leftri rightri

This is PART 33: Centers X(64001) - X(66000)

PART 1: Introduction and Centers X(1) - X(1000) PART 2: Centers X(1001) - X(3000) PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000) PART 5: Centers X(7001) - X(10000) PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000) PART 8: Centers X(14001) - X(16000) PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000) PART 11: Centers X(20001) - X(22000) PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000) PART 14: Centers X(26001) - X(28000) PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000) PART 17: Centers X(32001) - X(34000) PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000) PART 20: Centers X(38001) - X(40000) PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000) PART 23: Centers X(44001) - X(46000) PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000) PART 26: Centers X(50001) - X(52000) PART 27: Centers X(52001) - X(54000)
PART 28: Centers X(54001) - X(56000) PART 29: Centers X(56001) - X(58000) PART 30: Centers X(58001) - X(60000)
PART 31: Centers X(60001) - X(62000) PART 32: Centers X(62001) - X(64000) PART 33: Centers X(64001) - X(66000)
PART 34: Centers X(66001) - X(68000) PART 35: Centers X(68001) - X(70000) PART 36: Centers X(70001) - X(72000)

X(64001) = ORTHOLOGY CENTER OF THESE TRIANGLES: ASCELLA AND X(1)-CROSSPEDAL-OF-X(72)

Barycentrics    2*a^7-a^6*(b+c)+a^4*(b-c)^2*(b+c)+a^2*(b-c)^2*(b+c)^3-(b-c)^4*(b+c)^3+4*a*b*c*(b^2-c^2)^2-4*a^5*(b^2+c^2)+2*a^3*(b-c)^2*(b^2+c^2) : :
X(64001) = 3*X[354]+X[6253], -3*X[553]+X[1071], -3*X[5587]+X[12527], 3*X[11246]+X[12688], -X[12680]+5*X[52783]

X(64001) lies on these lines: {1, 50701}, {2, 5715}, {3, 142}, {4, 57}, {5, 5745}, {7, 1490}, {9, 6864}, {10, 5709}, {20, 8726}, {30, 5806}, {40, 443}, {58, 53599}, {63, 6835}, {78, 55109}, {117, 53828}, {165, 37407}, {226, 3149}, {354, 6253}, {355, 2095}, {405, 63438}, {411, 5249}, {499, 1699}, {515, 942}, {517, 11793}, {519, 24474}, {527, 5777}, {553, 1071}, {580, 3008}, {581, 3664}, {603, 53592}, {631, 41867}, {908, 6915}, {936, 5735}, {943, 6905}, {944, 3296}, {950, 37468}, {962, 6282}, {971, 24470}, {1158, 21628}, {1389, 34485}, {1393, 40950}, {1466, 1836}, {1467, 4293}, {1473, 37387}, {1482, 12437}, {1730, 63397}, {1837, 40271}, {1838, 3075}, {2051, 51759}, {2262, 51490}, {2816, 52824}, {2817, 44545}, {2829, 16616}, {2949, 62777}, {3091, 5744}, {3218, 6894}, {3306, 6836}, {3333, 12573}, {3358, 63973}, {3428, 19520}, {3452, 5812}, {3474, 12705}, {3487, 52026}, {3586, 5804}, {3587, 5493}, {3600, 12650}, {3601, 5603}, {3634, 6881}, {3636, 24299}, {3656, 34707}, {3668, 57276}, {3671, 6261}, {3683, 7958}, {3811, 60895}, {3817, 6824}, {3911, 6831}, {3916, 8226}, {4294, 10383}, {4295, 54198}, {4297, 6869}, {4301, 6885}, {4304, 6934}, {4311, 34489}, {4312, 63962}, {4355, 63981}, {4652, 6837}, {4847, 12704}, {5044, 5762}, {5122, 22835}, {5219, 6927}, {5290, 64148}, {5436, 59345}, {5437, 6865}, {5587, 12527}, {5691, 5768}, {5703, 30275}, {5705, 6843}, {5708, 5787}, {5714, 63966}, {5719, 40262}, {5728, 12671}, {5755, 63978}, {5759, 17582}, {5771, 9956}, {5791, 10175}, {5798, 40942}, {5842, 11018}, {5850, 63967}, {5882, 12577}, {5930, 34042}, {6001, 37544}, {6259, 18541}, {6260, 19541}, {6284, 17603}, {6361, 37551}, {6684, 7680}, {6692, 6922}, {6700, 6911}, {6705, 7681}, {6734, 6839}, {6737, 37625}, {6796, 13405}, {6827, 9843}, {6828, 59491}, {6832, 21165}, {6841, 12571}, {6846, 31424}, {6848, 9612}, {6849, 7330}, {6851, 26333}, {6854, 55104}, {6857, 8227}, {6861, 10171}, {6895, 27003}, {6924, 58461}, {6956, 31231}, {6962, 31266}, {6988, 25525}, {6989, 10164}, {6991, 54357}, {7354, 37566}, {7367, 20263}, {7683, 15762}, {7956, 22793}, {7988, 38306}, {8732, 37434}, {9799, 21454}, {9812, 21164}, {9841, 52835}, {9842, 37822}, {9945, 64192}, {10123, 37447}, {10202, 28164}, {10310, 37270}, {10445, 54405}, {10532, 31397}, {10572, 30274}, {10857, 64005}, {10884, 50695}, {10893, 37545}, {11012, 37306}, {11019, 48482}, {11036, 54051}, {11227, 28150}, {11246, 12688}, {11372, 64190}, {11499, 59722}, {11500, 21620}, {11522, 30282}, {11826, 17612}, {12447, 31806}, {12575, 13464}, {12599, 26040}, {12664, 52819}, {12680, 52783}, {12684, 31672}, {13407, 44425}, {15325, 15911}, {15908, 37363}, {16004, 28174}, {17102, 40960}, {18482, 34862}, {19860, 64079}, {19925, 37532}, {20205, 39585}, {24178, 37570}, {25526, 37418}, {28194, 31793}, {28228, 37585}, {30424, 54227}, {33597, 63274}, {37273, 60634}, {37526, 41869}, {37530, 40940}, {37583, 44675}, {37584, 43174}, {37837, 64110}, {38073, 50739}, {38454, 58637}, {40273, 61534}, {40658, 52542}, {41854, 43177}, {44178, 55105}, {50205, 61595}, {52265, 58463}, {54318, 64075}, {63318, 63382}, {63980, 64124}

X(64001) = midpoint of X(i) and X(j) for these {i,j}: {4, 4292}, {942, 20420}, {950, 37468}, {1071, 63998}, {6737, 37625}, {10123, 37447}, {64003, 64004}
X(64001) = reflection of X(i) in X(j) for these {i,j}: {3, 12436}, {5882, 12577}, {6738, 31870}, {12572, 5}, {12575, 13464}, {31806, 12447}, {57284, 37281}, {63999, 13374}
X(64001) = complement of X(64004)
X(64001) = X(i)-Ceva conjugate of X(j) for these {i, j}: {58993, 514}
X(64001) = pole of line {21172, 21173} with respect to the incircle
X(64001) = pole of line {12688, 54198} with respect to the Feuerbach hyperbola
X(64001) = pole of line {1819, 4184} with respect to the Stammler hyperbola
X(64001) = pole of line {6, 278} with respect to the dual conic of Yff parabola
X(64001) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6245), X(63186)}}, {{A, B, C, X(14377), X(55110)}}
X(64001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64003, 64004}, {3, 55108, 1125}, {3, 5805, 946}, {4, 57, 6245}, {5, 37623, 5745}, {7, 50700, 1490}, {20, 9776, 8726}, {515, 31870, 6738}, {516, 12436, 3}, {553, 63998, 1071}, {936, 5735, 5758}, {942, 20420, 515}, {946, 31730, 11496}, {962, 6904, 6282}, {1699, 15803, 6847}, {1838, 3075, 34050}, {4293, 11023, 1467}, {4295, 63992, 54198}, {5709, 6826, 10}, {5759, 17582, 61122}, {6705, 18483, 8727}, {6849, 7330, 63970}, {6869, 18443, 4297}, {8727, 37582, 6705}, {19541, 57282, 6260}, {31424, 38150, 6846}, {31870, 40249, 942}, {37532, 44229, 51755}, {44229, 51755, 19925}

X(64002) = ANTICOMPLEMENT OF X(4292)

Barycentrics    2*a^4+a^3*(b+c)-(b^2-c^2)^2-a^2*(b^2+c^2)-a*(b^3+b^2*c+b*c^2+c^3) : :
X(64002) = -3*X[2]+2*X[4292], -3*X[392]+2*X[18990], -2*X[942]+3*X[11113], -3*X[3058]+2*X[34791], -3*X[3241]+4*X[12575], -5*X[3616]+4*X[4298], -6*X[3742]+5*X[52783], -4*X[3812]+3*X[11246], -3*X[3873]+4*X[63999], -5*X[3876]+3*X[17579], -3*X[3877]+2*X[10106], -5*X[3889]+6*X[64162] and many others

X(64002) lies on these lines: {1, 5905}, {2, 4292}, {3, 908}, {4, 63}, {5, 3916}, {6, 50065}, {7, 452}, {8, 144}, {9, 377}, {10, 191}, {12, 4640}, {20, 78}, {21, 226}, {29, 307}, {30, 72}, {31, 13161}, {33, 54289}, {34, 22464}, {35, 16154}, {36, 21616}, {37, 49745}, {40, 3436}, {46, 24982}, {56, 24703}, {57, 2478}, {65, 17768}, {75, 1890}, {79, 5251}, {84, 6836}, {100, 16113}, {142, 5047}, {145, 10624}, {165, 5552}, {190, 3710}, {200, 64005}, {213, 50175}, {224, 41854}, {225, 283}, {228, 37425}, {238, 23536}, {255, 1785}, {306, 1330}, {318, 18750}, {376, 4855}, {382, 3419}, {388, 5250}, {392, 18990}, {394, 64057}, {404, 3452}, {405, 5249}, {406, 56457}, {411, 6260}, {442, 31445}, {443, 3305}, {475, 56456}, {497, 62874}, {513, 22299}, {515, 3869}, {517, 16980}, {518, 6284}, {527, 950}, {529, 3057}, {535, 3878}, {540, 2901}, {550, 5440}, {631, 30852}, {651, 5930}, {664, 50563}, {748, 24178}, {758, 10572}, {894, 26117}, {896, 21935}, {912, 7491}, {936, 4190}, {938, 9965}, {942, 11113}, {944, 11682}, {946, 2975}, {956, 12699}, {958, 1836}, {960, 7354}, {962, 3872}, {964, 4357}, {971, 60979}, {993, 12047}, {997, 4299}, {1001, 10404}, {1012, 5812}, {1043, 4101}, {1058, 62832}, {1071, 31789}, {1072, 3073}, {1074, 3074}, {1104, 3782}, {1125, 16865}, {1155, 1329}, {1210, 3218}, {1211, 50054}, {1220, 24723}, {1259, 6259}, {1260, 48664}, {1385, 51409}, {1394, 57477}, {1453, 19785}, {1468, 24210}, {1473, 37415}, {1478, 12514}, {1479, 26015}, {1503, 43216}, {1512, 37821}, {1519, 11249}, {1532, 37623}, {1621, 21620}, {1657, 3940}, {1697, 60965}, {1699, 10527}, {1707, 5230}, {1709, 10522}, {1724, 23537}, {1737, 55873}, {1750, 50695}, {1759, 5179}, {1760, 1861}, {1761, 1826}, {1762, 1869}, {1782, 21368}, {1817, 27412}, {1834, 4641}, {1842, 24310}, {1877, 37591}, {1885, 12689}, {1891, 8680}, {1896, 1947}, {1959, 46483}, {1999, 20077}, {2003, 3193}, {2093, 5554}, {2096, 6865}, {2476, 5745}, {2549, 54406}, {2550, 60949}, {2551, 3474}, {2792, 4499}, {2817, 41733}, {2829, 14110}, {3011, 54354}, {3058, 34791}, {3085, 35258}, {3091, 5744}, {3149, 37822}, {3191, 48897}, {3220, 37231}, {3241, 12575}, {3243, 41864}, {3306, 5084}, {3421, 6361}, {3428, 64119}, {3434, 41869}, {3487, 11111}, {3488, 11520}, {3522, 27383}, {3523, 5748}, {3529, 3984}, {3543, 5175}, {3555, 15171}, {3560, 37826}, {3579, 17757}, {3583, 6763}, {3586, 12649}, {3601, 28609}, {3616, 4298}, {3647, 3822}, {3650, 18480}, {3662, 17697}, {3663, 5262}, {3671, 14450}, {3681, 28150}, {3682, 61220}, {3683, 25466}, {3687, 50697}, {3717, 5300}, {3742, 52783}, {3811, 4302}, {3812, 11246}, {3816, 32636}, {3825, 4973}, {3838, 24953}, {3847, 61649}, {3870, 4294}, {3873, 63999}, {3876, 17579}, {3877, 10106}, {3883, 4968}, {3889, 64162}, {3890, 34605}, {3897, 64160}, {3911, 4193}, {3912, 31015}, {3914, 5247}, {3924, 33098}, {3925, 5302}, {3928, 9581}, {3935, 20066}, {3962, 44669}, {3983, 49732}, {4001, 10449}, {4018, 37730}, {4067, 12532}, {4185, 24320}, {4186, 37581}, {4187, 37582}, {4188, 6700}, {4189, 13411}, {4192, 22345}, {4194, 56367}, {4195, 27184}, {4198, 18655}, {4200, 27509}, {4201, 27064}, {4202, 17353}, {4217, 17274}, {4220, 54337}, {4252, 17720}, {4293, 19861}, {4295, 19860}, {4297, 4511}, {4301, 4861}, {4304, 15680}, {4311, 20067}, {4313, 64143}, {4340, 5287}, {4355, 10582}, {4385, 63134}, {4414, 5530}, {4415, 37539}, {4419, 5716}, {4420, 21060}, {4450, 4696}, {4512, 5290}, {4645, 56311}, {4654, 5436}, {4662, 34612}, {4679, 25524}, {4683, 54331}, {4847, 51118}, {4853, 9589}, {4857, 49627}, {4880, 37702}, {4996, 21635}, {4999, 17605}, {5010, 59719}, {5015, 63147}, {5016, 32933}, {5044, 11112}, {5059, 20007}, {5081, 54107}, {5082, 63135}, {5086, 11684}, {5087, 5433}, {5122, 13747}, {5129, 9776}, {5134, 21073}, {5174, 52844}, {5176, 11362}, {5177, 5273}, {5183, 8256}, {5204, 25681}, {5219, 6910}, {5225, 24477}, {5248, 13407}, {5257, 14005}, {5259, 51706}, {5260, 20292}, {5265, 26129}, {5271, 6994}, {5279, 8804}, {5288, 49600}, {5294, 16062}, {5295, 49716}, {5303, 10165}, {5316, 17531}, {5325, 6175}, {5330, 63987}, {5434, 58679}, {5435, 6919}, {5438, 31142}, {5439, 24470}, {5441, 41696}, {5442, 31263}, {5445, 31160}, {5493, 6736}, {5534, 37000}, {5587, 54290}, {5657, 63144}, {5687, 63145}, {5692, 10483}, {5695, 10371}, {5703, 17576}, {5705, 6871}, {5706, 55400}, {5710, 64016}, {5714, 6857}, {5715, 6837}, {5717, 28606}, {5720, 6934}, {5730, 18481}, {5731, 56387}, {5759, 52684}, {5777, 37468}, {5791, 17532}, {5794, 12943}, {5811, 50701}, {5814, 50044}, {5815, 17784}, {5836, 28534}, {5840, 46685}, {5841, 5887}, {5842, 14872}, {5857, 12711}, {5882, 62826}, {5927, 20420}, {5932, 10433}, {6001, 11827}, {6147, 50241}, {6198, 52362}, {6245, 6840}, {6684, 11681}, {6690, 18977}, {6705, 6943}, {6737, 28164}, {6743, 28158}, {6745, 12512}, {6762, 9580}, {6765, 20075}, {6769, 64078}, {6825, 21165}, {6827, 63399}, {6850, 55104}, {6856, 55867}, {6868, 18446}, {6890, 52027}, {6894, 60970}, {6899, 7171}, {6902, 26877}, {6904, 18228}, {6920, 55108}, {6921, 30827}, {6923, 26921}, {6928, 24467}, {6929, 37532}, {6931, 31231}, {6936, 18443}, {6938, 37531}, {6947, 37534}, {6951, 26878}, {6962, 63966}, {6986, 61115}, {6987, 10884}, {6992, 8726}, {6998, 60701}, {7013, 44696}, {7080, 9778}, {7183, 51364}, {7292, 24171}, {7293, 37431}, {7308, 37462}, {7675, 61010}, {7682, 13729}, {7688, 49178}, {7962, 36977}, {8165, 26062}, {8544, 52457}, {8616, 28027}, {8666, 30384}, {8669, 21093}, {9597, 39248}, {9614, 10529}, {9780, 18250}, {9809, 54227}, {9812, 64081}, {9840, 30076}, {9843, 27003}, {9945, 12103}, {10032, 50796}, {10164, 27529}, {10436, 37314}, {10441, 26892}, {10448, 24725}, {10461, 14956}, {10528, 61763}, {10543, 28645}, {10895, 26066}, {10914, 28174}, {10915, 11010}, {10950, 44663}, {11012, 12608}, {11015, 12437}, {11107, 51382}, {11108, 18541}, {11115, 26580}, {11194, 11376}, {11239, 53053}, {11240, 51785}, {11319, 17184}, {11374, 16370}, {11518, 60933}, {11523, 50244}, {11551, 30143}, {11679, 54429}, {11680, 18483}, {11826, 17615}, {12053, 54391}, {12246, 63984}, {12433, 24473}, {12513, 12701}, {12573, 52653}, {12577, 38314}, {12579, 43223}, {12607, 37568}, {12618, 16566}, {12625, 60977}, {12679, 64077}, {12702, 51433}, {12704, 26333}, {13369, 28459}, {13408, 16585}, {13724, 30078}, {13731, 22060}, {13740, 54311}, {14020, 50116}, {14206, 41013}, {14213, 56875}, {14923, 28194}, {15326, 59691}, {15338, 56176}, {15717, 46873}, {16048, 51400}, {16049, 57281}, {16086, 52354}, {16091, 56382}, {16127, 50528}, {16143, 41690}, {16859, 27186}, {16948, 33133}, {17016, 33100}, {17023, 37076}, {17139, 54356}, {17257, 50408}, {17276, 37549}, {17332, 49734}, {17351, 50050}, {17526, 25527}, {17609, 49736}, {17676, 26223}, {17732, 17742}, {18193, 28074}, {18230, 37436}, {18669, 22005}, {19335, 22376}, {19513, 22344}, {19514, 23205}, {19540, 23085}, {19543, 23206}, {19648, 23169}, {20060, 31397}, {20101, 41261}, {21287, 52396}, {21578, 30144}, {22010, 56538}, {22129, 41344}, {22793, 24390}, {23151, 49130}, {23661, 30807}, {24231, 28082}, {24248, 54418}, {24430, 40950}, {24474, 37290}, {24695, 54421}, {24913, 25677}, {24929, 41571}, {25006, 41229}, {25083, 49132}, {25237, 49476}, {26364, 58887}, {26790, 40872}, {26792, 37256}, {27388, 37250}, {27410, 40880}, {27413, 37180}, {27504, 28774}, {27505, 28739}, {27559, 35991}, {27725, 37158}, {28146, 34790}, {28238, 30006}, {28628, 61716}, {29574, 50234}, {29817, 51724}, {29967, 37225}, {30264, 37837}, {30305, 36846}, {30332, 56936}, {30985, 52241}, {31141, 37828}, {31259, 41867}, {31775, 64107}, {31793, 51379}, {31993, 49728}, {33151, 34937}, {33864, 36007}, {34471, 34647}, {34632, 63133}, {34862, 37374}, {37002, 37611}, {37229, 64152}, {37285, 54430}, {37286, 41550}, {37524, 58405}, {37563, 49626}, {37584, 51432}, {40270, 62854}, {41228, 61003}, {41249, 50166}, {41325, 55337}, {41338, 52860}, {41540, 59321}, {41543, 44238}, {44694, 48890}, {44706, 56814}, {45701, 59316}, {48870, 50066}, {49721, 50046}, {50031, 64128}, {50055, 50127}, {50093, 50171}, {50306, 64184}, {50307, 59305}, {50725, 61006}, {50737, 53620}, {51090, 60969}, {54433, 56082}, {56078, 57808}, {56879, 63137}, {59355, 63998}, {62837, 63993}, {63211, 64123}, {63962, 64150}, {63985, 64111}, {63988, 64075}, {63992, 64079}, {64047, 64163}

X(64002) = reflection of X(i) in X(j) for these {i,j}: {8, 12527}, {20, 64004}, {65, 57288}, {145, 10624}, {1071, 31789}, {1770, 10}, {3555, 15171}, {3868, 950}, {4018, 37730}, {4292, 12572}, {7354, 960}, {10483, 17647}, {11826, 63976}, {24474, 37290}, {37468, 5777}, {41228, 61003}, {41575, 10572}, {45287, 3878}, {57287, 72}, {59355, 63998}, {64003, 4}, {64047, 64163}
X(64002) = anticomplement of X(4292)
X(64002) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40407, 7}, {57392, 3868}
X(64002) = pole of line {8058, 59926} with respect to the DeLongchamps circle
X(64002) = pole of line {17604, 26476} with respect to the Feuerbach hyperbola
X(64002) = pole of line {3239, 7265} with respect to the Steiner circumellipse
X(64002) = pole of line {648, 653} with respect to the Yff parabola
X(64002) = pole of line {57045, 57064} with respect to the dual conic of incircle
X(64002) = pole of line {14996, 33150} with respect to the dual conic of Yff parabola
X(64002) = intersection, other than A, B, C, of circumconics {{A, B, C, X(267), X(3062)}}, {{A, B, C, X(502), X(8806)}}, {{A, B, C, X(1029), X(10405)}}, {{A, B, C, X(1034), X(62883)}}, {{A, B, C, X(7282), X(39130)}}, {{A, B, C, X(21075), X(34922)}}
X(64002) = barycentric product X(i)*X(j) for these (i, j): {312, 64055}
X(64002) = barycentric quotient X(i)/X(j) for these (i, j): {64055, 57}
X(64002) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11415, 51423}, {3, 58798, 908}, {4, 63, 6734}, {7, 452, 54392}, {8, 144, 3951}, {9, 9579, 377}, {20, 329, 78}, {30, 72, 57287}, {40, 3436, 6735}, {56, 24703, 41012}, {79, 5251, 12609}, {144, 3146, 8}, {191, 3585, 10}, {382, 3927, 3419}, {388, 5698, 5250}, {405, 57282, 5249}, {442, 31445, 54357}, {527, 950, 3868}, {535, 3878, 45287}, {758, 10572, 41575}, {993, 12047, 24541}, {1043, 33066, 4101}, {1330, 7283, 306}, {1478, 12514, 24987}, {1479, 62858, 26015}, {1724, 23537, 26723}, {2975, 5057, 946}, {3218, 5046, 1210}, {3421, 6361, 63130}, {3436, 44447, 40}, {3487, 11111, 62829}, {3543, 54398, 5175}, {3586, 54422, 12649}, {3648, 5080, 56288}, {3868, 11114, 950}, {3876, 17579, 57284}, {3935, 20066, 64117}, {4188, 27131, 6700}, {4189, 31053, 13411}, {4190, 31018, 936}, {4292, 12572, 2}, {4298, 40998, 3616}, {4415, 64159, 37539}, {4847, 51118, 52367}, {4861, 5180, 4301}, {5247, 24851, 3914}, {5493, 6736, 63136}, {5691, 60905, 12526}, {5692, 10483, 17647}, {5714, 6857, 31266}, {5905, 6872, 1}, {6260, 63438, 411}, {6871, 55868, 5705}, {12649, 20078, 54422}, {12702, 64087, 51433}, {15680, 17484, 34772}, {15680, 34772, 4304}, {16865, 31019, 1125}, {17768, 57288, 65}, {17781, 57287, 72}, {21075, 31730, 100}, {27003, 37162, 9843}, {31164, 62829, 3487}, {31547, 31548, 45738}, {33151, 62802, 34937}, {37821, 59318, 1512}, {41869, 57279, 3434}, {60905, 64197, 144}, {64111, 64190, 63985}

X(64003) = ORTHOLOGY CENTER OF THESE TRIANGLES: CONWAY AND X(1)-CROSSPEDAL-OF-X(72)

Barycentrics    2*a^7-a^6*(b+c)+a^4*(b-c)^2*(b+c)+a^2*(b-c)^2*(b+c)^3-(b-c)^4*(b+c)^3+2*a*b*c*(b^2-c^2)^2+2*a^3*(b^2+c^2)^2-2*a^5*(2*b^2+b*c+2*c^2) : :
X(64003) = -7*X[3523]+8*X[12436], -3*X[3753]+2*X[31799], -4*X[5777]+3*X[17781], -4*X[5806]+3*X[11113], -4*X[9940]+3*X[37428], -2*X[9943]+3*X[11246], -3*X[10167]+4*X[24470], -3*X[11112]+2*X[31793], -3*X[28452]+2*X[31837], -4*X[37281]+3*X[64107], -5*X[52783]+4*X[58567]

X(64003) lies on these lines: {1, 7}, {2, 5715}, {3, 5249}, {4, 63}, {5, 54357}, {8, 20223}, {9, 6835}, {10, 6839}, {21, 946}, {27, 283}, {30, 1071}, {40, 377}, {57, 6836}, {72, 5762}, {78, 5758}, {84, 10431}, {142, 6986}, {165, 10198}, {191, 12617}, {224, 6934}, {225, 412}, {226, 411}, {255, 1838}, {307, 7513}, {329, 50700}, {405, 5805}, {443, 5759}, {497, 62836}, {515, 3868}, {517, 5562}, {518, 6253}, {527, 12528}, {550, 24299}, {580, 26723}, {908, 1259}, {944, 11520}, {950, 62864}, {958, 5832}, {971, 14054}, {1004, 10310}, {1006, 55108}, {1012, 11249}, {1072, 3072}, {1076, 3075}, {1125, 37106}, {1210, 6840}, {1212, 5829}, {1385, 44238}, {1479, 62810}, {1490, 5905}, {1512, 10526}, {1519, 37302}, {1698, 6993}, {1699, 6837}, {1724, 53599}, {1729, 5179}, {1754, 23537}, {1836, 26357}, {1839, 15656}, {1998, 6223}, {2000, 37104}, {2077, 35976}, {2096, 12116}, {2886, 15823}, {2894, 4847}, {2949, 3219}, {3091, 5273}, {3146, 9799}, {3182, 56544}, {3218, 6245}, {3305, 6864}, {3306, 6865}, {3428, 37228}, {3452, 6915}, {3474, 37550}, {3523, 12436}, {3543, 28610}, {3562, 5930}, {3583, 54432}, {3587, 6897}, {3647, 12558}, {3753, 31799}, {3817, 6884}, {3911, 6943}, {3916, 8727}, {4190, 6282}, {4197, 6684}, {4652, 6847}, {5046, 7682}, {5057, 63989}, {5219, 6962}, {5234, 5833}, {5279, 10445}, {5440, 5763}, {5493, 37163}, {5535, 12616}, {5536, 10916}, {5563, 16155}, {5584, 5880}, {5603, 59345}, {5691, 49168}, {5713, 37419}, {5745, 6828}, {5777, 17781}, {5784, 7957}, {5806, 11113}, {5842, 12671}, {5882, 63159}, {6260, 36002}, {6284, 10391}, {6361, 6916}, {6598, 24391}, {6824, 21165}, {6826, 55104}, {6831, 37623}, {6838, 9612}, {6851, 63399}, {6855, 55867}, {6869, 18446}, {6870, 55868}, {6886, 38150}, {6890, 15803}, {6899, 37534}, {6900, 26878}, {6905, 27385}, {6909, 37583}, {6917, 37584}, {6925, 9579}, {6927, 30852}, {6985, 37826}, {6987, 54392}, {6988, 31266}, {7354, 64043}, {7411, 10902}, {7549, 54337}, {7580, 57282}, {7680, 47516}, {7681, 37358}, {7686, 11827}, {7958, 15254}, {7989, 31446}, {8226, 31445}, {8557, 57286}, {9616, 45650}, {9776, 37423}, {9778, 10268}, {9812, 10527}, {9940, 37428}, {9943, 11246}, {10123, 33557}, {10167, 24470}, {10267, 37426}, {10306, 63145}, {10529, 54052}, {10572, 18389}, {10680, 48661}, {10724, 13243}, {10883, 18483}, {11020, 63999}, {11112, 31793}, {11220, 28150}, {11362, 59356}, {11415, 63992}, {11496, 20835}, {11826, 17616}, {12053, 62873}, {12512, 37105}, {12527, 54398}, {12609, 59320}, {12650, 20076}, {12688, 17768}, {12701, 26437}, {12705, 44447}, {13442, 64126}, {13739, 51382}, {14217, 48694}, {14798, 15228}, {15852, 49745}, {15931, 51706}, {17529, 31658}, {17558, 40998}, {17579, 28194}, {17590, 61595}, {19541, 58798}, {19645, 37530}, {20070, 37435}, {21077, 44425}, {21620, 62800}, {22753, 37248}, {22793, 26202}, {23144, 64057}, {23536, 37570}, {24320, 37387}, {26201, 28146}, {26921, 44229}, {28174, 31775}, {28198, 37429}, {28381, 30078}, {28452, 31837}, {28534, 34742}, {29639, 37443}, {34789, 48713}, {37194, 37581}, {37281, 64107}, {37374, 37582}, {37462, 61122}, {37579, 64074}, {37591, 40950}, {41228, 63146}, {41572, 44547}, {45700, 50865}, {49164, 64084}, {49170, 62874}, {51423, 63986}, {52783, 58567}, {52835, 60990}, {54289, 57276}, {57284, 61002}, {59323, 64155}, {61024, 63970}, {63995, 64046}

X(64003) = midpoint of X(i) and X(j) for these {i,j}: {3868, 59355}
X(64003) = reflection of X(i) in X(j) for these {i,j}: {20, 4292}, {72, 20420}, {11827, 7686}, {12528, 63998}, {33557, 10123}, {41575, 37625}, {57287, 37468}, {64002, 4}, {64004, 64001}
X(64003) = anticomplement of X(64004)
X(64003) = pole of line {354, 26475} with respect to the Feuerbach hyperbola
X(64003) = pole of line {2328, 10902} with respect to the Stammler hyperbola
X(64003) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(1105)}}, {{A, B, C, X(77), X(775)}}, {{A, B, C, X(84), X(4341)}}, {{A, B, C, X(269), X(55105)}}, {{A, B, C, X(347), X(43740)}}, {{A, B, C, X(10884), X(34402)}}
X(64003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5709, 6734}, {7, 20, 10884}, {20, 11036, 5731}, {84, 41869, 10431}, {515, 37625, 41575}, {516, 4292, 20}, {527, 63998, 12528}, {946, 11012, 24541}, {946, 63438, 21}, {1071, 24474, 39772}, {1699, 31424, 6837}, {3146, 9965, 9799}, {3149, 5812, 908}, {3218, 6895, 6245}, {3868, 59355, 515}, {5603, 59345, 62829}, {5905, 50695, 1490}, {6361, 6916, 63141}, {10431, 43740, 48482}, {11012, 49177, 946}, {64001, 64004, 2}

X(64004) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND EXTOUCH AND X(1)-CROSSPEDAL-OF-X(72)

Barycentrics    2*a^7-a^6*(b+c)+a^4*(b-c)^2*(b+c)+a^2*(b-c)^2*(b+c)^3-(b-c)^4*(b+c)^3+2*a^3*(b+c)^2*(b^2+c^2)-4*a^5*(b^2+b*c+c^2) : :
X(64004) = -3*X[210]+X[6253], -3*X[553]+4*X[9940], -5*X[631]+4*X[12436], -5*X[3876]+X[59355], -3*X[11227]+2*X[24470], -X[12528]+3*X[17781] -X[24474]+3*X[28459]

X(64004) lies on these lines: {1, 5758}, {2, 5715}, {3, 226}, {4, 9}, {7, 8726}, {20, 78}, {30, 5777}, {57, 6865}, {63, 6245}, {72, 515}, {144, 9799}, {165, 498}, {198, 9122}, {201, 40950}, {210, 6253}, {212, 225}, {228, 37409}, {255, 1076}, {376, 28609}, {389, 517}, {405, 946}, {411, 908}, {442, 6684}, {443, 61122}, {452, 962}, {497, 10396}, {519, 42456}, {527, 1071}, {553, 9940}, {580, 40940}, {602, 1072}, {631, 12436}, {936, 50701}, {938, 12848}, {942, 5762}, {943, 10902}, {944, 11523}, {954, 12573}, {971, 61003}, {997, 64075}, {1006, 1125}, {1068, 59645}, {1155, 50031}, {1210, 1708}, {1260, 11500}, {1385, 63274}, {1478, 59340}, {1479, 1728}, {1698, 6843}, {1699, 6846}, {1713, 40963}, {1750, 5811}, {1764, 63397}, {1785, 38857}, {1794, 1838}, {1836, 5584}, {1864, 6284}, {1935, 53592}, {2077, 3651}, {2096, 9841}, {2324, 9121}, {2328, 37383}, {2385, 52359}, {2478, 7682}, {2792, 10381}, {2817, 41600}, {2829, 13227}, {2894, 2949}, {2900, 37000}, {3085, 10268}, {3149, 3452}, {3219, 6895}, {3305, 6835}, {3419, 11362}, {3430, 30266}, {3474, 37560}, {3487, 3576}, {3488, 7982}, {3579, 6907}, {3586, 7991}, {3587, 6850}, {3601, 59345}, {3634, 6829}, {3817, 6832}, {3876, 59355}, {3911, 6922}, {3916, 6705}, {3927, 5787}, {4185, 26935}, {4294, 6769}, {4295, 30503}, {4297, 18446}, {4300, 41011}, {4301, 6936}, {4304, 6868}, {4311, 37611}, {4314, 37569}, {4652, 6890}, {4847, 48482}, {5044, 20420}, {5129, 60959}, {5175, 59417}, {5219, 6988}, {5249, 6986}, {5285, 7412}, {5316, 6918}, {5436, 5603}, {5552, 9778}, {5554, 20070}, {5705, 6844}, {5714, 35242}, {5717, 37528}, {5720, 6869}, {5722, 61014}, {5728, 63999}, {5732, 61010}, {5735, 60987}, {5745, 6831}, {5750, 5798}, {5755, 57719}, {5763, 24929}, {5768, 54422}, {5805, 11108}, {5806, 60972}, {5842, 63146}, {5905, 10884}, {5927, 11826}, {5928, 63436}, {5930, 7078}, {6244, 11499}, {6259, 64156}, {6260, 6745}, {6700, 6905}, {6738, 37625}, {6828, 54357}, {6833, 21165}, {6847, 31424}, {6851, 7330}, {6860, 55867}, {6864, 7308}, {6877, 51073}, {6878, 19862}, {6883, 55108}, {6889, 10164}, {6894, 27065}, {6899, 63399}, {6913, 12699}, {6916, 9579}, {6925, 63141}, {6926, 15803}, {6927, 30827}, {6928, 10395}, {6943, 59491}, {6947, 9843}, {6962, 30852}, {6990, 12571}, {6992, 54392}, {7013, 40657}, {7070, 7952}, {7085, 37194}, {7491, 37585}, {7680, 47510}, {7681, 14022}, {7992, 60905}, {8226, 15908}, {8227, 16845}, {8232, 37108}, {8273, 10404}, {8544, 54178}, {8727, 31445}, {8728, 31658}, {8807, 52097}, {9119, 12241}, {9441, 24851}, {9668, 10392}, {9943, 17768}, {9960, 60979}, {10056, 16208}, {10106, 31786}, {10123, 31659}, {10320, 58887}, {10572, 18397}, {10860, 64190}, {11019, 12704}, {11113, 28194}, {11227, 24470}, {11249, 44675}, {11415, 54198}, {11491, 59722}, {11496, 13615}, {12047, 59320}, {12053, 22770}, {12245, 12625}, {12246, 58808}, {12528, 17781}, {12565, 63962}, {13161, 37570}, {13257, 24466}, {13329, 23537}, {13407, 15931}, {14647, 54290}, {15796, 52954}, {15972, 48899}, {17857, 21060}, {18228, 50700}, {18650, 52673}, {19861, 64079}, {21015, 37368}, {21153, 37407}, {22003, 59163}, {22300, 58690}, {22753, 37244}, {24474, 28459}, {24703, 63989}, {26006, 36023}, {26364, 59614}, {26921, 51755}, {28146, 31777}, {28174, 31798}, {28198, 31797}, {30264, 50371}, {31018, 50695}, {33597, 44238}, {36029, 57281}, {37364, 37582}, {37426, 63413}, {37468, 57284}, {37530, 39595}, {37537, 50065}, {40212, 44696}, {41561, 41854}, {41572, 62864}, {43177, 61011}, {44447, 63985}, {50528, 54227}, {51706, 52769}, {54305, 57276}

X(64004) = midpoint of X(i) and X(j) for these {i,j}: {20, 64002}, {6284, 7957}, {7491, 37585}, {11827, 14110}
X(64004) = reflection of X(i) in X(j) for these {i,j}: {4, 12572}, {950, 31789}, {4292, 3}, {6737, 31806}, {7982, 12575}, {10106, 31786}, {20420, 5044}, {22300, 58690}, {37468, 57284}, {37625, 6738}, {52819, 51489}, {63146, 63976}, {63998, 5777}, {64003, 64001}
X(64004) = complement of X(64003)
X(64004) = anticomplement of X(64001)
X(64004) = X(i)-Dao conjugate of X(j) for these {i, j}: {64001, 64001}
X(64004) = pole of line {12, 1864} with respect to the Feuerbach hyperbola
X(64004) = pole of line {25259, 57245} with respect to the Steiner circumellipse
X(64004) = pole of line {3239, 60494} with respect to the Steiner inellipse
X(64004) = pole of line {101, 653} with respect to the Yff parabola
X(64004) = pole of line {21172, 36054} with respect to the dual conic of DeLongchamps circle
X(64004) = pole of line {4000, 37543} with respect to the dual conic of Yff parabola
X(64004) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(15830)}}, {{A, B, C, X(4), X(41514)}}, {{A, B, C, X(9), X(57643)}}, {{A, B, C, X(19), X(3345)}}, {{A, B, C, X(281), X(1034)}}, {{A, B, C, X(972), X(6197)}}, {{A, B, C, X(1826), X(8806)}}
X(64004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64003, 64001}, {3, 5812, 226}, {4, 55104, 10}, {4, 5759, 40}, {7, 37423, 8726}, {20, 329, 1490}, {30, 5777, 63998}, {63, 6836, 6245}, {165, 9612, 6908}, {226, 54430, 13411}, {255, 1076, 34050}, {515, 31806, 6737}, {516, 12572, 4}, {517, 31789, 950}, {950, 15556, 64163}, {3916, 37374, 6705}, {5709, 6827, 1210}, {5758, 6987, 1}, {5762, 51489, 52819}, {5842, 63976, 63146}, {6260, 31730, 7580}, {6922, 37623, 3911}, {6992, 55109, 54392}, {7580, 11517, 6796}, {7580, 58798, 6260}, {9579, 37551, 6916}, {11415, 64150, 54198}, {11827, 14110, 515}, {24703, 64077, 63989}, {31561, 31562, 8804}, {37468, 64107, 57284}

X(64005) = ORTHOLOGY CENTER OF THESE TRIANGLES: 6TH MIXTILINEAR AND X(1)-CROSSPEDAL-OF-X(72)

Barycentrics    5*a^4+a^3*(b+c)-a*(b-c)^2*(b+c)-2*(b^2-c^2)^2-a^2*(3*b^2+2*b*c+3*c^2) : :
X(64005) = -9*X[2]+7*X[10248], -4*X[3]+3*X[1699], -2*X[4]+3*X[165], -16*X[5]+17*X[19872], -3*X[354]+4*X[31805], -3*X[376]+2*X[946], -6*X[381]+7*X[31423], -8*X[546]+9*X[54447], -4*X[548]+3*X[5886], -4*X[549]+5*X[50812], -4*X[550]+3*X[3576], -2*X[551]+3*X[62120] and many others

X(64005) lies on these lines: {1, 7}, {2, 10248}, {3, 1699}, {4, 165}, {5, 19872}, {8, 5059}, {10, 3146}, {12, 35445}, {21, 12511}, {28, 52840}, {30, 40}, {35, 7580}, {36, 9614}, {43, 50694}, {46, 2955}, {55, 5290}, {56, 9580}, {57, 6284}, {63, 5178}, {72, 5696}, {79, 59337}, {80, 7285}, {84, 5842}, {144, 6743}, {145, 28228}, {200, 64002}, {354, 31805}, {376, 946}, {377, 4512}, {381, 31423}, {382, 3579}, {388, 53053}, {392, 56998}, {405, 11495}, {411, 5010}, {443, 63413}, {484, 920}, {485, 9582}, {497, 3361}, {498, 37421}, {511, 39878}, {515, 3529}, {517, 1657}, {518, 48872}, {519, 15683}, {527, 3189}, {528, 6762}, {529, 2136}, {546, 54447}, {548, 5886}, {549, 50812}, {550, 3576}, {551, 62120}, {553, 18217}, {631, 7988}, {758, 9961}, {846, 48890}, {936, 50695}, {942, 5918}, {944, 11001}, {950, 3339}, {952, 62155}, {958, 11661}, {960, 17668}, {971, 5904}, {978, 50702}, {1001, 35202}, {1012, 59320}, {1071, 3894}, {1097, 24014}, {1125, 3522}, {1131, 49618}, {1132, 49619}, {1151, 13888}, {1152, 13942}, {1155, 9581}, {1203, 37537}, {1210, 53056}, {1385, 3534}, {1386, 59411}, {1420, 12701}, {1478, 51784}, {1479, 15803}, {1482, 15681}, {1483, 7982}, {1490, 16127}, {1503, 9899}, {1571, 7747}, {1572, 7756}, {1593, 37557}, {1614, 9586}, {1697, 7354}, {1702, 6560}, {1703, 6561}, {1706, 57288}, {1724, 9441}, {1727, 59324}, {1750, 5811}, {1766, 16545}, {1768, 5709}, {1836, 3601}, {1837, 5128}, {1885, 7713}, {1902, 37196}, {2077, 6985}, {2093, 10572}, {2475, 35258}, {2478, 64112}, {2548, 31421}, {2550, 5234}, {2777, 2948}, {2792, 54209}, {2794, 12408}, {2829, 5541}, {3062, 5759}, {3070, 9616}, {3085, 31508}, {3091, 10164}, {3149, 59326}, {3241, 62148}, {3244, 62149}, {3245, 37711}, {3333, 15171}, {3336, 64129}, {3338, 9841}, {3359, 7491}, {3419, 54290}, {3434, 62824}, {3436, 63145}, {3485, 53054}, {3486, 18421}, {3523, 3817}, {3524, 30308}, {3528, 10165}, {3530, 61268}, {3543, 19875}, {3560, 7688}, {3583, 6836}, {3585, 6925}, {3616, 50693}, {3617, 50692}, {3622, 62124}, {3623, 16191}, {3626, 61252}, {3627, 18492}, {3634, 3832}, {3636, 62125}, {3647, 31446}, {3648, 3951}, {3651, 5715}, {3653, 15690}, {3655, 19710}, {3656, 15686}, {3681, 63280}, {3689, 48664}, {3751, 29181}, {3753, 50242}, {3828, 50687}, {3830, 9956}, {3839, 19876}, {3841, 10883}, {3843, 11231}, {3853, 61261}, {3855, 10172}, {3858, 61614}, {3861, 61263}, {3869, 9859}, {3870, 20066}, {3874, 11220}, {3876, 31871}, {3899, 14110}, {3911, 5225}, {3947, 5281}, {3973, 10443}, {4190, 8583}, {4197, 12558}, {4229, 25526}, {4652, 5231}, {4654, 37080}, {4668, 49140}, {4669, 62168}, {4677, 34632}, {4745, 62051}, {4816, 5881}, {4855, 5057}, {4880, 41709}, {4882, 12527}, {5056, 58441}, {5068, 51073}, {5070, 61265}, {5071, 50813}, {5073, 18480}, {5076, 38140}, {5086, 63144}, {5119, 9613}, {5122, 9669}, {5180, 56387}, {5204, 50443}, {5217, 5219}, {5221, 37723}, {5223, 63146}, {5229, 5726}, {5248, 7411}, {5250, 17579}, {5251, 5584}, {5268, 50698}, {5269, 50065}, {5272, 50699}, {5285, 15951}, {5302, 38200}, {5426, 44238}, {5434, 37556}, {5436, 5880}, {5438, 24703}, {5439, 10178}, {5475, 31422}, {5506, 61122}, {5531, 13199}, {5536, 63399}, {5537, 11500}, {5538, 6261}, {5550, 21734}, {5561, 59421}, {5563, 63991}, {5586, 11246}, {5603, 17538}, {5657, 31673}, {5692, 12688}, {5693, 37585}, {5697, 17644}, {5698, 45085}, {5705, 6895}, {5708, 31795}, {5727, 37567}, {5745, 51576}, {5789, 36999}, {5790, 33697}, {5818, 15682}, {5841, 49163}, {5844, 58203}, {5847, 14927}, {5882, 11224}, {5895, 40660}, {5902, 9943}, {5925, 6001}, {5927, 58637}, {5930, 34033}, {6173, 51715}, {6197, 15942}, {6264, 38753}, {6282, 6869}, {6459, 19004}, {6460, 19003}, {6744, 21454}, {6767, 31776}, {6827, 10270}, {6835, 21153}, {6840, 18514}, {6850, 10268}, {6868, 30503}, {6899, 16209}, {6904, 40998}, {6909, 7280}, {6934, 63992}, {6986, 38150}, {6996, 31183}, {6999, 17284}, {7171, 12704}, {7288, 50444}, {7379, 9746}, {7387, 9590}, {7406, 16832}, {7416, 39578}, {7737, 9593}, {7741, 37374}, {7745, 9574}, {7964, 31445}, {7965, 8728}, {7967, 16189}, {7993, 12248}, {7994, 63981}, {8148, 61291}, {8185, 39568}, {8226, 41859}, {8275, 10944}, {8580, 12572}, {8703, 38021}, {8804, 18594}, {8983, 42638}, {9575, 63548}, {9577, 64054}, {9578, 12943}, {9583, 42260}, {9587, 34148}, {9611, 18447}, {9622, 61752}, {9624, 13624}, {9626, 12083}, {9668, 37582}, {9670, 32636}, {9671, 61649}, {9779, 15717}, {9780, 17578}, {9782, 54392}, {9801, 54433}, {9819, 10106}, {9845, 34719}, {9860, 23698}, {9896, 9904}, {9897, 64189}, {9911, 21312}, {9948, 14646}, {10085, 58808}, {10124, 50807}, {10167, 18398}, {10171, 10303}, {10222, 62143}, {10246, 62131}, {10247, 62142}, {10283, 62126}, {10310, 37411}, {10389, 10404}, {10394, 12432}, {10431, 31424}, {10434, 37425}, {10574, 31757}, {10595, 51705}, {10724, 37718}, {10726, 14690}, {10789, 12203}, {10826, 17613}, {10857, 64001}, {10882, 37331}, {10895, 51790}, {10896, 31231}, {10912, 34716}, {10980, 63999}, {11106, 59412}, {11112, 31435}, {11260, 34620}, {11278, 61288}, {11362, 28172}, {11372, 20420}, {11413, 49553}, {11496, 15931}, {11523, 17768}, {12047, 30282}, {12053, 13462}, {12085, 15177}, {12103, 22791}, {12111, 31737}, {12119, 13253}, {12261, 38788}, {12263, 22676}, {12514, 59355}, {12526, 44447}, {12579, 39586}, {12635, 28534}, {12645, 28208}, {12653, 64145}, {12705, 37468}, {12717, 29291}, {12778, 34584}, {13442, 24342}, {13464, 30392}, {13528, 52851}, {13607, 46333}, {13893, 23251}, {13911, 42272}, {13912, 23249}, {13947, 23261}, {13971, 42637}, {13973, 42271}, {13975, 23259}, {14100, 37544}, {14217, 38761}, {14664, 44984}, {14872, 15104}, {14942, 44760}, {14986, 51783}, {15015, 24466}, {15017, 34474}, {15022, 31253}, {15072, 31732}, {15178, 62134}, {15305, 31752}, {15484, 31430}, {15640, 34648}, {15680, 19860}, {15684, 50821}, {15685, 28204}, {15687, 50826}, {15689, 51709}, {15691, 50820}, {15692, 50802}, {15697, 51110}, {16116, 16143}, {16117, 32613}, {16118, 33557}, {16132, 37533}, {16159, 31651}, {16173, 38759}, {16200, 28216}, {16208, 26332}, {16239, 61266}, {16371, 25522}, {16475, 44882}, {17502, 18493}, {17529, 42356}, {17554, 38204}, {17605, 63756}, {17606, 51792}, {18357, 62041}, {18513, 37437}, {18525, 28168}, {18527, 37545}, {18990, 31393}, {18991, 42258}, {18992, 42259}, {19065, 42413}, {19066, 42414}, {19645, 53591}, {19854, 37434}, {19861, 37256}, {19877, 50689}, {19878, 61820}, {19883, 50816}, {20007, 63975}, {20067, 36846}, {20077, 49495}, {20127, 33535}, {20292, 62829}, {21627, 34610}, {23512, 37603}, {23536, 62875}, {23708, 59319}, {24178, 60846}, {24309, 37399}, {24467, 24468}, {24851, 37552}, {24914, 63207}, {24987, 31295}, {25440, 36002}, {28082, 63583}, {28186, 61245}, {28190, 61246}, {28212, 37727}, {28224, 62156}, {28609, 34626}, {28850, 64184}, {29012, 39885}, {29024, 61087}, {29054, 49532}, {29598, 37416}, {30323, 36975}, {30343, 40270}, {31151, 52858}, {31158, 51698}, {31399, 62021}, {31441, 39590}, {31447, 62008}, {31658, 41872}, {31728, 64051}, {31789, 37560}, {31837, 61705}, {33179, 62140}, {33923, 38034}, {34379, 61044}, {34611, 62832}, {34627, 62165}, {34718, 62163}, {34747, 62153}, {34823, 45281}, {35004, 54145}, {35774, 42266}, {35775, 42267}, {37328, 63968}, {37400, 61124}, {37422, 52680}, {37524, 64128}, {37529, 48897}, {37531, 50528}, {37553, 49745}, {37569, 41854}, {37624, 62137}, {37692, 59325}, {37698, 48916}, {37705, 62164}, {37826, 49178}, {38022, 62101}, {38023, 50971}, {38028, 44245}, {38029, 48892}, {38042, 62026}, {38047, 51163}, {38066, 62046}, {38068, 41099}, {38074, 62049}, {38076, 62007}, {38083, 61993}, {38112, 62047}, {38220, 38747}, {38314, 50815}, {38454, 41863}, {39531, 52846}, {40663, 41348}, {41339, 64055}, {41430, 61109}, {42263, 49227}, {42264, 49226}, {42275, 49602}, {42276, 49601}, {43151, 59385}, {43174, 49135}, {43577, 43830}, {44682, 61269}, {44841, 52783}, {44903, 50831}, {46264, 64084}, {46853, 61272}, {46933, 50690}, {46934, 62102}, {47273, 62493}, {47357, 51723}, {47745, 50810}, {48482, 52027}, {48881, 64085}, {49132, 54287}, {49134, 61256}, {49719, 63135}, {50190, 58567}, {50419, 59311}, {50796, 62042}, {50799, 62015}, {50803, 62005}, {50806, 62088}, {50824, 62139}, {50825, 61978}, {50829, 50873}, {50862, 53620}, {50864, 62166}, {50869, 61985}, {51069, 62030}, {51071, 62145}, {51076, 61927}, {51084, 62068}, {51086, 61778}, {51088, 61883}, {51103, 62132}, {51109, 62099}, {51119, 61806}, {52026, 64119}, {52653, 56999}, {53057, 64124}, {54051, 54227}, {57278, 59323}, {57282, 63282}, {58188, 58215}, {58206, 61248}, {58219, 62075}, {58834, 64144}, {59388, 62171}, {59418, 63973}, {59503, 61250}, {61258, 62038}, {61262, 62006}, {61267, 61853}, {61270, 62062}, {61274, 62113}, {61275, 62121}, {61276, 62123}, {61524, 62036}, {62858, 63984}, {63138, 64087}, {63310, 63386}

X(64005) = midpoint of X(i) and X(j) for these {i,j}: {8, 5059}, {3529, 6361}, {12702, 17800}, {18525, 49137}, {34627, 62165}, {34632, 62160}, {34718, 62163}, {37705, 62164}, {50810, 62161}, {50864, 62166}
X(64005) = reflection of X(i) in X(j) for these {i,j}: {1, 20}, {2, 34638}, {4, 31730}, {8, 5493}, {382, 3579}, {962, 4297}, {3062, 5759}, {3146, 10}, {3543, 50808}, {3586, 10860}, {3632, 7991}, {3655, 19710}, {3656, 15686}, {3901, 15071}, {4312, 2951}, {4677, 34632}, {5073, 18480}, {5531, 13199}, {5691, 40}, {5693, 37585}, {5881, 12702}, {5895, 40660}, {5904, 7957}, {6253, 31777}, {6264, 38753}, {7982, 18481}, {7991, 6361}, {7992, 64190}, {7993, 12248}, {9589, 1}, {9812, 59420}, {9897, 64189}, {10724, 46684}, {10726, 14690}, {11531, 944}, {12111, 31737}, {12653, 64145}, {12688, 31793}, {12699, 550}, {13253, 12119}, {14217, 38761}, {15640, 34648}, {15684, 50821}, {16118, 33557}, {16159, 31651}, {18481, 15704}, {22791, 12103}, {28609, 34626}, {31162, 3534}, {33535, 20127}, {33703, 31673}, {34628, 11001}, {34773, 62144}, {34789, 24466}, {41869, 3}, {44984, 14664}, {48661, 1385}, {49136, 33697}, {50811, 15681}, {50824, 62139}, {50865, 376}, {51093, 34628}, {51118, 12512}, {52835, 11495}, {52851, 13528}, {52860, 10310}, {58245, 145}, {62036, 61524}, {62041, 18357}, {62042, 50796}, {62048, 50862}, {64000, 31799}, {64051, 31728}, {64084, 46264}, {64085, 48881}
X(64005) = anticomplement of X(51118)
X(64005) = X(i)-Dao conjugate of X(j) for these {i, j}: {51118, 51118}
X(64005) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56146, 1}
X(64005) = pole of line {4802, 44408} with respect to the circumcircle
X(64005) = pole of line {514, 39547} with respect to the Conway circle
X(64005) = pole of line {28155, 48407} with respect to the excircles-radical circle
X(64005) = pole of line {514, 39540} with respect to the incircle
X(64005) = pole of line {44432, 48174} with respect to the orthoptic circle of the Steiner Inellipse
X(64005) = pole of line {354, 50443} with respect to the Feuerbach hyperbola
X(64005) = pole of line {514, 44409} with respect to the Suppa-Cucoanes circle
X(64005) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {8, 5059, 36154}
X(64005) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1443), X(7285)}}, {{A, B, C, X(1458), X(44760)}}, {{A, B, C, X(9589), X(14942)}}, {{A, B, C, X(56382), X(60243)}}
X(64005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1770, 4312}, {1, 4292, 4355}, {1, 516, 9589}, {2, 10248, 12571}, {2, 12512, 16192}, {3, 1699, 3624}, {3, 22793, 8227}, {3, 28146, 41869}, {3, 41869, 1699}, {4, 165, 1698}, {4, 31730, 165}, {4, 6684, 7989}, {8, 5059, 28164}, {8, 5493, 63468}, {10, 28158, 3146}, {10, 9778, 63469}, {20, 962, 4297}, {30, 31777, 6253}, {30, 31799, 64000}, {30, 40, 5691}, {40, 1709, 191}, {40, 5691, 3679}, {40, 7701, 26921}, {55, 9579, 5290}, {56, 9580, 51785}, {145, 28228, 58245}, {165, 7989, 6684}, {376, 50865, 25055}, {376, 946, 7987}, {382, 3579, 5587}, {515, 6361, 7991}, {515, 64190, 7992}, {516, 4297, 962}, {550, 12699, 3576}, {550, 28178, 12699}, {631, 18483, 7988}, {944, 28194, 11531}, {950, 3474, 3339}, {1125, 3522, 58221}, {1125, 59420, 3522}, {1385, 28202, 48661}, {1385, 48661, 31162}, {1448, 4319, 1}, {1478, 61763, 51784}, {1836, 15338, 3601}, {3522, 9812, 1125}, {3523, 3817, 34595}, {3529, 6361, 515}, {3534, 48661, 1385}, {3576, 12699, 11522}, {3579, 28154, 382}, {3579, 5587, 9588}, {3585, 59316, 31434}, {3627, 26446, 18492}, {3634, 3832, 61264}, {3832, 64108, 3634}, {5119, 10483, 9613}, {5475, 31422, 31428}, {5657, 31673, 37714}, {5657, 33703, 31673}, {5790, 49136, 33697}, {6253, 34630, 31777}, {7987, 50865, 946}, {8227, 41869, 22793}, {9779, 15717, 19862}, {10310, 37411, 44425}, {10404, 63273, 10389}, {11001, 28194, 34628}, {11246, 11518, 5586}, {11495, 52835, 38052}, {11496, 37426, 15931}, {11531, 34628, 944}, {12512, 51118, 2}, {12571, 51118, 10248}, {12701, 15326, 1420}, {12702, 17800, 28160}, {12702, 28160, 5881}, {12943, 37568, 9578}, {15681, 28198, 50811}, {15704, 28174, 18481}, {18481, 28174, 7982}, {18493, 62100, 17502}, {18525, 49137, 28168}, {19883, 50816, 62063}, {24466, 34789, 15015}, {28150, 31730, 4}, {28194, 34628, 51093}, {28216, 62144, 34773}, {34618, 64000, 31799}, {34638, 51118, 12512}, {37022, 64077, 36}, {38314, 62129, 50815}, {44447, 57287, 12526}, {53620, 62048, 50862}

X(64006) = ORTHOLOGY CENTER OF THESE TRIANGLES: HUTSON INTOUCH AND X(1)-CROSSPEDAL-OF-X(75)

Barycentrics    a^2*(-2*a*b*c*(b+c)+a^2*(b^2+c^2)-(b^2+c^2)^2) : :
X(64006) = -5*X[25917]+4*X[63978]

X(64006) lies on these lines: {1, 256}, {2, 23638}, {8, 30092}, {10, 50580}, {11, 48888}, {12, 24220}, {35, 48929}, {36, 48886}, {37, 8679}, {38, 18210}, {39, 21760}, {42, 3917}, {43, 3819}, {51, 3720}, {55, 103}, {56, 573}, {63, 40966}, {65, 3664}, {69, 35628}, {72, 34379}, {75, 35104}, {181, 940}, {182, 20958}, {226, 21334}, {373, 20962}, {388, 10446}, {394, 54312}, {495, 48934}, {497, 48878}, {516, 3057}, {517, 50307}, {518, 3688}, {674, 49478}, {692, 4265}, {750, 51377}, {756, 61640}, {899, 5650}, {960, 4416}, {968, 26892}, {970, 37607}, {971, 11997}, {984, 2810}, {986, 17114}, {995, 50592}, {999, 48875}, {1001, 3271}, {1125, 50594}, {1193, 4263}, {1197, 3787}, {1201, 23659}, {1216, 37698}, {1350, 37580}, {1357, 17595}, {1365, 3782}, {1401, 3666}, {1402, 22097}, {1458, 2269}, {1463, 3663}, {1468, 22076}, {1478, 48902}, {1479, 48938}, {1697, 1742}, {1993, 20959}, {2092, 2274}, {2175, 36740}, {2292, 23154}, {2356, 12294}, {2646, 40944}, {2841, 17461}, {2876, 3242}, {2979, 17018}, {3030, 4413}, {3060, 29814}, {3098, 37576}, {3240, 7998}, {3295, 48908}, {3585, 48940}, {3601, 50658}, {3616, 63498}, {3622, 63523}, {3690, 32912}, {3736, 56837}, {3743, 23156}, {3750, 7186}, {3751, 3781}, {3775, 26012}, {3784, 17594}, {3786, 33297}, {3792, 4260}, {3794, 29839}, {3869, 17364}, {3874, 49564}, {3875, 54338}, {3878, 17770}, {3883, 9025}, {3931, 11573}, {3937, 4414}, {4014, 24248}, {4259, 52020}, {4271, 20470}, {4293, 48918}, {4334, 37555}, {4517, 5223}, {4553, 49524}, {4666, 63513}, {5052, 23660}, {5188, 18758}, {5220, 7064}, {5283, 23630}, {5542, 20358}, {5691, 10862}, {5697, 29309}, {5712, 10473}, {5718, 50362}, {5784, 40965}, {5919, 29353}, {5943, 26102}, {6007, 49470}, {6018, 47006}, {6688, 25502}, {7066, 22132}, {7143, 15832}, {7295, 47038}, {9026, 49515}, {9037, 15569}, {9052, 49490}, {9309, 52653}, {9310, 51436}, {9564, 14829}, {9957, 15310}, {10582, 63511}, {11793, 37699}, {12053, 45305}, {13405, 20359}, {14839, 24282}, {15082, 62711}, {15489, 37608}, {15644, 37529}, {16980, 59305}, {17365, 20718}, {17778, 35614}, {17794, 30547}, {18178, 25466}, {18671, 60586}, {19765, 50646}, {20036, 50577}, {20460, 63571}, {20961, 21969}, {20967, 25941}, {23155, 28606}, {23841, 50578}, {25306, 29843}, {25385, 38484}, {25917, 63978}, {26098, 35645}, {26893, 62819}, {27846, 28403}, {29661, 61643}, {30778, 51407}, {35633, 50623}, {37492, 60722}, {37568, 41430}, {37633, 56878}, {40419, 56154}, {40952, 62821}, {41228, 52562}, {43650, 61357}, {47021, 59807}, {50593, 58469}, {50597, 59301}

X(64006) = midpoint of X(i) and X(j) for these {i,j}: {3057, 49537}, {3869, 17364}
X(64006) = reflection of X(i) in X(j) for these {i,j}: {8, 64007}, {65, 3664}, {4416, 960}, {21746, 1}
X(64006) = pole of line {512, 4378} with respect to the incircle
X(64006) = pole of line {1912, 45902} with respect to the Brocard inellipse
X(64006) = pole of line {3666, 4356} with respect to the Feuerbach hyperbola
X(64006) = pole of line {512, 21343} with respect to the Suppa-Cucoanes circle
X(64006) = pole of line {28366, 30097} with respect to the dual conic of Yff parabola
X(64006) = intersection, other than A, B, C, of circumconics {{A, B, C, X(103), X(256)}}, {{A, B, C, X(1284), X(40419)}}, {{A, B, C, X(7015), X(36056)}}, {{A, B, C, X(21746), X(56154)}}
X(64006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50617, 58535}, {1, 511, 21746}, {1001, 37516, 3271}, {3057, 49537, 516}, {3057, 8581, 12721}, {3664, 29311, 65}, {3751, 3781, 20683}, {3792, 4649, 4260}, {20962, 30950, 373}

X(64007) = COMPLEMENT OF X(21746)

Barycentrics    a*(-2*b^2*c^2+a^2*(b^2+c^2)-a*(b^3+b^2*c+b*c^2+c^3)) : :
X(64007) = -3*X[2]+X[21746], -3*X[210]+X[4416], 3*X[3681]+X[17364], -5*X[17331]+9*X[63961], -3*X[49738]+2*X[58571]

X(64007) lies on circumconic {{A, B, C, X(9442), X(60320)}} and on these lines: {1, 28350}, {2, 21746}, {7, 56542}, {8, 30092}, {9, 1742}, {10, 511}, {37, 6007}, {39, 1740}, {43, 4263}, {51, 26037}, {72, 50307}, {75, 3688}, {86, 52020}, {101, 8424}, {141, 2876}, {190, 7064}, {210, 4416}, {219, 24264}, {256, 2664}, {261, 3110}, {319, 4111}, {513, 17332}, {516, 960}, {518, 3664}, {524, 22271}, {538, 21080}, {573, 1376}, {594, 4553}, {674, 3739}, {730, 59565}, {894, 20683}, {899, 23659}, {936, 6210}, {958, 991}, {978, 50616}, {993, 48929}, {995, 50620}, {997, 31394}, {1010, 10822}, {1015, 24575}, {1045, 1500}, {1086, 56537}, {1125, 39543}, {1329, 48888}, {1654, 3888}, {1958, 37586}, {1959, 21804}, {2223, 28287}, {2234, 21035}, {2388, 25124}, {2550, 10446}, {2551, 48878}, {2807, 3040}, {2808, 59620}, {2810, 49457}, {2886, 24220}, {3056, 4384}, {3271, 17277}, {3294, 45705}, {3452, 45305}, {3661, 25279}, {3678, 17770}, {3681, 17364}, {3686, 9025}, {3690, 4418}, {3696, 35104}, {3729, 4517}, {3740, 29353}, {3741, 3819}, {3779, 10436}, {3781, 50314}, {3786, 4645}, {3789, 17272}, {3878, 29309}, {3917, 31330}, {3963, 53338}, {4014, 6646}, {4260, 50302}, {4443, 17053}, {4447, 21061}, {4472, 22279}, {4640, 41430}, {4648, 35892}, {4667, 22312}, {4670, 22277}, {4871, 15082}, {4890, 16826}, {4972, 17202}, {5044, 15310}, {5650, 30942}, {5737, 50646}, {5745, 50658}, {5836, 29311}, {6682, 40649}, {7174, 54338}, {7227, 21865}, {9018, 17239}, {9024, 58379}, {9052, 24325}, {9054, 13476}, {9620, 33781}, {9708, 48908}, {9709, 48875}, {10176, 29349}, {10544, 16824}, {12782, 16571}, {13576, 17183}, {16569, 50613}, {17023, 61034}, {17065, 31198}, {17245, 57024}, {17331, 63961}, {17390, 44671}, {19858, 50597}, {20106, 25137}, {20358, 24199}, {20372, 25100}, {20544, 21246}, {21299, 30830}, {21320, 29382}, {21369, 25061}, {22299, 49734}, {22325, 49732}, {23638, 59296}, {25108, 62398}, {25120, 27076}, {25144, 29604}, {25440, 48886}, {26806, 62872}, {31419, 48934}, {32932, 40966}, {34379, 34790}, {40099, 61421}, {41276, 64170}, {41350, 43059}, {49738, 58571}, {50577, 59295}, {58679, 63977}

X(64007) = midpoint of X(i) and X(j) for these {i,j}: {8, 64006}, {72, 50307}, {75, 3688}, {3888, 20670}, {4416, 49537}
X(64007) = reflection of X(i) in X(j) for these {i,j}: {3686, 58655}, {17049, 3739}, {17332, 40607}, {39543, 1125}, {63977, 58679}
X(64007) = complement of X(21746)
X(64007) = X(i)-complementary conjugate of X(j) for these {i, j}: {3449, 37}, {40419, 10}, {63148, 142}, {63188, 1}
X(64007) = pole of line {512, 625} with respect to the Spieker circle
X(64007) = pole of line {52614, 57056} with respect to the Steiner inellipse
X(64007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 59562, 44418}, {75, 3688, 14839}, {141, 23305, 17047}, {256, 2664, 21796}, {513, 40607, 17332}, {674, 3739, 17049}, {960, 15587, 18252}, {9025, 58655, 3686}

X(64008) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(1)-CROSSPEDAL-OF-X(80)

Barycentrics    a^7-a^6*(b+c)+2*(b-c)^4*(b+c)^3+a^5*(-4*b^2+b*c-4*c^2)-a*(b^2-c^2)^2*(2*b^2-7*b*c+2*c^2)+4*a^4*(b^3+b^2*c+b*c^2+c^3)-a^2*(b-c)^2*(5*b^3+11*b^2*c+11*b*c^2+5*c^3)+a^3*(5*b^4-8*b^3*c-2*b^2*c^2-8*b*c^3+5*c^4) : :
X(64008) = -6*X[2]+X[104], 4*X[3]+X[10728], X[4]+4*X[3035], 4*X[5]+X[100], X[8]+4*X[11729], 4*X[10]+X[10698], -X[20]+6*X[38760], -X[80]+6*X[10175], 4*X[140]+X[10742], 4*X[141]+X[10759], -X[149]+11*X[5056], 2*X[214]+3*X[5587] and many others

X(64008) lies on circumconic {{A, B, C, X(3262), X(6713)}} and on these lines: {2, 104}, {3, 10728}, {4, 3035}, {5, 100}, {8, 11729}, {10, 10698}, {11, 1058}, {20, 38760}, {30, 38762}, {80, 10175}, {140, 10742}, {141, 10759}, {149, 5056}, {214, 5587}, {373, 58508}, {376, 52836}, {381, 10724}, {474, 18861}, {485, 19112}, {486, 19113}, {498, 6975}, {515, 31263}, {517, 64141}, {528, 5071}, {547, 1484}, {549, 38753}, {551, 50907}, {569, 3045}, {590, 19082}, {615, 19081}, {631, 2829}, {944, 34123}, {946, 64136}, {952, 1656}, {1006, 64188}, {1125, 12751}, {1145, 5603}, {1156, 38108}, {1317, 59388}, {1320, 5886}, {1329, 6949}, {1387, 31479}, {1537, 5328}, {1587, 13991}, {1588, 13922}, {1698, 2800}, {1768, 38133}, {2771, 15059}, {2783, 14061}, {2787, 64089}, {2801, 20195}, {2802, 8227}, {2828, 31257}, {2932, 6913}, {3060, 58522}, {3086, 10956}, {3091, 5840}, {3523, 38761}, {3524, 38759}, {3525, 12248}, {3526, 38602}, {3530, 38754}, {3544, 35023}, {3545, 6174}, {3560, 17100}, {3576, 58453}, {3614, 6901}, {3624, 11715}, {3628, 11698}, {3634, 21635}, {3679, 25485}, {3681, 58674}, {3740, 58613}, {3742, 58687}, {3814, 6905}, {3817, 14217}, {3819, 58543}, {3825, 64173}, {3828, 50908}, {3832, 64186}, {3851, 22938}, {3855, 59390}, {3873, 58604}, {4193, 11491}, {4413, 12332}, {4996, 6911}, {5054, 38756}, {5055, 10707}, {5067, 6667}, {5068, 10993}, {5070, 12773}, {5072, 38141}, {5079, 51517}, {5087, 48363}, {5094, 12138}, {5154, 11499}, {5219, 12736}, {5284, 59382}, {5432, 6965}, {5433, 12763}, {5541, 7988}, {5550, 38032}, {5552, 6981}, {5562, 58504}, {5660, 10172}, {5705, 46694}, {5714, 24465}, {5790, 12531}, {5817, 10427}, {5848, 40330}, {5854, 10595}, {5901, 64140}, {6068, 59386}, {6154, 61921}, {6246, 7989}, {6264, 32557}, {6265, 7504}, {6326, 6702}, {6594, 38150}, {6684, 34789}, {6825, 32554}, {6829, 8068}, {6830, 64154}, {6834, 64111}, {6850, 55297}, {6920, 10058}, {6940, 48695}, {6941, 12775}, {6946, 7951}, {6951, 12761}, {6959, 11681}, {6968, 59572}, {6969, 35514}, {6983, 10588}, {7173, 13274}, {7484, 9913}, {7486, 10587}, {7489, 38722}, {7509, 54065}, {7704, 63130}, {7705, 45770}, {7741, 10087}, {7808, 12199}, {7866, 38646}, {7914, 12499}, {8252, 48701}, {8253, 48700}, {8674, 64101}, {9306, 58056}, {9624, 64137}, {9940, 17661}, {10109, 61601}, {10165, 64145}, {10171, 21630}, {10516, 51157}, {10598, 59591}, {10755, 14561}, {10767, 36518}, {10768, 36519}, {10769, 23514}, {10775, 36520}, {10778, 23515}, {11230, 12737}, {11231, 12515}, {11571, 20117}, {12119, 19925}, {12245, 64192}, {12247, 34122}, {12611, 26446}, {12739, 17606}, {12752, 15184}, {12762, 24953}, {12767, 19876}, {12776, 26363}, {13226, 50726}, {13253, 19875}, {13271, 64123}, {13464, 64056}, {13913, 32785}, {13977, 32786}, {14450, 61530}, {14639, 53729}, {14644, 53743}, {14853, 51007}, {14872, 58591}, {15022, 20095}, {15558, 31434}, {16239, 61605}, {17566, 37821}, {17619, 21740}, {17660, 58631}, {19914, 38042}, {20418, 61886}, {30852, 64139}, {31262, 31399}, {31423, 46684}, {31659, 37162}, {33812, 38155}, {37071, 38643}, {38021, 50841}, {38072, 51158}, {38074, 50843}, {38076, 50844}, {38077, 61932}, {38084, 61908}, {38119, 63119}, {38128, 46933}, {38182, 62354}, {38636, 61970}, {38637, 61855}, {42262, 48714}, {42265, 48715}, {45310, 61899}, {47034, 58449}, {49176, 59419}, {51529, 55857}, {53055, 61017}, {55856, 61566}, {58666, 61686}, {59376, 61895}, {63344, 63346}

X(64008) = midpoint of X(i) and X(j) for these {i,j}: {1698, 15017}
X(64008) = reflection of X(i) in X(j) for these {i,j}: {631, 31235}, {31272, 1656}
X(64008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 153, 6713}, {4, 3035, 34474}, {5, 100, 59391}, {5, 61562, 10738}, {104, 119, 10711}, {119, 58421, 2}, {119, 6713, 153}, {140, 10742, 38693}, {149, 5056, 23513}, {153, 6713, 104}, {381, 33814, 10724}, {952, 1656, 31272}, {1698, 15017, 2800}, {2829, 31235, 631}, {3090, 20400, 38665}, {3525, 12248, 21154}, {3526, 38755, 38602}, {3628, 11698, 57298}, {5055, 12331, 60759}, {5072, 48680, 38141}, {5541, 7988, 16174}, {6667, 38758, 37725}, {7989, 15015, 6246}, {10738, 38752, 61562}, {10738, 61562, 100}, {11698, 57298, 38669}, {12331, 60759, 10707}, {12611, 26446, 64189}, {21154, 38757, 12248}

X(64009) = ANTICOMPLEMENT OF X(153)

Barycentrics    3*a^7-3*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-5*b^2+17*b*c-5*c^2)+a*(b^2-c^2)^2*(b^2-7*b*c+c^2)-a^2*(b-c)^2*(b^3-9*b^2*c-9*b*c^2+c^3)+a^4*(5*b^3-9*b^2*c-9*b*c^2+5*c^3)+a^3*(b^4-10*b^3*c+22*b^2*c^2-10*b*c^3+c^4) : :
X(64009) = -3*X[2]+4*X[104], -3*X[4]+4*X[1484], -4*X[100]+5*X[3522], -3*X[376]+2*X[12331], -5*X[631]+4*X[11698], -5*X[1656]+4*X[61605], -16*X[3035]+17*X[61820], -7*X[3090]+6*X[38755], -5*X[3091]+4*X[10742], -3*X[3241]+2*X[13253], -7*X[3523]+8*X[38602], -9*X[3524]+8*X[61562] and many others

X(64009) lies on these lines: {1, 9809}, {2, 104}, {4, 1484}, {8, 1768}, {11, 3600}, {20, 952}, {23, 9913}, {80, 4293}, {100, 3522}, {144, 2801}, {145, 2800}, {149, 2829}, {193, 48692}, {376, 12331}, {388, 63270}, {390, 1317}, {452, 13257}, {515, 3218}, {516, 7993}, {519, 12767}, {528, 15683}, {631, 11698}, {944, 2771}, {962, 6264}, {1320, 10307}, {1587, 35856}, {1588, 35857}, {1656, 61605}, {2096, 17654}, {2783, 20094}, {2787, 5984}, {2802, 20070}, {2826, 20097}, {2827, 20098}, {2828, 31293}, {2830, 20099}, {2932, 3421}, {2950, 12648}, {3035, 61820}, {3090, 38755}, {3091, 10742}, {3241, 13253}, {3474, 17636}, {3476, 17638}, {3486, 17660}, {3523, 38602}, {3524, 61562}, {3530, 38637}, {3543, 10738}, {3552, 38657}, {3616, 21635}, {3617, 12751}, {3622, 11715}, {3623, 10698}, {3830, 61601}, {3839, 22799}, {4294, 7972}, {4297, 4420}, {4299, 9897}, {4313, 37736}, {4317, 37718}, {5056, 57298}, {5059, 5840}, {5068, 20418}, {5129, 34123}, {5261, 12763}, {5274, 12764}, {5434, 42356}, {5541, 9778}, {5550, 15017}, {5603, 16128}, {5640, 58543}, {5731, 6326}, {6154, 62125}, {6174, 15705}, {6839, 18519}, {6872, 64191}, {6888, 26321}, {6894, 18990}, {6904, 13226}, {6906, 32213}, {6930, 19907}, {6942, 35451}, {6948, 19914}, {6960, 32153}, {6995, 12138}, {7080, 17100}, {7486, 61580}, {7585, 48700}, {7586, 48701}, {7967, 48667}, {8674, 64102}, {9024, 61044}, {9541, 35882}, {9812, 21630}, {9952, 50890}, {10074, 14986}, {10265, 59387}, {10303, 38752}, {10304, 33814}, {10465, 13244}, {10528, 48695}, {10529, 48694}, {10707, 50687}, {10728, 17578}, {10759, 51170}, {10993, 62124}, {11114, 30283}, {11219, 54448}, {12087, 13222}, {12114, 20060}, {12246, 36977}, {12247, 37002}, {12515, 59417}, {12531, 17784}, {12667, 22775}, {12690, 50696}, {12736, 21454}, {15022, 31272}, {15558, 60934}, {15717, 37725}, {17580, 34122}, {18861, 37307}, {19081, 63016}, {19082, 63015}, {20007, 46685}, {20050, 64076}, {20075, 52116}, {20400, 61848}, {21154, 61834}, {21734, 34474}, {22560, 34610}, {22938, 38631}, {24466, 62120}, {26792, 37611}, {32454, 44434}, {32965, 38646}, {33703, 48680}, {34126, 46936}, {34628, 50838}, {37421, 54441}, {37781, 51565}, {38133, 46931}, {38629, 58195}, {38636, 46853}, {38665, 38761}, {38754, 51525}, {38760, 61804}, {41819, 63346}, {43511, 48715}, {43512, 48714}, {45310, 61930}, {48684, 62987}, {48685, 62986}, {49176, 64079}, {50689, 59391}, {50690, 64186}, {56880, 63983}, {58613, 64149}, {58687, 63961}, {59377, 61944}, {62837, 64000}

X(64009) = midpoint of X(i) and X(j) for these {i,j}: {48692, 48693}
X(64009) = reflection of X(i) in X(j) for these {i,j}: {4, 12773}, {8, 1768}, {20, 12248}, {149, 38669}, {153, 104}, {962, 6264}, {3146, 149}, {5531, 4297}, {6224, 64145}, {9802, 7993}, {9809, 1}, {10728, 37726}, {10742, 51529}, {12667, 22775}, {13199, 38753}, {20085, 9803}, {20095, 20}, {22938, 38631}, {33703, 48680}, {38665, 38761}, {38756, 1484}
X(64009) = anticomplement of X(153)
X(64009) = X(i)-Dao conjugate of X(j) for these {i, j}: {153, 153}
X(64009) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57769, 2}
X(64009) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34182, 8}, {57769, 6327}
X(64009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 952, 20095}, {104, 10711, 6713}, {104, 153, 2}, {149, 2829, 3146}, {515, 9803, 20085}, {516, 7993, 9802}, {952, 38753, 13199}, {1484, 38756, 4}, {2801, 64145, 6224}, {2829, 38669, 149}, {12248, 13199, 38753}, {12773, 38756, 1484}, {13199, 38753, 20}, {38755, 61566, 3090}

X(64010) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-CONWAY AND X(1)-CROSSPEDAL-OF-X(81)

Barycentrics    a^3+a*b*c-a^2*(b+c)+2*b*c*(b+c) : :
X(64010) = -4*X[4425]+5*X[31247]

X(64010) lies on these lines: {1, 39711}, {2, 3712}, {8, 30}, {10, 32936}, {21, 4647}, {31, 49474}, {35, 42031}, {36, 4717}, {43, 41242}, {55, 28605}, {63, 2941}, {75, 1621}, {79, 21081}, {81, 740}, {86, 27804}, {88, 3840}, {98, 100}, {141, 33102}, {171, 4365}, {190, 4651}, {210, 4756}, {306, 20292}, {310, 874}, {333, 4427}, {345, 33108}, {354, 49485}, {516, 33075}, {519, 32940}, {528, 33090}, {536, 3920}, {594, 33083}, {612, 42044}, {614, 50126}, {726, 32945}, {758, 4720}, {846, 5235}, {893, 52893}, {894, 3896}, {896, 4921}, {1010, 64071}, {1043, 17164}, {1086, 33173}, {1211, 28530}, {1255, 3993}, {1278, 3891}, {1376, 4671}, {1738, 33157}, {1836, 33077}, {1962, 5333}, {2308, 4716}, {2321, 4987}, {2475, 3704}, {2550, 32862}, {2796, 4683}, {2886, 33168}, {2895, 4046}, {2975, 4221}, {3120, 30831}, {3175, 5297}, {3210, 24552}, {3218, 3706}, {3219, 3696}, {3315, 24165}, {3434, 33089}, {3661, 32950}, {3681, 3729}, {3685, 4359}, {3687, 5057}, {3702, 5253}, {3703, 33110}, {3711, 4942}, {3720, 4693}, {3741, 32845}, {3743, 14005}, {3744, 4686}, {3745, 28484}, {3757, 4980}, {3773, 32948}, {3782, 33175}, {3838, 27757}, {3869, 20223}, {3870, 4659}, {3873, 3886}, {3875, 62807}, {3914, 32779}, {3923, 32860}, {3925, 32849}, {3938, 49493}, {3957, 49483}, {3967, 4767}, {3969, 4645}, {3980, 32915}, {3996, 17165}, {4011, 37687}, {4023, 26792}, {4030, 20095}, {4037, 37675}, {4061, 17781}, {4062, 33097}, {4065, 25526}, {4184, 4436}, {4234, 39766}, {4358, 9342}, {4361, 17127}, {4363, 17018}, {4425, 31247}, {4430, 49460}, {4431, 63134}, {4461, 11683}, {4641, 49468}, {4653, 46895}, {4673, 62837}, {4685, 32938}, {4702, 29817}, {4706, 17020}, {4709, 32864}, {4722, 50016}, {4918, 49734}, {4954, 31161}, {4966, 26842}, {4970, 32772}, {4972, 62392}, {5014, 29032}, {5047, 28612}, {5260, 7283}, {5263, 17147}, {5271, 62838}, {5295, 56288}, {5311, 49452}, {5739, 24280}, {5880, 32858}, {5988, 30760}, {5992, 31089}, {6057, 49732}, {6535, 33079}, {7191, 42051}, {7262, 50086}, {8013, 24697}, {9791, 41809}, {10327, 50107}, {10436, 62840}, {11246, 32863}, {11680, 17740}, {11681, 30444}, {14450, 41014}, {14923, 35659}, {15523, 24715}, {15674, 59592}, {16736, 58401}, {16948, 24850}, {17016, 50054}, {17019, 49462}, {17024, 48805}, {17135, 32939}, {17140, 62863}, {17143, 33764}, {17150, 17160}, {17151, 62834}, {17155, 32941}, {17156, 62795}, {17162, 41629}, {17281, 29679}, {17301, 29648}, {17495, 32942}, {17536, 28611}, {17593, 31241}, {17719, 48642}, {17764, 32947}, {17889, 33156}, {19796, 26230}, {19822, 64168}, {20056, 44367}, {20653, 24851}, {21949, 29873}, {23407, 32104}, {24248, 32782}, {24592, 56658}, {24594, 26103}, {24693, 29854}, {24723, 56810}, {24943, 33149}, {25507, 27811}, {26227, 42029}, {26241, 31130}, {26280, 42034}, {28522, 32928}, {28606, 50314}, {29113, 63139}, {29634, 50102}, {29641, 50105}, {29667, 50048}, {29815, 49453}, {29846, 48643}, {29874, 50103}, {31037, 44006}, {31301, 50277}, {31330, 32934}, {32777, 33131}, {32778, 33094}, {32783, 33145}, {32842, 63979}, {32848, 33109}, {32855, 33104}, {32857, 33081}, {32912, 49459}, {32917, 62226}, {32921, 62855}, {32923, 50117}, {32924, 49482}, {32930, 37680}, {33067, 49560}, {33084, 33098}, {33091, 34612}, {33129, 59692}, {33136, 33167}, {33139, 44416}, {33146, 33171}, {37595, 49461}, {37685, 49486}, {39962, 58467}, {41812, 58380}, {41817, 46896}, {41915, 52653}, {42058, 50088}, {48863, 54315}, {49469, 62821}, {50302, 62851}, {54309, 59596}, {56082, 63961}, {57280, 64184}

X(64010) = reflection of X(i) in X(j) for these {i,j}: {81, 4418}, {2895, 4046}, {4683, 21085}, {33100, 1211}
X(64010) = anticomplement of X(4854)
X(64010) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {38811, 7}, {38825, 2895}, {63191, 2893}
X(64010) = pole of line {48389, 53257} with respect to the circumcircle
X(64010) = pole of line {644, 4115} with respect to the Kiepert parabola
X(64010) = pole of line {48580, 57059} with respect to the Steiner circumellipse
X(64010) = pole of line {3873, 17393} with respect to the Wallace hyperbola
X(64010) = intersection, other than A, B, C, of circumconics {{A, B, C, X(98), X(10308)}}, {{A, B, C, X(1821), X(56947)}}
X(64010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3648, 49716}, {8, 63996, 11684}, {10, 32936, 33761}, {75, 32929, 1621}, {321, 32932, 100}, {740, 4418, 81}, {846, 21020, 5235}, {1043, 17164, 34195}, {1211, 28530, 33100}, {1962, 24342, 5333}, {2796, 21085, 4683}, {3120, 33160, 30831}, {3685, 4359, 5284}, {3729, 63131, 3681}, {3923, 32860, 32911}, {3980, 32915, 37633}, {3996, 17165, 62236}, {4046, 17768, 2895}, {4427, 17163, 333}, {4683, 21085, 31143}, {6057, 49732, 60459}, {17135, 32939, 62235}, {17155, 32941, 62814}, {21949, 50104, 29873}, {24165, 32943, 3315}, {24850, 27368, 16948}, {31330, 32934, 62796}, {33100, 46918, 1211}, {42051, 49484, 7191}

X(64011) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 107 AND X(1)-CROSSPEDAL-OF-X(100)

Barycentrics    5*a^4-3*a^3*(b+c)+a^2*(-4*b^2+5*b*c-4*c^2)-(b^2-c^2)^2+a*(3*b^3-b^2*c-b*c^2+3*c^3) : :
X(64011) = -X[149]+3*X[38314], -4*X[1387]+5*X[51105], -5*X[1698]+2*X[62616], -4*X[3035]+X[9897], -4*X[3036]+5*X[51066], -3*X[3524]+X[12247], -3*X[3545]+2*X[6246], -7*X[3624]+4*X[12019]

X(64011) lies on these lines: {1, 528}, {2, 80}, {8, 50841}, {10, 50844}, {11, 13384}, {30, 6265}, {36, 100}, {57, 1317}, {104, 15931}, {149, 38314}, {320, 4597}, {376, 2800}, {515, 5660}, {527, 4867}, {529, 41689}, {535, 4511}, {549, 952}, {551, 6175}, {662, 56950}, {678, 24864}, {758, 35596}, {900, 30580}, {1125, 50889}, {1145, 4677}, {1320, 5425}, {1385, 47033}, {1387, 51105}, {1537, 50865}, {1644, 10713}, {1698, 62616}, {2094, 11570}, {2098, 34707}, {2771, 28460}, {2801, 5692}, {2802, 3241}, {2829, 34628}, {2932, 4421}, {3035, 9897}, {3036, 51066}, {3058, 12740}, {3065, 17525}, {3244, 50894}, {3416, 51158}, {3476, 41553}, {3524, 12247}, {3534, 48667}, {3545, 6246}, {3582, 10073}, {3584, 10057}, {3624, 12019}, {3626, 50845}, {3632, 50842}, {3633, 13996}, {3636, 50892}, {3653, 62354}, {3654, 33814}, {3656, 14217}, {3751, 51008}, {3828, 59415}, {3830, 12611}, {3878, 37299}, {4293, 60984}, {4311, 41696}, {4315, 14151}, {4316, 28534}, {4370, 16554}, {4428, 63281}, {4643, 25690}, {4669, 12531}, {4745, 64141}, {4855, 37707}, {4870, 13273}, {5010, 51636}, {5054, 12619}, {5055, 12747}, {5064, 12137}, {5131, 5855}, {5249, 9963}, {5251, 60986}, {5258, 6986}, {5270, 13272}, {5289, 57006}, {5434, 12739}, {5443, 17577}, {5531, 64191}, {5563, 35979}, {5730, 34620}, {5840, 31162}, {5854, 34747}, {5882, 6940}, {5904, 34610}, {6154, 11034}, {6264, 18443}, {6326, 28459}, {6922, 37725}, {7208, 63054}, {7865, 12498}, {7982, 10993}, {8703, 12515}, {9024, 47356}, {9845, 41229}, {9881, 53729}, {10199, 37702}, {10246, 31140}, {10265, 50828}, {10269, 12331}, {10304, 46684}, {10385, 15558}, {10483, 56387}, {10698, 28194}, {10738, 51709}, {10742, 28208}, {10755, 51005}, {10769, 12258}, {10896, 51577}, {10950, 17564}, {11015, 34649}, {11113, 45764}, {11114, 30144}, {11237, 18976}, {11238, 12743}, {11571, 44663}, {11729, 38021}, {12690, 25525}, {12730, 30379}, {12732, 51097}, {12737, 34612}, {12738, 34606}, {12749, 45701}, {12750, 21842}, {12751, 22935}, {12767, 38759}, {13146, 49736}, {13199, 25485}, {13253, 24466}, {13462, 41556}, {13846, 49240}, {13847, 49241}, {14799, 17549}, {15228, 36005}, {15679, 51569}, {15699, 61553}, {15702, 38133}, {15703, 38182}, {15863, 53620}, {15933, 18240}, {17528, 34471}, {17647, 24926}, {18395, 34700}, {18857, 64140}, {19077, 32788}, {19078, 32787}, {19876, 34122}, {19883, 31272}, {19914, 50821}, {20095, 64137}, {20119, 51100}, {20400, 37714}, {20418, 30389}, {22836, 34605}, {25558, 60963}, {31525, 50921}, {33709, 51109}, {34123, 37718}, {34544, 36910}, {35597, 37230}, {37298, 37616}, {37430, 40257}, {37438, 37726}, {37727, 51525}, {38161, 61936}, {38197, 63109}, {38484, 48858}, {47043, 53739}, {47359, 51157}, {48694, 59320}, {49524, 51199}, {49732, 51112}, {50808, 64189}, {50910, 64136}, {50950, 51007}, {50952, 51198}, {51035, 51062}, {55929, 62838}, {56425, 62703}, {63343, 63365}

X(64011) = midpoint of X(i) and X(j) for these {i,j}: {2, 6224}, {100, 10031}, {3534, 48667}, {5541, 51093}, {6326, 50811}, {10609, 50843}, {12119, 50908}, {13996, 50846}, {36005, 62826}, {50842, 62617}, {50910, 64136}
X(64011) = reflection of X(i) in X(j) for these {i,j}: {1, 50843}, {2, 214}, {8, 50841}, {10, 50844}, {80, 2}, {104, 51705}, {1320, 51071}, {3065, 17525}, {3241, 11274}, {3416, 51158}, {3626, 50845}, {3632, 50842}, {3633, 50846}, {3654, 33814}, {3656, 19907}, {3679, 6174}, {3751, 51008}, {3830, 12611}, {4677, 1145}, {7972, 10031}, {9881, 53729}, {10031, 33337}, {10265, 50828}, {10707, 551}, {10738, 51709}, {10755, 51005}, {10769, 12258}, {11219, 3576}, {12515, 8703}, {12531, 4669}, {12737, 50824}, {14217, 3656}, {15228, 36005}, {15679, 51569}, {19914, 50821}, {20119, 51100}, {21630, 51103}, {26726, 51093}, {34789, 50908}, {37718, 34123}, {47359, 51157}, {49524, 51199}, {50865, 1537}, {50889, 1125}, {50890, 10}, {50891, 1}, {50892, 3636}, {50893, 8}, {50894, 3244}, {50908, 6265}, {50921, 31525}, {50950, 51007}, {50952, 51198}, {51035, 51062}, {51071, 33812}, {51093, 1317}, {60963, 25558}, {64145, 50811}, {64189, 50808}
X(64011) = pole of line {23884, 48571} with respect to the Steiner circumellipse
X(64011) = pole of line {1638, 23884} with respect to the Steiner inellipse
X(64011) = pole of line {2826, 39771} with respect to the Suppa-Cucoanes circle
X(64011) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {7424, 36005, 62826}
X(64011) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3254), X(24858)}}, {{A, B, C, X(34578), X(37222)}}
X(64011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34701, 34719}, {1, 528, 50891}, {30, 50908, 34789}, {30, 6265, 50908}, {80, 214, 64012}, {100, 10031, 519}, {100, 33337, 7972}, {100, 7972, 64056}, {214, 6224, 80}, {519, 33337, 10031}, {528, 50843, 1}, {551, 10707, 16173}, {952, 3576, 11219}, {952, 6174, 3679}, {1125, 50889, 59377}, {1317, 5541, 26726}, {1317, 9945, 5541}, {2802, 11274, 3241}, {3679, 15015, 6174}, {6154, 12735, 12653}, {10609, 50843, 528}, {12119, 50908, 30}, {38104, 58453, 2}

X(64012) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(1)-CROSSPEDAL-OF-X(100)

Barycentrics    3*a^4-a^3*(b+c)+a^2*(-4*b^2+3*b*c-4*c^2)+(b^2-c^2)^2+a*(b^3+b^2*c+b*c^2+c^3) : :
X(64012) = 3*X[1]+2*X[1145], -6*X[2]+X[80], 3*X[3]+2*X[12611], 4*X[5]+X[12119], 3*X[9]+2*X[25558], 4*X[10]+X[7972], 3*X[21]+2*X[51569], 3*X[36]+2*X[908], X[40]+4*X[11729], X[72]+4*X[58591], X[100]+4*X[1125], 2*X[119]+3*X[3576] and many others

X(64012) lies on circumconic {{A, B, C, X(320), X(6702)}} and on these lines: {1, 1145}, {2, 80}, {3, 12611}, {5, 12119}, {9, 25558}, {10, 7972}, {11, 3601}, {21, 51569}, {36, 908}, {40, 11729}, {72, 58591}, {100, 1125}, {104, 5251}, {119, 3576}, {140, 6265}, {142, 10090}, {149, 5550}, {153, 54445}, {165, 1537}, {373, 58501}, {404, 5443}, {442, 38410}, {515, 31263}, {517, 38762}, {519, 64141}, {528, 20195}, {549, 12515}, {551, 1320}, {590, 19078}, {615, 19077}, {631, 2800}, {632, 952}, {946, 34474}, {960, 11571}, {1001, 2932}, {1156, 38059}, {1317, 3679}, {1319, 51362}, {1385, 12751}, {1387, 5541}, {1420, 10956}, {1484, 3925}, {1699, 24466}, {1768, 21154}, {2771, 25917}, {2801, 18230}, {2802, 3616}, {2829, 7987}, {3036, 19875}, {3065, 15670}, {3090, 6246}, {3523, 46684}, {3525, 12247}, {3526, 12619}, {3555, 58663}, {3582, 5440}, {3612, 39692}, {3622, 64137}, {3632, 12735}, {3634, 33337}, {3681, 58698}, {3814, 4881}, {3817, 10724}, {3825, 5441}, {3828, 10031}, {3869, 5442}, {3873, 58625}, {3911, 4867}, {4187, 37616}, {4316, 5087}, {4413, 12331}, {4511, 6681}, {4647, 58397}, {4679, 16128}, {4855, 37720}, {4996, 31019}, {4999, 41689}, {5044, 17660}, {5054, 48667}, {5056, 38161}, {5070, 12747}, {5083, 5904}, {5086, 20107}, {5094, 12137}, {5131, 51409}, {5150, 17248}, {5218, 15558}, {5248, 17100}, {5253, 37731}, {5258, 6700}, {5259, 10058}, {5428, 47034}, {5432, 12740}, {5433, 12739}, {5438, 5533}, {5445, 17566}, {5531, 20418}, {5563, 27385}, {5587, 58421}, {5657, 25485}, {5692, 5744}, {5703, 18240}, {5794, 53616}, {5840, 8227}, {5886, 14217}, {5902, 64139}, {5903, 6921}, {6068, 59372}, {6264, 38032}, {6326, 6713}, {6594, 38053}, {6667, 10609}, {6675, 34600}, {6684, 10698}, {6789, 33115}, {6878, 12691}, {7280, 25681}, {7483, 45764}, {7484, 9912}, {7808, 12198}, {7914, 12498}, {7951, 35262}, {7991, 64192}, {8252, 49241}, {8253, 49240}, {8983, 19112}, {8988, 32785}, {9624, 64138}, {9780, 15863}, {9897, 34122}, {9963, 59377}, {10057, 17614}, {10073, 47033}, {10164, 64189}, {10176, 12532}, {10179, 17652}, {10200, 37571}, {10707, 19883}, {10711, 50828}, {10738, 11230}, {10742, 13624}, {10755, 38049}, {11231, 19914}, {11274, 50893}, {11813, 13587}, {12524, 37308}, {12690, 45310}, {12701, 63752}, {12729, 15184}, {12732, 38026}, {12737, 38028}, {12738, 24953}, {12749, 21842}, {12750, 26363}, {12763, 37605}, {12764, 37600}, {12775, 59326}, {12832, 31231}, {13199, 16174}, {13253, 64193}, {13462, 34690}, {13464, 64136}, {13922, 18992}, {13971, 19113}, {13976, 32786}, {13991, 18991}, {14151, 61016}, {14740, 27383}, {15178, 64140}, {15325, 51463}, {15931, 64188}, {15950, 17564}, {16126, 34753}, {16371, 18393}, {16475, 51007}, {17502, 38753}, {17661, 58567}, {17728, 36867}, {18481, 61580}, {19862, 31254}, {19872, 62616}, {19878, 59419}, {19907, 26446}, {20095, 32558}, {20119, 38204}, {20400, 30389}, {20586, 47742}, {21578, 31160}, {21616, 59319}, {21635, 38693}, {22935, 24299}, {22938, 61268}, {24926, 24982}, {24954, 38602}, {25440, 37735}, {25542, 46816}, {28628, 38063}, {30478, 46694}, {32109, 40878}, {34126, 62354}, {34719, 37704}, {36936, 61478}, {38023, 51158}, {38197, 63119}, {38213, 46933}, {38220, 53729}, {38314, 50841}, {38759, 58221}, {41012, 59325}, {44675, 48696}, {55856, 61553}, {58659, 61686}, {63344, 63365}

X(64012) = midpoint of X(i) and X(j) for these {i,j}: {7987, 15017}
X(64012) = reflection of X(i) in X(j) for these {i,j}: {1698, 31235}, {31272, 19862}
X(64012) = pole of line {23884, 30725} with respect to the Steiner inellipse
X(64012) = pole of line {2323, 37680} with respect to the dual conic of Yff parabola
X(64012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1145, 26726}, {2, 214, 80}, {2, 6224, 6702}, {10, 33812, 12531}, {80, 214, 64011}, {100, 1125, 16173}, {119, 3576, 64145}, {149, 5550, 32557}, {214, 58453, 2}, {214, 6702, 6224}, {952, 31235, 1698}, {1001, 2932, 63281}, {1145, 26726, 64056}, {1385, 38752, 12751}, {1387, 5541, 50891}, {1387, 6174, 5541}, {3035, 34123, 1}, {3525, 12247, 38133}, {3624, 15015, 11}, {3634, 33337, 59415}, {3814, 4881, 36975}, {5070, 12747, 38182}, {5087, 35271, 4316}, {5541, 25055, 1387}, {5886, 33814, 14217}, {6326, 6713, 11219}, {6667, 10609, 37718}, {7987, 15017, 2829}, {10090, 64154, 35204}, {11274, 53620, 50893}, {11729, 38760, 40}, {11813, 13587, 15228}, {12531, 33812, 7972}, {17566, 30144, 5445}, {19883, 50844, 10707}, {22935, 57298, 49176}, {38028, 61562, 12737}

X(64013) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND X(1)-CROSSPEDAL-OF-X(190)

Barycentrics    a*(a^5+a*b*(b-c)^2*c-a^4*(b+c)+a^2*(b-c)^2*(b+c)-2*b*(b-c)^2*c*(b+c)-a^3*(b^2-3*b*c+c^2)) : :

X(64013) lies on these lines: {1, 651}, {2, 35281}, {3, 16686}, {4, 595}, {9, 61086}, {11, 109}, {31, 1699}, {36, 3000}, {40, 9519}, {44, 517}, {55, 45885}, {56, 4014}, {58, 946}, {80, 23592}, {98, 727}, {100, 5400}, {101, 15507}, {102, 759}, {103, 105}, {104, 106}, {149, 1331}, {153, 24222}, {165, 748}, {171, 3817}, {212, 9580}, {238, 516}, {244, 1768}, {255, 9614}, {386, 11496}, {511, 49706}, {513, 37815}, {515, 40091}, {528, 3939}, {572, 31394}, {576, 1482}, {580, 12699}, {582, 48661}, {601, 8227}, {602, 41869}, {603, 50443}, {614, 1709}, {650, 2291}, {675, 20295}, {741, 29310}, {750, 7988}, {761, 2700}, {812, 56896}, {896, 5536}, {899, 5537}, {902, 44425}, {917, 59074}, {952, 24828}, {962, 1724}, {971, 1279}, {984, 60911}, {990, 7290}, {991, 1001}, {993, 24708}, {995, 1012}, {1054, 46684}, {1064, 4653}, {1086, 15251}, {1104, 9856}, {1146, 45282}, {1158, 24046}, {1411, 10703}, {1421, 7004}, {1456, 43044}, {1468, 11522}, {1471, 4312}, {1496, 51785}, {1497, 9612}, {1532, 17734}, {1647, 11219}, {1736, 4318}, {1742, 15485}, {1743, 43166}, {1750, 62875}, {1754, 9812}, {1771, 10591}, {1777, 3086}, {1836, 55086}, {1935, 12053}, {2006, 2342}, {2078, 2635}, {2170, 10697}, {2263, 15299}, {2340, 60885}, {2382, 29352}, {2718, 28233}, {2723, 59019}, {2725, 28848}, {2726, 31286}, {2807, 3271}, {2810, 36280}, {2835, 16560}, {2975, 4499}, {3052, 19541}, {3062, 16487}, {3072, 18483}, {3074, 10624}, {3091, 5264}, {3120, 34789}, {3242, 5779}, {3246, 15726}, {3315, 13243}, {3583, 56419}, {3646, 35658}, {3667, 24813}, {3685, 29016}, {3722, 5531}, {3744, 5927}, {3756, 13226}, {3757, 59637}, {3883, 12618}, {3915, 5691}, {3961, 15064}, {4257, 22753}, {4300, 5259}, {4301, 5247}, {4307, 38037}, {4432, 24294}, {4512, 25885}, {4644, 5603}, {4674, 64189}, {4675, 5886}, {4858, 24410}, {5219, 52428}, {5255, 19925}, {5263, 48888}, {5272, 64129}, {5732, 60846}, {5805, 64016}, {5853, 23693}, {6001, 30117}, {6127, 63281}, {6180, 42884}, {6210, 63968}, {6244, 37679}, {6264, 10700}, {6909, 49997}, {6913, 30116}, {7045, 62723}, {7221, 15430}, {7299, 12701}, {7681, 45939}, {7743, 52407}, {7956, 37646}, {7993, 17460}, {8226, 63979}, {8692, 11495}, {9440, 30331}, {9442, 61480}, {9779, 17126}, {9809, 33148}, {10085, 28011}, {10164, 17123}, {10171, 17122}, {10310, 17749}, {10571, 62333}, {10738, 45926}, {12608, 24160}, {12764, 52383}, {13257, 17724}, {14511, 61476}, {14665, 53900}, {14942, 43672}, {15071, 28082}, {15253, 38357}, {15626, 23404}, {15908, 24880}, {15955, 45776}, {16020, 63971}, {16469, 24644}, {16486, 30283}, {16610, 17613}, {16670, 62182}, {17365, 20330}, {17719, 21635}, {20999, 38389}, {21214, 63983}, {23703, 60782}, {23858, 61672}, {24159, 63962}, {24227, 37607}, {24695, 60895}, {24833, 53792}, {27627, 59326}, {28345, 52084}, {28476, 53892}, {28485, 53899}, {29309, 37510}, {29315, 36716}, {30223, 34036}, {31849, 38674}, {33536, 41230}, {33771, 37732}, {34862, 52541}, {35338, 64154}, {35514, 37650}, {37076, 52653}, {37570, 51118}, {37610, 59387}, {37817, 63992}, {38031, 50677}, {38390, 53279}, {38531, 38575}, {39531, 60685}, {41166, 43048}, {44675, 62789}, {45035, 58738}, {45305, 49482}, {45763, 50371}, {45946, 61732}, {48900, 50300}, {49515, 64198}, {53296, 53307}, {60718, 64155}, {63969, 63970}

X(64013) = midpoint of X(i) and X(j) for these {i,j}: {1, 9355}
X(64013) = reflection of X(i) in X(j) for these {i,j}: {1086, 15251}, {13329, 238}, {53298, 53302}
X(64013) = perspector of circumconic {{A, B, C, X(9503), X(37139)}}
X(64013) = pole of line {891, 53297} with respect to the circumcircle
X(64013) = pole of line {3887, 35636} with respect to the Conway circle
X(64013) = pole of line {3887, 11028} with respect to the incircle
X(64013) = pole of line {1647, 4475} with respect to the orthoptic circle of the Steiner Inellipse
X(64013) = pole of line {103, 1155} with respect to the Feuerbach hyperbola
X(64013) = pole of line {17191, 62756} with respect to the Stammler hyperbola
X(64013) = pole of line {3887, 18413} with respect to the Suppa-Cucoanes circle
X(64013) = pole of line {673, 909} with respect to the dual conic of Yff parabola
X(64013) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1, 1054, 5540}, {11, 3022, 3271}, {190, 14888, 15343}
X(64013) = intersection, other than A, B, C, of circumconics {{A, B, C, X(103), X(36086)}}, {{A, B, C, X(516), X(2254)}}, {{A, B, C, X(517), X(3960)}}, {{A, B, C, X(650), X(2801)}}, {{A, B, C, X(651), X(2717)}}, {{A, B, C, X(1156), X(46649)}}, {{A, B, C, X(1168), X(6185)}}, {{A, B, C, X(2316), X(52377)}}, {{A, B, C, X(7045), X(44858)}}, {{A, B, C, X(9357), X(51766)}}, {{A, B, C, X(9441), X(61480)}}, {{A, B, C, X(9442), X(61477)}}
X(64013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 51768, 2310}, {1, 651, 44858}, {1, 9355, 2801}, {104, 32486, 106}, {238, 516, 13329}, {513, 53302, 53298}, {651, 53055, 1}, {946, 3073, 58}, {1742, 15485, 52769}, {7290, 11372, 990}, {9812, 17127, 1754}, {30223, 34036, 62811}

X(64014) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-ARTZT AND X(2)-CROSSPEDAL-OF-X(4)

Barycentrics    13*a^6-7*a^4*(b^2+c^2)-5*(b^2-c^2)^2*(b^2+c^2)-a^2*(b^4+6*b^2*c^2+c^4) : :
X(64014) = -5*X[4]+8*X[575], -4*X[141]+5*X[15692], -3*X[165]+2*X[50781], -4*X[182]+3*X[3545], -4*X[381]+5*X[3618], -4*X[382]+9*X[63062], -4*X[547]+5*X[12017], -8*X[549]+7*X[3619], -10*X[550]+7*X[55602], -4*X[576]+X[33703], -4*X[597]+3*X[3839], -5*X[631]+4*X[11178]

X(64014) lies on these lines: {2, 154}, {3, 11147}, {4, 575}, {6, 3543}, {20, 524}, {30, 1351}, {69, 74}, {98, 11172}, {141, 15692}, {146, 34319}, {147, 11150}, {159, 15078}, {165, 50781}, {182, 3545}, {193, 15683}, {381, 3618}, {382, 63062}, {511, 11001}, {516, 49543}, {541, 11061}, {547, 12017}, {549, 3619}, {550, 55602}, {576, 33703}, {597, 3839}, {599, 5921}, {631, 11178}, {671, 54859}, {962, 47356}, {1350, 11160}, {1352, 3524}, {1513, 63107}, {1899, 32225}, {2393, 15072}, {2482, 50641}, {2777, 41720}, {2794, 8593}, {3090, 10168}, {3091, 47352}, {3146, 5032}, {3522, 15069}, {3523, 21358}, {3525, 18553}, {3528, 34507}, {3529, 19924}, {3533, 55687}, {3534, 3564}, {3546, 51933}, {3589, 61936}, {3620, 62063}, {3629, 62166}, {3655, 39898}, {3763, 15721}, {3818, 5071}, {3830, 14853}, {3832, 53093}, {3845, 5050}, {3850, 55701}, {3853, 53092}, {4995, 39891}, {5026, 37690}, {5054, 40330}, {5055, 39884}, {5056, 10541}, {5059, 11477}, {5067, 20190}, {5092, 15702}, {5093, 62040}, {5102, 62051}, {5182, 16041}, {5298, 39892}, {5477, 43619}, {5480, 50687}, {5485, 38664}, {5596, 52069}, {5621, 10298}, {5622, 18918}, {5642, 16051}, {5655, 18531}, {5661, 51880}, {5731, 47358}, {5870, 33338}, {5871, 33339}, {5965, 51179}, {5999, 9770}, {6055, 58883}, {6146, 34621}, {6329, 61994}, {6353, 32267}, {7426, 37643}, {7492, 16010}, {7493, 9140}, {7735, 53499}, {8182, 10991}, {8584, 15640}, {8703, 10519}, {8718, 44470}, {8721, 11156}, {9143, 16063}, {9744, 63025}, {9830, 11177}, {10109, 50957}, {10336, 63006}, {10575, 15073}, {10989, 37645}, {11003, 31105}, {11008, 15681}, {11151, 47061}, {11155, 33215}, {11157, 61097}, {11158, 61096}, {11188, 64100}, {11317, 46034}, {11427, 31133}, {11456, 22151}, {11482, 62036}, {11646, 62992}, {11812, 55682}, {11898, 15689}, {12007, 62032}, {12100, 33750}, {12101, 50963}, {12154, 41023}, {12155, 41022}, {12156, 14912}, {12203, 33190}, {12279, 50649}, {12290, 44479}, {12324, 15062}, {13669, 39887}, {13789, 39888}, {13857, 64177}, {14269, 18583}, {14458, 62888}, {14561, 41099}, {14810, 62086}, {14826, 43957}, {14831, 64023}, {14848, 15687}, {15074, 64030}, {15077, 59349}, {15303, 36201}, {15533, 15697}, {15534, 29181}, {15577, 37941}, {15581, 22467}, {15677, 63070}, {15684, 21850}, {15685, 50962}, {15686, 33878}, {15688, 48876}, {15690, 50969}, {15694, 18358}, {15698, 55667}, {15701, 50954}, {15708, 20582}, {15709, 24206}, {15710, 55662}, {15716, 50980}, {15719, 17508}, {15740, 38323}, {16092, 36894}, {16646, 37172}, {16647, 37173}, {17538, 55597}, {17800, 64067}, {18911, 26255}, {18914, 34726}, {18928, 31383}, {19124, 62975}, {19130, 61980}, {19459, 54992}, {19708, 50977}, {19709, 38110}, {19710, 34380}, {20080, 48881}, {20192, 52301}, {20194, 63097}, {20583, 51163}, {20791, 29959}, {21167, 50958}, {21735, 40107}, {22165, 31884}, {22329, 60658}, {22487, 44667}, {22488, 44666}, {23046, 51732}, {23053, 40248}, {23269, 44656}, {23275, 44657}, {25555, 61964}, {25561, 61899}, {26864, 47097}, {26869, 37904}, {26883, 43815}, {26944, 33591}, {28194, 51192}, {28538, 34632}, {28708, 31180}, {29317, 51140}, {29323, 62049}, {30308, 38049}, {31152, 37669}, {31162, 39870}, {31166, 41257}, {31670, 55715}, {32124, 37909}, {32250, 45311}, {33251, 39141}, {33748, 51022}, {33749, 62021}, {34573, 61846}, {34628, 39878}, {34664, 34781}, {34776, 41256}, {34803, 58849}, {35237, 41617}, {36757, 41112}, {36758, 41113}, {37170, 41042}, {37171, 41043}, {37184, 53246}, {37517, 62169}, {37640, 53431}, {37641, 53443}, {37644, 37901}, {37952, 47556}, {38040, 50806}, {38072, 51171}, {38136, 61993}, {38165, 50797}, {38167, 50799}, {38314, 64085}, {38317, 50956}, {38335, 53091}, {38738, 50639}, {39561, 62009}, {40236, 63065}, {40341, 62122}, {40671, 54569}, {40672, 54570}, {41145, 52283}, {41149, 51166}, {41982, 55648}, {42085, 51203}, {42086, 51200}, {42602, 48780}, {42603, 48781}, {42850, 60654}, {43150, 62058}, {44280, 47473}, {44407, 51993}, {44456, 62158}, {45759, 61545}, {46267, 61947}, {46333, 48873}, {47355, 61912}, {47359, 50864}, {47545, 62288}, {48872, 62153}, {48874, 62137}, {48884, 62011}, {48889, 61967}, {48898, 55590}, {48901, 62029}, {48910, 51170}, {50664, 61973}, {50783, 59417}, {50801, 50953}, {50808, 50950}, {50811, 50999}, {50815, 51004}, {50865, 51005}, {50872, 51000}, {50959, 51185}, {50960, 61943}, {50961, 50966}, {50964, 61979}, {50973, 62132}, {50976, 50982}, {50981, 61779}, {50984, 51186}, {50986, 62154}, {50988, 61847}, {50989, 51134}, {50991, 51135}, {51025, 55703}, {51075, 51153}, {51077, 51146}, {51130, 51167}, {51132, 62168}, {51137, 61838}, {51143, 61805}, {51172, 62050}, {51181, 61956}, {51188, 55591}, {51211, 63125}, {52987, 62127}, {53142, 54996}, {55177, 63034}, {55580, 62144}, {55584, 62140}, {55595, 62123}, {55606, 62113}, {55614, 62110}, {55620, 62106}, {55622, 58194}, {55626, 62102}, {55629, 62098}, {55631, 62096}, {55638, 62090}, {55639, 62089}, {55646, 62081}, {55649, 62077}, {55654, 62072}, {55676, 61806}, {55679, 61817}, {55684, 55864}, {55688, 61868}, {55691, 61884}, {55692, 61887}, {55695, 61913}, {55697, 61920}, {55699, 61927}, {55706, 61961}, {55711, 61992}, {55722, 58204}, {55724, 62155}, {58445, 61889}, {60101, 60150}, {61044, 62148}, {62005, 63123}, {62145, 63116}, {62161, 62996}

X(64014) = midpoint of X(i) and X(j) for these {i,j}: {193, 15683}, {376, 39874}, {1992, 14927}, {11001, 50974}, {15681, 39899}, {15685, 50962}, {34628, 39878}, {44456, 62158}, {50986, 62154}, {51028, 62160}
X(64014) = reflection of X(i) in X(j) for these {i,j}: {2, 43273}, {4, 11179}, {69, 376}, {146, 34319}, {147, 51798}, {376, 46264}, {381, 48906}, {599, 44882}, {962, 47356}, {1992, 6776}, {3146, 54131}, {3543, 6}, {3830, 50979}, {5921, 599}, {9143, 32233}, {11160, 1350}, {11180, 3}, {11188, 64100}, {15069, 54169}, {15533, 50965}, {15534, 51136}, {15640, 51024}, {15682, 20423}, {15683, 48905}, {15684, 21850}, {18440, 549}, {22165, 50971}, {31162, 39870}, {32250, 45311}, {33878, 15686}, {36990, 597}, {39898, 3655}, {41735, 31166}, {41737, 5642}, {47353, 51737}, {50639, 38738}, {50641, 2482}, {50864, 47359}, {50865, 51005}, {50872, 51000}, {50950, 50808}, {50955, 8703}, {50967, 3534}, {50978, 15690}, {50989, 51134}, {50990, 50975}, {50991, 51135}, {50992, 50967}, {50994, 51177}, {50999, 50811}, {51004, 50815}, {51022, 63124}, {51023, 2}, {51024, 8584}, {51027, 22165}, {51028, 15534}, {51029, 63022}, {51163, 20583}, {51166, 41149}, {51211, 63125}, {51212, 1992}, {51214, 63064}, {51215, 15533}, {51216, 51185}, {51538, 14912}, {54131, 8550}, {54170, 20}, {62042, 31670}, {62048, 48910}, {62174, 59411}, {62288, 47545}, {63022, 51176}, {63064, 50974}, {63118, 50973}, {64023, 14831}
X(64014) = inverse of X(32817) in Wallace hyperbola
X(64014) = anticomplement of X(47353)
X(64014) = pole of line {3839, 7735} with respect to the Kiepert hyperbola
X(64014) = pole of line {2407, 35278} with respect to the Kiepert parabola
X(64014) = pole of line {1350, 1495} with respect to the Stammler hyperbola
X(64014) = pole of line {30, 32817} with respect to the Wallace hyperbola
X(64014) = pole of line {6333, 44552} with respect to the dual conic of orthoptic circle of the Steiner Inellipse
X(64014) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {193, 15683, 36181}
X(64014) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(32817)}}, {{A, B, C, X(598), X(42287)}}, {{A, B, C, X(1494), X(3424)}}, {{A, B, C, X(35140), X(51023)}}, {{A, B, C, X(36890), X(54859)}}
X(64014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1503, 51023}, {2, 43273, 25406}, {2, 64059, 35266}, {4, 11179, 59373}, {20, 524, 54170}, {30, 6776, 1992}, {182, 3545, 63109}, {376, 39874, 542}, {376, 542, 69}, {381, 55705, 38079}, {511, 63064, 51214}, {542, 46264, 376}, {597, 36990, 3839}, {599, 44882, 10304}, {616, 617, 32817}, {1503, 51737, 47353}, {1992, 14927, 30}, {3146, 5032, 54131}, {3534, 3564, 50967}, {3534, 51175, 55593}, {3564, 50967, 50992}, {3818, 38064, 5071}, {3830, 50979, 14853}, {5071, 38064, 63119}, {8550, 54131, 5032}, {8703, 50955, 10519}, {10516, 50983, 2}, {10519, 50955, 50990}, {10519, 50975, 8703}, {10602, 40196, 51212}, {11001, 50974, 511}, {11160, 62120, 1350}, {11179, 11645, 4}, {12101, 59399, 50963}, {14912, 15682, 20423}, {14912, 20423, 63022}, {14912, 29012, 51538}, {15533, 50965, 62174}, {15533, 59411, 50965}, {15534, 29181, 51028}, {15682, 51538, 51029}, {15690, 50978, 55610}, {15690, 55610, 50969}, {20423, 29012, 15682}, {20582, 53094, 15708}, {22165, 50971, 31884}, {29181, 51136, 15534}, {31884, 50971, 62094}, {38317, 50956, 61932}, {43273, 47353, 51737}, {50687, 63127, 5480}, {50965, 59411, 15697}, {50984, 55673, 61796}, {51022, 53023, 62007}, {51022, 63124, 53023}, {51025, 55703, 61958}, {51028, 62160, 29181}, {51171, 61985, 38072}, {51186, 55673, 50984}, {51537, 63109, 3545}, {64080, 64196, 20}

X(64015) = ANTICOMPLEMENT OF X(4644)

Barycentrics    5*a^2-3*b^2+2*b*c-3*c^2-2*a*(b+c) : :
X(64015) = -4*X[10]+3*X[35578], -5*X[3616]+4*X[4667], -5*X[3617]+4*X[4363], -7*X[3622]+8*X[4364], -5*X[4470]+6*X[17251], -16*X[4472]+17*X[46932], -7*X[4678]+8*X[4690]

X(64015) lies on these lines: {2, 44}, {7, 391}, {8, 527}, {9, 4869}, {10, 35578}, {37, 62999}, {45, 29621}, {69, 144}, {75, 20059}, {85, 60975}, {145, 524}, {192, 20080}, {193, 3672}, {200, 3000}, {239, 4346}, {279, 17950}, {319, 4461}, {321, 20214}, {329, 4001}, {344, 17361}, {347, 63782}, {536, 3621}, {545, 31145}, {597, 26104}, {599, 54389}, {651, 23151}, {742, 31302}, {894, 5232}, {966, 17365}, {1086, 24599}, {1330, 54398}, {1743, 31191}, {1944, 27541}, {1992, 4389}, {2287, 6180}, {2321, 4488}, {2345, 17344}, {2895, 20078}, {2975, 24328}, {3161, 17296}, {3616, 4667}, {3617, 4363}, {3618, 17273}, {3620, 17350}, {3622, 4364}, {3629, 17255}, {3630, 17262}, {3632, 17132}, {3662, 37681}, {3664, 5296}, {3686, 31995}, {3687, 28610}, {3707, 6173}, {3729, 32099}, {3731, 29606}, {3869, 34371}, {3886, 63975}, {3912, 6172}, {3943, 15533}, {3945, 16826}, {3973, 21255}, {4000, 17345}, {4307, 17770}, {4310, 50023}, {4360, 11008}, {4361, 4373}, {4402, 4862}, {4409, 17362}, {4422, 30833}, {4440, 50074}, {4450, 20015}, {4452, 5839}, {4465, 30948}, {4470, 17251}, {4472, 46932}, {4480, 17294}, {4555, 53212}, {4645, 5686}, {4648, 17332}, {4655, 4753}, {4678, 4690}, {4681, 4916}, {4684, 52653}, {4702, 4779}, {4725, 20014}, {4781, 24683}, {4887, 16833}, {4888, 63978}, {4896, 16832}, {4912, 20052}, {4969, 49747}, {4971, 20054}, {5220, 39570}, {5222, 17274}, {5223, 10005}, {5233, 64142}, {5257, 36834}, {5308, 50093}, {5739, 9965}, {5749, 17272}, {5815, 6552}, {5905, 14552}, {6144, 17246}, {6542, 11160}, {6604, 60998}, {7222, 17275}, {7229, 17270}, {7232, 37650}, {7277, 17253}, {9740, 37764}, {10453, 24705}, {11679, 64143}, {14555, 21454}, {14986, 53020}, {15534, 17395}, {15589, 56555}, {15668, 30712}, {16670, 50092}, {16713, 26125}, {16823, 30340}, {16885, 53665}, {17133, 20053}, {17236, 51171}, {17254, 26626}, {17261, 29618}, {17269, 22165}, {17277, 62778}, {17288, 26685}, {17298, 18230}, {17302, 51170}, {17305, 59373}, {17314, 17334}, {17316, 17333}, {17321, 17329}, {17323, 32455}, {17330, 62223}, {17343, 31300}, {17346, 42697}, {17348, 33800}, {17354, 21356}, {17360, 50107}, {17375, 29589}, {17378, 29624}, {17380, 62995}, {17383, 63123}, {17771, 50295}, {17781, 34255}, {19825, 43990}, {20019, 50065}, {20348, 60737}, {21384, 52896}, {23942, 53501}, {24248, 50016}, {24594, 63003}, {24702, 24712}, {25101, 60983}, {25278, 40875}, {26840, 63037}, {27039, 27334}, {27184, 37666}, {29585, 50133}, {29605, 50090}, {29611, 50127}, {30332, 49451}, {32086, 60982}, {32087, 60976}, {32098, 60953}, {34379, 64168}, {37652, 62208}, {37658, 51351}, {37668, 60729}, {40333, 60731}, {49709, 50999}, {49748, 50992}, {50095, 52709}, {50101, 62231}, {56201, 58463}, {56927, 60934}, {57037, 63499}, {60939, 63152}, {62424, 63590}

X(64015) = reflection of X(i) in X(j) for these {i,j}: {145, 4419}, {4454, 8}, {4644, 4643}
X(64015) = anticomplement of X(4644)
X(64015) = perspector of circumconic {{A, B, C, X(4597), X(57928)}}
X(64015) = X(i)-Dao conjugate of X(j) for these {i, j}: {4644, 4644}
X(64015) = pole of line {4777, 47784} with respect to the Steiner circumellipse
X(64015) = pole of line {4777, 53573} with respect to the Steiner inellipse
X(64015) = pole of line {2398, 4781} with respect to the Yff parabola
X(64015) = pole of line {5235, 14953} with respect to the Wallace hyperbola
X(64015) = pole of line {39470, 49280} with respect to the dual conic of polar circle
X(64015) = pole of line {551, 64168} with respect to the dual conic of Yff parabola
X(64015) = intersection, other than A, B, C, of circumconics {{A, B, C, X(89), X(36101)}}, {{A, B, C, X(1275), X(29616)}}, {{A, B, C, X(18025), X(39704)}}, {{A, B, C, X(44551), X(53212)}}
X(64015) = barycentric product X(i)*X(j) for these (i, j): {190, 44551}
X(64015) = barycentric quotient X(i)/X(j) for these (i, j): {44551, 514}
X(64015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4644, 4747}, {7, 4416, 391}, {8, 527, 4454}, {9, 21296, 4869}, {69, 17347, 144}, {69, 190, 29616}, {144, 29616, 190}, {190, 29616, 346}, {193, 6646, 3672}, {320, 54280, 2}, {329, 4001, 37655}, {524, 4419, 145}, {1992, 4389, 17014}, {2321, 60977, 4488}, {3686, 60933, 31995}, {3912, 6172, 62706}, {4000, 17345, 45789}, {4364, 63054, 3622}, {4470, 17251, 46933}, {4643, 4670, 4748}, {4643, 4715, 4644}, {4643, 4795, 4708}, {4644, 4748, 4670}, {5839, 17276, 4452}, {7277, 17253, 63055}, {11160, 20073, 6542}, {17257, 17364, 3945}, {17296, 60942, 3161}, {17334, 40341, 17314}, {20059, 63001, 75}, {32099, 60957, 3729}, {45789, 62985, 4000}

X(64016) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(6) AND X(2)-CROSSPEDAL-OF-X(8)

Barycentrics    3*a^3-(b-c)^2*(b+c) : :
X(64016) = -4*X[1386]+3*X[17301], -5*X[3616]+4*X[17235], -2*X[3663]+3*X[38315], -2*X[3821]+3*X[50300], -2*X[4133]+3*X[5695], -4*X[4353]+3*X[49747], -3*X[47352]+2*X[49630], -3*X[48805]+2*X[49511], -2*X[49524]+3*X[50127]

X(64016) lies on these lines: {1, 3255}, {6, 516}, {7, 1279}, {8, 17351}, {10, 16885}, {30, 63357}, {31, 1836}, {37, 4307}, {40, 4271}, {44, 2550}, {45, 51090}, {55, 41011}, {57, 3756}, {58, 12699}, {63, 63979}, {69, 28570}, {144, 49515}, {145, 3644}, {149, 62795}, {165, 37662}, {171, 24703}, {190, 50289}, {193, 28581}, {226, 3052}, {238, 5880}, {312, 20101}, {321, 20064}, {390, 4644}, {513, 1469}, {517, 37516}, {518, 24695}, {524, 3886}, {527, 3242}, {528, 3751}, {536, 24280}, {545, 49446}, {595, 57282}, {614, 11246}, {726, 49681}, {750, 4679}, {752, 3416}, {896, 33104}, {902, 17718}, {908, 37540}, {946, 4252}, {1001, 4675}, {1086, 4312}, {1100, 64168}, {1104, 4295}, {1108, 3332}, {1191, 4292}, {1284, 3941}, {1333, 5327}, {1386, 17301}, {1456, 4331}, {1468, 12701}, {1471, 60718}, {1616, 4298}, {1699, 37646}, {1707, 2886}, {1770, 16466}, {1834, 41869}, {1892, 8750}, {2163, 16173}, {2177, 61707}, {2245, 6210}, {2263, 53529}, {2305, 25354}, {2308, 33094}, {2549, 28897}, {2792, 64085}, {2796, 32921}, {2835, 32118}, {3011, 61716}, {3056, 20718}, {3058, 62819}, {3072, 64119}, {3218, 17721}, {3241, 4912}, {3243, 53534}, {3286, 31394}, {3419, 49500}, {3434, 4641}, {3474, 3752}, {3550, 33096}, {3600, 45219}, {3616, 17235}, {3629, 49495}, {3663, 38315}, {3666, 44447}, {3685, 4851}, {3729, 5846}, {3744, 5905}, {3759, 62392}, {3782, 62834}, {3815, 9746}, {3821, 50300}, {3823, 26685}, {3827, 12723}, {3875, 28530}, {3883, 4363}, {3915, 10404}, {3966, 4418}, {3973, 38200}, {4008, 16732}, {4133, 5695}, {4255, 31730}, {4257, 5886}, {4259, 15310}, {4260, 29349}, {4265, 63968}, {4277, 48918}, {4344, 4419}, {4349, 16777}, {4353, 49747}, {4356, 16884}, {4362, 48641}, {4414, 17723}, {4415, 5269}, {4427, 33070}, {4450, 26223}, {4454, 49525}, {4480, 49527}, {4512, 17056}, {4640, 26098}, {4643, 5263}, {4645, 4676}, {4646, 6361}, {4648, 52653}, {4650, 33106}, {4654, 62875}, {4655, 28508}, {4657, 24723}, {4660, 4672}, {4667, 63977}, {4673, 20077}, {4689, 63008}, {4715, 49467}, {4733, 17275}, {4779, 62999}, {4795, 49746}, {4849, 17784}, {4854, 62845}, {4863, 32912}, {4888, 38316}, {4891, 63057}, {4924, 5853}, {5021, 48944}, {5057, 17126}, {5096, 24309}, {5250, 49745}, {5264, 58798}, {5292, 22793}, {5313, 15228}, {5542, 62223}, {5710, 64002}, {5718, 35258}, {5762, 61086}, {5805, 64013}, {5839, 49468}, {5852, 16496}, {6173, 60846}, {6284, 54421}, {6327, 32777}, {7174, 17334}, {7262, 33109}, {7735, 44431}, {7968, 52805}, {7969, 52808}, {8557, 11372}, {8616, 33097}, {8818, 53424}, {9340, 29662}, {9580, 62812}, {9778, 63089}, {9791, 41312}, {9812, 37642}, {9965, 21342}, {11415, 37539}, {11496, 54431}, {12652, 38454}, {12722, 24476}, {13405, 21000}, {15492, 38057}, {15601, 17337}, {16468, 24715}, {16469, 17366}, {16686, 51687}, {17127, 20292}, {17132, 51000}, {17253, 19868}, {17262, 49476}, {17303, 50295}, {17350, 32850}, {17392, 50836}, {17469, 33098}, {17483, 62806}, {17491, 33122}, {17716, 33099}, {17724, 31164}, {17764, 49488}, {17766, 32935}, {17767, 49455}, {17770, 32941}, {17771, 49458}, {18481, 29301}, {18907, 28915}, {20072, 49450}, {21282, 33114}, {21747, 33128}, {24342, 50296}, {24349, 49709}, {24392, 62820}, {24691, 54291}, {24821, 49534}, {25681, 37603}, {28011, 52783}, {28146, 48837}, {28178, 48847}, {28198, 48870}, {28202, 48857}, {28329, 51001}, {28526, 49453}, {28546, 49472}, {28550, 49477}, {28558, 47358}, {28562, 47359}, {28580, 49486}, {28628, 54354}, {29671, 59536}, {30615, 32938}, {30652, 33133}, {30653, 33129}, {30741, 59769}, {30811, 35263}, {30828, 35261}, {31300, 49499}, {31489, 49631}, {33075, 50048}, {33083, 52786}, {33095, 62841}, {33100, 50068}, {33112, 62838}, {33863, 48900}, {34379, 49460}, {35227, 59372}, {35466, 36277}, {37650, 59412}, {37674, 40998}, {37817, 39542}, {38186, 53602}, {42314, 62789}, {44006, 50102}, {44417, 63140}, {47352, 49630}, {47595, 49706}, {48805, 49511}, {49462, 50284}, {49524, 50127}, {49680, 64073}, {49720, 60731}, {50065, 57280}, {50076, 50126}, {50118, 50783}, {50175, 63359}, {50865, 61661}, {51415, 64112}, {52682, 53599}, {61152, 62660}, {62240, 64162}, {62849, 64164}

X(64016) = midpoint of X(i) and X(j) for these {i,j}: {24280, 51192}
X(64016) = reflection of X(i) in X(j) for these {i,j}: {8, 17351}, {69, 49484}, {3242, 63969}, {3416, 3923}, {3755, 64017}, {4655, 49482}, {4660, 4672}, {17276, 1}, {17299, 5695}, {17301, 50303}, {24248, 1386}, {24476, 12722}, {49446, 51147}, {49453, 49684}, {49486, 51196}, {49495, 3629}, {49680, 64073}, {49688, 32935}, {49747, 50294}, {50076, 50126}, {50175, 63359}, {50783, 50118}
X(64016) = pole of line {18492, 62322} with respect to the Kiepert hyperbola
X(64016) = pole of line {60980, 62383} with respect to the dual conic of Yff parabola
X(64016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17768, 17276}, {31, 1836, 3772}, {390, 4644, 49478}, {516, 64017, 3755}, {527, 63969, 3242}, {545, 51147, 49446}, {902, 24725, 17718}, {1001, 50307, 4675}, {1386, 24248, 17301}, {1386, 28534, 24248}, {3242, 63969, 50130}, {3416, 3923, 17281}, {3755, 64017, 6}, {4307, 5698, 37}, {4344, 63975, 4419}, {4645, 4676, 17279}, {4660, 4672, 38047}, {4672, 28494, 4660}, {5057, 17126, 17720}, {5695, 5847, 17299}, {7174, 60905, 17334}, {15601, 38052, 17337}, {17766, 32935, 49688}, {24248, 50303, 1386}, {24280, 51192, 536}, {28526, 49684, 49453}, {28580, 51196, 49486}, {31300, 49704, 49499}, {33100, 62807, 50068}, {49486, 51196, 50131}, {51090, 64174, 45}, {53529, 60883, 2263}

X(64017) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(6) AND X(2)-CROSSPEDAL-OF-X(10)

Barycentrics    6*a^3+3*a^2*(b+c)-(b-c)^2*(b+c) : :
X(64017) = -X[3242]+3*X[50294], -X[3416]+3*X[50115], -X[3663]+3*X[16475], -X[3773]+3*X[4672], -X[4655]+3*X[38049], -X[4660]+3*X[59408], 3*X[16834]+X[24280], -X[24248]+3*X[50114], -X[49495]+5*X[51170], -X[49511]+3*X[50300], -X[49630]+3*X[59373]

X(64017) lies on these lines: {1, 144}, {6, 516}, {7, 16469}, {9, 4349}, {10, 391}, {31, 13405}, {44, 64174}, {58, 86}, {81, 40998}, {171, 20103}, {329, 62842}, {386, 1742}, {387, 51118}, {519, 1992}, {527, 1386}, {551, 60846}, {595, 9440}, {614, 62240}, {651, 12573}, {726, 41622}, {740, 4856}, {902, 61652}, {995, 4334}, {1001, 4667}, {1086, 4989}, {1104, 12563}, {1191, 12577}, {1203, 4292}, {1279, 7277}, {1449, 4356}, {1453, 3671}, {1456, 52819}, {1471, 62789}, {1699, 37666}, {1738, 16477}, {2257, 54370}, {2271, 48925}, {2308, 3120}, {2550, 16670}, {2784, 5477}, {2796, 4991}, {2809, 12722}, {3008, 16468}, {3011, 21747}, {3242, 50294}, {3244, 4779}, {3332, 63973}, {3361, 62787}, {3416, 50115}, {3589, 28570}, {3626, 28512}, {3629, 49484}, {3634, 50304}, {3635, 3993}, {3663, 16475}, {3672, 60905}, {3686, 4733}, {3696, 4700}, {3756, 51435}, {3758, 3883}, {3773, 4672}, {3791, 48641}, {3817, 37642}, {3828, 50301}, {3874, 14523}, {3879, 4676}, {3946, 17768}, {3950, 50284}, {4000, 30424}, {4054, 50754}, {4061, 63009}, {4253, 6210}, {4260, 29353}, {4298, 6180}, {4312, 5222}, {4344, 5223}, {4383, 41422}, {4416, 19868}, {4512, 63007}, {4644, 5542}, {4648, 15601}, {4649, 63977}, {4655, 38049}, {4656, 62845}, {4660, 59408}, {4663, 5853}, {4759, 29606}, {4852, 28557}, {4888, 16020}, {5021, 48932}, {5269, 21060}, {5292, 12571}, {5294, 48647}, {5327, 40963}, {5711, 18250}, {5717, 18249}, {6700, 27381}, {6738, 54421}, {6745, 17126}, {7585, 49632}, {7586, 49633}, {7736, 49631}, {8557, 60911}, {9746, 37665}, {9778, 62181}, {10164, 63089}, {10171, 37646}, {10521, 62785}, {11019, 62812}, {11038, 16487}, {12447, 54386}, {12527, 57280}, {12572, 62805}, {12652, 28228}, {13329, 43151}, {16667, 64168}, {16834, 24280}, {17014, 63975}, {17132, 32921}, {17350, 49476}, {17365, 43180}, {17766, 41623}, {17781, 62807}, {19003, 52805}, {19004, 52808}, {20106, 32946}, {20156, 31211}, {24248, 50114}, {24725, 61647}, {28150, 48847}, {28158, 48837}, {28526, 49477}, {28580, 49489}, {28581, 32455}, {28897, 63633}, {29604, 33082}, {31034, 35263}, {32935, 49684}, {32941, 64073}, {34379, 49482}, {36277, 63008}, {37492, 63968}, {37502, 41430}, {37650, 38204}, {37662, 58441}, {37681, 38052}, {39595, 62841}, {43035, 60883}, {43179, 49478}, {44431, 63005}, {44839, 64084}, {48856, 50834}, {49474, 50019}, {49495, 51170}, {49511, 50300}, {49630, 59373}, {50020, 50117}, {50302, 63978}, {50802, 61661}, {64110, 64166}

X(64017) = midpoint of X(i) and X(j) for these {i,j}: {3629, 49484}, {3663, 24695}, {3751, 63969}, {3755, 64016}, {3923, 51196}, {32935, 49684}, {32941, 64073}
X(64017) = reflection of X(i) in X(j) for these {i,j}: {4353, 1386}, {17355, 4672}, {50304, 3634}, {53598, 1125}
X(64017) = perspector of circumconic {{A, B, C, X(4610), X(9057)}}
X(64017) = pole of line {4765, 17161} with respect to the Steiner circumellipse
X(64017) = pole of line {86, 14953} with respect to the dual conic of Yff parabola
X(64017) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1509), X(56043)}}, {{A, B, C, X(11599), X(53598)}}
X(64017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 64016, 3755}, {238, 3664, 1125}, {527, 1386, 4353}, {1125, 17770, 53598}, {1449, 5698, 4356}, {1743, 4307, 10}, {2308, 41011, 40940}, {3751, 50303, 63969}, {3751, 63969, 519}, {3755, 64016, 516}, {4648, 15601, 38059}, {4672, 5847, 17355}, {4888, 16020, 38054}, {16468, 50307, 3008}, {21747, 61707, 3011}, {52653, 62997, 1}

X(64018) = ANTICOMPLEMENT OF X(7737)

Barycentrics    5*a^4-3*b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2+c^2) : :
X(64018) = -2*X[6]+3*X[32986], -4*X[141]+3*X[14033], -5*X[3618]+6*X[11287], -7*X[3619]+6*X[11286], -5*X[3620]+4*X[3734], -8*X[4045]+7*X[51171], -15*X[5032]+16*X[61046], -6*X[7739]+5*X[51170], -2*X[11159]+3*X[21356], -3*X[14853]+4*X[37242], -4*X[35930]+5*X[40330], -5*X[50990]+4*X[59780] and many others

X(64018) lies on these lines: {2, 187}, {3, 1007}, {4, 183}, {5, 32867}, {6, 32986}, {20, 99}, {30, 69}, {32, 32974}, {39, 33023}, {40, 55418}, {76, 3146}, {83, 33202}, {84, 55419}, {86, 48813}, {115, 37667}, {141, 14033}, {148, 9939}, {193, 754}, {194, 32997}, {230, 16041}, {274, 37435}, {325, 376}, {340, 49670}, {378, 15574}, {381, 34229}, {382, 7767}, {385, 33017}, {393, 40889}, {394, 3331}, {439, 3788}, {491, 9541}, {512, 62642}, {524, 44526}, {538, 20080}, {543, 11160}, {549, 34803}, {550, 6337}, {574, 62988}, {620, 35287}, {621, 44463}, {622, 44459}, {626, 32973}, {631, 7773}, {637, 49038}, {638, 49039}, {671, 9740}, {892, 53201}, {1078, 3091}, {1285, 7792}, {1350, 10008}, {1369, 20062}, {1384, 33184}, {1597, 63155}, {1657, 3933}, {1799, 7378}, {1968, 28724}, {1975, 3529}, {1992, 5077}, {2080, 9752}, {2386, 12220}, {2407, 35923}, {2548, 7830}, {2896, 14035}, {2996, 7751}, {3053, 14064}, {3096, 33198}, {3314, 33007}, {3329, 7791}, {3522, 7763}, {3523, 7752}, {3528, 32823}, {3534, 6390}, {3543, 7811}, {3545, 37688}, {3552, 53033}, {3618, 11287}, {3619, 11286}, {3620, 3734}, {3767, 7842}, {3793, 63034}, {3815, 33215}, {3830, 64093}, {3832, 32832}, {3839, 32885}, {3854, 32870}, {3934, 32979}, {4045, 51171}, {4340, 51356}, {4967, 48807}, {5013, 33226}, {5023, 32970}, {5024, 8354}, {5032, 61046}, {5056, 32883}, {5059, 7768}, {5149, 33014}, {5206, 31274}, {5207, 10519}, {5210, 33216}, {5224, 48817}, {5254, 33238}, {5286, 6655}, {5304, 7790}, {5319, 7872}, {5395, 7808}, {5468, 36163}, {5564, 48798}, {5939, 9862}, {5971, 16063}, {6101, 53796}, {6189, 35914}, {6190, 35913}, {6194, 39266}, {6392, 7748}, {6644, 34883}, {6658, 7929}, {6722, 7825}, {6776, 39099}, {6781, 7818}, {7396, 33651}, {7408, 40022}, {7620, 8597}, {7694, 8722}, {7710, 54993}, {7735, 7841}, {7736, 8356}, {7738, 7762}, {7739, 51170}, {7745, 16043}, {7746, 32980}, {7747, 7800}, {7749, 32988}, {7754, 19695}, {7756, 7758}, {7757, 63091}, {7769, 15717}, {7774, 7833}, {7775, 63077}, {7777, 33008}, {7778, 32985}, {7779, 33264}, {7780, 54097}, {7782, 32831}, {7783, 33253}, {7784, 14001}, {7785, 31400}, {7788, 11001}, {7789, 33239}, {7793, 14063}, {7795, 7873}, {7799, 62120}, {7803, 7910}, {7806, 33251}, {7809, 10304}, {7810, 62203}, {7812, 37665}, {7814, 21734}, {7815, 32987}, {7824, 31404}, {7827, 63005}, {7828, 33200}, {7832, 33201}, {7836, 33244}, {7840, 53142}, {7843, 31401}, {7845, 34511}, {7850, 10513}, {7857, 33199}, {7868, 14039}, {7871, 32841}, {7879, 19687}, {7881, 33250}, {7885, 16925}, {7891, 33254}, {7893, 33256}, {7897, 33265}, {7899, 33203}, {7900, 33260}, {7904, 16924}, {7906, 33267}, {7911, 33180}, {7912, 32964}, {7924, 16989}, {7928, 16898}, {7931, 33255}, {7938, 14037}, {7939, 33257}, {7941, 33275}, {7946, 33209}, {7947, 33268}, {8352, 63029}, {8353, 31859}, {8357, 30435}, {8359, 15484}, {8362, 14535}, {8591, 52943}, {8667, 53419}, {8716, 50771}, {8781, 38747}, {9723, 35243}, {9770, 35955}, {10303, 32884}, {11008, 22253}, {11111, 37664}, {11159, 21356}, {11179, 51396}, {11184, 47061}, {11295, 63105}, {11296, 63106}, {11317, 42850}, {11318, 63104}, {11359, 63014}, {11361, 16990}, {12042, 39647}, {14031, 46226}, {14041, 17008}, {14068, 31276}, {14532, 14927}, {14615, 16251}, {14731, 38940}, {14853, 37242}, {15031, 61982}, {15271, 32983}, {15640, 32892}, {15682, 37671}, {15696, 32891}, {16589, 33051}, {16999, 33032}, {17004, 33006}, {17128, 33280}, {17538, 32818}, {17578, 32834}, {17579, 45962}, {19691, 20081}, {22676, 51373}, {23055, 37350}, {26233, 31099}, {26288, 44364}, {26289, 44365}, {31295, 34284}, {32152, 58851}, {32805, 35256}, {32806, 35255}, {32819, 32878}, {32820, 62147}, {32821, 62127}, {32822, 32890}, {32840, 62152}, {32869, 62048}, {32871, 61804}, {32873, 62060}, {32874, 62032}, {32877, 49140}, {32886, 50688}, {32887, 62067}, {32888, 50691}, {32889, 62083}, {32893, 62005}, {32898, 61816}, {32976, 44535}, {32984, 37637}, {32991, 39590}, {33019, 43449}, {33228, 62992}, {33247, 63548}, {33263, 63017}, {33273, 63083}, {33278, 63048}, {33285, 46453}, {33532, 52437}, {34254, 59343}, {34604, 63045}, {34608, 45201}, {35297, 37690}, {35474, 55972}, {35930, 40330}, {36187, 47291}, {36891, 41522}, {36987, 51386}, {37187, 60428}, {37190, 56442}, {38741, 46236}, {40123, 52397}, {40680, 44128}, {44369, 63428}, {48838, 62999}, {48869, 63001}, {50057, 63013}, {50990, 59780}, {50992, 52229}, {52718, 61945}, {53491, 60204}, {53492, 60205}, {58188, 62362}, {59634, 62130}, {62427, 63536}, {62995, 63633}

X(64018) = reflection of X(i) in X(j) for these {i,j}: {193, 2549}, {1992, 5077}, {7737, 7761}, {11008, 22253}, {14927, 14532}, {32815, 69}, {43618, 3734}
X(64018) = anticomplement of X(7737)
X(64018) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {30541, 8}
X(64018) = pole of line {597, 32983} with respect to the Kiepert hyperbola
X(64018) = pole of line {34211, 35356} with respect to the Kiepert parabola
X(64018) = pole of line {574, 26864} with respect to the Stammler hyperbola
X(64018) = pole of line {3906, 6333} with respect to the Steiner circumellipse
X(64018) = pole of line {376, 599} with respect to the Wallace hyperbola
X(64018) = pole of line {3265, 9209} with respect to the dual conic of orthoptic circle of the Steiner Inellipse
X(64018) = intersection, other than A, B, C, of circumconics {{A, B, C, X(376), X(11180)}}, {{A, B, C, X(598), X(35140)}}, {{A, B, C, X(1297), X(1383)}}, {{A, B, C, X(18023), X(32827)}}, {{A, B, C, X(23334), X(36882)}}, {{A, B, C, X(23582), X(37668)}}, {{A, B, C, X(41522), X(56687)}}, {{A, B, C, X(44552), X(51541)}}, {{A, B, C, X(50967), X(54667)}}
X(64018) = barycentric product X(i)*X(j) for these (i, j): {44552, 99}
X(64018) = barycentric quotient X(i)/X(j) for these (i, j): {44552, 523}
X(64018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 316, 32827}, {3, 32006, 32816}, {4, 3785, 32828}, {4, 7750, 3785}, {20, 315, 3926}, {20, 37668, 99}, {30, 69, 32815}, {69, 54170, 51438}, {76, 3146, 32826}, {99, 315, 37668}, {148, 9939, 63046}, {193, 33272, 2549}, {315, 7802, 20}, {316, 11057, 14907}, {316, 14907, 2}, {385, 33017, 43448}, {550, 7776, 6337}, {625, 47101, 21843}, {754, 2549, 193}, {1078, 3091, 32838}, {1285, 33190, 7792}, {2548, 7830, 32990}, {3523, 7752, 32839}, {3543, 15589, 11185}, {3767, 7842, 32982}, {3849, 7761, 7737}, {5210, 44377, 33216}, {5304, 33210, 7790}, {6337, 7776, 32825}, {6655, 20065, 5286}, {7747, 7800, 32971}, {7748, 14023, 6392}, {7762, 33234, 7738}, {7785, 32965, 31400}, {7803, 7910, 33025}, {7811, 11185, 15589}, {7850, 32833, 10513}, {7898, 14976, 14712}, {8359, 15484, 63041}, {11287, 18907, 3618}, {15271, 53418, 32983}, {32831, 50693, 7782}, {33192, 63046, 148}

X(64019) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(2)-CROSSPEDAL-OF-X(99)

Barycentrics    7*a^4+4*b^4-b^2*c^2+4*c^4-7*a^2*(b^2+c^2) : :
X(64019) = 4*X[2]+X[99], 4*X[5]+X[12117], 4*X[10]+X[9884], -X[98]+6*X[5054], 2*X[114]+3*X[3524], 4*X[140]+X[8724], 4*X[141]+X[8593], X[147]+9*X[15708], X[316]+4*X[27088], 2*X[325]+3*X[26613], -X[376]+6*X[38748], 2*X[381]+3*X[21166] and many others

X(64019) lies on these lines: {2, 99}, {3, 11149}, {5, 12117}, {10, 9884}, {30, 38750}, {76, 8860}, {83, 42010}, {88, 29609}, {98, 5054}, {114, 3524}, {140, 8724}, {141, 8593}, {147, 15708}, {316, 27088}, {325, 26613}, {376, 38748}, {381, 21166}, {385, 5215}, {531, 36770}, {542, 631}, {547, 14639}, {549, 6054}, {590, 19058}, {597, 7807}, {599, 1078}, {615, 19057}, {625, 9855}, {635, 5464}, {636, 5463}, {662, 31144}, {691, 46986}, {1125, 9881}, {1153, 8587}, {1385, 50880}, {1551, 38704}, {1916, 60645}, {1992, 7763}, {2782, 15694}, {2794, 15692}, {2796, 19862}, {2936, 40916}, {3090, 9880}, {3314, 5569}, {3455, 7496}, {3523, 20399}, {3525, 12243}, {3526, 23235}, {3534, 61575}, {3543, 36519}, {3545, 6721}, {3619, 45018}, {3624, 12258}, {3763, 9830}, {3788, 7883}, {3839, 38738}, {3849, 7925}, {3934, 11152}, {3972, 11184}, {4413, 12326}, {4590, 9164}, {5026, 10488}, {5055, 33813}, {5066, 38730}, {5067, 10992}, {5070, 12355}, {5071, 23698}, {5094, 12132}, {5149, 33273}, {5432, 12351}, {5433, 12350}, {5459, 11308}, {5460, 11307}, {5503, 11174}, {5590, 33343}, {5591, 33342}, {5690, 50883}, {5969, 7786}, {5972, 11006}, {5976, 51588}, {5984, 61830}, {6033, 12100}, {6036, 15709}, {6055, 15702}, {6189, 22245}, {6190, 22244}, {6321, 15699}, {6390, 11054}, {6669, 9116}, {6670, 9114}, {6684, 50881}, {6778, 36768}, {7484, 9876}, {7752, 32985}, {7760, 62204}, {7769, 8369}, {7778, 50571}, {7782, 11318}, {7792, 12040}, {7796, 11160}, {7799, 22329}, {7801, 7907}, {7802, 35287}, {7808, 12191}, {7809, 22110}, {7810, 7909}, {7811, 33216}, {7812, 16925}, {7815, 58765}, {7817, 33245}, {7832, 20582}, {7833, 7899}, {7836, 34506}, {7840, 10352}, {7841, 7940}, {7846, 33197}, {7856, 33203}, {7857, 34511}, {7859, 8365}, {7868, 52088}, {7888, 9939}, {7914, 9878}, {7931, 8786}, {7934, 35955}, {7944, 8359}, {7970, 50821}, {7983, 25055}, {8252, 49215}, {8253, 49214}, {8352, 32459}, {8594, 44383}, {8595, 44382}, {8597, 32456}, {8598, 44377}, {8703, 10722}, {8781, 18842}, {8859, 39785}, {8997, 19053}, {9681, 39387}, {9741, 63104}, {9771, 35954}, {9862, 15719}, {9864, 50828}, {10124, 38224}, {10303, 14981}, {10753, 50977}, {10754, 47352}, {10769, 59376}, {10991, 61820}, {11053, 51226}, {11163, 11288}, {11177, 15721}, {11539, 11632}, {11623, 55864}, {11694, 15545}, {11711, 19875}, {11724, 50810}, {11812, 51872}, {12042, 15701}, {12093, 16175}, {12188, 26614}, {12347, 15184}, {12349, 24953}, {12356, 26364}, {12357, 26363}, {13172, 61899}, {13188, 61864}, {13586, 31173}, {13846, 19108}, {13847, 19109}, {13908, 32785}, {13968, 32786}, {13989, 19054}, {14067, 31457}, {14069, 55767}, {14568, 44401}, {14645, 63127}, {14651, 61859}, {14692, 14890}, {14869, 52090}, {14891, 38742}, {14916, 57216}, {14928, 63121}, {15031, 59545}, {15092, 61901}, {15682, 38736}, {15687, 38731}, {15688, 22505}, {15698, 38749}, {15700, 38743}, {15705, 38747}, {15706, 38744}, {15713, 38739}, {15717, 38745}, {15723, 34127}, {16508, 63647}, {16988, 43535}, {17023, 49549}, {17504, 38741}, {18800, 21356}, {18823, 31998}, {19883, 50886}, {20398, 61867}, {20774, 35486}, {21636, 50829}, {22515, 61920}, {23055, 32833}, {23514, 61895}, {25561, 37334}, {27195, 35103}, {31275, 32479}, {33220, 42849}, {33231, 62348}, {34229, 60103}, {35378, 41146}, {38229, 61880}, {38314, 50888}, {38635, 61925}, {38732, 61883}, {38733, 61908}, {38734, 61886}, {38740, 61856}, {38746, 61806}, {39061, 40553}, {39805, 43572}, {39809, 41106}, {39838, 62120}, {41139, 47286}, {41672, 50992}, {41985, 61600}, {44010, 57152}, {44580, 61599}, {46210, 54918}, {46219, 51524}, {46980, 47288}, {47005, 52034}, {47290, 53136}, {50567, 59373}, {50641, 51737}, {50990, 55820}, {50991, 64092}, {50993, 55730}, {51523, 55863}, {52094, 62686}, {53729, 59377}, {54494, 56064}, {54509, 54841}, {55726, 55813}, {55728, 55812}, {55740, 55807}, {55742, 55806}, {55743, 55805}, {55758, 55797}, {55761, 55796}, {55764, 55795}, {55768, 55793}, {55771, 55791}, {55783, 55786}, {55817, 55829}, {60073, 60200}, {61560, 61851}, {61576, 61887}, {63344, 63347}

X(64019) = reflection of X(i) in X(j) for these {i,j}: {2, 31274}, {14061, 2}, {38739, 15713}
X(64019) = inverse of X(5461) in Wallace hyperbola
X(64019) = pole of line {2793, 14424} with respect to the orthoptic circle of the Steiner Inellipse
X(64019) = pole of line {187, 20977} with respect to the Stammler hyperbola
X(64019) = pole of line {690, 14610} with respect to the Steiner inellipse
X(64019) = pole of line {524, 625} with respect to the Wallace hyperbola
X(64019) = pole of line {27759, 50755} with respect to the dual conic of Yff parabola
X(64019) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(44010)}}, {{A, B, C, X(111), X(10153)}}, {{A, B, C, X(115), X(9164)}}, {{A, B, C, X(523), X(14971)}}, {{A, B, C, X(524), X(5461)}}, {{A, B, C, X(543), X(36953)}}, {{A, B, C, X(671), X(57926)}}, {{A, B, C, X(4590), X(9166)}}, {{A, B, C, X(7617), X(9516)}}, {{A, B, C, X(8591), X(51226)}}, {{A, B, C, X(9180), X(36523)}}, {{A, B, C, X(14061), X(18823)}}, {{A, B, C, X(14360), X(52094)}}, {{A, B, C, X(18842), X(52450)}}, {{A, B, C, X(31125), X(42010)}}, {{A, B, C, X(41134), X(42349)}}, {{A, B, C, X(60239), X(63853)}}, {{A, B, C, X(60645), X(60863)}}
X(64019) = barycentric product X(i)*X(j) for these (i, j): {44010, 99}
X(64019) = barycentric quotient X(i)/X(j) for these (i, j): {44010, 523}, {57152, 9178}
X(64019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 148, 14971}, {2, 31128, 42008}, {2, 32480, 7844}, {2, 41134, 99}, {2, 41135, 6722}, {2, 543, 14061}, {2, 620, 41134}, {2, 7618, 7790}, {2, 7664, 52141}, {2, 8591, 5461}, {2, 99, 9166}, {115, 14971, 41148}, {115, 8596, 671}, {549, 15561, 6054}, {549, 6054, 34473}, {620, 22247, 2482}, {2482, 22247, 2}, {2482, 5461, 8591}, {2482, 9167, 22247}, {5026, 21358, 11161}, {6722, 15300, 41135}, {7807, 62362, 55085}, {7883, 33274, 43459}, {11177, 15721, 38737}, {11539, 61561, 11632}, {11711, 19875, 50885}, {12188, 61843, 26614}, {14971, 36521, 148}, {15709, 64090, 6036}, {18823, 44397, 31998}, {19883, 51578, 50886}, {22110, 35297, 51224}, {22110, 51224, 7809}, {27088, 41133, 316}, {33376, 33377, 8593}, {39785, 58448, 8859}

X(64020) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ANTI-EXTOUCH AND X(3)-CROSSPEDAL-OF-X(1)

Barycentrics    a^2*(a+b-c)*(a-b+c)*(a^3-b^3-b^2*c-b*c^2-c^3+a^2*(b+c)-a*(b+c)^2) : :

X(64020) lies on these lines: {1, 90}, {3, 47}, {6, 19}, {8, 45729}, {11, 41344}, {12, 5711}, {25, 14529}, {31, 73}, {33, 1898}, {40, 54301}, {46, 36754}, {55, 581}, {56, 58}, {57, 1203}, {81, 3485}, {109, 386}, {171, 37694}, {184, 3556}, {201, 2911}, {212, 4300}, {223, 37550}, {225, 41011}, {226, 62805}, {238, 37523}, {255, 1064}, {278, 14016}, {388, 651}, {394, 960}, {405, 7299}, {497, 3562}, {517, 36747}, {578, 2818}, {595, 11510}, {601, 22350}, {602, 4303}, {603, 1193}, {611, 5252}, {613, 37549}, {774, 20277}, {920, 37565}, {940, 11375}, {958, 55400}, {959, 5323}, {999, 23070}, {1001, 54356}, {1038, 54386}, {1042, 1451}, {1046, 37591}, {1066, 1497}, {1106, 1450}, {1118, 3194}, {1124, 8978}, {1155, 36745}, {1181, 6001}, {1191, 1319}, {1214, 16471}, {1386, 23144}, {1388, 16483}, {1407, 32636}, {1411, 36750}, {1420, 5315}, {1421, 6126}, {1425, 5320}, {1452, 44086}, {1454, 1465}, {1457, 1468}, {1466, 2122}, {1467, 16469}, {1478, 8757}, {1479, 60691}, {1480, 5697}, {1498, 12688}, {1707, 54320}, {1724, 37558}, {1745, 3072}, {1771, 11502}, {1777, 63982}, {1788, 32911}, {1836, 1838}, {1837, 39574}, {1854, 17824}, {1950, 54423}, {1993, 3869}, {1994, 64047}, {2099, 15955}, {2323, 12526}, {2390, 11402}, {2646, 36746}, {2650, 61356}, {2964, 36152}, {2999, 37744}, {3057, 64069}, {3149, 5348}, {3193, 11415}, {3256, 5312}, {3295, 23071}, {3303, 39789}, {3339, 52423}, {3476, 62804}, {3516, 34935}, {3649, 37543}, {3812, 10601}, {3868, 45728}, {3924, 61396}, {4347, 15556}, {4383, 24914}, {4551, 5264}, {4559, 54416}, {4642, 61357}, {5021, 43039}, {5083, 30148}, {5119, 56535}, {5219, 37559}, {5221, 52424}, {5247, 24806}, {5292, 34029}, {5302, 55438}, {5396, 11507}, {5398, 59317}, {5399, 11508}, {5707, 12047}, {5902, 16472}, {5903, 16473}, {6147, 15253}, {6180, 10404}, {7074, 37568}, {7098, 17080}, {7288, 17074}, {7354, 64057}, {7355, 11428}, {7592, 64021}, {7686, 10982}, {7702, 23537}, {8071, 52407}, {8192, 8679}, {8270, 41538}, {9777, 58493}, {10106, 62828}, {10372, 28369}, {10693, 17847}, {10895, 52383}, {11425, 63435}, {11553, 54358}, {12161, 14988}, {12514, 45126}, {13567, 58459}, {13750, 37697}, {14110, 37498}, {14793, 58738}, {15071, 33178}, {16140, 20182}, {16790, 28037}, {17811, 25917}, {18360, 37541}, {18445, 40266}, {18451, 31937}, {18961, 64172}, {19860, 54444}, {19861, 22128}, {20306, 23292}, {20967, 22119}, {20992, 54411}, {22654, 26892}, {22766, 34586}, {22768, 37469}, {22769, 23154}, {24954, 25934}, {26098, 26481}, {26888, 37538}, {31165, 37672}, {34339, 36752}, {34435, 58737}, {36279, 37509}, {36749, 64044}, {37501, 37600}, {37542, 37738}, {37836, 52271}, {39150, 54402}, {39151, 54403}, {39523, 50193}, {40292, 52408}, {41687, 60689}, {44663, 63094}, {54339, 62841}, {54354, 60682}, {56634, 58741}

X(64020) = perspector of circumconic {{A, B, C, X(108), X(4565)}}
X(64020) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 56225}, {9, 60156}, {33, 57832}, {312, 46010}, {318, 57667}, {4086, 59130}, {6332, 59083}
X(64020) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 60156}, {5517, 4391}, {32664, 56225}
X(64020) = X(i)-Ceva conjugate of X(j) for these {i, j}: {959, 56}, {45126, 36744}
X(64020) = pole of line {1946, 2605} with respect to the circumcircle
X(64020) = pole of line {3, 33} with respect to the Feuerbach hyperbola
X(64020) = pole of line {513, 58888} with respect to the Orthic inconic
X(64020) = pole of line {8, 1812} with respect to the Stammler hyperbola
X(64020) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(52033)}}, {{A, B, C, X(6), X(1069)}}, {{A, B, C, X(19), X(58)}}, {{A, B, C, X(34), X(1412)}}, {{A, B, C, X(56), X(1880)}}, {{A, B, C, X(65), X(222)}}, {{A, B, C, X(406), X(859)}}, {{A, B, C, X(478), X(603)}}, {{A, B, C, X(607), X(2194)}}, {{A, B, C, X(608), X(1408)}}, {{A, B, C, X(915), X(3560)}}, {{A, B, C, X(1193), X(56905)}}, {{A, B, C, X(1409), X(7335)}}, {{A, B, C, X(1829), X(5739)}}, {{A, B, C, X(2178), X(60154)}}, {{A, B, C, X(2221), X(4185)}}, {{A, B, C, X(2262), X(57666)}}, {{A, B, C, X(2331), X(2360)}}, {{A, B, C, X(5341), X(34435)}}, {{A, B, C, X(7105), X(24430)}}, {{A, B, C, X(52413), X(57709)}}
X(64020) = barycentric product X(i)*X(j) for these (i, j): {1, 45126}, {56, 5739}, {222, 406}, {348, 44086}, {1408, 42707}, {1452, 63}, {12514, 57}, {14258, 1460}, {27174, 65}, {36744, 7}
X(64020) = barycentric quotient X(i)/X(j) for these (i, j): {31, 56225}, {56, 60156}, {222, 57832}, {406, 7017}, {1397, 46010}, {1452, 92}, {5739, 3596}, {12514, 312}, {27174, 314}, {36744, 8}, {44086, 281}, {45126, 75}, {52411, 57667}
X(64020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3073, 62333}, {31, 73, 37579}, {34, 54421, 65}, {40, 54301, 61397}, {56, 8614, 222}, {57, 34043, 1406}, {109, 386, 11509}, {184, 42448, 3556}, {212, 4300, 37601}, {222, 16466, 56}, {255, 1064, 26357}, {602, 4303, 37578}, {603, 1193, 1470}, {651, 57280, 388}, {1042, 2308, 1451}, {1066, 1497, 33925}, {1191, 34046, 1319}, {1191, 62207, 34046}, {1203, 34043, 57}, {1457, 1468, 26437}, {1479, 63339, 60691}, {1771, 37732, 11502}, {4551, 5264, 11501}, {5710, 9370, 5252}, {5711, 34048, 12}, {5903, 16473, 44414}, {14529, 42450, 25}

X(64021) = ANTICOMPLEMENT OF X(5887)

Barycentrics    a*(a^5*(b+c)-2*a^3*(b-c)^2*(b+c)+a*(b-c)^4*(b+c)+2*a^2*(b^2-c^2)^2-(b^2-c^2)^2*(b^2-b*c+c^2)-a^4*(b^2+b*c+c^2)) : :
X(64021) = -3*X[2]+2*X[5887], -2*X[72]+3*X[5657], -3*X[165]+2*X[31806], -6*X[354]+5*X[10595], -3*X[376]+4*X[9943], -3*X[381]+4*X[61541], -3*X[392]+4*X[9940], -5*X[631]+4*X[960], -4*X[942]+3*X[5603], -2*X[946]+3*X[5902], -4*X[1125]+5*X[15016], -4*X[1385]+3*X[3877] and many others

X(64021) lies on these lines: {1, 104}, {2, 5887}, {3, 3417}, {4, 65}, {5, 10129}, {7, 10532}, {8, 912}, {10, 5693}, {11, 7704}, {20, 145}, {24, 3556}, {30, 9961}, {34, 45225}, {35, 40256}, {36, 40257}, {40, 758}, {46, 6261}, {55, 45288}, {56, 26877}, {57, 7971}, {72, 5657}, {74, 30250}, {78, 3359}, {84, 1389}, {100, 37700}, {119, 25005}, {153, 355}, {165, 31806}, {185, 2818}, {214, 59332}, {221, 1181}, {318, 38955}, {354, 10595}, {376, 9943}, {381, 61541}, {389, 42448}, {392, 9940}, {404, 45770}, {411, 59318}, {484, 6796}, {496, 1537}, {497, 64045}, {515, 1770}, {516, 4084}, {518, 12245}, {519, 37430}, {580, 49500}, {581, 4424}, {631, 960}, {938, 10531}, {942, 5603}, {946, 5902}, {952, 14923}, {962, 5768}, {971, 7672}, {986, 1064}, {997, 6940}, {1000, 10305}, {1006, 12514}, {1012, 62864}, {1125, 15016}, {1155, 6942}, {1210, 1519}, {1385, 3877}, {1479, 53615}, {1482, 3873}, {1483, 64191}, {1490, 2093}, {1512, 4848}, {1614, 14529}, {1621, 37615}, {1698, 20117}, {1699, 31870}, {1709, 21669}, {1735, 10571}, {1737, 6941}, {1771, 45272}, {1788, 6834}, {1854, 6198}, {2077, 22836}, {2099, 12114}, {2390, 5890}, {2646, 6950}, {2650, 37529}, {2778, 12244}, {2801, 5881}, {2802, 61296}, {2829, 10950}, {2975, 24467}, {3057, 4305}, {3062, 16615}, {3073, 3924}, {3085, 64041}, {3086, 18838}, {3090, 3812}, {3091, 31937}, {3149, 36279}, {3185, 37115}, {3218, 11249}, {3241, 23340}, {3295, 37287}, {3338, 45977}, {3339, 63992}, {3419, 12529}, {3474, 6934}, {3485, 6833}, {3486, 6938}, {3487, 12709}, {3488, 12711}, {3523, 40296}, {3524, 31165}, {3525, 25917}, {3567, 42450}, {3576, 3878}, {3577, 10308}, {3579, 33597}, {3616, 6892}, {3622, 13373}, {3649, 7680}, {3655, 26201}, {3656, 6583}, {3679, 63967}, {3681, 5690}, {3698, 58631}, {3753, 5177}, {3754, 5587}, {3817, 33815}, {3827, 6776}, {3838, 6874}, {3870, 49163}, {3871, 64189}, {3874, 7982}, {3876, 5694}, {3881, 16200}, {3889, 10222}, {3890, 10246}, {3894, 11531}, {3899, 7987}, {3901, 7991}, {3918, 15064}, {3919, 19925}, {3957, 37622}, {3962, 63976}, {4004, 5927}, {4067, 43174}, {4227, 62843}, {4294, 41537}, {4338, 5691}, {4640, 6875}, {4642, 37699}, {4744, 51118}, {4757, 41869}, {4855, 34474}, {4867, 59326}, {5044, 18231}, {5057, 6928}, {5086, 6923}, {5119, 64173}, {5128, 52026}, {5221, 22753}, {5250, 18443}, {5253, 37612}, {5534, 38665}, {5537, 41696}, {5658, 41539}, {5692, 6684}, {5697, 5882}, {5698, 6936}, {5709, 64150}, {5714, 10599}, {5727, 10728}, {5731, 13369}, {5770, 10527}, {5794, 6951}, {5836, 14872}, {5880, 6901}, {5883, 8227}, {5885, 5886}, {5901, 13226}, {5904, 11362}, {5918, 17538}, {6147, 63257}, {6197, 64022}, {6237, 37098}, {6256, 10573}, {6265, 18861}, {6326, 25440}, {6705, 30274}, {6827, 11415}, {6829, 12609}, {6830, 12047}, {6831, 33899}, {6832, 28629}, {6852, 28628}, {6853, 26066}, {6868, 44447}, {6895, 12699}, {6902, 24703}, {6909, 62830}, {6917, 20292}, {6920, 54318}, {6922, 51409}, {6924, 9352}, {6949, 24914}, {6952, 11375}, {6963, 21616}, {6968, 54361}, {6990, 12617}, {7098, 52270}, {7330, 19860}, {7501, 40660}, {7592, 64020}, {7705, 12619}, {7741, 10265}, {7992, 18421}, {8148, 30283}, {8166, 61660}, {8256, 37725}, {8666, 11014}, {9581, 12736}, {9612, 59392}, {9624, 58565}, {9778, 37585}, {9781, 58493}, {9803, 52367}, {9856, 31794}, {9946, 35262}, {9947, 38074}, {9952, 18357}, {9960, 37468}, {10085, 25415}, {10167, 31786}, {10176, 31423}, {10178, 21735}, {10199, 50908}, {10247, 62854}, {10267, 18444}, {10273, 40263}, {10284, 61287}, {10310, 12635}, {10391, 14646}, {10394, 37730}, {10598, 64131}, {10605, 63435}, {10806, 30305}, {10893, 61717}, {10894, 61716}, {10942, 12532}, {11041, 12246}, {11219, 37735}, {11248, 34772}, {11372, 30329}, {11376, 17638}, {11431, 44545}, {11500, 37567}, {11507, 45230}, {11509, 59366}, {11529, 12705}, {11682, 37611}, {11684, 26921}, {11826, 44669}, {11827, 17768}, {12248, 37740}, {12515, 26285}, {12526, 30503}, {12559, 37569}, {12650, 30304}, {12678, 41687}, {12831, 26482}, {12832, 26476}, {13464, 18398}, {13465, 18259}, {13528, 56176}, {13754, 46483}, {14450, 37826}, {14526, 37719}, {15622, 53252}, {15726, 33703}, {15803, 40249}, {15829, 37526}, {17016, 36742}, {17637, 37724}, {17660, 25414}, {17857, 54286}, {17916, 53560}, {18237, 37541}, {18242, 40663}, {18393, 63963}, {18395, 63964}, {18492, 31871}, {19861, 37534}, {20612, 37531}, {20718, 30273}, {21165, 54290}, {24476, 39898}, {24806, 44706}, {27383, 41389}, {27529, 37713}, {28194, 34719}, {30144, 37561}, {31787, 64107}, {31798, 37427}, {31835, 63961}, {31838, 54445}, {32214, 64138}, {32613, 33858}, {34043, 59285}, {34195, 37533}, {34789, 37702}, {34862, 50194}, {36746, 37614}, {37006, 40264}, {37305, 64040}, {37403, 63391}, {37535, 48667}, {37624, 62835}, {37721, 52860}, {41538, 64148}, {44861, 56273}, {50317, 62831}, {50371, 64128}, {51379, 59591}, {59330, 64188}, {64106, 64132}

X(64021) = midpoint of X(i) and X(j) for these {i,j}: {20, 64047}, {3901, 7991}, {5903, 15071}
X(64021) = reflection of X(i) in X(j) for these {i,j}: {1, 5884}, {4, 65}, {8, 37562}, {72, 31788}, {355, 35004}, {944, 1071}, {962, 24474}, {1482, 24475}, {3057, 12675}, {3869, 3}, {3885, 37727}, {3962, 63976}, {4067, 43174}, {5693, 10}, {5694, 13145}, {5697, 5882}, {5887, 34339}, {5904, 11362}, {7982, 3874}, {9856, 31794}, {10698, 11570}, {11372, 30329}, {12246, 17649}, {12247, 17654}, {12528, 355}, {12666, 6256}, {12672, 942}, {12688, 7686}, {12758, 15528}, {14110, 9943}, {14872, 5836}, {14923, 25413}, {31803, 3754}, {37625, 4084}, {39898, 24476}, {40266, 5}, {42448, 389}, {59387, 10273}, {61705, 3919}
X(64021) = inverse of X(7704) in Feuerbach hyperbola
X(64021) = anticomplement of X(5887)
X(64021) = perspector of circumconic {{A, B, C, X(37136), X(54240)}}
X(64021) = X(i)-Dao conjugate of X(j) for these {i, j}: {5887, 5887}
X(64021) = pole of line {48390, 53305} with respect to the circumcircle
X(64021) = pole of line {3738, 50332} with respect to the Conway circle
X(64021) = pole of line {3738, 6129} with respect to the incircle
X(64021) = pole of line {521, 16228} with respect to the polar circle
X(64021) = pole of line {4, 1319} with respect to the Feuerbach hyperbola
X(64021) = pole of line {860, 58889} with respect to the Jerabek hyperbola
X(64021) = pole of line {650, 22086} with respect to the Orthic inconic
X(64021) = pole of line {1459, 3738} with respect to the Suppa-Cucoanes circle
X(64021) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 1364, 15614}
X(64021) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(1795)}}, {{A, B, C, X(104), X(158)}}, {{A, B, C, X(318), X(6906)}}, {{A, B, C, X(522), X(5450)}}, {{A, B, C, X(603), X(1875)}}, {{A, B, C, X(1118), X(3417)}}, {{A, B, C, X(1243), X(1887)}}, {{A, B, C, X(1389), X(15501)}}, {{A, B, C, X(1857), X(2342)}}
X(64021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1158, 6906}, {1, 1768, 5450}, {1, 63399, 104}, {3, 14988, 3869}, {20, 64047, 517}, {40, 12520, 3651}, {40, 18446, 11491}, {46, 6261, 6905}, {57, 7971, 63986}, {65, 12688, 7686}, {65, 1858, 18391}, {72, 31788, 5657}, {354, 45776, 10595}, {355, 2771, 12528}, {516, 4084, 37625}, {517, 1071, 944}, {517, 37727, 3885}, {912, 37562, 8}, {942, 12672, 5603}, {944, 2096, 37002}, {944, 6361, 37000}, {952, 25413, 14923}, {962, 5768, 12116}, {997, 59333, 6940}, {1155, 37837, 6942}, {1210, 54198, 1519}, {1482, 24475, 3873}, {1737, 12608, 6941}, {1837, 64119, 4}, {2646, 64118, 6950}, {2771, 17654, 12247}, {2771, 35004, 355}, {2800, 11570, 10698}, {2800, 15528, 12758}, {2800, 5884, 1}, {3057, 12675, 7967}, {3485, 14647, 6833}, {3486, 64190, 6938}, {3753, 5777, 5818}, {3754, 31803, 5587}, {4848, 6260, 1512}, {5534, 63130, 38665}, {5694, 13145, 26446}, {5836, 14872, 59388}, {5887, 34339, 2}, {5903, 15071, 515}, {6001, 7686, 12688}, {9943, 14110, 376}, {9943, 44663, 14110}, {11500, 37567, 48363}, {12047, 12616, 6830}, {12515, 37733, 26285}, {12526, 30503, 55104}, {12709, 50195, 3487}, {14986, 18419, 942}, {17660, 25414, 37738}, {18838, 64042, 3086}, {24467, 61146, 2975}, {33899, 39542, 6831}, {63391, 64129, 37403}

X(64022) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXTANGENTS AND X(3)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a^6+3*a^5*(b+c)-a*(b-c)^2*(b+c)^3+a^2*(b^2-c^2)^2-2*(b^2-c^2)^2*(b^2+c^2)-2*a^3*(b^3+b^2*c+b*c^2+c^3)) : :
X(64022) = -2*X[1]+3*X[154], -4*X[10]+3*X[1853], -X[145]+3*X[11206], -6*X[165]+5*X[8567], -4*X[206]+3*X[38315], -4*X[946]+5*X[64024], -8*X[1125]+9*X[61680], -4*X[1385]+5*X[17821], -4*X[1386]+5*X[19132], -10*X[1698]+9*X[61735], -4*X[3579]+3*X[10606]

X(64022) lies on these lines: {1, 154}, {3, 1782}, {6, 19}, {8, 1503}, {10, 1853}, {20, 54107}, {40, 64}, {55, 976}, {56, 26934}, {92, 5786}, {145, 11206}, {159, 3242}, {161, 9798}, {165, 8567}, {184, 11396}, {198, 201}, {206, 38315}, {209, 2390}, {219, 18598}, {355, 64037}, {394, 64039}, {405, 1726}, {484, 10076}, {515, 17845}, {516, 5895}, {517, 1498}, {518, 9924}, {524, 34730}, {774, 20991}, {912, 17834}, {942, 21370}, {944, 34782}, {946, 64024}, {952, 9833}, {958, 1762}, {960, 10319}, {962, 2883}, {1118, 51421}, {1125, 61680}, {1181, 41722}, {1191, 40959}, {1211, 20306}, {1385, 17821}, {1386, 19132}, {1482, 6759}, {1619, 12410}, {1698, 61735}, {1714, 51410}, {1834, 52082}, {1836, 1869}, {1837, 1842}, {1902, 15811}, {2093, 3987}, {2098, 10535}, {2099, 10537}, {2192, 3057}, {2393, 16980}, {2771, 17835}, {2778, 17812}, {2818, 5752}, {2836, 32276}, {2935, 12778}, {2948, 17847}, {3101, 3869}, {3176, 6525}, {3303, 18621}, {3579, 10606}, {3611, 42448}, {3616, 10192}, {3617, 32064}, {3622, 35260}, {3623, 64059}, {3812, 9816}, {3868, 7291}, {3913, 62393}, {3927, 48882}, {4295, 54294}, {4498, 8676}, {4663, 17813}, {5090, 36990}, {5221, 32065}, {5550, 58434}, {5584, 7085}, {5596, 5846}, {5603, 16252}, {5657, 6247}, {5690, 14216}, {5709, 13095}, {5790, 18381}, {5878, 28174}, {5887, 8251}, {5893, 9812}, {5894, 9778}, {5928, 46878}, {6000, 12702}, {6197, 64021}, {6225, 20070}, {6254, 26893}, {6354, 37384}, {6361, 15311}, {7074, 52359}, {7713, 17810}, {7957, 7959}, {7968, 17820}, {7969, 17819}, {7982, 40658}, {7984, 15647}, {7991, 58795}, {8141, 14988}, {8148, 32063}, {8185, 56924}, {9536, 40571}, {9780, 23332}, {9899, 63468}, {9928, 37498}, {10060, 11010}, {10117, 49553}, {10246, 10282}, {10247, 14530}, {10533, 44635}, {10534, 44636}, {10536, 14529}, {11435, 42450}, {11471, 12688}, {11645, 34713}, {12135, 31383}, {12245, 34781}, {12324, 59417}, {12335, 23858}, {12645, 64033}, {12671, 36986}, {13094, 49163}, {14543, 27410}, {15071, 63434}, {15509, 37591}, {15583, 59406}, {17811, 37613}, {17822, 31788}, {17823, 61726}, {17824, 37625}, {18400, 18525}, {18405, 18480}, {18453, 40266}, {18493, 61747}, {19087, 49227}, {19088, 49226}, {22802, 48661}, {26446, 40686}, {28629, 58459}, {30503, 54305}, {31166, 51000}, {32345, 32371}, {34774, 51192}, {34780, 59503}, {36851, 49524}, {37260, 62811}, {37549, 41230}, {39690, 41320}, {40933, 47848}, {41362, 59387}, {41869, 61721}, {44662, 64069}, {59388, 64034}

X(64022) = midpoint of X(i) and X(j) for these {i,j}: {6225, 20070}, {12245, 34781}, {12645, 64033}
X(64022) = reflection of X(i) in X(j) for these {i,j}: {1, 40660}, {64, 40}, {944, 34782}, {962, 2883}, {1482, 6759}, {1854, 3556}, {2099, 10537}, {2935, 12778}, {3242, 159}, {5895, 12779}, {7973, 1498}, {7982, 40658}, {7984, 15647}, {14216, 5690}, {17847, 2948}, {32345, 32371}, {36851, 49524}, {37498, 9928}, {48661, 22802}, {51000, 31166}, {51192, 34774}, {64037, 355}
X(64022) = perspector of circumconic {{A, B, C, X(108), X(56235)}}
X(64022) = pole of line {521, 58333} with respect to the Bevan circle
X(64022) = pole of line {656, 1946} with respect to the circumcircle
X(64022) = pole of line {33, 1104} with respect to the Feuerbach hyperbola
X(64022) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(19), X(44692)}}, {{A, B, C, X(34), X(2184)}}, {{A, B, C, X(64), X(608)}}, {{A, B, C, X(72), X(30456)}}, {{A, B, C, X(200), X(7156)}}, {{A, B, C, X(4185), X(27404)}}, {{A, B, C, X(34187), X(52413)}}
X(64022) = barycentric product X(i)*X(j) for these (i, j): {27404, 65}
X(64022) = barycentric quotient X(i)/X(j) for these (i, j): {27404, 314}
X(64022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40660, 154}, {40, 6001, 64}, {65, 2264, 54418}, {165, 12262, 8567}, {516, 12779, 5895}, {517, 1498, 7973}, {1829, 64040, 6}, {7713, 44547, 17810}

X(64023) = ANTICOMPLEMENT OF X(3313)

Barycentrics    a^2*(-b^6+a^2*b^2*c^2-c^6+a^4*(b^2+c^2)) : :
X(64023) = -3*X[2]+2*X[3313], -6*X[51]+5*X[3618], -4*X[141]+3*X[2979], -4*X[143]+3*X[5050], -4*X[182]+5*X[3567], -18*X[373]+17*X[63120], -4*X[389]+3*X[25406], -3*X[428]+2*X[13562], -3*X[568]+2*X[48906], -3*X[599]+4*X[41579], -4*X[1216]+5*X[40330], -3*X[1992]+2*X[6467] and many others

X(64023) lies on these lines: {2, 3313}, {4, 69}, {6, 22}, {20, 19161}, {23, 206}, {25, 20806}, {30, 10938}, {51, 3618}, {52, 6776}, {66, 7391}, {67, 13201}, {110, 20987}, {141, 2979}, {143, 5050}, {159, 1993}, {182, 3567}, {185, 14927}, {193, 2393}, {237, 50645}, {287, 60521}, {297, 40052}, {343, 3867}, {373, 63120}, {389, 25406}, {394, 7716}, {399, 10752}, {428, 13562}, {524, 9973}, {542, 7731}, {568, 48906}, {570, 37184}, {571, 37183}, {576, 11423}, {599, 41579}, {895, 32262}, {1007, 51412}, {1112, 19118}, {1154, 18440}, {1205, 11800}, {1216, 40330}, {1350, 7503}, {1351, 7387}, {1353, 14449}, {1503, 5889}, {1513, 39113}, {1609, 14060}, {1974, 22151}, {1992, 6467}, {1994, 64028}, {2781, 10733}, {2854, 6144}, {2871, 56017}, {3095, 20775}, {3098, 35921}, {3146, 20079}, {3547, 5446}, {3564, 6243}, {3580, 23300}, {3589, 5640}, {3619, 3917}, {3620, 29959}, {3629, 8705}, {3763, 7998}, {3819, 63121}, {3852, 7823}, {4259, 37231}, {5032, 22829}, {5085, 15043}, {5092, 15045}, {5093, 15074}, {5157, 6636}, {5166, 53059}, {5182, 39835}, {5392, 55028}, {5480, 13160}, {5523, 19595}, {5622, 12236}, {5890, 44831}, {5943, 63119}, {5946, 12017}, {5965, 13423}, {6101, 63475}, {6241, 29012}, {6353, 28708}, {6515, 36851}, {6660, 14575}, {6697, 31074}, {7403, 37484}, {7404, 10519}, {7517, 19139}, {7558, 9781}, {7566, 10516}, {7999, 24206}, {8681, 11008}, {9465, 16285}, {9730, 21852}, {9737, 44180}, {9818, 13391}, {9821, 22062}, {9909, 19125}, {9924, 11477}, {9936, 34382}, {10510, 56918}, {10565, 58550}, {10574, 44882}, {11002, 51171}, {11061, 13417}, {11328, 20819}, {11387, 64035}, {11422, 35707}, {11433, 41256}, {11451, 47355}, {11455, 48884}, {11465, 58445}, {11482, 16982}, {11513, 26894}, {11514, 26919}, {11646, 39836}, {11649, 37517}, {12086, 63431}, {12111, 36990}, {12160, 39879}, {12167, 37491}, {12223, 42258}, {12224, 42259}, {12225, 29181}, {12273, 14982}, {12282, 14531}, {12283, 63722}, {12329, 56878}, {13321, 55705}, {14118, 54374}, {14831, 64014}, {14957, 41760}, {15072, 48905}, {15577, 34148}, {15583, 34751}, {15760, 18438}, {16475, 31757}, {16981, 32366}, {18358, 23039}, {18374, 19122}, {18382, 50435}, {18436, 39884}, {18583, 34002}, {19124, 46730}, {19128, 44469}, {19136, 63069}, {19137, 34417}, {19197, 61362}, {19924, 22950}, {20022, 40073}, {20794, 48673}, {20960, 28710}, {21243, 46026}, {21849, 59373}, {22972, 55722}, {27375, 31360}, {30717, 54096}, {31099, 61664}, {31304, 36989}, {31810, 64033}, {32248, 64104}, {33879, 51128}, {33884, 61676}, {35500, 52987}, {36852, 47096}, {37446, 57805}, {37488, 39588}, {37511, 64096}, {39125, 53777}, {39571, 41257}, {40670, 44299}, {40673, 58555}, {40981, 50666}, {41584, 62382}, {45170, 64095}, {48892, 52989}, {50649, 59349}, {52276, 61629}, {53097, 63664}, {55629, 63414}, {58470, 63109}

X(64023) = reflection of X(i) in X(j) for these {i,j}: {20, 19161}, {69, 1843}, {110, 40949}, {1205, 11800}, {1351, 10263}, {1353, 14449}, {1992, 21969}, {2979, 9971}, {3313, 9969}, {6101, 63475}, {6776, 52}, {9967, 5446}, {11061, 13417}, {11412, 1352}, {12111, 36990}, {12220, 6}, {12272, 9973}, {12273, 14982}, {12283, 63722}, {12294, 13598}, {13201, 67}, {14927, 185}, {15073, 1351}, {18436, 39884}, {18438, 21850}, {32248, 64104}, {37484, 48876}, {39836, 11646}, {41716, 4}, {51212, 45186}, {62188, 29959}, {64014, 14831}, {64050, 1350}
X(64023) = anticomplement of X(3313)
X(64023) = perspector of circumconic {{A, B, C, X(827), X(6331)}}
X(64023) = X(i)-Dao conjugate of X(j) for these {i, j}: {3313, 3313}
X(64023) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {66, 21289}, {82, 5596}, {83, 21288}, {251, 21215}, {2156, 2896}, {2353, 21217}, {16277, 8}, {40404, 4329}, {46765, 6360}, {53657, 7192}, {58113, 4560}
X(64023) = pole of line {1899, 3618} with respect to the Jerabek hyperbola
X(64023) = pole of line {1180, 5133} with respect to the Kiepert hyperbola
X(64023) = pole of line {141, 184} with respect to the Stammler hyperbola
X(64023) = pole of line {850, 2485} with respect to the Steiner circumellipse
X(64023) = pole of line {3, 8024} with respect to the Wallace hyperbola
X(64023) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(20960)}}, {{A, B, C, X(6), X(1235)}}, {{A, B, C, X(76), X(1176)}}, {{A, B, C, X(251), X(264)}}, {{A, B, C, X(315), X(18124)}}, {{A, B, C, X(317), X(55028)}}, {{A, B, C, X(1501), X(1843)}}, {{A, B, C, X(5012), X(31360)}}, {{A, B, C, X(6664), X(19127)}}, {{A, B, C, X(17984), X(56975)}}, {{A, B, C, X(18049), X(44129)}}, {{A, B, C, X(33632), X(54412)}}, {{A, B, C, X(34207), X(44146)}}, {{A, B, C, X(44132), X(51862)}}
X(64023) = barycentric product X(i)*X(j) for these (i, j): {1, 18049}, {20960, 76}, {28710, 4}
X(64023) = barycentric quotient X(i)/X(j) for these (i, j): {18049, 75}, {20960, 6}, {28710, 69}
X(64023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 511, 41716}, {6, 22, 1176}, {6, 9019, 12220}, {23, 63063, 206}, {51, 11574, 3618}, {69, 1843, 11188}, {193, 7500, 5596}, {511, 1352, 11412}, {511, 13598, 12294}, {511, 1843, 69}, {511, 45186, 51212}, {524, 9973, 12272}, {3186, 44443, 3260}, {3313, 9969, 2}, {3917, 9822, 3619}, {5085, 32191, 15043}, {5446, 9967, 14853}, {11002, 51171, 58471}, {11477, 15581, 15801}, {12294, 13598, 51538}, {20859, 31390, 6}, {20987, 64195, 110}, {34775, 48910, 52842}, {34777, 40318, 895}, {40673, 58555, 62995}, {47355, 58532, 11451}

X(64024) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(3)-CROSSPEDAL-OF-X(4)

Barycentrics    a^10-3*a^2*(b^2-c^2)^4-6*a^8*(b^2+c^2)-4*a^4*(b^2-c^2)^2*(b^2+c^2)+2*(b^2-c^2)^4*(b^2+c^2)+2*a^6*(5*b^4-2*b^2*c^2+5*c^4) : :
X(64024) = -6*X[2]+X[64], 2*X[4]+3*X[154], 4*X[5]+X[1498], 4*X[10]+X[7973], X[20]+4*X[5893], 4*X[140]+X[5878], X[155]+4*X[15761], 4*X[156]+X[12293], -9*X[373]+4*X[58492], 3*X[376]+2*X[51491], X[382]+4*X[10282], 4*X[546]+X[9833] and many others

X(64024) lies on these lines: {2, 64}, {3, 113}, {4, 154}, {5, 1498}, {6, 235}, {10, 7973}, {11, 221}, {12, 2192}, {20, 5893}, {25, 43831}, {30, 17821}, {54, 62974}, {69, 32605}, {125, 12174}, {140, 5878}, {155, 15761}, {156, 12293}, {159, 3574}, {161, 1598}, {184, 37197}, {185, 26958}, {206, 7507}, {373, 58492}, {376, 51491}, {381, 569}, {382, 10282}, {403, 1181}, {427, 15811}, {468, 1192}, {546, 9833}, {549, 20427}, {550, 61606}, {568, 63697}, {590, 19088}, {599, 64031}, {615, 19087}, {631, 8567}, {946, 64022}, {1125, 12779}, {1204, 37453}, {1249, 5922}, {1350, 28419}, {1495, 12173}, {1503, 3091}, {1568, 11414}, {1593, 51403}, {1614, 18396}, {1619, 11479}, {1656, 6000}, {1657, 11202}, {1660, 11424}, {1699, 40660}, {1854, 11375}, {2781, 11444}, {2888, 11061}, {2917, 7517}, {3070, 17820}, {3071, 17819}, {3089, 12233}, {3090, 5656}, {3146, 35260}, {3147, 37487}, {3357, 3526}, {3462, 41372}, {3523, 5894}, {3524, 64187}, {3525, 12250}, {3527, 43834}, {3533, 15105}, {3542, 9786}, {3545, 34781}, {3589, 41735}, {3624, 12262}, {3763, 34146}, {3818, 6145}, {3830, 34785}, {3832, 11206}, {3843, 14530}, {3851, 14862}, {3855, 23324}, {4413, 12335}, {4846, 16238}, {5054, 48672}, {5055, 12315}, {5056, 12324}, {5068, 32064}, {5070, 13093}, {5072, 23325}, {5079, 32767}, {5085, 6816}, {5094, 11381}, {5318, 17827}, {5321, 17826}, {5339, 11243}, {5340, 11244}, {5432, 12950}, {5433, 12940}, {5439, 6001}, {5448, 7387}, {5480, 9924}, {5587, 40658}, {5654, 37498}, {5706, 37372}, {5786, 52248}, {5907, 6293}, {6241, 15738}, {6353, 13568}, {6525, 6621}, {6616, 10002}, {6622, 13567}, {6623, 12241}, {6689, 9818}, {6804, 34944}, {6823, 17811}, {7378, 16656}, {7386, 32602}, {7484, 9914}, {7487, 41424}, {7505, 10605}, {7547, 14157}, {7566, 32395}, {7568, 32620}, {7592, 44958}, {7691, 45014}, {7729, 9729}, {7778, 59530}, {7808, 12202}, {7914, 12502}, {7958, 7959}, {8252, 49251}, {8253, 49250}, {8718, 31180}, {8798, 20208}, {8991, 32785}, {9781, 63737}, {9820, 37497}, {9934, 61574}, {9968, 61737}, {10024, 18451}, {10110, 34751}, {10151, 19467}, {10193, 55863}, {10201, 12163}, {10274, 15089}, {10303, 54050}, {10516, 13160}, {10533, 23261}, {10534, 23251}, {10535, 10895}, {10594, 56924}, {10675, 42095}, {10676, 42098}, {10896, 26888}, {10984, 16072}, {10996, 53415}, {11064, 37201}, {11204, 15720}, {11245, 45004}, {11403, 61743}, {11439, 31236}, {11449, 16165}, {11456, 15081}, {11457, 35487}, {11464, 35490}, {11563, 12161}, {11745, 31860}, {11799, 36747}, {12111, 37638}, {12164, 64060}, {12279, 30744}, {12290, 52296}, {12791, 15184}, {12930, 24953}, {12964, 42262}, {12970, 42265}, {13094, 26364}, {13095, 26363}, {13367, 44438}, {13406, 14852}, {13526, 13613}, {13881, 32445}, {13980, 32786}, {14094, 63695}, {14128, 44544}, {14249, 15274}, {14853, 17040}, {14864, 61937}, {15028, 32184}, {15046, 32743}, {15056, 41715}, {15068, 61750}, {15118, 19153}, {15125, 15139}, {15577, 48910}, {15581, 23049}, {15585, 51212}, {15760, 17814}, {16261, 63728}, {16619, 31815}, {17812, 23315}, {17834, 22660}, {17840, 45861}, {17843, 45860}, {17846, 20424}, {18376, 45185}, {18382, 63666}, {18386, 61139}, {18390, 19347}, {18435, 41725}, {18504, 43273}, {18913, 47296}, {19130, 39879}, {20791, 36983}, {21659, 26864}, {22051, 39522}, {22662, 22968}, {22804, 32379}, {23041, 37444}, {23047, 31383}, {25563, 35450}, {26105, 58459}, {26881, 32391}, {26882, 35480}, {30402, 42093}, {30403, 42094}, {30771, 46850}, {31267, 53094}, {31282, 64101}, {31636, 45031}, {31670, 61610}, {31804, 37984}, {31829, 59543}, {31884, 58437}, {32111, 37119}, {33546, 53852}, {34007, 35264}, {34469, 52292}, {34786, 50414}, {34787, 54131}, {35602, 44440}, {36518, 63716}, {37440, 40909}, {37672, 61607}, {39571, 44960}, {45248, 63631}, {46265, 61799}, {46372, 62947}, {47355, 63420}, {47391, 61608}, {49673, 64098}, {50689, 64059}, {52102, 61905}, {53097, 61683}, {54211, 55864}, {55856, 61540}, {56297, 59424}, {58652, 61686}, {63344, 63371}, {63671, 64036}

X(64024) = midpoint of X(i) and X(j) for these {i,j}: {3843, 14530}
X(64024) = reflection of X(i) in X(j) for these {i,j}: {8567, 631}, {40686, 1656}, {53094, 31267}
X(64024) = pole of line {1593, 3087} with respect to the Kiepert hyperbola
X(64024) = pole of line {2071, 8567} with respect to the Stammler hyperbola
X(64024) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6696), X(14615)}}, {{A, B, C, X(11744), X(31361)}}, {{A, B, C, X(14457), X(37878)}}, {{A, B, C, X(14528), X(40082)}}
X(64024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2883, 64}, {2, 6225, 6696}, {3, 22802, 5925}, {4, 154, 17845}, {4, 16252, 154}, {20, 5893, 61721}, {140, 5878, 10606}, {381, 64033, 18383}, {546, 9833, 18405}, {631, 15311, 8567}, {1614, 35488, 18396}, {1656, 6000, 40686}, {2883, 6696, 6225}, {3089, 12233, 17810}, {3090, 5656, 6247}, {3090, 6247, 61735}, {3525, 12250, 23328}, {3574, 5198, 53023}, {3589, 41735, 52028}, {3832, 11206, 41362}, {3843, 14530, 18400}, {3855, 64034, 23324}, {5054, 48672, 64027}, {5055, 12315, 20299}, {5070, 13093, 23329}, {5656, 6247, 58795}, {5893, 10192, 20}, {5894, 58434, 3523}, {5925, 22802, 5895}, {6759, 18383, 64033}, {7507, 26883, 36990}, {9729, 36982, 7729}, {11441, 34117, 17824}, {12111, 63657, 37638}, {13406, 32139, 14852}, {14862, 18381, 32063}, {17825, 41602, 1853}, {18383, 64033, 64037}, {22802, 61747, 64063}, {22802, 64063, 3}, {35450, 46219, 25563}, {61749, 64063, 22802}

X(64025) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(3)-CROSSPEDAL-OF-X(4) AND CIRCUMCEVIAN OF X(64)

Barycentrics    a^2*(2*a^6*(b^2+c^2)+a^4*(-6*b^4+3*b^2*c^2-6*c^4)-(b^2-c^2)^2*(2*b^4+5*b^2*c^2+2*c^4)+a^2*(6*b^6-4*b^4*c^2-4*b^2*c^4+6*c^6)) : :
X(64025) = -3*X[2]+4*X[185], -6*X[51]+5*X[11439], -4*X[52]+3*X[3543], -8*X[140]+9*X[61136], -9*X[376]+8*X[10627], -15*X[381]+16*X[58531], -3*X[382]+4*X[14449], -8*X[389]+7*X[3832], -5*X[631]+4*X[5876], -8*X[1216]+9*X[10304], -5*X[1656]+6*X[45956], -2*X[1885]+3*X[45968] and many others

X(64025) lies on circumconic {{A, B, C, X(6344), X(11270)}} and on these lines: {2, 185}, {3, 9544}, {4, 94}, {20, 6193}, {22, 12174}, {23, 1498}, {30, 34799}, {49, 32138}, {51, 11439}, {52, 3543}, {64, 1993}, {68, 50009}, {74, 1147}, {110, 1204}, {113, 26917}, {140, 61136}, {145, 2807}, {155, 2071}, {156, 21844}, {184, 11440}, {186, 32139}, {193, 34146}, {323, 11413}, {376, 10627}, {381, 58531}, {382, 14449}, {389, 3832}, {399, 37814}, {511, 5059}, {542, 12278}, {569, 43602}, {578, 15062}, {631, 5876}, {1131, 12239}, {1132, 12240}, {1154, 3529}, {1181, 11003}, {1192, 35264}, {1216, 10304}, {1425, 11446}, {1593, 1994}, {1614, 7689}, {1656, 45956}, {1885, 45968}, {2883, 3580}, {2979, 45187}, {3060, 11381}, {3090, 13630}, {3091, 5462}, {3146, 5889}, {3153, 11457}, {3167, 34469}, {3270, 19367}, {3357, 9716}, {3431, 9704}, {3515, 35265}, {3520, 9545}, {3522, 5562}, {3523, 11459}, {3524, 11591}, {3528, 23039}, {3533, 14128}, {3544, 45958}, {3545, 37481}, {3564, 52071}, {3567, 3839}, {3819, 61804}, {3854, 5640}, {3855, 5946}, {3861, 13321}, {3917, 21734}, {4550, 43596}, {5056, 9730}, {5067, 15060}, {5068, 13382}, {5071, 12006}, {5154, 34462}, {5169, 12233}, {5446, 11455}, {5447, 62067}, {5448, 16003}, {5654, 12281}, {5656, 41725}, {5878, 52403}, {5891, 10303}, {5892, 46936}, {6101, 17538}, {6225, 6293}, {6240, 34796}, {6243, 33703}, {6247, 31074}, {6254, 9536}, {6285, 9539}, {6640, 22584}, {6642, 15052}, {7352, 9538}, {7391, 12324}, {7464, 16266}, {7486, 15045}, {7488, 7712}, {7492, 7691}, {7509, 64097}, {7517, 12112}, {7526, 15032}, {7527, 7592}, {7729, 37645}, {7998, 61791}, {7999, 15692}, {8567, 40928}, {8718, 37478}, {9242, 31296}, {9306, 43601}, {9703, 10226}, {9707, 38448}, {9781, 16194}, {9786, 13595}, {9812, 31732}, {9820, 43607}, {10095, 41099}, {10110, 61985}, {10170, 61856}, {10248, 31757}, {10255, 10264}, {10263, 15682}, {10299, 15067}, {10539, 14094}, {10540, 44879}, {10605, 11441}, {10620, 11250}, {10628, 20427}, {10937, 16270}, {11001, 37484}, {11017, 61932}, {11411, 44440}, {11424, 62990}, {11442, 34007}, {11444, 15717}, {11449, 21663}, {11451, 15012}, {11454, 13367}, {11468, 12038}, {11469, 63031}, {11479, 15018}, {11592, 15715}, {11793, 20791}, {12084, 56292}, {12087, 17834}, {12103, 54048}, {12160, 13093}, {12161, 14865}, {12219, 17854}, {12244, 34350}, {12254, 22815}, {12270, 14683}, {12284, 64183}, {12294, 51170}, {12308, 45735}, {12363, 41726}, {12825, 18931}, {13340, 62127}, {13346, 13445}, {13348, 62102}, {13363, 61921}, {13391, 49138}, {13451, 61990}, {13474, 14831}, {13596, 36749}, {13598, 16981}, {14379, 14919}, {14531, 50692}, {14805, 64180}, {14855, 62097}, {14915, 49135}, {15021, 17853}, {15024, 61936}, {15026, 61945}, {15028, 61914}, {15083, 43574}, {15644, 52093}, {15683, 64050}, {16226, 61944}, {16621, 62963}, {16625, 32062}, {16836, 61834}, {16881, 61984}, {17704, 61816}, {17714, 32608}, {18451, 44802}, {18474, 43895}, {18559, 64036}, {18562, 45731}, {18565, 32423}, {18914, 52069}, {19206, 43768}, {20379, 45622}, {21849, 62005}, {21969, 62032}, {22802, 50435}, {23040, 32210}, {23293, 43831}, {25711, 54037}, {26864, 38438}, {26879, 62947}, {26882, 32110}, {27082, 41673}, {30552, 63174}, {31304, 34781}, {31728, 59387}, {31751, 54445}, {31752, 64108}, {31804, 34005}, {31978, 63092}, {32111, 41587}, {32142, 61138}, {32392, 36982}, {33586, 58795}, {34484, 37490}, {34545, 63664}, {34780, 52842}, {35494, 43844}, {35497, 47391}, {36987, 62125}, {37201, 45794}, {37498, 37944}, {37643, 52003}, {37784, 64031}, {37913, 46730}, {40247, 61848}, {41398, 61752}, {43392, 43838}, {43845, 63682}, {43903, 59553}, {44003, 57451}, {46106, 57517}, {46852, 61966}, {48675, 50006}, {52525, 63425}, {54001, 61702}, {54041, 62083}, {54042, 62092}, {54047, 62104}, {54376, 64177}, {58470, 61962}, {59373, 63723}, {61128, 61753}, {62130, 63414}, {63063, 63420}

X(64025) = reflection of X(i) in X(j) for these {i,j}: {3, 45957}, {4, 34783}, {20, 6241}, {146, 7722}, {3146, 5889}, {3529, 64030}, {5059, 12279}, {6225, 6293}, {11412, 10575}, {12111, 185}, {12219, 17854}, {12279, 64029}, {12290, 52}, {14683, 12270}, {18436, 13491}, {18439, 6102}, {18562, 45731}, {33703, 6243}, {36982, 32392}, {45187, 46850}, {49135, 64051}, {64183, 12284}
X(64025) = anticomplement of X(12111)
X(64025) = perspector of circumconic {{A, B, C, X(46456), X(47269)}}
X(64025) = X(i)-Dao conjugate of X(j) for these {i, j}: {12111, 12111}
X(64025) = pole of line {20, 13851} with respect to the Jerabek hyperbola
X(64025) = pole of line {382, 10539} with respect to the Stammler hyperbola
X(64025) = pole of line {41079, 52584} with respect to the Steiner circumellipse
X(64025) = pole of line {12086, 44136} with respect to the Wallace hyperbola
X(64025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 43605, 9544}, {4, 12317, 32140}, {49, 32138, 35473}, {51, 11439, 50689}, {52, 12290, 3543}, {64, 1993, 12086}, {185, 12111, 2}, {185, 5907, 10574}, {389, 15305, 3832}, {511, 12279, 5059}, {511, 64029, 12279}, {1154, 64030, 3529}, {1181, 14118, 11003}, {2979, 46850, 50693}, {3060, 11381, 17578}, {3146, 5889, 62187}, {3522, 5562, 33884}, {5446, 11455, 50688}, {5562, 15072, 3522}, {5640, 44870, 3854}, {5663, 34783, 4}, {5663, 6102, 18439}, {5663, 7722, 146}, {5889, 6000, 3146}, {5890, 12162, 3091}, {6241, 11412, 10575}, {9730, 15058, 5056}, {9781, 16194, 61982}, {10574, 12111, 5907}, {10575, 11412, 20}, {10575, 13754, 11412}, {11444, 64100, 15717}, {11456, 12163, 7488}, {11468, 12038, 35493}, {11793, 20791, 61820}, {13491, 18436, 376}, {13630, 18435, 3090}, {14915, 64051, 49135}, {15030, 15043, 5068}, {15054, 34148, 3357}, {15644, 52093, 62120}, {16981, 50690, 13598}, {18439, 34783, 6102}, {32392, 36982, 41715}, {37481, 45959, 3545}, {45187, 46850, 2979}

X(64026) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-CONWAY AND X(3)-CROSSPEDAL-OF-X(5)

Barycentrics    a^2*(2*a^8-7*a^6*(b^2+c^2)-5*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4+c^4)+a^4*(9*b^4+4*b^2*c^2+9*c^4)) : :
X(64026) = 3*X[3796]+X[12160], X[11414]+3*X[63094]

X(64026) lies on these lines: {2, 43844}, {3, 13382}, {4, 11423}, {5, 542}, {6, 1598}, {20, 11422}, {24, 184}, {25, 50414}, {26, 16625}, {30, 32136}, {39, 39839}, {49, 9730}, {51, 1199}, {52, 2937}, {54, 74}, {64, 44731}, {110, 58498}, {140, 41597}, {154, 11432}, {155, 182}, {156, 5462}, {195, 10625}, {216, 14152}, {217, 30263}, {372, 8908}, {373, 43598}, {394, 37515}, {397, 35714}, {398, 35715}, {427, 12242}, {511, 12161}, {524, 16197}, {550, 1493}, {567, 12162}, {569, 5907}, {576, 7387}, {578, 1181}, {631, 3292}, {1092, 16836}, {1147, 9729}, {1173, 52294}, {1216, 5092}, {1495, 3567}, {1498, 11426}, {1503, 16198}, {1596, 14862}, {1597, 22334}, {1899, 32767}, {1993, 10984}, {1994, 12087}, {3047, 16223}, {3089, 44102}, {3167, 37514}, {3357, 11425}, {3518, 44110}, {3547, 63722}, {3574, 34224}, {3796, 12160}, {3819, 13336}, {3917, 56292}, {4232, 11431}, {5012, 5562}, {5050, 17814}, {5097, 5446}, {5449, 43588}, {5889, 11003}, {5890, 13367}, {5891, 13353}, {5892, 61753}, {5943, 10539}, {6101, 14810}, {6102, 15872}, {6146, 18383}, {6240, 10619}, {6467, 8537}, {6622, 14912}, {6636, 15801}, {6643, 11179}, {6644, 15012}, {6756, 45185}, {6776, 18381}, {7395, 40247}, {7488, 14831}, {7512, 14531}, {7514, 15083}, {7516, 20190}, {7517, 21849}, {7530, 22330}, {8681, 19458}, {8887, 41204}, {9306, 11695}, {9544, 15043}, {9545, 10574}, {9704, 37481}, {9705, 43600}, {9706, 15020}, {9716, 15717}, {9781, 34565}, {9786, 11202}, {9936, 34507}, {10018, 64064}, {10024, 61713}, {10112, 15760}, {10170, 55706}, {10263, 55716}, {10575, 37472}, {10594, 15004}, {11001, 53860}, {11004, 64050}, {11225, 41587}, {11264, 46029}, {11381, 15033}, {11412, 22352}, {11414, 63094}, {11424, 11456}, {11427, 14216}, {11438, 15750}, {11457, 61743}, {12006, 43586}, {12007, 16252}, {12022, 43831}, {12038, 13630}, {12088, 21969}, {12164, 37476}, {12233, 18400}, {12235, 58480}, {12241, 44226}, {12359, 58447}, {13335, 39805}, {13348, 16266}, {13352, 46850}, {13371, 18128}, {13419, 45089}, {13421, 23060}, {13434, 15030}, {13567, 64063}, {13598, 36749}, {13754, 32046}, {13861, 58470}, {14157, 44111}, {14530, 17810}, {14855, 37495}, {14865, 64029}, {15018, 43614}, {15037, 18350}, {15067, 55695}, {15068, 50664}, {15516, 46261}, {15761, 58806}, {16225, 58049}, {16226, 44802}, {16238, 61681}, {17836, 52016}, {18376, 18945}, {18420, 61751}, {18436, 37513}, {18909, 23329}, {18914, 20299}, {18925, 34785}, {18951, 61646}, {19122, 33748}, {19153, 44489}, {19362, 50649}, {19468, 21284}, {20958, 37699}, {20959, 37529}, {21663, 23040}, {24206, 31831}, {26882, 44108}, {26928, 62207}, {26938, 62245}, {32139, 44870}, {32379, 58489}, {34117, 44495}, {34148, 64100}, {34781, 63030}, {35921, 45187}, {36987, 55038}, {37471, 50461}, {37777, 58551}, {38633, 43807}, {39504, 45732}, {43130, 44494}, {43394, 43604}, {43592, 61900}, {43837, 64101}, {45298, 59659}, {45979, 58482}, {46030, 58807}, {46851, 57714}, {51031, 56298}, {58555, 64052}, {61607, 64038}, {63658, 63697}

X(64026) = midpoint of X(i) and X(j) for these {i,j}: {578, 1181}, {12160, 46728}, {12161, 64049}, {12227, 13198}, {12233, 31804}
X(64026) = pole of line {186, 578} with respect to the Jerabek hyperbola
X(64026) = pole of line {187, 1595} with respect to the Kiepert hyperbola
X(64026) = pole of line {1568, 3091} with respect to the Stammler hyperbola
X(64026) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(31504)}}, {{A, B, C, X(97), X(10110)}}, {{A, B, C, X(3527), X(56347)}}, {{A, B, C, X(13472), X(46090)}}, {{A, B, C, X(14528), X(34818)}}
X(64026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11423, 13366}, {4, 13366, 37505}, {6, 19347, 6759}, {6, 6759, 10110}, {49, 43845, 9730}, {54, 43602, 3520}, {155, 182, 11793}, {184, 389, 10282}, {184, 7592, 389}, {185, 11430, 64027}, {185, 44109, 54}, {569, 18445, 5907}, {578, 1181, 6000}, {1181, 11402, 578}, {1199, 1614, 51}, {1993, 10984, 15644}, {1994, 52525, 45186}, {3520, 15032, 43602}, {3520, 43602, 185}, {3796, 12160, 46728}, {6146, 18388, 18383}, {9306, 36752, 11695}, {9545, 10574, 51394}, {9704, 37481, 51393}, {10539, 36753, 5943}, {11424, 11456, 13474}, {12161, 64049, 511}, {12227, 13198, 10628}, {12233, 31804, 18400}, {13434, 43605, 15030}, {14862, 40240, 1596}, {15032, 44109, 11430}, {18914, 23292, 20299}, {43394, 45956, 43604}, {56292, 61134, 3917}

X(64027) = ORTHOLOGY CENTER OF THESE TRIANGLES: TRINH AND X(3)-CROSSPEDAL-OF-X(5)

Barycentrics    a^2*(2*a^8-3*a^6*(b^2+c^2)+7*a^2*(b^2-c^2)^2*(b^2+c^2)-3*a^4*(b^4-4*b^2*c^2+c^4)-(b^2-c^2)^2*(3*b^4+8*b^2*c^2+3*c^4)) : :
X(64027) = 3*X[3]+X[64], -2*X[140]+3*X[10193], -X[159]+3*X[55649], 3*X[376]+X[14216], 3*X[381]+X[5925], -X[382]+3*X[23325], -3*X[549]+X[2883], -X[576]+3*X[10249], -5*X[631]+X[5878], -5*X[1656]+X[5895], X[1657]+3*X[1853], -X[3146]+3*X[18376] and many others

X(64027) lies on these lines: {2, 18504}, {3, 64}, {4, 11270}, {5, 1539}, {6, 44763}, {20, 11454}, {24, 13474}, {30, 5449}, {49, 10620}, {51, 14865}, {54, 74}, {66, 48898}, {110, 35497}, {113, 32415}, {125, 18560}, {140, 10193}, {143, 32184}, {159, 55649}, {182, 34778}, {184, 35477}, {186, 11381}, {206, 55674}, {235, 44673}, {343, 63441}, {373, 43597}, {376, 14216}, {378, 389}, {381, 5925}, {382, 23325}, {511, 7689}, {517, 58579}, {541, 43839}, {546, 44801}, {548, 1503}, {549, 2883}, {550, 6247}, {567, 17835}, {575, 2781}, {576, 10249}, {578, 3516}, {631, 5878}, {632, 30507}, {924, 14809}, {1181, 11410}, {1192, 1597}, {1216, 31978}, {1350, 9226}, {1495, 12290}, {1593, 10110}, {1598, 37487}, {1614, 64029}, {1620, 3517}, {1656, 5895}, {1657, 1853}, {1658, 14915}, {1971, 15513}, {1986, 43904}, {2071, 5562}, {2393, 15579}, {2693, 13997}, {2778, 5885}, {2779, 43901}, {2818, 26285}, {2917, 52099}, {2935, 9730}, {3098, 33543}, {3146, 18376}, {3426, 55570}, {3518, 32062}, {3522, 9833}, {3523, 12250}, {3524, 6225}, {3527, 3532}, {3528, 12324}, {3530, 10182}, {3534, 64037}, {3579, 12262}, {3627, 23332}, {3628, 5893}, {3843, 61735}, {3851, 61721}, {5010, 7355}, {5054, 48672}, {5085, 34779}, {5092, 15578}, {5204, 10060}, {5217, 10076}, {5351, 11244}, {5352, 11243}, {5448, 23336}, {5621, 50649}, {5643, 7527}, {5656, 15717}, {5663, 10226}, {5876, 34152}, {5890, 34566}, {5892, 63682}, {6001, 31663}, {6101, 37950}, {6143, 12244}, {6200, 49251}, {6221, 19087}, {6240, 32340}, {6241, 13367}, {6285, 7280}, {6288, 38788}, {6293, 37513}, {6396, 49250}, {6398, 19088}, {6455, 17819}, {6456, 17820}, {6636, 23358}, {6644, 44870}, {6697, 31830}, {7393, 46373}, {7488, 13445}, {7502, 14641}, {7503, 16836}, {7506, 46847}, {7514, 17704}, {7526, 9729}, {7691, 36987}, {7729, 10564}, {8549, 52987}, {8681, 12301}, {8703, 34782}, {8991, 42216}, {9818, 11695}, {9914, 33540}, {9919, 38633}, {9924, 55629}, {9927, 34350}, {9934, 43598}, {9968, 55679}, {10018, 51403}, {10117, 33539}, {10168, 63699}, {10192, 14862}, {10250, 11477}, {10274, 18364}, {10295, 61139}, {10298, 12279}, {10304, 34781}, {10533, 35865}, {10534, 35864}, {10535, 59319}, {10625, 12307}, {10990, 37118}, {11206, 21735}, {11216, 55721}, {11250, 13754}, {11413, 15644}, {11449, 35493}, {11455, 44879}, {11464, 23040}, {11550, 35471}, {11572, 34797}, {11645, 34118}, {11744, 38728}, {12085, 46730}, {12086, 45186}, {12106, 46849}, {12107, 63728}, {12108, 58434}, {12111, 51394}, {12163, 13346}, {12316, 37495}, {12383, 43895}, {13289, 15030}, {13352, 47524}, {13399, 34224}, {13403, 20417}, {13452, 44108}, {13491, 18475}, {13851, 23294}, {13980, 42215}, {14118, 41725}, {14157, 17506}, {14363, 40664}, {14516, 16163}, {15018, 43603}, {15033, 35478}, {15054, 43605}, {15058, 61128}, {15577, 55653}, {15581, 55647}, {15582, 55650}, {15583, 48874}, {15606, 37480}, {15688, 64033}, {15696, 17845}, {15704, 41362}, {15761, 20191}, {15811, 55572}, {16003, 44076}, {16105, 43823}, {16111, 24572}, {16194, 45735}, {16655, 37931}, {16976, 59659}, {17502, 40658}, {17508, 19149}, {17538, 32064}, {17800, 18405}, {17813, 55580}, {17825, 40284}, {17834, 54992}, {18390, 26937}, {18488, 38321}, {18553, 36201}, {18570, 32392}, {18909, 60765}, {18931, 39571}, {19124, 21851}, {19132, 55682}, {19153, 55687}, {19467, 35485}, {19506, 20127}, {20190, 34117}, {20300, 48895}, {21312, 46728}, {21659, 35491}, {21849, 37490}, {23041, 55672}, {23042, 53094}, {23300, 29317}, {23324, 62036}, {23330, 38323}, {26879, 61744}, {26883, 32534}, {26888, 59325}, {29323, 51756}, {32046, 46374}, {32205, 63737}, {32445, 37512}, {33282, 51521}, {33541, 37955}, {33878, 52028}, {33923, 45185}, {34484, 41448}, {34775, 48896}, {34777, 55587}, {34780, 62100}, {34783, 34986}, {34788, 53097}, {34864, 41580}, {35228, 55657}, {35260, 61138}, {35479, 44082}, {35494, 43844}, {37515, 54994}, {37853, 44240}, {38937, 61462}, {39125, 55719}, {39879, 55646}, {40928, 40932}, {41593, 55695}, {43574, 45187}, {43586, 43615}, {44226, 47296}, {44242, 44407}, {44247, 64035}, {44249, 44829}, {44668, 55594}, {44762, 62069}, {44958, 61691}, {47748, 56924}, {50693, 64034}, {50709, 62026}, {54211, 61820}, {58085, 59291}, {58188, 64059}, {61606, 61810}, {61680, 61811}

X(64027) = midpoint of X(i) and X(j) for these {i,j}: {3, 3357}, {5, 5894}, {20, 18381}, {64, 6759}, {66, 48898}, {74, 13293}, {182, 34778}, {548, 61540}, {550, 6247}, {1216, 31978}, {1657, 34786}, {2693, 13997}, {3098, 63420}, {3579, 12262}, {7689, 12084}, {8549, 52987}, {9927, 34350}, {10606, 11204}, {11202, 35450}, {11250, 32138}, {11598, 12041}, {12085, 46730}, {12163, 13346}, {14216, 34785}, {14677, 23315}, {15583, 48874}, {15704, 41362}, {19506, 20127}, {20427, 22802}, {34775, 48896}, {34777, 55587}, {34788, 53097}, {44883, 63431}, {54050, 61747}
X(64027) = reflection of X(i) in X(j) for these {i,j}: {4, 32767}, {5, 25563}, {143, 32184}, {206, 55674}, {1498, 50414}, {2883, 64063}, {5092, 15578}, {5448, 23336}, {5893, 3628}, {10282, 3}, {12038, 10226}, {14864, 6247}, {15577, 55653}, {15761, 20191}, {16252, 3530}, {18383, 20299}, {20299, 6696}, {34117, 20190}, {34785, 32903}, {48889, 6697}, {48895, 20300}, {52102, 61540}, {55719, 39125}, {61749, 140}
X(64027) = complement of X(22802)
X(64027) = pole of line {186, 1204} with respect to the Jerabek hyperbola
X(64027) = pole of line {20, 1568} with respect to the Stammler hyperbola
X(64027) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 3357, 53716}, {74, 2693, 13293}, {107, 6080, 53757}
X(64027) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(11202)}}, {{A, B, C, X(54), X(11589)}}, {{A, B, C, X(74), X(8798)}}, {{A, B, C, X(1073), X(44763)}}, {{A, B, C, X(5897), X(10282)}}, {{A, B, C, X(11270), X(14379)}}
X(64027) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20427, 22802}, {3, 10606, 3357}, {3, 12315, 17821}, {3, 13093, 154}, {3, 14059, 12096}, {3, 1498, 11202}, {3, 18350, 43898}, {3, 18439, 51393}, {3, 35450, 1498}, {3, 8567, 11204}, {4, 11468, 21663}, {4, 23329, 32767}, {5, 12041, 43604}, {5, 23328, 25563}, {30, 20299, 18383}, {30, 6696, 20299}, {64, 17821, 12315}, {74, 13293, 10628}, {74, 32607, 17855}, {140, 15311, 61749}, {185, 11430, 64026}, {185, 3520, 11430}, {185, 44109, 43602}, {376, 34785, 32903}, {382, 40686, 23325}, {548, 61540, 1503}, {549, 2883, 64063}, {550, 6247, 18400}, {578, 10605, 13382}, {631, 54050, 5878}, {631, 5878, 61747}, {1498, 11202, 50414}, {1503, 61540, 52102}, {1593, 11438, 10110}, {1657, 1853, 34786}, {2071, 11440, 5562}, {2777, 25563, 5}, {3357, 6759, 64}, {3516, 10605, 578}, {3530, 16252, 10182}, {5054, 48672, 64024}, {6247, 18400, 14864}, {10606, 11204, 6000}, {10620, 35498, 49}, {11202, 50414, 10282}, {11250, 32138, 13754}, {11410, 34469, 1181}, {11413, 63425, 15644}, {11598, 12041, 2777}, {12162, 43898, 18350}, {12162, 43907, 3}, {12290, 21844, 1495}, {12315, 17821, 6759}, {13293, 32401, 3520}, {15032, 43806, 185}, {15055, 15062, 22467}, {15062, 22467, 15030}, {15105, 15712, 14862}, {15578, 34146, 5092}, {18859, 63392, 10625}, {43394, 51522, 45957}, {43615, 45959, 43586}, {44883, 63431, 511}

X(64028) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-CONWAY AND X(3)-CROSSPEDAL-OF-X(6)

Barycentrics    a^4*(a^4-b^4-4*b^2*c^2-c^4) : :
X(64028) = -3*X[3796]+X[37485]

X(64028) lies on these lines: {3, 43725}, {6, 25}, {32, 160}, {39, 157}, {49, 5050}, {54, 66}, {69, 5012}, {110, 3618}, {140, 141}, {156, 18583}, {185, 63431}, {193, 1176}, {237, 13345}, {389, 15577}, {511, 12161}, {518, 31811}, {524, 19126}, {526, 58317}, {542, 12228}, {567, 18440}, {569, 1352}, {570, 40947}, {571, 20775}, {575, 9822}, {576, 11536}, {578, 1503}, {597, 10128}, {1092, 5085}, {1154, 3098}, {1177, 17040}, {1181, 34146}, {1204, 32333}, {1205, 32226}, {1350, 10984}, {1353, 44470}, {1437, 36741}, {1576, 5065}, {1614, 14853}, {1899, 6697}, {1992, 19121}, {1993, 3313}, {1994, 64023}, {2781, 12227}, {2904, 45110}, {2909, 42444}, {3043, 5622}, {3044, 5182}, {3047, 52699}, {3048, 36696}, {3147, 14912}, {3148, 5421}, {3589, 9306}, {3629, 19127}, {3763, 43650}, {3796, 37485}, {5038, 41277}, {5039, 40643}, {5063, 14575}, {5480, 6759}, {5651, 47355}, {5889, 54374}, {5965, 44491}, {6146, 51756}, {6329, 25488}, {6403, 11423}, {6995, 43726}, {7078, 22769}, {7592, 19161}, {7669, 13351}, {8546, 11511}, {8548, 19141}, {8675, 58310}, {8717, 48880}, {8963, 44198}, {9002, 58315}, {9009, 57206}, {9010, 58314}, {9027, 58357}, {9544, 51171}, {9605, 33582}, {9677, 35841}, {9697, 39764}, {9703, 55705}, {9704, 53091}, {9744, 41770}, {9755, 61684}, {9968, 12294}, {9976, 55710}, {10272, 60764}, {10519, 61134}, {10539, 14561}, {11179, 15812}, {11422, 12220}, {11424, 36990}, {11425, 63420}, {11426, 39879}, {11427, 36851}, {11430, 44883}, {11438, 35228}, {11574, 34986}, {12007, 15585}, {12017, 22115}, {12166, 37514}, {12234, 44668}, {12329, 20986}, {13198, 32245}, {13346, 44882}, {13347, 21167}, {13352, 46264}, {13382, 14810}, {13567, 58437}, {13622, 19151}, {14528, 34817}, {15472, 36201}, {15580, 63688}, {15581, 37505}, {15582, 32191}, {15583, 51744}, {16187, 51127}, {16543, 19149}, {16776, 39561}, {17811, 31521}, {18382, 18388}, {18911, 28408}, {18925, 36989}, {18935, 23327}, {19124, 64080}, {19130, 46261}, {19131, 47525}, {19139, 44479}, {21660, 32341}, {21850, 61752}, {23042, 44489}, {23292, 23300}, {25406, 34148}, {26883, 53023}, {26926, 54347}, {29181, 31802}, {29317, 31815}, {29959, 63183}, {31810, 46728}, {32217, 47464}, {32375, 43838}, {33748, 43815}, {33872, 40981}, {34382, 44480}, {34945, 40146}, {35219, 41580}, {37645, 41256}, {38110, 61753}, {39588, 52432}, {39840, 41672}, {40330, 43651}, {41274, 64092}, {41622, 54332}, {41714, 44494}, {46288, 62194}, {47449, 51733}, {51212, 52525}, {51962, 52668}, {53022, 63612}, {63658, 63699}

X(64028) = midpoint of X(i) and X(j) for these {i,j}: {6, 19459}, {1350, 12160}, {13198, 32245}
X(64028) = reflection of X(i) in X(j) for these {i,j}: {182, 32046}
X(64028) = inverse of X(15435) in Stammler hyperbola
X(64028) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 43726}
X(64028) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 43726}, {26880, 3091}
X(64028) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39955, 32}
X(64028) = pole of line {3566, 23300} with respect to the 1st Brocard circle
X(64028) = pole of line {427, 7746} with respect to the Kiepert hyperbola
X(64028) = pole of line {3050, 8673} with respect to the MacBeath circumconic
X(64028) = pole of line {69, 3060} with respect to the Stammler hyperbola
X(64028) = pole of line {2485, 6563} with respect to the Steiner inellipse
X(64028) = pole of line {305, 5133} with respect to the Wallace hyperbola
X(64028) = pole of line {339, 34981} with respect to the dual conic of Wallace hyperbola
X(64028) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {6, 19459, 59796}
X(64028) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(58471)}}, {{A, B, C, X(25), X(7485)}}, {{A, B, C, X(32), X(44091)}}, {{A, B, C, X(51), X(66)}}, {{A, B, C, X(54), X(206)}}, {{A, B, C, X(69), X(9969)}}, {{A, B, C, X(1176), X(19136)}}, {{A, B, C, X(1843), X(5486)}}, {{A, B, C, X(2393), X(17040)}}, {{A, B, C, X(7716), X(14259)}}, {{A, B, C, X(9971), X(13622)}}, {{A, B, C, X(17810), X(34817)}}, {{A, B, C, X(19151), X(56918)}}, {{A, B, C, X(44079), X(52455)}}
X(64028) = barycentric product X(i)*X(j) for these (i, j): {6, 7485}, {5065, 52455}, {14259, 30435}
X(64028) = barycentric quotient X(i)/X(j) for these (i, j): {32, 43726}, {7485, 76}
X(64028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 10602, 39125}, {6, 159, 9969}, {6, 184, 206}, {6, 19125, 41593}, {6, 19459, 2393}, {6, 206, 19136}, {6, 20987, 51}, {6, 32621, 32366}, {69, 5012, 5157}, {182, 52016, 141}, {184, 13366, 44077}, {193, 11003, 1176}, {11402, 19459, 6}, {12167, 34397, 1974}, {20775, 34396, 571}, {23042, 44489, 51730}, {30398, 30399, 182}

X(64029) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-WASAT AND X(3)-CROSSPEDAL-OF-X(20)

Barycentrics    a^2*(3*a^6*(b^2+c^2)+9*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(-9*b^4+10*b^2*c^2-9*c^4)-(b^2-c^2)^2*(3*b^4+10*b^2*c^2+3*c^4)) : :
X(64029) = -8*X[4]+9*X[51], -4*X[140]+3*X[12162], -27*X[373]+26*X[5068], -2*X[382]+3*X[14831], -8*X[546]+9*X[16226], -4*X[550]+3*X[5562], -9*X[568]+8*X[12002], -6*X[1216]+7*X[62100], -10*X[1656]+9*X[15030], -3*X[1853]+4*X[22967], -9*X[2979]+11*X[62124], -9*X[3060]+7*X[50690] and many others

X(64029) lies on these lines: {3, 33556}, {4, 51}, {5, 13399}, {20, 45187}, {25, 58795}, {30, 14531}, {52, 45957}, {64, 184}, {74, 10282}, {125, 2883}, {140, 12162}, {154, 3532}, {373, 5068}, {382, 14831}, {468, 36982}, {511, 5059}, {541, 18563}, {542, 52071}, {546, 16226}, {550, 5562}, {567, 33541}, {568, 12002}, {1154, 62159}, {1181, 13093}, {1192, 44082}, {1204, 1495}, {1216, 62100}, {1425, 6285}, {1533, 41587}, {1593, 13366}, {1594, 52102}, {1614, 64027}, {1656, 15030}, {1657, 13754}, {1853, 22967}, {2777, 34224}, {2979, 62124}, {3060, 50690}, {3146, 21969}, {3270, 7355}, {3292, 11413}, {3357, 11456}, {3426, 10982}, {3517, 10605}, {3518, 43806}, {3519, 10293}, {3522, 3917}, {3523, 5650}, {3524, 40247}, {3533, 15058}, {3543, 16625}, {3819, 61791}, {3832, 15012}, {3850, 9730}, {3854, 5943}, {3858, 13630}, {5056, 9729}, {5073, 14915}, {5094, 31978}, {5446, 62023}, {5447, 62082}, {5462, 61970}, {5656, 26937}, {5876, 14855}, {5889, 49135}, {5891, 15712}, {5892, 61919}, {5895, 16879}, {6101, 62136}, {6102, 62026}, {6243, 49133}, {6247, 43831}, {6467, 30443}, {6759, 21663}, {7488, 15054}, {7998, 62060}, {7999, 62061}, {8550, 12294}, {8567, 26864}, {9707, 11204}, {9786, 44106}, {9899, 64040}, {9968, 44102}, {10018, 14862}, {10019, 41580}, {10170, 61832}, {10192, 43903}, {10295, 45185}, {10299, 11793}, {10540, 43604}, {10606, 44108}, {10619, 15105}, {10625, 62144}, {11403, 15004}, {11412, 62147}, {11424, 44111}, {11430, 35478}, {11444, 62067}, {11459, 21735}, {11585, 15063}, {11591, 62069}, {11695, 61136}, {12084, 43844}, {12086, 34986}, {12112, 47486}, {12250, 19467}, {13148, 13417}, {13348, 52093}, {13421, 62047}, {13433, 32339}, {13445, 43605}, {13452, 23040}, {13596, 16835}, {13598, 50691}, {14128, 61824}, {14641, 18436}, {14865, 64026}, {15010, 15752}, {15043, 46847}, {15056, 17704}, {15067, 62064}, {15311, 21659}, {15331, 51522}, {15606, 17538}, {15644, 62127}, {15720, 18435}, {15738, 17853}, {15761, 16003}, {15811, 34417}, {16982, 35404}, {17578, 21849}, {18364, 18475}, {18396, 48672}, {18859, 41597}, {18913, 61645}, {18914, 61744}, {18945, 54211}, {19206, 38808}, {19357, 35450}, {20791, 61856}, {21637, 63420}, {21639, 64031}, {21640, 49250}, {21641, 49251}, {21844, 50414}, {22112, 33537}, {23039, 62107}, {30439, 43424}, {30440, 43425}, {31834, 41981}, {32063, 55574}, {32111, 44959}, {32137, 45956}, {32139, 51394}, {32171, 43907}, {35487, 61749}, {37481, 46849}, {40928, 52293}, {43392, 43846}, {43577, 64036}, {43607, 64063}, {44960, 51403}, {45958, 61907}, {45959, 55856}, {50689, 58470}, {63670, 63728}

X(64029) = midpoint of X(i) and X(j) for these {i,j}: {12279, 64025}
X(64029) = reflection of X(i) in X(j) for these {i,j}: {52, 45957}, {185, 6241}, {5562, 10575}, {5895, 32392}, {11381, 185}, {12111, 46850}, {12162, 13491}, {12290, 389}, {18436, 14641}, {18439, 40647}, {21650, 17854}, {45186, 34783}, {45187, 20}, {62047, 13421}, {64036, 43577}
X(64029) = inverse of X(43592) in Jerabek hyperbola
X(64029) = pole of line {4, 1192} with respect to the Jerabek hyperbola
X(64029) = pole of line {647, 34569} with respect to the Orthic inconic
X(64029) = pole of line {1092, 3529} with respect to the Stammler hyperbola
X(64029) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1093), X(43719)}}, {{A, B, C, X(14249), X(14528)}}
X(64029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64, 12174, 184}, {185, 11381, 51}, {185, 32062, 389}, {389, 12290, 32062}, {389, 6000, 12290}, {568, 62016, 12002}, {1204, 1498, 1495}, {5663, 10575, 5562}, {6000, 6241, 185}, {10574, 44870, 373}, {10605, 12315, 26883}, {11457, 22802, 13851}, {12162, 13491, 64100}, {12279, 64025, 511}, {12290, 32062, 11381}, {13596, 43602, 37505}, {14641, 18436, 36987}, {14862, 20417, 10018}, {14915, 34783, 45186}, {16835, 43602, 13596}, {18439, 40647, 15030}

X(64030) = ORTHOLOGY CENTER OF THESE TRIANGLES: EHRMANN-SIDE AND X(3)-CROSSPEDAL-OF-X(20)

Barycentrics    a^2*(a^6*(b^2+c^2)+a^4*(-3*b^4+5*b^2*c^2-3*c^4)-(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)+a^2*(3*b^6-4*b^4*c^2-4*b^2*c^4+3*c^6)) : :
X(64030) = -9*X[2]+8*X[45958], -6*X[51]+5*X[5076], -4*X[140]+3*X[15305], -4*X[143]+3*X[3543], -9*X[373]+8*X[46852], -3*X[376]+2*X[5876], -3*X[381]+2*X[11381], -4*X[389]+3*X[3830], -4*X[546]+5*X[10574], -4*X[548]+3*X[11459], -6*X[549]+5*X[15058], -5*X[631]+4*X[45959] and many others

X(64030) lies on these lines: {2, 45958}, {3, 64}, {4, 3521}, {5, 7703}, {20, 5663}, {22, 63392}, {30, 5889}, {49, 11456}, {51, 5076}, {52, 5073}, {68, 10293}, {74, 1658}, {140, 15305}, {143, 3543}, {155, 37477}, {156, 2071}, {185, 382}, {265, 11457}, {373, 46852}, {376, 5876}, {381, 11381}, {389, 3830}, {399, 1092}, {511, 17800}, {546, 10574}, {548, 11459}, {549, 15058}, {550, 12111}, {567, 1593}, {631, 45959}, {1075, 34334}, {1147, 18859}, {1154, 3529}, {1181, 37472}, {1192, 51519}, {1204, 2070}, {1216, 15696}, {1425, 9642}, {1495, 43604}, {1503, 40929}, {1597, 36753}, {1614, 11250}, {1656, 64100}, {1657, 13754}, {1899, 31725}, {2072, 2883}, {2777, 6293}, {2931, 2937}, {2979, 12103}, {3060, 62036}, {3091, 32137}, {3146, 6102}, {3520, 61752}, {3522, 11591}, {3523, 15060}, {3524, 14128}, {3526, 15030}, {3528, 15067}, {3530, 15056}, {3534, 5562}, {3548, 5656}, {3567, 3853}, {3581, 7387}, {3627, 5890}, {3628, 20791}, {3832, 12006}, {3839, 15026}, {3843, 9730}, {3845, 15043}, {3850, 15045}, {3851, 9729}, {3855, 13363}, {3857, 11451}, {3858, 15024}, {3861, 5640}, {3917, 62100}, {5055, 44870}, {5059, 13391}, {5066, 15028}, {5070, 16836}, {5072, 5892}, {5447, 15688}, {5449, 13399}, {5462, 32062}, {5650, 61799}, {5878, 7728}, {5895, 41725}, {5899, 22550}, {5943, 61970}, {5944, 35473}, {6225, 18531}, {6247, 10024}, {6285, 18447}, {6288, 12324}, {6688, 61935}, {7355, 18455}, {7391, 15800}, {7464, 43605}, {7486, 11017}, {7488, 32138}, {7502, 8718}, {7503, 64098}, {7505, 12292}, {7517, 10605}, {7540, 13568}, {7542, 61540}, {7556, 51522}, {7722, 34584}, {7723, 38788}, {7729, 18381}, {7998, 46853}, {7999, 33923}, {8703, 11444}, {9538, 32143}, {9781, 15687}, {9818, 37471}, {9968, 45016}, {10020, 43607}, {10110, 62008}, {10170, 61811}, {10226, 11464}, {10254, 20299}, {10255, 61749}, {10263, 33703}, {10298, 32210}, {10304, 32142}, {10625, 15681}, {10627, 17538}, {10897, 35864}, {10898, 35865}, {10984, 33541}, {11002, 62021}, {11270, 43720}, {11412, 15704}, {11413, 22115}, {11424, 43845}, {11438, 18378}, {11449, 34152}, {11465, 12811}, {11468, 15331}, {11472, 13339}, {11541, 62187}, {11562, 38790}, {11563, 26917}, {11585, 36983}, {11592, 62067}, {11597, 18466}, {11645, 37473}, {11695, 19709}, {11820, 12309}, {12041, 21844}, {12083, 12163}, {12085, 12174}, {12106, 43601}, {12112, 22467}, {12281, 14677}, {12308, 37480}, {12606, 20427}, {12825, 38723}, {13321, 62016}, {13346, 35452}, {13348, 15689}, {13364, 50689}, {13382, 62023}, {13406, 23294}, {13416, 64059}, {13564, 63425}, {13598, 15684}, {14070, 34469}, {14130, 14805}, {14157, 37814}, {14449, 62044}, {14531, 62170}, {14708, 46431}, {14831, 62040}, {14845, 61968}, {14865, 32046}, {15012, 61991}, {15041, 21650}, {15074, 64014}, {15311, 18563}, {15606, 62128}, {15644, 62131}, {15646, 26882}, {15692, 55286}, {15694, 17704}, {16111, 22584}, {16196, 54039}, {16226, 44863}, {16625, 62035}, {16655, 38321}, {16658, 31830}, {16835, 61134}, {16868, 45622}, {17702, 17856}, {17834, 44457}, {17853, 36253}, {17855, 38724}, {18128, 61744}, {18323, 51491}, {18400, 18565}, {18403, 22802}, {18438, 34146}, {18449, 64031}, {18457, 49250}, {18459, 49251}, {18534, 37490}, {18564, 44829}, {18570, 52525}, {18874, 41099}, {18912, 44276}, {19129, 63420}, {19357, 47524}, {21849, 62027}, {21969, 62045}, {23293, 61750}, {25739, 44279}, {26883, 45735}, {26913, 44235}, {32140, 44440}, {32254, 52987}, {33879, 61821}, {33884, 62113}, {34007, 34514}, {34351, 43903}, {34439, 45788}, {34782, 44246}, {34798, 61299}, {35495, 44110}, {36749, 47527}, {36987, 62134}, {37198, 64097}, {37478, 47748}, {37483, 61150}, {37511, 48662}, {37944, 56292}, {43577, 61139}, {43613, 49671}, {43809, 46261}, {44299, 61808}, {44324, 62091}, {44544, 64187}, {44866, 52102}, {44958, 51548}, {45186, 49136}, {45187, 54048}, {46847, 61953}, {50693, 54042}, {52863, 64037}, {54041, 62104}, {54044, 62092}, {54047, 62119}, {58470, 61996}, {62147, 62188}, {62155, 64050}, {63671, 63728}

X(64030) = midpoint of X(i) and X(j) for these {i,j}: {3529, 64025}, {6241, 12279}
X(64030) = reflection of X(i) in X(j) for these {i,j}: {3, 10575}, {4, 13491}, {265, 17854}, {382, 185}, {3146, 6102}, {5073, 52}, {5562, 14641}, {5889, 45957}, {5895, 41725}, {6243, 34783}, {11381, 40647}, {11412, 15704}, {12111, 550}, {12162, 46850}, {12281, 14677}, {12290, 5}, {18436, 20}, {18439, 3}, {18562, 11750}, {22584, 16111}, {33703, 10263}, {34783, 6241}, {37484, 1657}, {38790, 11562}, {46431, 14708}, {48662, 37511}, {49136, 45186}, {61139, 43577}, {62040, 14831}, {62044, 14449}, {62045, 21969}, {64050, 62155}, {64187, 44544}
X(64030) = pole of line {381, 1204} with respect to the Jerabek hyperbola
X(64030) = pole of line {20, 10540} with respect to the Stammler hyperbola
X(64030) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(10540)}}, {{A, B, C, X(64), X(15424)}}, {{A, B, C, X(3521), X(14379)}}, {{A, B, C, X(5897), X(18439)}}
X(64030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1498, 10540}, {3, 18439, 18435}, {3, 6000, 18439}, {20, 18436, 13340}, {20, 5663, 18436}, {30, 34783, 6243}, {30, 45957, 5889}, {30, 6241, 34783}, {185, 14915, 382}, {185, 382, 568}, {373, 46852, 61946}, {1614, 13445, 11250}, {2777, 11750, 18562}, {2937, 10620, 7689}, {3853, 45956, 3567}, {5462, 32062, 61984}, {5562, 14641, 3534}, {5878, 18404, 7728}, {5889, 6241, 45957}, {6000, 46850, 12162}, {6241, 12279, 30}, {8718, 11440, 7502}, {9729, 16194, 3851}, {9730, 13474, 3843}, {10574, 11455, 546}, {10575, 12162, 46850}, {10620, 52100, 2937}, {11381, 40647, 381}, {11456, 12084, 49}, {11459, 52093, 548}, {12085, 12174, 18445}, {12085, 18445, 37495}, {12162, 46850, 3}, {12290, 15072, 5}, {14130, 64049, 14805}

X(64031) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND EHRMANN AND X(3)-CROSSPEDAL-OF-X(20)

Barycentrics    a^2*(a^10-5*a^8*(b^2+c^2)+2*a^4*(b^2-c^2)^2*(b^2+c^2)+6*a^6*(b^4+c^4)-a^2*(b^2-c^2)^2*(7*b^4+6*b^2*c^2+7*c^4)+(b^2-c^2)^2*(3*b^6+5*b^4*c^2+5*b^2*c^4+3*c^6)) : :
X(64031) = -3*X[2]+4*X[63699], -4*X[5]+3*X[61737], -3*X[6]+X[64], -X[20]+3*X[41719], -3*X[381]+2*X[34118], -3*X[597]+2*X[6696], -3*X[599]+5*X[64024], 3*X[1992]+X[6225], -2*X[3098]+3*X[23041], -3*X[5085]+4*X[41593], -3*X[5476]+2*X[20299], -X[5925]+3*X[43273] and many others

X(64031) lies on these lines: {2, 63699}, {3, 1177}, {5, 61737}, {6, 64}, {20, 41719}, {25, 15139}, {30, 63702}, {54, 32357}, {66, 3527}, {154, 3292}, {155, 159}, {182, 34778}, {193, 41735}, {206, 1092}, {235, 63129}, {381, 34118}, {382, 1351}, {394, 41580}, {524, 2883}, {542, 12293}, {575, 3357}, {576, 6000}, {597, 6696}, {599, 64024}, {1181, 9914}, {1204, 44102}, {1498, 2393}, {1594, 63656}, {1598, 61723}, {1619, 1993}, {1657, 54215}, {1660, 37672}, {1853, 9777}, {1992, 6225}, {2003, 7169}, {2323, 3556}, {2937, 15577}, {3088, 51744}, {3098, 23041}, {3167, 37928}, {3515, 18374}, {3517, 63663}, {3827, 37625}, {5050, 14130}, {5085, 41593}, {5093, 45034}, {5095, 5895}, {5198, 9971}, {5476, 20299}, {5596, 51212}, {5621, 34469}, {5656, 62344}, {5663, 8548}, {5925, 43273}, {6090, 17847}, {6247, 11432}, {6285, 19369}, {6515, 41602}, {6776, 18560}, {7355, 8540}, {7973, 64070}, {8537, 12290}, {8538, 10575}, {8541, 11381}, {8550, 15311}, {8567, 10541}, {8743, 10766}, {9019, 39568}, {9786, 19136}, {9813, 44870}, {9818, 44480}, {9924, 55722}, {10110, 61664}, {10117, 26864}, {10169, 35484}, {10192, 62217}, {10250, 22330}, {10282, 52987}, {10519, 58437}, {10606, 53093}, {10628, 44493}, {10752, 11456}, {11179, 20427}, {11202, 55606}, {11204, 20190}, {11206, 37900}, {11245, 34944}, {11413, 22151}, {11416, 12279}, {11431, 14853}, {11441, 63180}, {11479, 63723}, {11482, 13093}, {11511, 46850}, {11744, 12165}, {12017, 15578}, {12063, 12112}, {12085, 41725}, {12111, 41614}, {12161, 44544}, {12163, 44470}, {12167, 32340}, {12316, 39879}, {13292, 21850}, {13293, 25556}, {13382, 44489}, {13754, 44492}, {14070, 15136}, {14216, 20423}, {14530, 15582}, {14810, 23042}, {14912, 61088}, {14982, 15063}, {14984, 32139}, {15274, 53569}, {15579, 35450}, {15581, 32063}, {15905, 63419}, {16252, 61683}, {16789, 59349}, {17811, 45979}, {17813, 58795}, {17824, 21660}, {18381, 23049}, {18449, 64030}, {18535, 63688}, {18917, 47571}, {18931, 47457}, {19132, 31884}, {19142, 43616}, {19151, 34438}, {19161, 45045}, {19459, 44439}, {19924, 34785}, {21639, 64029}, {23329, 25555}, {25406, 34005}, {26206, 43813}, {26869, 32125}, {26937, 62375}, {29181, 34774}, {29317, 34776}, {31166, 34726}, {32368, 64099}, {34507, 61749}, {34613, 34781}, {34775, 48901}, {34788, 55718}, {35228, 55610}, {37198, 54334}, {37485, 41716}, {37489, 41613}, {37784, 64025}, {38136, 61542}, {40107, 61747}, {40647, 44503}, {41729, 46264}, {41736, 45968}, {41761, 44704}, {43810, 53091}, {44656, 48766}, {44657, 48767}, {46372, 53019}, {47546, 62288}, {50414, 55583}, {50977, 64063}, {51739, 55571}, {51756, 53023}, {54131, 64037}, {59351, 62174}, {63673, 63728}

X(64031) = midpoint of X(i) and X(j) for these {i,j}: {193, 41735}, {1498, 11477}, {5596, 51212}, {5878, 63722}, {5895, 64080}, {7973, 64070}, {9924, 55722}, {11744, 64104}, {39879, 44456}
X(64031) = reflection of X(i) in X(j) for these {i,j}: {3, 34117}, {66, 5480}, {159, 19149}, {1350, 206}, {1498, 9968}, {3357, 575}, {8549, 576}, {12085, 44469}, {12163, 44470}, {13293, 25556}, {15141, 9970}, {19149, 34779}, {33878, 15577}, {34507, 61749}, {34775, 48901}, {34777, 1351}, {34778, 182}, {34787, 6759}, {34788, 55718}, {36989, 34774}, {46264, 41729}, {52987, 10282}, {63420, 6}, {63431, 41593}
X(64031) = pole of line {9517, 39228} with respect to the circumcircle
X(64031) = pole of line {2485, 8673} with respect to the cosine circle
X(64031) = pole of line {9517, 15451} with respect to the Stammler circle
X(64031) = pole of line {2485, 30211} with respect to the MacBeath circumconic
X(64031) = pole of line {858, 32064} with respect to the Stammler hyperbola
X(64031) = intersection, other than A, B, C, of circumconics {{A, B, C, X(64), X(18876)}}, {{A, B, C, X(1177), X(41489)}}
X(64031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 34117, 19153}, {6, 34146, 63420}, {185, 11470, 6}, {511, 19149, 159}, {511, 34779, 19149}, {511, 6759, 34787}, {575, 3357, 10249}, {576, 6000, 8549}, {1351, 1503, 34777}, {1498, 11477, 2393}, {1993, 41715, 1619}, {2393, 9968, 1498}, {2781, 34117, 3}, {2781, 9970, 15141}, {5878, 63722, 1503}, {5895, 64080, 36201}, {8538, 10575, 54183}, {10602, 12174, 64080}, {19149, 34787, 6759}, {39879, 44456, 44668}

X(64032) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH ANTI-EULER AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    2*a^10-4*a^8*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(b^4+3*b^2*c^2+c^4)+a^2*(b^8-b^6*c^2-b^2*c^6+c^8) : :
X(64032) = -3*X[2]+2*X[11750], -2*X[185]+3*X[18559], -9*X[568]+8*X[32165], -5*X[631]+4*X[44829], -5*X[1656]+4*X[13470], -2*X[1885]+3*X[16658], -3*X[3060]+4*X[11819], -17*X[3533]+16*X[44862], -5*X[3567]+4*X[6146], -4*X[3575]+3*X[5890], -8*X[6756]+7*X[9781], -3*X[7540]+2*X[12370] and many others

X(64032) lies on these lines: {2, 11750}, {3, 18432}, {4, 54}, {5, 26882}, {20, 3410}, {23, 9927}, {24, 25739}, {26, 58922}, {30, 11412}, {32, 15340}, {49, 44288}, {52, 34799}, {68, 31304}, {69, 3529}, {70, 74}, {110, 18569}, {125, 44879}, {146, 3146}, {154, 7547}, {155, 52842}, {156, 31724}, {185, 18559}, {186, 18381}, {265, 37440}, {378, 17845}, {382, 1993}, {403, 18394}, {468, 11704}, {542, 11663}, {546, 14389}, {550, 37636}, {567, 63672}, {568, 32165}, {631, 44829}, {1092, 46450}, {1141, 34449}, {1495, 16868}, {1498, 35480}, {1503, 6240}, {1594, 11464}, {1656, 13470}, {1657, 61299}, {1658, 23293}, {1853, 32534}, {1885, 16658}, {2888, 12380}, {2937, 48675}, {3060, 11819}, {3153, 10539}, {3357, 13619}, {3517, 61701}, {3520, 11550}, {3521, 50006}, {3533, 44862}, {3542, 12140}, {3567, 6146}, {3575, 5890}, {3581, 18356}, {3627, 32111}, {3818, 35500}, {5876, 41590}, {6000, 34797}, {6143, 11202}, {6243, 7731}, {6247, 10295}, {6288, 7502}, {6293, 13423}, {6756, 9781}, {7391, 12118}, {7487, 18912}, {7488, 18474}, {7507, 9707}, {7517, 50435}, {7540, 12370}, {7544, 43651}, {7566, 37506}, {7574, 61753}, {7577, 10282}, {7579, 58407}, {7592, 18494}, {7747, 41367}, {7999, 64035}, {8907, 12084}, {10024, 26881}, {10304, 17712}, {10540, 18377}, {10546, 50143}, {10574, 38321}, {10594, 18396}, {10733, 31725}, {11002, 58806}, {11423, 31804}, {11439, 52070}, {11449, 13371}, {11454, 44242}, {11455, 16655}, {11456, 12173}, {11457, 18533}, {11459, 12134}, {11465, 64038}, {11565, 15026}, {11816, 22261}, {11818, 13434}, {12038, 31074}, {12103, 35257}, {12112, 22802}, {12163, 43895}, {12250, 32247}, {12363, 18564}, {12383, 13346}, {12605, 15058}, {12897, 17578}, {13203, 43391}, {13367, 52295}, {13406, 18430}, {13851, 44958}, {14269, 15807}, {14530, 18386}, {14790, 43574}, {14805, 50138}, {14864, 21663}, {14940, 23325}, {15043, 31830}, {15072, 40241}, {15305, 18563}, {15581, 35502}, {15761, 18392}, {15801, 31815}, {16013, 37970}, {17506, 23329}, {17821, 52296}, {18390, 34484}, {18405, 35488}, {18420, 61134}, {18504, 46817}, {18531, 43598}, {18945, 37122}, {20299, 21844}, {22660, 46818}, {23324, 35487}, {26879, 37458}, {26913, 45735}, {31723, 34148}, {34780, 37196}, {34938, 43576}, {35472, 40686}, {37481, 38322}, {37779, 63652}, {37931, 43607}, {38848, 39571}, {39874, 43596}, {44234, 45622}, {44279, 52863}, {44665, 64051}, {47486, 61645}, {50688, 63082}, {54001, 61747}, {56292, 61751}

X(64032) = reflection of X(i) in X(j) for these {i,j}: {4, 61139}, {6241, 6240}, {11412, 14516}, {11750, 45286}, {12111, 64036}, {12225, 12134}, {12289, 4}, {12290, 16659}, {18560, 16655}, {21659, 13419}, {34224, 3575}, {34799, 52}, {40242, 18560}, {44076, 11819}
X(64032) = anticomplement of X(11750)
X(64032) = X(i)-Dao conjugate of X(j) for these {i, j}: {11750, 11750}
X(64032) = pole of line {389, 23294} with respect to the Jerabek hyperbola
X(64032) = pole of line {156, 5562} with respect to the Stammler hyperbola
X(64032) = pole of line {550, 52347} with respect to the Wallace hyperbola
X(64032) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(8884), X(57640)}}, {{A, B, C, X(16835), X(61362)}}
X(64032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 12254, 578}, {4, 18400, 12289}, {4, 19467, 15033}, {4, 9833, 1614}, {24, 25739, 26917}, {24, 64037, 25739}, {30, 14516, 11412}, {30, 16659, 12290}, {30, 64036, 12111}, {186, 18381, 23294}, {403, 41362, 18394}, {1495, 18383, 16868}, {1503, 6240, 6241}, {1594, 34782, 11464}, {1853, 32534, 43608}, {3575, 34224, 5890}, {6146, 7576, 3567}, {6247, 10295, 11468}, {6756, 12022, 9781}, {10282, 11572, 7577}, {11455, 40242, 18560}, {11550, 34785, 3520}, {11819, 44076, 3060}, {12134, 12225, 11459}, {12173, 64033, 11456}, {13419, 18400, 21659}, {13419, 21659, 4}, {14216, 35471, 74}, {16655, 18560, 11455}, {18533, 64034, 11457}, {21659, 61139, 13419}

X(64033) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-INCIRCLE-CIRCLES AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    5*a^10-12*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+3*a^2*(b^4-c^4)^2+4*a^6*(2*b^4+b^2*c^2+2*c^4) : :
X(64033) = -2*X[5]+3*X[11206], -3*X[26]+2*X[18356], -2*X[64]+3*X[3534], -2*X[68]+3*X[9909], -4*X[140]+3*X[32064], -6*X[154]+5*X[1656], -4*X[1147]+3*X[34609], -2*X[1216]+3*X[34750], -3*X[1657]+2*X[5925], -6*X[1853]+7*X[3526], -4*X[2883]+3*X[3830], -7*X[3090]+9*X[64059] and many others

X(64033) lies on these lines: {3, 66}, {4, 11402}, {5, 11206}, {6, 13419}, {20, 13093}, {22, 2888}, {24, 26944}, {25, 18912}, {26, 18356}, {30, 6193}, {52, 39899}, {54, 5064}, {64, 3534}, {68, 9909}, {110, 40241}, {140, 32064}, {154, 1656}, {155, 44407}, {161, 2937}, {195, 382}, {206, 13353}, {381, 569}, {389, 9971}, {399, 40285}, {428, 3527}, {542, 17834}, {550, 12324}, {567, 34775}, {578, 36990}, {1147, 34609}, {1181, 18494}, {1216, 34750}, {1351, 5596}, {1593, 16659}, {1594, 26864}, {1595, 18925}, {1596, 18945}, {1597, 16655}, {1598, 6146}, {1614, 7507}, {1619, 7517}, {1657, 5925}, {1660, 18350}, {1853, 3526}, {1899, 3517}, {2393, 6243}, {2777, 49137}, {2883, 3830}, {3090, 64059}, {3167, 14790}, {3332, 7546}, {3357, 15696}, {3515, 11457}, {3518, 26869}, {3522, 61540}, {3564, 31305}, {3627, 5656}, {3628, 35260}, {3818, 37476}, {3843, 41362}, {3851, 16252}, {5050, 7528}, {5054, 17821}, {5056, 61606}, {5070, 10192}, {5072, 61747}, {5073, 5878}, {5076, 34786}, {5079, 23325}, {5093, 34774}, {5094, 9707}, {5198, 12022}, {5790, 40660}, {5890, 11387}, {5893, 62008}, {5894, 62131}, {5895, 49136}, {5921, 59346}, {6090, 47528}, {6240, 12174}, {6241, 37196}, {6445, 8991}, {6446, 13980}, {6756, 6776}, {7387, 12429}, {7401, 48906}, {7404, 39884}, {7405, 12017}, {7487, 18914}, {7526, 32354}, {7530, 45731}, {7540, 37493}, {7566, 11003}, {7715, 11433}, {7776, 57275}, {8549, 36753}, {8567, 52102}, {8780, 11585}, {8976, 10533}, {9545, 31133}, {9654, 26888}, {9669, 10535}, {9714, 25738}, {9715, 11442}, {9781, 62968}, {9825, 45073}, {9914, 44457}, {9919, 32423}, {9924, 11898}, {9934, 12902}, {10182, 61850}, {10193, 61793}, {10263, 41715}, {10295, 34469}, {10534, 13951}, {10606, 62100}, {10675, 42127}, {10676, 42126}, {11202, 14864}, {11204, 62082}, {11243, 42988}, {11244, 42989}, {11245, 37122}, {11403, 16658}, {11414, 14516}, {11427, 16198}, {11456, 12173}, {11482, 41719}, {11484, 64038}, {11550, 19357}, {11645, 13346}, {11750, 18451}, {12103, 54050}, {12111, 41590}, {12112, 35490}, {12241, 18535}, {12250, 15704}, {12254, 35502}, {12289, 44438}, {12359, 16195}, {12645, 64022}, {13142, 58764}, {13403, 15811}, {14070, 32140}, {14130, 63422}, {14156, 51933}, {14157, 37197}, {14627, 34117}, {14848, 31166}, {14862, 18376}, {15039, 15131}, {15069, 46728}, {15105, 62142}, {15311, 17800}, {15583, 53091}, {15644, 48905}, {15647, 38724}, {15681, 20427}, {15684, 51491}, {15688, 64027}, {16266, 61299}, {17814, 18536}, {17826, 42817}, {17827, 42818}, {18396, 26883}, {18405, 61749}, {18534, 44076}, {18909, 37458}, {18918, 44960}, {19149, 36749}, {20079, 48876}, {20850, 41587}, {21970, 37440}, {22051, 32346}, {22115, 44679}, {22660, 34725}, {22804, 32402}, {23236, 36201}, {23324, 61953}, {23329, 61811}, {23332, 46219}, {25563, 61803}, {26879, 55578}, {26882, 37453}, {26917, 62965}, {26937, 55570}, {29012, 37498}, {30402, 42132}, {30403, 42129}, {31810, 64023}, {32048, 37928}, {32306, 38885}, {32609, 63716}, {32767, 55857}, {34146, 37484}, {34776, 36752}, {37444, 46818}, {37505, 53023}, {37515, 43273}, {39568, 44665}, {40280, 58492}, {43605, 52842}, {44544, 64051}, {49138, 54211}, {50709, 58207}, {55858, 61735}, {55860, 58434}

X(64033) = midpoint of X(i) and X(j) for these {i,j}: {49138, 54211}
X(64033) = reflection of X(i) in X(j) for these {i,j}: {3, 9833}, {64, 34785}, {195, 32359}, {382, 1498}, {1351, 5596}, {1657, 17845}, {5073, 5878}, {5878, 44762}, {11898, 9924}, {12250, 15704}, {12315, 34781}, {12324, 550}, {12429, 7387}, {12645, 64022}, {12902, 9934}, {13093, 20}, {14216, 34782}, {18381, 45185}, {18440, 39879}, {20079, 48876}, {32306, 38885}, {34780, 3}, {37498, 61751}, {48672, 12315}, {49136, 5895}, {64034, 5}, {64037, 6759}, {64051, 44544}
X(64033) = pole of line {525, 37084} with respect to the circumcircle
X(64033) = pole of line {525, 15781} with respect to the Stammler circle
X(64033) = pole of line {3767, 16198} with respect to the Kiepert hyperbola
X(64033) = pole of line {22, 14530} with respect to the Stammler hyperbola
X(64033) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(14376), X(60161)}}, {{A, B, C, X(34168), X(34780)}}
X(64033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1503, 34780}, {4, 31804, 11426}, {5, 11206, 14530}, {30, 12315, 48672}, {30, 34781, 12315}, {64, 34785, 3534}, {154, 18381, 1656}, {161, 32321, 2937}, {550, 12324, 35450}, {1181, 61139, 18494}, {1498, 18400, 382}, {1498, 18445, 48669}, {1503, 34782, 14216}, {1503, 39879, 18440}, {6000, 17845, 1657}, {6146, 31383, 1598}, {6240, 12174, 64094}, {6759, 18383, 64024}, {7487, 39874, 18914}, {9833, 14216, 34782}, {11202, 14864, 40686}, {11202, 40686, 15720}, {11206, 64034, 5}, {14216, 34782, 3}, {16655, 19467, 1597}, {18381, 45185, 154}, {18383, 64024, 381}, {18400, 32359, 195}, {18405, 61749, 61984}, {29012, 61751, 37498}, {32767, 61680, 55857}, {64024, 64037, 18383}

X(64034) = ANTICOMPLEMENT OF X(9833)

Barycentrics    5*a^10-11*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(5*b^4+6*b^2*c^2+5*c^4)+a^6*(6*b^4+4*b^2*c^2+6*c^4) : :
X(64034) = -3*X[2]+2*X[9833], -2*X[3]+3*X[32064], -4*X[5]+3*X[11206], -4*X[66]+3*X[10519], -6*X[154]+7*X[3090], -3*X[193]+4*X[34788], -3*X[376]+4*X[6247], -4*X[546]+3*X[32063], -5*X[631]+6*X[1853], -10*X[1656]+9*X[35260], -2*X[1657]+3*X[54050], -5*X[3522]+8*X[14864] and many others

X(64034) lies on these lines: {2, 9833}, {3, 32064}, {4, 6}, {5, 11206}, {20, 2888}, {23, 32321}, {24, 23291}, {30, 11411}, {64, 3529}, {66, 10519}, {68, 31305}, {154, 3090}, {159, 7509}, {161, 7512}, {184, 43841}, {186, 58378}, {193, 34788}, {195, 31723}, {206, 43651}, {235, 18918}, {343, 59346}, {376, 6247}, {382, 6225}, {427, 18925}, {511, 20079}, {546, 32063}, {578, 7378}, {631, 1853}, {1092, 7396}, {1352, 44829}, {1370, 14516}, {1619, 10594}, {1656, 35260}, {1657, 54050}, {1660, 43598}, {1899, 7487}, {2393, 11412}, {2777, 49135}, {3088, 11550}, {3089, 31383}, {3091, 5012}, {3146, 5889}, {3424, 40448}, {3448, 31304}, {3517, 37643}, {3520, 63422}, {3522, 14864}, {3523, 20299}, {3524, 40686}, {3525, 17821}, {3528, 6696}, {3533, 61735}, {3534, 61540}, {3542, 25739}, {3543, 5878}, {3545, 16252}, {3547, 18474}, {3575, 18909}, {3619, 61542}, {3627, 12315}, {3832, 18383}, {3839, 61749}, {3855, 23324}, {5056, 23325}, {5059, 20427}, {5067, 10192}, {5068, 61747}, {5079, 61606}, {5446, 41715}, {5562, 5921}, {5667, 58797}, {5818, 40660}, {5894, 11001}, {5895, 15682}, {5925, 49138}, {6145, 7558}, {6193, 14790}, {6523, 6761}, {6623, 26883}, {6643, 12134}, {6756, 11433}, {6995, 13419}, {7383, 36989}, {7386, 64035}, {7391, 34799}, {7392, 64038}, {7395, 39879}, {7399, 25406}, {7400, 46264}, {7401, 15805}, {7408, 10110}, {7486, 64063}, {7525, 9920}, {7550, 15581}, {7553, 64048}, {7566, 63085}, {7576, 18916}, {8889, 19357}, {9781, 41580}, {9899, 28150}, {9909, 61544}, {10112, 31670}, {10182, 61856}, {10193, 61788}, {10303, 11202}, {10323, 63420}, {10535, 10591}, {10590, 26888}, {10606, 17538}, {10610, 32354}, {11003, 32379}, {11180, 11821}, {11204, 62097}, {11245, 11431}, {11414, 14927}, {11426, 16198}, {11427, 31804}, {11455, 36982}, {11457, 18533}, {11479, 39884}, {11645, 34621}, {11793, 34750}, {11819, 18951}, {12118, 41738}, {12362, 18440}, {12383, 63716}, {13203, 32423}, {13886, 17819}, {13939, 17820}, {14458, 60174}, {14788, 23300}, {14831, 15741}, {15022, 50414}, {15081, 15647}, {15105, 62171}, {15138, 35471}, {15311, 33703}, {15559, 41602}, {15595, 28717}, {15644, 33523}, {15692, 25563}, {15704, 35450}, {15717, 23329}, {16391, 37183}, {17578, 22802}, {18376, 50689}, {18494, 18914}, {18531, 64036}, {18912, 37122}, {21735, 23328}, {23294, 35486}, {26937, 37460}, {26944, 37458}, {31099, 34148}, {31802, 39899}, {32359, 61715}, {32816, 57275}, {32903, 62102}, {34146, 64051}, {34286, 40664}, {34664, 51023}, {34938, 44665}, {35864, 42275}, {35865, 42276}, {37498, 44442}, {38672, 45037}, {40241, 58922}, {40285, 43605}, {41736, 44076}, {43407, 49251}, {43408, 49250}, {43666, 54865}, {46729, 60166}, {47090, 53050}, {48672, 62036}, {50693, 64027}, {51491, 58795}, {54486, 60163}, {58434, 60781}, {59388, 64022}, {61680, 61886}, {61721, 62021}

X(64034) = reflection of X(i) in X(j) for these {i,j}: {20, 14216}, {3529, 64}, {5059, 20427}, {5878, 34786}, {6193, 14790}, {6225, 382}, {9833, 18381}, {12250, 12324}, {12315, 3627}, {12324, 34780}, {12383, 63716}, {17845, 6247}, {31305, 68}, {34781, 4}, {34785, 14864}, {48672, 62036}, {49138, 5925}, {58795, 51491}, {64033, 5}, {64187, 3146}
X(64034) = anticomplement of X(9833)
X(64034) = X(i)-Dao conjugate of X(j) for these {i, j}: {9833, 9833}
X(64034) = pole of line {1859, 10591} with respect to the Feuerbach hyperbola
X(64034) = pole of line {1632, 35311} with respect to the Kiepert parabola
X(64034) = pole of line {394, 9715} with respect to the Stammler hyperbola
X(64034) = pole of line {33294, 52585} with respect to the Steiner circumellipse
X(64034) = pole of line {3926, 59346} with respect to the Wallace hyperbola
X(64034) = intersection, other than A, B, C, of circumconics {{A, B, C, X(393), X(15319)}}, {{A, B, C, X(10002), X(40448)}}, {{A, B, C, X(10282), X(46728)}}
X(64034) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1503, 34781}, {4, 34224, 6776}, {4, 34781, 5656}, {5, 64033, 11206}, {30, 12324, 12250}, {30, 34780, 12324}, {68, 44407, 31305}, {1498, 8549, 7592}, {1899, 61139, 7487}, {3146, 6000, 64187}, {5878, 34786, 3543}, {6247, 17845, 376}, {6643, 12134, 14826}, {9833, 18381, 2}, {11442, 14216, 32337}, {11457, 18533, 18913}, {11457, 64032, 18533}, {11550, 19467, 3088}, {13419, 39571, 6995}, {14216, 18400, 20}, {16655, 18396, 4}, {23324, 64024, 3855}

X(64035) = COMPLEMENT OF X(6146)

Barycentrics    2*a^10-5*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+4*a^6*(b^2+c^2)^2-2*a^4*(b^2+c^2)^3+2*a^2*(b^4-c^4)^2 : :
X(64035) = -3*X[2]+X[6146], 3*X[376]+X[16659], -3*X[428]+X[45186], -3*X[547]+X[45970], -5*X[631]+X[34224], -5*X[632]+X[45731], -5*X[1656]+X[44076], -X[1885]+3*X[15030], -7*X[3090]+3*X[12022], -5*X[3091]+3*X[16657], -X[3146]+3*X[16654], X[3529]+3*X[16658] and many others

X(64035) lies on these lines: {2, 6146}, {3, 66}, {4, 394}, {5, 578}, {6, 6193}, {20, 16655}, {24, 343}, {30, 1216}, {49, 15872}, {52, 524}, {54, 14788}, {68, 6642}, {69, 7487}, {110, 13160}, {140, 13561}, {154, 3547}, {155, 12233}, {182, 31804}, {184, 7399}, {265, 50143}, {287, 26155}, {297, 8884}, {376, 16659}, {378, 63631}, {382, 16656}, {389, 3564}, {403, 43598}, {427, 1092}, {428, 45186}, {511, 6756}, {539, 5462}, {542, 9729}, {547, 45970}, {569, 3589}, {631, 34224}, {632, 45731}, {952, 55307}, {1154, 31830}, {1181, 6815}, {1209, 7542}, {1350, 31305}, {1368, 18381}, {1506, 59558}, {1514, 15052}, {1568, 23047}, {1594, 11064}, {1595, 3818}, {1656, 44076}, {1658, 44201}, {1853, 3546}, {1885, 15030}, {1993, 7544}, {2072, 6288}, {2883, 18451}, {2888, 3580}, {3088, 28419}, {3090, 12022}, {3091, 16657}, {3146, 16654}, {3147, 37638}, {3292, 3574}, {3357, 44241}, {3410, 22467}, {3518, 32269}, {3529, 16658}, {3541, 35602}, {3542, 35259}, {3548, 23332}, {3549, 10192}, {3567, 61658}, {3575, 5562}, {3628, 5972}, {3629, 37493}, {3631, 37478}, {3796, 7383}, {3819, 44829}, {3917, 61139}, {5020, 12429}, {5133, 34148}, {5159, 32767}, {5447, 44407}, {5449, 16238}, {5480, 7528}, {5576, 22115}, {5876, 34798}, {5891, 12605}, {5892, 10116}, {5921, 18909}, {5943, 10112}, {5944, 7568}, {5946, 32358}, {5965, 16625}, {6000, 31829}, {6090, 7507}, {6101, 11819}, {6240, 11459}, {6639, 58434}, {6643, 17811}, {6644, 12359}, {6676, 10282}, {6677, 61544}, {6759, 6823}, {6776, 6803}, {6804, 18945}, {6816, 18396}, {6997, 10982}, {7386, 64034}, {7395, 19467}, {7400, 11206}, {7403, 13352}, {7404, 10516}, {7488, 37636}, {7506, 41587}, {7511, 10441}, {7529, 15873}, {7540, 37484}, {7546, 48902}, {7550, 12254}, {7552, 35266}, {7553, 10625}, {7558, 9707}, {7565, 40112}, {7575, 21230}, {7576, 11412}, {7706, 15083}, {7819, 15595}, {7999, 64032}, {8263, 34507}, {8550, 36752}, {8681, 46363}, {9545, 14389}, {9715, 43653}, {9786, 11411}, {9815, 11432}, {9818, 12118}, {9826, 32166}, {10024, 18350}, {10095, 23410}, {10110, 13142}, {10115, 16881}, {10263, 13490}, {10519, 59346}, {10539, 15760}, {10564, 18488}, {10961, 35836}, {10963, 35837}, {10996, 34781}, {11017, 15807}, {11180, 18913}, {11264, 13363}, {11387, 64023}, {11414, 31383}, {11426, 14561}, {11430, 18358}, {11442, 17928}, {11444, 12225}, {11487, 17845}, {11550, 43652}, {11585, 18474}, {11695, 45298}, {11746, 58496}, {11793, 12362}, {11818, 16266}, {12006, 43588}, {12007, 36753}, {12038, 52262}, {12106, 63734}, {12111, 38323}, {12140, 41673}, {12162, 15311}, {12166, 63180}, {12278, 15056}, {12290, 44458}, {12324, 61113}, {12383, 35500}, {12428, 37696}, {13348, 29012}, {13353, 15462}, {13383, 15448}, {13434, 37990}, {13488, 44870}, {13568, 13754}, {14128, 30522}, {14156, 32144}, {14457, 40917}, {14533, 19179}, {14786, 37506}, {14852, 61507}, {15043, 45968}, {15058, 18560}, {15060, 52070}, {15062, 16386}, {15066, 37444}, {15068, 22660}, {15305, 52071}, {15559, 43574}, {16196, 20299}, {16976, 25563}, {17810, 64048}, {18388, 61607}, {18436, 38321}, {18531, 41362}, {18565, 50709}, {18583, 37505}, {18912, 37648}, {18970, 37697}, {19176, 58408}, {20428, 54306}, {20429, 54307}, {21659, 34664}, {22804, 51391}, {22833, 44686}, {30714, 32274}, {31834, 45971}, {32139, 50008}, {33586, 37122}, {34573, 37513}, {34603, 64050}, {34726, 54173}, {34826, 44452}, {34938, 36990}, {35018, 43575}, {37119, 45303}, {37472, 50137}, {37480, 39884}, {37515, 48906}, {37814, 44158}, {43084, 53169}, {43130, 51994}, {43150, 44683}, {43607, 61128}, {43614, 50435}, {43821, 50139}, {43841, 64177}, {43995, 52280}, {44247, 64027}, {44261, 50991}, {44804, 46852}, {46029, 61608}, {46728, 48876}, {46817, 61750}, {46818, 52525}, {56965, 63649}, {58545, 63659}, {63667, 64063}, {64066, 64095}

X(64035) = midpoint of X(i) and X(j) for these {i,j}: {3, 12134}, {20, 16655}, {1216, 45286}, {3575, 5562}, {6101, 11819}, {6146, 14516}, {7553, 10625}, {7576, 64062}, {12140, 41673}, {13419, 15644}, {16654, 54040}, {31831, 31833}, {31834, 45971}
X(64035) = reflection of X(i) in X(j) for these {i,j}: {52, 11745}, {382, 16656}, {389, 9825}, {6146, 64038}, {12241, 5}, {12362, 11793}, {13142, 10110}, {13292, 5462}, {13488, 44870}, {13568, 31833}, {15807, 11017}, {18914, 9729}, {43575, 35018}, {43588, 12006}, {52073, 14128}
X(64035) = complement of X(6146)
X(64035) = anticomplement of X(64038)
X(64035) = X(i)-Dao conjugate of X(j) for these {i, j}: {64038, 64038}
X(64035) = pole of line {577, 3767} with respect to the Kiepert hyperbola
X(64035) = pole of line {22, 1181} with respect to the Stammler hyperbola
X(64035) = pole of line {3265, 57065} with respect to the Steiner inellipse
X(64035) = pole of line {315, 40680} with respect to the Wallace hyperbola
X(64035) = pole of line {421, 2501} with respect to the dual conic of DeLongchamps circle
X(64035) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {125, 16178, 45258}
X(64035) = intersection, other than A, B, C, of circumconics {{A, B, C, X(66), X(1217)}}, {{A, B, C, X(14376), X(60114)}}, {{A, B, C, X(27356), X(41168)}}
X(64035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14516, 6146}, {2, 18925, 37476}, {2, 6146, 64038}, {3, 12134, 1503}, {3, 18440, 14216}, {3, 64033, 46264}, {4, 14826, 17814}, {5, 1147, 23292}, {5, 44665, 12241}, {5, 61753, 9820}, {5, 9306, 59659}, {54, 14788, 37649}, {68, 6642, 13567}, {69, 7487, 17834}, {141, 34782, 3}, {155, 18420, 12233}, {182, 61751, 31804}, {524, 11745, 52}, {539, 5462, 13292}, {542, 9729, 18914}, {569, 7405, 3589}, {1147, 9927, 23307}, {1209, 51393, 7542}, {1216, 45286, 30}, {1993, 7544, 45089}, {2888, 44802, 3580}, {3564, 9825, 389}, {3818, 13346, 1595}, {5020, 12429, 39571}, {5449, 16238, 47296}, {5449, 43586, 16238}, {6193, 7401, 6}, {6776, 6803, 37514}, {7528, 36747, 5480}, {7553, 10625, 29181}, {7558, 9707, 13394}, {9786, 15069, 11411}, {9815, 63722, 11432}, {10024, 18350, 51425}, {10127, 13292, 5462}, {10516, 11425, 7404}, {10539, 15760, 16252}, {12278, 15056, 52069}, {13565, 58407, 3628}, {13754, 31833, 13568}, {14128, 30522, 52073}, {17811, 64037, 6643}, {31831, 31833, 13754}

X(64036) = ORTHOLOGY CENTER OF THESE TRIANGLES: EHRMANN-SIDE AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    2*a^10-5*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+2*a^2*(b^4-c^4)^2+2*a^6*(2*b^4+b^2*c^2+2*c^4)-2*a^4*(b^6+c^6) : :
X(64036) = -3*X[51]+2*X[10116], -4*X[143]+3*X[45968], -2*X[185]+3*X[38321], -3*X[381]+2*X[6146], -3*X[428]+2*X[13292], -3*X[568]+4*X[6756], -3*X[1843]+2*X[12585], -3*X[3060]+2*X[32358], -5*X[3567]+6*X[13490], -3*X[3830]+4*X[16621], -5*X[3843]+4*X[12241], -3*X[3845]+2*X[45970] and many others

X(64036) lies on these lines: {3, 66}, {4, 1994}, {5, 1614}, {20, 15108}, {23, 63734}, {24, 32140}, {25, 25738}, {26, 11442}, {30, 11412}, {49, 427}, {51, 10116}, {52, 542}, {68, 7517}, {110, 13371}, {113, 18383}, {143, 45968}, {154, 6639}, {155, 31723}, {156, 1594}, {184, 5576}, {185, 38321}, {235, 265}, {343, 2937}, {381, 6146}, {382, 9936}, {389, 43129}, {399, 22660}, {428, 13292}, {524, 11663}, {539, 45186}, {546, 11423}, {550, 13445}, {567, 7403}, {568, 6756}, {569, 3818}, {858, 61753}, {1112, 46443}, {1147, 11550}, {1495, 5449}, {1595, 37472}, {1843, 12585}, {1853, 6640}, {1899, 7506}, {1907, 43595}, {1995, 18952}, {2070, 12359}, {2072, 10539}, {2883, 48669}, {2888, 12088}, {3060, 32358}, {3357, 44246}, {3410, 7512}, {3448, 3518}, {3548, 32064}, {3549, 11206}, {3564, 6243}, {3567, 13490}, {3575, 34783}, {3580, 18356}, {3627, 7728}, {3830, 16621}, {3843, 12241}, {3845, 45970}, {3858, 43575}, {5055, 64038}, {5076, 16654}, {5133, 32046}, {5448, 11572}, {5480, 14627}, {5562, 44407}, {5663, 6240}, {5876, 12225}, {5889, 11819}, {5890, 31830}, {5891, 44829}, {5907, 11750}, {5921, 31305}, {5946, 45732}, {6101, 61299}, {6102, 7576}, {6288, 15760}, {6644, 11457}, {6759, 10024}, {6776, 7528}, {7391, 16266}, {7401, 39874}, {7405, 37471}, {7487, 18917}, {7505, 61702}, {7525, 37636}, {7527, 12254}, {7555, 21230}, {7577, 61608}, {7592, 11818}, {9306, 37452}, {9544, 52295}, {9704, 23292}, {9707, 61700}, {9927, 11799}, {10018, 13561}, {10020, 23293}, {10110, 61713}, {10111, 46682}, {10254, 16252}, {10255, 51425}, {10263, 34603}, {10282, 32415}, {10295, 32138}, {10625, 29012}, {10627, 52397}, {11381, 17702}, {11411, 54149}, {11430, 18488}, {11440, 44242}, {11441, 18569}, {11444, 40241}, {11449, 23336}, {11468, 47335}, {11585, 18350}, {11645, 15644}, {12024, 61968}, {12086, 12383}, {12106, 26879}, {12112, 50009}, {12162, 12606}, {12289, 15305}, {12293, 31725}, {12429, 18534}, {12605, 18435}, {12897, 32062}, {13160, 61752}, {13198, 20303}, {13352, 61751}, {13399, 43604}, {13403, 16194}, {13470, 15060}, {13491, 38323}, {13567, 13621}, {13595, 43808}, {13754, 61139}, {13861, 18912}, {14157, 15761}, {14389, 50138}, {14449, 41628}, {14683, 56292}, {14787, 37476}, {14805, 63679}, {14940, 35265}, {15024, 23410}, {15058, 52073}, {15068, 37444}, {15069, 37486}, {15087, 45089}, {15311, 18565}, {15646, 43607}, {15704, 54040}, {16656, 62008}, {16657, 61984}, {16868, 46817}, {18323, 34786}, {18378, 41587}, {18394, 23323}, {18403, 41362}, {18404, 18451}, {18531, 64034}, {18559, 64025}, {18560, 30522}, {18859, 63631}, {18914, 37481}, {18925, 51023}, {18951, 37122}, {20299, 51393}, {21243, 45185}, {22115, 23335}, {22146, 27376}, {23039, 31831}, {23236, 37495}, {23294, 44452}, {23307, 41615}, {23315, 54073}, {24981, 41597}, {26886, 55534}, {26917, 44232}, {32111, 44279}, {32171, 37118}, {32321, 44259}, {35283, 55857}, {36747, 36990}, {36752, 64080}, {37347, 64049}, {37493, 39899}, {37505, 48889}, {37971, 61544}, {37981, 52432}, {41171, 52525}, {43577, 64029}, {44110, 44516}, {44795, 45177}, {44911, 45622}, {45730, 45967}, {45957, 45971}, {45959, 52069}, {46849, 61744}, {63671, 64024}

X(64036) = midpoint of X(i) and X(j) for these {i,j}: {12111, 64032}, {12278, 12290}, {14516, 16659}
X(64036) = reflection of X(i) in X(j) for these {i,j}: {3, 12134}, {52, 13419}, {185, 45286}, {382, 16655}, {5889, 11819}, {6243, 7553}, {10111, 46682}, {11750, 5907}, {12225, 5876}, {12289, 52070}, {18563, 12162}, {34224, 5}, {34783, 3575}, {34799, 12370}, {44076, 4}, {45731, 546}, {45957, 45971}, {64029, 43577}
X(64036) = pole of line {59744, 59932} with respect to the polar circle
X(64036) = pole of line {2965, 3767} with respect to the Kiepert hyperbola
X(64036) = pole of line {22, 156} with respect to the Stammler hyperbola
X(64036) = intersection, other than A, B, C, of circumconics {{A, B, C, X(66), X(11816)}}, {{A, B, C, X(13579), X(14376)}}, {{A, B, C, X(27361), X(41168)}}
X(64036) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 34799, 12370}, {52, 13419, 7540}, {68, 31383, 7517}, {399, 31724, 22660}, {542, 13419, 52}, {546, 45731, 12022}, {569, 3818, 50137}, {1503, 12134, 3}, {1594, 46818, 156}, {3564, 7553, 6243}, {6759, 18474, 10024}, {7403, 31804, 567}, {7405, 48906, 37471}, {7728, 52863, 3627}, {9927, 26883, 11799}, {10539, 18381, 2072}, {12111, 64032, 30}, {12162, 18400, 18563}, {12289, 15305, 52070}, {12370, 34799, 44076}, {13490, 43588, 3567}, {14157, 58922, 15761}, {16655, 44665, 382}, {18356, 37440, 3580}, {18451, 64037, 18404}, {23293, 26882, 10020}, {31804, 39884, 7403}

X(64037) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST EXCOSINE AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    3*a^10-6*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+2*a^6*(b^2+c^2)^2+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4) : :
X(64037) = -6*X[2]+5*X[17821], -4*X[5]+3*X[154], -2*X[26]+3*X[14852], -8*X[140]+9*X[61735], -3*X[376]+4*X[6696], -4*X[550]+5*X[8567], -3*X[568]+2*X[41725], -3*X[599]+4*X[34118], -5*X[631]+6*X[23332], -5*X[1656]+4*X[10282], -2*X[1658]+3*X[61702], -2*X[1660]+3*X[16072] and many others

X(64037) lies on these lines: {2, 17821}, {3, 161}, {4, 6}, {5, 154}, {20, 343}, {22, 58922}, {24, 25739}, {25, 61139}, {26, 14852}, {30, 64}, {52, 382}, {66, 1350}, {98, 46729}, {125, 3515}, {140, 61735}, {155, 18569}, {159, 7395}, {184, 7507}, {185, 12173}, {221, 1478}, {235, 31383}, {265, 7517}, {355, 64022}, {376, 6696}, {378, 12289}, {381, 569}, {389, 18494}, {394, 14516}, {399, 19506}, {403, 20303}, {427, 11425}, {485, 17819}, {486, 17820}, {511, 12429}, {542, 12164}, {550, 8567}, {568, 41725}, {599, 34118}, {631, 23332}, {858, 35602}, {973, 5890}, {1147, 15139}, {1192, 18533}, {1204, 15138}, {1351, 10112}, {1352, 9924}, {1479, 2192}, {1529, 13854}, {1593, 11550}, {1594, 19357}, {1595, 41602}, {1597, 13403}, {1598, 1619}, {1614, 7547}, {1624, 38281}, {1656, 10282}, {1657, 3357}, {1658, 61702}, {1660, 16072}, {1699, 40658}, {1854, 10572}, {1899, 3575}, {1971, 13881}, {1993, 32346}, {2393, 5562}, {2777, 5073}, {2781, 25335}, {2854, 12271}, {2888, 17846}, {2931, 38450}, {2935, 9937}, {3089, 18918}, {3090, 10192}, {3091, 11206}, {3146, 6515}, {3153, 11441}, {3167, 61751}, {3172, 51363}, {3424, 60618}, {3448, 17835}, {3518, 61701}, {3522, 23328}, {3526, 11202}, {3529, 5894}, {3534, 64027}, {3543, 6225}, {3567, 41589}, {3574, 11402}, {3580, 31304}, {3627, 5878}, {3763, 7509}, {3796, 13160}, {3818, 11479}, {3827, 14872}, {3830, 12315}, {3832, 63085}, {3843, 18376}, {3851, 14530}, {5012, 32369}, {5050, 34776}, {5055, 64063}, {5056, 35260}, {5059, 54050}, {5064, 11424}, {5067, 58434}, {5068, 64059}, {5072, 50414}, {5085, 7399}, {5094, 13367}, {5449, 14070}, {5576, 37506}, {5587, 40660}, {5663, 52843}, {5691, 5903}, {5889, 52842}, {5904, 32356}, {5907, 9967}, {5922, 18017}, {6102, 40909}, {6193, 37672}, {6240, 10605}, {6241, 35480}, {6285, 12953}, {6353, 15153}, {6560, 19087}, {6561, 19088}, {6642, 45286}, {6643, 17811}, {6756, 17810}, {6823, 46264}, {6995, 15873}, {7355, 12943}, {7383, 53094}, {7387, 9927}, {7400, 44882}, {7401, 17825}, {7487, 13567}, {7488, 37638}, {7514, 13470}, {7526, 34514}, {7544, 10601}, {7550, 15582}, {7564, 32046}, {7566, 13434}, {7568, 61612}, {7569, 32391}, {7576, 18912}, {7577, 9707}, {7703, 51033}, {7706, 18128}, {7715, 31860}, {7729, 10575}, {7773, 57275}, {7973, 12699}, {8991, 9541}, {9657, 32065}, {9670, 11189}, {9714, 63735}, {9815, 45298}, {9914, 16010}, {9934, 10113}, {9935, 38433}, {10076, 10483}, {10110, 41580}, {10182, 46219}, {10264, 32316}, {10323, 44883}, {10463, 60018}, {10533, 42265}, {10534, 42262}, {10535, 10896}, {10540, 34116}, {10619, 61743}, {10895, 26888}, {10984, 43273}, {11204, 15696}, {11243, 42156}, {11244, 42153}, {11381, 44438}, {11403, 61744}, {11412, 40341}, {11413, 12278}, {11414, 48905}, {11433, 11745}, {11438, 26944}, {11442, 12225}, {11449, 30744}, {11464, 52296}, {11472, 52070}, {11482, 23048}, {11541, 50709}, {11585, 59767}, {11645, 44470}, {11744, 12295}, {11793, 18536}, {11827, 63435}, {12084, 30522}, {12118, 23335}, {12134, 17814}, {12160, 34777}, {12161, 17824}, {12235, 14915}, {12250, 33703}, {12254, 52295}, {12290, 22535}, {12370, 44413}, {12383, 23315}, {12664, 52849}, {12667, 60689}, {12688, 15942}, {12779, 31673}, {13142, 31670}, {13203, 64183}, {13289, 38724}, {13346, 34609}, {13352, 44679}, {13371, 47391}, {13399, 34469}, {13474, 36982}, {13561, 18324}, {13568, 18909}, {13851, 15125}, {14118, 61700}, {14157, 18394}, {14269, 43835}, {14458, 45300}, {14528, 44836}, {14561, 19132}, {14644, 15647}, {14788, 20300}, {14790, 37498}, {14831, 32392}, {14862, 61970}, {14927, 52404}, {15087, 32365}, {15105, 49135}, {15131, 30714}, {15270, 54004}, {15305, 63728}, {15585, 40330}, {15653, 44886}, {15682, 64187}, {15688, 32903}, {15704, 61540}, {16000, 37932}, {16195, 61646}, {16266, 17847}, {16419, 44862}, {17578, 63012}, {17800, 35450}, {17809, 31804}, {17813, 31802}, {17826, 18582}, {17827, 18581}, {18377, 32139}, {18386, 43831}, {18388, 19347}, {18392, 40241}, {18404, 18451}, {18420, 37514}, {18434, 40441}, {18439, 58789}, {18445, 31724}, {18925, 23292}, {18952, 31830}, {19457, 44795}, {19459, 45015}, {20079, 51212}, {21841, 41424}, {23293, 38444}, {23294, 32534}, {23327, 53093}, {25738, 37489}, {26881, 63657}, {26937, 37487}, {29012, 37488}, {30402, 42098}, {30403, 42095}, {31152, 43652}, {31166, 38072}, {31283, 32171}, {31723, 36747}, {31815, 32358}, {31833, 37475}, {31867, 57528}, {31884, 59778}, {32274, 38885}, {32344, 61134}, {32351, 32354}, {32609, 32743}, {33537, 34664}, {34146, 45186}, {34170, 51342}, {34286, 41425}, {34778, 48872}, {34938, 34944}, {35472, 43608}, {35503, 43607}, {39522, 45970}, {40448, 46727}, {41427, 47090}, {42263, 49250}, {42264, 49251}, {42457, 51358}, {43651, 47352}, {44479, 44870}, {44673, 55570}, {46265, 61840}, {46443, 57584}, {50691, 54211}, {52863, 64030}, {54131, 64031}, {55578, 61645}, {58492, 64100}, {58579, 63432}, {58762, 63441}

X(64037) = midpoint of X(i) and X(j) for these {i,j}: {382, 34780}, {3146, 12324}, {5073, 13093}, {12250, 33703}, {13203, 64183}, {20079, 51212}
X(64037) = reflection of X(i) in X(j) for these {i,j}: {3, 18381}, {20, 6247}, {64, 14216}, {155, 18569}, {159, 51756}, {161, 18474}, {382, 34786}, {399, 19506}, {1350, 66}, {1498, 4}, {1619, 18390}, {1657, 3357}, {2917, 6145}, {2935, 63716}, {3357, 14864}, {3529, 5894}, {5596, 5480}, {5878, 3627}, {5895, 382}, {5925, 64}, {6225, 51491}, {6293, 52}, {6759, 18383}, {6776, 15583}, {7387, 9927}, {7973, 12699}, {9833, 5}, {9924, 1352}, {9934, 10113}, {10117, 265}, {10606, 32064}, {11206, 23324}, {11744, 12295}, {12118, 23335}, {12163, 32140}, {12315, 22802}, {12383, 23315}, {12779, 31673}, {15704, 61540}, {17834, 68}, {17835, 3448}, {17845, 3}, {17846, 2888}, {19149, 18382}, {32063, 18376}, {32139, 18377}, {32354, 32351}, {32359, 3574}, {34781, 2883}, {34785, 20299}, {34787, 34118}, {36982, 13474}, {36989, 23300}, {37498, 14790}, {38885, 32274}, {39879, 3818}, {48669, 32365}, {48872, 34778}, {48905, 63420}, {58795, 5878}, {64022, 355}, {64033, 6759}
X(64037) = anticomplement of X(34782)
X(64037) = perspector of circumconic {{A, B, C, X(107), X(16039)}}
X(64037) = X(i)-Dao conjugate of X(j) for these {i, j}: {34782, 34782}
X(64037) = pole of line {6368, 39201} with respect to the circumcircle
X(64037) = pole of line {8799, 42733} with respect to the orthocentroidal circle
X(64037) = pole of line {6368, 53255} with respect to the Stammler circle
X(64037) = pole of line {1859, 10896} with respect to the Feuerbach hyperbola
X(64037) = pole of line {51, 7507} with respect to the Jerabek hyperbola
X(64037) = pole of line {394, 7488} with respect to the Stammler hyperbola
X(64037) = pole of line {6587, 60597} with respect to the Steiner inellipse
X(64037) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(64), X(8745)}}, {{A, B, C, X(68), X(1249)}}, {{A, B, C, X(393), X(6145)}}, {{A, B, C, X(6530), X(46729)}}, {{A, B, C, X(10002), X(60618)}}, {{A, B, C, X(15262), X(38260)}}, {{A, B, C, X(34438), X(52418)}}
X(64037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 34782, 17821}, {3, 161, 2917}, {3, 18381, 1853}, {3, 18400, 17845}, {4, 12022, 10982}, {4, 16655, 15811}, {4, 18945, 12241}, {4, 34224, 1181}, {4, 34781, 2883}, {4, 5656, 5893}, {4, 6146, 6}, {4, 6776, 12233}, {5, 9833, 154}, {20, 32064, 6247}, {20, 6247, 10606}, {30, 14216, 64}, {30, 32140, 12163}, {30, 64, 5925}, {30, 68, 17834}, {52, 6000, 6293}, {68, 17834, 64060}, {159, 51756, 10516}, {184, 11572, 7507}, {381, 64033, 6759}, {382, 34780, 6000}, {1498, 18405, 4}, {1503, 15583, 6776}, {1503, 18382, 19149}, {1503, 2883, 34781}, {1503, 5480, 5596}, {1656, 10282, 61680}, {1899, 3575, 9786}, {2883, 34781, 1498}, {3091, 11206, 16252}, {3146, 12324, 15311}, {3543, 6225, 51491}, {3627, 5878, 61721}, {3830, 12315, 22802}, {3843, 32063, 61749}, {3851, 14530, 61747}, {5073, 13093, 2777}, {6000, 34786, 382}, {6240, 11457, 10605}, {6293, 34751, 52}, {6643, 64035, 17811}, {6756, 39571, 17810}, {6759, 18383, 381}, {7401, 64038, 17825}, {7517, 32321, 10117}, {9927, 44407, 7387}, {10282, 23325, 1656}, {11550, 21659, 1593}, {11750, 18474, 3}, {12118, 23335, 37497}, {12134, 18531, 17814}, {13419, 18390, 1598}, {13851, 26883, 37197}, {14157, 18394, 35488}, {14790, 44665, 37498}, {16252, 23324, 3091}, {17702, 63716, 2935}, {17845, 18381, 40686}, {18376, 61749, 3843}, {18381, 18474, 6145}, {18381, 34785, 20299}, {18383, 64033, 64024}, {18396, 34775, 18405}, {18400, 18474, 161}, {18400, 20299, 34785}, {18404, 64036, 18451}, {20300, 23041, 47355}, {23300, 36989, 5085}, {25739, 64032, 24}, {31723, 44076, 36747}, {34780, 34786, 5895}, {44288, 45731, 12161}, {45185, 61747, 14530}, {58795, 61721, 5878}

X(64038) = ORTHOLOGY CENTER OF THESE TRIANGLES: SUBMEDIAL AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    2*a^10+2*a^2*(b^2-c^2)^4-5*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+4*a^6*(b^4+c^4)-2*a^4*(b^6-5*b^4*c^2-5*b^2*c^4+c^6) : :
X(64038) = 3*X[2]+X[6146], X[20]+3*X[16657], X[185]+3*X[34664], -9*X[373]+X[61139], -3*X[381]+X[16621], 3*X[549]+X[12370], 5*X[631]+3*X[12022], X[1885]+3*X[64100], 7*X[3090]+X[34224], -5*X[3091]+X[16655], 7*X[3526]+3*X[12024], -9*X[3545]+X[16659] and many others

X(64038) lies on circumconic {{A, B, C, X(2980), X(14457)}} and on these lines: {2, 6146}, {3, 12241}, {4, 10601}, {5, 182}, {6, 6643}, {20, 16657}, {24, 37648}, {30, 5462}, {54, 11064}, {68, 141}, {140, 5449}, {155, 8550}, {184, 59659}, {185, 34664}, {235, 10984}, {323, 43838}, {343, 7509}, {373, 61139}, {381, 16621}, {389, 12362}, {403, 61134}, {441, 10600}, {511, 44862}, {524, 1216}, {546, 16656}, {549, 12370}, {550, 64095}, {567, 37452}, {569, 11585}, {576, 53022}, {578, 1368}, {631, 12022}, {858, 13434}, {1092, 30739}, {1147, 53415}, {1181, 6816}, {1350, 64048}, {1370, 10982}, {1498, 18537}, {1594, 37649}, {1598, 46264}, {1656, 8780}, {1853, 7404}, {1885, 64100}, {1899, 7395}, {2072, 13353}, {3066, 37122}, {3089, 25406}, {3090, 34224}, {3091, 16655}, {3526, 12024}, {3527, 31670}, {3530, 43575}, {3542, 3796}, {3545, 16659}, {3546, 11425}, {3547, 5085}, {3548, 37506}, {3564, 11793}, {3580, 37126}, {3628, 58435}, {3819, 10112}, {3832, 16654}, {3855, 16658}, {4846, 51491}, {5020, 9833}, {5055, 64036}, {5067, 35283}, {5092, 16197}, {5422, 37444}, {5446, 29181}, {5447, 58806}, {5480, 14790}, {5562, 11245}, {5892, 31833}, {5894, 49669}, {5907, 18914}, {5943, 6756}, {6193, 17811}, {6240, 15045}, {6243, 45967}, {6247, 9818}, {6642, 34782}, {6677, 10282}, {6696, 7526}, {6723, 16239}, {6776, 6804}, {6803, 18945}, {6815, 18396}, {6823, 18390}, {7386, 37498}, {7387, 15873}, {7392, 64034}, {7399, 43650}, {7401, 17825}, {7405, 18474}, {7487, 18928}, {7503, 18911}, {7505, 13394}, {7512, 32269}, {7514, 12359}, {7542, 37513}, {7550, 43808}, {7558, 61701}, {7568, 63839}, {7574, 15047}, {7576, 15024}, {7667, 45186}, {7829, 51746}, {7999, 64062}, {8718, 44803}, {9306, 31804}, {9715, 61506}, {9730, 12605}, {9815, 18494}, {9820, 32046}, {9825, 11695}, {10024, 37471}, {10116, 10170}, {10127, 45286}, {10151, 64179}, {10295, 43597}, {10540, 50139}, {10574, 52069}, {10610, 44452}, {10691, 13142}, {11179, 19347}, {11262, 11802}, {11412, 61658}, {11430, 16196}, {11432, 18536}, {11433, 17834}, {11444, 45968}, {11465, 64032}, {11479, 14216}, {11484, 64033}, {11487, 15069}, {11591, 43588}, {11819, 15026}, {12007, 12161}, {12225, 15043}, {12233, 18531}, {12429, 16419}, {13336, 15760}, {13339, 43821}, {13363, 13470}, {13403, 16836}, {13488, 46850}, {13630, 52073}, {14531, 61712}, {14788, 25739}, {14791, 44480}, {14896, 62490}, {15067, 32358}, {15153, 37347}, {15311, 40647}, {15606, 34380}, {15717, 54040}, {15805, 18420}, {16198, 19130}, {16238, 18475}, {16625, 32068}, {17810, 31305}, {18855, 52288}, {18874, 61299}, {19467, 54012}, {20299, 63679}, {20791, 52071}, {26879, 35921}, {26937, 54994}, {34002, 63735}, {34005, 43601}, {36153, 51391}, {37470, 44240}, {41588, 46728}, {43614, 46818}, {43836, 44569}, {44516, 44911}, {44920, 61749}, {45731, 55856}, {49673, 61619}, {50140, 61608}, {50143, 51425}, {58465, 64063}, {61607, 64026}

X(64038) = midpoint of X(i) and X(j) for these {i,j}: {3, 12241}, {389, 12362}, {1216, 13292}, {3530, 43575}, {5447, 58806}, {5907, 18914}, {6146, 64035}, {6756, 44829}, {10116, 31831}, {11591, 43588}, {12605, 13568}, {13142, 15644}, {13403, 31829}, {13470, 31830}, {13488, 46850}, {13630, 52073}
X(64038) = reflection of X(i) in X(j) for these {i,j}: {9825, 11695}, {11745, 5462}, {16656, 546}
X(64038) = complement of X(64035)
X(64038) = pole of line {14531, 54384} with respect to the Jerabek hyperbola
X(64038) = pole of line {32, 7401} with respect to the Kiepert hyperbola
X(64038) = pole of line {2979, 17834} with respect to the Stammler hyperbola
X(64038) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 12241, 14895}, {389, 12362, 14894}
X(64038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6146, 64035}, {5, 48906, 6759}, {5, 64049, 16252}, {30, 5462, 11745}, {68, 7393, 141}, {1216, 13292, 524}, {1216, 43573, 13292}, {1594, 43651, 37649}, {5422, 37444, 45089}, {5943, 44829, 6756}, {6776, 6804, 17814}, {7509, 18912, 343}, {7514, 18952, 12359}, {7542, 43817, 47296}, {9730, 12605, 13568}, {10116, 10170, 31831}, {10691, 13142, 15644}, {12362, 45298, 389}, {13363, 13470, 31830}, {13403, 16836, 31829}, {15873, 44882, 7387}, {17825, 64037, 7401}, {18390, 37515, 6823}, {18531, 36752, 12233}, {37126, 43816, 3580}, {37513, 43817, 7542}

X(64039) = ANTICOMPLEMENT OF X(1829)

Barycentrics    a*(-2*a^2*b^2*c^2+a^5*(b+c)+a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)-a*(b^5+b^4*c+b*c^4+c^5)) : :
X(64039) = -3*X[2]+2*X[1829], -3*X[3060]+4*X[44547], -4*X[5044]+3*X[61726], -5*X[25917]+4*X[41591], -3*X[34603]+4*X[49542]

X(64039) lies on circumconic {{A, B, C, X(8048), X(43712)}} and on these lines: {1, 22}, {2, 1829}, {3, 11396}, {8, 1370}, {10, 858}, {20, 145}, {21, 41340}, {23, 11363}, {30, 12135}, {40, 11413}, {65, 81}, {69, 3827}, {72, 2895}, {74, 13397}, {92, 37191}, {100, 52359}, {109, 12089}, {110, 40660}, {172, 21861}, {283, 1782}, {355, 37444}, {394, 64022}, {515, 12225}, {516, 52071}, {518, 12220}, {519, 52397}, {857, 26157}, {901, 2694}, {912, 11412}, {942, 7520}, {960, 32782}, {962, 37201}, {1038, 24611}, {1060, 11337}, {1076, 1845}, {1214, 4225}, {1385, 7488}, {1386, 19121}, {1426, 37798}, {1482, 11414}, {1633, 38885}, {1698, 30744}, {1824, 2475}, {1828, 5046}, {1870, 37231}, {1871, 6839}, {1872, 37437}, {1902, 3146}, {1905, 35996}, {1935, 21368}, {1993, 64040}, {1995, 7713}, {2071, 3579}, {2771, 12219}, {2836, 3962}, {2915, 18447}, {2937, 51696}, {3007, 34434}, {3057, 3100}, {3060, 44547}, {3151, 6542}, {3152, 62314}, {3153, 18480}, {3534, 34729}, {3576, 38444}, {3616, 7493}, {3617, 7396}, {3622, 10565}, {3623, 59343}, {3877, 27505}, {4197, 9895}, {4216, 37565}, {4393, 7560}, {4456, 18669}, {4463, 7270}, {4640, 57590}, {4663, 11416}, {5044, 61726}, {5090, 7391}, {5285, 52362}, {5603, 59349}, {5903, 16474}, {6001, 12111}, {7293, 33178}, {7500, 7718}, {7512, 24301}, {7691, 14110}, {7957, 22528}, {7967, 59346}, {7968, 11418}, {7969, 11417}, {7982, 33524}, {7987, 38438}, {8227, 63657}, {9537, 31788}, {9538, 9957}, {9625, 51694}, {9627, 20872}, {9715, 10246}, {9778, 30552}, {9798, 26283}, {9840, 21318}, {10296, 33697}, {10298, 13624}, {10319, 59359}, {11230, 58805}, {11440, 12262}, {12245, 52398}, {12699, 44440}, {12702, 21312}, {14923, 52365}, {15178, 38435}, {16386, 31730}, {16826, 26252}, {17014, 37544}, {17441, 34772}, {17502, 38448}, {18455, 20833}, {18589, 26167}, {18659, 20911}, {19367, 62402}, {20080, 34381}, {20254, 28348}, {20291, 20718}, {22793, 50009}, {23361, 45916}, {24474, 36029}, {24584, 26203}, {25917, 41591}, {25962, 51410}, {26910, 64132}, {26911, 45120}, {30769, 46932}, {34603, 49542}, {34642, 47313}, {34773, 44239}, {37404, 37562}, {37405, 41502}, {38480, 56951}, {40959, 62802}, {41538, 56878}, {44450, 50821}, {44545, 63013}, {44661, 57287}, {47090, 61524}, {51223, 56050}, {52345, 53349}, {59348, 61286}, {59351, 61276}, {59357, 63159}

X(64039) = reflection of X(i) in X(j) for these {i,j}: {1829, 37613}, {3146, 1902}, {3868, 18732}, {3869, 41600}, {41722, 3}
X(64039) = inverse of X(20067) in DeLongchamps circle
X(64039) = anticomplement of X(1829)
X(64039) = X(i)-Dao conjugate of X(j) for these {i, j}: {1829, 1829}
X(64039) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {3, 5484}, {961, 12649}, {1169, 3187}, {1220, 4}, {1240, 11442}, {1791, 8}, {1798, 1}, {2298, 5905}, {2359, 2}, {2363, 3868}, {6648, 46400}, {8707, 20293}, {14534, 17220}, {15420, 150}, {30710, 21270}, {32736, 25259}, {36098, 521}, {36147, 4391}, {57690, 4388}, {57853, 17135}
X(64039) = pole of line {513, 17496} with respect to the DeLongchamps circle
X(64039) = pole of line {7191, 11376} with respect to the Feuerbach hyperbola
X(64039) = pole of line {960, 52143} with respect to the Stammler hyperbola
X(64039) = pole of line {905, 15420} with respect to the Steiner circumellipse
X(64039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 18732, 3868}, {1829, 37613, 2}, {3101, 4296, 16049}, {3827, 41600, 3869}, {7270, 18719, 4463}

X(64040) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ANTI-EXTOUCH AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a^2-b^2-c^2)*(a^4+2*a^3*(b+c)+(b^2-c^2)^2) : :
X(64040) = -X[11396]+3*X[11402]

X(64040) lies on these lines: {1, 184}, {3, 63}, {6, 19}, {8, 6776}, {9, 37225}, {10, 1899}, {25, 40660}, {37, 44101}, {40, 185}, {41, 2312}, {43, 46}, {48, 201}, {51, 7713}, {57, 1425}, {73, 26934}, {125, 1698}, {154, 11363}, {165, 1204}, {197, 41538}, {212, 18673}, {217, 1572}, {355, 6146}, {377, 894}, {387, 52082}, {394, 37613}, {429, 5928}, {515, 19467}, {517, 1181}, {518, 8192}, {581, 1782}, {672, 23620}, {774, 2187}, {944, 18925}, {952, 31804}, {960, 37246}, {970, 24611}, {974, 12778}, {997, 37247}, {1011, 12514}, {1060, 1437}, {1158, 37195}, {1175, 14015}, {1211, 26066}, {1385, 19357}, {1386, 19125}, {1426, 34032}, {1452, 19366}, {1482, 19347}, {1498, 1902}, {1503, 5090}, {1571, 3269}, {1593, 6001}, {1697, 3270}, {1699, 43830}, {1708, 13738}, {1728, 13724}, {1788, 18915}, {1824, 5706}, {1837, 1884}, {1858, 3556}, {1864, 4186}, {1867, 5786}, {1868, 5776}, {1885, 12779}, {1992, 34730}, {1993, 64039}, {2083, 2200}, {2194, 17520}, {2268, 2292}, {2771, 19457}, {2836, 32251}, {3057, 19354}, {3145, 10393}, {3157, 18732}, {3176, 6618}, {3416, 26926}, {3516, 12262}, {3549, 12259}, {3576, 13367}, {3579, 10605}, {3622, 64058}, {3661, 63471}, {3751, 6467}, {3868, 37231}, {3869, 37399}, {3955, 54289}, {4196, 4295}, {4206, 62843}, {4224, 62864}, {4225, 55873}, {4663, 10602}, {5130, 37239}, {5657, 18909}, {5690, 18914}, {5691, 21659}, {5752, 59318}, {5767, 41013}, {6684, 26937}, {6910, 38000}, {7078, 17441}, {7289, 23154}, {7592, 41722}, {7718, 11206}, {7968, 19356}, {7969, 19355}, {9620, 39643}, {9780, 23291}, {9899, 64029}, {9905, 10619}, {10319, 22076}, {10394, 28029}, {11396, 11402}, {12609, 25453}, {12664, 37194}, {12785, 32377}, {13851, 18492}, {14054, 37547}, {14557, 36279}, {16049, 40571}, {16475, 21637}, {16560, 37523}, {18396, 18480}, {18397, 57281}, {18923, 19065}, {18924, 19066}, {18935, 59406}, {18945, 59387}, {18991, 21640}, {18992, 21641}, {19119, 51192}, {19360, 34339}, {19361, 61726}, {19362, 64044}, {20672, 53560}, {21663, 35242}, {24914, 26955}, {25055, 64064}, {26377, 37538}, {26866, 64132}, {26867, 45120}, {26890, 54305}, {28348, 62810}, {30076, 50426}, {31383, 49542}, {31811, 44662}, {32607, 33535}, {37305, 64021}, {37400, 56288}, {43218, 49500}, {45126, 54349}, {50581, 62393}, {52359, 61397}

X(64040) = perspector of circumconic {{A, B, C, X(108), X(1332)}}
X(64040) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7649, 59104}
X(64040) = pole of line {1946, 15313} with respect to the circumcircle
X(64040) = pole of line {33, 62333} with respect to the Feuerbach hyperbola
X(64040) = pole of line {1, 10974} with respect to the Jerabek hyperbola
X(64040) = pole of line {28, 1812} with respect to the Stammler hyperbola
X(64040) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(608)}}, {{A, B, C, X(6), X(1259)}}, {{A, B, C, X(19), X(78)}}, {{A, B, C, X(34), X(63)}}, {{A, B, C, X(65), X(3998)}}, {{A, B, C, X(72), X(1880)}}, {{A, B, C, X(607), X(1260)}}, {{A, B, C, X(1841), X(2217)}}, {{A, B, C, X(1876), X(25083)}}, {{A, B, C, X(14571), X(51379)}}
X(64040) = barycentric product X(i)*X(j) for these (i, j): {5230, 63}, {5336, 69}
X(64040) = barycentric quotient X(i)/X(j) for these (i, j): {906, 59104}, {5230, 92}, {5336, 4}
X(64040) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 64022, 1829}, {65, 2182, 4185}, {40660, 44547, 25}

X(64041) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST JOHNSON-YFF AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a+b-c)*(a-b+c)*(b+c)*(a^3+b^3-a*(b-c)^2+b^2*c+b*c^2+c^3-a^2*(b+c)) : :
X(64041) = -3*X[392]+2*X[993], -5*X[3616]+4*X[58578], -4*X[3812]+5*X[31266], -X[7672]+3*X[61027], -5*X[17609]+4*X[62852], -3*X[17718]+2*X[50195]

X(64041) lies on these lines: {1, 90}, {2, 18419}, {4, 64043}, {5, 64045}, {8, 5555}, {10, 12}, {11, 51755}, {35, 16132}, {37, 1409}, {38, 1457}, {40, 11501}, {46, 31837}, {55, 6001}, {56, 63}, {57, 4880}, {73, 2292}, {78, 11509}, {109, 30115}, {191, 37583}, {201, 1042}, {354, 15950}, {377, 7702}, {388, 3869}, {392, 993}, {495, 14988}, {498, 34339}, {499, 942}, {515, 3057}, {517, 1478}, {518, 2099}, {527, 5434}, {551, 5083}, {612, 54400}, {651, 54292}, {846, 60682}, {946, 10957}, {950, 1898}, {984, 24806}, {986, 37694}, {997, 1470}, {1038, 1406}, {1046, 54339}, {1071, 2646}, {1104, 7299}, {1155, 64107}, {1210, 20117}, {1214, 1464}, {1317, 2801}, {1367, 1439}, {1376, 51379}, {1388, 58679}, {1399, 37539}, {1400, 3958}, {1452, 41609}, {1469, 34377}, {1479, 31937}, {1770, 37585}, {1776, 62873}, {1788, 3876}, {1837, 5777}, {1868, 1882}, {1880, 4016}, {2098, 45776}, {2357, 10901}, {2594, 3931}, {2771, 10058}, {2778, 12373}, {2792, 49537}, {2800, 10956}, {2836, 52392}, {3085, 64021}, {3189, 12529}, {3295, 40266}, {3340, 5904}, {3476, 3877}, {3485, 3868}, {3486, 12528}, {3555, 11011}, {3556, 10831}, {3584, 11571}, {3585, 49177}, {3586, 61705}, {3600, 20078}, {3601, 15071}, {3612, 13369}, {3616, 58578}, {3812, 31266}, {3827, 12588}, {3874, 64160}, {3878, 10106}, {3884, 63987}, {3911, 10176}, {3940, 37541}, {3955, 30285}, {4292, 31806}, {4415, 51421}, {4419, 56821}, {4424, 4551}, {4640, 5172}, {4642, 56198}, {4870, 24473}, {5044, 24914}, {5119, 50528}, {5204, 21165}, {5217, 9943}, {5219, 5902}, {5250, 11510}, {5261, 64047}, {5433, 5745}, {5570, 5886}, {5603, 18839}, {5697, 37709}, {5720, 11502}, {5728, 44840}, {5794, 18961}, {5795, 12059}, {5841, 45287}, {5884, 13411}, {5903, 9578}, {6261, 26357}, {6713, 10202}, {6906, 56941}, {7082, 57278}, {7098, 11684}, {7288, 55868}, {7354, 14110}, {7672, 61027}, {7686, 10895}, {7951, 53615}, {7957, 17634}, {7962, 11372}, {7965, 17642}, {8071, 45770}, {8543, 63159}, {9028, 39897}, {9370, 37614}, {9579, 30290}, {9612, 37625}, {9613, 40271}, {9654, 64044}, {9856, 12701}, {9957, 37738}, {10039, 26482}, {10167, 37600}, {10175, 12736}, {10320, 11374}, {10372, 41600}, {10572, 40263}, {10592, 61541}, {10914, 44784}, {10949, 12053}, {10950, 14872}, {10966, 63986}, {11237, 31164}, {11376, 50196}, {11507, 37700}, {11529, 18397}, {11715, 17660}, {12047, 24474}, {12115, 63962}, {12514, 37579}, {12520, 37601}, {12526, 37550}, {12532, 29007}, {12559, 14054}, {12675, 34471}, {12711, 37080}, {12721, 29069}, {12832, 18254}, {13601, 34790}, {14882, 56176}, {15253, 39544}, {15325, 61539}, {15326, 63438}, {17609, 62852}, {17614, 34880}, {17718, 50195}, {18967, 62874}, {18982, 46179}, {21867, 62753}, {22766, 24467}, {22768, 63399}, {24333, 36487}, {24475, 37737}, {25080, 63295}, {26437, 62858}, {26470, 39599}, {26741, 49992}, {26921, 59317}, {31821, 64131}, {31838, 37618}, {34048, 57277}, {34293, 52836}, {37564, 37837}, {37567, 63976}, {41003, 52385}, {41558, 47320}, {51792, 61740}, {54408, 63992}, {60936, 64139}, {63332, 63447}, {63396, 64055}, {63967, 64163}

X(64041) = midpoint of X(i) and X(j) for these {i,j}: {3869, 5905}
X(64041) = reflection of X(i) in X(j) for these {i,j}: {63, 960}, {65, 226}, {3555, 62822}, {18389, 64110}
X(64041) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 998}, {58, 30513}, {2194, 58028}, {3737, 9058}
X(64041) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 30513}, {1060, 11103}, {1214, 58028}, {40611, 998}
X(64041) = pole of line {4017, 4895} with respect to the incircle
X(64041) = pole of line {3, 950} with respect to the Feuerbach hyperbola
X(64041) = pole of line {41538, 51377} with respect to the Jerabek hyperbola
X(64041) = pole of line {60, 3193} with respect to the Stammler hyperbola
X(64041) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(21077)}}, {{A, B, C, X(10), X(90)}}, {{A, B, C, X(37), X(17757)}}, {{A, B, C, X(65), X(1470)}}, {{A, B, C, X(72), X(1069)}}, {{A, B, C, X(210), X(7072)}}, {{A, B, C, X(442), X(4227)}}, {{A, B, C, X(758), X(9001)}}, {{A, B, C, X(1211), X(26637)}}, {{A, B, C, X(2357), X(11383)}}, {{A, B, C, X(3560), X(60154)}}, {{A, B, C, X(3753), X(52148)}}, {{A, B, C, X(3754), X(60089)}}, {{A, B, C, X(17740), X(31993)}}
X(64041) = barycentric product X(i)*X(j) for these (i, j): {12, 26637}, {226, 997}, {1470, 321}, {4552, 9001}, {11383, 1231}, {17740, 65}, {26942, 4227}
X(64041) = barycentric quotient X(i)/X(j) for these (i, j): {37, 30513}, {226, 58028}, {997, 333}, {1400, 998}, {1470, 81}, {4227, 46103}, {4559, 9058}, {9001, 4560}, {11383, 1172}, {17740, 314}, {26637, 261}
X(64041) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5693, 1858}, {1, 5887, 64042}, {1, 7330, 22760}, {12, 45288, 65}, {65, 210, 40663}, {65, 72, 41538}, {392, 17625, 1319}, {950, 31803, 1898}, {1836, 5252, 64086}, {3057, 12688, 6284}, {3671, 4067, 15556}, {3962, 44782, 72}, {8581, 31165, 64106}, {8581, 64106, 5434}, {11529, 18397, 61663}, {11684, 57283, 7098}, {13601, 34790, 41687}, {18389, 64110, 354}, {25917, 37566, 5433}, {44840, 61722, 5728}

X(64042) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND JOHNSON-YFF AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a-b-c)*(b^5-b^4*c+2*a*b*(b-c)^2*c-b*c^4+c^5+a^4*(b+c)-2*a^2*(b-c)^2*(b+c)) : :
X(64042) = -2*X[942]+3*X[10072], -5*X[3616]+4*X[58585], -X[3868]+3*X[11240], -5*X[3876]+4*X[58657], -2*X[4848]+3*X[61653], -5*X[5439]+6*X[10199], -X[37711]+3*X[61709]

X(64042) lies on these lines: {1, 90}, {8, 30513}, {10, 10958}, {11, 65}, {31, 43703}, {37, 2288}, {40, 11502}, {55, 78}, {56, 6001}, {63, 10966}, {72, 519}, {210, 5837}, {354, 12563}, {390, 20013}, {392, 2646}, {496, 14988}, {497, 3869}, {499, 34339}, {515, 1898}, {517, 1479}, {518, 2098}, {595, 45272}, {758, 10959}, {774, 1457}, {920, 11249}, {942, 10072}, {958, 7082}, {999, 40266}, {1071, 1319}, {1158, 1470}, {1191, 1854}, {1201, 7004}, {1387, 24475}, {1388, 12675}, {1399, 1795}, {1420, 15071}, {1454, 22753}, {1476, 13243}, {1478, 31937}, {1482, 37493}, {1621, 45230}, {1697, 5692}, {1737, 26476}, {1776, 2975}, {1824, 34434}, {1831, 1856}, {1836, 9856}, {1871, 42385}, {2099, 44547}, {2771, 10074}, {2778, 12374}, {2801, 63987}, {3024, 10693}, {3086, 18838}, {3216, 45269}, {3244, 15558}, {3304, 62836}, {3340, 61663}, {3476, 12528}, {3486, 3877}, {3555, 5048}, {3556, 10832}, {3612, 31838}, {3616, 58585}, {3623, 40269}, {3753, 17606}, {3811, 26358}, {3827, 12589}, {3868, 11240}, {3870, 10965}, {3876, 58657}, {3890, 10394}, {3893, 17658}, {3913, 51379}, {3962, 10866}, {4067, 4342}, {4301, 15556}, {4640, 37564}, {4848, 61653}, {5119, 31837}, {5172, 37837}, {5204, 9943}, {5252, 5777}, {5274, 64047}, {5315, 33178}, {5432, 6700}, {5439, 10199}, {5570, 11373}, {5694, 9957}, {5697, 5727}, {5720, 11501}, {5836, 31140}, {5882, 41562}, {5884, 44675}, {5886, 13750}, {5902, 50443}, {5903, 9581}, {5904, 7962}, {5919, 37734}, {6261, 37579}, {6284, 14110}, {7069, 10459}, {7354, 12688}, {7686, 10896}, {7982, 18397}, {8069, 45770}, {8758, 10571}, {9613, 61705}, {9614, 37625}, {9624, 30274}, {9669, 64044}, {10106, 31803}, {10122, 17609}, {10167, 37605}, {10391, 34471}, {10531, 18391}, {10543, 14100}, {10593, 61541}, {10624, 31806}, {10914, 25414}, {10915, 18254}, {10944, 14872}, {10953, 24703}, {10955, 20117}, {10957, 51755}, {11011, 61722}, {11112, 17646}, {11238, 44663}, {11246, 17634}, {11375, 50195}, {11436, 40964}, {11508, 37700}, {11510, 18446}, {11928, 25413}, {12514, 26357}, {12520, 37578}, {12526, 54408}, {12640, 14740}, {12758, 23340}, {13369, 37618}, {13464, 18389}, {13601, 64157}, {16583, 38345}, {17604, 41539}, {17615, 32049}, {17625, 20323}, {17637, 30538}, {17660, 41554}, {18961, 64119}, {19861, 22768}, {21935, 35015}, {22767, 24467}, {24474, 26475}, {24914, 31788}, {26437, 62810}, {30323, 41686}, {34195, 53055}, {37550, 63992}, {37568, 64107}, {37711, 61709}, {37720, 53615}, {37722, 45288}, {40263, 45287}, {52541, 53525}, {54382, 62372}, {54386, 61397}, {63295, 63450}

X(64042) = midpoint of X(i) and X(j) for these {i,j}: {3869, 12649}, {30323, 41686}
X(64042) = reflection of X(i) in X(j) for these {i,j}: {65, 1210}, {78, 960}, {1837, 64131}, {17660, 41554}, {64045, 496}, {64046, 12053}
X(64042) = inverse of X(12616) in Feuerbach hyperbola
X(64042) = X(i)-Ceva conjugate of X(j) for these {i, j}: {44765, 650}
X(64042) = pole of line {1769, 15313} with respect to the incircle
X(64042) = pole of line {3, 10} with respect to the Feuerbach hyperbola
X(64042) = pole of line {3193, 5323} with respect to the Stammler hyperbola
X(64042) = pole of line {1465, 40688} with respect to the dual conic of Yff parabola
X(64042) = intersection, other than A, B, C, of circumconics {{A, B, C, X(90), X(44040)}}, {{A, B, C, X(1036), X(30513)}}, {{A, B, C, X(7040), X(22758)}}
X(64042) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30223, 22760}, {1, 5887, 64041}, {1, 7330, 22759}, {1, 90, 22758}, {65, 17638, 12672}, {392, 12711, 2646}, {497, 3869, 64043}, {517, 64131, 1837}, {758, 12053, 64046}, {950, 3878, 3057}, {1210, 2800, 65}, {1864, 3057, 10950}, {3057, 9848, 3058}, {3086, 64021, 18838}, {3962, 10866, 17642}, {10391, 58679, 34471}, {12688, 64106, 7354}, {44547, 45776, 2099}

X(64043) = ORTHOLOGY CENTER OF THESE TRIANGLES: MANDART-INCIRCLE AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a-b-c)*(-2*a^3*b*c+a^4*(b+c)+(b-c)^4*(b+c)-2*a^2*(b^3+c^3)) : :
X(64043) =

X(64043) lies on these lines: {1, 3}, {4, 64041}, {8, 43740}, {11, 960}, {12, 1512}, {60, 3193}, {63, 22760}, {71, 8609}, {72, 1837}, {78, 11502}, {209, 22299}, {212, 3924}, {225, 1888}, {283, 18178}, {388, 55109}, {390, 64047}, {392, 11376}, {497, 3869}, {518, 10950}, {758, 950}, {908, 10958}, {912, 10572}, {946, 26481}, {952, 31831}, {1000, 10597}, {1104, 2361}, {1210, 31806}, {1329, 51379}, {1364, 10544}, {1479, 5887}, {1737, 31837}, {1776, 11684}, {1829, 1831}, {1836, 12709}, {1864, 3962}, {1898, 3586}, {1938, 11934}, {2264, 2323}, {2269, 2294}, {2292, 2654}, {2550, 14923}, {2650, 14547}, {2771, 12743}, {2778, 3028}, {2800, 10624}, {2802, 63146}, {3056, 3827}, {3058, 34695}, {3059, 3893}, {3189, 3885}, {3476, 64079}, {3486, 3868}, {3522, 18419}, {3555, 37740}, {3556, 10833}, {3562, 54292}, {3583, 16155}, {3753, 10198}, {3812, 5432}, {3876, 54361}, {3877, 10527}, {3878, 10916}, {3899, 51785}, {3925, 5836}, {4018, 12711}, {4084, 4314}, {4294, 41537}, {4304, 5884}, {4330, 11571}, {4342, 49627}, {5044, 17606}, {5252, 26332}, {5692, 9581}, {5705, 25522}, {5715, 10895}, {5727, 5904}, {5735, 8581}, {5806, 17605}, {6001, 6284}, {6046, 22464}, {6253, 10944}, {6598, 44782}, {6684, 12736}, {6738, 15556}, {6850, 7702}, {7078, 57277}, {7098, 62873}, {7354, 64003}, {8256, 51378}, {8557, 21871}, {9668, 40266}, {9943, 15338}, {10391, 10543}, {10393, 12559}, {10693, 12904}, {10947, 12672}, {10957, 45776}, {10959, 26015}, {11238, 31165}, {11240, 34744}, {11570, 13369}, {11997, 20718}, {12019, 31835}, {12116, 30305}, {12514, 62333}, {12526, 30223}, {12688, 12953}, {12721, 56819}, {12739, 33597}, {12740, 48713}, {12758, 37726}, {13274, 17638}, {13374, 15950}, {13375, 63256}, {13411, 31870}, {14988, 15171}, {15326, 64132}, {17097, 62800}, {17619, 62357}, {17622, 45700}, {17625, 64075}, {17636, 64056}, {17660, 64145}, {18239, 37001}, {18391, 41538}, {18395, 58630}, {18406, 37710}, {18673, 53557}, {20586, 48694}, {21616, 26476}, {21853, 54359}, {22072, 24443}, {22074, 40941}, {24541, 58679}, {24914, 64107}, {26470, 30384}, {29639, 34434}, {30143, 54430}, {34195, 45230}, {34791, 37734}, {37721, 41686}, {40663, 63976}, {43214, 44545}, {54418, 61397}, {54421, 61398}

X(64043) = midpoint of X(i) and X(j) for these {i,j}: {6284, 45288}
X(64043) = reflection of X(i) in X(j) for these {i,j}: {1858, 950}, {15556, 6738}
X(64043) = pole of line {1, 442} with respect to the Feuerbach hyperbola
X(64043) = pole of line {21, 64041} with respect to the Stammler hyperbola
X(64043) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(8), X(37579)}}, {{A, B, C, X(56), X(43740)}}, {{A, B, C, X(60), X(1470)}}, {{A, B, C, X(64), X(8069)}}, {{A, B, C, X(943), X(24299)}}, {{A, B, C, X(1000), X(10267)}}, {{A, B, C, X(5559), X(14798)}}, {{A, B, C, X(6598), X(37583)}}, {{A, B, C, X(40292), X(53089)}}, {{A, B, C, X(54339), X(60662)}}
X(64043) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5709, 56}, {65, 3057, 55}, {497, 3869, 64042}, {758, 950, 1858}, {3586, 5693, 1898}, {5697, 7962, 3057}, {6284, 45288, 6001}, {6738, 15556, 61663}, {10916, 12053, 26475}, {41012, 64139, 960}

X(64044) = ORTHOLOGY CENTER OF THESE TRIANGLES: X3-ABC REFLECTIONS AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a^5*(b+c)-2*a^3*(b-c)^2*(b+c)+a*(b-c)^4*(b+c)-(b-c)^4*(b+c)^2-a^4*(b^2+3*b*c+c^2)+a^2*(2*b^4+b^3*c-4*b^2*c^2+b*c^3+2*c^4)) : :
X(64044) = -3*X[2]+4*X[61541], -2*X[72]+3*X[5790], -3*X[381]+2*X[5887], -4*X[960]+5*X[1656], -2*X[1483]+3*X[3873], -7*X[3526]+8*X[3812], -3*X[3534]+4*X[9943], -7*X[3622]+8*X[58561], -3*X[3655]+4*X[12005], -3*X[3681]+4*X[61510], -5*X[3698]+4*X[58630], -3*X[3753]+2*X[31837] and many others

X(64044) lies on these lines: {1, 3}, {2, 61541}, {4, 14988}, {5, 3869}, {8, 6917}, {30, 9961}, {47, 1411}, {49, 14529}, {52, 2818}, {72, 5790}, {145, 6934}, {221, 36747}, {355, 758}, {377, 12245}, {381, 5887}, {382, 6001}, {442, 5690}, {515, 4084}, {518, 11898}, {519, 34688}, {912, 4018}, {944, 24475}, {952, 3868}, {960, 1656}, {970, 994}, {997, 45976}, {1351, 3827}, {1389, 2975}, {1478, 45288}, {1483, 3873}, {1484, 37356}, {1709, 54145}, {1737, 6971}, {1766, 21863}, {1788, 6958}, {2650, 37698}, {2771, 5691}, {2778, 10620}, {2800, 10738}, {3218, 32153}, {3485, 6863}, {3526, 3812}, {3534, 9943}, {3556, 7517}, {3577, 6597}, {3617, 6984}, {3622, 58561}, {3654, 10197}, {3655, 12005}, {3679, 44782}, {3681, 61510}, {3698, 58630}, {3753, 31837}, {3754, 26446}, {3811, 12331}, {3830, 12688}, {3843, 31937}, {3874, 37727}, {3876, 38042}, {3877, 5901}, {3878, 5886}, {3881, 61287}, {3884, 61276}, {3889, 61286}, {3890, 10283}, {3892, 61284}, {3894, 61296}, {3898, 61277}, {3899, 8227}, {3901, 5881}, {3919, 6684}, {4004, 64107}, {4185, 41722}, {4295, 6923}, {4297, 4744}, {4301, 12616}, {4511, 6924}, {4757, 5884}, {5055, 31165}, {5070, 25917}, {5330, 45977}, {5439, 31838}, {5446, 42448}, {5587, 5694}, {5603, 6862}, {5657, 5761}, {5692, 9956}, {5693, 18480}, {5730, 6911}, {5754, 34465}, {5762, 7672}, {5812, 15556}, {5818, 31835}, {5836, 59503}, {5837, 55108}, {5841, 10950}, {5844, 14923}, {5918, 62131}, {6261, 62359}, {6796, 37733}, {6831, 22791}, {6842, 39542}, {6889, 59417}, {6905, 62830}, {6910, 10595}, {6914, 56288}, {6928, 18391}, {6929, 11415}, {6980, 12047}, {7489, 12514}, {7491, 37730}, {8261, 28443}, {8581, 51514}, {9654, 64041}, {9669, 64042}, {10107, 63976}, {10165, 33815}, {10178, 62085}, {10483, 11571}, {10526, 10573}, {10693, 38724}, {10827, 51518}, {11362, 12609}, {11374, 15865}, {11491, 34195}, {11499, 12635}, {11604, 12247}, {11928, 12672}, {12520, 16117}, {12736, 57298}, {12737, 62825}, {13747, 61530}, {14054, 18499}, {14663, 38579}, {15064, 61258}, {15071, 28160}, {15726, 49136}, {16616, 61984}, {17528, 34718}, {17638, 51517}, {17647, 28234}, {18389, 37739}, {18524, 37700}, {19362, 64040}, {19860, 26921}, {19914, 41687}, {20117, 61261}, {20306, 41587}, {20430, 20718}, {21147, 23070}, {24467, 26321}, {26201, 50811}, {28194, 34649}, {32049, 41688}, {32141, 34772}, {35976, 64136}, {36749, 64020}, {36750, 54421}, {37227, 41723}, {37251, 45770}, {37489, 63435}, {37509, 54418}, {37714, 56762}, {37721, 61722}, {37740, 62859}, {37820, 49168}, {38066, 50740}, {38752, 64139}, {48661, 64094}, {48667, 63986}, {51700, 64149}, {54400, 64053}, {55287, 58535}, {56691, 58739}, {61283, 62854}, {63159, 64173}

X(64044) = midpoint of X(i) and X(j) for these {i,j}: {4, 64047}, {3901, 5881}
X(64044) = reflection of X(i) in X(j) for these {i,j}: {3, 65}, {944, 24475}, {3869, 5}, {3878, 31870}, {5693, 18480}, {5884, 4757}, {5887, 7686}, {7491, 37730}, {18481, 5884}, {31806, 3754}, {37727, 3874}, {40266, 4}, {42448, 5446}, {55287, 58535}, {63976, 10107}
X(64044) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 10771, 64047}
X(64044) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(32613)}}, {{A, B, C, X(484), X(56148)}}, {{A, B, C, X(3576), X(6597)}}, {{A, B, C, X(11604), X(26286)}}
X(64044) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 14988, 40266}, {4, 64047, 14988}, {65, 517, 3}, {3878, 31870, 5886}, {5887, 7686, 381}, {7686, 44663, 5887}, {34772, 48363, 32141}

X(64045) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-YFF AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a^5*(b+c)-2*a^3*(b-c)^2*(b+c)+a*(b-c)^4*(b+c)-a^4*(b+c)^2-(b-c)^4*(b+c)^2+2*a^2*(b^4+c^4)) : :
X(64045) = -5*X[1698]+4*X[58649], -3*X[3753]+2*X[8256], -3*X[3873]+X[36977], -4*X[5044]+5*X[31246], -5*X[5439]+4*X[6691]

X(64045) lies on these lines: {1, 3}, {4, 12666}, {5, 64041}, {10, 12736}, {11, 5887}, {20, 18419}, {47, 1104}, {72, 1329}, {79, 54145}, {80, 14872}, {210, 18395}, {226, 31870}, {255, 3924}, {392, 4999}, {495, 61541}, {496, 14988}, {497, 64021}, {498, 3812}, {499, 960}, {518, 10573}, {529, 24473}, {613, 3827}, {758, 1210}, {912, 1837}, {920, 57278}, {938, 11415}, {950, 5884}, {971, 37001}, {1071, 2829}, {1406, 64053}, {1426, 1785}, {1437, 18178}, {1478, 7686}, {1479, 6001}, {1698, 58649}, {1781, 2262}, {1788, 10321}, {1828, 1844}, {1858, 5722}, {1864, 37702}, {1898, 2771}, {2778, 10081}, {2800, 12053}, {2955, 40953}, {3086, 3869}, {3157, 57277}, {3419, 41559}, {3436, 3868}, {3486, 37002}, {3555, 38455}, {3556, 10046}, {3562, 54315}, {3582, 31165}, {3583, 12688}, {3586, 15071}, {3698, 41859}, {3752, 54427}, {3753, 8256}, {3754, 31397}, {3873, 36977}, {3874, 64163}, {3878, 44675}, {3884, 18240}, {3901, 18397}, {3911, 31806}, {3918, 61029}, {4004, 25557}, {4084, 11019}, {4299, 64132}, {4302, 9943}, {4317, 63994}, {4324, 5918}, {4337, 15852}, {4744, 21625}, {4857, 11571}, {4880, 54432}, {5044, 31246}, {5083, 5882}, {5270, 8581}, {5439, 6691}, {5533, 17638}, {5693, 9581}, {5719, 61530}, {5728, 17768}, {5777, 10826}, {5784, 47033}, {5836, 12647}, {5854, 10914}, {5883, 13411}, {6738, 18389}, {6797, 10057}, {6923, 7702}, {7681, 12047}, {8068, 17606}, {8070, 17605}, {8679, 24476}, {9669, 40266}, {10050, 49171}, {10051, 10052}, {10058, 64118}, {10072, 44663}, {10090, 59691}, {10320, 24914}, {10483, 63995}, {10785, 14647}, {10896, 31937}, {10948, 12672}, {10954, 13407}, {11502, 37700}, {12758, 17622}, {12832, 32554}, {13375, 39779}, {13405, 33815}, {14986, 64047}, {15518, 41712}, {15733, 41709}, {16118, 31391}, {17625, 45287}, {17646, 52367}, {17861, 52385}, {18239, 41698}, {18594, 55120}, {22134, 40941}, {22350, 24443}, {22760, 24467}, {24248, 45963}, {24465, 31775}, {24475, 37730}, {25681, 41389}, {26364, 51379}, {28075, 36574}, {28645, 44547}, {31141, 41686}, {37708, 54134}, {37737, 61534}, {40985, 54368}

X(64045) = midpoint of X(i) and X(j) for these {i,j}: {3436, 3868}, {15071, 52860}
X(64045) = reflection of X(i) in X(j) for these {i,j}: {56, 942}, {72, 1329}, {4299, 64132}, {64042, 496}
X(64045) = pole of line {1, 6923} with respect to the Feuerbach hyperbola
X(64045) = pole of line {513, 2077} with respect to the Suppa-Cucoanes circle
X(64045) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(8069)}}, {{A, B, C, X(7), X(22766)}}, {{A, B, C, X(8), X(11508)}}, {{A, B, C, X(998), X(37550)}}, {{A, B, C, X(3478), X(40255)}}, {{A, B, C, X(5172), X(17101)}}, {{A, B, C, X(5665), X(59335)}}, {{A, B, C, X(36052), X(37583)}}, {{A, B, C, X(37531), X(42464)}}, {{A, B, C, X(37579), X(42019)}}
X(64045) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 45288, 5887}, {496, 14988, 64042}, {517, 942, 56}, {5902, 5903, 3339}, {10572, 11570, 1071}

X(64046) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a-b-c)*(-2*a*b*(b-c)^2*c+a^4*(b+c)+(b-c)^4*(b+c)-2*a^2*(b^3+c^3)) : :
X(64046) = -3*X[210]+4*X[1329], -5*X[1698]+4*X[58645], -3*X[11238]+2*X[64131], -3*X[35262]+4*X[58585]

X(64046) lies on these lines: {1, 3}, {10, 50208}, {11, 72}, {38, 2654}, {63, 62333}, {210, 1329}, {212, 28082}, {219, 39943}, {244, 22072}, {283, 18191}, {392, 24953}, {497, 1858}, {499, 31837}, {518, 1837}, {758, 10959}, {908, 26476}, {912, 1479}, {938, 61663}, {946, 10957}, {950, 3874}, {960, 10527}, {971, 12953}, {1071, 6284}, {1210, 41538}, {1364, 59809}, {1512, 26482}, {1698, 58645}, {1827, 1828}, {1836, 55109}, {1864, 14054}, {2194, 3193}, {2260, 17452}, {2771, 12374}, {2778, 12382}, {2829, 12680}, {2836, 32290}, {3056, 24476}, {3058, 12711}, {3254, 6598}, {3486, 3873}, {3555, 10950}, {3556, 10835}, {3583, 40263}, {3681, 54361}, {3698, 3826}, {3811, 11502}, {3827, 12595}, {3869, 10529}, {3876, 10589}, {3877, 30478}, {3893, 5854}, {3901, 51785}, {3927, 7082}, {3962, 26015}, {4084, 4342}, {4297, 5083}, {4302, 13369}, {4304, 12005}, {4420, 60782}, {5130, 12586}, {5225, 12528}, {5252, 7686}, {5432, 5439}, {5433, 64107}, {5692, 50443}, {5693, 9614}, {5694, 7743}, {5705, 31246}, {5722, 10953}, {5728, 60919}, {5735, 31391}, {5777, 10896}, {5806, 10895}, {5884, 10624}, {5887, 10943}, {5904, 9581}, {6001, 12116}, {6067, 21677}, {6260, 12831}, {7074, 17054}, {7354, 17625}, {7681, 17605}, {8261, 42819}, {8581, 45634}, {8609, 21871}, {9578, 38036}, {9580, 15071}, {9668, 41685}, {10167, 15338}, {10587, 38053}, {10593, 31835}, {10806, 30305}, {10936, 10941}, {10947, 12699}, {10949, 12672}, {10958, 21077}, {11019, 15556}, {11214, 45022}, {11238, 64131}, {11240, 44663}, {11362, 12736}, {11375, 13374}, {11684, 53055}, {11920, 12686}, {12675, 37002}, {12688, 48482}, {12739, 37837}, {12740, 13279}, {12764, 15094}, {12776, 20586}, {13081, 31588}, {13082, 31589}, {13122, 32383}, {14100, 16142}, {14872, 37821}, {14988, 32214}, {15171, 24475}, {17638, 37726}, {17658, 21031}, {18251, 31140}, {18389, 63999}, {18412, 37723}, {18419, 20070}, {18543, 40266}, {18544, 31937}, {20118, 32554}, {22277, 22298}, {22760, 62858}, {22798, 60384}, {24465, 31777}, {24914, 63976}, {25681, 51379}, {25917, 26363}, {30223, 54422}, {31165, 45700}, {31397, 31870}, {31806, 44675}, {34791, 36977}, {35262, 58585}, {36052, 52408}, {37828, 51378}, {38455, 41575}, {40659, 59414}, {43740, 46354}, {45230, 63159}, {46677, 55016}, {49168, 64087}, {53557, 54360}, {57277, 64069}, {58578, 62829}, {63327, 63396}, {63995, 64003}, {64047, 64151}

X(64046) = midpoint of X(i) and X(j) for these {i,j}: {3868, 11415}
X(64046) = reflection of X(i) in X(j) for these {i,j}: {46, 942}, {72, 21616}, {1898, 1479}, {3057, 2098}, {14872, 37821}, {36977, 34791}, {37002, 12675}, {41538, 1210}, {64042, 12053}
X(64046) = pole of line {513, 59977} with respect to the incircle
X(64046) = pole of line {21302, 44426} with respect to the polar circle
X(64046) = pole of line {513, 59977} with respect to the DeLongchamps ellipse
X(64046) = pole of line {1, 224} with respect to the Feuerbach hyperbola
X(64046) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(40505)}}, {{A, B, C, X(8), X(11510)}}, {{A, B, C, X(56), X(46354)}}, {{A, B, C, X(1000), X(16202)}}, {{A, B, C, X(2078), X(6598)}}, {{A, B, C, X(3254), X(37583)}}, {{A, B, C, X(7742), X(42019)}}, {{A, B, C, X(32760), X(56587)}}, {{A, B, C, X(34489), X(39943)}}, {{A, B, C, X(37569), X(42464)}}, {{A, B, C, X(37579), X(43740)}}
X(64046) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {354, 3057, 2646}, {497, 3868, 1858}, {517, 2098, 3057}, {517, 942, 46}, {758, 12053, 64042}, {912, 1479, 1898}, {1210, 41538, 61653}, {12053, 49627, 10959}, {31246, 58649, 61686}

X(64047) = ANTICOMPLEMENT OF X(3869)

Barycentrics    a*(-2*b^3-a*b*c+b^2*c+b*c^2-2*c^3+2*a^2*(b+c)) : :
X(64047) = -3*X[2]+4*X[65], -4*X[72]+5*X[3617], -3*X[210]+4*X[10107], -6*X[354]+5*X[3890], -3*X[392]+4*X[31794], -8*X[942]+7*X[3622], -4*X[1125]+3*X[3899], -5*X[1698]+6*X[3919], -4*X[3057]+5*X[3623], -3*X[3060]+2*X[42448], -7*X[3090]+8*X[61541], -5*X[3091]+4*X[5887] and many others

X(64047) lies on these lines: {1, 89}, {2, 65}, {3, 62830}, {4, 14988}, {7, 21273}, {8, 79}, {10, 25958}, {20, 145}, {23, 3556}, {35, 62822}, {36, 45392}, {40, 34772}, {46, 4188}, {55, 34195}, {56, 18419}, {57, 11682}, {63, 3340}, {72, 3617}, {78, 2093}, {81, 37614}, {100, 12635}, {144, 7672}, {149, 151}, {191, 30147}, {192, 20718}, {193, 3827}, {210, 10107}, {214, 37524}, {221, 1993}, {244, 28370}, {329, 5554}, {346, 21853}, {354, 3890}, {388, 17483}, {390, 64043}, {392, 31794}, {404, 5730}, {405, 1159}, {484, 22836}, {512, 49303}, {516, 41575}, {518, 1278}, {519, 1770}, {535, 37706}, {760, 40868}, {908, 4848}, {942, 3622}, {958, 11684}, {994, 9534}, {997, 17572}, {999, 5330}, {1046, 49487}, {1104, 30653}, {1122, 33800}, {1125, 3899}, {1155, 37307}, {1158, 7982}, {1191, 55437}, {1210, 51423}, {1265, 60459}, {1320, 8148}, {1389, 22758}, {1479, 5180}, {1482, 6906}, {1616, 3315}, {1697, 3957}, {1698, 3919}, {1706, 3984}, {1722, 63096}, {1737, 5154}, {1829, 63009}, {1836, 5086}, {1837, 5057}, {1854, 9539}, {1938, 17494}, {1994, 64020}, {1999, 12435}, {2094, 4308}, {2098, 62837}, {2099, 2975}, {2262, 62985}, {2263, 63088}, {2306, 5239}, {2345, 21863}, {2390, 62187}, {2476, 39542}, {2551, 26792}, {2646, 17548}, {2650, 17018}, {2651, 11101}, {2771, 20084}, {2778, 64102}, {2802, 20050}, {2818, 5889}, {2899, 30578}, {3057, 3623}, {3060, 42448}, {3086, 53615}, {3090, 61541}, {3091, 5887}, {3146, 6001}, {3189, 20095}, {3210, 20040}, {3212, 20347}, {3219, 5234}, {3240, 4642}, {3241, 3874}, {3244, 3894}, {3245, 8715}, {3295, 37285}, {3306, 15829}, {3336, 30144}, {3339, 19861}, {3436, 17484}, {3474, 37256}, {3486, 15680}, {3522, 14110}, {3523, 34339}, {3580, 20306}, {3601, 63144}, {3616, 3878}, {3624, 33815}, {3632, 4338}, {3633, 4333}, {3651, 3871}, {3671, 24987}, {3678, 53620}, {3679, 4067}, {3681, 3962}, {3698, 63961}, {3727, 63066}, {3740, 3922}, {3746, 62860}, {3753, 3876}, {3754, 5692}, {3811, 63136}, {3832, 7686}, {3839, 31937}, {3870, 7991}, {3872, 54422}, {3880, 20014}, {3881, 20057}, {3884, 18398}, {3889, 9957}, {3895, 41863}, {3897, 3916}, {3898, 50190}, {3924, 17127}, {3935, 11523}, {3951, 9623}, {3959, 37657}, {3999, 45219}, {4004, 5044}, {4193, 51409}, {4296, 54400}, {4299, 6224}, {4301, 26015}, {4313, 39772}, {4323, 5744}, {4420, 54286}, {4424, 19767}, {4454, 34377}, {4525, 4691}, {4536, 51068}, {4537, 4745}, {4671, 17751}, {4855, 5128}, {4861, 25415}, {4867, 25440}, {4880, 8666}, {4881, 15803}, {4930, 13587}, {4973, 21842}, {5046, 11415}, {5059, 9961}, {5080, 10573}, {5083, 6049}, {5119, 12559}, {5141, 12047}, {5176, 41687}, {5183, 56176}, {5221, 5253}, {5240, 33654}, {5248, 5425}, {5249, 5837}, {5250, 11529}, {5255, 36565}, {5261, 64041}, {5265, 18838}, {5274, 64042}, {5303, 34471}, {5311, 11533}, {5535, 40257}, {5550, 5883}, {5603, 6888}, {5657, 26487}, {5690, 6937}, {5693, 59387}, {5694, 5818}, {5704, 12736}, {5710, 29815}, {5731, 5884}, {5770, 6847}, {5777, 54448}, {5794, 20292}, {5795, 17781}, {5835, 32782}, {5855, 7354}, {5918, 62124}, {5919, 62854}, {6553, 59263}, {6845, 22791}, {6850, 12245}, {6892, 10595}, {6908, 10528}, {7226, 10459}, {7673, 15185}, {7962, 62832}, {7967, 24475}, {8261, 15676}, {9335, 21214}, {9352, 59691}, {9536, 40571}, {9544, 14529}, {9578, 31164}, {9654, 59416}, {9778, 20612}, {9943, 50693}, {10176, 19877}, {10178, 62078}, {10273, 31837}, {10306, 64189}, {10381, 31037}, {10441, 37639}, {10480, 58820}, {10526, 12247}, {10587, 11036}, {10680, 10698}, {10914, 31145}, {10944, 34605}, {10950, 17768}, {11002, 42450}, {11010, 16126}, {11041, 13100}, {11114, 37730}, {11280, 22837}, {11509, 37293}, {11518, 29817}, {11526, 60990}, {11531, 36846}, {11681, 40663}, {11851, 19993}, {12432, 31018}, {12437, 63145}, {12513, 62235}, {12514, 16865}, {12532, 41686}, {12560, 60969}, {12688, 17578}, {13463, 51463}, {14497, 61148}, {14986, 64045}, {14997, 54386}, {15016, 54445}, {15692, 40296}, {15726, 50692}, {16150, 18525}, {16466, 54315}, {16610, 27645}, {16616, 61985}, {16704, 41723}, {16828, 22307}, {16859, 54318}, {17016, 37685}, {17024, 37549}, {17137, 24282}, {17154, 17480}, {17364, 29311}, {17479, 64071}, {17490, 34434}, {17495, 20036}, {17512, 46441}, {17521, 62843}, {17576, 62864}, {17609, 62835}, {17755, 30057}, {17784, 20013}, {18201, 32577}, {18412, 63975}, {18467, 37583}, {18607, 37548}, {18663, 20011}, {18664, 52364}, {19582, 46938}, {19784, 56463}, {19836, 56459}, {19998, 22300}, {20087, 51192}, {20109, 21216}, {21272, 36854}, {21281, 31130}, {21285, 33867}, {21677, 33108}, {21740, 59318}, {21767, 56000}, {21866, 27396}, {22299, 41839}, {23154, 45955}, {23839, 43983}, {24174, 27625}, {24471, 45789}, {24558, 64142}, {24982, 27131}, {25965, 26688}, {27086, 59317}, {27383, 64139}, {27525, 51379}, {27571, 61172}, {29350, 47676}, {29849, 49609}, {30329, 52653}, {30652, 62802}, {31393, 62861}, {33650, 34242}, {34040, 55399}, {34610, 35596}, {34698, 37430}, {34790, 50736}, {37433, 54161}, {37542, 62814}, {37556, 62815}, {37568, 61157}, {37700, 48363}, {37709, 60933}, {38074, 56762}, {41600, 63057}, {41712, 61026}, {41717, 44545}, {44840, 62870}, {49168, 52367}, {49492, 63996}, {52682, 59356}, {53356, 53562}, {54344, 62999}, {54382, 63004}, {54383, 62392}, {54418, 63074}, {58679, 64149}, {59265, 59760}, {59491, 64160}, {62370, 63524}, {62825, 63210}, {64002, 64163}, {64046, 64151}

X(64047) = reflection of X(i) in X(j) for these {i,j}: {1, 4084}, {4, 64044}, {8, 5903}, {20, 64021}, {72, 50193}, {144, 7672}, {145, 3868}, {962, 37625}, {3621, 14923}, {3868, 4018}, {3869, 65}, {3878, 4757}, {3885, 3555}, {3899, 4744}, {3962, 5836}, {5059, 9961}, {5697, 3874}, {6224, 11571}, {7673, 15185}, {12245, 25413}, {33650, 34242}, {37433, 54161}, {54213, 3651}, {63975, 18412}, {64002, 64163}
X(64047) = anticomplement of X(3869)
X(64047) = perspector of circumconic {{A, B, C, X(4604), X(15455)}}
X(64047) = X(i)-Dao conjugate of X(j) for these {i, j}: {3869, 3869}
X(64047) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2995, 2}
X(64047) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {56, 56819}, {2217, 8}, {2995, 6327}, {10570, 3436}, {13478, 69}, {15232, 1330}, {15386, 100}, {19607, 20245}, {26704, 20293}, {32653, 514}, {36050, 513}, {40160, 2893}, {44765, 20295}, {54951, 512}, {57757, 3888}, {57906, 315}, {59005, 523}
X(64047) = pole of line {16228, 54244} with respect to the polar circle
X(64047) = pole of line {3486, 3622} with respect to the Feuerbach hyperbola
X(64047) = pole of line {6758, 53349} with respect to the Kiepert parabola
X(64047) = pole of line {4653, 17104} with respect to the Stammler hyperbola
X(64047) = pole of line {905, 1577} with respect to the Steiner circumellipse
X(64047) = intersection, other than A, B, C, of circumconics {{A, B, C, X(79), X(959)}}, {{A, B, C, X(89), X(30690)}}, {{A, B, C, X(2320), X(31359)}}, {{A, B, C, X(5267), X(60079)}}, {{A, B, C, X(6757), X(53114)}}, {{A, B, C, X(42485), X(44663)}}
X(64047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5267, 2320}, {1, 56288, 4189}, {8, 14450, 1478}, {8, 17164, 28605}, {8, 4295, 2475}, {8, 5905, 20060}, {46, 4511, 4188}, {65, 31165, 3812}, {65, 3869, 2}, {65, 44663, 3869}, {145, 20067, 944}, {145, 20070, 20075}, {145, 3868, 4430}, {145, 9965, 20076}, {517, 3555, 3885}, {517, 4018, 3868}, {517, 64021, 20}, {518, 14923, 3621}, {758, 5903, 8}, {908, 4848, 25005}, {942, 3877, 3622}, {962, 12649, 149}, {962, 9803, 48482}, {1697, 11520, 3957}, {2650, 37598, 17018}, {2800, 37625, 962}, {3057, 3873, 3623}, {3245, 41696, 8715}, {3339, 19861, 27003}, {3486, 44447, 15680}, {3555, 3885, 145}, {3671, 24987, 31019}, {3753, 3876, 46933}, {3754, 5692, 9780}, {3868, 3885, 3555}, {3874, 5697, 3241}, {3878, 4757, 5902}, {3878, 5902, 3616}, {3884, 18398, 38314}, {3916, 50194, 3897}, {3962, 5836, 3681}, {4880, 11009, 8666}, {5221, 5289, 5253}, {5255, 49454, 36565}, {5730, 36279, 404}, {9957, 24473, 3889}, {11523, 63130, 3935}, {11531, 62823, 36846}, {12526, 18421, 19860}, {12635, 37567, 100}, {14988, 64044, 4}, {15803, 56387, 4881}, {17016, 54421, 37685}, {37549, 62804, 17024}

X(64048) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-ATIK AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a^10-5*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(5*b^4-2*b^2*c^2+5*c^4)+2*a^6*(5*b^4+6*b^2*c^2+5*c^4)-2*a^4*(5*b^6-b^4*c^2-b^2*c^4+5*c^6) : :
X(64048) = -3*X[18950]+X[52398]

X(64048) lies on these lines: {2, 36747}, {3, 11433}, {4, 52}, {5, 69}, {6, 3547}, {20, 12022}, {24, 54217}, {25, 6193}, {26, 18925}, {30, 18909}, {49, 35260}, {51, 7401}, {54, 7493}, {140, 18928}, {143, 18420}, {155, 193}, {185, 18910}, {235, 12160}, {265, 38442}, {317, 1093}, {343, 7404}, {371, 24246}, {372, 24245}, {376, 43573}, {381, 31802}, {382, 12324}, {511, 6643}, {524, 15873}, {539, 7714}, {567, 47525}, {568, 63709}, {569, 7494}, {571, 56891}, {631, 13352}, {1092, 61506}, {1147, 6353}, {1181, 61658}, {1216, 6804}, {1350, 64038}, {1352, 10110}, {1353, 19347}, {1370, 18912}, {1596, 12164}, {1598, 3564}, {1899, 34938}, {1992, 12161}, {1993, 3542}, {2777, 18932}, {2794, 39804}, {2888, 7394}, {2895, 6846}, {3088, 12359}, {3090, 23061}, {3091, 45794}, {3146, 34796}, {3147, 34148}, {3167, 21841}, {3410, 63666}, {3528, 32110}, {3541, 3580}, {3546, 13567}, {3548, 37643}, {3549, 11427}, {3567, 6815}, {3629, 16252}, {3832, 37779}, {3855, 12325}, {5050, 16197}, {5422, 7383}, {5449, 8889}, {5462, 6803}, {5562, 18537}, {5654, 6622}, {5739, 6824}, {5890, 37201}, {6146, 31305}, {6225, 34783}, {6243, 18531}, {6337, 52278}, {6403, 11382}, {6503, 52014}, {6623, 22660}, {6676, 11426}, {6756, 12429}, {6759, 41719}, {6776, 7387}, {6816, 11412}, {6823, 11432}, {6862, 14555}, {6959, 18141}, {6964, 32863}, {6995, 12134}, {6997, 9781}, {7386, 10625}, {7393, 10519}, {7399, 9777}, {7400, 36752}, {7487, 44665}, {7492, 43838}, {7500, 34224}, {7505, 37645}, {7517, 11206}, {7529, 14826}, {7530, 32358}, {7544, 11002}, {7553, 64034}, {7558, 63085}, {7592, 59349}, {7689, 64096}, {9715, 47582}, {9730, 10996}, {9818, 64066}, {9820, 63092}, {9833, 10112}, {9896, 49542}, {9909, 31804}, {9936, 46261}, {10116, 39874}, {10201, 15806}, {10243, 19459}, {10263, 14790}, {10539, 63174}, {11003, 59351}, {11008, 15068}, {11245, 11414}, {11424, 41586}, {11441, 41628}, {11477, 63129}, {12084, 18931}, {12085, 18913}, {12106, 22550}, {12118, 64095}, {12241, 17834}, {12295, 12317}, {12605, 41465}, {13347, 32068}, {13383, 63656}, {13391, 18952}, {13450, 37192}, {13598, 14216}, {13630, 15740}, {14070, 43595}, {14449, 18569}, {14516, 37122}, {14912, 19121}, {15022, 15108}, {15043, 45073}, {15077, 16982}, {15741, 40909}, {15760, 37493}, {16051, 43817}, {16063, 43816}, {16266, 37669}, {16881, 50008}, {17702, 18947}, {17810, 64035}, {18381, 31670}, {18534, 34781}, {18911, 64050}, {18914, 39568}, {18915, 64053}, {18922, 64054}, {18950, 52398}, {19119, 64052}, {19357, 32269}, {19458, 40318}, {21850, 61544}, {23291, 23335}, {23698, 39833}, {24243, 49029}, {24244, 49028}, {25738, 32064}, {26871, 37532}, {34608, 61713}, {34780, 58764}, {35513, 40647}, {37444, 62187}, {37483, 63081}, {37672, 59659}, {37814, 53050}, {38282, 64181}, {39522, 63734}, {40698, 47731}, {43839, 52290}, {43995, 52448}, {44262, 63022}, {44275, 63064}, {44862, 52987}, {56292, 62961}, {58806, 59346}, {61607, 64067}, {62979, 63649}

X(64048) = reflection of X(i) in X(j) for these {i,j}: {6643, 39571}, {11411, 18934}, {17814, 15873}, {18909, 18951}
X(64048) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {62886, 4329}
X(64048) = pole of line {5013, 7404} with respect to the Kiepert hyperbola
X(64048) = pole of line {1147, 5892} with respect to the Stammler hyperbola
X(64048) = pole of line {631, 9723} with respect to the Wallace hyperbola
X(64048) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(317), X(11411)}}, {{A, B, C, X(847), X(8797)}}, {{A, B, C, X(3527), X(14593)}}, {{A, B, C, X(5962), X(38442)}}
X(64048) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 69, 11487}, {20, 37644, 18916}, {30, 18951, 18909}, {68, 5446, 4}, {193, 3089, 155}, {343, 10982, 7404}, {382, 18917, 12324}, {524, 15873, 17814}, {1899, 45186, 34938}, {6146, 33586, 31305}, {7387, 13292, 6776}, {10263, 14790, 51212}, {12359, 44413, 3088}, {13142, 41588, 3}, {13567, 37498, 3546}, {13754, 18934, 11411}, {18912, 64051, 1370}

X(64049) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-CONWAY AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a^4*(a^2-b^2-c^2)*(a^4+b^4-4*b^2*c^2+c^4-2*a^2*(b^2+c^2)) : :
X(64049) = 3*X[11402]+X[11414], X[12174]+3*X[54994]

X(64049) lies on these lines: {2, 1614}, {3, 49}, {4, 569}, {5, 182}, {6, 5446}, {20, 54}, {22, 52}, {23, 3567}, {24, 6800}, {25, 5462}, {26, 389}, {30, 578}, {51, 7517}, {68, 1176}, {69, 9936}, {74, 56071}, {110, 631}, {125, 6639}, {140, 156}, {141, 31831}, {143, 17714}, {154, 5892}, {186, 10574}, {195, 37484}, {215, 5217}, {216, 23128}, {217, 10316}, {343, 34002}, {371, 9687}, {372, 9677}, {376, 34148}, {378, 10575}, {381, 11572}, {382, 567}, {511, 12161}, {542, 44491}, {548, 37480}, {549, 13347}, {550, 13346}, {568, 2937}, {575, 7530}, {576, 8546}, {577, 46394}, {597, 63663}, {601, 52434}, {692, 10267}, {974, 12893}, {1154, 7525}, {1173, 63076}, {1199, 3060}, {1205, 45016}, {1209, 7558}, {1352, 5157}, {1368, 9820}, {1370, 17712}, {1495, 7506}, {1498, 9818}, {1499, 57206}, {1579, 8909}, {1593, 14915}, {1598, 1974}, {1656, 10540}, {1657, 37472}, {1658, 11438}, {1660, 6644}, {1899, 3549}, {1993, 10323}, {1994, 11423}, {2070, 37481}, {2194, 36754}, {2393, 44480}, {2477, 5204}, {2777, 12228}, {2794, 39805}, {2914, 13201}, {2917, 11802}, {2931, 11806}, {2979, 56292}, {3043, 15055}, {3044, 21166}, {3045, 34474}, {3046, 38690}, {3047, 15035}, {3048, 38698}, {3053, 9604}, {3089, 19128}, {3091, 14157}, {3098, 6101}, {3146, 8718}, {3200, 5351}, {3201, 5352}, {3202, 13334}, {3203, 5171}, {3205, 5237}, {3206, 5238}, {3309, 58314}, {3357, 10274}, {3518, 15043}, {3520, 15072}, {3521, 18562}, {3522, 9545}, {3523, 9544}, {3526, 5651}, {3527, 53091}, {3528, 9706}, {3534, 37495}, {3538, 64177}, {3544, 46865}, {3546, 14156}, {3548, 43839}, {3564, 12229}, {3574, 31723}, {3575, 7706}, {3867, 18583}, {3955, 24467}, {4550, 7503}, {5020, 14530}, {5067, 43614}, {5070, 22112}, {5085, 7393}, {5092, 7516}, {5133, 16659}, {5135, 5707}, {5198, 44863}, {5206, 9697}, {5320, 37509}, {5422, 10594}, {5432, 9652}, {5433, 9667}, {5448, 18531}, {5504, 15740}, {5576, 11550}, {5609, 32305}, {5622, 36253}, {5640, 34484}, {5654, 6643}, {5878, 49669}, {5889, 7512}, {5890, 7488}, {5891, 7509}, {5899, 11692}, {5907, 7514}, {5943, 13861}, {5944, 11202}, {5946, 37440}, {6000, 7526}, {6102, 7502}, {6146, 9927}, {6153, 9920}, {6193, 7400}, {6241, 14118}, {6243, 13564}, {6247, 44679}, {6413, 8961}, {6449, 9686}, {6636, 11412}, {6676, 12359}, {6689, 14216}, {6823, 31804}, {6862, 37527}, {6914, 13323}, {7193, 26921}, {7395, 18451}, {7399, 12134}, {7401, 11206}, {7403, 16655}, {7404, 34781}, {7464, 52093}, {7493, 18916}, {7494, 11411}, {7505, 18911}, {7527, 12290}, {7528, 31383}, {7529, 10601}, {7542, 13394}, {7545, 15047}, {7550, 15056}, {7552, 43808}, {7553, 45089}, {7569, 61700}, {7712, 43600}, {7987, 9587}, {7999, 15246}, {8151, 8723}, {8550, 13292}, {8883, 59172}, {9517, 58316}, {9586, 16192}, {9603, 15815}, {9622, 35242}, {9653, 15326}, {9666, 15338}, {9696, 15515}, {9705, 15717}, {9707, 17928}, {9715, 37489}, {9735, 52909}, {9736, 52910}, {9781, 34545}, {9786, 14070}, {9826, 15647}, {9833, 18420}, {9909, 11432}, {9934, 46686}, {10117, 11557}, {10192, 16238}, {10201, 18952}, {10298, 43611}, {10311, 41334}, {10535, 37696}, {10620, 11597}, {10661, 11516}, {10662, 11515}, {10665, 11514}, {10666, 11513}, {10982, 18534}, {11134, 22236}, {11137, 22238}, {11179, 39571}, {11245, 41587}, {11248, 20986}, {11402, 11414}, {11413, 14855}, {11422, 64050}, {11425, 12085}, {11426, 39568}, {11427, 34938}, {11429, 64054}, {11430, 12084}, {11439, 12112}, {11449, 20791}, {11459, 37126}, {11464, 22467}, {11472, 12315}, {11479, 32063}, {11565, 18379}, {11574, 19139}, {11695, 50414}, {11818, 13419}, {11935, 62085}, {12006, 12106}, {12042, 57011}, {12083, 13366}, {12111, 35921}, {12118, 12318}, {12160, 37486}, {12174, 54994}, {12235, 32048}, {12254, 12278}, {12279, 14865}, {12289, 34007}, {12362, 22660}, {12901, 44573}, {13160, 18474}, {13198, 17702}, {13247, 51536}, {13289, 14708}, {13335, 52278}, {13369, 47371}, {13371, 61619}, {13383, 13567}, {13391, 32136}, {13445, 35475}, {13470, 18377}, {13474, 31861}, {13482, 15683}, {13505, 14652}, {13509, 26216}, {13595, 15024}, {13598, 37505}, {13621, 44082}, {14130, 14805}, {14133, 37242}, {14389, 15559}, {14529, 34339}, {14531, 37494}, {14790, 46264}, {14810, 15606}, {14852, 19129}, {14861, 16867}, {14912, 19121}, {14940, 26913}, {15037, 18378}, {15045, 26882}, {15053, 44879}, {15067, 17508}, {15132, 20417}, {15139, 40686}, {15305, 35500}, {15462, 16534}, {15463, 16111}, {15580, 41579}, {15581, 43130}, {15644, 16266}, {15692, 43572}, {15696, 37477}, {15712, 40111}, {15761, 18390}, {15873, 51730}, {16187, 16239}, {16194, 63664}, {16226, 51519}, {17809, 35243}, {17821, 37475}, {18356, 45732}, {18374, 53093}, {18388, 18569}, {18404, 43831}, {18435, 34864}, {18438, 19362}, {18559, 41482}, {18580, 25563}, {18912, 63735}, {18917, 47525}, {18923, 19061}, {18924, 19062}, {18931, 43617}, {19123, 63069}, {19153, 44503}, {19365, 64053}, {19456, 19468}, {19458, 19459}, {19548, 34465}, {20191, 26937}, {20299, 58447}, {21243, 32140}, {21659, 64179}, {21841, 45298}, {21844, 43601}, {22234, 37967}, {22758, 55098}, {22802, 34114}, {23239, 58048}, {23292, 23335}, {23698, 39834}, {25337, 43588}, {26864, 43586}, {26884, 37612}, {26888, 37697}, {26889, 37532}, {26917, 58805}, {26925, 53061}, {30209, 58310}, {31725, 61744}, {31833, 34782}, {31834, 33533}, {31837, 42463}, {32110, 38444}, {32284, 32621}, {32338, 45839}, {32767, 40276}, {33540, 55692}, {33556, 43898}, {33586, 37493}, {33749, 44490}, {34117, 44479}, {34473, 58058}, {34513, 45956}, {34779, 44544}, {34786, 44263}, {35473, 51033}, {35477, 52416}, {36153, 39561}, {36742, 44085}, {36750, 44104}, {37198, 37483}, {37347, 64036}, {37510, 44120}, {37644, 59351}, {38064, 43811}, {38691, 58060}, {38692, 58057}, {38693, 58056}, {38694, 58053}, {38695, 58052}, {38696, 58050}, {38697, 58051}, {38699, 58049}, {38706, 58062}, {38710, 58068}, {38712, 58055}, {38713, 58054}, {38714, 58067}, {38715, 58063}, {38716, 58059}, {38717, 58064}, {38718, 58066}, {38728, 54073}, {40280, 43809}, {40320, 52438}, {40920, 61878}, {44489, 50979}, {45959, 49671}, {47528, 51392}, {48876, 52016}, {51739, 64196}, {55711, 56918}, {57482, 58925}, {58407, 61736}, {58465, 61606}, {58806, 59349}, {61701, 63657}

X(64049) = midpoint of X(i) and X(j) for these {i,j}: {3, 1181}, {6823, 31804}, {11414, 36747}, {12160, 37486}
X(64049) = reflection of X(i) in X(j) for these {i,j}: {578, 32046}, {3867, 18583}, {12161, 64026}, {46728, 7525}
X(64049) = inverse of X(11487) in Stammler hyperbola
X(64049) = X(i)-isoconjugate-of-X(j) for these {i, j}: {158, 42021}, {24006, 43351}
X(64049) = X(i)-Dao conjugate of X(j) for these {i, j}: {1147, 42021}
X(64049) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5395, 32}, {5422, 13345}, {56338, 577}
X(64049) = pole of line {525, 10279} with respect to the 1st Brocard circle
X(64049) = pole of line {3, 54384} with respect to the Jerabek hyperbola
X(64049) = pole of line {8673, 57135} with respect to the Johnson circumconic
X(64049) = pole of line {32, 7403} with respect to the Kiepert hyperbola
X(64049) = pole of line {4, 1216} with respect to the Stammler hyperbola
X(64049) = pole of line {33294, 52584} with respect to the Steiner inellipse
X(64049) = pole of line {264, 1238} with respect to the Wallace hyperbola
X(64049) = pole of line {2970, 53575} with respect to the dual conic of Wallace hyperbola
X(64049) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 1181, 18338}
X(64049) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(1179)}}, {{A, B, C, X(4), X(1216)}}, {{A, B, C, X(68), X(3917)}}, {{A, B, C, X(69), X(5447)}}, {{A, B, C, X(394), X(5422)}}, {{A, B, C, X(1092), X(40441)}}, {{A, B, C, X(1147), X(1176)}}, {{A, B, C, X(3521), X(23039)}}, {{A, B, C, X(3527), X(62217)}}, {{A, B, C, X(3796), X(42065)}}, {{A, B, C, X(4846), X(5562)}}, {{A, B, C, X(5446), X(6504)}}, {{A, B, C, X(5504), X(43652)}}, {{A, B, C, X(13623), X(34783)}}, {{A, B, C, X(13754), X(15740)}}, {{A, B, C, X(14861), X(18436)}}, {{A, B, C, X(20574), X(41597)}}, {{A, B, C, X(32832), X(36212)}}, {{A, B, C, X(51394), X(56071)}}
X(64049) = barycentric product X(i)*X(j) for these (i, j): {3, 5422}, {184, 32832}, {10594, 394}, {13345, 69}
X(64049) = barycentric quotient X(i)/X(j) for these (i, j): {577, 42021}, {5422, 264}, {10594, 2052}, {13345, 4}, {32661, 43351}, {32832, 18022}
X(64049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1614, 10539}, {2, 61134, 13336}, {3, 1181, 13754}, {3, 155, 1216}, {3, 184, 1147}, {3, 18445, 5562}, {3, 185, 7689}, {3, 19347, 155}, {3, 19357, 12038}, {3, 22115, 43652}, {3, 34783, 63425}, {3, 394, 5447}, {3, 49, 1092}, {3, 9704, 22115}, {4, 5012, 569}, {5, 61752, 6759}, {6, 7387, 5446}, {20, 11003, 54}, {20, 4846, 43577}, {20, 54, 13352}, {22, 7592, 52}, {25, 36752, 5462}, {26, 389, 64095}, {30, 32046, 578}, {68, 6776, 10116}, {140, 156, 9306}, {154, 37514, 6642}, {182, 19137, 38110}, {182, 61752, 46261}, {184, 1092, 49}, {382, 567, 11424}, {511, 64026, 12161}, {1154, 7525, 46728}, {1176, 6776, 19131}, {1181, 3796, 3}, {1199, 12088, 3060}, {1498, 37476, 9818}, {1658, 13630, 11438}, {1899, 3549, 5449}, {1993, 10323, 10625}, {2909, 40643, 206}, {2937, 43845, 568}, {3522, 9545, 43574}, {3526, 18350, 5651}, {3546, 64181, 14156}, {3547, 6776, 68}, {5012, 52525, 4}, {5085, 17814, 7393}, {5092, 11793, 7516}, {5447, 41597, 394}, {5449, 18128, 1899}, {5562, 18445, 15083}, {5889, 15080, 7512}, {5944, 37814, 11202}, {6102, 7502, 46730}, {6146, 15760, 9927}, {7393, 17814, 10170}, {7503, 11456, 12162}, {7505, 18911, 43817}, {7509, 11441, 5891}, {7512, 15032, 5889}, {7514, 32139, 5907}, {7516, 15068, 11793}, {7517, 36753, 51}, {8550, 19127, 44470}, {8718, 15033, 3146}, {9707, 17928, 51393}, {9833, 18420, 45286}, {10539, 13336, 2}, {10540, 37471, 1656}, {10610, 13491, 18570}, {11402, 11414, 36747}, {11423, 64051, 1994}, {11426, 39568, 44413}, {11430, 46850, 12084}, {11456, 37513, 4550}, {12083, 36749, 45186}, {12084, 64098, 46850}, {12162, 37513, 7503}, {12229, 12230, 19126}, {13160, 34224, 18474}, {13366, 45186, 36749}, {13491, 18570, 3357}, {13564, 15087, 6243}, {13598, 37505, 39522}, {14157, 43651, 3091}, {14805, 64030, 14130}, {15032, 15080, 37478}, {15043, 26881, 3518}, {15045, 26882, 44802}, {15644, 34986, 16266}, {16252, 64038, 5}, {16655, 37649, 7403}, {21844, 61136, 43601}, {25337, 43588, 63734}, {32621, 44492, 32284}, {37126, 43605, 11459}, {55692, 56516, 33540}

X(64050) = ORTHOLOGY CENTER OF THESE TRIANGLES: 3RD ANTI-EULER AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a^2*(a^6*(b^2+c^2)-(b^2-c^2)^2*(b^4-b^2*c^2+c^4)-a^4*(3*b^4+7*b^2*c^2+3*c^4)+3*a^2*(b^6+b^4*c^2+b^2*c^4+c^6)) : :
X(64050) = -9*X[2]+8*X[10110], -5*X[3]+4*X[143], -3*X[4]+4*X[1216], -8*X[5]+9*X[7998], -3*X[20]+2*X[185], -6*X[51]+7*X[3523], -2*X[52]+3*X[376], -8*X[140]+7*X[9781], -18*X[373]+19*X[55864], -6*X[381]+7*X[7999], -4*X[389]+5*X[3522], -4*X[548]+3*X[568] and many others

X(64050) lies on these lines: {2, 10110}, {3, 143}, {4, 1216}, {5, 7998}, {20, 185}, {22, 19357}, {23, 1092}, {24, 15107}, {26, 11449}, {30, 11412}, {51, 3523}, {52, 376}, {54, 15080}, {64, 44668}, {110, 7387}, {140, 9781}, {155, 12082}, {323, 6759}, {373, 55864}, {378, 6152}, {381, 7999}, {382, 6101}, {389, 3522}, {411, 37482}, {548, 568}, {549, 15024}, {550, 5890}, {578, 6636}, {631, 5446}, {1112, 15051}, {1147, 12088}, {1154, 1657}, {1181, 11577}, {1350, 7503}, {1351, 37198}, {1568, 18504}, {1593, 6403}, {1595, 37636}, {1598, 15066}, {1614, 12083}, {1656, 44299}, {1658, 37477}, {1843, 62174}, {1907, 48876}, {1941, 35474}, {1993, 11414}, {1994, 10984}, {2071, 46730}, {2393, 12324}, {2777, 12273}, {2781, 17845}, {2794, 39807}, {2888, 11550}, {2937, 11464}, {3090, 5447}, {3091, 3917}, {3098, 11424}, {3146, 5562}, {3313, 6815}, {3357, 37944}, {3520, 37478}, {3524, 5462}, {3528, 9730}, {3529, 12271}, {3534, 6102}, {3538, 63084}, {3543, 5907}, {3544, 44863}, {3564, 12274}, {3575, 54040}, {3627, 15058}, {3819, 5056}, {3830, 11591}, {3832, 11793}, {3843, 11017}, {3851, 32142}, {3853, 16261}, {3855, 10170}, {3858, 44324}, {5012, 10323}, {5054, 10095}, {5059, 6000}, {5067, 33879}, {5070, 12046}, {5073, 5876}, {5076, 15060}, {5189, 18381}, {5198, 62217}, {5650, 7486}, {5663, 17800}, {5691, 31737}, {5752, 6909}, {5892, 10299}, {5899, 61753}, {5943, 10303}, {6146, 52397}, {6515, 52398}, {6688, 61856}, {6696, 34751}, {6746, 11410}, {6800, 9706}, {6834, 33852}, {6850, 41723}, {6932, 37536}, {6960, 37521}, {7391, 33523}, {7393, 41462}, {7416, 48928}, {7464, 7689}, {7485, 10982}, {7488, 13346}, {7502, 37495}, {7509, 44413}, {7512, 13352}, {7525, 37472}, {7527, 52987}, {7530, 43598}, {7544, 31670}, {7556, 12038}, {7574, 18394}, {7592, 35243}, {7667, 13142}, {7731, 12121}, {7957, 9037}, {7987, 31757}, {8703, 14449}, {8718, 18445}, {9019, 15062}, {9047, 12680}, {9729, 10304}, {9821, 54003}, {9833, 20062}, {9927, 46450}, {9967, 10996}, {10282, 37913}, {10310, 56878}, {10441, 37437}, {10539, 37925}, {10546, 34484}, {10564, 21844}, {10575, 11001}, {10733, 15738}, {11002, 15717}, {11004, 64026}, {11270, 58871}, {11381, 49135}, {11413, 17834}, {11416, 44492}, {11422, 64049}, {11440, 12085}, {11441, 39568}, {11442, 34938}, {11446, 64054}, {11454, 12084}, {11457, 41724}, {11468, 18859}, {11592, 15694}, {11649, 55583}, {11695, 61820}, {11704, 37938}, {12002, 14845}, {12063, 38397}, {12086, 63425}, {12118, 41482}, {12162, 33703}, {12163, 13445}, {12173, 41590}, {12239, 42638}, {12240, 42637}, {12272, 63428}, {12282, 14984}, {12283, 34380}, {12284, 20127}, {12307, 13423}, {12824, 15020}, {12834, 15805}, {13201, 15100}, {13336, 44832}, {13347, 15004}, {13363, 61811}, {13364, 46219}, {13367, 38435}, {13382, 62124}, {13383, 63660}, {13421, 62100}, {13451, 14869}, {13491, 15681}, {13568, 44439}, {13630, 15696}, {13734, 48936}, {14118, 46728}, {14128, 61984}, {14216, 45794}, {14389, 16197}, {14641, 62147}, {14790, 58922}, {14831, 62120}, {14855, 62127}, {14915, 49138}, {15012, 62083}, {15026, 15720}, {15030, 15606}, {15036, 16222}, {15055, 16270}, {15057, 45237}, {15074, 43612}, {15318, 62308}, {15683, 64025}, {15684, 32137}, {15692, 21849}, {15704, 34783}, {15708, 58470}, {16063, 39571}, {16194, 62028}, {16196, 47582}, {16226, 62063}, {16621, 64062}, {16625, 62097}, {16658, 31831}, {16836, 16981}, {16868, 51392}, {16881, 40280}, {16978, 38701}, {16980, 59417}, {17538, 40647}, {17704, 62067}, {17710, 55722}, {17712, 61713}, {17714, 22115}, {17928, 33586}, {18392, 18569}, {18435, 62036}, {18438, 31829}, {18874, 55857}, {18911, 64048}, {18914, 41628}, {19122, 64052}, {19367, 64053}, {22467, 37480}, {23293, 23335}, {23294, 63734}, {23698, 39836}, {26883, 37945}, {26910, 37532}, {26913, 41587}, {27355, 46936}, {29181, 41716}, {29317, 61139}, {30438, 31806}, {31738, 41869}, {31760, 35242}, {31834, 62041}, {32006, 51439}, {32062, 50691}, {32138, 35452}, {32139, 44457}, {32191, 55646}, {32205, 55863}, {32338, 34797}, {33748, 58555}, {34545, 37515}, {34603, 64035}, {34782, 41715}, {36749, 61134}, {36752, 53863}, {36836, 36978}, {36843, 36980}, {36979, 42434}, {36981, 42433}, {37409, 48921}, {37444, 50435}, {37489, 43601}, {37497, 38444}, {38730, 39837}, {38741, 39808}, {43602, 64098}, {43613, 64105}, {43650, 45308}, {43652, 44802}, {44450, 48914}, {44479, 54132}, {44837, 51033}, {44870, 50688}, {45187, 49140}, {45956, 62123}, {45957, 62151}, {45958, 62008}, {46517, 61544}, {46849, 62021}, {47092, 61540}, {47748, 61752}, {50693, 64100}, {51024, 63723}, {54039, 64187}, {54445, 58469}, {55286, 62093}, {58378, 60774}, {58487, 64108}, {58533, 61799}, {61136, 62113}, {62155, 64030}

X(64050) = reflection of X(i) in X(j) for these {i,j}: {4, 10625}, {382, 6101}, {3146, 5562}, {5073, 5876}, {5691, 31737}, {5889, 20}, {6241, 1657}, {6243, 550}, {6403, 33878}, {7731, 12121}, {10263, 63414}, {11412, 37484}, {11455, 54048}, {12111, 11412}, {12272, 63428}, {12279, 3529}, {12284, 20127}, {12290, 18436}, {13423, 12307}, {14531, 46850}, {15100, 13201}, {15305, 62188}, {33703, 12162}, {34783, 15704}, {39808, 38741}, {39837, 38730}, {41869, 31738}, {45186, 15644}, {45957, 62151}, {49135, 11381}, {51212, 3313}, {55722, 17710}, {55724, 15074}, {62041, 31834}, {62187, 36987}, {64023, 1350}, {64030, 62155}, {64051, 3}
X(64050) = anticomplement of X(45186)
X(64050) = X(i)-Dao conjugate of X(j) for these {i, j}: {45186, 45186}
X(64050) = pole of line {13337, 63534} with respect to the Kiepert hyperbola
X(64050) = pole of line {140, 156} with respect to the Stammler hyperbola
X(64050) = pole of line {1232, 1975} with respect to the Wallace hyperbola
X(64050) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1173), X(9307)}}, {{A, B, C, X(5422), X(40684)}}, {{A, B, C, X(9289), X(31626)}}
X(64050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10263, 3567}, {3, 13391, 64051}, {3, 143, 15045}, {3, 3060, 15043}, {3, 39522, 43651}, {3, 64051, 3060}, {4, 10625, 2979}, {4, 1216, 15056}, {20, 185, 52093}, {20, 511, 5889}, {22, 37498, 34148}, {30, 18436, 12290}, {30, 37484, 11412}, {51, 13348, 3523}, {51, 3523, 15028}, {52, 376, 10574}, {140, 9781, 11451}, {185, 52093, 15072}, {323, 12087, 6759}, {378, 37486, 7691}, {382, 11459, 11439}, {382, 6101, 11459}, {389, 36987, 3522}, {511, 46850, 14531}, {631, 5446, 5640}, {1147, 12088, 26881}, {1154, 1657, 6241}, {1216, 15056, 11444}, {1216, 46852, 5891}, {1598, 15066, 43614}, {1993, 11414, 52525}, {1994, 16661, 10984}, {2979, 15056, 1216}, {3146, 5562, 15305}, {3146, 62188, 5562}, {3529, 13754, 12279}, {3627, 23039, 15058}, {3832, 33884, 11793}, {3917, 13598, 3091}, {5054, 10095, 11465}, {5073, 54048, 5876}, {5073, 5876, 11455}, {5889, 52093, 185}, {10263, 63414, 3}, {11412, 12290, 18436}, {12083, 16266, 1614}, {12118, 44831, 41482}, {12290, 18436, 12111}, {13391, 63414, 10263}, {15026, 54044, 15720}, {16881, 46853, 40280}, {17714, 22115, 26882}, {19467, 48873, 20}, {36987, 62187, 20791}, {37494, 43576, 11454}

X(64051) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH ANTI-EULER AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a^2*(a^6*(b^2+c^2)-(b^2-c^2)^2*(b^4-b^2*c^2+c^4)-a^4*(3*b^4+5*b^2*c^2+3*c^4)+a^2*(3*b^6+b^4*c^2+b^2*c^4+3*c^6)) : :
X(64051) = -3*X[2]+4*X[5446], -3*X[3]+4*X[143], -4*X[5]+3*X[2979], -6*X[51]+5*X[631], -8*X[140]+9*X[5640], -3*X[165]+4*X[31760], -18*X[373]+17*X[3533], -3*X[376]+4*X[389], -3*X[381]+2*X[6101], -8*X[546]+7*X[15056], -8*X[548]+9*X[20791], -12*X[549]+13*X[15028] and many others

X(64051) lies on these lines: {2, 5446}, {3, 143}, {4, 69}, {5, 2979}, {6, 10323}, {20, 52}, {22, 54}, {23, 1147}, {24, 33586}, {26, 11464}, {30, 5889}, {49, 17714}, {51, 631}, {68, 7391}, {74, 12085}, {110, 7517}, {140, 5640}, {154, 9705}, {155, 14157}, {156, 5899}, {165, 31760}, {184, 12088}, {185, 3529}, {186, 13346}, {193, 12283}, {195, 61752}, {265, 13201}, {323, 10539}, {343, 15559}, {373, 3533}, {376, 389}, {378, 17834}, {381, 6101}, {382, 1154}, {394, 10594}, {428, 11387}, {477, 16978}, {524, 16655}, {546, 15056}, {548, 20791}, {549, 15028}, {550, 568}, {567, 7525}, {569, 6636}, {576, 1199}, {578, 7512}, {599, 63688}, {632, 13451}, {858, 26917}, {970, 6950}, {1092, 3518}, {1112, 3515}, {1181, 8718}, {1204, 7464}, {1209, 5169}, {1216, 3091}, {1350, 7509}, {1351, 7592}, {1370, 18912}, {1498, 44668}, {1568, 44958}, {1597, 43613}, {1614, 1993}, {1656, 7998}, {1657, 6102}, {1658, 37495}, {1699, 31738}, {1994, 11423}, {2070, 11449}, {2392, 37625}, {2393, 34781}, {2698, 16979}, {2777, 12284}, {2781, 25335}, {2794, 39808}, {2883, 62344}, {2888, 62967}, {2972, 38281}, {3088, 47328}, {3090, 3917}, {3146, 12282}, {3313, 7383}, {3516, 6746}, {3520, 46730}, {3522, 9730}, {3523, 5462}, {3524, 13348}, {3525, 5943}, {3526, 10095}, {3527, 7484}, {3528, 9729}, {3534, 13630}, {3543, 12162}, {3545, 11793}, {3564, 12285}, {3576, 31757}, {3580, 23294}, {3581, 11250}, {3627, 15305}, {3819, 5067}, {3830, 5876}, {3832, 5891}, {3843, 11591}, {3851, 15067}, {3853, 18435}, {3855, 15606}, {5012, 36749}, {5054, 15026}, {5055, 32142}, {5056, 33884}, {5059, 10575}, {5064, 11576}, {5068, 10170}, {5070, 13364}, {5073, 5663}, {5076, 45959}, {5102, 17710}, {5198, 58764}, {5449, 31074}, {5480, 14788}, {5587, 31737}, {5650, 61886}, {5752, 6906}, {5892, 15717}, {6000, 14531}, {6033, 39807}, {6143, 61646}, {6146, 29181}, {6152, 35502}, {6193, 7500}, {6247, 34751}, {6321, 39836}, {6515, 11457}, {6642, 38848}, {6662, 46977}, {6688, 61867}, {6759, 37925}, {6823, 18438}, {6905, 37482}, {6923, 41723}, {6932, 39271}, {6937, 18180}, {6941, 37536}, {6949, 37521}, {6959, 33852}, {7395, 33878}, {7399, 21850}, {7400, 9967}, {7403, 37636}, {7420, 48907}, {7486, 14845}, {7488, 13352}, {7502, 37472}, {7503, 37486}, {7526, 7691}, {7529, 15066}, {7530, 23061}, {7550, 52987}, {7553, 14516}, {7556, 13367}, {7689, 12086}, {7699, 10024}, {7703, 34826}, {7728, 12273}, {7731, 15102}, {7773, 51440}, {8537, 44492}, {8703, 16881}, {9047, 14872}, {9306, 34484}, {9541, 12239}, {9545, 37913}, {9707, 9909}, {9821, 54004}, {9826, 15036}, {9833, 41715}, {9862, 39817}, {9969, 10519}, {9973, 16621}, {10018, 32269}, {10112, 29317}, {10706, 16105}, {10733, 12281}, {11001, 14831}, {11017, 61968}, {11248, 56878}, {11381, 15682}, {11411, 43895}, {11413, 37489}, {11424, 35921}, {11425, 13482}, {11432, 37198}, {11441, 18534}, {11456, 12160}, {11458, 37784}, {11461, 64054}, {11468, 12084}, {11479, 55584}, {11563, 18504}, {11592, 55863}, {11649, 37946}, {11692, 44450}, {11704, 63735}, {12022, 13142}, {12046, 61892}, {12061, 16656}, {12083, 12161}, {12110, 41262}, {12112, 55723}, {12118, 31304}, {12134, 34603}, {12164, 12271}, {12219, 12295}, {12233, 44439}, {12236, 15055}, {12241, 37473}, {12244, 21649}, {12245, 16980}, {12272, 16658}, {12291, 15801}, {12293, 52842}, {12307, 32196}, {12316, 37949}, {12383, 13417}, {12824, 15034}, {12902, 15100}, {13172, 39846}, {13336, 34545}, {13358, 15041}, {13363, 15720}, {13368, 54202}, {13382, 62147}, {13383, 63661}, {13474, 45187}, {13488, 44935}, {13491, 17800}, {13564, 15080}, {13568, 44458}, {14118, 37478}, {14249, 62345}, {14269, 45958}, {14389, 34002}, {14641, 15683}, {14790, 25739}, {14865, 63425}, {14869, 58531}, {14915, 49135}, {15004, 37515}, {15012, 62092}, {15018, 45308}, {15032, 37517}, {15051, 16222}, {15060, 61984}, {15087, 47748}, {15110, 16622}, {15111, 36160}, {15360, 18281}, {15531, 64067}, {15687, 31834}, {15694, 32205}, {15695, 55286}, {15702, 58470}, {15704, 52093}, {15800, 32338}, {16194, 50688}, {16226, 17704}, {16624, 16880}, {16625, 17538}, {16836, 21735}, {17928, 37483}, {18378, 61753}, {18392, 31724}, {18394, 18569}, {18439, 62036}, {18475, 38435}, {18492, 31752}, {18916, 52398}, {19123, 63063}, {19368, 64053}, {19467, 44831}, {19924, 44829}, {20299, 41586}, {20574, 63172}, {21166, 39835}, {21653, 49048}, {21654, 49049}, {22115, 37440}, {22236, 36978}, {22238, 36980}, {22352, 37505}, {22467, 64095}, {22660, 47096}, {22712, 27375}, {23293, 63734}, {23698, 39837}, {26216, 41480}, {26879, 41588}, {26914, 37532}, {27082, 52000}, {30771, 43866}, {31101, 43817}, {31152, 43836}, {31423, 58474}, {31723, 58922}, {31728, 64005}, {31817, 61705}, {31833, 54040}, {31884, 32191}, {32062, 62021}, {32137, 62023}, {32138, 32608}, {32140, 41724}, {32411, 37948}, {32534, 37497}, {32816, 51439}, {32823, 51386}, {33873, 37466}, {33879, 55856}, {33923, 40280}, {34146, 64034}, {34473, 39806}, {34621, 51028}, {34799, 44407}, {35237, 43596}, {35243, 37493}, {35474, 56298}, {36753, 53863}, {36979, 42157}, {36981, 42158}, {37186, 47740}, {37453, 43823}, {37477, 37814}, {37490, 43601}, {37491, 39588}, {37496, 45735}, {37511, 61044}, {37732, 50599}, {37932, 63725}, {37945, 43605}, {39571, 47528}, {40241, 61299}, {40805, 62260}, {41673, 64101}, {43586, 48912}, {43608, 44441}, {43812, 54183}, {43896, 44442}, {44516, 59771}, {44544, 64033}, {44665, 64032}, {44879, 51394}, {45956, 62144}, {46450, 48914}, {46849, 50687}, {47093, 61607}, {47391, 63683}, {50593, 63982}, {50649, 54132}, {54044, 58533}, {58486, 61132}, {61136, 62127}, {61873, 63632}, {63684, 64182}

X(64051) = midpoint of X(i) and X(j) for these {i,j}: {49135, 64025}
X(64051) = reflection of X(i) in X(j) for these {i,j}: {3, 10263}, {4, 45186}, {20, 52}, {376, 21969}, {477, 16978}, {550, 14449}, {1657, 6102}, {2698, 16979}, {3529, 185}, {5059, 10575}, {5562, 13598}, {5889, 6243}, {5890, 62187}, {6102, 13421}, {6241, 5889}, {9862, 39817}, {10625, 5446}, {11001, 14831}, {11412, 4}, {12111, 382}, {12219, 12295}, {12220, 1351}, {12244, 21649}, {12245, 16980}, {12271, 12164}, {12273, 7728}, {12279, 34783}, {12281, 10733}, {12283, 193}, {12290, 3146}, {12291, 15801}, {12307, 32196}, {12383, 13417}, {13172, 39846}, {13201, 265}, {14516, 7553}, {15073, 11477}, {15100, 12902}, {15102, 7731}, {17800, 13491}, {18436, 3627}, {18439, 62036}, {32338, 15800}, {37484, 5}, {39807, 6033}, {39836, 6321}, {41716, 31670}, {44831, 54384}, {45187, 13474}, {46450, 48914}, {49048, 21653}, {49049, 21654}, {54202, 13368}, {61044, 37511}, {63414, 16982}, {64005, 31728}, {64033, 44544}, {64050, 3}
X(64051) = anticomplement of X(10625)
X(64051) = X(i)-Dao conjugate of X(j) for these {i, j}: {10625, 10625}
X(64051) = pole of line {1899, 3090} with respect to the Jerabek hyperbola
X(64051) = pole of line {5254, 18353} with respect to the Kiepert hyperbola
X(64051) = pole of line {140, 184} with respect to the Stammler hyperbola
X(64051) = pole of line {3, 1232} with respect to the Wallace hyperbola
X(64051) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(1232)}}, {{A, B, C, X(76), X(31626)}}, {{A, B, C, X(264), X(1173)}}, {{A, B, C, X(340), X(17711)}}, {{A, B, C, X(3260), X(38260)}}, {{A, B, C, X(59164), X(61378)}}
X(64051) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5446, 9781}, {3, 10263, 3060}, {3, 13321, 12006}, {3, 13391, 64050}, {3, 143, 15043}, {3, 3567, 15045}, {3, 39522, 13434}, {4, 11412, 11459}, {4, 511, 11412}, {4, 5562, 15058}, {4, 5907, 16261}, {5, 2979, 7999}, {5, 37484, 2979}, {6, 10323, 61134}, {20, 52, 5890}, {20, 62187, 52}, {22, 36747, 54}, {23, 1147, 26882}, {24, 37498, 43574}, {26, 34148, 11464}, {30, 34783, 12279}, {30, 6243, 5889}, {49, 17714, 26881}, {51, 631, 15024}, {140, 5640, 11465}, {381, 6101, 11444}, {382, 1154, 12111}, {382, 12111, 11455}, {394, 10594, 43598}, {511, 31670, 41716}, {511, 45186, 4}, {546, 23039, 15056}, {548, 37481, 20791}, {550, 14449, 568}, {550, 568, 10574}, {631, 15644, 54041}, {858, 41587, 26917}, {1181, 12082, 8718}, {1351, 11414, 7592}, {1370, 64048, 18912}, {1656, 10627, 7998}, {1657, 6102, 15072}, {1993, 7387, 1614}, {3060, 15043, 143}, {3146, 13754, 12290}, {3523, 11002, 5462}, {3526, 10095, 11451}, {3580, 23335, 23294}, {3627, 18436, 15305}, {3830, 5876, 11439}, {3843, 54048, 11591}, {3917, 10110, 3090}, {5446, 10625, 2}, {5562, 45186, 13598}, {5889, 12279, 34783}, {5946, 10263, 16982}, {6515, 34938, 11457}, {7517, 16266, 110}, {7526, 37494, 7691}, {9019, 11477, 15073}, {9729, 36987, 3528}, {10263, 13391, 3}, {10263, 64050, 3567}, {11412, 15058, 5562}, {11424, 46728, 35921}, {12083, 12161, 52525}, {12160, 39568, 11456}, {12164, 14984, 12271}, {12279, 34783, 6241}, {13391, 16982, 63414}, {13564, 32046, 15080}, {15024, 54041, 631}, {15107, 34148, 26}, {16982, 63414, 5946}, {18569, 50435, 18394}, {33586, 37498, 24}, {37486, 44413, 7503}, {37925, 56292, 6759}, {39568, 44456, 12160}, {49135, 64025, 14915}, {63063, 64052, 19123}

X(64052) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-HONSBERGER AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a^4*(a^8-b^8-2*a^4*b^2*c^2+6*b^6*c^2-2*b^4*c^4+6*b^2*c^6-c^8-2*a^6*(b^2+c^2)+2*a^2*(b^2-c^2)^2*(b^2+c^2)) : :
X(64052) = -X[1350]+3*X[14070], -3*X[5085]+X[12085], -X[9925]+4*X[50414], -3*X[10201]+2*X[24206], -4*X[10226]+5*X[55672], -2*X[11250]+3*X[17508], -2*X[11255]+3*X[15520], -2*X[12038]+3*X[23041], -4*X[12107]+X[52987], -X[13346]+3*X[23042], -2*X[13371]+3*X[38317]

X(64052) lies on circumconic {{A, B, C, X(1485), X(45819)}} and on these lines: {3, 1974}, {4, 19121}, {5, 19126}, {6, 5446}, {20, 19128}, {22, 9967}, {23, 6403}, {24, 37511}, {26, 206}, {30, 182}, {49, 10244}, {66, 5449}, {68, 5596}, {69, 10539}, {110, 63428}, {140, 19137}, {141, 13383}, {154, 41619}, {155, 10243}, {156, 34380}, {159, 32048}, {184, 1351}, {193, 1614}, {382, 19124}, {539, 31166}, {567, 34726}, {569, 1176}, {576, 11536}, {577, 52967}, {578, 21850}, {611, 9645}, {1092, 16195}, {1177, 17702}, {1216, 37485}, {1350, 14070}, {1352, 46261}, {1353, 61752}, {1428, 64053}, {1503, 9927}, {1658, 3098}, {1660, 14984}, {1843, 7517}, {2080, 41277}, {2211, 10316}, {2330, 64054}, {2777, 19138}, {2781, 12893}, {2794, 39811}, {2854, 15580}, {2937, 11470}, {3167, 16199}, {3564, 6759}, {3589, 23335}, {3618, 13336}, {3620, 43598}, {3818, 15761}, {5012, 34608}, {5050, 10982}, {5085, 12085}, {5092, 12084}, {5097, 8547}, {5157, 14561}, {5622, 12295}, {5899, 8541}, {5921, 14157}, {6321, 41274}, {6644, 52520}, {6660, 30258}, {6776, 61713}, {7506, 44091}, {7689, 34146}, {8538, 12088}, {9306, 10154}, {9687, 19145}, {9813, 63475}, {9822, 13861}, {9925, 50414}, {9969, 44480}, {10201, 24206}, {10226, 55672}, {10245, 22115}, {10323, 26206}, {10540, 11898}, {10625, 20806}, {11178, 44278}, {11250, 17508}, {11255, 15520}, {11414, 19118}, {12038, 23041}, {12083, 44102}, {12107, 52987}, {12241, 48906}, {12283, 37784}, {12584, 20773}, {13346, 23042}, {13352, 51212}, {13371, 38317}, {13391, 19155}, {13417, 44078}, {13754, 19141}, {14530, 19588}, {14810, 18324}, {14912, 52525}, {14915, 41613}, {15331, 55649}, {15462, 38726}, {18281, 58445}, {18382, 29012}, {18440, 26883}, {18569, 19130}, {19119, 64048}, {19122, 64050}, {19123, 63063}, {19125, 36747}, {19132, 37498}, {19161, 64095}, {19459, 32284}, {21637, 45186}, {23698, 39840}, {26283, 44084}, {26923, 37532}, {26926, 41587}, {29181, 64061}, {31267, 43839}, {32144, 51126}, {33851, 55587}, {34350, 48892}, {34417, 37972}, {34609, 43650}, {34779, 46730}, {35268, 37928}, {37478, 41716}, {37480, 48874}, {37515, 38110}, {39871, 47093}, {40279, 61532}, {41593, 44469}, {41714, 44493}, {43572, 54174}, {43574, 61044}, {43652, 55610}, {44213, 50977}, {44242, 48880}, {44279, 48884}, {48895, 52843}, {51171, 61134}, {52404, 57388}, {58555, 64026}

X(64052) = midpoint of X(i) and X(j) for these {i,j}: {6, 7387}, {68, 5596}, {155, 37491}, {159, 44492}, {19149, 37488}, {34779, 46730}
X(64052) = reflection of X(i) in X(j) for these {i,j}: {66, 5449}, {141, 13383}, {182, 19154}, {1147, 206}, {3098, 1658}, {3818, 15761}, {11178, 44278}, {12084, 5092}, {12584, 20773}, {18569, 19130}, {23335, 3589}, {34350, 48892}, {44469, 41593}, {48880, 44242}, {48884, 44279}, {50977, 44213}, {52016, 156}, {52843, 48895}
X(64052) = pole of line {5475, 7403} with respect to the Kiepert hyperbola
X(64052) = pole of line {7386, 7998} with respect to the Stammler hyperbola
X(64052) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {6, 1316, 7387}
X(64052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 19154, 182}, {156, 34380, 52016}, {206, 511, 1147}, {382, 19129, 19124}, {19149, 37488, 13754}, {32217, 44882, 51730}

X(64053) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a*(a^6+(b-c)^4*(b+c)^2-a^4*(b^2-4*b*c+c^2)-a^2*(b^4+2*b^3*c-2*b^2*c^2+2*b*c^3+c^4)) : :

X(64053) lies on circumconic {{A, B, C, X(79), X(42464)}} and on these lines: {1, 30}, {3, 34}, {4, 1060}, {5, 1038}, {12, 23335}, {20, 1062}, {26, 36}, {33, 382}, {35, 12084}, {40, 52408}, {46, 1399}, {55, 12085}, {56, 7387}, {65, 36742}, {72, 8757}, {73, 37533}, {92, 37157}, {109, 59318}, {140, 19372}, {221, 517}, {222, 24474}, {223, 37531}, {225, 6923}, {227, 11248}, {255, 37584}, {278, 6850}, {355, 8270}, {388, 34938}, {475, 52366}, {498, 44441}, {511, 7352}, {515, 4347}, {516, 59285}, {534, 4667}, {546, 9817}, {550, 1040}, {601, 1254}, {603, 37532}, {612, 9654}, {614, 5370}, {912, 64057}, {942, 1407}, {944, 4318}, {970, 52830}, {999, 4320}, {1012, 37565}, {1068, 6925}, {1069, 1498}, {1076, 1877}, {1147, 26888}, {1214, 3560}, {1385, 34036}, {1393, 37612}, {1394, 5709}, {1398, 11414}, {1406, 64045}, {1419, 7982}, {1425, 45186}, {1428, 64052}, {1455, 11249}, {1456, 14110}, {1478, 14790}, {1479, 4351}, {1490, 1807}, {1503, 18970}, {1657, 18455}, {1658, 7280}, {1718, 58887}, {1745, 37700}, {1766, 56906}, {1828, 37034}, {1829, 37241}, {1838, 6917}, {1875, 56414}, {1935, 26921}, {2003, 5903}, {2093, 8141}, {2263, 62183}, {2331, 38292}, {2777, 19469}, {2794, 39815}, {3100, 3529}, {3146, 6198}, {3419, 54289}, {3554, 42459}, {3564, 19473}, {3585, 18569}, {3627, 37729}, {3920, 44442}, {4252, 37582}, {4293, 31305}, {4295, 54292}, {4303, 37615}, {4324, 34350}, {4348, 9655}, {5010, 11250}, {5059, 9538}, {5088, 7210}, {5204, 14070}, {5268, 10592}, {5272, 10154}, {5307, 46704}, {5399, 37569}, {5433, 13383}, {5446, 19366}, {5722, 43036}, {6000, 6238}, {6149, 59324}, {6285, 14915}, {6851, 34231}, {6861, 54346}, {6897, 37800}, {6906, 17080}, {6914, 54320}, {6985, 46974}, {7078, 37585}, {7191, 34608}, {7355, 13754}, {7530, 54428}, {7562, 55875}, {7741, 15761}, {7951, 13371}, {9539, 49135}, {9632, 22644}, {9634, 13886}, {9641, 49137}, {9642, 49136}, {9643, 17800}, {9644, 33703}, {9931, 17702}, {9957, 61086}, {10055, 14216}, {10076, 12163}, {10895, 54401}, {11399, 18534}, {11436, 40647}, {11496, 15832}, {12107, 38458}, {12702, 22117}, {13391, 32143}, {13730, 40985}, {14986, 34621}, {15941, 41227}, {15951, 24929}, {17437, 52440}, {18324, 59319}, {18377, 18513}, {18514, 44279}, {18915, 64048}, {19349, 36747}, {19365, 64049}, {19367, 64050}, {19368, 64051}, {21842, 51696}, {23698, 39844}, {24467, 37591}, {24537, 56875}, {26611, 58798}, {26955, 41587}, {31837, 34048}, {34043, 37625}, {34120, 46878}, {34586, 63391}, {36011, 46883}, {36279, 54418}, {37022, 60415}, {37437, 37798}, {37438, 37695}, {37482, 39598}, {37613, 56960}, {51755, 53592}, {54400, 64044}, {55475, 55890}, {55481, 55885}, {56148, 63435}

X(64053) = reflection of X(i) in X(j) for these {i,j}: {1, 32047}, {3157, 64055}, {64054, 1}
X(64053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30, 64054}, {3, 34, 37697}, {4, 4296, 1060}, {30, 32047, 1}, {221, 37498, 3157}, {999, 39568, 9645}, {1394, 5709, 52407}

X(64054) = ORTHOLOGY CENTER OF THESE TRIANGLES: INTANGENTS AND X(3)-CROSSPEDAL-OF-X(155)

Barycentrics    a*(a^6+(b-c)^2*(b+c)^4-a^4*(b^2+4*b*c+c^2)-a^2*(b^4-2*b^3*c-2*b^2*c^2-2*b*c^3+c^4)) : :

X(64054) lies on these lines: {1, 30}, {3, 33}, {4, 1062}, {5, 1040}, {11, 23335}, {19, 20831}, {20, 1060}, {26, 35}, {34, 382}, {36, 12084}, {55, 7387}, {56, 9629}, {78, 55917}, {84, 52407}, {90, 2361}, {140, 9817}, {355, 36985}, {406, 52365}, {485, 9631}, {497, 34938}, {499, 44441}, {511, 6238}, {517, 1854}, {534, 30145}, {546, 19372}, {550, 1038}, {582, 1728}, {602, 2310}, {612, 7302}, {614, 9669}, {920, 53524}, {942, 990}, {971, 1498}, {1068, 10431}, {1069, 2192}, {1071, 60691}, {1074, 44229}, {1103, 18528}, {1147, 10535}, {1478, 4354}, {1479, 14790}, {1503, 12428}, {1614, 9637}, {1657, 9642}, {1658, 5010}, {1722, 12019}, {1807, 3345}, {1824, 13730}, {1864, 36754}, {1870, 3146}, {1936, 24467}, {2000, 3916}, {2330, 64052}, {2654, 37615}, {2777, 12888}, {2794, 39822}, {3149, 60415}, {3270, 45186}, {3295, 4319}, {3465, 37700}, {3529, 4296}, {3553, 42459}, {3564, 12910}, {3583, 18569}, {3586, 33178}, {3920, 34608}, {4123, 7283}, {4294, 31305}, {4316, 34350}, {4347, 28150}, {5217, 14070}, {5268, 10154}, {5272, 10593}, {5432, 13383}, {5446, 11436}, {5691, 9576}, {5707, 10391}, {6000, 7352}, {6285, 9931}, {6644, 54428}, {6851, 7952}, {6923, 40950}, {6985, 17102}, {7004, 37532}, {7070, 7330}, {7071, 11414}, {7078, 40263}, {7129, 38292}, {7191, 44442}, {7221, 9668}, {7280, 11250}, {7355, 14915}, {7517, 52427}, {7580, 37565}, {7741, 13371}, {7745, 9594}, {7747, 9635}, {7756, 9636}, {7951, 15761}, {8141, 61763}, {9371, 11499}, {9577, 64005}, {9595, 63548}, {9627, 12943}, {9630, 12953}, {9632, 42260}, {9638, 34148}, {9640, 57288}, {9798, 44670}, {10060, 12163}, {10071, 14216}, {10118, 17702}, {11248, 51361}, {11363, 37241}, {11398, 18534}, {11429, 64049}, {11446, 64050}, {11461, 64051}, {12684, 23072}, {13369, 41344}, {13391, 32168}, {14872, 41339}, {18324, 59325}, {18377, 18514}, {18513, 44279}, {18922, 64048}, {19354, 36747}, {19366, 40647}, {21147, 28160}, {22793, 34036}, {23698, 39851}, {24430, 26921}, {26956, 41587}, {27378, 38462}, {27505, 56876}, {28164, 59285}, {31424, 56317}, {34351, 52793}, {34586, 63988}, {35194, 55104}, {37504, 56225}, {37525, 51696}, {37584, 44706}, {53592, 59647}, {55476, 55885}, {55482, 55890}

X(64054) = reflection of X(i) in X(j) for these {i,j}: {1, 8144}, {64053, 1}
X(64054) = pole of line {942, 64020} with respect to the Feuerbach hyperbola
X(64054) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3345), X(56844)}}, {{A, B, C, X(52372), X(55917)}}
X(64054) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30, 64053}, {3, 33, 37696}, {4, 1062, 37697}, {4, 3100, 1062}, {20, 6198, 1060}, {30, 8144, 1}, {34, 9643, 18455}, {382, 18455, 34}, {550, 37729, 1038}, {1657, 9642, 18447}, {2192, 37498, 1069}, {3146, 9538, 1870}, {6198, 9539, 9644}, {9641, 18455, 9643}, {36985, 54295, 355}

X(64055) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(1) AND AYME

Barycentrics    a*(a+b-c)*(a-b+c)*(2*a^4+a^3*(b+c)-(b^2-c^2)^2-a^2*(b^2+c^2)-a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64055) lies on these lines: {1, 971}, {3, 223}, {4, 18623}, {5, 34050}, {6, 1448}, {28, 1439}, {30, 5930}, {34, 222}, {40, 22117}, {56, 56848}, {58, 1427}, {65, 267}, {72, 651}, {73, 500}, {77, 405}, {109, 227}, {221, 517}, {225, 6357}, {226, 37594}, {241, 1724}, {269, 1453}, {278, 57282}, {307, 49716}, {355, 34049}, {443, 54425}, {478, 37613}, {518, 4347}, {603, 1465}, {610, 38292}, {664, 7283}, {859, 1410}, {912, 32047}, {948, 4340}, {1038, 5044}, {1040, 31805}, {1060, 5777}, {1071, 1870}, {1079, 8069}, {1103, 6244}, {1104, 4306}, {1214, 1935}, {1385, 1455}, {1386, 4298}, {1406, 57277}, {1413, 9940}, {1422, 6913}, {1426, 1437}, {1457, 24928}, {1461, 2360}, {1466, 56418}, {1482, 34039}, {1498, 56294}, {1745, 46974}, {1785, 22792}, {1828, 26884}, {1875, 7335}, {1876, 18732}, {1892, 18629}, {1943, 5295}, {2122, 31788}, {2771, 19469}, {3074, 31658}, {3468, 17102}, {3555, 4318}, {3560, 34052}, {3671, 4667}, {3745, 5290}, {3824, 37695}, {3916, 17080}, {3947, 4682}, {4292, 43035}, {4314, 30621}, {4320, 16466}, {4334, 16478}, {4663, 12432}, {5018, 5247}, {5045, 34036}, {5439, 17074}, {5709, 23072}, {5728, 34028}, {5787, 34231}, {5806, 41344}, {5814, 56367}, {5932, 7498}, {6001, 59285}, {6223, 63965}, {6259, 7952}, {6260, 15252}, {7013, 37408}, {7053, 13737}, {7078, 31793}, {7100, 52384}, {7282, 18631}, {7290, 60897}, {7330, 47848}, {8099, 34025}, {8100, 34034}, {8270, 9370}, {8727, 53592}, {8808, 52260}, {9121, 38288}, {9840, 51647}, {9947, 34041}, {9955, 34029}, {9956, 34030}, {9957, 34040}, {9959, 34027}, {10361, 34120}, {10441, 34044}, {11018, 36746}, {11214, 26888}, {11363, 56816}, {11700, 37837}, {12488, 34037}, {12489, 34038}, {12490, 34031}, {12491, 34026}, {12514, 15832}, {12709, 54292}, {15803, 36636}, {16869, 18243}, {18447, 40263}, {18480, 51421}, {18481, 56821}, {20122, 39791}, {20211, 24565}, {23070, 24474}, {23071, 37585}, {24025, 64128}, {26892, 40985}, {28160, 56819}, {30456, 59681}, {33178, 63995}, {33649, 61231}, {33697, 38945}, {34045, 35631}, {34491, 37565}, {34823, 36949}, {36118, 44698}, {37257, 51413}, {37305, 51490}, {37404, 52097}, {37424, 59613}, {37623, 52407}, {40152, 48882}, {40611, 43924}, {41339, 64005}, {48883, 63203}, {50193, 54400}, {54289, 64171}, {57477, 58798}, {63396, 64041}

X(64055) = midpoint of X(i) and X(j) for these {i,j}: {1, 64057}, {221, 21147}, {3157, 64053}
X(64055) = reflection of X(i) in X(j) for these {i,j}: {19904, 1385}
X(64055) = X(i)-Dao conjugate of X(j) for these {i, j}: {4292, 23661}
X(64055) = intersection, other than A, B, C, of circumconics {{A, B, C, X(267), X(3062)}}, {{A, B, C, X(972), X(12688)}}, {{A, B, C, X(5932), X(15881)}}, {{A, B, C, X(7037), X(57392)}}
X(64055) = barycentric product X(i)*X(j) for these (i, j): {57, 64002}
X(64055) = barycentric quotient X(i)/X(j) for these (i, j): {64002, 312}
X(64055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 64057, 971}, {6, 1448, 37544}, {34, 222, 942}, {109, 227, 3579}, {221, 21147, 517}, {223, 1394, 3}, {223, 3182, 15881}, {603, 1465, 37582}, {1060, 8757, 5777}, {1104, 6610, 4306}, {6259, 59606, 7952}, {34036, 34046, 5045}

X(64056) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTIPEDAL-OF-X(80) AND X(4)-CROSSPEDAL-OF-X(1)

Barycentrics    a^4+9*a^2*b*c-3*a^3*(b+c)-(b^2-c^2)^2+a*(3*b^3-5*b^2*c-5*b*c^2+3*c^3) : :
X(64056) = -3*X[2]+2*X[64137], -2*X[11]+3*X[3679], -3*X[165]+2*X[64191], -3*X[392]+4*X[58663], -4*X[1125]+5*X[64141], -4*X[1387]+5*X[1698], -4*X[3036]+5*X[4668], -5*X[3617]+4*X[6702]

X(64056) lies on these lines: {1, 1145}, {2, 64137}, {8, 80}, {10, 1320}, {11, 3679}, {35, 25438}, {36, 100}, {40, 550}, {46, 18802}, {104, 5288}, {119, 7982}, {145, 214}, {165, 64191}, {244, 24864}, {355, 14217}, {392, 58663}, {484, 38455}, {515, 64136}, {517, 10742}, {518, 11571}, {528, 4677}, {551, 50894}, {643, 56950}, {956, 13205}, {958, 63281}, {960, 17652}, {1125, 64141}, {1317, 1420}, {1387, 1698}, {1484, 11524}, {1512, 4867}, {1537, 11531}, {1647, 10700}, {1737, 41702}, {1749, 44669}, {1788, 41554}, {1862, 54397}, {2093, 34690}, {2316, 21942}, {2550, 12647}, {2800, 5904}, {2829, 7991}, {2932, 12513}, {3036, 4668}, {3120, 4792}, {3241, 50841}, {3340, 10956}, {3583, 13271}, {3585, 32537}, {3617, 6702}, {3621, 6224}, {3622, 58453}, {3625, 11684}, {3626, 21630}, {3654, 38602}, {3656, 61580}, {3680, 5533}, {3689, 22935}, {3698, 58587}, {3746, 13278}, {3880, 10073}, {3885, 37702}, {3893, 19914}, {3913, 59334}, {4302, 34711}, {4530, 4752}, {4669, 10707}, {4678, 38213}, {4711, 58683}, {4745, 59377}, {4816, 62616}, {4863, 62354}, {4996, 8715}, {5119, 10050}, {5258, 10058}, {5425, 49626}, {5442, 56036}, {5445, 22837}, {5537, 48695}, {5587, 64138}, {5657, 11715}, {5687, 22560}, {5690, 12737}, {5727, 34719}, {5818, 16174}, {5840, 5881}, {5844, 6265}, {5853, 41700}, {5855, 41689}, {5882, 34474}, {5902, 11046}, {5903, 10052}, {6174, 12735}, {6246, 59388}, {6264, 11219}, {6667, 19875}, {6735, 63210}, {6788, 17460}, {7989, 38038}, {8148, 12611}, {8197, 13230}, {8204, 13228}, {8666, 17100}, {9024, 49688}, {9588, 21154}, {9589, 52836}, {9624, 58421}, {9780, 32557}, {9945, 62617}, {10057, 10914}, {10087, 12640}, {10222, 38752}, {10609, 58887}, {10728, 28194}, {10755, 49529}, {10912, 18395}, {10915, 11009}, {11024, 12736}, {11224, 15017}, {11249, 12331}, {11280, 12607}, {11698, 50908}, {11729, 16200}, {12248, 50810}, {12619, 59503}, {12702, 36972}, {12747, 51515}, {12750, 49168}, {12773, 34718}, {13143, 64200}, {13253, 37725}, {13464, 64008}, {14923, 37710}, {15178, 38762}, {15343, 62666}, {16189, 20400}, {16496, 51007}, {17636, 64043}, {17638, 34790}, {19077, 49233}, {19078, 49232}, {19876, 38026}, {20052, 20085}, {20095, 31145}, {20586, 40663}, {23153, 34151}, {24914, 47746}, {25055, 31235}, {25522, 34122}, {26725, 31397}, {30323, 39692}, {31419, 63270}, {31423, 38032}, {32157, 37616}, {32558, 46933}, {33814, 37727}, {34600, 41701}, {34641, 50890}, {34747, 35023}, {35616, 35636}, {36922, 52050}, {36975, 63136}, {36977, 37524}, {37546, 54065}, {37707, 59330}, {37711, 64202}, {38141, 61258}, {38665, 64188}, {38693, 43174}, {38757, 58245}, {38759, 63469}, {45310, 51066}, {46684, 59417}, {48680, 50798}, {49469, 51062}, {49681, 51157}, {58625, 62854}, {59400, 61553}

X(64056) = midpoint of X(i) and X(j) for these {i,j}: {3621, 6224}, {3632, 5541}
X(64056) = reflection of X(i) in X(j) for these {i,j}: {1, 1145}, {36, 51433}, {46, 18802}, {80, 8}, {104, 11362}, {145, 214}, {149, 15863}, {1320, 10}, {3241, 50841}, {3633, 1317}, {3679, 50842}, {5541, 13996}, {5697, 64139}, {5903, 39776}, {7972, 100}, {7982, 119}, {8148, 12611}, {9589, 52836}, {10707, 4669}, {10755, 49529}, {11219, 63143}, {11531, 1537}, {12531, 3625}, {12653, 11}, {12737, 5690}, {12751, 64140}, {12758, 14740}, {13143, 64200}, {13253, 37725}, {14217, 355}, {16496, 51007}, {17638, 34790}, {17652, 960}, {21630, 3626}, {23153, 34151}, {25416, 3035}, {26726, 1}, {30323, 55016}, {34747, 50843}, {34789, 12751}, {36975, 63136}, {37727, 33814}, {41702, 1737}, {49176, 19914}, {49469, 51062}, {49681, 51157}, {50890, 34641}, {50891, 3679}, {50893, 31145}, {50894, 551}, {51093, 6174}, {62617, 9945}, {63210, 6735}, {64145, 40}
X(64056) = anticomplement of X(64137)
X(64056) = X(i)-Dao conjugate of X(j) for these {i, j}: {64137, 64137}
X(64056) = pole of line {1537, 39771} with respect to the Suppa-Cucoanes circle
X(64056) = intersection, other than A, B, C, of circumconics {{A, B, C, X(36), X(2802)}}, {{A, B, C, X(80), X(2718)}}, {{A, B, C, X(765), X(50914)}}, {{A, B, C, X(5559), X(38544)}}, {{A, B, C, X(12641), X(52409)}}, {{A, B, C, X(18359), X(37222)}}
X(64056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5854, 26726}, {8, 149, 15863}, {8, 3952, 50914}, {10, 1320, 16173}, {11, 12653, 50891}, {40, 952, 64145}, {100, 519, 7972}, {100, 7972, 64011}, {149, 15863, 80}, {517, 12751, 34789}, {517, 64140, 12751}, {519, 51433, 36}, {952, 13996, 5541}, {1145, 25416, 3035}, {1145, 26726, 64012}, {1145, 5854, 1}, {2802, 14740, 12758}, {2802, 15863, 149}, {2802, 64139, 5697}, {3035, 5854, 25416}, {3626, 21630, 59415}, {3632, 5541, 952}, {3633, 15015, 1317}, {3679, 12653, 11}, {4668, 37718, 3036}, {11224, 15017, 64192}, {12758, 14740, 5692}, {13278, 51506, 3746}, {39776, 49169, 12749}

X(64057) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(1) AND CEVIAN OF X(280)

Barycentrics    a*(a^6-2*a^4*(b-c)^2+a^5*(b+c)-2*b*c*(b^2-c^2)^2+a^2*(b-c)^2*(b^2+c^2)-2*a^3*(b^3+c^3)+a*(b^5-b^4*c-b*c^4+c^5)) : :
X(64057) = -3*X[3576]+2*X[19904]

X(64057) lies on circumconic {{A, B, C, X(3062), X(3362)}} and on these lines: {1, 971}, {3, 1745}, {4, 222}, {6, 4292}, {10, 55406}, {20, 651}, {30, 3157}, {34, 1071}, {40, 2956}, {46, 4641}, {55, 1777}, {73, 1012}, {84, 223}, {109, 11500}, {212, 37426}, {221, 515}, {226, 36746}, {227, 1158}, {238, 60897}, {241, 1728}, {255, 7580}, {269, 10396}, {280, 20211}, {377, 55400}, {382, 23070}, {394, 64002}, {405, 4303}, {443, 55432}, {475, 26932}, {513, 3556}, {516, 64069}, {603, 2635}, {610, 3182}, {912, 64053}, {940, 9612}, {944, 34040}, {946, 34046}, {1035, 61227}, {1038, 5777}, {1044, 5247}, {1060, 40263}, {1068, 6357}, {1076, 58798}, {1103, 10860}, {1191, 4311}, {1210, 1407}, {1214, 7330}, {1259, 61220}, {1394, 1490}, {1406, 1837}, {1413, 6260}, {1427, 62810}, {1433, 6223}, {1448, 44547}, {1455, 6261}, {1461, 37818}, {1464, 22760}, {1465, 63399}, {1466, 37732}, {1478, 5711}, {1498, 5930}, {1617, 3073}, {1657, 23071}, {1753, 51490}, {1763, 15498}, {1785, 6259}, {1838, 7534}, {1854, 59285}, {1936, 23072}, {2003, 5706}, {2122, 12667}, {2183, 37273}, {2801, 4347}, {2823, 7973}, {2829, 56819}, {3075, 19541}, {3091, 17074}, {3146, 3562}, {3173, 37498}, {3176, 32714}, {3330, 18641}, {3468, 12684}, {3576, 19904}, {3784, 37415}, {4185, 26892}, {4186, 26884}, {4200, 26871}, {4293, 16466}, {4295, 4644}, {4296, 12528}, {4306, 57278}, {4333, 56535}, {4383, 15803}, {4551, 10310}, {5691, 34043}, {5710, 9613}, {5784, 54305}, {5787, 56814}, {5881, 60689}, {5932, 40836}, {6001, 21147}, {6245, 34042}, {6256, 51421}, {6734, 22129}, {6759, 36059}, {6834, 43043}, {6891, 52659}, {6913, 37523}, {6985, 52407}, {7074, 31730}, {7299, 37578}, {7354, 64020}, {7497, 20122}, {7971, 34039}, {8270, 14872}, {8614, 12943}, {9121, 47848}, {9122, 40152}, {9799, 34035}, {9940, 19372}, {10404, 61398}, {10571, 12114}, {11573, 56960}, {12410, 15310}, {12436, 17825}, {12572, 17811}, {12675, 34036}, {13369, 37697}, {13411, 37501}, {15836, 34052}, {16127, 38357}, {18242, 34030}, {18541, 36750}, {19349, 37468}, {20744, 49130}, {22097, 37062}, {22350, 37022}, {23144, 64003}, {26888, 47371}, {34028, 36991}, {34029, 63980}, {34033, 63981}, {36984, 52097}, {37387, 45963}, {37404, 63436}, {37413, 63397}, {37507, 46887}, {37530, 64152}, {37537, 54301}, {37541, 37699}, {39796, 54394}, {40267, 56825}, {41227, 63434}, {48482, 51424}, {51616, 54227}, {56821, 64120}, {56940, 60876}

X(64057) = reflection of X(i) in X(j) for these {i,j}: {1, 64055}, {1854, 59285}
X(64057) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 8757, 34048}, {84, 223, 17102}, {603, 2635, 3149}, {1456, 12680, 1}, {2003, 9579, 5706}, {6223, 18623, 7952}, {23072, 37411, 1936}, {36742, 57282, 37543}

X(64058) = PERSPECTOR OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(2) AND PEDAL-OF-X(6)

Barycentrics    (a^2-b^2-c^2)*(3*a^2+b^2-c^2)*(3*a^2-b^2+c^2) : :

X(64058) lies on these lines: {2, 98}, {3, 40911}, {4, 14530}, {6, 4232}, {20, 6800}, {22, 61044}, {23, 47571}, {25, 63030}, {49, 3547}, {54, 3089}, {69, 13394}, {107, 40138}, {154, 5480}, {156, 7404}, {185, 7998}, {193, 7493}, {217, 9463}, {323, 62174}, {376, 64094}, {378, 38396}, {468, 14912}, {549, 44833}, {631, 6090}, {1147, 7400}, {1181, 3523}, {1204, 41462}, {1249, 37070}, {1370, 61655}, {1495, 14853}, {1503, 52284}, {1614, 3088}, {1992, 32269}, {1993, 10565}, {1995, 18919}, {2452, 46869}, {2883, 14528}, {3066, 35266}, {3090, 31804}, {3091, 14389}, {3146, 41482}, {3167, 7494}, {3292, 10519}, {3431, 10293}, {3522, 13367}, {3525, 18914}, {3533, 26944}, {3549, 9704}, {3618, 35259}, {3620, 7495}, {3622, 64040}, {3796, 37669}, {3832, 19467}, {3854, 10619}, {4233, 44094}, {4549, 18475}, {4846, 38726}, {5020, 51732}, {5032, 7426}, {5050, 40132}, {5056, 6146}, {5068, 18945}, {5093, 37897}, {5094, 39874}, {5265, 19349}, {5281, 19354}, {5640, 6467}, {5646, 50983}, {5656, 11430}, {6353, 11402}, {6618, 56297}, {6676, 11898}, {6755, 60161}, {7378, 11206}, {7386, 59553}, {7392, 8780}, {7398, 35264}, {7408, 44110}, {7409, 31383}, {7487, 9707}, {7585, 19356}, {7586, 19355}, {8550, 37643}, {8779, 14930}, {8972, 18924}, {9545, 59349}, {9777, 62979}, {9833, 43841}, {10132, 55897}, {10133, 55893}, {10154, 61624}, {10192, 11433}, {10303, 18909}, {10304, 40112}, {10602, 26255}, {10605, 15692}, {10721, 49670}, {10783, 62957}, {10784, 62956}, {11002, 15073}, {11064, 25406}, {11101, 19783}, {11160, 47596}, {11169, 51990}, {11245, 38282}, {11422, 21637}, {11464, 37460}, {13171, 35473}, {13352, 34621}, {13851, 61954}, {13941, 18923}, {15032, 35486}, {15360, 63027}, {15504, 44535}, {15705, 21663}, {16051, 48906}, {17578, 43831}, {17825, 59699}, {18913, 61820}, {18918, 61936}, {18950, 37453}, {19363, 63033}, {19364, 63032}, {20423, 32237}, {21640, 63016}, {21641, 63015}, {21659, 50689}, {25320, 62516}, {26869, 52290}, {26874, 61374}, {26937, 61834}, {31099, 59771}, {32621, 37962}, {33201, 46900}, {33522, 37672}, {33748, 63084}, {34148, 52404}, {35265, 63036}, {35283, 63119}, {35484, 41450}, {37665, 38918}, {40947, 54375}, {44109, 61506}, {44210, 63428}, {44212, 53091}, {47391, 61113}, {47597, 54218}, {48873, 59343}, {53093, 61507}, {58378, 61842}, {61657, 62981}

X(64058) = pole of line {511, 5032} with respect to the Jerabek hyperbola
X(64058) = pole of line {230, 52284} with respect to the Kiepert hyperbola
X(64058) = pole of line {511, 1597} with respect to the Stammler hyperbola
X(64058) = pole of line {325, 52284} with respect to the Wallace hyperbola
X(64058) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(46328)}}, {{A, B, C, X(98), X(1285)}}, {{A, B, C, X(287), X(60193)}}, {{A, B, C, X(647), X(22112)}}, {{A, B, C, X(5651), X(43718)}}, {{A, B, C, X(11653), X(55981)}}, {{A, B, C, X(43650), X(51336)}}, {{A, B, C, X(45088), X(53174)}}
X(64058) = barycentric product X(i)*X(j) for these (i, j): {184, 46328}, {1285, 69}
X(64058) = barycentric quotient X(i)/X(j) for these (i, j): {1285, 4}, {46328, 18022}
X(64058) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 26864, 64059}, {6, 35260, 4232}, {154, 11427, 6995}, {468, 14912, 63081}, {1495, 14853, 52301}, {6353, 11402, 63031}, {6800, 37645, 20}, {8550, 61680, 37643}, {10192, 11433, 62973}, {10192, 17809, 11433}, {11206, 23292, 7378}, {26864, 61690, 4}, {35264, 63085, 7398}, {37643, 61680, 53857}

X(64059) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(2) AND X(4)-CIRCUMCONCEVIAN OF X(2)

Barycentrics    11*a^6-3*a^2*(b^2-c^2)^2-7*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2) : :
X(64059) = -X[2]+4*X[154], -X[4]+10*X[14530], -4*X[64]+13*X[21734], X[145]+8*X[40660], 8*X[156]+X[31305], 8*X[550]+X[54211], 4*X[1498]+5*X[3522], 8*X[1660]+X[7500], 8*X[2883]+X[5059], X[3060]+2*X[34750], 7*X[3090]+2*X[64033], 5*X[3091]+4*X[9833] and many others

X(64059) lies on these lines: {2, 154}, {3, 44833}, {4, 14530}, {6, 52301}, {20, 110}, {22, 62174}, {23, 159}, {25, 14912}, {30, 64177}, {64, 21734}, {107, 15258}, {125, 53857}, {145, 40660}, {156, 31305}, {161, 63012}, {184, 6995}, {206, 7693}, {323, 19149}, {376, 6090}, {390, 10535}, {394, 59343}, {468, 39874}, {523, 45292}, {550, 54211}, {1495, 4232}, {1498, 3522}, {1614, 7487}, {1619, 6636}, {1660, 7500}, {1899, 62973}, {1971, 5304}, {1995, 39879}, {2393, 5032}, {2883, 5059}, {3060, 34750}, {3079, 56296}, {3088, 9707}, {3089, 12022}, {3090, 64033}, {3091, 9833}, {3146, 34782}, {3167, 34608}, {3357, 41462}, {3426, 35483}, {3523, 10282}, {3525, 34780}, {3528, 12315}, {3566, 9168}, {3600, 26888}, {3620, 5596}, {3623, 64022}, {3832, 14389}, {3839, 18400}, {3854, 41362}, {5012, 7398}, {5056, 23325}, {5068, 64037}, {5071, 61606}, {5159, 21968}, {5286, 44116}, {5640, 33748}, {5650, 33750}, {5893, 50690}, {5894, 62102}, {5895, 62152}, {5921, 7493}, {5925, 62125}, {6000, 7998}, {6225, 50693}, {6247, 61820}, {6353, 26869}, {6696, 61804}, {6794, 61207}, {7378, 31383}, {7386, 8780}, {7392, 38110}, {7408, 11427}, {7409, 23292}, {7486, 18381}, {7492, 15577}, {7495, 61610}, {7496, 63420}, {7519, 63082}, {7585, 10533}, {7586, 10534}, {7605, 23327}, {7714, 11402}, {8549, 15018}, {8550, 41424}, {8567, 62060}, {8721, 35282}, {9143, 11160}, {9463, 32445}, {9485, 55121}, {9543, 19088}, {9909, 34380}, {9924, 51170}, {10117, 15582}, {10182, 10303}, {10193, 61805}, {10295, 41450}, {10519, 35268}, {10536, 17784}, {10537, 20075}, {10565, 26881}, {10606, 62063}, {11004, 34117}, {11064, 14927}, {11180, 61644}, {11202, 15692}, {11204, 62059}, {11241, 63059}, {11242, 63058}, {11243, 63079}, {11244, 63080}, {11245, 62979}, {11456, 37460}, {12007, 31860}, {12112, 35485}, {12225, 32605}, {12250, 62097}, {12283, 44084}, {12289, 46682}, {12324, 15717}, {12964, 43511}, {12970, 43512}, {13093, 21735}, {13171, 21844}, {13416, 64030}, {13419, 43841}, {14002, 15581}, {14227, 62956}, {14242, 62957}, {14528, 16656}, {14683, 15647}, {14862, 50691}, {14925, 37423}, {15139, 61088}, {15311, 62120}, {15428, 40884}, {15448, 37643}, {15580, 56924}, {15589, 57275}, {15683, 40112}, {15721, 23329}, {16063, 41735}, {16654, 19357}, {16657, 18925}, {16981, 44668}, {17576, 26637}, {17578, 17845}, {17813, 63000}, {17819, 63015}, {17820, 63016}, {18376, 61966}, {18533, 40114}, {18621, 61155}, {18919, 47459}, {18950, 62978}, {19132, 23326}, {19153, 63127}, {19708, 35450}, {20070, 40658}, {20079, 61737}, {20080, 34774}, {20299, 61856}, {20427, 62110}, {22802, 49140}, {23049, 63036}, {23061, 34779}, {23291, 61691}, {23324, 61944}, {30402, 63032}, {30403, 63033}, {31099, 36989}, {31101, 41602}, {32111, 49670}, {32237, 63722}, {33884, 34146}, {34785, 49135}, {35325, 41367}, {35356, 37668}, {35502, 38396}, {36851, 62937}, {37897, 39899}, {37904, 50974}, {37910, 44456}, {37980, 54184}, {40132, 48906}, {40686, 61842}, {40885, 53016}, {41374, 51358}, {41580, 62187}, {41715, 62188}, {44082, 61712}, {44442, 59553}, {44762, 61791}, {46034, 62950}, {46936, 64063}, {47313, 51028}, {48672, 62127}, {48912, 63026}, {50688, 61749}, {50689, 64024}, {51350, 54961}, {52404, 54040}, {56923, 63017}, {58188, 64027}, {58795, 62078}, {59767, 64196}, {61138, 61540}, {61655, 62964}, {61721, 62048}

X(64059) = midpoint of X(i) and X(j) for these {i,j}: {11206, 35260}
X(64059) = reflection of X(i) in X(j) for these {i,j}: {2, 35260}, {32064, 61735}, {35260, 154}, {61735, 10192}
X(64059) = pole of line {4240, 9189} with respect to the Kiepert parabola
X(64059) = pole of line {1350, 6000} with respect to the Stammler hyperbola
X(64059) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1294), X(3424)}}, {{A, B, C, X(42287), X(60193)}}
X(64059) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 26864, 64058}, {154, 1503, 35260}, {184, 6995, 63030}, {1495, 6776, 4232}, {1503, 10192, 61735}, {1503, 61735, 32064}, {3522, 15066, 40911}, {4232, 6776, 63081}, {10192, 32064, 2}, {10282, 34781, 3523}, {11206, 35260, 1503}, {12324, 17821, 15717}, {15448, 64080, 37643}

X(64060) = ISOTOMIC CONJUGATE OF X(54496)

Barycentrics    a^6-4*a^4*(b^2+c^2)-2*(b^2-c^2)^2*(b^2+c^2)+a^2*(5*b^4-2*b^2*c^2+5*c^4) : :
X(64060) = X[1498]+2*X[11411], -2*X[6193]+5*X[17821], -X[9936]+4*X[13383], -7*X[10244]+4*X[45185], -X[12085]+4*X[52104], -2*X[12164]+5*X[64024], -4*X[12359]+X[37498], 2*X[12429]+X[17845], -5*X[16195]+2*X[61751], -4*X[34477]+3*X[47391], -4*X[58434]+3*X[64177]

X(64060) lies on these lines: {2, 6}, {3, 10112}, {22, 41724}, {25, 15069}, {30, 64}, {51, 10516}, {52, 381}, {76, 54629}, {154, 3564}, {155, 10201}, {161, 542}, {376, 6146}, {427, 11477}, {428, 47353}, {441, 14023}, {511, 1853}, {539, 2917}, {549, 13292}, {569, 5054}, {1151, 11090}, {1152, 11091}, {1154, 14852}, {1209, 5055}, {1350, 1899}, {1351, 21243}, {1352, 17810}, {1370, 53097}, {1494, 47269}, {1498, 11411}, {1503, 34608}, {1620, 63631}, {2052, 54922}, {2781, 54038}, {2888, 52008}, {3060, 53023}, {3167, 5965}, {3292, 37453}, {3448, 48872}, {3519, 7506}, {3532, 30552}, {3534, 37478}, {3545, 45089}, {3592, 56506}, {3594, 56504}, {3796, 45968}, {3830, 18474}, {3917, 26869}, {4641, 53816}, {5020, 34507}, {5050, 11225}, {5064, 12294}, {5085, 11245}, {5392, 54666}, {5485, 54867}, {5562, 16072}, {6090, 61645}, {6145, 34725}, {6193, 17821}, {6293, 36982}, {6425, 56498}, {6426, 56497}, {6503, 8553}, {6509, 40995}, {6617, 15526}, {6676, 17809}, {7232, 54284}, {7494, 8550}, {7499, 53093}, {7507, 14531}, {7539, 15004}, {7571, 15019}, {7714, 11180}, {7734, 48876}, {7751, 52251}, {7768, 41235}, {7784, 40814}, {8280, 9974}, {8281, 9975}, {8538, 30771}, {8716, 35937}, {8780, 32223}, {9225, 63611}, {9306, 11898}, {9936, 13383}, {10192, 63174}, {10244, 45185}, {10302, 54910}, {10519, 18950}, {10605, 44458}, {10691, 54173}, {11178, 58470}, {11402, 61644}, {11412, 31180}, {11441, 46451}, {11442, 33586}, {11469, 50687}, {11550, 48910}, {11750, 15681}, {12085, 52104}, {12164, 64024}, {12359, 37498}, {12429, 17845}, {13361, 61545}, {13428, 23261}, {13439, 23251}, {13881, 60524}, {13966, 55471}, {14457, 34664}, {15068, 44270}, {15360, 51027}, {15644, 26944}, {15685, 20127}, {15693, 37513}, {16195, 61751}, {16266, 61736}, {16419, 40107}, {17814, 41587}, {18573, 63805}, {18951, 37514}, {20266, 62244}, {20977, 63541}, {21974, 51175}, {23061, 30744}, {23291, 63428}, {25738, 37486}, {25893, 33087}, {26932, 55405}, {26942, 55406}, {27376, 62955}, {29181, 32064}, {31236, 38397}, {31383, 47582}, {32000, 37873}, {32225, 44077}, {32599, 44260}, {32859, 48381}, {33522, 44882}, {33529, 42156}, {33530, 42153}, {34048, 63844}, {34351, 63649}, {34380, 61735}, {34477, 47391}, {34505, 52282}, {35603, 37943}, {36749, 48411}, {37197, 45187}, {37454, 53858}, {37487, 44268}, {37489, 38321}, {38317, 61677}, {39284, 54636}, {40996, 45200}, {41615, 44470}, {44518, 51481}, {47558, 55977}, {51024, 62964}, {54132, 62975}, {54772, 60221}, {54776, 54778}, {56456, 62245}, {56457, 62207}, {58434, 64177}, {58891, 63735}, {59343, 64196}, {59699, 62973}, {61700, 62187}

X(64060) = reflection of X(i) in X(j) for these {i,j}: {155, 10201}, {3167, 61646}, {10201, 63734}, {16266, 61736}, {34751, 61666}, {37498, 44441}, {44441, 12359}, {63174, 10192}, {63649, 34351}
X(64060) = isotomic conjugate of X(54496)
X(64060) = X(i)-complementary conjugate of X(j) for these {i, j}: {54930, 2887}
X(64060) = pole of line {6467, 15069} with respect to the Jerabek hyperbola
X(64060) = pole of line {2, 54930} with respect to the Kiepert hyperbola
X(64060) = pole of line {6, 9545} with respect to the Stammler hyperbola
X(64060) = pole of line {2, 54496} with respect to the Wallace hyperbola
X(64060) = pole of line {525, 7658} with respect to the dual conic of 2nd DrozFarny circle
X(64060) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(54629)}}, {{A, B, C, X(64), X(1993)}}, {{A, B, C, X(68), X(37669)}}, {{A, B, C, X(394), X(54922)}}, {{A, B, C, X(597), X(54910)}}, {{A, B, C, X(671), X(37672)}}, {{A, B, C, X(1992), X(54867)}}, {{A, B, C, X(1994), X(56361)}}, {{A, B, C, X(2052), X(61658)}}, {{A, B, C, X(2407), X(47269)}}, {{A, B, C, X(11427), X(14457)}}, {{A, B, C, X(13157), X(39113)}}, {{A, B, C, X(13854), X(37689)}}, {{A, B, C, X(37688), X(59756)}}, {{A, B, C, X(39284), X(63094)}}, {{A, B, C, X(41770), X(62545)}}, {{A, B, C, X(52154), X(53414)}}, {{A, B, C, X(54636), X(64062)}}
X(64060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 17834, 64037}, {68, 64066, 17834}, {343, 6515, 6}, {511, 61666, 34751}, {1352, 41588, 17810}, {3167, 61646, 61680}, {3292, 37453, 59551}, {5064, 21969, 54131}, {5965, 61646, 3167}, {6676, 63722, 17809}, {11442, 33586, 36990}, {12359, 37498, 40686}, {34751, 61739, 1853}

X(64061) = PERSPECTOR OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(3) AND MCCAY

Barycentrics    a^2*(a^10-2*a^8*(b^2+c^2)-b^2*c^2*(b^2-c^2)^2*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^4+c^4)+a^4*(2*b^6+b^4*c^2+b^2*c^4+2*c^6)) : :
X(64061) = X[159]+3*X[5050], 5*X[631]+3*X[41719], X[1498]+3*X[10249], -7*X[3526]+3*X[61737], 3*X[5476]+X[34785], X[9924]+7*X[55711], -3*X[10168]+X[20299], -3*X[10182]+X[40107], -3*X[10250]+7*X[55708], -3*X[10606]+11*X[55684], -3*X[11204]+7*X[55681], -3*X[11216]+7*X[53092] and many others

X(64061) lies on these lines: {2, 15139}, {3, 1177}, {4, 18374}, {5, 182}, {6, 24}, {25, 63688}, {26, 9019}, {30, 63699}, {49, 8262}, {50, 37114}, {64, 1176}, {110, 15069}, {140, 44491}, {141, 7542}, {154, 1995}, {156, 542}, {159, 5050}, {161, 5422}, {184, 468}, {186, 37473}, {216, 37813}, {427, 44078}, {511, 1658}, {524, 1147}, {567, 41613}, {569, 597}, {575, 2393}, {576, 7575}, {578, 11745}, {631, 41719}, {685, 52641}, {1350, 19121}, {1352, 6639}, {1498, 10249}, {1511, 44493}, {1614, 5622}, {1656, 32379}, {1660, 44212}, {1971, 5038}, {1974, 3575}, {1992, 9545}, {2854, 8548}, {2883, 10984}, {2937, 61723}, {3043, 64104}, {3044, 64091}, {3047, 64103}, {3060, 62291}, {3147, 63129}, {3202, 39840}, {3205, 51200}, {3206, 51203}, {3357, 9968}, {3398, 15270}, {3518, 9971}, {3526, 61737}, {3542, 63658}, {3564, 10020}, {3566, 39501}, {3618, 7544}, {3827, 5885}, {3852, 39750}, {5026, 59530}, {5092, 15578}, {5097, 21852}, {5157, 34774}, {5476, 34785}, {5621, 6241}, {5640, 56924}, {5944, 15074}, {5946, 44494}, {5965, 47360}, {5969, 39811}, {6000, 15579}, {6146, 62375}, {6247, 13336}, {6293, 37126}, {6642, 40441}, {6644, 44480}, {6696, 37515}, {6697, 58445}, {6756, 51744}, {6776, 7505}, {6800, 15647}, {7488, 22151}, {7493, 58357}, {7507, 63629}, {7512, 54334}, {7526, 63723}, {7530, 63737}, {7547, 36990}, {7555, 63714}, {7556, 10510}, {7568, 34177}, {7569, 47355}, {7577, 32353}, {7998, 17847}, {8540, 9666}, {8541, 12061}, {8743, 28343}, {8989, 11265}, {9306, 58434}, {9407, 54003}, {9653, 19369}, {9707, 32246}, {9833, 13353}, {9924, 55711}, {9977, 32367}, {10018, 62376}, {10117, 15080}, {10168, 20299}, {10182, 40107}, {10250, 55708}, {10274, 21230}, {10297, 64196}, {10516, 43614}, {10606, 55684}, {10628, 33533}, {11003, 35260}, {11204, 55681}, {11206, 62937}, {11216, 53092}, {11255, 11649}, {11444, 17824}, {11454, 51941}, {11456, 15738}, {11459, 52697}, {11477, 34148}, {12007, 15585}, {12017, 12315}, {12022, 47455}, {12111, 56568}, {12605, 44882}, {13198, 26864}, {13289, 34513}, {13352, 32217}, {13367, 44102}, {13434, 17845}, {14076, 24206}, {14216, 14787}, {14530, 55701}, {14561, 18382}, {14853, 56918}, {14984, 32171}, {15135, 37920}, {15274, 32713}, {15448, 44080}, {15516, 39125}, {15533, 43572}, {15580, 50664}, {16813, 58079}, {17508, 34779}, {17714, 63697}, {18377, 29012}, {18378, 45034}, {18380, 39569}, {18400, 25555}, {18404, 46264}, {18475, 44479}, {18504, 43273}, {18583, 31830}, {19122, 41716}, {19124, 23047}, {19161, 21637}, {19165, 22240}, {19596, 26882}, {20423, 37472}, {20987, 39588}, {22234, 34788}, {22352, 41580}, {23292, 44077}, {23332, 37454}, {29181, 64052}, {32184, 37514}, {32299, 39562}, {32445, 39560}, {34545, 34751}, {34777, 53091}, {34778, 53094}, {35225, 61378}, {36201, 61749}, {37488, 64195}, {37511, 43898}, {37644, 61685}, {39879, 55705}, {43574, 53097}, {43651, 47352}, {43652, 54169}, {43813, 55676}, {44232, 61610}, {44492, 47391}, {50414, 55704}, {52028, 55699}, {52432, 54347}, {58058, 64092}

X(64061) = midpoint of X(i) and X(j) for these {i,j}: {3, 34117}, {6, 15577}, {26, 44469}, {141, 41729}, {182, 206}, {575, 10282}, {1147, 44470}, {3357, 9968}, {8549, 15581}, {9977, 32367}, {12007, 15585}, {18382, 36989}, {19149, 44883}, {34776, 51756}, {34779, 63431}, {37488, 64195}
X(64061) = reflection of X(i) in X(j) for these {i,j}: {6697, 58445}, {15578, 5092}, {15582, 10282}, {20300, 3589}, {24206, 58450}, {39125, 15516}
X(64061) = inverse of X(38397) in Stammler hyperbola
X(64061) = complement of X(34118)
X(64061) = pole of line {525, 34507} with respect to the 1st Brocard circle
X(64061) = pole of line {9517, 15451} with respect to the circumcircle
X(64061) = pole of line {13366, 50649} with respect to the Jerabek hyperbola
X(64061) = pole of line {32, 1594} with respect to the Kiepert hyperbola
X(64061) = pole of line {343, 858} with respect to the Stammler hyperbola
X(64061) = pole of line {16040, 33294} with respect to the Steiner inellipse
X(64061) = pole of line {1236, 7796} with respect to the Wallace hyperbola
X(64061) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 18338, 34117}
X(64061) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(39575)}}, {{A, B, C, X(54), X(18876)}}, {{A, B, C, X(64), X(27366)}}, {{A, B, C, X(1176), X(33629)}}, {{A, B, C, X(1177), X(2980)}}, {{A, B, C, X(3527), X(60589)}}, {{A, B, C, X(6403), X(60527)}}, {{A, B, C, X(14533), X(19151)}}, {{A, B, C, X(19189), X(36823)}}, {{A, B, C, X(34787), X(63154)}}, {{A, B, C, X(42313), X(44668)}}
X(64061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1576, 61748}, {3, 19153, 34117}, {3, 34117, 2781}, {4, 18374, 63663}, {6, 15577, 44668}, {6, 17821, 34787}, {6, 19128, 51730}, {26, 44469, 9019}, {154, 53093, 8549}, {154, 8549, 15581}, {182, 206, 1503}, {182, 23042, 206}, {575, 10282, 2393}, {1147, 44470, 524}, {1498, 10541, 10249}, {1503, 3589, 20300}, {1614, 5622, 64080}, {2393, 10282, 15582}, {5012, 43815, 53093}, {5085, 19132, 19149}, {5085, 19149, 44883}, {5092, 34146, 15578}, {5622, 38851, 32274}, {10192, 13567, 58439}, {13367, 44102, 50649}, {14561, 36989, 18382}, {17508, 34779, 63431}, {17821, 34787, 15577}, {23041, 34787, 17821}, {34776, 38317, 51756}, {51739, 63663, 4}

X(64062) = ISOGONAL CONJUGATE OF X(33631)

Barycentrics    (a^2-b^2-c^2)*(2*a^4+(b^2-c^2)^2-3*a^2*(b^2+c^2)) : :
X(64062) = -3*X[51]+4*X[10128], -4*X[5447]+3*X[43934], -3*X[5650]+2*X[45298], -4*X[6688]+3*X[61657], -3*X[7998]+X[45968], -7*X[7999]+4*X[64038], -4*X[9825]+X[14531], -5*X[11444]+2*X[12241], -5*X[11591]+2*X[15807], -3*X[15082]+2*X[32068], 2*X[16621]+X[64050], 2*X[31829]+X[45187] and many others

X(64062) lies on these lines: {2, 6}, {3, 9936}, {20, 15105}, {22, 15582}, {30, 5562}, {51, 10128}, {52, 10127}, {76, 52281}, {97, 1238}, {140, 1493}, {184, 48876}, {287, 57852}, {297, 7768}, {315, 52282}, {340, 52280}, {376, 63631}, {427, 34507}, {428, 511}, {465, 40712}, {466, 40711}, {472, 634}, {473, 633}, {487, 5406}, {488, 5407}, {539, 1216}, {542, 7667}, {549, 1092}, {553, 62402}, {576, 37439}, {671, 54922}, {1232, 6748}, {1352, 5064}, {1353, 43650}, {1370, 15069}, {1503, 2979}, {1531, 12101}, {1568, 5066}, {1899, 11898}, {3167, 13394}, {3260, 45793}, {3292, 6676}, {3519, 37452}, {3524, 35602}, {3564, 3917}, {3785, 59211}, {3796, 10519}, {3819, 5965}, {5133, 23061}, {5447, 43934}, {5485, 54785}, {5650, 45298}, {5651, 41588}, {5891, 16657}, {5907, 62962}, {6090, 62965}, {6504, 54776}, {6677, 41586}, {6688, 61657}, {6997, 11477}, {7484, 63722}, {7485, 8550}, {7499, 34986}, {7500, 53097}, {7576, 11412}, {7714, 14826}, {7767, 36212}, {7799, 34386}, {7811, 35937}, {7998, 45968}, {7999, 64038}, {8703, 63425}, {9306, 32269}, {9825, 14531}, {10154, 35266}, {10982, 11487}, {11140, 54783}, {11180, 44442}, {11206, 62174}, {11444, 12241}, {11540, 46452}, {11591, 15807}, {12100, 44683}, {12325, 26879}, {12359, 44752}, {14023, 37344}, {14831, 31810}, {14918, 53506}, {15004, 64067}, {15082, 32068}, {15311, 54040}, {15605, 32767}, {15690, 16163}, {16197, 43844}, {16266, 60763}, {16276, 51438}, {16621, 64050}, {17363, 54284}, {17713, 18282}, {17810, 54013}, {18553, 52285}, {20290, 23541}, {22115, 44201}, {22128, 26942}, {22129, 26872}, {23039, 44665}, {23140, 56457}, {23983, 42033}, {25962, 64072}, {26611, 33066}, {26871, 55466}, {27082, 62095}, {29181, 62188}, {31166, 37485}, {31383, 33878}, {31829, 45187}, {32000, 41244}, {32142, 32358}, {32820, 51350}, {32833, 35941}, {33524, 44762}, {34002, 41597}, {34116, 34351}, {34384, 44137}, {34565, 61624}, {34603, 41716}, {34608, 50967}, {34609, 50955}, {35259, 62979}, {36790, 42052}, {37943, 59659}, {39284, 54911}, {41008, 46832}, {41594, 58439}, {44078, 44213}, {44111, 51732}, {44134, 62953}, {44278, 51425}, {44324, 44325}, {44935, 46847}, {45089, 56965}, {45185, 59348}, {45303, 62980}, {47353, 62964}, {52193, 52348}, {52194, 52349}, {52283, 56865}, {53050, 62063}, {54496, 54636}, {54772, 60143}, {54867, 60114}, {56448, 62245}, {56449, 62207}, {59553, 61644}, {61677, 63632}

X(64062) = midpoint of X(i) and X(j) for these {i,j}: {7576, 11412}
X(64062) = reflection of X(i) in X(j) for these {i,j}: {52, 10127}, {7576, 64035}, {11245, 3819}, {16657, 5891}, {44935, 46847}, {62962, 5907}
X(64062) = isogonal conjugate of X(33631)
X(64062) = isotomic conjugate of X(39284)
X(64062) = complement of X(41628)
X(64062) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 33631}, {19, 1173}, {31, 39284}, {288, 2181}, {798, 33513}, {1096, 31626}, {1973, 40410}, {2179, 39286}, {2190, 59142}, {24019, 39180}, {31610, 62268}, {32676, 39183}
X(64062) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 39284}, {3, 33631}, {5, 59142}, {6, 1173}, {140, 53}, {233, 4}, {1493, 6}, {5421, 15559}, {6337, 40410}, {6503, 31626}, {11792, 2501}, {15526, 39183}, {22052, 3518}, {31998, 33513}, {33549, 393}, {35071, 39180}, {35442, 12077}, {52032, 31610}, {62569, 62727}, {62573, 62724}, {62603, 39286}
X(64062) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1232, 140}, {14570, 52613}, {54911, 2}
X(64062) = X(i)-complementary conjugate of X(j) for these {i, j}: {661, 53986}, {2148, 39171}, {20185, 4369}
X(64062) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {54911, 6327}
X(64062) = X(i)-cross conjugate of X(j) for these {i, j}: {22052, 140}
X(64062) = pole of line {6467, 11577} with respect to the Jerabek hyperbola
X(64062) = pole of line {99, 33513} with respect to the Kiepert parabola
X(64062) = pole of line {6, 1173} with respect to the Stammler hyperbola
X(64062) = pole of line {523, 44450} with respect to the Steiner circumellipse
X(64062) = pole of line {2, 10979} with respect to the Wallace hyperbola
X(64062) = pole of line {525, 15340} with respect to the dual conic of polar circle
X(64062) = pole of line {115, 53986} with respect to the dual conic of Wallace hyperbola
X(64062) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(140)}}, {{A, B, C, X(3), X(5422)}}, {{A, B, C, X(6), X(6748)}}, {{A, B, C, X(69), X(1232)}}, {{A, B, C, X(86), X(17168)}}, {{A, B, C, X(97), X(1493)}}, {{A, B, C, X(230), X(55280)}}, {{A, B, C, X(287), X(3589)}}, {{A, B, C, X(302), X(40712)}}, {{A, B, C, X(303), X(40711)}}, {{A, B, C, X(325), X(57852)}}, {{A, B, C, X(333), X(20879)}}, {{A, B, C, X(343), X(34386)}}, {{A, B, C, X(524), X(54922)}}, {{A, B, C, X(525), X(37779)}}, {{A, B, C, X(671), X(61658)}}, {{A, B, C, X(966), X(21012)}}, {{A, B, C, X(1494), X(45198)}}, {{A, B, C, X(1799), X(37688)}}, {{A, B, C, X(1992), X(54785)}}, {{A, B, C, X(2303), X(17438)}}, {{A, B, C, X(3289), X(61355)}}, {{A, B, C, X(3519), X(13431)}}, {{A, B, C, X(3763), X(42313)}}, {{A, B, C, X(6515), X(54776)}}, {{A, B, C, X(10601), X(54910)}}, {{A, B, C, X(11433), X(44732)}}, {{A, B, C, X(14389), X(57875)}}, {{A, B, C, X(15066), X(36609)}}, {{A, B, C, X(17825), X(63154)}}, {{A, B, C, X(32078), X(59208)}}, {{A, B, C, X(34211), X(35311)}}, {{A, B, C, X(34545), X(36153)}}, {{A, B, C, X(34564), X(39284)}}, {{A, B, C, X(34897), X(37636)}}, {{A, B, C, X(35324), X(61198)}}, {{A, B, C, X(37672), X(54774)}}, {{A, B, C, X(41435), X(48261)}}, {{A, B, C, X(51171), X(56267)}}, {{A, B, C, X(54496), X(63094)}}, {{A, B, C, X(54772), X(59373)}}
X(64062) = barycentric product X(i)*X(j) for these (i, j): {140, 69}, {233, 34386}, {343, 59183}, {394, 40684}, {1232, 3}, {3265, 35311}, {3267, 35324}, {3926, 6748}, {3964, 44732}, {4143, 61217}, {4563, 55280}, {11064, 62730}, {13366, 305}, {15414, 35318}, {17168, 306}, {17206, 21012}, {17438, 304}, {18022, 61355}, {20879, 63}, {21103, 4561}, {22052, 76}, {32078, 34384}, {57811, 97}
X(64062) = barycentric quotient X(i)/X(j) for these (i, j): {2, 39284}, {3, 1173}, {6, 33631}, {69, 40410}, {95, 39286}, {97, 288}, {99, 33513}, {140, 4}, {216, 59142}, {233, 53}, {343, 31610}, {394, 31626}, {520, 39180}, {525, 39183}, {1232, 264}, {1493, 3518}, {1799, 39289}, {3078, 62261}, {3265, 62724}, {3519, 1487}, {4563, 55279}, {6748, 393}, {11064, 62727}, {13366, 25}, {14978, 13450}, {17168, 27}, {17438, 19}, {19210, 20574}, {20879, 92}, {21012, 1826}, {21103, 7649}, {22052, 6}, {26861, 26862}, {32078, 51}, {34386, 31617}, {34483, 34110}, {35311, 107}, {35318, 61193}, {35324, 112}, {35441, 12077}, {36153, 34484}, {36422, 6748}, {40684, 2052}, {43704, 43657}, {44732, 1093}, {53386, 14569}, {55280, 2501}, {57811, 324}, {59164, 60828}, {59183, 275}, {61217, 6529}, {61355, 184}, {62730, 16080}
X(64062) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 394, 343}, {1232, 40684, 57811}, {3167, 43653, 13394}, {3819, 5965, 11245}, {9936, 42021, 3}, {10519, 63174, 3796}, {10625, 31831, 16655}, {11898, 62217, 1899}, {14826, 63428, 33586}, {34986, 40107, 7499}, {40711, 44718, 466}, {40712, 44719, 465}

X(64063) = COMPLEMENT OF X(20299)

Barycentrics    2*a^10-6*a^8*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-3*a^2*(b^2-c^2)^2*(b^4+c^4)+a^6*(5*b^4+4*b^2*c^2+5*c^4) : :
X(64063) = 3*X[2]+X[6759], X[4]+3*X[11202], -X[64]+9*X[5054], 3*X[154]+5*X[1656], X[155]+3*X[61646], X[159]+3*X[38317], -X[182]+5*X[31267], 3*X[381]+5*X[17821], 3*X[549]+X[2883], X[576]+3*X[61683], -5*X[631]+X[3357], -5*X[632]+X[6247] and many others

X(64063) lies on these lines: {2, 6759}, {3, 113}, {4, 11202}, {5, 5944}, {17, 11244}, {18, 11243}, {24, 18388}, {30, 32903}, {49, 10112}, {51, 6152}, {52, 32223}, {54, 37943}, {64, 5054}, {107, 3462}, {110, 2888}, {125, 1614}, {140, 6000}, {143, 10096}, {154, 1656}, {155, 61646}, {156, 542}, {159, 38317}, {182, 31267}, {184, 7505}, {185, 10018}, {186, 43831}, {195, 51885}, {206, 24206}, {235, 11430}, {381, 17821}, {389, 468}, {403, 13367}, {436, 6750}, {511, 9820}, {523, 6663}, {541, 32210}, {546, 58407}, {548, 5893}, {549, 2883}, {550, 14156}, {576, 61683}, {578, 3542}, {620, 59530}, {631, 3357}, {632, 6247}, {1147, 10201}, {1154, 18282}, {1181, 37453}, {1209, 18350}, {1216, 45979}, {1352, 23042}, {1495, 1594}, {1498, 3526}, {1503, 3628}, {1506, 1971}, {1511, 61750}, {1533, 12086}, {1568, 7488}, {1620, 64094}, {1658, 5448}, {1853, 5070}, {2070, 15800}, {2072, 44829}, {2393, 25488}, {2781, 32142}, {2917, 13621}, {2937, 51392}, {3090, 9833}, {3091, 34786}, {3147, 11438}, {3518, 3574}, {3520, 51403}, {3521, 37955}, {3523, 5878}, {3524, 20427}, {3530, 15311}, {3533, 12324}, {3547, 59543}, {3549, 9306}, {3580, 43844}, {3589, 61610}, {3818, 23041}, {3819, 34002}, {3851, 17845}, {3934, 59706}, {4232, 43841}, {5055, 64037}, {5067, 11206}, {5072, 18405}, {5447, 25337}, {5462, 44232}, {5476, 34787}, {5642, 7552}, {5651, 7558}, {5654, 46730}, {5656, 10303}, {5663, 10125}, {5876, 16534}, {5891, 32348}, {5894, 15712}, {5907, 7542}, {5965, 41593}, {6053, 12111}, {6143, 14157}, {6241, 17853}, {6639, 10539}, {6676, 11793}, {6677, 11695}, {6699, 13491}, {6723, 60780}, {6756, 15448}, {6761, 38808}, {6863, 14925}, {7393, 32321}, {7486, 64034}, {7493, 46728}, {7540, 32267}, {7553, 32237}, {7568, 10170}, {7577, 26882}, {7592, 61645}, {7687, 11464}, {7749, 32445}, {8254, 13364}, {8567, 61811}, {8703, 51491}, {8960, 11242}, {8976, 17820}, {9704, 61713}, {9729, 16238}, {9920, 21308}, {10020, 13754}, {10024, 51393}, {10095, 44668}, {10110, 21841}, {10116, 63839}, {10224, 44407}, {10255, 11750}, {10257, 46850}, {10272, 10628}, {10516, 34776}, {10533, 10577}, {10534, 10576}, {10594, 61743}, {10606, 15720}, {10675, 33416}, {10676, 33417}, {11064, 15644}, {11230, 40660}, {11231, 40658}, {11241, 58866}, {11381, 37118}, {11423, 61712}, {11424, 62961}, {11440, 15063}, {11444, 52300}, {11550, 52296}, {11563, 12897}, {11565, 15088}, {12010, 32423}, {12038, 15761}, {12088, 51360}, {12241, 37942}, {12250, 61820}, {12254, 14644}, {12315, 15694}, {12900, 49673}, {13093, 55863}, {13154, 44883}, {13346, 64181}, {13348, 16618}, {13371, 29012}, {13399, 43608}, {13406, 17702}, {13434, 21451}, {13561, 34330}, {13567, 64026}, {13568, 37935}, {13598, 37971}, {13630, 44234}, {13851, 35487}, {13861, 15577}, {13951, 17819}, {14076, 32379}, {14249, 48361}, {14363, 56297}, {14641, 15122}, {14852, 61751}, {14864, 23332}, {14869, 23328}, {14915, 23336}, {15105, 61824}, {15585, 18583}, {15646, 43577}, {15647, 32743}, {15692, 64187}, {15693, 48672}, {15696, 61721}, {16163, 50009}, {16197, 53415}, {16655, 62958}, {16966, 30403}, {16967, 30402}, {17714, 29317}, {17826, 42129}, {17827, 42132}, {18369, 56924}, {18378, 61711}, {18390, 19357}, {18568, 34472}, {18909, 52290}, {18914, 47296}, {19153, 34507}, {19347, 26958}, {19506, 64101}, {20773, 33547}, {22467, 64179}, {22660, 34351}, {25338, 63737}, {26879, 61691}, {26883, 37119}, {32063, 40686}, {32064, 61886}, {32330, 54007}, {32340, 62982}, {32350, 38458}, {32401, 34864}, {32734, 58923}, {33549, 56298}, {34117, 40107}, {34224, 44110}, {34780, 55857}, {34986, 41587}, {35268, 47528}, {35450, 61832}, {36253, 45731}, {37471, 41603}, {37480, 59349}, {37505, 61690}, {37513, 50143}, {38848, 61715}, {39879, 47355}, {40647, 44452}, {41586, 56292}, {41729, 43150}, {43392, 52003}, {43573, 44282}, {43607, 64029}, {44236, 46849}, {44762, 55859}, {44870, 52262}, {44958, 61744}, {45089, 62978}, {45780, 58484}, {46114, 63414}, {46936, 64059}, {50709, 62123}, {50977, 64031}, {51756, 53999}, {52398, 62708}, {54050, 61814}, {54211, 61816}, {58454, 61609}, {58465, 64038}, {58795, 61850}, {63667, 64035}

X(64063) = midpoint of X(i) and X(j) for these {i,j}: {3, 61749}, {5, 10282}, {140, 16252}, {156, 5449}, {206, 24206}, {548, 5893}, {1498, 52102}, {1658, 5448}, {2883, 64027}, {3589, 61610}, {6759, 20299}, {9820, 13383}, {10020, 61608}, {10182, 61747}, {10201, 61681}, {11591, 41589}, {12038, 15761}, {13406, 32171}, {14076, 32379}, {14862, 25563}, {15577, 19130}, {15585, 18583}, {15647, 32743}, {18381, 45185}, {18383, 34782}, {20773, 33547}, {32767, 50414}, {34117, 40107}, {41597, 63734}, {41729, 43150}, {58434, 61606}, {58439, 61619}
X(64063) = reflection of X(i) in X(j) for these {i,j}: {14862, 16252}, {20191, 10125}, {25563, 140}, {32767, 3628}, {43839, 58435}, {58445, 58450}
X(64063) = complement of X(20299)
X(64063) = pole of line {13382, 35491} with respect to the Jerabek hyperbola
X(64063) = pole of line {2071, 7691} with respect to the Stammler hyperbola
X(64063) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1304, 53757, 53881}
X(64063) = intersection, other than A, B, C, of circumconics {{A, B, C, X(11744), X(15619)}}, {{A, B, C, X(40082), X(48361)}}
X(64063) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6759, 20299}, {3, 64024, 22802}, {5, 10192, 10282}, {5, 34782, 18383}, {5, 44516, 58447}, {30, 58435, 43839}, {49, 63735, 10112}, {140, 16252, 6000}, {140, 6000, 25563}, {140, 61606, 16252}, {154, 1656, 18381}, {154, 18381, 45185}, {156, 5449, 542}, {403, 13367, 13403}, {549, 2883, 64027}, {631, 3357, 10193}, {1495, 1594, 13419}, {1498, 23329, 52102}, {1498, 3526, 23329}, {1503, 3628, 32767}, {1503, 58450, 58445}, {3090, 35260, 9833}, {3523, 5878, 11204}, {3851, 17845, 18376}, {5070, 14530, 1853}, {5663, 10125, 20191}, {6000, 16252, 14862}, {6639, 10539, 21243}, {6676, 59659, 11793}, {7542, 51425, 5907}, {7577, 26882, 61139}, {9820, 13383, 511}, {10020, 61608, 13754}, {10096, 15806, 143}, {10182, 61747, 2777}, {10182, 61749, 3}, {10272, 34577, 11591}, {10282, 18383, 34782}, {11464, 16868, 21659}, {11563, 43394, 12897}, {13406, 32171, 17702}, {16252, 58434, 140}, {16868, 21659, 7687}, {18383, 34782, 18400}, {21841, 23292, 10110}, {22802, 61747, 64024}, {22802, 64024, 61749}, {32063, 46219, 40686}, {32767, 50414, 1503}, {34780, 55857, 61735}, {44232, 61619, 5462}, {61680, 61747, 10182}

X(64064) = PERSPECTOR OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(5) AND PEDAL-OF-X(54)

Barycentrics    (a^2-b^2-c^2)*(2*a^2+b^2-c^2)*(2*a^2-b^2+c^2) : :
X(64064) = 2*X[7542]+X[43844]

X(64064) lies on these lines: {2, 98}, {3, 14861}, {5, 10619}, {6, 62965}, {30, 5944}, {49, 539}, {51, 10192}, {52, 44213}, {54, 37943}, {143, 21660}, {154, 5064}, {185, 549}, {381, 19357}, {395, 21647}, {396, 21648}, {427, 44110}, {428, 1495}, {436, 62261}, {468, 13366}, {511, 61655}, {524, 21637}, {547, 6146}, {550, 34563}, {578, 62961}, {597, 6467}, {599, 19125}, {1181, 5054}, {1204, 3524}, {1425, 5298}, {1493, 18282}, {1503, 44108}, {1568, 18475}, {1624, 16030}, {1994, 32223}, {3167, 61644}, {3270, 4995}, {3292, 6676}, {3431, 13202}, {3518, 12242}, {3545, 19467}, {3549, 63649}, {3574, 7576}, {3917, 13394}, {4175, 37894}, {5020, 44300}, {5066, 13851}, {5071, 18925}, {5189, 54036}, {5448, 18564}, {5449, 9704}, {5655, 32607}, {5890, 10182}, {5892, 59648}, {6102, 15330}, {6353, 8537}, {6689, 18350}, {7426, 21849}, {7484, 59551}, {7542, 43844}, {7667, 13857}, {7714, 35260}, {7753, 14585}, {8550, 52297}, {8779, 9300}, {9706, 10112}, {9707, 61139}, {10018, 64026}, {10095, 11577}, {10124, 18914}, {10128, 37649}, {10154, 21969}, {10539, 60763}, {10602, 51185}, {10605, 15693}, {10691, 11064}, {10984, 64181}, {10990, 35473}, {11245, 58434}, {11402, 61645}, {11423, 34564}, {11425, 62966}, {11427, 34417}, {11430, 51403}, {11464, 18388}, {11550, 26864}, {11694, 17701}, {12038, 64179}, {12100, 21663}, {13399, 37118}, {13450, 33549}, {13567, 44109}, {13621, 19468}, {13846, 19356}, {13847, 19355}, {14528, 37197}, {14831, 34351}, {14862, 14865}, {15032, 44673}, {15063, 18570}, {15116, 19151}, {15448, 44106}, {15559, 50414}, {15681, 61771}, {15694, 19347}, {15699, 31804}, {15702, 26937}, {15709, 18909}, {15721, 18913}, {15723, 26944}, {16226, 44211}, {16252, 62962}, {16644, 19364}, {16645, 19363}, {16657, 61606}, {17809, 37453}, {18396, 19709}, {18400, 62982}, {18918, 61926}, {18931, 61822}, {18945, 61924}, {19459, 47352}, {20582, 26926}, {21639, 63124}, {21640, 32788}, {21641, 32787}, {22660, 35240}, {25055, 64040}, {26881, 59771}, {30714, 46029}, {31383, 62975}, {32225, 61658}, {32340, 34782}, {34566, 61657}, {34986, 41586}, {37439, 59699}, {37672, 50973}, {37760, 53863}, {38795, 50140}, {41589, 43581}, {43653, 64177}, {43817, 58435}, {44091, 51745}, {44210, 54384}, {44407, 61711}, {44450, 52525}, {45185, 52295}, {48891, 51360}, {51393, 61619}, {52298, 64080}, {58378, 61846}, {61744, 61747}, {62073, 64094}

X(64064) = pole of line {511, 548} with respect to the Jerabek hyperbola
X(64064) = pole of line {511, 6242} with respect to the Stammler hyperbola
X(64064) = intersection, other than A, B, C, of circumconics {{A, B, C, X(98), X(14861)}}, {{A, B, C, X(43891), X(53174)}}
X(64064) = barycentric product X(i)*X(j) for these (i, j): {343, 40634}, {11064, 16243}
X(64064) = barycentric quotient X(i)/X(j) for these (i, j): {16243, 16080}, {40634, 275}
X(64064) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 61690, 61659}, {9544, 21243, 24981}, {9706, 58805, 10112}, {10192, 61690, 51}, {11245, 58434, 61691}, {11402, 61680, 61645}, {13394, 59553, 3917}

X(64065) = MIDPOINT OF X(3)X(144)

Barycentrics    4*a^6-4*a^5*(b+c)-(b-c)^4*(b+c)^2-2*a*(b-c)^2*(b+c)^3-7*a^4*(b^2+c^2)+2*a^2*(b-c)^2*(2*b^2+3*b*c+2*c^2)+6*a^3*(b^3+b^2*c+b*c^2+c^3) : :
X(64065) = -4*X[2]+3*X[38080], -X[4]+3*X[51516], -4*X[10]+3*X[38170], -4*X[142]+5*X[632], 3*X[165]+X[41705], -2*X[546]+3*X[5817], -2*X[547]+3*X[61023], -2*X[548]+3*X[59418], -5*X[631]+X[20059], -4*X[1001]+3*X[10283], -4*X[1125]+3*X[38041], -5*X[1656]+3*X[59386] and many others

X(64065) lies on these lines: {2, 38080}, {3, 144}, {4, 51516}, {5, 9}, {7, 140}, {10, 38170}, {20, 60884}, {30, 5759}, {63, 13226}, {142, 632}, {165, 41705}, {390, 5844}, {442, 61025}, {480, 32141}, {495, 60883}, {496, 60919}, {511, 51144}, {516, 3627}, {517, 51090}, {518, 1353}, {527, 549}, {528, 50823}, {542, 51191}, {546, 5817}, {547, 61023}, {548, 59418}, {550, 971}, {590, 60915}, {615, 60916}, {631, 20059}, {912, 51489}, {942, 61014}, {952, 5223}, {954, 11048}, {1001, 10283}, {1125, 38041}, {1385, 5850}, {1482, 50243}, {1484, 5856}, {1536, 51352}, {1595, 60879}, {1656, 59386}, {2550, 38112}, {3219, 8727}, {3243, 61283}, {3526, 51514}, {3530, 21151}, {3564, 50995}, {3589, 38164}, {3628, 18230}, {3634, 38172}, {3845, 63970}, {3850, 59385}, {3858, 18482}, {3927, 5768}, {4187, 61026}, {4312, 26446}, {5054, 60984}, {5220, 37705}, {5446, 58534}, {5499, 17768}, {5542, 38028}, {5657, 63975}, {5686, 61510}, {5698, 37290}, {5708, 60941}, {5719, 61007}, {5728, 15935}, {5732, 8703}, {5733, 16675}, {5763, 31445}, {5845, 48876}, {5851, 33814}, {5852, 52769}, {6147, 52819}, {6173, 11539}, {6666, 38171}, {6667, 38173}, {6668, 38174}, {6883, 12848}, {6907, 60935}, {6914, 60940}, {6922, 60970}, {8236, 61597}, {8728, 26878}, {8981, 60913}, {10109, 38073}, {10124, 59374}, {10386, 14100}, {10398, 12433}, {10861, 17563}, {11038, 51700}, {11108, 61009}, {11372, 28174}, {11662, 21617}, {11812, 38065}, {12108, 60976}, {13329, 17334}, {13966, 60914}, {14869, 38122}, {15026, 58472}, {15171, 60910}, {15254, 20330}, {15325, 60924}, {15492, 53599}, {15587, 58630}, {15687, 52835}, {15694, 59375}, {15699, 60986}, {15704, 64197}, {15712, 21153}, {15713, 38067}, {16239, 60996}, {17502, 43176}, {17527, 61012}, {18990, 60909}, {20195, 55859}, {22117, 59611}, {22792, 43174}, {24393, 59400}, {24470, 60937}, {28194, 50837}, {28204, 50834}, {29007, 37438}, {30424, 38130}, {31663, 43182}, {31672, 62036}, {34380, 51190}, {37356, 61024}, {37424, 55104}, {37532, 51559}, {37582, 60961}, {38036, 61272}, {38057, 52682}, {38075, 61956}, {38082, 61910}, {38093, 61869}, {38110, 51150}, {38318, 61900}, {38454, 60911}, {40273, 63974}, {43177, 44682}, {44222, 60973}, {44455, 54204}, {50205, 60959}, {51732, 59405}, {58433, 61876}, {59389, 61988}, {60905, 61524}, {60962, 61837}, {60980, 61853}, {60999, 61874}, {61020, 61852}, {63374, 63384}

X(64065) = midpoint of X(i) and X(j) for these {i,j}: {3, 144}, {20, 60884}, {5759, 5779}, {44455, 54204}
X(64065) = reflection of X(i) in X(j) for these {i,j}: {5, 9}, {7, 140}, {3627, 60901}, {5446, 58534}, {5779, 61596}, {5805, 61511}, {15587, 58630}, {20330, 15254}, {31657, 31658}, {31671, 546}, {38111, 59381}, {43182, 31663}, {60901, 64198}, {60922, 61509}, {62036, 31672}, {63974, 40273}, {64198, 61000}
X(64065) = complement of X(60922)
X(64065) = anticomplement of X(61509)
X(64065) = X(i)-Dao conjugate of X(j) for these {i, j}: {61509, 61509}
X(64065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60922, 61509}, {3, 144, 5843}, {4, 61006, 51516}, {7, 140, 38111}, {9, 5735, 38108}, {9, 5805, 61511}, {30, 61596, 5779}, {142, 38113, 632}, {144, 21168, 3}, {516, 60901, 3627}, {516, 61000, 64198}, {516, 64198, 60901}, {527, 31658, 31657}, {631, 20059, 59380}, {1353, 51046, 1483}, {3526, 51514, 62778}, {5759, 5779, 30}, {5762, 61511, 5805}, {5779, 6172, 61596}, {5805, 61511, 5}, {5817, 31671, 546}, {6666, 38171, 55856}, {15254, 20330, 38043}, {18230, 38107, 3628}, {18482, 38139, 3858}, {31657, 31658, 549}

X(64066) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF ANTI-CONWAY AND X(4)-CROSSPEDAL-OF-X(5)

Barycentrics    (-(b^2-c^2)^2+a^2*(b^2+c^2))*(3*a^6-7*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(5*b^4+2*b^2*c^2+5*c^4)) : :
X(64066) = -3*X[154]+X[9936], -2*X[156]+3*X[10154], -X[6193]+3*X[14070], -2*X[9820]+3*X[61646], -4*X[10020]+3*X[59553], -3*X[10192]+2*X[41597], -3*X[10201]+2*X[61607], -5*X[17821]+3*X[63649], -3*X[37672]+5*X[64181]

X(64066) lies on these lines: {2, 37493}, {3, 6515}, {4, 45383}, {5, 51}, {6, 140}, {24, 45794}, {25, 31831}, {26, 159}, {30, 64}, {54, 41628}, {69, 6642}, {141, 5462}, {154, 9936}, {155, 13383}, {156, 10154}, {161, 17714}, {186, 46443}, {195, 61690}, {235, 18436}, {323, 10018}, {394, 16238}, {427, 6243}, {467, 56303}, {468, 35603}, {511, 12235}, {524, 1147}, {539, 34782}, {549, 569}, {550, 1204}, {568, 7399}, {578, 44201}, {631, 63012}, {632, 37649}, {1181, 16618}, {1199, 7495}, {1216, 13567}, {1353, 19131}, {1368, 6101}, {1595, 10263}, {1596, 5876}, {1657, 46349}, {1894, 32128}, {1899, 37486}, {1906, 18435}, {1993, 7542}, {2883, 13754}, {2888, 7576}, {2917, 12107}, {2979, 26879}, {3060, 7403}, {3133, 52347}, {3517, 11898}, {3518, 12325}, {3526, 63085}, {3530, 37476}, {3542, 58891}, {3546, 63428}, {3549, 12160}, {3567, 7405}, {3580, 11412}, {3627, 18474}, {3630, 43586}, {5447, 44479}, {5663, 32263}, {5889, 15760}, {5965, 10282}, {6102, 6823}, {6193, 14070}, {6247, 52104}, {6676, 12161}, {6755, 14978}, {7387, 11411}, {7393, 11433}, {7488, 37779}, {7499, 36753}, {7502, 31804}, {7509, 37644}, {7512, 45968}, {7516, 45298}, {7517, 47582}, {7525, 43588}, {7526, 13142}, {7553, 11442}, {7555, 32599}, {7592, 34002}, {7691, 12022}, {8263, 12106}, {8703, 61713}, {9777, 14786}, {9818, 64048}, {9820, 61646}, {9935, 32423}, {9967, 10627}, {10020, 59553}, {10192, 41597}, {10201, 61607}, {10539, 32269}, {10990, 62159}, {11402, 47525}, {11414, 18917}, {11441, 37971}, {11695, 40107}, {11750, 15704}, {13346, 44158}, {13371, 61724}, {13391, 61666}, {13622, 40441}, {14449, 21850}, {14516, 41596}, {14864, 29317}, {15068, 21841}, {15083, 16252}, {15107, 16659}, {15559, 62187}, {15712, 37513}, {15912, 41523}, {16789, 63722}, {17712, 48881}, {17810, 23411}, {17814, 44233}, {17821, 63649}, {18128, 44882}, {18350, 62978}, {18569, 61544}, {18859, 43903}, {18909, 35243}, {20303, 37938}, {23307, 45780}, {25738, 37494}, {26937, 37483}, {26944, 33878}, {27361, 27364}, {27377, 37127}, {31833, 37489}, {31834, 46030}, {32110, 63631}, {32348, 37505}, {34116, 40111}, {34224, 41724}, {34785, 44665}, {36747, 52262}, {36752, 43653}, {37452, 54048}, {37672, 64181}, {38136, 50136}, {39522, 63679}, {41589, 44322}, {44076, 44239}, {44077, 61753}, {44277, 63612}, {45088, 64105}, {64035, 64095}

X(64066) = midpoint of X(i) and X(j) for these {i,j}: {68, 17834}, {7387, 11411}
X(64066) = reflection of X(i) in X(j) for these {i,j}: {5, 63734}, {155, 13383}, {6247, 52104}, {13346, 44158}, {15083, 16252}, {16266, 140}, {18569, 61544}, {23335, 12359}
X(64066) = perspector of circumconic {{A, B, C, X(14570), X(43351)}}
X(64066) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2169, 36612}, {2190, 38260}
X(64066) = X(i)-Dao conjugate of X(j) for these {i, j}: {5, 38260}, {14363, 36612}
X(64066) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8800, 5}
X(64066) = pole of line {5891, 6146} with respect to the Jerabek hyperbola
X(64066) = pole of line {570, 1656} with respect to the Kiepert hyperbola
X(64066) = pole of line {54, 5422} with respect to the Stammler hyperbola
X(64066) = pole of line {18314, 47122} with respect to the Steiner inellipse
X(64066) = pole of line {95, 32832} with respect to the Wallace hyperbola
X(64066) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(3147)}}, {{A, B, C, X(52), X(64)}}, {{A, B, C, X(54), X(9827)}}, {{A, B, C, X(343), X(42021)}}, {{A, B, C, X(1209), X(13622)}}, {{A, B, C, X(27361), X(41588)}}, {{A, B, C, X(27362), X(62545)}}, {{A, B, C, X(42459), X(46200)}}, {{A, B, C, X(45088), X(45089)}}
X(64066) = barycentric product X(i)*X(j) for these (i, j): {3147, 343}
X(64066) = barycentric quotient X(i)/X(j) for these (i, j): {53, 36612}, {216, 38260}, {3147, 275}
X(64066) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6515, 13292}, {52, 1209, 45089}, {68, 17834, 30}, {140, 34380, 16266}, {343, 45089, 1209}, {511, 12359, 23335}, {1154, 63734, 5}, {3567, 37636, 7405}, {3580, 11412, 11585}, {5562, 41586, 41587}, {6146, 37478, 550}, {7502, 32358, 31804}, {7525, 43588, 48906}, {9937, 37488, 26}, {13142, 44683, 7526}, {17834, 64060, 68}

X(64067) = REFLECTION OF X(5) IN X(576)

Barycentrics    4*a^6-11*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(8*b^4-4*b^2*c^2+8*c^4) : :
X(64067) = -3*X[2]+5*X[11482], -X[3]+3*X[1992], X[4]+3*X[193], -3*X[6]+2*X[140], -3*X[69]+5*X[1656], -6*X[182]+5*X[15712], -3*X[376]+X[55580], -X[382]+3*X[54132], -2*X[548]+3*X[11179], -3*X[549]+4*X[575], -6*X[597]+5*X[632], -3*X[599]+4*X[3628] and many others

X(64067) lies on these lines: {2, 11482}, {3, 1992}, {4, 193}, {5, 524}, {6, 140}, {20, 55724}, {25, 9925}, {30, 11477}, {52, 5095}, {67, 13371}, {69, 1656}, {141, 5097}, {154, 47630}, {155, 63702}, {182, 15712}, {185, 54218}, {235, 15801}, {262, 50251}, {317, 59661}, {340, 42873}, {376, 55580}, {381, 63064}, {382, 54132}, {397, 51206}, {398, 51207}, {427, 8537}, {468, 1993}, {495, 19369}, {496, 8540}, {511, 550}, {517, 64073}, {542, 3627}, {546, 15069}, {547, 15533}, {548, 11179}, {549, 575}, {597, 632}, {599, 3628}, {631, 5032}, {1147, 15471}, {1154, 50649}, {1216, 44495}, {1350, 33923}, {1352, 3850}, {1368, 8538}, {1503, 34788}, {1513, 7837}, {1570, 7755}, {1595, 8541}, {1596, 11470}, {1657, 6776}, {1843, 13431}, {1899, 47315}, {1994, 7495}, {2393, 10263}, {3060, 10301}, {3090, 11160}, {3091, 50955}, {3098, 12007}, {3146, 50974}, {3167, 4232}, {3180, 37464}, {3181, 37463}, {3292, 44212}, {3416, 38165}, {3522, 14912}, {3523, 5050}, {3524, 55701}, {3525, 51179}, {3526, 59373}, {3528, 54174}, {3529, 51028}, {3530, 53093}, {3533, 51171}, {3541, 11405}, {3545, 63116}, {3580, 52293}, {3589, 15520}, {3618, 46219}, {3619, 55860}, {3620, 61886}, {3630, 24206}, {3631, 38317}, {3763, 61877}, {3818, 55717}, {3843, 11180}, {3845, 63115}, {3851, 11008}, {3853, 54131}, {3857, 47354}, {3858, 5480}, {3861, 47353}, {3933, 39099}, {4663, 5690}, {4857, 39873}, {5054, 63022}, {5055, 50992}, {5056, 7941}, {5066, 51187}, {5070, 21356}, {5071, 63118}, {5072, 51175}, {5073, 39899}, {5076, 51023}, {5085, 61792}, {5092, 61789}, {5094, 6515}, {5107, 5254}, {5189, 45968}, {5201, 52274}, {5270, 39897}, {5305, 63043}, {5446, 8681}, {5477, 10992}, {5486, 12161}, {5622, 37495}, {5844, 64070}, {5858, 52266}, {5859, 52263}, {5882, 51196}, {6101, 44479}, {6243, 15073}, {6329, 55714}, {6403, 46444}, {6676, 63094}, {6677, 37672}, {6696, 10250}, {6998, 63052}, {7380, 50074}, {7387, 53019}, {7426, 9716}, {7540, 11061}, {7575, 47549}, {7583, 9974}, {7584, 9975}, {7607, 22329}, {7608, 37688}, {7715, 34382}, {7752, 44369}, {7805, 11623}, {7862, 44395}, {7926, 39663}, {7982, 50952}, {8548, 36747}, {8703, 41149}, {9027, 43130}, {9740, 53099}, {9766, 10011}, {10018, 63063}, {10095, 29959}, {10096, 47448}, {10109, 51188}, {10124, 51185}, {10154, 34986}, {10168, 61837}, {10257, 47462}, {10299, 12017}, {10303, 63000}, {10304, 55602}, {10516, 61940}, {10519, 15720}, {10541, 12100}, {10542, 63633}, {10552, 63719}, {10602, 18914}, {10605, 47337}, {10625, 40673}, {10753, 52090}, {10993, 51198}, {11004, 52300}, {11245, 16063}, {11255, 23335}, {11422, 44210}, {11456, 47281}, {11539, 63124}, {11585, 18449}, {11645, 62041}, {12061, 32196}, {12103, 43273}, {12108, 38064}, {12584, 41595}, {12811, 38072}, {13169, 15027}, {13292, 14791}, {13330, 18907}, {13464, 34379}, {13860, 63093}, {13861, 63180}, {14216, 17813}, {14561, 35018}, {14614, 56370}, {14831, 44241}, {14864, 15583}, {14869, 20583}, {14927, 49139}, {15004, 64062}, {15066, 61657}, {15122, 44469}, {15178, 51005}, {15531, 64051}, {15582, 37936}, {15696, 54170}, {15699, 22165}, {15703, 50990}, {15704, 51140}, {15711, 55679}, {15714, 55644}, {15759, 55641}, {16239, 47352}, {16619, 34117}, {16981, 46818}, {17504, 55687}, {17800, 64014}, {18919, 26944}, {19116, 44501}, {19117, 44502}, {19136, 61753}, {19139, 21841}, {19924, 62155}, {20190, 44682}, {20299, 23326}, {20582, 55861}, {21167, 50664}, {21358, 48154}, {21554, 63049}, {21734, 55620}, {21735, 55610}, {21970, 64177}, {23061, 30739}, {23236, 41720}, {25338, 47276}, {25406, 55584}, {29012, 55719}, {29181, 55720}, {31670, 62026}, {31884, 62064}, {32244, 61543}, {32247, 39562}, {32273, 32365}, {32423, 64104}, {33586, 37910}, {33748, 61791}, {33749, 46853}, {33750, 55616}, {33751, 55586}, {33813, 41672}, {34200, 55614}, {34351, 53777}, {34774, 45185}, {35484, 45034}, {36749, 41614}, {36990, 62013}, {37118, 37784}, {37439, 53863}, {37450, 63038}, {37451, 41624}, {37473, 54215}, {37489, 37934}, {37645, 52292}, {37900, 62187}, {38040, 49511}, {38164, 47595}, {39561, 61824}, {39874, 49135}, {40330, 61919}, {41152, 61890}, {41585, 41597}, {41981, 55582}, {41991, 50959}, {42147, 51200}, {42148, 51203}, {44245, 50976}, {44452, 47460}, {44453, 61625}, {44500, 49111}, {45016, 56292}, {45186, 61692}, {45298, 46336}, {45759, 55631}, {46264, 55722}, {46267, 61851}, {47356, 61286}, {47358, 61278}, {47599, 50993}, {48310, 61876}, {48662, 51538}, {48873, 62136}, {48898, 55723}, {48905, 62156}, {50689, 51215}, {50954, 61955}, {50963, 61964}, {50965, 51180}, {50966, 62083}, {50970, 55611}, {50972, 55583}, {50982, 61852}, {50983, 55708}, {50987, 55704}, {50988, 61810}, {50989, 61896}, {50991, 61885}, {50994, 61887}, {51024, 62034}, {51136, 62162}, {51138, 55694}, {51143, 61879}, {51172, 51178}, {51173, 61968}, {51176, 62146}, {51181, 55698}, {51183, 61900}, {51186, 61880}, {52290, 63092}, {52301, 63174}, {53094, 61784}, {54347, 63734}, {55593, 62082}, {55597, 62079}, {55604, 62074}, {55626, 58190}, {55629, 62067}, {55637, 62062}, {55639, 62061}, {55643, 62060}, {55650, 62057}, {55678, 61783}, {55681, 61785}, {55682, 61787}, {55684, 61790}, {55697, 61794}, {55705, 61803}, {55711, 61813}, {55858, 63109}, {55863, 63062}, {61044, 62127}, {61607, 64048}, {61832, 63073}, {61834, 63122}, {61855, 63011}, {61856, 63123}, {61875, 63119}, {62217, 63031}

X(64067) = midpoint of X(i) and X(j) for these {i,j}: {20, 55724}, {193, 1351}, {381, 63064}, {1352, 6144}, {1992, 50962}, {6243, 15073}, {6776, 44456}, {11008, 11898}, {11160, 51174}, {11477, 63722}, {39899, 51212}, {46264, 55722}, {48898, 55723}
X(64067) = reflection of X(i) in X(j) for these {i,j}: {5, 576}, {6, 61624}, {69, 18583}, {141, 5097}, {155, 63702}, {182, 32455}, {549, 8584}, {550, 8550}, {1216, 44495}, {1353, 3629}, {3098, 12007}, {3630, 24206}, {5480, 55716}, {5690, 4663}, {6101, 44479}, {7575, 47549}, {11898, 18358}, {12584, 41595}, {15069, 546}, {15074, 32284}, {15122, 47464}, {15533, 547}, {21850, 1351}, {23335, 11255}, {24206, 55715}, {32244, 61543}, {33813, 41672}, {38136, 5102}, {39884, 21850}, {40107, 22330}, {40341, 61545}, {44453, 61625}, {47276, 25338}, {48874, 48906}, {48876, 6}, {48906, 1353}, {49111, 44500}, {50977, 20583}, {50978, 597}, {50979, 1992}, {50985, 599}, {53097, 548}, {55586, 33751}, {55606, 33749}, {62155, 64196}, {63612, 19139}
X(64067) = pole of line {1499, 39503} with respect to the nine-point circle
X(64067) = pole of line {574, 1656} with respect to the Kiepert hyperbola
X(64067) = pole of line {3167, 5422} with respect to the Stammler hyperbola
X(64067) = pole of line {14341, 47122} with respect to the Steiner inellipse
X(64067) = pole of line {3525, 6337} with respect to the Wallace hyperbola
X(64067) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {381, 9169, 63064}
X(64067) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2996), X(42021)}}, {{A, B, C, X(14248), X(34154)}}, {{A, B, C, X(22100), X(52454)}}, {{A, B, C, X(34208), X(53098)}}
X(64067) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 34380, 48876}, {6, 48876, 38110}, {69, 5093, 18583}, {141, 25555, 55856}, {141, 5097, 59399}, {193, 1351, 3564}, {511, 1353, 48906}, {511, 32284, 15074}, {511, 3629, 1353}, {511, 48906, 48874}, {511, 8550, 550}, {524, 576, 5}, {550, 1353, 8550}, {597, 40107, 632}, {631, 5032, 53092}, {1351, 3564, 21850}, {1993, 41588, 59553}, {3528, 54174, 55595}, {3564, 21850, 39884}, {5102, 6144, 1352}, {5480, 18553, 3858}, {5486, 44492, 16618}, {5965, 55716, 5480}, {10519, 62995, 53091}, {11008, 14853, 11898}, {11179, 53097, 548}, {11477, 15534, 63722}, {11898, 14853, 18358}, {14561, 40341, 61545}, {15069, 20423, 546}, {19924, 64196, 62155}, {20190, 54169, 44682}, {22330, 40107, 597}, {33749, 55606, 51737}, {34380, 61624, 6}, {38079, 50985, 599}, {42149, 42152, 44535}, {51170, 63428, 5050}, {51737, 55606, 46853}, {53093, 54173, 3530}, {55856, 59399, 25555}

X(64068) = COMPLEMENT OF X(12632)

Barycentrics    (a-b-c)*(a^3+a^2*(b+c)+(b-c)^2*(b+c)+a*(b^2-6*b*c+c^2)) : :
X(64068) = -4*X[3]+3*X[34607], -4*X[5]+3*X[34619], -2*X[40]+3*X[24477], -3*X[376]+4*X[8666], -4*X[548]+3*X[34707], -5*X[631]+4*X[8715], -4*X[1125]+3*X[3158], -5*X[1698]+6*X[24386], -7*X[3090]+8*X[24387], -5*X[3091]+6*X[11235], -5*X[3522]+6*X[11194], -7*X[3523]+6*X[4421] and many others

X(64068) lies on these lines: {1, 142}, {2, 3303}, {3, 34607}, {4, 519}, {5, 34619}, {7, 9797}, {8, 210}, {9, 12575}, {10, 1058}, {11, 7080}, {20, 528}, {21, 10385}, {40, 24477}, {55, 30478}, {56, 17784}, {65, 36845}, {69, 17144}, {72, 30305}, {80, 56089}, {100, 7288}, {145, 388}, {149, 3436}, {153, 13271}, {200, 12053}, {278, 15954}, {329, 12701}, {355, 13600}, {376, 8666}, {377, 3241}, {390, 958}, {392, 45085}, {404, 11240}, {405, 47357}, {452, 3058}, {474, 52804}, {475, 56183}, {495, 31418}, {499, 48696}, {515, 12629}, {516, 6762}, {517, 5787}, {518, 962}, {522, 12534}, {527, 9589}, {529, 3146}, {535, 33703}, {548, 34707}, {631, 8715}, {936, 63993}, {938, 5836}, {944, 12520}, {946, 6765}, {950, 4853}, {952, 12667}, {956, 4294}, {966, 3169}, {999, 17563}, {1000, 6598}, {1001, 7674}, {1056, 3244}, {1125, 3158}, {1210, 63137}, {1320, 43740}, {1329, 5274}, {1376, 14986}, {1392, 43741}, {1478, 3633}, {1479, 3421}, {1482, 44229}, {1500, 31405}, {1697, 4847}, {1698, 24386}, {1706, 11019}, {1788, 26015}, {1953, 17314}, {2334, 63007}, {2476, 11239}, {2802, 6903}, {2900, 3487}, {2975, 20075}, {3085, 24390}, {3086, 5687}, {3090, 24387}, {3091, 11235}, {3214, 63126}, {3243, 3671}, {3295, 6675}, {3296, 3892}, {3297, 31413}, {3304, 6904}, {3419, 45039}, {3452, 4882}, {3474, 62874}, {3476, 36846}, {3485, 3870}, {3486, 3872}, {3522, 11194}, {3523, 4421}, {3555, 4295}, {3576, 64117}, {3616, 3748}, {3622, 56177}, {3623, 33110}, {3624, 59584}, {3625, 36922}, {3656, 6849}, {3674, 3875}, {3679, 5084}, {3689, 11376}, {3742, 11024}, {3746, 6857}, {3811, 5603}, {3812, 10580}, {3829, 5056}, {3832, 11236}, {3871, 5218}, {3895, 6734}, {3900, 48089}, {3928, 5493}, {4097, 16828}, {4190, 49719}, {4293, 56998}, {4297, 35514}, {4302, 5288}, {4309, 5258}, {4317, 57000}, {4323, 12630}, {4342, 6743}, {4428, 17558}, {4647, 24394}, {4677, 4857}, {4685, 6822}, {4695, 28074}, {4915, 5795}, {4999, 5281}, {5080, 20053}, {5086, 12648}, {5100, 54433}, {5129, 49736}, {5175, 5252}, {5177, 15888}, {5187, 10707}, {5204, 6154}, {5221, 64151}, {5229, 20050}, {5255, 37642}, {5270, 34747}, {5289, 20007}, {5302, 52653}, {5434, 37435}, {5436, 30331}, {5437, 21625}, {5552, 10589}, {5657, 10806}, {5691, 11519}, {5698, 10624}, {5704, 37828}, {5731, 11260}, {5734, 6835}, {5744, 37568}, {5745, 53053}, {5800, 49681}, {5809, 9848}, {5815, 24703}, {5818, 10596}, {5837, 9819}, {5838, 30618}, {5850, 28647}, {5880, 11037}, {5882, 6916}, {6361, 62858}, {6366, 48083}, {6555, 59598}, {6600, 17590}, {6604, 62790}, {6653, 54098}, {6700, 37704}, {6735, 54361}, {6736, 9581}, {6737, 7962}, {6745, 50443}, {6767, 31419}, {6821, 42057}, {6824, 37622}, {6826, 10222}, {6834, 38665}, {6850, 37727}, {6856, 10056}, {6864, 13464}, {6865, 11362}, {6872, 34611}, {6891, 37726}, {6899, 50810}, {6919, 11238}, {6942, 48713}, {6957, 32537}, {6986, 42842}, {7319, 56090}, {7736, 20691}, {7738, 17448}, {7967, 22837}, {7991, 24391}, {8164, 25639}, {8227, 59722}, {8236, 51715}, {8732, 51773}, {9580, 12527}, {9614, 21075}, {9623, 63999}, {9657, 34749}, {9670, 34606}, {9708, 15172}, {9776, 17609}, {9802, 18719}, {10072, 17567}, {10179, 59413}, {10431, 44663}, {10449, 35634}, {10525, 47746}, {10528, 10588}, {10531, 49169}, {10578, 28628}, {10587, 33108}, {10591, 17757}, {10595, 22836}, {10914, 18391}, {11036, 42871}, {11108, 15170}, {11278, 18517}, {11375, 63168}, {11512, 53618}, {12433, 40587}, {12635, 13463}, {12641, 15863}, {12642, 26117}, {12649, 14923}, {12700, 63962}, {13729, 34700}, {13736, 49746}, {14647, 49163}, {15676, 61155}, {15704, 34740}, {16610, 28016}, {17480, 62392}, {17528, 31420}, {17552, 38025}, {17576, 63273}, {17578, 34706}, {17580, 49732}, {17658, 64131}, {17728, 26062}, {17749, 61222}, {17762, 42696}, {20013, 62826}, {20014, 20060}, {20047, 63010}, {20095, 22560}, {20344, 39567}, {21384, 41325}, {24389, 31435}, {24803, 34860}, {24982, 63142}, {25439, 26363}, {25681, 64083}, {26007, 28756}, {26333, 47745}, {26364, 47743}, {28194, 54422}, {28234, 48482}, {30145, 56317}, {30283, 31777}, {30513, 56091}, {30748, 39581}, {31106, 33090}, {31295, 34605}, {31458, 50739}, {32049, 59387}, {33137, 37588}, {34626, 50693}, {34739, 50688}, {34748, 47032}, {35104, 56542}, {36574, 64176}, {37230, 50805}, {37433, 50872}, {37462, 38314}, {37567, 51463}, {40663, 63133}, {41709, 64203}, {48805, 56986}, {48837, 50637}, {49627, 54286}, {50581, 63089}

X(64068) = midpoint of X(i) and X(j) for these {i,j}: {8, 12541}, {962, 6764}, {3680, 12625}, {5691, 11519}
X(64068) = reflection of X(i) in X(j) for these {i,j}: {1, 21627}, {20, 12513}, {145, 10912}, {153, 13271}, {2136, 10}, {2550, 6601}, {3189, 1}, {3811, 49600}, {3913, 3813}, {6361, 62858}, {6765, 946}, {7674, 1001}, {7991, 24391}, {11523, 4301}, {12245, 49168}, {12437, 64205}, {12632, 3913}, {12635, 13463}, {12641, 15863}, {20095, 22560}, {34607, 34625}, {63962, 12700}, {64202, 11362}
X(64068) = complement of X(12632)
X(64068) = anticomplement of X(3913)
X(64068) = perspector of circumconic {{A, B, C, X(646), X(37206)}}
X(64068) = X(i)-Dao conjugate of X(j) for these {i, j}: {3913, 3913}
X(64068) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34860, 3436}, {39956, 329}, {40012, 21286}, {40151, 27835}, {42304, 69}, {56155, 8}
X(64068) = pole of line {3583, 3667} with respect to the anticomplementary circle
X(64068) = pole of line {3667, 43923} with respect to the polar circle
X(64068) = pole of line {8, 17642} with respect to the Feuerbach hyperbola
X(64068) = pole of line {4462, 7178} with respect to the Steiner circumellipse
X(64068) = pole of line {3676, 20317} with respect to the Steiner inellipse
X(64068) = pole of line {9, 24175} with respect to the dual conic of Yff parabola
X(64068) = pole of line {21945, 53540} with respect to the dual conic of Wallace hyperbola
X(64068) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(44720)}}, {{A, B, C, X(8), X(2191)}}, {{A, B, C, X(80), X(42020)}}, {{A, B, C, X(277), X(312)}}, {{A, B, C, X(341), X(6601)}}, {{A, B, C, X(1265), X(3680)}}, {{A, B, C, X(3701), X(43745)}}, {{A, B, C, X(4662), X(30479)}}, {{A, B, C, X(4723), X(43740)}}
X(64068) = barycentric product X(i)*X(j) for these (i, j): {28011, 312}
X(64068) = barycentric quotient X(i)/X(j) for these (i, j): {28011, 57}
X(64068) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38052, 51723}, {1, 5082, 2550}, {1, 5853, 3189}, {2, 12632, 3913}, {7, 9797, 34791}, {8, 12541, 3880}, {8, 18228, 4662}, {8, 2899, 44720}, {8, 36926, 42020}, {8, 3702, 3974}, {8, 497, 2551}, {8, 9785, 960}, {10, 1058, 26105}, {20, 12513, 34610}, {55, 64081, 30478}, {100, 10529, 7288}, {145, 3434, 388}, {149, 3436, 5225}, {149, 3621, 3436}, {499, 48696, 59591}, {519, 4301, 11523}, {528, 12513, 20}, {946, 6765, 25568}, {962, 6764, 518}, {1479, 3632, 3421}, {1837, 3893, 8}, {2136, 24392, 10}, {2476, 64199, 11239}, {2802, 49168, 12245}, {3086, 5687, 59572}, {3304, 34612, 6904}, {3616, 64146, 56176}, {3680, 12625, 519}, {3689, 11376, 27383}, {3811, 49600, 5603}, {3813, 3913, 2}, {3871, 10527, 5218}, {4309, 5258, 11111}, {4342, 6743, 15829}, {4882, 51785, 3452}, {5046, 31145, 56879}, {5258, 34719, 4309}, {5853, 64205, 12437}, {5880, 58609, 11037}, {7991, 24391, 34744}, {8715, 45700, 631}, {10528, 11680, 10588}, {10624, 57279, 5698}, {10912, 44669, 145}, {11235, 12607, 3091}, {11238, 21031, 6919}, {11362, 64202, 34711}, {12116, 12245, 64111}, {12437, 21627, 64205}, {12437, 64205, 1}, {15888, 31140, 5177}, {24387, 45701, 3090}, {26015, 63130, 1788}, {36846, 57287, 3476}, {49719, 62837, 4190}, {56936, 64081, 55}

X(64069) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND ANTI-CONWAY AND X(4)-CROSSPEDAL-OF-X(8)

Barycentrics    a^2*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4+6*b^2*c^2+c^4)) : :
X(64069) = -3*X[154]+2*X[9798]

X(64069) lies on these lines: {1, 6}, {3, 947}, {4, 9370}, {8, 394}, {10, 17811}, {20, 23144}, {25, 16980}, {33, 14872}, {35, 37501}, {40, 222}, {42, 1496}, {46, 1407}, {47, 3052}, {55, 255}, {56, 1066}, {57, 1103}, {64, 2807}, {73, 3428}, {109, 1413}, {145, 1993}, {154, 9798}, {155, 952}, {184, 8192}, {221, 517}, {227, 5709}, {323, 3621}, {355, 17814}, {388, 5706}, {495, 5707}, {498, 37674}, {499, 37679}, {511, 12410}, {515, 1498}, {516, 64057}, {519, 22130}, {576, 58535}, {580, 1617}, {602, 10964}, {603, 10310}, {607, 20752}, {651, 962}, {692, 22654}, {774, 32912}, {912, 1854}, {940, 3085}, {942, 44414}, {944, 1181}, {946, 34048}, {961, 51497}, {971, 7959}, {999, 36754}, {1038, 63976}, {1040, 12675}, {1071, 54295}, {1074, 10404}, {1125, 17825}, {1167, 55086}, {1201, 61357}, {1350, 8193}, {1376, 3075}, {1385, 37514}, {1394, 6769}, {1398, 53548}, {1406, 24028}, {1433, 6765}, {1455, 37531}, {1465, 12704}, {1482, 23071}, {1483, 12161}, {1697, 2003}, {1745, 64077}, {1771, 5687}, {1783, 40836}, {1834, 10629}, {1935, 11496}, {1936, 11500}, {1994, 3623}, {2093, 7273}, {2123, 15501}, {2361, 11510}, {2594, 26357}, {2810, 42461}, {3057, 64020}, {3076, 19000}, {3077, 18999}, {3086, 4383}, {3149, 4551}, {3189, 22145}, {3241, 63094}, {3295, 22117}, {3303, 61398}, {3333, 52424}, {3445, 52186}, {3556, 8679}, {3616, 10601}, {3617, 15066}, {3622, 5422}, {3811, 46974}, {4252, 8069}, {4255, 8071}, {4292, 20744}, {4293, 37537}, {4295, 6180}, {4303, 5584}, {4306, 44858}, {5020, 23841}, {5022, 13006}, {5045, 39523}, {5119, 62207}, {5250, 55400}, {5255, 20745}, {5348, 11501}, {5452, 11022}, {5534, 51361}, {5550, 63128}, {5570, 17054}, {5603, 10982}, {5691, 15811}, {5711, 23131}, {5758, 34032}, {5844, 16266}, {5906, 23541}, {6149, 21000}, {6767, 36750}, {6851, 51424}, {7046, 40396}, {7080, 63068}, {7373, 37509}, {7592, 7967}, {7982, 34040}, {7991, 34043}, {8757, 12699}, {9052, 42460}, {9053, 64195}, {9371, 63399}, {9817, 58631}, {10246, 36752}, {10247, 36749}, {10267, 52408}, {10321, 37646}, {10571, 22770}, {10680, 34586}, {11248, 52407}, {11365, 17810}, {12001, 15306}, {12245, 60689}, {12514, 55406}, {12647, 63339}, {12680, 41339}, {12702, 23070}, {13138, 46355}, {13374, 19372}, {14110, 19349}, {14986, 32911}, {15068, 37705}, {15805, 38028}, {17102, 55405}, {17824, 32394}, {18445, 18526}, {18451, 18525}, {19855, 25878}, {19862, 59777}, {21620, 37543}, {22118, 37504}, {22128, 63130}, {22129, 56288}, {22753, 37694}, {22767, 54427}, {22791, 44413}, {23120, 41575}, {23129, 64163}, {23140, 63137}, {26935, 45963}, {28224, 32139}, {31884, 37557}, {34634, 43273}, {34657, 51024}, {35645, 37415}, {36753, 37624}, {37257, 51377}, {37546, 53097}, {37559, 51784}, {37576, 50630}, {38293, 51773}, {38866, 59813}, {38902, 40957}, {41227, 57193}, {44662, 64022}, {54286, 62244}, {55399, 62874}, {57277, 64046}

X(64069) = reflection of X(i) in X(j) for these {i,j}: {221, 3157}
X(64069) = inverse of X(62326) in MacBeath circumconic
X(64069) = X(i)-Dao conjugate of X(j) for these {i, j}: {7011, 347}
X(64069) = X(i)-Ceva conjugate of X(j) for these {i, j}: {280, 3}
X(64069) = pole of line {521, 3239} with respect to the MacBeath circumconic
X(64069) = pole of line {81, 14986} with respect to the Stammler hyperbola
X(64069) = pole of line {14344, 17494} with respect to the Steiner circumellipse
X(64069) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(53995)}}, {{A, B, C, X(6), X(52218)}}, {{A, B, C, X(9), X(947)}}, {{A, B, C, X(56), X(3554)}}, {{A, B, C, X(59), X(46355)}}, {{A, B, C, X(960), X(51497)}}, {{A, B, C, X(961), X(57278)}}, {{A, B, C, X(1002), X(44547)}}, {{A, B, C, X(1037), X(9119)}}, {{A, B, C, X(1433), X(22124)}}, {{A, B, C, X(1743), X(52186)}}, {{A, B, C, X(2334), X(3553)}}, {{A, B, C, X(16667), X(57709)}}, {{A, B, C, X(31435), X(51498)}}
X(64069) = barycentric product X(i)*X(j) for these (i, j): {312, 52218}, {1753, 63}, {56544, 9}
X(64069) = barycentric quotient X(i)/X(j) for these (i, j): {1753, 92}, {52218, 57}, {56544, 85}
X(64069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3074, 1001}, {47, 11508, 3052}, {56, 61397, 36745}, {517, 3157, 221}, {1124, 1335, 9}, {5353, 5357, 3973}, {7074, 34046, 3}, {10306, 23072, 109}

X(64070) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND EHRMANN AND X(4)-CROSSPEDAL-OF-X(8)

Barycentrics    a*(a^2+3*a*(b+c)-2*(b^2+c^2)) : :
X(64070) = -2*X[1]+3*X[6], -4*X[10]+3*X[599], -3*X[69]+5*X[3617], -6*X[141]+7*X[9780], -6*X[165]+5*X[55614], 3*X[193]+X[3621], -4*X[551]+5*X[51185], -4*X[575]+3*X[10246], -6*X[597]+5*X[3616], -8*X[1125]+9*X[47352], -3*X[1350]+4*X[3579], -3*X[1351]+X[8148] and many others

X(64070) lies on these lines: {1, 6}, {8, 524}, {10, 599}, {31, 41711}, {40, 53097}, {42, 36263}, {43, 18201}, {55, 896}, {56, 4557}, {57, 4849}, {63, 4689}, {65, 9004}, {69, 3617}, {81, 4661}, {141, 9780}, {145, 190}, {165, 55614}, {193, 3621}, {210, 37674}, {239, 49499}, {312, 38473}, {354, 14924}, {355, 15069}, {511, 12702}, {515, 64080}, {517, 11477}, {519, 5695}, {528, 24695}, {536, 49495}, {537, 49453}, {542, 18525}, {551, 51185}, {575, 10246}, {576, 1482}, {597, 3616}, {726, 49486}, {740, 49680}, {750, 3711}, {894, 49450}, {899, 4860}, {940, 3681}, {944, 8550}, {952, 63722}, {982, 17779}, {999, 45763}, {1002, 2238}, {1046, 3913}, {1125, 47352}, {1155, 54281}, {1350, 3579}, {1351, 8148}, {1352, 18357}, {1353, 61295}, {1376, 5524}, {1385, 53093}, {1407, 41539}, {1445, 42314}, {1458, 4878}, {1469, 3214}, {1698, 21358}, {1707, 21000}, {1854, 32276}, {2097, 2810}, {2098, 8540}, {2099, 19369}, {2292, 2334}, {2393, 16980}, {2550, 17365}, {2836, 5903}, {2930, 32278}, {2999, 21342}, {3000, 3779}, {3008, 51002}, {3052, 3870}, {3056, 9049}, {3158, 62820}, {3189, 64159}, {3240, 17595}, {3241, 8584}, {3244, 47356}, {3245, 9037}, {3305, 4883}, {3315, 14997}, {3339, 21896}, {3416, 3626}, {3445, 62832}, {3564, 37705}, {3576, 10541}, {3589, 5550}, {3618, 46934}, {3619, 46931}, {3622, 59373}, {3623, 5032}, {3624, 51003}, {3625, 5847}, {3629, 9053}, {3632, 28538}, {3633, 4693}, {3634, 3763}, {3636, 38023}, {3664, 24393}, {3679, 15533}, {3696, 17118}, {3699, 37684}, {3715, 3720}, {3717, 4851}, {3729, 28581}, {3740, 37682}, {3752, 62823}, {3755, 5850}, {3756, 63126}, {3786, 18166}, {3790, 17309}, {3811, 4252}, {3823, 17298}, {3828, 51186}, {3873, 4383}, {3874, 17054}, {3875, 28582}, {3879, 4899}, {3886, 17351}, {3923, 49460}, {3932, 17311}, {3935, 37540}, {3938, 4722}, {3951, 37548}, {3967, 39594}, {3979, 4428}, {4026, 17253}, {4042, 32771}, {4134, 62844}, {4255, 37599}, {4260, 5708}, {4265, 5217}, {4307, 7277}, {4310, 17366}, {4360, 31302}, {4361, 24349}, {4387, 32938}, {4413, 21805}, {4421, 4650}, {4423, 62867}, {4429, 7232}, {4430, 17597}, {4437, 29583}, {4646, 54422}, {4648, 5686}, {4654, 21949}, {4655, 48829}, {4659, 49468}, {4660, 17771}, {4668, 50950}, {4669, 51188}, {4672, 48805}, {4677, 51187}, {4678, 11160}, {4684, 17279}, {4716, 49532}, {4724, 9029}, {4745, 50989}, {4753, 16825}, {4784, 9040}, {4848, 62789}, {4852, 49446}, {4863, 41011}, {4888, 38200}, {4891, 30568}, {4896, 38185}, {4924, 5853}, {4966, 17267}, {4981, 19701}, {5085, 13624}, {5095, 32298}, {5096, 5204}, {5102, 11278}, {5128, 7289}, {5135, 37606}, {5308, 50996}, {5476, 18493}, {5480, 39898}, {5529, 40726}, {5542, 17278}, {5698, 50997}, {5718, 64153}, {5790, 34507}, {5844, 64067}, {5848, 62616}, {5852, 24248}, {5880, 49772}, {6180, 7672}, {7226, 20182}, {7973, 64031}, {7987, 55684}, {8185, 19596}, {8192, 32621}, {8270, 62207}, {8541, 11396}, {8787, 9884}, {9015, 47721}, {9052, 37516}, {9620, 10542}, {9955, 38072}, {9974, 35641}, {9975, 35642}, {10005, 62999}, {10222, 53858}, {10247, 11482}, {10516, 61261}, {10980, 16602}, {11038, 37650}, {11179, 34773}, {11235, 33096}, {11364, 39560}, {12699, 54131}, {12782, 44453}, {13330, 14839}, {14561, 61272}, {15808, 59408}, {16020, 51099}, {16823, 51055}, {16830, 50075}, {16831, 51050}, {16834, 49463}, {16948, 41610}, {17012, 62868}, {17070, 33137}, {17119, 49483}, {17126, 62236}, {17151, 49525}, {17162, 17165}, {17243, 27549}, {17245, 38057}, {17259, 60731}, {17262, 49470}, {17318, 49447}, {17330, 39581}, {17334, 64168}, {17337, 38053}, {17364, 32850}, {17599, 61358}, {17718, 31187}, {17723, 61652}, {17724, 24597}, {17728, 60414}, {18480, 47353}, {18481, 43273}, {18483, 53023}, {19604, 24471}, {19862, 47355}, {19875, 50993}, {19877, 20582}, {19878, 38089}, {20011, 32933}, {20012, 32939}, {20014, 63027}, {20049, 63117}, {20053, 51001}, {20057, 20583}, {20423, 22791}, {21356, 46933}, {22165, 53620}, {23841, 29959}, {24476, 31794}, {24477, 37662}, {24725, 31140}, {24821, 49452}, {25557, 38086}, {25568, 37646}, {27065, 62866}, {29649, 59597}, {30332, 51190}, {30340, 51150}, {30567, 59596}, {30811, 33114}, {31145, 63064}, {31663, 55626}, {31673, 36990}, {31884, 35242}, {32113, 47506}, {32455, 51147}, {32921, 49685}, {33136, 61716}, {33682, 49504}, {34046, 41538}, {34253, 37138}, {34381, 50193}, {36480, 49449}, {37501, 63976}, {37624, 53092}, {37660, 46897}, {38029, 55711}, {38116, 48876}, {38165, 61545}, {38314, 63124}, {39567, 63086}, {39586, 51034}, {39587, 50835}, {39885, 61250}, {41869, 51024}, {42289, 60909}, {43180, 50011}, {44497, 51691}, {44498, 51689}, {44656, 45572}, {44657, 45573}, {47276, 47321}, {47455, 47477}, {47458, 51725}, {48922, 48927}, {49451, 49484}, {49455, 49489}, {49461, 55998}, {49477, 50283}, {49493, 50016}, {49510, 50302}, {49520, 50281}, {49560, 50313}, {49698, 50289}, {49747, 50282}, {49752, 49766}, {50587, 50591}, {51006, 63127}, {51066, 51189}, {51093, 63125}, {51198, 62617}, {52923, 62837}, {54173, 61524}, {55671, 58219}, {55682, 58224}, {55701, 58230}, {60446, 62998}, {60942, 63977}, {62814, 63074}, {62855, 63095}

X(64070) = midpoint of X(i) and X(j) for these {i,j}: {31145, 63064}
X(64070) = reflection of X(i) in X(j) for these {i,j}: {1, 4663}, {6, 3751}, {69, 49524}, {599, 47359}, {944, 8550}, {1469, 22277}, {1482, 576}, {1992, 51124}, {2930, 32278}, {3241, 8584}, {3242, 6}, {3416, 49529}, {3886, 17351}, {5695, 32935}, {7973, 64031}, {9884, 8787}, {11160, 50949}, {15069, 355}, {15533, 3679}, {17276, 3755}, {32113, 47506}, {32298, 5095}, {32921, 49685}, {39898, 5480}, {40341, 3416}, {44453, 12782}, {47276, 47321}, {49446, 4852}, {49451, 49484}, {49453, 49488}, {49455, 49489}, {49458, 4672}, {49460, 3923}, {49486, 49497}, {49679, 51192}, {49681, 51196}, {49688, 49536}, {49747, 50282}, {50790, 47356}, {50998, 20583}, {50999, 597}, {51000, 1992}, {51147, 32455}, {51192, 3629}, {51689, 44498}, {51691, 44497}, {53097, 40}
X(64070) = pole of line {55, 11284} with respect to the Feuerbach hyperbola
X(64070) = pole of line {521, 39521} with respect to the MacBeath circumconic
X(64070) = pole of line {4789, 17494} with respect to the Steiner circumellipse
X(64070) = pole of line {1018, 56797} with respect to the Yff parabola
X(64070) = pole of line {274, 17588} with respect to the Wallace hyperbola
X(64070) = pole of line {11927, 14300} with respect to the Privalov conic
X(64070) = pole of line {142, 17323} with respect to the dual conic of Yff parabola
X(64070) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29573)}}, {{A, B, C, X(9), X(7241)}}, {{A, B, C, X(37), X(56314)}}, {{A, B, C, X(56), X(16784)}}, {{A, B, C, X(219), X(55977)}}, {{A, B, C, X(1001), X(43760)}}, {{A, B, C, X(1002), X(4663)}}, {{A, B, C, X(1279), X(42290)}}, {{A, B, C, X(1449), X(19604)}}, {{A, B, C, X(2334), X(16785)}}, {{A, B, C, X(2991), X(3242)}}, {{A, B, C, X(3731), X(56179)}}, {{A, B, C, X(5220), X(55935)}}, {{A, B, C, X(10308), X(56527)}}, {{A, B, C, X(16469), X(42315)}}, {{A, B, C, X(16503), X(55919)}}, {{A, B, C, X(16779), X(37129)}}, {{A, B, C, X(23704), X(37138)}}, {{A, B, C, X(38316), X(39273)}}
X(64070) = barycentric product X(i)*X(j) for these (i, j): {1, 29573}
X(64070) = barycentric quotient X(i)/X(j) for these (i, j): {29573, 75}
X(64070) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3751, 4663}, {1, 4663, 6}, {1, 5220, 45}, {6, 518, 3242}, {210, 62819, 37674}, {518, 4663, 1}, {519, 32935, 5695}, {537, 49488, 49453}, {599, 47359, 38087}, {726, 49497, 49486}, {899, 54352, 4860}, {1743, 3243, 1279}, {1992, 9041, 51000}, {3240, 62235, 17595}, {3416, 34379, 40341}, {3416, 49529, 59407}, {3629, 9053, 51192}, {3640, 5589, 7969}, {3641, 5588, 7968}, {3755, 5850, 17276}, {3870, 4641, 3052}, {3935, 62795, 37540}, {3979, 7262, 4428}, {4430, 32911, 17597}, {4672, 49458, 48805}, {5695, 32935, 49721}, {5847, 49536, 49688}, {9026, 22277, 1469}, {9041, 51124, 1992}, {9053, 51192, 49679}, {34379, 49529, 3416}, {38047, 49511, 3763}, {49451, 50127, 49484}, {49453, 49488, 50120}, {49470, 62222, 17262}

X(64071) = ANTICOMPLEMENT OF X(4647)

Barycentrics    (b+c)*(-a^3-2*a^2*(b+c)+b*c*(b+c)-a*(b^2-b*c+c^2)) : :
X(64071) = -3*X[2]+4*X[3743], -10*X[1698]+9*X[27812], -2*X[2650]+3*X[3241], -7*X[3523]+8*X[58392], -7*X[3622]+8*X[58380], -5*X[3623]+4*X[63354], -7*X[3624]+8*X[58387], -11*X[5550]+12*X[10180], -7*X[9780]+6*X[21020], -3*X[11239]+2*X[17874], -13*X[19877]+12*X[27798], -4*X[49564]+3*X[64164]

X(64071) lies on these lines: {1, 596}, {2, 3743}, {8, 192}, {10, 3995}, {21, 39766}, {37, 19874}, {42, 56318}, {58, 4427}, {65, 4552}, {72, 3896}, {75, 62831}, {79, 44006}, {81, 41813}, {99, 763}, {145, 758}, {191, 16704}, {194, 7985}, {312, 26030}, {321, 3931}, {386, 25253}, {442, 4442}, {519, 50165}, {523, 64199}, {525, 62399}, {536, 4968}, {595, 17150}, {690, 21222}, {726, 25295}, {846, 27368}, {964, 5695}, {986, 32915}, {1010, 64010}, {1089, 4868}, {1125, 17495}, {1193, 4970}, {1201, 14752}, {1203, 45222}, {1330, 33100}, {1468, 32934}, {1698, 27812}, {1834, 4918}, {1962, 3210}, {1999, 56288}, {2650, 3241}, {2667, 24349}, {2783, 15971}, {2796, 50234}, {2901, 4424}, {3120, 3178}, {3159, 3293}, {3161, 40977}, {3175, 3701}, {3187, 12514}, {3214, 3971}, {3244, 6758}, {3295, 3891}, {3303, 49453}, {3454, 27558}, {3523, 58392}, {3622, 58380}, {3623, 63354}, {3624, 58387}, {3666, 3702}, {3670, 29824}, {3672, 18697}, {3678, 19998}, {3685, 5262}, {3695, 4972}, {3704, 4854}, {3710, 3755}, {3712, 56778}, {3725, 4734}, {3746, 20045}, {3797, 26965}, {3868, 20718}, {3869, 18662}, {3871, 32926}, {3875, 5250}, {3878, 20040}, {3879, 20291}, {3881, 17154}, {3914, 57808}, {3915, 32921}, {3936, 63997}, {3951, 25237}, {3993, 56185}, {4016, 17314}, {4037, 27040}, {4062, 56949}, {4068, 32922}, {4075, 31855}, {4099, 16600}, {4356, 45744}, {4359, 6051}, {4360, 17141}, {4385, 42044}, {4387, 5192}, {4414, 17733}, {4425, 20653}, {4436, 35978}, {4452, 18698}, {4560, 38348}, {4642, 63800}, {4696, 64175}, {4717, 19863}, {4850, 26094}, {4903, 25123}, {5247, 32936}, {5255, 32928}, {5492, 48877}, {5550, 10180}, {5625, 16710}, {5710, 17318}, {5904, 20011}, {6048, 64178}, {7283, 17016}, {8720, 54310}, {9780, 21020}, {9957, 62401}, {10528, 23555}, {11239, 17874}, {11684, 56018}, {12632, 24394}, {12699, 33070}, {14210, 18600}, {14450, 17778}, {16705, 17762}, {16711, 41875}, {17034, 25248}, {17148, 50281}, {17162, 64072}, {17183, 39774}, {17479, 64047}, {17480, 20057}, {17539, 63292}, {17588, 54335}, {17756, 40986}, {17759, 25263}, {18135, 35544}, {19877, 27798}, {20691, 30730}, {20896, 50071}, {21081, 31037}, {21295, 37588}, {24159, 29830}, {24620, 53034}, {24883, 56313}, {25080, 64081}, {25268, 56311}, {25271, 48304}, {25294, 32925}, {25307, 33296}, {26097, 29840}, {28530, 49745}, {30122, 31031}, {30170, 31058}, {30438, 50579}, {31025, 42031}, {31036, 49488}, {31339, 49474}, {32845, 37607}, {35550, 50101}, {36845, 56839}, {37592, 50122}, {37614, 49492}, {40085, 52555}, {40091, 43993}, {41261, 63136}, {41814, 43990}, {43677, 62908}, {44661, 56936}, {44671, 49447}, {46901, 50608}, {49564, 64164}, {50043, 59760}, {52541, 58401}, {53037, 54389}, {53043, 62874}

X(64071) = reflection of X(i) in X(j) for these {i,j}: {1, 4065}, {8, 2292}, {4647, 3743}, {4968, 37548}, {17164, 1}, {24349, 2667}, {48877, 5492}
X(64071) = anticomplement of X(4647)
X(64071) = perspector of circumconic {{A, B, C, X(27805), X(37205)}}
X(64071) = X(i)-Dao conjugate of X(j) for these {i, j}: {4647, 4647}
X(64071) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7303, 26772}, {40438, 2}
X(64071) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58, 2891}, {1126, 1330}, {1171, 69}, {1255, 21287}, {1333, 41821}, {1576, 14779}, {4596, 21301}, {4629, 20295}, {4632, 21304}, {6578, 512}, {28615, 2895}, {32014, 315}, {40438, 6327}, {47947, 21294}, {50344, 3448}, {52558, 17135}, {53688, 20558}, {57685, 1370}, {62535, 17217}
X(64071) = pole of line {46542, 54229} with respect to the polar circle
X(64071) = pole of line {3952, 4010} with respect to the Kiepert parabola
X(64071) = pole of line {661, 1019} with respect to the Steiner circumellipse
X(64071) = pole of line {15309, 25666} with respect to the Steiner inellipse
X(64071) = pole of line {4360, 17103} with respect to the Wallace hyperbola
X(64071) = pole of line {17184, 24199} with respect to the dual conic of Yff parabola
X(64071) = intersection, other than A, B, C, of circumconics {{A, B, C, X(256), X(39949)}}, {{A, B, C, X(257), X(6539)}}, {{A, B, C, X(596), X(6538)}}, {{A, B, C, X(3995), X(8025)}}, {{A, B, C, X(4451), X(41683)}}
X(64071) = barycentric product X(i)*X(j) for these (i, j): {24067, 86}
X(64071) = barycentric quotient X(i)/X(j) for these (i, j): {24067, 10}
X(64071) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4065, 27804}, {8, 9791, 26064}, {145, 31888, 20086}, {321, 3931, 26115}, {536, 37548, 4968}, {740, 2292, 8}, {1962, 49598, 3616}, {3704, 4854, 5051}, {17164, 27804, 1}, {21020, 58386, 9780}, {25253, 64161, 386}, {27784, 28611, 2}, {41813, 63996, 81}

X(64072) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND X(4)-CROSSPEDAL-OF-X(10)

Barycentrics    (a+b)*(a+c)*(a^2+a*(b+c)-(b+c)^2) : :
X(64072) = -4*X[59723]+5*X[63286]

X(64072) lies on these lines: {1, 333}, {2, 4658}, {6, 10479}, {8, 58}, {10, 81}, {21, 519}, {27, 54422}, {28, 24391}, {29, 55956}, {35, 56181}, {36, 59303}, {38, 43993}, {46, 18206}, {63, 64184}, {69, 1714}, {72, 18178}, {79, 17770}, {86, 1698}, {99, 28502}, {100, 4278}, {145, 4653}, {191, 740}, {239, 3670}, {274, 17731}, {283, 49168}, {284, 5839}, {314, 1089}, {386, 1150}, {387, 14552}, {405, 18185}, {442, 524}, {518, 18180}, {527, 31902}, {540, 2475}, {551, 17557}, {595, 17135}, {596, 62235}, {599, 56780}, {758, 27368}, {849, 7058}, {859, 12513}, {940, 56767}, {956, 4267}, {1010, 3679}, {1043, 3632}, {1046, 4647}, {1125, 5235}, {1126, 26115}, {1203, 3741}, {1210, 2287}, {1211, 25441}, {1333, 17362}, {1408, 40663}, {1412, 1788}, {1724, 10449}, {1737, 1812}, {1746, 10441}, {1778, 2321}, {1780, 51978}, {1834, 49716}, {1838, 56014}, {2303, 3686}, {2323, 34831}, {2360, 24477}, {2650, 54335}, {2895, 3454}, {2901, 3219}, {2975, 4276}, {3017, 3578}, {3085, 16713}, {3193, 10916}, {3214, 17187}, {3216, 14829}, {3218, 64185}, {3241, 17588}, {3286, 5687}, {3293, 3736}, {3555, 18165}, {3625, 4720}, {3634, 5333}, {3650, 28530}, {3678, 17763}, {3710, 50606}, {3811, 54356}, {3813, 37357}, {3828, 17551}, {3831, 27644}, {3841, 32949}, {3874, 32914}, {3913, 17524}, {3915, 50625}, {3936, 24880}, {4001, 23537}, {4038, 25512}, {4042, 5711}, {4066, 32938}, {4067, 24624}, {4078, 63158}, {4184, 8715}, {4205, 49724}, {4221, 11362}, {4225, 8666}, {4229, 63469}, {4234, 4677}, {4273, 4969}, {4362, 5904}, {4416, 56019}, {4641, 5295}, {4649, 27164}, {4669, 51669}, {4683, 36250}, {4685, 13588}, {4716, 56023}, {4753, 51285}, {4847, 62843}, {4848, 5323}, {4877, 17314}, {5084, 37654}, {5192, 63060}, {5259, 35633}, {5277, 50252}, {5292, 5739}, {5312, 32916}, {5315, 50608}, {5361, 19767}, {5439, 17348}, {5563, 37442}, {5692, 17733}, {5741, 45939}, {5752, 5769}, {5788, 10478}, {5847, 41610}, {6048, 18792}, {6734, 40571}, {6765, 17194}, {7751, 52257}, {7760, 52256}, {7991, 37422}, {8025, 9780}, {8258, 21085}, {8822, 17151}, {9534, 37522}, {9612, 56020}, {11108, 19723}, {11523, 25516}, {12514, 17156}, {12607, 47515}, {13407, 34379}, {14007, 19875}, {14008, 24387}, {15523, 41822}, {16047, 17310}, {16050, 17294}, {16053, 29573}, {16054, 16833}, {16454, 48852}, {16825, 18398}, {17162, 64071}, {17167, 21077}, {17178, 26029}, {17185, 41229}, {17197, 21075}, {17206, 62755}, {17313, 50207}, {17346, 52258}, {17514, 49730}, {17539, 31145}, {17553, 51071}, {17589, 53620}, {17751, 27660}, {17778, 25446}, {18163, 57279}, {18169, 50581}, {18192, 59294}, {18646, 49636}, {19280, 46922}, {20083, 32782}, {20086, 26131}, {20653, 41814}, {22299, 35636}, {24271, 50153}, {24902, 41878}, {24982, 26637}, {25543, 25548}, {25639, 32843}, {25645, 35466}, {25669, 41806}, {25962, 64062}, {26030, 27163}, {26051, 49744}, {26117, 49723}, {26643, 50095}, {26860, 46933}, {27174, 50306}, {27798, 41812}, {28612, 30599}, {29473, 33825}, {29633, 30966}, {29674, 33295}, {30171, 32861}, {30172, 32852}, {30939, 46937}, {30984, 33139}, {31330, 62805}, {32911, 50605}, {32917, 59301}, {32945, 39673}, {33296, 34016}, {33766, 50312}, {34378, 41718}, {35099, 54160}, {37373, 37720}, {37402, 43174}, {37685, 43531}, {37693, 62998}, {38456, 47033}, {40773, 49488}, {45923, 48887}, {48837, 54429}, {48862, 56992}, {49728, 64167}, {50159, 56968}, {50755, 56949}, {53594, 58786}, {59723, 63286}

X(64072) = reflection of X(i) in X(j) for these {i,j}: {35637, 18180}
X(64072) = pole of line {995, 1203} with respect to the Stammler hyperbola
X(64072) = pole of line {3624, 4389} with respect to the Wallace hyperbola
X(64072) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(996), X(1224)}}, {{A, B, C, X(2258), X(28502)}}, {{A, B, C, X(5331), X(18812)}}, {{A, B, C, X(17126), X(57705)}}, {{A, B, C, X(37870), X(55942)}}
X(64072) = barycentric product X(i)*X(j) for these (i, j): {17299, 86}, {24914, 333}, {48266, 99}, {50504, 799}
X(64072) = barycentric quotient X(i)/X(j) for these (i, j): {17299, 10}, {24914, 226}, {48266, 523}, {50504, 661}
X(64072) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 28619, 28618}, {2, 4658, 28619}, {8, 16704, 58}, {10, 81, 25526}, {72, 18178, 18417}, {333, 56018, 1}, {518, 18180, 35637}, {2895, 24883, 3454}, {9534, 37683, 37522}, {10449, 37652, 1724}, {33295, 33297, 33953}, {35466, 41014, 25645}

X(64073) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND EHRMANN AND X(4)-CROSSPEDAL-OF-X(10)

Barycentrics    4*a^3-b^3-b^2*c-b*c^2-c^3+5*a^2*(b+c)-2*a*(b^2+c^2) : :
X(64073) = -X[1]+3*X[1992], -3*X[6]+2*X[1125], X[8]+3*X[193], -3*X[69]+5*X[1698], -6*X[141]+7*X[51073], -X[145]+9*X[63027], -4*X[575]+3*X[10165], -6*X[597]+5*X[19862], -3*X[599]+4*X[3634], -3*X[1351]+X[12699], -2*X[1352]+3*X[38146], -3*X[1353]+X[34773] and many others

X(64073) lies on circumconic {{A, B, C, X(55949), X(56044)}} and on these lines: {1, 1992}, {6, 1125}, {8, 193}, {10, 524}, {31, 50744}, {69, 1698}, {81, 4104}, {141, 51073}, {145, 63027}, {226, 19369}, {306, 4722}, {511, 31728}, {515, 63722}, {516, 11477}, {517, 64067}, {518, 3244}, {519, 5695}, {527, 49488}, {542, 31673}, {551, 8584}, {575, 10165}, {576, 946}, {597, 19862}, {599, 3634}, {726, 13330}, {1150, 61652}, {1351, 12699}, {1352, 38146}, {1353, 34773}, {1386, 32455}, {1738, 17364}, {1757, 3879}, {2784, 64091}, {2836, 4084}, {3214, 53541}, {3241, 63117}, {3271, 3555}, {3416, 4691}, {3564, 18480}, {3616, 5032}, {3617, 50950}, {3618, 34595}, {3621, 51001}, {3622, 16475}, {3623, 16496}, {3624, 59373}, {3625, 28538}, {3626, 47359}, {3630, 3844}, {3633, 51192}, {3636, 47358}, {3663, 17771}, {3679, 63064}, {3696, 7277}, {3712, 4028}, {3755, 17770}, {3759, 24231}, {3828, 15533}, {3874, 9004}, {3914, 17491}, {3986, 5625}, {4001, 61358}, {4061, 4697}, {4133, 17351}, {4266, 62858}, {4297, 8550}, {4349, 49457}, {4416, 4649}, {4464, 49445}, {4480, 49452}, {4527, 50118}, {4655, 50091}, {4669, 63115}, {4676, 49763}, {4684, 16468}, {4689, 4831}, {4700, 16825}, {4743, 28558}, {4745, 51187}, {4746, 50783}, {4780, 17768}, {4852, 5852}, {4856, 5850}, {4924, 17765}, {4966, 16669}, {4969, 49483}, {4974, 5542}, {4982, 16973}, {5093, 18493}, {5102, 64085}, {5223, 50284}, {5550, 63127}, {5819, 51194}, {5846, 49536}, {5880, 50022}, {5886, 11482}, {8540, 12053}, {9780, 11160}, {9798, 53019}, {10175, 34507}, {10609, 51198}, {11008, 59406}, {11180, 18492}, {11711, 41672}, {12263, 44500}, {12512, 53097}, {12702, 50962}, {13624, 50979}, {14848, 61268}, {15069, 19925}, {15481, 17390}, {15808, 20583}, {16020, 63086}, {16473, 41614}, {16491, 63026}, {16823, 63049}, {16830, 63052}, {16980, 61692}, {17197, 21077}, {17330, 39580}, {18483, 20423}, {19875, 50992}, {19876, 50990}, {19878, 47352}, {19883, 63124}, {20080, 46933}, {20086, 60459}, {20090, 60731}, {21358, 31253}, {24695, 28580}, {24725, 50758}, {25055, 63022}, {28164, 64080}, {28526, 49486}, {29602, 50996}, {29959, 58474}, {31738, 44479}, {32938, 50292}, {32940, 50306}, {32941, 64017}, {34380, 61524}, {34381, 44545}, {35242, 50967}, {37639, 37762}, {37705, 50986}, {38023, 51156}, {38047, 40341}, {38118, 48876}, {38167, 61545}, {38187, 47595}, {39586, 63054}, {39878, 51212}, {41149, 51071}, {41610, 63259}, {41869, 54132}, {43180, 51002}, {46934, 63000}, {47549, 51693}, {49451, 50303}, {49453, 50131}, {49476, 49712}, {49493, 49770}, {49499, 49783}, {49560, 50115}, {49680, 64016}, {49987, 54352}, {50600, 50611}, {50955, 61261}, {51069, 51188}, {51103, 63125}, {51178, 61256}, {51190, 60905}, {53620, 63116}, {62819, 63009}, {63279, 63280}

X(64073) = midpoint of X(i) and X(j) for these {i,j}: {193, 3751}, {1992, 50952}, {3416, 6144}, {3679, 63064}, {24695, 49495}, {39878, 51212}, {49680, 64016}
X(64073) = reflection of X(i) in X(j) for these {i,j}: {10, 4663}, {551, 8584}, {946, 576}, {1386, 32455}, {3630, 3844}, {3663, 49489}, {3755, 49685}, {4133, 17351}, {4297, 8550}, {11711, 41672}, {12263, 44500}, {15069, 19925}, {15533, 3828}, {31738, 44479}, {32921, 4856}, {32941, 64017}, {39870, 1353}, {49505, 1386}, {49511, 6}, {49529, 3751}, {49684, 51196}, {50091, 50283}, {50611, 50600}, {51003, 20583}, {51004, 597}, {51005, 1992}, {51089, 47356}, {51196, 3629}, {51693, 47549}, {53097, 12512}
X(64073) = pole of line {6590, 26777} with respect to the Steiner circumellipse
X(64073) = pole of line {4789, 25594} with respect to the Steiner inellipse
X(64073) = pole of line {15668, 17304} with respect to the dual conic of Yff parabola
X(64073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 34379, 49511}, {6, 49511, 38049}, {193, 3751, 5847}, {518, 3629, 51196}, {518, 51196, 49684}, {524, 4663, 10}, {1757, 3879, 4078}, {3751, 5847, 49529}, {4028, 4641, 59544}, {4416, 4649, 50290}, {4856, 5850, 32921}, {17770, 49685, 3755}, {17771, 49489, 3663}

X(64074) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    a*(a^6-a^5*(b+c)-a*(b-c)^2*(b+c)^3-2*b*c*(b^2-c^2)^2-2*a^4*(b^2-3*b*c+c^2)+2*a^3*(b^3+b^2*c+b*c^2+c^3)+a^2*(b^4-4*b^3*c-2*b^2*c^2-4*b*c^3+c^4)) : :
X(64074) = -3*X[3158]+X[63981], -4*X[5450]+3*X[11194], -X[6223]+3*X[25568], -2*X[6261]+3*X[56177], -3*X[11235]+4*X[63980], -3*X[34647]+2*X[54198], -4*X[64123]+3*X[64148]

X(64074) lies on circumconic {{A, B, C, X(346), X(9943)}} and on these lines: {1, 1407}, {2, 34630}, {3, 142}, {4, 1329}, {5, 35238}, {9, 58637}, {10, 6244}, {11, 6890}, {12, 6925}, {20, 55}, {21, 5584}, {30, 4421}, {31, 37537}, {34, 9371}, {35, 7580}, {36, 9589}, {40, 958}, {46, 17613}, {56, 962}, {57, 12651}, {63, 7957}, {65, 62836}, {72, 1709}, {78, 12688}, {84, 518}, {100, 3146}, {109, 41402}, {165, 405}, {197, 39568}, {355, 35448}, {376, 4428}, {382, 11499}, {404, 9812}, {411, 5217}, {412, 54394}, {474, 1699}, {480, 36991}, {497, 1466}, {511, 39877}, {515, 3913}, {517, 1158}, {519, 9948}, {529, 8668}, {550, 10267}, {601, 5706}, {631, 8167}, {692, 13346}, {908, 12679}, {936, 11372}, {939, 948}, {942, 64129}, {950, 37541}, {954, 2951}, {956, 7991}, {960, 6282}, {971, 3811}, {988, 12652}, {990, 5266}, {993, 5493}, {997, 9856}, {999, 4301}, {1071, 37569}, {1151, 13887}, {1152, 13940}, {1155, 62333}, {1259, 6253}, {1260, 63998}, {1470, 12701}, {1476, 4345}, {1479, 37374}, {1482, 3881}, {1490, 15726}, {1503, 12335}, {1593, 37577}, {1604, 21068}, {1621, 3522}, {1657, 11849}, {1721, 37552}, {1742, 37573}, {1770, 8069}, {1777, 7078}, {1802, 5781}, {1885, 11383}, {1935, 7074}, {1975, 20449}, {2077, 3149}, {2478, 50031}, {2550, 37434}, {2646, 64150}, {2777, 13204}, {2794, 12340}, {2801, 12684}, {2807, 37482}, {2829, 13205}, {2886, 6847}, {2932, 34789}, {2975, 20070}, {3035, 6848}, {3052, 37570}, {3073, 36745}, {3090, 61158}, {3091, 4413}, {3158, 63981}, {3189, 9799}, {3244, 30283}, {3295, 4297}, {3303, 5731}, {3333, 43166}, {3359, 7686}, {3361, 42884}, {3428, 6361}, {3436, 64000}, {3487, 8255}, {3523, 4423}, {3529, 11491}, {3534, 37621}, {3555, 10085}, {3560, 3579}, {3577, 10107}, {3586, 59329}, {3601, 12565}, {3627, 18491}, {3655, 12000}, {3656, 16203}, {3678, 5779}, {3742, 37526}, {3812, 37560}, {3816, 6926}, {3817, 16408}, {3826, 6846}, {3870, 12680}, {3880, 12650}, {3916, 41338}, {3925, 6837}, {3940, 31803}, {4068, 58389}, {4200, 25882}, {4267, 37422}, {4299, 11508}, {4300, 19765}, {4302, 11507}, {4333, 32760}, {4512, 19520}, {4999, 6935}, {5044, 54370}, {5047, 64108}, {5057, 38901}, {5068, 9342}, {5073, 18524}, {5080, 37001}, {5218, 37421}, {5220, 7330}, {5251, 63469}, {5258, 63468}, {5259, 16192}, {5265, 53055}, {5284, 15717}, {5285, 37046}, {5289, 12672}, {5293, 64134}, {5432, 6838}, {5433, 6966}, {5440, 63988}, {5450, 11194}, {5537, 5687}, {5538, 5730}, {5603, 37403}, {5657, 18253}, {5690, 18761}, {5709, 64118}, {5758, 17768}, {5777, 16112}, {5812, 12676}, {5840, 12332}, {5842, 6851}, {5881, 8168}, {5918, 10884}, {6001, 12635}, {6147, 60896}, {6223, 25568}, {6259, 21077}, {6261, 56177}, {6284, 6836}, {6459, 19000}, {6460, 18999}, {6684, 6913}, {6690, 6908}, {6765, 10864}, {6796, 28150}, {6833, 15908}, {6835, 7965}, {6840, 11502}, {6850, 7680}, {6864, 42356}, {6882, 10893}, {6883, 31663}, {6888, 31245}, {6891, 7681}, {6895, 36999}, {6911, 22793}, {6914, 35239}, {6916, 25466}, {6918, 18483}, {6922, 26333}, {6923, 10894}, {6934, 12775}, {6938, 11827}, {6943, 10896}, {6945, 31246}, {6962, 52793}, {6974, 24953}, {6985, 26285}, {7098, 22760}, {7171, 12675}, {7956, 10200}, {7958, 37462}, {7988, 16862}, {7992, 11523}, {7994, 57279}, {7996, 60723}, {8142, 8641}, {8158, 8666}, {8715, 28164}, {8726, 10178}, {8727, 31777}, {9441, 54354}, {9708, 43174}, {9709, 19925}, {9746, 16849}, {9779, 17531}, {9842, 20103}, {9961, 34772}, {10058, 59317}, {10164, 11108}, {10171, 16863}, {10198, 37424}, {10269, 22791}, {10525, 37356}, {10679, 18481}, {10827, 59328}, {10895, 37437}, {10902, 37426}, {11235, 63980}, {11246, 55109}, {11249, 28174}, {11490, 12203}, {11501, 12943}, {11510, 15326}, {12178, 23698}, {12260, 43178}, {12327, 12328}, {12329, 29181}, {12410, 63429}, {12514, 31793}, {12520, 24929}, {12545, 23853}, {12607, 12667}, {12702, 22758}, {13374, 37534}, {15228, 36152}, {15254, 61122}, {15852, 17594}, {16370, 59320}, {16371, 50865}, {16418, 50808}, {16853, 58441}, {17538, 61159}, {17582, 38037}, {17928, 20988}, {18540, 58631}, {19541, 25440}, {19763, 49130}, {19843, 35514}, {21628, 57284}, {22560, 48695}, {24328, 24683}, {24470, 60895}, {25681, 63989}, {25968, 27505}, {26086, 28202}, {26118, 30778}, {26286, 28198}, {26332, 31775}, {26446, 37234}, {28212, 32153}, {30304, 41863}, {30384, 40293}, {31162, 37561}, {31787, 54318}, {33597, 50528}, {33899, 49168}, {34247, 51063}, {34620, 34688}, {34647, 54198}, {34773, 37622}, {34791, 63430}, {35251, 63753}, {35258, 37228}, {35772, 42266}, {35773, 42267}, {36002, 62710}, {36746, 37529}, {37078, 61124}, {37267, 54348}, {37429, 63257}, {37544, 62839}, {37579, 64003}, {37592, 61086}, {37606, 51717}, {37611, 45776}, {37727, 44455}, {38150, 50203}, {41854, 42885}, {42258, 44590}, {42259, 44591}, {42843, 52026}, {43577, 43847}, {44431, 56774}, {44663, 54156}, {49140, 61154}, {50371, 63986}, {50688, 61152}, {50689, 61156}, {50693, 61155}, {57288, 64111}, {59301, 62183}, {59691, 63992}, {61157, 62152}, {63266, 64107}, {63304, 63386}, {64123, 64148}

X(64074) = midpoint of X(i) and X(j) for these {i,j}: {84, 6769}, {3189, 9799}, {5758, 64190}, {6765, 10864}, {7992, 11523}
X(64074) = reflection of X(i) in X(j) for these {i,j}: {1490, 56176}, {3913, 10306}, {5709, 64118}, {6259, 21077}, {6985, 26285}, {8158, 8666}, {10525, 37356}, {11500, 11248}, {12513, 12114}, {12635, 37531}, {12667, 12607}, {22560, 48695}, {22770, 5450}, {37411, 6796}, {49168, 33899}, {62858, 34862}, {64075, 550}, {64077, 3}
X(64074) = pole of line {4184, 8273} with respect to the Stammler hyperbola
X(64074) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10860, 9943}, {1, 37022, 63991}, {1, 9841, 58567}, {3, 11496, 1001}, {3, 12699, 22753}, {3, 31730, 11495}, {3, 516, 64077}, {3, 946, 25524}, {4, 10310, 1376}, {21, 9778, 5584}, {30, 11248, 11500}, {35, 64005, 7580}, {40, 1012, 958}, {84, 6769, 518}, {382, 35000, 11499}, {515, 10306, 3913}, {517, 12114, 12513}, {517, 34862, 62858}, {962, 6909, 56}, {1621, 3522, 8273}, {1699, 59326, 474}, {2077, 41869, 3149}, {3870, 63984, 12680}, {4301, 63983, 999}, {5248, 12512, 3}, {5450, 22770, 11194}, {5450, 28194, 22770}, {5918, 37080, 10884}, {6361, 6906, 3428}, {6796, 28150, 37411}, {6836, 64078, 6284}, {8666, 28228, 8158}, {10178, 51715, 8726}, {11248, 11500, 4421}, {15726, 56176, 1490}, {25440, 51118, 19541}, {26285, 28146, 6985}

X(64075) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-INNER-YFF AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    3*a^7-3*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-5*b^2+2*b*c-5*c^2)+a*(b^2-c^2)^2*(b^2+c^2)-a^2*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)+a^4*(5*b^3-3*b^2*c-3*b*c^2+5*c^3)+a^3*(b^4-2*b^3*c+10*b^2*c^2-2*b*c^3+c^4) : :
X(64075) = -2*X[5763]+3*X[56177], -4*X[6796]+3*X[45701], -2*X[21077]+3*X[52026]

X(64075) lies on these lines: {1, 7}, {3, 6690}, {4, 993}, {5, 35250}, {10, 50701}, {30, 10525}, {36, 6836}, {40, 6934}, {165, 4190}, {376, 10532}, {377, 59320}, {382, 26470}, {405, 7958}, {411, 1478}, {452, 3817}, {498, 14794}, {499, 6840}, {511, 49164}, {515, 5709}, {528, 8158}, {535, 12667}, {550, 10267}, {944, 3874}, {946, 6868}, {956, 6253}, {958, 20420}, {997, 64004}, {1012, 30264}, {1125, 5715}, {1151, 45650}, {1152, 45651}, {1376, 31799}, {1503, 49185}, {1657, 10680}, {1699, 6872}, {1885, 26377}, {1936, 56819}, {2777, 49203}, {2794, 49153}, {2801, 64144}, {2829, 37411}, {2975, 59355}, {3011, 50699}, {3146, 10527}, {3149, 11827}, {3428, 37468}, {3436, 44425}, {3485, 51717}, {3486, 62852}, {3529, 12116}, {3534, 16202}, {3576, 51706}, {3585, 6838}, {3624, 6992}, {3627, 45630}, {3814, 6927}, {3822, 6988}, {5059, 10529}, {5073, 18544}, {5129, 10171}, {5204, 37374}, {5230, 50702}, {5231, 50696}, {5248, 59345}, {5251, 6835}, {5267, 6847}, {5450, 6851}, {5536, 12649}, {5584, 11112}, {5603, 35016}, {5691, 6734}, {5705, 19925}, {5758, 22836}, {5762, 12635}, {5763, 56177}, {5812, 37837}, {5840, 48694}, {5841, 6256}, {5842, 22770}, {6284, 26437}, {6459, 26464}, {6460, 26458}, {6598, 24477}, {6684, 6885}, {6796, 45701}, {6827, 10200}, {6839, 19854}, {6890, 7280}, {6897, 7688}, {6899, 37561}, {6904, 10164}, {6905, 26364}, {6909, 36152}, {6916, 12511}, {6925, 10483}, {6930, 18483}, {6933, 52850}, {6936, 8227}, {6938, 41869}, {6948, 31730}, {6955, 35242}, {6962, 7951}, {6966, 59319}, {7354, 7580}, {7491, 26333}, {7982, 37000}, {9778, 37256}, {9799, 54302}, {9812, 15680}, {10268, 12512}, {10587, 50693}, {10597, 17538}, {10806, 11001}, {10894, 52265}, {10916, 28164}, {11106, 38037}, {11240, 15683}, {11269, 50694}, {11531, 20075}, {12001, 15681}, {12203, 26431}, {12248, 49176}, {12514, 63438}, {12595, 48872}, {12617, 31424}, {12675, 18481}, {12680, 14054}, {12704, 37002}, {12943, 26481}, {12953, 26475}, {13095, 17845}, {13907, 42638}, {13965, 42637}, {15326, 37022}, {15951, 63429}, {16371, 50031}, {17580, 58441}, {17625, 64043}, {17702, 49151}, {17800, 37726}, {18543, 49137}, {19049, 42259}, {19050, 42258}, {19541, 57288}, {20076, 41575}, {21077, 52026}, {21168, 45085}, {22753, 31789}, {23698, 49147}, {24390, 36999}, {25440, 64111}, {26308, 39568}, {28150, 40265}, {29181, 45728}, {29639, 50698}, {31452, 59421}, {32214, 62155}, {33108, 59356}, {34617, 64173}, {37550, 64129}, {37583, 63983}, {37821, 62359}, {41338, 57287}, {42266, 45640}, {42267, 45641}, {54318, 64001}, {63308, 63386}, {63988, 64002}

X(64075) = reflection of X(i) in X(j) for these {i,j}: {5758, 22836}, {5812, 37837}, {6256, 6985}, {6851, 5450}, {48482, 11249}, {49168, 5709}, {64074, 550}
X(64075) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 26332, 10198}, {4, 11012, 26363}, {20, 4293, 4297}, {20, 962, 4302}, {30, 11249, 48482}, {382, 35252, 26470}, {5709, 49170, 62858}, {5841, 6985, 6256}, {11249, 48482, 45700}

X(64076) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    3*a^7-5*a^5*(b-c)^2-3*a^6*(b+c)-(b-c)^4*(b+c)^3+a*(b^2-c^2)^2*(b^2-4*b*c+c^2)+a^4*(5*b^3+b^2*c+b*c^2+5*c^3)+a^3*(b^4-6*b^3*c+2*b^2*c^2-6*b*c^3+c^4)-a^2*(b^5-b^4*c-b*c^4+c^5) : :
X(64076) = -4*X[5450]+3*X[45700], -2*X[10916]+3*X[52027]

X(64076) lies on these lines: {1, 7}, {3, 3816}, {4, 2077}, {5, 35249}, {30, 4421}, {35, 6925}, {40, 6938}, {119, 382}, {165, 6872}, {376, 10531}, {452, 10164}, {497, 63983}, {498, 37437}, {511, 49165}, {515, 12640}, {519, 54156}, {550, 10269}, {758, 64190}, {908, 52860}, {946, 6948}, {950, 64129}, {958, 31777}, {1012, 11826}, {1151, 45652}, {1152, 45653}, {1158, 49168}, {1470, 6284}, {1479, 6909}, {1503, 49186}, {1519, 6934}, {1657, 10679}, {1699, 4190}, {1709, 57287}, {1768, 12649}, {1788, 46684}, {1837, 17613}, {1885, 26378}, {2096, 3874}, {2478, 59326}, {2777, 49204}, {2794, 49154}, {2801, 3189}, {2829, 10306}, {3146, 5552}, {3149, 24466}, {3359, 6868}, {3436, 5537}, {3529, 12115}, {3534, 16203}, {3583, 6890}, {3627, 45631}, {3647, 5657}, {3817, 6904}, {5010, 6838}, {5059, 10528}, {5073, 18542}, {5129, 58441}, {5248, 6916}, {5436, 64113}, {5440, 12679}, {5450, 45700}, {5538, 11415}, {5554, 9778}, {5584, 57002}, {5603, 51714}, {5687, 64000}, {5691, 6735}, {5722, 64128}, {5840, 48482}, {6244, 57288}, {6259, 56176}, {6459, 26465}, {6460, 26459}, {6684, 6930}, {6836, 59327}, {6850, 10198}, {6869, 12608}, {6885, 18483}, {6906, 26363}, {6935, 25639}, {6936, 35242}, {6943, 10724}, {6955, 8227}, {6962, 59325}, {6966, 7741}, {6976, 31423}, {6987, 10270}, {6992, 16192}, {7354, 26358}, {7580, 15338}, {7958, 56997}, {7982, 37002}, {8148, 38753}, {8715, 12667}, {9812, 37256}, {9961, 11015}, {10171, 17580}, {10572, 63985}, {10586, 50693}, {10596, 17538}, {10680, 38761}, {10805, 11001}, {10915, 28164}, {10916, 52027}, {10993, 18518}, {11239, 15683}, {11496, 31775}, {11531, 20076}, {12000, 15681}, {12203, 26432}, {12511, 59345}, {12594, 48872}, {12607, 40267}, {12648, 20066}, {12688, 41389}, {12703, 37000}, {12705, 17647}, {12751, 13199}, {12943, 26482}, {12953, 26476}, {13094, 17845}, {13906, 42638}, {13964, 42637}, {15171, 63991}, {15704, 37622}, {16127, 37700}, {17702, 49152}, {17757, 37001}, {18481, 23340}, {18545, 49137}, {19047, 42259}, {19048, 42258}, {20050, 64009}, {21164, 59420}, {21635, 27383}, {22836, 63962}, {23698, 49148}, {26309, 39568}, {27385, 50695}, {28154, 37713}, {28158, 59719}, {29181, 45729}, {30513, 50244}, {32213, 62155}, {34630, 57006}, {35000, 37821}, {35238, 37290}, {36977, 64145}, {37404, 49553}, {38037, 56999}, {42266, 45642}, {42267, 45643}, {50701, 51118}, {54370, 57284}, {55297, 64186}, {63309, 63386}

X(64076) = midpoint of X(i) and X(j) for these {i,j}: {3189, 12246}
X(64076) = reflection of X(i) in X(j) for these {i,j}: {6256, 11248}, {6259, 56176}, {12667, 8715}, {16127, 37700}, {40267, 12607}, {49168, 1158}, {49169, 49163}, {63962, 22836}, {64077, 550}
X(64076) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 26333, 10200}, {4, 2077, 26364}, {20, 4294, 4297}, {20, 962, 4299}, {30, 11248, 6256}, {382, 35251, 119}, {515, 49163, 49169}, {3146, 5552, 41698}, {3189, 12246, 2801}, {6256, 11248, 45701}

X(64077) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP TANGENTIAL AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    a*(a^6-a^5*(b+c)+2*a^3*(b-c)^2*(b+c)-a*(b-c)^4*(b+c)+2*b*c*(b^2-c^2)^2-2*a^4*(b^2+b*c+c^2)+a^2*(b^4+6*b^2*c^2+c^4)) : :
X(64077) = -X[3189]+3*X[54051], -3*X[3928]+X[7992], -3*X[4421]+4*X[6796], -X[6769]+3*X[52026], -X[9799]+3*X[24477], -3*X[11236]+4*X[18242], -2*X[12607]+3*X[64148], 3*X[28610]+X[54228]

X(64077) lies on these lines: {1, 1427}, {2, 5584}, {3, 142}, {4, 958}, {5, 35239}, {8, 36002}, {10, 19541}, {11, 6836}, {12, 6838}, {20, 56}, {21, 9812}, {30, 10525}, {35, 9589}, {36, 9614}, {40, 936}, {55, 411}, {57, 9943}, {63, 12688}, {64, 24310}, {65, 64150}, {72, 41338}, {78, 7957}, {84, 15726}, {85, 62385}, {100, 20070}, {104, 3529}, {165, 474}, {221, 1936}, {354, 10884}, {376, 40726}, {382, 22758}, {388, 37421}, {390, 57283}, {392, 59340}, {404, 9778}, {405, 1699}, {499, 37374}, {511, 39883}, {515, 12513}, {517, 3811}, {518, 1490}, {519, 8158}, {527, 54227}, {529, 12667}, {535, 40267}, {550, 10269}, {940, 4300}, {942, 12520}, {954, 63974}, {956, 5691}, {971, 62858}, {978, 9441}, {988, 1721}, {990, 37592}, {993, 51118}, {997, 31793}, {999, 4297}, {1004, 19861}, {1012, 11012}, {1044, 1407}, {1058, 43161}, {1064, 5706}, {1071, 12704}, {1106, 3000}, {1151, 22763}, {1152, 22764}, {1155, 63985}, {1158, 37623}, {1191, 37570}, {1193, 37537}, {1259, 11415}, {1329, 6848}, {1350, 10476}, {1465, 54295}, {1466, 3474}, {1479, 57278}, {1496, 6180}, {1503, 22778}, {1593, 1848}, {1617, 12053}, {1657, 22765}, {1708, 64131}, {1709, 3916}, {1742, 37501}, {1745, 64069}, {1750, 57279}, {1754, 16466}, {1766, 25066}, {1770, 8071}, {1836, 26357}, {1854, 37591}, {1885, 22479}, {2095, 5884}, {2099, 45230}, {2550, 50700}, {2635, 9370}, {2777, 22586}, {2794, 19159}, {2807, 5752}, {2829, 22560}, {2883, 3556}, {2951, 3361}, {2975, 3146}, {3035, 6927}, {3189, 54051}, {3218, 9961}, {3286, 37422}, {3295, 4301}, {3304, 5731}, {3333, 5572}, {3338, 10167}, {3434, 6253}, {3522, 5253}, {3534, 37535}, {3560, 22793}, {3576, 37426}, {3579, 6911}, {3601, 12651}, {3616, 7411}, {3622, 35986}, {3627, 18761}, {3646, 21153}, {3649, 55109}, {3651, 5603}, {3655, 12001}, {3656, 16202}, {3742, 8726}, {3812, 30503}, {3816, 6865}, {3817, 11108}, {3826, 6864}, {3832, 5260}, {3838, 5715}, {3925, 6835}, {3927, 31803}, {3928, 7992}, {4188, 54348}, {4192, 5799}, {4267, 5327}, {4299, 22767}, {4302, 22766}, {4413, 6915}, {4421, 6796}, {4423, 6986}, {4428, 10902}, {4640, 12705}, {4847, 63998}, {4999, 6847}, {5047, 9779}, {5073, 26321}, {5120, 40963}, {5173, 10393}, {5204, 6909}, {5220, 5777}, {5250, 37229}, {5266, 61086}, {5289, 14110}, {5432, 6962}, {5433, 6890}, {5450, 28150}, {5493, 6244}, {5536, 15071}, {5687, 7991}, {5690, 18491}, {5693, 24468}, {5709, 6001}, {5719, 12260}, {5720, 63976}, {5744, 9800}, {5745, 21628}, {5758, 38454}, {5779, 31871}, {5787, 10916}, {5791, 12617}, {5806, 54318}, {5812, 12608}, {5840, 22775}, {5841, 40255}, {5842, 6869}, {5887, 37584}, {5918, 32636}, {5927, 41229}, {6147, 60895}, {6282, 59691}, {6361, 6905}, {6459, 19014}, {6460, 19013}, {6684, 6918}, {6690, 6988}, {6691, 6926}, {6762, 63981}, {6765, 6766}, {6769, 52026}, {6825, 7680}, {6827, 7681}, {6828, 31245}, {6837, 7965}, {6840, 10896}, {6842, 10894}, {6846, 42356}, {6851, 63980}, {6883, 9955}, {6894, 33108}, {6895, 11680}, {6907, 26332}, {6908, 25466}, {6913, 18483}, {6914, 63754}, {6924, 35238}, {6925, 7354}, {6928, 10893}, {6932, 10895}, {6934, 11826}, {6938, 30264}, {6979, 31246}, {7074, 37694}, {7330, 16112}, {7688, 8167}, {7742, 30384}, {7959, 55405}, {7964, 25917}, {7971, 44663}, {7987, 41853}, {7988, 16842}, {7995, 54290}, {8168, 12245}, {8226, 19854}, {8301, 12335}, {8583, 37270}, {8666, 28164}, {8715, 28228}, {8727, 26363}, {9580, 37583}, {9708, 19925}, {9709, 43174}, {9746, 16852}, {9799, 24477}, {9842, 18250}, {9856, 12514}, {10085, 41860}, {10164, 16408}, {10171, 16853}, {10178, 37526}, {10200, 37364}, {10246, 16117}, {10267, 22791}, {10431, 10527}, {10526, 37406}, {10680, 18481}, {10826, 59322}, {10860, 15803}, {11236, 18242}, {11248, 28174}, {11260, 12650}, {11372, 31424}, {11375, 37601}, {11376, 37578}, {11424, 55098}, {11499, 12702}, {11502, 37567}, {11517, 51409}, {11522, 15931}, {12047, 40292}, {12203, 22520}, {12607, 64148}, {12652, 37552}, {12675, 41854}, {12679, 64002}, {12680, 62874}, {12701, 37579}, {12943, 22759}, {12953, 22760}, {13205, 64188}, {13374, 18443}, {14100, 62836}, {15338, 22768}, {15622, 23853}, {16370, 50865}, {16371, 59326}, {16417, 50808}, {16435, 29598}, {16678, 37195}, {16845, 38037}, {16857, 50802}, {16863, 58441}, {17170, 59242}, {17531, 64108}, {17542, 30308}, {17613, 58887}, {17702, 22583}, {17733, 28850}, {17742, 44424}, {17768, 63962}, {18251, 55869}, {19517, 31191}, {19521, 38052}, {19544, 39586}, {19762, 49130}, {20835, 24541}, {20991, 27621}, {22504, 23698}, {22654, 39568}, {22769, 29181}, {23708, 59321}, {24470, 60896}, {24703, 63989}, {25055, 35202}, {25893, 37282}, {25968, 27379}, {26105, 37423}, {26285, 28198}, {26286, 28146}, {26319, 26413}, {26320, 26389}, {26333, 31789}, {26921, 31937}, {27802, 49132}, {28212, 32141}, {28610, 54228}, {29054, 64170}, {30283, 62825}, {30478, 37434}, {31423, 61158}, {31445, 54370}, {31798, 54286}, {31805, 43178}, {33597, 37569}, {34626, 34741}, {35250, 37290}, {35784, 42266}, {35785, 42267}, {36999, 52367}, {37244, 40998}, {37252, 63438}, {37258, 54394}, {37412, 57281}, {37531, 37837}, {37582, 64129}, {37585, 45770}, {38329, 53284}, {40270, 43175}, {42258, 44606}, {42259, 44607}, {42884, 51785}, {43577, 43848}, {44431, 56775}, {46730, 53291}, {50696, 64081}, {59387, 61032}, {59421, 63272}, {63316, 63386}

X(64077) = midpoint of X(i) and X(j) for these {i,j}: {6762, 63981}, {6765, 6766}, {22770, 37411}
X(64077) = reflection of X(i) in X(j) for these {i,j}: {1158, 37623}, {3913, 11500}, {5787, 10916}, {5812, 12608}, {6769, 56176}, {6851, 63980}, {10306, 6796}, {10526, 37406}, {11500, 6985}, {12114, 11249}, {12513, 22770}, {12635, 6261}, {12650, 11260}, {13205, 64188}, {37531, 37837}, {64074, 3}, {64076, 550}
X(64077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12699, 11496}, {3, 22753, 25524}, {3, 516, 64074}, {3, 946, 1001}, {3, 9911, 20872}, {4, 3428, 958}, {20, 56, 63991}, {30, 11249, 12114}, {36, 64005, 37022}, {40, 3149, 1376}, {40, 936, 58637}, {57, 12565, 9943}, {517, 11500, 3913}, {517, 6261, 12635}, {517, 6985, 11500}, {1125, 12511, 3}, {1479, 59317, 57278}, {2951, 3361, 9841}, {3333, 5732, 58567}, {3434, 50695, 6253}, {3616, 7411, 8273}, {5493, 25440, 6244}, {6769, 52026, 56176}, {6796, 10306, 4421}, {6796, 28194, 10306}, {6925, 64079, 7354}, {7965, 24953, 6837}, {10860, 15803, 64128}, {11012, 41869, 1012}, {11249, 12114, 11194}, {12702, 62359, 11499}, {22770, 37411, 515}, {37282, 41012, 25893}, {37531, 37837, 56177}, {52367, 59355, 36999}

X(64078) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-YFF TANGENTS AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    3*a^7-3*a^6*(b+c)-a^2*(b-c)^2*(b+c)^3-(b-c)^4*(b+c)^3+a^5*(-5*b^2+8*b*c-5*c^2)+a*(b^2-c^2)^2*(b^2-4*b*c+c^2)+a^4*(5*b^3+3*b^2*c+3*b*c^2+5*c^3)+a^3*(b^4-4*b^3*c-2*b^2*c^2-4*b*c^3+c^4) : :
X(64078) = -4*X[2886]+5*X[6974]

X(64078) lies on these lines: {1, 7}, {2, 2077}, {3, 10531}, {4, 100}, {5, 35251}, {8, 7330}, {11, 6966}, {30, 10679}, {35, 6838}, {40, 5554}, {55, 6925}, {56, 38759}, {104, 11240}, {145, 2800}, {146, 49204}, {147, 49202}, {148, 49148}, {149, 48695}, {153, 25438}, {165, 6992}, {193, 49165}, {355, 63266}, {376, 10269}, {377, 11496}, {382, 10942}, {388, 26358}, {405, 31777}, {452, 24982}, {497, 1470}, {511, 39902}, {515, 3895}, {517, 6938}, {550, 16203}, {944, 9961}, {946, 4190}, {950, 63985}, {1012, 3434}, {1151, 13906}, {1152, 13964}, {1158, 12649}, {1376, 6957}, {1479, 6890}, {1482, 37002}, {1484, 10785}, {1503, 13094}, {1519, 9812}, {1621, 6916}, {1657, 12000}, {1885, 11400}, {2096, 3873}, {2478, 10310}, {2550, 6912}, {2777, 13217}, {2794, 13118}, {2829, 13278}, {2886, 6974}, {2950, 9803}, {3058, 63991}, {3085, 37437}, {3086, 10058}, {3091, 26364}, {3146, 6256}, {3189, 12528}, {3359, 6987}, {3436, 10306}, {3448, 49152}, {3474, 18838}, {3522, 10586}, {3523, 10200}, {3529, 10805}, {3543, 41698}, {3579, 6936}, {3627, 18542}, {3868, 64190}, {3871, 12667}, {3913, 64000}, {4420, 5811}, {4855, 63989}, {5073, 18545}, {5217, 6962}, {5218, 6932}, {5225, 6943}, {5229, 26482}, {5248, 37112}, {5265, 17010}, {5450, 10529}, {5603, 6948}, {5657, 6930}, {5691, 10915}, {5693, 20013}, {5722, 17613}, {5819, 60419}, {5842, 10431}, {5886, 6955}, {5905, 37569}, {6244, 11113}, {6284, 6836}, {6361, 6868}, {6459, 19048}, {6460, 19047}, {6560, 45643}, {6561, 45642}, {6735, 17784}, {6769, 64002}, {6833, 10525}, {6834, 26285}, {6835, 42356}, {6847, 52367}, {6869, 33596}, {6888, 31418}, {6906, 10527}, {6910, 15908}, {6921, 7681}, {6929, 35000}, {6931, 10893}, {6934, 12699}, {6935, 11680}, {6945, 59572}, {6947, 35238}, {6953, 25440}, {6958, 10598}, {6959, 38762}, {6970, 34474}, {6972, 10591}, {6976, 26446}, {6978, 55297}, {7354, 10965}, {7956, 16371}, {7982, 20076}, {9668, 37374}, {9799, 49171}, {9841, 41864}, {9911, 16049}, {10270, 37423}, {10530, 48482}, {10786, 11849}, {10803, 12203}, {10834, 39568}, {10956, 12943}, {10958, 12953}, {11111, 35514}, {11114, 30513}, {11236, 52836}, {11415, 37531}, {11495, 34630}, {11684, 12245}, {11827, 50244}, {12189, 23698}, {12296, 49156}, {12297, 49158}, {12324, 49186}, {12381, 12430}, {12384, 49206}, {12512, 16209}, {12594, 29181}, {12607, 37001}, {12608, 41869}, {12679, 56176}, {12705, 57287}, {12751, 20095}, {13219, 49154}, {15171, 37022}, {15338, 22768}, {15680, 16113}, {18961, 63270}, {21077, 52860}, {22753, 24466}, {25722, 41389}, {26015, 52027}, {26332, 31295}, {27385, 50700}, {28164, 49626}, {31730, 59333}, {31799, 50242}, {34550, 49207}, {34772, 63962}, {35448, 37290}, {35816, 42266}, {35817, 42267}, {36845, 54052}, {41575, 54156}, {42258, 44643}, {42259, 44644}, {43577, 43861}, {45729, 51212}, {49169, 51897}, {51118, 59719}, {63341, 63386}

X(64078) = reflection of X(i) in X(j) for these {i,j}: {20, 4302}, {3434, 1012}, {5905, 37569}, {6925, 55}, {12115, 10679}, {12648, 12703}
X(64078) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(77), X(45393)}}, {{A, B, C, X(269), X(915)}}, {{A, B, C, X(279), X(37203)}}
X(64078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11248, 5552}, {20, 390, 5731}, {30, 10679, 12115}, {515, 12703, 12648}, {516, 4302, 20}, {3146, 10528, 6256}, {3522, 10586, 37561}, {6284, 64074, 6836}, {10679, 12115, 11239}, {11496, 11826, 377}

X(64079) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    3*a^7-3*a^6*(b+c)+5*a^4*(b-c)^2*(b+c)-(b-c)^4*(b+c)^3+a^5*(-5*b^2+4*b*c-5*c^2)+a*(b^2-c^2)^2*(b^2+c^2)-a^2*(b-c)^2*(b^3-5*b^2*c-5*b*c^2+c^3)+a^3*(b^4-4*b^3*c+14*b^2*c^2-4*b*c^3+c^4) : :
X(64079) =

X(64079) lies on these lines: {1, 7}, {2, 11012}, {3, 10532}, {4, 2975}, {5, 35252}, {8, 5709}, {12, 6962}, {30, 10680}, {36, 6890}, {40, 4190}, {56, 6836}, {104, 6851}, {145, 37625}, {146, 49203}, {147, 49201}, {148, 49147}, {149, 48694}, {153, 48713}, {193, 49164}, {355, 64153}, {376, 10267}, {377, 3428}, {382, 10943}, {388, 411}, {404, 64111}, {452, 5715}, {474, 31799}, {497, 26437}, {511, 39903}, {515, 12649}, {517, 6934}, {550, 16202}, {944, 3873}, {946, 6872}, {956, 20420}, {958, 6835}, {993, 6837}, {1125, 6992}, {1151, 13907}, {1152, 13965}, {1478, 6838}, {1482, 37000}, {1503, 13095}, {1621, 59345}, {1657, 12001}, {1885, 11401}, {2096, 9961}, {2478, 11827}, {2551, 6915}, {2777, 13218}, {2794, 13119}, {2829, 13279}, {3086, 6840}, {3091, 26363}, {3146, 10529}, {3149, 3436}, {3434, 22770}, {3448, 49151}, {3476, 64043}, {3522, 10587}, {3523, 10198}, {3529, 10806}, {3543, 45700}, {3562, 56821}, {3579, 6955}, {3616, 6987}, {3627, 18544}, {3813, 36999}, {4511, 5758}, {4999, 6860}, {5073, 18543}, {5080, 6848}, {5204, 6966}, {5225, 26475}, {5229, 6932}, {5250, 63438}, {5251, 6886}, {5253, 6865}, {5260, 6864}, {5303, 6935}, {5536, 49168}, {5552, 6905}, {5603, 6868}, {5657, 6885}, {5691, 10916}, {5693, 20078}, {5696, 54204}, {5730, 5762}, {5840, 12776}, {5882, 62861}, {5886, 6936}, {5905, 6261}, {6253, 12513}, {6256, 10530}, {6284, 18967}, {6361, 6948}, {6459, 19050}, {6460, 19049}, {6560, 45641}, {6561, 45640}, {6734, 50700}, {6796, 10528}, {6828, 30478}, {6833, 26286}, {6834, 10526}, {6839, 19843}, {6863, 10599}, {6897, 35239}, {6899, 10269}, {6904, 24987}, {6909, 37579}, {6910, 7680}, {6925, 7354}, {6927, 11681}, {6933, 10894}, {6938, 12699}, {6943, 7288}, {6957, 57288}, {6960, 10590}, {6976, 9955}, {6985, 12115}, {6993, 19854}, {7491, 10531}, {7580, 18990}, {7982, 20075}, {9799, 49170}, {9800, 54052}, {9911, 35998}, {10431, 12114}, {10585, 52265}, {10724, 12248}, {10785, 22765}, {10804, 12203}, {10835, 39568}, {10941, 50528}, {10957, 12943}, {10959, 12953}, {11235, 52837}, {11239, 11491}, {11415, 63986}, {11496, 30264}, {11510, 15326}, {12190, 23698}, {12296, 49155}, {12297, 49157}, {12324, 49185}, {12382, 12431}, {12384, 49205}, {12512, 16208}, {12595, 29181}, {12667, 36002}, {12672, 44447}, {13219, 49153}, {14054, 64144}, {15680, 49177}, {17647, 41338}, {19860, 64001}, {19861, 64004}, {20060, 64148}, {20070, 37256}, {26015, 50696}, {26228, 50699}, {28164, 49627}, {31777, 56998}, {34486, 50693}, {35514, 57000}, {35818, 42266}, {35819, 42267}, {37112, 59320}, {37423, 54445}, {37530, 50702}, {42258, 44645}, {42259, 44646}, {43577, 43862}, {43740, 54391}, {45728, 51212}, {49176, 64009}, {55296, 59392}, {63342, 63386}, {63992, 64002}

X(64079) = midpoint of X(i) and X(j) for these {i,j}: {20076, 50695}
X(64079) = reflection of X(i) in X(j) for these {i,j}: {20, 4299}, {3436, 3149}, {6836, 56}, {11415, 63986}, {12116, 10680}, {12649, 12704}
X(64079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11249, 10527}, {20, 3600, 5731}, {30, 10680, 12116}, {515, 12704, 12649}, {516, 4299, 20}, {3146, 10529, 48482}, {3146, 20067, 64120}, {3522, 10587, 10902}, {5886, 35250, 6936}, {7354, 64077, 6925}, {10680, 12116, 11240}, {12687, 12704, 62874}, {20076, 50695, 515}

X(64080) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND EHRMANN AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    5*a^6+a^2*(b^2-c^2)^2-4*a^4*(b^2+c^2)-2*(b^2-c^2)^2*(b^2+c^2) : :
X(64080) = -6*X[2]+7*X[10541], -2*X[4]+3*X[6], -2*X[5]+3*X[11179], -3*X[69]+5*X[3522], -4*X[140]+3*X[1352], -6*X[141]+7*X[3523], -6*X[182]+5*X[1656], 3*X[193]+X[5059], -3*X[381]+4*X[575], -4*X[389]+3*X[9971], -8*X[546]+9*X[38072], -4*X[548]+3*X[54173] and many others

X(64080) lies on these lines: {2, 10541}, {3, 67}, {4, 6}, {5, 11179}, {20, 524}, {22, 41724}, {24, 15581}, {26, 45732}, {30, 11477}, {51, 62968}, {54, 51739}, {64, 5486}, {66, 14528}, {68, 16618}, {69, 3522}, {76, 45018}, {98, 7607}, {110, 59767}, {125, 26864}, {140, 1352}, {141, 3523}, {146, 25329}, {147, 7778}, {154, 468}, {155, 14791}, {156, 15114}, {159, 2929}, {182, 1656}, {183, 5984}, {184, 1853}, {185, 2393}, {186, 15582}, {193, 5059}, {230, 7710}, {235, 31166}, {253, 59246}, {262, 54857}, {287, 11331}, {376, 15533}, {381, 575}, {382, 576}, {383, 49948}, {389, 9971}, {394, 16063}, {427, 17809}, {511, 1657}, {515, 64070}, {516, 49486}, {518, 39878}, {539, 35243}, {546, 38072}, {548, 54173}, {549, 51186}, {550, 1350}, {578, 34780}, {597, 3091}, {611, 5270}, {613, 4857}, {631, 11180}, {754, 14532}, {1080, 49947}, {1151, 61097}, {1152, 61096}, {1192, 18909}, {1351, 5073}, {1353, 5102}, {1370, 37672}, {1386, 11522}, {1428, 39892}, {1495, 26869}, {1593, 32621}, {1614, 5622}, {1620, 18913}, {1691, 61754}, {1885, 58795}, {1992, 3146}, {1993, 5189}, {2076, 39882}, {2330, 39891}, {2548, 40927}, {2549, 10542}, {2777, 64104}, {2781, 5925}, {2784, 5695}, {2794, 44526}, {2836, 15071}, {2854, 15072}, {2916, 9937}, {3053, 8721}, {3090, 47354}, {3098, 11898}, {3242, 5882}, {3292, 31152}, {3416, 43174}, {3424, 7736}, {3448, 6800}, {3516, 10619}, {3517, 20987}, {3519, 34436}, {3520, 15579}, {3524, 50993}, {3525, 50983}, {3526, 11178}, {3527, 22336}, {3528, 54169}, {3529, 50974}, {3533, 40330}, {3534, 51188}, {3543, 8584}, {3545, 15153}, {3567, 63688}, {3589, 5056}, {3592, 36709}, {3594, 36714}, {3618, 5068}, {3619, 61834}, {3620, 21167}, {3627, 20423}, {3628, 38064}, {3629, 49135}, {3630, 55607}, {3631, 55656}, {3796, 7495}, {3815, 53015}, {3818, 3851}, {3830, 11482}, {3832, 59373}, {3839, 63124}, {3843, 5476}, {3850, 14561}, {3854, 51171}, {3858, 18583}, {4232, 11206}, {4301, 47356}, {4663, 5691}, {5013, 59363}, {5023, 15993}, {5026, 50641}, {5032, 17578}, {5054, 55687}, {5055, 55701}, {5064, 13366}, {5070, 10168}, {5072, 55708}, {5076, 22330}, {5079, 25561}, {5092, 15720}, {5093, 48901}, {5095, 5895}, {5097, 48884}, {5182, 7887}, {5422, 7533}, {5471, 54570}, {5472, 54569}, {5477, 7748}, {5493, 5847}, {5562, 54334}, {5663, 15074}, {5878, 54218}, {5889, 9019}, {5965, 33878}, {5999, 9766}, {6000, 50649}, {6033, 44507}, {6090, 24981}, {6222, 13882}, {6247, 18925}, {6329, 33748}, {6399, 13934}, {6409, 12257}, {6410, 12256}, {6419, 36711}, {6420, 36712}, {6425, 21736}, {6467, 30443}, {6593, 41737}, {6642, 18128}, {6759, 18374}, {6770, 16644}, {6773, 16645}, {6811, 13846}, {6813, 13847}, {7000, 32788}, {7374, 32787}, {7387, 10116}, {7390, 17330}, {7391, 63094}, {7486, 48310}, {7488, 35707}, {7500, 61658}, {7527, 8546}, {7544, 25488}, {7556, 54162}, {7574, 18445}, {7608, 53100}, {7610, 11177}, {7612, 60337}, {7716, 39871}, {7735, 59252}, {7755, 40825}, {7784, 12203}, {7841, 8593}, {7890, 40268}, {7901, 39141}, {7982, 51000}, {7991, 28538}, {8252, 45510}, {8253, 45511}, {8289, 43529}, {8537, 35480}, {8540, 12953}, {8541, 12173}, {8548, 12293}, {8667, 37182}, {8681, 46850}, {8703, 50989}, {8716, 54996}, {8960, 19145}, {9004, 12680}, {9140, 62516}, {9544, 30745}, {9716, 10989}, {9729, 29959}, {9730, 43130}, {9744, 9756}, {9755, 43460}, {9786, 9833}, {9830, 34505}, {9862, 44541}, {9919, 10114}, {9924, 17818}, {9968, 11470}, {9973, 13382}, {9974, 35820}, {9975, 35821}, {9976, 12902}, {9977, 48675}, {10018, 23041}, {10112, 39568}, {10151, 47460}, {10192, 23291}, {10249, 11457}, {10250, 18383}, {10282, 26944}, {10295, 10605}, {10296, 15826}, {10299, 55673}, {10301, 11245}, {10303, 20582}, {10304, 22165}, {10387, 39897}, {10519, 21735}, {10574, 11188}, {10601, 62937}, {10606, 35485}, {10706, 63694}, {11001, 51187}, {11003, 61700}, {11008, 61044}, {11063, 52276}, {11160, 50693}, {11255, 52843}, {11257, 32469}, {11305, 51012}, {11306, 51015}, {11318, 18800}, {11362, 50783}, {11381, 40673}, {11402, 11550}, {11410, 13399}, {11422, 31133}, {11425, 14216}, {11432, 13419}, {11433, 52301}, {11438, 12367}, {11541, 51132}, {11579, 14852}, {11623, 11646}, {12017, 24206}, {12103, 50973}, {12134, 37514}, {12162, 44479}, {12164, 44829}, {12177, 14880}, {12215, 32821}, {12254, 32247}, {12279, 15531}, {12283, 32339}, {12294, 32366}, {12315, 13403}, {12594, 49165}, {12595, 49164}, {12811, 38079}, {12943, 19369}, {13169, 15021}, {13367, 61737}, {13464, 38315}, {13473, 47462}, {13474, 44495}, {13491, 14984}, {13608, 57466}, {13622, 43719}, {13665, 44656}, {13785, 44657}, {14093, 55644}, {14157, 43812}, {14232, 31411}, {14458, 60142}, {14614, 40236}, {14683, 15066}, {14810, 62082}, {14848, 22234}, {14864, 44679}, {14915, 32284}, {14982, 16534}, {15004, 62976}, {15022, 51138}, {15028, 40670}, {15034, 49672}, {15043, 16776}, {15054, 34792}, {15063, 34319}, {15087, 45034}, {15105, 61088}, {15118, 19153}, {15122, 47391}, {15303, 38791}, {15305, 63723}, {15311, 49670}, {15321, 43908}, {15448, 37643}, {15520, 48895}, {15577, 32534}, {15640, 41149}, {15681, 55580}, {15682, 63125}, {15683, 63064}, {15688, 55631}, {15689, 55602}, {15692, 50991}, {15693, 55679}, {15696, 55606}, {15700, 55675}, {15704, 51182}, {15705, 50994}, {15708, 51143}, {15712, 55676}, {15717, 21356}, {16013, 35477}, {16196, 45248}, {16252, 62375}, {16270, 61665}, {16964, 51203}, {16965, 51200}, {17506, 35228}, {17508, 43150}, {17538, 50967}, {17702, 64103}, {17710, 41716}, {17800, 19924}, {17811, 46336}, {17821, 35486}, {18358, 55699}, {18381, 19347}, {18390, 32063}, {18451, 44503}, {18510, 44481}, {18512, 44482}, {18534, 61713}, {18911, 35259}, {18916, 54149}, {19124, 64028}, {19125, 51756}, {19127, 52525}, {19130, 53091}, {19136, 26883}, {19146, 58866}, {19708, 51189}, {20062, 41628}, {20080, 62124}, {20583, 50688}, {20775, 63421}, {20818, 41327}, {21850, 62026}, {21970, 32237}, {22151, 43605}, {22236, 41035}, {22238, 41034}, {22466, 63181}, {23292, 32064}, {23332, 62960}, {23698, 64091}, {24273, 35423}, {25331, 51941}, {25556, 38789}, {25565, 50957}, {26336, 44483}, {26346, 44484}, {26937, 61683}, {28164, 64073}, {29317, 44456}, {29323, 37517}, {30389, 51003}, {30771, 59551}, {31492, 37334}, {32113, 37487}, {32135, 38743}, {32139, 56568}, {32255, 34799}, {32273, 39562}, {32423, 64098}, {32455, 50691}, {33586, 37900}, {33703, 54132}, {33750, 61787}, {33751, 55639}, {33923, 48876}, {34147, 37072}, {34156, 34369}, {34380, 48873}, {34573, 61856}, {34609, 34986}, {34624, 54993}, {34778, 35491}, {34788, 64094}, {35018, 38110}, {35260, 47296}, {35283, 59777}, {36752, 64036}, {36757, 42992}, {36758, 42993}, {36992, 42127}, {36994, 42126}, {36997, 44499}, {37070, 51939}, {37197, 44102}, {37453, 44110}, {37727, 50790}, {37910, 41588}, {37931, 47446}, {37984, 47458}, {38005, 51745}, {38317, 55705}, {38397, 47596}, {38757, 51008}, {39561, 48889}, {39838, 41672}, {40947, 63419}, {41022, 41745}, {41023, 41746}, {41036, 42815}, {41037, 42816}, {41040, 42156}, {41041, 42153}, {41152, 62059}, {41153, 61958}, {41424, 61506}, {41731, 48679}, {41981, 55618}, {42096, 44667}, {42097, 44666}, {42262, 48467}, {42265, 48466}, {42271, 48477}, {42272, 48476}, {42431, 51206}, {42432, 51207}, {43537, 62992}, {43621, 62047}, {43845, 44494}, {44076, 44492}, {44245, 50961}, {44470, 45730}, {44500, 52854}, {44509, 45376}, {44510, 45375}, {44513, 48656}, {44514, 48655}, {46267, 61920}, {46935, 51126}, {47337, 58762}, {47455, 47474}, {47464, 61721}, {47549, 62288}, {47629, 59553}, {48874, 62136}, {48880, 55584}, {48881, 55591}, {48885, 55593}, {48891, 55587}, {48892, 55610}, {48904, 55716}, {48920, 55585}, {48942, 55715}, {49136, 51140}, {49137, 50962}, {49140, 51028}, {50664, 61937}, {50687, 63022}, {50689, 50959}, {50690, 51170}, {50692, 63027}, {50861, 62245}, {50950, 63469}, {50954, 55694}, {50958, 61820}, {50963, 61991}, {50971, 51215}, {50972, 58195}, {50975, 62092}, {50976, 50978}, {50982, 51177}, {50984, 61804}, {50985, 58196}, {50986, 62162}, {50987, 55861}, {50990, 62063}, {50992, 62120}, {50997, 64197}, {51130, 51216}, {51135, 62083}, {51137, 61831}, {51142, 61781}, {51164, 62028}, {51175, 55597}, {51178, 62146}, {51179, 62133}, {51732, 61940}, {51733, 61701}, {52102, 55575}, {52293, 61735}, {52298, 64064}, {53098, 60150}, {55583, 62143}, {55588, 62134}, {55595, 62121}, {55620, 62105}, {55622, 62096}, {55629, 62093}, {55637, 62085}, {55647, 62075}, {55649, 62074}, {55650, 62073}, {55654, 62069}, {55671, 61545}, {55674, 61794}, {55677, 61799}, {55681, 61811}, {55682, 61815}, {55692, 61855}, {55695, 61875}, {55697, 55860}, {55698, 55857}, {59399, 61976}, {60118, 60324}, {60147, 60328}, {62048, 63117}, {62129, 63118}, {62148, 63116}, {62160, 63115}

X(64080) = midpoint of X(i) and X(j) for these {i,j}: {193, 14927}, {6144, 48872}, {6241, 15073}, {11008, 61044}, {15683, 63064}, {17800, 55724}
X(64080) = reflection of X(i) in X(j) for these {i,j}: {4, 8550}, {6, 6776}, {20, 64196}, {69, 44882}, {146, 25329}, {382, 576}, {599, 43273}, {1350, 46264}, {1352, 48906}, {1992, 51136}, {2930, 32233}, {3543, 8584}, {5691, 4663}, {5895, 64031}, {5921, 141}, {9924, 36989}, {9973, 19161}, {10296, 15826}, {11160, 50965}, {11180, 51737}, {11477, 63722}, {11898, 3098}, {12162, 44479}, {12293, 8548}, {12294, 32366}, {12902, 9976}, {13474, 44495}, {15069, 3}, {15533, 376}, {16176, 32234}, {18440, 182}, {25335, 16010}, {31670, 1353}, {32250, 15118}, {32272, 49116}, {32306, 32305}, {33878, 48898}, {36992, 44498}, {36994, 44497}, {36997, 44499}, {37473, 185}, {39838, 41672}, {39879, 34776}, {40341, 1350}, {41716, 17710}, {41737, 6593}, {44439, 6467}, {44453, 11257}, {47276, 10295}, {47353, 11179}, {48662, 3818}, {48675, 9977}, {48679, 41731}, {48872, 48905}, {48884, 5097}, {48904, 55716}, {48910, 1351}, {48942, 55715}, {50641, 5026}, {51022, 20583}, {51023, 597}, {51024, 1992}, {51027, 599}, {51163, 32455}, {51212, 3629}, {52843, 11255}, {52854, 44500}, {53097, 20}, {55582, 48873}, {55584, 48880}, {55585, 48920}, {55587, 48891}, {55722, 193}, {62288, 47549}, {63428, 48881}, {64085, 39870}
X(64080) = perspector of circumconic {{A, B, C, X(107), X(17708)}}
X(64080) = pole of line {690, 9420} with respect to the 2nd Brocard circle
X(64080) = pole of line {690, 39201} with respect to the circumcircle
X(64080) = pole of line {525, 13196} with respect to the cosine circle
X(64080) = pole of line {690, 42658} with respect to the 2nd DrozFarny circle
X(64080) = pole of line {9191, 9209} with respect to the orthoptic circle of the Steiner Inellipse
X(64080) = pole of line {51, 5094} with respect to the Jerabek hyperbola
X(64080) = pole of line {4, 1384} with respect to the Kiepert hyperbola
X(64080) = pole of line {1632, 5467} with respect to the Kiepert parabola
X(64080) = pole of line {523, 47464} with respect to the Orthic inconic
X(64080) = pole of line {23, 394} with respect to the Stammler hyperbola
X(64080) = pole of line {6587, 14417} with respect to the Steiner inellipse
X(64080) = pole of line {316, 3146} with respect to the Wallace hyperbola
X(64080) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(8744)}}, {{A, B, C, X(4), X(34897)}}, {{A, B, C, X(67), X(393)}}, {{A, B, C, X(69), X(33630)}}, {{A, B, C, X(287), X(36990)}}, {{A, B, C, X(1249), X(5486)}}, {{A, B, C, X(2207), X(3455)}}, {{A, B, C, X(2697), X(15069)}}, {{A, B, C, X(3087), X(22336)}}, {{A, B, C, X(6530), X(7607)}}, {{A, B, C, X(8743), X(14528)}}, {{A, B, C, X(10002), X(53099)}}, {{A, B, C, X(14357), X(60428)}}, {{A, B, C, X(22466), X(43448)}}, {{A, B, C, X(33971), X(54857)}}, {{A, B, C, X(35907), X(53232)}}, {{A, B, C, X(38005), X(40065)}}, {{A, B, C, X(58070), X(59007)}}
X(64080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15069, 599}, {3, 50955, 40107}, {3, 542, 15069}, {4, 15258, 1990}, {4, 6776, 8550}, {5, 11179, 53093}, {20, 524, 53097}, {20, 64014, 64196}, {24, 15581, 19596}, {30, 63722, 11477}, {69, 44882, 31884}, {125, 26864, 61680}, {141, 25406, 53094}, {154, 1899, 26958}, {182, 10516, 47355}, {182, 18553, 1656}, {185, 2393, 37473}, {193, 14927, 29181}, {193, 29181, 55722}, {382, 576, 54131}, {397, 398, 5286}, {511, 48905, 48872}, {524, 64196, 20}, {542, 16010, 25335}, {542, 32233, 2930}, {542, 32305, 32306}, {542, 49116, 32272}, {542, 599, 51027}, {548, 54173, 55626}, {576, 11645, 382}, {631, 51737, 55684}, {1181, 8549, 6}, {1350, 3564, 40341}, {1350, 46264, 59411}, {1351, 29012, 48910}, {1352, 48906, 5085}, {1352, 5085, 3763}, {1353, 31670, 5102}, {1503, 8550, 4}, {1614, 5622, 64061}, {1656, 18440, 18553}, {1656, 18553, 10516}, {2781, 32234, 16176}, {2883, 8550, 15471}, {3448, 6800, 37638}, {3564, 46264, 1350}, {3818, 25555, 3851}, {3843, 53092, 5476}, {3851, 5050, 25555}, {5050, 48662, 3818}, {5476, 33749, 53092}, {5870, 10783, 3070}, {5871, 10784, 3071}, {5921, 25406, 141}, {5965, 48898, 33878}, {6144, 48872, 511}, {6241, 15073, 2781}, {6467, 34146, 44439}, {6776, 34224, 8549}, {9744, 9756, 31489}, {9833, 18914, 9786}, {10249, 34118, 40686}, {10602, 12174, 64031}, {11179, 47353, 47352}, {11180, 51737, 21358}, {11245, 31383, 17810}, {11477, 63722, 15534}, {12174, 21659, 5895}, {12241, 34781, 15811}, {15069, 43273, 3}, {17800, 55724, 19924}, {18909, 34782, 1192}, {18911, 46818, 35259}, {21358, 55684, 631}, {34380, 48873, 55582}, {37643, 64059, 15448}, {39870, 64085, 38315}, {39899, 48905, 6144}, {47353, 53093, 5}, {48881, 63428, 55591}

X(64081) = ANTICOMPLEMENT OF X(3085)

Barycentrics    (a-b-c)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b^2-6*b*c+c^2)) : :

X(64081) lies on these lines: {1, 2}, {3, 5082}, {4, 956}, {5, 3421}, {7, 54303}, {9, 12053}, {11, 2551}, {20, 2894}, {21, 390}, {36, 37267}, {40, 5744}, {55, 30478}, {56, 2550}, {63, 962}, {65, 24477}, {69, 55082}, {72, 5603}, {75, 280}, {100, 3523}, {140, 59591}, {144, 11415}, {149, 6872}, {210, 11376}, {219, 391}, {226, 6762}, {278, 318}, {279, 20880}, {321, 60157}, {329, 946}, {341, 28808}, {344, 31269}, {345, 4673}, {346, 3702}, {354, 28629}, {355, 6848}, {377, 3600}, {388, 2886}, {404, 1617}, {405, 1058}, {442, 1056}, {443, 999}, {452, 497}, {475, 7046}, {495, 6856}, {496, 5084}, {515, 5175}, {516, 62824}, {517, 6847}, {518, 3485}, {529, 5229}, {631, 5687}, {668, 32828}, {908, 5815}, {942, 64151}, {944, 3419}, {950, 24392}, {952, 6825}, {960, 17642}, {966, 2256}, {993, 4294}, {1006, 10806}, {1071, 12529}, {1108, 2345}, {1145, 6967}, {1150, 5706}, {1212, 56937}, {1259, 1621}, {1260, 16845}, {1329, 10589}, {1376, 7288}, {1385, 37407}, {1420, 57284}, {1468, 4307}, {1478, 5288}, {1479, 5258}, {1482, 6824}, {1519, 5811}, {1697, 5745}, {1699, 12527}, {1706, 3911}, {1788, 5836}, {2098, 21677}, {2185, 56945}, {2192, 20306}, {2242, 31416}, {2257, 5749}, {2475, 20076}, {2476, 5261}, {2478, 5274}, {2646, 3189}, {3059, 17609}, {3088, 56876}, {3090, 17757}, {3091, 3436}, {3146, 52367}, {3243, 63274}, {3295, 6857}, {3303, 24953}, {3304, 3925}, {3306, 11024}, {3332, 54429}, {3333, 9776}, {3340, 24391}, {3452, 26129}, {3475, 28628}, {3476, 5794}, {3487, 3555}, {3522, 43161}, {3541, 56877}, {3576, 63146}, {3598, 41826}, {3601, 5853}, {3614, 34689}, {3649, 42014}, {3668, 31995}, {3671, 62823}, {3681, 6886}, {3685, 26059}, {3698, 17728}, {3713, 63055}, {3714, 28830}, {3717, 56466}, {3740, 46677}, {3832, 5080}, {3868, 5173}, {3869, 6837}, {3871, 5281}, {3873, 11036}, {3876, 5686}, {3877, 17622}, {3880, 26066}, {3883, 27509}, {3885, 18231}, {3889, 11038}, {3895, 12541}, {3913, 4999}, {3916, 6361}, {3926, 17143}, {3927, 22791}, {3940, 5901}, {3951, 51423}, {3983, 24954}, {4187, 47743}, {4188, 7742}, {4189, 20075}, {4190, 33110}, {4193, 8165}, {4194, 5081}, {4208, 33108}, {4220, 8192}, {4224, 12410}, {4293, 8666}, {4295, 9965}, {4301, 12526}, {4317, 31420}, {4318, 54289}, {4342, 18249}, {4344, 62809}, {4388, 5906}, {4441, 32830}, {4461, 25252}, {4512, 12575}, {4514, 27505}, {4546, 47795}, {4652, 9778}, {4662, 25681}, {4665, 59609}, {4684, 25521}, {4855, 54445}, {4875, 6554}, {4901, 56446}, {4996, 17548}, {5044, 11373}, {5046, 10522}, {5056, 11681}, {5068, 56880}, {5086, 6838}, {5129, 5260}, {5176, 6953}, {5178, 37112}, {5204, 34612}, {5217, 31157}, {5223, 11522}, {5225, 11235}, {5234, 40998}, {5248, 31458}, {5249, 11037}, {5250, 5273}, {5253, 17580}, {5284, 17554}, {5286, 16975}, {5303, 10304}, {5433, 59572}, {5436, 64162}, {5558, 42015}, {5657, 6926}, {5690, 6891}, {5698, 12701}, {5710, 37642}, {5730, 6832}, {5731, 37108}, {5734, 11682}, {5748, 8227}, {5770, 37562}, {5790, 6944}, {5791, 9957}, {5795, 9581}, {5809, 24389}, {5818, 6964}, {5837, 7962}, {5844, 6862}, {5881, 64148}, {5886, 34790}, {5930, 52358}, {6154, 63756}, {6392, 21226}, {6502, 31413}, {6553, 37887}, {6653, 32965}, {6675, 6767}, {6684, 63137}, {6826, 10680}, {6827, 10943}, {6829, 10597}, {6833, 12245}, {6834, 59388}, {6842, 18545}, {6843, 10532}, {6844, 26470}, {6854, 45977}, {6855, 63257}, {6861, 10247}, {6863, 12645}, {6871, 20060}, {6881, 12001}, {6883, 32214}, {6884, 62826}, {6885, 22765}, {6889, 7967}, {6890, 14110}, {6892, 10679}, {6920, 10596}, {6935, 10306}, {6937, 10805}, {6948, 32153}, {6958, 59503}, {6959, 61510}, {6972, 64201}, {6987, 12116}, {6988, 55300}, {6989, 10246}, {7091, 60992}, {7173, 31141}, {7354, 31140}, {7373, 8728}, {7677, 37282}, {7738, 21956}, {7987, 43175}, {8158, 8727}, {8168, 64123}, {9614, 12572}, {9709, 15325}, {9710, 25524}, {9798, 35988}, {9799, 64150}, {9812, 64002}, {9858, 51774}, {10085, 63971}, {10106, 54366}, {10386, 17571}, {10430, 12565}, {10588, 12607}, {10590, 25639}, {10591, 24387}, {10624, 31424}, {10896, 34606}, {11111, 15171}, {11249, 50701}, {11281, 42871}, {11375, 25568}, {11523, 64160}, {12437, 13384}, {12514, 30305}, {12537, 18241}, {12573, 59412}, {12667, 15908}, {13279, 45043}, {14450, 20059}, {14552, 23151}, {14740, 16173}, {15170, 17561}, {15172, 16418}, {15299, 61009}, {15346, 30340}, {15717, 15931}, {15888, 31245}, {16284, 52422}, {16471, 19742}, {16704, 62843}, {17164, 56839}, {17552, 31494}, {17625, 18251}, {17740, 37528}, {18228, 41012}, {18481, 37427}, {18543, 28459}, {19582, 27549}, {20067, 31295}, {20070, 41338}, {20220, 56943}, {20999, 36510}, {22754, 37462}, {23542, 32773}, {23853, 27621}, {24320, 28028}, {24349, 30543}, {24552, 56986}, {24597, 62804}, {25009, 30235}, {25080, 64071}, {25083, 62857}, {25304, 62174}, {25917, 28778}, {26027, 43533}, {26036, 56530}, {26105, 37722}, {27334, 50314}, {27530, 28796}, {27540, 40960}, {28194, 54290}, {30282, 64117}, {30283, 37424}, {30384, 41229}, {31231, 63990}, {31272, 55016}, {31401, 52959}, {31402, 31466}, {31405, 54416}, {31408, 31484}, {31409, 31488}, {31435, 63993}, {31888, 52126}, {32942, 56987}, {34605, 50736}, {34611, 50742}, {34632, 63144}, {34720, 52793}, {35262, 59413}, {35466, 37542}, {35514, 37022}, {36844, 52364}, {37244, 42884}, {37313, 42842}, {37543, 37655}, {37602, 41859}, {37666, 57280}, {41863, 64110}, {41867, 51723}, {44189, 60599}, {44229, 62318}, {44447, 62827}, {44448, 47796}, {45036, 51102}, {50696, 64077}, {52366, 52404}, {53997, 55392}, {55905, 63134}, {55907, 63140}, {55910, 63147}, {59340, 63136}, {59491, 63130}, {62773, 64124}, {63974, 63975}, {63980, 64111}

X(64081) = anticomplement of X(3085)
X(64081) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 7160}
X(64081) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 7160}, {3085, 3085}, {7308, 4328}
X(64081) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {55105, 4}, {55106, 11442}, {55107, 317}, {58992, 513}
X(64081) = pole of line {4391, 20294} with respect to the DeLongchamps circle
X(64081) = pole of line {3057, 3189} with respect to the Feuerbach hyperbola
X(64081) = pole of line {58, 1617} with respect to the Stammler hyperbola
X(64081) = pole of line {514, 4131} with respect to the Steiner circumellipse
X(64081) = pole of line {86, 6604} with respect to the Wallace hyperbola
X(64081) = pole of line {3239, 4811} with respect to the dual conic of incircle
X(64081) = pole of line {4025, 57101} with respect to the dual conic of polar circle
X(64081) = pole of line {2, 24213} with respect to the dual conic of Yff parabola
X(64081) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1440)}}, {{A, B, C, X(2), X(9776)}}, {{A, B, C, X(4), X(31397)}}, {{A, B, C, X(8), X(309)}}, {{A, B, C, X(9), X(6765)}}, {{A, B, C, X(10), X(6601)}}, {{A, B, C, X(21), X(3870)}}, {{A, B, C, X(42), X(52384)}}, {{A, B, C, X(75), X(7080)}}, {{A, B, C, X(78), X(1219)}}, {{A, B, C, X(200), X(280)}}, {{A, B, C, X(278), X(2999)}}, {{A, B, C, X(333), X(34255)}}, {{A, B, C, X(347), X(1103)}}, {{A, B, C, X(348), X(64082)}}, {{A, B, C, X(386), X(51502)}}, {{A, B, C, X(596), X(59722)}}, {{A, B, C, X(899), X(14300)}}, {{A, B, C, X(936), X(59760)}}, {{A, B, C, X(1210), X(55076)}}, {{A, B, C, X(1320), X(19860)}}, {{A, B, C, X(3615), X(24564)}}, {{A, B, C, X(3680), X(9623)}}, {{A, B, C, X(4373), X(10528)}}, {{A, B, C, X(4882), X(42015)}}, {{A, B, C, X(5558), X(10578)}}, {{A, B, C, X(6553), X(34772)}}, {{A, B, C, X(6735), X(43533)}}, {{A, B, C, X(7318), X(14986)}}, {{A, B, C, X(10587), X(30712)}}, {{A, B, C, X(12260), X(18241)}}, {{A, B, C, X(12864), X(15998)}}, {{A, B, C, X(13405), X(51512)}}, {{A, B, C, X(15909), X(51784)}}, {{A, B, C, X(20007), X(51565)}}, {{A, B, C, X(23511), X(37887)}}, {{A, B, C, X(24987), X(43740)}}, {{A, B, C, X(25006), X(43745)}}, {{A, B, C, X(29611), X(41791)}}, {{A, B, C, X(31434), X(60158)}}, {{A, B, C, X(36845), X(60668)}}, {{A, B, C, X(44675), X(60164)}}, {{A, B, C, X(52158), X(56809)}}, {{A, B, C, X(56102), X(59296)}}
X(64081) = barycentric product X(i)*X(j) for these (i, j): {8, 9776}, {312, 3333}, {346, 62782}, {14300, 668}
X(64081) = barycentric quotient X(i)/X(j) for these (i, j): {9, 7160}, {3333, 57}, {9776, 7}, {14300, 513}, {62782, 279}
X(64081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4847, 8}, {2, 8, 7080}, {3, 5082, 17784}, {8, 3616, 78}, {8, 4861, 145}, {10, 3086, 2}, {11, 2551, 6919}, {55, 64068, 56936}, {56, 2550, 6904}, {377, 54391, 3600}, {388, 2886, 5177}, {495, 31493, 6856}, {496, 9708, 5084}, {497, 958, 452}, {908, 63135, 5815}, {946, 57279, 329}, {956, 24390, 4}, {958, 3813, 497}, {993, 4294, 17576}, {999, 31419, 443}, {1698, 4915, 6736}, {1706, 3911, 26062}, {2646, 4863, 3189}, {2886, 12513, 388}, {2975, 3434, 20}, {3436, 11680, 3091}, {3452, 50443, 26129}, {3624, 4882, 6745}, {3869, 64153, 54398}, {3871, 6910, 5281}, {3913, 4999, 5218}, {4295, 62858, 9965}, {4853, 5231, 10}, {5234, 51785, 40998}, {5249, 62832, 11037}, {5273, 9785, 5250}, {5281, 12632, 3871}, {5657, 10785, 6926}, {5657, 10914, 63133}, {5703, 6764, 3870}, {5745, 21627, 1697}, {5794, 11260, 3476}, {5795, 24386, 9581}, {5837, 64205, 7962}, {8227, 21075, 5748}, {9709, 15325, 17567}, {9710, 25524, 26040}, {11235, 57288, 5225}, {12514, 49600, 30305}, {28628, 34791, 3475}, {30478, 64068, 55}, {43161, 59320, 3522}

X(64082) = ISOGONAL CONJUGATE OF X(7129)

Barycentrics    a*(a^2-b^2-c^2)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b+c)^2) : :

X(64082) lies on these lines: {1, 2}, {3, 23168}, {6, 25091}, {9, 16577}, {20, 9121}, {34, 37279}, {40, 1817}, {48, 10319}, {57, 2289}, {63, 77}, {81, 2327}, {92, 27413}, {100, 7070}, {101, 1763}, {152, 2822}, {189, 53997}, {223, 329}, {241, 55405}, {269, 9965}, {278, 908}, {307, 6349}, {321, 56216}, {322, 2331}, {326, 345}, {333, 55392}, {440, 18446}, {464, 10884}, {469, 57276}, {511, 28379}, {515, 37185}, {517, 11347}, {527, 56848}, {610, 3101}, {651, 47848}, {664, 18750}, {914, 56456}, {940, 25939}, {1040, 1818}, {1073, 3692}, {1108, 4383}, {1172, 55478}, {1259, 6617}, {1260, 38288}, {1332, 3719}, {1385, 21483}, {1427, 6603}, {1442, 5273}, {1443, 28610}, {1445, 55399}, {1498, 63985}, {1630, 24611}, {1708, 2323}, {1801, 2328}, {1802, 37755}, {1813, 6507}, {1944, 20223}, {1953, 9816}, {2192, 9371}, {2256, 3666}, {2257, 26669}, {2318, 20277}, {2336, 56328}, {2910, 6260}, {2989, 39700}, {2990, 39947}, {3218, 4341}, {3219, 63088}, {3305, 40937}, {3306, 37543}, {3428, 11350}, {3434, 40960}, {3436, 5930}, {3452, 56418}, {3553, 5712}, {3576, 53815}, {3668, 5905}, {3752, 25934}, {3875, 17862}, {3929, 47057}, {3936, 25013}, {3949, 25915}, {3951, 56839}, {4350, 62799}, {4354, 56583}, {4552, 28950}, {4561, 52406}, {4641, 37672}, {5227, 18675}, {5249, 7190}, {5250, 16368}, {5294, 11427}, {5437, 26741}, {5534, 30809}, {5709, 37263}, {6360, 45738}, {6513, 52351}, {6611, 7368}, {6678, 37533}, {6769, 24604}, {7011, 7013}, {7290, 54348}, {7490, 37531}, {8257, 52423}, {8555, 54305}, {8747, 27412}, {8897, 20769}, {9370, 52384}, {9536, 18594}, {10025, 18663}, {10310, 40658}, {10601, 54358}, {11340, 59320}, {11349, 39592}, {11433, 25019}, {15500, 18678}, {16054, 37529}, {16413, 17614}, {16435, 31786}, {16438, 24590}, {17073, 26942}, {17147, 26651}, {17776, 26668}, {17825, 25067}, {17976, 20254}, {18134, 55391}, {18599, 21376}, {18621, 37577}, {18652, 56367}, {19542, 63986}, {19684, 25001}, {19822, 24553}, {20182, 25878}, {22119, 22132}, {22134, 23112}, {22136, 26921}, {22356, 26934}, {22770, 37269}, {23113, 23131}, {23292, 32777}, {24554, 62851}, {25243, 26223}, {25252, 56082}, {26065, 63092}, {27382, 56943}, {27411, 64194}, {28606, 37659}, {30852, 37695}, {31164, 55010}, {33116, 44179}, {35312, 45742}, {37248, 62809}, {37419, 64150}, {37887, 56352}, {40911, 63395}, {46352, 55015}, {46831, 52386}, {56178, 64135}, {57233, 57245}, {57287, 62970}, {61012, 63074}

X(64082) = isogonal conjugate of X(7129)
X(64082) = perspector of circumconic {{A, B, C, X(190), X(6516)}}
X(64082) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 7129}, {2, 7151}, {4, 1436}, {6, 40836}, {7, 7154}, {19, 84}, {21, 2358}, {25, 189}, {27, 2357}, {28, 1903}, {33, 1422}, {34, 282}, {55, 55110}, {56, 7003}, {57, 7008}, {92, 2208}, {162, 55242}, {268, 1118}, {273, 7118}, {278, 2192}, {280, 608}, {281, 1413}, {285, 1880}, {309, 1973}, {393, 1433}, {513, 40117}, {604, 7020}, {607, 1440}, {1096, 41081}, {1119, 7367}, {1172, 52384}, {1249, 60803}, {1256, 2331}, {1395, 34404}, {1396, 53013}, {1407, 57492}, {1474, 39130}, {1857, 55117}, {1974, 44190}, {2299, 8808}, {3064, 8059}, {3209, 46355}, {5317, 52389}, {6059, 34400}, {6591, 13138}, {6612, 7046}, {7337, 44189}, {7649, 36049}, {8747, 41087}, {8752, 56939}, {17924, 32652}, {18344, 37141}, {41084, 41489}
X(64082) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 7003}, {3, 7129}, {6, 84}, {9, 40836}, {57, 278}, {125, 55242}, {223, 55110}, {226, 8808}, {281, 158}, {3161, 7020}, {3351, 7149}, {5452, 7008}, {5514, 7649}, {6337, 309}, {6503, 41081}, {6505, 189}, {7078, 1741}, {11517, 282}, {14298, 7004}, {14390, 60799}, {14837, 4858}, {16596, 17924}, {22391, 2208}, {24018, 26932}, {24771, 57492}, {32664, 7151}, {36033, 1436}, {39026, 40117}, {40591, 1903}, {40611, 2358}, {51574, 39130}, {55044, 3064}, {55063, 522}, {57055, 24026}, {61075, 44426}, {62584, 34404}, {62647, 280}
X(64082) = X(i)-Ceva conjugate of X(j) for these {i, j}: {322, 40}, {326, 78}, {345, 63}, {7045, 1331}, {27398, 329}
X(64082) = X(i)-cross conjugate of X(j) for these {i, j}: {2324, 78}, {7011, 63}, {7078, 7013}, {16596, 57213}, {52097, 69}
X(64082) = pole of line {7649, 55242} with respect to the polar circle
X(64082) = pole of line {905, 57042} with respect to the MacBeath circumconic
X(64082) = pole of line {58, 84} with respect to the Stammler hyperbola
X(64082) = pole of line {514, 59973} with respect to the Steiner inellipse
X(64082) = pole of line {644, 56235} with respect to the Hutson-Moses hyperbola
X(64082) = pole of line {86, 309} with respect to the Wallace hyperbola
X(64082) = pole of line {4025, 17899} with respect to the dual conic of excircles-radical circle
X(64082) = pole of line {4025, 4391} with respect to the dual conic of polar circle
X(64082) = pole of line {52616, 57054} with respect to the dual conic of Orthic inconic
X(64082) = pole of line {2, 11023} with respect to the dual conic of Yff parabola
X(64082) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(222)}}, {{A, B, C, X(2), X(77)}}, {{A, B, C, X(3), X(936)}}, {{A, B, C, X(8), X(63)}}, {{A, B, C, X(10), X(40)}}, {{A, B, C, X(42), X(1409)}}, {{A, B, C, X(57), X(1210)}}, {{A, B, C, X(69), X(34255)}}, {{A, B, C, X(78), X(394)}}, {{A, B, C, X(81), X(938)}}, {{A, B, C, X(88), X(5704)}}, {{A, B, C, X(196), X(2982)}}, {{A, B, C, X(198), X(612)}}, {{A, B, C, X(200), X(219)}}, {{A, B, C, X(208), X(5230)}}, {{A, B, C, X(221), X(54418)}}, {{A, B, C, X(226), X(15836)}}, {{A, B, C, X(271), X(55987)}}, {{A, B, C, X(278), X(3086)}}, {{A, B, C, X(287), X(1999)}}, {{A, B, C, X(306), X(322)}}, {{A, B, C, X(312), X(7183)}}, {{A, B, C, X(345), X(7080)}}, {{A, B, C, X(387), X(3194)}}, {{A, B, C, X(499), X(37887)}}, {{A, B, C, X(614), X(6611)}}, {{A, B, C, X(905), X(44675)}}, {{A, B, C, X(997), X(45127)}}, {{A, B, C, X(1041), X(56345)}}, {{A, B, C, X(1193), X(7114)}}, {{A, B, C, X(1255), X(5703)}}, {{A, B, C, X(1737), X(14837)}}, {{A, B, C, X(1790), X(19861)}}, {{A, B, C, X(1797), X(36846)}}, {{A, B, C, X(1807), X(36609)}}, {{A, B, C, X(1814), X(36845)}}, {{A, B, C, X(1815), X(3870)}}, {{A, B, C, X(1998), X(60047)}}, {{A, B, C, X(2340), X(10397)}}, {{A, B, C, X(2989), X(3187)}}, {{A, B, C, X(2990), X(12649)}}, {{A, B, C, X(3011), X(6129)}}, {{A, B, C, X(3085), X(7952)}}, {{A, B, C, X(3577), X(52037)}}, {{A, B, C, X(3719), X(4564)}}, {{A, B, C, X(3872), X(22129)}}, {{A, B, C, X(4025), X(26001)}}, {{A, B, C, X(4047), X(4061)}}, {{A, B, C, X(4511), X(6513)}}, {{A, B, C, X(5271), X(8822)}}, {{A, B, C, X(5552), X(6505)}}, {{A, B, C, X(6510), X(6745)}}, {{A, B, C, X(6518), X(7360)}}, {{A, B, C, X(6734), X(18607)}}, {{A, B, C, X(6735), X(57245)}}, {{A, B, C, X(6765), X(54414)}}, {{A, B, C, X(7074), X(28043)}}, {{A, B, C, X(7177), X(14986)}}, {{A, B, C, X(10527), X(52381)}}, {{A, B, C, X(10529), X(27832)}}, {{A, B, C, X(13411), X(25430)}}, {{A, B, C, X(14919), X(34772)}}, {{A, B, C, X(15524), X(47848)}}, {{A, B, C, X(17896), X(39700)}}, {{A, B, C, X(20007), X(56355)}}, {{A, B, C, X(21482), X(40435)}}, {{A, B, C, X(21717), X(37755)}}, {{A, B, C, X(22350), X(57233)}}, {{A, B, C, X(27383), X(56234)}}, {{A, B, C, X(28118), X(40971)}}, {{A, B, C, X(40212), X(51375)}}, {{A, B, C, X(42287), X(56328)}}
X(64082) = barycentric product X(i)*X(j) for these (i, j): {3, 322}, {40, 69}, {72, 8822}, {196, 3719}, {198, 304}, {200, 57479}, {219, 40702}, {221, 3718}, {223, 345}, {227, 332}, {271, 55015}, {283, 57810}, {312, 7011}, {326, 7952}, {329, 63}, {347, 78}, {1214, 27398}, {1259, 342}, {1264, 208}, {1331, 17896}, {1332, 14837}, {1441, 1819}, {1444, 21075}, {1817, 306}, {2187, 305}, {2199, 57919}, {2289, 40701}, {2324, 348}, {2331, 3926}, {3194, 52396}, {3596, 7114}, {3964, 47372}, {3998, 41083}, {4552, 57213}, {4561, 6129}, {4563, 55212}, {4998, 53557}, {6516, 8058}, {7013, 8}, {7045, 7358}, {7074, 7182}, {7078, 75}, {7080, 77}, {10397, 4554}, {14256, 3692}, {16596, 4564}, {17206, 21871}, {20336, 2360}, {35518, 57118}, {40212, 44189}, {40417, 52097}, {40971, 7055}, {52406, 6611}, {55111, 85}, {55112, 57}, {55116, 7183}, {55241, 647}, {57101, 664}, {57233, 6335}, {57245, 651}
X(64082) = barycentric quotient X(i)/X(j) for these (i, j): {1, 40836}, {3, 84}, {6, 7129}, {8, 7020}, {9, 7003}, {31, 7151}, {40, 4}, {41, 7154}, {48, 1436}, {55, 7008}, {57, 55110}, {63, 189}, {69, 309}, {71, 1903}, {72, 39130}, {73, 52384}, {77, 1440}, {78, 280}, {101, 40117}, {184, 2208}, {198, 19}, {200, 57492}, {208, 1118}, {212, 2192}, {219, 282}, {221, 34}, {222, 1422}, {223, 278}, {227, 225}, {228, 2357}, {255, 1433}, {271, 46355}, {283, 285}, {304, 44190}, {322, 264}, {329, 92}, {332, 57795}, {345, 34404}, {347, 273}, {394, 41081}, {603, 1413}, {647, 55242}, {906, 36049}, {1071, 52571}, {1103, 7952}, {1214, 8808}, {1259, 271}, {1264, 57783}, {1331, 13138}, {1332, 44327}, {1400, 2358}, {1433, 1256}, {1802, 7367}, {1804, 56972}, {1813, 37141}, {1817, 27}, {1819, 21}, {2187, 25}, {2199, 608}, {2289, 268}, {2318, 53013}, {2324, 281}, {2331, 393}, {2360, 28}, {3194, 8747}, {3195, 1096}, {3342, 7149}, {3682, 52389}, {3718, 57793}, {3719, 44189}, {3990, 41087}, {3998, 56944}, {4563, 55211}, {4855, 56940}, {5440, 56939}, {6056, 2188}, {6129, 7649}, {6516, 53642}, {6611, 1435}, {7011, 57}, {7013, 7}, {7074, 33}, {7078, 1}, {7080, 318}, {7099, 6612}, {7114, 56}, {7125, 55117}, {7183, 34400}, {7358, 24026}, {7368, 7079}, {7952, 158}, {8058, 44426}, {8822, 286}, {10397, 650}, {14256, 1847}, {14298, 3064}, {14379, 60799}, {14837, 17924}, {15501, 36123}, {16596, 4858}, {17896, 46107}, {19614, 60803}, {21075, 41013}, {21871, 1826}, {23067, 61229}, {27398, 31623}, {32656, 32652}, {36059, 8059}, {37755, 13853}, {40152, 52037}, {40212, 196}, {40702, 331}, {40971, 1857}, {47372, 1093}, {47432, 2310}, {52097, 946}, {52386, 53010}, {52425, 7118}, {53557, 11}, {55015, 342}, {55044, 7004}, {55111, 9}, {55112, 312}, {55212, 2501}, {55241, 6331}, {57101, 522}, {57118, 108}, {57213, 4560}, {57233, 905}, {57241, 61040}, {57245, 4391}, {57479, 1088}, {57810, 57809}
X(64082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3190, 3870}, {1, 3682, 78}, {3, 23168, 23204}, {63, 6505, 77}, {223, 2324, 329}, {326, 37669, 41081}, {6349, 26872, 307}, {18607, 55466, 63}, {40399, 63068, 62798}

X(64083) = ISOTOMIC CONJUGATE OF X(36620)

Barycentrics    (a-b-c)*(3*a^2-(b-c)^2-2*a*(b+c)) : :

X(64083) lies on these lines: {1, 2}, {3, 5815}, {7, 480}, {9, 1200}, {20, 21075}, {40, 54199}, {55, 18228}, {63, 64108}, {72, 31787}, {75, 56331}, {100, 329}, {144, 165}, {210, 5218}, {226, 46917}, {318, 461}, {345, 3699}, {346, 19605}, {355, 5828}, {390, 3158}, {474, 11037}, {497, 3689}, {518, 5435}, {631, 34790}, {664, 31527}, {728, 2125}, {908, 9812}, {944, 37364}, {950, 8165}, {956, 54445}, {962, 5687}, {971, 11678}, {1088, 30806}, {1155, 28610}, {1215, 7229}, {1259, 7411}, {1320, 56090}, {1329, 3189}, {1699, 46873}, {1709, 60935}, {1837, 12536}, {2077, 54052}, {2094, 9352}, {2325, 59599}, {2550, 3838}, {2551, 4313}, {2886, 7679}, {2900, 5809}, {2968, 32862}, {3035, 14151}, {3059, 3740}, {3091, 63146}, {3160, 16284}, {3161, 3693}, {3218, 20588}, {3243, 6692}, {3421, 5440}, {3434, 5748}, {3474, 64143}, {3475, 4413}, {3486, 21031}, {3487, 9709}, {3488, 3820}, {3522, 12527}, {3523, 57279}, {3555, 17567}, {3600, 5438}, {3681, 5744}, {3684, 5838}, {3685, 8055}, {3694, 27382}, {3697, 6857}, {3701, 52346}, {3711, 5432}, {3713, 5296}, {3715, 4995}, {3717, 6555}, {3744, 63126}, {3751, 59593}, {3868, 26062}, {3869, 31798}, {3873, 17658}, {3880, 4345}, {3913, 8169}, {3930, 40127}, {3940, 5657}, {3947, 37161}, {3965, 5749}, {3996, 28808}, {4073, 26685}, {4308, 59691}, {4323, 5836}, {4344, 63089}, {4417, 43290}, {4421, 5698}, {4447, 17081}, {4488, 10025}, {4551, 18623}, {4640, 6172}, {4644, 25355}, {4661, 14740}, {4662, 30478}, {4671, 17860}, {4679, 10385}, {4734, 20895}, {4849, 37642}, {4863, 10589}, {4998, 7055}, {5015, 36682}, {5080, 10431}, {5081, 57534}, {5175, 8226}, {5223, 10164}, {5253, 16411}, {5261, 57284}, {5265, 6762}, {5274, 5853}, {5290, 56999}, {5316, 10389}, {5437, 11038}, {5534, 6926}, {5537, 64130}, {5686, 5745}, {5696, 15064}, {5728, 58650}, {5734, 10914}, {5758, 11499}, {5775, 26446}, {5811, 11248}, {5825, 46694}, {5850, 53056}, {5927, 25722}, {6223, 10310}, {6224, 55016}, {6557, 14942}, {6684, 54398}, {6690, 38057}, {6865, 64116}, {6913, 61628}, {6921, 46677}, {6935, 18908}, {6988, 58643}, {7046, 52412}, {8236, 26105}, {8727, 17757}, {9436, 21296}, {9776, 37271}, {9799, 17857}, {9874, 22991}, {9954, 10167}, {10307, 17613}, {10860, 60966}, {11106, 18250}, {11246, 61152}, {11415, 36002}, {11523, 63990}, {11680, 51416}, {11682, 63133}, {12053, 12632}, {14100, 18227}, {14450, 35990}, {15717, 62824}, {15733, 18236}, {17183, 56181}, {17296, 62388}, {17580, 21620}, {17718, 26040}, {18220, 21627}, {20075, 27131}, {20196, 64162}, {21454, 64112}, {24703, 30332}, {25525, 40333}, {25681, 64068}, {25718, 36620}, {27065, 42012}, {27398, 56182}, {27541, 51972}, {27542, 28826}, {30305, 48696}, {30628, 64157}, {31018, 58328}, {31508, 51090}, {31995, 40719}, {32099, 40999}, {32849, 53673}, {33144, 56009}, {33168, 53661}, {33677, 61413}, {34784, 62775}, {36624, 36626}, {36922, 38127}, {37669, 62391}, {38200, 58463}, {38255, 56088}, {39959, 44794}, {41012, 56936}, {41867, 46916}, {42014, 61023}, {42361, 51567}, {44785, 60971}, {50808, 60905}, {51362, 59388}, {51364, 53997}, {54051, 64111}, {54228, 63985}, {54389, 59596}, {54422, 59675}, {55998, 59732}, {56180, 56349}, {56201, 60668}, {60714, 64168}, {61012, 62839}, {62823, 64142}, {63961, 64171}

X(64083) = reflection of X(i) in X(j) for these {i,j}: {5274, 30827}, {5435, 59572}
X(64083) = isotomic conjugate of X(36620)
X(64083) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 61380}, {31, 36620}, {41, 60831}, {56, 3062}, {57, 11051}, {604, 10405}, {649, 61240}, {667, 53640}, {1106, 63165}, {1397, 44186}, {1407, 19605}, {1416, 56718}, {1436, 42872}, {9316, 60813}, {51641, 55284}
X(64083) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3062}, {2, 36620}, {7, 279}, {478, 61380}, {3160, 60831}, {3161, 10405}, {4130, 1146}, {5375, 61240}, {5452, 11051}, {6552, 63165}, {6631, 53640}, {7658, 11}, {13609, 3676}, {24771, 19605}, {39026, 53622}, {40133, 60992}, {40609, 56718}, {45252, 60813}, {55285, 4934}, {59573, 59170}, {62585, 44186}
X(64083) = X(i)-Ceva conjugate of X(j) for these {i, j}: {346, 8}, {1275, 644}, {16284, 144}
X(64083) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {56355, 69}
X(64083) = X(i)-cross conjugate of X(j) for these {i, j}: {144, 8}, {45203, 31627}, {45228, 9}
X(64083) = pole of line {3057, 52653} with respect to the Feuerbach hyperbola
X(64083) = pole of line {190, 53640} with respect to the Yff parabola
X(64083) = pole of line {86, 36620} with respect to the Wallace hyperbola
X(64083) = pole of line {3239, 3900} with respect to the dual conic of incircle
X(64083) = pole of line {2, 4936} with respect to the dual conic of Yff parabola
X(64083) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(165)}}, {{A, B, C, X(2), X(144)}}, {{A, B, C, X(7), X(11019)}}, {{A, B, C, X(8), X(16284)}}, {{A, B, C, X(9), X(8580)}}, {{A, B, C, X(10), X(21060)}}, {{A, B, C, X(21), X(8583)}}, {{A, B, C, X(80), X(30286)}}, {{A, B, C, X(145), X(14942)}}, {{A, B, C, X(280), X(3616)}}, {{A, B, C, X(281), X(13405)}}, {{A, B, C, X(312), X(29616)}}, {{A, B, C, X(314), X(35613)}}, {{A, B, C, X(318), X(9780)}}, {{A, B, C, X(345), X(26006)}}, {{A, B, C, X(519), X(56090)}}, {{A, B, C, X(522), X(38254)}}, {{A, B, C, X(1026), X(31343)}}, {{A, B, C, X(1034), X(6734)}}, {{A, B, C, X(1193), X(3207)}}, {{A, B, C, X(1200), X(45228)}}, {{A, B, C, X(1210), X(41561)}}, {{A, B, C, X(1280), X(36846)}}, {{A, B, C, X(1419), X(2999)}}, {{A, B, C, X(2340), X(58835)}}, {{A, B, C, X(2398), X(3699)}}, {{A, B, C, X(3008), X(7658)}}, {{A, B, C, X(3241), X(51565)}}, {{A, B, C, X(3617), X(60668)}}, {{A, B, C, X(3621), X(56088)}}, {{A, B, C, X(3680), X(11519)}}, {{A, B, C, X(3693), X(56714)}}, {{A, B, C, X(3705), X(56349)}}, {{A, B, C, X(3870), X(41798)}}, {{A, B, C, X(3912), X(6557)}}, {{A, B, C, X(4384), X(56201)}}, {{A, B, C, X(4518), X(39570)}}, {{A, B, C, X(4847), X(50560)}}, {{A, B, C, X(4853), X(39959)}}, {{A, B, C, X(4998), X(5423)}}, {{A, B, C, X(5222), X(9533)}}, {{A, B, C, X(5552), X(36624)}}, {{A, B, C, X(6738), X(56144)}}, {{A, B, C, X(6745), X(57064)}}, {{A, B, C, X(7155), X(30567)}}, {{A, B, C, X(9778), X(55346)}}, {{A, B, C, X(10307), X(36620)}}, {{A, B, C, X(10580), X(21453)}}, {{A, B, C, X(17023), X(34277)}}, {{A, B, C, X(19861), X(56098)}}, {{A, B, C, X(21872), X(59305)}}, {{A, B, C, X(22117), X(22350)}}, {{A, B, C, X(26015), X(42361)}}, {{A, B, C, X(27383), X(36626)}}, {{A, B, C, X(29627), X(38255)}}, {{A, B, C, X(36845), X(51567)}}, {{A, B, C, X(40869), X(58877)}}
X(64083) = barycentric product X(i)*X(j) for these (i, j): {144, 8}, {165, 312}, {200, 31627}, {220, 50560}, {345, 63965}, {1419, 341}, {1697, 44797}, {2322, 50563}, {3160, 346}, {3207, 3596}, {3699, 7658}, {4554, 58835}, {5423, 9533}, {13609, 4998}, {16284, 9}, {17106, 30693}, {21060, 333}, {21872, 314}, {22117, 7017}, {45203, 56026}, {50559, 7046}, {50561, 728}, {50562, 56182}, {55285, 645}, {57064, 664}, {62533, 650}
X(64083) = barycentric quotient X(i)/X(j) for these (i, j): {2, 36620}, {7, 60831}, {8, 10405}, {9, 3062}, {40, 42872}, {55, 11051}, {56, 61380}, {100, 61240}, {101, 53622}, {144, 7}, {165, 57}, {190, 53640}, {200, 19605}, {312, 44186}, {346, 63165}, {497, 62544}, {645, 55284}, {1419, 269}, {3160, 279}, {3207, 56}, {3693, 56718}, {7658, 3676}, {9533, 479}, {13609, 11}, {16284, 85}, {17106, 738}, {21060, 226}, {21872, 65}, {22117, 222}, {31627, 1088}, {41006, 59170}, {43182, 60992}, {45203, 11019}, {45228, 40133}, {50559, 7056}, {50560, 57792}, {50561, 23062}, {50563, 56382}, {55285, 7178}, {57064, 522}, {58835, 650}, {58877, 7658}, {62533, 4554}, {63594, 24856}, {63965, 278}
X(64083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 4511, 3241}, {9, 59584, 5281}, {55, 18228, 52653}, {78, 2057, 4420}, {100, 329, 9778}, {145, 6736, 8}, {165, 21060, 144}, {200, 6745, 2}, {210, 5218, 5273}, {329, 9778, 63975}, {345, 3699, 5423}, {497, 3689, 64146}, {518, 59572, 5435}, {908, 17784, 9812}, {908, 64135, 17784}, {1376, 25568, 7}, {2551, 56176, 4313}, {3035, 24477, 64114}, {3158, 3452, 390}, {3421, 5440, 5731}, {3434, 5748, 9779}, {3487, 9709, 11024}, {5328, 64146, 497}, {5745, 62218, 5686}, {5853, 30827, 5274}, {24703, 34607, 30332}, {57279, 59587, 3523}

X(64084) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(3)-CIRCUMCONCEVIAN OF X(6) AND X(4)-CROSSPEDAL-OF-X(40)

Barycentrics    a*(a^5+b^5-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)+a^3*(-4*b^2+2*b*c-4*c^2)+a*(b+c)^2*(3*b^2-4*b*c+3*c^2)) : :
X(64084) = -2*X[3]+3*X[16475], -2*X[10]+3*X[14853], -4*X[141]+5*X[8227], -3*X[165]+4*X[182], -8*X[575]+5*X[63469], -4*X[576]+X[7991], -2*X[599]+3*X[38021], -5*X[631]+6*X[38049], -4*X[1125]+3*X[10519]

X(64084) lies on circumconic {{A, B, C, X(937), X(1432)}} and on these lines: {1, 256}, {3, 16475}, {4, 5847}, {6, 40}, {10, 14853}, {20, 39870}, {57, 613}, {69, 946}, {78, 25304}, {141, 8227}, {165, 182}, {193, 962}, {265, 32261}, {355, 21850}, {376, 51005}, {381, 50950}, {515, 51192}, {516, 4780}, {517, 1351}, {518, 5693}, {519, 54132}, {524, 31162}, {542, 50865}, {551, 50967}, {575, 63469}, {576, 7991}, {599, 38021}, {611, 1697}, {631, 38049}, {674, 33536}, {936, 17792}, {944, 49684}, {966, 39605}, {990, 29353}, {1125, 10519}, {1350, 1386}, {1352, 1699}, {1353, 28174}, {1385, 16491}, {1428, 15803}, {1482, 16496}, {1503, 41869}, {1571, 5034}, {1572, 5028}, {1698, 14561}, {1721, 15310}, {1743, 6211}, {1770, 39901}, {1836, 39897}, {1902, 12167}, {1992, 28194}, {2077, 36741}, {2093, 8540}, {2330, 61763}, {2771, 48679}, {2781, 33535}, {2800, 10755}, {2802, 10759}, {2809, 10758}, {2817, 10764}, {2836, 51941}, {2948, 9970}, {2999, 20368}, {3094, 9592}, {3098, 7987}, {3241, 51028}, {3242, 16200}, {3333, 24471}, {3416, 5480}, {3428, 37492}, {3543, 51001}, {3545, 50781}, {3564, 12699}, {3579, 5050}, {3589, 31423}, {3616, 62174}, {3618, 6684}, {3679, 20423}, {3731, 7609}, {3779, 6769}, {3817, 40330}, {3827, 37625}, {3844, 54447}, {3875, 29057}, {4220, 62845}, {4259, 63391}, {4260, 6282}, {4301, 34379}, {4663, 5102}, {5032, 34632}, {5039, 12197}, {5052, 9620}, {5085, 35242}, {5092, 16192}, {5093, 12702}, {5097, 63468}, {5250, 15988}, {5272, 37521}, {5476, 19875}, {5603, 49511}, {5691, 31670}, {5731, 61044}, {5818, 38146}, {5846, 5881}, {5848, 14217}, {5886, 48876}, {5921, 9812}, {6326, 9024}, {6361, 14912}, {7289, 12704}, {7988, 24206}, {7989, 19130}, {9025, 63992}, {9589, 39878}, {9612, 12588}, {9614, 12589}, {9616, 19145}, {9625, 15577}, {9904, 11579}, {9911, 19459}, {9924, 40658}, {9943, 58621}, {10222, 55724}, {10246, 55584}, {10268, 19133}, {10319, 61398}, {11012, 36740}, {11178, 30308}, {11203, 62816}, {11224, 55720}, {11362, 59406}, {11531, 37517}, {12017, 31663}, {12164, 34381}, {12177, 13174}, {12194, 13355}, {12245, 49529}, {12555, 37676}, {12701, 39873}, {12703, 45729}, {12782, 35439}, {13605, 32247}, {13624, 55610}, {14810, 58221}, {14848, 50821}, {14927, 28150}, {15178, 55580}, {16189, 55721}, {16468, 18788}, {16834, 24257}, {17502, 55629}, {18440, 22793}, {18492, 53023}, {18583, 26446}, {19924, 34628}, {20070, 51170}, {22791, 34380}, {24728, 49477}, {25055, 54173}, {25406, 31730}, {28212, 61624}, {28538, 54131}, {29054, 49496}, {29311, 61086}, {30389, 52987}, {30392, 55587}, {31421, 50659}, {31666, 55602}, {31673, 51538}, {35774, 35841}, {35775, 35840}, {38023, 54169}, {38034, 61545}, {38036, 47595}, {38068, 63109}, {38118, 51171}, {38136, 61261}, {38314, 54174}, {38315, 53097}, {39899, 48661}, {43174, 59408}, {43216, 57279}, {44839, 64017}, {46264, 64005}, {47321, 47571}, {47356, 50811}, {49164, 64003}, {49524, 63143}, {49653, 53994}, {49681, 61296}, {51147, 61291}, {51705, 54170}, {55597, 58229}, {55623, 58225}, {55657, 58217}, {55663, 58215}, {55718, 58245}, {59399, 61524}, {63356, 63385}

X(64084) = midpoint of X(i) and X(j) for these {i,j}: {193, 962}, {1482, 44456}, {3241, 51028}, {3242, 55722}, {3543, 51001}, {9589, 39878}, {39899, 48661}, {51192, 51212}
X(64084) = reflection of X(i) in X(j) for these {i,j}: {20, 39870}, {40, 6}, {69, 946}, {355, 21850}, {376, 51005}, {944, 49684}, {1350, 1386}, {2948, 9970}, {3416, 5480}, {3679, 20423}, {3751, 1351}, {5691, 31670}, {6776, 51196}, {7289, 45728}, {9904, 11579}, {9924, 40658}, {9943, 58621}, {12245, 49529}, {12782, 35439}, {13174, 12177}, {16496, 1482}, {18440, 22793}, {19459, 31812}, {24728, 49477}, {32247, 13605}, {32261, 265}, {33878, 1385}, {39878, 63722}, {39885, 4}, {39898, 4301}, {47321, 47571}, {50811, 47356}, {50950, 381}, {50967, 551}, {54170, 51705}, {61296, 49681}, {63428, 49511}, {64005, 46264}
X(64084) = perspector of circumconic {{A, B, C, X(37137), X(58991)}}
X(64084) = pole of line {3063, 22154} with respect to the cosine circle
X(64084) = pole of line {3666, 9817} with respect to the Feuerbach hyperbola
X(64084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5847, 39885}, {141, 38035, 8227}, {516, 51196, 6776}, {517, 1351, 3751}, {1350, 1386, 3576}, {1702, 12698, 40}, {3098, 38029, 7987}, {3416, 5480, 5587}, {4301, 34379, 39898}, {51192, 51212, 515}

X(64085) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF ANTI-HONSBERGER AND X(4)-CROSSPEDAL-OF-X(40)

Barycentrics    a^6+a^5*(b+c)+2*a^3*b*c*(b+c)-a^4*(b+c)^2+a^2*(b-c)^2*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)-a*(b^5-b^4*c-b*c^4+c^5) : :
X(64085) = -4*X[5]+3*X[38047], -2*X[10]+3*X[10516], -2*X[182]+3*X[5886], -2*X[597]+3*X[38021], -4*X[1125]+3*X[5085], -2*X[1386]+3*X[5603], -3*X[1699]+X[3751], -5*X[3091]+3*X[59406]

X(64085) lies on these lines: {1, 1503}, {4, 518}, {5, 38047}, {6, 946}, {10, 10516}, {30, 47358}, {40, 141}, {65, 12589}, {69, 962}, {74, 32238}, {113, 32278}, {182, 5886}, {354, 26118}, {355, 3818}, {376, 51003}, {381, 47359}, {497, 5928}, {511, 12699}, {515, 3242}, {516, 1350}, {517, 1352}, {519, 47353}, {524, 31162}, {542, 3656}, {551, 43273}, {597, 38021}, {599, 28194}, {611, 12047}, {613, 30384}, {944, 49465}, {952, 39884}, {960, 26939}, {1012, 22769}, {1125, 5085}, {1385, 46264}, {1386, 5603}, {1428, 11376}, {1469, 1836}, {1482, 18440}, {1519, 45729}, {1537, 5848}, {1699, 3751}, {1892, 53548}, {2098, 39891}, {2099, 39892}, {2330, 11375}, {2778, 2892}, {2784, 32921}, {2792, 64016}, {2807, 19161}, {3056, 12701}, {3057, 12588}, {3091, 59406}, {3149, 12329}, {3241, 51023}, {3543, 50999}, {3564, 22791}, {3576, 44882}, {3589, 8227}, {3616, 25406}, {3620, 20070}, {3654, 11178}, {3655, 11645}, {3679, 47354}, {3763, 6684}, {3827, 12586}, {3844, 5657}, {3873, 37456}, {3877, 63470}, {4260, 5805}, {4295, 24471}, {4297, 48905}, {4301, 5847}, {4307, 10401}, {4310, 30617}, {4643, 6210}, {4663, 14853}, {5050, 18493}, {5102, 64073}, {5250, 26543}, {5587, 49524}, {5596, 40658}, {5690, 18358}, {5691, 16496}, {5693, 9021}, {5731, 14927}, {5784, 11677}, {5820, 45776}, {5845, 11372}, {5846, 7982}, {5881, 9053}, {5901, 38029}, {5921, 51192}, {6001, 24476}, {6211, 17279}, {6361, 10519}, {7289, 12705}, {7983, 50641}, {7984, 41737}, {8196, 39881}, {8203, 39880}, {8550, 11522}, {9024, 14217}, {9812, 51212}, {9830, 50881}, {9856, 34381}, {9911, 37485}, {9943, 58581}, {9955, 14561}, {9956, 38116}, {10165, 53094}, {10247, 48662}, {10387, 10624}, {10404, 15971}, {10445, 50995}, {10595, 39874}, {11179, 38023}, {11180, 28538}, {11415, 43216}, {11477, 34379}, {11496, 36740}, {11579, 12261}, {11720, 32233}, {12197, 42534}, {12262, 61088}, {12512, 55646}, {12571, 38146}, {12594, 12608}, {13211, 32274}, {13464, 38315}, {13605, 16010}, {14848, 50806}, {15668, 39605}, {16200, 51147}, {17276, 29057}, {17301, 24257}, {17642, 36844}, {18481, 29012}, {18483, 53023}, {18583, 38034}, {18788, 33087}, {19542, 41338}, {19925, 38144}, {20330, 38046}, {21167, 35242}, {21279, 60926}, {21356, 34632}, {21850, 40273}, {22753, 36741}, {22793, 31670}, {24206, 26446}, {24851, 50612}, {25055, 51737}, {26929, 63994}, {28146, 48873}, {28150, 48872}, {28174, 48876}, {28178, 48874}, {28198, 54173}, {28212, 61545}, {29054, 49509}, {29181, 41869}, {29207, 61086}, {31423, 34573}, {31730, 31884}, {31803, 34378}, {33878, 48661}, {36728, 51002}, {37984, 47506}, {38036, 51150}, {38049, 53093}, {38072, 50802}, {38110, 61272}, {38118, 47355}, {38145, 42356}, {38165, 61259}, {38314, 64014}, {38317, 61268}, {47745, 49690}, {48881, 64005}, {48910, 49505}, {48922, 48931}, {49531, 64088}, {51414, 54408}, {51537, 59387}, {60895, 64126}

X(64085) = midpoint of X(i) and X(j) for these {i,j}: {4, 39898}, {69, 962}, {1482, 18440}, {3241, 51023}, {3242, 36990}, {3543, 50999}, {5691, 16496}, {5921, 51192}, {7982, 39885}, {7983, 50641}, {7984, 41737}, {33878, 48661}, {49505, 51118}
X(64085) = reflection of X(i) in X(j) for these {i,j}: {6, 946}, {40, 141}, {74, 32238}, {355, 3818}, {376, 51003}, {944, 49465}, {1350, 49511}, {3416, 1352}, {3654, 11178}, {3679, 47354}, {3751, 5480}, {5596, 40658}, {5690, 18358}, {6776, 1386}, {9943, 58581}, {11179, 51709}, {11579, 12261}, {13211, 32274}, {16010, 13605}, {21850, 40273}, {31670, 22793}, {32233, 11720}, {32278, 113}, {39870, 13464}, {39878, 8550}, {43273, 551}, {46264, 1385}, {47356, 3656}, {47359, 381}, {47506, 37984}, {48905, 4297}, {48906, 5901}, {48910, 51118}, {48922, 48931}, {49529, 19925}, {49531, 64088}, {49681, 1482}, {49688, 355}, {49690, 47745}, {61088, 12262}, {64005, 48881}, {64080, 39870}
X(64085) = pole of line {36844, 40959} with respect to the Feuerbach hyperbola
X(64085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 39898, 518}, {6, 946, 38035}, {516, 49511, 1350}, {542, 3656, 47356}, {1699, 3751, 5480}, {3242, 36990, 515}, {5603, 6776, 1386}, {11179, 51709, 38023}, {11522, 39878, 16475}, {13464, 39870, 38315}, {16475, 39878, 8550}, {19925, 49529, 38144}, {22753, 39877, 36741}, {38315, 64080, 39870}

X(64086) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST JOHNSON-YFF AND X(4)-CROSSPEDAL-OF-X(55)

Barycentrics    (a+b-c)*(a-b+c)*(a^5-a^4*(b+c)+(b-c)^2*(b+c)^3-a*(b+c)^2*(b^2+c^2)) : :

X(64086) lies on these lines: {1, 6917}, {2, 5172}, {3, 26481}, {4, 12}, {5, 8069}, {8, 18962}, {11, 6826}, {30, 40292}, {56, 377}, {65, 3419}, {145, 388}, {197, 1894}, {347, 39751}, {355, 1858}, {442, 37579}, {443, 5433}, {497, 6839}, {498, 6928}, {517, 1478}, {528, 10956}, {674, 12588}, {942, 10044}, {1056, 1317}, {1454, 6734}, {1457, 33104}, {1470, 11112}, {1479, 9955}, {1486, 1884}, {1617, 17528}, {1770, 37584}, {1824, 11392}, {1837, 50195}, {2098, 10532}, {2478, 6690}, {2550, 12848}, {2646, 48482}, {3057, 26332}, {3086, 6901}, {3295, 18499}, {3304, 10949}, {3428, 6850}, {3476, 18467}, {3485, 52367}, {3583, 5219}, {3585, 5119}, {3586, 18406}, {3614, 6893}, {3813, 18967}, {4185, 10831}, {4293, 6951}, {4295, 45288}, {4680, 6358}, {5046, 10588}, {5080, 5698}, {5173, 10404}, {5204, 6897}, {5217, 6836}, {5218, 6840}, {5225, 6894}, {5229, 37437}, {5261, 20075}, {5270, 25415}, {5432, 6827}, {5434, 31140}, {5587, 30223}, {5603, 10947}, {5693, 37710}, {5697, 49177}, {5721, 61398}, {5726, 18513}, {5800, 39897}, {5820, 34372}, {5880, 18838}, {6256, 12688}, {6835, 10896}, {6851, 15338}, {6862, 59334}, {6864, 7173}, {6865, 52793}, {6867, 10321}, {6899, 63756}, {6900, 10591}, {6916, 15326}, {6918, 26476}, {6925, 12943}, {6929, 7951}, {6934, 37564}, {6957, 12764}, {6959, 8070}, {7294, 17582}, {7497, 10833}, {7742, 37438}, {9579, 41338}, {9612, 37569}, {9654, 10679}, {9655, 47032}, {9659, 37117}, {9673, 36009}, {10039, 10526}, {10106, 22837}, {10522, 12607}, {10525, 12047}, {10572, 18517}, {10592, 61533}, {10596, 13274}, {10629, 15888}, {10826, 17699}, {10827, 37821}, {11372, 41698}, {11509, 15844}, {11510, 25466}, {12116, 34471}, {12678, 12859}, {16915, 28773}, {17605, 26333}, {17700, 45632}, {21859, 31409}, {22766, 26470}, {22768, 63980}, {24390, 26437}, {24806, 33109}, {26126, 56782}, {26326, 45627}, {26327, 45628}, {26357, 37468}, {26358, 63257}, {30116, 38945}, {30274, 49176}, {33111, 60682}, {37155, 57288}, {37550, 42012}, {37736, 56790}, {37738, 50194}, {38454, 60909}, {41538, 64171}, {45287, 61146}, {45625, 48454}, {45626, 48455}, {63326, 63393}, {63750, 63852}

X(64086) = pole of line {5722, 5812} with respect to the Feuerbach hyperbola
X(64086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3085, 10953}, {55, 10895, 7680}, {55, 36999, 6284}, {388, 2475, 18961}, {388, 3434, 2099}, {1836, 5252, 64041}, {3085, 37000, 55}, {18407, 24929, 1479}, {26388, 26412, 1}

X(64087) = ISOGONAL CONJUGATE OF X(15617)

Barycentrics    a^4+4*a^2*b*c-a^3*(b+c)-(b^2-c^2)^2+a*(b^3-3*b^2*c-3*b*c^2+c^3) : :
X(64087) = -3*X[2]+2*X[24928], -4*X[1125]+5*X[31246], -5*X[1698]+4*X[6691], -4*X[3626]+X[37567], -5*X[3697]+4*X[58649], -2*X[4311]+3*X[16371], 4*X[4701]+X[63209], -3*X[17728]+2*X[62825], -3*X[35262]+4*X[47742], -3*X[38042]+2*X[61534], -2*X[49627]+3*X[61717]

X(64087) lies on these lines: {1, 1329}, {2, 24928}, {3, 6735}, {4, 8}, {5, 3872}, {6, 21074}, {7, 4004}, {10, 56}, {30, 63130}, {36, 37828}, {40, 1145}, {46, 529}, {55, 10915}, {63, 5690}, {78, 952}, {80, 3632}, {100, 18481}, {145, 5722}, {150, 16284}, {153, 6259}, {200, 5881}, {322, 41004}, {341, 21290}, {388, 3753}, {392, 2551}, {405, 5795}, {442, 9578}, {443, 4002}, {495, 19860}, {496, 36846}, {499, 5123}, {515, 5687}, {516, 37001}, {518, 10573}, {519, 1837}, {604, 21030}, {758, 41687}, {908, 1482}, {936, 37709}, {938, 16215}, {942, 5554}, {944, 5440}, {958, 8069}, {960, 12647}, {997, 10944}, {998, 5724}, {999, 24982}, {1056, 5439}, {1125, 31246}, {1146, 17742}, {1155, 37829}, {1265, 59586}, {1319, 26364}, {1320, 47744}, {1376, 40293}, {1385, 5552}, {1420, 13747}, {1478, 5836}, {1479, 3880}, {1483, 56387}, {1512, 22770}, {1657, 63145}, {1697, 11113}, {1698, 6691}, {1737, 12513}, {2057, 37611}, {2099, 21077}, {2136, 3586}, {2321, 54008}, {2390, 4680}, {2478, 9957}, {2646, 45701}, {2800, 12059}, {2802, 12701}, {2841, 13532}, {2886, 10827}, {2932, 63983}, {2975, 6940}, {3035, 12749}, {3036, 10057}, {3057, 41389}, {3086, 17619}, {3254, 43731}, {3303, 49626}, {3337, 34690}, {3416, 8679}, {3476, 17614}, {3486, 34619}, {3555, 18391}, {3612, 64123}, {3616, 5828}, {3617, 6904}, {3625, 4863}, {3626, 37567}, {3633, 37702}, {3654, 37430}, {3697, 58649}, {3754, 10404}, {3811, 10950}, {3813, 10826}, {3814, 11376}, {3820, 19861}, {3870, 14022}, {3884, 4679}, {3885, 5046}, {3895, 15171}, {3913, 10572}, {3916, 5657}, {3927, 59503}, {3940, 12645}, {3962, 36920}, {4193, 11373}, {4308, 17567}, {4311, 16371}, {4420, 61244}, {4511, 6963}, {4513, 5179}, {4652, 61524}, {4668, 5223}, {4678, 37435}, {4701, 63209}, {4853, 5587}, {4855, 34773}, {4861, 5886}, {4865, 20498}, {4875, 56746}, {4882, 37712}, {4915, 37714}, {5084, 20789}, {5087, 33895}, {5119, 57288}, {5126, 6921}, {5187, 7743}, {5258, 26066}, {5270, 5880}, {5288, 18395}, {5330, 27131}, {5533, 11256}, {5691, 63137}, {5697, 24703}, {5705, 38058}, {5725, 10459}, {5727, 6765}, {5731, 59591}, {5748, 10595}, {5790, 6734}, {5818, 6964}, {5844, 11682}, {5882, 6745}, {5901, 30852}, {5904, 41684}, {5905, 50193}, {6244, 52683}, {6261, 37725}, {6361, 63133}, {6554, 41391}, {6700, 63987}, {6737, 47745}, {6925, 31798}, {6929, 23340}, {6983, 9956}, {7354, 54286}, {7483, 31434}, {7967, 27383}, {7971, 13257}, {7982, 51409}, {7991, 52860}, {8050, 38955}, {8148, 51423}, {9580, 64202}, {9581, 12629}, {9654, 40587}, {9708, 24987}, {9940, 10805}, {10200, 20323}, {10246, 27385}, {10371, 41822}, {10528, 24929}, {10531, 13600}, {10624, 12640}, {10742, 39776}, {10896, 49600}, {10912, 30384}, {10942, 61146}, {11009, 34647}, {11236, 12047}, {11237, 12609}, {11362, 12527}, {11525, 18492}, {11680, 61261}, {11826, 63132}, {11827, 20588}, {12115, 31788}, {12514, 34606}, {12526, 63143}, {12531, 62354}, {12666, 17661}, {12702, 51433}, {13463, 64203}, {14110, 46677}, {14740, 31806}, {15813, 59327}, {15888, 54318}, {15955, 17720}, {16086, 44720}, {16980, 31778}, {17275, 21061}, {17299, 21078}, {17533, 50443}, {17606, 45700}, {17613, 64120}, {17671, 40872}, {17718, 30147}, {17721, 50637}, {17728, 62825}, {17781, 34718}, {18525, 35448}, {19537, 59675}, {19914, 46685}, {20060, 57282}, {20270, 21244}, {20895, 21286}, {22836, 37740}, {23831, 63139}, {24541, 31479}, {25005, 54391}, {25006, 37240}, {26127, 62835}, {28224, 64135}, {28628, 37719}, {30144, 37738}, {31160, 34640}, {31436, 57003}, {31786, 51380}, {32157, 59316}, {32213, 37615}, {32850, 56799}, {34123, 63208}, {34471, 59719}, {34625, 54361}, {34772, 37739}, {35262, 47742}, {37281, 37532}, {37585, 51378}, {37711, 44669}, {37717, 59310}, {38042, 61534}, {38126, 60970}, {38176, 64153}, {40663, 62858}, {41006, 56536}, {46937, 60452}, {49163, 56545}, {49168, 64046}, {49627, 61717}, {51984, 52478}, {54176, 61296}, {57002, 61763}, {63138, 64005}, {64139, 64140}

X(64087) = midpoint of X(i) and X(j) for these {i,j}: {8, 3436}, {2098, 36972}, {3632, 30323}, {5881, 63391}, {7991, 52860}, {18525, 35448}
X(64087) = reflection of X(i) in X(j) for these {i,j}: {1, 1329}, {46, 8256}, {56, 10}, {2098, 21616}, {3555, 50196}, {4311, 63990}, {5687, 6736}, {5730, 21075}, {8256, 33559}, {20076, 37582}, {36846, 496}, {36977, 24928}, {37738, 30144}, {54134, 47745}, {58798, 3436}, {61296, 54176}, {63987, 6700}
X(64087) = inverse of X(10914) in Fuhrmann circle
X(64087) = isogonal conjugate of X(15617)
X(64087) = complement of X(36977)
X(64087) = anticomplement of X(24928)
X(64087) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 15617}, {24928, 24928}
X(64087) = pole of line {2804, 57155} with respect to the Bevan circle
X(64087) = pole of line {513, 10914} with respect to the Fuhrmann circle
X(64087) = pole of line {1837, 10914} with respect to the Feuerbach hyperbola
X(64087) = pole of line {1437, 15617} with respect to the Stammler hyperbola
X(64087) = pole of line {1444, 15617} with respect to the Wallace hyperbola
X(64087) = pole of line {6692, 17720} with respect to the dual conic of Yff parabola
X(64087) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(15952)}}, {{A, B, C, X(69), X(12245)}}, {{A, B, C, X(92), X(60085)}}, {{A, B, C, X(318), X(996)}}, {{A, B, C, X(3680), X(5081)}}, {{A, B, C, X(3869), X(42019)}}, {{A, B, C, X(8050), X(53151)}}, {{A, B, C, X(10914), X(34406)}}
X(64087) = barycentric product X(i)*X(j) for these (i, j): {15952, 321}
X(64087) = barycentric quotient X(i)/X(j) for these (i, j): {6, 15617}, {15952, 81}
X(64087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36977, 24928}, {4, 8, 10914}, {8, 329, 12245}, {8, 3421, 72}, {8, 3436, 517}, {8, 355, 3419}, {8, 5080, 14923}, {8, 5176, 355}, {8, 56879, 34790}, {8, 56880, 3869}, {8, 59387, 5082}, {10, 10106, 474}, {10, 8666, 24914}, {46, 3679, 8256}, {515, 6736, 5687}, {517, 3436, 58798}, {519, 21075, 5730}, {529, 8256, 46}, {944, 7080, 5440}, {960, 32537, 12647}, {1329, 38455, 1}, {1385, 51362, 5552}, {1706, 9613, 11112}, {2098, 31141, 21616}, {2098, 36972, 519}, {2478, 12648, 9957}, {3632, 30323, 5854}, {3632, 9614, 3680}, {3679, 37710, 5794}, {3679, 9613, 1706}, {3814, 22837, 11376}, {4193, 38460, 11373}, {4311, 63990, 16371}, {4853, 5587, 24390}, {4861, 11681, 5886}, {5080, 14923, 12699}, {5123, 11260, 499}, {5795, 31397, 405}, {8256, 33559, 3679}, {9578, 9623, 442}, {10944, 21031, 997}, {20895, 21286, 64122}, {31141, 36972, 2098}, {51433, 64002, 12702}

X(64088) = COMPLEMENT OF X(30273)

Barycentrics    a^5*(b+c)-a*(b-c)^2*(b+c)^3-2*b*c*(b^2-c^2)^2+2*a^2*b*c*(b^2+c^2) : :
X(64088) = -3*X[2]+X[30273], -X[20]+5*X[4699], -4*X[140]+5*X[31238], -X[192]+5*X[3091], -3*X[262]+X[32453], X[382]+4*X[4739], 4*X[546]+X[4686], -5*X[631]+7*X[4751], -X[984]+3*X[5587], X[1278]+7*X[3832], -5*X[1656]+4*X[4698], 3*X[1699]+X[49474] and many others

X(64088) lies on these lines: {2, 30273}, {3, 3739}, {4, 75}, {5, 37}, {10, 29054}, {20, 4699}, {30, 4688}, {65, 23690}, {72, 20236}, {114, 14680}, {119, 25642}, {140, 31238}, {192, 3091}, {262, 32453}, {346, 36694}, {354, 23689}, {355, 518}, {376, 51049}, {381, 536}, {382, 4739}, {389, 58499}, {511, 21443}, {515, 24325}, {517, 3696}, {537, 50796}, {546, 4686}, {547, 51045}, {549, 51042}, {631, 4751}, {726, 6248}, {740, 946}, {742, 5480}, {942, 17861}, {952, 49478}, {971, 48938}, {984, 5587}, {1071, 48937}, {1210, 4032}, {1278, 3832}, {1427, 20256}, {1479, 11997}, {1482, 28581}, {1503, 49481}, {1656, 4698}, {1699, 49474}, {1733, 12723}, {1824, 14213}, {1867, 6734}, {1882, 37591}, {1893, 22464}, {2182, 24332}, {2345, 36670}, {2805, 10738}, {3090, 4687}, {3146, 4772}, {3149, 54410}, {3543, 51044}, {3545, 4664}, {3576, 40328}, {3644, 3855}, {3655, 51061}, {3672, 36695}, {3752, 37365}, {3797, 7384}, {3817, 3993}, {3821, 17062}, {3839, 4740}, {3842, 10175}, {3843, 4726}, {3850, 4718}, {3851, 4681}, {3854, 4788}, {3914, 5515}, {4008, 12722}, {4192, 31993}, {4301, 4709}, {4411, 8760}, {4463, 20886}, {4704, 5068}, {4732, 11362}, {4755, 5055}, {4764, 61964}, {4812, 36557}, {4821, 50689}, {5056, 27268}, {5066, 61623}, {5071, 51043}, {5295, 15488}, {5307, 37581}, {5603, 49470}, {5709, 5788}, {5720, 27471}, {5817, 51052}, {5832, 54008}, {5881, 49490}, {5886, 15569}, {5887, 20718}, {6327, 54151}, {6817, 54284}, {6835, 20171}, {7201, 9612}, {7982, 49459}, {8229, 49512}, {8680, 15762}, {9955, 49462}, {10222, 49475}, {10436, 37474}, {10516, 49509}, {11178, 51050}, {11499, 15624}, {11522, 49469}, {12571, 28522}, {12618, 36654}, {12675, 58583}, {13464, 49471}, {14206, 61662}, {14853, 49496}, {15687, 51048}, {15852, 15973}, {15908, 21926}, {15971, 20892}, {16200, 49678}, {16732, 24476}, {17225, 50959}, {17280, 36692}, {17302, 36693}, {17321, 36672}, {17348, 37510}, {17441, 20242}, {17755, 29243}, {18357, 49515}, {18480, 49483}, {18492, 49493}, {18531, 37820}, {19540, 44417}, {19546, 30818}, {20544, 24269}, {21279, 24701}, {22791, 49468}, {24209, 32118}, {24212, 37592}, {24220, 29016}, {24257, 48900}, {24349, 59387}, {24357, 36526}, {24828, 63970}, {24993, 52245}, {25384, 36530}, {25939, 37370}, {26011, 47522}, {26470, 37361}, {27483, 63402}, {27487, 63444}, {28194, 50096}, {29057, 45305}, {29069, 48888}, {29331, 48934}, {31162, 50086}, {31302, 54448}, {33878, 43169}, {34627, 51055}, {34648, 51060}, {34718, 51036}, {37712, 49498}, {37714, 49448}, {38034, 49461}, {38074, 50075}, {38076, 50777}, {38140, 49523}, {38150, 51058}, {38155, 49510}, {49450, 59388}, {49503, 61256}, {49531, 64085}, {51047, 61942}, {51051, 54131}, {51064, 61985}, {58655, 63976}, {63318, 63398}

X(64088) = midpoint of X(i) and X(j) for these {i,j}: {4, 75}, {376, 51065}, {381, 51040}, {3543, 51044}, {4301, 4709}, {5881, 49490}, {6327, 54151}, {7982, 49459}, {15687, 51048}, {30271, 52852}, {31162, 50086}, {34627, 51055}, {34648, 51060}, {49531, 64085}, {51051, 54131}, {51063, 63427}
X(64088) = reflection of X(i) in X(j) for these {i,j}: {3, 3739}, {37, 5}, {376, 51049}, {381, 51041}, {389, 58499}, {3655, 51061}, {11362, 4732}, {12675, 58583}, {34718, 51036}, {49471, 13464}, {49475, 10222}, {51038, 381}, {51042, 549}, {51045, 547}, {51046, 61522}, {51050, 11178}, {63976, 58655}
X(64088) = complement of X(30273)
X(64088) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 75, 10779}
X(64088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 63427, 51063}, {5, 29010, 37}, {5, 51046, 61522}, {75, 51063, 63427}, {355, 5805, 1352}, {381, 536, 51038}, {536, 51041, 381}, {4688, 52852, 30271}, {5071, 51043, 51488}, {29010, 61522, 51046}, {30271, 52852, 30}

X(64089) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(4)-CROSSPEDAL-OF-X(98)

Barycentrics    a^8-5*a^6*(b^2+c^2)+(b^2-c^2)^2*(2*b^4-b^2*c^2+2*c^4)+a^4*(7*b^4+3*b^2*c^2+7*c^4)+a^2*(-5*b^6+b^4*c^2+b^2*c^4-5*c^6) : :
X(64089) = -6*X[2]+X[98], X[4]+4*X[620], 4*X[5]+X[99], X[8]+4*X[11724], 4*X[10]+X[7970], -X[20]+6*X[38748], -2*X[115]+7*X[3090], 4*X[140]+X[6033], 4*X[141]+X[10753], -X[148]+11*X[5056], 3*X[262]+2*X[5976], X[316]+4*X[37459] and many others

X(64089) lies on these lines: {2, 98}, {3, 7899}, {4, 620}, {5, 99}, {8, 11724}, {10, 7970}, {20, 38748}, {30, 38750}, {69, 9754}, {115, 3090}, {140, 6033}, {141, 10753}, {148, 5056}, {183, 54103}, {262, 5976}, {316, 37459}, {325, 10011}, {373, 58502}, {376, 9167}, {381, 10723}, {485, 19108}, {486, 19109}, {511, 7925}, {543, 5071}, {546, 38730}, {547, 8724}, {549, 38741}, {551, 50880}, {569, 3044}, {575, 16984}, {576, 63021}, {590, 19056}, {597, 64091}, {615, 19055}, {619, 36765}, {625, 11676}, {631, 2794}, {632, 31268}, {671, 5055}, {690, 64101}, {842, 36170}, {1007, 9753}, {1125, 9864}, {1503, 40336}, {1513, 5103}, {1587, 13989}, {1588, 8997}, {1656, 2782}, {1916, 7608}, {1995, 39828}, {2023, 31489}, {2080, 7809}, {2482, 3545}, {2783, 31272}, {2784, 19862}, {2787, 64008}, {2790, 31255}, {3035, 10768}, {3054, 12830}, {3055, 12055}, {3060, 58517}, {3091, 23698}, {3146, 38736}, {3523, 38749}, {3524, 22247}, {3525, 7914}, {3526, 12042}, {3530, 38742}, {3533, 10991}, {3544, 35022}, {3614, 13182}, {3624, 11710}, {3627, 38731}, {3628, 7859}, {3634, 21636}, {3679, 50883}, {3742, 58681}, {3788, 37446}, {3815, 44534}, {3817, 51578}, {3819, 58537}, {3828, 50881}, {3832, 39809}, {3851, 22515}, {4193, 38556}, {4413, 12178}, {4993, 39814}, {5020, 39803}, {5026, 10516}, {5054, 22566}, {5067, 6722}, {5068, 10992}, {5070, 7943}, {5072, 38733}, {5079, 15092}, {5094, 12131}, {5097, 36859}, {5133, 39816}, {5149, 37334}, {5171, 7912}, {5219, 24472}, {5418, 50719}, {5420, 50720}, {5422, 39810}, {5432, 12185}, {5433, 12184}, {5461, 61899}, {5476, 50639}, {5503, 14494}, {5562, 58503}, {5587, 11711}, {5640, 39806}, {5886, 7983}, {5943, 39817}, {5965, 63047}, {5978, 52266}, {5979, 52263}, {5988, 17593}, {5999, 29323}, {6114, 42580}, {6115, 42581}, {6248, 32967}, {6390, 39663}, {6656, 61104}, {6669, 61634}, {6670, 36776}, {6811, 12123}, {6813, 12124}, {6997, 39813}, {7173, 13183}, {7308, 24469}, {7484, 9861}, {7509, 39857}, {7527, 39831}, {7607, 60073}, {7697, 8179}, {7709, 7844}, {7741, 10086}, {7752, 12110}, {7775, 10788}, {7777, 36849}, {7778, 22712}, {7808, 12176}, {7828, 32467}, {7835, 37348}, {7858, 20576}, {7866, 38642}, {7887, 11257}, {7888, 12251}, {7901, 13334}, {7907, 54393}, {7909, 49111}, {7919, 11171}, {7931, 15819}, {7951, 10089}, {7988, 13174}, {8252, 49213}, {8253, 49212}, {8290, 15850}, {8591, 61924}, {8980, 32785}, {9749, 33386}, {9750, 33387}, {9751, 22664}, {9752, 63098}, {9771, 9877}, {9880, 52695}, {10109, 61600}, {10153, 53103}, {10171, 11599}, {10175, 13178}, {10185, 60136}, {10256, 54996}, {10272, 15545}, {10358, 39652}, {10601, 39820}, {10754, 14561}, {10769, 23513}, {10896, 15452}, {11184, 42536}, {11318, 63424}, {11412, 39835}, {11539, 14830}, {11606, 53108}, {11623, 61886}, {11632, 15699}, {11668, 60103}, {11793, 39846}, {12181, 15184}, {12183, 24953}, {12189, 26364}, {12190, 26363}, {12243, 14971}, {12355, 61925}, {12829, 37637}, {13335, 33245}, {13449, 13586}, {13967, 32786}, {14137, 36763}, {14643, 15342}, {14644, 53735}, {14853, 50567}, {14872, 58590}, {15022, 20094}, {15024, 39808}, {15081, 50711}, {15300, 61926}, {15703, 49102}, {15723, 26614}, {16239, 61599}, {16760, 36173}, {17004, 34507}, {17006, 36864}, {20398, 46936}, {20774, 37453}, {21445, 58448}, {23515, 33512}, {30745, 62490}, {31839, 34512}, {32152, 33259}, {32829, 62348}, {32970, 36998}, {33219, 52771}, {34803, 46236}, {35005, 60192}, {35018, 38229}, {35921, 39854}, {35951, 62203}, {36521, 61932}, {36523, 61913}, {36770, 41023}, {37690, 58883}, {38634, 61855}, {38635, 61970}, {38740, 60781}, {39804, 63084}, {39812, 63664}, {39825, 44802}, {39834, 43651}, {41135, 61912}, {42010, 54920}, {42262, 49266}, {42265, 49267}, {43150, 53104}, {43460, 56370}, {44972, 46987}, {47290, 57307}, {48657, 61887}, {50726, 52821}, {51387, 59397}, {51388, 59398}, {51523, 55857}, {52090, 55856}, {53729, 59391}, {54978, 60213}, {58661, 61686}, {58728, 60504}, {60144, 60280}, {61911, 62427}, {63344, 63345}

X(64089) = reflection of X(i) in X(j) for these {i,j}: {631, 31274}, {14061, 1656}, {38739, 632}
X(64089) = inverse of X(24981) in orthoptic circle of the Steiner Inellipse
X(64089) = pole of line {690, 24981} with respect to the orthoptic circle of the Steiner Inellipse
X(64089) = pole of line {230, 5111} with respect to the Kiepert hyperbola
X(64089) = pole of line {325, 5965} with respect to the Wallace hyperbola
X(64089) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {99, 15342, 58098}, {115, 15357, 45161}
X(64089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(98), X(60034)}}, {{A, B, C, X(182), X(52091)}}, {{A, B, C, X(262), X(51820)}}, {{A, B, C, X(287), X(56064)}}, {{A, B, C, X(325), X(6036)}}, {{A, B, C, X(1976), X(5966)}}, {{A, B, C, X(5967), X(11669)}}, {{A, B, C, X(7608), X(40820)}}, {{A, B, C, X(8781), X(46806)}}
X(64089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 147, 6036}, {2, 23234, 6054}, {4, 620, 21166}, {5, 15561, 99}, {5, 61561, 6321}, {5, 99, 14639}, {98, 23234, 114}, {114, 6036, 147}, {114, 6721, 2}, {140, 6033, 34473}, {148, 5056, 23514}, {325, 10011, 38227}, {381, 33813, 10723}, {620, 36519, 4}, {2794, 31274, 631}, {3090, 20399, 23235}, {3525, 9862, 38737}, {3526, 38743, 12042}, {3628, 51872, 38224}, {5055, 13188, 61576}, {5070, 12188, 34127}, {5079, 38732, 15092}, {5640, 39807, 39806}, {6321, 15561, 61561}, {6722, 14981, 14651}, {6722, 38746, 14981}, {7752, 37466, 12110}, {10723, 33813, 12117}, {11177, 35021, 98}, {13188, 61576, 671}, {15092, 51524, 38732}, {38224, 51872, 38664}, {38737, 38745, 9862}, {52695, 61936, 9880}

X(64090) = ANTICOMPLEMENT OF X(11632)

Barycentrics    a^8-9*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4+5*b^2*c^2+c^4)+a^4*(10*b^4+13*b^2*c^2+10*c^4)-a^2*(3*b^6+5*b^4*c^2+5*b^2*c^4+3*c^6) : :
X(64090) = -4*X[5]+3*X[41135], -X[20]+4*X[51524], -4*X[115]+5*X[5071], -8*X[620]+7*X[15702], -5*X[631]+4*X[6055], -7*X[3090]+6*X[9166], X[3146]+8*X[38628], -7*X[3523]+4*X[51523], -11*X[3525]+12*X[9167], -7*X[3528]+4*X[10991], -X[3529]+4*X[10992], -17*X[3533]+20*X[38751]

X(64090) lies on these lines: {2, 2782}, {3, 11177}, {4, 543}, {5, 41135}, {20, 51524}, {30, 147}, {69, 74}, {98, 2482}, {114, 671}, {115, 5071}, {148, 381}, {186, 2936}, {385, 37461}, {524, 11676}, {530, 36776}, {531, 61634}, {538, 9890}, {549, 12188}, {599, 60653}, {620, 15702}, {631, 6055}, {1285, 5477}, {1327, 35698}, {1328, 35699}, {1352, 57633}, {1513, 52229}, {1569, 7739}, {1634, 37991}, {1916, 54826}, {1992, 10788}, {2080, 44367}, {2784, 50811}, {2793, 63250}, {2794, 11001}, {2796, 21636}, {3023, 12350}, {3027, 12351}, {3090, 9166}, {3146, 38628}, {3523, 51523}, {3525, 9167}, {3528, 10991}, {3529, 10992}, {3533, 38751}, {3543, 6033}, {3564, 8598}, {3817, 50887}, {3839, 6321}, {3845, 12355}, {3855, 38734}, {4027, 33255}, {4226, 9143}, {5054, 61561}, {5066, 38732}, {5067, 14971}, {5182, 12176}, {5461, 61899}, {5463, 6773}, {5464, 6770}, {5476, 7757}, {5478, 22577}, {5479, 22578}, {5485, 9877}, {5587, 50884}, {5603, 50886}, {5613, 51482}, {5617, 51483}, {5642, 22265}, {5969, 32474}, {5976, 32836}, {5984, 10304}, {5988, 48818}, {5989, 59634}, {6036, 15709}, {6298, 41042}, {6299, 41043}, {6337, 53765}, {6390, 61102}, {6721, 61889}, {6722, 61888}, {6776, 51798}, {7470, 32820}, {7665, 14694}, {7783, 37345}, {7799, 39266}, {7801, 11257}, {7970, 34631}, {8550, 35950}, {8584, 22521}, {8593, 50974}, {8716, 47353}, {8719, 15533}, {8787, 64091}, {8859, 37459}, {9114, 41022}, {9116, 41023}, {9140, 35922}, {9302, 60099}, {9740, 16508}, {9753, 32469}, {9830, 11180}, {9864, 34627}, {9875, 50796}, {9876, 39803}, {9880, 41099}, {9881, 50810}, {9884, 50818}, {10086, 10385}, {10303, 26614}, {10553, 34245}, {10722, 62042}, {10723, 62017}, {11165, 13860}, {11178, 52691}, {11179, 35925}, {11599, 38021}, {11656, 33512}, {12042, 15692}, {12184, 18969}, {12185, 12354}, {13174, 28194}, {13178, 38074}, {14061, 61895}, {14639, 41106}, {14831, 39808}, {14912, 18800}, {15092, 61927}, {15534, 39656}, {15682, 23698}, {15683, 38730}, {15687, 38733}, {15694, 61560}, {15697, 38731}, {15698, 34473}, {15708, 38750}, {15715, 35022}, {15716, 38634}, {15719, 38748}, {15721, 38739}, {19708, 21166}, {19905, 21356}, {19911, 63029}, {20398, 61886}, {21445, 27088}, {22247, 61861}, {22505, 50687}, {22515, 35369}, {23514, 61926}, {31274, 61865}, {32480, 37242}, {32516, 46226}, {32815, 35705}, {33260, 34510}, {34505, 37446}, {34507, 55164}, {35750, 36362}, {35751, 36319}, {35930, 63028}, {35951, 63722}, {35954, 50979}, {35955, 50955}, {36318, 47867}, {36320, 36769}, {36329, 36344}, {36331, 36363}, {36519, 36523}, {37939, 39828}, {38071, 61600}, {38229, 61920}, {38627, 61820}, {38635, 62073}, {38654, 51737}, {38737, 61822}, {38738, 62130}, {38740, 61867}, {38741, 62120}, {38742, 62094}, {38746, 61913}, {38747, 62086}, {39652, 63093}, {39809, 62011}, {39838, 62029}, {43572, 57011}, {44237, 51860}, {47367, 57628}, {47368, 57629}, {50639, 63428}, {50885, 59388}, {51795, 63993}, {55009, 60201}, {61575, 61936}, {61576, 61924}

X(64090) = midpoint of X(i) and X(j) for these {i,j}: {147, 8591}, {3543, 20094}, {6054, 23235}, {13188, 48657}, {14692, 14830}
X(64090) = reflection of X(i) in X(j) for these {i,j}: {2, 8724}, {4, 6054}, {98, 2482}, {147, 48657}, {148, 381}, {376, 99}, {381, 51872}, {385, 37461}, {671, 114}, {1992, 12177}, {3543, 6033}, {5485, 9877}, {5984, 14830}, {6054, 14981}, {6321, 22566}, {6770, 5464}, {6773, 5463}, {6776, 51798}, {8591, 13188}, {8596, 6321}, {9740, 16508}, {9862, 376}, {9875, 50796}, {11001, 12117}, {11177, 3}, {11656, 33512}, {12117, 15300}, {12188, 549}, {12243, 2}, {12355, 3845}, {13172, 8591}, {14830, 33813}, {15683, 38730}, {15687, 61599}, {22265, 5642}, {22577, 5478}, {22578, 5479}, {31162, 21636}, {34627, 9864}, {34631, 7970}, {38664, 6055}, {38733, 15687}, {39808, 14831}, {44367, 2080}, {50810, 9881}, {50818, 9884}, {50974, 8593}, {51482, 5613}, {51483, 5617}, {62042, 10722}, {63029, 19911}, {63428, 50639}, {64091, 8787}
X(64090) = anticomplement of X(11632)
X(64090) = X(i)-Dao conjugate of X(j) for these {i, j}: {11632, 11632}
X(64090) = pole of line {44822, 53247} with respect to the circumcircle
X(64090) = pole of line {804, 9125} with respect to the orthoptic circle of the Steiner Inellipse
X(64090) = pole of line {2407, 53379} with respect to the Kiepert parabola
X(64090) = pole of line {1495, 2080} with respect to the Stammler hyperbola
X(64090) = pole of line {3268, 39905} with respect to the Steiner circumellipse
X(64090) = pole of line {30, 39099} with respect to the Wallace hyperbola
X(64090) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {99, 12074, 47288}, {147, 8591, 9143}
X(64090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(46316)}}, {{A, B, C, X(1494), X(43532)}}, {{A, B, C, X(12243), X(46142)}}, {{A, B, C, X(14494), X(36890)}}, {{A, B, C, X(45018), X(54501)}}
X(64090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12243, 14651}, {2, 2782, 12243}, {30, 13188, 8591}, {30, 48657, 147}, {98, 2482, 3524}, {99, 542, 376}, {114, 671, 3545}, {115, 23234, 5071}, {147, 13188, 13172}, {376, 542, 9862}, {543, 14981, 6054}, {599, 63424, 60653}, {2794, 12117, 11001}, {2794, 15300, 12117}, {2796, 21636, 31162}, {5461, 64089, 61899}, {5984, 10304, 14830}, {6036, 64019, 15709}, {6054, 23235, 543}, {6055, 41134, 631}, {6321, 22566, 3839}, {11177, 52695, 3}, {12355, 38743, 3845}, {13188, 48657, 30}, {14692, 33813, 5984}, {14830, 33813, 10304}, {14981, 23235, 4}, {15561, 49102, 2}, {38664, 41134, 6055}, {51524, 52090, 20}, {51898, 51899, 54173}

X(64091) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND EHRMANN AND X(4)-CROSSPEDAL-OF-X(98)

Barycentrics    3*a^10-b^10+b^8*c^2+b^2*c^8-c^10-7*a^8*(b^2+c^2)+a^6*(11*b^4+5*b^2*c^2+11*c^4)-2*a^4*(5*b^6+b^4*c^2+b^2*c^4+5*c^6)+a^2*(4*b^8-5*b^6*c^2+10*b^4*c^4-5*b^2*c^6+4*c^8) : :
X(64091) = -3*X[6]+2*X[114], -X[147]+3*X[1992], -6*X[182]+5*X[38750], -4*X[575]+3*X[15561], -6*X[597]+5*X[64089], -3*X[599]+4*X[6036], -4*X[620]+5*X[53093], -2*X[1352]+3*X[6034], -2*X[5026]+3*X[14912], -3*X[5085]+2*X[50567], -3*X[5182]+4*X[12007]

X(64091) lies on these lines: {6, 114}, {98, 524}, {99, 8550}, {115, 15069}, {147, 1992}, {182, 38750}, {193, 1916}, {511, 38741}, {542, 1351}, {575, 15561}, {576, 6033}, {597, 64089}, {599, 6036}, {620, 53093}, {671, 54475}, {690, 64103}, {1350, 14645}, {1352, 6034}, {1353, 12177}, {1503, 10723}, {2393, 39817}, {2782, 7737}, {2784, 64073}, {2794, 11477}, {3044, 64061}, {3564, 5111}, {3629, 10753}, {4663, 9864}, {5026, 14912}, {5085, 50567}, {5182, 12007}, {5480, 50641}, {5621, 39831}, {5969, 6776}, {5986, 41628}, {6054, 8584}, {6055, 15533}, {6721, 47352}, {7762, 38664}, {7776, 11623}, {8540, 12185}, {8724, 11842}, {8787, 64090}, {9830, 50974}, {9971, 39806}, {9974, 50720}, {9975, 50719}, {9976, 15545}, {10541, 38748}, {11177, 63064}, {11179, 33813}, {11482, 38743}, {11632, 31173}, {12184, 19369}, {12243, 23334}, {12829, 63043}, {13188, 51798}, {14692, 51140}, {14830, 47618}, {14848, 25562}, {14981, 30435}, {15073, 39808}, {19120, 39872}, {19569, 51212}, {20423, 22505}, {23234, 63124}, {23698, 64080}, {29959, 58502}, {32532, 60176}, {32621, 39803}, {34507, 38224}, {35021, 40341}, {38738, 43273}, {38739, 40107}, {38742, 52987}, {38745, 53858}, {38749, 53097}, {39804, 63129}, {50639, 51737}, {50979, 61561}

X(64091) = midpoint of X(i) and X(j) for these {i,j}: {11177, 63064}, {15073, 39808}
X(64091) = reflection of X(i) in X(j) for these {i,j}: {99, 8550}, {6033, 576}, {6054, 8584}, {9864, 4663}, {10753, 3629}, {12177, 1353}, {14981, 41672}, {15069, 115}, {15533, 6055}, {15545, 9976}, {50639, 51737}, {50641, 5480}, {53097, 38749}, {64090, 8787}, {64092, 63722}
X(64091) = pole of line {6321, 56370} with respect to the Kiepert hyperbola
X(64091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2782, 63722, 64092}, {49040, 49041, 3424}

X(64092) = ISOGONAL CONJUGATE OF X(14565)

Barycentrics    3*a^6-3*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(2*b^4-b^2*c^2+2*c^4) : :
X(64092) = -2*X[141]+3*X[5182], -X[148]+3*X[1992], -2*X[325]+3*X[12151], -3*X[599]+4*X[620], -3*X[1350]+4*X[38736], -3*X[1351]+X[38733], -3*X[1352]+4*X[61575], -6*X[3630]+13*X[52886], -4*X[6036]+5*X[53093], -8*X[6722]+9*X[47352], -X[8596]+5*X[63117], -3*X[9166]+4*X[63124]

X(64092) lies on these lines: {2, 8587}, {4, 60176}, {6, 13}, {30, 8586}, {32, 52090}, {53, 20774}, {69, 5026}, {98, 3815}, {99, 524}, {110, 1648}, {112, 32234}, {114, 15069}, {141, 5182}, {147, 7735}, {148, 1992}, {182, 9696}, {187, 8724}, {193, 5969}, {230, 6054}, {325, 12151}, {385, 35705}, {511, 38730}, {530, 41746}, {531, 41745}, {543, 10488}, {574, 14830}, {575, 7603}, {576, 6321}, {590, 13640}, {597, 11161}, {599, 620}, {615, 13760}, {671, 8584}, {690, 64104}, {694, 25046}, {732, 50249}, {1285, 50974}, {1350, 38736}, {1351, 38733}, {1352, 61575}, {1384, 48657}, {1499, 44677}, {1503, 5111}, {1506, 33749}, {1569, 38741}, {1641, 10554}, {1691, 3564}, {1915, 45968}, {1993, 62298}, {2023, 5984}, {2076, 5965}, {2079, 2930}, {2393, 39846}, {2482, 5210}, {2502, 6792}, {2548, 51523}, {2782, 7737}, {2794, 44526}, {3044, 62289}, {3053, 14981}, {3054, 23234}, {3094, 3269}, {3124, 14683}, {3292, 39602}, {3314, 4027}, {3448, 8288}, {3629, 10754}, {3630, 52886}, {4663, 13178}, {5013, 10991}, {5017, 44532}, {5107, 11645}, {5461, 18584}, {5463, 9117}, {5464, 9115}, {5480, 54571}, {5609, 15546}, {5613, 6782}, {5617, 6783}, {5621, 39860}, {5648, 48654}, {5913, 9225}, {5939, 7774}, {5976, 63046}, {5986, 14153}, {6032, 11422}, {6036, 53093}, {6055, 31489}, {6114, 22509}, {6115, 22507}, {6144, 14645}, {6722, 47352}, {6770, 61331}, {6772, 41621}, {6773, 61332}, {6775, 41620}, {6779, 6780}, {6791, 20998}, {6811, 33430}, {6813, 33431}, {7736, 11177}, {7745, 38664}, {7762, 53765}, {7777, 58765}, {7779, 8289}, {7837, 14931}, {8030, 10717}, {8540, 13183}, {8591, 63064}, {8592, 44367}, {8596, 63117}, {8627, 37779}, {9140, 41939}, {9146, 62658}, {9166, 63124}, {9167, 50993}, {9169, 58854}, {9971, 39835}, {9974, 37839}, {10418, 46276}, {10541, 38737}, {10765, 41720}, {10987, 12350}, {11061, 48945}, {11152, 14712}, {11179, 12042}, {11477, 23698}, {11482, 38732}, {12007, 53484}, {13182, 19369}, {13653, 32787}, {13773, 32788}, {13881, 38745}, {14561, 15092}, {14567, 41724}, {15073, 39837}, {15300, 51187}, {15342, 25329}, {15514, 29012}, {15545, 32761}, {15561, 32135}, {15820, 34986}, {16010, 34866}, {16529, 36766}, {16530, 60069}, {18553, 39601}, {19108, 58033}, {19109, 58032}, {19780, 36776}, {19781, 61634}, {19905, 50979}, {20399, 44535}, {20423, 22515}, {21358, 31274}, {22165, 41134}, {22247, 51186}, {22330, 39590}, {22501, 22502}, {22512, 47863}, {22513, 47864}, {22566, 43620}, {23004, 44498}, {23005, 44497}, {29959, 58503}, {31415, 49102}, {32525, 35279}, {32552, 45880}, {32553, 45879}, {32621, 39832}, {33876, 56788}, {34369, 60504}, {35022, 40341}, {35324, 63700}, {35356, 45291}, {35369, 63027}, {35948, 49267}, {35949, 49266}, {36521, 51188}, {36883, 56760}, {38731, 52987}, {38734, 53858}, {38738, 53097}, {38749, 43273}, {38750, 40107}, {38940, 45672}, {39809, 54131}, {39833, 63129}, {40866, 62551}, {41060, 42094}, {41061, 42093}, {41135, 63022}, {41274, 64028}, {46249, 53132}, {47276, 47326}, {50641, 53475}, {50991, 64019}, {50992, 52695}, {58058, 64061}

X(64092) = midpoint of X(i) and X(j) for these {i,j}: {8591, 63064}, {10488, 15534}, {10754, 45018}, {15073, 39837}
X(64092) = reflection of X(i) in X(j) for these {i,j}: {2, 8787}, {6, 5477}, {69, 5026}, {98, 8550}, {115, 41672}, {599, 18800}, {671, 8584}, {5104, 53499}, {6321, 576}, {6772, 41621}, {6775, 41620}, {10754, 3629}, {11161, 597}, {11646, 6}, {13178, 4663}, {15069, 114}, {15342, 25329}, {15533, 2482}, {19905, 50979}, {22512, 47863}, {22513, 47864}, {23004, 44498}, {23005, 44497}, {34507, 32135}, {40341, 50567}, {44453, 1569}, {47276, 47326}, {51798, 8593}, {53097, 38738}, {64091, 63722}
X(64092) = inverse of X(34155) in cosine circle
X(64092) = inverse of X(18424) in orthocentroidal circle
X(64092) = isogonal conjugate of X(14565)
X(64092) = perspector of circumconic {{A, B, C, X(476), X(9170)}}
X(64092) = pole of line {690, 34155} with respect to the cosine circle
X(64092) = pole of line {690, 18424} with respect to the orthocentroidal circle
X(64092) = pole of line {30, 9166} with respect to the Kiepert hyperbola
X(64092) = pole of line {9182, 53274} with respect to the Kiepert parabola
X(64092) = pole of line {323, 2502} with respect to the Stammler hyperbola
X(64092) = pole of line {9168, 11176} with respect to the Steiner circumellipse
X(64092) = pole of line {543, 7799} with respect to the Wallace hyperbola
X(64092) = intersection, other than A, B, C, of circumconics {{A, B, C, X(265), X(53605)}}, {{A, B, C, X(843), X(11060)}}, {{A, B, C, X(1989), X(8587)}}, {{A, B, C, X(7608), X(14356)}}, {{A, B, C, X(45103), X(51226)}}
X(64092) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11646, 6034}, {6, 542, 11646}, {115, 41672, 6}, {115, 5477, 41672}, {524, 53499, 5104}, {524, 8593, 51798}, {2782, 63722, 64091}, {5471, 43457, 14}, {5472, 43457, 13}, {6777, 6778, 6033}, {6792, 9143, 2502}, {10488, 15534, 543}, {12188, 15484, 115}, {22501, 22502, 22505}, {22997, 22998, 8724}, {31862, 31863, 18424}, {32135, 34507, 15561}, {47859, 47860, 6321}, {50719, 50720, 381}

X(64093) = ISOTOMIC CONJUGATE OF X(11169)

Barycentrics    -b^4+6*b^2*c^2-c^4+a^2*(b^2+c^2) : :
X(64093) = -X[7774]+3*X[44543], 3*X[33016]+X[63046]

X(64093) lies on these lines: {2, 2418}, {3, 32815}, {4, 7767}, {5, 76}, {11, 3761}, {12, 3760}, {20, 32872}, {30, 183}, {32, 50774}, {39, 15491}, {69, 381}, {75, 3820}, {99, 549}, {115, 141}, {140, 1975}, {148, 8356}, {187, 13468}, {193, 15484}, {194, 31406}, {230, 3734}, {235, 1235}, {264, 1596}, {274, 17527}, {298, 31694}, {299, 31693}, {302, 37351}, {303, 37352}, {308, 16098}, {310, 37355}, {311, 339}, {315, 546}, {316, 3845}, {350, 495}, {376, 32893}, {382, 3785}, {384, 63047}, {385, 8370}, {427, 39998}, {442, 18135}, {491, 18538}, {492, 18762}, {496, 1909}, {524, 3363}, {538, 3815}, {543, 11168}, {547, 32833}, {550, 1078}, {574, 58446}, {597, 5355}, {599, 7615}, {620, 3054}, {621, 41017}, {622, 41016}, {626, 63534}, {637, 6215}, {638, 6214}, {671, 7831}, {754, 53418}, {1003, 17008}, {1007, 5055}, {1153, 36521}, {1236, 46030}, {1329, 20888}, {1368, 40022}, {1384, 14033}, {1565, 20925}, {1595, 54412}, {1656, 3926}, {1657, 32826}, {1906, 44142}, {2482, 15597}, {2549, 8359}, {2782, 37451}, {2886, 6381}, {2896, 33229}, {2996, 16043}, {3090, 32830}, {3091, 7776}, {3143, 44155}, {3265, 14566}, {3314, 33228}, {3329, 19570}, {3523, 32822}, {3525, 32870}, {3526, 6337}, {3533, 32897}, {3545, 32874}, {3564, 37348}, {3589, 5309}, {3620, 16041}, {3627, 7750}, {3628, 7763}, {3629, 7753}, {3630, 7845}, {3631, 7818}, {3767, 7819}, {3793, 7737}, {3830, 64018}, {3843, 32006}, {3850, 7773}, {3851, 32816}, {3858, 7768}, {3934, 4045}, {3972, 19661}, {4187, 34284}, {4441, 17757}, {5020, 22241}, {5054, 32885}, {5056, 32818}, {5066, 7788}, {5067, 32831}, {5068, 32823}, {5070, 32829}, {5071, 32869}, {5072, 32888}, {5077, 7620}, {5224, 16052}, {5305, 7770}, {5306, 7804}, {5468, 57618}, {5480, 14994}, {6031, 47313}, {6376, 31419}, {6392, 9605}, {6623, 32000}, {6656, 16986}, {6661, 7806}, {6683, 9607}, {6722, 7880}, {6787, 20326}, {6823, 41009}, {7405, 28706}, {7486, 32840}, {7530, 15574}, {7603, 7813}, {7610, 21843}, {7617, 7908}, {7694, 15069}, {7735, 11286}, {7736, 22253}, {7745, 7751}, {7746, 7789}, {7749, 59545}, {7754, 16924}, {7761, 18546}, {7762, 16044}, {7765, 31239}, {7766, 53489}, {7769, 32820}, {7771, 8703}, {7774, 44543}, {7775, 50771}, {7778, 43620}, {7779, 33013}, {7782, 15712}, {7792, 14568}, {7793, 19687}, {7794, 39565}, {7795, 8361}, {7797, 16987}, {7798, 9300}, {7799, 15699}, {7800, 8357}, {7801, 44377}, {7802, 62036}, {7807, 17128}, {7809, 38071}, {7810, 15598}, {7811, 15687}, {7812, 50251}, {7815, 63548}, {7826, 39590}, {7828, 33185}, {7832, 33186}, {7836, 33249}, {7839, 33020}, {7841, 16990}, {7848, 47617}, {7850, 23046}, {7851, 8364}, {7860, 61976}, {7865, 63543}, {7868, 8360}, {7879, 14063}, {7881, 32961}, {7893, 33018}, {7898, 8352}, {7904, 19695}, {7906, 33002}, {7913, 34573}, {7929, 14062}, {7930, 33212}, {7939, 32993}, {7941, 33024}, {7942, 33211}, {8024, 37439}, {8354, 8556}, {8363, 46226}, {8367, 11174}, {8584, 9731}, {8728, 18140}, {8859, 35954}, {9606, 32450}, {9723, 18462}, {9766, 31415}, {9771, 39785}, {10170, 51386}, {10301, 26233}, {10303, 52718}, {11007, 51258}, {11054, 63101}, {11057, 33699}, {11064, 33509}, {11113, 37670}, {11159, 63029}, {11287, 43448}, {11288, 62992}, {11539, 59634}, {11548, 34254}, {11799, 44135}, {12188, 48906}, {12215, 38110}, {13877, 53480}, {13930, 53479}, {14039, 37689}, {14041, 63044}, {14532, 46034}, {14535, 51171}, {14651, 37450}, {14829, 36728}, {14928, 51737}, {15022, 32882}, {15067, 51439}, {15655, 35927}, {15703, 32837}, {15980, 18906}, {16921, 20081}, {17004, 35297}, {17556, 45962}, {18122, 52628}, {18142, 44150}, {18145, 37664}, {18152, 47514}, {18531, 41008}, {18840, 33180}, {18859, 34883}, {20094, 33273}, {20112, 22165}, {21031, 32104}, {21309, 63034}, {24206, 51397}, {24240, 42055}, {25278, 64200}, {26235, 30739}, {27269, 33033}, {30435, 32971}, {30444, 44140}, {31026, 37096}, {31455, 59546}, {31467, 32975}, {31489, 34511}, {32455, 41748}, {32456, 34506}, {32458, 61576}, {32821, 35018}, {32824, 32867}, {32825, 32878}, {32835, 61886}, {32839, 55857}, {32841, 46936}, {32871, 61881}, {32875, 61903}, {32877, 61911}, {32880, 61914}, {32883, 55858}, {32884, 61878}, {32892, 61920}, {32896, 61901}, {33016, 63046}, {33025, 55732}, {33416, 59540}, {33417, 59539}, {34127, 62348}, {36719, 58804}, {36733, 58803}, {37347, 52347}, {37638, 44216}, {37663, 62755}, {37678, 48847}, {37984, 44134}, {38907, 44224}, {43459, 46853}, {44180, 54006}, {46999, 62431}, {48874, 60702}, {48913, 61956}, {50955, 57634}, {51389, 59197}, {51441, 52145}, {54488, 60212}, {54718, 60217}, {58445, 59552}, {59773, 59776}, {61876, 62362}

X(64093) = midpoint of X(i) and X(j) for these {i,j}: {183, 11185}, {5475, 17131}
X(64093) = reflection of X(i) in X(j) for these {i,j}: {574, 58446}
X(64093) = isotomic conjugate of X(11169)
X(64093) = complement of X(31859)
X(64093) = perspector of circumconic {{A, B, C, X(35179), X(57813)}}
X(64093) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 11169}, {560, 57817}
X(64093) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 11169}, {6374, 57817}
X(64093) = pole of line {25423, 37350} with respect to the nine-point circle
X(64093) = pole of line {669, 34014} with respect to the orthoptic circle of the Steiner Inellipse
X(64093) = pole of line {538, 599} with respect to the Kiepert hyperbola
X(64093) = pole of line {6334, 37350} with respect to the MacBeath inconic
X(64093) = pole of line {1384, 34396} with respect to the Stammler hyperbola
X(64093) = pole of line {1499, 9148} with respect to the Steiner inellipse
X(64093) = pole of line {182, 1992} with respect to the Wallace hyperbola
X(64093) = pole of line {523, 39099} with respect to the dual conic of orthoptic circle of the Steiner Inellipse
X(64093) = pole of line {3134, 9191} with respect to the dual conic of Stammler hyperbola
X(64093) = pole of line {6784, 6791} with respect to the dual conic of Wallace hyperbola
X(64093) = intersection, other than A, B, C, of circumconics {{A, B, C, X(262), X(373)}}, {{A, B, C, X(327), X(5485)}}, {{A, B, C, X(15048), X(17983)}}
X(64093) = barycentric product X(i)*X(j) for these (i, j): {305, 33842}, {373, 76}
X(64093) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11169}, {76, 57817}, {373, 6}, {33842, 25}
X(64093) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47286, 15048}, {5, 76, 3933}, {76, 59635, 5}, {99, 37688, 549}, {115, 141, 33184}, {115, 9466, 141}, {183, 11185, 30}, {193, 32983, 15484}, {194, 32992, 31406}, {230, 3734, 8369}, {316, 37671, 14929}, {339, 15760, 41005}, {385, 8370, 18907}, {599, 7615, 37350}, {1078, 32819, 550}, {1975, 32832, 140}, {2549, 15271, 8359}, {3845, 14929, 316}, {3934, 32457, 4045}, {3934, 5254, 8362}, {4045, 32457, 5254}, {5475, 17131, 524}, {6337, 32838, 3526}, {6392, 32968, 9605}, {7603, 14711, 7813}, {7620, 42850, 5077}, {7737, 8667, 3793}, {7746, 17130, 7789}, {7761, 18546, 53419}, {7795, 13881, 8361}, {7800, 44518, 8357}, {8367, 63633, 11174}, {14033, 37667, 1384}, {15271, 34505, 2549}, {16044, 17129, 7762}, {16509, 59780, 2}, {20112, 22165, 31173}, {32815, 32828, 34229}, {32815, 34229, 3}

X(64094) = ORTHOLOGY CENTER OF THESE TRIANGLES: X3-ABC REFLECTIONS AND X(6)-CROSSPEDAL-OF-X(3)

Barycentrics    (a^2-b^2-c^2)*(3*a^8-13*a^4*(b^2-c^2)^2+2*(b^2-c^2)^4+3*a^6*(b^2+c^2)+5*a^2*(b^2-c^2)^2*(b^2+c^2)) : :
X(64094) = -3*X[3]+2*X[4549], -3*X[1597]+4*X[5480], -7*X[3526]+6*X[32620], -3*X[5050]+2*X[49669], -3*X[5093]+2*X[64096], -3*X[14912]+X[49670], -3*X[35513]+X[61044], -3*X[38789]+2*X[45019], -8*X[52101]+11*X[61990]

X(64094) lies on these lines: {3, 4549}, {4, 3426}, {5, 18931}, {6, 2777}, {20, 19347}, {22, 34796}, {24, 43905}, {25, 32111}, {30, 1351}, {64, 32395}, {74, 5094}, {125, 381}, {146, 1995}, {155, 43577}, {184, 3534}, {185, 382}, {195, 1181}, {262, 43956}, {287, 11159}, {376, 64058}, {378, 12244}, {389, 5895}, {399, 19403}, {427, 35450}, {512, 53320}, {525, 62350}, {546, 18913}, {550, 41465}, {578, 5925}, {974, 38790}, {1112, 5890}, {1192, 61749}, {1204, 1656}, {1499, 58346}, {1514, 61506}, {1593, 18431}, {1594, 34469}, {1595, 12250}, {1597, 5480}, {1598, 5878}, {1620, 64063}, {1885, 11432}, {1899, 3830}, {1990, 38920}, {2453, 32417}, {2883, 3517}, {3070, 19044}, {3071, 19043}, {3088, 32601}, {3146, 18914}, {3269, 15484}, {3521, 34801}, {3526, 32620}, {3527, 13488}, {3529, 31804}, {3537, 40911}, {3566, 62339}, {3567, 43599}, {3575, 12315}, {3627, 18909}, {3845, 23291}, {3851, 26937}, {5050, 49669}, {5054, 21663}, {5073, 6146}, {5076, 34563}, {5093, 64096}, {5169, 64102}, {5562, 11850}, {5622, 14848}, {5640, 16270}, {5656, 37458}, {5663, 11188}, {5667, 37070}, {5894, 55575}, {6000, 9971}, {6102, 22979}, {6225, 6756}, {6240, 12174}, {6241, 7730}, {9786, 22802}, {10295, 26864}, {10606, 18388}, {10706, 47597}, {10745, 37072}, {10982, 19361}, {10990, 61743}, {11165, 60704}, {11402, 35481}, {11455, 62976}, {11456, 37196}, {11799, 21970}, {11898, 13754}, {12121, 18445}, {12160, 52071}, {12233, 20427}, {12429, 34783}, {12902, 61724}, {13352, 34622}, {13367, 62100}, {13419, 58795}, {13851, 38335}, {14912, 49670}, {15054, 61700}, {15061, 40920}, {15063, 35259}, {15341, 21309}, {15448, 55572}, {15687, 18918}, {15696, 19357}, {15704, 18925}, {16252, 55570}, {17702, 39899}, {17800, 19467}, {18390, 61721}, {18533, 32063}, {18536, 64100}, {18550, 34802}, {18569, 18948}, {18877, 60588}, {18919, 21850}, {18923, 42225}, {18924, 42226}, {18929, 42144}, {18930, 42145}, {18945, 62036}, {20417, 61735}, {21659, 49136}, {23039, 40912}, {23251, 44639}, {23261, 44640}, {29317, 33534}, {34788, 64080}, {35260, 37934}, {35485, 61690}, {35513, 61044}, {37197, 43589}, {37487, 61747}, {37643, 37984}, {37644, 62288}, {38726, 47391}, {38789, 45019}, {39571, 51491}, {41398, 47596}, {46349, 47092}, {47474, 63129}, {48661, 64044}, {50008, 64097}, {52101, 61990}, {62073, 64064}

X(64094) = midpoint of X(i) and X(j) for these {i,j}: {35512, 64187}
X(64094) = reflection of X(i) in X(j) for these {i,j}: {3, 4846}, {382, 40909}, {1657, 35237}, {3426, 4}, {10938, 185}, {11472, 7706}, {41465, 550}, {64097, 50008}
X(64094) = inverse of X(381) in Jerabek hyperbola
X(64094) = pole of line {3049, 9033} with respect to the cosine circle
X(64094) = pole of line {7687, 9003} with respect to the orthocentroidal circle
X(64094) = pole of line {373, 381} with respect to the Jerabek hyperbola
X(64094) = pole of line {16303, 37984} with respect to the Kiepert hyperbola
X(64094) = pole of line {9003, 9209} with respect to the Orthic inconic
X(64094) = pole of line {378, 6090} with respect to the Stammler hyperbola
X(64094) = pole of line {32817, 35483} with respect to the Wallace hyperbola
X(64094) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3521), X(51471)}}, {{A, B, C, X(3527), X(58082)}}, {{A, B, C, X(4846), X(44556)}}, {{A, B, C, X(10293), X(56270)}}, {{A, B, C, X(11064), X(61135)}}, {{A, B, C, X(52452), X(61116)}}
X(64094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {185, 14915, 10938}, {541, 7706, 11472}, {5878, 13568, 1598}, {6240, 12174, 64033}, {6241, 12173, 34780}, {7706, 11472, 381}, {12233, 20427, 55571}, {14915, 40909, 382}

X(64095) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(25) AND X(6)-CROSSPEDAL-OF-X(3)

Barycentrics    a^2*(a^4-2*(b^2-c^2)^2+a^2*(b^2+c^2))*(a^4+b^4+c^4-2*a^2*(b^2+c^2)) : :
X(64095) = -X[18531]+3*X[61506], -3*X[35259]+X[58891]

X(64095) lies on these lines: {2, 37478}, {3, 51}, {4, 5449}, {5, 11745}, {6, 14070}, {20, 12897}, {22, 9730}, {23, 5890}, {24, 52}, {25, 13754}, {26, 389}, {30, 11438}, {54, 62990}, {68, 7487}, {74, 3543}, {110, 47485}, {113, 62961}, {125, 31723}, {140, 46728}, {141, 10127}, {143, 578}, {155, 3517}, {182, 5946}, {184, 568}, {185, 7517}, {186, 3060}, {193, 63649}, {376, 15053}, {378, 32110}, {381, 1531}, {382, 1204}, {394, 43586}, {511, 6644}, {517, 9639}, {539, 6515}, {547, 33533}, {549, 3098}, {550, 64038}, {567, 13321}, {569, 3567}, {571, 5961}, {576, 7575}, {912, 41611}, {1092, 6243}, {1112, 12893}, {1154, 9306}, {1181, 9714}, {1192, 12085}, {1209, 7544}, {1216, 6642}, {1351, 44102}, {1495, 14831}, {1511, 34155}, {1595, 44158}, {1598, 12163}, {1899, 44407}, {1974, 2931}, {1994, 11464}, {1995, 5891}, {2072, 61645}, {2355, 40263}, {2777, 44276}, {2917, 10115}, {2937, 10984}, {3090, 7691}, {3091, 38848}, {3133, 15827}, {3147, 43839}, {3357, 3627}, {3515, 12038}, {3516, 12002}, {3518, 5889}, {3522, 43597}, {3524, 43584}, {3529, 43601}, {3541, 20191}, {3542, 5448}, {3564, 41585}, {3574, 6639}, {3575, 9927}, {3580, 7576}, {3818, 13490}, {3843, 63392}, {3853, 32138}, {3917, 37494}, {4232, 16534}, {4549, 18537}, {5012, 7556}, {5020, 10170}, {5071, 10545}, {5198, 46849}, {5422, 37513}, {5447, 37486}, {5480, 52262}, {5504, 63184}, {5562, 7506}, {5640, 35921}, {5651, 23039}, {5654, 6353}, {5888, 61859}, {5907, 13861}, {5943, 7514}, {6000, 7530}, {6102, 6759}, {6238, 54428}, {6403, 37784}, {6623, 46686}, {6636, 15045}, {6699, 31670}, {6756, 12359}, {7387, 9786}, {7512, 13336}, {7516, 11695}, {7519, 16003}, {7525, 12006}, {7526, 10110}, {7540, 11550}, {7542, 45089}, {7545, 18435}, {7550, 11451}, {7687, 18568}, {7706, 15760}, {8717, 12083}, {9715, 36752}, {9737, 44221}, {9777, 37506}, {9781, 14118}, {9818, 17810}, {9820, 31802}, {9833, 10116}, {9973, 12412}, {10117, 11806}, {10201, 18388}, {10255, 15800}, {10263, 13346}, {10264, 48884}, {10282, 12161}, {10298, 11002}, {10540, 44082}, {10564, 15078}, {10574, 12088}, {10594, 12162}, {10605, 14915}, {10625, 17928}, {11064, 44211}, {11262, 32196}, {11412, 44802}, {11422, 37953}, {11430, 18324}, {11432, 16195}, {11433, 43573}, {11439, 26863}, {11454, 13596}, {11459, 13595}, {11470, 15136}, {11472, 18535}, {11649, 44490}, {11750, 18912}, {11818, 21243}, {11819, 18381}, {12082, 14855}, {12084, 13598}, {12107, 16881}, {12111, 34484}, {12118, 64048}, {12160, 41597}, {12227, 20773}, {12233, 13383}, {12235, 19908}, {12236, 13289}, {12370, 34785}, {12828, 17702}, {13292, 34782}, {13364, 49671}, {13367, 36749}, {13391, 37480}, {13419, 32140}, {13445, 15682}, {13621, 18436}, {13630, 17714}, {14516, 63652}, {14561, 54374}, {14641, 39568}, {14805, 15038}, {14852, 18494}, {14984, 41618}, {15024, 37126}, {15030, 44106}, {15032, 26881}, {15035, 16981}, {15072, 37925}, {15074, 44489}, {15305, 52294}, {15361, 44287}, {15473, 46085}, {15702, 41462}, {16222, 22109}, {16226, 22352}, {16657, 44249}, {18128, 18916}, {18281, 44673}, {18378, 26883}, {18418, 58885}, {18531, 61506}, {18559, 50435}, {18911, 44831}, {18917, 31383}, {18952, 44829}, {19130, 60763}, {19161, 64052}, {19357, 37493}, {19467, 58806}, {20300, 23329}, {20397, 31099}, {21841, 22660}, {21969, 51394}, {22112, 54006}, {22467, 64051}, {23292, 34351}, {23325, 44288}, {25738, 61139}, {26913, 46450}, {31830, 63734}, {31860, 64097}, {32284, 34787}, {32333, 58557}, {32358, 61751}, {32392, 40285}, {34148, 44879}, {34513, 39561}, {34798, 44271}, {34826, 63672}, {35243, 37475}, {35259, 58891}, {37122, 52104}, {37347, 61644}, {37444, 43817}, {37458, 41588}, {37484, 43652}, {37644, 61713}, {37936, 61752}, {37947, 45956}, {37984, 63721}, {38435, 61134}, {39806, 39854}, {39825, 39835}, {43574, 62187}, {43613, 50689}, {44213, 61619}, {44883, 58494}, {45170, 64023}, {47066, 48365}, {47068, 48366}, {47316, 61606}, {47486, 56292}, {51425, 62978}, {52842, 61701}, {52987, 54042}, {54992, 58764}, {58439, 61747}, {64035, 64066}

X(64095) = midpoint of X(i) and X(j) for these {i,j}: {3, 33586}, {25, 37489}, {10605, 18534}, {18917, 31383}, {37458, 41588}
X(64095) = reflection of X(i) in X(j) for these {i,j}: {394, 43586}, {9306, 12106}, {46261, 25}
X(64095) = X(i)-isoconjugate-of-X(j) for these {i, j}: {91, 3431}, {1820, 43530}, {20571, 58941}
X(64095) = X(i)-Dao conjugate of X(j) for these {i, j}: {577, 56266}, {4550, 68}, {34116, 3431}
X(64095) = X(i)-Ceva conjugate of X(j) for these {i, j}: {58785, 381}
X(64095) = pole of line {567, 1181} with respect to the Jerabek hyperbola
X(64095) = pole of line {68, 631} with respect to the Stammler hyperbola
X(64095) = pole of line {20563, 44149} with respect to the Wallace hyperbola
X(64095) = intersection, other than A, B, C, of circumconics {{A, B, C, X(24), X(381)}}, {{A, B, C, X(52), X(5158)}}, {{A, B, C, X(317), X(1531)}}, {{A, B, C, X(571), X(3581)}}, {{A, B, C, X(1147), X(43689)}}, {{A, B, C, X(1993), X(5961)}}, {{A, B, C, X(18475), X(60256)}}, {{A, B, C, X(34417), X(44077)}}, {{A, B, C, X(52000), X(63184)}}, {{A, B, C, X(52432), X(58785)}}
X(64095) = barycentric product X(i)*X(j) for these (i, j): {24, 37638}, {317, 5158}, {1748, 18477}, {1993, 381}, {4993, 52}, {11547, 63425}, {18883, 3581}, {34417, 7763}, {44135, 571}, {46808, 51393}, {52032, 58785}
X(64095) = barycentric quotient X(i)/X(j) for these (i, j): {24, 43530}, {381, 5392}, {571, 3431}, {1147, 56266}, {1993, 57822}, {3581, 37802}, {4993, 34385}, {5158, 68}, {8745, 16263}, {34416, 60501}, {34417, 2165}, {37638, 20563}, {44135, 57904}, {51393, 46809}, {52436, 58941}, {61208, 58994}, {63425, 52350}
X(64095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14070, 18475}, {24, 1993, 51393}, {24, 52000, 44077}, {25, 13754, 46261}, {25, 37489, 13754}, {26, 389, 64049}, {52, 51393, 1993}, {68, 7487, 45286}, {143, 1658, 578}, {186, 3060, 13352}, {376, 15053, 37470}, {381, 3581, 63425}, {567, 13321, 15004}, {568, 2070, 184}, {1154, 12106, 9306}, {1192, 12085, 43604}, {1495, 14831, 18445}, {1993, 51393, 1147}, {1994, 37940, 11464}, {2937, 37481, 10984}, {3515, 36747, 12038}, {3518, 5889, 10539}, {3575, 41587, 9927}, {3580, 7576, 18474}, {3581, 34417, 4550}, {5889, 10539, 15083}, {5946, 7502, 182}, {6102, 37440, 6759}, {7387, 9786, 40647}, {7512, 15043, 13336}, {7517, 37490, 185}, {7525, 12006, 37515}, {7545, 32608, 18435}, {9833, 18951, 10116}, {10263, 37814, 13346}, {10282, 16625, 12161}, {10298, 11002, 15033}, {10298, 15033, 39242}, {10605, 18534, 14915}, {11430, 21849, 39522}, {12083, 64100, 8717}, {12107, 16881, 32046}, {15032, 37939, 26881}, {15053, 15107, 376}, {18324, 39522, 11430}, {18378, 34783, 26883}, {18388, 32223, 10201}, {18445, 51519, 1495}, {18912, 31304, 11750}, {34417, 63425, 381}, {37458, 41588, 44665}, {37484, 43809, 43652}, {44288, 63839, 23325}

X(64096) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(3)-CIRCUMCONCEVIAN OF X(6) AND X(6)-CROSSPEDAL-OF-X(3)

Barycentrics    3*a^10-7*a^8*(b^2+c^2)-4*a^4*b^2*c^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4-10*b^2*c^2+c^4)+4*a^6*(b^4+5*b^2*c^2+c^4) : :
X(64096) = -2*X[141]+3*X[9818], -3*X[1597]+X[18440], -3*X[5093]+X[64094], -2*X[7706]+3*X[14853], -2*X[8717]+3*X[25406], -3*X[14561]+2*X[50008], -3*X[18420]+4*X[19130], -3*X[32620]+2*X[48876], -4*X[33533]+3*X[54173]

X(64096) lies on these lines: {2, 10564}, {3, 16657}, {4, 110}, {5, 37497}, {6, 30}, {20, 3567}, {64, 13292}, {68, 1593}, {69, 4550}, {74, 37644}, {141, 9818}, {143, 34350}, {146, 11004}, {155, 13488}, {184, 1533}, {193, 13754}, {235, 64181}, {323, 37077}, {376, 15053}, {378, 3580}, {381, 11064}, {382, 19347}, {511, 4549}, {524, 56966}, {541, 1992}, {542, 45019}, {550, 37475}, {568, 974}, {569, 37201}, {576, 2777}, {1352, 31861}, {1498, 43595}, {1511, 44275}, {1514, 3830}, {1595, 12293}, {1596, 47391}, {1597, 18440}, {1885, 36747}, {1902, 9933}, {1993, 12364}, {2433, 46984}, {2696, 6792}, {2931, 44274}, {2935, 10264}, {3060, 35481}, {3087, 18850}, {3088, 9927}, {3089, 12038}, {3146, 11423}, {3357, 18951}, {3426, 39899}, {3516, 41587}, {3543, 63082}, {3564, 11472}, {3627, 9833}, {5093, 64094}, {5422, 44458}, {5663, 63722}, {5878, 12161}, {5892, 61113}, {6102, 7729}, {6146, 47527}, {6622, 43839}, {6699, 37643}, {6776, 14915}, {6800, 62344}, {7464, 18911}, {7493, 39242}, {7529, 63631}, {7689, 64048}, {7703, 50435}, {7706, 14853}, {7731, 64102}, {8717, 25406}, {9936, 12162}, {10113, 15131}, {10116, 12324}, {11403, 12134}, {11438, 37853}, {11442, 13596}, {11473, 19062}, {11474, 19061}, {11744, 55980}, {12028, 56403}, {12084, 39571}, {12085, 12241}, {12086, 18912}, {12121, 41670}, {12163, 13142}, {12254, 62028}, {12359, 55571}, {12370, 14216}, {12900, 62708}, {13403, 14790}, {14561, 50008}, {15033, 44440}, {15311, 32455}, {16063, 43576}, {16163, 34417}, {18281, 20304}, {18390, 44441}, {18400, 48884}, {18420, 19130}, {18451, 62962}, {18531, 51360}, {18533, 44084}, {18909, 58806}, {19121, 35513}, {19456, 38790}, {31723, 58789}, {31725, 37472}, {32110, 35485}, {32620, 48876}, {33533, 54173}, {33586, 44249}, {33703, 43818}, {33878, 35254}, {34664, 37483}, {35484, 61700}, {36989, 48901}, {37511, 64023}, {37638, 44218}, {37827, 44882}, {38794, 59495}, {40890, 47740}, {44158, 55575}, {44239, 44935}, {44276, 51548}, {44285, 47582}, {46030, 59543}, {51425, 62966}, {58871, 63081}

X(64096) = midpoint of X(i) and X(j) for these {i,j}: {3426, 39899}
X(64096) = reflection of X(i) in X(j) for these {i,j}: {69, 4550}, {1352, 31861}, {4549, 49669}, {4846, 6}, {31670, 64099}, {33878, 35254}, {35237, 48906}, {40909, 21850}
X(64096) = perspector of circumconic {{A, B, C, X(687), X(1302)}}
X(64096) = pole of line {13754, 15066} with respect to the Stammler hyperbola
X(64096) = pole of line {32833, 62338} with respect to the Wallace hyperbola
X(64096) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1300), X(34288)}}, {{A, B, C, X(2986), X(4846)}}
X(64096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 30, 4846}, {6, 54131, 47571}, {30, 21850, 40909}, {30, 48906, 35237}, {30, 64099, 31670}, {113, 13352, 37645}, {113, 37645, 5654}, {376, 63084, 37470}, {511, 49669, 4549}, {10653, 10654, 34288}, {10733, 15472, 113}, {13352, 44080, 5504}, {40909, 44413, 21850}

X(64097) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF ANTI-HONSBERGER AND X(6)-CROSSPEDAL-OF-X(3)

Barycentrics    a^2*(a^8+2*a^6*(b^2+c^2)-4*a^4*(3*b^4-b^2*c^2+3*c^4)-(b^2-c^2)^2*(5*b^4+14*b^2*c^2+5*c^4)+2*a^2*(7*b^6-b^4*c^2-b^2*c^4+7*c^6)) : :
X(64097) = -2*X[182]+3*X[32620], -3*X[5050]+4*X[49671], -6*X[7514]+5*X[12017], -2*X[7706]+3*X[10516], -2*X[8717]+3*X[31884], -2*X[37517]+3*X[44413]

X(64097) lies on these lines: {3, 74}, {4, 45383}, {5, 37643}, {6, 4550}, {20, 31831}, {22, 12112}, {24, 15052}, {25, 3581}, {30, 69}, {64, 1216}, {113, 37638}, {140, 18931}, {141, 4846}, {155, 11430}, {159, 3098}, {182, 32620}, {185, 7393}, {323, 378}, {343, 1514}, {376, 46818}, {381, 3580}, {394, 10564}, {511, 11472}, {524, 56966}, {541, 599}, {550, 13093}, {1154, 1597}, {1181, 37513}, {1350, 12367}, {1351, 31861}, {1495, 14070}, {1503, 4549}, {1593, 18436}, {1598, 45959}, {1657, 16659}, {1993, 13482}, {2070, 40914}, {2777, 34507}, {2781, 44754}, {2782, 48991}, {2854, 34802}, {2888, 35490}, {2931, 40291}, {3167, 18570}, {3410, 35480}, {3515, 63392}, {3531, 55978}, {3534, 50434}, {3564, 49669}, {3631, 15311}, {3818, 40909}, {3851, 34826}, {5020, 15060}, {5024, 35934}, {5050, 49671}, {5462, 33537}, {5562, 12085}, {5656, 16618}, {5888, 20791}, {5891, 10605}, {5892, 59777}, {5907, 6642}, {6102, 11479}, {6243, 11403}, {6699, 59767}, {6985, 48917}, {7387, 12162}, {7395, 34783}, {7502, 32063}, {7503, 15032}, {7509, 64025}, {7514, 12017}, {7516, 45957}, {7526, 12164}, {7527, 11004}, {7529, 15058}, {7687, 14852}, {7689, 17814}, {7706, 10516}, {7712, 41450}, {8717, 31884}, {8780, 18324}, {9730, 63128}, {9973, 55582}, {10170, 37475}, {10606, 58871}, {10628, 44493}, {10752, 41614}, {10938, 19459}, {11381, 37486}, {11410, 22115}, {11412, 47527}, {11414, 18439}, {11425, 15083}, {11426, 63682}, {11455, 44454}, {11539, 61774}, {11820, 33532}, {12084, 31834}, {12429, 52070}, {13382, 15805}, {14269, 18551}, {14643, 52292}, {14805, 18445}, {15030, 34417}, {15056, 43584}, {15063, 61644}, {15069, 17702}, {15105, 42021}, {15107, 15305}, {15435, 18358}, {15687, 58764}, {15750, 18350}, {16194, 33586}, {16266, 55571}, {16534, 61680}, {17928, 54434}, {18532, 37954}, {18537, 63081}, {18859, 52055}, {18917, 34664}, {19140, 19153}, {20126, 32216}, {21312, 23039}, {21970, 44275}, {22241, 35002}, {26206, 55705}, {31860, 64095}, {32110, 35259}, {34514, 34725}, {35254, 46264}, {35265, 41398}, {35450, 62217}, {36747, 45187}, {36990, 54147}, {37077, 37779}, {37198, 64030}, {37493, 63664}, {37506, 44109}, {37517, 44413}, {37645, 44218}, {39522, 40318}, {39874, 46442}, {40916, 61136}, {41424, 46261}, {41464, 55604}, {41735, 48876}, {50008, 64094}, {54202, 62023}

X(64097) = midpoint of X(i) and X(j) for these {i,j}: {3426, 33878}
X(64097) = reflection of X(i) in X(j) for these {i,j}: {3, 64105}, {6, 4550}, {1351, 31861}, {4846, 141}, {11820, 33532}, {35237, 3098}, {40909, 3818}, {44456, 64099}, {46264, 35254}, {64094, 50008}, {64098, 33533}
X(64097) = inverse of X(26864) in Stammler hyperbola
X(64097) = perspector of circumconic {{A, B, C, X(44769), X(53958)}}
X(64097) = pole of line {21663, 35243} with respect to the Jerabek hyperbola
X(64097) = pole of line {15760, 52703} with respect to the Kiepert hyperbola
X(64097) = pole of line {1636, 8675} with respect to the MacBeath circumconic
X(64097) = pole of line {30, 26864} with respect to the Stammler hyperbola
X(64097) = pole of line {376, 3260} with respect to the Wallace hyperbola
X(64097) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(26864)}}, {{A, B, C, X(74), X(36889)}}, {{A, B, C, X(3426), X(40352)}}, {{A, B, C, X(14919), X(34801)}}
X(64097) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 399, 26864}, {6, 4550, 9818}, {74, 11459, 15066}, {74, 12825, 399}, {74, 399, 12412}, {1154, 64099, 44456}, {1597, 44456, 64099}, {3098, 35237, 35243}, {3098, 6000, 35237}, {3426, 33878, 30}, {4550, 13754, 6}, {5663, 33533, 64098}, {5907, 12163, 6642}, {7689, 43586, 37487}, {11820, 55610, 33532}, {17814, 37487, 43586}, {18451, 63425, 14070}, {33533, 64098, 3}, {41450, 44837, 7712}, {64098, 64105, 33533}

X(64098) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-HONSBERGER AND X(6)-CROSSPEDAL-OF-X(4)

Barycentrics    a^2*(a^8-4*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)+a^4*(6*b^4-8*b^2*c^2+6*c^4)-2*a^2*(2*b^6-5*b^4*c^2-5*b^2*c^4+2*c^6)) : :
X(64098) = 3*X[5050]+X[11820], -3*X[5085]+X[11472], -3*X[15462]+X[45019], -3*X[25406]+X[49669], -3*X[32620]+5*X[53094]

X(64098) lies on these lines: {2, 12112}, {3, 74}, {4, 15018}, {5, 54012}, {6, 30}, {20, 11004}, {22, 3581}, {23, 61136}, {26, 11438}, {54, 52093}, {66, 18358}, {140, 1498}, {143, 39568}, {155, 548}, {182, 14915}, {184, 10564}, {185, 37478}, {186, 7712}, {195, 62131}, {206, 4550}, {323, 376}, {378, 14805}, {381, 51548}, {382, 13470}, {394, 8703}, {511, 8547}, {541, 19140}, {546, 37514}, {547, 59777}, {549, 18451}, {550, 1181}, {568, 12082}, {578, 14641}, {631, 15052}, {1154, 19459}, {1176, 3426}, {1192, 12107}, {1199, 5059}, {1495, 6644}, {1503, 50008}, {1597, 19118}, {1598, 12006}, {1657, 7592}, {1658, 37487}, {1853, 46029}, {1993, 3534}, {1994, 11001}, {1995, 40280}, {2071, 3431}, {2696, 32730}, {2697, 32732}, {2777, 25556}, {3060, 44457}, {3098, 13754}, {3146, 36753}, {3516, 10610}, {3523, 54434}, {3528, 43605}, {3529, 36749}, {3530, 17814}, {3543, 63040}, {3546, 61608}, {3587, 62246}, {3627, 36752}, {3796, 18570}, {3830, 5422}, {3843, 52100}, {3845, 10601}, {3850, 15805}, {5050, 11820}, {5055, 7703}, {5066, 17825}, {5085, 11472}, {5198, 15026}, {5453, 19765}, {5585, 45769}, {5621, 44754}, {5878, 52073}, {5889, 43596}, {5890, 12083}, {5946, 18534}, {6101, 37198}, {6102, 11414}, {6243, 33524}, {6696, 40285}, {6759, 31978}, {6776, 41617}, {6823, 32140}, {7387, 13630}, {7393, 12315}, {7464, 11003}, {7484, 15060}, {7485, 18435}, {7502, 10605}, {7503, 64030}, {7506, 43584}, {7509, 18439}, {7516, 12162}, {7517, 8718}, {7525, 12163}, {7526, 10575}, {7530, 9730}, {7706, 29012}, {7708, 57634}, {8548, 9976}, {9729, 13861}, {9777, 44454}, {9786, 17714}, {9919, 11561}, {10201, 47296}, {10264, 37638}, {10272, 59767}, {10282, 46372}, {10323, 34783}, {10540, 41450}, {10545, 15045}, {10546, 14157}, {10627, 12164}, {10821, 50009}, {10982, 62036}, {11002, 37946}, {11381, 13336}, {11422, 43576}, {11430, 12084}, {11479, 32137}, {11799, 18911}, {12085, 32046}, {12088, 37490}, {12100, 17811}, {12103, 37498}, {12106, 37475}, {12121, 52124}, {12220, 13391}, {12244, 51882}, {12279, 61134}, {12364, 34966}, {12370, 37201}, {12429, 45732}, {12900, 15113}, {13154, 13347}, {13321, 37949}, {13348, 15083}, {13352, 44109}, {13353, 35502}, {13363, 62209}, {13364, 18535}, {13394, 18580}, {14627, 49137}, {15024, 63665}, {15038, 15684}, {15047, 62008}, {15053, 51519}, {15087, 15681}, {15462, 45019}, {15640, 63076}, {15682, 34545}, {15688, 50461}, {15689, 52099}, {15690, 37672}, {15704, 36747}, {15760, 61702}, {16003, 61644}, {16194, 43650}, {16619, 61506}, {16836, 46261}, {16936, 62123}, {17800, 43845}, {17821, 43615}, {18388, 31181}, {18475, 58871}, {18494, 61299}, {18531, 58885}, {18909, 63734}, {18951, 52404}, {19127, 19138}, {19139, 44882}, {19142, 19154}, {19150, 48898}, {19710, 63094}, {20126, 32227}, {20481, 40248}, {25406, 49669}, {26958, 44278}, {31152, 51391}, {32110, 35268}, {32344, 63420}, {32366, 37517}, {32423, 64080}, {32620, 53094}, {34128, 52292}, {37471, 63664}, {37489, 45956}, {37648, 44275}, {37925, 48912}, {38794, 49672}, {41463, 63720}, {43602, 64050}, {44441, 61619}, {44480, 64196}, {44750, 45016}, {44829, 52843}, {48892, 64195}, {49673, 64024}, {50693, 56292}, {54042, 58891}, {54044, 62217}, {62160, 62990}, {63663, 63727}

X(64098) = midpoint of X(i) and X(j) for these {i,j}: {6, 35237}, {4846, 46264}, {40909, 48905}
X(64098) = reflection of X(i) in X(j) for these {i,j}: {4550, 5092}, {11472, 49671}, {31861, 182}, {33532, 8717}, {64097, 33533}, {64099, 6}, {64105, 3}
X(64098) = inverse of X(15066) in Stammler hyperbola
X(64098) = perspector of circumconic {{A, B, C, X(1302), X(44769)}}
X(64098) = pole of line {7624, 8675} with respect to the 1st Brocard circle
X(64098) = pole of line {526, 42660} with respect to the circumcircle
X(64098) = pole of line {523, 47465} with respect to the cosine circle
X(64098) = pole of line {7514, 21663} with respect to the Jerabek hyperbola
X(64098) = pole of line {1636, 9007} with respect to the MacBeath circumconic
X(64098) = pole of line {30, 15066} with respect to the Stammler hyperbola
X(64098) = pole of line {8552, 9209} with respect to the Steiner inellipse
X(64098) = pole of line {3260, 32833} with respect to the Wallace hyperbola
X(64098) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {6, 14685, 15919}
X(64098) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(15066)}}, {{A, B, C, X(74), X(34288)}}, {{A, B, C, X(841), X(47322)}}, {{A, B, C, X(3426), X(46147)}}, {{A, B, C, X(4846), X(14919)}}, {{A, B, C, X(35910), X(56925)}}
X(64098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11456, 15068}, {3, 12174, 5876}, {3, 26864, 1511}, {3, 399, 15066}, {3, 5663, 64105}, {3, 64097, 33533}, {6, 30, 64099}, {6, 64099, 39522}, {182, 14915, 31861}, {511, 8717, 33532}, {1495, 64100, 37470}, {1511, 61752, 26864}, {3426, 12017, 9818}, {4550, 5092, 7514}, {5085, 11472, 49671}, {5092, 6000, 4550}, {5663, 33533, 64097}, {7393, 12315, 45959}, {8718, 10574, 7517}, {10264, 44262, 37638}, {10575, 10984, 7526}, {11456, 15066, 399}, {11456, 15068, 32139}, {12041, 34513, 3}, {15072, 15080, 74}, {15805, 15811, 3850}, {40909, 48905, 30}, {46850, 64049, 12084}

X(64099) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND EHRMANN AND X(6)-CROSSPEDAL-OF-X(4)

Barycentrics    a^2*(a^8-4*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4-8*b^2*c^2+c^4)+2*a^4*(3*b^4+8*b^2*c^2+3*c^4)-2*a^2*(2*b^6+b^4*c^2+b^2*c^4+2*c^6)) : :
X(64099) = -2*X[3098]+3*X[7514], -5*X[11482]+X[11820], -5*X[12017]+3*X[35243], -3*X[32620]+X[53097], -X[41465]+3*X[49669]

X(64099) lies on these lines: {3, 5640}, {4, 323}, {5, 37483}, {6, 30}, {20, 63040}, {22, 14805}, {23, 3431}, {25, 1511}, {26, 11430}, {51, 37470}, {74, 3060}, {140, 59777}, {143, 12085}, {155, 3853}, {182, 33532}, {186, 48912}, {195, 62023}, {265, 31133}, {376, 15018}, {378, 3581}, {381, 15066}, {382, 11456}, {394, 3845}, {399, 1539}, {511, 4550}, {541, 9976}, {546, 37498}, {549, 63128}, {550, 10982}, {567, 12082}, {575, 8717}, {576, 14915}, {611, 1480}, {613, 6580}, {895, 1351}, {1154, 1597}, {1181, 62036}, {1199, 49135}, {1350, 49671}, {1495, 7530}, {1498, 62026}, {1514, 44276}, {1593, 10263}, {1657, 15037}, {1885, 31815}, {1994, 15682}, {1995, 37477}, {3088, 63734}, {3098, 7514}, {3146, 15032}, {3527, 12006}, {3529, 36753}, {3531, 5020}, {3534, 5422}, {3543, 11004}, {3567, 43603}, {3627, 32139}, {3832, 54434}, {3861, 17814}, {5012, 44457}, {5066, 17811}, {5073, 7592}, {5076, 11441}, {5198, 61753}, {5446, 11438}, {5480, 50008}, {5876, 11403}, {5888, 54041}, {5946, 21312}, {6000, 55716}, {6102, 47527}, {6243, 35502}, {6644, 10564}, {6800, 37924}, {6985, 51340}, {7393, 63414}, {7464, 11002}, {7517, 11464}, {7526, 37478}, {7527, 37494}, {7712, 37925}, {7728, 52124}, {8703, 10601}, {9301, 32444}, {9714, 43394}, {9818, 13391}, {9977, 44493}, {10113, 15106}, {10546, 43574}, {10594, 37495}, {10627, 11479}, {11001, 34545}, {11003, 37946}, {11064, 44275}, {11250, 37487}, {11255, 22830}, {11264, 34780}, {11402, 44454}, {11424, 37513}, {11425, 17714}, {11472, 11477}, {11482, 11820}, {12017, 35243}, {12083, 15033}, {12086, 37490}, {12100, 17825}, {12101, 37672}, {12103, 37514}, {12106, 31860}, {12163, 14449}, {12164, 32137}, {12279, 43596}, {12383, 62963}, {12897, 52843}, {13142, 32140}, {13154, 13348}, {13321, 35452}, {13346, 13861}, {13353, 33524}, {13364, 62209}, {13482, 26881}, {13491, 37493}, {13596, 15110}, {13754, 37517}, {14070, 58764}, {14627, 49136}, {14791, 16657}, {14855, 15004}, {15035, 41448}, {15038, 15681}, {15047, 62121}, {15081, 31074}, {15087, 15684}, {15122, 61506}, {15640, 62990}, {15687, 18451}, {15690, 46945}, {15704, 36752}, {15760, 44935}, {15800, 35490}, {15805, 33923}, {15811, 62013}, {16261, 23061}, {16419, 54044}, {16982, 32138}, {17702, 19139}, {18281, 47296}, {18390, 31181}, {18534, 26864}, {18540, 62246}, {18570, 33586}, {18571, 41447}, {18580, 32269}, {18911, 62332}, {19121, 55705}, {22233, 43600}, {25338, 61680}, {26958, 40685}, {32046, 39568}, {32368, 64031}, {32423, 36990}, {32620, 53097}, {33699, 63094}, {37406, 49743}, {37484, 63664}, {37486, 63682}, {37638, 44287}, {37643, 44441}, {37645, 46817}, {38335, 50461}, {41424, 47391}, {41465, 49669}, {41614, 56966}, {41617, 54132}, {43605, 62021}, {43845, 49134}, {44107, 64100}, {44218, 47582}, {47092, 61657}, {48895, 64195}, {50688, 56292}, {52099, 62137}, {62160, 63076}, {62967, 64183}, {63673, 63727}

X(64099) = midpoint of X(i) and X(j) for these {i,j}: {11472, 11477}, {31670, 64096}, {44456, 64097}, {49669, 51212}
X(64099) = reflection of X(i) in X(j) for these {i,j}: {1350, 49671}, {8717, 575}, {33532, 182}, {33878, 33533}, {39522, 44413}, {50008, 5480}, {64098, 6}, {64105, 31861}
X(64099) = pole of line {523, 14398} with respect to the cosine circle
X(64099) = pole of line {549, 15066} with respect to the Stammler hyperbola
X(64099) = pole of line {32833, 44148} with respect to the Wallace hyperbola
X(64099) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11472, 11477, 14687}
X(64099) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4846), X(55982)}}, {{A, B, C, X(14483), X(34288)}}
X(64099) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 30, 64098}, {30, 44413, 39522}, {511, 31861, 64105}, {1597, 44456, 64097}, {3543, 11004, 12112}, {3627, 36747, 32139}, {5640, 43576, 3}, {9818, 33878, 33533}, {11004, 12112, 18445}, {13391, 33533, 33878}, {31670, 64096, 30}, {39522, 64098, 6}

X(64100) = COMPLEMENT OF X(15305)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4-4*b^2*c^2+c^4)) : :
X(64100) = 2*X[5]+X[10575], X[20]+2*X[389], X[52]+2*X[550], X[110]+2*X[17855], -4*X[140]+X[12162], 2*X[143]+X[15704], -3*X[373]+2*X[381], -X[382]+4*X[5462], -8*X[546]+11*X[27355], 2*X[548]+X[6102], -5*X[631]+2*X[5907], -5*X[632]+2*X[45959] and many others

X(64100) lies on these lines: {2, 5656}, {3, 49}, {4, 5943}, {5, 10575}, {6, 21312}, {20, 389}, {22, 11438}, {23, 15053}, {25, 37475}, {30, 51}, {39, 47620}, {52, 550}, {64, 7395}, {69, 3537}, {74, 827}, {110, 17855}, {125, 15760}, {140, 12162}, {141, 15151}, {143, 15704}, {154, 7729}, {182, 378}, {187, 52438}, {216, 3269}, {217, 22401}, {265, 13623}, {287, 35928}, {373, 381}, {376, 511}, {382, 5462}, {517, 37428}, {541, 61679}, {542, 61667}, {546, 27355}, {548, 6102}, {549, 5642}, {567, 18859}, {568, 3534}, {569, 12084}, {575, 7464}, {578, 11413}, {631, 5907}, {632, 45959}, {858, 18388}, {916, 64107}, {970, 3651}, {974, 6467}, {1060, 3270}, {1062, 1425}, {1105, 56298}, {1154, 8703}, {1192, 9715}, {1350, 32621}, {1368, 1568}, {1495, 6644}, {1498, 31978}, {1503, 29959}, {1514, 44920}, {1531, 4846}, {1533, 1596}, {1593, 37514}, {1597, 10601}, {1656, 64030}, {1657, 5446}, {1843, 18533}, {1885, 64038}, {1986, 37853}, {1993, 37480}, {2071, 5012}, {2393, 43273}, {2549, 50387}, {2772, 10176}, {2777, 12824}, {2781, 15303}, {2807, 3576}, {2935, 41593}, {2979, 10304}, {3066, 11820}, {3090, 10219}, {3091, 11695}, {3146, 10110}, {3357, 7503}, {3426, 63128}, {3516, 37476}, {3518, 8718}, {3520, 61134}, {3521, 14861}, {3522, 5889}, {3523, 11793}, {3524, 3819}, {3525, 15058}, {3526, 18439}, {3528, 11412}, {3529, 3567}, {3530, 5876}, {3543, 5640}, {3545, 6688}, {3547, 26937}, {3574, 23335}, {3587, 26893}, {3611, 15941}, {3627, 12006}, {3832, 15028}, {3839, 11451}, {3845, 13363}, {3849, 31743}, {3851, 46849}, {3853, 15026}, {3854, 40284}, {3855, 11465}, {3858, 32205}, {4303, 40944}, {5050, 54992}, {5054, 10170}, {5056, 11439}, {5071, 16261}, {5072, 46852}, {5076, 44863}, {5085, 10606}, {5097, 43576}, {5157, 44883}, {5158, 51990}, {5254, 15575}, {5448, 37452}, {5651, 18451}, {5691, 58487}, {5752, 37426}, {5878, 6816}, {5894, 41589}, {5944, 43615}, {5972, 17854}, {6001, 41581}, {6030, 7488}, {6101, 33923}, {6146, 31829}, {6225, 6804}, {6240, 44829}, {6243, 15696}, {6247, 7399}, {6293, 8567}, {6642, 26883}, {6699, 21650}, {6723, 12292}, {6759, 17928}, {6776, 8681}, {6800, 11202}, {6803, 12324}, {6815, 14216}, {6876, 15489}, {6899, 10441}, {6903, 15488}, {6907, 34462}, {7171, 26892}, {7400, 18913}, {7430, 48886}, {7494, 18931}, {7495, 20417}, {7496, 15054}, {7502, 32110}, {7509, 13347}, {7526, 13336}, {7527, 13445}, {7530, 44106}, {7576, 29012}, {7592, 13346}, {7706, 31723}, {7998, 15692}, {7999, 10299}, {8541, 54183}, {8679, 63432}, {8717, 12083}, {9019, 19161}, {9306, 11456}, {9781, 33703}, {9786, 11414}, {9818, 43650}, {9825, 16655}, {9826, 13202}, {9969, 48905}, {10095, 62036}, {10192, 40928}, {10201, 61691}, {10226, 10610}, {10263, 12103}, {10282, 22467}, {10295, 11649}, {10298, 15080}, {10303, 15056}, {10323, 46730}, {10540, 43586}, {10564, 44109}, {10620, 54006}, {10627, 46853}, {10628, 15055}, {10721, 41671}, {10722, 58503}, {10723, 58502}, {10724, 58508}, {10725, 58507}, {10726, 58513}, {10727, 58505}, {10728, 58504}, {10732, 58506}, {10733, 58498}, {10938, 37638}, {10990, 25711}, {10996, 18909}, {11001, 21849}, {11002, 15683}, {11017, 61900}, {11188, 64014}, {11328, 44437}, {11402, 37497}, {11424, 12085}, {11433, 35513}, {11440, 37126}, {11444, 15717}, {11464, 61128}, {11468, 43896}, {11470, 44503}, {11472, 22112}, {11550, 18420}, {11557, 20127}, {11561, 14677}, {11562, 12041}, {11585, 43831}, {11591, 15712}, {11592, 61789}, {11806, 12121}, {12002, 49139}, {12022, 44458}, {12045, 61895}, {12086, 13434}, {12087, 43603}, {12100, 15067}, {12107, 63729}, {12118, 21651}, {12174, 17814}, {12203, 35474}, {12220, 21851}, {12239, 42259}, {12240, 42258}, {12317, 43150}, {12512, 31732}, {12825, 48378}, {13160, 20299}, {13335, 52279}, {13340, 15688}, {13352, 13366}, {13364, 15687}, {13369, 23154}, {13403, 52071}, {13417, 14708}, {13595, 43584}, {14070, 35268}, {14093, 54048}, {14118, 41725}, {14128, 14869}, {14130, 37471}, {14133, 35476}, {14449, 62123}, {14805, 58871}, {14810, 44832}, {14865, 43651}, {14872, 58690}, {14880, 63556}, {14891, 44324}, {14913, 39874}, {15003, 62026}, {15004, 44413}, {15032, 34986}, {15037, 35452}, {15038, 35001}, {15063, 30739}, {15082, 15702}, {15087, 37477}, {15122, 61619}, {15311, 34664}, {15606, 21734}, {15682, 58470}, {15694, 62184}, {15708, 44299}, {15721, 33879}, {15738, 38729}, {15761, 43817}, {15801, 43612}, {16072, 45979}, {16252, 36982}, {16625, 17538}, {16881, 62144}, {16980, 18481}, {16981, 62129}, {17713, 64180}, {17821, 22967}, {17834, 37198}, {18114, 46585}, {18128, 44076}, {18369, 52100}, {18383, 34007}, {18390, 18911}, {18400, 38323}, {18474, 50008}, {18534, 34417}, {18536, 64094}, {18537, 54012}, {18563, 43577}, {18570, 37513}, {18874, 61988}, {19129, 19457}, {19708, 54041}, {21163, 47426}, {22109, 45170}, {22278, 34746}, {22350, 39796}, {23292, 47090}, {25555, 35484}, {26206, 34779}, {31670, 41256}, {31804, 63631}, {31833, 61139}, {31834, 61792}, {32063, 35259}, {32142, 44682}, {32171, 43898}, {32184, 41362}, {32237, 47485}, {32352, 44242}, {32423, 45730}, {33843, 59208}, {33884, 62063}, {34002, 44158}, {34128, 34330}, {34148, 64026}, {34200, 54042}, {34224, 43904}, {34545, 37944}, {34565, 39522}, {34624, 61727}, {35243, 37489}, {35283, 44838}, {35480, 58480}, {35481, 52000}, {35485, 44479}, {35497, 51033}, {36978, 42088}, {36980, 42087}, {37118, 58447}, {37182, 40254}, {37196, 47328}, {37201, 39571}, {37484, 62100}, {37495, 43845}, {38321, 44407}, {38322, 61299}, {38738, 39817}, {38749, 39846}, {40247, 61820}, {41257, 48901}, {41463, 52987}, {41543, 56885}, {41715, 54050}, {41869, 58469}, {43602, 56292}, {43846, 43866}, {44084, 44438}, {44107, 64099}, {44110, 51393}, {44249, 54384}, {44441, 61743}, {44831, 48898}, {44871, 61991}, {44935, 61657}, {44983, 58509}, {44984, 58510}, {44985, 58511}, {44986, 58512}, {44987, 58514}, {44988, 58515}, {45759, 54044}, {45958, 55856}, {45968, 54040}, {46945, 55582}, {47353, 61676}, {47549, 50649}, {48897, 50594}, {48904, 58549}, {48910, 58471}, {50693, 64050}, {52003, 63441}, {52661, 59529}, {52687, 59710}, {53093, 58762}, {54047, 62073}, {58492, 64037}, {58531, 62034}, {58533, 62164}, {62104, 63414}, {62120, 62187}

X(64100) = midpoint of X(i) and X(j) for these {i,j}: {2, 15072}, {20, 3060}, {154, 7729}, {185, 3917}, {376, 5890}, {568, 3534}, {5642, 17853}, {5889, 62188}, {5943, 46850}, {8703, 45956}, {9730, 14855}, {10192, 40928}, {10575, 16194}, {11188, 64014}, {12022, 44458}, {13491, 15060}, {14831, 36987}, {34624, 61727}, {41715, 54050}, {45968, 54040}
X(64100) = reflection of X(i) in X(j) for these {i,j}: {2, 16836}, {4, 5943}, {51, 9730}, {373, 40280}, {381, 5892}, {3060, 389}, {3845, 13363}, {3917, 3}, {5562, 3917}, {5891, 549}, {5943, 9729}, {7998, 55166}, {11381, 16194}, {11455, 46847}, {11459, 3819}, {12162, 15060}, {14831, 5890}, {15030, 2}, {15060, 140}, {15067, 12100}, {15687, 13364}, {16194, 5}, {16261, 63632}, {16657, 45298}, {18435, 10170}, {21969, 568}, {32062, 381}, {34746, 22278}, {36987, 376}, {40673, 11179}, {44324, 14891}, {44870, 10219}, {45186, 3060}, {46847, 6688}, {47353, 61676}, {54042, 34200}, {62188, 15644}
X(64100) = complement of X(15305)
X(64100) = X(i)-Dao conjugate of X(j) for these {i, j}: {1596, 36876}, {37648, 44134}
X(64100) = pole of line {8675, 10516} with respect to the orthocentroidal circle
X(64100) = pole of line {3, 4549} with respect to the Jerabek hyperbola
X(64100) = pole of line {4, 5651} with respect to the Stammler hyperbola
X(64100) = pole of line {44560, 52584} with respect to the Steiner inellipse
X(64100) = pole of line {264, 1597} with respect to the Wallace hyperbola
X(64100) = pole of line {850, 53369} with respect to the dual conic of polar circle
X(64100) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {2, 15072, 61734}
X(64100) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(43652)}}, {{A, B, C, X(74), X(3917)}}, {{A, B, C, X(394), X(37648)}}, {{A, B, C, X(1092), X(15740)}}, {{A, B, C, X(1176), X(1533)}}, {{A, B, C, X(4846), X(51990)}}, {{A, B, C, X(5447), X(43689)}}, {{A, B, C, X(13623), X(22115)}}, {{A, B, C, X(15030), X(54988)}}
X(64100) = barycentric product X(i)*X(j) for these (i, j): {3, 37648}, {1596, 394}, {14919, 1533}
X(64100) = barycentric quotient X(i)/X(j) for these (i, j): {1533, 46106}, {1596, 2052}, {37648, 264}
X(64100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15072, 6000}, {2, 20791, 16836}, {3, 10605, 63425}, {3, 1181, 1092}, {3, 13754, 3917}, {3, 155, 43652}, {3, 184, 51394}, {3, 18436, 5447}, {3, 19347, 35602}, {3, 34783, 1216}, {3, 40647, 185}, {3, 43807, 63392}, {3, 64049, 13367}, {4, 15045, 5943}, {5, 10575, 11381}, {20, 389, 45186}, {30, 45298, 16657}, {30, 9730, 51}, {51, 9730, 16226}, {140, 13491, 12162}, {185, 3917, 13754}, {185, 45187, 34783}, {373, 32062, 381}, {376, 511, 36987}, {376, 61136, 5890}, {381, 14915, 32062}, {511, 11179, 40673}, {511, 5890, 14831}, {549, 5663, 5891}, {550, 13630, 52}, {631, 6241, 5907}, {974, 16163, 21649}, {1092, 1181, 43844}, {1216, 34783, 45187}, {1216, 45187, 5562}, {1657, 37481, 5446}, {2071, 5012, 11430}, {3090, 12290, 44870}, {3091, 12279, 13474}, {3146, 15043, 10110}, {3357, 37515, 7503}, {3522, 5889, 15644}, {3523, 12111, 11793}, {3528, 11412, 13348}, {3529, 3567, 13598}, {3545, 11455, 46847}, {3845, 13363, 14845}, {5054, 18435, 10170}, {5085, 10606, 54994}, {5462, 14641, 382}, {5642, 17853, 5663}, {5907, 17704, 631}, {5943, 9729, 15045}, {6102, 10625, 14531}, {6688, 46847, 3545}, {6800, 15078, 11202}, {8717, 64095, 12083}, {8718, 43597, 3518}, {9729, 46850, 4}, {9730, 14855, 30}, {10627, 55286, 46853}, {11695, 13474, 3091}, {12085, 36752, 11424}, {12162, 13491, 64029}, {13382, 15644, 5889}, {13598, 15012, 3567}, {14708, 16111, 13417}, {14831, 36987, 511}, {14915, 40280, 373}, {15032, 43574, 34986}, {15043, 52093, 3146}, {15072, 16836, 15030}, {15072, 20791, 2}, {15712, 45957, 11591}, {15717, 64025, 11444}, {18911, 44440, 18390}, {21663, 22352, 3}, {22467, 52525, 10282}, {37470, 64098, 1495}, {37511, 48906, 6467}, {51393, 61752, 44110}

X(64101) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(6)-CROSSPEDAL-OF-X(67)

Barycentrics    a^10-5*a^8*(b^2+c^2)+2*(b^2-c^2)^4*(b^2+c^2)-a^4*(b^2+c^2)^3-a^2*(b^2-c^2)^2*(4*b^4-3*b^2*c^2+4*c^4)+a^6*(7*b^4+3*b^2*c^2+7*c^4) : :
X(64101) = -6*X[2]+X[74], 3*X[3]+2*X[1539], X[4]+4*X[5972], X[8]+4*X[11723], 4*X[10]+X[7978], -2*X[20]+7*X[15036], 4*X[114]+X[22265], -2*X[125]+7*X[3090], 4*X[140]+X[7728], 4*X[141]+X[10752], X[147]+4*X[33511], X[148]+4*X[33512] and many others

X(64101) lies on these lines: {2, 74}, {3, 1539}, {4, 5972}, {5, 49}, {8, 11723}, {10, 7978}, {20, 15036}, {30, 15051}, {114, 22265}, {125, 3090}, {140, 7728}, {141, 10752}, {147, 33511}, {148, 33512}, {182, 41737}, {185, 43866}, {186, 1531}, {373, 58498}, {376, 13202}, {381, 1511}, {399, 5055}, {403, 11064}, {477, 36169}, {485, 19110}, {486, 19111}, {542, 3618}, {546, 12121}, {547, 5655}, {549, 20127}, {551, 50877}, {569, 3047}, {590, 19060}, {597, 64103}, {615, 19059}, {631, 2777}, {632, 15021}, {690, 64089}, {895, 14561}, {974, 15045}, {1112, 11412}, {1125, 12368}, {1209, 43580}, {1352, 32234}, {1568, 32223}, {1587, 13990}, {1588, 8998}, {1651, 38246}, {1656, 5663}, {1986, 11459}, {1995, 2931}, {2072, 14157}, {2771, 5439}, {2772, 31273}, {2778, 25917}, {2779, 31262}, {2781, 3763}, {2914, 34155}, {2948, 7988}, {3035, 10767}, {3043, 9306}, {3060, 58516}, {3091, 15034}, {3146, 38726}, {3448, 5056}, {3470, 39170}, {3518, 22109}, {3523, 16111}, {3524, 37853}, {3525, 12244}, {3526, 12041}, {3528, 48375}, {3530, 38788}, {3533, 10990}, {3545, 5642}, {3564, 47461}, {3581, 44282}, {3589, 5622}, {3614, 12903}, {3624, 11709}, {3627, 38723}, {3628, 15054}, {3742, 58680}, {3818, 7577}, {3819, 58536}, {3828, 50878}, {3832, 12295}, {3843, 15040}, {3850, 34153}, {3851, 10113}, {3858, 22251}, {3917, 11807}, {4193, 38555}, {4413, 12327}, {5020, 12168}, {5054, 38790}, {5066, 13392}, {5067, 6723}, {5068, 30714}, {5070, 10620}, {5072, 12902}, {5079, 5609}, {5094, 12133}, {5133, 23306}, {5159, 32111}, {5181, 14853}, {5219, 59818}, {5422, 19456}, {5432, 12374}, {5433, 12373}, {5465, 23234}, {5504, 15033}, {5562, 41671}, {5587, 11720}, {5627, 14611}, {5640, 12236}, {5654, 37644}, {5656, 15113}, {5886, 7984}, {5889, 16222}, {5890, 9826}, {5891, 11557}, {5892, 54037}, {5907, 7722}, {5943, 21649}, {6143, 43613}, {6353, 15473}, {6564, 10820}, {6565, 10819}, {6593, 10516}, {6698, 51941}, {6997, 12319}, {7173, 12904}, {7484, 9919}, {7486, 16003}, {7509, 10117}, {7527, 12901}, {7569, 15102}, {7603, 14901}, {7723, 15056}, {7731, 12358}, {7741, 10088}, {7808, 12192}, {7844, 15920}, {7866, 38641}, {7887, 38520}, {7914, 9984}, {7951, 10091}, {7999, 63657}, {8252, 49217}, {8253, 49216}, {8674, 64008}, {8718, 11585}, {8994, 32785}, {9143, 61924}, {9820, 63710}, {9934, 32743}, {9955, 12778}, {9970, 24206}, {10171, 13605}, {10175, 13211}, {10255, 27866}, {10257, 50434}, {10590, 46683}, {10591, 46687}, {10601, 17838}, {10657, 42914}, {10658, 42915}, {10745, 44891}, {10778, 23513}, {10817, 35255}, {10818, 35256}, {11005, 36519}, {11178, 25556}, {11439, 31283}, {11440, 60780}, {11441, 11704}, {11455, 30744}, {11464, 20771}, {11561, 15060}, {11579, 38317}, {11693, 61954}, {11694, 38071}, {11793, 13417}, {11799, 43576}, {12068, 38700}, {12111, 14708}, {12261, 61268}, {12281, 25711}, {12284, 15024}, {12290, 44573}, {12292, 52296}, {12302, 63664}, {12308, 20379}, {12369, 15184}, {12372, 24953}, {12381, 26364}, {12382, 26363}, {12812, 15027}, {12827, 18932}, {12893, 44802}, {12898, 18357}, {13198, 43651}, {13289, 35921}, {13969, 32786}, {14128, 38898}, {14156, 52403}, {14457, 43841}, {14639, 53735}, {14683, 15022}, {14695, 14932}, {14789, 43578}, {14872, 58601}, {14912, 32300}, {14915, 30745}, {14989, 47084}, {15023, 15704}, {15032, 43836}, {15039, 61935}, {15041, 46219}, {15042, 15681}, {15107, 51391}, {15463, 16868}, {15699, 20126}, {16072, 20772}, {16239, 61598}, {16252, 63716}, {17847, 63695}, {18279, 51835}, {18332, 61575}, {18538, 19052}, {18583, 63700}, {18762, 19051}, {18917, 26917}, {19122, 39899}, {19506, 64063}, {20396, 61911}, {20397, 46936}, {20417, 61886}, {20957, 60603}, {21315, 33505}, {21451, 38848}, {21650, 54000}, {22115, 46031}, {22750, 45177}, {23323, 59648}, {24981, 61921}, {25321, 32275}, {25564, 61128}, {25739, 46818}, {28408, 31670}, {30771, 46431}, {31180, 48905}, {31267, 36201}, {31282, 64024}, {31378, 57471}, {31379, 36172}, {31945, 34150}, {32274, 52697}, {32607, 35500}, {33851, 53023}, {35487, 59659}, {36184, 60605}, {36208, 37835}, {36209, 37832}, {37071, 38650}, {37477, 44961}, {37779, 63735}, {37942, 47582}, {38581, 45694}, {38633, 61855}, {38638, 61970}, {38729, 60781}, {40410, 43767}, {40948, 57526}, {41462, 44262}, {41673, 64051}, {42262, 49268}, {42265, 49269}, {42274, 49223}, {42277, 49222}, {43572, 50435}, {43597, 43831}, {43599, 43604}, {43602, 43817}, {43837, 64026}, {43966, 57316}, {44214, 58885}, {45311, 61899}, {46451, 51392}, {47571, 62382}, {48895, 52294}, {49673, 52525}, {50726, 52820}, {51033, 58435}, {51522, 55857}, {53743, 59391}, {55856, 61548}, {56567, 61912}, {58654, 61686}, {59495, 62974}, {61936, 64183}, {63344, 63348}

X(64101) = midpoint of X(i) and X(j) for these {i,j}: {3843, 15040}, {3858, 22251}, {15081, 20125}
X(64101) = reflection of X(i) in X(j) for these {i,j}: {15021, 38728}, {15051, 38794}, {15059, 1656}, {38728, 632}
X(64101) = pole of line {9003, 24981} with respect to the orthoptic circle of the Steiner Inellipse
X(64101) = pole of line {974, 1154} with respect to the Stammler hyperbola
X(64101) = pole of line {24978, 46229} with respect to the Steiner inellipse
X(64101) = pole of line {1273, 10257} with respect to the Wallace hyperbola
X(64101) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1141), X(57747)}}, {{A, B, C, X(3260), X(6699)}}
X(64101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 146, 6699}, {3, 15046, 61574}, {4, 5972, 15035}, {5, 10272, 265}, {5, 110, 14644}, {20, 38793, 15036}, {30, 38794, 15051}, {74, 113, 10706}, {113, 12900, 2}, {113, 6699, 146}, {125, 6053, 12317}, {140, 7728, 15055}, {146, 6699, 74}, {265, 10272, 110}, {265, 14643, 10272}, {381, 1511, 10733}, {399, 20304, 9140}, {399, 5055, 20304}, {3448, 5056, 23515}, {3525, 12244, 38727}, {3526, 38789, 12041}, {3545, 12383, 7687}, {3589, 14982, 5622}, {3851, 32609, 10113}, {5071, 20125, 15081}, {5079, 38724, 15088}, {5640, 12273, 12236}, {5907, 16223, 7722}, {5972, 36518, 4}, {6053, 12317, 14094}, {6723, 38792, 15063}, {9826, 12825, 5890}, {10620, 34128, 15057}, {11561, 15060, 22584}, {12068, 46045, 38700}, {12358, 12824, 7731}, {13202, 48378, 376}, {15046, 61574, 15029}, {15081, 20125, 542}, {15088, 38724, 15025}, {16534, 23515, 3448}, {32743, 61747, 9934}, {38727, 38791, 12244}, {38793, 46686, 20}

X(64102) = ANTICOMPLEMENT OF X(146)

Barycentrics    3*a^10-a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(-14*b^4+23*b^2*c^2-14*c^4)-a^2*(b^2-c^2)^2*(5*b^4+19*b^2*c^2+5*c^4)+2*a^4*(9*b^6-8*b^4*c^2-8*b^2*c^4+9*c^6) : :
X(64102) = -3*X[2]+4*X[74], -9*X[3]+8*X[13392], -3*X[4]+4*X[10264], -4*X[110]+5*X[3522], -8*X[125]+7*X[3832], -4*X[265]+3*X[3543], -3*X[376]+2*X[399], -5*X[631]+6*X[15041], -8*X[1511]+9*X[10304], -8*X[1539]+9*X[3839], -5*X[1656]+4*X[61598], -2*X[2948]+3*X[9778] and many others

X(64102) lies on these lines: {2, 74}, {3, 13392}, {4, 10264}, {8, 9904}, {20, 5663}, {23, 9919}, {30, 12317}, {64, 13203}, {110, 3522}, {125, 3832}, {185, 43838}, {193, 2781}, {265, 3543}, {323, 17838}, {376, 399}, {390, 3028}, {542, 15683}, {550, 12308}, {631, 15041}, {690, 5984}, {962, 33535}, {1147, 43391}, {1204, 21451}, {1511, 10304}, {1539, 3839}, {1587, 35826}, {1588, 35827}, {1656, 61598}, {1885, 18947}, {2071, 12412}, {2771, 6361}, {2772, 20096}, {2775, 20097}, {2776, 20098}, {2777, 3146}, {2778, 64047}, {2779, 20066}, {2780, 20099}, {2854, 61044}, {2931, 37913}, {2935, 37645}, {2948, 9778}, {3024, 3600}, {3043, 35485}, {3090, 38789}, {3091, 7728}, {3184, 14919}, {3426, 62963}, {3486, 11670}, {3523, 12041}, {3524, 10272}, {3528, 32609}, {3529, 32423}, {3530, 38633}, {3552, 38653}, {3580, 15311}, {3617, 12368}, {3618, 5621}, {3620, 14982}, {3622, 11709}, {3623, 7978}, {3854, 46686}, {4293, 7727}, {4294, 19470}, {5056, 15061}, {5059, 17702}, {5068, 20417}, {5071, 40685}, {5094, 41428}, {5169, 64094}, {5189, 12319}, {5261, 12373}, {5274, 12374}, {5609, 38788}, {5622, 63123}, {5640, 58536}, {5642, 15705}, {5655, 15692}, {5656, 13289}, {5894, 17847}, {5921, 32247}, {5925, 34799}, {5972, 15021}, {6000, 15100}, {6053, 15051}, {6225, 10117}, {6636, 12168}, {6776, 41731}, {6904, 52820}, {6995, 12133}, {7391, 36853}, {7408, 15473}, {7486, 61574}, {7487, 12292}, {7519, 46431}, {7533, 11472}, {7585, 49216}, {7586, 49217}, {7687, 61985}, {7731, 64096}, {8674, 64009}, {9140, 13202}, {9143, 16163}, {9541, 12375}, {9812, 13605}, {9976, 54132}, {10081, 14986}, {10113, 38626}, {10303, 14643}, {10528, 49152}, {10529, 49151}, {10565, 32227}, {10575, 15102}, {10605, 18933}, {10628, 20427}, {10721, 16003}, {10752, 51170}, {11002, 11807}, {11004, 19456}, {11457, 59493}, {11561, 61136}, {11694, 15042}, {12087, 12310}, {12270, 46264}, {12273, 62188}, {12295, 50690}, {12358, 54037}, {12824, 15151}, {12902, 33703}, {13171, 14118}, {13293, 35494}, {13393, 62023}, {13445, 51360}, {14094, 16111}, {14508, 14731}, {14644, 50689}, {14853, 32305}, {14912, 48679}, {14915, 20063}, {15022, 15059}, {15034, 62078}, {15035, 21734}, {15036, 62060}, {15039, 62084}, {15040, 21735}, {15046, 61886}, {15055, 15063}, {15057, 36518}, {15101, 18439}, {15108, 44458}, {15680, 38497}, {15697, 64182}, {16010, 51212}, {16534, 61791}, {17538, 34153}, {19059, 63016}, {19060, 63015}, {19457, 63036}, {20079, 36201}, {20379, 61982}, {21454, 59818}, {21649, 62187}, {24981, 62125}, {25328, 51538}, {25330, 51163}, {25336, 64196}, {25406, 51941}, {29181, 32255}, {30714, 62124}, {31074, 35450}, {32111, 37760}, {32138, 58805}, {32254, 48874}, {32965, 38641}, {33260, 38520}, {34128, 46936}, {34584, 49135}, {34796, 40909}, {38632, 58195}, {38638, 46853}, {38723, 62110}, {38726, 62102}, {38727, 61834}, {38728, 55864}, {38793, 61804}, {41819, 63348}, {43511, 49269}, {43512, 49268}, {43806, 43816}, {44287, 52055}, {44450, 51391}, {45311, 61930}, {46451, 51548}, {49313, 62987}, {49314, 62986}, {56567, 62081}, {58680, 63961}

X(64102) = midpoint of X(i) and X(j) for these {i,j}: {49044, 49045}
X(64102) = reflection of X(i) in X(j) for these {i,j}: {4, 10620}, {8, 9904}, {20, 12244}, {110, 10990}, {146, 74}, {323, 50434}, {399, 14677}, {962, 33535}, {3146, 3448}, {3448, 15054}, {5921, 32247}, {6225, 10117}, {7728, 51522}, {10113, 38626}, {10721, 16003}, {12308, 550}, {12383, 20127}, {13203, 64}, {14094, 16111}, {14683, 20}, {14731, 14508}, {15102, 10575}, {17847, 5894}, {18439, 15101}, {25336, 64196}, {32254, 48874}, {33703, 12902}, {38790, 10264}, {51212, 16010}, {64183, 12317}
X(64102) = anticomplement of X(146)
X(64102) = X(i)-Dao conjugate of X(j) for these {i, j}: {146, 146}
X(64102) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57766, 2}
X(64102) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34178, 8}, {57766, 6327}
X(64102) = pole of line {6723, 9003} with respect to the orthoptic circle of the Steiner Inellipse
X(64102) = pole of line {10540, 10564} with respect to the Stammler hyperbola
X(64102) = pole of line {8552, 14566} with respect to the Steiner circumellipse
X(64102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 5663, 14683}, {30, 12317, 64183}, {74, 10706, 6699}, {74, 146, 2}, {74, 541, 146}, {399, 14677, 376}, {1539, 15081, 3839}, {1539, 20126, 15081}, {2777, 3448, 3146}, {5663, 20127, 12383}, {10264, 38790, 4}, {10620, 38790, 10264}, {12244, 12383, 20127}, {12383, 20127, 20}, {38789, 61548, 3090}, {49044, 49045, 2781}

X(64103) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND EHRMANN AND X(6)-CROSSPEDAL-OF-X(67)

Barycentrics    3*a^12-7*a^10*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)^2+3*a^8*(b^4+7*b^2*c^2+c^4)+4*a^6*(b^6-4*b^4*c^2-4*b^2*c^4+c^6)+a^2*(b^2-c^2)^2*(3*b^6-5*b^4*c^2-5*b^2*c^4+3*c^6)+a^4*(-5*b^8+11*b^6*c^2-4*b^4*c^4+11*b^2*c^6-5*c^8) : :
X(64103) = -2*X[141]+3*X[5622], -X[146]+3*X[1992], -6*X[182]+5*X[38794], -4*X[575]+3*X[14643], -6*X[597]+5*X[64101], -3*X[599]+4*X[6699], -3*X[1350]+4*X[37853], -3*X[1351]+X[38790], -3*X[1352]+4*X[20304], -4*X[1511]+3*X[5648], -2*X[1539]+3*X[20423], -3*X[5085]+2*X[5181] and many others

X(64103) lies on these lines: {6, 13}, {67, 3564}, {69, 59495}, {74, 524}, {110, 8550}, {125, 6090}, {141, 5622}, {146, 1992}, {182, 38794}, {184, 32227}, {193, 2781}, {511, 20127}, {541, 15534}, {575, 14643}, {576, 7728}, {597, 64101}, {599, 6699}, {690, 64091}, {895, 1503}, {974, 2854}, {1350, 37853}, {1351, 38790}, {1352, 20304}, {1353, 9970}, {1511, 5648}, {1539, 20423}, {2393, 21649}, {2777, 11477}, {2935, 16010}, {3047, 64061}, {3448, 9716}, {3629, 10752}, {4663, 12368}, {5085, 5181}, {5093, 32271}, {5095, 12165}, {5480, 41737}, {5621, 12901}, {5663, 63722}, {5921, 25320}, {5965, 32305}, {5972, 53093}, {6593, 14912}, {8540, 12374}, {8548, 63710}, {8549, 63716}, {8584, 10706}, {9140, 11064}, {9143, 63084}, {9730, 23236}, {9971, 12236}, {9972, 32423}, {10250, 32743}, {10272, 50979}, {10516, 15118}, {10541, 38793}, {10564, 20126}, {11180, 15081}, {11482, 38789}, {11898, 49116}, {12007, 52699}, {12168, 32621}, {12284, 15073}, {12317, 50974}, {12364, 51391}, {12373, 19369}, {12900, 47352}, {13202, 54131}, {13289, 41583}, {13392, 15462}, {14094, 16657}, {14683, 41670}, {14984, 46264}, {15051, 51737}, {15061, 34507}, {15472, 32234}, {16003, 37497}, {16111, 53097}, {16163, 43273}, {17702, 64080}, {18932, 63129}, {19459, 32114}, {24981, 30734}, {25406, 33851}, {29959, 58498}, {30714, 37475}, {32110, 47276}, {32111, 47549}, {34777, 36201}, {37470, 64182}, {38728, 40107}, {38788, 52987}, {38791, 53858}

X(64103) = midpoint of X(i) and X(j) for these {i,j}: {12284, 15073}
X(64103) = reflection of X(i) in X(j) for these {i,j}: {67, 11579}, {110, 8550}, {265, 9976}, {5648, 11179}, {5921, 32274}, {7728, 576}, {9970, 1353}, {10706, 8584}, {10752, 3629}, {11898, 49116}, {12368, 4663}, {14094, 25329}, {14982, 6}, {15069, 125}, {32111, 47549}, {32233, 6776}, {41737, 5480}, {47276, 32110}, {51941, 5095}, {53097, 16111}, {63700, 182}, {63710, 8548}, {63716, 8549}, {64104, 63722}
X(64103) = pole of line {323, 12824} with respect to the Stammler hyperbola
X(64103) = intersection, other than A, B, C, of circumconics {{A, B, C, X(67), X(56403)}}, {{A, B, C, X(2696), X(41392)}}, {{A, B, C, X(11744), X(56395)}}, {{A, B, C, X(14559), X(48373)}}
X(64103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 542, 14982}, {542, 9976, 265}, {2854, 6776, 32233}, {3564, 11579, 67}, {5663, 63722, 64104}, {5921, 25320, 32274}

X(64104) = ORTHOLOGY CENTER OF THESE TRIANGLES: UNARY COFACTOR TRIANGLE OF 2ND EHRMANN AND X(6)-CROSSPEDAL-OF-X(67)

Barycentrics    3*a^8-3*a^6*(b^2+c^2)+3*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(-2*b^4+7*b^2*c^2-2*c^4)-(b^4-c^4)^2 : :
X(64104) = -6*X[182]+5*X[38728], -4*X[575]+3*X[15061], -3*X[599]+4*X[5972], -4*X[1112]+3*X[9971], -3*X[1350]+4*X[38726], -3*X[1352]+4*X[61574], -3*X[1992]+X[3448]

X(64104) lies on circumconic {{A, B, C, X(2770), X(8791)}} and on these lines: {6, 67}, {69, 6593}, {74, 8550}, {110, 524}, {113, 15069}, {141, 32244}, {159, 32240}, {182, 38728}, {193, 2854}, {265, 576}, {511, 11562}, {518, 32298}, {542, 1351}, {575, 15061}, {597, 13169}, {599, 5972}, {690, 64092}, {868, 60739}, {895, 3629}, {1112, 9971}, {1177, 13622}, {1205, 32366}, {1350, 38726}, {1352, 61574}, {1353, 11579}, {1495, 47276}, {1503, 10721}, {1986, 37473}, {1992, 3448}, {2393, 13417}, {2777, 64080}, {2781, 6776}, {2892, 18919}, {2930, 6144}, {3043, 64061}, {3564, 9970}, {3580, 47549}, {3618, 6698}, {3763, 32257}, {3815, 9769}, {3818, 32272}, {4563, 36883}, {4663, 13211}, {5039, 32242}, {5050, 49116}, {5093, 32306}, {5181, 40341}, {5477, 59793}, {5480, 43580}, {5505, 22336}, {5621, 13293}, {5622, 12007}, {5642, 15533}, {5663, 63722}, {5847, 32278}, {5965, 19140}, {5987, 7837}, {6699, 53093}, {6723, 47352}, {7731, 15073}, {8262, 52238}, {8537, 44795}, {8540, 12904}, {8584, 9140}, {8787, 11006}, {9027, 61679}, {9143, 63064}, {9969, 32260}, {9974, 49222}, {9975, 49223}, {10113, 20423}, {10516, 32275}, {10541, 38727}, {10628, 50649}, {11004, 52191}, {11008, 40342}, {11179, 12041}, {11477, 17702}, {11482, 38724}, {11744, 12165}, {11746, 61665}, {11898, 45016}, {12167, 32239}, {12596, 15133}, {12903, 19369}, {13171, 32621}, {13248, 47277}, {13654, 32787}, {13774, 32788}, {14561, 15088}, {14643, 25556}, {14850, 32135}, {14853, 32274}, {14912, 32247}, {14984, 38898}, {15027, 22330}, {15036, 54169}, {15357, 41672}, {15462, 34477}, {15471, 47455}, {15520, 20301}, {15647, 41719}, {16111, 43273}, {16163, 53097}, {16475, 32238}, {18440, 32271}, {18457, 19398}, {18459, 19399}, {18947, 41618}, {19051, 44501}, {19052, 44502}, {19459, 32262}, {22251, 50978}, {24206, 34155}, {24981, 37750}, {25320, 51170}, {25328, 32455}, {29959, 41671}, {32227, 41586}, {32248, 64023}, {32255, 62996}, {32273, 55716}, {32289, 39897}, {32290, 39873}, {32300, 47355}, {32309, 45729}, {32310, 45728}, {32423, 64067}, {33851, 63428}, {34774, 38885}, {36253, 53858}, {37779, 57271}, {38723, 52987}, {38794, 40107}, {38851, 46444}, {39899, 48679}, {41617, 51882}, {41670, 54013}, {43391, 43812}, {44102, 47453}, {45311, 51185}, {46686, 47353}, {47284, 51431}, {47296, 47458}, {47457, 62376}, {50979, 61548}, {59399, 61543}, {63379, 63385}

X(64104) = midpoint of X(i) and X(j) for these {i,j}: {6, 16176}, {193, 11061}, {2930, 6144}, {7731, 15073}, {9143, 63064}, {10752, 32234}, {32248, 64023}, {39899, 48679}
X(64104) = reflection of X(i) in X(j) for these {i,j}: {6, 5095}, {67, 6}, {69, 6593}, {74, 8550}, {110, 25329}, {141, 41595}, {265, 576}, {599, 15303}, {895, 3629}, {1205, 32366}, {2930, 56565}, {3580, 47549}, {5648, 34319}, {9140, 8584}, {9973, 40949}, {11006, 8787}, {11579, 1353}, {11744, 64031}, {13169, 597}, {13211, 4663}, {14982, 9970}, {15069, 113}, {15133, 12596}, {15357, 41672}, {15533, 5642}, {18440, 32271}, {25328, 32455}, {32244, 141}, {32260, 9969}, {32272, 3818}, {32273, 55716}, {34319, 41720}, {34507, 25556}, {37473, 1986}, {38851, 46444}, {38885, 34774}, {40341, 5181}, {41721, 32217}, {47276, 1495}, {47284, 51431}, {53097, 16163}, {59793, 5477}, {63129, 41618}, {63428, 33851}, {63700, 19140}, {63716, 13248}, {64103, 63722}
X(64104) = pole of line {39477, 42659} with respect to the circumcircle
X(64104) = pole of line {1637, 18424} with respect to the orthocentroidal circle
X(64104) = pole of line {2393, 47450} with respect to the Jerabek hyperbola
X(64104) = pole of line {690, 41672} with respect to the Orthic inconic
X(64104) = pole of line {2854, 22151} with respect to the Stammler hyperbola
X(64104) = pole of line {30745, 37804} with respect to the Wallace hyperbola
X(64104) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {10752, 10753, 32234}
X(64104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {67, 19379, 15131}, {69, 25321, 6593}, {110, 25329, 34319}, {110, 41720, 25329}, {141, 41595, 52699}, {193, 11061, 2854}, {524, 25329, 110}, {524, 32217, 41721}, {524, 34319, 5648}, {2854, 40949, 9973}, {2930, 25331, 56565}, {3564, 9970, 14982}, {5663, 63722, 64103}, {5965, 19140, 63700}, {6144, 25331, 2930}, {25556, 34507, 14643}, {32244, 52699, 141}, {32252, 32280, 67}, {40341, 52697, 5181}

X(64105) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTIPEDAL-OF-X(6) AND X(6)-CROSSPEDAL-OF-X(182)

Barycentrics    a^2*(a^8-6*a^4*(b^4+c^4)-(b^2-c^2)^2*(3*b^4+8*b^2*c^2+3*c^4)+2*a^2*(4*b^6+b^4*c^2+b^2*c^4+4*c^6)) : :
X(64105) = -2*X[182]+3*X[7514], X[3426]+3*X[55610], -3*X[10516]+X[40909], -X[11820]+3*X[35243], -3*X[18420]+5*X[40330], -3*X[31884]+X[35237], -X[33534]+5*X[55614], -3*X[44413]+X[55722]

X(64105) lies on these lines: {3, 74}, {4, 37494}, {5, 3066}, {6, 32599}, {22, 18435}, {25, 15060}, {26, 5907}, {30, 599}, {64, 548}, {68, 52073}, {69, 49669}, {113, 61644}, {140, 5646}, {141, 50008}, {143, 11479}, {155, 31834}, {182, 7514}, {183, 61188}, {185, 7516}, {186, 41398}, {378, 23039}, {381, 15360}, {382, 41171}, {394, 18570}, {511, 4550}, {541, 50977}, {542, 8547}, {546, 17834}, {549, 10605}, {567, 7503}, {569, 45187}, {1154, 1351}, {1216, 12084}, {1498, 7525}, {1503, 35254}, {1593, 6101}, {1597, 6403}, {1598, 45958}, {1658, 17814}, {1995, 3581}, {2421, 30541}, {2777, 40107}, {2979, 43576}, {3090, 37490}, {3098, 14915}, {3292, 39242}, {3357, 5447}, {3426, 55610}, {3516, 64180}, {3564, 5486}, {3627, 37486}, {3628, 9786}, {3843, 12307}, {3845, 33586}, {3850, 33537}, {5055, 7699}, {5066, 17810}, {5094, 51391}, {5544, 13363}, {5562, 7526}, {5650, 37470}, {5651, 5891}, {5655, 47596}, {6000, 8717}, {6102, 7395}, {6243, 63664}, {6642, 14128}, {7387, 45959}, {7393, 13630}, {7403, 31815}, {7464, 33884}, {7492, 12112}, {7493, 46817}, {7496, 61136}, {7502, 18451}, {7506, 15056}, {7509, 13339}, {7517, 7691}, {7530, 15030}, {7556, 15052}, {7566, 15800}, {7574, 61700}, {7575, 35259}, {7592, 34864}, {7689, 11793}, {7706, 24206}, {7730, 54202}, {8548, 12596}, {9306, 18324}, {9729, 13154}, {9730, 22112}, {10170, 11438}, {10201, 44201}, {10272, 17835}, {10323, 18439}, {10516, 40909}, {10540, 44837}, {10606, 44324}, {10627, 12085}, {10628, 34117}, {11003, 18445}, {11064, 18580}, {11188, 33878}, {11455, 44457}, {11674, 32444}, {11801, 14852}, {11820, 35243}, {11935, 50461}, {12083, 15305}, {12105, 41424}, {12164, 32046}, {12362, 32140}, {13445, 54041}, {13596, 62188}, {13861, 46730}, {14644, 38397}, {14805, 63720}, {15069, 32423}, {15107, 16261}, {15361, 47597}, {15689, 33544}, {16072, 63839}, {17702, 34507}, {17928, 63392}, {18350, 38444}, {18420, 40330}, {18531, 61702}, {21312, 54042}, {25561, 51993}, {26958, 50140}, {31884, 35237}, {32137, 39568}, {32269, 44275}, {33534, 55614}, {33539, 62008}, {33540, 48154}, {33541, 62131}, {33542, 62142}, {33543, 61150}, {34477, 59543}, {34778, 61683}, {35450, 54044}, {35452, 54047}, {35500, 36749}, {35502, 37484}, {36747, 63682}, {38728, 49672}, {40280, 40916}, {41714, 55587}, {41721, 56966}, {43613, 64050}, {43807, 61811}, {44413, 55722}, {45088, 64066}, {51797, 56568}, {54994, 58891}

X(64105) = midpoint of X(i) and X(j) for these {i,j}: {3, 64097}, {69, 49669}, {1350, 11472}, {1352, 4549}
X(64105) = reflection of X(i) in X(j) for these {i,j}: {3, 33533}, {6, 49671}, {7706, 24206}, {8717, 14810}, {31861, 4550}, {33532, 3098}, {39522, 9818}, {50008, 141}, {51993, 25561}, {64098, 3}, {64099, 31861}
X(64105) = inverse of X(6800) in Stammler hyperbola
X(64105) = pole of line {39520, 55219} with respect to the cosine circle
X(64105) = pole of line {30, 6800} with respect to the Stammler hyperbola
X(64105) = pole of line {3260, 14907} with respect to the Wallace hyperbola
X(64105) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {69, 36163, 49669}, {1350, 11472, 14687}
X(64105) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(6800)}}, {{A, B, C, X(14906), X(40352)}}
X(64105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11459, 15068}, {3, 26864, 34513}, {3, 399, 6800}, {3, 5663, 64098}, {3, 5876, 32139}, {3, 6090, 1511}, {3, 64097, 5663}, {6, 32620, 49671}, {110, 12281, 12308}, {511, 31861, 64099}, {511, 4550, 31861}, {1154, 9818, 39522}, {1350, 11472, 30}, {1352, 54173, 32113}, {3098, 14915, 33532}, {5562, 7526, 16266}, {5609, 34513, 26864}, {5651, 63425, 32110}, {5891, 32110, 5651}, {6000, 14810, 8717}, {7691, 15058, 7517}, {11820, 55629, 35243}, {15030, 37478, 7530}, {32138, 32142, 3}, {33543, 61150, 62123}

X(64106) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(57) AND X(7)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+6*b*c+c^2)) : :
X(64106) = -3*X[210]+2*X[3421], -8*X[3820]+9*X[61686], -7*X[3983]+8*X[58650], -5*X[4005]+4*X[9954], -2*X[18391]+3*X[61660]

X(64106) lies on these lines: {1, 3}, {7, 3877}, {11, 7682}, {12, 3452}, {31, 1455}, {34, 1191}, {72, 10106}, {108, 1905}, {208, 1829}, {210, 3421}, {221, 4320}, {226, 392}, {227, 1193}, {278, 957}, {329, 388}, {347, 24471}, {515, 1864}, {518, 3476}, {519, 41539}, {527, 5434}, {758, 4315}, {944, 44547}, {946, 57285}, {956, 1708}, {961, 40399}, {995, 1465}, {1046, 9363}, {1071, 4311}, {1108, 1400}, {1122, 1358}, {1201, 1254}, {1317, 15185}, {1320, 60948}, {1359, 2823}, {1360, 47006}, {1386, 54292}, {1393, 52541}, {1407, 54400}, {1408, 62843}, {1418, 53530}, {1427, 1457}, {1445, 3872}, {1448, 34040}, {1450, 3752}, {1453, 34039}, {1469, 34371}, {1471, 49487}, {1478, 37822}, {1788, 5836}, {1858, 12680}, {1887, 54200}, {2094, 44663}, {2096, 4293}, {2097, 3827}, {2256, 2285}, {2300, 8898}, {2650, 4322}, {2802, 41556}, {2982, 57664}, {3086, 7686}, {3241, 7672}, {3244, 12432}, {3319, 47007}, {3485, 58679}, {3555, 15556}, {3598, 23839}, {3600, 3869}, {3671, 3884}, {3698, 19843}, {3753, 3911}, {3812, 7288}, {3820, 61686}, {3868, 4308}, {3878, 4298}, {3880, 36845}, {3889, 6049}, {3893, 41687}, {3962, 9850}, {3983, 58650}, {4005, 9954}, {4292, 12672}, {4295, 45776}, {4296, 62804}, {4297, 12711}, {4301, 17622}, {4305, 12710}, {4318, 62848}, {4847, 40663}, {4848, 10914}, {5044, 9578}, {5083, 24473}, {5433, 6692}, {5603, 54366}, {5666, 52181}, {5691, 64131}, {5727, 64157}, {5728, 43175}, {5731, 10391}, {5777, 9613}, {5806, 50443}, {5887, 18990}, {5918, 15326}, {5930, 14557}, {6284, 9848}, {6604, 18156}, {6737, 10944}, {7175, 36942}, {7354, 12688}, {8101, 10506}, {9370, 54386}, {9579, 9856}, {9655, 31937}, {10176, 51782}, {10396, 12650}, {10591, 16616}, {10693, 46683}, {10866, 12701}, {11237, 31142}, {11374, 31838}, {12648, 51378}, {12758, 24465}, {12832, 17636}, {14100, 43161}, {14872, 45287}, {15239, 63992}, {15325, 61535}, {15558, 38055}, {15844, 24987}, {16466, 21147}, {16483, 34036}, {17638, 31391}, {18391, 61660}, {21578, 63432}, {23840, 43065}, {30294, 50865}, {30384, 64127}, {31397, 39779}, {32049, 46677}, {34046, 54421}, {34434, 42549}, {34790, 37709}, {36973, 60909}, {37740, 61663}, {39542, 64115}, {39783, 41537}, {41572, 64139}, {41576, 44669}, {54135, 60910}, {64021, 64132}

X(64106) = midpoint of X(i) and X(j) for these {i,j}: {3869, 9965}
X(64106) = reflection of X(i) in X(j) for these {i,j}: {65, 57}, {329, 960}, {5727, 64157}, {17625, 4315}, {63995, 4293}
X(64106) = pole of line {1, 3427} with respect to the Feuerbach hyperbola
X(64106) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31397)}}, {{A, B, C, X(3), X(957)}}, {{A, B, C, X(4), X(22770)}}, {{A, B, C, X(19), X(30503)}}, {{A, B, C, X(28), X(9940)}}, {{A, B, C, X(34), X(3333)}}, {{A, B, C, X(40), X(34434)}}, {{A, B, C, X(105), X(17603)}}, {{A, B, C, X(354), X(1411)}}, {{A, B, C, X(517), X(14493)}}, {{A, B, C, X(942), X(57664)}}, {{A, B, C, X(961), X(37566)}}, {{A, B, C, X(994), X(2093)}}, {{A, B, C, X(999), X(39779)}}, {{A, B, C, X(1243), X(2095)}}, {{A, B, C, X(1320), X(17642)}}, {{A, B, C, X(3427), X(3428)}}, {{A, B, C, X(3666), X(26591)}}, {{A, B, C, X(10428), X(22765)}}, {{A, B, C, X(10966), X(57666)}}, {{A, B, C, X(11529), X(13476)}}, {{A, B, C, X(20615), X(26437)}}, {{A, B, C, X(37558), X(52384)}}
X(64106) = barycentric product X(i)*X(j) for these (i, j): {278, 64107}, {26591, 56}, {31397, 57}
X(64106) = barycentric quotient X(i)/X(j) for these (i, j): {26591, 3596}, {31397, 312}, {39779, 28808}, {64107, 345}
X(64106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1617, 1319}, {57, 517, 65}, {65, 1319, 354}, {65, 5919, 2099}, {758, 4315, 17625}, {3878, 4298, 12709}, {4292, 12672, 17634}, {4293, 6001, 63995}, {5434, 64041, 8581}, {7354, 64042, 12688}, {8581, 31165, 64041}, {39779, 64107, 31397}

X(64107) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(165) AND X(7)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a^2-b^2-c^2)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+6*b*c+c^2)) : :
X(64107) = -X[4]+4*X[5044], 2*X[5]+X[37585], X[20]+5*X[3876], -X[80]+4*X[58666], -8*X[140]+5*X[5439], -2*X[355]+5*X[3697], X[550]+2*X[31835], -5*X[631]+2*X[942], -4*X[1385]+X[3555], -X[1482]+4*X[31838], -5*X[1698]+2*X[7686], -7*X[3090]+4*X[5806] and many others

X(64107) lies on these lines: {1, 5920}, {2, 392}, {3, 63}, {4, 5044}, {5, 37585}, {8, 6865}, {9, 1012}, {10, 6831}, {20, 3876}, {21, 44861}, {29, 1872}, {30, 5927}, {35, 12711}, {36, 17625}, {37, 63982}, {40, 936}, {46, 12709}, {65, 5432}, {71, 34591}, {80, 58666}, {104, 60970}, {140, 5439}, {144, 2096}, {165, 5692}, {191, 17649}, {201, 17102}, {210, 515}, {212, 46974}, {307, 1565}, {329, 6916}, {354, 5298}, {355, 3697}, {376, 971}, {377, 5812}, {386, 37528}, {404, 37623}, {405, 37531}, {411, 3579}, {443, 5758}, {474, 5709}, {516, 10176}, {518, 3576}, {549, 10202}, {550, 31835}, {580, 37539}, {602, 5266}, {631, 942}, {758, 10164}, {908, 6907}, {916, 64100}, {938, 9957}, {944, 20007}, {946, 3925}, {956, 17658}, {958, 63391}, {962, 6864}, {965, 1766}, {975, 5706}, {993, 50371}, {997, 3428}, {999, 1445}, {1001, 37569}, {1006, 5728}, {1038, 7078}, {1155, 64041}, {1210, 3057}, {1214, 22350}, {1385, 3555}, {1387, 61016}, {1420, 17624}, {1482, 31838}, {1490, 37426}, {1512, 3820}, {1532, 3452}, {1593, 41609}, {1698, 7686}, {1807, 47487}, {1858, 5217}, {1864, 4304}, {1871, 7513}, {1898, 15338}, {2077, 4640}, {2095, 3306}, {2287, 4221}, {2551, 58649}, {2646, 41538}, {2771, 15055}, {2800, 6174}, {2801, 4134}, {2949, 37583}, {3090, 5806}, {3219, 6909}, {3305, 6913}, {3359, 41389}, {3419, 6827}, {3421, 51380}, {3487, 37407}, {3488, 64157}, {3522, 12528}, {3523, 3868}, {3524, 11227}, {3528, 31805}, {3530, 24475}, {3587, 5720}, {3601, 44547}, {3624, 13374}, {3678, 4297}, {3681, 5731}, {3740, 5587}, {3786, 7415}, {3812, 31423}, {3832, 31822}, {3869, 6988}, {3872, 51378}, {3873, 54445}, {3878, 6700}, {3880, 63143}, {3884, 9843}, {3890, 13600}, {3921, 5790}, {3928, 21164}, {3929, 52027}, {3956, 38155}, {3962, 5884}, {4004, 64044}, {4005, 12680}, {4018, 34339}, {4294, 64131}, {4420, 64116}, {4533, 18481}, {4641, 37469}, {4662, 5881}, {4679, 26333}, {5218, 50195}, {5220, 63991}, {5223, 63430}, {5250, 10306}, {5251, 5538}, {5265, 58576}, {5273, 6935}, {5293, 37570}, {5316, 7682}, {5328, 6969}, {5433, 64046}, {5584, 6261}, {5658, 37427}, {5690, 6734}, {5691, 58631}, {5693, 9943}, {5694, 31663}, {5697, 17622}, {5705, 5836}, {5722, 6947}, {5759, 50701}, {5761, 6989}, {5763, 8728}, {5771, 59491}, {5780, 37411}, {5784, 63438}, {5787, 6899}, {5791, 6833}, {5804, 17559}, {5805, 6854}, {5883, 58441}, {5903, 9588}, {5904, 7987}, {5918, 63276}, {5919, 28234}, {6051, 37529}, {6211, 63423}, {6326, 7688}, {6361, 9856}, {6769, 31435}, {6828, 9956}, {6835, 12699}, {6850, 58798}, {6855, 9780}, {6870, 61261}, {6876, 40262}, {6883, 37533}, {6889, 11374}, {6894, 22793}, {6895, 18480}, {6897, 57282}, {6906, 26878}, {6911, 37584}, {6912, 27065}, {6918, 12702}, {6925, 31018}, {6927, 31798}, {6932, 27131}, {6936, 9844}, {6940, 37582}, {6955, 60946}, {6966, 55868}, {6987, 64171}, {6991, 9955}, {7288, 50196}, {7330, 37022}, {7982, 58679}, {7989, 16616}, {7991, 45776}, {8100, 8127}, {8128, 12491}, {8583, 50203}, {8726, 11523}, {9021, 21167}, {9568, 57719}, {9864, 58662}, {9945, 12691}, {10039, 15844}, {10175, 44847}, {10179, 16200}, {10270, 54290}, {10304, 11220}, {10310, 12514}, {10391, 18397}, {10519, 34381}, {10531, 50399}, {10902, 56176}, {10953, 54304}, {10984, 42463}, {11012, 59691}, {11248, 11344}, {11249, 17614}, {11495, 50528}, {11500, 59340}, {11827, 17647}, {12114, 41229}, {12368, 58671}, {12512, 31803}, {12526, 37560}, {12616, 21677}, {12664, 40661}, {12665, 38759}, {12688, 20117}, {12704, 25524}, {12751, 58663}, {12784, 58673}, {13145, 31447}, {13178, 58661}, {13211, 58654}, {13329, 30115}, {13348, 29958}, {14740, 64191}, {15064, 28164}, {15071, 16192}, {15185, 52769}, {15325, 17626}, {15726, 61705}, {15852, 37732}, {15908, 21616}, {16139, 35979}, {16371, 17612}, {16410, 19861}, {16418, 59381}, {16465, 37106}, {17529, 55108}, {17603, 18389}, {17613, 35238}, {17642, 44675}, {17654, 64139}, {17661, 38761}, {18236, 62357}, {18254, 24466}, {18412, 53054}, {18641, 22076}, {19262, 27396}, {20013, 37727}, {20846, 26285}, {21617, 39542}, {21629, 38386}, {21871, 40942}, {21872, 46830}, {22753, 41338}, {22937, 26086}, {24914, 64043}, {26286, 37301}, {27385, 37562}, {28381, 48882}, {28466, 33595}, {30267, 54150}, {31162, 38150}, {31397, 39779}, {31775, 64002}, {31787, 64021}, {31789, 57287}, {31836, 34783}, {31937, 50695}, {34862, 37403}, {35239, 45770}, {36029, 59681}, {37180, 51490}, {37229, 59318}, {37281, 64003}, {37374, 51755}, {37462, 55109}, {37468, 57284}, {37526, 54422}, {37568, 64042}, {37600, 54192}, {37613, 58378}, {37837, 59320}, {38113, 50202}, {38127, 61032}, {38140, 52269}, {39885, 58653}, {40659, 43161}, {41012, 50206}, {41228, 51489}, {43652, 47371}, {45186, 58497}, {50896, 58665}, {50899, 58670}, {50903, 58664}, {54145, 58449}, {54433, 55112}, {54447, 58451}, {58648, 64111}, {58688, 59388}, {58808, 64197}, {59387, 63961}, {63266, 64074}

X(64107) = midpoint of X(i) and X(j) for these {i,j}: {1, 15104}, {72, 10167}, {165, 5692}, {3681, 5731}, {3877, 59417}, {10157, 31793}
X(64107) = reflection of X(i) in X(j) for these {i,j}: {4, 10157}, {354, 10165}, {942, 10156}, {1071, 10167}, {3753, 26446}, {5587, 3740}, {5883, 58441}, {10157, 5044}, {10167, 3}, {10202, 549}, {11227, 33575}, {15104, 63976}, {16200, 10179}, {18908, 210}, {24473, 10202}, {38155, 3956}
X(64107) = pole of line {3303, 37740} with respect to the Feuerbach hyperbola
X(64107) = pole of line {1071, 22076} with respect to the Jerabek hyperbola
X(64107) = pole of line {28, 9940} with respect to the Stammler hyperbola
X(64107) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(957)}}, {{A, B, C, X(63), X(30500)}}, {{A, B, C, X(72), X(44861)}}, {{A, B, C, X(78), X(7160)}}, {{A, B, C, X(104), X(10167)}}, {{A, B, C, X(1071), X(1791)}}, {{A, B, C, X(3998), X(26591)}}
X(64107) = barycentric product X(i)*X(j) for these (i, j): {345, 64106}, {26591, 3}, {30680, 39779}, {31397, 63}
X(64107) = barycentric quotient X(i)/X(j) for these (i, j): {26591, 264}, {31397, 92}, {64106, 278}
X(64107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 26921, 3916}, {3, 31837, 72}, {3, 3927, 63399}, {3, 3940, 18446}, {3, 72, 1071}, {3, 78, 33597}, {3, 912, 10167}, {9, 6282, 1012}, {20, 3876, 5777}, {40, 936, 3149}, {40, 960, 12672}, {72, 10167, 912}, {140, 24474, 5439}, {165, 5692, 6001}, {191, 59326, 64118}, {201, 22072, 17102}, {210, 515, 18908}, {517, 26446, 3753}, {550, 31835, 40263}, {960, 58637, 40}, {1490, 37551, 37426}, {3523, 3868, 9940}, {3587, 5720, 7580}, {3678, 4297, 14872}, {3877, 59417, 517}, {4005, 12680, 63967}, {5044, 31793, 4}, {5693, 35242, 9943}, {5904, 7987, 12675}, {6684, 31806, 65}, {6925, 31018, 37822}, {6986, 34772, 1385}, {7957, 25917, 946}, {11227, 33575, 3524}, {18397, 30282, 10391}, {20007, 37423, 944}, {20117, 31730, 12688}, {21677, 50031, 12616}, {24929, 31658, 1006}, {31397, 64106, 39779}, {31423, 37625, 3812}, {54051, 59418, 376}, {57284, 64004, 37468}, {64139, 64193, 17654}

X(64108) = ANTICOMPLEMENT OF X(7988)

Barycentrics    7*a^3-3*a*(b-c)^2-5*a^2*(b+c)+(b-c)^2*(b+c) : :
X(64108) = -2*X[1]+11*X[15717], X[2]+2*X[165], 8*X[3]+X[8], -X[4]+4*X[11231], -16*X[5]+7*X[10248], 4*X[10]+5*X[3522], X[20]+2*X[5587], 8*X[140]+X[6361], -X[145]+10*X[7987], X[210]+2*X[10178], 2*X[355]+7*X[3528], X[376]+2*X[26446] and many others

X(64108) lies on these lines: {1, 15717}, {2, 165}, {3, 8}, {4, 11231}, {5, 10248}, {7, 1155}, {9, 56263}, {10, 3522}, {11, 30312}, {20, 5587}, {21, 26062}, {30, 61260}, {35, 938}, {40, 3306}, {46, 5703}, {55, 5435}, {57, 5281}, {63, 64083}, {140, 6361}, {144, 6745}, {145, 7987}, {189, 39558}, {210, 10178}, {226, 63207}, {329, 21168}, {355, 3528}, {376, 26446}, {381, 28182}, {382, 61262}, {390, 3911}, {392, 33575}, {404, 5584}, {497, 61649}, {515, 10304}, {517, 3524}, {519, 15705}, {548, 38138}, {549, 5603}, {550, 5818}, {551, 61806}, {631, 962}, {632, 48661}, {658, 3160}, {750, 5308}, {899, 1742}, {908, 62710}, {927, 43080}, {946, 10303}, {971, 63961}, {990, 5297}, {991, 3240}, {1000, 5126}, {1006, 35238}, {1054, 16020}, {1056, 5122}, {1125, 20070}, {1158, 54228}, {1253, 9364}, {1293, 9095}, {1376, 5273}, {1385, 10299}, {1482, 15712}, {1483, 61790}, {1621, 6244}, {1697, 5265}, {1698, 3146}, {1709, 27065}, {1768, 60912}, {1770, 5556}, {1776, 60954}, {1788, 4313}, {2077, 37106}, {2094, 21151}, {2320, 50371}, {2476, 50031}, {2807, 7998}, {3035, 5328}, {3085, 58887}, {3086, 59316}, {3091, 10172}, {3161, 5205}, {3218, 63168}, {3219, 64129}, {3241, 3576}, {3305, 10860}, {3338, 5558}, {3416, 59581}, {3474, 5226}, {3475, 4995}, {3485, 52793}, {3486, 63756}, {3525, 12699}, {3526, 61269}, {3529, 9956}, {3530, 5734}, {3533, 9955}, {3534, 38042}, {3543, 10175}, {3545, 28146}, {3599, 17093}, {3617, 4297}, {3622, 7991}, {3623, 30389}, {3624, 5493}, {3625, 58217}, {3634, 3832}, {3654, 7967}, {3655, 15715}, {3656, 15719}, {3667, 6544}, {3679, 62063}, {3681, 10167}, {3697, 31805}, {3740, 5918}, {3757, 10856}, {3826, 10883}, {3828, 15683}, {3830, 50813}, {3839, 28150}, {3844, 14927}, {3868, 58637}, {3869, 31787}, {3870, 10857}, {3871, 8273}, {3873, 11227}, {3876, 9943}, {3890, 31798}, {3916, 5815}, {3928, 59584}, {4031, 30340}, {4188, 59320}, {4189, 59326}, {4229, 5235}, {4294, 5704}, {4295, 37572}, {4301, 46934}, {4302, 37718}, {4305, 59325}, {4308, 5204}, {4323, 37567}, {4344, 17726}, {4413, 11495}, {4420, 10884}, {4421, 24477}, {4430, 15104}, {4511, 30503}, {4640, 18228}, {4652, 7080}, {4666, 7994}, {4669, 62054}, {4745, 62072}, {4816, 58215}, {5010, 17010}, {5044, 9961}, {5047, 64074}, {5054, 28174}, {5055, 28178}, {5056, 41869}, {5059, 19925}, {5067, 22793}, {5068, 51118}, {5070, 61267}, {5080, 6916}, {5088, 52715}, {5131, 10056}, {5180, 6954}, {5212, 62985}, {5220, 13243}, {5222, 11200}, {5249, 38123}, {5260, 37022}, {5274, 31231}, {5278, 37078}, {5286, 31422}, {5304, 9574}, {5537, 52769}, {5552, 10270}, {5554, 17548}, {5660, 9809}, {5686, 46917}, {5691, 46933}, {5697, 18240}, {5745, 38200}, {5748, 44447}, {5749, 37499}, {5766, 54366}, {5790, 8703}, {5817, 7580}, {5844, 17504}, {5846, 55673}, {5851, 6172}, {5852, 25568}, {5881, 58188}, {5882, 20053}, {5901, 61811}, {5984, 51578}, {6049, 37605}, {6223, 64118}, {6409, 19065}, {6410, 19066}, {6764, 8715}, {6796, 9799}, {6857, 11024}, {6865, 52367}, {6908, 27529}, {6937, 38109}, {6940, 35239}, {6963, 23513}, {6986, 10310}, {6988, 11415}, {7074, 17074}, {7229, 29828}, {7288, 9785}, {7292, 61086}, {7320, 20323}, {7486, 18483}, {7492, 9590}, {7586, 9616}, {7671, 61660}, {7672, 17603}, {7676, 62775}, {7705, 50244}, {7718, 15750}, {7735, 31443}, {7982, 61798}, {7989, 17578}, {8055, 26265}, {8148, 61280}, {8185, 16661}, {8227, 55864}, {8582, 11106}, {9342, 19541}, {9352, 9776}, {9582, 13975}, {9589, 19862}, {9782, 55109}, {9800, 12511}, {9801, 24309}, {9960, 58660}, {10222, 61795}, {10246, 12100}, {10247, 15700}, {10268, 10527}, {10385, 17728}, {10431, 26040}, {10434, 10453}, {10449, 61124}, {10528, 16209}, {10529, 16208}, {11019, 31508}, {11037, 37582}, {11041, 37606}, {11230, 15702}, {11239, 21164}, {11362, 20050}, {11539, 28216}, {11680, 37364}, {11681, 37424}, {12245, 13624}, {12518, 58708}, {12527, 27525}, {12571, 19872}, {12577, 53057}, {12630, 51463}, {12701, 63213}, {13329, 17126}, {13405, 21454}, {13883, 43511}, {13911, 42637}, {13936, 43512}, {13973, 42638}, {14647, 54051}, {14664, 17777}, {14869, 18493}, {14891, 34718}, {14986, 61763}, {15022, 51073}, {15305, 52796}, {15338, 54361}, {15599, 27013}, {15682, 38140}, {15688, 28186}, {15689, 28190}, {15690, 50826}, {15693, 38028}, {15694, 38034}, {15696, 18357}, {15697, 50796}, {15706, 58230}, {15708, 28194}, {15709, 28198}, {15710, 28204}, {15714, 59400}, {15716, 50824}, {15720, 22791}, {15721, 31162}, {15726, 61023}, {15759, 50798}, {15931, 36845}, {15933, 59337}, {16173, 30305}, {16200, 50828}, {17051, 61159}, {17484, 60896}, {17531, 64077}, {17538, 18480}, {17558, 63141}, {17566, 26129}, {17576, 24982}, {17601, 64168}, {17613, 31658}, {17784, 59491}, {17800, 61259}, {18231, 57284}, {18250, 51576}, {18481, 21735}, {18492, 49135}, {18525, 33923}, {18788, 26626}, {19649, 26241}, {19708, 50821}, {19860, 38399}, {19875, 28164}, {19876, 34638}, {19883, 61830}, {20368, 59297}, {21629, 60423}, {22467, 37557}, {24987, 37267}, {24988, 36652}, {25055, 28228}, {26038, 37400}, {26112, 27002}, {26245, 62300}, {27003, 41338}, {27383, 37560}, {28158, 50687}, {28168, 62130}, {28202, 61899}, {28208, 62086}, {28224, 38066}, {28232, 38021}, {28236, 62056}, {28472, 42049}, {28537, 52620}, {28877, 33156}, {30116, 62320}, {30295, 60995}, {30315, 50690}, {31019, 64113}, {31145, 61778}, {31424, 59675}, {31427, 61322}, {31452, 37524}, {31752, 64025}, {31852, 63851}, {31884, 59406}, {32917, 37416}, {32931, 59620}, {33108, 37374}, {33697, 62147}, {33703, 61261}, {34122, 57006}, {34200, 34627}, {34595, 61848}, {34628, 38155}, {34648, 62129}, {34744, 56177}, {35595, 54370}, {35986, 36991}, {37163, 38134}, {37583, 41824}, {37624, 61794}, {37705, 58190}, {37714, 62102}, {37789, 54408}, {38076, 62032}, {38081, 41982}, {38083, 62017}, {38116, 55649}, {38127, 50811}, {38454, 59374}, {38759, 64141}, {38941, 56543}, {39570, 59779}, {40127, 41423}, {40256, 54199}, {40273, 46219}, {40333, 63413}, {41106, 50873}, {41348, 64160}, {42316, 51406}, {43182, 61006}, {44682, 61283}, {46853, 61251}, {46904, 54474}, {46930, 50689}, {48919, 50420}, {49524, 55651}, {50696, 59389}, {50799, 62049}, {50800, 62154}, {50803, 62018}, {50806, 61851}, {50807, 61904}, {50809, 51709}, {50812, 62160}, {50814, 51105}, {50815, 51066}, {50818, 61777}, {50819, 62073}, {50823, 61779}, {50862, 62145}, {50867, 62165}, {50872, 61805}, {51067, 51080}, {51086, 51110}, {51088, 61838}, {51192, 53094}, {51622, 51630}, {51700, 61802}, {51705, 61781}, {54052, 64148}, {54290, 59587}, {55863, 61272}, {56507, 59298}, {58487, 64050}, {61122, 63985}, {61247, 62066}, {61258, 62117}, {61293, 61785}, {61510, 62069}

X(64108) = midpoint of X(i) and X(j) for these {i,j}: {40, 61275}, {9778, 9779}, {54448, 62120}
X(64108) = reflection of X(i) in X(j) for these {i,j}: {4, 61263}, {3839, 54447}, {9779, 2}, {9812, 9779}, {38314, 54445}, {54445, 3524}, {54447, 38068}, {54448, 19875}, {61254, 10}, {61263, 11231}, {61270, 140}, {61275, 10165}
X(64108) = anticomplement of X(7988)
X(64108) = perspector of circumconic {{A, B, C, X(13136), X(32040)}}
X(64108) = X(i)-Dao conjugate of X(j) for these {i, j}: {7988, 7988}
X(64108) = pole of line {514, 48163} with respect to the orthoptic circle of the Steiner Inellipse
X(64108) = pole of line {28151, 39534} with respect to the polar circle
X(64108) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(9779), X(18025)}}, {{A, B, C, X(34234), X(55937)}}, {{A, B, C, X(38955), X(54668)}}
X(64108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 165, 9778}, {2, 35258, 52653}, {2, 516, 9779}, {2, 9778, 9812}, {3, 5657, 5731}, {3, 61524, 944}, {10, 16192, 3522}, {20, 6684, 9780}, {40, 3523, 3616}, {55, 5435, 10580}, {57, 5281, 10578}, {100, 5744, 8}, {145, 61791, 7987}, {165, 10164, 2}, {165, 1699, 50808}, {165, 21153, 35258}, {210, 10178, 11220}, {376, 26446, 59387}, {517, 3524, 54445}, {517, 54445, 38314}, {631, 3579, 962}, {631, 962, 5550}, {944, 5657, 59503}, {1125, 63469, 20070}, {1155, 5218, 7}, {1698, 12512, 3146}, {1788, 5217, 4313}, {3474, 5432, 5226}, {3576, 59417, 3241}, {3617, 21734, 4297}, {3634, 64005, 3832}, {3654, 17502, 7967}, {3817, 10164, 50829}, {3911, 35445, 390}, {3916, 59591, 5815}, {4413, 11495, 36002}, {4421, 24477, 64146}, {5059, 46932, 19925}, {5273, 7411, 10430}, {5432, 63212, 3474}, {5537, 52769, 61155}, {6684, 35242, 20}, {7288, 37568, 9785}, {7967, 15698, 17502}, {7987, 43174, 145}, {9778, 9779, 516}, {10164, 50808, 58441}, {11231, 28154, 61263}, {12245, 61138, 13624}, {12571, 19872, 61914}, {13405, 53056, 21454}, {15692, 59417, 3576}, {17578, 46931, 7989}, {19875, 28164, 54448}, {19876, 34638, 61985}, {20070, 61820, 1125}, {28150, 38068, 54447}, {28150, 54447, 3839}, {28154, 61263, 4}, {30332, 31188, 11}, {31018, 63971, 9809}, {31423, 31730, 3091}, {31425, 35242, 6684}, {34474, 38693, 17100}, {35986, 61156, 44425}, {46933, 50693, 5691}, {50808, 58441, 1699}, {50809, 61822, 51709}, {54448, 62120, 28164}, {59503, 61524, 5657}, {62710, 63975, 908}

X(64109) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 110 AND X(7)-CROSSPEDAL-OF-X(8)

Barycentrics    2*a^3*(b+c)+(b^2-c^2)^2-a^2*(b^2+12*b*c+c^2)-2*a*(b^3+b^2*c+b*c^2+c^3) : :
X(64109) = 3*X[2]+X[1000], X[144]+3*X[1056], -3*X[551]+X[14563], -X[1159]+3*X[38053], -X[3577]+3*X[5886], -5*X[3616]+X[11041], 7*X[3624]+X[8275], -3*X[9708]+5*X[18230], -3*X[10246]+X[64147], -X[16236]+9*X[25055], -X[24297]+5*X[31272]

X(64109) lies on circumconic {{A, B, C, X(42285), X(51564)}} and on these lines: {1, 5791}, {2, 1000}, {5, 58679}, {8, 16842}, {10, 10179}, {11, 17057}, {30, 60964}, {37, 50027}, {55, 9945}, {142, 517}, {144, 1056}, {145, 31259}, {355, 7966}, {392, 495}, {442, 3890}, {496, 24987}, {514, 4364}, {515, 60901}, {518, 63643}, {519, 6666}, {551, 14563}, {632, 1125}, {952, 1001}, {996, 4422}, {999, 5744}, {1086, 17461}, {1159, 38053}, {1385, 6705}, {1483, 58415}, {1484, 3816}, {1621, 6224}, {1698, 11524}, {2320, 50843}, {2800, 31657}, {2802, 3826}, {2886, 3898}, {3057, 8728}, {3295, 19520}, {3419, 15170}, {3476, 16418}, {3577, 5886}, {3616, 11041}, {3624, 8275}, {3626, 14150}, {3634, 64205}, {3654, 5437}, {3656, 25525}, {3740, 49626}, {3820, 5316}, {3822, 38034}, {3824, 4301}, {3841, 13463}, {3877, 31019}, {3878, 6147}, {3884, 5499}, {4423, 12647}, {4752, 17369}, {4867, 37703}, {4900, 13602}, {5045, 5837}, {5218, 35272}, {5248, 31649}, {5250, 18990}, {5259, 10944}, {5284, 12531}, {5289, 5719}, {5432, 12740}, {5434, 16140}, {5436, 37727}, {5730, 10587}, {5745, 51788}, {5790, 26105}, {5794, 15172}, {5844, 54318}, {5880, 28212}, {5901, 10198}, {6690, 6713}, {6692, 50821}, {8148, 28629}, {8256, 19862}, {8583, 47742}, {9708, 18230}, {9780, 32634}, {9957, 31419}, {10039, 17527}, {10246, 64147}, {10386, 17647}, {10592, 41012}, {10609, 61155}, {10914, 24564}, {11682, 16137}, {14077, 40551}, {14923, 17529}, {16236, 25055}, {17248, 41779}, {17528, 30305}, {17563, 37568}, {18253, 62825}, {24297, 31272}, {24473, 58813}, {24864, 45213}, {25524, 61524}, {26446, 31190}, {27383, 31480}, {31794, 51723}, {32198, 58453}, {33812, 50824}, {37424, 45776}, {38025, 38211}, {45287, 50241}, {51103, 54288}, {51709, 58463}

X(64109) = midpoint of X(i) and X(j) for these {i,j}: {355, 7966}, {1000, 40587}, {36867, 36922}
X(64109) = reflection of X(i) in X(j) for these {i,j}: {15935, 42819}
X(64109) = complement of X(40587)
X(64109) = X(i)-Ceva conjugate of X(j) for these {i, j}: {52925, 900}
X(64109) = X(i)-complementary conjugate of X(j) for these {i, j}: {1000, 21251}, {2163, 40587}, {34446, 16590}
X(64109) = pole of line {62620, 63217} with respect to the Steiner inellipse
X(64109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 36922, 36867}, {2, 1000, 40587}, {519, 42819, 15935}, {3884, 25466, 22791}, {5316, 51362, 3820}, {5730, 10587, 63282}

X(64110) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(55) AND X(7)-CROSSPEDAL-OF-X(10)

Barycentrics    2*a^4-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(3*b^2+2*b*c+3*c^2) : :
X(64110) = -X[8]+5*X[31266], X[2099]+3*X[17718], 7*X[3622]+X[5905], -11*X[5550]+7*X[55867], X[8545]+3*X[11038], 3*X[10056]+X[25415], 3*X[11237]+X[37740], -X[11608]+3*X[38220], X[31164]+3*X[38314], 3*X[38316]+X[61011], -13*X[46934]+5*X[55868]

X(64110) lies on these lines: {1, 4}, {2, 5775}, {3, 3671}, {5, 6738}, {7, 3576}, {8, 31266}, {10, 3940}, {11, 4870}, {12, 64163}, {36, 553}, {40, 5281}, {55, 28194}, {57, 10165}, {63, 3333}, {65, 5432}, {72, 24066}, {102, 58993}, {104, 60961}, {140, 31794}, {142, 997}, {214, 60980}, {354, 15950}, {355, 3947}, {376, 4312}, {390, 31162}, {442, 6737}, {495, 519}, {496, 6744}, {498, 4848}, {516, 8255}, {517, 5719}, {527, 551}, {535, 25405}, {631, 3339}, {758, 942}, {912, 5045}, {936, 28629}, {938, 8227}, {943, 59320}, {952, 51782}, {954, 3428}, {962, 16134}, {995, 26728}, {1000, 11224}, {1006, 52819}, {1060, 18589}, {1100, 40963}, {1159, 26446}, {1210, 11375}, {1385, 4298}, {1386, 9028}, {1387, 2801}, {1537, 63258}, {1565, 2792}, {1621, 51423}, {1737, 5425}, {1770, 37571}, {1836, 4304}, {1858, 10122}, {2093, 5218}, {2099, 17718}, {2140, 52542}, {2294, 34591}, {2476, 41575}, {2646, 3649}, {2800, 50195}, {3074, 55101}, {3085, 3340}, {3086, 11518}, {3243, 34625}, {3244, 64205}, {3295, 4301}, {3361, 21165}, {3452, 54318}, {3474, 30282}, {3524, 53056}, {3577, 64148}, {3601, 4295}, {3622, 5905}, {3634, 54288}, {3636, 12577}, {3656, 4342}, {3679, 8164}, {3686, 54335}, {3743, 37565}, {3753, 6745}, {3754, 59719}, {3812, 6700}, {3817, 5722}, {3838, 44669}, {3868, 24541}, {3902, 50744}, {3911, 5902}, {3945, 41010}, {3946, 17761}, {3962, 24953}, {3982, 37525}, {4018, 7483}, {4054, 49492}, {4293, 4654}, {4297, 57282}, {4305, 9579}, {4311, 10404}, {4313, 41869}, {4314, 12699}, {4315, 10246}, {4323, 7982}, {4353, 29069}, {4355, 30389}, {4511, 5249}, {4653, 5327}, {4667, 24316}, {4757, 58404}, {4758, 25363}, {4867, 26725}, {4881, 26842}, {4995, 5183}, {5126, 43180}, {5219, 10175}, {5226, 5587}, {5261, 5881}, {5274, 15933}, {5550, 55867}, {5556, 49135}, {5657, 18421}, {5665, 6908}, {5693, 62864}, {5704, 18221}, {5726, 59388}, {5727, 10590}, {5795, 21077}, {5836, 59722}, {5837, 10198}, {5841, 15178}, {5880, 56177}, {5883, 6692}, {5884, 6705}, {5886, 11019}, {5903, 63259}, {5919, 37703}, {6001, 11018}, {6051, 25080}, {6282, 12560}, {6326, 21617}, {6666, 10176}, {6690, 44663}, {6734, 34195}, {6743, 31419}, {6766, 7160}, {6847, 9948}, {6857, 12526}, {7373, 22758}, {7675, 50528}, {8068, 41558}, {8275, 34631}, {8543, 62873}, {8545, 11038}, {8680, 15569}, {8728, 12447}, {9578, 47745}, {9623, 25568}, {9624, 14986}, {9654, 37739}, {9708, 21060}, {9843, 25681}, {9856, 12710}, {9955, 12433}, {9957, 63282}, {10039, 37731}, {10056, 25415}, {10107, 64123}, {10164, 36279}, {10283, 51788}, {10389, 30305}, {10394, 61705}, {10527, 11520}, {10529, 62861}, {10578, 31393}, {10580, 37704}, {10588, 31399}, {10591, 37723}, {10624, 37080}, {10895, 37724}, {10902, 57283}, {10916, 62860}, {10980, 25055}, {11011, 15888}, {11235, 51071}, {11237, 37740}, {11240, 62815}, {11246, 37600}, {11263, 17647}, {11373, 21625}, {11415, 62829}, {11496, 18237}, {11523, 19843}, {11608, 38220}, {11729, 18240}, {12005, 16193}, {12245, 51784}, {12263, 46180}, {12268, 31570}, {12269, 31569}, {12432, 31837}, {12436, 59691}, {12559, 24391}, {12575, 22791}, {12609, 22836}, {12625, 31418}, {12735, 50892}, {13462, 59372}, {13624, 24470}, {14794, 63288}, {15170, 43179}, {15252, 44916}, {15368, 49744}, {15844, 63963}, {15935, 18527}, {17084, 53597}, {18454, 21623}, {18456, 21624}, {19860, 21075}, {19925, 37730}, {20117, 44547}, {21454, 54445}, {21616, 30143}, {22465, 24424}, {24231, 37617}, {24331, 25353}, {24389, 42871}, {24987, 62830}, {25639, 31936}, {26015, 63159}, {28172, 61716}, {28212, 51787}, {28232, 59337}, {28236, 37728}, {29639, 49454}, {30115, 64174}, {30144, 51706}, {30284, 41857}, {30350, 61274}, {30424, 37606}, {30478, 54422}, {31164, 38314}, {31434, 38127}, {31795, 40273}, {33110, 34772}, {33815, 58405}, {34790, 58699}, {35272, 38054}, {35670, 35886}, {37605, 52783}, {37836, 42443}, {37837, 64001}, {38316, 61011}, {40256, 59335}, {40663, 61648}, {40998, 51409}, {41863, 64081}, {42289, 63982}, {43174, 50193}, {43177, 63991}, {44858, 50898}, {45770, 55108}, {46934, 55868}, {50742, 63975}, {50757, 60116}, {50908, 53055}, {51105, 53058}, {52769, 60945}, {54286, 59584}, {54424, 59644}, {54430, 59317}, {58576, 58578}, {60885, 60972}, {60937, 63430}, {63137, 63168}, {64017, 64166}

X(64110) = midpoint of X(i) and X(j) for these {i,j}: {1, 226}, {10, 62822}, {495, 50194}, {1836, 4304}, {2099, 31397}, {18389, 64041}, {24929, 39542}
X(64110) = reflection of X(i) in X(j) for these {i,j}: {10, 58463}, {942, 58626}, {5745, 1125}, {13405, 5719}, {34790, 58699}, {54288, 3634}, {62852, 5045}
X(64110) = X(i)-complementary conjugate of X(j) for these {i, j}: {3577, 3454}, {50442, 21245}, {55938, 141}
X(64110) = pole of line {522, 4707} with respect to the incircle
X(64110) = pole of line {65, 4304} with respect to the Feuerbach hyperbola
X(64110) = pole of line {4560, 14837} with respect to the Steiner inellipse
X(64110) = pole of line {57, 2245} with respect to the dual conic of Yff parabola
X(64110) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(55091)}}, {{A, B, C, X(102), X(14547)}}, {{A, B, C, X(278), X(55090)}}, {{A, B, C, X(515), X(60041)}}, {{A, B, C, X(3486), X(54972)}}, {{A, B, C, X(5745), X(39768)}}, {{A, B, C, X(23987), X(58993)}}
X(64110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10106, 13607}, {1, 11522, 1058}, {1, 12047, 950}, {1, 12053, 40270}, {1, 13407, 10106}, {1, 1699, 3488}, {1, 226, 515}, {1, 3485, 946}, {1, 3487, 21620}, {1, 388, 5882}, {1, 5290, 944}, {1, 9612, 3486}, {36, 11551, 553}, {65, 13411, 6684}, {354, 15950, 44675}, {354, 64041, 18389}, {495, 50194, 519}, {517, 5719, 13405}, {551, 5542, 999}, {758, 1125, 5745}, {912, 5045, 62852}, {942, 16137, 12563}, {942, 37737, 1125}, {950, 12047, 18483}, {1125, 12563, 942}, {1125, 18249, 6675}, {1385, 6147, 4298}, {1836, 4304, 28150}, {2099, 17718, 31397}, {2099, 31397, 28234}, {2646, 3649, 4292}, {3486, 9612, 31673}, {3601, 4295, 31730}, {3616, 11036, 3333}, {3622, 11037, 61762}, {3636, 12577, 24928}, {3754, 59719, 63990}, {4293, 13384, 51705}, {4312, 53054, 376}, {4654, 13384, 4293}, {5219, 18391, 10175}, {5425, 37701, 1737}, {5727, 10590, 50796}, {5886, 15934, 11019}, {10404, 34471, 4311}, {12559, 26363, 24391}, {12563, 37737, 64124}, {12609, 22836, 57284}, {12635, 28628, 10}, {24929, 39542, 516}, {41870, 61762, 11037}

X(64111) = ANTICOMPLEMENT OF X(22753)

Barycentrics    a^7-a^6*(b+c)-a^5*(b+c)^2+a*(b-c)^4*(b+c)^2-(b-c)^4*(b+c)^3-a^3*(b+c)^2*(b^2-6*b*c+c^2)+a^4*(b^3-5*b^2*c-5*b*c^2+c^3)+a^2*(b-c)^2*(b^3+7*b^2*c+7*b*c^2+c^3) : :
X(64111) =

X(64111) lies on these lines: {1, 6865}, {2, 3428}, {3, 388}, {4, 9}, {5, 19855}, {8, 3427}, {12, 5584}, {20, 100}, {30, 6244}, {35, 59345}, {46, 10629}, {55, 6987}, {56, 6926}, {63, 14647}, {65, 5758}, {80, 55964}, {84, 12527}, {104, 34610}, {165, 1478}, {197, 36029}, {200, 515}, {226, 30503}, {329, 6001}, {347, 56874}, {355, 6851}, {376, 535}, {382, 31777}, {404, 64079}, {411, 5552}, {443, 6684}, {452, 11496}, {496, 8158}, {497, 517}, {498, 6988}, {518, 5768}, {529, 63991}, {631, 10198}, {908, 64150}, {938, 7672}, {944, 3811}, {946, 5084}, {950, 6769}, {956, 37374}, {958, 6847}, {962, 2478}, {993, 6935}, {999, 37364}, {1056, 3576}, {1058, 4342}, {1064, 63089}, {1072, 4000}, {1103, 5930}, {1329, 6848}, {1376, 50701}, {1479, 7991}, {1490, 21075}, {1621, 6992}, {1698, 6864}, {1699, 6939}, {1737, 41338}, {1788, 5709}, {1837, 7957}, {2096, 64129}, {2723, 2742}, {2802, 6903}, {2886, 6844}, {2975, 6890}, {3086, 6922}, {3091, 15908}, {3146, 11826}, {3176, 61178}, {3359, 3474}, {3434, 6840}, {3452, 63992}, {3475, 18443}, {3476, 37611}, {3486, 37531}, {3488, 37569}, {3522, 20060}, {3524, 10197}, {3579, 5229}, {3583, 63468}, {3585, 63469}, {3586, 7994}, {3617, 6895}, {3651, 10786}, {3654, 37820}, {3814, 6969}, {3820, 19541}, {3925, 6843}, {3927, 33899}, {4222, 9911}, {4292, 37560}, {4294, 10306}, {4295, 5812}, {4297, 59722}, {4298, 37526}, {4299, 59326}, {4302, 5537}, {4321, 8726}, {4329, 57810}, {5046, 20070}, {5080, 6925}, {5082, 11362}, {5177, 10894}, {5217, 18962}, {5225, 6928}, {5260, 6837}, {5261, 37108}, {5270, 16192}, {5285, 37028}, {5603, 6947}, {5658, 50528}, {5731, 50371}, {5762, 36279}, {5787, 34790}, {5794, 58637}, {5811, 12688}, {5815, 9799}, {5841, 6948}, {5842, 17784}, {5881, 6743}, {5883, 60895}, {5918, 12678}, {6245, 57279}, {6247, 63435}, {6256, 31730}, {6260, 12565}, {6600, 34619}, {6705, 62824}, {6713, 6891}, {6745, 52026}, {6796, 59591}, {6825, 10588}, {6826, 26040}, {6831, 19843}, {6833, 30478}, {6834, 64008}, {6835, 9780}, {6838, 11681}, {6849, 9956}, {6855, 19854}, {6868, 11248}, {6869, 11499}, {6882, 10589}, {6893, 12699}, {6894, 46933}, {6902, 10531}, {6905, 59572}, {6907, 10590}, {6917, 61524}, {6919, 7681}, {6927, 26364}, {6929, 28174}, {6937, 10599}, {6943, 10527}, {6956, 26363}, {6957, 9812}, {6961, 26286}, {6962, 27529}, {7070, 51375}, {7074, 51421}, {7412, 8193}, {7491, 35448}, {7580, 17757}, {7688, 8164}, {7952, 54295}, {8227, 17559}, {8270, 34231}, {8273, 15888}, {8727, 9708}, {9441, 37716}, {9578, 37551}, {9654, 37424}, {9709, 20420}, {10039, 59340}, {10056, 15931}, {10321, 59317}, {10365, 52097}, {10385, 10679}, {10431, 59387}, {10522, 56288}, {10595, 11014}, {10953, 37567}, {11114, 30513}, {11236, 11495}, {11929, 37401}, {12432, 37625}, {12520, 21077}, {15177, 37441}, {17582, 31423}, {17857, 64144}, {18242, 37421}, {18446, 25568}, {18481, 64116}, {18516, 28146}, {18908, 40659}, {20368, 26929}, {22350, 56821}, {22793, 31797}, {23512, 23600}, {24987, 49183}, {25440, 64075}, {25466, 37407}, {26285, 35250}, {26333, 28194}, {26935, 37384}, {26942, 63436}, {27383, 37837}, {28466, 61533}, {31141, 34618}, {31787, 57282}, {34607, 37000}, {34612, 36999}, {34620, 38759}, {34630, 52836}, {35513, 36984}, {36986, 52398}, {37002, 37403}, {37022, 64120}, {37822, 64130}, {54051, 64083}, {54133, 60975}, {57288, 64074}, {58648, 64107}, {58798, 63962}, {60086, 60158}, {63980, 64081}, {63985, 64002}

X(64111) = midpoint of X(i) and X(j) for these {i,j}: {3586, 7994}
X(64111) = reflection of X(i) in X(j) for these {i,j}: {497, 6827}, {999, 37364}, {2096, 64129}, {3474, 3359}, {3476, 37611}, {4293, 3}, {6948, 35238}, {7982, 4342}, {19541, 3820}, {50701, 1376}, {63992, 3452}, {64130, 37822}
X(64111) = anticomplement of X(22753)
X(64111) = X(i)-Dao conjugate of X(j) for these {i, j}: {22753, 22753}
X(64111) = pole of line {1864, 5252} with respect to the Feuerbach hyperbola
X(64111) = pole of line {101, 2406} with respect to the Yff parabola
X(64111) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(19), X(1295)}}, {{A, B, C, X(281), X(1065)}}, {{A, B, C, X(3345), X(7713)}}, {{A, B, C, X(46878), X(60158)}}
X(64111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 38149, 18406}, {4, 5657, 2550}, {12, 5584, 6908}, {20, 3436, 12667}, {20, 7080, 11500}, {56, 50031, 6926}, {165, 1478, 6916}, {498, 59320, 6988}, {517, 6827, 497}, {1329, 64077, 6848}, {3579, 10526, 6850}, {5080, 9778, 6925}, {5603, 6947, 26105}, {5657, 5759, 40}, {5657, 6361, 48363}, {5812, 31788, 4295}, {5815, 9799, 14872}, {6684, 26332, 443}, {6826, 26446, 26040}, {6840, 59417, 3434}, {6850, 10526, 5229}, {6891, 11249, 7288}, {6903, 12245, 12116}, {6922, 22770, 3086}, {7580, 17757, 64148}, {10310, 11827, 20}, {63985, 64002, 64190}

X(64112) = CENTROID OF X(7)-CROSSPEDAL-OF-X(57)

Barycentrics    a*(3*a^2-b^2+6*b*c-c^2-2*a*(b+c)) : :
X(64112) = 2*X[10]+X[4293], 2*X[57]+X[200], -X[329]+4*X[20103], -X[497]+4*X[6692], 2*X[997]+X[2093], 2*X[999]+X[63137], -4*X[1125]+X[30305], X[3359]+2*X[6911], 2*X[3452]+X[3474], -5*X[3616]+2*X[4342], -4*X[3816]+X[9580], X[7171]+2*X[18491] and many others

X(64112) lies on these lines: {1, 88}, {2, 165}, {3, 38399}, {4, 10270}, {7, 6745}, {8, 3361}, {9, 1155}, {10, 4293}, {11, 31190}, {20, 8582}, {21, 16192}, {31, 23511}, {35, 37282}, {36, 9623}, {40, 392}, {43, 62812}, {46, 936}, {55, 5437}, {56, 1706}, {57, 200}, {63, 5785}, {65, 5438}, {78, 3339}, {142, 5218}, {171, 2999}, {193, 5212}, {210, 3928}, {226, 59572}, {238, 54390}, {269, 9364}, {329, 20103}, {354, 3158}, {355, 13226}, {377, 1698}, {388, 63990}, {405, 35242}, {442, 16113}, {443, 6684}, {452, 12512}, {480, 60955}, {497, 6692}, {513, 2441}, {515, 21164}, {517, 16417}, {519, 64151}, {535, 5131}, {553, 25568}, {612, 46901}, {614, 8056}, {631, 10268}, {658, 9312}, {896, 3973}, {899, 1743}, {902, 60846}, {908, 4312}, {946, 17567}, {960, 5128}, {968, 17124}, {997, 2093}, {999, 63137}, {1001, 35445}, {1004, 5732}, {1103, 3075}, {1125, 30305}, {1201, 45047}, {1329, 9579}, {1385, 17573}, {1420, 5836}, {1490, 59333}, {1512, 6955}, {1621, 31508}, {1697, 10179}, {1707, 2239}, {1709, 61740}, {1722, 37091}, {1730, 11358}, {1750, 35990}, {1768, 64197}, {1788, 57284}, {1836, 30827}, {2077, 37249}, {2094, 5850}, {2136, 3304}, {2270, 2297}, {2475, 7989}, {2478, 64005}, {2550, 3911}, {2771, 5720}, {2829, 5587}, {2886, 31231}, {2951, 36002}, {3011, 4859}, {3035, 5219}, {3052, 16602}, {3062, 61012}, {3085, 12436}, {3149, 12565}, {3174, 60985}, {3218, 5223}, {3219, 30393}, {3243, 3689}, {3246, 39963}, {3305, 9342}, {3333, 5687}, {3336, 54422}, {3338, 6765}, {3340, 59691}, {3359, 6911}, {3452, 3474}, {3475, 59584}, {3487, 59587}, {3501, 4936}, {3523, 11024}, {3550, 5272}, {3576, 3753}, {3577, 50371}, {3579, 16408}, {3600, 6736}, {3601, 3812}, {3616, 4342}, {3617, 53057}, {3624, 6921}, {3634, 5177}, {3646, 16862}, {3671, 27383}, {3679, 64153}, {3680, 20323}, {3683, 51780}, {3698, 5204}, {3729, 5205}, {3731, 4414}, {3740, 3929}, {3742, 4421}, {3744, 5573}, {3749, 17063}, {3751, 56009}, {3752, 5269}, {3816, 9580}, {3826, 37363}, {3848, 4428}, {3870, 10980}, {3872, 13462}, {3873, 64135}, {3877, 36006}, {3880, 40726}, {3922, 34471}, {3957, 30350}, {3961, 18193}, {4061, 37655}, {4187, 41869}, {4188, 7987}, {4190, 5691}, {4191, 10434}, {4294, 9843}, {4295, 6700}, {4297, 37267}, {4298, 7080}, {4326, 10177}, {4402, 50754}, {4418, 26265}, {4423, 63211}, {4511, 18421}, {4640, 7308}, {4652, 5234}, {4847, 5435}, {4869, 50753}, {4881, 30392}, {4882, 62874}, {4902, 32856}, {4915, 54391}, {4917, 62854}, {5010, 37300}, {5044, 54290}, {5082, 64124}, {5084, 31730}, {5122, 9708}, {5126, 40587}, {5217, 5436}, {5221, 11523}, {5250, 17531}, {5255, 11512}, {5268, 17596}, {5275, 9574}, {5277, 9593}, {5283, 31421}, {5290, 5552}, {5316, 5698}, {5330, 58245}, {5338, 57534}, {5432, 25525}, {5440, 11529}, {5534, 37612}, {5537, 43166}, {5542, 63168}, {5563, 12629}, {5708, 41863}, {5745, 26040}, {5790, 19706}, {5819, 8568}, {5853, 31146}, {5856, 6173}, {5881, 17583}, {5886, 17564}, {6175, 19876}, {6205, 54330}, {6244, 16411}, {6690, 41867}, {6691, 50443}, {6762, 32636}, {6796, 8726}, {6872, 25011}, {6905, 30503}, {6915, 63985}, {6918, 12705}, {6919, 51118}, {6933, 19872}, {7171, 18491}, {7174, 17595}, {7290, 16610}, {7292, 16487}, {7982, 17614}, {7991, 17572}, {8167, 63214}, {8227, 13747}, {8256, 37709}, {8257, 60782}, {8581, 51380}, {8727, 25973}, {9337, 17715}, {9350, 62820}, {9441, 16412}, {9458, 53337}, {9578, 37828}, {9588, 24987}, {9589, 41012}, {9612, 26364}, {9614, 10200}, {9616, 31473}, {9709, 37582}, {9776, 13405}, {9814, 60935}, {9819, 63136}, {9957, 63138}, {9965, 21060}, {10241, 10860}, {10310, 12651}, {10382, 11502}, {10856, 37261}, {10857, 35977}, {10914, 61762}, {11019, 17784}, {11108, 31663}, {11231, 17528}, {11246, 28609}, {11329, 35291}, {11372, 17613}, {11499, 37534}, {11500, 37526}, {11518, 56176}, {11680, 31224}, {12560, 37541}, {12650, 37561}, {12699, 25522}, {13587, 58221}, {13588, 17194}, {14022, 52835}, {14439, 40131}, {15254, 61158}, {15599, 25955}, {15733, 61660}, {15829, 37567}, {15931, 37309}, {16059, 37619}, {16208, 24541}, {16451, 61124}, {16469, 17126}, {16485, 37589}, {16496, 18201}, {16589, 31422}, {16832, 32917}, {17022, 17122}, {17151, 17763}, {17529, 31425}, {17532, 54447}, {17566, 34595}, {17577, 61264}, {17619, 18492}, {17642, 58623}, {17721, 43055}, {17728, 24392}, {17768, 31142}, {18229, 32918}, {19329, 61221}, {19877, 37161}, {19925, 37435}, {20196, 24703}, {20292, 30852}, {21454, 64083}, {21620, 59591}, {21625, 56936}, {24174, 37552}, {24280, 62297}, {24309, 33849}, {25005, 37714}, {25557, 35023}, {25590, 29828}, {26229, 53381}, {28043, 51302}, {28522, 29649}, {30282, 54318}, {30567, 32932}, {31018, 60905}, {31140, 61649}, {31673, 57000}, {32845, 55998}, {32916, 37092}, {33144, 59593}, {33153, 63584}, {34123, 61275}, {34247, 62739}, {34607, 64162}, {34790, 37545}, {35238, 50204}, {35595, 36835}, {35613, 63131}, {35994, 55478}, {36277, 37680}, {36603, 42040}, {37248, 59326}, {37278, 39585}, {37524, 41229}, {37553, 37674}, {37684, 49495}, {37764, 48627}, {38057, 46916}, {38460, 53058}, {42819, 61153}, {43151, 60959}, {43182, 61009}, {43290, 49499}, {46684, 54370}, {47742, 57282}, {48696, 51816}, {49446, 62300}, {50240, 61261}, {50843, 61285}, {51066, 51113}, {51415, 64016}, {59415, 61254}, {60982, 61035}

X(64112) = midpoint of X(i) and X(j) for these {i,j}: {57, 46917}
X(64112) = reflection of X(i) in X(j) for these {i,j}: {200, 46917}, {46917, 1376}
X(64112) = perspector of circumconic {{A, B, C, X(3257), X(32040)}}
X(64112) = pole of line {2827, 54261} with respect to the incircle
X(64112) = pole of line {3243, 5048} with respect to the Feuerbach hyperbola
X(64112) = pole of line {52680, 58221} with respect to the Stammler hyperbola
X(64112) = pole of line {908, 5222} with respect to the dual conic of Yff parabola
X(64112) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(4454)}}, {{A, B, C, X(100), X(55993)}}, {{A, B, C, X(106), X(52013)}}, {{A, B, C, X(294), X(46917)}}, {{A, B, C, X(513), X(62695)}}, {{A, B, C, X(1320), X(39959)}}, {{A, B, C, X(4674), X(54668)}}, {{A, B, C, X(5223), X(50836)}}
X(64112) = barycentric product X(i)*X(j) for these (i, j): {1, 4454}
X(64112) = barycentric quotient X(i)/X(j) for these (i, j): {4454, 75}
X(64112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1054, 62695}, {2, 165, 4512}, {2, 9778, 40998}, {10, 15803, 62824}, {40, 474, 8583}, {46, 936, 12526}, {55, 5437, 10582}, {57, 200, 62823}, {57, 46917, 518}, {63, 9352, 53056}, {100, 3306, 1}, {171, 2999, 62842}, {497, 6692, 31249}, {518, 1376, 46917}, {518, 46917, 200}, {1054, 9324, 58863}, {1155, 4413, 9}, {3035, 5880, 5219}, {3149, 37560, 12565}, {3359, 6911, 63992}, {3550, 5272, 62875}, {3579, 16408, 31435}, {3689, 4860, 3243}, {3742, 4421, 10389}, {3753, 16371, 3576}, {3870, 27003, 10980}, {4188, 19860, 7987}, {4190, 24982, 5691}, {4652, 9780, 5234}, {5268, 17596, 62818}, {6904, 26062, 10}, {7308, 63207, 4640}, {8580, 53056, 63}, {16610, 37540, 7290}, {17122, 17594, 17022}, {17619, 50239, 18492}, {17784, 62773, 11019}, {62837, 63142, 11519}

X(64113) = ORTHOLOGY CENTER OF THESE TRIANGLES: K798I AND X(7)-CROSSPEDAL-OF-X(100)

Barycentrics    a^5*(b+c)-(b-c)^4*(b+c)^2+2*a^2*(b-c)^2*(b^2+c^2)-a^4*(b^2-6*b*c+c^2)-2*a^3*(b^3+2*b^2*c+2*b*c^2+c^3)+a*(b^5-b^4*c-b*c^4+c^5) : :
X(64113) = X[40]+3*X[6173], -5*X[631]+X[5698], X[944]+3*X[2550], -X[962]+9*X[59374], -X[1482]+9*X[38065], -5*X[1698]+X[64197], X[4312]+3*X[21153], -X[5220]+3*X[26446], -5*X[8227]+9*X[38093], 5*X[10595]+3*X[35514], -X[11531]+9*X[38024], X[12245]+3*X[51099] and many others

X(64113) lies on circumconic {{A, B, C, X(5553), X(14377)}} and on these lines: {1, 30379}, {2, 1709}, {3, 142}, {4, 43178}, {5, 15726}, {7, 46}, {9, 2252}, {10, 1071}, {35, 63254}, {40, 6173}, {65, 5542}, {72, 61035}, {140, 12608}, {165, 5249}, {226, 1155}, {377, 5691}, {390, 3612}, {442, 38204}, {443, 12520}, {498, 8545}, {517, 25557}, {518, 5690}, {527, 6684}, {528, 1385}, {549, 28534}, {551, 50371}, {631, 5698}, {908, 60905}, {942, 8255}, {944, 2550}, {954, 11509}, {962, 59374}, {971, 3826}, {991, 1738}, {1158, 6989}, {1445, 17700}, {1454, 52819}, {1478, 8544}, {1482, 38065}, {1698, 64197}, {1737, 10394}, {1742, 53599}, {1768, 54357}, {1770, 6986}, {1890, 37117}, {2646, 30331}, {2886, 11227}, {2951, 6836}, {3057, 38055}, {3254, 34486}, {3336, 60932}, {3452, 58441}, {3523, 12047}, {3576, 6955}, {3579, 38454}, {3584, 60952}, {3624, 6966}, {3634, 6260}, {3652, 58449}, {3671, 54205}, {3754, 54178}, {3812, 37424}, {3816, 10156}, {3817, 7965}, {3833, 7682}, {3836, 12618}, {3838, 37364}, {3841, 6245}, {3848, 7956}, {3874, 41570}, {3925, 10167}, {4190, 43161}, {4295, 30275}, {4297, 6253}, {4312, 21153}, {5119, 60926}, {5218, 64115}, {5220, 26446}, {5231, 11407}, {5316, 21635}, {5436, 64076}, {5445, 41700}, {5696, 6734}, {5729, 24914}, {5759, 60991}, {5794, 43176}, {5843, 15481}, {5851, 11231}, {5853, 13607}, {5918, 8226}, {6147, 58637}, {6666, 60911}, {6675, 64128}, {6712, 49631}, {6825, 8257}, {6831, 63973}, {6833, 11372}, {6854, 50528}, {6862, 58433}, {6863, 15297}, {6890, 38037}, {6908, 60987}, {6910, 16209}, {6916, 54318}, {6940, 64154}, {6984, 59389}, {7483, 38059}, {8227, 38093}, {8727, 10178}, {8728, 9943}, {9612, 30353}, {9746, 51400}, {9778, 27186}, {9809, 35595}, {9842, 50740}, {9940, 10916}, {10177, 15908}, {10198, 37560}, {10269, 42842}, {10572, 37163}, {10595, 35514}, {10860, 41867}, {11019, 17603}, {11531, 38024}, {12005, 61030}, {12053, 37600}, {12245, 51099}, {12514, 37407}, {12573, 59317}, {12645, 38121}, {12647, 30318}, {12679, 16842}, {12688, 17529}, {12704, 54158}, {13257, 61686}, {13329, 50307}, {13405, 37541}, {13750, 30329}, {14110, 38054}, {15064, 41561}, {15299, 60925}, {15570, 61597}, {15931, 36003}, {16112, 38108}, {16203, 42886}, {17167, 35997}, {17528, 19925}, {17768, 22937}, {18450, 45287}, {18482, 38172}, {19862, 63266}, {20070, 59340}, {20330, 38111}, {21075, 44785}, {21620, 36279}, {22768, 42884}, {25466, 31787}, {25993, 39531}, {26363, 37526}, {27385, 60885}, {27529, 60935}, {30332, 30384}, {30340, 59417}, {31019, 64108}, {31419, 58567}, {31777, 51715}, {33149, 54474}, {36866, 38130}, {36976, 59316}, {36996, 38057}, {37356, 42356}, {37428, 38094}, {37462, 63988}, {37606, 63993}, {37612, 54203}, {38030, 42871}, {41012, 50836}, {41555, 49627}, {41861, 63265}, {42819, 51700}, {48888, 59688}, {51102, 61296}, {55104, 61011}, {59318, 60980}, {59637, 62673}

X(64113) = midpoint of X(i) and X(j) for these {i,j}: {3, 5880}, {4, 43178}, {9, 60896}, {10, 43177}, {40, 60895}, {5805, 11495}, {6916, 54318}, {19925, 43181}, {43174, 43180}, {43182, 63970}, {54370, 63971}
X(64113) = reflection of X(i) in X(j) for these {i,j}: {15254, 140}, {42356, 61595}, {60911, 6666}, {60912, 6684}
X(64113) = complement of X(54370)
X(64113) = pole of line {3887, 48012} with respect to the excircles-radical circle
X(64113) = pole of line {21185, 47887} with respect to the incircle
X(64113) = pole of line {3935, 44435} with respect to the orthoptic circle of the Steiner Inellipse
X(64113) = pole of line {6, 7190} with respect to the dual conic of Yff parabola
X(64113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 63971, 54370}, {3, 5880, 516}, {10, 43177, 2801}, {40, 6173, 60895}, {142, 5880, 12609}, {527, 6684, 60912}, {3836, 59620, 12618}, {8728, 9943, 12617}, {10394, 30312, 1737}, {21620, 61022, 43180}, {31590, 31591, 5074}, {33428, 33429, 34847}, {37438, 40296, 12616}, {38204, 43182, 63970}, {60925, 61019, 15299}

X(64114) = ISOTOMIC CONJUGATE OF X(38255)

Barycentrics    (5*a-3*(b+c))*(a+b-c)*(a-b+c) : :

X(64114) lies on these lines: {1, 10303}, {2, 7}, {3, 5704}, {4, 5122}, {8, 1319}, {10, 4308}, {11, 9778}, {36, 59387}, {56, 9780}, {65, 3848}, {77, 23511}, {140, 5703}, {145, 59584}, {165, 5274}, {190, 6557}, {222, 37680}, {241, 16602}, {278, 39962}, {279, 31183}, {348, 31189}, {388, 19877}, {390, 10164}, {479, 37757}, {484, 499}, {497, 61649}, {498, 11037}, {547, 18541}, {549, 3488}, {631, 938}, {632, 5708}, {651, 37679}, {653, 17917}, {658, 31192}, {673, 38254}, {748, 9364}, {942, 3525}, {944, 11545}, {950, 15717}, {997, 5775}, {1000, 50821}, {1056, 11231}, {1058, 51787}, {1125, 4323}, {1155, 9812}, {1210, 3523}, {1376, 7677}, {1387, 50810}, {1388, 20050}, {1420, 3617}, {1429, 29579}, {1442, 2999}, {1443, 54390}, {1458, 16569}, {1465, 18624}, {1466, 5047}, {1471, 17122}, {1479, 5442}, {1532, 54052}, {1538, 14646}, {1698, 3600}, {1737, 5731}, {1788, 2099}, {1876, 38282}, {1892, 52299}, {1997, 3161}, {2003, 14997}, {2886, 30312}, {3008, 3160}, {3035, 14151}, {3085, 51816}, {3086, 5119}, {3090, 37582}, {3091, 15803}, {3146, 51792}, {3158, 12630}, {3212, 31225}, {3241, 40663}, {3339, 19862}, {3340, 46934}, {3361, 3634}, {3474, 9779}, {3476, 5298}, {3487, 3526}, {3522, 9581}, {3524, 5722}, {3533, 11374}, {3579, 47743}, {3582, 30305}, {3586, 10304}, {3587, 6926}, {3601, 61820}, {3621, 63208}, {3622, 4848}, {3628, 5714}, {3660, 3681}, {3669, 63246}, {3671, 34595}, {3742, 7672}, {3748, 5218}, {3772, 31201}, {3816, 52653}, {3817, 53056}, {3832, 51790}, {3876, 37566}, {3947, 19872}, {4021, 31326}, {4188, 5175}, {4292, 5056}, {4304, 15692}, {4307, 49631}, {4312, 10171}, {4315, 19875}, {4318, 5272}, {4322, 6048}, {4344, 24239}, {4345, 44675}, {4383, 17074}, {4552, 17490}, {4652, 6919}, {4661, 5083}, {4855, 12536}, {4860, 5326}, {4887, 33795}, {5054, 15933}, {5067, 57282}, {5068, 9579}, {5070, 24470}, {5123, 34610}, {5126, 59388}, {5204, 7319}, {5221, 7294}, {5222, 24581}, {5228, 37682}, {5281, 8236}, {5284, 37541}, {5290, 51073}, {5393, 17805}, {5405, 17802}, {5432, 10578}, {5493, 50444}, {5543, 29571}, {5657, 15325}, {5658, 5825}, {5686, 20103}, {5692, 18419}, {5705, 17580}, {5719, 15694}, {5728, 10156}, {5758, 6958}, {5768, 6880}, {5804, 6977}, {5811, 6959}, {5815, 26364}, {5927, 11575}, {5936, 18229}, {6147, 46219}, {6223, 6834}, {6244, 53055}, {6610, 37650}, {6667, 63975}, {6684, 14986}, {6700, 54398}, {6762, 27525}, {6764, 59591}, {6767, 61614}, {6891, 37584}, {6927, 9799}, {6954, 13151}, {7176, 16832}, {7269, 17022}, {7292, 8270}, {7486, 9612}, {7991, 18220}, {8051, 31227}, {8055, 37758}, {8056, 36640}, {8165, 62824}, {8167, 8543}, {8581, 58451}, {8583, 18231}, {8972, 51842}, {9316, 17123}, {9578, 46932}, {9843, 17558}, {10106, 46933}, {10178, 17604}, {10394, 11227}, {10527, 26062}, {10529, 12541}, {10571, 27625}, {10588, 32636}, {10591, 58887}, {11020, 61660}, {11024, 26363}, {11036, 61856}, {11041, 38028}, {11518, 61848}, {11530, 61630}, {11812, 15935}, {12433, 15720}, {12690, 19705}, {13405, 30350}, {13411, 55864}, {13941, 51841}, {14189, 36620}, {14256, 31185}, {14829, 32099}, {14996, 52423}, {15104, 18240}, {16408, 57283}, {16577, 26742}, {16610, 17080}, {17020, 45126}, {17081, 31994}, {17091, 43063}, {17092, 31197}, {17093, 31203}, {17277, 40420}, {17566, 27383}, {17572, 37583}, {17625, 63961}, {18391, 37525}, {18623, 43043}, {18625, 31204}, {18633, 31215}, {19843, 58405}, {20057, 41687}, {20070, 50443}, {20182, 37634}, {21578, 50864}, {22464, 24175}, {24471, 63119}, {24599, 25718}, {25255, 53042}, {25502, 42289}, {25568, 62710}, {25934, 62243}, {26007, 31527}, {26015, 64146}, {26129, 56288}, {26446, 51788}, {27818, 36621}, {28346, 51766}, {29627, 32003}, {29628, 43054}, {30318, 62218}, {30331, 50829}, {30384, 34632}, {30608, 63164}, {31187, 37800}, {31232, 31598}, {31272, 44447}, {31273, 34929}, {31423, 64124}, {31721, 50114}, {32079, 58904}, {32087, 55095}, {34048, 37687}, {36638, 45202}, {37364, 59418}, {37520, 41825}, {37578, 60782}, {37633, 52424}, {37681, 45204}, {37723, 61816}, {37771, 43055}, {41539, 64149}, {41802, 41803}, {41806, 41808}, {43037, 59601}, {45675, 53544}, {46931, 51789}, {47761, 57167}, {51302, 62788}, {51578, 51795}, {51781, 63990}, {56331, 60733}, {61686, 63994}, {62208, 62695}, {63261, 63263}

X(64114) = isotomic conjugate of X(38255)
X(64114) = complement of X(46873)
X(64114) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 38255}, {41, 36606}, {55, 36603}, {650, 8699}, {1253, 36621}, {2175, 40026}, {3063, 58131}
X(64114) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 38255}, {145, 3161}, {223, 36603}, {3160, 36606}, {10001, 58131}, {17113, 36621}, {40593, 40026}
X(64114) = X(i)-Ceva conjugate of X(j) for these {i, j}: {27818, 7}
X(64114) = X(i)-cross conjugate of X(j) for these {i, j}: {3973, 3621}
X(64114) = pole of line {100, 13252} with respect to the Yff parabola
X(64114) = pole of line {333, 5328} with respect to the Wallace hyperbola
X(64114) = pole of line {1, 5056} with respect to the dual conic of Yff parabola
X(64114) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3621)}}, {{A, B, C, X(8), X(30827)}}, {{A, B, C, X(9), X(3973)}}, {{A, B, C, X(57), X(63163)}}, {{A, B, C, X(63), X(39962)}}, {{A, B, C, X(75), X(45789)}}, {{A, B, C, X(144), X(42318)}}, {{A, B, C, X(189), X(30852)}}, {{A, B, C, X(333), X(5328)}}, {{A, B, C, X(527), X(4962)}}, {{A, B, C, X(672), X(2516)}}, {{A, B, C, X(673), X(20059)}}, {{A, B, C, X(1255), X(3306)}}, {{A, B, C, X(1400), X(38296)}}, {{A, B, C, X(3452), X(56201)}}, {{A, B, C, X(3911), X(8051)}}, {{A, B, C, X(3928), X(8056)}}, {{A, B, C, X(3929), X(39963)}}, {{A, B, C, X(3982), X(60085)}}, {{A, B, C, X(4072), X(5257)}}, {{A, B, C, X(4373), X(33800)}}, {{A, B, C, X(4998), X(16078)}}, {{A, B, C, X(5219), X(63164)}}, {{A, B, C, X(5226), X(40420)}}, {{A, B, C, X(5435), X(36621)}}, {{A, B, C, X(5748), X(34234)}}, {{A, B, C, X(6692), X(7320)}}, {{A, B, C, X(9436), X(38254)}}, {{A, B, C, X(18228), X(30608)}}, {{A, B, C, X(25417), X(27003)}}, {{A, B, C, X(36620), X(51351)}}, {{A, B, C, X(56054), X(58463)}}
X(64114) = barycentric product X(i)*X(j) for these (i, j): {1434, 4072}, {2516, 4554}, {3621, 7}, {3973, 85}, {4572, 58154}, {4573, 59589}, {4962, 664}, {20942, 57}, {21000, 6063}, {22147, 331}, {38296, 76}, {63208, 75}
X(64114) = barycentric quotient X(i)/X(j) for these (i, j): {2, 38255}, {7, 36606}, {57, 36603}, {85, 40026}, {109, 8699}, {279, 36621}, {664, 58131}, {2516, 650}, {3621, 8}, {3973, 9}, {4072, 2321}, {4962, 522}, {20942, 312}, {21000, 55}, {22147, 219}, {38296, 6}, {58154, 663}, {59589, 3700}, {63208, 1}
X(64114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21454, 5219}, {2, 3218, 5748}, {2, 3911, 5435}, {2, 5435, 7}, {2, 57, 5226}, {2, 5744, 18228}, {2, 5745, 18230}, {2, 63, 5328}, {10, 5265, 4308}, {57, 3982, 21454}, {57, 5219, 3982}, {165, 5274, 30332}, {1155, 10589, 9812}, {1210, 3523, 4313}, {1788, 5433, 3616}, {3361, 3634, 5261}, {3526, 34753, 3487}, {3628, 37545, 5714}, {5218, 17728, 10580}, {5226, 5435, 57}, {5281, 11019, 8236}, {7288, 24914, 8}, {31187, 43056, 37800}

X(64115) = TRIPOLE OF PERSPECTIVITY AXIS OF THESE TRIANGLES: X(8)-CROSSPEDAL-OF-X(1) AND FUHRMANN

Barycentrics    (a+b-c)*(a-b+c)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+c^2)) : :

X(64115) lies on these lines: {1, 6850}, {2, 7}, {4, 34489}, {5, 37566}, {11, 971}, {12, 3824}, {30, 1319}, {34, 24159}, {56, 3560}, {65, 495}, {73, 23537}, {85, 20920}, {104, 1519}, {109, 3011}, {119, 912}, {222, 3772}, {223, 23681}, {225, 4306}, {278, 4341}, {354, 64127}, {388, 12609}, {499, 7330}, {514, 3064}, {516, 2078}, {518, 51416}, {614, 34029}, {651, 33129}, {675, 32689}, {902, 60718}, {914, 48380}, {920, 10052}, {942, 6842}, {946, 1420}, {950, 18444}, {1086, 1465}, {1155, 5762}, {1210, 6941}, {1214, 3782}, {1412, 17167}, {1441, 20887}, {1442, 33155}, {1443, 37798}, {1444, 17182}, {1456, 15253}, {1458, 3120}, {1466, 11374}, {1467, 6893}, {1471, 24725}, {1479, 41854}, {1512, 12736}, {1617, 1836}, {1738, 4551}, {1758, 32857}, {1770, 7702}, {1788, 21077}, {1877, 30117}, {2003, 40940}, {2006, 34050}, {2635, 53599}, {2886, 17625}, {3057, 37424}, {3086, 12608}, {3256, 13405}, {3340, 21620}, {3485, 51706}, {3487, 6897}, {3811, 41540}, {3838, 63994}, {3912, 38468}, {3927, 24914}, {4000, 56418}, {4292, 6906}, {4298, 11263}, {4304, 37430}, {4318, 33148}, {4861, 10106}, {5045, 49107}, {5057, 7677}, {5083, 26015}, {5126, 38032}, {5137, 36059}, {5218, 64113}, {5252, 17528}, {5433, 31445}, {5443, 13370}, {5714, 6898}, {5727, 64147}, {5731, 12053}, {5768, 6260}, {5770, 6981}, {5805, 64152}, {5832, 37240}, {5843, 61649}, {5853, 37736}, {6180, 37695}, {6357, 6610}, {6831, 64132}, {6848, 11023}, {6868, 37618}, {6917, 45287}, {6940, 13411}, {6961, 15803}, {7011, 18588}, {7125, 18651}, {7175, 34830}, {7269, 37635}, {7284, 23708}, {7288, 21616}, {7741, 61740}, {7743, 51774}, {8270, 33144}, {8727, 63995}, {9316, 33127}, {9364, 17719}, {9580, 43161}, {10320, 45639}, {10321, 59333}, {10395, 12528}, {10400, 16580}, {10404, 22759}, {10571, 23536}, {10572, 18961}, {11376, 41426}, {11509, 63259}, {12709, 25466}, {13161, 37558}, {13462, 18393}, {13601, 15888}, {15528, 34293}, {15845, 17626}, {15908, 50196}, {16610, 52659}, {17074, 33133}, {17080, 33146}, {17603, 31657}, {17718, 37541}, {17862, 45206}, {17923, 37136}, {18467, 63987}, {18541, 28444}, {18593, 22464}, {19785, 45126}, {24789, 34048}, {24929, 28458}, {25558, 41556}, {26011, 26932}, {30284, 64162}, {30305, 37427}, {30312, 63961}, {31776, 33592}, {33136, 53531}, {34371, 51410}, {34529, 38459}, {34855, 57442}, {37163, 63274}, {39542, 64106}, {40663, 51362}, {41011, 55086}, {44425, 64155}, {50443, 63989}, {52212, 53546}, {52456, 61231}, {54408, 60924}

X(64115) = midpoint of X(i) and X(j) for these {i,j}: {37136, 56869}
X(64115) = trilinear pole of line {12832, 55126}
X(64115) = perspector of circumconic {{A, B, C, X(273), X(664)}}
X(64115) = center of circumconic {{A, B, C, X(37136), X(56869)}}
X(64115) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 45393}, {8, 32655}, {9, 36052}, {55, 2990}, {78, 913}, {100, 61214}, {212, 37203}, {219, 915}, {220, 63190}, {521, 32698}, {652, 36106}, {3657, 5546}, {39173, 52663}, {46133, 52425}
X(64115) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 45393}, {119, 9}, {223, 2990}, {478, 36052}, {8054, 61214}, {8609, 6735}, {39002, 652}, {40837, 37203}, {42769, 2170}, {56761, 61238}, {62602, 46133}
X(64115) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7, 11570}, {17923, 34050}, {37136, 514}
X(64115) = X(i)-complementary conjugate of X(j) for these {i, j}: {46435, 141}
X(64115) = X(i)-cross conjugate of X(j) for these {i, j}: {8609, 1737}
X(64115) = pole of line {3668, 3676} with respect to the incircle
X(64115) = pole of line {9, 3064} with respect to the polar circle
X(64115) = pole of line {11570, 14100} with respect to the Feuerbach hyperbola
X(64115) = pole of line {522, 12649} with respect to the Steiner circumellipse
X(64115) = pole of line {522, 1210} with respect to the Steiner inellipse
X(64115) = pole of line {3719, 6332} with respect to the dual conic of polar circle
X(64115) = pole of line {1, 104} with respect to the dual conic of Yff parabola
X(64115) = pole of line {8611, 21044} with respect to the dual conic of Wallace hyperbola
X(64115) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1737)}}, {{A, B, C, X(9), X(3064)}}, {{A, B, C, X(57), X(18838)}}, {{A, B, C, X(63), X(514)}}, {{A, B, C, X(104), X(12665)}}, {{A, B, C, X(119), X(908)}}, {{A, B, C, X(278), X(5905)}}, {{A, B, C, X(307), X(4077)}}, {{A, B, C, X(329), X(59935)}}, {{A, B, C, X(527), X(12831)}}, {{A, B, C, X(579), X(57173)}}, {{A, B, C, X(675), X(33864)}}, {{A, B, C, X(1025), X(5236)}}, {{A, B, C, X(1400), X(55208)}}, {{A, B, C, X(1708), X(4564)}}, {{A, B, C, X(2051), X(30852)}}, {{A, B, C, X(3218), X(11570)}}, {{A, B, C, X(3306), X(17758)}}, {{A, B, C, X(3911), X(12832)}}, {{A, B, C, X(5249), X(23595)}}, {{A, B, C, X(5744), X(14266)}}, {{A, B, C, X(7130), X(56549)}}, {{A, B, C, X(8257), X(27475)}}, {{A, B, C, X(26743), X(54357)}}, {{A, B, C, X(37131), X(60974)}}, {{A, B, C, X(38461), X(56543)}}, {{A, B, C, X(40152), X(51649)}}, {{A, B, C, X(53337), X(56881)}}, {{A, B, C, X(55871), X(56231)}}
X(64115) = barycentric product X(i)*X(j) for these (i, j): {85, 8609}, {264, 51649}, {273, 912}, {278, 914}, {1737, 7}, {2252, 331}, {3658, 4077}, {3676, 56881}, {11570, 18815}, {12831, 62723}, {12832, 903}, {14266, 22464}, {18838, 75}, {24002, 61239}, {46107, 56410}, {48380, 57}, {52456, 9436}, {55126, 664}, {61231, 693}
X(64115) = barycentric quotient X(i)/X(j) for these (i, j): {1, 45393}, {34, 915}, {56, 36052}, {57, 2990}, {108, 36106}, {109, 6099}, {119, 6735}, {269, 63190}, {273, 46133}, {278, 37203}, {604, 32655}, {608, 913}, {649, 61214}, {912, 78}, {914, 345}, {1457, 39173}, {1737, 8}, {2252, 219}, {3658, 643}, {4017, 3657}, {8609, 9}, {11570, 4511}, {12831, 6745}, {12832, 519}, {14266, 51565}, {18838, 1}, {32674, 32698}, {41552, 10916}, {48380, 312}, {51649, 3}, {51824, 2342}, {52456, 14942}, {53314, 61043}, {55126, 522}, {56410, 1331}, {56881, 3699}, {61231, 100}, {61239, 644}
X(64115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {142, 226, 5219}, {226, 3911, 908}, {7702, 37579, 1770}, {21578, 33593, 30384}

X(64116) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(8)-CROSSPEDAL-OF-X(1) AND CEVIAN OF X(84)

Barycentrics    a*(2*a^6-3*a^5*(b+c)-2*a^2*b*c*(b+c)^2+(b-c)^2*(b+c)^4-3*a^4*(b^2+c^2)-a*(b-c)^2*(3*b^3+7*b^2*c+7*b*c^2+3*c^3)+a^3*(6*b^3+4*b^2*c+4*b*c^2+6*c^3)) : :
X(64116) = -X[1158]+3*X[4421], X[1490]+3*X[3158], X[3189]+3*X[64148], -X[5812]+3*X[25568], -X[6245]+3*X[59584], -2*X[9955]+3*X[37713], -2*X[10943]+3*X[11230], -3*X[17502]+2*X[32153], 3*X[34607]+X[63962]

X(64116) lies on these lines: {1, 6918}, {3, 200}, {4, 63168}, {5, 13405}, {8, 6988}, {10, 140}, {21, 18908}, {35, 5531}, {40, 3689}, {55, 1898}, {72, 11491}, {78, 31786}, {100, 1071}, {153, 11015}, {210, 10902}, {228, 15623}, {355, 3085}, {392, 64173}, {411, 3935}, {480, 51489}, {515, 12607}, {516, 18243}, {517, 3811}, {518, 6796}, {519, 37837}, {528, 12608}, {580, 4849}, {912, 3579}, {942, 11499}, {944, 5440}, {971, 6600}, {1006, 3697}, {1158, 4421}, {1319, 61296}, {1376, 9940}, {1483, 6738}, {1490, 3158}, {1872, 56316}, {2077, 12680}, {2095, 41863}, {2646, 5881}, {2801, 64118}, {3057, 6326}, {3149, 3870}, {3174, 64156}, {3189, 64148}, {3295, 5720}, {3419, 10786}, {3517, 7719}, {3555, 6905}, {3560, 9947}, {3625, 51717}, {3694, 64121}, {3744, 37732}, {3748, 8227}, {3871, 12672}, {3880, 40257}, {3893, 11014}, {3957, 6915}, {4018, 48363}, {4294, 37822}, {4420, 64107}, {4533, 26878}, {4640, 63967}, {4847, 52265}, {4857, 5660}, {5044, 10267}, {5045, 6911}, {5248, 58631}, {5266, 37699}, {5587, 37080}, {5687, 18446}, {5690, 6743}, {5693, 37568}, {5731, 56879}, {5768, 59591}, {5780, 31435}, {5790, 24299}, {5806, 18491}, {5812, 25568}, {5815, 59345}, {5840, 22792}, {5842, 21077}, {5887, 12738}, {6001, 8715}, {6244, 41854}, {6245, 59584}, {6260, 64117}, {6745, 6922}, {6765, 22770}, {6769, 37411}, {6864, 10578}, {6865, 64083}, {6907, 63146}, {6927, 36845}, {6929, 31795}, {6970, 18391}, {7680, 10942}, {7686, 10222}, {7958, 63287}, {7967, 17614}, {8726, 46917}, {9709, 18443}, {9856, 10679}, {9955, 37713}, {9956, 10198}, {9957, 45770}, {10157, 63271}, {10175, 51715}, {10246, 16863}, {10572, 37725}, {10884, 64135}, {10914, 21740}, {10943, 11230}, {11249, 40262}, {11501, 50195}, {11502, 50196}, {11508, 64131}, {11517, 51380}, {11849, 40263}, {12053, 41553}, {12331, 37562}, {12432, 24475}, {12616, 64123}, {12675, 25440}, {12704, 41711}, {12751, 41541}, {13528, 15071}, {13600, 63986}, {15178, 54318}, {17502, 32153}, {17606, 49176}, {18481, 64111}, {18518, 37533}, {18524, 24474}, {18525, 33596}, {19904, 20760}, {20323, 61291}, {21075, 31789}, {21620, 37281}, {24467, 31663}, {25081, 58382}, {25439, 45776}, {25917, 34486}, {26285, 34862}, {28204, 45701}, {29670, 36477}, {31445, 32613}, {31658, 40659}, {31805, 35238}, {31821, 51787}, {33595, 34627}, {34607, 63962}, {35016, 38155}, {37000, 58798}, {37571, 37712}, {37582, 41539}, {37594, 37698}, {37733, 50194}, {55108, 63282}, {56762, 64198}, {59326, 63432}, {59329, 63995}, {59719, 63980}

X(64116) = midpoint of X(i) and X(j) for these {i,j}: {3, 5534}, {1490, 10306}, {3174, 64156}, {3811, 11500}, {3913, 6261}, {6260, 64117}, {6765, 22770}, {6769, 37411}
X(64116) = reflection of X(i) in X(j) for these {i,j}: {3579, 32141}, {11249, 40262}, {12616, 64123}, {18480, 10942}, {24467, 31663}, {34862, 26285}, {37623, 6796}, {63980, 59719}
X(64116) = pole of line {1728, 7982} with respect to the Feuerbach hyperbola
X(64116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 200, 58643}, {35, 5531, 14872}, {55, 17857, 5777}, {518, 6796, 37623}, {912, 32141, 3579}, {1490, 3158, 10306}, {3811, 11500, 517}, {5687, 18446, 31788}, {5882, 59691, 1385}, {6765, 52026, 22770}

X(64117) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(8)-CROSSPEDAL-OF-X(1) AND CEVIAN OF X(273)

Barycentrics    4*a^4-a^3*(b+c)-3*a^2*(b+c)^2+a*(b+c)^3-(b^2-c^2)^2 : :
X(64117) = -X[4]+3*X[3158], -2*X[5]+3*X[59584], -4*X[140]+3*X[24386], -5*X[631]+3*X[24392], -5*X[3522]+X[6764], -3*X[3576]+X[64068], -X[3680]+3*X[7967], -2*X[3813]+3*X[10165], -3*X[4421]+2*X[6684], -3*X[5657]+X[12625], -X[5691]+3*X[34619], -3*X[5731]+X[12629]

X(64117) lies on circumconic {{A, B, C, X(39697), X(56146)}} and on these lines: {1, 6904}, {2, 51724}, {3, 5853}, {4, 3158}, {5, 59584}, {8, 3977}, {10, 55}, {11, 59587}, {19, 3950}, {20, 6765}, {35, 4847}, {40, 376}, {65, 1317}, {78, 10624}, {100, 1210}, {140, 24386}, {145, 2093}, {149, 27385}, {200, 4294}, {210, 63273}, {380, 17355}, {386, 63969}, {390, 936}, {443, 10389}, {474, 64162}, {497, 6700}, {515, 3913}, {516, 1490}, {517, 9942}, {518, 31730}, {527, 34707}, {528, 946}, {551, 17614}, {631, 24392}, {678, 21935}, {758, 5493}, {910, 21096}, {952, 12640}, {975, 63977}, {997, 12575}, {1058, 1125}, {1066, 35338}, {1376, 9843}, {1385, 21627}, {1479, 6745}, {1706, 3488}, {1855, 21090}, {2264, 59579}, {2478, 64135}, {2900, 37000}, {2901, 3198}, {3059, 3678}, {3073, 3939}, {3295, 57284}, {3434, 13411}, {3452, 15171}, {3474, 41863}, {3486, 63137}, {3522, 6764}, {3576, 64068}, {3579, 24391}, {3586, 7080}, {3601, 5082}, {3625, 37568}, {3633, 21578}, {3635, 11529}, {3636, 28629}, {3646, 47357}, {3680, 7967}, {3689, 6284}, {3722, 23536}, {3755, 5266}, {3779, 50590}, {3813, 10165}, {3817, 6896}, {3820, 31795}, {3868, 63145}, {3870, 4292}, {3871, 31397}, {3874, 64132}, {3880, 5882}, {3925, 19862}, {3935, 20066}, {4101, 4450}, {4301, 22836}, {4302, 12527}, {4305, 4853}, {4309, 40998}, {4313, 9623}, {4342, 30144}, {4349, 59301}, {4356, 30142}, {4421, 6684}, {4432, 59685}, {4669, 17525}, {4855, 44675}, {4863, 5217}, {5044, 10386}, {5049, 17563}, {5084, 41864}, {5119, 6737}, {5175, 31434}, {5267, 37601}, {5281, 5705}, {5415, 49548}, {5416, 49547}, {5440, 12053}, {5528, 30424}, {5584, 8666}, {5657, 12625}, {5691, 34619}, {5722, 63990}, {5731, 12629}, {5732, 7674}, {6245, 11248}, {6253, 21077}, {6260, 64116}, {6361, 11523}, {6600, 11496}, {6675, 61031}, {6736, 10572}, {6738, 54286}, {6743, 12514}, {7682, 11499}, {7987, 34625}, {8236, 17580}, {8728, 63271}, {9581, 59591}, {9612, 63168}, {9614, 27383}, {9778, 54422}, {9858, 9957}, {9945, 24928}, {10107, 14563}, {10164, 10902}, {10175, 64123}, {10246, 64205}, {10268, 43174}, {10385, 31435}, {10912, 13607}, {10915, 12751}, {11019, 25440}, {11260, 51705}, {11362, 44669}, {11406, 49542}, {11500, 52804}, {11849, 51755}, {12513, 22777}, {12536, 59417}, {12607, 31673}, {12616, 13205}, {12635, 28194}, {13464, 56177}, {15733, 54175}, {15803, 36845}, {16842, 46916}, {16845, 38200}, {17558, 59413}, {17647, 25439}, {17715, 24178}, {17857, 59687}, {18527, 47742}, {19133, 59408}, {19925, 45701}, {20095, 34772}, {20323, 34699}, {21616, 51783}, {24393, 31445}, {24477, 35242}, {24850, 49529}, {25524, 40270}, {25568, 41869}, {26066, 61153}, {28236, 49169}, {30282, 64081}, {31728, 34372}, {32157, 38127}, {33597, 34709}, {34611, 41012}, {36977, 51786}, {37462, 62856}, {37579, 49627}, {37700, 54198}, {41575, 63136}, {43166, 50700}, {49732, 51715}, {49772, 54354}, {50739, 51102}, {52541, 53534}, {59388, 64204}, {59678, 59728}, {59691, 63993}, {62836, 63130}

X(64117) = midpoint of X(i) and X(j) for these {i,j}: {20, 6765}, {40, 3189}, {145, 64202}, {944, 2136}, {2900, 37000}, {5732, 7674}, {6361, 11523}, {12629, 12632}
X(64117) = reflection of X(i) in X(j) for these {i,j}: {4, 59722}, {10, 8715}, {946, 56176}, {4301, 22836}, {6245, 11248}, {6260, 64116}, {10912, 13607}, {21627, 1385}, {24391, 3579}, {31673, 12607}, {49168, 43174}, {51118, 21077}, {54198, 37700}, {62858, 12512}, {63970, 6600}
X(64117) = pole of line {329, 24789} with respect to the dual conic of Yff parabola
X(64117) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {20, 6765, 6790}
X(64117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3158, 59722}, {20, 64146, 6765}, {40, 3189, 519}, {55, 63146, 10}, {78, 20075, 10624}, {100, 1210, 59675}, {200, 4294, 12572}, {519, 12512, 62858}, {528, 56176, 946}, {1058, 5438, 1125}, {1376, 63999, 9843}, {2136, 34701, 944}, {3174, 6769, 3811}, {3189, 34607, 40}, {3689, 6284, 21075}, {3871, 57287, 31397}, {3935, 20066, 64002}, {5731, 12632, 12629}, {10572, 48696, 6736}, {41864, 46917, 5084}

X(64118) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTERS-MIDPOINTS AND X(8)-CROSSPEDAL-OF-X(3)

Barycentrics    a*(2*a^6-a^5*(b+c)-a*(b-c)^2*(b+c)^3+a^4*(-5*b^2+4*b*c-5*c^2)-(b^2-c^2)^2*(b^2+c^2)+4*a^2*(b-c)^2*(b^2+b*c+c^2)+2*a^3*(b^3+b^2*c+b*c^2+c^3)) : :
X(64118) = -3*X[2]+X[64119], X[84]+3*X[165], -X[1490]+5*X[35242], -5*X[3876]+X[12666], 3*X[3928]+X[6769], -3*X[4421]+X[5534], -X[6223]+9*X[64108], -X[7971]+5*X[7987], X[7992]+7*X[16192], -3*X[10165]+X[54198], X[12246]+3*X[64148], X[12667]+3*X[54052] and many others

X(64118) lies on circumconic {{A, B, C, X(39167), X(55918)}} and on these lines: {2, 64119}, {3, 960}, {4, 1155}, {5, 58405}, {8, 13528}, {9, 10270}, {10, 2829}, {20, 5086}, {21, 54442}, {30, 12616}, {35, 1071}, {36, 12672}, {40, 956}, {46, 1012}, {55, 12675}, {56, 45776}, {57, 11496}, {63, 10310}, {65, 6906}, {72, 2077}, {84, 165}, {100, 14872}, {104, 3057}, {109, 17102}, {140, 12608}, {191, 17649}, {210, 56941}, {255, 9371}, {354, 26877}, {392, 2950}, {405, 59333}, {499, 22835}, {515, 550}, {516, 6705}, {517, 5450}, {518, 11248}, {601, 3666}, {631, 3683}, {912, 26285}, {944, 37568}, {946, 15325}, {958, 3359}, {971, 6796}, {993, 31788}, {1001, 37534}, {1214, 40658}, {1376, 7330}, {1385, 2800}, {1465, 1777}, {1490, 35242}, {1512, 64000}, {1519, 5433}, {1699, 37524}, {1707, 36745}, {1709, 3149}, {1727, 59327}, {1770, 6831}, {1836, 6833}, {1837, 6938}, {2096, 3085}, {2646, 6950}, {2771, 26086}, {2801, 64116}, {3073, 3752}, {3091, 9352}, {3219, 18239}, {3358, 11495}, {3428, 4652}, {3474, 6847}, {3523, 62838}, {3560, 3812}, {3576, 19535}, {3647, 6260}, {3651, 5918}, {3652, 64188}, {3742, 37612}, {3820, 6684}, {3838, 6862}, {3869, 50371}, {3876, 12666}, {3911, 7681}, {3928, 6769}, {3931, 37469}, {4292, 7680}, {4295, 6935}, {4297, 15862}, {4301, 4973}, {4414, 37528}, {4421, 5534}, {4512, 37526}, {4679, 6967}, {4857, 11219}, {4861, 64189}, {5010, 15071}, {5057, 6972}, {5087, 6958}, {5122, 9856}, {5123, 37821}, {5204, 63986}, {5217, 18446}, {5248, 9940}, {5252, 37002}, {5302, 6256}, {5440, 5693}, {5445, 41698}, {5499, 11231}, {5537, 6763}, {5584, 21165}, {5587, 50239}, {5603, 32636}, {5657, 37829}, {5691, 37572}, {5698, 6926}, {5709, 64074}, {5777, 18232}, {5794, 6948}, {5811, 59572}, {5836, 22758}, {5842, 6245}, {5880, 6824}, {5884, 24929}, {5927, 7701}, {6223, 64108}, {6282, 54290}, {6734, 11826}, {6834, 12679}, {6850, 26066}, {6888, 20292}, {6890, 44447}, {6891, 24703}, {6892, 28628}, {6905, 12688}, {6909, 14110}, {6914, 34339}, {6916, 15823}, {6918, 54370}, {6924, 31937}, {6927, 64130}, {6940, 25917}, {6952, 17605}, {6961, 25681}, {6966, 11415}, {6977, 11375}, {6985, 15726}, {6988, 63971}, {7289, 39877}, {7411, 12671}, {7971, 7987}, {7992, 16192}, {8762, 47372}, {9579, 10894}, {9616, 19067}, {9803, 11015}, {9841, 10268}, {9960, 37105}, {10058, 64045}, {10085, 59316}, {10165, 54198}, {10167, 10902}, {10179, 16203}, {10202, 51715}, {10222, 52074}, {10225, 18480}, {10267, 58567}, {10269, 58679}, {10306, 62858}, {10309, 18228}, {10391, 11507}, {10531, 17728}, {10679, 34791}, {10785, 12701}, {10786, 12678}, {11491, 12680}, {11509, 44547}, {12053, 20418}, {12246, 64148}, {12513, 49163}, {12515, 37562}, {12547, 61124}, {12617, 37281}, {12667, 54052}, {12686, 16209}, {12687, 16208}, {12700, 45700}, {12705, 15803}, {12761, 17619}, {12767, 37616}, {13226, 15171}, {13369, 32613}, {13373, 42819}, {13600, 62825}, {13624, 40257}, {15644, 22276}, {15837, 36996}, {15908, 59491}, {16116, 45065}, {16118, 52850}, {16197, 59701}, {17594, 36746}, {17614, 59332}, {17638, 18861}, {18243, 31658}, {18482, 33335}, {18515, 25413}, {19919, 22937}, {21154, 52116}, {21164, 31435}, {21669, 41542}, {21740, 37600}, {22769, 26928}, {22793, 41347}, {24466, 57287}, {26202, 38140}, {26364, 37822}, {26921, 35238}, {28202, 40265}, {31424, 37560}, {31786, 63983}, {33810, 37558}, {36866, 40263}, {37541, 62810}, {37579, 64132}, {37622, 58609}, {38901, 51379}, {41539, 54432}, {48363, 63206}, {51889, 55315}, {54199, 54445}, {59417, 62827}, {59458, 59647}, {61763, 63430}

X(64118) = midpoint of X(i) and X(j) for these {i,j}: {3, 1158}, {40, 12114}, {84, 11500}, {550, 33899}, {1768, 12332}, {2950, 22775}, {3358, 11495}, {3579, 34862}, {5450, 40256}, {5709, 64074}, {6245, 31730}, {7289, 39877}, {10306, 62858}, {11248, 24467}, {12513, 49163}, {12515, 48695}, {18238, 63976}, {49171, 56889}, {64119, 64190}
X(64118) = reflection of X(i) in X(j) for these {i,j}: {6796, 31663}, {11260, 32153}, {12608, 140}, {18242, 6684}, {22792, 63964}, {22793, 63963}, {32159, 58630}, {37837, 3}, {40257, 13624}, {56176, 26285}, {63980, 6705}
X(64118) = complement of X(64119)
X(64118) = pole of line {1388, 21740} with respect to the Feuerbach hyperbola
X(64118) = pole of line {16049, 50371} with respect to the Stammler hyperbola
X(64118) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 1158, 53752}, {104, 2745, 53748}, {109, 2765, 53742}, {124, 1364, 52114}
X(64118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64190, 64119}, {3, 1158, 6001}, {3, 5887, 59691}, {3, 6001, 37837}, {35, 1768, 1071}, {40, 52027, 12114}, {46, 1012, 7686}, {55, 63399, 12675}, {57, 11496, 13374}, {63, 10310, 63976}, {84, 165, 11500}, {191, 59326, 64107}, {516, 6705, 63980}, {517, 32153, 11260}, {631, 14646, 63962}, {971, 31663, 6796}, {971, 58630, 32159}, {1376, 7330, 58631}, {1709, 58887, 3149}, {3579, 34862, 515}, {3916, 17613, 40}, {4640, 64128, 3}, {4652, 63985, 3428}, {5010, 15071, 33597}, {5450, 40256, 517}, {6245, 31730, 5842}, {6909, 56288, 14110}, {7992, 16192, 52026}, {11231, 22792, 63964}, {11248, 24467, 518}, {12680, 63211, 11491}, {12705, 15803, 22753}, {18232, 25440, 62357}, {26921, 35238, 58637}, {54432, 59329, 41539}

X(64119) = ORTHOLOGY CENTER OF THESE TRIANGLES: GARCIA-REFLECTION AND X(8)-CROSSPEDAL-OF-X(3)

Barycentrics    a^7-a^4*(b-c)^2*(b+c)-(b-c)^4*(b+c)^3+a^3*(b^2-c^2)^2-2*a*b*c*(b^2-c^2)^2-2*a^5*(b^2-b*c+c^2)+2*a^2*(b^5-b^4*c-b*c^4+c^5) : :
X(64119) = -3*X[2]+2*X[64118], -3*X[165]+5*X[63966], -3*X[381]+2*X[12616], -7*X[3090]+3*X[14646], -5*X[3091]+3*X[14647], -3*X[3817]+2*X[6705], -2*X[5450]+3*X[5886], -3*X[5587]+X[54156], X[6223]+3*X[9812], -X[6361]+3*X[64148], -X[6769]+3*X[28609], -3*X[10157]+2*X[58660]

X(64119) lies on these lines: {1, 1537}, {2, 64118}, {3, 12608}, {4, 65}, {5, 1158}, {7, 10309}, {10, 37822}, {11, 7702}, {20, 5057}, {30, 6261}, {40, 17757}, {46, 1532}, {56, 1519}, {57, 7681}, {63, 15908}, {78, 11826}, {79, 84}, {104, 11376}, {119, 37828}, {153, 14923}, {165, 63966}, {185, 38389}, {208, 25640}, {221, 1785}, {226, 11496}, {278, 40658}, {281, 54009}, {318, 33650}, {329, 63976}, {354, 10531}, {355, 2800}, {381, 12616}, {382, 515}, {388, 45776}, {411, 45392}, {497, 12675}, {516, 5812}, {517, 6256}, {519, 12700}, {528, 5534}, {546, 33899}, {601, 17720}, {603, 35015}, {631, 4679}, {908, 10310}, {912, 10525}, {942, 26333}, {944, 5048}, {946, 999}, {960, 6850}, {962, 3885}, {971, 16127}, {997, 31775}, {1012, 12047}, {1064, 50065}, {1068, 1456}, {1070, 6180}, {1071, 1479}, {1155, 6834}, {1210, 10893}, {1319, 37002}, {1329, 3359}, {1478, 10043}, {1490, 5842}, {1498, 1838}, {1503, 46467}, {1512, 37567}, {1538, 37582}, {1709, 6831}, {1768, 7741}, {1770, 3149}, {1839, 5776}, {1853, 39574}, {1854, 56814}, {1872, 3827}, {2096, 3086}, {2099, 37001}, {2550, 5811}, {2646, 6938}, {2886, 7330}, {2956, 31516}, {3057, 12115}, {3072, 64016}, {3073, 3772}, {3090, 14646}, {3091, 14647}, {3358, 42356}, {3417, 14127}, {3419, 5693}, {3427, 5556}, {3428, 64002}, {3434, 14872}, {3474, 6848}, {3527, 15320}, {3560, 28628}, {3576, 49178}, {3583, 15071}, {3656, 34698}, {3683, 6889}, {3812, 6893}, {3816, 37534}, {3817, 6705}, {3838, 6824}, {3841, 60911}, {3868, 12666}, {3869, 37437}, {4187, 59333}, {4292, 22753}, {4302, 33597}, {4640, 6825}, {4855, 24466}, {5087, 6891}, {5225, 5768}, {5252, 25414}, {5450, 5886}, {5552, 13528}, {5587, 54156}, {5603, 10404}, {5691, 7971}, {5698, 6908}, {5706, 41011}, {5708, 5805}, {5709, 17768}, {5715, 11372}, {5722, 5884}, {5731, 50244}, {5787, 16159}, {5794, 5887}, {5832, 31418}, {5840, 37700}, {5903, 41698}, {5905, 18239}, {5918, 6899}, {5919, 10805}, {6223, 9812}, {6247, 39585}, {6284, 18446}, {6361, 64148}, {6684, 51090}, {6769, 28609}, {6796, 35000}, {6827, 9943}, {6833, 17605}, {6838, 44447}, {6840, 9961}, {6842, 26066}, {6851, 9942}, {6865, 63971}, {6888, 10129}, {6897, 25917}, {6906, 11375}, {6907, 12514}, {6913, 12609}, {6917, 31937}, {6922, 64129}, {6925, 11415}, {6929, 34339}, {6932, 56288}, {6940, 24954}, {6941, 24914}, {6948, 59691}, {6968, 17606}, {6979, 9352}, {6985, 40245}, {6989, 15254}, {7082, 63437}, {7354, 63986}, {7680, 9612}, {7956, 24470}, {7987, 59347}, {8148, 52683}, {8227, 41865}, {8256, 38757}, {9579, 63992}, {9614, 63430}, {9809, 12528}, {9856, 26332}, {9940, 60896}, {9955, 34862}, {9960, 37433}, {10157, 58660}, {10165, 17571}, {10248, 54228}, {10270, 30827}, {10307, 43733}, {10400, 41010}, {10429, 38306}, {10431, 12671}, {10593, 13226}, {10596, 17609}, {10698, 37738}, {10728, 37740}, {10786, 37568}, {10950, 52836}, {11813, 63983}, {11827, 64150}, {12001, 48664}, {12116, 12680}, {12330, 19541}, {12332, 21635}, {12520, 31789}, {12607, 49163}, {12611, 32612}, {12650, 31162}, {12677, 31673}, {13253, 37707}, {13257, 17857}, {14216, 39529}, {14217, 25416}, {14450, 54145}, {16005, 43732}, {16116, 17637}, {17102, 34029}, {17728, 26877}, {18407, 31828}, {18481, 40257}, {18961, 64042}, {20418, 50443}, {21164, 25522}, {24210, 36746}, {26285, 37713}, {26446, 40256}, {34231, 54010}, {34719, 50865}, {34772, 48697}, {35635, 48899}, {36846, 40290}, {37406, 59318}, {37468, 63988}, {37562, 37821}, {37725, 63130}, {37820, 40263}, {38121, 51572}, {38454, 52684}, {44455, 48661}, {45637, 58576}, {51409, 63391}, {52026, 64005}, {54175, 60905}, {54199, 59387}, {62810, 64127}, {63324, 63450}

X(64119) = midpoint of X(i) and X(j) for these {i,j}: {4, 63962}, {962, 12667}, {1482, 40267}, {1490, 41869}, {3868, 12666}, {5691, 7971}, {6259, 12699}, {8148, 52683}, {16127, 48482}, {34789, 46435}, {51118, 54227}
X(64119) = reflection of X(i) in X(j) for these {i,j}: {3, 12608}, {20, 37837}, {40, 18242}, {84, 63980}, {1158, 5}, {1490, 18243}, {3358, 42356}, {6245, 18483}, {6256, 22792}, {10306, 21077}, {11500, 6260}, {12114, 946}, {12332, 21635}, {18238, 13374}, {18481, 40257}, {33899, 546}, {34862, 9955}, {40256, 63964}, {48482, 22793}, {48695, 12611}, {49163, 12607}, {59318, 37406}, {64190, 64118}
X(64119) = inverse of X(7702) in Feuerbach hyperbola
X(64119) = complement of X(64190)
X(64119) = anticomplement of X(64118)
X(64119) = X(i)-Dao conjugate of X(j) for these {i, j}: {64118, 64118}
X(64119) = pole of line {3738, 6246} with respect to the Fuhrmann circle
X(64119) = pole of line {2804, 6129} with respect to the incircle
X(64119) = pole of line {4, 5553} with respect to the Feuerbach hyperbola
X(64119) = pole of line {2804, 21189} with respect to the Suppa-Cucoanes circle
X(64119) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 3318, 5514}
X(64119) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(79), X(47372)}}, {{A, B, C, X(158), X(46435)}}, {{A, B, C, X(1118), X(60843)}}, {{A, B, C, X(1857), X(10309)}}
X(64119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64190, 64118}, {4, 4295, 7686}, {4, 63962, 6001}, {4, 64021, 1837}, {84, 1699, 63980}, {516, 21077, 10306}, {516, 6260, 11500}, {517, 22792, 6256}, {971, 22793, 48482}, {1479, 10052, 5570}, {1482, 40267, 515}, {1490, 41869, 5842}, {1836, 12679, 4}, {2550, 5811, 58631}, {4292, 63989, 22753}, {5087, 64128, 6891}, {5842, 18243, 1490}, {5887, 6923, 5794}, {6925, 11415, 14110}, {9612, 12705, 7680}, {9809, 52367, 12528}, {10742, 25413, 355}, {12678, 12701, 944}, {16127, 48482, 971}, {34789, 46435, 2829}

X(64120) = ANTICOMPLEMENT OF X(6256)

Barycentrics    3*a^7-3*a^6*(b+c)+5*a^4*(b-c)^2*(b+c)-(b-c)^4*(b+c)^3+a^5*(-5*b^2+14*b*c-5*c^2)+a^3*(b-c)^2*(b^2-6*b*c+c^2)+a*(b^2-c^2)^2*(b^2-6*b*c+c^2)-a^2*(b-c)^2*(b^3-5*b^2*c-5*b*c^2+c^3) : :
X(64120) = -3*X[2]+4*X[5450], -3*X[376]+2*X[11500], -5*X[631]+4*X[18242], -3*X[3241]+X[54199], -5*X[3522]+4*X[6796], -5*X[3616]+4*X[12608], -7*X[3832]+8*X[63963], -5*X[3876]+4*X[32159], -3*X[5587]+4*X[6705], -3*X[5731]+X[6223], -3*X[5886]+2*X[22792], -2*X[9942]+3*X[63432] and many others

X(64120) lies on these lines: {1, 10309}, {2, 5450}, {3, 1603}, {4, 11}, {5, 40267}, {8, 20}, {10, 10270}, {12, 6935}, {30, 22770}, {36, 6848}, {65, 2096}, {90, 3427}, {119, 6961}, {144, 31806}, {145, 2800}, {153, 5552}, {329, 63391}, {355, 6948}, {376, 11500}, {388, 1012}, {390, 5882}, {452, 3576}, {497, 18237}, {499, 41698}, {516, 12650}, {517, 17648}, {519, 54156}, {529, 8668}, {631, 18242}, {944, 3057}, {946, 3600}, {950, 63430}, {958, 6916}, {960, 18239}, {962, 20076}, {971, 5698}, {993, 6908}, {997, 1490}, {1056, 11496}, {1071, 3486}, {1155, 6934}, {1319, 12679}, {1376, 40290}, {1385, 6259}, {1420, 63989}, {1436, 55116}, {1455, 7952}, {1478, 6847}, {1532, 7288}, {1699, 4317}, {1709, 10043}, {1737, 4299}, {1768, 10573}, {1854, 51422}, {2077, 7080}, {2217, 37414}, {2550, 31775}, {2646, 12678}, {2950, 49169}, {2975, 6925}, {3085, 6906}, {3146, 10529}, {3241, 54199}, {3333, 15239}, {3338, 5804}, {3361, 7682}, {3421, 10310}, {3435, 7412}, {3436, 6909}, {3476, 12672}, {3488, 12675}, {3522, 6796}, {3529, 5842}, {3585, 6844}, {3616, 12608}, {3832, 63963}, {3876, 32159}, {4188, 64188}, {4190, 12616}, {4302, 7992}, {4305, 18446}, {4311, 63992}, {4679, 5658}, {5080, 6890}, {5082, 11826}, {5129, 10165}, {5204, 6927}, {5229, 6831}, {5251, 37407}, {5253, 6957}, {5303, 6962}, {5433, 6969}, {5587, 6705}, {5603, 10404}, {5657, 37829}, {5690, 52683}, {5704, 31673}, {5731, 6223}, {5768, 10051}, {5770, 5787}, {5795, 37560}, {5805, 31776}, {5818, 6955}, {5841, 6851}, {5854, 52116}, {5886, 22792}, {6282, 12527}, {6713, 6981}, {6826, 18761}, {6833, 10590}, {6850, 19843}, {6863, 18515}, {6865, 57288}, {6885, 18480}, {6891, 37821}, {6893, 10269}, {6897, 19855}, {6907, 30478}, {6921, 38693}, {6923, 26321}, {6926, 63983}, {6939, 25524}, {6944, 18516}, {6950, 10786}, {6956, 10895}, {6958, 10742}, {6959, 33898}, {6966, 11681}, {6971, 38756}, {6973, 26492}, {7967, 10543}, {8581, 45776}, {8582, 21164}, {8727, 9655}, {9798, 37404}, {9910, 28029}, {9942, 63432}, {9965, 37625}, {10106, 12705}, {10175, 17580}, {10246, 48664}, {10307, 60919}, {10465, 35635}, {10527, 37437}, {10532, 21669}, {10902, 17576}, {10916, 28164}, {10935, 12686}, {10936, 12687}, {11001, 34630}, {11012, 37421}, {11240, 48694}, {11248, 34619}, {11499, 38761}, {11715, 46435}, {12116, 40272}, {12119, 12665}, {12245, 14646}, {12664, 45120}, {12677, 33597}, {12758, 64145}, {13199, 13996}, {14986, 26333}, {15171, 30283}, {16127, 40257}, {17613, 64087}, {18340, 34030}, {18391, 63399}, {18525, 33899}, {18908, 58660}, {20007, 63967}, {20013, 54193}, {21454, 31870}, {21578, 63988}, {22654, 37305}, {26332, 37434}, {28204, 34711}, {30147, 60896}, {30384, 52860}, {33811, 44075}, {34286, 37395}, {37022, 64111}, {37234, 38037}, {37423, 52026}, {37427, 59320}, {37725, 59591}, {38031, 50243}, {40260, 46932}, {41010, 55119}, {44696, 47372}, {45634, 49170}, {45635, 49171}, {45770, 48697}, {56821, 64057}, {56936, 61296}, {63986, 64130}

X(64120) = midpoint of X(i) and X(j) for these {i,j}: {944, 12246}
X(64120) = reflection of X(i) in X(j) for these {i,j}: {4, 12114}, {8, 1158}, {65, 18238}, {153, 48695}, {355, 34862}, {1490, 4297}, {3146, 48482}, {5691, 6245}, {6223, 6261}, {6256, 5450}, {6259, 1385}, {7971, 5882}, {12666, 5887}, {12667, 3}, {16127, 40257}, {18239, 960}, {18525, 33899}, {33898, 38602}, {40267, 5}, {46435, 11715}, {52683, 5690}, {63962, 1}
X(64120) = inverse of X(3086) in Feuerbach hyperbola
X(64120) = anticomplement of X(6256)
X(64120) = X(i)-Dao conjugate of X(j) for these {i, j}: {6256, 6256}
X(64120) = pole of line {42337, 53304} with respect to the circumcircle
X(64120) = pole of line {8058, 53522} with respect to the incircle
X(64120) = pole of line {2804, 54239} with respect to the polar circle
X(64120) = pole of line {3086, 6001} with respect to the Feuerbach hyperbola
X(64120) = pole of line {23681, 34050} with respect to the dual conic of Yff parabola
X(64120) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(104), X(271)}}, {{A, B, C, X(280), X(10309)}}
X(64120) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12667, 64148}, {4, 104, 3086}, {4, 10785, 10591}, {4, 12248, 37002}, {4, 37002, 4293}, {4, 47743, 10893}, {8, 54052, 1158}, {84, 1158, 56941}, {104, 47744, 20418}, {355, 34862, 14647}, {515, 1158, 8}, {944, 12246, 6001}, {944, 6938, 4294}, {971, 5887, 12666}, {1071, 3486, 64147}, {3146, 20067, 64079}, {4299, 5691, 50701}, {5450, 6256, 2}, {5731, 6223, 6261}, {6713, 45631, 6981}, {6868, 18481, 43161}, {6906, 12115, 3085}, {10085, 10572, 5768}, {10893, 20418, 47743}, {10896, 52836, 4}, {12114, 56889, 56}, {12114, 59366, 104}, {18516, 32612, 6944}, {57288, 63991, 6865}

X(64121) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTERS-MIDPOINTS AND X(8)-CROSSPEDAL-OF-X(6)

Barycentrics    a*(2*a^4-a^3*(b+c)-(b^2-c^2)^2-a^2*(b^2-4*b*c+c^2)+a*(b^3-3*b^2*c-3*b*c^2+c^3)) : :
X(64121) = -3*X[2]+X[64122], -X[990]+3*X[5085], X[10444]+3*X[50127]

X(64121) lies on these lines: {2, 64122}, {3, 9}, {4, 5749}, {5, 5750}, {6, 517}, {7, 7397}, {10, 29207}, {19, 31788}, {30, 10445}, {37, 572}, {40, 1743}, {44, 573}, {45, 13624}, {57, 19517}, {63, 16435}, {71, 2265}, {72, 37399}, {140, 5257}, {142, 19512}, {165, 2348}, {169, 31787}, {218, 31793}, {219, 2261}, {266, 59470}, {284, 15952}, {346, 944}, {355, 2345}, {374, 16547}, {380, 10306}, {391, 5657}, {478, 37613}, {515, 17355}, {516, 4085}, {518, 63968}, {579, 19543}, {604, 24928}, {631, 5296}, {672, 4192}, {894, 6996}, {942, 2285}, {952, 2321}, {960, 24265}, {966, 26446}, {990, 5085}, {1030, 26086}, {1071, 5279}, {1100, 10222}, {1108, 5053}, {1172, 1872}, {1213, 11231}, {1375, 25019}, {1377, 6212}, {1378, 6213}, {1400, 19513}, {1404, 17452}, {1428, 12721}, {1449, 1482}, {1503, 12618}, {1723, 3428}, {1746, 31993}, {1764, 4641}, {1824, 26890}, {1864, 5285}, {2082, 31798}, {2098, 38296}, {2171, 50194}, {2178, 32612}, {2257, 22770}, {2262, 16548}, {2267, 40937}, {2268, 24929}, {2270, 3359}, {2287, 4221}, {2297, 63992}, {2317, 21801}, {2323, 21871}, {2324, 20818}, {2325, 34773}, {2330, 12723}, {2944, 5247}, {3101, 14557}, {3161, 5731}, {3207, 34524}, {3247, 10246}, {3576, 3731}, {3589, 12610}, {3654, 37654}, {3666, 21375}, {3683, 10434}, {3686, 5690}, {3694, 64116}, {3707, 61524}, {3713, 34790}, {3758, 10446}, {3929, 10856}, {3950, 5882}, {3986, 10165}, {4007, 12645}, {4034, 59503}, {4058, 47745}, {4220, 5927}, {4254, 11248}, {4268, 8609}, {4287, 26287}, {4297, 30618}, {4519, 13244}, {4640, 9564}, {4663, 29311}, {4670, 24220}, {4856, 28234}, {4873, 18526}, {4898, 61291}, {5091, 17635}, {5120, 8557}, {5294, 19542}, {5341, 13145}, {5356, 5885}, {5746, 5812}, {5788, 39564}, {5790, 59772}, {5805, 36670}, {5816, 9956}, {5817, 7390}, {5838, 35514}, {5886, 63055}, {5909, 8251}, {5928, 56366}, {6259, 50425}, {6361, 61330}, {6554, 59578}, {6684, 63978}, {6796, 59689}, {6865, 27382}, {6922, 40942}, {6926, 27508}, {7085, 64171}, {7377, 17368}, {7485, 17616}, {7957, 17745}, {7982, 16667}, {8804, 31789}, {9940, 54405}, {9957, 54359}, {10157, 19544}, {10164, 59624}, {10167, 19649}, {10319, 34048}, {10443, 31730}, {10444, 50127}, {10855, 16419}, {10884, 56536}, {11227, 16434}, {11230, 17398}, {11278, 16666}, {11349, 61012}, {12034, 15492}, {12329, 15733}, {12572, 40660}, {12680, 17744}, {12702, 16670}, {13006, 40590}, {13323, 37594}, {13329, 30271}, {13478, 44417}, {13732, 16601}, {14100, 40910}, {15178, 16777}, {15726, 24309}, {16554, 52405}, {16566, 43216}, {16677, 31662}, {16814, 17502}, {16884, 33179}, {16885, 31663}, {17281, 28204}, {17314, 37727}, {17330, 50821}, {17350, 37416}, {17351, 29069}, {17369, 18480}, {17754, 19540}, {18481, 54389}, {18482, 36654}, {18589, 36949}, {18594, 37560}, {19645, 26223}, {20262, 59671}, {21061, 37620}, {21062, 23292}, {21370, 55406}, {21495, 26699}, {21796, 62371}, {23512, 27064}, {23617, 33950}, {24328, 60973}, {24604, 61009}, {24611, 51413}, {25078, 37837}, {26039, 61261}, {26285, 36744}, {26286, 36743}, {26685, 36698}, {26938, 58643}, {27396, 33597}, {28739, 41004}, {30456, 41340}, {31781, 54421}, {32431, 38140}, {32613, 54285}, {34543, 62370}, {37062, 55104}, {37364, 40869}, {37581, 64157}, {37597, 56547}, {39048, 43182}, {40968, 43065}, {41006, 59588}, {44424, 49127}, {50123, 51087}, {50810, 63086}, {52015, 58608}, {54008, 54283}, {59417, 62985}

X(64121) = midpoint of X(i) and X(j) for these {i,j}: {6, 1766}
X(64121) = reflection of X(i) in X(j) for these {i,j}: {12610, 3589}
X(64121) = complement of X(64122)
X(64121) = perspector of circumconic {{A, B, C, X(9058), X(13138)}}
X(64121) = pole of line {3910, 50453} with respect to the excircles-radical circle
X(64121) = pole of line {5269, 30223} with respect to the Feuerbach hyperbola
X(64121) = pole of line {26470, 30444} with respect to the Kiepert hyperbola
X(64121) = pole of line {1817, 26637} with respect to the Stammler hyperbola
X(64121) = pole of line {40134, 57055} with respect to the Steiner inellipse
X(64121) = intersection, other than A, B, C, of circumconics {{A, B, C, X(40), X(5438)}}, {{A, B, C, X(84), X(998)}}
X(64121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9, 64125}, {6, 1766, 517}, {9, 2182, 59681}, {9, 5776, 5777}, {9, 5783, 5044}, {37, 572, 1385}, {894, 6996, 64126}, {5816, 17303, 9956}, {32555, 32556, 5438}

X(64122) = ORTHOLOGY CENTER OF THESE TRIANGLES: GARCIA-REFLECTION AND X(8)-CROSSPEDAL-OF-X(6)

Barycentrics    a^5-b^5-a^3*(b-c)^2+b^4*c-2*a*b*(b-c)^2*c+b*c^4-c^5+a^2*(b-c)^2*(b+c) : :
X(64122) = -3*X[2]+2*X[64121], -3*X[10516]+2*X[12618]

X(64122) lies on these lines: {1, 10401}, {2, 64121}, {3, 4357}, {4, 7}, {5, 10436}, {6, 12610}, {19, 26932}, {30, 10444}, {40, 17272}, {57, 5928}, {63, 5755}, {69, 517}, {75, 355}, {77, 41007}, {79, 10435}, {84, 15314}, {86, 5886}, {141, 1766}, {150, 39126}, {222, 1848}, {226, 2050}, {269, 1565}, {286, 57816}, {307, 3149}, {320, 10446}, {326, 45770}, {381, 50116}, {515, 3663}, {516, 1350}, {527, 10445}, {572, 4657}, {573, 4643}, {604, 20270}, {857, 26651}, {894, 7377}, {944, 3672}, {946, 3664}, {952, 3875}, {962, 21296}, {990, 1503}, {1012, 18650}, {1122, 12688}, {1266, 18525}, {1370, 17616}, {1385, 17321}, {1407, 21621}, {1444, 26286}, {1482, 3879}, {1699, 4888}, {1746, 24789}, {1829, 8048}, {1836, 10473}, {2182, 42857}, {2995, 34387}, {3146, 45789}, {3654, 17271}, {3655, 17320}, {3656, 17378}, {3662, 6996}, {3665, 63988}, {3667, 21202}, {3739, 5816}, {3772, 13478}, {3927, 39591}, {3945, 5603}, {4021, 5882}, {4056, 12679}, {4329, 12672}, {4360, 37727}, {4389, 18481}, {4654, 10888}, {4675, 24220}, {4858, 54008}, {4862, 5691}, {4887, 31673}, {4896, 18483}, {4967, 5790}, {5224, 26446}, {5232, 5657}, {5587, 25590}, {5690, 17270}, {5732, 49131}, {5749, 7402}, {5784, 50861}, {5786, 23537}, {5881, 17151}, {5903, 58800}, {5933, 50193}, {6001, 24471}, {6173, 36728}, {6245, 24213}, {6261, 41003}, {6265, 44179}, {6646, 6999}, {7198, 10085}, {7272, 12678}, {7384, 26806}, {7487, 19904}, {7595, 17610}, {8727, 40719}, {8804, 61002}, {9436, 19541}, {9535, 33066}, {9856, 17170}, {9948, 10521}, {10167, 26118}, {10367, 23661}, {10441, 10452}, {10442, 41869}, {10454, 50065}, {10468, 37620}, {10516, 12618}, {10884, 13442}, {10889, 15171}, {11220, 37456}, {11230, 63014}, {11677, 17668}, {12245, 32099}, {12586, 44670}, {12588, 12721}, {12589, 12723}, {15726, 58581}, {16412, 25023}, {16435, 54311}, {17160, 61244}, {17184, 19645}, {17236, 37416}, {17253, 37499}, {17257, 36698}, {17276, 29069}, {17282, 19512}, {17308, 59680}, {17393, 61287}, {17394, 61276}, {17578, 33800}, {17625, 36844}, {17811, 21062}, {18480, 42697}, {18655, 37468}, {20245, 51558}, {20246, 38955}, {20895, 21286}, {21244, 24334}, {21246, 24702}, {21375, 32777}, {21554, 38122}, {22753, 53596}, {23512, 27184}, {24179, 63980}, {24251, 26066}, {24265, 25681}, {24474, 54344}, {24728, 28845}, {25019, 37272}, {27509, 59681}, {28204, 50101}, {29010, 49518}, {29057, 33869}, {29369, 36685}, {31995, 59387}, {32087, 59388}, {35635, 63997}, {37774, 59578}, {39579, 41344}, {41847, 61268}, {43172, 51118}, {50099, 50798}, {51709, 63110}, {62789, 63989}

X(64122) = reflection of X(i) in X(j) for these {i,j}: {6, 12610}, {1766, 141}
X(64122) = anticomplement of X(64121)
X(64122) = X(i)-Dao conjugate of X(j) for these {i, j}: {64121, 64121}
X(64122) = pole of line {3910, 4063} with respect to the Conway circle
X(64122) = pole of line {905, 3910} with respect to the incircle
X(64122) = pole of line {1836, 7595} with respect to the Feuerbach hyperbola
X(64122) = pole of line {1792, 4221} with respect to the Wallace hyperbola
X(64122) = pole of line {1734, 3910} with respect to the Suppa-Cucoanes circle
X(64122) = pole of line {2217, 2385} with respect to the dual conic of Yff parabola
X(64122) = intersection, other than A, B, C, of circumconics {{A, B, C, X(342), X(15314)}}, {{A, B, C, X(1439), X(57816)}}, {{A, B, C, X(7282), X(10435)}}
X(64122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 7, 64126}, {17257, 36698, 64125}, {20895, 21286, 64087}

X(64123) = COMPLEMENT OF X(3813)

Barycentrics    (a-b-c)*(2*a^3+2*a^2*(b+c)-(b-c)^2*(b+c)-a*(b^2+c^2)) : :
X(64123) = X[4]+3*X[4421], X[20]+3*X[11236], -3*X[549]+X[8666], 3*X[551]+X[12640], -5*X[631]+X[12513], -5*X[1656]+3*X[3829], 5*X[1698]+3*X[3158], X[2136]+7*X[3624], -7*X[3090]+3*X[11235], 5*X[3091]+3*X[34607], X[3146]+3*X[34626], X[3189]+7*X[9780] and many others

X(64123) lies on these lines: {1, 1145}, {2, 3303}, {3, 529}, {4, 4421}, {5, 528}, {8, 4999}, {10, 6675}, {11, 3871}, {12, 100}, {20, 11236}, {21, 4995}, {35, 17757}, {55, 1329}, {56, 10528}, {119, 11849}, {140, 519}, {145, 5433}, {149, 7173}, {200, 26066}, {210, 17637}, {230, 20691}, {388, 37267}, {404, 6174}, {405, 9711}, {442, 3584}, {443, 1376}, {451, 56183}, {474, 10056}, {495, 17563}, {496, 6667}, {497, 3847}, {498, 2886}, {513, 53002}, {517, 32157}, {518, 5771}, {522, 4075}, {535, 548}, {549, 8666}, {551, 12640}, {594, 46823}, {631, 12513}, {758, 11277}, {908, 37568}, {950, 5123}, {952, 26287}, {958, 5218}, {960, 6745}, {1001, 8668}, {1125, 3880}, {1158, 5851}, {1259, 15843}, {1385, 10915}, {1388, 12648}, {1478, 56998}, {1483, 6713}, {1656, 3829}, {1697, 25681}, {1698, 3158}, {1706, 28628}, {1788, 63168}, {1834, 60714}, {2136, 3624}, {2334, 63078}, {2476, 34612}, {2550, 59476}, {2551, 5281}, {2646, 6735}, {2802, 5901}, {2829, 10942}, {2975, 52793}, {3036, 10950}, {3039, 25082}, {3057, 27385}, {3058, 4193}, {3090, 11235}, {3091, 34607}, {3146, 34626}, {3169, 17398}, {3189, 9780}, {3214, 35466}, {3241, 17566}, {3244, 15325}, {3295, 3816}, {3304, 6921}, {3436, 5217}, {3475, 26062}, {3523, 11194}, {3525, 34625}, {3526, 45700}, {3528, 34620}, {3529, 34739}, {3576, 32049}, {3579, 17768}, {3612, 64087}, {3614, 6154}, {3616, 10912}, {3617, 24953}, {3626, 58404}, {3628, 24387}, {3634, 5853}, {3635, 6681}, {3678, 58640}, {3679, 7483}, {3680, 25055}, {3689, 6734}, {3698, 52638}, {3699, 56313}, {3701, 3712}, {3704, 7081}, {3746, 4187}, {3753, 11281}, {3754, 5719}, {3811, 26446}, {3812, 13405}, {3814, 15171}, {3820, 5248}, {3825, 15172}, {3826, 6600}, {3828, 50205}, {3832, 34706}, {3843, 34707}, {3870, 24914}, {3881, 34753}, {3895, 11376}, {3910, 59515}, {3911, 34791}, {3915, 37663}, {3919, 16137}, {3925, 31254}, {3956, 58449}, {3983, 54357}, {4188, 5434}, {4189, 34606}, {4190, 11237}, {4294, 61153}, {4309, 17556}, {4317, 19537}, {4330, 31160}, {4420, 21677}, {4428, 5084}, {4640, 21075}, {4662, 5745}, {4855, 5252}, {4857, 17533}, {5045, 58405}, {5046, 63273}, {5047, 50038}, {5080, 15338}, {5087, 10624}, {5141, 49719}, {5154, 34611}, {5187, 9670}, {5253, 22560}, {5255, 37662}, {5258, 37298}, {5260, 15676}, {5289, 27383}, {5298, 62837}, {5438, 51784}, {5440, 10039}, {5443, 5541}, {5657, 12635}, {5690, 5855}, {5734, 34711}, {5794, 31434}, {5836, 13411}, {5842, 32141}, {5844, 26087}, {5846, 17748}, {5880, 41865}, {5882, 32537}, {5883, 63282}, {5884, 64193}, {5886, 13463}, {6265, 32198}, {6284, 11681}, {6583, 61530}, {6700, 58679}, {6765, 31423}, {6767, 10200}, {6845, 34746}, {6851, 11500}, {6872, 31141}, {6903, 11491}, {6906, 37725}, {6919, 10385}, {6931, 11238}, {6933, 31140}, {6945, 34709}, {6952, 38665}, {6959, 37622}, {7680, 11499}, {7681, 10679}, {7751, 17224}, {7789, 25102}, {7991, 34647}, {8069, 15867}, {8162, 10586}, {8168, 64081}, {8582, 51715}, {8728, 10197}, {9352, 52783}, {9588, 11523}, {9624, 34640}, {9656, 31295}, {9785, 62710}, {9797, 31188}, {9843, 42819}, {9956, 61533}, {10107, 64110}, {10165, 11260}, {10175, 64117}, {10246, 49169}, {10284, 11729}, {10306, 42843}, {10310, 10786}, {10588, 17784}, {10589, 56936}, {10609, 37710}, {10896, 20075}, {10916, 11231}, {10955, 55016}, {11010, 51409}, {11011, 51433}, {11108, 52804}, {11112, 37719}, {11230, 49600}, {11248, 18242}, {11362, 52265}, {11374, 54286}, {11375, 63130}, {11501, 15844}, {11507, 15813}, {11680, 52795}, {12331, 26470}, {12616, 64116}, {12625, 19875}, {12642, 56778}, {12701, 30852}, {12953, 61154}, {13271, 64008}, {13607, 33956}, {13731, 15621}, {14923, 15950}, {15326, 20060}, {15625, 37331}, {15717, 34610}, {15845, 26358}, {15932, 41548}, {16408, 31480}, {16610, 28027}, {17043, 59711}, {17044, 59516}, {17144, 37688}, {17549, 56880}, {17603, 46677}, {17663, 20612}, {17724, 24443}, {19335, 55362}, {19589, 29633}, {19862, 21627}, {19877, 64146}, {20418, 37727}, {21620, 59675}, {22837, 32426}, {24386, 51073}, {24390, 48696}, {24703, 61763}, {24928, 49626}, {24982, 37080}, {25438, 38752}, {25524, 59572}, {26007, 28742}, {26629, 26752}, {27526, 30847}, {28609, 63469}, {29958, 61166}, {30827, 53053}, {31157, 37291}, {31397, 59587}, {31410, 57000}, {31466, 31501}, {32213, 32612}, {33179, 61534}, {33771, 37715}, {34122, 37702}, {34372, 58487}, {34605, 37307}, {34701, 37714}, {34772, 40663}, {36926, 52352}, {37162, 44847}, {37339, 48801}, {37535, 38760}, {37646, 50581}, {37720, 45310}, {38058, 47033}, {38930, 60711}, {43174, 44663}, {45976, 48713}, {56311, 59592}, {58609, 64124}, {58798, 59316}, {59671, 59733}, {61292, 61566}, {61510, 61520}, {61521, 61597}, {63211, 64002}, {64074, 64148}

X(64123) = midpoint of X(i) and X(j) for these {i,j}: {3, 12607}, {5, 8715}, {10, 56176}, {1385, 10915}, {3579, 21077}, {3813, 3913}, {3826, 6600}, {5690, 22836}, {5882, 32537}, {6265, 32198}, {6684, 59722}, {10942, 26285}, {11248, 18242}, {12616, 64116}, {12640, 33895}
X(64123) = reflection of X(i) in X(j) for these {i,j}: {24387, 3628}
X(64123) = complement of X(3813)
X(64123) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 5511, 61079}
X(64123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3035, 6691}, {2, 3913, 3813}, {3, 12607, 529}, {3, 45701, 12607}, {5, 8715, 528}, {8, 5432, 4999}, {10, 56176, 44669}, {10, 59584, 56176}, {35, 17757, 57288}, {55, 5552, 1329}, {498, 2886, 6668}, {498, 5687, 2886}, {551, 12640, 33895}, {631, 34619, 12513}, {1376, 3085, 25466}, {1385, 10915, 38455}, {3085, 59591, 1376}, {3295, 26364, 3816}, {3579, 21077, 17768}, {3614, 6154, 52367}, {3746, 4187, 49736}, {3753, 63259, 11281}, {3871, 27529, 11}, {4995, 21031, 21}, {5218, 7080, 958}, {5281, 27525, 2551}, {5690, 22836, 5855}, {6174, 15888, 404}, {6684, 59722, 518}, {6921, 11239, 3304}, {9624, 64202, 34640}, {9709, 10198, 3826}, {10942, 26285, 2829}, {13405, 63990, 3812}, {31397, 59587, 59691}

X(64124) = COMPLEMENT OF X(21075)

Barycentrics    2*a^4-3*a^2*(b-c)^2+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2 : :
X(64124) = X[46]+3*X[10072], 3*X[1479]+X[4333], 3*X[10090]+X[12750], 3*X[11240]+X[63130], X[12649]+3*X[35262]

X(64124) lies on these lines: {1, 631}, {2, 3333}, {3, 4314}, {4, 3361}, {5, 4298}, {7, 8227}, {8, 61762}, {10, 999}, {11, 1354}, {12, 10172}, {31, 28018}, {35, 64162}, {36, 950}, {40, 5435}, {46, 10072}, {55, 40270}, {56, 515}, {57, 946}, {65, 13464}, {104, 13370}, {140, 5045}, {142, 26363}, {165, 1058}, {200, 17567}, {226, 499}, {227, 43068}, {329, 25522}, {354, 5433}, {355, 4315}, {388, 10175}, {390, 35242}, {404, 26015}, {443, 5231}, {474, 4847}, {495, 3634}, {496, 516}, {497, 15803}, {498, 51816}, {517, 34753}, {518, 6691}, {519, 8256}, {527, 10199}, {537, 59731}, {546, 31776}, {548, 31795}, {550, 18527}, {553, 1776}, {758, 942}, {861, 40956}, {912, 58573}, {936, 24477}, {938, 3576}, {944, 13462}, {956, 8582}, {958, 9843}, {962, 37704}, {982, 34937}, {997, 24391}, {1056, 1698}, {1066, 3216}, {1104, 3756}, {1155, 10624}, {1159, 61276}, {1208, 33811}, {1319, 13607}, {1375, 40940}, {1385, 6738}, {1387, 50193}, {1420, 5882}, {1445, 12704}, {1447, 53597}, {1458, 37732}, {1467, 6261}, {1470, 37287}, {1471, 37530}, {1478, 6896}, {1479, 4333}, {1519, 26877}, {1565, 10521}, {1617, 6796}, {1647, 37009}, {1656, 3947}, {1699, 47743}, {1706, 34625}, {1737, 5563}, {1770, 37720}, {1887, 23711}, {2257, 59644}, {2260, 40942}, {2646, 5298}, {2886, 12436}, {3035, 34791}, {3075, 55086}, {3085, 31231}, {3090, 5290}, {3218, 31888}, {3244, 56177}, {3295, 10164}, {3296, 34595}, {3297, 13912}, {3298, 13975}, {3304, 24914}, {3306, 10527}, {3336, 30384}, {3339, 5603}, {3452, 10200}, {3474, 9614}, {3476, 47745}, {3486, 51705}, {3487, 3624}, {3488, 7987}, {3523, 10580}, {3555, 6745}, {3579, 12575}, {3600, 5587}, {3616, 11529}, {3632, 53058}, {3636, 50194}, {3646, 5273}, {3660, 12005}, {3671, 5708}, {3698, 39779}, {3701, 62621}, {3743, 53042}, {3748, 52793}, {3772, 24171}, {3816, 12572}, {3817, 57282}, {3870, 6921}, {3873, 27385}, {3881, 6681}, {3889, 17566}, {3913, 59675}, {3916, 40998}, {3946, 37565}, {4031, 23708}, {4187, 12527}, {4253, 40869}, {4293, 9581}, {4297, 5722}, {4299, 28172}, {4301, 11373}, {4304, 5204}, {4305, 37723}, {4308, 5881}, {4312, 50444}, {4317, 10826}, {4323, 61275}, {4342, 12702}, {4355, 5714}, {4666, 6910}, {4860, 11375}, {5044, 58577}, {5049, 58441}, {5082, 64112}, {5084, 31249}, {5121, 5247}, {5122, 12512}, {5126, 37730}, {5128, 30305}, {5220, 5542}, {5221, 11376}, {5234, 17559}, {5236, 7537}, {5250, 10586}, {5253, 6734}, {5261, 54447}, {5267, 37292}, {5274, 41869}, {5294, 26094}, {5316, 41229}, {5432, 17609}, {5434, 17606}, {5437, 19843}, {5443, 11551}, {5445, 37602}, {5450, 57278}, {5534, 6970}, {5550, 11036}, {5552, 31224}, {5558, 61856}, {5570, 15556}, {5690, 51788}, {5717, 6998}, {5719, 50192}, {5744, 31435}, {5777, 63994}, {5794, 40726}, {5795, 8666}, {5853, 25440}, {5884, 37566}, {5901, 31794}, {5902, 64160}, {6049, 61291}, {6147, 11230}, {6245, 18237}, {6260, 10396}, {6361, 51785}, {6712, 14760}, {6713, 12432}, {6735, 62837}, {6737, 17614}, {6744, 24929}, {6762, 31190}, {6765, 59572}, {6848, 63430}, {6857, 10582}, {6964, 7091}, {7294, 61648}, {7373, 26446}, {7677, 10902}, {7682, 12114}, {7686, 20418}, {7956, 34862}, {8074, 40133}, {8166, 12246}, {8555, 29821}, {8568, 17742}, {8732, 37526}, {9578, 31399}, {9579, 10591}, {9612, 10589}, {9613, 50796}, {9669, 51118}, {9844, 63432}, {9850, 18908}, {9856, 13226}, {9948, 63992}, {9955, 24470}, {9956, 51782}, {9957, 43174}, {9965, 26129}, {10021, 58586}, {10090, 12750}, {10156, 16201}, {10198, 51723}, {10265, 48694}, {10303, 10578}, {10310, 42884}, {10573, 63987}, {10593, 12571}, {10595, 18421}, {10916, 57284}, {11038, 61016}, {11227, 12710}, {11240, 63130}, {11263, 60980}, {11512, 33137}, {12433, 13624}, {12608, 62810}, {12649, 35262}, {12667, 33994}, {12675, 64157}, {12699, 37545}, {12701, 28232}, {12908, 58440}, {12915, 63976}, {13373, 62852}, {13374, 37544}, {13600, 64193}, {13883, 35769}, {13936, 35768}, {15172, 31663}, {15299, 60992}, {15841, 38059}, {16174, 24465}, {16485, 28080}, {16572, 40127}, {16869, 62811}, {17051, 51715}, {17353, 25492}, {17527, 18250}, {17531, 25006}, {17605, 52783}, {17625, 63967}, {18398, 63274}, {18990, 19925}, {20103, 34790}, {20323, 40663}, {21151, 30330}, {21578, 37702}, {21627, 54286}, {23536, 29662}, {23537, 51751}, {24178, 33140}, {24982, 54391}, {26062, 63137}, {26105, 31424}, {27383, 41863}, {28027, 46190}, {28096, 54310}, {29817, 37291}, {30340, 61015}, {31423, 64114}, {31479, 51073}, {31792, 61524}, {33593, 41551}, {34120, 62388}, {34198, 34502}, {35620, 43223}, {36489, 37608}, {37534, 62839}, {37561, 62873}, {37587, 45287}, {37589, 51615}, {37592, 39595}, {37646, 52541}, {38036, 60939}, {38037, 60955}, {38130, 62775}, {38859, 51364}, {39605, 61018}, {43151, 63972}, {43179, 63271}, {50190, 63259}, {50191, 63282}, {51706, 58463}, {51775, 52542}, {53057, 64005}, {54302, 61002}, {54370, 61022}, {58570, 61521}, {58587, 61566}, {58609, 64123}, {60924, 61014}, {62773, 64081}, {63980, 64001}, {64131, 64132}

X(64124) = midpoint of X(i) and X(j) for these {i,j}: {1, 4848}, {10, 62825}, {46, 12053}, {56, 1210}, {496, 37582}, {1837, 4311}, {10573, 63987}, {15299, 60992}, {21075, 62874}, {25440, 49627}, {60924, 61014}, {63399, 63989}, {64131, 64132}
X(64124) = reflection of X(i) in X(j) for these {i,j}: {6700, 6691}, {63990, 58405}
X(64124) = complement of X(21075)
X(64124) = X(i)-complementary conjugate of X(j) for these {i, j}: {58, 6260}, {84, 3454}, {189, 21245}, {285, 1329}, {1014, 20307}, {1333, 223}, {1408, 7952}, {1412, 20206}, {1413, 442}, {1422, 17052}, {1433, 21530}, {1436, 1211}, {2193, 55113}, {2194, 38015}, {2203, 46836}, {2206, 40943}, {2208, 1213}, {3733, 7358}, {3737, 46663}, {4565, 20314}, {6612, 18635}, {7118, 38930}, {7151, 50036}, {7254, 53833}, {13138, 31946}, {32652, 661}, {36049, 4129}, {52384, 34829}, {55117, 18642}, {55211, 21262}
X(64124) = pole of line {6006, 7661} with respect to the incircle
X(64124) = pole of line {5882, 5919} with respect to the Feuerbach hyperbola
X(64124) = pole of line {223, 5219} with respect to the dual conic of Yff parabola
X(64124) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1000), X(55091)}}, {{A, B, C, X(11362), X(40446)}}
X(64124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1788, 11362}, {1, 3911, 6684}, {1, 4848, 28234}, {1, 7288, 10165}, {2, 3333, 21620}, {2, 62874, 21075}, {3, 11019, 63999}, {11, 32636, 4292}, {11, 4292, 18483}, {40, 14986, 63993}, {46, 12053, 28194}, {56, 17728, 1210}, {56, 1837, 4311}, {57, 50443, 4295}, {65, 44675, 13464}, {140, 5045, 13405}, {354, 5433, 13411}, {404, 26015, 63146}, {496, 37582, 516}, {497, 15803, 31730}, {499, 3338, 226}, {518, 6691, 6700}, {519, 58405, 63990}, {942, 3742, 58566}, {942, 37737, 12563}, {1125, 12563, 37737}, {1210, 4311, 1837}, {1737, 5563, 10106}, {1837, 4311, 515}, {3035, 34791, 59722}, {3086, 4295, 50443}, {3304, 24914, 31397}, {3337, 12047, 553}, {3337, 3582, 12047}, {3555, 13747, 6745}, {3600, 5704, 5587}, {3624, 10980, 3487}, {3634, 12577, 495}, {3742, 4999, 1125}, {3881, 6681, 59719}, {4293, 9581, 31673}, {4295, 50443, 946}, {4355, 7988, 5714}, {5122, 15171, 12512}, {5435, 14986, 40}, {5542, 19862, 11374}, {5708, 5886, 3671}, {9613, 54361, 50796}, {10164, 21625, 3295}, {10396, 54366, 6260}, {11373, 36279, 4301}, {12563, 37737, 64110}, {24239, 37607, 5717}, {27383, 64151, 41863}, {31249, 62824, 5084}, {34790, 52264, 20103}, {51785, 53056, 6361}

X(64125) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTERS-MIDPOINTS AND X(8)-CROSSPEDAL-OF-X(37)

Barycentrics    a*(3*a^3*(b+c)+(b^2-c^2)^2-a^2*(b^2+4*b*c+c^2)+a*(-3*b^3+b^2*c+b*c^2-3*c^3)) : :
X(64125) = -3*X[2]+X[64126], 3*X[165]+X[64134], -5*X[4687]+X[10446]

X(64125) lies on these lines: {2, 64126}, {3, 9}, {4, 5296}, {5, 5257}, {6, 1385}, {37, 517}, {40, 3731}, {44, 572}, {45, 1766}, {71, 31788}, {72, 61109}, {140, 5750}, {165, 64134}, {210, 10434}, {228, 64171}, {346, 5657}, {355, 966}, {391, 944}, {392, 19256}, {515, 63978}, {516, 3842}, {549, 50115}, {579, 9940}, {604, 5126}, {631, 5749}, {672, 11227}, {942, 1400}, {946, 3986}, {952, 3686}, {1030, 33862}, {1100, 15178}, {1108, 4266}, {1213, 9956}, {1334, 31798}, {1423, 37597}, {1449, 10246}, {1482, 3247}, {1696, 3428}, {1743, 3576}, {1764, 44307}, {2171, 50193}, {2178, 26286}, {2183, 31786}, {2245, 34339}, {2264, 10902}, {2265, 22054}, {2269, 9957}, {2285, 37582}, {2287, 33597}, {2321, 5690}, {2322, 45766}, {2325, 29327}, {2345, 26446}, {2347, 43065}, {2348, 15931}, {3161, 46937}, {3185, 58648}, {3294, 9856}, {3305, 16435}, {3509, 19516}, {3655, 37654}, {3666, 21363}, {3683, 20989}, {3693, 37619}, {3694, 58643}, {3707, 34773}, {3723, 33179}, {3730, 31787}, {3739, 29069}, {3931, 9548}, {3950, 11362}, {3965, 21061}, {3973, 7987}, {4007, 59503}, {4034, 12645}, {4058, 38127}, {4192, 10157}, {4205, 39591}, {4210, 17616}, {4245, 37620}, {4254, 8557}, {4268, 18857}, {4270, 37698}, {4271, 8609}, {4364, 12610}, {4557, 40659}, {4687, 10446}, {4698, 24220}, {4856, 13607}, {4877, 15952}, {4969, 32900}, {5036, 21853}, {5120, 10269}, {5124, 23961}, {5356, 41347}, {5759, 7390}, {5816, 18480}, {5836, 59727}, {5839, 37727}, {5927, 37400}, {6051, 31779}, {6666, 19512}, {6684, 17355}, {6907, 8804}, {6908, 27508}, {6988, 27382}, {6996, 17260}, {7308, 10856}, {7377, 17248}, {7397, 18230}, {7686, 25081}, {7982, 16673}, {8074, 59588}, {8245, 9441}, {8273, 61037}, {9840, 16601}, {10156, 17754}, {10222, 16777}, {10786, 27522}, {10855, 16059}, {10882, 25917}, {11231, 17303}, {11278, 16672}, {11349, 60969}, {11575, 56546}, {12555, 25430}, {12702, 16676}, {14557, 62857}, {14636, 21033}, {15254, 63968}, {15489, 25092}, {15569, 29311}, {15586, 16814}, {15624, 15733}, {15726, 41430}, {15837, 40910}, {16590, 28208}, {16671, 31662}, {16885, 17502}, {17257, 36698}, {17281, 50821}, {17330, 28204}, {18482, 36526}, {18591, 23980}, {19262, 27396}, {19514, 25068}, {19544, 40131}, {19547, 37623}, {21074, 51362}, {21511, 26699}, {21871, 37562}, {22027, 59658}, {24328, 60974}, {24471, 25065}, {25019, 30810}, {26285, 54285}, {28244, 34460}, {30618, 59682}, {31781, 59305}, {31837, 48930}, {31993, 54035}, {32612, 36743}, {32613, 36744}, {34524, 42316}, {35652, 62189}, {36670, 38108}, {37320, 55104}, {38869, 41391}, {40942, 52265}, {43174, 59585}, {59387, 62608}, {59733, 63976}

X(64125) = midpoint of X(i) and X(j) for these {i,j}: {37, 573}
X(64125) = reflection of X(i) in X(j) for these {i,j}: {24220, 4698}
X(64125) = complement of X(64126)
X(64125) = pole of line {4791, 14838} with respect to the Spieker circle
X(64125) = pole of line {30223, 37553} with respect to the Feuerbach hyperbola
X(64125) = intersection, other than A, B, C, of circumconics {{A, B, C, X(84), X(994)}}, {{A, B, C, X(1436), X(46018)}}
X(64125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9, 64121}, {9, 198, 59681}, {37, 573, 517}, {45, 37499, 1766}, {198, 54322, 15817}, {1766, 37499, 3579}, {3965, 21061, 34790}, {3986, 10443, 946}, {5257, 10445, 5}, {6684, 17355, 59680}, {7308, 10856, 19517}, {17257, 36698, 64122}, {44424, 59207, 10157}

X(64126) = ORTHOLOGY CENTER OF THESE TRIANGLES: GARCIA-REFLECTION AND X(8)-CROSSPEDAL-OF-X(37)

Barycentrics    a^3*(b-c)^2+a^4*(b+c)-a^2*(b-c)^2*(b+c)-2*b*(b-c)^2*c*(b+c)-a*(b-c)^2*(b^2+c^2) : :
X(64126) = -3*X[2]+2*X[64125]

X(64126) lies on these lines: {1, 10435}, {2, 64125}, {3, 10436}, {4, 7}, {5, 4357}, {8, 31781}, {10, 43172}, {30, 50116}, {37, 24220}, {40, 10442}, {57, 2050}, {65, 45189}, {69, 355}, {72, 20245}, {75, 517}, {86, 1385}, {104, 1014}, {142, 10445}, {222, 5307}, {226, 51414}, {286, 6528}, {307, 6831}, {314, 35631}, {320, 18480}, {379, 26651}, {381, 17274}, {392, 17183}, {511, 21443}, {515, 3664}, {516, 24325}, {527, 36728}, {572, 4670}, {573, 3739}, {894, 6996}, {912, 54344}, {944, 3945}, {946, 3663}, {952, 3879}, {962, 31995}, {982, 1699}, {1012, 18655}, {1086, 12610}, {1108, 17197}, {1111, 1122}, {1266, 22791}, {1350, 43169}, {1400, 53526}, {1418, 24237}, {1478, 10401}, {1482, 3875}, {1565, 3668}, {1721, 48944}, {1746, 4641}, {1764, 31993}, {1766, 4363}, {1826, 26932}, {1836, 7595}, {1867, 2995}, {1882, 30493}, {1944, 59681}, {2051, 3752}, {2262, 4858}, {3295, 10889}, {3655, 63110}, {3656, 50101}, {3662, 7377}, {3666, 10478}, {3667, 23810}, {3672, 5603}, {3696, 29311}, {3706, 10439}, {3753, 24993}, {3812, 50037}, {3817, 6682}, {3832, 45789}, {4021, 13464}, {4059, 4888}, {4301, 53594}, {4328, 63992}, {4360, 10222}, {4389, 9955}, {4459, 12723}, {4643, 5816}, {4887, 18483}, {4896, 31673}, {4909, 13607}, {4955, 15071}, {4967, 5690}, {5155, 8048}, {5224, 9956}, {5232, 5818}, {5249, 19542}, {5295, 10441}, {5439, 51558}, {5480, 53599}, {5587, 17272}, {5736, 33597}, {5749, 7397}, {5755, 28287}, {5778, 23151}, {5790, 17270}, {5799, 23537}, {5817, 36694}, {5832, 50861}, {5886, 17321}, {5887, 17139}, {5927, 20347}, {6173, 36731}, {6354, 21621}, {6646, 7384}, {6821, 10855}, {6999, 26806}, {7190, 63986}, {7321, 22793}, {7682, 24213}, {7686, 17861}, {7982, 17151}, {8233, 30380}, {8727, 9436}, {8728, 39591}, {9535, 19804}, {9856, 17753}, {10157, 30946}, {10455, 19259}, {10456, 10476}, {10573, 58800}, {10914, 20895}, {11230, 17322}, {11231, 28653}, {11278, 17160}, {12245, 32087}, {12545, 49598}, {12672, 17220}, {12699, 42697}, {13442, 64003}, {13624, 41847}, {14110, 18698}, {15178, 17394}, {15488, 20888}, {15726, 58583}, {15971, 20880}, {16465, 20242}, {17257, 36662}, {17273, 38140}, {17320, 51709}, {17345, 32431}, {17353, 19512}, {17378, 28204}, {17393, 33179}, {17614, 24540}, {17619, 24986}, {17885, 43037}, {18443, 56959}, {18650, 37468}, {19541, 40719}, {19925, 53598}, {20236, 43216}, {20258, 25066}, {20430, 49518}, {20907, 32475}, {21233, 24705}, {21246, 24336}, {21296, 59387}, {21554, 31658}, {22464, 41007}, {22753, 24179}, {23661, 43213}, {24474, 46704}, {24728, 48900}, {24774, 28351}, {25083, 30035}, {27633, 34460}, {28208, 39704}, {29010, 48934}, {29207, 50307}, {29347, 49462}, {30097, 37597}, {30949, 44424}, {32025, 38176}, {32099, 59388}, {33800, 50689}, {39550, 58787}, {39553, 50314}, {41010, 62780}, {44179, 46920}, {44307, 54035}, {45770, 55391}, {53596, 63980}, {54404, 59318}, {60895, 64085}

X(64126) = midpoint of X(i) and X(j) for these {i,j}: {75, 10446}
X(64126) = reflection of X(i) in X(j) for these {i,j}: {37, 24220}, {573, 3739}
X(64126) = anticomplement of X(64125)
X(64126) = X(i)-Dao conjugate of X(j) for these {i, j}: {64125, 64125}
X(64126) = pole of line {23880, 48320} with respect to the Conway circle
X(64126) = pole of line {905, 1577} with respect to the incircle
X(64126) = pole of line {1836, 10473} with respect to the Feuerbach hyperbola
X(64126) = pole of line {1734, 23880} with respect to the Suppa-Cucoanes circle
X(64126) = pole of line {3668, 3827} with respect to the dual conic of Yff parabola
X(64126) = intersection, other than A, B, C, of circumconics {{A, B, C, X(273), X(10435)}}, {{A, B, C, X(1439), X(18816)}}
X(64126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 7, 64122}, {7, 21279, 41004}, {7, 44735, 942}, {57, 10888, 2050}, {75, 10446, 517}, {894, 6996, 64121}, {10436, 10444, 3}, {10442, 25590, 40}, {17183, 24547, 392}

X(64127) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(56) AND X(8)-CROSSPEDAL-OF-X(55)

Barycentrics    (a+b-c)*(a-b+c)*(-2*a*(b-c)^2*(b+c)+(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(64127) lies on these lines: {1, 6907}, {2, 8543}, {4, 18237}, {5, 65}, {6, 34029}, {7, 11680}, {10, 13601}, {11, 57}, {12, 3340}, {30, 56}, {43, 52659}, {46, 6922}, {109, 37646}, {124, 13567}, {140, 11509}, {196, 37372}, {221, 5292}, {222, 11269}, {226, 518}, {354, 64115}, {388, 17532}, {442, 3485}, {495, 2099}, {497, 1617}, {499, 1466}, {553, 3829}, {613, 26098}, {651, 33142}, {908, 18236}, {959, 3142}, {999, 6923}, {1012, 3086}, {1118, 15763}, {1155, 37364}, {1159, 6980}, {1210, 6001}, {1214, 24210}, {1329, 4848}, {1368, 18588}, {1420, 37722}, {1454, 37356}, {1457, 64172}, {1465, 3914}, {1467, 50528}, {1470, 6914}, {1532, 18391}, {1538, 64157}, {1595, 1887}, {1596, 1875}, {1621, 37797}, {1708, 14022}, {1758, 33095}, {1788, 4187}, {1834, 10571}, {1837, 63988}, {2078, 3058}, {2646, 37424}, {3256, 5432}, {3339, 7741}, {3361, 37720}, {3474, 37374}, {3585, 34697}, {3649, 26481}, {3660, 10391}, {3671, 15844}, {3772, 15253}, {3813, 10106}, {3816, 3911}, {3820, 5692}, {3925, 5219}, {4292, 63980}, {4295, 6831}, {4298, 24387}, {4318, 33133}, {4915, 9578}, {5057, 37358}, {5128, 50031}, {5221, 10593}, {5226, 33108}, {5230, 34040}, {5259, 5433}, {5274, 10431}, {5305, 56913}, {5434, 31159}, {5435, 44447}, {5533, 37587}, {5563, 10948}, {5729, 8226}, {5843, 61716}, {5903, 10523}, {6051, 54346}, {6067, 60937}, {6284, 37583}, {6354, 62221}, {6604, 32816}, {6734, 12709}, {6882, 36279}, {6925, 14986}, {7288, 16370}, {7354, 26475}, {7672, 31053}, {7677, 35989}, {7678, 60939}, {7702, 24470}, {7951, 18421}, {8270, 17720}, {8728, 11375}, {9316, 29662}, {9955, 37544}, {10177, 30379}, {10306, 10321}, {10404, 10957}, {10473, 15986}, {10589, 38037}, {10629, 22770}, {10943, 18961}, {10947, 33925}, {10953, 31799}, {11235, 42886}, {11507, 52265}, {11510, 15172}, {12608, 44547}, {12699, 37550}, {14257, 37368}, {15048, 43039}, {15171, 37579}, {15518, 41338}, {15726, 60992}, {15804, 26105}, {15950, 26725}, {17064, 37695}, {17080, 33134}, {17527, 24914}, {17625, 26015}, {18242, 64163}, {18243, 41562}, {21616, 50206}, {21617, 61028}, {22766, 31775}, {23304, 53566}, {24806, 37715}, {25466, 64160}, {25568, 51416}, {25760, 26942}, {25973, 30827}, {26013, 41883}, {26333, 57278}, {26470, 57282}, {26482, 41696}, {28628, 47510}, {28997, 33114}, {30311, 60975}, {30384, 64106}, {31789, 59317}, {33105, 42289}, {33137, 34048}, {37321, 60681}, {37406, 37730}, {37438, 37737}, {37591, 63997}, {37738, 41709}, {38357, 62811}, {41871, 63994}, {42356, 52819}, {52367, 57283}, {62810, 64119}

X(64127) = pole of line {971, 10572} with respect to the Feuerbach hyperbola
X(64127) = pole of line {37597, 43035} with respect to the dual conic of Yff parabola
X(64127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 1836, 8727}, {497, 54366, 1617}, {1210, 63989, 64131}, {3671, 25639, 15844}, {3772, 34036, 15253}, {9316, 29662, 43043}, {18961, 26437, 18990}

X(64128) = COMPLEMENT OF X(12679)

Barycentrics    a*(2*a^6-a^5*(b+c)-a*(b-c)^2*(b+c)^3+a^4*(-5*b^2+8*b*c-5*c^2)-(b^2-c^2)^2*(b^2+c^2)+2*a^3*(b^3+b^2*c+b*c^2+c^3)+4*a^2*(b^4-2*b^3*c-2*b*c^3+c^4)) : :
X(64128) = -3*X[2]+X[12679], -3*X[16371]+X[63988], -3*X[17556]+X[52860]

X(64128) lies on these lines: {1, 17613}, {2, 12679}, {3, 960}, {10, 34862}, {20, 1155}, {30, 61530}, {35, 10167}, {40, 3880}, {46, 37022}, {55, 58567}, {56, 63985}, {57, 12651}, {63, 58637}, {65, 6909}, {72, 1768}, {84, 1376}, {100, 12680}, {104, 11260}, {165, 3916}, {404, 12688}, {411, 1776}, {474, 1709}, {496, 516}, {515, 8256}, {517, 62825}, {518, 10310}, {548, 952}, {601, 1386}, {603, 9371}, {631, 15254}, {944, 13528}, {958, 37560}, {962, 32636}, {971, 25440}, {993, 31787}, {1001, 37526}, {1012, 3812}, {1071, 2077}, {1385, 3898}, {1728, 7580}, {1770, 37374}, {1836, 6890}, {2551, 54052}, {2886, 6705}, {3035, 6260}, {3146, 9352}, {3149, 15297}, {3218, 7957}, {3358, 15587}, {3359, 5836}, {3523, 3683}, {3555, 5537}, {3647, 31658}, {3740, 7330}, {3742, 11496}, {3814, 22792}, {3838, 6833}, {3893, 38669}, {3913, 63430}, {4018, 5538}, {4188, 9961}, {4324, 10073}, {4420, 13243}, {4652, 5584}, {4973, 5493}, {5087, 6891}, {5123, 6256}, {5193, 17622}, {5204, 64150}, {5217, 10884}, {5220, 5732}, {5248, 11227}, {5289, 54156}, {5302, 6684}, {5438, 7992}, {5440, 15071}, {5450, 31788}, {5552, 12678}, {5660, 41690}, {5691, 56998}, {5722, 64076}, {5731, 37568}, {5794, 14647}, {5880, 6847}, {6223, 59572}, {6244, 62858}, {6259, 26364}, {6675, 64113}, {6691, 63989}, {6914, 40296}, {6916, 26066}, {6925, 24914}, {6926, 24703}, {6935, 28628}, {6966, 11375}, {6972, 17605}, {7171, 11500}, {8069, 64132}, {8227, 63266}, {8273, 35258}, {8666, 31798}, {9940, 51715}, {10164, 31445}, {10268, 12687}, {10269, 45776}, {10306, 34791}, {10391, 11509}, {10860, 15803}, {10916, 13226}, {11248, 12675}, {11277, 22936}, {11374, 60896}, {11491, 63432}, {12515, 48694}, {12616, 31775}, {12667, 37828}, {12672, 37561}, {12704, 42886}, {12705, 21164}, {12740, 37605}, {12775, 58591}, {13348, 22276}, {13369, 26285}, {13374, 37612}, {14110, 37403}, {15717, 62838}, {15823, 37108}, {15852, 17596}, {16141, 61653}, {16196, 40560}, {16371, 63988}, {16408, 54370}, {17502, 51717}, {17556, 52860}, {17567, 64130}, {17594, 37501}, {17606, 37437}, {17619, 41698}, {17647, 33899}, {18239, 56941}, {19862, 38123}, {19925, 50240}, {20586, 64189}, {22835, 26492}, {24025, 64055}, {24467, 35238}, {24982, 64000}, {25681, 63962}, {26927, 37577}, {31663, 31805}, {31730, 37623}, {31786, 40256}, {33557, 41542}, {37524, 64005}, {37572, 37711}, {41561, 59587}, {44663, 63391}, {50031, 64002}, {50371, 64021}, {57278, 59336}

X(64128) = midpoint of X(i) and X(j) for these {i,j}: {20, 1837}, {46, 37022}, {56, 63985}, {1768, 2932}, {5687, 10085}, {10310, 63399}, {20586, 64189}
X(64128) = reflection of X(i) in X(j) for these {i,j}: {59691, 3}, {63989, 6691}
X(64128) = complement of X(12679)
X(64128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1158, 960}, {3, 6001, 59691}, {3, 64118, 4640}, {3, 64129, 9943}, {84, 10270, 1376}, {165, 10085, 5687}, {1012, 59333, 3812}, {1071, 2077, 56176}, {1709, 16209, 474}, {1768, 59326, 72}, {3359, 12114, 5836}, {4297, 46684, 3579}, {10860, 15803, 64077}, {11496, 37534, 3742}, {12705, 21164, 25524}, {24467, 35238, 63976}

X(64129) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTERS-MIDPOINTS AND X(8)-CROSSPEDAL-OF-X(57)

Barycentrics    a*(a^5-b^5+a*(b-c)^4+b^4*c+b*c^4-c^5-a^4*(b+c)-2*a^3*(b^2-4*b*c+c^2)+2*a^2*(b^3-2*b^2*c-2*b*c^2+c^3)) : :
X(64129) = -3*X[21164]+X[63992]

X(64129) lies on these lines: {1, 1106}, {2, 1709}, {3, 960}, {4, 59333}, {8, 10085}, {9, 2272}, {10, 84}, {20, 46}, {35, 10884}, {36, 64150}, {40, 376}, {55, 10167}, {57, 497}, {63, 100}, {65, 37022}, {78, 15071}, {90, 6838}, {109, 1040}, {169, 43163}, {171, 990}, {191, 16192}, {214, 2950}, {222, 9371}, {223, 24025}, {226, 60896}, {355, 28458}, {404, 9961}, {411, 920}, {443, 12617}, {474, 12688}, {515, 3359}, {517, 63991}, {518, 6244}, {550, 59318}, {553, 60895}, {603, 54295}, {649, 15487}, {758, 6282}, {912, 35238}, {936, 7992}, {942, 64074}, {946, 37534}, {950, 64076}, {952, 63132}, {958, 31787}, {962, 3338}, {971, 1376}, {982, 61086}, {991, 17594}, {993, 30503}, {1001, 11227}, {1012, 54318}, {1026, 38502}, {1071, 3811}, {1125, 6935}, {1155, 1708}, {1210, 59336}, {1214, 2192}, {1329, 6259}, {1377, 49234}, {1378, 49235}, {1385, 4428}, {1445, 2951}, {1466, 12711}, {1490, 10270}, {1699, 3306}, {1706, 10864}, {1707, 13329}, {1728, 37421}, {1737, 6925}, {1742, 17596}, {1750, 35990}, {1754, 30265}, {1764, 39594}, {1766, 3509}, {1770, 6836}, {1779, 37419}, {1836, 37374}, {2057, 12059}, {2077, 18446}, {2082, 9315}, {2096, 64111}, {2285, 43173}, {2551, 12246}, {2720, 2739}, {2800, 37611}, {2807, 3784}, {2884, 40537}, {3218, 9778}, {3219, 64108}, {3295, 58567}, {3333, 4301}, {3336, 64005}, {3337, 9589}, {3339, 62836}, {3358, 5745}, {3522, 56288}, {3560, 40296}, {3576, 6950}, {3577, 3919}, {3579, 24467}, {3651, 63437}, {3740, 5779}, {3817, 5437}, {3870, 5537}, {3874, 6769}, {3878, 54156}, {3880, 30283}, {3885, 7991}, {3899, 12767}, {3911, 30223}, {3916, 5584}, {3927, 58637}, {3929, 43181}, {3931, 37501}, {4187, 12679}, {4292, 10629}, {4413, 5927}, {4414, 63395}, {4512, 10857}, {4650, 9441}, {4652, 59320}, {4845, 56380}, {5046, 52860}, {5119, 5731}, {5220, 58696}, {5248, 8726}, {5250, 7987}, {5272, 64013}, {5274, 37789}, {5281, 15298}, {5325, 6684}, {5435, 15299}, {5536, 31146}, {5587, 6951}, {5687, 12680}, {5691, 17579}, {5698, 14646}, {5709, 31730}, {5744, 42012}, {5794, 33899}, {5880, 8727}, {5882, 49163}, {5884, 12559}, {6175, 7989}, {6260, 26364}, {6361, 10806}, {6690, 60964}, {6700, 54227}, {6705, 26363}, {6745, 41561}, {6763, 63469}, {6796, 41854}, {6847, 12609}, {6848, 58405}, {6850, 12616}, {6865, 64190}, {6890, 12047}, {6891, 12608}, {6905, 50528}, {6922, 64119}, {6926, 21616}, {6972, 37692}, {7004, 8270}, {7291, 28124}, {7308, 58441}, {7688, 21165}, {7701, 31423}, {7967, 12703}, {7971, 30144}, {7994, 62823}, {7995, 8583}, {8167, 10156}, {8193, 26927}, {8257, 15726}, {8580, 15064}, {8730, 11495}, {9352, 36002}, {9355, 16569}, {9709, 12684}, {9746, 56518}, {9809, 27131}, {9812, 27003}, {9856, 25524}, {9940, 11496}, {9948, 57284}, {10157, 16112}, {10175, 18540}, {10200, 63989}, {10306, 12675}, {10391, 37541}, {10393, 11509}, {10446, 60717}, {10582, 11407}, {10826, 37437}, {10980, 43166}, {11015, 63141}, {11248, 13369}, {11522, 35010}, {11531, 62832}, {12114, 31788}, {12115, 45633}, {12436, 21628}, {12513, 31798}, {12515, 38759}, {12560, 58626}, {12565, 15803}, {12652, 18193}, {12678, 17757}, {12699, 37612}, {13257, 41706}, {13388, 61094}, {13389, 61095}, {13405, 43177}, {13528, 63432}, {15621, 53296}, {15931, 35258}, {17122, 64134}, {18444, 59337}, {21164, 63992}, {21635, 30827}, {24477, 35514}, {24703, 37364}, {25568, 36996}, {26066, 37424}, {26921, 31663}, {28164, 58808}, {28236, 63137}, {29068, 53898}, {29844, 61087}, {31419, 61556}, {32916, 59620}, {34628, 36005}, {35242, 55104}, {35986, 55873}, {37403, 63391}, {37550, 64075}, {37551, 54290}, {37561, 63986}, {37582, 64077}, {39635, 53892}, {43174, 57279}, {47848, 59645}, {48697, 52026}, {49500, 62320}, {50031, 58798}, {51786, 61294}, {55870, 62838}, {56941, 64148}, {58678, 61005}, {59458, 59606}, {59624, 59677}, {59646, 60784}, {59665, 59674}, {60786, 62811}, {60938, 63974}

X(64129) = midpoint of X(i) and X(j) for these {i,j}: {20, 18391}, {40, 63430}, {57, 10860}, {200, 30304}, {2096, 64111}, {3359, 7171}, {7994, 62823}
X(64129) = reflection of X(i) in X(j) for these {i,j}: {997, 3}, {24703, 37364}, {54286, 3359}, {59687, 20103}
X(64129) = complement of X(64130)
X(64129) = X(i)-Dao conjugate of X(j) for these {i, j}: {6180, 9312}
X(64129) = pole of line {3667, 53395} with respect to the Bevan circle
X(64129) = pole of line {521, 53278} with respect to the circumcircle
X(64129) = pole of line {6735, 59969} with respect to the orthoptic circle of the Steiner Inellipse
X(64129) = pole of line {8581, 20323} with respect to the Feuerbach hyperbola
X(64129) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {20, 6790, 18391}
X(64129) = intersection, other than A, B, C, of circumconics {{A, B, C, X(103), X(3435)}}, {{A, B, C, X(7045), X(20588)}}, {{A, B, C, X(10307), X(36101)}}, {{A, B, C, X(44040), X(63985)}}
X(64129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1709, 54370}, {3, 1158, 12514}, {3, 6001, 997}, {3, 9943, 12520}, {40, 63399, 62858}, {40, 63430, 519}, {40, 9841, 4297}, {40, 9845, 2136}, {57, 10860, 516}, {63, 100, 20588}, {165, 1768, 63}, {165, 30304, 200}, {200, 30304, 2801}, {404, 9961, 63988}, {515, 3359, 54286}, {936, 7992, 31803}, {1155, 5918, 7580}, {1490, 10270, 25440}, {3218, 9778, 41338}, {3359, 7171, 515}, {3522, 56288, 59340}, {4512, 10857, 52769}, {4640, 10178, 3}, {5437, 11372, 3817}, {5884, 37531, 12559}, {5918, 7580, 43178}, {6361, 26877, 12704}, {6916, 14647, 10}, {8580, 64197, 15064}, {10164, 59687, 20103}, {12705, 37526, 1125}, {16209, 63988, 404}, {37403, 64021, 63391}, {58441, 60911, 7308}

X(64130) = ORTHOLOGY CENTER OF THESE TRIANGLES: GARCIA-REFLECTION AND X(8)-CROSSPEDAL-OF-X(57)

Barycentrics    a^6-3*a^4*(b-c)^2-8*a*b*(b-c)^2*c*(b+c)-(b-c)^4*(b+c)^2+3*a^2*(b^2-c^2)^2 : :
X(64130) =

X(64130) lies on these lines: {1, 6223}, {2, 1709}, {4, 65}, {7, 1699}, {8, 12059}, {10, 7995}, {20, 997}, {36, 54052}, {40, 5811}, {55, 5658}, {56, 12246}, {79, 10429}, {84, 3086}, {144, 41338}, {149, 152}, {165, 18228}, {189, 24026}, {200, 329}, {210, 35514}, {226, 11372}, {278, 2192}, {281, 20307}, {354, 36996}, {388, 6259}, {452, 12520}, {496, 12684}, {497, 971}, {515, 7962}, {519, 962}, {938, 15071}, {944, 3058}, {946, 4654}, {1056, 12678}, {1058, 12680}, {1155, 14646}, {1158, 6848}, {1210, 7992}, {1456, 63965}, {1479, 9799}, {1490, 4294}, {1532, 14647}, {1538, 10589}, {1768, 5435}, {1770, 50700}, {1851, 38389}, {2096, 22753}, {2400, 20295}, {2478, 9961}, {2550, 5927}, {2886, 16112}, {2999, 53087}, {3085, 6260}, {3146, 11415}, {3149, 64190}, {3332, 41011}, {3427, 46435}, {3452, 10860}, {3474, 19541}, {3715, 5657}, {3817, 9776}, {3925, 5817}, {3982, 38036}, {4293, 63992}, {4302, 54051}, {4305, 6261}, {4423, 21151}, {4679, 5918}, {4847, 64197}, {5057, 10431}, {5084, 9943}, {5154, 10940}, {5177, 12617}, {5180, 52851}, {5225, 5787}, {5226, 60925}, {5229, 22792}, {5249, 38037}, {5437, 10863}, {5531, 64146}, {5536, 28610}, {5537, 64083}, {5553, 10308}, {5698, 7580}, {5732, 40998}, {5748, 21635}, {5758, 41869}, {5768, 26333}, {5804, 5884}, {5813, 28124}, {5815, 7991}, {5903, 54199}, {6245, 10591}, {6284, 64144}, {6847, 12608}, {6850, 31937}, {6927, 64118}, {6964, 59333}, {6987, 50528}, {7288, 34862}, {7952, 15811}, {7964, 21168}, {7965, 61716}, {7987, 50742}, {7989, 11024}, {8166, 17728}, {8226, 60987}, {9355, 33137}, {9581, 9948}, {9612, 21628}, {9778, 31018}, {9949, 19925}, {10085, 14986}, {10157, 26040}, {10167, 26105}, {10241, 64157}, {10248, 14450}, {10446, 39594}, {10525, 31828}, {10582, 43177}, {10624, 63981}, {10857, 43182}, {10864, 12053}, {11037, 11522}, {11051, 13609}, {11381, 52082}, {11496, 18243}, {12047, 37434}, {12247, 33519}, {12514, 37421}, {12565, 12572}, {12667, 12672}, {13257, 25568}, {15726, 24703}, {15733, 61010}, {15931, 52653}, {17484, 20015}, {17567, 64128}, {17613, 59572}, {17650, 31788}, {18990, 48664}, {26098, 64134}, {27521, 28966}, {30223, 54366}, {31146, 60895}, {33899, 54361}, {36002, 44447}, {37822, 64111}, {38385, 40218}, {41012, 63984}, {41325, 44424}, {41698, 59387}, {41853, 59418}, {59412, 61740}, {63986, 64120}

X(64130) = reflection of X(i) in X(j) for these {i,j}: {20, 997}, {200, 59687}, {2096, 22753}, {3474, 19541}, {4293, 63992}, {5768, 26333}, {7994, 21060}, {10860, 3452}, {18391, 4}, {30304, 11019}, {63430, 946}, {64111, 37822}, {64157, 10241}
X(64130) = anticomplement of X(64129)
X(64130) = pole of line {6129, 7658} with respect to the incircle
X(64130) = pole of line {4, 10307} with respect to the Feuerbach hyperbola
X(64130) = pole of line {279, 1422} with respect to the dual conic of Yff parabola
X(64130) = intersection, other than A, B, C, of circumconics {{A, B, C, X(158), X(36620)}}, {{A, B, C, X(1857), X(3062)}}, {{A, B, C, X(10309), X(47372)}}
X(64130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6001, 18391}, {4, 63962, 4295}, {84, 63989, 3086}, {354, 41706, 36996}, {516, 21060, 7994}, {516, 59687, 200}, {938, 54228, 15071}, {1699, 30304, 11019}, {3817, 60896, 9776}, {6259, 9856, 388}, {9809, 9812, 5905}, {12679, 12688, 4}

X(64131) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(56) AND X(8)-CROSSPEDAL-OF-X(65)

Barycentrics    a*(a-b-c)*(2*a^3*b*c+2*a*b*(b-c)^2*c+a^4*(b+c)-2*a^2*(b-c)^2*(b+c)+(b-c)^2*(b+c)^3) : :
X(64131) = -3*X[10072]+2*X[58576], -3*X[11238]+X[64046], -X[37567]+3*X[61653]

X(64131) lies on circumconic {{A, B, C, X(9375), X(34048)}} and on these lines: {1, 1864}, {2, 12529}, {3, 30223}, {4, 3427}, {5, 50195}, {11, 113}, {12, 10157}, {33, 16466}, {36, 16143}, {55, 5044}, {56, 971}, {57, 7992}, {65, 1699}, {72, 497}, {78, 15733}, {90, 8071}, {145, 17615}, {210, 1697}, {354, 50443}, {388, 5927}, {390, 3876}, {392, 3486}, {496, 912}, {499, 9940}, {517, 1479}, {518, 10392}, {595, 51361}, {774, 1465}, {920, 37623}, {938, 12709}, {946, 5173}, {950, 960}, {962, 41539}, {999, 40263}, {1001, 10393}, {1071, 3086}, {1104, 45272}, {1125, 10391}, {1193, 2310}, {1210, 6001}, {1385, 22760}, {1420, 12680}, {1466, 1709}, {1470, 34862}, {1490, 1617}, {1682, 11997}, {1708, 64077}, {1728, 3428}, {1737, 15908}, {1776, 3916}, {1836, 37544}, {1857, 1871}, {1903, 2257}, {2057, 52804}, {2136, 46677}, {2646, 5259}, {2886, 10395}, {3057, 3632}, {3059, 10384}, {3073, 46974}, {3216, 9371}, {3333, 61705}, {3339, 17634}, {3340, 61718}, {3361, 63995}, {3485, 5728}, {3579, 11502}, {3586, 14110}, {3601, 5696}, {3616, 10177}, {3624, 17603}, {3646, 10383}, {3678, 12575}, {3681, 9785}, {3753, 31418}, {3868, 5274}, {3889, 18220}, {3911, 9943}, {3913, 51380}, {3927, 54408}, {4294, 64107}, {4298, 31871}, {4314, 10176}, {4383, 54295}, {5045, 11376}, {5048, 41696}, {5119, 58643}, {5172, 40262}, {5204, 31805}, {5250, 58648}, {5252, 9947}, {5253, 17616}, {5265, 11220}, {5433, 11227}, {5435, 9961}, {5439, 10589}, {5570, 37720}, {5572, 63274}, {5687, 58649}, {5691, 64106}, {5694, 18527}, {5711, 9817}, {5722, 5887}, {5784, 8583}, {5882, 32159}, {5886, 16193}, {5904, 17642}, {5919, 17632}, {6051, 14547}, {6261, 57278}, {6282, 10092}, {6284, 31793}, {6904, 17668}, {6918, 59335}, {7008, 57276}, {7080, 18236}, {7082, 26357}, {7288, 10167}, {7741, 13750}, {7743, 26475}, {7957, 9580}, {7962, 9954}, {8581, 30330}, {8715, 62357}, {9119, 40963}, {9614, 18397}, {9668, 37585}, {9669, 24474}, {9956, 10958}, {9957, 10950}, {10072, 58576}, {10382, 31435}, {10396, 12664}, {10572, 31786}, {10598, 64021}, {10624, 63976}, {10629, 37822}, {10785, 58588}, {10916, 15845}, {10980, 30290}, {11018, 11375}, {11019, 31803}, {11238, 64046}, {11379, 18421}, {11508, 64116}, {11522, 18412}, {11531, 30294}, {12528, 14986}, {12589, 34381}, {12617, 15844}, {12672, 13601}, {12675, 41562}, {12705, 37541}, {12706, 62775}, {12710, 13411}, {12915, 37722}, {13369, 15325}, {13374, 18389}, {14054, 51409}, {15071, 37566}, {15171, 31837}, {15172, 31835}, {15254, 54430}, {16201, 17718}, {16469, 58906}, {17609, 41861}, {17637, 26725}, {17658, 64068}, {18239, 41426}, {18398, 50444}, {18732, 56884}, {18961, 22792}, {19541, 37550}, {20117, 63999}, {20789, 37738}, {22753, 62810}, {23537, 38357}, {24430, 37592}, {24914, 31787}, {24929, 62333}, {26476, 34339}, {31397, 58631}, {31658, 37601}, {31792, 37740}, {31798, 40663}, {31821, 64041}, {33575, 63756}, {37080, 63972}, {37462, 60925}, {37567, 61653}, {37594, 61398}, {37711, 54134}, {45776, 64163}, {51413, 52359}, {51489, 59320}, {63967, 63993}, {64124, 64132}

X(64131) = midpoint of X(i) and X(j) for these {i,j}: {56, 1898}, {1837, 64042}, {12701, 41538}
X(64131) = reflection of X(i) in X(j) for these {i,j}: {5687, 58649}, {37738, 20789}, {50196, 496}, {64132, 64124}
X(64131) = pole of line {53527, 59972} with respect to the incircle
X(64131) = pole of line {30, 40} with respect to the Feuerbach hyperbola
X(64131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 1858, 942}, {56, 1898, 971}, {65, 10896, 5806}, {65, 17604, 9581}, {210, 9848, 1697}, {392, 9844, 3486}, {496, 912, 50196}, {946, 44547, 5173}, {1071, 3086, 3660}, {1210, 63989, 64127}, {5904, 51785, 17642}, {7082, 26357, 31445}, {9856, 64157, 65}, {12528, 14986, 17625}, {12672, 18391, 13601}, {12701, 41538, 517}, {14100, 25917, 3601}, {15299, 63988, 56}, {17634, 61660, 3339}, {18220, 40269, 3889}, {41562, 44675, 12675}

X(64132) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(56) AND X(8)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a^5*(b+c)-2*a^3*(b-c)^2*(b+c)+a*(b-c)^4*(b+c)+2*a^2*(b-c)^2*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)-a^4*(b^2-4*b*c+c^2)) : :
X(64132) = -X[1898]+3*X[17728], -X[6928]+3*X[10202]

X(64132) lies on these lines: {1, 1407}, {4, 10305}, {7, 6836}, {30, 553}, {35, 10178}, {36, 191}, {40, 17625}, {46, 518}, {56, 6001}, {57, 1071}, {63, 37282}, {65, 944}, {72, 3928}, {79, 3255}, {84, 1467}, {142, 50206}, {226, 6922}, {241, 44706}, {354, 1058}, {376, 3057}, {495, 40296}, {496, 58573}, {516, 50196}, {517, 4311}, {774, 61376}, {912, 6924}, {936, 17612}, {938, 11220}, {946, 3660}, {971, 1210}, {982, 1044}, {990, 41344}, {1012, 34489}, {1066, 9371}, {1076, 3782}, {1086, 1838}, {1122, 15498}, {1155, 63976}, {1158, 1617}, {1319, 6906}, {1376, 59336}, {1408, 4227}, {1420, 12672}, {1466, 18446}, {1470, 37837}, {1473, 40660}, {1478, 3812}, {1479, 15726}, {1745, 3752}, {1770, 5570}, {1788, 14872}, {1829, 3937}, {1836, 10531}, {1858, 32636}, {1898, 17728}, {2093, 2136}, {2094, 3868}, {2771, 41547}, {2956, 7290}, {3085, 8581}, {3086, 12688}, {3218, 35979}, {3333, 12711}, {3361, 15071}, {3468, 6610}, {3486, 63432}, {3487, 17603}, {3576, 12709}, {3624, 30290}, {3666, 4303}, {3671, 16193}, {3742, 12047}, {3753, 9613}, {3848, 37692}, {3873, 56936}, {3874, 64117}, {3911, 5777}, {4188, 51379}, {4294, 5918}, {4298, 50195}, {4299, 64045}, {4304, 31805}, {4306, 17102}, {4312, 5572}, {4325, 53615}, {4640, 7742}, {5044, 11575}, {5122, 31837}, {5173, 12005}, {5204, 21165}, {5252, 6897}, {5435, 12528}, {5439, 6173}, {5603, 17634}, {5728, 60955}, {5768, 12671}, {5836, 11112}, {5882, 13601}, {5885, 31776}, {5903, 24473}, {5904, 53056}, {6361, 17642}, {6734, 17616}, {6763, 59323}, {6831, 64115}, {6848, 18239}, {6875, 37605}, {6915, 37789}, {6928, 10202}, {6991, 60988}, {7354, 7686}, {7962, 17624}, {8069, 64128}, {9614, 17626}, {9856, 44675}, {9961, 14986}, {10106, 31788}, {10179, 21842}, {10396, 30304}, {10609, 11570}, {10624, 12915}, {10827, 44217}, {11227, 13411}, {12053, 58576}, {12059, 58649}, {12136, 51359}, {12262, 26927}, {12664, 54366}, {12680, 17632}, {12943, 16616}, {13373, 39542}, {14058, 26011}, {15325, 31937}, {15326, 64043}, {15528, 24465}, {16370, 37618}, {17646, 45700}, {17649, 63992}, {17660, 38665}, {18191, 31900}, {18389, 37544}, {18990, 34339}, {21454, 50695}, {22053, 37528}, {24914, 58631}, {25415, 58609}, {26201, 31794}, {26866, 64040}, {26910, 64039}, {26914, 41722}, {28381, 61412}, {30493, 46017}, {31391, 59386}, {31397, 31787}, {34880, 52270}, {37579, 64118}, {40293, 59691}, {41562, 64157}, {50193, 61292}, {51380, 59675}, {51489, 60961}, {58637, 58887}, {64021, 64106}, {64124, 64131}

X(64132) = midpoint of X(i) and X(j) for these {i,j}: {1071, 3149}, {4299, 64045}
X(64132) = reflection of X(i) in X(j) for these {i,j}: {496, 58573}, {6922, 9940}, {12053, 58576}, {12059, 58649}, {45120, 37282}, {64131, 64124}
X(64132) = pole of line {3737, 7254} with respect to the incircle
X(64132) = pole of line {3304, 3649} with respect to the Feuerbach hyperbola
X(64132) = pole of line {47921, 50346} with respect to the Suppa-Cucoanes circle
X(64132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 1071, 44547}, {84, 1467, 57278}, {942, 13369, 10391}, {7354, 18838, 7686}, {9943, 63994, 1}, {37566, 63995, 4}

X(64133) = ISOTOMIC CONJUGATE OF X(4492)

Barycentrics    b*c*(2*a^2+b*c) : :

X(64133) lies on these lines: {1, 76}, {2, 668}, {6, 40859}, {8, 274}, {10, 24524}, {12, 7752}, {32, 6645}, {33, 58782}, {35, 7782}, {36, 7771}, {37, 34283}, {39, 330}, {55, 99}, {56, 1078}, {69, 1056}, {75, 519}, {83, 16502}, {85, 10106}, {86, 996}, {142, 49774}, {145, 17143}, {148, 9664}, {172, 6179}, {183, 999}, {192, 538}, {194, 1500}, {264, 1870}, {304, 33941}, {305, 3920}, {310, 17018}, {312, 29574}, {313, 17394}, {315, 388}, {316, 1478}, {321, 17389}, {325, 495}, {334, 29659}, {335, 3735}, {346, 48869}, {384, 2241}, {385, 2242}, {386, 34063}, {390, 32815}, {496, 59635}, {497, 11185}, {498, 7769}, {513, 56129}, {514, 36494}, {551, 6381}, {612, 57518}, {664, 6063}, {693, 14421}, {811, 7017}, {873, 7257}, {874, 4363}, {894, 10027}, {940, 41232}, {956, 16992}, {995, 37678}, {1007, 8164}, {1060, 62698}, {1107, 24656}, {1125, 6376}, {1215, 27808}, {1221, 21746}, {1269, 17393}, {1438, 36548}, {1509, 5711}, {1574, 27318}, {1698, 25280}, {1914, 3972}, {1930, 7278}, {1965, 29651}, {1975, 3295}, {2176, 17499}, {2275, 7786}, {2276, 7757}, {2388, 25295}, {3085, 7763}, {3086, 32832}, {3096, 26561}, {3212, 50626}, {3230, 24514}, {3241, 4441}, {3244, 17144}, {3263, 50286}, {3264, 41847}, {3600, 3785}, {3616, 18140}, {3622, 18135}, {3632, 32092}, {3633, 32104}, {3636, 20943}, {3672, 48838}, {3679, 52716}, {3734, 4366}, {3758, 3997}, {3765, 16826}, {3770, 16777}, {3809, 46897}, {3907, 52619}, {3934, 31999}, {3948, 29570}, {3963, 17379}, {3975, 16831}, {4293, 14907}, {4359, 29617}, {4385, 18156}, {4393, 20913}, {4406, 4844}, {4413, 56801}, {4479, 51071}, {4505, 17369}, {4506, 4670}, {4555, 34230}, {4561, 41276}, {4666, 18153}, {4692, 14210}, {4696, 33932}, {4710, 43997}, {4737, 30758}, {4890, 21299}, {4968, 33935}, {5152, 10053}, {5194, 39266}, {5204, 43459}, {5209, 51356}, {5261, 32816}, {5264, 17103}, {5270, 7860}, {5280, 7894}, {5283, 21226}, {5291, 16998}, {5297, 11059}, {5299, 7878}, {5311, 51857}, {5434, 7811}, {5712, 30710}, {5750, 17786}, {6198, 54412}, {6382, 18059}, {6384, 6685}, {6655, 9651}, {7049, 59528}, {7191, 40022}, {7200, 24326}, {7208, 43262}, {7354, 7802}, {7750, 18990}, {7760, 54416}, {7770, 16781}, {7773, 9654}, {7774, 31409}, {7777, 31476}, {7783, 31451}, {7785, 9650}, {7790, 26590}, {7796, 15888}, {7799, 10056}, {7809, 11237}, {7814, 37719}, {7835, 26629}, {7847, 9597}, {7857, 26686}, {7858, 9596}, {7930, 30104}, {7942, 30103}, {8024, 29815}, {9331, 11055}, {9466, 30998}, {9665, 16044}, {9780, 25278}, {10009, 24325}, {10459, 30092}, {10589, 53127}, {10896, 15031}, {11132, 22929}, {11133, 22884}, {12577, 16284}, {14615, 55392}, {14839, 24282}, {14986, 32828}, {15171, 32819}, {15325, 37688}, {16085, 16394}, {16549, 29699}, {16552, 29383}, {16589, 41838}, {16604, 25102}, {16748, 20011}, {16784, 60855}, {16788, 18047}, {16971, 17027}, {17023, 20917}, {17024, 39998}, {17030, 17448}, {17033, 20963}, {17045, 18144}, {17140, 21272}, {17149, 43223}, {17165, 53332}, {17234, 30109}, {17280, 48864}, {17302, 48840}, {17321, 44139}, {17350, 52963}, {17351, 52964}, {17358, 48860}, {17380, 18143}, {17381, 18040}, {17383, 48844}, {17391, 20891}, {17397, 52043}, {17398, 30473}, {17750, 17752}, {17762, 49564}, {18064, 19684}, {18145, 38314}, {18147, 48855}, {18152, 29814}, {18447, 41009}, {18827, 24464}, {19804, 50095}, {19807, 42028}, {19810, 62808}, {20017, 30599}, {20055, 60736}, {20925, 62697}, {20955, 33945}, {21219, 27269}, {21223, 21838}, {21232, 24631}, {24254, 31317}, {24331, 39044}, {24512, 30114}, {25286, 26037}, {25296, 46933}, {25298, 29576}, {25528, 59562}, {26035, 26759}, {26100, 26807}, {26234, 30806}, {26959, 63493}, {27846, 31005}, {28809, 29624}, {29605, 60730}, {29612, 59212}, {29634, 51861}, {29822, 30964}, {30022, 59305}, {30179, 34542}, {31416, 33028}, {31456, 33047}, {31477, 31859}, {31488, 33045}, {31490, 33036}, {31625, 55919}, {32005, 32450}, {32025, 48852}, {32937, 33948}, {33296, 52572}, {33682, 52138}, {33937, 33943}, {33938, 33942}, {34020, 59297}, {35102, 49516}, {35957, 35961}, {36871, 41142}, {37670, 54391}, {40790, 41259}, {41849, 56250}, {44140, 48858}, {46180, 49528}, {49470, 60719}, {49481, 49777}, {49753, 51058}, {51314, 55245}, {55470, 59335}, {61413, 62705}

X(64133) = isotomic conjugate of X(4492)
X(64133) = anticomplement of X(1573)
X(64133) = trilinear pole of line {4406, 47762}
X(64133) = perspector of circumconic {{A, B, C, X(889), X(37133)}}
X(64133) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4492}, {32, 57725}, {560, 30635}, {1501, 57920}, {4775, 8695}
X(64133) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4492}, {1573, 1573}, {6374, 30635}, {6376, 57725}, {17237, 46901}, {25760, 3764}
X(64133) = X(i)-cross conjugate of X(j) for these {i, j}: {46897, 3758}
X(64133) = pole of line {891, 47780} with respect to the Steiner circumellipse
X(64133) = pole of line {891, 47779} with respect to the Steiner inellipse
X(64133) = pole of line {995, 1001} with respect to the Wallace hyperbola
X(64133) = pole of line {4389, 4871} with respect to the dual conic of Yff parabola
X(64133) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(609)}}, {{A, B, C, X(2), X(47762)}}, {{A, B, C, X(32), X(4161)}}, {{A, B, C, X(257), X(3760)}}, {{A, B, C, X(335), X(3761)}}, {{A, B, C, X(513), X(16975)}}, {{A, B, C, X(519), X(4844)}}, {{A, B, C, X(668), X(56129)}}, {{A, B, C, X(870), X(3227)}}, {{A, B, C, X(996), X(1002)}}, {{A, B, C, X(1015), X(55919)}}, {{A, B, C, X(1573), X(4492)}}, {{A, B, C, X(1911), X(4116)}}, {{A, B, C, X(2230), X(52205)}}, {{A, B, C, X(3679), X(50086)}}, {{A, B, C, X(4406), X(53219)}}, {{A, B, C, X(18359), X(33936)}}, {{A, B, C, X(18836), X(40365)}}, {{A, B, C, X(20569), X(31002)}}, {{A, B, C, X(58027), X(59255)}}
X(64133) = barycentric product X(i)*X(j) for these (i, j): {190, 4406}, {274, 46897}, {310, 3997}, {350, 43262}, {561, 609}, {3227, 62627}, {3758, 75}, {4554, 47729}, {4761, 799}, {7035, 7208}, {17126, 76}, {47762, 668}, {52379, 7276}
X(64133) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4492}, {75, 57725}, {76, 30635}, {561, 57920}, {609, 31}, {3758, 1}, {3809, 2276}, {3997, 42}, {4406, 514}, {4604, 8695}, {4761, 661}, {4844, 4893}, {7208, 244}, {7276, 2171}, {17126, 6}, {43262, 291}, {46897, 37}, {47729, 650}, {47762, 513}, {62627, 536}
X(64133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1909, 76}, {1, 3510, 4116}, {1, 3761, 350}, {2, 9263, 16975}, {75, 3879, 34282}, {75, 49779, 33936}, {85, 39731, 33940}, {145, 34284, 17143}, {350, 1909, 3761}, {384, 2241, 53680}, {551, 6381, 30963}, {1107, 24656, 27255}, {1909, 25303, 1}, {2275, 27020, 7786}, {3679, 52716, 60706}, {3765, 16826, 30830}, {4692, 14210, 33931}, {6381, 30963, 18146}, {16604, 25102, 27091}, {18059, 32771, 6382}, {24524, 31997, 10}, {26234, 30806, 33934}, {33938, 41875, 33942}

X(64134) = ORTHOLOGY CENTER OF THESE TRIANGLES: GARCIA-REFLECTION AND X(8)-CROSSPEDAL-OF-X(75)

Barycentrics    a*(-2*a*(b-c)^2*(b+c)+a^2*(b^2-3*b*c+c^2)+(b-c)^2*(b^2+3*b*c+c^2)) : :
X(64134) = -3*X[165]+4*X[64125], -3*X[7611]+2*X[48929]

X(64134) lies on circumconic {{A, B, C, X(3062), X(41796)}} and on these lines: {1, 971}, {2, 10868}, {3, 8245}, {4, 240}, {6, 9355}, {7, 2310}, {9, 1721}, {10, 9950}, {37, 1742}, {38, 9812}, {40, 7996}, {43, 5927}, {45, 11495}, {65, 41680}, {75, 45305}, {84, 37607}, {165, 64125}, {170, 16601}, {171, 1709}, {192, 28850}, {238, 990}, {241, 31391}, {244, 9779}, {355, 29327}, {382, 5492}, {386, 31871}, {513, 18161}, {516, 984}, {517, 49448}, {651, 4336}, {740, 48878}, {756, 9778}, {846, 7580}, {894, 48900}, {900, 27471}, {946, 3976}, {982, 1699}, {1086, 42356}, {1253, 29007}, {1376, 34524}, {1423, 12723}, {1490, 37573}, {1736, 4312}, {1738, 63970}, {1750, 17594}, {1754, 7262}, {1756, 33536}, {1757, 5779}, {1758, 64152}, {1765, 53402}, {1836, 24430}, {1854, 2647}, {2170, 9309}, {2292, 3146}, {2340, 25722}, {2783, 48938}, {2801, 49490}, {2808, 7201}, {2826, 24098}, {2938, 24450}, {2951, 3731}, {2957, 38530}, {3061, 24274}, {3091, 7613}, {3120, 10883}, {3332, 24695}, {3474, 7069}, {3551, 18208}, {3663, 63973}, {3667, 21191}, {3673, 34848}, {3720, 11220}, {3729, 4073}, {3751, 64197}, {3782, 7965}, {3817, 17063}, {3821, 36652}, {3832, 24443}, {3912, 59688}, {3923, 13727}, {3944, 8727}, {4014, 41777}, {4319, 8545}, {4357, 21629}, {4414, 36002}, {4416, 28849}, {4488, 4712}, {4695, 54448}, {4890, 14520}, {4902, 24802}, {5121, 10863}, {5228, 60910}, {5255, 12705}, {5268, 10860}, {5293, 64074}, {5400, 61740}, {5691, 37598}, {5693, 52524}, {5713, 16127}, {5805, 32857}, {5851, 17365}, {5918, 44307}, {6172, 21039}, {6837, 24161}, {6996, 24728}, {7126, 30301}, {7174, 12652}, {7271, 9814}, {7274, 30330}, {7377, 41886}, {7611, 48929}, {7701, 37530}, {7982, 55724}, {8226, 17889}, {9364, 9817}, {9801, 17257}, {9809, 24725}, {9944, 27626}, {9947, 59294}, {9961, 59305}, {9962, 28287}, {10157, 16569}, {10167, 26102}, {10394, 42289}, {11203, 37400}, {11227, 25502}, {11358, 17628}, {11531, 62179}, {12571, 24046}, {12618, 32784}, {12699, 29369}, {13161, 21628}, {13329, 60911}, {15310, 20430}, {15837, 51300}, {16496, 43166}, {17122, 64129}, {17333, 28854}, {17334, 38454}, {17363, 28870}, {17596, 19541}, {17601, 44425}, {17613, 56010}, {17635, 37555}, {17747, 24449}, {17861, 23821}, {18216, 60953}, {18360, 63676}, {19551, 30300}, {19925, 24440}, {24010, 63165}, {24280, 44694}, {24372, 32431}, {24708, 40937}, {25072, 43151}, {25375, 25521}, {26098, 64130}, {28043, 60966}, {29016, 49452}, {29301, 48902}, {29349, 31395}, {29571, 43182}, {30854, 59621}, {33149, 53599}, {34852, 59573}, {34862, 37608}, {36991, 64168}, {37365, 45782}, {37529, 40263}, {37617, 63992}, {39126, 63597}, {53524, 61716}, {57022, 60933}, {59387, 64176}, {61705, 63982}

X(64134) = reflection of X(i) in X(j) for these {i,j}: {75, 45305}, {1742, 37}
X(64134) = anticomplement of X(59620)
X(64134) = X(i)-Dao conjugate of X(j) for these {i, j}: {41796, 3177}, {59620, 59620}
X(64134) = pole of line {3900, 4885} with respect to the incircle
X(64134) = pole of line {1577, 3900} with respect to the Suppa-Cucoanes circle
X(64134) = pole of line {9311, 41777} with respect to the dual conic of Yff parabola
X(64134) = barycentric product X(i)*X(j) for these (i, j): {41796, 7}
X(64134) = barycentric quotient X(i)/X(j) for these (i, j): {41796, 8}
X(64134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16112, 9355}, {9, 1721, 9441}, {37, 15726, 1742}, {4319, 8545, 9440}, {4907, 60937, 1}

X(64135) = CENTROID OF X(8)-CROSSPEDAL-OF-X(78)

Barycentrics    a*(3*a^2+b^2+4*b*c+c^2-4*a*(b+c)) : :
X(64135) = -X[1898]+4*X[58657], 2*X[4848]+X[20013], -4*X[10310]+X[63984], -X[12649]+4*X[63990], 2*X[17857]+X[63985], -4*X[25440]+X[62874], -X[36846]+4*X[59691]

X(64135) lies on these lines: {1, 3833}, {2, 3158}, {3, 63135}, {8, 3523}, {10, 31452}, {40, 3984}, {42, 62808}, {43, 56510}, {55, 3305}, {57, 3935}, {63, 100}, {72, 43719}, {78, 517}, {145, 5438}, {149, 30827}, {210, 4421}, {312, 43290}, {329, 63145}, {345, 49991}, {354, 1376}, {377, 59722}, {404, 6765}, {474, 5049}, {480, 15726}, {519, 35262}, {612, 17592}, {614, 56009}, {678, 748}, {899, 3749}, {908, 9812}, {936, 3871}, {956, 17502}, {997, 3895}, {1051, 42043}, {1054, 62850}, {1259, 18908}, {1260, 5927}, {1319, 8168}, {1420, 3621}, {1445, 61030}, {1621, 8580}, {1698, 5178}, {1699, 49719}, {1706, 34772}, {1707, 21805}, {1898, 58657}, {2078, 62776}, {2177, 5268}, {2321, 26258}, {2325, 53673}, {2478, 64117}, {2550, 31266}, {2975, 4882}, {3030, 63513}, {3035, 4863}, {3174, 7671}, {3189, 24982}, {3214, 37552}, {3219, 35445}, {3240, 5269}, {3243, 27003}, {3256, 8545}, {3293, 62809}, {3315, 8056}, {3419, 38042}, {3434, 3817}, {3436, 28164}, {3452, 20075}, {3550, 5524}, {3579, 3951}, {3601, 3617}, {3612, 3626}, {3625, 37618}, {3678, 59316}, {3683, 61153}, {3692, 54316}, {3699, 56082}, {3711, 4640}, {3715, 61154}, {3722, 5272}, {3811, 5902}, {3848, 4413}, {3869, 63468}, {3872, 5440}, {3873, 64112}, {3875, 26229}, {3876, 61763}, {3913, 5919}, {3921, 16418}, {3928, 4661}, {3957, 5437}, {3961, 17591}, {3989, 17594}, {4126, 59536}, {4188, 6762}, {4297, 56879}, {4428, 61686}, {4429, 56522}, {4434, 17156}, {4511, 16200}, {4512, 63961}, {4650, 9337}, {4652, 34790}, {4662, 5217}, {4677, 10031}, {4847, 58441}, {4848, 20013}, {4849, 37540}, {4853, 30392}, {4881, 31145}, {4901, 33168}, {5082, 27385}, {5131, 62858}, {5175, 27525}, {5218, 25006}, {5219, 33110}, {5220, 63211}, {5249, 63168}, {5250, 8715}, {5281, 54357}, {5297, 37553}, {5330, 64202}, {5426, 51066}, {5432, 61032}, {5435, 20015}, {5436, 46933}, {5552, 6886}, {5554, 12437}, {5574, 41798}, {5828, 7080}, {6154, 24703}, {6326, 63132}, {6600, 61028}, {6602, 41795}, {6734, 59591}, {6735, 6935}, {6736, 28236}, {7081, 63131}, {7308, 61155}, {7994, 36002}, {9004, 56179}, {9342, 10582}, {9352, 62236}, {9580, 20095}, {9709, 54392}, {9778, 17781}, {9782, 41870}, {10164, 64153}, {10247, 10914}, {10310, 63984}, {10527, 59587}, {10528, 57284}, {10884, 64116}, {11224, 14923}, {11269, 59593}, {11415, 28232}, {11500, 63141}, {11681, 12558}, {11684, 63469}, {12329, 63180}, {12527, 59420}, {12541, 24558}, {12625, 25005}, {12649, 63990}, {13384, 51781}, {13405, 61029}, {16192, 62827}, {16670, 30652}, {16842, 63271}, {17127, 54309}, {17718, 49732}, {17780, 32929}, {17783, 21949}, {17857, 63985}, {18141, 50744}, {19860, 56176}, {20050, 61762}, {20052, 45036}, {21060, 44447}, {21075, 28150}, {23511, 62806}, {23705, 45829}, {24393, 55868}, {25440, 62874}, {25568, 31164}, {26015, 31224}, {27065, 61157}, {28043, 54474}, {28178, 58798}, {28224, 64087}, {29822, 41930}, {31508, 62838}, {31855, 37817}, {32141, 55104}, {35989, 60949}, {36278, 46973}, {36846, 59691}, {37162, 41864}, {37611, 38665}, {37680, 62875}, {37687, 60846}, {41711, 61152}, {49492, 51284}, {52026, 59417}, {53056, 62235}, {55478, 56316}, {56010, 62819}, {56178, 64082}, {56309, 61192}, {57106, 58835}, {58688, 64171}, {63090, 63969}

X(64135) = intersection, other than A, B, C, of circumconics {{A, B, C, X(103), X(945)}}, {{A, B, C, X(36101), X(39962)}}, {{A, B, C, X(56088), X(56091)}}
X(64135) = barycentric product X(i)*X(j) for these (i, j): {1332, 39532}
X(64135) = barycentric quotient X(i)/X(j) for these (i, j): {39532, 17924}
X(64135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 4420, 3984}, {78, 5687, 63130}, {78, 63130, 11682}, {100, 200, 63}, {100, 3681, 165}, {165, 200, 3681}, {210, 4421, 35258}, {404, 6765, 62832}, {997, 48696, 3895}, {1376, 3689, 3870}, {1376, 3870, 3306}, {3158, 46917, 2}, {3306, 3870, 62815}, {3434, 6745, 30852}, {3722, 9350, 5272}, {3957, 61156, 5437}, {5218, 25006, 55867}, {9352, 62236, 62823}, {17784, 64083, 908}, {20095, 27131, 9580}, {26015, 59572, 31224}, {35445, 62218, 3219}

X(64136) = ORTHOLOGY CENTER OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a*(a^6+a^5*(b+c)-(b^2-c^2)^2*(2*b^2-5*b*c+2*c^2)-a^4*(4*b^2+7*b*c+4*c^2)+a*(b-c)^2*(b^3-11*b^2*c-11*b*c^2+c^3)-2*a^3*(b^3-6*b^2*c-6*b*c^2+c^3)+a^2*(5*b^4+2*b^3*c-22*b^2*c^2+2*b*c^3+5*c^4)) : :
X(64136) = -2*X[1]+3*X[34474], -3*X[2]+2*X[64138], -4*X[5]+5*X[64141], -2*X[11]+3*X[5657], -3*X[165]+2*X[11715], -3*X[376]+2*X[64191], -5*X[631]+4*X[1387], -4*X[946]+5*X[64008], -5*X[1698]+4*X[16174], -X[1768]+3*X[63468], -4*X[3035]+3*X[5603]

X(64136) lies on these lines: {1, 34474}, {2, 64138}, {3, 1320}, {4, 1145}, {5, 64141}, {8, 5840}, {10, 14217}, {11, 5657}, {20, 952}, {30, 50907}, {40, 104}, {80, 11362}, {100, 517}, {119, 962}, {149, 6827}, {153, 20070}, {165, 11715}, {214, 7982}, {355, 10724}, {376, 64191}, {484, 10074}, {515, 64056}, {516, 10728}, {519, 12119}, {528, 5759}, {631, 1387}, {944, 5854}, {946, 64008}, {1000, 6955}, {1006, 5119}, {1056, 24465}, {1155, 20586}, {1317, 37567}, {1482, 4188}, {1490, 2800}, {1537, 5763}, {1697, 12736}, {1698, 16174}, {1768, 63468}, {1770, 12749}, {2093, 5083}, {2095, 34631}, {2829, 6361}, {2932, 22770}, {3035, 5603}, {3057, 6940}, {3090, 38038}, {3245, 7972}, {3339, 46681}, {3428, 13205}, {3523, 38032}, {3526, 38044}, {3576, 64137}, {3579, 12737}, {3616, 38760}, {3654, 10707}, {3655, 50894}, {3679, 6246}, {3871, 25413}, {3957, 10273}, {4295, 10956}, {4996, 11248}, {5046, 5690}, {5253, 10284}, {5697, 10090}, {5709, 12776}, {5720, 63130}, {5779, 59388}, {5790, 22938}, {5836, 6920}, {5856, 35514}, {5882, 26726}, {5901, 38762}, {5903, 10087}, {6174, 64192}, {6224, 10993}, {6594, 43166}, {6684, 16173}, {6797, 31658}, {6906, 14923}, {6909, 35460}, {6919, 34122}, {6926, 64193}, {6946, 54286}, {6970, 11729}, {6979, 22791}, {6985, 12331}, {7491, 19914}, {7967, 25416}, {7970, 53729}, {7978, 53743}, {7983, 53720}, {7984, 53711}, {8148, 19907}, {9588, 38133}, {9624, 58453}, {9778, 38761}, {9780, 23513}, {9802, 37726}, {10031, 36004}, {10058, 11010}, {10246, 61157}, {10310, 18861}, {10595, 34123}, {10679, 37300}, {10695, 53741}, {10696, 53742}, {10697, 53739}, {10700, 41343}, {10703, 53740}, {10711, 28194}, {10742, 28174}, {11249, 17100}, {11491, 25438}, {11531, 15015}, {11698, 28212}, {11822, 13230}, {11823, 13228}, {12246, 52116}, {12703, 64154}, {12735, 36279}, {12743, 41687}, {12747, 34718}, {12758, 60782}, {12775, 39776}, {13099, 53745}, {13272, 32198}, {13274, 40663}, {13278, 18444}, {13464, 64012}, {14193, 38576}, {14740, 63137}, {15035, 31523}, {15702, 38026}, {15803, 41554}, {15863, 63143}, {16139, 33856}, {17638, 63976}, {17652, 31786}, {17654, 31798}, {18240, 31393}, {19081, 49227}, {19082, 49226}, {19112, 35775}, {19113, 35774}, {19877, 38319}, {21630, 43174}, {21635, 28228}, {22799, 48661}, {23340, 45977}, {24297, 41166}, {24475, 64199}, {26446, 31272}, {31162, 50841}, {31423, 32557}, {31730, 64145}, {34627, 50842}, {34711, 37430}, {35976, 64044}, {38513, 53790}, {38705, 52478}, {39898, 51007}, {48667, 51525}, {48668, 61246}, {48680, 59503}, {50821, 59377}, {50910, 64011}, {57298, 61524}, {59387, 64186}, {63138, 63986}, {63399, 64202}

X(64136) = midpoint of X(i) and X(j) for these {i,j}: {153, 20070}, {5541, 7991}, {12245, 13199}
X(64136) = reflection of X(i) in X(j) for these {i,j}: {4, 1145}, {80, 11362}, {104, 40}, {944, 24466}, {962, 119}, {1320, 3}, {1482, 33814}, {6224, 10993}, {6264, 46684}, {6905, 63136}, {6909, 35460}, {7970, 53729}, {7978, 53743}, {7982, 214}, {7983, 53720}, {7984, 53711}, {8148, 19907}, {9802, 37726}, {10695, 53741}, {10696, 53742}, {10697, 53739}, {10698, 100}, {10703, 53740}, {10707, 3654}, {10724, 355}, {10728, 12751}, {10738, 5690}, {11531, 25485}, {12246, 52116}, {12653, 11715}, {12737, 3579}, {13099, 53745}, {13272, 32198}, {14217, 10}, {17638, 63976}, {17652, 31786}, {17654, 31798}, {21630, 43174}, {26726, 5882}, {31162, 50841}, {34627, 50842}, {34631, 50843}, {38665, 5541}, {38669, 12515}, {39898, 51007}, {43166, 6594}, {48661, 22799}, {48667, 51525}, {50890, 34718}, {50894, 3655}, {50910, 64011}, {60782, 63132}, {64145, 31730}, {64189, 12702}
X(64136) = anticomplement of X(64138)
X(64136) = X(i)-Dao conjugate of X(j) for these {i, j}: {64138, 64138}
X(64136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 14217, 59391}, {40, 2802, 104}, {40, 6264, 46684}, {100, 517, 10698}, {165, 12653, 11715}, {516, 12751, 10728}, {517, 63136, 6905}, {952, 12702, 64189}, {2800, 5541, 38665}, {2802, 46684, 6264}, {3579, 12737, 38693}, {5541, 7991, 2800}, {5657, 30305, 6963}, {5690, 10738, 59415}, {5854, 24466, 944}, {10310, 22560, 18861}, {11531, 15015, 25485}, {12245, 13199, 952}, {39776, 49163, 12775}

X(64137) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-AQUILA AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a*(2*a^3+3*b^3-4*b^2*c-4*b*c^2+3*c^3-3*a^2*(b+c)-2*a*(b^2-5*b*c+c^2)) : :
X(64137) = -3*X[2]+X[64056], -X[153]+5*X[5734], -3*X[551]+2*X[3035], X[1768]+3*X[11224], -2*X[2550]+3*X[38207], -3*X[3576]+X[64136], -5*X[3616]+4*X[58453], -5*X[3617]+9*X[32558], -7*X[3622]+5*X[64012]

X(64137) lies on these lines: {1, 88}, {2, 64056}, {8, 6702}, {10, 1387}, {11, 519}, {65, 15999}, {80, 145}, {104, 7982}, {119, 13464}, {149, 1478}, {153, 5734}, {355, 16174}, {515, 64138}, {516, 64191}, {517, 4973}, {528, 5542}, {546, 946}, {551, 3035}, {758, 2611}, {891, 41191}, {900, 48296}, {944, 14217}, {956, 2098}, {962, 64145}, {993, 7962}, {997, 11525}, {999, 13205}, {1001, 3898}, {1023, 2170}, {1125, 1145}, {1317, 1365}, {1482, 2800}, {1768, 11224}, {2099, 3892}, {2550, 38207}, {2771, 34791}, {2801, 3243}, {2829, 4301}, {2932, 3304}, {2975, 63281}, {3036, 3625}, {3057, 30538}, {3254, 14497}, {3295, 22560}, {3555, 17638}, {3576, 64136}, {3616, 58453}, {3617, 32558}, {3622, 64012}, {3623, 6224}, {3624, 64141}, {3626, 33709}, {3632, 59415}, {3633, 12531}, {3636, 13996}, {3656, 10742}, {3678, 5330}, {3679, 31272}, {3680, 45391}, {3738, 24457}, {3746, 4996}, {3756, 14028}, {3828, 38026}, {3872, 10176}, {3873, 11571}, {3880, 6797}, {3881, 11009}, {3884, 4861}, {3887, 14421}, {3919, 51788}, {4084, 11278}, {4315, 24465}, {4511, 41702}, {4649, 62481}, {4669, 45310}, {4677, 59377}, {4745, 59376}, {4752, 4919}, {4757, 11280}, {4939, 51975}, {5049, 58591}, {5223, 53055}, {5289, 46694}, {5493, 38759}, {5563, 17100}, {5603, 12751}, {5690, 38133}, {5836, 58587}, {5840, 5882}, {5844, 12619}, {5848, 49684}, {5856, 30331}, {5881, 59391}, {5886, 64140}, {6154, 44840}, {6174, 51103}, {6265, 10247}, {6594, 42819}, {6681, 51433}, {6684, 38032}, {6713, 11362}, {6734, 15862}, {7743, 33956}, {7967, 12119}, {7991, 38693}, {7993, 11379}, {7995, 12559}, {8068, 24387}, {8148, 12515}, {8666, 10058}, {8988, 49232}, {9024, 49465}, {9623, 36835}, {9624, 64008}, {9802, 20057}, {9897, 10707}, {9951, 62860}, {9956, 38044}, {9957, 35016}, {10074, 25415}, {10246, 61153}, {10265, 49627}, {10609, 33812}, {10728, 31162}, {10738, 37727}, {10755, 16496}, {10912, 30144}, {10956, 64160}, {11256, 12635}, {11366, 13230}, {11367, 13228}, {11369, 12550}, {11531, 64189}, {11729, 49626}, {11731, 25377}, {11813, 38455}, {12260, 30143}, {12560, 14151}, {12630, 45043}, {12641, 26364}, {12690, 62617}, {12729, 16211}, {12740, 22836}, {12743, 37734}, {13143, 64199}, {13243, 16191}, {13271, 34640}, {13272, 37739}, {13273, 37738}, {13274, 37740}, {13976, 49233}, {14988, 23960}, {15178, 33814}, {16137, 51569}, {17609, 58625}, {17636, 33176}, {17719, 24864}, {18802, 58405}, {19907, 33179}, {19925, 38038}, {20049, 50893}, {20095, 64011}, {21154, 43174}, {22938, 28204}, {24390, 63270}, {24393, 38216}, {25681, 47746}, {25697, 49467}, {25917, 58698}, {26139, 50915}, {28194, 38761}, {31397, 38062}, {31399, 38319}, {31788, 58595}, {34747, 50890}, {36846, 47320}, {37524, 56036}, {37525, 61157}, {38021, 50907}, {38182, 61510}, {38197, 49524}, {38752, 61276}, {40587, 61158}, {46685, 62826}, {47115, 53742}, {50846, 50892}, {51529, 58240}, {51709, 61580}, {53530, 61225}, {61278, 61562}

X(64137) = midpoint of X(i) and X(j) for these {i,j}: {1, 1320}, {8, 26726}, {11, 25416}, {65, 17652}, {80, 145}, {100, 12653}, {104, 7982}, {149, 7972}, {944, 14217}, {962, 64145}, {1482, 12737}, {3241, 50891}, {3244, 21630}, {3555, 17638}, {3633, 12531}, {3679, 50894}, {4511, 41702}, {6264, 10698}, {8148, 12515}, {10707, 51093}, {10738, 37727}, {10755, 16496}, {11256, 12635}, {11531, 64189}, {12690, 62617}, {13143, 64199}, {13253, 38669}, {20049, 50893}, {34747, 50890}, {38460, 63210}
X(64137) = reflection of X(i) in X(j) for these {i,j}: {8, 6702}, {10, 1387}, {119, 13464}, {214, 1}, {355, 16174}, {1145, 1125}, {1317, 3635}, {3625, 3036}, {3626, 33709}, {3878, 15558}, {4669, 45310}, {5493, 38759}, {5836, 58587}, {6174, 51103}, {6594, 42819}, {6797, 58611}, {10609, 33812}, {11274, 51071}, {11362, 6713}, {11570, 3881}, {15863, 11}, {18802, 58405}, {19907, 33179}, {21635, 64192}, {25485, 10222}, {31788, 58595}, {33337, 12735}, {33814, 15178}, {38213, 16173}, {39776, 3754}, {46684, 11715}, {50841, 551}, {50842, 3828}, {51433, 6681}, {51569, 16137}, {53742, 47115}, {61562, 61278}, {64139, 3884}
X(64137) = inverse of X(5048) in Feuerbach hyperbola
X(64137) = complement of X(64056)
X(64137) = pole of line {2827, 12758} with respect to the incircle
X(64137) = pole of line {2802, 5048} with respect to the Feuerbach hyperbola
X(64137) = pole of line {908, 43055} with respect to the dual conic of Yff parabola
X(64137) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1, 1320, 10703}, {11, 1357, 3937}, {80, 145, 38950}, {100, 12653, 58124}, {6264, 10696, 10698}, {7984, 13869, 31523}
X(64137) = intersection, other than A, B, C, of circumconics {{A, B, C, X(106), X(24302)}}, {{A, B, C, X(1392), X(62703)}}, {{A, B, C, X(11717), X(46972)}}
X(64137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 12653, 100}, {1, 1320, 2802}, {1, 244, 11717}, {1, 2802, 214}, {8, 16173, 6702}, {8, 6702, 38213}, {10, 1387, 32557}, {11, 25416, 519}, {11, 519, 15863}, {100, 1320, 12653}, {149, 3241, 7972}, {355, 16174, 38161}, {517, 11715, 46684}, {528, 12735, 33337}, {952, 10222, 25485}, {952, 64192, 21635}, {1387, 5854, 10}, {1482, 12737, 2800}, {2098, 22837, 3878}, {2099, 20586, 5083}, {2802, 3754, 39776}, {3244, 21630, 952}, {3625, 59419, 3036}, {3626, 33709, 34122}, {3880, 58611, 6797}, {6264, 10698, 2801}, {6264, 16200, 10698}, {7972, 50891, 149}, {10090, 13278, 8715}, {11280, 62837, 4757}, {12735, 33337, 11274}, {16173, 26726, 8}, {33337, 51071, 12735}, {38026, 50842, 3828}, {38460, 63210, 758}

X(64138) = ORTHOLOGY CENTER OF THESE TRIANGLES: EULER AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    2*a^6*(b+c)-a*(b-c)^4*(b+c)^2-(b-c)^4*(b+c)^3-a^5*(b^2+10*b*c+c^2)+a^4*(-5*b^3+11*b^2*c+11*b*c^2-5*c^3)+2*a^2*(b-c)^2*(2*b^3-3*b^2*c-3*b*c^2+2*c^3)+2*a^3*(b^4+4*b^3*c-12*b^2*c^2+4*b*c^3+c^4) : :
X(64138) = -3*X[2]+X[64136], -X[100]+3*X[5603], -2*X[140]+3*X[38044], -2*X[182]+3*X[38050], -3*X[381]+X[64140], -2*X[549]+3*X[38026], -4*X[1125]+3*X[38760], -5*X[1698]+6*X[38319], 3*X[1699]+X[12653], -2*X[3035]+3*X[5886]

X(64138) lies on these lines: {1, 5840}, {2, 64136}, {3, 1387}, {4, 145}, {5, 1145}, {8, 11928}, {10, 16174}, {11, 517}, {12, 10284}, {30, 64191}, {40, 5442}, {55, 38033}, {80, 7982}, {100, 5603}, {104, 962}, {119, 946}, {140, 38044}, {182, 38050}, {214, 10993}, {355, 5854}, {381, 64140}, {390, 6948}, {404, 5901}, {496, 25413}, {515, 64137}, {516, 11715}, {519, 6246}, {528, 3656}, {549, 38026}, {944, 10724}, {999, 24465}, {1000, 6982}, {1125, 38760}, {1317, 10222}, {1385, 24466}, {1476, 24470}, {1484, 37356}, {1698, 38319}, {1699, 12653}, {1836, 20586}, {2095, 13226}, {2098, 10525}, {2099, 13274}, {2102, 10782}, {2103, 10781}, {2800, 4084}, {2829, 12676}, {3035, 5886}, {3057, 6842}, {3090, 64141}, {3254, 43166}, {3476, 10247}, {3485, 12000}, {3579, 21154}, {3616, 34474}, {3649, 33179}, {3654, 45310}, {3671, 46681}, {3839, 50907}, {3885, 10942}, {3890, 37438}, {3895, 37713}, {4190, 10595}, {4193, 5690}, {4292, 41554}, {4295, 12001}, {4861, 37290}, {5048, 18976}, {5176, 5844}, {5187, 12245}, {5298, 10225}, {5531, 50908}, {5533, 5903}, {5541, 11522}, {5587, 64056}, {5657, 31272}, {5697, 8068}, {5734, 6224}, {5759, 53055}, {5761, 9802}, {5790, 6973}, {5881, 26726}, {5887, 49600}, {6154, 22935}, {6174, 51709}, {6264, 31162}, {6361, 38693}, {6667, 26446}, {6684, 32557}, {6702, 11362}, {6841, 45776}, {6885, 9945}, {6890, 64189}, {6891, 12702}, {6909, 22765}, {6915, 12732}, {6944, 18493}, {6945, 38034}, {6961, 18220}, {6981, 63133}, {7491, 12701}, {7970, 10769}, {7972, 12831}, {7978, 10778}, {7983, 10768}, {7984, 10767}, {8148, 12019}, {8196, 13230}, {8203, 13228}, {8227, 58421}, {9624, 64012}, {9785, 16202}, {9812, 10728}, {9897, 11224}, {9943, 58595}, {9955, 13996}, {10035, 37425}, {10057, 30323}, {10058, 11249}, {10073, 25415}, {10087, 11501}, {10090, 11248}, {10202, 18240}, {10273, 11019}, {10427, 20330}, {10526, 12764}, {10543, 33281}, {10609, 19907}, {10695, 10772}, {10696, 10777}, {10697, 10770}, {10703, 10771}, {10707, 12247}, {10755, 39898}, {10780, 13099}, {10912, 37821}, {10914, 55016}, {10956, 12047}, {11011, 12743}, {11012, 63281}, {11230, 31235}, {11278, 62616}, {11280, 53616}, {11496, 22560}, {11499, 25438}, {11531, 37718}, {11723, 53743}, {11724, 53729}, {11725, 53720}, {11726, 53741}, {11727, 53742}, {11728, 53739}, {11734, 53740}, {11735, 53711}, {12053, 12736}, {12515, 20418}, {12575, 24299}, {12611, 13600}, {12650, 46435}, {12665, 31937}, {12684, 34256}, {12738, 12858}, {12773, 60922}, {12775, 13279}, {12776, 55109}, {13205, 22753}, {13253, 49176}, {13271, 37820}, {13913, 49226}, {13977, 49227}, {14690, 29008}, {15863, 28234}, {15908, 63270}, {16125, 25485}, {17567, 38762}, {17579, 50843}, {17702, 31523}, {18357, 38141}, {18480, 59390}, {22793, 52836}, {24833, 38576}, {25557, 61279}, {28194, 46684}, {28212, 61566}, {31658, 38060}, {31659, 37563}, {31788, 58587}, {31835, 64200}, {32214, 64021}, {33593, 37401}, {33668, 61281}, {33709, 38133}, {34126, 61524}, {34627, 50894}, {34631, 50890}, {34862, 52116}, {35004, 37722}, {37375, 61553}, {37611, 64155}, {38028, 61155}, {38077, 50842}, {38753, 48661}, {41869, 64145}, {44455, 60782}, {46685, 51423}, {49163, 55297}, {50810, 59377}, {50821, 59376}, {53800, 56761}

X(64138) = midpoint of X(i) and X(j) for these {i,j}: {1, 14217}, {4, 1320}, {80, 7982}, {104, 962}, {149, 10698}, {944, 10724}, {1482, 10738}, {2102, 10782}, {2103, 10781}, {3254, 43166}, {4301, 21630}, {5881, 26726}, {6264, 34789}, {7970, 10769}, {7978, 10778}, {7983, 10768}, {7984, 10767}, {8148, 19914}, {9802, 38665}, {10695, 10772}, {10696, 10777}, {10697, 10770}, {10703, 10771}, {10755, 39898}, {10780, 13099}, {12650, 46435}, {12653, 12751}, {12699, 12737}, {13253, 49176}, {31162, 50891}, {34627, 50894}, {34631, 50890}, {38753, 48661}, {41869, 64145}
X(64138) = reflection of X(i) in X(j) for these {i,j}: {3, 1387}, {10, 16174}, {40, 6713}, {100, 11729}, {119, 946}, {214, 13464}, {1145, 5}, {1317, 10222}, {1537, 22791}, {3654, 45310}, {5690, 60759}, {6154, 22935}, {6174, 51709}, {6265, 64192}, {6882, 30384}, {9943, 58595}, {10427, 20330}, {10609, 19907}, {10993, 214}, {11362, 6702}, {12515, 20418}, {12665, 31937}, {12702, 64193}, {12732, 51525}, {14690, 29008}, {19914, 12019}, {22799, 40273}, {24466, 1385}, {31788, 58587}, {33814, 5901}, {37401, 33593}, {37425, 10035}, {37562, 12736}, {37725, 12611}, {37726, 21630}, {38761, 11715}, {43174, 33709}, {52116, 34862}, {52836, 22793}, {53711, 11735}, {53720, 11725}, {53729, 11724}, {53739, 11728}, {53740, 11734}, {53741, 11726}, {53742, 11727}, {53743, 11723}
X(64138) = complement of X(64136)
X(64138) = pole of line {24457, 55126} with respect to the incircle
X(64138) = pole of line {952, 5570} with respect to the Feuerbach hyperbola
X(64138) = pole of line {23838, 55126} with respect to the Suppa-Cucoanes circle
X(64138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 14217, 5840}, {10, 16174, 23513}, {40, 16173, 6713}, {100, 5603, 11729}, {516, 11715, 38761}, {517, 30384, 6882}, {528, 64192, 6265}, {946, 2802, 119}, {952, 22791, 1537}, {952, 40273, 22799}, {1145, 38038, 5}, {1482, 10738, 952}, {1699, 12653, 12751}, {2800, 21630, 37726}, {3656, 6265, 64192}, {4301, 21630, 2800}, {5533, 5903, 12832}, {5690, 60759, 34122}, {5901, 33814, 34123}, {6264, 31162, 34789}, {6702, 11362, 38128}, {8148, 51517, 19914}, {12699, 12737, 2829}, {12702, 57298, 64193}

X(64139) = ANTICOMPLEMENT OF X(12736)

Barycentrics    a*(a-b-c)*(a^2-b^2+b*c-c^2)*(-2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :
X(64139) = -3*X[2]+2*X[12736], -3*X[210]+2*X[3036], -3*X[392]+2*X[1387], -2*X[942]+3*X[34123], -3*X[3576]+2*X[15528], -5*X[3616]+4*X[18240], -3*X[3681]+X[12531], -4*X[3812]+5*X[31235], -3*X[3873]+4*X[46681], -5*X[3876]+4*X[46694], -4*X[4015]+3*X[38213], -3*X[5790]+4*X[58674]

X(64139) lies on the Yff contact circle and on these lines: {1, 1331}, {2, 12736}, {8, 80}, {9, 644}, {10, 8068}, {11, 960}, {21, 6596}, {36, 214}, {40, 78}, {63, 104}, {65, 3035}, {72, 952}, {119, 517}, {144, 2801}, {145, 18397}, {153, 329}, {190, 51565}, {200, 3899}, {210, 3036}, {392, 1387}, {515, 12665}, {518, 1317}, {528, 3059}, {643, 1793}, {942, 34123}, {956, 12737}, {997, 10090}, {1259, 5730}, {1260, 48667}, {1420, 3868}, {1445, 64154}, {1697, 13278}, {1768, 12526}, {2057, 7991}, {2099, 42843}, {2320, 56117}, {2771, 3650}, {2804, 53549}, {2829, 14110}, {2932, 12515}, {2950, 6282}, {2975, 11715}, {3032, 3687}, {3057, 5854}, {3241, 18412}, {3419, 10738}, {3434, 14217}, {3436, 12751}, {3555, 12735}, {3576, 15528}, {3588, 21078}, {3616, 18240}, {3681, 12531}, {3738, 3904}, {3754, 27529}, {3811, 10087}, {3812, 31235}, {3827, 51007}, {3873, 46681}, {3876, 46694}, {3884, 4861}, {3885, 5727}, {3916, 38602}, {3927, 12773}, {3939, 10703}, {3940, 12331}, {3951, 38669}, {3962, 17660}, {3984, 38665}, {4015, 38213}, {4067, 33337}, {4652, 38693}, {4847, 21630}, {4853, 12653}, {4855, 34474}, {5044, 6797}, {5086, 6246}, {5119, 25438}, {5219, 64141}, {5223, 7993}, {5289, 12740}, {5440, 14988}, {5533, 10916}, {5552, 5903}, {5587, 14923}, {5660, 7080}, {5693, 12119}, {5720, 63130}, {5790, 58674}, {5794, 13273}, {5836, 58663}, {5840, 5887}, {5883, 58453}, {5884, 59332}, {5902, 64012}, {5904, 7972}, {6001, 24466}, {6174, 44663}, {6264, 11920}, {6667, 25917}, {6702, 10176}, {6713, 59491}, {6737, 31938}, {6925, 46435}, {9957, 25416}, {9963, 41228}, {10031, 34716}, {10057, 10522}, {10058, 12514}, {10073, 49168}, {10074, 62858}, {10527, 16173}, {10698, 11682}, {10742, 58798}, {10914, 61510}, {11415, 34789}, {11523, 37736}, {11571, 15015}, {11679, 35636}, {11680, 16174}, {11729, 24474}, {12513, 20586}, {12635, 12739}, {12641, 30513}, {12690, 64171}, {12701, 13271}, {12709, 24465}, {12730, 34784}, {12743, 44669}, {12746, 44694}, {12764, 24703}, {12775, 37531}, {13279, 15829}, {15175, 56105}, {15556, 62830}, {16585, 63346}, {16586, 34586}, {17100, 46684}, {17652, 17658}, {17654, 64107}, {17880, 53332}, {18467, 37313}, {20007, 20095}, {20612, 22836}, {21616, 39692}, {24028, 61482}, {25413, 37713}, {25440, 59330}, {25485, 62826}, {25522, 31272}, {27383, 64047}, {30196, 61185}, {30852, 64008}, {31786, 64191}, {31838, 38032}, {31937, 64186}, {34339, 38760}, {34591, 61233}, {38099, 58629}, {38128, 58630}, {38156, 58631}, {38177, 58632}, {38192, 58633}, {38202, 58634}, {38211, 58635}, {38215, 58636}, {38752, 64044}, {38901, 40256}, {41554, 54391}, {41572, 64106}, {44425, 63136}, {45288, 59691}, {48695, 63391}, {60936, 64041}, {61033, 63159}, {64087, 64140}

X(64139) = midpoint of X(i) and X(j) for these {i,j}: {100, 3869}, {3962, 17660}, {4067, 33337}, {5693, 12119}, {5697, 64056}, {5904, 7972}, {6224, 12532}, {12730, 34784}
X(64139) = reflection of X(i) in X(j) for these {i,j}: {8, 14740}, {11, 960}, {65, 3035}, {80, 18254}, {908, 41389}, {1320, 15558}, {3555, 12735}, {3868, 5083}, {5836, 58663}, {6246, 20117}, {6735, 51379}, {6797, 5044}, {9802, 9951}, {11570, 214}, {12758, 3878}, {15863, 3678}, {17636, 3036}, {17654, 64193}, {24474, 11729}, {25416, 9957}, {39776, 1145}, {46685, 72}, {64137, 3884}, {64186, 31937}, {64191, 31786}
X(64139) = anticomplement of X(12736)
X(64139) = perspector of circumconic {{A, B, C, X(2397), X(4585)}}
X(64139) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 40437}, {104, 1411}, {649, 53811}, {655, 2423}, {909, 2006}, {2161, 34051}, {2401, 32675}, {10428, 14584}, {15635, 52377}, {18815, 34858}, {32669, 60074}, {41933, 52212}
X(64139) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 40437}, {44, 40218}, {908, 7}, {1145, 80}, {1737, 14266}, {2245, 57}, {5375, 53811}, {10015, 1111}, {12736, 12736}, {13999, 43933}, {16586, 18815}, {23980, 2006}, {35128, 2401}, {35204, 104}, {40584, 34051}, {40613, 1411}, {42761, 4077}, {45247, 1168}, {46974, 56638}, {55153, 60074}, {57434, 43728}
X(64139) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8, 6735}, {40436, 22350}
X(64139) = pole of line {3036, 3689} with respect to the Feuerbach hyperbola
X(64139) = pole of line {759, 2720} with respect to the Stammler hyperbola
X(64139) = pole of line {2397, 24029} with respect to the Yff parabola
X(64139) = pole of line {14616, 54953} with respect to the Wallace hyperbola
X(64139) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {100, 3869, 34151}
X(64139) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(119)}}, {{A, B, C, X(8), X(4996)}}, {{A, B, C, X(9), X(214)}}, {{A, B, C, X(21), X(39778)}}, {{A, B, C, X(36), X(80)}}, {{A, B, C, X(104), X(1512)}}, {{A, B, C, X(758), X(2804)}}, {{A, B, C, X(908), X(1320)}}, {{A, B, C, X(1089), X(4736)}}, {{A, B, C, X(1519), X(1870)}}, {{A, B, C, X(1532), X(17515)}}, {{A, B, C, X(1537), X(3577)}}, {{A, B, C, X(2170), X(3259)}}, {{A, B, C, X(2323), X(12641)}}, {{A, B, C, X(2677), X(38982)}}, {{A, B, C, X(2800), X(7012)}}, {{A, B, C, X(3262), X(56105)}}, {{A, B, C, X(3724), X(34857)}}, {{A, B, C, X(4511), X(6735)}}, {{A, B, C, X(4867), X(51362)}}, {{A, B, C, X(4881), X(51433)}}, {{A, B, C, X(4973), X(51409)}}, {{A, B, C, X(6073), X(24028)}}, {{A, B, C, X(11604), X(17139)}}, {{A, B, C, X(14260), X(15906)}}, {{A, B, C, X(15175), X(56416)}}, {{A, B, C, X(18254), X(34544)}}, {{A, B, C, X(24026), X(57434)}}, {{A, B, C, X(27950), X(51381)}}, {{A, B, C, X(30513), X(39776)}}, {{A, B, C, X(46398), X(57435)}}, {{A, B, C, X(51380), X(58328)}}, {{A, B, C, X(51390), X(53045)}}, {{A, B, C, X(53046), X(61672)}}, {{A, B, C, X(55016), X(56101)}}
X(64139) = barycentric product X(i)*X(j) for these (i, j): {100, 53045}, {312, 34586}, {1332, 53047}, {1845, 345}, {2323, 3262}, {2397, 3738}, {2804, 4585}, {3218, 6735}, {4511, 908}, {4564, 57434}, {16586, 8}, {17078, 51380}, {17515, 51367}, {17923, 51379}, {26611, 56757}, {32851, 517}, {42768, 645}, {46398, 765}, {53046, 668}, {53562, 55258}
X(64139) = barycentric quotient X(i)/X(j) for these (i, j): {9, 40437}, {36, 34051}, {100, 53811}, {214, 40218}, {517, 2006}, {908, 18815}, {1145, 14628}, {1845, 278}, {1983, 2720}, {2183, 1411}, {2323, 104}, {2361, 909}, {2397, 35174}, {2427, 2222}, {2804, 60074}, {3738, 2401}, {4511, 34234}, {4585, 54953}, {5081, 16082}, {6735, 18359}, {8648, 2423}, {16586, 7}, {17757, 60091}, {21801, 52383}, {24028, 52212}, {32851, 18816}, {34586, 57}, {38353, 7004}, {42768, 7178}, {46398, 1111}, {51379, 52351}, {51380, 36910}, {52426, 34858}, {53045, 693}, {53046, 513}, {53047, 17924}, {53285, 61238}, {53562, 55259}, {56416, 34535}, {56757, 59196}, {57434, 4858}, {58328, 52663}
X(64139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 6326, 64188}, {72, 952, 46685}, {80, 5692, 18254}, {100, 3869, 2800}, {210, 17636, 3036}, {214, 758, 11570}, {517, 1145, 39776}, {517, 41389, 908}, {908, 51433, 1512}, {960, 64043, 41012}, {1145, 55016, 6735}, {1320, 3877, 15558}, {2802, 14740, 8}, {2802, 18254, 80}, {2802, 3678, 15863}, {2802, 3878, 12758}, {2802, 9951, 9802}, {3876, 59415, 46694}, {4511, 4996, 214}, {4867, 58328, 4511}, {5044, 6797, 34122}, {5289, 22560, 12740}, {5697, 64056, 2802}, {6224, 12532, 2801}, {17100, 56288, 46684}, {17654, 64107, 64193}

X(64140) = ORTHOLOGY CENTER OF THESE TRIANGLES: JOHNSON AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a^7-3*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(b^2+13*b*c+c^2)+a*(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)-a^2*(b-c)^2*(b^3-13*b^2*c-13*b*c^2+c^3)+a^4*(5*b^3-13*b^2*c-13*b*c^2+5*c^3)-a^3*(5*b^4+5*b^3*c-26*b^2*c^2+5*b*c^3+5*c^4) : :
X(64140) = -2*X[1]+3*X[38752], -2*X[11]+3*X[5790], -4*X[140]+5*X[64141], -3*X[381]+2*X[64138], -4*X[1387]+5*X[1656], -X[1768]+3*X[63143], -4*X[3035]+3*X[10246], -7*X[3090]+6*X[38044], -7*X[3526]+6*X[38032], -4*X[3579]+3*X[38754], 2*X[3625]+X[12738]

X(64140) lies on these lines: {1, 38752}, {3, 8}, {5, 1320}, {10, 12737}, {11, 5790}, {30, 50907}, {40, 38753}, {65, 12749}, {80, 3057}, {119, 1482}, {140, 64141}, {145, 6959}, {149, 6929}, {153, 12245}, {214, 37727}, {355, 2802}, {381, 64138}, {515, 35460}, {517, 10742}, {519, 6265}, {528, 5779}, {962, 22799}, {1317, 10573}, {1319, 7972}, {1385, 37829}, {1387, 1656}, {1483, 13747}, {1484, 4187}, {1532, 5844}, {1537, 8148}, {1737, 20586}, {1768, 63143}, {2098, 39692}, {2800, 6259}, {2829, 12702}, {3035, 10246}, {3036, 9711}, {3090, 38044}, {3526, 38032}, {3579, 38754}, {3621, 6834}, {3625, 12738}, {3626, 10265}, {3632, 6326}, {3652, 47745}, {3654, 46684}, {3655, 50841}, {3679, 6264}, {3851, 38038}, {4668, 7993}, {4677, 5531}, {4678, 6967}, {5119, 9897}, {5260, 34352}, {5541, 5881}, {5554, 34123}, {5587, 12653}, {5603, 61580}, {5697, 12764}, {5818, 60759}, {5840, 13996}, {5886, 64137}, {5901, 64008}, {5903, 12763}, {6838, 20052}, {6938, 20095}, {7982, 12611}, {8200, 13230}, {8207, 13228}, {8256, 37535}, {9780, 34126}, {9956, 16173}, {10057, 17636}, {10074, 40663}, {10087, 10950}, {10090, 10944}, {10176, 15863}, {10222, 26726}, {10247, 11729}, {10707, 61553}, {10728, 28174}, {10916, 11256}, {11113, 50890}, {11248, 54134}, {11249, 36972}, {11362, 12515}, {11499, 22560}, {11570, 41687}, {11715, 26446}, {11849, 25438}, {12119, 13528}, {12248, 59417}, {12641, 23340}, {12665, 40266}, {12735, 18391}, {12743, 37711}, {12832, 41426}, {12898, 53743}, {13205, 22758}, {13243, 37429}, {13273, 37710}, {14077, 42547}, {14217, 18480}, {14643, 31523}, {15015, 61296}, {15017, 16200}, {15178, 64012}, {15703, 38026}, {16174, 61261}, {17660, 36920}, {18357, 59391}, {18857, 64011}, {18976, 37708}, {20418, 38128}, {21635, 28234}, {22765, 38455}, {22938, 59387}, {25413, 39776}, {26363, 38135}, {31272, 38042}, {31399, 33709}, {32049, 41688}, {32537, 37230}, {34689, 34718}, {34748, 50843}, {34880, 37707}, {35000, 48695}, {35842, 35883}, {35843, 35882}, {37621, 51506}, {37725, 48667}, {38112, 61566}, {38161, 61258}, {45776, 58687}, {48661, 52836}, {52478, 57313}, {53055, 61511}, {64087, 64139}

X(64140) = midpoint of X(i) and X(j) for these {i,j}: {153, 12245}, {3632, 6326}, {5541, 5881}, {12331, 12645}, {12531, 38665}, {12751, 64056}
X(64140) = reflection of X(i) in X(j) for these {i,j}: {3, 1145}, {104, 5690}, {145, 19907}, {944, 33814}, {962, 22799}, {1320, 5}, {1482, 119}, {1483, 61562}, {1484, 61510}, {3655, 50841}, {6224, 51525}, {6264, 12619}, {7972, 22935}, {7982, 12611}, {8148, 1537}, {10265, 3626}, {10698, 11698}, {10738, 355}, {10742, 12751}, {11256, 10916}, {12515, 11362}, {12737, 10}, {12898, 53743}, {14217, 18480}, {19914, 8}, {25413, 39776}, {25416, 11729}, {26726, 10222}, {34718, 50842}, {34748, 50843}, {37726, 3036}, {37727, 214}, {38753, 40}, {40266, 12665}, {45776, 58687}, {48661, 52836}, {48667, 37725}, {62354, 15863}, {64145, 3579}
X(64140) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {12751, 50914, 64056}
X(64140) = intersection, other than A, B, C, of circumconics {{A, B, C, X(104), X(17101)}}, {{A, B, C, X(517), X(17100)}}, {{A, B, C, X(1809), X(34901)}}, {{A, B, C, X(5559), X(56757)}}, {{A, B, C, X(36944), X(38544)}}
X(64140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 952, 19914}, {10, 12737, 57298}, {119, 5854, 1482}, {355, 2802, 10738}, {517, 12751, 10742}, {952, 1145, 3}, {952, 33814, 944}, {952, 51525, 6224}, {952, 5690, 104}, {1484, 61510, 59415}, {3579, 64145, 38754}, {3679, 6264, 12619}, {5844, 11698, 10698}, {8148, 38755, 1537}, {11729, 25416, 10247}, {12331, 12645, 952}, {12751, 64056, 517}

X(64141) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a^4+2*a^3*(b+c)+2*(b^2-c^2)^2-a^2*(3*b^2+5*b*c+3*c^2)+a*(-2*b^3+5*b^2*c+5*b*c^2-2*c^3) : :
X(64141) = -3*X[1]+8*X[58453], 4*X[5]+X[64136], 3*X[8]+2*X[1317], X[65]+4*X[58663], -X[104]+6*X[26446], 2*X[119]+3*X[5657], 4*X[140]+X[64140], -X[145]+6*X[34123], 3*X[190]+2*X[19636], -6*X[210]+X[12532], 2*X[214]+3*X[3679], 2*X[355]+3*X[34474] and many others

X(64141) lies on these lines: {1, 58453}, {2, 1000}, {5, 64136}, {7, 55016}, {8, 1317}, {10, 21}, {11, 9710}, {65, 58663}, {88, 24222}, {104, 26446}, {119, 5657}, {140, 64140}, {145, 34123}, {149, 5084}, {153, 6916}, {190, 19636}, {210, 12532}, {214, 3679}, {319, 55094}, {355, 34474}, {404, 5252}, {517, 64008}, {519, 64012}, {528, 18230}, {549, 50907}, {551, 26726}, {631, 952}, {644, 21013}, {944, 38760}, {958, 17100}, {1125, 64056}, {1156, 38057}, {1210, 64199}, {1376, 4996}, {1537, 6969}, {1621, 25438}, {1698, 2802}, {1788, 10956}, {2771, 3697}, {2800, 3876}, {2932, 9708}, {3036, 6174}, {3090, 64138}, {3218, 51362}, {3219, 10711}, {3523, 64191}, {3525, 38032}, {3579, 10728}, {3616, 5854}, {3621, 12735}, {3622, 25416}, {3624, 64137}, {3626, 7972}, {3634, 16173}, {3654, 12611}, {3678, 11571}, {3681, 11570}, {3698, 31254}, {3740, 17638}, {3826, 63270}, {3828, 21630}, {3868, 14740}, {3871, 5722}, {3877, 39776}, {3885, 37704}, {3911, 5193}, {3921, 58659}, {3956, 47320}, {4002, 6797}, {4193, 30305}, {4413, 22560}, {4420, 12739}, {4511, 36920}, {4662, 17660}, {4669, 33812}, {4745, 64011}, {4861, 37829}, {5056, 38038}, {5070, 38044}, {5123, 37375}, {5176, 13587}, {5178, 10073}, {5219, 64139}, {5261, 24465}, {5330, 26364}, {5445, 10074}, {5541, 6702}, {5552, 62830}, {5587, 10724}, {5603, 58421}, {5686, 10427}, {5690, 6949}, {5692, 58698}, {5790, 6950}, {5818, 5840}, {5836, 7504}, {5856, 40333}, {6068, 59412}, {6175, 16140}, {6264, 38133}, {6594, 20119}, {6666, 53055}, {6667, 13996}, {6684, 12751}, {6883, 12331}, {6930, 13199}, {6931, 63133}, {6965, 10738}, {7705, 63130}, {8068, 33108}, {8256, 15950}, {9588, 46684}, {9778, 52836}, {9897, 38213}, {9945, 20085}, {9956, 59391}, {10039, 17531}, {10087, 18395}, {10164, 64145}, {10175, 14217}, {10265, 25006}, {10742, 61524}, {10755, 38047}, {11231, 12737}, {11698, 16006}, {11715, 31423}, {11729, 12245}, {12019, 20095}, {12247, 38128}, {12619, 38665}, {12653, 32557}, {12702, 61580}, {12730, 64154}, {12736, 31434}, {12747, 38177}, {12755, 40659}, {12763, 56880}, {12832, 14151}, {13243, 37725}, {13271, 32157}, {13278, 24982}, {13279, 24987}, {13911, 19112}, {13922, 19065}, {13973, 19113}, {13991, 19066}, {14193, 21290}, {14923, 23708}, {15015, 15863}, {15678, 63211}, {16174, 54447}, {17484, 17757}, {17577, 54286}, {17661, 31787}, {17725, 54315}, {18240, 51784}, {18254, 63961}, {19907, 59503}, {19914, 38112}, {21041, 36237}, {21042, 31143}, {24466, 59387}, {25055, 50894}, {25485, 63143}, {30855, 34587}, {31231, 41554}, {33709, 50891}, {34789, 43174}, {37797, 40663}, {38050, 63119}, {38066, 48667}, {38087, 51158}, {38098, 50844}, {38314, 50842}, {38759, 64108}, {45701, 63159}, {51007, 59406}

X(64141) = reflection of X(i) in X(j) for these {i,j}: {3616, 31235}, {31272, 1698}
X(64141) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1000), X(56950)}}, {{A, B, C, X(6740), X(36596)}}
X(64141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1145, 1320}, {10, 100, 59415}, {80, 100, 9963}, {100, 5260, 10058}, {119, 5657, 64189}, {149, 46933, 34122}, {214, 12531, 10031}, {214, 3679, 12531}, {1698, 2802, 31272}, {3036, 6174, 6224}, {3036, 6224, 50890}, {5123, 63136, 37375}, {5541, 19875, 6702}, {5690, 38752, 10698}, {5854, 31235, 3616}, {6224, 53620, 3036}, {6594, 38200, 20119}, {6684, 12751, 38693}, {6702, 50841, 5541}, {9963, 59415, 80}, {19875, 50841, 10707}, {38112, 61562, 19914}

X(64142) = ANTICOMPLEMENT OF X(5328)

Barycentrics    (5*a-b-c)*(a+b-c)*(a-b+c) : :

X(64142) lies on these lines: {1, 15717}, {2, 7}, {3, 15935}, {4, 13226}, {8, 3361}, {12, 46931}, {20, 5722}, {43, 61376}, {46, 14986}, {56, 100}, {65, 3622}, {77, 17012}, {80, 4293}, {81, 44794}, {85, 24589}, {88, 279}, {109, 9095}, {165, 10580}, {196, 56297}, {223, 17020}, {241, 4850}, {278, 26745}, {319, 37655}, {354, 5281}, {388, 46933}, {390, 1155}, {404, 20007}, {474, 54398}, {499, 11552}, {631, 5708}, {651, 14997}, {673, 56274}, {750, 39587}, {899, 4334}, {927, 2384}, {938, 3522}, {942, 3523}, {950, 50693}, {962, 37704}, {999, 1000}, {1014, 16704}, {1150, 7268}, {1210, 3146}, {1323, 5222}, {1371, 5393}, {1372, 5405}, {1387, 6966}, {1407, 32911}, {1418, 16610}, {1420, 3623}, {1427, 39975}, {1429, 29585}, {1434, 5235}, {1442, 17013}, {1443, 56418}, {1458, 3240}, {1465, 17092}, {1466, 4189}, {1467, 34772}, {1471, 9364}, {1659, 17804}, {1737, 54448}, {1788, 3600}, {1876, 4232}, {1892, 52284}, {2078, 61157}, {2263, 7292}, {2646, 18221}, {3008, 21314}, {3085, 3337}, {3086, 3336}, {3090, 24470}, {3210, 32105}, {3212, 35312}, {3241, 13462}, {3321, 26007}, {3339, 3616}, {3474, 5274}, {3475, 52638}, {3476, 31145}, {3487, 10303}, {3488, 5122}, {3524, 15934}, {3525, 6147}, {3528, 12433}, {3545, 18541}, {3576, 14563}, {3586, 15683}, {3601, 61791}, {3621, 4308}, {3634, 4355}, {3660, 7672}, {3671, 5550}, {3672, 17595}, {3681, 63994}, {3711, 50835}, {3752, 37666}, {3832, 4292}, {3873, 51378}, {3916, 5129}, {3945, 37520}, {4000, 37798}, {4032, 4772}, {4294, 37524}, {4295, 23708}, {4297, 53057}, {4298, 5726}, {4307, 17722}, {4310, 17725}, {4312, 9779}, {4313, 21734}, {4327, 5297}, {4346, 17720}, {4358, 39126}, {4373, 37759}, {4384, 52715}, {4413, 5686}, {4430, 41539}, {4452, 62300}, {4454, 28808}, {4488, 62297}, {4652, 11106}, {4661, 17625}, {4678, 10106}, {4860, 5218}, {4869, 32851}, {5056, 57282}, {5126, 11041}, {5128, 9785}, {5131, 54342}, {5154, 57285}, {5221, 7288}, {5228, 29624}, {5231, 59412}, {5233, 64015}, {5261, 24914}, {5290, 19877}, {5439, 17558}, {5556, 12571}, {5703, 61820}, {5714, 7486}, {5728, 11575}, {5729, 13243}, {5903, 18240}, {6180, 37680}, {6604, 51583}, {6684, 11037}, {6734, 56999}, {6744, 16192}, {6848, 26877}, {6908, 37612}, {6926, 37532}, {6939, 61535}, {6964, 24467}, {7091, 63135}, {7175, 63050}, {7176, 16816}, {7190, 17021}, {7191, 60786}, {7195, 63591}, {7271, 54390}, {7277, 63089}, {7613, 33140}, {7677, 37541}, {7682, 54052}, {7956, 14646}, {7988, 30424}, {8046, 40218}, {8236, 35445}, {8270, 17024}, {8581, 63961}, {9316, 17127}, {9352, 17784}, {9533, 17093}, {9579, 50689}, {9581, 17578}, {9588, 12577}, {9612, 15022}, {9778, 11019}, {9802, 11240}, {10004, 37757}, {10164, 10578}, {10385, 63212}, {10394, 61660}, {10404, 46930}, {10405, 34234}, {10527, 15932}, {10529, 37550}, {10588, 52783}, {10589, 11246}, {11020, 11227}, {11220, 64157}, {11374, 55864}, {11518, 61804}, {11529, 54445}, {12649, 37267}, {12730, 41556}, {12832, 20085}, {13390, 17801}, {13411, 61834}, {14829, 42696}, {15511, 55937}, {15680, 41547}, {15692, 24929}, {15705, 15933}, {17051, 47357}, {17074, 37685}, {17079, 63233}, {17366, 37642}, {17572, 57283}, {17612, 41228}, {17718, 30340}, {17740, 24593}, {18391, 21578}, {18421, 38314}, {18593, 26742}, {20014, 63987}, {20043, 37639}, {20054, 41687}, {20121, 31183}, {21625, 63469}, {24471, 51171}, {24558, 64047}, {24599, 24620}, {25934, 62799}, {25939, 45227}, {26062, 62874}, {26723, 62781}, {26866, 33849}, {27191, 31232}, {27797, 60085}, {29627, 59779}, {30652, 55086}, {30711, 63164}, {30829, 62706}, {31721, 59215}, {31888, 41697}, {33129, 62783}, {33150, 57477}, {34048, 63096}, {34632, 63993}, {37108, 37534}, {37139, 37222}, {37307, 37583}, {37423, 37623}, {37646, 62208}, {37723, 62102}, {38399, 54392}, {40420, 56086}, {41712, 62235}, {42290, 43063}, {43052, 52620}, {43055, 63126}, {43056, 63008}, {45204, 62820}, {46017, 63030}, {50810, 51788}, {51301, 54310}, {51415, 54281}, {51790, 61992}, {51792, 62005}, {51841, 63016}, {51842, 63015}, {52423, 63095}, {55437, 63068}, {56075, 62621}, {58800, 63057}, {62787, 62795}, {62823, 64083}, {63003, 63152}, {63207, 64162}

X(64142) = isotomic conjugate of X(56075)
X(64142) = anticomplement of X(5328)
X(64142) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4900}, {9, 41436}, {31, 56075}, {41, 36588}, {55, 39963}, {284, 56159}, {650, 6014}, {2175, 40029}, {3063, 53659}
X(64142) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 56075}, {9, 4900}, {223, 39963}, {478, 41436}, {3160, 36588}, {3679, 4873}, {5328, 5328}, {10001, 53659}, {40590, 56159}, {40593, 40029}, {52593, 11}, {52659, 36915}
X(64142) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {55993, 3436}
X(64142) = X(i)-cross conjugate of X(j) for these {i, j}: {16236, 7}, {16670, 3241}
X(64142) = pole of line {17136, 23831} with respect to the Kiepert parabola
X(64142) = pole of line {522, 30725} with respect to the Steiner circumellipse
X(64142) = pole of line {333, 56075} with respect to the Wallace hyperbola
X(64142) = pole of line {3669, 4453} with respect to the dual conic of Spieker circle
X(64142) = pole of line {1, 3832} with respect to the dual conic of Yff parabola
X(64142) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1120)}}, {{A, B, C, X(9), X(88)}}, {{A, B, C, X(27), X(28610)}}, {{A, B, C, X(57), X(8686)}}, {{A, B, C, X(63), X(1811)}}, {{A, B, C, X(80), X(31142)}}, {{A, B, C, X(81), X(5437)}}, {{A, B, C, X(89), X(3306)}}, {{A, B, C, X(92), X(46873)}}, {{A, B, C, X(144), X(34234)}}, {{A, B, C, X(226), X(44794)}}, {{A, B, C, X(278), X(31231)}}, {{A, B, C, X(279), X(3911)}}, {{A, B, C, X(527), X(6006)}}, {{A, B, C, X(672), X(2384)}}, {{A, B, C, X(673), X(6172)}}, {{A, B, C, X(908), X(8046)}}, {{A, B, C, X(1000), X(5316)}}, {{A, B, C, X(3218), X(55921)}}, {{A, B, C, X(3452), X(56086)}}, {{A, B, C, X(3929), X(36603)}}, {{A, B, C, X(3982), X(60076)}}, {{A, B, C, X(4029), X(5257)}}, {{A, B, C, X(4031), X(60085)}}, {{A, B, C, X(4373), X(17274)}}, {{A, B, C, X(4671), X(36593)}}, {{A, B, C, X(5219), X(16236)}}, {{A, B, C, X(5226), X(8051)}}, {{A, B, C, X(5235), X(36911)}}, {{A, B, C, X(5328), X(56075)}}, {{A, B, C, X(7308), X(8056)}}, {{A, B, C, X(8545), X(43760)}}, {{A, B, C, X(9436), X(56274)}}, {{A, B, C, X(14621), X(35578)}}, {{A, B, C, X(18228), X(30711)}}, {{A, B, C, X(21446), X(60953)}}, {{A, B, C, X(21454), X(40420)}}, {{A, B, C, X(21870), X(59207)}}, {{A, B, C, X(24029), X(61240)}}, {{A, B, C, X(24624), X(60942)}}, {{A, B, C, X(26580), X(27797)}}, {{A, B, C, X(27475), X(59374)}}, {{A, B, C, X(27776), X(30590)}}, {{A, B, C, X(30712), X(50116)}}, {{A, B, C, X(36100), X(60966)}}, {{A, B, C, X(36101), X(36973)}}, {{A, B, C, X(37131), X(56551)}}, {{A, B, C, X(39962), X(51780)}}, {{A, B, C, X(40869), X(63851)}}, {{A, B, C, X(42290), X(52896)}}, {{A, B, C, X(42318), X(61023)}}, {{A, B, C, X(57663), X(59173)}}, {{A, B, C, X(60169), X(60980)}}
X(64142) = barycentric product X(i)*X(j) for these (i, j): {279, 62706}, {1434, 4029}, {3241, 7}, {4572, 8656}, {6006, 664}, {13462, 75}, {16236, 39704}, {16670, 85}, {21870, 57785}, {23073, 331}, {30829, 57}
X(64142) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4900}, {2, 56075}, {7, 36588}, {56, 41436}, {57, 39963}, {65, 56159}, {85, 40029}, {109, 6014}, {664, 53659}, {1317, 36924}, {3241, 8}, {3911, 36915}, {4029, 2321}, {4982, 3686}, {6006, 522}, {8656, 663}, {13462, 1}, {16236, 3679}, {16670, 9}, {21870, 210}, {23073, 219}, {30829, 312}, {36911, 4873}, {52593, 4944}, {62706, 346}
X(64142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20059, 908}, {2, 23958, 9965}, {2, 3218, 144}, {2, 57, 21454}, {7, 5435, 3911}, {46, 14986, 20070}, {57, 1445, 3218}, {57, 5219, 4031}, {65, 5265, 3622}, {100, 64151, 145}, {631, 5708, 11036}, {908, 2094, 20059}, {938, 15803, 3522}, {1471, 9364, 17126}, {1788, 32636, 3600}, {1788, 3600, 3617}, {3306, 5744, 2}, {3488, 5122, 10304}, {3911, 4031, 5219}, {3928, 6692, 18228}, {4031, 5219, 7}, {4292, 5704, 3832}, {4860, 5218, 11038}, {10164, 10980, 10578}, {11019, 53056, 9778}, {17074, 52424, 37685}, {34753, 37545, 4}

X(64143) = ANTICOMPLEMENT OF X(3928)

Barycentrics    3*a^3+3*a^2*(b+c)-3*(b-c)^2*(b+c)-a*(3*b^2+2*b*c+3*c^2) : :
X(64143) = X[3146]+2*X[11523], -5*X[3616]+4*X[11194], -7*X[3832]+4*X[24391], -4*X[4421]+3*X[9778], -X[5059]+4*X[12437], -4*X[5763]+X[12246], -4*X[5812]+X[9799], -X[6764]+4*X[12699], 2*X[9589]+X[12632], -2*X[12625]+5*X[17578], -13*X[19877]+4*X[28646], -3*X[25055]+2*X[34646]

X(64143) lies on these lines: {2, 7}, {8, 1836}, {20, 41561}, {30, 5758}, {37, 41825}, {55, 63975}, {65, 18247}, {69, 42034}, {145, 9580}, {210, 59412}, {223, 36640}, {312, 21296}, {320, 20942}, {321, 32099}, {345, 4488}, {376, 33597}, {381, 5811}, {388, 31165}, {516, 64146}, {518, 9812}, {519, 962}, {524, 42047}, {528, 9809}, {529, 2098}, {545, 42049}, {551, 11037}, {651, 18624}, {758, 59387}, {938, 24473}, {944, 4930}, {1211, 7229}, {1699, 5850}, {1743, 62208}, {1864, 3868}, {2999, 4346}, {3083, 31601}, {3084, 31602}, {3091, 30326}, {3146, 11523}, {3161, 18134}, {3175, 36854}, {3339, 8165}, {3474, 64083}, {3475, 52653}, {3487, 16418}, {3616, 11194}, {3679, 4295}, {3681, 59413}, {3687, 4454}, {3715, 9780}, {3782, 5222}, {3811, 41860}, {3829, 5852}, {3832, 24391}, {3839, 55109}, {3870, 30332}, {3897, 20323}, {3927, 5714}, {3945, 4656}, {3947, 18231}, {3951, 5177}, {3984, 37435}, {4052, 10446}, {4054, 14552}, {4102, 55948}, {4312, 21060}, {4313, 64002}, {4344, 41011}, {4345, 51423}, {4402, 63037}, {4415, 4644}, {4421, 9778}, {4428, 5698}, {4552, 18663}, {4645, 5423}, {4703, 39581}, {4869, 30568}, {4887, 23511}, {4902, 24175}, {4980, 5739}, {5057, 36845}, {5059, 12437}, {5128, 27525}, {5175, 62969}, {5221, 44847}, {5261, 12526}, {5274, 62823}, {5658, 5762}, {5703, 16370}, {5704, 17533}, {5735, 59687}, {5743, 7222}, {5761, 28444}, {5763, 12246}, {5764, 16403}, {5775, 10590}, {5812, 9799}, {5880, 58629}, {5927, 59385}, {6049, 20076}, {6147, 16857}, {6175, 11236}, {6361, 41543}, {6764, 12699}, {8055, 18141}, {8580, 30424}, {9579, 20007}, {9589, 12632}, {9612, 54398}, {9797, 12701}, {10157, 59386}, {10327, 17491}, {10580, 24703}, {10582, 30340}, {11024, 19875}, {11036, 12572}, {11038, 40998}, {11106, 63274}, {11113, 15933}, {11552, 51066}, {11678, 41539}, {11679, 64015}, {12625, 17578}, {13405, 60905}, {13587, 27383}, {14555, 31995}, {15683, 34701}, {16020, 33103}, {16833, 17753}, {17139, 41629}, {17170, 29573}, {17183, 42028}, {17276, 63089}, {17294, 33867}, {19346, 21319}, {19877, 28646}, {23681, 37681}, {24248, 42043}, {24695, 33101}, {24725, 42039}, {25055, 34646}, {25930, 62788}, {26105, 58560}, {27398, 58786}, {28194, 63962}, {28534, 34607}, {30305, 51093}, {30807, 32003}, {30854, 32098}, {31146, 60926}, {31888, 41550}, {32857, 36634}, {32859, 34255}, {33099, 42042}, {34048, 62799}, {34611, 50839}, {34619, 34632}, {36850, 41830}, {37631, 42050}, {37656, 41915}, {39595, 39980}, {39948, 62997}, {41792, 50079}, {41823, 62229}, {44447, 63168}, {45116, 51067}, {49736, 51099}, {50802, 60895}, {50808, 63971}, {52374, 56355}, {54113, 56927}, {62798, 63094}

X(64143) = reflection of X(i) in X(j) for these {i,j}: {944, 4930}, {9778, 25568}, {15683, 34701}, {34610, 34647}, {34632, 34619}, {34744, 11236}
X(64143) = anticomplement of X(3928)
X(64143) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 7285}
X(64143) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 7285}, {3928, 3928}
X(64143) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {7319, 69}, {41441, 8}
X(64143) = pole of line {3812, 14100} with respect to the Feuerbach hyperbola
X(64143) = pole of line {522, 21052} with respect to the Steiner circumellipse
X(64143) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(27525)}}, {{A, B, C, X(8), X(3929)}}, {{A, B, C, X(57), X(5128)}}, {{A, B, C, X(553), X(55948)}}, {{A, B, C, X(1121), X(28610)}}, {{A, B, C, X(2094), X(56947)}}, {{A, B, C, X(3219), X(56355)}}, {{A, B, C, X(4102), X(6172)}}, {{A, B, C, X(5435), X(60167)}}, {{A, B, C, X(18228), X(34401)}}, {{A, B, C, X(31231), X(55962)}}, {{A, B, C, X(52819), X(54928)}}
X(64143) = barycentric product X(i)*X(j) for these (i, j): {5128, 75}, {27525, 7}
X(64143) = barycentric quotient X(i)/X(j) for these (i, j): {1, 7285}, {5128, 1}, {27525, 8}
X(64143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 3929}, {2, 17781, 6172}, {7, 329, 18228}, {144, 226, 5273}, {226, 3929, 2}, {329, 5905, 7}, {908, 9965, 5435}, {5905, 17484, 329}, {11236, 34744, 53620}, {17768, 25568, 9778}, {34610, 34647, 38314}

X(64144) = ANTICOMPLEMENT OF X(5787)

Barycentrics    3*a^7-5*a^6*(b+c)-(b-c)^4*(b+c)^3-3*a^3*(b^2-c^2)^2-a^5*(3*b^2+2*b*c+3*c^2)+a*(b^2-c^2)^2*(3*b^2+2*b*c+3*c^2)-a^2*(b-c)^2*(3*b^3+b^2*c+b*c^2+3*c^3)+a^4*(9*b^3-b^2*c-b*c^2+9*c^3) : :
X(64144) = -3*X[2]+2*X[5787], -2*X[84]+3*X[376], -3*X[165]+2*X[9948], -5*X[631]+4*X[6245], -5*X[3522]+4*X[34862], -7*X[3523]+8*X[40262], -9*X[3524]+8*X[6705], -7*X[3528]+6*X[52027], -3*X[3543]+4*X[22792], -9*X[3545]+10*X[63966], -4*X[6796]+3*X[14647], -2*X[7992]+3*X[14646]

X(64144) lies on these lines: {1, 4}, {2, 5787}, {3, 5273}, {7, 20420}, {8, 7580}, {9, 4297}, {12, 33993}, {20, 72}, {30, 5758}, {40, 6743}, {84, 376}, {145, 50696}, {165, 9948}, {220, 5776}, {279, 41004}, {355, 6908}, {390, 9856}, {405, 5731}, {442, 59387}, {443, 10884}, {452, 5927}, {516, 3189}, {517, 12632}, {519, 6766}, {550, 12684}, {631, 6245}, {912, 6869}, {938, 19541}, {942, 50700}, {943, 1012}, {952, 6764}, {954, 4313}, {958, 45039}, {960, 43161}, {1006, 8273}, {1071, 37544}, {1260, 10430}, {1385, 6846}, {1708, 10085}, {1728, 21578}, {1788, 44425}, {1837, 54366}, {2096, 6934}, {2550, 12520}, {2801, 64075}, {3146, 6259}, {3149, 5768}, {3160, 6356}, {3419, 37421}, {3474, 15071}, {3522, 34862}, {3523, 40262}, {3524, 6705}, {3528, 52027}, {3543, 22792}, {3545, 63966}, {3576, 16845}, {3600, 5728}, {3616, 8226}, {3651, 5584}, {3868, 50695}, {3962, 6001}, {4190, 11220}, {4292, 36996}, {4293, 12680}, {4294, 12688}, {4295, 6253}, {4299, 18397}, {4301, 52835}, {4308, 5809}, {4311, 10396}, {4314, 11372}, {4315, 9845}, {4317, 10399}, {5044, 37423}, {5082, 64150}, {5129, 10157}, {5175, 52683}, {5222, 19542}, {5436, 63970}, {5450, 35202}, {5554, 35990}, {5698, 31803}, {5703, 8727}, {5720, 6865}, {5732, 57284}, {5777, 6987}, {5802, 40133}, {5805, 11036}, {5811, 31789}, {5812, 28160}, {5815, 31799}, {5818, 6889}, {5842, 63962}, {5905, 59355}, {5920, 12249}, {6224, 13257}, {6284, 64130}, {6796, 14647}, {6829, 18242}, {6832, 37837}, {6835, 18444}, {6843, 18480}, {6847, 33597}, {6849, 37615}, {6851, 37700}, {6864, 18443}, {6868, 40263}, {6885, 13369}, {6887, 13151}, {6904, 10167}, {6907, 18525}, {6909, 11517}, {6913, 34773}, {6916, 41854}, {6938, 18239}, {6955, 18238}, {6988, 51755}, {6990, 7958}, {7288, 10395}, {7330, 59345}, {7686, 64147}, {7992, 14646}, {8726, 17582}, {8987, 43509}, {9541, 49234}, {9579, 41561}, {9778, 11684}, {9851, 10398}, {9910, 12082}, {10381, 54181}, {10431, 34772}, {10465, 10477}, {10950, 64152}, {11111, 52684}, {11201, 28901}, {11227, 17580}, {12247, 54441}, {12248, 12691}, {12565, 35514}, {12625, 28236}, {12635, 61010}, {12649, 36002}, {12664, 45120}, {12779, 41339}, {13442, 48923}, {13974, 43510}, {14054, 64079}, {15998, 56273}, {17532, 50864}, {17554, 38108}, {17857, 64111}, {19925, 25525}, {21168, 52665}, {24929, 37434}, {27383, 37374}, {28174, 54199}, {35844, 42260}, {35845, 42261}, {37441, 57281}, {38037, 51715}, {41869, 54227}, {44696, 56299}, {51773, 57278}, {58834, 64005}, {63297, 63445}

X(64144) = reflection of X(i) in X(j) for these {i,j}: {4, 1490}, {3146, 6259}, {6764, 8158}, {6851, 37700}, {7992, 31730}, {9799, 3}, {10864, 4297}, {12246, 20}, {12684, 550}, {41869, 54227}
X(64144) = anticomplement of X(5787)
X(64144) = X(i)-Dao conjugate of X(j) for these {i, j}: {5787, 5787}
X(64144) = pole of line {522, 59992} with respect to the polar circle
X(64144) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1838), X(10429)}}, {{A, B, C, X(7580), X(31793)}}
X(64144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1490, 5658}, {4, 18446, 3487}, {4, 944, 3488}, {20, 20007, 31793}, {20, 72, 5759}, {20, 971, 12246}, {226, 5691, 4}, {443, 10884, 21151}, {550, 12684, 54052}, {5777, 18481, 6987}, {7992, 31730, 14646}, {9799, 54051, 3}, {12565, 63146, 35514}

X(64145) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND SCHIFFLER AND X(8)-CROSSPEDAL-OF-X(145)

Barycentrics    3*a^7-4*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-4*b^2+15*b*c-4*c^2)+2*a*(b^2-c^2)^2*(b^2-3*b*c+c^2)-a^3*(b-c)^2*(b^2+11*b*c+c^2)-a^2*(b-c)^2*(2*b^3-7*b^2*c-7*b*c^2+2*c^3)+a^4*(7*b^3-8*b^2*c-8*b*c^2+7*c^3) : :
X(64145) = -3*X[1]+2*X[1537], -2*X[10]+3*X[38693], -2*X[119]+3*X[3576], -3*X[165]+2*X[1145], -5*X[355]+6*X[38177], -3*X[1319]+2*X[1538], -4*X[1387]+3*X[1699], -5*X[1698]+6*X[21154], -4*X[3035]+5*X[7987], -4*X[3036]+3*X[37712]

X(64145) lies on circumconic {{A, B, C, X(40437), X(46435)}} and on these lines: {1, 1537}, {3, 12751}, {4, 11715}, {8, 46684}, {10, 38693}, {11, 1420}, {20, 2802}, {30, 12737}, {35, 12749}, {36, 80}, {40, 550}, {100, 4297}, {103, 43353}, {119, 3576}, {144, 2801}, {153, 214}, {165, 1145}, {355, 38177}, {497, 41554}, {516, 1320}, {517, 26726}, {519, 64189}, {528, 2951}, {529, 5538}, {944, 2800}, {946, 10728}, {960, 17661}, {962, 64137}, {971, 17638}, {1012, 63281}, {1071, 11571}, {1158, 37707}, {1317, 7962}, {1319, 1538}, {1385, 10742}, {1387, 1699}, {1388, 40267}, {1484, 28186}, {1698, 21154}, {2646, 12763}, {2771, 12680}, {2932, 63991}, {2950, 5119}, {3035, 7987}, {3036, 37712}, {3091, 32557}, {3476, 15558}, {3486, 5083}, {3488, 46681}, {3579, 38754}, {3583, 12761}, {3600, 18240}, {3601, 10956}, {3655, 12678}, {3679, 64193}, {3746, 12775}, {3832, 32558}, {4293, 12736}, {4316, 17654}, {5204, 52683}, {5434, 20330}, {5441, 5882}, {5450, 37710}, {5531, 10609}, {5537, 25438}, {5587, 6713}, {5692, 12665}, {5727, 12832}, {5818, 38133}, {5840, 6264}, {5854, 7991}, {5886, 22799}, {5902, 15528}, {5903, 37002}, {6256, 21842}, {6265, 34773}, {6284, 20586}, {6326, 28459}, {6667, 7989}, {6702, 59387}, {6796, 18861}, {7580, 22560}, {7967, 25485}, {8227, 38032}, {8727, 63270}, {9615, 13922}, {9864, 53733}, {9897, 58887}, {9952, 63207}, {10057, 12114}, {10058, 45287}, {10073, 22775}, {10074, 10572}, {10164, 64141}, {10165, 64008}, {10246, 12611}, {10304, 50841}, {10465, 38484}, {10711, 51705}, {10724, 21630}, {10738, 28160}, {10759, 39870}, {11224, 60933}, {11249, 12773}, {11260, 13271}, {11531, 25416}, {11570, 64147}, {12115, 37525}, {12138, 54397}, {12247, 37572}, {12331, 35238}, {12368, 53753}, {12531, 28236}, {12619, 18525}, {12641, 38455}, {12653, 64005}, {12743, 30283}, {12750, 48694}, {12757, 15096}, {12758, 64120}, {12762, 33597}, {12767, 30304}, {12784, 53755}, {13178, 53722}, {13205, 37022}, {13211, 53715}, {13226, 62616}, {13532, 36944}, {13624, 38752}, {13729, 51714}, {15015, 37725}, {15017, 25522}, {15931, 51506}, {17100, 63983}, {17502, 38762}, {17660, 64043}, {18480, 57298}, {18492, 23513}, {18519, 60743}, {18908, 58666}, {18976, 37579}, {19077, 48701}, {19078, 48700}, {19914, 28204}, {19925, 31272}, {20418, 37718}, {21635, 41012}, {30308, 38026}, {30384, 52851}, {31673, 59391}, {31730, 64136}, {33557, 38669}, {33812, 41561}, {33858, 47034}, {34122, 37714}, {34126, 61261}, {34648, 59377}, {34690, 37569}, {36977, 64076}, {37618, 39692}, {37706, 59330}, {37708, 52027}, {38084, 50799}, {41869, 64138}, {50896, 53750}, {50899, 53752}, {50903, 53746}, {51529, 62354}, {51897, 57002}, {53055, 63973}, {54445, 58453}

X(64145) = midpoint of X(i) and X(j) for these {i,j}: {944, 12248}, {6224, 64009}, {12653, 64005}
X(64145) = reflection of X(i) in X(j) for these {i,j}: {1, 64191}, {4, 11715}, {8, 46684}, {40, 38761}, {80, 104}, {100, 4297}, {153, 214}, {355, 38602}, {962, 64137}, {1145, 38759}, {5531, 10609}, {5541, 24466}, {5660, 5731}, {5691, 11}, {6265, 34773}, {7972, 944}, {9864, 53733}, {10698, 5882}, {10711, 51705}, {10724, 21630}, {10728, 946}, {10742, 1385}, {10759, 39870}, {11531, 25416}, {11571, 1071}, {12119, 18481}, {12368, 53753}, {12751, 3}, {12784, 53755}, {13178, 53722}, {13211, 53715}, {13253, 1317}, {13271, 11260}, {13532, 53748}, {14217, 12737}, {15096, 12757}, {16128, 19907}, {17661, 960}, {18525, 12619}, {34789, 1}, {38756, 12611}, {41698, 1319}, {41869, 64138}, {44425, 21578}, {47034, 33858}, {49176, 12773}, {50896, 53750}, {50899, 53752}, {50903, 53746}, {50908, 3655}, {51897, 57002}, {52836, 1387}, {52851, 30384}, {62354, 51529}, {62616, 13226}, {64011, 50811}, {64056, 40}, {64136, 31730}, {64140, 3579}
X(64145) = pole of line {11219, 17638} with respect to the Feuerbach hyperbola
X(64145) = pole of line {2804, 25416} with respect to the Suppa-Cucoanes circle
X(64145) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {6224, 20098, 64009}
X(64145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2829, 34789}, {4, 11715, 16173}, {30, 12737, 14217}, {40, 952, 64056}, {80, 104, 11219}, {104, 515, 80}, {104, 64188, 36}, {119, 3576, 64012}, {153, 214, 5660}, {153, 5731, 214}, {515, 21578, 44425}, {944, 12248, 2800}, {944, 2800, 7972}, {952, 18481, 12119}, {952, 24466, 5541}, {952, 38761, 40}, {1145, 38759, 165}, {1387, 52836, 1699}, {2829, 64191, 1}, {3655, 16128, 19907}, {6224, 64009, 2801}, {10246, 38756, 12611}, {12737, 14217, 50891}, {12764, 33898, 41698}, {15017, 30389, 34123}, {16128, 19907, 50908}, {21630, 28164, 10724}, {34123, 38757, 15017}, {38754, 64140, 3579}

X(64146) = ANTICOMPLEMENT OF X(24392)

Barycentrics    (a-b-c)*(5*a^2+(b-c)^2-2*a*(b+c)) : :
X(64146) = -4*X[3]+X[6764], -X[7]+4*X[3174], X[20]+2*X[6765], -X[962]+4*X[3811], -5*X[3091]+8*X[59722], -5*X[3522]+2*X[6762], -5*X[3617]+2*X[12625], -X[3621]+4*X[12640], -7*X[3622]+4*X[21627], -5*X[3623]+2*X[3680], -8*X[3813]+11*X[5550], -4*X[5534]+X[6223] and many others

X(64146) lies on these lines: {1, 11024}, {2, 3158}, {3, 6764}, {7, 3174}, {8, 21}, {10, 17554}, {20, 6765}, {42, 4344}, {56, 9797}, {57, 145}, {63, 20015}, {78, 9785}, {100, 1617}, {149, 5748}, {165, 519}, {200, 390}, {210, 10385}, {329, 2900}, {354, 3241}, {479, 664}, {497, 3689}, {516, 64143}, {517, 54051}, {518, 5918}, {521, 30613}, {528, 9812}, {672, 3169}, {758, 34632}, {910, 17314}, {938, 5687}, {944, 6244}, {962, 3811}, {1002, 35104}, {1155, 20050}, {1190, 4513}, {1202, 3501}, {1260, 5809}, {1376, 10580}, {1621, 6600}, {1697, 20007}, {1997, 43290}, {2078, 12649}, {2094, 4430}, {2280, 5749}, {2348, 3161}, {2550, 10578}, {3091, 59722}, {3160, 8270}, {3208, 8012}, {3210, 53552}, {3243, 21454}, {3244, 10980}, {3256, 12648}, {3434, 5226}, {3474, 6154}, {3475, 34612}, {3522, 6762}, {3598, 3875}, {3599, 25718}, {3616, 3748}, {3617, 12625}, {3621, 12640}, {3622, 21627}, {3623, 3680}, {3632, 4305}, {3633, 53056}, {3681, 6172}, {3684, 6602}, {3685, 5423}, {3693, 5838}, {3740, 47357}, {3744, 5222}, {3753, 15933}, {3813, 5550}, {3872, 10383}, {3885, 17642}, {3886, 7172}, {3896, 4460}, {3939, 17127}, {3957, 9776}, {3961, 64168}, {4097, 4651}, {4105, 20537}, {4294, 5815}, {4314, 4882}, {4323, 34772}, {4339, 10460}, {4345, 4511}, {4421, 24477}, {4428, 38057}, {4512, 5686}, {4685, 52155}, {4779, 6555}, {4847, 5281}, {4848, 20008}, {4863, 5218}, {4917, 57287}, {4924, 62820}, {4939, 46938}, {5082, 5703}, {5173, 14923}, {5175, 10528}, {5274, 6745}, {5325, 59414}, {5531, 64130}, {5534, 6223}, {5704, 59591}, {5734, 22836}, {5766, 64171}, {5839, 42316}, {5854, 10031}, {5855, 34711}, {5856, 60971}, {5905, 20095}, {6049, 36846}, {6601, 56028}, {6743, 53053}, {7965, 12607}, {7967, 11227}, {8580, 30331}, {8715, 15931}, {8730, 35977}, {9053, 42049}, {9581, 27525}, {9799, 10306}, {9803, 25438}, {9965, 63145}, {10005, 56078}, {10394, 17658}, {10589, 62710}, {10857, 12629}, {10912, 20057}, {10914, 11018}, {11523, 20070}, {16020, 17715}, {16845, 63271}, {17018, 54308}, {17316, 19589}, {17576, 63135}, {17592, 48856}, {18391, 48696}, {19877, 64123}, {20036, 28272}, {20054, 63214}, {24388, 29679}, {24394, 27804}, {26015, 64114}, {26062, 33925}, {27818, 40154}, {28451, 59503}, {30628, 41539}, {32087, 63131}, {32099, 63134}, {34619, 59387}, {34625, 54445}, {34639, 63468}, {36802, 52210}, {37553, 39587}, {37655, 49451}, {37681, 62875}, {38053, 49732}, {38092, 61029}, {38314, 56177}, {39350, 41837}, {41575, 63133}, {44447, 60957}, {47375, 61023}, {47387, 60995}, {51615, 63621}, {54398, 61763}, {55868, 61157}, {58615, 61287}, {59374, 63261}, {63132, 64147}

X(64146) = reflection of X(i) in X(j) for these {i,j}: {2, 3158}, {9778, 34607}, {9812, 25568}, {24392, 59584}, {24477, 4421}, {28610, 9778}, {59387, 34619}, {63468, 34639}
X(64146) = anticomplement of X(24392)
X(64146) = X(i)-Dao conjugate of X(j) for these {i, j}: {4515, 2321}, {24392, 24392}, {53665, 24797}
X(64146) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1434, 9}, {17158, 37681}
X(64146) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {56081, 21286}, {56314, 3436}
X(64146) = pole of line {960, 4345} with respect to the Feuerbach hyperbola
X(64146) = pole of line {30719, 31605} with respect to the Steiner circumellipse
X(64146) = pole of line {27834, 37206} with respect to the Yff parabola
X(64146) = pole of line {18228, 31183} with respect to the dual conic of Yff parabola
X(64146) = centroid of X(8)-crosspedal-of-X(145)
X(64146) = intersection, other than A, B, C, of circumconics {{A, B, C, X(21), X(2137)}}, {{A, B, C, X(333), X(8051)}}, {{A, B, C, X(345), X(22040)}}, {{A, B, C, X(479), X(4076)}}, {{A, B, C, X(1002), X(3913)}}, {{A, B, C, X(1043), X(6553)}}, {{A, B, C, X(3161), X(40154)}}, {{A, B, C, X(8668), X(28471)}}, {{A, B, C, X(42470), X(56182)}}, {{A, B, C, X(44301), X(52352)}}
X(64146) = barycentric product X(i)*X(j) for these (i, j): {1, 56085}, {21, 22040}, {312, 62875}, {17158, 9}, {18153, 55}, {23819, 644}, {37681, 8}
X(64146) = barycentric quotient X(i)/X(j) for these (i, j): {17158, 85}, {18153, 6063}, {22040, 1441}, {23819, 24002}, {37681, 7}, {56085, 75}, {62875, 57}
X(64146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 12632, 12541}, {8, 3189, 12536}, {8, 55, 5273}, {78, 56936, 9785}, {100, 36845, 5435}, {145, 37267, 62832}, {200, 390, 18228}, {210, 10385, 52653}, {329, 20075, 30332}, {497, 3689, 64083}, {497, 64083, 5328}, {518, 34607, 9778}, {518, 9778, 28610}, {528, 25568, 9812}, {2136, 12437, 145}, {3158, 24392, 59584}, {3174, 7674, 7}, {3189, 3913, 8}, {3434, 63168, 5226}, {3475, 34612, 59412}, {3748, 26040, 3616}, {3935, 20075, 329}, {4421, 24477, 64108}, {4779, 6555, 30568}, {5435, 12630, 36845}, {5601, 5602, 3913}, {5853, 59584, 24392}, {6154, 41711, 3474}, {6765, 64117, 20}, {24392, 59584, 2}

X(64147) = ISOTOMIC CONJUGATE OF X(49496)

Barycentrics    (a^3*b-2*b*c^3+a*(b^3-b*c^2-2*c^3))*(a^3*c-2*b^3*c+a*(-2*b^3-b^2*c+c^3)) : :

X(64147) lies on these lines: {984, 3729}, {3864, 9902}, {3869, 52029}, {7146, 9312}, {26643, 40773}

X(64147) = isotomic conjugate of X(49496)
X(64147) = trilinear pole of line {1491, 4885}
X(64147) = Kimberling-Pavlov X(2)-conjugate of X(1) and X(4)
X(64147) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(76)}}, {{A, B, C, X(4), X(274)}}, {{A, B, C, X(19), X(6385)}}, {{A, B, C, X(83), X(56051)}}, {{A, B, C, X(105), X(40030)}}, {{A, B, C, X(239), X(35158)}}, {{A, B, C, X(330), X(2481)}}, {{A, B, C, X(671), X(36871)}}, {{A, B, C, X(894), X(10435)}}, {{A, B, C, X(981), X(56066)}}, {{A, B, C, X(3062), X(27447)}}, {{A, B, C, X(3226), X(42359)}}, {{A, B, C, X(3227), X(5485)}}, {{A, B, C, X(3869), X(18206)}}, {{A, B, C, X(4384), X(60149)}}, {{A, B, C, X(5395), X(39736)}}, {{A, B, C, X(6383), X(8769)}}, {{A, B, C, X(9311), X(18827)}}, {{A, B, C, X(18785), X(60244)}}, {{A, B, C, X(18840), X(32009)}}, {{A, B, C, X(27424), X(33676)}}, {{A, B, C, X(34860), X(35167)}}, {{A, B, C, X(35172), X(43676)}}, {{A, B, C, X(38247), X(43681)}}, {{A, B, C, X(38259), X(39740)}}, {{A, B, C, X(39738), X(60285)}}, {{A, B, C, X(39954), X(40017)}}, {{A, B, C, X(40014), X(52209)}}, {{A, B, C, X(46274), X(53222)}}

X(64148) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(165) AND X(9)-CROSSPEDAL-OF-X(1)

Barycentrics    (a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b+c)^2)*(a^4-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)-(b^2-c^2)^2) : :
X(64148) = X[8]+2*X[6261], 2*X[10]+X[1490], -X[145]+4*X[40257], 2*X[550]+X[40267], -5*X[631]+2*X[12114], -5*X[1698]+2*X[6245], -7*X[3090]+4*X[63980], -X[3189]+4*X[64116], -7*X[3523]+4*X[5450], 2*X[3579]+X[6259], -11*X[5056]+8*X[63963], -X[5758]+4*X[21077] and many others

X(64148) lies on these lines: {1, 5804}, {2, 515}, {3, 1603}, {4, 12}, {5, 26105}, {8, 6261}, {10, 1490}, {11, 6969}, {20, 2077}, {40, 329}, {56, 6927}, {84, 5273}, {100, 6925}, {104, 6880}, {119, 6827}, {145, 40257}, {153, 4996}, {165, 37427}, {197, 37305}, {198, 5514}, {210, 5657}, {223, 51375}, {227, 7952}, {355, 6825}, {376, 2829}, {381, 38037}, {387, 37699}, {388, 3149}, {390, 26333}, {393, 21854}, {411, 3436}, {452, 10902}, {480, 35514}, {495, 19541}, {497, 1532}, {498, 5691}, {516, 45701}, {517, 25568}, {550, 40267}, {631, 12114}, {944, 1319}, {946, 5226}, {952, 34625}, {958, 6988}, {962, 10528}, {971, 14647}, {1001, 6939}, {1012, 5218}, {1056, 22753}, {1058, 7681}, {1071, 1788}, {1125, 6964}, {1155, 2096}, {1158, 3219}, {1329, 6865}, {1376, 6916}, {1385, 6944}, {1440, 5923}, {1470, 4293}, {1478, 44425}, {1512, 18391}, {1519, 30305}, {1528, 40971}, {1621, 6957}, {1697, 63989}, {1698, 6245}, {1699, 10056}, {1737, 5768}, {1745, 51660}, {1750, 31434}, {1770, 15867}, {1857, 45766}, {2267, 26063}, {2478, 54348}, {2550, 6907}, {2800, 59417}, {2975, 6962}, {3035, 63991}, {3090, 63980}, {3091, 34486}, {3189, 64116}, {3359, 52684}, {3421, 3428}, {3434, 6932}, {3486, 33597}, {3487, 7686}, {3523, 5450}, {3577, 64110}, {3579, 6259}, {3616, 6953}, {3822, 6843}, {3911, 63430}, {3947, 5715}, {4194, 39574}, {4297, 6926}, {4302, 41698}, {4870, 5603}, {5056, 63963}, {5082, 15908}, {5084, 25893}, {5217, 64000}, {5229, 37468}, {5230, 40958}, {5261, 26332}, {5290, 64001}, {5432, 6935}, {5535, 9965}, {5584, 21031}, {5698, 37822}, {5758, 21077}, {5780, 45085}, {5787, 6989}, {5791, 9947}, {5811, 12514}, {5818, 6889}, {5881, 64081}, {5882, 6049}, {6282, 6745}, {6361, 64119}, {6705, 10864}, {6735, 64150}, {6767, 7956}, {6769, 59722}, {6824, 18480}, {6826, 18491}, {6828, 10585}, {6831, 10588}, {6833, 37600}, {6836, 11681}, {6842, 18518}, {6844, 7951}, {6846, 10198}, {6850, 11499}, {6862, 38114}, {6863, 18525}, {6864, 25466}, {6867, 18517}, {6868, 37821}, {6869, 10526}, {6887, 61261}, {6890, 27529}, {6891, 18481}, {6892, 18761}, {6893, 10267}, {6923, 18524}, {6930, 18516}, {6941, 10591}, {6942, 37002}, {6949, 10785}, {6954, 22758}, {6959, 34773}, {6960, 10527}, {6970, 10269}, {6982, 37820}, {6985, 10942}, {7491, 18542}, {7501, 20989}, {7580, 17757}, {7966, 63993}, {7971, 11362}, {7991, 54198}, {7992, 9588}, {8165, 37423}, {8582, 8726}, {8727, 31479}, {9654, 20420}, {9709, 37424}, {9780, 9799}, {9942, 14872}, {9943, 18239}, {10039, 63988}, {10164, 52027}, {10265, 61019}, {10268, 12572}, {10270, 59675}, {10310, 59591}, {10321, 10572}, {10531, 64173}, {10884, 24982}, {11036, 31870}, {11372, 60995}, {12246, 64118}, {12528, 32159}, {12607, 64077}, {12664, 58631}, {12671, 26066}, {12679, 37568}, {12680, 24914}, {12683, 56313}, {12686, 60935}, {12761, 13199}, {13912, 19068}, {13975, 19067}, {14646, 63276}, {15177, 35988}, {15325, 30283}, {15338, 37001}, {16127, 40256}, {17576, 59331}, {17649, 31787}, {18528, 51755}, {18529, 63970}, {19854, 37714}, {20060, 64079}, {21155, 34697}, {23600, 53815}, {26062, 59333}, {27383, 63391}, {27525, 31730}, {28236, 45700}, {30478, 52265}, {30513, 37300}, {31397, 63992}, {31673, 37434}, {31803, 58636}, {33814, 33898}, {34231, 51361}, {36996, 41712}, {37560, 63990}, {37569, 63168}, {38149, 50741}, {41538, 64021}, {41570, 54159}, {43174, 54156}, {54052, 64108}, {54398, 63967}, {56941, 64129}, {57288, 59345}, {59388, 61032}, {64074, 64123}

X(64148) = midpoint of X(i) and X(j) for these {i,j}: {5657, 5658}, {54051, 59387}
X(64148) = reflection of X(i) in X(j) for these {i,j}: {14647, 26446}, {52027, 10164}
X(64148) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1413, 56101}
X(64148) = X(i)-Dao conjugate of X(j) for these {i, j}: {281, 55963}, {38957, 61040}
X(64148) = pole of line {11041, 44547} with respect to the Feuerbach hyperbola
X(64148) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(329), X(40573)}}, {{A, B, C, X(943), X(7952)}}, {{A, B, C, X(1512), X(55116)}}, {{A, B, C, X(7080), X(18391)}}
X(64148) = barycentric product X(i)*X(j) for these (i, j): {322, 8557}, {6350, 7952}, {18391, 329}, {54366, 7080}, {57810, 62691}
X(64148) = barycentric quotient X(i)/X(j) for these (i, j): {2324, 56101}, {7952, 55963}, {8557, 84}, {18391, 189}, {18446, 41081}, {19350, 1433}, {54366, 1440}, {62691, 285}
X(64148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12667, 64120}, {4, 10786, 3085}, {4, 11491, 4294}, {4, 8164, 7680}, {40, 6260, 63962}, {498, 5691, 6847}, {944, 6834, 3086}, {971, 26446, 14647}, {1155, 12678, 2096}, {1478, 44425, 50701}, {1512, 18446, 18391}, {1698, 63981, 6245}, {3579, 6259, 64190}, {4297, 26364, 6926}, {5261, 50700, 26332}, {5657, 5658, 6001}, {5818, 6889, 19855}, {6256, 6796, 20}, {6905, 12115, 4293}, {7080, 37421, 40}, {7580, 17757, 64111}, {9780, 9799, 12616}, {10198, 19925, 6846}, {10864, 31423, 6705}, {11500, 18242, 4}, {18391, 18446, 64147}, {18480, 26487, 6824}, {18516, 32613, 6930}, {18761, 31659, 6892}, {43174, 54227, 54156}, {48482, 63964, 3091}, {54051, 59387, 515}

X(64149) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(9)-CROSSPEDAL-OF-X(2) AND ANTIPEDAL-OF-X(9)

Barycentrics    a*(-b^2+3*b*c-c^2+a*(b+c)) : :
X(64149) = -5*X[2]+2*X[210], X[3]+8*X[58561], X[4]+8*X[13373], X[5]+8*X[58605], -5*X[8]+14*X[4002], X[9]+8*X[58607], 4*X[10]+5*X[3889], X[20]+8*X[13374], 2*X[51]+X[23155], 2*X[65]+7*X[3622], X[69]+8*X[58562], -2*X[72]+11*X[5550] and many others

X(64149) lies on these lines: {1, 88}, {2, 210}, {3, 58561}, {4, 13373}, {5, 58605}, {6, 7292}, {7, 3660}, {8, 4002}, {9, 58607}, {10, 3889}, {11, 10129}, {20, 13374}, {21, 3338}, {31, 29820}, {37, 3999}, {38, 22220}, {42, 17063}, {43, 62867}, {51, 23155}, {55, 9352}, {56, 20846}, {57, 1621}, {63, 5284}, {65, 3622}, {69, 58562}, {72, 5550}, {75, 29824}, {80, 58625}, {81, 614}, {85, 35312}, {89, 3246}, {104, 58604}, {142, 11025}, {144, 58563}, {145, 3812}, {146, 58582}, {147, 58589}, {148, 58590}, {149, 5880}, {150, 58592}, {151, 58593}, {152, 58594}, {153, 58595}, {165, 62856}, {171, 62806}, {190, 24359}, {192, 58583}, {193, 58581}, {194, 58584}, {200, 9342}, {238, 62795}, {312, 17140}, {329, 58577}, {373, 2810}, {390, 17603}, {392, 942}, {405, 62827}, {443, 5178}, {495, 34122}, {497, 20292}, {513, 6548}, {517, 3524}, {537, 64178}, {551, 3877}, {612, 62814}, {658, 55082}, {674, 7998}, {748, 32913}, {756, 25502}, {758, 15671}, {896, 15485}, {899, 49490}, {908, 5542}, {936, 62861}, {938, 5086}, {940, 7191}, {946, 9961}, {960, 46934}, {962, 9940}, {968, 18193}, {971, 9779}, {982, 3720}, {984, 17449}, {997, 63159}, {1001, 3218}, {1056, 5176}, {1086, 33134}, {1100, 17025}, {1122, 30712}, {1125, 3868}, {1150, 16823}, {1155, 42819}, {1215, 30957}, {1278, 58620}, {1279, 17126}, {1376, 3957}, {1385, 6876}, {1386, 14996}, {1420, 51683}, {1647, 17717}, {1698, 3881}, {1699, 11220}, {1757, 17125}, {1788, 10587}, {1836, 26842}, {1962, 17591}, {1995, 22769}, {2094, 52653}, {2320, 5126}, {2346, 60985}, {2475, 58568}, {2476, 51706}, {2650, 21214}, {2771, 5886}, {2800, 61275}, {2801, 7988}, {2805, 17301}, {2836, 38023}, {2886, 27186}, {2975, 3333}, {2979, 58574}, {3006, 17234}, {3035, 37703}, {3086, 62864}, {3091, 12675}, {3120, 24217}, {3121, 63493}, {3146, 58567}, {3219, 4423}, {3240, 16610}, {3241, 3753}, {3242, 5297}, {3243, 62236}, {3290, 63066}, {3296, 5084}, {3305, 62823}, {3337, 5248}, {3361, 5303}, {3434, 9776}, {3436, 11037}, {3448, 58601}, {3485, 10586}, {3533, 58630}, {3543, 63432}, {3555, 9780}, {3617, 34791}, {3621, 3698}, {3623, 5836}, {3624, 3874}, {3633, 3918}, {3636, 5903}, {3646, 3951}, {3648, 58586}, {3664, 50003}, {3666, 29814}, {3670, 62831}, {3673, 16727}, {3677, 5287}, {3678, 34595}, {3679, 3833}, {3689, 15570}, {3705, 18139}, {3711, 61158}, {3736, 16753}, {3745, 4906}, {3751, 37680}, {3752, 4883}, {3756, 5718}, {3758, 16482}, {3794, 42025}, {3811, 17531}, {3816, 31053}, {3817, 61740}, {3820, 58813}, {3826, 51463}, {3827, 35260}, {3832, 12680}, {3834, 25959}, {3836, 33120}, {3840, 32771}, {3846, 33069}, {3870, 5437}, {3879, 49987}, {3894, 10176}, {3896, 17490}, {3897, 5563}, {3898, 51105}, {3899, 51110}, {3909, 17723}, {3911, 7672}, {3912, 24629}, {3919, 51103}, {3920, 17597}, {3935, 4413}, {3938, 17122}, {3952, 17146}, {3956, 19876}, {3961, 17124}, {3966, 32863}, {3967, 46938}, {3968, 4677}, {3976, 59305}, {3980, 32943}, {3983, 46931}, {3994, 49532}, {4003, 15569}, {4004, 31792}, {4011, 32940}, {4015, 19872}, {4038, 17017}, {4083, 14474}, {4131, 17427}, {4188, 37080}, {4189, 32636}, {4193, 13407}, {4197, 10916}, {4358, 24349}, {4359, 10453}, {4414, 16484}, {4420, 16408}, {4429, 29835}, {4438, 29851}, {4440, 58618}, {4442, 4890}, {4511, 15934}, {4640, 23958}, {4645, 58627}, {4648, 25279}, {4662, 46932}, {4663, 14997}, {4671, 49483}, {4675, 17721}, {4679, 17484}, {4682, 29815}, {4687, 13476}, {4694, 30116}, {4706, 49475}, {4712, 56510}, {4751, 58379}, {4795, 24482}, {4847, 38204}, {4851, 32842}, {4853, 30343}, {4861, 7373}, {4871, 32931}, {4881, 40726}, {4891, 42051}, {4966, 33077}, {4972, 29843}, {5046, 10404}, {5047, 62858}, {5056, 14872}, {5080, 58570}, {5082, 16216}, {5083, 5219}, {5121, 37651}, {5173, 5435}, {5208, 5333}, {5211, 17300}, {5218, 18839}, {5220, 35595}, {5226, 10584}, {5231, 20116}, {5249, 10861}, {5250, 38399}, {5256, 5573}, {5260, 62874}, {5263, 26627}, {5268, 62850}, {5272, 32911}, {5274, 10391}, {5281, 17642}, {5302, 17570}, {5311, 17598}, {5536, 52769}, {5558, 56879}, {5572, 25722}, {5603, 10202}, {5640, 8679}, {5650, 9052}, {5651, 43149}, {5697, 33815}, {5703, 50196}, {5704, 10585}, {5708, 56288}, {5734, 31788}, {5748, 10569}, {5884, 9624}, {5885, 61276}, {5888, 41454}, {5901, 13226}, {5904, 19862}, {5905, 26105}, {6173, 7671}, {6193, 58580}, {6223, 58588}, {6224, 58587}, {6225, 58579}, {6542, 58628}, {6679, 29853}, {6688, 61640}, {6703, 29648}, {6744, 57287}, {6767, 63136}, {6986, 12704}, {7226, 21342}, {7486, 58631}, {7673, 35445}, {7705, 37719}, {7951, 59419}, {7957, 15717}, {8025, 18165}, {8083, 8125}, {8126, 11033}, {8167, 27065}, {8227, 12005}, {8583, 11520}, {9004, 59373}, {9024, 17392}, {9037, 11002}, {9047, 33884}, {9049, 33879}, {9318, 37143}, {9330, 49515}, {9778, 11227}, {9807, 58614}, {9812, 10167}, {9960, 63980}, {10199, 37701}, {10283, 38032}, {10303, 63976}, {10458, 18601}, {10529, 28629}, {10578, 12915}, {10595, 34339}, {10609, 15935}, {10883, 12669}, {10914, 20057}, {11021, 35614}, {11246, 49736}, {11263, 37720}, {11269, 33129}, {11375, 13751}, {11407, 43166}, {11412, 58575}, {11415, 58573}, {11465, 58647}, {11518, 19861}, {11529, 62826}, {11681, 21620}, {11684, 31435}, {11691, 58616}, {12111, 58617}, {12329, 40916}, {12529, 12564}, {12530, 17304}, {12531, 46681}, {12586, 18911}, {12649, 58585}, {13219, 58603}, {13243, 54370}, {13464, 15016}, {13587, 59337}, {13747, 63282}, {14360, 58602}, {14439, 17754}, {14450, 58619}, {14475, 37998}, {14828, 26229}, {15066, 45728}, {15104, 58441}, {15185, 60996}, {15726, 59375}, {15733, 59374}, {15888, 25005}, {16020, 24597}, {16706, 29829}, {16825, 32919}, {16831, 62872}, {16856, 51572}, {16973, 37675}, {17016, 17054}, {17019, 17599}, {17022, 62833}, {17049, 17391}, {17056, 29680}, {17074, 34036}, {17092, 55340}, {17117, 38473}, {17123, 32912}, {17135, 19804}, {17145, 49450}, {17154, 31035}, {17155, 28516}, {17164, 58393}, {17165, 18743}, {17232, 48647}, {17241, 22279}, {17278, 33139}, {17279, 33170}, {17387, 62667}, {17394, 50362}, {17451, 63500}, {17469, 37604}, {17483, 24703}, {17495, 49470}, {17536, 41229}, {17566, 63259}, {17572, 56176}, {17596, 62849}, {17716, 29818}, {17720, 33148}, {18141, 33078}, {18191, 26860}, {18260, 63962}, {18444, 22753}, {18450, 64152}, {19860, 62837}, {19877, 34790}, {20059, 58608}, {20080, 58621}, {20081, 58622}, {20094, 58610}, {20095, 58611}, {20096, 58612}, {20195, 34784}, {20330, 37374}, {20344, 58596}, {20358, 29570}, {20683, 29581}, {20718, 27811}, {21290, 58597}, {21346, 24554}, {21454, 44447}, {21805, 49498}, {21808, 26690}, {22112, 43146}, {22294, 29822}, {24003, 49491}, {24165, 28522}, {24210, 33146}, {24216, 29639}, {24231, 33151}, {24325, 30942}, {24331, 32917}, {24391, 24564}, {24512, 26242}, {24635, 59217}, {24789, 33142}, {24929, 35271}, {24987, 51723}, {25082, 35341}, {25295, 30090}, {25413, 61278}, {25522, 41870}, {25524, 34772}, {25760, 49676}, {25815, 25817}, {25957, 29655}, {25960, 33064}, {25961, 29673}, {26103, 32937}, {26127, 58798}, {26128, 29845}, {26234, 30962}, {26724, 33137}, {26805, 63587}, {27147, 52020}, {27812, 44671}, {28011, 62804}, {28082, 37607}, {28395, 63520}, {28465, 38028}, {28611, 50625}, {28620, 35637}, {29578, 56542}, {29635, 33123}, {29642, 33119}, {29649, 32923}, {29651, 32918}, {29662, 33130}, {29665, 37634}, {29668, 32772}, {29677, 32780}, {29681, 37646}, {29685, 33174}, {29687, 33169}, {29821, 62821}, {29830, 32851}, {29837, 32774}, {29844, 33072}, {29848, 58443}, {30148, 37559}, {30274, 44675}, {30331, 63145}, {30565, 30704}, {30852, 31249}, {30967, 31317}, {30970, 40328}, {31146, 38052}, {31164, 59372}, {31179, 50533}, {31266, 62852}, {31526, 59181}, {32860, 42057}, {32925, 42055}, {33071, 63056}, {33131, 40688}, {33650, 58600}, {34186, 58598}, {34188, 58599}, {34381, 64177}, {34611, 64162}, {35004, 61277}, {36277, 60846}, {36845, 58623}, {37541, 37789}, {37624, 61541}, {37677, 63522}, {38026, 61273}, {38093, 61030}, {38205, 41556}, {38869, 47299}, {40401, 46972}, {41539, 64114}, {41611, 62973}, {41847, 57024}, {49459, 50001}, {49529, 60423}, {49688, 60459}, {51380, 62710}, {51700, 64044}, {51816, 54318}, {52254, 61013}, {52255, 60991}, {52367, 58569}, {53381, 62697}, {55857, 58632}, {58613, 64009}, {58633, 63120}, {58637, 61820}, {58675, 61876}, {58679, 64047}

X(64149) = midpoint of X(i) and X(j) for these {i,j}: {3873, 63961}
X(64149) = reflection of X(i) in X(j) for these {i,j}: {3681, 63961}, {61740, 3817}, {62835, 38314}, {63961, 2}
X(64149) = anticomplement of X(61686)
X(64149) = perspector of circumconic {{A, B, C, X(3257), X(32041)}}
X(64149) = X(i)-Dao conjugate of X(j) for these {i, j}: {4403, 4411}, {61686, 61686}
X(64149) = pole of line {2827, 42322} with respect to the incircle
X(64149) = pole of line {390, 5048} with respect to the Feuerbach hyperbola
X(64149) = pole of line {3751, 33538} with respect to the Stammler hyperbola
X(64149) = pole of line {4762, 21222} with respect to the Steiner circumellipse
X(64149) = pole of line {3960, 4762} with respect to the Steiner inellipse
X(64149) = pole of line {26227, 30758} with respect to the Wallace hyperbola
X(64149) = pole of line {908, 24635} with respect to the dual conic of Yff parabola
X(64149) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(52620)}}, {{A, B, C, X(88), X(27475)}}, {{A, B, C, X(100), X(39704)}}, {{A, B, C, X(106), X(1002)}}, {{A, B, C, X(513), X(2177)}}, {{A, B, C, X(1320), X(60668)}}, {{A, B, C, X(3681), X(57785)}}, {{A, B, C, X(3722), X(40401)}}, {{A, B, C, X(3873), X(32021)}}, {{A, B, C, X(4674), X(39954)}}, {{A, B, C, X(4792), X(6548)}}, {{A, B, C, X(4850), X(46972)}}, {{A, B, C, X(8715), X(43972)}}, {{A, B, C, X(9348), X(21806)}}, {{A, B, C, X(25439), X(60078)}}, {{A, B, C, X(34919), X(59269)}}
X(64149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1054, 2177}, {1, 244, 4850}, {1, 3306, 100}, {1, 3754, 3885}, {1, 37633, 9347}, {1, 56010, 3722}, {2, 354, 3873}, {2, 3873, 3681}, {2, 4430, 210}, {2, 4661, 3740}, {2, 518, 63961}, {2, 64151, 64153}, {8, 5045, 62854}, {10, 50190, 3889}, {11, 25557, 31019}, {11, 31019, 10129}, {37, 3999, 4392}, {55, 27003, 9352}, {55, 29817, 62862}, {63, 10582, 5284}, {65, 3622, 3890}, {142, 11025, 30628}, {142, 26015, 33108}, {200, 30350, 62815}, {210, 3848, 2}, {244, 17450, 1}, {354, 3848, 4430}, {517, 38314, 62835}, {940, 7191, 62807}, {942, 3616, 3869}, {982, 3720, 28606}, {984, 17449, 62868}, {1001, 4860, 3218}, {1125, 18398, 3868}, {1155, 42819, 61155}, {1279, 37520, 17126}, {1962, 42040, 17591}, {3361, 62829, 5303}, {3624, 3874, 3876}, {3666, 29814, 62840}, {3742, 58560, 354}, {3745, 4906, 17024}, {3752, 4883, 17018}, {3753, 5049, 3241}, {3812, 17609, 145}, {3870, 44841, 62863}, {3873, 63961, 518}, {3952, 17146, 49499}, {4038, 17017, 62801}, {4666, 35258, 38316}, {4675, 17721, 33112}, {4871, 49479, 32931}, {5045, 5439, 8}, {5211, 17300, 33070}, {5249, 11019, 11680}, {5272, 62819, 32911}, {5437, 44841, 3870}, {8227, 12005, 12528}, {9335, 17018, 3752}, {9776, 10580, 3434}, {11018, 17626, 10580}, {11518, 19861, 34195}, {16484, 18201, 4414}, {16610, 49478, 3240}, {17051, 25557, 11}, {17124, 62869, 3961}, {17125, 54352, 1757}, {17154, 31035, 49447}, {17449, 30950, 984}, {17597, 37674, 3920}, {21342, 44307, 7226}, {24165, 32915, 50106}, {25502, 62865, 756}, {28082, 37607, 62802}, {35258, 38316, 1621}, {38054, 41861, 10861}, {49498, 62711, 21805}, {51816, 54318, 54391}

X(64150) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTIPEDAL-OF-X(9) AND X(9)-CROSSPEDAL-OF-X(55)

Barycentrics    a*(a^6-2*a^5*(b+c)+4*a^3*(b-c)^2*(b+c)-2*a*(b-c)^4*(b+c)-a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(b^4-10*b^2*c^2+c^4)) : :
X(64150) = -4*X[7680]+5*X[31266], -3*X[38693]+2*X[41166]

X(64150) lies on these lines: {1, 7}, {2, 30503}, {3, 392}, {4, 19860}, {8, 1490}, {10, 6838}, {19, 37258}, {21, 12705}, {30, 61146}, {33, 24806}, {36, 64129}, {40, 78}, {56, 9943}, {63, 3428}, {64, 19611}, {65, 64077}, {72, 64156}, {84, 2975}, {104, 7171}, {165, 997}, {185, 23526}, {200, 59417}, {207, 1895}, {224, 11682}, {376, 37611}, {404, 37560}, {405, 9856}, {412, 57276}, {474, 31787}, {515, 3434}, {517, 3870}, {529, 12678}, {550, 19907}, {573, 54330}, {758, 41338}, {908, 64111}, {936, 59675}, {944, 36846}, {946, 6836}, {956, 971}, {958, 12688}, {960, 5584}, {993, 1709}, {999, 10167}, {1040, 1457}, {1064, 5256}, {1071, 22770}, {1125, 6890}, {1158, 4652}, {1319, 5918}, {1385, 37022}, {1420, 9841}, {1467, 14986}, {1519, 6827}, {1537, 37428}, {1538, 17556}, {1616, 16936}, {1621, 3576}, {1698, 6960}, {1699, 6840}, {1750, 9623}, {1766, 57015}, {1936, 54400}, {2478, 63989}, {2646, 64074}, {2739, 14733}, {2950, 4996}, {3149, 31788}, {3304, 58567}, {3306, 22753}, {3340, 10393}, {3359, 6905}, {3421, 5658}, {3436, 6260}, {3523, 8583}, {3555, 8158}, {3579, 45770}, {3612, 51717}, {3616, 8726}, {3624, 6972}, {3753, 19541}, {3811, 7991}, {3877, 7411}, {3878, 12511}, {3951, 5693}, {3984, 63976}, {4188, 10270}, {4229, 18465}, {4511, 6282}, {4512, 37106}, {4666, 5603}, {4853, 63981}, {4855, 10310}, {4861, 12650}, {5082, 64144}, {5178, 5881}, {5204, 64128}, {5251, 54370}, {5253, 37526}, {5287, 23512}, {5289, 11495}, {5440, 6244}, {5493, 22836}, {5534, 12245}, {5587, 6932}, {5657, 5720}, {5687, 31798}, {5691, 37437}, {5709, 64021}, {5730, 31793}, {5768, 26015}, {5787, 24390}, {5840, 12700}, {5884, 12704}, {5886, 37374}, {5887, 35239}, {5927, 9708}, {6245, 10527}, {6361, 21740}, {6684, 6962}, {6735, 64148}, {6766, 41863}, {6769, 20070}, {6837, 21628}, {6847, 24541}, {6848, 24982}, {6865, 41012}, {6908, 24987}, {6912, 11372}, {6943, 8227}, {6953, 8582}, {6964, 25011}, {6966, 10165}, {6985, 37562}, {6986, 31435}, {6992, 40998}, {7680, 31266}, {7957, 12635}, {7964, 31165}, {7966, 7982}, {7992, 62824}, {7993, 16143}, {7994, 34632}, {7995, 31424}, {8270, 45272}, {8273, 58679}, {8666, 10085}, {9799, 64081}, {9800, 37434}, {9960, 12529}, {10058, 37618}, {10306, 33597}, {10461, 12548}, {10571, 54295}, {10680, 13369}, {10857, 54445}, {11220, 54391}, {11249, 63399}, {11362, 17857}, {11415, 54198}, {11491, 49163}, {11496, 62829}, {11500, 63130}, {11681, 63966}, {11827, 64119}, {12053, 34489}, {12114, 63984}, {12120, 54228}, {12512, 30144}, {12513, 12680}, {12514, 59320}, {12527, 54227}, {12528, 57279}, {12617, 19854}, {12675, 62832}, {12679, 57288}, {12702, 37700}, {12711, 62836}, {12740, 38759}, {12775, 37403}, {13734, 31394}, {14647, 59491}, {14872, 63135}, {14988, 37584}, {15071, 62858}, {15829, 37551}, {15852, 37614}, {16821, 48878}, {17784, 54051}, {18528, 59388}, {18529, 54448}, {21147, 61227}, {22791, 37615}, {24564, 37407}, {24928, 31805}, {25681, 50031}, {25930, 36698}, {26921, 40266}, {28164, 41860}, {28174, 37533}, {28194, 37569}, {28291, 43363}, {30147, 51118}, {31730, 40257}, {31786, 37426}, {31799, 58798}, {31803, 41229}, {34526, 41325}, {34611, 50811}, {34618, 34647}, {35445, 59421}, {37305, 55472}, {37380, 55478}, {37419, 64082}, {37422, 54356}, {38693, 41166}, {44425, 54286}, {44447, 63438}, {48697, 51433}, {51361, 60689}, {51616, 57477}, {54156, 56288}, {61148, 62155}, {63962, 64002}

X(64150) = reflection of X(i) in X(j) for these {i,j}: {63, 3428}, {1709, 993}, {3870, 18446}, {4302, 4297}, {44447, 63438}
X(64150) = pole of line {9001, 44408} with respect to the circumcircle
X(64150) = pole of line {44432, 46399} with respect to the orthoptic circle of the Steiner Inellipse
X(64150) = pole of line {2328, 4221} with respect to the Stammler hyperbola
X(64150) = pole of line {3732, 24029} with respect to the Yff parabola
X(64150) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(64), X(4320)}}, {{A, B, C, X(102), X(269)}}, {{A, B, C, X(279), X(36100)}}, {{A, B, C, X(1323), X(2739)}}, {{A, B, C, X(5731), X(56098)}}
X(64150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1044, 4320}, {1, 12520, 10884}, {1, 12565, 20}, {1, 5732, 5731}, {3, 12672, 5250}, {3, 63986, 19861}, {40, 52026, 100}, {40, 6261, 78}, {40, 7971, 3869}, {516, 4297, 4302}, {517, 18446, 3870}, {962, 5731, 390}, {1071, 22770, 62874}, {1319, 5918, 63991}, {1750, 9623, 59387}, {2975, 9961, 84}, {3428, 6001, 63}, {3576, 10860, 6909}, {3878, 12511, 59340}, {4511, 9778, 6282}, {5603, 18443, 4666}, {5887, 35239, 55104}, {6361, 21740, 37531}, {10310, 37837, 4855}, {11220, 54391, 63430}, {11682, 63141, 14110}, {20070, 34772, 6769}, {30503, 63992, 2}, {31730, 40257, 63391}

X(64151) = CENTROID OF X(9)-CROSSPEDAL-OF-X(57)

Barycentrics    a^3+3*a^2*(b+c)+(b-c)^2*(b+c)+a*(-5*b^2+6*b*c-5*c^2) : :
X(64151) = -2*X[200]+5*X[62773], 2*X[497]+X[9965], -4*X[1376]+X[20015], -7*X[3622]+4*X[5289], -X[20214]+4*X[24703], -2*X[21060]+5*X[31249]

X(64151) lies on these lines: {1, 5744}, {2, 210}, {7, 24389}, {8, 3306}, {20, 12704}, {46, 56936}, {56, 100}, {57, 5853}, {63, 10580}, {69, 26240}, {144, 62235}, {193, 5211}, {200, 62773}, {279, 20247}, {329, 5850}, {346, 2260}, {387, 3953}, {390, 3218}, {391, 54385}, {442, 3296}, {452, 62858}, {497, 9965}, {516, 2094}, {519, 64112}, {553, 24392}, {658, 6604}, {938, 62874}, {942, 64081}, {1219, 17751}, {1376, 20015}, {1482, 13226}, {1732, 62706}, {1788, 34791}, {2191, 7292}, {2550, 4860}, {2646, 3623}, {2800, 11240}, {3006, 4869}, {3085, 3881}, {3086, 3874}, {3189, 32636}, {3241, 3576}, {3243, 3911}, {3315, 24597}, {3338, 6904}, {3434, 21454}, {3555, 7080}, {3600, 12649}, {3616, 11520}, {3622, 5289}, {3660, 8732}, {3672, 4392}, {3751, 24216}, {3756, 63126}, {3868, 14986}, {3870, 5435}, {3889, 16193}, {3894, 10072}, {3928, 64162}, {3957, 5281}, {3999, 4000}, {4253, 35341}, {4295, 49627}, {4298, 5175}, {4308, 41575}, {4310, 11269}, {4346, 33134}, {4373, 4442}, {4402, 50758}, {4427, 4779}, {4644, 17721}, {4654, 24386}, {4666, 5273}, {4847, 9776}, {5057, 20059}, {5082, 5708}, {5083, 54366}, {5126, 36867}, {5177, 10916}, {5178, 56999}, {5218, 42871}, {5220, 17051}, {5221, 64068}, {5231, 5542}, {5247, 28080}, {5253, 20007}, {5265, 34772}, {5274, 5905}, {5437, 46916}, {5536, 43161}, {5603, 24473}, {5703, 62861}, {5745, 44841}, {5791, 50191}, {5851, 10707}, {5856, 12848}, {5902, 34625}, {5919, 34744}, {6067, 33108}, {6734, 11037}, {6744, 62824}, {6765, 26062}, {6887, 58561}, {7191, 37666}, {7613, 33136}, {7674, 60948}, {8166, 13257}, {8236, 35258}, {9779, 31164}, {9797, 63130}, {10527, 11036}, {10569, 64171}, {10578, 59491}, {10582, 38059}, {10584, 46873}, {10587, 18231}, {11106, 62827}, {12526, 21625}, {12635, 24558}, {12675, 37421}, {13373, 37407}, {17162, 24435}, {17375, 60446}, {17597, 37642}, {17726, 63054}, {18398, 19843}, {19855, 58565}, {19993, 37538}, {20075, 23958}, {20214, 24703}, {21060, 31249}, {22769, 35988}, {24953, 46934}, {26241, 37683}, {27334, 35892}, {27383, 41863}, {27549, 30947}, {28016, 54386}, {28512, 29844}, {28808, 49499}, {29616, 33089}, {29817, 55868}, {29840, 63057}, {30275, 41555}, {30340, 31019}, {33070, 62999}, {33142, 62208}, {34753, 59591}, {34879, 61157}, {37633, 39587}, {40127, 51194}, {40270, 54290}, {41711, 59572}, {62814, 63078}, {62819, 63007}, {64046, 64047}

X(64151) = pole of line {390, 62835} with respect to the Feuerbach hyperbola
X(64151) = pole of line {4762, 30181} with respect to the Steiner circumellipse
X(64151) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1002), X(8686)}}, {{A, B, C, X(1120), X(60668)}}
X(64151) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 36845, 17784}, {145, 64142, 100}, {3189, 32636, 37267}, {3243, 3911, 63168}, {3756, 64070, 63126}, {4847, 10980, 9776}, {4860, 51463, 2550}, {5437, 59414, 46916}, {11019, 62823, 329}, {11269, 17449, 4310}, {17728, 25568, 2}, {37684, 58371, 145}, {59491, 62815, 10578}

X(64152) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(57) AND X(9)-CROSSPEDAL-OF-X(63)

Barycentrics    a*(a^5-2*a^4*(b+c)+2*a^2*(b-c)^2*(b+c)+4*b*(b-c)^2*c*(b+c)-a*(b^2-c^2)^2) : :

X(64152) lies on circumconic {{A, B, C, X(36123), X(56144)}} and on these lines: {1, 37411}, {3, 5219}, {4, 11}, {6, 2635}, {7, 36002}, {9, 1155}, {12, 5584}, {33, 1427}, {36, 6913}, {40, 17634}, {46, 5777}, {55, 226}, {57, 971}, {65, 1490}, {72, 3711}, {79, 11507}, {198, 851}, {218, 45885}, {225, 1035}, {241, 9817}, {243, 342}, {329, 1376}, {354, 4321}, {388, 37421}, {404, 5328}, {405, 5204}, {442, 10895}, {452, 25524}, {474, 5316}, {480, 61010}, {497, 50696}, {513, 61238}, {535, 17532}, {750, 3000}, {908, 1004}, {950, 3304}, {958, 5177}, {990, 1465}, {999, 3586}, {1001, 1005}, {1012, 17010}, {1254, 1854}, {1260, 28609}, {1402, 10888}, {1454, 12664}, {1466, 3149}, {1478, 3428}, {1482, 37736}, {1617, 1699}, {1696, 8804}, {1708, 5927}, {1721, 9371}, {1728, 37582}, {1745, 5706}, {1754, 34048}, {1758, 64134}, {1770, 5812}, {1776, 16112}, {1781, 15831}, {1837, 63998}, {1857, 40837}, {1936, 6180}, {2099, 18446}, {2263, 51361}, {2771, 18397}, {2802, 41701}, {2900, 41711}, {3011, 21002}, {3146, 57283}, {3303, 3487}, {3306, 8544}, {3452, 37270}, {3543, 62873}, {3585, 59317}, {3651, 5217}, {3668, 16870}, {3772, 37385}, {3911, 63970}, {3947, 12511}, {4295, 11500}, {4299, 31789}, {4312, 37541}, {4331, 38357}, {4342, 63274}, {4423, 13615}, {4860, 5728}, {5128, 9709}, {5175, 12513}, {5218, 8232}, {5221, 44547}, {5226, 7411}, {5348, 34032}, {5433, 6846}, {5436, 37605}, {5531, 5903}, {5658, 11246}, {5703, 33557}, {5708, 10399}, {5715, 37579}, {5732, 17603}, {5748, 35977}, {5758, 11501}, {5805, 64115}, {5806, 34489}, {5851, 12848}, {5856, 12831}, {6838, 15844}, {6911, 37822}, {6918, 15803}, {6937, 9656}, {6985, 57282}, {6987, 15326}, {7308, 37271}, {7367, 13609}, {7677, 9779}, {7989, 59323}, {8158, 37709}, {8273, 11375}, {8581, 54408}, {9613, 22770}, {9654, 35239}, {9655, 11249}, {9657, 10966}, {10123, 11517}, {10396, 32636}, {10483, 22766}, {10883, 37797}, {10950, 64144}, {11269, 51424}, {11376, 51773}, {12688, 37550}, {13411, 37426}, {15239, 63992}, {15447, 15972}, {16118, 59334}, {16411, 20196}, {18450, 64149}, {18518, 50193}, {18541, 62359}, {20835, 31266}, {21677, 45039}, {22053, 37674}, {24320, 47522}, {24928, 31822}, {30295, 60995}, {30326, 53056}, {30852, 37309}, {33925, 52835}, {36482, 37581}, {37229, 64002}, {37377, 42379}, {37530, 64057}, {37537, 37694}, {50195, 50528}, {54430, 63756}, {59389, 61649}

X(64152) = pole of line {47123, 53522} with respect to the incircle
X(64152) = pole of line {5728, 6001} with respect to the Feuerbach hyperbola
X(64152) = pole of line {5228, 34050} with respect to the dual conic of Yff parabola
X(64152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 54366, 11}, {9, 37240, 4413}, {57, 1750, 1864}, {108, 46009, 56}, {226, 7580, 55}, {329, 35990, 1376}, {3149, 4292, 1466}, {4312, 44425, 37541}, {13615, 25525, 4423}

X(64153) = ANTICOMPLEMENT OF X(17718)

Barycentrics    a^3+a^2*(b+c)+(b-c)^2*(b+c)-3*a*(b^2+c^2) : :
X(64153) = -2*X[55]+5*X[55868], -4*X[495]+7*X[9780], 2*X[1836]+X[20078], X[3621]+2*X[37740], -X[3870]+4*X[5745], 2*X[4640]+X[4863], -11*X[5550]+8*X[5719], -4*X[6690]+X[41711], -X[10679]+4*X[61539], -X[12647]+4*X[54288], -4*X[13405]+7*X[55867], -X[20050]+4*X[37728]

X(64153) lies on these lines: {1, 24597}, {2, 210}, {3, 8}, {6, 17726}, {7, 15346}, {9, 26015}, {10, 3306}, {11, 5220}, {20, 5178}, {38, 19785}, {44, 17721}, {55, 55868}, {57, 25006}, {63, 516}, {69, 3006}, {72, 5886}, {78, 10165}, {144, 5057}, {145, 37080}, {149, 5698}, {193, 33070}, {200, 59491}, {329, 5817}, {333, 4228}, {344, 29824}, {345, 17135}, {348, 35312}, {355, 64079}, {377, 62858}, {390, 62838}, {392, 11240}, {495, 9780}, {497, 3219}, {499, 3678}, {517, 61662}, {519, 59337}, {553, 61031}, {583, 2345}, {584, 5839}, {611, 32911}, {612, 63078}, {631, 4420}, {658, 33298}, {908, 5223}, {938, 5260}, {946, 3951}, {954, 5284}, {958, 12649}, {960, 10529}, {962, 11684}, {984, 11269}, {1001, 51463}, {1104, 36579}, {1125, 3984}, {1260, 38031}, {1386, 63067}, {1482, 16617}, {1621, 5273}, {1699, 17781}, {1757, 29676}, {1788, 3600}, {1836, 20078}, {2094, 59412}, {2478, 10916}, {2550, 3218}, {2646, 20013}, {2886, 5852}, {3011, 16496}, {3035, 3711}, {3086, 3876}, {3189, 4189}, {3241, 15670}, {3242, 26228}, {3303, 18253}, {3305, 11019}, {3315, 16020}, {3416, 31091}, {3419, 28160}, {3421, 6854}, {3436, 5587}, {3452, 10584}, {3474, 33110}, {3555, 5791}, {3564, 3578}, {3620, 48647}, {3621, 37740}, {3626, 4311}, {3640, 55877}, {3641, 55876}, {3647, 4309}, {3650, 48661}, {3660, 40659}, {3677, 26723}, {3679, 64112}, {3690, 35645}, {3705, 5739}, {3712, 49460}, {3715, 3816}, {3741, 33163}, {3751, 29639}, {3769, 20020}, {3811, 6910}, {3826, 4860}, {3868, 19843}, {3869, 6837}, {3870, 5745}, {3872, 6974}, {3874, 19854}, {3875, 50758}, {3877, 34625}, {3886, 3977}, {3911, 24393}, {3920, 37642}, {3927, 11415}, {3929, 24392}, {3935, 5218}, {3936, 30741}, {3952, 28808}, {3999, 17278}, {4000, 4392}, {4005, 25681}, {4126, 53673}, {4307, 62795}, {4310, 33129}, {4339, 16948}, {4358, 27549}, {4383, 12594}, {4419, 33134}, {4423, 42885}, {4427, 21283}, {4438, 33171}, {4511, 6878}, {4640, 4863}, {4644, 33112}, {4652, 63146}, {4662, 24914}, {4663, 17723}, {4679, 15481}, {4855, 6743}, {4865, 28498}, {4884, 28472}, {4915, 51433}, {5014, 63140}, {5015, 54429}, {5082, 56288}, {5086, 50695}, {5211, 17349}, {5221, 9710}, {5227, 61668}, {5235, 39581}, {5249, 5785}, {5258, 49168}, {5281, 20015}, {5288, 36977}, {5325, 64162}, {5328, 31272}, {5361, 33090}, {5372, 33091}, {5550, 5719}, {5552, 11231}, {5557, 41862}, {5660, 46685}, {5692, 16173}, {5705, 10585}, {5712, 29664}, {5718, 64070}, {5730, 10283}, {5762, 9812}, {5794, 20076}, {5815, 11681}, {5818, 56880}, {5832, 9965}, {5837, 36846}, {5848, 17346}, {5850, 31164}, {5851, 42014}, {5853, 35258}, {5856, 6172}, {5857, 28610}, {5904, 26363}, {6601, 55960}, {6690, 41711}, {6762, 24987}, {6765, 38399}, {6838, 14872}, {6886, 13374}, {6890, 63976}, {6933, 21077}, {6953, 58631}, {6962, 17857}, {6967, 58630}, {7226, 33142}, {7292, 37650}, {7465, 22769}, {7957, 14923}, {7964, 17784}, {8229, 39898}, {9342, 62773}, {9347, 39587}, {9778, 49719}, {10057, 38213}, {10072, 10176}, {10164, 64135}, {10172, 21075}, {10327, 14829}, {10453, 17776}, {10528, 26066}, {10586, 25917}, {10587, 34791}, {10589, 27131}, {10679, 61539}, {10785, 31837}, {11200, 24635}, {11246, 61032}, {11523, 24541}, {11679, 63147}, {12116, 26921}, {12329, 37449}, {12513, 21677}, {12588, 37653}, {12647, 54288}, {12675, 37112}, {12702, 64200}, {13243, 63971}, {13405, 55867}, {14268, 37206}, {14552, 33075}, {14555, 26265}, {14647, 59417}, {15296, 26105}, {16439, 32862}, {16552, 35341}, {16704, 29832}, {17134, 42696}, {17145, 29830}, {17155, 19819}, {17163, 53043}, {17242, 38473}, {17321, 29829}, {17343, 24752}, {17558, 62870}, {17575, 51572}, {17717, 49712}, {17719, 49503}, {17720, 49515}, {17724, 31187}, {17768, 31140}, {17772, 32853}, {17860, 20879}, {19822, 31330}, {19860, 24391}, {20050, 37728}, {20103, 31224}, {20693, 31497}, {21060, 30852}, {21242, 32935}, {21342, 24789}, {24239, 63090}, {24248, 33136}, {24389, 60949}, {24552, 26065}, {24695, 33104}, {24892, 33144}, {26034, 29673}, {26040, 27003}, {26098, 29690}, {26258, 37658}, {29010, 50043}, {29640, 49498}, {29680, 63089}, {29828, 49529}, {29840, 37652}, {29857, 49511}, {30393, 31249}, {30478, 34772}, {30608, 49714}, {31136, 33161}, {31157, 56177}, {31231, 62218}, {31302, 37759}, {32087, 50144}, {32851, 49450}, {32917, 36479}, {33071, 63009}, {33078, 37655}, {33120, 50295}, {33138, 62865}, {33140, 49448}, {33156, 50316}, {35263, 56523}, {36277, 63969}, {36922, 61285}, {37032, 56945}, {37660, 49524}, {37666, 62807}, {38176, 64087}, {40940, 62833}, {41573, 60958}, {43174, 63142}, {46904, 50282}, {46917, 59414}, {47824, 52620}, {49451, 59779}, {49455, 50755}, {49467, 59769}, {49505, 50752}, {52255, 61010}, {52806, 55398}, {52809, 55397}, {53014, 62799}, {53337, 54280}, {57287, 62824}, {60446, 62989}, {60731, 63003}, {61414, 62482}, {62236, 63168}, {62796, 64168}

X(64153) = reflection of X(i) in X(j) for these {i,j}: {5905, 61716}, {10057, 38213}, {61716, 2886}
X(64153) = anticomplement of X(17718)
X(64153) = perspector of circumconic {{A, B, C, X(13136), X(32041)}}
X(64153) = X(i)-Dao conjugate of X(j) for these {i, j}: {17718, 17718}
X(64153) = pole of line {3309, 48182} with respect to the orthoptic circle of the Steiner Inellipse
X(64153) = pole of line {859, 22769} with respect to the Stammler hyperbola
X(64153) = pole of line {3904, 4762} with respect to the Steiner circumellipse
X(64153) = pole of line {51357, 62669} with respect to the Yff parabola
X(64153) = pole of line {7474, 17139} with respect to the Wallace hyperbola
X(64153) = centroid of X(9)-crosspedal-of-X(63)
X(64153) = intersection, other than A, B, C, of circumconics {{A, B, C, X(104), X(1002)}}, {{A, B, C, X(27475), X(34234)}}, {{A, B, C, X(51565), X(60668)}}
X(64153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4430, 3475}, {2, 4661, 25568}, {2, 5686, 63961}, {2, 64151, 64149}, {8, 5744, 100}, {10, 3338, 37462}, {10, 63135, 56879}, {11, 5220, 31018}, {38, 33137, 19785}, {63, 3434, 44447}, {63, 4847, 3434}, {2886, 5852, 61716}, {3242, 35466, 26228}, {3751, 29639, 63008}, {3927, 24390, 11415}, {4392, 33139, 4000}, {4640, 4863, 20075}, {5178, 62827, 20}, {5223, 5231, 908}, {5273, 36845, 1621}, {5852, 61716, 5905}, {6734, 57279, 3436}, {10916, 41229, 2478}, {16704, 29832, 51192}, {29690, 32912, 26098}, {33108, 62235, 7}, {33114, 46909, 2}, {33129, 62868, 4310}, {33136, 36263, 24248}, {54398, 64081, 3869}

X(64154) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-INNER-GARCIA AND X(9)-CROSSPEDAL-OF-X(100)

Barycentrics    a*(a^5+a^3*b*c-2*a^4*(b+c)-b*(b-c)^2*c*(b+c)+a^2*(2*b^3+b^2*c+b*c^2+2*c^3)-a*(b^4-b^3*c+4*b^2*c^2-b*c^3+c^4)) : :
X(64154) = -X[80]+4*X[6666], X[144]+2*X[25558], -3*X[4881]+X[18450], X[6224]+5*X[18230], X[6265]+2*X[31658], X[7972]+2*X[24393], X[12119]+2*X[63970], X[12730]+5*X[64141], X[12751]+2*X[43175], -5*X[20195]+8*X[58453], -3*X[38093]+2*X[38207]

X(64154) lies on these lines: {1, 3939}, {2, 11}, {3, 1633}, {7, 1470}, {8, 42842}, {9, 48}, {10, 34486}, {21, 662}, {36, 527}, {56, 6068}, {59, 518}, {80, 6666}, {119, 6827}, {142, 10090}, {144, 25558}, {145, 42886}, {153, 6992}, {200, 41553}, {210, 41701}, {238, 1818}, {294, 5701}, {329, 12831}, {404, 5880}, {405, 4305}, {411, 25681}, {480, 1317}, {499, 10093}, {516, 1519}, {758, 60989}, {900, 53287}, {943, 1125}, {952, 6883}, {954, 5856}, {956, 50843}, {958, 38669}, {960, 6986}, {971, 48697}, {999, 51099}, {1005, 4679}, {1145, 6600}, {1259, 7288}, {1260, 24477}, {1320, 2346}, {1387, 50204}, {1445, 64139}, {1458, 23693}, {1610, 13732}, {1617, 25568}, {1708, 5083}, {1737, 5853}, {1768, 10857}, {1769, 14414}, {1836, 35977}, {1890, 4231}, {2078, 6745}, {2361, 63068}, {2551, 37725}, {2800, 21153}, {2802, 31393}, {2829, 6987}, {2834, 51419}, {2975, 5220}, {3059, 41541}, {3086, 11517}, {3185, 19649}, {3243, 45391}, {3303, 13996}, {3428, 25606}, {3452, 5660}, {3474, 37309}, {3485, 37282}, {3486, 25875}, {3616, 13279}, {3646, 5248}, {3651, 21616}, {3685, 37788}, {3742, 62800}, {3746, 63990}, {3871, 37828}, {3911, 58328}, {4432, 24410}, {4512, 41166}, {4557, 53302}, {4881, 18450}, {4915, 51767}, {5010, 50836}, {5044, 12738}, {5047, 5794}, {5057, 36003}, {5087, 36002}, {5172, 61035}, {5223, 10074}, {5251, 60986}, {5253, 25557}, {5259, 57284}, {5440, 15733}, {5450, 64197}, {5531, 30393}, {5572, 45395}, {5732, 48695}, {5745, 11219}, {5766, 26357}, {5779, 18515}, {5840, 6826}, {5851, 37106}, {6224, 18230}, {6265, 31658}, {6700, 10902}, {6829, 59391}, {6830, 64008}, {6839, 10724}, {6854, 13199}, {6858, 23513}, {6859, 58421}, {6879, 38149}, {6880, 35514}, {6881, 10738}, {6882, 18524}, {6906, 54370}, {6909, 15726}, {6911, 33814}, {6913, 38159}, {6920, 17647}, {6924, 52682}, {6940, 64113}, {6946, 7704}, {6954, 38760}, {6963, 11491}, {6970, 11248}, {6978, 11499}, {7080, 11510}, {7280, 60905}, {7411, 24703}, {7688, 50908}, {7972, 24393}, {8236, 13278}, {8545, 35262}, {8583, 54430}, {8932, 22390}, {9024, 38048}, {9709, 51525}, {10058, 15015}, {10177, 24929}, {10269, 60940}, {10394, 15297}, {10742, 28459}, {10965, 63133}, {10966, 24558}, {11019, 59614}, {11038, 42885}, {11108, 12019}, {11500, 20400}, {11507, 17567}, {11508, 59591}, {11570, 60974}, {12047, 58461}, {12119, 63970}, {12532, 61024}, {12703, 64136}, {12730, 64141}, {12740, 15837}, {12751, 43175}, {12755, 39778}, {12776, 30144}, {12832, 62775}, {13243, 62777}, {13272, 25466}, {13587, 28534}, {14740, 37736}, {15325, 41555}, {15804, 24465}, {16370, 51636}, {16410, 28629}, {16857, 38102}, {17100, 52653}, {17566, 30312}, {17579, 30311}, {17605, 35990}, {17768, 27086}, {18461, 60419}, {18861, 21151}, {19843, 37726}, {20195, 58453}, {20418, 30478}, {21161, 51090}, {21362, 53298}, {24434, 33761}, {24466, 50701}, {25438, 30331}, {25439, 50841}, {26129, 30332}, {26481, 27529}, {27383, 37579}, {28466, 38602}, {28922, 36741}, {28930, 32932}, {30284, 61012}, {30556, 60886}, {33925, 63168}, {34789, 41853}, {34919, 55966}, {35338, 64013}, {35892, 45394}, {37403, 43178}, {37561, 43177}, {37621, 47742}, {38093, 38207}, {40269, 61026}, {45036, 63983}, {47387, 57278}, {53741, 58037}, {54445, 60997}, {55871, 62815}, {56177, 62873}

X(64154) = midpoint of X(i) and X(j) for these {i,j}: {36, 60885}, {4511, 37787}, {4915, 51767}, {18450, 60935}
X(64154) = reflection of X(i) in X(j) for these {i,j}: {38053, 34123}, {41555, 15325}, {64155, 142}
X(64154) = complement of X(45043)
X(64154) = perspector of circumconic {{A, B, C, X(666), X(31615)}}
X(64154) = pole of line {659, 6366} with respect to the circumcircle
X(64154) = pole of line {518, 1776} with respect to the Feuerbach hyperbola
X(64154) = pole of line {1155, 3286} with respect to the Stammler hyperbola
X(64154) = pole of line {918, 43991} with respect to the Steiner circumellipse
X(64154) = pole of line {918, 43050} with respect to the Steiner inellipse
X(64154) = pole of line {53337, 61239} with respect to the Yff parabola
X(64154) = pole of line {1252, 2284} with respect to the Hutson-Moses hyperbola
X(64154) = pole of line {30806, 30941} with respect to the Wallace hyperbola
X(64154) = pole of line {2323, 3008} with respect to the dual conic of Yff parabola
X(64154) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {100, 934, 53055}, {4915, 51767, 51811}
X(64154) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(56850)}}, {{A, B, C, X(2), X(36819)}}, {{A, B, C, X(7), X(52456)}}, {{A, B, C, X(11), X(518)}}, {{A, B, C, X(59), X(105)}}, {{A, B, C, X(104), X(673)}}, {{A, B, C, X(765), X(14942)}}, {{A, B, C, X(1156), X(13576)}}, {{A, B, C, X(2550), X(14947)}}, {{A, B, C, X(4998), X(60782)}}, {{A, B, C, X(6065), X(28071)}}, {{A, B, C, X(6174), X(43946)}}, {{A, B, C, X(34068), X(56853)}}, {{A, B, C, X(34591), X(51379)}}
X(64154) = barycentric product X(i)*X(j) for these (i, j): {100, 62306}
X(64154) = barycentric quotient X(i)/X(j) for these (i, j): {62306, 693}
X(64154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15507, 1633}, {36, 60885, 527}, {55, 25893, 26105}, {55, 6174, 100}, {100, 5284, 10707}, {214, 51506, 104}, {404, 8543, 5880}, {954, 37249, 60987}, {4511, 37787, 518}, {4679, 34879, 1005}, {4881, 60935, 18450}, {5856, 34123, 38053}, {15254, 59691, 5784}, {24036, 28345, 9}, {24646, 24647, 2550}, {35204, 64012, 10090}, {39778, 60970, 12755}

X(64155) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-YFF AND X(9)-CROSSPEDAL-OF-X(100)

Barycentrics    a^6-a^5*(b+c)-(b-c)^4*(b+c)^2-a^4*(b^2-3*b*c+c^2)+a^2*(b-c)^2*(b^2-b*c+c^2)+a*(b^5-b^4*c-b*c^4+c^5) : :
X(64155) = 2*X[7]+X[80], -X[144]+4*X[6702], -2*X[214]+5*X[62778], -5*X[1698]+2*X[6068], 2*X[6246]+X[36996], -X[6265]+4*X[61509], 2*X[6797]+X[8581], -X[10031]+4*X[51098], X[10724]+2*X[43182], -X[12119]+4*X[31657]

X(64155) lies on these lines: {1, 528}, {2, 38207}, {7, 80}, {9, 6506}, {11, 57}, {35, 63254}, {36, 516}, {46, 5735}, {56, 52682}, {79, 1156}, {100, 5249}, {104, 15909}, {119, 60937}, {142, 10090}, {144, 6702}, {149, 10580}, {214, 62778}, {226, 5660}, {390, 37525}, {481, 60886}, {484, 38454}, {498, 6594}, {499, 5698}, {515, 60993}, {518, 10057}, {527, 1737}, {942, 38543}, {952, 11529}, {971, 13273}, {1001, 14793}, {1387, 3576}, {1462, 50307}, {1479, 11023}, {1698, 6068}, {1736, 32857}, {1749, 14527}, {1781, 5829}, {1838, 32714}, {2095, 54133}, {2550, 12647}, {2792, 24618}, {2800, 59386}, {2802, 59412}, {3035, 25525}, {3062, 46435}, {3086, 45035}, {3256, 11218}, {3333, 37726}, {3338, 10042}, {3361, 20418}, {3474, 41166}, {3475, 41553}, {3582, 28534}, {3583, 15726}, {3675, 24836}, {3679, 38202}, {3812, 13272}, {3814, 60935}, {4298, 38669}, {4654, 12831}, {4679, 59376}, {5057, 59377}, {5220, 18395}, {5223, 38211}, {5290, 37725}, {5425, 5542}, {5443, 8543}, {5445, 30312}, {5535, 5762}, {5541, 10059}, {5570, 15733}, {5586, 12019}, {5692, 52457}, {5697, 60926}, {5708, 45630}, {5728, 10073}, {5784, 47033}, {5832, 5856}, {5840, 18443}, {5850, 59415}, {5851, 9814}, {5853, 41702}, {5886, 38173}, {5903, 10043}, {6147, 12738}, {6172, 38216}, {6246, 36996}, {6265, 61509}, {6797, 8581}, {6835, 30290}, {7676, 14799}, {7702, 9581}, {7741, 54370}, {7951, 8545}, {8544, 10483}, {10031, 51098}, {10044, 12750}, {10074, 12573}, {10202, 10738}, {10265, 52819}, {10394, 37702}, {10404, 62616}, {10572, 43177}, {10590, 60998}, {10707, 11019}, {10724, 43182}, {10773, 11028}, {10826, 64197}, {10980, 41556}, {11045, 50190}, {11495, 63281}, {12119, 31657}, {12609, 48713}, {12619, 41712}, {12740, 20330}, {12764, 18482}, {13271, 58611}, {13274, 63972}, {15251, 53529}, {15254, 16153}, {15558, 35514}, {16155, 59319}, {16159, 34753}, {16475, 38188}, {17059, 24410}, {17606, 64198}, {18397, 61011}, {18450, 36975}, {18483, 47744}, {19077, 60913}, {19078, 60914}, {21168, 38133}, {21620, 38665}, {24644, 38038}, {24703, 45310}, {25055, 38095}, {25558, 61020}, {26726, 64203}, {26842, 62852}, {30274, 41861}, {30318, 37707}, {31231, 38131}, {31272, 51090}, {31397, 51100}, {32557, 52653}, {34474, 38123}, {36279, 36971}, {37582, 49177}, {37606, 38065}, {37611, 64138}, {37701, 38209}, {37826, 61007}, {38060, 50836}, {38150, 39692}, {38172, 38752}, {38182, 51516}, {39542, 50908}, {41694, 63970}, {43180, 64163}, {44425, 64115}, {52769, 60988}, {59323, 64003}, {60718, 64013}, {60919, 63270}

X(64155) = midpoint of X(i) and X(j) for these {i,j}: {7, 45043}, {4312, 51768}, {14151, 20119}
X(64155) = reflection of X(i) in X(j) for these {i,j}: {1, 38055}, {2, 38207}, {36, 30379}, {80, 45043}, {1699, 38152}, {3576, 38124}, {3679, 38202}, {5223, 38211}, {5886, 38173}, {6172, 38216}, {7972, 14151}, {14151, 5542}, {15228, 30295}, {16475, 38188}, {21168, 38133}, {24644, 38038}, {25055, 38095}, {34474, 38123}, {36975, 18450}, {37701, 38209}, {38752, 38172}, {41700, 1737}, {50836, 38060}, {51516, 38182}, {51768, 11}, {52653, 32557}, {60935, 3814}, {64154, 142}
X(64155) = inverse of X(34789) in Feuerbach hyperbola
X(64155) = pole of line {676, 2826} with respect to the incircle
X(64155) = pole of line {971, 13274} with respect to the Feuerbach hyperbola
X(64155) = pole of line {36038, 48571} with respect to the Steiner circumellipse
X(64155) = pole of line {2254, 2826} with respect to the Suppa-Cucoanes circle
X(64155) = pole of line {527, 651} with respect to the dual conic of Yff parabola
X(64155) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 1358, 55370}
X(64155) = intersection, other than A, B, C, of circumconics {{A, B, C, X(36), X(59813)}}, {{A, B, C, X(79), X(38543)}}, {{A, B, C, X(80), X(42064)}}, {{A, B, C, X(3254), X(18815)}}
X(64155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 45043, 2801}, {11, 24465, 1768}, {11, 57, 11219}, {226, 60782, 5660}, {516, 30295, 15228}, {516, 30379, 36}, {527, 1737, 41700}, {528, 38055, 1}, {2801, 45043, 80}, {5542, 20119, 7972}, {30312, 60912, 5445}, {39144, 39145, 34789}

X(64156) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTIPEDAL-OF-X(9) AND X(9)-CROSSPEDAL-OF-X(142)

Barycentrics    a^2*(a^7-3*a^6*(b+c)-a^2*(b-c)^2*(b+c)^3+a^5*(b^2+4*b*c+c^2)+a*(b^2-c^2)^2*(3*b^2+4*b*c+3*c^2)+5*a^4*(b^3+b^2*c+b*c^2+c^3)-a^3*(5*b^4+8*b^3*c-2*b^2*c^2+8*b*c^3+5*c^4)-(b-c)^2*(b^5+3*b^4*c+12*b^3*c^2+12*b^2*c^3+3*b*c^4+c^5)) : :
X(64156) = -X[9799]+5*X[18230], -X[9948]+3*X[38130], -X[12650]+3*X[38316], -3*X[38150]+5*X[63966]

X(64156) lies on these lines: {3, 9}, {4, 390}, {7, 3149}, {35, 3062}, {40, 480}, {55, 1750}, {56, 10398}, {72, 64150}, {100, 329}, {104, 5825}, {142, 6918}, {144, 411}, {223, 38288}, {226, 5805}, {404, 61009}, {405, 5731}, {474, 21151}, {515, 1001}, {516, 5812}, {517, 47387}, {518, 6261}, {944, 5809}, {999, 5728}, {1012, 36991}, {1071, 1445}, {1259, 60966}, {1617, 1864}, {1728, 12680}, {2183, 63434}, {2371, 28291}, {2550, 6907}, {2801, 22775}, {2947, 34048}, {2951, 10310}, {3059, 17857}, {3174, 64116}, {3243, 54159}, {3428, 5223}, {3487, 20330}, {3560, 60901}, {3651, 21168}, {3746, 24644}, {4304, 31672}, {4312, 37541}, {5177, 38149}, {5220, 18237}, {5542, 22753}, {5687, 35514}, {5715, 18482}, {5729, 18450}, {5762, 6985}, {5766, 11491}, {5787, 11108}, {5843, 60950}, {5851, 64188}, {5927, 13615}, {6223, 37426}, {6245, 6666}, {6256, 42843}, {6259, 64004}, {6767, 7966}, {6796, 11495}, {6831, 60943}, {6883, 61511}, {6905, 12848}, {6908, 9709}, {6911, 31657}, {6915, 62778}, {6927, 8732}, {7070, 54414}, {7675, 33597}, {8158, 11523}, {8273, 10864}, {9799, 18230}, {9845, 51773}, {9942, 60974}, {9948, 38130}, {9960, 61024}, {10382, 63972}, {10392, 30283}, {10394, 37302}, {10445, 37502}, {10679, 52835}, {10884, 16410}, {11220, 37309}, {11227, 16411}, {11344, 60969}, {11496, 63973}, {11509, 31391}, {12114, 52769}, {12528, 60970}, {12608, 42885}, {12650, 38316}, {12667, 31789}, {12669, 37787}, {12688, 15837}, {15298, 63988}, {15804, 63995}, {15931, 30326}, {16202, 59389}, {16408, 38122}, {16417, 60972}, {16853, 38318}, {18397, 41712}, {20846, 61025}, {25440, 43182}, {25525, 61595}, {26357, 60909}, {31822, 37622}, {34032, 61227}, {35262, 37244}, {37251, 59380}, {37282, 61012}, {37301, 61026}, {37579, 60910}, {37623, 60990}, {38107, 60991}, {38150, 63966}, {40257, 42871}, {42356, 48482}, {51090, 59687}, {54203, 64171}, {55432, 63395}, {60922, 61011}

X(64156) = midpoint of X(i) and X(j) for these {i,j}: {9, 1490}, {12667, 43161}
X(64156) = reflection of X(i) in X(j) for these {i,j}: {3174, 64116}, {3358, 31658}, {6245, 6666}, {10306, 6600}, {11495, 6796}, {12114, 52769}, {42871, 40257}, {48482, 42356}, {60990, 37623}
X(64156) = pole of line {6362, 59935} with respect to the polar circle
X(64156) = pole of line {10398, 30223} with respect to the Feuerbach hyperbola
X(64156) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(268), X(2346)}}, {{A, B, C, X(329), X(971)}}, {{A, B, C, X(972), X(1436)}}, {{A, B, C, X(7367), X(44861)}}, {{A, B, C, X(52389), X(60229)}}
X(64156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 1490, 971}, {9, 5732, 51489}, {516, 6600, 10306}, {971, 31658, 3358}, {1001, 63970, 6913}, {1260, 7580, 6244}, {6260, 11500, 37411}

X(64157) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(57) AND X(9)-CROSSPEDAL-OF-X(142)

Barycentrics    a*(a^4*(b+c)-(b-c)^2*(b+c)^3-2*a^3*(b^2+b*c+c^2)+2*a*(b-c)^2*(b^2+3*b*c+c^2)) : :
X(64157) = -3*X[17612]+5*X[62773]

X(64157) lies on these lines: {1, 210}, {2, 955}, {3, 10382}, {4, 10429}, {5, 226}, {6, 20310}, {7, 5927}, {9, 46675}, {11, 5173}, {20, 9844}, {33, 52424}, {55, 15299}, {57, 971}, {63, 5729}, {65, 1699}, {72, 938}, {145, 20789}, {165, 14100}, {200, 58650}, {218, 28070}, {273, 56299}, {354, 5219}, {388, 9947}, {389, 5908}, {474, 9858}, {497, 517}, {499, 16193}, {518, 3452}, {950, 31793}, {954, 3305}, {960, 6738}, {999, 5720}, {1001, 58648}, {1056, 18908}, {1071, 5658}, {1125, 58699}, {1155, 41853}, {1202, 3119}, {1212, 8958}, {1260, 1998}, {1376, 8257}, {1400, 44424}, {1445, 7580}, {1466, 34862}, {1538, 64127}, {1708, 51489}, {1709, 60910}, {1728, 31445}, {1736, 3666}, {1737, 3925}, {1743, 22117}, {1788, 12711}, {1836, 18482}, {1871, 3176}, {1876, 37372}, {1898, 5221}, {2000, 10601}, {2257, 38288}, {2801, 63994}, {3057, 15104}, {3059, 8580}, {3085, 16201}, {3086, 3475}, {3295, 58643}, {3304, 12128}, {3333, 14872}, {3339, 12688}, {3361, 12680}, {3488, 64107}, {3555, 14986}, {3634, 12564}, {3660, 17728}, {3678, 6744}, {3681, 10580}, {3715, 15298}, {3740, 5572}, {3742, 58463}, {3752, 62811}, {3811, 58649}, {3812, 18251}, {3817, 30329}, {3868, 6919}, {3870, 42884}, {3873, 5748}, {3911, 10391}, {3983, 51784}, {4187, 14054}, {4314, 58637}, {4640, 60994}, {4848, 31798}, {4863, 10573}, {5020, 59681}, {5049, 5719}, {5218, 15008}, {5222, 63965}, {5274, 7672}, {5281, 7671}, {5435, 10167}, {5437, 5784}, {5439, 5704}, {5440, 62873}, {5480, 21621}, {5542, 15064}, {5703, 12537}, {5708, 40263}, {5727, 64106}, {5732, 33995}, {5761, 11373}, {5763, 12053}, {5780, 7373}, {5804, 12672}, {5844, 9957}, {5918, 53056}, {5943, 29957}, {6001, 7682}, {6354, 53599}, {6684, 12710}, {6825, 9940}, {6849, 57282}, {6866, 31794}, {6883, 24929}, {6985, 37582}, {7675, 62776}, {7991, 9848}, {7994, 10384}, {8581, 10980}, {9817, 37543}, {10156, 17603}, {10171, 58626}, {10241, 64130}, {10389, 58688}, {10399, 41867}, {10578, 63961}, {10866, 11531}, {11220, 64142}, {11496, 58660}, {12005, 32159}, {12675, 64124}, {12709, 31821}, {13369, 34753}, {13411, 50205}, {13601, 64042}, {15185, 18236}, {15252, 40940}, {15254, 58651}, {15803, 31805}, {17441, 51413}, {17612, 62773}, {17616, 27003}, {17625, 58577}, {17658, 36845}, {17706, 20117}, {17718, 38318}, {17810, 21370}, {18240, 45310}, {18397, 31142}, {18838, 61722}, {21620, 58631}, {24928, 37700}, {27065, 62800}, {30223, 37541}, {30282, 33575}, {30326, 60937}, {30628, 64083}, {30946, 44735}, {31786, 37730}, {33994, 40269}, {37581, 64121}, {37583, 40262}, {39779, 59388}, {40962, 63511}, {40963, 58472}, {41338, 41712}, {41561, 60992}, {41562, 64132}, {41861, 61686}, {46974, 64166}, {50192, 56762}, {51361, 55086}, {54462, 58897}, {63976, 63999}

X(64157) = midpoint of X(i) and X(j) for these {i,j}: {57, 1864}, {497, 41539}, {5727, 64106}, {17658, 36845}, {61660, 61718}
X(64157) = reflection of X(i) in X(j) for these {i,j}: {200, 58650}, {3940, 5044}, {12915, 11019}, {17625, 58577}, {21060, 18227}, {64130, 10241}
X(64157) = perspector of circumconic {{A, B, C, X(4606), X(46964)}}
X(64157) = X(i)-complementary conjugate of X(j) for these {i, j}: {25, 52818}, {1170, 18589}, {1435, 45226}, {1803, 6389}, {2346, 34823}, {10482, 42018}, {10509, 18639}, {21453, 1368}, {53243, 20315}, {58322, 123}, {61373, 34822}
X(64157) = pole of line {1697, 5252} with respect to the Feuerbach hyperbola
X(64157) = pole of line {17924, 47965} with respect to the Steiner inellipse
X(64157) = pole of line {650, 663} with respect to the dual conic of DeLongchamps circle
X(64157) = intersection, other than A, B, C, of circumconics {{A, B, C, X(955), X(2334)}}, {{A, B, C, X(4866), X(57719)}}
X(64157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5728, 11018}, {11, 61663, 5173}, {57, 1864, 971}, {57, 61718, 1864}, {65, 17604, 1699}, {65, 64131, 9856}, {65, 9581, 5806}, {210, 7308, 5044}, {497, 41539, 517}, {518, 11019, 12915}, {518, 18227, 21060}, {942, 10157, 226}, {1210, 44547, 942}, {1788, 12711, 31787}, {1864, 61660, 57}, {3555, 14986, 16215}, {3740, 5572, 13405}, {3911, 10391, 11227}, {5435, 10167, 11575}, {5435, 10394, 10167}, {5437, 5784, 10855}, {5704, 62864, 5439}, {12433, 31837, 9957}, {15185, 18236, 25568}

X(64158) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST SAVIN AND X(10)-CROSSPEDAL-OF-X(8)

Barycentrics    2*a^4-2*a^3*(b+c)-2*a*b*c*(b+c)-(b^2-c^2)^2-a^2*(3*b^2+4*b*c+3*c^2) : :
X(64158) = -3*X[2]+2*X[49734], -4*X[1125]+3*X[50169], -3*X[3578]+X[3621], -5*X[3616]+3*X[50171], -5*X[3617]+6*X[49730], -7*X[3622]+3*X[50172], -5*X[3623]+3*X[42045], -2*X[3626]+3*X[49729], -4*X[3636]+3*X[50226], X[20014]+3*X[50277], X[20050]+3*X[50215], -7*X[20057]+3*X[50234]

X(64158) lies on these lines: {1, 30}, {2, 49734}, {3, 37634}, {4, 5718}, {6, 6872}, {8, 4918}, {10, 3712}, {11, 15973}, {12, 37573}, {20, 940}, {21, 1834}, {35, 37715}, {37, 57287}, {42, 57288}, {46, 48915}, {55, 9840}, {56, 15447}, {58, 57002}, {81, 15680}, {141, 17676}, {145, 524}, {171, 15338}, {230, 23903}, {306, 50050}, {386, 11113}, {387, 11111}, {390, 28369}, {405, 48837}, {442, 4653}, {452, 4383}, {497, 15971}, {511, 3057}, {515, 37548}, {528, 10459}, {538, 49466}, {540, 3244}, {543, 50235}, {546, 37693}, {550, 37522}, {613, 48922}, {758, 63415}, {846, 21677}, {855, 4267}, {938, 17595}, {950, 3666}, {968, 5794}, {980, 49131}, {1043, 1211}, {1125, 50169}, {1155, 48919}, {1201, 49736}, {1319, 48893}, {1479, 46704}, {1503, 1854}, {1616, 28368}, {1697, 48883}, {1714, 16418}, {1724, 48847}, {1764, 31782}, {1837, 17594}, {2098, 48909}, {2177, 12607}, {2292, 44669}, {2303, 31293}, {2475, 17056}, {2478, 4255}, {2646, 24210}, {2650, 17768}, {2886, 10448}, {3017, 17525}, {3120, 11281}, {3146, 5712}, {3152, 18635}, {3419, 62871}, {3476, 48923}, {3488, 37549}, {3529, 4340}, {3560, 5721}, {3564, 37740}, {3578, 3621}, {3589, 11319}, {3601, 17720}, {3616, 50171}, {3617, 49730}, {3622, 50172}, {3623, 42045}, {3626, 49729}, {3632, 49718}, {3636, 50226}, {3670, 12433}, {3743, 63360}, {3744, 4314}, {3750, 15888}, {3772, 62829}, {3912, 50167}, {3931, 5724}, {3945, 5059}, {3999, 6744}, {4026, 54331}, {4187, 4256}, {4189, 37646}, {4190, 37674}, {4265, 35998}, {4294, 5710}, {4298, 4883}, {4302, 5711}, {4304, 37539}, {4313, 48890}, {4324, 37559}, {4346, 15936}, {4415, 34772}, {4424, 37730}, {4513, 15984}, {4648, 37435}, {4656, 12437}, {4720, 26064}, {4884, 36500}, {4933, 21712}, {4995, 50421}, {5046, 37662}, {5119, 48882}, {5132, 13724}, {5217, 14636}, {5218, 50420}, {5248, 64172}, {5252, 48937}, {5255, 63273}, {5292, 16370}, {5347, 37399}, {5396, 37290}, {5432, 37574}, {5436, 24789}, {5691, 37553}, {5706, 6868}, {5716, 20182}, {5835, 32929}, {6003, 14284}, {6051, 17647}, {6097, 14793}, {6175, 24936}, {6658, 20132}, {6675, 24902}, {6690, 21935}, {6703, 11115}, {6707, 17589}, {6936, 36745}, {6938, 36746}, {6987, 37537}, {8359, 29438}, {8572, 10586}, {9534, 48814}, {9612, 17775}, {10039, 48887}, {10106, 63977}, {10385, 50422}, {10386, 37610}, {10449, 37038}, {10589, 50417}, {10950, 24430}, {11010, 48924}, {11112, 48841}, {11114, 19767}, {11238, 50415}, {11346, 48845}, {11520, 17276}, {11827, 37529}, {11997, 41600}, {12575, 50627}, {12625, 62818}, {12953, 26098}, {13161, 17724}, {13411, 37691}, {13728, 48863}, {13736, 19732}, {13743, 63318}, {14450, 63333}, {15048, 16783}, {15326, 37607}, {15670, 24880}, {15672, 24898}, {15676, 31204}, {15677, 16948}, {16052, 25645}, {16617, 45926}, {16859, 17337}, {17023, 50168}, {17164, 28530}, {17246, 63394}, {17261, 44728}, {17316, 50166}, {17576, 37642}, {17579, 48846}, {17588, 62689}, {17677, 25650}, {17751, 44419}, {17757, 33771}, {18165, 58889}, {19312, 23947}, {19684, 50322}, {19701, 50408}, {19722, 19783}, {19758, 36474}, {19766, 48817}, {20014, 50277}, {20050, 50215}, {20057, 50234}, {20834, 40980}, {21031, 60714}, {23536, 51715}, {23675, 42819}, {24512, 63548}, {24928, 48926}, {25988, 36797}, {26626, 50170}, {30305, 48941}, {30384, 48931}, {31156, 48842}, {31789, 63982}, {31792, 49557}, {31880, 33961}, {32479, 50262}, {32819, 37632}, {33100, 34195}, {34231, 46468}, {34606, 50581}, {34612, 59311}, {35016, 36250}, {35203, 37568}, {36479, 50156}, {37162, 51415}, {37256, 37633}, {37298, 45939}, {37617, 37722}, {38357, 45230}, {38814, 52360}, {40688, 54392}, {41002, 59303}, {43531, 50391}, {44307, 57284}, {46467, 56814}, {48859, 50321}, {49762, 50220}, {49770, 50270}, {50038, 56009}, {50260, 52229}, {50745, 63271}, {57285, 60682}, {62804, 63359}, {63354, 63376}

X(64158) = reflection of X(i) in X(j) for these {i,j}: {8, 49728}, {3632, 49718}, {37631, 49739}, {49557, 31792}, {49724, 49735}, {49745, 1}, {63360, 3743}
X(64158) = anticomplement of X(49734)
X(64158) = X(i)-Dao conjugate of X(j) for these {i, j}: {49734, 49734}
X(64158) = pole of line {523, 4833} with respect to the incircle
X(64158) = pole of line {942, 24239} with respect to the Feuerbach hyperbola
X(64158) = pole of line {391, 6871} with respect to the Kiepert hyperbola
X(64158) = pole of line {523, 48337} with respect to the Suppa-Cucoanes circle
X(64158) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6740), X(49745)}}, {{A, B, C, X(50811), X(54613)}}
X(64158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 24851, 3649}, {1, 30, 49745}, {1, 49745, 37631}, {1, 50065, 3782}, {1, 6284, 63979}, {4, 19765, 5718}, {8, 49728, 49724}, {8, 49735, 49728}, {21, 1834, 35466}, {56, 37425, 15447}, {81, 15680, 64159}, {1043, 26117, 1211}, {2478, 4255, 37663}, {3486, 64168, 37614}, {3632, 49723, 49718}, {3931, 10572, 5724}, {4854, 10543, 1}, {13161, 37080, 17724}, {48847, 50241, 1724}, {57002, 64167, 58}

X(64159) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(58) AND X(10)-CROSSPEDAL-OF-X(8)

Barycentrics    4*a^4-a^2*(b-c)^2+2*a^3*(b+c)-(b^2-c^2)^2 : :
X(64159) = -2*X[10]+3*X[59574], -X[1330]+3*X[4234], -3*X[5429]+X[24851], -4*X[6693]+3*X[16052]

X(64159) lies on these lines: {1, 3255}, {3, 37662}, {4, 4252}, {5, 4257}, {6, 20}, {10, 59574}, {21, 17056}, {30, 58}, {31, 7354}, {32, 49131}, {42, 15338}, {44, 57284}, {56, 855}, {81, 15680}, {141, 4195}, {171, 57288}, {172, 17747}, {191, 63360}, {230, 7379}, {325, 59538}, {333, 49734}, {376, 4255}, {382, 5292}, {386, 550}, {387, 3529}, {388, 3052}, {404, 51415}, {405, 17245}, {442, 24902}, {443, 17337}, {452, 37674}, {524, 1043}, {529, 5255}, {540, 41014}, {546, 45939}, {548, 4256}, {580, 31775}, {582, 28458}, {594, 50054}, {595, 18990}, {601, 11827}, {896, 21677}, {902, 15888}, {940, 6872}, {961, 1633}, {1010, 1213}, {1012, 54431}, {1030, 37402}, {1046, 44669}, {1064, 30264}, {1086, 1104}, {1150, 50322}, {1191, 4293}, {1193, 15326}, {1203, 4316}, {1211, 11115}, {1220, 44419}, {1279, 4298}, {1329, 37603}, {1330, 4234}, {1333, 1901}, {1399, 51421}, {1430, 1852}, {1453, 17366}, {1468, 6284}, {1616, 3600}, {1657, 48837}, {1707, 5794}, {1714, 50239}, {1724, 11112}, {1990, 44698}, {2163, 37720}, {2238, 56984}, {2245, 48883}, {2475, 16948}, {2646, 41011}, {2650, 10543}, {2829, 3072}, {2975, 63979}, {3053, 36706}, {3146, 37642}, {3178, 59592}, {3189, 64070}, {3242, 4339}, {3286, 9840}, {3436, 37540}, {3522, 63089}, {3534, 48870}, {3550, 12607}, {3589, 4201}, {3629, 20018}, {3704, 24850}, {3756, 32636}, {3763, 56986}, {3772, 9579}, {3782, 62802}, {3816, 37608}, {3915, 5434}, {3924, 11246}, {3936, 17539}, {3943, 7283}, {4188, 37663}, {4189, 5718}, {4190, 4383}, {4221, 54371}, {4225, 15447}, {4229, 18755}, {4253, 18907}, {4265, 37399}, {4267, 37425}, {4278, 48930}, {4299, 16466}, {4304, 7277}, {4313, 4644}, {4314, 49478}, {4315, 45219}, {4317, 16483}, {4325, 5315}, {4330, 16474}, {4340, 11111}, {4415, 37539}, {4427, 4918}, {4641, 57287}, {4646, 31730}, {4648, 11106}, {4653, 49743}, {4675, 5436}, {4957, 56875}, {5021, 7737}, {5046, 37634}, {5059, 37666}, {5096, 37328}, {5129, 37682}, {5177, 31187}, {5224, 51674}, {5230, 12943}, {5241, 19284}, {5277, 38930}, {5303, 33107}, {5323, 28029}, {5347, 35998}, {5429, 24851}, {5706, 6938}, {5712, 17576}, {5724, 56288}, {5737, 50408}, {5793, 63140}, {6693, 16052}, {6703, 26117}, {6748, 7513}, {6781, 20970}, {6868, 36746}, {6904, 37679}, {6948, 36745}, {6987, 37501}, {7263, 19851}, {7270, 44416}, {7745, 13727}, {9711, 56010}, {10026, 11104}, {10479, 50391}, {10483, 64172}, {10544, 20718}, {11001, 48842}, {11036, 62223}, {11113, 37522}, {11269, 12953}, {11281, 33097}, {12625, 62820}, {12635, 24695}, {13408, 13743}, {13725, 17398}, {13736, 15668}, {13745, 25526}, {15676, 63344}, {15677, 37631}, {15678, 49739}, {15681, 48857}, {15704, 48847}, {15852, 63438}, {15955, 28174}, {16696, 50622}, {17034, 19687}, {17234, 56989}, {17262, 20009}, {17313, 51606}, {17330, 51668}, {17340, 54433}, {17525, 49744}, {17563, 17749}, {17698, 48835}, {17778, 52352}, {18191, 58889}, {18541, 24159}, {19262, 19759}, {19312, 59625}, {19710, 48861}, {20067, 62804}, {20076, 37542}, {20131, 33059}, {20135, 33040}, {20154, 33058}, {20156, 33039}, {21024, 50164}, {21077, 37589}, {21358, 51675}, {21871, 35669}, {23537, 64166}, {24470, 30117}, {24565, 26958}, {24597, 31295}, {24632, 50168}, {25466, 54354}, {26051, 62689}, {26064, 51669}, {28082, 52783}, {28453, 63323}, {31789, 37469}, {31880, 63332}, {32911, 37256}, {33100, 63280}, {34620, 50303}, {34791, 53534}, {35016, 63366}, {37267, 63126}, {37298, 37693}, {37307, 37651}, {37331, 54300}, {37614, 44447}, {37650, 56999}, {37722, 54310}, {37817, 57282}, {44238, 48897}, {48866, 56734}, {48881, 50591}, {48892, 50595}, {48906, 50600}, {48939, 53425}, {50061, 54429}, {50065, 62809}, {50738, 63054}, {62843, 63386}, {63292, 63997}

X(64159) = midpoint of X(i) and X(j) for these {i,j}: {1043, 20077}
X(64159) = reflection of X(i) in X(j) for these {i,j}: {1834, 58}, {3704, 24850}, {63997, 63292}
X(64159) = pole of line {3091, 32431} with respect to the Kiepert hyperbola
X(64159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 4252, 37646}, {21, 49745, 17056}, {30, 58, 1834}, {58, 1834, 61661}, {81, 15680, 64158}, {1010, 49728, 1213}, {1043, 20077, 524}, {2475, 16948, 35466}, {37539, 64002, 4415}

X(64160) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST SAVIN AND X(10)-CROSSPEDAL-OF-X(12)

Barycentrics    (a+b-c)*(a-b+c)*(2*a^2-3*a*(b+c)-(b+c)^2) : :
X(64160) = 3*X[3584]+X[11280]

X(64160) lies on these lines: {1, 4}, {2, 3340}, {5, 50194}, {7, 1420}, {8, 5219}, {10, 2099}, {11, 6738}, {12, 519}, {20, 13384}, {21, 41551}, {35, 28194}, {46, 10165}, {55, 4301}, {56, 551}, {57, 3616}, {65, 392}, {79, 21578}, {109, 37607}, {140, 50193}, {142, 19861}, {145, 5226}, {181, 28389}, {238, 55101}, {354, 12563}, {377, 56387}, {381, 37739}, {404, 3256}, {495, 10222}, {496, 15844}, {498, 11362}, {516, 2646}, {517, 13411}, {527, 2975}, {595, 54339}, {631, 2093}, {908, 5795}, {936, 46916}, {938, 50443}, {940, 34040}, {942, 5901}, {945, 54972}, {958, 34647}, {960, 5173}, {962, 3601}, {993, 26437}, {999, 61276}, {1001, 52819}, {1012, 54198}, {1191, 37543}, {1201, 30097}, {1210, 5886}, {1279, 41003}, {1284, 10475}, {1319, 3636}, {1323, 4059}, {1385, 4292}, {1387, 2771}, {1388, 4315}, {1389, 1512}, {1393, 4424}, {1421, 5262}, {1465, 37548}, {1476, 3255}, {1482, 11374}, {1621, 37583}, {1697, 5703}, {1706, 27383}, {1708, 31435}, {1737, 5443}, {1770, 37525}, {1788, 3624}, {1836, 4297}, {1837, 3817}, {1858, 62852}, {2078, 57283}, {2098, 17718}, {2136, 63168}, {2171, 5750}, {2325, 25253}, {2362, 13971}, {2800, 13750}, {2886, 6737}, {3035, 10107}, {3057, 13405}, {3085, 7982}, {3086, 9624}, {3090, 11041}, {3091, 5727}, {3241, 5261}, {3243, 8232}, {3244, 3947}, {3295, 3656}, {3303, 4342}, {3304, 5542}, {3333, 61275}, {3339, 7288}, {3361, 4031}, {3428, 54430}, {3434, 12437}, {3452, 19860}, {3474, 7987}, {3523, 5128}, {3576, 4295}, {3577, 6848}, {3584, 11280}, {3600, 4654}, {3612, 31730}, {3633, 5726}, {3634, 40663}, {3635, 10944}, {3655, 9655}, {3664, 41007}, {3665, 58816}, {3674, 55082}, {3676, 44315}, {3679, 10588}, {3698, 20103}, {3702, 6358}, {3720, 37558}, {3741, 10474}, {3753, 6700}, {3812, 13601}, {3854, 7319}, {3869, 5745}, {3870, 21627}, {3874, 64041}, {3897, 64002}, {3919, 58405}, {3925, 12447}, {3984, 11526}, {4004, 13747}, {4032, 15569}, {4114, 13462}, {4294, 31162}, {4299, 51705}, {4304, 12699}, {4305, 41869}, {4311, 10246}, {4312, 30389}, {4313, 9580}, {4314, 12701}, {4355, 51105}, {4511, 57284}, {4666, 34489}, {4847, 12635}, {4853, 25568}, {4930, 31493}, {4955, 7181}, {4999, 44663}, {5048, 15888}, {5057, 51683}, {5126, 24470}, {5183, 52793}, {5217, 5493}, {5218, 7991}, {5221, 15808}, {5274, 37723}, {5289, 28628}, {5298, 51108}, {5323, 28619}, {5425, 17706}, {5432, 43174}, {5434, 51103}, {5435, 46934}, {5550, 31231}, {5554, 30852}, {5558, 7285}, {5563, 11551}, {5665, 54366}, {5697, 63259}, {5698, 61021}, {5719, 9957}, {5722, 18493}, {5731, 9579}, {5734, 7962}, {5797, 37693}, {5836, 6745}, {5853, 21617}, {5881, 10590}, {5887, 18389}, {5902, 64124}, {5903, 6684}, {6001, 16193}, {6051, 16577}, {6147, 10283}, {6361, 30282}, {6666, 7672}, {6705, 30274}, {6734, 62830}, {6744, 37722}, {6847, 7971}, {6863, 15865}, {6935, 54156}, {6940, 59329}, {7176, 25723}, {7280, 50828}, {7373, 26321}, {7677, 60945}, {7743, 12433}, {7988, 54361}, {8227, 18391}, {8545, 62832}, {8582, 25681}, {8583, 28629}, {8666, 18967}, {8983, 16232}, {9436, 17084}, {9589, 53054}, {9654, 37727}, {9776, 24558}, {9785, 10389}, {9856, 10391}, {9955, 37730}, {10039, 11009}, {10056, 30323}, {10164, 37567}, {10167, 17634}, {10171, 17606}, {10172, 18395}, {10175, 10573}, {10176, 41538}, {10386, 10624}, {10392, 38037}, {10527, 24391}, {10528, 12640}, {10529, 11520}, {10578, 37556}, {10580, 18220}, {10591, 38021}, {10827, 47745}, {10895, 37740}, {10896, 37724}, {10914, 59722}, {10916, 62822}, {10950, 17605}, {10954, 63964}, {10956, 64137}, {11019, 11376}, {11028, 11728}, {11036, 62836}, {11038, 34497}, {11224, 51784}, {11237, 37738}, {11240, 62861}, {11246, 37605}, {11281, 58679}, {11373, 15934}, {11501, 25439}, {11518, 14986}, {11523, 64081}, {11544, 31776}, {11680, 41575}, {11724, 24472}, {11725, 59815}, {11726, 59813}, {11727, 12016}, {11729, 12736}, {11734, 59816}, {11735, 59817}, {12245, 31434}, {12436, 17614}, {12512, 37600}, {12526, 30478}, {12559, 45700}, {12560, 38053}, {12572, 51409}, {12573, 16888}, {12575, 37080}, {12577, 20323}, {12588, 49684}, {12609, 30144}, {12649, 24386}, {12739, 21630}, {12832, 32557}, {13273, 33337}, {13902, 51841}, {13959, 51842}, {13975, 38235}, {14563, 23708}, {15174, 31795}, {15178, 18990}, {15325, 31794}, {15368, 49745}, {15558, 64192}, {15717, 63207}, {16609, 19868}, {16818, 28777}, {16865, 41572}, {17097, 24987}, {17397, 62774}, {17451, 40869}, {17609, 17625}, {17700, 40256}, {18249, 24953}, {18480, 37728}, {18838, 58565}, {18976, 33812}, {19862, 24914}, {20070, 35445}, {20076, 31164}, {20118, 33709}, {20616, 25092}, {21616, 30147}, {21746, 63603}, {22759, 62825}, {22836, 63146}, {24387, 26481}, {25405, 61278}, {25466, 64127}, {25524, 37541}, {25557, 60993}, {25917, 41539}, {26015, 34195}, {26127, 41012}, {26364, 44848}, {27385, 63990}, {28228, 37568}, {28236, 37734}, {28385, 62739}, {30312, 60999}, {30318, 61027}, {31391, 43176}, {31410, 61288}, {31792, 63282}, {31937, 41562}, {32086, 47444}, {34625, 41863}, {37228, 61002}, {37236, 51687}, {37267, 45036}, {37582, 38028}, {37711, 50796}, {37731, 63210}, {38059, 41712}, {40719, 52563}, {41348, 64108}, {43040, 49768}, {44307, 45890}, {45776, 50195}, {49627, 62860}, {50398, 60947}, {50603, 50626}, {50808, 63756}, {54286, 59587}, {59491, 64047}, {59584, 63130}

X(64160) = midpoint of X(i) and X(j) for these {i,j}: {1, 12047}, {12, 11011}, {6734, 62830}, {10039, 11009}
X(64160) = reflection of X(i) in X(j) for these {i,j}: {13411, 37737}, {13750, 58566}
X(64160) = inverse of X(38945) in the incircle
X(64160) = perspector of circumconic {{A, B, C, X(653), X(46480)}}
X(64160) = X(i)-Dao conjugate of X(j) for these {i, j}: {63978, 5745}
X(64160) = pole of line {522, 17950} with respect to the incircle
X(64160) = pole of line {65, 4297} with respect to the Feuerbach hyperbola
X(64160) = pole of line {14837, 48321} with respect to the Steiner inellipse
X(64160) = pole of line {332, 4923} with respect to the Wallace hyperbola
X(64160) = pole of line {57, 4888} with respect to the dual conic of Yff parabola
X(64160) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(17588)}}, {{A, B, C, X(225), X(35576)}}, {{A, B, C, X(581), X(945)}}, {{A, B, C, X(944), X(54972)}}, {{A, B, C, X(1065), X(5882)}}, {{A, B, C, X(10106), X(60041)}}
X(64160) = barycentric product X(i)*X(j) for these (i, j): {7, 63978}, {17588, 226}
X(64160) = barycentric quotient X(i)/X(j) for these (i, j): {17588, 333}, {63978, 8}
X(64160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11522, 497}, {1, 12047, 515}, {1, 1478, 5882}, {1, 1699, 3486}, {1, 18393, 10572}, {1, 226, 10106}, {1, 3485, 226}, {1, 5290, 3476}, {1, 5603, 12053}, {1, 946, 950}, {1, 9612, 944}, {1, 9613, 7967}, {1, 9614, 3488}, {2, 11682, 5837}, {2, 3340, 4848}, {2, 4323, 3340}, {5, 50194, 64163}, {7, 3622, 1420}, {12, 11011, 519}, {56, 3671, 553}, {65, 1125, 3911}, {65, 15950, 1125}, {79, 24926, 21578}, {145, 5226, 9578}, {498, 25415, 11362}, {517, 37737, 13411}, {551, 3671, 56}, {942, 5901, 44675}, {960, 5173, 15556}, {1319, 3649, 4298}, {1385, 39542, 4292}, {1387, 16137, 5045}, {1388, 10404, 4315}, {1482, 11374, 31397}, {1836, 34471, 4297}, {2099, 11375, 10}, {2800, 58566, 13750}, {3241, 5261, 37709}, {3244, 3947, 5252}, {3339, 25055, 7288}, {3487, 10595, 1}, {3600, 38314, 63208}, {3624, 18421, 1788}, {3636, 4298, 1319}, {3649, 4298, 3982}, {3869, 24541, 5745}, {4654, 63208, 3600}, {4870, 11011, 12}, {5714, 7967, 9613}, {6147, 10283, 24928}, {10039, 11009, 28234}, {10246, 57282, 4311}, {10572, 18393, 18483}, {10950, 17605, 19925}, {11009, 37701, 10039}, {11526, 60943, 24393}, {12560, 38053, 60992}, {20616, 43039, 25092}, {22791, 24929, 10624}, {24470, 51700, 5126}, {24953, 31165, 18249}, {37722, 44840, 6744}

X(64161) = CENTROID OF X(10)-CROSSPEDAL-OF-X(42)

Barycentrics    3*a^2*(b+c)-b*c*(b+c)+a*(b^2+c^2) : :
X(64161) = -X[8]+4*X[4868], 2*X[38]+X[20011], 2*X[3666]+X[3896], -X[4365]+4*X[6685]

X(64161) lies on circumconic {{A, B, C, X(27483), X(39706)}} and on these lines: {1, 17495}, {2, 740}, {6, 4427}, {8, 4868}, {31, 45222}, {38, 20011}, {42, 726}, {43, 3995}, {55, 17150}, {75, 29822}, {100, 4360}, {145, 986}, {192, 872}, {244, 49471}, {321, 28484}, {386, 25253}, {404, 41813}, {514, 38349}, {519, 46901}, {536, 46897}, {750, 50281}, {846, 19742}, {896, 49489}, {899, 3993}, {902, 49477}, {984, 19998}, {1150, 17162}, {2177, 20045}, {2321, 26251}, {2796, 61707}, {2802, 3241}, {2901, 26030}, {3006, 3755}, {3187, 17594}, {3210, 17018}, {3216, 4065}, {3244, 17449}, {3616, 6533}, {3666, 3896}, {3685, 17012}, {3722, 49472}, {3750, 32924}, {3759, 62838}, {3821, 4062}, {3875, 26227}, {3946, 26230}, {3980, 8025}, {3989, 4685}, {4000, 29830}, {4003, 49475}, {4028, 17184}, {4085, 31079}, {4353, 50744}, {4358, 49462}, {4359, 37593}, {4365, 6685}, {4393, 4781}, {4414, 16704}, {4418, 19717}, {4442, 5718}, {4649, 32845}, {4651, 28606}, {4655, 63071}, {4664, 62296}, {4689, 4852}, {4693, 32944}, {4704, 9330}, {4706, 15569}, {4709, 30970}, {4716, 32917}, {4743, 33136}, {4780, 29639}, {4850, 29824}, {4854, 5741}, {4937, 51059}, {4946, 49520}, {4991, 21747}, {5108, 62644}, {5256, 32929}, {5297, 17319}, {5312, 56318}, {6155, 26035}, {6542, 33086}, {6758, 25241}, {7226, 20012}, {8620, 20691}, {9347, 17393}, {9791, 37656}, {11246, 42045}, {14459, 33082}, {16062, 27558}, {16347, 27368}, {16834, 35258}, {17011, 32932}, {17146, 49478}, {17154, 49490}, {17155, 42042}, {17164, 19767}, {17243, 24988}, {17301, 33122}, {17302, 33175}, {17318, 17780}, {17366, 24542}, {17490, 29814}, {17491, 24248}, {17593, 32919}, {17596, 37639}, {17600, 32945}, {17718, 50102}, {17740, 29829}, {17778, 33102}, {17861, 63168}, {18133, 61174}, {19740, 24342}, {19804, 62840}, {20017, 26034}, {20040, 37598}, {20290, 32950}, {21282, 33070}, {21805, 49456}, {21806, 24325}, {21870, 49523}, {24725, 44006}, {25568, 50071}, {26115, 64184}, {26250, 32928}, {28516, 31161}, {28526, 61652}, {28599, 33088}, {28605, 59297}, {28611, 58380}, {29584, 31348}, {29823, 32941}, {29839, 33150}, {30564, 50018}, {30665, 47776}, {30818, 49461}, {30942, 49469}, {30964, 53363}, {31025, 49474}, {31037, 32776}, {31179, 53372}, {32925, 42043}, {32931, 49452}, {32934, 61358}, {33100, 62998}, {33112, 62392}, {33161, 50287}, {33296, 56431}, {35263, 50114}, {36263, 49497}, {38047, 50105}, {48630, 52786}, {49510, 49983}, {49987, 63977}, {50101, 53381}, {56520, 59547}

X(64161) = midpoint of X(i) and X(j) for these {i,j}: {3896, 46909}
X(64161) = reflection of X(i) in X(j) for these {i,j}: {2, 46904}, {17135, 46909}, {46909, 3666}
X(64161) = pole of line {3768, 28840} with respect to the Steiner circumellipse
X(64161) = pole of line {24603, 26580} with respect to the dual conic of Yff parabola
X(64161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 17147, 17165}, {42, 4970, 17147}, {145, 4392, 17145}, {192, 3240, 3952}, {899, 3993, 31035}, {1150, 49486, 17162}, {2177, 32921, 20045}, {3210, 17018, 17140}, {3666, 28581, 46909}, {3821, 4062, 31017}, {3896, 46909, 28581}, {4085, 32848, 31079}, {4414, 49488, 16704}, {4706, 15569, 24589}, {17592, 32860, 2}, {24248, 31034, 17491}, {32931, 49452, 62227}

X(64162) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST SAVIN AND X(10)-CROSSPEDAL-OF-X(210)

Barycentrics    2*a^3+2*a*(b-c)^2-3*a^2*(b+c)-(b-c)^2*(b+c) : :
X(64162) = -X[65]+4*X[6744], 2*X[942]+X[10624], -X[1770]+7*X[50190], X[3057]+2*X[6738], X[3555]+2*X[12572], -7*X[3622]+X[57287], -4*X[3636]+X[17647], 5*X[3889]+X[64002], 5*X[3890]+X[41575], -X[4292]+4*X[5045], 2*X[4298]+X[6284], -3*X[4731]+X[34720] and many others

X(64162) lies on these lines: {1, 4}, {2, 3158}, {7, 9580}, {8, 7308}, {9, 36845}, {10, 3303}, {11, 3748}, {20, 41864}, {30, 5049}, {35, 64124}, {38, 49989}, {55, 3911}, {56, 4314}, {57, 390}, {65, 6744}, {79, 36946}, {100, 6692}, {140, 63271}, {142, 3434}, {145, 3984}, {149, 5249}, {165, 10385}, {200, 5316}, {210, 392}, {312, 49466}, {329, 3243}, {354, 516}, {377, 51723}, {405, 51724}, {452, 6762}, {474, 64117}, {495, 18527}, {496, 11230}, {514, 11193}, {517, 15170}, {518, 40998}, {527, 3873}, {528, 3742}, {551, 31140}, {614, 3755}, {908, 3957}, {938, 1697}, {940, 63969}, {942, 10624}, {952, 10157}, {962, 11518}, {999, 4304}, {1001, 1260}, {1100, 17747}, {1125, 3925}, {1210, 3295}, {1279, 40940}, {1420, 4313}, {1621, 5745}, {1706, 56936}, {1738, 29820}, {1770, 50190}, {1788, 53053}, {1836, 3982}, {1837, 38155}, {1914, 61688}, {2099, 4342}, {2280, 40869}, {2325, 63147}, {2346, 5284}, {2550, 10582}, {2809, 41581}, {2886, 42819}, {2887, 49768}, {3057, 6738}, {3085, 54447}, {3189, 8583}, {3241, 31142}, {3242, 4656}, {3244, 4679}, {3304, 4297}, {3305, 24393}, {3306, 20075}, {3333, 4294}, {3338, 4309}, {3340, 9785}, {3452, 3870}, {3474, 4031}, {3555, 12572}, {3584, 10172}, {3599, 32079}, {3601, 14986}, {3616, 37436}, {3621, 7320}, {3622, 57287}, {3626, 45081}, {3632, 30393}, {3636, 17647}, {3663, 17597}, {3664, 4883}, {3666, 63977}, {3671, 12701}, {3677, 64168}, {3681, 61718}, {3683, 51463}, {3685, 36483}, {3686, 17135}, {3689, 20103}, {3720, 13576}, {3744, 39595}, {3746, 6684}, {3750, 24239}, {3813, 51715}, {3816, 6745}, {3817, 11238}, {3848, 49732}, {3871, 63990}, {3879, 30946}, {3883, 10453}, {3889, 64002}, {3890, 41575}, {3896, 49987}, {3912, 4514}, {3913, 8582}, {3928, 64151}, {3929, 52653}, {3946, 7191}, {3947, 10896}, {4011, 49529}, {4021, 29215}, {4061, 49460}, {4082, 49688}, {4104, 49458}, {4114, 4312}, {4187, 59722}, {4292, 5045}, {4298, 6284}, {4302, 51816}, {4305, 61762}, {4311, 7373}, {4326, 60992}, {4343, 30097}, {4353, 4854}, {4356, 17599}, {4388, 4684}, {4415, 4864}, {4430, 17781}, {4432, 59664}, {4512, 24477}, {4654, 9812}, {4689, 51615}, {4703, 49505}, {4731, 34720}, {4855, 10586}, {4891, 5846}, {4995, 58441}, {5057, 62863}, {5083, 10391}, {5084, 6765}, {5121, 60714}, {5129, 6764}, {5173, 5572}, {5178, 24564}, {5219, 5274}, {5221, 5493}, {5248, 49627}, {5250, 24391}, {5252, 8162}, {5281, 31231}, {5294, 29835}, {5325, 64153}, {5434, 28164}, {5435, 35445}, {5436, 64081}, {5437, 17784}, {5554, 12640}, {5563, 41853}, {5687, 9843}, {5698, 62823}, {5703, 50443}, {5719, 7743}, {5722, 5790}, {5727, 51779}, {5728, 17642}, {5741, 50744}, {5743, 49467}, {5750, 24552}, {5837, 12649}, {5844, 9957}, {5847, 42057}, {5902, 28194}, {5903, 17706}, {5905, 62815}, {6600, 25893}, {6737, 58679}, {6743, 25917}, {6872, 62832}, {7354, 12577}, {7580, 43175}, {9053, 35652}, {9371, 26740}, {9578, 54448}, {9579, 11037}, {9670, 10404}, {9848, 12709}, {9955, 63282}, {10056, 10175}, {10072, 10165}, {10122, 41551}, {10177, 60972}, {10179, 44669}, {10200, 59587}, {10386, 37582}, {10529, 62829}, {10543, 20323}, {10569, 63995}, {10857, 35514}, {10950, 17604}, {11025, 60945}, {11415, 62861}, {11529, 30305}, {11680, 58463}, {12437, 19861}, {12512, 32636}, {12527, 34791}, {12710, 50196}, {13388, 31568}, {13389, 31567}, {14100, 17625}, {14555, 49451}, {14563, 25415}, {15104, 28234}, {15174, 15178}, {15185, 61003}, {15558, 41558}, {15888, 19925}, {15935, 50194}, {16465, 61002}, {17059, 25970}, {17067, 33131}, {17123, 49772}, {17155, 28557}, {17319, 56555}, {17596, 24216}, {17603, 17626}, {17605, 37703}, {17715, 24217}, {17764, 42053}, {18391, 31393}, {18839, 62852}, {18990, 28168}, {19860, 21627}, {20015, 62218}, {20196, 64083}, {20292, 60980}, {20358, 28858}, {21454, 30332}, {21578, 37602}, {21617, 63261}, {21856, 23653}, {24165, 28580}, {24231, 33095}, {24389, 47387}, {24470, 50191}, {24541, 62870}, {24703, 42871}, {24929, 38028}, {25430, 39587}, {25439, 44848}, {27003, 63145}, {28070, 41006}, {28526, 42055}, {29639, 62849}, {29652, 50290}, {29655, 59692}, {29814, 30949}, {29824, 63134}, {30143, 49600}, {30284, 64115}, {30330, 61014}, {30827, 63168}, {30947, 63139}, {31249, 59572}, {31770, 58616}, {31792, 37730}, {32861, 49763}, {32926, 49771}, {33595, 34123}, {34607, 64112}, {34611, 64149}, {36479, 53663}, {37587, 54342}, {37617, 53618}, {37642, 62875}, {37720, 63259}, {37721, 47745}, {41011, 62867}, {41166, 41556}, {41839, 49527}, {50294, 62845}, {50843, 50892}, {50865, 59372}, {51423, 63159}, {51784, 54361}, {53055, 62800}, {54408, 62839}, {57288, 58609}, {59491, 61155}, {62240, 64016}, {63207, 64142}

X(64162) = midpoint of X(i) and X(j) for these {i,j}: {354, 3058}, {4430, 17781}
X(64162) = reflection of X(i) in X(j) for these {i,j}: {553, 354}, {40998, 49736}, {49732, 3848}, {60972, 10177}
X(64162) = pole of line {522, 3935} with respect to the incircle
X(64162) = pole of line {65, 5542} with respect to the Feuerbach hyperbola
X(64162) = pole of line {57, 24796} with respect to the dual conic of Yff parabola
X(64162) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(56088)}}, {{A, B, C, X(33), X(10390)}}, {{A, B, C, X(34), X(60666)}}, {{A, B, C, X(278), X(42318)}}, {{A, B, C, X(1067), X(21620)}}
X(64162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1058, 12053}, {1, 1479, 21620}, {1, 1699, 3475}, {1, 3586, 1056}, {1, 4857, 13407}, {1, 497, 226}, {1, 950, 10106}, {1, 9614, 3487}, {2, 64146, 46917}, {2, 8236, 10389}, {11, 3748, 13405}, {11, 61648, 10171}, {55, 17728, 10164}, {149, 29817, 5249}, {200, 26105, 5316}, {354, 3058, 516}, {354, 516, 553}, {390, 10580, 57}, {497, 3475, 1699}, {518, 49736, 40998}, {938, 1697, 4848}, {1621, 26015, 5745}, {1836, 5542, 3982}, {3244, 21060, 41711}, {3338, 4309, 31730}, {3434, 4666, 142}, {3474, 10980, 4031}, {3748, 61648, 63287}, {4314, 21625, 56}, {4423, 4863, 10}, {4512, 31146, 24477}, {4857, 13407, 18483}, {4883, 63979, 3664}, {5045, 15171, 4292}, {5274, 10578, 5219}, {5284, 25006, 6666}, {5542, 51783, 1836}, {5722, 6767, 31397}, {6284, 17609, 4298}, {6744, 12575, 65}, {6767, 18530, 5722}, {9580, 44841, 7}, {9670, 10404, 51118}, {9812, 11038, 4654}, {9957, 12433, 64163}, {10164, 11019, 17728}, {10164, 17728, 3911}, {10171, 13405, 61648}, {10391, 12915, 5083}, {10596, 18446, 946}, {11019, 30331, 55}, {11238, 17718, 3817}, {12915, 63972, 10391}, {13405, 43179, 3748}, {24392, 38316, 2}, {24477, 47357, 4512}, {32636, 63273, 12512}, {37080, 37722, 1125}

X(64163) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(65) AND X(21)-CROSSPEDAL-OF-X(1)

Barycentrics    2*a^4-a^2*(b-c)^2-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)-(b^2-c^2)^2 : :
X(64163) = -3*X[354]+X[10944], -3*X[553]+2*X[18990], -3*X[3753]+2*X[57284], -2*X[3878]+3*X[40998], -X[3962]+3*X[34606], -5*X[4004]+3*X[11112], -2*X[4298]+3*X[5902], -3*X[5692]+4*X[18250], -3*X[5919]+4*X[40270], -4*X[12577]+5*X[18398]

X(64163) lies on these lines: {1, 2}, {3, 4848}, {4, 3340}, {5, 50194}, {7, 9613}, {11, 11011}, {12, 64110}, {20, 2093}, {30, 41551}, {35, 17010}, {40, 3486}, {41, 8074}, {46, 4297}, {55, 11362}, {56, 5882}, {57, 944}, {65, 515}, {72, 5795}, {79, 37006}, {80, 7548}, {91, 53114}, {92, 56814}, {150, 3674}, {165, 4305}, {214, 58405}, {218, 41006}, {226, 355}, {322, 3879}, {354, 10944}, {376, 5128}, {388, 5881}, {389, 517}, {390, 10398}, {405, 5837}, {484, 12512}, {495, 63274}, {496, 10222}, {497, 7982}, {516, 5903}, {518, 14454}, {527, 4018}, {535, 4757}, {553, 18990}, {581, 24806}, {611, 49529}, {613, 49684}, {631, 13384}, {664, 53597}, {758, 12527}, {908, 62830}, {912, 41569}, {942, 952}, {946, 1837}, {954, 24393}, {956, 24391}, {960, 5855}, {962, 3586}, {993, 11507}, {999, 11499}, {1000, 7160}, {1056, 11518}, {1058, 7962}, {1109, 2650}, {1111, 58816}, {1126, 36123}, {1159, 18525}, {1317, 20323}, {1319, 13607}, {1385, 3911}, {1387, 33179}, {1388, 17728}, {1420, 7967}, {1433, 10570}, {1441, 3664}, {1445, 43175}, {1449, 54283}, {1457, 37732}, {1468, 1771}, {1478, 3671}, {1479, 4301}, {1482, 5722}, {1483, 24928}, {1497, 37610}, {1512, 21740}, {1697, 3488}, {1728, 5250}, {1735, 4642}, {1736, 63977}, {1770, 28164}, {1785, 5174}, {1788, 3576}, {1834, 8286}, {1836, 31673}, {1858, 2800}, {1864, 12672}, {1905, 49542}, {1953, 40963}, {2078, 64173}, {2098, 63993}, {2346, 5559}, {2478, 11682}, {2646, 6684}, {2784, 18413}, {2802, 37999}, {3057, 28234}, {3072, 55101}, {3091, 4323}, {3189, 63137}, {3245, 5441}, {3256, 6906}, {3295, 54430}, {3304, 37738}, {3333, 3476}, {3336, 21578}, {3338, 4315}, {3339, 4293}, {3421, 11523}, {3452, 5730}, {3485, 5587}, {3487, 9578}, {3528, 63207}, {3553, 20262}, {3601, 5657}, {3612, 10164}, {3614, 4870}, {3649, 12831}, {3656, 9669}, {3663, 56927}, {3692, 3950}, {3748, 45081}, {3753, 57284}, {3754, 13750}, {3812, 16193}, {3817, 10826}, {3822, 10954}, {3839, 7319}, {3869, 12572}, {3871, 51433}, {3874, 64045}, {3878, 40998}, {3881, 5570}, {3897, 59491}, {3901, 5850}, {3946, 63844}, {3947, 10827}, {3962, 34606}, {4004, 11112}, {4067, 41686}, {4294, 7991}, {4295, 5691}, {4298, 5902}, {4302, 5493}, {4313, 59417}, {4314, 5119}, {4342, 30323}, {4424, 44706}, {4513, 21096}, {4646, 17102}, {4654, 34627}, {4656, 26872}, {4855, 59675}, {4857, 11280}, {4904, 52542}, {5046, 51423}, {5048, 37722}, {5082, 12625}, {5084, 15829}, {5126, 34753}, {5173, 7686}, {5176, 34195}, {5183, 15338}, {5204, 51705}, {5219, 5818}, {5225, 31162}, {5251, 18249}, {5252, 14563}, {5270, 9897}, {5274, 5734}, {5290, 37712}, {5425, 12563}, {5440, 63990}, {5443, 10171}, {5445, 58441}, {5450, 11509}, {5542, 30318}, {5603, 9581}, {5687, 12437}, {5690, 24929}, {5692, 18250}, {5697, 12575}, {5708, 18526}, {5717, 5724}, {5719, 61510}, {5728, 5853}, {5731, 15803}, {5768, 12650}, {5790, 11374}, {5809, 43166}, {5836, 8261}, {5844, 9957}, {5919, 40270}, {5920, 13867}, {5933, 10444}, {6001, 13601}, {6147, 37705}, {6198, 51359}, {6284, 28194}, {6603, 21049}, {6692, 17614}, {6740, 46441}, {6909, 59329}, {7190, 24213}, {7674, 30330}, {7682, 63986}, {8069, 8715}, {8071, 8666}, {8227, 54361}, {8232, 38154}, {8256, 56176}, {8275, 30337}, {9588, 53054}, {9612, 59387}, {9624, 10589}, {9955, 12019}, {9956, 11545}, {10073, 21630}, {10090, 33337}, {10165, 24914}, {10175, 11375}, {10247, 11373}, {10391, 31788}, {10399, 14923}, {10543, 37568}, {10569, 17644}, {10571, 37699}, {10590, 37714}, {10591, 11522}, {10593, 51709}, {10595, 50443}, {10629, 12559}, {10698, 47744}, {10895, 50796}, {11009, 30384}, {11015, 63145}, {11023, 11037}, {11031, 63134}, {11224, 51785}, {11278, 18527}, {11376, 61717}, {11491, 37583}, {11502, 26437}, {11508, 25439}, {11517, 12640}, {11531, 16236}, {11715, 12832}, {12005, 18838}, {12114, 37541}, {12436, 30274}, {12571, 18393}, {12573, 30329}, {12577, 18398}, {12579, 30358}, {12580, 18399}, {12581, 18409}, {12582, 18408}, {12635, 21075}, {12645, 15934}, {12667, 41561}, {12688, 17632}, {12709, 14872}, {13375, 24225}, {14110, 41539}, {14584, 59283}, {15178, 15325}, {15299, 30331}, {15888, 44840}, {15950, 17606}, {18242, 64127}, {18480, 39542}, {18481, 36279}, {20789, 58645}, {21077, 62822}, {21933, 40942}, {22766, 25440}, {22767, 62825}, {23129, 64069}, {24470, 28224}, {25405, 61286}, {26393, 49555}, {26417, 49556}, {26475, 63963}, {28451, 34718}, {31410, 61252}, {31730, 37567}, {31792, 58630}, {33956, 58609}, {34231, 54396}, {34434, 58493}, {34607, 63138}, {34744, 54290}, {34773, 37582}, {34790, 40661}, {34791, 38455}, {34851, 46974}, {36920, 37080}, {36977, 62832}, {37828, 56177}, {38074, 43734}, {38134, 61649}, {39574, 60681}, {40950, 56285}, {41012, 62826}, {43180, 64155}, {44663, 57288}, {44848, 47742}, {45776, 64131}, {52682, 61021}, {53058, 61289}, {53615, 62859}, {54286, 59335}, {54432, 56288}, {56311, 59576}, {56936, 64202}, {56943, 62812}, {57287, 62864}, {61291, 61762}, {62836, 63130}, {63360, 64174}, {63967, 64041}, {64002, 64047}

X(64163) = midpoint of X(i) and X(j) for these {i,j}: {65, 10950}, {5903, 10572}, {37706, 45287}, {64002, 64047}
X(64163) = reflection of X(i) in X(j) for these {i,j}: {1, 6738}, {72, 5795}, {950, 37730}, {3057, 63999}, {3869, 12572}, {4292, 65}, {5697, 12575}, {6737, 10}, {9957, 12433}, {10106, 942}, {10624, 950}, {12573, 30329}, {17647, 3754}, {18990, 31794}, {34434, 58493}, {45287, 4298}, {63146, 5836}
X(64163) = inverse of X(47622) in incircle
X(64163) = inverse of X(63257) in Feuerbach hyperbola
X(64163) = X(i)-complementary conjugate of X(j) for these {i, j}: {1389, 1329}
X(64163) = pole of line {1459, 3667} with respect to the incircle
X(64163) = pole of line {12, 946} with respect to the Feuerbach hyperbola
X(64163) = pole of line {514, 28834} with respect to the Steiner inellipse
X(64163) = pole of line {663, 3667} with respect to the Suppa-Cucoanes circle
X(64163) = pole of line {3239, 36054} with respect to the dual conic of DeLongchamps circle
X(64163) = intersection, other than A, B, C, of circumconics {{A, B, C, X(78), X(3577)}}, {{A, B, C, X(80), X(6737)}}, {{A, B, C, X(91), X(3679)}}, {{A, B, C, X(996), X(3085)}}, {{A, B, C, X(1125), X(36123)}}, {{A, B, C, X(1126), X(22350)}}, {{A, B, C, X(1220), X(13411)}}, {{A, B, C, X(1222), X(31397)}}, {{A, B, C, X(2346), X(4861)}}, {{A, B, C, X(3872), X(7160)}}, {{A, B, C, X(4511), X(17097)}}, {{A, B, C, X(4847), X(5559)}}, {{A, B, C, X(5705), X(31359)}}, {{A, B, C, X(7080), X(10570)}}, {{A, B, C, X(26363), X(42285)}}, {{A, B, C, X(27383), X(54972)}}
X(64163) = barycentric product X(i)*X(j) for these (i, j): {33597, 92}
X(64163) = barycentric quotient X(i)/X(j) for these (i, j): {33597, 63}
X(64163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1737, 1125}, {1, 3679, 3085}, {1, 499, 551}, {4, 11041, 3340}, {5, 50194, 64160}, {8, 145, 6765}, {10, 519, 6737}, {11, 11011, 13464}, {55, 41687, 11362}, {56, 37740, 5882}, {57, 944, 4311}, {65, 10950, 515}, {65, 515, 4292}, {78, 5554, 10}, {80, 12047, 19925}, {145, 5554, 78}, {145, 938, 1}, {517, 37730, 950}, {517, 950, 10624}, {942, 6797, 61541}, {942, 952, 10106}, {950, 15556, 64004}, {999, 37727, 63987}, {1159, 18525, 57282}, {1479, 25415, 4301}, {1837, 2099, 946}, {2646, 40663, 6684}, {3057, 41538, 31806}, {3333, 61296, 3476}, {3340, 5727, 4}, {3487, 59388, 9578}, {3488, 12245, 1697}, {3754, 62852, 13750}, {3947, 38155, 10827}, {4298, 28236, 45287}, {5425, 13407, 12563}, {5691, 18421, 4295}, {5836, 44669, 63146}, {5844, 12433, 9957}, {5881, 11529, 388}, {5902, 45287, 4298}, {5903, 10572, 516}, {7962, 37723, 1058}, {9957, 12433, 64162}, {11009, 37702, 30384}, {11518, 37709, 1056}, {12563, 51782, 13407}, {13407, 37710, 51782}, {13607, 64124, 1319}, {14563, 47745, 21620}, {18990, 31794, 553}, {21620, 47745, 5252}, {25415, 37721, 1479}, {28204, 31794, 18990}, {28234, 63999, 3057}, {37706, 45287, 28236}, {37724, 41687, 55}

X(64164) = CENTROID OF X(21)-CROSSPEDAL-OF-X(1)

Barycentrics    2*a^3+2*a*b*c+2*a^2*(b+c)-(b-c)^2*(b+c) : :
X(64164) = -X[2292]+4*X[49743], -7*X[3622]+4*X[12579], -X[5492]+4*X[63374], -3*X[27812]+X[50277], -4*X[49564]+X[64071]

X(64164) lies on these lines: {1, 5180}, {2, 17770}, {7, 17017}, {10, 20290}, {31, 29689}, {38, 17365}, {42, 50307}, {58, 26725}, {63, 29682}, {79, 4658}, {81, 3120}, {86, 4683}, {191, 27577}, {226, 29683}, {320, 32772}, {321, 49995}, {354, 513}, {514, 62663}, {524, 21020}, {527, 3989}, {614, 4888}, {740, 42045}, {748, 4675}, {758, 49744}, {846, 37635}, {894, 15523}, {896, 17056}, {940, 24725}, {942, 20961}, {1046, 21674}, {1100, 33145}, {1330, 27714}, {1647, 33107}, {1707, 29661}, {1836, 62821}, {1961, 17484}, {1962, 17768}, {1999, 48642}, {2292, 49743}, {2308, 5249}, {2392, 3060}, {2650, 44669}, {2795, 50181}, {2796, 27804}, {2895, 8013}, {3218, 29688}, {3578, 27798}, {3622, 12579}, {3649, 51654}, {3662, 29684}, {3664, 3720}, {3681, 50301}, {3745, 32856}, {3758, 25957}, {3772, 62846}, {3821, 19717}, {3877, 48825}, {3879, 4365}, {3914, 4667}, {3923, 63056}, {3925, 4722}, {3936, 4697}, {3938, 4307}, {3944, 14996}, {3980, 31034}, {4001, 30970}, {4024, 52208}, {4038, 5057}, {4046, 4938}, {4062, 4418}, {4138, 29863}, {4349, 29816}, {4363, 32852}, {4414, 5712}, {4416, 59306}, {4425, 8025}, {4610, 40164}, {4644, 32912}, {4649, 20292}, {4654, 33143}, {4655, 19684}, {4672, 18139}, {4795, 31134}, {4831, 62689}, {4854, 63401}, {4980, 17772}, {4981, 17771}, {5311, 5905}, {5333, 8040}, {5492, 63374}, {5542, 29818}, {5692, 48868}, {5852, 42039}, {5880, 61358}, {6147, 62847}, {6327, 29685}, {6535, 32846}, {6690, 9340}, {7321, 32924}, {8682, 50258}, {9345, 24703}, {9347, 33101}, {10180, 28558}, {11246, 46904}, {11263, 17173}, {13486, 14844}, {16468, 27186}, {16477, 26724}, {17011, 32857}, {17019, 33099}, {17120, 29850}, {17155, 50128}, {17163, 50256}, {17184, 33682}, {17187, 53541}, {17298, 29677}, {17300, 32930}, {17350, 29854}, {17364, 31330}, {17378, 32915}, {17379, 32776}, {17599, 62223}, {17726, 42038}, {17889, 37685}, {18165, 53542}, {20064, 29651}, {21027, 32864}, {21085, 63071}, {21141, 23763}, {24231, 29819}, {24392, 33104}, {24892, 62812}, {25385, 37639}, {26223, 29687}, {26842, 29821}, {27812, 50277}, {29639, 62240}, {29675, 30652}, {29686, 33069}, {29690, 32913}, {31019, 62841}, {31037, 59628}, {31053, 37604}, {32780, 48650}, {32859, 50302}, {32919, 62230}, {32940, 33073}, {33096, 37633}, {33103, 62807}, {33111, 62795}, {33154, 62801}, {38456, 50234}, {41814, 42437}, {49564, 64071}, {53388, 59584}, {62849, 64016}, {62867, 63979}

X(64164) = midpoint of X(i) and X(j) for these {i,j}: {17163, 50256}
X(64164) = reflection of X(i) in X(j) for these {i,j}: {2, 23812}, {1962, 37631}, {3578, 27798}
X(64164) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2248, 41821}, {13610, 2891}
X(64164) = pole of line {21192, 31010} with respect to the Steiner circumellipse
X(64164) = pole of line {8013, 32101} with respect to the Wallace hyperbola
X(64164) = pole of line {17169, 17190} with respect to the dual conic of Yff parabola
X(64164) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4024), X(14844)}}, {{A, B, C, X(6628), X(43972)}}, {{A, B, C, X(13486), X(52208)}}
X(64164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {86, 4683, 6536}, {1046, 26131, 21674}, {2895, 24342, 8013}, {3664, 41011, 3720}, {3925, 7277, 4722}, {4418, 17778, 4062}, {5333, 24697, 8040}, {8025, 17491, 4425}, {17768, 37631, 1962}, {17770, 23812, 2}, {33100, 41819, 1}

X(64165) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(37)-CROSSPEDAL-OF-X(1) AND ASCELLA

Barycentrics    a*(a^2+5*a*(b+c)-2*(b^2-b*c+c^2)) : :
X(64165) = -2*X[4364]+3*X[48830], -2*X[4407]+3*X[48822], -4*X[4472]+3*X[48802], -2*X[4690]+3*X[48851]

X(64165) lies on these lines: {1, 6}, {8, 17378}, {10, 17313}, {42, 17595}, {55, 62795}, {75, 49680}, {81, 41711}, {88, 1002}, {89, 100}, {145, 5695}, {190, 3241}, {239, 51055}, {320, 48829}, {519, 4363}, {524, 36479}, {528, 4644}, {537, 17318}, {599, 29659}, {651, 2099}, {678, 37540}, {894, 49460}, {999, 4557}, {1086, 50282}, {1155, 59234}, {1159, 2809}, {1376, 37520}, {1443, 7672}, {1456, 11526}, {2242, 52965}, {2334, 3868}, {3052, 3979}, {3244, 32935}, {3306, 21870}, {3617, 17300}, {3621, 20090}, {3634, 17265}, {3679, 17374}, {3681, 17021}, {3711, 37633}, {3715, 29814}, {3717, 29601}, {3729, 49475}, {3736, 18198}, {3742, 54390}, {3755, 4887}, {3758, 48805}, {3789, 30950}, {3873, 17012}, {3879, 49688}, {3912, 47359}, {3932, 29583}, {3939, 56177}, {3940, 62844}, {4085, 7232}, {4361, 49479}, {4364, 48830}, {4383, 62867}, {4393, 24841}, {4407, 48822}, {4413, 54309}, {4423, 62866}, {4428, 4641}, {4430, 17013}, {4472, 48802}, {4657, 49505}, {4675, 49772}, {4684, 29596}, {4690, 48851}, {4693, 49721}, {4702, 50127}, {4753, 24331}, {4851, 49529}, {4883, 8167}, {4896, 5880}, {4924, 64174}, {4942, 32915}, {4954, 24344}, {4966, 29579}, {5222, 51099}, {5228, 53531}, {5542, 17067}, {5550, 17352}, {5708, 50587}, {5852, 64168}, {9053, 50284}, {9330, 40434}, {9347, 14969}, {9780, 17234}, {11269, 37691}, {12702, 29311}, {14077, 53535}, {14190, 60698}, {14996, 62236}, {15668, 49457}, {16694, 37507}, {16826, 50075}, {16831, 51034}, {16832, 51061}, {17018, 62796}, {17023, 47358}, {17051, 63126}, {17118, 49459}, {17119, 31178}, {17160, 24349}, {17262, 49471}, {17269, 49764}, {17281, 49763}, {17290, 50287}, {17293, 50315}, {17311, 33165}, {17319, 49501}, {17369, 50316}, {17461, 41434}, {17597, 61358}, {17601, 32913}, {17721, 61652}, {19654, 52981}, {20072, 49746}, {21358, 36478}, {23344, 37606}, {23345, 29350}, {23511, 58560}, {24342, 49689}, {24594, 62296}, {24597, 37703}, {24715, 62223}, {26626, 50999}, {28600, 62711}, {29598, 51003}, {29624, 50835}, {29660, 47352}, {32846, 59407}, {32921, 49535}, {33076, 40341}, {36534, 46922}, {40587, 53114}, {41847, 49450}, {46934, 63051}, {47356, 49771}, {49453, 49499}, {49483, 49495}, {49488, 49491}, {49714, 50286}, {49740, 54280}, {50017, 50131}, {50023, 50283}, {50303, 53534}, {50310, 62231}, {50311, 61344}, {51463, 63008}, {62230, 63139}, {62863, 63074}

X(64165) = X(i)-isoconjugate-of-X(j) for these {i, j}: {514, 28911}
X(64165) = pole of line {17494, 47767} with respect to the Steiner circumellipse
X(64165) = pole of line {100, 28911} with respect to the Hutson-Moses hyperbola
X(64165) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(39428)}}, {{A, B, C, X(37), X(56151)}}, {{A, B, C, X(44), X(1002)}}, {{A, B, C, X(45), X(55935)}}, {{A, B, C, X(88), X(1001)}}, {{A, B, C, X(89), X(3246)}}, {{A, B, C, X(518), X(28910)}}, {{A, B, C, X(1023), X(37138)}}, {{A, B, C, X(1390), X(16672)}}, {{A, B, C, X(16676), X(39959)}}, {{A, B, C, X(34893), X(36404)}}
X(64165) = barycentric product X(i)*X(j) for these (i, j): {100, 28910}
X(64165) = barycentric quotient X(i)/X(j) for these (i, j): {692, 28911}, {28910, 693}
X(64165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3751, 44}, {1, 44, 1001}, {17601, 32913, 54281}, {49764, 50313, 17269}

X(64166) = MIDPOINT OF X(1)X(4641)

Barycentrics    a*(4*a^3+2*a*b*c+3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(64166) = -5*X[3616]+X[32859]

X(64166) lies on these lines: {1, 3683}, {3, 1453}, {6, 24929}, {10, 50059}, {21, 17011}, {30, 40940}, {31, 517}, {43, 37589}, {44, 30115}, {56, 56848}, {58, 942}, {72, 62802}, {204, 7497}, {238, 5429}, {239, 4234}, {376, 5222}, {392, 17127}, {405, 5287}, {500, 1193}, {518, 49480}, {519, 44416}, {527, 39544}, {536, 49683}, {540, 1125}, {551, 3246}, {580, 31793}, {593, 51420}, {595, 9957}, {601, 31787}, {759, 58970}, {859, 40956}, {902, 51787}, {956, 62834}, {960, 63292}, {964, 39564}, {993, 1386}, {995, 5126}, {999, 7290}, {1064, 20978}, {1100, 4653}, {1191, 3157}, {1203, 2646}, {1279, 5049}, {1319, 2003}, {1325, 33774}, {1385, 16466}, {1419, 13462}, {1451, 37544}, {1455, 55086}, {1468, 5045}, {1724, 5044}, {1743, 3940}, {1829, 14015}, {1999, 13735}, {2257, 38292}, {3073, 9856}, {3419, 24597}, {3488, 37666}, {3576, 16469}, {3579, 54418}, {3616, 32859}, {3666, 52680}, {3745, 5251}, {3748, 16474}, {3752, 4257}, {3753, 17126}, {3824, 49745}, {3838, 50757}, {3877, 30653}, {3914, 28146}, {3915, 31792}, {3916, 5262}, {3924, 31794}, {3931, 54354}, {3961, 5247}, {4195, 5295}, {4245, 37609}, {4252, 37582}, {4304, 48847}, {4384, 19276}, {4665, 50053}, {4708, 49729}, {4719, 5267}, {5230, 18480}, {5256, 16370}, {5269, 9708}, {5271, 16394}, {5302, 30142}, {5313, 37600}, {5396, 40958}, {5440, 32911}, {5482, 34281}, {5716, 5791}, {5717, 6675}, {5722, 37642}, {5806, 37530}, {5814, 37176}, {6679, 38456}, {6767, 62875}, {9955, 13408}, {11018, 54321}, {11108, 37554}, {11112, 26723}, {11227, 37469}, {11269, 18527}, {11354, 11679}, {11357, 16831}, {13151, 51340}, {13587, 17020}, {15934, 16485}, {16417, 23511}, {16478, 37592}, {16483, 51788}, {16498, 62865}, {16572, 43136}, {16832, 19332}, {16857, 17022}, {16858, 17019}, {16861, 17021}, {17012, 17549}, {17014, 50742}, {17365, 26728}, {17564, 45204}, {18541, 23681}, {20083, 50050}, {21764, 43065}, {23168, 28383}, {23536, 31776}, {23537, 64159}, {24299, 36750}, {24473, 62795}, {28082, 50192}, {28154, 33128}, {28160, 61647}, {28202, 33094}, {28466, 54369}, {29571, 50202}, {29603, 50410}, {29816, 62847}, {29821, 37599}, {29833, 49735}, {29841, 48814}, {33596, 37509}, {34255, 51673}, {37732, 40262}, {42819, 62844}, {44417, 48866}, {44663, 49682}, {46974, 64157}, {47040, 50124}, {50759, 63979}, {64017, 64110}

X(64166) = midpoint of X(i) and X(j) for these {i,j}: {1, 4641}
X(64166) = pole of line {1710, 3601} with respect to the Feuerbach hyperbola
X(64166) = pole of line {18465, 34772} with respect to the Stammler hyperbola
X(64166) = barycentric product X(i)*X(j) for these (i, j): {64167, 81}
X(64166) = barycentric quotient X(i)/X(j) for these (i, j): {64167, 321}
X(64166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58, 1104, 942}, {405, 62809, 37594}, {3752, 4257, 5122}, {16485, 62812, 15934}

X(64167) = COMPLEMENT OF X(4720)

Barycentrics    (b+c)*(4*a^3+2*a*b*c+3*a^2*(b+c)+(b-c)^2*(b+c)) : :
X(64167) = -3*X[2]+X[4720]

X(64167) lies on these lines: {1, 442}, {2, 4720}, {3, 63078}, {4, 41083}, {5, 19767}, {6, 11113}, {8, 4205}, {10, 4046}, {12, 59301}, {29, 56301}, {30, 81}, {42, 12081}, {58, 57002}, {69, 50056}, {72, 4656}, {79, 63310}, {80, 11069}, {86, 50169}, {145, 5051}, {333, 13745}, {381, 63008}, {386, 4187}, {387, 405}, {407, 1068}, {429, 6198}, {440, 3488}, {495, 3136}, {496, 3142}, {517, 40952}, {519, 1211}, {529, 16474}, {551, 21242}, {758, 4854}, {851, 999}, {857, 17014}, {860, 63965}, {938, 18641}, {940, 11112}, {942, 58889}, {952, 17015}, {956, 4199}, {1046, 3650}, {1100, 12690}, {1145, 2092}, {1213, 3247}, {1329, 5312}, {1449, 1901}, {1483, 30449}, {1532, 5396}, {1837, 51557}, {2238, 50282}, {2245, 5119}, {2475, 41819}, {2650, 63997}, {3017, 4653}, {3057, 10974}, {3058, 62828}, {3178, 58399}, {3216, 17575}, {3240, 3820}, {3241, 3936}, {3244, 3454}, {3295, 37225}, {3543, 62997}, {3555, 10381}, {3649, 36250}, {3663, 24473}, {3743, 21677}, {3753, 3755}, {3816, 5313}, {3868, 50067}, {3946, 4904}, {3948, 4737}, {4065, 4918}, {4204, 9708}, {4255, 13747}, {4256, 37634}, {4340, 50239}, {4383, 48857}, {4393, 26601}, {4487, 62588}, {4648, 44217}, {4649, 53501}, {4658, 49745}, {4692, 53478}, {4780, 50083}, {4868, 16577}, {5256, 5722}, {5262, 12433}, {5292, 7483}, {5315, 49736}, {5331, 37357}, {5434, 62844}, {5439, 24175}, {5440, 39595}, {5453, 37401}, {5707, 37468}, {5712, 17532}, {5718, 17530}, {5719, 33133}, {5721, 8226}, {5739, 54367}, {5799, 10454}, {5902, 11809}, {6155, 21965}, {6175, 37635}, {6284, 62805}, {6675, 24883}, {6925, 62183}, {8025, 50171}, {8614, 63309}, {9844, 58890}, {9957, 22076}, {10149, 30447}, {10449, 13728}, {10459, 64200}, {10543, 63292}, {10950, 30446}, {11111, 37666}, {11114, 37685}, {11355, 15048}, {11361, 20145}, {14020, 19742}, {14986, 37154}, {14996, 17579}, {15170, 62848}, {15171, 57280}, {15172, 62804}, {15934, 19785}, {16086, 34064}, {16137, 63333}, {16370, 37642}, {16394, 63013}, {16418, 24597}, {16589, 49772}, {16704, 49735}, {17276, 50066}, {17300, 17678}, {17372, 50051}, {17381, 50323}, {17525, 52680}, {17533, 37662}, {17537, 19743}, {17542, 37650}, {17556, 63089}, {17677, 17778}, {18134, 48858}, {19684, 37150}, {19732, 51679}, {20018, 52258}, {21024, 29659}, {21031, 50587}, {23905, 50016}, {24210, 51409}, {25526, 49734}, {26064, 49718}, {26117, 49716}, {26728, 50103}, {26860, 50172}, {27081, 31145}, {29829, 49492}, {31156, 63067}, {31782, 37399}, {31938, 63396}, {32782, 50058}, {32847, 53423}, {33134, 39542}, {33155, 39544}, {33172, 48815}, {36195, 54315}, {36750, 37290}, {37038, 37683}, {37230, 63296}, {37298, 37646}, {37374, 63982}, {37447, 48903}, {37594, 57287}, {37652, 48814}, {37655, 51665}, {37674, 48842}, {37716, 42042}, {37722, 50604}, {40721, 47286}, {41015, 53387}, {44094, 56960}, {44150, 62697}, {47032, 63338}, {48813, 63057}, {48819, 62850}, {48861, 63074}, {48863, 51672}, {49459, 56953}, {49490, 53476}, {49728, 64072}, {49744, 63401}, {50749, 63287}

X(64167) = reflection of X(i) in X(j) for these {i,j}: {4046, 10}
X(64167) = complement of X(4720)
X(64167) = X(i)-complementary conjugate of X(j) for these {i, j}: {65, 21251}, {89, 21246}, {1042, 17057}, {1402, 16590}, {2163, 960}, {4017, 15614}, {28607, 5745}, {28658, 3452}, {30588, 21244}, {51641, 61073}, {53114, 1329}, {55246, 124}
X(64167) = pole of line {9, 484} with respect to the Kiepert hyperbola
X(64167) = pole of line {7178, 50449} with respect to the Steiner inellipse
X(64167) = pole of line {5745, 7359} with respect to the dual conic of Yff parabola
X(64167) = intersection, other than A, B, C, of circumconics {{A, B, C, X(37887), X(60243)}}, {{A, B, C, X(41501), X(54786)}}
X(64167) = barycentric product X(i)*X(j) for these (i, j): {321, 64166}
X(64167) = barycentric quotient X(i)/X(j) for these (i, j): {64166, 81}
X(64167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1834, 442}, {940, 48837, 11112}, {3017, 4653, 35466}, {3017, 49739, 15670}, {33155, 63159, 39544}, {35466, 49739, 4653}, {36250, 63354, 3649}, {48903, 63318, 37447}

X(64168) = ORTHOLOGY CENTER OF THESE TRIANGLES: MIXTILINEAR AND X(57)-CROSSPEDAL-OF-X(1)

Barycentrics    a^3-3*a^2*(b+c)-(b-c)^2*(b+c)-a*(b+c)^2 : :
X(64168) = -9*X[38314]+8*X[50293], -8*X[50312]+9*X[53620]

X(64168) lies on these lines: {1, 7}, {2, 968}, {4, 941}, {6, 5698}, {8, 192}, {9, 3755}, {10, 346}, {11, 56755}, {37, 2550}, {38, 36845}, {40, 1400}, {42, 329}, {43, 18228}, {45, 38057}, {55, 1284}, {65, 11997}, {69, 24723}, {75, 39581}, {81, 44447}, {142, 7613}, {144, 3751}, {145, 5847}, {165, 39595}, {171, 9778}, {190, 59406}, {200, 4656}, {226, 37553}, {238, 5222}, {344, 4429}, {345, 32773}, {377, 62831}, {387, 1723}, {388, 37548}, {391, 4780}, {443, 6051}, {452, 54418}, {497, 3666}, {517, 7961}, {518, 4419}, {528, 48856}, {536, 48849}, {581, 52024}, {612, 17784}, {726, 36479}, {752, 3241}, {774, 938}, {846, 5273}, {894, 24280}, {940, 3474}, {944, 29207}, {950, 4907}, {954, 28071}, {958, 45705}, {966, 3696}, {982, 10580}, {988, 14986}, {1001, 4000}, {1058, 37592}, {1086, 38053}, {1100, 64016}, {1125, 4779}, {1159, 28905}, {1193, 41828}, {1253, 5766}, {1279, 17301}, {1402, 37400}, {1423, 1697}, {1463, 5919}, {1469, 3057}, {1486, 41230}, {1503, 1854}, {1621, 19785}, {1633, 36740}, {1698, 25072}, {1707, 37666}, {1711, 62777}, {1722, 5129}, {1736, 4424}, {1743, 51090}, {1757, 6172}, {1836, 5712}, {1962, 33094}, {1999, 63140}, {2177, 63168}, {2269, 6210}, {2285, 12717}, {2310, 5809}, {2345, 4026}, {2551, 4646}, {2796, 35578}, {2899, 59299}, {2999, 40998}, {3027, 19637}, {3058, 17599}, {3086, 17077}, {3091, 5530}, {3161, 4085}, {3175, 3974}, {3194, 21148}, {3240, 31018}, {3242, 17246}, {3247, 64174}, {3295, 28015}, {3416, 17314}, {3421, 64175}, {3434, 28606}, {3475, 3782}, {3485, 19765}, {3487, 48944}, {3551, 7320}, {3586, 52856}, {3616, 16484}, {3617, 3790}, {3618, 4676}, {3622, 26806}, {3673, 60720}, {3677, 64162}, {3679, 50100}, {3720, 9776}, {3736, 17183}, {3744, 10385}, {3750, 10578}, {3752, 26105}, {3757, 30699}, {3823, 41313}, {3836, 29627}, {3869, 54383}, {3875, 3883}, {3886, 4357}, {3891, 50071}, {3896, 5739}, {3920, 20075}, {3923, 5749}, {3932, 48829}, {3944, 5226}, {3946, 7290}, {3961, 64146}, {3971, 5423}, {3993, 4660}, {3995, 10327}, {4008, 17863}, {4078, 39570}, {4183, 17903}, {4360, 51192}, {4363, 28530}, {4366, 26626}, {4402, 16825}, {4414, 5744}, {4415, 25568}, {4416, 49495}, {4427, 29829}, {4428, 17061}, {4454, 28526}, {4488, 32935}, {4512, 40940}, {4640, 37642}, {4643, 28581}, {4644, 17768}, {4645, 17316}, {4648, 5880}, {4649, 24695}, {4653, 62389}, {4655, 21296}, {4657, 49484}, {4659, 28557}, {4664, 32850}, {4679, 63126}, {4684, 17274}, {4689, 5218}, {4693, 29611}, {4716, 50296}, {4732, 62608}, {4847, 62818}, {4899, 50090}, {4972, 17776}, {5057, 63008}, {5250, 28287}, {5263, 17321}, {5274, 24239}, {5281, 9746}, {5308, 20533}, {5435, 17596}, {5550, 17383}, {5554, 25245}, {5657, 37715}, {5686, 49772}, {5703, 37573}, {5711, 6361}, {5716, 6284}, {5717, 41869}, {5758, 37529}, {5772, 29659}, {5811, 37699}, {5815, 50581}, {5839, 49486}, {5846, 17318}, {5852, 64165}, {5853, 7174}, {5905, 17018}, {6007, 35628}, {6244, 56218}, {6327, 27804}, {6650, 29570}, {6767, 28915}, {6872, 17016}, {7071, 7952}, {7080, 27282}, {8055, 59511}, {8143, 18517}, {8543, 37800}, {9441, 59418}, {9779, 17717}, {9780, 17280}, {9812, 17592}, {9965, 62819}, {10030, 62697}, {10186, 37617}, {10198, 36250}, {10480, 39780}, {10572, 15430}, {10582, 24177}, {11415, 19767}, {11529, 28881}, {11533, 12536}, {12053, 30097}, {12541, 59310}, {13097, 20760}, {13161, 26125}, {13576, 60108}, {13736, 16824}, {14267, 56854}, {14450, 17481}, {14523, 63972}, {14552, 17156}, {14956, 25060}, {15254, 37650}, {15507, 37502}, {15933, 28854}, {16469, 50114}, {16475, 17014}, {16667, 64017}, {16676, 38200}, {17258, 49450}, {17261, 27549}, {17262, 49524}, {17275, 49468}, {17276, 49478}, {17299, 49461}, {17319, 50289}, {17334, 64070}, {17358, 19877}, {17395, 38315}, {17593, 24217}, {17601, 64108}, {17772, 20050}, {17869, 26165}, {17950, 28849}, {18141, 33068}, {19822, 64010}, {19823, 26230}, {19843, 62871}, {19855, 54287}, {20057, 28494}, {20073, 62222}, {20101, 58820}, {20182, 63979}, {20292, 62840}, {20539, 41269}, {21806, 24725}, {23793, 26824}, {23903, 53424}, {24325, 31995}, {24597, 62838}, {24703, 63089}, {24929, 60751}, {25421, 59311}, {26034, 32915}, {26040, 44307}, {26132, 29839}, {26228, 33155}, {27286, 27517}, {28081, 34937}, {28534, 63054}, {28610, 32913}, {29327, 36474}, {29571, 38052}, {29573, 49630}, {29814, 33102}, {29965, 41012}, {31183, 38059}, {31189, 31289}, {31393, 52896}, {31730, 37554}, {32087, 49474}, {32099, 33082}, {32776, 33171}, {32922, 49746}, {32936, 33163}, {32947, 33088}, {33097, 41825}, {33099, 42042}, {33142, 55868}, {33145, 62849}, {34379, 64015}, {36706, 44735}, {36746, 64190}, {36991, 64134}, {37574, 48932}, {37608, 48925}, {37655, 39594}, {38037, 53599}, {38047, 54389}, {38314, 50293}, {40718, 59297}, {41011, 63007}, {49446, 49466}, {49523, 49688}, {49747, 51099}, {50044, 59760}, {50079, 51054}, {50122, 51665}, {50312, 53620}, {53020, 62183}, {56809, 60785}, {59408, 61330}, {60714, 64083}, {62796, 64153}

X(64168) = reflection of X(i) in X(j) for these {i,j}: {1, 4356}, {8, 50295}, {4307, 1}, {35578, 48830}, {50284, 50281}, {50314, 50290}
X(64168) = anticomplement of X(50314)
X(64168) = perspector of circumconic {{A, B, C, X(658), X(27805)}}
X(64168) = X(i)-Dao conjugate of X(j) for these {i, j}: {50314, 50314}
X(64168) = pole of line {514, 50508} with respect to the incircle
X(64168) = pole of line {4367, 26275} with respect to the mixtilinear incircles radical circle
X(64168) = pole of line {905, 44432} with respect to the orthoptic circle of the Steiner Inellipse
X(64168) = pole of line {23880, 54229} with respect to the polar circle
X(64168) = pole of line {354, 1469} with respect to the Feuerbach hyperbola
X(64168) = pole of line {14543, 21295} with respect to the Kiepert parabola
X(64168) = pole of line {661, 4025} with respect to the Steiner circumellipse
X(64168) = pole of line {7658, 25666} with respect to the Steiner inellipse
X(64168) = pole of line {3732, 53332} with respect to the Yff parabola
X(64168) = pole of line {1043, 17103} with respect to the Wallace hyperbola
X(64168) = pole of line {514, 4170} with respect to the Suppa-Cucoanes circle
X(64168) = pole of line {4529, 47130} with respect to the dual conic of incircle
X(64168) = pole of line {7, 391} with respect to the dual conic of Yff parabola
X(64168) = pole of line {52335, 53559} with respect to the dual conic of Wallace hyperbola
X(64168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(4451)}}, {{A, B, C, X(8), X(7176)}}, {{A, B, C, X(77), X(941)}}, {{A, B, C, X(256), X(269)}}, {{A, B, C, X(257), X(279)}}, {{A, B, C, X(346), X(3945)}}, {{A, B, C, X(3551), X(7271)}}, {{A, B, C, X(3664), X(56144)}}, {{A, B, C, X(4073), X(7184)}}, {{A, B, C, X(4307), X(14942)}}, {{A, B, C, X(4321), X(43751)}}, {{A, B, C, X(7675), X(28071)}}, {{A, B, C, X(56382), X(60321)}}
X(64168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1770, 4340}, {1, 3663, 4310}, {1, 4294, 4339}, {1, 4312, 3664}, {1, 4862, 5542}, {1, 516, 4307}, {8, 9791, 17257}, {175, 176, 7176}, {390, 3672, 1}, {740, 50295, 8}, {752, 50281, 50284}, {846, 33137, 5273}, {1836, 37593, 5712}, {2796, 48830, 35578}, {3416, 49462, 17314}, {3750, 33144, 10578}, {4026, 5695, 2345}, {5222, 52653, 238}, {5880, 15569, 4648}, {17018, 33100, 5905}, {17592, 33095, 26098}, {17594, 24210, 2}, {26098, 33095, 9812}, {28580, 50290, 50314}, {33155, 61155, 26228}, {37548, 50065, 388}, {37614, 64158, 3486}, {50281, 50284, 3241}

X(64169) = PERSPECTOR OF THESE TRIANGLES: X(65)-CROSSPEDAL-OF-X(1) AND CEVIAN OF X(81)

Barycentrics    a^2*(b+c)*(a^2-b*c-a*(b+c)) : :

X(64169) lies on these lines: {1, 5132}, {3, 4497}, {6, 31}, {9, 22271}, {10, 1001}, {35, 3286}, {37, 4068}, {43, 16690}, {81, 40433}, {82, 39971}, {86, 100}, {171, 18166}, {226, 15320}, {228, 37593}, {238, 3293}, {239, 16684}, {284, 692}, {497, 44411}, {584, 2175}, {594, 4433}, {673, 2346}, {869, 16685}, {872, 3747}, {894, 4436}, {941, 23381}, {956, 49680}, {958, 59302}, {993, 49497}, {1018, 21865}, {1030, 17798}, {1100, 2223}, {1260, 4061}, {1334, 4878}, {1376, 15668}, {1439, 53321}, {1442, 2283}, {1449, 3941}, {1486, 4254}, {1500, 41333}, {1621, 3996}, {1626, 54312}, {1631, 36744}, {1634, 38814}, {1697, 22299}, {1826, 7071}, {1911, 40519}, {2082, 22297}, {2174, 35327}, {2183, 4343}, {2200, 4258}, {2245, 52020}, {2270, 3185}, {2667, 20964}, {3256, 7175}, {3285, 7122}, {3294, 40607}, {3303, 59305}, {3589, 8299}, {3663, 24405}, {3666, 18183}, {3693, 58633}, {3724, 21806}, {3736, 33771}, {3745, 54327}, {3750, 45223}, {3757, 20174}, {3759, 23407}, {3870, 22275}, {3871, 5263}, {3931, 52359}, {3939, 55100}, {4263, 4749}, {4267, 37573}, {4271, 21746}, {4361, 22316}, {4366, 18082}, {4423, 59306}, {4428, 4685}, {4447, 17390}, {4667, 41430}, {4689, 23845}, {4705, 58336}, {4854, 21319}, {4946, 61159}, {5276, 20875}, {5312, 16287}, {5313, 22083}, {7083, 23855}, {7234, 53535}, {7289, 17594}, {8300, 56131}, {8641, 57232}, {8715, 50302}, {9669, 39583}, {10013, 34445}, {10389, 22278}, {11248, 37474}, {13405, 34830}, {13476, 20367}, {15485, 31855}, {15571, 49471}, {15622, 63434}, {16484, 19265}, {16503, 22279}, {16666, 16694}, {16667, 16688}, {16678, 17018}, {16687, 17011}, {16777, 34247}, {16792, 61172}, {16884, 21010}, {17246, 21320}, {17261, 23343}, {17262, 21080}, {17318, 64170}, {17332, 45705}, {17349, 19998}, {17463, 25065}, {18755, 21788}, {19763, 23383}, {19765, 23361}, {20162, 41233}, {20713, 22021}, {20878, 41328}, {20963, 23370}, {21061, 44671}, {21796, 39688}, {21801, 42446}, {21840, 58384}, {21858, 40732}, {22298, 54359}, {22313, 63522}, {22328, 41239}, {23398, 60724}, {23846, 37548}, {23851, 40728}, {23854, 23868}, {23865, 50487}, {24394, 59727}, {27164, 56181}, {29437, 29824}, {37510, 37621}, {37575, 49478}, {37677, 61157}, {37679, 59309}, {40954, 51377}, {42819, 53307}, {49462, 60723}, {49486, 54410}, {52024, 55323}, {52897, 60714}

X(64169) = isogonal conjugate of X(39734)
X(64169) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 39734}, {2, 39950}, {6, 40004}, {58, 40216}, {81, 17758}, {86, 13476}, {274, 2350}, {513, 53649}, {693, 43076}, {1014, 55076}, {1019, 54118}, {1414, 60478}
X(64169) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 39734}, {9, 40004}, {10, 40216}, {1500, 321}, {3720, 20888}, {3925, 20880}, {17761, 693}, {32664, 39950}, {39026, 53649}, {40586, 17758}, {40600, 13476}, {40608, 60478}
X(64169) = X(i)-Ceva conjugate of X(j) for these {i, j}: {81, 213}, {100, 4040}, {1621, 3294}, {2346, 37}, {40433, 6}, {40435, 220}
X(64169) = pole of line {649, 2664} with respect to the circumcircle
X(64169) = pole of line {86, 5284} with respect to the Stammler hyperbola
X(64169) = pole of line {4468, 6586} with respect to the Steiner inellipse
X(64169) = pole of line {310, 29824} with respect to the Wallace hyperbola
X(64169) = pole of line {2140, 17278} with respect to the dual conic of Yff parabola
X(64169) = pole of line {21207, 62429} with respect to the dual conic of Wallace hyperbola
X(64169) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(8053)}}, {{A, B, C, X(6), X(3294)}}, {{A, B, C, X(10), X(22277)}}, {{A, B, C, X(31), X(1621)}}, {{A, B, C, X(37), X(672)}}, {{A, B, C, X(42), X(4651)}}, {{A, B, C, X(55), X(3996)}}, {{A, B, C, X(71), X(20616)}}, {{A, B, C, X(86), X(4040)}}, {{A, B, C, X(210), X(14547)}}, {{A, B, C, X(226), X(40606)}}, {{A, B, C, X(256), X(20954)}}, {{A, B, C, X(523), X(21804)}}, {{A, B, C, X(674), X(4151)}}, {{A, B, C, X(1011), X(14004)}}, {{A, B, C, X(1334), X(2293)}}, {{A, B, C, X(1500), X(21035)}}, {{A, B, C, X(1914), X(21007)}}, {{A, B, C, X(2276), X(4043)}}, {{A, B, C, X(2486), X(4516)}}, {{A, B, C, X(3286), X(4068)}}, {{A, B, C, X(4557), X(54325)}}, {{A, B, C, X(10013), X(20992)}}, {{A, B, C, X(18152), X(39967)}}, {{A, B, C, X(22301), X(43073)}}, {{A, B, C, X(24388), X(40599)}}, {{A, B, C, X(36635), X(55919)}}, {{A, B, C, X(39734), X(40586)}}
X(64169) = barycentric product X(i)*X(j) for these (i, j): {1, 3294}, {10, 4251}, {31, 4043}, {101, 4151}, {1018, 4040}, {1252, 2486}, {1334, 55082}, {1400, 3996}, {1621, 37}, {2205, 40088}, {2321, 55086}, {4069, 58324}, {4651, 6}, {14004, 71}, {17143, 213}, {17277, 42}, {17494, 4557}, {18098, 56537}, {18152, 1918}, {20616, 21}, {21007, 3952}, {21727, 662}, {38859, 4515}, {40094, 41333}, {40433, 62646}, {40521, 57148}, {40607, 81}, {43915, 6605}, {55340, 56255}, {58361, 692}
X(64169) = barycentric quotient X(i)/X(j) for these (i, j): {1, 40004}, {6, 39734}, {31, 39950}, {37, 40216}, {42, 17758}, {101, 53649}, {213, 13476}, {1334, 55076}, {1621, 274}, {1918, 2350}, {2486, 23989}, {3294, 75}, {3709, 60478}, {3996, 28660}, {4040, 7199}, {4043, 561}, {4151, 3261}, {4251, 86}, {4557, 54118}, {4651, 76}, {14004, 44129}, {17143, 6385}, {17277, 310}, {17494, 52619}, {20616, 1441}, {21007, 7192}, {21727, 1577}, {22160, 15419}, {32739, 43076}, {38346, 17205}, {38365, 17197}, {40607, 321}, {43915, 59181}, {55086, 1434}, {55340, 16708}, {56537, 16703}, {58361, 40495}, {62646, 20888}
X(64169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 15624, 20990}, {1, 5132, 20470}, {6, 55, 8053}, {35, 4649, 3286}, {37, 21889, 21804}, {42, 1918, 6}, {42, 2269, 22301}, {42, 55, 52139}, {42, 71, 22277}, {1100, 2223, 16679}, {3295, 37502, 1001}, {4068, 4557, 37}, {36744, 37580, 1631}

X(64170) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(65)-CROSSPEDAL-OF-X(1) AND PEDAL-OF-X(31)

Barycentrics    a*(-2*b^2*c^2+a^3*(b+c)+a*b*c*(b+c)-a^2*(b^2+b*c+c^2)) : :

X(64170) lies on these lines: {1, 6}, {2, 20487}, {3, 726}, {7, 4447}, {8, 1284}, {35, 49445}, {36, 49532}, {43, 28358}, {55, 192}, {56, 24349}, {63, 20359}, {69, 21320}, {75, 183}, {86, 24672}, {100, 1278}, {105, 38869}, {190, 7155}, {198, 8301}, {344, 24477}, {346, 8299}, {354, 25099}, {519, 31394}, {536, 4421}, {537, 11194}, {572, 22779}, {573, 14839}, {664, 34057}, {740, 3913}, {742, 24328}, {758, 31395}, {894, 21010}, {983, 1580}, {993, 49520}, {999, 49479}, {1011, 32925}, {1265, 28265}, {1423, 17792}, {1486, 20475}, {1621, 4704}, {1818, 54338}, {2223, 3729}, {2241, 20688}, {2319, 20674}, {2330, 52134}, {2975, 31302}, {2998, 56853}, {3009, 28365}, {3271, 29497}, {3295, 3993}, {3329, 4423}, {3434, 21927}, {3507, 41886}, {3644, 61153}, {3739, 15271}, {3740, 25887}, {3811, 46475}, {3840, 4438}, {3891, 56185}, {3923, 37590}, {3938, 22167}, {3941, 17351}, {3971, 16058}, {4026, 12607}, {4068, 58400}, {4078, 24391}, {4097, 17133}, {4191, 17155}, {4360, 41527}, {4361, 4557}, {4362, 20760}, {4363, 20990}, {4387, 22016}, {4413, 4699}, {4428, 4664}, {4517, 28287}, {4657, 6685}, {4687, 8167}, {4688, 8556}, {4751, 61158}, {5132, 49453}, {5201, 20840}, {5205, 30090}, {5284, 62994}, {5687, 49474}, {6179, 11490}, {6180, 41350}, {7232, 24405}, {7751, 12338}, {7754, 32453}, {8053, 17262}, {8168, 49459}, {8177, 9055}, {8616, 34252}, {8715, 28522}, {10267, 51046}, {10310, 63427}, {11495, 24728}, {11496, 20430}, {11500, 29010}, {13587, 51056}, {16059, 24165}, {16367, 27481}, {16370, 51035}, {16373, 64178}, {16412, 27478}, {16417, 51060}, {16418, 50777}, {16678, 17157}, {17132, 41430}, {17259, 24742}, {17261, 23407}, {17277, 24753}, {17318, 64169}, {17319, 52136}, {17321, 25568}, {17349, 52923}, {17350, 36635}, {17597, 21330}, {18201, 39742}, {19308, 27494}, {20358, 21371}, {20718, 31785}, {20872, 23843}, {20876, 23853}, {21080, 52139}, {21319, 33088}, {22220, 28082}, {24325, 25524}, {24357, 29670}, {24655, 30097}, {24826, 27472}, {25440, 50117}, {26245, 28353}, {27697, 32771}, {28351, 56714}, {29054, 64077}, {30273, 39646}, {30948, 44304}, {31178, 40726}, {32921, 37502}, {32935, 37507}, {33147, 50199}, {37575, 49446}, {37580, 49528}, {41276, 64007}, {49535, 62825}

X(64170) = X(i)-Dao conjugate of X(j) for these {i, j}: {20284, 33890}
X(64170) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2053, 1376}
X(64170) = pole of line {667, 17072} with respect to the circumcircle
X(64170) = pole of line {3903, 4436} with respect to the Kiepert parabola
X(64170) = pole of line {81, 63527} with respect to the Stammler hyperbola
X(64170) = pole of line {3287, 17494} with respect to the Steiner circumellipse
X(64170) = pole of line {274, 3794} with respect to the Wallace hyperbola
X(64170) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(56358)}}, {{A, B, C, X(9), X(7033)}}, {{A, B, C, X(75), X(3061)}}, {{A, B, C, X(220), X(56180)}}, {{A, B, C, X(518), X(2998)}}, {{A, B, C, X(1107), X(41527)}}, {{A, B, C, X(20359), X(24752)}}
X(64170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1403, 7081, 1376}

X(64171) = COMPLEMENT OF X(16465)

Barycentrics    a*(a-b-c)^2*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :
X(64171) = -3*X[375]+2*X[58490], -3*X[3740]+2*X[6690], -X[26892]+3*X[61662]

X(64171) lies on these lines: {1, 37224}, {2, 955}, {4, 8}, {9, 55}, {10, 13567}, {21, 12867}, {25, 59681}, {33, 219}, {37, 3190}, {40, 12664}, {57, 5784}, {63, 971}, {65, 18251}, {69, 21609}, {78, 405}, {100, 51489}, {144, 50696}, {165, 5696}, {169, 17810}, {212, 56178}, {218, 28043}, {226, 518}, {228, 64125}, {333, 7360}, {354, 5231}, {375, 58490}, {377, 37544}, {388, 45039}, {392, 3488}, {394, 2000}, {404, 9858}, {440, 2968}, {442, 942}, {452, 3876}, {461, 27382}, {519, 59638}, {528, 14740}, {573, 3198}, {674, 9969}, {756, 2340}, {908, 8226}, {912, 6907}, {936, 10396}, {950, 960}, {954, 3870}, {956, 18446}, {958, 10393}, {990, 55405}, {997, 25893}, {1005, 3219}, {1006, 5440}, {1071, 6908}, {1145, 12691}, {1259, 31445}, {1329, 10395}, {1350, 21370}, {1376, 1708}, {1445, 37270}, {1490, 3428}, {1621, 63972}, {1698, 10399}, {1728, 8069}, {1731, 40970}, {1736, 25091}, {1737, 25973}, {1750, 5223}, {1858, 21677}, {1861, 26942}, {1887, 7066}, {2099, 4853}, {2182, 5285}, {2287, 2326}, {2318, 7069}, {2321, 41509}, {2323, 56317}, {2550, 41539}, {2893, 4872}, {3056, 40962}, {3057, 12625}, {3195, 22131}, {3218, 17616}, {3306, 10855}, {3452, 14022}, {3474, 17668}, {3475, 15185}, {3487, 3555}, {3522, 9859}, {3586, 5692}, {3611, 31788}, {3651, 3916}, {3678, 6743}, {3679, 18397}, {3686, 9119}, {3696, 17860}, {3697, 7080}, {3706, 24026}, {3729, 12689}, {3740, 6690}, {3812, 61029}, {3868, 5177}, {3872, 50194}, {3878, 51783}, {3925, 61663}, {3927, 37411}, {3928, 63995}, {3940, 6913}, {4046, 4081}, {4061, 8804}, {4082, 51972}, {4199, 44694}, {4312, 41866}, {4413, 61653}, {4511, 5284}, {4531, 23638}, {4640, 58651}, {4652, 31805}, {4662, 6736}, {4882, 5119}, {4915, 25415}, {5045, 10527}, {5220, 20588}, {5273, 10394}, {5435, 17612}, {5436, 25917}, {5437, 61660}, {5562, 5908}, {5687, 55104}, {5729, 58650}, {5744, 10167}, {5745, 10391}, {5759, 17784}, {5766, 64146}, {5779, 56545}, {5809, 18228}, {5836, 15556}, {5842, 63146}, {5904, 9612}, {5928, 50861}, {6067, 60991}, {6068, 33519}, {6260, 32159}, {6598, 44782}, {6889, 9940}, {6987, 64107}, {7085, 64121}, {7308, 61718}, {7411, 60970}, {7522, 10477}, {7680, 21075}, {7957, 36999}, {8232, 34784}, {8255, 58634}, {8270, 34032}, {8580, 10398}, {8581, 62823}, {9534, 52346}, {9778, 25722}, {10310, 58660}, {10392, 18227}, {10529, 16215}, {10530, 16218}, {10538, 30266}, {10569, 64151}, {10578, 30628}, {10861, 21454}, {10916, 50196}, {11035, 62832}, {11113, 51379}, {11227, 59491}, {11517, 32613}, {11997, 40966}, {12128, 62837}, {12526, 12688}, {12527, 63998}, {12528, 37421}, {12680, 62824}, {12690, 64139}, {12915, 26015}, {13257, 46685}, {13405, 58699}, {13754, 49718}, {14547, 40937}, {15064, 21060}, {15569, 63393}, {15587, 52819}, {16053, 27399}, {16193, 26363}, {16845, 27383}, {17355, 58697}, {17532, 31164}, {17625, 24477}, {17642, 24392}, {17728, 58623}, {17768, 41871}, {18255, 56936}, {18607, 61220}, {18750, 48878}, {20344, 22321}, {22027, 29016}, {24473, 50741}, {24644, 30326}, {25006, 51416}, {25939, 62811}, {26040, 60987}, {26052, 41004}, {26892, 61662}, {28125, 61358}, {28609, 31140}, {29331, 59520}, {31053, 52255}, {31789, 31837}, {31793, 57287}, {34791, 63274}, {38454, 61003}, {40292, 41229}, {40958, 43065}, {41015, 60586}, {41538, 64086}, {41559, 63437}, {47373, 58633}, {54203, 64156}, {54289, 64055}, {54430, 56176}, {55016, 58659}, {58632, 61533}, {58636, 59722}, {58688, 64135}, {60969, 62800}, {60978, 61035}, {63961, 64083}

X(64171) = midpoint of X(i) and X(j) for these {i,j}: {72, 3419}, {1824, 26893}, {3059, 42014}, {3428, 14872}, {7957, 36999}, {37584, 40263}
X(64171) = reflection of X(i) in X(j) for these {i,j}: {55, 58648}, {4640, 58651}, {5173, 2886}, {7680, 58631}, {8069, 58649}, {8255, 58634}, {10391, 5745}, {13405, 58699}, {16465, 11018}, {24929, 5044}, {32613, 58630}, {47373, 58633}, {50195, 10}, {61533, 58632}
X(64171) = complement of X(16465)
X(64171) = anticomplement of X(11018)
X(64171) = perspector of circumconic {{A, B, C, X(644), X(6335)}}
X(64171) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 60041}, {57, 2982}, {58, 52560}, {65, 63193}, {222, 40573}, {269, 943}, {279, 2259}, {513, 36048}, {514, 32651}, {1042, 40412}, {1106, 40422}, {1119, 1794}, {1175, 3668}, {1407, 40435}, {1412, 60188}, {1459, 58993}, {1461, 56320}, {3676, 15439}, {7099, 40447}, {40395, 52373}, {40570, 56382}, {43924, 54952}
X(64171) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 60041}, {10, 52560}, {442, 7}, {942, 1439}, {5452, 2982}, {6552, 40422}, {6600, 943}, {7358, 63245}, {11018, 11018}, {15607, 513}, {16585, 1088}, {18591, 279}, {24771, 40435}, {35508, 56320}, {38966, 14775}, {39026, 36048}, {40599, 60188}, {40602, 63193}, {40937, 1446}
X(64171) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3952, 3239}, {6734, 40937}, {36797, 57055}
X(64171) = pole of line {4394, 48383} with respect to the circumcircle
X(64171) = pole of line {513, 14775} with respect to the polar circle
X(64171) = pole of line {9, 1837} with respect to the Feuerbach hyperbola
X(64171) = pole of line {1014, 1175} with respect to the Stammler hyperbola
X(64171) = pole of line {4552, 35341} with respect to the Yff parabola
X(64171) = pole of line {1444, 40412} with respect to the Wallace hyperbola
X(64171) = pole of line {4131, 63245} with respect to the dual conic of polar circle
X(64171) = pole of line {24177, 24181} with respect to the dual conic of Yff parabola
X(64171) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(5758)}}, {{A, B, C, X(4), X(55)}}, {{A, B, C, X(8), X(1260)}}, {{A, B, C, X(9), X(92)}}, {{A, B, C, X(200), X(318)}}, {{A, B, C, X(210), X(442)}}, {{A, B, C, X(219), X(26872)}}, {{A, B, C, X(220), X(14054)}}, {{A, B, C, X(321), X(2287)}}, {{A, B, C, X(329), X(55111)}}, {{A, B, C, X(380), X(46884)}}, {{A, B, C, X(480), X(7046)}}, {{A, B, C, X(517), X(23207)}}, {{A, B, C, X(962), X(4303)}}, {{A, B, C, X(1824), X(40952)}}, {{A, B, C, X(1828), X(40956)}}, {{A, B, C, X(1829), X(20967)}}, {{A, B, C, X(1838), X(10382)}}, {{A, B, C, X(1841), X(2161)}}, {{A, B, C, X(1851), X(7083)}}, {{A, B, C, X(1902), X(61427)}}, {{A, B, C, X(1903), X(2294)}}, {{A, B, C, X(2328), X(5174)}}, {{A, B, C, X(3683), X(42064)}}, {{A, B, C, X(3689), X(38462)}}, {{A, B, C, X(3693), X(46108)}}, {{A, B, C, X(3715), X(3824)}}, {{A, B, C, X(3900), X(56877)}}, {{A, B, C, X(4254), X(46882)}}, {{A, B, C, X(4512), X(5342)}}, {{A, B, C, X(5081), X(58328)}}, {{A, B, C, X(6600), X(59269)}}, {{A, B, C, X(7008), X(45926)}}, {{A, B, C, X(13386), X(60848)}}, {{A, B, C, X(13387), X(60847)}}, {{A, B, C, X(14557), X(14597)}}, {{A, B, C, X(18607), X(30807)}}, {{A, B, C, X(28071), X(40659)}}, {{A, B, C, X(39791), X(43213)}}, {{A, B, C, X(52345), X(56839)}}
X(64171) = barycentric product X(i)*X(j) for these (i, j): {37, 51978}, {200, 5249}, {321, 8021}, {333, 40967}, {346, 942}, {522, 61233}, {1043, 2294}, {1098, 21675}, {1265, 1841}, {1792, 1865}, {1838, 3692}, {1859, 345}, {2260, 341}, {2287, 442}, {2321, 54356}, {2322, 56839}, {3239, 61220}, {3701, 46882}, {3710, 46884}, {4303, 7101}, {4397, 61197}, {6734, 9}, {14547, 312}, {15416, 53323}, {18607, 7046}, {23207, 7017}, {23752, 7259}, {31938, 7110}, {33525, 668}, {36421, 59163}, {40937, 8}, {40956, 59761}, {50354, 6558}, {55010, 56182}, {57055, 61180}, {61161, 7253}, {62779, 728}
X(64171) = barycentric quotient X(i)/X(j) for these (i, j): {9, 60041}, {33, 40573}, {37, 52560}, {55, 2982}, {101, 36048}, {200, 40435}, {210, 60188}, {220, 943}, {284, 63193}, {346, 40422}, {442, 1446}, {644, 54952}, {692, 32651}, {942, 279}, {1253, 2259}, {1783, 58993}, {1802, 1794}, {1838, 1847}, {1841, 1119}, {1859, 278}, {2260, 269}, {2287, 40412}, {2294, 3668}, {3900, 56320}, {4183, 40395}, {4303, 7177}, {5249, 1088}, {6734, 85}, {7046, 40447}, {8021, 81}, {14547, 57}, {14597, 7053}, {18591, 1439}, {18607, 7056}, {23207, 222}, {31938, 17095}, {33525, 513}, {40937, 7}, {40952, 1427}, {40956, 1407}, {40967, 226}, {40978, 1042}, {41393, 20618}, {46882, 1014}, {50354, 58817}, {51978, 274}, {53323, 32714}, {54356, 1434}, {56839, 56382}, {57055, 63245}, {61161, 4566}, {61169, 1020}, {61180, 13149}, {61197, 934}, {61220, 658}, {61233, 664}, {61236, 36118}, {62779, 23062}
X(64171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16465, 11018}, {8, 318, 5295}, {8, 3681, 17658}, {9, 10382, 13615}, {9, 200, 1260}, {55, 210, 58648}, {55, 42014, 42012}, {72, 5927, 329}, {200, 210, 51380}, {210, 1864, 9}, {210, 3059, 200}, {210, 3711, 58696}, {210, 3715, 58635}, {329, 3681, 72}, {329, 5175, 9812}, {442, 14054, 942}, {518, 2886, 5173}, {936, 10396, 37244}, {950, 40661, 960}, {1824, 26893, 517}, {3059, 42014, 15733}, {3678, 12572, 45120}, {3681, 17615, 9954}, {9954, 34790, 3681}, {14547, 40967, 40937}, {15733, 58648, 55}

X(64172) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(31) AND X(75)-CROSSPEDAL-OF-X(1)

Barycentrics    2*a^3*(b+c)+(b^2-c^2)^2+a^2*(b^2+c^2) : :
X(64172) = -3*X[33122]+X[49687], -3*X[33143]+2*X[39544]

X(64172) lies on circumconic {{A, B, C, X(37887), X(60084)}} and on these lines: {1, 442}, {2, 37715}, {3, 5230}, {4, 3195}, {5, 1193}, {6, 1478}, {8, 3891}, {10, 3666}, {11, 995}, {12, 386}, {30, 31}, {36, 37646}, {41, 5305}, {42, 495}, {43, 17757}, {55, 48837}, {56, 5292}, {57, 51421}, {58, 7354}, {65, 23537}, {72, 13161}, {80, 17366}, {149, 62848}, {171, 11112}, {204, 15942}, {213, 5254}, {218, 5286}, {238, 11113}, {355, 54418}, {377, 5711}, {387, 388}, {392, 24210}, {404, 54355}, {496, 1201}, {497, 16483}, {498, 4255}, {515, 5721}, {517, 1072}, {519, 2887}, {524, 4805}, {528, 37610}, {580, 11827}, {595, 6284}, {601, 31775}, {602, 31789}, {607, 41361}, {614, 5722}, {672, 15048}, {758, 3782}, {899, 3820}, {942, 23536}, {952, 30448}, {956, 33137}, {958, 1714}, {978, 4187}, {993, 35466}, {997, 17720}, {999, 11269}, {1064, 6907}, {1074, 50195}, {1086, 5902}, {1104, 10572}, {1145, 41886}, {1191, 1479}, {1203, 3585}, {1329, 3216}, {1448, 34041}, {1453, 5691}, {1457, 64127}, {1460, 37241}, {1466, 34030}, {1468, 18990}, {1470, 43043}, {1724, 57288}, {1737, 3752}, {1738, 3753}, {2251, 5306}, {2292, 50067}, {2475, 57280}, {2650, 6147}, {2975, 24883}, {2999, 5587}, {3011, 24929}, {3017, 5434}, {3052, 4302}, {3058, 40091}, {3072, 37468}, {3120, 39542}, {3293, 12607}, {3436, 55399}, {3583, 5315}, {3586, 7290}, {3617, 41821}, {3679, 7174}, {3704, 64184}, {3736, 47515}, {3755, 31397}, {3791, 38456}, {3814, 37663}, {3816, 49997}, {3822, 5718}, {3826, 56191}, {3869, 63997}, {3877, 33134}, {3878, 36250}, {3915, 15171}, {3924, 37730}, {3925, 30116}, {3931, 24987}, {3932, 30903}, {3933, 24995}, {3944, 51409}, {3987, 8256}, {4000, 4904}, {4202, 17751}, {4205, 31339}, {4245, 27628}, {4252, 4299}, {4256, 5432}, {4257, 15326}, {4293, 37642}, {4300, 37424}, {4361, 51571}, {4388, 17677}, {4415, 5692}, {4511, 33133}, {4642, 5690}, {4645, 17678}, {4646, 10039}, {4647, 5835}, {4680, 5846}, {4692, 49524}, {4720, 33175}, {4766, 33184}, {5021, 9597}, {5045, 23675}, {5080, 32911}, {5086, 5262}, {5222, 7377}, {5248, 64158}, {5256, 5725}, {5266, 57287}, {5312, 37719}, {5313, 7951}, {5398, 5841}, {5433, 45939}, {5439, 24178}, {5706, 26332}, {5719, 33127}, {5774, 11359}, {5793, 19784}, {5883, 40688}, {6175, 33112}, {6656, 17033}, {6675, 10448}, {6734, 37592}, {6737, 34937}, {6739, 16613}, {7078, 10629}, {7680, 63982}, {8360, 30816}, {8728, 59305}, {9598, 14974}, {10056, 48842}, {10198, 19765}, {10459, 31419}, {10483, 64159}, {10523, 54427}, {10526, 36754}, {10571, 57285}, {10590, 63089}, {10609, 29658}, {10944, 15955}, {11114, 17127}, {11237, 48857}, {11529, 23681}, {12433, 28082}, {12514, 50065}, {15325, 29662}, {16052, 25760}, {16086, 32926}, {16287, 28265}, {16600, 40997}, {17017, 50325}, {17034, 26561}, {17126, 17579}, {17527, 27627}, {17530, 17717}, {17532, 26098}, {17577, 33107}, {17602, 30115}, {17647, 37539}, {17670, 41240}, {17698, 54331}, {17747, 54981}, {17768, 49500}, {18242, 37732}, {18393, 62221}, {18481, 63318}, {18907, 21764}, {18961, 64020}, {18970, 56295}, {19241, 28250}, {20255, 24366}, {21258, 24790}, {23850, 40980}, {24231, 24473}, {24514, 47286}, {24789, 54318}, {24880, 24953}, {25639, 50604}, {26582, 30114}, {26590, 40859}, {26728, 44840}, {28160, 61647}, {28174, 33094}, {28257, 51559}, {29821, 37717}, {32772, 37150}, {32781, 48815}, {33122, 49687}, {33132, 60353}, {33140, 37617}, {33142, 54391}, {33143, 39544}, {33148, 63159}, {33150, 54315}, {37096, 41233}, {37529, 63257}, {37549, 49168}, {37599, 59491}, {38455, 49494}, {38945, 55086}, {48813, 63140}, {48819, 62833}, {49745, 62805}, {50056, 50295}, {50169, 50302}, {52367, 62804}, {54354, 57002}, {54366, 56821}, {54386, 58798}, {54421, 57282}, {59310, 64200}, {59582, 59685}, {62828, 63979}, {62860, 63415}

X(64172) = midpoint of X(i) and X(j) for these {i,j}: {8, 3891}
X(64172) = reflection of X(i) in X(j) for these {i,j}: {1, 17061}, {3703, 10}, {49454, 39544}
X(64172) = complement of X(49492)
X(64172) = X(i)-complementary conjugate of X(j) for these {i, j}: {994, 1329}, {46018, 3452}, {60071, 21244}
X(64172) = pole of line {50621, 64043} with respect to the Feuerbach hyperbola
X(64172) = pole of line {7178, 14349} with respect to the Steiner inellipse
X(64172) = pole of line {5745, 22001} with respect to the dual conic of Yff parabola
X(64172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5794, 63360}, {495, 48847, 42}, {1193, 21935, 5}, {3755, 31397, 64175}, {5313, 7951, 37662}, {5774, 11359, 26034}, {17061, 44669, 1}, {33143, 49454, 39544}

X(64173) = ORTHOLOGY CENTER OF THESE TRIANGLES: 5TH MIXTILINEAR AND X(79)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a^6-a^5*(b+c)+b*c*(b^2-c^2)^2+a^2*(b-c)^2*(b^2+4*b*c+c^2)-a^4*(2*b^2+3*b*c+2*c^2)+2*a^3*(b^3+2*b^2*c+2*b*c^2+c^3)-a*(b-c)^2*(b^3+5*b^2*c+5*b*c^2+c^3)) : :
X(64173) = -2*X[946]+3*X[11218], -3*X[5659]+4*X[6684], -X[11524]+7*X[30389]

X(64173) lies on circumconic {{A, B, C, X(5844), X(10914)}} and on these lines: {1, 1389}, {2, 10806}, {3, 145}, {4, 390}, {8, 1006}, {10, 34486}, {20, 10679}, {21, 952}, {30, 13100}, {35, 104}, {36, 13607}, {40, 3243}, {55, 944}, {56, 11041}, {57, 8000}, {100, 1385}, {140, 12331}, {149, 6842}, {153, 37290}, {355, 1621}, {376, 10306}, {388, 37000}, {392, 64116}, {404, 10246}, {405, 59388}, {411, 1482}, {484, 12005}, {496, 6949}, {497, 6941}, {515, 3746}, {516, 49178}, {517, 3651}, {519, 10902}, {581, 37610}, {602, 50581}, {631, 5687}, {942, 48363}, {943, 31397}, {946, 11218}, {947, 35057}, {956, 6875}, {962, 37622}, {993, 15862}, {999, 6942}, {1001, 5818}, {1056, 6934}, {1058, 6834}, {1064, 37588}, {1317, 37564}, {1512, 63999}, {1519, 12575}, {1532, 15172}, {1697, 7971}, {2078, 64163}, {2136, 3576}, {2800, 37563}, {2829, 63273}, {2975, 32613}, {3057, 10698}, {3058, 18242}, {3085, 6830}, {3091, 18518}, {3149, 6767}, {3241, 11249}, {3244, 11012}, {3256, 4311}, {3303, 5603}, {3421, 6936}, {3434, 6937}, {3476, 11507}, {3486, 11508}, {3522, 35448}, {3525, 9709}, {3528, 6244}, {3560, 61155}, {3579, 26877}, {3584, 63963}, {3601, 7966}, {3616, 6946}, {3617, 6883}, {3621, 37106}, {3622, 6911}, {3623, 10680}, {3655, 26285}, {3748, 7686}, {3825, 64008}, {3873, 59318}, {3877, 37700}, {3881, 5535}, {3884, 6326}, {3885, 61146}, {3889, 37532}, {3890, 45770}, {3913, 5657}, {3915, 37699}, {3920, 4231}, {3935, 31837}, {3957, 24474}, {4188, 16203}, {4220, 20045}, {4294, 12115}, {4304, 12775}, {4309, 6256}, {4428, 34627}, {4857, 59391}, {4881, 24927}, {5046, 10942}, {5047, 5790}, {5082, 6889}, {5119, 64021}, {5172, 37734}, {5204, 39777}, {5218, 10785}, {5248, 5881}, {5250, 5534}, {5251, 47745}, {5253, 15178}, {5281, 6977}, {5284, 9956}, {5303, 32900}, {5396, 62804}, {5531, 20117}, {5552, 6963}, {5584, 50810}, {5659, 6684}, {5690, 6986}, {5731, 11248}, {5804, 8236}, {5842, 15888}, {5884, 11010}, {5901, 6915}, {5919, 37837}, {6003, 14812}, {6264, 51111}, {6361, 38454}, {6583, 62863}, {6605, 48263}, {6762, 21165}, {6765, 55104}, {6826, 10587}, {6827, 10528}, {6833, 12333}, {6848, 10596}, {6850, 20075}, {6853, 24390}, {6876, 22770}, {6880, 14986}, {6888, 61533}, {6897, 17784}, {6902, 17757}, {6908, 56936}, {6909, 11849}, {6912, 18525}, {6914, 18526}, {6924, 37624}, {6947, 7080}, {6952, 63263}, {6954, 10529}, {6967, 59591}, {6970, 10586}, {6985, 12000}, {7411, 12702}, {7421, 15626}, {7489, 37705}, {7491, 20060}, {7504, 59382}, {7508, 61295}, {7992, 53053}, {8158, 34631}, {8666, 59331}, {8728, 38170}, {9957, 33597}, {10056, 48482}, {10057, 10572}, {10074, 14792}, {10093, 12647}, {10283, 37251}, {10385, 12667}, {10525, 34611}, {10531, 64148}, {10532, 63256}, {10597, 50701}, {10884, 49163}, {10965, 30305}, {11362, 15931}, {11510, 18391}, {11524, 30389}, {11680, 26487}, {11715, 37616}, {12249, 63258}, {12515, 26201}, {12520, 12703}, {12675, 37568}, {13143, 37518}, {13199, 31775}, {13278, 18444}, {13407, 16153}, {13464, 44425}, {13528, 58567}, {13587, 37535}, {13743, 28224}, {14497, 56030}, {14988, 35989}, {16117, 28212}, {16370, 50818}, {16615, 56035}, {16858, 50798}, {17531, 38028}, {17536, 38042}, {17549, 32153}, {17577, 34745}, {18443, 63130}, {19544, 26245}, {19649, 29832}, {20070, 44455}, {20095, 37163}, {20418, 52793}, {22765, 61286}, {22791, 36002}, {25438, 34474}, {25440, 45036}, {25542, 31399}, {26086, 38693}, {26286, 59421}, {26878, 34790}, {28174, 33557}, {28204, 28461}, {28234, 59320}, {28466, 31145}, {31393, 63986}, {31659, 37726}, {32905, 48694}, {33110, 37438}, {34339, 63136}, {34353, 35979}, {34617, 64075}, {37468, 62800}, {37556, 52026}, {37601, 64147}, {37698, 57280}, {37718, 40260}, {37719, 59392}, {37732, 40091}, {37733, 62826}, {37739, 62873}, {38513, 55287}, {45976, 51700}, {50194, 57283}, {51705, 59326}, {61288, 62825}, {61597, 62318}, {61763, 63399}, {63159, 64044}

X(64173) = reflection of X(i) in X(j) for these {i,j}: {4, 63257}, {21, 37621}, {1389, 1}, {5603, 63287}, {10532, 63256}
X(64173) = pole of line {6905, 28217} with respect to the circumcircle
X(64173) = pole of line {11011, 61663} with respect to the Feuerbach hyperbola
X(64173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11491, 6905}, {1, 6905, 45977}, {3, 1483, 54391}, {8, 10267, 1006}, {35, 5882, 104}, {55, 944, 6906}, {100, 1385, 6940}, {355, 1621, 6920}, {497, 10786, 6941}, {3057, 21740, 10698}, {3085, 12116, 6830}, {3149, 6767, 10595}, {3303, 11500, 5603}, {3616, 11499, 6946}, {4857, 63964, 59391}, {5731, 11248, 37403}, {5901, 18524, 6915}, {7491, 32213, 20060}, {10246, 32141, 404}, {11849, 34773, 6909}, {26286, 61287, 62837}, {32613, 37727, 2975}, {59421, 62837, 26286}

X(64174) = COMPLEMENT OF X(3883)

Barycentrics    2*a^3+a^2*(b+c)-(b-c)^2*(b+c)+2*a*(b+c)^2 : :
X(64174) = -3*X[2]+X[3883], -5*X[3617]+X[17363], 3*X[17378]+X[49450], -3*X[29574]+X[49470], 3*X[31178]+X[49534], X[31302]+3*X[50128], -5*X[40328]+X[49506], -X[49461]+3*X[50113], -X[49525]+3*X[49727]

X(64174) lies on these lines: {1, 142}, {2, 3883}, {4, 53009}, {6, 10}, {7, 7174}, {8, 3879}, {9, 4307}, {12, 1456}, {37, 516}, {38, 553}, {40, 3332}, {44, 64017}, {45, 51090}, {55, 11347}, {65, 3688}, {75, 49476}, {81, 25006}, {86, 32850}, {141, 19868}, {145, 17117}, {149, 17021}, {171, 5745}, {192, 28557}, {200, 5712}, {226, 612}, {238, 6666}, {241, 12573}, {269, 388}, {329, 7322}, {341, 34283}, {355, 62183}, {390, 5308}, {405, 21002}, {495, 25365}, {497, 17022}, {515, 991}, {518, 3664}, {519, 3696}, {527, 984}, {528, 15569}, {551, 48829}, {750, 1471}, {752, 3842}, {756, 41011}, {894, 3717}, {899, 46916}, {908, 5297}, {940, 4847}, {942, 9052}, {946, 975}, {950, 2293}, {976, 63274}, {1001, 21514}, {1086, 4353}, {1125, 1279}, {1386, 3008}, {1418, 4298}, {1419, 9578}, {1449, 38200}, {1453, 19855}, {1458, 10106}, {1698, 16469}, {1706, 3169}, {1707, 5325}, {1743, 38057}, {1836, 4656}, {1961, 20539}, {2321, 50314}, {2325, 3923}, {2886, 4682}, {2999, 26040}, {3072, 6684}, {3242, 4675}, {3244, 49486}, {3247, 64168}, {3434, 5287}, {3452, 5268}, {3474, 62818}, {3589, 3823}, {3616, 17282}, {3617, 17363}, {3624, 16487}, {3626, 4733}, {3634, 17337}, {3663, 5880}, {3672, 59412}, {3677, 9776}, {3679, 63054}, {3687, 33073}, {3720, 13576}, {3731, 5698}, {3739, 5846}, {3745, 3925}, {3751, 4667}, {3773, 49766}, {3812, 17049}, {3844, 29604}, {3886, 17316}, {3912, 5263}, {3914, 5311}, {3920, 5249}, {3932, 17355}, {3935, 37635}, {3950, 5695}, {3993, 28580}, {4001, 4981}, {4085, 50293}, {4097, 5687}, {4104, 32946}, {4297, 50677}, {4300, 63998}, {4304, 47042}, {4310, 6173}, {4312, 4419}, {4315, 42314}, {4318, 21617}, {4327, 60992}, {4339, 5436}, {4340, 57279}, {4356, 16777}, {4357, 4645}, {4384, 51192}, {4413, 17723}, {4429, 17023}, {4644, 5223}, {4646, 20227}, {4649, 49772}, {4660, 50290}, {4670, 49524}, {4676, 25101}, {4681, 28530}, {4684, 17300}, {4698, 28566}, {4702, 29606}, {4712, 50261}, {4726, 28472}, {4732, 17772}, {4747, 10005}, {4758, 29659}, {4780, 50281}, {4924, 64165}, {4982, 49489}, {5121, 17722}, {5222, 40333}, {5257, 16970}, {5264, 21059}, {5275, 40869}, {5530, 63990}, {5604, 31569}, {5605, 31570}, {5710, 25878}, {5718, 6745}, {5733, 11362}, {5749, 39570}, {5795, 20258}, {5800, 21620}, {5836, 35104}, {5850, 17365}, {6051, 10624}, {6610, 51782}, {6692, 17122}, {7123, 62901}, {7179, 41354}, {7228, 28582}, {7263, 49463}, {8286, 13405}, {8580, 63089}, {8581, 62789}, {9049, 13476}, {9347, 33108}, {9580, 25430}, {9780, 37681}, {10039, 63319}, {10327, 53663}, {11019, 37674}, {12436, 37592}, {12527, 49745}, {12609, 30142}, {15251, 61595}, {15254, 25072}, {15287, 25524}, {15601, 18230}, {16020, 20195}, {16610, 17726}, {16688, 52241}, {16825, 49684}, {16884, 38201}, {16975, 61326}, {17019, 33110}, {17051, 51615}, {17126, 54357}, {17132, 49523}, {17133, 49474}, {17243, 49484}, {17276, 30424}, {17278, 38204}, {17301, 51100}, {17319, 62392}, {17332, 28570}, {17369, 49756}, {17378, 49450}, {17388, 49468}, {17390, 28581}, {17450, 49989}, {17599, 24177}, {17784, 37553}, {19808, 39597}, {19843, 37554}, {20103, 37662}, {20716, 59517}, {20964, 28375}, {21026, 30768}, {21027, 50756}, {21674, 61399}, {21805, 61652}, {24199, 32922}, {24231, 60980}, {24295, 49769}, {24342, 32847}, {24349, 49527}, {24563, 24982}, {24564, 62804}, {24589, 49987}, {24693, 32921}, {24695, 60942}, {24789, 61029}, {24987, 37659}, {25496, 62673}, {25557, 49465}, {26015, 37633}, {26051, 41261}, {26627, 29832}, {26723, 62807}, {26724, 62855}, {27186, 29815}, {27549, 50127}, {28301, 49445}, {28337, 51036}, {28346, 52969}, {28526, 49456}, {28858, 52964}, {29574, 49470}, {29600, 48805}, {29653, 59692}, {29657, 56010}, {29664, 59491}, {30115, 64110}, {30145, 51706}, {30172, 39559}, {30621, 51617}, {31025, 50000}, {31178, 49534}, {31302, 50128}, {31397, 44356}, {31419, 37594}, {31730, 62871}, {32944, 60423}, {33082, 36531}, {33111, 58463}, {33137, 61031}, {34379, 49457}, {34612, 37593}, {34790, 49743}, {34824, 51147}, {35658, 37434}, {36124, 38825}, {36480, 49511}, {37675, 60360}, {40328, 49506}, {40998, 44307}, {41141, 48810}, {41312, 49630}, {42697, 49446}, {43179, 53534}, {44858, 50896}, {46897, 49991}, {48809, 50781}, {48854, 50092}, {49453, 53594}, {49461, 50113}, {49473, 49768}, {49479, 49531}, {49525, 49727}, {49719, 62840}, {50303, 60986}, {63360, 64163}

X(64174) = midpoint of X(i) and X(j) for these {i,j}: {8, 3879}, {65, 3688}, {75, 49476}, {984, 50307}, {3883, 50289}, {17365, 49515}, {17388, 49468}, {24325, 50288}, {24349, 49527}, {29574, 49720}, {50116, 50286}, {50291, 50301}
X(64174) = reflection of X(i) in X(j) for these {i,j}: {3686, 10}, {17049, 3812}, {63977, 15569}
X(64174) = complement of X(3883)
X(64174) = perspector of circumconic {{A, B, C, X(835), X(37206)}}
X(64174) = X(i)-complementary conjugate of X(j) for these {i, j}: {1390, 1329}, {59120, 20317}
X(64174) = pole of line {4205, 18250} with respect to the Kiepert hyperbola
X(64174) = pole of line {47659, 47676} with respect to the Steiner circumellipse
X(64174) = pole of line {3676, 4379} with respect to the Steiner inellipse
X(64174) = pole of line {9, 3589} with respect to the dual conic of Yff parabola
X(64174) = intersection, other than A, B, C, of circumconics {{A, B, C, X(277), X(39716)}}, {{A, B, C, X(1818), X(38825)}}, {{A, B, C, X(2191), X(2214)}}, {{A, B, C, X(3946), X(36124)}}, {{A, B, C, X(6601), X(60152)}}
X(64174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1738, 3946}, {1, 2550, 3755}, {1, 38052, 4000}, {2, 4344, 7290}, {2, 50289, 3883}, {7, 39587, 7174}, {10, 4349, 6}, {10, 50302, 5750}, {10, 5847, 3686}, {528, 15569, 63977}, {750, 29639, 3911}, {984, 50301, 50307}, {1279, 17245, 1125}, {1386, 3008, 4989}, {1386, 3826, 3008}, {1698, 16469, 37650}, {1961, 33109, 24210}, {2886, 4682, 39595}, {3242, 4675, 5542}, {3745, 3925, 40940}, {4344, 7290, 50294}, {4645, 16830, 4357}, {4667, 24393, 3751}, {12609, 30142, 34937}, {17365, 49515, 5850}, {24325, 50288, 519}, {24349, 50286, 49527}, {29571, 63969, 1001}, {39586, 50295, 5257}, {40328, 49506, 50305}, {49527, 50116, 24349}, {50288, 50299, 24325}, {50291, 50301, 527}, {50291, 50307, 984}

X(64175) = COMPLEMENT OF X(3902)

Barycentrics    a*(a^2*(b+c)+(b-c)^2*(b+c)+2*a*(b^2+3*b*c+c^2)) : :
X(64175) = -3*X[2]+X[3902]

X(64175) lies on these lines: {1, 474}, {2, 3902}, {6, 5119}, {8, 3896}, {10, 3706}, {37, 3679}, {40, 36746}, {42, 517}, {43, 392}, {55, 37817}, {58, 37568}, {65, 4306}, {72, 37598}, {73, 13601}, {75, 50083}, {81, 63136}, {100, 17015}, {145, 37339}, {192, 4737}, {227, 3340}, {244, 5049}, {312, 50122}, {386, 3057}, {484, 16474}, {495, 3914}, {518, 4424}, {519, 3666}, {536, 4692}, {551, 16610}, {614, 6767}, {756, 49984}, {902, 51787}, {910, 16785}, {940, 54286}, {942, 4642}, {956, 17594}, {960, 3293}, {968, 9708}, {986, 3555}, {993, 4689}, {995, 5919}, {1100, 5541}, {1104, 3746}, {1107, 50016}, {1145, 2092}, {1193, 9957}, {1201, 31792}, {1203, 37563}, {1319, 4256}, {1386, 37610}, {1427, 18421}, {1453, 53053}, {1455, 3256}, {1465, 2099}, {1468, 3579}, {1500, 16601}, {1697, 7074}, {1698, 21896}, {1834, 10039}, {2177, 24929}, {2276, 43065}, {2292, 34790}, {2334, 37567}, {2646, 15955}, {2650, 50193}, {2999, 16483}, {3214, 5044}, {3216, 58679}, {3240, 3877}, {3241, 4850}, {3247, 51781}, {3290, 50291}, {3295, 54418}, {3421, 64168}, {3434, 5725}, {3617, 62831}, {3626, 3743}, {3670, 34791}, {3689, 30115}, {3697, 59294}, {3720, 4695}, {3739, 4714}, {3740, 31855}, {3744, 25439}, {3748, 30117}, {3750, 60353}, {3755, 31397}, {3772, 10056}, {3811, 37614}, {3871, 5266}, {3878, 50587}, {3892, 3999}, {3895, 5256}, {3946, 21232}, {3953, 58609}, {3957, 54315}, {3971, 59586}, {3992, 35652}, {3995, 4723}, {4252, 59316}, {4257, 63211}, {4263, 11113}, {4270, 21871}, {4300, 31798}, {4663, 49500}, {4681, 4738}, {4696, 64071}, {4698, 19870}, {4711, 62325}, {4720, 25060}, {4849, 5692}, {4875, 25092}, {4883, 5883}, {4891, 49999}, {5045, 24443}, {5122, 54310}, {5252, 48837}, {5312, 5697}, {5530, 24390}, {5711, 62808}, {5774, 17156}, {5902, 49478}, {6690, 50759}, {6735, 37715}, {7991, 15852}, {8715, 37539}, {9623, 37553}, {10179, 49997}, {10391, 45269}, {11231, 29662}, {11239, 19785}, {11269, 26446}, {11362, 37528}, {12672, 37699}, {12702, 54421}, {13528, 37469}, {14923, 19767}, {15569, 56191}, {15888, 23537}, {16469, 53052}, {16602, 25055}, {16605, 25086}, {17012, 62848}, {17061, 50745}, {17461, 21870}, {17609, 24046}, {17720, 45701}, {17757, 24210}, {18677, 38462}, {20691, 29659}, {20925, 50101}, {24028, 50195}, {24473, 49490}, {25099, 50620}, {26728, 37703}, {28174, 41011}, {28212, 61652}, {30116, 37593}, {30305, 63089}, {30384, 37662}, {30411, 61072}, {32777, 48831}, {32945, 60684}, {35460, 51340}, {36279, 62819}, {37520, 62844}, {37562, 37698}, {37599, 54391}, {37728, 60415}, {37732, 45776}, {39523, 61356}, {40937, 56926}, {41261, 41813}, {45126, 60689}, {60751, 63168}, {63146, 63360}

X(64175) = midpoint of X(i) and X(j) for these {i,j}: {8, 3896}
X(64175) = reflection of X(i) in X(j) for these {i,j}: {3666, 4868}, {3706, 10}
X(64175) = complement of X(3902)
X(64175) = X(i)-complementary conjugate of X(j) for these {i, j}: {28210, 59971}, {40434, 21244}, {41434, 1329}
X(64175) = pole of line {2098, 31514} with respect to the Feuerbach hyperbola
X(64175) = pole of line {3669, 47777} with respect to the Steiner inellipse
X(64175) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3742), X(36125)}}, {{A, B, C, X(25524), X(57705)}}
X(64175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1739, 3742}, {1, 24440, 5439}, {1, 3987, 3812}, {1, 60714, 5440}, {1, 64176, 3753}, {10, 37548, 6051}, {519, 4868, 3666}, {1500, 41015, 16601}, {2999, 31393, 16483}, {3755, 31397, 64172}, {3871, 17016, 5266}, {51787, 64166, 902}

X(64176) = REFLECTION OF X(312) IN X(10)

Barycentrics    a*(b^3-2*b^2*c-2*b*c^2+c^3+a*(b^2+3*b*c+c^2)) : :

X(64176) lies on these lines: {1, 474}, {2, 4695}, {6, 21888}, {8, 38}, {10, 312}, {31, 63136}, {36, 49494}, {39, 4051}, {40, 1707}, {43, 517}, {55, 60353}, {65, 50581}, {72, 59294}, {100, 49487}, {145, 3976}, {171, 54286}, {238, 5119}, {244, 3241}, {291, 50282}, {392, 16569}, {484, 4650}, {495, 17889}, {519, 982}, {536, 984}, {614, 3895}, {668, 49518}, {726, 4737}, {750, 17015}, {756, 53620}, {846, 9708}, {899, 3877}, {956, 17596}, {960, 6048}, {978, 3057}, {988, 4853}, {993, 17601}, {995, 2802}, {997, 56009}, {999, 1054}, {1046, 37567}, {1145, 41886}, {1193, 14923}, {1201, 3885}, {1266, 20925}, {1453, 63138}, {1478, 24715}, {1697, 1722}, {1724, 11010}, {1725, 10573}, {1736, 30286}, {1737, 33141}, {1738, 31397}, {1743, 63468}, {1834, 8256}, {2093, 3751}, {2170, 17756}, {2276, 21332}, {2292, 3617}, {3085, 24161}, {3125, 51058}, {3208, 16583}, {3214, 3869}, {3216, 5697}, {3242, 8168}, {3244, 24046}, {3245, 49500}, {3293, 5903}, {3421, 24248}, {3434, 37717}, {3436, 24851}, {3452, 38471}, {3501, 41015}, {3632, 3670}, {3633, 3953}, {3663, 63151}, {3681, 49984}, {3684, 9620}, {3698, 37548}, {3735, 52959}, {3744, 16498}, {3750, 54318}, {3831, 4673}, {3871, 3924}, {3872, 37617}, {3874, 50575}, {3884, 17749}, {3890, 27627}, {3902, 30942}, {3914, 6735}, {3931, 59311}, {3935, 49454}, {3938, 54315}, {3940, 5524}, {3944, 17757}, {3959, 20691}, {3979, 15934}, {4000, 21232}, {4002, 6051}, {4342, 45204}, {4392, 31145}, {4398, 18159}, {4457, 48850}, {4641, 5183}, {4674, 5902}, {4692, 49493}, {4694, 51093}, {4711, 49515}, {4723, 32925}, {4731, 44307}, {4738, 49517}, {4742, 30957}, {4849, 44663}, {4868, 17592}, {5080, 33094}, {5121, 63993}, {5255, 16478}, {5272, 31393}, {5289, 5529}, {5293, 37614}, {5295, 59313}, {5429, 37540}, {5541, 37610}, {5657, 33137}, {5692, 22325}, {5724, 34612}, {5725, 33109}, {5727, 45269}, {5919, 16610}, {6736, 13161}, {6767, 29820}, {7174, 51781}, {7275, 62541}, {7757, 35957}, {7991, 54386}, {9352, 54310}, {9623, 17594}, {9819, 23511}, {9957, 21214}, {10056, 33130}, {10176, 17461}, {10179, 16602}, {10915, 23537}, {12782, 46180}, {15955, 25440}, {16284, 24214}, {16821, 32916}, {17064, 31434}, {17158, 24172}, {17715, 25439}, {17719, 45701}, {18183, 49690}, {18391, 24028}, {18419, 53531}, {19860, 37573}, {21870, 53115}, {22316, 49459}, {24168, 51071}, {24464, 50016}, {24473, 49498}, {25073, 27304}, {25079, 26029}, {26446, 33140}, {27002, 38475}, {28850, 52517}, {29659, 35101}, {30147, 33771}, {31433, 60711}, {32107, 41775}, {32780, 48831}, {32913, 36279}, {33144, 34619}, {36574, 64068}, {37562, 37699}, {37568, 54354}, {37591, 41687}, {37592, 59310}, {42039, 51072}, {42041, 51068}, {49503, 62325}, {53052, 60846}, {59305, 62840}, {59387, 64134}

X(64176) = midpoint of X(i) and X(j) for these {i,j}: {8, 3210}
X(64176) = reflection of X(i) in X(j) for these {i,j}: {1, 3752}, {312, 10}
X(64176) = X(i)-complementary conjugate of X(j) for these {i, j}: {56150, 1329}
X(64176) = pole of line {38406, 56953} with respect to the Kiepert hyperbola
X(64176) = pole of line {47759, 48131} with respect to the Steiner circumellipse
X(64176) = pole of line {3669, 47760} with respect to the Steiner inellipse
X(64176) = pole of line {4106, 30198} with respect to the Suppa-Cucoanes circle
X(64176) = pole of line {3452, 19804} with respect to the dual conic of Yff parabola
X(64176) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3445), X(4492)}}, {{A, B, C, X(8056), X(34258)}}, {{A, B, C, X(17063), X(36125)}}
X(64176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1739, 17063}, {1, 24440, 24174}, {1, 3987, 24440}, {8, 4642, 986}, {960, 21896, 6048}, {3679, 4424, 984}, {3752, 3880, 1}, {3914, 6735, 37716}, {4868, 30116, 17592}, {5255, 54418, 16478}, {17063, 24440, 1739}, {54418, 63130, 5255}

X(64177) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(69)-CROSSPEDAL-OF-X(2) AND PEDAL-OF-X(25)

Barycentrics    (a^2-b^2-c^2)*(7*a^4-(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :
X(64177) = X[2]+2*X[3167], -4*X[68]+13*X[5067], 4*X[155]+5*X[631], 8*X[156]+X[34938], 7*X[3090]+2*X[6193], 7*X[3523]+2*X[12164], -11*X[3525]+2*X[11411], -7*X[3528]+16*X[12038], X[3529]+8*X[22660], -17*X[3533]+8*X[12359], -17*X[3544]+8*X[9927], -11*X[5056]+2*X[12429] and many others

X(64177) lies on these lines: {2, 3167}, {3, 40911}, {4, 110}, {6, 40132}, {20, 26864}, {25, 63092}, {30, 64059}, {49, 6643}, {54, 6804}, {68, 5067}, {69, 3292}, {125, 62708}, {154, 29181}, {155, 631}, {156, 34938}, {184, 7386}, {193, 468}, {323, 7493}, {373, 8681}, {376, 6800}, {394, 7494}, {443, 41608}, {450, 1249}, {511, 35260}, {524, 61680}, {525, 9168}, {539, 61899}, {542, 30775}, {852, 20794}, {858, 39874}, {912, 17561}, {925, 56633}, {1007, 47200}, {1092, 10996}, {1285, 32661}, {1351, 4232}, {1353, 63081}, {1370, 9544}, {1495, 51212}, {1614, 52398}, {1885, 32605}, {1992, 5642}, {1993, 6353}, {1994, 34966}, {1995, 63082}, {3060, 62979}, {3090, 6193}, {3147, 56292}, {3316, 49224}, {3317, 49225}, {3523, 12164}, {3524, 7998}, {3525, 11411}, {3528, 12038}, {3529, 22660}, {3533, 12359}, {3538, 64049}, {3544, 9927}, {3545, 44665}, {3580, 52290}, {3618, 5651}, {3796, 33750}, {4563, 6337}, {5012, 41619}, {5020, 59399}, {5032, 47597}, {5056, 12429}, {5071, 63649}, {5093, 44212}, {5094, 5921}, {5159, 39899}, {5422, 52077}, {5449, 60781}, {5462, 12271}, {5640, 34382}, {5656, 37497}, {5967, 17932}, {5972, 37643}, {6240, 25712}, {6391, 63123}, {6515, 38282}, {6677, 63031}, {6776, 11064}, {6816, 9545}, {6857, 26637}, {6995, 8780}, {7392, 9306}, {7401, 61753}, {7486, 61544}, {7503, 38396}, {7582, 8909}, {7605, 63036}, {7689, 41462}, {7714, 35264}, {7763, 57216}, {8057, 14401}, {8548, 15018}, {8550, 59767}, {8889, 61700}, {9155, 32985}, {9463, 61199}, {9703, 18531}, {9707, 59346}, {9716, 37644}, {9777, 14914}, {9925, 16042}, {9928, 10595}, {9936, 43839}, {10192, 37672}, {10299, 12163}, {10516, 14826}, {10554, 58046}, {11002, 14984}, {11003, 41615}, {11008, 41586}, {11180, 45303}, {11206, 29012}, {11284, 19588}, {11422, 63084}, {11433, 34986}, {11442, 52299}, {11451, 61666}, {11477, 15448}, {12293, 61964}, {12310, 14002}, {13303, 45325}, {13366, 18928}, {13416, 34783}, {13567, 59551}, {13568, 45248}, {13857, 64014}, {13881, 15504}, {14039, 46900}, {14853, 35259}, {14927, 51360}, {15024, 21651}, {15061, 18917}, {15082, 38064}, {15083, 61814}, {15139, 36851}, {17040, 63069}, {17809, 53415}, {17810, 59699}, {18420, 40111}, {18440, 52284}, {18909, 43844}, {18931, 38727}, {18935, 28708}, {19119, 28419}, {19597, 37338}, {21850, 52301}, {21970, 64067}, {31099, 46818}, {32001, 41203}, {32225, 63064}, {32235, 32255}, {34381, 64149}, {34511, 35282}, {35266, 54132}, {35513, 43574}, {36181, 47148}, {37897, 44456}, {37904, 51028}, {41588, 62973}, {43653, 64064}, {43841, 64035}, {44109, 54012}, {44210, 62174}, {51170, 63612}, {54376, 64025}, {58434, 64060}

X(64177) = inverse of X(1992) in Thomson-Gibert-Moses hyperbola
X(64177) = perspector of circumconic {{A, B, C, X(687), X(20187)}}
X(64177) = X(i)-Ceva conjugate of X(j) for these {i, j}: {11169, 3}
X(64177) = pole of line {16051, 37637} with respect to the Kiepert hyperbola
X(64177) = pole of line {9191, 30512} with respect to the Kiepert parabola
X(64177) = pole of line {352, 1499} with respect to the MacBeath circumconic
X(64177) = pole of line {47236, 50644} with respect to the Orthic inconic
X(64177) = pole of line {1351, 1597} with respect to the Stammler hyperbola
X(64177) = pole of line {8598, 44427} with respect to the Steiner circumellipse
X(64177) = pole of line {1007, 5094} with respect to the Wallace hyperbola
X(64177) = pole of line {1499, 54259} with respect to the dual conic of DeLongchamps circle
X(64177) = pole of line {3906, 45688} with respect to the dual conic of polar circle
X(64177) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1300), X(7612)}}, {{A, B, C, X(2986), X(56267)}}, {{A, B, C, X(44080), X(47390)}}
X(64177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3167, 63174}, {110, 34148, 44080}, {110, 37645, 4}, {184, 37669, 7386}, {323, 7493, 63428}, {394, 13394, 10519}, {631, 15066, 44833}, {3167, 59553, 2}, {6776, 11064, 16051}, {9306, 11427, 7392}, {10519, 13394, 7494}, {11411, 64181, 3525}, {14389, 54013, 3090}, {34986, 59543, 11433}, {41597, 64181, 11411}

X(64178) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(75)-CROSSPEDAL-OF-X(2) AND PEDAL-OF-X(31)

Barycentrics    -b*c*(b+c)+a*(b^2+3*b*c+c^2) : :
X(64178) = X[551]+2*X[59718], -4*X[596]+13*X[34595], 5*X[1698]+4*X[3159], X[3175]+2*X[3740], 7*X[3624]+2*X[24068], -X[3681]+4*X[4096], X[3873]+2*X[42054], 5*X[3876]+4*X[63800], X[4661]+2*X[42057], -10*X[4687]+X[17157], 5*X[4704]+4*X[59565], 2*X[10179]+X[50078] and many others

X(64178) lies on these lines: {1, 3952}, {2, 726}, {9, 17763}, {10, 4671}, {37, 4009}, {38, 18743}, {42, 27538}, {43, 3995}, {45, 32917}, {75, 3994}, {190, 750}, {192, 899}, {210, 28581}, {226, 29854}, {244, 30829}, {312, 756}, {321, 26037}, {329, 32949}, {344, 29632}, {373, 14839}, {522, 6544}, {536, 61686}, {537, 64149}, {551, 59718}, {596, 34595}, {612, 30568}, {714, 51488}, {740, 42056}, {748, 32926}, {896, 17336}, {908, 4078}, {940, 32938}, {984, 4358}, {1001, 32927}, {1089, 31339}, {1376, 32936}, {1698, 3159}, {1961, 26223}, {1978, 6376}, {2177, 3699}, {2292, 46937}, {3011, 25101}, {3175, 3740}, {3219, 29649}, {3240, 3993}, {3305, 32914}, {3452, 29849}, {3501, 61163}, {3624, 24068}, {3663, 60423}, {3666, 59506}, {3681, 4096}, {3703, 25960}, {3715, 32864}, {3717, 33120}, {3720, 32937}, {3731, 29828}, {3782, 25961}, {3807, 4664}, {3836, 33151}, {3840, 7226}, {3846, 32862}, {3873, 42054}, {3876, 63800}, {3891, 17123}, {3912, 33065}, {3920, 4011}, {3923, 5297}, {3931, 59582}, {3932, 25760}, {3943, 4023}, {3967, 32771}, {3999, 49513}, {4052, 61029}, {4062, 17242}, {4090, 17018}, {4103, 9331}, {4135, 28605}, {4362, 27065}, {4365, 59296}, {4383, 32928}, {4387, 32945}, {4392, 4871}, {4413, 17262}, {4414, 5205}, {4415, 25957}, {4416, 49990}, {4418, 5268}, {4422, 17602}, {4423, 32923}, {4425, 29679}, {4427, 56010}, {4434, 62838}, {4439, 33089}, {4656, 32776}, {4660, 60459}, {4661, 42057}, {4672, 9347}, {4679, 32844}, {4687, 17157}, {4703, 33078}, {4704, 59565}, {4706, 4718}, {4756, 32935}, {4759, 30653}, {4850, 24003}, {4918, 9711}, {4938, 17386}, {5220, 32919}, {5233, 32848}, {5284, 32920}, {5294, 29847}, {5311, 27064}, {5741, 33092}, {5743, 6057}, {6048, 64071}, {6541, 33077}, {6745, 59585}, {7292, 49455}, {8026, 40087}, {8580, 59638}, {8669, 16865}, {8720, 17572}, {9458, 42720}, {10179, 50078}, {10327, 32947}, {10459, 19582}, {11269, 27549}, {14459, 17314}, {14997, 49477}, {15485, 20045}, {16373, 64170}, {16569, 17147}, {16610, 49523}, {16825, 35595}, {16831, 31063}, {17122, 32933}, {17124, 32939}, {17125, 32922}, {17140, 25502}, {17165, 26102}, {17234, 32856}, {17264, 33156}, {17279, 32775}, {17349, 50756}, {17353, 29636}, {17363, 49995}, {17397, 59735}, {17449, 30947}, {17450, 49499}, {17495, 49445}, {17717, 30566}, {17718, 41313}, {17720, 33115}, {17721, 24709}, {17725, 24542}, {17776, 29846}, {17777, 33104}, {18139, 33101}, {18140, 36863}, {18228, 33088}, {19765, 59598}, {19872, 24176}, {19875, 27812}, {19998, 49469}, {20942, 42041}, {21020, 42034}, {21080, 27268}, {21093, 31019}, {21805, 49470}, {24067, 59772}, {24080, 31996}, {24210, 33117}, {24349, 30950}, {24589, 49493}, {24703, 33072}, {24988, 33149}, {25055, 59717}, {25253, 59311}, {25959, 49769}, {26580, 29674}, {26688, 29821}, {26792, 32946}, {27131, 29671}, {27184, 29687}, {27804, 42043}, {28557, 46916}, {28606, 59511}, {29574, 61652}, {29635, 33166}, {29639, 62297}, {29642, 33153}, {29653, 31053}, {29824, 49448}, {29845, 33163}, {29851, 33144}, {30578, 33112}, {31018, 32843}, {31197, 49522}, {32129, 36847}, {32916, 33761}, {32921, 37680}, {32924, 37679}, {32940, 37674}, {33125, 62673}, {34064, 61358}, {36479, 53661}, {37548, 59577}, {37553, 59599}, {37593, 59596}, {37598, 52353}, {41242, 50302}, {42051, 58451}, {49474, 62227}

X(64178) = reflection of X(i) in X(j) for these {i,j}: {63961, 42056}
X(64178) = pole of line {4785, 21385} with respect to the Steiner circumellipse
X(64178) = pole of line {3807, 24004} with respect to the Yff parabola
X(64178) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(17155), X(55997)}}, {{A, B, C, X(27494), X(39698)}}, {{A, B, C, X(52654), X(56162)}}
X(64178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 32925, 17155}, {2, 3971, 32925}, {37, 4009, 32931}, {210, 35652, 32915}, {312, 756, 31330}, {612, 30568, 32930}, {740, 42056, 63961}, {908, 4078, 29643}, {984, 4358, 30942}, {3952, 31035, 1}, {3967, 44307, 32771}, {3971, 59517, 2}, {4671, 9330, 10}, {4756, 37633, 32935}, {4871, 49520, 4392}, {5205, 17261, 4414}, {5268, 56082, 4418}, {7226, 46938, 3840}, {24003, 49456, 4850}, {27538, 41839, 42}, {30829, 49447, 244}, {49445, 62711, 17495}

X(64179) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS AND X(54)-CROSSPEDAL-OF-X(3)

Barycentrics    (a^2-b^2-c^2)*((b^2-c^2)^4+2*a^6*(b^2+c^2)+a^4*(-3*b^4+10*b^2*c^2-3*c^4)) : :
X(64179) = -X[20]+3*X[6030], 5*X[631]+X[43599], 5*X[632]+X[44755], 3*X[5890]+X[15103], 2*X[12103]+X[53779], 7*X[15043]+X[15086], -2*X[37472]+3*X[61659]

X(64179) lies on circumconic {{A, B, C, X(3521), X(32085)}} and on these lines: {2, 3357}, {3, 1568}, {4, 83}, {5, 10575}, {20, 6030}, {30, 3574}, {113, 140}, {125, 10024}, {184, 12118}, {185, 12359}, {265, 18128}, {381, 15805}, {382, 3796}, {403, 9729}, {541, 45619}, {548, 51392}, {550, 13394}, {567, 12897}, {569, 61744}, {578, 44440}, {631, 43599}, {632, 44755}, {1092, 15438}, {1105, 3462}, {1181, 12429}, {1204, 3549}, {1209, 5663}, {1495, 31833}, {1498, 47353}, {1519, 6831}, {1531, 12362}, {1594, 46850}, {1656, 11472}, {2777, 14118}, {2883, 7399}, {2916, 11414}, {3090, 15740}, {3520, 58447}, {3530, 44796}, {3543, 54036}, {3547, 63425}, {3580, 13382}, {3690, 31837}, {3850, 51548}, {3851, 5544}, {3917, 22660}, {5012, 13403}, {5133, 13474}, {5462, 11799}, {5489, 6368}, {5562, 6823}, {5576, 14915}, {5642, 61608}, {5654, 43652}, {5890, 15103}, {5893, 34664}, {5895, 54994}, {5907, 15063}, {6000, 13160}, {6102, 41586}, {6241, 21243}, {6689, 14130}, {6800, 34785}, {6815, 44679}, {7395, 9914}, {7400, 11821}, {7403, 32062}, {7503, 22802}, {7509, 32600}, {7517, 7706}, {7542, 21663}, {7550, 38791}, {7574, 17712}, {7728, 34864}, {9019, 12233}, {9730, 15761}, {10095, 43893}, {10110, 47096}, {10112, 15032}, {10151, 64038}, {10254, 45622}, {10282, 38323}, {10539, 50008}, {10619, 15089}, {10982, 14848}, {11430, 52071}, {11559, 14861}, {11560, 14708}, {11563, 12006}, {11745, 47093}, {11750, 44263}, {12038, 64064}, {12085, 61743}, {12103, 53779}, {12162, 34115}, {12163, 61644}, {12605, 22352}, {13202, 37513}, {13339, 46686}, {13353, 31726}, {13367, 16163}, {13371, 14855}, {13399, 13491}, {13406, 43817}, {13434, 52403}, {13488, 37649}, {13630, 61750}, {14788, 32111}, {15037, 58807}, {15043, 15086}, {15045, 44958}, {15058, 24206}, {15072, 20299}, {15321, 15811}, {15720, 21968}, {15800, 47748}, {15807, 44267}, {16003, 34826}, {16836, 32743}, {16868, 43846}, {17928, 61747}, {18364, 20127}, {18400, 34007}, {18420, 26883}, {18555, 34564}, {20191, 44753}, {21451, 43584}, {21659, 64049}, {22467, 64063}, {26917, 61136}, {31074, 52093}, {31371, 56069}, {31829, 51394}, {32068, 43600}, {32340, 44407}, {33923, 51391}, {34152, 58407}, {34350, 39242}, {34545, 40240}, {37197, 37514}, {37472, 61659}, {37476, 44438}, {37648, 44960}, {37943, 43597}, {38793, 58435}, {41464, 52404}, {43392, 53781}, {43595, 44109}, {43601, 44673}, {43845, 58806}, {46849, 50137}, {46852, 50135}

X(64179) = midpoint of X(i) and X(j) for these {i,j}: {3, 3521}, {4, 8718}, {3543, 54036}, {15800, 47748}, {18488, 44866}, {34007, 52525}, {34563, 35240}, {43585, 64180}
X(64179) = reflection of X(i) in X(j) for these {i,j}: {11560, 14708}, {14130, 6689}, {18488, 5}, {34563, 3521}, {35240, 3}, {64180, 140}
X(64179) = inverse of X(40647) in Jerabek hyperbola
X(64179) = complement of X(15062)
X(64179) = pole of line {826, 1092} with respect to the 1st Brocard circle
X(64179) = pole of line {12605, 40647} with respect to the Jerabek hyperbola
X(64179) = pole of line {3520, 3917} with respect to the Stammler hyperbola
X(64179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 43831, 1568}, {4, 8718, 29012}, {2883, 7399, 15030}, {3549, 4846, 1204}, {5012, 50009, 13403}, {13630, 61750, 63735}, {14788, 32111, 44870}, {34007, 52525, 18400}

X(64180) = COMPLEMENT OF X(3521)

Barycentrics    a^2*(2*a^4-3*(b^2-c^2)^2+a^2*(b^2+c^2))*(a^4+b^4+3*b^2*c^2+c^4-2*a^2*(b^2+c^2)) : :
X(64180) = -3*X[2]+X[3521], -5*X[3]+3*X[6030], -5*X[2916]+9*X[55654], -4*X[3530]+X[44866], -9*X[7998]+X[15086], -5*X[11444]+X[15103], -X[12316]+3*X[13482], -7*X[14869]+X[44755], -3*X[15688]+X[54036], -5*X[41464]+11*X[55632]

X(64180) lies on these lines: {2, 3521}, {3, 6030}, {4, 18442}, {5, 20191}, {6, 6102}, {30, 1209}, {35, 34586}, {74, 34864}, {110, 11559}, {113, 140}, {141, 550}, {143, 7527}, {185, 63729}, {186, 45958}, {206, 3357}, {378, 6101}, {389, 46084}, {399, 51033}, {546, 44106}, {548, 16655}, {549, 2883}, {632, 43604}, {960, 31663}, {1147, 5876}, {1154, 14130}, {1176, 43719}, {1204, 49671}, {1493, 13754}, {1498, 34513}, {1510, 14809}, {1511, 5907}, {1539, 10024}, {1656, 11454}, {1658, 44082}, {2070, 43613}, {2071, 32142}, {2916, 55654}, {3516, 64105}, {3520, 11591}, {3526, 11468}, {3530, 44866}, {3580, 15807}, {3627, 16254}, {3628, 21663}, {3850, 32110}, {4550, 37814}, {5237, 34328}, {5238, 34327}, {5447, 37950}, {5449, 43865}, {5609, 13367}, {5663, 10610}, {5891, 10226}, {5944, 12162}, {5946, 7689}, {6000, 32391}, {6152, 13391}, {6368, 57128}, {6593, 20190}, {6644, 33537}, {6759, 34472}, {7488, 32137}, {7503, 32138}, {7516, 10606}, {7568, 15311}, {7575, 44870}, {7998, 15086}, {8542, 9019}, {8567, 32620}, {9306, 33556}, {9704, 12111}, {9818, 15026}, {9909, 56069}, {10113, 34826}, {10170, 11598}, {10193, 32415}, {10212, 38793}, {10263, 63425}, {10620, 61134}, {10627, 45973}, {10984, 13491}, {11017, 44802}, {11188, 12085}, {11250, 15067}, {11413, 33533}, {11440, 13630}, {11444, 15103}, {11672, 37512}, {11793, 22966}, {12006, 35500}, {12084, 54042}, {12086, 63414}, {12107, 16194}, {12167, 55571}, {12316, 13482}, {13382, 55709}, {13561, 52069}, {13565, 34007}, {14805, 64025}, {14869, 44755}, {15030, 15331}, {15116, 20582}, {15246, 55286}, {15688, 54036}, {15748, 17814}, {16656, 47342}, {17713, 64100}, {18435, 32171}, {22333, 47391}, {23039, 35475}, {26206, 55697}, {30522, 34005}, {33539, 37922}, {33542, 35452}, {34577, 51403}, {35473, 43846}, {35478, 37477}, {35498, 40930}, {37936, 46849}, {37955, 43614}, {41464, 55632}, {41614, 45034}, {43611, 46865}, {45248, 61753}, {45956, 55706}

X(64180) = midpoint of X(i) and X(j) for these {i,j}: {3, 15062}, {4, 18442}, {110, 11559}, {3520, 44753}, {8718, 33541}, {16835, 52100}, {18488, 35240}
X(64180) = reflection of X(i) in X(j) for these {i,j}: {185, 63729}, {10610, 14118}, {34007, 13565}, {43585, 64179}, {46027, 546}, {53779, 46027}, {64179, 140}
X(64180) = inverse of X(57713) in Stammler hyperbola
X(64180) = complement of X(3521)
X(64180) = center of circumconic {{A, B, C, X(110), X(11559)}}
X(64180) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 10024}, {2190, 12006}, {3520, 10}
X(64180) = pole of line {550, 3521} with respect to the Stammler hyperbola
X(64180) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {110, 11559, 16166}
X(64180) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(46027)}}, {{A, B, C, X(546), X(3520)}}, {{A, B, C, X(550), X(6030)}}
X(64180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 33541, 8718}, {3, 52100, 6030}, {5663, 14118, 10610}, {5876, 18570, 43394}, {6030, 15062, 16835}, {6030, 16835, 52100}, {7527, 63392, 143}, {7689, 63682, 5946}, {8718, 15062, 33541}, {18488, 35240, 30}, {34826, 52070, 10113}

X(64181) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(64)-CROSSPEDAL-OF-X(3)

Barycentrics    (a^2-b^2-c^2)*(3*a^8-(b^2-c^2)^4-6*a^6*(b^2+c^2)+2*a^2*(b^2-c^2)^2*(b^2+c^2)+2*a^4*(b^4+c^4)) : :
X(64181) = 4*X[10]+X[9933], X[20]+4*X[5448], 4*X[140]+X[155], 3*X[154]+2*X[23335], 4*X[156]+X[14216], -9*X[373]+4*X[58496], -6*X[549]+X[12163], 4*X[1125]+X[9928], -3*X[1853]+8*X[32144], -7*X[3090]+2*X[9927], 3*X[3167]+7*X[3526], -7*X[3523]+2*X[7689] and many others

X(64181) lies on these lines: {2, 54}, {3, 4549}, {4, 11449}, {5, 11425}, {6, 16238}, {10, 9933}, {20, 5448}, {30, 17821}, {49, 1899}, {52, 3147}, {110, 37119}, {140, 155}, {146, 35494}, {154, 23335}, {156, 14216}, {184, 3548}, {235, 64096}, {373, 58496}, {394, 7542}, {468, 36747}, {511, 31267}, {549, 12163}, {550, 41427}, {567, 63701}, {578, 5504}, {590, 19062}, {615, 8909}, {631, 10574}, {632, 3564}, {858, 9707}, {912, 25917}, {1069, 5432}, {1092, 3549}, {1125, 9928}, {1181, 10257}, {1216, 37669}, {1352, 61753}, {1593, 51425}, {1656, 44665}, {1853, 32144}, {1993, 10018}, {1995, 32048}, {2072, 19467}, {2548, 32661}, {2931, 9815}, {3088, 46261}, {3090, 9927}, {3091, 15034}, {3157, 5433}, {3167, 3526}, {3523, 7689}, {3525, 11411}, {3533, 63174}, {3541, 10539}, {3542, 13352}, {3546, 14156}, {3547, 44516}, {3567, 45780}, {3618, 34382}, {3624, 12259}, {3628, 14852}, {3917, 47525}, {4413, 12328}, {5054, 12164}, {5070, 12429}, {5094, 12134}, {5159, 31804}, {5418, 10666}, {5420, 10665}, {5446, 6353}, {5447, 7494}, {5462, 11427}, {5642, 15115}, {5651, 14786}, {5876, 18580}, {5878, 11250}, {5944, 14791}, {6143, 11442}, {6623, 12897}, {6639, 22115}, {6642, 23292}, {6643, 18475}, {6699, 18913}, {6759, 44441}, {7387, 10192}, {7391, 26882}, {7393, 53415}, {7401, 43586}, {7403, 35259}, {7405, 23307}, {7484, 9908}, {7493, 10625}, {7505, 34148}, {7506, 59648}, {7509, 19908}, {7525, 46114}, {7528, 61743}, {7568, 19139}, {7575, 31815}, {7592, 61655}, {7808, 12193}, {7914, 9923}, {8252, 49225}, {8253, 49224}, {8912, 18510}, {9544, 11457}, {9703, 25738}, {9705, 23294}, {9706, 26913}, {9818, 59659}, {9833, 13371}, {9937, 37649}, {9967, 28708}, {10020, 16266}, {10116, 23291}, {10182, 46730}, {10201, 58435}, {10272, 12302}, {10282, 14790}, {10303, 15083}, {10564, 37201}, {10601, 15316}, {10661, 42089}, {10662, 42092}, {10984, 64064}, {11202, 32364}, {11441, 37118}, {11464, 37444}, {11469, 16534}, {11585, 19357}, {12084, 61608}, {12085, 16252}, {12161, 44452}, {12235, 63085}, {12383, 33547}, {12418, 15184}, {12421, 45298}, {12423, 24953}, {12430, 26364}, {12431, 26363}, {12901, 35475}, {13292, 26958}, {13346, 64063}, {13353, 54012}, {13367, 18531}, {13383, 37498}, {13392, 50138}, {13909, 32785}, {13970, 32786}, {14516, 52296}, {14643, 63685}, {14984, 15026}, {15024, 63036}, {15559, 35264}, {15760, 35602}, {15805, 19458}, {17814, 52262}, {17834, 34351}, {18356, 34331}, {18445, 26937}, {18569, 32171}, {18917, 43844}, {18925, 62708}, {18951, 34986}, {19131, 28419}, {20302, 37347}, {21841, 44413}, {23128, 31401}, {23306, 32609}, {23336, 32139}, {26492, 47371}, {30744, 34224}, {31670, 37440}, {31802, 37935}, {32140, 61736}, {32539, 43808}, {32767, 61751}, {34007, 38942}, {34938, 35260}, {36749, 61506}, {36752, 61690}, {36753, 58726}, {37453, 41587}, {37471, 41615}, {37472, 54148}, {37476, 59767}, {37481, 38794}, {37484, 63683}, {37490, 44214}, {37672, 64066}, {38282, 64048}, {39522, 44232}, {42021, 43653}, {43595, 44911}, {43843, 61199}, {44469, 61683}, {44802, 59771}, {45184, 61863}, {48876, 63702}, {51732, 63612}, {52016, 58445}, {52104, 55864}, {54217, 58465}, {55856, 61544}, {62376, 63722}, {63344, 63353}

X(64181) = pole of line {15905, 53414} with respect to the Kiepert hyperbola
X(64181) = pole of line {52, 378} with respect to the Stammler hyperbola
X(64181) = pole of line {39113, 44134} with respect to the Wallace hyperbola
X(64181) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(96), X(4846)}}, {{A, B, C, X(317), X(5449)}}
X(64181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1147, 68}, {2, 6193, 5449}, {2, 9545, 18912}, {3, 9820, 5654}, {5, 47391, 12118}, {49, 6640, 1899}, {68, 1147, 63649}, {140, 59553, 155}, {156, 18281, 14216}, {549, 61607, 12163}, {615, 8909, 19061}, {1147, 43839, 2}, {1147, 5449, 6193}, {3147, 37645, 52}, {3167, 12359, 9936}, {3167, 3526, 12359}, {3525, 64177, 11411}, {5054, 12164, 44158}, {11411, 64177, 41597}, {14156, 64049, 3546}, {37498, 61680, 13383}

X(64182) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 107 AND X(74)-CROSSPEDAL-OF-X(3)

Barycentrics    5*a^10-2*a^2*b^2*c^2*(b^2-c^2)^2-12*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(7*b^4+19*b^2*c^2+7*c^4)+a^4*(b^6-8*b^4*c^2-8*b^2*c^4+c^6) : :
X(64182) = X[20]+2*X[5609], -2*X[125]+3*X[5054], -4*X[140]+7*X[15020], -3*X[186]+2*X[15361], -X[382]+7*X[15039], -4*X[468]+3*X[15362], -4*X[547]+3*X[14644], -4*X[548]+X[15054], 2*X[550]+X[14094]

X(64182) lies on these lines: {2, 265}, {3, 67}, {5, 11694}, {20, 5609}, {30, 110}, {49, 38323}, {74, 8703}, {113, 3830}, {125, 5054}, {140, 15020}, {146, 11001}, {186, 15361}, {376, 5663}, {381, 5642}, {382, 15039}, {394, 399}, {428, 15472}, {468, 15362}, {511, 34319}, {519, 12778}, {524, 3581}, {539, 12893}, {543, 18332}, {547, 14644}, {548, 15054}, {549, 9140}, {550, 14094}, {567, 597}, {568, 1992}, {671, 51478}, {690, 53275}, {895, 50979}, {1351, 15303}, {1385, 50921}, {1483, 50923}, {1539, 15682}, {1657, 15063}, {1989, 32761}, {2771, 28460}, {2777, 15681}, {2781, 13340}, {2854, 11179}, {2948, 50811}, {3043, 18559}, {3058, 10091}, {3448, 3524}, {3519, 15331}, {3522, 51522}, {3523, 20379}, {3525, 20396}, {3526, 36253}, {3545, 10113}, {3564, 47333}, {3580, 18579}, {3582, 12904}, {3584, 12903}, {3656, 11720}, {3839, 61574}, {3845, 10272}, {3851, 38795}, {3858, 15029}, {5055, 5972}, {5064, 12140}, {5066, 13392}, {5073, 38791}, {5095, 50962}, {5434, 10088}, {5465, 6321}, {5504, 11597}, {5622, 13339}, {5690, 50920}, {5987, 60654}, {6053, 15685}, {6055, 14849}, {6243, 25711}, {6288, 12038}, {6593, 20423}, {6684, 50919}, {6699, 15693}, {6723, 61864}, {7540, 37495}, {7552, 32171}, {7574, 13857}, {7575, 15360}, {7576, 15463}, {7687, 19709}, {7706, 11935}, {7722, 35489}, {7768, 45993}, {7865, 12501}, {7984, 50824}, {9033, 20128}, {9126, 36255}, {9759, 56370}, {10264, 12100}, {10295, 63720}, {10304, 12041}, {10546, 39487}, {10564, 11645}, {10620, 15688}, {10657, 36968}, {10658, 36967}, {10748, 63767}, {10819, 19052}, {10820, 19051}, {10990, 15696}, {11006, 33813}, {11061, 50967}, {11064, 58789}, {11178, 39242}, {11237, 18968}, {11238, 12896}, {11430, 25561}, {11464, 44262}, {11539, 15059}, {11557, 21969}, {11579, 37283}, {11632, 53725}, {11699, 28198}, {11799, 35266}, {11801, 15699}, {12117, 15342}, {12244, 62120}, {12261, 25055}, {12295, 14269}, {12308, 15689}, {12317, 19708}, {12355, 16278}, {12368, 28208}, {12407, 19875}, {12828, 55572}, {12889, 34612}, {12890, 34606}, {12900, 61920}, {12905, 45701}, {12906, 45700}, {13169, 48876}, {13202, 62040}, {13211, 50821}, {13393, 61790}, {13605, 50828}, {13846, 49222}, {13847, 49223}, {14093, 15041}, {14559, 52056}, {14677, 15690}, {14892, 22250}, {14980, 43969}, {15021, 33923}, {15023, 61792}, {15025, 55856}, {15036, 17504}, {15042, 15716}, {15055, 34200}, {15057, 15712}, {15088, 61899}, {15131, 18400}, {15454, 58733}, {15683, 34584}, {15684, 38789}, {15694, 38638}, {15695, 37853}, {15697, 64102}, {15700, 38727}, {15701, 48378}, {15702, 34128}, {15703, 23515}, {15713, 40685}, {15718, 48375}, {15720, 20397}, {16176, 50973}, {16270, 18925}, {17538, 38632}, {18331, 52695}, {18564, 54073}, {18571, 41724}, {19059, 52048}, {19060, 52047}, {19140, 19924}, {22467, 25714}, {25328, 50983}, {25566, 48901}, {25712, 37484}, {32114, 39899}, {32234, 37934}, {32244, 50978}, {32271, 51024}, {32438, 54973}, {33851, 54173}, {33878, 56565}, {34148, 38322}, {34331, 58922}, {36208, 41100}, {36209, 41101}, {36966, 43597}, {37470, 64103}, {37483, 56568}, {37958, 41586}, {38335, 46686}, {38626, 62092}, {38729, 61811}, {38738, 56566}, {38792, 61996}, {40115, 53499}, {41512, 51345}, {41595, 51132}, {43573, 43809}, {43836, 45970}, {44214, 44569}, {44282, 50435}, {46817, 62380}, {46818, 54995}, {49216, 53130}, {49217, 53131}, {51224, 57268}, {52697, 54131}, {63343, 63352}, {63684, 64051}

X(64182) = midpoint of X(i) and X(j) for these {i,j}: {2, 12383}, {146, 11001}, {376, 9143}, {399, 3534}, {2930, 43273}, {2948, 50811}, {5648, 32233}, {5655, 12121}, {11061, 50967}, {12117, 15342}, {15685, 38790}, {16176, 50973}, {20126, 23236}, {38738, 56566}, {46818, 54995}
X(64182) = reflection of X(i) in X(j) for these {i,j}: {2, 1511}, {5, 11694}, {67, 50977}, {74, 8703}, {265, 2}, {381, 5642}, {895, 50979}, {1351, 15303}, {3534, 16163}, {3580, 18579}, {3581, 44265}, {3656, 11720}, {3830, 113}, {3845, 10272}, {5055, 11693}, {5066, 13392}, {5648, 12584}, {5655, 110}, {6321, 5465}, {7574, 13857}, {7728, 5655}, {7984, 50824}, {8724, 53735}, {9140, 549}, {10264, 12100}, {10733, 3845}, {11006, 33813}, {11579, 51737}, {11632, 53725}, {11799, 35266}, {12355, 16278}, {13169, 48876}, {13211, 50821}, {13605, 50828}, {14643, 32609}, {14677, 15690}, {15061, 15035}, {15360, 7575}, {15682, 1539}, {20126, 3}, {20127, 3534}, {20423, 6593}, {21969, 11557}, {25328, 50983}, {32244, 50978}, {32272, 50955}, {36255, 9126}, {38724, 38793}, {38788, 38723}, {44555, 15361}, {48901, 25566}, {50435, 44282}, {50878, 11699}, {50919, 6684}, {50920, 5690}, {50921, 1385}, {50923, 1483}, {50955, 5181}, {50962, 5095}, {51024, 32271}, {51132, 41595}, {54173, 33851}, {62040, 13202}, {63700, 5648}
X(64182) = perspector of circumconic {{A, B, C, X(17708), X(30528)}}
X(64182) = pole of line {690, 46616} with respect to the circumcircle
X(64182) = pole of line {43291, 61656} with respect to the Kiepert hyperbola
X(64182) = pole of line {5467, 7471} with respect to the Kiepert parabola
X(64182) = pole of line {23, 3581} with respect to the Stammler hyperbola
X(64182) = pole of line {14417, 45681} with respect to the Steiner inellipse
X(64182) = pole of line {316, 35520} with respect to the Wallace hyperbola
X(64182) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {2, 11006, 12383}, {146, 11001, 36172}, {399, 3534, 13188}, {476, 14480, 53872}, {15300, 38738, 56566}, {20126, 23236, 52056}
X(64182) = intersection, other than A, B, C, of circumconics {{A, B, C, X(67), X(477)}}, {{A, B, C, X(2697), X(20126)}}, {{A, B, C, X(3431), X(34210)}}, {{A, B, C, X(39985), X(61116)}}
X(64182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 30714, 23236}, {3, 542, 20126}, {30, 110, 5655}, {110, 12121, 7728}, {110, 34153, 12121}, {186, 44555, 15361}, {265, 1511, 38794}, {376, 9143, 5663}, {381, 32609, 5642}, {382, 15039, 16534}, {399, 16163, 20127}, {399, 3534, 541}, {524, 44265, 3581}, {541, 16163, 3534}, {542, 12584, 5648}, {542, 50955, 32272}, {542, 50977, 67}, {542, 5181, 50955}, {542, 53735, 8724}, {549, 32423, 9140}, {1511, 12383, 265}, {5642, 17702, 381}, {5655, 12121, 30}, {5663, 38723, 38788}, {9140, 15035, 549}, {11699, 28198, 50878}, {12584, 32233, 63700}, {15035, 32423, 15061}, {15694, 38724, 45311}, {17702, 32609, 14643}, {20126, 23236, 542}, {24981, 38726, 10620}, {38638, 38724, 38793}, {38793, 45311, 15694}

X(64183) = ANTICOMPLEMENT OF X(12383)

Barycentrics    5*a^10-11*a^8*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(5*b^4-b^2*c^2+5*c^4)+a^6*(6*b^4+17*b^2*c^2+6*c^4)-2*a^4*(b^6+2*b^4*c^2+2*b^2*c^4+c^6) : :
X(64183) = -3*X[2]+4*X[265], -4*X[67]+3*X[62174], -8*X[113]+9*X[3839], -8*X[125]+7*X[3523], -2*X[323]+3*X[3153], -3*X[376]+4*X[10264], -6*X[381]+5*X[20125], -5*X[631]+4*X[34153], -10*X[632]+9*X[38638], -8*X[1495]+9*X[46451], -8*X[1539]+9*X[50687], -2*X[2935]+3*X[32064] and many others

X(64183) lies on circumconic {{A, B, C, X(68), X(3471)}} and on these lines: {2, 265}, {4, 195}, {6, 40640}, {8, 12407}, {20, 68}, {23, 12412}, {30, 12317}, {52, 15102}, {67, 62174}, {110, 578}, {113, 3839}, {125, 3523}, {146, 148}, {147, 48982}, {323, 3153}, {376, 10264}, {381, 20125}, {390, 12896}, {511, 15100}, {541, 15640}, {631, 34153}, {632, 38638}, {1478, 6126}, {1479, 7343}, {1495, 46451}, {1503, 17812}, {1514, 17838}, {1539, 50687}, {1587, 35834}, {1588, 35835}, {2771, 20084}, {2777, 49135}, {2781, 20079}, {2854, 5921}, {2888, 21659}, {2931, 10298}, {2935, 32064}, {2948, 59387}, {3088, 44795}, {3090, 11801}, {3146, 5663}, {3410, 4550}, {3522, 12121}, {3524, 15042}, {3525, 15040}, {3528, 61548}, {3529, 10620}, {3544, 15039}, {3545, 10272}, {3564, 10296}, {3575, 18947}, {3581, 30522}, {3600, 18968}, {3617, 12778}, {3622, 12261}, {3623, 12898}, {3627, 12308}, {3832, 10113}, {3854, 61574}, {5055, 13392}, {5056, 12900}, {5059, 12244}, {5068, 14643}, {5070, 22251}, {5076, 61598}, {5261, 10088}, {5274, 10091}, {5334, 36209}, {5335, 36208}, {5504, 43949}, {5505, 53021}, {5609, 50689}, {5642, 61924}, {5655, 61985}, {5731, 13605}, {5972, 7486}, {5984, 57611}, {6053, 61989}, {6288, 43818}, {6699, 15692}, {6723, 15020}, {6776, 9976}, {6995, 12140}, {7378, 15472}, {7488, 12310}, {7527, 12168}, {7585, 49222}, {7586, 49223}, {7728, 17578}, {7731, 62187}, {8972, 10819}, {8994, 9542}, {9140, 10304}, {9919, 37945}, {9927, 11464}, {10116, 43596}, {10303, 15035}, {10421, 62606}, {10528, 49160}, {10529, 49159}, {10546, 18390}, {10564, 25739}, {10657, 42134}, {10658, 42133}, {10706, 62007}, {10721, 50691}, {10820, 13941}, {11001, 14677}, {11002, 11557}, {11430, 58922}, {11438, 12278}, {11456, 12293}, {11694, 61899}, {12022, 15018}, {12041, 50693}, {12112, 52403}, {12133, 54037}, {12219, 14984}, {12270, 21649}, {12273, 21650}, {12284, 64025}, {12295, 14094}, {12375, 23249}, {12376, 23259}, {12584, 40330}, {12901, 35493}, {12904, 14986}, {13172, 15545}, {13203, 64037}, {13211, 59417}, {13393, 62131}, {14516, 15052}, {14853, 25556}, {14901, 43448}, {14927, 16010}, {15027, 61820}, {15032, 34007}, {15034, 23515}, {15036, 20397}, {15037, 43838}, {15041, 17538}, {15046, 61945}, {15054, 49140}, {15055, 62097}, {15057, 58188}, {15059, 55864}, {15061, 15717}, {15066, 18396}, {15101, 37484}, {15106, 37444}, {15107, 18400}, {15682, 38790}, {15683, 20127}, {15697, 37853}, {15721, 48378}, {15816, 62213}, {17701, 38942}, {17847, 41362}, {18331, 20094}, {18420, 63040}, {18440, 37077}, {19051, 63016}, {19052, 63015}, {20126, 62120}, {20379, 21734}, {20396, 61842}, {20417, 62110}, {24981, 61982}, {25320, 32233}, {25328, 25406}, {25330, 44882}, {25335, 29181}, {32247, 61044}, {32254, 39884}, {32306, 63428}, {34128, 61834}, {34584, 50692}, {35826, 43408}, {35827, 43407}, {37477, 60455}, {37496, 46450}, {37638, 50007}, {38448, 61544}, {38633, 44245}, {38726, 62067}, {38727, 61788}, {38728, 61791}, {38788, 62124}, {38793, 61856}, {39874, 44440}, {41465, 45794}, {41819, 63352}, {42522, 46688}, {42523, 46689}, {43584, 43816}, {44456, 52842}, {45311, 61844}, {49319, 62987}, {49320, 62986}, {51522, 62152}, {51538, 51941}, {56567, 61994}, {61936, 64101}, {62967, 64099}

X(64183) = midpoint of X(i) and X(j) for these {i,j}: {49050, 49051}
X(64183) = reflection of X(i) in X(j) for these {i,j}: {4, 12902}, {8, 12407}, {20, 3448}, {146, 10733}, {3529, 10620}, {5059, 12244}, {12270, 21649}, {12273, 21650}, {12308, 3627}, {12383, 265}, {13172, 15545}, {13203, 64037}, {14094, 12295}, {14683, 4}, {14927, 16010}, {15102, 52}, {17847, 41362}, {20094, 18331}, {23236, 10113}, {32254, 39884}, {37484, 15101}, {61044, 32247}, {63428, 32306}, {64025, 12284}, {64102, 12317}
X(64183) = anticomplement of X(12383)
X(64183) = X(i)-Dao conjugate of X(j) for these {i, j}: {12383, 12383}
X(64183) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {35372, 8}
X(64183) = pole of line {16163, 55121} with respect to the DeLongchamps circle
X(64183) = pole of line {3153, 61656} with respect to the Kiepert hyperbola
X(64183) = pole of line {3581, 37922} with respect to the Stammler hyperbola
X(64183) = pole of line {1637, 6334} with respect to the Steiner circumellipse
X(64183) = pole of line {52149, 59634} with respect to the Wallace hyperbola
X(64183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 32423, 14683}, {30, 12317, 64102}, {110, 15044, 36518}, {146, 10733, 3543}, {265, 1511, 15081}, {265, 64182, 20304}, {542, 10733, 146}, {1511, 15081, 2}, {3448, 17702, 20}, {11801, 32609, 3090}, {12293, 34799, 50009}, {12383, 15081, 1511}, {12902, 32423, 4}, {34153, 38724, 631}, {49050, 49051, 542}

X(64184) = ANTICOMPLEMENT OF X(2901)

Barycentrics    a^3*(b+c)-a*b*c*(b+c)-b*c*(b+c)^2+a^2*(b^2+b*c+c^2) : :
X(64184) = -3*X[2]+2*X[2901], -4*X[596]+3*X[3873], -2*X[942]+3*X[42051], -4*X[970]+3*X[54035], -4*X[1125]+3*X[32915], -5*X[1698]+4*X[63800], -4*X[3159]+5*X[3876], -3*X[3175]+4*X[5044], -4*X[3678]+3*X[32925], -3*X[3681]+2*X[24068], -2*X[3874]+3*X[17155], -8*X[4075]+9*X[63961] and many others

X(64184) lies on these lines: {1, 75}, {2, 2901}, {6, 50044}, {8, 4424}, {10, 4970}, {20, 29016}, {35, 4362}, {36, 17733}, {43, 1089}, {58, 3187}, {63, 64072}, {72, 536}, {78, 20237}, {79, 32946}, {145, 4340}, {191, 32934}, {192, 9534}, {239, 1724}, {306, 23537}, {312, 3216}, {321, 386}, {341, 31855}, {345, 1714}, {405, 4361}, {443, 17314}, {519, 3868}, {551, 25056}, {594, 13728}, {595, 32929}, {596, 3873}, {726, 5904}, {942, 42051}, {960, 28484}, {970, 54035}, {984, 22316}, {993, 27368}, {995, 3702}, {1008, 33941}, {1125, 32915}, {1193, 4365}, {1203, 3923}, {1211, 50067}, {1215, 5312}, {1278, 20018}, {1698, 63800}, {1770, 5847}, {1999, 37522}, {2049, 20182}, {3100, 56146}, {3159, 3876}, {3175, 5044}, {3190, 23661}, {3191, 40564}, {3210, 3670}, {3293, 4385}, {3338, 39594}, {3454, 33077}, {3555, 28581}, {3666, 5295}, {3678, 32925}, {3681, 24068}, {3682, 20320}, {3704, 64172}, {3706, 37592}, {3743, 31339}, {3772, 25645}, {3780, 50156}, {3782, 41014}, {3791, 24850}, {3841, 29643}, {3874, 17155}, {3896, 4968}, {3902, 50637}, {3953, 10453}, {3969, 4202}, {3980, 37559}, {3992, 6048}, {3993, 27785}, {4028, 13407}, {4065, 62831}, {4066, 32931}, {4075, 63961}, {4259, 9022}, {4299, 39765}, {4358, 17749}, {4384, 54287}, {4399, 49728}, {4418, 62805}, {4692, 50581}, {4714, 59311}, {4716, 5247}, {4717, 50604}, {4742, 56804}, {4850, 50605}, {4852, 50054}, {4894, 32866}, {4967, 19857}, {4971, 11112}, {4975, 21214}, {5132, 56538}, {5248, 32914}, {5259, 16825}, {5262, 48863}, {5264, 32932}, {5271, 62871}, {5292, 17740}, {5692, 28522}, {5695, 16466}, {5814, 50065}, {5836, 50083}, {5844, 31774}, {6051, 49462}, {6533, 26102}, {6734, 25094}, {6763, 32853}, {7951, 17748}, {9555, 21333}, {10448, 54335}, {10483, 38456}, {11104, 56138}, {13725, 42696}, {13745, 50098}, {14005, 62851}, {16394, 50120}, {16458, 16777}, {16817, 17117}, {16834, 50049}, {17011, 43531}, {17045, 56985}, {17133, 57284}, {17156, 62858}, {17161, 29066}, {17233, 33833}, {17243, 17529}, {17281, 21802}, {17362, 49716}, {17380, 37036}, {17495, 24046}, {17763, 25440}, {18398, 24165}, {19270, 55095}, {19767, 28605}, {19789, 24159}, {19835, 54426}, {19846, 33132}, {19858, 21020}, {19871, 50096}, {20016, 20077}, {20017, 39700}, {20083, 32779}, {20222, 52365}, {20336, 37819}, {21070, 26242}, {21831, 55180}, {22021, 37093}, {24174, 49999}, {24851, 32861}, {24880, 33113}, {24883, 33168}, {25639, 29849}, {25760, 36250}, {26115, 64161}, {26227, 33771}, {27798, 39708}, {28612, 59305}, {28850, 64005}, {29617, 49723}, {29653, 41859}, {30142, 32928}, {30145, 32945}, {30148, 32943}, {30171, 32855}, {30172, 32848}, {31327, 50086}, {32771, 59301}, {32842, 52367}, {32939, 56018}, {33080, 41822}, {33932, 37042}, {34064, 56766}, {37038, 50088}, {39584, 51816}, {41229, 62817}, {42057, 50190}, {48842, 50041}, {48847, 50042}, {48857, 50043}, {48870, 50045}, {49500, 63996}, {49683, 62802}, {50112, 51672}, {50113, 51671}, {50122, 58679}, {50306, 64002}, {57280, 64010}

X(64184) = reflection of X(i) in X(j) for these {i,j}: {984, 22316}, {2901, 64185}, {5904, 59302}
X(64184) = anticomplement of X(2901)
X(64184) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {15376, 8}, {39700, 21287}
X(64184) = pole of line {6002, 48281} with respect to the Conway circle
X(64184) = pole of line {7192, 14349} with respect to the Steiner circumellipse
X(64184) = pole of line {4369, 48054} with respect to the Steiner inellipse
X(64184) = pole of line {6002, 43924} with respect to the Suppa-Cucoanes circle
X(64184) = pole of line {4357, 33146} with respect to the dual conic of Yff parabola
X(64184) = intersection, other than A, B, C, of circumconics {{A, B, C, X(86), X(15315)}}, {{A, B, C, X(2296), X(28619)}}, {{A, B, C, X(4647), X(56138)}}
X(64184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10436, 28619}, {1, 49474, 4647}, {239, 7283, 1724}, {726, 59302, 5904}, {1010, 4360, 1}, {2901, 64185, 2}, {3210, 10449, 3670}, {3666, 5295, 10479}, {3876, 42044, 3159}, {24165, 35633, 18398}

X(64185) = COMPLEMENT OF X(2901)

Barycentrics    a^3*(b+c)-2*a*b*c*(b+c)-b*c*(b+c)^2+a^2*(b^2+c^2) : :
X(64185) = -3*X[2]+X[2901], X[72]+3*X[42051], -3*X[210]+X[24068], X[3057]+3*X[50083], -7*X[3624]+3*X[32915], -3*X[3740]+2*X[4075], -3*X[3742]+4*X[6532], -X[3874]+3*X[24165], 5*X[3876]+3*X[50106], X[5904]+3*X[17155]

X(64185) lies on these lines: {1, 3896}, {2, 2901}, {3, 4361}, {8, 3670}, {10, 3666}, {35, 32914}, {36, 27368}, {58, 239}, {72, 42051}, {75, 386}, {79, 32843}, {191, 32845}, {210, 24068}, {312, 17749}, {321, 3216}, {518, 596}, {519, 942}, {524, 24470}, {536, 3159}, {540, 4292}, {594, 56734}, {595, 32932}, {726, 3678}, {740, 1125}, {758, 59303}, {899, 1089}, {936, 17151}, {970, 29069}, {975, 3875}, {978, 20891}, {1040, 56146}, {1043, 30117}, {1086, 41014}, {1193, 4647}, {1203, 4418}, {1575, 52535}, {1714, 17740}, {1739, 17751}, {1962, 25512}, {2321, 40941}, {3057, 50083}, {3187, 37522}, {3210, 9534}, {3214, 4692}, {3218, 64072}, {3290, 21070}, {3293, 4968}, {3337, 32919}, {3338, 17156}, {3454, 3687}, {3624, 32915}, {3634, 63800}, {3696, 37592}, {3701, 59669}, {3702, 49997}, {3720, 6533}, {3736, 20174}, {3740, 4075}, {3742, 6532}, {3743, 4970}, {3752, 5295}, {3757, 33771}, {3822, 17748}, {3841, 29671}, {3846, 36250}, {3874, 24165}, {3876, 50106}, {3920, 43993}, {3953, 17135}, {3969, 17674}, {3976, 49459}, {3980, 62805}, {3993, 27784}, {4028, 51706}, {4065, 6051}, {4066, 59511}, {4255, 17119}, {4256, 17117}, {4340, 20043}, {4360, 56766}, {4362, 25440}, {4365, 27627}, {4383, 50044}, {4384, 62871}, {4653, 16817}, {4696, 31855}, {4709, 50608}, {4714, 10459}, {4716, 37607}, {4818, 19992}, {4850, 10479}, {4852, 37594}, {4974, 24850}, {4975, 28352}, {5045, 28581}, {5248, 16825}, {5256, 43531}, {5312, 32771}, {5743, 50067}, {5814, 48835}, {5904, 17155}, {5956, 57039}, {6007, 58469}, {6147, 7263}, {6693, 40940}, {6763, 32864}, {9895, 49558}, {10449, 17490}, {10916, 34822}, {12512, 28850}, {15489, 29010}, {16458, 20182}, {16777, 56767}, {16833, 31424}, {17011, 25526}, {17293, 56736}, {17314, 17582}, {17348, 31445}, {17366, 17698}, {19786, 24931}, {19863, 21020}, {20108, 44417}, {20367, 62858}, {20911, 62755}, {21196, 29066}, {21240, 49560}, {22316, 24325}, {24880, 32851}, {25079, 49992}, {25645, 33129}, {26060, 33093}, {27474, 30110}, {28611, 59305}, {29643, 41859}, {30142, 32921}, {30148, 32941}, {30172, 32855}, {33085, 41822}, {34790, 59717}, {35633, 58565}, {37539, 49683}, {37732, 59637}, {40959, 63146}, {42696, 56737}, {47040, 62829}, {48836, 50050}, {48866, 50054}, {49468, 52541}, {49479, 50590}, {49609, 54288}, {50088, 54345}

X(64185) = midpoint of X(i) and X(j) for these {i,j}: {2901, 64184}, {3874, 59302}, {22316, 24325}
X(64185) = reflection of X(i) in X(j) for these {i,j}: {942, 24176}, {3159, 5044}, {35633, 58565}, {63800, 3634}
X(64185) = complement of X(2901)
X(64185) = X(i)-complementary conjugate of X(j) for these {i, j}: {1333, 62564}, {15376, 10}, {29014, 4129}, {39700, 21245}
X(64185) = pole of line {7192, 14349} with respect to the Steiner inellipse
X(64185) = pole of line {1213, 4054} with respect to the dual conic of Yff parabola
X(64185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64184, 2901}, {8, 17495, 3670}, {519, 24176, 942}, {536, 5044, 3159}, {899, 1089, 59666}, {3687, 23537, 3454}, {3752, 5295, 50605}, {3976, 49459, 50625}, {10449, 17490, 24046}, {24165, 59302, 3874}

X(64186) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-EXCENTERS-REFLECTIONS AND X(104)-CROSSPEDAL-OF-X(3)

Barycentrics    4*a^7-5*a^5*(b-c)^2-4*a^6*(b+c)+2*a^2*(b-c)^2*(b+c)^3-3*(b-c)^4*(b+c)^3+a*(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)+a^4*(5*b^3-b^2*c-b*c^2+5*c^3)-2*a^3*(b^4+b^3*c-2*b^2*c^2+b*c^3+c^4) : :
X(64186) = -3*X[4]+X[100], -2*X[40]+3*X[38128], -2*X[140]+3*X[38141], X[149]+3*X[3543], -X[153]+5*X[17578], -2*X[182]+3*X[38147], -3*X[376]+5*X[31272], -3*X[381]+2*X[3035], -2*X[548]+3*X[34126], -2*X[549]+3*X[38077], -2*X[550]+3*X[21154], -5*X[631]+6*X[38319] and many others

X(64186) lies on these lines: {3, 3847}, {4, 100}, {5, 24466}, {11, 30}, {20, 6713}, {40, 38128}, {80, 36599}, {104, 3146}, {140, 38141}, {149, 3543}, {153, 17578}, {182, 38147}, {214, 18483}, {376, 31272}, {381, 3035}, {382, 2829}, {515, 64137}, {516, 6246}, {517, 38389}, {528, 3830}, {546, 33814}, {548, 34126}, {549, 38077}, {550, 21154}, {631, 38319}, {952, 3627}, {956, 10525}, {1001, 6923}, {1145, 18480}, {1317, 22791}, {1385, 38038}, {1387, 9614}, {1484, 62036}, {1537, 22793}, {1597, 13222}, {1657, 38759}, {1699, 11729}, {1728, 5128}, {1770, 12832}, {2771, 12690}, {2783, 39838}, {2787, 39809}, {2800, 51118}, {2802, 31673}, {2828, 38956}, {3036, 12702}, {3045, 14157}, {3091, 34474}, {3529, 38693}, {3534, 45310}, {3579, 34122}, {3585, 10956}, {3656, 12735}, {3818, 51007}, {3829, 18515}, {3832, 64008}, {3843, 38752}, {3845, 6174}, {3851, 38762}, {3853, 22799}, {3861, 61562}, {4297, 16174}, {4413, 6929}, {4996, 21669}, {5073, 20418}, {5076, 12331}, {5251, 37290}, {5533, 10483}, {5690, 38156}, {5722, 24465}, {5732, 38124}, {5848, 31670}, {5851, 31671}, {5854, 18525}, {5856, 31672}, {6068, 60901}, {6154, 11698}, {6265, 63992}, {6361, 59415}, {6564, 13922}, {6565, 13991}, {6684, 38161}, {6702, 31730}, {6882, 24042}, {6985, 10058}, {7687, 53711}, {7972, 31162}, {8068, 37406}, {8674, 12295}, {8703, 59376}, {9730, 58475}, {9812, 10698}, {9897, 50865}, {9955, 34123}, {10427, 18482}, {10609, 12611}, {10707, 12248}, {10711, 20095}, {10721, 10778}, {10722, 10769}, {10723, 10768}, {10725, 10772}, {10726, 10777}, {10727, 10770}, {10732, 10771}, {10733, 10767}, {10736, 10782}, {10737, 10781}, {10759, 51538}, {10773, 44983}, {10774, 44984}, {10775, 44985}, {10776, 44986}, {10779, 44987}, {10780, 44988}, {11001, 59377}, {11510, 12953}, {11715, 28164}, {12102, 51525}, {12512, 38133}, {12619, 28146}, {12650, 12737}, {12943, 13274}, {13271, 34706}, {13913, 42258}, {13977, 42259}, {14269, 35023}, {15863, 28194}, {17556, 35249}, {17800, 38754}, {18254, 37585}, {18514, 37356}, {18518, 25438}, {18534, 54065}, {19112, 23259}, {19113, 23249}, {19907, 40273}, {19914, 48661}, {20400, 61984}, {21850, 51198}, {25416, 28204}, {28150, 46684}, {28160, 64191}, {28178, 61553}, {31512, 44979}, {31657, 38152}, {31658, 38159}, {31659, 38163}, {31663, 38182}, {31937, 64139}, {33899, 52116}, {34200, 38084}, {37234, 51506}, {37468, 51636}, {37736, 51790}, {38119, 44882}, {38131, 63413}, {38636, 61968}, {38665, 50688}, {38669, 62028}, {38755, 62008}, {38756, 62023}, {38758, 61990}, {41686, 62616}, {42271, 48700}, {42272, 48701}, {42283, 48715}, {42284, 48714}, {46686, 53743}, {46850, 58508}, {50240, 61268}, {50690, 64009}, {51529, 61601}, {52835, 54159}, {55297, 64076}, {59387, 64136}

X(64186) = midpoint of X(i) and X(j) for these {i,j}: {4, 10724}, {80, 41869}, {104, 3146}, {149, 10728}, {382, 10738}, {1484, 62036}, {5073, 38753}, {5691, 14217}, {10707, 15682}, {10721, 10778}, {10722, 10769}, {10723, 10768}, {10725, 10772}, {10726, 10777}, {10727, 10770}, {10732, 10771}, {10733, 10767}, {10736, 10782}, {10737, 10781}, {10742, 48680}, {10773, 44983}, {10774, 44984}, {10775, 44985}, {10776, 44986}, {10779, 44987}, {10780, 44988}, {19914, 48661}, {31512, 44979}, {61601, 62034}
X(64186) = reflection of X(i) in X(j) for these {i,j}: {11, 22938}, {20, 6713}, {119, 4}, {214, 18483}, {550, 60759}, {1145, 18480}, {1317, 22791}, {1537, 22793}, {1657, 38759}, {3534, 45310}, {4297, 16174}, {6068, 60901}, {6154, 11698}, {6174, 3845}, {6882, 24042}, {10427, 18482}, {10609, 12611}, {10993, 119}, {12119, 11729}, {12331, 38757}, {12515, 12019}, {12702, 3036}, {18481, 1387}, {19907, 40273}, {22799, 3853}, {24466, 5}, {31730, 6702}, {33814, 546}, {37585, 18254}, {37725, 22799}, {37726, 10738}, {38753, 20418}, {38760, 59390}, {38761, 11}, {46850, 58508}, {51007, 3818}, {51198, 21850}, {51529, 61601}, {52116, 33899}, {52836, 3627}, {53711, 7687}, {53743, 46686}, {61562, 3861}, {64139, 31937}
X(64186) = pole of line {10728, 55126} with respect to the polar circle
X(64186) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 10724, 10731}, {104, 3146, 46618}, {149, 10728, 10776}
X(64186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 10724, 5840}, {4, 5840, 119}, {11, 30, 38761}, {30, 22938, 11}, {119, 5840, 10993}, {149, 3543, 10728}, {382, 10738, 2829}, {550, 60759, 21154}, {952, 3627, 52836}, {1657, 57298, 38759}, {1699, 12119, 11729}, {2829, 10738, 37726}, {3091, 34474, 58421}, {3830, 48680, 10742}, {5073, 51517, 38753}, {5691, 14217, 952}, {10742, 48680, 528}, {24466, 59390, 5}, {38753, 51517, 20418}

X(64187) = ORTHOLOGY CENTER OF THESE TRIANGLES: CIRCUMORTHIC AND X(68)-CROSSPEDAL-OF-X(4)

Barycentrics    5*a^10-18*a^6*(b^2-c^2)^2-3*a^8*(b^2+c^2)+22*a^4*(b^2-c^2)^2*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)-a^2*(b^2-c^2)^2*(3*b^4+26*b^2*c^2+3*c^4) : :
X(64187) = -11*X[3]+12*X[61606], -3*X[4]+2*X[64], -6*X[154]+5*X[17538], -3*X[376]+4*X[2883], -4*X[546]+3*X[35450], -8*X[548]+9*X[35260], -5*X[631]+4*X[5894], -2*X[1657]+3*X[11206], -7*X[3090]+8*X[5893], -5*X[3091]+4*X[3357], -7*X[3523]+8*X[61749], -9*X[3524]+10*X[64024] and many others

X(64187) lies on these lines: {2, 18504}, {3, 61606}, {4, 64}, {5, 40920}, {20, 110}, {24, 46373}, {30, 6193}, {54, 43695}, {66, 57715}, {68, 541}, {74, 58378}, {154, 17538}, {376, 2883}, {378, 9914}, {382, 12324}, {389, 30443}, {546, 35450}, {548, 35260}, {631, 5894}, {1204, 6623}, {1498, 3529}, {1503, 6144}, {1514, 6622}, {1657, 11206}, {1658, 9919}, {1941, 18850}, {3090, 5893}, {3091, 3357}, {3146, 5889}, {3184, 31377}, {3426, 38442}, {3523, 61749}, {3524, 64024}, {3525, 8567}, {3527, 13488}, {3528, 16252}, {3541, 7699}, {3543, 14216}, {3545, 6696}, {3548, 7728}, {3567, 31978}, {3627, 13093}, {3839, 20299}, {3843, 61540}, {3854, 32767}, {3855, 40686}, {4293, 12950}, {4294, 12940}, {5059, 9833}, {5067, 23328}, {5068, 23329}, {5225, 10076}, {5229, 10060}, {5890, 22967}, {6241, 18945}, {6293, 7722}, {6361, 12779}, {6403, 12290}, {6776, 18560}, {7486, 25563}, {7505, 11270}, {7731, 22535}, {9899, 31673}, {10117, 21844}, {10151, 34469}, {10152, 59424}, {10182, 61788}, {10192, 21735}, {10193, 61856}, {10282, 50693}, {10303, 11204}, {10575, 41715}, {10721, 11457}, {11001, 34782}, {11202, 62097}, {11381, 11387}, {11412, 36982}, {11431, 16657}, {11541, 58795}, {11738, 38447}, {12086, 32321}, {12103, 14530}, {12289, 32234}, {12964, 43408}, {12970, 43407}, {13203, 18404}, {13754, 36983}, {14853, 43599}, {14862, 62110}, {15139, 35471}, {15318, 16251}, {15319, 31361}, {15682, 64037}, {15683, 34785}, {15692, 64063}, {15704, 32063}, {15717, 61747}, {15740, 34664}, {15751, 36518}, {16835, 38443}, {17578, 18381}, {17845, 49138}, {18383, 50687}, {18400, 49135}, {18405, 62021}, {18533, 22750}, {18909, 44438}, {18931, 37197}, {19087, 23273}, {19088, 23267}, {19467, 49670}, {20725, 45771}, {22615, 35865}, {22644, 35864}, {23061, 49140}, {23249, 49250}, {23259, 49251}, {23325, 61982}, {23332, 61964}, {32125, 44958}, {32337, 32340}, {32605, 51394}, {32903, 62129}, {34622, 61607}, {34778, 40330}, {34780, 62036}, {34786, 50691}, {34787, 41735}, {35481, 59279}, {35488, 63726}, {37643, 44226}, {37669, 63441}, {41362, 62028}, {44544, 64030}, {44762, 50709}, {46372, 56292}, {50414, 62125}, {54039, 64050}, {58434, 61807}, {61138, 61680}, {61735, 61945}

X(64187) = midpoint of X(i) and X(j) for these {i,j}: {3146, 54211}
X(64187) = reflection of X(i) in X(j) for these {i,j}: {4, 5895}, {20, 5878}, {64, 51491}, {3529, 1498}, {5059, 9833}, {5925, 2883}, {6225, 48672}, {6361, 12779}, {9899, 31673}, {11412, 36982}, {12244, 11744}, {12250, 4}, {12324, 382}, {13093, 3627}, {13203, 38790}, {20427, 22802}, {30443, 389}, {34780, 62036}, {34781, 6225}, {35512, 64094}, {49138, 17845}, {64030, 44544}, {64034, 3146}
X(64187) = anticomplement of X(20427)
X(64187) = pole of line {6623, 11381} with respect to the Jerabek hyperbola
X(64187) = pole of line {6000, 35602} with respect to the Stammler hyperbola
X(64187) = pole of line {41077, 52585} with respect to the Steiner circumellipse
X(64187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(51385)}}, {{A, B, C, X(54), X(39268)}}, {{A, B, C, X(1294), X(6526)}}, {{A, B, C, X(10152), X(12250)}}, {{A, B, C, X(33893), X(41425)}}, {{A, B, C, X(38442), X(58758)}}
X(64187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 15311, 12250}, {4, 3183, 51385}, {4, 32601, 10605}, {4, 36965, 41425}, {4, 40664, 6526}, {20, 5878, 5656}, {30, 48672, 6225}, {30, 6225, 34781}, {64, 5895, 51491}, {2777, 5878, 20}, {2883, 5925, 376}, {3146, 54211, 6000}, {3146, 6000, 64034}, {5893, 10606, 3090}, {5895, 15311, 4}, {15311, 51491, 64}

X(64188) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST CIRCUMPERP AND X(80)-CROSSPEDAL-OF-X(4)

Barycentrics    a*(a^9-2*a^8*(b+c)+b*(b-c)^4*c*(b+c)^3+a^7*(-2*b^2+5*b*c-2*c^2)-3*a^5*b*c*(3*b^2-2*b*c+3*c^2)+a^6*(6*b^3-b^2*c-b*c^2+6*c^3)-a*(b^2-c^2)^2*(b^4-b^3*c-2*b^2*c^2-b*c^3+c^4)+a^3*(b-c)^2*(2*b^4+7*b^3*c+4*b^2*c^2+7*b*c^3+2*c^4)+a^2*(b-c)^2*(2*b^5-3*b^4*c-5*b^3*c^2-5*b^2*c^3-3*b*c^4+2*c^5)-a^4*(6*b^5-9*b^4*c+b^3*c^2+b^2*c^3-9*b*c^4+6*c^5)) : :
X(64188) = -3*X[165]+X[2950], X[9803]+3*X[54051]

X(64188) lies on circumconic {{A, B, C, X(34256), X(36100)}} and on these lines: {3, 119}, {4, 8068}, {9, 34256}, {11, 3149}, {20, 17100}, {21, 63964}, {30, 12761}, {35, 12608}, {36, 80}, {40, 78}, {55, 1537}, {56, 64191}, {57, 15528}, {63, 12665}, {84, 35976}, {153, 4996}, {165, 2950}, {214, 37611}, {404, 5450}, {474, 21154}, {517, 25438}, {908, 2077}, {944, 10074}, {952, 11249}, {1006, 64008}, {1012, 52836}, {1145, 3428}, {1158, 5720}, {1376, 64193}, {1387, 22753}, {1420, 11715}, {1490, 1768}, {1519, 32760}, {1532, 5172}, {1699, 63281}, {1793, 3658}, {1795, 61231}, {1809, 13532}, {2801, 60974}, {2932, 7580}, {3295, 64192}, {3651, 5660}, {3652, 64118}, {3916, 17661}, {4188, 64120}, {4491, 44805}, {5251, 6940}, {5260, 40260}, {5533, 12116}, {5692, 40256}, {5697, 10087}, {5840, 6985}, {5842, 10738}, {5851, 64156}, {5854, 22770}, {6001, 6100}, {6264, 13279}, {6265, 37837}, {6667, 6918}, {6713, 6911}, {6834, 36152}, {6883, 58421}, {6906, 7951}, {6914, 22799}, {6915, 18406}, {6924, 12114}, {6942, 12248}, {7962, 25485}, {7972, 12776}, {7982, 13278}, {8069, 26333}, {9803, 54051}, {9942, 12738}, {10175, 17009}, {10267, 11729}, {10724, 36002}, {10902, 41012}, {10956, 26357}, {11012, 12751}, {11495, 12332}, {11499, 59366}, {11502, 12832}, {11570, 18446}, {11698, 12762}, {11700, 15737}, {12115, 14793}, {12611, 32613}, {12616, 35979}, {12739, 33597}, {12758, 63986}, {12763, 37564}, {13205, 64077}, {13273, 37468}, {13528, 41389}, {13743, 38109}, {15501, 34913}, {15931, 64012}, {16049, 45396}, {16174, 53055}, {16371, 34697}, {17857, 46685}, {18524, 19914}, {21155, 37286}, {21669, 52850}, {22792, 26086}, {22935, 40262}, {26285, 37713}, {31870, 57283}, {37251, 57298}, {37305, 54090}, {38606, 40535}, {38665, 64056}, {40255, 49169}, {52769, 58453}, {53752, 60018}, {58698, 60912}, {59330, 64021}, {59331, 63966}

X(64188) = midpoint of X(i) and X(j) for these {i,j}: {1490, 1768}, {11500, 22775}, {12248, 12667}, {13205, 64077}, {33898, 38753}
X(64188) = reflection of X(i) in X(j) for these {i,j}: {100, 6796}, {1158, 46684}, {6265, 37837}, {10698, 40257}, {10742, 18242}, {12114, 38602}, {12332, 33814}, {12762, 11698}, {17661, 32159}, {22935, 40262}, {34789, 12608}, {48482, 11}, {48694, 22775}, {48695, 3}
X(64188) = inverse of X(49207) in circumcircle
X(64188) = X(i)-vertex conjugate of X(j) for these {i, j}: {2804, 49207}
X(64188) = pole of line {2804, 25438} with respect to the circumcircle
X(64188) = pole of line {24029, 46605} with respect to the Yff parabola
X(64188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 119, 51506}, {3, 2829, 48695}, {35, 34789, 12775}, {36, 44425, 1512}, {36, 64145, 104}, {40, 6326, 64139}, {104, 60782, 10265}, {104, 6905, 10090}, {952, 22775, 48694}, {2800, 6796, 100}, {2829, 18242, 10742}, {2932, 7580, 24466}, {6942, 12248, 18861}, {10698, 11491, 10087}, {11500, 22775, 952}, {33898, 38753, 2829}

X(64189) = ANTICOMPLEMENT OF X(1537)

Barycentrics    a*(a^6+a^5*(b+c)-(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)-a^4*(4*b^2+3*b*c+4*c^2)+a*(b-c)^2*(b^3-7*b^2*c-7*b*c^2+c^3)-2*a^3*(b^3-4*b^2*c-4*b*c^2+c^3)+a^2*(5*b^4-14*b^2*c^2+5*c^4)) : :
X(64189) = -2*X[1]+3*X[38693], -3*X[2]+2*X[1537], -2*X[4]+3*X[59415], -2*X[119]+3*X[5657], -3*X[165]+2*X[214], -5*X[631]+4*X[11729], -4*X[946]+5*X[31272], -2*X[1317]+3*X[5731], -3*X[1699]+4*X[6702], -5*X[3091]+6*X[34122], -7*X[3523]+6*X[34123], -3*X[3576]+2*X[25485]

X(64189) lies on these lines: {1, 38693}, {2, 1537}, {3, 5330}, {4, 59415}, {8, 2829}, {10, 34789}, {11, 962}, {20, 952}, {21, 12775}, {30, 19914}, {40, 78}, {46, 12758}, {57, 15558}, {63, 2950}, {80, 516}, {88, 32486}, {104, 517}, {119, 5657}, {144, 153}, {145, 64191}, {149, 6836}, {165, 214}, {329, 55016}, {355, 10728}, {376, 10031}, {484, 10090}, {497, 12832}, {515, 12531}, {519, 64145}, {528, 9803}, {631, 11729}, {651, 24028}, {758, 25438}, {944, 38761}, {946, 31272}, {1155, 12740}, {1158, 14923}, {1295, 35011}, {1317, 5731}, {1387, 6966}, {1445, 2093}, {1482, 38602}, {1484, 28212}, {1697, 5083}, {1699, 6702}, {1706, 46694}, {1768, 2802}, {1770, 10057}, {2077, 62826}, {2096, 12648}, {2771, 15054}, {2801, 2951}, {2818, 38512}, {2821, 13266}, {2827, 21385}, {2932, 6244}, {2975, 40256}, {3036, 16112}, {3091, 34122}, {3339, 18240}, {3359, 3877}, {3428, 4996}, {3523, 34123}, {3576, 25485}, {3579, 6265}, {3587, 9946}, {3616, 21154}, {3654, 10711}, {3655, 50910}, {3681, 12665}, {3699, 30196}, {3753, 61012}, {3868, 13278}, {3871, 64021}, {3873, 12703}, {3885, 63399}, {3890, 59333}, {4193, 32554}, {4297, 7972}, {4301, 16173}, {4511, 13528}, {4674, 64013}, {4861, 64118}, {4880, 26726}, {5080, 12761}, {5119, 7676}, {5183, 17638}, {5221, 5734}, {5303, 11014}, {5531, 12565}, {5603, 6713}, {5690, 10742}, {5691, 15863}, {5697, 10074}, {5709, 13279}, {5790, 22799}, {5818, 38128}, {5840, 6361}, {5855, 54193}, {5903, 10058}, {5927, 58659}, {6001, 12532}, {6224, 9778}, {6246, 41869}, {6735, 46435}, {6840, 10738}, {6890, 64138}, {6906, 25413}, {6915, 12672}, {6923, 59416}, {6960, 38752}, {6972, 22791}, {6986, 31788}, {7012, 36121}, {7580, 12331}, {7962, 41554}, {7970, 53733}, {7978, 53753}, {7982, 11715}, {7983, 53722}, {7984, 53715}, {8227, 38133}, {9588, 15017}, {9589, 37718}, {9809, 37725}, {9897, 64005}, {9943, 17660}, {9952, 12690}, {10087, 11010}, {10164, 64012}, {10265, 10707}, {10304, 50843}, {10306, 64047}, {10310, 17100}, {10595, 38032}, {10679, 63159}, {10695, 53750}, {10696, 53752}, {10697, 53746}, {10703, 23703}, {10884, 37736}, {11219, 21630}, {11248, 62830}, {11249, 18861}, {11362, 11684}, {11522, 32557}, {11531, 64137}, {11822, 12463}, {11823, 12462}, {12119, 31730}, {12512, 33337}, {12526, 14740}, {12528, 46685}, {12533, 63141}, {12611, 26446}, {12619, 12699}, {12701, 20118}, {12730, 43161}, {12739, 37568}, {12764, 40663}, {12773, 37022}, {13099, 53755}, {13257, 37421}, {14988, 35460}, {15015, 63469}, {15055, 31525}, {16174, 31162}, {17549, 61146}, {17566, 55297}, {17661, 34790}, {17768, 32198}, {18254, 54286}, {18493, 34126}, {19081, 35775}, {19082, 35774}, {19112, 49227}, {19113, 49226}, {20586, 64128}, {21635, 43174}, {22938, 48661}, {23340, 26877}, {23832, 53292}, {25722, 63137}, {28234, 62235}, {30308, 38104}, {31254, 33594}, {31393, 46681}, {31397, 60936}, {33814, 48667}, {34718, 50907}, {34773, 38754}, {35000, 38722}, {36002, 48363}, {37714, 38213}, {38084, 50806}, {38756, 59503}, {48668, 61249}, {50808, 64011}, {53409, 60990}

X(64189) = midpoint of X(i) and X(j) for these {i,j}: {149, 20070}, {1768, 7991}, {5541, 12767}, {6361, 12247}, {9897, 64005}, {12245, 12248}
X(64189) = reflection of X(i) in X(j) for these {i,j}: {1, 46684}, {100, 40}, {104, 12515}, {145, 64191}, {153, 1145}, {944, 38761}, {962, 11}, {1317, 38759}, {1320, 104}, {1482, 38602}, {1537, 64193}, {4511, 13528}, {5691, 15863}, {6224, 24466}, {6265, 3579}, {7970, 53733}, {7972, 4297}, {7978, 53753}, {7982, 11715}, {7983, 53722}, {7984, 53715}, {9809, 37725}, {9963, 13199}, {10031, 376}, {10695, 53750}, {10696, 53752}, {10697, 53746}, {10698, 3}, {10703, 53748}, {10711, 3654}, {10724, 80}, {10728, 355}, {10742, 5690}, {11531, 64137}, {12119, 31730}, {12528, 46685}, {12690, 9952}, {12699, 12619}, {12730, 43161}, {12751, 11362}, {13099, 53755}, {13253, 214}, {14217, 10265}, {17660, 9943}, {17661, 34790}, {20586, 64128}, {21635, 43174}, {33337, 12512}, {34789, 10}, {36002, 48363}, {38669, 1768}, {41869, 6246}, {48661, 22938}, {48667, 33814}, {48695, 40256}, {50907, 34718}, {50910, 3655}, {52836, 3036}, {62826, 2077}, {64011, 50808}, {64136, 12702}
X(64189) = anticomplement of X(1537)
X(64189) = pole of line {2401, 56234} with respect to the Steiner circumellipse
X(64189) = intersection, other than A, B, C, of circumconics {{A, B, C, X(102), X(10428)}}, {{A, B, C, X(1145), X(17613)}}, {{A, B, C, X(1295), X(52478)}}
X(64189) = barycentric product X(i)*X(j) for these (i, j): {38886, 75}
X(64189) = barycentric quotient X(i)/X(j) for these (i, j): {38886, 1}
X(64189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 46684, 38693}, {40, 2800, 100}, {80, 516, 10724}, {104, 517, 1320}, {119, 5657, 64141}, {153, 59417, 1145}, {165, 13253, 214}, {517, 12515, 104}, {952, 12702, 64136}, {952, 13199, 9963}, {1317, 38759, 5731}, {1768, 2802, 38669}, {1768, 7991, 2802}, {3036, 52836, 59387}, {5541, 12767, 2801}, {6224, 9778, 24466}, {10265, 14217, 10707}, {10265, 28194, 14217}, {10310, 22775, 17100}, {11010, 11571, 10087}, {12245, 12248, 952}, {12611, 26446, 64008}, {12619, 12699, 59391}, {12767, 63468, 5541}, {21154, 64192, 3616}, {54156, 63130, 12528}

X(64190) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-GARCIA AND X(80)-CROSSPEDAL-OF-X(4)

Barycentrics    3*a^7-a^6*(b+c)+a^2*(b-c)^4*(b+c)+a^4*(b+c)^3-(b-c)^4*(b+c)^3-a*(b-c)^2*(b+c)^4+a^5*(-7*b^2+6*b*c-7*c^2)+a^3*(b-c)^2*(5*b^2+6*b*c+5*c^2) : :
X(64190) = -3*X[2]+4*X[64118], -3*X[376]+2*X[6261], -5*X[631]+4*X[12608], -3*X[1699]+4*X[6705], -5*X[3522]+4*X[37837], -3*X[3576]+2*X[54198], -2*X[5534]+3*X[34607], -3*X[5658]+4*X[6796], -3*X[5770]+2*X[10525], -3*X[5918]+2*X[9942], -3*X[5927]+4*X[58660], -3*X[9812]+4*X[63980]

X(64190) lies on circumconic {{A, B, C, X(2123), X(7040)}} and on these lines: {1, 2096}, {2, 64118}, {3, 1633}, {4, 46}, {7, 11496}, {8, 2829}, {20, 3869}, {30, 34744}, {40, 2123}, {63, 49171}, {72, 12666}, {78, 48697}, {84, 516}, {109, 7952}, {144, 18239}, {165, 5924}, {191, 2950}, {278, 1777}, {329, 10309}, {347, 40658}, {376, 6261}, {382, 33899}, {390, 12675}, {497, 63399}, {499, 11665}, {515, 3529}, {517, 17648}, {527, 6769}, {631, 12608}, {758, 64076}, {912, 3189}, {944, 2800}, {946, 3361}, {962, 12114}, {1012, 4295}, {1071, 4294}, {1155, 6848}, {1376, 5811}, {1479, 1768}, {1490, 2951}, {1519, 7288}, {1699, 6705}, {1721, 57276}, {1836, 6847}, {2550, 7330}, {2551, 3359}, {2956, 5930}, {3073, 4000}, {3149, 64130}, {3427, 9800}, {3452, 10270}, {3476, 37002}, {3485, 6906}, {3486, 6938}, {3487, 60923}, {3488, 5884}, {3522, 37837}, {3556, 37404}, {3560, 28629}, {3576, 54198}, {3579, 6259}, {3600, 45776}, {3648, 6223}, {3683, 37407}, {3868, 64078}, {3927, 31777}, {4292, 12705}, {4293, 12672}, {4297, 7971}, {4640, 6908}, {4644, 37529}, {5057, 6890}, {5084, 59333}, {5221, 5804}, {5248, 60896}, {5330, 5731}, {5435, 7681}, {5450, 5563}, {5534, 34607}, {5536, 40265}, {5553, 12775}, {5658, 6796}, {5690, 40267}, {5694, 35249}, {5696, 63967}, {5704, 10893}, {5744, 15908}, {5758, 17768}, {5768, 6284}, {5770, 10525}, {5777, 17668}, {5787, 28146}, {5842, 9799}, {5880, 6846}, {5887, 6948}, {5918, 9942}, {5927, 58660}, {6245, 41869}, {6837, 20292}, {6864, 54370}, {6865, 64129}, {6885, 31937}, {6909, 11415}, {6916, 12514}, {6925, 56288}, {6926, 24703}, {6927, 58887}, {6930, 34339}, {6935, 12047}, {6950, 14803}, {6953, 9352}, {6987, 9943}, {7080, 13528}, {7580, 12330}, {7956, 37545}, {8726, 45084}, {9121, 53087}, {9669, 13226}, {9809, 12332}, {9812, 63980}, {9948, 28150}, {9965, 18238}, {10164, 63966}, {10531, 26877}, {10571, 33810}, {10595, 11551}, {10624, 63430}, {10860, 64004}, {11023, 24465}, {11248, 25568}, {11372, 64001}, {12512, 52026}, {12515, 37821}, {12520, 59345}, {12565, 63438}, {12572, 15239}, {12650, 28194}, {12664, 15726}, {12676, 17613}, {12678, 37568}, {12688, 50701}, {12699, 34862}, {12700, 34625}, {13374, 21454}, {14872, 17784}, {15803, 63989}, {17574, 54445}, {18237, 37022}, {22792, 26446}, {24467, 24477}, {26105, 37534}, {26364, 46435}, {36746, 64168}, {37001, 40663}, {37112, 62838}, {37526, 40998}, {37567, 64000}, {49170, 63984}, {51090, 61122}, {54051, 54228}, {63985, 64002}

X(64190) = midpoint of X(i) and X(j) for these {i,j}: {6361, 12246}, {7992, 64005}
X(64190) = reflection of X(i) in X(j) for these {i,j}: {4, 1158}, {382, 33899}, {962, 12114}, {1490, 31730}, {5758, 64074}, {6223, 11500}, {6256, 40256}, {6259, 3579}, {7971, 4297}, {9809, 12332}, {10309, 56889}, {12666, 72}, {12667, 40}, {12699, 34862}, {14647, 14646}, {16127, 6796}, {18239, 63976}, {40267, 5690}, {41869, 6245}, {46435, 46684}, {54227, 12512}, {63962, 3}, {64119, 64118}
X(64190) = anticomplement of X(64119)
X(64190) = X(i)-Dao conjugate of X(j) for these {i, j}: {64119, 64119}
X(64190) = pole of line {7649, 53532} with respect to the Suppa-Cucoanes circle
X(64190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1158, 14647}, {4, 14646, 1158}, {962, 54052, 12114}, {1155, 12679, 6848}, {1709, 1770, 4}, {3579, 6259, 64148}, {4302, 15071, 944}, {6223, 9778, 11500}, {6256, 40256, 5657}, {6361, 12246, 515}, {6796, 16127, 5658}, {12512, 54227, 52026}, {17768, 64074, 5758}, {24703, 64128, 6926}, {63985, 64002, 64111}

X(64191) = ORTHOLOGY CENTER OF THESE TRIANGLES: HUTSON INTOUCH AND X(80)-CROSSPEDAL-OF-X(4)

Barycentrics    4*a^7-6*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-5*b^2+22*b*c-5*c^2)-2*a^3*(b-c)^2*(b^2+9*b*c+c^2)+a*(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)-2*a^2*(b-c)^2*(2*b^3-5*b^2*c-5*b*c^2+2*c^3)+a^4*(11*b^3-13*b^2*c-13*b*c^2+11*c^3) : :
X(64191) = -2*X[5]+3*X[38032], -2*X[10]+3*X[21154], -3*X[165]+X[64056], -3*X[376]+X[64136], -2*X[381]+3*X[38026], -3*X[392]+X[17661], -2*X[546]+3*X[38044], -2*X[3035]+3*X[3576]

X(64191) lies on these lines: {1, 1537}, {3, 8}, {4, 1387}, {5, 38032}, {10, 21154}, {11, 515}, {20, 1320}, {30, 64138}, {40, 5854}, {55, 45635}, {56, 64188}, {65, 15528}, {80, 20418}, {119, 1385}, {145, 64189}, {149, 6925}, {153, 2478}, {165, 64056}, {214, 6700}, {355, 6713}, {376, 64136}, {381, 38026}, {390, 6938}, {392, 17661}, {516, 64137}, {517, 3937}, {519, 13528}, {528, 5732}, {546, 38044}, {855, 13265}, {946, 52836}, {950, 41554}, {960, 12665}, {1012, 3476}, {1071, 1317}, {1158, 37738}, {1388, 6256}, {1389, 24470}, {1478, 38039}, {1479, 12761}, {1482, 37002}, {1483, 64021}, {1484, 37406}, {1512, 5126}, {1519, 25405}, {1697, 2950}, {1768, 5119}, {1862, 37391}, {2077, 38455}, {2096, 3241}, {2646, 10956}, {2771, 24981}, {2777, 31523}, {2801, 33337}, {2802, 4297}, {3035, 3576}, {3036, 5881}, {3149, 41426}, {3295, 10935}, {3523, 64141}, {3524, 50907}, {3612, 12749}, {3655, 6265}, {3756, 41343}, {3895, 12515}, {4186, 12138}, {4293, 24465}, {4311, 12736}, {4315, 18240}, {4861, 31775}, {5450, 10944}, {5480, 38050}, {5531, 64011}, {5587, 6667}, {5603, 10728}, {5691, 16173}, {5697, 54176}, {5805, 38055}, {5840, 12700}, {5842, 36975}, {5844, 35460}, {5856, 43161}, {5884, 37734}, {5901, 22799}, {6001, 12758}, {6174, 51705}, {6261, 12740}, {6282, 34716}, {6702, 38156}, {6831, 45287}, {6834, 12019}, {6872, 64009}, {6921, 59415}, {6929, 10246}, {6955, 40587}, {6959, 10785}, {6962, 20085}, {7294, 40260}, {7686, 58595}, {7991, 26726}, {8068, 63980}, {8104, 9837}, {8256, 59332}, {9845, 59347}, {9897, 11219}, {10031, 13243}, {10035, 46704}, {10043, 10058}, {10051, 10074}, {10087, 12332}, {10090, 11500}, {10106, 63257}, {10165, 31235}, {10265, 37605}, {10306, 13278}, {10310, 25438}, {10543, 13607}, {10738, 12116}, {10786, 38752}, {10936, 12776}, {10950, 12832}, {10966, 45634}, {10993, 12732}, {11570, 12675}, {11826, 22837}, {12611, 15178}, {12619, 18857}, {12650, 34489}, {12672, 15558}, {12680, 17638}, {12690, 37726}, {12702, 38754}, {12763, 34471}, {13205, 63991}, {13273, 48482}, {13624, 38760}, {13867, 46681}, {13913, 49601}, {13977, 49602}, {14740, 64107}, {14872, 18254}, {15017, 30392}, {15863, 28236}, {16116, 61281}, {16174, 31673}, {17009, 21677}, {17757, 32554}, {18242, 21842}, {18357, 34126}, {18480, 23513}, {18908, 46694}, {19907, 21740}, {19925, 32557}, {20400, 30389}, {22938, 28186}, {28160, 64186}, {28224, 61566}, {31272, 59387}, {31786, 64139}, {31788, 39776}, {33709, 38161}, {34628, 50891}, {34632, 50894}, {34648, 38077}, {36991, 53055}, {37136, 56690}, {37568, 62617}, {37624, 38756}, {37720, 56036}, {37829, 47745}, {38028, 61580}, {38060, 63970}, {38177, 61249}, {38319, 61261}, {39870, 51198}, {40257, 41543}, {46685, 51379}, {50796, 59376}, {50864, 59377}

X(64191) = midpoint of X(i) and X(j) for these {i,j}: {1, 64145}, {20, 1320}, {104, 944}, {145, 64189}, {1482, 38753}, {1768, 7972}, {6224, 38669}, {6264, 12119}, {7991, 26726}, {10698, 12248}, {12515, 37727}, {12680, 17638}, {12737, 18481}, {18526, 19914}, {34628, 50891}, {34632, 50894}
X(64191) = reflection of X(i) in X(j) for these {i,j}: {4, 1387}, {8, 64193}, {11, 11715}, {40, 38759}, {65, 15528}, {80, 20418}, {119, 1385}, {355, 6713}, {1145, 3}, {1317, 5882}, {1512, 5126}, {1519, 25405}, {1532, 1319}, {1537, 1}, {5881, 3036}, {6174, 51705}, {7686, 58595}, {10698, 12735}, {10742, 11729}, {11570, 12675}, {12247, 13226}, {12611, 15178}, {12665, 960}, {12672, 15558}, {12690, 37726}, {12732, 10993}, {12751, 3035}, {13257, 6265}, {14872, 18254}, {21677, 17009}, {22799, 5901}, {24466, 4297}, {25485, 13607}, {31673, 16174}, {34789, 64192}, {37725, 214}, {38665, 9945}, {39776, 31788}, {46704, 10035}, {50843, 3655}, {51198, 39870}, {52836, 946}, {62616, 10265}, {64139, 31786}
X(64191) = inverse of X(44675) in Feuerbach hyperbola
X(64191) = pole of line {2804, 25416} with respect to the incircle
X(64191) = pole of line {2800, 18838} with respect to the Feuerbach hyperbola
X(64191) = pole of line {2804, 26726} with respect to the Suppa-Cucoanes circle
X(64191) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1, 61481, 64145}, {11, 3318, 58893}, {1768, 7972, 56423}
X(64191) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1145), X(2734)}}, {{A, B, C, X(10305), X(36944)}}, {{A, B, C, X(46435), X(51565)}}
X(64191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2829, 1537}, {1, 34789, 64192}, {1, 64145, 2829}, {3, 952, 1145}, {4, 1387, 38038}, {8, 38693, 64193}, {104, 11491, 18861}, {104, 12247, 13226}, {104, 944, 952}, {119, 1385, 34123}, {515, 1319, 1532}, {952, 13226, 12247}, {952, 64193, 8}, {952, 9945, 38665}, {2800, 5882, 1317}, {2802, 4297, 24466}, {2829, 64192, 34789}, {3576, 12751, 3035}, {5854, 38759, 40}, {6264, 12119, 528}, {6264, 50811, 12119}, {7967, 10698, 12735}, {7967, 12248, 10698}, {10246, 10742, 11729}, {11491, 18861, 33814}, {12737, 18481, 5840}, {13257, 50843, 6265}, {16174, 31673, 59390}

X(64192) = ORTHOLOGY CENTER OF THESE TRIANGLES: INCIRCLE-CIRCLES AND X(80)-CROSSPEDAL-OF-X(4)

Barycentrics    2*a^7-6*a^6*(b+c)-8*a^2*(b-c)^4*(b+c)+(b-c)^4*(b+c)^3-a^5*(b^2-20*b*c+c^2)-4*a^3*(b-c)^2*(b^2+6*b*c+c^2)+a*(b^2-c^2)^2*(3*b^2-4*b*c+3*c^2)+a^4*(13*b^3-17*b^2*c-17*b*c^2+13*c^3) : :
X(64192) = -X[40]+3*X[34123], -X[80]+5*X[11522], -3*X[551]+X[46684], -X[1320]+5*X[5734], -5*X[1656]+3*X[38128], 3*X[1699]+X[7972], -5*X[3091]+X[12531]

X(64192) lies on these lines: {1, 1537}, {4, 1317}, {5, 3036}, {11, 2099}, {40, 34123}, {56, 11047}, {80, 11522}, {100, 22753}, {104, 3296}, {119, 1482}, {145, 10893}, {214, 4301}, {388, 12761}, {515, 12735}, {517, 3035}, {519, 22835}, {528, 3656}, {546, 946}, {551, 46684}, {942, 1387}, {944, 52836}, {962, 24466}, {999, 45637}, {1012, 10074}, {1125, 64193}, {1145, 7982}, {1320, 5734}, {1385, 38759}, {1466, 12332}, {1483, 22799}, {1519, 5048}, {1532, 63210}, {1656, 38128}, {1699, 7972}, {1768, 11034}, {2098, 10956}, {2802, 7686}, {2950, 3333}, {3091, 12531}, {3149, 10087}, {3295, 64188}, {3545, 50910}, {3555, 12665}, {3577, 5660}, {3616, 21154}, {3622, 38693}, {3816, 32554}, {3817, 15863}, {3878, 5771}, {5045, 15528}, {5071, 38099}, {5083, 6001}, {5330, 15908}, {5531, 50891}, {5533, 6831}, {5542, 11715}, {5552, 18802}, {5657, 31235}, {5690, 58421}, {5715, 12690}, {5720, 34640}, {5840, 19907}, {5844, 61580}, {5851, 12773}, {5882, 22792}, {5883, 5901}, {5886, 6667}, {6174, 64136}, {6256, 54176}, {6264, 13257}, {6326, 12658}, {6691, 25413}, {7956, 11698}, {7967, 10728}, {7991, 64012}, {8068, 63257}, {8148, 38752}, {8227, 34122}, {9945, 64001}, {10051, 15845}, {10058, 11045}, {10246, 38761}, {10247, 10742}, {10283, 38602}, {10427, 43166}, {10531, 12764}, {10532, 13273}, {10609, 14217}, {10738, 26332}, {10894, 59391}, {11009, 39692}, {11048, 12776}, {11224, 15017}, {11278, 38758}, {11376, 12832}, {11570, 12672}, {12019, 16174}, {12119, 31162}, {12245, 64008}, {12515, 37612}, {12560, 38055}, {12619, 45310}, {12675, 46681}, {12702, 38760}, {12730, 59385}, {12736, 13374}, {12739, 63986}, {12751, 16200}, {12831, 20586}, {13253, 16173}, {13463, 45770}, {13756, 46044}, {14151, 36991}, {15558, 64160}, {16189, 26726}, {18493, 19914}, {18861, 45977}, {20119, 38152}, {22770, 51506}, {24042, 28224}, {26087, 37290}, {28234, 51362}, {33594, 44669}, {34339, 58604}, {34627, 50846}, {34631, 50842}, {37624, 38753}, {37726, 48667}, {37736, 63992}, {38077, 50890}, {38319, 61272}, {39898, 51198}, {43174, 58453}, {45636, 48694}, {56890, 59816}, {59390, 62617}

X(64192) = midpoint of X(i) and X(j) for these {i,j}: {1, 1537}, {4, 1317}, {11, 10698}, {119, 1482}, {214, 4301}, {944, 52836}, {946, 25485}, {962, 24466}, {1145, 7982}, {1320, 37725}, {1483, 22799}, {1519, 5048}, {1532, 63210}, {3555, 12665}, {6264, 13257}, {6265, 64138}, {10222, 12611}, {10427, 43166}, {10609, 14217}, {11570, 12672}, {12751, 25416}, {13756, 46044}, {19907, 22791}, {21635, 64137}, {31162, 50843}, {34627, 50846}, {34631, 50842}, {34789, 64191}, {37726, 48667}, {39898, 51198}
X(64192) = reflection of X(i) in X(j) for these {i,j}: {1145, 20400}, {1387, 13464}, {3035, 11729}, {3036, 5}, {5690, 58421}, {6713, 5901}, {12019, 16174}, {12675, 46681}, {12736, 13374}, {15528, 5045}, {20418, 1387}, {34339, 58604}, {38757, 12611}, {38759, 1385}, {43174, 58453}, {45310, 51709}, {64193, 1125}
X(64192) = pole of line {2804, 64056} with respect to the incircle
X(64192) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 1317, 1359}, {11, 3318, 10698}
X(64192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1537, 2829}, {1, 34789, 64191}, {80, 11522, 38038}, {119, 1482, 5854}, {517, 11729, 3035}, {952, 12611, 38757}, {1387, 2800, 20418}, {1537, 64191, 34789}, {2800, 13464, 1387}, {3091, 12531, 38156}, {3616, 64189, 21154}, {3656, 6265, 64138}, {6264, 50908, 13257}, {6265, 64138, 528}, {10222, 12611, 952}, {12515, 61276, 38032}, {12751, 16200, 25416}, {18493, 19914, 23513}, {19907, 22791, 5840}

X(64193) = COMPLEMENT OF X(1537)

Barycentrics    2*a^7-3*a*(b-c)^4*(b+c)^2+(b-c)^4*(b+c)^3-7*a^5*(b^2+c^2)-2*a^2*(b-c)^2*(b^3+6*b^2*c+6*b*c^2+c^3)+a^4*(b^3+9*b^2*c+9*b*c^2+c^3)+2*a^3*(4*b^4-3*b^3*c-6*b^2*c^2-3*b*c^3+4*c^4) : :
X(64193) = -X[1]+3*X[21154], -3*X[2]+X[1537], -X[4]+3*X[34122], X[20]+3*X[59415], X[80]+3*X[165], -3*X[210]+X[12665], -X[214]+3*X[10164], -X[355]+3*X[38128], -3*X[549]+X[19907], -5*X[631]+X[10698], -X[962]+5*X[31272], -X[1317]+3*X[3576] and many others

X(64193) lies on these lines: {1, 21154}, {2, 1537}, {3, 8}, {4, 34122}, {5, 32554}, {9, 119}, {10, 2829}, {11, 40}, {20, 59415}, {30, 1512}, {46, 24465}, {55, 12832}, {63, 55016}, {80, 165}, {140, 392}, {149, 6865}, {153, 6916}, {210, 12665}, {214, 10164}, {355, 38128}, {405, 12775}, {484, 8068}, {515, 3036}, {516, 6702}, {517, 1387}, {518, 15528}, {528, 10265}, {549, 19907}, {631, 10698}, {653, 21664}, {912, 51380}, {946, 6667}, {958, 48695}, {960, 2800}, {962, 31272}, {971, 58659}, {1000, 5281}, {1071, 46685}, {1108, 50650}, {1125, 64192}, {1158, 37828}, {1317, 3576}, {1320, 59417}, {1329, 40256}, {1376, 64188}, {1385, 12735}, {1482, 6961}, {1484, 37364}, {1656, 11024}, {1698, 34789}, {1737, 13528}, {1768, 9588}, {1772, 15253}, {1788, 10306}, {1862, 7412}, {2077, 40663}, {2095, 8732}, {2771, 20417}, {2801, 40659}, {2802, 20418}, {3428, 10090}, {3524, 50843}, {3579, 5840}, {3654, 12737}, {3656, 38069}, {3679, 64145}, {3697, 17661}, {3872, 18802}, {4297, 15863}, {4301, 32557}, {5083, 9940}, {5128, 5812}, {5316, 11231}, {5445, 15908}, {5450, 8256}, {5493, 59419}, {5533, 11010}, {5535, 63270}, {5537, 63281}, {5541, 11219}, {5587, 52836}, {5603, 61535}, {5660, 12767}, {5691, 38156}, {5708, 12872}, {5762, 60363}, {5777, 46694}, {5790, 6948}, {5818, 10728}, {5841, 10225}, {5851, 15481}, {5854, 11260}, {5855, 54192}, {5882, 32157}, {5884, 64123}, {5885, 63282}, {5886, 31190}, {5887, 47742}, {5901, 25413}, {6001, 18254}, {6154, 10268}, {6174, 6326}, {6246, 31730}, {6264, 13996}, {6265, 38760}, {6361, 59391}, {6797, 31793}, {6825, 38752}, {6827, 10738}, {6842, 61580}, {6850, 10742}, {6882, 28174}, {6891, 12702}, {6908, 13257}, {6918, 26062}, {6923, 22799}, {6926, 64136}, {6928, 22938}, {6951, 38058}, {6954, 38762}, {6958, 22791}, {6971, 40273}, {6978, 8166}, {6982, 40333}, {6987, 12690}, {7080, 10305}, {7491, 61553}, {7972, 7987}, {7991, 16173}, {8164, 60934}, {8726, 37736}, {9616, 19077}, {9709, 45039}, {9778, 10724}, {9897, 16192}, {9943, 32159}, {9955, 38319}, {9956, 44848}, {10031, 15692}, {10057, 58887}, {10058, 10310}, {10073, 59316}, {10165, 25485}, {10270, 12751}, {10304, 50890}, {10523, 59330}, {10679, 42884}, {10944, 59332}, {10956, 59333}, {10993, 62354}, {11248, 57278}, {11499, 33899}, {11698, 37424}, {11826, 18395}, {11827, 37572}, {11849, 12433}, {12119, 35242}, {12138, 37305}, {12245, 25416}, {12332, 51506}, {12699, 23513}, {12703, 17728}, {12743, 63211}, {12749, 16209}, {12750, 16208}, {12758, 55301}, {13145, 31659}, {13243, 37108}, {13253, 64012}, {13600, 64124}, {13913, 35774}, {13977, 35775}, {14647, 38211}, {14740, 58643}, {14988, 41389}, {16174, 28194}, {17009, 44669}, {17652, 61566}, {17654, 64107}, {18232, 18242}, {18253, 38757}, {18259, 19919}, {18525, 38754}, {20095, 37423}, {20118, 37568}, {20119, 59418}, {20400, 21635}, {22793, 38182}, {22935, 31447}, {24028, 43043}, {24954, 31235}, {26285, 37730}, {28228, 33709}, {31162, 59376}, {31525, 38727}, {32486, 43055}, {34196, 34311}, {34632, 59377}, {35004, 37737}, {36279, 54366}, {37256, 38215}, {37374, 48363}, {37718, 63469}, {38060, 43166}, {38077, 50865}, {38112, 61539}, {38152, 63974}, {38161, 51118}, {38216, 63973}, {39776, 59491}, {41869, 59390}, {45122, 52830}, {45776, 58405}, {47032, 61622}, {53055, 62775}, {55305, 59320}, {58441, 58453}

X(64193) = midpoint of X(i) and X(j) for these {i,j}: {8, 64191}, {10, 46684}, {11, 40}, {80, 24466}, {104, 1145}, {119, 12515}, {355, 38761}, {1071, 46685}, {1512, 17613}, {1537, 64189}, {1737, 13528}, {1768, 37725}, {2077, 40663}, {3036, 38759}, {3579, 12619}, {4297, 15863}, {5690, 38602}, {6154, 49176}, {6246, 31730}, {6264, 13996}, {6797, 31793}, {9945, 9952}, {10609, 12247}, {10993, 62354}, {11362, 11715}, {12119, 62616}, {12245, 25416}, {12690, 13199}, {12702, 64138}, {17654, 64139}, {37374, 48363}, {46435, 52116}
X(64193) = reflection of X(i) in X(j) for these {i,j}: {946, 6667}, {1387, 6713}, {3035, 6684}, {5083, 9940}, {5777, 46694}, {9945, 33814}, {11729, 140}, {12019, 12619}, {12611, 58421}, {12735, 1385}, {14740, 58643}, {18254, 58666}, {21635, 20400}, {64192, 1125}
X(64193) = complement of X(1537)
X(64193) = pole of line {1387, 2804} with respect to the Spieker circle
X(64193) = pole of line {1317, 12665} with respect to the Feuerbach hyperbola
X(64193) = pole of line {2401, 56234} with respect to the Steiner inellipse
X(64193) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 40, 14115}, {1768, 37725, 56423}
X(64193) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(38243)}}, {{A, B, C, X(10305), X(52178)}}, {{A, B, C, X(34234), X(46435)}}
X(64193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64189, 1537}, {8, 38693, 64191}, {10, 46684, 2829}, {80, 165, 24466}, {104, 1145, 952}, {104, 5657, 1145}, {517, 6713, 1387}, {631, 10698, 34123}, {946, 38133, 6667}, {952, 33814, 9945}, {956, 5657, 5690}, {962, 31272, 38038}, {1512, 17613, 30}, {2800, 6684, 3035}, {3036, 38759, 515}, {3359, 26446, 6907}, {3579, 12619, 5840}, {5771, 61524, 5657}, {5840, 12619, 12019}, {6001, 58666, 18254}, {6684, 31788, 52265}, {11231, 12611, 58421}, {11362, 11715, 5854}, {12247, 34474, 10609}, {12515, 26446, 119}, {12515, 37822, 52116}, {12702, 57298, 64138}, {33814, 38602, 38722}, {37562, 55297, 11729}, {38128, 38761, 355}

X(64194) = ANTICOMPLEMENT OF X(1465)

Barycentrics    b*c*(-2*a^4+a^2*(b-c)^2+a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :

X(64194) lies on these lines: {1, 27378}, {2, 92}, {3, 23661}, {4, 52366}, {5, 56875}, {8, 3427}, {9, 26591}, {10, 1076}, {20, 318}, {30, 38462}, {40, 23528}, {46, 17869}, {57, 17862}, {63, 321}, {69, 189}, {75, 5744}, {78, 52345}, {85, 50442}, {100, 2723}, {144, 4671}, {158, 27379}, {165, 17860}, {201, 34831}, {225, 24984}, {226, 18726}, {241, 26011}, {242, 33849}, {306, 57837}, {345, 20928}, {348, 21588}, {394, 28950}, {484, 23580}, {514, 661}, {516, 24026}, {517, 38955}, {535, 15065}, {655, 3218}, {860, 60427}, {894, 26587}, {927, 36796}, {971, 61185}, {1038, 24537}, {1060, 5136}, {1089, 12527}, {1096, 27403}, {1146, 26005}, {1229, 45738}, {1231, 20926}, {1295, 1309}, {1817, 31623}, {1829, 51558}, {1895, 27402}, {1896, 13614}, {1897, 3100}, {1944, 63068}, {1999, 62798}, {2094, 39126}, {2968, 37374}, {2975, 4968}, {3091, 5342}, {3101, 23512}, {3187, 55399}, {3262, 20920}, {3306, 20905}, {3436, 3701}, {3666, 18662}, {3702, 3869}, {3911, 4858}, {3952, 17615}, {4224, 7009}, {4296, 11109}, {4329, 32000}, {4359, 14213}, {4554, 7112}, {4723, 5176}, {4742, 62826}, {4980, 20879}, {5057, 33650}, {5081, 6840}, {5090, 36496}, {5174, 6895}, {5287, 5736}, {5435, 54284}, {5745, 6358}, {5748, 18743}, {5812, 5906}, {5905, 26871}, {5942, 31018}, {6357, 36949}, {6757, 58404}, {6851, 56876}, {6882, 34332}, {6996, 46108}, {7046, 52365}, {7102, 26118}, {7718, 28104}, {7952, 27505}, {8747, 27405}, {8758, 26095}, {14058, 42456}, {14212, 30834}, {14829, 54107}, {15252, 33305}, {15803, 20320}, {15988, 27064}, {16414, 59642}, {17102, 20222}, {17350, 26612}, {17484, 37781}, {17720, 53510}, {17740, 20895}, {18151, 37758}, {18607, 52358}, {19785, 55905}, {19799, 61414}, {20887, 51583}, {20927, 28808}, {20940, 40704}, {20999, 39572}, {21318, 37354}, {22129, 28968}, {23689, 29658}, {23690, 33140}, {23978, 46109}, {24627, 26538}, {24983, 46878}, {25001, 54357}, {26163, 27059}, {26223, 55400}, {27411, 64082}, {28765, 33157}, {28956, 37788}, {30007, 30029}, {30034, 30076}, {30699, 55907}, {32774, 55900}, {34822, 53008}, {34851, 56285}, {35516, 51414}, {36100, 36795}, {37365, 59520}, {39351, 63002}, {42709, 56883}, {46421, 60853}, {46422, 60854}, {46873, 46938}, {50102, 55906}, {51368, 59205}, {53816, 57810}, {56082, 56545}

X(64194) = isogonal conjugate of X(32677)
X(64194) = isotomic conjugate of X(36100)
X(64194) = anticomplement of X(1465)
X(64194) = trilinear pole of line {14304, 24034}
X(64194) = perspector of circumconic {{A, B, C, X(75), X(18026)}}
X(64194) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 32677}, {6, 102}, {19, 36055}, {31, 36100}, {32, 34393}, {48, 36121}, {56, 15629}, {109, 2432}, {110, 55255}, {184, 52780}, {251, 46359}, {521, 32667}, {522, 32643}, {650, 36040}, {652, 36067}, {2161, 58741}, {2342, 60000}, {6589, 35183}, {8607, 15379}, {8999, 32683}, {15633, 23979}, {32656, 60584}, {32660, 53152}, {32675, 61042}
X(64194) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 15629}, {2, 36100}, {3, 32677}, {6, 36055}, {9, 102}, {11, 2432}, {244, 55255}, {515, 2182}, {1249, 36121}, {1465, 1465}, {6376, 34393}, {8607, 1735}, {10017, 650}, {23986, 1}, {34050, 43058}, {35128, 61042}, {36944, 52663}, {40584, 58741}, {40585, 46359}, {40624, 2399}, {46974, 2323}, {51221, 19}, {57291, 46391}, {62605, 52780}
X(64194) = X(i)-Ceva conjugate of X(j) for these {i, j}: {75, 24034}, {36795, 2}
X(64194) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1, 36918}, {9, 153}, {104, 7}, {909, 145}, {1309, 46400}, {1795, 347}, {1809, 4329}, {2250, 2475}, {2342, 2}, {2423, 58371}, {2720, 4025}, {10428, 1266}, {13136, 21302}, {15501, 5932}, {18816, 21285}, {32641, 522}, {34051, 36845}, {34234, 3434}, {34858, 3210}, {36037, 693}, {36110, 17896}, {36123, 56927}, {36795, 6327}, {37136, 3900}, {38955, 2893}, {41933, 38460}, {43728, 150}, {51565, 69}, {52663, 8}, {54953, 46402}, {61238, 149}
X(64194) = X(i)-cross conjugate of X(j) for these {i, j}: {24034, 75}
X(64194) = pole of line {693, 10444} with respect to the Conway circle
X(64194) = pole of line {347, 693} with respect to the DeLongchamps circle
X(64194) = pole of line {19, 650} with respect to the polar circle
X(64194) = pole of line {693, 1441} with respect to the MacBeath inconic
X(64194) = pole of line {163, 2193} with respect to the Stammler hyperbola
X(64194) = pole of line {8, 521} with respect to the Steiner circumellipse
X(64194) = pole of line {10, 521} with respect to the Steiner inellipse
X(64194) = pole of line {522, 4551} with respect to the Yff parabola
X(64194) = pole of line {662, 1812} with respect to the Wallace hyperbola
X(64194) = pole of line {2, 2417} with respect to the dual conic of Adams circle
X(64194) = pole of line {321, 15416} with respect to the dual conic of circumcircle
X(64194) = pole of line {2, 2417} with respect to the dual conic of Conway circle
X(64194) = pole of line {2, 2417} with respect to the dual conic of incircle
X(64194) = pole of line {63, 57184} with respect to the dual conic of polar circle
X(64194) = pole of line {651, 4391} with respect to the dual conic of Feuerbach hyperbola
X(64194) = pole of line {244, 1210} with respect to the dual conic of Yff parabola
X(64194) = pole of line {661, 53560} with respect to the dual conic of Wallace hyperbola
X(64194) = pole of line {2, 2417} with respect to the dual conic of Suppa-Cucoanes circle
X(64194) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6332)}}, {{A, B, C, X(63), X(17080)}}, {{A, B, C, X(69), X(347)}}, {{A, B, C, X(92), X(4391)}}, {{A, B, C, X(189), X(278)}}, {{A, B, C, X(273), X(309)}}, {{A, B, C, X(281), X(3239)}}, {{A, B, C, X(655), X(908)}}, {{A, B, C, X(661), X(1880)}}, {{A, B, C, X(857), X(7452)}}, {{A, B, C, X(1214), X(24018)}}, {{A, B, C, X(1295), X(1465)}}, {{A, B, C, X(1309), X(2405)}}, {{A, B, C, X(1441), X(14208)}}, {{A, B, C, X(1577), X(40149)}}, {{A, B, C, X(2006), X(32706)}}, {{A, B, C, X(2861), X(8048)}}, {{A, B, C, X(3762), X(26736)}}, {{A, B, C, X(3904), X(17923)}}, {{A, B, C, X(3948), X(55254)}}, {{A, B, C, X(4358), X(42718)}}, {{A, B, C, X(4728), X(53522)}}, {{A, B, C, X(4791), X(59283)}}, {{A, B, C, X(5089), X(51361)}}, {{A, B, C, X(6087), X(34371)}}, {{A, B, C, X(6590), X(8755)}}, {{A, B, C, X(14304), X(37805)}}, {{A, B, C, X(14349), X(53082)}}, {{A, B, C, X(29069), X(55128)}}, {{A, B, C, X(34255), X(51375)}}, {{A, B, C, X(36795), X(59205)}}, {{A, B, C, X(37695), X(56261)}}, {{A, B, C, X(37800), X(55963)}}, {{A, B, C, X(40188), X(48335)}}, {{A, B, C, X(42549), X(48334)}}, {{A, B, C, X(48131), X(51414)}}, {{A, B, C, X(48398), X(61411)}}, {{A, B, C, X(50457), X(51421)}}, {{A, B, C, X(52412), X(57066)}}
X(64194) = barycentric product X(i)*X(j) for these (i, j): {1, 35516}, {264, 46974}, {304, 8755}, {309, 51375}, {312, 34050}, {314, 51421}, {320, 59283}, {515, 75}, {1455, 3596}, {2182, 76}, {2406, 4391}, {3262, 56638}, {11700, 20566}, {14208, 7452}, {14304, 664}, {18026, 39471}, {23987, 35518}, {24034, 34393}, {24035, 6332}, {30710, 51414}, {30806, 63857}, {31623, 51368}, {36100, 59205}, {42718, 514}, {46391, 46404}, {51361, 6063}, {51424, 57815}, {53522, 668}, {55254, 661}
X(64194) = barycentric quotient X(i)/X(j) for these (i, j): {1, 102}, {2, 36100}, {3, 36055}, {4, 36121}, {6, 32677}, {9, 15629}, {36, 58741}, {38, 46359}, {75, 34393}, {92, 52780}, {108, 36067}, {109, 36040}, {117, 1735}, {515, 1}, {650, 2432}, {661, 55255}, {1359, 1455}, {1415, 32643}, {1455, 56}, {1465, 60000}, {1735, 54242}, {2182, 6}, {2406, 651}, {2425, 1415}, {3738, 61042}, {4391, 2399}, {6001, 56634}, {6087, 6129}, {7452, 162}, {8755, 19}, {9056, 36088}, {10017, 35014}, {11700, 36}, {13138, 6081}, {14304, 522}, {17924, 60584}, {23986, 2182}, {23987, 108}, {24026, 15633}, {24034, 515}, {24035, 653}, {26704, 36108}, {26715, 36135}, {32674, 32667}, {34050, 57}, {35516, 75}, {36050, 35183}, {38554, 46974}, {39471, 521}, {42718, 190}, {42755, 1769}, {44426, 53152}, {46391, 652}, {46974, 3}, {51361, 55}, {51368, 1214}, {51375, 40}, {51408, 1155}, {51414, 3666}, {51421, 65}, {51422, 1319}, {51424, 354}, {53522, 513}, {55128, 21189}, {55254, 799}, {56638, 104}, {57291, 53557}, {57446, 53525}, {59283, 80}, {63857, 1156}
X(64194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37798, 17923}, {2, 6360, 17080}, {3, 41013, 23661}, {92, 6350, 1441}, {225, 34823, 24984}, {312, 18750, 329}, {908, 14206, 30807}, {908, 914, 3936}, {1038, 54396, 24537}, {3218, 18359, 48380}, {4358, 30807, 908}, {14058, 42456, 44706}, {14213, 59491, 4359}, {18743, 20921, 5748}, {18743, 20930, 30828}, {20222, 27506, 17102}, {20920, 32851, 3262}

X(64195) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(69)-CROSSPEDAL-OF-X(6) AND 1ST EHRMANN

Barycentrics    a^2*(a^6+b^6+b^4*c^2+b^2*c^4+c^6-a^4*(b^2+c^2)-a^2*(b^2+c^2)^2) : :
X(64195) = -X[159]+3*X[3167], -X[6391]+3*X[11216], -X[15581]+4*X[41597], -X[17834]+3*X[23041], -3*X[19153]+X[37491], -X[34778]+3*X[37497], -2*X[35228]+3*X[47391], X[36851]+3*X[63174], -2*X[58437]+3*X[59553], -4*X[58450]+3*X[61646]

X(64195) lies on these lines: {2, 6}, {26, 206}, {50, 9723}, {68, 20300}, {76, 53485}, {110, 20987}, {125, 30803}, {155, 1503}, {157, 50645}, {159, 3167}, {182, 1216}, {184, 3313}, {195, 5050}, {287, 20564}, {297, 8746}, {338, 56017}, {542, 31181}, {571, 36212}, {575, 13154}, {576, 19137}, {651, 18626}, {732, 23128}, {1092, 19161}, {1176, 2979}, {1181, 44882}, {1236, 7754}, {1350, 7512}, {1351, 7506}, {1352, 5576}, {1576, 23163}, {1609, 34990}, {1843, 3292}, {2393, 34966}, {2781, 5504}, {2854, 13248}, {2892, 17847}, {2904, 19128}, {2911, 20808}, {2916, 6800}, {2965, 52275}, {3001, 40947}, {3098, 18475}, {3157, 9021}, {3431, 55646}, {3448, 31114}, {3518, 11477}, {3564, 13371}, {3818, 15068}, {3917, 5157}, {5017, 46288}, {5020, 58532}, {5026, 39839}, {5085, 7592}, {5169, 46448}, {5480, 7528}, {5505, 38263}, {5621, 12219}, {5965, 8548}, {6090, 16776}, {6391, 11216}, {6593, 19118}, {6642, 32191}, {6689, 19150}, {6776, 18948}, {7540, 31670}, {7568, 44480}, {7758, 14376}, {7760, 53490}, {7780, 58454}, {8265, 43183}, {8547, 17710}, {8705, 9924}, {9022, 22130}, {9027, 39125}, {9053, 64069}, {9306, 9969}, {9605, 23133}, {9973, 63183}, {10020, 34380}, {11441, 36990}, {11456, 48905}, {11511, 32366}, {11574, 34986}, {12007, 44503}, {12017, 15087}, {12163, 15578}, {12164, 63420}, {12167, 51994}, {12319, 34775}, {12383, 48910}, {13346, 34146}, {13367, 54374}, {13490, 21850}, {13754, 44883}, {14561, 36749}, {14615, 19221}, {14927, 43605}, {15069, 39588}, {15135, 38396}, {15321, 31133}, {15581, 41597}, {15583, 52077}, {16473, 38047}, {17834, 23041}, {18382, 44665}, {18440, 50461}, {18445, 46264}, {19121, 23061}, {19125, 19127}, {19130, 39522}, {19149, 29181}, {19153, 37491}, {20423, 43726}, {20771, 44456}, {20819, 34396}, {21852, 43586}, {21969, 44091}, {24206, 53999}, {29012, 32139}, {32001, 52418}, {34148, 41716}, {34778, 37497}, {35228, 47391}, {36851, 63174}, {37452, 63722}, {37483, 48881}, {37488, 64061}, {37813, 61629}, {38435, 53097}, {44668, 44752}, {45286, 48901}, {48892, 64098}, {48895, 64099}, {51739, 58891}, {52124, 58770}, {58437, 59553}, {58450, 61646}

X(64195) = midpoint of X(i) and X(j) for these {i,j}: {12164, 63420}, {16266, 19139}, {19149, 37498}, {19588, 34777}
X(64195) = reflection of X(i) in X(j) for these {i,j}: {68, 20300}, {12163, 15578}, {15577, 1147}, {34117, 19139}, {37488, 64061}
X(64195) = inverse of X(62376) in MacBeath circumconic
X(64195) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 18124}, {661, 1286}
X(64195) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 18124}, {10316, 22}, {36830, 1286}
X(64195) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18018, 3}
X(64195) = pole of line {5157, 6467} with respect to the Jerabek hyperbola
X(64195) = pole of line {2, 44527} with respect to the Kiepert hyperbola
X(64195) = pole of line {99, 1286} with respect to the Kiepert parabola
X(64195) = pole of line {525, 23285} with respect to the MacBeath circumconic
X(64195) = pole of line {6, 5133} with respect to the Stammler hyperbola
X(64195) = pole of line {523, 37978} with respect to the Steiner circumellipse
X(64195) = pole of line {525, 23285} with respect to the dual conic of nine-point circle
X(64195) = pole of line {525, 55228} with respect to the dual conic of orthoptic circle of the Steiner Inellipse
X(64195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1485)}}, {{A, B, C, X(69), X(59169)}}, {{A, B, C, X(76), X(59778)}}, {{A, B, C, X(141), X(56004)}}, {{A, B, C, X(249), X(62376)}}, {{A, B, C, X(325), X(20564)}}, {{A, B, C, X(343), X(6664)}}, {{A, B, C, X(2987), X(45794)}}, {{A, B, C, X(3431), X(3619)}}, {{A, B, C, X(3580), X(34207)}}, {{A, B, C, X(5504), X(28419)}}, {{A, B, C, X(5505), X(20080)}}, {{A, B, C, X(14376), X(28408)}}, {{A, B, C, X(37636), X(40802)}}, {{A, B, C, X(37644), X(43726)}}, {{A, B, C, X(37649), X(56347)}}, {{A, B, C, X(42295), X(46288)}}
X(64195) = barycentric product X(i)*X(j) for these (i, j): {21213, 69}
X(64195) = barycentric quotient X(i)/X(j) for these (i, j): {3, 18124}, {110, 1286}, {21213, 4}
X(64195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 394, 141}, {110, 64023, 20987}, {511, 1147, 15577}, {511, 19139, 34117}, {576, 19137, 58471}, {1994, 3618, 6}, {11574, 34986, 64028}, {16266, 19139, 511}, {17710, 19459, 8547}, {19125, 37485, 19127}, {19149, 37498, 29181}, {19588, 34777, 2854}

X(64196) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST EHRMANN AND X(141)-CROSSPEDAL-OF-X(6)

Barycentrics    8*a^6-3*a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^2+c^2)^2 : :
X(64196) = -9*X[2]+11*X[55684], -2*X[4]+3*X[597], -5*X[5]+6*X[10168], -3*X[6]+X[3146], -3*X[67]+5*X[15021], -4*X[140]+3*X[47354], -3*X[182]+2*X[546], -3*X[376]+X[15069], -X[382]+3*X[11179], -3*X[549]+2*X[18553], -3*X[599]+5*X[3522], -5*X[631]+3*X[47353] and many others

X(64196) lies on these lines: {2, 55684}, {3, 66}, {4, 597}, {5, 10168}, {6, 3146}, {20, 524}, {23, 13567}, {30, 576}, {67, 15021}, {69, 43691}, {140, 47354}, {154, 16051}, {182, 546}, {184, 46517}, {185, 9019}, {193, 48872}, {343, 7492}, {376, 15069}, {382, 11179}, {511, 13491}, {516, 4852}, {542, 550}, {548, 34507}, {549, 18553}, {575, 3627}, {599, 3522}, {631, 47353}, {632, 5092}, {895, 52071}, {1204, 47558}, {1350, 3630}, {1351, 49137}, {1353, 29317}, {1368, 59699}, {1513, 55177}, {1656, 50957}, {1657, 50962}, {1992, 5059}, {2393, 22967}, {2777, 25329}, {2781, 10575}, {2883, 6593}, {2930, 63631}, {3090, 5085}, {3091, 3589}, {3313, 45187}, {3416, 63469}, {3424, 15271}, {3523, 20582}, {3525, 10516}, {3528, 11180}, {3529, 3629}, {3530, 11178}, {3534, 55595}, {3543, 63124}, {3564, 12103}, {3618, 50689}, {3619, 55673}, {3620, 55651}, {3628, 3818}, {3631, 5921}, {3763, 61820}, {3832, 47352}, {3845, 25555}, {3851, 38064}, {3853, 5476}, {3854, 63109}, {3857, 38110}, {3933, 14928}, {4663, 28164}, {5026, 38745}, {5032, 50692}, {5038, 53418}, {5050, 5076}, {5056, 51025}, {5068, 50960}, {5072, 12017}, {5073, 20423}, {5093, 43621}, {5159, 10192}, {5182, 33229}, {5207, 59552}, {5254, 53499}, {5305, 20194}, {5306, 40236}, {5486, 34622}, {5493, 28538}, {5596, 58795}, {5621, 7488}, {5622, 8718}, {5846, 7991}, {5882, 50998}, {5893, 19153}, {5895, 41719}, {5965, 48874}, {6144, 61044}, {6146, 12082}, {6329, 50688}, {6698, 32250}, {7390, 49731}, {7530, 15873}, {7550, 16659}, {7555, 12359}, {7710, 44377}, {7982, 51147}, {8538, 41729}, {8542, 31829}, {8703, 40107}, {8705, 15072}, {9306, 10300}, {9589, 47356}, {9729, 16776}, {9730, 63688}, {9830, 10991}, {9968, 11511}, {9969, 15012}, {9970, 18563}, {9971, 10574}, {9974, 42276}, {9975, 42275}, {10297, 64061}, {10299, 50984}, {10303, 34573}, {10304, 50991}, {10510, 12225}, {10519, 55641}, {11001, 63115}, {11206, 53415}, {11284, 31383}, {11381, 63723}, {11482, 12007}, {11522, 51006}, {11541, 14912}, {11550, 37454}, {11585, 38795}, {11898, 55602}, {12022, 37946}, {12088, 22533}, {12102, 18583}, {12108, 17508}, {12111, 54334}, {12241, 37827}, {12362, 44762}, {12811, 38317}, {13468, 37182}, {13910, 53513}, {13972, 53516}, {14002, 37648}, {14094, 32233}, {14561, 55701}, {14810, 62091}, {14848, 62023}, {14853, 62028}, {14869, 24206}, {14915, 44479}, {14982, 15034}, {15019, 34603}, {15020, 41737}, {15022, 47355}, {15080, 45303}, {15152, 16072}, {15331, 61543}, {15533, 62120}, {15534, 15683}, {15692, 51143}, {15696, 54173}, {15705, 51186}, {15717, 21358}, {16003, 44261}, {16010, 34224}, {17574, 63470}, {17578, 59373}, {17704, 61676}, {17710, 34146}, {17809, 44442}, {19127, 41362}, {19130, 55704}, {19596, 22467}, {19924, 62155}, {20062, 61658}, {20080, 55591}, {20300, 63674}, {20397, 32274}, {20583, 49135}, {21356, 21734}, {21659, 53777}, {21735, 50958}, {21850, 22330}, {22234, 48901}, {23046, 46267}, {23061, 52397}, {23292, 31099}, {25336, 64102}, {25561, 55856}, {25565, 50987}, {28662, 38801}, {30734, 54012}, {32154, 61139}, {32184, 61664}, {32218, 37957}, {32455, 49140}, {32599, 44076}, {33532, 44665}, {33703, 54131}, {33749, 62041}, {33750, 61807}, {33751, 43150}, {33878, 62134}, {33923, 50977}, {34117, 51491}, {34380, 48880}, {34624, 54996}, {35237, 44492}, {36775, 41020}, {38079, 51129}, {38136, 50664}, {38757, 51157}, {39560, 63534}, {39899, 48873}, {40330, 55676}, {40341, 62125}, {41149, 62160}, {41152, 62094}, {41153, 62007}, {41989, 55693}, {42117, 44511}, {42118, 44512}, {42144, 44497}, {42145, 44498}, {42225, 44501}, {42226, 44502}, {42785, 55707}, {42786, 55685}, {43174, 50949}, {43632, 51203}, {43633, 51200}, {44480, 64098}, {46936, 51127}, {47336, 51733}, {47341, 61752}, {48876, 48892}, {48885, 55597}, {48896, 55721}, {49138, 54132}, {49681, 58245}, {50687, 51185}, {50690, 51130}, {50691, 51026}, {50954, 61794}, {50955, 51134}, {50956, 61919}, {50967, 62127}, {50972, 51027}, {50974, 62147}, {50976, 62096}, {50979, 62036}, {50982, 62107}, {50990, 62095}, {50992, 62129}, {50993, 62063}, {50994, 62081}, {51131, 51216}, {51132, 62159}, {51139, 61834}, {51140, 62156}, {51144, 64197}, {51176, 62171}, {51187, 62145}, {51188, 62132}, {51189, 62099}, {51739, 64049}, {51756, 63667}, {53015, 58446}, {53091, 62024}, {55600, 58196}, {55644, 62087}, {55646, 62084}, {55649, 61545}, {55671, 61795}, {55672, 61801}, {55674, 61808}, {55675, 61810}, {55678, 61831}, {55682, 61850}, {55692, 61923}, {55697, 61955}, {55705, 61991}, {58445, 61900}, {59343, 64060}, {59767, 64059}, {62048, 63022}, {62133, 63428}, {62148, 63064}, {62168, 63125}

X(64196) = midpoint of X(i) and X(j) for these {i,j}: {6, 14927}, {20, 64080}, {193, 48872}, {1350, 39874}, {1657, 63722}, {3529, 11477}, {6144, 61044}, {6776, 48905}, {15534, 15683}, {25336, 64102}, {39899, 48873}, {62155, 64067}
X(64196) = reflection of X(i) in X(j) for these {i,j}: {141, 44882}, {597, 43273}, {599, 50971}, {3543, 63124}, {3627, 575}, {3629, 6776}, {3630, 1350}, {5480, 48906}, {5921, 3631}, {11160, 50970}, {11381, 63723}, {20582, 51135}, {22165, 376}, {31670, 12007}, {32250, 6698}, {34507, 548}, {36990, 3589}, {39884, 5092}, {43150, 33751}, {44882, 46264}, {48874, 48891}, {48876, 48892}, {48881, 48898}, {48884, 18583}, {51022, 597}, {51023, 20582}, {51024, 20583}, {51163, 6}, {51166, 1992}, {51212, 32455}, {51491, 34117}, {52987, 12103}
X(64196) = pole of line {3906, 23301} with respect to the Steiner circle
X(64196) = pole of line {3767, 3832} with respect to the Kiepert hyperbola
X(64196) = pole of line {22, 55614} with respect to the Stammler hyperbola
X(64196) = pole of line {315, 5059} with respect to the Wallace hyperbola
X(64196) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {6, 2452, 14927}
X(64196) = intersection, other than A, B, C, of circumconics {{A, B, C, X(66), X(52443)}}, {{A, B, C, X(2353), X(43691)}}, {{A, B, C, X(14376), X(18842)}}
X(64196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 64014, 64080}, {20, 64080, 524}, {69, 50693, 55614}, {548, 34507, 54169}, {575, 29012, 3627}, {1352, 21167, 141}, {1503, 46264, 44882}, {3091, 25406, 10541}, {3529, 11477, 29181}, {3529, 6776, 11477}, {3564, 12103, 52987}, {3627, 48906, 575}, {3818, 55687, 3628}, {5965, 48891, 48874}, {6776, 29181, 3629}, {10519, 62092, 55641}, {10541, 36990, 3091}, {11477, 48905, 3529}, {11482, 49136, 31670}, {11898, 62119, 55602}, {12103, 52987, 48881}, {24206, 55679, 14869}, {25406, 36990, 3589}, {29012, 48906, 5480}, {33751, 55650, 62079}, {38072, 51138, 597}, {39899, 62143, 55580}, {48876, 62104, 55631}, {48892, 55631, 62104}, {48898, 52987, 12103}, {55580, 62143, 48873}, {55614, 59411, 50693}, {55701, 61984, 14561}, {62155, 64067, 19924}

X(64197) = ORTHOLOGY CENTER OF THESE TRIANGLES: FUHRMANN AND X(80)-CROSSPEDAL-OF-X(7)

Barycentrics    a*(a^5+a^4*(b+c)-3*(b-c)^2*(b+c)^3+a^3*(-6*b^2+4*b*c-6*c^2)+a*(b-c)^2*(5*b^2+6*b*c+5*c^2)+2*a^2*(b^3+b^2*c+b*c^2+c^3)) : :
X(64197) = -2*X[3]+3*X[9], -4*X[5]+3*X[6173], -X[20]+3*X[6172], -6*X[142]+7*X[3090], -4*X[546]+3*X[5805], -4*X[576]+3*X[51194], -5*X[631]+6*X[60986], -10*X[632]+9*X[38122], -10*X[1656]+9*X[38093], -5*X[1698]+4*X[64113], -3*X[3243]+4*X[10222], -7*X[3523]+9*X[61023] and many others

X(64197) lies on these lines: {1, 651}, {2, 11407}, {3, 9}, {4, 527}, {5, 6173}, {7, 1210}, {8, 144}, {10, 6223}, {20, 6172}, {40, 4662}, {46, 30353}, {57, 5729}, {63, 1750}, {72, 36973}, {78, 60935}, {90, 56262}, {142, 3090}, {165, 3219}, {169, 38668}, {191, 2938}, {200, 1709}, {210, 10860}, {223, 24430}, {269, 1736}, {355, 54156}, {381, 60963}, {443, 60972}, {515, 5698}, {518, 5693}, {528, 5881}, {546, 5805}, {576, 51194}, {631, 60986}, {632, 38122}, {912, 18540}, {938, 60998}, {942, 60953}, {960, 10864}, {990, 1743}, {991, 3731}, {1445, 6915}, {1656, 38093}, {1698, 64113}, {1699, 5905}, {1706, 9947}, {1721, 1757}, {1768, 64112}, {2093, 59387}, {2475, 37714}, {2550, 6256}, {2551, 9948}, {3241, 18452}, {3243, 10222}, {3247, 62183}, {3303, 14100}, {3304, 8581}, {3305, 10857}, {3306, 13243}, {3339, 9814}, {3523, 61023}, {3525, 6666}, {3529, 5759}, {3530, 38067}, {3544, 60980}, {3576, 15254}, {3585, 4312}, {3586, 60946}, {3627, 5762}, {3628, 20195}, {3646, 58567}, {3679, 6925}, {3681, 7994}, {3715, 5918}, {3746, 4326}, {3751, 64134}, {3817, 10980}, {3832, 60984}, {3839, 60971}, {3855, 38073}, {3876, 63984}, {3925, 41706}, {3928, 19541}, {3929, 7580}, {3973, 13329}, {3984, 41228}, {4292, 12848}, {4304, 5766}, {4321, 5563}, {4654, 8226}, {4847, 64130}, {4857, 36599}, {4862, 53599}, {4866, 43174}, {5047, 12669}, {5056, 59374}, {5067, 60999}, {5068, 59375}, {5070, 38065}, {5072, 38107}, {5076, 31671}, {5079, 59380}, {5219, 13257}, {5234, 12520}, {5290, 12617}, {5400, 62695}, {5437, 10157}, {5450, 64154}, {5493, 50834}, {5528, 51525}, {5542, 14986}, {5587, 5851}, {5658, 5745}, {5705, 6260}, {5715, 61011}, {5728, 11518}, {5809, 60934}, {5811, 6245}, {5825, 8732}, {5850, 63973}, {5882, 47357}, {5887, 12650}, {5904, 12651}, {6001, 9623}, {6244, 62218}, {6762, 9856}, {6765, 12705}, {6769, 63967}, {6835, 60932}, {6837, 61027}, {6839, 60951}, {6860, 21617}, {6872, 50836}, {6908, 31446}, {6920, 60964}, {6926, 54178}, {6946, 8257}, {6957, 60952}, {6982, 51755}, {6999, 60927}, {7082, 41341}, {7282, 39531}, {7308, 10167}, {7675, 29007}, {7681, 41555}, {7701, 17857}, {7988, 21635}, {7989, 7997}, {8227, 25557}, {8544, 15803}, {8580, 15064}, {8583, 10085}, {8727, 28609}, {9579, 61007}, {9614, 60926}, {9799, 12572}, {9812, 20214}, {9819, 28236}, {9842, 61022}, {9845, 58679}, {9851, 11106}, {10164, 30393}, {10171, 24645}, {10177, 12675}, {10303, 18230}, {10392, 60961}, {10427, 20400}, {10431, 17781}, {10442, 35615}, {10826, 64155}, {10861, 17531}, {10883, 31164}, {10884, 60981}, {10940, 24982}, {11227, 51780}, {11240, 11522}, {11495, 15481}, {11524, 58245}, {12103, 61596}, {12108, 38113}, {12246, 57284}, {12514, 63981}, {12560, 18412}, {12565, 41229}, {12618, 17272}, {12652, 49448}, {12680, 31435}, {12688, 42014}, {12767, 61254}, {12811, 38139}, {12812, 38171}, {13226, 31190}, {13411, 60995}, {13464, 51099}, {13727, 50127}, {15012, 58534}, {15022, 62778}, {15178, 38316}, {15704, 64065}, {15829, 31821}, {16189, 24644}, {16239, 38082}, {16814, 50677}, {16865, 19861}, {17274, 36652}, {17538, 21168}, {17572, 61012}, {17613, 46917}, {17768, 41705}, {18229, 59637}, {18446, 61004}, {18480, 52682}, {18482, 60922}, {19647, 56509}, {19843, 54227}, {20059, 50689}, {20190, 38117}, {20420, 34742}, {21669, 60973}, {24393, 35514}, {24467, 60989}, {25590, 48888}, {29016, 55998}, {30223, 33925}, {30282, 60944}, {30557, 60903}, {31142, 37374}, {31391, 41712}, {31828, 54203}, {31871, 62858}, {34507, 51152}, {36279, 55922}, {36660, 50116}, {36682, 50092}, {36706, 50093}, {37161, 51100}, {37436, 60959}, {37560, 58631}, {38036, 42356}, {38055, 50443}, {38059, 43176}, {38111, 61900}, {38137, 41991}, {38145, 51150}, {38318, 55857}, {38454, 41869}, {41857, 59372}, {43161, 51090}, {43175, 52653}, {43879, 60920}, {43880, 60921}, {46936, 60996}, {50688, 60957}, {50693, 59418}, {50995, 53097}, {50997, 64080}, {51144, 64196}, {51514, 61968}, {53513, 60913}, {53516, 60914}, {54179, 54205}, {57282, 60982}, {58035, 59216}, {58433, 60781}, {58808, 64107}, {59386, 60962}, {60983, 62097}, {61001, 61870}, {61705, 63992}, {62824, 63988}

X(64197) = midpoint of X(i) and X(j) for these {i,j}: {144, 36991}, {3062, 5223}, {5691, 60905}, {5779, 60884}, {10394, 12528}, {52835, 60977}
X(64197) = reflection of X(i) in X(j) for these {i,j}: {1, 54370}, {3, 64198}, {7, 63970}, {9, 5779}, {40, 5220}, {1490, 52684}, {5732, 9}, {5735, 4}, {5759, 60942}, {5784, 5777}, {5805, 60901}, {11372, 16112}, {11495, 15481}, {18446, 61004}, {30424, 19925}, {35514, 24393}, {36996, 142}, {43161, 51090}, {43166, 11372}, {43178, 60912}, {52682, 18480}, {52835, 31672}, {54159, 54135}, {54179, 54205}, {60922, 18482}, {60933, 5805}, {60963, 381}, {63413, 61000}, {63971, 10}
X(64197) = anticomplement of X(43177)
X(64197) = perspector of circumconic {{A, B, C, X(13138), X(37139)}}
X(64197) = X(i)-Dao conjugate of X(j) for these {i, j}: {43177, 43177}
X(64197) = pole of line {28292, 59935} with respect to the polar circle
X(64197) = pole of line {1155, 10860} with respect to the Feuerbach hyperbola
X(64197) = pole of line {1817, 62756} with respect to the Stammler hyperbola
X(64197) = pole of line {664, 61237} with respect to the Yff parabola
X(64197) = pole of line {3887, 21188} with respect to the Suppa-Cucoanes circle
X(64197) = pole of line {347, 30379} with respect to the dual conic of Yff parabola
X(64197) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(56763)}}, {{A, B, C, X(84), X(10405)}}, {{A, B, C, X(165), X(60905)}}, {{A, B, C, X(268), X(60047)}}, {{A, B, C, X(282), X(1156)}}, {{A, B, C, X(1436), X(3062)}}, {{A, B, C, X(1903), X(62764)}}, {{A, B, C, X(4845), X(7367)}}
X(64197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5779, 64198}, {3, 64198, 9}, {4, 527, 5735}, {7, 63970, 38150}, {9, 5732, 21153}, {84, 5777, 936}, {84, 5784, 5732}, {144, 36991, 516}, {144, 64002, 60905}, {518, 11372, 43166}, {518, 16112, 11372}, {527, 54135, 54159}, {971, 5777, 5784}, {971, 64198, 3}, {1490, 7330, 31424}, {2801, 54370, 1}, {3062, 52665, 5223}, {3146, 3951, 7991}, {3305, 11220, 10857}, {3339, 9814, 30424}, {5044, 12684, 9841}, {5220, 15726, 40}, {5223, 60905, 12526}, {5762, 31672, 52835}, {5779, 40263, 52684}, {5779, 60884, 971}, {5805, 5843, 60933}, {5805, 60901, 59389}, {5817, 36996, 142}, {5843, 60901, 5805}, {6223, 60997, 63971}, {7330, 40263, 1490}, {8544, 37787, 15803}, {10394, 12528, 2801}, {12705, 14872, 6765}, {30304, 30326, 2}, {31657, 38108, 20195}, {43178, 60912, 165}, {52835, 60977, 5762}, {61000, 63413, 21168}

X(64198) = ORTHOLOGY CENTER OF THESE TRIANGLES: K798I AND X(80)-CROSSPEDAL-OF-X(7)

Barycentrics    a*(2*a^5-a^4*(b+c)-3*(b-c)^2*(b+c)^3+a^3*(-6*b^2+2*b*c-6*c^2)+4*a^2*(b+c)*(b^2+c^2)+2*a*(b-c)^2*(2*b^2+3*b*c+2*c^2))*S^2 : :
X(64198) = -X[3]+3*X[9], X[4]+3*X[6172], -3*X[7]+7*X[3090], -3*X[142]+4*X[3628], 3*X[144]+5*X[3091], -3*X[381]+X[5735], -5*X[631]+9*X[61023], -5*X[632]+6*X[6666], -3*X[1001]+2*X[15178], -5*X[1656]+3*X[6173], 3*X[3062]+5*X[63469], X[3146]+3*X[5759] and many others

X(64198) lies on these lines: {3, 9}, {4, 6172}, {5, 527}, {7, 3090}, {10, 22792}, {63, 10157}, {65, 41700}, {72, 6912}, {140, 43177}, {142, 3628}, {144, 3091}, {210, 5537}, {355, 5698}, {381, 5735}, {392, 38669}, {516, 3627}, {517, 5220}, {518, 576}, {528, 37290}, {546, 5762}, {631, 61023}, {632, 6666}, {912, 61004}, {942, 5729}, {958, 31821}, {990, 16885}, {991, 16814}, {1001, 15178}, {1071, 60981}, {1156, 18908}, {1212, 38666}, {1385, 2801}, {1656, 6173}, {1709, 3715}, {1768, 61686}, {2550, 37821}, {3057, 51768}, {3062, 63469}, {3146, 5759}, {3219, 5927}, {3303, 15298}, {3304, 15299}, {3305, 11227}, {3523, 38067}, {3525, 18230}, {3529, 21168}, {3544, 59386}, {3579, 15726}, {3652, 58658}, {3731, 62183}, {3746, 14100}, {3824, 60987}, {3826, 38179}, {3851, 38075}, {3857, 38139}, {3927, 5806}, {3929, 19541}, {3951, 60966}, {4301, 50834}, {4312, 10895}, {4640, 15064}, {5047, 60969}, {5055, 60963}, {5056, 60984}, {5067, 59374}, {5068, 38073}, {5070, 38093}, {5071, 60971}, {5072, 38150}, {5076, 52835}, {5079, 38107}, {5122, 8544}, {5183, 51790}, {5223, 7982}, {5302, 31803}, {5316, 13226}, {5325, 59687}, {5563, 8581}, {5587, 52682}, {5708, 60953}, {5714, 60975}, {5728, 6920}, {5791, 5811}, {5837, 51090}, {5850, 20330}, {5851, 11231}, {5880, 9956}, {5881, 50836}, {5882, 50243}, {6244, 58688}, {6829, 60951}, {6832, 61027}, {6915, 60970}, {6946, 37582}, {6978, 52457}, {6982, 37822}, {6984, 41563}, {7082, 33925}, {7308, 10156}, {7377, 60927}, {7486, 59375}, {7743, 60926}, {7991, 11372}, {8167, 58615}, {8226, 17781}, {8257, 24467}, {8543, 50194}, {8668, 15733}, {8728, 60972}, {9612, 61007}, {9856, 41229}, {9947, 12514}, {9954, 42012}, {9955, 60895}, {10167, 27065}, {10175, 30424}, {10303, 21151}, {10394, 24929}, {10398, 11518}, {10427, 38763}, {10541, 38117}, {10861, 17572}, {11230, 25557}, {11374, 60995}, {11477, 50995}, {11482, 51194}, {12103, 63413}, {12618, 17332}, {12812, 60962}, {12848, 57282}, {13243, 35595}, {13257, 54357}, {13329, 15492}, {14869, 38113}, {14872, 34486}, {15022, 20059}, {15069, 50997}, {15587, 18232}, {16625, 58534}, {16865, 61025}, {17333, 36652}, {17334, 53599}, {17336, 48878}, {17351, 48888}, {17531, 61012}, {17538, 59418}, {17606, 64155}, {17613, 63961}, {17668, 36866}, {18250, 33899}, {18542, 38121}, {19546, 56509}, {20195, 55857}, {22793, 38454}, {24644, 58245}, {25405, 30318}, {26446, 63971}, {30332, 59388}, {30389, 38031}, {31391, 41694}, {31399, 51100}, {31663, 43178}, {31666, 52769}, {31671, 59389}, {34753, 61022}, {34790, 42014}, {35514, 38126}, {37436, 61009}, {37560, 51572}, {37622, 49184}, {37727, 47357}, {38052, 41705}, {38065, 46219}, {38080, 61907}, {38082, 55856}, {38111, 55861}, {38130, 43182}, {38149, 63975}, {38171, 60980}, {43879, 60913}, {43880, 60914}, {46936, 62778}, {49515, 64013}, {51099, 61276}, {51514, 61923}, {55862, 61001}, {56762, 64116}, {59385, 61964}, {60781, 60996}, {61020, 61903}

X(64198) = midpoint of X(i) and X(j) for these {i,j}: {3, 64197}, {9, 5779}, {144, 5805}, {355, 5698}, {5220, 54370}, {5732, 60884}, {5759, 31672}, {37822, 60940}, {38031, 52665}, {52682, 60905}, {60901, 64065}, {60922, 60977}, {60942, 63970}
X(64198) = reflection of X(i) in X(j) for these {i,j}: {7, 61595}, {142, 61511}, {1385, 15254}, {3579, 60912}, {5880, 9956}, {18482, 63970}, {31657, 6666}, {31658, 9}, {43177, 140}, {43178, 31663}, {60895, 9955}, {60942, 61596}, {60962, 61509}, {64065, 61000}
X(64198) = pole of line {30223, 35445} with respect to the Feuerbach hyperbola
X(64198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5779, 64197}, {3, 64197, 971}, {7, 38108, 61595}, {9, 5732, 59381}, {9, 64197, 3}, {9, 971, 31658}, {142, 61511, 38318}, {144, 5817, 5805}, {516, 61000, 64065}, {2801, 15254, 1385}, {3929, 30326, 19541}, {5044, 7330, 34862}, {5220, 54370, 517}, {5587, 60905, 52682}, {5729, 8545, 942}, {5762, 61596, 60942}, {5762, 63970, 18482}, {5779, 51516, 9}, {5779, 59381, 60884}, {5843, 61511, 142}, {15298, 60910, 63972}, {15726, 60912, 3579}, {18230, 36996, 38122}, {36991, 60983, 21168}, {38150, 60977, 60922}, {43177, 60986, 140}, {59381, 60884, 5732}, {60901, 64065, 516}, {60942, 63970, 5762}

X(64199) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND X(79)-CROSSPEDAL-OF-X(8)

Barycentrics    a*(a^3+3*b*c*(b+c)-a*(b^2+9*b*c+c^2)) : :
X(64199) = -5*X[3091]+6*X[63257], -5*X[3616]+6*X[63287], -4*X[5270]+3*X[15679], -3*X[6175]+4*X[15888], -X[13144]+3*X[15015], -3*X[15678]+4*X[63273]

X(64199) lies on these lines: {1, 3833}, {2, 31480}, {3, 145}, {8, 344}, {10, 17546}, {21, 519}, {35, 32633}, {55, 17574}, {56, 39777}, {65, 14151}, {100, 3244}, {149, 546}, {224, 13375}, {377, 12632}, {404, 3241}, {405, 31145}, {517, 33557}, {523, 64071}, {952, 21669}, {956, 20014}, {958, 20053}, {962, 18243}, {1000, 20013}, {1210, 64141}, {1317, 1476}, {1320, 1389}, {1376, 20057}, {1621, 3632}, {1697, 3951}, {1995, 20020}, {2136, 11518}, {2476, 11239}, {2550, 63256}, {2802, 34195}, {2975, 3633}, {3058, 56880}, {3090, 10528}, {3091, 63257}, {3146, 40267}, {3295, 3621}, {3315, 3987}, {3525, 10529}, {3529, 20075}, {3555, 26201}, {3616, 63287}, {3617, 6767}, {3622, 16862}, {3623, 5687}, {3625, 5260}, {3626, 5284}, {3627, 20060}, {3635, 5253}, {3636, 9342}, {3679, 17536}, {3680, 56030}, {3754, 62863}, {3811, 5330}, {3813, 7504}, {3868, 3895}, {3870, 3885}, {3876, 31393}, {3877, 3984}, {3878, 62236}, {3881, 5541}, {3889, 63130}, {3897, 12629}, {3935, 9957}, {3957, 10914}, {3979, 63333}, {4189, 20049}, {4193, 34619}, {4393, 21540}, {4420, 5919}, {4430, 12702}, {4669, 17547}, {4677, 16861}, {4701, 5259}, {4898, 38869}, {5086, 49626}, {5270, 15679}, {5550, 8162}, {6175, 15888}, {6542, 21516}, {6909, 37727}, {6912, 12648}, {6940, 61286}, {6946, 52074}, {6985, 34631}, {7301, 49534}, {7677, 41687}, {8168, 9780}, {8666, 34747}, {8702, 57093}, {8715, 13587}, {9708, 17544}, {9963, 45287}, {10527, 63263}, {10915, 59415}, {11010, 62235}, {11240, 17566}, {11349, 17389}, {11520, 64202}, {11530, 54392}, {11684, 37563}, {12000, 59388}, {12103, 20067}, {12331, 45977}, {12513, 17549}, {12521, 63137}, {12524, 44669}, {12607, 34699}, {12732, 24470}, {12737, 35597}, {13143, 64137}, {13144, 15015}, {13278, 38669}, {15170, 37162}, {15178, 38460}, {15678, 63273}, {15704, 20066}, {16371, 51092}, {16373, 20012}, {16477, 37588}, {16855, 46933}, {17014, 21519}, {17314, 37503}, {17388, 54409}, {17534, 53620}, {17535, 38314}, {17538, 20076}, {18990, 20095}, {19292, 20037}, {19316, 39587}, {19526, 20054}, {19993, 40916}, {20070, 36996}, {20084, 28216}, {21496, 29616}, {24475, 64136}, {25416, 51525}, {28174, 63285}, {32537, 50890}, {32911, 50575}, {33176, 60782}, {34486, 41575}, {34749, 36005}, {34791, 63136}, {35000, 61292}, {36006, 51071}, {37411, 50872}, {44685, 50194}, {48713, 50894}, {50581, 62848}, {51573, 56115}, {54286, 62854}, {62874, 63469}

X(64199) = reflection of X(i) in X(j) for these {i,j}: {8, 45081}, {3632, 15862}, {11684, 37563}, {13143, 64137}, {14923, 13375}, {56091, 64201}, {64201, 1}
X(64199) = anticomplement of X(64200)
X(64199) = X(i)-Dao conjugate of X(j) for these {i, j}: {64200, 64200}
X(64199) = pole of line {13587, 28217} with respect to the circumcircle
X(64199) = pole of line {7321, 17169} with respect to the Wallace hyperbola
X(64199) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5559), X(56135)}}, {{A, B, C, X(32008), X(39962)}}, {{A, B, C, X(56091), X(56118)}}
X(64199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3303, 5047}, {145, 3871, 54391}, {3241, 3913, 404}, {3870, 3885, 62830}, {8715, 51093, 62837}, {8715, 62837, 13587}, {10222, 38665, 6915}, {11239, 64068, 2476}, {12331, 61597, 45977}

X(64200) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH EULER AND X(79)-CROSSPEDAL-OF-X(8)

Barycentrics    6*a*b*c*(b+c)-(b^2-c^2)^2+a^2*(b^2-6*b*c+c^2) : :
X(64200) = -2*X[3746]+3*X[15670], -9*X[5659]+7*X[9588], X[13144]+3*X[37718], -3*X[17525]+2*X[63273], -6*X[38054]+5*X[63258]

X(64200) lies on these lines: {1, 3826}, {2, 31480}, {5, 8}, {10, 3893}, {11, 3626}, {12, 3625}, {20, 956}, {55, 31458}, {56, 17583}, {72, 4301}, {78, 61276}, {100, 3530}, {145, 4197}, {200, 9624}, {210, 49600}, {224, 3872}, {381, 56879}, {382, 3434}, {388, 31420}, {392, 21627}, {405, 47357}, {442, 519}, {443, 38092}, {474, 34625}, {495, 3621}, {496, 1000}, {498, 8168}, {517, 22798}, {523, 764}, {528, 4330}, {546, 56880}, {548, 2975}, {550, 49719}, {631, 5687}, {858, 33090}, {952, 5178}, {958, 4309}, {960, 38211}, {962, 5779}, {1124, 31486}, {1125, 34501}, {1145, 6734}, {1329, 4668}, {1484, 32634}, {1490, 3419}, {1500, 31491}, {1697, 31446}, {1907, 56876}, {2136, 31436}, {2276, 31469}, {2346, 15998}, {2476, 31145}, {2550, 56997}, {2802, 21677}, {2886, 3632}, {2894, 59356}, {3057, 10395}, {3241, 8728}, {3244, 3925}, {3295, 31494}, {3421, 3832}, {3436, 3843}, {3526, 10527}, {3528, 17784}, {3555, 5784}, {3633, 25466}, {3648, 28216}, {3650, 28174}, {3656, 3984}, {3679, 3680}, {3681, 22791}, {3695, 3902}, {3697, 12053}, {3698, 49627}, {3746, 15670}, {3754, 51463}, {3814, 4746}, {3820, 4678}, {3853, 52367}, {3861, 5080}, {3895, 5791}, {3913, 7483}, {3935, 37737}, {4002, 11019}, {4015, 21630}, {4293, 57001}, {4317, 11112}, {4325, 5288}, {4420, 5901}, {4511, 61278}, {4662, 30384}, {4669, 17533}, {4677, 12607}, {4701, 25639}, {4745, 50038}, {4816, 7951}, {4847, 10914}, {4861, 61286}, {4863, 37724}, {4882, 11218}, {4915, 37714}, {4999, 48696}, {5047, 15170}, {5067, 7080}, {5070, 5552}, {5086, 61249}, {5176, 61255}, {5260, 15172}, {5267, 6154}, {5303, 58190}, {5563, 49732}, {5659, 9588}, {5692, 13463}, {5718, 50575}, {5836, 13375}, {6736, 31399}, {6845, 12245}, {6857, 12632}, {6990, 34631}, {7765, 21956}, {7982, 8226}, {8582, 45115}, {8666, 34612}, {8715, 34720}, {9589, 38454}, {9607, 16975}, {9623, 37723}, {9656, 31140}, {9670, 11113}, {9698, 52959}, {9709, 10529}, {9780, 45116}, {9957, 25006}, {10385, 19526}, {10459, 64167}, {10528, 31493}, {10609, 63146}, {10915, 38058}, {10942, 51515}, {10943, 59503}, {10957, 36920}, {11240, 16408}, {11684, 28212}, {12620, 63993}, {12623, 44669}, {12649, 40587}, {12699, 63135}, {12702, 64153}, {12732, 37568}, {13143, 64056}, {13144, 37718}, {13747, 45700}, {15559, 56877}, {15908, 47745}, {17525, 63273}, {17532, 31410}, {17619, 24386}, {18253, 37563}, {18990, 33110}, {19535, 34607}, {20050, 33108}, {20691, 31462}, {21927, 49510}, {24953, 25439}, {25278, 64093}, {26446, 63142}, {27529, 48154}, {31447, 59491}, {31478, 37661}, {31835, 64138}, {33895, 50208}, {34605, 50240}, {34610, 56998}, {34611, 50241}, {34718, 37356}, {34790, 51409}, {37406, 50798}, {38054, 63258}, {38455, 47033}, {38665, 52265}, {55864, 59591}, {59310, 64172}, {63143, 63980}

X(64200) = midpoint of X(i) and X(j) for these {i,j}: {8, 64201}, {5559, 11524}, {13143, 64056}
X(64200) = reflection of X(i) in X(j) for these {i,j}: {13375, 5836}, {15862, 3626}, {37563, 18253}, {45081, 10}, {57002, 5258}
X(64200) = complement of X(64199)
X(64200) = pole of line {17533, 28217} with respect to the nine-point circle
X(64200) = pole of line {28217, 37374} with respect to the Steiner circle
X(64200) = pole of line {16814, 46196} with respect to the Kiepert hyperbola
X(64200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 9710, 17529}, {8, 24390, 17757}, {8, 64201, 5844}, {10, 37722, 17575}, {528, 5258, 57002}, {958, 4309, 57003}, {3679, 11524, 5559}, {3679, 37720, 9711}, {3679, 3813, 4187}, {3813, 9711, 37720}, {4669, 24387, 21031}, {21031, 24387, 17533}, {45081, 61032, 10}

X(64201) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-GARCIA AND X(79)-CROSSPEDAL-OF-X(8)

Barycentrics    a*(a^3+2*b^3-5*b^2*c-5*b*c^2+2*c^3-2*a^2*(b+c)-a*(b^2-7*b*c+c^2)) : :
X(64201) = -7*X[3622]+6*X[63287]

X(64201) lies on these lines: {1, 3833}, {2, 10912}, {5, 8}, {10, 1320}, {21, 2802}, {40, 2975}, {72, 26200}, {78, 11525}, {100, 1385}, {145, 2550}, {404, 22837}, {517, 3652}, {518, 63275}, {519, 5178}, {523, 1222}, {758, 12786}, {944, 28458}, {952, 47032}, {1125, 41702}, {1145, 34126}, {1621, 3885}, {2098, 3617}, {2099, 3621}, {2136, 63260}, {2346, 3680}, {2475, 38455}, {2476, 49169}, {3057, 5260}, {3241, 11024}, {3244, 32924}, {3336, 54391}, {3338, 13375}, {3340, 60953}, {3434, 12667}, {3616, 40587}, {3622, 63287}, {3625, 11009}, {3626, 63210}, {3632, 10129}, {3633, 63159}, {3648, 28212}, {3679, 5330}, {3681, 7982}, {3869, 4853}, {3871, 37571}, {3873, 12629}, {3876, 30323}, {3880, 37080}, {3884, 5506}, {3890, 9623}, {3893, 34772}, {3898, 17536}, {3935, 11011}, {3984, 11224}, {4420, 10222}, {4511, 33179}, {4547, 56115}, {4678, 5289}, {4701, 4867}, {4900, 56030}, {4915, 11682}, {4999, 13996}, {5046, 13463}, {5080, 40273}, {5082, 6951}, {5086, 12531}, {5176, 19925}, {5220, 63209}, {5253, 5836}, {5284, 9957}, {5303, 31663}, {5541, 51111}, {5659, 51433}, {5687, 37624}, {5853, 63265}, {5854, 63270}, {5903, 62235}, {6736, 11218}, {6920, 10284}, {6972, 64081}, {7173, 33559}, {7987, 63130}, {7991, 62827}, {9802, 15171}, {10707, 49600}, {10861, 11519}, {10944, 33110}, {12127, 62815}, {12541, 50839}, {12635, 31145}, {12640, 24541}, {13995, 44669}, {15888, 32426}, {17619, 59377}, {20054, 41711}, {22560, 37293}, {22791, 56880}, {24387, 59415}, {24928, 44685}, {24982, 64205}, {28174, 63280}, {28629, 63256}, {32157, 37291}, {32633, 63211}, {36006, 51714}, {37562, 38669}, {43177, 57287}, {49494, 57280}, {50637, 54315}, {50894, 63254}, {62870, 63255}

X(64201) = midpoint of X(i) and X(j) for these {i,j}: {1, 11524}, {12653, 13144}, {56091, 64199}
X(64201) = reflection of X(i) in X(j) for these {i,j}: {8, 64200}, {5559, 10}, {56091, 11524}, {64199, 1}
X(64201) = anticomplement of X(45081)
X(64201) = X(i)-Dao conjugate of X(j) for these {i, j}: {45081, 45081}
X(64201) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1385), X(5844)}}, {{A, B, C, X(1389), X(28219)}}, {{A, B, C, X(5559), X(56323)}}, {{A, B, C, X(13143), X(56135)}}
X(64201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3632, 62830, 62236}, {3872, 14923, 2975}, {4853, 11531, 63135}, {4861, 10914, 100}, {5836, 38460, 5253}, {5844, 64200, 8}, {11531, 63135, 3869}

X(64202) = ORTHOLOGY CENTER OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND X(84)-CROSSPEDAL-OF-X(8)

Barycentrics    a*(a^3-3*b^3+7*b^2*c+7*b*c^2-3*c^3+3*a^2*(b+c)-a*(b^2+14*b*c+c^2)) : :
X(64202) = -4*X[5]+5*X[64204], -4*X[550]+3*X[34716], -5*X[631]+4*X[64205], -2*X[1482]+3*X[3158], -3*X[1699]+4*X[10915], -3*X[3576]+2*X[10912], -2*X[4301]+3*X[34619], -3*X[4421]+2*X[33895], -3*X[5657]+2*X[21627], -4*X[5690]+3*X[24392], -2*X[5882]+3*X[34607], -5*X[7987]+4*X[22837] and many others

X(64202) lies on these lines: {1, 88}, {3, 3680}, {4, 12640}, {5, 64204}, {8, 3586}, {10, 5274}, {20, 519}, {35, 64203}, {40, 3880}, {56, 63138}, {145, 2093}, {200, 5697}, {405, 1697}, {517, 1490}, {518, 55582}, {528, 5881}, {550, 34716}, {631, 64205}, {936, 3057}, {952, 52116}, {958, 11525}, {1000, 57284}, {1125, 30337}, {1145, 9581}, {1210, 63133}, {1420, 19537}, {1482, 3158}, {1698, 10584}, {1699, 10915}, {1706, 9957}, {1837, 13996}, {2478, 3679}, {3149, 3913}, {3174, 37625}, {3189, 28234}, {3241, 37267}, {3243, 50193}, {3244, 3339}, {3303, 16410}, {3576, 10912}, {3625, 5223}, {3632, 12526}, {3633, 36977}, {3635, 10980}, {3746, 37248}, {3753, 37556}, {3811, 11531}, {3868, 51786}, {3872, 4189}, {3877, 63142}, {3878, 4882}, {3884, 8580}, {3893, 57279}, {3922, 8162}, {3951, 31145}, {4002, 16856}, {4004, 44841}, {4084, 8544}, {4301, 34619}, {4421, 33895}, {4512, 37563}, {4669, 4866}, {4677, 11114}, {4853, 5119}, {4861, 30282}, {4915, 12514}, {4917, 62830}, {4936, 5540}, {5044, 51781}, {5177, 31397}, {5187, 6735}, {5248, 53052}, {5290, 49626}, {5330, 64135}, {5436, 40587}, {5437, 31792}, {5439, 51779}, {5657, 21627}, {5687, 7962}, {5690, 24392}, {5691, 49169}, {5759, 5853}, {5836, 31393}, {5840, 12641}, {5854, 12119}, {5882, 34607}, {6154, 37738}, {6736, 30305}, {6762, 7171}, {6865, 11362}, {6933, 31434}, {6953, 11522}, {7320, 17580}, {7963, 47622}, {7966, 31788}, {7987, 22837}, {7992, 28236}, {7997, 37712}, {8227, 13463}, {8666, 63469}, {8668, 11012}, {9580, 64087}, {9588, 45700}, {9613, 12648}, {9624, 34640}, {10106, 57000}, {10595, 59584}, {10866, 58649}, {10993, 34701}, {11010, 62824}, {11108, 11530}, {11224, 22836}, {11238, 37829}, {11260, 35242}, {11519, 62858}, {11520, 64199}, {12120, 31798}, {12448, 58637}, {12541, 59417}, {12607, 31162}, {12625, 31789}, {12650, 49163}, {13528, 15347}, {13729, 37714}, {15803, 36846}, {16113, 44669}, {16200, 56176}, {16486, 56174}, {17151, 21271}, {17648, 37560}, {19875, 24387}, {21153, 42842}, {21630, 50444}, {22560, 59332}, {24391, 50810}, {25405, 45036}, {30323, 48696}, {30350, 33815}, {30568, 56799}, {31423, 32157}, {31775, 34709}, {32049, 41869}, {34625, 43174}, {34719, 37721}, {34773, 47746}, {36002, 58245}, {37307, 38460}, {37618, 41702}, {37704, 37828}, {37711, 64056}, {45047, 54319}, {45763, 52181}, {53056, 62825}, {56936, 64163}, {63399, 64136}

X(64202) = reflection of X(i) in X(j) for these {i,j}: {4, 12640}, {145, 64117}, {3680, 3}, {5691, 49169}, {6762, 12702}, {6765, 2136}, {7982, 3913}, {11519, 62858}, {11531, 3811}, {12448, 58637}, {12629, 40}, {12650, 49163}, {12653, 25438}, {41869, 32049}, {47746, 34773}, {54422, 7991}, {64068, 11362}
X(64202) = pole of line {30198, 53392} with respect to the Bevan circle
X(64202) = pole of line {5048, 12629} with respect to the Feuerbach hyperbola
X(64202) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(106), X(38271)}}, {{A, B, C, X(1320), X(36624)}}
X(64202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 3880, 12629}, {517, 2136, 6765}, {519, 7991, 54422}, {1320, 4855, 1}, {1697, 10914, 9623}, {2802, 25438, 12653}, {3057, 63137, 936}, {4853, 5119, 31424}, {11519, 63468, 62858}, {34640, 64123, 9624}, {34711, 64068, 11362}, {36846, 63136, 15803}

X(64203) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-YFF AND X(84)-CROSSPEDAL-OF-X(8)

Barycentrics    a*(a^3+3*b^3-7*b^2*c-7*b*c^2+3*c^3-3*a^2*(b+c)-a*(b^2-12*b*c+c^2)) : :
X(64203) = -2*X[3895]+3*X[59337]

X(64203) lies on these lines: {1, 474}, {8, 5187}, {9, 13143}, {10, 10584}, {11, 3679}, {35, 64202}, {40, 32153}, {46, 14923}, {145, 10044}, {200, 63210}, {355, 546}, {498, 12640}, {499, 64205}, {517, 1709}, {519, 1478}, {952, 12678}, {993, 2802}, {997, 1320}, {1482, 3893}, {1621, 3885}, {1698, 11373}, {3057, 9708}, {3243, 34747}, {3244, 11045}, {3338, 36846}, {3340, 3633}, {3359, 6264}, {3419, 5854}, {3576, 5541}, {3577, 4867}, {3612, 4861}, {3625, 11682}, {3655, 6154}, {3689, 10247}, {3895, 59337}, {3984, 4701}, {4312, 34690}, {4316, 34716}, {4423, 9957}, {4668, 15829}, {4677, 11235}, {4853, 5697}, {4915, 5692}, {5010, 13205}, {5251, 9819}, {5288, 7991}, {5691, 12700}, {5727, 10947}, {5790, 44784}, {5853, 60923}, {5881, 10525}, {5903, 10042}, {5904, 11531}, {5919, 40587}, {6735, 23708}, {6765, 11009}, {7280, 63138}, {7993, 17654}, {8068, 12641}, {8148, 31937}, {9589, 64000}, {9897, 13271}, {10045, 11519}, {10522, 37711}, {10573, 21627}, {10785, 11362}, {10827, 49169}, {10829, 37546}, {10893, 37714}, {10915, 37692}, {10949, 41687}, {11260, 58887}, {11280, 11523}, {11529, 34612}, {11544, 16126}, {12245, 12616}, {12448, 44547}, {12546, 22787}, {12559, 20050}, {13463, 64087}, {13996, 26446}, {16152, 44669}, {16496, 36814}, {17098, 56091}, {17613, 63468}, {17622, 30393}, {17625, 18421}, {17757, 34640}, {18223, 63146}, {18480, 36972}, {18516, 31162}, {18961, 37709}, {22837, 37618}, {24392, 41684}, {26726, 64155}, {30144, 63142}, {35249, 50811}, {38460, 54286}, {41709, 64068}, {45700, 51433}

X(64203) = reflection of X(i) in X(j) for these {i,j}: {3632, 4863}, {5119, 3872}, {37708, 3434}
X(64203) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3445), X(56152)}}, {{A, B, C, X(8056), X(13143)}}
X(64203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 49600, 10826}, {519, 3434, 37708}, {2802, 3872, 5119}, {3679, 12653, 7962}, {4853, 5697, 41229}, {4863, 5844, 3632}, {7962, 11525, 3679}, {10912, 10914, 1}, {10944, 47746, 3633}, {22837, 63130, 37618}

X(64204) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(84)-CROSSPEDAL-OF-X(8)

Barycentrics    (a-b-c)*(a^3+4*a^2*(b+c)-2*(b-c)^2*(b+c)+a*(b^2-6*b*c+c^2)) : :
X(64204) = -6*X[2]+X[3680], -8*X[3]+3*X[34716], 4*X[5]+X[64202], 2*X[8]+3*X[3158], X[40]+4*X[10915], -X[145]+6*X[59584], 3*X[165]+2*X[32049], X[3189]+4*X[3626], 3*X[3576]+2*X[49169], -X[3633]+6*X[56177], -6*X[3654]+X[54422], 2*X[3811]+3*X[63143] and many others

X(64204) lies on these lines: {1, 1145}, {2, 3680}, {3, 34716}, {5, 64202}, {8, 3158}, {9, 6736}, {10, 1058}, {40, 10915}, {100, 37709}, {145, 59584}, {165, 32049}, {226, 63133}, {405, 3679}, {443, 1706}, {517, 63966}, {519, 631}, {528, 37714}, {529, 63469}, {646, 44720}, {1000, 6700}, {1329, 9819}, {1420, 12648}, {1478, 63138}, {1697, 2478}, {1698, 3880}, {1837, 47375}, {2475, 3882}, {2802, 8227}, {2900, 4882}, {3057, 30827}, {3169, 59772}, {3174, 21677}, {3189, 3626}, {3208, 23058}, {3243, 4848}, {3303, 37829}, {3333, 49626}, {3340, 10528}, {3576, 49169}, {3617, 5853}, {3632, 37525}, {3633, 56177}, {3654, 54422}, {3698, 20195}, {3811, 63143}, {3816, 30337}, {3829, 30315}, {3871, 5727}, {3885, 50443}, {3890, 20196}, {3893, 5231}, {3895, 9581}, {3919, 41870}, {3928, 43174}, {3929, 56879}, {4097, 59307}, {4301, 34711}, {4421, 32537}, {4595, 31638}, {4668, 44669}, {4669, 50739}, {4677, 37298}, {4915, 26066}, {5123, 51785}, {5219, 14923}, {5251, 8668}, {5531, 32198}, {5541, 10827}, {5552, 7962}, {5554, 10389}, {5657, 6762}, {5690, 6765}, {5795, 11106}, {5836, 25525}, {5837, 62218}, {5881, 6906}, {6173, 15888}, {6675, 9623}, {6834, 7982}, {6908, 11362}, {7080, 15829}, {7987, 38455}, {7988, 13463}, {7991, 12607}, {8583, 45081}, {9579, 63136}, {9588, 12513}, {9589, 11236}, {9613, 56998}, {9780, 21627}, {10039, 63137}, {10106, 37267}, {10179, 17648}, {10914, 31434}, {11239, 11518}, {11375, 13996}, {11525, 26363}, {12245, 59722}, {12247, 61296}, {12448, 58451}, {12541, 24386}, {12629, 26446}, {12649, 61016}, {16200, 59719}, {18634, 59711}, {20076, 63207}, {20420, 34687}, {24299, 59503}, {24982, 37556}, {24987, 38200}, {25055, 33895}, {31231, 36846}, {34471, 44784}, {34647, 58245}, {36972, 37600}, {37567, 60933}, {37711, 46816}, {38028, 47746}, {38763, 61276}, {42020, 56078}, {45036, 63987}, {49600, 54447}, {57002, 61763}, {59216, 63620}, {59388, 64117}

X(64204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37828, 31190}, {2, 12640, 3680}, {10, 2136, 24392}, {3679, 31436, 405}, {3679, 3913, 12625}, {5836, 51784, 25525}, {5881, 8715, 34701}, {7991, 12607, 28609}, {10528, 51433, 3340}, {11362, 34619, 11523}, {12541, 46933, 24386}, {32049, 32157, 165}

X(64205) = COMPLEMENT OF X(12640)

Barycentrics    (a-b-c)*(2*a^3-a^2*(b+c)-(b-c)^2*(b+c)-4*a*(b^2-3*b*c+c^2)) : :
X(64205) = 3*X[2]+X[3680], -3*X[551]+X[3913], -5*X[631]+X[64202], -X[2136]+5*X[3616], X[3146]+3*X[34716], -3*X[3158]+7*X[3622], 3*X[3742]+X[12448], -3*X[3817]+X[32049], -X[5493]+3*X[11194], 3*X[5603]+X[12629], -5*X[5734]+X[11523], 3*X[5790]+X[47746] and many others

X(64205) lies on circumconic {{A, B, C, X(277), X(38255)}} and on these lines: {1, 142}, {2, 3680}, {5, 519}, {8, 18220}, {10, 10912}, {145, 5226}, {226, 36846}, {499, 64203}, {515, 10525}, {516, 11260}, {517, 6705}, {518, 31821}, {521, 23808}, {527, 4301}, {551, 3913}, {553, 62837}, {631, 64202}, {950, 4861}, {958, 4342}, {1000, 5705}, {1125, 3880}, {1320, 6734}, {1387, 6700}, {1420, 37267}, {1482, 51755}, {2098, 4847}, {2136, 3616}, {2170, 52528}, {2475, 10106}, {2478, 3872}, {2802, 6684}, {3008, 45219}, {3057, 5745}, {3146, 34716}, {3158, 3622}, {3243, 4323}, {3244, 64110}, {3434, 63987}, {3445, 24175}, {3452, 4853}, {3626, 5854}, {3634, 64109}, {3635, 6701}, {3636, 56176}, {3742, 12448}, {3817, 32049}, {3884, 58415}, {3893, 6745}, {3900, 19947}, {3911, 14923}, {4051, 40869}, {4311, 56998}, {4345, 15829}, {4696, 4939}, {4848, 10529}, {5048, 6737}, {5258, 50891}, {5267, 22560}, {5493, 11194}, {5603, 12629}, {5734, 11523}, {5790, 47746}, {5836, 6692}, {5837, 7962}, {5882, 6850}, {5901, 59722}, {6553, 15590}, {6666, 58679}, {6675, 9957}, {6736, 11376}, {6762, 60965}, {6765, 10595}, {6766, 60974}, {6847, 7982}, {6891, 11362}, {8666, 28194}, {8732, 61630}, {8834, 10005}, {9588, 34711}, {9589, 34610}, {9623, 17559}, {9624, 34619}, {9785, 11106}, {9819, 30478}, {9843, 40587}, {10039, 41702}, {10171, 32426}, {10175, 49169}, {10246, 64117}, {10624, 57002}, {10914, 13747}, {10916, 28234}, {11035, 12446}, {11256, 21635}, {11519, 25568}, {11531, 24477}, {12436, 51788}, {12577, 60980}, {12632, 38314}, {12635, 24389}, {12641, 31272}, {13272, 21630}, {13384, 56936}, {17460, 28027}, {17528, 51071}, {17563, 24928}, {17784, 63208}, {19925, 38455}, {21949, 37743}, {24558, 46917}, {24982, 64201}, {28352, 61222}, {28661, 59599}, {30147, 40270}, {30389, 34607}, {31231, 63133}, {32157, 58441}, {34744, 58245}, {34937, 50637}

X(64205) = midpoint of X(i) and X(j) for these {i,j}: {1, 21627}, {10, 10912}, {3680, 12640}, {3813, 33895}, {4301, 12513}, {7982, 24391}, {11256, 21635}, {11260, 13463}, {12437, 64068}, {22837, 49600}
X(64205) = reflection of X(i) in X(j) for these {i,j}: {56176, 3636}, {59722, 5901}
X(64205) = complement of X(12640)
X(64205) = X(i)-complementary conjugate of X(j) for these {i, j}: {1476, 2885}, {59095, 20317}
X(64205) = pole of line {3676, 27830} with respect to the Steiner inellipse
X(64205) = pole of line {9, 63621} with respect to the dual conic of Yff parabola
X(64205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 21627, 5853}, {1, 64068, 12437}, {2, 3680, 12640}, {8, 18220, 30827}, {2136, 3616, 59584}, {3622, 12541, 3158}, {3813, 33895, 519}, {3872, 12053, 5795}, {4301, 12513, 527}, {7962, 64081, 5837}, {7982, 34625, 24391}, {10914, 44675, 63990}, {11260, 13463, 516}, {12437, 21627, 64068}, {12513, 34640, 4301}, {22837, 49600, 515}

X(64206) = X(6)X(41) ∩ X(77)X(674)

Barycentrics    a^2*(a+b-c)*(a-b+c)*((b+c)*a-(b-c)^2)*((b+c)*a-b^2-b*c-c^2) : :
X(64206) = 3*X(354)-X(1827) = 3*X(354)-2*X(40646)

Let (I) be the incircle of a triangle ABC. Let ωa be the circle tangent to (I) and passing through B and C. Define ωb and ωc cyclically. Let Ab, Ac be the second intersections of ωa and AC and AB, respectively, and define Bc, Ba and Ca, Cb cyclically. Let A'=BcBa∩CaCb, and define B', C' cyclically. Finally, let A* be the second intersection of ωb and ωc, and define B* and C* cyclically. Then: 1) A'B'C' and the intouch triangle are perspective (at X(64206)) and, 2) A'B'C' and A*B*C* are perspective (homothetic center X(64207)). (Keita Miyamoto, June 26, 2024 - Centers found by César Lozada).

X(64206) lies on the cubic K1089 and these lines: {6, 41}, {7, 15320}, {37, 1362}, {77, 674}, {222, 1486}, {226, 58571}, {241, 22277}, {354, 1827}, {946, 971}, {1037, 47373}, {1418, 52020}, {2807, 11700}, {3668, 5173}, {5083, 16888}, {6610, 21746}, {10481, 43915}, {14548, 21279}, {17625, 41003}, {21239, 44411}, {22300, 37544}, {22440, 41339}, {35312, 63227}, {55102, 60932}, {55340, 63203}

X(64206) = reflection of X(1827) in X(40646)
X(64206) = X(35338)-beth conjugate of-X(142)
X(64206) = X(i)-Ceva conjugate of-X(j) for these (i, j): (7, 1418), (56005, 20229)
X(64206) = X(i)-Dao conjugate of-X(j) for these (i, j): (116, 62725), (354, 8)
X(64206) = X(i)-isoconjugate of-X(j) for these {i, j}: {6605, 14377}, {43190, 62747}
X(64206) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3681, 63239), (3730, 56118), (6586, 62725), (15624, 6605), (35312, 31624), (40606, 8), (61376, 14377)
X(64206) = pole of the line {46110, 62725} with respect to the polar circle
X(64206) = pole of the line {1418, 24220} with respect to the circumhyperbola dual of Yff parabola
X(64206) = pole of the line {1418, 11246} with respect to the Feuerbach circumhyperbola
X(64206) = barycentric product X(i)*X(j) for these {i,j}: {7, 40606}, {1418, 3681}, {1475, 33298}, {1734, 63203}, {3730, 10481}, {4184, 52023}, {6586, 35312}, {15624, 59181}, {17233, 61376}
X(64206) = trilinear product X(i)*X(j) for these {i,j}: {57, 40606}, {1418, 3730}, {3681, 61376}, {6586, 63203}, {10481, 15624}
X(64206) = trilinear quotient X(i)/X(j) for these (i,j): (1418, 14377), (1734, 62725), (3681, 56118), (3730, 6605), (6586, 62747), (15624, 10482), (17233, 63239), (33298, 57815), (40606, 9), (53237, 57497), (63203, 43190)
X(64206) = (X(354), X(1827))-harmonic conjugate of X(40646)

X(64207) = X(1)X(3) ∩ X(479)X(1119)

Barycentrics    a*(a+b-c)*(a-b+c)*((b+c)*a^5-3*(b^2+c^2)*a^4+2*(b+c)*(b^2-3*b*c+c^2)*a^3+2*(b^2+3*b*c+c^2)*(b-c)^2*a^2-3*(b^4-c^4)*(b-c)*a+(b^2-c^2)^2*(b-c)^2) : :

X(64207) lies on these lines: {1, 3}, {479, 1119}, {1439, 3598}, {5745, 58623}, {8581, 41867}, {8732, 34784}, {10391, 60992}, {17612, 59413}, {58564, 60945}

X(64207) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (57, 34489, 55), (1467, 37566, 942)

X(64208) = X(37)X(56) ∩ X(518)X(1125)

Barycentrics    a*((b+c)*a^4+2*b*c*a^3+10*(b+c)*b*c*a^2+4*(b^2+4*b*c+c^2)*b*c*a-(b^2-c^2)^2*(b+c)) : :

Let (Ia) be the A-excircle of a triangle ABC. Let ωa be the circle tangent to (Ia) and passing through B and C. Define ωb and ωc cyclically. Let Ab, Ac be the second intersections of ωa and AC and AB, respectively, and define Bc, Ba and Ca, Cb cyclically. Let A'=BcBa∩CaCb, and define B', C' cyclically. Finally, let A* be the second intersection of ωb and ωc, and define B* and C* cyclically. Then: 1) A'B'C' and the extouch triangle are perspective (at X(22276)) and, 2) A'B'C' and A*B*C* are perspective (homothetic center X(64208)). (Keita Miyamoto, June 26, 2024 - Centers found by César Lozada).

X(64208) lies on these lines: {1, 21867}, {37, 56}, {518, 1125}, {614, 49478}, {960, 28639}, {975, 12329}, {984, 51816}, {3742, 29642}, {5173, 22276}, {5287, 40635}, {6051, 8053}, {12721, 16672}, {15569, 24929}, {20718, 37544}, {28627, 54344}

X(64209) = ISOGONAL CONJUGATE OF X(3083)

Barycentrics    a*(a*b + S)*(a*c + S) : :

X(64209) lies on the cirumconic {A,B,C,X(1),X(6)}, the cubic K678, and these lines: {1, 1123}, {6, 7133}, {19, 5412}, {33, 42}, {34, 61392}, {56, 2362}, {58, 606}, {86, 3084}, {106, 6135}, {158, 55404}, {190, 8393}, {269, 13437}, {386, 55498}, {1124, 37885}, {1126, 18992}, {1609, 44590}, {1659, 4000}, {1887, 16232}, {2334, 7968}, {3068, 8941}, {3299, 52186}, {3301, 57709}, {3445, 44635}, {4644, 52814}, {13387, 56328}, {13435, 56427}, {14571, 42013}, {17365, 58839}, {19004, 56343}, {30354, 60887}, {41515, 52033}, {54396, 55454}

X(64209) = isogonal conjugate of X(3083)
X(64209) = polar conjugate of X(46744)
X(64209) = polar conjugate of the isotomic conjugate of X(6213)
X(64209) = X(i)-Ceva conjugate of X(j) for these (i,j): {1123, 13456}, {13437, 13438}
X(64209) = X(60850)-cross conjugate of X(19)
X(64209) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3083}, {2, 1124}, {3, 13386}, {6, 1267}, {7, 60848}, {9, 52419}, {19, 55388}, {48, 46744}, {55, 13453}, {56, 13425}, {63, 6212}, {69, 34125}, {75, 605}, {100, 6364}, {394, 1336}, {898, 14440}, {1252, 22107}, {1259, 13459}, {1335, 13424}, {1804, 13426}, {3297, 38488}, {3299, 39312}, {3719, 13460}, {4131, 6136}, {6502, 56385}, {7183, 13427}, {10252, 15890}, {13389, 30556}, {31547, 46376}, {38003, 56354}, {40650, 42019}, {55442, 63689}
X(64209) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 13425}, {3, 3083}, {6, 55388}, {9, 1267}, {206, 605}, {223, 13453}, {478, 52419}, {661, 22107}, {1249, 46744}, {3162, 6212}, {8054, 6364}, {32664, 1124}, {36103, 13386}, {49171, 40650}
X(64209) = cevapoint of X(i) and X(j) for these (i,j): {1, 8941}, {6, 44590}
X(64209) = crosspoint of X(i) and X(j) for these (i,j): {6, 37882}, {1123, 13437}
X(64209) = crosssum of X(i) and X(j) for these (i,j): {1, 38004}, {2, 37881}, {1124, 60848}
X(64209) = crossdifference of every pair of points on line {4091, 6364}
X(64209) = barycentric product X(i)*X(j) for these {i,j}: {1, 1123}, {4, 6213}, {7, 13456}, {8, 13438}, {9, 13437}, {19, 13387}, {25, 46745}, {57, 13454}, {92, 34121}, {158, 1335}, {393, 3084}, {514, 6135}, {606, 2052}, {1096, 5391}, {1659, 7133}, {1857, 52420}, {2362, 7090}, {6524, 55387}, {30557, 61392}, {60850, 60854}
X(64209) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1267}, {3, 55388}, {4, 46744}, {6, 3083}, {9, 13425}, {19, 13386}, {25, 6212}, {31, 1124}, {32, 605}, {41, 60848}, {56, 52419}, {57, 13453}, {244, 22107}, {606, 394}, {649, 6364}, {1096, 1336}, {1123, 75}, {1335, 326}, {1973, 34125}, {3084, 3926}, {3554, 40650}, {3768, 14440}, {6059, 13427}, {6135, 190}, {6213, 69}, {6365, 30805}, {7133, 56385}, {7337, 13460}, {13387, 304}, {13437, 85}, {13438, 7}, {13454, 312}, {13456, 8}, {34121, 63}, {46378, 31547}, {46745, 305}, {52420, 7055}, {55387, 4176}, {60847, 3719}, {60850, 13389}, {60851, 30556}, {61386, 10252}
X(64209) = {X(37885),X(42019)}-harmonic conjugate of X(1124)

X(64210) = ISOGONAL CONJUGATE OF X(3084)

Barycentrics    a*(a*b - S)*(a*c - S) : :

X(64210) lies on the cirumconic {A,B,C,X(1),X(6)}, the cubic K678, and these lines: {1, 1336}, {6, 9043}, {19, 5413}, {33, 42}, {34, 61393}, {56, 7968}, {58, 605}, {86, 3083}, {106, 6136}, {158, 55403}, {190, 8394}, {269, 13459}, {386, 55497}, {1126, 18991}, {1335, 42019}, {1609, 44591}, {1887, 2362}, {2334, 7969}, {3069, 8945}, {3299, 57709}, {3301, 52186}, {3445, 44636}, {4000, 13390}, {4644, 52812}, {7133, 14571}, {13386, 56328}, {13424, 56384}, {17365, 58837}, {19003, 56343}, {41516, 52033}, {54396, 55425}

X(64210) = isogonal conjugate of X(3084)
X(64210) = polar conjugate of X(46745)
X(64210) = polar conjugate of the isotomic conjugate of X(6212)
X(64210) = X(i)-Ceva conjugate of X(j) for these (i,j): {1336, 13427}, {13459, 13460}
X(64210) = X(60849)-cross conjugate of X(19)
X(64210) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3084}, {2, 1335}, {3, 13387}, {6, 5391}, {7, 60847}, {9, 52420}, {19, 55387}, {48, 46745}, {55, 13436}, {56, 13458}, {63, 6213}, {69, 34121}, {75, 606}, {100, 6365}, {394, 1123}, {898, 14445}, {1124, 13435}, {1252, 22106}, {1259, 13437}, {1804, 13454}, {2067, 56386}, {3719, 13438}, {4131, 6135}, {7183, 13456}, {10253, 15889}, {13388, 30557}, {31548, 46377}
X(64210) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 13458}, {3, 3084}, {6, 55387}, {9, 5391}, {206, 606}, {223, 13436}, {478, 52420}, {661, 22106}, {1249, 46745}, {3162, 6213}, {8054, 6365}, {32664, 1335}, {36103, 13387}
X(64210) = cevapoint of X(i) and X(j) for these (i,j): {1, 8945}, {6, 44591}
X(64210) = crosspoint of X(1336) and X(13459)
X(64210) = crosssum of X(1335) and X(60847)
X(64210) = crossdifference of every pair of points on line {4091, 6365}
X(64210) = barycentric product X(i)*X(j) for these {i,j}: {1, 1336}, {4, 6212}, {7, 13427}, {8, 13460}, {9, 13459}, {19, 13386}, {25, 46744}, {57, 13426}, {92, 34125}, {158, 1124}, {393, 3083}, {514, 6136}, {605, 2052}, {1096, 1267}, {1857, 52419}, {6524, 55388}, {13390, 42013}, {14121, 16232}, {30556, 61393}, {60849, 60853}
X(64210) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 5391}, {3, 55387}, {4, 46745}, {6, 3084}, {9, 13458}, {19, 13387}, {25, 6213}, {31, 1335}, {32, 606}, {41, 60847}, {56, 52420}, {57, 13436}, {244, 22106}, {605, 394}, {649, 6365}, {1096, 1123}, {1124, 326}, {1336, 75}, {1973, 34121}, {3083, 3926}, {3768, 14445}, {6059, 13456}, {6136, 190}, {6212, 69}, {6364, 30805}, {7337, 13438}, {13386, 304}, {13426, 312}, {13427, 8}, {13459, 85}, {13460, 7}, {34125, 63}, {42013, 56386}, {46379, 31548}, {46744, 305}, {52419, 7055}, {55388, 4176}, {60848, 3719}, {60849, 13388}, {60852, 30557}, {61387, 10253}

X(64211) = POLAR CONJUGATE OF X(84)

Barycentrics    b*c*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-a^3 - a^2*b + a*b^2 + b^3 - a^2*c + 2*a*b*c - b^2*c + a*c^2 - b*c^2 + c^3) : :

X(64211) lies on the cubics K366 and K973, and these lines: {2, 92}, {4, 3753}, {8, 1034}, {9, 40444}, {10, 158}, {19, 24511}, {27, 55478}, {29, 19860}, {40, 47372}, {63, 653}, {72, 1148}, {75, 7017}, {107, 56375}, {196, 329}, {200, 1897}, {242, 62972}, {243, 1376}, {297, 25977}, {312, 6335}, {321, 459}, {322, 2331}, {469, 30687}, {648, 56440}, {860, 25003}, {958, 1940}, {1118, 2551}, {1784, 3679}, {1826, 30686}, {1838, 8582}, {1847, 26563}, {1857, 2550}, {3673, 17862}, {3681, 61180}, {3698, 42385}, {3916, 8762}, {4385, 60516}, {5081, 11433}, {5125, 24982}, {5174, 5554}, {5342, 11109}, {6336, 52140}, {6820, 7282}, {7020, 23528}, {7080, 7952}, {7182, 46404}, {7719, 26003}, {8056, 16082}, {8270, 36127}, {13149, 31627}, {13567, 21933}, {14571, 25091}, {15621, 53317}, {16080, 43683}, {17784, 44695}, {17861, 24177}, {18692, 20239}, {18928, 55393}, {20307, 38357}, {20905, 62349}, {24703, 52167}, {24993, 62970}, {26062, 37417}, {26942, 62605}, {28654, 59206}, {30758, 40703}, {33673, 41081}, {40701, 40702}, {56296, 56300}, {57531, 61012}

X(64211) = isotomic conjugate of X(41081)
X(64211) = polar conjugate of X(84)
X(64211) = isotomic conjugate of the isogonal conjugate of X(2331)
X(64211) = isotomic conjugate of the polar conjugate of X(47372)
X(64211) = polar conjugate of the isotomic conjugate of X(322)
X(64211) = polar conjugate of the isogonal conjugate of X(40)
X(64211) = X(i)-Ceva conjugate of X(j) for these (i,j): {75, 318}, {7017, 92}, {24032, 1897}, {40701, 342}
X(64211) = X(i)-cross conjugate of X(j) for these (i,j): {40, 322}, {196, 92}, {2331, 47372}, {7952, 342}, {20321, 75}, {53009, 7952}, {57049, 1897}
X(64211) = X(i)-isoconjugate of X(j) for these (i,j): {3, 1436}, {6, 1433}, {31, 41081}, {41, 56972}, {48, 84}, {55, 55117}, {56, 268}, {57, 2188}, {58, 41087}, {63, 2208}, {77, 7118}, {184, 189}, {212, 1422}, {219, 1413}, {222, 2192}, {255, 7129}, {271, 604}, {280, 52411}, {282, 603}, {285, 1409}, {309, 9247}, {394, 7151}, {577, 40836}, {610, 60799}, {652, 8059}, {849, 53010}, {905, 32652}, {1260, 6612}, {1333, 52389}, {1397, 44189}, {1415, 61040}, {1437, 1903}, {1440, 52425}, {1459, 36049}, {1790, 2357}, {1804, 7154}, {1946, 37141}, {2175, 34400}, {2193, 52384}, {2194, 52037}, {2206, 56944}, {4575, 55242}, {6056, 55110}, {7003, 7335}, {7008, 7125}, {7053, 7367}, {7152, 46881}, {8886, 28783}, {13138, 22383}, {14575, 44190}, {14642, 41084}, {15905, 60803}, {23224, 40117}, {32659, 56939}
X(64211) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 268}, {2, 41081}, {9, 1433}, {10, 41087}, {37, 52389}, {40, 22124}, {57, 222}, {136, 55242}, {223, 55117}, {281, 1}, {946, 22063}, {1108, 1071}, {1146, 61040}, {1214, 52037}, {1249, 84}, {3160, 56972}, {3161, 271}, {3162, 2208}, {4075, 53010}, {5452, 2188}, {5514, 1459}, {6129, 34591}, {6523, 7129}, {7952, 282}, {14092, 60799}, {16596, 905}, {17898, 40616}, {23050, 7367}, {36103, 1436}, {39053, 37141}, {39060, 53642}, {40593, 34400}, {40603, 56944}, {40837, 1422}, {47345, 52384}, {55044, 652}, {55063, 57241}, {57055, 24031}, {61075, 521}, {62576, 309}, {62585, 44189}, {62602, 1440}, {62605, 189}
X(64211) = cevapoint of X(i) and X(j) for these (i,j): {40, 2331}, {281, 3176}, {7952, 55116}
X(64211) = crosspoint of X(75) and X(40702)
X(64211) = crosssum of X(i) and X(j) for these (i,j): {3, 23168}, {31, 7118}
X(64211) = trilinear pole of line {1528, 8058}
X(64211) = barycentric product X(i)*X(j) for these {i,j}: {4, 322}, {8, 342}, {9, 40701}, {29, 57810}, {40, 264}, {69, 47372}, {75, 7952}, {76, 2331}, {85, 55116}, {92, 329}, {190, 59935}, {196, 312}, {198, 1969}, {208, 3596}, {223, 7017}, {227, 44130}, {273, 7080}, {274, 53009}, {281, 40702}, {286, 21075}, {313, 3194}, {318, 347}, {321, 41083}, {331, 2324}, {561, 3195}, {668, 54239}, {1897, 17896}, {2187, 18022}, {2501, 55241}, {3176, 47634}, {3209, 28659}, {6063, 40971}, {6331, 55212}, {6335, 14837}, {7020, 55015}, {7035, 38362}, {7074, 57787}, {7078, 57806}, {7101, 14256}, {7358, 24032}, {8058, 18026}, {8822, 41013}, {13149, 57049}, {14298, 46404}, {21871, 44129}, {27398, 40149}, {52938, 57101}, {54240, 57245}
X(64211) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1433}, {2, 41081}, {4, 84}, {7, 56972}, {8, 271}, {9, 268}, {10, 52389}, {19, 1436}, {25, 2208}, {29, 285}, {33, 2192}, {34, 1413}, {37, 41087}, {40, 3}, {55, 2188}, {57, 55117}, {64, 60799}, {85, 34400}, {92, 189}, {108, 8059}, {158, 40836}, {196, 57}, {198, 48}, {208, 56}, {221, 603}, {223, 222}, {225, 52384}, {226, 52037}, {227, 73}, {264, 309}, {273, 1440}, {278, 1422}, {281, 282}, {312, 44189}, {318, 280}, {321, 56944}, {322, 69}, {329, 63}, {342, 7}, {347, 77}, {393, 7129}, {522, 61040}, {594, 53010}, {607, 7118}, {653, 37141}, {1096, 7151}, {1103, 7078}, {1435, 6612}, {1490, 46881}, {1528, 6001}, {1712, 8886}, {1783, 36049}, {1817, 1790}, {1824, 2357}, {1826, 1903}, {1857, 7008}, {1895, 41084}, {1897, 13138}, {1969, 44190}, {2187, 184}, {2199, 52411}, {2324, 219}, {2331, 6}, {2360, 1437}, {2501, 55242}, {3176, 3341}, {3194, 58}, {3195, 31}, {3209, 604}, {3318, 53557}, {3596, 57783}, {5514, 34591}, {6129, 1459}, {6260, 1071}, {6331, 55211}, {6335, 44327}, {6611, 7099}, {7011, 7125}, {7013, 1804}, {7017, 34404}, {7020, 46355}, {7074, 212}, {7078, 255}, {7079, 7367}, {7080, 78}, {7114, 7335}, {7358, 24031}, {7368, 1802}, {7952, 1}, {8058, 521}, {8750, 32652}, {8802, 28784}, {8822, 1444}, {8894, 47851}, {10397, 36054}, {14256, 7177}, {14298, 652}, {14837, 905}, {15501, 1795}, {17896, 4025}, {18026, 53642}, {21075, 72}, {21871, 71}, {25022, 24560}, {27398, 1812}, {37410, 3576}, {37421, 10884}, {38357, 7004}, {38362, 244}, {38462, 56939}, {40149, 8808}, {40212, 7011}, {40701, 85}, {40702, 348}, {40836, 1256}, {40943, 22063}, {40971, 55}, {41013, 39130}, {41083, 81}, {41088, 19614}, {44130, 57795}, {47372, 4}, {47432, 2638}, {51375, 46974}, {52097, 63397}, {53008, 53013}, {53009, 37}, {53011, 41086}, {53557, 1364}, {54239, 513}, {55015, 7013}, {55111, 2289}, {55112, 3719}, {55116, 9}, {55212, 647}, {55241, 4563}, {57049, 57055}, {57101, 57241}, {57118, 36059}, {57810, 307}, {59935, 514}, {60431, 56763}, {61178, 61229}, {63383, 55979}
X(64211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 158, 318}, {196, 55116, 329}, {281, 40149, 92}

X(64212) = X(468)-CEVA CONJUGATE OF X(6)

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 4*a^2*b^6 - b^8 - 4*a^6*c^2 + 13*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 7*a^2*b^2*c^4 + 2*b^4*c^4 + 4*a^2*c^6 - c^8) : :

X(64212) lies on the cubic K478 and these lines: {3, 67}, {6, 14908}, {25, 1560}, {110, 6091}, {154, 5191}, {186, 13200}, {187, 18374}, {378, 9756}, {574, 34106}, {671, 33900}, {1576, 3053}, {2493, 8753}, {5013, 20975}, {5023, 20993}, {5461, 34010}, {6636, 34883}, {8573, 35133}, {9125, 42659}, {9127, 35266}, {9142, 53095}, {9145, 47412}, {9409, 57261}, {32113, 61443}, {37457, 56308}, {38463, 58309}, {41336, 44102}, {44533, 56957}, {47113, 51393}, {52144, 52169}, {52166, 53265}

X(64212) = X(468)-Ceva conjugate of X(6)
X(64212) = X(895)-Dao conjugate of X(30786)
X(64212) = crosssum of X(525) and X(5099)
X(64212) = crossdifference of every pair of points on line {2492, 6719}
X(64212) = barycentric product X(10424)*X(14961)
X(64212) = {X(14908),X(47426)}-harmonic conjugate of X(6)

X(64213) = X(468)-CEVA CONJUGATE OF X(25)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6 + a^4*b^2 - a^2*b^4 - b^6 + a^4*c^2 - 5*a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 + 3*b^2*c^4 - c^6) : :

X(64213) lies on the cubics K478 and X(535), and these lines: {2, 8792}, {6, 67}, {19, 47232}, {24, 41394}, {25, 111}, {115, 1184}, {187, 8428}, {232, 52166}, {352, 41363}, {399, 54380}, {427, 5354}, {468, 8744}, {648, 34336}, {858, 22121}, {1194, 34866}, {1609, 2493}, {1611, 10418}, {1995, 36415}, {2030, 34397}, {2207, 62981}, {2492, 42665}, {2502, 61206}, {2965, 10985}, {3162, 37453}, {3172, 21448}, {3291, 38463}, {5359, 62980}, {8585, 52905}, {8743, 20481}, {11284, 52951}, {30739, 59657}, {31128, 41676}, {36828, 45016}, {37981, 43291}, {45141, 47228}, {46276, 61207}, {47097, 52058}, {47230, 57262}

X(64213) = polar conjugate of the isotomic conjugate of X(2930)
X(64213) = X(i)-Ceva conjugate of X(j) for these (i,j): {468, 25}, {8744, 6}
X(64213) = X(i)-isoconjugate of X(j) for these (i,j): {63, 13574}, {304, 22259}
X(64213) = X(i)-Dao conjugate of X(j) for these (i,j): {111, 30786}, {3162, 13574}
X(64213) = crosssum of X(i) and X(j) for these (i,j): {6, 32262}, {520, 55048}, {525, 62594}
X(64213) = crossdifference of every pair of points on line {9517, 14417}
X(64213) = barycentric product X(i)*X(j) for these {i,j}: {4, 2930}, {19, 16563}, {25, 14360}, {112, 18310}, {468, 15899}, {5095, 61499}, {8753, 62664}
X(64213) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 13574}, {1974, 22259}, {2930, 69}, {14360, 305}, {15899, 30786}, {16563, 304}, {18310, 3267}, {44102, 41498}
X(64213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {112, 44467, 25}, {1560, 6103, 8791}, {1560, 8791, 5094}, {8744, 11580, 468}

X(64214) = MIDPOINT OF X(6391) AND X(12310)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - a^8*c^2 + 9*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 11*a^2*b^6*c^2 + 5*b^8*c^2 - 2*a^6*c^4 - 6*a^4*b^2*c^4 + 24*a^2*b^4*c^4 - 4*b^6*c^4 + 2*a^4*c^6 - 11*a^2*b^2*c^6 - 4*b^4*c^6 + a^2*c^8 + 5*b^2*c^8 - c^10) : :
X(64214) = 4 X[8548] - 3 X[39562], 2 X[155] - 3 X[45016], 2 X[2930] - 3 X[45082], 3 X[3167] - 4 X[6593], 3 X[5050] - 2 X[5504], 3 X[9909] - 2 X[38885], 4 X[9925] - 7 X[15039], 4 X[19138] - 3 X[32609], 2 X[52016] - 3 X[52697]

X(64214) lies on the Feuerbach circumhyperbola of the tangential triangle, the cubic K478, and these lines: {2, 23296}, {3, 895}, {6, 5181}, {68, 32306}, {110, 19118}, {155, 5095}, {159, 1177}, {193, 19504}, {195, 1992}, {394, 34470}, {399, 3564}, {468, 37784}, {511, 2935}, {524, 15141}, {542, 1498}, {1205, 7689}, {2393, 37928}, {2781, 46373}, {2917, 44470}, {2930, 8681}, {2931, 32127}, {2948, 34381}, {3167, 6593}, {5050, 5504}, {7493, 52124}, {8541, 45034}, {8542, 58495}, {8549, 34622}, {8780, 63181}, {9909, 38885}, {9925, 15039}, {9970, 12164}, {9976, 46945}, {11579, 15151}, {12038, 40673}, {13754, 48679}, {15106, 32244}, {15128, 30771}, {15462, 45045}, {17702, 35237}, {18440, 32239}, {19138, 32609}, {20772, 21313}, {32241, 53021}, {32245, 41612}, {32255, 52100}, {38851, 63180}, {52016, 52697}

X(64214) = midpoint of X(6391) and X(12310)
X(64214) = reflection of X(i) in X(j) for these {i,j}: {12164, 9970}, {18440, 63710}, {19588, 110}, {32306, 68}, {41615, 53777}
X(64214) = anticomplement of X(23296)
X(64214) = tangential-isogonal conjugate of X(37928)
X(64214) = X(i)-Ceva conjugate of X(j) for these (i,j): {468, 3}, {37784, 6}
X(64214) = crosssum of X(523) and X(48317)
X(64214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {895, 32251, 39562}, {895, 41614, 32251}

X(64215) = X(1)X(20595)∩X(31)X(48)

Barycentrics    a^3*(a + b)*(a + c)*(a^2 + a*b - b^2 + a*c - b*c - c^2) : :

X(64215) lies on the cubic K1021 and these lines: {1, 20595}, {6, 2248}, {31, 48}, {32, 17104}, {37, 2185}, {39, 501}, {58, 21008}, {60, 172}, {86, 25345}, {101, 5006}, {110, 1914}, {163, 2251}, {187, 5127}, {213, 849}, {593, 60697}, {662, 1575}, {798, 33882}, {1101, 19622}, {1326, 17735}, {1408, 41526}, {1500, 15792}, {1790, 62692}, {1922, 56388}, {2109, 5009}, {2210, 18268}, {2220, 3051}, {2242, 9275}, {2276, 40214}, {2277, 61409}, {6043, 21904}, {9456, 36142}, {16568, 62801}

X(64215) = X(64215) = isogonal conjugate of the isotomic conjugate of X(1931)
X(64215) = X(i)-Ceva conjugate of X(j) for these (i,j): {2210, 56388}, {18268, 1333}
X(64215) = X(18266)-cross conjugate of X(1326)
X(64215) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11599}, {4, 57848}, {10, 6650}, {37, 18032}, {75, 9278}, {76, 2054}, {86, 6543}, {190, 18014}, {264, 57681}, {306, 17982}, {313, 17962}, {321, 1929}, {523, 35148}, {740, 63896}, {850, 2702}, {1230, 53688}, {1577, 37135}, {1978, 18001}, {3948, 9505}, {4024, 17930}, {9506, 35544}, {17940, 52623}, {20536, 30586}, {39921, 63885}, {40725, 43534}
X(64215) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 9278}, {1326, 20648}, {20546, 20634}, {32664, 11599}, {35080, 20948}, {36033, 57848}, {39041, 313}, {39042, 76}, {40589, 18032}, {40600, 6543}, {41841, 27801}, {55053, 18014}
X(64215) = crosssum of X(i) and X(j) for these (i,j): {1, 20607}, {2, 20349}
X(64215) = crossdifference of every pair of points on line {1577, 4647}
X(64215) = barycentric product X(i)*X(j) for these {i,j}: {1, 1326}, {6, 1931}, {28, 17976}, {31, 17731}, {32, 52137}, {48, 423}, {58, 1757}, {81, 17735}, {86, 18266}, {110, 9508}, {163, 2786}, {513, 17943}, {593, 20693}, {662, 5029}, {667, 17934}, {741, 8298}, {757, 58287}, {849, 6541}, {1333, 6542}, {1437, 17927}, {2206, 20947}, {5009, 40794}, {6651, 18268}, {9456, 31059}, {17990, 52935}
X(64215) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 11599}, {32, 9278}, {48, 57848}, {58, 18032}, {163, 35148}, {213, 6543}, {423, 1969}, {560, 2054}, {667, 18014}, {1326, 75}, {1333, 6650}, {1576, 37135}, {1757, 313}, {1931, 76}, {1980, 18001}, {2203, 17982}, {2206, 1929}, {2786, 20948}, {5029, 1577}, {6542, 27801}, {8298, 35544}, {9247, 57681}, {9508, 850}, {17731, 561}, {17735, 321}, {17934, 6386}, {17943, 668}, {17976, 20336}, {17990, 4036}, {18266, 10}, {18268, 63896}, {20693, 28654}, {52137, 1502}, {58287, 1089}
X(64215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20607, 20595}, {6, 20472, 20461}

X(64216) = X(1)X(20589)∩X(6)X(692)

Barycentrics    a^3*(a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2) : :

X(64216) lies on the cubic K1021 and these lines: {1, 20589}, {6, 692}, {31, 9447}, {41, 42079}, {55, 7123}, {81, 105}, {182, 29349}, {184, 57656}, {294, 2264}, {518, 2991}, {560, 604}, {608, 1974}, {666, 18825}, {673, 1492}, {685, 54235}, {739, 919}, {884, 2423}, {1083, 4437}, {1177, 10099}, {1190, 7050}, {1333, 1576}, {1357, 1397}, {1415, 61055}, {1428, 1456}, {1691, 51333}, {1911, 2210}, {1976, 55261}, {2162, 20986}, {2203, 61206}, {2214, 16972}, {2221, 36057}, {2330, 14100}, {2481, 4577}, {3056, 56003}, {3573, 32029}, {3683, 40406}, {5317, 8751}, {5377, 5381}, {6654, 55940}, {8659, 43929}, {9061, 15636}, {9455, 32724}, {9456, 32666}, {13576, 51743}, {14776, 51726}, {14942, 56046}, {17938, 56388}, {19136, 51987}, {20332, 36086}, {32734, 41604}, {36404, 40401}, {36614, 59232}, {36942, 37492}, {40400, 52927}, {53971, 59049}

X(64216) = midpoint of X(6) and X(16686)
X(64216) = isogonal conjugate of X(3263)
X(64216) = isogonal conjugate of the anticomplement of X(3290)
X(64216) = isogonal conjugate of the isotomic conjugate of X(105)
X(64216) = isogonal conjugate of the polar conjugate of X(8751)
X(64216) = polar conjugate of the isotomic conjugate of X(32658)
X(64216) = X(i)-Ceva conjugate of X(j) for these (i,j): {105, 32658}, {5377, 919}, {15382, 6}, {32735, 43929}, {35185, 2440}, {41934, 32}
X(64216) = X(i)-cross conjugate of X(j) for these (i,j): {32, 41934}, {1922, 34077}, {9455, 32}, {14599, 1333}
X(64216) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3263}, {2, 3912}, {7, 3717}, {8, 9436}, {9, 40704}, {10, 30941}, {37, 18157}, {63, 46108}, {69, 1861}, {75, 518}, {76, 672}, {85, 3693}, {86, 3932}, {92, 25083}, {99, 4088}, {190, 918}, {239, 40217}, {241, 312}, {264, 1818}, {274, 3930}, {304, 5089}, {305, 2356}, {306, 15149}, {310, 20683}, {313, 3286}, {321, 18206}, {334, 8299}, {335, 17755}, {341, 34855}, {345, 5236}, {346, 62786}, {350, 22116}, {514, 42720}, {522, 883}, {561, 2223}, {646, 53544}, {661, 55260}, {664, 50333}, {665, 1978}, {666, 53583}, {668, 2254}, {673, 4437}, {693, 1026}, {765, 62429}, {799, 24290}, {850, 54353}, {908, 56753}, {926, 4572}, {1001, 63231}, {1025, 4391}, {1268, 4966}, {1458, 3596}, {1502, 9454}, {1876, 3718}, {1921, 3252}, {1928, 9455}, {1969, 20752}, {2283, 35519}, {2284, 3261}, {2340, 6063}, {2414, 4468}, {2481, 4712}, {2991, 20431}, {3126, 51560}, {3161, 10029}, {3262, 36819}, {3264, 34230}, {3675, 7035}, {3699, 43042}, {3952, 23829}, {4238, 14208}, {4373, 4899}, {4X(64216) = 384, 62622}, {4397, 41353}, {4447, 7018}, {4518, 39775}, {4562, 62552}, {4684, 5936}, {4925, 53647}, {5383, 23773}, {6184, 18031}, {6385, 39258}, {7257, 53551}, {9311, 40883}, {9502, 57996}, {14439, 20568}, {16284, 56718}, {16593, 36807}, {17789, 40781}, {18025, 50441}, {18891, 40730}, {20336, 54407}, {20504, 35574}, {21959, 56053}, {27919, 40098}, {28659, 52635}, {30701, 51400}, {31637, 34337}, {32008, 51384}, {32023, 56714}, {34234, 51390}, {35160, 40609}, {36086, 62430}, {40495, 54325}, {40869, 56668}, {42722, 52228}, {46406, 52614}, {50357, 53658}, {53553, 56241}, {54440, 63223}
X(64216) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 3263}, {206, 518}, {478, 40704}, {513, 62429}, {798, 23773}, {1438, 20642}, {3162, 46108}, {20540, 20628}, {22391, 25083}, {32664, 3912}, {33675, 1502}, {36830, 55260}, {38986, 4088}, {38989, 62430}, {38996, 24290}, {39025, 50333}, {40368, 2223}, {40369, 9455}, {40589, 18157}, {40600, 3932}, {55053, 918}, {62554, 76}, {62599, 561}
X(64216) = cevapoint of X(i) and X(j) for these (i,j): {31, 2210}, {32, 9455}
X(64216) = crosspoint of X(i) and X(j) for these (i,j): {6, 34183}, {105, 8751}, {919, 5377}, {1416, 1438}
X(64216) = crosssum of X(i) and X(j) for these (i,j): {1, 20601}, {2, 20344}, {518, 25083}, {918, 3675}, {3717, 3912}, {4437, 23102}
X(64216) = trilinear pole of line {32, 667}
X(64216) = crossdifference of every pair of points on line {918, 4437}
X(64216) = X(1083)-line conjugate of X(4437)
X(64216) = barycentric product X(i)*X(j) for these {i,j}: {1, 1438}, {3, 8751}, {4, 32658}, {6, 105}, {9, 1416}, {19, 36057}, {25, 1814}, {31, 673}, {32, 2481}, {41, 56783}, {48, 36124}, {55, 1462}, {56, 294}, {57, 2195}, {58, 18785}, {81, 56853}, {100, 43929}, {101, 1027}, {104, 51987}, {109, 1024}, {110, 55261}, {112, 10099}, {184, 54235}, {238, 51866}, {251, 46149}, {513, 919}, {514, 32666}, {518, 41934}, {560, 18031}, {604, 14942}, {649, 36086}, {650, 32735}, {651, 884}, {663, 36146}, {666, 667}, {672, 51838}, {692, 62635}, {739, 52902}, {840, 51922}, {885, 1415}, {909, 54364}, {911, 56639}, {927, 3063}, {1015, 5377}, {1106, 6559}, {1252, 43921}, {1292, 2440}, {1333, 13576}, {1397, 36796}, {1407, 28071}, {1492, 29956}, {1643, 59021}, {1911, 6654}, {1914, 52030}, {1919, 51560}, {1973, 31637}, {1980, 36803}, {2175, 34018}, {2210, 52209}, {2223, 6185}, {3290, 15382}, {3309, 32644}, {3669, 52927}, {4724, 36138}, {4762, 32724}, {5091, 59049}, {6169, 9316}, {8659, 39272}, {8852, 40754}, {9310, 51845}, {9455, 57537}, {18108, 46163}, {23696, 32674}, {26703, 51961}, {32655, 52456}, {34183, 62554}, {36802, 57181}, {40746, 52029}, {51333, 56856}, {52635, 62715}
X(64216) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3263}, {25, 46108}, {31, 3912}, {32, 518}, {41, 3717}, {56, 40704}, {58, 18157}, {105, 76}, {110, 55260}, {184, 25083}, {213, 3932}, {294, 3596}, {560, 672}, {604, 9436}, {665, 62430}, {666, 6386}, {667, 918}, {669, 24290}, {673, 561}, {692, 42720}, {798, 4088}, {884, 4391}, {919, 668}, {1015, 62429}, {1024, 35519}, {1027, 3261}, {1106, 62786}, {1333, 30941}, {1395, 5236}, {1397, 241}, {1415, 883}, {1416, 85}, {1438, 75}, {1462, 6063}, {1501, 2223}, {1814, 305}, {1911, 40217}, {1917, 9454}, {1918, 3930}, {1919, 2254}, {1922, 22116}, {1973, 1861}, {1974, 5089}, {1977, 3675}, {1980, 665}, {2175, 3693}, {2195, 312}, {2203, 15149}, {2205, 20683}, {2206, 18206}, {2210, 17755}, {2223, 4437}, {2279, 63231}, {2481, 1502}, {3063, 50333}, {5377, 31625}, {6654, 18891}, {8751, 264}, {9233, 9455}, {9247, 1818}, {9447, 2340}, {9454, 4712}, {9455, 6184}, {9459, 14439}, {10099, 3267}, {13576, 27801}, {14575, 20752}, {14598, 3252}, {14599, 8299}, {14942, 28659}, {16945, 10029}, {18031, 1928}, {18785, 313}, {18897, 40730}, {28071, 59761}, {29956, 62415}, {31637, 40364}, {32644, 54987}, {32658, 69}, {32666, 190}, {32724, 32041}, {32735, 4554}, {32739, 1026}, {34018, 41283}, {34858, 56753}, {36057, 304}, {36086, 1978}, {36124, 1969}, {36146, 4572}, {36796, 40363}, {38986, 23773}, {39686, 23102}, {41280, 52635}, {41934, 2481}, {43921, 23989}, {43929, 693}, {46149, 8024}, {51838, 18031}, {51866, 334}, {51987, 3262}, {52030, 18895}, {52209, 44172}, {52410, 34855}, {52902, 35543}, {52927, 646}, {54235, 18022}, {55261, 850}, {56783, 20567}, {56853, 321}, {57129, 23829}, {57181, 43042}, {61206, 4238}, {62635, 40495}
X(64216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20601, 20589}, {6, 20468, 20455}, {105, 1814, 46149}, {1438, 2195, 56853}

X(64217) = X(524)-CROSS CONJUGATE OF X(523)

Barycentrics    (b^2 - c^2)*(a^2 + b^2 - 2*c^2)*(-a^2 + 2*b^2 - c^2)*(2*a^4 - 3*a^2*b^2 + 2*b^4 - a^2*c^2 - b^2*c^2 + c^4)*(2*a^4 - a^2*b^2 + b^4 - 3*a^2*c^2 - b^2*c^2 + 2*c^4) : :
X(64217) = 3 X[36953] - X[36955], 3 X[14588] + 5 X[42345]

X(64217) lies on the X-parabola of ABC (see X(12065)), the cubic K241, and these lines: {523, 620}, {2501, 14052}, {4024, 21047}, {5466, 45291}, {8029, 62672}, {9178, 62645}, {14588, 42345}, {58784, 62629}

X(64217) = X(i)-cross conjugate of X(j) for these (i,j): {524, 523}, {45212, 57539}
X(64217) = X(i)-isoconjugate of X(j) for these (i,j): {163, 45291}, {896, 33803}, {922, 33799}, {14567, 33809}, {23889, 39024}
X(64217) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 45291}, {15899, 33803}, {39061, 33799}
X(64217) = cevapoint of X(i) and X(j) for these (i,j): {524, 36953}, {690, 8029}, {1648, 42553}
X(64217) = trilinear pole of line {115, 11123}
X(64217) = barycentric product X(i)*X(j) for these {i,j}: {671, 36955}, {5466, 36953}, {14052, 14977}
X(64217) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 33803}, {523, 45291}, {671, 33799}, {5466, 14061}, {9178, 39024}, {10097, 14060}, {14052, 4235}, {36953, 5468}, {36955, 524}, {46277, 33809}

X(64218) = X(32)-CROSS CONJUGATE OF X(111)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4) : :

X(64218) lies on the cubics K531 and K7664 and these lines: {6, 10558}, {67, 524}, {111, 18374}, {141, 8869}, {187, 2393}, {249, 2854}, {598, 14246}, {691, 9019}, {843, 39413}, {3124, 32741}, {6593, 15398}, {8262, 10416}, {8541, 51428}, {8542, 14357}, {8753, 60428}, {8859, 10511}, {8877, 40057}, {9971, 52142}, {10422, 32246}, {14580, 32740}, {14608, 36820}, {19127, 57481}, {19596, 32729}, {21639, 57467}, {22151, 46783}, {22258, 32251}, {22259, 41936}, {22826, 22827}, {38294, 46105}, {41511, 53929}

X(64218) = isogonal conjugate of X(7664)
X(64218) = isogonal conjugate of the complement of X(31125)
X(64218) = isogonal conjugate of the isotomic conjugate of X(10415)
X(64218) = X(i)-cross conjugate of X(j) for these (i,j): {32, 111}, {3005, 691}, {20975, 9178}, {51962, 32740}, {59175, 3455}
X(64218) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7664}, {23, 14210}, {75, 6593}, {187, 20944}, {316, 896}, {524, 16568}, {662, 18311}, {897, 62661}, {922, 40074}, {2492, 24039}, {2642, 55226}, {5099, 24041}, {9979, 23889}, {14246, 24038}, {16702, 21094}, {18715, 52898}, {42081, 52551}, {46254, 47415}
X(64218) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 7664}, {206, 6593}, {1084, 18311}, {3005, 5099}, {6593, 62661}, {15477, 23}, {15899, 316}, {15900, 3266}, {39061, 40074}
X(64218) = cevapoint of X(i) and X(j) for these (i,j): {6, 46154}, {895, 8869}, {3455, 59175}
X(64218) = crosspoint of X(10422) and X(10630)
X(64218) = crosssum of X(i) and X(j) for these (i,j): {2482, 5181}, {5099, 18311}, {6390, 62664}
X(64218) = trilinear pole of line {351, 3455}
X(64218) = crossdifference of every pair of points on line {18311, 62661}
X(64218) = barycentric product X(i)*X(j) for these {i,j}: {6, 10415}, {67, 111}, {671, 3455}, {690, 39413}, {895, 8791}, {897, 2157}, {935, 10097}, {8753, 34897}, {9076, 46154}, {9139, 60496}, {9178, 17708}, {10511, 42007}, {10630, 14357}, {14908, 46105}, {18019, 32740}, {22258, 61494}, {23288, 58953}, {57539, 59175}
X(64218) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7664}, {32, 6593}, {67, 3266}, {111, 316}, {187, 62661}, {512, 18311}, {671, 40074}, {691, 55226}, {895, 37804}, {897, 20944}, {923, 16568}, {2157, 14210}, {3124, 5099}, {3455, 524}, {6041, 32313}, {7316, 17088}, {8753, 37765}, {8791, 44146}, {9178, 9979}, {10415, 76}, {10630, 52551}, {14357, 36792}, {14908, 22151}, {19626, 18374}, {20975, 62594}, {32729, 52630}, {32740, 23}, {39413, 892}, {41272, 9019}, {41936, 14246}, {59175, 2482}
X(64218) = {X(895),X(15899)}-harmonic conjugate of X(10510)

X(64219) = X(3)X(51)∩X(4)X(95)

Barycentrics    a^4*(a^2 - b^2 - c^2)^2*(a^4 - 4*a^2*b^2 + 3*b^4 - 2*a^2*c^2 - 4*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - 4*a^2*c^2 - 4*b^2*c^2 + 3*c^4) : :

X(64219) lies on the cubic K737 and these lines: {2, 11282}, {3, 51}, {4, 95}, {20, 8796}, {30, 60007}, {97, 6759}, {184, 19210}, {217, 577}, {376, 1105}, {418, 1092}, {511, 56337}, {578, 26874}, {1294, 3522}, {3785, 6394}, {3964, 5562}, {10110, 37068}, {10323, 56307}, {11414, 34818}, {12362, 44156}, {13346, 26876}, {16391, 61363}, {18564, 31392}, {23217, 43652}, {26865, 37498}, {26907, 36747}, {27372, 63433}, {28783, 41376}, {34786, 52681}, {35268, 37081}

X(64219) = isogonal conjugate of the polar conjugate of X(63154)
X(64219) = X(61394)-cross conjugate of X(577)
X(64219) = X(i)-isoconjugate of X(j) for these (i,j): {75, 61348}, {92, 3087}, {158, 631}, {823, 47122}, {1096, 44149}, {6521, 36748}, {6755, 40440}, {11402, 57806}
X(64219) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 61348}, {1147, 631}, {6503, 44149}, {22391, 3087}
X(64219) = cevapoint of X(i) and X(j) for these (i,j): {577, 26880}, {578, 6759}
X(64219) = crosssum of X(i) and X(j) for these (i,j): {3087, 61348}, {37192, 43981}
X(64219) = trilinear pole of line {32320, 42293}
X(64219) = barycentric product X(i)*X(j) for these {i,j}: {3, 63154}, {97, 63176}, {255, 56033}, {394, 3527}, {577, 8797}, {1092, 8796}, {3964, 34818}, {52613, 58950}
X(64219) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 61348}, {184, 3087}, {217, 6755}, {394, 44149}, {577, 631}, {3527, 2052}, {8797, 18027}, {14585, 11402}, {23606, 36748}, {34818, 1093}, {39201, 47122}, {56033, 57806}, {58950, 15352}, {63154, 264}, {63176, 324}
X(64219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3527, 63154}, {3527, 63154, 63176}

X(64220) = X(6)X(351)∩X(187)X(54274)

Barycentrics    a^2*(b^2 - c^2)*(2*a^2 - b^2 - c^2)*(a^4 - 4*a^2*b^2 + b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 2*c^4)*(a^4 + 2*a^2*b^2 - 2*b^4 - 4*a^2*c^2 + 2*b^2*c^2 + c^4) : :

X(64220) lies on the cubics K229 and K978 and these lines: {6, 351}, {187, 54274}, {249, 5467}, {512, 21906}, {524, 1649}, {598, 804}, {9170, 23342}, {9178, 10630}, {14608, 51226}, {17994, 17999}, {18823, 35146}, {18872, 62412}, {23348, 53690}

X(64220) = isogonal conjugate of X(34760)
X(64220) = isogonal conjugate of the anticomplement of X(41176)
X(64220) = isogonal conjugate of the isotomic conjugate of X(34763)
X(64220) = X(53690)-Ceva conjugate of X(843)
X(64220) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34760}, {75, 23348}, {99, 17955}, {543, 36085}, {662, 17948}, {799, 17964}, {897, 9182}, {9181, 46277}, {17993, 24037}, {18007, 24041}, {36142, 45809}
X(64220) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 34760}, {206, 23348}, {512, 17993}, {1084, 17948}, {3005, 18007}, {6593, 9182}, {21905, 8371}, {23992, 45809}, {38986, 17955}, {38988, 543}, {38996, 17964}
X(64220) = crosspoint of X(843) and X(53690)
X(64220) = crosssum of X(i) and X(j) for these (i,j): {2, 45294}, {543, 33921}, {1641, 8371}, {17948, 18007}
X(64220) = trilinear pole of line {351, 59801}
X(64220) = crossdifference of every pair of points on line {543, 9182}
X(64220) = barycentric product X(i)*X(j) for these {i,j}: {6, 34763}, {187, 9180}, {351, 18823}, {512, 51226}, {523, 48450}, {690, 843}, {9170, 21906}, {23992, 53690}
X(64220) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34760}, {32, 23348}, {187, 9182}, {351, 543}, {512, 17948}, {669, 17964}, {690, 45809}, {798, 17955}, {843, 892}, {1084, 17993}, {3124, 18007}, {9180, 18023}, {14567, 9181}, {18823, 53080}, {21906, 8371}, {34763, 76}, {48450, 99}, {51226, 670}, {53690, 57552}, {54274, 1641}, {59801, 33921}

X(64221) = X(30)X(50)∩X(110)X(476)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 - b^2*c^6) : :

X(64221) lies on the cubics K147, K192, and K1072, and these lines: {30, 50}, {94, 36188}, {110, 476}, {250, 23290}, {1316, 43084}, {2410, 4226}, {3564, 34209}, {5467, 39295}, {5877, 39170}, {14995, 54554}, {18883, 47348}, {36192, 57482}, {38896, 41205}, {39290, 51262}, {43090, 45921}, {51263, 54959}, {56397, 62490}

X(64221) = midpoint of X(476) and X(60053)
X(64221) = trilinear pole of line {32761, 56396}
X(64221) = crossdifference of every pair of points on line {2088, 60342}
X(64221) = barycentric product X(i)*X(j) for these {i,j}: {99, 56396}, {476, 40879}, {32761, 35139}, {39295, 62489}
X(64221) = barycentric quotient X(i)/X(j) for these {i,j}: {32761, 526}, {39295, 53192}, {40879, 3268}, {56396, 523}, {62489, 62551}
X(64221) = {X(5467),X(56398)}-harmonic conjugate of X(39295)

X(64222) = X(75)X(3123)∩X(76)X(335)

Barycentrics    b^3*c^3*(-a^2 + b*c)^2 : :

X(64222) lies on the cubic K986 and these lines: {75, 3123}, {76, 335}, {244, 310}, {312, 561}, {350, 1926}, {756, 40087}, {1089, 18833}, {1111, 4602}, {1921, 3797}, {1928, 3760}, {3673, 18837}, {6385, 18032}, {10009, 31323}, {17738, 37133}, {17755, 27853}, {18037, 63878}, {20448, 20651}

X(64222) = isogonal conjugate of X(18267)
X(64222) = isotomic conjugate of the isogonal conjugate of X(39044)
X(64222) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 1926}, {18833, 35544}
X(64222) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18267}, {6, 51856}, {32, 52205}, {291, 14598}, {292, 1922}, {334, 18893}, {335, 18897}, {560, 30663}, {875, 34067}, {1501, 40098}, {1927, 18787}, {7104, 30657}, {8789, 30669}, {61364, 62714}
X(64222) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 18267}, {9, 51856}, {740, 872}, {812, 3248}, {1966, 6}, {3912, 40730}, {3948, 40155}, {6374, 30663}, {6376, 52205}, {6651, 1911}, {18277, 291}, {19557, 1922}, {35119, 875}, {39028, 292}, {39029, 14598}, {39030, 30669}, {39786, 798}, {62610, 18787}
X(64222) = barycentric product X(i)*X(j) for these {i,j}: {75, 56660}, {76, 39044}, {238, 44169}, {239, 18891}, {350, 1921}, {561, 4366}, {1502, 8300}, {1914, 44171}, {1926, 17493}, {1928, 51328}, {1978, 27855}, {3766, 27853}, {3975, 18033}, {4087, 10030}, {4368, 6385}, {4375, 6386}, {6652, 44172}, {14603, 18786}, {18901, 61385}, {30940, 35544}, {35068, 57992}
X(64222) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 51856}, {6, 18267}, {75, 52205}, {76, 30663}, {238, 1922}, {239, 1911}, {350, 292}, {561, 40098}, {812, 875}, {874, 813}, {1909, 30657}, {1914, 14598}, {1921, 291}, {1926, 30669}, {2210, 18897}, {3570, 34067}, {3684, 18265}, {3685, 51858}, {3766, 3572}, {3802, 40728}, {3975, 7077}, {3978, 18787}, {4087, 4876}, {4094, 7109}, {4366, 31}, {4368, 213}, {4375, 667}, {6652, 2210}, {8300, 32}, {14599, 18893}, {17493, 1967}, {17755, 40730}, {18035, 40794}, {18786, 9468}, {18891, 335}, {27853, 660}, {27855, 649}, {27919, 2223}, {27926, 18266}, {30940, 741}, {33295, 18268}, {35068, 872}, {35119, 3248}, {39044, 6}, {40767, 18263}, {44169, 334}, {44171, 18895}, {51328, 560}, {52379, 62714}, {53681, 7122}, {56660, 1}, {57992, 57554}, {61385, 8789}, {62553, 40155}
v{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {350, 19581, 20356}, {350, 44169, 1926}

X(64223) = X(8)X(76)∩X(75)X(141)

Barycentrics    b*c*(-a^2 + b*c)*(-(a*b) + b^2 - a*c + c^2) : :

X(64223) lies on the cubic K986 and these lines: {8, 76}, {10, 4986}, {69, 2876}, {75, 141}, {150, 10449}, {239, 350}, {305, 10453}, {313, 22271}, {314, 7261}, {319, 42554}, {320, 36792}, {321, 20630}, {511, 20561}, {799, 19642}, {883, 53548}, {1111, 4647}, {1227, 62430}, {1500, 28598}, {1926, 4087}, {1930, 49560}, {1978, 21404}, {2254, 23829}, {3123, 3728}, {3263, 3912}, {3266, 29824}, {3766, 4010}, {3925, 18052}, {4479, 29617}, {4499, 36216}, {4554, 52160}, {4651, 39998}, {4710, 21443}, {4738, 6381}, {4847, 51861}, {4966, 18157}, {5222, 30830}, {6184, 42720}, {6376, 40609}, {8024, 17135}, {11059, 30947}, {14210, 49764}, {16589, 26965}, {17033, 29983}, {17230, 31130}, {17244, 30758}, {17292, 60706}, {17367, 30963}, {17752, 30045}, {18032, 60678}, {18067, 32865}, {20333, 27918}, {20549, 20861}, {21415, 33081}, {21416, 33064}, {23989, 53363}, {25125, 57033}, {27844, 27853}, {28616, 41828}, {29611, 30866}, {29615, 43270}, {29674, 33937}, {31625, 53219}, {33141, 59510}, {36791, 41314}, {40022, 59296}, {40619, 61174}, {42721, 51583}, {44312, 61165}

X(64223) = reflection of X(20861) in X(20549)
X(64223) = isotomic conjugate of X(52030)
X(64223) = isotomic conjugate of the isogonal conjugate of X(8299)
X(64223) = X(i)-Ceva conjugate of X(j) for these (i,j): {75, 3263}, {76, 3948}, {668, 3766}, {31625, 42720}, {56241, 50333}, {56660, 62553}
X(64223) = X(38989)-cross conjugate of X(62552)
X(64223) = X(i)-isoconjugate of X(j) for these (i,j): {6, 51866}, {31, 52030}, {32, 52209}, {105, 1911}, {292, 1438}, {673, 1922}, {741, 56853}, {813, 43929}, {875, 36086}, {876, 32666}, {919, 3572}, {1027, 34067}, {1397, 33676}, {1416, 7077}, {1462, 51858}, {2196, 8751}, {2481, 14598}, {3252, 41934}, {6654, 51856}, {18031, 18897}, {18265, 56783}, {18268, 18785}, {40730, 51838}
X(64223) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 52030}, {9, 51866}, {518, 40730}, {665, 1015}, {1966, 6654}, {2238, 6}, {3716, 3271}, {3912, 1}, {6184, 292}, {6376, 52209}, {6651, 105}, {8299, 56853}, {17755, 291}, {18277, 2481}, {19557, 1438}, {27918, 513}, {35068, 18785}, {35094, 876}, {35119, 1027}, {38980, 3572}, {38989, 875}, {39028, 673}, {39046, 1911}, {40609, 7077}, {40623, 43929}, {52656, 52205}, {62552, 43921}, {62553, 13576}, {62585, 33676}, {62587, 335}
X(64223) = cevapoint of X(38989) and X(62552)
X(64223) = crosspoint of X(75) and X(350)
X(64223) = crosssum of X(31) and X(1911)
X(64223) = crossdifference of every pair of points on line {875, 1922}
X(64223) = barycentric product X(i)*X(j) for these {i,j}: {75, 17755}, {76, 8299}, {239, 3263}, {241, 4087}, {312, 39775}, {334, 27919}, {350, 3912}, {518, 1921}, {668, 62552}, {672, 18891}, {740, 18157}, {874, 918}, {1969, 20778}, {2223, 44169}, {2254, 27853}, {3596, 34253}, {3685, 40704}, {3693, 18033}, {3717, 10030}, {3766, 42720}, {3932, 30940}, {3948, 30941}, {3975, 9436}, {4010, 55260}, {9454, 44171}, {18206, 35544}, {22116, 56660}, {25083, 40717}, {28659, 51329}, {31625, 38989}, {39044, 40217}
X(64223) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 51866}, {2, 52030}, {75, 52209}, {238, 1438}, {239, 105}, {242, 8751}, {312, 33676}, {350, 673}, {518, 292}, {659, 43929}, {665, 875}, {672, 1911}, {740, 18785}, {812, 1027}, {874, 666}, {918, 876}, {1026, 813}, {1281, 40754}, {1429, 1416}, {1447, 1462}, {1818, 2196}, {1921, 2481}, {2223, 1922}, {2238, 56853}, {2254, 3572}, {2284, 34067}, {2340, 51858}, {3263, 335}, {3286, 18268}, {3570, 36086}, {3573, 919}, {3684, 2195}, {3685, 294}, {3693, 7077}, {3716, 1024}, {3717, 4876}, {3766, 62635}, {3797, 52029}, {3912, 291}, {3948, 13576}, {3975, 14942}, {4010, 55261}, {4087, 36796}, {4435, 884}, {4437, 22116}, {4465, 52902}, {4712, 3252}, {6184, 40730}, {6654, 51838}, {7193, 32658}, {8299, 6}, {9454, 14598}, {9455, 18897}, {10030, 56783}, {15507, 51987}, {17755, 1}, {18033, 34018}, {18037, 40724}, {18157, 18827}, {18206, 741}, {18891, 18031}, {20769, 36057}, {20778, 48}, {22116, 52205}, {24459, 10099}, {25083, 295}, {27853, 51560}, {27918, 43921}, {27919, 238}, {30665, 29956}, {30941, 37128}, {33701, 2111}, {34253, 56}, {38989, 1015}, {39044, 6654}, {39775, 57}, {39916, 56856}, {40217, 30663}, {40704, 7233}, {40717, 54235}, {40730, 51856}, {40781, 30648}, {42720, 660}, {51329, 604}, {51381, 54364}, {55260, 4589}, {62552, 513}
X(64223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17794, 52029}, {75, 52151, 334}, {668, 2481, 20345}, {4441, 20345, 2481}

X(64224) = X(86)-DAO CONJUGATE OF X(6)

Barycentrics    b^2*(a + b)*c^2*(a + c)*(-a^2 + a*b + b^2 + a*c + b*c + c^2) : :

X(64224) lies on the cubic K986 and these lines: {69, 8044}, {75, 23928}, {76, 6625}, {86, 310}, {141, 18152}, {257, 1921}, {274, 17302}, {313, 670}, {314, 7261}, {1654, 51857}, {1963, 8033}, {3948, 34021}, {4043, 55239}, {4610, 40589}, {6385, 18032}, {7199, 54256}, {17787, 36860}, {38814, 40722}, {49676, 57992}, {52619, 52629}
on K986

X(64224) = isotomic conjugate of the isogonal conjugate of X(6626)
X(64224) = X(76)-Ceva conjugate of X(310)
X(64224) = X(i)-isoconjugate of X(j) for these (i,j): {32, 52208}, {42, 18757}, {213, 2248}, {560, 63885}, {1918, 13610}, {1973, 15377}, {2205, 6625}, {50487, 53628}
X(64224) = X(i)-Dao conjugate of X(j) for these (i,j): {86, 6}, {6337, 15377}, {6374, 63885}, {6376, 52208}, {6626, 2248}, {6627, 512}, {34021, 13610}, {40592, 18757}
X(64224) = cevapoint of X(17762) and X(51857)
X(64224) = crosspoint of X(76) and X(51857)
X(64224) = barycentric product X(i)*X(j) for these {i,j}: {76, 6626}, {86, 51857}, {274, 17762}, {305, 2905}, {310, 1654}, {561, 38814}, {670, 21196}, {799, 50451}, {846, 6385}, {873, 27569}, {1921, 52207}, {3261, 57060}, {17084, 28660}, {18021, 27691}, {18891, 45783}, {21879, 57992}, {44169, 51867}
X(64224) = barycentric quotient X(i)/X(j) for these {i,j}: {69, 15377}, {75, 52208}, {76, 63885}, {81, 18757}, {86, 2248}, {274, 13610}, {310, 6625}, {846, 213}, {1654, 42}, {2905, 25}, {4213, 2333}, {4610, 53628}, {6385, 51865}, {6626, 6}, {17084, 1400}, {17762, 37}, {18755, 1918}, {21085, 1500}, {21196, 512}, {21879, 872}, {22139, 2200}, {27569, 756}, {27691, 181}, {27954, 20964}, {38814, 31}, {39921, 2054}, {45783, 1911}, {50451, 661}, {51857, 10}, {51867, 1922}, {52207, 292}, {52612, 53655}, {57060, 101}, {63627, 40729}

X(64225) = X(64225) = X(1575)-DAO CONJUGATE OF X(43)

Barycentrics    b*c*(-a^2 + b*c)*(a*b - a*c + b*c)*(-(a*b) + a*c + b*c)*(-(a*b^2) + b^2*c - a*c^2 + b*c^2) : :

X(64225) lies on the cubic K986 and these lines: {76, 330}, {312, 335}, {350, 39914}, {726, 20366}, {812, 14296}, {1921, 1926}, {4440, 18830}, {12263, 23493}, {17793, 56663}, {20913, 52655}, {20936, 33890}, {20943, 27424}, {29960, 30026}, {45782, 49493}, {59802, 62234}

X(64225) = X(56663)-Ceva conjugate of X(62553)
X(64225) = X(i)-isoconjugate of X(j) for these (i,j): {32, 33680}, {727, 51973}, {1911, 62421}, {2176, 63881}, {14598, 40844}, {34077, 41531}
X(64225) = X(i)-Dao conjugate of X(j) for these (i,j): {1575, 43}, {3837, 6377}, {3948, 192}, {6376, 33680}, {6651, 62421}, {17793, 51973}, {18277, 40844}, {20532, 41531}, {27846, 20979}
X(64225) = barycentric product X(i)*X(j) for these {i,j}: {75, 56663}, {330, 62553}, {1921, 40881}, {6383, 17475}, {6384, 17793}, {34252, 35538}, {39914, 52043}, {44169, 51864}
X(64225) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 33680}, {87, 63881}, {239, 62421}, {726, 41531}, {1575, 51973}, {1921, 40844}, {8850, 1403}, {17475, 2176}, {17793, 43}, {20663, 2209}, {34252, 727}, {39914, 20332}, {40881, 292}, {51321, 34077}, {51864, 1922}, {52043, 40848}, {56663, 1}, {62553, 192}, {62558, 20979}

X(64226) = X(75)-DAO CONJUGATE OF X(1575)

Barycentrics    b^2*c^2*(-(a*b) - a*c + b*c)*(-(a^2*b) - a*b^2 + a^2*c + b^2*c)*(a^2*b - a^2*c - a*c^2 + b*c^2) : :

X(64226) lies on the cubic K986 and these lines: {75, 3123}, {76, 330}, {192, 23643}, {257, 18035}, {310, 55947}, {350, 3226}, {1978, 20532}, {2998, 27809}, {6376, 21337}, {7233, 18033}, {18037, 36799}, {20971, 33296}, {52136, 62421}

X(64226) = X(57535)-Ceva conjugate of X(40087)
X(64226) = X(i)-isoconjugate of X(j) for these (i,j): {6, 51864}, {32, 40881}, {2162, 21760}, {3009, 7121}, {14598, 56663}
X(64226) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 51864}, {75, 1575}, {6376, 40881}, {6377, 6373}, {18277, 56663}, {33678, 2162}, {40598, 3009}
X(64226) = cevapoint of X(726) and X(59518)
X(64226) = crosspoint of X(32020) and X(40844)
X(64226) = crosssum of X(21760) and X(51864)
X(64226) = trilinear pole of line {3835, 6382}
X(64226) = barycentric product X(i)*X(j) for these {i,j}: {75, 40844}, {561, 62421}, {727, 40367}, {1921, 33680}, {3226, 6382}, {3835, 54985}, {6376, 32020}
X(64226) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 51864}, {43, 21760}, {75, 40881}, {192, 3009}, {1921, 56663}, {3226, 2162}, {3253, 51321}, {3835, 6373}, {3971, 21830}, {6376, 1575}, {6382, 726}, {8709, 34071}, {8851, 57264}, {18793, 21759}, {20332, 7121}, {21138, 52633}, {22370, 20777}, {27809, 23493}, {30545, 1463}, {31008, 18792}, {32020, 87}, {33680, 292}, {36799, 2053}, {40367, 35538}, {40844, 1}, {40848, 40155}, {54985, 4598}, {62421, 31}

X(64227) = X(5)-DAO CONJUGATE OF X(40804)

Barycentrics    (a^2 - b^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 + a^4*c^4 - 2*b^4*c^4 + b^2*c^6) : :

X(64227) lies on the cubic K976 and these lines: {3, 525}, {5, 217}, {54, 276}, {98, 185}, {184, 14265}, {287, 575}, {401, 32545}, {631, 36893}, {1614, 52491}, {6146, 51441}, {6759, 52641}, {14585, 48452}, {18925, 36874}, {19357, 36822}, {19467, 56688}, {21659, 34175}, {44088, 60594}, {58728, 60700}

X(64227) = X(290)-Ceva conjugate of X(401)
X(64227) = X(32428)-cross conjugate of X(53174)
X(64227) = X(i)-isoconjugate of X(j) for these (i,j): {240, 1298}, {1956, 19189}, {2190, 40804}, {40440, 57500}
X(64227) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 40804}, {14382, 276}, {39045, 19189}, {39085, 1298}, {52128, 511}
X(64227) = barycentric product X(i)*X(j) for these {i,j}: {287, 32428}, {336, 2313}, {343, 32545}, {401, 53174}, {61196, 62523}
X(64227) = barycentric quotient X(i)/X(j) for these {i,j}: {216, 40804}, {217, 57500}, {248, 1298}, {685, 41210}, {1971, 19189}, {2313, 240}, {2966, 41208}, {32428, 297}, {32545, 275}, {53174, 1972}

X(64228) = X(1511)-DAO CONJUGATE OF X(1154)

Barycentrics    (a^2 - b^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4) : :

X(64228) lies on the cubic K976 and these lines: {3, 6368}, {5, 49}, {95, 46751}, {276, 46138}, {933, 7728}, {1568, 51254}, {1970, 1989}, {2420, 52945}, {4240, 14254}, {5944, 38896}, {7691, 43965}, {8884, 58733}, {10282, 58704}, {10610, 58926}, {12121, 15958}, {14980, 46966}, {15469, 52010}, {18400, 58746}, {18475, 58729}, {39170, 44516}, {41334, 50433}, {46064, 58789}
on K976

X(64228) = X(46138)-Ceva conjugate of X(43768)
X(64228) = X(30)-cross conjugate of X(265)
X(64228) = X(i)-isoconjugate of X(j) for these (i,j): {74, 51801}, {1154, 36119}, {1953, 57487}, {2159, 14918}, {2290, 16080}, {2349, 11062}, {36131, 41078}, {61354, 62273}
X(64228) = X(i)-Dao conjugate of X(j) for these (i,j): {1511, 1154}, {3163, 14918}, {39008, 41078}, {39170, 5}, {62569, 1273}
X(64228) = trilinear pole of line {3284, 14391}
X(64228) = crossdifference of every pair of points on line {2081, 11062}
X(64228) = barycentric product X(i)*X(j) for these {i,j}: {54, 57482}, {95, 56399}, {97, 14254}, {265, 43768}, {275, 51254}, {933, 18557}, {1141, 11064}, {3260, 11077}, {3284, 46138}, {14583, 34386}, {18558, 18831}, {41392, 62428}, {43752, 50433}, {46106, 50463}
X(64228) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 14918}, {54, 57487}, {265, 62722}, {1141, 16080}, {1495, 11062}, {2173, 51801}, {3284, 1154}, {9033, 41078}, {9409, 2081}, {11064, 1273}, {11077, 74}, {14254, 324}, {14391, 55132}, {14533, 14385}, {14583, 53}, {18558, 6368}, {32662, 36831}, {36298, 6117}, {36299, 6116}, {41392, 35360}, {43768, 340}, {50433, 44715}, {50463, 14919}, {51254, 343}, {56399, 5}, {57482, 311}, {62270, 61354}
X(64228) = {X(1141),X(50463)}-harmonic conjugate of X(265)

X(64229) = X(223)-DAO CONJUGATE OF X(7090)

Barycentrics    a*(a+b-c)*(a-b+c)*(2*S+(a+b-c)*(a-b+c)) : :
Barycentrics    1-Sec[A/2]^2-Tan[A/2] : :

X(6422) lies on the cubic K631 and these lines: {1, 16213}, {6, 57}, {7, 1659}, {77, 2066}, {176, 20070}, {241, 6204}, {279, 16232}, {348, 13453}, {481, 946}, {738, 18992}, {948, 30276}, {1014, 61400}, {1323, 35775}, {1440, 13390}, {2067, 4350}, {4292, 31529}, {6180, 6203}, {6502, 7177}, {7053, 34125}, {10481, 31541}, {35774, 59813}, {42013, 43736}, {44624, 51364}, {60849, 63150}, {60852, 63178}

X(64229) = isotomic conjugate of the polar conjugate of X(61400)
X(64229) = X(6502)-cross conjugate of X(13389)
X(64229) = X(i)-isoconjugate of X(j) for these (i,j): {8, 60851}, {9, 7133}, {33, 30557}, {41, 60854}, {55, 7090}, {200, 2362}, {220, 1659}, {281, 5414}, {318, 53066}, {346, 60850}, {607, 56386}, {728, 61401}, {1260, 61392}, {1805, 53008}, {2066, 13454}, {2067, 7046}, {3239, 54018}, {3939, 58840}, {7079, 13388}, {7101, 53063}, {13456, 30556}, {34911, 46378}
X(64229) = X(i)-Dao conjugate of X(j) for these (i,j): {223, 7090}, {478, 7133}, {3160, 60854}, {6609, 2362}, {13388, 8}, {40617, 58840}
X(64229) = barycentric product X(i)*X(j) for these {i,j}: {7, 13389}, {69, 61400}, {77, 13390}, {85, 6502}, {269, 56385}, {279, 30556}, {348, 16232}, {934, 54019}, {1088, 2066}, {1267, 61401}, {1446, 1806}, {1659, 52419}, {2362, 13453}, {6063, 53064}, {7053, 60853}, {7056, 42013}, {7177, 14121}, {7182, 60849}, {7183, 61393}, {53065, 57792}
X(64229) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 60854}, {56, 7133}, {57, 7090}, {77, 56386}, {222, 30557}, {269, 1659}, {603, 5414}, {604, 60851}, {1106, 60850}, {1407, 2362}, {1435, 61392}, {1806, 2287}, {2066, 200}, {2362, 13454}, {3669, 58840}, {6502, 9}, {7023, 61401}, {7053, 13388}, {7099, 2067}, {13389, 8}, {13390, 318}, {14121, 7101}, {16232, 281}, {30556, 346}, {42013, 7046}, {46376, 34911}, {52411, 53066}, {52419, 56385}, {53064, 55}, {53065, 220}, {54016, 56183}, {54019, 4397}, {56385, 341}, {60849, 33}, {60850, 13456}, {60852, 7079}, {61400, 4}, {61401, 1123}
X(64229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 1419, 51842}, {77, 52419, 13389}

X(64230) = X(223)-DAO CONJUGATE OF X(14121)

Barycentrics    a*(a+b-c)^2*(a-b+c)^2*(-2*S*b+(c+a)*(a+b-c)*(-a+b+c))*(-2*S*c+(a+b)*(-a+b+c)*(a-b+c)) : :
Barycentrics    1 - Sec[A/2]^2 + Tan[A/2] : :

X(64230) lies on the cubic K631 and these lines: {1, 16214}, {6, 57}, {7, 13389}, {77, 5414}, {175, 20070}, {241, 6203}, {279, 2362}, {348, 13436}, {482, 946}, {738, 18991}, {948, 30277}, {1014, 61401}, {1071, 60903}, {1323, 35774}, {1440, 1659}, {2067, 7177}, {4292, 31528}, {4350, 6502}, {5572, 60878}, {6180, 6204}, {7053, 34121}, {7133, 43736}, {10481, 31540}, {35775, 59813}, {44623, 51364}, {60850, 63150}, {60851, 63178}

X(64230) = isotomic conjugate of the polar conjugate of X(61401)
X(64230) = X(2067)-cross conjugate of X(13388)
X(64230) = X(i)-isoconjugate of X(j) for these (i,j): {8, 60852}, {9, 42013}, {33, 30556}, {41, 60853}, {55, 14121}, {200, 16232}, {220, 13390}, {281, 2066}, {318, 53065}, {346, 60849}, {607, 56385}, {728, 61400}, {1260, 61393}, {1806, 53008}, {3239, 54016}, {3939, 58838}, {5414, 13426}, {6502, 7046}, {7079, 13389}, {7101, 53064}, {13427, 30557}, {34912, 46379}
X(64230) = X(i)-Dao conjugate of X(j) for these (i,j): {223, 14121}, {478, 42013}, {3160, 60853}, {6609, 16232}, {13389, 8}, {40617, 58838}
X(64230) = barycentric product X(i)*X(j) for these {i,j}: {7, 13388}, {69, 61401}, {77, 1659}, {85, 2067}, {269, 56386}, {279, 30557}, {348, 2362}, {934, 54017}, {1088, 5414}, {1446, 1805}, {5391, 61400}, {6063, 53063}, {7053, 60854}, {7056, 7133}, {7090, 7177}, {7182, 60850}, {7183, 61392}, {13390, 52420}, {13436, 16232}, {53066, 57792}
X(64230) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 60853}, {56, 42013}, {57, 14121}, {77, 56385}, {222, 30556}, {269, 13390}, {603, 2066}, {604, 60852}, {1106, 60849}, {1407, 16232}, {1435, 61393}, {1659, 318}, {1805, 2287}, {2067, 9}, {2362, 281}, {3669, 58838}, {5414, 200}, {7023, 61400}, {7053, 13389}, {7090, 7101}, {7099, 6502}, {7133, 7046}, {13388, 8}, {16232, 13426}, {30557, 346}, {46377, 34912}, {52411, 53065}, {52420, 56386}, {53063, 55}, {53066, 220}, {54017, 4397}, {54018, 56183}, {56386, 341}, {60849, 13427}, {60850, 33}, {60851, 7079}, {61400, 1336}, {61401, 4}
X(64230) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 1419, 51841}, {77, 52420, 13388}

X(64231) = X(1966)-DAO CONJUGATE OF X(1281)

Barycentrics    b*c*(-a^2 + b*c)*(a^3 + b^3 - a*b*c - c^3)*(-a^3 + b^3 + a*b*c - c^3) : :

X(64231) lies on the cubics K744 and K1077 and these lines: {1, 56706}, {8, 7261}, {10, 33676}, {76, 3496}, {330, 348}, {1655, 40781}, {1909, 52085}, {4560, 16705}, {9239, 19581}, {17760, 24479}, {27855, 42455}

X(64231) = X(i)-Ceva conjugate of X(j) for these (i,j): {18036, 350}, {63875, 40846}
X(64231) = X(4366)-cross conjugate of X(350)
0 X(64231) = X(i)-isoconjugate of X(j) for these (i,j): {32, 52085}, {291, 19554}, {292, 17798}, {335, 18262}, {560, 51859}, {1281, 51856}, {1911, 3509}, {1922, 4645}, {5018, 51858}, {14598, 17789}, {18037, 18267}, {18038, 30663}, {18268, 20715}, {18787, 41882}, {19561, 52205}, {40730, 40754}
X(64231) = X(i)-Dao conjugate of X(j) for these (i,j): {1966, 1281}, {6374, 51859}, {6376, 52085}, {96651, 3509}, {7261, 8933}, {18277, 17789}, {19557, 17798}, {35068, 20715}, {39028, 4645}, {39029, 19554}, {62553, 4071}
X(64231) = cevapoint of X(3512) and X(56706)
X(64231) = barycentric product X(i)*X(j) for these {i,j}: {238, 18036}, {239, 40845}, {350, 7261}, {1921, 3512}, {3766, 51614}, {4366, 63895}, {7281, 18033}, {8852, 18891}, {17493, 40846}, {24479, 56660}, {39044, 63875}
X(64231) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 52085}, {76, 51859}, {238, 17798}, {239, 3509}, {350, 4645}, {740, 20715}, {1447, 5018}, {1914, 19554}, {1921, 17789}, {2210, 18262}, {3512, 292}, {3766, 4458}, {3948, 4071}, {4366, 19557}, {6654, 40754}, {7061, 18787}, {7261, 291}, {7281, 7077}, {8300, 19561}, {8852, 1911}, {17493, 40873}, {18036, 334}, {18786, 41532}, {20769, 20741}, {24479, 52205}, {39044, 1281}, {40781, 3252}, {40845, 335}, {40846, 30669}, {51328, 18038}, {51614, 660}, {56660, 18037}, {56697, 40791}, {56706, 9470}, {63875, 30663}, {63895, 40098}
X(64231) = {X(3512),X(18036)}-harmonic conjugate of X(40846)

X(64232) = X(75)-DAO CONJUGATE OF X(40795)

Barycentrics    b^2*c^2*(-(a^3*b^3) - 2*a^4*b*c - a^2*b^2*c^2 - a^3*c^3 + b^3*c^3) : :

X(64232) lies on the cubic K744 and these lines: {1, 7168}, {8, 3978}, {10, 1920}, {76, 257}, {274, 330}, {1909, 18275}, {1921, 30038}, {3727, 44169}, {6374, 59509}, {6376, 18277}, {6386, 59515}, {6645, 37133}, {18059, 27880}, {18760, 52085}, {19573, 64133}

X(64232) = isotomic conjugate of the isogonal conjugate of X(30661)
X(64232) = X(1909)-Ceva conjugate of X(76)
X(64232) = X(i)-isoconjugate of X(j) for these (i,j): {32, 52176}, {7104, 63888}, {16360, 51856}
X(64232) = X(i)-Dao conjugate of X(j) for these (i,j): {75, 40795}, {1966, 16360}, {6376, 52176}, {7018, 256}
X(64232) = barycentric product X(i)*X(j) for these {i,j}: {76, 30661}, {561, 18754}, {1920, 39917}, {6382, 40741}, {16362, 18891}
X(64232) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 52176}, {1909, 63888}, {6376, 40795}, {16362, 1911}, {18754, 31}, {30661, 6}, {39044, 16360}, {39917, 893}, {40741, 2162}, {40768, 7121}
v{X(257),X(1926)}-harmonic conjugate of X(76)

X(64233) = X(1921)-DAO CONJUGATE OF X(56660)

Barycentrics    (b^2 - a*c)*(a*b - c^2)*(a^3*b^3 - a^2*b^2*c^2 + a^3*c^3 - b^3*c^3) : :

X(64233) lies on the cubic K744 and these lines: {1, 18795}, {8, 291}, {10, 30663}, {39, 62557}, {76, 335}, {172, 37207}, {194, 40155}, {257, 52085}, {334, 20255}, {1500, 35956}, {1655, 40796}, {1909, 52205}, {1911, 7346}, {4444, 48131}, {4562, 20691}, {6376, 52656}, {7187, 40098}, {17739, 18787}, {17762, 18298}, {19567, 51868}, {22116, 25918}, {26752, 36906}

X(64233) = X(i)-Ceva conjugate of X(j) for these (i,j): {1909, 52085}, {52205, 335}
X(64233) = X(i)-cross conjugate of X(j) for these (i,j): {18275, 335}, {19581, 40849}
X(64233) = X(i)-isoconjugate of X(j) for these (i,j): {238, 51919}, {1914, 7168}, {8300, 63893}, {24576, 51328}, {39933, 61385}
X(64233) = X(i)-Dao conjugate of X(j) for these (i,j): {1921, 56660}, {9470, 51919}, {22116, 40782}, {36906, 7168}
X(64233) = barycentric product X(i)*X(j) for these {i,j}: {1, 51868}, {291, 19567}, {292, 18275}, {334, 3510}, {335, 19565}, {8875, 51859}, {18277, 52205}, {18278, 18895}, {19579, 40098}, {19581, 30663}, {30669, 40849}
X(64233) = barycentric quotient X(i)/X(j) for these {i,j}: {291, 7168}, {292, 51919}, {3510, 238}, {18274, 51328}, {18275, 1921}, {18277, 56660}, {18278, 1914}, {18787, 51920}, {19565, 239}, {19567, 350}, {19579, 4366}, {19580, 8300}, {19581, 39044}, {23186, 7193}, {30663, 24576}, {30669, 39933}, {40849, 17493}, {51868, 75}, {52205, 63893}, {52656, 40782}, {56695, 40798}, {57265, 61385}

X(64234) = X(1)X(88)∩X(10)X(90)

Barycentrics    a*(a^3 + a^2*b - 2*a*b^2 - 2*b^3 + a^2*c - 3*a*b*c + 4*b^2*c - 2*a*c^2 + 4*b*c^2 - 2*c^3) : :
X(64234) = 2 X[1] - 3 X[106], X[1] - 3 X[1054], 4 X[1] - 3 X[10700], 5 X[1] - 6 X[11717], 5 X[1] - 3 X[13541], 5 X[106] - 4 X[11717], 5 X[106] - 2 X[13541], 4 X[1054] - X[10700], 5 X[1054] - 2 X[11717], 5 X[1054] - X[13541], 5 X[10700] - 8 X[11717], 5 X[10700] - 4 X[13541], 4 X[10] - 3 X[10713], 6 X[121] - 7 X[9780], 7 X[9780] - 3 X[17777], 3 X[1293] - 4 X[3579], 4 X[1125] - 3 X[50915], 5 X[3617] - 3 X[21290], X[3621] + 3 X[20098], 4 X[3626] - 3 X[50914], 4 X[3634] - 3 X[11814], 4 X[4663] - 3 X[10761], 11 X[5550] - 12 X[6715], X[8148] - 3 X[38576], 3 X[10730] - 4 X[31673], 3 X[10744] - 4 X[18357], 3 X[10774] - 4 X[12019], 12 X[11731] - 13 X[46934], 8 X[13624] - 9 X[38695], 6 X[14664] - 5 X[35242], 4 X[14664] - 3 X[38713], 10 X[35242] - 9 X[38713], 9 X[57300] - 8 X[61272]

X(64234) lies on the cubic K299 and these lines: {1, 88}, {10, 190}, {40, 9519}, {44, 5011}, {58, 3987}, {101, 21888}, {121, 9780}, {484, 896}, {517, 38671}, {519, 18201}, {528, 6788}, {595, 24440}, {758, 5524}, {759, 1293}, {846, 3968}, {899, 3245}, {1125, 50915}, {1126, 7312}, {1357, 5221}, {1482, 51531}, {1739, 7292}, {2097, 2810}, {2254, 2832}, {2836, 34893}, {2840, 5128}, {2841, 3030}, {2842, 3214}, {3227, 49488}, {3339, 51765}, {3617, 21290}, {3621, 20098}, {3626, 50914}, {3634, 11814}, {3679, 36263}, {3753, 4653}, {3899, 9350}, {3919, 60714}, {4413, 17461}, {4424, 5297}, {4646, 4658}, {4663, 10761}, {4880, 49984}, {5204, 34139}, {5225, 12534}, {5400, 64189}, {5550, 6715}, {5708, 52827}, {5836, 37599}, {6163, 17960}, {8148, 38576}, {9352, 49494}, {9432, 55926}, {10730, 31673}, {10744, 18357}, {10774, 12019}, {11731, 46934}, {12702, 17749}, {13329, 48363}, {13624, 38695}, {13996, 24864}, {14026, 38938}, {14664, 35242}, {16611, 41322}, {17070, 17734}, {17160, 57029}, {21222, 53356}, {21944, 56952}, {21949, 50821}, {24880, 61524}, {28212, 51415}, {30384, 60414}, {31514, 46901}, {32486, 64136}, {38945, 40663}, {57300, 61272}, {62235, 62325}

X(64234) = reflection of X(i) in X(j) for these {i,j}: {106, 1054}, {1482, 51531}, {10700, 106}, {13541, 11717}, {17777, 121}, {38685, 40}
X(64234) = reflection of X(45763) in the anti-Orthic axis
X(64234) = {X(1739),X(63136)}-harmonic conjugate of X(40091)

X(64235) = X(524)-CEVA CONJUGATE OF X(69)

Barycentrics    (a^2 - b^2 - c^2)*(3*a^6 - 2*a^4*b^2 - 4*a^2*b^4 + b^6 - 2*a^4*c^2 + 7*a^2*b^2*c^2 - 4*a^2*c^4 + c^6) : :
X(64235) = 3 X[1992] - 2 X[41909], 3 X[69] - 4 X[52881], 3 X[4563] - 2 X[52881], 5 X[3618] - 4 X[6388]

X(64235) lies on the cubic K534 and these lines: {6, 8788}, {32, 1992}, {69, 125}, {99, 5095}, {193, 4576}, {524, 62310}, {690, 11061}, {2407, 46236}, {2930, 10553}, {3618, 6388}, {3785, 20975}, {3933, 22143}, {6340, 50992}, {6393, 47277}, {7752, 8541}, {9035, 25332}, {10330, 25321}, {10765, 11008}, {19583, 63064}, {32114, 57216}, {39099, 47526}

X(64235) = reflection of X(69) in X(4563)
X(64235) = isotomic conjugate of the polar conjugate of X(7665)
X(64235) = X(i)-Ceva conjugate of X(j) for these (i,j): {524, 69}, {62310, 6337}
X(64235) = X(i)-isoconjugate of X(j) for these (i,j): {923, 63900}, {15390, 36128}
X(64235) = X(i)-Dao conjugate of X(j) for these (i,j): {2482, 63900}, {30786, 671}
X(64235) = barycentric product X(i)*X(j) for these {i,j}: {69, 7665}, {524, 62607}
X(64235) = barycentric quotient X(i)/X(j) for these {i,j}: {524, 63900}, {3292, 15390}, {7665, 4}, {62607, 671}

X(64236) = X(9505)-CEVA CONJUGATE OF X(11599)

Barycentrics    (a^2 + a*b + b^2 - a*c - b*c - c^2)*(a^2 - a*b - b^2 + a*c - b*c + c^2)*(a*b^2 - b^2*c + a*c^2 - b*c^2) : :

X(64236) lies on the cubic K744 and these lines: {1, 40725}, {8, 6650}, {10, 40098}, {58, 17930}, {76, 4485}, {330, 1929}, {514, 1125}, {596, 9278}, {1655, 40793}, {1909, 9505}, {19929, 19936}, {21140, 62636}, {35148, 35172}

X(64236) = X(9505)-Ceva conjugate of X(11599)
X(64236) = X(17793)-cross conjugate of X(726)
X(64236) = X(i)-isoconjugate of X(j) for these (i,j): {727, 1757}, {1326, 18793}, {3226, 18266}, {6542, 34077}, {8298, 63881}, {17735, 20332}
X(64236) = X(i)-Dao conjugate of X(j) for these (i,j): {726, 59724}, {1575, 6651}, {17793, 1757}, {20532, 6542}, {22116, 40794}, {27846, 38348}
X(64236) = crosspoint of X(18032) and X(63896)
X(64236) = barycentric product X(i)*X(j) for these {i,j}: {726, 6650}, {1575, 18032}, {1929, 52043}, {3837, 35148}, {9505, 62553}, {11599, 62636}, {17793, 63896}, {17930, 21053}, {17962, 35538}, {20908, 37135}
X(64236) = barycentric quotient X(i)/X(j) for these {i,j}: {726, 6542}, {1575, 1757}, {1929, 20332}, {3009, 17735}, {3837, 2786}, {6373, 5029}, {6650, 3226}, {9278, 18793}, {9506, 63881}, {11599, 27809}, {17475, 8298}, {17793, 6651}, {17962, 727}, {18032, 32020}, {18792, 1931}, {20532, 59724}, {20785, 17976}, {21053, 18004}, {21760, 18266}, {21830, 58287}, {35148, 8709}, {40725, 3253}, {52043, 20947}, {52656, 40794}, {62558, 38348}, {62636, 17731}

X(64237) = ANTITOMIC IMAGE OF X(1022)

Barycentrics    a*(b - c)*(a^2*b + a*b^2 - 2*a^2*c - 2*b^2*c + a*c^2 + b*c^2)*(2*a^2*b - a*b^2 - a^2*c - b^2*c - a*c^2 + 2*b*c^2) : :

X(64237) lies on the circumconic {{A,B,C,X(1),X(2)}}, the cubic K324, and these lines: {1, 659}, {2, 812}, {81, 50456}, {88, 649}, {100, 38349}, {101, 5376}, {105, 2382}, {190, 4375}, {244, 43928}, {291, 513}, {330, 21222}, {514, 3227}, {900, 35030}, {1015, 1022}, {1280, 48572}, {2832, 54977}, {3768, 36275}, {4724, 55935}, {4893, 56170}, {9263, 63246}, {17494, 39698}, {36805, 48008}, {48244, 52654}

X(64237) = midpoint of X(9263) and X(63246)
X(64237) = reflection of X(1022) in X(1015)
X(64237) = antitomic image of X(1022)
X(64237) = X(52745)-cross conjugate of X(513)
X(64237) = X(i)-isoconjugate of X(j) for these (i,j): {6, 56811}, {44, 59486}, {100, 20331}, {101, 537}, {765, 52745}, {813, 52908}, {1252, 36848}, {23344, 46795}
X(64237) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 56811}, {513, 52745}, {661, 36848}, {1015, 537}, {8054, 20331}, {40595, 59486}, {40623, 52908}
X(64237) = cevapoint of X(513) and X(52745)
X(64237) = crosssum of X(20331) and X(52745)
X(64237) = trilinear pole of line {513, 16507}
X(64237) = barycentric product X(i)*X(j) for these {i,j}: {291, 47070}, {335, 52226}, {513, 18822}, {693, 2382}, {903, 59487}, {1022, 46797}, {3227, 46782}, {51923, 62619}
X(64237) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 56811}, {106, 59486}, {244, 36848}, {513, 537}, {649, 20331}, {659, 52908}, {1015, 52745}, {1022, 46795}, {2382, 100}, {3227, 46780}, {18822, 668}, {21123, 52960}, {42753, 42765}, {43928, 52768}, {46782, 536}, {46797, 24004}, {47070, 350}, {51923, 23891}, {52226, 239}, {52745, 35123}, {59487, 519}
X(64237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21385, 52226, 51923}, {47070, 47776, 46797}

X(64238) = X(1)X(33674)∩X(8)X(76)

Barycentrics    b*c*(a^2 + b^2 - a*c - b*c)*(-a^2 + a*b + b*c - c^2)*(-(a^2*b^2) - a^2*b*c + a*b^2*c - a^2*c^2 + a*b*c^2 + b^2*c^2) : :

X(64238) lies on the cubic K744 and these lines: {1, 33674}, {8, 76}, {213, 666}, {274, 52085}, {1107, 46798}, {1909, 52209}, {3061, 36796}, {6376, 56697}, {7176, 34085}, {17739, 18298}, {17760, 30633}, {32009, 62635}, {36803, 59504}, {40874, 56856}

X(64238) = isotomic conjugate of the isogonal conjugate of X(56856)
X(64238) = X(52209)-Ceva conjugate of X(2481)
X(64238) = X(39916)-cross conjugate of X(40874)
X(64238) = X(i)-isoconjugate of X(j) for these (i,j): {672, 51333}, {2107, 3286}, {2223, 2665}, {9454, 39925}, {40730, 40769}
X(64238) = X(i)-Dao conjugate of X(j) for these (i,j): {350, 17755}, {673, 8934}, {33675, 39925}, {39056, 672}, {39057, 18206}, {62554, 51333}, {62599, 2665}
X(64238) = cevapoint of X(39028) and X(52049)
X(64238) = barycentric product X(i)*X(j) for these {i,j}: {76, 56856}, {673, 52049}, {2481, 17759}, {2664, 18031}, {13576, 40874}, {18785, 41535}, {39028, 52209}
X(64238) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 51333}, {666, 53624}, {673, 2665}, {2106, 3286}, {2481, 39925}, {2664, 672}, {2669, 18206}, {6654, 40769}, {13576, 54980}, {17759, 518}, {18785, 2107}, {20796, 20752}, {21788, 2223}, {21897, 20683}, {36803, 53216}, {39028, 17755}, {39916, 8299}, {40796, 3252}, {40874, 30941}, {41535, 18157}, {52030, 63874}, {52049, 3912}, {52209, 63892}, {56697, 40798}, {56856, 6}, {58367, 3932}, {62599, 8934}
X(64238) = {X(18031),X(52029)}-harmonic conjugate of X(2481)

X(64239) = X(1)X(1655)∩X(10)X(30663)

Barycentrics    (a*b - b^2 + a*c - c^2)*(a^2*b^2 + a^2*b*c + a*b^2*c - a^2*c^2 - a*b*c^2 - b^2*c^2)*(a^2*b^2 - a^2*b*c + a*b^2*c - a^2*c^2 - a*b*c^2 + b^2*c^2) : :

X(64239) lies on the cubic K744 and these lines: {1, 1655}, {10, 30663}, {514, 20888}, {1909, 52209}, {2725, 53624}, {3503, 36215}, {6376, 27475}, {9499, 17739}, {12194, 40769}, {17755, 40788}, {17758, 43685}, {18206, 27919}, {24579, 39273}, {35167, 53216}, {39957, 54980}

X(64239) = X(i)-isoconjugate of X(j) for these (i,j): {6, 56856}, {105, 21788}, {1438, 2664}, {2106, 56853}, {8751, 20796}, {13576, 56388}, {18785, 56837}, {51331, 52030}
X(64239) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 56856}, {3912, 39916}, {6184, 2664}, {17755, 17759}, {27918, 27854}, {39046, 21788}, {52656, 40796}, {62587, 52049}
X(64239) = crosssum of X(21788) and X(51331)
X(64239) = barycentric product X(i)*X(j) for these {i,j}: {2254, 53216}, {2665, 3263}, {3912, 39925}, {18157, 54980}, {18206, 43685}
X(64239) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 56856}, {518, 2664}, {672, 21788}, {1818, 20796}, {2107, 56853}, {2665, 105}, {3263, 52049}, {3286, 56837}, {3912, 17759}, {3930, 21897}, {17755, 39916}, {18157, 40874}, {18206, 2106}, {22116, 40796}, {30941, 2669}, {39925, 673}, {40798, 56854}, {51333, 1438}, {53216, 51560}, {53624, 36086}, {54407, 15148}, {54980, 18785}, {62552, 27854}, {63874, 51866}, {63892, 52030}

X(64240) = X(6)-CROSS CONJUGATE OF X(7)

Barycentrics    (a + b - c)*(a - b + c)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - b^2*c + a*c^2 + b*c^2 - c^3)*(a^3 - a^2*b + a*b^2 - b^3 - a^2*c + b^2*c - a*c^2 - b*c^2 + c^3) : :

X(64240) lies on the cubic K631 and these lines: {7, 1486}, {77, 3870}, {279, 41788}, {344, 348}, {651, 30705}, {1014, 4233}, {1445, 4253}, {1565, 7071}, {2175, 3323}, {2346, 54236}, {2402, 4000}, {9061, 40615}, {10029, 17353}, {17092, 17093}, {37800, 57792}

X(64240) = isogonal conjugate of X(5452)
X(64240) = isogonal conjugate of the anticomplement of X(18214)
X(64240) = isogonal conjugate of the complement of X(13577)
X(64240) = isotomic conjugate of the anticomplement of X(20269)
X(64240) = X(i)-cross conjugate of X(j) for these (i,j): {6, 7}, {650, 26706}, {665, 35185}, {5089, 43736}, {20269, 2}, {44178, 13577}, {47431, 34855}, {61663, 42311}
X(64240) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5452}, {9, 1486}, {33, 22131}, {41, 3434}, {55, 169}, {101, 11934}, {200, 56913}, {212, 17905}, {220, 34036}, {284, 21867}, {650, 57250}, {657, 40576}, {1253, 37800}, {1334, 4228}, {2175, 20927}, {2194, 21073}, {2212, 28420}
X(64240) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 5452}, {223, 169}, {478, 1486}, {1015, 11934}, {1214, 21073}, {3160, 3434}, {3676, 5511}, {6609, 56913}, {17113, 37800}, {40590, 21867}, {40593, 20927}, {40615, 21185}, {40837, 17905}
X(64240) = cevapoint of X(i) and X(j) for these (i,j): {3, 34960}, {6, 3433}, {650, 1565}, {665, 3323}, {3669, 40615}, {40141, 54236}
X(64240) = trilinear pole of line {3309, 4897}
X(64240) = barycentric product X(i)*X(j) for these {i,j}: {7, 13577}, {57, 57773}, {85, 44178}, {664, 26721}, {3433, 6063}, {7131, 41788}, {40141, 57792}
X(64240) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5452}, {7, 3434}, {56, 1486}, {57, 169}, {65, 21867}, {85, 20927}, {109, 57250}, {222, 22131}, {226, 21073}, {269, 34036}, {278, 17905}, {279, 37800}, {348, 28420}, {513, 11934}, {934, 40576}, {1014, 4228}, {1407, 56913}, {3433, 55}, {3676, 21185}, {13577, 8}, {15728, 61491}, {24002, 26546}, {24471, 41581}, {26706, 56183}, {26721, 522}, {27818, 27826}, {35185, 52927}, {40141, 220}, {40154, 14268}, {40615, 5511}, {43042, 55133}, {44178, 9}, {54236, 6600}, {57773, 312}

X(64241) = X(100)X(2742)∩X(513)X(644)

Barycentrics    a*(a - b)*(a - c)*(a^4 - 2*a^3*b - a^2*b^2 + 4*a*b^3 - 2*b^4 - 2*a^3*c + 7*a^2*b*c - 5*a*b^2*c + 4*b^3*c - a^2*c^2 - 5*a*b*c^2 - 4*b^2*c^2 + 4*a*c^3 + 4*b*c^3 - 2*c^4) : :
X(64241) = 2 X[100] - 3 X[6065]

X(64241) lies on the cubic K299 and these lines: {100, 2742}, {513, 644}, {518, 1156}, {666, 671}, {840, 898}, {899, 5526}, {900, 60488}, {901, 1026}, {956, 14661}, {1001, 47007}, {1023, 1308}, {1025, 14733}, {2254, 5548}, {2691, 6099}, {3241, 60698}, {14513, 54440}

X(64241) = reflection of X(840) in X(1083)

X(64242) = X(7)X(3174)∩X(57)X(218)

Barycentrics    a*(a + b - c)*(a - b + c)*(a^3 - a^2*b - a*b^2 + b^3 - 3*a^2*c + 2*a*b*c - 3*b^2*c + 3*a*c^2 + 3*b*c^2 - c^3)*(a^3 - 3*a^2*b + 3*a*b^2 - b^3 - a^2*c + 2*a*b*c + 3*b^2*c - a*c^2 - 3*b*c^2 + c^3) : :

X(64242) lies on the cubic K1059 and these lines: {1, 40154}, {7, 3174}, {57, 218}, {63, 43760}, {142, 60832}, {165, 15728}, {200, 40615}, {223, 1462}, {269, 1617}, {479, 4350}, {2999, 42315}, {5173, 63459}, {5236, 55110}, {5273, 8051}, {6602, 53538}, {8817, 63897}, {10389, 19604}, {29627, 63164}, {37611, 59490}

X(64242) = isogonal conjugate of X(3174)
X(64242) = isogonal conjugate of the anticomplement of X(24389)
X(64242) = X(i)-cross conjugate of X(j) for these (i,j): {55, 57}, {2191, 1}
X(64242) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3174}, {6, 56937}, {8, 21002}, {9, 16572}, {41, 20946}, {55, 36845}, {57, 24771}, {220, 8732}, {281, 22153}, {284, 21096}, {651, 59979}, {10482, 41573}
X(64242) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 3174}, {9, 56937}, {223, 36845}, {478, 16572}, {3160, 20946}, {5452, 24771}, {38991, 59979}, {40590, 21096}
X(64242) = cevapoint of X(663) and X(53538)
X(64242) = barycentric product X(i)*X(j) for these {i,j}: {57, 42361}, {279, 42470}, {2191, 63897}, {3669, 53653}, {4350, 60832}, {24002, 53888}
X(64242) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 56937}, {6, 3174}, {7, 20946}, {55, 24771}, {56, 16572}, {57, 36845}, {65, 21096}, {269, 8732}, {603, 22153}, {604, 21002}, {663, 59979}, {1418, 41573}, {42361, 312}, {42470, 346}, {53653, 646}, {53888, 644}

X(64243) = X(2)X(1350)∩X(3)X(9740)

Barycentrics    13*a^8 + 48*a^6*b^2 - 38*a^4*b^4 - 24*a^2*b^6 + b^8 + 48*a^6*c^2 - 20*a^4*b^2*c^2 - 104*a^2*b^4*c^2 + 12*b^6*c^2 - 38*a^4*c^4 - 104*a^2*b^2*c^4 - 26*b^4*c^4 - 24*a^2*c^6 + 12*b^2*c^6 + c^8 : :
X(64243) = X[14484] + 2 X[46944], 3 X[3524] - X[14482]

X(64243) lies on the cubic K765 and these lines: {2, 1350}, {3, 9740}, {20, 55164}, {99, 10304}, {376, 3424}, {385, 15705}, {549, 51588}, {551, 9746}, {3524, 5024}, {3543, 31168}, {5485, 55167}, {6054, 10519}, {6194, 7757}, {7875, 61830}, {8974, 38425}, {9748, 15702}, {9755, 15715}, {11180, 55177}, {13950, 38426}, {15717, 63065}, {16986, 50687}, {16988, 61930}, {16989, 61812}, {16990, 62120}, {31884, 42850}, {37455, 54174}, {37665, 44839}, {37668, 60654}, {50977, 60658}, {50983, 63005}

X(64243) = midpoint of X(i) and X(j) for these {i,j}: {2, 46944}, {376, 60143}, {44839, 50967}
X(64243) = reflection of X(i) in X(j) for these {i,j}: {14484, 2}, {51588, 549}
on K765
X(64243) = Thomson-isogonal conjugate of X(5024)

X(64244) = X(1)X(87)∩X(3)X(8616)

Barycentrics    a*(a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - 2*a^4*b*c - 2*a^3*b^2*c + a^4*c^2 - 2*a^3*b*c^2 + 5*a^2*b^2*c^2 - 2*a*b^3*c^2 - b^4*c^2 + 2*a^3*c^3 - 2*a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 - b^2*c^4) : :

X(64244) lies on the cubic K077 and these lines: {1, 87}, {3, 8616}, {43, 5255}, {519, 979}, {595, 978}, {962, 56805}, {1050, 5438}, {1191, 1740}, {3915, 4203}, {4673, 18194}, {6762, 9359}, {7220, 50621}, {7240, 11037}, {12565, 56630}, {13740, 59311}, {15654, 54354}, {16483, 36646}, {20036, 27663}, {39748, 51093}, {39949, 51105}, {47623, 63986}, {50581, 62828}

X(64244) = reflection of X(39969) in X(979)

X(64245) = X(6)-DAO CONJUGATE OF (622)

Barycentrics    a^2*(a^2 - b^2 - c^2)/(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 2*(a^2 - b^2 - c^2)*S) : :

X(64245) lies on the cubic K390 and these lines: {6, 470}, {15, 184}, {17, 125}, {577, 44718}, {3269, 11130}, {7836, 14972}, {10662, 50466}, {11131, 14585}, {14533, 19295}, {18877, 19294}, {36209, 46059}, {40710, 50433}
on K390

X(64245) = isotomic conjugate of the polar conjugate of X(3439)
X(64245) = isogonal conjugate of the polar conjugate of X(2993)
X(64245) = X(2993)-Ceva conjugate of X(3439)
X(64245) = X(i)-cross conjugate of X(j) for these (i,j): {46113, 3}, {51243, 2993}
X(64245) = X(i)-isoconjugate of X(j) for these (i,j): {19, 622}, {92, 3130}, {2153, 11094}
X(64245) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 622}, {22391, 3130}, {40580, 11094}
X(64245) = cevapoint of X(i) and X(j) for these (i,j): {6, 10676}, {3269, 60009}
X(64245) = trilinear pole of line {39201, 60010}
X(64245) = barycentric product X(i)*X(j) for these {i,j}: {3, 2993}, {69, 3439}, {95, 51243}, {14373, 52437}, {40157, 40710}
X(64245) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 622}, {15, 11094}, {184, 3130}, {2993, 264}, {3439, 4}, {14373, 6344}, {22115, 14369}, {36297, 51277}, {40157, 471}, {46113, 40581}, {51243, 5}

X(64246) = X(6)-DAO CONJUGATE OF X(621)

Barycentrics    a^2*(a^2 - b^2 - c^2)/(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 2*(a^2 - b^2 - c^2)*S) : :

X(64246) lies on the cubic K390 and these lines: {6, 471}, {16, 184}, {18, 125}, {577, 44719}, {3269, 11131}, {7836, 14972}, {10661, 50465}, {11130, 14585}, {14533, 19294}, {18877, 19295}, {36208, 46058}, {40709, 50433}
on K390

X(64246) = isotomic conjugate of the polar conjugate of X(3438)
X(64246) = isogonal conjugate of the polar conjugate of X(2992)
X(64246) = X(2992)-Ceva conjugate of X(3438)
X(64246) = X(i)-cross conjugate of X(j) for these (i,j): {46112, 3}, {51242, 2992}
X(64246) = X(i)-isoconjugate of X(j) for these (i,j): {19, 621}, {92, 3129}, {2154, 11093}
X(64246) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 621}, {22391, 3129}, {40581, 11093}
X(64246) = cevapoint of X(i) and X(j) for these (i,j): {6, 10675}, {3269, 60010}
X(64246) = trilinear pole of line {39201, 60009}
X(64246) = barycentric product X(i)*X(j) for these {i,j}: {3, 2992}, {69, 3438}, {95, 51242}, {14372, 52437}, {40156, 40709}
X(64246) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 621}, {16, 11093}, {184, 3129}, {2992, 264}, {3438, 4}, {14372, 6344}, {22115, 14368}, {36296, 51270}, {40156, 470}, {46112, 40580}, {51242, 5}

X(64247) = X(1)X(14261)∩X(40)X(376))

Barycentrics    a*(a^5*b + 2*a^4*b^2 - 2*a^2*b^4 - a*b^5 + a^5*c - 11*a^4*b*c + a^3*b^2*c + 9*a^2*b^3*c - 2*a*b^4*c + 2*b^5*c + 2*a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 + 9*a^2*b*c^3 - a*b^2*c^3 - 4*b^3*c^3 - 2*a^2*c^4 - 2*a*b*c^4 - a*c^5 + 2*b*c^5) : :
X(64247) = X[40] - 3 X[47639], 4 X[1385] - 3 X[56804], 5 X[7987] - 3 X[21214], 3 X[6048] - 7 X[16192]

X(64247) lies on the cubic K100 and these lines: {1, 14261}, {3, 17749}, {4, 16528}, {40, 376}, {56, 33551}, {386, 48921}, {573, 3522}, {1285, 4253}, {1293, 3913}, {1385, 56804}, {1482, 10700}, {1742, 7963}, {1764, 50693}, {2137, 17107}, {3158, 47302}, {3336, 34196}, {3667, 19582}, {4257, 6011}, {6048, 16192}, {10304, 48883}, {10476, 59420}, {15688, 48882}, {15689, 48915}, {21363, 21734}, {24466, 44075}, {28352, 45829}, {46362, 56799}, {48924, 62098}, {63442, 63983}

X(64247) = reflection of X(i) in X(j) for these {i,j}: {14261, 1}, {17749, 3}
X(64247) = X(52352)-Ceva conjugate of X(1)

X(64248) = X(1)X(1326)∩X(9)X(6626))

Barycentrics    a*(a + b)*(a + c)*(a^5*b + a^4*b^2 + a^3*b^3 - a^2*b^4 - a*b^5 - b^6 + a^5*c + a^3*b^2*c + 2*a^2*b^3*c - a*b^4*c - 2*b^5*c + a^4*c^2 + a^3*b*c^2 + 2*a^2*b^2*c^2 - a*b^3*c^2 + a^3*c^3 + 2*a^2*b*c^3 - a*b^2*c^3 - a^2*c^4 - a*b*c^4 - a*c^5 - 2*b*c^5 - c^6) : :

X(64248) lies on the cubic K1025 and these lines: {1, 1326}, {9, 6626}, {1019, 2786}, {1282, 8935}, {1756, 25354}, {1757, 45783}, {1929, 18786}, {3509, 52207}, {3512, 18206}, {10583, 63053}, {17738, 52137}, {18189, 54308}, {18789, 43747}

X(64248) = X(i)-Ceva conjugate of X(j) for these (i,j): {3509, 18206}, {52207, 1}
X(64248) = barycentric product X(8846)*X(18827)
X(64248) = barycentric quotient X(8846)/X(740)

X(64249) = X(3913)-CEVA CONJUGATE OF X(1)

Barycentrics    a*(a^5*b + 4*a^4*b^2 + 2*a^3*b^3 - 4*a^2*b^4 - 3*a*b^5 + a^5*c - 13*a^4*b*c - 6*a^3*b^2*c + 10*a^2*b^3*c + 5*a*b^4*c + 3*b^5*c + 4*a^4*c^2 - 6*a^3*b*c^2 + 16*a^2*b^2*c^2 - 10*a*b^3*c^2 + 2*a^3*c^3 + 10*a^2*b*c^3 - 10*a*b^2*c^3 - 6*b^3*c^3 - 4*a^2*c^4 + 5*a*b*c^4 - 3*a*c^5 + 3*b*c^5) : :
X(64249) = 3 X[1] - 2 X[14261], 4 X[3] - 3 X[21214], 2 X[3] - 3 X[47639], 3 X[165] - 2 X[17749], 3 X[6048] - 5 X[63469], 7 X[30389] - 6 X[56804]

X(64249) lies on the cubic K077 and these lines: {1, 14261}, {3, 8616}, {20, 519}, {40, 48936}, {57, 33551}, {165, 17749}, {573, 3973}, {1695, 9778}, {7982, 13541}, {11512, 46946}, {11518, 63580}, {26102, 53002}, {30389, 56804}, {44039, 64005}

X(64249) = reflection of X(21214) in X(47639)
X(64249) = excentral-isogonal conjugate of X(62858)
X(64249) = X(3913)-Ceva conjugate of X(1)

X(64250) = X(471)-CEVA CONJUGATE OF X(186)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2 - b^2 + c^2)*(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 2*(a^2 - b^2 - c^2)*S) : :

X(64250) lies on the cubic K390 and these lines: {6, 471}, {15, 186}, {16, 11587}, {216, 11145}, {323, 340}, {621, 11093}, {2914, 6116}, {2981, 8882}, {3171, 8740}, {5353, 35201}, {5357, 51801}, {6110, 36209}, {6151, 8749}, {11062, 19295}, {19294, 39176}

X(64250) = polar conjugate of the isotomic conjugate of X(14368)
X(64250) = X(471)-Ceva conjugate of X(186)
X(64250) = X(63)-isoconjugate of X(14372)
X(64250) = X(i)-Dao conjugate of X(j) for these (i,j): {15, 40710}, {3162, 14372}, {46666, 14582}
X(64250) = crosspoint of X(471) and X(11093)
X(64250) = barycentric product X(i)*X(j) for these {i,j}: {4, 14368}, {15, 11093}, {186, 621}, {340, 3129}, {471, 40580}
X(64250) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 14372}, {186, 2992}, {621, 328}, {3129, 265}, {11093, 300}, {14368, 69}, {34397, 3438}, {40580, 40710}

X(64251) = X(470)-CEVA CONJUGATE OF X(186)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2 - b^2 + c^2)*(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 2*(a^2 - b^2 - c^2)*S) : :

X(64251) lies on the cubic K390 and these lines: {6, 470}, {15, 11587}, {16, 186}, {216, 11146}, {323, 340}, {622, 11094}, {2914, 6117}, {2981, 8749}, {3170, 8739}, {5353, 51801}, {5357, 35201}, {6111, 36208}, {6151, 8882}, {11062, 19294}, {19295, 39176}

X(64251) = polar conjugate of the isotomic conjugate of X(14369)
X(64251) = X(470)-Ceva conjugate of X(186)
X(64251) = X(63)-isoconjugate of X(14373)
X(64251) = X(i)-Dao conjugate of X(j) for these (i,j): {16, 40709}, {3162, 14373}, {46667, 14582}
X(64251) = crosspoint of X(470) and X(11094)
X(64251) = barycentric product X(i)*X(j) for these {i,j}: {4, 14369}, {16, 11094}, {186, 622}, {340, 3130}, {470, 40581}
X(64251) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 14373}, {186, 2993}, {622, 328}, {3130, 265}, {11094, 301}, {14369, 69}, {34397, 3439}, {40581, 40709}

X(64252) = X(2)X(3470)∩X(4)X(523)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(2*a^8 - 7*a^6*b^2 + 9*a^4*b^4 - 5*a^2*b^6 + b^8 - 7*a^6*c^2 - 6*a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 4*b^6*c^2 + 9*a^4*c^4 + 5*a^2*b^2*c^4 + 6*b^4*c^4 - 5*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(64252) lies on the cubic K917 and these lines: {2, 3470}, {4, 523}, {20, 52130}, {74, 3522}, {140, 9717}, {631, 40630}, {1656, 12079}, {3091, 5627}, {3523, 14385}, {3541, 57487}, {3546, 14919}, {5056, 39239}, {7592, 63856}, {8749, 56865}, {14989, 50691}, {16080, 60159}, {17578, 57471}, {18916, 57488}, {19467, 34329}, {32820, 36890}, {43681, 60119}

X(64252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14264, 36875, 56686}, {14264, 56686, 52488}

X(64253) = X(6)X(3170)∩X(13)X(533)

Barycentrics    a^2*(Sqrt[3]*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 - 2*b^4 - 2*a^2*c^2 + 7*b^2*c^2 - 2*c^4) - 2*(a^4 - 2*a^2*b^2 + 4*b^4 - 2*a^2*c^2 - 5*b^2*c^2 + 4*c^4)*S) : :

X(64253) lies on the cubic K390 and these lines: {6, 3170}, {13, 533}, {15, 3438}, {16, 14368}, {2379, 33958}, {3171, 8740}, {3441, 5669}, {6106, 22850}, {8604, 19294}, {10677, 34321}, {11081, 19295}, {16460, 36209}, {44719, 53032}

X(64253) = X(323)-cross conjugate of X(16)
X(64253) = X(i)-isoconjugate of X(j) for these (i,j): {2154, 3180}, {2166, 3170}
X(64253) = X(i)-Dao conjugate of X(j) for these (i,j): {11597, 3170}, {40581, 3180}, {40604, 30471}
X(64253) = barycentric product X(i)*X(j) for these {i,j}: {16, 11121}, {323, 53029}, {11078, 53031}, {23871, 36515}
X(64253) = barycentric quotient X(i)/X(j) for these {i,j}: {16, 3180}, {50, 3170}, {323, 30471}, {11121, 301}, {34395, 19780}, {36515, 23896}, {53029, 94}, {53031, 11092}

X(64254) = X(6)X(3171)∩X(14)X(532)

Barycentrics    a^2*(Sqrt[3]*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 - 2*b^4 - 2*a^2*c^2 + 7*b^2*c^2 - 2*c^4) + 2*(a^4 - 2*a^2*b^2 + 4*b^4 - 2*a^2*c^2 - 5*b^2*c^2 + 4*c^4)*S) : :

X(64254) lies on the cubic K390 and these lines: {6, 3171}, {14, 532}, {15, 14369}, {16, 3439}, {2378, 33957}, {3170, 8739}, {3440, 5668}, {6107, 22894}, {8603, 19295}, {10678, 34322}, {11080, 41889}, {11086, 19294}, {16459, 36208}, {44718, 53031}

X(64254) = X(323)-cross conjugate of X(15)
X(64254) = X(i)-isoconjugate of X(j) for these (i,j): {2153, 3181}, {2166, 3171}
X(64254) = X(i)-Dao conjugate of X(j) for these (i,j): {11597, 3171}, {40580, 3181}, {40604, 30472}
X(64254) = barycentric product X(i)*X(j) for these {i,j}: {15, 11122}, {323, 53030}, {11092, 53032}, {23870, 36514}
X(64254) = barycentric quotient X(i)/X(j) for these {i,j}: {15, 3181}, {50, 3171}, {323, 30472}, {11122, 300}, {34394, 19781}, {36514, 23895}, {53030, 94}, {53032, 11078}

X(64255) = X(3)X(8157)∩X(4)X(195)

Barycentrics    a^2*(a^14-5*(b^2+c^2)*a^12+3*(3*b^4+4*b^2*c^2+3*c^4)*a^10-(b^2+c^2)*(5*b^4+4*b^2*c^2+5*c^4)*a^8-(5*b^8+5*c^8-b^2*c^2*(6*b^4-b^2*c^2+6*c^4))*a^6+3*(b^2+c^2)*(3*b^8+3*c^8-b^2*c^2*(6*b^4-7*b^2*c^2+6*c^4))*a^4-(b^2-c^2)^2*(5*b^8+5*c^8+2*b^2*c^2*(2*b^4+b^2*c^2+2*c^4))*a^2+(b^4-c^4)^3*(b^2-c^2)) : :
X(64255) = 3 X[17824] + X[17847], X[399] + 2 X[2914], 2 X[399] + X[43704], 4 X[2914] - X[43704], 3 X[38789] - X[48675], 3 X[54] - 4 X[47117], 3 X[11702] - 2 X[47117], 2 X[1209] - 3 X[14643], 2 X[1493] + X[14094], X[12307] - 3 X[32609], X[3448] - 3 X[61715], 2 X[11804] - 3 X[61715], X[3519] - 4 X[16534], 2 X[5609] + X[15801], X[6242] - 4 X[63684], 4 X[6689] - 3 X[15061], X[9972] - 4 X[63694], X[12308] + 2 X[15089], X[12308] + 4 X[32226], X[12308] + 3 X[55039], 2 X[15089] - 3 X[55039], 4 X[32226] - 3 X[55039], 2 X[11802] - 3 X[16223], 4 X[15091] - X[37496], X[12325] - 5 X[20125], 4 X[13565] - 5 X[64101], 2 X[15647] - 3 X[32379], 4 X[32348] - 5 X[38794]

X(64255) lies on the cubic K465 and these lines: {3, 8157}, {4, 195}, {5, 33565}, {49, 43581}, {54, 5663}, {74, 10610}, {110, 1154}, {113, 6288}, {125, 15037}, {140, 40640}, {146, 12254}, {155, 5898}, {265, 3574}, {539, 5655}, {542, 19150}, {1157, 24772}, {1209, 14643}, {1351, 56568}, {1352, 10254}, {1493, 14094}, {1511, 7691}, {1658, 12307}, {2888, 13406}, {2937, 7731}, {3024, 10066}, {3028, 10082}, {3043, 47360}, {3448, 11804}, {3519, 16534}, {5012, 15101}, {5609, 14668}, {5878, 18562}, {5899, 13417}, {5965, 19140}, {6242, 63684}, {6639, 11487}, {6689, 15061}, {7545, 7730}, {7687, 12234}, {7722, 37970}, {7727, 47378}, {7728, 18400}, {8254, 10264}, {9704, 12412}, {9970, 44668}, {9972, 63694}, {9977, 25556}, {10088, 13079}, {10091, 18984}, {10115, 21649}, {10203, 11591}, {10228, 43598}, {10272, 21230}, {10298, 15040}, {10620, 11003}, {10657, 10678}, {10658, 10677}, {11472, 12308}, {11557, 13621}, {11561, 43809}, {11563, 46440}, {11801, 15038}, {11802, 16223}, {12121, 15091}, {12227, 12242}, {12300, 15463}, {12325, 20125}, {12375, 12971}, {12376, 12965}, {12893, 45025}, {13392, 54201}, {13565, 64101}, {14049, 15063}, {15100, 32046}, {15647, 22815}, {15800, 17702}, {18912, 32341}, {19506, 32349}, {21308, 41671}, {22051, 33332}, {22955, 25711}, {25714, 37440}, {27552, 43816}, {27866, 54006}, {32339, 45735}, {32348, 38794}, {35197, 62316}, {35707, 48679}, {36966, 43605}, {51933, 54202}, {54157, 56292}, {63064, 63703}

X(64255) = midpoint of X(i) and X(j) for these {i,j}: {110, 43580}, {146, 12254}, {195, 399}, {5898, 12316}, {7731, 32338}, {14049, 15063}
X(64255) = reflection of X(i) in X(j) for these {i,j}: {3, 11597}, {4, 11805}, {54, 11702}, {74, 10610}, {195, 2914}, {265, 3574}, {3448, 11804}, {6288, 113}, {7691, 1511}, {9977, 25556}, {10264, 8254}, {11559, 14130}, {15089, 32226}, {15137, 15091}, {21230, 10272}, {21649, 10115}, {32352, 11557}, {33565, 5}, {36853, 20424}, {37496, 15137}, {43704, 195}, {54201, 13392}
X(64255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 38898, 2070}, {399, 2914, 43704}, {399, 19504, 12902}, {3448, 61715, 11804}, {11561, 58881, 43809}, {15089, 32226, 55039}, {22815, 32379, 44515}

X(64256) = X(3)X(8157)∩X(5)X(18401)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - a^8*c^2 + 3*a^6*b^2*c^2 - 4*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - b^8*c^2 - 2*a^6*c^4 - 2*b^6*c^4 + 2*a^4*c^6 - a^2*b^2*c^6 + 2*b^4*c^6 + a^2*c^8 + b^2*c^8 - c^10)*(a^10 - a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 + a^2*b^8 - b^10 - 3*a^8*c^2 + 3*a^6*b^2*c^2 - a^2*b^6*c^2 + b^8*c^2 + 2*a^6*c^4 - 4*a^4*b^2*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 3*a^2*b^2*c^6 - 2*b^4*c^6 - 3*a^2*c^8 - b^2*c^8 + c^10) : :
X(64256) = 3 X[381] - 2 X[10214]

X(64256) lies on the cubics K039 and K465 and these lines: {3, 8157}, {5, 18402}, {186, 18401}, {264, 13219}, {381, 10214}, {933, 14118}, {1154, 34900}, {3153, 61441}, {6662, 45971}, {10296, 44977}, {12111, 13506}, {13754, 50463}, {14980, 18403}, {15478, 61471}, {21650, 43083}, {32352, 35442}, {40079, 61445}

X(64256) = midpoint of X(12111) and X(13506)
X(64256) = isogonal conjugate of X(61440)
X(64256) = antigonal image of X(6798)
X(64256) = X(i)-isoconjugate of X(j) for these (i,j): {1, 61440}, {2190, 3153}, {40440, 56924}
X(64256) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 61440}, {5, 3153}
X(64256) = barycentric product X(53962)*X(60597)
X(64256) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 61440}, {216, 3153}, {217, 56924}, {53962, 16813}

X(64257) = X(4)X(7730)∩X(5)X(18402)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^18 - 5*a^16*b^2 + 8*a^14*b^4 - 14*a^10*b^8 + 14*a^8*b^10 - 8*a^4*b^14 + 5*a^2*b^16 - b^18 - 5*a^16*c^2 + 20*a^14*b^2*c^2 - 26*a^12*b^4*c^2 + 4*a^10*b^6*c^2 + 20*a^8*b^8*c^2 - 20*a^6*b^10*c^2 + 10*a^4*b^12*c^2 - 4*a^2*b^14*c^2 + b^16*c^2 + 8*a^14*c^4 - 26*a^12*b^2*c^4 + 33*a^10*b^4*c^4 - 19*a^8*b^6*c^4 - a^6*b^8*c^4 + 9*a^4*b^10*c^4 - 4*a^2*b^12*c^4 + 4*a^10*b^2*c^6 - 19*a^8*b^4*c^6 + 24*a^6*b^6*c^6 - 11*a^4*b^8*c^6 - 2*a^2*b^10*c^6 + 4*b^12*c^6 - 14*a^10*c^8 + 20*a^8*b^2*c^8 - a^6*b^4*c^8 - 11*a^4*b^6*c^8 + 10*a^2*b^8*c^8 - 4*b^10*c^8 + 14*a^8*c^10 - 20*a^6*b^2*c^10 + 9*a^4*b^4*c^10 - 2*a^2*b^6*c^10 - 4*b^8*c^10 + 10*a^4*b^2*c^12 - 4*a^2*b^4*c^12 + 4*b^6*c^12 - 8*a^4*c^14 - 4*a^2*b^2*c^14 + 5*a^2*c^16 + b^2*c^16 - c^18) : :
X(64257) = 3 X[5890] - X[13506]

X(64257) lies on the cubic K465 and these lines: {4, 7730}, {5, 18402}, {24, 8157}, {186, 933}, {1154, 44057}, {5889, 6801}, {5890, 13506}, {10018, 11701}, {11561, 52057}, {13310, 30258}, {14118, 18401}, {15331, 38616}, {38585, 45735}, {52169, 54067}

X(64257) = reflection of X(4) in X(10214)

X(64258) = X(111)X(230)∩X(115)X(523)

Barycentrics    (b - c)^2*(b + c)^2*(a^2 + b^2 - 2*c^2)*(-a^2 + 2*b^2 - c^2) : :
X(64258) = 5 X[115] - 3 X[23991], 3 X[115] - X[23992], 2 X[115] - 3 X[31644], 7 X[115] - 3 X[45212], 7 X[115] - 6 X[57515], X[115] - 3 X[61339], 9 X[23991] - 5 X[23992], 2 X[23991] - 5 X[31644], 6 X[23991] - 5 X[44398], 7 X[23991] - 5 X[45212], 7 X[23991] - 10 X[57515], X[23991] - 5 X[61339], 2 X[23992] - 9 X[31644], 2 X[23992] - 3 X[44398], 7 X[23992] - 9 X[45212], 7 X[23992] - 18 X[57515], X[23992] - 9 X[61339], 3 X[31644] - X[44398], 7 X[31644] - 2 X[45212], 7 X[31644] - 4 X[57515], 7 X[44398] - 6 X[45212], 7 X[44398] - 12 X[57515], X[44398] - 6 X[61339], X[45212] - 7 X[61339], 2 X[57515] - 7 X[61339], 3 X[671] + X[892], 5 X[671] + 3 X[39061], X[671] + 3 X[57539], X[892] - 3 X[17948], 5 X[892] - 9 X[39061], X[892] - 9 X[57539], 5 X[17948] - 3 X[39061], X[17948] - 3 X[57539], X[39061] - 5 X[57539], 4 X[40553] - 3 X[44397], 3 X[5461] - 2 X[40486], 3 X[14588] - X[20094], X[39356] - 9 X[41135], 5 X[40429] - 4 X[40511]

X(64258) lies on the X-parabola of ABC (see X(12065)), the cubic K239, and these lines: {2, 62655}, {6, 9214}, {30, 17964}, {111, 230}, {115, 523}, {141, 52756}, {148, 9182}, {316, 524}, {325, 31125}, {338, 850}, {395, 52749}, {396, 52748}, {543, 40553}, {597, 60867}, {685, 1990}, {868, 23288}, {895, 44768}, {897, 60055}, {1213, 52747}, {1503, 48983}, {1648, 5466}, {2395, 9178}, {2501, 6791}, {2502, 58856}, {2549, 45143}, {2872, 15630}, {3018, 48721}, {3124, 8599}, {3589, 52551}, {3815, 5968}, {3943, 6543}, {4024, 21043}, {5254, 14263}, {5306, 51926}, {5461, 40486}, {5523, 52490}, {5913, 46783}, {6071, 9009}, {7745, 14246}, {8030, 54607}, {8753, 60428}, {9012, 44011}, {9164, 15300}, {10097, 15328}, {10415, 47245}, {10418, 46980}, {10556, 20998}, {10561, 34294}, {11053, 34760}, {14588, 20094}, {14609, 15048}, {14977, 62551}, {14995, 35606}, {15993, 46154}, {16278, 57429}, {17056, 52764}, {18023, 18896}, {20578, 30452}, {20579, 30453}, {22110, 42008}, {23292, 52767}, {23302, 52750}, {23303, 52751}, {24855, 52232}, {24975, 50941}, {30508, 39022}, {30509, 39023}, {30786, 44377}, {36877, 43448}, {39356, 41135}, {40350, 47238}, {40429, 40511}, {40879, 44526}, {41176, 62662}, {41936, 47242}, {44396, 46799}, {44401, 52141}, {44518, 59423}, {44677, 50711}, {52483, 53418}, {52760, 53414}, {60042, 62626}

X(64258) = midpoint of X(i) and X(j) for these {i,j}: {148, 9182}, {671, 17948}, {61472, 61474}
X(64258) = reflection of X(i) in X(j) for these {i,j}: {15300, 9164}, {31644, 61339}, {44398, 115}, {45212, 57515}
X(64258) = polar conjugate of the isotomic conjugate of X(51258)
X(64258) = X(i)-Ceva conjugate of X(j) for these (i,j): {671, 5466}, {17983, 9178}, {57539, 523}, {57552, 10278}
X(64258) = X(i)-cross conjugate of X(j) for these (i,j): {1648, 115}, {33919, 523}, {42344, 8029}, {58908, 10415}
X(64258) = X(i)-isoconjugate of X(j) for these (i,j): {110, 23889}, {163, 5468}, {187, 24041}, {249, 896}, {524, 1101}, {662, 5467}, {922, 4590}, {1576, 24039}, {2642, 59152}, {3266, 23995}, {4235, 4575}, {4570, 16702}, {4592, 61207}, {14210, 23357}, {14567, 24037}, {23200, 46254}, {44102, 62719}
X(64258) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 5468}, {136, 4235}, {244, 23889}, {512, 14567}, {523, 524}, {620, 62658}, {647, 6390}, {690, 8030}, {1084, 5467}, {1649, 2482}, {2492, 62661}, {3005, 187}, {4858, 24039}, {4988, 6629}, {5139, 61207}, {15477, 23357}, {15899, 249}, {17436, 39785}, {18314, 3266}, {21905, 39689}, {39061, 4590}, {50330, 16702}, {55267, 50567}, {62568, 27088}, {62577, 36792}, {62607, 47389}
X(64258) = cevapoint of X(i) and X(j) for these (i,j): {115, 1648}, {690, 11123}, {8029, 42344}, {33919, 61339}
X(64258) = crosspoint of X(671) and X(5466)
X(64258) = crosssum of X(187) and X(5467)
X(64258) = trilinear pole of line {115, 8029}
X(64258) = crossdifference of every pair of points on line {5467, 44814}
X(64258) = barycentric product X(i)*X(j) for these {i,j}: {4, 51258}, {67, 10555}, {111, 338}, {115, 671}, {125, 17983}, {339, 8753}, {512, 52632}, {523, 5466}, {691, 23105}, {850, 9178}, {868, 9154}, {892, 8029}, {895, 2970}, {897, 1109}, {923, 23994}, {1577, 23894}, {1648, 57539}, {2395, 62629}, {2501, 14977}, {2643, 46277}, {3124, 18023}, {4024, 62626}, {8288, 18818}, {8430, 43665}, {8599, 23288}, {8754, 30786}, {9139, 58261}, {9180, 18007}, {9213, 10412}, {9214, 12079}, {10097, 14618}, {10630, 52628}, {14728, 42553}, {15359, 39450}, {20902, 36128}, {20975, 46111}, {22260, 53080}, {23962, 32740}, {30465, 36307}, {30468, 36310}, {31125, 34294}, {42344, 57552}, {52940, 61339}
X(64258) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 249}, {115, 524}, {125, 6390}, {338, 3266}, {512, 5467}, {523, 5468}, {661, 23889}, {671, 4590}, {691, 59152}, {868, 50567}, {892, 31614}, {897, 24041}, {923, 1101}, {1084, 14567}, {1109, 14210}, {1365, 7181}, {1577, 24039}, {1648, 2482}, {2489, 61207}, {2501, 4235}, {2643, 896}, {2970, 44146}, {2971, 44102}, {3120, 6629}, {3124, 187}, {3125, 16702}, {4036, 42721}, {4092, 3712}, {5099, 62661}, {5466, 99}, {6388, 32459}, {6791, 27088}, {8029, 690}, {8288, 39785}, {8430, 2421}, {8753, 250}, {8754, 468}, {9154, 57991}, {9178, 110}, {9213, 10411}, {10097, 4558}, {10555, 316}, {10561, 52630}, {12079, 36890}, {14443, 33915}, {14908, 47390}, {14977, 4563}, {15475, 14559}, {16732, 16741}, {17983, 18020}, {17993, 9181}, {18007, 9182}, {18023, 34537}, {19626, 23963}, {20975, 3292}, {21043, 4062}, {21131, 4750}, {21833, 21839}, {21906, 39689}, {22260, 351}, {23105, 35522}, {23288, 9146}, {23894, 662}, {23991, 62658}, {23992, 8030}, {30452, 52039}, {30453, 52040}, {30786, 47389}, {31644, 45291}, {32740, 23357}, {33919, 1649}, {34294, 52898}, {34574, 45773}, {39691, 7813}, {41221, 41586}, {42344, 23992}, {42553, 33906}, {44114, 9155}, {46277, 24037}, {51258, 69}, {51428, 45662}, {51441, 5967}, {52628, 36792}, {52632, 670}, {57539, 52940}, {57552, 42370}, {61339, 1648}, {62626, 4610}, {62629, 2396}
X(64258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 16092, 230}, {671, 10630, 34169}, {671, 34169, 53419}, {671, 57539, 17948}, {9214, 52450, 6}, {14263, 59422, 5254}, {31644, 44398, 115}, {36307, 36310, 16092}, {52551, 60863, 52758}, {52758, 60863, 3589}, {60867, 63853, 597}

X(64259) = X(4)X(54)∩X(6368)X(39201)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^20 - 8*a^18*b^2 + 10*a^16*b^4 - 3*a^14*b^6 + 4*a^12*b^8 - 17*a^10*b^10 + 18*a^8*b^12 - 5*a^6*b^14 - 2*a^4*b^16 + a^2*b^18 - 8*a^18*c^2 + 22*a^16*b^2*c^2 - 17*a^14*b^4*c^2 - 3*a^12*b^6*c^2 + 19*a^10*b^8*c^2 - 27*a^8*b^10*c^2 + 13*a^6*b^12*c^2 + 7*a^4*b^14*c^2 - 7*a^2*b^16*c^2 + b^18*c^2 + 10*a^16*c^4 - 17*a^14*b^2*c^4 + 10*a^12*b^4*c^4 - 2*a^10*b^6*c^4 + 2*a^8*b^8*c^4 - 9*a^6*b^10*c^4 - 6*a^4*b^12*c^4 + 20*a^2*b^14*c^4 - 8*b^16*c^4 - 3*a^14*c^6 - 3*a^12*b^2*c^6 - 2*a^10*b^4*c^6 + 14*a^8*b^6*c^6 + a^6*b^8*c^6 - 7*a^4*b^10*c^6 - 28*a^2*b^12*c^6 + 28*b^14*c^6 + 4*a^12*c^8 + 19*a^10*b^2*c^8 + 2*a^8*b^4*c^8 + a^6*b^6*c^8 + 16*a^4*b^8*c^8 + 14*a^2*b^10*c^8 - 56*b^12*c^8 - 17*a^10*c^10 - 27*a^8*b^2*c^10 - 9*a^6*b^4*c^10 - 7*a^4*b^6*c^10 + 14*a^2*b^8*c^10 + 70*b^10*c^10 + 18*a^8*c^12 + 13*a^6*b^2*c^12 - 6*a^4*b^4*c^12 - 28*a^2*b^6*c^12 - 56*b^8*c^12 - 5*a^6*c^14 + 7*a^4*b^2*c^14 + 20*a^2*b^4*c^14 + 28*b^6*c^14 - 2*a^4*c^16 - 7*a^2*b^2*c^16 - 8*b^4*c^16 + a^2*c^18 + b^2*c^18) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6287.

X(64259) lies on these lines: {4, 54}, {6368, 39201}

X(64260) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND ANTI-AQUILA

Barycentrics    a*(9*a^3+3*b^3-11*b^2*c-11*b*c^2+3*c^3-3*a^2*(b+c)-9*a*(b+c)^2) : :
X(64260) = -6*X[551]+X[43733]

X(64260) lies on these lines: {1, 3683}, {9, 3988}, {10, 3158}, {11, 3601}, {20, 946}, {40, 4004}, {145, 36922}, {405, 4533}, {551, 43733}, {942, 51576}, {1001, 5785}, {1125, 45036}, {1385, 11372}, {1420, 3649}, {1621, 7982}, {3295, 11525}, {3333, 51715}, {3612, 45035}, {3632, 10389}, {3636, 5542}, {3646, 24929}, {3711, 37080}, {3878, 64263}, {3922, 61763}, {4018, 4512}, {4757, 5248}, {5223, 16866}, {5259, 64342}, {5438, 19878}, {6284, 25055}, {6744, 50739}, {8226, 18242}, {9352, 35242}, {10179, 17624}, {10912, 31393}, {10980, 17571}, {11108, 36835}, {11379, 30389}, {12688, 30392}, {13384, 62333}, {14100, 51577}, {15079, 59337}, {16860, 30393}, {16865, 41863}, {19526, 62823}, {20057, 62856}, {22791, 63974}, {30223, 30538}, {31435, 64369}, {37704, 51724}, {38036, 59345}, {51506, 64137}, {57279, 62870}, {58560, 63754}, {64147, 64324}

X(64260) = inverse of X(3601) in Feuerbach hyperbola

X(64261) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND INFINITE-ALTITUDE

Barycentrics    3*a^7-4*a^6*(b+c)+4*a^2*b*(b-c)^2*c*(b+c)-2*(b-c)^4*(b+c)^3+a^5*(-3*b^2+2*b*c-3*c^2)-3*a^3*(b^2-c^2)^2+a*(b^2-c^2)^2*(3*b^2-2*b*c+3*c^2)+a^4*(6*b^3-2*b^2*c-2*b*c^2+6*c^3) : :
X(64261) = -3*X[165]+4*X[12616], -3*X[376]+4*X[6705], -5*X[1656]+4*X[40262], -5*X[3091]+3*X[54051], -3*X[3543]+X[6223], -3*X[3830]+2*X[22792], -X[5059]+3*X[54052], -5*X[8227]+4*X[37837], -3*X[9812]+2*X[54198], -3*X[14647]+2*X[31730]

X(64261) lies on these lines: {1, 4}, {3, 5705}, {5, 5436}, {8, 64004}, {9, 355}, {10, 6987}, {20, 4652}, {30, 84}, {40, 1726}, {57, 37468}, {65, 36999}, {72, 5881}, {78, 6840}, {80, 1728}, {149, 64267}, {165, 12616}, {376, 6705}, {377, 8726}, {381, 24299}, {382, 971}, {405, 5587}, {442, 3576}, {452, 24987}, {484, 63437}, {516, 49168}, {517, 5924}, {519, 5758}, {936, 6827}, {938, 64001}, {942, 12671}, {943, 51784}, {952, 5812}, {962, 41575}, {1006, 1698}, {1071, 9579}, {1125, 6843}, {1158, 64005}, {1210, 50701}, {1385, 25525}, {1449, 5798}, {1453, 5721}, {1512, 10395}, {1621, 64272}, {1656, 40262}, {1657, 34862}, {1753, 50530}, {1768, 4333}, {1836, 52837}, {1837, 6253}, {1998, 10431}, {2323, 5776}, {2475, 10884}, {2800, 9589}, {2829, 10864}, {2893, 10444}, {2900, 37531}, {2950, 5840}, {3072, 56959}, {3091, 54051}, {3146, 9799}, {3149, 9581}, {3244, 16204}, {3347, 48358}, {3543, 6223}, {3577, 37730}, {3601, 6831}, {3624, 6829}, {3627, 6259}, {3651, 5450}, {3671, 64147}, {3679, 55104}, {3830, 22792}, {4018, 5895}, {4190, 21164}, {4292, 5768}, {4297, 6908}, {4304, 6847}, {4311, 54366}, {4312, 5884}, {4355, 12005}, {4855, 6943}, {4930, 28204}, {5059, 54052}, {5073, 12684}, {5177, 5731}, {5219, 33597}, {5231, 7580}, {5437, 37281}, {5438, 6922}, {5534, 10526}, {5665, 57282}, {5720, 6928}, {5722, 20420}, {5727, 44547}, {5728, 7686}, {5732, 6850}, {5745, 59345}, {5759, 11362}, {5777, 18525}, {5802, 10445}, {5805, 12433}, {6282, 6836}, {6284, 12705}, {6560, 19067}, {6561, 19068}, {6828, 62829}, {6832, 7989}, {6833, 30282}, {6839, 54392}, {6844, 13411}, {6846, 10198}, {6865, 57284}, {6868, 31424}, {6877, 34595}, {6889, 7987}, {6897, 10857}, {6907, 18481}, {6913, 10267}, {6917, 18443}, {6920, 64269}, {6923, 41854}, {6934, 15803}, {6936, 16208}, {6984, 30389}, {6990, 63964}, {7330, 7491}, {7354, 63430}, {7548, 31266}, {7682, 50700}, {7971, 12699}, {8226, 18242}, {8227, 37837}, {8987, 9541}, {9580, 12672}, {9668, 9856}, {9812, 54198}, {9841, 31775}, {9848, 64332}, {9897, 12691}, {9942, 37723}, {9948, 28150}, {9960, 39772}, {10085, 10483}, {10167, 50239}, {10175, 16845}, {10389, 63257}, {10399, 37721}, {10477, 39885}, {10527, 37421}, {10826, 36152}, {10860, 11826}, {10916, 28164}, {10943, 28186}, {11112, 37526}, {11249, 28160}, {11491, 31434}, {11827, 57279}, {12136, 44438}, {12246, 33703}, {12565, 64320}, {12575, 64322}, {12677, 41863}, {12680, 12943}, {12687, 15239}, {12688, 12953}, {14110, 64171}, {14647, 31730}, {15704, 61556}, {15726, 17649}, {16202, 59389}, {16206, 61294}, {17532, 50811}, {18397, 37711}, {18406, 64328}, {18499, 37562}, {18528, 37821}, {18540, 37290}, {18908, 45120}, {21370, 36986}, {22770, 24392}, {22791, 64263}, {26015, 50696}, {26437, 64152}, {26475, 57285}, {31794, 52682}, {31822, 33697}, {33576, 64330}, {36991, 60934}, {37000, 61763}, {37001, 64046}, {37230, 37615}, {37428, 37551}, {37718, 64188}, {38122, 50238}, {38150, 44229}, {41004, 62780}, {42263, 49234}, {42264, 49235}, {43740, 56273}, {45632, 54154}, {46435, 64186}, {47033, 59340}, {49177, 64119}, {50741, 51705}, {51118, 63962}, {52367, 64150}, {54408, 64000}, {58588, 63432}, {61146, 64281}, {63146, 64111}, {63974, 64295}

X(64261) = midpoint of X(i) and X(j) for these {i,j}: {3146, 9799}, {5073, 12684}, {12246, 33703}
X(64261) = reflection of X(i) in X(j) for these {i,j}: {20, 6245}, {84, 5787}, {1490, 4}, {1657, 34862}, {5534, 10526}, {6259, 3627}, {7971, 12699}, {11523, 5812}, {12667, 31673}, {12671, 942}, {15704, 61556}, {40267, 33697}, {46435, 64186}, {63962, 51118}, {64005, 1158}, {64075, 10916}, {64190, 9948}, {64267, 149}, {64276, 64265}, {64298, 64272}
X(64261) = pole of line {65, 5715} with respect to the Feuerbach hyperbola
X(64261) = intersection, other than A, B, C, of circumconics {{A, B, C, X(29), X(5715)}}, {{A, B, C, X(278), X(64265)}}, {{A, B, C, X(6598), X(7952)}}
X(64261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4, 5715}, {4, 18446, 9612}, {4, 3488, 946}, {4, 515, 1490}, {4, 944, 226}, {20, 6245, 52027}, {30, 5787, 84}, {515, 31673, 12667}, {3146, 12649, 64003}, {3586, 5691, 4}, {6836, 57287, 6282}, {9948, 28150, 64190}, {10864, 12704, 49170}, {10916, 28164, 64075}

X(64262) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND INTOUCH

Barycentrics    (a^2-2*(b-c)^2+a*(b+c))*(3*a^3-5*a^2*(b+c)+(b-c)^2*(b+c)+a*(b+c)^2) : :
X(64262) = -2*X[10]+3*X[60987], X[145]+3*X[60975]

X(64262) lies on these lines: {1, 527}, {7, 24389}, {9, 17718}, {10, 60987}, {57, 10427}, {65, 12625}, {145, 60975}, {516, 64147}, {518, 36922}, {1071, 5735}, {1156, 31164}, {1317, 3243}, {1537, 5851}, {1699, 64264}, {1836, 3254}, {1998, 60932}, {2078, 61007}, {3174, 52819}, {3333, 25557}, {3632, 13375}, {3649, 60953}, {3870, 60951}, {3951, 60997}, {4312, 11570}, {4860, 5231}, {5853, 16236}, {6006, 38371}, {7672, 39776}, {7982, 38454}, {9814, 10052}, {12848, 41570}, {14100, 18839}, {16006, 49177}, {22791, 64277}, {31053, 63254}, {39771, 47123}, {42871, 61285}, {43180, 45700}, {60895, 63962}, {63974, 64295}

X(64262) = reflection of X(i) in X(j) for these {i,j}: {63264, 34917}
X(64262) = X(i)-Dao conjugate of X(j) for these {i, j}: {5231, 8}
X(64262) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7, 6173}
X(64262) = pole of line {6173, 17603} with respect to the Feuerbach hyperbola
X(64262) = pole of line {27486, 30181} with respect to the Steiner circumellipse
X(64262) = pole of line {28292, 43050} with respect to the Suppa-Cucoanes circle
X(64262) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15346)}}, {{A, B, C, X(5231), X(34919)}}, {{A, B, C, X(6173), X(12848)}}, {{A, B, C, X(42014), X(47375)}}
X(64262) = barycentric product X(i)*X(j) for these (i, j): {6173, 63168}, {12848, 5231}
X(64262) = barycentric quotient X(i)/X(j) for these (i, j): {12848, 63166}, {63168, 55954}
X(64262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4860, 44785, 6173}

X(64263) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 5TH MIXTILINEAR

Barycentrics    a*(9*a^3+15*b^3-11*b^2*c-11*b*c^2+15*c^3-15*a^2*(b+c)+a*(-9*b^2+6*b*c-9*c^2)) : :
X(64263) = 3*X[3241]+X[5556]

X(64263) lies on circumconic {{A, B, C, X(39980), X(56030)}} and on these lines: {1, 3052}, {9, 56030}, {10, 11041}, {65, 45036}, {100, 3340}, {145, 226}, {390, 20057}, {944, 3635}, {1482, 7966}, {2099, 2136}, {2886, 3632}, {3241, 5556}, {3243, 11011}, {3576, 4757}, {3616, 5837}, {3878, 64260}, {3889, 15558}, {4004, 5438}, {4423, 15829}, {5441, 64289}, {5730, 51780}, {6762, 62822}, {7971, 10222}, {7972, 9613}, {7982, 64173}, {7990, 16189}, {8000, 11523}, {10389, 63260}, {10698, 12705}, {18492, 21635}, {22791, 64261}, {31794, 51577}, {63974, 64295}, {64147, 64324}

X(64264) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 6TH MIXTILINEAR

Barycentrics    a*(a^7-a^6*(b+c)-3*(b-c)^4*(b+c)^3-7*a^5*(b^2-b*c+c^2)-a^2*(b-c)^2*(11*b^3-7*b^2*c-7*b*c^2+11*c^3)+a^4*(15*b^3-7*b^2*c-7*b*c^2+15*c^3)-a^3*(5*b^4+14*b^3*c-30*b^2*c^2+14*b*c^3+5*c^4)+a*(b-c)^2*(11*b^4+5*b^3*c-8*b^2*c^2+5*b*c^3+11*c^4)) : :
X(64264) = -3*X[165]+2*X[5528], -4*X[1484]+3*X[38036], -4*X[10265]+3*X[38052], -2*X[10427]+3*X[11219], -X[15096]+3*X[41861]

X(64264) lies on these lines: {1, 651}, {3, 5696}, {9, 5531}, {11, 30330}, {80, 10398}, {149, 63974}, {150, 56933}, {165, 5528}, {214, 5785}, {516, 9803}, {518, 7993}, {528, 7991}, {952, 5223}, {1484, 38036}, {1699, 64262}, {1709, 36868}, {1768, 2951}, {2771, 11372}, {3062, 3254}, {4882, 38665}, {5536, 15726}, {5537, 15733}, {5735, 37433}, {5787, 7992}, {7982, 64288}, {8226, 34917}, {9809, 63973}, {10045, 64155}, {10085, 16143}, {10265, 38052}, {10268, 51525}, {10384, 17638}, {10427, 11219}, {10573, 12848}, {12560, 12755}, {14100, 64372}, {14872, 34486}, {15096, 41861}, {17660, 60937}, {21635, 61013}, {33593, 59372}, {33925, 60910}, {64147, 64324}

X(64264) = reflection of X(i) in X(j) for these {i,j}: {2951, 1768}, {5531, 9}, {9809, 63973}, {63974, 149}, {64295, 149}

X(64265) = ISOGONAL CONJUGATE OF X(11012)

Barycentrics    (a^5+(b-c)^3*(b+c)^2-a^4*(2*b+c)+a^3*(b^2+b*c-2*c^2)+a^2*(b^3-4*b^2*c+b*c^2+2*c^3)+a*(-2*b^4+b^3*c+b^2*c^2-b*c^3+c^4))*(a^5-(b-c)^3*(b+c)^2-a^4*(b+2*c)+a^3*(-2*b^2+b*c+c^2)+a^2*(2*b^3+b^2*c-4*b*c^2+c^3)+a*(b^4-b^3*c+b^2*c^2+b*c^3-2*c^4)) : :
X(64265) = -3*X[2]+2*X[64286], -3*X[381]+2*X[64271]

X(64265) lies on the Feuerbach hyperbola and on these lines: {1, 6831}, {2, 64286}, {4, 64272}, {5, 64285}, {7, 5884}, {8, 6840}, {9, 355}, {10, 64280}, {21, 515}, {30, 6597}, {79, 6001}, {81, 64296}, {84, 7354}, {90, 5691}, {104, 4311}, {225, 36121}, {314, 35516}, {381, 64271}, {517, 6598}, {943, 31397}, {944, 56027}, {946, 17097}, {952, 6596}, {971, 3255}, {1000, 12116}, {1156, 31673}, {1172, 8755}, {1320, 41575}, {1389, 64163}, {1699, 17098}, {1837, 3577}, {2320, 6888}, {2771, 6599}, {2800, 11604}, {2829, 3065}, {2949, 31799}, {3254, 24474}, {3296, 10532}, {3680, 5763}, {4295, 38306}, {5303, 6705}, {5556, 63962}, {5561, 64119}, {5665, 5715}, {5787, 34773}, {5794, 10268}, {5842, 15910}, {5881, 56101}, {6003, 43728}, {6261, 31266}, {6601, 49168}, {6765, 56278}, {7091, 12687}, {7160, 45081}, {7284, 49170}, {7686, 15909}, {10597, 18490}, {11012, 12616}, {12114, 15446}, {12247, 24298}, {12667, 34919}, {12688, 13273}, {12750, 24302}, {12751, 45393}, {13408, 63335}, {13464, 56030}, {14647, 64075}, {15175, 37710}, {18483, 55924}, {19860, 64274}, {35057, 43737}, {35097, 50899}, {37625, 43740}, {37714, 64319}, {40396, 40950}, {63974, 64295}, {64147, 64324}

X(64265) = midpoint of X(i) and X(j) for these {i,j}: {64261, 64276}
X(64265) = reflection of X(i) in X(j) for these {i,j}: {1, 64266}, {4, 64272}, {6261, 64273}, {64268, 12616}, {64276, 64275}, {64279, 64274}, {64280, 10}, {64283, 64293}, {64285, 5}, {64287, 1}
X(64265) = isogonal conjugate of X(11012)
X(64265) = anticomplement of X(64286)
X(64265) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 11012}, {1167, 40249}
X(64265) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 79}
X(64265) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 11012}, {6260, 40249}, {64286, 64286}
X(64265) = pole of line {3577, 6362} with respect to the Fuhrmann circle
X(64265) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(994)}}, {{A, B, C, X(10), X(1065)}}, {{A, B, C, X(19), X(56148)}}, {{A, B, C, X(27), X(31789)}}, {{A, B, C, X(28), X(6840)}}, {{A, B, C, X(29), X(6831)}}, {{A, B, C, X(33), X(26332)}}, {{A, B, C, X(34), X(48482)}}, {{A, B, C, X(40), X(37550)}}, {{A, B, C, X(64), X(34441)}}, {{A, B, C, X(65), X(947)}}, {{A, B, C, X(74), X(20419)}}, {{A, B, C, X(92), X(355)}}, {{A, B, C, X(102), X(31806)}}, {{A, B, C, X(158), X(10570)}}, {{A, B, C, X(225), X(515)}}, {{A, B, C, X(516), X(28473)}}, {{A, B, C, X(517), X(5174)}}, {{A, B, C, X(519), X(41575)}}, {{A, B, C, X(758), X(30200)}}, {{A, B, C, X(946), X(40950)}}, {{A, B, C, X(957), X(44759)}}, {{A, B, C, X(996), X(57724)}}, {{A, B, C, X(998), X(55105)}}, {{A, B, C, X(1068), X(5691)}}, {{A, B, C, X(1072), X(49542)}}, {{A, B, C, X(1121), X(54882)}}, {{A, B, C, X(1126), X(1243)}}, {{A, B, C, X(1220), X(15844)}}, {{A, B, C, X(1224), X(60112)}}, {{A, B, C, X(1441), X(56133)}}, {{A, B, C, X(2051), X(40435)}}, {{A, B, C, X(2078), X(24474)}}, {{A, B, C, X(2342), X(5884)}}, {{A, B, C, X(2716), X(63750)}}, {{A, B, C, X(2730), X(35174)}}, {{A, B, C, X(2788), X(28850)}}, {{A, B, C, X(2800), X(8674)}}, {{A, B, C, X(2990), X(55027)}}, {{A, B, C, X(3424), X(9103)}}, {{A, B, C, X(3426), X(41487)}}, {{A, B, C, X(3667), X(5844)}}, {{A, B, C, X(3679), X(54758)}}, {{A, B, C, X(3870), X(49168)}}, {{A, B, C, X(4311), X(22464)}}, {{A, B, C, X(5903), X(36152)}}, {{A, B, C, X(6001), X(35057)}}, {{A, B, C, X(6734), X(31397)}}, {{A, B, C, X(6765), X(12649)}}, {{A, B, C, X(14584), X(49176)}}, {{A, B, C, X(18815), X(56143)}}, {{A, B, C, X(20615), X(28233)}}, {{A, B, C, X(23710), X(31673)}}, {{A, B, C, X(28292), X(38454)}}, {{A, B, C, X(29057), X(29298)}}, {{A, B, C, X(30199), X(61030)}}, {{A, B, C, X(31359), X(54972)}}, {{A, B, C, X(34892), X(54691)}}, {{A, B, C, X(34914), X(54630)}}, {{A, B, C, X(37579), X(37625)}}, {{A, B, C, X(37710), X(56419)}}, {{A, B, C, X(38008), X(42464)}}, {{A, B, C, X(40442), X(43724)}}, {{A, B, C, X(41434), X(44835)}}, {{A, B, C, X(41506), X(60634)}}, {{A, B, C, X(47033), X(51760)}}, {{A, B, C, X(54933), X(56132)}}, {{A, B, C, X(57723), X(60079)}}
X(64265) = barycentric quotient X(i)/X(j) for these (i, j): {6, 11012}, {1108, 40249}
X(64265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64291, 64292, 1}

X(64266) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-AQUILA AND 1ST ANTI-PAVLOV

Barycentrics    a^8*(b-c)^2-(b-c)^6*(b+c)^4-4*a^4*b*c*(b^2-c^2)^2+2*a*(b-c)^4*(b+c)^3*(b^2+c^2)-2*a^7*(b^3+c^3)+2*a^5*(b-c)^2*(3*b^3+5*b^2*c+5*b*c^2+3*c^3)-2*a^6*(b^4-3*b^3*c-2*b^2*c^2-3*b*c^3+c^4)+2*a^2*(b^2-c^2)^2*(b^4-b^3*c-2*b^2*c^2-b*c^3+c^4)-2*a^3*(b-c)^2*(3*b^5+4*b^4*c+b^3*c^2+b^2*c^3+4*b*c^4+3*c^5) : :
X(64266) = -3*X[2]+X[64280], -3*X[5886]+X[64285]

X(64266) lies on these lines: {1, 6831}, {2, 64280}, {4, 37579}, {5, 1001}, {10, 6882}, {11, 7686}, {442, 5842}, {515, 6841}, {523, 53047}, {946, 64284}, {1125, 64286}, {1389, 18391}, {1532, 14798}, {2829, 37447}, {3011, 37362}, {3085, 6830}, {3646, 4187}, {3649, 6001}, {4973, 6705}, {5542, 6245}, {5587, 37359}, {5705, 49183}, {5709, 38454}, {5715, 11372}, {5844, 10912}, {5886, 64285}, {6260, 12558}, {6734, 63976}, {6796, 6881}, {6828, 64298}, {6833, 26357}, {6845, 10532}, {6922, 26363}, {6943, 10527}, {6963, 19855}, {6971, 18544}, {6990, 64148}, {7510, 23843}, {7741, 59342}, {8226, 18242}, {8227, 64328}, {8727, 12114}, {9955, 64271}, {10265, 12432}, {10785, 26437}, {10883, 12667}, {10957, 45081}, {11012, 37374}, {11249, 37356}, {11525, 64200}, {12616, 24474}, {14647, 55109}, {15932, 64155}, {18238, 63254}, {36152, 37468}, {37726, 64137}, {54318, 64279}, {63292, 64296}, {63974, 64295}, {64003, 64118}, {64147, 64324}

X(64266) = midpoint of X(i) and X(j) for these {i,j}: {1, 64265}, {48482, 64269}, {64281, 64291}
X(64266) = reflection of X(i) in X(j) for these {i,j}: {64271, 9955}, {64274, 63963}, {64286, 1125}
X(64266) = complement of X(64280)
X(64266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6830, 12116, 26481}, {10198, 48482, 11500}

X(64267) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND ANTI-INNER-GARCIA

Barycentrics    a*(a^9+13*a^7*b*c-3*a^8*(b+c)+(b-c)^6*(b+c)^3+2*a^6*(4*b^3-9*b^2*c-9*b*c^2+4*c^3)-2*a^2*b*(b-c)^2*c*(9*b^3-11*b^2*c-11*b*c^2+9*c^3)-a*(b^2-c^2)^2*(3*b^4-17*b^3*c+24*b^2*c^2-17*b*c^3+3*c^4)-a^5*(6*b^4+9*b^3*c-50*b^2*c^2+9*b*c^3+6*c^4)+a^3*(b-c)^2*(8*b^4-5*b^3*c-50*b^2*c^2-5*b*c^3+8*c^4)-2*a^4*(3*b^5-21*b^4*c+20*b^3*c^2+20*b^2*c^3-21*b*c^4+3*c^5)) : :
X(64267) = -3*X[3576]+2*X[12332], -4*X[11698]+5*X[63966], -2*X[12331]+3*X[52026]

X(64267) lies on these lines: {1, 104}, {9, 48667}, {40, 2932}, {57, 17654}, {80, 63992}, {84, 12773}, {119, 9623}, {149, 64261}, {153, 3872}, {200, 1145}, {214, 30503}, {515, 7993}, {952, 1490}, {956, 5693}, {1320, 56273}, {1512, 41684}, {2771, 7971}, {2829, 6264}, {3576, 12332}, {3632, 5531}, {4853, 12751}, {4861, 9809}, {5541, 64188}, {5657, 40257}, {5720, 19914}, {6224, 64150}, {6265, 38760}, {6282, 64189}, {6765, 12641}, {7982, 17652}, {9803, 26015}, {9897, 63988}, {11698, 63966}, {12119, 12565}, {12247, 63986}, {12331, 52026}, {12515, 37611}, {12520, 33337}, {12672, 64372}, {12737, 43166}, {17638, 30223}, {18443, 19907}, {19067, 35857}, {19068, 35856}, {22791, 64281}, {22837, 63962}, {38460, 64009}, {46685, 63135}, {51636, 63391}, {54154, 64278}, {63974, 64295}, {64147, 64324}

X(64267) = reflection of X(i) in X(j) for these {i,j}: {40, 22775}, {84, 12773}, {1768, 48694}, {2950, 104}, {5531, 6261}, {5541, 64188}, {9809, 54198}, {12650, 6264}, {54156, 1768}, {64261, 149}
X(64267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {104, 10698, 15558}, {104, 2800, 2950}, {104, 2950, 52027}, {1768, 2800, 54156}, {2800, 48694, 1768}, {2829, 6264, 12650}

X(64268) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST CIRCUMPERP AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9-2*a^8*(b+c)-b*(b-c)^4*c*(b+c)^3+a^5*b*c*(-5*b^2+14*b*c-5*c^2)+a^7*(-2*b^2+5*b*c-2*c^2)+a^6*(6*b^3-3*b^2*c-3*b*c^2+6*c^3)-a*(b^2-c^2)^2*(b^4-5*b^3*c+6*b^2*c^2-5*b*c^3+c^4)+a^3*(b-c)^2*(2*b^4-b^3*c-12*b^2*c^2-b*c^3+2*c^4)+a^2*(b-c)^2*(2*b^5-b^4*c+9*b^3*c^2+9*b^2*c^3-b*c^4+2*c^5)-a^4*(6*b^5-11*b^4*c+11*b^3*c^2+11*b^2*c^3-11*b*c^4+6*c^5)) : :
X(64268) = -3*X[2]+2*X[64273], -3*X[165]+X[64276]

X(64268) lies on these lines: {1, 3215}, {2, 64273}, {3, 64269}, {4, 64274}, {9, 1630}, {10, 64188}, {21, 2800}, {30, 12519}, {35, 104}, {36, 64291}, {40, 2975}, {55, 64283}, {56, 63257}, {57, 64284}, {100, 64270}, {140, 22775}, {165, 64276}, {515, 3651}, {550, 11495}, {692, 1385}, {958, 6256}, {993, 1158}, {1006, 40257}, {1376, 64294}, {1389, 5903}, {2829, 47032}, {3295, 64282}, {3428, 24390}, {3476, 59334}, {3652, 6001}, {5251, 12608}, {5260, 63964}, {5445, 6905}, {5563, 11218}, {5844, 11248}, {5887, 51506}, {6796, 64298}, {8666, 37531}, {10902, 64287}, {11012, 12616}, {11249, 37356}, {11500, 61510}, {12119, 57287}, {12515, 37562}, {13464, 52819}, {15228, 59322}, {18861, 64290}, {22770, 38454}, {26332, 59317}, {33596, 34791}, {34352, 38602}, {40255, 45700}, {63974, 64295}, {64119, 64271}, {64147, 64324}

X(64268) = midpoint of X(i) and X(j) for these {i,j}: {40, 64281}, {1158, 64279}, {64276, 64288}
X(64268) = reflection of X(i) in X(j) for these {i,j}: {4, 64274}, {6261, 64286}, {64119, 64271}, {64265, 12616}, {64269, 3}, {64298, 6796}
X(64268) = anticomplement of X(64273)
X(64268) = X(i)-Dao conjugate of X(j) for these {i, j}: {64273, 64273}
X(64268) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {165, 64288, 64276}

X(64269) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9-2*a^8*(b+c)+b*(b-c)^4*c*(b+c)^3+a^7*(-2*b^2+b*c-2*c^2)-a^5*b*c*(3*b^2+2*b*c+3*c^2)+a^6*(6*b^3+5*b^2*c+5*b*c^2+6*c^3)-a*(b^2-c^2)^2*(b^4+b^3*c-2*b^2*c^2+b*c^3+c^4)-3*a^4*(2*b^5+b^4*c-b^3*c^2-b^2*c^3+b*c^4+2*c^5)+a^2*(b-c)^2*(2*b^5+3*b^4*c-3*b^3*c^2-3*b^2*c^3+3*b*c^4+2*c^5)+a^3*(2*b^6+3*b^5*c-10*b^3*c^3+3*b*c^5+2*c^6)) : :
X(64269) = -3*X[2]+2*X[64274], -3*X[3576]+X[64281], -5*X[7987]+X[64288]

X(64269) lies on these lines: {1, 1389}, {2, 64274}, {3, 64268}, {4, 64273}, {5, 1001}, {21, 515}, {30, 12524}, {35, 64291}, {40, 224}, {55, 26332}, {56, 64283}, {80, 10395}, {100, 11012}, {411, 40257}, {548, 12332}, {944, 36152}, {958, 64294}, {999, 64282}, {1158, 5732}, {1490, 16208}, {1610, 37812}, {1621, 7548}, {2800, 3651}, {2975, 64270}, {3072, 3736}, {3149, 15950}, {3576, 64281}, {3579, 53291}, {3746, 11218}, {3871, 37625}, {3878, 6261}, {3913, 5844}, {4297, 48695}, {4324, 12775}, {5046, 64148}, {5248, 64272}, {5443, 44425}, {5709, 8715}, {5842, 37230}, {5882, 37583}, {6256, 7491}, {6265, 37837}, {6915, 34486}, {6920, 64261}, {6949, 10589}, {7411, 40256}, {7508, 12114}, {7987, 64288}, {9964, 56288}, {10306, 38454}, {10950, 37579}, {11219, 34890}, {11248, 64075}, {11499, 26363}, {11510, 26475}, {12005, 15932}, {12329, 49164}, {12616, 15931}, {12687, 35242}, {16202, 37251}, {18389, 37550}, {18524, 26470}, {26357, 45081}, {37000, 63262}, {63974, 64295}, {64147, 64324}

X(64269) = midpoint of X(i) and X(j) for these {i,j}: {1, 64276}, {64173, 64280}
X(64269) = reflection of X(i) in X(j) for these {i,j}: {4, 64273}, {48482, 64266}, {64268, 3}, {64279, 64286}, {64280, 6796}, {64285, 37837}
X(64269) = anticomplement of X(64274)
X(64269) = X(i)-Dao conjugate of X(j) for these {i, j}: {64274, 64274}
X(64269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6905, 64173, 1389}, {10267, 11500, 48482}

X(64270) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-CONWAY AND 1ST ANTI-PAVLOV

Barycentrics    3*a^7+15*a^5*b*c-7*a^6*(b+c)-2*(b-c)^4*(b+c)^3+a*(b^2-c^2)^2*(6*b^2-7*b*c+6*c^2)-3*a^2*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)+2*a^4*(6*b^3-5*b^2*c-5*b*c^2+6*c^3)-a^3*(9*b^4+8*b^3*c-22*b^2*c^2+8*b*c^3+9*c^4) : :
X(64270) = -3*X[2]+2*X[64283], -2*X[3244]+3*X[11218], -5*X[3616]+4*X[64282], -4*X[3626]+3*X[5659], -3*X[3873]+4*X[64284]

X(64270) lies on these lines: {2, 64283}, {4, 3621}, {8, 411}, {21, 952}, {30, 12535}, {63, 64276}, {78, 64281}, {100, 64268}, {145, 6828}, {200, 64288}, {355, 1389}, {515, 11684}, {517, 52841}, {519, 52269}, {944, 55868}, {1156, 5559}, {1483, 6852}, {2476, 10942}, {2975, 64269}, {3244, 11218}, {3486, 45081}, {3616, 64282}, {3623, 6855}, {3626, 5659}, {3632, 34784}, {3869, 5881}, {3873, 64284}, {4678, 6988}, {5086, 12531}, {5693, 40264}, {6326, 40260}, {6734, 64287}, {6853, 61510}, {6870, 20014}, {6873, 10247}, {6875, 18526}, {6876, 59503}, {6909, 33899}, {6912, 12648}, {6932, 64200}, {6985, 51515}, {7491, 61245}, {10039, 63263}, {10592, 43734}, {11415, 54134}, {11680, 64273}, {11681, 64274}, {11682, 64272}, {12245, 59355}, {12514, 15862}, {12532, 14872}, {12738, 21740}, {13375, 37708}, {17577, 50798}, {17857, 64279}, {20052, 50695}, {20117, 64278}, {21617, 64163}, {37700, 59416}, {37709, 62864}, {57287, 64189}, {59356, 64044}, {64147, 64324}

X(64270) = reflection of X(i) in X(j) for these {i,j}: {145, 63257}, {944, 64275}, {1389, 355}, {64283, 64294}
X(64270) = anticomplement of X(64283)
X(64270) = X(i)-Dao conjugate of X(j) for these {i, j}: {64283, 64283}
X(64270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 62830, 7548}, {64283, 64294, 2}

X(64271) = ORTHOLOGY CENTER OF THESE TRIANGLES: EHRMANN-MID AND 1ST ANTI-PAVLOV

Barycentrics    a^9*(b+c)-(b-c)^6*(b+c)^4+a*(b-c)^4*(b+c)^3*(b^2+c^2)-a^8*(b^2+4*b*c+c^2)+a^7*(-4*b^3+3*b^2*c+3*b*c^2-4*c^3)-2*a^4*(b-c)^2*(3*b^4+4*b^3*c-b^2*c^2+4*b*c^3+3*c^4)+a^2*(b^2-c^2)^2*(4*b^4-7*b^3*c+10*b^2*c^2-7*b*c^3+4*c^4)+a^6*(4*b^4+5*b^3*c-16*b^2*c^2+5*b*c^3+4*c^4)+2*a^5*(3*b^5-5*b^4*c+5*b^3*c^2+5*b^2*c^3-5*b*c^4+3*c^5)-a^3*(b-c)^2*(4*b^5+b^4*c+9*b^3*c^2+9*b^2*c^3+b*c^4+4*c^5) : :

X(64271) lies on these lines: {4, 64285}, {30, 12639}, {381, 64265}, {515, 33592}, {546, 64272}, {946, 5719}, {1519, 63257}, {2829, 49107}, {6001, 22798}, {7681, 64284}, {9955, 64266}, {10284, 18242}, {10895, 64291}, {10896, 64292}, {12608, 18480}, {12609, 34862}, {12611, 64273}, {12699, 64280}, {18525, 64287}, {31871, 60901}, {63317, 64296}, {63966, 64276}, {63974, 64295}, {64119, 64268}, {64147, 64324}

X(64271) = midpoint of X(i) and X(j) for these {i,j}: {4, 64285}, {12699, 64280}, {18525, 64287}, {64119, 64268}
X(64271) = reflection of X(i) in X(j) for these {i,j}: {64266, 9955}, {64272, 546}

X(64272) = ORTHOLOGY CENTER OF THESE TRIANGLES: EULER AND 1ST ANTI-PAVLOV

Barycentrics    2*a^10+10*a^8*b*c-5*a^9*(b+c)+21*a^5*b*(b-c)^2*c*(b+c)-2*(b-c)^6*(b+c)^4+4*a^2*b*c*(b^2-c^2)^2*(2*b^2-5*b*c+2*c^2)+a*(b-c)^4*(b+c)^3*(5*b^2-3*b*c+5*c^2)-2*a^6*(b-c)^2*(5*b^2+12*b*c+5*c^2)+a^7*(10*b^3-7*b^2*c-7*b*c^2+10*c^3)+2*a^4*(b-c)^2*(5*b^4+b^3*c-10*b^2*c^2+b*c^3+5*c^4)-a^3*(b-c)^2*(10*b^5+21*b^4*c-3*b^3*c^2-3*b^2*c^3+21*b*c^4+10*c^5) : :
X(64272) = -3*X[381]+X[64285], -3*X[5587]+X[64280], -3*X[5603]+X[64287]

X(64272) lies on these lines: {4, 64265}, {5, 64286}, {355, 3878}, {381, 64285}, {515, 6841}, {546, 64271}, {946, 37730}, {950, 63257}, {1389, 5727}, {1478, 64292}, {1479, 64291}, {1621, 64261}, {3884, 48482}, {5248, 64269}, {5250, 64276}, {5587, 64280}, {5603, 64287}, {5804, 37702}, {5805, 30329}, {5837, 64294}, {5901, 64293}, {6001, 16125}, {7704, 63986}, {9578, 64173}, {11682, 64270}, {18480, 63970}, {18493, 40257}, {25639, 64274}, {26332, 45636}, {51717, 63963}, {63318, 64296}, {63974, 64295}, {64147, 64324}, {64160, 64283}

X(64272) = midpoint of X(i) and X(j) for these {i,j}: {4, 64265}, {64261, 64298}
X(64272) = reflection of X(i) in X(j) for these {i,j}: {64271, 546}, {64286, 5}

X(64273) = ORTHOLOGY CENTER OF THESE TRIANGLES: 3RD EULER AND 1ST ANTI-PAVLOV

Barycentrics    a^8*(b+c)^2-2*a^7*(b+c)^3-(b-c)^6*(b+c)^4-2*a^6*(b+c)^2*(b^2-3*b*c+c^2)+2*a*(b-c)^4*(b+c)^3*(b^2-b*c+c^2)-2*a^4*b*(b-c)^2*c*(4*b^2+9*b*c+4*c^2)+2*a^2*(b^2-c^2)^2*(b^4+b^3*c-3*b^2*c^2+b*c^3+c^4)-2*a^3*(b-c)^2*(3*b^5+5*b^4*c-b^3*c^2-b^2*c^3+5*b*c^4+3*c^5)+a^5*(6*b^5+8*b^4*c-8*b^3*c^2-8*b^2*c^3+8*b*c^4+6*c^5) : :
X(64273) = -3*X[2]+X[64268], 3*X[1699]+X[64276], -9*X[7988]+X[64288], -5*X[8227]+X[64281]

X(64273) lies on these lines: {2, 64268}, {4, 64269}, {5, 30147}, {11, 64283}, {12, 946}, {30, 12615}, {119, 15863}, {142, 12616}, {226, 64284}, {442, 2800}, {496, 64282}, {515, 6841}, {546, 18242}, {950, 6246}, {1389, 6941}, {1479, 64173}, {1699, 64276}, {2829, 31649}, {2886, 64294}, {3822, 12608}, {3878, 6842}, {5248, 37290}, {5450, 25466}, {5844, 12607}, {6001, 49107}, {6256, 6912}, {6261, 31266}, {6796, 7680}, {6828, 51683}, {6882, 51717}, {7951, 63986}, {7988, 64288}, {8227, 64281}, {9956, 21252}, {11218, 37719}, {11680, 64270}, {12611, 64271}, {17757, 40260}, {18446, 64292}, {37438, 40256}, {48482, 64298}, {51700, 63980}, {63974, 64295}, {64147, 64324}

X(64273) = midpoint of X(i) and X(j) for these {i,j}: {4, 64269}, {6261, 64265}, {48482, 64298}, {64279, 64291}
X(64273) = reflection of X(i) in X(j) for these {i,j}: {64274, 5}
X(64273) = complement of X(64268)

X(64274) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH EULER AND 1ST ANTI-PAVLOV

Barycentrics    a^8*(b-c)^2+6*a^4*b^2*(b-c)^2*c^2-2*a^7*(b-c)^2*(b+c)-(b-c)^6*(b+c)^4+2*a*(b-c)^4*(b+c)^3*(b^2+c^2)+6*a^5*(b+c)*(b^2-b*c+c^2)^2+2*a^2*(b^2-c^2)^2*(b^4-2*b^3*c+b^2*c^2-2*b*c^3+c^4)-2*a^6*(b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)-2*a^3*(b-c)^2*(3*b^5+3*b^4*c+5*b^3*c^2+5*b^2*c^3+3*b*c^4+3*c^5) : :
X(64274) = -3*X[2]+X[64269], -5*X[1698]+X[64276], 3*X[5587]+X[64281], 7*X[7989]+X[64288]

X(64274) lies on these lines: {2, 64269}, {4, 64268}, {5, 30147}, {10, 6882}, {11, 11011}, {12, 64283}, {30, 12623}, {140, 3826}, {214, 58461}, {442, 515}, {495, 64282}, {498, 64173}, {946, 10395}, {1006, 19854}, {1210, 64284}, {1329, 64294}, {1389, 6830}, {1698, 64276}, {2800, 6841}, {2886, 31789}, {3754, 12616}, {3813, 5844}, {5289, 6971}, {5428, 5842}, {5587, 64281}, {5659, 55104}, {6001, 22798}, {6831, 40663}, {7741, 64291}, {7989, 64288}, {8727, 40256}, {10943, 22836}, {10957, 13411}, {11218, 37720}, {11681, 64270}, {12047, 12691}, {12608, 63970}, {17662, 45081}, {19860, 64265}, {24390, 31806}, {25639, 64272}, {63974, 64295}, {64147, 64324}

X(64274) = midpoint of X(i) and X(j) for these {i,j}: {4, 64268}, {48482, 64280}, {64265, 64279}
X(64274) = reflection of X(i) in X(j) for these {i,j}: {64266, 63963}, {64273, 5}
X(64274) = complement of X(64269)

X(64275) = COMPLEMENT OF X(1389)

Barycentrics    (2*a^3-a^2*(b+c)+(b-c)^2*(b+c)-2*a*(b^2-b*c+c^2))*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+4*b*c+c^2)) : :
X(64275) = -3*X[2]+X[1389], -X[7982]+3*X[11218], -3*X[10246]+2*X[64282], -X[64144]+3*X[64298]

X(64275) lies on these lines: {1, 140}, {2, 1389}, {3, 64268}, {5, 17057}, {8, 1006}, {9, 355}, {10, 6882}, {12, 34353}, {30, 13089}, {40, 64291}, {100, 64290}, {119, 960}, {142, 3754}, {214, 6684}, {404, 5657}, {442, 517}, {515, 3647}, {519, 24299}, {758, 12639}, {944, 55868}, {952, 5258}, {997, 64279}, {1145, 6734}, {1385, 59491}, {1482, 10198}, {1737, 31838}, {2092, 8609}, {2323, 59680}, {2800, 37401}, {3035, 55296}, {3126, 28473}, {3617, 12116}, {3626, 6594}, {3654, 5709}, {3679, 64292}, {3878, 6842}, {4297, 51570}, {4511, 31659}, {5176, 26878}, {5252, 26921}, {5289, 6863}, {5692, 10942}, {5705, 11530}, {5730, 26487}, {5771, 37583}, {5790, 48482}, {5818, 45630}, {5837, 5887}, {5881, 16208}, {5882, 54288}, {5903, 37438}, {5904, 32213}, {6265, 52265}, {6600, 16202}, {6700, 38763}, {6735, 58630}, {6853, 62826}, {6883, 10573}, {6986, 12247}, {7483, 46920}, {7508, 15446}, {7982, 11218}, {8256, 26363}, {8702, 57095}, {10039, 13375}, {10246, 64282}, {10268, 18481}, {10427, 31788}, {10527, 64201}, {10532, 59417}, {10609, 33862}, {10680, 22754}, {10916, 12640}, {10943, 38112}, {10944, 36152}, {10993, 37568}, {11012, 61524}, {11231, 24541}, {11499, 64280}, {12647, 37579}, {12649, 64199}, {12702, 15346}, {12757, 13369}, {14794, 33814}, {15347, 38066}, {15556, 31397}, {16206, 61275}, {18395, 26475}, {18518, 64335}, {23513, 41012}, {25466, 64044}, {26287, 37298}, {26358, 63262}, {28212, 49177}, {28458, 40256}, {30379, 31794}, {31835, 37725}, {32198, 48713}, {37562, 41540}, {37611, 64281}, {37621, 44669}, {37625, 41862}, {38116, 45728}, {38121, 60895}, {45036, 64287}, {45770, 64285}, {50810, 55109}, {51463, 61286}, {61276, 64109}, {63974, 64295}, {64144, 64298}, {64147, 64324}

X(64275) = midpoint of X(i) and X(j) for these {i,j}: {8, 64173}, {40, 64291}, {100, 64290}, {944, 64270}, {5690, 34352}, {64265, 64276}
X(64275) = reflection of X(i) in X(j) for these {i,j}: {355, 64294}, {24474, 64284}, {45081, 34352}, {61032, 38112}, {64283, 1385}
X(64275) = complement of X(1389)
X(64275) = center of circumconic {{A, B, C, X(100), X(64290)}}
X(64275) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 9956}, {56, 64163}, {58, 37737}, {106, 11545}, {1385, 10}, {2317, 2}, {56814, 5}, {59491, 141}
X(64275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(13375)}}, {{A, B, C, X(5559), X(10039)}}, {{A, B, C, X(59491), X(64265)}}
X(64275) = barycentric product X(i)*X(j) for these (i, j): {10039, 59491}
X(64275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 5690, 40663}, {5444, 31423, 140}, {5690, 34352, 5844}, {5844, 34352, 45081}, {16202, 59503, 49168}

X(64276) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTRAL AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9-a^8*(b+c)-(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)-a^7*(4*b^2+7*b*c+4*c^2)+4*a^6*(b^3+4*b^2*c+4*b*c^2+c^3)+a*(b^2-c^2)^2*(b^4-11*b^3*c+16*b^2*c^2-11*b*c^3+c^4)-a^3*(b-c)^2*(4*b^4-7*b^3*c-30*b^2*c^2-7*b*c^3+4*c^4)+a^5*(6*b^4+3*b^3*c-22*b^2*c^2+3*b*c^3+6*c^4)+4*a^2*(b-c)^2*(b^5+3*b^4*c-3*b^3*c^2-3*b^2*c^3+3*b*c^4+c^5)-6*a^4*(b^5+4*b^4*c-3*b^3*c^2-3*b^2*c^3+4*b*c^4+c^5)) : :
X(64276) = -3*X[165]+2*X[64268], -5*X[1698]+4*X[64274], -3*X[1699]+4*X[64273], -3*X[52026]+2*X[64285], -5*X[63966]+4*X[64271]

X(64276) lies on these lines: {1, 1389}, {3, 64281}, {8, 2949}, {9, 355}, {20, 2950}, {30, 12660}, {40, 49170}, {57, 64283}, {63, 64270}, {165, 64268}, {191, 515}, {952, 54302}, {993, 10268}, {1158, 16558}, {1490, 3869}, {1697, 5715}, {1698, 64274}, {1699, 64273}, {2136, 5709}, {2800, 13146}, {2951, 54156}, {3333, 64282}, {3646, 4187}, {5119, 64291}, {5250, 64272}, {5506, 5818}, {5528, 12702}, {5541, 12245}, {5730, 6326}, {5882, 15932}, {6001, 63267}, {7991, 56583}, {10902, 37308}, {10914, 11012}, {12658, 64199}, {13144, 48694}, {37550, 37740}, {52026, 64285}, {59342, 64292}, {63966, 64271}, {63974, 64295}, {64147, 64324}

X(64276) = reflection of X(i) in X(j) for these {i,j}: {1, 64269}, {1389, 64286}, {1490, 64298}, {64261, 64265}, {64265, 64275}, {64279, 6796}, {64281, 3}, {64288, 64268}
X(64276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {165, 64288, 64268}

X(64277) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND EXTOUCH

Barycentrics    a*(a^9-4*a^7*(b-c)^2-a^8*(b+c)-(b-c)^4*(b+c)^5+4*a^6*(b^3-3*b^2*c-3*b*c^2+c^3)-2*a^4*(b-c)^2*(3*b^3-7*b^2*c-7*b*c^2+3*c^3)-4*a^3*(b-c)^2*(b^4+4*b^3*c+10*b^2*c^2+4*b*c^3+c^4)+a*(b^2-c^2)^2*(b^4+8*b^3*c-2*b^2*c^2+8*b*c^3+c^4)+a^5*(6*b^4-8*b^3*c+20*b^2*c^2-8*b*c^3+6*c^4)+4*a^2*(b-c)^2*(b^5-b^4*c+4*b^3*c^2+4*b^2*c^3-b*c^4+c^5)) : :
X(64277) = -2*X[12330]+3*X[52027]

X(64277) lies on these lines: {1, 84}, {9, 1630}, {40, 6737}, {515, 6762}, {942, 64320}, {956, 56273}, {971, 22770}, {1158, 9841}, {1385, 3358}, {1490, 3428}, {3333, 6245}, {3427, 7091}, {3632, 41338}, {4847, 12667}, {4882, 11500}, {5437, 12616}, {5691, 15239}, {6223, 64081}, {6260, 19843}, {7171, 31786}, {9799, 62874}, {9942, 30503}, {9960, 12529}, {10309, 34625}, {10396, 12664}, {10860, 14110}, {10864, 41869}, {11372, 54198}, {12330, 52027}, {12565, 12671}, {12666, 64369}, {14647, 37526}, {19854, 63966}, {22791, 64262}, {33899, 37534}, {37837, 61122}, {52026, 59320}, {56889, 63981}, {58808, 64190}, {63974, 64295}, {64118, 64312}, {64147, 64324}

X(64277) = reflection of X(i) in X(j) for these {i,j}: {84, 49170}, {1490, 18237}, {63981, 56889}
X(64277) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {84, 12687, 63430}, {84, 7971, 12705}, {6001, 49170, 84}

X(64278) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND FUHRMANN

Barycentrics    3*a^7-6*a^6*(b+c)-2*(b-c)^4*(b+c)^3-a^5*(b^2-13*b*c+c^2)+a*(b^2-c^2)^2*(5*b^2-8*b*c+5*c^2)-a^2*(b-c)^2*(2*b^3-9*b^2*c-9*b*c^2+2*c^3)+a^4*(10*b^3-9*b^2*c-9*b*c^2+10*c^3)-a^3*(7*b^4+5*b^3*c-20*b^2*c^2+5*b*c^3+7*c^4) : :
X(64278) = -4*X[104]+3*X[50811], -5*X[1698]+4*X[22935], -3*X[1699]+2*X[48667], -3*X[1768]+2*X[38753], -3*X[3576]+2*X[6224], -3*X[3656]+4*X[61601], -3*X[3679]+2*X[12331], -4*X[6713]+3*X[64011], -3*X[10707]+2*X[25485], -5*X[11522]+6*X[51517], -3*X[12119]+4*X[38759], -4*X[12619]+3*X[15015]

X(64278) lies on circumconic {{A, B, C, X(2006), X(64290)}} and on these lines: {1, 5}, {8, 64369}, {9, 64290}, {30, 12767}, {40, 12247}, {100, 59331}, {104, 50811}, {149, 7982}, {153, 3577}, {515, 3218}, {912, 37006}, {1512, 28236}, {1698, 22935}, {1699, 48667}, {1768, 38753}, {2771, 5691}, {2800, 10724}, {2801, 41577}, {2802, 12625}, {3576, 6224}, {3586, 17638}, {3656, 61601}, {3679, 12331}, {3681, 12531}, {3811, 6596}, {5251, 37621}, {5541, 19914}, {5692, 12645}, {6713, 64011}, {9579, 11571}, {9589, 48680}, {9613, 17660}, {9625, 9912}, {9802, 28234}, {9809, 31673}, {9952, 24466}, {10222, 52850}, {10246, 17057}, {10572, 64372}, {10707, 25485}, {10738, 13253}, {11362, 20095}, {11499, 14804}, {11522, 51517}, {11529, 41558}, {12119, 38759}, {12619, 15015}, {12653, 41709}, {12690, 14217}, {12736, 12757}, {12773, 26286}, {15096, 18525}, {15863, 38665}, {16200, 21630}, {16858, 50890}, {18492, 21635}, {19875, 61562}, {20117, 64270}, {22765, 28204}, {30389, 61566}, {31425, 34474}, {31434, 41541}, {31447, 38636}, {34627, 38073}, {34717, 42843}, {38021, 50889}, {38669, 64188}, {43161, 60994}, {44254, 61510}, {54154, 64267}, {63974, 64295}, {64147, 64324}

X(64278) = midpoint of X(i) and X(j) for these {i,j}: {9803, 20085}
X(64278) = reflection of X(i) in X(j) for these {i,j}: {40, 12247}, {5531, 355}, {5541, 19914}, {5691, 12747}, {5881, 9897}, {6224, 10265}, {6326, 80}, {7972, 37726}, {7982, 149}, {9589, 48680}, {9809, 31673}, {12757, 12736}, {13253, 10738}, {14217, 12690}, {20095, 11362}, {24466, 9952}, {38665, 15863}
X(64278) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {80, 7972, 8068}, {80, 952, 6326}, {355, 952, 5531}, {952, 37726, 7972}, {952, 9897, 5881}, {2771, 12747, 5691}, {5541, 19914, 63143}, {5727, 5881, 5587}, {6224, 10265, 3576}, {6265, 37718, 8227}, {9803, 20085, 515}, {10738, 13253, 31162}, {12619, 15015, 31423}

X(64279) = ORTHOLOGY CENTER OF THESE TRIANGLES: FUHRMANN AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9+9*a^7*b*c-3*a^8*(b+c)+8*a^6*(b-c)^2*(b+c)+(b-c)^6*(b+c)^3-2*a^2*b*(b-c)^2*c*(4*b^3-7*b^2*c-7*b*c^2+4*c^3)-a*(b^2-c^2)^2*(3*b^4-11*b^3*c+18*b^2*c^2-11*b*c^3+3*c^4)-a^5*(6*b^4+7*b^3*c-30*b^2*c^2+7*b*c^3+6*c^4)+a^3*(b-c)^2*(8*b^4+3*b^3*c-20*b^2*c^2+3*b*c^3+8*c^4)-2*a^4*(3*b^5-11*b^4*c+11*b^3*c^2+11*b^2*c^3-11*b*c^4+3*c^5)) : :

X(64279) lies on these lines: {1, 1389}, {8, 6326}, {40, 45392}, {191, 2800}, {355, 2886}, {515, 2475}, {993, 1158}, {997, 64275}, {1490, 64288}, {2771, 12745}, {3576, 37293}, {3811, 5844}, {3872, 64287}, {5080, 12608}, {5220, 5694}, {5697, 10093}, {5731, 10940}, {5880, 31657}, {6001, 48668}, {6924, 34353}, {6949, 64290}, {7951, 63986}, {10094, 21842}, {11375, 63257}, {11524, 38665}, {17857, 64270}, {18446, 37706}, {18524, 37837}, {19860, 64265}, {30147, 48482}, {33281, 40262}, {37740, 64283}, {40249, 48694}, {51717, 64188}, {54176, 64282}, {54318, 64266}, {63974, 64295}, {64147, 64324}

X(64279) = midpoint of X(i) and X(j) for these {i,j}: {1389, 64280}, {1490, 64288}
X(64279) = reflection of X(i) in X(j) for these {i,j}: {1158, 64268}, {6261, 64285}, {64265, 64274}, {64269, 64286}, {64276, 6796}, {64291, 64273}

X(64280) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-GARCIA AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9-2*a^8*(b+c)+b*(b-c)^4*c*(b+c)^3+a^7*(-2*b^2+b*c-2*c^2)-a^5*b*c*(b^2-10*b*c+c^2)+3*a^6*(2*b^3+b^2*c+b*c^2+2*c^3)-a*(b^2-c^2)^2*(b^4-b^3*c+4*b^2*c^2-b*c^3+c^4)+a^3*(b-c)^2*(2*b^4+3*b^3*c-2*b^2*c^2+3*b*c^3+2*c^4)+a^4*(-6*b^5+b^4*c-7*b^3*c^2-7*b^2*c^3+b*c^4-6*c^5)+a^2*(b-c)^2*(2*b^5+b^4*c+5*b^3*c^2+5*b^2*c^3+b*c^4+2*c^5)) : :
X(64280) = -3*X[2]+2*X[64266], -3*X[5587]+2*X[64272]

X(64280) lies on these lines: {1, 1389}, {2, 64266}, {3, 1602}, {4, 40292}, {8, 411}, {10, 64265}, {21, 5842}, {84, 12511}, {100, 14110}, {404, 11024}, {515, 3651}, {517, 64285}, {519, 64287}, {943, 946}, {944, 59317}, {1006, 19854}, {1490, 5223}, {1737, 64292}, {2346, 5703}, {2829, 33557}, {3085, 3149}, {3811, 52026}, {4294, 37302}, {4847, 11012}, {5173, 33597}, {5536, 40249}, {5584, 14647}, {5587, 64272}, {5731, 35976}, {5758, 38454}, {5844, 22770}, {6001, 11684}, {6245, 7688}, {6261, 41338}, {6847, 37601}, {6927, 10321}, {6940, 15931}, {6942, 7742}, {6985, 10942}, {6986, 63980}, {7411, 12114}, {7580, 12667}, {7680, 63263}, {10039, 44425}, {10592, 19541}, {11218, 63259}, {11496, 30332}, {11499, 64275}, {11501, 45081}, {11525, 64316}, {12666, 50528}, {12675, 18450}, {12699, 64271}, {12777, 64200}, {18242, 36002}, {26357, 50701}, {30384, 63262}, {34772, 37837}, {37000, 52270}, {38665, 64056}, {63319, 64296}, {63974, 64295}, {64147, 64324}, {64199, 64312}

X(64280) = reflection of X(i) in X(j) for these {i,j}: {1, 64286}, {1389, 64279}, {12699, 64271}, {48482, 64274}, {64173, 64269}, {64265, 10}, {64269, 6796}, {64298, 11500}
X(64280) = anticomplement of X(64266)
X(64280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1389, 11491, 64173}, {11500, 59366, 54051}

X(64281) = ORTHOLOGY CENTER OF THESE TRIANGLES: HEXYL AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9+13*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)-a^5*(b-c)^2*(6*b^2+23*b*c+6*c^2)-2*a^4*(b-c)^2*(3*b^3-10*b^2*c-10*b*c^2+3*c^3)+2*a^6*(4*b^3-7*b^2*c-7*b*c^2+4*c^3)-2*a^2*b*(b-c)^2*c*(5*b^3-9*b^2*c-9*b*c^2+5*c^3)-a*(b^2-c^2)^2*(3*b^4-15*b^3*c+20*b^2*c^2-15*b*c^3+3*c^4)+a^3*(b-c)^2*(8*b^4-b^3*c-30*b^2*c^2-b*c^3+8*c^4)) : :

X(64281) lies on these lines: {1, 6831}, {3, 64276}, {30, 12845}, {40, 2975}, {78, 64270}, {84, 1389}, {145, 6264}, {515, 2475}, {517, 54302}, {936, 64294}, {1768, 5903}, {1836, 12676}, {2829, 16118}, {3333, 64284}, {3576, 64269}, {3601, 7966}, {5537, 11524}, {5587, 64274}, {5732, 5832}, {5844, 12629}, {5882, 30284}, {6261, 7548}, {6326, 11681}, {7704, 63986}, {7962, 11920}, {7971, 10394}, {7982, 45632}, {8227, 64273}, {10042, 63430}, {10050, 12705}, {11014, 48482}, {11529, 12687}, {12664, 50194}, {13375, 59335}, {19860, 52026}, {20612, 38669}, {22791, 64267}, {37611, 64275}, {59331, 64359}, {61146, 64261}, {63974, 64295}, {64147, 64324}

X(64281) = midpoint of X(i) and X(j) for these {i,j}: {1, 64288}
X(64281) = reflection of X(i) in X(j) for these {i,j}: {40, 64268}, {1490, 64285}, {63257, 64293}, {64276, 3}, {64287, 64283}, {64291, 64266}, {64298, 64286}
X(64281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64286, 64298, 52026}

X(64282) = ORTHOLOGY CENTER OF THESE TRIANGLES: INCIRCLE-CIRCLES AND 1ST ANTI-PAVLOV

Barycentrics    6*a^7-12*a^6*(b+c)-(b-c)^4*(b+c)^3-5*a^5*(b^2-4*b*c+c^2)-8*a^3*(b-c)^2*(b^2+3*b*c+c^2)+a*(b^2-c^2)^2*(7*b^2-12*b*c+7*c^2)-2*a^2*(b-c)^2*(5*b^3-b^2*c-b*c^2+5*c^3)+a^4*(23*b^3-11*b^2*c-11*b*c^2+23*c^3) : :
X(64282) = -5*X[3616]+X[64270], X[3633]+3*X[5659], -3*X[10246]+X[64275], 5*X[61288]+X[64200]

X(64282) lies on these lines: {1, 6831}, {30, 12909}, {56, 11041}, {495, 64274}, {496, 64273}, {515, 15911}, {942, 13607}, {952, 11281}, {999, 64269}, {1125, 64294}, {1385, 3244}, {1389, 3296}, {1482, 38454}, {1483, 31419}, {2099, 11048}, {2800, 15174}, {3295, 64268}, {3333, 64276}, {3616, 64270}, {3633, 5659}, {4999, 15178}, {5045, 64284}, {5542, 5882}, {5855, 24299}, {7686, 58626}, {9952, 12735}, {10246, 64275}, {18242, 37724}, {22753, 64298}, {25466, 37727}, {26286, 50824}, {28224, 33592}, {34471, 45081}, {36996, 64120}, {37615, 38122}, {37730, 63964}, {37837, 64297}, {38306, 56030}, {45776, 63972}, {46920, 61283}, {54176, 64279}, {61288, 64200}, {63974, 64295}, {63999, 64192}, {64147, 64324}

X(64282) = midpoint of X(i) and X(j) for these {i,j}: {1, 64283}
X(64282) = reflection of X(i) in X(j) for these {i,j}: {64284, 5045}, {64294, 1125}

X(64283) = ORTHOLOGY CENTER OF THESE TRIANGLES: INTOUCH AND 1ST ANTI-PAVLOV

Barycentrics    (2*a^3-a^2*(b+c)+(b-c)^2*(b+c)-2*a*(b^2-b*c+c^2))*(2*a^4-a^2*(b-c)^2-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)-(b^2-c^2)^2) : :
X(64283) = -3*X[2]+X[64270], -3*X[354]+2*X[64284], -X[3632]+3*X[5659]

X(64283) lies on circumconic {{A, B, C, X(33597), X(56030)}} and on these lines: {1, 6831}, {2, 64270}, {3, 145}, {4, 56030}, {7, 944}, {11, 64273}, {12, 64274}, {30, 12913}, {46, 7966}, {55, 64268}, {56, 64269}, {57, 64276}, {65, 4311}, {224, 3872}, {354, 64284}, {355, 31266}, {442, 952}, {515, 3649}, {517, 39772}, {519, 39783}, {946, 39782}, {950, 1537}, {1155, 39777}, {1159, 6934}, {1317, 2646}, {1385, 59491}, {1482, 10941}, {1532, 21740}, {2099, 45638}, {2800, 10543}, {3057, 41537}, {3149, 64298}, {3174, 12629}, {3241, 37428}, {3244, 14110}, {3270, 9957}, {3486, 63962}, {3612, 5559}, {3623, 6836}, {3632, 5659}, {3655, 59318}, {3957, 37374}, {4084, 30264}, {4297, 4757}, {5794, 61296}, {5855, 10902}, {5881, 28628}, {6261, 37724}, {6862, 10587}, {6917, 10805}, {7483, 10246}, {7982, 38454}, {9803, 51683}, {10247, 10806}, {10427, 17647}, {10595, 15935}, {10609, 32900}, {10698, 15172}, {10940, 11112}, {11570, 12675}, {11827, 62822}, {12616, 32905}, {12672, 14100}, {13375, 13750}, {14988, 57002}, {17528, 50818}, {17757, 37733}, {18446, 37739}, {20418, 24926}, {24927, 50843}, {28224, 37230}, {31789, 62830}, {33281, 37726}, {33597, 64163}, {34352, 37298}, {34773, 64044}, {35010, 64011}, {37356, 61283}, {37438, 61295}, {37740, 64279}, {39779, 63987}, {44222, 61293}, {51093, 59340}, {61288, 63391}, {63974, 64295}, {64147, 64324}, {64160, 64272}

X(64283) = midpoint of X(i) and X(j) for these {i,j}: {944, 1389}, {64281, 64287}
X(64283) = reflection of X(i) in X(j) for these {i,j}: {1, 64282}, {63257, 1}, {64265, 64293}, {64270, 64294}, {64275, 1385}
X(64283) = complement of X(64270)
X(64283) = anticomplement of X(64294)
X(64283) = X(i)-Dao conjugate of X(j) for these {i, j}: {64163, 8}, {64286, 1389}, {64294, 64294}
X(64283) = pole of line {13464, 64284} with respect to the Feuerbach hyperbola
X(64283) = barycentric product X(i)*X(j) for these (i, j): {59491, 64163}
X(64283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64270, 64294}, {21740, 37730, 1532}, {64286, 64297, 33597}

X(64284) = ORTHOLOGY CENTER OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^8*(b+c)-2*a^7*(b+c)^2-(b-c)^4*(b+c)^3*(b^2-3*b*c+c^2)+2*a^5*(b+c)^2*(3*b^2-5*b*c+3*c^2)+a^4*b*c*(-5*b^3+11*b^2*c+11*b*c^2-5*c^3)+a^6*(-2*b^3+3*b^2*c+3*b*c^2-2*c^3)+2*a*(b^2-c^2)^2*(b^4-3*b^3*c+3*b^2*c^2-3*b*c^3+c^4)-2*a^3*(b-c)^2*(3*b^4+2*b^3*c-3*b^2*c^2+2*b*c^3+3*c^4)+a^2*(b-c)^2*(2*b^5+b^4*c-13*b^3*c^2-13*b^2*c^3+b*c^4+2*c^5)) : :
X(64284) = -3*X[354]+X[64283], 3*X[3873]+X[64270], X[5903]+3*X[11218]

X(64284) lies on these lines: {1, 1389}, {4, 18224}, {7, 5884}, {30, 12917}, {57, 64268}, {65, 41552}, {142, 3754}, {226, 64273}, {354, 64283}, {515, 10122}, {517, 11281}, {518, 64294}, {938, 18226}, {946, 64266}, {1210, 64274}, {1387, 13374}, {2800, 33593}, {3333, 64281}, {3873, 64270}, {4298, 15528}, {5045, 64282}, {5572, 7686}, {5761, 10198}, {5804, 48482}, {5836, 5844}, {5883, 11249}, {5902, 10532}, {5903, 11218}, {6001, 11544}, {6003, 13408}, {7681, 64271}, {10980, 64288}, {11012, 27003}, {15016, 64079}, {18221, 64287}, {20117, 31053}, {22753, 64285}, {31788, 38454}, {37625, 59417}, {45081, 64046}, {49168, 61030}, {63974, 64295}, {64147, 64324}

X(64284) = midpoint of X(i) and X(j) for these {i,j}: {65, 63257}, {1389, 13375}, {24474, 64275}
X(64284) = reflection of X(i) in X(j) for these {i,j}: {64282, 5045}
X(64284) = pole of line {11011, 64283} with respect to the Feuerbach hyperbola

X(64285) = ORTHOLOGY CENTER OF THESE TRIANGLES: JOHNSON AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9+7*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2-b*c+c^2)-2*a^2*b*(b-c)^2*c*(3*b^3-4*b^2*c-4*b*c^2+3*c^3)+a^6*(8*b^3-4*b^2*c-4*b*c^2+8*c^3)-a*(b^2-c^2)^2*(3*b^4-8*b^3*c+14*b^2*c^2-8*b*c^3+3*c^4)-2*a^5*(3*b^4+3*b^3*c-11*b^2*c^2+3*b*c^3+3*c^4)+a^3*(b-c)^2*(8*b^4+7*b^3*c-8*b^2*c^2+7*b*c^3+8*c^4)-3*a^4*(2*b^5-5*b^4*c+5*b^3*c^2+5*b^2*c^3-5*b*c^4+2*c^5)) : :
X(64285) = -3*X[381]+2*X[64272], -3*X[5886]+2*X[64266], -3*X[52026]+X[64276]

X(64285) lies on these lines: {1, 5805}, {3, 64286}, {4, 64271}, {5, 64265}, {11, 64292}, {12, 64291}, {355, 2886}, {381, 64272}, {515, 11263}, {517, 64280}, {952, 6598}, {958, 5779}, {971, 17653}, {1389, 17097}, {1482, 11500}, {2800, 16139}, {3625, 12738}, {3652, 6001}, {4511, 40262}, {4915, 17857}, {5659, 21677}, {5720, 64294}, {5844, 6765}, {5886, 64266}, {6260, 10742}, {6265, 37837}, {7971, 26921}, {8158, 12635}, {9957, 33597}, {10950, 64127}, {11374, 63257}, {18446, 37739}, {18481, 41688}, {18518, 64318}, {22753, 64284}, {22765, 40249}, {24953, 33899}, {35250, 63962}, {37615, 64293}, {45770, 64275}, {52026, 64276}, {63323, 64296}, {63974, 64295}, {64147, 64324}

X(64285) = midpoint of X(i) and X(j) for these {i,j}: {1389, 64298}, {1490, 64281}, {6261, 64279}
X(64285) = reflection of X(i) in X(j) for these {i,j}: {3, 64286}, {4, 64271}, {64265, 5}, {64269, 37837}

X(64286) = ORTHOLOGY CENTER OF THESE TRIANGLES: MEDIAL AND 1ST ANTI-PAVLOV

Barycentrics    a*(2*a^4-a^2*(b-c)^2-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)-(b^2-c^2)^2)*(a^5-a^4*(b+c)+a^3*(-2*b^2+b*c-2*c^2)-(b-c)^2*(b^3+c^3)+a^2*(2*b^3-b^2*c-b*c^2+2*c^3)+a*(b^4-b^3*c+4*b^2*c^2-b*c^3+c^4)) : :
X(64286) = -3*X[2]+X[64265]

X(64286) lies on these lines: {1, 1389}, {2, 64265}, {3, 64285}, {5, 64272}, {8, 64287}, {9, 1630}, {10, 37837}, {30, 12639}, {142, 1385}, {214, 31786}, {442, 515}, {498, 64291}, {499, 64292}, {997, 49183}, {1125, 64266}, {1145, 6737}, {1158, 51576}, {2092, 8607}, {2800, 35204}, {2829, 51569}, {3035, 55305}, {3428, 5730}, {3647, 6001}, {4297, 41540}, {5780, 51572}, {5818, 6853}, {5842, 35016}, {5844, 12640}, {5884, 59317}, {6260, 57288}, {6594, 31837}, {6600, 22770}, {6901, 41862}, {11012, 40249}, {11499, 40587}, {11500, 30147}, {12114, 15346}, {12520, 49171}, {13411, 63257}, {14110, 54192}, {15348, 61030}, {15556, 21740}, {15909, 56027}, {17056, 64296}, {19524, 52148}, {19860, 52026}, {33597, 64163}, {51409, 64004}, {51570, 64118}, {54430, 63986}, {59691, 64315}, {63974, 64295}, {64147, 64324}

X(64286) = midpoint of X(i) and X(j) for these {i,j}: {1, 64280}, {3, 64285}, {8, 64287}, {1389, 64276}, {6261, 64268}, {64269, 64279}, {64281, 64298}
X(64286) = reflection of X(i) in X(j) for these {i,j}: {64266, 1125}, {64272, 5}
X(64286) = complement of X(64265)
X(64286) = X(i)-complementary conjugate of X(j) for these {i, j}: {11012, 10}
X(64286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33597, 64283, 64297}, {52026, 64281, 64298}

X(64287) = ORTHOLOGY CENTER OF THESE TRIANGLES: 5TH MIXTILINEAR AND 1ST ANTI-PAVLOV

Barycentrics    3*a^10-9*a^9*(b+c)-(b-c)^6*(b+c)^4+a^8*(b^2+25*b*c+c^2)+a*(b-c)^4*(b+c)^3*(5*b^2-6*b*c+5*c^2)-4*a^5*(b-c)^2*(3*b^3-7*b^2*c-7*b*c^2+3*c^3)+2*a^7*(11*b^3-9*b^2*c-9*b*c^2+11*c^3)-a^2*(b^2-c^2)^2*(7*b^4-25*b^3*c+40*b^2*c^2-25*b*c^3+7*c^4)-a^6*(20*b^4+21*b^3*c-58*b^2*c^2+21*b*c^3+20*c^4)+a^4*(b-c)^2*(24*b^4+17*b^3*c-26*b^2*c^2+17*b*c^3+24*c^4)-2*a^3*(b-c)^2*(3*b^5+13*b^4*c-8*b^3*c^2-8*b^2*c^3+13*b*c^4+3*c^5) : :
X(64287) = -3*X[5603]+2*X[64272]

X(64287) lies on these lines: {1, 6831}, {8, 64286}, {100, 11012}, {145, 37625}, {515, 34195}, {519, 64280}, {952, 6598}, {2136, 5709}, {3243, 5735}, {3872, 64279}, {3957, 32905}, {5441, 6001}, {5603, 64272}, {5705, 64294}, {5715, 37739}, {5734, 48482}, {6261, 54154}, {6284, 7971}, {6734, 64270}, {7966, 12687}, {10902, 64268}, {11680, 40257}, {13607, 63260}, {18221, 64284}, {18525, 64271}, {22791, 64261}, {37291, 54445}, {41575, 64298}, {45036, 64275}, {63333, 64296}, {63974, 64295}, {64147, 64324}

X(64287) = reflection of X(i) in X(j) for these {i,j}: {8, 64286}, {18525, 64271}, {64265, 1}, {64281, 64283}

X(64288) = ORTHOLOGY CENTER OF THESE TRIANGLES: 6TH MIXTILINEAR AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9+17*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2-6*b*c+c^2)-2*a^4*(b-c)^2*(3*b^3-17*b^2*c-17*b*c^2+3*c^3)-2*a^2*b*(b-c)^2*c*(7*b^3-15*b^2*c-15*b*c^2+7*c^3)+a^6*(8*b^3-22*b^2*c-22*b*c^2+8*c^3)-a*(b^2-c^2)^2*(3*b^4-21*b^3*c+28*b^2*c^2-21*b*c^3+3*c^4)-a^5*(6*b^4+13*b^3*c-50*b^2*c^2+13*b*c^3+6*c^4)+a^3*(b-c)^2*(8*b^4-9*b^3*c-54*b^2*c^2-9*b*c^3+8*c^4)) : :
X(64288) = -3*X[165]+4*X[64268], -5*X[7987]+4*X[64269], -9*X[7988]+8*X[64273], -7*X[7989]+8*X[64274]

X(64288) lies on these lines: {1, 6831}, {30, 13101}, {84, 12767}, {165, 64268}, {200, 64270}, {515, 16143}, {1158, 6763}, {1389, 3062}, {1490, 64279}, {2951, 11826}, {3633, 7993}, {5844, 6769}, {7982, 64264}, {7987, 64269}, {7988, 64273}, {7989, 64274}, {7990, 64173}, {8580, 64294}, {9623, 64298}, {9851, 10970}, {10980, 64284}, {11009, 12664}, {11010, 12114}, {11224, 45648}, {61763, 64320}, {63974, 64295}, {63984, 64201}, {64147, 64324}

X(64288) = reflection of X(i) in X(j) for these {i,j}: {1, 64281}, {1490, 64279}, {64276, 64268}

X(64289) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 1ST SCHIFFLER

Barycentrics    3*a^4+3*a^3*(b+c)-2*(b^2-c^2)^2-a^2*(b^2-b*c+c^2)+a*(-3*b^3+b^2*c+b*c^2-3*c^3) : :
X(64289) = -8*X[21]+9*X[25055], -3*X[1699]+2*X[7701], -4*X[2475]+3*X[3679], -3*X[3576]+4*X[33668], -7*X[3624]+4*X[3648], -3*X[3652]+4*X[46028], -3*X[4654]+2*X[37292], -8*X[5499]+7*X[9588], -3*X[5587]+2*X[13465], -4*X[6675]+3*X[63278], -5*X[8227]+4*X[22936], -7*X[9624]+6*X[28453] and many others

X(64289) lies on these lines: {1, 5180}, {9, 46}, {10, 31888}, {21, 25055}, {30, 7982}, {63, 13089}, {224, 34600}, {758, 3632}, {1420, 3649}, {1699, 7701}, {1768, 37356}, {1836, 6763}, {2475, 3679}, {2771, 5691}, {3336, 4193}, {3337, 5057}, {3339, 41551}, {3576, 33668}, {3624, 3648}, {3652, 46028}, {3746, 28534}, {3811, 13146}, {3894, 41869}, {3901, 12625}, {4654, 37292}, {5141, 61703}, {5219, 45065}, {5231, 52126}, {5441, 64263}, {5499, 9588}, {5557, 49736}, {5587, 13465}, {5735, 37433}, {6675, 63278}, {6841, 41691}, {8227, 22936}, {9579, 36922}, {9624, 28453}, {10032, 31254}, {10389, 13995}, {11246, 17527}, {11522, 13743}, {11544, 26725}, {11552, 64002}, {11604, 18514}, {12519, 14799}, {15677, 51105}, {16116, 16143}, {17365, 63376}, {17718, 63290}, {19872, 58449}, {25415, 33961}, {28558, 64072}, {35016, 63280}, {35989, 63288}, {41550, 59316}, {45632, 49177}, {49163, 49178}, {52860, 54145}, {54447, 61622}, {63974, 64295}, {64147, 64324}

X(64289) = midpoint of X(i) and X(j) for these {i,j}: {14450, 20084}
X(64289) = reflection of X(i) in X(j) for these {i,j}: {1, 14450}, {191, 79}, {3648, 11263}, {7701, 16159}, {12845, 49193}, {16143, 16116}, {31888, 10}, {41691, 6841}, {63280, 35016}, {64005, 16143}
X(64289) = pole of line {1019, 5957} with respect to the Bevan circle
X(64289) = pole of line {3946, 26842} with respect to the dual conic of Yff parabola
X(64289) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7110), X(10266)}}, {{A, B, C, X(8818), X(43732)}}
X(64289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {79, 17768, 191}, {7701, 16159, 1699}, {10266, 14450, 17483}, {33100, 63366, 1}

X(64290) = ISOGONAL CONJUGATE OF X(22765)

Barycentrics    (a^5+(b-c)^3*(b+c)^2-a^4*(3*b+c)+a^3*(2*b^2+3*b*c-2*c^2)+2*a^2*(b^3-3*b^2*c+b*c^2+c^3)+a*(-3*b^4+3*b^3*c+2*b^2*c^2-3*b*c^3+c^4))*(a^5-(b-c)^3*(b+c)^2-a^4*(b+3*c)+a^3*(-2*b^2+3*b*c+2*c^2)+2*a^2*(b^3+b^2*c-3*b*c^2+c^3)+a*(b^4-3*b^3*c+2*b^2*c^2+3*b*c^3-3*c^4)) : :
X(64290) = -3*X[11218]+2*X[25485], 2*X[15862]+X[49176]

X(64290) lies on the Feuerbach hyperbola and on these lines: {1, 6952}, {4, 17638}, {7, 17654}, {8, 6902}, {9, 64278}, {11, 1389}, {21, 952}, {30, 6595}, {65, 61105}, {79, 2800}, {84, 12248}, {100, 64275}, {104, 5172}, {515, 3065}, {517, 11604}, {519, 6596}, {523, 46041}, {758, 6599}, {943, 45081}, {944, 14795}, {1320, 1484}, {1537, 55924}, {2320, 7967}, {2475, 34353}, {2771, 10266}, {2801, 3255}, {2802, 6598}, {2829, 10308}, {3467, 9897}, {6224, 32613}, {6246, 17501}, {6597, 23016}, {6949, 64279}, {8674, 43728}, {8702, 14224}, {10057, 13375}, {10573, 21398}, {10698, 17097}, {11218, 25485}, {11219, 56036}, {12245, 43740}, {12531, 45393}, {12647, 15175}, {12736, 34485}, {12737, 56105}, {12764, 23959}, {13143, 41684}, {14497, 18391}, {15862, 49176}, {15863, 34918}, {16615, 59391}, {17636, 24298}, {18861, 64268}, {20418, 37518}, {30513, 59388}, {32635, 64140}, {55929, 64145}, {63335, 63365}, {63974, 64295}, {64147, 64324}

X(64290) = reflection of X(i) in X(j) for these {i,j}: {100, 64275}, {1389, 11}, {10698, 63257}
X(64290) = isogonal conjugate of X(22765)
X(64290) = X(i)-vertex conjugate of X(j) for these {i, j}: {4, 34442}
X(64290) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(28), X(6902)}}, {{A, B, C, X(29), X(6952)}}, {{A, B, C, X(54), X(34434)}}, {{A, B, C, X(65), X(37621)}}, {{A, B, C, X(74), X(517)}}, {{A, B, C, X(513), X(28219)}}, {{A, B, C, X(519), X(41558)}}, {{A, B, C, X(523), X(952)}}, {{A, B, C, X(528), X(28473)}}, {{A, B, C, X(900), X(5844)}}, {{A, B, C, X(959), X(13472)}}, {{A, B, C, X(996), X(60112)}}, {{A, B, C, X(1016), X(54739)}}, {{A, B, C, X(1173), X(46187)}}, {{A, B, C, X(1220), X(60173)}}, {{A, B, C, X(1411), X(62354)}}, {{A, B, C, X(2161), X(14987)}}, {{A, B, C, X(2771), X(8702)}}, {{A, B, C, X(2783), X(29298)}}, {{A, B, C, X(2800), X(35057)}}, {{A, B, C, X(2802), X(6003)}}, {{A, B, C, X(2829), X(56092)}}, {{A, B, C, X(2994), X(43757)}}, {{A, B, C, X(3431), X(41446)}}, {{A, B, C, X(3459), X(55036)}}, {{A, B, C, X(5397), X(42285)}}, {{A, B, C, X(5697), X(14804)}}, {{A, B, C, X(5903), X(14795)}}, {{A, B, C, X(6882), X(37168)}}, {{A, B, C, X(7612), X(9093)}}, {{A, B, C, X(9803), X(36921)}}, {{A, B, C, X(10265), X(40437)}}, {{A, B, C, X(12245), X(56876)}}, {{A, B, C, X(12247), X(51565)}}, {{A, B, C, X(12531), X(14266)}}, {{A, B, C, X(13576), X(53873)}}, {{A, B, C, X(15337), X(43078)}}, {{A, B, C, X(15381), X(38882)}}, {{A, B, C, X(19914), X(36944)}}, {{A, B, C, X(26707), X(47645)}}, {{A, B, C, X(46872), X(60158)}}, {{A, B, C, X(60157), X(63169)}}

X(64291) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-YFF AND 1ST ANTI-PAVLOV

Barycentrics    a^7+5*a^5*b*c-2*a^6*(b+c)+7*a^2*b*(b-c)^2*c*(b+c)-(b-c)^4*(b+c)^3+2*a*(b^2-c^2)^2*(b^2-b*c+c^2)-3*a^3*(b-c)^2*(b^2+3*b*c+c^2)+3*a^4*(b^3-2*b^2*c-2*b*c^2+c^3) : :
X(64291) = 2*X[4]+X[5559], -4*X[10]+3*X[5659], X[962]+2*X[15862], -3*X[3679]+4*X[64294]

X(64291) lies on these lines: {1, 6831}, {4, 5559}, {5, 11014}, {8, 6894}, {10, 5659}, {12, 64285}, {30, 34352}, {35, 64269}, {36, 64268}, {40, 64275}, {65, 64155}, {79, 2800}, {80, 946}, {153, 31871}, {355, 546}, {388, 15071}, {498, 64286}, {515, 3746}, {517, 37230}, {519, 52269}, {952, 16160}, {962, 15862}, {1478, 13375}, {1479, 64272}, {1482, 45630}, {1697, 5252}, {1709, 9613}, {1768, 18990}, {1837, 11522}, {2006, 33177}, {3419, 11531}, {3583, 45776}, {3584, 37837}, {3585, 10057}, {3586, 10059}, {3679, 64294}, {3881, 9803}, {3884, 6840}, {3899, 5812}, {4301, 5086}, {4317, 14647}, {4325, 64118}, {4915, 37714}, {5119, 64276}, {5176, 19925}, {5270, 6001}, {5288, 51755}, {5434, 33899}, {5537, 17647}, {5563, 11219}, {5587, 52050}, {5603, 37702}, {5690, 24468}, {5715, 25415}, {5787, 63287}, {5794, 7991}, {5805, 41687}, {5842, 37563}, {5855, 6598}, {5902, 10532}, {5903, 26332}, {6003, 15971}, {6261, 37719}, {6830, 37735}, {6833, 21842}, {6888, 51111}, {6906, 14795}, {7686, 41684}, {7741, 64274}, {7951, 63986}, {8727, 10944}, {9578, 63988}, {9856, 41698}, {10039, 44425}, {10058, 45287}, {10222, 49176}, {10265, 45977}, {10597, 50190}, {10738, 12751}, {10827, 63992}, {10894, 18393}, {10895, 64271}, {11010, 37468}, {11045, 30274}, {12247, 31870}, {12541, 59387}, {12625, 32049}, {13865, 61253}, {15064, 56880}, {15888, 33857}, {16173, 63963}, {17699, 49170}, {18395, 22753}, {18406, 64056}, {18525, 37622}, {20060, 31803}, {21740, 37731}, {24987, 35979}, {31397, 64298}, {37701, 40257}, {53616, 64192}, {63339, 64296}, {63974, 64295}, {64147, 64324}

X(64291) = reflection of X(i) in X(j) for these {i,j}: {1, 63257}, {40, 64275}, {1389, 946}, {59320, 24987}, {64279, 64273}, {64281, 64266}
X(64291) = pole of line {5691, 28217} with respect to the Fuhrmann circle
X(64291) = pole of line {64157, 64292} with respect to the Feuerbach hyperbola
X(64291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63257, 11218}, {1, 64265, 64292}, {355, 22791, 54154}, {3585, 12672, 34789}, {5563, 12616, 11219}

X(64292) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-YFF AND 1ST ANTI-PAVLOV

Barycentrics    a^10-3*a^9*(b+c)-(b-c)^6*(b+c)^4+a^8*(b^2+5*b*c+c^2)+a*(b-c)^4*(b+c)^3*(3*b^2-2*b*c+3*c^2)+2*a^5*b*c*(4*b^3-7*b^2*c-7*b*c^2+4*c^3)+a^7*(6*b^3-2*b^2*c-2*b*c^2+6*c^3)-a^2*(b^2-c^2)^2*(b^4-5*b^3*c+12*b^2*c^2-5*b*c^3+c^4)-a^6*(8*b^4+b^3*c-16*b^2*c^2+b*c^3+8*c^4)+a^4*(b-c)^2*(8*b^4+5*b^3*c-8*b^2*c^2+5*b*c^3+8*c^4)-2*a^3*(b-c)^2*(3*b^5+5*b^4*c-3*b^3*c^2-3*b^2*c^3+5*b*c^4+3*c^5) : :

X(64292) lies on these lines: {1, 6831}, {4, 18224}, {11, 64285}, {80, 10395}, {499, 64286}, {528, 6598}, {971, 17637}, {1478, 64272}, {1737, 64280}, {1837, 15299}, {2800, 16155}, {3419, 16208}, {3679, 64275}, {3893, 19914}, {5434, 5787}, {5659, 6734}, {5768, 11046}, {5790, 10267}, {6001, 16153}, {10039, 64173}, {10052, 15071}, {10573, 12116}, {10896, 64271}, {10902, 47033}, {11012, 11219}, {15104, 49168}, {18446, 64273}, {24299, 28204}, {37702, 48482}, {59342, 64276}, {63340, 64296}, {63974, 64295}, {64147, 64324}

X(64292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 64265, 64291}

X(64293) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ZANIAH AND 1ST ANTI-PAVLOV

Barycentrics    2*a^10-6*a^9*(b+c)-6*a*b*(b-c)^4*c*(b+c)^3+(b-c)^6*(b+c)^4-a^8*(b^2-24*b*c+c^2)+2*a^7*(9*b^3-10*b^2*c-10*b*c^2+9*c^3)-2*a^5*(b-c)^2*(9*b^3-8*b^2*c-8*b*c^2+9*c^3)-2*a^2*(b^2-c^2)^2*(4*b^4-13*b^3*c+14*b^2*c^2-13*b*c^3+4*c^4)-2*a^6*(5*b^4+13*b^3*c-24*b^2*c^2+13*b*c^3+5*c^4)+2*a^4*(b-c)^2*(8*b^4+5*b^3*c-14*b^2*c^2+5*b*c^3+8*c^4)+2*a^3*(b-c)^2*(3*b^5-4*b^4*c+13*b^3*c^2+13*b^2*c^3-4*b*c^4+3*c^5) : :
X(64293) = -5*X[3616]+X[64298]

X(64293) lies on these lines: {1, 6831}, {7, 12114}, {56, 11023}, {142, 1385}, {404, 11024}, {515, 11281}, {1389, 10785}, {2829, 33593}, {3427, 56030}, {3616, 64298}, {4999, 5836}, {5572, 13464}, {5901, 64272}, {6001, 10122}, {6261, 42356}, {6839, 51683}, {6972, 64081}, {12736, 20418}, {14110, 59491}, {15528, 58588}, {18242, 31266}, {22770, 38454}, {37615, 64285}, {63974, 64295}, {64147, 64324}

X(64293) = midpoint of X(i) and X(j) for these {i,j}: {63257, 64281}, {64265, 64283}

X(64294) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ZANIAH AND 1ST ANTI-PAVLOV

Barycentrics    2*a^7-6*a^6*(b+c)+14*a^2*b*(b-c)^2*c*(b+c)-3*(b-c)^4*(b+c)^3+a^5*(3*b^2+16*b*c+3*c^2)+a*(b^2-c^2)^2*(7*b^2-6*b*c+7*c^2)+a^4*(9*b^3-11*b^2*c-11*b*c^2+9*c^3)-2*a^3*(6*b^4+5*b^3*c-10*b^2*c^2+5*b*c^3+6*c^4) : :
X(64294) = 3*X[2]+X[64270], X[3632]+3*X[11218], 3*X[3679]+X[64291]

X(64294) lies on these lines: {2, 64270}, {3, 18231}, {5, 8}, {9, 355}, {10, 37837}, {30, 18259}, {405, 59388}, {515, 18253}, {517, 15911}, {518, 64284}, {936, 64281}, {952, 6675}, {958, 64269}, {960, 58636}, {1125, 64282}, {1158, 5794}, {1329, 64274}, {1376, 64268}, {1385, 64297}, {1837, 31393}, {2346, 43734}, {2886, 64273}, {3036, 38758}, {3149, 3617}, {3577, 61261}, {3626, 7686}, {3632, 11218}, {3679, 64291}, {4678, 6835}, {5428, 28224}, {5559, 10826}, {5690, 20420}, {5705, 64287}, {5720, 64285}, {5837, 64272}, {5901, 41575}, {6861, 12645}, {6907, 45039}, {8580, 64288}, {9623, 45770}, {9956, 11545}, {10395, 31397}, {11362, 38454}, {12019, 15558}, {15587, 31788}, {15862, 21616}, {18254, 58631}, {19860, 38042}, {37724, 63287}, {38149, 44229}, {57284, 64193}, {63974, 64295}, {64147, 64324}, {64318, 64335}

X(64294) = midpoint of X(i) and X(j) for these {i,j}: {8, 63257}, {355, 64275}, {64270, 64283}
X(64294) = reflection of X(i) in X(j) for these {i,j}: {64282, 1125}
X(64294) = complement of X(64283)
X(64294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64270, 64283}, {8, 63257, 5844}, {5730, 5818, 5}, {5780, 5790, 5818}

X(64295) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(83)

Barycentrics    a^2*(a^2+2*b^2+2*a*c+c^2)*(a^2+2*a*b+b^2+2*c^2) : :

X(64295) lies on these lines: {35, 595}, {44, 3219}, {83, 17495}, {1404, 2003}, {2985, 45222}, {3285, 40153}, {14829, 29833}, {16704, 16705}, {17366, 24624}, {32779, 62620}, {40215, 60809}

X(64295) = trilinear pole of line {1960, 2605}
X(64295) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 17369}, {6, 4692}, {9, 5434}
X(64295) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 17369}, {9, 4692}, {478, 5434}
X(64295) = X(i)-cross conjugate of X(j) for these {i, j}: {5109, 1}
X(64295) = X(i)-cross conjugate of X(j) for these {i, j}: {5109, 1}
X(64295) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5315)}}, {{A, B, C, X(2), X(56)}}, {{A, B, C, X(6), X(44)}}, {{A, B, C, X(27), X(14829)}}, {{A, B, C, X(31), X(3108)}}, {{A, B, C, X(35), X(57)}}, {{A, B, C, X(55), X(39955)}}, {{A, B, C, X(58), X(88)}}, {{A, B, C, X(81), X(83)}}, {{A, B, C, X(106), X(40434)}}, {{A, B, C, X(111), X(40746)}}, {{A, B, C, X(222), X(30680)}}, {{A, B, C, X(251), X(893)}}, {{A, B, C, X(264), X(45746)}}, {{A, B, C, X(292), X(39389)}}, {{A, B, C, X(386), X(29833)}}, {{A, B, C, X(513), X(60258)}}, {{A, B, C, X(603), X(14919)}}, {{A, B, C, X(967), X(26745)}}, {{A, B, C, X(1014), X(57881)}}, {{A, B, C, X(1029), X(46331)}}, {{A, B, C, X(1219), X(16466)}}, {{A, B, C, X(1245), X(39724)}}, {{A, B, C, X(1255), X(1412)}}, {{A, B, C, X(1407), X(25417)}}, {{A, B, C, X(1432), X(18359)}}, {{A, B, C, X(1797), X(57658)}}, {{A, B, C, X(2163), X(39963)}}, {{A, B, C, X(2999), X(56354)}}, {{A, B, C, X(3112), X(7303)}}, {{A, B, C, X(3218), X(3449)}}, {{A, B, C, X(3478), X(56075)}}, {{A, B, C, X(3752), X(33168)}}, {{A, B, C, X(4850), X(32779)}}, {{A, B, C, X(5109), X(17369)}}, {{A, B, C, X(5256), X(17016)}}, {{A, B, C, X(5337), X(62739)}}, {{A, B, C, X(7304), X(38830)}}, {{A, B, C, X(7316), X(14621)}}, {{A, B, C, X(8700), X(60665)}}, {{A, B, C, X(10623), X(42467)}}, {{A, B, C, X(17191), X(40215)}}, {{A, B, C, X(17495), X(61406)}}, {{A, B, C, X(17946), X(60097)}}, {{A, B, C, X(17961), X(45785)}}, {{A, B, C, X(20332), X(55942)}}, {{A, B, C, X(21739), X(57666)}}, {{A, B, C, X(24471), X(52442)}}, {{A, B, C, X(28513), X(39962)}}, {{A, B, C, X(30651), X(39951)}}, {{A, B, C, X(34434), X(59265)}}, {{A, B, C, X(37128), X(39706)}}, {{A, B, C, X(39747), X(57749)}}, {{A, B, C, X(39961), X(57656)}}, {{A, B, C, X(41436), X(56039)}}, {{A, B, C, X(53083), X(57721)}}, {{A, B, C, X(60191), X(63750)}}

X(64296) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND PAVLOV AND 1ST ANTI-PAVLOV

Barycentrics    2*a^10-3*a^9*(b+c)-(b-c)^6*(b+c)^4+a^8*(-3*b^2+8*b*c-3*c^2)+2*a^2*b*c*(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)+a*(b-c)^4*(b+c)^3*(3*b^2-b*c+3*c^2)+a^7*(6*b^3-7*b^2*c-7*b*c^2+6*c^3)+a^5*b*c*(19*b^3-15*b^2*c-15*b*c^2+19*c^3)-2*a^6*(b^4+3*b^3*c-14*b^2*c^2+3*b*c^3+c^4)+2*a^4*(b-c)^2*(2*b^4-b^3*c-10*b^2*c^2-b*c^3+2*c^4)-a^3*(b-c)^2*(6*b^5+17*b^4*c+b^3*c^2+b^2*c^3+17*b*c^4+6*c^5) : :

X(64296) lies on these lines: {1, 4}, {81, 64265}, {6001, 63366}, {10265, 55101}, {17056, 64286}, {63257, 63446}, {63292, 64266}, {63317, 64271}, {63318, 64272}, {63319, 64280}, {63323, 64285}, {63333, 64287}, {63339, 64291}, {63340, 64292}, {63974, 64295}, {64147, 64324}

X(64297) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(55) AND 1ST ANTI-PAVLOV

Barycentrics    a*(2*a^4-a^2*(b-c)^2-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)-(b^2-c^2)^2)*(a^4+a^2*b*c-2*a^3*(b+c)-(b-c)^2*(b^2+b*c+c^2)+2*a*(b^3+c^3)) : :

X(64297) lies on these lines: {1, 64298}, {8, 5659}, {515, 10543}, {516, 41571}, {944, 56027}, {971, 41546}, {1385, 64294}, {1697, 7971}, {2346, 3062}, {3870, 41338}, {5531, 58699}, {6003, 42758}, {10578, 11218}, {11531, 62822}, {15931, 60970}, {18389, 37550}, {33597, 64163}, {37525, 64321}, {37837, 64282}, {38454, 41570}, {41575, 51717}, {44425, 58626}, {47387, 61030}, {63974, 64295}, {64147, 64324}

X(64297) = midpoint of X(i) and X(j) for these {i,j}: {18446, 64173}
X(64297) = X(i)-Dao conjugate of X(j) for these {i, j}: {64286, 15909}
X(64297) = barycentric product X(i)*X(j) for these (i, j): {60970, 64163}
X(64297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33597, 64283, 64286}

X(64298) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(9)-CIRCUMCONCEVIAN-OF-X(8) AND 1ST ANTI-PAVLOV

Barycentrics    a*(a^9-2*a^8*(b+c)+3*b*(b-c)^4*c*(b+c)^3+a^5*b*c*(b^2-6*b*c+c^2)-a^7*(2*b^2+3*b*c+2*c^2)+a^2*(b-c)^4*(2*b^3+9*b^2*c+9*b*c^2+2*c^3)+a^6*(6*b^3+11*b^2*c+11*b*c^2+6*c^3)-a*(b^2-c^2)^2*(b^4+5*b^3*c-4*b^2*c^2+5*b*c^3+c^4)+a^3*(b-c)^2*(2*b^4+11*b^3*c+22*b^2*c^2+11*b*c^3+2*c^4)-a^4*(6*b^5+13*b^4*c-7*b^3*c^2-7*b^2*c^3+13*b*c^4+6*c^5)) : :
X(64298) = -5*X[3616]+4*X[64293]

X(64298) lies on these lines: {1, 64297}, {3, 18231}, {4, 390}, {8, 411}, {20, 12330}, {21, 515}, {40, 9960}, {56, 64321}, {78, 64316}, {1389, 17097}, {1490, 3869}, {1621, 64261}, {2476, 64148}, {3149, 64283}, {3577, 56030}, {3616, 64293}, {3870, 3885}, {3871, 59355}, {3913, 38454}, {5842, 52841}, {5844, 6985}, {6001, 33557}, {6223, 63975}, {6796, 64268}, {6825, 18518}, {6828, 64266}, {6866, 16202}, {6909, 45392}, {6915, 37837}, {7098, 12680}, {7548, 18242}, {9623, 64288}, {9819, 63988}, {12514, 63981}, {12671, 56288}, {19860, 52026}, {22753, 64282}, {26332, 62800}, {31397, 64291}, {41575, 64287}, {44425, 64163}, {48482, 64273}, {63974, 64295}, {64144, 64275}, {64147, 64324}, {64201, 64319}

X(64298) = midpoint of X(i) and X(j) for these {i,j}: {1490, 64276}
X(64298) = reflection of X(i) in X(j) for these {i,j}: {1389, 64285}, {48482, 64273}, {64261, 64272}, {64268, 6796}, {64280, 11500}, {64281, 64286}
X(64298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {52026, 64281, 64286}, {63257, 64173, 2346}

X(64299) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-ARTZT AND ANTI-AGUILERA-PAVLOV

Barycentrics    5*a^3-4*b^3+2*b^2*c+2*b*c^2-4*c^3-4*a^2*(b+c)-a*(b^2+c^2) : :
X(64299) = -4*X[551]+5*X[17304], -4*X[3821]+3*X[25055], -2*X[3923]+3*X[19875], -4*X[4655]+X[49451], -2*X[17351]+3*X[38087], -3*X[21358]+2*X[49484], -3*X[38314]+2*X[63969], -3*X[49747]+X[50790], -6*X[50081]+7*X[50785]

X(64299) lies on circumconic {{A, B, C, X(41895), X(55937)}} and on these lines: {1, 24692}, {2, 165}, {8, 17132}, {10, 41895}, {40, 17677}, {148, 1654}, {517, 60929}, {519, 11160}, {524, 49495}, {528, 17274}, {536, 50783}, {551, 17304}, {597, 64016}, {599, 3886}, {726, 4677}, {740, 50950}, {752, 16834}, {1992, 3755}, {2177, 31177}, {2550, 50093}, {3241, 3663}, {3416, 50089}, {3751, 28558}, {3821, 25055}, {3875, 28538}, {3877, 9519}, {3923, 19875}, {4201, 9589}, {4312, 50128}, {4346, 49771}, {4384, 24715}, {4450, 50102}, {4645, 29573}, {4655, 49451}, {4669, 28526}, {4933, 31134}, {5250, 17679}, {5853, 50999}, {5880, 49740}, {6173, 49746}, {9041, 17276}, {9580, 33068}, {10444, 17579}, {11159, 28897}, {11354, 28202}, {11359, 28198}, {11679, 33094}, {13587, 63968}, {15533, 28581}, {15534, 28570}, {16475, 28494}, {16831, 50299}, {17294, 28580}, {17351, 38087}, {17549, 24309}, {17601, 27759}, {17738, 50126}, {17766, 51093}, {17768, 47359}, {17770, 50952}, {18252, 31165}, {19860, 50165}, {21358, 49484}, {21937, 48900}, {24280, 50118}, {24710, 54309}, {24723, 49720}, {24728, 34628}, {24807, 28877}, {26227, 53372}, {28194, 48813}, {28503, 50789}, {28530, 50949}, {28534, 48829}, {28546, 50953}, {28550, 51066}, {28566, 51000}, {29574, 64168}, {29597, 50301}, {29617, 62392}, {30567, 33095}, {30568, 32948}, {31143, 63131}, {32850, 49748}, {33869, 50310}, {34747, 49455}, {35227, 48629}, {35955, 64301}, {38314, 63969}, {48830, 50307}, {48849, 50119}, {49543, 51001}, {49741, 50130}, {49747, 50790}, {50075, 51102}, {50081, 50785}, {50087, 50782}, {50091, 50303}, {50109, 51192}, {50316, 50787}, {50533, 62695}, {51055, 60963}, {51678, 64005}, {63127, 64017}, {63974, 64295}, {64147, 64324}

X(64299) = reflection of X(i) in X(j) for these {i,j}: {2, 49630}, {1992, 3755}, {3241, 3663}, {3679, 4660}, {3729, 3679}, {3886, 599}, {16834, 50080}, {24280, 50118}, {31165, 18252}, {34628, 24728}, {34747, 49455}, {50089, 3416}, {50127, 48829}, {50130, 49741}, {50303, 50091}, {51001, 49543}, {51192, 50109}, {64016, 597}
X(64299) = pole of line {28565, 54261} with respect to the incircle
X(64299) = pole of line {4120, 47757} with respect to the Steiner circumellipse
X(64299) = pole of line {5222, 50128} with respect to the dual conic of Yff parabola
X(64299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 49630, 2}, {752, 50080, 16834}, {2796, 3679, 3729}, {2796, 4660, 3679}, {24280, 53620, 50118}, {28534, 48829, 50127}

X(64300) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-AGUILERA-PAVLOV AND ASCELLA

Barycentrics    2*a*(-b^2-c^2+a*(b+c))+(a+b+c)*S : :

X(64300) lies on circumconic {{A, B, C, X(27475), X(63689)}} and on these lines: {1, 7585}, {2, 210}, {8, 176}, {10, 30341}, {145, 45714}, {519, 52809}, {1267, 49450}, {1386, 63015}, {1991, 9053}, {3068, 3242}, {3069, 64070}, {3100, 46421}, {3241, 13639}, {3616, 3640}, {3621, 45720}, {3622, 45713}, {3623, 45719}, {3751, 7586}, {4663, 63016}, {5223, 30412}, {5391, 49499}, {5591, 49524}, {5604, 8975}, {5605, 19066}, {5846, 5861}, {6351, 49515}, {6352, 49478}, {7374, 39898}, {7968, 61323}, {8972, 16496}, {16475, 63059}, {19054, 38315}, {24349, 32794}, {30333, 31547}, {36553, 49706}, {49465, 63023}, {63974, 64295}, {64147, 64324}

X(64301) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND ANTI-AGUILERA-PAVLOV

Barycentrics    3*a^5+6*a^4*(b+c)-2*b*(b-c)^2*c*(b+c)-a*(b^2-c^2)^2-6*a^3*(b^2+c^2)-2*a^2*(b^3+2*b^2*c+2*b*c^2+c^3) : :
X(64301) = -3*X[2]+2*X[64303], -5*X[3522]+X[64308], -3*X[3524]+2*X[49631], -5*X[7987]+2*X[48900], -4*X[13624]+X[48944]

X(64301) lies on these lines: {1, 1434}, {2, 64303}, {3, 9305}, {4, 64302}, {20, 44431}, {40, 7709}, {56, 64306}, {99, 3886}, {165, 16833}, {376, 516}, {515, 48802}, {519, 9741}, {726, 32474}, {993, 4221}, {1125, 54668}, {1285, 64017}, {1499, 30580}, {1742, 22676}, {2784, 50811}, {2938, 3875}, {3522, 64308}, {3524, 49631}, {3534, 28897}, {3941, 11495}, {4297, 15428}, {4512, 35935}, {5250, 35915}, {5263, 40840}, {5731, 28849}, {7415, 50302}, {7987, 48900}, {8703, 28915}, {8716, 28581}, {8719, 37620}, {9778, 11200}, {12512, 35658}, {13624, 48944}, {28160, 53018}, {28881, 51705}, {31859, 49495}, {35955, 64299}, {39586, 49130}, {63402, 64084}, {63974, 64295}, {64147, 64324}

X(64301) = midpoint of X(i) and X(j) for these {i,j}: {1, 64304}, {20, 44431}, {9778, 11200}
X(64301) = reflection of X(i) in X(j) for these {i,j}: {4, 64302}, {9746, 3}, {54668, 1125}
X(64301) = inverse of X(3886) in Wallace hyperbola
X(64301) = anticomplement of X(64303)
X(64301) = X(i)-Dao conjugate of X(j) for these {i, j}: {64303, 64303}
X(64301) = pole of line {693, 24622} with respect to the orthoptic circle of the Steiner Inellipse

X(64302) = COMPLEMENT OF X(9746)

Barycentrics    3*a^4*(b+c)+2*a*(b^2-c^2)^2-6*a^3*(b^2+c^2)-2*a^2*(b^3+2*b^2*c+2*b*c^2+c^3)+(b-c)^2*(3*b^3+7*b^2*c+7*b*c^2+3*c^3) : :
X(64302) = -5*X[8227]+X[64305], -X[48944]+7*X[61268]

X(64302) lies on these lines: {1, 9742}, {2, 165}, {4, 64301}, {5, 64303}, {10, 262}, {11, 64306}, {226, 64307}, {511, 50158}, {517, 48853}, {519, 9770}, {547, 28915}, {549, 28897}, {551, 2784}, {726, 9764}, {740, 24386}, {946, 39580}, {1007, 3886}, {1125, 7710}, {1447, 30424}, {1513, 25354}, {2796, 9877}, {3424, 56226}, {3634, 35663}, {3663, 5988}, {3667, 25381}, {3755, 3815}, {3816, 50290}, {3821, 9743}, {3923, 40926}, {4297, 7379}, {4356, 24239}, {5542, 7179}, {5587, 10186}, {5731, 53018}, {5886, 28849}, {6998, 48925}, {7407, 19925}, {7410, 41869}, {7735, 64017}, {8227, 64305}, {9748, 63978}, {9751, 19862}, {9755, 33682}, {9756, 50302}, {9765, 17766}, {9774, 19883}, {10165, 28845}, {10175, 28850}, {13468, 28570}, {13634, 59420}, {22664, 49482}, {28236, 48854}, {28901, 38028}, {28913, 61270}, {30827, 50295}, {37637, 64016}, {38155, 50291}, {40131, 60911}, {44377, 49484}, {48944, 61268}, {49495, 62988}, {63974, 64295}, {64147, 64324}

X(64302) = midpoint of X(i) and X(j) for these {i,j}: {4, 64301}, {5587, 10186}, {5731, 53018}, {9746, 44431}
X(64302) = reflection of X(i) in X(j) for these {i,j}: {49631, 2}, {64303, 5}
X(64302) = complement of X(9746)
X(64302) = pole of line {4785, 4913} with respect to the excircles-radical circle
X(64302) = pole of line {239, 514} with respect to the orthoptic circle of the Steiner Inellipse
X(64302) = pole of line {5222, 7735} with respect to the dual conic of Yff parabola
X(64302) = intersection, other than A, B, C, of circumconics {{A, B, C, X(262), X(55937)}}, {{A, B, C, X(18025), X(49631)}}
X(64302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 44431, 9746}, {2, 516, 49631}, {7380, 39605, 10}, {7407, 39586, 19925}, {9746, 44431, 516}

X(64303) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH EULER AND ANTI-AGUILERA-PAVLOV

Barycentrics    (b+c)*(-3*a^4+4*a*(b-c)^2*(b+c)+a^2*(-4*b^2+2*b*c-4*c^2)+(b-c)^2*(3*b^2+8*b*c+3*c^2)) : :
X(64303) = -3*X[2]+X[64301], -5*X[1698]+X[64304], -5*X[3091]+X[44431], 7*X[3832]+X[64308], -3*X[7988]+X[10186], 2*X[19925]+X[48900], X[31673]+2*X[48932], X[48944]+5*X[61261], X[53014]+3*X[54448]

X(64303) lies on these lines: {2, 64301}, {4, 9746}, {5, 64302}, {10, 17747}, {12, 64306}, {30, 49631}, {115, 3755}, {381, 516}, {515, 48822}, {519, 40727}, {946, 7697}, {1210, 64307}, {1698, 64304}, {2784, 11632}, {3091, 44431}, {3817, 28850}, {3822, 30444}, {3832, 64308}, {3845, 28897}, {4078, 21090}, {4429, 40840}, {5066, 28915}, {5587, 28849}, {6684, 36675}, {7988, 10186}, {10164, 36728}, {12571, 35664}, {15484, 64017}, {19925, 48900}, {22682, 45305}, {28845, 36722}, {28854, 38076}, {28870, 38155}, {28913, 61260}, {31673, 48932}, {36677, 39605}, {36687, 44430}, {37350, 49630}, {48944, 61261}, {53014, 54448}, {59261, 60634}, {63974, 64295}, {64147, 64324}

X(64303) = midpoint of X(i) and X(j) for these {i,j}: {4, 9746}, {10, 54668}
X(64303) = reflection of X(i) in X(j) for these {i,j}: {64302, 5}
X(64303) = inverse of X(3755) in Kiepert hyperbola
X(64303) = complement of X(64301)
X(64303) = pole of line {6590, 11068} with respect to the orthoptic circle of the Steiner Inellipse
X(64303) = pole of line {30792, 61673} with respect to the dual conic of Wallace hyperbola

X(64304) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTRAL AND ANTI-AGUILERA-PAVLOV

Barycentrics    3*a^5+12*a^4*(b+c)-4*b*(b-c)^2*c*(b+c)-5*a*(b^2-c^2)^2-6*a^3*(b^2+c^2)-4*a^2*(b^3+2*b^2*c+2*b*c^2+c^3) : :
X(64304) = -5*X[1698]+4*X[64303], -5*X[7987]+8*X[48925], -7*X[16192]+4*X[48900], -5*X[35242]+2*X[48944]

X(64304) lies on the Wallace hyperbola and on these lines: {1, 1434}, {2, 165}, {3, 64305}, {20, 61151}, {40, 16552}, {57, 64306}, {63, 2941}, {194, 7991}, {376, 28881}, {519, 11148}, {1499, 62634}, {1621, 41930}, {1698, 64303}, {1764, 10860}, {2784, 8591}, {2938, 25590}, {2951, 58035}, {4061, 17784}, {4356, 21454}, {5493, 8915}, {7987, 48925}, {10167, 10439}, {10434, 37078}, {11200, 28228}, {12565, 52676}, {16192, 48900}, {17147, 62823}, {20368, 46946}, {28850, 63468}, {35242, 48944}, {40840, 50314}, {63974, 64295}, {64147, 64324}

X(64304) = reflection of X(i) in X(j) for these {i,j}: {1, 64301}, {64305, 3}
X(64304) = anticomplement of X(54668)
X(64304) = X(i)-Dao conjugate of X(j) for these {i, j}: {42290, 62784}, {54668, 54668}
X(64304) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3886, 1}
X(64304) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {5223, 1330}, {29616, 21287}, {42316, 2895}, {59215, 2893}
X(64304) = pole of line {28840, 48037} with respect to the Conway circle
X(64304) = pole of line {28840, 54261} with respect to the incircle
X(64304) = pole of line {514, 30765} with respect to the orthoptic circle of the Steiner Inellipse
X(64304) = pole of line {3886, 64304} with respect to the Wallace hyperbola

X(64305) = ORTHOLOGY CENTER OF THESE TRIANGLES: HEXYL AND ANTI-AGUILERA-PAVLOV

Barycentrics    3*a^5-6*a^4*(b+c)-2*a^2*(b-c)^2*(b+c)+4*b*(b-c)^2*c*(b+c)+5*a*(b^2-c^2)^2 : :
X(64305) = -5*X[8227]+4*X[64302], -5*X[35242]+8*X[48932]

X(64305) lies on these lines: {1, 4059}, {2, 28881}, {3, 64304}, {4, 1886}, {40, 6998}, {376, 516}, {515, 53014}, {885, 3577}, {946, 16020}, {962, 64308}, {1565, 4312}, {1699, 33132}, {2784, 12243}, {2795, 51121}, {3333, 64307}, {3424, 60634}, {3656, 28915}, {4295, 41403}, {4301, 35667}, {4307, 63993}, {5480, 38386}, {5587, 28849}, {5805, 52826}, {7290, 17761}, {7982, 12251}, {7988, 28913}, {8227, 64302}, {11372, 58036}, {14651, 54657}, {16200, 28850}, {19288, 31435}, {26446, 28905}, {28854, 38021}, {28858, 54447}, {28877, 53018}, {28897, 50865}, {35242, 48932}, {50898, 60963}, {54933, 56144}, {63974, 64295}, {63982, 63992}, {64110, 64168}, {64147, 64324}

X(64305) = midpoint of X(i) and X(j) for these {i,j}: {962, 64308}
X(64305) = reflection of X(i) in X(j) for these {i,j}: {4, 54668}, {40, 9746}, {9746, 48900}, {44431, 946}, {64304, 3}
X(64305) = pole of line {661, 3676} with respect to the orthoptic circle of the Steiner Inellipse

X(64306) = ORTHOLOGY CENTER OF THESE TRIANGLES: INTOUCH AND ANTI-AGUILERA-PAVLOV

Barycentrics    (b+c)*(-a^2+2*b*c+a*(b+c))*(3*a^2+(b-c)^2) : :

X(64306) lies on these lines: {1, 4059}, {11, 64302}, {12, 64303}, {37, 13576}, {55, 9746}, {56, 64301}, {57, 64304}, {210, 740}, {226, 4356}, {354, 516}, {390, 3598}, {497, 3666}, {1699, 17592}, {3021, 30331}, {3475, 50068}, {3696, 59207}, {3925, 50290}, {3930, 49462}, {3931, 20616}, {4037, 49468}, {4307, 4883}, {4387, 7308}, {4423, 50314}, {4863, 50295}, {4995, 49631}, {5919, 28850}, {12575, 35671}, {15170, 28915}, {15569, 30949}, {30946, 49470}, {37080, 48900}, {41539, 56326}, {63974, 64295}, {64147, 64324}

X(64306) = X(i)-isoconjugate-of-X(j) for these {i, j}: {39959, 51443}
X(64306) = pole of line {4702, 4724} with respect to the incircle
X(64306) = pole of line {1469, 5542} with respect to the Feuerbach hyperbola
X(64306) = pole of line {4693, 4762} with respect to the Suppa-Cucoanes circle
X(64306) = intersection, other than A, B, C, of circumconics {{A, B, C, X(390), X(42289)}}, {{A, B, C, X(3424), X(37658)}}, {{A, B, C, X(3598), X(59207)}}, {{A, B, C, X(3696), X(3755)}}, {{A, B, C, X(28809), X(43951)}}
X(64306) = barycentric product X(i)*X(j) for these (i, j): {3696, 5222}, {3755, 4384}, {4044, 7290}, {30854, 42289}, {59207, 62697}
X(64306) = barycentric quotient X(i)/X(j) for these (i, j): {3696, 39749}, {3755, 27475}, {7290, 42302}, {42289, 21446}, {59207, 39959}

X(64307) = ORTHOLOGY CENTER OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND ANTI-AGUILERA-PAVLOV

Barycentrics    6*a^3*b*c+3*a^4*(b+c)-b*(b-c)^2*c*(b+c)-2*a*(b^2-c^2)^2-a^2*(b^3-4*b^2*c-4*b*c^2+c^3) : :

X(64307) lies on these lines: {1, 1434}, {7, 43751}, {57, 9746}, {63, 4697}, {226, 64302}, {354, 516}, {740, 3873}, {982, 4307}, {1210, 64303}, {1621, 40592}, {2784, 5434}, {3333, 64305}, {3338, 48900}, {3666, 4349}, {4312, 62697}, {4356, 4883}, {4512, 10180}, {4645, 24631}, {4974, 24596}, {5018, 33765}, {5902, 28850}, {9776, 50295}, {9778, 17592}, {11019, 54668}, {17784, 50284}, {24628, 52133}, {27475, 52155}, {32636, 48932}, {37080, 48925}, {49563, 50307}, {50281, 62815}, {50314, 62823}, {63974, 64295}, {64147, 64324}

X(64307) = pole of line {4724, 4817} with respect to the incircle

X(64308) = ORTHOLOGY CENTER OF THESE TRIANGLES: CEVIAN-OF-X(75) AND ANTI-AGUILERA-PAVLOV

Barycentrics    (3*a^2+(b-c)^2)*(3*a^3-3*b^3-b^2*c-b*c^2-3*c^3-a^2*(b+c)+a*(b+c)^2) : :
X(64308) = -5*X[3522]+4*X[64301], -7*X[3832]+8*X[64303], -13*X[46934]+16*X[48932]

X(64308) lies on these lines: {2, 165}, {10, 60327}, {20, 20880}, {40, 39570}, {105, 11495}, {144, 4073}, {145, 33890}, {321, 3198}, {376, 28915}, {390, 3598}, {962, 64305}, {982, 4307}, {1447, 30332}, {1503, 3578}, {2292, 20070}, {2784, 31145}, {3522, 64301}, {3543, 28897}, {3617, 17741}, {3667, 53583}, {3749, 64168}, {3755, 63005}, {3832, 64303}, {4297, 39567}, {4373, 24728}, {5749, 43951}, {6361, 7390}, {7710, 51583}, {11200, 28885}, {12512, 16020}, {18788, 29621}, {20097, 43161}, {20344, 35514}, {21129, 28296}, {28158, 48851}, {28164, 48849}, {28228, 48856}, {28292, 53045}, {28866, 54448}, {28881, 34632}, {37665, 64016}, {39581, 64005}, {46934, 48932}, {56776, 64077}, {56777, 64074}, {63974, 64295}, {64147, 64324}

X(64308) = reflection of X(i) in X(j) for these {i,j}: {962, 64305}, {44431, 9746}
X(64308) = anticomplement of X(44431)
X(64308) = X(i)-Dao conjugate of X(j) for these {i, j}: {7290, 1}, {44431, 44431}
X(64308) = X(i)-Ceva conjugate of X(j) for these {i, j}: {75, 5222}
X(64308) = pole of line {514, 4521} with respect to the orthoptic circle of the Steiner Inellipse
X(64308) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3424), X(3598)}}, {{A, B, C, X(5222), X(43951)}}, {{A, B, C, X(55937), X(60327)}}
X(64308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 9746, 44431}, {9746, 44431, 2}

X(64309) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: ANTI-AGUILERA AND ASCELLA

Barycentrics    a*(-2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c))-a*(a-b-c)*S : :

X(64309) lies on these lines: {1, 371}, {3, 51955}, {8, 31562}, {9, 374}, {10, 36690}, {40, 30556}, {102, 6136}, {175, 31540}, {221, 1124}, {515, 64336}, {934, 52419}, {946, 14121}, {962, 31561}, {1699, 44038}, {1743, 35774}, {1766, 31438}, {2093, 6203}, {3428, 60848}, {4252, 7968}, {4301, 31594}, {6213, 7991}, {7090, 11362}, {7955, 34494}, {7982, 30557}, {8957, 12053}, {12702, 51957}, {16469, 45500}, {28234, 64314}, {30324, 31397}, {30412, 59417}, {31547, 31552}, {63974, 64295}, {64147, 64324}

X(64309) = intersection, other than A, B, C, of circumconics {{A, B, C, X(102), X(2067)}}, {{A, B, C, X(3577), X(16232)}}, {{A, B, C, X(14121), X(32556)}}, {{A, B, C, X(48308), X(60849)}}
X(64309) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6212, 32556}, {40, 30556, 32555}

X(64310) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: ASCELLA AND ANTI-AGUILERA

Barycentrics    4*a^10-11*a^9*(b+c)-(b-c)^6*(b+c)^4-a^8*(b^2-10*b*c+c^2)+a*(b-c)^4*(b+c)^3*(5*b^2-2*b*c+5*c^2)-4*a^3*(b-c)^4*(b^3+4*b^2*c+4*b*c^2+c^3)+4*a^7*(7*b^3+2*b^2*c+2*b*c^2+7*c^3)-8*a^2*(b^2-c^2)^2*(b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)-4*a^6*(5*b^4-6*b^2*c^2+5*c^4)+2*a^4*(b-c)^2*(13*b^4+12*b^3*c+6*b^2*c^2+12*b*c^3+13*c^4)-2*a^5*(9*b^5-5*b^4*c+12*b^3*c^2+12*b^2*c^3-5*b*c^4+9*c^5) : :

X(64310) lies on these lines: {3, 5837}, {57, 64147}, {142, 515}, {519, 8730}, {942, 4315}, {944, 1467}, {1319, 64327}, {1490, 5084}, {1656, 5787}, {2095, 36867}, {2800, 63413}, {3244, 12439}, {3306, 54051}, {3427, 3576}, {3577, 50701}, {3601, 64322}, {3911, 5768}, {4297, 9942}, {5709, 12437}, {5732, 56273}, {5744, 64313}, {5745, 64335}, {6245, 6675}, {6260, 6928}, {6796, 24391}, {6987, 61002}, {7966, 63987}, {8726, 64320}, {8732, 64321}, {11018, 64325}, {12444, 12608}, {17603, 64332}, {17612, 64331}, {18481, 64326}, {37230, 55108}, {63974, 64295}

X(64310) = midpoint of X(i) and X(j) for these {i,j}: {944, 64319}, {18481, 64326}, {64147, 64316}, {64316, 64324}
X(64310) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {64147, 64316, 64324}

X(64311) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: 1ST CIRCUMPERP AND ANTI-AGUILERA

Barycentrics    a*(a^9-2*a^8*(b+c)+6*a^5*b*c*(b+c)^2-2*b*(b-c)^4*c*(b+c)^3+2*a^3*(b^2-c^2)^2*(b^2-9*b*c+c^2)-2*a^7*(b^2-b*c+c^2)+a^6*(6*b^3-4*b^2*c-4*b*c^2+6*c^3)-a*(b^2-c^2)^2*(b^4-10*b^3*c+10*b^2*c^2-10*b*c^3+c^4)+2*a^2*(b-c)^2*(b^5+11*b^3*c^2+11*b^2*c^3+c^5)-2*a^4*(3*b^5-6*b^4*c+11*b^3*c^2+11*b^2*c^3-6*b*c^4+3*c^5)) : :

X(64311) lies on these lines: {3, 5837}, {9, 3197}, {10, 56889}, {40, 956}, {55, 104}, {56, 64322}, {57, 64325}, {65, 11496}, {84, 64319}, {100, 64313}, {165, 64316}, {405, 54156}, {515, 11495}, {516, 64333}, {517, 60974}, {958, 1158}, {1001, 2800}, {1012, 2093}, {1155, 64332}, {1376, 64188}, {1490, 3697}, {2077, 36922}, {2550, 2829}, {3295, 64323}, {3427, 3428}, {3651, 5584}, {3652, 64326}, {3911, 22753}, {5047, 54199}, {5450, 10306}, {5771, 33899}, {5842, 35514}, {6261, 58660}, {6684, 18237}, {6705, 22770}, {6906, 11041}, {7676, 64321}, {7680, 54366}, {7966, 61763}, {10269, 64109}, {10679, 36867}, {11108, 54198}, {11529, 42884}, {12515, 22758}, {12616, 64077}, {17649, 41229}, {17784, 24466}, {18238, 57279}, {22775, 52148}, {40256, 64074}, {63974, 64295}

X(64311) = midpoint of X(i) and X(j) for these {i,j}: {40, 64320}, {84, 64319}
X(64311) = reflection of X(i) in X(j) for these {i,j}: {64312, 3}
X(64311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {956, 52027, 12114}

X(64312) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: 2ND CIRCUMPERP AND ANTI-AGUILERA

Barycentrics    a*(a^9-2*a^8*(b+c)+2*b*(b-c)^4*c*(b+c)^3-2*a^7*(b^2+3*b*c+c^2)+2*a^5*b*c*(3*b^2-10*b*c+3*c^2)+2*a^6*(3*b^3+8*b^2*c+8*b*c^2+3*c^3)+2*a^3*(b-c)^2*(b^4+5*b^3*c+16*b^2*c^2+5*b*c^3+c^4)-a*(b^2-c^2)^2*(b^4+6*b^3*c-6*b^2*c^2+6*b*c^3+c^4)+2*a^2*(b-c)^2*(b^5+6*b^4*c-3*b^3*c^2-3*b^2*c^3+6*b*c^4+c^5)-2*a^4*(3*b^5+12*b^4*c-7*b^3*c^2-7*b^2*c^3+12*b*c^4+3*c^5)) : :

X(64312) lies on these lines: {1, 227}, {3, 5837}, {11, 6969}, {21, 3427}, {55, 64322}, {56, 64147}, {100, 3428}, {224, 11682}, {390, 5842}, {392, 1490}, {515, 1001}, {944, 57278}, {958, 64335}, {999, 64323}, {1000, 11491}, {1125, 64333}, {1385, 64334}, {2646, 64332}, {2800, 11495}, {2829, 43161}, {2975, 64313}, {3091, 18242}, {3576, 38399}, {3616, 64293}, {3913, 6796}, {4304, 11496}, {5250, 12671}, {5289, 6261}, {5450, 63754}, {5732, 6001}, {5805, 6767}, {6265, 64326}, {6855, 63980}, {6905, 11041}, {7677, 64321}, {7971, 37426}, {10267, 64109}, {10680, 36867}, {11012, 36922}, {11499, 40587}, {11510, 64327}, {17614, 64331}, {18446, 64106}, {40257, 64077}, {48695, 63991}, {59320, 63752}, {63974, 64295}, {64118, 64277}, {64199, 64280}

X(64312) = midpoint of X(i) and X(j) for these {i,j}: {1, 64316}, {944, 64317}, {7966, 64319}
X(64312) = reflection of X(i) in X(j) for these {i,j}: {64311, 3}, {64318, 64328}, {64328, 37837}, {64333, 1125}, {64334, 1385}
X(64312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7966, 52026, 64319}

X(64313) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: INNER-CONWAY AND ANTI-AGUILERA

Barycentrics    5*a^7-13*a^6*(b+c)-7*a^2*(b-c)^4*(b+c)-3*(b-c)^4*(b+c)^3+a^5*(b^2+18*b*c+c^2)+a*(b^2-c^2)^2*(11*b^2-6*b*c+11*c^2)+a^4*(23*b^3-11*b^2*c-11*b*c^2+23*c^3)-a^3*(17*b^4+12*b^3*c-26*b^2*c^2+12*b*c^3+17*c^4) : :
X(64313) = -2*X[1159]+3*X[38149], -2*X[3577]+3*X[59387], -5*X[3616]+4*X[64323], -3*X[3873]+4*X[64325], -3*X[5587]+2*X[14563], -3*X[5603]+2*X[36867], -3*X[5731]+4*X[64315], -3*X[7967]+4*X[64109], -X[16236]+3*X[37712], -2*X[40587]+3*X[59388]

X(64313) lies on these lines: {2, 6326}, {8, 1490}, {9, 64321}, {20, 11684}, {78, 64320}, {100, 64311}, {144, 515}, {145, 64322}, {153, 3434}, {355, 5714}, {390, 952}, {517, 34784}, {518, 64332}, {519, 43166}, {908, 64333}, {944, 31445}, {946, 20008}, {962, 3621}, {1159, 38149}, {2975, 64312}, {3091, 34195}, {3146, 5693}, {3427, 56101}, {3577, 59387}, {3616, 64323}, {3617, 17857}, {3869, 14872}, {3873, 64325}, {4511, 64334}, {5059, 12535}, {5250, 7966}, {5587, 14563}, {5603, 36867}, {5731, 64315}, {5744, 64310}, {5775, 52026}, {5884, 56999}, {6001, 25722}, {6737, 9799}, {6864, 18221}, {7967, 64109}, {7971, 11525}, {8275, 10624}, {9859, 17649}, {12536, 12705}, {12665, 20085}, {16112, 44669}, {16236, 37712}, {17615, 64331}, {17620, 39779}, {17784, 64189}, {18231, 33597}, {28172, 41705}, {33108, 37725}, {40587, 59388}, {63974, 64295}

X(64313) = reflection of X(i) in X(j) for these {i,j}: {145, 64322}, {11041, 355}, {11525, 47745}, {64147, 64335}, {64321, 9}, {64324, 64335}
X(64313) = anticomplement of X(64147)
X(64313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64147, 64335, 2}

X(64314) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: ANTI-AGUILERA AND EXCENTERS-MIDPOINTS

Barycentrics    (a-b-c)*(2*a^3-2*a*(b-c)^2-a^2*(b+c)+(b-c)^2*(b+c)-2*a*S) : :

X(64314) lies on these lines: {1, 1123}, {8, 14121}, {9, 519}, {10, 3316}, {145, 30556}, {517, 64336}, {944, 6213}, {956, 60847}, {2099, 30324}, {2551, 49592}, {3241, 30412}, {3244, 31595}, {3476, 6203}, {3625, 31594}, {3880, 13360}, {4297, 51957}, {5233, 56385}, {5252, 30325}, {5414, 51565}, {5881, 31561}, {5882, 32555}, {6212, 12245}, {7586, 18234}, {7982, 31562}, {8957, 10573}, {11362, 32556}, {13387, 13390}, {13388, 46422}, {13461, 32851}, {17805, 31535}, {28234, 64309}, {30478, 49625}, {34790, 34910}, {44038, 59388}, {63974, 64295}, {64147, 64324}

X(64314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1000), X(1123)}}, {{A, B, C, X(7090), X(51565)}}, {{A, B, C, X(7967), X(13390)}}, {{A, B, C, X(42013), X(64209)}}
X(64314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 30557, 14121}

X(64315) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: EXCENTERS-MIDPOINTS AND ANTI-AGUILERA

Barycentrics    (3*a^3-a^2*(b+c)+(b-c)^2*(b+c)+a*(-3*b^2+2*b*c-3*c^2))*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+6*b*c+c^2)) : :

X(64315) lies on these lines: {1, 631}, {2, 3577}, {3, 5837}, {8, 7966}, {9, 515}, {10, 6922}, {40, 6904}, {100, 64330}, {104, 15931}, {119, 3452}, {142, 517}, {214, 10164}, {355, 51572}, {392, 442}, {516, 15346}, {519, 6600}, {936, 64319}, {952, 6594}, {956, 5882}, {960, 6260}, {997, 64328}, {1056, 52819}, {1108, 2092}, {1145, 4847}, {1159, 38122}, {1385, 5771}, {1484, 24386}, {1512, 5316}, {2256, 34261}, {2800, 10427}, {2829, 51090}, {3035, 55300}, {3126, 28292}, {3219, 64009}, {3306, 59417}, {3340, 37407}, {3428, 16371}, {3576, 5744}, {3647, 4297}, {3878, 41540}, {4640, 38759}, {5250, 64078}, {5325, 22758}, {5690, 12640}, {5731, 64313}, {5745, 37611}, {5836, 12864}, {5853, 15348}, {6001, 43182}, {6261, 56273}, {6700, 64318}, {6705, 64320}, {6713, 50821}, {6889, 64160}, {6908, 15829}, {6916, 61002}, {6934, 31730}, {7971, 37108}, {8732, 11529}, {9948, 51576}, {10106, 55104}, {10246, 36867}, {10267, 12437}, {11500, 12447}, {11525, 64081}, {11530, 19843}, {11682, 37112}, {12114, 18249}, {12514, 49171}, {12616, 64331}, {12639, 33668}, {12736, 17642}, {19854, 44848}, {21620, 31806}, {22754, 22770}, {24474, 51723}, {26446, 40587}, {28194, 35514}, {31397, 39779}, {31837, 32213}, {36845, 63143}, {37424, 54198}, {38056, 38123}, {54366, 64110}, {59691, 64286}

X(64315) = midpoint of X(i) and X(j) for these {i,j}: {8, 7966}, {40, 64322}, {100, 64330}, {3427, 64316}, {36922, 64147}, {36922, 64324}
X(64315) = reflection of X(i) in X(j) for these {i,j}: {64320, 6705}, {64323, 1385}
X(64315) = complement of X(3577)
X(64315) = center of circumconic {{A, B, C, X(100), X(64330)}}
X(64315) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 10175}, {6, 5219}, {56, 18391}, {58, 64110}, {2163, 14563}, {3576, 10}, {5744, 141}, {34231, 5}, {36922, 21251}
X(64315) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {36922, 64147, 64324}
X(64315) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39779)}}, {{A, B, C, X(1000), X(31397)}}, {{A, B, C, X(3427), X(5744)}}
X(64315) = barycentric product X(i)*X(j) for these (i, j): {26591, 3576}, {31397, 5744}
X(64315) = barycentric quotient X(i)/X(j) for these (i, j): {31397, 50442}
X(64315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1000, 3911, 14563}, {1512, 5316, 10175}, {3427, 64316, 515}

X(64316) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: EXCENTRAL AND ANTI-AGUILERA

Barycentrics    a*(a^9-a^8*(b+c)-(b-c)^4*(b+c)^3*(b^2-6*b*c+c^2)-4*a^7*(b^2+4*b*c+c^2)+4*a^6*(b^3+7*b^2*c+7*b*c^2+c^3)+a*(b^2-c^2)^2*(b^4-16*b^3*c+14*b^2*c^2-16*b*c^3+c^4)-4*a^3*(b-c)^2*(b^4-2*b^3*c-10*b^2*c^2-2*b*c^3+c^4)+2*a^5*(3*b^4+8*b^3*c-14*b^2*c^2+8*b*c^3+3*c^4)+4*a^2*(b-c)^2*(b^5+5*b^4*c-2*b^3*c^2-2*b^2*c^3+5*b*c^4+c^5)-2*a^4*(3*b^5+23*b^4*c-10*b^3*c^2-10*b^2*c^3+23*b*c^4+3*c^5)) : :

X(64316) lies on these lines: {1, 227}, {2, 64333}, {3, 64320}, {9, 515}, {40, 6737}, {55, 64332}, {57, 64147}, {63, 64313}, {78, 64298}, {84, 191}, {165, 64311}, {517, 3174}, {1376, 64331}, {1445, 64321}, {1490, 14110}, {1697, 64322}, {1706, 6796}, {2136, 28234}, {2800, 5528}, {2949, 57279}, {2950, 10860}, {2951, 6001}, {3333, 64323}, {3428, 63137}, {3576, 64334}, {3646, 5084}, {4302, 12705}, {4867, 15239}, {5219, 64148}, {5541, 41338}, {5692, 63981}, {5720, 31786}, {7580, 56273}, {7971, 56583}, {11525, 64280}, {12526, 12671}, {12650, 37244}, {18481, 55305}, {21578, 63430}, {28160, 52684}, {31435, 64261}, {47848, 60018}, {63264, 64109}, {63974, 64295}

X(64316) = reflection of X(i) in X(j) for these {i,j}: {1, 64312}, {3427, 64315}, {3577, 64328}, {64147, 64310}, {64319, 11500}, {64320, 3}, {64324, 64310}
X(64316) = anticomplement of X(64333)
X(64316) = X(i)-Dao conjugate of X(j) for these {i, j}: {64333, 64333}
X(64316) = X(i)-Ceva conjugate of X(j) for these {i, j}: {54051, 1490}
X(64316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 64315, 3427}, {3577, 52026, 64328}

X(64317) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: EXTOUCH AND ANTI-AGUILERA

Barycentrics    (a^4-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)-(b^2-c^2)^2)*(a^6-2*a^5*(b+c)+(b-c)^4*(b+c)^2-a^4*(b^2-10*b*c+c^2)+4*a^3*(b^3+c^3)-a^2*(b^4+8*b^3*c-2*b^2*c^2+8*b*c^3+c^4)-2*a*(b^5-b^4*c-b*c^4+c^5)) : :
X(64317) = -3*X[2]+2*X[64334], -3*X[5587]+2*X[64333]

X(64317) lies on these lines: {2, 64334}, {4, 1000}, {8, 1490}, {9, 515}, {10, 64320}, {72, 12667}, {104, 37578}, {153, 329}, {226, 3577}, {355, 45039}, {517, 61010}, {610, 38923}, {938, 64323}, {944, 57278}, {950, 7966}, {952, 64156}, {1056, 64325}, {1145, 7580}, {1512, 18391}, {1750, 12647}, {2829, 5759}, {2950, 9778}, {3059, 6001}, {3487, 18242}, {3522, 9799}, {3650, 64190}, {3651, 5584}, {3911, 5768}, {5587, 64333}, {5731, 37313}, {5744, 54051}, {5758, 6256}, {5804, 63274}, {6223, 31938}, {6260, 11523}, {6907, 40587}, {6913, 64109}, {11041, 64318}, {12666, 41559}, {31789, 52683}, {51380, 64111}, {55104, 64120}, {63974, 64295}

X(64317) = reflection of X(i) in X(j) for these {i,j}: {944, 64312}, {3427, 64335}, {11041, 64318}, {64147, 64328}, {64320, 10}, {64324, 64328}
X(64317) = anticomplement of X(64334)
X(64317) = X(i)-Dao conjugate of X(j) for these {i, j}: {54366, 7}, {64328, 56273}, {64334, 64334}
X(64317) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8, 18391}
X(64317) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1000), X(18446)}}, {{A, B, C, X(3427), X(54366)}}, {{A, B, C, X(6282), X(56273)}}
X(64317) = barycentric quotient X(i)/X(j) for these (i, j): {8557, 56273}
X(64317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 64335, 3427}, {1512, 18446, 54366}, {64147, 64148, 64328}

X(64318) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: FUHRMANN AND ANTI-AGUILERA

Barycentrics    a*(a^9-4*a^8*(b+c)+2*(b-c)^4*(b+c)^3*(b^2-3*b*c+c^2)+2*a^7*(b^2+7*b*c+c^2)+2*a^6*(5*b^3-8*b^2*c-8*b*c^2+5*c^3)-6*a^5*(2*b^4+b^3*c-10*b^2*c^2+b*c^3+2*c^4)-a*(b^2-c^2)^2*(5*b^4-22*b^3*c+42*b^2*c^2-22*b*c^3+5*c^4)+2*a^3*(b-c)^2*(7*b^4-b^3*c-24*b^2*c^2-b*c^3+7*c^4)-2*a^2*(b-c)^2*(b^5+6*b^4*c-19*b^3*c^2-19*b^2*c^3+6*b*c^4+c^5)-2*a^4*(3*b^5-18*b^4*c+23*b^3*c^2+23*b^2*c^3-18*b*c^4+3*c^5)) : :

X(64318) lies on these lines: {1, 227}, {8, 6932}, {355, 6260}, {515, 5880}, {944, 11023}, {958, 1158}, {1000, 10786}, {2099, 64148}, {2475, 12667}, {2800, 5220}, {2829, 63971}, {6001, 9623}, {6700, 64315}, {7971, 18908}, {9940, 64334}, {10310, 45392}, {10864, 18238}, {10894, 63989}, {10912, 40257}, {10950, 64147}, {11041, 64317}, {11236, 12608}, {11525, 17857}, {12114, 19860}, {12635, 28234}, {18518, 64285}, {26487, 64109}, {34606, 63962}, {37739, 64323}, {63974, 64295}, {64294, 64335}

X(64318) = midpoint of X(i) and X(j) for these {i,j}: {3577, 64319}, {11041, 64317}, {40587, 64326}
X(64318) = reflection of X(i) in X(j) for these {i,j}: {64312, 64328}

X(64319) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: OUTER-GARCIA AND ANTI-AGUILERA

Barycentrics    a*(a^9+4*a^7*b*c-3*a^8*(b+c)+(b-c)^6*(b+c)^3-4*a^2*b*(b-c)^2*c*(b^3-9*b^2*c-9*b*c^2+c^3)+a^6*(8*b^3-4*b^2*c-4*b*c^2+8*c^3)+a^5*(-6*b^4+4*b^3*c+52*b^2*c^2+4*b*c^3-6*c^4)+4*a^3*(b-c)^2*(2*b^4-b^3*c-10*b^2*c^2-b*c^3+2*c^4)-a*(b^2-c^2)^2*(3*b^4-12*b^3*c+34*b^2*c^2-12*b*c^3+3*c^4)-2*a^4*(3*b^5-7*b^4*c+20*b^3*c^2+20*b^2*c^3-7*b*c^4+3*c^5)) : :

X(64319) lies on these lines: {1, 227}, {8, 1490}, {10, 3427}, {40, 12330}, {84, 64311}, {100, 6282}, {515, 2550}, {517, 47387}, {936, 64315}, {944, 1467}, {1000, 63986}, {1837, 64327}, {2802, 42470}, {2829, 2951}, {3872, 54051}, {4853, 12777}, {5223, 6001}, {5531, 64056}, {5726, 18242}, {5731, 6904}, {6261, 6765}, {6762, 9942}, {7160, 45776}, {9708, 51489}, {9960, 63135}, {11041, 18446}, {11684, 54156}, {12565, 12667}, {12751, 50528}, {16143, 37712}, {17857, 36922}, {18450, 64321}, {31397, 63992}, {37714, 64265}, {43175, 54318}, {63257, 63966}, {63974, 64295}, {64147, 64163}, {64201, 64298}

X(64319) = reflection of X(i) in X(j) for these {i,j}: {1, 64328}, {84, 64311}, {944, 64310}, {3427, 10}, {3577, 64318}, {7966, 64312}, {12650, 64334}, {64316, 11500}
X(64319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7966, 52026, 64312}

X(64320) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: HEXYL AND ANTI-AGUILERA

Barycentrics    a*(a^9+12*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2-6*b*c+c^2)+4*a^3*(b^2-c^2)^2*(2*b^2-7*b*c+2*c^2)-2*a^5*(b-c)^2*(3*b^2+8*b*c+3*c^2)-8*a^2*b*(b-c)^2*c*(b^3-3*b^2*c-3*b*c^2+c^3)+8*a^6*(b^3-2*b^2*c-2*b*c^2+c^3)-2*a^4*(b-c)^2*(3*b^3-11*b^2*c-11*b*c^2+3*c^3)-a*(b^2-c^2)^2*(3*b^4-20*b^3*c+18*b^2*c^2-20*b*c^3+3*c^4)) : :

X(64320) lies on these lines: {1, 3427}, {3, 64316}, {4, 207}, {10, 64317}, {11, 63992}, {40, 956}, {55, 7966}, {56, 64332}, {65, 84}, {78, 64313}, {442, 1490}, {515, 2550}, {517, 3358}, {936, 12616}, {942, 64277}, {952, 3174}, {971, 64326}, {1158, 54302}, {1709, 10050}, {1768, 2093}, {1998, 9803}, {2800, 43166}, {2817, 18725}, {2829, 30353}, {3333, 64325}, {3576, 38399}, {4413, 52026}, {5450, 10268}, {5728, 6001}, {6260, 28629}, {6261, 6855}, {6264, 25416}, {6282, 14647}, {6705, 64315}, {6769, 12629}, {7171, 31788}, {7675, 64321}, {7957, 12842}, {8164, 18446}, {8726, 64310}, {9121, 37558}, {9799, 19860}, {9948, 14563}, {10042, 10085}, {10864, 18238}, {11471, 38870}, {11920, 64043}, {12565, 64261}, {12651, 37625}, {33899, 37531}, {36922, 63391}, {37704, 63980}, {50195, 63430}, {54318, 63970}, {61763, 64288}, {63974, 64295}

X(64320) = midpoint of X(i) and X(j) for these {i,j}: {84, 3577}, {9948, 14563}
X(64320) = reflection of X(i) in X(j) for these {i,j}: {1, 64334}, {4, 64333}, {40, 64311}, {1490, 64328}, {3427, 6245}, {64315, 6705}, {64316, 3}, {64317, 10}, {64335, 12616}
X(64320) = inverse of X(63992) in Feuerbach hyperbola
X(64320) = pole of line {15239, 63992} with respect to the Feuerbach hyperbola

X(64321) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: HONSBERGER AND ANTI-AGUILERA

Barycentrics    7*a^7-13*a^6*(b+c)-7*a^2*(b-c)^4*(b+c)-3*(b-c)^4*(b+c)^3+a^5*(-5*b^2+14*b*c-5*c^2)+a*(b^2-c^2)^2*(9*b^2-10*b*c+9*c^2)-a^3*(b-c)^2*(11*b^2+26*b*c+11*c^2)+a^4*(23*b^3-11*b^2*c-11*b*c^2+23*c^3) : :
X(64321) = -3*X[5603]+4*X[15935], -3*X[8236]+2*X[64322], -5*X[11025]+4*X[64325], -3*X[11038]+4*X[64323], -5*X[18230]+4*X[64335]

X(64321) lies on these lines: {3, 8}, {7, 515}, {9, 64313}, {20, 41575}, {40, 12536}, {56, 64298}, {517, 30628}, {519, 7674}, {938, 22753}, {1445, 64316}, {2346, 3427}, {2800, 30332}, {3218, 63430}, {3339, 4293}, {3486, 9799}, {3616, 6855}, {4208, 18444}, {4302, 12767}, {4323, 48482}, {4345, 25485}, {5174, 18283}, {5328, 6326}, {5572, 64332}, {5603, 15935}, {5704, 37837}, {5722, 8166}, {5727, 54366}, {5734, 12116}, {5882, 64340}, {6223, 10572}, {6261, 18467}, {6284, 54199}, {6737, 37423}, {6738, 50700}, {6843, 18446}, {6866, 21740}, {7675, 64320}, {7676, 64311}, {7677, 64312}, {7967, 10578}, {8236, 64322}, {8732, 64310}, {9623, 28236}, {9780, 33597}, {10265, 31188}, {11025, 64325}, {11038, 64323}, {11495, 44669}, {12115, 50864}, {12630, 28234}, {12730, 36976}, {13253, 30305}, {16133, 36991}, {17097, 38306}, {17620, 64331}, {18221, 64001}, {18230, 64335}, {18391, 44425}, {18450, 64319}, {21578, 53056}, {21617, 64333}, {28160, 36996}, {30284, 64334}, {31397, 53054}, {34632, 37000}, {37525, 64297}, {37706, 59323}, {37730, 64144}, {37797, 64148}, {38307, 48697}, {63974, 64295}

X(64321) = reflection of X(i) in X(j) for these {i,j}: {7, 64147}, {64313, 9}, {64332, 5572}
X(64321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 64147, 7}, {944, 5768, 5731}, {5731, 5775, 3}, {5731, 9803, 5744}

X(64322) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: HUTSON INTOUCH AND ANTI-AGUILERA

Barycentrics    a^7-3*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(b^2+10*b*c+c^2)+a*(b^2-c^2)^2*(3*b^2-2*b*c+3*c^2)-a^3*(b-c)^2*(5*b^2+18*b*c+5*c^2)-a^2*(b-c)^2*(b^3-13*b^2*c-13*b*c^2+c^3)+a^4*(5*b^3-13*b^2*c-13*b*c^2+5*c^3) : :
X(64322) = 3*X[1699]+X[8275], -X[4900]+5*X[37714], -3*X[8236]+X[64321], -3*X[9708]+4*X[61511], -X[24297]+3*X[59391]

X(64322) lies on these lines: {1, 3427}, {3, 64109}, {4, 1000}, {5, 40587}, {7, 2800}, {8, 908}, {10, 6964}, {11, 2099}, {40, 6904}, {55, 64312}, {56, 64311}, {65, 11023}, {104, 33925}, {145, 64313}, {149, 6246}, {355, 13600}, {381, 64138}, {388, 12672}, {390, 515}, {392, 64111}, {495, 64326}, {517, 2550}, {519, 63970}, {938, 13464}, {944, 3303}, {952, 60901}, {962, 2475}, {999, 13226}, {1012, 3476}, {1056, 6001}, {1058, 13867}, {1158, 3600}, {1159, 20330}, {1319, 6935}, {1320, 10883}, {1478, 12758}, {1479, 64272}, {1482, 6841}, {1519, 10590}, {1697, 64316}, {1699, 8275}, {1953, 53994}, {2095, 34744}, {2096, 5434}, {3085, 63986}, {3241, 6264}, {3485, 63257}, {3545, 22835}, {3601, 64310}, {3616, 6972}, {3632, 12599}, {3679, 7682}, {3748, 7967}, {3878, 5758}, {3890, 6836}, {4295, 7702}, {4298, 54156}, {4301, 5715}, {4308, 5450}, {4315, 52027}, {4413, 5657}, {4861, 6837}, {4863, 59388}, {4900, 37714}, {5119, 50701}, {5154, 5554}, {5176, 6957}, {5261, 10935}, {5290, 54198}, {5703, 40257}, {5720, 34619}, {5731, 34486}, {5734, 12649}, {5771, 22770}, {5787, 31792}, {5790, 7956}, {5804, 10573}, {5815, 20117}, {5818, 7681}, {5836, 6864}, {5854, 42356}, {5882, 9799}, {5884, 11037}, {5886, 6978}, {5920, 12858}, {6326, 63168}, {6705, 61762}, {6766, 11362}, {6835, 14923}, {6844, 10051}, {6848, 10039}, {6865, 58679}, {6896, 7686}, {6906, 11510}, {6956, 11376}, {7320, 64329}, {7373, 33899}, {7971, 21620}, {7991, 64001}, {8236, 64321}, {9578, 63989}, {9708, 61511}, {9785, 48482}, {9803, 25485}, {9850, 18238}, {9856, 12667}, {10043, 12047}, {10106, 12705}, {10222, 36867}, {10284, 18517}, {10309, 30290}, {10430, 50811}, {10525, 26200}, {10597, 64021}, {11046, 11570}, {12053, 64333}, {12115, 64130}, {12575, 64261}, {12616, 14986}, {12650, 21628}, {12703, 17784}, {13227, 61705}, {13253, 33593}, {16200, 36845}, {17622, 64331}, {17624, 58588}, {18990, 64190}, {19925, 49169}, {24297, 59391}, {28212, 52682}, {28292, 44431}, {31397, 63992}, {34625, 51755}, {34627, 34699}, {38073, 38202}, {41824, 64124}, {45085, 58643}, {63974, 64295}

X(64322) = midpoint of X(i) and X(j) for these {i,j}: {4, 1000}, {145, 64313}, {3057, 64332}, {7982, 36922}, {12672, 39779}
X(64322) = reflection of X(i) in X(j) for these {i,j}: {3, 64109}, {8, 64335}, {40, 64315}, {65, 64325}, {1159, 20330}, {3577, 946}, {14563, 13464}, {36867, 10222}, {40587, 5}, {64147, 1}, {64324, 1}
X(64322) = inverse of X(18391) in Feuerbach hyperbola
X(64322) = pole of line {18391, 61660} with respect to the Feuerbach hyperbola
X(64322) = pole of line {43068, 54366} with respect to the dual conic of Yff parabola
X(64322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 13600, 64068}, {388, 12672, 63962}, {946, 28234, 3577}, {7982, 36922, 28234}, {10106, 12705, 64120}, {10573, 11522, 5804}, {28234, 64335, 8}, {31397, 63992, 64148}

X(64323) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: INCIRCLE-CIRCLES AND ANTI-AGUILERA

Barycentrics    4*a^7-2*a^5*(b-c)^2-9*a^6*(b+c)-(b-c)^4*(b+c)^3-4*a^3*(b-c)^2*(2*b^2+3*b*c+2*c^2)+2*a*(b^2-c^2)^2*(3*b^2-4*b*c+3*c^2)-a^2*(b-c)^2*(7*b^3+5*b^2*c+5*b*c^2+7*c^3)+a^4*(17*b^3-b^2*c-b*c^2+17*c^3) : :
X(64323) = 3*X[3488]+X[36996], -5*X[3616]+X[64313], X[4900]+7*X[61289], 3*X[11038]+X[64321], X[11525]+3*X[61291], -9*X[15933]+X[36991], -5*X[17609]+X[64332]

X(64323) lies on these lines: {1, 3427}, {3, 3244}, {10, 37615}, {57, 7966}, {142, 952}, {145, 8726}, {443, 61296}, {515, 5542}, {517, 43175}, {519, 18443}, {551, 6265}, {938, 64317}, {942, 4315}, {944, 3296}, {946, 16137}, {971, 15935}, {999, 64312}, {1000, 3601}, {1125, 64335}, {1159, 60945}, {1210, 6949}, {1317, 17603}, {1385, 5771}, {1483, 9940}, {2095, 3655}, {2800, 30331}, {3241, 6282}, {3295, 64311}, {3333, 64316}, {3358, 43179}, {3488, 36996}, {3616, 64313}, {3626, 6989}, {3632, 37407}, {3636, 6824}, {4292, 11048}, {4297, 12005}, {4298, 45636}, {4314, 5884}, {4900, 61289}, {5045, 64325}, {5083, 64191}, {5745, 10246}, {5787, 13464}, {5887, 51724}, {6001, 63972}, {6260, 12433}, {6261, 6744}, {6738, 64328}, {6826, 28236}, {6861, 15808}, {6881, 38155}, {7682, 18446}, {8275, 30282}, {8728, 47745}, {9843, 37700}, {10164, 13151}, {10202, 33337}, {10857, 51093}, {11034, 50701}, {11036, 64261}, {11038, 64321}, {11500, 17706}, {11520, 64004}, {11525, 61291}, {11529, 12573}, {11715, 12735}, {12247, 31397}, {12563, 48482}, {12853, 37544}, {12909, 16159}, {15178, 64109}, {15803, 16236}, {15933, 36991}, {17609, 64332}, {17624, 64331}, {21620, 64333}, {21625, 40257}, {24473, 63438}, {28172, 31671}, {28452, 51082}, {34339, 64117}, {34489, 64163}, {37526, 61288}, {37533, 51071}, {37566, 37734}, {37727, 40587}, {37739, 64318}, {39779, 63987}, {41867, 59388}, {54198, 63999}, {63974, 64295}, {63993, 64192}

X(64323) = midpoint of X(i) and X(j) for these {i,j}: {1, 64147}, {1, 64324}, {3, 36867}, {944, 3577}, {5882, 14563}, {7966, 11041}, {37727, 40587}
X(64323) = reflection of X(i) in X(j) for these {i,j}: {6245, 64334}, {64109, 15178}, {64315, 1385}, {64325, 5045}, {64335, 1125}
X(64323) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1, 64147, 64324}
X(64323) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 36867, 28234}, {944, 11518, 64001}, {1483, 9940, 12437}, {7967, 11041, 7966}

X(64324) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: INTOUCH AND ANTI-AGUILERA

Barycentrics    (3*a^3-a^2*(b+c)+(b-c)^2*(b+c)+a*(-3*b^2+2*b*c-3*c^2))*(a^4-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)-(b^2-c^2)^2) : :
X(64324) = -3*X[354]+2*X[64325], X[4900]+3*X[61294], -3*X[10246]+2*X[64109], -3*X[15934]+2*X[20330]

X(64324) lies on these lines: {1, 3427}, {2, 6326}, {3, 39783}, {4, 3649}, {7, 515}, {8, 224}, {20, 5884}, {40, 145}, {55, 104}, {56, 64312}, {57, 64310}, {65, 944}, {354, 64325}, {355, 3824}, {390, 2800}, {452, 5693}, {497, 1537}, {516, 64262}, {517, 15185}, {519, 3174}, {631, 21677}, {758, 6987}, {938, 6261}, {950, 63962}, {952, 2550}, {962, 10941}, {1056, 63258}, {1071, 3486}, {1158, 4313}, {1385, 5770}, {1483, 10306}, {1490, 6738}, {1512, 18391}, {1538, 5722}, {1788, 33597}, {2093, 16236}, {2094, 50811}, {2099, 64327}, {2320, 11715}, {2771, 6930}, {2829, 36996}, {3086, 21740}, {3146, 12913}, {3189, 31788}, {3241, 37569}, {3244, 6769}, {3476, 39779}, {3488, 6001}, {3576, 5744}, {3600, 12005}, {3655, 34744}, {3671, 64261}, {3689, 5657}, {3925, 59388}, {4294, 41537}, {4295, 45638}, {4305, 63399}, {4314, 54156}, {4900, 61294}, {5129, 20117}, {5274, 16174}, {5584, 12245}, {5603, 39782}, {5691, 11551}, {5703, 12616}, {5715, 12563}, {5727, 64115}, {5758, 12559}, {5775, 6684}, {5804, 63988}, {5885, 6885}, {5902, 50701}, {6224, 15528}, {6253, 34502}, {6737, 8726}, {6825, 33858}, {6836, 34195}, {6846, 30143}, {6855, 11281}, {6865, 12635}, {6891, 37733}, {6904, 15016}, {6905, 64341}, {6908, 49168}, {6916, 44669}, {6926, 22836}, {6938, 33667}, {6969, 61717}, {6982, 62354}, {7686, 64144}, {7688, 59417}, {7964, 50810}, {7971, 63999}, {7994, 51093}, {8275, 61763}, {10044, 45287}, {10052, 10572}, {10246, 64109}, {10382, 56273}, {10884, 41575}, {10902, 45392}, {10950, 64318}, {11036, 26332}, {11525, 61296}, {11570, 64145}, {12247, 41701}, {12437, 37560}, {12667, 37730}, {12680, 37724}, {12767, 54342}, {13226, 37606}, {14647, 24929}, {14986, 18467}, {15934, 20330}, {16132, 37421}, {17625, 64331}, {18221, 31870}, {20015, 63143}, {30283, 37728}, {31019, 59387}, {31806, 37423}, {34612, 50818}, {34618, 34631}, {34625, 61146}, {37080, 39781}, {37537, 63415}, {37567, 39777}, {37601, 64173}, {37723, 63989}, {63132, 64146}, {63974, 64295}, {64163, 64319}

X(64324) = midpoint of X(i) and X(j) for these {i,j}: {7, 64321}, {944, 11041}, {11525, 61296}
X(64324) = reflection of X(i) in X(j) for these {i,j}: {1, 64323}, {3427, 64334}, {3577, 14563}, {7966, 5882}, {12667, 64326}, {36922, 64315}, {64313, 64335}, {64316, 64310}, {64317, 64328}, {64322, 1}, {64330, 11715}, {64332, 64325}
X(64324) = complement of X(64313)
X(64324) = anticomplement of X(64335)
X(64324) = X(i)-Dao conjugate of X(j) for these {i, j}: {18391, 8}, {64147, 64313}, {64328, 3577}, {64335, 64335}
X(64324) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7, 54366}, {64147, 64147}
X(64324) = X(i)-cross conjugate of X(j) for these {i, j}: {64147, 64147}
X(64324) = pole of line {5603, 54366} with respect to the Feuerbach hyperbola
X(64324) = pole of line {54366, 62780} with respect to the dual conic of Yff parabola
X(64324) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1000), X(1512)}}, {{A, B, C, X(3427), X(18391)}}, {{A, B, C, X(5744), X(54366)}}, {{A, B, C, X(18446), X(34231)}}
X(64324) = barycentric product X(i)*X(j) for these (i, j): {2, 64147}, {18391, 5744}, {34231, 6350}
X(64324) = barycentric quotient X(i)/X(j) for these (i, j): {8557, 3577}, {18391, 50442}, {34231, 55963}, {64147, 2}
X(64324) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64313, 64335}, {7, 64321, 515}, {354, 64332, 64325}, {515, 14563, 3577}, {1071, 3486, 64120}, {3576, 36922, 64315}, {5882, 28234, 7966}, {18221, 50700, 31870}, {18391, 18446, 64148}

X(64325) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: INVERSE-IN-INCIRCLE AND ANTI-AGUILERA

Barycentrics    a*(a^8*(b+c)-(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)-2*a^7*(b^2+3*b*c+c^2)+2*a^4*b*c*(-3*b^3+11*b^2*c+11*b*c^2-3*c^3)-2*a^6*(b^3-2*b^2*c-2*b*c^2+c^3)+2*a*(b^2-c^2)^2*(b^4-3*b^3*c-3*b*c^3+c^4)+2*a^5*(3*b^4+3*b^3*c-8*b^2*c^2+3*b*c^3+3*c^4)-2*a^3*(b-c)^2*(3*b^4+3*b^3*c-8*b^2*c^2+3*b*c^3+3*c^4)+2*a^2*(b-c)^2*(b^5-13*b^3*c^2-13*b^2*c^3+c^5)) : :
X(64325) = -3*X[354]+X[64147], 3*X[3873]+X[64313], -5*X[11025]+X[64321]

X(64325) lies on these lines: {1, 227}, {7, 3427}, {57, 64311}, {65, 11023}, {142, 517}, {354, 64147}, {515, 5572}, {518, 64335}, {999, 64334}, {1000, 17642}, {1056, 64317}, {1320, 45395}, {1537, 33593}, {2829, 12573}, {3306, 3428}, {3333, 64320}, {3812, 22770}, {3873, 64313}, {3890, 14110}, {4298, 18238}, {4355, 17649}, {5045, 64323}, {5173, 12736}, {5603, 54366}, {5836, 28234}, {6738, 18241}, {9856, 11544}, {10122, 12675}, {10179, 11281}, {10532, 44547}, {11018, 64310}, {11019, 64333}, {11024, 37462}, {11025, 64321}, {12114, 18219}, {12677, 26332}, {15528, 63994}, {17626, 64331}, {63974, 64295}

X(64325) = midpoint of X(i) and X(j) for these {i,j}: {65, 64322}, {3577, 39779}, {64147, 64332}, {64324, 64332}
X(64325) = reflection of X(i) in X(j) for these {i,j}: {64323, 5045}
X(64325) = pole of line {2099, 64147} with respect to the Feuerbach hyperbola
X(64325) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {64147, 64324, 64332}

X(64326) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: JOHNSON AND ANTI-AGUILERA

Barycentrics    a*(a^9-4*a^8*(b+c)+2*(b-c)^6*(b+c)^3+2*a^7*(b^2+5*b*c+c^2)+2*a^6*(5*b^3-3*b^2*c-3*b*c^2+5*c^3)-a*(b^2-c^2)^2*(5*b^4-14*b^3*c+34*b^2*c^2-14*b*c^3+5*c^4)-2*a^5*(6*b^4+3*b^3*c-22*b^2*c^2+3*b*c^3+6*c^4)+2*a^3*(b-c)^2*(7*b^4+5*b^3*c-8*b^2*c^2+5*b*c^3+7*c^4)-2*a^2*(b-c)^2*(b^5+3*b^4*c-12*b^3*c^2-12*b^2*c^3+3*b*c^4+c^5)-2*a^4*(3*b^5-9*b^4*c+14*b^3*c^2+14*b^2*c^3-9*b*c^4+3*c^5)) : :
X(64326) = 3*X[5658]+X[11041]

X(64326) lies on these lines: {3, 64328}, {5, 3427}, {355, 6260}, {495, 64322}, {515, 5542}, {517, 47387}, {952, 6601}, {971, 64320}, {1479, 64327}, {1482, 6261}, {1490, 3577}, {3421, 13257}, {3652, 64311}, {3940, 64148}, {5658, 11041}, {5779, 6001}, {5787, 64333}, {5795, 54227}, {6256, 37230}, {6265, 64312}, {7971, 34790}, {9942, 64334}, {12667, 37730}, {18242, 64335}, {18481, 64310}, {31799, 63962}, {39779, 63986}, {40267, 41688}, {63974, 64295}, {63988, 64332}

X(64326) = midpoint of X(i) and X(j) for these {i,j}: {1490, 3577}, {12667, 64147}, {12667, 64324}
X(64326) = reflection of X(i) in X(j) for these {i,j}: {3, 64328}, {3427, 5}, {5787, 64333}, {18481, 64310}, {40587, 64318}, {64335, 18242}
X(64326) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {12667, 64147, 64324}

X(64327) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: MANDART-INCIRCLE AND ANTI-AGUILERA

Barycentrics    2*a^10-6*a^9*(b+c)-(b-c)^6*(b+c)^4+4*a*(b-c)^4*(b+c)^3*(b^2+c^2)+a^8*(b^2+6*b*c+c^2)-2*a^3*(b-c)^4*(3*b^3+13*b^2*c+13*b*c^2+3*c^3)+2*a^7*(7*b^3+b^2*c+b*c^2+7*c^3)-4*a^2*(b^2-c^2)^2*(b^4-2*b^3*c+6*b^2*c^2-2*b*c^3+c^4)+16*a^4*(b-c)^2*(b^4+b^3*c-b^2*c^2+b*c^3+c^4)-2*a^6*(7*b^4-22*b^2*c^2+7*c^4)-2*a^5*(3*b^5-5*b^4*c+18*b^3*c^2+18*b^2*c^3-5*b*c^4+3*c^5) : :
X(64327) =

X(64327) lies on these lines: {11, 64328}, {55, 3427}, {515, 14100}, {944, 3303}, {952, 5223}, {1319, 64310}, {1479, 64326}, {1837, 64319}, {2099, 64147}, {5768, 51463}, {6001, 60919}, {6067, 30503}, {7966, 10944}, {7982, 36867}, {10950, 44547}, {11510, 64312}, {18446, 37703}, {34486, 64109}, {63974, 64295}

X(64327) = reflection of X(i) in X(j) for these {i,j}: {10944, 7966}
X(64327) = pole of line {7680, 64325} with respect to the Feuerbach hyperbola

X(64328) = COMPLEMENT OF X(3427)

Barycentrics    a*(a^4-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)-(b^2-c^2)^2)*(a^5-a^4*(b+c)+2*a^2*(b-c)^2*(b+c)-(b-c)^4*(b+c)-2*a^3*(b^2+c^2)+a*(b^4+6*b^2*c^2+c^4)) : :

X(64328) lies on these lines: {1, 227}, {2, 3427}, {3, 64326}, {9, 3197}, {10, 5720}, {11, 64327}, {40, 11517}, {84, 5251}, {100, 56101}, {142, 515}, {165, 12332}, {200, 1145}, {214, 37611}, {442, 1490}, {517, 6600}, {518, 15348}, {908, 64111}, {958, 9942}, {960, 49183}, {971, 15346}, {997, 64315}, {1158, 3647}, {1385, 22754}, {1467, 12675}, {1482, 12631}, {1512, 18391}, {1841, 34261}, {2092, 3553}, {2800, 6594}, {2829, 5732}, {3035, 55302}, {3085, 63986}, {3126, 30199}, {3576, 52148}, {3811, 12640}, {4326, 5842}, {5219, 7680}, {5258, 12687}, {5260, 9960}, {5534, 49168}, {5660, 52050}, {5692, 7971}, {5727, 34489}, {6184, 34526}, {6256, 41540}, {6260, 12520}, {6738, 64323}, {6796, 37531}, {7951, 63966}, {7992, 13089}, {8227, 64266}, {8726, 12114}, {9943, 49171}, {10884, 12667}, {11014, 11525}, {11041, 21740}, {12330, 31787}, {12565, 64119}, {14647, 54357}, {15347, 64116}, {18406, 64261}, {28473, 57095}, {37302, 59335}, {40249, 62858}, {40587, 61146}, {41862, 63981}, {45770, 64275}, {51506, 64129}, {51576, 64118}, {57276, 59305}, {63974, 64295}

X(64328) = midpoint of X(i) and X(j) for these {i,j}: {1, 64319}, {3, 64326}, {1490, 64320}, {3577, 64316}, {64147, 64317}, {64312, 64318}, {64317, 64324}
X(64328) = reflection of X(i) in X(j) for these {i,j}: {64312, 37837}
X(64328) = complement of X(3427)
X(64328) = center of circumconic {{A, B, C, X(100), X(36127)}}
X(64328) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 8557}
X(64328) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 7680}, {31, 8557}, {3428, 10}, {34042, 142}
X(64328) = pole of line {7680, 8557} with respect to the Kiepert hyperbola
X(64328) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {64147, 64317, 64324}
X(64328) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3427), X(8557)}}, {{A, B, C, X(3577), X(18391)}}, {{A, B, C, X(54366), X(56273)}}
X(64328) = barycentric quotient X(i)/X(j) for these (i, j): {8557, 3427}
X(64328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {958, 9942, 49170}, {3577, 52026, 64316}, {64147, 64148, 64317}

X(64329) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: 1ST SCHIFFLER AND ANTI-AGUILERA

Barycentrics    (a^5+(b-c)^3*(b+c)^2-a^4*(2*b+c)+a^3*(b^2-3*b*c-2*c^2)-a*(b+c)^2*(2*b^2-b*c-c^2)+a^2*(b^3-4*b^2*c+b*c^2+2*c^3))*(a^5-(b-c)^3*(b+c)^2-a^4*(b+2*c)+a*(b+c)^2*(b^2+b*c-2*c^2)+a^3*(-2*b^2-3*b*c+c^2)+a^2*(2*b^3+b^2*c-4*b*c^2+c^3)) : :

X(64329) lies on the Feuerbach hyperbola and on these lines: {1, 6357}, {4, 61718}, {8, 14206}, {9, 30}, {20, 56203}, {21, 18653}, {80, 41539}, {84, 16141}, {515, 2346}, {758, 6601}, {943, 4304}, {971, 34917}, {1012, 15175}, {1071, 5557}, {1172, 52954}, {1320, 51077}, {2771, 3254}, {3296, 10122}, {3467, 37468}, {3887, 14224}, {4292, 10308}, {4866, 47033}, {5252, 7160}, {5556, 16125}, {5558, 9799}, {5665, 5722}, {5691, 7162}, {6001, 15909}, {6597, 16138}, {7320, 64322}, {7688, 54357}, {8809, 62781}, {9963, 56121}, {10390, 20330}, {10431, 64335}, {14563, 17097}, {16116, 43733}, {16118, 36599}, {16236, 56152}, {22798, 35239}, {28234, 56091}, {31673, 32635}, {37434, 64344}, {38306, 64130}, {41691, 64003}, {42317, 45929}, {42325, 43728}, {42470, 44669}, {43740, 49177}, {44256, 63267}, {63974, 64295}, {64147, 64324}, {64330, 64332}

X(64329) = isogonal conjugate of X(7688)
X(64329) = trilinear pole of line {650, 11125}
X(64329) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 15909}
X(64329) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(10), X(24564)}}, {{A, B, C, X(20), X(31902)}}, {{A, B, C, X(27), X(30)}}, {{A, B, C, X(28), X(37433)}}, {{A, B, C, X(29), X(37447)}}, {{A, B, C, X(57), X(3587)}}, {{A, B, C, X(63), X(4846)}}, {{A, B, C, X(75), X(54516)}}, {{A, B, C, X(86), X(54526)}}, {{A, B, C, X(103), X(1243)}}, {{A, B, C, X(272), X(54533)}}, {{A, B, C, X(335), X(54692)}}, {{A, B, C, X(515), X(6362)}}, {{A, B, C, X(517), X(42325)}}, {{A, B, C, X(673), X(54882)}}, {{A, B, C, X(758), X(3309)}}, {{A, B, C, X(994), X(3423)}}, {{A, B, C, X(996), X(54687)}}, {{A, B, C, X(1065), X(43672)}}, {{A, B, C, X(1224), X(57720)}}, {{A, B, C, X(1268), X(57719)}}, {{A, B, C, X(1847), X(31672)}}, {{A, B, C, X(2051), X(56228)}}, {{A, B, C, X(2771), X(3887)}}, {{A, B, C, X(3649), X(41506)}}, {{A, B, C, X(3679), X(54789)}}, {{A, B, C, X(5936), X(54787)}}, {{A, B, C, X(13476), X(28193)}}, {{A, B, C, X(14621), X(54729)}}, {{A, B, C, X(15474), X(60167)}}, {{A, B, C, X(16251), X(41514)}}, {{A, B, C, X(17768), X(28292)}}, {{A, B, C, X(18850), X(55963)}}, {{A, B, C, X(28217), X(28234)}}, {{A, B, C, X(28626), X(54790)}}, {{A, B, C, X(30598), X(54972)}}, {{A, B, C, X(42285), X(54517)}}, {{A, B, C, X(54754), X(57725)}}, {{A, B, C, X(57661), X(60155)}}

X(64330) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: 2ND SCHIFFLER AND ANTI-AGUILERA

Barycentrics    (a^5+(b-c)^3*(b+c)^2-a^4*(4*b+c)+a^3*(3*b^2+3*b*c-2*c^2)+a^2*(3*b^3-8*b^2*c+3*b*c^2+2*c^3)+a*(-4*b^4+3*b^3*c+3*b^2*c^2-3*b*c^3+c^4))*(a^5-(b-c)^3*(b+c)^2-a^4*(b+4*c)+a^3*(-2*b^2+3*b*c+3*c^2)+a^2*(2*b^3+3*b^2*c-8*b*c^2+3*c^3)+a*(b^4-3*b^3*c+3*b^2*c^2+3*b*c^3-4*c^4)) : :
X(64330) =

X(64330) lies on the Feuerbach hyperbola and on these lines: {1, 11219}, {7, 2800}, {8, 49176}, {9, 952}, {11, 3577}, {21, 5882}, {65, 34485}, {79, 12672}, {100, 64315}, {104, 2078}, {514, 46041}, {515, 1156}, {517, 3254}, {519, 34894}, {944, 55918}, {946, 55924}, {1000, 12247}, {1210, 1389}, {1320, 10265}, {1392, 6972}, {1476, 48694}, {1768, 7284}, {2320, 11715}, {2771, 3255}, {2801, 34919}, {2802, 6601}, {2826, 23838}, {2829, 3062}, {3065, 64145}, {3680, 6922}, {3887, 43728}, {4900, 64056}, {5551, 10597}, {5556, 26332}, {5559, 12750}, {5561, 34789}, {5691, 55934}, {5854, 42470}, {6264, 36922}, {6265, 64109}, {6596, 12737}, {7162, 51767}, {7317, 10806}, {7319, 48482}, {7972, 15175}, {10532, 43733}, {11041, 14497}, {11522, 17098}, {11604, 14217}, {12116, 43734}, {12619, 40587}, {12629, 56278}, {12641, 19914}, {12751, 30513}, {12776, 15179}, {13464, 17097}, {14496, 59391}, {17638, 46435}, {23710, 36121}, {33576, 64261}, {43174, 48713}, {49168, 56089}, {55931, 62616}, {63974, 64295}, {64329, 64332}

X(64330) = midpoint of X(i) and X(j) for these {i,j}: {1000, 12247}, {6264, 36922}
X(64330) = reflection of X(i) in X(j) for these {i,j}: {100, 64315}, {3577, 11}, {6265, 64109}, {12751, 64335}, {40587, 12619}, {64147, 11715}, {64324, 11715}
X(64330) = X(i)-vertex conjugate of X(j) for these {i, j}: {34442, 46435}
X(64330) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(41487)}}, {{A, B, C, X(65), X(34486)}}, {{A, B, C, X(98), X(36935)}}, {{A, B, C, X(103), X(517)}}, {{A, B, C, X(105), X(47645)}}, {{A, B, C, X(225), X(5882)}}, {{A, B, C, X(513), X(28233)}}, {{A, B, C, X(514), X(952)}}, {{A, B, C, X(515), X(6366)}}, {{A, B, C, X(519), X(2826)}}, {{A, B, C, X(528), X(28292)}}, {{A, B, C, X(900), X(28234)}}, {{A, B, C, X(947), X(34434)}}, {{A, B, C, X(1065), X(42285)}}, {{A, B, C, X(1222), X(57719)}}, {{A, B, C, X(1243), X(41434)}}, {{A, B, C, X(1411), X(49176)}}, {{A, B, C, X(2161), X(2716)}}, {{A, B, C, X(2342), X(2800)}}, {{A, B, C, X(2801), X(14077)}}, {{A, B, C, X(2802), X(3309)}}, {{A, B, C, X(3632), X(11240)}}, {{A, B, C, X(4248), X(6922)}}, {{A, B, C, X(7972), X(56419)}}, {{A, B, C, X(9093), X(43537)}}, {{A, B, C, X(11219), X(40437)}}, {{A, B, C, X(11510), X(37625)}}, {{A, B, C, X(12531), X(52178)}}, {{A, B, C, X(12629), X(12649)}}, {{A, B, C, X(13464), X(40950)}}, {{A, B, C, X(13478), X(55956)}}, {{A, B, C, X(14528), X(34442)}}, {{A, B, C, X(14536), X(43655)}}, {{A, B, C, X(20418), X(36123)}}, {{A, B, C, X(24857), X(54679)}}, {{A, B, C, X(24858), X(54528)}}, {{A, B, C, X(28535), X(41446)}}, {{A, B, C, X(29374), X(53907)}}, {{A, B, C, X(34892), X(54739)}}, {{A, B, C, X(36846), X(49168)}}, {{A, B, C, X(38669), X(38955)}}, {{A, B, C, X(43908), X(57396)}}, {{A, B, C, X(53180), X(53774)}}, {{A, B, C, X(56145), X(57724)}}

X(64331) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: URSA-MAJOR AND ANTI-AGUILERA

Barycentrics    a*(a^11*(b+c)-(b-c)^6*(b+c)^4*(b^2-4*b*c+c^2)-a^10*(3*b^2+14*b*c+3*c^2)-a^9*(b^3-35*b^2*c-35*b*c^2+c^3)+a*(b-c)^4*(b+c)^3*(3*b^4-22*b^3*c+46*b^2*c^2-22*b*c^3+3*c^4)-2*a^6*(b-c)^2*(7*b^4-28*b^3*c-102*b^2*c^2-28*b*c^3+7*c^4)+a^8*(11*b^4-2*b^3*c-114*b^2*c^2-2*b*c^3+11*c^4)-2*a^7*(3*b^5+43*b^4*c-62*b^3*c^2-62*b^2*c^3+43*b*c^4+3*c^5)+2*a^5*(b-c)^2*(7*b^5+33*b^4*c-88*b^3*c^2-88*b^2*c^3+33*b*c^4+7*c^5)+a^2*(b^2-c^2)^2*(b^6+26*b^5*c-145*b^4*c^2+204*b^3*c^3-145*b^2*c^4+26*b*c^5+c^6)+2*a^4*(b-c)^2*(3*b^6-44*b^5*c+5*b^4*c^2+136*b^3*c^3+5*b^2*c^4-44*b*c^5+3*c^6)-a^3*(b-c)^2*(11*b^7-15*b^6*c-117*b^5*c^2+153*b^4*c^3+153*b^3*c^4-117*b^2*c^5-15*b*c^6+11*c^7)) : :
X(64331) =

X(64331) lies on these lines: {11, 64332}, {40, 956}, {355, 45039}, {515, 17668}, {517, 60950}, {950, 12664}, {1000, 3427}, {1376, 64316}, {2800, 36868}, {3577, 15239}, {11041, 12246}, {12616, 64315}, {17612, 64310}, {17614, 64312}, {17615, 64313}, {17620, 64321}, {17622, 64322}, {17624, 64323}, {17625, 64147}, {17626, 64325}, {17634, 64000}, {17648, 28234}, {18236, 64335}, {39779, 64334}, {63974, 64295}

X(64331) = reflection of X(i) in X(j) for these {i,j}: {39779, 64334}, {64332, 64333}

X(64332) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: URSA-MINOR AND ANTI-AGUILERA

Barycentrics    a*(a^8*(b+c)-32*a^4*b*(b-c)^2*c*(b+c)-(b-c)^4*(b+c)^3*(b^2-6*b*c+c^2)-2*a^7*(b^2+6*b*c+c^2)+2*a^5*(b-c)^2*(3*b^2+10*b*c+3*c^2)-2*a^6*(b^3-9*b^2*c-9*b*c^2+c^3)+2*a*(b^2-c^2)^2*(b^4-8*b^3*c+6*b^2*c^2-8*b*c^3+c^4)-2*a^3*(b-c)^2*(3*b^4-4*b^3*c-22*b^2*c^2-4*b*c^3+3*c^4)+2*a^2*(b-c)^2*(b^5+5*b^4*c-14*b^3*c^2-14*b^2*c^3+5*b*c^4+c^5)) : :
X(64332) = -3*X[210]+4*X[64335], -3*X[354]+2*X[64147], -5*X[17609]+4*X[64323]

X(64332) lies on these lines: {4, 1000}, {11, 64331}, {55, 64316}, {56, 64320}, {65, 64001}, {210, 64335}, {354, 64147}, {515, 14100}, {517, 3059}, {518, 64313}, {1155, 64311}, {1319, 64334}, {2099, 3577}, {2646, 64312}, {3149, 3698}, {3303, 7966}, {3427, 64106}, {3893, 28234}, {3900, 42755}, {5572, 64321}, {5836, 50700}, {6001, 31391}, {7686, 11041}, {8727, 64109}, {9848, 64261}, {10866, 48482}, {11510, 37252}, {12672, 44782}, {12680, 17637}, {12688, 12943}, {17603, 64310}, {17609, 64323}, {17638, 52836}, {18222, 31393}, {19541, 40587}, {56273, 64152}, {63988, 64326}, {64329, 64330}

X(64332) = reflection of X(i) in X(j) for these {i,j}: {3057, 64322}, {11041, 7686}, {64147, 64325}, {64321, 5572}, {64324, 64325}, {64331, 64333}
X(64332) = inverse of X(64333) in Feuerbach hyperbola
X(64332) = pole of line {3427, 3577} with respect to the Feuerbach hyperbola
X(64332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64147, 64325, 354}

X(64333) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: WASAT AND ANTI-AGUILERA

Barycentrics    a^9*(b+c)-(b-c)^6*(b+c)^4+4*a^6*(b-c)^2*(b^2+4*b*c+c^2)+a*(b-c)^4*(b+c)^3*(b^2+10*b*c+c^2)-a^8*(b^2+14*b*c+c^2)-2*a^4*(b^2-c^2)^2*(3*b^2-14*b*c+3*c^2)-4*a^7*(b^3-5*b^2*c-5*b*c^2+c^3)+2*a^5*(b-c)^2*(3*b^3-11*b^2*c-11*b*c^2+3*c^3)+4*a^2*(b^2-c^2)^2*(b^4-6*b^3*c+6*b^2*c^2-6*b*c^3+c^4)-4*a^3*(b-c)^2*(b^5+b^4*c+10*b^3*c^2+10*b^2*c^3+b*c^4+c^5) : :
X(64333) = -3*X[2]+X[64316], -3*X[5587]+X[64317]

X(64333) lies on these lines: {2, 64316}, {4, 207}, {10, 6922}, {11, 64331}, {142, 515}, {226, 64147}, {516, 64311}, {517, 24389}, {908, 64313}, {946, 5722}, {1125, 64312}, {3085, 7966}, {3427, 3577}, {3452, 64335}, {5587, 64317}, {5787, 64326}, {6001, 30329}, {6245, 7686}, {6260, 11263}, {7680, 63993}, {10165, 11500}, {11019, 64325}, {12053, 64322}, {21617, 64321}, {21620, 64323}, {21627, 28234}, {21631, 63976}, {63974, 64295}

X(64333) = midpoint of X(i) and X(j) for these {i,j}: {4, 64320}, {3427, 3577}, {5787, 64326}, {64331, 64332}
X(64333) = inverse of X(64332) in Feuerbach hyperbola
X(64333) = complement of X(64316)

X(64334) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: 1ST ZANIAH AND ANTI-AGUILERA

Barycentrics    a*(a^9+8*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)-2*a^5*(b+c)^2*(3*b^2-4*b*c+3*c^2)-2*a^2*b*(b-c)^2*c*(b^3-5*b^2*c-5*b*c^2+c^3)-2*a^4*(b-c)^2*(3*b^3-2*b^2*c-2*b*c^2+3*c^3)+a^6*(8*b^3-6*b^2*c-6*b*c^2+8*c^3)+8*a^3*(b-c)^2*(b^4-b^2*c^2+c^4)-a*(b^2-c^2)^2*(3*b^4-12*b^3*c+10*b^2*c^2-12*b*c^3+3*c^4)) : :
X(64334) = -3*X[2]+X[64317], -3*X[3576]+X[64316]

X(64334) lies on these lines: {1, 3427}, {2, 64317}, {3, 5836}, {4, 34489}, {7, 56273}, {57, 104}, {78, 6972}, {84, 10122}, {142, 515}, {514, 37628}, {517, 60974}, {912, 60973}, {942, 12114}, {997, 51755}, {999, 64325}, {1000, 6935}, {1158, 24474}, {1319, 64332}, {1385, 64312}, {1387, 8727}, {1467, 4293}, {1490, 3091}, {1699, 33593}, {1709, 11570}, {1870, 34492}, {2475, 10884}, {2800, 3358}, {2829, 5805}, {3218, 52027}, {3576, 64316}, {3601, 7966}, {3671, 45654}, {3811, 12616}, {3870, 9803}, {3872, 5744}, {4511, 64313}, {5219, 6830}, {5450, 5709}, {5572, 6001}, {5720, 6978}, {5731, 6904}, {5745, 37611}, {5770, 6705}, {5787, 5886}, {5806, 56889}, {5882, 12855}, {6256, 55108}, {6896, 64144}, {6913, 60964}, {6946, 52026}, {7682, 54366}, {9940, 64318}, {9942, 64326}, {11544, 64119}, {11551, 18224}, {12005, 49170}, {12520, 48482}, {12737, 36867}, {13374, 18237}, {14647, 37569}, {18223, 64120}, {21578, 50701}, {22758, 55869}, {30284, 64321}, {30503, 43161}, {39779, 64331}, {54135, 60363}, {63974, 64295}

X(64334) = midpoint of X(i) and X(j) for these {i,j}: {1, 64320}, {3427, 64147}, {3427, 64324}, {6245, 64323}, {12650, 64319}, {39779, 64331},
X(64334) = reflection of X(i) in X(j) for these {i,j}: {64312, 1385}
X(64334) = complement of X(64317)
X(64334) = pole of line {8557, 54366} with respect to the dual conic of Yff parabola
X(64334) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3427, 64147, 64324}
X(64334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5787, 37615, 6261}

X(64335) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: 2ND ZANIAH AND ANTI-AGUILERA

Barycentrics    a^7-3*a^6*(b+c)-(b-c)^4*(b+c)^3+3*a*(b^2-c^2)^2*(b^2+c^2)+a^5*(b^2+6*b*c+c^2)-a^2*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)+a^4*(5*b^3-3*b^2*c-3*b*c^2+5*c^3)-a^3*(5*b^4+6*b^3*c-6*b^2*c^2+6*b*c^3+5*c^4) : :
X(64335) = 3*X[210]+X[64332], -3*X[5886]+X[36867], -5*X[18230]+X[64321]

X(64335) lies on circumconic {{A, B, C, X(3427), X(50442)}} and on these lines: {1, 6832}, {2, 6326}, {3, 18253}, {4, 5692}, {5, 12635}, {8, 908}, {9, 515}, {10, 5720}, {20, 7701}, {30, 16112}, {40, 50695}, {72, 26332}, {80, 497}, {119, 2886}, {145, 24148}, {191, 6934}, {210, 64332}, {355, 960}, {377, 5693}, {388, 18397}, {443, 5884}, {498, 45230}, {514, 24316}, {517, 18482}, {518, 64325}, {519, 24389}, {758, 6826}, {936, 12616}, {944, 5251}, {952, 1001}, {958, 64312}, {962, 18406}, {997, 51755}, {1056, 18412}, {1125, 64323}, {1158, 57284}, {1329, 5780}, {1376, 64188}, {1512, 3679}, {1537, 31140}, {1656, 11281}, {1768, 6955}, {2550, 2800}, {2771, 60896}, {2829, 5779}, {3090, 15079}, {3149, 21677}, {3419, 26333}, {3434, 14217}, {3452, 64333}, {3485, 5818}, {3576, 54357}, {3940, 7680}, {4867, 5603}, {5219, 10175}, {5252, 18908}, {5657, 44425}, {5660, 12247}, {5690, 18491}, {5694, 6917}, {5727, 37556}, {5745, 64310}, {5768, 10165}, {5777, 5794}, {5791, 37837}, {5817, 60885}, {5881, 7966}, {5886, 36867}, {5902, 6854}, {5904, 10532}, {6001, 15587}, {6245, 12447}, {6260, 45039}, {6684, 18231}, {6824, 22836}, {6827, 10176}, {6835, 37625}, {6849, 16134}, {6850, 16127}, {6861, 37733}, {6864, 31870}, {6865, 45085}, {6877, 26725}, {6887, 30143}, {6897, 15071}, {6898, 37702}, {6913, 42843}, {6923, 16128}, {6925, 61705}, {6930, 60911}, {6935, 54192}, {6950, 35204}, {6957, 54154}, {6982, 21635}, {6991, 34195}, {7330, 17647}, {8227, 12649}, {8275, 9614}, {9534, 49652}, {9709, 18237}, {9956, 28628}, {10051, 37718}, {10198, 37700}, {10431, 64329}, {10526, 31835}, {11529, 21617}, {12115, 12691}, {12559, 55108}, {12617, 37531}, {12751, 30513}, {15016, 37462}, {15064, 18254}, {15175, 46816}, {16132, 37112}, {16236, 41684}, {17857, 24987}, {18230, 64321}, {18236, 64331}, {18242, 64326}, {18518, 64275}, {19843, 40257}, {19854, 21740}, {20418, 35272}, {22758, 51506}, {26363, 45770}, {26921, 64075}, {28160, 64198}, {28172, 36991}, {31018, 59387}, {31142, 50796}, {31160, 38074}, {31821, 64119}, {37727, 51715}, {49736, 50798}, {63974, 64295}, {64294, 64318}

X(64335) = midpoint of X(i) and X(j) for these {i,j}: {8, 64322}, {3427, 64317}, {3577, 36922}, {5881, 7966}, {12751, 64330}, {64147, 64313}, {64313, 64324}
X(64335) = reflection of X(i) in X(j) for these {i,j}: {6930, 60911}, {64320, 12616}, {64323, 1125}, {64326, 18242}
X(64335) = complement of X(64147)
X(64335) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {64147, 64313, 64324}
X(64335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 960, 48482}, {3427, 64317, 515}, {3577, 36922, 28234}, {5587, 36922, 3577}, {5777, 5794, 6256}, {6850, 31803, 16127}

X(64336) = ORTHOLOGY CENTER OF THESE TRIANGLES: THESE TRIANGLES: ANTI-AGUILERA AND AGUILERA

Barycentrics    (a+b+c)*(2*a^3-a^2*(b+c)-(b-c)^2*(b+c))-2*a*(a-b-c)*S : :

X(64336) lies on cubic K202 and on these lines: {1, 6459}, {2, 45704}, {4, 9}, {6, 52805}, {7, 13389}, {20, 30556}, {37, 52808}, {55, 30324}, {144, 13386}, {390, 16232}, {497, 6204}, {515, 64309}, {517, 64314}, {527, 5860}, {528, 49338}, {946, 32556}, {962, 30557}, {971, 34910}, {1100, 52809}, {1124, 64057}, {1336, 4312}, {1479, 8957}, {1659, 2066}, {1836, 30325}, {2951, 38004}, {3062, 13426}, {3474, 6203}, {5393, 9616}, {5853, 12627}, {7580, 60848}, {9778, 30412}, {9812, 30413}, {11495, 34125}, {13359, 15726}, {13459, 52819}, {14100, 58896}, {16777, 52806}, {17768, 49339}, {30355, 64210}, {31432, 31533}, {31730, 32555}, {43178, 55497}, {51364, 52419}, {63974, 64295}, {64147, 64324}

X(64336) = isogonal conjugate of X(46377)
X(64336) = anticomplement of X(45704)
X(64336) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46377}, {2067, 15892}, {13388, 30335}, {40700, 53063}
X(64336) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46377}, {7090, 13387}, {45704, 45704}
X(64336) = X(i)-Ceva conjugate of X(j) for these {i, j}: {13386, 14121}
X(64336) = pole of line {1864, 30325} with respect to the Feuerbach hyperbola
X(64336) = pole of line {1790, 46377} with respect to the Stammler hyperbola
X(64336) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(176)}}, {{A, B, C, X(9), X(13389)}}, {{A, B, C, X(19), X(61400)}}, {{A, B, C, X(189), X(9778)}}, {{A, B, C, X(281), X(13390)}}, {{A, B, C, X(3062), X(6213)}}, {{A, B, C, X(7079), X(42013)}}
X(64336) = barycentric product X(i)*X(j) for these (i, j): {1336, 31548}, {13390, 30412}, {14121, 176}, {46379, 75}, {51842, 60853}
X(64336) = barycentric quotient X(i)/X(j) for these (i, j): {6, 46377}, {14121, 40700}, {30412, 56386}, {31548, 5391}, {42013, 15892}, {46379, 1}, {51842, 13388}, {60852, 30335}
X(64336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6212, 14121}, {40, 31562, 7090}, {5493, 31595, 51957}

X(64337) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 2ND ANTI-CIRCUMPERP-TANGENTIAL

Barycentrics    a*(a+b-c)*(a-b+c)*(2*a^4-3*a^3*(b+c)-a^2*(b^2+c^2)-(b+c)^2*(b^2-b*c+c^2)+3*a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64337) lies on these lines: {1, 6924}, {10, 41541}, {12, 6841}, {35, 11571}, {55, 21740}, {56, 3889}, {73, 43924}, {90, 37700}, {214, 10914}, {952, 30538}, {1317, 1385}, {1319, 3244}, {1388, 3913}, {2646, 5882}, {3057, 25485}, {3085, 56027}, {3358, 3601}, {4857, 11375}, {4870, 34649}, {5172, 7098}, {5252, 37571}, {5427, 41538}, {5432, 24299}, {5433, 5440}, {5434, 33595}, {5703, 64086}, {5719, 61552}, {6284, 12608}, {7354, 33596}, {11015, 13273}, {11510, 56177}, {11570, 26086}, {12053, 15950}, {12743, 63964}, {13755, 56884}, {14563, 20323}, {32760, 37733}, {33598, 49600}, {37525, 37738}, {37605, 54192}, {37616, 37736}, {39781, 41554}, {40663, 41575}, {41537, 64107}, {41553, 51111}, {62616, 64116}, {63974, 64295}, {64147, 64324}

X(64337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 12739, 45288}

X(64338) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND ANTI-MANDART-INCIRCLE

Barycentrics    a^2*(a^7-3*a^6*(b+c)+a^5*(b^2+4*b*c+c^2)+a*(b^2-c^2)^2*(3*b^2+4*b*c+3*c^2)+5*a^4*(b^3+b^2*c+b*c^2+c^3)-a^3*(5*b^4+8*b^3*c-2*b^2*c^2+8*b*c^3+5*c^4)-a^2*(b^5+b^4*c+10*b^3*c^2+10*b^2*c^3+b*c^4+c^5)-(b-c)^2*(b^5+3*b^4*c+3*b*c^4+c^5)) : :

X(64338) lies on these lines: {3, 10122}, {9, 1998}, {11, 954}, {55, 1708}, {100, 60987}, {226, 5805}, {405, 21677}, {950, 11496}, {1001, 1260}, {1005, 60950}, {1071, 10393}, {1709, 10382}, {2949, 10399}, {3295, 54430}, {3488, 12247}, {3651, 45084}, {5083, 22775}, {5722, 10395}, {6913, 62354}, {7580, 11246}, {11495, 37541}, {11507, 63437}, {11517, 37080}, {14022, 42843}, {16293, 40661}, {22753, 63274}, {26921, 44547}, {33925, 64351}, {33993, 60782}, {47387, 61028}, {63974, 64295}, {64147, 64324}

X(64338) = inverse of X(954) in Feuerbach hyperbola

X(64339) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND AAOA

Barycentrics    a*(a^6+(b^2-c^2)^2*(b^2+c^2)-a^4*(b^2-b*c+c^2)-a^2*(b^4+b^3*c+b*c^3+c^4)) : :

X(64339) lies on these lines: {1, 3}, {4, 63676}, {11, 13160}, {12, 1594}, {30, 9628}, {33, 4348}, {34, 7507}, {37, 52413}, {50, 31880}, {73, 6145}, {197, 11396}, {201, 2361}, {388, 37444}, {442, 45946}, {495, 13371}, {500, 17702}, {516, 38336}, {518, 52362}, {566, 63493}, {601, 18477}, {611, 44469}, {612, 5094}, {613, 44480}, {858, 3920}, {912, 8614}, {976, 20277}, {1056, 47528}, {1068, 64086}, {1399, 44706}, {1478, 18569}, {1479, 37729}, {1717, 28146}, {1718, 9956}, {1829, 20989}, {1836, 4347}, {1935, 24431}, {2293, 22954}, {2594, 8555}, {3056, 37473}, {3058, 38323}, {3085, 37119}, {3086, 7558}, {3091, 63669}, {3100, 15338}, {3585, 31724}, {3715, 54305}, {4294, 35471}, {4296, 7354}, {4302, 8144}, {4351, 18990}, {4354, 44242}, {5252, 59285}, {5270, 7574}, {5310, 21284}, {6020, 53772}, {6198, 6240}, {6872, 9639}, {7191, 7495}, {7568, 15325}, {9673, 11399}, {10056, 18281}, {10088, 15132}, {10149, 10295}, {10896, 37696}, {10950, 54292}, {10953, 34231}, {11363, 20988}, {12184, 39844}, {12373, 19505}, {12588, 34118}, {12903, 15133}, {12943, 64053}, {13182, 39815}, {13407, 63326}, {16063, 29815}, {17718, 30142}, {18580, 31452}, {18984, 41590}, {20833, 51692}, {32330, 32378}, {37697, 54401}, {40635, 40985}, {41335, 62211}, {63974, 64295}, {64147, 64324}

X(64339) = pole of line {21, 9630} with respect to the Stammler hyperbola
X(64339) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6145)}}, {{A, B, C, X(21), X(9630)}}, {{A, B, C, X(943), X(18455)}}, {{A, B, C, X(1036), X(9672)}}, {{A, B, C, X(1037), X(9659)}}, {{A, B, C, X(2346), X(9627)}}
X(64339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1060, 56}, {6198, 6284, 9629}

X(64340) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND ANTICOMPLEMENTARY

Barycentrics    15*a^3+a*(b-c)^2-21*a^2*(b+c)+5*(b-c)^2*(b+c) : :

X(64340) lies on these lines: {1, 31188}, {2, 12630}, {7, 35445}, {8, 31205}, {11, 7679}, {55, 16133}, {100, 59374}, {354, 5218}, {390, 1699}, {495, 4313}, {3035, 38314}, {3475, 63212}, {3616, 31233}, {3622, 12640}, {4345, 5703}, {4460, 26245}, {4661, 5273}, {5281, 5542}, {5550, 34501}, {5558, 52793}, {5882, 64321}, {5905, 12850}, {6172, 41570}, {6767, 38022}, {7674, 60996}, {8162, 61158}, {9897, 10056}, {10177, 18230}, {10580, 63263}, {11034, 11038}, {11041, 34718}, {12247, 12735}, {17718, 30332}, {20119, 33993}, {28169, 31992}, {33108, 64146}, {35023, 38053}, {35258, 60976}, {37703, 64108}, {37787, 64346}, {42819, 62710}, {58451, 64083}, {63974, 64295}, {64147, 64324}

X(64340) = inverse of X(8236) in Feuerbach hyperbola
X(64340) = anticomplement of X(64371)
X(64340) = X(i)-Dao conjugate of X(j) for these {i, j}: {64371, 64371}

X(64341) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 1ST CIRCUMPERP

Barycentrics    a*(a^5+6*a^3*b*c-2*a^4*(b+c)+2*a^2*(b-c)^2*(b+c)+2*b*(b-c)^2*c*(b+c)-a*(b-c)^2*(b^2+6*b*c+c^2)) : :

X(64341) lies on these lines: {1, 26742}, {2, 42843}, {3, 5427}, {6, 650}, {7, 12831}, {11, 37541}, {55, 3911}, {56, 5882}, {57, 11502}, {63, 61653}, {65, 22753}, {100, 33925}, {104, 1470}, {140, 64342}, {142, 480}, {354, 1376}, {474, 5883}, {519, 52148}, {999, 1317}, {1001, 61649}, {1012, 10265}, {1155, 1445}, {1210, 11509}, {1406, 37732}, {1466, 1837}, {1768, 61718}, {1788, 26357}, {2099, 12736}, {2346, 5218}, {3058, 6244}, {3149, 5221}, {3174, 60985}, {3244, 3304}, {3295, 15720}, {3303, 10165}, {3333, 11501}, {3336, 6985}, {3338, 11499}, {3649, 6918}, {3913, 20323}, {4000, 45946}, {4317, 18518}, {4848, 10966}, {4860, 5083}, {5348, 52424}, {5435, 37578}, {5563, 61291}, {5902, 6326}, {6174, 6600}, {6180, 45885}, {6181, 43046}, {6713, 10072}, {6738, 22768}, {6883, 15175}, {6905, 64147}, {7071, 23711}, {7742, 34753}, {7972, 15180}, {8069, 33814}, {9709, 15888}, {10246, 64351}, {10306, 37722}, {10950, 30283}, {11038, 61156}, {11246, 19541}, {11500, 32636}, {11510, 64124}, {11517, 58405}, {14986, 26358}, {17366, 51408}, {17572, 18221}, {21635, 61716}, {25524, 56387}, {25954, 59405}, {26866, 53279}, {31190, 58328}, {33519, 60884}, {37723, 59326}, {37730, 40293}, {37734, 41426}, {52819, 64152}, {55870, 58651}, {63974, 64295}

X(64342) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 2ND CIRCUMPERP

Barycentrics    a*(a^6-a^5*(b+c)-2*b*c*(b^2-c^2)^2-2*a^4*(b^2+3*b*c+c^2)+2*a^3*(b^3+2*b^2*c+2*b*c^2+c^3)-a*(b-c)^2*(b^3+5*b^2*c+5*b*c^2+c^3)+a^2*(b^4+8*b^3*c+6*b^2*c^2+8*b*c^3+c^4)) : :

X(64342) lies on these lines: {1, 6883}, {3, 3649}, {10, 3303}, {11, 498}, {21, 42843}, {37, 7124}, {55, 946}, {56, 954}, {78, 1001}, {140, 64341}, {354, 55104}, {405, 10176}, {497, 6991}, {943, 26357}, {958, 3984}, {1125, 11517}, {1260, 24953}, {1898, 7675}, {2346, 43745}, {2646, 12114}, {3058, 7958}, {3085, 6830}, {3485, 37601}, {3487, 37578}, {3560, 6326}, {3601, 11372}, {3616, 13279}, {3646, 10389}, {3746, 8227}, {3748, 12260}, {4654, 35202}, {4870, 64077}, {4995, 10306}, {5047, 45085}, {5217, 12511}, {5259, 64260}, {5506, 61718}, {5552, 26105}, {5687, 31245}, {5703, 37579}, {5719, 7742}, {5919, 10912}, {6737, 37724}, {6767, 10573}, {6913, 10543}, {6949, 10596}, {6985, 37701}, {7288, 62800}, {7992, 10383}, {8273, 10404}, {8544, 37600}, {10056, 16202}, {10267, 63259}, {10679, 31452}, {11281, 37282}, {11500, 61648}, {11510, 13405}, {11525, 37556}, {11553, 37537}, {11715, 12739}, {12267, 16370}, {13384, 22759}, {19854, 37722}, {21319, 22654}, {24457, 48297}, {24929, 62333}, {25542, 37723}, {30147, 64137}, {37228, 56177}, {37426, 61716}, {37541, 52793}, {37737, 40292}, {42885, 62874}, {63974, 64295}, {64147, 64324}

X(64342) = midpoint of X(i) and X(j) for these {i,j}: {1, 7162}
X(64342) = inverse of X(3295) in Feuerbach hyperbola
X(64342) = pole of line {3295, 26921} with respect to the Feuerbach hyperbola
X(64342) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {52769, 63274, 56}

X(64343) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND INNER-CONWAY

Barycentrics    a*(4*a^2+2*b^2+b*c+2*c^2-6*a*(b+c)) : :
X(64343) = -2*X[51570]+3*X[51817]

X(64343) lies on these lines: {1, 61156}, {2, 3689}, {7, 41553}, {8, 5424}, {9, 3935}, {55, 4661}, {89, 678}, {100, 4860}, {145, 1385}, {149, 5660}, {165, 3218}, {192, 4777}, {200, 35595}, {214, 3241}, {518, 61157}, {519, 2320}, {1100, 17756}, {1320, 6911}, {1621, 3711}, {2646, 20014}, {3158, 3306}, {3240, 3722}, {3621, 18231}, {3623, 56176}, {3651, 3871}, {3749, 63074}, {3895, 7982}, {3897, 20054}, {3911, 64353}, {4361, 4954}, {4393, 31020}, {4421, 23958}, {4660, 30991}, {4678, 37080}, {4867, 25439}, {5218, 64351}, {5541, 39778}, {5658, 20075}, {5659, 36845}, {6846, 10528}, {7674, 62778}, {9803, 12648}, {10385, 26792}, {16669, 30653}, {16777, 37675}, {16858, 56115}, {17242, 62668}, {17483, 34607}, {20053, 37571}, {20085, 34627}, {24344, 49479}, {24929, 31145}, {25417, 42042}, {25959, 50748}, {28465, 50823}, {29817, 64135}, {33110, 64146}, {34791, 37307}, {37651, 53534}, {51570, 51817}, {56028, 58433}, {60962, 63145}, {61153, 62235}, {63974, 64295}, {64147, 64324}

X(64343) = reflection of X(i) in X(j) for these {i,j}: {64361, 52638}
X(64343) = anticomplement of X(64361)
X(64343) = X(i)-Dao conjugate of X(j) for these {i, j}: {64361, 64361}
X(64343) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {52638, 64361, 2}

X(64344) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND CONWAY

Barycentrics    a*(2*a^3+2*b^3-b^2*c-2*b*c^2+c^3-a^2*(2*b+c)-2*a*(b^2+b*c+c^2))*(2*a^3+b^3-2*b^2*c-b*c^2+2*c^3-a^2*(b+2*c)-2*a*(b^2+b*c+c^2)) : :

X(64344) lies on the Feuerbach hyperbola and on these lines: {1, 37106}, {2, 6598}, {4, 4313}, {7, 2646}, {8, 33116}, {9, 3984}, {20, 79}, {21, 12635}, {35, 15173}, {55, 17097}, {80, 3085}, {377, 11604}, {390, 15909}, {405, 12867}, {943, 62873}, {1012, 10308}, {1058, 24298}, {1172, 13739}, {1319, 5558}, {1320, 3303}, {1385, 3296}, {1389, 3295}, {1392, 5919}, {1420, 10390}, {1442, 8809}, {1476, 34471}, {2099, 56030}, {2320, 3868}, {2335, 62802}, {3062, 7675}, {3254, 3622}, {3255, 17576}, {3488, 6861}, {3601, 5665}, {3616, 43740}, {3680, 10389}, {3748, 7320}, {3811, 4866}, {4292, 43732}, {4304, 5561}, {4323, 51512}, {5424, 10122}, {5557, 11036}, {5560, 19925}, {5694, 55918}, {5732, 31507}, {5758, 24299}, {6601, 8236}, {7091, 13384}, {7284, 18444}, {9957, 14497}, {10039, 43731}, {10246, 15179}, {10528, 34918}, {10543, 10883}, {11491, 16615}, {15180, 24926}, {15910, 22836}, {17098, 59337}, {17544, 61718}, {17558, 35016}, {18490, 24928}, {30389, 45834}, {31660, 37300}, {34917, 60975}, {37434, 64329}, {40430, 56948}, {56027, 62864}, {56203, 61722}, {57287, 58463}, {63974, 64295}, {64147, 64324}

X(64344) = trilinear pole of line {650, 6003}
X(64344) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 25525}
X(64344) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 5558}
X(64344) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 25525}
X(64344) = X(i)-cross conjugate of X(j) for these {i, j}: {11020, 7}
X(64344) = pole of line {11020, 64344} with respect to the Feuerbach hyperbola
X(64344) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(13739)}}, {{A, B, C, X(3), X(24929)}}, {{A, B, C, X(20), X(1442)}}, {{A, B, C, X(27), X(16865)}}, {{A, B, C, X(29), X(37106)}}, {{A, B, C, X(35), X(11270)}}, {{A, B, C, X(37), X(12635)}}, {{A, B, C, X(55), X(2646)}}, {{A, B, C, X(56), X(3477)}}, {{A, B, C, X(59), X(939)}}, {{A, B, C, X(63), X(1255)}}, {{A, B, C, X(77), X(1792)}}, {{A, B, C, X(78), X(5703)}}, {{A, B, C, X(272), X(5331)}}, {{A, B, C, X(280), X(56104)}}, {{A, B, C, X(573), X(55100)}}, {{A, B, C, X(759), X(51223)}}, {{A, B, C, X(945), X(41432)}}, {{A, B, C, X(951), X(37741)}}, {{A, B, C, X(959), X(2218)}}, {{A, B, C, X(963), X(41431)}}, {{A, B, C, X(1002), X(2217)}}, {{A, B, C, X(1043), X(60041)}}, {{A, B, C, X(1170), X(42318)}}, {{A, B, C, X(1222), X(56314)}}, {{A, B, C, X(1257), X(5936)}}, {{A, B, C, X(1259), X(33597)}}, {{A, B, C, X(1319), X(3303)}}, {{A, B, C, X(1385), X(3295)}}, {{A, B, C, X(1388), X(5919)}}, {{A, B, C, X(1411), X(37724)}}, {{A, B, C, X(1420), X(10389)}}, {{A, B, C, X(1697), X(13384)}}, {{A, B, C, X(1807), X(11374)}}, {{A, B, C, X(2167), X(41514)}}, {{A, B, C, X(2334), X(18772)}}, {{A, B, C, X(3006), X(36565)}}, {{A, B, C, X(3057), X(34471)}}, {{A, B, C, X(3085), X(4511)}}, {{A, B, C, X(3160), X(7675)}}, {{A, B, C, X(3304), X(3748)}}, {{A, B, C, X(3423), X(3445)}}, {{A, B, C, X(3449), X(34430)}}, {{A, B, C, X(3612), X(59337)}}, {{A, B, C, X(3616), X(3811)}}, {{A, B, C, X(3622), X(3935)}}, {{A, B, C, X(3746), X(37525)}}, {{A, B, C, X(3868), X(4653)}}, {{A, B, C, X(4350), X(8236)}}, {{A, B, C, X(4567), X(58012)}}, {{A, B, C, X(5208), X(10448)}}, {{A, B, C, X(6740), X(54972)}}, {{A, B, C, X(6767), X(24928)}}, {{A, B, C, X(6884), X(17515)}}, {{A, B, C, X(7269), X(11036)}}, {{A, B, C, X(8544), X(31721)}}, {{A, B, C, X(9957), X(10246)}}, {{A, B, C, X(18359), X(27789)}}, {{A, B, C, X(19765), X(37539)}}, {{A, B, C, X(25252), X(25255)}}, {{A, B, C, X(27475), X(55986)}}, {{A, B, C, X(27818), X(39273)}}, {{A, B, C, X(36626), X(60158)}}, {{A, B, C, X(41013), X(56221)}}, {{A, B, C, X(44178), X(56054)}}, {{A, B, C, X(54051), X(57643)}}, {{A, B, C, X(54357), X(60247)}}, {{A, B, C, X(55965), X(57826)}}, {{A, B, C, X(55991), X(60077)}}, {{A, B, C, X(56098), X(56331)}}, {{A, B, C, X(60666), X(61373)}}, {{A, B, C, X(60975), X(60981)}}
X(64344) = barycentric quotient X(i)/X(j) for these (i, j): {1, 25525}

X(64345) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 3RD EULER

Barycentrics    a^5*(b+c)-(b-c)^4*(b+c)^2-a^4*(b^2+c^2)+a^2*(b-c)^2*(2*b^2+3*b*c+2*c^2)-a^3*(2*b^3+b^2*c+b*c^2+2*c^3)+a*(b^5-b^4*c-b*c^4+c^5) : :

X(64345) lies on circumconic {{A, B, C, X(17758), X(38543)}} and on these lines: {1, 48501}, {3, 79}, {5, 14526}, {12, 5884}, {55, 11218}, {65, 495}, {100, 5880}, {142, 44785}, {226, 1155}, {354, 2886}, {442, 5883}, {550, 12047}, {946, 2646}, {1156, 61008}, {1454, 31423}, {1768, 5219}, {1836, 7411}, {3244, 12609}, {3475, 33110}, {3485, 37163}, {3649, 31806}, {4500, 17758}, {4870, 28458}, {6839, 33857}, {6881, 61722}, {6884, 16141}, {6906, 11375}, {7489, 16152}, {7701, 16767}, {7702, 11374}, {8255, 63254}, {8727, 17603}, {9956, 13750}, {11112, 11263}, {13996, 15888}, {15079, 61718}, {15346, 34917}, {17451, 38543}, {17528, 47033}, {17728, 27186}, {18393, 37606}, {20323, 51706}, {21617, 31391}, {33592, 37571}, {44782, 47516}, {63974, 64295}, {64147, 64324}

X(64346) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND EXCENTRAL

Barycentrics    a*(a^5-a^4*(b+c)+a*(b^2-c^2)^2-2*a^3*(b^2+8*b*c+c^2)-(b-c)^2*(b^3+7*b^2*c+7*b*c^2+c^3)+2*a^2*(b^3+11*b^2*c+11*b*c^2+c^3)) : :

X(64346) lies on these lines: {1, 58643}, {9, 63168}, {10, 37556}, {11, 31393}, {40, 3649}, {55, 1750}, {57, 3475}, {200, 1001}, {518, 38399}, {946, 1697}, {1768, 15298}, {3303, 3646}, {3333, 37703}, {3601, 12114}, {3711, 37080}, {3811, 35016}, {5316, 7080}, {5531, 46816}, {5919, 11525}, {6600, 46917}, {7160, 13411}, {7966, 31397}, {7988, 45035}, {10179, 10912}, {11379, 53053}, {11495, 30353}, {11518, 63976}, {11715, 13384}, {18391, 51779}, {31435, 59722}, {31452, 37560}, {33993, 48363}, {33995, 44675}, {35258, 60965}, {37787, 64340}, {40659, 61718}, {41539, 44841}, {51780, 64162}, {52638, 54408}, {54318, 64137}, {61763, 64152}, {63974, 64295}, {64147, 64324}

X(64346) = inverse of X(31393) in Feuerbach hyperbola
X(64346) = pole of line {10398, 31393} with respect to the Feuerbach hyperbola

X(64347) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 3RD EXTOUCH

Barycentrics    a*(a^2-b^2-c^2)*(a^4+2*a^3*(b+c)-2*a*(b-c)^2*(b+c)-(b^2-c^2)^2) : :

X(64347) lies on these lines: {1, 4}, {3, 77}, {9, 18675}, {40, 37755}, {46, 18593}, {48, 1449}, {56, 37310}, {57, 7114}, {63, 3157}, {65, 46009}, {72, 64082}, {78, 1060}, {84, 1419}, {221, 43058}, {222, 1181}, {228, 20764}, {241, 36745}, {255, 21165}, {347, 5758}, {386, 51775}, {389, 45963}, {495, 10367}, {500, 7675}, {517, 37413}, {651, 7330}, {936, 53996}, {942, 5256}, {943, 8809}, {975, 20281}, {982, 45984}, {999, 13737}, {1012, 64055}, {1038, 10360}, {1040, 4303}, {1062, 10884}, {1103, 5657}, {1125, 20262}, {1148, 2331}, {1158, 34043}, {1210, 56418}, {1214, 7078}, {1385, 5909}, {1394, 6906}, {1422, 6935}, {1427, 5706}, {1442, 5703}, {1445, 36754}, {1448, 63982}, {1452, 56842}, {1456, 11496}, {1465, 41344}, {1697, 53557}, {1708, 54301}, {1763, 2360}, {2003, 62810}, {2200, 51210}, {2263, 7138}, {2286, 37592}, {2323, 62858}, {2646, 15498}, {2658, 54418}, {3085, 10365}, {3100, 41854}, {3182, 3601}, {3295, 10373}, {3358, 34028}, {3562, 5709}, {3612, 11700}, {3646, 34591}, {3651, 7070}, {3811, 63802}, {3870, 5399}, {3916, 23072}, {4292, 56848}, {4296, 37531}, {4347, 37569}, {4652, 52407}, {4989, 22063}, {5044, 25930}, {5287, 11374}, {5719, 58799}, {5902, 54360}, {6147, 7190}, {6508, 31435}, {6675, 59613}, {6833, 34050}, {6846, 54425}, {6847, 18623}, {7412, 55311}, {7532, 37697}, {8164, 8282}, {8758, 64020}, {8766, 37554}, {8808, 13411}, {9576, 16143}, {10366, 17718}, {10374, 37080}, {10379, 37324}, {10786, 51375}, {11022, 17609}, {11036, 17011}, {11529, 18673}, {14110, 15832}, {14377, 45128}, {15881, 33597}, {17074, 37534}, {17421, 19861}, {18210, 64040}, {18447, 37700}, {19349, 63437}, {20211, 37054}, {20280, 30115}, {20581, 63962}, {23070, 24467}, {23071, 26921}, {24025, 59333}, {24929, 37046}, {26892, 34956}, {28011, 62266}, {32047, 37533}, {33587, 61762}, {34032, 52384}, {36742, 62836}, {37800, 55108}, {39791, 40944}, {45929, 46835}, {58617, 64206}, {59215, 61122}, {63974, 64295}, {64147, 64324}

X(64347) = X(i)-Dao conjugate of X(j) for these {i, j}: {12514, 406}, {52118, 522}
X(64347) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57832, 63}
X(64347) = pole of line {65, 11022} with respect to the Feuerbach hyperbola
X(64347) = pole of line {283, 2000} with respect to the Stammler hyperbola
X(64347) = pole of line {4397, 4467} with respect to the dual conic of polar circle
X(64347) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1804)}}, {{A, B, C, X(3), X(33)}}, {{A, B, C, X(4), X(77)}}, {{A, B, C, X(34), X(7053)}}, {{A, B, C, X(78), X(6198)}}, {{A, B, C, X(225), X(1439)}}, {{A, B, C, X(278), X(6349)}}, {{A, B, C, X(943), X(44695)}}, {{A, B, C, X(1410), X(57652)}}, {{A, B, C, X(1785), X(62402)}}, {{A, B, C, X(1838), X(8809)}}, {{A, B, C, X(7013), X(7952)}}, {{A, B, C, X(14547), X(19614)}}, {{A, B, C, X(45126), X(56216)}}
X(64347) = barycentric product X(i)*X(j) for these (i, j): {1, 6349}, {4295, 63}
X(64347) = barycentric quotient X(i)/X(j) for these (i, j): {4295, 92}, {6349, 75}
X(64347) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1079, 1478}, {1, 1490, 6198}, {1, 1745, 33}, {1, 223, 4}, {1, 3468, 34}, {1, 73, 18446}, {73, 20277, 1}, {222, 17102, 63399}, {255, 54320, 21165}, {1214, 7078, 55104}, {3562, 17080, 5709}

X(64348) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 4TH EXTOUCH

Barycentrics    a*(a^6-a^4*(b-c)^2-4*a^3*b*c*(b+c)-4*a*b^2*c^2*(b+c)+(b^2-c^2)^2*(b^2+c^2)-a^2*(b^4+6*b^3*c+6*b^2*c^2+6*b*c^3+c^4)) : :

X(64348) lies on these lines: {1, 3}, {33, 64158}, {34, 5718}, {37, 37228}, {69, 34772}, {78, 1211}, {442, 975}, {612, 5794}, {997, 13728}, {1837, 37360}, {2303, 16049}, {3486, 26118}, {3672, 4190}, {3772, 47516}, {3811, 10371}, {4296, 5712}, {4657, 19861}, {5262, 6910}, {5530, 57277}, {5716, 6836}, {5928, 10393}, {8895, 52362}, {11112, 50068}, {12610, 64160}, {17016, 37642}, {17647, 30142}, {26066, 35466}, {26215, 64415}, {37224, 44307}, {37428, 50070}, {37468, 50065}, {37715, 54401}, {54417, 64040}, {63974, 64295}, {64147, 64324}

X(64348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1038, 940}

X(64349) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND 5TH EXTOUCH

Barycentrics    a*(a+b-c)*(a-b+c)*(a^4-(b+c)^2*(b^2+c^2)) : :

X(64349) lies on these lines: {1, 3}, {5, 54401}, {6, 41538}, {8, 54292}, {9, 7299}, {10, 57277}, {11, 7399}, {12, 34}, {21, 28709}, {31, 201}, {33, 3575}, {37, 608}, {38, 603}, {47, 26921}, {63, 1399}, {66, 73}, {72, 64020}, {77, 3665}, {78, 3416}, {90, 35194}, {172, 571}, {197, 1829}, {210, 54305}, {221, 64041}, {225, 64086}, {226, 4347}, {227, 11501}, {348, 1442}, {388, 1370}, {495, 23335}, {497, 6815}, {498, 37697}, {500, 44665}, {518, 54289}, {570, 2275}, {601, 44706}, {614, 5433}, {750, 1393}, {774, 52428}, {943, 1063}, {975, 11375}, {984, 1935}, {1394, 7174}, {1411, 19860}, {1421, 3624}, {1428, 5157}, {1448, 10404}, {1451, 62847}, {1455, 22759}, {1469, 3313}, {1478, 14790}, {1479, 18420}, {1486, 11363}, {1788, 5262}, {1791, 3869}, {1870, 3085}, {1950, 7251}, {2003, 5904}, {2263, 3649}, {2330, 19365}, {2361, 55104}, {2594, 3811}, {2999, 31230}, {3011, 54346}, {3028, 54376}, {3056, 19161}, {3073, 7082}, {3083, 56504}, {3084, 56506}, {3086, 7383}, {3242, 34046}, {3485, 4318}, {3585, 31723}, {3600, 29815}, {3614, 63669}, {3688, 7066}, {3782, 7702}, {3870, 52362}, {3961, 36493}, {4185, 40635}, {4294, 6198}, {4302, 64054}, {4319, 63273}, {4320, 5434}, {4327, 52783}, {4330, 9644}, {4332, 5311}, {5160, 47340}, {5248, 16577}, {5252, 6357}, {5256, 43053}, {5261, 31099}, {5265, 17024}, {5268, 19372}, {5293, 37694}, {5297, 10588}, {5310, 21213}, {5336, 56325}, {5576, 7951}, {6253, 57276}, {7098, 17126}, {7179, 7210}, {7190, 7198}, {7191, 7288}, {7286, 46517}, {7330, 24431}, {7713, 20989}, {7741, 37347}, {8728, 15253}, {8900, 10944}, {9673, 54428}, {9817, 10896}, {10055, 19471}, {10056, 44441}, {10106, 30145}, {10149, 37931}, {10571, 30115}, {10830, 22479}, {10833, 11399}, {10953, 56814}, {11237, 34609}, {11396, 52359}, {12701, 61086}, {12953, 18494}, {13161, 18961}, {13740, 14594}, {15171, 31833}, {15338, 44239}, {15556, 62805}, {15852, 51361}, {17602, 57285}, {20986, 64040}, {24609, 28713}, {26060, 37771}, {26926, 39897}, {31397, 59285}, {40663, 54418}, {43039, 54317}, {43054, 59301}, {43214, 54394}, {44547, 61398}, {45288, 54400}, {52347, 55392}, {52440, 62833}, {54304, 64172}, {56384, 56497}, {56427, 56498}, {61397, 63976}, {63974, 64295}, {64147, 64324}

X(64349) = pole of line {1, 45015} with respect to the Feuerbach hyperbola
X(64349) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(66)}}, {{A, B, C, X(3), X(4280)}}, {{A, B, C, X(9), X(33178)}}, {{A, B, C, X(37), X(41340)}}, {{A, B, C, X(57), X(56366)}}, {{A, B, C, X(942), X(1063)}}, {{A, B, C, X(943), X(1062)}}, {{A, B, C, X(947), X(15177)}}, {{A, B, C, X(1036), X(10832)}}, {{A, B, C, X(1037), X(10831)}}, {{A, B, C, X(1060), X(1791)}}, {{A, B, C, X(1155), X(46380)}}, {{A, B, C, X(2218), X(40959)}}, {{A, B, C, X(3666), X(55936)}}, {{A, B, C, X(5903), X(56136)}}, {{A, B, C, X(10319), X(52351)}}
X(64349) = barycentric product X(i)*X(j) for these (i, j): {1, 56366}, {1441, 4280}, {11392, 63}, {46380, 664}
X(64349) = barycentric quotient X(i)/X(j) for these (i, j): {4280, 21}, {11392, 92}, {46380, 522}, {56366, 75}
X(64349) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1038, 56}, {1, 35, 1062}, {34, 612, 12}, {612, 4348, 34}, {975, 34036, 11375}, {3811, 45126, 2594}, {3920, 4296, 388}, {4347, 30142, 226}

X(64350) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND OUTER-GARCIA

Barycentrics    3*a^4+2*a^3*(b+c)-2*a*(b-c)^2*(b+c)+3*(b^2-c^2)^2-2*a^2*(3*b^2+10*b*c+3*c^2) : :

X(64350) lies on these lines: {1, 3525}, {4, 5726}, {8, 6675}, {10, 38316}, {12, 13865}, {40, 30424}, {55, 21669}, {226, 31436}, {388, 59316}, {495, 6361}, {498, 16173}, {631, 61762}, {942, 5657}, {944, 3601}, {950, 38074}, {1000, 13411}, {1056, 15803}, {1058, 31434}, {1145, 3616}, {1317, 12247}, {1387, 7320}, {1697, 8164}, {1788, 50190}, {3057, 3085}, {3090, 31393}, {3146, 51787}, {3295, 5818}, {3476, 31452}, {3486, 9897}, {3487, 5903}, {3488, 10039}, {3529, 51782}, {3545, 12575}, {3634, 51781}, {3654, 11036}, {3876, 10528}, {3895, 6856}, {4313, 34627}, {4315, 10299}, {4662, 34619}, {5067, 63993}, {5071, 51785}, {5119, 5714}, {5129, 51362}, {5218, 37618}, {5550, 64201}, {5556, 28216}, {5586, 21620}, {5690, 10578}, {5703, 31480}, {6736, 16845}, {6767, 9780}, {9785, 31479}, {9957, 18220}, {10303, 51788}, {10385, 10827}, {11037, 61524}, {11530, 19862}, {12245, 13405}, {12433, 53620}, {12541, 31493}, {13462, 61814}, {17538, 31508}, {18483, 53052}, {19875, 40270}, {21201, 23757}, {30478, 49626}, {31795, 54448}, {37556, 47743}, {37571, 41553}, {37704, 61886}, {50444, 61899}, {51783, 61964}, {58463, 64202}, {63974, 64295}, {64147, 64324}

X(64350) = reflection of X(i) in X(j) for these {i,j}: {64370, 10}

X(64351) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND MANDART-INCIRCLE

Barycentrics    a*(a-b-c)*(2*a^4-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)-a^2*(b^2+c^2)-(b-c)^2*(b^2-b*c+c^2)) : :

X(64351) lies on these lines: {11, 42819}, {55, 3218}, {214, 3753}, {226, 3058}, {1317, 24929}, {1319, 14563}, {1709, 10389}, {2293, 53535}, {2646, 3244}, {3295, 45288}, {3654, 37525}, {3689, 4847}, {3744, 63332}, {3746, 24475}, {3913, 4861}, {4995, 51463}, {5218, 64343}, {5424, 7972}, {5882, 37080}, {5919, 25485}, {10246, 64341}, {10385, 17483}, {10395, 10950}, {10543, 45287}, {11238, 62862}, {15950, 34746}, {16484, 52371}, {16777, 62372}, {17660, 41166}, {21677, 37734}, {25094, 49465}, {33925, 64338}, {37571, 61287}, {41341, 60948}, {41553, 52638}, {60919, 60962}, {63974, 64295}, {64147, 64324}

X(64351) = inverse of X(42819) in Feuerbach hyperbola
X(64351) = pole of line {3898, 30329} with respect to the Feuerbach hyperbola

X(64352) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND WASAT

Barycentrics    a^5*(b+c)+(b-c)^4*(b+c)^2+2*a^2*(b-c)^2*(b^2-4*b*c+c^2)-a^4*(3*b^2+2*b*c+3*c^2)+2*a^3*(b^3+2*b^2*c+2*b*c^2+c^3)-a*(b-c)^2*(3*b^3-5*b^2*c-5*b*c^2+3*c^3) : :

X(64352) lies on these lines: {1, 1512}, {9, 26015}, {55, 3911}, {226, 1538}, {392, 10916}, {496, 10395}, {497, 1709}, {956, 49627}, {1000, 1737}, {1145, 5919}, {1210, 5690}, {1385, 15174}, {1387, 11230}, {1388, 21625}, {1484, 51755}, {1698, 12654}, {3035, 42819}, {3058, 17613}, {3475, 8166}, {3660, 5572}, {3663, 3676}, {3679, 46947}, {3740, 3816}, {5218, 33994}, {8071, 41565}, {8582, 10179}, {9001, 17115}, {9843, 44848}, {10265, 15558}, {10389, 31190}, {10580, 30284}, {12053, 45776}, {13226, 41166}, {14100, 41556}, {15170, 64193}, {15935, 25405}, {17721, 62372}, {24388, 59998}, {60961, 63973}, {63974, 64295}, {64147, 64324}

X(64352) = midpoint of X(i) and X(j) for these {i,j}: {1, 10051}
X(64352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3816, 51380, 5316}, {12915, 15845, 226}

X(64353) = EQUICENTER OF THESE TRIANGLES: 1ST PAVLOV AND GEMINI 29

Barycentrics    a*(a+b-c)*(a-b+c)*(4*a^3-2*b^3-b^2*c-b*c^2-2*c^3-10*a^2*(b+c)+a*(8*b^2+9*b*c+8*c^2)) : :

X(64353) lies on these lines: {2, 41553}, {55, 14151}, {57, 3957}, {390, 34789}, {497, 3748}, {1317, 2320}, {1319, 3241}, {1388, 64199}, {1621, 60944}, {2099, 18467}, {3158, 38460}, {3689, 31188}, {3870, 37787}, {3911, 64343}, {5083, 61157}, {5119, 18444}, {5281, 37525}, {5768, 6935}, {6049, 41824}, {7675, 30304}, {8545, 10389}, {12730, 31140}, {21617, 56028}, {30275, 63261}, {31526, 57090}, {36845, 64114}, {37736, 61155}, {60954, 62236}, {63974, 64295}, {64147, 64324}

X(64354) = EQUICENTER OF THESE TRIANGLES: 2ND PAVLOV AND 1ST ANTI-AURIGA

Barycentrics    -(a*(a+b+c)*(2*a^4*(b+c)+b*(b-c)^2*c*(b+c)-2*a^3*(b^2+b*c+c^2)-2*a^2*(b+c)*(b^2+b*c+c^2)+a*(2*b^4-b^3*c-4*b^2*c^2-b*c^3+2*c^4)))+4*a*(a^3-a^2*(b+c)+(b-c)^2*(b+c)-a*(b^2+b*c+c^2))*sqrt(R*(r+4*R))*S : :

X(64354) lies on these lines: {1, 442}, {81, 5597}, {5453, 48460}, {13408, 48454}, {18496, 63296}, {26290, 63291}, {26296, 63310}, {26302, 63311}, {26310, 63315}, {26319, 63316}, {26326, 63318}, {26334, 63321}, {26344, 63322}, {26351, 63332}, {26365, 63292}, {26371, 63293}, {26379, 63294}, {26380, 63295}, {26381, 63297}, {26383, 63320}, {26384, 63298}, {26385, 63299}, {26386, 63323}, {26387, 63327}, {26388, 63326}, {26389, 63325}, {26390, 63324}, {26393, 63304}, {26394, 37635}, {26395, 63333}, {26396, 63305}, {26397, 63306}, {26398, 63307}, {26399, 63308}, {26400, 63309}, {26401, 63342}, {26402, 63341}, {37631, 45696}, {44582, 63328}, {44583, 63329}, {45345, 63300}, {45348, 63301}, {45349, 63302}, {45352, 63303}, {45354, 63313}, {45355, 63317}, {45357, 63330}, {45360, 63331}, {45365, 63336}, {45366, 63337}, {45369, 63338}, {45371, 63339}, {45373, 63340}, {45711, 63354}, {45724, 63359}, {48456, 63355}, {48458, 63364}, {48462, 63345}, {48464, 63346}, {48470, 63347}, {48472, 63348}, {48474, 63349}, {48478, 63350}, {48480, 63351}, {48483, 63352}, {48485, 63353}, {48487, 63356}, {48489, 63357}, {48491, 63358}, {48495, 63361}, {48497, 63362}, {48499, 63363}, {48501, 63365}, {48503, 63366}, {48505, 63367}, {48507, 63368}, {48509, 63369}, {48511, 63370}, {48513, 63371}, {48515, 63372}, {48517, 63373}, {48519, 63374}, {48521, 63375}, {48523, 63376}, {48525, 63377}, {48527, 63378}, {48529, 63379}, {60880, 63381}, {63974, 64295}, {64147, 64324}

X(64354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63393, 64355}

X(64355) = EQUICENTER OF THESE TRIANGLES: 2ND PAVLOV AND 2ND ANTI-AURIGA

Barycentrics    a*(a+b+c)*(2*a^4*(b+c)+b*(b-c)^2*c*(b+c)-2*a^3*(b^2+b*c+c^2)-2*a^2*(b+c)*(b^2+b*c+c^2)+a*(2*b^4-b^3*c-4*b^2*c^2-b*c^3+2*c^4))+4*a*(a^3-a^2*(b+c)+(b-c)^2*(b+c)-a*(b^2+b*c+c^2))*sqrt(R*(r+4*R))*S : :

X(64355) lies on these lines: {1, 442}, {81, 5598}, {5453, 48461}, {13408, 48455}, {18498, 63296}, {26291, 63291}, {26297, 63310}, {26303, 63311}, {26311, 63315}, {26320, 63316}, {26327, 63318}, {26335, 63321}, {26345, 63322}, {26352, 63332}, {26366, 63292}, {26372, 63293}, {26403, 63294}, {26404, 63295}, {26405, 63297}, {26407, 63320}, {26408, 63298}, {26409, 63299}, {26410, 63323}, {26411, 63327}, {26412, 63326}, {26413, 63325}, {26414, 63324}, {26417, 63304}, {26418, 37635}, {26419, 63333}, {26420, 63305}, {26421, 63306}, {26422, 63307}, {26423, 63308}, {26424, 63309}, {26425, 63342}, {26426, 63341}, {37631, 45697}, {44584, 63328}, {44585, 63329}, {45346, 63301}, {45347, 63300}, {45350, 63303}, {45351, 63302}, {45353, 63312}, {45356, 63317}, {45358, 63331}, {45359, 63330}, {45367, 63337}, {45368, 63336}, {45370, 63338}, {45372, 63339}, {45374, 63340}, {45712, 63354}, {45725, 63359}, {48457, 63355}, {48459, 63364}, {48463, 63345}, {48465, 63346}, {48471, 63347}, {48473, 63348}, {48475, 63349}, {48479, 63350}, {48481, 63351}, {48484, 63352}, {48486, 63353}, {48488, 63356}, {48490, 63357}, {48492, 63358}, {48496, 63361}, {48498, 63362}, {48500, 63363}, {48502, 63365}, {48504, 63366}, {48506, 63367}, {48508, 63368}, {48510, 63369}, {48512, 63370}, {48514, 63371}, {48516, 63372}, {48518, 63373}, {48520, 63374}, {48522, 63375}, {48524, 63376}, {48526, 63377}, {48528, 63378}, {48530, 63379}, {60881, 63381}, {63974, 64295}, {64147, 64324}

X(64355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63393, 64354}

X(64356) = EQUICENTER OF THESE TRIANGLES: 2ND PAVLOV AND 2ND INNER-SODDY

Barycentrics    a*(a+b+c)*(a^3-a^2*(b+c)+(b-c)^2*(b+c)-a*(b^2+b*c+c^2))-2*a*(a+b)*(a+c)*S : :

X(64356) lies on these lines: {1, 21}, {9, 63298}, {37, 63329}, {176, 18625}, {323, 56384}, {482, 55010}, {1100, 63328}, {1449, 63299}, {5393, 35466}, {5405, 17056}, {6357, 31538}, {7969, 61661}, {13389, 18593}, {31583, 32419}, {34494, 47057}, {63974, 64295}, {64147, 64324}

X(64357) = EQUICENTER OF THESE TRIANGLES: 2ND PAVLOV AND 2ND OUTER-SODDY

Barycentrics    a*(a+b+c)*(a^3-a^2*(b+c)+(b-c)^2*(b+c)-a*(b^2+b*c+c^2))+2*a*(a+b)*(a+c)*S : :

X(64357) lies on these lines: {1, 21}, {9, 63299}, {37, 63328}, {175, 18625}, {323, 56427}, {481, 55010}, {1100, 63329}, {1449, 63298}, {5393, 17056}, {5405, 35466}, {6357, 31539}, {7968, 61661}, {13388, 18593}, {31582, 32421}, {34495, 47057}, {63974, 64295}, {64147, 64324}

X(64358) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND ANTI-EULER

Barycentrics    a*(a^5*(b+c)-a^4*(b^2-3*b*c+c^2)+2*a^2*(b-c)^2*(b^2+b*c+c^2)-(b^2-c^2)^2*(b^2+b*c+c^2)-2*a^3*(b^3+c^3)+a*(b^5-b^4*c-b*c^4+c^5)) : :
X(64358) = -3*X[2]+4*X[13369], -2*X[72]+3*X[376], -3*X[165]+2*X[63967], -5*X[631]+4*X[5777], -3*X[944]+2*X[3057], -6*X[946]+7*X[50190], -2*X[960]+3*X[63432], -4*X[1125]+3*X[61705], -3*X[1699]+4*X[12005], -7*X[3090]+6*X[5927], -5*X[3091]+6*X[10202], -5*X[3522]+4*X[31837] and many others

X(64358) lies on these lines: {1, 10308}, {2, 13369}, {3, 3219}, {4, 7}, {5, 27186}, {11, 18243}, {20, 912}, {30, 3868}, {40, 2801}, {57, 41562}, {63, 3651}, {72, 376}, {75, 48877}, {78, 7171}, {84, 943}, {90, 104}, {165, 63967}, {222, 6198}, {226, 6845}, {329, 6899}, {355, 6951}, {382, 24475}, {411, 13243}, {443, 17616}, {500, 28606}, {515, 1770}, {517, 3529}, {518, 6361}, {553, 10399}, {603, 3465}, {631, 5777}, {651, 1062}, {916, 11412}, {944, 3057}, {946, 50190}, {956, 12529}, {960, 63432}, {993, 16132}, {1006, 7330}, {1012, 12684}, {1056, 12711}, {1058, 17625}, {1125, 61705}, {1158, 11491}, {1479, 16127}, {1490, 1708}, {1519, 54227}, {1614, 47371}, {1699, 12005}, {1745, 7004}, {1768, 6796}, {1776, 7742}, {1836, 16116}, {1858, 4293}, {1864, 64132}, {1870, 64057}, {1898, 3086}, {2096, 6934}, {2771, 3648}, {2772, 23156}, {2808, 5562}, {3090, 5927}, {3091, 10202}, {3100, 3157}, {3146, 24474}, {3149, 26877}, {3218, 6985}, {3487, 10391}, {3522, 31837}, {3524, 5044}, {3525, 11227}, {3528, 31805}, {3545, 5439}, {3560, 18444}, {3562, 64054}, {3576, 31803}, {3579, 3681}, {3583, 41690}, {3587, 3951}, {3616, 31937}, {3652, 62838}, {3655, 3890}, {3656, 62854}, {3660, 47743}, {3678, 35242}, {3698, 38074}, {3873, 12699}, {3874, 41869}, {3877, 34773}, {3878, 50811}, {3881, 31162}, {3885, 18526}, {3889, 22791}, {3897, 12919}, {3916, 6876}, {3918, 61256}, {3927, 37426}, {3935, 35448}, {3982, 18398}, {4297, 5693}, {4303, 24430}, {4305, 64041}, {4420, 35238}, {4654, 10122}, {4662, 5657}, {5067, 10157}, {5083, 9614}, {5225, 5570}, {5229, 13750}, {5248, 7701}, {5249, 6990}, {5450, 37616}, {5492, 62831}, {5534, 63985}, {5603, 12675}, {5658, 6834}, {5691, 5884}, {5720, 6940}, {5731, 5887}, {5732, 55104}, {5758, 10430}, {5770, 6838}, {5791, 58658}, {5811, 6947}, {5836, 34627}, {5883, 18492}, {5886, 26201}, {5902, 31673}, {5904, 31730}, {5905, 6851}, {5918, 63976}, {6000, 23154}, {6147, 11020}, {6197, 63434}, {6245, 6830}, {6260, 6941}, {6326, 63983}, {6763, 16143}, {6833, 12664}, {6841, 31019}, {6848, 41560}, {6895, 37826}, {6896, 9776}, {6902, 37822}, {6903, 58798}, {6909, 37700}, {6912, 37615}, {6915, 37612}, {6920, 18443}, {6922, 13257}, {6927, 11575}, {6937, 51755}, {6946, 37534}, {6950, 33597}, {6972, 37713}, {7411, 26921}, {7491, 9964}, {7967, 12672}, {7971, 10698}, {7986, 17016}, {7987, 20117}, {7992, 53053}, {8143, 62840}, {8144, 23070}, {8227, 31871}, {8581, 12710}, {8726, 64197}, {8728, 10861}, {9021, 48905}, {9579, 18389}, {9638, 36059}, {9780, 40296}, {9856, 10595}, {9859, 37429}, {9955, 64149}, {9965, 14054}, {10156, 61867}, {10404, 17637}, {10531, 64130}, {10728, 11570}, {10786, 14647}, {10806, 54228}, {11108, 60884}, {11459, 11573}, {11523, 58808}, {12082, 37547}, {12114, 21740}, {12116, 18839}, {12532, 38761}, {12665, 34474}, {12691, 52026}, {12701, 17660}, {12775, 49171}, {13151, 16865}, {13624, 56203}, {13754, 20243}, {14923, 28204}, {15016, 19925}, {15045, 58497}, {15064, 31423}, {15528, 59391}, {15682, 24473}, {16138, 62870}, {17074, 37696}, {17483, 37433}, {17538, 31793}, {17613, 64116}, {17615, 59591}, {17857, 64129}, {18517, 20292}, {18525, 50239}, {18540, 54392}, {18623, 38295}, {18908, 31787}, {19904, 37441}, {21161, 31424}, {21312, 42461}, {23361, 53252}, {24468, 63267}, {25413, 28224}, {26040, 45084}, {26200, 61284}, {26871, 56876}, {28164, 37625}, {28186, 64044}, {28461, 62829}, {29958, 64100}, {30290, 64110}, {31053, 37356}, {31418, 41871}, {31788, 59388}, {31822, 62021}, {33557, 37584}, {33575, 61787}, {33815, 34648}, {34339, 59387}, {34381, 39874}, {36002, 37532}, {37000, 64190}, {37427, 54398}, {37430, 57287}, {37460, 41609}, {37531, 63984}, {41465, 64039}, {41706, 64119}, {42463, 43574}, {43177, 60978}, {44547, 63995}, {45977, 63992}, {46475, 63158}, {50528, 62858}, {50558, 62801}, {56762, 63961}, {58630, 64108}, {60961, 63999}, {61762, 63430}, {62871, 63291}, {63974, 64295}, {64147, 64324}

X(64358) = reflection of X(i) in X(j) for these {i,j}: {4, 1071}, {382, 24475}, {944, 12680}, {3146, 24474}, {3869, 18481}, {3885, 18526}, {5691, 5884}, {5693, 4297}, {5904, 31730}, {10728, 11570}, {12528, 3}, {12532, 38761}, {12664, 18238}, {12666, 6261}, {12688, 12675}, {14872, 9943}, {15682, 24473}, {18239, 9942}, {31828, 26201}, {40263, 13369}, {40266, 34773}, {41869, 3874}, {64021, 15071}, {64144, 12671}
X(64358) = anticomplement of X(40263)
X(64358) = X(i)-Dao conjugate of X(j) for these {i, j}: {40263, 40263}
X(64358) = pole of line {905, 35057} with respect to the incircle
X(64358) = pole of line {1836, 3086} with respect to the Feuerbach hyperbola
X(64358) = pole of line {37584, 52012} with respect to the Stammler hyperbola
X(64358) = pole of line {17896, 25593} with respect to the Steiner circumellipse
X(64358) = pole of line {1459, 1734} with respect to the Suppa-Cucoanes circle
X(64358) = intersection, other than A, B, C, of circumconics {{A, B, C, X(273), X(10308)}}, {{A, B, C, X(342), X(943)}}, {{A, B, C, X(942), X(2188)}}
X(64358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 41854, 3651}, {78, 7171, 37403}, {84, 18446, 6906}, {411, 13243, 24467}, {515, 15071, 64021}, {944, 12246, 6938}, {1490, 30304, 63399}, {1490, 63399, 6905}, {2096, 64144, 6934}, {2771, 18481, 3869}, {5768, 6223, 4}, {5927, 9940, 3090}, {6001, 12680, 944}, {6261, 10085, 104}, {9942, 18239, 5658}, {9943, 14872, 5657}, {9960, 12669, 1071}, {11220, 12528, 3}, {12675, 12688, 5603}, {26201, 31828, 5886}, {31805, 64107, 3528}, {33597, 34862, 6950}

X(64359) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND ANTI-MANDART-INCIRCLE

Barycentrics    a^2*(a^4-b^4+a^2*b*c+b^3*c+b^2*c^2+b*c^3-c^4-2*a^3*(b+c)+2*a*(b^3+c^3)) : :

X(64359) lies on these lines: {2, 15931}, {3, 3897}, {7, 2078}, {21, 18481}, {35, 145}, {36, 2320}, {55, 3218}, {100, 34879}, {104, 3655}, {535, 15175}, {993, 6224}, {1001, 10129}, {1617, 29817}, {1621, 1836}, {1768, 35258}, {3869, 16761}, {3872, 4996}, {3877, 37286}, {3935, 6600}, {4188, 11024}, {4189, 5450}, {4293, 10587}, {4679, 63917}, {4881, 52148}, {5217, 8668}, {5248, 10483}, {5250, 16132}, {5267, 45392}, {5744, 64146}, {6636, 10434}, {6796, 37291}, {6986, 25005}, {7987, 37293}, {8053, 16874}, {10267, 18444}, {10404, 63269}, {11113, 22799}, {11220, 20835}, {13589, 31394}, {16112, 60969}, {20045, 25241}, {20060, 54430}, {20846, 59366}, {27003, 37578}, {31660, 62858}, {35202, 37307}, {36867, 54391}, {38460, 40292}, {41341, 64149}, {51111, 64362}, {59331, 64281}, {63974, 64295}, {64147, 64324}

X(64359) = X(i)-vertex conjugate of X(j) for these {i, j}: {3218, 50359}
X(64359) = pole of line {3218, 50359} with respect to the circumcircle

X(64360) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND ANTI-TANGENTIAL-MIDARC

Barycentrics    a*(a+b-c)*(a-b+c)*(3*a^4+2*a^3*(b+c)-(b^2-c^2)^2-2*a^2*(b^2+c^2)-2*a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64360) lies on circumconic {{A, B, C, X(10308), X(55105)}} and on these lines: {1, 10308}, {33, 64057}, {34, 222}, {56, 6610}, {58, 56848}, {65, 62207}, {73, 991}, {77, 1935}, {84, 20277}, {109, 59316}, {208, 7335}, {221, 3057}, {223, 580}, {225, 18623}, {269, 1451}, {651, 1038}, {1406, 54418}, {1413, 17603}, {1448, 2003}, {1455, 34471}, {1456, 17609}, {1457, 61762}, {1465, 37545}, {3157, 37483}, {3468, 63399}, {4320, 64020}, {4662, 9370}, {5903, 21147}, {6357, 57282}, {8614, 54421}, {10394, 34028}, {10404, 62845}, {10571, 37618}, {12514, 61225}, {17074, 19372}, {23070, 64053}, {23154, 32065}, {26892, 39791}, {31792, 34040}, {31938, 54289}, {34033, 53053}, {34036, 50190}, {36986, 47371}, {47057, 62871}, {63974, 64295}, {64147, 64324}

X(64360) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {222, 64055, 34}, {1394, 1419, 73}, {21147, 34043, 54400}

X(64361) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND ANTICOMPLEMENTARY

Barycentrics    a^2*(b+c)+2*(b-c)^2*(b+c)+a*(-3*b^2+b*c-3*c^2) : :

X(64361) lies on circumconic {{A, B, C, X(6548), X(14497)}} and on these lines: {1, 31254}, {2, 3689}, {8, 3090}, {9, 10707}, {11, 63961}, {63, 10032}, {75, 693}, {100, 5231}, {142, 11025}, {144, 5057}, {149, 62838}, {442, 62854}, {518, 10129}, {519, 17057}, {908, 3681}, {1000, 53620}, {1145, 1484}, {1320, 3679}, {1621, 24392}, {2886, 3873}, {2975, 33557}, {3006, 17233}, {3120, 62868}, {3218, 31140}, {3219, 11235}, {3419, 3655}, {3434, 5744}, {3626, 7705}, {3813, 3890}, {3816, 61032}, {3829, 27131}, {3838, 4430}, {3869, 6841}, {3872, 6326}, {3876, 24387}, {3877, 21630}, {3925, 17051}, {3957, 31245}, {4080, 49501}, {4197, 49627}, {4384, 30857}, {4431, 33089}, {4661, 17605}, {4662, 5154}, {4678, 17606}, {4691, 15079}, {4850, 29676}, {4861, 58744}, {4956, 17262}, {5086, 6838}, {5176, 38074}, {5178, 6989}, {5219, 62236}, {5316, 24386}, {5745, 34611}, {6067, 25722}, {6601, 18230}, {6734, 6943}, {6764, 10585}, {7704, 31835}, {9347, 11269}, {9352, 33110}, {9780, 14150}, {11238, 27065}, {12625, 51683}, {12730, 51102}, {17064, 62814}, {17236, 46909}, {17241, 29824}, {17246, 33134}, {17721, 33139}, {20292, 24477}, {21026, 31137}, {21242, 33120}, {21283, 32851}, {24892, 62806}, {25525, 62863}, {26738, 49490}, {27757, 49460}, {28606, 29690}, {29664, 62840}, {33104, 62795}, {33111, 62866}, {33142, 62807}, {36922, 62826}, {37651, 49772}, {41556, 60988}, {49719, 59491}, {52367, 62827}, {60933, 62235}, {60964, 64375}, {61156, 61649}, {62835, 64109}, {63974, 64295}, {64147, 64324}

X(64361) = reflection of X(i) in X(j) for these {i,j}: {64343, 52638}
X(64361) = complement of X(64343)
X(64361) = anticomplement of X(52638)
X(64361) = X(i)-Dao conjugate of X(j) for these {i, j}: {52638, 52638}
X(64361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64343, 52638}, {2886, 51463, 31019}, {4847, 11680, 3681}, {26015, 33108, 64149}, {29676, 33136, 4850}, {29690, 33141, 28606}, {31019, 51463, 3873}

X(64362) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 2ND CIRCUMPERP TANGENTIAL

Barycentrics    a^2*(a^5-b^5+2*b^4*c-2*b^3*c^2-2*b^2*c^3+2*b*c^4-c^5-a^4*(b+c)+a^3*(-2*b^2+b*c-2*c^2)+a^2*(2*b^3-b^2*c-b*c^2+2*c^3)+a*(b^4-b^3*c+5*b^2*c^2-b*c^3+c^4)) : :

X(64362) lies on these lines: {1, 27086}, {3, 4861}, {8, 6796}, {21, 5832}, {35, 2320}, {36, 145}, {40, 4996}, {56, 3889}, {100, 26286}, {165, 34758}, {404, 17662}, {517, 45392}, {993, 15680}, {1476, 13587}, {2975, 3419}, {3241, 37583}, {3428, 56288}, {3522, 43161}, {3616, 5766}, {3869, 48667}, {3885, 5172}, {3890, 37308}, {4057, 23361}, {4420, 35252}, {4511, 11249}, {5541, 7280}, {6224, 8666}, {6261, 12532}, {6987, 10527}, {10966, 37300}, {14804, 25439}, {16143, 62824}, {22754, 37282}, {22767, 37301}, {32612, 64173}, {36152, 38460}, {36867, 62837}, {37293, 54286}, {40255, 52270}, {51111, 64359}, {63974, 64295}, {64147, 64324}

X(64363) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 1ST CIRCUMPERP

Barycentrics    a*(4*a^5+7*a^3*b*c-8*a^4*(b+c)+2*b*(b-c)^2*c*(b+c)+a^2*(8*b^3-2*b^2*c-2*b*c^2+8*c^3)+a*(-4*b^4+b^3*c+2*b^2*c^2+b*c^3-4*c^4)) : :

X(64363) lies on these lines: {36, 4421}, {55, 6173}, {57, 3957}, {993, 21161}, {1376, 15931}, {1621, 9580}, {3158, 60989}, {3576, 54286}, {10914, 63752}, {11034, 61153}, {30827, 64154}, {35271, 37525}, {37578, 52804}, {58328, 60977}, {63974, 64295}, {64147, 64324}

X(64364) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 2ND CIRCUMPERP

Barycentrics    a*(4*a^6-4*a^5*(b+c)-2*b*c*(b^2-c^2)^2-a^4*(8*b^2+b*c+8*c^2)+a^3*(8*b^3-3*b^2*c-3*b*c^2+8*c^3)+a^2*(4*b^4+3*b^3*c+14*b^2*c^2+3*b*c^3+4*c^4)+a*(-4*b^5+7*b^4*c+b^3*c^2+b^2*c^3+7*b*c^4-4*c^5)) : :

X(64364) lies on these lines: {35, 3633}, {40, 5267}, {56, 60982}, {104, 59331}, {993, 3651}, {3243, 3601}, {3340, 4189}, {3576, 63437}, {3652, 31424}, {11495, 37022}, {12767, 51576}, {15829, 37106}, {63974, 64295}, {64147, 64324}

X(64365) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 5TH CONWAY

Barycentrics    a*(a^5*(b+c)+3*a^3*b*c*(b+c)-b*c*(b+c)^2*(b^2+c^2)+2*a^4*(b^2+b*c+c^2)-a^2*(2*b^4+b^3*c+4*b^2*c^2+b*c^3+2*c^4)-a*(b^5+4*b^4*c+3*b^3*c^2+3*b^2*c^3+4*b*c^4+c^5)) : :
X(64365) = -3*X[2]+2*X[10408]

X(64365) lies on these lines: {1, 21}, {2, 10408}, {8, 1764}, {12, 29472}, {56, 16574}, {72, 37620}, {78, 10882}, {405, 35620}, {908, 19863}, {956, 10441}, {958, 10473}, {960, 10475}, {1215, 15825}, {3436, 10479}, {3649, 29382}, {3741, 12527}, {3872, 12435}, {3895, 12546}, {4385, 6996}, {4388, 48883}, {4652, 10434}, {4847, 12545}, {4861, 11521}, {8583, 21371}, {10404, 29788}, {10446, 64081}, {10455, 20245}, {10478, 10527}, {10480, 12513}, {11021, 54392}, {12053, 24705}, {12544, 42012}, {12547, 64150}, {16828, 30007}, {17733, 24068}, {21061, 56318}, {23361, 46877}, {24390, 48899}, {63974, 64295}, {64147, 64324}

X(64365) = anticomplement of X(10408)
X(64365) = X(i)-Dao conjugate of X(j) for these {i, j}: {10408, 10408}
X(64365) = pole of line {3882, 21859} with respect to the Yff parabola
X(64365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2975, 35614, 1}, {10476, 57279, 11679}

X(64366) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND EXCENTERS-MIDPOINTS

Barycentrics    a*(9*a^5-15*a^4*(b+c)+a^3*(-6*b^2+4*b*c-6*c^2)-a*(b+c)^2*(3*b^2-10*b*c+3*c^2)-(b-c)^2*(3*b^3+b^2*c+b*c^2+3*c^3)+2*a^2*(9*b^3+b^2*c+b*c^2+9*c^3)) : :

X(64366) lies on these lines: {1, 63382}, {7, 35258}, {55, 3243}, {165, 2550}, {1155, 38399}, {1836, 4512}, {3035, 21153}, {3174, 35445}, {3633, 61763}, {4297, 10268}, {4640, 5732}, {5794, 18253}, {30503, 46684}, {63974, 64295}, {64147, 64324}

X(64367) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND EXCENTERS-REFLECTIONS

Barycentrics    a*(a^6-4*a^5*(b+c)+a^4*(b^2+14*b*c+c^2)+(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)+a^3*(8*b^3-6*b^2*c-6*b*c^2+8*c^3)-a^2*(5*b^4+6*b^3*c-2*b^2*c^2+6*b*c^3+5*c^4)-2*a*(2*b^5-5*b^4*c+b^3*c^2+b^2*c^3-5*b*c^4+2*c^5)) : :

X(64367) lies on these lines: {1, 35979}, {8, 5187}, {149, 41709}, {517, 63437}, {1001, 3057}, {1482, 3870}, {3340, 60982}, {3680, 27826}, {3692, 17444}, {5506, 9623}, {6765, 12653}, {7354, 11520}, {7962, 24987}, {7982, 41575}, {10941, 25415}, {12559, 14450}, {12773, 62874}, {63974, 64295}, {64147, 64324}

X(64368) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND EXTOUCH

Barycentrics    a*(a-b-c)*(a^4+2*a^3*(b+c)-4*a^2*(b^2+c^2)+(b-c)^2*(3*b^2+14*b*c+3*c^2)-2*a*(b^3+5*b^2*c+5*b*c^2+c^3)) : :

X(64368) lies on these lines: {100, 21153}, {142, 5231}, {200, 1001}, {329, 1699}, {497, 24393}, {956, 1490}, {1482, 4853}, {2886, 4654}, {3243, 64171}, {3358, 10860}, {4882, 5506}, {4915, 12653}, {5082, 11362}, {5785, 26015}, {6734, 10941}, {6745, 36835}, {9614, 31018}, {12526, 12699}, {14450, 54422}, {15733, 38399}, {31435, 51572}, {63974, 64295}, {64147, 64324}, {64153, 64197}

X(64369) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND INNER-GARCIA

Barycentrics    a*(a^6-3*a^3*b*c*(b+c)-(b-c)^2*(b+c)^4-a^4*(3*b^2+b*c+3*c^2)+a*b*c*(3*b^3+5*b^2*c+5*b*c^2+3*c^3)+3*a^2*(b^4+b^3*c+b*c^3+c^4)) : :

X(64369) lies on these lines: {1, 15910}, {3, 5696}, {8, 64278}, {9, 943}, {40, 1726}, {57, 26481}, {63, 2894}, {90, 3929}, {191, 6284}, {224, 3576}, {946, 60979}, {956, 5693}, {1697, 3632}, {1728, 21031}, {1836, 6763}, {1858, 5258}, {2886, 54302}, {2975, 16132}, {3333, 25557}, {3646, 15299}, {3683, 3746}, {3869, 3872}, {3962, 11009}, {5250, 36922}, {5288, 64041}, {5535, 6734}, {5692, 62333}, {5709, 18407}, {5762, 7330}, {5775, 40256}, {6597, 24298}, {6743, 26878}, {6762, 62822}, {10902, 64171}, {11012, 12671}, {12514, 12625}, {12666, 64277}, {14100, 31445}, {15901, 50205}, {24390, 49177}, {31419, 60883}, {31435, 64260}, {31730, 60970}, {41852, 60966}, {41870, 60964}, {50528, 62824}, {60933, 62858}, {62777, 63999}, {64147, 64324}

X(64369) = reflection of X(i) in X(j) for these {i,j}: {40, 2949}
X(64369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2949, 5842, 40}

X(64370) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND OUTER-GARCIA

Barycentrics    3*a^4-7*a^3*(b+c)-6*(b^2-c^2)^2+a^2*(3*b^2-2*b*c+3*c^2)+a*(7*b^3+9*b^2*c+9*b*c^2+7*c^3) : :

X(64370) lies on these lines: {8, 5056}, {10, 38316}, {11, 4668}, {40, 5775}, {3419, 62824}, {3617, 3646}, {3626, 3680}, {3632, 17057}, {3679, 3893}, {3869, 31162}, {3872, 58744}, {3884, 24392}, {4677, 11375}, {4847, 5881}, {4853, 6326}, {4866, 12019}, {5587, 5806}, {6734, 31423}, {6736, 21631}, {6737, 61275}, {6743, 54447}, {10914, 63143}, {24390, 36922}, {24473, 41865}, {28161, 44314}, {41869, 63277}, {61291, 64081}, {63974, 64295}, {64147, 64324}

X(64370) = reflection of X(i) in X(j) for these {i,j}: {64350, 10}

X(64371) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND MEDIAL

Barycentrics    5*a^3-2*a^2*(b+c)+10*(b-c)^2*(b+c)-a*(13*b^2+2*b*c+13*c^2) : :

X(64371) lies on these lines: {2, 12630}, {9, 9779}, {10, 61275}, {1698, 10179}, {2550, 10164}, {2886, 50865}, {3035, 38200}, {3059, 5231}, {3740, 30827}, {3828, 11525}, {3873, 25525}, {4007, 30741}, {5528, 38399}, {6265, 9623}, {6667, 19875}, {7320, 46932}, {9780, 64205}, {14475, 28169}, {36835, 45310}, {63974, 64295}, {64147, 64324}

X(64371) = complement of X(64340)

X(64372) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND 2ND SCHIFFLER

Barycentrics    a*(a^5-a^4*(b+c)+2*a^2*(b-c)^2*(b+c)-(b-c)^2*(b+c)^3+a^3*(-2*b^2+5*b*c-2*c^2)+a*(b-c)^2*(b^2+b*c+c^2)) : :

X(64372) lies on these lines: {1, 399}, {9, 100}, {11, 57}, {35, 1898}, {40, 80}, {46, 12764}, {55, 5531}, {63, 149}, {65, 12767}, {84, 104}, {109, 2310}, {153, 9578}, {165, 7082}, {191, 6284}, {200, 13205}, {214, 31435}, {226, 9809}, {484, 28146}, {516, 1776}, {528, 3929}, {920, 41869}, {936, 2932}, {950, 9803}, {952, 1697}, {971, 2078}, {1158, 9581}, {1317, 37556}, {1320, 6762}, {1376, 58683}, {1421, 7004}, {1479, 5770}, {1484, 9614}, {1706, 59415}, {1708, 45043}, {1717, 2964}, {1727, 3583}, {1728, 5128}, {1864, 3256}, {2006, 38357}, {2093, 6797}, {2136, 12531}, {2800, 3340}, {2801, 10389}, {2802, 57279}, {2958, 5532}, {3035, 7308}, {3057, 7993}, {3073, 33178}, {3219, 20095}, {3254, 60990}, {3333, 16173}, {3336, 10896}, {3359, 12619}, {3577, 48360}, {3586, 62354}, {3601, 6326}, {3612, 45764}, {3646, 64012}, {3652, 15171}, {3811, 47320}, {3928, 10707}, {4551, 9355}, {4654, 62839}, {4939, 34234}, {5083, 11020}, {5119, 9897}, {5218, 60911}, {5219, 21635}, {5227, 9024}, {5250, 6224}, {5285, 13222}, {5290, 63270}, {5437, 31272}, {5438, 17100}, {5506, 52793}, {5541, 41229}, {5709, 10738}, {5727, 12247}, {5825, 9778}, {5851, 60937}, {6264, 7962}, {6265, 13384}, {6597, 15680}, {6713, 37526}, {6763, 12701}, {7098, 51118}, {7171, 38602}, {7284, 55929}, {7972, 31393}, {7991, 17636}, {7992, 34489}, {8068, 59335}, {8069, 61705}, {8545, 63261}, {9612, 16128}, {9841, 38693}, {10085, 12740}, {10106, 64009}, {10396, 12736}, {10572, 64278}, {10582, 58591}, {10742, 18540}, {10768, 24469}, {10777, 53404}, {10860, 46684}, {10864, 64145}, {11010, 59503}, {11518, 11570}, {11523, 12532}, {11529, 11571}, {11698, 31434}, {11715, 63430}, {12331, 61763}, {12629, 17652}, {12672, 64267}, {12688, 37583}, {12691, 12775}, {12699, 54432}, {12735, 51779}, {13199, 55104}, {13273, 37550}, {13274, 54408}, {14100, 64264}, {15071, 62333}, {15297, 64112}, {15298, 41701}, {15558, 38669}, {15863, 63137}, {16138, 18990}, {16370, 33598}, {17654, 54156}, {17661, 64197}, {19914, 49163}, {20418, 49171}, {21630, 62858}, {22560, 62824}, {22775, 63992}, {22935, 30282}, {24466, 37551}, {31231, 64129}, {34474, 61122}, {36278, 61223}, {37532, 51517}, {37534, 57298}, {37541, 60910}, {37584, 48680}, {38761, 58808}, {39692, 59333}, {39778, 62829}, {41546, 62800}, {41689, 59337}, {44547, 63266}, {46685, 56545}, {50443, 63399}, {63974, 64295}, {64147, 64324}

X(64372) = pole of line {53300, 55126} with respect to the Bevan circle
X(64372) = pole of line {676, 8674} with respect to the incircle
X(64372) = pole of line {36, 971} with respect to the Feuerbach hyperbola
X(64372) = pole of line {8674, 10015} with respect to the Suppa-Cucoanes circle
X(64372) = intersection, other than A, B, C, of circumconics {{A, B, C, X(104), X(48357)}}, {{A, B, C, X(3065), X(41798)}}
X(64372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 1768, 57}, {1727, 3583, 5535}, {1768, 51768, 11}, {7004, 64013, 1421}, {13243, 53055, 5083}, {37541, 60910, 61718}

X(64373) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND WASAT

Barycentrics    -7*a^4*b*c+a^5*(b+c)-2*(b-c)^4*(b+c)^2+a^2*(b-c)^2*(2*b^2+3*b*c+2*c^2)+a^3*(-4*b^3+5*b^2*c+5*b*c^2-4*c^3)+a*(b-c)^2*(3*b^3+4*b^2*c+4*b*c^2+3*c^3) : :

X(64373) lies on these lines: {1, 52269}, {2, 36976}, {8, 5087}, {11, 7672}, {92, 44426}, {226, 7671}, {390, 33993}, {497, 3748}, {908, 7678}, {1156, 31164}, {1621, 9580}, {1699, 53055}, {2346, 5219}, {2886, 3877}, {3452, 11680}, {3577, 16174}, {3817, 4342}, {3838, 47357}, {3870, 10707}, {5274, 5603}, {7673, 33108}, {7956, 38038}, {8727, 38055}, {10865, 42356}, {11522, 17097}, {12528, 41685}, {20015, 46873}, {24392, 62826}, {45035, 64163}, {63974, 64295}, {64147, 64324}

X(64373) = inverse of X(7672) in Feuerbach hyperbola

X(64374) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND MOSES-MIYAMOTO

Barycentrics    a*(a^6-4*a^5*(b+c)+12*a^3*b*c*(b+c)+5*a^4*(b^2+c^2)-(b-c)^4*(b^2+c^2)+4*a*(b-c)^2*(b^3+c^3)-a^2*(5*b^4+4*b^3*c+14*b^2*c^2+4*b*c^3+5*c^4)) : :

X(64374) lies on these lines: {1, 21}, {144, 16572}, {219, 4350}, {220, 1445}, {279, 60990}, {329, 15662}, {1212, 7190}, {5228, 15853}, {5543, 61024}, {10025, 27304}, {20111, 55337}, {25930, 55466}, {38459, 60974}, {63974, 64295}, {64147, 64324}

X(64375) = EQUICENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV AND GEMINI 29

Barycentrics    a*(a^5-a^4*(b+c)-2*a^3*(b^2+c^2)-(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)+2*a^2*(b^3+4*b^2*c+4*b*c^2+c^3)+a*(b^4-12*b^3*c+10*b^2*c^2-12*b*c^3+c^4)) : :

X(64375) lies on these lines: {3, 3895}, {9, 26015}, {63, 3058}, {145, 3338}, {354, 1376}, {1260, 4666}, {1317, 51786}, {1320, 37569}, {1445, 41556}, {1998, 5531}, {2320, 38460}, {2900, 3873}, {3218, 9778}, {3555, 18518}, {3875, 4025}, {7674, 60948}, {10051, 12649}, {10707, 60973}, {12704, 36977}, {15185, 60938}, {15680, 62858}, {18481, 62874}, {32636, 63130}, {41860, 62823}, {60964, 64361}, {63974, 64295}, {64147, 64324}

X(64376) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ABC-X3 REFLECTIONS

Barycentrics    a*(a+b)*(a+c)*(a^4-4*a^3*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)+4*a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64376) lies on circumconic {{A, B, C, X(3345), X(3577)}} and on these lines: {2, 64400}, {3, 81}, {4, 5235}, {5, 64425}, {8, 7415}, {20, 333}, {21, 40}, {30, 64402}, {35, 64420}, {36, 64421}, {55, 64382}, {56, 64414}, {58, 165}, {86, 3523}, {182, 64381}, {283, 1817}, {285, 1816}, {371, 64386}, {372, 64385}, {376, 4921}, {382, 64399}, {411, 573}, {474, 24557}, {515, 64401}, {517, 64415}, {601, 39673}, {631, 5333}, {946, 17557}, {962, 11110}, {1014, 15803}, {1043, 59417}, {1151, 64410}, {1152, 64411}, {1155, 5323}, {1350, 37105}, {1593, 64378}, {1657, 64383}, {1764, 6986}, {2077, 64394}, {2303, 37499}, {2941, 3647}, {3098, 64398}, {3193, 11012}, {3428, 4225}, {3522, 16704}, {3524, 42025}, {3576, 64377}, {3579, 4221}, {3651, 48882}, {3916, 7291}, {4184, 10310}, {4188, 21766}, {4220, 35203}, {4267, 5584}, {4276, 59320}, {4278, 59326}, {4281, 4300}, {4297, 64072}, {4653, 7991}, {4658, 7987}, {4720, 11362}, {5273, 54294}, {5324, 7964}, {5731, 56018}, {5759, 25516}, {6200, 64412}, {6244, 17524}, {6282, 54356}, {6284, 64409}, {6396, 64413}, {6684, 14005}, {6876, 37783}, {6904, 26638}, {6915, 21363}, {7354, 64408}, {7957, 18165}, {8025, 15717}, {8273, 18185}, {9540, 64417}, {9778, 37422}, {10164, 25526}, {10303, 25507}, {10304, 41629}, {10461, 56182}, {11248, 64422}, {11249, 64423}, {11414, 64395}, {11822, 64396}, {11823, 64397}, {11824, 64403}, {11825, 64404}, {11826, 64406}, {11827, 64407}, {12305, 64387}, {12306, 64388}, {13935, 64418}, {14008, 15908}, {14110, 41723}, {15692, 42028}, {16451, 63068}, {17551, 31423}, {17553, 28194}, {17588, 20070}, {18163, 37551}, {18180, 31793}, {19543, 37680}, {21669, 48915}, {25060, 37528}, {26290, 64379}, {26291, 64380}, {26294, 64391}, {26295, 64392}, {26860, 61791}, {26935, 27652}, {31445, 56204}, {33557, 48883}, {36745, 61409}, {37264, 37659}, {37418, 56840}, {45498, 64389}, {45499, 64390}, {46877, 64150}, {52680, 63469}, {63974, 64295}, {64147, 64324}

X(64376) = reflection of X(i) in X(j) for these {i,j}: {63291, 3}
X(64376) = pole of line {405, 1490} with respect to the Stammler hyperbola
X(64376) = pole of line {33672, 44140} with respect to the Wallace hyperbola
X(64376) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 48924, 63400}, {3, 64419, 64393}, {58, 165, 37402}, {64393, 64419, 81}

X(64377) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-AQUILA

Barycentrics    a*(a+b)*(a+c)*(a+3*(b+c)) : :

X(64377) lies on these lines: {1, 21}, {2, 41014}, {3, 14996}, {6, 5047}, {8, 86}, {10, 5333}, {27, 11036}, {28, 11396}, {29, 10405}, {30, 63297}, {56, 18185}, {60, 44840}, {65, 1014}, {72, 17019}, {100, 37559}, {145, 1010}, {193, 37314}, {274, 33770}, {284, 11518}, {314, 4968}, {333, 3616}, {354, 18178}, {377, 3945}, {386, 17531}, {387, 4197}, {404, 940}, {405, 37685}, {411, 5707}, {442, 37635}, {445, 56301}, {452, 56020}, {453, 13750}, {496, 14008}, {500, 33557}, {515, 64400}, {517, 37402}, {519, 25526}, {524, 26064}, {551, 4921}, {581, 36002}, {582, 6986}, {759, 28166}, {859, 7373}, {942, 1817}, {961, 10474}, {964, 17379}, {978, 9345}, {999, 4225}, {1043, 3241}, {1058, 14956}, {1100, 2303}, {1125, 5235}, {1126, 56191}, {1193, 4038}, {1201, 4281}, {1203, 5284}, {1319, 64382}, {1330, 42045}, {1386, 41610}, {1408, 11011}, {1412, 3340}, {1434, 3160}, {1449, 2287}, {1459, 57093}, {1482, 4221}, {1697, 18164}, {1698, 28620}, {1724, 16861}, {1778, 16777}, {1790, 11529}, {1816, 41344}, {1834, 6175}, {1870, 54340}, {1963, 35991}, {2099, 5323}, {2363, 31503}, {2475, 41819}, {2476, 5712}, {2478, 63007}, {2646, 64414}, {2895, 4205}, {2906, 30733}, {3017, 63343}, {3146, 62183}, {3247, 3951}, {3285, 16884}, {3286, 3303}, {3295, 4184}, {3304, 4267}, {3445, 5331}, {3559, 63965}, {3576, 64376}, {3617, 14007}, {3621, 17589}, {3622, 11110}, {3623, 11115}, {3624, 64425}, {3634, 28618}, {3649, 18625}, {3651, 5453}, {3672, 58786}, {3710, 29574}, {3736, 64199}, {3745, 56182}, {3746, 4278}, {3811, 9347}, {3871, 5711}, {3876, 5287}, {3895, 17207}, {4083, 57058}, {4193, 63008}, {4202, 17300}, {4203, 19714}, {4220, 48909}, {4228, 17024}, {4229, 20070}, {4252, 17574}, {4276, 5563}, {4340, 17579}, {4383, 17534}, {4393, 26643}, {4420, 4682}, {4646, 16700}, {4649, 27644}, {4667, 64002}, {4697, 58399}, {4854, 14450}, {5044, 17021}, {5045, 18180}, {5051, 17778}, {5247, 55103}, {5361, 16343}, {5372, 19273}, {5396, 6915}, {5439, 17012}, {5603, 64384}, {5687, 35983}, {5706, 7411}, {5710, 18166}, {5718, 7504}, {5751, 12111}, {5886, 64405}, {5902, 37294}, {6147, 31902}, {6186, 51624}, {6505, 14868}, {6744, 17188}, {6767, 17524}, {6905, 45931}, {6912, 11441}, {6920, 36750}, {7968, 64410}, {7969, 64411}, {8543, 64020}, {8951, 17022}, {9780, 25507}, {9955, 64399}, {10246, 64419}, {10247, 15952}, {10449, 19684}, {10618, 22937}, {10974, 61728}, {11108, 63074}, {11114, 63054}, {11363, 64378}, {11364, 64381}, {11365, 64395}, {11366, 64396}, {11367, 64397}, {11368, 64398}, {11370, 64403}, {11371, 64404}, {11373, 64406}, {11374, 64407}, {11375, 64408}, {11376, 64409}, {11381, 14520}, {11553, 16133}, {11831, 64402}, {12112, 21669}, {13408, 52841}, {13587, 37522}, {13728, 32863}, {13740, 19717}, {13869, 57589}, {13883, 64417}, {13936, 64418}, {14016, 38295}, {14020, 63052}, {14815, 63519}, {14997, 16842}, {15671, 61661}, {15678, 49739}, {15679, 49744}, {16048, 63004}, {16050, 29585}, {16053, 29624}, {16054, 17014}, {16062, 63056}, {16137, 37369}, {16139, 32167}, {16342, 37683}, {16454, 20018}, {16466, 29814}, {16696, 37548}, {16845, 63067}, {16853, 63096}, {16859, 63095}, {16865, 63039}, {16916, 20145}, {17016, 17518}, {17056, 24883}, {17097, 54292}, {17164, 41813}, {17167, 21620}, {17175, 49495}, {17483, 50067}, {17514, 49718}, {17535, 37674}, {17536, 32911}, {17546, 37680}, {17549, 19765}, {17553, 38314}, {17609, 18165}, {17637, 44913}, {17686, 20132}, {17697, 37677}, {18465, 34772}, {18493, 64383}, {18991, 64385}, {18992, 64386}, {19270, 37639}, {19280, 19740}, {19742, 37035}, {19743, 56983}, {19783, 63057}, {19859, 41930}, {19874, 25508}, {20077, 49735}, {20086, 49716}, {20090, 26117}, {20970, 37675}, {21161, 63307}, {23059, 54417}, {23544, 25429}, {24474, 37418}, {24851, 64164}, {24880, 63344}, {24936, 35466}, {25055, 64424}, {25060, 37592}, {25441, 30831}, {26365, 64379}, {26366, 64380}, {26369, 64391}, {26370, 64392}, {27804, 63996}, {30143, 37783}, {30966, 32004}, {31034, 52258}, {31660, 63304}, {32772, 35633}, {33100, 63285}, {33296, 51356}, {33953, 49476}, {34064, 56318}, {35762, 64412}, {35763, 64413}, {35981, 60691}, {35997, 36279}, {37224, 63088}, {37230, 63374}, {37296, 61155}, {37492, 63183}, {37538, 59354}, {37593, 56288}, {39948, 63157}, {45398, 64387}, {45399, 64388}, {45500, 64389}, {45501, 64390}, {47033, 63370}, {47115, 51966}, {48282, 57189}, {48283, 57246}, {49745, 63401}, {52269, 63318}, {54358, 56000}, {56023, 64071}, {56936, 56984}, {63974, 64295}, {64147, 64324}

X(64377) = reflection of X(i) in X(j) for these {i,j}: {37402, 64393}
X(64377) = perspector of circumconic {{A, B, C, X(662), X(4633)}}
X(64377) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 60243}, {37, 39948}, {42, 28626}, {512, 58135}, {523, 28148}, {1400, 30711}
X(64377) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 60243}, {3624, 42031}, {39054, 58135}, {40582, 30711}, {40589, 39948}, {40592, 28626}
X(64377) = X(i)-Ceva conjugate of X(j) for these {i, j}: {63157, 21}
X(64377) = X(i)-cross conjugate of X(j) for these {i, j}: {3247, 25507}
X(64377) = pole of line {24006, 55285} with respect to the polar circle
X(64377) = pole of line {4197, 5949} with respect to the Kiepert hyperbola
X(64377) = pole of line {100, 43356} with respect to the Kiepert parabola
X(64377) = pole of line {23090, 57093} with respect to the MacBeath circumconic
X(64377) = pole of line {1, 3683} with respect to the Stammler hyperbola
X(64377) = pole of line {4560, 57112} with respect to the Steiner circumellipse
X(64377) = pole of line {101, 43356} with respect to the Hutson-Moses hyperbola
X(64377) = pole of line {75, 3616} with respect to the Wallace hyperbola
X(64377) = pole of line {5249, 58786} with respect to the dual conic of Yff parabola
X(64377) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3247)}}, {{A, B, C, X(7), X(31424)}}, {{A, B, C, X(8), X(4512)}}, {{A, B, C, X(10), X(58380)}}, {{A, B, C, X(21), X(40438)}}, {{A, B, C, X(28), X(4658)}}, {{A, B, C, X(31), X(2334)}}, {{A, B, C, X(58), X(56048)}}, {{A, B, C, X(63), X(3951)}}, {{A, B, C, X(65), X(1962)}}, {{A, B, C, X(81), X(25507)}}, {{A, B, C, X(105), X(62821)}}, {{A, B, C, X(283), X(57685)}}, {{A, B, C, X(758), X(3947)}}, {{A, B, C, X(896), X(48026)}}, {{A, B, C, X(993), X(1476)}}, {{A, B, C, X(1320), X(5250)}}, {{A, B, C, X(1442), X(3647)}}, {{A, B, C, X(1468), X(3445)}}, {{A, B, C, X(2292), X(31503)}}, {{A, B, C, X(2298), X(54354)}}, {{A, B, C, X(2346), X(5248)}}, {{A, B, C, X(2363), X(64415)}}, {{A, B, C, X(3743), X(53114)}}, {{A, B, C, X(3747), X(50509)}}, {{A, B, C, X(3869), X(56030)}}, {{A, B, C, X(5331), X(16948)}}, {{A, B, C, X(12514), X(17097)}}, {{A, B, C, X(28606), X(42029)}}, {{A, B, C, X(39948), X(62812)}}
X(64377) = barycentric product X(i)*X(j) for these (i, j): {1, 25507}, {27, 3951}, {81, 9780}, {333, 3339}, {2185, 3947}, {3247, 86}, {28147, 662}, {42029, 58}, {48026, 99}, {50509, 799}
X(64377) = barycentric quotient X(i)/X(j) for these (i, j): {1, 60243}, {21, 30711}, {58, 39948}, {81, 28626}, {163, 28148}, {662, 58135}, {3247, 10}, {3339, 226}, {3947, 6358}, {3951, 306}, {9780, 321}, {25507, 75}, {28147, 1577}, {42029, 313}, {48026, 523}, {50509, 661}
X(64377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1046, 1962}, {1, 191, 58380}, {1, 4658, 81}, {1, 81, 21}, {2, 56018, 64401}, {8, 86, 14005}, {10, 28619, 5333}, {10, 5333, 17551}, {81, 3193, 46441}, {145, 8025, 1010}, {333, 3616, 17557}, {517, 64393, 37402}, {940, 19767, 404}, {1125, 64072, 5235}, {1834, 37631, 26131}, {2475, 41819, 49743}, {3241, 42028, 51669}, {3622, 16704, 11110}, {5453, 45923, 3651}, {5711, 17018, 3871}, {17056, 24883, 31254}, {37559, 59301, 100}, {38314, 41629, 17553}, {49743, 64167, 2475}

X(64378) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-ARA

Barycentrics    a*(a+b)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2-c^2-2*a*(b+c))*(a^2-b^2+c^2) : :

X(64378) lies on these lines: {4, 333}, {19, 1707}, {21, 1829}, {24, 64393}, {25, 81}, {27, 1851}, {28, 34}, {33, 64414}, {86, 6353}, {162, 4206}, {171, 2333}, {235, 64400}, {242, 44734}, {256, 1172}, {427, 5235}, {428, 4921}, {429, 26064}, {444, 27644}, {468, 5333}, {511, 1812}, {573, 4219}, {1593, 64376}, {1598, 64419}, {1824, 3219}, {1828, 54340}, {1843, 41610}, {2212, 38832}, {2303, 44103}, {2355, 14014}, {3060, 7466}, {3193, 26377}, {3559, 52082}, {3736, 40976}, {4183, 17185}, {4184, 11383}, {4213, 30966}, {4225, 22479}, {4232, 8025}, {5064, 64424}, {5090, 64401}, {5094, 64425}, {5146, 31902}, {5331, 34260}, {5410, 64386}, {5411, 64385}, {5412, 64410}, {5413, 64411}, {6995, 16704}, {7009, 56014}, {7487, 64384}, {7714, 41629}, {7718, 56018}, {11363, 64377}, {11380, 64381}, {11384, 64396}, {11385, 64397}, {11386, 64398}, {11388, 64403}, {11389, 64404}, {11390, 64406}, {11391, 64407}, {11392, 64408}, {11393, 64409}, {11396, 64415}, {11398, 64420}, {11399, 64421}, {11400, 64422}, {11401, 64423}, {11832, 64402}, {13884, 64417}, {13937, 64418}, {18494, 64383}, {25507, 38282}, {26371, 64379}, {26372, 64380}, {26375, 64391}, {26376, 64392}, {26378, 64394}, {26637, 35973}, {35764, 64412}, {35765, 64413}, {42025, 62978}, {42028, 62979}, {44086, 61409}, {45400, 64387}, {45401, 64388}, {45502, 64389}, {45503, 64390}, {49542, 64072}, {63974, 64295}, {64147, 64324}

X(64378) = X(i)-isoconjugate-of-X(j) for these {i, j}: {71, 56044}, {73, 56205}
X(64378) = pole of line {4086, 48047} with respect to the polar circle
X(64378) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(256)}}, {{A, B, C, X(603), X(7116)}}, {{A, B, C, X(4104), X(35650)}}, {{A, B, C, X(5323), X(5331)}}, {{A, B, C, X(48136), X(51654)}}
X(64378) = barycentric product X(i)*X(j) for these (i, j): {17257, 28}, {17594, 27}, {48136, 648}
X(64378) = barycentric quotient X(i)/X(j) for these (i, j): {28, 56044}, {1172, 56205}, {4104, 52369}, {17257, 20336}, {17594, 306}, {48136, 525}
X(64378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58, 7713, 28}

X(64379) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST ANTI-AURIGA

Barycentrics    a*(a+b)*(a+c)*(a+b+c)*(a^3-3*a^2*(b+c)+(b-c)^2*(b+c)+a*(b^2+4*b*c+c^2))-8*a*(a+b)*(a+c)*(b+c)*sqrt(R*(r+4*R))*S : :

X(64379) lies on these lines: {1, 64380}, {21, 45711}, {58, 26296}, {81, 5597}, {333, 26394}, {3193, 26399}, {4184, 26393}, {4225, 26319}, {4921, 45696}, {5235, 26359}, {18496, 64383}, {26290, 64376}, {26302, 64395}, {26310, 64398}, {26326, 64400}, {26334, 64403}, {26344, 64404}, {26351, 64414}, {26365, 64377}, {26371, 64378}, {26379, 64381}, {26380, 64382}, {26381, 64384}, {26382, 64401}, {26383, 64402}, {26384, 64385}, {26385, 64386}, {26386, 64405}, {26387, 64409}, {26388, 64408}, {26389, 64407}, {26390, 64406}, {26395, 64415}, {26396, 64391}, {26397, 64392}, {26398, 64393}, {26400, 64394}, {26401, 64423}, {26402, 64422}, {41610, 45724}, {44582, 64410}, {44583, 64411}, {45345, 64387}, {45348, 64388}, {45349, 64389}, {45352, 64390}, {45354, 64397}, {45355, 64399}, {45357, 64412}, {45360, 64413}, {45365, 64417}, {45366, 64418}, {45369, 64419}, {45371, 64420}, {45373, 64421}, {48511, 64072}, {63974, 64295}, {64147, 64324}

X(64380) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND ANTI-AURIGA

Barycentrics    a*(a+b)*(a+c)*(a+b+c)*(a^3-3*a^2*(b+c)+(b-c)^2*(b+c)+a*(b^2+4*b*c+c^2))+8*a*(a+b)*(a+c)*(b+c)*sqrt(R*(r+4*R))*S : :

X(64380) lies on these lines: {1, 64379}, {21, 45712}, {58, 26297}, {81, 5598}, {333, 26418}, {3193, 26423}, {4184, 26417}, {4225, 26320}, {4921, 45697}, {5235, 26360}, {18498, 64383}, {26291, 64376}, {26303, 64395}, {26311, 64398}, {26327, 64400}, {26335, 64403}, {26345, 64404}, {26352, 64414}, {26366, 64377}, {26372, 64378}, {26403, 64381}, {26404, 64382}, {26405, 64384}, {26406, 64401}, {26407, 64402}, {26408, 64385}, {26409, 64386}, {26410, 64405}, {26411, 64409}, {26412, 64408}, {26413, 64407}, {26414, 64406}, {26419, 64415}, {26420, 64391}, {26421, 64392}, {26422, 64393}, {26424, 64394}, {26425, 64423}, {26426, 64422}, {41610, 45725}, {44584, 64410}, {44585, 64411}, {45346, 64388}, {45347, 64387}, {45350, 64390}, {45351, 64389}, {45353, 64396}, {45356, 64399}, {45358, 64413}, {45359, 64412}, {45367, 64418}, {45368, 64417}, {45370, 64419}, {45372, 64420}, {45374, 64421}, {48512, 64072}, {63974, 64295}, {64147, 64324}

X(64381) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 5TH ANTI-BROCARD

Barycentrics    a*(a+b)*(a+c)*(b^2*c^2+2*a^3*(b+c)+a^2*(b^2+c^2)) : :

X(64381) lies on these lines: {21, 12194}, {32, 81}, {58, 10789}, {83, 5235}, {86, 7793}, {98, 64400}, {182, 64376}, {333, 7787}, {1078, 5333}, {2080, 64393}, {3193, 26431}, {3216, 4279}, {4184, 11490}, {4225, 22520}, {4921, 12150}, {7808, 64425}, {10788, 64384}, {10790, 64395}, {10791, 64401}, {10792, 64403}, {10793, 64404}, {10794, 64406}, {10795, 64407}, {10796, 64405}, {10797, 64408}, {10798, 64409}, {10799, 64414}, {10800, 64415}, {10801, 64420}, {10802, 64421}, {10803, 64422}, {10804, 64423}, {11364, 64377}, {11380, 64378}, {11837, 64396}, {11838, 64397}, {11839, 64402}, {11842, 64419}, {12212, 41610}, {12835, 64382}, {13885, 64417}, {13938, 64418}, {18501, 64383}, {18502, 64399}, {18993, 64385}, {18994, 64386}, {26379, 64379}, {26403, 64380}, {26429, 64391}, {26430, 64392}, {26432, 64394}, {35766, 64412}, {35767, 64413}, {44586, 64410}, {44587, 64411}, {45402, 64387}, {45403, 64388}, {45504, 64389}, {45505, 64390}, {49545, 64072}, {63974, 64295}, {64147, 64324}

X(64382) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND ANTI-CIRCUMPERP-TANGENTIAL

Barycentrics    a*(a+b)*(a+b-c)*(a+c)*(a-b+c)*(a^2-2*a*(b+c)-(b+c)^2) : :

X(64382) lies on these lines: {1, 58392}, {3, 64420}, {4, 64409}, {6, 27621}, {11, 64400}, {12, 5235}, {21, 65}, {27, 1118}, {28, 34}, {36, 64393}, {46, 4221}, {55, 64376}, {56, 81}, {60, 757}, {73, 4281}, {86, 7288}, {201, 35623}, {333, 388}, {404, 4259}, {859, 62843}, {940, 61109}, {999, 64419}, {1010, 1788}, {1155, 37402}, {1319, 64377}, {1399, 39673}, {1400, 2303}, {1405, 37694}, {1412, 3361}, {1420, 4658}, {1434, 7195}, {1454, 16049}, {1466, 3286}, {1468, 1610}, {1469, 41610}, {1470, 64394}, {1478, 64405}, {1708, 47512}, {1778, 2285}, {1780, 17560}, {1792, 5208}, {1812, 37442}, {1817, 54417}, {1875, 54340}, {1940, 44734}, {2067, 64410}, {2099, 64415}, {3193, 26437}, {3339, 52680}, {3340, 4653}, {3474, 37422}, {3476, 56018}, {3485, 11110}, {3486, 7415}, {3585, 64399}, {3600, 16704}, {3911, 25526}, {4184, 11509}, {4228, 56840}, {4276, 37583}, {4288, 54320}, {4293, 64384}, {4720, 41687}, {4921, 5434}, {5221, 11101}, {5252, 64401}, {5253, 26637}, {5265, 8025}, {5298, 42025}, {5333, 5433}, {6502, 64411}, {7342, 30581}, {7412, 37530}, {9655, 64383}, {10106, 64072}, {11237, 64424}, {11337, 36740}, {11375, 17557}, {12835, 64381}, {14005, 24914}, {14016, 14257}, {15556, 35637}, {15952, 36279}, {17524, 37541}, {18178, 64106}, {18954, 64395}, {18955, 64396}, {18956, 64397}, {18957, 64398}, {18958, 64402}, {18959, 64403}, {18960, 64404}, {18961, 64406}, {18962, 64407}, {18965, 64417}, {18966, 64418}, {18967, 64423}, {18995, 64385}, {18996, 64386}, {19366, 27653}, {22097, 37607}, {26380, 64379}, {26404, 64380}, {26435, 64391}, {26436, 64392}, {35768, 64412}, {35769, 64413}, {37357, 64127}, {37384, 37642}, {40571, 57283}, {45404, 64387}, {45405, 64388}, {45506, 64389}, {45507, 64390}, {51966, 59816}, {63974, 64295}, {64147, 64324}

X(64382) = X(i)-isoconjugate-of-X(j) for these {i, j}: {210, 969}, {967, 2321}, {1334, 58012}
X(64382) = X(i)-Dao conjugate of X(j) for these {i, j}: {38960, 4086}
X(64382) = pole of line {78, 210} with respect to the Stammler hyperbola
X(64382) = pole of line {3701, 3718} with respect to the Wallace hyperbola
X(64382) = intersection, other than A, B, C, of circumconics {{A, B, C, X(28), X(757)}}, {{A, B, C, X(34), X(959)}}, {{A, B, C, X(57), X(54320)}}, {{A, B, C, X(58), X(4288)}}, {{A, B, C, X(60), X(2299)}}, {{A, B, C, X(966), X(7713)}}, {{A, B, C, X(968), X(5338)}}, {{A, B, C, X(1395), X(1408)}}, {{A, B, C, X(1396), X(63194)}}, {{A, B, C, X(1443), X(1835)}}, {{A, B, C, X(5323), X(63193)}}
X(64382) = barycentric product X(i)*X(j) for these (i, j): {27, 54320}, {273, 4288}, {1014, 966}, {1414, 45745}, {1434, 968}, {2271, 57785}, {3485, 81}, {4565, 7650}, {4573, 48099}, {11110, 57}
X(64382) = barycentric quotient X(i)/X(j) for these (i, j): {966, 3701}, {968, 2321}, {1014, 58012}, {1408, 967}, {1412, 969}, {1434, 58013}, {2271, 210}, {3485, 321}, {4288, 78}, {11110, 312}, {45745, 4086}, {48099, 3700}, {54320, 306}
X(64382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 58, 5323}, {333, 388, 64408}, {999, 64419, 64421}, {1408, 32636, 1014}

X(64383) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-EHRMANN-MID

Barycentrics    (a+b)*(a+c)*(a^5+a^4*(b+c)-2*(b-c)^2*(b+c)^3+a*(b^2-c^2)^2-2*a^3*(b^2+c^2)+a^2*(b^3+b^2*c+b*c^2+c^3)) : :

X(64383) lies on these lines: {3, 5235}, {4, 5769}, {5, 86}, {21, 18525}, {30, 333}, {58, 18480}, {81, 381}, {355, 15952}, {547, 25507}, {859, 18519}, {999, 64409}, {1010, 18357}, {1043, 37705}, {1408, 10826}, {1656, 64393}, {1657, 64376}, {3091, 26860}, {3193, 18544}, {3286, 18491}, {3295, 64408}, {3534, 64424}, {3545, 8025}, {3830, 4921}, {3843, 64400}, {3845, 41629}, {4184, 18524}, {4221, 5790}, {4225, 26321}, {4267, 18761}, {4653, 28204}, {4658, 9955}, {4720, 50798}, {5054, 64425}, {5055, 5333}, {5066, 42028}, {5690, 37422}, {6740, 37227}, {7415, 28186}, {9654, 64420}, {9655, 64382}, {9668, 64414}, {9669, 64421}, {11110, 34773}, {12699, 64072}, {12702, 64401}, {13665, 64410}, {13785, 64411}, {17194, 18528}, {17524, 18518}, {17556, 26637}, {18163, 18540}, {18178, 31937}, {18180, 40263}, {18440, 41610}, {18493, 64377}, {18494, 64378}, {18496, 64379}, {18498, 64380}, {18501, 64381}, {18503, 64398}, {18508, 64402}, {18510, 64385}, {18512, 64386}, {18526, 64415}, {18539, 64391}, {18542, 64394}, {18543, 64423}, {18545, 64422}, {18653, 52012}, {19543, 37660}, {19709, 42025}, {22791, 56018}, {23251, 64412}, {23261, 64413}, {25526, 61261}, {26336, 64403}, {26346, 64404}, {26438, 64392}, {28619, 61268}, {33295, 36729}, {40266, 41723}, {45375, 64387}, {45376, 64388}, {45377, 64389}, {45378, 64390}, {45379, 64396}, {45380, 64397}, {45384, 64417}, {45385, 64418}, {63974, 64295}, {64147, 64324}

X(64383) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {81, 64399, 381}

X(64384) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-EULER

Barycentrics    (a+b)*(a+c)*(a^5+a^4*(b+c)-(b-c)^2*(b+c)^3+a*(b^2-c^2)^2-2*a^3*(b^2+c^2)) : :

X(64384) lies on these lines: {1, 58383}, {2, 64393}, {3, 333}, {4, 81}, {5, 86}, {8, 4221}, {20, 5767}, {21, 944}, {24, 64395}, {27, 1071}, {28, 5768}, {29, 1437}, {30, 41629}, {40, 64072}, {58, 515}, {84, 18163}, {104, 4225}, {110, 17584}, {119, 14011}, {284, 6245}, {355, 1010}, {376, 4921}, {381, 42028}, {388, 64420}, {405, 26638}, {497, 64421}, {500, 7413}, {517, 37422}, {581, 13478}, {631, 5235}, {946, 4658}, {952, 1043}, {1210, 1412}, {1385, 11110}, {1408, 1837}, {1434, 5708}, {1444, 5770}, {1587, 64410}, {1588, 64411}, {1656, 25507}, {1812, 6827}, {1858, 62342}, {1943, 41340}, {2287, 6865}, {2478, 26637}, {3073, 38832}, {3085, 64408}, {3086, 64409}, {3090, 5333}, {3091, 8025}, {3193, 12116}, {3286, 11500}, {3524, 64424}, {3525, 64425}, {3545, 42025}, {3559, 45766}, {3579, 4229}, {3651, 48923}, {3736, 37699}, {3832, 26860}, {4184, 11491}, {4187, 24556}, {4220, 48877}, {4234, 28204}, {4248, 51420}, {4267, 12114}, {4276, 5450}, {4278, 6796}, {4281, 15486}, {4293, 64382}, {4294, 64414}, {4653, 5882}, {5323, 18391}, {5327, 48482}, {5587, 25526}, {5603, 64377}, {5657, 37402}, {5693, 18417}, {5709, 18206}, {5752, 23512}, {5769, 29767}, {5786, 36746}, {5788, 27164}, {5811, 17183}, {5812, 56020}, {5818, 14005}, {6001, 18178}, {6260, 17197}, {6560, 64412}, {6561, 64413}, {6776, 6851}, {6836, 40571}, {6882, 31631}, {6891, 14868}, {6903, 37783}, {6908, 16713}, {6922, 27398}, {6996, 37536}, {6998, 48887}, {7330, 17185}, {7379, 9958}, {7415, 18481}, {7474, 39572}, {7487, 64378}, {7581, 64386}, {7582, 64385}, {7967, 64415}, {8227, 28619}, {8982, 64392}, {9862, 64398}, {9940, 16054}, {9956, 14007}, {10269, 37442}, {10449, 56960}, {10783, 64403}, {10784, 64404}, {10785, 64406}, {10786, 64407}, {10788, 64381}, {10805, 64422}, {10806, 64423}, {11064, 25647}, {11248, 56181}, {11496, 18185}, {11499, 13588}, {11843, 64396}, {11844, 64397}, {11845, 64402}, {12115, 64394}, {12616, 54323}, {12675, 18165}, {12680, 18191}, {13886, 64417}, {13939, 64418}, {14009, 26470}, {14829, 19543}, {17559, 24557}, {17731, 32515}, {18283, 52891}, {18446, 25516}, {18465, 45770}, {18526, 52352}, {19648, 29766}, {19839, 21277}, {26381, 64379}, {26405, 64380}, {26441, 64391}, {26921, 30273}, {30941, 36670}, {32613, 37296}, {33295, 36674}, {34627, 51669}, {36675, 51356}, {37088, 37482}, {37354, 54349}, {37527, 48937}, {37611, 46877}, {41723, 64021}, {41810, 48917}, {45406, 64387}, {45407, 64388}, {45510, 64389}, {45511, 64390}, {46704, 51340}, {48924, 63402}, {51558, 61409}, {58389, 59624}, {63974, 64295}, {64147, 64324}

X(64384) = midpoint of X(i) and X(j) for these {i,j}: {37422, 56018}
X(64384) = reflection of X(i) in X(j) for these {i,j}: {4, 63318}, {1043, 15952}
X(64384) = pole of line {11249, 13738} with respect to the Stammler hyperbola
X(64384) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37402, 64401, 5657}, {37422, 56018, 517}, {64393, 64405, 2}

X(64385) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-INNER-GREBE

Barycentrics    a*(a+b)*(a+c)*(2*a*(b+c)-S) : :

X(64385) lies on these lines: {2, 6}, {21, 18992}, {58, 19003}, {372, 64376}, {605, 39673}, {1014, 51841}, {1587, 64400}, {1702, 37402}, {3193, 26458}, {3299, 64420}, {3301, 64421}, {3311, 64393}, {4184, 18999}, {4225, 19013}, {4658, 19004}, {5411, 64378}, {6418, 64419}, {6420, 64413}, {7582, 64384}, {7584, 64405}, {7968, 64415}, {13785, 64399}, {13883, 14005}, {13888, 28620}, {13893, 17551}, {13936, 64401}, {13971, 17557}, {18510, 64383}, {18991, 64377}, {18993, 64381}, {18995, 64382}, {19005, 64395}, {19007, 64396}, {19009, 64397}, {19011, 64398}, {19017, 64402}, {19023, 64406}, {19025, 64407}, {19027, 64408}, {19029, 64409}, {19037, 64414}, {19047, 64422}, {19049, 64423}, {25526, 49548}, {26384, 64379}, {26408, 64380}, {26459, 64394}, {35770, 64412}, {45512, 64389}, {45514, 64390}, {49547, 64072}, {63974, 64295}, {64147, 64324}

X(64385) = pole of line {6, 55441} with respect to the Stammler hyperbola

X(64386) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-OUTER-GREBE

Barycentrics    a*(a+b)*(a+c)*(2*a*(b+c)+S) : :

X(64386) lies on these lines: {2, 6}, {21, 18991}, {58, 19004}, {371, 64376}, {606, 39673}, {1014, 51842}, {1588, 64400}, {1703, 37402}, {3193, 26464}, {3299, 64421}, {3301, 64420}, {3312, 64393}, {4184, 19000}, {4225, 19014}, {4658, 19003}, {5410, 64378}, {6417, 64419}, {6419, 64412}, {7581, 64384}, {7583, 64405}, {7969, 64415}, {8983, 17557}, {13665, 64399}, {13883, 64401}, {13936, 14005}, {13942, 28620}, {13947, 17551}, {18512, 64383}, {18992, 64377}, {18994, 64381}, {18996, 64382}, {19006, 64395}, {19008, 64396}, {19010, 64397}, {19012, 64398}, {19018, 64402}, {19024, 64406}, {19026, 64407}, {19028, 64408}, {19030, 64409}, {19038, 64414}, {19048, 64422}, {19050, 64423}, {25526, 49547}, {26385, 64379}, {26409, 64380}, {26465, 64394}, {35771, 64413}, {45513, 64390}, {45515, 64389}, {49548, 64072}, {63974, 64295}, {64147, 64324}

X(64386) = pole of line {6, 55442} with respect to the Stammler hyperbola

X(64387) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST ANTI-KENMOTU CENTERS

Barycentrics    a*(a+b)*(a+c)*(a^2+b^2+c^2-2*a*(b+c)+2*S) : :

X(64387) lies on these lines: {2, 6}, {3, 64389}, {21, 45713}, {58, 45426}, {3102, 64413}, {3193, 45422}, {4184, 45416}, {4225, 45436}, {6289, 64405}, {12305, 64376}, {43119, 64393}, {45345, 64379}, {45347, 64380}, {45375, 64383}, {45398, 64377}, {45400, 64378}, {45402, 64381}, {45404, 64382}, {45406, 64384}, {45411, 64390}, {45424, 64394}, {45428, 64395}, {45430, 64396}, {45432, 64397}, {45434, 64398}, {45438, 64399}, {45440, 64400}, {45444, 64401}, {45446, 64402}, {45454, 64406}, {45456, 64407}, {45458, 64408}, {45460, 64409}, {45462, 64412}, {45470, 64414}, {45476, 64415}, {45488, 64419}, {45490, 64420}, {45492, 64421}, {45494, 64422}, {45496, 64423}, {49347, 64072}, {63974, 64295}, {64147, 64324}

X(64388) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND ANTI-KENMOTU CENTERS

Barycentrics    a*(a+b)*(a+c)*(a^2+b^2+c^2-2*a*(b+c)-2*S) : :

X(64388) lies on these lines: {2, 6}, {3, 64390}, {21, 45714}, {58, 45427}, {3103, 64412}, {3193, 45423}, {4184, 45417}, {4225, 45437}, {6290, 64405}, {12306, 64376}, {43118, 64393}, {45346, 64380}, {45348, 64379}, {45376, 64383}, {45399, 64377}, {45401, 64378}, {45403, 64381}, {45405, 64382}, {45407, 64384}, {45410, 64389}, {45425, 64394}, {45429, 64395}, {45431, 64396}, {45433, 64397}, {45435, 64398}, {45439, 64399}, {45441, 64400}, {45445, 64401}, {45447, 64402}, {45455, 64406}, {45457, 64407}, {45459, 64408}, {45461, 64409}, {45463, 64413}, {45471, 64414}, {45477, 64415}, {45489, 64419}, {45491, 64420}, {45493, 64421}, {45495, 64422}, {45497, 64423}, {49348, 64072}, {63974, 64295}, {64147, 64324}

X(64389) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST ANTI-KENMOTU-FREE-VERTICES

Barycentrics    a*(a+b)*(a+c)*(a^3*(a+2*b+2*c)+(b^2-c^2)^2-2*a*(a+b+c)*(b^2+c^2)-2*(a^2+b^2+c^2-2*a*(b+c))*S) : :

X(64389) lies on these lines: {3, 64387}, {21, 45715}, {39, 64411}, {58, 45530}, {81, 372}, {182, 41610}, {333, 45508}, {641, 5235}, {3193, 45526}, {4184, 45520}, {4225, 45540}, {4921, 41490}, {5062, 64410}, {45349, 64379}, {45351, 64380}, {45377, 64383}, {45410, 64388}, {45498, 64376}, {45500, 64377}, {45502, 64378}, {45504, 64381}, {45506, 64382}, {45510, 64384}, {45512, 64385}, {45515, 64386}, {45522, 64391}, {45525, 64392}, {45528, 64394}, {45532, 64395}, {45534, 64396}, {45536, 64397}, {45538, 64398}, {45542, 64399}, {45544, 64400}, {45546, 64401}, {45548, 64402}, {45550, 64403}, {45553, 64404}, {45554, 64405}, {45556, 64406}, {45558, 64407}, {45560, 64408}, {45562, 64409}, {45565, 64413}, {45570, 64414}, {45572, 64415}, {45574, 64417}, {45577, 64418}, {45578, 64419}, {45580, 64420}, {45582, 64421}, {45584, 64422}, {45586, 64423}, {48764, 64072}, {63974, 64295}, {64147, 64324}

X(64389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {41610, 64393, 64390}

X(64390) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND ANTI-KENMOTU-FREE-VERTICES

Barycentrics    a*(a+b)*(a+c)*(a^3*(a+2*b+2*c)+(b^2-c^2)^2-2*a*(a+b+c)*(b^2+c^2)+2*(a^2+b^2+c^2-2*a*(b+c))*S) : :

X(64390) lies on these lines: {3, 64388}, {21, 45716}, {39, 64410}, {58, 45531}, {81, 371}, {182, 41610}, {333, 45509}, {642, 5235}, {3193, 45527}, {4184, 45521}, {4225, 45541}, {4921, 41491}, {5058, 64411}, {45350, 64380}, {45352, 64379}, {45378, 64383}, {45411, 64387}, {45499, 64376}, {45501, 64377}, {45503, 64378}, {45505, 64381}, {45507, 64382}, {45511, 64384}, {45513, 64386}, {45514, 64385}, {45523, 64392}, {45524, 64391}, {45529, 64394}, {45533, 64395}, {45535, 64396}, {45537, 64397}, {45539, 64398}, {45543, 64399}, {45545, 64400}, {45547, 64401}, {45549, 64402}, {45551, 64404}, {45552, 64403}, {45555, 64405}, {45557, 64406}, {45559, 64407}, {45561, 64408}, {45563, 64409}, {45564, 64412}, {45571, 64414}, {45573, 64415}, {45575, 64418}, {45576, 64417}, {45579, 64419}, {45581, 64420}, {45583, 64421}, {45585, 64422}, {45587, 64423}, {48765, 64072}, {63974, 64295}, {64147, 64324}

X(64390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {41610, 64393, 64389}

X(64391) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 3RD ANTI-TRI-SQUARES-CENTRAL

Barycentrics    (a+b)*(a+c)*(a*(a^2+b^2+c^2-2*a*(b+c))-2*(b+c-2*a)*S) : :

X(64391) lies on these lines: {2, 6}, {21, 45719}, {58, 26300}, {3193, 26517}, {4184, 26512}, {4225, 26324}, {18539, 64383}, {26294, 64376}, {26306, 64395}, {26314, 64398}, {26330, 64400}, {26355, 64414}, {26369, 64377}, {26375, 64378}, {26396, 64379}, {26420, 64380}, {26429, 64381}, {26435, 64382}, {26441, 64384}, {26444, 64401}, {26449, 64402}, {26468, 64405}, {26473, 64409}, {26479, 64408}, {26485, 64407}, {26490, 64406}, {26514, 64415}, {26516, 64393}, {26518, 64394}, {26519, 64423}, {26520, 64422}, {45522, 64389}, {45524, 64390}, {49012, 64396}, {49014, 64397}, {49016, 64399}, {49018, 64412}, {49028, 64419}, {49030, 64420}, {49032, 64421}, {49078, 64072}, {63974, 64295}, {64147, 64324}

X(64392) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 4TH ANTI-TRI-SQUARES-CENTRAL

Barycentrics    (a+b)*(a+c)*(a*(a^2+b^2+c^2-2*a*(b+c))+2*(b+c-2*a)*S) : :

X(64392) lies on these lines: {2, 6}, {21, 45720}, {58, 26301}, {3193, 26522}, {4184, 26513}, {4225, 26325}, {8982, 64384}, {26295, 64376}, {26307, 64395}, {26315, 64398}, {26331, 64400}, {26356, 64414}, {26370, 64377}, {26376, 64378}, {26397, 64379}, {26421, 64380}, {26430, 64381}, {26436, 64382}, {26438, 64383}, {26445, 64401}, {26450, 64402}, {26469, 64405}, {26474, 64409}, {26480, 64408}, {26486, 64407}, {26491, 64406}, {26515, 64415}, {26521, 64393}, {26523, 64394}, {26524, 64423}, {26525, 64422}, {45523, 64390}, {45525, 64389}, {49013, 64396}, {49015, 64397}, {49017, 64399}, {49019, 64413}, {49029, 64419}, {49031, 64420}, {49033, 64421}, {49079, 64072}, {63974, 64295}, {64147, 64324}

X(64393) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-X3-ABC REFLECTIONS

Barycentrics    a*(a+b)*(a+c)*(a^4+2*a^3*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)-2*a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64393) lies on circumconic {{A, B, C, X(104), X(51223)}} and on these lines: {1, 1412}, {2, 64384}, {3, 81}, {4, 86}, {5, 5333}, {20, 8025}, {21, 104}, {24, 64378}, {28, 1790}, {30, 42025}, {35, 64414}, {36, 64382}, {40, 4658}, {55, 64421}, {56, 64420}, {58, 602}, {60, 13151}, {140, 5235}, {182, 41610}, {191, 58392}, {284, 8726}, {333, 631}, {355, 14005}, {371, 64411}, {372, 64410}, {376, 42028}, {394, 13726}, {498, 64408}, {499, 64409}, {500, 4220}, {501, 5358}, {515, 25526}, {517, 37402}, {549, 4921}, {572, 2303}, {601, 38832}, {741, 1292}, {942, 1014}, {943, 3955}, {944, 1010}, {946, 28619}, {991, 52564}, {1006, 1092}, {1043, 7967}, {1396, 4303}, {1408, 2646}, {1442, 41340}, {1656, 64383}, {1817, 9940}, {1871, 14014}, {2080, 64381}, {2185, 4227}, {2360, 17194}, {3090, 25507}, {3193, 4184}, {3194, 44709}, {3286, 62843}, {3311, 64385}, {3312, 64386}, {3522, 26860}, {3523, 16704}, {3524, 41629}, {3526, 64425}, {3580, 24907}, {3651, 37527}, {3653, 17553}, {3655, 51669}, {4225, 10269}, {4229, 6361}, {4276, 37561}, {4278, 10902}, {4697, 58389}, {4720, 37727}, {5054, 64424}, {5084, 24556}, {5450, 12547}, {5603, 37422}, {5657, 56018}, {5706, 18166}, {5707, 37400}, {5767, 16738}, {5818, 14007}, {5884, 18417}, {6176, 6920}, {6200, 64413}, {6396, 64412}, {6642, 64395}, {6684, 64072}, {6857, 26638}, {6947, 31631}, {6986, 34148}, {6998, 48877}, {7125, 37523}, {7583, 64417}, {7584, 64418}, {8227, 28620}, {9956, 17551}, {10246, 15952}, {10310, 18185}, {10470, 37469}, {11064, 24933}, {11108, 24557}, {11491, 13588}, {11499, 35983}, {12005, 35637}, {13731, 27644}, {15852, 16726}, {16202, 64423}, {16203, 64422}, {16287, 63068}, {16290, 37659}, {16696, 37528}, {16713, 37407}, {17167, 31902}, {17185, 63399}, {18163, 37526}, {18206, 55104}, {18446, 47512}, {18653, 31901}, {19262, 36746}, {19543, 37633}, {21669, 48894}, {26316, 64398}, {26341, 64403}, {26348, 64404}, {26398, 64379}, {26422, 64380}, {26446, 64401}, {26451, 64402}, {26487, 64407}, {26492, 64406}, {26516, 64391}, {26521, 64392}, {26818, 37108}, {30389, 52680}, {30944, 54349}, {33557, 48926}, {34339, 41723}, {36742, 61109}, {37320, 62183}, {37399, 50317}, {38856, 60703}, {43118, 64388}, {43119, 64387}, {46475, 63158}, {48930, 51340}, {63974, 64295}, {64147, 64324}

X(64393) = midpoint of X(i) and X(j) for these {i,j}: {3, 63338}, {37402, 64377}
X(64393) = pole of line {405, 517} with respect to the Stammler hyperbola
X(64393) = pole of line {3262, 5761} with respect to the Wallace hyperbola
X(64393) = barycentric product X(i)*X(j) for these (i, j): {2185, 54346}
X(64393) = barycentric quotient X(i)/X(j) for these (i, j): {54346, 6358}
X(64393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64384, 64405}, {3, 48909, 63400}, {3, 64419, 64376}, {81, 64376, 64419}, {1790, 54356, 28}, {2360, 17194, 17560}, {10246, 15952, 64415}, {37402, 64377, 517}, {37527, 48893, 3651}, {64389, 64390, 41610}

X(64394) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ANTI-OUTER-YFF

Barycentrics    a*(a+b)*(a-b-c)*(a+c)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b^2-4*b*c+c^2)) : :

X(64394) lies on these lines: {1, 21}, {2, 36742}, {5, 64406}, {6, 6910}, {28, 10202}, {34, 17074}, {60, 5324}, {86, 7318}, {110, 17560}, {119, 64405}, {285, 3615}, {323, 15674}, {333, 5552}, {377, 5721}, {404, 581}, {442, 51340}, {452, 14996}, {453, 54323}, {500, 35979}, {631, 5422}, {859, 16203}, {940, 2478}, {991, 35976}, {1010, 5554}, {1125, 22128}, {1181, 6974}, {1325, 15016}, {1408, 18165}, {1437, 4228}, {1470, 64382}, {1816, 54411}, {1817, 37534}, {1993, 6857}, {2077, 64376}, {2287, 3707}, {2475, 63318}, {2979, 7523}, {3286, 11509}, {3359, 37402}, {3616, 64020}, {4184, 11248}, {4193, 37633}, {4221, 37562}, {4225, 10269}, {4267, 22768}, {4276, 14803}, {4278, 59327}, {4921, 45701}, {5047, 63068}, {5235, 26364}, {5323, 18838}, {5333, 10200}, {5453, 37308}, {5707, 6872}, {6735, 64401}, {6892, 7592}, {6921, 10601}, {6931, 37674}, {6962, 10982}, {6966, 37514}, {6977, 36752}, {7465, 37482}, {7483, 36750}, {8025, 10586}, {8614, 11281}, {10527, 61398}, {10528, 16704}, {10531, 14956}, {10679, 17524}, {10915, 64072}, {10942, 47515}, {11110, 26637}, {11113, 45931}, {11220, 57276}, {11239, 41629}, {12115, 64384}, {12608, 17167}, {12648, 56018}, {13323, 37231}, {13411, 54444}, {14005, 24982}, {15066, 16845}, {15670, 22136}, {15988, 56778}, {16049, 18180}, {17379, 26091}, {17811, 31259}, {18191, 54417}, {18542, 64383}, {19047, 64411}, {19048, 64410}, {19717, 27506}, {26309, 64395}, {26318, 64398}, {26333, 64400}, {26343, 64403}, {26350, 64404}, {26358, 64414}, {26378, 64378}, {26400, 64379}, {26424, 64380}, {26432, 64381}, {26453, 64402}, {26459, 64385}, {26465, 64386}, {26476, 64409}, {26482, 64408}, {26518, 64391}, {26523, 64392}, {26625, 37314}, {27086, 63291}, {34545, 37291}, {37229, 62183}, {37286, 63307}, {37298, 37509}, {41610, 45729}, {44734, 56047}, {45424, 64387}, {45425, 64388}, {45528, 64389}, {45529, 64390}, {45627, 64396}, {45628, 64397}, {45631, 64399}, {45642, 64412}, {45643, 64413}, {45652, 64417}, {45653, 64418}, {45923, 57002}, {48909, 52273}, {63974, 64295}, {64147, 64324}

X(64394) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 56231}, {65, 7162}
X(64394) = X(i)-Dao conjugate of X(j) for these {i, j}: {40589, 56231}, {40602, 7162}
X(64394) = pole of line {5949, 6933} with respect to the Kiepert hyperbola
X(64394) = pole of line {100, 43351} with respect to the Kiepert parabola
X(64394) = pole of line {1, 6883} with respect to the Stammler hyperbola
X(64394) = pole of line {101, 43351} with respect to the Hutson-Moses hyperbola
X(64394) = pole of line {75, 5552} with respect to the Wallace hyperbola
X(64394) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3338)}}, {{A, B, C, X(31), X(61398)}}, {{A, B, C, X(60), X(1780)}}, {{A, B, C, X(86), X(3193)}}, {{A, B, C, X(191), X(3255)}}, {{A, B, C, X(285), X(35193)}}, {{A, B, C, X(758), X(12609)}}, {{A, B, C, X(896), X(13401)}}, {{A, B, C, X(1320), X(3890)}}, {{A, B, C, X(4512), X(42012)}}, {{A, B, C, X(5248), X(45393)}}, {{A, B, C, X(5250), X(30513)}}
X(64394) = barycentric product X(i)*X(j) for these (i, j): {274, 61398}, {333, 3338}, {1434, 42012}, {10527, 81}, {12609, 2185}, {13401, 99}, {17412, 4625}, {32561, 57785}
X(64394) = barycentric quotient X(i)/X(j) for these (i, j): {58, 56231}, {284, 7162}, {3338, 226}, {10527, 321}, {12609, 6358}, {13401, 523}, {17412, 4041}, {32561, 210}, {42012, 2321}, {61398, 37}
X(64394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 81, 3193}, {283, 17194, 21}

X(64395) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND ARA

Barycentrics    a^2*(a+b)*(a+c)*(-2*a*b^2*c^2+a^4*(b+c)-(b-c)^2*(b+c)^3) : :

X(64395) lies on these lines: {3, 5235}, {21, 9798}, {22, 333}, {23, 16704}, {24, 64384}, {25, 81}, {58, 8185}, {86, 1995}, {100, 16876}, {159, 41610}, {197, 4184}, {859, 20999}, {1460, 39673}, {1598, 64400}, {3193, 26308}, {3286, 20989}, {3556, 41723}, {4225, 22654}, {4921, 9909}, {5020, 5333}, {5594, 64404}, {5595, 64403}, {6642, 64393}, {7484, 64425}, {7517, 64419}, {8025, 13595}, {8190, 64396}, {8191, 64397}, {8192, 64415}, {8193, 64401}, {9818, 64399}, {10037, 64420}, {10046, 64421}, {10790, 64381}, {10828, 64398}, {10829, 64406}, {10830, 64407}, {10831, 64408}, {10832, 64409}, {10833, 64414}, {10834, 64422}, {10835, 64423}, {11365, 64377}, {11414, 64376}, {11853, 64402}, {13889, 64417}, {13943, 64418}, {14002, 26860}, {16713, 35988}, {18185, 20988}, {18954, 64382}, {19005, 64385}, {19006, 64386}, {23381, 62838}, {26302, 64379}, {26303, 64380}, {26306, 64391}, {26307, 64392}, {26309, 64394}, {35776, 64412}, {35777, 64413}, {44598, 64410}, {44599, 64411}, {45428, 64387}, {45429, 64388}, {45532, 64389}, {45533, 64390}, {49553, 64072}, {54356, 57281}, {63974, 64295}, {64147, 64324}

X(64395) = pole of line {5848, 37058} with respect to the Stammler hyperbola

X(64396) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST AURIGA

Barycentrics    a*(a+b)*(a+c)*(-a+b+c)*(a^2*(b+c)+a*(b+c)^2-2*sqrt(R*(r+4*R))*S) : :

X(64396) lies on these lines: {8, 21}, {58, 8186}, {81, 5597}, {3193, 45625}, {4184, 11492}, {4225, 11493}, {4653, 8187}, {4921, 11207}, {5235, 5599}, {5598, 64415}, {8190, 64395}, {8196, 64400}, {8198, 64403}, {8199, 64404}, {8200, 64405}, {11366, 64377}, {11384, 64378}, {11822, 64376}, {11837, 64381}, {11843, 64384}, {11861, 64398}, {11863, 64402}, {11865, 64406}, {11867, 64407}, {11869, 64408}, {11871, 64409}, {11873, 64414}, {11875, 64419}, {11877, 64420}, {11879, 64421}, {11881, 64422}, {11883, 64423}, {12452, 41610}, {13890, 64417}, {13944, 64418}, {18495, 64399}, {18955, 64382}, {19007, 64385}, {19008, 64386}, {35778, 64412}, {35781, 64413}, {44600, 64410}, {44601, 64411}, {45353, 64380}, {45379, 64383}, {45430, 64387}, {45431, 64388}, {45534, 64389}, {45535, 64390}, {45627, 64394}, {49012, 64391}, {49013, 64392}, {49555, 64072}, {63974, 64295}, {64147, 64324}

X(64396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 55, 64397}

X(64397) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND AURIGA

Barycentrics    a*(a+b)*(a+c)*(-a+b+c)*(a^2*(b+c)+a*(b+c)^2+2*sqrt(R*(r+4*R))*S) : :

X(64397) lies on these lines: {8, 21}, {58, 8187}, {81, 5598}, {3193, 45626}, {4184, 11493}, {4225, 11492}, {4653, 8186}, {4921, 11208}, {5235, 5600}, {5597, 64415}, {8191, 64395}, {8203, 64400}, {8205, 64403}, {8206, 64404}, {8207, 64405}, {11367, 64377}, {11385, 64378}, {11823, 64376}, {11838, 64381}, {11844, 64384}, {11862, 64398}, {11864, 64402}, {11866, 64406}, {11868, 64407}, {11870, 64408}, {11872, 64409}, {11874, 64414}, {11876, 64419}, {11878, 64420}, {11880, 64421}, {11882, 64422}, {11884, 64423}, {12453, 41610}, {13891, 64417}, {13945, 64418}, {18497, 64399}, {18956, 64382}, {19009, 64385}, {19010, 64386}, {35779, 64413}, {35780, 64412}, {44602, 64410}, {44603, 64411}, {45354, 64379}, {45380, 64383}, {45432, 64387}, {45433, 64388}, {45536, 64389}, {45537, 64390}, {45628, 64394}, {49014, 64391}, {49015, 64392}, {49556, 64072}, {63974, 64295}, {64147, 64324}

X(64397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 55, 64396}

X(64398) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 5TH BROCARD

Barycentrics    a*(a+b)*(a+c)*(a^4+b^4+b^2*c^2+c^4-2*a^3*(b+c)+a^2*(b^2+c^2)) : :

X(64398) lies on these lines: {21, 9941}, {32, 81}, {58, 3099}, {86, 10583}, {333, 2896}, {3094, 41610}, {3096, 5235}, {3098, 64376}, {3193, 26317}, {4184, 11494}, {4225, 22744}, {4921, 7811}, {5333, 7846}, {7865, 64424}, {7914, 64425}, {9301, 64419}, {9857, 64401}, {9862, 64384}, {9993, 64400}, {9994, 64403}, {9995, 64404}, {9996, 64405}, {9997, 64415}, {10038, 64420}, {10047, 64421}, {10828, 64395}, {10871, 64406}, {10872, 64407}, {10873, 64408}, {10874, 64409}, {10877, 64414}, {10878, 64422}, {10879, 64423}, {11368, 64377}, {11386, 64378}, {11861, 64396}, {11862, 64397}, {11885, 64402}, {13892, 64417}, {13946, 64418}, {18500, 64399}, {18503, 64383}, {18957, 64382}, {19011, 64385}, {19012, 64386}, {26310, 64379}, {26311, 64380}, {26314, 64391}, {26315, 64392}, {26316, 64393}, {26318, 64394}, {35782, 64412}, {35783, 64413}, {44604, 64410}, {44605, 64411}, {45434, 64387}, {45435, 64388}, {45538, 64389}, {45539, 64390}, {49561, 64072}, {63974, 64295}, {64147, 64324}

X(64399) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND EHRMANN-MID

Barycentrics    (a+b)*(a+c)*(a^5+2*a^4*(b+c)-4*(b-c)^2*(b+c)^3+a*(b^2-c^2)^2-2*a^3*(b^2+c^2)+2*a^2*(b^3+b^2*c+b*c^2+c^3)) : :

X(64399) lies on these lines: {3, 64425}, {4, 333}, {5, 5333}, {21, 18480}, {30, 5235}, {58, 18492}, {81, 381}, {86, 3545}, {355, 4720}, {382, 64376}, {546, 64400}, {1478, 64409}, {1479, 64408}, {2303, 32431}, {3091, 8025}, {3193, 45630}, {3583, 64414}, {3585, 64382}, {3818, 41610}, {3830, 64424}, {3839, 16704}, {3843, 64419}, {3845, 4921}, {4184, 18491}, {4221, 5587}, {4225, 18761}, {5066, 42025}, {5071, 25507}, {5323, 10826}, {5818, 37422}, {6564, 64410}, {6565, 64411}, {9818, 64395}, {9955, 64377}, {9956, 37402}, {9958, 37433}, {10895, 64420}, {10896, 64421}, {12699, 64401}, {13665, 64386}, {13785, 64385}, {14005, 61261}, {17194, 18529}, {17557, 18481}, {18483, 64072}, {18495, 64396}, {18497, 64397}, {18500, 64398}, {18502, 64381}, {18507, 64402}, {18509, 64403}, {18511, 64404}, {18516, 64406}, {18517, 64407}, {18525, 64415}, {18538, 64417}, {18542, 64422}, {18544, 64423}, {18762, 64418}, {26637, 37375}, {26860, 61954}, {31937, 41723}, {35786, 64412}, {35787, 64413}, {40571, 50435}, {41099, 41629}, {41106, 42028}, {45355, 64379}, {45356, 64380}, {45438, 64387}, {45439, 64388}, {45542, 64389}, {45543, 64390}, {45631, 64394}, {49016, 64391}, {49017, 64392}, {63974, 64295}, {64147, 64324}

X(64400) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND EULER

Barycentrics    (a+b)*(a+c)*(a^5-2*a^4*(b+c)+2*(b-c)^2*(b+c)^3+a*(b^2-c^2)^2-2*a^3*(b^2+c^2)) : :

X(64400) lies on these lines: {2, 64376}, {3, 5333}, {4, 81}, {5, 5235}, {11, 64382}, {12, 64414}, {20, 86}, {21, 946}, {28, 5805}, {30, 42025}, {40, 14005}, {58, 1699}, {98, 64381}, {229, 4227}, {235, 64378}, {283, 5715}, {333, 3091}, {371, 64417}, {372, 64418}, {381, 4921}, {411, 10478}, {443, 24557}, {515, 64377}, {516, 25526}, {546, 64399}, {962, 1010}, {1014, 4292}, {1412, 9579}, {1437, 31902}, {1478, 64421}, {1479, 64420}, {1587, 64385}, {1588, 64386}, {1598, 64395}, {1812, 5799}, {1817, 64001}, {1836, 5323}, {2051, 6915}, {2287, 6835}, {2475, 26637}, {3070, 64411}, {3071, 64410}, {3073, 39673}, {3090, 64425}, {3146, 8025}, {3193, 26332}, {3523, 25507}, {3543, 42028}, {3545, 64424}, {3616, 7415}, {3651, 48931}, {3832, 16704}, {3839, 41629}, {3843, 64383}, {4184, 11496}, {4220, 48899}, {4221, 12699}, {4225, 22753}, {4229, 17201}, {4297, 28619}, {4653, 11522}, {4658, 5691}, {4720, 7982}, {5177, 26638}, {5480, 41610}, {5587, 64401}, {5603, 64415}, {5706, 61409}, {5806, 18180}, {6201, 64404}, {6202, 64403}, {6564, 64413}, {6565, 64412}, {6684, 17551}, {6894, 40571}, {6904, 24556}, {6986, 24220}, {7681, 14008}, {7683, 52269}, {7686, 41723}, {7956, 37357}, {7987, 28620}, {8196, 64396}, {8203, 64397}, {8227, 17557}, {9812, 37422}, {9993, 64398}, {10310, 35983}, {10531, 64422}, {10532, 64423}, {10893, 64406}, {10894, 64407}, {10895, 64408}, {10896, 64409}, {11897, 64402}, {17139, 55109}, {17553, 38021}, {17578, 26860}, {17589, 20070}, {19925, 64072}, {24949, 47296}, {26326, 64379}, {26327, 64380}, {26330, 64391}, {26331, 64392}, {26333, 64394}, {27643, 36745}, {30966, 36693}, {31162, 51669}, {31901, 51420}, {37093, 37659}, {37399, 48902}, {37537, 52897}, {37783, 44229}, {45440, 64387}, {45441, 64388}, {45544, 64389}, {45545, 64390}, {56018, 59387}, {63974, 64295}, {64147, 64324}

X(64400) = midpoint of X(i) and X(j) for these {i,j}: {4, 63297}
X(64400) = reflection of X(i) in X(j) for these {i,j}: {37402, 25526}
X(64400) = pole of line {10902, 37057} with respect to the Stammler hyperbola
X(64400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 64419, 64405}, {516, 25526, 37402}

X(64401) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND OUTER-GARCIA

Barycentrics    (a+b)*(a-b-c)*(a+c)*(a+2*(b+c)) : :

X(64401) lies on these lines: {1, 5235}, {2, 41014}, {3, 5361}, {5, 37656}, {8, 21}, {10, 81}, {27, 54398}, {29, 30711}, {58, 3679}, {65, 64408}, {69, 4197}, {72, 41723}, {75, 58786}, {86, 9780}, {145, 11110}, {191, 64010}, {200, 54356}, {210, 18178}, {274, 30806}, {284, 4034}, {314, 3701}, {319, 57808}, {377, 14552}, {391, 2478}, {404, 1150}, {442, 2895}, {474, 5372}, {515, 64376}, {517, 64405}, {519, 17553}, {524, 26131}, {594, 1778}, {914, 14868}, {956, 4225}, {964, 37652}, {1010, 3617}, {1014, 1788}, {1046, 21020}, {1125, 64425}, {1211, 24883}, {1325, 47321}, {1330, 3578}, {1434, 31994}, {1444, 37294}, {1654, 5051}, {1698, 4658}, {1714, 32782}, {1737, 64421}, {1834, 26064}, {1837, 64414}, {2049, 37685}, {2287, 2323}, {2303, 17275}, {2475, 49716}, {2476, 5739}, {2651, 5016}, {2901, 33761}, {2975, 39578}, {3057, 64409}, {3214, 3736}, {3219, 5295}, {3416, 41610}, {3454, 31143}, {3559, 7046}, {3621, 17588}, {3626, 16948}, {3632, 4653}, {3634, 28619}, {3678, 18417}, {3696, 56288}, {3868, 5271}, {3872, 46877}, {3876, 11679}, {3927, 28605}, {3932, 63158}, {3936, 25446}, {4007, 4877}, {4015, 51285}, {4023, 27529}, {4066, 4756}, {4184, 5687}, {4193, 14555}, {4202, 37653}, {4221, 5690}, {4228, 33090}, {4273, 50082}, {4276, 5258}, {4281, 10459}, {4400, 4690}, {4647, 11684}, {4651, 13588}, {4668, 52680}, {4678, 11115}, {4869, 50393}, {4882, 17194}, {5047, 5278}, {5082, 14956}, {5090, 64378}, {5125, 56014}, {5177, 56020}, {5192, 17349}, {5247, 59307}, {5252, 64382}, {5264, 39673}, {5323, 40663}, {5587, 64400}, {5657, 37402}, {5688, 64404}, {5689, 64403}, {5737, 19767}, {5741, 7504}, {5790, 64419}, {5791, 33077}, {5814, 40571}, {6735, 64394}, {7080, 16713}, {8025, 14007}, {8193, 64395}, {8582, 24557}, {8728, 32863}, {8822, 32087}, {9656, 21291}, {9709, 35983}, {9857, 64398}, {10039, 64420}, {10381, 61699}, {10458, 50581}, {10461, 63135}, {10479, 32911}, {10791, 64381}, {10914, 64406}, {10915, 64422}, {10916, 64423}, {11900, 64402}, {12699, 64399}, {12702, 64383}, {13740, 19742}, {13883, 64386}, {13893, 64417}, {13911, 64410}, {13936, 64385}, {13947, 64418}, {13973, 64411}, {14008, 24390}, {14829, 17531}, {14996, 16458}, {15679, 50215}, {15952, 59503}, {16053, 29616}, {16342, 20018}, {16454, 37683}, {16738, 59299}, {17156, 62831}, {17162, 41813}, {17163, 63996}, {17167, 21075}, {17277, 17536}, {17346, 17577}, {17549, 48850}, {17579, 54429}, {18169, 59294}, {18180, 34790}, {18249, 56204}, {19280, 19717}, {19859, 62808}, {19875, 42025}, {19877, 25507}, {20077, 50171}, {20086, 49743}, {20293, 57093}, {20653, 42334}, {24632, 50095}, {24880, 30831}, {24936, 62689}, {25005, 26637}, {25441, 31247}, {25645, 31204}, {26115, 27164}, {26382, 64379}, {26406, 64380}, {26444, 64391}, {26445, 64392}, {26446, 64393}, {28618, 51073}, {31330, 57280}, {31339, 32853}, {32917, 59302}, {33075, 62843}, {33557, 48877}, {34195, 54335}, {35788, 64412}, {35789, 64413}, {36568, 50308}, {37037, 63067}, {37422, 59417}, {37442, 54391}, {37462, 37655}, {37522, 48852}, {37639, 56766}, {37680, 50605}, {41629, 53620}, {43533, 54760}, {45444, 64387}, {45445, 64388}, {45546, 64389}, {45547, 64390}, {48935, 52841}, {52258, 63100}, {55095, 56318}, {62796, 64184}, {63974, 64295}, {64147, 64324}

X(64401) = reflection of X(i) in X(j) for these {i,j}: {17553, 64424}, {63319, 10}
X(64401) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 56221}, {57, 28625}, {65, 56343}, {226, 34819}, {604, 60203}, {1042, 56203}, {1400, 25417}, {1402, 30598}, {1880, 56070}, {4017, 8652}, {4559, 48074}, {7180, 37211}, {32042, 51641}
X(64401) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 56221}, {1698, 3671}, {3161, 60203}, {5452, 28625}, {34961, 8652}, {40582, 25417}, {40602, 56343}, {40605, 30598}, {51572, 65}, {53167, 7178}, {55067, 48074}, {62648, 226}
X(64401) = X(i)-cross conjugate of X(j) for these {i, j}: {3715, 4877}, {4877, 5333}
X(64401) = pole of line {960, 4720} with respect to the Feuerbach hyperbola
X(64401) = pole of line {56, 1203} with respect to the Stammler hyperbola
X(64401) = pole of line {7, 5550} with respect to the Wallace hyperbola
X(64401) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(1224)}}, {{A, B, C, X(21), X(4658)}}, {{A, B, C, X(55), X(3715)}}, {{A, B, C, X(333), X(3615)}}, {{A, B, C, X(345), X(28605)}}, {{A, B, C, X(958), X(1320)}}, {{A, B, C, X(1259), X(3927)}}, {{A, B, C, X(2323), X(4880)}}, {{A, B, C, X(3686), X(52344)}}, {{A, B, C, X(3701), X(4046)}}, {{A, B, C, X(3712), X(4820)}}, {{A, B, C, X(3871), X(56115)}}, {{A, B, C, X(4042), X(52133)}}, {{A, B, C, X(4654), X(5273)}}, {{A, B, C, X(4802), X(44669)}}, {{A, B, C, X(12867), X(31660)}}, {{A, B, C, X(42030), X(43260)}}
X(64401) = barycentric product X(i)*X(j) for these (i, j): {21, 28605}, {274, 3715}, {284, 30596}, {312, 4658}, {1043, 4654}, {1698, 333}, {2185, 4066}, {3699, 4960}, {4007, 86}, {4560, 4756}, {4631, 48005}, {4802, 645}, {4813, 7257}, {4820, 99}, {4823, 643}, {4834, 62534}, {4840, 646}, {4877, 75}, {5333, 8}, {16777, 314}, {28660, 61358}, {30589, 4720}, {31623, 3927}, {31902, 345}, {36800, 4716}
X(64401) = barycentric quotient X(i)/X(j) for these (i, j): {8, 60203}, {9, 56221}, {21, 25417}, {55, 28625}, {283, 56070}, {284, 56343}, {333, 30598}, {643, 37211}, {645, 32042}, {1043, 42030}, {1698, 226}, {2194, 34819}, {2287, 56203}, {3715, 37}, {3737, 48074}, {3824, 55010}, {3927, 1214}, {4007, 10}, {4066, 6358}, {4654, 3668}, {4658, 57}, {4716, 16609}, {4720, 30590}, {4727, 40663}, {4756, 4552}, {4802, 7178}, {4810, 7212}, {4813, 4017}, {4820, 523}, {4823, 4077}, {4834, 7180}, {4840, 3669}, {4877, 1}, {4880, 18593}, {4898, 4848}, {4958, 30572}, {4960, 3676}, {5221, 1427}, {5333, 7}, {5546, 8652}, {16777, 65}, {28605, 1441}, {30596, 349}, {31902, 278}, {36074, 53321}, {48005, 57185}, {61358, 1400}, {62648, 3671}
X(64401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5235, 17557}, {2, 56018, 64377}, {8, 21, 4720}, {8, 333, 21}, {10, 64072, 81}, {10, 81, 14005}, {86, 9780, 17551}, {519, 64424, 17553}, {1150, 9534, 404}, {1698, 4658, 5333}, {1834, 49724, 26064}, {3617, 16704, 1010}, {3679, 4921, 51669}, {3701, 60731, 32635}, {3936, 25446, 31254}, {5278, 10449, 5047}, {5657, 64384, 37402}, {8025, 46933, 14007}

X(64402) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND GOSSARD

Barycentrics    (a+b)*(a+c)*(2*a^4-(b^2-c^2)^2-a^2*(b^2+c^2))*(a^9-2*a^8*(b+c)-a^7*(b^2+c^2)-6*a^2*(b-c)^2*(b+c)^3*(b^2+c^2)+5*a^3*(b^2-c^2)^2*(b^2+c^2)+2*a^6*(b^3+b^2*c+b*c^2+c^3)+a^5*(-3*b^4+7*b^2*c^2-3*c^4)+2*(b-c)^2*(b+c)^3*(b^4+3*b^2*c^2+c^4)-a*(b^2-c^2)^2*(2*b^4+5*b^2*c^2+2*c^4)+2*a^4*(2*b^5+2*b^4*c-5*b^3*c^2-5*b^2*c^3+2*b*c^4+2*c^5)) : :

X(64402) lies on these lines: {21, 12438}, {30, 64376}, {58, 11852}, {81, 402}, {333, 4240}, {1650, 5235}, {1651, 4921}, {3193, 26452}, {4184, 11848}, {4225, 22755}, {5333, 15183}, {11831, 64377}, {11832, 64378}, {11839, 64381}, {11845, 64384}, {11853, 64395}, {11863, 64396}, {11864, 64397}, {11885, 64398}, {11897, 64400}, {11900, 64401}, {11901, 64403}, {11902, 64404}, {11903, 64406}, {11904, 64407}, {11905, 64408}, {11906, 64409}, {11909, 64414}, {11910, 64415}, {11911, 64419}, {11912, 64420}, {11913, 64421}, {11914, 64422}, {11915, 64423}, {12583, 41610}, {13894, 64417}, {13948, 64418}, {15184, 64425}, {16212, 56018}, {18507, 64399}, {18508, 64383}, {18958, 64382}, {19017, 64385}, {19018, 64386}, {26383, 64379}, {26407, 64380}, {26449, 64391}, {26450, 64392}, {26451, 64393}, {26453, 64394}, {35790, 64412}, {35791, 64413}, {44610, 64410}, {44611, 64411}, {45446, 64387}, {45447, 64388}, {45548, 64389}, {45549, 64390}, {49585, 64072}, {63974, 64295}, {64147, 64324}

X(64402) = reflection of X(i) in X(j) for these {i,j}: {63320, 402}

X(64403) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND INNER-GREBE

Barycentrics    a*(a+b)*(a+c)*(a^2+b^2+c^2-2*a*(b+c)-S) : :

X(64403) lies on these lines: {2, 6}, {21, 3641}, {58, 5589}, {3193, 26342}, {4184, 11497}, {4225, 22756}, {5595, 64395}, {5605, 64415}, {5689, 64401}, {6202, 64400}, {6215, 64405}, {8198, 64396}, {8205, 64397}, {9994, 64398}, {10040, 64420}, {10048, 64421}, {10783, 64384}, {10792, 64381}, {10919, 64406}, {10921, 64407}, {10923, 64408}, {10925, 64409}, {10927, 64414}, {10929, 64422}, {10931, 64423}, {11370, 64377}, {11388, 64378}, {11824, 64376}, {11901, 64402}, {11916, 64419}, {18509, 64399}, {18959, 64382}, {26334, 64379}, {26335, 64380}, {26336, 64383}, {26341, 64393}, {26343, 64394}, {35792, 64412}, {35795, 64413}, {45550, 64389}, {45552, 64390}, {49586, 64072}, {63974, 64295}, {64147, 64324}

X(64404) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND OUTER-GREBE

Barycentrics    a*(a+b)*(a+c)*(a^2+b^2+c^2-2*a*(b+c)+S) : :

X(64404) lies on these lines: {2, 6}, {21, 3640}, {58, 5588}, {3193, 26349}, {4184, 11498}, {4225, 22757}, {5594, 64395}, {5604, 64415}, {5688, 64401}, {6201, 64400}, {6214, 64405}, {8199, 64396}, {8206, 64397}, {9995, 64398}, {10041, 64420}, {10049, 64421}, {10784, 64384}, {10793, 64381}, {10920, 64406}, {10922, 64407}, {10924, 64408}, {10926, 64409}, {10928, 64414}, {10930, 64422}, {10932, 64423}, {11371, 64377}, {11389, 64378}, {11825, 64376}, {11902, 64402}, {11917, 64419}, {18511, 64399}, {18960, 64382}, {26344, 64379}, {26345, 64380}, {26346, 64383}, {26348, 64393}, {26350, 64394}, {35793, 64413}, {35794, 64412}, {45551, 64390}, {45553, 64389}, {49587, 64072}, {63974, 64295}, {64147, 64324}

X(64405) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND JOHNSON

Barycentrics    (a+b)*(a+c)*(a^5-2*(b-c)^2*(b+c)^3+a*(b^2-c^2)^2-2*a^3*(b^2+c^2)+2*a^2*(b^3+b^2*c+b*c^2+c^3)) : :

X(64405) lies on these lines: {1, 64408}, {2, 64384}, {3, 5235}, {4, 333}, {5, 81}, {10, 4221}, {11, 64421}, {12, 64420}, {21, 355}, {28, 51755}, {30, 64376}, {58, 5587}, {86, 3090}, {104, 37442}, {119, 64394}, {140, 64425}, {381, 4921}, {485, 64410}, {486, 64411}, {517, 64401}, {944, 11110}, {946, 64072}, {952, 64415}, {1010, 5818}, {1043, 59388}, {1352, 6990}, {1385, 17557}, {1408, 17606}, {1478, 64382}, {1479, 64414}, {1656, 5333}, {1737, 5323}, {1746, 37431}, {1812, 6830}, {2287, 6831}, {2303, 5816}, {3091, 16704}, {3193, 14008}, {3545, 41629}, {3651, 48937}, {4184, 11499}, {4193, 26637}, {4220, 48887}, {4225, 22758}, {4234, 38074}, {4653, 5881}, {4658, 8227}, {5055, 42025}, {5056, 8025}, {5067, 25507}, {5071, 42028}, {5084, 26638}, {5603, 56018}, {5657, 37422}, {5720, 54356}, {5777, 18180}, {5778, 56000}, {5786, 19262}, {5789, 52012}, {5790, 15952}, {5791, 37418}, {5810, 6828}, {5886, 64377}, {5887, 41723}, {6214, 64404}, {6215, 64403}, {6289, 64387}, {6290, 64388}, {6564, 64412}, {6565, 64413}, {6848, 16713}, {6873, 56439}, {6879, 31631}, {6952, 14868}, {6956, 27398}, {7330, 31902}, {7413, 48877}, {7583, 64386}, {7584, 64385}, {8200, 64396}, {8207, 64397}, {8976, 64417}, {9956, 14005}, {9958, 37456}, {9996, 64398}, {10175, 25526}, {10458, 37699}, {10796, 64381}, {10942, 64422}, {10943, 64423}, {13951, 64418}, {14872, 18165}, {15022, 26860}, {16948, 18357}, {17527, 24557}, {17553, 28204}, {18417, 20117}, {24883, 30444}, {26386, 64379}, {26410, 64380}, {26446, 37402}, {26468, 64391}, {26469, 64392}, {33295, 36651}, {35637, 63967}, {37714, 52680}, {45554, 64389}, {45555, 64390}, {63974, 64295}, {64147, 64324}

X(64405) = reflection of X(i) in X(j) for these {i,j}: {63323, 5}
X(64405) = pole of line {26286, 37058} with respect to the Stammler hyperbola
X(64405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64384, 64393}, {381, 64419, 64400}, {4921, 64400, 64419}, {64408, 64409, 1}

X(64406) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND INNER-JOHNSON

Barycentrics    (a+b)*(a+c)*(a^4-a^3*(b+c)+3*a*(b-c)^2*(b+c)-2*(b^2-c^2)^2-a^2*(b^2-4*b*c+c^2)) : :

X(64406) lies on these lines: {2, 37474}, {5, 64394}, {11, 81}, {12, 64422}, {21, 355}, {58, 10826}, {86, 10584}, {333, 3434}, {859, 18519}, {1376, 4184}, {1746, 37449}, {3193, 10943}, {4225, 12114}, {4653, 37708}, {4921, 11235}, {5324, 24624}, {5788, 6872}, {10523, 64420}, {10785, 64384}, {10794, 64381}, {10829, 64395}, {10871, 64398}, {10883, 11442}, {10893, 64400}, {10914, 64401}, {10919, 64403}, {10920, 64404}, {10944, 64408}, {10947, 64414}, {10948, 64421}, {10949, 64423}, {11373, 64377}, {11390, 64378}, {11826, 64376}, {11865, 64396}, {11866, 64397}, {11903, 64402}, {11928, 64419}, {12586, 41610}, {12616, 16049}, {12672, 41723}, {13478, 35996}, {13895, 64417}, {13952, 64418}, {14005, 17619}, {17557, 17614}, {18180, 31937}, {18516, 64399}, {18961, 64382}, {19023, 64385}, {19024, 64386}, {22139, 46521}, {26390, 64379}, {26414, 64380}, {26490, 64391}, {26491, 64392}, {26492, 64393}, {26637, 37373}, {34612, 64424}, {35796, 64412}, {35797, 64413}, {35979, 48937}, {44618, 64410}, {44619, 64411}, {45454, 64387}, {45455, 64388}, {45556, 64389}, {45557, 64390}, {49600, 64072}, {63974, 64295}, {64147, 64324}

X(64406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 64405, 64407}

X(64407) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND OUTER-JOHNSON

Barycentrics    (a+b)*(a+c)*(a^5-2*(b-c)^2*(b+c)^3+a*(b^2-c^2)^2-2*a^3*(b^2+b*c+c^2)+2*a^2*(b^3+2*b^2*c+2*b*c^2+c^3)) : :

X(64407) lies on these lines: {2, 5788}, {5, 3193}, {10, 16049}, {11, 64423}, {12, 81}, {21, 355}, {58, 10827}, {68, 6829}, {72, 41723}, {86, 10585}, {283, 5587}, {333, 3436}, {958, 4225}, {1437, 9956}, {1698, 1790}, {1792, 5086}, {1812, 11681}, {1817, 5791}, {1867, 3219}, {2476, 5810}, {4184, 11500}, {4653, 37711}, {4921, 11236}, {5130, 54340}, {5260, 15232}, {5790, 37227}, {5818, 11103}, {6684, 35997}, {7989, 62756}, {10523, 64421}, {10786, 64384}, {10795, 64381}, {10830, 64395}, {10872, 64398}, {10894, 64400}, {10921, 64403}, {10922, 64404}, {10942, 47515}, {10950, 64409}, {10953, 64414}, {10954, 64420}, {10955, 64422}, {11374, 64377}, {11391, 64378}, {11827, 64376}, {11867, 64396}, {11868, 64397}, {11904, 64402}, {11929, 64419}, {12587, 41610}, {13896, 64417}, {13953, 64418}, {14011, 26637}, {14868, 27529}, {17167, 21077}, {17518, 25005}, {17524, 18518}, {17857, 54356}, {18517, 64399}, {18962, 64382}, {19025, 64385}, {19026, 64386}, {21677, 37369}, {24953, 64425}, {26389, 64379}, {26413, 64380}, {26485, 64391}, {26486, 64392}, {26487, 64393}, {26921, 31902}, {27174, 39566}, {34606, 64424}, {35798, 64412}, {35799, 64413}, {35989, 48937}, {37277, 51755}, {44620, 64410}, {44621, 64411}, {45456, 64387}, {45457, 64388}, {45558, 64389}, {45559, 64390}, {63974, 64295}, {64147, 64324}

X(64407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 64405, 64406}

X(64408) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST JOHNSON-YFF

Barycentrics    (a+b)*(a+b-c)*(a+c)*(a-b+c)*(a^3-a*(b+c)^2+2*(b+c)^3) : :

X(64408) lies on these lines: {1, 64405}, {4, 64414}, {5, 64421}, {10, 5323}, {12, 81}, {21, 5252}, {56, 5235}, {58, 9578}, {65, 64401}, {86, 10588}, {226, 64072}, {333, 388}, {495, 64420}, {498, 64393}, {1014, 24914}, {1319, 17557}, {1408, 14005}, {1412, 1698}, {1479, 64399}, {2287, 15844}, {2476, 5820}, {2551, 26638}, {3085, 64384}, {3193, 26481}, {3295, 64383}, {3476, 11110}, {3485, 56018}, {3736, 56198}, {4184, 11501}, {4221, 10039}, {4225, 22759}, {4653, 37709}, {4658, 5219}, {4921, 11237}, {5261, 16704}, {5433, 64425}, {5434, 64424}, {5712, 5788}, {7354, 64376}, {9654, 64419}, {10797, 64381}, {10831, 64395}, {10873, 64398}, {10895, 64400}, {10923, 64403}, {10924, 64404}, {10944, 64406}, {10956, 64422}, {10957, 14008}, {11375, 64377}, {11392, 64378}, {11681, 26637}, {11869, 64396}, {11870, 64397}, {11905, 64402}, {12588, 41610}, {13897, 64417}, {13954, 64418}, {19027, 64385}, {19028, 64386}, {26388, 64379}, {26412, 64380}, {26479, 64391}, {26480, 64392}, {26482, 64394}, {31472, 64410}, {35800, 64412}, {35801, 64413}, {41723, 64041}, {44622, 64411}, {45458, 64387}, {45459, 64388}, {45560, 64389}, {45561, 64390}, {63974, 64295}, {64147, 64324}

X(64408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {333, 388, 64382}

X(64409) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND JOHNSON-YFF

Barycentrics    (a+b)*(a-b-c)*(a+c)*(a^3-a*(b-c)^2+2*(b-c)^2*(b+c)) : :

X(64409) lies on these lines: {1, 64405}, {4, 64382}, {5, 64420}, {11, 81}, {21, 1837}, {27, 1857}, {55, 5235}, {58, 9581}, {86, 10589}, {333, 497}, {496, 64421}, {499, 64393}, {999, 64383}, {1010, 54361}, {1014, 17728}, {1210, 5323}, {1396, 37372}, {1478, 64399}, {1737, 4221}, {1788, 37422}, {1812, 37373}, {1864, 18165}, {2074, 5358}, {2646, 17557}, {2654, 4281}, {3057, 64401}, {3058, 64424}, {3086, 64384}, {3193, 26475}, {3486, 11110}, {4183, 5324}, {4184, 11502}, {4207, 37642}, {4225, 22760}, {4228, 24624}, {4653, 5727}, {4658, 50443}, {4921, 11238}, {5274, 16704}, {5348, 39673}, {5432, 64425}, {6284, 64376}, {7069, 35623}, {7424, 16948}, {9669, 64419}, {10395, 47512}, {10798, 64381}, {10832, 64395}, {10874, 64398}, {10896, 64400}, {10925, 64403}, {10926, 64404}, {10950, 64407}, {10958, 64422}, {10959, 64423}, {11376, 64377}, {11393, 64378}, {11871, 64396}, {11872, 64397}, {11906, 64402}, {12053, 64072}, {12589, 41610}, {13588, 60782}, {13898, 64417}, {13955, 64418}, {14005, 17606}, {17604, 18191}, {18180, 64131}, {19029, 64385}, {19030, 64386}, {24914, 37402}, {26105, 26638}, {26387, 64379}, {26411, 64380}, {26473, 64391}, {26474, 64392}, {26476, 64394}, {27762, 42025}, {35802, 64412}, {35803, 64413}, {37357, 62843}, {41723, 64042}, {44623, 64410}, {44624, 64411}, {45460, 64387}, {45461, 64388}, {45562, 64389}, {45563, 64390}, {63974, 64295}, {64147, 64324}

X(64409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 64405, 64408}, {333, 497, 64414}

X(64410) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST KENMOTU-CENTERS

Barycentrics    a*(a+b)*(a+c)*(a*(b+c)+S) : :

X(64410) lies on these lines: {2, 6}, {21, 7969}, {39, 64390}, {58, 606}, {371, 64412}, {372, 64393}, {485, 64405}, {605, 38832}, {1010, 19065}, {1124, 64421}, {1151, 64376}, {1335, 64420}, {1412, 51842}, {1587, 64384}, {2066, 64414}, {2067, 64382}, {2362, 5323}, {3071, 64400}, {3193, 19050}, {3286, 19000}, {3311, 64419}, {4184, 44590}, {4221, 35774}, {4225, 44606}, {4267, 19014}, {4658, 18992}, {5062, 64389}, {5412, 64378}, {6419, 64413}, {6564, 64399}, {7968, 64377}, {11110, 13902}, {13665, 64383}, {13883, 64072}, {13911, 64401}, {13936, 25526}, {13971, 28619}, {13973, 14005}, {18185, 18999}, {19048, 64394}, {19066, 56018}, {31472, 64408}, {37402, 49227}, {44582, 64379}, {44584, 64380}, {44586, 64381}, {44598, 64395}, {44600, 64396}, {44602, 64397}, {44604, 64398}, {44610, 64402}, {44618, 64406}, {44620, 64407}, {44623, 64409}, {44635, 64415}, {44643, 64422}, {44645, 64423}, {63974, 64295}, {64147, 64324}

X(64410) = pole of line {6, 3083} with respect to the Stammler hyperbola
X(64410) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(64209)}}, {{A, B, C, X(69), X(6213)}}, {{A, B, C, X(394), X(606)}}, {{A, B, C, X(7347), X(14555)}}
X(64410) = barycentric product X(i)*X(j) for these (i, j): {6351, 81}
X(64410) = barycentric quotient X(i)/X(j) for these (i, j): {6351, 321}

X(64411) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND KENMOTU-CENTERS

Barycentrics    a*(a+b)*(a+c)*(a*(b+c)-S) : :

X(64411) lies on these lines: {2, 6}, {21, 7968}, {39, 64389}, {58, 605}, {371, 64393}, {372, 64413}, {486, 64405}, {606, 38832}, {1010, 19066}, {1124, 64420}, {1152, 64376}, {1172, 7595}, {1335, 64421}, {1412, 51841}, {1588, 64384}, {3070, 64400}, {3193, 19049}, {3286, 18999}, {3312, 64419}, {4184, 44591}, {4221, 35775}, {4225, 44607}, {4267, 19013}, {4658, 18991}, {5058, 64390}, {5323, 16232}, {5413, 64378}, {5414, 64414}, {6420, 64412}, {6502, 64382}, {6565, 64399}, {7969, 64377}, {8983, 28619}, {11110, 13959}, {13785, 64383}, {13883, 25526}, {13911, 14005}, {13936, 64072}, {13973, 64401}, {18185, 19000}, {19047, 64394}, {19065, 56018}, {37402, 49226}, {44583, 64379}, {44585, 64380}, {44587, 64381}, {44599, 64395}, {44601, 64396}, {44603, 64397}, {44605, 64398}, {44611, 64402}, {44619, 64406}, {44621, 64407}, {44622, 64408}, {44624, 64409}, {44636, 64415}, {44644, 64422}, {44646, 64423}, {63974, 64295}, {64147, 64324}

X(64411) = pole of line {6, 3084} with respect to the Stammler hyperbola
X(64411) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(64210)}}, {{A, B, C, X(69), X(6212)}}, {{A, B, C, X(394), X(605)}}, {{A, B, C, X(7348), X(14555)}}
X(64411) = barycentric product X(i)*X(j) for these (i, j): {6352, 81}
X(64411) = barycentric quotient X(i)/X(j) for these (i, j): {6352, 321}

X(64412) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 1ST KENMOTU-FREE-VERTICES

Barycentrics    a*(a+b)*(a+c)*(a^4-a^3*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)+a*(b+c)*(b^2+c^2-2*S)) : :

X(64412) lies on these lines: {6, 19543}, {21, 35641}, {58, 35774}, {81, 372}, {86, 5420}, {333, 485}, {371, 64410}, {1587, 16704}, {3103, 64388}, {3193, 45640}, {4184, 35772}, {4221, 35611}, {4225, 35784}, {4921, 35822}, {5235, 10576}, {6200, 64376}, {6396, 64393}, {6419, 64386}, {6420, 64411}, {6560, 64384}, {6564, 64405}, {6565, 64400}, {8025, 13935}, {23251, 64383}, {35762, 64377}, {35764, 64378}, {35766, 64381}, {35768, 64382}, {35769, 64421}, {35770, 64385}, {35776, 64395}, {35778, 64396}, {35780, 64397}, {35782, 64398}, {35786, 64399}, {35788, 64401}, {35790, 64402}, {35792, 64403}, {35794, 64404}, {35796, 64406}, {35798, 64407}, {35800, 64408}, {35802, 64409}, {35808, 64414}, {35809, 64420}, {35810, 64415}, {35812, 64417}, {35814, 64418}, {35816, 64422}, {35818, 64423}, {35840, 41610}, {45357, 64379}, {45359, 64380}, {45462, 64387}, {45564, 64390}, {45642, 64394}, {49018, 64391}, {49601, 64072}, {63974, 64295}, {64147, 64324}

X(64413) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 2ND KENMOTU-FREE-VERTICES

Barycentrics    a*(a+b)*(a+c)*(a^4-a^3*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)+a*(b+c)*(b^2+c^2+2*S)) : :

X(64413) lies on these lines: {6, 19543}, {21, 35642}, {58, 35775}, {81, 371}, {86, 5418}, {333, 486}, {372, 64411}, {1588, 16704}, {3102, 64387}, {3193, 45641}, {4184, 35773}, {4221, 35610}, {4225, 35785}, {4921, 35823}, {5235, 10577}, {6200, 64393}, {6396, 64376}, {6419, 64410}, {6420, 64385}, {6561, 64384}, {6564, 64400}, {6565, 64405}, {8025, 9540}, {23261, 64383}, {35763, 64377}, {35765, 64378}, {35767, 64381}, {35768, 64421}, {35769, 64382}, {35771, 64386}, {35777, 64395}, {35779, 64397}, {35781, 64396}, {35783, 64398}, {35787, 64399}, {35789, 64401}, {35791, 64402}, {35793, 64404}, {35795, 64403}, {35797, 64406}, {35799, 64407}, {35801, 64408}, {35803, 64409}, {35808, 64420}, {35809, 64414}, {35811, 64415}, {35813, 64418}, {35815, 64417}, {35817, 64422}, {35819, 64423}, {35841, 41610}, {45358, 64380}, {45360, 64379}, {45463, 64388}, {45565, 64389}, {45643, 64394}, {49019, 64392}, {49602, 64072}, {63974, 64295}, {64147, 64324}

X(64413) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 64419, 64412}

X(64414) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND MANDART-INCIRCLE

Barycentrics    a*(a+b)*(a-b-c)*(a+c)*(a^2-(b-c)^2-2*a*(b+c)) : :

X(64414) lies on these lines: {1, 58392}, {3, 64421}, {4, 64408}, {11, 5235}, {12, 64400}, {21, 643}, {33, 64378}, {35, 64393}, {40, 5323}, {55, 81}, {56, 64376}, {58, 1697}, {86, 5218}, {100, 26637}, {165, 1412}, {212, 38832}, {243, 56014}, {284, 62756}, {333, 497}, {390, 16704}, {896, 42446}, {950, 64072}, {1005, 37516}, {1014, 1155}, {1253, 62740}, {1408, 37402}, {1479, 64405}, {1776, 11997}, {1778, 54359}, {1812, 56181}, {1837, 64401}, {1936, 2269}, {2066, 64410}, {2098, 64415}, {2328, 5324}, {2550, 26638}, {2646, 64377}, {2651, 3056}, {3058, 4921}, {3193, 26357}, {3295, 64419}, {3476, 7415}, {3486, 56018}, {3583, 64399}, {3601, 4658}, {4221, 5119}, {4225, 10966}, {4271, 33849}, {4294, 64384}, {4413, 24557}, {4414, 18161}, {4653, 7962}, {4995, 42025}, {5132, 63068}, {5281, 8025}, {5333, 5432}, {5414, 64411}, {7074, 40153}, {9371, 16696}, {9668, 64383}, {9819, 52680}, {10385, 41629}, {10388, 17194}, {10799, 64381}, {10833, 64395}, {10877, 64398}, {10927, 64403}, {10928, 64404}, {10947, 64406}, {10953, 64407}, {10965, 64422}, {11238, 64424}, {11376, 17557}, {11873, 64396}, {11874, 64397}, {11909, 64402}, {13901, 64417}, {13958, 64418}, {14935, 40403}, {17642, 18165}, {19037, 64385}, {19038, 64386}, {24556, 59572}, {26351, 64379}, {26352, 64380}, {26355, 64391}, {26356, 64392}, {26358, 64394}, {35808, 64412}, {35809, 64413}, {40467, 57093}, {41723, 64043}, {45470, 64387}, {45471, 64388}, {45570, 64389}, {45571, 64390}, {61397, 61409}, {63974, 64295}, {64147, 64324}

X(64414) = pole of line {4511, 15569} with respect to the Feuerbach hyperbola
X(64414) = pole of line {1001, 1319} with respect to the Stammler hyperbola
X(64414) = intersection, other than A, B, C, of circumconics {{A, B, C, X(294), X(17126)}}, {{A, B, C, X(1002), X(1320)}}
X(64414) = barycentric product X(i)*X(j) for these (i, j): {21, 4419}, {47757, 643}, {48332, 645}
X(64414) = barycentric quotient X(i)/X(j) for these (i, j): {4419, 1441}, {47757, 4077}, {48332, 7178}
X(64414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {333, 497, 64409}, {1408, 37568, 37402}, {2328, 18163, 5324}, {3295, 64419, 64420}

X(64415) = ISOGONAL CONJUGATE OF X(31503)

Barycentrics    a*(a+b)*(a-3*(b+c))*(a+c) : :

X(64415) lies on these lines: {1, 21}, {2, 1043}, {3, 37633}, {6, 16865}, {8, 5235}, {10, 4720}, {12, 14008}, {23, 54371}, {27, 4313}, {28, 1255}, {29, 5703}, {30, 26131}, {33, 54340}, {37, 2287}, {42, 5260}, {55, 4225}, {56, 4184}, {72, 33761}, {86, 3445}, {88, 5439}, {100, 37442}, {104, 59012}, {105, 43359}, {110, 54417}, {145, 333}, {229, 2646}, {284, 3247}, {314, 24547}, {386, 5047}, {388, 14956}, {405, 19767}, {442, 24936}, {452, 63008}, {495, 37357}, {496, 47515}, {500, 21669}, {517, 64376}, {519, 17553}, {551, 25526}, {581, 6912}, {582, 1006}, {663, 57189}, {741, 58117}, {750, 37574}, {759, 8652}, {859, 3295}, {940, 4189}, {952, 64405}, {958, 2334}, {962, 7415}, {988, 64149}, {999, 17524}, {1001, 27644}, {1010, 3616}, {1014, 1420}, {1100, 1778}, {1104, 17011}, {1125, 14005}, {1150, 56769}, {1172, 13739}, {1191, 61409}, {1193, 5284}, {1201, 3736}, {1220, 29822}, {1279, 63158}, {1319, 5323}, {1325, 37571}, {1330, 49735}, {1333, 3723}, {1385, 4221}, {1412, 63208}, {1449, 4877}, {1616, 40153}, {1724, 16858}, {1790, 13384}, {1792, 25060}, {1817, 3601}, {1963, 37032}, {2098, 64414}, {2099, 64382}, {2177, 59311}, {2217, 39737}, {2256, 56000}, {2298, 40452}, {2303, 3285}, {2360, 40214}, {2475, 17056}, {2654, 27653}, {2895, 49728}, {3017, 15671}, {3057, 18165}, {3194, 11107}, {3216, 17536}, {3241, 4921}, {3242, 41610}, {3244, 64072}, {3286, 3304}, {3303, 4267}, {3305, 8951}, {3315, 37592}, {3487, 33151}, {3488, 25516}, {3559, 34231}, {3576, 37402}, {3623, 16704}, {3624, 17551}, {3636, 28619}, {3649, 33100}, {3651, 48903}, {3663, 26729}, {3664, 58786}, {3720, 5253}, {3731, 3984}, {3746, 4276}, {3748, 5324}, {3750, 10459}, {3870, 46877}, {3871, 30116}, {3876, 54287}, {3896, 16824}, {3920, 4228}, {3924, 17592}, {3936, 26117}, {3945, 8822}, {4021, 17189}, {4188, 37674}, {4190, 4648}, {4195, 19684}, {4197, 48837}, {4201, 18139}, {4205, 31247}, {4220, 48894}, {4234, 38314}, {4252, 14996}, {4256, 17531}, {4257, 17574}, {4278, 5563}, {4383, 16859}, {4511, 6051}, {4683, 12579}, {4719, 7292}, {4850, 54392}, {4854, 11281}, {4855, 17022}, {5046, 5718}, {5051, 25650}, {5084, 37651}, {5129, 63090}, {5222, 16053}, {5251, 59301}, {5256, 5436}, {5262, 47512}, {5276, 17522}, {5278, 20018}, {5283, 63087}, {5297, 56176}, {5303, 37607}, {5308, 16054}, {5358, 30145}, {5396, 6920}, {5428, 45923}, {5440, 17581}, {5453, 13743}, {5550, 14007}, {5597, 64397}, {5598, 64396}, {5603, 64400}, {5604, 64404}, {5605, 64403}, {5706, 37106}, {5707, 6875}, {5710, 61155}, {5711, 37303}, {5712, 6872}, {5721, 6884}, {5731, 37422}, {5736, 7538}, {5739, 13736}, {5919, 18178}, {6284, 33112}, {6675, 24883}, {6690, 54355}, {6740, 56417}, {6906, 50317}, {6986, 63982}, {7508, 45931}, {7967, 64384}, {7968, 64385}, {7969, 64386}, {8025, 17539}, {8143, 33858}, {8167, 27625}, {8192, 64395}, {8543, 10571}, {9345, 37608}, {9347, 37552}, {9612, 26738}, {9957, 18180}, {9997, 64398}, {10246, 15952}, {10247, 64419}, {10449, 16342}, {10543, 37369}, {10800, 64381}, {10944, 64406}, {10950, 64407}, {11106, 63007}, {11108, 37687}, {11396, 64378}, {11441, 36746}, {11681, 37373}, {11910, 64402}, {12053, 17167}, {12549, 63968}, {13725, 32782}, {13745, 26064}, {13902, 64417}, {13959, 64418}, {14829, 16347}, {14953, 29624}, {14997, 17544}, {15672, 61661}, {15674, 35466}, {15677, 37631}, {15678, 49744}, {15680, 37635}, {15808, 28618}, {16046, 29580}, {16050, 26626}, {16749, 62697}, {16754, 58329}, {16826, 26643}, {16919, 20131}, {17016, 37593}, {17019, 27174}, {17021, 54387}, {17234, 56782}, {17319, 56019}, {17392, 37299}, {17526, 19766}, {17534, 17749}, {17549, 37522}, {17558, 24597}, {17570, 37679}, {17577, 48841}, {17589, 25507}, {17676, 18134}, {17692, 20132}, {18163, 37556}, {18525, 64399}, {18526, 64383}, {18755, 19318}, {19245, 19763}, {19312, 26243}, {19860, 25059}, {19861, 24554}, {20077, 42045}, {21935, 29640}, {21997, 29569}, {22464, 64160}, {22836, 27785}, {24553, 24565}, {24556, 24558}, {24632, 29574}, {24953, 33142}, {25524, 35983}, {25906, 50622}, {26215, 64348}, {26395, 64379}, {26419, 64380}, {26514, 64391}, {26515, 64392}, {26690, 62707}, {26725, 36250}, {27714, 33160}, {28443, 63307}, {28453, 63338}, {28628, 33134}, {30143, 54315}, {31019, 50065}, {31649, 51340}, {33557, 52524}, {33771, 56191}, {34028, 41402}, {35810, 64412}, {35811, 64413}, {35981, 57283}, {35997, 37600}, {36011, 54313}, {36565, 40980}, {36740, 63183}, {36742, 56292}, {37162, 37662}, {37228, 37659}, {37291, 37634}, {37375, 37693}, {37433, 63386}, {37538, 59359}, {37614, 56946}, {37650, 50398}, {38316, 54308}, {39766, 41813}, {43223, 54331}, {44635, 64410}, {44636, 64411}, {45476, 64387}, {45477, 64388}, {45572, 64389}, {45573, 64390}, {45924, 52841}, {46897, 56311}, {48307, 57246}, {48930, 63400}, {49598, 64010}, {49743, 57002}, {50677, 50693}, {53707, 59135}, {62692, 63493}, {63974, 64295}, {64147, 64324}

X(64415) = reflection of X(i) in X(j) for these {i,j}: {64424, 17553}
X(64415) = isogonal conjugate of X(31503)
X(64415) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 31503}, {6, 56226}, {37, 39980}, {42, 30712}, {512, 58132}, {523, 28162}, {1400, 56201}
X(64415) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 31503}, {9, 56226}, {11530, 10}, {39054, 58132}, {40582, 56201}, {40589, 39980}, {40592, 30712}, {62221, 4815}
X(64415) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56048, 81}
X(64415) = pole of line {3733, 57189} with respect to the circumcircle
X(64415) = pole of line {24006, 30591} with respect to the polar circle
X(64415) = pole of line {81, 2646} with respect to the Feuerbach hyperbola
X(64415) = pole of line {966, 5949} with respect to the Kiepert hyperbola
X(64415) = pole of line {100, 645} with respect to the Kiepert parabola
X(64415) = pole of line {1, 3052} with respect to the Stammler hyperbola
X(64415) = pole of line {4560, 4897} with respect to the Steiner circumellipse
X(64415) = pole of line {2487, 14838} with respect to the Steiner inellipse
X(64415) = pole of line {101, 643} with respect to the Hutson-Moses hyperbola
X(64415) = pole of line {75, 145} with respect to the Wallace hyperbola
X(64415) = pole of line {5235, 5249} with respect to the dual conic of Yff parabola
X(64415) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3340)}}, {{A, B, C, X(2), X(62812)}}, {{A, B, C, X(31), X(3445)}}, {{A, B, C, X(37), X(2650)}}, {{A, B, C, X(63), X(1255)}}, {{A, B, C, X(79), X(5426)}}, {{A, B, C, X(81), X(40430)}}, {{A, B, C, X(86), X(16948)}}, {{A, B, C, X(104), X(5248)}}, {{A, B, C, X(105), X(62841)}}, {{A, B, C, X(191), X(5424)}}, {{A, B, C, X(758), X(28161)}}, {{A, B, C, X(759), X(4658)}}, {{A, B, C, X(943), X(993)}}, {{A, B, C, X(1320), X(3897)}}, {{A, B, C, X(1390), X(32913)}}, {{A, B, C, X(1420), X(3622)}}, {{A, B, C, X(1468), X(2334)}}, {{A, B, C, X(1476), X(1621)}}, {{A, B, C, X(1824), X(1962)}}, {{A, B, C, X(2217), X(62821)}}, {{A, B, C, X(2298), X(10448)}}, {{A, B, C, X(2320), X(5250)}}, {{A, B, C, X(2346), X(2975)}}, {{A, B, C, X(3573), X(58117)}}, {{A, B, C, X(3647), X(6198)}}, {{A, B, C, X(3743), X(4058)}}, {{A, B, C, X(3747), X(48338)}}, {{A, B, C, X(3869), X(39737)}}, {{A, B, C, X(3884), X(37518)}}, {{A, B, C, X(4512), X(62218)}}, {{A, B, C, X(12514), X(56027)}}, {{A, B, C, X(18206), X(56066)}}, {{A, B, C, X(28606), X(42034)}}, {{A, B, C, X(40434), X(40436)}}, {{A, B, C, X(43359), X(54353)}}
X(64415) = barycentric product X(i)*X(j) for these (i, j): {21, 5226}, {27, 3984}, {333, 3340}, {1434, 62218}, {2287, 62783}, {3617, 81}, {3731, 86}, {4058, 757}, {4567, 62221}, {10563, 41629}, {28161, 662}, {42034, 58}, {48338, 799}, {56048, 62608}
X(64415) = barycentric quotient X(i)/X(j) for these (i, j): {1, 56226}, {6, 31503}, {21, 56201}, {58, 39980}, {81, 30712}, {163, 28162}, {662, 58132}, {3340, 226}, {3617, 321}, {3731, 10}, {3984, 306}, {4058, 1089}, {5226, 1441}, {10563, 4052}, {14350, 4404}, {28161, 1577}, {42034, 313}, {48338, 661}, {62218, 2321}, {62221, 16732}, {62783, 1446}
X(64415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10448, 2975}, {1, 21, 81}, {1, 2292, 34195}, {1, 4653, 21}, {1, 5248, 57280}, {1, 52680, 4658}, {1, 846, 2650}, {1, 968, 3869}, {8, 11110, 5235}, {10, 17557, 64425}, {21, 81, 16948}, {86, 52352, 11115}, {386, 5047, 37680}, {405, 19767, 32911}, {442, 24936, 63344}, {519, 17553, 64424}, {846, 2650, 11684}, {1010, 3616, 5333}, {3057, 18165, 41723}, {3622, 11115, 86}, {4234, 38314, 42025}, {4720, 17557, 10}, {5051, 25650, 30831}, {6675, 64167, 24883}, {10246, 15952, 64393}, {13745, 41014, 26064}, {15680, 37635, 49745}, {17056, 64158, 2475}, {17589, 46934, 25507}, {26064, 41014, 31143}, {35016, 58380, 1}, {37573, 59305, 100}

X(64416) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 6TH MIXTILINEAR

Barycentrics    a*(a+b)*(a-b-c)*(b-c)^2*(a+c)*(a^3-3*b*c*(b+c)-a*(b^2+b*c+c^2)) : :

X(64416) lies on circumconic {{A, B, C, X(3737), X(50346)}} and on these lines: {1, 54399}, {11, 3737}, {21, 53388}, {58, 21669}, {81, 16133}, {284, 37675}, {333, 61223}, {846, 18163}, {1021, 38347}, {2611, 48293}, {3120, 17197}, {3125, 55067}, {3736, 7413}, {3746, 4267}, {4516, 18191}, {4551, 24624}, {17194, 56317}, {19642, 35338}, {26856, 34589}, {37019, 53389}, {46816, 52680}, {63974, 64295}, {64147, 64324}

X(64416) = inverse of X(3737) in Feuerbach hyperbola
X(64416) = perspector of circumconic {{A, B, C, X(57093), X(57189)}}
X(64416) = X(i)-Dao conjugate of X(j) for these {i, j}: {4560, 75}
X(64416) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1, 3737}, {62670, 1019}
X(64416) = pole of line {20653, 42708} with respect to the dual conic of Wallace hyperbola
X(64416) = barycentric product X(i)*X(j) for these (i, j): {1, 40625}, {21, 24224}, {514, 57093}, {522, 57189}, {4560, 50346}, {17197, 5260}, {18191, 55095}, {57248, 650}
X(64416) = barycentric quotient X(i)/X(j) for these (i, j): {18191, 55090}, {24224, 1441}, {40625, 75}, {50346, 4552}, {57093, 190}, {57189, 664}, {57248, 4554}, {58302, 21859}

X(64417) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 3RD TRI-SQUARES-CENTRAL

Barycentrics    (a+b)*(a+c)*(2*a^2*(b+c)+(a+2*(b+c))*S) : :

X(64417) lies on these lines: {2, 6}, {21, 8983}, {58, 13888}, {371, 64400}, {3193, 45650}, {4184, 13887}, {4225, 22763}, {7583, 64393}, {8976, 64405}, {9540, 64376}, {13883, 64377}, {13884, 64378}, {13885, 64381}, {13886, 64384}, {13889, 64395}, {13890, 64396}, {13891, 64397}, {13892, 64398}, {13893, 64401}, {13894, 64402}, {13895, 64406}, {13896, 64407}, {13897, 64408}, {13898, 64409}, {13901, 64414}, {13902, 64415}, {13903, 64419}, {13904, 64420}, {13905, 64421}, {13906, 64422}, {13907, 64423}, {13936, 17551}, {14005, 18991}, {18538, 64399}, {18965, 64382}, {19000, 35983}, {19003, 28620}, {28619, 49548}, {35812, 64412}, {35815, 64413}, {45365, 64379}, {45368, 64380}, {45384, 64383}, {45574, 64389}, {45576, 64390}, {45652, 64394}, {49618, 64072}, {63974, 64295}, {64147, 64324}

X(64418) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND 4TH TRI-SQUARES-CENTRAL

Barycentrics    (a+b)*(a+c)*(2*a^2*(b+c)-(a+2*(b+c))*S) : :

X(64418) lies on these lines: {2, 6}, {21, 13971}, {58, 13942}, {372, 64400}, {3193, 45651}, {4184, 13940}, {4225, 22764}, {7584, 64393}, {13883, 17551}, {13935, 64376}, {13936, 64377}, {13937, 64378}, {13938, 64381}, {13939, 64384}, {13943, 64395}, {13944, 64396}, {13945, 64397}, {13946, 64398}, {13947, 64401}, {13948, 64402}, {13951, 64405}, {13952, 64406}, {13953, 64407}, {13954, 64408}, {13955, 64409}, {13958, 64414}, {13959, 64415}, {13961, 64419}, {13962, 64420}, {13963, 64421}, {13964, 64422}, {13965, 64423}, {14005, 18992}, {18762, 64399}, {18966, 64382}, {18999, 35983}, {19004, 28620}, {28619, 49547}, {35813, 64413}, {35814, 64412}, {45366, 64379}, {45367, 64380}, {45385, 64383}, {45575, 64390}, {45577, 64389}, {45653, 64394}, {49619, 64072}, {63974, 64295}, {64147, 64324}

X(64419) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND X3-ABC REFLECTIONS

Barycentrics    a*(a+b)*(a+c)*(a^4-a^3*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)+a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64419) lies on circumconic {{A, B, C, X(14497), X(51223)}} and on these lines: {1, 58382}, {3, 81}, {4, 5769}, {5, 333}, {6, 19543}, {21, 1482}, {28, 2095}, {30, 41629}, {46, 1408}, {58, 517}, {86, 140}, {283, 18180}, {284, 37623}, {355, 64072}, {381, 4921}, {394, 16415}, {474, 26637}, {500, 46623}, {549, 42028}, {580, 37536}, {582, 37521}, {602, 62740}, {631, 8025}, {632, 25507}, {859, 3193}, {952, 56018}, {999, 64382}, {1010, 5690}, {1014, 37545}, {1043, 5844}, {1330, 30449}, {1351, 6985}, {1385, 4658}, {1396, 23072}, {1412, 37582}, {1437, 37532}, {1598, 64378}, {1656, 5235}, {1754, 37482}, {1780, 18191}, {1812, 6911}, {1944, 59642}, {2194, 12704}, {2287, 6918}, {2303, 19547}, {2651, 22791}, {2906, 7436}, {3149, 12160}, {3286, 11248}, {3295, 64414}, {3311, 64410}, {3312, 64411}, {3523, 26860}, {3526, 5333}, {3559, 21664}, {3580, 25646}, {3651, 48907}, {3843, 64399}, {4184, 11849}, {4192, 36750}, {4220, 48928}, {4221, 12702}, {4225, 22765}, {4227, 11396}, {4267, 11249}, {4276, 26286}, {4278, 26285}, {4653, 10222}, {5054, 42025}, {5055, 64424}, {5070, 64425}, {5323, 36279}, {5398, 10441}, {5482, 13329}, {5709, 18163}, {5752, 37530}, {5754, 6905}, {5790, 64401}, {5901, 11110}, {6147, 22161}, {6417, 64386}, {6418, 64385}, {6675, 22139}, {6824, 16713}, {6924, 9567}, {6926, 26818}, {7413, 48933}, {7415, 34773}, {7517, 64395}, {7982, 52680}, {8148, 16948}, {8728, 26638}, {9301, 64398}, {9654, 64408}, {9669, 64409}, {9840, 45923}, {10246, 64377}, {10247, 64415}, {10267, 18185}, {10595, 17588}, {10679, 17524}, {11115, 12245}, {11842, 64381}, {11875, 64396}, {11876, 64397}, {11911, 64402}, {11916, 64403}, {11917, 64404}, {11928, 64406}, {11929, 64407}, {12000, 64422}, {12001, 64423}, {13731, 45931}, {13903, 64417}, {13961, 64418}, {16117, 48921}, {16414, 63068}, {16863, 24557}, {17185, 26921}, {18164, 37534}, {18169, 37529}, {18206, 24467}, {19513, 37509}, {19549, 27644}, {19550, 36754}, {22136, 28258}, {22458, 62798}, {22770, 62843}, {24556, 52264}, {25526, 26446}, {28174, 37422}, {30444, 49716}, {31837, 56770}, {32141, 56181}, {33814, 37288}, {34718, 51669}, {35631, 38832}, {37227, 41723}, {37251, 37783}, {37425, 51340}, {37527, 48882}, {37533, 54356}, {37625, 40980}, {45369, 64379}, {45370, 64380}, {45488, 64387}, {45489, 64388}, {45578, 64389}, {45579, 64390}, {49028, 64391}, {49029, 64392}, {54417, 59318}, {58383, 59624}, {63974, 64295}, {64147, 64324}

X(64419) = reflection of X(i) in X(j) for these {i,j}: {3, 63307}, {1330, 30449}, {15952, 58}
X(64419) = pole of line {405, 3897} with respect to the Stammler hyperbola
X(64419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58, 517, 15952}, {81, 64376, 64393}, {283, 18180, 36011}, {4921, 64400, 64405}, {64376, 64393, 3}, {64382, 64421, 999}, {64400, 64405, 381}, {64412, 64413, 6}, {64414, 64420, 3295}

X(64420) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND INNER-YFF

Barycentrics    a*(a+b)*(a+c)*(a^4-4*a*b*c*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(64420) lies on these lines: {1, 21}, {3, 64382}, {4, 940}, {5, 64409}, {6, 6857}, {12, 64405}, {28, 1905}, {35, 64376}, {46, 37402}, {56, 64393}, {57, 37418}, {60, 4228}, {65, 4221}, {86, 3086}, {90, 56048}, {158, 44734}, {222, 3485}, {284, 2270}, {285, 17188}, {333, 3085}, {354, 1408}, {388, 64384}, {411, 991}, {495, 64408}, {498, 5235}, {499, 5333}, {611, 41610}, {942, 5323}, {1010, 18391}, {1014, 3338}, {1124, 64411}, {1210, 25526}, {1335, 64410}, {1412, 3333}, {1437, 16193}, {1448, 17074}, {1479, 64400}, {1737, 14005}, {1812, 11110}, {1817, 54323}, {2193, 17102}, {2194, 17560}, {2287, 13411}, {2303, 25516}, {2476, 37633}, {3075, 35981}, {3295, 64414}, {3299, 64385}, {3301, 64386}, {3486, 5711}, {3584, 64424}, {3616, 26637}, {3624, 24557}, {3664, 12047}, {3931, 7098}, {3945, 6837}, {4184, 11507}, {4225, 22766}, {4259, 7523}, {4281, 22350}, {4295, 37422}, {4303, 37607}, {4305, 7415}, {4921, 10056}, {5324, 11018}, {5327, 18166}, {5358, 9275}, {5703, 40571}, {5706, 59345}, {5707, 6868}, {5712, 6824}, {5718, 6852}, {6841, 49743}, {6853, 37634}, {6856, 37674}, {6872, 14996}, {6875, 19765}, {6985, 48927}, {7491, 45931}, {7952, 14016}, {8025, 14986}, {9654, 64383}, {10037, 64395}, {10038, 64398}, {10039, 64401}, {10040, 64403}, {10041, 64404}, {10072, 42025}, {10393, 37554}, {10523, 64406}, {10572, 37559}, {10801, 64381}, {10895, 64399}, {10954, 64407}, {11111, 48846}, {11398, 64378}, {11877, 64396}, {11878, 64397}, {11912, 64402}, {13323, 35612}, {13404, 39949}, {13750, 16049}, {13904, 64417}, {13962, 64418}, {14017, 36740}, {14868, 37442}, {15988, 25650}, {16471, 17558}, {17577, 48868}, {18180, 50195}, {19714, 30943}, {24624, 56417}, {28619, 44675}, {31397, 64072}, {35808, 64413}, {35809, 64412}, {37261, 50597}, {44547, 47512}, {45371, 64379}, {45372, 64380}, {45490, 64387}, {45491, 64388}, {45580, 64389}, {45581, 64390}, {46883, 54340}, {49030, 64391}, {49031, 64392}, {49744, 52269}, {63974, 64295}, {64147, 64324}

X(64420) = pole of line {6003, 21192} with respect to the incircle
X(64420) = pole of line {2646, 4221} with respect to the Feuerbach hyperbola
X(64420) = pole of line {5949, 6856} with respect to the Kiepert hyperbola
X(64420) = pole of line {1, 55399} with respect to the Stammler hyperbola
X(64420) = pole of line {75, 3085} with respect to the Wallace hyperbola
X(64420) = pole of line {1014, 5249} with respect to the dual conic of Yff parabola
X(64420) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(19843)}}, {{A, B, C, X(4), X(5250)}}, {{A, B, C, X(63), X(60076)}}, {{A, B, C, X(90), X(4512)}}, {{A, B, C, X(595), X(13404)}}, {{A, B, C, X(3193), X(56048)}}, {{A, B, C, X(3877), X(17097)}}, {{A, B, C, X(5330), X(56030)}}
X(64420) = barycentric product X(i)*X(j) for these (i, j): {19843, 81}
X(64420) = barycentric quotient X(i)/X(j) for these (i, j): {19843, 321}
X(64420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {940, 36746, 4340}, {3295, 64419, 64414}, {18165, 54417, 28}

X(64421) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND OUTER-YFF

Barycentrics    a*(a+b)*(a+c)*(a^4+4*a*b*c*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)) : :

X(64421) lies on these lines: {1, 21}, {3, 64414}, {5, 64408}, {6, 5084}, {8, 26637}, {11, 64405}, {28, 18178}, {36, 64376}, {40, 1412}, {46, 1014}, {55, 64393}, {86, 3085}, {158, 56014}, {284, 8602}, {333, 3086}, {386, 63068}, {387, 394}, {496, 64409}, {497, 64384}, {498, 5333}, {499, 5235}, {517, 5323}, {613, 41610}, {631, 940}, {938, 40571}, {999, 64382}, {1000, 5710}, {1124, 64410}, {1210, 2287}, {1335, 64411}, {1408, 3057}, {1437, 15524}, {1478, 64400}, {1698, 24557}, {1714, 37659}, {1737, 64401}, {1792, 18465}, {1812, 18391}, {2303, 41344}, {2360, 18163}, {3194, 34546}, {3299, 64386}, {3301, 64385}, {3582, 64424}, {3945, 37112}, {4184, 11508}, {4222, 37516}, {4225, 22767}, {4340, 5706}, {4854, 8614}, {4921, 10072}, {5119, 37402}, {5142, 5820}, {5324, 12915}, {5707, 5712}, {5716, 60691}, {5718, 6949}, {5733, 6932}, {6357, 63997}, {6930, 36742}, {6950, 19765}, {6965, 56292}, {7162, 56048}, {7952, 53020}, {9669, 64383}, {10039, 14005}, {10046, 64395}, {10047, 64398}, {10048, 64403}, {10049, 64404}, {10056, 42025}, {10523, 64407}, {10802, 64381}, {10896, 64399}, {10948, 64406}, {11023, 16054}, {11399, 64378}, {11879, 64396}, {11880, 64397}, {11913, 64402}, {13411, 28619}, {13905, 64417}, {13963, 64418}, {14868, 56181}, {14986, 16704}, {15501, 54417}, {16471, 37666}, {17560, 18191}, {17566, 37633}, {18180, 50196}, {19843, 26638}, {23070, 50067}, {25446, 25897}, {25526, 31397}, {30305, 37422}, {33849, 50594}, {35768, 64413}, {35769, 64412}, {37401, 45923}, {37431, 44085}, {39595, 54301}, {40153, 64069}, {41723, 64045}, {45373, 64379}, {45374, 64380}, {45492, 64387}, {45493, 64388}, {45582, 64389}, {45583, 64390}, {49032, 64391}, {49033, 64392}, {49745, 63297}, {50633, 59353}, {56293, 62691}, {63974, 64295}, {64147, 64324}

X(64421) = pole of line {443, 5949} with respect to the Kiepert hyperbola
X(64421) = pole of line {1, 55400} with respect to the Stammler hyperbola
X(64421) = pole of line {75, 3086} with respect to the Wallace hyperbola
X(64421) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(8602)}}, {{A, B, C, X(31), X(42019)}}, {{A, B, C, X(63), X(34546)}}, {{A, B, C, X(81), X(24556)}}, {{A, B, C, X(1000), X(5250)}}, {{A, B, C, X(4512), X(7162)}}
X(64421) = barycentric product X(i)*X(j) for these (i, j): {1, 24556}, {33969, 4573}
X(64421) = barycentric quotient X(i)/X(j) for these (i, j): {24556, 75}, {33969, 3700}
X(64421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {999, 64419, 64382}, {1408, 3057, 4221}

X(64422) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND INNER-YFF TANGENTS

Barycentrics    a*(a+b)*(a+c)*(a^4-6*a*b*c*(b+c)+(b^2-c^2)^2-2*a^2*(b^2-b*c+c^2)) : :

X(64422) lies on these lines: {1, 21}, {4, 37633}, {12, 64406}, {60, 17560}, {86, 10586}, {333, 10528}, {940, 6872}, {1812, 17588}, {4184, 11509}, {4221, 34339}, {4225, 22768}, {4228, 54417}, {4921, 11239}, {5235, 5552}, {5554, 51978}, {6837, 36746}, {6841, 26131}, {6857, 32911}, {6871, 37674}, {10531, 64400}, {10803, 64381}, {10805, 64384}, {10834, 64395}, {10878, 64398}, {10915, 64401}, {10929, 64403}, {10930, 64404}, {10942, 64405}, {10955, 64407}, {10956, 64408}, {10958, 64409}, {10965, 64414}, {11248, 64376}, {11400, 64378}, {11881, 64396}, {11882, 64397}, {11914, 64402}, {12000, 64419}, {12594, 41610}, {13906, 64417}, {13964, 64418}, {16049, 18165}, {16203, 64393}, {16617, 51340}, {18542, 64399}, {18545, 64383}, {19047, 64385}, {19048, 64386}, {26364, 64425}, {26402, 64379}, {26426, 64380}, {26520, 64391}, {26525, 64392}, {35816, 64412}, {35817, 64413}, {37402, 59333}, {37418, 37534}, {37501, 50695}, {44643, 64410}, {44644, 64411}, {45494, 64387}, {45495, 64388}, {45584, 64389}, {45585, 64390}, {45701, 64424}, {49626, 64072}, {63974, 64295}, {64147, 64324}

X(64422) = pole of line {75, 10528} with respect to the Wallace hyperbola
X(64422) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(63), X(60169)}}, {{A, B, C, X(3890), X(17097)}}

X(64423) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND OUTER-YFF TANGENTS

Barycentrics    a*(a+b)*(a+c)*(a^4+6*a*b*c*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+b*c+c^2)) : :

X(64423) lies on these lines: {1, 21}, {11, 64407}, {86, 10587}, {145, 1812}, {155, 6930}, {229, 64043}, {333, 10529}, {631, 5707}, {1043, 26637}, {1068, 33151}, {1069, 3488}, {1437, 9957}, {1697, 1790}, {2287, 5839}, {2990, 63157}, {3057, 16049}, {3871, 14868}, {4184, 11510}, {4225, 10966}, {4228, 18178}, {4921, 11240}, {5084, 32911}, {5235, 10527}, {5292, 37680}, {5706, 37112}, {5713, 6932}, {5919, 54417}, {10528, 31631}, {10532, 64400}, {10804, 64381}, {10806, 64384}, {10835, 64395}, {10879, 64398}, {10916, 64401}, {10931, 64403}, {10932, 64404}, {10943, 64405}, {10949, 64406}, {10957, 14008}, {10959, 64409}, {11249, 64376}, {11401, 64378}, {11883, 64396}, {11884, 64397}, {11915, 64402}, {12001, 64419}, {12595, 41610}, {13907, 64417}, {13965, 64418}, {14923, 17518}, {16202, 64393}, {18543, 64383}, {18544, 64399}, {18967, 64382}, {19049, 64385}, {19050, 64386}, {22136, 64167}, {24557, 24987}, {26131, 37401}, {26363, 64425}, {26401, 64379}, {26425, 64380}, {26519, 64391}, {26524, 64392}, {35818, 64412}, {35819, 64413}, {35997, 37568}, {41723, 64046}, {44645, 64410}, {44646, 64411}, {45496, 64387}, {45497, 64388}, {45586, 64389}, {45587, 64390}, {45700, 64424}, {49627, 64072}, {63974, 64295}, {64147, 64324}

X(64423) = pole of line {75, 10529} with respect to the Wallace hyperbola
X(64423) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1000), X(12514)}}, {{A, B, C, X(2990), X(62812)}}
X(64423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3193, 81}

X(64424) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND GEMINI 107

Barycentrics    (a+b)*(3*a-4*(b+c))*(a+c) : :

X(64424) lies on these lines: {2, 6}, {10, 16948}, {21, 3679}, {30, 64376}, {58, 19875}, {519, 17553}, {551, 17557}, {1817, 25057}, {3058, 64409}, {3175, 33761}, {3241, 11110}, {3524, 64384}, {3534, 64383}, {3545, 64400}, {3582, 64421}, {3584, 64420}, {3794, 63961}, {3828, 14005}, {3830, 64399}, {4197, 48834}, {4221, 50821}, {4234, 53620}, {4606, 5325}, {4653, 4677}, {4668, 17782}, {4669, 4720}, {4678, 52352}, {4685, 32917}, {5054, 64393}, {5055, 64419}, {5064, 64378}, {5271, 50106}, {5434, 64408}, {6175, 49723}, {7415, 50864}, {7865, 64398}, {10458, 42043}, {11237, 64382}, {11238, 64414}, {15952, 38066}, {16052, 26064}, {16833, 40773}, {16865, 48862}, {17549, 48852}, {17551, 19876}, {17577, 48839}, {17588, 31145}, {18169, 36634}, {24936, 49718}, {25055, 64377}, {29582, 33297}, {30564, 32939}, {31165, 41723}, {34606, 64407}, {34612, 64406}, {35623, 42041}, {37870, 56037}, {38314, 56018}, {41310, 63158}, {41821, 59583}, {45313, 57112}, {45700, 64423}, {45701, 64422}, {50428, 54429}, {51066, 52680}, {56519, 62586}, {59624, 64010}, {63974, 64295}, {64147, 64324}

X(64424) = midpoint of X(i) and X(j) for these {i,j}: {17553, 64401}
X(64424) = reflection of X(i) in X(j) for these {i,j}: {64415, 17553}
X(64424) = trilinear pole of line {28205, 58159}
X(64424) = X(i)-Dao conjugate of X(j) for these {i, j}: {36830, 28206}
X(64424) = pole of line {99, 28206} with respect to the Kiepert parabola
X(64424) = pole of line {2, 15492} with respect to the Wallace hyperbola
X(64424) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4668)}}, {{A, B, C, X(6), X(17782)}}, {{A, B, C, X(391), X(36910)}}, {{A, B, C, X(524), X(28205)}}, {{A, B, C, X(940), X(56037)}}, {{A, B, C, X(1751), X(19738)}}, {{A, B, C, X(3231), X(58159)}}, {{A, B, C, X(3936), X(60267)}}, {{A, B, C, X(4383), X(39962)}}, {{A, B, C, X(4585), X(4606)}}, {{A, B, C, X(4921), X(60235)}}, {{A, B, C, X(24624), X(42028)}}, {{A, B, C, X(31205), X(56947)}}, {{A, B, C, X(37639), X(55953)}}, {{A, B, C, X(37674), X(40434)}}
X(64424) = barycentric product X(i)*X(j) for these (i, j): {4668, 86}, {17782, 310}, {28205, 99}, {58159, 670}
X(64424) = barycentric quotient X(i)/X(j) for these (i, j): {110, 28206}, {4668, 10}, {17782, 42}, {28205, 523}, {58159, 512}
X(64424) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 333, 4921}, {2, 4921, 81}, {519, 17553, 64415}, {4921, 5235, 2}, {17553, 64401, 519}

X(64425) = EQUICENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND GEMINI 109

Barycentrics    (a+b)*(a-4*(b+c))*(a+c) : :

X(64425) lies on these lines: {2, 6}, {3, 64399}, {5, 64376}, {10, 4720}, {21, 1698}, {58, 17124}, {100, 59306}, {140, 64405}, {229, 17581}, {274, 39962}, {750, 39673}, {1010, 19877}, {1014, 31231}, {1043, 46933}, {1125, 64401}, {1621, 59312}, {3090, 64400}, {3525, 64384}, {3526, 64393}, {3624, 64377}, {3634, 14005}, {3828, 17553}, {3925, 14008}, {4184, 4413}, {4221, 11231}, {4653, 19875}, {4658, 34595}, {4803, 51066}, {5054, 64383}, {5070, 64419}, {5094, 64378}, {5208, 63961}, {5257, 33133}, {5260, 37442}, {5271, 62851}, {5273, 7359}, {5284, 30970}, {5316, 17167}, {5432, 64409}, {5433, 64408}, {5550, 56018}, {5745, 7110}, {6557, 27825}, {7484, 64395}, {7808, 64381}, {7914, 64398}, {8040, 33135}, {9342, 13588}, {9534, 19334}, {9780, 11110}, {10458, 16569}, {11115, 46931}, {14956, 26040}, {15184, 64402}, {16054, 62400}, {16457, 19767}, {16700, 31197}, {16832, 40773}, {17125, 38832}, {17151, 25081}, {17197, 31271}, {17357, 63158}, {17514, 24883}, {17588, 46932}, {17589, 46930}, {18165, 61686}, {18229, 25058}, {19827, 37095}, {19858, 62804}, {19859, 62802}, {19862, 64072}, {19876, 52680}, {19878, 28619}, {24624, 60243}, {24953, 64407}, {24988, 33730}, {25060, 44307}, {25526, 51073}, {25917, 41723}, {26363, 64423}, {26364, 64422}, {27003, 31238}, {27798, 64010}, {28653, 56520}, {29576, 33113}, {29581, 33297}, {31286, 57112}, {31423, 37402}, {31993, 33761}, {33108, 37373}, {37870, 40434}, {47794, 57189}, {51505, 54357}, {53039, 59624}, {60203, 60235}, {63974, 64295}, {64147, 64324}

X(64425) = trilinear pole of line {28165, 58165}
X(64425) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 28166}
X(64425) = X(i)-Dao conjugate of X(j) for these {i, j}: {16675, 4002}, {36830, 28166}
X(64425) = pole of line {99, 28166} with respect to the Kiepert parabola
X(64425) = pole of line {6, 7280} with respect to the Stammler hyperbola
X(64425) = pole of line {2, 16669} with respect to the Wallace hyperbola
X(64425) = pole of line {1125, 17551} with respect to the dual conic of Yff parabola
X(64425) = pole of line {4024, 57066} with respect to the dual conic of Suppa-Cucoanes circle
X(64425) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5560)}}, {{A, B, C, X(6), X(16675)}}, {{A, B, C, X(88), X(37685)}}, {{A, B, C, X(391), X(7110)}}, {{A, B, C, X(524), X(28165)}}, {{A, B, C, X(940), X(40434)}}, {{A, B, C, X(1255), X(14996)}}, {{A, B, C, X(3231), X(58165)}}, {{A, B, C, X(3936), X(60243)}}, {{A, B, C, X(5333), X(60235)}}, {{A, B, C, X(17056), X(60203)}}, {{A, B, C, X(17346), X(56062)}}, {{A, B, C, X(24624), X(25507)}}, {{A, B, C, X(26860), X(37870)}}, {{A, B, C, X(37639), X(56058)}}, {{A, B, C, X(42028), X(52393)}}, {{A, B, C, X(56204), X(56440)}}
X(64425) = barycentric product X(i)*X(j) for these (i, j): {16675, 274}, {28165, 99}, {58165, 670}
X(64425) = barycentric quotient X(i)/X(j) for these (i, j): {110, 28166}, {16675, 37}, {28165, 523}, {58165, 512}
X(64425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 333, 5333}, {2, 5235, 81}, {10, 17557, 64415}, {5235, 5333, 333}





leftri   Composites: X(64426) - X(64437)  rightri

Contributed by Clark Kimberling and Peter Moses, July 3, 2024

Suppose that P = p(a,b,c) : p(b,c,a) : p(c,a,b) and U = u(a,b,c) : u(b,c,a) : u(c,a,b) are triangle centers, where p(a,b,c) and u(a,b,c) are polynomials in standard form (i.e., p(a,b,c) and p(b,c,a) are relatively prime, and the coefficient of the highest power of a is positive, or if p(a,b,c) is invariant of a then the coefficient of highest power of b is positive.)

Define the composite P-of-U to be the triangle center given by

P-of-U = p(u(a,b,c), u(b,c,a), u(c,a,b)) : p(u(b,c,a), u(c,a,b), u(a,b,c)) : p(u(c,a,b), u(a,b,c), u(b,c,a)).

For example, X(3)-of-X(3) = X(1147) = a^4(a^2 - b^2 - c^2)(a^4 + b^4 + c^4 - 2 a^2 b^2 - 2 a^2 c^2) : :

Suppose next that the Euler line is represented as a linear combination of X(3) and X(4) as follows:

V(r,s) = a^2 (a^2 - b^2 - c^2)*r + (b^2 - c^2 - a^2)(c^2 - a^2 - b^2)*s : : ,

where r and s are not both 0. Let P = X(10) = b + c : c + a : a + b.

Then "X(10)-of-Euler-line" is the line given by

X(10)-of-V(r,s), which as the linear combination

(a^2 (b^2 + c^2) + (b^2 - c^2)^2)*r - 2 a^2(a^2 - b^2 - c^2)*s : :

is essentially X(5)*r + X(3)*s, the Euler line.

Reversing the order of the composition gives "the Euler line of X(10)", consisting of points

W(r,s) = (b + c)^2 (a^2 - b c + a b + a c)*r + 2(b^2 - c a + b c + b a)(c^2 - a b + c a + c b)*s : :,

which is essentially X(4075)*r + X(596)*s.

The appearance of (r,s,k) in the following list means that r and s are not both 0 and W(r,s) = X(k):

(r,0,4075), (0,s,596), (r,r,6532), (r,-r,6534), (2r,r,2), (2r,-r,24068), and in general, we have the combo

W(r,s) = 3*r*X(2) + (3*s - r)*X(596). The list continues:

(-4,1,46426), (-10,3,46427), (-3,1, 46428), (-2,3,46429), (1,2,46430), (2,3,46431), (4,3,46432), (3,2,46433), (3,1,46434), (10,3,46435), (-1,1,46436), (-1,3,46437).

A selection of points of the form X(i)-of-X(i) appear next:

X(1)-of-X(1) = X(1)
X(2)-of-X(2) = X(2)
X(3)-of-X(3) = X(1147)
X(4)-of-X(4) = X(3346)
X(5)-of-X(5) = X(64452)
X(6)-of-X(6) = X(32)
X(7)-of-X(7) = X(10405)
X(8)-of-X(8) = X(145)
X(9)-of-X(9) = X(1)
X(10)-of-X(10) = X(1125)
X(11)-of-X(11) = X(3126)
X(39)-of-X(39) = X(64453)
X(42)-of-X(42) = X(64454)
X(63)-of-X(63) = X(64455)
X(72)-of-X(72) = X(64456)
X(81)-of-X(81) = X(64457)
X(85)-of-X(85) = X(64458)
X(88)-of-X(88) = X(64459)
X(99)-of-X(99) = X(64460)
X(526)-of-X(526) = X64461)
X(527)-of-X(527) = X64462)
X(545)-of-X(545) = X(64463)
--------------------------------------------------------

The appearance of (i,j,k) in the following list means that X(i)-of-X(j) = X(k):

(3,3,1147), (3,4,6523), (3,5,6663), (3,6,206), (3,7,17113), (3,8,6552), (3,9,6600), (3,10,4075), (3,11,64440), (4,1,4), (4,2,2), (4,3,68), (4,4,3346), (4,5,6662), (4,6,66), (4,7,42483), (4,8,6553), (4,9,6601), (4,10,596), (4,11,43974), (5,1,5), (5,2,2), (5,3,5449), (5,4,59361), (5,5,64452), (5,6,6697), (5,7,64441), (5,8,64442, (5,9,64443), (5,10,6532), (5,11,64445), (6,1,6), (6,2,2), (6,3,577), (6,4,393), (6,5,36412), (6,6,32), (6,7,279), (6,8,346), (6,9,220), (6,10,594), (7,1,7), (7,2,2), (7,3,69), (7,4,253), (7,5,264), (7,6,4), (7,7,10405), (7,8,4373), (7,9,8), (7,10,75), (7,11,693), (8,1,8), (8,2,2), (8,3,4), (8,4,20), (8,5,3), (8,6,69), (8,7,144), (8,8,145), (8,9,7), (8,10,1), (8,11,100), (9,1,9), (9,2,2), (9,3,6), (9,4,1249), (9,5,216), (9,6,3), (9,7,3160), (9,8,3161), (9,9,1), (9,10,37), (9,11,650), (10,1,10), (10,2,2), (10,3,5), (10,4,3), (10,5,140), (10,6,141), (10,7,9), (10,8,1), (10,9,142), (10,10,1125), (10,11,3035), (11,1,11), (11,3,125), (11,4,122), (11,5,2972), (11,6,125), (11,7,13609), (11,8,3756), (11,9,11), (11,10,244), (11,11,3126), (15,3,64464), (16,3,64465), (17,3,64466), (18,3,64467)

underbar



X(64426) = X(2)X(596)∩X(72)X(519)

Barycentrics    3*a^2*b^2 + 3*a*b^3 + 2*a^2*b*c + 5*a*b^2*c - 3*b^3*c + 3*a^2*c^2 + 5*a*b*c^2 - 6*b^2*c^2 + 3*a*c^3 - 3*b*c^3 : :
X(64426) = 5 X[2] - 4 X[6532], X[596] - 4 X[4075], 5 X[596] - 8 X[6532], X[596] + 2 X[24068], 5 X[4075] - 2 X[6532], 2 X[4075] + X[24068], 4 X[6532] + 5 X[24068], X[551] - 3 X[3971], X[3828] - 3 X[59718], X[3679] + 3 X[32925], 3 X[17155] - 7 X[19876]

X(64426) lies on these lines: {2, 596}, {10, 4980}, {72, 519}, {537, 13476}, {551, 3971}, {726, 3828}, {1089, 42039}, {1125, 3967}, {3679, 17163}, {3956, 28516}, {4125, 20891}, {4360, 6540}, {4692, 42285}, {17155, 19876}, {18146, 21208}, {21080, 50777}, {24067, 50113}, {58629, 64185}

X(64426) = midpoint of X(i) and X(j) for these {i,j}: {2, 24068}, {21080, 50777}
X(64426) = reflection of X(i) in X(j) for these {i,j}: {2, 4075}, {596, 2}, {64185, 58629}
X(64426) = {X(4075),X(24068)}-harmonic conjugate of X(596)

X(64427) = X(2)X(596)∩X(8)X(4365)

Barycentrics    2*a^2*b^2 + 2*a*b^3 + a^2*b*c + 3*a*b^2*c - 2*b^3*c + 2*a^2*c^2 + 3*a*b*c^2 - 4*b^2*c^2 + 2*a*c^3 - 2*b*c^3 : :
X(64427) = 15 X[2] - 8 X[596], 9 X[2] - 16 X[4075], 39 X[2] - 32 X[6532], 3 X[2] + 4 X[24068], 3 X[596] - 10 X[4075], 13 X[596] - 20 X[6532], 2 X[596] + 5 X[24068], 13 X[4075] - 6 X[6532], 4 X[4075] + 3 X[24068], 8 X[6532] + 13 X[24068], X[8] + 6 X[32925], X[145] - 8 X[3159], 5 X[1698] - 12 X[59718], 4 X[2901] + 3 X[4661], 5 X[3616] - 12 X[3971], 10 X[3697] - 3 X[50106], X[3885] + 6 X[50078], 5 X[3889] - 12 X[35652], 11 X[5550] - 18 X[64178], 6 X[17155] - 13 X[19877], 16 X[24176] - 23 X[46931], 4 X[34790] + 3 X[42044]

X(64427) lies on these lines: {2, 596}, {8, 4365}, {145, 3159}, {726, 4772}, {1089, 7226}, {1698, 59718}, {2901, 4661}, {3214, 49445}, {3616, 3971}, {3622, 59717}, {3697, 50106}, {3701, 49447}, {3871, 17262}, {3885, 50078}, {3889, 35652}, {3953, 46938}, {3983, 28555}, {4193, 4884}, {4361, 32635}, {4756, 16466}, {4903, 26094}, {5550, 64178}, {14997, 43993}, {17155, 19877}, {19767, 32937}, {21080, 26115}, {24176, 46931}, {24443, 49517}, {25248, 29510}, {27385, 59732}, {34790, 42044}

X(64428) = X(2)X(596)∩X(519)X(4536)

Barycentrics    5*a^2*b^2 + 5*a*b^3 + 2*a^2*b*c + 7*a*b^2*c - 5*b^3*c + 5*a^2*c^2 + 7*a*b*c^2 - 10*b^2*c^2 + 5*a*c^3 - 5*b*c^3 : :
X(64428) = 9 X[2] - 5 X[596], 3 X[2] - 5 X[4075], 6 X[2] - 5 X[6532], 3 X[2] + 5 X[24068], X[596] - 3 X[4075], 2 X[596] - 3 X[6532], X[596] + 3 X[24068], X[6532] + 2 X[24068], 5 X[3159] - X[3244], X[3632] + 15 X[32925], 15 X[3971] - 7 X[15808], X[24176] - 3 X[59718]

X(64428) lies on these lines: {2, 596}, {519, 4536}, {726, 4739}, {3159, 3244}, {3632, 32925}, {3636, 59717}, {3971, 15808}, {4540, 28554}, {24176, 59718}

X(64428) = midpoint of X(4075) and X(24068)
X(64428) = reflection of X(6532) in X(4075)

X(64429) = X(1)X(87)∩X(2)X(596)

Barycentrics    a^2*b^2 + a*b^3 - a^2*b*c - b^3*c + a^2*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64429) = 3 X[2] - 4 X[596], 9 X[2] - 8 X[4075], 15 X[2] - 16 X[6532], 3 X[596] - 2 X[4075], 5 X[596] - 4 X[6532], 5 X[4075] - 6 X[6532], 4 X[4075] - 3 X[24068], 8 X[6532] - 5 X[24068], 2 X[10] - 3 X[17155], 4 X[1125] - 3 X[32925], 5 X[1698] - 6 X[24165], 2 X[2901] - 3 X[3873], 4 X[3159] - 5 X[3616], 3 X[3175] - 4 X[5045], 7 X[3624] - 6 X[3971], 3 X[3681] - 4 X[64185], 4 X[3881] - 3 X[32915], 5 X[3889] - 3 X[42044], 7 X[9780] - 8 X[24176], 5 X[18398] - 6 X[42055], 5 X[18398] - 4 X[63800], 3 X[42055] - 2 X[63800], 10 X[19862] - 9 X[64178], 13 X[34595] - 12 X[59517], 2 X[34790] - 3 X[42051], 3 X[50122] - 4 X[58609], 7 X[51073] - 6 X[59718]

X(64429) lies on these lines: {1, 87}, {2, 596}, {6, 43993}, {8, 20068}, {10, 7226}, {35, 32920}, {38, 10479}, {58, 3891}, {69, 33868}, {72, 28582}, {79, 4865}, {312, 3953}, {341, 1739}, {386, 17165}, {442, 4884}, {518, 64184}, {519, 1770}, {522, 12534}, {536, 3555}, {537, 5904}, {595, 32933}, {714, 4647}, {982, 1089}, {986, 4692}, {995, 56318}, {1125, 32925}, {1203, 32935}, {1698, 24165}, {1724, 32922}, {2275, 22036}, {2901, 3873}, {3159, 3616}, {3175, 5045}, {3210, 3293}, {3216, 32937}, {3242, 50044}, {3337, 29649}, {3454, 33089}, {3624, 3971}, {3670, 4385}, {3681, 64185}, {3701, 24046}, {3746, 32934}, {3881, 32915}, {3889, 42044}, {3952, 17749}, {3987, 4737}, {3992, 24174}, {4066, 30942}, {4082, 24171}, {4125, 24167}, {4362, 6763}, {4365, 50625}, {4392, 50605}, {4418, 30145}, {4434, 37524}, {4694, 34860}, {4857, 29844}, {4894, 24851}, {5010, 8720}, {5069, 40085}, {5248, 32923}, {5264, 32939}, {5274, 44040}, {6051, 49523}, {7080, 44311}, {7280, 8669}, {8715, 32845}, {9534, 31302}, {9780, 24176}, {10449, 36862}, {10624, 17132}, {16602, 59582}, {16828, 21080}, {17756, 21067}, {18135, 24166}, {18393, 49613}, {18398, 42055}, {19846, 33147}, {19862, 64178}, {19871, 51060}, {20077, 20087}, {20083, 33170}, {23537, 63147}, {25440, 32927}, {25645, 33144}, {27091, 31348}, {27481, 31996}, {27785, 49456}, {28542, 34719}, {28555, 34791}, {30148, 32930}, {32026, 36494}, {32092, 49521}, {32926, 37522}, {32940, 62805}, {33120, 36250}, {34595, 59517}, {34790, 42051}, {37610, 63996}, {41011, 50589}, {42471, 62227}, {50122, 58609}, {51073, 59718}, {56800, 62636}, {59730, 63259}

X(64429) = reflection of X(i) in X(j) for these {i,j}: {24068, 596}, {49445, 42027}
X(64429) = anticomplement of X(24068)
X(64429) = anticomplement of the isotomic conjugate of X(39693)
X(64429) = X(39693)-anticomplementary conjugate of X(6327)
X(64429) = X(39693)-Ceva conjugate of X(2)
X(64429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {596, 24068, 2}, {42055, 63800, 18398}

X(64430) = X(2)X(596)∩X(519)X(942)

Barycentrics    3*a^2*b^2 + 3*a*b^3 - 10*a^2*b*c - 7*a*b^2*c - 3*b^3*c + 3*a^2*c^2 - 7*a*b*c^2 - 6*b^2*c^2 + 3*a*c^3 - 3*b*c^3 : :
X(64430) = 5 X[2] - X[24068], 2 X[596] + X[4075], X[596] + 2 X[6532], 5 X[596] + X[24068], X[4075] - 4 X[6532], 5 X[4075] - 2 X[24068], 10 X[6532] - X[24068], X[551] + 3 X[24165], X[3159] - 3 X[19883]

X(64430) lies on these lines: {2, 596}, {10, 42038}, {519, 942}, {537, 40607}, {551, 1962}, {594, 35076}, {726, 4755}, {3159, 19883}, {3828, 59717}, {4013, 44847}, {4151, 45657}, {4714, 39697}, {6533, 42039}, {7263, 58898}

X(64430) = midpoint of X(2) and X(596)
X(64430) = reflection of X(i) in X(j) for these {i,j}: {2, 6532}, {4075, 2}
X(64430) = {X(596),X(6532)}-harmonic conjugate of X(4075)

X(64431) = X(2)X(596)∩X(10)X(982)

Barycentrics    a^2*b^2 + a*b^3 - 4*a^2*b*c - 3*a*b^2*c - b^3*c + a^2*c^2 - 3*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64431) = X[1] + 4 X[24176], 3 X[2] + 2 X[596], 9 X[2] - 4 X[4075], 3 X[2] - 8 X[6532], 6 X[2] - X[24068], 3 X[596] + 2 X[4075], X[596] + 4 X[6532], 4 X[596] + X[24068], X[4075] - 6 X[6532], 8 X[4075] - 3 X[24068], 16 X[6532] - X[24068], 3 X[354] + 2 X[64185], 2 X[1125] + 3 X[24165], X[2901] - 6 X[3742], 2 X[3159] - 7 X[3624], 2 X[3159] + 3 X[17155], 7 X[3624] + 3 X[17155], 2 X[3678] + 3 X[42055], X[3874] - 6 X[42053], 3 X[3971] - 8 X[19878], 3 X[32860] + 7 X[50190], 3 X[32925] - 13 X[34595], 9 X[64149] + X[64184]

X(64431) lies on these lines: {1, 17495}, {2, 596}, {10, 982}, {38, 6533}, {244, 50605}, {274, 24166}, {354, 64185}, {496, 7263}, {519, 3889}, {540, 52783}, {726, 4687}, {1125, 24165}, {1698, 59717}, {2901, 3742}, {3159, 3624}, {3210, 4065}, {3216, 17140}, {3337, 32914}, {3678, 42055}, {3874, 42053}, {3953, 4359}, {3971, 19878}, {3976, 28612}, {3980, 30148}, {4066, 4871}, {4385, 49993}, {4568, 27318}, {10527, 44311}, {10589, 44040}, {16602, 59666}, {16825, 18206}, {17205, 33945}, {17749, 24349}, {20108, 32771}, {21208, 34284}, {25512, 46901}, {28581, 50191}, {31025, 42471}, {31348, 31996}, {31997, 57029}, {32860, 50190}, {32925, 34595}, {37607, 49683}, {37633, 43993}, {64149, 64184}

X(64431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 596, 24068}, {596, 6532, 2}, {3624, 17155, 3159}

X(64432) = X(2)X(596)∩X(10)X(4487)

Barycentrics    a^2*b^2 + a*b^3 - 10*a^2*b*c - 9*a*b^2*c - b^3*c + a^2*c^2 - 9*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64432) = 6 X[2] + X[596], 9 X[2] - 2 X[4075], 3 X[2] + 4 X[6532], 15 X[2] - X[24068], 3 X[596] + 4 X[4075], X[596] - 8 X[6532], 5 X[596] + 2 X[24068], X[4075] + 6 X[6532], 10 X[4075] - 3 X[24068], 20 X[6532] + X[24068], X[3159] - 8 X[19878], 6 X[3848] + X[64185], 5 X[19862] + 2 X[24176]

X(64432) lies on these lines: {2, 596}, {10, 4487}, {519, 4002}, {1125, 3752}, {3159, 19878}, {3848, 64185}, {4850, 58387}, {19862, 24176}, {24443, 42285}, {51073, 59717}

X(64432) = {X(2),X(6532)}-harmonic conjugate of X(596)

X(64433) = X(2)X(596)∩X(10)X(46190)

Barycentrics    a^2*b^2 + a*b^3 - 14*a^2*b*c - 13*a*b^2*c - b^3*c + a^2*c^2 - 13*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64433) = 9 X[2] + X[596], 6 X[2] - X[4075], 3 X[2] + 2 X[6532], 21 X[2] - X[24068], 2 X[596] + 3 X[4075], X[596] - 6 X[6532], 7 X[596] + 3 X[24068], X[4075] + 4 X[6532], 7 X[4075] - 2 X[24068], 14 X[6532] + X[24068], 4 X[19878] + X[24176]

X(64433) lies on these lines: {2, 596}, {10, 46190}, {519, 45777}, {1125, 4868}, {3752, 58387}, {19878, 24176}, {24174, 42285}, {30957, 39708}, {31253, 59717}

X(64433) = {X(2),X(6532)}-harmonic conjugate of X(4075)

X(64434) = X(2)X(596)∩X(10)X(3902)

Barycentrics    a^2*b^2 + a*b^3 + 10*a^2*b*c + 11*a*b^2*c - b^3*c + a^2*c^2 + 11*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64434) = 9 X[2] - X[596], 3 X[2] + X[4075], 15 X[2] + X[24068], X[596] + 3 X[4075], X[596] - 3 X[6532], 5 X[596] + 3 X[24068], 5 X[4075] - X[24068], 5 X[6532] + X[24068], X[3159] + 7 X[51073], X[24176] - 5 X[31253], X[24176] + 3 X[59517], 5 X[31253] + 3 X[59517]

X(64434) lies on these lines: {2, 596}, {10, 3902}, {519, 4540}, {1125, 17724}, {3159, 51073}, {3634, 17070}, {19878, 59717}, {24176, 31253}, {44307, 58387}

X(64434) = midpoint of X(4075) and X(6532)
X(64434) = complement of X(6532)
X(64434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4075, 6532}, {31253, 59517, 24176}

X(64435) = X(2)X(596)∩X(10)X(4673)

Barycentrics    a^2*b^2 + a*b^3 + 8*a^2*b*c + 9*a*b^2*c - b^3*c + a^2*c^2 + 9*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64435) = 15 X[2] - 2 X[596], 9 X[2] + 4 X[4075], 21 X[2] - 8 X[6532], 12 X[2] + X[24068], 3 X[596] + 10 X[4075], 7 X[596] - 20 X[6532], 8 X[596] + 5 X[24068], 7 X[4075] + 6 X[6532], 16 X[4075] - 3 X[24068], 32 X[6532] + 7 X[24068], X[2901] + 12 X[58451], 3 X[3971] + 10 X[31253], 17 X[19872] - 4 X[24176], 17 X[19872] + 9 X[64178], 4 X[24176] + 9 X[64178], 9 X[42056] + 4 X[58565], 7 X[51073] + 6 X[59517]

X(64435) lies on these lines: {2, 596}, {10, 4673}, {2901, 58451}, {3971, 31253}, {19872, 24176}, {34595, 59717}, {42056, 58565}, {51073, 59517}

X(64435) = {X(19872),X(64178)}-harmonic conjugate of X(24176)

X(64436) = X(2)X(596)∩X(10)X(3702)

Barycentrics    a^2*b^2 + a*b^3 + 6*a^2*b*c + 7*a*b^2*c - b^3*c + a^2*c^2 + 7*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64436) = 6 X[2] - X[596], 3 X[2] + 2 X[4075], 9 X[2] - 4 X[6532], 9 X[2] + X[24068], X[596] + 4 X[4075], 3 X[596] - 8 X[6532], 3 X[596] + 2 X[24068], 3 X[4075] + 2 X[6532], 6 X[4075] - X[24068], 4 X[6532] + X[24068], X[2901] + 9 X[61686], X[3159] + 4 X[3634], X[3159] - 6 X[59517], 2 X[3634] + 3 X[59517], X[3874] + 9 X[42056], 3 X[3971] + 2 X[24176], 3 X[3971] + 7 X[51073], 2 X[24176] - 7 X[51073], 3 X[4096] + 2 X[58565], 17 X[19872] + 3 X[32925], 6 X[58451] - X[64185]

X(64436) lies on these lines: {2, 596}, {10, 3702}, {519, 3697}, {726, 31238}, {1125, 59511}, {2901, 61686}, {3159, 3634}, {3874, 42056}, {3971, 24176}, {4013, 25466}, {4065, 31035}, {4096, 58565}, {5432, 44040}, {6051, 59669}, {19862, 31264}, {19872, 32925}, {20108, 24003}, {25248, 29406}, {26364, 59638}, {44307, 59666}, {58451, 64185}

X(64436) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4075, 596}, {2, 24068, 6532}, {3634, 59517, 3159}, {3971, 51073, 24176}, {4075, 6532, 24068}, {6532, 24068, 596}

X(64437) = X(1)X(56150)∩X(2)X(596)

Barycentrics    a^2*b^2 + a*b^3 + 5*a^2*b*c + 6*a*b^2*c - b^3*c + a^2*c^2 + 6*a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(64437) = 21 X[2] - 4 X[596], 9 X[2] + 8 X[4075], 33 X[2] - 16 X[6532], 15 X[2] + 2 X[24068], 3 X[596] + 14 X[4075], 11 X[596] - 28 X[6532], 10 X[596] + 7 X[24068], 11 X[4075] + 6 X[6532], 20 X[4075] - 3 X[24068], 40 X[6532] + 11 X[24068], 5 X[1698] + 12 X[59517], 4 X[3159] + 13 X[19877], 8 X[3634] + 9 X[64178], 12 X[4096] + 5 X[18398], X[5904] - 18 X[42056], 3 X[17155] - 20 X[31253], 3 X[32925] + 14 X[51073], 18 X[61686] - X[64184]

X(64437) lies on these lines: {1, 56150}, {2, 596}, {726, 19872}, {1698, 30863}, {3159, 19877}, {3634, 64178}, {4096, 18398}, {4434, 41872}, {5904, 42056}, {9330, 50605}, {17155, 31253}, {32925, 51073}, {59669, 62831}, {61686, 64184}

X(64438) = X(1)X(1088)∩X(4)X(390)

Barycentrics    (a^2+(b-c)^2)*(a-b-c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6320.

X(64438) lies on these lines: {1, 1088}, {4, 390}, {8, 6605}, {10, 10482}, {20, 61373}, {55, 17682}, {145, 62728}, {341, 3886}, {497, 17671}, {516, 10509}, {938, 1170}, {942, 52507}, {950, 1174}, {1067, 47487}, {1697, 56255}, {3673, 4319}, {4294, 40443}, {9440, 34848}, {17681, 28071}

X(64438) = cevapoint of X(497) and X(4319)
X(64438) = crosspoint of X(21453) and X(56118)
X(64438) = crosssum of X(2293) and X(61376)
X(64438) = X(i)-Dao conjugate of-X(j) for these (i, j): (1040, 15185), (4000, 4847), (6554, 10481), (14936, 21127), (15487, 1418), (59619, 20880)
X(64438) = X(i)-isoconjugate of-X(j) for these {i, j}: {354, 1037}, {1041, 22053}, {1418, 7123}, {1475, 7131}, {2293, 56359}, {2488, 8269}, {7084, 10481}, {8012, 63178}, {20229, 30705}, {56179, 61376}
X(64438) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (497, 142), (614, 1418), (1170, 56359), (1174, 1037), (1633, 63203), (1863, 1855), (2082, 354), (2346, 7131), (3673, 59181), (3732, 35312), (3914, 52023), (4000, 10481), (4012, 51972), (4319, 1212), (5324, 18164), (6554, 4847), (6605, 56179), (7083, 1475), (7124, 22053), (10482, 7123), (16502, 61376), (17115, 21127), (21453, 30705), (28070, 3059), (30706, 2293), (32008, 8817), (40965, 21808), (56118, 30701), (59141, 7084), (61373, 63178), (62725, 48070), (63239, 57925)
X(64438) = barycentric product of X(i) and X(j) for these {i, j}: {497, 32008}, {614, 63239}, {2082, 57815}, {3673, 6605}, {3732, 62725}
X(64438) = barycentric quotient of X(i) and X(j) for these (i, j): (497, 142), (614, 1418), (1170, 56359), (1174, 1037), (1633, 63203)
X(64438) = trilinear product of X(i) and X(j) for these {i, j}: {497, 2346}, {614, 56118}, {1170, 6554}, {1633, 62725}, {1863, 40443}
X(64438) = trilinear quotient of X(i) and X(j) for these (i, j): (497, 354), (614, 61376), (1040, 22053), (1863, 1827), (2082, 1475)

X(64439) = X(51)X(684)∩X(389)X(2797)

Barycentrics    a^2 (b - c) (b + c) (a^10 b^2 - 4 a^8 b^4 + 6 a^6 b^6 - 4 a^4 b^8 + a^2 b^10 + a^10 c^2 - 4 a^8 b^2 c^2 + 5 a^6 b^4 c^2 - 3 a^4 b^6 c^2 + 2 a^2 b^8 c^2 - b^10 c^2 - 4 a^8 c^4 + 5 a^6 b^2 c^4 - 6 a^4 b^4 c^4 + a^2 b^6 c^4 + 4 b^8 c^4 + 6 a^6 c^6 - 3 a^4 b^2 c^6 + a^2 b^4 c^6 - 6 b^6 c^6 - 4 a^4 c^8 + 2 a^2 b^2 c^8 + 4 b^4 c^8 + a^2 c^10 - b^2 c^10) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6332.

X(64439) lies on these lines: {51, 684}, {52, 41079}, {389, 2797}, {511, 6130}, {520, 16230}, {526, 11800}, {1112, 9033}, {2799, 39806}, {3060, 53345}, {5446, 9517}, {5462, 8552}, {7387, 58316}, {9409, 45186}, {15644, 44818}, {31953, 39817}, {35360, 58071}, {45319, 58470}, {47214, 58481}

X(64440) = X(3)-OF-X(11)

Barycentrics    (b - c)^4*(-a + b + c)^2*(-((a - b)^4*(a + b - c)^2) - (-a + c)^4*(a - b + c)^2 + (b - c)^4*(-a + b + c)^2) : :
X(64440) = X[11] + 3 X[42454], X[15914] - 3 X[42454]

Regarding the names of X(64440)-X(64445) and X(64452)-X(64467), see the preamble just before X(64426).

X(64440) lies on these lines: {2, 43974}, {11, 15914}, {100, 885}, {244, 21132}, {513, 24465}, {514, 18240}, {522, 46694}, {523, 58388}, {676, 15253}, {2804, 3716}, {2826, 13226}, {2968, 42455}, {3119, 42462}, {4885, 6667}, {5840, 11247}, {21201, 24025}

X(64440) = midpoint of X(11) and X(15914)
X(64440) = complement of X(43974)
X(64440) = complement of the isogonal conjugate of X(1618)
X(64440) = complement of the isotomic conjugate of X(54110)
X(64440) = X(i)-complementary conjugate of X(j) for these (i,j): {1618, 10}, {24203, 21252}, {32666, 2284}, {54110, 2887}
X(64440) = crosspoint of X(2) and X(54110)
X(64440) = barycentric product X(i)*X(j) for these {i,j}: {17924, 34949}, {24203, 42462}
X(64440) = barycentric quotient X(34949)/X(1332)
X(64440) = {X(11),X(42454)}-harmonic conjugate of X(15914)

X(64441) = X(5)-OF-X(7)

Barycentrics    (a + b - c)^4*(a - b + c)^2*(-a + b + c)^2 + (a + b - c)^2*(a - b + c)^4*(-a + b + c)^2 - (a + b - c)^4*(-a + b + c)^4 + 2*(a + b - c)^2*(a - b + c)^2*(-a + b + c)^4 - (a - b + c)^4*(-a + b + c)^4 : :
X(64441) = 3 X[2] + X[42483], X[15913] - 5 X[18230]

X(64441) lies on these lines: {2, 17113}, {7, 13609}, {9, 2272}, {4000, 35508}, {5514, 42356}, {6554, 17279}, {6666, 56857}, {15837, 28123}, {15913, 18230}, {17112, 58635}, {19605, 63973}

X(64441) = midpoint of X(17113) and X(42483)
X(64441) = complement of X(17113)
X(64441) = X(i)-complementary conjugate of X(j) for these (i,j): {1253, 17113}, {2125, 2886}, {8917, 21258}, {63904, 17046}
X(64441) = {X(2),X(42483)}-harmonic conjugate of X(17113)

X(64442) = X(5)-OF-X(8)

Barycentrics    (a + b - c)^4 - 2*(a + b - c)^2*(a - b + c)^2 + (a - b + c)^4 - (a + b - c)^2*(-a + b + c)^2 - (a - b + c)^2*(-a + b + c)^2 : :
X(64442) = X[1] + 3 X[26718], 3 X[2] + X[6553], X[4] - 3 X[26719], 5 X[3616] - X[8834]

X(644) lies on these lines: {1, 6692}, {2, 6552}, {4, 26719}, {8, 1120}, {56, 28016}, {106, 944}, {279, 57033}, {344, 26111}, {388, 28018}, {513, 56155}, {614, 40132}, {1015, 6554}, {1125, 7174}, {1149, 1788}, {1279, 5265}, {1319, 28080}, {1616, 5435}, {1647, 54361}, {1997, 17480}, {2136, 56798}, {2191, 30478}, {2345, 16604}, {3333, 4644}, {3475, 46190}, {3476, 28074}, {3486, 32577}, {3616, 6703}, {3622, 58414}, {3680, 60374}, {4000, 14986}, {4313, 8572}, {4339, 40726}, {4962, 21172}, {5657, 56804}, {5853, 45047}, {6714, 16020}, {6738, 15839}, {7288, 28011}, {7963, 12437}, {8056, 21627}, {8688, 44669}, {10589, 23675}, {11512, 53618}, {12245, 54319}, {12625, 51615}, {17213, 24797}, {17321, 41879}, {21214, 24477}, {24171, 37704}, {24216, 56630}, {24391, 46943}, {27195, 30701}, {37542, 62773}, {38053, 63520}, {41436, 45081}, {41850, 46934}, {44722, 58371}, {62832, 63126}

X(64442) = midpoint of X(6552) and X(6553)
X(64442) = complement of X(6552)
X(64442) = X(i)-complementary conjugate of X(j) for these (i,j): {604, 24151}, {1106, 6552}, {2137, 1329}, {8051, 21244}
X(64442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6553, 6552}, {3445, 3756, 8}, {11512, 53618, 64068}, {14986, 52541, 4000}

X(64443) = X(5)-OF-X(9)

Barycentrics    (a - b - c)*(a^2*b^2 - 2*a*b^3 + b^4 + 2*a*b^2*c - 4*b^3*c + a^2*c^2 + 2*a*b*c^2 + 6*b^2*c^2 - 2*a*c^3 - 4*b*c^3 + c^4) : :
X(64443) = 3 X[2] + X[6601], 9 X[2] - X[7674], 3 X[6600] - X[7674], 3 X[6601] + X[7674], X[142] + 3 X[24386], 3 X[24386] - X[24389], 3 X[3829] - X[42356], 3 X[1699] + X[60990], X[3174] - 5 X[20195], X[3174] + 3 X[24392], 5 X[20195] + 3 X[24392], 3 X[24477] + X[61010], 3 X[11235] + X[11495], 5 X[31245] - X[47387], 5 X[31272] - X[34894]

X(64443) lies on these lines: {2, 2346}, {5, 518}, {7, 11680}, {9, 11}, {12, 3243}, {141, 17059}, {142, 2886}, {144, 7678}, {145, 7679}, {149, 7676}, {226, 41573}, {354, 60991}, {390, 6910}, {442, 38053}, {474, 2550}, {495, 42871}, {496, 1001}, {516, 6705}, {521, 40551}, {522, 7263}, {527, 3829}, {528, 549}, {997, 1387}, {1125, 3813}, {1329, 24393}, {1699, 60990}, {1836, 60968}, {2000, 15253}, {2476, 11038}, {3174, 3925}, {3189, 17529}, {3434, 37309}, {3452, 58635}, {3739, 24388}, {3816, 6666}, {3820, 3956}, {3838, 58563}, {3873, 61013}, {3880, 64109}, {3928, 7965}, {3939, 17337}, {4187, 38057}, {4193, 5686}, {4321, 57285}, {4847, 40659}, {5220, 10593}, {5223, 7741}, {5542, 25639}, {5732, 15908}, {5805, 5857}, {5832, 15299}, {6701, 20116}, {6744, 25466}, {7677, 35979}, {7681, 63970}, {7958, 11523}, {8226, 24477}, {8580, 42470}, {8583, 38200}, {8727, 60974}, {9710, 10179}, {10283, 22836}, {10427, 25722}, {10527, 11344}, {10943, 42842}, {11235, 11495}, {11269, 54358}, {12329, 19512}, {12447, 64205}, {15185, 21617}, {15254, 58415}, {15935, 44669}, {16160, 17768}, {17530, 51099}, {17668, 30379}, {17728, 60985}, {20059, 30311}, {21031, 59414}, {22312, 44411}, {22753, 45700}, {23305, 53564}, {24179, 47595}, {24181, 60375}, {24703, 61005}, {26019, 27484}, {26040, 52804}, {30628, 41548}, {31245, 47387}, {31272, 34894}, {33108, 60996}, {37358, 61024}, {37722, 38316}, {38097, 44847}, {38454, 60994}, {49168, 64294}, {52254, 64153}, {52255, 64151}, {56284, 60489}, {58608, 63643}, {58626, 61033}

X(64443) = midpoint of X(i) and X(j) for these {i,j}: {142, 24389}, {3813, 3826}, {6600, 6601}
X(64443) = complement of X(6600)
X(64443) = complement of the isogonal conjugate of X(40154)
X(64443) = X(i)-complementary conjugate of X(j) for these (i,j): {269, 6600}, {277, 3452}, {1292, 4521}, {2191, 9}, {3669, 40615}, {3676, 5511}, {17107, 2}, {37206, 20317}, {40154, 10}, {54987, 59971}, {57656, 1212}, {57791, 21244}
X(64443) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6601, 6600}, {9, 3254, 60919}, {11, 6067, 9}, {142, 11019, 58564}, {142, 24386, 24389}, {20195, 24392, 3174}, {21617, 26015, 15185}, {25722, 60988, 10427}, {30628, 61008, 41548}

X(64444) = X(5)-OF-X(11)

Barycentrics    (a - b)^8*(a + b - c)^4 - 2*(a - b)^4*(a + b - c)^2*(-a + c)^4*(a - b + c)^2 + (-a + c)^8*(a - b + c)^4 - (a - b)^4*(b - c)^4*(a + b - c)^2*(-a + b + c)^2 - (b - c)^4*(-a + c)^4*(a - b + c)^2*(-a + b + c)^2 : :
X(64444) = 3 X[2] + X[43974], X[15914] - 5 X[31235]

X(64444) lies on these lines: {2, 43974}, {11, 3126}, {2804, 25380}, {15914, 31235}, {53573, 55126}

X(64445) = X(6)-OF-X(11)

Barycentrics    (b - c)^4*(-a + b + c)^2 : :

X(64445) lies on these lines: {2, 31611}, {11, 650}, {44, 17747}, {115, 661}, {116, 59522}, {149, 1252}, {294, 5375}, {497, 14827}, {528, 14589}, {607, 9665}, {649, 6075}, {666, 17036}, {693, 35094}, {1015, 6591}, {1086, 3676}, {1090, 52316}, {1146, 3239}, {1262, 34529}, {2161, 61066}, {2310, 6608}, {2520, 3271}, {2611, 55280}, {2886, 5701}, {3120, 35505}, {3700, 51442}, {3911, 9356}, {4516, 42771}, {4976, 51402}, {5532, 52334}, {6547, 24198}, {7336, 52338}, {10947, 16283}, {11238, 30706}, {13401, 14115}, {14300, 33646}, {17435, 35015}, {21044, 35506}, {23653, 64127}, {45320, 62683}, {51407, 62297}, {53529, 59798}

X(64445) = complement of X(54110)
X(64445) = complement of the isotomic conjugate of X(43974)
X(64445) = X(i)-complementary conjugate of X(j) for these (i,j): {43947, 17072}, {43974, 2887}
X(64445) = X(i)-Ceva conjugate of X(j) for these (i,j): {1086, 21132}, {1090, 5532}, {1146, 42462}, {2170, 55195}, {23978, 42455}, {26856, 56283}, {31611, 11}, {34529, 513}, {57536, 885}
X(64445) = X(i)-isoconjugate of X(j) for these (i,j): {59, 4564}, {100, 4619}, {109, 31615}, {644, 59151}, {765, 1262}, {934, 59149}, {1016, 24027}, {1025, 59101}, {1110, 1275}, {1252, 7045}, {1461, 57731}, {2149, 4998}, {7012, 44717}, {7035, 23979}
X(64445) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 31615}, {513, 1262}, {514, 1275}, {522, 1016}, {650, 4998}, {661, 7045}, {2968, 6632}, {4885, 61415}, {6615, 4564}, {8054, 4619}, {14714, 59149}, {17115, 1252}, {35508, 57731}, {35509, 883}, {40625, 55194}, {52305, 35094}, {52873, 62721}
X(64445) = crosspoint of X(i) and X(j) for these (i,j): {2, 43974}, {11, 40166}, {885, 57536}, {1086, 21132}, {1146, 42462}, {2969, 6545}, {23978, 42455}, {24026, 40213}, {26856, 56283}
X(64445) = crosssum of X(i) and X(j) for these (i,j): {6, 1618}, {219, 39189}, {1262, 4619}, {2283, 35505}
X(64445) = crossdifference of every pair of points on line {2283, 4619}
X(64445) = barycentric product X(i)*X(j) for these {i,j}: {1, 1090}, {7, 5532}, {8, 7336}, {11, 11}, {115, 26856}, {244, 24026}, {513, 42455}, {514, 42462}, {522, 21132}, {523, 56283}, {650, 40166}, {657, 23100}, {661, 40213}, {764, 4397}, {885, 52305}, {1015, 23978}, {1086, 1146}, {1111, 2310}, {1358, 4081}, {1565, 42069}, {2170, 4858}, {2401, 52316}, {2968, 2969}, {2973, 3270}, {3239, 6545}, {3271, 34387}, {3676, 23615}, {3937, 21666}, {4530, 60578}, {4560, 55195}, {6362, 56284}, {8735, 26932}, {14936, 23989}, {16727, 36197}, {17197, 21044}, {17205, 52335}, {21143, 52622}, {23104, 43924}, {31611, 46101}, {34529, 34530}, {35509, 57536}, {42454, 60478}, {46384, 60074}, {52303, 57645}, {52304, 62715}, {52334, 60479}, {52338, 60480}, {52946, 60491}
X(64445) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 4998}, {244, 7045}, {649, 4619}, {650, 31615}, {657, 59149}, {764, 934}, {884, 59101}, {1015, 1262}, {1086, 1275}, {1090, 75}, {1146, 1016}, {1357, 7339}, {1358, 59457}, {1977, 23979}, {2170, 4564}, {2310, 765}, {2969, 55346}, {3022, 6065}, {3239, 6632}, {3248, 24027}, {3271, 59}, {3900, 57731}, {4081, 4076}, {4397, 57950}, {4560, 55194}, {4953, 44724}, {5532, 8}, {6545, 658}, {7117, 44717}, {7336, 7}, {8034, 53321}, {8042, 4637}, {8735, 46102}, {14936, 1252}, {17197, 4620}, {21131, 4605}, {21132, 664}, {21143, 1461}, {23100, 46406}, {23615, 3699}, {23978, 31625}, {24026, 7035}, {24188, 62789}, {26856, 4590}, {31611, 31619}, {35509, 35094}, {40166, 4554}, {40213, 799}, {42069, 15742}, {42455, 668}, {42462, 190}, {43924, 59151}, {46384, 4585}, {52303, 4996}, {52305, 883}, {52315, 55016}, {52316, 2397}, {52333, 6068}, {52336, 14027}, {52337, 1317}, {52338, 62669}, {52946, 62721}, {55195, 4552}, {56283, 99}, {56284, 6606}, {61050, 6066}, {63462, 4559}
X(64445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 650, 46101}, {46101, 52946, 650}





leftri  Miyamoto-mixtilinear related centers: X(64446) - X(64451)  rightri

This preamble and centers X(64446)-X(64451) were contributed by César Eliud Lozada, July 8, 2024.

The following conjectures are due to Keita Miyamoto, July 02, 2024:

In a triangle ABC with circumcircle ω, denote:
  1. a1, b1, c1: the A-, B-, C- mixtilinear excircles of ABC, respectively.
  2. o1: the outer-Apollonius circle of a1, b1, c1.
  3. a2: the circle, other than ω, passing through B and C and internally tangent to a1. Cyclically b2 and c2.
  4. o2: the outer-Apollonius circle of a2, b2, c2.
  5. Ab, Ac: the second intersections of a2 and AC, AB, respectively. Similarly Bc, Ba and Ca, Cb.
  6. A': the second intersection of b2 and c2, and, cyclically B', C'.
  7. ta: the common tangent of a1 and a2, and, cyclically tb, tc.

Then:

  1. (a) o1 and o2 are tangent.
  2. (b) A'B'C' and the triangle bounded by the lines AbAc, BcBa, CaCb are perspective.
  3. (c) ABC and the triangle bounded by the lines ta, tb, tc are perspective.

Results:

Similar points can be found by using mixtilinear incircles instead of mixtilinear excircles and inner-Apollonius circles instead of outer Apollonius circles. With this new construction:

underbar

X(64446) = X(9)X(644) ∩ X(56)X(101)

Barycentrics    a^2*(-a+b+c)*(a^4-3*(b+c)*a^3+(b^2+7*b*c+c^2)*a^2+(b+c)*(3*b^2-8*b*c+3*c^2)*a-(2*b^2-b*c+2*c^2)*(b-c)^2) : :

X(64446) lies on the apollonian circle of mixtilinear excircles and these lines: {9, 644}, {56, 101}, {672, 32625}, {2246, 5128}, {2291, 6244}, {2348, 5011}, {3022, 58368}, {4534, 4752}, {5540, 7991}, {8158, 35599}, {8165, 26074}, {11224, 52184}

X(64446) = cross-difference of every pair of points on the line X(53523)X(53528)
X(64446) = touchpoint of outer apollonian circle of mixtilinear excircles and line {22108, 64446}

X(64447) = (name pending)

Barycentrics    a^2*(a^8-2*(b+c)*a^7-2*(b^2-b*c+c^2)*a^6+2*(b+c)*(3*b^2+2*b*c+3*c^2)*a^5-2*(5*b^2+2*b*c+5*c^2)*b*c*a^4-2*(b^2-c^2)*(b-c)*(b+3*c)*(3*b+c)*a^3+2*(b^4+c^4+3*b*c*(3*b^2+4*b*c+3*c^2))*(b-c)^2*a^2+2*(b^2-c^2)^2*(b+c)^3*a-(b^2-c^2)^2*(b^4+c^4+6*b*c*(b^2+3*b*c+c^2))) : :

X(64447) lies on these lines: {3, 9}

X(64448) = (name pending)

Barycentrics    a^2*(-a+b+c)*(a^4-2*(b+2*c)*a^3-2*(b+c)*(2*b-3*c)*a^2+2*(b-c)*(5*b^2+b*c+2*c^2)*a-(5*b^2-c^2)*(b-c)^2)*(a^4-2*(2*b+c)*a^3+2*(b+c)*(3*b-2*c)*a^2-2*(b-c)*(2*b^2+b*c+5*c^2)*a+(b^2-5*c^2)*(b-c)^2) : :

X(64448) lies on these lines: {5572, 16112}

X(64449) = X(1)X(84) ∩ X(3)X(595)

Barycentrics    a^2*(a^5+(b+c)*a^4-2*(b^2+c^2)*a^3-2*(b^2-c^2)*(b-c)*a^2+(b^4-10*b^2*c^2+c^4)*a+(b^2-c^2)*(b-c)^3) : :
X(64449) = X(6)+2*X(1480) = 5*X(6)-4*X(39523) = 3*X(6)-2*X(44414) = 5*X(1480)+2*X(39523) = 3*X(1480)+X(44414) = 6*X(39523)-5*X(44414) = 4*X(41455)-7*X(55676)

X(64449) lies on these lines: {1, 84}, {3, 595}, {4, 5710}, {6, 517}, {20, 62804}, {31, 3428}, {40, 2999}, {55, 1064}, {56, 601}, {58, 22770}, {165, 5315}, {171, 22753}, {380, 22124}, {386, 10306}, {392, 17811}, {394, 3877}, {500, 16202}, {515, 63969}, {516, 62828}, {578, 55287}, {581, 3295}, {602, 5584}, {912, 3242}, {940, 5603}, {944, 37542}, {946, 2050}, {952, 12594}, {956, 55406}, {958, 3073}, {962, 5706}, {988, 64118}, {991, 40091}, {999, 1407}, {1056, 6180}, {1057, 52830}, {1072, 1836}, {1158, 37592}, {1181, 37614}, {1193, 10310}, {1203, 7991}, {1279, 18443}, {1351, 45955}, {1385, 1616}, {1399, 10966}, {1406, 3304}, {1457, 34042}, {1464, 33925}, {1482, 36742}, {1519, 17720}, {1697, 7078}, {2003, 7962}, {2093, 52424}, {2099, 61398}, {2390, 22769}, {2594, 26358}, {2808, 6767}, {2818, 36740}, {3057, 64020}, {3072, 64077}, {3149, 5264}, {3157, 9957}, {3194, 56887}, {3297, 8978}, {3359, 3752}, {3434, 5721}, {3445, 16203}, {3562, 9785}, {3576, 16483}, {3744, 18446}, {3753, 17825}, {3872, 55400}, {3880, 45729}, {3913, 37699}, {3915, 4300}, {4221, 40153}, {4252, 11249}, {4255, 11248}, {4301, 62805}, {4383, 5657}, {4646, 49163}, {5050, 53790}, {5119, 7074}, {5230, 15908}, {5250, 16368}, {5255, 11500}, {5266, 6261}, {5269, 63992}, {5313, 5537}, {5396, 10679}, {5687, 37732}, {5707, 22791}, {5731, 62848}, {5886, 37674}, {6361, 37537}, {6684, 45204}, {6905, 37540}, {6913, 30116}, {7290, 30503}, {7680, 26098}, {8148, 36750}, {8192, 42448}, {8572, 32612}, {9623, 55432}, {9856, 15811}, {10106, 64057}, {10246, 16486}, {10247, 51340}, {10532, 49745}, {11224, 16474}, {11230, 37682}, {11522, 37559}, {12053, 41344}, {12595, 14988}, {12702, 36754}, {12703, 64175}, {13161, 64119}, {16489, 30392}, {17054, 34339}, {18391, 60689}, {18444, 62806}, {21000, 32613}, {22129, 54391}, {24806, 57278}, {25413, 36752}, {26333, 37715}, {26446, 37679}, {28194, 50114}, {30145, 31803}, {31397, 34048}, {31785, 37415}, {32911, 59417}, {34036, 50195}, {34937, 54198}, {37474, 55004}, {37514, 37562}, {37534, 52541}, {37539, 63986}, {37549, 64021}, {37552, 37837}, {37622, 37698}, {41455, 55676}, {43166, 54358}, {44663, 45728}, {54386, 63976}, {62834, 64150}, {64042, 64349}

X(64449) = cross-difference of every pair of points on the line X(9001)X(14298)
X(64449) = perspector of the circumconic through X(9058) and X(37141)
X(64449) = pole of the line {6371, 23224} with respect to the circumcircle
X(64449) = pole of the line {56, 7395} with respect to the Feuerbach circumhyperbola
X(64449) = pole of the line {9051, 40137} with respect to the MacBeath circumconic
X(64449) = pole of the line {11115, 26637} with respect to the Stammler hyperbola
X(64449) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (40, 16466, 36745), (962, 57280, 5706), (1616, 37501, 1385), (3057, 64020, 64069), (30116, 64013, 6913)

X(64450) = (name pending)

Barycentrics    a^2*(a^11+(b+c)*a^10-(5*b^2-24*b*c+5*c^2)*a^9-(b+c)*(5*b^2-8*b*c+5*c^2)*a^8+2*(5*b^4+5*c^4-2*b*c*(16*b^2-35*b*c+16*c^2))*a^7+2*(b+c)*(5*b^4+5*c^4-2*b*c*(8*b^2+9*b*c+8*c^2))*a^6-2*(5*b^6+5*c^6-(24*b^4+24*c^4-b*c*(139*b^2-160*b*c+139*c^2))*b*c)*a^5-2*(b+c)*(5*b^6+5*c^6-(24*b^4+24*c^4-b*c*(67*b^2+48*b*c+67*c^2))*b*c)*a^4+(5*b^8+5*c^8-2*(82*b^4+82*c^4+b*c*(128*b^2-159*b*c+128*c^2))*b^2*c^2)*a^3+(b+c)*(5*b^8+5*c^8-2*(16*b^6+16*c^6+(26*b^4+26*c^4-7*b*c*(16*b^2-39*b*c+16*c^2))*b*c)*b*c)*a^2-(b^2-c^2)^2*(b^6+c^6+(8*b^4+8*c^4-b*c*(49*b^2-144*b*c+49*c^2))*b*c)*a+(b^2-c^2)^3*(b-c)*(-b^4-c^4+6*b*c*(b^2-3*b*c+c^2))) : :

X(64450) lies on these lines: {2999, 11505}

X(64451) = (name pending)

Barycentrics    a^2*(a^3-(b+c)*a^2-(5*b^2-10*b*c+c^2)*a+(b-c)*(5*b^2-c^2))*(a^3-(b+c)*a^2-(b^2-10*b*c+5*c^2)*a+(b-c)*(b^2-5*c^2))*(a^2+2*(b+c)*a+(b-c)^2) : :

X(64451) lies on these lines: {518, 7962}

X(64452) = X(5)-OF-X(5)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)^4 - (a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)^2*(-(a^2*b^2) + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)^2 - 2*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)^2*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)^2 - (-(a^2*b^2) + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)^2*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)^2 + (a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)^4 : :
X(64452) = 3 X[2] + X[6662], 5 X[632] - X[15912], 9 X[11539] - X[41481], 3 X[42453] - 11 X[55859], 7 X[55862] - 3 X[59531]

Regarding the names of X(64452)-X(64467), see the preamble just before X(64426).

X(64452) lies on these lines: {2, 6662}, {5, 2972}, {30, 5447}, {140, 12012}, {632, 15912}, {11017, 53803}, {11539, 41481}, {16239, 58454}, {33539, 36162}, {42453, 55859}, {42466, 63175}, {55862, 59531}

X(64452) = midpoint of X(6662) and X(6663)
X(64452) = complement of X(6663)
X(64452) = {X(2),X(6662)}-harmonic conjugate of X(6663)

X(64453) = X(39)-OF-X(39)

Barycentrics    a^4*(b^2 + c^2)^2*((a^2 + b^2)^2*c^4 + b^4*(a^2 + c^2)^2) : :

X(64453) lies on these lines: {2, 31622}, {39, 55050}, {574, 57503}, {1506, 35971}, {3229, 6292}, {3934, 9496}, {6683, 30736}, {52042, 59994}

X(64453) = complement of the isotomic conjugate of X(59994)
X(64453) = X(i)-complementary conjugate of X(j) for these (i,j): {1917, 7829}, {1923, 3934}, {2531, 21253}, {3051, 21238}, {8041, 21235}, {41331, 1215}, {59994, 2887}
X(64453) = crosspoint of X(2) and X(59994)

X(64454) = X(42)-OF-X(42)

Barycentrics    a^4*(b + c)^2*((a + b)*c^2 + b^2*(a + c)) : :

X(64454) lies on these lines: {1, 2}, {872, 6378}, {1918, 62420}, {1964, 22199}, {2667, 22184}, {21700, 21838}, {21820, 62550}, {23610, 53581}

X(64454) = isogonal conjugate of X(59148)
X(64454) = isogonal conjugate of the isotomic conjugate of X(21700)
X(64454) = X(i)-Ceva conjugate of X(j) for these (i,j): {42, 21838}, {4557, 53581}
X(64454) = X(i)-isoconjugate of X(j) for these (i,j): {1, 59148}, {274, 40409}, {873, 40418}, {1221, 1509}, {57399, 57992}, {57949, 60230}
X(64454) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 59148}, {3122, 52619}, {3741, 310}, {51575, 57992}
X(64454) = crosspoint of X(42) and X(7109)
X(64454) = crossdifference of every pair of points on line {649, 16737}
X(64454) = barycentric product X(i)*X(j) for these {i,j}: {6, 21700}, {31, 22206}, {32, 21713}, {42, 21838}, {213, 3728}, {669, 61165}, {756, 1197}, {872, 1107}, {1334, 39780}, {1500, 2309}, {1826, 23212}, {1918, 21024}, {3741, 7109}, {3971, 45217}, {4079, 53268}, {4557, 40627}, {6378, 45216}, {20691, 45209}, {27880, 40729}, {50487, 61234}, {53338, 53581}
X(64454) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 59148}, {872, 1221}, {1107, 57992}, {1197, 873}, {1918, 40409}, {3728, 6385}, {7109, 40418}, {21700, 76}, {21713, 1502}, {21838, 310}, {22206, 561}, {23212, 17206}, {40627, 52619}, {53268, 52612}, {61165, 4609}

X(64455) = X(63)-OF-X(63)

Barycentrics    a*(a^2 - b^2 - c^2)*(a^2*(a^2 - b^2 - c^2)^2 - b^2*(-a^2 + b^2 - c^2)^2 - c^2*(-a^2 - b^2 + c^2)^2) : :

X(64455) lies on the Kiepert circumhyperbola of the anticomplementary triangle and these lines: {1, 91}, {2, 914}, {19, 63808}, {20, 224}, {48, 63}, {92, 31631}, {487, 13386}, {488, 13387}, {662, 1748}, {811, 6521}, {1096, 2617}, {1707, 4575}, {1708, 1813}, {1764, 24611}, {1800, 12514}, {1848, 37181}, {1944, 46717}, {1958, 45224}, {1959, 18596}, {2128, 17442}, {3869, 14868}, {18597, 18713}, {21378, 51304}, {52676, 56875}

X(64455) = anticomplement of X(60249)
X(64455) = anticomplement of the isotomic conjugate of X(31631)
X(64455) = isotomic conjugate of the polar conjugate of X(920)
X(64455) = isogonal conjugate of the polar conjugate of X(33808)
X(64455) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {46, 2893}, {112, 44426}, {284, 11415}, {1333, 10529}, {1800, 4329}, {2150, 62858}, {2178, 2475}, {2194, 20078}, {2299, 2994}, {3157, 2897}, {3193, 69}, {3559, 21270}, {5552, 21287}, {31631, 6327}, {46389, 3448}, {59973, 13219}, {61397, 2895}
X(64455) = X(i)-Ceva conjugate of X(j) for these (i,j): {92, 63}, {31631, 2}, {33808, 920}, {44179, 1}
X(64455) = X(i)-isoconjugate of X(j) for these (i,j): {2, 39109}, {4, 60775}, {6, 254}, {19, 921}, {25, 6504}, {32, 46746}, {54, 41536}, {69, 60779}, {96, 47732}, {393, 15316}, {571, 52582}, {924, 39416}, {1609, 57697}, {1973, 57998}, {1993, 59189}, {2165, 34756}, {2501, 13398}, {6753, 63958}, {8745, 32132}, {8800, 8882}, {14593, 57484}, {14910, 16172}, {39114, 41271}, {40388, 59497}
X(64455) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 921}, {9, 254}, {394, 63}, {2165, 91}, {6337, 57998}, {6376, 46746}, {6505, 6504}, {32664, 39109}, {36033, 60775}
X(64455) = crosspoint of X(811) and X(62719)
X(64455) = barycentric product X(i)*X(j) for these {i,j}: {1, 40697}, {3, 33808}, {63, 6515}, {69, 920}, {75, 155}, {91, 59155}, {92, 6503}, {304, 1609}, {326, 3542}, {454, 57998}, {8883, 18695}, {34853, 44179}, {41587, 62277}
X(64455) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 254}, {3, 921}, {31, 39109}, {47, 34756}, {48, 60775}, {63, 6504}, {69, 57998}, {75, 46746}, {91, 52582}, {155, 1}, {255, 15316}, {454, 920}, {920, 4}, {921, 57697}, {1609, 19}, {1725, 16172}, {1953, 41536}, {1973, 60779}, {2180, 47732}, {3542, 158}, {4575, 13398}, {6503, 63}, {6515, 92}, {8883, 2190}, {15478, 36053}, {33808, 264}, {34853, 91}, {36145, 39416}, {39116, 57716}, {40697, 75}, {44706, 8800}, {51425, 1784}, {57998, 57868}, {58888, 3064}, {59155, 44179}, {63801, 40678}, {63808, 39114}
X(64455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6505, 6513, 2}, {6507, 6508, 63}

X(64456) = X(72)-OF-X(72)

Barycentrics    a*(b + c)*(a^2 - b^2 - c^2)*(a^2*b - b^3 + a^2*c + 2*a*b*c + b^2*c + b*c^2 - c^3)*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c - 5*a^4*b*c - 2*a^3*b^2*c + 2*a^2*b^3*c - a*b^4*c - b^5*c - 2*a^4*c^2 - 2*a^3*b*c^2 + 2*a^2*b^2*c^2 + 2*a*b^3*c^2 + 2*a^3*c^3 + 2*a^2*b*c^3 + 2*a*b^2*c^3 + 2*b^3*c^3 + a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5) : :

X(64456) lies on these lines: {1, 15656}, {65, 23604}, {72, 18591}, {500, 912}, {1838, 45038}, {1841, 14054}, {2252, 18673}, {4303, 18607}

X(64456) = X(3868)-Ceva conjugate of X(942)
X(64456) = barycentric product X(942)*X(56728)
X(64456) = barycentric quotient X(i)/X(j) for these {i,j}: {1612, 40395}, {56728, 40422}

X(64457) = X(81)-OF-X(81)

Barycentrics    a*(a + b)^2*(a + c)^2*(a^2 + b^2 + a*c + b*c)*(a^2 + a*b + b*c + c^2) : :

X(64457) lies on the circumconic {{A,B,C,X(1),X(2)} and these lines: {1, 849}, {2, 261}, {57, 757}, {60, 959}, {81, 18202}, {88, 30581}, {105, 58982}, {274, 763}, {279, 552}, {961, 1325}, {1220, 1224}, {1255, 2298}, {1333, 37870}, {1412, 1432}, {1798, 51223}, {4581, 60043}, {5839, 7058}, {7132, 7305}, {15420, 60044}, {17946, 40153}, {19623, 30710}, {34914, 42028}

X(64457) = isogonal conjugate of X(21810)
X(64457) = X(i)-cross conjugate of X(j) for these (i,j): {81, 14534}, {3733, 52935}, {5262, 86}, {57058, 662}, {57246, 1414}
X(64457) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21810}, {6, 20653}, {9, 52567}, {10, 2092}, {12, 2269}, {37, 2292}, {42, 1211}, {56, 61377}, {65, 21033}, {71, 429}, {181, 3687}, {190, 42661}, {213, 18697}, {226, 40966}, {306, 44092}, {312, 59174}, {321, 3725}, {523, 61168}, {594, 1193}, {661, 61172}, {756, 3666}, {762, 54308}, {872, 20911}, {960, 2171}, {1018, 50330}, {1089, 2300}, {1228, 1918}, {1254, 3965}, {1334, 41003}, {1400, 3704}, {1500, 4357}, {1826, 22076}, {1829, 3949}, {1848, 3690}, {2197, 46878}, {2298, 6042}, {2354, 3695}, {3674, 7064}, {3882, 4705}, {3971, 45218}, {4024, 53280}, {4064, 61205}, {4079, 53332}, {4103, 6371}, {4557, 21124}, {6057, 61412}, {6358, 20967}, {6535, 40153}, {7140, 22097}, {17420, 21859}, {20691, 45197}, {21035, 27067}, {21078, 42550}, {22074, 56285}, {26942, 40976}, {40521, 48131}, {51870, 52087}, {55232, 61226}, {56914, 59305}, {57185, 61223}
X(64457) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 61377}, {3, 21810}, {9, 20653}, {478, 52567}, {6626, 18697}, {34021, 1228}, {36830, 61172}, {40582, 3704}, {40589, 2292}, {40592, 1211}, {40602, 21033}, {52087, 6042}, {55053, 42661}
X(64457) = cevapoint of X(i) and X(j) for these (i,j): {60, 1333}, {81, 593}, {1169, 2363}
X(64457) = barycentric product X(i)*X(j) for these {i,j}: {28, 57853}, {56, 52550}, {60, 31643}, {81, 14534}, {86, 2363}, {261, 961}, {274, 1169}, {286, 1798}, {593, 30710}, {693, 58982}, {757, 1220}, {763, 14624}, {849, 1240}, {1333, 40827}, {1414, 57161}, {1509, 2298}, {4581, 52935}, {4610, 62749}
X(64457) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 20653}, {6, 21810}, {9, 61377}, {21, 3704}, {28, 429}, {56, 52567}, {58, 2292}, {60, 960}, {81, 1211}, {86, 18697}, {110, 61172}, {163, 61168}, {270, 46878}, {274, 1228}, {284, 21033}, {593, 3666}, {667, 42661}, {757, 4357}, {763, 16705}, {849, 1193}, {961, 12}, {1014, 41003}, {1019, 21124}, {1169, 37}, {1193, 6042}, {1220, 1089}, {1333, 2092}, {1397, 59174}, {1434, 45196}, {1437, 22076}, {1509, 20911}, {1791, 3695}, {1798, 72}, {2150, 2269}, {2185, 3687}, {2194, 40966}, {2203, 44092}, {2206, 3725}, {2298, 594}, {2359, 3949}, {2363, 10}, {3733, 50330}, {4556, 3882}, {4581, 4036}, {4636, 61223}, {6628, 16739}, {7054, 3965}, {7303, 59191}, {7341, 24471}, {8687, 21859}, {14534, 321}, {16948, 4918}, {30710, 28654}, {31643, 34388}, {32736, 40521}, {36147, 4103}, {40453, 51870}, {40827, 27801}, {52376, 27067}, {52550, 3596}, {52935, 53332}, {57161, 4086}, {57853, 20336}, {58982, 100}, {59159, 21803}, {62749, 4024}

X(64458) = X(85)-OF-X(85)

Barycentrics    a*(a - b - c)*(a^3*b - 2*a^2*b^2 + a*b^3 - a^3*c + a^2*b*c + a*b^2*c - b^3*c + 2*a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 - b*c^3)*(a^3*b - 2*a^2*b^2 + a*b^3 - a^3*c - a^2*b*c + a*b^2*c + b^3*c + 2*a^2*c^2 - a*b*c^2 - 2*b^2*c^2 - a*c^3 + b*c^3) : :

X(64458) lies on these lines: {9, 3177}, {85, 52064}, {142, 63905}, {220, 1376}, {480, 4513}, {728, 28058}, {1223, 60811}, {2125, 5437}, {2338, 17754}, {2371, 53632}, {4147, 23058}, {6376, 6559}, {7367, 41239}, {14943, 63601}, {41796, 63603}

X(64458) = isogonal conjugate of X(34497)
X(64458) = isotomic conjugate of X(40593)
X(64458) = isotomic conjugate of the complement of X(56265)
X(64458) = X(2)-cross conjugate of X(9)
X(64458) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34497}, {6, 31526}, {7, 20995}, {31, 40593}, {56, 3177}, {57, 1742}, {109, 21195}, {278, 20793}, {604, 20935}, {1014, 21856}, {1412, 21084}, {1458, 51846}, {10481, 38835}
X(64458) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 3177}, {2, 40593}, {3, 34497}, {9, 31526}, {11, 21195}, {3161, 20935}, {5452, 1742}, {40599, 21084}
X(64458) = cevapoint of X(i) and X(j) for these (i,j): {1, 41680}, {2, 56265}, {3900, 52064}
X(64458) = trilinear pole of line {4105, 54266}
X(64458) = barycentric product X(i)*X(j) for these {i,j}: {9, 56265}, {200, 43750}, {480, 60811}, {4163, 53632}
X(64458) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 31526}, {2, 40593}, {6, 34497}, {8, 20935}, {9, 3177}, {41, 20995}, {55, 1742}, {210, 21084}, {212, 20793}, {294, 51846}, {650, 21195}, {1334, 21856}, {43750, 1088}, {53632, 4626}, {56265, 85}, {59141, 38835}, {60811, 57880}

X(64459) = X(88)-OF-X(88)

Barycentrics    a*(a + b - 2*c)*(a - 2*b + c)*(a^2 - 4*a*b + b^2 + 2*a*c + 2*b*c - 2*c^2)*(a^2 + 2*a*b - 2*b^2 - 4*a*c + 2*b*c + c^2) : :

X(64459) lies on the circumconic {{A,B,C,X(1),X(2)} and these lines: {1, 3257}, {2, 4555}, {44, 5376}, {81, 4622}, {88, 2087}, {89, 2384}, {274, 4634}, {291, 4792}, {679, 1022}, {1002, 61422}, {1320, 55935}, {24841, 24858}

X(64459) = X(i)-cross conjugate of X(j) for these (i,j): {14421, 4618}, {51908, 88}
X(64459) = X(i)-isoconjugate of X(j) for these (i,j): {6, 1644}, {101, 33920}, {519, 8649}, {545, 902}, {678, 51908}, {1023, 14421}, {1960, 6633}, {4604, 14410}, {14475, 23344}
X(64459) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 1644}, {1015, 33920}, {40594, 545}
X(64459) = cevapoint of X(i) and X(j) for these (i,j): {88, 51908}, {2087, 14421}
X(64459) = trilinear pole of line {88, 513}
X(64459) = barycentric product X(i)*X(j) for these {i,j}: {88, 35168}, {2384, 20568}, {3257, 62623}, {4618, 34764}, {51908, 57567}
X(64459) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1644}, {88, 545}, {513, 33920}, {1022, 14475}, {2226, 51908}, {2384, 44}, {3257, 6633}, {4618, 34762}, {4775, 14410}, {9456, 8649}, {23345, 14421}, {35168, 4358}, {51908, 35121}, {52225, 6544}, {56049, 43038}, {62623, 3762}

X(64460) = X(99)-OF-X(99)

Barycentrics    (a^2 - b^2)^3*(a^2 - c^2)^3*(a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2) : :

X(64460) lies on the Steiner circumellipse and these lines: {99, 11123}, {249, 35146}, {543, 31632}, {648, 55270}, {671, 1641}, {691, 18829}, {886, 32729}, {892, 42370}, {2482, 4590}, {3228, 19626}, {4577, 53735}, {5466, 14728}, {5641, 47389}, {31998, 52883}, {35136, 52035}, {35138, 59152}, {35139, 53080}

X(64460) = isotomic conjugate of X(33919)
X(64460) = isotomic conjugate of the isogonal conjugate of X(45773)
X(64460) = X(42370)-Ceva conjugate of X(52940)
X(64460) = X(i)-cross conjugate of X(j) for these (i,j): {99, 57552}, {892, 52940}, {5468, 4590}, {33919, 2}, {52940, 42370}, {53367, 18020}, {53379, 39292}, {55226, 34537}, {61190, 892}
X(64460) = X(i)-isoconjugate of X(j) for these (i,j): {31, 33919}, {110, 45775}, {163, 42344}, {351, 2643}, {661, 21906}, {798, 1648}, {896, 22260}, {922, 8029}, {923, 14443}, {1924, 52628}, {2642, 3124}, {4117, 35522}, {14210, 23099}, {23894, 59801}
X(64460) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 33919}, {115, 42344}, {244, 45775}, {524, 46049}, {2482, 14443}, {9428, 52628}, {15477, 23099}, {15899, 22260}, {31998, 1648}, {35087, 14423}, {36830, 21906}, {39061, 8029}, {62613, 2682}
X(64460) = cevapoint of X(i) and X(j) for these (i,j): {2, 33919}, {523, 11053}, {524, 10190}, {620, 690}, {892, 52940}, {4590, 5468}
X(64460) = trilinear pole of line {2, 4590}
X(64460) = barycentric product X(i)*X(j) for these {i,j}: {76, 45773}, {99, 52940}, {249, 53080}, {523, 42370}, {671, 31614}, {691, 34537}, {892, 4590}, {5468, 57552}, {18023, 59152}, {24037, 36085}, {30786, 55270}, {32729, 44168}
X(64460) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 33919}, {99, 1648}, {110, 21906}, {111, 22260}, {249, 351}, {523, 42344}, {524, 14443}, {543, 14423}, {661, 45775}, {670, 52628}, {671, 8029}, {691, 3124}, {892, 115}, {2396, 51429}, {2407, 2682}, {2482, 46049}, {4590, 690}, {5380, 21833}, {5466, 61339}, {5467, 59801}, {5468, 23992}, {18020, 14273}, {18023, 23105}, {19626, 23610}, {24041, 2642}, {31614, 524}, {32729, 1084}, {32740, 23099}, {34537, 35522}, {34539, 9178}, {36085, 2643}, {41294, 33918}, {42370, 99}, {45773, 6}, {47389, 14417}, {47443, 44102}, {50941, 51428}, {52940, 523}, {53080, 338}, {55226, 5099}, {55270, 468}, {57552, 5466}, {57991, 52038}, {59152, 187}, {59762, 2970}, {61190, 23991}

X(64461) = X(526)-OF-X(526)

Barycentrics    a^2*(b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 2*b^6*c^2 - 2*a^4*c^4 + 4*b^4*c^4 + a^2*c^6 - 2*b^2*c^6) : :

X(64461) lies on these lines: {30, 511}, {2088, 16186}, {3581, 14270}, {5118, 52603}, {32110, 39477}, {35139, 35316}, {37477, 44826}, {37496, 53247}

X(64461) = crossdifference of every pair of points on line {6, 476}

X(64462) = X(527)-OF-X(527)

Barycentrics    2*a^4 - 2*a^3*b - 3*a^2*b^2 + 4*a*b^3 - b^4 - 2*a^3*c + 8*a^2*b*c - 4*a*b^2*c - 2*b^3*c - 3*a^2*c^2 - 4*a*b*c^2 + 6*b^2*c^2 + 4*a*c^3 - 2*b*c^3 - c^4 : :

X(64462) lies on these lines: {2, 664}, {8, 42050}, {10, 59609}, {11, 60692}, {30, 511}, {551, 62674}, {1212, 25719}, {1275, 57563}, {1317, 9318}, {1565, 10708}, {1952, 55956}, {3036, 24318}, {3241, 14942}, {3679, 50441}, {3870, 42064}, {4370, 40865}, {4437, 30225}, {4530, 26007}, {4534, 9317}, {4904, 34578}, {4945, 31048}, {4957, 17392}, {6554, 25718}, {8301, 11194}, {9312, 21258}, {10710, 18328}, {16833, 45749}, {17264, 40872}, {17294, 51390}, {17389, 20173}, {24712, 62616}, {25716, 46835}, {25726, 37774}, {31145, 52164}, {31169, 55954}, {38941, 61673}, {39542, 60083}, {41006, 58458}, {43066, 48381}, {47037, 47043}

X(64462) = isotomic conjugate of X(53212)
X(64462) = trilinear pole of line {14476, 14477}
X(64462) = crossdifference of every pair of points on line {6, 6139}
X(64462) = barycentric product X(4437)*X(43570)
X(64462) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 664, 35110}, {2, 1121, 1146}, {2, 35110, 17044}, {2, 39351, 1121}, {2, 39357, 664}, {664, 1121, 2}, {664, 1146, 17044}, {664, 39351, 1146}, {1121, 39357, 35110}, {1146, 17044, 40483}, {1146, 35110, 2}, {39351, 39357, 2}

X(64463) = X(545)-OF-X(545)

Barycentrics    2*a^4 - 4*a^3*b - 6*a^2*b^2 + 8*a*b^3 - b^4 - 4*a^3*c + 24*a^2*b*c - 12*a*b^2*c - 4*b^3*c - 6*a^2*c^2 - 12*a*b*c^2 + 12*b^2*c^2 + 8*a*c^3 - 4*b*c^3 - c^4 : :

X(64463) lies on these lines: {2, 4555}, {30, 511}, {1016, 62413}, {3241, 24407}, {4370, 6633}, {6547, 9460}, {6549, 36525}, {6630, 54974}, {6631, 41138}, {17310, 30566}, {24441, 24864}, {36522, 53582}, {41140, 43055}, {49751, 50112}, {57564, 57567}

X(64463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4555, 35121}, {2, 35168, 35092}, {2, 39349, 35168}, {4555, 35168, 2}, {4555, 39349, 35092}, {35092, 35121, 2}

X(64464) = X(15)-OF-X(3)

Barycentrics    a^4*(a^2 - b^2 - c^2)*(Sqrt[3]*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4) + 2*(a^2 - b^2 - c^2)*S) : :

X(64464) lies on these lines: {2, 51268}, {3, 10662}, {15, 1511}, {62, 1493}, {539, 52204}, {577, 1147}, {621, 52605}, {1154, 3165}, {3200, 11136}, {5334, 11556}, {9703, 46113}, {10217, 38414}, {10633, 11127}, {10635, 44719}, {10661, 50465}, {11486, 16022}, {15091, 18470}, {17714, 41089}, {22115, 46112}, {36296, 43704}, {42121, 54297}, {50469, 52349}

X(64464) = isotomic conjugate of the polar conjugate of X(11136)
X(64464) = isogonal conjugate of the polar conjugate of X(11127)
X(64464) = X(11127)-Ceva conjugate of X(11136)
X(64464) = X(i)-isoconjugate of X(j) for these (i,j): {92, 11082}, {158, 52204}, {11083, 63764}
X(64464) = X(i)-Dao conjugate of X(j) for these (i,j): {1147, 52204}, {11131, 264}, {22391, 11082}, {63834, 11126}
X(64464) = crosspoint of X(38414) and X(47390)
X(64464) = crossdifference of every pair of points on line {23283, 23290}
X(64464) = barycentric product X(i)*X(j) for these {i,j}: {3, 11127}, {15, 52349}, {62, 44718}, {63, 35198}, {69, 11136}, {184, 11133}, {303, 46112}, {323, 50469}, {394, 10633}, {3200, 40709}, {6105, 44719}, {8603, 44180}, {8836, 22115}, {10677, 52348}, {11088, 52437}, {11145, 50466}, {46113, 52221}, {52606, 60010}
X(64464) = barycentric quotient X(i)/X(j) for these {i,j}: {49, 8838}, {184, 11082}, {577, 52204}, {3200, 470}, {8603, 93}, {8836, 18817}, {10633, 2052}, {11088, 6344}, {11127, 264}, {11133, 18022}, {11136, 4}, {34394, 8742}, {35198, 92}, {44718, 34390}, {46112, 18}, {46113, 11601}, {50469, 94}, {52349, 300}, {63837, 11126}

X(64465) = X(16)-OF-X(3)

Barycentrics    (a^4*(a^2 - b^2 - c^2)*(-(Sqrt[3]*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4)) + 2*(a^2 - b^2 - c^2)*S)) : :

X(64465) lies on these lines: {2, 51275}, {3, 10661}, {16, 1511}, {61, 1493}, {539, 52203}, {577, 1147}, {622, 52606}, {1154, 3166}, {3201, 11135}, {5335, 11555}, {9703, 46112}, {10218, 38413}, {10632, 11126}, {10634, 44718}, {10662, 50466}, {11485, 16021}, {15091, 18468}, {17714, 41090}, {22115, 46113}, {36297, 43704}, {42124, 54298}, {50468, 52348}

X(64465) = isotomic conjugate of the polar conjugate of X(11135)
X(64465) = isogonal conjugate of the polar conjugate of X(11126)
X(64465) = X(11126)-Ceva conjugate of X(11135)
X(64465) = X(i)-isoconjugate of X(j) for these (i,j): {92, 11087}, {158, 52203}, {11088, 63764}
X(64465) = X(i)-Dao conjugate of X(j) for these (i,j): {1147, 52203}, {11130, 264}, {22391, 11087}, {63834, 11127}
X(64465) = crosspoint of X(38413) and X(47390)
X(64465) = crossdifference of every pair of points on line {23284, 23290}
X(64465) = barycentric product X(i)*X(j) for these {i,j}: {3, 11126}, {16, 52348}, {61, 44719}, {63, 35199}, {69, 11135}, {184, 11132}, {302, 46113}, {323, 50468}, {394, 10632}, {3201, 40710}, {6104, 44718}, {8604, 44180}, {8838, 22115}, {10678, 52349}, {11083, 52437}, {11146, 50465}, {46112, 52220}, {52605, 60009}
X(64465) = barycentric quotient X(i)/X(j) for these {i,j}: {49, 8836}, {184, 11087}, {577, 52203}, {3201, 471}, {8604, 93}, {8838, 18817}, {10632, 2052}, {11083, 6344}, {11126, 264}, {11132, 18022}, {11135, 4}, {34395, 8741}, {35199, 92}, {44719, 34389}, {46112, 11600}, {46113, 17}, {50468, 94}, {52348, 301}, {63837, 11127}

X(64466) = X(17)-OF-X(3)

Barycentrics    1/((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4 + 2*Sqrt[3]*(a^2 - b^2 - c^2)*S)) : :

X(64466) lies on these lines: {3, 44714}, {5, 16}, {324, 471}, {343, 44719}, {1147, 52204}, {3166, 10125}, {5449, 52203}, {44713, 50465}

X(64466) = trilinear pole of line {6368, 60009}

X(64467) = X(18)-OF-X(3)

Barycentrics    1/((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4 - 2*Sqrt[3]*(a^2 - b^2 - c^2)*S)) : :

X(64467) lies on these lines: {3, 44713}, {5, 15}, {324, 470}, {343, 44718}, {1147, 52203}, {3165, 10125}, {5449, 52204}, {44714, 50466}

X(64467) = trilinear pole of line {6368, 60010}

X(64468) = ISOGONAL CONJUGATE OF X(64466)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4 + 2*Sqrt[3]*(a^2 - b^2 - c^2)*S) : :

X(64468) lies on these lines: {3, 56514}, {4, 14}, {6, 24}, {13, 16868}, {15, 21844}, {16, 3520}, {17, 14940}, {18, 7577}, {32, 23717}, {61, 186}, {378, 22238}, {395, 1594}, {396, 10018}, {397, 403}, {398, 6240}, {470, 11126}, {933, 39406}, {1593, 11486}, {1595, 42634}, {1598, 11409}, {1614, 11244}, {1885, 42924}, {2937, 11268}, {3147, 37640}, {3200, 59279}, {3411, 52295}, {3518, 8740}, {3542, 42998}, {5237, 35473}, {5238, 17506}, {5339, 35480}, {5340, 35488}, {6198, 7127}, {7487, 63080}, {7505, 40693}, {7507, 42989}, {7547, 42153}, {7576, 43229}, {7722, 36209}, {8737, 8929}, {8839, 46113}, {10019, 43416}, {10295, 42147}, {10635, 37126}, {10642, 34484}, {10646, 23040}, {10654, 35471}, {10661, 11453}, {11243, 26882}, {11466, 30403}, {11475, 34755}, {11485, 15750}, {11543, 23047}, {12173, 42975}, {13619, 42157}, {16268, 62982}, {16645, 52296}, {16773, 37118}, {16964, 34797}, {18533, 42999}, {18560, 42148}, {21648, 64026}, {22236, 32534}, {35472, 36836}, {35477, 36843}, {35481, 42151}, {35487, 42166}, {35489, 41101}, {35490, 42155}, {35491, 42943}, {35503, 42150}, {37119, 42149}, {37453, 42988}, {37777, 54363}, {37931, 42925}, {37943, 61719}, {42165, 57584}, {42990, 44958}, {43632, 56369}, {44102, 44512}

X(64468) = isogonal conjugate oof X(64466)
X(64468) = crossdifference of every pair of points on line {6368, 60009}
X(64468) = barycentric quotient X(3205)/X(52348)
X(64468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 62, 56515}, {6, 10633, 10632}, {62, 8739, 4}, {10880, 10881, 10633}

X(64469) = ISOGONAL CONJUGATE OF X(64467)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4 - 2*Sqrt[3]*(a^2 - b^2 - c^2)*S) : :

X(64469) lies on these lines: {3, 56515}, {4, 13}, {6, 24}, {14, 16868}, {15, 3520}, {16, 21844}, {17, 7577}, {18, 14940}, {32, 23716}, {62, 186}, {378, 22236}, {395, 10018}, {396, 1594}, {397, 6240}, {398, 403}, {471, 11127}, {933, 39407}, {1593, 11485}, {1595, 42633}, {1598, 11408}, {1614, 11243}, {1870, 2307}, {1885, 42925}, {2937, 11267}, {3147, 37641}, {3201, 59279}, {3412, 52295}, {3518, 8739}, {3542, 42999}, {5237, 17506}, {5238, 35473}, {5339, 35488}, {5340, 35480}, {7487, 63079}, {7505, 40694}, {7507, 42988}, {7547, 42156}, {7576, 43228}, {7722, 36208}, {8738, 8930}, {8837, 46112}, {10019, 43417}, {10295, 42148}, {10634, 37126}, {10641, 34484}, {10645, 23040}, {10653, 35471}, {10662, 11452}, {11244, 26882}, {11467, 30402}, {11476, 34754}, {11486, 15750}, {11542, 23047}, {12173, 42974}, {13619, 42158}, {16267, 62982}, {16644, 52296}, {16772, 37118}, {16965, 34797}, {18533, 42998}, {18559, 61719}, {18560, 42147}, {21647, 64026}, {22238, 32534}, {35472, 36843}, {35477, 36836}, {35481, 42150}, {35487, 42163}, {35489, 41100}, {35490, 42154}, {35491, 42942}, {35503, 42151}, {37119, 42152}, {37453, 42989}, {37777, 54362}, {37931, 42924}, {42164, 57584}, {42991, 44958}, {43633, 56369}, {44102, 44511}

X(64469) = isogonal conjugate oof X(64467)
X(64469) = crossdifference of every pair of points on line {6368, 60010}
X(64469) = barycentric quotient X(3206)/X(52349)
X(64469) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 61, 56514}, {6, 10632, 10633}, {61, 8740, 4}, {10880, 10881, 10632}

X(64470) = X(5)X(25043)∩X(570)X(15345)

Barycentrics    (-a^2 b^2 + b^4 - a^2 c^2 - 2 b^2 c^2 + c^4) (a^4 b^2 - 2 a^2 b^4 + b^6 + a^4 c^2 - 2 a^2 b^2 c^2 - b^4 c^2 - 2 a^2 c^4 - b^2 c^4 + c^6) (-a^18 + 6 a^16 b^2 - 16 a^14 b^4 + 26 a^12 b^6 - 30 a^10 b^8 + 26 a^8 b^10 - 16 a^6 b^12 + 6 a^4 b^14 - a^2 b^16 + 6 a^16 c^2 - 22 a^14 b^2 c^2 + 30 a^12 b^4 c^2 - 15 a^10 b^6 c^2 - 9 a^8 b^8 c^2 + 20 a^6 b^10 c^2 - 12 a^4 b^12 c^2 + a^2 b^14 c^2 + b^16 c^2 - 16 a^14 c^4 + 30 a^12 b^2 c^4 - 19 a^10 b^4 c^4 + 13 a^8 b^6 c^4 - 22 a^6 b^8 c^4 + 22 a^4 b^10 c^4 - 3 a^2 b^12 c^4 - 5 b^14 c^4 + 26 a^12 c^6 - 15 a^10 b^2 c^6 + 13 a^8 b^4 c^6 - 16 a^4 b^8 c^6 + 19 a^2 b^10 c^6 + 9 b^12 c^6 - 30 a^10 c^8 - 9 a^8 b^2 c^8 - 22 a^6 b^4 c^8 - 16 a^4 b^6 c^8 - 32 a^2 b^8 c^8 - 5 b^10 c^8 + 26 a^8 c^10 + 20 a^6 b^2 c^10 + 22 a^4 b^4 c^10 + 19 a^2 b^6 c^10 - 5 b^8 c^10 - 16 a^6 c^12 - 12 a^4 b^2 c^12 - 3 a^2 b^4 c^12 + 9 b^6 c^12 + 6 a^4 c^14 + a^2 b^2 c^14 - 5 b^4 c^14 - a^2 c^16 + b^2 c^16) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6368.

X(64470) lies on these lines: {5, 25043}, {570, 15345}

X(64471) = 81ST HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 - 5*a^4*c^2 - 12*a^2*b^2*c^2 + b^4*c^2 + 4*a^2*c^4 + b^2*c^4 - c^6) : :
X(64471) = X[3] - 3 X[44212], X[4] + 3 X[25], X[4] - 3 X[1596], 5 X[4] + 3 X[18533], 3 X[4] + X[37196], 7 X[4] - 3 X[44438], 5 X[4] - 9 X[62966], 3 X[5] - X[14791], X[5] - 3 X[44275], X[20] - 9 X[26255], X[20] - 3 X[44273], 5 X[25] - X[18533], 9 X[25] - X[37196], 3 X[25] - X[37458], 7 X[25] + X[44438], 5 X[25] + 3 X[62966], 2 X[140] - 3 X[6677], X[140] - 3 X[44233], X[550] - 3 X[6644], 5 X[631] - 9 X[47597], 3 X[1368] - 5 X[1656], 3 X[1370] - 11 X[5056], 5 X[1596] + X[18533], 9 X[1596] + X[37196], 3 X[1596] + X[37458], 7 X[1596] - X[44438], 5 X[1596] - 3 X[62966], 5 X[1656] + 3 X[18534], X[1657] - 3 X[44241], 7 X[3090] - 3 X[31152], 7 X[3523] - 3 X[21312], 4 X[3850] - 3 X[44920], 2 X[3850] - 3 X[46030], 7 X[3851] - 3 X[18531], 13 X[5067] - 9 X[32216], 13 X[5068] + 3 X[7500], 13 X[5068] - 9 X[16072], X[7500] + 3 X[16072], 3 X[7530] + X[14791], X[7530] + 3 X[44275], X[10295] - 3 X[44272], X[14791] - 9 X[44275], 9 X[18533] - 5 X[37196], 3 X[18533] - 5 X[37458], 7 X[18533] + 5 X[44438], X[18533] + 3 X[62966], 3 X[26255] - X[44273], 15 X[31255] - 19 X[61886], X[37196] - 3 X[37458], 7 X[37196] + 9 X[44438], 5 X[37196] + 27 X[62966], 7 X[37458] + 3 X[44438], 5 X[37458] + 9 X[62966], 9 X[37951] - X[56369], 3 X[44276] - X[62036], 5 X[44438] - 21 X[62966], 3 X[44454] + 13 X[46219], 7 X[44904] - 6 X[50140], X[5882] - 3 X[51695], X[8550] - 3 X[19136], 3 X[20772] - X[30714], X[37480] - 3 X[61507]

See Antreas Hatzipolakis and Peter Moses, euclid 6378.

X(64471) lies on these lines: {2, 3}, {53, 43291}, {54, 40114}, {113, 11566}, {125, 16654}, {155, 63702}, {230, 33842}, {232, 63633}, {389, 63714}, {397, 63681}, {398, 63680}, {1495, 16657}, {1629, 51385}, {1843, 46817}, {1974, 61752}, {1990, 3199}, {2393, 10110}, {2790, 11623}, {3426, 18931}, {3527, 10602}, {3564, 46261}, {5095, 5609}, {5446, 14984}, {5480, 61610}, {5654, 7716}, {5882, 51695}, {5946, 44079}, {6152, 10294}, {6390, 58782}, {6749, 33871}, {6759, 8550}, {7583, 35765}, {7584, 35764}, {7713, 22791}, {7718, 37705}, {8263, 17814}, {10539, 13142}, {10546, 54040}, {10985, 60428}, {11245, 14157}, {11398, 15172}, {11430, 15448}, {11433, 32063}, {11459, 47582}, {11576, 22051}, {11743, 12242}, {11745, 61749}, {11793, 63723}, {11801, 46682}, {11803, 63693}, {12294, 15067}, {13382, 41589}, {13392, 15472}, {13451, 47328}, {13464, 44662}, {13474, 20417}, {13570, 58447}, {13598, 59659}, {14852, 39884}, {14862, 58483}, {15030, 32269}, {15032, 61657}, {15048, 59229}, {15068, 34380}, {15118, 15465}, {15251, 23711}, {16318, 33885}, {16656, 20299}, {18357, 49542}, {18388, 61612}, {18451, 41588}, {18914, 26883}, {18990, 54428}, {19347, 54149}, {20772, 30714}, {23292, 61606}, {32223, 46847}, {32234, 32358}, {36201, 63695}, {37480, 61507}, {39571, 64080}, {40240, 50414}, {43574, 44935}, {44106, 51403}, {44158, 46849}, {44413, 59553}, {59649, 63634}, {63477, 63739}, {63683, 63686}, {63685, 63721}, {63690, 63726}

X(64471) = midpoint of X(i) and X(j) for these {i,j}: {4, 37458}, {5, 7530}, {25, 1596}, {1368, 18534}, {18451, 41588}, {54149, 54218}
X(64471) = reflection of X(i) in X(j) for these {i,j}: {6677, 44233}, {44920, 46030}
X(64471) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 37897, 33591}, {4, 25, 37458}, {4, 235, 37984}, {4, 3517, 550}, {4, 3518, 10295}, {4, 3542, 5094}, {4, 4232, 3}, {4, 5094, 1595}, {4, 10295, 1885}, {4, 10301, 6756}, {4, 10594, 10301}, {4, 21841, 140}, {4, 35486, 1593}, {4, 37984, 546}, {4, 44959, 10019}, {4, 44960, 3850}, {4, 47486, 35491}, {4, 52290, 3088}, {5, 16618, 140}, {5, 16619, 16618}, {24, 1906, 13488}, {24, 13488, 548}, {25, 1598, 7530}, {25, 62966, 18533}, {140, 16618, 16197}, {140, 25338, 13383}, {235, 6756, 546}, {235, 10301, 4}, {235, 10594, 6756}, {378, 37935, 12100}, {378, 62978, 37935}, {381, 37971, 6676}, {403, 52294, 428}, {427, 37942, 547}, {427, 62961, 37942}, {546, 13383, 63679}, {546, 25338, 140}, {1593, 62981, 35486}, {1595, 3542, 3628}, {1596, 37458, 4}, {1597, 6353, 549}, {1598, 3089, 5}, {3518, 44803, 1885}, {3542, 5198, 1595}, {3575, 44226, 3853}, {5000, 5001, 43957}, {5094, 5198, 4}, {6623, 7714, 18494}, {6623, 18494, 3845}, {6644, 7530, 7387}, {6756, 37984, 4}, {7530, 44233, 16197}, {7530, 44275, 5}, {10096, 14893, 44236}, {10295, 44803, 4}, {15030, 32269, 44683}, {15122, 16238, 140}, {16252, 63737, 63699}, {34621, 40132, 3}, {37458, 44274, 37934}, {42807, 42808, 11479}, {63665, 63667, 546}, {63688, 63737, 10110}

X(64472) = 82ND HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^10 - 5*a^8*b^2 + 2*a^6*b^4 + 4*a^4*b^6 - 4*a^2*b^8 + b^10 - 5*a^8*c^2 - 4*a^6*b^2*c^2 + 2*a^4*b^4*c^2 + 10*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 + 2*a^4*b^2*c^4 - 12*a^2*b^4*c^4 + 2*b^6*c^4 + 4*a^4*c^6 + 10*a^2*b^2*c^6 + 2*b^4*c^6 - 4*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(64472) = X[3] - 3 X[44213], X[4] + 3 X[26], X[4] - 3 X[15761], 7 X[4] - 3 X[52843], X[5] - 3 X[44278], X[20] - 3 X[48368], 7 X[26] + X[52843], 7 X[140] - 6 X[5498], 2 X[140] - 3 X[10020], 5 X[140] - 6 X[10125], X[140] - 3 X[13383], 4 X[140] - 3 X[23336], 13 X[140] - 12 X[34421], 19 X[140] - 18 X[34478], 3 X[547] - 4 X[12010], X[550] - 3 X[1658], X[550] - 9 X[10154], 5 X[1656] + 3 X[7387], 5 X[1656] - 9 X[10201], 5 X[1656] - 3 X[13371], 25 X[1656] - 9 X[34609], X[1657] - 9 X[14070], X[1657] - 3 X[44242], X[1658] - 3 X[10154], 7 X[3090] - 3 X[31181], 5 X[3522] - 9 X[18324], 7 X[3523] - 3 X[12084], 7 X[3523] - 9 X[34477], 2 X[3530] - 3 X[15330], 17 X[3533] - 9 X[44441], 2 X[3850] - 3 X[13406], 7 X[3851] + 9 X[9909], 7 X[3851] - 3 X[18569], 5 X[3858] - 3 X[18377], 11 X[5056] - 3 X[14790], 13 X[5068] + 3 X[31305], X[5073] + 15 X[16195], 4 X[5498] - 7 X[10020], 5 X[5498] - 7 X[10125], 2 X[5498] - 7 X[13383], 3 X[5498] - 7 X[18282], 8 X[5498] - 7 X[23336], 13 X[5498] - 14 X[34421], 19 X[5498] - 21 X[34478], X[7387] + 3 X[10201], 5 X[7387] + 3 X[34609], 3 X[9909] + X[18569], 5 X[10020] - 4 X[10125], 3 X[10020] - 4 X[18282], 13 X[10020] - 8 X[34421], 19 X[10020] - 12 X[34478], 2 X[10125] - 5 X[13383], 3 X[10125] - 5 X[18282], 8 X[10125] - 5 X[23336], 13 X[10125] - 10 X[34421], 19 X[10125] - 15 X[34478], 3 X[10201] - X[13371], 5 X[10201] - X[34609], 3 X[10224] - 4 X[35018], 3 X[10226] - 4 X[61792], 21 X[10244] + 11 X[61970], 27 X[10245] + 5 X[62023], 3 X[11250] - 5 X[15712], X[11250] - 3 X[34351], X[12084] - 3 X[34477], 3 X[12085] - 11 X[15720], 5 X[13371] - 3 X[34609], 3 X[13383] - 2 X[18282], 4 X[13383] - X[23336], 13 X[13383] - 4 X[34421], 19 X[13383] - 6 X[34478], 3 X[14070] - X[44242], 3 X[15331] - 2 X[33923], 3 X[15332] - 2 X[62136], 5 X[15712] - 9 X[34351], 7 X[15761] - X[52843], X[17714] + 3 X[44278], 3 X[18281] + X[39568], 9 X[18281] - 13 X[46219], 8 X[18282] - 3 X[23336], 13 X[18282] - 6 X[34421], 19 X[18282] - 9 X[34478], 9 X[18568] - 13 X[61975], 3 X[23044] + X[50008], 3 X[23335] - 7 X[55856], 13 X[23336] - 16 X[34421], 19 X[23336] - 24 X[34478], 5 X[31283] - X[34938], 15 X[31283] - 19 X[61886], 2 X[32144] - 3 X[34330], 3 X[32144] - 4 X[61877], 9 X[33591] - X[62144], X[33923] - 3 X[44277], 9 X[34330] - 8 X[61877], 3 X[34350] - 7 X[62100], 38 X[34421] - 39 X[34478], 9 X[34608] + 23 X[61921], 9 X[34621] + 23 X[61834], 3 X[34938] - 19 X[61886], 3 X[39568] + 13 X[46219], 3 X[44279] - X[62036], 9 X[54992] - 25 X[61815], 11 X[55859] - 9 X[61736], 3 X[5449] - X[14864], X[5882] - 3 X[51696], X[8550] - 3 X[19154], 3 X[12359] + X[44762], X[15105] - 3 X[32138], 3 X[20773] - X[30714], X[34507] + 3 X[64052]

See Antreas Hatzipolakis and Peter Moses, euclid 6381.

X(64472) lies on these lines: {2, 3}, {397, 11268}, {398, 11267}, {511, 61608}, {539, 50414}, {1154, 16252}, {1614, 32358}, {3471, 16104}, {3519, 10540}, {3589, 18874}, {5446, 12242}, {5449, 14864}, {5562, 46817}, {5663, 41674}, {5882, 51696}, {6101, 51425}, {6102, 32269}, {6759, 61612}, {8550, 19154}, {9820, 13391}, {10272, 41673}, {10610, 16657}, {10619, 12370}, {10627, 59659}, {11803, 14449}, {12359, 44762}, {13431, 43844}, {13598, 44516}, {13754, 14862}, {14641, 44673}, {15105, 32138}, {15647, 32423}, {16655, 34826}, {17710, 18583}, {20773, 30714}, {26881, 44076}, {32111, 63392}, {32223, 40647}, {32237, 45286}, {32379, 50708}, {34117, 34380}, {34507, 64052}, {41587, 43588}, {44201, 45959}, {58439, 61749}, {61685, 64066}

X(64472) = midpoint of X(i) and X(j) for these {i,j}: {5, 17714}, {26, 15761}, {6759, 63734}, {7387, 13371}
X(64472) = reflection of X(i) in X(j) for these {i,j}: {140, 18282}, {10020, 13383}, {15331, 44277}, {23336, 10020}
X(64472) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 62961, 5}, {5, 428, 546}, {5, 34002, 140}, {5, 37947, 7553}, {23, 10024, 11819}, {26, 7517, 17714}, {140, 13383, 18282}, {140, 18282, 10020}, {140, 25337, 34002}, {140, 25338, 21841}, {140, 64471, 3850}, {235, 7502, 52073}, {468, 550, 140}, {548, 10096, 16238}, {1657, 10018, 15122}, {1658, 17714, 22}, {3627, 7542, 44236}, {3853, 34577, 52262}, {7387, 10201, 13371}, {7488, 11799, 52070}, {7488, 52070, 548}, {7517, 10024, 428}, {7542, 47093, 3627}, {7555, 44235, 12362}, {7556, 47336, 12103}, {10018, 15122, 140}, {10024, 11819, 546}, {10619, 18555, 12370}, {11563, 12605, 546}, {12103, 44234, 16196}, {13160, 18378, 13490}, {15760, 37440, 31830}, {16197, 44233, 3628}, {16618, 21841, 140}, {17714, 44278, 5}, {31723, 63657, 5}, {37936, 61750, 3575}, {41587, 61752, 43588}, {59351, 62961, 3}

X(64473) = 83RD HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c + 2*a^5*b*c - a^4*b^2*c - 3*a^3*b^3*c + a^2*b^4*c + a*b^5*c + b^6*c - a^5*c^2 - a^4*b*c^2 + 2*a^3*b^2*c^2 - 2*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + a^4*c^3 - 3*a^3*b*c^3 - 2*a^2*b^2*c^3 - 2*a*b^3*c^3 - 3*b^4*c^3 - a^3*c^4 + a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 + a^2*c^5 + a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :
X(64473) = X[3] - 3 X[44217], X[4] + 3 X[377], X[4] - 3 X[44229], X[20] - 3 X[44284], 2 X[140] - 3 X[8728], 3 X[405] - 5 X[1656], X[550] - 3 X[44222], X[550] - 6 X[50238], 5 X[631] - 9 X[50793], 5 X[632] - 6 X[50395], X[1657] - 3 X[37426], X[1657] - 15 X[50713], 7 X[3090] - 3 X[31156], 5 X[3522] - 21 X[50794], 7 X[3523] - 15 X[50237], 17 X[3533] - 21 X[50393], 4 X[3628] - 3 X[50202], 4 X[3850] + 3 X[50240], 7 X[3851] - 3 X[37234], 7 X[3851] + 3 X[50239], 11 X[5056] - 3 X[6872], 13 X[5068] + 3 X[31295], 11 X[5070] - 9 X[50714], 15 X[31259] - 19 X[61886], 8 X[35018] - 3 X[50241], X[37426] - 5 X[50713], 3 X[44286] - X[62036], 13 X[46219] - 15 X[50207], 29 X[46935] - 21 X[50398], 6 X[50205] - 7 X[55856], 3 X[50242] - 17 X[61919], 6 X[50243] - 13 X[61907], 3 X[50244] - 23 X[61921], 12 X[50394] - 11 X[55859], 21 X[50795] - 23 X[55860], X[5882] - 3 X[51706], X[8550] - 3 X[51738], 4 X[25555] - 3 X[51743]

See Antreas Hatzipolakis and Peter Moses, euclid 6381.

X(64473) lies on these lines: {2, 3}, {355, 5270}, {388, 37705}, {496, 64086}, {518, 34507}, {1056, 61295}, {1074, 8144}, {1125, 18407}, {1478, 5221}, {1479, 61272}, {1714, 63307}, {3336, 5587}, {3583, 61268}, {3585, 24914}, {3812, 13369}, {4857, 5886}, {5131, 7989}, {5289, 22791}, {5302, 9956}, {5535, 41229}, {5690, 26332}, {5692, 16159}, {5706, 15068}, {5790, 56880}, {5844, 10532}, {5882, 51706}, {5891, 58889}, {5901, 37820}, {7171, 18492}, {8148, 33110}, {8550, 51738}, {9654, 11698}, {9782, 59387}, {9955, 59691}, {10170, 15488}, {10176, 16125}, {10441, 15067}, {10525, 38034}, {10526, 38042}, {10597, 61597}, {11545, 18962}, {12116, 51700}, {13273, 61580}, {18397, 57282}, {18406, 18481}, {18493, 52367}, {18517, 34773}, {19767, 63323}, {20292, 40266}, {22836, 33592}, {23039, 41723}, {25524, 45630}, {25555, 51743}, {31835, 37826}, {34862, 38140}, {37522, 45926}, {37821, 61259}, {38028, 48482}, {38149, 61251}, {48835, 48887}, {56879, 61510}, {61552, 61716}

X(64473) = midpoint of X(i) and X(j) for these {i,j}: {355, 10404}, {377, 44229}, {381, 50397}, {37234, 50239}
X(64473) = reflection of X(i) in X(j) for these {i,j}: {5302, 9956}, {44222, 50238}
X(64473) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 381, 6845}, {4, 37163, 1657}, {5, 550, 16617}, {5, 37281, 6924}, {377, 2475, 50397}, {550, 16617, 6914}, {2475, 6900, 381}, {6826, 6917, 5}, {6829, 6845, 4193}, {6835, 6923, 546}, {6839, 6901, 3}, {6843, 6862, 5}, {6843, 6885, 6862}, {6854, 6928, 3628}, {6861, 6934, 7508}, {6864, 6929, 5}, {6867, 6959, 5}, {6894, 6951, 382}, {6934, 6993, 6861}, {6946, 7548, 6971}, {6985, 17528, 5499}, {6990, 17579, 13743}, {8703, 44258, 6851}, {14784, 14785, 16865}, {42807, 42808, 6831}

X(64474) = 84TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics   (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 - 5*a^4*c^2 + 12*a^2*b^2*c^2 + b^4*c^2 + 4*a^2*c^4 + b^2*c^4 - c^6) : :
X(64474) = X[3] - 3 X[44218], 5 X[3] - 3 X[44261], X[4] + 3 X[378], X[4] - 3 X[427], 7 X[4] - 3 X[35480], 5 X[4] + 3 X[35481], X[5] - 3 X[44287], X[20] + 3 X[31133], X[20] - 3 X[44285], 3 X[22] - 7 X[3523], 4 X[140] - 3 X[6676], 5 X[140] - 3 X[25337], X[140] - 3 X[44236], 2 X[140] - 3 X[52262], 7 X[378] + X[35480], 5 X[378] - X[35481], 7 X[427] - X[35480], 5 X[427] + X[35481], X[550] - 3 X[18570], 5 X[631] - X[12082], 5 X[631] - 3 X[44210], 5 X[632] - 3 X[44262], 5 X[1656] - 3 X[15760], X[1657] + 3 X[31723], X[1657] - 3 X[44249], X[3146] - 9 X[31105], 5 X[3522] + 3 X[7391], 5 X[3522] - 3 X[44239], 2 X[3850] - 3 X[39504], 5 X[3858] - 3 X[44263], 11 X[5056] - 15 X[31236], 11 X[5056] - 3 X[44440], X[5059] + 3 X[52842], 3 X[6676] - 2 X[16618], 5 X[6676] - 4 X[25337], X[6676] - 4 X[44236], 3 X[7502] - 5 X[15712], X[10295] - 3 X[44281], 13 X[10299] - 9 X[44837], 13 X[10303] - 9 X[47596], X[12082] - 3 X[44210], 3 X[12083] - 11 X[15720], 6 X[13413] - 5 X[61940], 5 X[16618] - 6 X[25337], X[16618] - 6 X[44236], X[16618] - 3 X[52262], 3 X[20062] - 19 X[61791], 11 X[21735] - 3 X[44831], X[25337] - 5 X[44236], 2 X[25337] - 5 X[52262], 5 X[31236] - X[44440], 4 X[35018] - 3 X[46029], 5 X[35480] + 7 X[35481], X[37458] - 3 X[44274], 5 X[44218] - X[44261], 3 X[44288] - X[62036], 3 X[44457] - 19 X[61832], X[8550] - 3 X[51739], X[5882] - 3 X[51707], X[11456] - 3 X[61690], 2 X[13464] - 3 X[51718]

See Antreas Hatzipolakis and Peter Moses, euclid 6381.

X(64474) lies on these lines: {2, 3}, {32, 6749}, {33, 15325}, {39, 1990}, {53, 574}, {125, 16657}, {141, 37480}, {185, 61540}, {187, 6748}, {230, 33843}, {264, 6390}, {340, 7767}, {389, 2781}, {393, 5024}, {511, 44683}, {523, 52600}, {575, 15471}, {578, 6247}, {1112, 61548}, {1204, 45089}, {1352, 37497}, {1353, 18917}, {1384, 3087}, {1495, 16654}, {1503, 11430}, {1785, 37599}, {1829, 61524}, {1862, 61566}, {1876, 5719}, {1902, 5901}, {2207, 31406}, {3092, 13966}, {3093, 8981}, {3098, 3867}, {3357, 12233}, {3426, 5656}, {3564, 13352}, {3567, 43607}, {3574, 10990}, {3589, 16836}, {3793, 27377}, {3926, 52710}, {3933, 44134}, {5007, 39176}, {5090, 34773}, {5095, 16003}, {5185, 61565}, {5186, 61560}, {5305, 6103}, {5412, 35255}, {5413, 35256}, {5446, 44158}, {5480, 11438}, {5486, 8549}, {5654, 11472}, {5663, 15120}, {5882, 51707}, {5893, 15125}, {5972, 46847}, {6000, 23292}, {6152, 54201}, {6225, 43841}, {6403, 13340}, {6689, 14641}, {6746, 14449}, {7583, 11474}, {7584, 11473}, {7687, 15113}, {7735, 39662}, {8548, 36747}, {8739, 42913}, {8740, 42912}, {9019, 15644}, {9300, 14581}, {9605, 40138}, {9729, 25555}, {9730, 12294}, {9820, 15115}, {10110, 25563}, {10182, 15448}, {10264, 15472}, {10272, 12133}, {10282, 16621}, {10294, 22948}, {10564, 18358}, {10982, 26937}, {11064, 15030}, {11245, 15033}, {11386, 42787}, {11425, 14216}, {11426, 18909}, {11432, 18913}, {11456, 61690}, {11464, 16658}, {11475, 11543}, {11476, 11542}, {12131, 61561}, {12134, 18488}, {12138, 61562}, {12143, 32516}, {12145, 61573}, {12162, 61607}, {12163, 31802}, {12241, 20299}, {12242, 31978}, {12300, 22051}, {12324, 19347}, {12359, 13142}, {12897, 15123}, {13339, 19128}, {13346, 34507}, {13348, 51994}, {13363, 44084}, {13366, 13399}, {13367, 16655}, {13391, 47328}, {13393, 32165}, {13403, 15126}, {13431, 16622}, {13464, 51718}, {13474, 16252}, {13561, 55295}, {13567, 23329}, {13568, 64027}, {13624, 49542}, {14357, 41522}, {14389, 15072}, {14561, 37475}, {14830, 20774}, {14852, 64096}, {14853, 18931}, {15116, 32274}, {15117, 22833}, {15121, 23294}, {15129, 36253}, {15311, 18388}, {16194, 51425}, {16235, 47206}, {16318, 63633}, {18390, 23332}, {18451, 59553}, {18553, 64035}, {18925, 34780}, {19127, 37515}, {21309, 40065}, {21850, 37489}, {23296, 63700}, {27371, 63548}, {30435, 62213}, {32062, 61606}, {32137, 61608}, {32140, 43595}, {32234, 37472}, {32247, 32251}, {32447, 59661}, {34380, 39588}, {35370, 63688}, {36412, 40349}, {36990, 61610}, {37477, 39871}, {37483, 48876}, {37487, 53023}, {37506, 48906}, {37589, 56814}, {37649, 64100}, {37688, 58782}, {39571, 40686}, {41585, 50977}, {41588, 44413}, {41602, 63422}, {43839, 46849}, {44870, 59659}, {46878, 47742}, {52102, 64026}, {52848, 61626}, {54050, 64094}, {54944, 60138}

X(64474) = midpoint of X(i) and X(j) for these {i,j}: {378, 427}, {7391, 44239}, {31133, 44285}, {31723, 44249}, {41602, 63422}
X(64474) = reflection of X(i) in X(j) for these {i,j}: {6676, 52262}, {7555, 3530}, {16618, 140}, {52262, 44236}
X(64474) = polar conjugate of X(54926)
X(64474) = X(48)-isoconjugate of X(54926)
X(64474) = X(1249)-Dao conjugate of X(54926)
X(64474) = barycentric quotient X(4)/X(54926)
X(64474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1596, 37942}, {2, 1597, 1596}, {3, 4, 37458}, {3, 1595, 6756}, {3, 3088, 1595}, {3, 7403, 9825}, {3, 37458, 37934}, {4, 5, 37984}, {4, 24, 10301}, {4, 140, 21841}, {4, 468, 64471}, {4, 631, 4232}, {4, 1656, 44960}, {4, 3515, 7715}, {4, 3516, 550}, {4, 3520, 10295}, {4, 3523, 3517}, {4, 3541, 5094}, {4, 4232, 1598}, {4, 5094, 5}, {4, 10295, 3575}, {4, 35478, 35491}, {4, 35483, 20}, {4, 35485, 37196}, {4, 35486, 25}, {4, 37118, 468}, {4, 37458, 6756}, {4, 37984, 44226}, {4, 49670, 382}, {4, 52290, 3089}, {5, 550, 50008}, {5, 1593, 13488}, {5, 12084, 31829}, {5, 13488, 44226}, {5, 15122, 140}, {5, 18281, 5159}, {25, 549, 37935}, {140, 3853, 25338}, {140, 15122, 16196}, {140, 16197, 7495}, {140, 16618, 6676}, {140, 25338, 10020}, {140, 64471, 468}, {235, 37119, 3628}, {376, 7378, 18494}, {381, 10257, 6677}, {403, 13596, 62962}, {403, 62958, 547}, {427, 44218, 44274}, {468, 37118, 140}, {468, 64471, 21841}, {546, 23336, 16238}, {548, 16198, 3575}, {550, 12084, 47337}, {550, 50008, 31829}, {578, 6247, 18914}, {631, 12082, 44210}, {858, 7527, 34664}, {1593, 3541, 5}, {1593, 5094, 4}, {1594, 1885, 546}, {1594, 14865, 1885}, {1595, 37458, 4}, {1907, 10301, 4}, {3516, 37196, 35485}, {3516, 62977, 37196}, {3520, 3575, 548}, {3520, 15559, 3575}, {3524, 6995, 55572}, {3575, 15559, 16198}, {3845, 44452, 44233}, {3861, 5498, 44232}, {5054, 18535, 6353}, {5064, 11410, 18533}, {5480, 23328, 11438}, {6623, 52299, 5055}, {6756, 37934, 37458}, {7499, 47091, 376}, {7526, 23335, 12362}, {7530, 18580, 34351}, {7530, 34351, 37897}, {7556, 34613, 37899}, {7576, 35473, 37931}, {7577, 10151, 5066}, {7715, 15712, 3515}, {9818, 44441, 1368}, {10295, 15559, 4}, {11250, 31833, 44247}, {11410, 18533, 8703}, {11425, 14216, 31804}, {12084, 50008, 550}, {12362, 47315, 14791}, {13488, 37984, 4}, {14782, 14783, 40132}, {14791, 23335, 47315}, {14813, 14814, 6823}, {14865, 35482, 1594}, {15118, 20417, 16270}, {15765, 18585, 44212}, {16618, 52262, 140}, {18281, 31861, 5}, {18560, 23047, 3853}, {18560, 52295, 23047}, {31829, 47337, 550}, {35473, 37931, 34200}, {35484, 37118, 4}, {35485, 37196, 550}, {35490, 63662, 12102}, {35502, 37119, 235}, {37196, 62977, 4}, {37931, 52285, 7576}, {42789, 42790, 7550}, {42807, 42808, 6642}, {44804, 44911, 46030}, {46030, 61736, 44911}, {62958, 62962, 403}

X(64475) = 85TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^7 - 2*a^6*b - 5*a^5*b^2 + 5*a^4*b^3 + 4*a^3*b^4 - 4*a^2*b^5 - a*b^6 + b^7 - 2*a^6*c + 4*a^5*b*c + a^4*b^2*c - 12*a^3*b^3*c + 2*a^2*b^4*c + 8*a*b^5*c - b^6*c - 5*a^5*c^2 + a^4*b*c^2 + 4*a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - 3*b^5*c^2 + 5*a^4*c^3 - 12*a^3*b*c^3 + 2*a^2*b^2*c^3 - 16*a*b^3*c^3 + 3*b^4*c^3 + 4*a^3*c^4 + 2*a^2*b*c^4 + a*b^2*c^4 + 3*b^3*c^4 - 4*a^2*c^5 + 8*a*b*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6 + c^7 : :
X(64475) = X[4] + 3 X[404], 2 X[140] - 3 X[52264], 5 X[1656] - 3 X[4187], 5 X[1656] + 3 X[37251], 7 X[3523] - 3 X[37403], 3 X[5046] - 11 X[5056], 13 X[5068] + 3 X[37256], 3 X[6903] - 19 X[61886], 3 X[57004] + 19 X[61937], X[5882] - 3 X[51714]

See Antreas Hatzipolakis and Peter Moses, euclid 6381.

X(64475) lies on these lines: {2, 3}, {119, 5270}, {355, 61534}, {496, 11501}, {952, 20323}, {2802, 11729}, {3035, 9955}, {3476, 37705}, {3847, 18407}, {4420, 5844}, {5432, 61268}, {5433, 61261}, {5557, 5660}, {5843, 60948}, {5882, 51714}, {5887, 61530}, {5901, 5919}, {6691, 18480}, {6692, 13369}, {6713, 19925}, {8227, 61533}, {10170, 34466}, {10200, 18491}, {10584, 18544}, {10680, 56879}, {10916, 38455}, {11230, 14150}, {11522, 12703}, {15325, 17606}, {22791, 25681}, {24474, 61551}, {24475, 61535}, {25917, 61524}, {30384, 61272}, {31937, 58405}, {38752, 63257}, {51709, 64123}, {61013, 61509}, {61259, 61521}, {61562, 64138}

X(64475) = midpoint of X(4187) and X(37251)
X(64475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 140, 16617}, {5, 6924, 37290}, {3560, 6964, 5}, {6911, 6944, 5}, {6918, 6959, 5}, {6946, 6979, 6842}, {6964, 6970, 3560}, {42807, 42808, 1012}

X(64476) = 86TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^7 - 2*a^6*b - 5*a^5*b^2 + 5*a^4*b^3 + 4*a^3*b^4 - 4*a^2*b^5 - a*b^6 + b^7 - 2*a^6*c + 4*a^5*b*c + a^4*b^2*c + 6*a^3*b^3*c + 2*a^2*b^4*c - 10*a*b^5*c - b^6*c - 5*a^5*c^2 + a^4*b*c^2 + 4*a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - 3*b^5*c^2 + 5*a^4*c^3 + 6*a^3*b*c^3 + 2*a^2*b^2*c^3 + 20*a*b^3*c^3 + 3*b^4*c^3 + 4*a^3*c^4 + 2*a^2*b*c^4 + a*b^2*c^4 + 3*b^3*c^4 - 4*a^2*c^5 - 10*a*b*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6 + c^7 : :
X(64476) = X[3] - 3 X[50202], X[4] + 3 X[405], 2 X[140] - 3 X[50205], 3 X[377] - 11 X[5056], 5 X[631] - 9 X[50714], 5 X[1656] - 3 X[8728], 5 X[1656] + 3 X[37234], 7 X[3090] - 3 X[44217], 5 X[3091] + 3 X[31156], 5 X[3522] - 21 X[50398], 7 X[3523] - 15 X[31259], 7 X[3523] - 3 X[37426], 7 X[3526] - 3 X[44284], 17 X[3533] - 21 X[50795], 4 X[3628] - 3 X[50395], 4 X[3850] + 3 X[50243], 7 X[3851] - 3 X[44229], 7 X[3851] + 3 X[50241], 3 X[5055] - X[50396], 13 X[5068] + 3 X[6872], 5 X[5071] - X[50397], 17 X[7486] - 9 X[50793], 5 X[31259] - X[37426], 8 X[35018] - 3 X[50238], 3 X[44222] - 7 X[55856], 3 X[44286] - 7 X[61976], 29 X[46935] - 21 X[50393], 15 X[50207] - 19 X[61886], 3 X[50239] - 23 X[61921], 3 X[50240] - 17 X[61919], 6 X[50394] - 7 X[55856], X[5882] - 3 X[51715], 5 X[8227] - X[10404], X[8550] - 3 X[51743], 5 X[11522] + 3 X[41229]

See Antreas Hatzipolakis and Peter Moses, euclid 6381.

X(64476) lies on these lines: {2, 3}, {9, 22791}, {226, 61272}, {329, 18493}, {355, 10389}, {518, 13464}, {946, 5302}, {950, 18357}, {1385, 63970}, {1490, 38028}, {1728, 39542}, {1864, 37737}, {3488, 37705}, {3586, 61261}, {3968, 43174}, {5049, 5777}, {5436, 34773}, {5771, 5806}, {5812, 38034}, {5817, 10283}, {5882, 51715}, {6147, 10396}, {6260, 11230}, {6684, 31822}, {7373, 8232}, {8227, 10404}, {8550, 51743}, {9612, 15325}, {9624, 30326}, {9955, 12572}, {10399, 16137}, {11522, 41229}, {18446, 51700}, {20418, 21635}, {22770, 38037}, {28212, 55104}, {31837, 61511}, {37531, 38108}, {38043, 64156}, {40273, 64004}, {56880, 63257}, {61259, 61533}

X(64476) = midpoint of X(i) and X(j) for these {i,j}: {946, 5302}, {8728, 37234}, {44229, 50241}
X(64476) = reflection of X(44222) in X(50394)
X(64476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 3560, 37281}, {5, 16617, 140}, {381, 16866, 6869}, {6832, 6907, 3628}, {6846, 6913, 5}, {6920, 8226, 31789}, {8226, 31789, 546}, {14784, 14785, 37436}, {16845, 37411, 549}, {42807, 42808, 19541}

X(64477) = 87TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^7 - 2*a^6*b - 5*a^5*b^2 + 5*a^4*b^3 + 4*a^3*b^4 - 4*a^2*b^5 - a*b^6 + b^7 - 2*a^6*c - 4*a^5*b*c + a^4*b^2*c + 2*a^2*b^4*c + 4*a*b^5*c - b^6*c - 5*a^5*c^2 + a^4*b*c^2 + 4*a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - 3*b^5*c^2 + 5*a^4*c^3 + 2*a^2*b^2*c^3 - 8*a*b^3*c^3 + 3*b^4*c^3 + 4*a^3*c^4 + 2*a^2*b*c^4 + a*b^2*c^4 + 3*b^3*c^4 - 4*a^2*c^5 + 4*a*b*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6 + c^7 : :
X(64477) = X[4] + 3 X[411], X[4] - 3 X[6842], 5 X[4] - 9 X[17577], 2 X[140] - 3 X[52265], 5 X[411] + 3 X[17577], 5 X[1656] - 3 X[6831], 5 X[3522] + 3 X[37437], 7 X[3523] - 3 X[6906], 7 X[3851] - 9 X[17530], 11 X[5056] - 3 X[6895], 5 X[6842] - 3 X[17577], 13 X[10299] - 9 X[17549], 11 X[15720] - 9 X[37298], 9 X[37299] - 17 X[62067], X[49135] - 9 X[62969], X[5882] - 3 X[51717]

See Antreas Hatzipolakis and Peter Moses, euclid 6381.

X(64477) lies on these lines: {2, 3}, {40, 37713}, {119, 59320}, {516, 31659}, {1319, 12433}, {2800, 31837}, {3035, 31663}, {3057, 5719}, {3428, 10942}, {3576, 61534}, {3579, 12608}, {4857, 14798}, {4999, 28160}, {5086, 28224}, {5119, 11374}, {5219, 59316}, {5690, 6261}, {5722, 37618}, {5844, 21740}, {5882, 49627}, {5887, 61524}, {6684, 31937}, {6690, 22793}, {6691, 17502}, {10572, 15325}, {11231, 12617}, {11729, 31786}, {12047, 28174}, {12115, 35252}, {12514, 47742}, {12699, 61533}, {22770, 32213}, {26446, 63988}, {26487, 64077}, {28150, 58404}, {28178, 61520}, {32760, 63273}, {34466, 40647}, {34753, 61660}, {38113, 54370}, {40263, 61539}, {61551, 64107}

X(64477) = midpoint of X(411) and X(6842)
X(64477) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 381, 6936}, {3, 6838, 37406}, {3, 37406, 37290}, {3, 37429, 548}, {4, 140, 16617}, {3560, 6988, 549}, {3651, 6960, 6882}, {6825, 6985, 5}, {6841, 6853, 3628}, {6848, 6883, 5}, {6853, 36002, 6841}, {6856, 6985, 44286}, {6863, 7580, 37356}, {6876, 6932, 7491}, {6876, 7491, 548}, {6908, 6911, 44222}, {14813, 14814, 37356}, {42807, 42808, 405}

X(64478) = (name pending)

Barycentrics    a^2*(a^6+b^6-3*b^5*c-4*b^4*c^2+7*b^3*c^3+2*b^2*c^4-4*b*c^5+c^6-2*a^5*(2*b+c)+a^4*(2*b^2+12*b*c-c^2)+a^3*(7*b^3-15*b^2*c-8*b*c^2+4*c^3)-a^2*(4*b^4+13*b^3*c-30*b^2*c^2+8*b*c^3+c^4)-a*(3*b^5-21*b^4*c+13*b^3*c^2+15*b^2*c^3-12*b*c^4+2*c^5))*(a^6+b^6-4*b^5*c+2*b^4*c^2+7*b^3*c^3-4*b^2*c^4-3*b*c^5+c^6-2*a^5*(b+2*c)+a^4*(-b^2+12*b*c+2*c^2)+a^3*(4*b^3-8*b^2*c-15*b*c^2+7*c^3)-a^2*(b^4+8*b^3*c-30*b^2*c^2+13*b*c^3+4*c^4)-a*(2*b^5-12*b^4*c+15*b^3*c^2+13*b^2*c^3-21*b*c^4+3*c^5)) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6386.

X(64478) lies on these lines: { }

X(64478) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(1293)}}, {{A, B, C, X(7), X(2827)}}, {{A, B, C, X(106), X(3531)}}, {{A, B, C, X(14484), X(53933)}}, {{A, B, C, X(52518), X(61424)}}

X(64479) = X(99)X(11332)∩X(1316)X(3734)

Barycentrics    (a^6*c^2+b^4*c^2*(b^2-c^2)+a^4*(b^4-2*b^2*c^2-c^4)+a^2*(-2*b^4*c^2+3*b^2*c^4))*(a^6*b^2-b^4*c^4+b^2*c^6+a^4*(-b^4-2*b^2*c^2+c^4)+a^2*(3*b^4*c^2-2*b^2*c^4)) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6386.

X(64479) lies on these lines: {99, 11332}, {543, 38947}, {1316, 3734}, {2782, 48947}, {23342, 44155}, {47285, 62489}

X(64479) = trilinear pole of line {3231, 47229}
X(64479) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5108)}}, {{A, B, C, X(4), X(1316)}}, {{A, B, C, X(6), X(99)}}, {{A, B, C, X(25), X(56957)}}, {{A, B, C, X(30), X(14052)}}, {{A, B, C, X(66), X(54925)}}, {{A, B, C, X(98), X(1344)}}, {{A, B, C, X(115), X(264)}}, {{A, B, C, X(148), X(1031)}}, {{A, B, C, X(262), X(690)}}, {{A, B, C, X(378), X(56962)}}, {{A, B, C, X(427), X(40856)}}, {{A, B, C, X(468), X(57594)}}, {{A, B, C, X(512), X(53704)}}, {{A, B, C, X(538), X(34537)}}, {{A, B, C, X(543), X(598)}}, {{A, B, C, X(669), X(11332)}}, {{A, B, C, X(671), X(3114)}}, {{A, B, C, X(843), X(46302)}}, {{A, B, C, X(1003), X(10754)}}, {{A, B, C, X(1593), X(56961)}}, {{A, B, C, X(1597), X(44889)}}, {{A, B, C, X(1916), X(45096)}}, {{A, B, C, X(1975), X(60501)}}, {{A, B, C, X(2418), X(5967)}}, {{A, B, C, X(2549), X(54124)}}, {{A, B, C, X(2787), X(2795)}}, {{A, B, C, X(2794), X(2797)}}, {{A, B, C, X(2799), X(60266)}}, {{A, B, C, X(3407), X(57552)}}, {{A, B, C, X(3613), X(9293)}}, {{A, B, C, X(3972), X(5969)}}, {{A, B, C, X(4185), X(56958)}}, {{A, B, C, X(5026), X(7757)}}, {{A, B, C, X(5094), X(56967)}}, {{A, B, C, X(5182), X(31859)}}, {{A, B, C, X(5186), X(9307)}}, {{A, B, C, X(9180), X(18575)}}, {{A, B, C, X(10484), X(57561)}}, {{A, B, C, X(10630), X(53919)}}, {{A, B, C, X(13481), X(42345)}}, {{A, B, C, X(32815), X(47735)}}, {{A, B, C, X(35906), X(47285)}}, {{A, B, C, X(36897), X(53221)}}, {{A, B, C, X(40513), X(60178)}}, {{A, B, C, X(43664), X(52239)}}, {{A, B, C, X(46648), X(54713)}}, {{A, B, C, X(48452), X(53196)}}, {{A, B, C, X(53603), X(62672)}}

X(64480) = 6TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    -a^16 b^2 + 5 a^14 b^4 - 9 a^12 b^6 + 5 a^10 b^8 + 5 a^8 b^10 - 9 a^6 b^12 + 5 a^4 b^14 - a^2 b^16 - a^16 c^2 - 2 a^14 b^2 c^2 + 3 a^12 b^4 c^2 + 13 a^10 b^6 c^2 - 23 a^8 b^8 c^2 + 13 a^6 b^10 c^2 - 6 a^4 b^12 c^2 + 4 a^2 b^14 c^2 - b^16 c^2 + 5 a^14 c^4 + 3 a^12 b^2 c^4 - 28 a^10 b^4 c^4 + 17 a^8 b^6 c^4 + 17 a^6 b^8 c^4 - 7 a^4 b^10 c^4 - 12 a^2 b^12 c^4 + 5 b^14 c^4 - 9 a^12 c^6 + 13 a^10 b^2 c^6 + 17 a^8 b^4 c^6 - 42 a^6 b^6 c^6 + 8 a^4 b^8 c^6 + 28 a^2 b^10 c^6 - 9 b^12 c^6 + 5 a^10 c^8 - 23 a^8 b^2 c^8 + 17 a^6 b^4 c^8 + 8 a^4 b^6 c^8 - 38 a^2 b^8 c^8 + 5 b^10 c^8 + 5 a^8 c^10 + 13 a^6 b^2 c^10 - 7 a^4 b^4 c^10 + 28 a^2 b^6 c^10 + 5 b^8 c^10 - 9 a^6 c^12 - 6 a^4 b^2 c^12 - 12 a^2 b^4 c^12 - 9 b^6 c^12 + 5 a^4 c^14 + 4 a^2 b^2 c^14 + 5 b^4 c^14 - a^2 c^16 - b^2 c^16 + 4 a^13 b c OH S - 6 a^11 b^3 c OH S - 6 a^9 b^5 c OH S + 10 a^7 b^7 c OH S + 6 a^5 b^9 c OH S - 12 a^3 b^11 c OH S + 4 a b^13 c OH S - 6 a^11 b c^3 OH S + 24 a^9 b^3 c^3 OH S - 12 a^7 b^5 c^3 OH S - 24 a^5 b^7 c^3 OH S + 30 a^3 b^9 c^3 OH S - 12 a b^11 c^3 OH S - 6 a^9 b c^5 OH S - 12 a^7 b^3 c^5 OH S + 36 a^5 b^5 c^5 OH S - 18 a^3 b^7 c^5 OH S + 12 a b^9 c^5 OH S + 10 a^7 b c^7 OH S - 24 a^5 b^3 c^7 OH S - 18 a^3 b^5 c^7 OH S - 8 a b^7 c^7 OH S + 6 a^5 b c^9 OH S + 30 a^3 b^3 c^9 OH S + 12 a b^5 c^9 OH S - 12 a^3 b c^11 OH S - 12 a b^3 c^11 OH S + 4 a b c^13 OH S : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6388.

X(64480) lies on these lines: {2, 3), {542, 44123}, {1989, 8106}, {8115, 45016}, {13415, 18374}, {15360, 24650}, {32225, 44125}

X(64481) = 7TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    -a^16 b^2 + 5 a^14 b^4 - 9 a^12 b^6 + 5 a^10 b^8 + 5 a^8 b^10 - 9 a^6 b^12 + 5 a^4 b^14 - a^2 b^16 - a^16 c^2 - 2 a^14 b^2 c^2 + 3 a^12 b^4 c^2 + 13 a^10 b^6 c^2 - 23 a^8 b^8 c^2 + 13 a^6 b^10 c^2 - 6 a^4 b^12 c^2 + 4 a^2 b^14 c^2 - b^16 c^2 + 5 a^14 c^4 + 3 a^12 b^2 c^4 - 28 a^10 b^4 c^4 + 17 a^8 b^6 c^4 + 17 a^6 b^8 c^4 - 7 a^4 b^10 c^4 - 12 a^2 b^12 c^4 + 5 b^14 c^4 - 9 a^12 c^6 + 13 a^10 b^2 c^6 + 17 a^8 b^4 c^6 - 42 a^6 b^6 c^6 + 8 a^4 b^8 c^6 + 28 a^2 b^10 c^6 - 9 b^12 c^6 + 5 a^10 c^8 - 23 a^8 b^2 c^8 + 17 a^6 b^4 c^8 + 8 a^4 b^6 c^8 - 38 a^2 b^8 c^8 + 5 b^10 c^8 + 5 a^8 c^10 + 13 a^6 b^2 c^10 - 7 a^4 b^4 c^10 + 28 a^2 b^6 c^10 + 5 b^8 c^10 - 9 a^6 c^12 - 6 a^4 b^2 c^12 - 12 a^2 b^4 c^12 - 9 b^6 c^12 + 5 a^4 c^14 + 4 a^2 b^2 c^14 + 5 b^4 c^14 - a^2 c^16 - b^2 c^16 - 4 a^13 b c OH S + 6 a^11 b^3 c OH S + 6 a^9 b^5 c OH S - 10 a^7 b^7 c OH S - 6 a^5 b^9 c OH S + 12 a^3 b^11 c OH S - 4 a b^13 c OH S + 6 a^11 b c^3 OH S - 24 a^9 b^3 c^3 OH S + 12 a^7 b^5 c^3 OH S + 24 a^5 b^7 c^3 OH S - 30 a^3 b^9 c^3 OH S + 12 a b^11 c^3 OH S + 6 a^9 b c^5 OH S + 12 a^7 b^3 c^5 OH S - 36 a^5 b^5 c^5 OH S + 18 a^3 b^7 c^5 OH S - 12 a b^9 c^5 OH S - 10 a^7 b c^7 OH S + 24 a^5 b^3 c^7 OH S + 18 a^3 b^5 c^7 OH S + 8 a b^7 c^7 OH S - 6 a^5 b c^9 OH S - 30 a^3 b^3 c^9 OH S - 12 a b^5 c^9 OH S + 12 a^3 b c^11 OH S + 12 a b^3 c^11 OH S - 4 a b c^13 OH S : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6388.

X(64481) lies on these lines: {2, 3}, {542, 44124}, {1989, 8105}, {8116, 45016}, {13414, 18374}, {15360, 24651}, {32225, 44126}

X(64482) = 8TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    -2 a^12 + 6 a^10 b^2 - 13 a^8 b^4 + 5 a^6 b^6 + 7 a^4 b^8 - 5 a^2 b^10 + 2 b^12 + 6 a^10 c^2 - 2 a^8 b^2 c^2 + 11 a^6 b^4 c^2 - 19 a^4 b^6 c^2 + 7 a^2 b^8 c^2 - 9 b^10 c^2 - 13 a^8 c^4 + 11 a^6 b^2 c^4 + 6 a^4 b^4 c^4 + 22 b^8 c^4 + 5 a^6 c^6 - 19 a^4 b^2 c^6 - 30 b^6 c^6 + 7 a^4 c^8 + 7 a^2 b^2 c^8 + 22 b^4 c^8 - 5 a^2 c^10 - 9 b^2 c^10 + 2 c^12 - 2 a^10 W + 5 a^8 b^2 W + 6 a^6 b^4 W - 7 a^4 b^6 W - 4 a^2 b^8 W + 2 b^10 W + 5 a^8 c^2 W - 30 a^6 b^2 c^2 W + 14 a^4 b^4 c^2 W + 25 a^2 b^6 c^2 W - 8 b^8 c^2 W + 6 a^6 c^4 W + 14 a^4 b^2 c^4 W - 46 a^2 b^4 c^4 W + 6 b^6 c^4 W - 7 a^4 c^6 W + 25 a^2 b^2 c^6 W + 6 b^4 c^6 W - 4 a^2 c^8 W - 8 b^2 c^8 W + 2 c^10 W : : where W^2 = a^4 - a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2 + c^4

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6388.

X(64482) lies on these lines: {2, 3}, {2028, 31862}, {3413, 6321}

X(64483) = 9TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    -2 a^12 + 6 a^10 b^2 - 13 a^8 b^4 + 5 a^6 b^6 + 7 a^4 b^8 - 5 a^2 b^10 + 2 b^12 + 6 a^10 c^2 - 2 a^8 b^2 c^2 + 11 a^6 b^4 c^2 - 19 a^4 b^6 c^2 + 7 a^2 b^8 c^2 - 9 b^10 c^2 - 13 a^8 c^4 + 11 a^6 b^2 c^4 + 6 a^4 b^4 c^4 + 22 b^8 c^4 + 5 a^6 c^6 - 19 a^4 b^2 c^6 - 30 b^6 c^6 + 7 a^4 c^8 + 7 a^2 b^2 c^8 + 22 b^4 c^8 - 5 a^2 c^10 - 9 b^2 c^10 + 2 c^12 + 2 a^10 W - 5 a^8 b^2 W - 6 a^6 b^4 W + 7 a^4 b^6 W + 4 a^2 b^8 W - 2 b^10 W - 5 a^8 c^2 W + 30 a^6 b^2 c^2 W - 14 a^4 b^4 c^2 W - 25 a^2 b^6 c^2 W + 8 b^8 c^2 W - 6 a^6 c^4 W - 14 a^4 b^2 c^4 W + 46 a^2 b^4 c^4 W - 6 b^6 c^4 W + 7 a^4 c^6 W - 25 a^2 b^2 c^6 W - 6 b^4 c^6 W + 4 a^2 c^8 W + 8 b^2 c^8 W - 2 c^10 W : : where W^2 = a^4 - a^2 b^2 + b^4 - a^2 c^2 - b^2 c^2 + c^4

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6388.

X(64483) lies on these lines: {2, 3}, {2029, 31863}, {3414, 6321}

X(64484) = 88TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(2*a^5 - a^4*b - a^3*b^2 - a^2*b^3 - 2*a*b^4 + b^5 - a^4*c + 2*a^2*b^2*c + b^4*c - a^3*c^2 + 2*a^2*b*c^2 + 4*a*b^2*c^2 - 2*b^3*c^2 - a^2*c^3 - 2*b^2*c^3 - 2*a*c^4 + b*c^4 + c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6416.

X(64484) lies on these lines: {2, 3}, {99, 44435}, {110, 2692}, {476, 1293}, {523, 4427}, {691, 9059}, {1290, 34594}, {1291, 26713}, {4570, 15343}, {9088, 53895}, {10420, 32704}

X(64484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7475, 7477, 36167}, {7477, 50403, 7479}

X(64485) = 89TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - 3*a^2*b^10 + b^12 + a^10*c^2 - 4*a^8*b^2*c^2 + 5*a^6*b^4*c^2 - 6*a^4*b^6*c^2 + 8*a^2*b^8*c^2 - 4*b^10*c^2 - 3*a^8*c^4 + 5*a^6*b^2*c^4 + 2*a^4*b^4*c^4 - 5*a^2*b^6*c^4 + 7*b^8*c^4 + 2*a^6*c^6 - 6*a^4*b^2*c^6 - 5*a^2*b^4*c^6 - 8*b^6*c^6 + 2*a^4*c^8 + 8*a^2*b^2*c^8 + 7*b^4*c^8 - 3*a^2*c^10 - 4*b^2*c^10 + c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6416.

X(64485) lies on these lines: {2, 3}, {107, 53960}, {110, 1291}, {476, 930}, {523, 50947}, {691, 58975}, {925, 39198}, {933, 10420}, {1304, 20185}, {1624, 60605}, {1634, 14480}, {9060, 53884}, {13398, 53962}, {16166, 33639}, {20626, 53953}, {25150, 38896}, {53695, 53945}

X(64485) = X(656)-isoconjugate of X(53930)
X(64485) = X(i)-Dao conjugate of X(j) for these (i,j): {40596, 53930}, {45180, 523}
X(64485) = crossdifference of every pair of points on line {647, 10413}
X(64485) = barycentric product X(99)*X(47226)
X(64485) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 53930}, {47226, 523}
X(64485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7468, 40049, 7471}, {7471, 40049, 15329}

X(64486) = X(5)X(49)∩X(30)X(6689)

Barycentrics    2 a^10 - 9 a^8 b^2 + 12 a^6 b^4 - 2 a^4 b^6 - 6 a^2 b^8 + 3 b^10 - 9 a^8 c^2 + 6 a^6 b^2 c^2 + 11 a^4 b^4 c^2 + a^2 b^6 c^2 - 9 b^8 c^2 + 12 a^6 c^4 + 11 a^4 b^2 c^4 + 10 a^2 b^4 c^4 + 6 b^6 c^4 - 2 a^4 c^6 + a^2 b^2 c^6 + 6 b^4 c^6 - 6 a^2 c^8 - 9 b^2 c^8 + 3 c^10 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6418.

X(64486) lies on these lines: {2, 12307}, {5, 49}, {30, 6689}, {140, 3574}, {195, 3090}, {539, 10109}, {546, 10610}, {547, 1209}, {549, 15800}, {632, 7691}, {973, 58531}, {1154, 3628}, {1216, 44056}, {1493, 12812}, {1656, 11803}, {2888, 5055}, {3519, 61907}, {3545, 48675}, {3850, 18400}, {3851, 12254}, {5066, 22804}, {5079, 55039}, {6759, 32351}, {7173, 47378}, {7486, 12325}, {9827, 58465}, {9905, 61268}, {10066, 10593}, {10082, 10592}, {10115, 11591}, {10289, 10615}, {10619, 61940}, {10628, 12006}, {11271, 61911}, {11424, 46029}, {11576, 37942}, {11702, 23515}, {11802, 13363}, {11805, 61548}, {11808, 12010}, {12046, 12900}, {12060, 32744}, {12242, 13565}, {12266, 18357}, {12300, 62958}, {12363, 63667}, {12965, 42583}, {12971, 42582}, {13163, 44516}, {13365, 15350}, {13376, 18874}, {13595, 44515}, {14071, 23516}, {14449, 41590}, {14845, 44325}, {15026, 32352}, {15061, 43899}, {15801, 21357}, {15957, 61594}, {16239, 32348}, {18538, 49257}, {18762, 49256}, {20193, 58805}, {20376, 64027}, {31834, 37454}, {32401, 51491}, {34599, 58432}, {44904, 61659}, {48154, 54201}, {54157, 55856}, {54202, 55857}

X(64487) = X(5)X(14)∩X(511)X(6673)

Barycentrics    3 (2 a^20-11 a^18 b^2+16 a^16 b^4+35 a^14 b^6-179 a^12 b^8+321 a^10 b^10-311 a^8 b^12+171 a^6 b^14-49 a^4 b^16+4 a^2 b^18+b^20-11 a^18 c^2+20 a^16 b^2 c^2+55 a^14 b^4 c^2-219 a^12 b^6 c^2+182 a^10 b^8 c^2+173 a^8 b^10 c^2-372 a^6 b^12 c^2+227 a^4 b^14 c^2-54 a^2 b^16 c^2-b^18 c^2+16 a^16 c^4+55 a^14 b^2 c^4-220 a^12 b^4 c^4+335 a^10 b^6 c^4-277 a^8 b^8 c^4+486 a^6 b^10 c^4-456 a^4 b^12 c^4+210 a^2 b^14 c^4-23 b^16 c^4+35 a^14 c^6-219 a^12 b^2 c^6+335 a^10 b^4 c^6-276 a^8 b^6 c^6-168 a^6 b^8 c^6+459 a^4 b^10 c^6-361 a^2 b^12 c^6+114 b^14 c^6-179 a^12 c^8+182 a^10 b^2 c^8-277 a^8 b^4 c^8-168 a^6 b^6 c^8-326 a^4 b^8 c^8+201 a^2 b^10 c^8-258 b^12 c^8+321 a^10 c^10+173 a^8 b^2 c^10+486 a^6 b^4 c^10+459 a^4 b^6 c^10+201 a^2 b^8 c^10+334 b^10 c^10-311 a^8 c^12-372 a^6 b^2 c^12-456 a^4 b^4 c^12-361 a^2 b^6 c^12-258 b^8 c^12+171 a^6 c^14+227 a^4 b^2 c^14+210 a^2 b^4 c^14+114 b^6 c^14-49 a^4 c^16-54 a^2 b^2 c^16-23 b^4 c^16+4 a^2 c^18-b^2 c^18+c^20)+2 (6 a^18-43 a^16 b^2+141 a^14 b^4-266 a^12 b^6+281 a^10 b^8-126 a^8 b^10-35 a^6 b^12+68 a^4 b^14-33 a^2 b^16+7 b^18-43 a^16 c^2+158 a^14 b^2 c^2-228 a^12 b^4 c^2+27 a^10 b^6 c^2+294 a^8 b^8 c^2-233 a^6 b^10 c^2-8 a^4 b^12 c^2+73 a^2 b^14 c^2-40 b^16 c^2+141 a^14 c^4-228 a^12 b^2 c^4+300 a^10 b^4 c^4-192 a^8 b^6 c^4+361 a^6 b^8 c^4-96 a^4 b^10 c^4+12 a^2 b^12 c^4+107 b^14 c^4-266 a^12 c^6+27 a^10 b^2 c^6-192 a^8 b^4 c^6-660 a^6 b^6 c^6+135 a^4 b^8 c^6-318 a^2 b^10 c^6-151 b^12 c^6+281 a^10 c^8+294 a^8 b^2 c^8+361 a^6 b^4 c^8+135 a^4 b^6 c^8+532 a^2 b^8 c^8+77 b^10 c^8-126 a^8 c^10-233 a^6 b^2 c^10-96 a^4 b^4 c^10-318 a^2 b^6 c^10+77 b^8 c^10-35 a^6 c^12-8 a^4 b^2 c^12+12 a^2 b^4 c^12-151 b^6 c^12+68 a^4 c^14+73 a^2 b^2 c^14+107 b^4 c^14-33 a^2 c^16-40 b^2 c^16+7 c^18) T : : where T= S Sqrt[3]

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6418.

X(64487) lies on these lines: {5, 14}, {511, 6673}, {629, 61538}, {1656, 44776}, {20252, 22832}, {23514, 25608}, {31705, 39590}, {49106, 51753}

X(64488) = X(5)X(13)∩X(511)X(6674)

Barycentrics    3 (2 a^20-11 a^18 b^2+16 a^16 b^4+35 a^14 b^6-179 a^12 b^8+321 a^10 b^10-311 a^8 b^12+171 a^6 b^14-49 a^4 b^16+4 a^2 b^18+b^20-11 a^18 c^2+20 a^16 b^2 c^2+55 a^14 b^4 c^2-219 a^12 b^6 c^2+182 a^10 b^8 c^2+173 a^8 b^10 c^2-372 a^6 b^12 c^2+227 a^4 b^14 c^2-54 a^2 b^16 c^2-b^18 c^2+16 a^16 c^4+55 a^14 b^2 c^4-220 a^12 b^4 c^4+335 a^10 b^6 c^4-277 a^8 b^8 c^4+486 a^6 b^10 c^4-456 a^4 b^12 c^4+210 a^2 b^14 c^4-23 b^16 c^4+35 a^14 c^6-219 a^12 b^2 c^6+335 a^10 b^4 c^6-276 a^8 b^6 c^6-168 a^6 b^8 c^6+459 a^4 b^10 c^6-361 a^2 b^12 c^6+114 b^14 c^6-179 a^12 c^8+182 a^10 b^2 c^8-277 a^8 b^4 c^8-168 a^6 b^6 c^8-326 a^4 b^8 c^8+201 a^2 b^10 c^8-258 b^12 c^8+321 a^10 c^10+173 a^8 b^2 c^10+486 a^6 b^4 c^10+459 a^4 b^6 c^10+201 a^2 b^8 c^10+334 b^10 c^10-311 a^8 c^12-372 a^6 b^2 c^12-456 a^4 b^4 c^12-361 a^2 b^6 c^12-258 b^8 c^12+171 a^6 c^14+227 a^4 b^2 c^14+210 a^2 b^4 c^14+114 b^6 c^14-49 a^4 c^16-54 a^2 b^2 c^16-23 b^4 c^16+4 a^2 c^18-b^2 c^18+c^20)-2 (6 a^18-43 a^16 b^2+141 a^14 b^4-266 a^12 b^6+281 a^10 b^8-126 a^8 b^10-35 a^6 b^12+68 a^4 b^14-33 a^2 b^16+7 b^18-43 a^16 c^2+158 a^14 b^2 c^2-228 a^12 b^4 c^2+27 a^10 b^6 c^2+294 a^8 b^8 c^2-233 a^6 b^10 c^2-8 a^4 b^12 c^2+73 a^2 b^14 c^2-40 b^16 c^2+141 a^14 c^4-228 a^12 b^2 c^4+300 a^10 b^4 c^4-192 a^8 b^6 c^4+361 a^6 b^8 c^4-96 a^4 b^10 c^4+12 a^2 b^12 c^4+107 b^14 c^4-266 a^12 c^6+27 a^10 b^2 c^6-192 a^8 b^4 c^6-660 a^6 b^6 c^6+135 a^4 b^8 c^6-318 a^2 b^10 c^6-151 b^12 c^6+281 a^10 c^8+294 a^8 b^2 c^8+361 a^6 b^4 c^8+135 a^4 b^6 c^8+532 a^2 b^8 c^8+77 b^10 c^8-126 a^8 c^10-233 a^6 b^2 c^10-96 a^4 b^4 c^10-318 a^2 b^6 c^10+77 b^8 c^10-35 a^6 c^12-8 a^4 b^2 c^12+12 a^2 b^4 c^12-151 b^6 c^12+68 a^4 c^14+73 a^2 b^2 c^14+107 b^4 c^14-33 a^2 c^16-40 b^2 c^16+7 c^18) T : : where T= S Sqrt[3]

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6418.

X(64488) lies on these lines: {5, 13}, {511, 6674}, {630, 61537}, {1656, 44777}, {20253, 22831}, {23514, 25609}, {31706, 39590}, {49105, 51754}

X(64489) = X(2)X(3937)∩X(511)X(3911)

Barycentrics    a (a^3 b^2 - a b^4 - 4 a^3 b c + 2 a^2 b^2 c + 4 a b^3 c - 2 b^4 c + a^3 c^2 + 2 a^2 b c^2 - 8 a b^2 c^2 + 2 b^3 c^2 + 4 a b c^3 + 2 b^2 c^3 - a c^4 - 2 b c^4) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6429.

X(64489) lies on these lines: {2, 3937}, {5, 44313}, {11, 29349}, {100, 61674}, {140, 46174}, {182, 36059}, {405, 36058}, {496, 53002}, {511, 3911}, {513, 6667}, {517, 18240}, {1086, 52827}, {1125, 2841}, {1155, 29309}, {1357,17719}, {1387, 53790}, {2808, 13226}, {2810, 3035}, {2818, 6713}, {2842, 58453}, {2850, 6723}, {3784, 31231}, {3819,59491}, {5265, 31785}, {5435, 37521}, {5439, 15906}, {5482, 12109}, {6085, 53580}, {6688, 6692}, {6705, 44870}, {7413, 40420}, {9957, 59812}, {11028, 11227}, {12433, 14131}, {13747, 29958}, {14115, 22102}, {15082, 54357}, {15325, 35059}, {15488, 15803}, {15507, 53389}, {15635, 55317}, {17566, 23154}, {18191, 43055}, {21154, 31849}, {23841, 58405}, {24465, 53792}, {25524, 53294}, {26892, 31224}, {28239, 53393}, {31272, 38389}, {37365, 40687}, {37646, 40649}, {38390, 45310}, {38604, 60687}, {58447, 58460}, {58535, 64124}

X(64490) = X(99)X(6784)∩X(115)X(3111)

Barycentrics    a^2 (a^4 b^4 - a^2 b^6 - 4 a^4 b^2 c^2 + 3 a^2 b^4 c^2 - 2 b^6 c^2 + a^4 c^4 + 3 a^2 b^2 c^4 + 2 b^4 c^4 - a^2 c^6 - 2 b^2 c^6) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6429.

X(64490) lies on these lines: {99, 6784}, {115, 3111}, {140, 46172}, {182, 32661}, {230, 35060}, {368, 369}, {512, 6722}, {620, 34383}, {2387, 58448}, {2871, 58503}, {2882, 3589}, {4173, 7907}, {5254, 58211}, {6723, 9517}, {7807, 63556}, {7857, 40951}, {9292, 32969}, {9429, 40478}, {11285, 17970}, {14113, 22103}, {14984, 48378}, {15630, 55312}, {31850, 38737}, {32970, 63555}, {33233, 63554}, {37514, 52170}, {38739, 41330}, {39469, 44818}

X(64491) = X(49)X(182)∩X(64)X(399)

Barycentrics    a^2 (4 a^8 - 12 a^6 b^2 + 12 a^4 b^4 - 4 a^2 b^6 - 12 a^6 c^2 + 15 a^4 b^2 c^2 - 5 a^2 b^4 c^2 + 2 b^6 c^2 + 12 a^4 c^4 - 5 a^2 b^2 c^4 - 4 b^4 c^4 - 4 a^2 c^6 + 2 b^2 c^6) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6435.

X(64491) lies on these lines: {3, 9544}, {5, 11935}, {24, 2914}, {49, 182}, {54, 1656}, {64, 399}, {110, 382}, {155, 12893}, {156, 3534}, {184, 15720}, {381, 1147}, {567, 61911}, {569, 61887}, {578, 61937}, {1092, 8717}, {1385, 3683}, {1614, 62100}, {1657, 5895}, {2070, 8907}, {2937, 15577}, {3043, 37197}, {3167, 9932}, {3200, 42988}, {3201, 42989}, {3527, 18369}, {5012, 61850}, {5054, 9704}, {5055, 9545}, {5072, 43614}, {5076, 10539}, {5079, 9306}, {5093, 7506}, {6090, 40913}, {9586, 18493}, {9705, 61811}, {9706, 61878}, {9716, 16881}, {10282, 54048}, {10540, 49136}, {10984, 15706}, {11003, 55863}, {11477, 12584}, {11898, 64061}, {12111, 35496}, {12164, 37955}, {12307, 17821}, {12315, 18859}, {13346, 62040}, {13352, 61990}, {13353, 61875}, {13432, 52417}, {14093, 52525}, {14157, 49133}, {15040, 45248}, {18445, 22962}, {20125, 44271}, {32046, 55858}, {34148, 61984}, {34783, 43898}, {35495, 64027}, {37453, 59279}, {37471, 61847}, {37477, 62170}, {37495, 62016}, {43574, 49137}, {43598, 61946}, {43651, 61883}, {43652, 62073}, {44470, 51175} ,{45831, 50461}, {60462, 64033}, {61134, 61826}, {61752, 62085}, {61799, 64049}

X(64491) = reflection of X(11999) in X(3)

X(64492) = 10TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    4 a^16-12 a^14 b^2+14 a^12 b^4-26 a^10 b^6+60 a^8 b^8-64 a^6 b^10+22 a^4 b^12+6 a^2 b^14-4 b^16-12 a^14 c^2+62 a^12 b^2 c^2-93 a^10 b^4 c^2+104 a^6 b^8 c^2-60 a^4 b^10 c^2-15 a^2 b^12 c^2+14 b^14 c^2+14 a^12 c^4-93 a^10 b^2 c^4+108 a^8 b^4 c^4-16 a^6 b^6 c^4-18 a^4 b^8 c^4+9 a^2 b^10 c^4-4 b^12 c^4-26 a^10 c^6-16 a^6 b^4 c^6+112 a^4 b^6 c^6-46 b^10 c^6+60 a^8 c^8+104 a^6 b^2 c^8-18 a^4 b^4 c^8+80 b^8 c^8-64 a^6 c^10-60 a^4 b^2 c^10+9 a^2 b^4 c^10-46 b^6 c^10+22 a^4 c^12-15 a^2 b^2 c^12-4 b^4 c^12+6 a^2 c^14+14 b^2 c^14-4 c^16-8 Sqrt[3] (2 a^8 b^2-4 a^6 b^4+4 a^2 b^8-2 b^10+2 a^8 c^2+6 a^6 b^2 c^2-7 a^4 b^4 c^2-7 a^2 b^6 c^2+6 b^8 c^2-4 a^6 c^4-7 a^4 b^2 c^4+6 a^2 b^4 c^4-4 b^6 c^4-7 a^2 b^2 c^6-4 b^4 c^6+4 a^2 c^8+6 b^2 c^8-2 c^10) S^3 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6444.

X(64492) lies on these lines: {2, 3}, {10217, 54556}, {13202, 46833}, {13598, 33957}, {16657, 61537}

X(64493) = 11TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    4 a^16-12 a^14 b^2+14 a^12 b^4-26 a^10 b^6+60 a^8 b^8-64 a^6 b^10+22 a^4 b^12+6 a^2 b^14-4 b^16-12 a^14 c^2+62 a^12 b^2 c^2-93 a^10 b^4 c^2+104 a^6 b^8 c^2-60 a^4 b^10 c^2-15 a^2 b^12 c^2+14 b^14 c^2+14 a^12 c^4-93 a^10 b^2 c^4+108 a^8 b^4 c^4-16 a^6 b^6 c^4-18 a^4 b^8 c^4+9 a^2 b^10 c^4-4 b^12 c^4-26 a^10 c^6-16 a^6 b^4 c^6+112 a^4 b^6 c^6-46 b^10 c^6+60 a^8 c^8+104 a^6 b^2 c^8-18 a^4 b^4 c^8+80 b^8 c^8-64 a^6 c^10-60 a^4 b^2 c^10+9 a^2 b^4 c^10-46 b^6 c^10+22 a^4 c^12-15 a^2 b^2 c^12-4 b^4 c^12+6 a^2 c^14+14 b^2 c^14-4 c^16+8 Sqrt[3] (2 a^8 b^2-4 a^6 b^4+4 a^2 b^8-2 b^10+2 a^8 c^2+6 a^6 b^2 c^2-7 a^4 b^4 c^2-7 a^2 b^6 c^2+6 b^8 c^2-4 a^6 c^4-7 a^4 b^2 c^4+6 a^2 b^4 c^4-4 b^6 c^4-7 a^2 b^2 c^6-4 b^4 c^6+4 a^2 c^8+6 b^2 c^8-2 c^10) S^3 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6344.

X(64493) lies on these lines: {2, 3}, {10218, 54557}, {13202, 46834}, {13598, 33958}, {16657, 61538}

X(64494) = X(3)X(1369)∩X(114)X(140)

Barycentrics   2 a^10 + 3 a^8 b^2 - 2 a^6 b^4 - 2 a^4 b^6 - b^10 + 3 a^8 c^2 - 6 a^6 b^2 c^2 - 9 a^4 b^4 c^2 - a^2 b^6 c^2 + b^8 c^2 - 2 a^6 c^4 - 9 a^4 b^2 c^4 - 6 a^2 b^4 c^4 - 2 a^4 c^6 - a^2 b^2 c^6 + b^2 c^8 - c^10 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6444.

X(64494) lies on these lines: {3, 1369}, {5, 8793}, {114, 140}, {14880, 50136}, {15321, 40441}

X(64495) = X(4)X(69)∩X(95)X(1975)

Barycentrics    b^2*c^2*(a^4+3*(b^2-c^2)^2-4*a^2*(b^2+c^2)) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6455.

X(64495) lies on these lines: {2, 54636}, {4, 69}, {95, 1975}, {183, 16276}, {305, 7539}, {1238, 7752}, {3589, 40814}, {3763, 41760}, {7499, 37688}, {7782, 18354}, {8024, 63098}, {8797, 32818}, {9723, 52712}, {15466, 37638}, {16197, 41009}, {18022, 62275}, {20563, 63173}, {30737, 59343}, {31995, 34388}, {32087, 34387}, {32807, 34392}, {32832, 40697}, {32834, 40680}, {39998, 62698}, {40032, 57897}, {45198, 64093}, {51128, 53474}, {51171, 51481}, {52347, 59635}, {52581, 57909}

X(64495) = isotomic conjugate of X(43908)
X(64495) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 43908}, {560, 36948}, {9247, 60161}
X(64495) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43908}, {3090, 17809}, {6374, 36948}, {11427, 19357}, {62576, 60161}
X(64495) = pole of line {3, 13366} with respect to the Wallace hyperbola
X(64495) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(3090)}}, {{A, B, C, X(95), X(32001)}}, {{A, B, C, X(264), X(54636)}}, {{A, B, C, X(305), X(1232)}}, {{A, B, C, X(317), X(63173)}}, {{A, B, C, X(511), X(36751)}}, {{A, B, C, X(1843), X(9777)}}, {{A, B, C, X(14615), X(57909)}}, {{A, B, C, X(18022), X(44149)}}, {{A, B, C, X(32000), X(57897)}}, {{A, B, C, X(54412), X(55553)}}, {{A, B, C, X(57907), X(58782)}}
X(64495) = barycentric product X(i)*X(j) for these (i, j): {1502, 9777}, {3090, 76}, {18022, 36751}
X(64495) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43908}, {76, 36948}, {264, 60161}, {3090, 6}, {9777, 32}, {36751, 184} X(64495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 11185, 32002}, {76, 14615, 1232}, {76, 264, 44149}, {264, 44149, 44133}, {311, 1232, 44135}, {1232, 44135, 14615}, {14615, 44135, 264}

X(64496) = (name pending)

Barycentrics    (a-b) (a+b) (a-c) (a+c) (a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^6-a^4 b^2-4 a^2 b^4+3 b^6-2 a^4 c^2+7 a^2 b^2 c^2-4 b^4 c^2-2 a^2 c^4-b^2 c^4+2 c^6) (2 a^6-2 a^4 b^2-2 a^2 b^4+2 b^6-a^4 c^2+7 a^2 b^2 c^2-b^4 c^2-4 a^2 c^4-4 b^2 c^4+3 c^6) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6457.

X(64496) lies on this line: {107,14480}

X(64497) = X(74)X(323)∩X(526)X(5961)

Barycentrics    a^2 (a^20-5 a^18 b^2+8 a^16 b^4+a^14 b^6-21 a^12 b^8+35 a^10 b^10-35 a^8 b^12+27 a^6 b^14-16 a^4 b^16+6 a^2 b^18-b^20-5 a^18 c^2+24 a^16 b^2 c^2-43 a^14 b^4 c^2+31 a^12 b^6 c^2-3 a^10 b^8 c^2+5 a^8 b^10 c^2-29 a^6 b^12 c^2+33 a^4 b^14 c^2-16 a^2 b^16 c^2+3 b^18 c^2+8 a^16 c^4-43 a^14 b^2 c^4+81 a^12 b^4 c^4-67 a^10 b^6 c^4+17 a^8 b^8 c^4+18 a^6 b^10 c^4-22 a^4 b^12 c^4+8 a^2 b^14 c^4+a^14 c^6+31 a^12 b^2 c^6-67 a^10 b^4 c^6+52 a^8 b^6 c^6-18 a^6 b^8 c^6-a^4 b^10 c^6+12 a^2 b^12 c^6-10 b^14 c^6-21 a^12 c^8-3 a^10 b^2 c^8+17 a^8 b^4 c^8-18 a^6 b^6 c^8+12 a^4 b^8 c^8-10 a^2 b^10 c^8+17 b^12 c^8+35 a^10 c^10+5 a^8 b^2 c^10+18 a^6 b^4 c^10-a^4 b^6 c^10-10 a^2 b^8 c^10-18 b^10 c^10-35 a^8 c^12-29 a^6 b^2 c^12-22 a^4 b^4 c^12+12 a^2 b^6 c^12+17 b^8 c^12+27 a^6 c^14+33 a^4 b^2 c^14+8 a^2 b^4 c^14-10 b^6 c^14-16 a^4 c^16-16 a^2 b^2 c^16+6 a^2 c^18+3 b^2 c^18-c^20) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6461.

X(64497) lies on these lines: {74, 323}, {526, 5961}, {924, 13289}, {5663, 13496}, {13557, 22584}

X(64498) = X(3)X(74)∩X(26)X(5504)

Barycentrics    a^2 (2 a^14-7 a^12 b^2+6 a^10 b^4+5 a^8 b^6-10 a^6 b^8+3 a^4 b^10+2 a^2 b^12-b^14-7 a^12 c^2+22 a^10 b^2 c^2-24 a^8 b^4 c^2+8 a^6 b^6 c^2+5 a^4 b^8 c^2-6 a^2 b^10 c^2+2 b^12 c^2+6 a^10 c^4-24 a^8 b^2 c^4+24 a^6 b^4 c^4-10 a^4 b^6 c^4+4 a^2 b^8 c^4+5 a^8 c^6+8 a^6 b^2 c^6-10 a^4 b^4 c^6-b^8 c^6-10 a^6 c^8+5 a^4 b^2 c^8+4 a^2 b^4 c^8-b^6 c^8+3 a^4 c^10-6 a^2 b^2 c^10+2 a^2 c^12+2 b^2 c^12-c^14) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6461.

X(64498) lies on these lines: {3, 74}, {5, 20771}, {24, 12236}, {26, 5504}, {30, 15647}, {49,1986}, {54,16222}, {113,13367}, {125,44452}, {154, 12302}, {184, 14708}, {186, 3047}, {265, 7505}, {403, 10113}, {542, 34477}, {550, 59495}, {578, 58516}, {974, 37814}, {1147, 13289}, {1495, 12295}, {1539, 18560}, {2777, 12038}, {2931, 17821}, {3515, 19456}, {5654, 11744}, {5972, 18475}, {6644, 13198}, {6723, 43586}, {6759, 12901}, {7502, 41673}, {7722, 9544}, {7728, 35481}, {9826, 32046}, {9934, 12084}, {10020, 32391}, {10117, 47391}, {10201, 63710}, {10226, 11598}, {10272, 52073}, {10282, 15761}, {10539, 32607}, {10540, 12292}, {10610, 58435}, {10733, 26882},{11202, 12893}, {11430, 46686}, {11746, 12106}, {12017, 49125}, {12121, 44440}, {12228, 19357}, {12419, 15061}, {12596, 34787}, {13358, 37917}, {13561, 34128}, {14984, 15577}, {15059, 61702}, {15089, 45237}, {16003, 17701}, {16111, 51394}, {16165, 34153}, {18281, 63716}, {18400, 33547}, {19138, 23041}, {19155, 44439}, {19479, 34785}, {20772, 61574}, {23306, 34782}, {32743, 43839}, {37472, 63738}, {41674, 44213}, {45735, 46430}

X(64499) = CENTER OF THE PŁATEK CIRCLE

Barycentrics    (a - b - c)*(5*a^3 + 3*a^2*b - a*b^2 + b^3 + 3*a^2*c - 18*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + c^3) : :
X(64499) = 3 X[25567] - 2 X[64442]

The circle, denoted here by O*, is named after Miłosz Płatek, who constructed it as follows. Let Oa be the larger of two circles through X(8) tangent to lines AB and AC, and define Ob and Oc cyclically. Then O* is the circle tangent to Oa, Ob, Oc. The radius of O* is 4r^3/(|r2-|X(1)X(8)|2|), where r = radius of the incircle. (Miłosz Płatek, June 14, 2024, see here).

The radius of O* is 4*r^3 / (4*r (r - 4*R) + s^2). Let A' = Oa∩O*, and define B' and C' cyclically. Then A'B'C' is perspective to ABC, and the perspector is X(15519). For a GeoGebra figure, see X(64449). (Peter Moses, July 21, 2024)

X(64499) lies on these lines: {1, 2}, {2136, 6555}, {2137, 6762}, {3161, 3913}, {3699, 12541}, {3880, 8834}, {5853, 6552}, {6553, 45047}, {6556, 12625}, {6557, 64068}, {8055, 12632}, {12536, 42020}, {24150, 62985}, {25567, 64442}, {38255, 50444}, {44720, 64146}, {48921, 49718}

X(64499) = reflection of X(6553) in X(45047)
X(64499) = incircle-of-anticomplementary-triangle-inverse of X(60374)
X(64499) = X(8051)-Ceva conjugate of X(3161)
X(64499) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8, 15519, 1), (3699, 12541, 28661)

X(64500) = X(3)X(118)∩X(4)X(103)

Barycentrics    2*a^8 - 2*a^7*b - 3*a^5*b^3 + a^4*b^4 + 4*a^3*b^5 - 2*a^2*b^6 + a*b^7 - b^8 - 2*a^7*c + 2*a^6*b*c + 3*a^5*b^2*c - 3*a^4*b^3*c - a*b^6*c + b^7*c + 3*a^5*b*c^2 + 4*a^4*b^2*c^2 - 4*a^3*b^3*c^2 - 2*a^2*b^4*c^2 - 3*a*b^5*c^2 + 2*b^6*c^2 - 3*a^5*c^3 - 3*a^4*b*c^3 - 4*a^3*b^2*c^3 + 8*a^2*b^3*c^3 + 3*a*b^4*c^3 - b^5*c^3 + a^4*c^4 - 2*a^2*b^2*c^4 + 3*a*b^3*c^4 - 2*b^4*c^4 + 4*a^3*c^5 - 3*a*b^2*c^5 - b^3*c^5 - 2*a^2*c^6 - a*b*c^6 + 2*b^2*c^6 + a*c^7 + b*c^7 - c^8 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64500) lies on these lines: {2, 38692}, {3, 118}, {4, 103}, {5, 6712}, {11, 53750}, {20, 101}, {30, 511}, {40, 50903}, {104, 10772}, {113, 53751}, {114, 53732}, {119, 53741}, {125, 53714}, {140, 58420}, {150, 3146}, {376, 10710}, {381, 57297}, {382, 10739}, {546, 61565}, {548, 61563}, {550, 35024}, {944, 10697}, {946, 11714}, {950, 59813}, {962, 10695}, {1282, 64005}, {1362, 6284}, {1385, 11728}, {1530, 5074}, {1536, 17729}, {1541, 51775}, {1565, 31851}, {1614, 58057}, {1657, 33520}, {1770, 18413}, {1885, 5185}, {3022, 7354}, {3046, 34148}, {3091, 31273}, {3529, 38666}, {3543, 10708}, {3627, 51528}, {4292, 11028}, {4297, 11712}, {4298, 14760}, {5059, 20096}, {5462, 58521}, {5691, 39156}, {6776, 10758}, {9729, 58505}, {10110, 58507}, {10724, 10770}, {10756, 51212}, {12512, 28346}, {13374, 58594}, {14512, 44975}, {15704, 51526}, {16111, 53712}, {16163, 53747}, {17747, 51633}, {20420, 52825}, {24466, 53739}, {28345, 63413}, {37437, 38558}, {38630, 58203}, {38738, 53730}, {38749, 53721}, {38761, 53746}, {50808, 50902}, {50810, 50904}, {50811, 50905}, {50862, 50895}, {50864, 50897}, {50865, 50898}, {58567, 58592}, {58631, 58665}, {58637, 58664}, {59783, 63406}, {61602, 62026}

X(64500) = Thomson isogonal conjugate of X(35184)
X(64590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 118, 6710}, {3, 10741, 118}, {3, 38764, 38772}, {3, 38765, 38773}, {3, 38767, 38764}, {3, 38768, 10741}, {3, 38769, 20401}, {3, 38773, 38771}, {4, 103, 116}, {4, 26705, 20622}, {4, 63418, 103}, {5, 6712, 58418}, {5, 38601, 6712}, {20, 101, 63403}, {20, 152, 101}, {103, 10727, 4}, {103, 63418, 33521}, {116, 33521, 103}, {118, 6710, 20401}, {118, 10741, 38769}, {118, 38764, 38770}, {118, 38765, 38771}, {118, 38772, 38764}, {118, 38773, 3}, {140, 61579, 58420}, {150, 3146, 10725}, {382, 38574, 10739}, {546, 61565, 61577}, {548, 61604, 61563}, {946, 11714, 11726}, {5691, 39156, 50896}, {6710, 38769, 118}, {6710, 38770, 38764}, {6710, 38771, 3}, {9729, 58542, 58505}, {10110, 58507, 58519}, {10725, 38668, 150}, {10727, 63418, 116}, {10741, 38764, 38767}, {10741, 38765, 3}, {10741, 38766, 38764}, {10741, 38771, 20401}, {10741, 38773, 6710}, {38764, 38765, 38766}, {38764, 38766, 3}, {38764, 38767, 118}, {38764, 38770, 20401}, {38764, 38772, 6710}, {38765, 38768, 118}, {38766, 38767, 38772}, {38767, 38772, 38770}, {38768, 38773, 38769}, {38769, 38771, 6710}, {38774, 38775, 6710}, {58637, 58686, 58664}

X(64501) = X(3)X(124)∩X(4)X(109)

Barycentrics    2*a^10 - 2*a^9*b - 4*a^8*b^2 + 5*a^7*b^3 + a^6*b^4 - 3*a^5*b^5 + a^4*b^6 - a^3*b^7 + a^2*b^8 + a*b^9 - b^10 - 2*a^9*c + 6*a^8*b*c - a^7*b^2*c - 9*a^6*b^3*c + 5*a^5*b^4*c + a^4*b^5*c + a^3*b^6*c + a^2*b^7*c - 3*a*b^8*c + b^9*c - 4*a^8*c^2 - a^7*b*c^2 + 12*a^6*b^2*c^2 - 2*a^5*b^3*c^2 - 5*a^4*b^4*c^2 + 3*a^3*b^5*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 + 5*a^7*c^3 - 9*a^6*b*c^3 - 2*a^5*b^2*c^3 + 6*a^4*b^3*c^3 - 3*a^3*b^4*c^3 - a^2*b^5*c^3 + 8*a*b^6*c^3 - 4*b^7*c^3 + a^6*c^4 + 5*a^5*b*c^4 - 5*a^4*b^2*c^4 - 3*a^3*b^3*c^4 + 10*a^2*b^4*c^4 - 6*a*b^5*c^4 - 2*b^6*c^4 - 3*a^5*c^5 + a^4*b*c^5 + 3*a^3*b^2*c^5 - a^2*b^3*c^5 - 6*a*b^4*c^5 + 6*b^5*c^5 + a^4*c^6 + a^3*b*c^6 - 6*a^2*b^2*c^6 + 8*a*b^3*c^6 - 2*b^4*c^6 - a^3*c^7 + a^2*b*c^7 - 4*b^3*c^7 + a^2*c^8 - 3*a*b*c^8 + 3*b^2*c^8 + a*c^9 + b*c^9 - c^10 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64501) lies on these lines: {2, 38697}, {3, 124}, {4, 109}, {5, 6718}, {10, 14690}, {11, 53752}, {20, 102}, {30, 511}, {40, 13532}, {104, 10777}, {113, 53758}, {114, 53734}, {115, 53724}, {119, 53742}, {125, 53717}, {140, 58426}, {151, 3146}, {376, 10716}, {381, 57303}, {382, 10740}, {546, 61571}, {548, 61564}, {550, 38600}, {944, 10703}, {946, 11700}, {950, 12016}, {962, 10696}, {1158, 56424}, {1361, 7354}, {1364, 6284}, {1385, 11734}, {1479, 1795}, {1614, 58051}, {1657, 38573}, {1770, 1845}, {3040, 57288}, {3529, 38667}, {3543, 10709}, {3627, 51534}, {4292, 59816}, {4297, 11713}, {5462, 58526}, {5512, 53759}, {5691, 50899}, {6261, 61228}, {6776, 10764}, {7421, 39992}, {9729, 58506}, {10110, 58513}, {10483, 52129}, {10724, 10771}, {10757, 51212}, {12005, 34956}, {12114, 54081}, {13374, 58600}, {13464, 47115}, {15704, 51527}, {16111, 53713}, {16163, 53749}, {16174, 29008}, {20420, 52830}, {24466, 53740}, {31866, 38357}, {34148, 58060}, {34242, 64021}, {37437, 38559}, {38738, 53731}, {38761, 53748}, {42464, 63130}, {44927, 55315}, {50811, 50918}, {50864, 50900}, {50865, 50901}, {58567, 58593}, {58631, 58670}, {61603, 62026}

X(64501) = Thomson isogonal conjugate of X(35187)
X(64501) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 124, 6711}, {3, 10747, 124}, {3, 38776, 38784}, {3, 38777, 38785}, {3, 38779, 38776}, {3, 38780, 10747}, {3, 38785, 38783}, {4, 109, 117}, {4, 32706, 20620}, {5, 6718, 58419}, {5, 38607, 6718}, {20, 102, 63404}, {20, 33650, 102}, {109, 10732, 4}, {124, 10747, 38781}, {124, 38776, 38782}, {124, 38777, 38783}, {124, 38784, 38776}, {124, 38785, 3}, {140, 61585, 58426}, {151, 3146, 10726}, {382, 38579, 10740}, {546, 61571, 61578}, {946, 11700, 11727}, {6711, 38781, 124}, {6711, 38782, 38776}, {6711, 38783, 3}, {10110, 58513, 58520}, {10726, 38674, 151}, {10747, 38776, 38779}, {10747, 38777, 3}, {10747, 38778, 38776}, {10747, 38785, 6711}, {38357, 38554, 31866}, {38776, 38777, 38778}, {38776, 38778, 3}, {38776, 38779, 124}, {38776, 38784, 6711}, {38777, 38780, 124}, {38778, 38779, 38784}, {38779, 38784, 38782}, {38780, 38785, 38781}, {38781, 38783, 6711}, {38786, 38787, 6711}

X(64502) = X(3)X(116)∩X(4)X(101)

Barycentrics    2*a^8 - 2*a^7*b - 2*a^6*b^2 + a^5*b^3 + a^4*b^4 + a*b^7 - b^8 - 2*a^7*c + 2*a^6*b*c + 3*a^5*b^2*c - 3*a^4*b^3*c - a*b^6*c + b^7*c - 2*a^6*c^2 + 3*a^5*b*c^2 - 3*a*b^5*c^2 + 2*b^6*c^2 + a^5*c^3 - 3*a^4*b*c^3 + 3*a*b^4*c^3 - b^5*c^3 + a^4*c^4 + 3*a*b^3*c^4 - 2*b^4*c^4 - 3*a*b^2*c^5 - b^3*c^5 - a*b*c^6 + 2*b^2*c^6 + a*c^7 + b*c^7 - c^8 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64502) lies on these lines: {2, 38690}, {3, 116}, {4, 101}, {5, 6710}, {11, 53746}, {20, 103}, {30, 511}, {40, 50896}, {104, 10770}, {113, 53747}, {114, 53730}, {115, 53721}, {119, 53739}, {125, 53712}, {140, 58418}, {152, 3146}, {376, 10708}, {381, 38764}, {382, 10741}, {546, 20401}, {548, 61565}, {550, 38601}, {631, 31273}, {944, 10695}, {946, 11712}, {950, 11028}, {962, 10697}, {1146, 31852}, {1282, 5691}, {1362, 7354}, {1385, 11726}, {1478, 56144}, {1530, 6603}, {1536, 51633}, {1614, 3046}, {1656, 38774}, {1657, 33521}, {3022, 6284}, {3041, 57288}, {3091, 38775}, {3332, 44858}, {3529, 38668}, {3534, 38766}, {3543, 10710}, {3575, 5185}, {3627, 38769}, {3732, 18328}, {3830, 38767}, {3845, 38770}, {4292, 59813}, {4297, 11714}, {4872, 47621}, {5073, 38768}, {5462, 58519}, {5510, 59783}, {5870, 34112}, {6776, 10756}, {7430, 39993}, {9729, 58507}, {9812, 15735}, {10110, 58505}, {10454, 38479}, {10572, 18413}, {10724, 10772}, {10758, 51212}, {13374, 58592}, {14760, 63999}, {15704, 51528}, {16111, 53714}, {16163, 53751}, {19925, 28346}, {20420, 52823}, {24466, 53741}, {24929, 34929}, {28345, 63970}, {34148, 58057}, {37437, 38560}, {38630, 62034}, {38738, 53732}, {38761, 53750}, {39156, 64005}, {44975, 60065}, {50808, 50895}, {50810, 50897}, {50811, 50898}, {50862, 50902}, {50864, 50904}, {50865, 50905}, {58567, 58594}, {58631, 58664}, {58637, 58665}, {61604, 62026}

X(64502) = Thomson isogonal conjugate of X(35182)
X(64502) = barycentric quotient X(6444)/X(19181)
X(64502) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 38690, 38772}, {3, 116, 6712}, {3, 10739, 116}, {4, 101, 118}, {4, 917, 5190}, {4, 63416, 101}, {5, 6710, 58420}, {5, 38599, 6710}, {20, 103, 38773}, {20, 150, 103}, {101, 10725, 4}, {101, 63416, 33520}, {116, 63403, 3}, {118, 33520, 101}, {140, 61577, 58418}, {152, 3146, 10727}, {152, 20096, 38666}, {382, 38572, 10741}, {546, 61563, 61579}, {548, 61602, 61565}, {550, 38601, 38771}, {946, 11712, 11728}, {1282, 5691, 50903}, {1657, 38574, 38765}, {3146, 20096, 152}, {3627, 51526, 38769}, {9729, 58540, 58507}, {10110, 58505, 58521}, {10725, 63416, 118}, {10727, 38666, 152}, {10739, 63403, 6712}, {20401, 35024, 61563}, {38574, 38765, 33521}, {58567, 58612, 58594}, {58637, 58684, 58665}, {61563, 61579, 20401}

X(64503) = X(4)X(120)∩X(20)X(105)

Barycentrics    2*a^8 - 4*a^7*b + 3*a^6*b^2 - 2*a^5*b^3 - a^4*b^4 + 4*a^3*b^5 - 3*a^2*b^6 + 2*a*b^7 - b^8 - 4*a^7*c + 8*a^5*b^2*c - 10*a^4*b^3*c + 4*a^3*b^4*c + 2*b^7*c + 3*a^6*c^2 + 8*a^5*b*c^2 + 2*a^4*b^2*c^2 - 4*a^3*b^3*c^2 - a^2*b^4*c^2 - 8*a*b^5*c^2 - 2*a^5*c^3 - 10*a^4*b*c^3 - 4*a^3*b^2*c^3 + 8*a^2*b^3*c^3 + 6*a*b^4*c^3 - 2*b^5*c^3 - a^4*c^4 + 4*a^3*b*c^4 - a^2*b^2*c^4 + 6*a*b^3*c^4 + 2*b^4*c^4 + 4*a^3*c^5 - 8*a*b^2*c^5 - 2*b^3*c^5 - 3*a^2*c^6 + 2*a*c^7 + 2*b*c^7 - c^8 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64503) lies on these lines: {2, 38712}, {3, 5511}, {4, 120}, {5, 38619}, {20, 105}, {30, 511}, {169, 3039}, {376, 38694}, {381, 57327}, {382, 10743}, {546, 61581}, {548, 61567}, {550, 38603}, {946, 11730}, {962, 10699}, {1083, 38386}, {1358, 6284}, {1614, 58055}, {1657, 38575}, {3021, 7354}, {3146, 10729}, {3529, 38670}, {3543, 10712}, {4292, 59814}, {4297, 11716}, {5059, 20097}, {5540, 64005}, {5691, 50911}, {9729, 58509}, {10724, 10773}, {10760, 51212}, {11113, 34124}, {15704, 51530}, {16163, 53756}, {24466, 46409}, {33970, 38759}, {34148, 58053}, {37000, 61491}, {37437, 38561}, {48454, 48541}, {48455, 48542}, {50864, 50912}, {50865, 50913}, {58567, 58596}

X(64503) = barycentric quotient X(29349)/X(47305)
X(64503) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5511, 6714}, {3, 15521, 5511}, {4, 1292, 120}, {4, 15344, 53990}, {20, 105, 63405}, {20, 34547, 105}, {382, 38589, 10743}, {1292, 44983, 4}, {3146, 20344, 10729}, {10729, 38684, 20344}

X(64504) = X(4)X(121)∩X(20)X(106)

Barycentrics    2*a^7 - 4*a^6*b - 6*a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 + 2*a^2*b^5 + 2*a*b^6 - b^7 - 4*a^6*c + 18*a^5*b*c + 3*a^4*b^2*c - 9*a^3*b^3*c - a^2*b^4*c - 9*a*b^5*c + 2*b^6*c - 6*a^5*c^2 + 3*a^4*b*c^2 - 6*a^3*b^2*c^2 + 3*a^2*b^3*c^2 - 2*a*b^4*c^2 + 4*b^5*c^2 + 3*a^4*c^3 - 9*a^3*b*c^3 + 3*a^2*b^2*c^3 + 18*a*b^3*c^3 - 5*b^4*c^3 + 2*a^3*c^4 - a^2*b*c^4 - 2*a*b^2*c^4 - 5*b^3*c^4 + 2*a^2*c^5 - 9*a*b*c^5 + 4*b^2*c^5 + 2*a*c^6 + 2*b*c^6 - c^7 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64504) lies on these lines: {2, 38713}, {3, 5510}, {4, 121}, {5, 38620}, {20, 106}, {30, 511}, {376, 38695}, {381, 57328}, {382, 10744}, {546, 61582}, {548, 61568}, {550, 38604}, {946, 11731}, {962, 10700}, {1054, 64005}, {1357, 6284}, {1614, 58054}, {1657, 38576}, {3146, 10730}, {3529, 38671}, {3543, 10713}, {4292, 59812}, {4297, 11717}, {4311, 63774}, {5059, 20098}, {5691, 50914}, {6018, 7354}, {6789, 38384}, {9589, 13541}, {9729, 58510}, {10110, 58523}, {10724, 10774}, {10761, 51212}, {11814, 51118}, {14664, 31730}, {15704, 51531}, {34139, 64077}, {34148, 58052}, {37437, 38562}, {50865, 50915}, {58567, 58597}, {58637, 58667}, {59783, 63403}

X(64504) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5510, 6715}, {3, 15522, 5510}, {4, 1293, 121}, {20, 106, 63406}, {20, 34548, 106}, {382, 38590, 10744}, {1293, 44984, 4}, {3146, 21290, 10730}, {10730, 38685, 21290}

X(64505) = X(3)X(133)∩X(4)X(122)

Barycentrics    2*a^16 - 2*a^14*b^2 - 15*a^12*b^4 + 36*a^10*b^6 - 25*a^8*b^8 - 2*a^6*b^10 + 7*a^4*b^12 - b^16 - 2*a^14*c^2 + 32*a^12*b^2*c^2 - 36*a^10*b^4*c^2 - 54*a^8*b^6*c^2 + 86*a^6*b^8*c^2 - 12*a^4*b^10*c^2 - 16*a^2*b^12*c^2 + 2*b^14*c^2 - 15*a^12*c^4 - 36*a^10*b^2*c^4 + 158*a^8*b^4*c^4 - 84*a^6*b^6*c^4 - 79*a^4*b^8*c^4 + 48*a^2*b^10*c^4 + 8*b^12*c^4 + 36*a^10*c^6 - 54*a^8*b^2*c^6 - 84*a^6*b^4*c^6 + 168*a^4*b^6*c^6 - 32*a^2*b^8*c^6 - 34*b^10*c^6 - 25*a^8*c^8 + 86*a^6*b^2*c^8 - 79*a^4*b^4*c^8 - 32*a^2*b^6*c^8 + 50*b^8*c^8 - 2*a^6*c^10 - 12*a^4*b^2*c^10 + 48*a^2*b^4*c^10 - 34*b^6*c^10 + 7*a^4*c^12 - 16*a^2*b^2*c^12 + 8*b^4*c^12 + 2*b^2*c^14 - c^16 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64505) lies on these lines: {2, 38714}, {3, 133}, {4, 122}, {5, 34842}, {20, 107}, {24, 5879}, {30, 511}, {125, 36162}, {140, 58431}, {376, 23239}, {381, 36520}, {382, 10745}, {546, 61583}, {548, 61569}, {550, 38605}, {946, 11732}, {962, 10701}, {1515, 34147}, {1559, 12096}, {1614, 58067}, {1657, 23240}, {3146, 3346}, {3183, 3529}, {3324, 6284}, {3543, 10714}, {3627, 20329}, {4292, 59824}, {4297, 11718}, {5462, 58530}, {5691, 50916}, {6529, 39020}, {7158, 7354}, {7387, 14703}, {9729, 58511}, {10110, 58524}, {10724, 10775}, {10762, 51212}, {11001, 42452}, {11251, 47087}, {11589, 51385}, {13155, 34782}, {14673, 39568}, {15704, 51532}, {16111, 53716}, {16163, 53757}, {23241, 36965}, {24930, 37853}, {33897, 42465}, {34109, 51358}, {34148, 58048}, {37437, 38563}, {38749, 53723}, {46472, 47204}, {58567, 58598}, {58637, 58668}

X(64505) = Thomson isogonal conjugate of X(46968)
X(64505) = barycentric quotient X(i)/X(j) for these {i,j}: {14338, 16676}, {23184, 55296}
X(64505) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 133, 6716}, {3, 22337, 133}, {4, 1294, 122}, {4, 1301, 50937}, {4, 44985, 38956}, {5, 34842, 58424}, {5, 38621, 34842}, {20, 107, 3184}, {20, 34549, 107}, {122, 38956, 4}, {133, 63411, 3}, {140, 61592, 58431}, {381, 57329, 36520}, {382, 38591, 10745}, {1294, 44985, 4}, {1657, 38577, 23240}, {3146, 34186, 10152}, {10152, 38686, 34186}, {22337, 63411, 6716}, {23240, 38577, 52057}

X(64506) = X(4)X(123)∩X(20)X(108)

Barycentrics    2*a^13 - 2*a^12*b - 5*a^11*b^2 + 5*a^10*b^3 + a^9*b^4 - a^8*b^5 + 6*a^7*b^6 - 6*a^6*b^7 - 4*a^5*b^8 + 4*a^4*b^9 - a^3*b^10 + a^2*b^11 + a*b^12 - b^13 - 2*a^12*c + 12*a^11*b*c - 5*a^10*b^2*c - 18*a^9*b^3*c + 21*a^8*b^4*c - 12*a^7*b^5*c - 14*a^6*b^6*c + 24*a^5*b^7*c - 4*a^4*b^8*c + 3*a^2*b^10*c - 6*a*b^11*c + b^12*c - 5*a^11*c^2 - 5*a^10*b*c^2 + 34*a^9*b^2*c^2 - 20*a^8*b^3*c^2 - 34*a^7*b^4*c^2 + 46*a^6*b^5*c^2 - 12*a^5*b^6*c^2 - 8*a^4*b^7*c^2 + 15*a^3*b^8*c^2 - 17*a^2*b^9*c^2 + 2*a*b^10*c^2 + 4*b^11*c^2 + 5*a^10*c^3 - 18*a^9*b*c^3 - 20*a^8*b^2*c^3 + 80*a^7*b^3*c^3 - 26*a^6*b^4*c^3 - 40*a^5*b^5*c^3 + 40*a^4*b^6*c^3 - 40*a^3*b^7*c^3 + 5*a^2*b^8*c^3 + 18*a*b^9*c^3 - 4*b^10*c^3 + a^9*c^4 + 21*a^8*b*c^4 - 34*a^7*b^2*c^4 - 26*a^6*b^3*c^4 + 64*a^5*b^4*c^4 - 32*a^4*b^5*c^4 - 14*a^3*b^6*c^4 + 42*a^2*b^7*c^4 - 17*a*b^8*c^4 - 5*b^9*c^4 - a^8*c^5 - 12*a^7*b*c^5 + 46*a^6*b^2*c^5 - 40*a^5*b^3*c^5 - 32*a^4*b^4*c^5 + 80*a^3*b^5*c^5 - 34*a^2*b^6*c^5 - 12*a*b^7*c^5 + 5*b^8*c^5 + 6*a^7*c^6 - 14*a^6*b*c^6 - 12*a^5*b^2*c^6 + 40*a^4*b^3*c^6 - 14*a^3*b^4*c^6 - 34*a^2*b^5*c^6 + 28*a*b^6*c^6 - 6*a^6*c^7 + 24*a^5*b*c^7 - 8*a^4*b^2*c^7 - 40*a^3*b^3*c^7 + 42*a^2*b^4*c^7 - 12*a*b^5*c^7 - 4*a^5*c^8 - 4*a^4*b*c^8 + 15*a^3*b^2*c^8 + 5*a^2*b^3*c^8 - 17*a*b^4*c^8 + 5*b^5*c^8 + 4*a^4*c^9 - 17*a^2*b^2*c^9 + 18*a*b^3*c^9 - 5*b^4*c^9 - a^3*c^10 + 3*a^2*b*c^10 + 2*a*b^2*c^10 - 4*b^3*c^10 + a^2*c^11 - 6*a*b*c^11 + 4*b^2*c^11 + a*c^12 + b*c^12 - c^13 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64506) lies on these lines: {2, 38715}, {3, 6717}, {4, 123}, {5, 38622}, {20, 108}, {30, 511}, {376, 38696}, {381, 57330}, {382, 10746}, {546, 61584}, {548, 61570}, {550, 38606}, {946, 11733}, {962, 10702}, {1359, 6284}, {1614, 58063}, {1657, 38578}, {3146, 10731}, {3318, 7354}, {3529, 38673}, {3543, 10715}, {4292, 59820}, {4297, 11719}, {5691, 50917}, {7387, 54064}, {9729, 58512}, {10110, 58525}, {10724, 10776}, {10763, 51212}, {15704, 51533}, {34148, 58050}, {37437, 38564}, {38759, 56890}, {49207, 64076}, {52112, 64000}, {58567, 58599}, {58637, 58669}

X(64506) = X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 25640, 6717}, {3, 33566, 25640}, {4, 1295, 123}, {4, 40097, 53991}, {20, 108, 63407}, {20, 34550, 108}, {382, 38592, 10746}, {1295, 44986, 4}, {3146, 34188, 10731}, {10731, 38687, 34188}

X(64507) = X(3)X(117)∩X(4)X(102)

Barycentrics    2*a^10 - 2*a^9*b - 2*a^8*b^2 + 5*a^7*b^3 - 5*a^6*b^4 - 3*a^5*b^5 + 7*a^4*b^6 - a^3*b^7 - a^2*b^8 + a*b^9 - b^10 - 2*a^9*c + 6*a^8*b*c - 5*a^7*b^2*c - 5*a^6*b^3*c + 13*a^5*b^4*c - 7*a^4*b^5*c - 3*a^3*b^6*c + 5*a^2*b^7*c - 3*a*b^8*c + b^9*c - 2*a^8*c^2 - 5*a^7*b*c^2 + 20*a^6*b^2*c^2 - 10*a^5*b^3*c^2 - 11*a^4*b^4*c^2 + 15*a^3*b^5*c^2 - 10*a^2*b^6*c^2 + 3*b^8*c^2 + 5*a^7*c^3 - 5*a^6*b*c^3 - 10*a^5*b^2*c^3 + 22*a^4*b^3*c^3 - 11*a^3*b^4*c^3 - 5*a^2*b^5*c^3 + 8*a*b^6*c^3 - 4*b^7*c^3 - 5*a^6*c^4 + 13*a^5*b*c^4 - 11*a^4*b^2*c^4 - 11*a^3*b^3*c^4 + 22*a^2*b^4*c^4 - 6*a*b^5*c^4 - 2*b^6*c^4 - 3*a^5*c^5 - 7*a^4*b*c^5 + 15*a^3*b^2*c^5 - 5*a^2*b^3*c^5 - 6*a*b^4*c^5 + 6*b^5*c^5 + 7*a^4*c^6 - 3*a^3*b*c^6 - 10*a^2*b^2*c^6 + 8*a*b^3*c^6 - 2*b^4*c^6 - a^3*c^7 + 5*a^2*b*c^7 - 4*b^3*c^7 - a^2*c^8 - 3*a*b*c^8 + 3*b^2*c^8 + a*c^9 + b*c^9 - c^10 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64507) lies on these lines: {2, 38691}, {3, 117}, {4, 102}, {5, 6711}, {11, 53748}, {20, 109}, {30, 511}, {40, 50899}, {104, 10771}, {113, 53749}, {114, 53731}, {119, 53740}, {125, 53713}, {140, 58419}, {376, 10709}, {381, 38776}, {382, 10747}, {546, 61564}, {548, 61571}, {550, 38607}, {944, 10696}, {946, 11713}, {950, 59816}, {962, 10703}, {1361, 6284}, {1364, 7354}, {1385, 11727}, {1542, 50366}, {1614, 58060}, {1656, 38786}, {1657, 38579}, {1795, 4299}, {1845, 10572}, {3042, 57288}, {3091, 38787}, {3146, 10732}, {3486, 52167}, {3529, 38674}, {3534, 38778}, {3543, 10716}, {3627, 38781}, {3830, 38779}, {3845, 38782}, {4292, 12016}, {4297, 11700}, {5073, 38780}, {5462, 58520}, {5691, 13532}, {6776, 10757}, {9729, 58513}, {10110, 58506}, {10724, 10777}, {10764, 51212}, {13374, 58593}, {14690, 31730}, {15704, 51534}, {16111, 53717}, {16163, 53758}, {20420, 52824}, {21147, 61227}, {21664, 31866}, {24466, 53742}, {34148, 58051}, {37420, 38945}, {37437, 38565}, {38738, 53734}, {38749, 53724}, {38761, 53752}, {44927, 55318}, {50810, 50900}, {50811, 50901}, {50865, 50918}, {51421, 54083}, {53759, 63408}, {54081, 64077}, {56148, 63986}, {58567, 58600}, {58637, 58670}

X(64507) = Thomson isogonal conjugate of X(35183)
X(64507) = barycentric product X(6640)*X(37678)
X(64507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 38691, 38784}, {3, 117, 6718}, {3, 10740, 117}, {4, 102, 124}, {4, 26704, 51221}, {4, 63417, 102}, {5, 6711, 58426}, {5, 38600, 6711}, {20, 109, 38785}, {20, 151, 109}, {102, 10726, 4}, {117, 63404, 3}, {140, 61578, 58419}, {382, 38573, 10747}, {546, 61564, 61585}, {548, 61603, 61571}, {550, 38607, 38783}, {946, 11713, 11734}, {1657, 38579, 38777}, {3146, 33650, 10732}, {3627, 51527, 38781}, {9729, 58541, 58513}, {10110, 58506, 58526}, {10726, 63417, 124}, {10732, 38667, 33650}, {10740, 63404, 6718}, {58637, 58685, 58670}

X(64508) = X(4)X(126)∩X(20)X(111)

Barycentrics    2*a^10 - 8*a^8*b^2 - 5*a^6*b^4 + 9*a^4*b^6 + 3*a^2*b^8 - b^10 - 8*a^8*c^2 + 52*a^6*b^2*c^2 - 31*a^4*b^4*c^2 - 26*a^2*b^6*c^2 + 5*b^8*c^2 - 5*a^6*c^4 - 31*a^4*b^2*c^4 + 62*a^2*b^4*c^4 - 4*b^6*c^4 + 9*a^4*c^6 - 26*a^2*b^2*c^6 - 4*b^4*c^6 + 3*a^2*c^8 + 5*b^2*c^8 - c^10 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64508) lies on these lines: {2, 38716}, {3, 5512}, {4, 126}, {5, 38623}, {20, 111}, {30, 511}, {99, 57614}, {265, 35447}, {376, 9172}, {381, 57331}, {382, 10748}, {485, 11835}, {486, 11836}, {546, 40340}, {548, 61572}, {550, 14650}, {620, 57594}, {962, 10704}, {1614, 58059}, {1657, 11258}, {3048, 34148}, {3146, 10734}, {3325, 6284}, {3529, 14654}, {3534, 52698}, {3543, 10717}, {4292, 59819}, {4297, 11721}, {5059, 20099}, {5108, 14856}, {5461, 57620}, {5477, 58768}, {5480, 14688}, {5691, 50924}, {6019, 7354}, {6722, 57610}, {7387, 14657}, {9129, 16163}, {9729, 58514}, {10110, 58527}, {10418, 57599}, {10724, 10779}, {10765, 51212}, {14666, 15681}, {14689, 50381}, {14866, 44574}, {15704, 51535}, {16111, 53718}, {22247, 57619}, {24466, 53744}, {25406, 36696}, {28662, 44882}, {36883, 36990}, {38738, 53736}, {38749, 53726}, {38761, 53754}, {38785, 53759}, {43618, 45012}, {47325, 62288}, {49669, 52036}, {50864, 50925}, {50865, 50926}, {58567, 58602}, {58637, 58672}, {63386, 63454}

X(64508) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5512, 6719}, {3, 22338, 5512}, {3, 38796, 38804}, {3, 38797, 38805}, {3, 38799, 38796}, {3, 38800, 22338}, {3, 38805, 38803}, {4, 1296, 126}, {4, 2374, 53992}, {5, 38623, 40556}, {5, 40556, 58427}, {20, 111, 63408}, {382, 38593, 10748}, {1296, 44987, 4}, {3146, 14360, 10734}, {3543, 37749, 10717}, {5512, 22338, 38801}, {5512, 38796, 38802}, {5512, 38797, 38803}, {5512, 38804, 38796}, {5512, 38805, 3}, {6719, 38801, 5512}, {6719, 38802, 38796}, {6719, 38803, 3}, {10734, 38688, 14360}, {22338, 38796, 38799}, {22338, 38797, 3}, {22338, 38798, 38796}, {22338, 38805, 6719}, {36990, 37751, 36883}, {38796, 38797, 38798}, {38796, 38798, 3}, {38796, 38799, 5512}, {38796, 38804, 6719}, {38797, 38800, 5512}, {38798, 38799, 38804}, {38799, 38804, 38802}, {38800, 38805, 38801}, {38801, 38803, 6719}, {38806, 38807, 6719}

X(64509) = X(3)X(132)∩X(4)X(127)

Barycentrics    2*a^14 - 2*a^12*b^2 - a^10*b^4 - a^8*b^6 + 4*a^4*b^10 - a^2*b^12 - b^14 - 2*a^12*c^2 + 4*a^10*b^2*c^2 + a^8*b^4*c^2 - 2*a^6*b^6*c^2 - 2*a^4*b^8*c^2 - 2*a^2*b^10*c^2 + 3*b^12*c^2 - a^10*c^4 + a^8*b^2*c^4 + 4*a^6*b^4*c^4 - 2*a^4*b^6*c^4 + a^2*b^8*c^4 - 3*b^10*c^4 - a^8*c^6 - 2*a^6*b^2*c^6 - 2*a^4*b^4*c^6 + 4*a^2*b^6*c^6 + b^8*c^6 - 2*a^4*b^2*c^8 + a^2*b^4*c^8 + b^6*c^8 + 4*a^4*c^10 - 2*a^2*b^2*c^10 - 3*b^4*c^10 - a^2*c^12 + 3*b^2*c^12 - c^14 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64509) lies on these lines: {2, 38717}, {3, 132}, {4, 127}, {5, 19160}, {20, 112}, {22, 14983}, {26, 34217}, {30, 511}, {40, 12784}, {55, 12945}, {56, 12955}, {140, 58430}, {376, 38699}, {381, 57332}, {382, 10749}, {485, 13918}, {486, 13985}, {546, 61586}, {548, 61573}, {550, 38608}, {944, 13099}, {946, 12265}, {962, 10705}, {1151, 13923}, {1152, 13992}, {1478, 13116}, {1479, 13117}, {1529, 54075}, {1587, 19094}, {1588, 19093}, {1614, 58064}, {1657, 13310}, {1885, 13166}, {3070, 49218}, {3071, 49219}, {3146, 10735}, {3320, 6284}, {3529, 13200}, {3543, 10718}, {3575, 12145}, {3627, 19163}, {4292, 59821}, {4297, 11722}, {4299, 13312}, {4302, 13311}, {5073, 48681}, {5462, 58529}, {5480, 44885}, {5691, 12408}, {5870, 12806}, {5871, 12805}, {6020, 7354}, {6256, 49154}, {6459, 19115}, {6460, 19114}, {6529, 14944}, {7387, 19165}, {9157, 34608}, {9729, 58515}, {9730, 16224}, {9834, 12478}, {9835, 12479}, {9838, 12996}, {9839, 12997}, {9873, 12503}, {10110, 58528}, {10724, 10780}, {10766, 51212}, {11500, 12340}, {11605, 52842}, {11641, 39568}, {12110, 12207}, {12113, 12796}, {12114, 12925}, {12115, 13118}, {12116, 13119}, {12203, 13195}, {12225, 53772}, {12943, 13296}, {12953, 13297}, {13206, 64074}, {13221, 64005}, {13313, 64078}, {13314, 64079}, {13408, 63349}, {13526, 15048}, {13748, 49315}, {13749, 49316}, {15689, 38639}, {15704, 51536}, {16111, 53719}, {16163, 53760}, {16225, 64100}, {18533, 18876}, {19162, 64077}, {19164, 31305}, {20410, 52069}, {24270, 63431}, {24466, 53745}, {28343, 44882}, {34148, 58049}, {35820, 35828}, {35821, 35829}, {35880, 42266}, {35881, 42267}, {37437, 38567}, {37921, 51389}, {38738, 53737}, {38749, 53727}, {38761, 53755}, {38971, 46620}, {42258, 49270}, {42259, 49271}, {42426, 46631}, {44438, 46186}, {44704, 52950}, {48454, 48474}, {48455, 48475}, {48466, 48732}, {48467, 48733}, {48468, 49386}, {48469, 49385}, {48476, 49046}, {48477, 49047}, {48482, 49153}, {49205, 64075}, {49206, 64076}, {50381, 63408}, {58567, 58603}, {58637, 58673}

X(64509) = Thomson isogonal conjugate of X(46967)
X(64509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 132, 6720}, {3, 12918, 132}, {3, 48658, 12918}, {4, 1289, 50938}, {4, 1297, 127}, {4, 12253, 1297}, {5, 34841, 58428}, {5, 38624, 34841}, {20, 112, 14689}, {20, 12384, 112}, {132, 63410, 3}, {140, 61591, 58430}, {382, 13115, 10749}, {1297, 44988, 4}, {3146, 13219, 10735}, {5691, 12408, 13280}, {10735, 38689, 13219}, {12253, 44988, 127}, {12918, 63410, 6720}, {19160, 38624, 5}

X(64510) = X(4)X(477)∩X(20)X(476)

Barycentrics    2*a^16 - 4*a^14*b^2 - 6*a^12*b^4 + 21*a^10*b^6 - 15*a^8*b^8 - 2*a^6*b^10 + 4*a^4*b^12 + a^2*b^14 - b^16 - 4*a^14*c^2 + 24*a^12*b^2*c^2 - 25*a^10*b^4*c^2 - 26*a^8*b^6*c^2 + 45*a^6*b^8*c^2 - 5*a^4*b^10*c^2 - 12*a^2*b^12*c^2 + 3*b^14*c^2 - 6*a^12*c^4 - 25*a^10*b^2*c^4 + 84*a^8*b^4*c^4 - 43*a^6*b^6*c^4 - 42*a^4*b^8*c^4 + 30*a^2*b^10*c^4 + 2*b^12*c^4 + 21*a^10*c^6 - 26*a^8*b^2*c^6 - 43*a^6*b^4*c^6 + 86*a^4*b^6*c^6 - 19*a^2*b^8*c^6 - 19*b^10*c^6 - 15*a^8*c^8 + 45*a^6*b^2*c^8 - 42*a^4*b^4*c^8 - 19*a^2*b^6*c^8 + 30*b^8*c^8 - 2*a^6*c^10 - 5*a^4*b^2*c^10 + 30*a^2*b^4*c^10 - 19*b^6*c^10 + 4*a^4*c^12 - 12*a^2*b^2*c^12 + 2*b^4*c^12 + a^2*c^14 + 3*b^2*c^14 - c^16 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6462.

X(64510) lies on these lines: {2, 38701}, {3, 16177}, {4, 477}, {5, 31379}, {20, 476}, {30, 511}, {74, 6070}, {110, 1553}, {113, 14934}, {125, 34150}, {133, 31510}, {146, 14480}, {186, 34170}, {376, 38700}, {381, 57306}, {382, 20957}, {403, 46424}, {546, 63715}, {550, 18319}, {950, 59823}, {1495, 47347}, {1514, 47148}, {1657, 38580}, {2072, 12096}, {3146, 14731}, {3154, 7687}, {3357, 53785}, {3448, 14508}, {3529, 38677}, {3543, 34312}, {4292, 59825}, {5627, 60740}, {5972, 36169}, {6284, 33964}, {6760, 18403}, {6761, 13619}, {7354, 33965}, {7422, 47220}, {7471, 16163}, {7740, 11251}, {9179, 63408}, {10110, 12052}, {10113, 16340}, {10295, 47204}, {10733, 17511}, {11589, 44246}, {11749, 62036}, {12041, 34209}, {12068, 48378}, {12079, 20417}, {12121, 36193}, {12295, 36184}, {13202, 46045}, {13383, 63708}, {13403, 36179}, {13997, 18381}, {14611, 15063}, {14643, 31378}, {14644, 57471}, {14993, 38788}, {16111, 46632}, {16978, 45186}, {18323, 34147}, {18376, 18870}, {18508, 53319}, {20304, 21316}, {21315, 34128}, {38738, 53738}, {38749, 53728}, {47222, 52546}, {47324, 62288}, {51939, 56369}, {53716, 57424}

X(64510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 25641, 22104}, {4, 477, 3258}, {4, 1304, 18809}, {5, 38610, 31379}, {5, 38625, 40557}, {20, 34193, 476}, {110, 36172, 1553}, {113, 14934, 55308}, {125, 36164, 55319}, {382, 38581, 20957}, {477, 14989, 4}, {550, 18319, 38609}, {1304, 44992, 4}, {3146, 14731, 44967}, {10295, 47323, 47327}, {16340, 21269, 10113}, {34150, 36164, 125}, {36169, 47084, 5972}, {38678, 44967, 14731}

X(64511) = X(114)X(3566)∩X(115)X(1570)

Barycentrics    (2*a^8 - 4*a^6*b^2 + 3*a^4*b^4 - b^8 - 4*a^6*c^2 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 4*b^6*c^2 + 3*a^4*c^4 - 2*a^2*b^2*c^4 - 6*b^4*c^4 + 4*b^2*c^6 - c^8)*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + a^8*c^2 - a^4*b^4*c^2 + 6*a^2*b^6*c^2 - 2*b^8*c^2 - 4*a^6*c^4 - a^4*b^2*c^4 - 8*a^2*b^4*c^4 + b^6*c^4 + 6*a^4*c^6 + 6*a^2*b^2*c^6 + b^4*c^6 - 4*a^2*c^8 - 2*b^2*c^8 + c^10) : :
X(64511) = 5 X[1656] - 3 X[57372]

See Antreas Hatzipolakis and Peter Moses, euclid 6464.

X(64511) lies on the nine-point circle and these lines: {2, 23700}, {4, 10425}, {5, 36472}, {114, 3566}, {115, 1570}, {136, 13449}, {511, 5139}, {512, 31842}, {1352, 48317}, {1656, 57372}, {2679, 31848}, {3258, 36163}, {5099, 48876}, {22401, 38974}, {25641, 55131}, {38970, 54393}

X(64511) = midpoint of X(4) and X(10425)
X(64511) = reflection of X(36472) in X(5)
X(64511) = complement of X(23700)
X(64511) = orthic-isogonal conjugate of X(23698)
X(64511) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23698}, {23698, 10}
X(64511) = X(4)-Ceva conjugate of X(23698)

X(64512) = X(119)X(521)∩X(122)X(856)

Barycentrics    (2*a^7 - 2*a^6*b - 3*a^5*b^2 + 3*a^4*b^3 + a*b^6 - b^7 - 2*a^6*c + 8*a^5*b*c - 3*a^4*b^2*c - 4*a^3*b^3*c + 4*a^2*b^4*c - 4*a*b^5*c + b^6*c - 3*a^5*c^2 - 3*a^4*b*c^2 + 8*a^3*b^2*c^2 - 4*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + 3*a^4*c^3 - 4*a^3*b*c^3 - 4*a^2*b^2*c^3 + 8*a*b^3*c^3 - 3*b^4*c^3 + 4*a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 - 4*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7)*(a^7*b^2 - a^6*b^3 - 3*a^5*b^4 + 3*a^4*b^5 + 3*a^3*b^6 - 3*a^2*b^7 - a*b^8 + b^9 - a^6*b^2*c + 4*a^5*b^3*c + a^4*b^4*c - 8*a^3*b^5*c + a^2*b^6*c + 4*a*b^7*c - b^8*c + a^7*c^2 - a^6*b*c^2 - 4*a^4*b^3*c^2 + a^3*b^4*c^2 + 7*a^2*b^5*c^2 - 2*a*b^6*c^2 - 2*b^7*c^2 - a^6*c^3 + 4*a^5*b*c^3 - 4*a^4*b^2*c^3 + 8*a^3*b^3*c^3 - 5*a^2*b^4*c^3 - 4*a*b^5*c^3 + 2*b^6*c^3 - 3*a^5*c^4 + a^4*b*c^4 + a^3*b^2*c^4 - 5*a^2*b^3*c^4 + 6*a*b^4*c^4 + 3*a^4*c^5 - 8*a^3*b*c^5 + 7*a^2*b^2*c^5 - 4*a*b^3*c^5 + 3*a^3*c^6 + a^2*b*c^6 - 2*a*b^2*c^6 + 2*b^3*c^6 - 3*a^2*c^7 + 4*a*b*c^7 - 2*b^2*c^7 - a*c^8 - b*c^8 + c^9) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6464.

X(64512) lies on the nine-point circle and these lines: {1, 10017}, {2, 2745}, {4, 2720}, {5, 63757}, {11, 1519}, {115, 3330}, {119, 521}, {122, 856}, {123, 517}, {513, 25640}, {1877, 20620}, {2829, 28347}, {3259, 7681}, {3814, 46663}, {5514, 62326}, {5520, 7686}, {7680, 46415}, {15612, 26333}, {20619, 59976}, {25641, 55146}

X(64512) = midpoint of X(4) and X(2720)
X(64512) = reflection of X(63757) in X(5)
X(64512) = complement of X(2745)
X(64512) = orthic-isogonal conjugate of X(2829)
X(64512) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2829}, {2829, 10}
X(64512) = X(4)-Ceva conjugate of X(2829)

X(64513) = X(4)X(6099)∩X(11)X(912)

Barycentrics    (2*a^7 - 2*a^6*b - 3*a^5*b^2 + 3*a^4*b^3 + a*b^6 - b^7 - 2*a^6*c + 4*a^5*b*c + a^4*b^2*c - 2*a^3*b^3*c - 2*a*b^5*c + b^6*c - 3*a^5*c^2 + a^4*b*c^2 - a*b^4*c^2 + 3*b^5*c^2 + 3*a^4*c^3 - 2*a^3*b*c^3 + 4*a*b^3*c^3 - 3*b^4*c^3 - a*b^2*c^4 - 3*b^3*c^4 - 2*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7)*(a^7*b^2 - a^6*b^3 - 3*a^5*b^4 + 3*a^4*b^5 + 3*a^3*b^6 - 3*a^2*b^7 - a*b^8 + b^9 - a^6*b^2*c + 2*a^5*b^3*c + a^4*b^4*c - 4*a^3*b^5*c + a^2*b^6*c + 2*a*b^7*c - b^8*c + a^7*c^2 - a^6*b*c^2 - 3*a^3*b^4*c^2 + 3*a^2*b^5*c^2 + 2*a*b^6*c^2 - 2*b^7*c^2 - a^6*c^3 + 2*a^5*b*c^3 + 4*a^3*b^3*c^3 - a^2*b^4*c^3 - 2*a*b^5*c^3 + 2*b^6*c^3 - 3*a^5*c^4 + a^4*b*c^4 - 3*a^3*b^2*c^4 - a^2*b^3*c^4 - 2*a*b^4*c^4 + 3*a^4*c^5 - 4*a^3*b*c^5 + 3*a^2*b^2*c^5 - 2*a*b^3*c^5 + 3*a^3*c^6 + a^2*b*c^6 + 2*a*b^2*c^6 + 2*b^3*c^6 - 3*a^2*c^7 + 2*a*b*c^7 - 2*b^2*c^7 - a*c^8 - b*c^8 + c^9) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6464.

X(64513) lies on the nine-point circle and these lines: {2, 43078}, {4, 6099}, {5, 15608}, {11, 912}, {115, 45886}, {119, 15313}, {355, 53985}, {513, 42423}, {517, 5521}, {1062, 10017}, {3259, 31847}, {5520, 31837}, {5777, 53988}, {5887, 13999}, {25641, 55147}

X(64513) = midpoint of X(4) and X(6099)
X(64513) = reflection of X(15608) in X(5)
X(64513) = complement of X(43078)
X(64513) = orthic-isogonal conjugate of X(5840)
X(64513) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 5840}, {5840, 10}
X(64513) = X(4)-Ceva conjugate of X(5840)

X(64514) = 1ST HATZIPOLAKIS-GARCÍA CAPITÁN-MOSES-EULER POINT

Barycentrics    3*Sqrt[3]*a^2*(a^16 - 6*a^14*b^2 + 14*a^12*b^4 - 14*a^10*b^6 + 14*a^6*b^10 - 14*a^4*b^12 + 6*a^2*b^14 - b^16 - 6*a^14*c^2 + 19*a^12*b^2*c^2 - 22*a^10*b^4*c^2 + 13*a^8*b^6*c^2 - 8*a^6*b^8*c^2 + 7*a^4*b^10*c^2 - 4*a^2*b^12*c^2 + b^14*c^2 + 14*a^12*c^4 - 22*a^10*b^2*c^4 + 13*a^8*b^4*c^4 - 4*a^6*b^6*c^4 - 3*a^4*b^8*c^4 - 2*a^2*b^10*c^4 + 4*b^12*c^4 - 14*a^10*c^6 + 13*a^8*b^2*c^6 - 4*a^6*b^4*c^6 + 13*a^4*b^6*c^6 - 9*b^10*c^6 - 8*a^6*b^2*c^8 - 3*a^4*b^4*c^8 + 10*b^8*c^8 + 14*a^6*c^10 + 7*a^4*b^2*c^10 - 2*a^2*b^4*c^10 - 9*b^6*c^10 - 14*a^4*c^12 - 4*a^2*b^2*c^12 + 4*b^4*c^12 + 6*a^2*c^14 + b^2*c^14 - c^16) - 2*(4*a^16 - 5*a^14*b^2 - 35*a^12*b^4 + 109*a^10*b^6 - 125*a^8*b^8 + 61*a^6*b^10 - 5*a^4*b^12 - 5*a^2*b^14 + b^16 - 5*a^14*c^2 + 22*a^12*b^2*c^2 - 27*a^10*b^4*c^2 - 14*a^8*b^6*c^2 + 61*a^6*b^8*c^2 - 54*a^4*b^10*c^2 + 19*a^2*b^12*c^2 - 2*b^14*c^2 - 35*a^12*c^4 - 27*a^10*b^2*c^4 + 114*a^8*b^4*c^4 - 95*a^6*b^6*c^4 + 78*a^4*b^8*c^4 - 27*a^2*b^10*c^4 - 8*b^12*c^4 + 109*a^10*c^6 - 14*a^8*b^2*c^6 - 95*a^6*b^4*c^6 - 38*a^4*b^6*c^6 + 13*a^2*b^8*c^6 + 34*b^10*c^6 - 125*a^8*c^8 + 61*a^6*b^2*c^8 + 78*a^4*b^4*c^8 + 13*a^2*b^6*c^8 - 50*b^8*c^8 + 61*a^6*c^10 - 54*a^4*b^2*c^10 - 27*a^2*b^4*c^10 + 34*b^6*c^10 - 5*a^4*c^12 + 19*a^2*b^2*c^12 - 8*b^4*c^12 - 5*a^2*c^14 - 2*b^2*c^14 + c^16)*S : :

See Antreas Hatzipolakis, Francisco Javier García Capitán and Peter Moses, euclid 6476.

X(64514) lies on this line: {2, 3}

X(64515) = 2ND HATZIPOLAKIS-GARCÍA CAPITÁN-MOSES-EULER POINT

Barycentrics    3*Sqrt[3]*a^2*(a^16 - 6*a^14*b^2 + 14*a^12*b^4 - 14*a^10*b^6 + 14*a^6*b^10 - 14*a^4*b^12 + 6*a^2*b^14 - b^16 - 6*a^14*c^2 + 19*a^12*b^2*c^2 - 22*a^10*b^4*c^2 + 13*a^8*b^6*c^2 - 8*a^6*b^8*c^2 + 7*a^4*b^10*c^2 - 4*a^2*b^12*c^2 + b^14*c^2 + 14*a^12*c^4 - 22*a^10*b^2*c^4 + 13*a^8*b^4*c^4 - 4*a^6*b^6*c^4 - 3*a^4*b^8*c^4 - 2*a^2*b^10*c^4 + 4*b^12*c^4 - 14*a^10*c^6 + 13*a^8*b^2*c^6 - 4*a^6*b^4*c^6 + 13*a^4*b^6*c^6 - 9*b^10*c^6 - 8*a^6*b^2*c^8 - 3*a^4*b^4*c^8 + 10*b^8*c^8 + 14*a^6*c^10 + 7*a^4*b^2*c^10 - 2*a^2*b^4*c^10 - 9*b^6*c^10 - 14*a^4*c^12 - 4*a^2*b^2*c^12 + 4*b^4*c^12 + 6*a^2*c^14 + b^2*c^14 - c^16) + 2*(4*a^16 - 5*a^14*b^2 - 35*a^12*b^4 + 109*a^10*b^6 - 125*a^8*b^8 + 61*a^6*b^10 - 5*a^4*b^12 - 5*a^2*b^14 + b^16 - 5*a^14*c^2 + 22*a^12*b^2*c^2 - 27*a^10*b^4*c^2 - 14*a^8*b^6*c^2 + 61*a^6*b^8*c^2 - 54*a^4*b^10*c^2 + 19*a^2*b^12*c^2 - 2*b^14*c^2 - 35*a^12*c^4 - 27*a^10*b^2*c^4 + 114*a^8*b^4*c^4 - 95*a^6*b^6*c^4 + 78*a^4*b^8*c^4 - 27*a^2*b^10*c^4 - 8*b^12*c^4 + 109*a^10*c^6 - 14*a^8*b^2*c^6 - 95*a^6*b^4*c^6 - 38*a^4*b^6*c^6 + 13*a^2*b^8*c^6 + 34*b^10*c^6 - 125*a^8*c^8 + 61*a^6*b^2*c^8 + 78*a^4*b^4*c^8 + 13*a^2*b^6*c^8 - 50*b^8*c^8 + 61*a^6*c^10 - 54*a^4*b^2*c^10 - 27*a^2*b^4*c^10 + 34*b^6*c^10 - 5*a^4*c^12 + 19*a^2*b^2*c^12 - 8*b^4*c^12 - 5*a^2*c^14 - 2*b^2*c^14 + c^16)*S : :

See Antreas Hatzipolakis, Francisco Javier García Capitán and Peter Moses, euclid 6476.

X(64515) lies on this line: {2, 3}

X(64516) = ISOGONAL CONJUGATE OF X(2081)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6481.

X(64516) lies on these lines: {95, 5649}, {97, 30528}, {249, 14570}, {250, 476}, {523, 14587}, {648, 20577}, {687, 40427}, {691, 1141}, {925, 46966}, {1157, 14859}, {1972, 50433}, {2407, 2413}, {2966, 11077}, {14590, 14592}, {16813, 23582}, {18831, 54959}, {18883, 57758}, {23286, 64221}, {32680, 62735}, {34487, 62727}, {37779, 43768}, {46155, 57742}, {57474, 57482}, {57486, 57489}, {62746, 63202}

X(64516) = isogonal conjugate of X(2081)
X(64516) = isotomic conjugate of X(41078)
X(64516) = trilinear pole of line {5, 49}
X(64516) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2081}, {5, 2624}, {31, 41078}, {50, 2618}, {51, 32679}, {523, 2290}, {526, 1953}, {647, 51801}, {654, 2599}, {656, 11062}, {661, 1154}, {798, 1273}, {810, 14918}, {2088, 2617}, {2148, 55132}, {2179, 3268}, {2181, 8552}, {2594, 2600}, {6149, 12077}, {6369, 21741}, {14213, 14270}, {15451, 52414}, {21828, 35194}, {41218, 63202}, {44427, 62266}, {44706, 47230}
X(64516) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41078}, {3, 2081}, {216, 55132}, {14993, 12077}, {15295, 55219}, {31998, 1273}, {36830, 1154}, {39052, 51801}, {39062, 14918}, {39170, 14391}, {40596, 11062}, {62603, 3268}
X(64516) = X(i)-cross conjugate of X(j) for these {i, j}: {50, 14587}, {94, 39295}, {648, 39290}, {655, 32680}, {24978, 2}
X(64516) = pole of line {2081, 47423} with respect to the Stammler hyperbola
X(64516) = pole of line {43083, 43965} with respect to the Steiner circumellipse
X(64516) = pole of line {2081, 41078} with respect to the Wallace hyperbola
X(64516) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(63202)}}, {{A, B, C, X(94), X(648)}}, {{A, B, C, X(249), X(250)}}, {{A, B, C, X(476), X(39290)}}, {{A, B, C, X(933), X(16813)}}, {{A, B, C, X(1291), X(14590)}}, {{A, B, C, X(2407), X(37779)}}, {{A, B, C, X(2421), X(44376)}}, {{A, B, C, X(4558), X(46963)}}, {{A, B, C, X(15412), X(39182)}}, {{A, B, C, X(16039), X(38342)}}, {{A, B, C, X(18316), X(30247)}}, {{A, B, C, X(24624), X(34357)}}, {{A, B, C, X(24978), X(41078)}}, {{A, B, C, X(53199), X(54554)}}
X(64516) = barycentric product X(i)*X(j) for these (i, j): {110, 46138}, {275, 60053}, {276, 32662}, {311, 46966}, {328, 933}, {476, 95}, {1141, 99}, {2167, 32680}, {4993, 54959}, {10411, 14859}, {11060, 55218}, {11077, 6331}, {14560, 34384}, {14586, 20573}, {15412, 39295}, {15958, 18817}, {16077, 64228}, {18315, 94}, {18831, 265}, {23895, 51268}, {23896, 51275}, {32678, 62276}, {35139, 54}, {36061, 40440}, {36129, 62277}, {36134, 63759}, {39277, 6742}, {39287, 46155}, {39290, 43768}, {42405, 50433}, {46456, 97}, {50463, 6528}
X(64516) = barycentric quotient X(i)/X(j) for these (i, j): {2, 41078}, {5, 55132}, {6, 2081}, {54, 526}, {94, 18314}, {95, 3268}, {97, 8552}, {99, 1273}, {110, 1154}, {112, 11062}, {162, 51801}, {163, 2290}, {265, 6368}, {275, 44427}, {476, 5}, {648, 14918}, {933, 186}, {1141, 523}, {1157, 8562}, {1989, 12077}, {2148, 2624}, {2166, 2618}, {2167, 32679}, {2222, 2599}, {2623, 2088}, {3615, 6369}, {6344, 23290}, {8882, 47230}, {8883, 44816}, {11060, 55219}, {11077, 647}, {14559, 41586}, {14560, 51}, {14586, 50}, {14587, 52603}, {14859, 10412}, {15395, 36831}, {15412, 62551}, {15475, 41221}, {15958, 22115}, {16813, 14165}, {18315, 323}, {18384, 51513}, {18831, 340}, {18883, 63829}, {20573, 15415}, {23286, 16186}, {23895, 33530}, {23896, 33529}, {25044, 44809}, {30529, 20577}, {32662, 216}, {32678, 1953}, {32680, 14213}, {34386, 45792}, {35139, 311}, {36061, 44706}, {36078, 2594}, {36134, 6149}, {36306, 6116}, {36309, 6117}, {38413, 44711}, {38414, 44712}, {39277, 4467}, {39290, 62722}, {39295, 14570}, {41392, 52945}, {41512, 63735}, {43083, 35442}, {43768, 5664}, {43965, 21230}, {45147, 43958}, {46138, 850}, {46456, 324}, {46966, 54}, {50433, 17434}, {50463, 520}, {51268, 23870}, {51275, 23871}, {52153, 15451}, {54034, 14270}, {56399, 14391}, {60053, 343}, {64228, 9033}

X(64517) =  (name pending)

Barycentrics    22 a^16-97 a^14 b^2+218 a^12 b^4-330 a^10 b^6+347 a^8 b^8-249 a^6 b^10+116 a^4 b^12-28 a^2 b^14+b^16-97 a^14 c^2+262 a^12 b^2 c^2-325 a^10 b^4 c^2+181 a^8 b^6 c^2+61 a^6 b^8 c^2-148 a^4 b^10 c^2+73 a^2 b^12 c^2-7 b^14 c^2+218 a^12 c^4-325 a^10 b^2 c^4+296 a^8 b^4 c^4-176 a^6 b^6 c^4+176 a^4 b^8 c^4-103 a^2 b^10 c^4+26 b^12 c^4-330 a^10 c^6+181 a^8 b^2 c^6-176 a^6 b^4 c^6-128 a^4 b^6 c^6+58 a^2 b^8 c^6-57 b^10 c^6+347 a^8 c^8+61 a^6 b^2 c^8+176 a^4 b^4 c^8+58 a^2 b^6 c^8+74 b^8 c^8-249 a^6 c^10-148 a^4 b^2 c^10-103 a^2 b^4 c^10-57 b^6 c^10+116 a^4 c^12+73 a^2 b^2 c^12+26 b^4 c^12-28 a^2 c^14-7 b^2 c^14+c^16 : :
Barycentrics    44 S^6+3 SB SC (8 R^2-3 SW) SW^3+S^4 (-36 SB SC+24 R^2 SW-37 SW^2)-S^2 SW (72 R^2 SB SC-39 SB SC SW+24 R^2 SW^2-11 SW^3) : :

As a point on the Euler line, X(64517) has Shinagawa coefficients {(E+F)^3 (5 E+11 F)-(E+F) (31 E+37 F) S^2+44 S^4,-3 (E+F)^3 (E+3 F)+3 (E+F) (7 E+13 F) S^2-36 S^4}.

See Antreas Hatzipolakis and Ercole Suppa, euclid 6488.

X(64517) lies on this line: {2, 3}

X(64518) =  EULER LINE INTERCEPT OF X(1153)X(44386)

Barycentrics    14 a^10-37 a^8 b^2+14 a^6 b^4+32 a^4 b^6-28 a^2 b^8+5 b^10-37 a^8 c^2+110 a^6 b^2 c^2-87 a^4 b^4 c^2+65 a^2 b^6 c^2-19 b^8 c^2+14 a^6 c^4-87 a^4 b^2 c^4-42 a^2 b^4 c^4+14 b^6 c^4+32 a^4 c^6+65 a^2 b^2 c^6+14 b^4 c^6-28 a^2 c^8-19 b^2 c^8+5 c^10 : :
Barycentrics    3 S^2 (81 R^2-14 SW)+18 SB SC SW-81 R^2 SB SC-4 SW^3 : :
X(64518) = 5*X(2)-X(46067), 2*X(2)-X(46068), 7*X(2)+X(46069)

As a point on the Euler line, X(64518) has Shinagawa coefficients {16 (E+F)^3-3 (25 E-56 F) S^2,9 (E-8 F) S^2}.

See Antreas Hatzipolakis and Ercole Suppa, euclid 6490.

X(64518) lies on these lines: {2, 3}, {1153, 44386}, {11694, 18800}, {15597, 52036}, {18122, 63647}

X(64518) = midpoint of X(i) and X(j) for these (i, j): {2, 46066}, {14694, 57623}
X(64518) = reflection of X(46068) in X(2)

X(64519) =  X(573)X(5975)∩X(4297)X(53902)

Barycentrics    a^2 (a-b) (a-c) (a+b+c)^4 (a^4+a^3 b+a b^3+b^4-a^3 c+a^2 b c+a b^2 c-b^3 c-2 a^2 c^2-5 a b c^2-2 b^2 c^2-a c^3-b c^3-c^4) (a^4-a^3 b-2 a^2 b^2-a b^3-b^4+a^3 c+a^2 b c-5 a b^2 c-b^3 c+a b c^2-2 b^2 c^2+a c^3-b c^3+c^4) : :
X(64519) = 2*X(3)-X(38453)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6502.

X(64519) lies on the circumcircle and these lines: {3, 38453}, {572, 53689}, {573, 5975}, {4297, 53902}

X(64519) = isogonal conjugate of the circumnormal-isogonal conjugate of X(38453)
X(64519) = circumperp conjugate of X(38453)
X(64519) = circumnormal-isogonal conjugate of X(38456)
X(64519) = intersection, other than A, B, C, of the circumcircle and the circumconic {{A, B, C, X(1), X(61223)}}
X(64519) = antipode in circumcircle of X(38453)

X(64520) =  (name pending)

Barycentrics    a^2 (a^8-2 a^7 b+2 a^5 b^3-2 a^4 b^4+2 a^3 b^5-2 a b^7+b^8-2 a^7 c+5 a^6 b c-3 a^5 b^2 c-3 a^2 b^5 c+5 a b^6 c-2 b^7 c+a^6 c^2-3 a^5 b c^2+5 a^4 b^2 c^2-6 a^3 b^3 c^2+5 a^2 b^4 c^2-3 a b^5 c^2+b^6 c^2-3 a^4 b c^3+3 a^3 b^2 c^3+3 a^2 b^3 c^3-3 a b^4 c^3+a^4 c^4+3 a^3 b c^4-10 a^2 b^2 c^4+3 a b^3 c^4+b^4 c^4-2 a^3 c^5+6 a^2 b c^5+6 a b^2 c^5-2 b^3 c^5-a^2 c^6-10 a b c^6-b^2 c^6+4 a c^7+4 b c^7-2 c^8) (a^8-2 a^7 b+a^6 b^2+a^4 b^4-2 a^3 b^5-a^2 b^6+4 a b^7-2 b^8-2 a^7 c+5 a^6 b c-3 a^5 b^2 c-3 a^4 b^3 c+3 a^3 b^4 c+6 a^2 b^5 c-10 a b^6 c+4 b^7 c-3 a^5 b c^2+5 a^4 b^2 c^2+3 a^3 b^3 c^2-10 a^2 b^4 c^2+6 a b^5 c^2-b^6 c^2+2 a^5 c^3-6 a^3 b^2 c^3+3 a^2 b^3 c^3+3 a b^4 c^3-2 b^5 c^3-2 a^4 c^4+5 a^2 b^2 c^4-3 a b^3 c^4+b^4 c^4+2 a^3 c^5-3 a^2 b c^5-3 a b^2 c^5+5 a b c^6+b^2 c^6-2 a c^7-2 b c^7+c^8) : :

See Antreas Hatzipolakis, Elias Hagos and Ercole Suppa, euclid 6502.

X(64520) lies on the circumcircle and this line: {2222, 55335}

X(64520) = intersection, other than A, B, C, of the circumcircle and the circumconic {{A, B, C, X(11), X(59)}}

X(64521) =  (name pending)

Barycentrics    a^2 (a-b) (a-c) (a-b-c)^2 (a+b-c)^2 (a-b+c)^2 (a^3-a^2 b-a b^2+b^3-a^2 c+3 a b c-b^2 c-a c^2-b c^2+c^3)^2 (a^6-a^4 b^2-a^2 b^4+b^6-a^5 c+a^3 b^2 c+a^2 b^3 c-b^5 c-2 a^4 c^2+2 a^3 b c^2+2 a^2 b^2 c^2+2 a b^3 c^2-2 b^4 c^2+2 a^3 c^3-5 a^2 b c^3-5 a b^2 c^3+2 b^3 c^3+a^2 c^4+4 a b c^4+b^2 c^4-a c^5-b c^5) (a^6-a^5 b-2 a^4 b^2+2 a^3 b^3+a^2 b^4-a b^5+2 a^3 b^2 c-5 a^2 b^3 c+4 a b^4 c-b^5 c-a^4 c^2+a^3 b c^2+2 a^2 b^2 c^2-5 a b^3 c^2+b^4 c^2+a^2 b c^3+2 a b^2 c^3+2 b^3 c^3-a^2 c^4-2 b^2 c^4-b c^5+c^6) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6502.

X(64521) lies on the circumcircle and this line: {100, 35100}

X(64521) = antipode in the circumcircle of X(64520)

leftri

Points related to the 1st Pavlov-Altintaş triangle: X(64522)-X(64584)

rightri

This preamble and centers X(64522)-X(64584) were contributed by Ivan Pavlov on July 25, 2024.

Let IaIbIc be the intouch triangle. Let AI intersect IaIb and IaIc at points Ab and Ac resp. Let Na be the nine-point center of IaAbAc and similarly define Nb and Nc. In the following, NaNbNc is called the 1st Pavlov-Altintaş triangle. Its inverse triangle is called the 1st anti-Pavlov-Altintaş triangle. The barycentric coordinates of their A-vertices are:

1st Pavlov-Altintaş: -a*(b-c)^2 : b*((b-c)*c+a*(b+c)) : c*(b*(-b+c)+a*(b+c))
1st anti-Pavlov-Altintaş: a-b-c : c : b

The 1st Pavlov-Altintaş triangle is perspective to ABC with perspector X(13476). It is also bilogic to the intouch triangle and has the same centroid - X(354). The perspector of the intouch and 1st Pavlov-Altintaş triangles is an infinite point, X(513). Some other triangles perspective to the 1st Pavlov-Altintas include: AAOA, Aquila, Artzt, 8th Brocard, circumsymmedial, Lucas central, Lucas inner, Lucas reflection, Lucas tangents, 1st Pamfilos-Zhou, 1st and 2nd Sharygin, symmedial, tangential, inner-Yff, outer-Yff.
The 1st anti-Pavlov-Altintaş triangle is perspective to ABC with perspector X(75). Some other triangles perspective to it include: Gemini 16, Gemini 17, Gemini 111, Aquila, inner-Conway, inner-Garcia, Yff contact, inner-Yff, outer-Yff.
The 1st anti-Pavlov-Altintaş triangle is orthologic to the intouch with orhtology center X(3869). It is also orthologic to the 5th Conway and 1st Savin triangles with orthology centers resp. X(64002) and X(8).
For more information on some related triangles see this Euclid thread.

X(64522) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND ANTI-TANGENTIAL-MIDARC

Barycentrics    a*(a+b-c)*(a-b+c)*(-(a^2*b*(b-c)^2*c*(b+c))+a^5*(b+c)^2+b*(b-c)^2*c*(b+c)^3+a*(b^2-c^2)^2*(b^2-b*c+c^2)-a^3*(2*b^4+b^3*c+2*b^2*c^2+b*c^3+2*c^4)) : :

X(64522) lies on these lines: {1, 15622}, {11, 1425}, {12, 21252}, {56, 64548}, {57, 23383}, {65, 1193}, {109, 37806}, {225, 1876}, {354, 2654}, {496, 942}, {513, 30493}, {1465, 22300}, {4296, 50362}, {4347, 37536}, {5665, 11021}, {5842, 40644}, {6583, 51751}, {11680, 19367}, {15832, 35645}, {18838, 28013}, {20718, 37591}, {28087, 28109}

X(64522) = pole of line {1459, 1946} with respect to the DeLongchamps ellipse
X(64522) = pole of line {1042, 7354} with respect to the Feuerbach hyperbola
X(64522) = pole of line {1427, 2051} with respect to the dual conic of Yff parabola
X(64522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 1393, 64550}, {65, 1457, 34434}

X(64523) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND SYMMEDIAL

Barycentrics    a*(b-c)^2*(a^2-b*c-a*(b+c)) : :
X(64523) = -X[190]+3*X[16482], -3*X[597]+X[25323], 3*X[903]+X[4499], -5*X[3618]+X[25050], -X[3888]+5*X[27191], X[4440]+3*X[24482], -3*X[25316]+7*X[51171]

X(64523) lies on these lines: {1, 4557}, {2, 4553}, {6, 13476}, {9, 64553}, {11, 125}, {31, 64550}, {37, 17445}, {41, 64551}, {42, 64559}, {44, 20358}, {75, 61183}, {88, 34583}, {105, 692}, {116, 53835}, {190, 16482}, {238, 20718}, {239, 44671}, {244, 659}, {354, 2246}, {373, 17602}, {513, 1086}, {517, 3246}, {518, 4753}, {521, 17059}, {523, 24225}, {597, 25323}, {614, 53312}, {650, 38990}, {674, 3008}, {872, 64555}, {903, 4499}, {942, 2836}, {1015, 1084}, {1100, 58571}, {1111, 4965}, {1918, 40504}, {1964, 64556}, {2170, 17463}, {2209, 64557}, {2486, 17761}, {2643, 4132}, {2807, 15251}, {3011, 38472}, {3056, 17278}, {3120, 38390}, {3122, 27846}, {3125, 4164}, {3589, 17049}, {3618, 25050}, {3666, 38998}, {3675, 7202}, {3688, 17337}, {3722, 22313}, {3739, 19563}, {3742, 24685}, {3744, 22278}, {3756, 38992}, {3757, 58644}, {3772, 63511}, {3834, 9025}, {3888, 27191}, {3924, 34434}, {4000, 63498}, {4083, 55055}, {4124, 16732}, {4384, 58379}, {4395, 6007}, {4403, 29198}, {4422, 14839}, {4436, 16494}, {4440, 24482}, {4700, 9038}, {4802, 23772}, {4926, 24840}, {5091, 16686}, {5943, 17061}, {6594, 9957}, {7292, 50362}, {9024, 40480}, {9359, 16495}, {14523, 21867}, {14717, 23982}, {14973, 32914}, {15888, 46187}, {16602, 20359}, {17067, 29353}, {17197, 53564}, {17277, 40607}, {17348, 22271}, {17349, 64581}, {17353, 21865}, {17356, 17792}, {17366, 21746}, {17417, 17419}, {17724, 61166}, {18165, 29821}, {21278, 29484}, {21299, 29802}, {21362, 24405}, {21762, 38996}, {23560, 50516}, {24168, 35059}, {24191, 50514}, {24542, 61172}, {24789, 63513}, {25316, 51171}, {28597, 29396}, {31947, 38987}, {38346, 38347}, {38979, 55045}, {40137, 43960}, {40216, 55026}, {40601, 40941}, {55340, 64169}, {56805, 57039}

X(64523) = midpoint of X(i) and X(j) for these {i,j}: {6, 46149}, {44, 20358}, {239, 57024}, {354, 61708}, {1086, 3271}, {4553, 25048}
X(64523) = reflection of X(i) in X(j) for these {i,j}: {40521, 4422}
X(64523) = isogonal conjugate of X(63918)
X(64523) = complement of X(4553)
X(64523) = perspector of circumconic {{A, B, C, X(1019), X(4040)}}
X(64523) = center of circumconic {{A, B, C, X(6), X(17187)}}
X(64523) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 63918}, {59, 55076}, {765, 13476}, {1016, 2350}, {1110, 40216}, {1252, 17758}, {3952, 43076}, {4557, 53649}
X(64523) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 63918}, {513, 13476}, {514, 40216}, {661, 17758}, {693, 76}, {1015, 54118}, {1500, 61402}, {6615, 55076}, {17761, 3952}, {50337, 17165}
X(64523) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6, 513}, {1621, 4040}, {17143, 17494}, {17761, 38347}, {18785, 659}, {38859, 58324}, {39797, 649}, {55026, 514}, {60075, 650}, {61403, 1015}
X(64523) = X(i)-complementary conjugate of X(j) for these {i, j}: {58, 3005}, {82, 513}, {83, 3835}, {251, 514}, {308, 21262}, {513, 21249}, {514, 21248}, {649, 6292}, {667, 16587}, {1176, 20315}, {1474, 23285}, {2206, 52591}, {3112, 21260}, {3120, 46654}, {3122, 15449}, {4628, 4422}, {10566, 141}, {18070, 21245}, {18082, 31946}, {18098, 4129}, {18101, 124}, {18105, 1213}, {18107, 21250}, {18108, 10}, {18113, 5510}, {21207, 55070}, {32085, 20316}, {39179, 3739}, {43924, 17055}, {46288, 6586}, {46289, 650}, {51906, 6627}, {52376, 4369}, {52394, 512}, {55240, 1211}, {56245, 20317}, {58784, 3454}, {61404, 116}
X(64523) = X(i)-cross conjugate of X(j) for these {i, j}: {38365, 38347}
X(64523) = pole of line {3675, 53524} with respect to the incircle
X(64523) = pole of line {38346, 38365} with respect to the Brocard inellipse
X(64523) = pole of line {244, 665} with respect to the DeLongchamps ellipse
X(64523) = pole of line {523, 4724} with respect to the Feuerbach hyperbola
X(64523) = pole of line {650, 21260} with respect to the Kiepert hyperbola
X(64523) = pole of line {765, 63918} with respect to the Stammler hyperbola
X(64523) = pole of line {3121, 14296} with respect to the Steiner inellipse
X(64523) = pole of line {7035, 63918} with respect to the Wallace hyperbola
X(64523) = pole of line {812, 14838} with respect to the dual conic of Yff parabola
X(64523) = pole of line {442, 1089} with respect to the dual conic of Wallace hyperbola
X(64523) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {44, 1155, 20358}
X(64523) = X(4553)-of-medial-triangle
X(64523) = intersection, other than A, B, C, of circumconics {{A, B, C, X(244), X(2486)}}, {{A, B, C, X(513), X(21007)}}, {{A, B, C, X(1086), X(13476)}}, {{A, B, C, X(2973), X(21252)}}, {{A, B, C, X(3294), X(16507)}}, {{A, B, C, X(4557), X(7192)}}, {{A, B, C, X(16726), X(17761)}}, {{A, B, C, X(17494), X(43931)}}, {{A, B, C, X(18191), X(38347)}}, {{A, B, C, X(26846), X(61403)}}, {{A, B, C, X(38346), X(43921)}}
X(64523) = barycentric product X(i)*X(j) for these (i, j): {1, 17761}, {522, 58324}, {523, 57148}, {1015, 17143}, {1019, 4151}, {1086, 1621}, {1111, 4251}, {1146, 38859}, {1977, 40088}, {2170, 55082}, {2310, 33765}, {2486, 81}, {3733, 58361}, {3996, 53538}, {4040, 514}, {4858, 55086}, {13476, 26846}, {14004, 3942}, {16726, 4651}, {16727, 64169}, {17205, 3294}, {17277, 244}, {17494, 513}, {17924, 22160}, {18152, 3248}, {20954, 649}, {21007, 693}, {26847, 34434}, {38346, 75}, {38347, 7}, {38365, 85}, {40607, 61403}, {40619, 6}, {42454, 651}, {56537, 61404}, {57167, 650}, {57247, 663}
X(64523) = barycentric quotient X(i)/X(j) for these (i, j): {6, 63918}, {244, 17758}, {513, 54118}, {1015, 13476}, {1019, 53649}, {1086, 40216}, {1621, 1016}, {2170, 55076}, {2486, 321}, {3248, 2350}, {4040, 190}, {4151, 4033}, {4251, 765}, {16726, 39734}, {17143, 31625}, {17205, 40004}, {17277, 7035}, {17494, 668}, {17761, 75}, {20954, 1978}, {21007, 100}, {21727, 4103}, {22160, 1332}, {26846, 17143}, {38346, 1}, {38347, 8}, {38365, 9}, {38859, 1275}, {40607, 61402}, {40619, 76}, {42454, 4391}, {55086, 4564}, {56537, 61406}, {57129, 43076}, {57148, 99}, {57167, 4554}, {57247, 4572}, {58324, 664}, {58361, 27808}
X(64523) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 53391, 4557}, {1, 64554, 64552}, {2, 25048, 4553}, {6, 13476, 64561}, {6, 64524, 13476}, {239, 57024, 44671}, {244, 3248, 16726}, {1086, 3271, 513}, {3589, 17049, 22279}, {4422, 14839, 40521}, {16507, 16726, 3248}, {17277, 56537, 40607}, {18165, 29821, 58572}

X(64524) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND TANGENTIAL

Barycentrics    a*(-(b*(b-c)^2*c)-a*(b-c)^2*(b+c)+a^2*(b^2+c^2)) : :

X(64524) lies on these lines: {1, 5132}, {2, 22279}, {6, 13476}, {7, 513}, {10, 9049}, {11, 42447}, {31, 64559}, {37, 20358}, {44, 63522}, {48, 354}, {55, 64549}, {57, 3941}, {65, 1279}, {71, 59217}, {75, 57024}, {116, 44412}, {141, 17049}, {142, 674}, {206, 942}, {244, 1964}, {344, 40521}, {511, 25557}, {517, 42819}, {518, 16825}, {869, 64556}, {946, 58617}, {982, 16696}, {1001, 20718}, {1015, 8265}, {1026, 29439}, {1086, 21746}, {1125, 58410}, {1486, 5228}, {1918, 64557}, {1953, 17463}, {2389, 24389}, {2807, 20330}, {2808, 42356}, {2809, 61033}, {2875, 29957}, {2876, 51150}, {3008, 22277}, {3056, 4675}, {3271, 17365}, {3688, 17245}, {3742, 25523}, {3754, 49473}, {3759, 3873}, {3779, 17278}, {3826, 9052}, {3834, 17792}, {3870, 22278}, {3874, 4974}, {3881, 49489}, {4022, 21352}, {4083, 59857}, {4090, 24742}, {4361, 35892}, {4384, 22271}, {4553, 17234}, {4644, 63498}, {4670, 58583}, {4852, 64546}, {4890, 17395}, {5045, 52495}, {5091, 38863}, {5256, 22290}, {5542, 8679}, {5572, 44670}, {5836, 49467}, {5902, 16110}, {6007, 7263}, {6147, 58469}, {6697, 16608}, {7032, 16726}, {8053, 20367}, {9025, 17376}, {10473, 21769}, {10980, 18725}, {11019, 58574}, {12109, 25466}, {14839, 17243}, {15185, 21867}, {16014, 18180}, {16482, 17350}, {16507, 23524}, {16574, 16684}, {16777, 64552}, {17065, 57039}, {17142, 18137}, {17259, 40607}, {17277, 62872}, {17279, 21865}, {17300, 25048}, {17337, 20683}, {17366, 52020}, {17394, 50362}, {17443, 17447}, {17445, 21330}, {17718, 38472}, {18040, 20352}, {18143, 21278}, {18621, 37543}, {20116, 44661}, {21238, 30982}, {21258, 23305}, {21620, 58493}, {22299, 54392}, {22325, 29651}, {23343, 29380}, {23839, 50360}, {24220, 53564}, {24482, 31300}, {29353, 60980}, {29830, 61172}, {34371, 58563}, {34824, 64007}, {35612, 58572}, {37536, 50293}, {37703, 51377}, {38390, 61716}, {39734, 55026}, {43035, 64206}, {50516, 63527}

X(64524) = midpoint of X(i) and X(j) for these {i,j}: {4361, 35892}, {15185, 21867}
X(64524) = perspector of circumconic {{A, B, C, X(34018), X(46725)}}
X(64524) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 2141}
X(64524) = X(i)-Dao conjugate of X(j) for these {i, j}: {2140, 3681}, {23989, 40495}, {32664, 2141}
X(64524) = X(i)-Ceva conjugate of X(j) for these {i, j}: {692, 513}
X(64524) = pole of line {44319, 47970} with respect to the Bevan circle
X(64524) = pole of line {4040, 22160} with respect to the circumcircle
X(64524) = pole of line {241, 514} with respect to the DeLongchamps ellipse
X(64524) = pole of line {16580, 40690} with respect to the dual conic of Yff parabola
X(64524) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(57167)}}, {{A, B, C, X(2140), X(39797)}}, {{A, B, C, X(13476), X(24002)}}, {{A, B, C, X(20990), X(39734)}}, {{A, B, C, X(34444), X(43930)}}, {{A, B, C, X(55026), X(64169)}}
X(64524) = barycentric product X(i)*X(j) for these (i, j): {1, 2140}, {101, 19594}, {46725, 513}
X(64524) = barycentric quotient X(i)/X(j) for these (i, j): {31, 2141}, {2140, 75}, {19594, 3261}, {46725, 668}
X(64524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 39797, 40638}, {6, 64560, 13476}, {244, 64555, 1964}, {4361, 35892, 44671}, {13476, 64523, 6}, {17259, 56542, 40607}, {17277, 62872, 64581}, {64553, 64554, 37}, {64557, 64558, 1918}

X(64525) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(b*c*(b^2-c^2)^2+a^4*(b^2-6*b*c+c^2)+a^3*(b^3+b^2*c+b*c^2+c^3)-a^2*(b^4-5*b^3*c-5*b*c^3+c^4)-a*(b^5+b^4*c+b*c^4+c^5)) : :
X(64525) = 3*X[376]+X[37482], -X[970]+3*X[8703], X[1657]+3*X[37521], -5*X[3522]+X[5752], 3*X[3534]+X[10441], -3*X[3576]+X[64532], -5*X[3616]+X[64527], -5*X[7987]+X[64537]

X(64525) lies on these lines: {1, 16528}, {2, 64529}, {3, 1724}, {4, 64528}, {5, 14131}, {20, 37536}, {30, 5482}, {36, 33656}, {55, 64533}, {56, 64534}, {373, 17583}, {376, 37482}, {404, 34461}, {511, 548}, {517, 550}, {581, 64247}, {901, 3871}, {952, 53002}, {958, 64542}, {970, 8703}, {1125, 64541}, {1149, 1385}, {1657, 37521}, {2646, 64539}, {2975, 64526}, {3246, 13624}, {3522, 5752}, {3534, 10441}, {3576, 64532}, {3616, 64527}, {4324, 50362}, {4855, 56885}, {5650, 57003}, {5754, 62320}, {5901, 29349}, {6011, 37469}, {7677, 64547}, {7987, 64537}, {9945, 29958}, {10108, 19765}, {10572, 35059}, {11112, 64544}, {15488, 15704}, {15489, 33923}, {15622, 26285}, {18180, 37256}, {19513, 48916}, {22392, 34463}, {24929, 64538}, {29229, 48934}, {34583, 37702}, {36005, 41723}, {48927, 64540}, {53790, 61286}, {57004, 58889}

X(64525) = midpoint of X(i) and X(j) for these {i,j}: {1, 64531}, {20, 37536}, {15488, 15704}
X(64525) = reflection of X(i) in X(j) for these {i,j}: {4, 64528}, {5, 14131}, {15489, 33923}, {34466, 3}, {64541, 1125}
X(64525) = anticomplement of X(64529)
X(64525) = X(3853)-of-anti-Artzt-triangle
X(64525) = X(3988)-of-inner-Garcia-triangle
X(64525) = X(6662)-of-2nd-circumperp-triangle
X(64525) = X(6663)-of-hexyl-triangle

X(64526) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-CONWAY AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+b*c*(b^2-c^2)^2-a^2*(b+c)^2*(b^2-3*b*c+c^2)+a^3*(b^3+b^2*c+b*c^2+c^3)-a*(b^5+b^4*c+4*b^3*c^2+4*b^2*c^3+b*c^4+c^5)) : :
X(64526) = -3*X[3819]+2*X[15172], -3*X[3873]+4*X[64535], -3*X[22278]+2*X[31757], -3*X[49732]+2*X[58469]

X(64526) lies on these lines: {2, 64534}, {9, 64547}, {30, 64567}, {63, 64531}, {72, 4450}, {78, 64532}, {100, 34466}, {145, 64533}, {200, 56885}, {219, 12912}, {329, 64527}, {517, 5562}, {518, 64539}, {908, 64541}, {2975, 64525}, {3434, 37536}, {3555, 64538}, {3819, 15172}, {3873, 64535}, {4416, 15310}, {4420, 56884}, {5082, 37482}, {5482, 24390}, {5752, 17784}, {5853, 11573}, {10108, 17018}, {10916, 35059}, {11680, 64528}, {11681, 64529}, {11682, 64530}, {18180, 33110}, {22278, 31757}, {31419, 64544}, {31855, 57666}, {49732, 58469}

X(64526) = reflection of X(i) in X(j) for these {i,j}: {145, 64533}, {3555, 64538}, {64534, 64542}, {64547, 9}
X(64526) = anticomplement of X(64534)
X(64526) = X(6662)-of-inner-Conway-triangle
X(64526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {200, 64537, 56885}, {64534, 64542, 2}

X(64527) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CONWAY AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^3+2*b*c*(b+c)-a*(b+c)^2)*((b-c)^2*(b+c)+a*(b^2-3*b*c+c^2)) : :
X(64527) = -X[40]+3*X[45829], -5*X[1656]+4*X[53002], -5*X[3616]+4*X[64525], -3*X[9778]+4*X[34466], -9*X[9779]+8*X[64528], -7*X[9780]+8*X[64529], -3*X[9812]+2*X[37536], -X[12435]+3*X[41869], -3*X[37521]+4*X[40273]

X(64527) lies on cubics K461, K655 and on these lines: {2, 64531}, {3, 16686}, {7, 64534}, {20, 64532}, {30, 64568}, {40, 45829}, {145, 64530}, {320, 10446}, {329, 64526}, {355, 56799}, {497, 64539}, {511, 48661}, {516, 5752}, {517, 3146}, {1058, 64538}, {1482, 14261}, {1656, 53002}, {2818, 5895}, {3616, 64525}, {3627, 31785}, {5687, 38389}, {5886, 26111}, {9519, 63967}, {9580, 11573}, {9778, 34466}, {9779, 64528}, {9780, 64529}, {9785, 64533}, {9812, 37536}, {10525, 14266}, {10580, 64535}, {10591, 35059}, {12435, 41869}, {12645, 53790}, {12912, 34048}, {17784, 56885}, {18228, 64542}, {18257, 26932}, {18480, 36919}, {18541, 58535}, {26046, 26446}, {26364, 38390}, {31778, 51118}, {37521, 40273}

X(64527) = reflection of X(i) in X(j) for these {i,j}: {20, 64532}, {145, 64530}, {5752, 64537}, {31778, 51118}, {31785, 3627}, {37482, 12699}, {64531, 64541}
X(64527) = anticomplement of X(64531)
X(64527) = X(i)-Dao conjugate of X(j) for these {i, j}: {38389, 513}, {64531, 64531}
X(64527) = pole of line {4063, 48293} with respect to the Conway circle
X(64527) = X(6662)-of-2nd-Conway-triangle
X(64527) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 64537, 5752}, {12699, 15310, 37482}, {64531, 64541, 2}

X(64528) = ORTHOLOGY CENTER OF THESE TRIANGLES: 3RD EULER AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2-3*b*c*(b^2-c^2)^2+a^3*(b^3+b^2*c+b*c^2+c^3)-a^2*(b^4-5*b^3*c-5*b*c^3+c^4)-a*(b^5+b^4*c+b*c^4+c^5)) : :
X(64528) = -9*X[2]+X[5752], 3*X[549]+X[15488], -5*X[632]+X[970], 5*X[1656]+3*X[37521], 3*X[1699]+X[64531], 7*X[3090]+X[37482], 7*X[3526]+X[10441], 7*X[3624]+X[31778], -3*X[3817]+X[64541], -9*X[7988]+X[64537], -5*X[8227]+X[64532], -9*X[9779]+X[64527] and many others

X(64528) lies on these lines: {2, 5752}, {3, 52524}, {4, 64525}, {5, 5482}, {11, 64534}, {12, 64533}, {30, 14131}, {79, 34583}, {140, 517}, {226, 64535}, {229, 37431}, {500, 19546}, {511, 3628}, {549, 15488}, {632, 970}, {942, 37634}, {952, 64570}, {1201, 10222}, {1385, 19513}, {1656, 37521}, {1699, 64531}, {2051, 49641}, {2886, 64542}, {3090, 37482}, {3526, 10441}, {3579, 30950}, {3624, 31778}, {3817, 64541}, {3831, 9956}, {3911, 15443}, {4187, 64544}, {4871, 9955}, {5400, 48907}, {5718, 10108}, {5777, 62621}, {5810, 18141}, {5886, 26094}, {6667, 58469}, {6915, 34461}, {7504, 33852}, {7678, 64547}, {7988, 64537}, {8227, 64532}, {8610, 50650}, {9779, 64527}, {11230, 19864}, {11231, 35631}, {11522, 64530}, {11680, 64526}, {12047, 35059}, {17575, 61643}, {17605, 64539}, {19335, 48903}, {19547, 37682}, {19549, 50317}, {19648, 48926}, {23383, 26285}, {24470, 64489}, {30852, 56885}, {33656, 63963}, {37693, 49557}, {40273, 53002}

X(64528) = midpoint of X(i) and X(j) for these {i,j}: {4, 64525}, {5, 5482}, {34466, 37536}, {40273, 53002}
X(64528) = reflection of X(i) in X(j) for these {i,j}: {64529, 5}
X(64528) = complement of X(34466)
X(64528) = X(6662)-of-3rd-Euler-triangle
X(64528) = X(6663)-of-Wasat-triangle
X(64528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37536, 34466}

X(64529) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH EULER AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+5*b*c*(b^2-c^2)^2+a^3*(b^3+b^2*c+b*c^2+c^3)-a^2*(b^4+3*b^3*c+3*b*c^3+c^4)-a*(b^5+b^4*c+b*c^4+c^5)) : :
X(64529) = -3*X[5]+X[5482], -9*X[381]+X[10441], X[970]+3*X[3845], -5*X[1698]+X[64531], -5*X[3091]+X[37536], -9*X[3545]+X[37482], 3*X[3679]+X[64530], 7*X[3832]+X[5752], -5*X[3858]+X[15488], -11*X[5072]+3*X[37521], 3*X[5587]+X[64532] and many others

X(64529) lies on these lines: {2, 64525}, {4, 34466}, {5, 5482}, {10, 38390}, {11, 64533}, {12, 64534}, {21, 34461}, {30, 64570}, {381, 10441}, {511, 3850}, {517, 546}, {952, 64569}, {970, 3845}, {1210, 64535}, {1329, 64542}, {1698, 64531}, {3091, 37536}, {3259, 24390}, {3545, 37482}, {3628, 14131}, {3679, 64530}, {3822, 33656}, {3832, 5752}, {3853, 15489}, {3858, 15488}, {5072, 37521}, {5587, 64532}, {7679, 64547}, {7989, 64537}, {9780, 64527}, {11681, 64526}, {17530, 64544}, {17606, 64539},

X(64529) = midpoint of X(i) and X(j) for these {i,j}: {4, 34466}, {10, 64541}, {3853, 15489}
X(64529) = reflection of X(i) in X(j) for these {i,j}: {14131, 3628}, {64528, 5}
X(64529) = complement of X(64525)
X(64529) = X(6662)-of-4th-Euler-triangle

X(64530) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTERS-REFLECTIONS AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(b*c*(b^2-c^2)^2+a^4*(b^2+c^2)+a^3*(b^3-5*b^2*c-5*b*c^2+c^3)-a^2*(b^4+b^3*c-12*b^2*c^2+b*c^3+c^4)-a*(b^5-5*b^4*c+6*b^3*c^2+6*b^2*c^3-5*b*c^4+c^5)) : :
X(64530) = -3*X[3656]+2*X[5482], -3*X[3679]+4*X[64529], -3*X[10283]+2*X[53002], -5*X[11522]+4*X[64528], -4*X[14131]+5*X[61276]

X(64530) lies on circumconic {{A, B, C, X(20615), X(38462)}} and on these lines: {1, 16528}, {4, 8}, {5, 121}, {30, 64571}, {145, 64527}, {946, 49993}, {1483, 29349}, {2098, 64539}, {2841, 13463}, {3340, 64534}, {3656, 5482}, {3679, 64529}, {3877, 17690}, {4301, 37536}, {7962, 64533}, {7991, 34466}, {8715, 34461}, {10222, 14261}, {10283, 53002}, {11278, 15310}, {11522, 64528}, {11526, 64547}, {11531, 64537}, {11682, 64526}, {14131, 61276}, {15829, 64542},

X(64530) = midpoint of X(i) and X(j) for these {i,j}: {145, 64527}, {11531, 64537}
X(64530) = reflection of X(i) in X(j) for these {i,j}: {8, 64541}, {7991, 34466}, {37536, 4301}, {64531, 1}
X(64530) = pole of line {1837, 4694} with respect to the Feuerbach hyperbola
X(64530) = X(6662)-of-excenters-reflections-triangle
X(64530) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 64541, 8}

X(64531) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTRAL AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^3*(b-c)^2*(b+c)+b*c*(b^2-c^2)^2+a^4*(b^2-4*b*c+c^2)-a^2*(b^4-3*b^3*c-4*b^2*c^2-3*b*c^3+c^4)-a*(b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+c^5)) : :
X(64531) = -3*X[165]+2*X[34466], -5*X[1698]+4*X[64529], -3*X[1699]+4*X[64528], -X[5752]+3*X[9778], -3*X[5886]+4*X[14131], -7*X[31423]+3*X[45829], -3*X[37521]+X[48661]

X(64531) lies on these lines: {1, 16528}, {2, 64527}, {3, 49997}, {5, 29349}, {9, 64542}, {20, 145}, {30, 44039}, {40, 48928}, {44, 573}, {55, 64539}, {57, 64534}, {63, 64526}, {100, 56885}, {165, 34466}, {222, 12912}, {513, 8715}, {516, 37536}, {1385, 56804}, {1445, 64547}, {1479, 35059}, {1483, 53790}, {1657, 31785}, {1697, 64533}, {1698, 64529}, {1699, 64528}, {1742, 48926}, {2818, 5894}, {3295, 64538}, {3336, 33656}, {3753, 50322}, {4324, 64580}, {5482, 12699}, {5752, 9778}, {5886, 14131}, {9519, 12005}, {10108, 37553}, {15488, 28178}, {18046, 22793}, {25440, 34461}, {26285, 52005}, {28198, 35631}, {31423, 45829}, {31778, 64005}, {33555, 37743}, {34463, 37732}, {34583, 37720}, {37521, 48661}

X(64531) = midpoint of X(i) and X(j) for these {i,j}: {1657, 31785}, {6361, 37482}, {31778, 64005}
X(64531) = reflection of X(i) in X(j) for these {i,j}: {1, 64525}, {5, 53002}, {12699, 5482}, {64527, 64541}, {64530, 1}, {64532, 3}, {64537, 34466}
X(64531) = complement of X(64527)
X(64531) = anticomplement of X(64541)
X(64531) = X(i)-Dao conjugate of X(j) for these {i, j}: {64541, 64541}
X(64531) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3871, 1}
X(64531) = pole of line {4694, 11376} with respect to the Feuerbach hyperbola
X(64531) = X(6662)-of-excentral-triangle
X(64531) = X(6663)-of-6th-mixtilinear-triangle
X(64531) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6361, 37482, 517}, {29349, 53002, 5}

X(64532) = ORTHOLOGY CENTER OF THESE TRIANGLES: HEXYL AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^3*(b-c)^2*(b+c)+b*c*(b^2-c^2)^2+a^4*(b^2+c^2)-a^2*(b-c)^2*(b^2+3*b*c+c^2)-a*(b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+c^5)) : :
X(64532) = -3*X[381]+X[31785], -3*X[549]+2*X[53002], -3*X[1699]+X[31778], -3*X[3576]+2*X[64525], -2*X[5482]+3*X[5886], -3*X[5587]+4*X[64529], -3*X[5603]+X[37482], -5*X[8227]+4*X[64528], -5*X[18493]+3*X[37521]

X(64532) lies on these lines: {1, 10108}, {3, 49997}, {4, 8}, {20, 64527}, {30, 64572}, {40, 5400}, {56, 64539}, {78, 64526}, {381, 31785}, {392, 17676}, {499, 35059}, {511, 22791}, {513, 8666}, {549, 53002}, {550, 29349}, {916, 54198}, {936, 64542}, {942, 17721}, {946, 37536}, {957, 37435}, {970, 28174}, {991, 1279}, {999, 64538}, {1537, 5562}, {1699, 31778}, {2390, 10916}, {2818, 2883}, {3333, 64535}, {3576, 64525}, {3579, 5956}, {3583, 64580}, {3784, 11373}, {5482, 5886}, {5587, 64529}, {5603, 37482}, {6147, 58535}, {6796, 34461}, {7675, 64547}, {8227, 64528}, {8679, 49600}, {11230, 25492}, {11573, 12053}, {13464, 29353}, {13624, 28370}, {15488, 40273}, {18481, 50419}, {18493, 37521}, {19858, 49641}, {20039, 37727}, {21630, 23156}, {24390, 42448}, {27625, 31663}, {28160, 64568}, {28389, 37589}, {50621, 63997}, {61640, 64200}

X(64532) = midpoint of X(i) and X(j) for these {i,j}: {1, 64537}, {20, 64527}, {962, 5752}
X(64532) = reflection of X(i) in X(j) for these {i,j}: {4, 64541}, {40, 34466}, {15488, 40273}, {37536, 946}, {64531, 3}
X(64532) = pole of line {1837, 3670} with respect to the Feuerbach hyperbola
X(64532) = pole of line {1437, 35978} with respect to the Stammler hyperbola
X(64532) = X(6662)-of-hexyl-triangle
X(64532) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1, 51634, 64537}
X(64532) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 56884, 56885}, {517, 64541, 4}, {962, 5752, 517}

X(64533) = ORTHOLOGY CENTER OF THESE TRIANGLES: HUTSON INTOUCH AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+b*c*(b^2-c^2)^2+a^3*(b^3+b^2*c+b*c^2+c^3)-a^2*(b^4-b^3*c+8*b^2*c^2-b*c^3+c^4)-a*(b^5+b^4*c+b*c^4+c^5)) : :
X(64533) = -3*X[8236]+X[64547]

X(64533) lies on these lines: {1, 10108}, {8, 64542}, {10, 41682}, {11, 64529}, {12, 64528}, {55, 64525}, {56, 34466}, {65, 64535}, {73, 1385}, {145, 64526}, {388, 37536}, {495, 5482}, {513, 3884}, {517, 4292}, {942, 5724}, {952, 64573}, {1056, 37482}, {1697, 64531}, {3057, 64539}, {3600, 5752}, {4187, 6075}, {5045, 5717}, {5270, 50362}, {7962, 64530}, {8236, 64547}, {9655, 35645}, {9785, 64527}, {10039, 35059}, {12053, 64541}, {15310, 31792}, {19861, 56885}, {23156, 34434}, {24470, 45955}, {34790, 49991}

X(64533) = midpoint of X(i) and X(j) for these {i,j}: {145, 64526}, {3057, 64539}, {10106, 11573}, {23156, 34434}
X(64533) = reflection of X(i) in X(j) for these {i,j}: {8, 64542}, {65, 64535}, {64534, 1}
X(64533) = pole of line {4132, 48281} with respect to the incircle
X(64533) = pole of line {3670, 37722} with respect to the Feuerbach hyperbola
X(64533) = X(6662)-of-Hutson-intouch-triangle
X(64533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10106, 11573, 517}

X(64534) = ORTHOLOGY CENTER OF THESE TRIANGLES: INTOUCH AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^2-b*c+a*(b+c))*(a^2*(b-c)^2+2*a*b*c*(b+c)-(b^2-c^2)^2) : :
X(64534) = -3*X[354]+2*X[64535], -X[11573]+3*X[64162]

X(64534) lies on these lines: {1, 10108}, {2, 64526}, {7, 64527}, {11, 64528}, {12, 64529}, {30, 58535}, {55, 34466}, {56, 64525}, {57, 64531}, {65, 33656}, {149, 18180}, {226, 64541}, {354, 64535}, {389, 517}, {390, 5752}, {496, 5482}, {497, 37536}, {511, 15172}, {513, 3881}, {516, 58617}, {528, 58469}, {942, 63979}, {952, 44865}, {970, 10386}, {1058, 37482}, {3340, 64530}, {3664, 5045}, {3870, 56885}, {5853, 58497}, {10095, 58539}, {10222, 45046}, {11573, 64162}, {12109, 28174}, {12699, 17220}, {12912, 52424}, {14131, 15325}, {16608, 18257}, {24390, 64544}, {24470, 29349}, {29353, 40270}, {34753, 53002}

X(64534) = midpoint of X(i) and X(j) for these {i,j}: {7, 64547},
X(64534) = reflection of X(i) in X(j) for these {i,j}: {64526, 64542}, {64533, 1}, {64538, 5045}, {64539, 64535}
X(64534) = complement of X(64526)
X(64534) = anticomplement of X(64542)
X(64534) = X(i)-Dao conjugate of X(j) for these {i, j}: {24390, 8}, {64542, 64542}
X(64534) = pole of line {4057, 4063} with respect to the incircle
X(64534) = pole of line {12, 3670} with respect to the Feuerbach hyperbola
X(64534) = pole of line {4132, 4491} with respect to the Suppa-Cucoanes circle
X(64534) = X(6662)-of-intouch-triangle
X(64534) = X(6663)-of-Ursa-minor-triangle
X(64534) = barycentric product X(i)*X(j) for these (i, j): {3995, 64544}, {24390, 32911}
X(64534) = barycentric quotient X(i)/X(j) for these (i, j): {24390, 40013}, {64544, 39747}
X(64534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64526, 64542}, {354, 64539, 64535}, {5045, 15310, 64538}

X(64535) = ORTHOLOGY CENTER OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+b*c*(b^2-c^2)^2+a^3*(b^3-3*b^2*c-3*b*c^2+c^3)-a^2*(b^4-b^3*c+8*b^2*c^2-b*c^3+c^4)-a*(b^5-3*b^4*c+4*b^3*c^2+4*b^2*c^3-3*b*c^4+c^5)) : :
X(64535) = -3*X[354]+X[64534], 3*X[553]+X[11573], 3*X[3873]+X[64526], -5*X[11025]+X[64547], X[23156]+3*X[64550]

X(64535) lies on these lines: {1, 16528}, {5, 24237}, {7, 37536}, {57, 34466}, {65, 64533}, {226, 64528}, {354, 64534}, {513, 43972}, {517, 4298}, {518, 64542}, {553, 11573}, {942, 49745}, {1042, 1385}, {1210, 64529}, {3306, 56885}, {3333, 64532}, {3666, 10108}, {3670, 49557}, {3873, 64526}, {3937, 64544}, {4355, 31778}, {5482, 6147}, {5719, 14131}, {5752, 21454}, {5810, 63152}, {5885, 20617}, {9940, 62789}, {10580, 64527}, {10980, 64537}, {11019, 64541}, {11025, 64547}, {13407, 35059}, {15310, 50192}, {18180, 26842}, {23156, 64550}, {34583, 37731}

X(64535) = midpoint of X(i) and X(j) for these {i,j}: {65, 64533}, {942, 64538}, {64534, 64539}
X(64535) = pole of line {4694, 63997} with respect to the Feuerbach hyperbola
X(64535) = X(6662)-of-inverse-in-incircle-triangle
X(64535) = X(6663)-of-intouch-triangle
X(64535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {354, 64539, 64534}

X(64536) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND 1ST JENKINS

Barycentrics    2*a^3*(b+c)-a*(b-c)^2*(b+c)-b*c*(b+c)^2+a^2*(b^2+6*b*c+c^2) : :
X(64536) = -3*X[210]+5*X[64436], -3*X[354]+X[596], X[942]+3*X[4891], -3*X[3740]+4*X[64434], -3*X[3742]+2*X[6532], -6*X[3848]+5*X[64433], 3*X[3873]+X[24068], 5*X[18398]+3*X[32915], 3*X[39550]+X[44039], -9*X[63961]+13*X[64435], -9*X[64149]+X[64184]

X(64536) lies on these lines: {1, 2}, {210, 64436}, {354, 596}, {516, 37536}, {518, 4075}, {536, 50192}, {726, 13476}, {740, 24176}, {942, 4891}, {1089, 62867}, {1126, 13741}, {1269, 3664}, {1574, 17388}, {2260, 3950}, {2650, 4975}, {3159, 3874}, {3315, 43993}, {3454, 4966}, {3670, 4065}, {3740, 64434}, {3742, 6532}, {3848, 64433}, {3873, 24068}, {3879, 18133}, {3881, 59717}, {3934, 17390}, {3993, 4022}, {4066, 49479}, {4360, 24170}, {4658, 32942}, {4857, 32949}, {4970, 24167}, {5204, 47040}, {5259, 32919}, {5284, 64072}, {6682, 58380}, {8715, 20470}, {13374, 29016}, {15569, 58387}, {16887, 41851}, {17376, 22793}, {17770, 57024}, {18398, 32915}, {18483, 48933}, {21070, 24512}, {21746, 50610}, {24046, 49470}, {25542, 32864}, {28228, 31778}, {32943, 37559}, {35631, 64566}, {36250, 49676}, {39550, 44039}, {50601, 64006}, {58560, 64430}, {63961, 64435}, {64149, 64184}

X(64536) = midpoint of X(i) and X(j) for these {i,j}: {596, 2901}, {3159, 3874}, {3881, 63800}, {35631, 64566}
X(64536) = reflection of X(i) in X(j) for these {i,j}: {24176, 58565}, {64185, 6532}, {64430, 58560}
X(64536) = pole of line {514, 26822} with respect to the Steiner inellipse
X(64536) = pole of line {86, 33771} with respect to the Wallace hyperbola
X(64536) = pole of line {21207, 55065} with respect to the dual conic of Stammler hyperbola
X(64536) = intersection, other than A, B, C, of circumconics {{A, B, C, X(42), X(43972)}}, {{A, B, C, X(3216), X(13476)}}, {{A, B, C, X(4651), X(42471)}}, {{A, B, C, X(20011), X(60617)}}
X(64536) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 3720, 1125}, {740, 58565, 24176}, {3742, 64185, 6532}, {64149, 64184, 64431}

X(64537) = ORTHOLOGY CENTER OF THESE TRIANGLES: 6TH MIXTILINEAR AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(-(a^2*(b^2-c^2)^2)+b*c*(b^2-c^2)^2+a^4*(b^2-b*c+c^2)+a^3*(b^3+c^3)-a*(b^5+b^3*c^2+b^2*c^3+c^5)) : :
X(64537) = -3*X[165]+4*X[34466], -3*X[1699]+2*X[37536], -4*X[5482]+5*X[8227], -5*X[7987]+4*X[64525], -9*X[7988]+8*X[64528], -7*X[7989]+8*X[64529], -4*X[9955]+3*X[37521]

X(64537) lies on these lines: {1, 10108}, {3, 238}, {4, 6327}, {5, 25957}, {30, 64575}, {40, 31855}, {57, 64539}, {78, 56884}, {165, 34466}, {200, 56885}, {355, 44865}, {382, 517}, {496, 3784}, {497, 11573}, {500, 31394}, {511, 12699}, {513, 62858}, {516, 5752}, {916, 63962}, {944, 62401}, {946, 29353}, {970, 29349}, {1699, 37536}, {2201, 20739}, {2390, 49168}, {2550, 58497}, {2818, 12779}, {3056, 63997}, {3333, 64538}, {3419, 42448}, {4326, 64547}, {4655, 50603}, {5178, 30438}, {5482, 8227}, {5880, 58469}, {7074, 12912}, {7987, 64525}, {7988, 64528}, {7989, 64529}, {8580, 64542}, {8757, 12410}, {9548, 64540}, {9955, 37521}, {10441, 22793}, {10974, 64016}, {10980, 64535}, {11531, 64530}, {17646, 44545}, {18480, 31785}, {24390, 26892}, {24851, 50617}, {25306, 63996}, {31781, 31822}, {33096, 50585}, {34462, 63985}, {38389, 58798}, {41014, 44151}, {49641, 59312}, {58617, 60896}

X(64537) = midpoint of X(i) and X(j) for these {i,j}: {5752, 64527}
X(64537) = reflection of X(i) in X(j) for these {i,j}: {1, 64532}, {10441, 22793}, {11531, 64530}, {31778, 4}, {31781, 31822}, {31785, 18480}, {37482, 946}, {37536, 64541}, {64531, 34466}
X(64537) = pole of line {4132, 4834} with respect to the Conway circle
X(64537) = pole of line {3670, 9581} with respect to the Feuerbach hyperbola
X(64537) = X(1351)-of-4th-Brocard-triangle
X(64537) = X(1351)-of-orthocentroidal-triangle
X(64537) = X(6662)-of-6th-mixtilinear-triangle
X(64537) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {946, 29353, 37482}, {5752, 64527, 516}, {34466, 64531, 165}, {37536, 64541, 1699}

X(64538) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST SAVIN AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+a^3*(b-c)^2*(b+c)+b*c*(b^2-c^2)^2-a^2*(b^4-b^3*c+4*b^2*c^2-b*c^3+c^4)-a*(b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+c^5)) : :
X(64538) = 3*X[11112]+X[23154], 3*X[17616]+X[18732]

X(64538) lies on these lines: {1, 64539}, {3, 6180}, {5, 40687}, {7, 37482}, {8, 50003}, {12, 35059}, {79, 50362}, {226, 5482}, {442, 3937}, {474, 56885}, {496, 64541}, {511, 24470}, {513, 1125}, {517, 4292}, {942, 49745}, {999, 64532}, {1058, 64527}, {1385, 1457}, {1463, 5266}, {2476, 26910}, {3295, 64531}, {3333, 64537}, {3555, 64526}, {3579, 22097}, {3628, 64489}, {3664, 5045}, {3666, 49557}, {3784, 37536}, {3953, 20615}, {4001, 34790}, {4014, 63997}, {5044, 17332}, {5249, 64544}, {5253, 56884}, {5762, 13348}, {5810, 26929}, {6937, 26914}, {9940, 40644}, {10441, 18541}, {11112, 23154}, {12436, 58497}, {12907, 30621}, {13411, 14131}, {15172, 29349}, {17365, 50597}, {17616, 18732}, {20367, 48928}, {22300, 23156}, {24929, 64525}, {34339, 45122}, {34466, 37582}, {37592, 49537}, {41340, 63995}, {58073, 62304}

X(64538) = midpoint of X(i) and X(j) for these {i,j}: {1, 64539}, {3555, 64526}, {4292, 11573}, {22300, 23156}
X(64538) = reflection of X(i) in X(j) for these {i,j}: {942, 64535}, {34790, 64542}, {58497, 12436}, {64534, 5045}
X(64538) = pole of line {3733, 4063} with respect to the incircle
X(64538) = pole of line {3953, 37722} with respect to the Feuerbach hyperbola
X(64538) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3784, 57282, 37536}, {4292, 11573, 517}, {5045, 15310, 64534}

X(64539) = ORTHOLOGY CENTER OF THESE TRIANGLES: URSA-MINOR AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+a^3*(b-c)^2*(b+c)+b*c*(b^2-c^2)^2-a^2*(b-c)^2*(b^2+b*c+c^2)-a*(b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+c^5)) : :
X(64539) = -3*X[210]+4*X[64542], -3*X[354]+2*X[64534], -3*X[11112]+X[42448], -2*X[31757]+3*X[64550]

X(64539) lies on these lines: {1, 64538}, {3, 1777}, {5, 35059}, {10, 513}, {30, 64577}, {55, 64531}, {56, 64532}, {57, 64537}, {210, 64542}, {354, 64534}, {404, 56884}, {497, 64527}, {516, 11573}, {517, 1770}, {518, 64526}, {942, 15310}, {1155, 34466}, {1376, 56885}, {1385, 4337}, {1739, 57666}, {1836, 37536}, {2098, 64530}, {2390, 17647}, {2392, 22300}, {2646, 64525}, {2818, 31775}, {3057, 64533}, {3474, 5752}, {3650, 3690}, {3784, 12699}, {3825, 38390}, {3888, 63996}, {3931, 49537}, {3937, 24390}, {4187, 38389}, {4295, 37482}, {4694, 20615}, {5044, 31895}, {5482, 12047}, {5530, 64540}, {5572, 64547}, {9579, 31778}, {9655, 31785}, {10108, 37593}, {10483, 64580}, {11112, 42448}, {12609, 64544}, {15171, 29349}, {17605, 64528}, {17606, 64529}, {18180, 20292}, {20718, 31737}, {31757, 64550}, {35645, 48661}, {41682, 49600}

X(64539) = midpoint of X(i) and X(j) for these {i,j}: {10483, 64580}
X(64539) = reflection of X(i) in X(j) for these {i,j}: {1, 64538}, {3057, 64533}, {64534, 64535}, {64547, 5572}
X(64539) = pole of line {667, 4694} with respect to the incircle
X(64539) = pole of line {496, 3782} with respect to the Feuerbach hyperbola
X(64539) = pole of line {4358, 24793} with respect to the Steiner inellipse
X(64539) = pole of line {3733, 4063} with respect to the Suppa-Cucoanes circle
X(64539) = X(6662)-of-Ursa-minor-triangle
X(64539) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3931, 49537, 49557}, {64534, 64535, 354}

X(64540) = ORTHOLOGY CENTER OF THESE TRIANGLES: VIJAY POLAR EXCENTRAL AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^6*(b-c)^2*(b+c)+b^2*(b-c)^2*c^2*(b+c)^3-a*b^2*c^2*(b+c)^2*(b^2+c^2)+a^5*(b-c)^2*(2*b^2+3*b*c+2*c^2)+a^4*b*c*(b^3+b^2*c+b*c^2+c^3)-a^3*(b+c)^2*(2*b^4-5*b^3*c+3*b^2*c^2-5*b*c^3+2*c^4)-a^2*(b^7-b^5*c^2+2*b^4*c^3+2*b^3*c^4-b^2*c^5+c^7)) : :

X(64540) lies on these lines: {4, 36926}, {5, 49641}, {44, 573}, {513, 17748}, {517, 2901}, {550, 970}, {2051, 5482}, {5530, 64539}, {5752, 18481}, {9535, 37482}, {9548, 64537}, {9567, 16528}, {28370, 61109}, {34466, 35203}, {48927, 64525}

X(64540) = pole of line {31946, 50493} with respect to the excircles-radical circle

X(64541) = ORTHOLOGY CENTER OF THESE TRIANGLES: WASAT AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+a^3*(b-c)^2*(b+c)+3*b*c*(b^2-c^2)^2-a^2*(b-c)^2*(b^2+3*b*c+c^2)-a*(b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+c^5)) : :
X(64541) = 3*X[2]+X[64527], -3*X[1699]+X[37536], -3*X[3817]+2*X[64528], -5*X[3843]+X[31785], 5*X[8227]+3*X[45829], -3*X[11230]+2*X[14131]

X(64541) lies on these lines: {2, 64527}, {4, 8}, {5, 49993}, {10, 38390}, {30, 64578}, {35, 34461}, {140, 29349}, {226, 64534}, {496, 64538}, {511, 40273}, {513, 24387}, {516, 34466}, {908, 64526}, {946, 48933}, {1125, 64525}, {1385, 32486}, {1699, 37536}, {2818, 5893}, {3452, 64542}, {3579, 19648}, {3628, 53002}, {3817, 64528}, {3834, 5482}, {3843, 31785}, {7741, 35059}, {8227, 45829}, {11019, 64535}, {11230, 14131}, {11263, 33656}, {12053, 64533}, {15489, 28178}, {17173, 64544}, {18257, 41883}, {18514, 64580}, {19543, 29229}, {21617, 64547}, {24390, 38389}, {28208, 64568}, {53790, 61510}

X(64541) = midpoint of X(i) and X(j) for these {i,j}: {4, 64532}, {8, 64530}, {37536, 64537}, {64527, 64531},
X(64541) = reflection of X(i) in X(j) for these {i,j}: {10, 64529}, {5482, 9955}, {53002, 3628}, {64525, 1125}
X(64541) = complement of X(64531)
X(64541) = X(6662)-of-Wasat-triangle-triangle
X(64541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64527, 64531}, {4, 64532, 517}, {1699, 64537, 37536}, {9955, 15310, 5482}

X(64542) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ZANIAH AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^4*(b-c)^2+b*c*(b^2-c^2)^2-a^2*(b-c)^2*(b^2+b*c+c^2)+a^3*(b^3+b^2*c+b*c^2+c^3)-a*(b^5+b^4*c+8*b^3*c^2+8*b^2*c^3+b*c^4+c^5)) : :
X(64542) = 3*X[2]+X[64526], 3*X[210]+X[64539], -5*X[18230]+X[64547], 3*X[22278]+X[31737]

X(64542) lies on these lines: {2, 64526}, {8, 64533}, {9, 64531}, {10, 49641}, {42, 10108}, {71, 2173}, {210, 64539}, {513, 4015}, {517, 11793}, {518, 64535}, {936, 64532}, {958, 64525}, {1329, 64529}, {1376, 34466}, {2550, 37536}, {2886, 64528}, {3293, 49557}, {3452, 64541}, {4001, 34790}, {5044, 44419}, {5482, 31419}, {5782, 9709}, {8580, 64537}, {15310, 63978}, {15829, 64530}, {18228, 64527}, {18230, 64547}, {22278, 31737}, {35338, 48926}

X(64542) = midpoint of X(i) and X(j) for these {i,j}: {8, 64533}, {34790, 64538}, {64526, 64534}
X(64542) = complement of X(64534)
X(64542) = pole of line {4132, 44316} with respect to the Spieker circle
X(64542) = X(6662)-of-2nd-Zaniah-triangle
X(64542) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64526, 64534}

X(64543) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND ANTIPEDAL-OF-X(19)

Barycentrics    a*(a^6*(b+c)+2*a^3*b*c*(b+c)^2-a^2*(b-c)^2*(b+c)^3-2*a^5*(b^2+c^2)+2*a*(b^2-c^2)^2*(b^2-b*c+c^2)+a^4*(b^3-2*b^2*c-2*b*c^2+c^3)-(b-c)^4*(b^3+2*b^2*c+2*b*c^2+c^3)) : :
X(64543) = -3*X[354]+X[3668], 3*X[3873]+X[45738]

X(64543) lies on these lines: {1, 19}, {37, 11028}, {57, 4319}, {142, 17059}, {226, 1827}, {354, 3668}, {497, 1119}, {516, 942}, {518, 59646}, {938, 50861}, {950, 1876}, {1439, 14100}, {2263, 11518}, {2809, 30621}, {2835, 12016}, {3333, 30265}, {3873, 45738}, {4329, 10580}, {5728, 8804}, {8680, 13476}, {9440, 18413}, {11018, 40646}, {11019, 18589}, {11020, 18655}, {13405, 40530}, {14760, 24929}, {59483, 62674}

X(64543) = X(571)-of-inverse-in-incircle
X(64543) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {942, 9944, 60945}, {31571, 31572, 63999}

X(64544) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(21) AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a+b)*(a+c)*(a^2*(b-c)^2+2*a*b*c*(b+c)-(b^2-c^2)^2) : :
X(64544) = -X[442]+3*X[61643], -3*X[15670]+X[22076], X[15680]+3*X[61699]

X(64544) lies on circumconic {{A, B, C, X(1389), X(24390)}} and on these lines: {1, 18174}, {2, 5482}, {3, 1730}, {21, 517}, {28, 9940}, {51, 7483}, {58, 942}, {60, 58569}, {65, 52680}, {81, 5045}, {140, 5446}, {333, 34790}, {373, 13747}, {375, 59719}, {392, 17588}, {404, 14131}, {405, 37536}, {442, 61643}, {496, 17197}, {500, 28258}, {511, 6675}, {513, 11263}, {851, 48926}, {859, 1385}, {991, 16415}, {1071, 37113}, {1125, 2392}, {1154, 10021}, {1212, 14964}, {1408, 3660}, {1437, 4228}, {1764, 57523}, {1780, 5173}, {1828, 5439}, {1872, 52891}, {2194, 16193}, {2328, 64419}, {2810, 63282}, {2836, 58568}, {3035, 58501}, {3286, 37582}, {3295, 18163}, {3555, 16704}, {3579, 17524}, {3647, 20718}, {3753, 11115}, {3794, 11110}, {3812, 35059}, {3819, 50205}, {3937, 64535}, {3953, 64559}, {3976, 18192}, {4184, 31663}, {4187, 64528}, {4221, 31787}, {4225, 13624}, {4267, 24929}, {4278, 5122}, {4653, 9957}, {4658, 5049}, {4999, 58469}, {5249, 64538}, {5259, 50362}, {5324, 11018}, {5358, 54417}, {5650, 17590}, {5719, 29958}, {5752, 6857}, {5777, 25516}, {5885, 11101}, {5901, 61638}, {6688, 52264}, {6888, 34462}, {7419, 15178}, {7489, 39271}, {7535, 36746}, {8021, 37623}, {8731, 48882}, {9895, 10391}, {9947, 64405}, {9955, 17167}, {9956, 47515}, {10110, 52265}, {10167, 31900}, {10441, 16418}, {10470, 19251}, {11108, 37521}, {11112, 64525}, {11227, 52012}, {11374, 56885}, {11451, 17566}, {12609, 64539}, {13411, 58497}, {13754, 16617}, {14956, 22793}, {15488, 50241}, {15670, 22076}, {15680, 61699}, {15952, 31788}, {16049, 40296}, {16164, 41592}, {16215, 64421}, {16948, 31794}, {17056, 49557}, {17173, 64541}, {17185, 35631}, {17530, 64529}, {17536, 33852}, {17810, 19547}, {18169, 37592}, {18792, 63522}, {19531, 19860}, {20831, 37527}, {24390, 64534}, {25514, 36742}, {27000, 46498}, {28383, 50317}, {31419, 64526}, {31792, 64415}, {34339, 37227}, {34381, 41582}, {37292, 46623}, {37370, 48931}, {37544, 64382}, {37693, 57666}, {37730, 64582}, {38472, 58404}, {40980, 50195}, {44253, 58619}, {46882, 59681}, {52541, 52564}, {57002, 58889}

X(64544) = midpoint of X(i) and X(j) for these {i,j}: {21, 18180}, {57002, 58889}
X(64544) = pole of line {1385, 3555} with respect to the Stammler hyperbola
X(64544) = X(5045)-of-2nd-anti-Pavlov-triangle
X(64544) = barycentric product X(i)*X(j) for these (i, j): {24390, 81}, {39747, 64534}
X(64544) = barycentric quotient X(i)/X(j) for these (i, j): {24390, 321}, {64534, 3995}
X(64544) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 18180, 517}, {51, 7483, 34466}, {58, 18165, 942}, {859, 54356, 1385}, {4228, 64394, 1437}, {4653, 18178, 9957}, {17167, 37357, 9955}, {58404, 58474, 38472}

X(64545) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND PEDAL-OF-X(31)

Barycentrics    -(a*b*(b-c)^2*c)+a^2*b*c*(b+c)-b^2*c^2*(b+c)+a^3*(b+c)^2 : :
X(64545) = -3*X[354]+X[42027], -3*X[4688]+X[22316], -7*X[4772]+3*X[32860], -X[17157]+3*X[42055], -2*X[58693]+3*X[59517]

X(64545) lies on these lines: {1, 75}, {37, 3840}, {42, 20892}, {43, 30090}, {192, 982}, {244, 56185}, {354, 42027}, {518, 59565}, {519, 64007}, {536, 42053}, {537, 21080}, {714, 13476}, {726, 942}, {730, 3664}, {742, 25371}, {872, 25106}, {899, 30044}, {1215, 20891}, {1278, 17450}, {2901, 50117}, {3739, 6685}, {3831, 3842}, {3950, 6184}, {3993, 37592}, {4688, 22316}, {4699, 59297}, {4704, 30948}, {4772, 32860}, {17157, 42055}, {17755, 51902}, {18743, 53676}, {20256, 29671}, {20923, 59511}, {21796, 46843}, {22167, 29824}, {24003, 29982}, {24357, 29668}, {25295, 62867}, {27633, 40533}, {28850, 64126}, {29649, 64170}, {58693, 59517}

X(64545) = midpoint of X(i) and X(j) for these {i,j}: {2901, 50117}
X(64545) = reflection of X(i) in X(j) for these {i,j}: {59716, 58620}
X(64545) = pole of line {4369, 27315} with respect to the Steiner inellipse
X(64545) = intersection, other than A, B, C, of circumconics {{A, B, C, X(274), X(30045)}}, {{A, B, C, X(13476), X(34063)}}
X(64545) = barycentric product X(i)*X(j) for these (i, j): {1, 30045}
X(64545) = barycentric quotient X(i)/X(j) for these (i, j): {30045, 75}
X(64545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {536, 58620, 59716}

X(64546) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND ANTIPEDAL-OF-X(37)

Barycentrics    a*(a^2*(b+c)^2-b*c*(b^2+c^2)-a*(b^3-2*b^2*c-2*b*c^2+c^3)) : :
X(64546) = -X[75]+3*X[354], X[192]+3*X[3873], -3*X[210]+5*X[4687], -X[3059]+3*X[27475], -3*X[3681]+7*X[27268], -X[3688]+3*X[29574], -3*X[3740]+4*X[4698], -3*X[3753]+X[49459], -6*X[3848]+5*X[31238], -3*X[3892]+X[49479], 3*X[4430]+5*X[4704] and many others

X(64546) lies on these lines: {1, 6}, {2, 58655}, {42, 21330}, {65, 24523}, {75, 354}, {192, 3873}, {210, 4687}, {346, 1002}, {517, 49471}, {519, 17049}, {536, 13476}, {674, 17390}, {714, 4891}, {726, 3881}, {740, 942}, {758, 58400}, {1764, 10178}, {2260, 8299}, {2277, 63515}, {2667, 3666}, {2805, 38484}, {2810, 58554}, {3059, 27475}, {3664, 6007}, {3681, 27268}, {3688, 29574}, {3696, 3812}, {3702, 3889}, {3720, 3728}, {3726, 17446}, {3739, 3741}, {3740, 4698}, {3753, 49459}, {3759, 63522}, {3779, 17316}, {3783, 28244}, {3842, 34790}, {3848, 31238}, {3870, 34247}, {3874, 3993}, {3875, 64560}, {3879, 9025}, {3880, 49475}, {3892, 49479}, {3912, 52020}, {4032, 5173}, {4111, 24603}, {4357, 4890}, {4360, 20358}, {4430, 4704}, {4446, 20691}, {4688, 58560}, {4699, 64149}, {4709, 5883}, {4755, 40607}, {4851, 17792}, {4852, 64524}, {4871, 25106}, {5045, 24325}, {5208, 8822}, {5249, 21926}, {5836, 22316}, {5847, 39543}, {5902, 49469}, {7201, 17625}, {9038, 17332}, {9507, 40941}, {9943, 10441}, {10167, 35621}, {10446, 15726}, {10473, 63994}, {10476, 30271}, {10914, 49678}, {12675, 35631}, {12680, 51063}, {12710, 35632}, {12723, 49518}, {13374, 64088}, {14520, 21629}, {15624, 23853}, {17065, 21857}, {17157, 32915}, {17165, 22016}, {17229, 22279}, {17231, 25144}, {17234, 61034}, {17243, 22277}, {17303, 28600}, {17319, 62872}, {17348, 64554}, {17356, 24653}, {17378, 49537}, {17609, 26106}, {17755, 58618}, {18398, 49474}, {20891, 25295}, {20992, 62853}, {21238, 25102}, {21443, 58584}, {22167, 62867}, {24210, 53476}, {24471, 39775}, {25277, 29982}, {25384, 29652}, {27261, 46897}, {27482, 31342}, {27633, 63497}, {28849, 50658}, {35612, 39594}, {35620, 39584}, {37676, 40934}, {44663, 48858}, {49481, 58562}, {58561, 61549}

X(64546) = midpoint of X(i) and X(j) for these {i,j}: {65, 49470}, {984, 3555}, {3874, 3993}, {3879, 21746}, {10914, 49678}, {11997, 54344}, {12680, 51063}, {12723, 49518}
X(64546) = reflection of X(i) in X(j) for these {i,j}: {75, 58583}, {960, 15569}, {3696, 3812}, {3739, 58571}, {3740, 64552}, {4688, 58560}, {17755, 58618}, {21443, 58584}, {22271, 4698}, {24325, 5045}, {30271, 58567}, {34790, 3842}, {49481, 58562}, {61549, 58561}, {64088, 13374}
X(64546) = anticomplement of X(58655)
X(64546) = X(i)-Dao conjugate of X(j) for these {i, j}: {58655, 58655}
X(64546) = X(i)-complementary conjugate of X(j) for these {i, j}: {34445, 1213}, {39741, 3454}, {39970, 1211}, {40025, 21245}, {59113, 661}
X(64546) = pole of line {3309, 47948} with respect to the Conway circle
X(64546) = pole of line {4083, 8640} with respect to the DeLongchamps ellipse
X(64546) = pole of line {55, 86} with respect to the Feuerbach hyperbola
X(64546) = pole of line {650, 7199} with respect to the Steiner inellipse
X(64546) = pole of line {1018, 25310} with respect to the Yff parabola
X(64546) = pole of line {274, 32932} with respect to the Wallace hyperbola
X(64546) = pole of line {142, 16589} with respect to the dual conic of Yff parabola
X(64546) = X(6748)-of-inverse-in-Conway-triangle
X(64546) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29968)}}, {{A, B, C, X(2176), X(13476)}}, {{A, B, C, X(3294), X(42027)}}, {{A, B, C, X(56537), X(62541)}}
X(64546) = barycentric product X(i)*X(j) for these (i, j): {1, 29968}
X(64546) = barycentric quotient X(i)/X(j) for these (i, j): {29968, 75}
X(64546) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 354, 58583}, {518, 15569, 960}, {984, 3555, 518}, {2667, 4022, 3666}, {3739, 58571, 3742}, {3741, 25124, 3739}, {4698, 22271, 3740}, {22271, 64552, 4698}, {25295, 29824, 20891}

X(64547) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(1)-CIRCUMCONCEVIAN OF X(7) AND 1ST-PAVLOV-ALTINTAŞ

Barycentrics    a*(a^6*(b-c)^2+b*(b-c)^4*c*(b+c)^2-a^5*(b^3-3*b^2*c-3*b*c^2+c^3)+a^2*(b+c)^2*(b^4+6*b^3*c-10*b^2*c^2+6*b*c^3+c^4)-a^4*(2*b^4+7*b^3*c-14*b^2*c^2+7*b*c^3+2*c^4)+2*a^3*(b^5-b^4*c-7*b^3*c^2-7*b^2*c^3-b*c^4+c^5)-a*(b-c)^2*(b^5+3*b^4*c+10*b^3*c^2+10*b^2*c^3+3*b*c^4+c^5)) : :
X(64547) = -3*X[8236]+2*X[64533], -5*X[11025]+4*X[64535], -5*X[18230]+4*X[64542]

X(64547) lies on these lines: {7, 64527}, {9, 64526}, {1445, 64531}, {3174, 56885}, {4326, 64537}, {5572, 64539}, {7675, 64532}, {7676, 34466}, {7677, 64525}, {7678, 64528}, {7679, 64529}, {8236, 64533}, {11025, 64535}, {11526, 64530}, {11573, 15006}, {15310, 63972}, {18230, 64542}, {21617, 64541}

X(64547) = reflection of X(i) in X(j) for these {i,j}: {7, 64534}, {11573, 15006}, {64526, 9}, {64539, 5572}
X(64547) = X(6662)-of-Honsberger-triangle

X(64548) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF 1ST CIRCUMPERP

Barycentrics    a*(-(b*(b-c)^2*c*(b+c))+a^3*(b+c)^2-a*(b-c)^2*(b^2-b*c+c^2)) : :

X(64548) lies on these lines: {1, 15621}, {2, 58644}, {37, 38}, {56, 64522}, {57, 18613}, {65, 1149}, {181, 3756}, {244, 64550}, {513, 1401}, {518, 3840}, {528, 40649}, {551, 942}, {614, 53312}, {959, 64442}, {982, 20718}, {1201, 34434}, {1420, 20617}, {3555, 49999}, {3677, 64553}, {3742, 22325}, {3873, 3952}, {4430, 30861}, {4553, 29840}, {4884, 40521}, {7191, 50362}, {7248, 64016}, {10453, 44671}, {10473, 21769}, {10582, 64554}, {14973, 30942}, {16610, 22278}, {16969, 64560}, {18165, 29820}, {18240, 58624}, {24471, 57033}, {30148, 37536}, {31330, 58379}, {37663, 61166}, {40588, 40959}, {62819, 64561}

X(64548) = pole of line {51662, 57155} with respect to the circumcircle
X(64548) = pole of line {44319, 62739} with respect to the incircle
X(64548) = pole of line {649, 854} with respect to the DeLongchamps ellipse

X(64549) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF 2ND SAVIN

Barycentrics    a*(3*a^2*b*c*(b+c)-b*(b-c)^2*c*(b+c)+a^3*(b^2-b*c+c^2)-a*(b-c)^2*(b^2+3*b*c+c^2)) : :

X(64549) lies on these lines: {1, 228}, {2, 9052}, {6, 64559}, {31, 64560}, {51, 3475}, {55, 64524}, {105, 5320}, {154, 354}, {373, 25568}, {517, 62856}, {518, 19723}, {942, 62834}, {968, 20358}, {1011, 55340}, {1824, 5572}, {3917, 38053}, {4228, 43149}, {5045, 62808}, {5542, 26892}, {5603, 6000}, {7190, 15503}, {7191, 35612}, {10578, 51377}, {11036, 42448}, {17049, 33171}, {17597, 18165}, {17728, 58574}, {19785, 39543}, {24477, 61643}, {26885, 52015}, {29817, 35645}, {32914, 35892}, {37521, 64149}, {38314, 39550}, {51099, 61678}

X(64549) = pole of line {4802, 21104} with respect to the DeLongchamps ellipse

X(64550) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 2

Barycentrics    a*(-(b*(b-c)^2*c*(b+c))+a^3*(b+c)^2-a*(b-c)^2*(b^2+3*b*c+c^2)) : :
X(64550) = 2*X[942]+X[22300], -4*X[3812]+X[22299], X[4292]+2*X[58493], X[16980]+5*X[52783], -X[23156]+4*X[64535], 2*X[31757]+X[64539], 2*X[37544]+X[44545]

X(64550) lies on circumconic {{A, B, C, X(34434), X(41797)}} and on these lines: {2, 20718}, {31, 64523}, {42, 13476}, {51, 513}, {55, 64524}, {57, 53297}, {65, 1193}, {72, 28611}, {75, 14973}, {142, 22276}, {181, 1086}, {197, 5228}, {210, 4688}, {226, 38472}, {244, 64548}, {354, 42040}, {375, 527}, {517, 549}, {518, 4685}, {553, 8679}, {612, 64553}, {902, 64559}, {942, 22300}, {968, 64554}, {1202, 2262}, {1836, 38390}, {1962, 64552}, {2051, 53566}, {3185, 43915}, {3336, 18180}, {3725, 64556}, {3754, 6682}, {3812, 22299}, {4292, 58493}, {4359, 22275}, {4850, 58572}, {5903, 17063}, {5943, 17768}, {5959, 34093}, {8049, 40619}, {9052, 49732}, {11263, 34466}, {11281, 15489}, {11552, 56884}, {11553, 28238}, {15443, 24914}, {16453, 42443}, {16610, 27635}, {16980, 52783}, {17049, 44419}, {17140, 22294}, {17245, 40966}, {17365, 23638}, {17596, 18165}, {18139, 61172}, {20367, 52139}, {22325, 24325}, {23156, 64535}, {26037, 40607}, {26842, 56878}, {27003, 50362}, {29309, 49736}, {31757, 64539}, {31993, 58642}, {32771, 58644}, {32860, 44671}, {32932, 57024}, {37544, 44545}, {37593, 58571}, {37662, 39793}, {39550, 40726}, {58574, 64162}, {59296, 64581}, {61358, 64561}, {63511, 64016}

X(64550) = midpoint of X(i) and X(j) for these {i,j}: {51, 11246}
X(64550) = reflection of X(i) in X(j) for these {i,j}: {64162, 58574}
X(64550) = X(i)-Dao conjugate of X(j) for these {i, j}: {41797, 17135}
X(64550) = pole of line {676, 1459} with respect to the DeLongchamps ellipse
X(64550) = pole of line {2051, 40515} with respect to the dual conic of Yff parabola
X(64550) = barycentric product X(i)*X(j) for these (i, j): {41797, 57}
X(64550) = barycentric quotient X(i)/X(j) for these (i, j): {41797, 312}
X(64550) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 11246, 513}, {65, 1393, 64522}

X(64551) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 13

Barycentrics    a*(a^4+b*(b-c)^2*c+a*(b-c)^2*(b+c)-2*a^2*(b^2+c^2)) : :

X(64551) lies on circumconic {{A, B, C, X(2224), X(55161)}} and on these lines: {1, 692}, {41, 64523}, {48, 354}, {560, 64555}, {604, 13476}, {674, 52086}, {999, 20470}, {1319, 1471}, {2268, 64553}, {2278, 20358}, {3204, 63522}, {4851, 25523}, {5050, 42885}, {7113, 64560}, {9310, 64554}, {10246, 23344}, {15934, 51687}, {17438, 21346}, {22356, 59217}, {35327, 52015}, {52134, 57024}

X(64551) = barycentric product X(i)*X(j) for these (i, j): {1, 55161}
X(64551) = barycentric quotient X(i)/X(j) for these (i, j): {55161, 75}

X(64552) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 68

Barycentrics    a*(-(b*(b-c)^2*c)+a^2*(b+c)^2-a*(b^3-5*b^2*c-5*b*c^2+c^3)) : :
X(64552) = -X[3681]+5*X[4687], X[3873]+3*X[51488], X[4430]+7*X[27268], X[4664]+3*X[64149], X[4681]+2*X[58583], 5*X[5439]+X[49462], X[7671]+3*X[27475], 5*X[17609]+X[49515]

X(64552) lies on these lines: {1, 4557}, {2, 44671}, {9, 64561}, {37, 38}, {513, 17392}, {517, 6176}, {518, 551}, {536, 3742}, {740, 3833}, {1149, 49478}, {1962, 64550}, {2486, 17758}, {2667, 64556}, {3247, 64553}, {3681, 4687}, {3696, 49999}, {3739, 3840}, {3740, 4698}, {3873, 51488}, {4430, 27268}, {4553, 29569}, {4664, 64149}, {4681, 58583}, {4890, 17245}, {5045, 27784}, {5439, 49462}, {5883, 50111}, {5902, 20718}, {6007, 49738}, {7671, 27475}, {10177, 51057}, {10389, 15624}, {16482, 46922}, {16672, 64560}, {16777, 64524}, {16826, 57024}, {17243, 22279}, {17359, 28600}, {17463, 21808}, {17609, 49515}, {20913, 57034}, {25078, 58564}, {26102, 58572}, {34583, 37633}, {37635, 61729}, {49491, 52875}

X(64552) = midpoint of X(i) and X(j) for these {i,j}: {37, 354}, {3740, 64546}, {3848, 58620}, {3892, 50094}, {4430, 64581}, {5883, 50111}, {10177, 51057}
X(64552) = reflection of X(i) in X(j) for these {i,j}: {354, 58571}, {3681, 40607}, {3739, 3848}, {3740, 4698}, {13476, 354}, {22271, 3740}, {58379, 2}
X(64552) = pole of line {649, 891} with respect to the DeLongchamps ellipse
X(64552) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 64554, 64523}, {2, 44671, 58379}, {37, 58571, 13476}, {3892, 50094, 518}

X(64553) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 80

Barycentrics    a*(-(b*(b-c)^2*c)+a^2*(b^2+c^2)-a*(b^3+b^2*c+b*c^2+c^3)) : :
X(64553) = -X[3779]+3*X[17301]

X(64553) lies on these lines: {1, 3286}, {2, 21865}, {8, 18144}, {9, 64523}, {37, 20358}, {38, 1755}, {65, 7225}, {75, 17142}, {141, 14839}, {192, 57024}, {239, 64581}, {354, 3723}, {513, 3056}, {517, 3098}, {518, 4523}, {612, 64550}, {674, 3663}, {758, 49472}, {1086, 3688}, {1449, 64561}, {2268, 64551}, {3057, 4864}, {3247, 64552}, {3270, 60919}, {3271, 17334}, {3662, 4553}, {3677, 64548}, {3747, 64557}, {3755, 9049}, {3779, 17301}, {3789, 28634}, {3799, 17283}, {3873, 17393}, {3875, 44671}, {3891, 22275}, {3946, 22277}, {4111, 50098}, {4271, 21320}, {4360, 62872}, {4361, 22271}, {4364, 17049}, {4384, 40607}, {4392, 50362}, {4446, 57039}, {4517, 17278}, {4657, 22279}, {4735, 28358}, {6385, 17143}, {6646, 25048}, {7064, 17337}, {7190, 43915}, {7263, 64007}, {8049, 27807}, {9025, 17345}, {9957, 15570}, {10477, 49453}, {15624, 37555}, {16482, 17336}, {16684, 62817}, {16777, 58571}, {16814, 63522}, {17144, 30938}, {17235, 17792}, {17246, 21746}, {17279, 40521}, {17318, 35892}, {17366, 20683}, {17395, 52020}, {17444, 17447}, {17452, 17463}, {17761, 55076}, {18040, 28597}, {18133, 20352}, {18191, 36263}, {20367, 20990}, {20964, 64558}, {21278, 39995}, {21334, 21342}, {22299, 37549}, {22325, 32920}, {23051, 34434}, {24661, 39742}, {25279, 48629}, {28593, 30982}, {28639, 58583}, {33122, 61172}, {46149, 49509}

X(64553) = midpoint of X(i) and X(j) for these {i,j}: {3056, 17276}, {10477, 49453}
X(64553) = reflection of X(i) in X(j) for these {i,j}: {17792, 17235}, {22277, 3946}
X(64553) = anticomplement of X(21865)
X(64553) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34443, 1654}, {55026, 1330}
X(64553) = pole of line {1019, 44319} with respect to the circumcircle
X(64553) = pole of line {512, 4162} with respect to the DeLongchamps ellipse
X(64553) = pole of line {27918, 36488} with respect to the Feuerbach hyperbola
X(64553) = pole of line {1621, 18042} with respect to the Stammler hyperbola
X(64553) = pole of line {16755, 33891} with respect to the Steiner circumellipse
X(64553) = pole of line {17143, 33764} with respect to the Wallace hyperbola
X(64553) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(8049), X(16679)}}, {{A, B, C, X(8053), X(27807)}}
X(64553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 20358, 64524}, {37, 64524, 64554}, {3056, 17276, 513}, {4361, 56542, 22271}, {16777, 64560, 58571}

X(64554) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 81

Barycentrics    a*(-(b*(b-c)^2*c)+a^2*(b^2+c^2)-a*(b^3-3*b^2*c-3*b*c^2+c^3)) : :
X(64554) =

X(64554) lies on these lines: {1, 4557}, {2, 57024}, {6, 58571}, {9, 13476}, {37, 20358}, {44, 354}, {45, 64560}, {344, 21865}, {513, 4675}, {518, 24331}, {674, 29571}, {942, 15254}, {968, 64550}, {1100, 63522}, {1445, 43915}, {1743, 64561}, {2140, 2486}, {2183, 3720}, {3271, 17392}, {3707, 9038}, {3742, 4670}, {3747, 64558}, {3753, 4702}, {3758, 16482}, {3812, 49484}, {3826, 39543}, {3834, 30953}, {3873, 17335}, {3892, 4753}, {4384, 44671}, {4432, 5883}, {4553, 17244}, {4663, 5045}, {4672, 58565}, {4687, 56537}, {4852, 58620}, {4890, 17366}, {4965, 7278}, {5272, 58572}, {5311, 64559}, {6007, 34824}, {6384, 30938}, {6666, 22277}, {8167, 35612}, {9054, 31285}, {9310, 64551}, {9345, 18191}, {10582, 64548}, {11375, 45963}, {15950, 53548}, {16832, 58379}, {17049, 17243}, {17063, 24696}, {17245, 21746}, {17259, 22271}, {17260, 64581}, {17279, 22279}, {17337, 52020}, {17348, 64546}, {17351, 58583}, {17451, 17463}, {18165, 26102}, {20964, 64557}, {20990, 55340}, {24327, 46843}, {25048, 29569}, {40131, 53312}, {40521, 41313}, {42356, 50658}, {47373, 52015}

X(64554) = midpoint of X(i) and X(j) for these {i,j}: {45, 64560}
X(64554) = pole of line {891, 54249} with respect to the DeLongchamps ellipse
X(64554) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64523, 64552, 1}

X(64555) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 89

Barycentrics    a*(-(b*(b-c)^2*c)-a*(b-c)^2*(b+c)+2*a^2*(b^2+c^2)) : :

X(64555) lies on these lines: {1, 1258}, {244, 1964}, {354, 63504}, {560, 64551}, {756, 56537}, {872, 64523}, {1015, 21815}, {1100, 3726}, {1279, 61399}, {1386, 2650}, {2170, 9449}, {2309, 20358}, {3123, 21746}, {3248, 13476}, {3663, 23634}, {3725, 64559}, {3728, 21352}, {3747, 55340}, {3873, 18194}, {4259, 28403}, {7032, 64560}, {16507, 64561}, {16696, 42038}, {16710, 42053}, {17348, 21805}, {17394, 17450}, {17445, 22167}, {20090, 63526}, {20706, 23660}, {21278, 30982}, {23633, 28358}, {24661, 64149}, {27846, 52020}

X(64555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17445, 57024, 22167}

X(64556) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 94

Barycentrics    a*(b*(b-c)^2*c+a*(b-c)^2*(b+c)+a^2*(b+c)^2) : :

X(64556) lies on these lines: {2, 37}, {6, 16726}, {38, 40607}, {39, 17337}, {42, 58571}, {44, 16574}, {213, 39797}, {239, 29437}, {244, 872}, {335, 29483}, {386, 5045}, {518, 3216}, {614, 15624}, {714, 25106}, {800, 37646}, {869, 64524}, {899, 4022}, {980, 17259}, {982, 64581}, {1086, 21796}, {1104, 16453}, {1279, 5132}, {1333, 11349}, {1418, 5165}, {1921, 29454}, {1964, 64523}, {2092, 17245}, {2664, 56537}, {2667, 64552}, {3589, 39798}, {3696, 50605}, {3725, 64550}, {3728, 58379}, {3840, 22316}, {3912, 21858}, {3946, 8610}, {4032, 43048}, {4255, 50203}, {4263, 17392}, {4271, 28350}, {4277, 4648}, {4446, 22323}, {4553, 24478}, {5069, 37650}, {6532, 20108}, {7032, 16507}, {7201, 26742}, {7277, 53543}, {10449, 21896}, {16696, 17277}, {16700, 32911}, {16716, 17682}, {16727, 39735}, {16728, 17352}, {17053, 17366}, {17231, 21857}, {17237, 21892}, {17348, 37596}, {17398, 31198}, {17749, 49515}, {18040, 59715}, {18143, 26772}, {18148, 59526}, {18150, 26756}, {19512, 50650}, {19543, 30271}, {20363, 29438}, {20718, 24443}, {21330, 44671}, {23488, 29557}, {24897, 41805}, {25125, 59514}, {28014, 37503}, {28248, 58642}, {29571, 56926}, {39974, 49738}, {49725, 50620}, {51415, 53476}, {58401, 64161}

X(64556) = reflection of X(i) in X(j) for these {i,j}: {20892, 3739}
X(64556) = complement of X(18137)
X(64556) = X(i)-Ceva conjugate of X(j) for these {i, j}: {53651, 513}
X(64556) = X(i)-complementary conjugate of X(j) for these {i, j}: {32, 40586}, {6577, 3835}, {8049, 626}, {34444, 141}, {39735, 21235}, {39797, 2887}, {40005, 40379}, {40147, 3454}, {40504, 21245}, {53651, 21262}
X(64556) = pole of line {1333, 63087} with respect to the Stammler hyperbola
X(64556) = pole of line {513, 23506} with respect to the Steiner inellipse
X(64556) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3995), X(39957)}}, {{A, B, C, X(18137), X(39797)}}
X(64556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {244, 872, 13476}, {536, 3739, 20892}, {614, 15624, 64557}, {3666, 4698, 37}

X(64557) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 99

Barycentrics    a*(b*(b-c)^2*c+2*a^3*(b+c)+a*(b-c)^2*(b+c)-a^2*(b^2+c^2)) : :

X(64557) lies on circumconic {{A, B, C, X(3970), X(13476)}} and on these lines: {1, 6}, {31, 13476}, {75, 62806}, {105, 2220}, {540, 48823}, {614, 15624}, {748, 40607}, {1621, 33760}, {1918, 64524}, {2209, 64523}, {3739, 3744}, {3747, 64553}, {3915, 20718}, {3938, 22271}, {3941, 16726}, {4022, 29818}, {16696, 23407}, {17135, 17279}, {17357, 31330}, {18137, 20045}, {20964, 64554}, {22316, 50023}, {34444, 56853}, {41312, 50257}

X(64557) = pole of line {274, 62814} with respect to the Wallace hyperbola
X(64557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {614, 15624, 64556}, {1918, 64524, 64558}

X(64558) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 100

Barycentrics    a*(-(b*(b-c)^2*c)+2*a^3*(b+c)-a*(b-c)^2*(b+c)+a^2*(b^2+c^2)) : :

X(64558) lies on these lines: {6, 20367}, {31, 64523}, {37, 21371}, {43, 22323}, {44, 4363}, {57, 16726}, {980, 1100}, {1086, 4274}, {1386, 24464}, {1449, 18186}, {1918, 64524}, {2209, 13476}, {3747, 64554}, {3759, 62636}, {4641, 63060}, {5165, 5222}, {5256, 16666}, {9352, 36289}, {20964, 64553}, {28254, 46838}, {29966, 41310}, {33882, 62797}

X(64558) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1918, 64524, 64557}

X(64559) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 105

Barycentrics    a*(a^3*(b-c)^2+2*a^2*b*c*(b+c)-b*(b-c)^2*c*(b+c)-a*(b-c)^2*(b^2+3*b*c+c^2)) : :

X(64559) lies on these lines: {1, 4245}, {6, 64549}, {31, 64524}, {42, 64523}, {55, 55340}, {65, 595}, {81, 105}, {210, 3757}, {518, 19742}, {902, 64550}, {2223, 39797}, {2308, 13476}, {3057, 51715}, {3475, 63498}, {3683, 20358}, {3722, 22278}, {3725, 64555}, {3953, 64544}, {4553, 29851}, {5311, 64554}, {5943, 17724}, {13407, 57666}, {14523, 43214}, {14746, 40972}, {16482, 32938}, {17625, 51708}, {17718, 63511}, {23415, 38347}, {23638, 37703}, {28027, 58493}, {29820, 50362}, {32914, 57024}

X(64559) = pole of line {3100, 20222} with respect to the Feuerbach hyperbola
X(64559) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7191, 18165, 354}

X(64560) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 110

Barycentrics    a*(-(b*(b-c)^2*c)-a*(b-c)^2*(b+c)+a^2*(b^2+b*c+c^2)) : :
X(64560) =

X(64560) lies on these lines: {1, 3}, {2, 20683}, {6, 13476}, {7, 2481}, {31, 64549}, {38, 5283}, {45, 64554}, {69, 17049}, {75, 35892}, {105, 60722}, {142, 3779}, {181, 3475}, {210, 16832}, {213, 614}, {239, 3873}, {244, 869}, {274, 5208}, {497, 17753}, {513, 62223}, {518, 4384}, {672, 59217}, {674, 4675}, {758, 24331}, {948, 1362}, {1001, 62817}, {1002, 5222}, {1015, 3117}, {1107, 21342}, {1334, 3720}, {1401, 7195}, {1463, 59372}, {1469, 5542}, {1743, 63522}, {1836, 4056}, {2082, 20229}, {2171, 21346}, {2276, 60677}, {2664, 17063}, {3041, 28827}, {3056, 3664}, {3218, 23407}, {3271, 4644}, {3294, 4423}, {3315, 62813}, {3672, 4890}, {3681, 16815}, {3688, 4648}, {3706, 32104}, {3742, 16831}, {3754, 49458}, {3763, 22279}, {3789, 24603}, {3799, 29572}, {3868, 16823}, {3874, 16825}, {3875, 64546}, {3881, 49488}, {4000, 52020}, {4042, 29773}, {4191, 40638}, {4259, 25557}, {4363, 57024}, {4392, 40773}, {4430, 16816}, {4517, 29571}, {4553, 17313}, {4847, 17050}, {4859, 61034}, {4888, 49537}, {4896, 29353}, {5439, 39586}, {5572, 12723}, {5836, 49451}, {5883, 36480}, {6007, 42697}, {7032, 64555}, {7113, 64551}, {7353, 31570}, {7362, 31569}, {9054, 34824}, {10436, 58583}, {10453, 17143}, {10477, 24325}, {10521, 15658}, {11037, 50626}, {14154, 63822}, {14839, 17316}, {15668, 56537}, {16476, 32913}, {16672, 64552}, {16777, 58571}, {16826, 64149}, {16969, 64548}, {16972, 58562}, {16975, 17449}, {17119, 44671}, {17154, 31036}, {17259, 64581}, {17267, 21865}, {17278, 22277}, {17298, 17792}, {17378, 25048}, {17794, 30830}, {18165, 18206}, {20116, 32118}, {20455, 59405}, {20544, 30985}, {20680, 24578}, {20992, 55340}, {21240, 31330}, {21384, 62823}, {24248, 39543}, {24268, 62852}, {24471, 58563}, {28600, 29603}, {29597, 58560}, {29988, 63147}, {34791, 49495}, {38989, 56697}, {39341, 49490}, {40730, 52209}, {49478, 60673}

X(64560) = reflection of X(i) in X(j) for these {i,j}: {45, 64554}, {4517, 29571}
X(64560) = X(i)-Dao conjugate of X(j) for these {i, j}: {30949, 49450}
X(64560) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8693, 513}
X(64560) = pole of line {513, 665} with respect to the incircle
X(64560) = pole of line {513, 665} with respect to the DeLongchamps ellipse
X(64560) = pole of line {1, 4059} with respect to the Feuerbach hyperbola
X(64560) = pole of line {21, 56542} with respect to the Stammler hyperbola
X(64560) = pole of line {226, 40784} with respect to the dual conic of Yff parabola
X(64560) = X(458)-of-intouch
X(64560) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(2223)}}, {{A, B, C, X(55), X(2481)}}, {{A, B, C, X(57), X(30949)}}, {{A, B, C, X(241), X(13476)}}, {{A, B, C, X(981), X(3744)}}, {{A, B, C, X(2283), X(4569)}}, {{A, B, C, X(3296), X(37609)}}
X(64560) = barycentric product X(i)*X(j) for these (i, j): {1, 30949}
X(64560) = barycentric quotient X(i)/X(j) for these (i, j): {30949, 75}
X(64560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 57, 2223}, {1, 982, 980}, {2, 62872, 56542}, {105, 62797, 60722}, {13476, 64524, 6}, {58571, 64553, 16777}

X(64561) = PERSPECTOR OF THESE TRIANGLES: 1ST-PAVLOV-ALTINTAŞ AND UNARY COFACTOR TRIANGLE OF GEMINI 111

Barycentrics    a*(-(b*(b-c)^2*c)-a*(b-c)^2*(b+c)+a^2*(b^2+6*b*c+c^2)) : :
X(64561) = -3*X[46922]+X[56537]

X(64561) lies on these lines: {6, 13476}, {9, 64552}, {44, 58571}, {86, 40607}, {354, 4722}, {513, 7277}, {518, 33682}, {524, 22279}, {651, 43915}, {757, 17943}, {872, 16726}, {894, 44671}, {1449, 64553}, {1743, 64554}, {2663, 16696}, {3879, 21865}, {4553, 20090}, {4557, 18164}, {4649, 20718}, {4667, 22277}, {4670, 22271}, {5750, 9038}, {9440, 40636}, {10436, 58379}, {16507, 64555}, {16668, 20358}, {17049, 32455}, {17120, 57024}, {17379, 64581}, {17390, 40521}, {20683, 63401}, {32913, 58572}, {38390, 61707}, {38472, 61652}, {46922, 56537}, {61358, 64550}, {62819, 64548}

X(64561) = midpoint of X(i) and X(j) for these {i,j}: {7277, 52020}
X(64561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {651, 55102, 43915}

X(64562) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND ANTI-AQUILA

Barycentrics    9*a^2*b*c+a^3*(b+c)+2*b*c*(b+c)^2-a*(b^3-4*b^2*c-4*b*c^2+c^3) : :
X(64562) =

X(64562) lies on these lines: {1, 39711}, {8, 443}, {75, 62854}, {192, 3622}, {229, 8666}, {244, 1698}, {596, 62831}, {1125, 3971}, {1201, 31178}, {2975, 45738}, {3646, 4756}, {3869, 17140}, {3875, 56048}, {3889, 50625}, {4329, 42697}, {4968, 64149}, {5880, 21289}, {17154, 31359}, {17164, 62835}, {17609, 28605}, {28581, 39739}, {31264, 34595}, {31339, 62868}, {49499, 64581}, {52352, 62870}

X(64562) = midpoint of X(i) and X(j) for these {i,j}: {1, 39711}
X(64562) = anticomplement of X(56237)
X(64562) = X(i)-Dao conjugate of X(j) for these {i, j}: {56237, 56237}
X(64562) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58, 3617}, {60, 12526}, {81, 32099}, {110, 4778}, {593, 10436}, {662, 48079}, {1333, 41839}, {1412, 62999}, {1449, 2895}, {2363, 3714}, {3361, 2475}, {3616, 1330}, {4565, 48268}, {4570, 4756}, {4652, 52364}, {4778, 3448}, {4790, 21221}, {4801, 21294}, {17553, 21291}, {19804, 21287}, {21454, 2893}, {31903, 4}, {42028, 69}, {48580, 150}, {58140, 148}
X(64562) = pole of line {4790, 4801} with respect to the Steiner circumellipse
X(64562) = pole of line {17393, 63158} with respect to the Wallace hyperbola
X(64562) = pole of line {4656, 33172} with respect to the dual conic of Yff parabola

X(64563) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND 5TH MIXTILINEAR

Barycentrics    (a-b-c)*(2*a^2*(b+c)-b*c*(b+c)+a*(2*b^2-5*b*c+2*c^2)) : :
X(64563) = -4*X[1125]+3*X[24174]

X(64563) lies on these lines: {1, 4234}, {2, 56174}, {8, 210}, {75, 3890}, {145, 3175}, {190, 36846}, {192, 3623}, {320, 4329}, {643, 3915}, {1125, 24174}, {1222, 56082}, {1997, 63133}, {2098, 3685}, {2136, 3699}, {2802, 46937}, {3210, 45219}, {3244, 24068}, {3445, 62300}, {3622, 3666}, {3656, 25650}, {3680, 30568}, {3878, 50625}, {3922, 26103}, {3996, 15829}, {4301, 18134}, {5057, 64584}, {5836, 30829}, {7270, 30305}, {10107, 30947}, {10912, 56311}, {11682, 45738}, {12632, 44722}, {12640, 62297}, {12699, 34548}, {12701, 60452}, {13463, 29641}, {14923, 18743}, {17154, 39702}, {17158, 53332}, {17164, 62835}, {17777, 32049}, {19804, 58679}, {20041, 42044}, {21272, 33780}, {22016, 49450}, {29824, 64580}, {56078, 64205}

X(64563) = reflection of X(i) in X(j) for these {i,j}: {8, 59577}, {34860, 1}, {44720, 19582}
X(64563) = anticomplement of X(56174)
X(64563) = X(i)-Dao conjugate of X(j) for these {i, j}: {56174, 56174}
X(64563) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58, 3621}, {60, 11682}, {81, 21296}, {110, 3667}, {145, 1330}, {593, 17151}, {662, 4106}, {1333, 17490}, {1412, 4373}, {1420, 2475}, {1743, 2895}, {3052, 1654}, {3667, 3448}, {4248, 4}, {4394, 21221}, {4462, 21294}, {4556, 4897}, {4565, 3676}, {4570, 3699}, {4591, 4927}, {4855, 52364}, {5435, 2893}, {8643, 148}, {16948, 8}, {18743, 21287}, {20818, 3151}, {33628, 2}, {41629, 69}, {52352, 3436}
X(64563) = pole of line {3699, 25268} with respect to the Kiepert parabola
X(64563) = pole of line {1408, 3915} with respect to the Stammler hyperbola
X(64563) = pole of line {4394, 4462} with respect to the Steiner circumellipse
X(64563) = pole of line {1014, 3875} with respect to the Wallace hyperbola
X(64563) = pole of line {5233, 24175} with respect to the dual conic of Yff parabola
X(64563) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(59577)}}, {{A, B, C, X(8), X(28370)}}, {{A, B, C, X(3701), X(34860)}}
X(64563) = barycentric product X(i)*X(j) for these (i, j): {28370, 312}
X(64563) = barycentric quotient X(i)/X(j) for these (i, j): {28370, 57}
X(64563) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 19582, 59577}, {3880, 19582, 44720}, {3880, 59577, 8}

X(64564) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND INNER-YFF

Barycentrics    b*c*(a^8-2*a^7*(b+c)-2*a^6*(b+c)^2-2*a*b*(b-c)^2*c*(b+c)^3+2*a^4*(b+c)^4-2*a^2*(b-c)^2*(b+c)^4+(b^2-c^2)^4+2*a^5*(2*b^3+b^2*c+b*c^2+2*c^3)-2*a^3*(b^5-b^4*c-4*b^3*c^2-4*b^2*c^3-b*c^4+c^5)) : :

X(64564) lies on circumconic {{A, B, C, X(1441), X(56727)}} and on these lines: {2, 158}, {4, 1441}, {8, 6515}, {21, 92}, {75, 51978}, {192, 6392}, {5271, 62810}, {6358, 10393}, {7650, 42455}, {12514, 45738}, {14361, 23661}, {17134, 37418}, {20320, 25935}, {24068, 31397}, {37095, 64420}

X(64564) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {28, 55109}, {58, 64081}, {3085, 1330}, {3553, 2895}, {19349, 3152}, {37383, 4}, {37550, 2475}, {55104, 52364}, {60494, 13219}, {62843, 8}

X(64565) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST CIRCUMPERP AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    2*a^6*(b+c)-a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3+a^5*(b^2-6*b*c+c^2)-a*(b^2-c^2)^2*(b^2-b*c+c^2)+a^3*b*c*(5*b^2-2*b*c+5*c^2)-2*a^4*(b^3+c^3) : :
X(64565) = -3*X[165]+X[44039], -5*X[3522]+X[10454], 3*X[9778]+X[64568]

X(64565) lies on these lines: {1, 24237}, {2, 64569}, {3, 48863}, {4, 17749}, {10, 37331}, {20, 391}, {30, 15489}, {39, 49131}, {40, 64572}, {55, 64573}, {100, 64567}, {165, 44039}, {515, 550}, {516, 64578}, {517, 596}, {759, 6906}, {952, 53002}, {1155, 64577}, {2051, 15971}, {2654, 40687}, {3522, 10454}, {3667, 31803}, {4220, 64576}, {4292, 29307}, {4297, 41430}, {5881, 16528}, {7991, 64571}, {9778, 64568}, {13442, 50650}, {13478, 37022}, {17355, 30618}, {21363, 50419}, {29069, 31793}, {29353, 59303}, {51558, 62320}

X(64565) = midpoint of X(i) and X(j) for these {i,j}: {40, 64572}, {7991, 64571}, {44039, 64575}
X(64565) = reflection of X(i) in X(j) for these {i,j}: {4, 64570}, {64566, 3}
X(64565) = anticomplement of X(64569)
X(64565) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {165, 64575, 44039}

X(64566) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    2*a^6*(b+c)-a^2*b*(b-c)^2*c*(b+c)+a^5*(b+c)^2-b*(b-c)^2*c*(b+c)^3-a*(b^2-c^2)^2*(b^2-b*c+c^2)-a^3*b*c*(3*b^2+2*b*c+3*c^2)-2*a^4*(b^3+c^3) : :
X(64566) = 3*X[2]+X[10454], -3*X[3576]+X[64572], -5*X[3616]+X[64568], X[3868]+3*X[54035], -3*X[4891]+X[31779], -3*X[10440]+X[59302]

X(64566) lies on these lines: {1, 2051}, {2, 10454}, {3, 48863}, {4, 991}, {5, 515}, {8, 9568}, {10, 13731}, {20, 64247}, {21, 64576}, {30, 5482}, {56, 64573}, {225, 40677}, {405, 13478}, {411, 6011}, {516, 15488}, {519, 970}, {572, 13740}, {573, 10449}, {942, 29069}, {944, 995}, {950, 19542}, {952, 34466}, {1746, 5047}, {2646, 64577}, {2975, 64567}, {3185, 56861}, {3244, 9569}, {3576, 64572}, {3616, 64568}, {3840, 4192}, {3868, 54035}, {4891, 31779}, {5046, 17182}, {5188, 49132}, {5396, 5882}, {5400, 21214}, {5691, 26102}, {5718, 10106}, {5743, 5795}, {5754, 37727}, {5755, 24391}, {5786, 11108}, {5799, 63999}, {7987, 29827}, {9567, 50588}, {10440, 59302}, {10479, 61109}, {10882, 30942}, {13244, 27368}, {13323, 48866}, {16607, 29065}, {16678, 52357}, {18481, 19648}, {23361, 34589}, {29307, 64004}, {29311, 35633}, {35631, 64536}, {35635, 54318}, {37365, 48894}, {37646, 64582}, {37693, 45287}, {43174, 48886}, {43739, 52087}, {57719, 60135}

X(64566) = midpoint of X(i) and X(j) for these {i,j}: {1, 44039}
X(64566) = reflection of X(i) in X(j) for these {i,j}: {4, 64569}, {35631, 64536}, {64565, 3}, {64578, 1125}
X(64566) = anticomplement of X(64570)
X(64566) = X(i)-Dao conjugate of X(j) for these {i, j}: {64570, 64570}
X(64566) = pole of line {8714, 17420} with respect to the excircles-radical circle
X(64566) = pole of line {2260, 37646} with respect to the dual conic of Yff parabola
X(64566) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 51558, 2051}, {5, 6176, 1125}, {8, 21363, 9568}, {515, 1125, 64578}

X(64567) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-CONWAY AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    a^5*(b-c)^2+2*a^6*(b+c)-b*(b-c)^2*c*(b+c)^3+a^3*b*c*(b^2-6*b*c+c^2)-a*(b^2-c^2)^2*(b^2-b*c+c^2)-2*a^4*(b^3+c^3)-a^2*b*c*(b^3-5*b^2*c-5*b*c^2+c^3) : :

X(64567) lies on these lines: {2, 64573}, {8, 48883}, {10, 22345}, {30, 64526}, {63, 44039}, {72, 515}, {78, 64572}, {100, 64565}, {200, 64575}, {329, 64568}, {355, 22458}, {518, 64577}, {519, 16980}, {908, 64578}, {952, 29958}, {2975, 64566}, {4696, 57287}, {8192, 48863}, {11680, 64569}, {11681, 64570}, {11682, 64571}, {11688, 64576}, {17499, 20096}, {23361, 52357}, {25237, 28598}

X(64567) = anticomplement of X(64573)

X(64568) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CONWAY AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    2*a^6*(b+c)-2*a^4*(b-c)^2*(b+c)-3*a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3-a*(b^2-c^2)^2*(b^2+c^2)+a^3*b*c*(b^2-6*b*c+c^2)+a^5*(b^2-b*c+c^2) : :
X(64568) = -4*X[960]+3*X[54035], -5*X[1698]+4*X[64574], -5*X[3616]+4*X[64566], -3*X[9778]+4*X[64565], -9*X[9779]+8*X[64569], -7*X[9780]+8*X[64570]

X(64568) lies on circumconic {{A, B, C, X(10454), X(51565)}} and on these lines: {1, 4}, {2, 44039}, {7, 64573}, {8, 1764}, {10, 10882}, {20, 64572}, {30, 64527}, {145, 10446}, {329, 64567}, {355, 10479}, {516, 64575}, {517, 64184}, {519, 12126}, {952, 10441}, {956, 5786}, {958, 1746}, {960, 54035}, {995, 51558}, {1125, 10887}, {1193, 50037}, {1482, 48899}, {1698, 64574}, {1837, 10475}, {2975, 13478}, {3146, 20037}, {3616, 64566}, {3741, 19647}, {3869, 29069}, {4297, 10434}, {5484, 10468}, {5587, 19863}, {5731, 10470}, {5793, 16435}, {5795, 18229}, {5853, 10442}, {5881, 10476}, {6738, 11021}, {7354, 29207}, {9535, 20036}, {9778, 64565}, {9779, 64569}, {9780, 64570}, {9791, 64576}, {9799, 10463}, {10435, 10890}, {10439, 28236}, {10444, 57287}, {10473, 10950}, {10474, 37740}, {10480, 10944}, {10856, 57284}, {10886, 19925}, {12550, 16124}, {18525, 19648}, {28160, 64532}, {28164, 45829}, {28204, 35631}, {28208, 64541}, {28224, 39550}, {35620, 37730}, {35634, 38455}, {37558, 45189}, {54331, 63968}

X(64568) = reflection of X(i) in X(j) for these {i,j}: {20, 64572}, {145, 64571}, {10454, 1}, {12435, 12545}, {44039, 64578}
X(64568) = anticomplement of X(44039)
X(64568) = pole of line {522, 4318} with respect to the Conway circle
X(64568) = X(185)-of-3rd-Conway-triangle
X(64568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 515, 10454}, {8, 10465, 1764}, {145, 10446, 11521}, {355, 37620, 10479}, {519, 12545, 12435}

X(64569) = ORTHOLOGY CENTER OF THESE TRIANGLES: 3RD EULER AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    a^5*(b-c)^2+2*a^6*(b+c)-a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3-a*(b^2-c^2)^2*(b^2-5*b*c+c^2)-a^3*b*c*(3*b^2+2*b*c+3*c^2)-2*a^4*(b^3+c^3) : :
X(64569) = 3*X[1699]+X[44039], -3*X[3817]+X[64578], 7*X[3832]+X[10454], -9*X[7988]+X[64575], -5*X[8227]+X[64572], -9*X[9779]+X[64568], -5*X[11522]+X[64571]

X(64569) lies on these lines: {2, 64565}, {4, 991}, {5, 20108}, {10, 15507}, {11, 64573}, {30, 14131}, {515, 546}, {517, 4075}, {952, 64529}, {1699, 44039}, {3817, 64578}, {3832, 10454}, {5806, 29069}, {6842, 31845}, {7988, 64575}, {8227, 64572}, {8229, 64576}, {9779, 64568}, {11522, 64571}, {11680, 64567}, {12572, 29307}, {17605, 64577},

X(64569) = midpoint of X(i) and X(j) for these {i,j}: {4, 64566}
X(64569) = reflection of X(i) in X(j) for these {i,j}: {64570, 5}
X(64569) = complement of X(64565)

X(64570) = ORTHOLOGY CENTER OF THESE TRIANGLES: 4TH EULER AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    a^5*(b-c)^2+2*a^6*(b+c)-a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3-a*(b^2-c^2)^2*(b^2+3*b*c+c^2)+a^3*b*c*(5*b^2-2*b*c+5*c^2)-2*a^4*(b^3+c^3) : :
X(64570) = -9*X[2]+X[10454], -5*X[1698]+X[44039], 3*X[3679]+X[64571], -3*X[3828]+X[64574], 3*X[5587]+X[64572], 7*X[7989]+X[64575], 7*X[9780]+X[64568], 3*X[10440]+X[12545]

X(64570) lies on these lines: {2, 10454}, {3, 17259}, {4, 17749}, {5, 20108}, {10, 15825}, {12, 64573}, {30, 64529}, {73, 40687}, {140, 515}, {386, 24220}, {404, 1746}, {474, 13478}, {516, 15489}, {572, 56766}, {950, 54387}, {952, 64528}, {1698, 44039}, {1764, 9568}, {2051, 3216}, {3667, 31871}, {3679, 64571}, {3828, 64574}, {5044, 29069}, {5051, 64576}, {5400, 15971}, {5587, 64572}, {5691, 62711}, {5786, 16408}, {5816, 56737}, {6686, 19925}, {6831, 42425}, {7989, 64575}, {9569, 48899}, {9780, 64568}, {10106, 37634}, {10440, 12545}, {10465, 26038}, {10882, 26037}, {11681, 64567}, {16569, 50037}, {17606, 64577}, {19335, 48937}, {19549, 50605}, {21363, 50702}, {23361, 41797}, {24618, 57283}, {29307, 64001}, {37662, 64582}

X(64570) = midpoint of X(i) and X(j) for these {i,j}: {4, 64565}, {10, 64578}
X(64570) = reflection of X(i) in X(j) for these {i,j}: {64569, 5}
X(64570) = complement of X(64566)

X(64571) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXCENTERS-REFLECTIONS AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    2*a^6*(b+c)-7*a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3+a^5*(b^2-4*b*c+c^2)-a*(b^2-c^2)^2*(b^2-b*c+c^2)+a^3*b*c*(3*b^2-14*b*c+3*c^2)-2*a^4*(b^3-3*b^2*c-3*b*c^2+c^3) : :
X(64571) = -3*X[551]+2*X[64574], -3*X[3241]+X[10454], -3*X[3679]+4*X[64570], -5*X[3890]+3*X[54035], -5*X[11522]+4*X[64569]

X(64571) lies on these lines: {1, 2051}, {4, 50637}, {8, 64578}, {10, 19549}, {30, 64530}, {145, 10446}, {382, 515}, {517, 64572}, {519, 10441}, {551, 64574}, {952, 15488}, {996, 37415}, {1222, 6996}, {2098, 64577}, {3057, 29069}, {3146, 14261}, {3241, 10454}, {3340, 64573}, {3663, 10106}, {3679, 64570}, {3890, 54035}, {5853, 43172}, {5881, 50625}, {7982, 48941}, {7991, 64565}, {10459, 24220}, {11522, 64569}, {11531, 64575}, {11533, 64576}, {11682, 64567}, {12513, 13478},

X(64571) = midpoint of X(i) and X(j) for these {i,j}: {145, 64568}, {11531, 64575}
X(64571) = reflection of X(i) in X(j) for these {i,j}: {8, 64578}, {7991, 64565}, {44039, 1}

X(64572) = ORTHOLOGY CENTER OF THESE TRIANGLES: HEXYL AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    3*a^3*b*(b-c)^2*c+2*a^6*(b+c)-2*a^4*(b-c)^2*(b+c)-3*a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3+a^5*(b^2-4*b*c+c^2)-a*(b^2-c^2)^2*(b^2-b*c+c^2) : :
X(64572) = -3*X[3576]+2*X[64566], -3*X[5587]+4*X[64570], -3*X[5731]+X[10454], -5*X[8227]+4*X[64569]

X(64572) lies on circumconic {{A, B, C, X(41904), X(44039)}} and on these lines: {1, 15971}, {3, 10}, {4, 995}, {20, 64568}, {30, 64532}, {40, 64565}, {56, 64577}, {78, 64567}, {222, 5710}, {516, 54338}, {517, 64571}, {519, 31785}, {944, 991}, {950, 17721}, {978, 5400}, {1503, 18990}, {3576, 64566}, {3878, 29057}, {5014, 57287}, {5264, 45287}, {5587, 64570}, {5731, 10454}, {7683, 64172}, {8227, 64569}, {8235, 64576}, {10572, 24239}, {11322, 24997}, {14110, 29069}, {28470, 48075}, {34773, 48893}

X(64572) = midpoint of X(i) and X(j) for these {i,j}: {1, 64575}, {20, 64568}
X(64572) = reflection of X(i) in X(j) for these {i,j}: {4, 64578}, {40, 64565}, {44039, 3}
X(64572) = pole of line {3772, 61412} with respect to the dual conic of Yff parabola
X(64572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 515, 44039}

X(64573) = ORTHOLOGY CENTER OF THESE TRIANGLES: INTOUCH AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    (a^3-b*c*(b+c)-a*(b^2-b*c+c^2))*(a^2*(b-c)^2+2*a^3*(b+c)+(b^2-c^2)^2) : :

X(64573) lies on these lines: {1, 15971}, {2, 64567}, {7, 64568}, {11, 64569}, {12, 64570}, {30, 58535}, {55, 64565}, {56, 64566}, {57, 44039}, {150, 5484}, {226, 64578}, {515, 942}, {944, 4306}, {952, 64533}, {1284, 64576}, {1401, 10950}, {3340, 64571}, {3600, 10454}, {3664, 10106}, {3953, 10572}, {5260, 24618}, {6284, 33551}, {7354, 21746}, {10570, 22769}, {18689, 20880}, {23536, 40677}, {24237, 37558}, {34589, 55362}, {40687, 59305}

X(64573) = complement of X(64567)
X(64573) = pole of line {17496, 21173} with respect to the incircle
X(64573) = pole of line {6354, 61412} with respect to the dual conic of Yff parabola
X(64573) = barycentric product X(i)*X(j) for these (i, j): {52358, 64582}
X(64573) = barycentric quotient X(i)/X(j) for these (i, j): {64582, 46880}

X(64574) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST JENKINS AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    2*a^6*(b+c)-4*a^2*b*(b-c)^2*c*(b+c)-a*(b-c)^4*(b+c)^2-b*(b-c)^2*c*(b+c)^3+a^5*(b^2+c^2)-2*a^3*b*c*(b^2+4*b*c+c^2)+a^4*(-2*b^3+3*b^2*c+3*b*c^2-2*c^3) : :
X(64574) = -3*X[551]+X[64571], -5*X[1698]+X[64568], 3*X[3679]+X[10454], -3*X[3828]+2*X[64570], X[5903]+3*X[54035]

X(64574) lies on circumconic {{A, B, C, X(573), X(15654)}} and on these lines: {3, 10}, {4, 33109}, {8, 9548}, {20, 47639}, {30, 49641}, {40, 7283}, {43, 944}, {102, 8707}, {145, 9549}, {181, 64163}, {386, 5882}, {517, 63800}, {519, 970}, {551, 64571}, {573, 2321}, {946, 30116}, {950, 5255}, {952, 59303}, {1385, 6685}, {1695, 12245}, {1698, 64568}, {2051, 13464}, {3550, 10572}, {3634, 64578}, {3679, 10454}, {3754, 29069}, {3828, 64570}, {3831, 37620}, {4203, 24996}, {4745, 62185}, {5530, 10106}, {5587, 19853}, {5657, 59313}, {5731, 59299}, {5818, 59312}, {5881, 9534}, {5903, 54035}, {7686, 29054}, {7982, 9535}, {9567, 37727}, {9623, 35635}, {10175, 19858}, {10406, 11011}, {10408, 64110}, {10459, 51558}, {13740, 39573}, {29057, 31788}, {35203, 43174}, {35633, 45955}

X(64574) = midpoint of X(i) and X(j) for these {i,j}: {10, 44039}
X(64574) = reflection of X(i) in X(j) for these {i,j}: {64578, 3634}
X(64574) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 44039, 515}, {2536, 2537, 15654}, {30116, 50037, 946}

X(64575) = ORTHOLOGY CENTER OF THESE TRIANGLES: 6TH MIXTILINEAR AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    2*a^3*b*(b-c)^2*c+2*a^6*(b+c)-2*a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3+a^5*(b^2-3*b*c+c^2)-a*(b^2-c^2)^2*(b^2-b*c+c^2)+a^4*(-2*b^3+b^2*c+b*c^2-2*c^3) : :
X(64575) = -3*X[165]+2*X[44039], -3*X[1699]+4*X[64578], -9*X[7988]+8*X[64569], -7*X[7989]+8*X[64570]

X(64575) lies on these lines: {1, 15971}, {3, 32918}, {4, 1193}, {8, 20}, {30, 64537}, {43, 5691}, {57, 64577}, {165, 44039}, {200, 64567}, {355, 37331}, {516, 64568}, {944, 4300}, {962, 20037}, {1469, 1503}, {1699, 64578}, {1742, 59310}, {3146, 20036}, {3220, 10570}, {3741, 4297}, {3869, 29057}, {4307, 10106}, {5587, 26030}, {5794, 18235}, {6210, 50419}, {7413, 10448}, {7987, 29827}, {7988, 64569}, {7989, 64570}, {8245, 64576}, {9840, 31339}, {11203, 31359}, {11531, 64571}, {12114, 37195}, {17016, 24257}, {17751, 20368}, {18481, 37425}, {19840, 37088}, {28164, 59303}, {31330, 50423}, {59299, 59387}

X(64575) = reflection of X(i) in X(j) for these {i,j}: {1, 64572}, {10454, 4297}, {11531, 64571}, {44039, 64565}
X(64575) = pole of line {21052, 21189} with respect to the excircles-radical circle
X(64575) = pole of line {6332, 20521} with respect to the Steiner circumellipse
X(64575) = pole of line {23681, 61412} with respect to the dual conic of Yff parabola
X(64575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {44039, 64565, 165}

X(64576) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST SHARYGIN AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    a^8*(b-c)^2+2*a^9*(b+c)-2*a^2*b*c*(b^2-c^2)^2*(b^2-3*b*c+c^2)-b*(b-c)^2*c*(b+c)^4*(b^2-b*c+c^2)-8*a^3*b^2*c^2*(b^3+c^3)-2*a^7*(b^3-3*b^2*c-3*b*c^2+c^3)-a*(b-c)^2*(b+c)^3*(b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)+2*a^6*(b^4+4*b^3*c-2*b^2*c^2+4*b*c^3+c^4)+a^5*(b^5-9*b^4*c+2*b^3*c^2+2*b^2*c^3-9*b*c^4+c^5)-a^4*(3*b^6+3*b^5*c+2*b^4*c^2+16*b^3*c^3+2*b^2*c^4+3*b*c^5+3*c^6) : :

X(64576) lies on these lines: {10, 9840}, {21, 64566}, {515, 9959}, {846, 44039}, {1284, 64573}, {4220, 64565}, {4425, 64578}, {5051, 64570}, {8229, 64569}, {8235, 64572}, {8245, 64575}, {9791, 64568}, {11533, 64571}, {11688, 64567}, {17611, 64577},

X(64577) = ORTHOLOGY CENTER OF THESE TRIANGLES: URSA-MINOR AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    a^5*(b-c)^2+a^3*b*(b-c)^2*c+2*a^6*(b+c)-2*a^4*(b-c)^2*(b+c)-3*a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3-a*(b^2-c^2)^2*(b^2-b*c+c^2) : :

X(64577) lies on these lines: {1, 4}, {10, 859}, {25, 10570}, {30, 64539}, {55, 44039}, {56, 64572}, {57, 64575}, {354, 64573}, {516, 64580}, {518, 64567}, {952, 5446}, {1155, 64565}, {1401, 7354}, {2098, 64571}, {2646, 64566}, {3575, 64507}, {5285, 40455}, {5724, 50622}, {5795, 28376}, {10457, 64582}, {10944, 50621}, {10950, 21746}, {11109, 41401}, {13478, 22760}, {15232, 52150}, {15971, 37558}, {17605, 64569}, {17606, 64570}, {17611, 64576}, {17647, 50605}, {17751, 57287}, {27621, 57284}, {28348, 56861}, {29069, 64043}, {37259, 56862}

X(64577) = pole of line {65, 2051} with respect to the Feuerbach hyperbola

X(64578) = ORTHOLOGY CENTER OF THESE TRIANGLES: WASAT AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    a^5*(b-c)^2+3*a^3*b*(b-c)^2*c+2*a^6*(b+c)-2*a^4*(b-c)^2*(b+c)-3*a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3-a*(b^2-c^2)^2*(b^2+b*c+c^2) : :
X(64578) = 3*X[1699]+X[64575], -5*X[3616]+X[10454], -3*X[3817]+2*X[64569]

X(64578) lies on these lines: {1, 9551}, {2, 44039}, {4, 995}, {5, 515}, {8, 64571}, {10, 15825}, {30, 64541}, {56, 13478}, {226, 64573}, {355, 50605}, {516, 64565}, {517, 64185}, {519, 35631}, {573, 10465}, {908, 64567}, {946, 36250}, {960, 29069}, {978, 50037}, {999, 5786}, {1042, 24237}, {1193, 2051}, {1699, 64575}, {1746, 2975}, {3616, 10454}, {3634, 64574}, {3667, 12688}, {3817, 64569}, {3840, 19546}, {4297, 9840}, {4425, 64576}, {5691, 21214}, {5793, 19517}, {10106, 39595}, {10446, 20036}, {10882, 31339}, {11521, 20040}, {15232, 34589}, {29311, 43164}, {29827, 37714}, {35649, 41723}, {37558, 40687}, {49997, 51558}, {64126, 64582}

X(64578) = midpoint of X(i) and X(j) for these {i,j}: {4, 64572}, {8, 64571}, {43164, 59303}, {44039, 64568},
X(64578) = reflection of X(i) in X(j) for these {i,j}: {10, 64570}, {64566, 1125}, {64574, 3634}
X(64578) = complement of X(44039)
X(64578) = pole of line {1400, 37646} with respect to the dual conic of Yff parabola
X(64578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64568, 44039}, {515, 1125, 64566}, {43164, 59303, 29311}

X(64579) = PERSPECTOR OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND X(9)-CIRCUMCONCEVIAN OF X(2)

Barycentrics    a*(a-b-c)*(a^3*(b+c)-(b-c)^2*(b^2+b*c+c^2)-a^2*(3*b^2+b*c+3*c^2)+a*(3*b^3-b^2*c-b*c^2+3*c^3)) : :

X(64579) lies on these lines: {2, 277}, {8, 15853}, {63, 15490}, {200, 6605}, {644, 3870}, {846, 8580}, {3161, 3693}, {3873, 35341}, {3971, 13405}, {5296, 44798}, {8012, 41228}, {8055, 40784}, {11019, 26690}, {17093, 28740}, {19541, 56536}, {27396, 40869}, {40997, 52818}

X(64579) = X(i)-Dao conjugate of X(j) for these {i, j}: {3059, 1212}
X(64579) = X(i)-Ceva conjugate of X(j) for these {i, j}: {31618, 8}
X(64579) = pole of line {522, 693} with respect to the dual conic of Adams circle
X(64579) = pole of line {693, 3900} with respect to the dual conic of incircle
X(64579) = pole of line {644, 3939} with respect to the dual conic of Feuerbach hyperbola
X(64579) = pole of line {693, 45755} with respect to the dual conic of Suppa-Cucoanes circle
X(64579) = intersection, other than A, B, C, of circumconics {{A, B, C, X(277), X(10482)}}, {{A, B, C, X(6605), X(30628)}}, {{A, B, C, X(20880), X(55337)}}
X(64579) = barycentric product X(i)*X(j) for these (i, j): {30628, 8}
X(64579) = barycentric quotient X(i)/X(j) for these (i, j): {30628, 7}
X(64579) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3870, 24771, 644}

X(64580) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND PEDAL-OF-X(21)

Barycentrics    a*(a^3*(b-c)^2*(b+c)+a^4*(b+c)^2-b*c*(b^2-c^2)^2-a^2*(b^4+b^3*c-2*b^2*c^2+b*c^3+c^4)-a*(b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+c^5)) : :

X(64580) lies on these lines: {1, 3}, {2, 34434}, {75, 14923}, {192, 20718}, {210, 59313}, {312, 3869}, {511, 10950}, {516, 64577}, {529, 23154}, {573, 56325}, {674, 41575}, {758, 24068}, {952, 6101}, {960, 25591}, {970, 40663}, {1829, 54396}, {1938, 48271}, {2390, 64002}, {2818, 11827}, {3175, 44663}, {3210, 20041}, {3583, 64532}, {3693, 20719}, {3827, 43216}, {3877, 26092}, {3878, 50605}, {3893, 49459}, {3922, 29825}, {4324, 64531}, {5752, 10573}, {5836, 31993}, {6327, 64584}, {8256, 51377}, {10459, 22097}, {10483, 64539}, {11573, 45287}, {12245, 59433}, {18178, 49487}, {18180, 30147}, {18395, 34466}, {18514, 64541}, {20647, 22298}, {21272, 21596}, {22300, 26028}, {25005, 38472}, {29824, 64563}, {29958, 34606}, {42448, 57288}

X(64580) = reflection of X(i) in X(j) for these {i,j}: {3869, 22299}, {10483, 64539}, {42448, 57288}, {45287, 11573}
X(64580) = anticomplement of X(34434)
X(64580) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1, 20060}, {6, 62998}, {58, 20040}, {59, 4551}, {572, 2}, {662, 18155}, {1252, 21362}, {2149, 56188}, {2185, 54121}, {2975, 8}, {4570, 53280}, {11109, 4}, {14534, 20028}, {14829, 69}, {17074, 7}, {17496, 150}, {17751, 1330}, {20986, 192}, {21061, 2895}, {21173, 149}, {22118, 6360}, {34278, 37653}, {37558, 2475}, {52139, 1654}, {52358, 2893}, {55323, 17778}, {57091, 33650}, {57165, 31290}, {57244, 21293}
X(64580) = pole of line {17496, 27346} with respect to the Steiner circumellipse
X(64580) = pole of line {21362, 56188} with respect to the Yff parabola
X(64580) = intersection, other than A, B, C, of circumconics {{A, B, C, X(56), X(55036)}}, {{A, B, C, X(312), X(1764)}}, {{A, B, C, X(10475), X(34434)}}
X(64580) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 3057, 3666}

X(64581) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND ANTIPEDAL-OF-X(37)

Barycentrics    a*(a^2*(b+c)^2-b*c*(b^2+c^2)-a*(b^3+b^2*c+b*c^2+c^3)) : :
X(64581) = -X[75]+3*X[3681], X[192]+3*X[4661], -3*X[210]+2*X[3739], -3*X[354]+4*X[4698], -6*X[3740]+5*X[31238], -3*X[3873]+5*X[4687], -4*X[3988]+X[49491], 2*X[4127]+X[49449], -3*X[4134]+X[49479], -3*X[4430]+7*X[27268], 3*X[4525]+X[49504] and many others

X(64581) lies on these lines: {1, 6}, {2, 13476}, {8, 3770}, {38, 872}, {63, 15624}, {69, 4553}, {75, 3681}, {76, 22289}, {141, 20683}, {192, 4661}, {210, 3739}, {239, 64553}, {291, 46838}, {354, 4698}, {513, 17347}, {517, 48938}, {524, 3688}, {668, 33769}, {674, 4416}, {692, 19121}, {726, 22316}, {740, 24068}, {758, 49457}, {869, 16696}, {982, 64556}, {1282, 1761}, {2895, 21289}, {3661, 21865}, {3663, 22312}, {3678, 24325}, {3696, 34790}, {3740, 31238}, {3779, 4643}, {3789, 17303}, {3799, 17295}, {3842, 3874}, {3868, 19874}, {3869, 20248}, {3873, 4687}, {3879, 9038}, {3883, 9049}, {3949, 4712}, {3952, 18137}, {3988, 49491}, {4043, 17135}, {4067, 49510}, {4111, 4665}, {4127, 49449}, {4134, 49479}, {4357, 22277}, {4364, 52020}, {4430, 27268}, {4517, 4851}, {4525, 49504}, {4537, 49535}, {4557, 16574}, {4688, 58655}, {4699, 58379}, {4715, 49537}, {4751, 63961}, {4878, 56509}, {5224, 22279}, {5697, 49689}, {6007, 17334}, {6376, 22293}, {6664, 9055}, {7064, 17243}, {9054, 17332}, {12329, 23151}, {12782, 21858}, {14839, 17362}, {14973, 32937}, {17049, 17330}, {17233, 40521}, {17235, 61034}, {17259, 64560}, {17260, 64554}, {17277, 62872}, {17344, 17792}, {17348, 20358}, {17349, 64523}, {17361, 25279}, {17365, 64007}, {17379, 64561}, {18206, 20990}, {21342, 27636}, {22285, 60719}, {25048, 62989}, {26125, 43915}, {29054, 63967}, {30271, 63976}, {34784, 51052}, {44670, 45738}, {49499, 64562}, {59296, 64550}, {62817, 64169}

X(64581) = midpoint of X(i) and X(j) for these {i,j}: {984, 5904}, {3869, 49450}, {4067, 49510}, {5697, 49689}, {34784, 51052}
X(64581) = reflection of X(i) in X(j) for these {i,j}: {75, 22271}, {3555, 15569}, {3696, 34790}, {3874, 3842}, {4430, 64552}, {13476, 40607}, {17365, 64007}, {21746, 17332}, {24325, 3678}, {30271, 63976}
X(64581) = anticomplement of X(13476)
X(64581) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 40008}
X(64581) = X(i)-Dao conjugate of X(j) for these {i, j}: {6376, 40008}, {13476, 13476}, {21753, 20963}
X(64581) = X(i)-Ceva conjugate of X(j) for these {i, j}: {17143, 2}
X(64581) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1, 33110}, {6, 17300}, {59, 35338}, {101, 26824}, {110, 4151}, {251, 17034}, {662, 7199}, {757, 13476}, {765, 4553}, {1110, 54118}, {1252, 1018}, {1621, 8}, {3294, 2895}, {3996, 3436}, {4040, 149}, {4043, 21287}, {4151, 3448}, {4251, 2}, {4570, 4436}, {4651, 1330}, {14004, 4}, {17143, 6327}, {17277, 69}, {17494, 150}, {18152, 315}, {20954, 21293}, {21007, 4440}, {33765, 6604}, {38346, 54102}, {38365, 17036}, {38859, 36845}, {40088, 21275}, {40408, 39734}, {55082, 3434}, {55086, 145}, {56537, 21289}, {58361, 21294}, {64169, 1654}
X(64581) = pole of line {55, 17259} with respect to the Feuerbach hyperbola
X(64581) = pole of line {81, 64524} with respect to the Stammler hyperbola
X(64581) = pole of line {17494, 20954} with respect to the Steiner circumellipse
X(64581) = pole of line {1018, 54118} with respect to the Yff parabola
X(64581) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(39735)}}, {{A, B, C, X(6), X(8049)}}, {{A, B, C, X(69), X(20811)}}, {{A, B, C, X(75), X(16552)}}, {{A, B, C, X(213), X(40504)}}, {{A, B, C, X(518), X(6664)}}, {{A, B, C, X(1218), X(16684)}}, {{A, B, C, X(13476), X(20963)}}, {{A, B, C, X(17135), X(40007)}}, {{A, B, C, X(40088), X(63918)}}
X(64581) = barycentric product X(i)*X(j) for these (i, j): {1, 40006}, {40638, 76}
X(64581) = barycentric quotient X(i)/X(j) for these (i, j): {75, 40008}, {40006, 75}, {40638, 6}
X(64581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 3681, 22271}, {518, 15569, 3555}, {984, 5904, 518}, {3740, 58583, 31238}, {3873, 4687, 58571}, {9054, 17332, 21746}, {13476, 40607, 2}, {17277, 62872, 64524}, {22271, 40504, 4651}

X(64582) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL-OF-X(58) AND 1ST ANTI-PAVLOV-ALTINTAŞ

Barycentrics    (a+b)*(a-b-c)*(a+c)*(a^2*(b-c)^2+2*a^3*(b+c)+(b^2-c^2)^2) : :

X(64582) lies on these lines: {1, 17197}, {8, 18163}, {10, 4267}, {20, 579}, {21, 950}, {39, 49131}, {58, 515}, {81, 10106}, {284, 1010}, {333, 5795}, {519, 18178}, {859, 1210}, {1043, 4483}, {1751, 37228}, {1834, 7683}, {1837, 56861}, {3286, 4297}, {3419, 19531}, {3452, 46877}, {3486, 17194}, {3600, 18164}, {3911, 4225}, {4266, 9534}, {4271, 9568}, {4276, 6684}, {4304, 17524}, {4308, 26818}, {4653, 63999}, {5837, 17185}, {6692, 37442}, {6738, 18165}, {8258, 54399}, {10454, 37642}, {10457, 64577}, {10461, 24391}, {10572, 52680}, {10950, 18191}, {11115, 57287}, {12437, 20258}, {13411, 47515}, {14953, 62774}, {15829, 17183}, {17167, 64160}, {17647, 54417}, {17754, 56984}, {18180, 64163}, {37646, 64566}, {37662, 64570}, {37730, 64544}, {62691, 63998}, {64126, 64578}, {64162, 64415}

X(64582) = pole of line {28274, 37583} with respect to the Stammler hyperbola
X(64582) = pole of line {37887, 53083} with respect to the dual conic of Yff parabola
X(64582) = barycentric product X(i)*X(j) for these (i, j): {46880, 64573}
X(64582) = barycentric quotient X(i)/X(j) for these (i, j): {64573, 52358}

X(64583) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND ANTIPEDAL-OF-X(158)

Barycentrics    b*c*(a^8-4*a^7*(b+c)+4*a*b*(b-c)^2*c*(b+c)^3-2*a^4*(b^2-c^2)^2+(b^2-c^2)^4+a^5*(8*b^3-4*b^2*c-4*b*c^2+8*c^3)-4*a^3*(b^5-b^4*c-b*c^4+c^5)) : :

X(64583) lies on circumconic {{A, B, C, X(3346), X(8747)}} and on these lines: {1, 29}, {2, 52384}, {8, 6001}, {75, 20246}, {85, 56872}, {189, 23661}, {192, 30694}, {318, 6260}, {322, 3436}, {1097, 14544}, {1441, 5932}, {1792, 18750}, {3346, 3998}, {5930, 64211}, {27383, 64194}, {37566, 54284}, {52346, 52366}

X(64583) = anticomplement of X(52384)
X(64583) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {21, 962}, {40, 2475}, {60, 62874}, {110, 8058}, {198, 17778}, {283, 280}, {284, 9965}, {329, 2893}, {333, 21279}, {643, 4397}, {662, 4131}, {1098, 20220}, {1790, 55119}, {1817, 7}, {1819, 20}, {2287, 189}, {2324, 2895}, {2360, 145}, {3194, 12649}, {5546, 6332}, {7054, 20223}, {7058, 20246}, {7074, 1654}, {7078, 3152}, {7080, 1330}, {7259, 20296}, {8058, 3448}, {8822, 3434}, {10397, 39352}, {13614, 34162}, {14298, 21221}, {27398, 69}, {41083, 56927}, {52378, 934}, {55111, 3151}, {57245, 13219}, {64082, 2897}

X(64584) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST ANTI-PAVLOV-ALTINTAŞ AND ANTIPEDAL-OF-X(225)

Barycentrics    a^7+4*a^5*b*c+2*a^2*b*(b-c)^2*c*(b+c)-2*a*b*c*(b^2-c^2)^2-(b-c)^2*(b+c)^3*(b^2-b*c+c^2)+a^4*(b^3-2*b^2*c-2*b*c^2+c^3)-a^3*(b^4+2*b^3*c-2*b^2*c^2+2*b*c^3+c^4) : :

X(64584) lies on circumconic {{A, B, C, X(34), X(40457)}} and on these lines: {1, 4}, {2, 2217}, {21, 23369}, {75, 5086}, {192, 20060}, {345, 3436}, {1610, 17555}, {2385, 45738}, {2551, 34851}, {3869, 33066}, {4329, 21287}, {5057, 64563}, {5794, 5928}, {6327, 64580}, {6875, 37812}, {7354, 51414}, {8229, 22760}, {29846, 30943}

X(64584) = anticomplement of X(2217)
X(64584) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1, 64047}, {2, 10446}, {6, 37683}, {59, 109}, {100, 57091}, {190, 35519}, {333, 2995}, {573, 2}, {3185, 192}, {3192, 193}, {3869, 8}, {4225, 1}, {4417, 69}, {6589, 4440}, {7012, 61178}, {7115, 44765}, {10571, 145}, {17080, 7}, {17555, 4}, {21078, 2895}, {21189, 149}, {22134, 6360}, {22276, 1654}, {40452, 17164}, {40590, 17778}, {51612, 1370}, {52310, 39352}, {53081, 28605}, {56553, 347}, {57111, 34188}

X(64585) = 1ST MIYAMOTO-MOSES-EULER CENTER

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 4*a^4*b^2*c^2 + 14*a^2*b^4*c^2 - 8*b^6*c^2 + 14*a^2*b^2*c^4 + 18*b^4*c^4 + 2*a^2*c^6 - 8*b^2*c^6 - c^8) : :
X(64585) = X[3]-4X[13154]

Let ABC be a triangle and MaMbMc the medial triangle. Let (Oa) be the circle passing through Mb and Mc and touching the circumcircle of ABC on the negative side of BC. Define (Ob) and (Oc) cyclically. Let A' be the intersection, other than O, of (Ob) and (Oc). Define B' and C' cyclically. (1) The center of the inner Apollonius circle of (Oa), (Ob), (Oc) lies on the Euler line. (2) The circumcenter of A'B'C' lies on the Euler line. (Keita Miyamoto, July 14, 2024)
The centers described in (1) and (2) are X(64585) and X(64586), respectively. (Centers found by Peter Moses, July 23, 2024)

X(64585) lies on these lines: {2,3}, {6,11793}, {54,6090}, {64,16836}, {68,19588}, {141,39571}, {155,5050}, {182,17814}, {185,22112}, {389,17825}, {394,11426}, {498,16541}, {511,3527}, {569,3167}, {578,17811}, {625,54091}, {1154,5644}, {1181,43650}, {1216,1351}, {1350,10110}, {1352,64038}, {1498,37515}, {1503,31521}, {2548,8573}, {3199,36751}, {3426,46850}, {3531,41462}, {3564,11487}, {3614,18954}, {3796,14530}, {3817,9911}, {3818,44862}, {3819,37498}, {3917,10982}, {3964,32828}, {5085,6759}, {5093,15067}, {5422,11444}, {5446,33878}, {5447,44413}, {5544,37489}, {5562,10601}, {5646,37480}, {5650,11424}, {5651,19357}, {5708,62770}, {5709,26938}, {5818,8192}, {5886,12410}, {5891,12164}, {5892,12163}, {5907,37514}, {5943,17834}, {6000,33537}, {6101,44456}, {6688,46730}, {6800,43614}, {7173,10833}, {7330,26928}, {7689,32620}, {7746,34809}, {7776,45198}, {7988,37557}, {8193,8227}, {8717,46852}, {9306,37476}, {9695,23275}, {9712,52795}, {9723,19418}, {9777,11412}, {9786,11695}, {9798,10175}, {9861,36519}, {9919,36518}, {10171,49553}, {10263,55584}, {10516,18381}, {10541,56516}, {10564,61774}, {10576,13889}, {10577,13943}, {10984,32063}, {11402,43651}, {11411,45298}, {11438,59777}, {11459,43600}, {11477,15606}, {11820,13474}, {11898,13292}, {12006,64105}, {12017,64049}, {12161,26206}, {12168,15059}, {12174,15058}, {12309,14852}, {12310,23515}, {12315,15030}, {12329,13374}, {13093,64100}, {13171,64101}, {13175,23514}, {13222,23513}, {13336,18451}, {13347,44870}, {13434,15066}, {13567,45015}, {13630,64097}, {13754,15805}, {14061,39803}, {14561,37491}, {14673,36520}, {14826,31804}, {15068,55705}, {15082,37497}, {16252,31267}, {17810,46728}, {18920,18925}, {19459,40330}, {21766,64050}, {22769,58631}, {23039,37493}, {23328,46373}, {23709,44914}, {26864,43598}, {31831,39899}, {32142,39522}, {32205,33533}, {34507,53019}, {34787,61676}, {34986,43908}, {35237,46849}, {36747,62217}, {36753,58891}, {37478,62209}, {37488,38317}, {37505,37672}, {38108,60897}, {38110,61607}, {39832,64089}, {42582,44598}, {42583,44599}, {43573,50955}, {45045,47296}, {45958,64098}, {48876,64048}, {52163,55602}, {53093,64026}, {54798,60171}, {55692,61752}

X(64585) = complement of X(6803)
X(64585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6804, 5}, {2, 6816, 7399}, {2, 7395, 3}, {2, 26205, 32954}, {3, 5, 1598}, {3, 381, 39568}, {3, 1656, 5020}, {3, 3851, 18534}, {3, 5020, 3517}, {3, 5055, 7529}, {3, 6642, 55572}, {3, 6644, 55574}, {3, 7506, 16195}, {3, 7529, 9909}, {3, 9818, 55571}, {3, 10244, 7512}, {3, 11479, 1597}, {3, 11484, 25}, {3, 18535, 11414}, {3, 35501, 11413}, {3, 61970, 44457}, {3, 62027, 47751}, {4, 7484, 3}, {5, 140, 3547}, {5, 7393, 3}, {5, 7516, 7387}, {5, 14790, 381}, {5, 16197, 3089}, {5, 16198, 3091}, {24, 5067, 11284}, {25, 3090, 11484}, {25, 7509, 3}, {25, 7512, 10244}, {140, 9818, 3}, {155, 33540, 10170}, {182, 17814, 19347}, {381, 10243, 1598}, {405, 474, 25876}, {468, 7464, 2070}, {549, 12085, 3}, {631, 1593, 3}, {631, 3089, 16197}, {1583, 1584, 37068}, {1656, 3526, 6639}, {1995, 37126, 9715}, {2045, 2046, 21841}, {2070, 7574, 62290}, {3090, 7509, 25}, {3091, 7485, 11414}, {3091, 11414, 18535}, {3515, 35921, 3}, {3523, 21312, 3}, {3523, 63664, 21312}, {3545, 10323, 5198}, {3628, 7514, 6642}, {3839, 45308, 33524}, {5020, 16195, 7506}, {5067, 7550, 24}, {5079, 54006, 7517}, {5422, 11444, 12160}, {5562, 10601, 11432}, {5891, 36752, 12164}, {6642, 7514, 3}, {6815, 34664, 382}, {6816, 7399, 381}, {6864, 37431, 7497}, {6905, 37246, 3}, {7387, 7393, 7516}, {7387, 7516, 3}, {7398, 59346, 7715}, {7401, 12362, 18494}, {7485, 11414, 3}, {7486, 37126, 1995}, {7506, 16195, 3517}, {7517, 54006, 3}, {7550, 11284, 3}, {9715, 37126, 3}, {10243, 14790, 39568}, {11313, 11314, 52251}, {11479, 16419, 3}, {13160, 16072, 3851}, {14709, 14710, 44273}, {14782, 14783, 7400}, {14784, 14785, 7392}, {16374, 37302, 3}, {17928, 54994, 3}, {30100, 52290, 24}, {35452, 61815, 3}, {37344, 54004, 3}

X(64586) = 2ND MIYAMOTO-MOSES-EULER CENTER

Barycentrics    a^2*(a^14 - 3*a^12*b^2 + a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - a^4*b^10 + 3*a^2*b^12 - b^14 - 3*a^12*c^2 + 10*a^10*b^2*c^2 - 13*a^8*b^4*c^2 + 4*a^6*b^6*c^2 + 11*a^4*b^8*c^2 - 14*a^2*b^10*c^2 + 5*b^12*c^2 + a^10*c^4 - 13*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 26*a^4*b^6*c^4 + 29*a^2*b^8*c^4 - 9*b^10*c^4 + 5*a^8*c^6 + 4*a^6*b^2*c^6 - 26*a^4*b^4*c^6 - 36*a^2*b^6*c^6 + 5*b^8*c^6 - 5*a^6*c^8 + 11*a^4*b^2*c^8 + 29*a^2*b^4*c^8 + 5*b^6*c^8 - a^4*c^10 - 14*a^2*b^2*c^10 - 9*b^4*c^10 + 3*a^2*c^12 + 5*b^2*c^12 - c^14) : :

See X(64585).

X(64586) lies on these lines: {2,3}, {159,44503}, {9306,9937}, {9822,44470}, {9908,13567}, {12301,18390}, {13754,45045}, {14457,44665}, {19137,44479}, {32048,43586}, {63701,64035}

X(64586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 7529, 235}, {3, 50143, 7395}, {24, 6816, 3}, {5020, 7506, 6642}, {6642, 7387, 6644}, {7503, 45172, 3}, {11479, 14130, 9818}, {16386, 37951, 2070}

X(64587) =  X(69)X(146)∩X(110)X(5895)

Barycentrics    2 a^16-a^14 b^2-16 a^12 b^4+27 a^10 b^6-27 a^6 b^10+16 a^4 b^12+a^2 b^14-2 b^16-a^14 c^2+22 a^12 b^2 c^2-18 a^10 b^4 c^2-68 a^8 b^6 c^2+99 a^6 b^8 c^2-18 a^4 b^10 c^2-24 a^2 b^12 c^2+8 b^14 c^2-16 a^12 c^4-18 a^10 b^2 c^4+128 a^8 b^4 c^4-72 a^6 b^6 c^4-80 a^4 b^8 c^4+66 a^2 b^10 c^4-8 b^12 c^4+27 a^10 c^6-68 a^8 b^2 c^6-72 a^6 b^4 c^6+164 a^4 b^6 c^6-43 a^2 b^8 c^6-8 b^10 c^6+99 a^6 b^2 c^8-80 a^4 b^4 c^8-43 a^2 b^6 c^8+20 b^8 c^8-27 a^6 c^10-18 a^4 b^2 c^10+66 a^2 b^4 c^10-8 b^6 c^10+16 a^4 c^12-24 a^2 b^2 c^12-8 b^4 c^12+a^2 c^14+8 b^2 c^14-2 c^16 : :
Barycentrics    S^2*(48*R^4-13*R^2*SA-11*R^2*SW+3*SA*SW)-(SB*SC*(48*R^2-11*SW)*(6*R^2-SW)) : :
X(64587) = 2*X(113)-X(11598), 2*X(2883)-X(15647), X(2935)-3*X(10706), X(5925)-3*X(15035), 2*X(6696)-3*X(36518), 3*X(10192)-2*X(37853), 3*X(10606)-5*X(64101), X(10733)-3*X(61721), 4*X(12900)-3*X(23328), 3*X(14643)-X(20427), 3*X(15055)-5*X(64024), 3*X(38789)+X(48672)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6506.

X(64587) lies on these lines: {4, 59654}, {69, 146}, {110, 5895}, {113, 10257}, {125, 5893}, {550, 1511}, {1498, 10721}, {1503, 5095}, {1539, 6000}, {2935, 10706}, {3357, 61574},{5663, 9927}, {5878, 7728}, {5894, 5972}, {5925, 15035}, {6225, 63716}, {6247, 46686}, {6696, 36518}, {6759, 34584}, {9934, 38790}, {10113, 45957}, {10117, 38444}, {10192, 37853}, {10606, 64101}, {10620, 63695}, {10733, 61721}, {12041, 61749}, {12373, 12950}, {12374, 12940}, {12900, 23328}, {13417, 36982}, {14643, 20427}, {15055, 64024},{16111, 16252}, {17702, 51491}, {17812, 19149}, {17854, 41589}, {19504, 46372}, {23315, 38791}, {31978, 41671}, {34128, 43585}, {34774, 36201}, {38789, 48672}, {39084, 47114}

X(64588) =  X(4)X(974)∩X(5)X(1539)

Barycentrics    2 a^16-3 a^14 b^2-8 a^12 b^4+17 a^10 b^6-17 a^6 b^10+8 a^4 b^12+3 a^2 b^14-2 b^16-3 a^14 c^2+22 a^12 b^2 c^2-18 a^10 b^4 c^2-48 a^8 b^6 c^2+69 a^6 b^8 c^2-6 a^4 b^10 c^2-24 a^2 b^12 c^2+8 b^14 c^2-8 a^12 c^4-18 a^10 b^2 c^4+96 a^8 b^4 c^4-52 a^6 b^6 c^4-64 a^4 b^8 c^4+54 a^2 b^10 c^4-8 b^12 c^4+17 a^10 c^6-48 a^8 b^2 c^6-52 a^6 b^4 c^6+124 a^4 b^6 c^6-33 a^2 b^8 c^6-8 b^10 c^6+69 a^6 b^2 c^8-64 a^4 b^4 c^8-33 a^2 b^6 c^8+20 b^8 c^8-17 a^6 c^10-6 a^4 b^2 c^10+54 a^2 b^4 c^10-8 b^6 c^10+8 a^4 c^12-24 a^2 b^2 c^12-8 b^4 c^12+3 a^2 c^14+8 b^2 c^14-2 c^16 : :
Barycentrics    S^2*(24*R^4-5*R^2*SA-5*R^2*SW+SA*SW)-SB*SC*(216*R^4-88*R^2*SW+9*SW^2) : :
X(64588) = 3*X(4)-X(63716), 2*X(5)-X(11598), X(64)-3*X(14644), X(5895)+2*X(63695), X(5925)-3*X(15055), 2*X(6696)-3*X(23515), 2*X(6698)-X(34778), 4*X(6723)-3*X(23328), X(10117)+3*X(61721), 3*X(10192)-2*X(38726), 3*X(10606)-5*X(15059), 3*X(10706)-X(17847), X(10721)-3*X(61721), 3*X(11744)+X(63716), X(12250)-5*X(15081), 3*X(15035)-5*X(64024),7*X(15036)-9*X(61680), 3*X(15061)-X(20427), 4*X(15088)-3*X(23329), 3*X(34128)-2*X(64027), 3*X(38724)+X(48672)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6506.

X(64588) lies on these lines: {4, 974}, {5, 1539}, {30, 15647}, {64, 14644}, {74, 5895}, {113, 5893}, {125, 10151}, {265, 5878}, {378, 7699}, {382, 9934}, {389, 22833}, {1177, 18550}, {1352, 2781}, {1498, 10733}, {1503, 12295}, {1511, 61749}, {1885, 3574}, {2778, 5777}, {2883, 17702}, {2935, 17928}, {3357, 20304}, {3521, 16222}, {5480, 10169}, {5663, 9927}, {5925, 15055}, {5972, 44241}, {6000, 10113}, {6247, 7687}, {6640, 20127}, {6696, 23515}, {6698, 34778}, {7706, 13364}, {10019, 10990},{10192, 38726}, {10257, 16111}, {10606, 15059}, {10706, 17847}, {11250, 13289}, {12133, 51757}, {12236, 44271}, {12250, 15081}, {12308, 64031}, {12825, 50009}, {12903, 12950}, {12904, 12940}, {13198, 44438}, {13293, 61574}, {13474, 32369}, {13851, 17856}, {15035, 64024}, {15036, 61680}, {15061, 20427}, {15088, 23329}, {15117, 37984}, {16163, 16252}, {18325, 44668}, {19456, 46372}, {20417, 43592}, {21649, 36982}, {23326, 48895}, {31978, 58498}, {32274, 34146}, {38724, 48672}, {38885, 48910}, {41673, 44440},{52071, 59495}

X(64588) = complement of the circumperp conjugate of X(40082)
X(64588) = pole of the line X(14391)X(46425) with respect to orthic inconic

X(64589) =  X(99)X(9544)∩X(184)X(543)

Barycentrics    a^2 (2 a^8-4 a^6 b^2+4 a^4 b^4-2 a^2 b^6-4 a^6 c^2+2 a^2 b^4 c^2+b^6 c^2+4 a^4 c^4+2 a^2 b^2 c^4-4 b^4 c^4-2 a^2 c^6+b^2 c^6) : :
Barycentrics    S^2*(-18*R^2*SA+9*SA^2-6*R^2*SW-6*SA*SW+SW^2))-2*(SB+SC)*(3*S^4-SA*(SA-2*SW)*SW^2 : :
X(64589) = X(3455)-3*X(6800)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6506.

X(64589) lies on these lines: {49, 10992}, {99, 9544}, {110, 2482}, {114, 10540}, {115, 5012}, {182, 5461}, {184, 543}, {542, 19127}, {567, 9880}, {620, 9306}, {671,11003}, {1614, 14981}, {2936, 26864}, {3455, 6800}, {5651, 22247}, {6722, 43650}, {6759, 38745}, {8787, 32217}, {10488, 51797}, {10539, 20399}, {10991, 52525}, {11623, 64049}, {15462, 61755}, {18350, 38751}, {18374, 18800}, {32046, 38734}, {33586, 39839}, {33813, 40111}, {38738, 43574}, {38740, 61134}, {38747, 57011}, {46301, 56980}

X(64590) =  EULER LINE INTERCEPT OF X(599)X(51730)

Barycentrics    5 a^10-12 a^8 b^2+4 a^6 b^4+10 a^4 b^6-9 a^2 b^8+2 b^10-12 a^8 c^2+18 a^6 b^2 c^2-18 a^4 b^4 c^2+18 a^2 b^6 c^2-6 b^8 c^2+4 a^6 c^4-18 a^4 b^2 c^4-18 a^2 b^4 c^4+4 b^6 c^4+10 a^4 c^6+18 a^2 b^2 c^6+4 b^4 c^6-9 a^2 c^8-6 b^2 c^8+2 c^10 : :
Barycentrics    S^2*(32*R^2-7*SW)-3*SB*SC*(2*R^2-SW) : :
X(64590) = 2*X(2)+X(24), 5*X(2)-2*X(11585), X(2)-4*X(16238), 4*X(2)-X(31180), 8*X(2)-5*X(31282), 7*X(2)-X(37444), X(2)+2*X(44211), X(3)+2*X(44270),X(4)+2*X(44268), 5*X(24)+4*X(11585),X(24)+8*X(16238), 2*X(24)+X(31180), 4*X(24)+5*X(31282), 11*X(24)-2*X(31304), 7*X(24)+2*X(37444), X(24)-4*X(44211), 2*X(235)+X(376), 4*X(381)-X(35490), X(381)+2*X(37814), X(599)+2*X(51730), X(3679)+2*X(51694), X(9140)+2*X(20771), X(21969)-4*X(58482), 2*X(33563)+X(63649), 4*X(51734)-X(54132)

As a point on the Euler line, X(64590) has Shinagawa coefficients {2*E-14*F,3*E+6*F}.

See Kadir Altintas and Ercole Suppa, euclid 6516.

X(64590) lies on these lines: {2, 3}, {599, 51730}, {3679, 51694}, {5642, 12227}, {7592, 61681}, {9140, 20771}, {15045, 61680}, {21969, 58482}, {33563, 63649}, {38794, 39522}, {43866,64037}, {44668, 47352}, {51734, 54132}

X(64590) = pole of the line X(5650)X(61701) with respect to Thomson-Gibert-Moses hyperbola

X(64591) =  EULER LINE INTERCEPT OF X(539)X(61646)

Barycentrics    5 a^10-12 a^8 b^2+4 a^6 b^4+10 a^4 b^6-9 a^2 b^8+2 b^10-12 a^8 c^2+8 a^6 b^2 c^2-4 a^4 b^4 c^2+14 a^2 b^6 c^2-6 b^8 c^2+4 a^6 c^4-4 a^4 b^2 c^4-10 a^2 b^4 c^4+4 b^6 c^4+10 a^4 c^6+14 a^2 b^2 c^6+4 b^4 c^6-9 a^2 c^8-6 b^2 c^8+2 c^10 : :
Barycentrics    S^2*(25*R^2-7*SW)-3*SB*SC*(R^2-SW) : :
X(64591) = 2*X(2)+X(26), X(2)-4*X(10020), 5*X(2)-2*X(13371), 7*X(2)-X(14790),4*X(2)-X(31181), 8*X(2)-5*X(31283), X(2)+2*X(44213), X(3)-4*X(15330), X(3)+8*X(18282), X(3)+2*X(44278), X(4)+2*X(48368), X(26)+8*X(10020), 5*X(26)+4*X(13371), 7*X(26)+2*X(14790), 2*X(26)+X(31181), 4*X(26)+5*X(31283), 11*X(26)-2*X(31305), X(26)-4*X(44213), X(376)+2*X(15761), X(381)+2*X(1658), 7*X(381)-4*X(18567),4*X(381)-X(52843), X(599)+2*X(19154), X(3679)+2*X(51696), X(9140)+2*X(20773), 2*X(11255)-5*X(51185), X(17834)+8*X(58435), X(21969)-4*X(58484), X(63649)+2*X(63734)

As a point on the Euler line, X(64591) has Shinagawa coefficients {3E+28F,-9E-12F}.

See Kadir Altintas and Ercole Suppa, euclid 6516.

X(64591) lies on these lines: {2, 3}, {539, 61646}, {599, 19154}, {1154, 61680}, {3679, 51696}, {9140, 20773}, {11255, 51185}, {11265, 13847}, {11266, 13846}, {11267, 16645}, {11268, 16644}, {12161, 64064}, {17834, 58435}, {21969, 58484}, {32223, 39522}, {33878, 46114}, {44673, 64098}, {61299, 61735}, {63649, 63734}

X(64591) = pole of the line X(5650)X(61702) with respect to Thomson-Gibert-Moses hyperbola

X(64592) =  EULER LINE INTERCEPT OF X(599)X(51731)

Barycentrics   5 a^6+a^5 b-2 a^4 b^2+4 a^3 b^3-5 a^2 b^4-5 a b^5+2 b^6+a^5 c+a^4 b c+4 a^3 b^2 c+4 a^2 b^3 c-5 a b^4 c-5 b^5 c-2 a^4 c^2+4 a^3 b c^2+18 a^2 b^2 c^2+10 a b^3 c^2-2 b^4 c^2+4 a^3 c^3+4 a^2 b c^3+10 a b^2 c^3+10 b^3 c^3-5 a^2 c^4-5 a b c^4-2 b^2 c^4-5 a c^5-5 b c^5+2 c^6 : :
X(64592) = 2*X(2)+X(27), 5*X(2)-2*X(440), 7*X(2)-X(3151), X(2)-4*X(6678), 4*X(2)-X(31153), 8*X(2)-5*X(31256), X(4)+2*X(48369), 5*X(27)+4*X(440),7*X(27)+2*X(3151), X(27)+8*X(6678),2*X(27)+X(31153),4*X(27)+5*X(31256), 11*X(27)-2*X(31292), X(376)+2*X(15762), 4*X(381)-X(52844), 14*X(440)-5*X(3151), X(440)-10*X(6678), 8*X(440)-5*X(31153), X(599)+2*X(51731), X(903)+2*X(62652), X(3679)+2*X(51697)

As a point on the Euler line, X(64592) has Shinagawa coefficients {9r^2+36r*R+36R^2-5s^2,6s^2}.

See Kadir Altintas and Ercole Suppa, euclid 6516.

X(64592) lies on these lines: {2, 3}, {599, 51731}, {903, 62652}, {3679, 51697}

X(64592) = pole of the line X(31153)X(40940) with respect to dual of Yff parabola

X(64593) =  EULER LINE INTERCEPT OF X(3679)X(51698)

Barycentrics    5 a^7+5 a^6 b-2 a^5 b^2-2 a^4 b^3-5 a^3 b^4-5 a^2 b^5+2 a b^6+2 b^7+5 a^6 c+a^5 b c-2 a^4 b^2 c+4 a^3 b^3 c-5 a^2 b^4 c-5 a b^5 c+2 b^6 c-2 a^5 c^2-2 a^4 b c^2+18 a^3 b^2 c^2+18 a^2 b^3 c^2-2 a b^4 c^2-2 b^5 c^2-2 a^4 c^3+4 a^3 b c^3+18 a^2 b^2 c^3+10 a b^3 c^3-2 b^4 c^3-5 a^3 c^4-5 a^2 b c^4-2 a b^2 c^4-2 b^3 c^4-5 a^2 c^5-5 a b c^5-2 b^2 c^5+2 a c^6+2 b c^6+2 c^7 : :
Barycentrics    (S^2*(4*r*R+36*R^2-7*SW)+3*SB*SC*(2*r*R+SW)) : :
X(64593) = 2*X(2)+X(28), 5*X(2)-2*X(21530), 4*X(2)-X(31154), 8*X(2)-5*X(31257), X(2)-4*X(52259), 7*X(2)-X(52364), X(4)+2*X(48370), 5*X(28)+4*X(21530), 2*X(28)+X(31154), 4*X(28)+5*X(31257),11*X(28)-2*X(31293), X(28)+8*X(52259), 7*X(28)+2*X(52364), X(376)+2*X(15763), X(381)+2*X(44220), 4*X(381)-X(52845), X(3679)+2*X(51698)

As a point on the Euler line, X(64593) has Shinagawa coefficients {7r^2+32r*R+36R^2-7s^2,-3(r^2+2r*R-s^2)}.

See Kadir Altintas and Ercole Suppa, euclid 6516.

X(64593) lies on these lines: {2, 3}, {3679, 51698}, {25055, 44661}

X(64594) =  EULER LINE INTERCEPT OF X(3679)X(51699)

Barycentrics    5 a^7+4 a^6 b-3 a^5 b^2-6 a^4 b^3-9 a^3 b^4+7 a b^6+2 b^7+4 a^6 c-a^5 b c-7 a^4 b^2 c-4 a^3 b^3 c-4 a^2 b^4 c+5 a b^5 c+7 b^6 c-3 a^5 c^2-7 a^4 b c^2+10 a^3 b^2 c^2+4 a^2 b^3 c^2-7 a b^4 c^2+3 b^5 c^2-6 a^4 c^3-4 a^3 b c^3+4 a^2 b^2 c^3-10 a b^3 c^3-12 b^4 c^3-9 a^3 c^4-4 a^2 b c^4-7 a b^2 c^4-12 b^3 c^4+5 a b c^5+3 b^2 c^5+7 a c^6+7 b c^6+2 c^7 : :
X(64594) = 2*X(2)+X(29), 7*X(2)-X(3152), 5*X(2)-2*X(18641), 4*X(2)-X(31155), 8*X(2)-5*X(31258), X(2)-4*X(52260), 7*X(29)+2*X(3152), 5*X(29)+4*X(18641), 2*X(29)+X(31155), 4*X(29)+5*X(31258), 11*X(29)-2*X(31294), X(29)+8*X(52260), X(376)+2*X(44225), 4*X(381)-X(52846), X(3679)+2*X(51699)

As a point on the Euler line, X(64594) has Shinagawa coefficients {5r^2+28r*R-9(-4R^2+s^2),-6r(r+2R)}.

See Kadir Altintas and Ercole Suppa, euclid 6516.

X(64594) lies on these lines: {2, 3}, {3679, 51699}

X(64595) =  (name pending)

Barycentrics    (a^2 - b^2 - c^2)*(a^12 - 3*a^10*b^2 + 2*a^8*b^4 + 2*a^6*b^6 - 3*a^4*b^8 + a^2*b^10 - 3*a^10*c^2 + 7*a^8*b^2*c^2 - 5*a^6*b^4*c^2 + 2*a^4*b^6*c^2 - 2*a^2*b^8*c^2 + b^10*c^2 + 2*a^8*c^4 - 5*a^6*b^2*c^4 + 2*a^4*b^4*c^4 + a^2*b^6*c^4 - 4*b^8*c^4 + 2*a^6*c^6 + 2*a^4*b^2*c^6 + a^2*b^4*c^6 + 6*b^6*c^6 - 3*a^4*c^8 - 2*a^2*b^2*c^8 - 4*b^4*c^8 + a^2*c^10 + b^2*c^10)*(2*a^12*b^2 - 7*a^10*b^4 + 7*a^8*b^6 + 2*a^6*b^8 - 8*a^4*b^10 + 5*a^2*b^12 - b^14 + 2*a^12*c^2 - 4*a^10*b^2*c^2 + 4*a^8*b^4*c^2 - 9*a^6*b^6*c^2 + 17*a^4*b^8*c^2 - 15*a^2*b^10*c^2 + 5*b^12*c^2 - 7*a^10*c^4 + 4*a^8*b^2*c^4 + 6*a^6*b^4*c^4 - 9*a^4*b^6*c^4 + 15*a^2*b^8*c^4 - 9*b^10*c^4 + 7*a^8*c^6 - 9*a^6*b^2*c^6 - 9*a^4*b^4*c^6 - 10*a^2*b^6*c^6 + 5*b^8*c^6 + 2*a^6*c^8 + 17*a^4*b^2*c^8 + 15*a^2*b^4*c^8 + 5*b^6*c^8 - 8*a^4*c^10 - 15*a^2*b^2*c^10 - 9*b^4*c^10 + 5*a^2*c^12 + 5*b^2*c^12 - c^14) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6519.

X(64595) lies on these lines: { }

X(64595) = complement of X(64596)

X(64596) = X(5)X(19192)∩X(11459)X(16868)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - 3*a^2*b^10 + b^12 + a^10*c^2 - 2*a^8*b^2*c^2 + 2*a^6*b^4*c^2 - 5*a^4*b^6*c^2 + 7*a^2*b^8*c^2 - 3*b^10*c^2 - 4*a^8*c^4 + a^6*b^2*c^4 + 2*a^4*b^4*c^4 - 5*a^2*b^6*c^4 + 2*b^8*c^4 + 6*a^6*c^6 + a^4*b^2*c^6 + 2*a^2*b^4*c^6 + 2*b^6*c^6 - 4*a^4*c^8 - 2*a^2*b^2*c^8 - 3*b^4*c^8 + a^2*c^10 + b^2*c^10)*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10 + a^10*c^2 - 2*a^8*b^2*c^2 + a^6*b^4*c^2 + a^4*b^6*c^2 - 2*a^2*b^8*c^2 + b^10*c^2 - 3*a^8*c^4 + 2*a^6*b^2*c^4 + 2*a^4*b^4*c^4 + 2*a^2*b^6*c^4 - 3*b^8*c^4 + 2*a^6*c^6 - 5*a^4*b^2*c^6 - 5*a^2*b^4*c^6 + 2*b^6*c^6 + 2*a^4*c^8 + 7*a^2*b^2*c^8 + 2*b^4*c^8 - 3*a^2*c^10 - 3*b^2*c^10 + c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6519.

X(64596) lies on these lines: {5, 19192}, {11459, 16868}, {36412, 62947}

X(64596) = isogonal conjugate of X(64597)
X(64596) = anticomplement of X(64595)
X(64596) = cevapoint of X(5) and X(403)

X(64597) = X(30)X(184)∩X(54)X(186)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 3*a^10*b^2 + 2*a^8*b^4 + 2*a^6*b^6 - 3*a^4*b^8 + a^2*b^10 - 3*a^10*c^2 + 7*a^8*b^2*c^2 - 5*a^6*b^4*c^2 + 2*a^4*b^6*c^2 - 2*a^2*b^8*c^2 + b^10*c^2 + 2*a^8*c^4 - 5*a^6*b^2*c^4 + 2*a^4*b^4*c^4 + a^2*b^6*c^4 - 4*b^8*c^4 + 2*a^6*c^6 + 2*a^4*b^2*c^6 + a^2*b^4*c^6 + 6*b^6*c^6 - 3*a^4*c^8 - 2*a^2*b^2*c^8 - 4*b^4*c^8 + a^2*c^10 + b^2*c^10) : :
X(64597) = X[2071] + 2 X[34986], 4 X[44907] - 3 X[61644], 2 X[57582] - 3 X[61743]

See Antreas Hatzipolakis and Peter Moses, euclid 6519.

X(64597) lies on these lines: {3, 16867}, {6, 37917}, {23, 48914}, {24, 32411}, {30, 184}, {49, 5448}, {51, 37951}, {54, 186}, {110, 13851}, {125, 539}, {185, 2071}, {403, 578}, {569, 44452}, {1092, 10257}, {1147, 2072}, {1181, 18859}, {1204, 34152}, {2070, 19357}, {3043, 25739}, {3153, 9545}, {5012, 37941}, {5097, 37940}, {5504, 21649}, {6000, 15463}, {6146, 36966}, {6759, 57584}, {6776, 44450}, {7574, 10619}, {9666, 10149}, {9703, 18396}, {9706, 10296}, {10151, 11424}, {10539, 23323}, {10540, 46686}, {12228, 51393}, {12289, 59279}, {12897, 31726}, {13198, 21663}, {13346, 16386}, {13473, 26883}, {13754, 32607}, {15004, 44272}, {15462, 21639}, {15646, 32046}, {16976, 43652}, {18383, 44905}, {18400, 52416}, {18925, 46450}, {19347, 35452}, {19457, 50461}, {22109, 45780}, {37505, 58551}, {38936, 58261}, {44246, 64049}, {44907, 61644}, {47277, 51733}, {57582, 61743}

X(64597) = isogonal conjugate of X(64596)
X(64597) = crosspoint of X(54) and X(5504)
X(64597) = crosssum of X(5) and X(403)
X(64597) = {X(13198),X(43574)}-harmonic conjugate of X(21663)

X(64598) = ISOGONAL CONJUGATE OF X(33562)

Barycentrics    a^2 (a^8-2 a^7 b+a^6 b^2-3 a^4 b^4+6 a^3 b^5-a^2 b^6-4 a b^7+2 b^8-2 a^7 c+5 a^6 b c-3 a^5 b^2 c+5 a^4 b^3 c-5 a^3 b^4 c-10 a^2 b^5 c+14 a b^6 c-4 b^7 c-3 a^5 b c^2+a^4 b^2 c^2-5 a^3 b^3 c^2+18 a^2 b^4 c^2-10 a b^5 c^2-b^6 c^2+2 a^5 c^3+2 a^3 b^2 c^3-5 a^2 b^3 c^3-5 a b^4 c^3+6 b^5 c^3-2 a^4 c^4+a^2 b^2 c^4+5 a b^3 c^4-3 b^4 c^4+2 a^3 c^5-3 a^2 b c^5-3 a b^2 c^5+5 a b c^6+b^2 c^6-2 a c^7-2 b c^7+c^8) (a^8-2 a^7 b+2 a^5 b^3-2 a^4 b^4+2 a^3 b^5-2 a b^7+b^8-2 a^7 c+5 a^6 b c-3 a^5 b^2 c-3 a^2 b^5 c+5 a b^6 c-2 b^7 c+a^6 c^2-3 a^5 b c^2+a^4 b^2 c^2+2 a^3 b^3 c^2+a^2 b^4 c^2-3 a b^5 c^2+b^6 c^2+5 a^4 b c^3-5 a^3 b^2 c^3-5 a^2 b^3 c^3+5 a b^4 c^3-3 a^4 c^4-5 a^3 b c^4+18 a^2 b^2 c^4-5 a b^3 c^4-3 b^4 c^4+6 a^3 c^5-10 a^2 b c^5-10 a b^2 c^5+6 b^3 c^5-a^2 c^6+14 a b c^6-b^2 c^6-4 a c^7-4 b c^7+2 c^8) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6525.

X(64598) lies on this line: {1421, 55335}

X(64598) = isogonal conjugate of X(33562)
X(64598) = intersection, other than A, B, C, of the circumconics {{A, B, C, X(1), X(1421)}} and {{A, B, C, X(11), X(59)}}

X(64599) = X(6)X(25)∩X(373)X(599)

Barycentrics   a^2 (a^4 b^2-b^6+a^4 c^2+10 a^2 b^2 c^2+b^4 c^2+b^2 c^4-c^6) : :
X(64599) = 5*X(6)+X(1843), 7*X(6)-X(6467), 2*X(6)+X(9969), 3*X(6)+X(9971), 5*X(6)-2*X(22829), 4*X(6)-X(32366), 3*X(6)-X(40673), X(6)+2*X(58471), 5*X(51)-X(1843), 7*X(51)+X(6467), 2*X(51)-X(9969), 3*X(51)-X(9971), 11*X(51)-X(9973), 5*X(51)+2*X(22829), 4*X(51)+X(32366), 3*X(51)+X(40673), X(69)-5*X(11451), X(141)+2*X(58555), 2*X(143)+X(44479),3*X(373)-X(599), X(568)+3*X(14848), 2*X(575)+X(5446), X(576)+2*X(5462), X(1216)-4*X(25555), X(1352)-3*X(14845), 2*X(1843)-5*X(9969), 3*X(1843)-5*X(9971), 11*X(1843)-5*X(9973), X(1843)+2*X(22829), 4*X(1843)+5*X(32366), 3*X(1843)+5*X(40673), X(1843)-10*X(58471), 3*X(5943)-2*X(40670), 2*X(5943)-X(61676), 2*X(6467)+7*X(9969), 3*X(6467)+7*X(9971), 4*X(6467)-7*X(32366), 3*X(6467)-7*X(40673), 3*X(9969)-2*X(9971), 11*X(9969)-2*X(9973), 5*X(9969)+4*X(22829), 2*X(9969)+X(32366), 3*X(9969)+2*X(40673), X(9969)-4*X(58471), 11*X(9971)-3*X(9973), 4*X(9971)+3*X(32366), X(9971)-6*X(58471), X(11216)+2*X(58544), 3*X(38110)-X(54042), 4*X(40670)-3*X(61676)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6525.

X(64599) lies on these lines: {4, 38005}, {6, 25}, {66, 18950}, {69, 11451}, {141, 6688}, {143, 44479}, {157, 13342}, {160, 13341}, {182, 39522}, {373, 599},{389, 2781}, {511, 549}, {524, 5943}, {542, 11232}, {568, 14848}, {575, 5446}, {576, 5462}, {1084, 46305}, {1154, 18583}, {1173, 1177}, {1216, 25555}, {1352, 14845}, {1493, 6153}, {1503, 51745}, {1576, 5007}, {1992, 5640}, {2854, 20583}, {2979, 3618}, {3060, 59373}, {3066, 63180}, {3148, 33872}, {3313, 51171}, {3527, 8549}, {3564, 13364}, {3567, 35486}, {3589, 3819}, {3629, 9822}, {3917, 47352}, {4663, 58469}, {5032, 11188}, {5085, 36987}, {5095, 58495}, {5097, 58549}, {5421, 40981}, {5476, 13754}, {5480, 6000}, {5890, 14853}, {5891, 14561}, {6329, 11574}, {6749, 34854}, {7998, 63109}, {8548, 58545}, {8550, 10110}, {8584, 8681}, {9019, 21849}, {9730, 20423}, {9977, 58557}, {10095, 43130}, {10250, 44489}, {11002, 63127}, {11255, 58484}, {11649, 47544}, {11692, 15516}, {11694, 14984}, {12039, 41614}, {12099, 61657}, {12220, 63011}, {12272, 63073}, {13338, 52144}, {14855, 31670}, {14912, 31166}, {14913, 32455}, {15019, 53777}, {15026, 64067}, {15030, 38072}, {15045, 54132}, {15067, 38079}, {15303, 45237}, {15471, 51994}, {15520, 34382}, {15531, 63022}, {15534, 61667}, {15826, 58481}, {16511, 16789}, {16657, 36201}, {20576, 46184}, {20582, 63632}, {20791, 51212}, {21969, 51185}, {22151, 53863}, {25322, 32450}, {32062, 53023}, {32155, 58546}, {32191, 32411}, {36851, 43726}, {37505, 64061}, {41672, 58518}, {41714, 55714}, {44299, 63119},{44496, 58552}, {44497, 58478}, {44498, 58477}, {44500, 58486}, {45186, 53093}, {46847, 50959}, {54131, 64100},{58492, 64031}, {63123, 64023}, {63663, 64026}, {63673, 63697}

X(64599) = inverse in orthic inconic of X(12367)
X(64599) = pole of the line X(6)X(22336) with respect to Jerabek hyperbola
X(64599) = pole of the line X(427)X(7603) with respect to Kiepert hyperbola
X(64599) = pole of the line X(512)X(5104) with respect to orthic inconic
X(64599) = pole of the line X(69)X(16511) with respect to Stammler hyperbola
X(64599) = pole of the line X(2485)X(36900) with respect to Steiner inellipse
X(64599) = pole of the line X(6090)X(47352) with respect to Thomson-Gibert-Moses hyperbola
X(64599) = pole of the tripolar of X(22336) with respect to Brocard inellipse

X(64600) = X(1836)X(42447)∩X(15726)X(29957)

Barycentrics    a^2 (a+b-c) (a-b+c) (a^5 b^2-3 a^4 b^3+2 a^3 b^4+2 a^2 b^5-3 a b^6+b^7-a^4 b^2 c+4 a^2 b^4 c-4 a b^5 c+b^6 c+a^5 c^2-a^4 b c^2-2 a^3 b^2 c^2+2 a^2 b^3 c^2+3 a b^4 c^2-3 b^5 c^2-3 a^4 c^3+2 a^2 b^2 c^3+8 a b^3 c^3+b^4 c^3+2 a^3 c^4+4 a^2 b c^4+3 a b^2 c^4+b^3 c^4+2 a^2 c^5-4 a b c^5-3 b^2 c^5-3 a c^6+b c^6+c^7) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6525.

X(64600) lies on these lines: {1836, 42447}, {15726, 29957}

X(64600) = pole of the line X(10581)X(22108) with respect to orthic inconic

X(64601) = X(30)X(113)∩X(110)X(237)

Barycentrics    a^2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 + a^2*b^4*c^2 - 2*a^4*c^4 + a^2*b^2*c^4 - b^4*c^4 + a^2*c^6) : :
X(64601) = X[7468] + 3 X[35265], 3 X[15035] - X[47620]

See Antreas Hatzipolakis and Peter Moses, euclid 6526.

X(64601) lies on these lines: {30, 113}, {110, 237}, {125, 52261}, {542, 44215}, {2854, 51735}, {5663, 44221}, {5972, 21531}, {7468, 35265}, {10546, 57618}, {11328, 15920}, {15035, 47620}, {17702, 44227}, {21177, 45082}, {35296, 54085}, {37906, 53735}, {45016, 63473}

X(64601) = midpoint of X(110) and X(237)
X(64601) = reflection of X(i) in X(j) for these {i,j}: {125, 52261}, {21531, 5972}
X(64601) = barycentric product X(11064)*X(54094)
X(64601) = barycentric quotient X(i)/X(j) for these {i,j}: {2420, 53603}, {54094, 16080}

X(64602) = X(30)X(113)∩X(110)X(384)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 + a^2*b^2*c^2 - b^4*c^2 - b^2*c^4) : :
X(64602) = X[3448] - 5 X[19689], X[7470] - 3 X[15035], 3 X[14643] - X[37243], X[14683] + 7 X[19692], 5 X[15059] - 7 X[19694], 4 X[19697] + X[24981]

See Antreas Hatzipolakis and Peter Moses, euclid 6526.

X(64602) lies on these lines: {30, 113}, {110, 384}, {125, 7819}, {542, 6661}, {698, 6593}, {2777, 44251}, {2854, 42421}, {3448, 19689}, {3972, 13210}, {5663, 44224}, {5972, 6656}, {7470, 15035}, {14643, 37243}, {14683, 19692}, {15059, 19694}, {17702, 44230}, {19697, 24981}, {32423, 44237}

X(64602) = midpoint of X(110) and X(384)
X(64602) = reflection of X(i) in X(j) for these {i,j}: {125, 7819}, {6656, 5972}
X(64602) = barycentric product X(11064)*X(37912)
X(64602) = barycentric quotient X(i)/X(j) for these {i,j}: {2420, 53918}, {37912, 16080}

X(64603) = X(30)X(113)∩X(110)X(401)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^8 - a^6*b^2 - a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 - 2*b^4*c^4 + b^2*c^6) : :
X(64603) = X[9140] - 3 X[44575], 3 X[15035] - X[35474], 3 X[36518] - 2 X[44228], 3 X[44578] - 2 X[45311]

See Antreas Hatzipolakis and Peter Moses, euclid 6526.

X(64603) lies on these lines: {30, 113}, {69, 34245}, {110, 401}, {125, 441}, {297, 5972}, {450, 23582}, {511, 7473}, {524, 46459}, {525, 3292}, {542, 40884}, {852, 22264}, {1316, 44127}, {1651, 58347}, {2777, 44252}, {2854, 51740}, {3284, 9033}, {3288, 3289}, {4240, 58343}, {5651, 40856}, {6090, 34360}, {9140, 44575}, {13414, 44332}, {13415, 44333}, {15035, 35474}, {15781, 19457}, {17702, 44231}, {30227, 64177}, {34982, 60774}, {36518, 44228}, {44578, 45311}

X(64603) = midpoint of X(110) and X(401)
X(64603) = reflection of X(i) in X(j) for these {i,j}: {125, 441}, {297, 5972}
X(64603) = X(i)-isoconjugate of X(j) for these (i,j): {9513, 36119}, {36131, 46245}
X(64603) = X(i)-Dao conjugate of X(j) for these (i,j): {1511, 9513}, {39008, 46245}, {39078, 16080}
X(64603) = crossdifference of every pair of points on line {2433, 6785}
X(64603) = barycentric product X(i)*X(j) for these {i,j}: {30, 63464}, {1316, 11064}, {3284, 44155}, {9033, 40866}
X(64603) = barycentric quotient X(i)/X(j) for these {i,j}: {1316, 16080}, {2420, 53699}, {3284, 9513}, {9033, 46245}, {35912, 53229}, {40866, 16077}, {44127, 8749}, {46249, 1304}, {47229, 18808}, {63464, 1494}

X(64604) = X(6)X(110)∩X(30)X(113)

Barycentrics    a^2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 9*a^2*b^2*c^2 - 4*b^4*c^2 - a^2*c^4 - 4*b^2*c^4 + c^6) : :

X(64604) lies on these lines: {2, 14982}, {3, 45019}, {6, 110}, {23, 33851}, {30, 113}, {67, 54013}, {125, 18358}, {323, 12824}, {394, 10752}, {399, 974}, {542, 37648}, {1112, 37517}, {1302, 40879}, {2781, 15066}, {2935, 15051}, {3531, 5504}, {4846, 5655}, {5092, 5972}, {5181, 32269}, {5609, 9730}, {5622, 63128}, {5648, 26255}, {5650, 12041}, {5651, 5663}, {6090, 9970}, {7426, 62381}, {7712, 13203}, {9143, 63084}, {9306, 19140}, {9976, 12099}, {10117, 55646}, {11284, 11579}, {11598, 12379}, {12367, 37980}, {12827, 47296}, {13198, 55705}, {14094, 37475}, {14643, 14805}, {14984, 34417}, {15034, 37497}, {15068, 25711}, {15080, 59767}, {15462, 26864}, {16105, 37483}, {16187, 32305}, {16534, 43586}, {16657, 30714}, {25556, 44084}, {33878, 41673}, {37511, 61679}, {37513, 38795}, {37962, 41617}, {39562, 62209}, {41671, 55715}, {61506, 63700}, {61574, 61743}, {64096, 64182}

X(64604) = midpoint of X(110) and X(1995)
X(64604) = reflection of X(30739) in X(5972)
X(64604) = X(2159)-isoconjugate of X(55973)
X(64604) = X(3163)-Dao conjugate of X(55973)
X(64604) = crossdifference of every pair of points on line {690, 2433}
X(64604) = barycentric product X(i)*X(j) for these {i,j}: {30, 41617}, {2407, 2780}, {11064, 37962}, {35266, 52496}
X(64604) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 55973}, {2420, 2696}, {2780, 2394}, {37962, 16080}, {41617, 1494}
X(64604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 35259, 62516}, {113, 5642, 11064}, {1495, 1511, 16165}, {1495, 5642, 1511}, {1511, 20772, 1495}, {5642, 20772, 16165}, {9143, 63084, 64103}, {11064, 16165, 59495}

X(64605) = X(30)X(113)∩X(51)X(110)

Barycentrics    a^2*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 7*a^2*b^2*c^2 - 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :
X(64605) = 5 X[7545] + 7 X[15039]

X(64605) lies on these lines: {30, 113}, {51, 110}, {185, 14094}, {394, 13417}, {1147, 7545}, {3292, 12824}, {5650, 15055}, {5651, 10620}, {5655, 43586}, {5972, 22352}, {6593, 21639}, {8541, 52697}, {9143, 10546}, {9306, 61679}, {11557, 50461}, {12827, 61691}, {13293, 15036}, {13366, 41670}, {14643, 18475}, {14708, 32235}, {14984, 44106}, {15462, 44110}, {15463, 52294}, {16223, 18445}, {18418, 61743}, {26881, 48898}, {43844, 62516}

X(64605) = midpoint of X(110) and X(13595)
X(64605) = {X(5642),X(20772)}-harmonic conjugate of X(1495)

X(64606) = X(30)X(113)∩X(69)X(110)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(4*a^6 - a^4*b^2 - 4*a^2*b^4 + b^6 - a^4*c^2 + 6*a^2*b^2*c^2 - b^4*c^2 - 4*a^2*c^4 - b^2*c^4 + c^6) : :
X(64606) = 2 X[18580] - 3 X[38793], 3 X[15035] - X[35485]

X(64606) lies on these lines: {30, 113}, {69, 110}, {125, 13394}, {154, 14982}, {184, 19138}, {265, 45082}, {394, 19140}, {542, 26864}, {895, 64058}, {1843, 41670}, {3066, 32300}, {3818, 5094}, {4232, 52699}, {5095, 32269}, {5609, 44683}, {5651, 18580}, {6053, 12168}, {6593, 15448}, {7426, 15303}, {12140, 64101}, {12295, 61743}, {12827, 46818}, {12828, 32223}, {15035, 35485}, {15131, 48905}, {15462, 44080}, {16003, 32235}, {16111, 35268}, {32233, 61680}, {32237, 32271}, {32250, 45303}, {32275, 61644}, {32366, 45237}, {41673, 61679}, {41737, 64059}, {46261, 52101}, {56567, 63425}

X(64606) = midpoint of X(i) and X(j) for these {i,j}: {110, 7493}, {26864, 32227}
X(64606) = reflection of X(5094) in X(5972)
X(64606) = X(5505)-isoconjugate of X(36119)
X(64606) = X(1511)-Dao conjugate of X(5505)
X(64606) = barycentric product X(i)*X(j) for these {i,j}: {7426, 11064}, {16163, 58875}
X(64606) = barycentric quotient X(i)/X(j) for these {i,j}: {2420, 10098}, {3284, 5505}, {7426, 16080}
X(64606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1495, 5642, 113}, {5642, 16163, 11064}, {11064, 16165, 16163}, {13394, 62516, 125}, {20772, 20773, 1495}

X(64607) = X(30)X(113)∩X(99)X(110)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) : :
X(64607) = 3 X[45662] - X[53132], X[7422] - 3 X[15035]

X(64607) lies on these lines: {2, 54501}, {30, 113}, {99, 110}, {125, 12042}, {247, 39809}, {476, 58979}, {526, 35345}, {542, 5191}, {685, 892}, {868, 5972}, {1316, 53725}, {1637, 2420}, {2407, 9033}, {5181, 39072}, {5467, 9003}, {5651, 57612}, {7422, 15035}, {7471, 9181}, {7473, 14999}, {9189, 57627}, {14270, 15329}, {14559, 53274}, {17702, 47200}, {34761, 50941}, {35259, 56967}, {51262, 60340}

X(64607) = midpoint of X(i) and X(j) for these {i,j}: {110, 4226}, {14559, 53274}
X(64607) = reflection of X(868) in X(5972)
X(64607) = X(i)-isoconjugate of X(j) for these (i,j): {2159, 14223}, {2349, 14998}, {35909, 36119}, {36096, 56792}
X(64607) = X(i)-Dao conjugate of X(j) for these (i,j): {1511, 35909}, {3163, 14223}, {23967, 2394}, {42426, 18808}, {62613, 5641}
X(64607) = crosssum of X(526) and X(34291)
X(64607) = trilinear pole of line {57431, 57464}
X(64607) = crossdifference of every pair of points on line {2433, 3124}
X(64607) = barycentric product X(i)*X(j) for these {i,j}: {30, 14999}, {542, 2407}, {2966, 57431}, {3233, 51227}, {5642, 50941}, {6148, 23968}, {7473, 11064}, {34761, 51389}, {36789, 51262}, {36885, 51372}, {42743, 60869}, {51457, 60511}
X(64607) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 14223}, {542, 2394}, {1495, 14998}, {1640, 12079}, {2407, 5641}, {2420, 842}, {3233, 51228}, {3284, 35909}, {5191, 2433}, {5642, 50942}, {6103, 18808}, {7473, 16080}, {14999, 1494}, {23968, 5627}, {41392, 54554}, {42743, 35910}, {51262, 40384}, {51389, 34765}, {51394, 35911}, {52951, 53177}, {57431, 2799}, {58348, 1637}, {60505, 17986}
X(64607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 5468, 6333}, {1511, 51430, 5642}, {5191, 45662, 47082}, {5642, 16163, 51389}, {5642, 51431, 113}, {35314, 35315, 3268}

X(64608) = X(396)X(3163)∩X(524)X(618)

Barycentrics    2 a^12-4 a^10 b^2+9 a^8 b^4-19 a^6 b^6+18 a^4 b^8-7 a^2 b^10+b^12-4 a^10 c^2-6 a^8 b^2 c^2+15 a^6 b^4 c^2-23 a^4 b^6 c^2+15 a^2 b^8 c^2-5 b^10 c^2+9 a^8 c^4+15 a^6 b^2 c^4+12 a^4 b^4 c^4-8 a^2 b^6 c^4+5 b^8 c^4-19 a^6 c^6-23 a^4 b^2 c^6-8 a^2 b^4 c^6-2 b^6 c^6+18 a^4 c^8+15 a^2 b^2 c^8+5 b^4 c^8-7 a^2 c^10-5 b^2 c^10+c^12-2 (2 a^10-4 a^8 b^2+3 a^6 b^4-4 a^4 b^6+4 a^2 b^8-b^10-4 a^8 c^2+6 a^6 b^2 c^2-3 a^2 b^6 c^2+3 a^6 c^4+b^6 c^4-4 a^4 c^6-3 a^2 b^2 c^6+b^4 c^6+4 a^2 c^8-c^10) T : : where T = Sqrt[3] S

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6537.

X(64608) lies on these lines: {298, 46833}, {396, 3163}, {524, 618}, {630, 44386}, {3180, 11131}, {5664, 14816}, {37786, 41887}

X(64609) = X(395)X(3163)∩X(524)X(619)

Barycentrics    2 a^12-4 a^10 b^2+9 a^8 b^4-19 a^6 b^6+18 a^4 b^8-7 a^2 b^10+b^12-4 a^10 c^2-6 a^8 b^2 c^2+15 a^6 b^4 c^2-23 a^4 b^6 c^2+15 a^2 b^8 c^2-5 b^10 c^2+9 a^8 c^4+15 a^6 b^2 c^4+12 a^4 b^4 c^4-8 a^2 b^6 c^4+5 b^8 c^4-19 a^6 c^6-23 a^4 b^2 c^6-8 a^2 b^4 c^6-2 b^6 c^6+18 a^4 c^8+15 a^2 b^2 c^8+5 b^4 c^8-7 a^2 c^10-5 b^2 c^10+c^12+2 (2 a^10-4 a^8 b^2+3 a^6 b^4-4 a^4 b^6+4 a^2 b^8-b^10-4 a^8 c^2+6 a^6 b^2 c^2-3 a^2 b^6 c^2+3 a^6 c^4+b^6 c^4-4 a^4 c^6-3 a^2 b^2 c^6+b^4 c^6+4 a^2 c^8-c^10) T : : where T = Sqrt[3] S

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6537.

X(64609) lies on these lines: {299, 46834}, {395, 3163}, {524, 619}, {629, 44386}, {3181, 11130}, {5664, 14817}, {23896, 62690}, {37785, 41888}

X(64610) = X(3)X(8254)∩(74)X(3574)

Barycentrics    (a^8 + 2*a^6*b^2 - 6*a^4*b^4 + 2*a^2*b^6 + b^8 - 2*a^6*c^2 - 3*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 2*b^6*c^2 - a^2*b^2*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 + 2*a^6*c^2 - 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 - 6*a^4*c^4 - 3*a^2*b^2*c^4 + 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :
X(64610) = X[6288] - 4 X[13566]

See Antreas Hatzipolakis and Peter Moses, euclid 6538.

X(64610) lies on the Jerabek circumhyperbola and these lines: {3, 8254}, {4, 58489}, {6, 12254}, {51, 43891}, {64, 32351}, {74, 3574}, {265, 10095}, {389, 33565}, {1154, 34483}, {1173, 18400}, {1176, 29317}, {1568, 32396}, {3567, 45736}, {5169, 45788}, {5189, 14861}, {5900, 10628}, {6145, 43808}, {6242, 13622}, {6288, 13566}, {7730, 45972}, {10619, 34567}, {11559, 33332}, {12242, 57713}, {13418, 32352}, {13623, 15800}, {14483, 40240}, {14865, 34437}, {15002, 38322}, {19151, 35471}, {21400, 63672}, {22466, 63659}, {32337, 38433}, {32639, 40640}, {33539, 50138}

X(64610) = isogonal conjugate of X(34864)
X(64610) = barycentric quotient X(6)/X(34864)

X(64611) = X(2)X(514)∩X(6)X(101)

Barycentrics    a^2*(a + b - 2*c)*(a - 2*b + c)*(a*b^2 - b^3 + a*c^2 - c^3) : :

X(64611) lies on the cubic K280 and these lines: {2, 514}, {6, 101}, {39, 39264}, {88, 24598}, {262, 24808}, {378, 8752}, {574, 17969}, {901, 38884}, {903, 7757}, {953, 32686}, {1168, 30116}, {3730, 14260}, {4080, 31036}, {4674, 17756}, {4997, 30830}, {5024, 45140}, {5701, 55244}, {15378, 31616}, {19250, 45144}, {23345, 24484}, {31227, 31234}, {32665, 62703}, {34179, 40150}, {34362, 35123}, {42723, 57015}

X(64611) = X(i)-isoconjugate of X(j) for these (i,j): {44, 675}, {519, 2224}, {900, 36087}, {902, 37130}, {2251, 43093}, {3762, 32682}, {23703, 60573}, {52680, 60135}
X(64611) = X(i)-Dao conjugate of X(j) for these (i,j): {9460, 43093}, {38990, 900}, {40594, 37130}, {40595, 675}, {53980, 8756}
X(64611) = crossdifference of every pair of points on line {900, 902}
X(64611) = barycentric product X(i)*X(j) for these {i,j}: {88, 57015}, {106, 3006}, {674, 903}, {901, 23887}, {1022, 42723}, {2225, 20568}, {4080, 14964}, {4997, 43039}, {8618, 57995}
X(64611) = barycentric quotient X(i)/X(j) for these {i,j}: {88, 37130}, {106, 675}, {674, 519}, {903, 43093}, {2225, 44}, {3006, 3264}, {4249, 46541}, {8618, 902}, {9456, 2224}, {14964, 16704}, {32665, 36087}, {32719, 32682}, {42723, 24004}, {43039, 3911}, {46150, 46158}, {51657, 1319}, {57015, 4358}

X(64612) = X(2)X(513)∩X(6)X(100)

Barycentrics    a*(2*a*b - a*c - b*c)*(a*b - 2*a*c + b*c)*(a*b - b^2 + a*c - c^2) : :

X(64612) lies on the cubic K280 and these lines: {2, 513}, {6, 100}, {7, 1357}, {59, 1397}, {192, 13476}, {518, 42720}, {672, 1026}, {840, 898}, {889, 4441}, {995, 62763}, {1002, 3227}, {1025, 1458}, {2414, 57469}, {3252, 14439}, {3286, 47048}, {3423, 37300}, {7032, 62769}, {8299, 34230}, {9309, 30610}, {16405, 45145}, {18771, 31628}, {24403, 64149}, {29824, 53340}, {30941, 55260}, {36294, 63961}, {41439, 42343}, {56753, 57468}, {60288, 60617}

X(64612) = isogonal conjugate of X(52902)
X(64612) = X(i)-isoconjugate of X(j) for these (i,j): {1, 52902}, {6, 36816}, {105, 899}, {294, 52896}, {536, 1438}, {666, 3768}, {673, 3230}, {890, 51560}, {891, 36086}, {919, 4728}, {1027, 23343}, {1416, 4009}, {2195, 43037}, {4465, 51866}, {4526, 36146}, {5377, 19945}, {6381, 64216}, {13576, 62740}, {14430, 32735}, {14942, 62739}, {18785, 52897}, {23891, 43929}, {36138, 45338}, {45145, 54364}, {56853, 62755}
X(64612) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 52902}, {9, 36816}, {2238, 4465}, {6184, 536}, {17755, 6381}, {38980, 4728}, {38989, 891}, {39012, 45338}, {39014, 4526}, {39046, 899}, {39063, 43037}, {40609, 4009}, {62587, 35543}
X(64612) = trilinear pole of line {518, 665}
X(64612) = crossdifference of every pair of points on line {891, 3230}
X(64612) = barycentric product X(i)*X(j) for these {i,j}: {241, 36798}, {518, 3227}, {665, 889}, {672, 31002}, {739, 3263}, {898, 918}, {1026, 62619}, {2254, 4607}, {3286, 60288}, {3675, 5381}, {3912, 37129}, {18157, 62763}, {18206, 41683}, {42720, 43928}, {56753, 63852}
X(64612) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36816}, {6, 52902}, {241, 43037}, {518, 536}, {665, 891}, {672, 899}, {739, 105}, {889, 36803}, {898, 666}, {926, 4526}, {1026, 23891}, {1458, 52896}, {2223, 3230}, {2254, 4728}, {2284, 23343}, {3227, 2481}, {3263, 35543}, {3286, 52897}, {3675, 52626}, {3693, 4009}, {3912, 6381}, {3930, 3994}, {4607, 51560}, {8299, 4465}, {18206, 62755}, {20683, 52959}, {23349, 43929}, {23892, 1027}, {24290, 14431}, {31002, 18031}, {32718, 919}, {34075, 36086}, {34230, 52900}, {36798, 36796}, {37129, 673}, {42720, 41314}, {42758, 42764}, {43928, 62635}, {52635, 62739}, {62763, 18785}
X(64612) = {X(36872),X(52768)}-harmonic conjugate of X(2)

X(64613) = X(30)X(599)∩X(67)X(7737)

Barycentrics    (a^4 + b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 3*c^4)*(a^4 + 2*a^2*b^2 - 3*b^4 + 2*b^2*c^2 + c^4) : :

X(64613) lies on the cubic K477 and these lines: {30, 599}, {67, 7737}, {125, 34288}, {1990, 3815}, {2452, 23327}, {3260, 9464}, {7493, 10130}, {9214, 9770}, {10002, 52661}, {11410, 63419}, {14981, 15454}, {16280, 35906}, {16303, 61735}, {18575, 31415}, {21765, 34417}, {21843, 30542}, {23288, 62384}, {31173, 46645}, {32133, 39602}, {37643, 39453}, {41359, 53015}, {45819, 61506}

X(64613) = isogonal conjugate of X(6800)
X(64613) = isotomic conjugate of X(14907)
X(64613) = isogonal conjugate of the anticomplement of X(45303)
X(64613) = isotomic conjugate of the anticomplement of X(5475)
X(64613) = isotomic conjugate of the isogonal conjugate of X(14906)
X(64613) = X(5475)-cross conjugate of X(2)
X(64613) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6800}, {31, 14907}
X(64613) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 14907}, {3, 6800}
X(64613) = trilinear pole of line {1637, 3906}
X(64613) = barycentric product X(76)*X(14906)
X(64613) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14907}, {6, 6800}, {14906, 6}

X(64614) = X(2)X(14248)∩X(3)X(8770)

Barycentrics    a^2*(a^2 + b^2 - 3*c^2)*(a^2 - b^2 - c^2)*(a^2 - 3*b^2 + c^2)*(a^4 + 2*a^2*b^2 + b^4 + 2*a^2*c^2 - 6*b^2*c^2 + c^4) : :

X(64614) lies on the cubic K168 and these lines: {2, 14248}, {3, 8770}, {6, 39128}, {25, 3565}, {69, 1368}, {1351, 31842}, {1370, 5203}, {2996, 7386}, {5020, 15261}, {5272, 8769}, {6337, 6341}, {7392, 52454}, {16419, 40809}, {19588, 53068}, {35136, 57518}, {46336, 47730}

X(64614) = complement of X(55023)
X(64614) = complement of the isogonal conjugate of X(19588)
X(64614) = complement of the isotomic conjugate of X(19583)
X(64614) = isotomic conjugate of the isogonal conjugate of X(53068)
X(64614) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 8770}, {48, 3926}, {1611, 226}, {1973, 6387}, {2128, 141}, {2519, 8287}, {4575, 58766}, {6392, 20305}, {6461, 18589}, {19583, 2887}, {19588, 10}, {33781, 5}, {33787, 21243}, {53068, 16605}
X(64614) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 8770}, {14248, 6391}
X(64614) = X(6461)-cross conjugate of X(19588)
X(64614) = X(i)-isoconjugate of X(j) for these (i,j): {19, 30558}, {92, 53067}, {193, 2129}, {1707, 55023}, {15369, 18156}
X(64614) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 30558}, {8770, 2}, {15261, 15369}, {22391, 53067}
X(64614) = crosspoint of X(2) and X(19583)
X(64614) = crosssum of X(6) and X(15369)
X(64614) = barycentric product X(i)*X(j) for these {i,j}: {76, 53068}, {1611, 6340}, {2128, 8769}, {2519, 35136}, {2996, 19588}, {6338, 14248}, {6391, 6392}, {6461, 34208}, {8770, 19583}
X(64614) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 30558}, {184, 53067}, {1611, 6353}, {2128, 18156}, {2519, 3566}, {6391, 6339}, {6392, 54412}, {6461, 6337}, {8770, 55023}, {14248, 63899}, {19583, 57518}, {19588, 193}, {38252, 2129}, {40319, 40322}, {53059, 15369}, {53068, 6}

X(64615) = X(22)X(1634)∩X(25)X(53575)

Barycentrics    a^2*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^2*b^2*c^2 - c^6)*(a^6 - b^6 - a^4*c^2 + a^2*b^2*c^2 - a^2*c^4 + c^6) : :

X(64615) lies on the cubic K488 and these lines: {22, 1634}, {25, 53575}, {30, 14634}, {206, 1511}, {339, 2980}, {1576, 6636}, {3455, 9479}, {5063, 17409}, {7485, 40559}, {33801, 35520}, {37969, 47150}, {38872, 48453}, {46608, 51869}

X(64615) = isogonal conjugate of the anticomplement of X(1495)
X(64615) = isogonal conjugate of the isotomic conjugate of X(55032)
X(64615) = X(9407)-cross conjugate of X(6)
X(64615) = cevapoint of X(i) and X(j) for these (i,j): {39, 1495}, {669, 2088}, {9409, 38356}
X(64615) = trilinear pole of line {3051, 9210}
X(64615) = barycentric product X(6)*X(55032)
X(64615) = barycentric quotient X(55032)/X(76)

X(64616) = X(4)X(218)∩X(100)X(24290)

Barycentrics    a*(a - b)*(a - c)*(a^5 - a^4*b + a*b^4 - b^5 - a^4*c + a^3*b*c + a*b^3*c + b^4*c - 4*a*b^2*c^2 + a*b*c^3 + a*c^4 + b*c^4 - c^5) : :

X(64616) lies on the cubic K299 and these lines: {4, 218}, {100, 24290}, {101, 2254}, {190, 644}, {919, 3309}, {1415, 57105}, {1618, 2509}, {2170, 10697}, {2246, 64234}, {20331, 20672}, {35349, 46392}, {52985, 64241}, {54230, 57192}

X(64616) = polar-circle-inverse of X(8735)
X(64616) = antigonal image of X(18343)
X(64616) = symgonal image of X(1083)
X(64616) = X(53213)-Ceva conjugate of X(100)
X(64616) = crossdifference of every pair of points on line {3271, 53550}
X(64616) = barycentric product X(100)*X(18343)
X(64616) = barycentric quotient X(18343)/X(693)

X(64617) = X(1)X(6460)∩X(4)X(9)

Barycentrics    2*a^4 + a^3*b - a^2*b^2 - a*b^3 - b^4 + a^3*c - 2*a^2*b*c + a*b^2*c - a^2*c^2 + a*b*c^2 + 2*b^2*c^2 - a*c^3 - c^4 + 2*a^2*S - 2*a*b*S - 2*a*c*S : :
Barycentrics    (a + b + c)*(2*a^3 - a^2*b - b^3 - a^2*c + b^2*c + b*c^2 - c^3) + 2*a*(a - b - c)*S : :

X(64617) lies on the cubic K202 and these lines: {1, 6460}, {4, 9}, {6, 52808}, {7, 1659}, {20, 30557}, {37, 52805}, {46, 8957}, {55, 30325}, {144, 13387}, {390, 2362}, {497, 6203}, {515, 64314}, {527, 5861}, {528, 49337}, {946, 32555}, {962, 30556}, {971, 34909}, {1100, 52806}, {1123, 4312}, {1335, 64057}, {1633, 8224}, {1836, 30324}, {3062, 13454}, {3474, 6204}, {5414, 13390}, {5853, 12628}, {7580, 60847}, {9778, 30413}, {9812, 30412}, {11495, 34121}, {13360, 15726}, {13437, 52819}, {14100, 58897}, {16777, 52809}, {17768, 49340}, {28194, 64309}, {30354, 60887}, {31730, 32556}, {43178, 55498}, {51364, 52420}

X(64617) = reflection of X(i) in X(j) for these {i,j}: {7, 45704}, {64336, 9}
X(64617) = isogonal conjugate of X(46376)
X(64617) = X(13387)-Ceva conjugate of X(7090)
X(64617) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46376}, {6502, 15891}, {13389, 30336}, {40699, 53064}
X(64617) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 46376}, {14121, 13386}
X(64617) = barycentric product X(i)*X(j) for these {i,j}: {75, 46378}, {175, 7090}, {1123, 31547}, {1659, 30413}, {51841, 60854}
X(64617) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46376}, {7090, 40699}, {7133, 15891}, {30413, 56385}, {31547, 1267}, {46378, 1}, {51841, 13389}, {60851, 30336}
X(64617) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6213, 7090}, {40, 31561, 14121}, {5493, 31594, 51955}

X(64618) = X(2)X(2987)∩X(6)X(10425)

Barycentrics    a^2*(a^4 + b^4 - 3*b^2*c^2 + c^4)*(a^4 - a^2*b^2 + 2*b^4 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + 2*c^4) : :

X(64618) lies on the cubics K250 and K280 and these lines: {2, 2987}, {6, 10425}, {39, 14253}, {83, 47736}, {182, 3563}, {378, 32697}, {2065, 5050}, {5013, 57728}, {7790, 35142}, {10601, 57493}, {13335, 61446}, {15018, 52515}

X(64618) = barycentric product X(2987)*X(14568)
X(64618) = barycentric quotient X(i)/X(j) for these {i,j}: {2872, 55122}, {10425, 2858}, {14568, 51481}

X(64619) = X(4)X(1499)∩X(24)X(111)

Barycentrics    a^2*(a^2 + b^2 - 2*c^2)*(a^2 + b^2 - c^2)*(a^2 - 2*b^2 + c^2)*(a^2 - b^2 + c^2)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(64619) lies on the cubic K620 and these lines: {4, 1499}, {24, 111}, {25, 41936}, {671, 43678}, {892, 56015}, {1235, 52756}, {1593, 45143}, {1968, 17964}, {2207, 8753}, {3162, 8877}, {5523, 59422}, {5968, 39575}, {8743, 14246}, {9214, 41361}, {11470, 52233}, {14262, 23701}, {14580, 34158}, {27376, 64258}, {44161, 59762}

X(64619) = isogonal conjugate of X(53784)
X(64619) = polar conjugate of the isotomic conjugate of X(57485)
X(64619) = polar conjugate of the isogonal conjugate of X(51962)
X(64619) = X(10630)-Ceva conjugate of X(8753)
X(64619) = X(51962)-cross conjugate of X(57485)
X(64619) = X(i)-isoconjugate of X(j) for these (i,j): {1, 53784}, {255, 58078}, {326, 51823}, {3292, 37220}, {14210, 18876}, {24038, 41511}
X(64619) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 53784}, {468, 36792}, {6523, 58078}, {15259, 51823}, {15477, 18876}, {38971, 45807}, {61067, 6390}
X(64619) = barycentric product X(i)*X(j) for these {i,j}: {4, 57485}, {25, 59422}, {111, 5523}, {264, 51962}, {671, 14580}, {858, 8753}, {1560, 10630}, {2052, 34158}, {2393, 17983}, {5466, 46592}, {6524, 51253}, {9178, 61181}, {10415, 20410}, {10561, 60507}, {18669, 36128}, {21459, 46154}, {39269, 52142}
X(64619) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 53784}, {393, 58078}, {1560, 36792}, {2207, 51823}, {2393, 6390}, {5523, 3266}, {8753, 2373}, {14580, 524}, {17983, 46140}, {20410, 7664}, {32740, 18876}, {34158, 394}, {36128, 37220}, {41936, 41511}, {46592, 5468}, {47138, 45807}, {51253, 4176}, {51962, 3}, {57485, 69}, {59422, 305}
X(64619) = {X(4),X(52490)}-harmonic conjugate of X(14263)

X(64620) = X(2)X(2393)∩X(6)X(2373)

Barycentrics    (a^2 - b^2 - c^2)*(a^4*b^2 - b^6 + 2*a^4*c^2 - 2*a^2*b^2*c^2 + 2*a^2*c^4 + b^2*c^4)*(2*a^4*b^2 + 2*a^2*b^4 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 - c^6) : :

X(64620) lies on the cubic K280 and these lines: {2, 2393}, {6, 2373}, {69, 14961}, {141, 57466}, {264, 5523}, {287, 33926}, {305, 62382}, {1180, 13575}, {1494, 7757}, {1799, 41614}, {3618, 10603}, {18018, 54347}, {19459, 40404}, {36879, 40413}

X(64620) = isogonal conjugate of X(52905)
X(64620) = X(1)-isoconjugate of X(52905)
X(64620) = X(3)-Dao conjugate of X(52905)
X(64620) = trilinear pole of line {525, 42665}
X(64620) = barycentric quotient X(6)/X(52905)

X(64621) = X(2)X(15265)∩X(4)X(16089)

Barycentrics    b^2*c^2*(3*a^6*b^2 - 2*a^4*b^4 - a^2*b^6 + 3*a^6*c^2 + 7*a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 - 2*a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6) : :

X(64621) lies on the cubic K412 and these lines: {2, 15265}, {4, 16089}, {5, 76}, {99, 11328}, {115, 40814}, {264, 19130}, {290, 381}, {297, 7790}, {316, 6785}, {458, 6528}, {598, 30491}, {850, 5640}, {1078, 47640}, {3066, 6331}, {3972, 10684}, {3978, 11185}, {5476, 44155}, {5480, 40822}, {5943, 51843}, {7757, 11672}, {7771, 35934}, {7827, 34235}, {9993, 44231}, {10796, 14382}, {14249, 18027}, {14561, 17984}, {14853, 44137}, {19573, 47846}, {32815, 63170}, {44133, 51396}, {46325, 63632}, {53127, 60707}

X(64621) = reflection of X(76) in X(14937)
X(64621) = complement of X(57450)

X(64622) = X(7)X(7090)∩X(9)X(13389)

Barycentrics    a*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 - 2*a^3*c - 8*a^2*b*c + 6*a*b^2*c + 4*b^3*c + 6*a*b*c^2 - 6*b^2*c^2 + 2*a*c^3 + 4*b*c^3 - c^4 - 2*a^2*S - 4*a*b*S + 6*b^2*S - 4*a*c*S + 4*b*c*S + 6*c^2*S) : :
Barycentrics    a*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 - 2*a^3*c - 8*a^2*b*c + 6*a*b^2*c + 4*b^3*c + 6*a*b*c^2 - 6*b^2*c^2 + 2*a*c^3 + 4*b*c^3 - c^4 - 2*(a^2 + 2*a*b - 3*b^2 + 2*a*c - 2*b*c - 3*c^2)*S) : :

X(64622) lies on the cubic K202 and these lines: {7, 7090}, {9, 13389}, {40, 971}, {63, 46377}, {69, 31548}, {72, 31564}, {77, 30557}, {144, 13386}, {480, 30298}, {518, 30335}, {1001, 16213}, {13387, 45704}, {31562, 61003}

X(64622) = isogonal conjugate of X(46379)
X(64622) = X(6213)-cross conjugate of X(13388)
X(64622) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46379}, {6, 64336}, {176, 60852}, {30412, 60849}, {42013, 51842}
X(64622) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 46379}, {9, 64336}, {13389, 176}
X(64622) = barycentric product X(i)*X(j) for these {i,j}: {75, 46377}, {13388, 40700}
X(64622) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 64336}, {6, 46379}, {2067, 51842}, {3084, 31548}, {13388, 176}, {15892, 14121}, {30335, 42013}, {30557, 30412}, {40700, 60853}, {46377, 1}, {64230, 16663}
X(64622) = {X(144),X(46422)}-harmonic conjugate of X(64336)

X(64623) = X(1)X(971)∩X(7)X(13389)

Barycentrics    a*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 - 2*a^3*c + 8*a^2*b*c - 2*a*b^2*c - 4*b^3*c - 2*a*b*c^2 + 10*b^2*c^2 + 2*a*c^3 - 4*b*c^3 - c^4 + 2*a^2*S - 4*a*b*S + 2*b^2*S - 4*a*c*S - 4*b*c*S + 2*c^2*S) : :
Barycentrics    a*((a + b - c)*(a - b + c)*(a^2 - 2*a*b + b^2 - 2*a*c + 6*b*c + c^2) + 2*(a^2 - 2*a*b + b^2 - 2*a*c - 2*b*c + c^2)*S) : :

X(64623) lies on the cubic K202 and these lines: {1, 971}, {7, 13389}, {9, 13388}, {55, 30354}, {144, 175}, {481, 52819}, {516, 31532}, {612, 30288}, {910, 6203}, {1372, 61007}, {3084, 60966}, {5405, 60992}, {6212, 39795}, {10911, 60883}, {20059, 55397}, {30325, 60887}, {30355, 31391}, {31565, 51190}, {32556, 34495}, {55398, 60969}

X(64623) = X(i)-Ceva conjugate of X(j) for these (i,j): {175, 13388}, {30557, 13389}
X(64623) = barycentric product X(75)*X(8833)
X(64623) = barycentric quotient X(8833)/X(1)
X(64623) = {X(42013),X(64230)}-harmonic conjugate of X(13389)

X(64624) = X(2)X(51548)∩X(3)X(1495)

Barycentrics    a^2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8 - a^6*c^2 + 13*a^4*b^2*c^2 - 8*a^2*b^4*c^2 - 4*b^6*c^2 - 3*a^4*c^4 - 8*a^2*b^2*c^4 + 12*b^4*c^4 + 5*a^2*c^6 - 4*b^2*c^6 - 2*c^8) : :
X(64624) = 3 X[3] - 2 X[1495], 3 X[3] - 4 X[58871], X[74] - 3 X[13445], 3 X[74] - X[15107], 2 X[3580] - 3 X[20126], X[3581] - 6 X[13445], 3 X[3581] - 2 X[15107], 9 X[13445] - X[15107], 3 X[14993] - 2 X[47323], X[323] - 3 X[7464], 2 X[323] - 3 X[37477], 4 X[323] - 3 X[63720], 4 X[7464] - X[63720], X[399] - 3 X[18859], and many others

X(64624) lies on the cubic K488 and these lines: {2, 51548}, {3, 1495}, {6, 18373}, {20, 41466}, {23, 12041}, {30, 74}, {49, 11456}, {64, 18436}, {110, 37950}, {125, 18325}, {146, 51391}, {186, 12133}, {323, 5663}, {376, 33533}, {378, 14805}, {381, 37470}, {382, 11438}, {399, 2935}, {468, 38728}, {511, 10620}, {512, 35002}, {541, 51360}, {546, 43584}, {548, 15062}, {550, 16659}, {567, 15072}, {568, 64099}, {599, 3098}, {858, 7728}, {1154, 37944}, {1204, 5073}, {1503, 12121}, {1511, 2071}, {1514, 2072}, {1531, 38790}, {1533, 6699}, {1597, 44084}, {1657, 3357}, {2393, 33878}, {2777, 7574}, {2916, 52099}, {2937, 64027}, {3231, 40115}, {3292, 12308}, {3431, 61752}, {3529, 32138}, {3530, 43613}, {3589, 13623}, {3830, 34417}, {3845, 10545}, {3853, 43601}, {3861, 43597}, {5092, 14855}, {5160, 10081}, {5189, 12244}, {5446, 43807}, {5505, 8705}, {5655, 11064}, {5888, 12100}, {5899, 21663}, {5907, 33541}, {6241, 37495}, {7286, 10065}, {7517, 37487}, {7527, 13339}, {7575, 15055}, {7687, 31726}, {7689, 17800}, {7691, 62144}, {7712, 35473}, {8703, 41462}, {10295, 38788}, {10296, 34584}, {10546, 11455}, {10575, 11430}, {10606, 12083}, {10610, 35478}, {10721, 18572}, {10752, 18449}, {11202, 35495}, {11250, 11464}, {11413, 15068}, {11440, 15704}, {11468, 17714}, {11563, 40685}, {11799, 15061}, {12085, 12160}, {12086, 13491}, {12088, 32210}, {12290, 18350}, {12302, 41615}, {12900, 51403}, {13202, 18403}, {13293, 15139}, {13353, 14865}, {13474, 43809}, {13596, 15018}, {13619, 61299}, {13754, 35452}, {14130, 37513}, {14157, 15051}, {14560, 14634}, {14643, 15122}, {14644, 44267}, {14851, 47324}, {14926, 15082}, {15021, 37967}, {15037, 40647}, {15041, 32110}, {15053, 15687}, {15054, 43576}, {15059, 44961}, {15066, 18435}, {15080, 18570}, {15081, 52403}, {15089, 17854}, {15681, 63425}, {15682, 48912}, {15684, 64095}, {16111, 29012}, {16117, 48919}, {18378, 43604}, {18445, 54992}, {18451, 58762}, {19596, 55646}, {21312, 23039}, {22462, 46852}, {30745, 61574}, {31861, 40280}, {32237, 37958}, {35498, 52100}, {35501, 44102}, {37923, 38633}, {38794, 46817}, {38848, 62013}, {41465, 54050}, {41613, 44883}, {43603, 58531}, {45959, 54434}, {46202, 55585}, {46728, 62143}, {46730, 49137}, {46818, 54995}, {47347, 57305}, {61136, 63040}, {63441, 64036}

X(64624) = midpoint of X(i) and X(j) for these {i,j}: {5189, 12244}, {10620, 35001}, {15054, 43576}
X(64624) = reflection of X(i) in X(j) for these {i,j}: {23, 12041}, {110, 37950}, {146, 51391}, {399, 10564}, {1495, 58871}, {1533, 6699}, {3581, 74}, {5899, 21663}, {7728, 858}, {10540, 2071}, {10721, 18572}, {12112, 1511}, {12308, 3292}, {12367, 3098}, {14157, 34152}, {14560, 14634}, {15139, 13293}, {18325, 125}, {20127, 50434}, {22115, 18859}, {32111, 15122}, {37477, 7464}, {37924, 32110}, {38790, 1531}, {41613, 44883}, {41615, 12302}, {63720, 37477}, {64182, 54995}
X(64624) = anticomplement of X(51548)
X(64624) = crossdifference of every pair of points on line {5306, 9209}
X(64624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {378, 64098, 14805}, {399, 10564, 22115}, {399, 18859, 10564}, {1495, 58871, 3}, {1511, 12112, 10540}, {1657, 3357, 63392}, {2071, 12112, 1511}, {12084, 64030, 49}, {12086, 13491, 37472}, {15041, 37924, 32110}, {15122, 32111, 14643}

X(64625) = X(2)X(647)∩X(6)X(98)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(2*a^4*b^4 - 2*a^2*b^6 + 2*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 - 2*a^2*c^6 - b^2*c^6) : :

X(64625) lies on the cubic K280 and these lines: {2, 647}, {6, 98}, {39, 14265}, {187, 7422}, {290, 7757}, {378, 6531}, {574, 48452}, {2549, 34175}, {2715, 47737}, {2966, 7771}, {3815, 51404}, {3972, 54086}, {5024, 36822}, {5092, 51963}, {5309, 54991}, {5999, 14966}, {6785, 7735}, {7736, 52451}, {7738, 56688}, {7786, 14382}, {8779, 35912}, {9744, 51943}, {12042, 60504}, {13366, 51820}, {14355, 41932}, {15048, 51441}, {22712, 34359}, {39575, 52641}, {47044, 52038}

X(64625) = {X(34235),X(52672)}-harmonic conjugate of X(43665)

X(64626) = X(2)X(42013)∩X(3)X(8949)

Barycentrics    a*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 4*a^4*b*c + 8*a^2*b^3*c - 4*b^5*c - a^4*c^2 - 6*a^2*b^2*c^2 - b^4*c^2 + 8*a^2*b*c^3 + 8*b^3*c^3 - a^2*c^4 - b^2*c^4 - 4*b*c^5 + c^6 - 2*a^4*S + 2*b^4*S + 4*a^2*b*c*S + 4*b^3*c*S - 12*b^2*c^2*S + 4*b*c^3*S + 2*c^4*S) : :
Barycentrics    a*(a^4 - b^4 - 2*a^2*b*c - 2*b^3*c + 6*b^2*c^2 - 2*b*c^3 - c^4 + 2*(a^2 + b^2 - 4*b*c + c^2)*S) : :

X(64626) lies on the cubics K168 and K1243 and these lines: {2, 42013}, {3, 8949}, {6, 6203}, {486, 31590}, {2067, 52420}, {2362, 17081}, {3084, 5408}, {5272, 8769}, {5391, 6337}, {13389, 24246}, {30336, 59691}

X(64626) = X(3)-cross conjugate of X(13388)
X(64626) = X(i)-isoconjugate of X(j) for these (i,j): {92, 53069}, {6204, 42013}, {57266, 60852}
X(64626) = X(i)-Dao conjugate of X(j) for these (i,j): {13389, 57266}, {22391, 53069}
X(64626) = barycentric product X(13388)*X(57270)
X(64626) = barycentric quotient X(i)/X(j) for these {i,j}: {184, 53069}, {2067, 6204}, {7347, 14121}, {13388, 57266}, {57270, 60853}

X(64627) = X(2)X(7133)∩X(3)X(8947)

Barycentrics    a*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 4*a^4*b*c + 8*a^2*b^3*c - 4*b^5*c - a^4*c^2 - 6*a^2*b^2*c^2 - b^4*c^2 + 8*a^2*b*c^3 + 8*b^3*c^3 - a^2*c^4 - b^2*c^4 - 4*b*c^5 + c^6 + 2*a^4*S - 2*b^4*S - 4*a^2*b*c*S - 4*b^3*c*S + 12*b^2*c^2*S - 4*b*c^3*S - 2*c^4*S) : :
Barycentrics    a*(-a^4 + b^4 + 2*a^2*b*c + 2*b^3*c - 6*b^2*c^2 + 2*b*c^3 + c^4 + 2*(a^2 + b^2 - 4*b*c + c^2)*S) : :

X(64627) lies on the cubics K168 and K1243 and these lines: {2, 7133}, {3, 8947}, {6, 6204}, {485, 31591}, {1267, 6337}, {2066, 3083}, {5272, 8769}, {6502, 52419}, {13388, 24245}, {16232, 17081}, {30335, 59691}

X(64627) = X(3)-cross conjugate of X(13389)
X(64627) = X(i)-isoconjugate of X(j) for these (i,j): {92, 53070}, {6203, 7133}, {57267, 60851}
X(64627) = X(i)-Dao conjugate of X(j) for these (i,j): {13388, 57267}, {22391, 53070}
X(64627) = barycentric product X(13389)*X(57269)
X(64627) = barycentric quotient X(i)/X(j) for these {i,j}: {184, 53070}, {6502, 6203}, {7348, 7090}, {13389, 57267}, {57269, 60854}

X(64628) = X(2)X(74)∩X(316)X(1494)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(3*a^8 - 8*a^4*b^4 + 4*a^2*b^6 + b^8 + 4*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 4*b^6*c^2 - 8*a^4*c^4 - 4*a^2*b^2*c^4 + 6*b^4*c^4 + 4*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(64628) lies on the cubic K477 and these lines: {2, 74}, {316, 1494}, {1304, 10295}, {2394, 9003}, {6334, 53383}, {10152, 35480}, {10296, 14989}, {10297, 12079}, {15341, 18877}, {39377, 44934}, {39378, 44933}, {40385, 52976}, {46339, 46808}

X(64628) = barycentric product X(4549)*X(16080)
X(64628) = barycentric quotient X(4549)/X(11064)
X(64628) = {X(74),X(52488)}-harmonic conjugate of X(60119)

X(64629) = X(2)X(24243)∩X(3)X(6406)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 12*a^4*b^2*c^2 + 22*a^2*b^4*c^2 - 8*b^6*c^2 + 22*a^2*b^2*c^4 + 18*b^4*c^4 + 2*a^2*c^6 - 8*b^2*c^6 - c^8 - 2*a^6*S + 10*a^4*b^2*S - 14*a^2*b^4*S + 6*b^6*S + 10*a^4*c^2*S - 12*a^2*b^2*c^2*S - 14*b^4*c^2*S - 14*a^2*c^4*S - 14*b^2*c^4*S + 6*c^6*S) : :
Barycentrics    a^2*(a^6 - 5*a^4*b^2 + 7*a^2*b^4 - 3*b^6 - 5*a^4*c^2 + 6*a^2*b^2*c^2 + 7*b^4*c^2 + 7*a^2*c^4 + 7*b^2*c^4 - 3*c^6 + 2*(a^4 - b^4 - 10*b^2*c^2 - c^4)*S) : :

X(64629) lies on the cubic K168 and these lines: {2, 24243}, {3, 6406}, {6, 494}, {372, 53062}, {485, 642}, {1147, 26507}, {1307, 6396}, {1327, 49435}, {1600, 5412}, {3068, 26506}, {5417, 45599}, {9738, 26293}, {12313, 49377}, {16419, 40809}, {56504, 59702}

X(64629) = isogonal conjugate of X(61391)
X(64629) = isotomic conjugate of the isogonal conjugate of X(53062)
X(64629) = X(i)-cross conjugate of X(j) for these (i,j): {3, 5409}, {32575, 372}
X(64629) = X(i)-isoconjugate of X(j) for these (i,j): {1, 61391}, {19, 24245}, {92, 53061}, {19216, 41516}
X(64629) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 61391}, {6, 24245}, {5408, 487}, {10960, 3069}, {22391, 53061}
X(64629) = cevapoint of X(3) and X(494)
X(64629) = barycentric product X(i)*X(j) for these {i,j}: {76, 53062}, {372, 5491}, {491, 494}, {1307, 54028}, {5409, 24243}, {26461, 45806}
X(64629) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 24245}, {6, 61391}, {184, 53061}, {372, 3069}, {494, 486}, {1307, 54030}, {1600, 39388}, {5409, 487}, {5412, 52291}, {5491, 34392}, {8946, 41516}, {26455, 8036}, {26461, 8576}, {26920, 10133}, {32575, 13934}, {53062, 6}
X(64629) = {X(45414),X(45595)}-harmonic conjugate of X(494)

X(64630) = X(2)X(24244)∩X(3)X(6291)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 12*a^4*b^2*c^2 + 22*a^2*b^4*c^2 - 8*b^6*c^2 + 22*a^2*b^2*c^4 + 18*b^4*c^4 + 2*a^2*c^6 - 8*b^2*c^6 - c^8 + 2*a^6*S - 10*a^4*b^2*S + 14*a^2*b^4*S - 6*b^6*S - 10*a^4*c^2*S + 12*a^2*b^2*c^2*S + 14*b^4*c^2*S + 14*a^2*c^4*S + 14*b^2*c^4*S - 6*c^6*S) : :
Barycentrics    a^2*(-a^6 + 5*a^4*b^2 - 7*a^2*b^4 + 3*b^6 + 5*a^4*c^2 - 6*a^2*b^2*c^2 - 7*b^4*c^2 - 7*a^2*c^4 - 7*b^2*c^4 + 3*c^6 + 2*(a^4 - b^4 - 10*b^2*c^2 - c^4)*S) : :

X(64630) lies on the cubic K168 and these lines: {2, 24244}, {3, 6291}, {6, 493}, {371, 8950}, {486, 641}, {1147, 26498}, {1151, 8913}, {1306, 6200}, {1328, 49434}, {1599, 5413}, {3069, 26496}, {5419, 45600}, {9739, 26292}, {12314, 49378}, {16419, 40809}, {56506, 59702}

X(64630) = isogonal conjugate of X(61390)
X(64630) = isotomic conjugate of the isogonal conjugate of X(8950)
X(64630) = X(i)-cross conjugate of X(j) for these (i,j): {3, 5408}, {32568, 371}
X(64630) = X(i)-isoconjugate of X(j) for these (i,j): {1, 61390}, {19, 24246}, {92, 53060}, {19215, 41515}
X(64630) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 61390}, {6, 24246}, {5409, 488}, {10962, 3068}, {22391, 53060}
X(64630) = cevapoint of X(i) and X(j) for these (i,j): {3, 493}, {5408, 8913}
X(64630) = barycentric product X(i)*X(j) for these {i,j}: {76, 8950}, {371, 5490}, {492, 493}, {1306, 54029}, {5408, 24244}, {26454, 45805}
X(64630) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 24246}, {6, 61390}, {184, 53060}, {371, 3068}, {493, 485}, {1306, 54031}, {1599, 39387}, {5408, 488}, {5413, 5200}, {5490, 34391}, {8911, 10132}, {8948, 41515}, {8950, 6}, {26454, 8577}, {26460, 8035}, {32568, 13882}
X(64630) = {X(45415),X(45596)}-harmonic conjugate of X(493)

X(64631) = X(2)X(7133)∩X(3)X(6213)

Barycentrics    a*(a^2 - b^2 - c^2)*(a^5 + a^4*b - 4*a^3*b^2 + 3*a*b^4 - b^5 + a^4*c - 4*a^3*b*c + 4*a^2*b^2*c - b^4*c - 4*a^3*c^2 + 4*a^2*b*c^2 - 6*a*b^2*c^2 + 2*b^3*c^2 + 2*b^2*c^3 + 3*a*c^4 - b*c^4 - c^5 + 2*a^3*S - 6*a^2*b*S + 2*a*b^2*S + 2*b^3*S - 6*a^2*c*S + 4*a*b*c*S - 2*b^2*c*S + 2*a*c^2*S - 2*b*c^2*S + 2*c^3*S) : :
Barycentrics    a*((a - b - c)*(a + b - c)*(a - b + c)*(a^2 - b^2 - c^2)*(a^2 + 2*a*b - b^2 + 2*a*c - 2*b*c - c^2) + 2*(a^2 - b^2 - c^2)*(a^3 - 3*a^2*b + a*b^2 + b^3 - 3*a^2*c + 2*a*b*c - b^2*c + a*c^2 - b*c^2 + c^3)*S) : :
X(64631) = 3 X[2] + X[52813]

X(64631) lies on the Feuerbach circumhyperbola of the medial triangle, the cubic K168, and these lines: {2, 7133}, {3, 6213}, {6, 8941}, {9, 9616}, {10, 486}, {37, 1376}, {69, 5391}, {100, 42013}, {119, 44038}, {142, 5393}, {214, 35774}, {443, 1123}, {474, 8965}, {485, 41540}, {1336, 59591}, {1766, 8224}, {2550, 6351}, {3084, 5408}, {6260, 31561}, {6352, 59572}, {25524, 38487}

X(64631) = midpoint of X(52813) and X(57269)
X(64631) = complement of X(57269)
X(64631) = complement of the isotomic conjugate of X(57267)
X(64631) = isotomic conjugate of the isogonal conjugate of X(53070)
X(64631) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 30557}, {6203, 141}, {57267, 2887}
X(64631) = X(2)-Ceva conjugate of X(30557)
X(64631) = X(i)-isoconjugate of X(j) for these (i,j): {7348, 16232}, {57269, 60849}
X(64631) = X(30557)-Dao conjugate of X(2)
X(64631) = crosspoint of X(2) and X(57267)
X(64631) = barycentric product X(i)*X(j) for these {i,j}: {76, 53070}, {6203, 56386}, {30557, 57267}
X(64631) = barycentric quotient X(i)/X(j) for these {i,j}: {5414, 7348}, {6203, 13390}, {30557, 57269}, {53070, 6}
X(64631) = {X(2),X(52813)}-harmonic conjugate of X(57269)

X(64632) = X(2)X(42013)∩X(3)X(6212)

Barycentrics    a*(a^2 - b^2 - c^2)*(a^5 + a^4*b - 4*a^3*b^2 + 3*a*b^4 - b^5 + a^4*c - 4*a^3*b*c + 4*a^2*b^2*c - b^4*c - 4*a^3*c^2 + 4*a^2*b*c^2 - 6*a*b^2*c^2 + 2*b^3*c^2 + 2*b^2*c^3 + 3*a*c^4 - b*c^4 - c^5 - 2*a^3*S + 6*a^2*b*S - 2*a*b^2*S - 2*b^3*S + 6*a^2*c*S - 4*a*b*c*S + 2*b^2*c*S - 2*a*c^2*S + 2*b*c^2*S - 2*c^3*S) : :
Barycentrics    a*((a - b - c)*(a + b - c)*(a - b + c)*(a^2 - b^2 - c^2)*(a^2 + 2*a*b - b^2 + 2*a*c - 2*b*c - c^2) - 2*(a^2 - b^2 - c^2)*(a^3 - 3*a^2*b + a*b^2 + b^3 - 3*a^2*c + 2*a*b*c - b^2*c + a*c^2 - b*c^2 + c^3)*S) : :
X(64632) = 3 X[2] + X[52811]

X(64632) lies on the Feuerbach circumhyperbola of the medial triangle, the cubic K168, and these lines: {2, 42013}, {3, 6212}, {6, 8945}, {9, 30355}, {10, 485}, {37, 1376}, {69, 1267}, {100, 7133}, {142, 5405}, {214, 35775}, {443, 1336}, {486, 41540}, {1123, 59591}, {2066, 3083}, {2550, 6352}, {3811, 8953}, {3913, 38487}, {5687, 8965}, {6260, 31562}, {6351, 59572}, {9616, 45036}, {30413, 31413}, {31453, 32556}, {40653, 40869}

X(64632) = midpoint of X(52811) and X(57270)
X(64632) = complement of X(57270)
X(64632) = complement of the isotomic conjugate of X(57266)
X(64632) = isotomic conjugate of the isogonal conjugate of X(53069)
X(64632) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 30556}, {6204, 141}, {57266, 2887}
X(64632) = X(2)-Ceva conjugate of X(30556)
X(64632) = X(i)-isoconjugate of X(j) for these (i,j): {2362, 7347}, {57270, 60850}
X(64632) = X(30556)-Dao conjugate of X(2)
X(64632) = crosspoint of X(2) and X(57266)
X(64632) = barycentric product X(i)*X(j) for these {i,j}: {76, 53069}, {6204, 56385}, {30556, 57266}
X(64632) = barycentric quotient X(i)/X(j) for these {i,j}: {2066, 7347}, {6204, 1659}, {30556, 57270}, {53069, 6}
X(64632) = {X(2),X(52811)}-harmonic conjugate of X(57270)

X(64633) = X(3)X(669)∩X(23)X(99)

Barycentrics    a^2*(a^10*b^2 - 4*a^8*b^4 + 4*a^4*b^8 - a^2*b^10 + a^10*c^2 - 4*a^8*b^2*c^2 + 14*a^6*b^4*c^2 - 17*a^4*b^6*c^2 + 5*a^2*b^8*c^2 - b^10*c^2 - 4*a^8*c^4 + 14*a^6*b^2*c^4 - 6*a^4*b^4*c^4 + 5*a^2*b^6*c^4 - b^8*c^4 - 17*a^4*b^2*c^6 + 5*a^2*b^4*c^6 + 4*a^4*c^8 + 5*a^2*b^2*c^8 - b^4*c^8 - a^2*c^10 - b^2*c^10) : :

X(64633) lies on the cubic K903 and these lines: {3, 669}, {23, 99}, {110, 187}, {237, 524}, {1995, 35606}, {5166, 33875}, {5912, 9149}, {5914, 33900}, {6792, 37465}, {9169, 11328}, {9212, 52773}, {14916, 37184}, {16042, 60863}, {32525, 37338}

X(64633) = circumcircle-inverse of X(5652)
X(64633) = crossdifference of every pair of points on line {3291, 8371}

X(64634) = X(3)X(512)∩X(23)X(110)

Barycentrics    a^2*(2*a^12 - 6*a^10*b^2 + 9*a^8*b^4 - 9*a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 - 2*b^12 - 6*a^10*c^2 + 10*a^8*b^2*c^2 - 7*a^6*b^4*c^2 + 3*a^4*b^6*c^2 - 5*a^2*b^8*c^2 + 5*b^10*c^2 + 9*a^8*c^4 - 7*a^6*b^2*c^4 + 6*a^4*b^4*c^4 - 10*b^8*c^4 - 9*a^6*c^6 + 3*a^4*b^2*c^6 + 14*b^6*c^6 + 3*a^4*c^8 - 5*a^2*b^2*c^8 - 10*b^4*c^8 + 3*a^2*c^10 + 5*b^2*c^10 - 2*c^12) : :
X(64634) = X[74] - 3 X[38704], 3 X[249] - 5 X[15034], 3 X[249] + X[38680], 5 X[15034] + X[38680], X[265] - 3 X[57311], X[691] - 3 X[15035], 3 X[9218] - 7 X[15020], 3 X[9218] - X[38679], 7 X[15020] - X[38679], X[14094] - 3 X[33803], 3 X[14643] - X[38953], 5 X[15040] - X[38582], 5 X[15051] - 3 X[38702], 4 X[20397] - 3 X[35605], 3 X[32609] + X[38583], 2 X[38734] - 3 X[58907], 5 X[38740] - 3 X[58908], 3 X[38793] - 2 X[40544], 5 X[38794] - 3 X[57307]

X(64634) lies on the cubic K903 and these lines: {3, 512}, {23, 110}, {30, 53735}, {74, 38704}, {125, 16760}, {182, 5968}, {187, 14702}, {249, 15034}, {265, 57311}, {523, 53725}, {525, 31854}, {542, 36166}, {575, 13137}, {576, 44127}, {625, 54076}, {690, 46634}, {691, 15035}, {1499, 46987}, {1503, 47570}, {1511, 9181}, {2682, 23698}, {3906, 18332}, {5099, 17702}, {5642, 7471}, {5651, 33927}, {5663, 38613}, {5972, 16188}, {5999, 6054}, {6036, 51428}, {6785, 14002}, {9168, 63767}, {9218, 15020}, {9717, 14687}, {12073, 46633}, {12106, 31850}, {13857, 34312}, {14094, 33803}, {14643, 38953}, {14915, 18860}, {15040, 38582}, {15051, 38702}, {15448, 47584}, {20397, 35605}, {22265, 47288}, {32478, 54248}, {32609, 38583}, {34175, 46512}, {35266, 47351}, {35912, 52076}, {37123, 52994}, {38734, 58907}, {38740, 58908}, {38793, 40544}, {38794, 57307}, {51393, 53760}

X(64634) = midpoint of X(i) and X(j) for these {i,j}: {110, 842}, {22265, 47288}
X(64634) = reflection of X(i) in X(j) for these {i,j}: {125, 16760}, {9181, 1511}, {16188, 5972}, {47584, 15448}, {51428, 6036}, {53710, 46987}
X(64634) = reflection of X(53728) in the Euler line
X(64634) = circumcircle-inverse of X(34291)
X(64634) = crossdifference of every pair of points on line {230, 1640}
X(64634) = {X(3),X(33928)}-harmonic conjugate of X(47049)

X(64635) = X(4)X(513)∩X(8)X(1309)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3)*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c + 2*a^3*b^2*c - 3*a*b^4*c - a^4*c^2 + 2*a^3*b*c^2 - 4*a^2*b^2*c^2 + 2*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + 2*a*b^2*c^3 + 2*a^2*c^4 - 3*a*b*c^4 + b^2*c^4 + a*c^5 - c^6) : :

X(64635) lies on the cubic K620 and these lines: {4, 513}, {8, 1309}, {24, 104}, {64, 38955}, {1093, 1118}, {1413, 34051}, {1593, 45145}, {2250, 41320}, {7435, 39175}, {12138, 56761}, {18816, 54412}, {34182, 36944}, {34234, 37258}, {36110, 56638}, {36819, 46878}, {51359, 51660}, {61429, 64120}

X(64635) = polar conjugate of the isotomic conjugate of X(57495)
X(64635) = X(1309)-Ceva conjugate of X(14312)
X(64635) = X(i)-isoconjugate of X(j) for these (i,j): {255, 54241}, {1295, 22350}, {2431, 24029}, {15405, 24028}
X(64635) = X(i)-Dao conjugate of X(j) for these (i,j): {6523, 54241}, {14571, 26611}, {53991, 517}
X(64635) = barycentric product X(i)*X(j) for these {i,j}: {4, 57495}, {2052, 39175}, {2405, 43728}, {6001, 16082}, {25640, 59196}, {34234, 51359}, {36795, 51399}
X(64635) = barycentric quotient X(i)/X(j) for these {i,j}: {393, 54241}, {2443, 23981}, {25640, 26611}, {39175, 394}, {41933, 15405}, {43058, 62402}, {43728, 2417}, {51359, 908}, {51399, 1465}, {57495, 69}

X(64636) = X(2)X(2592)∩X(4)X(39)

Barycentrics    (b^2 - c^2)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6)*((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - a^2*(-a^2 + b^2 + c^2)*(1 + J)) - a^2*(-((a^2 - b^2)*(a^2 + b^2 - c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4)*((a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2) - c^2*(a^2 + b^2 - c^2)*(1 + J))) + (a^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*((a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2) - b^2*(a^2 - b^2 + c^2)*(1 + J))) : :

X(64636) lies on the cubic K280 and these lines: {2, 2592}, {4, 39}, {6, 1114}, {376, 15167}, {1313, 15048}, {1344, 5024}, {1345, 45141}, {1346, 3815}, {1347, 5523}, {5013, 14709}, {5063, 41942}, {7735, 15166}, {7737, 15161}, {7757, 15165}, {8106, 40138}, {8743, 14710}, {10737, 44526}, {16070, 41518}, {41941, 52905}

X(64637) = X(2)X(2593)∩X(4)X(39)

Barycentrics    a^2*(-((a^2 - b^2)*(a^2 + b^2 - c^2)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4)*((a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2) - c^2*(a^2 + b^2 - c^2)*(1 - J))) + (a^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2)*((a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2) - b^2*(a^2 - b^2 + c^2)*(1 - J))) - (b^2 - c^2)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6)*((a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - a^2*(-a^2 + b^2 + c^2)*(1 - J)) : :

X(64637) lies on the cubic K280 and these lines: {2, 2593}, {4, 39}, {6, 1113}, {376, 15166}, {1312, 15048}, {1344, 45141}, {1345, 5024}, {1346, 5523}, {1347, 3815}, {5013, 14710}, {5063, 41941}, {7735, 15167}, {7737, 15160}, {7757, 15164}, {8105, 40138}, {8743, 14709}, {10736, 44526}, {16071, 41519}, {41942, 52905}

X(64638) = X(2)X(3)∩X(637)X(9873)

Barycentrics    (a^2 + b^2 + c^2) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) + (3 a^4 - 2 a^2 b^2 - b^4 - 2 a^2 c^2 + 2 b^2 c^2 - c^4) S : :
X(64638) = 5 X[3] - 3 X[36734], 4 X[140] - 3 X[36733], 2 X[3627] - 3 X[36719], X[5073] - 3 X[36718]

See Francisco Javier García Capitán , Sharing the centroid and more.

X(64638) lies on these lines: {2, 3}, {511, 39888}, {637, 9873}, {1503, 49038}, {1975, 58803}, {5490, 54935}, {5870, 9733}, {6201, 43119}, {6459, 31670}, {6460, 39876}, {6560, 7738}, {7690, 33364}, {7750, 58804}, {8982, 14927}, {10722, 33341}, {10784, 45488}, {26361, 45542}, {26429, 42413}, {26441, 51212}, {29181, 49039}, {29317, 42858}, {39874, 43133}, {41411, 42275}, {42258, 48910}, {42259, 48905}, {42264, 63548}

X(64638) = reflection of X(i) in X(j) for these {i,j}: {5870, 9733}, {64639, 20}
X(64638) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 36658}, {4, 376, 11292}, {20, 11293, 376}, {376, 7375, 3}, {3543, 32489, 4}

X(64639) = X(2)X(3)∩X(638)X(9873)

Barycentrics    (a^2 + b^2 + c^2) (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) + (-3 a^4 + 2 a^2 b^2 + b^4 + 2 a^2 c^2 - 2 b^2 c^2 + c^4) S : :
X(64639) = 5 X[3] - 3 X[36718], 4 X[140] - 3 X[36719], 2 X[3627] - 3 X[36733], X[5073] - 3 X[36734]

See Francisco Javier García Capitán , Sharing the centroid and more.

X(64639) lies on these lines: {2, 3}, {511, 39887}, {638, 9873}, {1503, 49039}, {1975, 58804}, {5491, 54936}, {5871, 9732}, {6202, 43118}, {6459, 39875}, {6460, 31670}, {6561, 7738}, {7692, 33365}, {7750, 58803}, {8982, 51212}, {10722, 33340}, {10783, 45489}, {14927, 26441}, 26362, 45543}, {26430, 42414}, {29181, 49038}, {29317, 42859}, {39874, 43134}, {41410, 42276}, {42258, 48905}, {42259, 48910}, {42263, 63548}

X(64639) = reflection of X(i) in X(j) for these {i,j}: {5871, 9732}, {64638, 20}
X(64639) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 36657}, {4, 376, 11291}, {20, 11294, 376}, {376, 7376, 3}, {3543, 32488, 4}

X(64640) = X(3)X(966)∩X(45)X(198)

Barycentrics    a^2 (a^6 + a^5 b - a^4 b^2 + a^2 b^4 - a b^5 - b^6 + a^5 c + 3 a^4 b c + 2 a^3 b^2 c - 2 a^2 b^3 c - 3 a b^4 c - b^5 c - a^4 c^2 + 2 a^3 b c^2 - 2 a^2 b^2 c^2 + b^4 c^2 - 2 a^2 b c^3 + 2 b^3 c^3 + a^2 c^4 - 3 a b c^4 + b^2 c^4 - a c^5 - b c^5 - c^6) : :

See Keita Miyamoto and Francisco Javier García Capitán, euclid 6555.

X(64640) lies on these lines: {3, 966}, {6, 16947}, {19, 5277}, {45, 198}, {48, 18755}, {197, 199}, {610, 35342}, {1213, 52273}, {1603, 1604}, {1609, 13738}, {1953, 40750}, {2183, 2305}, {4254, 20842}, {8573, 37257}, {17299, 23858}, {20876, 20877}, {35216, 56956}, {36744, 37259}, {38871, 38903}, {60544, 60564}

X(64641) =  EULER LINE INTERCEPT OF X(12383)X(36254)

Barycentrics    4 a^28-37 a^26 b^2+153 a^24 b^4-382 a^22 b^6+682 a^20 b^8-1023 a^18 b^10+1419 a^16 b^12-1716 a^14 b^14+1584 a^12 b^16-979 a^10 b^18+319 a^8 b^20+18 a^6 b^22-62 a^4 b^24+23 a^2 b^26-3 b^28-37 a^26 c^2+264 a^24 b^2 c^2-798 a^22 b^4 c^2+1330 a^20 b^6 c^2-1335 a^18 b^8 c^2+774 a^16 b^10 c^2+12 a^14 b^12 c^2-684 a^12 b^14 c^2+765 a^10 b^16 c^2-140 a^8 b^18 c^2-462 a^6 b^20 c^2+474 a^4 b^22 c^2-193 a^2 b^24 c^2+30 b^26 c^2+153 a^24 c^4-798 a^22 b^2 c^4+1806 a^20 b^4 c^4-2154 a^18 b^6 c^4+1017 a^16 b^8 c^4+564 a^14 b^10 c^4-744 a^12 b^12 c^4+108 a^10 b^14 c^4-561 a^8 b^16 c^4+1578 a^6 b^18 c^4-1542 a^4 b^20 c^4+702 a^2 b^22 c^4-129 b^24 c^4-382 a^22 c^6+1330 a^20 b^2 c^6-2154 a^18 b^4 c^6+2434 a^16 b^6 c^6-1540 a^14 b^8 c^6-552 a^12 b^10 c^6+1360 a^10 b^12 c^6+410 a^8 b^14 c^6-2562 a^6 b^16 c^6+2798 a^4 b^18 c^6-1442 a^2 b^20 c^6+300 b^22 c^6+682 a^20 c^8-1335 a^18 b^2 c^8+1017 a^16 b^4 c^8-1540 a^14 b^6 c^8+2622 a^12 b^8 c^8-1389 a^10 b^10 c^8-949 a^8 b^12 c^8+2568 a^6 b^14 c^8-3138 a^4 b^16 c^8+1825 a^2 b^18 c^8-363 b^20 c^8-1023 a^18 c^10+774 a^16 b^2 c^10+564 a^14 b^4 c^10-552 a^12 b^6 c^10-1389 a^10 b^8 c^10+1842 a^8 b^10 c^10-1140 a^6 b^12 c^10+2424 a^4 b^14 c^10-1431 a^2 b^16 c^10+66 b^18 c^10+1419 a^16 c^12+12 a^14 b^2 c^12-744 a^12 b^4 c^12+1360 a^10 b^6 c^12-949 a^8 b^8 c^12-1140 a^6 b^10 c^12-1908 a^4 b^12 c^12+516 a^2 b^14 c^12+495 b^16 c^12-1716 a^14 c^14-684 a^12 b^2 c^14+108 a^10 b^4 c^14+410 a^8 b^6 c^14+2568 a^6 b^8 c^14+2424 a^4 b^10 c^14+516 a^2 b^12 c^14-792 b^14 c^14+1584 a^12 c^16+765 a^10 b^2 c^16-561 a^8 b^4 c^16-2562 a^6 b^6 c^16-3138 a^4 b^8 c^16-1431 a^2 b^10 c^16+495 b^12 c^16-979 a^10 c^18-140 a^8 b^2 c^18+1578 a^6 b^4 c^18+2798 a^4 b^6 c^18+1825 a^2 b^8 c^18+66 b^10 c^18+319 a^8 c^20-462 a^6 b^2 c^20-1542 a^4 b^4 c^20-1442 a^2 b^6 c^20-363 b^8 c^20+18 a^6 c^22+474 a^4 b^2 c^22+702 a^2 b^4 c^22+300 b^6 c^22-62 a^4 c^24-193 a^2 b^2 c^24-129 b^4 c^24+23 a^2 c^26+30 b^2 c^26-3 c^28 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6567.

X(64641) lies on these lines: {2, 3}, {12383, 36254}

X(64642) =  EULER LINE INTERCEPT OF X(14643)X(33855)

Barycentrics    2 a^16-19 a^14 b^2+53 a^12 b^4-55 a^10 b^6+5 a^8 b^8+23 a^6 b^10-a^4 b^12-13 a^2 b^14+5 b^16-19 a^14 c^2+26 a^12 b^2 c^2-39 a^10 b^4 c^2+128 a^8 b^6 c^2-109 a^6 b^8 c^2-42 a^4 b^10 c^2+71 a^2 b^12 c^2-16 b^14 c^2+53 a^12 c^4-39 a^10 b^2 c^4-144 a^8 b^4 c^4+71 a^6 b^6 c^4+198 a^4 b^8 c^4-135 a^2 b^10 c^4-4 b^12 c^4-55 a^10 c^6+128 a^8 b^2 c^6+71 a^6 b^4 c^6-310 a^4 b^6 c^6+77 a^2 b^8 c^6+80 b^10 c^6+5 a^8 c^8-109 a^6 b^2 c^8+198 a^4 b^4 c^8+77 a^2 b^6 c^8-130 b^8 c^8+23 a^6 c^10-42 a^4 b^2 c^10-135 a^2 b^4 c^10+80 b^6 c^10-a^4 c^12+71 a^2 b^2 c^12-4 b^4 c^12-13 a^2 c^14-16 b^2 c^14+5 c^16 : :
Barycentrics    4*S^4-3*SB*SC*(297*R^4-108*R^2*SW+8*SW^2)-3*S^2*(117*R^4+4*SB*SC-60*R^2*SW+8*SW^2) : :
X(64642) = 7*X(5)-3*X(20124), 5*X(140)-2*X(36164), 3*X(14643)-X(33855)

As a point on the Euler line, X(64642) has Shinagawa coefficients {15*E^2+48*E*F+384*F^2-64*S^2,-21*E^2-528*E*F+384*F^2+192*S^2}.

See Antreas Hatzipolakis and Ercole Suppa, euclid 6567.

X(64642) lies on these lines: {2, 3}, {14643, 33855}, {16168, 20393}, {32417, 61598}, {34153, 57471}

X(64642) = reflection of X(140) in X(523)X(14643)
X(64642) = complement of the circumperp conjugate of X(15766)

X(64643) = X(76)-CEVA CONJUGATE OF X(513)

Barycentrics    a*(b - c)^2*(a^3 + a*b^2 + a*b*c - b^2*c + a*c^2 - b*c^2) : :

X(64643) lies on these lines: {1, 7239}, {2, 62587}, {11, 115}, {37, 24542}, {39, 17602}, {100, 26278}, {244, 21339}, {513, 1977}, {650, 6377}, {661, 8054}, {1194, 17061}, {1979, 24289}, {2275, 17720}, {2969, 6591}, {3121, 14296}, {3124, 64523}, {3666, 5976}, {3752, 24582}, {3756, 6588}, {4396, 57039}, {16604, 30818}, {16606, 64225}, {16726, 17198}, {16742, 16759}, {17475, 61172}, {17721, 63493}, {18037, 19786}, {22200, 64559}, {38347, 39786}, {40941, 47231}

X(64643) = complement of the isotomic conjugate of X(18108)
X(64643) = isotomic conjugate of the isogonal conjugate of X(55053)
X(64643) = X(i)-complementary conjugate of X(j) for these (i,j): {82, 21260}, {83, 21262}, {251, 3835}, {649, 21248}, {667, 21249}, {1919, 6292}, {1980, 16587}, {2206, 3005}, {3120, 55070}, {3122, 46654}, {4628, 27076}, {10547, 20315}, {10566, 626}, {18105, 3454}, {18108, 2887}, {39179, 21240}, {46288, 514}, {46289, 513}, {52376, 42327}, {52394, 23301}, {55240, 21245}, {61383, 3239}
X(64643) = X(76)-Ceva conjugate of X(513)
X(64643) = X(101)-isoconjugate of X(54458)
X(64643) = X(i)-Dao conjugate of X(j) for these (i,j): {667, 6}, {1015, 54458}
X(64643) = crosspoint of X(2) and X(18108)
X(64643) = crosssum of X(i) and X(j) for these (i,j): {1, 7239}, {6, 4553}, {213, 61172}
X(64643) = barycentric product X(i)*X(j) for these {i,j}: {1, 21210}, {76, 55053}, {244, 32926}, {513, 21301}, {514, 21389}, {649, 20952}, {693, 21005}, {1019, 21099}, {3261, 57047}, {6591, 28423}, {17924, 22157}, {40495, 57097}
X(64643) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 54458}, {20952, 1978}, {21005, 100}, {21099, 4033}, {21210, 75}, {21301, 668}, {21389, 190}, {22157, 1332}, {32926, 7035}, {55053, 6}, {57047, 101}, {57097, 692}

X(64644) = X(76)-CEVA CONJUGATE OF X(918)

Barycentrics    b*(b - c)^2*c*(-a^2 + b*c)*(-(a*b) + b^2 - a*c + c^2) : :

X(64644) lies on these lines: {11, 693}, {76, 4583}, {115, 1111}, {120, 3263}, {350, 1281}, {918, 35505}, {1565, 3777}, {1566, 4858}, {3760, 51989}, {4142, 21208}, {4358, 16593}, {4509, 7336}, {6063, 30959}, {20974, 48094}, {21207, 48393}, {23773, 53583}, {27918, 39786}, {35119, 40623}, {40075, 64222}

X(64644) = isotomic conjugate of the isogonal conjugate of X(38989)
X(64644) = X(i)-complementary conjugate of X(j) for these (i,j): {251, 3716}, {665, 21249}, {2254, 21248}, {10566, 20544}, {18108, 20335}, {46289, 918}
X(64644) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 918}, {1111, 62429}
X(64644) = X(i)-isoconjugate of X(j) for these (i,j): {660, 32666}, {813, 919}, {1110, 52030}, {1252, 51866}, {1911, 5377}, {5378, 64216}, {18265, 39293}, {23990, 52209}, {34067, 36086}
X(64644) = X(i)-Dao conjugate of X(j) for these (i,j): {514, 52030}, {661, 51866}, {665, 6}, {918, 22116}, {1577, 33676}, {2238, 1252}, {3126, 7077}, {3716, 55}, {3912, 765}, {6651, 5377}, {17755, 5378}, {27918, 100}, {35094, 660}, {35119, 36086}, {38980, 813}, {38989, 34067}, {40623, 919}, {62552, 105}, {62558, 1438}
X(64644) = crosspoint of X(i) and X(j) for these (i,j): {693, 3263}, {30940, 52619}
X(64644) = crosssum of X(i) and X(j) for these (i,j): {6, 46163}, {692, 64216}, {34067, 40730}
X(64644) = crossdifference of every pair of points on line {32666, 34067}
X(64644) = barycentric product X(i)*X(j) for these {i,j}: {76, 38989}, {239, 62429}, {693, 62552}, {918, 3766}, {1086, 64223}, {1111, 17755}, {1921, 3675}, {3263, 27918}, {4124, 40704}, {4858, 39775}, {8299, 23989}, {17435, 18033}, {34253, 34387}
X(64644) = barycentric quotient X(i)/X(j) for these {i,j}: {239, 5377}, {244, 51866}, {659, 919}, {665, 34067}, {812, 36086}, {918, 660}, {1086, 52030}, {1111, 52209}, {2254, 813}, {3675, 292}, {3766, 666}, {3912, 5378}, {4124, 294}, {4435, 52927}, {4858, 33676}, {8299, 1252}, {8632, 32666}, {10030, 39293}, {17435, 7077}, {17755, 765}, {23773, 41531}, {23829, 4584}, {27846, 1438}, {27918, 105}, {34253, 59}, {35094, 22116}, {35505, 40730}, {38989, 6}, {39775, 4564}, {39786, 56853}, {43041, 36146}, {51329, 2149}, {62429, 335}, {62552, 100}, {64223, 1016}

X(64645) = X(76)-CEVA CONJUGATE OF X(30)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 - b^6 - a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(64645) lies on these lines: {6, 13}, {30, 9408}, {146, 6794}, {339, 3589}, {1235, 14389}, {1531, 52950}, {1539, 52951}, {1990, 34334}, {2420, 6793}, {3124, 5305}, {3580, 44576}, {4846, 40354}, {5523, 15639}, {5664, 5976}, {6103, 6699}, {7664, 14316}, {9412, 20127}, {10317, 39008}, {12918, 48905}, {14398, 41079}, {14915, 41358}, {36435, 58789}, {37638, 62573}, {41361, 61206}

X(64645) = X(i)-complementary conjugate of X(j) for these (i,j): {1495, 21249}, {2173, 21248}, {9406, 6292}, {9407, 16587}, {36035, 55070}, {46288, 18593}, {46289, 30}
X(64645) = X(76)-Ceva conjugate of X(30)
X(64645) = X(i)-isoconjugate of X(j) for these (i,j): {2159, 55032}, {2349, 64615}
X(64645) = X(i)-Dao conjugate of X(j) for these (i,j): {1495, 6}, {3163, 55032}
X(64645) = crosssum of X(6) and X(46147)
X(64645) = crossdifference of every pair of points on line {526, 64615}
X(64645) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 55032}, {1495, 64615}

X(64646) = X(76)-CEVA CONJUGATE OF X(9019)

Barycentrics    a^2*(a^4 - b^4 + b^2*c^2 - c^4)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(64646) lies on these lines: {2, 339}, {3, 64213}, {6, 110}, {22, 112}, {23, 8744}, {39, 52533}, {115, 1194}, {187, 47181}, {216, 6103}, {230, 63846}, {232, 3163}, {250, 53929}, {647, 60510}, {648, 2373}, {858, 1560}, {1180, 31236}, {1184, 2079}, {1196, 10418}, {1249, 7493}, {1625, 46128}, {1986, 7418}, {2492, 7664}, {2781, 36828}, {3580, 15595}, {4232, 45245}, {4239, 40582}, {7492, 18472}, {8745, 26284}, {9475, 15329}, {9609, 38872}, {9832, 39078}, {10313, 39176}, {13351, 44529}, {15905, 26283}, {16165, 28343}, {16318, 16387}, {21208, 40940}, {22240, 47228}, {24855, 47182}, {26257, 37895}, {34349, 34834}, {37801, 37804}, {37980, 52058}, {38652, 47230}, {40937, 47232}, {40941, 47231}, {40948, 46594}, {44468, 53346}, {46425, 62612}, {47426, 57485}, {52950, 56922}, {57481, 60002}

X(64646) = complement of X(18019)
X(64646) = complement of the isogonal conjugate of X(18374)
X(64646) = complement of the isotomic conjugate of X(23)
X(64646) = isotomic conjugate of the polar conjugate of X(20410)
X(64646) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 21234}, {23, 2887}, {31, 858}, {32, 16581}, {316, 21235}, {560, 187}, {604, 18637}, {923, 6698}, {1973, 62376}, {2492, 21253}, {8744, 20305}, {10317, 18589}, {14246, 21256}, {16568, 626}, {18374, 10}, {20944, 40379}, {32676, 9517}, {42659, 34846}, {46289, 9019}, {52142, 4892}, {52630, 42327}, {52916, 21259}, {55226, 21263}
X(64646) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 858}, {76, 9019}, {250, 46592}, {648, 9517}, {57481, 23}, {59422, 2393}
X(64646) = X(47426)-cross conjugate of X(6593)
X(64646) = X(i)-isoconjugate of X(j) for these (i,j): {1910, 36884}, {2157, 2373}, {3455, 37220}
X(64646) = X(i)-Dao conjugate of X(j) for these (i,j): {468, 57496}, {858, 2}, {5099, 60040}, {5181, 34897}, {11672, 36884}, {39169, 41511}, {40583, 2373}, {47138, 339}, {61067, 67}
X(64646) = crosspoint of X(i) and X(j) for these (i,j): {2, 23}, {250, 52630}, {14246, 37765}
X(64646) = crosssum of X(6) and X(67)
X(64646) = crossdifference of every pair of points on line {690, 3455}
X(64646) = barycentric product X(i)*X(j) for these {i,j}: {23, 858}, {69, 20410}, {250, 38971}, {316, 2393}, {1236, 18374}, {1560, 57481}, {5181, 14246}, {5523, 22151}, {6593, 59422}, {7664, 57485}, {8744, 62382}, {9517, 61181}, {9979, 61198}, {14580, 37804}, {14961, 37765}, {16568, 18669}, {36415, 57476}, {47138, 52630}, {47426, 52551}
X(64646) = barycentric quotient X(i)/X(j) for these {i,j}: {23, 2373}, {316, 46140}, {511, 36884}, {858, 18019}, {1560, 57496}, {2393, 67}, {2492, 60040}, {5523, 46105}, {8744, 60133}, {9019, 46165}, {10317, 18876}, {14580, 8791}, {14961, 34897}, {16568, 37220}, {18374, 1177}, {20410, 4}, {36415, 60002}, {38971, 339}, {46592, 935}, {47426, 14357}, {51962, 64218}, {52142, 10422}, {57485, 10415}, {61198, 17708}
X(64646) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 40583, 36415}, {36415, 40583, 52951}

X(64647) = X(76)-CEVA CONJUGATE OF X(511)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^6*b^2 - a^2*b^6 + a^6*c^2 - b^6*c^2 + 2*b^4*c^4 - a^2*c^6 - b^2*c^6) : :

X(64647) lies on these lines: {2, 11794}, {5, 39}, {22, 61194}, {76, 39575}, {98, 5661}, {147, 34235}, {216, 15819}, {232, 511}, {262, 15355}, {339, 3934}, {343, 14994}, {1194, 3124}, {1196, 40377}, {2021, 47079}, {2491, 2799}, {3094, 47049}, {5052, 14984}, {5188, 53795}, {5305, 52536}, {10317, 14675}, {13236, 15915}, {14580, 36789}, {14965, 58355}, {15462, 57260}, {15905, 22655}, {16308, 47568}, {17980, 52471}, {22240, 22712}, {23584, 47200}, {34359, 46272}, {36471, 53981}, {38974, 44953}, {40810, 51511}

X(64647) = midpoint of X(76) and X(41676)
X(64647) = reflection of X(339) in X(3934)
X(64647) = complement of the isotomic conjugate of X(51862)
X(64647) = isotomic conjugate of the isogonal conjugate of X(40601)
X(64647) = X(i)-complementary conjugate of X(j) for these (i,j): {82, 21531}, {237, 21249}, {560, 8623}, {1755, 21248}, {3405, 626}, {9417, 6292}, {9418, 16587}, {20022, 21235}, {34072, 24284}, {46288, 16609}, {46289, 511}, {51862, 2887}
X(64647) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 511}, {41676, 2799}
X(64647) = X(1910)-isoconjugate of X(55033)
X(64647) = X(i)-Dao conjugate of X(j) for these (i,j): {237, 6}, {11672, 55033}
X(64647) = crosspoint of X(i) and X(j) for these (i,j): {2, 51862}, {2421, 27867}
X(64647) = crosssum of X(i) and X(j) for these (i,j): {6, 20021}, {2395, 7668}
X(64647) = crossdifference of every pair of points on line {879, 51869}
X(64647) = barycentric product X(i)*X(j) for these {i,j}: {76, 40601}, {297, 14965}, {325, 60514}, {511, 14957}, {1959, 16564}
X(64647) = barycentric quotient X(i)/X(j) for these {i,j}: {511, 55033}, {14957, 290}, {14965, 287}, {16564, 1821}, {40601, 6}, {58355, 17974}, {60514, 98}
X(64647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 60526, 2023}, {2023, 2493, 60526}

X(64648) = X(76)-CEVA CONJUGATE OF X(1503)

Barycentrics    (2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6)*(a^8 - b^8 - a^4*b^2*c^2 + b^6*c^2 + b^2*c^6 - c^8) : :

X(64648) lies on these lines: {2, 44766}, {4, 32}, {230, 39000}, {339, 5305}, {1289, 26269}, {1297, 45280}, {2508, 38652}, {23977, 50938}, {34137, 34237}, {36899, 39085}, {46425, 62612}

X(64648) = complement of the isotomic conjugate of X(21458)
X(64648) = X(i)-complementary conjugate of X(j) for these (i,j): {2312, 21248}, {21458, 2887}, {42671, 21249}, {46289, 1503}
X(64648) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 1503}, {53657, 55129}
X(64648) = X(i)-Dao conjugate of X(j) for these (i,j): {42671, 6}, {50938, 34129}
X(64648) = crosspoint of X(2) and X(21458)
X(64648) = crosssum of X(6) and X(46164)
X(64648) = barycentric product X(i)*X(j) for these {i,j}: {34137, 60516}, {38652, 57490}
X(64648) = barycentric quotient X(i)/X(j) for these {i,j}: {2508, 34212}, {16318, 34129}

X(64649) = ISOTOMIC CONJUGATE OF X(55085)

Barycentrics    (3*a^2*b^2 + b^4 + a^2*c^2 + 3*b^2*c^2)*(a^2*b^2 + 3*a^2*c^2 + 3*b^2*c^2 + c^4) : :

X(64649 lies on these lines: {385, 18092}, {732, 3589}, {7794, 45108}, {9466, 19609}, {16890, 42006}, {21022, 21684}, {35540, 39998}, {59739, 61063}

X(64649) = isotomic conjugate of X(55085)
X(64649) = isotomic conjugate of the isogonal conjugate of X(55075)
X(64649) = X(34294)-cross conjugate of X(523)
X(64649) = X(i)-isoconjugate of X(j) for these (i,j): {31, 55085}, {560, 55081}, {14990, 24041}
X(64649) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55085}, {3005, 14990}, {6374, 55081}
X(64649) = barycentric product X(i)*X(j) for these {i,j}: {76, 55075}, {19609, 52618}
X(64649) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55085}, {76, 55081}, {3124, 14990}, {19609, 1634}, {55075, 6}

X(64650) = X(76)-CEVA CONJUGATE OF X(512)

Barycentrics    a^2*(b - c)^2*(b + c)^2*(a^4 + a^2*b^2 + a^2*c^2 - b^2*c^2) : :

X(64650) lies on these lines: {32, 53273}, {39, 620}, {112, 19626}, {115, 804}, {148, 14700}, {512, 9427}, {733, 52034}, {1194, 7664}, {1196, 10418}, {2489, 2971}, {3124, 5113}, {3229, 56442}, {5305, 52536}, {5355, 8265}, {5475, 63557}, {6375, 9466}, {6377, 40619}, {6388, 62573}, {7761, 63572}, {7853, 63570}, {9431, 30229}, {14691, 32531}, {16589, 62587}, {35078, 52591}, {35971, 46665}, {39000, 47421}, {39018, 55152}

X(64650) = complement of the isotomic conjugate of X(18105)
X(64650) = isotomic conjugate of the isogonal conjugate of X(38996)
X(64650) = X(i)-complementary conjugate of X(j) for these (i,j): {82, 23301}, {83, 21263}, {251, 42327}, {560, 3005}, {669, 21249}, {798, 21248}, {1917, 52591}, {1924, 6292}, {2643, 55070}, {4117, 15449}, {4599, 36950}, {4630, 21254}, {9426, 16587}, {18070, 40379}, {18098, 21262}, {18105, 2887}, {46288, 4369}, {46289, 512}, {51906, 21253}, {55240, 626}, {58784, 21235}, {61383, 8062}
X(64650) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 512}, {1627, 21006}, {7760, 8711}
X(64650) = X(i)-isoconjugate of X(j) for these (i,j): {662, 55034}, {6664, 24041}
X(64650) = X(i)-Dao conjugate of X(j) for these (i,j): {669, 6}, {1084, 55034}, {3005, 6664}
X(64650) = crosspoint of X(i) and X(j) for these (i,j): {2, 18105}, {1627, 21006}
X(64650) = crosssum of X(i) and X(j) for these (i,j): {6, 4576}, {3051, 61219}, {6664, 55034}
X(64650) = crossdifference of every pair of points on line {1634, 10330}
X(64650) = barycentric product X(i)*X(j) for these {i,j}: {76, 38996}, {115, 1627}, {512, 44445}, {513, 22322}, {523, 21006}, {798, 20953}, {850, 57075}, {2501, 22159}, {2643, 33760}, {3124, 7760}, {8711, 58784}
X(64650) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 55034}, {1627, 4590}, {3124, 6664}, {7760, 34537}, {8711, 4576}, {18105, 6573}, {20953, 4602}, {21006, 99}, {22159, 4563}, {22322, 668}, {33760, 24037}, {38996, 6}, {44445, 670}, {57075, 110}
X(64650) = {X(115),X(1084)}-harmonic conjugate of X(51906)

X(64651) =  EULER LINE INTERCEPT OF X(399)X(14354)

Barycentrics    a^2 (a^26-7 a^24 b^2+12 a^22 b^4+44 a^20 b^6-275 a^18 b^8+693 a^16 b^10-1056 a^14 b^12+1056 a^12 b^14-693 a^10 b^16+275 a^8 b^18-44 a^6 b^20-12 a^4 b^22+7 a^2 b^24-b^26-7 a^24 c^2+45 a^22 b^2 c^2-105 a^20 b^4 c^2+67 a^18 b^6 c^2+162 a^16 b^8 c^2-414 a^14 b^10 c^2+462 a^12 b^12 c^2-378 a^10 b^14 c^2+333 a^8 b^16 c^2-287 a^6 b^18 c^2+171 a^4 b^20 c^2-57 a^2 b^22 c^2+8 b^24 c^2+12 a^22 c^4-105 a^20 b^2 c^4+357 a^18 b^4 c^4-573 a^16 b^6 c^4+450 a^14 b^8 c^4-318 a^12 b^10 c^4+642 a^10 b^12 c^4-972 a^8 b^14 c^4+798 a^6 b^16 c^4-405 a^4 b^18 c^4+141 a^2 b^20 c^4-27 b^22 c^4+44 a^20 c^6+67 a^18 b^2 c^6-573 a^16 b^4 c^6+1099 a^14 b^6 c^6-817 a^12 b^8 c^6-360 a^10 b^10 c^6+934 a^8 b^12 c^6-433 a^6 b^14 c^6+123 a^4 b^16 c^6-133 a^2 b^18 c^6+49 b^20 c^6-275 a^18 c^8+162 a^16 b^2 c^8+450 a^14 b^4 c^8-817 a^12 b^6 c^8+1260 a^10 b^8 c^8-543 a^8 b^10 c^8-811 a^6 b^12 c^8+531 a^4 b^14 c^8+93 a^2 b^16 c^8-50 b^18 c^8+693 a^16 c^10-414 a^14 b^2 c^10-318 a^12 b^4 c^10-360 a^10 b^6 c^10-543 a^8 b^8 c^10+1554 a^6 b^10 c^10-408 a^4 b^12 c^10-258 a^2 b^14 c^10+27 b^16 c^10-1056 a^14 c^12+462 a^12 b^2 c^12+642 a^10 b^4 c^12+934 a^8 b^6 c^12-811 a^6 b^8 c^12-408 a^4 b^10 c^12+414 a^2 b^12 c^12-6 b^14 c^12+1056 a^12 c^14-378 a^10 b^2 c^14-972 a^8 b^4 c^14-433 a^6 b^6 c^14+531 a^4 b^8 c^14-258 a^2 b^10 c^14-6 b^12 c^14-693 a^10 c^16+333 a^8 b^2 c^16+798 a^6 b^4 c^16+123 a^4 b^6 c^16+93 a^2 b^8 c^16+27 b^10 c^16+275 a^8 c^18-287 a^6 b^2 c^18-405 a^4 b^4 c^18-133 a^2 b^6 c^18-50 b^8 c^18-44 a^6 c^20+171 a^4 b^2 c^20+141 a^2 b^4 c^20+49 b^6 c^20-12 a^4 c^22-57 a^2 b^2 c^22-27 b^4 c^22+7 a^2 c^24+8 b^2 c^24-c^26) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6572.

X(64651) lies on these lines: {2, 3}, {399, 14354}

X(64652) =  EULER LINE INTERCEPT OF X(110)X(14993)

Barycentrics    4 a^16-17 a^14 b^2+25 a^12 b^4-11 a^10 b^6-5 a^8 b^8+a^6 b^10+7 a^4 b^12-5 a^2 b^14+b^16-17 a^14 c^2+46 a^12 b^2 c^2-51 a^10 b^4 c^2+34 a^8 b^6 c^2+a^6 b^8 c^2-30 a^4 b^10 c^2+19 a^2 b^12 c^2-2 b^14 c^2+25 a^12 c^4-51 a^10 b^2 c^4+18 a^8 b^4 c^4-11 a^6 b^6 c^4+54 a^4 b^8 c^4-27 a^2 b^10 c^4-8 b^12 c^4-11 a^10 c^6+34 a^8 b^2 c^6-11 a^6 b^4 c^6-62 a^4 b^6 c^6+13 a^2 b^8 c^6+34 b^10 c^6-5 a^8 c^8+a^6 b^2 c^8+54 a^4 b^4 c^8+13 a^2 b^6 c^8-50 b^8 c^8+a^6 c^10-30 a^4 b^2 c^10-27 a^2 b^4 c^10+34 b^6 c^10+7 a^4 c^12+19 a^2 b^2 c^12-8 b^4 c^12-5 a^2 c^14-2 b^2 c^14+c^16 : :
Barycentrics    2*S^4-3*SB*SC*(27*R^4-2*SW^2)-3*S^2*(99*R^4+2*SB*SC-48*R^2*SW+6*SW^2) : :
X(64652) = X(5)+2*X(7471), 5*X(5)-2*X(36184), 2*X(140)+X(36193), X(476)+2*X(10272), 2*X(1511)+X(18319), 2*X(1553)+X(14677), 2*X(3233)+X(34209), X(5627)-3*X(57305), X(5627)+3*X(60605), 2*X(5972)-X(45694), X(10264)-4*X(22104), 3*X(14643)+X(51345), 2*X(14934)-5*X(22251), 5*X(15027)+X(31876), 5*X(15040)+X(34193), 2*X(25641)+X(34153), 2*X(31378)-X(33855), X(51345)-3*X(60603), X(52056)+5*X(64101)

As a point on the Euler line, X(64652) has Shinagawa coefficients {9*E^2+288*F^2-32*S^2,-15*E^2-192*E*F-96*F^2+96*S^2}.

See Antreas Hatzipolakis and Ercole Suppa, euclid 6572.

X(64652) lies on these lines: {2, 3}, {110, 14993}, {476, 10272}, {523, 18285}, {1138, 38580}, {1511, 18319}, {1553, 14677}, {3233, 34209}, {5627, 32423}, {5972, 45694}, {10264, 22104}, {12121, 57471}, {14643, 51345}, {14934, 22251}, {15027,31876}, {15040, 34193}, {16168, 31378}, {25641, 34153}, {32417, 38609}, {52056, 64101}

X(64652) = reflection of X(5) in X(523)X(14643)

X(64653) = X(3)X(76)∩X(30)X(599)

Barycentrics    a^8 - a^6*b^2 + a^4*b^4 - a^2*b^6 - a^6*c^2 + 2*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 2*b^6*c^2 + a^4*c^4 - 5*a^2*b^2*c^4 - 4*b^4*c^4 - a^2*c^6 + 2*b^2*c^6 : :

See Kadir Altintas and Francisco Javier García Capitán, euclid 6576.

X(64653) lies on these lines: {3, 76}, {4, 3314}, {5, 7778}, {6, 22525}, {20, 63044}, {30, 599}, {114, 7801}, {140, 3767}, {141, 37242}, {182, 538}, {298, 44465}, {299, 44461}, {325, 37348}, {381, 47618}, {384, 10788}, {385, 35925}, {511, 3734}, {543, 50977}, {549, 7610}, {550, 59363}, {574, 15819}, {575, 7798}, {576, 7804}, {631, 7783}, {736, 35424}, {1003, 2080}, {1232, 40947}, {1316, 15066}, {1351, 10796}, {1499, 46778}, {1597, 43976}, {1656, 7832}, {1657, 9873}, {2452, 41614}, {2549, 53475}, {2709, 53919}, {2794, 34507}, {3054, 10256}, {3095, 7770}, {3098, 44774}, {3398, 7754}, {3526, 7828}, {3788, 6721}, {3934, 9737}, {5024, 40108}, {5050, 22253}, {5054, 8860}, {5070, 7930}, {5149, 32135}, {5171, 7816}, {6090, 51430}, {6194, 11676}, {6228, 6229}, {6248, 17130}, {6312, 12975}, {6316, 12974}, {6321, 7841}, {6390, 37451}, {6776, 32836}, {7485, 39906}, {7503, 26179}, {7697, 13860}, {7709, 37455}, {7751, 13335}, {7781, 13334}, {7789, 37466}, {7794, 39838}, {7799, 43461}, {7810, 38738}, {7818,13449},{7833, 13172}, {7835, 38227}, {7836, 37446}, {7839, 10359}, {7854, 32152}, {7870, 64089}, {7883, 10723}, {7934, 14639}, {7942, 46219}, {8591, 60653}, {9301, 10000}, {9466, 18860}, {9744, 32833}, {9755, 26316}, {9832, 46634}, {9996, 35456}, {10516, 40250}, {10519, 32815}, {10983, 11272}, {11007, 37638}, {11171, 31859}, {11174, 32447}, {11185, 15980}, {11288, 14693}, {11295, 13102}, {11296, 13103}, {11318, 61576}, {11842, 14614}, {12117, 55164}, {12215, 35429}, {13564, 33802}, {13732, 50156}, {13862, 43453}, {14001, 20576}, {14033, 63428}, {14494, 32968}, {14532, 55610}, {14538, 25167}, {14539, 25157}, {14931, 43532}, {14994, 35387}, {15684, 34681}, {15694, 55801}, {15718, 46941}, {16084, 59248}, {18768, 44224}, {18907, 34380}, {22594, 44476}, {22623, 44475}, {24271, 37521}, {31276, 37334}, {31981, 32448}, {33532, 53274}, {35259, 37906}, {35385, 37004}, {35606, 62191}, {37344, 63736}, {37450, 47286}, {38110, 63633}, {40727, 49102}, {40879, 57612}, {43449, 44526}, {44518, 61600}, {50008, 62551}, {50641, 50955}, {50978, 63945}, {51389, 61644}, {56370, 64093}, {57588, 59767}, {60654, 64090}

X(64654) = X(2)X(2064)∩X(39)X(1212)

Barycentrics    a (a b+b^2+a c+c^2) (a^3+b^3-b^2 c-b c^2+c^3) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6583.

X(64654) lies on these lines: {2, 2064}, {37, 20106}, {39, 1212}, {57, 5019}, {244, 40956}, {1104, 35650}, {1211, 2092}, {1214, 17053}, {1427, 20227}, {1447, 17080}, {1763, 16946}, {3772, 17861}, {3924, 36570}, {4646, 6743}, {4850, 5278}, {5437, 54317}, {16579, 28358}, {17054, 54431}, {18591, 40941}, {18592, 53387}, {19762, 24046}, {20254, 37819}, {20886, 33129}, {22380, 33945}, {40959, 40984}

X(64654) = complement of X(2064)
X(64654) = barycentric product of X(i) and X(j) for these (i,j): (1193, 17861), (1829, 41004), (1837, 24471), (1848, 26934), (2092, 16749), (2292, 17189)
X(64654) = barycentric quotient of X(i) and X(j) for these {i,j}: {1193, 40436}, {1829, 34406}, {2300, 56003}, {2354, 55994}, {3666, 59759}, {3772, 30710}
X(64654) = trilinear product of X(i) and X(j) for these (i,j): (960, 36570), (1193, 3772), (1829, 26934), (1837, 61412), (2092, 17189), (2300, 17861)
X(64654) = trilinear quotient of X(i) and X(j) for these (i,j): (1193, 56003), (1829, 55994), (1848, 34406), (2354, 56305), (3666, 40436), (3674, 34399)
X(64654) = pole of the line X(2886)X(49598) with respect to dual of Yff parabola
X(64654) = pole of the line X(17052)X(44417) with respect to Kiepert hyperbola
X(64654) = pole of the line X(663)X(832) with respect to Steiner inellipse}

X(64655) = X(216)X(53496)∩X(6509)X(11064)

Barycentrics    a^2 (a^2-b^2-c^2)^2 (a^10 b^2-3 a^8 b^4+2 a^6 b^6+2 a^4 b^8-3 a^2 b^10+b^12+a^10 c^2-2 a^6 b^4 c^2-3 a^4 b^6 c^2+7 a^2 b^8 c^2-3 b^10 c^2-3 a^8 c^4-2 a^6 b^2 c^4+2 a^4 b^4 c^4-4 a^2 b^6 c^4+3 b^8 c^4+2 a^6 c^6-3 a^4 b^2 c^6-4 a^2 b^4 c^6-2 b^6 c^6+2 a^4 c^8+7 a^2 b^2 c^8+3 b^4 c^8-3 a^2 c^10-3 b^2 c^10+c^12) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6583.

X(64655) lies on these lines: {216, 53496}, {6509, 11064}, {15526, 34834}

X(64656) = X(2)X(6)∩X(403)X(2883)

Barycentrics    a^10 b^2-3 a^8 b^4+2 a^6 b^6+2 a^4 b^8-3 a^2 b^10+b^12+a^10 c^2+6 a^8 b^2 c^2-2 a^6 b^4 c^2-20 a^4 b^6 c^2+17 a^2 b^8 c^2-2 b^10 c^2-3 a^8 c^4-2 a^6 b^2 c^4+36 a^4 b^4 c^4-14 a^2 b^6 c^4-b^8 c^4+2 a^6 c^6-20 a^4 b^2 c^6-14 a^2 b^4 c^6+4 b^6 c^6+2 a^4 c^8+17 a^2 b^2 c^8-b^4 c^8-3 a^2 c^10-2 b^2 c^10+c^12 : :
Barycentrics    64*R^4-6*R^2*SA-18*R^2*SW+SA*SW+SW^2 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6583.

X(64656) lies on these lines: {2, 6}, {125, 44079}, {235, 31978}, {403, 2883}, {427, 58483}, {441, 40320}, {468, 1660}, {1192, 15873}, {3003, 45200}, {6247, 6623}, {9729, 15760}, {9786, 18537}, {9818, 44158}, {10257, 13346}, {12233, 15024}, {13416, 41588}, {23291, 41735}, {26937, 46373}, {37197, 43695}, {44911, 61607}

X(64656) = complement of X(2063)
X(64656) = pole of the line X(2)X(14091) with respect to Kiepert hyperbola

X(64657) = X(39)X(8364)∩X(1180)X(7914)

Barycentrics    a^2 (a^6 b^2+a^4 b^4+a^2 b^6+b^8+a^6 c^2-a^2 b^4 c^2-b^6 c^2+a^4 c^4-a^2 b^2 c^4+a^2 c^6-b^2 c^6+c^8) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6583.

X(64657) lies on these lines: {39, 8364}, {1180, 7914}, {1194, 6292}, {1196, 7499}, {7815, 9465}

X(64658) = X(1)X(2)∩X(11)X(6245)

Barycentrics    a^6 b-2 a^5 b^2-a^4 b^3+4 a^3 b^4-a^2 b^5-2 a b^6+b^7+a^6 c+4 a^5 b c+a^4 b^2 c-12 a^3 b^3 c-a^2 b^4 c+8 a b^5 c-b^6 c-2 a^5 c^2+a^4 b c^2+16 a^3 b^2 c^2+2 a^2 b^3 c^2+2 a b^4 c^2-3 b^5 c^2-a^4 c^3-12 a^3 b c^3+2 a^2 b^2 c^3-16 a b^3 c^3+3 b^4 c^3+4 a^3 c^4-a^2 b c^4+2 a b^2 c^4+3 b^3 c^4-a^2 c^5+8 a b c^5-3 b^2 c^5-2 a c^6-b c^6+c^7 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6583.

X(64658) lies on these lines: {1, 2}, {5, 58576}, {11, 6245}, {56, 7682}, {57, 64190}, {496, 31788}, {497, 37560}, {515, 41426}, {516, 59336}, {631, 33994}, {1466, 17728}, {1699, 11023}, {1785, 24171}, {3452, 50196}, {3660, 6260}, {3820, 16215}, {3911, 10310}, {4187,17626}, {4292,52860}, {4301, 12736}, {4311, 64145}, {4848,15558}, {5450, 57278}, {5573, 7952}, {7681, 18238}, {7741, 63970}, {9581, 12667}, {11507, 51724}, {11508, 59675}, {12915, 17527}, {17054, 51616}, {18240, 21077}, {18838, 54198}, {24213, 62789}, {36123, 40446}

X(64658) = complement of X(2057)
X(64658) = pole of the line X(2)X(31600) with respect to dual of Yff parabola

X(64659) = X(1)X(3)∩X(78)X(9954)

Barycentrics    -a (2 a^6-3 a^5 (b+c)+a^4 (-3 b^2+16 b c-3 c^2)+a^3 (6 b^3-4 b^2 c-4 b c^2+6 c^3)-2 a^2 b c (7 b^2-6 b c+7 c^2)-a (b-c)^2 (3 b^3-b^2 c-b c^2+3 c^3)+(b-c)^4 (b+c)^2) : :
Barycentrics    a*(2*a^6 - 3*a^5*b - 3*a^4*b^2 + 6*a^3*b^3 - 3*a*b^5 + b^6 - 3*a^5*c + 16*a^4*b*c - 4*a^3*b^2*c - 14*a^2*b^3*c + 7*a*b^4*c - 2*b^5*c - 3*a^4*c^2 - 4*a^3*b*c^2 + 12*a^2*b^2*c^2 - 4*a*b^3*c^2 - b^4*c^2 + 6*a^3*c^3 - 14*a^2*b*c^3 - 4*a*b^2*c^3 + 4*b^3*c^3 + 7*a*b*c^4 - b^2*c^4 - 3*a*c^5 - 2*b*c^5 + c^6) : :
X(64659) = 3 X[3] - X[3359], X[57] - 5 X[7987], 3 X[165] + X[7962], X[999] - 3 X[3576], X[2093] - 9 X[58221], X[3359] + 3 X[37611], 3 X[3576] + X[6282], X[7994] + 7 X[30389], 3 X[21164] - X[36279], X[3421] + 3 X[5731], X[5691] - 5 X[20196], X[7682] - 3 X[10165], 3 X[35272] - X[63992]
X(64659) = r*X[1] + (r - 4*R)*X[3]

euclid 6586.

X(64659) lies on these lines: {1, 3}, {20, 17614}, {78, 9954}, {84, 31821}, {104, 60970}, {200, 30283}, {214, 38759}, {355, 6926}, {392, 6909}, {515, 3820}, {527,43176}, {936, 9947}, {958, 58650}, {960, 34862}, {971, 997}, {993, 31658}, {1125, 7956}, {1292, 38452}, {1519, 37429}, {1538, 6925}, {1768, 31165}, {2810, 11714}, {2975,17658}, {3421,5440}, {3452, 4297}, {3877, 17613}, {3897, 15717}, {3940, 63430}, {4298, 5763}, {4311, 31799}, {4511, 10167}, {4881, 7411}, {5044, 12114}, {5450, 31445}, {5493, 51714}, {5603, 62778}, {5658, 6987}, {5691, 20196}, {5806, 25524} ,{5812, 31776}, {5886, 6916}, {6261, 31805}, {6326, 63432}, {6827, 18516}, {6850, 9955}, {6865, 18481}, {6882, 38140}, {6891, 9956}, {6907, 11230}, {6922, 18480}, {6928, 33697}, {6948, 28146}, {7290, 8147}, {7580, 35262}, {7682, 10165}, {8583, 10241}, {8666, 58637}, {9709, 12650},{9856, 19861}, {9943, 30144}, {10156, 54318}, {10307, 54052}, {11260, 43174}, {12053, 31777}, {12672, 37403}, {18243, 37837}, {18446, 51489}, {21616, 22792}, {22793, 31775}, {22836, 58567}, {33597, 37423}, {34647, 60896}, {42819, 43151}, {45287, 50031}, {51705, 54192}, {52769, 58608}

X(64659) = midpoint of X(i) and X(j) for these {i,j}: {1, 6244}, {3, 37611}, {200, 30283}, {997, 63991}, {999, 6282}, {3452, 4297}, {3940, 63430}, {5289, 64129}, {12915, 31793}
X(64659) = reflection of X(i) in X(j) for these {i,j}: {7956, 1125}, {10269, 13624}, {51788, 1385}
X(64659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3, 31787}, {3, 1482, 37560}, {3, 10246, 30503}, {3, 12702, 10270}, {3, 31786, 3579}, {40, 3576, 13462}, {960, 63983, 34862}, {3428, 3576, 5126}, {3576, 6282, 999}, {3576, 24929, 1385}, {3576, 50371, 24929}, {3579, 17502, 23961}, {5049, 37569, 10222}, {7987, 59340, 5204}, {14110, 37561, 37582}, {17642, 37605, 5193}, {19861, 37022, 9856}, {38013, 38014, 24928}

X(64660) = X(376)X(930)∩X(378)X(933)

Barycentrics    a^2*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 + a^8*c^2 - 2*a^4*b^4*c^2 + b^8*c^2 - 7*a^6*c^4 + a^4*b^2*c^4 + a^2*b^4*c^4 - 7*b^6*c^4 + 5*a^4*c^6 + 5*b^4*c^6 + 2*a^2*c^8 + 2*b^2*c^8 - 2*c^10)*(a^10 + a^8*b^2 - 7*a^6*b^4 + 5*a^4*b^6 + 2*a^2*b^8 - 2*b^10 - 3*a^8*c^2 + a^4*b^4*c^2 + 2*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 + a^2*b^4*c^4 + 5*b^6*c^4 + 2*a^4*c^6 - 7*b^4*c^6 - 3*a^2*c^8 + b^2*c^8 + c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6605.

X(64660) lies on the circumcircle and these lines: {3, 58975}, {5, 1302}, {107, 7576}, {110, 5891}, {376, 930}, {378, 933}, {925, 44239}, {1291, 7464}, {2070, 9060}, {3153, 16167}, {3518, 9064}, {7422, 9076}, {7488, 53958}, {10295, 52998}, {12060, 46966}, {18533, 20626}, {20185, 21312}, {29011, 46585}, {32710, 53246}, {37943, 53944}, {50401, 53945}

X(64660) = reflection of X(58975) in X(3)

X(64661) = X(51)X(551)∩X(373)X(519)

Barycentrics    a^2 (a^3 b^2+a^2 b^3-a b^4-b^5+a^2 b^2 c-b^4 c+a^3 c^2+a^2 b c^2+10 a b^2 c^2+4 b^3 c^2+a^2 c^3+4 b^2 c^3-a c^4-b c^4-c^5) : :

See Keita Miyamoto and Francisco Javier García Capitán, euclid 6603.

X(64661) lies on these lines: {1, 5943}, {51, 551}, {373, 519}, {389, 9624}, {511, 25055}, {1125, 3917}, {1154, 38022}, {1386, 29959}, {1698, 10219}, {2393, 38023}, {3060, 3616}, {3241, 11451}, {3636, 16980}, {3656, 5892}, {3679, 6688}, {3796, 11365}, {3892, 61640}, {5313, 39543}, {5462, 61276}, {5603, 15045}, {5640, 38314}, {5650, 19883}, {5691, 13570}, {5734, 15028}, {5886, 13754}, {5901, 5946}, {6000, 38021}, {7982, 11695}, {8681, 16475}, {9589, 17704}, {9729, 11522}, {9730, 51709}, {9822, 16491}, {9955, 16194}, {10595, 58487}, {11735, 12824}, {13364, 50824}, {13391, 38028}, {13451, 51700}, {13598, 30389}, {14845, 28204}, {14984, 38040}, {15026, 61278}, {15060, 61272}, {15808, 31757}, {16776, 51006}, {16836, 31162}, {17609, 58497}, {19875, 63632}, {21746, 49997}, {21849, 51110}, {21969, 51108}, {22415, 40955}, {24473, 58574}, {25557, 56884}, {28352, 50597}, {29958, 50190}, {30308, 46847}, {32062, 50802}, {36987, 50828}, {42448, 58565}, {46934, 62188}, {47356, 61676}, {50759, 63522},{51005, 61667}, {51105, 58470}

X(64662) = X(1)X(389)∩X(351)X(515)

Barycentrics    a^2 (a^6 b^2-3 a^4 b^4+3 a^2 b^6-b^8+a^6 c^2+2 a^4 b^2 c^2-2 a^3 b^3 c^2-5 a^2 b^4 c^2+2 a b^5 c^2+2 b^6 c^2-2 a^3 b^2 c^3+4 a^2 b^3 c^3-2 a b^4 c^3-3 a^4 c^4-5 a^2 b^2 c^4-2 a b^3 c^4-2 b^4 c^4+2 a b^2 c^5+3 a^2 c^6+2 b^2 c^6-c^8) : :

See Keita Miyamoto and Francisco Javier García Capitán, euclid 6603.

X(64662) lies on these lines: {1, 389}, {2, 52796}, {3, 61398}, {4, 58469}, {8, 15043}, {40, 9729}, {51, 515}, {52, 1385}, {80, 58508}, {143, 34773}, {165, 16836}, {182, 15177}, {185, 946}, {355, 5462}, {373, 10175}, {375, 18908}, {511, 3576}, {517, 3058}, {519, 16226}, {551, 14831}, {568, 10246}, {578, 16472}, {602, 10974}, {912, 41581}, {944, 3567}, {952, 5946}, {962, 10574}, {970, 10902}, {1071, 42450}, {1125, 5562}, {1154, 38028}, {1181, 11365}, {1386, 19161}, {1482, 37481}, {1572, 50387}, {1698, 11695}, {1699, 6000}, {1843, 39870}, {1986, 11735}, {2801, 15049}, {2807, 5603}, {2808, 61705}, {2818, 5902}, {2979, 54445}, {3060, 5731}, {3616, 5889}, {3624, 11793}, {3817, 15030}, {3917, 10165}, {4297, 31757}, {5446, 18481}, {5550, 11444}, {5587, 5943}, {5640, 59387}, {5657, 15045}, {5663, 38034}, {5690, 12006}, {5691, 10110}, {5818, 15024}, {5876, 61272}, {5881, 23841}, {5882, 16980}, {5884, 42448}, {5886, 13754}, {5891, 11230}, {5892, 26446}, {5901, 6102}, {5907, 8227}, {6001, 41580}, {6688, 54447}, {7680, 34462}, {7968, 12239}, {7969, 12240}, {7982, 15012}, {7987, 15644}, {8193, 37514}, {9778, 20791}, {9779, 15305}, {9780, 15028}, {9812, 15072}, {9822, 39885}, {9864, 58503}, {9955, 12162}, {10575, 22793}, {10625, 13624}, {10984, 49553}, {11381, 18483}, {11522, 13382}, {11562, 12261}, {11709, 13417}, {11710, 39846}, {11711, 39817}, {11720, 21649}, {12005, 23154}, {12109, 37625}, {12266, 32352}, {12368, 41671}, {12699, 40647}, {12751, 58504}, {12784, 58515}, {13178, 58502}, {13211, 58498}, {13363, 38042}, {13464, 31728}, {13491, 40273}, {13532, 58506}, {13630, 22791}, {14531, 31738}, {14845, 38140}, {14855, 28146}, {14872, 58497}, {15026, 18357}, {15060, 61269}, {15489, 59331}, {17704, 35242}, {18493, 34783}, {19862, 31752}, {21849, 50811}, {21969, 51705}, {24474, 58575}, {31751, 45187}, {34146, 38035}, {34372, 56177}, {37515, 37557}, {41869, 46850}, {50896, 58507}, {50899, 58513}, {50903, 58505}, {51707, 54384}, {58548, 59388}

X(64663) = X(1)X(5462)∩X(52)X(3616)

Barycentrics    a^2 (a^6 b^2-3 a^4 b^4+3 a^2 b^6-b^8+a^6 c^2+4 a^4 b^2 c^2-4 a^3 b^3 c^2-9 a^2 b^4 c^2+4 a b^5 c^2+4 b^6 c^2-4 a^3 b^2 c^3+8 a^2 b^3 c^3-4 a b^4 c^3-3 a^4 c^4-9 a^2 b^2 c^4-4 a b^3 c^4-6 b^4 c^4+4 a b^2 c^5+3 a^2 c^6+4 b^2 c^6-c^8) : :

See Keita Miyamoto and Francisco Javier García Capitán, euclid 6603.

X(64663) lies on these lines: {1, 5462}, {51, 10246},{52, 3616}, {143, 51700}, {145, 15024}, {185, 18493}, {373, 5790}, {389, 5901}, {511, 38028}, {517, 5892}, {946, 40647}, {952, 5943}, {960, 58575}, {1125, 1216}, {1385, 5446}, {1483, 15026}, {1699, 14915}, {2807, 51709}, {3567, 3622}, {3617, 11465}, {3636, 31760}, {5603, 9730}, {5640, 7967}, {5690, 11695}, {5691, 44863}, {5844, 13363}, {5886, 13754}, {5907, 61272}, {5946, 10283}, {6000, 38034}, {6153, 12266}, {6688, 38042}, {9729, 22791},{9779, 16194}, {9812, 14855}, {10110, 34773}, {10170, 11230}, {10222, 58487}, {10595, 15043}, {11412, 46934}, {11451, 59388}, {11557, 11735}, {11692,51701}, {11723, 11806}, {12245, 15028}, {12410, 15805}, {13364, 28224}, {13373, 42450}, {13607, 58474}, {14641, 22793}, {14845, 59387}, {15060, 61270}, {15808, 31738}, {16475, 34382}, {16836, 28174}, {16980, 37624}, {19907, 58508}, {31937, 58617}, {32205, 61510}, {34791, 58647}, {40273, 46850}, {50824, 58470}

X(64664) = X(2)X(72)∩X(46)X(4428)

Barycentrics    a (3 a^2 b-3 b^3+3 a^2 c+8 a b c+5 b^2 c+5 b c^2-3 c^3) : :

See Keita Miyamoto and Francisco Javier García Capitán, euclid 6603.

X(64664) lies on these lines: {1, 4004},{2, 72},{8, 50192},{9, 19536}, {30, 10167}, {46, 4428}, {57, 16370}, {63, 16857}, {65, 551}, {145, 50191}, {210, 3833}, {226, 17533}, {354, 519}, {376, 9940}, {381, 1071}, {392, 3742}, {405, 3928}, {474, 11518}, {484, 42819}, {517, 3524}, {518, 3921}, {547, 24475}, {549, 24474}, {553, 11113}, {597, 24476}, {758, 19883}, {912, 5055}, {956, 10980}, {971, 3839}, {1125, 4018}, {1210, 17530}, {1453, 39980}, {1737, 25557}, {1739, 49478}, {2771, 59377}, {2800, 38026}, {2801, 38076}, {3057, 33815}, {3175, 43220}, {3218, 16858}, {3219, 17547}, {3241, 5045}, {3244, 3922}, {3306, 5440}, {3336, 51715}, {3338, 11194}, {3419, 9776}, {3543, 5806}, {3545, 5927}, {3555, 3679}, {3601, 19705}, {3616, 31794}, {3622, 50193}, {3634, 4533}, {3655, 13373}, {3656, 34339}, {3666, 48855}, {3697, 3828}, {3698, 3881}, {3740, 3894}, {3754, 17609}, {3816, 11551}, {3827, 38023}, {3830, 13369}, {3848, 5692}, {3873, 53620}, {3878, 51108}, {3889, 31145}, {3916, 5708}, {3918, 34641}, {3919, 5919}, {3929, 17542}, {3951, 16853}, {3962, 19862}, {3984, 16863}, {3999, 30116}, {4005, 51073}, {4084, 51109}, {4539, 61686}, {4654, 17556}, {4666, 36279}, {4677, 34791}, {4723, 17146}, {4731, 38098}, {4757, 15808}, {4860, 54318}, {4870, 10199}, {4880, 15254}, {4930, 19861}, {5066, 40263}, {5071, 5777}, {5542, 17757}, {5563, 19524}, {5570, 10056}, {5728, 6173}, {5731, 58615}, {5836, 50190}, {5885, 12672}, {5903, 51105}, {5904, 19876}, {6001, 38021}, {6583, 50821}, {6797, 10031}, {6940, 10222}, {6942, 15178}, {6977, 61276}, {7686, 50811}, {8581, 51098}, {9021, 48310}, {9709, 62861}, {9943, 50865}, {10072, 13750}, {10156, 15708}, {10157, 61924}, {10177, 28534}, {10197, 41539}, {10273, 10283}, {10304, 11227}, {10707, 58587}, {11018, 15933}, {11220, 50687}, {11237, 17625}, {11238, 12711}, {11274, 17636}, {11520, 16408}, {11523, 16862},{11570, 45310}, {11573, 21969}, {12005, 50796}, {12009, 18480}, {12100, 37585}, {12528, 61936}, {12625, 56997}, {12680, 34648}, {12688, 50802}, {12736, 50843}, {13374, 15016}, {13407, 17619}, {13476, 51034}, {13587, 24929}, {13747, 63274}, {14110, 50828}, {14523, 50301}, {14988, 38022}, {15071, 30308}, {15570, 48696}, {15677, 58619}, {15683, 31805}, {15692, 31793}, {15694, 31837}, {15803, 19704}, {16842, 54422}, {16861, 31445}, {17051, 30384}, {17529, 24391}, {17549, 37582}, {17626, 50195}, {17654, 58604}, {18180, 42028}, {18527, 20292}, {19290, 35612}, {19804, 48850}, {20116, 51100}, {21077, 44847}, {21161, 37623}, {21165, 28451}, {21342, 56191}, {24174, 42043}, {26728, 37634}, {26877, 28461}, {28466, 37532}, {30117, 37520}, {30143, 32636}, {30350, 63137}, {31178, 58583}, {31446, 50795}, {31663, 62870}, {31787, 34632}, {31798, 50872}, {31822, 62042}, {31835, 61885}, {31870, 51705}, {33575, 61812}, {34378, 38089}, {34381, 59373}, {34628, 58567}, {34747, 58609}, {34772, 36006}, {37545, 62829}, {37562, 58561}, {37592, 42040}, {37723, 50239}, {42038, 59305}, {42057, 50083}, {44566, 53550}, {47356, 58562}, {47357, 58564}, {49483, 49999}, {49499, 59586}, {50824, 61541}, {51110, 58679}, {51787, 62862}

X(64665) = X(140)X(17794)∩X(297)X(31626)

Barycentrics    (a^8 - 2 a^6 b^2 + 2 a^4 b^4 - 2 a^2 b^6 + b^8 - 3 a^6 c^2 + 2 a^4 b^2 c^2 + 3 a^2 b^4 c^2 - 2 b^6 c^2 + 4 a^4 c^4 + 2 a^2 b^2 c^4 + 2 b^4 c^4 - 3 a^2 c^6 - 2 b^2 c^6 + c^8) (a^8 - 3 a^6 b^2 + 4 a^4 b^4 - 3 a^2 b^6 + b^8 - 2 a^6 c^2 + 2 a^4 b^2 c^2 + 2 a^2 b^4 c^2 - 2 b^6 c^2 + 2 a^4 c^4 + 3 a^2 b^2 c^4 + 2 b^4 c^4 - 2 a^2 c^6 - 2 b^2 c^6 + c^8) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6609.

X(64665) lies on these lines: {140, 17974}, {297, 31626}, {6101, 54032}, {14767, 14938}, {28724, 39113}, {34828, 43994}, {52251, 63154}

X(64666) = 12TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    2 a^16 - 9 a^14 b^2 + 16 a^12 b^4 - 16 a^10 b^6 + 15 a^8 b^8 - 17 a^6 b^10 + 14 a^4 b^12 - 6 a^2 b^14 + b^16 - 9 a^14 c^2 + 26 a^12 b^2 c^2 - 29 a^10 b^4 c^2 + 15 a^8 b^6 c^2 + 9 a^6 b^8 c^2 - 28 a^4 b^10 c^2 + 21 a^2 b^12 c^2 - 5 b^14 c^2 + 16 a^12 c^4 - 29 a^10 b^2 c^4 + 12 a^8 b^4 c^4 - 4 a^6 b^6 c^4 + 22 a^4 b^8 c^4 - 27 a^2 b^10 c^4 + 10 b^12 c^4 - 16 a^10 c^6 + 15 a^8 b^2 c^6 - 4 a^6 b^4 c^6 - 16 a^4 b^6 c^6 + 12 a^2 b^8 c^6 - 11 b^10 c^6 + 15 a^8 c^8 + 9 a^6 b^2 c^8 + 22 a^4 b^4 c^8 + 12 a^2 b^6 c^8 + 10 b^8 c^8 - 17 a^6 c^10 - 28 a^4 b^2 c^10 - 27 a^2 b^4 c^10 - 11 b^6 c^10 + 14 a^4 c^12 + 21 a^2 b^2 c^12 + 10 b^4 c^12 - 6 a^2 c^14 - 5 b^2 c^14 + c^16 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6609.

X(64666) lies on these lines: {2, 3}, {18400, 61590}

X(64667) = X(1)X(2)∩X(57)X(4428)

Barycentrics    a*(3*a^2 - 6*a*b + 3*b^2 - 6*a*c - 10*b*c + 3*c^2) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64667) lies on these lines: {1, 2}, {31, 39980}, {57, 4428}, {63, 30350}, {81, 16487}, {165, 62856}, {269, 63110}, {354, 3928}, {376, 12651}, {553, 12560}, {940, 35227}, {968, 42038}, {1001, 3929}, {1279, 62842}, {1386, 39948}, {1490, 38021}, {1621, 10980}, {1743, 62867}, {1750, 50802}, {2177, 8056}, {2951, 59375}, {2975, 30343}, {3058, 4326}, {3174, 38093}, {3243, 4423}, {3247, 59216}, {3304, 13615}, {3305, 62863}, {3306, 62862}, {3333, 16370}, {3361, 17549}, {3524, 6769}, {3555, 17542}, {3601, 40726}, {3653, 37531}, {3656, 18443}, {3731, 42039}, {3742, 4421}, {3746, 37309}, {3748, 5437}, {3750, 62695}, {3839, 63981}, {3848, 46917}, {3889, 5234}, {4321, 4654}, {4328, 17320}, {4863, 20195}, {4864, 7322}, {4866, 17536}, {4883, 7290}, {5045, 16418}, {5055, 5534}, {5066, 18528}, {5223, 5284}, {5436, 17609}, {5528, 38095}, {5531, 59377}, {5558, 11106}, {5563, 20835}, {5665, 51773}, {5732, 38024}, {6282, 50828}, {6326, 38026}, {7308, 42871}, {7411, 30389}, {7987, 62870}, {8167, 15570}, {8226, 9624}, {8726, 28194}, {8727, 61276}, {9580, 25557}, {9776, 30331}, {10382, 11238}, {10383, 10385}, {10431, 11522}, {10439, 64549}, {10857, 50808}, {11038, 40998}, {11194, 51715}, {11220, 24644}, {11224, 62835}, {11518, 44663}, {12526, 24473}, {12565, 31162}, {15178, 19541}, {16484, 62818}, {16857, 57279}, {16858, 62874}, {17051, 31231}, {17093, 25723}, {17146, 25734}, {17194, 42028}, {17394, 40719}, {17642, 58564}, {17784, 43179}, {18153, 25303}, {18529, 41106}, {25430, 49465}, {25522, 63282}, {25590, 32943}, {27003, 31508}, {30827, 37703}, {31424, 50190}, {36946, 41229}, {37364, 61278}, {37700, 38022}, {37736, 45310}, {38053, 64162}, {41711, 51780}, {41815, 51699}, {42040, 62849}, {42041, 62869}, {50192, 54290}, {51709, 63992}, {53056, 61155}, {55082, 56309}, {56179, 63109}, {58565, 61763}, {60846, 62819}, {61159, 63214}

X(64667) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4666, 10582}, {1, 8580, 3957}, {1, 10582, 200}, {1, 29820, 2999}, {1, 54392, 4853}, {354, 38316, 4512}, {551, 45700, 25055}, {1001, 44841, 62823}, {3742, 10389, 64112}, {4428, 58560, 57}, {4666, 29817, 1}, {5284, 62815, 5223}, {42819, 58560, 4428}, {62856, 64149, 165}

X(64668) = X(1)X(3)∩X(4)X(4666)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c - 6*a^4*b*c + 4*a^3*b^2*c + 8*a^2*b^3*c - 2*a*b^4*c - 2*b^5*c - a^4*c^2 + 4*a^3*b*c^2 - 6*a^2*b^2*c^2 + 4*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 8*a^2*b*c^3 + 4*a*b^2*c^3 + 4*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 2*b*c^5 + c^6) : :
X(64668) = 3 X[3576] - X[37551]

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64668) lies on these lines: {1, 3}, {2, 5534}, {4, 4666}, {5, 10582}, {20, 29817}, {84, 38316}, {104, 62829}, {140, 200}, {381, 63981}, {496, 10382}, {515, 6849}, {550, 12651}, {551, 6261}, {602, 62819}, {631, 3870}, {912, 31435}, {944, 6864}, {946, 41854}, {997, 31458}, {1001, 7330}, {1006, 62874}, {1058, 7675}, {1064, 28011}, {1125, 5720}, {1279, 36746}, {1483, 4853}, {1490, 5886}, {1621, 63399}, {1750, 9955}, {1802, 17438}, {2951, 48661}, {2999, 37698}, {3174, 38122}, {3243, 61122}, {3244, 12521}, {3306, 11491}, {3523, 3957}, {3526, 8580}, {3553, 4253}, {3554, 4251}, {3560, 63430}, {3616, 6846}, {3622, 18444}, {3624, 17857}, {3655, 12650}, {3720, 36670}, {3742, 11500}, {3811, 10165}, {3851, 18529}, {3873, 55104}, {3881, 52769}, {3889, 6986}, {3935, 10303}, {4298, 6868}, {4314, 6948}, {4321, 6147}, {4326, 15172}, {4423, 14872}, {4428, 64118}, {4512, 24467}, {4847, 6989}, {5249, 12116}, {5272, 37699}, {5287, 7397}, {5290, 6928}, {5436, 22758}, {5437, 11499}, {5528, 38124}, {5531, 34595}, {5603, 10884}, {5732, 12699}, {5758, 11038}, {5840, 41864}, {5882, 54318}, {5901, 63992}, {6326, 38032}, {6713, 37736}, {6765, 26446}, {6825, 11019}, {6827, 21620}, {6850, 63999}, {6883, 57279}, {6889, 26015}, {6891, 13405}, {6908, 10580}, {6926, 10578}, {6954, 64124}, {6959, 31249}, {6987, 11037}, {7171, 11496}, {7191, 7390}, {7290, 36742}, {7967, 17582}, {8167, 58631}, {8583, 37700}, {9623, 37727}, {9624, 63988}, {9845, 18519}, {10177, 52684}, {10393, 44675}, {10595, 64150}, {10864, 37234}, {11522, 50528}, {12005, 12514}, {12114, 51715}, {12520, 13464}, {12526, 24475}, {12560, 24470}, {12565, 22791}, {12629, 61287}, {12680, 18540}, {12700, 15170}, {12705, 13369}, {12864, 57284}, {14520, 46475}, {14986, 30284}, {15570, 58637}, {16132, 61275}, {16408, 64116}, {16469, 36750}, {16487, 51340}, {16842, 18908}, {16845, 19861}, {17022, 19512}, {17560, 54356}, {17614, 50203}, {22153, 40937}, {25522, 37713}, {25525, 26470}, {26201, 30304}, {26877, 35258}, {26921, 62823}, {29820, 36526}, {30143, 64328}, {31231, 31659}, {31837, 41863}, {32141, 64112}, {36745, 49478}, {36845, 37407}, {38029, 43149}, {38053, 55108}, {42871, 63976}, {43175, 64001}, {47357, 64190}, {48482, 51706}, {49736, 64119}

X(64668) = midpoint of X(1) and X(8726)
X(64668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1385, 37611}, {1, 3576, 37531}, {1, 7987, 37569}, {1, 10383, 3295}, {1, 30389, 63391}, {1, 30503, 1482}, {40, 3576, 35202}, {1001, 12675, 7330}, {1385, 5045, 3}, {1385, 11249, 3576}, {3295, 9940, 3359}, {3622, 18444, 63986}, {5563, 24926, 37571}, {5563, 36946, 18398}, {10202, 16202, 40}, {10246, 16203, 24299}, {10246, 37615, 1}, {10267, 13373, 57}, {10268, 10980, 37532}, {10389, 37526, 11248}, {11496, 58567, 7171}, {15931, 50190, 12704}, {16203, 24299, 3576}, {37612, 37621, 165}, {37622, 40296, 40}, {37624, 61146, 1}, {37700, 38028, 8583}, {42819, 58567, 11496}

X(64669) = X(1)X(4)∩X(5)X(200)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c + 2*a^4*b*c + 4*a^3*b^2*c + 4*a^2*b^3*c - 2*a*b^4*c - 6*b^5*c - a^4*c^2 + 4*a^3*b*c^2 - 6*a^2*b^2*c^2 + 4*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 4*a^2*b*c^3 + 4*a*b^2*c^3 + 12*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 6*b*c^5 + c^6) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64669) lies on these lines: {1, 4}, {2, 6769}, {3, 10582}, {5, 200}, {10, 5804}, {20, 4666}, {40, 1001}, {42, 36694}, {57, 11496}, {84, 354}, {282, 1855}, {381, 5534}, {516, 8726}, {517, 11108}, {546, 18528}, {551, 37427}, {553, 64190}, {602, 60846}, {936, 2886}, {942, 3358}, {960, 7982}, {962, 30503}, {1012, 3333}, {1071, 5572}, {1103, 19372}, {1125, 6282}, {1389, 4866}, {1467, 4295}, {1482, 4853}, {1512, 51784}, {1621, 10268}, {1697, 7686}, {1709, 18398}, {1953, 7079}, {1998, 6828}, {2057, 30852}, {2093, 31870}, {2095, 54290}, {2951, 59386}, {2999, 37529}, {3057, 3577}, {3062, 64358}, {3072, 62875}, {3073, 62812}, {3085, 7682}, {3090, 8580}, {3091, 3870}, {3146, 29817}, {3174, 38150}, {3243, 14872}, {3295, 5806}, {3296, 12246}, {3304, 18237}, {3306, 10270}, {3338, 52027}, {3340, 45776}, {3361, 6906}, {3428, 5436}, {3560, 62824}, {3576, 37426}, {3601, 22753}, {3616, 37108}, {3632, 64335}, {3646, 64107}, {3742, 37526}, {3811, 3817}, {3832, 3957}, {3872, 5734}, {3874, 54370}, {3935, 5068}, {4208, 19861}, {4294, 10383}, {4301, 54318}, {4314, 50701}, {4321, 20330}, {4326, 5805}, {4328, 41010}, {4423, 7957}, {4512, 5709}, {4654, 64119}, {4847, 6846}, {4882, 5818}, {4915, 12654}, {5045, 63430}, {5129, 19860}, {5173, 10396}, {5219, 7681}, {5231, 6824}, {5234, 6920}, {5259, 41338}, {5272, 21554}, {5437, 10310}, {5439, 37560}, {5506, 11531}, {5528, 38152}, {5531, 59391}, {5587, 6765}, {5706, 7290}, {5707, 62842}, {5720, 9955}, {5732, 25557}, {5758, 40998}, {5768, 6744}, {5777, 41863}, {5842, 41864}, {5884, 7995}, {5886, 8583}, {5901, 37424}, {5902, 54156}, {6001, 11518}, {6223, 11038}, {6253, 12858}, {6326, 38038}, {6684, 7994}, {6745, 6964}, {6837, 26015}, {6847, 11019}, {6848, 13405}, {6864, 63146}, {6886, 25006}, {6891, 31249}, {6912, 62874}, {6913, 57279}, {6935, 64124}, {6936, 12120}, {6939, 21075}, {7171, 13373}, {7308, 63976}, {7330, 62823}, {7395, 40910}, {7671, 9960}, {7680, 9581}, {7956, 11374}, {7971, 64320}, {7992, 24644}, {8167, 58637}, {9624, 28628}, {9812, 10884}, {9856, 15934}, {9940, 10860}, {9947, 10222}, {10085, 50190}, {10384, 12710}, {10389, 11500}, {10580, 37434}, {10857, 31730}, {10980, 63399}, {11235, 38021}, {11248, 64112}, {11281, 61275}, {11529, 12672}, {12005, 30304}, {12526, 24474}, {12528, 62861}, {12565, 12699}, {12629, 12635}, {12675, 44841}, {12704, 31424}, {13462, 45977}, {15908, 25525}, {16204, 62826}, {17528, 51709}, {17718, 63966}, {18161, 41790}, {18493, 37533}, {22793, 41854}, {24389, 38037}, {30326, 63967}, {31162, 37428}, {37080, 52026}, {37275, 52015}, {37623, 38399}, {37700, 38034}, {37721, 64291}, {41012, 50399}, {54198, 64334}, {58565, 64129}, {58567, 58808}, {58660, 61660}, {64163, 64322}

X(64669) = midpoint of X(1) and X(8726)
X(64669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 946, 63992}, {1, 1479, 10382}, {1, 1699, 1490}, {946, 13464, 3485}, {946, 48482, 1699}, {946, 63999, 4}, {962, 54392, 30503}, {3742, 64074, 37526}, {4423, 7957, 61122}, {5886, 37531, 8583}, {6744, 21628, 5768}, {8227, 37569, 936}, {9614, 11522, 946}, {10582, 12651, 3}, {11496, 13374, 57}, {12699, 18443, 12565}, {51715, 64077, 3576}

X(64670) = X(1)X(5)∩X(3)X(4666)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c - 2*a^4*b*c + 4*a^3*b^2*c + 6*a^2*b^3*c - 2*a*b^4*c - 4*b^5*c - a^4*c^2 + 4*a^3*b*c^2 - 6*a^2*b^2*c^2 + 4*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 6*a^2*b*c^3 + 4*a*b^2*c^3 + 8*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 4*b*c^5 + c^6) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64670) lies on these lines: {1, 5}, {3, 4666}, {4, 29817}, {57, 58561}, {140, 10582}, {200, 3628}, {354, 24467}, {548, 12651}, {549, 6769}, {601, 17450}, {1001, 26921}, {1279, 5707}, {1385, 64077}, {1389, 62835}, {1482, 31838}, {1490, 38034}, {1621, 37532}, {1656, 3870}, {1697, 61541}, {3090, 3957}, {3174, 38171}, {3306, 11849}, {3333, 6914}, {3560, 5045}, {3616, 6989}, {3622, 6908}, {3656, 34618}, {3742, 11248}, {3748, 11499}, {3753, 12000}, {3811, 11230}, {3812, 37622}, {3845, 63981}, {3850, 18528}, {3857, 18529}, {3889, 6920}, {3935, 5067}, {4326, 61509}, {4853, 61597}, {4883, 36742}, {5439, 10679}, {5528, 38173}, {5603, 6851}, {5709, 38316}, {5732, 38041}, {6261, 51709}, {6583, 12514}, {6765, 38042}, {6824, 10580}, {6861, 26015}, {6862, 11019}, {6865, 10595}, {6887, 36845}, {6917, 63999}, {6929, 21620}, {6930, 11037}, {6944, 10578}, {6959, 13405}, {7330, 44841}, {7402, 17019}, {7407, 17024}, {7489, 62874}, {7516, 40910}, {7743, 10393}, {8167, 58630}, {8580, 55856}, {8583, 50394}, {8726, 28174}, {10222, 54318}, {10246, 37411}, {10247, 16853}, {10267, 13374}, {10383, 10386}, {10388, 61535}, {10389, 32141}, {10525, 51706}, {11249, 51715}, {11491, 62862}, {11496, 13373}, {11518, 14988}, {12650, 50824}, {15570, 58631}, {17609, 22758}, {18443, 22791}, {18446, 18493}, {19861, 50726}, {22765, 62829}, {29820, 37529}, {31231, 61520}, {31835, 41863}, {37531, 38028}, {37611, 51700}, {37612, 64149}, {37621, 62856}, {40273, 41854}, {45931, 62834}, {55108, 64162}, {58560, 64118}

X(64670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5886, 37700}, {1, 9624, 45770}, {355, 5886, 7958}, {5901, 10943, 5886}, {11373, 61276, 5901}, {13374, 42819, 10267}

X(64671) = X(1)X(6)∩X(69)X(4666)

Barycentrics    a*(a^4 - 2*a^3*b + 2*a^2*b^2 - 2*a*b^3 + b^4 - 2*a^3*c - 6*a^2*b*c - 2*a*b^2*c - 2*b^3*c + 2*a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 + c^4) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64671) lies on these lines: {1, 6}, {57, 58562}, {69, 4666}, {105, 54385}, {141, 10582}, {193, 29817}, {200, 3589}, {354, 7289}, {612, 37650}, {614, 4648}, {1038, 1471}, {1040, 2293}, {1253, 17469}, {1490, 38035}, {1721, 17301}, {2191, 3945}, {3174, 38186}, {3333, 36740}, {3361, 4265}, {3618, 3870}, {3666, 21002}, {3811, 38049}, {3827, 11518}, {3920, 37681}, {3957, 51171}, {4326, 51150}, {4344, 5262}, {4853, 51147}, {4915, 49679}, {5045, 37492}, {5085, 6769}, {5268, 17337}, {5272, 17245}, {5528, 38188}, {5534, 14561}, {5732, 38046}, {5800, 63999}, {6326, 38050}, {6765, 38047}, {8167, 58653}, {8580, 47355}, {9623, 49681}, {10383, 10387}, {10389, 12329}, {11025, 39273}, {12651, 44882}, {17024, 62997}, {18528, 19130}, {20978, 29819}, {21059, 62834}, {28194, 50294}, {37531, 38029}, {37700, 38040}, {49684, 54318}, {51192, 54392}, {53023, 63981}

X(64671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16667, 8271}, {1386, 45728, 16475}, {3945, 7191, 2191}, {3957, 51171, 56179}

X(64672) = X(1)X(7)∩X(9)X(354)

Barycentrics    a*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4 - 4*a^3*c + 8*a^2*b*c + 4*a*b^2*c - 8*b^3*c + 6*a^2*c^2 + 4*a*b*c^2 + 14*b^2*c^2 - 4*a*c^3 - 8*b*c^3 + c^4) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64672) lies on these lines: {1, 7}, {9, 354}, {55, 60955}, {57, 58563}, {142, 200}, {144, 4666}, {165, 2346}, {480, 5437}, {518, 11518}, {614, 14930}, {954, 3333}, {1001, 62824}, {1223, 27475}, {1445, 10980}, {1490, 38036}, {1699, 41857}, {3059, 3243}, {3062, 7671}, {3174, 6173}, {3296, 5759}, {3304, 38316}, {3338, 21153}, {3731, 21346}, {3811, 38054}, {3870, 62778}, {3874, 5223}, {4512, 60990}, {4860, 15837}, {4882, 40333}, {5045, 7330}, {5049, 63430}, {5231, 41573}, {5534, 38107}, {5558, 52653}, {5572, 16112}, {5809, 6744}, {6067, 25525}, {6326, 38055}, {6600, 64112}, {6765, 38052}, {6769, 21151}, {7673, 30337}, {7993, 14151}, {7994, 43151}, {8090, 8389}, {8167, 58678}, {8232, 11019}, {8257, 58607}, {8388, 8423}, {8543, 30343}, {8545, 11025}, {8580, 60996}, {8583, 38053}, {8732, 13405}, {9623, 34784}, {10177, 60965}, {10383, 60945}, {10388, 61022}, {10389, 11495}, {10398, 20116}, {10404, 52835}, {10865, 30318}, {11372, 12675}, {12669, 18219}, {13407, 38150}, {14100, 60953}, {15298, 18398}, {15299, 50190}, {15587, 42871}, {15888, 38200}, {16133, 24644}, {17718, 20195}, {20059, 29817}, {20330, 63992}, {21453, 50561}, {24389, 31146}, {25722, 62863}, {30628, 62815}, {31231, 59476}, {36973, 58608}, {37531, 38030}, {37700, 38041}, {38122, 63282}, {38399, 60974}, {41228, 42015}, {41861, 64197}, {47375, 60985}, {58635, 61660}, {59385, 63981}, {60919, 60982}, {60949, 62858}, {60964, 61033}, {60967, 63973}

X(64672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7, 4326}, {1, 5542, 4321}, {1, 7271, 2293}, {1, 7274, 4319}, {1, 59372, 5732}, {7, 4326, 30353}, {9, 10390, 354}, {2346, 60938, 165}, {5542, 60895, 59372}, {8545, 11025, 30330}, {13405, 15841, 8732}, {30330, 30350, 11025}, {30356, 30357, 1721}, {44841, 60937, 5572}, {59372, 63974, 7}

X(64673) = X(1)X(2)∩X(9)X(65)

Barycentrics    a*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - 2*a*b*c - 5*b^2*c - a*c^2 - 5*b*c^2 + c^3) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64673) lies on these lines: {1, 2}, {3, 38399}, {4, 12565}, {5, 63992}, {7, 12527}, {9, 65}, {12, 25525}, {20, 11024}, {21, 165}, {34, 281}, {35, 37248}, {37, 728}, {40, 405}, {46, 5251}, {55, 1706}, {56, 5437}, {57, 958}, {63, 3339}, {72, 11529}, {77, 31994}, {80, 41859}, {85, 269}, {86, 16284}, {100, 62829}, {140, 37611}, {142, 388}, {210, 11523}, {221, 55432}, {223, 37558}, {226, 2551}, {241, 7273}, {326, 28653}, {329, 3671}, {348, 62793}, {354, 6762}, {355, 8728}, {377, 5691}, {392, 3646}, {404, 7987}, {442, 1490}, {443, 515}, {452, 516}, {474, 3576}, {517, 11108}, {518, 11518}, {528, 41864}, {587, 55425}, {846, 25906}, {891, 25926}, {894, 27288}, {937, 43531}, {942, 9708}, {944, 17582}, {946, 5084}, {950, 2550}, {956, 3333}, {960, 3340}, {962, 5129}, {968, 4642}, {986, 62818}, {988, 24174}, {993, 15803}, {1001, 1697}, {1005, 12511}, {1006, 10268}, {1010, 17194}, {1012, 37560}, {1104, 5269}, {1203, 10601}, {1213, 3553}, {1320, 45830}, {1329, 5219}, {1376, 3601}, {1385, 16408}, {1420, 25524}, {1441, 34059}, {1453, 5711}, {1482, 16853}, {1512, 6889}, {1519, 6898}, {1621, 53053}, {1656, 61146}, {1699, 2478}, {1721, 26117}, {1742, 50408}, {1743, 54421}, {1750, 5177}, {1754, 16346}, {1757, 25903}, {1764, 19283}, {1788, 5745}, {1829, 7719}, {1837, 3925}, {1864, 18251}, {1891, 25993}, {2093, 3754}, {2099, 15829}, {2136, 3303}, {2263, 5749}, {2292, 3731}, {2295, 16970}, {2324, 5257}, {2345, 51972}, {2360, 17581}, {2476, 7989}, {2646, 4413}, {2647, 24570}, {2886, 9581}, {2951, 3146}, {2975, 3306}, {3036, 37736}, {3057, 4423}, {3062, 9961}, {3090, 63986}, {3091, 64150}, {3142, 10887}, {3158, 4731}, {3174, 12625}, {3243, 40659}, {3247, 3694}, {3295, 63137}, {3305, 3869}, {3338, 5258}, {3359, 3560}, {3421, 21620}, {3428, 16293}, {3436, 5249}, {3452, 3485}, {3486, 10383}, {3487, 21075}, {3488, 63146}, {3554, 17398}, {3577, 14110}, {3579, 16418}, {3649, 28609}, {3654, 50202}, {3677, 17054}, {3678, 12559}, {3680, 5919}, {3681, 4866}, {3683, 3922}, {3715, 3962}, {3729, 56311}, {3739, 5793}, {3740, 12635}, {3742, 12513}, {3748, 51781}, {3816, 50443}, {3817, 6919}, {3820, 11374}, {3824, 9654}, {3826, 5727}, {3833, 8666}, {3848, 11260}, {3868, 5223}, {3873, 63135}, {3876, 30393}, {3877, 11531}, {3880, 37556}, {3885, 30337}, {3889, 30350}, {3897, 17531}, {3899, 5506}, {3911, 30478}, {3913, 10389}, {3915, 60846}, {3918, 5248}, {3927, 31794}, {3928, 5221}, {3929, 5302}, {3930, 7323}, {3931, 25091}, {3951, 60969}, {3968, 8715}, {3983, 44840}, {3984, 34195}, {4002, 5687}, {4015, 62860}, {4026, 54295}, {4063, 25901}, {4160, 25900}, {4183, 11471}, {4187, 7680}, {4188, 58221}, {4189, 16192}, {4193, 7988}, {4197, 37714}, {4204, 58889}, {4208, 10884}, {4225, 61124}, {4293, 12436}, {4295, 12572}, {4297, 6904}, {4298, 9776}, {4312, 64002}, {4314, 17784}, {4328, 4357}, {4424, 54287}, {4640, 5128}, {4646, 37553}, {4652, 53056}, {4761, 26017}, {4855, 53054}, {4859, 23536}, {4968, 20905}, {4972, 25017}, {4999, 31231}, {5047, 5250}, {5082, 63999}, {5119, 5259}, {5141, 61264}, {5218, 63990}, {5226, 8165}, {5247, 62812}, {5252, 20195}, {5253, 13462}, {5255, 62875}, {5266, 16485}, {5283, 9593}, {5284, 9819}, {5288, 51816}, {5296, 42289}, {5315, 63128}, {5316, 64160}, {5330, 16189}, {5342, 11109}, {5433, 31190}, {5450, 21164}, {5528, 38202}, {5531, 59415}, {5534, 5790}, {5584, 13615}, {5603, 17559}, {5657, 6769}, {5686, 18221}, {5690, 50205}, {5697, 25542}, {5698, 60972}, {5706, 16416}, {5710, 7290}, {5716, 64174}, {5720, 9956}, {5722, 31419}, {5731, 17580}, {5785, 18412}, {5805, 31799}, {5815, 11036}, {5818, 18446}, {5835, 17279}, {5837, 6666}, {5880, 9579}, {5881, 17529}, {5883, 62858}, {5886, 17527}, {5901, 51559}, {5902, 41229}, {6173, 10404}, {6175, 16143}, {6261, 6856}, {6264, 34123}, {6282, 6684}, {6284, 63643}, {6326, 20400}, {6675, 26446}, {6690, 37828}, {6692, 7288}, {6708, 19372}, {6862, 55302}, {6872, 64005}, {6906, 10270}, {6912, 63985}, {6913, 12705}, {6939, 63989}, {7171, 18761}, {7174, 25892}, {7190, 32003}, {7271, 32086}, {7274, 32098}, {7330, 34339}, {7483, 31423}, {7672, 60958}, {7675, 40333}, {7688, 37284}, {7705, 30315}, {7713, 62972}, {7962, 8167}, {7994, 43174}, {7995, 54370}, {8236, 12632}, {9578, 25466}, {9612, 12609}, {9620, 16589}, {9624, 17575}, {9709, 24929}, {9710, 37723}, {9711, 11281}, {9778, 11106}, {9800, 63973}, {9940, 63430}, {9957, 40587}, {10107, 15254}, {10164, 26062}, {10165, 17567}, {10167, 10864}, {10172, 40257}, {10179, 10912}, {10222, 16855}, {10246, 16863}, {10267, 50204}, {10365, 20262}, {10371, 17296}, {10384, 58608}, {10396, 42012}, {10434, 13738}, {10441, 19282}, {10476, 19518}, {10543, 34701}, {10563, 27819}, {10588, 58463}, {10827, 25962}, {10860, 31787}, {10888, 50037}, {10892, 37225}, {10902, 37249}, {10914, 25893}, {10980, 62874}, {11111, 31730}, {11113, 41869}, {11221, 18673}, {11224, 17534}, {11344, 59320}, {11362, 17552}, {11375, 30827}, {11512, 37617}, {11522, 41012}, {11525, 12260}, {11681, 31266}, {12053, 26105}, {12114, 37526}, {12512, 17576}, {12563, 21060}, {12652, 17697}, {12702, 16857}, {12737, 38763}, {13151, 18518}, {13161, 23681}, {13384, 59691}, {13624, 16417}, {13745, 52524}, {14005, 54356}, {14077, 25925}, {14837, 58339}, {15071, 64197}, {15178, 35272}, {15832, 59215}, {15852, 37059}, {15931, 37282}, {15934, 34790}, {15950, 24954}, {16200, 16854}, {16232, 31438}, {16295, 39578}, {16343, 63982}, {16344, 37530}, {16347, 62320}, {16348, 37537}, {16370, 35242}, {16456, 50317}, {16466, 17825}, {16469, 57280}, {16483, 59777}, {16601, 59216}, {16608, 17306}, {16673, 59733}, {16844, 37529}, {16859, 63468}, {16862, 17614}, {16865, 35258}, {17151, 24547}, {17164, 56082}, {17274, 32007}, {17303, 21933}, {17355, 56937}, {17502, 17573}, {17528, 18480}, {17532, 18492}, {17535, 30392}, {17554, 59417}, {17571, 31663}, {17590, 63143}, {17594, 24440}, {17606, 31245}, {17612, 58567}, {17619, 54447}, {17698, 25968}, {17718, 21031}, {17861, 20880}, {18357, 18528}, {18529, 50741}, {18992, 31473}, {19003, 63072}, {19533, 20368}, {19885, 19890}, {19907, 55861}, {20060, 27186}, {20070, 52653}, {20196, 25681}, {21153, 59340}, {21921, 40131}, {22136, 39523}, {22758, 37534}, {22937, 59318}, {24291, 59255}, {24309, 28029}, {24554, 54315}, {24556, 28619}, {24557, 64377}, {24914, 24953}, {24984, 36985}, {25009, 29066}, {25019, 37314}, {25067, 37548}, {25099, 37598}, {25243, 64071}, {25440, 30282}, {25568, 63274}, {25909, 30675}, {25924, 29350}, {25974, 49516}, {26546, 47724}, {26638, 64072}, {26669, 62831}, {26690, 52705}, {26695, 48295}, {26921, 61541}, {27065, 64047}, {27410, 57810}, {28164, 37435}, {28383, 37619}, {30326, 31803}, {30331, 56936}, {30674, 41340}, {31359, 32008}, {31445, 36279}, {31453, 51841}, {32024, 50127}, {34043, 55400}, {34501, 37724}, {34711, 38025}, {34791, 44841}, {35202, 37309}, {37229, 44425}, {37308, 59331}, {37436, 38204}, {37614, 44307}, {37698, 50432}, {37700, 38042}, {37721, 44256}, {38074, 50727}, {40149, 54396}, {43178, 51100}, {45081, 63644}, {46196, 54330}, {46917, 56176}, {46947, 61275}, {48897, 50169}, {49454, 58697}, {50394, 61510}, {50621, 63511}, {51090, 61009}, {52027, 59333}, {52706, 62215}, {54343, 55478}, {55285, 58329}, {55392, 63014}, {55859, 61148}, {55924, 62838}, {56182, 63157}, {56244, 59682}, {56987, 61086}, {57277, 63592}, {62832, 64149}, {62835, 64201}, {62856, 63142}, {64068, 64162}, {64319, 64333}

X(64673) = reflection of X(31435) in X(11108)
X(64673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 8583}, {1, 10, 200}, {1, 1698, 936}, {1, 1722, 2999}, {1, 3679, 6765}, {1, 4882, 3870}, {1, 4915, 145}, {1, 8580, 78}, {1, 9623, 4853}, {1, 11519, 3241}, {1, 12127, 3623}, {1, 23511, 1193}, {2, 5554, 24987}, {2, 19860, 1}, {2, 24541, 3624}, {2, 24982, 1698}, {4, 30503, 12565}, {8, 54392, 1}, {9, 65, 12526}, {10, 551, 59722}, {10, 1125, 3085}, {10, 6738, 8}, {10, 10198, 31434}, {10, 13405, 7080}, {10, 30143, 3811}, {10, 49168, 3679}, {10, 54318, 1}, {40, 405, 4512}, {46, 5251, 31424}, {55, 3698, 1706}, {57, 958, 62824}, {63, 5260, 5234}, {78, 9780, 8580}, {142, 5795, 388}, {145, 4666, 1}, {388, 1467, 4321}, {392, 16842, 3646}, {405, 3753, 40}, {612, 3924, 1}, {614, 10459, 1}, {894, 27288, 30625}, {942, 9708, 57279}, {942, 57279, 62823}, {956, 5439, 3333}, {958, 3812, 57}, {962, 5129, 40998}, {988, 24174, 62695}, {997, 30147, 1}, {1001, 5836, 1697}, {1210, 19843, 5231}, {1329, 28628, 5219}, {1453, 5711, 62842}, {1621, 63130, 53053}, {1706, 5436, 55}, {1737, 19854, 5705}, {2099, 25917, 15829}, {2136, 38316, 3303}, {2551, 28629, 226}, {2646, 4413, 5438}, {2975, 3306, 3361}, {3083, 3084, 17019}, {3086, 9843, 31249}, {3339, 5234, 63}, {3340, 7308, 960}, {3436, 5249, 5290}, {3486, 26040, 57284}, {3577, 61122, 14110}, {3616, 3872, 1}, {3616, 7080, 13405}, {3617, 3870, 4882}, {3617, 20008, 8}, {3622, 36846, 1}, {3624, 31434, 10198}, {3634, 30147, 997}, {3646, 7982, 392}, {3671, 18250, 329}, {3683, 3922, 37567}, {3754, 12514, 2093}, {3811, 30143, 1}, {3811, 54318, 30143}, {3897, 17531, 35262}, {3897, 35262, 30389}, {3913, 51715, 10389}, {3918, 5248, 54286}, {4853, 10582, 1}, {5248, 54286, 61763}, {5287, 17016, 1}, {5554, 24987, 3679}, {5691, 38052, 377}, {5790, 37615, 5534}, {5880, 57288, 9579}, {5886, 17527, 25522}, {5902, 41229, 54422}, {6913, 31788, 12705}, {9578, 41867, 25466}, {10884, 59387, 63981}, {11109, 64211, 39585}, {11530, 38316, 2136}, {12520, 19925, 1750}, {15829, 51780, 25917}, {15934, 34790, 41863}, {18391, 19855, 10}, {18761, 40296, 7171}, {19890, 19900, 19885}, {21717, 27714, 10}, {24541, 25011, 2}, {29820, 59310, 1}, {31445, 36279, 54290}, {34195, 63961, 3984}, {54418, 59305, 1}

X(64674) = X(1)X(6)∩X(2)X(3174)

Barycentrics    a*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4 - 4*a^3*c + 8*a*b^2*c - 4*b^3*c + 6*a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 - 4*a*c^3 - 4*b*c^3 + c^4) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64674) lies on these lines: {1, 6}, {2, 3174}, {7, 4666}, {57, 58564}, {63, 11025}, {105, 380}, {142, 497}, {144, 29817}, {165, 60985}, {200, 6666}, {354, 60990}, {390, 54392}, {480, 3748}, {516, 8726}, {551, 63973}, {610, 52015}, {614, 4343}, {946, 5732}, {1445, 1621}, {1467, 12560}, {1490, 38037}, {1699, 60991}, {1750, 42356}, {2346, 42470}, {2550, 63999}, {2886, 20195}, {2951, 6173}, {3059, 4423}, {3305, 34784}, {3306, 7676}, {3485, 4321}, {3616, 7675}, {3742, 10857}, {3811, 38059}, {3870, 18230}, {3873, 60949}, {3890, 11526}, {4319, 59217}, {4335, 29820}, {4428, 7994}, {4512, 60974}, {5284, 30628}, {5528, 38205}, {5534, 38108}, {6282, 52769}, {6326, 38060}, {6600, 10389}, {6601, 64162}, {6765, 38057}, {6769, 21153}, {7308, 40659}, {7674, 8236}, {7677, 62829}, {7678, 31266}, {8167, 58634}, {8257, 10388}, {10580, 41573}, {10980, 60968}, {11235, 38093}, {11281, 16143}, {12514, 20116}, {12651, 63413}, {28070, 42449}, {28194, 30503}, {30331, 54318}, {30353, 60980}, {34919, 60961}, {35258, 60948}, {37531, 38031}, {37700, 38043}, {38036, 49177}, {38054, 43178}, {38150, 48482}, {40998, 61010}, {59389, 63981}, {60938, 64149}, {60979, 64262}, {61005, 61033}

X(64674) = reflection of X(31435) in X(1001)
X(64674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1001, 5572, 9}, {1001, 51715, 38316}, {4326, 10582, 142}, {5284, 30628, 60958}, {61005, 61033, 62823}

X(64675) = X(1)X(2)∩X(3)X(3742)

Barycentrics    a*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - 6*a*b*c - 3*b^2*c - a*c^2 - 3*b*c^2 + c^3) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64675) lies on these lines: {1, 2}, {3, 3742}, {4, 38053}, {9, 3874}, {11, 10393}, {21, 3338}, {35, 3306}, {36, 37285}, {38, 54287}, {40, 5883}, {46, 1621}, {55, 5439}, {56, 37284}, {57, 5248}, {63, 5259}, {72, 4423}, {86, 3673}, {142, 63999}, {169, 16503}, {210, 16842}, {224, 11680}, {354, 405}, {377, 19852}, {404, 59337}, {474, 37080}, {496, 28628}, {497, 12609}, {515, 6849}, {516, 8726}, {518, 11108}, {631, 37569}, {758, 11518}, {942, 1001}, {944, 6896}, {946, 6851}, {956, 17609}, {958, 5045}, {960, 12559}, {968, 3670}, {982, 62871}, {986, 16484}, {988, 4653}, {993, 3333}, {1006, 12704}, {1046, 15485}, {1058, 28629}, {1062, 17045}, {1071, 10177}, {1158, 10202}, {1279, 5711}, {1385, 5806}, {1446, 4341}, {1467, 3671}, {1468, 17450}, {1479, 5249}, {1482, 10179}, {1490, 3817}, {1697, 3754}, {1699, 10884}, {1706, 25439}, {1724, 62819}, {1750, 12571}, {1844, 55472}, {2093, 33815}, {2191, 43531}, {2257, 25081}, {2478, 13407}, {2802, 37556}, {2975, 51816}, {3090, 17857}, {3174, 38204}, {3189, 17582}, {3247, 25078}, {3295, 3812}, {3303, 3753}, {3305, 5904}, {3336, 35258}, {3337, 4652}, {3339, 60948}, {3340, 3884}, {3361, 5267}, {3475, 5084}, {3485, 34489}, {3487, 21616}, {3488, 17647}, {3560, 13373}, {3576, 3651}, {3579, 4428}, {3612, 5253}, {3646, 10176}, {3647, 3928}, {3678, 7308}, {3681, 17536}, {3697, 41711}, {3723, 4515}, {3740, 16853}, {3746, 62856}, {3748, 5687}, {3750, 24174}, {3816, 11374}, {3822, 9581}, {3824, 18527}, {3825, 5219}, {3833, 8715}, {3838, 9669}, {3841, 41867}, {3848, 16408}, {3868, 5284}, {3871, 62862}, {3873, 5047}, {3878, 11529}, {3881, 44841}, {3886, 28612}, {3889, 5260}, {3890, 25415}, {3892, 6762}, {3894, 3951}, {3898, 7982}, {3916, 4860}, {3918, 63137}, {3919, 7991}, {3927, 15254}, {3931, 17054}, {3991, 16777}, {4038, 16478}, {4187, 17718}, {4256, 11512}, {4294, 9776}, {4301, 30503}, {4314, 10383}, {4421, 63271}, {4430, 17570}, {4640, 5708}, {4658, 16475}, {4662, 15570}, {4888, 63366}, {4966, 5814}, {4999, 17051}, {5015, 17234}, {5044, 8167}, {5049, 12513}, {5129, 11038}, {5218, 58405}, {5234, 30350}, {5250, 5902}, {5251, 50190}, {5258, 62832}, {5266, 37674}, {5290, 61013}, {5302, 16857}, {5324, 52018}, {5358, 60721}, {5422, 56535}, {5425, 11682}, {5437, 25440}, {5493, 43166}, {5528, 38207}, {5531, 59419}, {5534, 10175}, {5542, 12572}, {5586, 50836}, {5603, 6899}, {5692, 11520}, {5719, 25681}, {5722, 25466}, {5730, 44840}, {5732, 38054}, {5749, 59728}, {5750, 21096}, {5768, 12617}, {5787, 5886}, {5794, 12433}, {5836, 6767}, {5837, 17706}, {5880, 15171}, {5901, 37356}, {6051, 37549}, {6147, 24703}, {6173, 41869}, {6198, 17917}, {6259, 38030}, {6326, 32557}, {6361, 47357}, {6583, 26921}, {6702, 37736}, {6706, 28639}, {6769, 10164}, {6845, 9624}, {6912, 10085}, {6913, 12675}, {6986, 41338}, {6990, 8227}, {7290, 62805}, {7330, 12005}, {7483, 17728}, {7741, 31266}, {7987, 37105}, {8236, 11024}, {8728, 64443}, {9345, 62847}, {9708, 34791}, {9799, 38037}, {9940, 11496}, {10013, 57748}, {10165, 37531}, {10246, 37837}, {10396, 62852}, {10404, 11113}, {10857, 12512}, {10980, 31424}, {11227, 64074}, {11230, 37700}, {11375, 37359}, {11415, 11551}, {11522, 64150}, {12631, 40587}, {12699, 49736}, {12738, 45310}, {13624, 40726}, {15299, 62864}, {15624, 16414}, {15829, 62822}, {16132, 38021}, {16137, 34647}, {16193, 57278}, {16203, 59366}, {16370, 32636}, {16418, 58560}, {16485, 63292}, {16589, 16973}, {16783, 40131}, {16845, 24477}, {16854, 61686}, {16855, 58451}, {16858, 62827}, {17063, 37573}, {17188, 17584}, {17321, 53596}, {17527, 63282}, {17534, 63961}, {17559, 25568}, {17594, 24046}, {17681, 27475}, {18219, 63973}, {18240, 51506}, {18444, 63988}, {18483, 41854}, {21346, 56839}, {22936, 24467}, {23681, 36250}, {24159, 24210}, {24161, 24217}, {24178, 48837}, {24443, 62849}, {24929, 25524}, {25086, 37658}, {25430, 56137}, {25525, 25639}, {25557, 57282}, {26127, 31053}, {26725, 37720}, {27003, 58887}, {27186, 52367}, {28609, 41870}, {28611, 63131}, {30852, 37731}, {31231, 58404}, {31259, 64153}, {31445, 50192}, {31926, 46883}, {32558, 39778}, {33124, 52258}, {34036, 37523}, {34790, 42871}, {34862, 58615}, {35202, 63141}, {35262, 37571}, {36946, 63135}, {37492, 58581}, {37554, 49480}, {37559, 62834}, {37607, 37817}, {37622, 63132}, {37869, 45126}, {48482, 55108}, {48897, 50226}, {50594, 63511}, {51111, 61762}, {54408, 54430}, {54422, 61024}, {59316, 61155}, {60895, 64004}, {61146, 61276}, {61302, 62216}

X(64675) = midpoint of X(11518) and X(31435)
X(64675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 3811}, {1, 1125, 997}, {1, 1698, 3870}, {1, 2999, 59301}, {1, 3624, 78}, {1, 4853, 3635}, {1, 5272, 386}, {1, 6048, 3979}, {1, 8583, 22836}, {1, 9623, 3244}, {1, 10582, 1125}, {1, 12629, 51071}, {1, 17022, 30142}, {1, 25055, 19861}, {1, 25502, 5293}, {1, 26102, 975}, {1, 54392, 54318}, {4, 38053, 51706}, {8, 29817, 1}, {21, 64149, 3338}, {354, 405, 62858}, {404, 62870, 59337}, {551, 30143, 1}, {942, 1001, 12514}, {946, 18443, 12520}, {960, 15934, 12559}, {1125, 6744, 10}, {1125, 10916, 2}, {1125, 11019, 26363}, {1125, 22836, 8583}, {3086, 3616, 1125}, {3295, 3812, 54286}, {3305, 62861, 5904}, {3333, 5436, 993}, {3475, 5084, 21077}, {3487, 26105, 21616}, {3636, 30147, 1}, {3646, 11523, 10176}, {3720, 28082, 1}, {3742, 51715, 3}, {3812, 42819, 3295}, {3848, 56176, 16408}, {3873, 5047, 41229}, {4666, 54392, 1}, {5248, 58565, 57}, {5251, 50190, 62874}, {5259, 18398, 63}, {5262, 29814, 1}, {5886, 37615, 6261}, {5904, 25542, 3305}, {7308, 41863, 3678}, {8583, 11519, 12447}, {8583, 22836, 997}, {9843, 13405, 26364}, {9940, 11496, 64129}, {10580, 19843, 49627}, {10857, 12651, 12512}, {22837, 51103, 1}, {44841, 57279, 3881}

X(64676) = X(1)X(5)∩X(100)X(4666)

Barycentrics    a*(a^5 - 3*a^4*b + 2*a^3*b^2 + 2*a^2*b^3 - 3*a*b^4 + b^5 - 3*a^4*c + 5*a^3*b*c - 4*a^2*b^2*c + 7*a*b^3*c - 5*b^4*c + 2*a^3*c^2 - 4*a^2*b*c^2 - 8*a*b^2*c^2 + 4*b^3*c^2 + 2*a^2*c^3 + 7*a*b*c^3 + 4*b^2*c^3 - 3*a*c^4 - 5*b*c^4 + c^5) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64676) lies on these lines: {1, 5}, {57, 18240}, {100, 4666}, {149, 5249}, {200, 6667}, {354, 1768}, {1320, 54392}, {1490, 38038}, {1697, 12736}, {1706, 13278}, {2800, 11518}, {2802, 37556}, {3035, 10582}, {3058, 31657}, {3174, 38205}, {3243, 46685}, {3256, 17626}, {3295, 58587}, {3303, 5541}, {3333, 10058}, {3338, 63281}, {3340, 15558}, {3475, 21635}, {3742, 13205}, {3811, 32557}, {3870, 31272}, {4654, 34789}, {4861, 5316}, {5049, 12773}, {5083, 11020}, {5290, 12764}, {5732, 9580}, {5840, 41864}, {5919, 12653}, {6765, 34122}, {6767, 6797}, {6769, 21154}, {7308, 14740}, {8167, 58663}, {8236, 20095}, {9623, 25416}, {9809, 11038}, {10222, 61660}, {11496, 58595}, {11529, 12758}, {12053, 18444}, {12532, 62861}, {12651, 38759}, {12705, 15528}, {15015, 37080}, {15570, 58683}, {17642, 31658}, {17660, 51768}, {18254, 41863}, {18443, 64138}, {22560, 51715}, {37531, 38032}, {42819, 58611}, {42871, 61718}, {54318, 64137}, {59390, 63981}

X(64676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {{1, 11, 37736}, {1, 16173, 6326}, {11, 17718, 15017}, {1387, 37726, 16173}, {5083, 53055, 64372}, {44841, 64372, 5083}

X(64677) = X(1)X(5)∩X(200)X(6668)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c - 3*a^4*b*c + 5*a^3*b^2*c + 7*a^2*b^3*c - 3*a*b^4*c - 4*b^5*c - a^4*c^2 + 5*a^3*b*c^2 + 4*a^2*b^2*c^2 + 5*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 7*a^2*b*c^3 + 5*a*b^2*c^3 + 8*b^3*c^3 - a^2*c^4 - 3*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 4*b*c^5 + c^6) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64677) lies on these lines: {1, 5}, {57, 58566}, {165, 63272}, {200, 6668}, {354, 5259}, {614, 31880}, {758, 11518}, {1490, 38039}, {2975, 4666}, {3174, 38206}, {3340, 61122}, {3811, 38062}, {4999, 10582}, {5221, 38031}, {5528, 38209}, {5732, 38056}, {5842, 41864}, {6765, 38058}, {6769, 21155}, {10389, 11491}, {10396, 44841}, {15829, 54392}, {20060, 29817}, {25542, 61663}, {31262, 61648}, {37080, 40262}, {37531, 38033}, {41012, 63274}

X(64677) = {X(26470),X(37737)}-harmonic conjugate of X(37701)

X(64678) = X(1)X(19)∩X(57)X(1486)

Barycentrics    a*(a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3 - a^3*b^4 + 3*a^2*b^5 - 3*a*b^6 + b^7 - 3*a^6*c - 2*a^5*b*c + 3*a^4*b^2*c - 4*a^3*b^3*c + 3*a^2*b^4*c + 6*a*b^5*c - 3*b^6*c + 3*a^5*c^2 + 3*a^4*b*c^2 - 6*a^3*b^2*c^2 - 6*a^2*b^3*c^2 + 3*a*b^4*c^2 + 3*b^5*c^2 - a^4*c^3 - 4*a^3*b*c^3 - 6*a^2*b^2*c^3 - 12*a*b^3*c^3 - b^4*c^3 - a^3*c^4 + 3*a^2*b*c^4 + 3*a*b^2*c^4 - b^3*c^4 + 3*a^2*c^5 + 6*a*b*c^5 + 3*b^2*c^5 - 3*a*c^6 - 3*b*c^6 + c^7) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64678) lies on these lines: {1, 19}, {57, 1486}, {142, 11677}, {200, 40530}, {516, 8726}, {1119, 34036}, {1467, 2263}, {3720, 4319}, {3827, 11518}, {4329, 4666}, {6769, 21160}, {8271, 59681}, {10582, 18589}, {18443, 55340}, {20061, 29817}, {23305, 41867}, {24388, 37382}

X(64678) = {X(51687),X(64543)}-harmonic conjugate of X(19)

X(64679) = X(1)X(7)∩X(3)X(200)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c - 14*a^4*b*c + 4*a^3*b^2*c + 12*a^2*b^3*c - 2*a*b^4*c + 2*b^5*c - a^4*c^2 + 4*a^3*b*c^2 - 6*a^2*b^2*c^2 + 4*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 12*a^2*b*c^3 + 4*a*b^2*c^3 - 4*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - b^2*c^4 - 2*a*c^5 + 2*b*c^5 + c^6) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64679) lies on these lines: {1, 7}, {2, 63981}, {3, 200}, {4, 10582}, {9, 8273}, {10, 10857}, {40, 3555}, {55, 9841}, {56, 10382}, {57, 58567}, {84, 4512}, {140, 18528}, {165, 6765}, {376, 6769}, {388, 10383}, {405, 1490}, {411, 3361}, {443, 515}, {518, 37551}, {572, 2297}, {573, 1208}, {610, 22654}, {936, 993}, {944, 4853}, {956, 9845}, {958, 58634}, {971, 31435}, {1071, 12526}, {1125, 1750}, {1385, 41854}, {1467, 3486}, {1621, 63984}, {1697, 9943}, {1699, 51706}, {1768, 16208}, {2999, 36698}, {3090, 18529}, {3146, 4666}, {3174, 5584}, {3243, 7957}, {3295, 10860}, {3303, 5918}, {3333, 7580}, {3339, 62852}, {3522, 3870}, {3523, 8580}, {3601, 63991}, {3624, 6886}, {3677, 15852}, {3744, 35658}, {3873, 63141}, {3874, 7991}, {3913, 10178}, {3935, 21734}, {3957, 50693}, {4847, 37108}, {5059, 29817}, {5231, 6908}, {5250, 7992}, {5269, 37501}, {5272, 7385}, {5290, 6836}, {5531, 38693}, {5587, 17529}, {5691, 6835}, {5720, 13624}, {6223, 40998}, {6245, 38399}, {6261, 11111}, {6796, 21164}, {6848, 31249}, {6912, 30389}, {6996, 17022}, {7070, 34046}, {7171, 10267}, {7411, 62874}, {7958, 59389}, {7994, 12512}, {9623, 17647}, {10085, 15931}, {10165, 17552}, {10268, 63399}, {10270, 11491}, {10304, 34646}, {10389, 64074}, {10430, 21628}, {10902, 49170}, {11019, 37421}, {11106, 19861}, {11112, 12650}, {11379, 16143}, {11495, 34791}, {11496, 58808}, {11500, 37526}, {11522, 41860}, {12514, 30304}, {12527, 37423}, {12612, 21620}, {14100, 51773}, {14872, 61122}, {16132, 57002}, {16408, 33574}, {16410, 52026}, {17554, 54445}, {18238, 64312}, {18443, 18481}, {19860, 56999}, {21153, 35202}, {25502, 36692}, {30282, 63983}, {31146, 37427}, {31787, 63137}, {31793, 41863}, {35445, 64128}, {36746, 62842}, {37198, 40910}, {37570, 62812}, {37736, 38759}, {53053, 63985}, {54422, 59340}, {61275, 63267}, {61763, 64129}

X(64679) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20, 12651}, {1, 2951, 962}, {1, 4292, 12560}, {1, 5732, 12565}, {1, 64005, 43166}, {3, 63430, 62824}, {40, 12675, 62823}, {944, 30503, 4853}, {1385, 41854, 63992}, {1490, 3576, 8583}, {3295, 31805, 10860}, {3576, 10864, 405}, {3600, 7675, 1}, {4297, 4298, 20}, {4319, 4322, 1}, {5234, 7987, 6986}, {5250, 11220, 7992}, {5731, 10884, 1}, {7987, 9851, 5234}, {8273, 12680, 9}, {10085, 15931, 31424}, {11500, 37526, 64112}, {35202, 41229, 21153}

X(64680) = X(1)X(21)∩X(200)X(6675)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c - 9*a^4*b*c + 7*a^3*b^2*c + 11*a^2*b^3*c - 5*a*b^4*c - 2*b^5*c - a^4*c^2 + 7*a^3*b*c^2 + 16*a^2*b^2*c^2 + 11*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 11*a^2*b*c^3 + 11*a*b^2*c^3 + 4*b^3*c^3 - a^2*c^4 - 5*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 2*b*c^5 + c^6) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64680) lies on these lines: {1, 21}, {57, 58568}, {200, 6675}, {442, 10582}, {1697, 8261}, {2475, 4666}, {3295, 58619}, {3333, 37286}, {3649, 4321}, {3870, 15674}, {3957, 15676}, {4298, 15680}, {4853, 12658}, {4857, 51706}, {5045, 37292}, {5542, 14450}, {6769, 21161}, {6904, 30143}, {7701, 12675}, {9614, 11263}, {11522, 16143}, {12651, 44238}, {13743, 63430}, {18528, 46028}, {25522, 63289}, {37282, 37571}, {52269, 63981}

X(64681) = X(1)X(6)∩X(75)X(4666)

Barycentrics    a*(a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c - 3*a^2*b*c - 5*a*b^2*c + b^3*c - 2*a^2*c^2 - 5*a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64681) lies on these lines: {1, 6}, {57, 58571}, {75, 4666}, {192, 29817}, {200, 4698}, {583, 52155}, {614, 2667}, {968, 4022}, {1742, 17392}, {1962, 21346}, {3672, 29814}, {3720, 4000}, {3739, 10582}, {3748, 34247}, {3870, 4687}, {3957, 27268}, {4068, 37555}, {4335, 4675}, {4343, 4648}, {4878, 17018}, {7308, 22271}, {8167, 58655}, {9623, 49475}, {10389, 15624}, {11518, 20718}, {13476, 44841}, {17278, 26102}, {21330, 62849}, {28194, 48855}, {37523, 42289}, {49470, 54392}, {49471, 54318}

X(64682) = X(1)X(39)∩X(200)X(6683)

Barycentrics    a*(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 2*a^3*b^2*c - 4*a^2*b^3*c + a^4*c^2 - 2*a^3*b*c^2 + 3*a^2*b^2*c^2 - 2*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 - 4*a^2*b*c^3 - 2*a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 + b^2*c^4) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64682) lies on these lines: {1, 39}, {76, 4666}, {194, 29817}, {200, 6683}, {2271, 18170}, {3742, 12338}, {3870, 7786}, {3934, 10582}, {6261, 22475}, {6769, 21163}, {7976, 54392}, {8167, 58656}, {15570, 58695}, {22682, 63981}, {22779, 51715}, {42819, 58622}

X(64683) = X(1)X(6)∩X(200)X(6687)

Barycentrics    a*(a^4 - 3*a^3*b + 4*a^2*b^2 - 3*a*b^3 + b^4 - 3*a^3*c - 3*a^2*b*c + 3*a*b^2*c - 3*b^3*c + 4*a^2*c^2 + 3*a*b*c^2 + 4*b^2*c^2 - 3*a*c^3 - 3*b*c^3 + c^4) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64683) lies on these lines: {1, 6}, {105, 2173}, {200, 6687}, {320, 4666}, {3834, 10582}, {4675, 29820}, {5053, 11716}, {9623, 49699}, {20072, 29817}, {28194, 30117}, {49700, 54318}, {49709, 54392}, {53534, 60353}

X(64684) = X(1)X(3)∩X(583)X(2324)

Barycentrics    a*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^5*c - 4*a^4*b*c - 2*a^3*b^2*c + 6*a^2*b^3*c + 4*a*b^4*c - 2*b^5*c - a^4*c^2 - 2*a^3*b*c^2 - 18*a^2*b^2*c^2 - 2*a*b^3*c^2 - b^4*c^2 + 4*a^3*c^3 + 6*a^2*b*c^3 - 2*a*b^2*c^3 + 4*b^3*c^3 - a^2*c^4 + 4*a*b*c^4 - b^2*c^4 - 2*a*c^5 - 2*b*c^5 + c^6) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64684) lies on these lines: {1, 3}, {79, 38036}, {200, 58405}, {583, 2324}, {936, 64153}, {1728, 17625}, {1750, 7681}, {3811, 64151}, {3870, 59675}, {4311, 50695}, {4321, 9612}, {4666, 11415}, {4857, 41860}, {5053, 54385}, {5084, 13407}, {5720, 61534}, {6835, 9613}, {6837, 44675}, {6854, 10106}, {9614, 10431}, {9623, 36977}, {10072, 63988}, {10582, 21616}, {17529, 64087}, {17567, 24477}, {17728, 17857}, {20076, 54392}, {37722, 50528}, {42884, 64132}

X(64684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {56, 354, 12704}, {56, 50196, 46}, {999, 34489, 1}, {1420, 18398, 61763}

X(64685) = X(1)X(51)∩X(200)X(6688)

Barycentrics    a^2*(2*a^2*b^2 - 2*b^4 - 3*a^2*b*c + 6*a*b^2*c - 3*b^3*c + 2*a^2*c^2 + 6*a*b*c^2 + 10*b^2*c^2 - 3*b*c^3 - 2*c^4) : :

See Keita Miyamoto and Peter Moses, euclid 6618.

X(64685) lies on these lines: {1, 51}, {57, 58574}, {200, 6688}, {1699, 64549}, {2390, 11518}, {2979, 4666}, {3819, 10582}, {3870, 11451}, {5534, 14845}, {9580, 64524}, {16487, 40952}, {26892, 30350}, {29817, 62187}

X(64686) = X(6)X(842)∩X(98)X(385)

Barycentrics    a^2 (a^4+b^4-a^2 c^2-b^2 c^2) (a^4-a^2 b^2-b^2 c^2+c^4) (a^4 b^4-2 a^2 b^6+b^8+a^4 b^2 c^2-a^2 b^4 c^2-b^6 c^2+a^4 c^4-a^2 b^2 c^4+3 b^4 c^4-2 a^2 c^6-b^2 c^6+c^8) : :
X(64686) = 3*X(98)-4*X(15630), 2*X(2679)-3*X(6785), 3*X(13137)-2*X(15630)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6620.

X(64686) lies on these lines: {4, 37841}, {6, 842}, {98, 385}, {265, 290}, {512, 10722}, {685, 1112}, {1976, 15107}, {2065, 51862}, {2679, 6785}, {2698, 12110}, {3060, 40820}, {3329, 61733}, {3972, 41330}, {5967, 11002}, {9301, 51869}, {11610, 35388}, {13558, 43754}, {14265, 53797}, {14984, 17932}, {20021, 37779}, {31670,52451}, {32540, 48673}, {36822, 38580}, {40428, 51440}, {51404, 52694}, {51820, 62187}

X(64686) = barycentric product of X(i) and X(j) for these (i,j): (43187, 45911), (43665, 60610), (45911, 43187), (60610, 43665)
X(64686) = trilinear product of X(i) and X(j) for these (i,j): (36036, 45911), (45911, 36036)

X(64687) = X(99)X(512)∩X(265)X(290)

Barycentrics    a^2 (a^2-b^2)(a^2-c^2)(a^4 b^4-2 a^2 b^6+b^8-a^4 b^2 c^2+a^2 b^4 c^2-3 b^6 c^2+a^4 c^4+a^2 b^2 c^4+5 b^4 c^4-2 a^2 c^6-3 b^2 c^6+c^8) : :
X(64687) = 3*X(99)-4*X(15631), X(805)-3*X(13170), 2*X(2679)-3*X(6787), 3*X(12833)-2*X(15631), 5*X(14061)-4*X(14113)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6620.

X(64687) lies on these lines: {76, 18321}, {99, 512}, {249, 1625}, {265, 290}, {511, 10723}, {526, 892}, {691, 10411}, {924, 31998}, {928, 17930}, {1078, 2698}, {1510, 4590}, {2679, 6787}, {2715, 52630}, {7752, 33330}, {7769, 57310}, {9517, 17932}, {10409, 14183}, {10410, 14184}, {14061, 14113}, {18440, 44969}, {20188, 33799}, {22999, 44361}, {23008, 44362}, {44042, 64133}

X(64687) = isotomic conjugate of the isogonal conjugate of X(60607)
X(64687) = barycentric product X(76)*X(60607)
X(64687) = trilinear product X(75)*X(60607)
X(64687) = pole of the line X(804)X(11616) with respect to Wallace hyperbola

X(64688) = X(2)X(3025)∩X(100)X(513)

Barycentrics    a (a-b) (a-c) (a^4 b^2-2 a^2 b^4+b^6-a^4 b c-a^3 b^2 c+3 a^2 b^3 c+a b^4 c-2 b^5 c+a^4 c^2-a^3 b c^2-a^2 b^2 c^2-a b^3 c^2-b^4 c^2+3 a^2 b c^3-a b^2 c^3+4 b^3 c^3-2 a^2 c^4+a b c^4-b^2 c^4-2 b c^5+c^6) : :
X(64688) = 3*X(100)-4*X(15632), 2*X(3259)-3*X(61729), 3*X(3873)-4*X(24201), 4*X(14115)-5*X(31272), 2*X(15632)-3*X(34151), 8*X(33646)-9*X(59377)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6620.

X(64688) lies on the incircle of the anticomplementary triangle and on these lines: {2, 3025}, {8, 53800}, {63, 34464}, {100, 513}, {145, 13756}, {265, 5080}, {517, 10724}, {518, 23152}, {519, 23153}, {758, 56691}, {953, 2975}, {956, 38586}, {1290, 3657}, {2222, 43355}, {3259, 11680}, {3738, 51562}, {3873, 24201}, {3909, 39185},{5176, 13532}, {5303, 38707}, {5375, 46389}, {5687, 38584}, {11681, 31841}, {14115, 31272}, {17483, 61696}, {17484, 60845}, {27529, 57313}, {31512, 38389}, {33646, 59377}, {40100, 52367}, {40263, 44982}, {53792, 56878}, {61185, 61637}

X(64688) = anticomplement of X(3025)
X(64688) = anticomplementary conjugate of the anticomplement of X(46649)
X(64688) = pole of the line X(2397)X(36804) with respect to Steiner circumellipse

X(64689) = X(3)X(64)∩X(343)X(1216)

Barycentrics    a^2 (a^2-b^2-c^2) (a^10 b^2-3 a^8 b^4+2 a^6 b^6+2 a^4 b^8-3 a^2 b^10+b^12+a^10 c^2-4 a^8 b^2 c^2+6 a^6 b^4 c^2-4 a^4 b^6 c^2+a^2 b^8 c^2-3 a^8 c^4+6 a^6 b^2 c^4-4 a^4 b^4 c^4+2 a^2 b^6 c^4-9 b^8 c^4+2 a^6 c^6-4 a^4 b^2 c^6+2 a^2 b^4 c^6+16 b^6 c^6+2 a^4 c^8+a^2 b^2 c^8-9 b^4 c^8-3 a^2 c^10+c^12) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6628.

X(64689) lies on these lines: {2, 52000}, {3, 64}, {30, 13416}, {52, 26958}, {68, 43587}, {185, 64181}, {339, 51386}, {343, 1216}, {389, 6640}, {511, 2072}, {599, 9967}, {974, 6699}, {1154, 5159}, {1368, 15067}, {3546, 11444}, {3548, 5562}, {3763, 37511}, {3917, 13851}, {5447, 12605}, {5663, 16976}, {5972, 44907}, {6643, 7999}, {7509, 52416}, {7723, 17855}, {10110, 10255}, {10170, 15760}, {11487, 41738}, {11574, 43150}, {11591, 16196}, {12362, 30522}, {13348, 18563}, {14128, 31829}, {15060, 44241}, {15644, 18404}, {23039, 30771}, {32607, 51394}, {34146, 51425}, {44084, 44911}, {44247, 45959}, {44495, 45967}

X(64690) = X(69)X(523)∩X(525)X(3589)

Barycentrics    (b-c)*(b+c)*(-a^6+3*b^6+b^4*c^2+b^2*c^4+3*c^6+5*a^4*(b^2+c^2)-a^2*(7*b^4+3*b^2*c^2+7*c^4)) : :
X(64690) = -5*X[3763]+3*X[45801], -9*X[18311]+5*X[51170], -9*X[53374]+17*X[63120]

See Ivan Pavlov, euclid 6629.

X(64690) lies on these lines: {69, 523}, {525, 3589}, {3763, 45801}, {6333, 45147}, {18311, 51170}, {53374, 63120}

X(64690) = perspector of circumconic {{A, B, C, X(8781), X(54459)}}
X(64690) = pole of line {2799, 6722} with respect to the Kiepert parabola
X(64690) = pole of line {325, 20063} with respect to the Steiner circumellipse
X(64690) = pole of line {23, 44377} with respect to the Steiner inellipse
X(64690) = pole of line {6390, 35296} with respect to the dual conic of the orthoptic circle of the Steiner inellipse

X(64691) = COMPLEMENT OF X(639)

Barycentrics    2*a^4 - 3*a^2*b^2 + b^4 - 3*a^2*c^2 - 2*b^2*c^2 + c^4 - 2*(2*a^2 + b^2 + c^2)*S : :
X(64691) = 3 X[2] + X[371], 9 X[2] - X[637], 15 X[2] + X[43134], 3 X[371] + X[637], 5 X[371] - X[43134], X[637] - 3 X[639], 5 X[637] + 3 X[43134], 5 X[639] + X[43134], X[490] + 3 X[35822], 3 X[597] - X[44502], 5 X[631] - X[11825], 7 X[3090] + X[26441], 7 X[3526] + X[45489], 5 X[3618] - X[35840], 3 X[9753] + X[11824], X[35820] + 3 X[35949]

X(64691) lies on these lines: {2, 371}, {3, 45440}, {5, 6118}, {6, 641}, {32, 590}, {140, 143}, {141, 8981}, {187, 53487}, {372, 39387}, {395, 33393}, {396, 33394}, {485, 11292}, {489, 6453}, {490, 35822}, {491, 35812}, {492, 6419}, {524, 44482}, {575, 48772}, {591, 6417}, {597, 13966}, {615, 1504}, {631, 11825}, {632, 45872}, {638, 8960}, {1151, 11313}, {1352, 48735}, {1506, 50374}, {1583, 8276}, {1991, 13903}, {2460, 6656}, {3071, 32491}, {3090, 26441}, {3102, 7807}, {3103, 7792}, {3311, 45472}, {3312, 41490}, {3525, 10517}, {3526, 45489}, {3618, 5420}, {3972, 60274}, {4045, 43144}, {5007, 51395}, {5050, 48734}, {5395, 10195}, {5943, 15896}, {6200, 7389}, {6222, 10516}, {6228, 13879}, {6420, 45508}, {6422, 45577}, {6423, 45574}, {6564, 11294}, {6567, 7852}, {6669, 34562}, {6670, 34559}, {6811, 45553}, {7376, 32785}, {7388, 10576}, {7581, 33364}, {7582, 26361}, {7583, 32421}, {7745, 32432}, {7803, 45564}, {7834, 9738}, {7874, 51401}, {8252, 12962}, {8253, 11314}, {8361, 32435}, {8976, 13663}, {9675, 32490}, {9681, 58804}, {9692, 51952}, {9753, 11824}, {10515, 12257}, {11316, 47355}, {12314, 15293}, {13758, 45512}, {13972, 31406}, {16925, 45565}, {22596, 49114}, {23311, 42215}, {24206, 48773}, {26615, 42414}, {26619, 31412}, {32489, 35821}, {32497, 49220}, {32790, 62241}, {32805, 42009}, {32807, 58866}, {33425, 42166}, {33426, 42163}, {35771, 62987}, {35815, 62986}, {35820, 35949}, {37340, 53456}, {37341, 53467}, {37343, 48467}, {37649, 55865}, {38110, 49103}, {39388, 40274}, {43119, 48466}, {43558, 54626}, {43880, 61310}, {44657, 52669}, {45398, 48746}, {45411, 45554}, {45510, 45551}, {45576, 62201}, {53480, 62206}

X(64691) = midpoint of X(i) and X(j) for these {i,j}: {5, 43120}, {32, 640}, {371, 639}
X(64691) = complement of X(639)
X(64691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 371, 639}, {2, 5418, 642}, {5, 45871, 6118}, {6, 11315, 641}

X(64692) = X(51)X(597)∩X(373)X(524)

Barycentrics    a^2*(a^4*b^2 - b^6 + a^4*c^2 + 12*a^2*b^2*c^2 + 3*b^4*c^2 + 3*b^2*c^4 - c^6) : :
X(64692) = X[2] + 2 X[64599], X[6] + 2 X[5943], 5 X[6] + 4 X[9822], 7 X[6] + 2 X[14913], 2 X[6] + X[29959], 5 X[5943] - 2 X[9822], 7 X[5943] - X[14913], 4 X[5943] - X[29959], 14 X[9822] - 5 X[14913], 8 X[9822] - 5 X[29959], 4 X[14913] - 7 X[29959], X[51] + 2 X[597], X[52] + 8 X[25555], X[599] - 4 X[6688], X[1843] + 8 X[6329], X[1992] + 5 X[11451], X[1992] + 2 X[61676], 5 X[11451] - 2 X[61676], X[2979] - 7 X[63109], 2 X[3060] + X[3313], X[3060] + 5 X[3618], X[3060] - 4 X[58471], X[3313] - 10 X[3618], X[3313] + 8 X[58471], 5 X[3618] + 4 X[58471], 4 X[3589] - X[3917], 5 X[3763] - 8 X[10219], 5 X[3763] + 4 X[58555], 2 X[10219] + X[58555], 8 X[5462] + X[50649], 2 X[5476] + X[9730], 2 X[5480] + X[64100], 2 X[5892] + X[20423], X[5946] + 2 X[18583], 4 X[5946] - X[19161], 8 X[18583] + X[19161], X[6467] + 8 X[58532], X[8584] + 2 X[40670], 2 X[8584] + X[61667], 4 X[40670] - X[61667], X[9967] + 8 X[58549], 2 X[9969] + 7 X[51171], X[9971] + 5 X[51185], X[9971] - 4 X[58470], 5 X[51185] + 4 X[58470], 4 X[10110] + 5 X[53093], 7 X[10541] + 2 X[13598], X[11188] + 5 X[63127], X[11477] + 8 X[11695], 2 X[12099] + X[15303], X[12824] + 2 X[15118], 2 X[13364] + X[50979], X[13451] + 2 X[51732], 4 X[13570] - X[36990], X[15074] + 8 X[58531], X[16194] - 4 X[19130], 2 X[16776] + X[40673], X[16776] + 2 X[63124], X[40673] - 4 X[63124], 2 X[16836] + X[54131], 4 X[20583] - X[61692], 2 X[21849] + X[54334], 4 X[22829] - 13 X[63011], 2 X[23327] + X[41580], X[32062] - 4 X[50959], 8 X[32205] + X[64067], 2 X[32366] - 11 X[63123], X[36987] - 4 X[50983], 4 X[41153] - X[44323], 2 X[43129] + 7 X[55712], 2 X[43130] + 7 X[53092]

See Antreas Hatzipolakis and Peter Moses, euclid 6637.

X(64692) lies on these lines: {2, 64599}, {6, 1196}, {51, 597}, {52, 25555}, {182, 12083}, {373, 524}, {511, 5054}, {518, 64661}, {542, 14845}, {575, 7545}, {599, 6688}, {1154, 38079}, {1843, 6329}, {1992, 11451}, {2393, 5640}, {2781, 16226}, {2979, 63109}, {3060, 3313}, {3066, 32621}, {3589, 3917}, {3763, 10219}, {5032, 9027}, {5422, 19136}, {5462, 50649}, {5476, 9730}, {5480, 64100}, {5650, 48310}, {5892, 20423}, {5946, 18583}, {6000, 38072}, {6467, 58532}, {8584, 40670}, {9967, 58549}, {9969, 51171}, {9971, 51185}, {10110, 53093}, {10541, 13598}, {11188, 63127}, {11477, 11695}, {11649, 47455}, {12039, 37784}, {12099, 15303}, {12824, 15118}, {13337, 59707}, {13364, 50979}, {13391, 38110}, {13451, 51732}, {13570, 36990}, {13754, 14561}, {14853, 15045}, {14984, 59399}, {15019, 22151}, {15074, 58531}, {16194, 19130}, {16776, 40673}, {16836, 54131}, {20583, 61692}, {21358, 63632}, {21849, 54334}, {22829, 63011}, {23327, 41580}, {32062, 50959}, {32205, 64067}, {32366, 63123}, {35264, 64028}, {35707, 44106}, {36987, 50983}, {38005, 46336}, {38402, 55606}, {41153, 44323}, {41256, 43726}, {41593, 61775}, {43129, 55712}, {43130, 53092}, {51797, 55709}, {52697, 55713}

X(64692) = midpoint of X(i) and X(j) for these {i,j}: {5640, 59373}, {14853, 15045}
X(64692) = reflection of X(i) in X(j) for these {i,j}: {5650, 48310}, {21358, 63632}
X(64692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5943, 29959}, {1992, 11451, 61676}, {3618, 58471, 3313}, {8584, 40670, 61667}, {16776, 63124, 40673}

leftri

Points related to crosspedal triangles, Part 2: X(64693)-X(64768)

rightri

This preamble and centers X(64693)-X(64768) were contributed by Ivan Pavlov on August 06, 2024.

Given a triangle ABC and two points P and Q not on its sides, let the line through Q parallel to AP intersect lines AB and AC at points Ab and Ac. Similarly define Ba, Bc, Ca, Cb. The lines BaCa, AbCb, AcBc form a triangle called here the P-crosspedal triangle of Q.

We remind the reader of two other definitions used below:
(1) Through Q construct a line parallel to AP and let A' be the intersection point with BC. Similarly define B' and C'; A'B'C' is called P-pedal triangle of Q
(2) The P-antipedal triangle of Q is the triangle A'B'C' such that ABC is P-pedal of Q wrt A'B'C'.

For more information and properties see Euclid 6286

X(64693) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ZANIAH AND X(1)-CROSSPEDAL-OF-X(5)

Barycentrics    a*(a^5*(b+c)-a^4*(b+c)^2-(b^2-c^2)^2*(b^2+3*b*c+c^2)-a^3*(2*b^3+b^2*c+b*c^2+2*c^3)+a^2*(2*b^4+5*b^3*c+2*b^2*c^2+5*b*c^3+2*c^4)+a*(b^5-b^3*c^2-b^2*c^3+c^5)) : :
X(64693) = -3*X[2]+X[12005], X[3]+3*X[15064], -X[40]+9*X[63961], -X[65]+5*X[31399], X[72]+3*X[10175], 3*X[210]+X[946], X[355]+3*X[10176], -3*X[375]+X[31760], 3*X[392]+X[47745], -3*X[547]+X[6583], -X[942]+3*X[10172], -X[1071]+9*X[61686] and many others

X(64693) lies on these lines: {2, 12005}, {3, 15064}, {5, 3678}, {9, 6796}, {10, 119}, {40, 63961}, {65, 31399}, {72, 10175}, {140, 2801}, {210, 946}, {355, 10176}, {375, 31760}, {392, 47745}, {515, 5044}, {516, 58630}, {517, 3850}, {547, 6583}, {756, 37732}, {758, 9956}, {912, 3634}, {936, 5450}, {942, 10172}, {958, 5780}, {960, 58636}, {1071, 61686}, {1158, 8580}, {1490, 30393}, {1656, 3874}, {1698, 5884}, {2551, 64335}, {2802, 58674}, {2816, 58668}, {3090, 5904}, {3149, 3715}, {3305, 17857}, {3452, 63963}, {3579, 31871}, {3628, 58565}, {3652, 46684}, {3681, 8227}, {3697, 11362}, {3740, 5777}, {3754, 5694}, {3820, 64763}, {3828, 34339}, {3833, 24475}, {3868, 54447}, {3876, 5587}, {3878, 5790}, {3881, 11230}, {3898, 12645}, {3901, 30315}, {3918, 14988}, {3956, 5690}, {3968, 35004}, {3983, 12672}, {4134, 24474}, {4547, 9955}, {4662, 28234}, {4669, 23340}, {4711, 13600}, {4973, 45976}, {5067, 18398}, {5220, 6918}, {5260, 6326}, {5432, 41562}, {5506, 5531}, {5660, 6853}, {5692, 5818}, {5693, 9780}, {5791, 40249}, {5840, 58698}, {5882, 18908}, {5927, 31730}, {6246, 47033}, {6705, 32159}, {6763, 6946}, {6985, 60912}, {7294, 17660}, {7951, 15556}, {9519, 64541}, {9708, 40257}, {9709, 40256}, {9940, 58451}, {10122, 61648}, {10157, 18483}, {10164, 40263}, {10165, 14872}, {10202, 51073}, {10225, 19919}, {10284, 59400}, {10588, 18397}, {10902, 27065}, {11248, 60911}, {12528, 31423}, {12616, 18236}, {12665, 38133}, {13369, 58441}, {13373, 19878}, {13464, 34790}, {14110, 50796}, {14740, 16174}, {15016, 19877}, {15254, 64116}, {15481, 37623}, {18228, 48482}, {19875, 64021}, {19925, 31837}, {20116, 38318}, {20752, 25064}, {21616, 40259}, {22936, 33814}, {24025, 35194}, {24206, 34378}, {26446, 31803}, {26878, 44425}, {27784, 37698}, {28150, 58637}, {28174, 58675}, {28194, 58629}, {28232, 58688}, {28236, 31838}, {29054, 40607}, {29958, 52796}, {31419, 64762}, {31452, 61709}, {31659, 58449}, {31673, 64107}, {31937, 43174}, {37162, 49176}, {38752, 47320}, {57284, 62357}, {58634, 58660}, {58658, 58666}, {61562, 61622}, {61628, 64123}, {64118, 64198}

X(64693) = midpoint of X(i) and X(j) for these {i,j}: {5, 3678}, {10, 20117}, {72, 31870}, {140, 56762}, {3579, 31871}, {3754, 5694}, {5044, 58631}, {5777, 6684}, {6705, 32159}, {9956, 31835}, {12005, 63967}, {13464, 34790}, {14740, 16174}, {18483, 63976}, {19925, 31837}, {31937, 43174}
X(64693) = reflection of X(i) in X(j) for these {i,j}: {4015, 58632}, {13373, 19878}, {58565, 3628}
X(64693) = complement of X(12005)
X(64693) = pole of line {3738, 8062} with respect to the Spieker circle
X(64693) = X(1216)-of-K798i triangle
X(64693) = X(5449)-of-2nd-Zaniah triangle
X(64693) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3035, 3042, 6710}
X(64693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 63967, 12005}, {10, 20117, 2800}, {72, 10175, 31870}, {140, 56762, 2801}, {517, 58632, 4015}, {3740, 5777, 6684}, {3876, 5587, 31806}, {3983, 12672, 38127}, {5044, 58631, 515}, {5694, 38042, 3754}, {9956, 31835, 758}, {10157, 63976, 18483}, {18908, 25917, 5882}

X(64694) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CONWAY AND X(1)-CROSSPEDAL-OF-X(6)

Barycentrics    a^5-b^5+2*a^3*b*c+b^4*c+b*c^4-c^5+a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b-c)^2*(b^2+4*b*c+c^2) : :
X(64694) = -3*X[2]+2*X[1766], -3*X[1699]+X[7996], -5*X[3091]+4*X[12618], -5*X[3616]+4*X[63968], -5*X[3618]+4*X[64121], -3*X[9778]+4*X[24309], -X[9801]+3*X[9812]

X(64694) lies on these lines: {1, 7}, {2, 1766}, {3, 17321}, {4, 75}, {8, 21273}, {19, 27509}, {30, 50101}, {37, 36698}, {40, 4357}, {69, 517}, {86, 4221}, {144, 5813}, {150, 2823}, {192, 6999}, {307, 39579}, {319, 12245}, {326, 63986}, {329, 3687}, {332, 945}, {345, 19542}, {348, 41007}, {355, 42696}, {376, 17320}, {377, 24547}, {388, 12721}, {497, 12723}, {515, 3875}, {534, 7289}, {572, 26626}, {573, 17257}, {631, 17322}, {938, 32118}, {944, 4360}, {946, 10436}, {971, 51212}, {1058, 12722}, {1111, 31598}, {1266, 41869}, {1267, 2048}, {1444, 11249}, {1460, 3474}, {1699, 7996}, {1764, 10468}, {1836, 17635}, {1848, 56367}, {2270, 40880}, {2345, 7377}, {2478, 24993}, {2550, 18252}, {2961, 53596}, {3057, 10401}, {3090, 28653}, {3091, 12618}, {3146, 4452}, {3421, 63151}, {3434, 12530}, {3436, 20895}, {3616, 63968}, {3618, 64121}, {3656, 63110}, {3739, 36662}, {3879, 7982}, {4000, 6996}, {4219, 37581}, {4364, 37499}, {4373, 39732}, {4384, 64701}, {4389, 6361}, {4398, 29291}, {4440, 17481}, {4464, 61296}, {4699, 7384}, {4872, 39126}, {4967, 5587}, {5224, 5657}, {5232, 59417}, {5564, 59388}, {5691, 17151}, {5722, 21848}, {5744, 16566}, {5886, 63014}, {5903, 5933}, {5905, 17147}, {6604, 41004}, {6836, 17863}, {7291, 20061}, {7397, 16706}, {7402, 17289}, {7595, 57269}, {7967, 17393}, {7991, 17272}, {9436, 41010}, {9776, 17304}, {9778, 24309}, {9801, 9812}, {9944, 62697}, {9962, 10431}, {9965, 36850}, {10447, 12549}, {10452, 12435}, {10464, 64568}, {10595, 17394}, {11115, 17183}, {11362, 17270}, {11415, 20245}, {12699, 42697}, {12725, 37443}, {14021, 24554}, {14557, 54113}, {16548, 56445}, {17132, 64143}, {17271, 50810}, {17274, 28194}, {17302, 37416}, {17355, 18228}, {17862, 37185}, {18162, 24683}, {19645, 19785}, {20070, 41826}, {20430, 36674}, {21068, 27384}, {21078, 45744}, {21370, 55907}, {21375, 26065}, {24259, 30946}, {24463, 64134}, {24590, 25019}, {26118, 26234}, {28228, 53598}, {28606, 37419}, {29054, 49518}, {29057, 39774}, {29207, 51192}, {30271, 36706}, {31162, 50116}, {32087, 59387}, {34188, 55024}, {34627, 50088}, {34631, 50132}, {36659, 64728}, {36686, 61549}, {36731, 50107}, {36861, 64130}, {37531, 55391}, {41003, 64077}, {51118, 53594}, {52082, 54109}

X(64694) = reflection of X(i) in X(j) for these {i,j}: {20, 990}, {69, 64122}, {1766, 12610}, {3729, 10445}, {7996, 21629}, {10444, 3663}, {12652, 4301}, {12717, 946}, {20070, 61087}, {50107, 36731}
X(64694) = anticomplement of X(1766)
X(64694) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57642, 2}
X(64694) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {3435, 2}, {8048, 69}, {15385, 651}, {34277, 3436}, {39167, 56943}, {40097, 4391}, {40454, 321}, {42467, 8}, {43703, 2895}, {46640, 513}, {57642, 6327}, {57777, 315}, {57781, 21275}, {58997, 3910}
X(64694) = pole of line {354, 10401} with respect to the Feuerbach hyperbola
X(64694) = pole of line {4025, 21174} with respect to the Steiner circumellipse
X(64694) = pole of line {3732, 14594} with respect to the Yff parabola
X(64694) = pole of line {944, 1043} with respect to the Wallace hyperbola
X(64694) = pole of line {7, 54418} with respect to the dual conic of Yff parabola
X(64694) = X(577)-of-2nd-Conway
X(64694) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(4320)}}, {{A, B, C, X(7), X(27539)}}, {{A, B, C, X(77), X(30479)}}, {{A, B, C, X(945), X(1042)}}, {{A, B, C, X(3668), X(58003)}}, {{A, B, C, X(56382), X(60197)}}
X(64694) = barycentric product X(i)*X(j) for these (i, j): {27539, 7}
X(64694) = barycentric quotient X(i)/X(j) for these (i, j): {27539, 8}
X(64694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 4329, 17170}, {7, 962, 10446}, {516, 3663, 10444}, {516, 4301, 12652}, {516, 990, 20}, {1699, 7996, 21629}, {1766, 12610, 2}, {4862, 9589, 10442}

X(64695) = ORTHOLOGY CENTER OF THESE TRIANGLES: HONSBERGER AND X(1)-CROSSPEDAL-OF-X(6)

Barycentrics    a^4-2*b*(b-c)^2*c+a^3*(b+c)-a*(b-c)^2*(b+c)-a^2*(b^2+4*b*c+c^2) : :
X(64695) = -4*X[3821]+3*X[38052], -4*X[3946]+3*X[59405], -3*X[7671]+X[12718], -2*X[50118]+3*X[61023]

X(64695) lies on these lines: {1, 7}, {9, 75}, {37, 62383}, {40, 3673}, {46, 7264}, {55, 40719}, {57, 62697}, {69, 5853}, {85, 1697}, {86, 38316}, {142, 16831}, {144, 239}, {150, 3586}, {165, 1447}, {200, 30946}, {348, 12053}, {350, 30567}, {497, 9436}, {518, 3875}, {527, 1992}, {528, 17274}, {536, 50995}, {545, 51144}, {664, 7962}, {672, 24600}, {726, 5223}, {910, 24352}, {950, 6604}, {1001, 10436}, {1058, 53597}, {1111, 5119}, {1266, 5698}, {1445, 1766}, {1699, 7179}, {1743, 53602}, {2082, 30625}, {2098, 25716}, {2136, 16284}, {2223, 11495}, {2550, 4357}, {2796, 50836}, {3057, 9312}, {3059, 18252}, {3062, 41527}, {3212, 7991}, {3243, 4360}, {3247, 27475}, {3263, 30568}, {3294, 60958}, {3303, 4059}, {3576, 24203}, {3598, 9778}, {3601, 55082}, {3662, 20533}, {3665, 12701}, {3821, 38052}, {3870, 20347}, {3895, 30806}, {3923, 25590}, {3946, 59405}, {4000, 16970}, {4393, 20059}, {4419, 5819}, {4441, 11679}, {4660, 17272}, {4859, 53600}, {4872, 9580}, {4911, 41869}, {4912, 50997}, {4967, 38057}, {5224, 38200}, {5232, 59413}, {5250, 20880}, {5493, 10521}, {5564, 59414}, {5572, 12723}, {5686, 32087}, {5691, 56928}, {5845, 16973}, {5850, 49488}, {5919, 7223}, {6172, 16833}, {6173, 17320}, {6284, 30617}, {6381, 51284}, {6646, 41845}, {6762, 17158}, {7247, 9579}, {7671, 12718}, {7676, 24309}, {7677, 63968}, {7996, 30330}, {8232, 10445}, {8237, 12610}, {8545, 29069}, {8822, 18206}, {9581, 33298}, {9614, 17181}, {10384, 39126}, {10389, 14828}, {10980, 60717}, {11372, 29057}, {11522, 17084}, {12530, 30628}, {12717, 44735}, {14100, 17635}, {14548, 64162}, {15185, 54344}, {15485, 55967}, {15956, 60932}, {16552, 60949}, {16566, 60974}, {16593, 17282}, {16816, 61006}, {16823, 24280}, {16825, 28526}, {16826, 62778}, {16830, 59412}, {16832, 17355}, {16972, 17301}, {17095, 50443}, {17116, 31347}, {17117, 27484}, {17133, 50996}, {17271, 51102}, {17322, 20195}, {19860, 20244}, {24179, 52769}, {24209, 60912}, {24393, 42696}, {26234, 56518}, {26563, 63130}, {29181, 50175}, {29580, 59375}, {29584, 60984}, {31130, 56082}, {32007, 41864}, {34855, 56309}, {35258, 53381}, {41842, 48627}, {47357, 50116}, {49458, 53598}, {49710, 60905}, {50118, 61023}, {51929, 56900}

X(64695) = midpoint of X(i) and X(j) for these {i,j}: {12530, 30628}, {14100, 17635}
X(64695) = reflection of X(i) in X(j) for these {i,j}: {7, 3663}, {3059, 18252}, {3729, 9}, {12723, 5572}, {60960, 53602}
X(64695) = perspector of circumconic {{A, B, C, X(658), X(51560)}}
X(64695) = pole of line {354, 40719} with respect to the Feuerbach hyperbola
X(64695) = pole of line {4025, 47798} with respect to the Steiner circumellipse
X(64695) = pole of line {3716, 7658} with respect to the Steiner inellipse
X(64695) = pole of line {1026, 3732} with respect to the Yff parabola
X(64695) = pole of line {1043, 6762} with respect to the Wallace hyperbola
X(64695) = pole of line {7, 1738} with respect to the dual conic of Yff parabola
X(64695) = X(577)-of-Honsberger
X(64695) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6559)}}, {{A, B, C, X(7), X(36796)}}, {{A, B, C, X(9), X(1458)}}, {{A, B, C, X(190), X(41353)}}, {{A, B, C, X(269), X(673)}}, {{A, B, C, X(279), X(2481)}}, {{A, B, C, X(1042), X(18785)}}, {{A, B, C, X(3062), X(4334)}}, {{A, B, C, X(3160), X(41527)}}, {{A, B, C, X(3254), X(4331)}}, {{A, B, C, X(3729), X(41355)}}, {{A, B, C, X(4350), X(31638)}}, {{A, B, C, X(10390), X(42289)}}
X(64695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 14189, 269}, {7, 8236, 3945}, {516, 3663, 7}, {673, 51052, 9}, {3875, 49518, 49446}

X(64696) = ORTHOLOGY CENTER OF THESE TRIANGLES: OUTER-GARCIA AND X(1)-CROSSPEDAL-OF-X(7)

Barycentrics    a^6-8*a^3*b*c*(b+c)-8*a*b*(b-c)^2*c*(b+c)-(b-c)^4*(b+c)^2-3*a^4*(b^2-6*b*c+c^2)+a^2*(b-c)^2*(3*b^2+2*b*c+3*c^2) : :
X(64696) = -4*X[3]+3*X[52653], -4*X[946]+5*X[62778], -4*X[1125]+3*X[24644], -5*X[1698]+4*X[64699], -5*X[3091]+6*X[38052], -7*X[3523]+8*X[43151], -5*X[3616]+6*X[21151], -3*X[3839]+4*X[51100], -11*X[5056]+12*X[38204], -2*X[5223]+3*X[59417], -11*X[5550]+12*X[38122], -3*X[5603]+4*X[31657] and many others

X(64696) lies on these lines: {1, 7}, {2, 10860}, {3, 52653}, {4, 11024}, {8, 971}, {9, 37421}, {10, 3062}, {40, 144}, {46, 60941}, {72, 54228}, {100, 329}, {165, 18228}, {376, 64659}, {377, 9800}, {388, 31391}, {411, 5698}, {497, 5918}, {515, 11525}, {517, 36996}, {519, 64697}, {527, 34632}, {631, 63266}, {938, 9943}, {946, 62778}, {1001, 6909}, {1058, 31805}, {1071, 30628}, {1125, 24644}, {1156, 5825}, {1158, 60970}, {1697, 60961}, {1698, 64699}, {1709, 5273}, {1788, 60910}, {2550, 6925}, {2801, 64056}, {2802, 56090}, {3059, 12528}, {3091, 38052}, {3358, 5744}, {3428, 54052}, {3434, 10430}, {3474, 60883}, {3522, 35262}, {3523, 43151}, {3579, 5811}, {3616, 21151}, {3826, 6932}, {3839, 51100}, {3895, 20059}, {4208, 21628}, {4229, 17183}, {4645, 9801}, {5056, 38204}, {5128, 61014}, {5223, 59417}, {5274, 64705}, {5435, 15299}, {5550, 38122}, {5603, 31657}, {5657, 5779}, {5686, 64197}, {5690, 60884}, {5691, 58834}, {5703, 64074}, {5762, 6361}, {5766, 7676}, {5785, 7995}, {5805, 9776}, {5817, 9780}, {5818, 38121}, {5843, 12702}, {5850, 7991}, {5851, 64189}, {5880, 6836}, {6001, 41228}, {6764, 12680}, {6838, 18230}, {6890, 38037}, {6943, 42356}, {6962, 15254}, {7080, 60966}, {7966, 28194}, {7992, 54398}, {7994, 41561}, {8227, 38123}, {9779, 37374}, {9799, 12777}, {9841, 10384}, {10167, 10580}, {10178, 26105}, {10248, 18482}, {10303, 38059}, {10304, 50836}, {10309, 11500}, {10595, 38030}, {11220, 36845}, {11522, 38054}, {12669, 15733}, {12686, 60935}, {12688, 15587}, {12699, 59386}, {12705, 37108}, {13374, 45084}, {14110, 54199}, {16112, 38057}, {17613, 31658}, {17650, 17668}, {17768, 33557}, {18493, 38111}, {19877, 38108}, {22791, 59380}, {24014, 31527}, {26062, 61012}, {28174, 60922}, {28610, 41338}, {30308, 38094}, {31162, 59375}, {31672, 38149}, {31730, 52026}, {31777, 64144}, {37714, 38201}, {38080, 50806}, {39581, 59620}, {40333, 63970}, {44280, 47470}, {45203, 45721}, {47033, 59413}, {50528, 54051}, {51516, 61524}, {51768, 64114}, {52457, 63413}, {52835, 60987}, {60911, 61023}, {60912, 60983}, {60979, 63141}, {63984, 64081}, {64190, 64280}

X(64696) = midpoint of X(i) and X(j) for these {i,j}: {5691, 58834}, {9961, 25722}, {20059, 20070}
X(64696) = reflection of X(i) in X(j) for these {i,j}: {8, 35514}, {20, 2951}, {144, 40}, {390, 5732}, {962, 7}, {3062, 10}, {5698, 11495}, {12528, 3059}, {12688, 15587}, {14100, 9943}, {30628, 1071}, {36991, 2550}, {54204, 41338}, {60884, 5690}, {63975, 5759}
X(64696) = anticomplement of X(11372)
X(64696) = pole of line {4025, 26695} with respect to the Steiner circumellipse
X(64696) = pole of line {934, 3732} with respect to the Yff parabola
X(64696) = X(1351)-of-2nd-Conway triangle
X(64696) = X(3062)-of-outer-Garcia triangle
X(64696) = intersection, other than A, B, C, of circumconics {{A, B, C, X(269), X(972)}}, {{A, B, C, X(279), X(55030)}}, {{A, B, C, X(971), X(6244)}}
X(64696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 516, 962}, {40, 6223, 5815}, {390, 5732, 5731}, {516, 2951, 20}, {516, 5732, 390}, {2550, 15726, 36991}, {2550, 36991, 59387}, {5658, 6244, 64083}, {5698, 11495, 59418}, {9778, 63975, 5759}, {9778, 64083, 6244}, {9961, 25722, 971}, {10384, 60992, 14986}, {24644, 64698, 1125}, {38037, 64113, 60996}, {38052, 63973, 3091}, {38121, 60901, 5818}, {59412, 60959, 11024}

X(64697) = ORTHOLOGY CENTER OF THESE TRIANGLES: 5TH MIXTILINEAR AND X(1)-CROSSPEDAL-OF-X(7)

Barycentrics    a*(a^5-7*a^4*(b+c)+2*a^2*(b-c)^2*(b+c)+2*a^3*(5*b^2-2*b*c+5*c^2)-a*(b-c)^2*(11*b^2+10*b*c+11*c^2)+(b-c)^2*(5*b^3+11*b^2*c+11*b*c^2+5*c^3)) : :
X(64697) = -4*X[10]+5*X[64698], -8*X[142]+7*X[7989], -5*X[355]+6*X[38170], -8*X[1001]+9*X[30392], -5*X[1698]+6*X[21151], -3*X[1699]+4*X[5542], -4*X[2550]+3*X[37712], -5*X[3091]+6*X[38054], -4*X[3243]+3*X[11224], -3*X[3576]+2*X[5779], -5*X[3616]+4*X[64699], -7*X[3624]+6*X[5817] and many others

X(64697) lies on circumconic {{A, B, C, X(19605), X(24644)}} and on these lines: {1, 971}, {2, 30291}, {4, 45834}, {7, 5691}, {8, 43182}, {9, 3207}, {10, 64698}, {20, 5850}, {36, 64156}, {57, 24645}, {63, 100}, {84, 15298}, {142, 7989}, {144, 4297}, {145, 516}, {355, 38170}, {480, 59326}, {515, 4312}, {518, 2136}, {519, 64696}, {527, 34628}, {952, 4900}, {1001, 30392}, {1071, 3339}, {1385, 60884}, {1420, 60910}, {1445, 53057}, {1490, 3361}, {1698, 21151}, {1699, 5542}, {1750, 5728}, {2550, 37712}, {3057, 7990}, {3091, 38054}, {3243, 11224}, {3340, 31391}, {3358, 30282}, {3486, 60961}, {3576, 5779}, {3586, 60924}, {3601, 60909}, {3616, 64699}, {3624, 5817}, {3632, 35514}, {3839, 51098}, {4321, 10394}, {4326, 7995}, {4355, 63998}, {4853, 25722}, {4866, 14872}, {4882, 9943}, {5234, 5785}, {5290, 9799}, {5572, 30343}, {5587, 31657}, {5658, 10392}, {5686, 9588}, {5731, 51090}, {5805, 12678}, {5818, 38123}, {5843, 18481}, {5851, 64145}, {6001, 7966}, {7672, 30353}, {7988, 63970}, {7992, 53053}, {8227, 38030}, {8544, 40269}, {8580, 10167}, {9355, 60846}, {9580, 41706}, {9613, 60923}, {9814, 12560}, {9948, 51784}, {10178, 62218}, {10202, 18529}, {10304, 50834}, {10483, 64766}, {10857, 30393}, {10861, 64673}, {11038, 11522}, {11379, 18222}, {11407, 17612}, {11715, 51768}, {12528, 64679}, {12575, 54228}, {12675, 41861}, {13462, 15299}, {13624, 51516}, {15733, 18452}, {15837, 34862}, {15909, 57282}, {16112, 38316}, {16189, 34195}, {16865, 19861}, {18446, 53054}, {18480, 59380}, {18492, 38107}, {19925, 62778}, {25011, 30315}, {25557, 59389}, {28160, 60922}, {30308, 38024}, {31658, 58221}, {31672, 38036}, {31673, 59386}, {34595, 38108}, {34648, 59375}, {37714, 38052}, {38080, 50799}, {38111, 61261}, {38154, 64113}, {38158, 60996}, {41690, 60926}, {41700, 52026}, {41705, 50811}, {41712, 53056}, {42871, 64263}, {43161, 60905}, {43175, 50836}, {43180, 59385}, {51489, 63432}, {51785, 54227}, {52819, 64144}, {61264, 61595}

X(64697) = midpoint of X(i) and X(j) for these {i,j}: {11531, 58834}
X(64697) = reflection of X(i) in X(j) for these {i,j}: {8, 43182}, {144, 4297}, {3062, 1}, {3632, 35514}, {4312, 36996}, {5223, 5732}, {5691, 7}, {7991, 2951}, {7995, 4326}, {18412, 1071}, {36991, 5542}, {60884, 1385}, {60905, 43161}
X(64697) = pole of line {3900, 48017} with respect to the Conway circle
X(64697) = pole of line {57, 24644} with respect to the Feuerbach hyperbola
X(64697) = pole of line {60992, 62783} with respect to the dual conic of Yff parabola
X(64697) = X(193)-of-excenters-reflections triangle
X(64697) = X(3062)-of-5th-mixtilinear triangle
X(64697) = X(5921)-of-excentral triangle
X(64697) = X(6776)-of-6th-mixtilinear triangle
X(64697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 12680, 9851}, {1, 3062, 24644}, {1, 971, 3062}, {515, 36996, 4312}, {518, 2951, 7991}, {1071, 63981, 3339}, {2801, 5732, 5223}, {4321, 10394, 30330}, {5223, 5732, 165}, {5542, 36991, 1699}, {5686, 43151, 9588}, {5732, 12669, 30304}, {11038, 63973, 11522}, {11531, 58834, 516}, {38030, 60901, 8227}

X(64698) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(1)-CROSSPEDAL-OF-X(7)

Barycentrics    a^5-3*a*(b-c)^4-6*a^4*(b+c)-4*a^2*(b-c)^2*(b+c)+2*(b-c)^4*(b+c)+2*a^3*(5*b^2-2*b*c+5*c^2) : :
X(64698) = -X[1]+6*X[21151], -6*X[2]+X[3062], 4*X[3]+X[4312], -X[4]+6*X[38123], 2*X[7]+3*X[165], X[8]+4*X[43176], 4*X[10]+X[64697], -8*X[142]+3*X[1699], -X[144]+6*X[10164], -X[382]+6*X[38172], -2*X[390]+7*X[30389], -X[962]+6*X[38054] and many others

X(64698) lies on these lines: {1, 21151}, {2, 3062}, {3, 4312}, {4, 38123}, {7, 165}, {8, 43176}, {9, 1768}, {10, 64697}, {40, 5586}, {142, 1699}, {144, 10164}, {377, 5691}, {382, 38172}, {390, 30389}, {516, 3522}, {518, 64204}, {954, 59326}, {962, 38054}, {971, 1698}, {1125, 24644}, {1387, 3576}, {1742, 4859}, {2093, 54178}, {2801, 64141}, {3146, 38151}, {3160, 60831}, {3339, 37108}, {3523, 51090}, {3543, 38094}, {3579, 59380}, {3624, 11372}, {3679, 9952}, {3872, 6224}, {4297, 59412}, {4326, 30379}, {4355, 5584}, {4428, 6173}, {4888, 9441}, {5218, 60961}, {5219, 31391}, {5223, 7080}, {5231, 25722}, {5290, 64111}, {5536, 60938}, {5542, 7991}, {5759, 16192}, {5762, 35242}, {5779, 31423}, {5785, 37112}, {5805, 64005}, {5833, 10884}, {5880, 15909}, {5881, 38121}, {5918, 41867}, {6684, 36996}, {6713, 51768}, {6895, 38150}, {6908, 10398}, {7320, 11038}, {7982, 38030}, {7988, 58834}, {7989, 36991}, {7992, 37407}, {7994, 61022}, {8232, 9814}, {8255, 41338}, {8273, 9589}, {8581, 31787}, {8732, 11407}, {9616, 60914}, {9940, 41861}, {9950, 29627}, {10167, 15587}, {10178, 25525}, {10430, 61029}, {10724, 38207}, {11227, 14100}, {11231, 60884}, {12630, 61289}, {12699, 38111}, {15298, 37560}, {15299, 37526}, {15717, 63975}, {15726, 20195}, {15803, 60923}, {15841, 30350}, {16208, 60895}, {16209, 21153}, {16832, 59688}, {17284, 59620}, {17549, 50836}, {19872, 38108}, {20059, 64108}, {21617, 30353}, {24465, 35445}, {30315, 38158}, {30331, 30392}, {30393, 41561}, {30424, 59418}, {31162, 38065}, {31183, 64741}, {31231, 60910}, {31508, 60993}, {31663, 60922}, {31730, 59386}, {33574, 37704}, {34628, 51100}, {34632, 51098}, {36838, 50561}, {37714, 40333}, {38093, 42356}, {38107, 41869}, {38115, 64084}, {38187, 51212}, {38454, 61020}, {39878, 47595}, {41705, 59381}, {41862, 61595}, {50808, 59375}, {50865, 59374}, {52819, 53056}, {54447, 60901}, {59215, 63625}, {60924, 61763}

X(64698) = reflection of X(i) in X(j) for these {i,j}: {37714, 40333}
X(64698) = X(3062)-of-Gemini-109 triangle
X(64698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43182, 3062}, {7, 43151, 165}, {40, 31657, 59372}, {142, 2951, 1699}, {1125, 64696, 24644}, {5732, 38052, 5691}, {5732, 64113, 38052}, {6173, 11495, 63974}, {7988, 58834, 63973}, {11372, 38122, 3624}, {21153, 60896, 60905}, {36991, 38204, 7989}, {38204, 43181, 36991}, {60996, 63973, 7988}

X(64699) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 110 AND X(1)-CROSSPEDAL-OF-X(7)

Barycentrics    2*a^5-3*a^4*(b+c)+10*a^2*(b-c)^2*(b+c)+(b-c)^4*(b+c)-6*a*(b^2-c^2)^2-4*a^3*(b^2-4*b*c+c^2) : :
X(64699) = 3*X[2]+X[3062], -5*X[5]+3*X[38172], -X[7]+3*X[3817], X[8]+3*X[24644], -2*X[142]+3*X[10171], X[144]+3*X[1699], X[153]+3*X[51768], -5*X[1656]+3*X[38123], -5*X[1698]+X[64696], -X[2951]+3*X[10164], -X[3059]+3*X[15064], -5*X[3091]+X[4312] and many others

X(64699) lies on circumconic {{A, B, C, X(281), X(38254)}} and on these lines: {2, 3062}, {4, 9}, {5, 38172}, {7, 3817}, {8, 24644}, {11, 60961}, {142, 10171}, {144, 1699}, {153, 51768}, {226, 60910}, {515, 60901}, {517, 58678}, {518, 31821}, {527, 3829}, {946, 5779}, {971, 1125}, {1156, 21617}, {1387, 2801}, {1656, 38123}, {1698, 64696}, {1742, 25072}, {1836, 61014}, {2807, 58534}, {2951, 10164}, {3008, 64134}, {3059, 15064}, {3091, 4312}, {3358, 12436}, {3616, 64697}, {3634, 9842}, {3664, 9355}, {3667, 40551}, {3671, 10398}, {3832, 63975}, {3911, 31391}, {4297, 11106}, {4298, 15299}, {4301, 5223}, {4326, 60995}, {4384, 9950}, {4847, 60966}, {4915, 18222}, {5057, 15909}, {5071, 38094}, {5248, 64156}, {5542, 14986}, {5691, 52653}, {5704, 30424}, {5728, 12563}, {5732, 17558}, {5762, 18483}, {5785, 37434}, {5789, 5805}, {5843, 9955}, {5851, 60980}, {5853, 32537}, {5886, 60884}, {5927, 13405}, {5942, 63598}, {6172, 63974}, {6666, 15726}, {6675, 43181}, {6684, 61511}, {6701, 61595}, {6738, 10392}, {6745, 25722}, {6846, 54227}, {7674, 50801}, {7678, 60936}, {7988, 62778}, {7989, 59412}, {8226, 52819}, {8227, 36996}, {8232, 59687}, {9779, 20059}, {9812, 61006}, {9949, 64673}, {10004, 15913}, {10157, 15587}, {10863, 60992}, {10883, 60979}, {11019, 60937}, {11495, 60986}, {11522, 52665}, {12053, 60909}, {12512, 31658}, {12528, 41861}, {12575, 15298}, {12699, 51516}, {13257, 63258}, {15841, 60953}, {16418, 52769}, {17618, 60993}, {18243, 31657}, {19862, 21151}, {19878, 38122}, {21060, 30326}, {22793, 64065}, {22992, 64198}, {24389, 60973}, {28164, 31672}, {28236, 30331}, {28850, 59585}, {29571, 64741}, {30291, 64083}, {30308, 60984}, {30311, 41572}, {30353, 62775}, {31162, 50834}, {31211, 59620}, {31253, 38318}, {31399, 38121}, {31730, 59381}, {31994, 59170}, {34648, 50836}, {38075, 51100}, {38204, 63971}, {38454, 61000}, {40273, 61596}, {40998, 60969}, {41705, 59386}, {50808, 61023}, {58433, 63643}, {59380, 61268}, {59385, 60905}, {59688, 62398}, {60959, 64130}

X(64699) = midpoint of X(i) and X(j) for these {i,j}: {4, 51090}, {10, 11372}, {142, 16112}, {946, 5779}, {1156, 21635}, {3062, 43182}, {4297, 36991}, {4301, 5223}, {5542, 64197}, {5728, 31803}, {5759, 51118}, {22793, 64065}, {24389, 60973}, {31162, 50834}, {34648, 50836}, {40273, 61596}
X(64699) = reflection of X(i) in X(j) for these {i,j}: {5805, 12571}, {6684, 61511}, {12512, 31658}, {43151, 6666}, {43176, 1125}
X(64699) = complement of X(43182)
X(64699) = pole of line {1864, 61014} with respect to the Feuerbach hyperbola
X(64699) = pole of line {3160, 4000} with respect to the dual conic of Yff parabola
X(64699) = X(3062)-of-Gemini-110 triangle
X(64699) = X(6467)-of-3rd-Euler triangle
X(64699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3062, 43182}, {10, 11372, 516}, {971, 1125, 43176}, {2951, 18230, 10164}, {3091, 4312, 38151}, {5817, 11372, 10}, {6666, 15726, 43151}, {6666, 43151, 58441}, {8227, 36996, 38054}, {38037, 64197, 5542}

X(64700) = ORTHOLOGY CENTER OF THESE TRIANGLES: CONWAY AND X(1)-CROSSPEDAL-OF-X(37)

Barycentrics    2*a^5-b^5+b^4*c-2*a*b*(b-c)^2*c+b*c^4-c^5+a^4*(b+c)-2*a^2*b*c*(b+c)-2*a^3*(b^2-b*c+c^2) : :
X(64700) = -3*X[2]+2*X[64701], -3*X[10167]+2*X[50658], -3*X[50093]+4*X[64125]

X(64700) lies on these lines: {1, 7}, {2, 64701}, {3, 4357}, {4, 10436}, {8, 20246}, {9, 36698}, {27, 30687}, {30, 50116}, {40, 69}, {55, 10401}, {63, 573}, {75, 515}, {84, 6210}, {86, 946}, {99, 102}, {142, 6996}, {165, 17272}, {198, 40880}, {226, 23512}, {307, 411}, {319, 11362}, {320, 31730}, {326, 6261}, {348, 41010}, {355, 4967}, {376, 17274}, {412, 39579}, {464, 30675}, {511, 1071}, {517, 3879}, {534, 18161}, {550, 29085}, {572, 12610}, {610, 27509}, {894, 6999}, {944, 3875}, {950, 44735}, {971, 49132}, {1012, 31394}, {1064, 54308}, {1122, 5918}, {1158, 54404}, {1266, 18481}, {1268, 31399}, {1444, 11012}, {1447, 24213}, {1503, 30271}, {1630, 6518}, {1764, 10452}, {1765, 28287}, {1766, 3912}, {1944, 8804}, {2093, 5933}, {2807, 52385}, {3084, 9789}, {3576, 17321}, {3596, 64574}, {3662, 37416}, {3673, 64706}, {3868, 29311}, {3883, 29207}, {4360, 5882}, {4464, 37727}, {4643, 37499}, {5224, 6684}, {5249, 19645}, {5273, 63978}, {5279, 16550}, {5564, 47745}, {5657, 17270}, {5691, 25590}, {5750, 7377}, {5784, 64007}, {5805, 49130}, {5816, 24603}, {5881, 42696}, {6011, 43363}, {6735, 21286}, {6837, 28627}, {6925, 21279}, {7282, 37420}, {7289, 24683}, {7385, 63970}, {7397, 17282}, {7411, 41430}, {7580, 9436}, {8227, 63014}, {8720, 17770}, {9778, 21296}, {9799, 48878}, {9943, 24471}, {9965, 17364}, {10165, 17322}, {10167, 50658}, {10175, 28653}, {10391, 21746}, {10434, 37175}, {10447, 10454}, {10468, 10882}, {10860, 63152}, {11220, 29353}, {11329, 25023}, {11349, 25019}, {11433, 39592}, {11495, 47595}, {12512, 53598}, {12555, 63057}, {13464, 17394}, {13607, 17393}, {15310, 49711}, {17183, 24550}, {17320, 51705}, {17353, 64121}, {17377, 28234}, {17378, 28194}, {18446, 50656}, {18483, 41847}, {20070, 62999}, {20245, 64002}, {20880, 48890}, {21078, 22003}, {21375, 56078}, {24540, 41012}, {26651, 31015}, {27633, 62371}, {28204, 50099}, {28845, 59620}, {29097, 44238}, {30273, 49518}, {31162, 63110}, {32025, 38127}, {32099, 59417}, {33800, 62124}, {34379, 54422}, {37443, 45305}, {37567, 58800}, {37774, 59644}, {40257, 44179}, {40590, 45270}, {45789, 50693}, {48881, 63390}, {49537, 63995}, {50093, 64125}, {50101, 50811}, {53597, 64077}, {55391, 63391}

X(64700) = reflection of X(i) in X(j) for these {i,j}: {4416, 573}, {10446, 3664}
X(64700) = anticomplement of X(64701)
X(64700) = pole of line {109, 3732} with respect to the Yff parabola
X(64700) = pole of line {515, 1043} with respect to the Wallace hyperbola
X(64700) = pole of line {7, 1468} with respect to the dual conic of Yff parabola
X(64700) = X(216)-of-Conway triangle
X(64700) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(34277)}}, {{A, B, C, X(84), X(4320)}}, {{A, B, C, X(102), X(1042)}}, {{A, B, C, X(269), X(42467)}}, {{A, B, C, X(279), X(8048)}}, {{A, B, C, X(347), X(30479)}}, {{A, B, C, X(2739), X(5018)}}, {{A, B, C, X(3668), X(34393)}}, {{A, B, C, X(10444), X(34402)}}
X(64700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 20, 10444}, {516, 3664, 10446}, {572, 12610, 17023}, {894, 6999, 10445}

X(64701) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND EXTOUCH AND X(1)-CROSSPEDAL-OF-X(37)

Barycentrics    2*a^5+4*a^3*b*c-a^4*(b+c)+2*a^2*(b-c)^2*(b+c)-(b-c)^2*(b+c)^3-2*a*(b^2-c^2)^2 : :
X(64701) = -3*X[2]+X[64700]

X(64701) lies on these lines: {2, 64700}, {3, 5257}, {4, 9}, {5, 5750}, {6, 946}, {20, 5296}, {30, 64125}, {37, 515}, {44, 18483}, {45, 31673}, {57, 24213}, {72, 29311}, {115, 117}, {142, 64122}, {198, 1012}, {219, 21068}, {222, 226}, {225, 46011}, {329, 4416}, {346, 59387}, {355, 2321}, {379, 25019}, {381, 50115}, {391, 962}, {442, 50035}, {511, 5777}, {517, 3686}, {527, 36728}, {546, 29085}, {572, 1125}, {579, 64001}, {604, 44675}, {610, 6847}, {894, 7384}, {944, 3247}, {948, 41010}, {950, 5724}, {971, 50658}, {975, 991}, {1100, 13464}, {1210, 2285}, {1213, 6684}, {1400, 1765}, {1449, 5603}, {1699, 1743}, {1742, 1750}, {1746, 40940}, {1777, 2199}, {1864, 21746}, {1903, 43724}, {2050, 3452}, {2171, 64163}, {2178, 5450}, {2182, 6831}, {2260, 58036}, {2262, 12672}, {2268, 13411}, {2269, 10624}, {2325, 18480}, {2348, 7965}, {2807, 9119}, {2808, 58554}, {2956, 9612}, {3008, 12610}, {3073, 4264}, {3091, 5749}, {3149, 54322}, {3330, 51759}, {3707, 12699}, {3713, 21075}, {3723, 13607}, {3731, 5691}, {3817, 29635}, {3965, 63146}, {3986, 4297}, {4007, 59388}, {4029, 18525}, {4034, 12245}, {4058, 38155}, {4148, 9525}, {4254, 11496}, {4270, 37529}, {4357, 6996}, {4384, 64694}, {4700, 22791}, {5120, 22753}, {5292, 5715}, {5307, 64708}, {5356, 10265}, {5393, 30324}, {5405, 30325}, {5720, 50656}, {5788, 5812}, {5798, 29307}, {5839, 7982}, {5881, 17314}, {5882, 16777}, {5927, 29353}, {6245, 54405}, {6260, 34261}, {6737, 21078}, {6796, 54285}, {6913, 31394}, {6999, 17260}, {7377, 17353}, {7397, 17306}, {7406, 10444}, {7580, 41430}, {8227, 63055}, {8232, 64702}, {8545, 21279}, {8557, 26332}, {8727, 40869}, {9778, 62608}, {9956, 59680}, {10175, 17303}, {10436, 36662}, {11362, 17275}, {11522, 16667}, {12512, 37508}, {12527, 21061}, {12616, 24005}, {13405, 55100}, {13442, 16601}, {16972, 39870}, {17248, 37416}, {17281, 50796}, {17299, 47745}, {17330, 28194}, {17362, 28234}, {17733, 34379}, {17770, 27871}, {19868, 63968}, {20623, 42425}, {21090, 59728}, {21239, 44356}, {24224, 52819}, {24275, 56959}, {25023, 37233}, {26118, 40131}, {27508, 37434}, {28244, 62371}, {29207, 64174}, {29649, 59687}, {31162, 37654}, {31397, 54359}, {31730, 37499}, {36694, 38150}, {36731, 60986}, {39898, 51194}, {41007, 43035}, {44424, 53413}, {46835, 59644}, {47299, 63430}, {48878, 54433}, {48938, 49781}, {50650, 64570}, {55432, 63989}

X(64701) = midpoint of X(i) and X(j) for these {i,j}: {4416, 10446}
X(64701) = reflection of X(i) in X(j) for these {i,j}: {3664, 24220}
X(64701) = complement of X(64700)
X(64701) = pole of line {181, 1864} with respect to the Feuerbach hyperbola
X(64701) = pole of line {515, 1834} with respect to the Kiepert hyperbola
X(64701) = pole of line {3239, 21186} with respect to the Steiner inellipse
X(64701) = pole of line {56, 4000} with respect to the dual conic of Yff parabola
X(64701) = X(216)-of-2nd-extouch triangle
X(64701) = intersection, other than A, B, C, of circumconics {{A, B, C, X(40), X(43724)}}, {{A, B, C, X(222), X(573)}}, {{A, B, C, X(281), X(13478)}}, {{A, B, C, X(1826), X(40160)}}, {{A, B, C, X(10445), X(40444)}}
X(64701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 9, 10445}, {5, 64121, 5750}, {19, 20262, 8074}, {1766, 5816, 10}, {7406, 17257, 10444}

X(64702) = ORTHOLOGY CENTER OF THESE TRIANGLES: HONSBERGER AND X(1)-CROSSPEDAL-OF-X(37)

Barycentrics    2*a^4-a^3*(b+c)+a*(b-c)^2*(b+c)-(b-c)^2*(b^2+c^2)-a^2*(b^2+4*b*c+c^2) : :
X(64702) = -X[17363]+3*X[27484]

X(64702) lies on these lines: {1, 7}, {2, 5838}, {3, 53597}, {9, 69}, {37, 5845}, {55, 9436}, {57, 14548}, {75, 5853}, {85, 950}, {86, 142}, {144, 17261}, {150, 31397}, {226, 4872}, {304, 34282}, {319, 24393}, {348, 3601}, {497, 40719}, {511, 5728}, {518, 3688}, {527, 4664}, {528, 50116}, {573, 1445}, {894, 20533}, {954, 41004}, {1001, 4357}, {1100, 51150}, {1429, 38855}, {1439, 50658}, {1447, 11019}, {1449, 59405}, {1565, 24929}, {1697, 6604}, {1890, 40983}, {1959, 60979}, {2082, 26101}, {2280, 51400}, {2550, 10436}, {3008, 16779}, {3059, 64007}, {3212, 6738}, {3303, 30617}, {3486, 9312}, {3598, 10580}, {3665, 37080}, {3673, 63999}, {3687, 45962}, {3875, 49771}, {4056, 13407}, {4059, 6284}, {4251, 34847}, {4262, 51775}, {4644, 41325}, {4648, 5819}, {4675, 62383}, {4851, 50995}, {4911, 21620}, {5223, 34379}, {5224, 6666}, {5232, 17284}, {5287, 36850}, {5572, 21746}, {5686, 32099}, {5736, 21617}, {5740, 61016}, {5795, 16284}, {5809, 48878}, {5850, 49520}, {6172, 29573}, {6173, 63110}, {6629, 51290}, {6744, 10521}, {7146, 52819}, {7179, 13405}, {7181, 37600}, {7198, 17609}, {7278, 45287}, {7671, 29353}, {7672, 29311}, {7676, 40910}, {7987, 17081}, {8232, 64701}, {9581, 52422}, {10384, 63152}, {10950, 25719}, {11495, 37580}, {12053, 55082}, {12527, 36854}, {13411, 17181}, {14100, 39775}, {15310, 63972}, {15589, 30567}, {15936, 60932}, {16593, 17353}, {16782, 28350}, {17060, 25964}, {17185, 30941}, {17243, 51144}, {17270, 38057}, {17271, 60986}, {17274, 47357}, {17321, 38316}, {17331, 29579}, {17363, 27484}, {17742, 60949}, {17770, 51090}, {20059, 29585}, {20195, 63014}, {21285, 24987}, {21296, 52653}, {24203, 63993}, {24701, 48902}, {25521, 40963}, {25590, 36479}, {25723, 34471}, {26626, 62778}, {26806, 41845}, {29571, 52084}, {29583, 61006}, {29598, 60996}, {29601, 60942}, {29602, 60957}, {29633, 38204}, {29637, 38059}, {30628, 64709}, {30946, 40998}, {30963, 32023}, {31394, 42884}, {33159, 38194}, {33949, 63274}, {41311, 51151}, {41313, 50997}, {41712, 58800}, {41826, 54392}, {49509, 49776}, {49768, 53598}, {50133, 60927}, {52769, 53596}, {54404, 60974}, {62697, 64162}

X(64702) = midpoint of X(i) and X(j) for these {i,j}: {144, 17364}, {14100, 49537}, {30628, 64709}, {50133, 60927}
X(64702) = reflection of X(i) in X(j) for these {i,j}: {7, 3664}, {3059, 64007}, {4416, 9}, {21746, 5572}
X(64702) = pole of line {514, 4435} with respect to the incircle
X(64702) = pole of line {354, 9436} with respect to the Feuerbach hyperbola
X(64702) = pole of line {672, 2328} with respect to the Stammler hyperbola
X(64702) = pole of line {4025, 48242} with respect to the Steiner circumellipse
X(64702) = pole of line {4458, 7658} with respect to the Steiner inellipse
X(64702) = pole of line {3732, 54440} with respect to the Yff parabola
X(64702) = pole of line {1043, 3912} with respect to the Wallace hyperbola
X(64702) = pole of line {7, 238} with respect to the dual conic of Yff parabola
X(64702) = X(216)-of-Honsberger triangle
X(64702) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(58004)}}, {{A, B, C, X(9), X(2263)}}, {{A, B, C, X(69), X(23603)}}, {{A, B, C, X(269), X(39273)}}, {{A, B, C, X(284), X(1458)}}, {{A, B, C, X(662), X(41353)}}, {{A, B, C, X(673), X(3668)}}, {{A, B, C, X(1042), X(1438)}}, {{A, B, C, X(2346), X(4318)}}, {{A, B, C, X(3912), X(16054)}}, {{A, B, C, X(4327), X(10390)}}, {{A, B, C, X(31637), X(56382)}}
X(64702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17170, 3674}, {7, 14189, 3668}, {7, 8236, 3672}, {142, 16503, 17023}, {516, 3664, 7}, {1001, 47595, 4357}, {4872, 14828, 226}

X(64703) = ORTHOLOGY CENTER OF THESE TRIANGLES: INCIRCLE-CIRCLES AND X(1)-CROSSPEDAL-OF-X(56)

Barycentrics    2*a^4-3*a^3*(b+c)+3*a*(b-c)^2*(b+c)+a^2*(-3*b^2+14*b*c-3*c^2)+(b^2-c^2)^2 : :
X(64703) = -7*X[3622]+3*X[35262], -X[4848]+3*X[10072], 3*X[11238]+X[37738], 3*X[11240]+X[11682], -5*X[17609]+X[64704]

X(64703) lies on these lines: {1, 4}, {3, 4342}, {8, 25522}, {10, 10912}, {35, 50828}, {40, 5265}, {56, 28194}, {145, 26129}, {496, 519}, {516, 24928}, {517, 34753}, {527, 42886}, {551, 3295}, {631, 9819}, {938, 16200}, {962, 61762}, {997, 21627}, {999, 4301}, {1000, 1698}, {1071, 10866}, {1125, 1387}, {1210, 2098}, {1319, 10624}, {1320, 24982}, {1376, 64767}, {1385, 10386}, {1388, 4304}, {1420, 30305}, {1482, 11019}, {1483, 18527}, {1697, 10165}, {2099, 17706}, {2800, 50196}, {3057, 5433}, {3086, 7962}, {3244, 5722}, {3333, 63985}, {3445, 24171}, {3555, 12059}, {3576, 9785}, {3600, 31162}, {3601, 11023}, {3616, 31393}, {3622, 35262}, {3635, 5087}, {3636, 12436}, {3656, 3671}, {3679, 47743}, {3746, 10090}, {3816, 33895}, {3847, 32537}, {3880, 6700}, {3884, 5745}, {3895, 59587}, {3911, 5697}, {3947, 18493}, {4292, 20323}, {4294, 51705}, {4298, 22791}, {4308, 41869}, {4311, 12701}, {4314, 10246}, {4315, 12699}, {4345, 7982}, {4701, 11545}, {4848, 10072}, {4861, 26127}, {5048, 37722}, {5049, 12563}, {5126, 12512}, {5261, 38021}, {5274, 5881}, {5330, 26015}, {5703, 61275}, {5704, 63143}, {5734, 11529}, {5795, 22837}, {5818, 50444}, {5837, 45700}, {5840, 15172}, {5853, 30144}, {5880, 30331}, {5901, 13405}, {5919, 13411}, {6001, 16215}, {6049, 50811}, {6361, 13462}, {6705, 17622}, {6738, 10222}, {6744, 50194}, {6767, 11499}, {7743, 19925}, {8227, 18220}, {9581, 47745}, {9589, 53058}, {9955, 51782}, {10039, 10172}, {10175, 50443}, {10589, 31399}, {10591, 37709}, {11036, 63984}, {11041, 16189}, {11236, 37739}, {11238, 37738}, {11240, 11682}, {11260, 12572}, {11376, 31397}, {11525, 56038}, {12433, 33179}, {12577, 39542}, {12640, 26364}, {12653, 44848}, {12654, 46947}, {12675, 46681}, {12688, 17624}, {12735, 38757}, {12915, 45776}, {13271, 17647}, {14028, 24167}, {15170, 51103}, {15171, 25405}, {15325, 43174}, {15829, 34625}, {15845, 63964}, {16137, 63972}, {17609, 64704}, {17642, 31806}, {18240, 34339}, {18481, 51783}, {21075, 36846}, {21669, 60961}, {23537, 47622}, {24927, 64138}, {25055, 30337}, {28228, 37582}, {30283, 54227}, {30960, 42057}, {38460, 41012}, {49600, 57284}, {51423, 62837}, {59572, 64202}, {63774, 63997}

X(64703) = midpoint of X(i) and X(j) for these {i,j}: {1, 12053}, {1210, 2098}, {3555, 12059}, {4301, 63983}, {4311, 12701}, {4848, 30323}, {21075, 36846}
X(64703) = reflection of X(i) in X(j) for these {i,j}: {63990, 1125}
X(64703) = pole of line {65, 17624} with respect to the Feuerbach hyperbola
X(64703) = pole of line {14837, 21222} with respect to the Steiner inellipse
X(64703) = pole of line {57, 51415} with respect to the dual conic of Yff parabola
X(64703) = X(1092)-of-incircle-circles triangle
X(64703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11522, 1056}, {1, 12053, 515}, {1, 30384, 10106}, {1, 497, 5882}, {1, 5603, 21620}, {1, 950, 13607}, {1, 9614, 3476}, {946, 5882, 6256}, {1125, 2802, 63990}, {1210, 2098, 28234}, {1387, 9957, 1125}, {1420, 30305, 31730}, {3057, 44675, 6684}, {3086, 7962, 11362}, {3476, 9614, 31673}, {3656, 7373, 3671}, {4294, 63208, 51705}, {4311, 12701, 28150}, {4345, 14986, 7982}, {5048, 37722, 64163}, {5901, 31792, 13405}, {10072, 30323, 4848}, {10106, 30384, 18483}, {10591, 37709, 50796}, {22791, 51788, 4298}

X(64704) = ORTHOLOGY CENTER OF THESE TRIANGLES: URSA-MINOR AND X(1)-CROSSPEDAL-OF-X(56)

Barycentrics    a*(-(a^4*(b-c)^2)+a^5*(b+c)-2*a^3*(b-c)^2*(b+c)+a*(b-c)^4*(b+c)-(b^2-c^2)^2*(b^2+c^2)+2*a^2*(b-c)^2*(b^2+b*c+c^2)) : :
X(64704) = -3*X[210]+2*X[12059], -4*X[3825]+5*X[5439], -3*X[10072]+4*X[58573], -5*X[17609]+4*X[64703], -3*X[17728]+2*X[64131]

X(64704) lies on circumconic {{A, B, C, X(5553), X(43724)}} and on these lines: {1, 1406}, {3, 64041}, {4, 5553}, {11, 6245}, {20, 64043}, {30, 64045}, {36, 5887}, {46, 912}, {55, 9943}, {56, 6001}, {57, 1858}, {65, 515}, {72, 1155}, {84, 22760}, {210, 12059}, {354, 3671}, {392, 5267}, {497, 9961}, {498, 40296}, {499, 31937}, {513, 1828}, {516, 64046}, {517, 4299}, {518, 8544}, {942, 1479}, {960, 4652}, {962, 18839}, {971, 1837}, {1042, 7004}, {1044, 37591}, {1158, 37579}, {1210, 1898}, {1319, 5450}, {1388, 45776}, {1407, 1854}, {1464, 17102}, {1466, 9942}, {1467, 7992}, {1470, 6261}, {1478, 34339}, {1490, 11502}, {1709, 34489}, {1737, 40263}, {1768, 37583}, {1770, 5840}, {1788, 12528}, {1872, 31849}, {2099, 12675}, {2292, 22053}, {2635, 24443}, {2646, 10167}, {2771, 10081}, {2800, 4311}, {2801, 4848}, {2802, 3555}, {3057, 4297}, {3146, 18419}, {3189, 3474}, {3304, 63994}, {3339, 61663}, {3340, 9845}, {3359, 11501}, {3486, 11220}, {3660, 9856}, {3745, 35672}, {3784, 41600}, {3812, 10895}, {3825, 5439}, {3911, 31803}, {4293, 64021}, {4295, 12116}, {4301, 5083}, {4306, 8758}, {4325, 11571}, {5122, 5694}, {5128, 5904}, {5172, 64118}, {5219, 30290}, {5221, 44547}, {5252, 31788}, {5570, 12699}, {5693, 15803}, {5720, 59336}, {5728, 17637}, {5777, 24914}, {5784, 21677}, {5794, 17616}, {5902, 9579}, {5903, 61296}, {5927, 17606}, {6260, 10958}, {6848, 12666}, {6958, 18856}, {7355, 40959}, {7686, 12943}, {8581, 15888}, {8614, 64722}, {9612, 15016}, {9940, 11375}, {10052, 37826}, {10072, 58573}, {10123, 47319}, {10178, 63756}, {10202, 12047}, {10391, 63984}, {10404, 50195}, {10483, 53615}, {10944, 16004}, {10966, 64150}, {11509, 18446}, {11575, 31821}, {12136, 51399}, {12514, 37578}, {12520, 26357}, {12529, 24477}, {12565, 54408}, {12664, 57285}, {12701, 50196}, {12736, 31673}, {12831, 21077}, {12832, 41560}, {12953, 15726}, {13601, 37740}, {13750, 57282}, {14110, 15326}, {14872, 40663}, {15104, 41348}, {17609, 64703}, {17615, 37828}, {17646, 24390}, {17654, 18976}, {17728, 64131}, {18391, 64358}, {18518, 36279}, {20420, 24465}, {23154, 52359}, {24467, 59317}, {26201, 50194}, {26892, 44545}, {31837, 58887}, {33178, 34043}, {34471, 58567}, {37562, 45287}, {40272, 41869}, {40293, 45770}, {57277, 64057}, {58637, 63212}

X(64704) = midpoint of X(i) and X(j) for these {i,j}: {15071, 63988}
X(64704) = reflection of X(i) in X(j) for these {i,j}: {56, 64132}, {72, 25440}, {1479, 942}, {1898, 1210}, {3057, 63987}, {12059, 63990}, {12688, 63989}, {12701, 50196}, {41538, 46}, {63985, 9943}, {64042, 56}
X(64704) = pole of line {5101, 16228} with respect to the Fuhrmann circle
X(64704) = pole of line {1459, 9001} with respect to the incircle
X(64704) = pole of line {946, 999} with respect to the Feuerbach hyperbola
X(64704) = pole of line {9001, 21173} with respect to the Suppa-Cucoanes circle
X(64704) = X(1092)-of-Ursa-minor triangle
X(64704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {46, 912, 41538}, {56, 6001, 64042}, {57, 15071, 1858}, {65, 12680, 10950}, {65, 63995, 7354}, {1770, 11570, 24474}, {3057, 5918, 15338}, {4292, 5884, 65}, {4293, 64021, 64721}, {6001, 64132, 56}, {10167, 12709, 2646}, {15326, 45288, 14110}

X(64705) = ORTHOLOGY CENTER OF THESE TRIANGLES: ASCELLA AND X(1)-CROSSPEDAL-OF-X(57)

Barycentrics    2*a^2*(b-c)^4+a^5*(b+c)+(b-c)^4*(b+c)^2+a^4*(-3*b^2+10*b*c-3*c^2)+2*a^3*(b^3-3*b^2*c-3*b*c^2+c^3)-a*(b-c)^2*(3*b^3+b^2*c+b*c^2+3*c^3) : :
X(64705) = -3*X[2]+X[1750], -3*X[15064]+4*X[18227], -X[50696]+5*X[62773]

X(64705) lies on these lines: {2, 1750}, {3, 10}, {4, 5437}, {5, 10156}, {11, 5918}, {20, 1210}, {30, 7682}, {40, 24477}, {55, 43175}, {57, 497}, {84, 6865}, {142, 1538}, {165, 4847}, {214, 64310}, {226, 10167}, {329, 30304}, {404, 64707}, {443, 19925}, {474, 63998}, {519, 5768}, {528, 13226}, {551, 18443}, {579, 10443}, {610, 53579}, {908, 11220}, {936, 9799}, {942, 4301}, {944, 3158}, {946, 3742}, {950, 1466}, {960, 9948}, {971, 3452}, {990, 39595}, {1040, 34050}, {1125, 6847}, {1447, 24213}, {1479, 64658}, {1490, 6700}, {1699, 9776}, {1709, 40998}, {1742, 24239}, {2095, 28194}, {2478, 63984}, {2551, 10864}, {2801, 21060}, {2886, 10178}, {2951, 8732}, {3085, 64679}, {3086, 12565}, {3244, 37531}, {3306, 10431}, {3358, 51090}, {3476, 3601}, {3522, 6734}, {3576, 6935}, {3587, 5770}, {3634, 37407}, {3671, 58626}, {3741, 10856}, {3840, 21629}, {3846, 59688}, {3880, 24391}, {3911, 7580}, {3928, 5759}, {4292, 6836}, {4304, 6909}, {4744, 24474}, {5273, 21153}, {5274, 64696}, {5281, 5731}, {5316, 5927}, {5325, 31658}, {5393, 31564}, {5405, 31563}, {5438, 64144}, {5493, 5709}, {5542, 11018}, {5657, 51781}, {5658, 30827}, {5691, 6904}, {5705, 37108}, {5717, 37501}, {5735, 21454}, {5817, 51780}, {5837, 33899}, {5853, 6244}, {6260, 6922}, {6692, 19541}, {6824, 19862}, {6827, 7171}, {6851, 26333}, {6857, 12617}, {6890, 10884}, {6891, 41854}, {6899, 63399}, {6905, 61115}, {6987, 52027}, {6989, 51073}, {7004, 64708}, {7411, 59491}, {7989, 37436}, {7994, 36845}, {8568, 44424}, {9614, 11023}, {9778, 26015}, {9842, 17527}, {9942, 21616}, {9961, 41012}, {10085, 12527}, {10171, 41867}, {10265, 38759}, {10310, 64117}, {10383, 13405}, {10445, 17754}, {10580, 43166}, {10624, 63985}, {10916, 12512}, {11219, 41853}, {11372, 26105}, {11495, 24389}, {11496, 51724}, {12053, 17626}, {12437, 38455}, {12680, 21075}, {13243, 17781}, {15064, 18227}, {15841, 60945}, {18228, 64197}, {20330, 58615}, {21151, 25525}, {21164, 28164}, {21620, 58567}, {21627, 31798}, {23512, 62774}, {24175, 53599}, {24392, 35514}, {24982, 37267}, {25006, 64108}, {28452, 50862}, {28609, 36996}, {30265, 40940}, {31424, 37423}, {31445, 61556}, {31673, 37281}, {31730, 37623}, {34742, 37428}, {35977, 44425}, {37276, 39531}, {37363, 64113}, {37533, 51071}, {37551, 43174}, {40249, 54198}, {44675, 64150}, {47621, 50114}, {50696, 62773}, {63430, 64111}, {63999, 64074}, {64077, 64124}

X(64705) = midpoint of X(i) and X(j) for these {i,j}: {4, 58808}, {20, 3586}, {329, 30304}, {497, 10860}, {1750, 10430}, {5768, 6282}, {6827, 7171}, {7994, 36845}, {63430, 64111}
X(64705) = reflection of X(i) in X(j) for these {i,j}: {3452, 37364}, {4297, 63991}, {4301, 63993}, {19541, 6692}, {51118, 26333}, {59687, 3452}, {63137, 43174}, {63992, 1125}
X(64705) = complement of X(1750)
X(64705) = X(i)-complementary conjugate of X(j) for these {i, j}: {36622, 2886}, {38268, 5}
X(64705) = pole of line {44448, 47808} with respect to the orthoptic circle of the Steiner Inellipse
X(64705) = pole of line {8581, 64042} with respect to the Feuerbach hyperbola
X(64705) = pole of line {948, 3772} with respect to the dual conic of Yff parabola
X(64705) = X(394)-of-Ascella triangle
X(64705) = X(1750)-of-medial triangle
X(64705) = X(6515)-of-Wasat triangle
X(64705) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 18339, 58808}
X(64705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10430, 1750}, {3, 5745, 10164}, {3, 5787, 57284}, {3, 64706, 4297}, {4, 37526, 12436}, {142, 8727, 3817}, {226, 10167, 43177}, {497, 10860, 516}, {908, 11220, 41561}, {971, 3452, 59687}, {1040, 34050, 59645}, {1699, 11407, 9776}, {6847, 8726, 1125}, {6851, 37534, 64001}, {6851, 64001, 51118}, {6890, 10884, 13411}, {6899, 63399, 64004}, {8727, 11227, 142}, {10167, 37374, 226}, {20205, 34822, 10}, {37533, 64323, 51071}

X(64706) = ORTHOLOGY CENTER OF THESE TRIANGLES: ASCELLA AND X(1)-CROSSPEDAL-OF-X(65)

Barycentrics    2*a^7-3*a^6*(b+c)-a^2*(b-c)^4*(b+c)-(b-c)^4*(b+c)^3+2*a*(b^2-c^2)^2*(b^2+c^2)-2*a^5*(b^2+4*b*c+c^2)+a^4*(5*b^3-b^2*c-b*c^2+5*c^3)-2*a^3*(b^4-4*b^3*c-2*b^2*c^2-4*b*c^3+c^4) : :
X(64706) = -3*X[2]+X[63998], -3*X[165]+X[63146], -3*X[553]+X[64003], -X[4292]+3*X[10167], 3*X[5918]+X[6284], 3*X[11220]+X[64002], X[11827]+3*X[63432], -X[12688]+3*X[40998]

X(64706) lies on circumconic {{A, B, C, X(41904), X(57284)}} and on these lines: {1, 7365}, {2, 63998}, {3, 10}, {4, 142}, {8, 37551}, {9, 9799}, {20, 57}, {30, 5806}, {40, 5768}, {84, 6987}, {165, 63146}, {226, 6836}, {388, 10383}, {411, 3911}, {443, 5691}, {452, 10430}, {497, 1467}, {516, 942}, {519, 31793}, {527, 1071}, {550, 37623}, {553, 64003}, {610, 6554}, {936, 64144}, {944, 6282}, {946, 6851}, {962, 11518}, {971, 12572}, {991, 5717}, {1001, 21628}, {1040, 5930}, {1125, 8727}, {1210, 7580}, {1446, 18650}, {1482, 64323}, {1490, 3452}, {1750, 5084}, {1766, 21096}, {1770, 30274}, {1817, 26001}, {2551, 63981}, {2784, 52822}, {3091, 41867}, {3146, 9776}, {3149, 6692}, {3295, 43175}, {3306, 50695}, {3358, 9948}, {3522, 5744}, {3576, 6847}, {3587, 11362}, {3601, 5731}, {3673, 64700}, {3833, 11227}, {3946, 30265}, {4219, 49542}, {4292, 10167}, {4294, 10860}, {4298, 11018}, {4301, 15934}, {4304, 37022}, {4314, 64074}, {4339, 35658}, {4757, 28228}, {4847, 5584}, {5129, 36991}, {5249, 6895}, {5436, 37434}, {5437, 50700}, {5438, 54051}, {5587, 37407}, {5698, 7992}, {5709, 31730}, {5759, 54422}, {5771, 31663}, {5805, 43182}, {5882, 37531}, {5918, 6284}, {6223, 52457}, {6244, 64117}, {6260, 6827}, {6261, 64310}, {6700, 37364}, {6701, 12571}, {6734, 7411}, {6738, 37544}, {6743, 58637}, {6745, 50031}, {6824, 10165}, {6826, 31673}, {6831, 58463}, {6857, 7987}, {6868, 7171}, {6869, 37534}, {6872, 63984}, {6899, 18446}, {6916, 64261}, {6922, 58461}, {6926, 52026}, {6989, 10175}, {7354, 17603}, {7415, 64582}, {7682, 37411}, {8582, 37270}, {8728, 19925}, {9121, 53996}, {9581, 37421}, {9843, 19541}, {9942, 31789}, {9960, 61002}, {10202, 28150}, {10268, 14647}, {10431, 54392}, {10454, 10856}, {10572, 15803}, {10916, 12511}, {10993, 46684}, {11019, 64077}, {11108, 63970}, {11220, 64002}, {11827, 63432}, {12053, 34489}, {12512, 64128}, {12527, 12680}, {12545, 35612}, {12547, 24705}, {12617, 52769}, {12649, 63141}, {12669, 61003}, {12688, 40998}, {13151, 51717}, {13226, 38759}, {13411, 37374}, {13464, 37615}, {13607, 37533}, {15852, 37597}, {16388, 18589}, {17612, 64000}, {18444, 63274}, {18483, 55108}, {22053, 40950}, {24474, 28194}, {24703, 54227}, {24982, 35977}, {25011, 35985}, {28160, 37281}, {28234, 37585}, {28849, 35633}, {30282, 31452}, {34619, 50811}, {34707, 50808}, {37523, 40960}, {37526, 50701}, {41561, 58798}, {41869, 63971}, {43177, 57282}, {50528, 63989}, {52027, 59345}, {52819, 62864}, {54398, 59418}, {63399, 63438}

X(64706) = midpoint of X(i) and X(j) for these {i,j}: {20, 950}, {1071, 64004}, {12527, 12680}, {12669, 61003}, {63998, 64707}
X(64706) = reflection of X(i) in X(j) for these {i,j}: {4298, 58567}, {4301, 40270}, {6743, 58637}, {20420, 12436}, {57284, 3}, {64001, 9940}
X(64706) = complement of X(63998)
X(64706) = pole of line {2257, 3772} with respect to the dual conic of Yff parabola
X(64706) = X(5562)-of-Ascella triangle
X(64706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 64707, 63998}, {3, 515, 57284}, {3, 51755, 6684}, {3, 5787, 10}, {3, 5791, 10164}, {3, 6245, 5745}, {4, 8726, 142}, {30, 9940, 64001}, {40, 5768, 24391}, {944, 6282, 12437}, {1071, 37428, 64004}, {1750, 5084, 9842}, {4297, 64705, 3}, {5691, 10857, 443}, {6827, 41854, 6260}, {6836, 10884, 226}, {6851, 18443, 946}, {11227, 20420, 12436}, {12436, 28164, 20420}, {24391, 63413, 40}

X(64707) = ORTHOLOGY CENTER OF THESE TRIANGLES: CONWAY AND X(1)-CROSSPEDAL-OF-X(65)

Barycentrics    2*a^7-3*a^6*(b+c)-a^2*(b-c)^4*(b+c)-(b-c)^4*(b+c)^3+2*a*(b^2-c^2)^2*(b^2+b*c+c^2)-2*a^5*(b^2+3*b*c+c^2)+a^4*(5*b^3-b^2*c-b*c^2+5*c^3)-2*a^3*(b^4-2*b^3*c-2*b^2*c^2-2*b*c^3+c^4) : :
X(64707) = -3*X[2]+2*X[63998], -2*X[5777]+3*X[37428], -3*X[10167]+2*X[20420], -3*X[11112]+4*X[31805], -2*X[12528]+3*X[17781]

X(64707) lies on these lines: {1, 10431}, {2, 63998}, {3, 54357}, {4, 5249}, {7, 950}, {8, 20}, {10, 7411}, {21, 4297}, {27, 25935}, {30, 1071}, {57, 50695}, {78, 64144}, {79, 51118}, {85, 1891}, {142, 6894}, {224, 908}, {226, 6895}, {355, 37426}, {377, 5691}, {388, 7675}, {390, 9800}, {404, 64705}, {411, 6245}, {452, 36991}, {516, 3868}, {938, 50696}, {946, 16132}, {962, 11520}, {971, 60979}, {1004, 24982}, {1012, 10267}, {1076, 3465}, {1125, 10883}, {1210, 36002}, {1259, 37022}, {1385, 37447}, {1621, 21628}, {1750, 2478}, {1770, 18389}, {2829, 12671}, {3100, 5930}, {3305, 37423}, {3306, 50700}, {3434, 12565}, {3436, 63981}, {3522, 5273}, {3576, 6837}, {3651, 51755}, {3746, 4304}, {3912, 19645}, {3951, 5759}, {4190, 9841}, {4197, 19925}, {4292, 5902}, {4293, 62836}, {4298, 11020}, {4299, 62810}, {4301, 63159}, {4311, 62873}, {4313, 10106}, {4314, 62800}, {4316, 54432}, {4384, 37419}, {4855, 54051}, {4872, 56382}, {5047, 63970}, {5057, 54227}, {5059, 9965}, {5208, 12545}, {5250, 43161}, {5279, 51972}, {5584, 25006}, {5587, 37112}, {5720, 6899}, {5731, 37434}, {5761, 6851}, {5777, 37428}, {5784, 57288}, {5787, 6734}, {5795, 38200}, {5853, 20070}, {6253, 9943}, {6260, 6840}, {6284, 15726}, {6505, 9121}, {6604, 18655}, {6684, 37105}, {6835, 8726}, {6839, 31673}, {6869, 63399}, {6870, 25525}, {6884, 10165}, {6890, 52026}, {6925, 64261}, {6934, 7171}, {6936, 18540}, {6993, 18492}, {7354, 10391}, {7965, 51715}, {7992, 44447}, {8273, 24564}, {9812, 11036}, {9842, 37162}, {10085, 64075}, {10167, 20420}, {10444, 10452}, {10857, 37462}, {10863, 26127}, {11112, 31805}, {12527, 41228}, {12528, 17781}, {12625, 60990}, {12680, 16465}, {13739, 18653}, {15683, 28610}, {16192, 31446}, {16208, 34628}, {16547, 41006}, {16823, 37443}, {17616, 64000}, {17647, 31424}, {18219, 64679}, {20835, 24987}, {20880, 48890}, {22937, 44238}, {26015, 64077}, {27385, 37374}, {28160, 34339}, {28186, 31775}, {28208, 37429}, {30030, 50424}, {35976, 44425}, {37104, 49542}, {37108, 59387}, {37248, 63991}, {37300, 63983}, {37302, 60743}, {41012, 63988}, {41860, 43740}, {41869, 55109}, {48482, 50528}, {54356, 63395}, {54422, 64005}, {61024, 63413}, {63430, 64079}

X(64707) = reflection of X(i) in X(j) for these {i,j}: {3146, 950}, {6253, 9943}, {12528, 64004}, {57287, 20}, {59355, 4292}, {63998, 64706}, {64003, 1071}
X(64707) = anticomplement of X(63998)
X(64707) = perspector of circumconic {{A, B, C, X(44327), X(50392)}}
X(64707) = pole of line {2360, 59320} with respect to the Stammler hyperbola
X(64707) = X(5562)-of-Conway triangle
X(64707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 10884, 5249}, {8, 20, 63141}, {20, 10430, 63984}, {20, 515, 57287}, {20, 54398, 9778}, {20, 9799, 63}, {30, 1071, 64003}, {1490, 6836, 908}, {4292, 28164, 59355}, {4297, 12617, 15931}, {5691, 5732, 377}, {11220, 59355, 4292}, {18444, 37433, 946}

X(64708) = PERSPECTOR OF THESE TRIANGLES: X(1)-CROSSPEDAL-OF-X(72) AND ANTICEVIAN OF X(226)

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b+c)^2) : :
X(64708) = -3*X[2]+X[20223]

X(64708) lies on these lines: {1, 5758}, {2, 20223}, {7, 5287}, {9, 278}, {10, 201}, {33, 516}, {34, 12572}, {37, 226}, {40, 196}, {56, 34937}, {57, 1766}, {63, 34050}, {65, 4854}, {72, 5930}, {73, 3191}, {77, 5905}, {81, 41572}, {92, 20262}, {108, 5285}, {144, 18623}, {197, 2385}, {212, 23710}, {219, 34032}, {220, 34048}, {222, 527}, {223, 329}, {227, 21075}, {241, 3782}, {306, 4552}, {307, 321}, {515, 5928}, {517, 46017}, {553, 49747}, {612, 4331}, {651, 17781}, {664, 33066}, {908, 17080}, {1020, 36908}, {1038, 4292}, {1068, 55104}, {1076, 6245}, {1210, 37591}, {1323, 56848}, {1393, 9843}, {1400, 41342}, {1407, 17276}, {1441, 25013}, {1445, 19785}, {1465, 3452}, {1659, 31561}, {1708, 8557}, {1834, 4848}, {1848, 10445}, {1943, 4416}, {1999, 17950}, {2318, 4551}, {2321, 26942}, {2635, 59687}, {2654, 4301}, {3160, 64143}, {3175, 21096}, {3219, 37798}, {3305, 37800}, {3428, 51616}, {3553, 45126}, {3671, 37558}, {3677, 64747}, {3729, 56367}, {3745, 60883}, {3755, 41539}, {3772, 3911}, {3946, 52424}, {3955, 41349}, {3977, 28774}, {3995, 56559}, {4054, 52358}, {4296, 64002}, {4419, 7365}, {4654, 10481}, {5018, 33099}, {5228, 50068}, {5236, 25087}, {5307, 64701}, {5759, 7070}, {5762, 59611}, {6172, 18624}, {6357, 60942}, {6737, 56819}, {7004, 64705}, {7069, 63970}, {7078, 10402}, {7147, 21809}, {7288, 24171}, {7330, 53592}, {7580, 16870}, {9436, 20173}, {12527, 21147}, {13390, 31562}, {13411, 54320}, {15286, 47848}, {17022, 62780}, {17075, 28997}, {17086, 27064}, {17304, 56460}, {17355, 56366}, {17811, 61002}, {18228, 36640}, {18625, 29007}, {18750, 40880}, {20205, 64194}, {21621, 29069}, {21801, 37755}, {22053, 43177}, {22117, 59606}, {23703, 50808}, {24175, 31231}, {24248, 60786}, {24310, 56549}, {26006, 28950}, {26723, 37787}, {26724, 61016}, {26885, 56910}, {27540, 45738}, {28194, 60689}, {28739, 56082}, {30379, 33146}, {31142, 36636}, {33298, 42029}, {34033, 60905}, {34035, 60979}, {34036, 40998}, {37543, 52819}, {37544, 50067}, {39126, 62229}, {40960, 64750}, {42707, 57807}, {46974, 63438}, {50114, 52423}, {52408, 59647}, {53011, 61178}, {59613, 64065}, {60091, 60249}

X(64708) = complement of X(20223)
X(64708) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 285}, {21, 1436}, {27, 2188}, {28, 268}, {32, 57795}, {58, 282}, {60, 1903}, {81, 2192}, {84, 284}, {86, 7118}, {112, 61040}, {189, 2194}, {270, 41087}, {271, 1474}, {280, 1333}, {283, 7129}, {309, 57657}, {333, 2208}, {593, 53013}, {1014, 7367}, {1021, 8059}, {1172, 1433}, {1413, 2287}, {1422, 2328}, {1437, 7003}, {1444, 7154}, {1790, 7008}, {1812, 7151}, {2150, 39130}, {2185, 2357}, {2189, 52389}, {2193, 40836}, {2203, 44189}, {2206, 34404}, {2299, 41081}, {2332, 56972}, {3737, 36049}, {4183, 55117}, {4560, 32652}, {4636, 55242}, {6612, 56182}, {7054, 52384}, {7252, 13138}, {13853, 23609}, {21789, 37141}, {23189, 40117}, {40979, 57422}
X(64708) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 285}, {10, 282}, {37, 280}, {57, 81}, {226, 41081}, {281, 29}, {1214, 189}, {5514, 3737}, {6376, 57795}, {16596, 4560}, {24018, 16731}, {34591, 61040}, {36908, 1422}, {40586, 2192}, {40590, 84}, {40591, 268}, {40600, 7118}, {40603, 34404}, {40611, 1436}, {47345, 40836}, {51574, 271}, {55044, 1021}, {55063, 57081}, {56325, 39130}, {59608, 1440}, {61075, 7253}, {62564, 44189}, {62570, 309}, {62614, 57783}
X(64708) = X(i)-Ceva conjugate of X(j) for these {i, j}: {307, 10}, {321, 226}, {347, 227}, {40702, 57810}, {57810, 21075}
X(64708) = X(i)-cross conjugate of X(j) for these {i, j}: {21871, 21075}, {53009, 10}
X(64708) = pole of line {4077, 50332} with respect to the incircle
X(64708) = pole of line {3737, 17926} with respect to the polar circle
X(64708) = pole of line {226, 21933} with respect to the Kiepert hyperbola
X(64708) = pole of line {656, 59976} with respect to the Steiner inellipse
X(64708) = pole of line {15411, 57213} with respect to the dual conic of polar circle
X(64708) = pole of line {17880, 23978} with respect to the dual conic of Stammler hyperbola
X(64708) = pole of line {355, 388} with respect to the dual conic of Yff parabola
X(64708) = pole of line {1146, 7004} with respect to the dual conic of Wallace hyperbola
X(64708) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(37410)}}, {{A, B, C, X(10), X(40)}}, {{A, B, C, X(37), X(2324)}}, {{A, B, C, X(196), X(347)}}, {{A, B, C, X(208), X(223)}}, {{A, B, C, X(226), X(329)}}, {{A, B, C, X(306), X(51368)}}, {{A, B, C, X(307), X(40212)}}, {{A, B, C, X(860), X(1817)}}, {{A, B, C, X(1826), X(1901)}}, {{A, B, C, X(2321), X(8804)}}, {{A, B, C, X(4082), X(57049)}}, {{A, B, C, X(6354), X(56285)}}, {{A, B, C, X(6356), X(6358)}}, {{A, B, C, X(7080), X(60188)}}, {{A, B, C, X(8058), X(8680)}}, {{A, B, C, X(8822), X(41003)}}, {{A, B, C, X(17056), X(27398)}}, {{A, B, C, X(18591), X(40967)}}, {{A, B, C, X(36908), X(51365)}}, {{A, B, C, X(41083), X(55010)}}, {{A, B, C, X(48357), X(54668)}}
X(64708) = barycentric product X(i)*X(j) for these (i, j): {1, 57810}, {10, 347}, {12, 8822}, {37, 40702}, {196, 306}, {198, 349}, {221, 313}, {223, 321}, {226, 329}, {227, 75}, {307, 7952}, {322, 65}, {342, 72}, {348, 53009}, {1214, 64211}, {1231, 2331}, {1441, 40}, {1446, 2324}, {1817, 6358}, {2199, 27801}, {2360, 34388}, {3194, 57807}, {3209, 40071}, {3668, 7080}, {4554, 55212}, {4566, 8058}, {14256, 2321}, {14837, 4552}, {17896, 4551}, {20336, 208}, {21075, 7}, {21871, 85}, {26942, 41083}, {27398, 6354}, {30713, 6611}, {39130, 55015}, {40149, 64082}, {40701, 71}, {41013, 7013}, {47372, 52385}, {52607, 57245}, {53008, 57479}, {55116, 56382}, {55241, 57185}, {57118, 850}, {57809, 7078}
X(64708) = barycentric quotient X(i)/X(j) for these (i, j): {1, 285}, {10, 280}, {12, 39130}, {37, 282}, {40, 21}, {42, 2192}, {65, 84}, {71, 268}, {72, 271}, {73, 1433}, {75, 57795}, {181, 2357}, {196, 27}, {198, 284}, {201, 52389}, {208, 28}, {213, 7118}, {221, 58}, {223, 81}, {225, 40836}, {226, 189}, {227, 1}, {228, 2188}, {306, 44189}, {313, 57793}, {321, 34404}, {322, 314}, {329, 333}, {342, 286}, {347, 86}, {349, 44190}, {656, 61040}, {756, 53013}, {1020, 37141}, {1042, 1413}, {1214, 41081}, {1254, 52384}, {1334, 7367}, {1400, 1436}, {1402, 2208}, {1427, 1422}, {1439, 56972}, {1441, 309}, {1817, 2185}, {1824, 7008}, {1826, 7003}, {1880, 7129}, {2171, 1903}, {2187, 2194}, {2197, 41087}, {2199, 1333}, {2324, 2287}, {2331, 1172}, {2333, 7154}, {2360, 60}, {3194, 270}, {3195, 2299}, {3209, 1474}, {3668, 1440}, {4551, 13138}, {4552, 44327}, {4554, 55211}, {4559, 36049}, {4566, 53642}, {4848, 56940}, {5930, 41084}, {6129, 3737}, {6354, 8808}, {6611, 1412}, {7011, 1790}, {7013, 1444}, {7074, 2328}, {7078, 283}, {7080, 1043}, {7114, 1437}, {7952, 29}, {8058, 7253}, {8803, 8886}, {8822, 261}, {10397, 23090}, {14256, 1434}, {14298, 1021}, {14837, 4560}, {17896, 18155}, {20336, 57783}, {21075, 8}, {21871, 9}, {26942, 56944}, {27398, 7058}, {37755, 52037}, {38374, 17205}, {39130, 46355}, {40212, 1817}, {40663, 56939}, {40701, 44129}, {40702, 274}, {40971, 4183}, {41013, 7020}, {41083, 46103}, {41088, 52158}, {47372, 1896}, {52023, 13156}, {52373, 55117}, {52384, 1256}, {53008, 57492}, {53009, 281}, {53321, 8059}, {55015, 8822}, {55111, 2327}, {55116, 2322}, {55212, 650}, {55241, 4631}, {56382, 34400}, {57101, 57081}, {57118, 110}, {57185, 55242}, {57245, 15411}, {57285, 52571}, {57652, 7151}, {57810, 75}, {59935, 57215}, {62192, 6612}, {64082, 1812}, {64211, 31623}
X(64708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 57477, 34050}, {201, 225, 10}, {212, 23710, 59645}, {329, 347, 223}, {1076, 44706, 6245}, {1427, 4415, 226}, {21062, 22001, 8804}

X(64709) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-CONWAY AND X(1)-CROSSPEDAL-OF-X(75)

Barycentrics    a*(-(b^2*c^2)+a^2*(b^2+c^2)-a*(b^3+c^3)) : :
X(64709) = -3*X[2]+2*X[21746], -6*X[210]+5*X[17331], -5*X[3616]+4*X[39543], -4*X[3664]+3*X[3873], -3*X[3681]+2*X[4416], -5*X[3890]+4*X[63977], -5*X[4699]+4*X[17049], -3*X[17346]+4*X[22271], -5*X[17391]+4*X[64546], -9*X[63961]+8*X[63978]

X(64709) lies on these lines: {1, 28375}, {2, 21746}, {6, 33760}, {7, 62872}, {8, 511}, {10, 50585}, {37, 3809}, {42, 50584}, {43, 23659}, {51, 59296}, {63, 1742}, {69, 2876}, {72, 15310}, {75, 674}, {78, 6210}, {86, 64751}, {87, 20456}, {100, 573}, {144, 4499}, {145, 64006}, {192, 3688}, {210, 17331}, {219, 3573}, {239, 3056}, {256, 869}, {306, 25308}, {319, 9018}, {346, 3799}, {513, 17347}, {516, 3869}, {518, 17364}, {660, 50995}, {662, 1631}, {668, 25291}, {894, 3779}, {908, 45305}, {956, 48908}, {978, 50603}, {991, 2975}, {1150, 50646}, {1193, 50616}, {1278, 14839}, {1740, 3778}, {1964, 4443}, {2234, 4446}, {2293, 23407}, {2388, 25295}, {2979, 17135}, {3059, 43216}, {3060, 4651}, {3190, 11688}, {3240, 4263}, {3271, 17349}, {3293, 50592}, {3434, 10446}, {3436, 48878}, {3596, 21278}, {3616, 39543}, {3661, 17792}, {3664, 3873}, {3681, 4416}, {3685, 3781}, {3687, 25306}, {3696, 9047}, {3758, 22277}, {3786, 50295}, {3789, 17252}, {3792, 32941}, {3794, 33137}, {3868, 50307}, {3890, 63977}, {3912, 25279}, {3917, 10453}, {3948, 21299}, {3963, 24351}, {4067, 28508}, {4093, 4493}, {4195, 10822}, {4259, 5263}, {4307, 54383}, {4361, 25048}, {4389, 56537}, {4398, 64553}, {4511, 31394}, {4517, 17261}, {4553, 17233}, {4579, 12329}, {4645, 10477}, {4699, 17049}, {4787, 24478}, {4890, 29570}, {5080, 48938}, {5650, 30947}, {5687, 48875}, {5744, 50658}, {5904, 17770}, {5943, 26038}, {6646, 56542}, {7032, 24575}, {7186, 32853}, {7998, 29824}, {8679, 49450}, {9024, 17362}, {9025, 17363}, {9049, 49499}, {9052, 24349}, {9054, 17365}, {11680, 24220}, {11681, 48888}, {14923, 29311}, {16574, 35338}, {16885, 24482}, {17065, 23633}, {17202, 32773}, {17234, 57024}, {17272, 60929}, {17300, 35892}, {17346, 22271}, {17350, 20683}, {17367, 61034}, {17377, 44671}, {17379, 52020}, {17391, 64546}, {20012, 50577}, {20036, 50621}, {20245, 20556}, {20248, 53358}, {20358, 48627}, {20535, 52562}, {20670, 62989}, {20684, 21387}, {20961, 26037}, {21035, 24696}, {21755, 21787}, {23305, 37796}, {23638, 59295}, {24390, 48934}, {24599, 63523}, {25144, 29613}, {25505, 46898}, {26806, 64560}, {26893, 32932}, {29497, 52923}, {29628, 63522}, {30628, 64702}, {31737, 50633}, {48902, 52367}, {50579, 59302}, {50617, 59303}, {63961, 63978}

X(64709) = reflection of X(i) in X(j) for these {i,j}: {145, 64006}, {192, 3688}, {3868, 50307}, {17347, 64581}, {17364, 49537}, {21746, 64007}, {30628, 64702}
X(64709) = anticomplement of X(21746)
X(64709) = X(i)-Dao conjugate of X(j) for these {i, j}: {21746, 21746}
X(64709) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {3449, 192}, {40419, 8}, {63148, 7}, {63188, 145}
X(64709) = pole of line {52614, 57056} with respect to the Steiner circumellipse
X(64709) = pole of line {1626, 16876} with respect to the Wallace hyperbola
X(64709) = X(264)-of-inner-Conway triangle
X(64709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43, 50613, 23659}, {513, 64581, 17347}, {518, 49537, 17364}, {1740, 3778, 24598}, {2293, 28287, 23407}, {3688, 6007, 192}, {3869, 25722, 12530}, {21278, 53338, 3596}, {21746, 64007, 2}

X(64710) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND PAVLOV AND X(1)-CROSSPEDAL-OF-X(80)

Barycentrics    a^2*(b^4+c^4+a^3*(b+c)-a^2*(b^2+c^2)-a*(b^3+c^3)) : :

X(64710) lies on these lines: {1, 149}, {11, 3136}, {21, 45066}, {30, 12081}, {38, 17660}, {42, 81}, {48, 54065}, {55, 53324}, {58, 35204}, {73, 12739}, {80, 59305}, {104, 63291}, {110, 1283}, {119, 63318}, {214, 1193}, {238, 63917}, {244, 58591}, {323, 902}, {386, 15015}, {500, 2292}, {511, 3724}, {522, 12080}, {528, 37631}, {581, 6326}, {612, 5531}, {649, 38018}, {899, 1818}, {900, 14752}, {952, 5453}, {968, 64372}, {991, 1768}, {1064, 6265}, {1066, 63388}, {1156, 63384}, {1201, 12746}, {1317, 63295}, {1320, 63333}, {1458, 5083}, {1757, 56808}, {1862, 2356}, {2177, 13205}, {2254, 3722}, {2310, 34976}, {2340, 14740}, {2594, 41541}, {2610, 21341}, {2654, 12743}, {2667, 2805}, {2783, 63345}, {2800, 4300}, {2801, 3989}, {2802, 63354}, {2829, 63386}, {2831, 4137}, {3190, 32912}, {3682, 51506}, {3920, 5483}, {3938, 36482}, {4303, 11570}, {4337, 11571}, {4343, 63387}, {4511, 32843}, {4653, 46816}, {4883, 58611}, {5396, 22935}, {5492, 5495}, {5541, 63310}, {5840, 13408}, {5848, 63394}, {5854, 63415}, {5856, 63381}, {6154, 63401}, {6174, 61661}, {9024, 63359}, {9897, 30116}, {9978, 47625}, {10087, 54350}, {10090, 63340}, {10707, 63343}, {10738, 63323}, {10755, 63385}, {12331, 37698}, {13194, 63294}, {13199, 37529}, {13222, 63311}, {13228, 63312}, {13230, 63313}, {13235, 63315}, {13268, 63320}, {13269, 63321}, {13270, 63322}, {13271, 63324}, {13272, 63325}, {13273, 63326}, {13274, 63327}, {13278, 63341}, {13279, 63342}, {13922, 63336}, {13991, 63337}, {15792, 54078}, {16585, 46685}, {17018, 20095}, {19112, 63298}, {19113, 63299}, {20962, 58504}, {21283, 22837}, {21674, 54356}, {21805, 58663}, {22067, 62739}, {22560, 63316}, {22836, 31034}, {22938, 63317}, {25438, 63309}, {27627, 64012}, {28257, 58453}, {28352, 34123}, {30115, 41689}, {30950, 31272}, {31880, 49745}, {33814, 63307}, {34442, 54371}, {35882, 63330}, {35883, 63331}, {37558, 41558}, {40958, 64154}, {44307, 58683}, {48303, 62492}, {48533, 64354}, {48534, 64355}, {48680, 63296}, {48703, 63300}, {48704, 63301}, {48705, 63302}, {48706, 63303}, {48711, 63305}, {48712, 63306}, {48713, 63308}, {48714, 63328}, {48715, 63329}, {50317, 62354}, {53280, 53542}, {56878, 58285}, {60718, 61228}

X(64710) = reflection of X(i) in X(j) for these {i,j}: {63346, 5453}, {63365, 63370}
X(64710) = perspector of circumconic {{A, B, C, X(4584), X(39137)}}
X(64710) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4444, 672}
X(64710) = pole of line {20718, 55335} with respect to the Feuerbach hyperbola
X(64710) = pole of line {672, 5954} with respect to the Kiepert hyperbola
X(64710) = pole of line {238, 5127} with respect to the Stammler hyperbola
X(64710) = X(100)-of-2nd-Pavlov triangle
X(64710) = X(4647)-of-anti-inner-Garcia triangle
X(64710) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(149), X(8674)}}, {{A, B, C, X(291), X(5620)}}, {{A, B, C, X(3120), X(4570)}}, {{A, B, C, X(3446), X(33148)}}, {{A, B, C, X(11604), X(42552)}}, {{A, B, C, X(21907), X(37128)}}
X(64710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 61220, 3120}, {952, 5453, 63346}

X(64711) = ORTHOLOGY CENTER OF THESE TRIANGLES: MCCAY AND X(2)-CROSSPEDAL-OF-X(4)

Barycentrics    a^8+5*a^6*(b^2+c^2)+3*a^2*(b^2-c^2)^2*(b^2+c^2)-2*(b^2-c^2)^2*(b^4+c^4)-a^4*(7*b^4+6*b^2*c^2+7*c^4) : :
X(64711) = 2*X[5]+X[8721], 3*X[3545]+X[15428], -4*X[5171]+X[63938], 3*X[10304]+X[53016], 3*X[41134]+X[60140]

X(64711) lies on these lines: {2, 154}, {3, 114}, {4, 3815}, {5, 8721}, {6, 1513}, {20, 1007}, {30, 7618}, {98, 7607}, {132, 15274}, {140, 30794}, {147, 183}, {159, 61682}, {182, 37071}, {230, 6776}, {232, 37074}, {262, 14492}, {316, 54993}, {325, 1350}, {376, 22110}, {381, 11171}, {382, 58851}, {383, 41039}, {511, 9766}, {542, 7610}, {599, 6054}, {858, 59231}, {1080, 41038}, {1151, 6811}, {1152, 6813}, {1352, 15271}, {1499, 45681}, {1529, 42854}, {1656, 12054}, {2023, 11257}, {2782, 13085}, {2784, 49608}, {3054, 39874}, {3091, 63041}, {3146, 63077}, {3522, 7885}, {3524, 50571}, {3543, 63025}, {3545, 15428}, {3564, 8667}, {5023, 36998}, {5050, 52669}, {5094, 53267}, {5102, 41624}, {5116, 13860}, {5171, 63938}, {5188, 7776}, {5304, 12007}, {5306, 9752}, {5480, 7736}, {5868, 37463}, {5869, 37464}, {5921, 34229}, {5965, 63951}, {5984, 17004}, {5999, 8350}, {6114, 41041}, {6115, 41040}, {6194, 7788}, {6795, 36170}, {7000, 14230}, {7374, 14233}, {7608, 60326}, {7612, 60185}, {7735, 8550}, {7774, 11477}, {7777, 40236}, {7782, 8781}, {7792, 53093}, {7809, 22676}, {7866, 37479}, {7868, 37455}, {7887, 12203}, {7928, 15717}, {8547, 18122}, {8860, 11177}, {9300, 14853}, {9742, 62174}, {9748, 63024}, {9755, 35006}, {9770, 60658}, {9774, 22664}, {9924, 45198}, {10011, 48906}, {10304, 53016}, {10722, 44541}, {11151, 35955}, {11163, 54131}, {11168, 11180}, {11174, 13862}, {11287, 21163}, {11318, 36519}, {11331, 45031}, {13083, 41022}, {13084, 41023}, {13881, 14651}, {14458, 53108}, {14484, 60118}, {14880, 34127}, {14927, 34803}, {15576, 16318}, {16989, 55711}, {19161, 51412}, {19164, 61748}, {26864, 47200}, {30549, 40680}, {35901, 38975}, {36173, 59227}, {36751, 41761}, {36997, 37512}, {37242, 52771}, {37450, 53094}, {38072, 63101}, {38383, 44453}, {40824, 59548}, {41134, 60140}, {43118, 48467}, {43119, 48466}, {43537, 54921}, {43951, 54522}, {44377, 44882}, {45279, 52703}, {45510, 49325}, {45511, 49326}, {46264, 56370}, {47619, 51580}, {48881, 63098}, {50771, 63428}, {51212, 62988}, {51426, 52520}, {51872, 64653}, {53099, 54706}, {53104, 54851}, {54815, 60333}, {61684, 61737}

X(64711) = midpoint of X(i) and X(j) for these {i,j}: {2, 7710}, {8719, 53017}, {9770, 60658}, {15428, 46034}
X(64711) = reflection of X(i) in X(j) for these {i,j}: {7610, 40248}, {9756, 2}, {53017, 7694}
X(64711) = complement of X(53015)
X(64711) = pole of line {525, 1636} with respect to the orthoptic circle of the Steiner Inellipse
X(64711) = pole of line {7735, 13860} with respect to the Kiepert hyperbola
X(64711) = pole of line {35278, 61213} with respect to the Kiepert parabola
X(64711) = pole of line {1350, 37183} with respect to the Stammler hyperbola
X(64711) = X(5503)-of-McCay triangle
X(64711) = X(9756)-of-Gemini-107 triangle
X(64711) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {2, 7710, 34235}, {98, 1297, 9769}
X(64711) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(7607), X(57504)}}, {{A, B, C, X(9756), X(35140)}}, {{A, B, C, X(14494), X(42287)}}
X(64711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1503, 9756}, {2, 7710, 1503}, {3, 114, 7778}, {4, 63424, 44526}, {30, 7694, 53017}, {132, 45141, 15274}, {147, 183, 15069}, {325, 37182, 1350}, {1513, 9744, 6}, {3545, 15428, 46034}, {6776, 58883, 230}, {9749, 9750, 3}, {9752, 14912, 5306}, {13860, 43460, 36990}, {13860, 43461, 31489}, {14912, 60657, 9752}, {31489, 36990, 13860}, {37446, 39646, 13881}, {37637, 64080, 98}

X(64712) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(2)-CROSSPEDAL-OF-X(10) AND ANTI-ARTZT

Barycentrics    2*a^2-3*b^2-4*b*c-3*c^2-2*a*(b+c) : :
X(64712) = -5*X[3617]+X[4363], X[3632]+3*X[41312], X[4419]+7*X[4678], -X[4644]+3*X[10022], -X[4795]+5*X[51066], -5*X[4798]+9*X[19875], -11*X[46933]+3*X[63054]

X(64712) lies on these lines: {1, 25358}, {2, 4969}, {8, 4364}, {9, 48636}, {10, 524}, {37, 4478}, {42, 50158}, {45, 50097}, {86, 60710}, {141, 4384}, {190, 594}, {306, 49730}, {319, 1213}, {320, 49733}, {391, 17293}, {519, 4708}, {527, 4691}, {536, 3626}, {545, 3679}, {597, 17308}, {599, 34824}, {966, 4445}, {1086, 17271}, {1125, 4725}, {1211, 33133}, {1268, 20090}, {3008, 20582}, {3589, 3686}, {3617, 4363}, {3629, 17303}, {3630, 10436}, {3631, 3739}, {3632, 41312}, {3661, 4422}, {3664, 28633}, {3707, 17359}, {3775, 50023}, {3834, 50991}, {3879, 6707}, {3912, 31285}, {3943, 17256}, {4021, 4545}, {4026, 42334}, {4029, 50084}, {4034, 4657}, {4060, 4681}, {4357, 4399}, {4361, 5232}, {4371, 17323}, {4389, 50098}, {4393, 5224}, {4395, 17237}, {4405, 17301}, {4407, 28503}, {4409, 6646}, {4415, 41816}, {4416, 7227}, {4419, 4678}, {4440, 62225}, {4555, 18823}, {4644, 10022}, {4651, 25349}, {4662, 34377}, {4669, 28309}, {4675, 22165}, {4687, 29618}, {4688, 7238}, {4698, 29606}, {4700, 63124}, {4701, 28329}, {4715, 4745}, {4733, 33082}, {4739, 53598}, {4741, 49727}, {4746, 17133}, {4755, 49765}, {4759, 62467}, {4795, 51066}, {4798, 19875}, {4967, 7228}, {5257, 17372}, {5296, 17309}, {5564, 17246}, {5750, 32455}, {5839, 17327}, {5846, 36480}, {6329, 17385}, {6542, 31144}, {7263, 17272}, {7277, 28604}, {9055, 49457}, {15534, 61313}, {15593, 39570}, {15668, 32099}, {15985, 60737}, {16672, 50079}, {16831, 50076}, {17014, 25503}, {17023, 50082}, {17119, 49741}, {17228, 17337}, {17229, 63978}, {17238, 17366}, {17245, 17287}, {17248, 17388}, {17250, 17395}, {17253, 42696}, {17255, 32087}, {17259, 29627}, {17277, 29587}, {17281, 61343}, {17295, 29589}, {17321, 62224}, {17325, 50112}, {17328, 17334}, {17331, 17340}, {17333, 62228}, {17338, 48640}, {17343, 17365}, {17346, 17369}, {17348, 31191}, {17360, 17392}, {17363, 17398}, {17374, 24603}, {17397, 50077}, {17768, 50312}, {20055, 50113}, {21296, 28635}, {25350, 59296}, {28301, 51070}, {28653, 63401}, {29069, 61510}, {29571, 50081}, {29574, 52706}, {29603, 50131}, {29610, 62231}, {29612, 50132}, {29628, 48639}, {37654, 61344}, {40999, 63782}, {41311, 49770}, {44416, 49724}, {46933, 63054}, {49726, 54280}, {50180, 59306}, {50275, 56191}

X(64712) = midpoint of X(i) and X(j) for these {i,j}: {8, 4364}, {10, 4690}, {4643, 4665}
X(64712) = reflection of X(i) in X(j) for these {i,j}: {1, 25358}, {4472, 10}
X(64712) = pole of line {18004, 28179} with respect to the Steiner circumellipse
X(64712) = pole of line {4789, 23770} with respect to the Steiner inellipse
X(64712) = pole of line {4927, 28340} with respect to the Suppa-Cucoanes circle
X(64712) = X(4472)-of-outer-Garcia triangle
X(64712) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4590), X(51353)}}, {{A, B, C, X(35162), X(55949)}}
X(64712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 4364, 4971}, {8, 4748, 17318}, {10, 4690, 524}, {10, 524, 4472}, {141, 4384, 40480}, {190, 32025, 51353}, {319, 1213, 17390}, {594, 1654, 17332}, {966, 4445, 17243}, {1654, 32025, 594}, {1654, 51353, 190}, {3661, 17330, 4422}, {3679, 4643, 4665}, {3686, 17239, 3589}, {3912, 49731, 31285}, {3943, 17256, 49737}, {4643, 4665, 545}, {4651, 49717, 25349}, {4748, 17318, 4364}, {4967, 17344, 7228}, {5224, 17362, 17045}, {5564, 17252, 17246}, {17237, 50095, 4395}, {17250, 29617, 17395}, {17251, 17318, 4748}, {17256, 29615, 3943}, {17270, 17275, 141}, {17328, 48628, 17334}, {17346, 29593, 17369}, {17360, 29576, 17392}, {17374, 24603, 49738}, {25358, 28337, 1}, {49724, 56810, 44416}, {54280, 61321, 49726}

X(64713) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(6) AND X(2)-CROSSPEDAL-OF-X(39)

Barycentrics    a^2*(b^4+4*b^2*c^2+c^4+3*a^2*(b^2+c^2)) : :
X(64713) = -X[69]+5*X[7786], -X[76]+5*X[3618], X[1916]+3*X[5182], X[7976]+3*X[59406], -3*X[9466]+5*X[40332], -3*X[10519]+7*X[61132], X[11257]+3*X[14853], -X[12263]+3*X[38049], X[12782]+3*X[16475], -X[22486]+5*X[63127], -5*X[31239]+7*X[47355], X[32448]+3*X[59399] and many others

X(64713) lies on these lines: {2, 11175}, {3, 6}, {51, 1180}, {69, 7786}, {76, 3618}, {83, 12215}, {115, 53484}, {141, 6683}, {194, 33198}, {230, 58445}, {232, 30499}, {251, 22352}, {262, 3424}, {352, 39389}, {373, 9465}, {394, 39951}, {524, 10007}, {538, 597}, {542, 2023}, {625, 51848}, {698, 6329}, {732, 3589}, {736, 44380}, {1176, 59996}, {1194, 3124}, {1196, 6688}, {1285, 22676}, {1352, 7736}, {1386, 3997}, {1428, 5280}, {1506, 53475}, {1594, 51434}, {1843, 39575}, {1916, 5182}, {1976, 3108}, {2330, 5299}, {2548, 3818}, {2549, 48901}, {2782, 18583}, {2854, 46337}, {3009, 25100}, {3051, 3819}, {3117, 34236}, {3202, 64028}, {3231, 15082}, {3291, 63632}, {3501, 50629}, {3506, 14153}, {3564, 11272}, {3763, 7888}, {3767, 38317}, {3815, 24206}, {3917, 62991}, {3981, 58470}, {4048, 7804}, {5026, 42421}, {5103, 7861}, {5207, 7858}, {5254, 19130}, {5286, 6248}, {5304, 22712}, {5306, 10168}, {5359, 43650}, {5475, 48889}, {5476, 7739}, {5480, 15048}, {5650, 9463}, {5969, 36521}, {6034, 39593}, {6194, 63005}, {6782, 22691}, {6783, 22692}, {7709, 14482}, {7735, 15819}, {7737, 48898}, {7738, 31670}, {7745, 29012}, {7747, 29323}, {7748, 48895}, {7753, 11645}, {7757, 9741}, {7792, 51373}, {7805, 8177}, {7819, 41651}, {7827, 39266}, {7839, 56789}, {7889, 41756}, {7976, 59406}, {8369, 59552}, {8617, 62184}, {8743, 19124}, {9466, 40332}, {9606, 40107}, {9865, 10336}, {9969, 58486}, {10333, 12216}, {10387, 31461}, {10519, 61132}, {11179, 44422}, {11257, 14853}, {12007, 41672}, {12263, 38049}, {12782, 16475}, {13196, 51828}, {13410, 46906}, {13474, 48262}, {14881, 48906}, {14885, 21637}, {14928, 53489}, {15484, 22682}, {15989, 39798}, {18907, 44882}, {19053, 22723}, {19054, 22722}, {19102, 22642}, {19105, 22613}, {20859, 21849}, {22486, 63127}, {22720, 22725}, {22721, 22724}, {23660, 39543}, {27375, 58471}, {29317, 63548}, {31088, 46900}, {31239, 47355}, {32448, 59399}, {32515, 51732}, {33201, 63123}, {33478, 61331}, {33479, 61332}, {33706, 64243}, {37334, 39872}, {37637, 44774}, {38064, 63006}, {38110, 49111}, {39141, 62994}, {39784, 44772}, {40108, 48876}, {40126, 63128}, {42288, 62696}, {43976, 47738}, {44102, 53026}, {44519, 48879}, {44526, 48904}, {47277, 47580}, {47459, 47573}, {48942, 62203}, {49792, 52669}, {51735, 64599}, {52854, 53023}, {58621, 58695}, {58622, 58694}

X(64713) = midpoint of X(i) and X(j) for these {i,j}: {6, 39}, {76, 41622}, {2024, 2025}, {11179, 44422}, {13196, 51828}, {14881, 48906}, {14994, 32451}, {24256, 32449}, {47277, 47580}, {58621, 58695}, {58622, 58694}
X(64713) = reflection of X(i) in X(j) for these {i,j}: {141, 6683}, {3934, 3589}, {9969, 58486}, {27375, 58471}
X(64713) = inverse of X(5039) in 1st Brocard circle
X(64713) = inverse of X(9605) in 2nd Brocard circle
X(64713) = inverse of X(2021) in half Moses circle
X(64713) = isogonal conjugate of X(62894)
X(64713) = complement of X(14994)
X(64713) = X(i)-Ceva conjugate of X(j) for these {i, j}: {43357, 512}
X(64713) = X(i)-complementary conjugate of X(j) for these {i, j}: {82, 52658}, {263, 21249}, {2186, 21248}, {3402, 6292}, {42288, 10}, {42299, 2887}, {46289, 15819}, {46319, 16587}, {55240, 46656}
X(64713) = pole of line {512, 5039} with respect to the 1st Brocard circle
X(64713) = pole of line {512, 9605} with respect to the 2nd Brocard circle
X(64713) = pole of line {512, 2021} with respect to the half Moses circle
X(64713) = pole of line {512, 39684} with respect to the Moses circle
X(64713) = pole of line {512, 39684} with respect to the Brocard inellipse
X(64713) = pole of line {184, 251} with respect to the Jerabek hyperbola
X(64713) = pole of line {5, 5188} with respect to the Kiepert hyperbola
X(64713) = pole of line {2, 5039} with respect to the Stammler hyperbola
X(64713) = pole of line {3804, 31296} with respect to the Steiner circumellipse
X(64713) = pole of line {647, 4108} with respect to the Steiner inellipse
X(64713) = pole of line {76, 9605} with respect to the Wallace hyperbola
X(64713) = pole of line {520, 23285} with respect to the dual conic of DeLongchamps circle
X(64713) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {76, 38527, 41622}
X(64713) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5039)}}, {{A, B, C, X(3), X(30499)}}, {{A, B, C, X(4), X(37479)}}, {{A, B, C, X(6), X(60099)}}, {{A, B, C, X(32), X(11175)}}, {{A, B, C, X(54), X(5188)}}, {{A, B, C, X(76), X(9605)}}, {{A, B, C, X(182), X(3424)}}, {{A, B, C, X(262), X(1350)}}, {{A, B, C, X(511), X(3108)}}, {{A, B, C, X(1976), X(5007)}}, {{A, B, C, X(2987), X(44500)}}, {{A, B, C, X(7772), X(27375)}}, {{A, B, C, X(12212), X(42288)}}, {{A, B, C, X(14994), X(42299)}}, {{A, B, C, X(30435), X(59996)}}
X(64713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {597, 32449, 24256}, {732, 3589, 3934}, {1194, 20965, 5943}, {1689, 1690, 1350}, {2024, 2025, 511}, {11205, 20965, 1194}, {24256, 32449, 538}

X(64714) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 107 AND X(3)-CROSSPEDAL-OF-X(4)

Barycentrics    a^10+6*a^8*(b^2+c^2)+20*a^4*(b^2-c^2)^2*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+a^6*(-22*b^4+28*b^2*c^2-22*c^4)-a^2*(b^2-c^2)^2*(3*b^4+26*b^2*c^2+3*c^4) : :
X(64714) = -5*X[3]+8*X[14862], 2*X[146]+X[17812], -3*X[154]+2*X[376], -4*X[381]+3*X[1853], -4*X[549]+3*X[10606], -4*X[597]+3*X[52028], -5*X[631]+2*X[15105], X[3146]+2*X[44762], -2*X[3357]+3*X[5054], -6*X[3524]+5*X[8567], -3*X[3545]+2*X[6247], -3*X[3839]+4*X[5893] and many others

X(64714) lies on circumconic {{A, B, C, X(51348), X(59496)}} and on these lines: {2, 64}, {3, 14862}, {4, 11431}, {6, 62962}, {20, 51261}, {30, 155}, {146, 17812}, {154, 376}, {185, 58483}, {221, 3058}, {381, 1853}, {428, 15811}, {519, 7973}, {524, 41735}, {541, 10117}, {542, 6391}, {549, 10606}, {597, 52028}, {599, 34146}, {631, 15105}, {1075, 51342}, {1192, 62978}, {1204, 62965}, {1249, 58758}, {1503, 1992}, {1619, 54992}, {1907, 22334}, {2071, 59551}, {2192, 5434}, {2777, 15681}, {2935, 5655}, {3146, 44762}, {3197, 34618}, {3357, 5054}, {3426, 18388}, {3516, 64064}, {3524, 8567}, {3534, 5925}, {3545, 6247}, {3582, 10076}, {3584, 10060}, {3830, 12315}, {3839, 5893}, {3845, 14216}, {3851, 52102}, {4846, 10127}, {5055, 13093}, {5064, 11381}, {5071, 61735}, {5894, 10304}, {6001, 24473}, {6241, 52003}, {6285, 11237}, {6293, 36982}, {6621, 58797}, {7355, 11238}, {7507, 15011}, {7714, 13568}, {7865, 12502}, {8703, 17821}, {9899, 19875}, {9968, 11470}, {10182, 15718}, {10192, 15692}, {10193, 61829}, {10282, 15688}, {10516, 15305}, {10605, 32111}, {10675, 42154}, {10676, 42155}, {10706, 31180}, {10990, 55576}, {11001, 34782}, {11064, 58762}, {11202, 14093}, {11204, 15700}, {11206, 15683}, {11472, 60763}, {12262, 25055}, {12290, 22948}, {12379, 59767}, {12920, 34612}, {12930, 34606}, {13094, 45701}, {13095, 45700}, {13846, 49250}, {13847, 49251}, {14269, 18381}, {14530, 15689}, {14864, 61984}, {15063, 21312}, {15069, 44440}, {15152, 37460}, {15534, 64031}, {15682, 34781}, {15684, 18400}, {15685, 34785}, {15687, 18405}, {15693, 64027}, {15694, 35450}, {15696, 50414}, {15699, 61540}, {15701, 64063}, {15702, 23328}, {15703, 23329}, {15721, 58434}, {17800, 45185}, {17819, 41945}, {17820, 41946}, {17824, 46372}, {17826, 42942}, {17827, 42943}, {18376, 61996}, {18383, 61993}, {19087, 32788}, {19088, 32787}, {19132, 51737}, {19149, 43273}, {19709, 20299}, {19924, 39879}, {23324, 61980}, {23332, 61936}, {25563, 61864}, {26958, 51403}, {28194, 64022}, {30402, 42626}, {30403, 42625}, {30552, 45248}, {32062, 53023}, {32064, 61985}, {32138, 64591}, {32602, 34608}, {32767, 61933}, {34117, 37077}, {34319, 36201}, {34774, 64014}, {34780, 38335}, {34786, 62020}, {35260, 62063}, {37197, 64029}, {37201, 64062}, {40658, 50811}, {41362, 50687}, {41715, 54039}, {43831, 62980}, {44837, 64759}, {47352, 63420}, {50709, 62166}, {50956, 61542}, {51892, 56296}, {62017, 64034}, {62040, 64033}, {62120, 64726}, {62129, 64059}, {63343, 63371}

X(64714) = midpoint of X(i) and X(j) for these {i,j}: {2, 6225}, {3534, 48672}, {3830, 12315}, {11001, 64187}, {15682, 34781}, {41715, 54039}, {62040, 64033}
X(64714) = reflection of X(i) in X(j) for these {i,j}: {2, 2883}, {64, 2}, {154, 5656}, {2935, 5655}, {3534, 6759}, {3830, 22802}, {5925, 3534}, {7729, 41580}, {11001, 34782}, {14216, 3845}, {15534, 64031}, {15682, 51491}, {15685, 34785}, {20427, 8703}, {35450, 61747}, {43273, 19149}, {50811, 40658}, {54050, 10192}, {61088, 51737}, {64014, 34774}, {64037, 3830}
X(64714) = pole of line {11441, 58795} with respect to the Stammler hyperbola
X(64714) = X(64)-of-Gemini-107 triangle
X(64714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64, 2883, 64024}, {1498, 5878, 5895}, {1498, 5895, 17845}, {2883, 6225, 64}, {5656, 15311, 154}, {6000, 41580, 7729}, {6759, 48672, 5925}, {12250, 16252, 8567}, {12315, 22802, 64037}, {13093, 61749, 40686}

X(64715) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(3)-CROSSPEDAL-OF-X(4) AND PEDAL OF X(28)

Barycentrics    a*(a^5*(b+c)-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)-2*a^3*(b^3+b^2*c+b*c^2+c^3)+2*a^2*(b^4-b^2*c^2+c^4)+a*(b^5+b^4*c+b*c^4+c^5)) : :
X(64715) = -3*X[2]+4*X[44547], -2*X[1829]+3*X[3060], -3*X[2979]+4*X[37613], -3*X[17616]+4*X[37544], -3*X[41717]+4*X[42450]

X(64715) lies on these lines: {1, 1993}, {2, 44547}, {3, 55873}, {4, 912}, {8, 6515}, {10, 3580}, {12, 41571}, {21, 72}, {22, 64040}, {23, 40660}, {24, 9928}, {37, 56000}, {49, 51696}, {52, 41722}, {54, 24301}, {63, 10393}, {65, 2475}, {78, 18397}, {100, 7098}, {110, 11363}, {144, 145}, {224, 1708}, {226, 39772}, {321, 51978}, {411, 1071}, {511, 64039}, {517, 5889}, {519, 41628}, {758, 10572}, {895, 43703}, {920, 3811}, {942, 2476}, {960, 16865}, {971, 59355}, {1319, 58744}, {1331, 1780}, {1351, 11396}, {1385, 34148}, {1386, 63063}, {1482, 12160}, {1594, 12259}, {1824, 41723}, {1829, 3060}, {1864, 5046}, {1876, 19367}, {1897, 3559}, {1898, 5057}, {1902, 12111}, {1994, 64722}, {1998, 54422}, {2003, 52362}, {2551, 14454}, {2646, 9637}, {2771, 4018}, {2975, 45230}, {2979, 37613}, {3146, 6001}, {3152, 17950}, {3176, 6820}, {3193, 6198}, {3485, 3873}, {3555, 5887}, {3562, 37782}, {3564, 12135}, {3616, 37645}, {3622, 63092}, {3681, 10528}, {3746, 3870}, {3751, 40318}, {3822, 47319}, {3827, 64023}, {3874, 12047}, {3876, 6857}, {3927, 37284}, {4189, 10391}, {4640, 17637}, {4641, 56840}, {4663, 37784}, {5090, 11442}, {5279, 62691}, {5728, 60969}, {5729, 25875}, {5777, 6828}, {6261, 62874}, {6734, 18389}, {6842, 24475}, {6853, 10202}, {6869, 64358}, {6875, 31837}, {6876, 13369}, {6895, 12664}, {6925, 64021}, {7672, 12529}, {7957, 20066}, {8543, 15185}, {8545, 11520}, {9943, 35986}, {9960, 9965}, {10025, 46713}, {10399, 54392}, {10530, 24477}, {10916, 62859}, {11015, 37585}, {11344, 55872}, {11415, 36845}, {11523, 56545}, {12086, 12262}, {12272, 34381}, {12635, 22760}, {12680, 20067}, {12709, 16133}, {12710, 61155}, {14872, 20060}, {15556, 41572}, {17577, 24473}, {17603, 37291}, {17616, 37544}, {18412, 19860}, {18480, 50435}, {20008, 20214}, {21318, 48909}, {21740, 54391}, {23958, 64132}, {24541, 62852}, {31728, 53781}, {31937, 36852}, {33586, 64022}, {34195, 64041}, {34379, 40316}, {34729, 50962}, {35989, 56288}, {36846, 63210}, {37435, 60975}, {37700, 52270}, {39599, 49627}, {40658, 43605}, {40661, 54357}, {41574, 57285}, {41717, 42450}, {45038, 62305}, {50582, 50619}, {52359, 56878}, {62823, 63988}, {62826, 64042}

X(64715) = reflection of X(i) in X(j) for these {i,j}: {3868, 14054}, {3869, 1858}, {12111, 1902}, {41722, 52}, {57287, 15556}, {64002, 41562}
X(64715) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34, 2894}, {943, 52366}, {2259, 56943}, {2982, 4329}, {14775, 33650}, {15439, 20294}, {40395, 20245}, {40447, 21286}, {40570, 63}, {40573, 69}, {58993, 21302}, {60041, 1370}, {63193, 20243}
X(64715) = pole of line {942, 41608} with respect to the Stammler hyperbola
X(64715) = pole of line {650, 17924} with respect to the Steiner circumellipse
X(64715) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1175), X(9309)}}, {{A, B, C, X(9311), X(56041)}}, {{A, B, C, X(18123), X(43740)}}
X(64715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 10393, 20846}, {72, 16465, 34772}, {224, 1708, 37301}, {518, 1858, 3869}, {758, 41562, 64002}, {912, 14054, 3868}, {3555, 5887, 62830}, {3868, 12528, 5905}, {3869, 10394, 6872}

X(64716) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID AND X(3)-CROSSPEDAL-OF-X(6)

Barycentrics    a^2*(a^10-5*a^8*(b^2+c^2)+3*(b^2-c^2)^2*(b^2+c^2)^3+a^6*(6*b^4-8*b^2*c^2+6*c^4)-a^2*(b^2-c^2)^2*(7*b^4+6*b^2*c^2+7*c^4)+2*a^4*(b^6+b^4*c^2+b^2*c^4+c^6)) : :
X(64716) = -3*X[3]+4*X[206], -3*X[4]+X[20079], -2*X[66]+3*X[381], -X[69]+3*X[5656], -3*X[154]+2*X[3098], -4*X[575]+3*X[52028], 2*X[576]+X[58795], -3*X[1853]+4*X[19130], -5*X[3091]+4*X[61542], -2*X[3357]+3*X[5085], -5*X[3763]+6*X[61747], -3*X[3830]+2*X[34775]

X(64716) lies on circumconic {{A, B, C, X(3426), X(52041)}} and on these lines: {3, 206}, {4, 20079}, {6, 1597}, {20, 64719}, {25, 41715}, {30, 5596}, {64, 182}, {66, 381}, {69, 5656}, {154, 3098}, {159, 399}, {193, 54219}, {378, 19125}, {382, 1351}, {511, 1498}, {542, 6391}, {575, 52028}, {576, 58795}, {611, 6285}, {613, 7355}, {1176, 54994}, {1177, 10620}, {1181, 12294}, {1350, 6759}, {1352, 2883}, {1428, 10076}, {1598, 19161}, {1619, 3167}, {1657, 36989}, {1853, 19130}, {1885, 6225}, {1907, 12324}, {1974, 10605}, {2330, 10060}, {2393, 44454}, {2777, 11820}, {2935, 19140}, {3091, 61542}, {3172, 34137}, {3357, 5085}, {3517, 44679}, {3527, 15321}, {3534, 31166}, {3564, 41735}, {3566, 62307}, {3763, 61747}, {3830, 34775}, {3843, 51756}, {5020, 41580}, {5050, 13093}, {5054, 31267}, {5055, 6697}, {5092, 10606}, {5093, 8549}, {5480, 11432}, {5544, 61735}, {5895, 29012}, {5925, 48898}, {6247, 14561}, {6293, 37488}, {7387, 44544}, {7716, 21851}, {8567, 17508}, {9777, 32064}, {9833, 29181}, {9969, 18535}, {10249, 41593}, {10282, 31884}, {10516, 61749}, {10519, 61610}, {10602, 39874}, {10752, 12165}, {11202, 55646}, {11204, 55676}, {11414, 41716}, {11456, 19459}, {11598, 15462}, {12017, 19153}, {12085, 19139}, {12160, 34781}, {12163, 64052}, {12250, 25406}, {12262, 38029}, {12290, 39588}, {12292, 32251}, {12606, 48669}, {13293, 52697}, {13445, 19122}, {13564, 14530}, {13754, 37491}, {14810, 17821}, {14927, 64187}, {15072, 26206}, {15311, 34774}, {15578, 55682}, {15579, 55701}, {15581, 55580}, {15582, 55595}, {15583, 20423}, {15585, 54173}, {15694, 58450}, {17813, 55716}, {17814, 52520}, {17845, 29317}, {17847, 52098}, {17856, 34470}, {18400, 48910}, {18405, 48895}, {18451, 37511}, {18563, 48672}, {19137, 37475}, {19145, 49250}, {19146, 49251}, {20427, 44882}, {20806, 21312}, {21850, 36851}, {22802, 36990}, {23042, 53094}, {23329, 47355}, {24206, 64024}, {28708, 47090}, {32271, 63716}, {34780, 37493}, {34782, 48873}, {34785, 48872}, {34787, 55584}, {35228, 55639}, {36201, 38790}, {36982, 44492}, {37473, 40285}, {38110, 61540}, {38317, 40686}, {40318, 54039}, {41719, 48906}, {41725, 56918}, {44440, 46442}, {44668, 55724}, {48662, 48675}, {48884, 61721}, {48901, 64037}, {50414, 55614}, {50955, 54146}, {51538, 64034}

X(64716) = midpoint of X(i) and X(j) for these {i,j}: {1351, 12315}, {6225, 6776}, {14927, 64187}, {34781, 51212}
X(64716) = reflection of X(i) in X(j) for these {i,j}: {3, 19149}, {6, 34779}, {20, 64719}, {64, 182}, {1350, 6759}, {1351, 64031}, {1352, 2883}, {1657, 36989}, {2935, 19140}, {3534, 31166}, {5925, 48898}, {10620, 1177}, {12085, 19139}, {12163, 64052}, {13093, 63420}, {14216, 5480}, {17847, 52098}, {19149, 9968}, {20427, 44882}, {33878, 159}, {34778, 206}, {35450, 19153}, {36851, 21850}, {36990, 22802}, {39879, 1498}, {46264, 34774}, {48872, 34785}, {48873, 34782}, {48905, 34776}, {55584, 34787}, {61088, 48906}, {63420, 34117}, {63716, 32271}, {64037, 48901}
X(64716) = inverse of X(54080) in Stammler circle
X(64716) = perspector of circumconic {{A, B, C, X(9064), X(56008)}}
X(64716) = pole of line {8552, 8673} with respect to the circumcircle
X(64716) = pole of line {647, 8673} with respect to the Stammler circle
X(64716) = pole of line {14396, 62176} with respect to the MacBeath circumconic
X(64716) = pole of line {1370, 46818} with respect to the Stammler hyperbola
X(64716) = X(66)-of-anti-Ehrmann-mid triangle
X(64716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {159, 2781, 33878}, {206, 34146, 34778}, {511, 1498, 39879}, {1351, 12315, 1503}, {1503, 64031, 1351}, {2777, 34776, 48905}, {5050, 13093, 63420}, {6000, 34779, 6}, {9968, 34146, 19149}, {12017, 35450, 44883}, {14530, 55610, 15577}, {19149, 34146, 3}, {19149, 34778, 206}, {23042, 64027, 53094}, {32063, 33878, 159}

X(64717) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-ASCELLA AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    5*a^10-12*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+8*a^6*(b^4+b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4) : :
X(64717) = -2*X[4]+3*X[11402], -4*X[578]+3*X[5064], -5*X[5076]+8*X[32136]

X(64717) lies on these lines: {3, 70}, {4, 11402}, {5, 26864}, {6, 61139}, {20, 3564}, {22, 12429}, {24, 26869}, {25, 6146}, {26, 45731}, {30, 12160}, {64, 13622}, {68, 9715}, {74, 15696}, {125, 17821}, {155, 11750}, {184, 7507}, {185, 2393}, {186, 26944}, {235, 11206}, {378, 12254}, {381, 1614}, {382, 11456}, {394, 44829}, {403, 14530}, {427, 18925}, {539, 37486}, {550, 34469}, {578, 5064}, {1092, 31152}, {1154, 1657}, {1181, 12173}, {1498, 21659}, {1503, 1593}, {1597, 16659}, {1598, 12022}, {1656, 9707}, {1853, 13367}, {1885, 34781}, {1899, 3515}, {1993, 64718}, {2883, 51998}, {3146, 31802}, {3167, 37444}, {3448, 38444}, {3516, 14216}, {3517, 18912}, {3526, 11464}, {3528, 43903}, {3574, 17809}, {3575, 6776}, {3580, 16195}, {5050, 7544}, {5054, 23294}, {5073, 31815}, {5076, 32136}, {5094, 18381}, {5198, 12241}, {5691, 31811}, {5889, 12283}, {5925, 64029}, {5944, 61702}, {6090, 6643}, {6247, 11410}, {6622, 64059}, {6756, 9777}, {6759, 18396}, {6800, 58922}, {6815, 48906}, {7387, 44076}, {7395, 12134}, {7484, 64035}, {7487, 11245}, {7493, 61544}, {7500, 13142}, {7503, 18440}, {7530, 45970}, {7539, 37476}, {7576, 11432}, {7592, 18494}, {8567, 13399}, {9638, 9669}, {9818, 64036}, {10110, 62968}, {10112, 33586}, {10116, 37489}, {10282, 37453}, {10539, 16072}, {10605, 34785}, {10619, 11425}, {10982, 13419}, {11284, 64038}, {11403, 16655}, {11411, 44239}, {11414, 44665}, {11424, 36990}, {11462, 18512}, {11463, 18510}, {11466, 42815}, {11467, 42816}, {11468, 15688}, {11819, 37493}, {12024, 15873}, {12111, 31807}, {12118, 12166}, {12164, 12225}, {12315, 18560}, {12370, 18534}, {13093, 35481}, {13171, 32423}, {13340, 43896}, {13353, 56965}, {13470, 15068}, {13567, 55578}, {13851, 64024}, {14070, 25738}, {15106, 23236}, {15683, 32601}, {15811, 61744}, {17702, 19458}, {18386, 41362}, {18390, 45185}, {18405, 43831}, {18533, 18914}, {18913, 37931}, {18916, 37458}, {19118, 64719}, {26879, 55572}, {26882, 61701}, {26883, 62966}, {26937, 55576}, {31304, 45968}, {31810, 64051}, {31812, 41869}, {32249, 52093}, {34148, 34609}, {34786, 45110}, {34797, 64094}, {35450, 35491}, {35485, 61540}, {36747, 44407}, {36752, 45286}, {37198, 46264}, {40242, 49136}, {41040, 45256}, {41041, 45257}, {43608, 61811}, {59346, 64756}

X(64717) = reflection of X(i) in X(j) for these {i,j}: {4, 31804}, {382, 12161}, {1593, 19467}, {3146, 31802}, {5073, 31815}, {5691, 31811}, {12111, 31807}, {12166, 12118}, {12167, 6776}, {12173, 1181}, {32333, 12254}, {36990, 64028}, {41869, 31812}, {64051, 31810}
X(64717) = pole of line {26, 8780} with respect to the Stammler hyperbola
X(64717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 31804, 11402}, {184, 64037, 7507}, {185, 17845, 37196}, {1181, 18400, 12173}, {1498, 21659, 44438}, {1503, 19467, 1593}, {6146, 9833, 25}, {6759, 18396, 37197}, {7592, 64032, 18494}, {9707, 25739, 1656}, {10619, 11550, 11425}, {10982, 13419, 62976}, {11206, 18945, 235}, {11456, 12289, 382}, {12241, 31383, 5198}, {17845, 64080, 185}, {18381, 19357, 5094}, {18925, 64034, 427}

X(64718) = ORTHOLOGY CENTER OF THESE TRIANGLES: 3RD ANTI-EULER AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    2*a^10-4*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(b^4+b^2*c^2+c^4)+a^4*(b^6+b^4*c^2+b^2*c^4+c^6)+a^2*(b^8-b^6*c^2-b^2*c^6+c^8) : :
X(64718) = -3*X[2]+4*X[44829], -5*X[52]+6*X[11232], -3*X[381]+4*X[13470], -5*X[631]+4*X[45286], -3*X[2979]+2*X[14516], -3*X[3060]+4*X[6146], -5*X[3091]+4*X[13419], -7*X[3528]+8*X[17712], -3*X[3543]+4*X[13403], -5*X[3567]+4*X[11819], -4*X[3575]+5*X[10574], -9*X[5640]+8*X[6756] and many others

X(64718) lies on circumconic {{A, B, C, X(1179), X(15319)}} and on these lines: {2, 44829}, {3, 18432}, {4, 569}, {5, 26881}, {20, 2888}, {22, 58922}, {24, 26913}, {26, 25739}, {30, 5889}, {52, 11232}, {54, 31723}, {68, 44831}, {110, 9833}, {156, 7574}, {265, 17714}, {323, 61751}, {381, 13470}, {382, 7592}, {511, 34799}, {576, 3146}, {631, 45286}, {858, 11449}, {1147, 46450}, {1181, 52842}, {1503, 12111}, {1568, 45185}, {1614, 18569}, {1657, 30522}, {1658, 23294}, {1853, 38444}, {1899, 31304}, {1993, 64717}, {2070, 26917}, {2071, 34785}, {2072, 26882}, {2979, 14516}, {3060, 6146}, {3091, 13419}, {3147, 12140}, {3153, 6759}, {3448, 46730}, {3528, 17712}, {3529, 11411}, {3541, 51033}, {3543, 13403}, {3547, 6030}, {3567, 11819}, {3574, 11003}, {3575, 10574}, {5189, 13346}, {5449, 7556}, {5640, 6756}, {6193, 23061}, {6225, 11061}, {6240, 15072}, {6247, 11454}, {6288, 7525}, {6800, 7507}, {7387, 50435}, {7391, 19467}, {7487, 18911}, {7488, 18381}, {7500, 18945}, {7512, 18474}, {7540, 9781}, {7553, 12022}, {7566, 37476}, {7576, 15043}, {7998, 64035}, {9714, 61701}, {9927, 12088}, {10112, 62187}, {10296, 22802}, {10297, 18504}, {10298, 20299}, {10316, 15340}, {10575, 34797}, {11381, 11645}, {11413, 17845}, {11422, 31804}, {11424, 62967}, {11425, 31133}, {11439, 16655}, {11441, 64033}, {11444, 12134}, {11451, 64038}, {11455, 52070}, {11459, 64036}, {11464, 13371}, {11468, 44242}, {11550, 14118}, {11818, 43651}, {12082, 12293}, {12173, 39588}, {12241, 34603}, {12254, 13352}, {12290, 18563}, {12362, 15056}, {12605, 15305}, {12897, 15682}, {13160, 15080}, {13201, 32423}, {13353, 63672}, {13367, 31074}, {13491, 32196}, {14157, 18404}, {14790, 34148}, {14805, 33332}, {14927, 36851}, {15004, 43838}, {15045, 31830}, {15055, 35503}, {15107, 31305}, {15360, 34726}, {15704, 50434}, {15761, 18394}, {15807, 62008}, {16661, 48898}, {17578, 61744}, {17821, 30744}, {17834, 41724}, {18324, 43608}, {18392, 41362}, {18430, 61750}, {18475, 52295}, {18533, 43601}, {18559, 40647}, {19122, 64719}, {20791, 31833}, {21451, 44082}, {23325, 58805}, {23329, 38448}, {31724, 61752}, {31976, 63421}, {32402, 45839}, {33523, 52397}, {33524, 48905}, {34786, 50009}, {35482, 39242}, {36990, 63664}, {38438, 40686}, {39138, 59290}, {43808, 64095}, {43817, 47485}, {44279, 58789}, {44491, 46264}, {44665, 64050}

X(64718) = midpoint of X(i) and X(j) for these {i,j}: {12111, 40241}
X(64718) = reflection of X(i) in X(j) for these {i,j}: {4, 11750}, {3146, 21659}, {5889, 34224}, {6243, 45731}, {12111, 12225}, {12278, 20}, {12290, 18563}, {16659, 12605}, {34797, 10575}, {61139, 44829}, {64032, 3}, {64051, 44076}
X(64718) = anticomplement of X(61139)
X(64718) = pole of line {1216, 7502} with respect to the Stammler hyperbola
X(64718) = pole of line {1238, 32820} with respect to the Wallace hyperbola
X(64718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 11442, 7691}, {20, 14216, 11440}, {20, 18400, 12278}, {20, 2888, 46728}, {20, 64034, 11442}, {22, 64037, 58922}, {30, 34224, 5889}, {30, 44076, 64051}, {30, 45731, 6243}, {1503, 12225, 12111}, {9833, 37444, 110}, {11750, 44407, 4}, {12111, 40241, 1503}, {12605, 16659, 15305}, {16655, 52069, 11439}, {21659, 29012, 3146}, {44829, 61139, 2}

X(64719) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-HONSBERGER AND X(3)-CROSSPEDAL-OF-X(52)

Barycentrics    4*a^12-7*a^10*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)^2+a^2*(b^2-c^2)^2*(b^2+c^2)^3-2*a^4*(b^2-c^2)^2*(b^4+c^4)-a^8*(b^4+6*b^2*c^2+c^4)+6*a^6*(b^6+b^4*c^2+b^2*c^4+c^6) : :
X(64719) = -3*X[2]+2*X[61542], -3*X[154]+X[1352], -5*X[631]+X[20079], -5*X[632]+4*X[6697], -X[1351]+3*X[41719], -X[2892]+3*X[32609], -5*X[3618]+X[64034], -4*X[3628]+5*X[31267], -3*X[5085]+X[14216], 3*X[5656]+X[14927]

X(64719) lies on these lines: {2, 61542}, {3, 5596}, {4, 19125}, {5, 182}, {6, 6756}, {20, 64716}, {24, 26926}, {25, 6776}, {26, 159}, {30, 19139}, {66, 140}, {69, 9715}, {141, 10282}, {154, 1352}, {161, 41588}, {184, 15809}, {511, 34774}, {542, 10154}, {546, 34775}, {548, 34778}, {550, 34146}, {575, 15583}, {631, 20079}, {632, 6697}, {973, 1843}, {1176, 7399}, {1177, 32423}, {1351, 41719}, {1353, 2393}, {1498, 12362}, {1619, 15818}, {1853, 11548}, {1974, 6146}, {2781, 34153}, {2883, 29012}, {2892, 32609}, {3542, 39874}, {3549, 14530}, {3618, 64034}, {3628, 31267}, {3827, 24475}, {3867, 13419}, {5050, 7528}, {5085, 14216}, {5092, 6247}, {5480, 18400}, {5656, 14927}, {5878, 48905}, {5893, 48884}, {5894, 48892}, {5921, 7493}, {6000, 44882}, {6193, 37491}, {6696, 17508}, {7395, 25406}, {7487, 19119}, {7488, 46442}, {7502, 15577}, {7514, 63420}, {7539, 32064}, {7568, 34118}, {7715, 8550}, {8703, 63431}, {8721, 20993}, {9714, 39899}, {9924, 63722}, {9934, 32233}, {9968, 15704}, {10192, 24206}, {11818, 18583}, {11819, 21850}, {12017, 14786}, {12134, 19131}, {12315, 61088}, {13383, 18356}, {13490, 50979}, {14516, 19121}, {14561, 19132}, {14912, 37122}, {15026, 58494}, {15073, 46444}, {15258, 41766}, {15311, 48898}, {15462, 41602}, {15516, 23326}, {15580, 37936}, {15581, 37440}, {15585, 34507}, {16072, 64014}, {16655, 19124}, {17845, 31670}, {18382, 38136}, {18531, 32063}, {19118, 64717}, {19122, 64718}, {19123, 64032}, {19126, 64035}, {19128, 34224}, {19129, 64036}, {19130, 41362}, {19161, 37458}, {20427, 59411}, {21637, 61139}, {21841, 64080}, {23327, 51732}, {23328, 55674}, {23332, 58445}, {29181, 34779}, {29323, 51491}, {32337, 46448}, {32455, 34788}, {32767, 51126}, {34380, 34787}, {35260, 40330}, {37942, 47453}, {41593, 59399}, {41716, 44239}, {42353, 42671}, {44665, 64052}, {44668, 64067}, {51437, 56866}, {55856, 58450}, {61545, 61683}

X(64719) = midpoint of X(i) and X(j) for these {i,j}: {3, 5596}, {6, 9833}, {20, 64716}, {1498, 46264}, {5878, 48905}, {6193, 37491}, {6759, 34776}, {6776, 39879}, {9924, 63722}, {9934, 32233}, {12315, 61088}, {17845, 31670}, {19149, 36989}, {34774, 34782}, {34779, 34785}, {36851, 64033}
X(64719) = reflection of X(i) in X(j) for these {i,j}: {5, 206}, {66, 140}, {141, 10282}, {1352, 61610}, {1353, 41729}, {3818, 16252}, {5894, 48892}, {6247, 5092}, {15583, 575}, {18381, 3589}, {18382, 63699}, {21850, 34117}, {23300, 64061}, {34118, 58437}, {34507, 15585}, {34775, 546}, {34778, 548}, {34788, 32455}, {41362, 19130}, {48876, 15577}, {48884, 5893}
X(64719) = anticomplement of X(61542)
X(64719) = X(5596)-of-anti-X3-ABC-reflections triangle
X(64719) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 5596, 18338}
X(64719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {154, 1352, 61610}, {206, 1503, 5}, {1503, 16252, 3818}, {1503, 3589, 18381}, {1503, 64061, 23300}, {5050, 64033, 36851}, {6759, 34776, 1503}, {6776, 11206, 39879}, {18381, 23042, 3589}, {18382, 63699, 38136}, {19132, 64037, 14561}, {19149, 36989, 30}, {23300, 64061, 38110}, {31166, 36989, 19149}, {34774, 34782, 511}, {34779, 34785, 29181}

X(64720) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ANTI-PAVLOV AND X(3)-CROSSPEDAL-OF-X(68)

Barycentrics    a*(a+b)*(a+c)*(a^4-2*a^3*(b+c)+(b^2-c^2)^2-2*a^2*(b^2+c^2)+2*a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64720) lies on circumconic {{A, B, C, X(1389), X(51223)}} and on these lines: {1, 58392}, {3, 81}, {4, 333}, {5, 5235}, {20, 5767}, {21, 517}, {28, 283}, {30, 4921}, {40, 58}, {46, 5323}, {55, 64420}, {56, 64421}, {86, 631}, {140, 5333}, {171, 43073}, {255, 1396}, {285, 52889}, {355, 64401}, {371, 64410}, {372, 64411}, {376, 41629}, {381, 64424}, {382, 64383}, {394, 37264}, {404, 7998}, {411, 5752}, {443, 26638}, {511, 3651}, {515, 64072}, {549, 42025}, {573, 2303}, {580, 1764}, {582, 19649}, {602, 10476}, {859, 22770}, {944, 7415}, {970, 1812}, {1006, 10441}, {1010, 5657}, {1014, 37582}, {1043, 12245}, {1064, 4281}, {1155, 1408}, {1160, 64404}, {1161, 64403}, {1172, 4269}, {1385, 64377}, {1412, 15803}, {1437, 1817}, {1478, 64408}, {1479, 64409}, {1482, 64415}, {1656, 64425}, {1766, 1778}, {1780, 5324}, {2077, 4278}, {2287, 3149}, {2328, 17560}, {2360, 62756}, {2817, 51966}, {2979, 35976}, {3193, 4225}, {3218, 18732}, {3286, 10310}, {3311, 64386}, {3312, 64385}, {3398, 64381}, {3428, 4267}, {3523, 8025}, {3524, 42028}, {3525, 25507}, {3576, 4658}, {3579, 37402}, {3654, 51669}, {3656, 17553}, {4184, 11248}, {4220, 48882}, {4227, 41722}, {4228, 35193}, {4234, 50810}, {4276, 11012}, {4653, 7982}, {5127, 5358}, {5398, 37399}, {5603, 11110}, {5706, 19262}, {5707, 61109}, {5755, 7549}, {5758, 25516}, {5886, 17557}, {6197, 23602}, {6361, 37422}, {6684, 25526}, {6769, 17194}, {6847, 16713}, {6876, 56439}, {6880, 31631}, {6915, 34466}, {6920, 15488}, {6927, 27398}, {6940, 15489}, {6942, 14868}, {6986, 37536}, {7387, 64395}, {7411, 37482}, {7413, 48941}, {7957, 18191}, {7991, 52680}, {8981, 64417}, {9525, 35055}, {9732, 64388}, {9733, 64387}, {9738, 64390}, {9739, 64389}, {9821, 64398}, {9895, 62777}, {10165, 28619}, {10306, 17524}, {10458, 37529}, {10525, 64406}, {10526, 64407}, {10679, 64422}, {10680, 64423}, {10902, 29311}, {11064, 24882}, {11115, 59417}, {11231, 17551}, {11251, 64402}, {11252, 64396}, {11253, 64397}, {11491, 56181}, {12702, 15952}, {13732, 37791}, {13966, 64418}, {14005, 26446}, {14110, 18178}, {15717, 26860}, {16049, 59318}, {16408, 24557}, {16415, 37659}, {16453, 63068}, {17185, 47512}, {17567, 24556}, {18164, 37526}, {18206, 63399}, {18417, 31806}, {19513, 27644}, {19543, 32911}, {19548, 48875}, {22139, 28258}, {22458, 62799}, {26064, 30444}, {33295, 36697}, {35203, 37527}, {36742, 37400}, {36745, 40153}, {36754, 61409}, {37531, 54356}, {37570, 63389}, {37584, 56840}, {44661, 54302}, {45923, 48930}, {45955, 64173}, {46877, 63986}, {48460, 64379}, {48461, 64380}, {49038, 64391}, {49039, 64392}

X(64720) = reflection of X(i) in X(j) for these {i,j}: {3651, 46623}
X(64720) = pole of line {405, 1385} with respect to the Stammler hyperbola
X(64720) = pole of line {5770, 44140} with respect to the Wallace hyperbola
X(64720) = X(3)-of-2nd-anti-Pavlov triangle
X(64720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 48909, 63291}, {3, 48917, 63400}, {3, 64419, 81}, {3, 81, 64393}, {4, 333, 64405}, {4, 64405, 64399}, {20, 16704, 64384}, {40, 58, 4221}, {371, 64412, 64410}, {372, 64413, 64411}, {511, 46623, 3651}, {580, 1764, 37431}, {5235, 64400, 5}, {7415, 56018, 944}, {48924, 63307, 3}, {64382, 64414, 1}

X(64721) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND ANTI-CIRCUMPERP-TANGENTIAL AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+4*b*c+c^2)) : :
X(64721) = -3*X[61663]+2*X[64163]

X(64721) lies on these lines: {1, 3}, {4, 64042}, {8, 20928}, {10, 26481}, {11, 7686}, {12, 908}, {63, 22759}, {72, 5252}, {78, 11501}, {90, 18761}, {145, 41537}, {201, 10459}, {225, 1829}, {226, 3878}, {388, 3869}, {392, 10198}, {515, 1858}, {518, 10944}, {519, 14054}, {758, 10106}, {912, 18970}, {920, 22758}, {952, 13292}, {961, 2990}, {1068, 41722}, {1104, 1411}, {1122, 62780}, {1201, 1393}, {1210, 26475}, {1254, 1457}, {1317, 34791}, {1359, 2778}, {1361, 1365}, {1399, 1455}, {1400, 1953}, {1406, 4320}, {1445, 42842}, {1450, 24443}, {1451, 49487}, {1452, 26377}, {1469, 3827}, {1478, 5887}, {1512, 10958}, {1572, 56913}, {1737, 26470}, {1788, 10527}, {1830, 1887}, {1836, 12672}, {1837, 48482}, {1841, 21770}, {1864, 64261}, {1898, 5691}, {2262, 8557}, {2285, 21853}, {2362, 19050}, {2771, 18968}, {2800, 4292}, {2802, 12432}, {2975, 7098}, {3193, 5323}, {3474, 64079}, {3476, 3868}, {3485, 3877}, {3555, 37738}, {3556, 18954}, {3585, 31937}, {3600, 64047}, {3698, 5705}, {3753, 24914}, {3754, 3911}, {3812, 5433}, {3874, 63987}, {3880, 41575}, {3884, 64160}, {3885, 7672}, {3897, 58578}, {3899, 5290}, {4018, 17625}, {4084, 4315}, {4293, 64021}, {4295, 7702}, {4311, 5884}, {4848, 10916}, {4863, 10914}, {5083, 33812}, {5230, 44545}, {5427, 8261}, {5434, 34742}, {5692, 9578}, {5693, 9613}, {5728, 37724}, {5794, 64086}, {5836, 6734}, {5853, 41577}, {5881, 18397}, {5882, 18389}, {5904, 36922}, {6001, 7354}, {6797, 20118}, {7195, 23839}, {8581, 60933}, {9655, 40266}, {9670, 9848}, {9856, 13273}, {9943, 15326}, {10039, 13375}, {10404, 12709}, {10543, 12710}, {10693, 12903}, {10806, 64747}, {10826, 45630}, {10941, 12648}, {10949, 26015}, {10950, 44547}, {10956, 64139}, {11237, 28609}, {12116, 18391}, {12607, 51379}, {12649, 14923}, {12688, 12943}, {12736, 64124}, {12758, 33593}, {12832, 37726}, {13369, 21578}, {13464, 64284}, {14988, 18990}, {15325, 61541}, {15950, 58679}, {15955, 55101}, {16232, 19049}, {16466, 57277}, {16685, 56908}, {17636, 49176}, {17646, 50239}, {17654, 48694}, {17705, 22464}, {18732, 30493}, {19366, 43217}, {19860, 55871}, {20718, 63398}, {21077, 26482}, {21147, 64020}, {22791, 64127}, {25917, 30827}, {27286, 31359}, {31397, 31806}, {31870, 44675}, {33597, 64269}, {37708, 41686}, {39779, 45638}, {41723, 64382}, {44662, 56819}, {45776, 57285}, {45946, 59816}, {49627, 64767}, {51422, 64159}, {54292, 57280}, {57283, 62826}, {60909, 60965}, {61663, 64163}, {64157, 64292}

X(64721) = reflection of X(i) in X(j) for these {i,j}: {1829, 34434}, {10950, 44547}
X(64721) = inverse of X(64266) in Feuerbach hyperbola
X(64721) = X(i)-isoconjugate-of-X(j) for these {i, j}: {522, 43345}
X(64721) = X(i)-Dao conjugate of X(j) for these {i, j}: {64275, 8}
X(64721) = pole of line {44426, 57091} with respect to the polar circle
X(64721) = pole of line {1, 6831} with respect to the Feuerbach hyperbola
X(64721) = pole of line {21, 64042} with respect to the Stammler hyperbola
X(64721) = X(65)-of-2nd-anti-circumperp-tangential triangle
X(64721) = X(6240)-of-intouch triangle
X(64721) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10039)}}, {{A, B, C, X(3), X(31837)}}, {{A, B, C, X(4), X(11249)}}, {{A, B, C, X(6), X(8071)}}, {{A, B, C, X(7), X(26437)}}, {{A, B, C, X(8), X(26357)}}, {{A, B, C, X(28), X(10202)}}, {{A, B, C, X(34), X(3338)}}, {{A, B, C, X(46), X(994)}}, {{A, B, C, X(225), X(37558)}}, {{A, B, C, X(513), X(22765)}}, {{A, B, C, X(942), X(1411)}}, {{A, B, C, X(957), X(10269)}}, {{A, B, C, X(959), X(1470)}}, {{A, B, C, X(961), X(18838)}}, {{A, B, C, X(998), X(17437)}}, {{A, B, C, X(1243), X(37532)}}, {{A, B, C, X(1389), X(24474)}}, {{A, B, C, X(1953), X(39271)}}, {{A, B, C, X(2990), X(3666)}}, {{A, B, C, X(3577), X(12704)}}, {{A, B, C, X(5563), X(13375)}}, {{A, B, C, X(10966), X(43740)}}, {{A, B, C, X(11012), X(64265)}}, {{A, B, C, X(22766), X(34430)}}, {{A, B, C, X(37601), X(41446)}}, {{A, B, C, X(41487), X(59334)}}
X(64721) = barycentric product X(i)*X(j) for these (i, j): {278, 31837}, {10039, 57}
X(64721) = barycentric quotient X(i)/X(j) for these (i, j): {1415, 43345}, {10039, 312}, {31837, 345}
X(64721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 5903, 65}, {65, 1319, 942}, {65, 3057, 2099}, {388, 3869, 64041}, {4293, 64021, 64704}, {4320, 54400, 1406}, {10914, 41539, 41687}

X(64722) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-CONWAY AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(2*a^6+a^5*(b+c)+a*(b-c)^2*(b+c)^3-3*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^3*(b^3+b^2*c+b*c^2+c^3)) : :
X(64722) = X[11396]+3*X[11402]

X(64722) lies on these lines: {1, 6}, {3, 45126}, {4, 40658}, {8, 11427}, {10, 23292}, {28, 2262}, {34, 5706}, {40, 11425}, {47, 4640}, {51, 11363}, {52, 24301}, {54, 65}, {56, 37310}, {58, 17102}, {81, 37277}, {143, 51696}, {145, 63030}, {154, 7713}, {182, 37613}, {184, 1829}, {185, 12262}, {212, 37528}, {222, 64132}, {227, 3072}, {255, 3666}, {386, 46974}, {387, 34231}, {389, 1385}, {498, 4682}, {515, 12233}, {517, 578}, {580, 1214}, {601, 9371}, {603, 43058}, {774, 2308}, {820, 1193}, {912, 12161}, {942, 1147}, {946, 12241}, {990, 64057}, {1038, 36745}, {1040, 36746}, {1060, 36754}, {1062, 10391}, {1071, 2003}, {1074, 49745}, {1103, 5269}, {1125, 13567}, {1175, 2906}, {1181, 6001}, {1192, 7987}, {1210, 52260}, {1319, 19366}, {1399, 64118}, {1427, 3468}, {1442, 6986}, {1451, 20277}, {1456, 4295}, {1465, 37530}, {1482, 11426}, {1496, 17017}, {1620, 58221}, {1834, 56814}, {1858, 2904}, {1864, 6198}, {1898, 38336}, {1902, 11424}, {1905, 2194}, {1994, 64715}, {2317, 18673}, {2646, 11436}, {2771, 12227}, {2778, 15472}, {2836, 32245}, {2999, 15524}, {3057, 11429}, {3075, 3752}, {3085, 3745}, {3149, 56418}, {3562, 5262}, {3576, 9786}, {3579, 11430}, {3616, 11433}, {3622, 63031}, {3624, 26958}, {3740, 54401}, {3827, 64028}, {4292, 43035}, {4294, 41339}, {4297, 13568}, {4641, 44706}, {4719, 8071}, {5012, 64039}, {5398, 37565}, {5480, 49542}, {5550, 37643}, {5707, 37697}, {5713, 37695}, {5721, 40950}, {5818, 43841}, {5886, 39571}, {6505, 37282}, {7498, 53994}, {7515, 45206}, {7686, 57277}, {7687, 11699}, {7718, 14853}, {8614, 64704}, {9538, 10394}, {9955, 18390}, {10222, 37505}, {10246, 11432}, {11179, 34643}, {11396, 11402}, {11398, 37538}, {11435, 37080}, {11438, 13624}, {11720, 11746}, {12259, 13292}, {12710, 61398}, {13403, 22793}, {13411, 37594}, {14110, 54292}, {14529, 44545}, {14557, 57281}, {16410, 53996}, {17809, 64022}, {18388, 18480}, {18447, 37509}, {18455, 36750}, {18593, 37582}, {19862, 47296}, {20986, 52359}, {22350, 37539}, {31728, 51707}, {34712, 54131}, {34977, 36052}, {37408, 54420}, {37600, 63291}, {37685, 62864}, {37699, 51361}, {41538, 64339}, {43822, 51694}, {44495, 58535}, {46934, 63081}, {50195, 62805}, {51695, 58469}, {54289, 55399}, {54427, 59691}, {61397, 63976}, {63339, 64045}, {63658, 63698}

X(64722) = midpoint of X(i) and X(j) for these {i,j}: {11396, 64040}
X(64722) = pole of line {24, 55} with respect to the Feuerbach hyperbola
X(64722) = pole of line {81, 44547} with respect to the Stammler hyperbola
X(64722) = pole of line {521, 3700} with respect to the dual conic of DeLongchamps circle
X(64722) = pole of line {142, 18588} with respect to the dual conic of Yff parabola
X(64722) = intersection, other than A, B, C, of circumconics {{A, B, C, X(9), X(2190)}}, {{A, B, C, X(54), X(219)}}, {{A, B, C, X(81), X(44547)}}
X(64722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3074, 37}, {184, 1829, 40660}, {580, 8555, 1214}, {1062, 36742, 10391}, {2003, 33178, 1071}, {11396, 11402, 64040}, {61397, 64349, 63976}

X(64723) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(1)-CIRCUMCONCEVIAN OF X(9) AND X(3)-CROSSPEDAL-OF-X(72)

Barycentrics    a*(a^4*(b+c)-(b-c)^4*(b+c)+2*a*(b+c)^2*(b^2+c^2)-2*a^3*(b^2+4*b*c+c^2)) : :
X(64723) = -3*X[392]+2*X[5542], -2*X[3243]+3*X[5919], -5*X[3616]+4*X[58563], -5*X[3698]+6*X[38057], -6*X[3740]+5*X[40333], -4*X[3812]+5*X[18230], -5*X[3876]+4*X[58634], -X[3901]+3*X[41861], -7*X[3983]+6*X[38200], -5*X[4005]+4*X[40659], -4*X[4015]+3*X[38201], -X[4312]+3*X[5692] and many others

X(64723) lies on circumconic {{A, B, C, X(5665), X(9311)}} and on these lines: {7, 960}, {9, 65}, {40, 480}, {56, 60990}, {63, 354}, {72, 516}, {78, 11495}, {142, 3649}, {144, 145}, {210, 329}, {219, 1456}, {220, 2263}, {392, 5542}, {517, 4915}, {527, 5434}, {528, 17781}, {758, 5728}, {908, 3826}, {946, 6067}, {954, 12514}, {958, 60949}, {971, 5693}, {1212, 42289}, {1260, 7964}, {1386, 62799}, {2262, 3958}, {2771, 63277}, {2800, 6068}, {2836, 36101}, {2951, 31793}, {2975, 42819}, {3243, 5919}, {3555, 30331}, {3616, 58563}, {3696, 30807}, {3698, 38057}, {3706, 18750}, {3740, 40333}, {3812, 18230}, {3827, 21871}, {3868, 5572}, {3876, 58634}, {3878, 5850}, {3880, 7673}, {3886, 30625}, {3899, 41707}, {3901, 41861}, {3916, 52769}, {3929, 5173}, {3940, 50528}, {3983, 38200}, {4005, 40659}, {4015, 38201}, {4018, 30329}, {4295, 45120}, {4312, 5692}, {4321, 15829}, {4326, 11523}, {4519, 64194}, {4662, 59413}, {4679, 61660}, {4847, 7965}, {5044, 38052}, {5220, 60966}, {5263, 10025}, {5423, 44792}, {5439, 38059}, {5686, 5836}, {5695, 45738}, {5696, 37585}, {5759, 6001}, {5762, 5887}, {5784, 17768}, {5817, 7686}, {5851, 64139}, {5853, 6284}, {5856, 17638}, {5918, 63413}, {6172, 7672}, {6600, 37568}, {6601, 12701}, {6734, 42356}, {7675, 12635}, {7676, 56176}, {8236, 34791}, {8261, 11684}, {8543, 61024}, {8583, 60955}, {9856, 63974}, {9943, 59418}, {9954, 15104}, {11038, 58679}, {11682, 42871}, {12680, 43161}, {12709, 52819}, {13257, 21060}, {14988, 64065}, {15481, 60935}, {15569, 24635}, {15570, 62826}, {15726, 41228}, {16133, 60981}, {17604, 24703}, {17609, 38316}, {17632, 57288}, {17642, 30223}, {18482, 49177}, {20116, 24473}, {21153, 54290}, {21168, 64021}, {25466, 41857}, {25524, 60938}, {25681, 61019}, {26066, 60943}, {28609, 58648}, {28610, 63994}, {30332, 34784}, {31658, 60885}, {31671, 31937}, {31838, 38030}, {32636, 60968}, {34339, 59381}, {34790, 41869}, {35514, 63962}, {37566, 60974}, {37722, 41573}, {38092, 58629}, {38121, 58630}, {38149, 58631}, {38170, 58632}, {38185, 58633}, {38202, 46694}, {38203, 58636}, {41389, 44785}, {42884, 62858}, {43166, 57279}, {45043, 58683}, {46873, 58451}, {50836, 63972}, {51516, 64044}, {52835, 64171}, {60909, 60965}, {60910, 64043}, {60919, 64042}, {61006, 64047}, {61035, 64107}

X(64723) = midpoint of X(i) and X(j) for these {i,j}: {144, 3869}, {3962, 14100}, {30332, 34784}, {41228, 63975}
X(64723) = reflection of X(i) in X(j) for these {i,j}: {7, 960}, {65, 9}, {2951, 31793}, {3059, 72}, {3555, 30331}, {3868, 5572}, {4018, 30329}, {5728, 51090}, {5836, 58678}, {12680, 43161}, {14100, 5698}, {31391, 5784}, {31671, 31937}, {35514, 63976}, {44785, 41389}, {63974, 9856}
X(64723) = pole of line {2, 5809} with respect to the Feuerbach hyperbola
X(64723) = X(5480)-of-inner-Conway triangle
X(64723) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {72, 516, 3059}, {144, 3869, 518}, {518, 5698, 14100}, {758, 51090, 5728}, {3868, 52653, 5572}, {3876, 59412, 58634}, {5223, 11372, 42014}, {5784, 17768, 31391}, {5836, 58678, 5686}, {38200, 58635, 3983}, {41228, 63975, 15726}, {60883, 64041, 8581}

X(64724) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(186) AND X(4)-CROSSPEDAL-OF-X(6)

Barycentrics    (2*a^2-b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^2+c^2) : :
X(64724) = 2*X[7575]+X[32275], X[13169]+2*X[32267], -7*X[15020]+X[54216], 2*X[15118]+X[47276], -X[16163]+4*X[47569], -4*X[16321]+X[51431], -X[18374]+3*X[47450], -X[21639]+3*X[61691], X[32244]+5*X[37760], X[32272]+5*X[37958], X[47279]+2*X[47296]

X(64724) lies on these lines: {2, 8541}, {4, 7883}, {6, 13622}, {23, 32239}, {24, 34507}, {25, 599}, {49, 12585}, {51, 54347}, {67, 19596}, {69, 1974}, {125, 2393}, {141, 427}, {184, 61683}, {186, 542}, {232, 15993}, {237, 15526}, {297, 8754}, {340, 419}, {343, 8263}, {378, 50977}, {403, 511}, {420, 648}, {428, 50991}, {468, 524}, {575, 10018}, {576, 7505}, {597, 52297}, {754, 37912}, {826, 21108}, {1205, 41603}, {1350, 44438}, {1352, 18533}, {1495, 47150}, {1503, 13399}, {1593, 54147}, {1596, 5891}, {1613, 36879}, {1992, 38282}, {2781, 51403}, {2930, 37920}, {3098, 35481}, {3147, 63722}, {3284, 44887}, {3515, 15069}, {3542, 11470}, {3564, 37935}, {3580, 8681}, {3619, 52299}, {3620, 6995}, {3630, 46444}, {3631, 44091}, {3763, 12167}, {3818, 35480}, {5032, 53857}, {5064, 50993}, {5094, 21358}, {5139, 44956}, {5201, 44896}, {5622, 44673}, {5965, 19128}, {5969, 46560}, {5972, 22151}, {6240, 18553}, {6403, 7577}, {6623, 50967}, {6697, 9973}, {6776, 11202}, {7575, 32275}, {7714, 50994}, {7716, 62976}, {7794, 27369}, {7826, 44162}, {8537, 14940}, {8623, 61218}, {9822, 37990}, {10295, 11645}, {10516, 18386}, {10602, 26958}, {11160, 62973}, {11179, 35486}, {11180, 37460}, {11188, 21243}, {11255, 60780}, {11405, 16511}, {11550, 61737}, {11574, 26156}, {12220, 31101}, {13169, 32267}, {13394, 53022}, {13473, 29181}, {13567, 40673}, {13619, 29012}, {14984, 63735}, {15020, 54216}, {15074, 43817}, {15118, 47276}, {15360, 37962}, {15533, 62965}, {15585, 26926}, {15750, 64080}, {16003, 37934}, {16163, 47569}, {16321, 51431}, {18374, 47450}, {18560, 55606}, {19118, 40341}, {19510, 37981}, {20582, 62958}, {21419, 34897}, {21637, 58437}, {21639, 61691}, {22165, 62978}, {23200, 35282}, {32127, 32263}, {32244, 37760}, {32272, 37958}, {34118, 61139}, {35325, 36824}, {35491, 55631}, {37196, 47353}, {37197, 53097}, {37347, 45118}, {37473, 43831}, {37765, 38294}, {37933, 63700}, {37977, 41724}, {40670, 41599}, {41614, 61646}, {43273, 55576}, {44084, 62381}, {44125, 62593}, {44126, 62592}, {44146, 50567}, {44375, 47200}, {45312, 50707}, {46151, 46157}, {47279, 47296}, {47328, 61676}, {50955, 55572}, {50990, 62979}, {51186, 62980}, {51438, 63547}, {52104, 55570}, {52290, 59373}, {59707, 62338}

X(64724) = midpoint of X(i) and X(j) for these {i,j}: {67, 19596}, {22151, 41721}, {32113, 62376}, {36824, 38303}
X(64724) = reflection of X(i) in X(j) for these {i,j}: {125, 62376}, {5095, 44102}, {5622, 44673}, {21639, 62375}, {22151, 5972}, {44102, 468}
X(64724) = complement of X(11416)
X(64724) = perspector of circumconic {{A, B, C, X(427), X(4235)}}
X(64724) = X(i)-isoconjugate-of-X(j) for these {i, j}: {82, 895}, {83, 36060}, {111, 34055}, {897, 1176}, {923, 1799}, {3112, 14908}, {4580, 36142}, {4599, 10097}, {10547, 46277}, {14977, 34072}, {28724, 36128}, {30786, 46289}
X(64724) = X(i)-Dao conjugate of X(j) for these {i, j}: {39, 30786}, {141, 895}, {1560, 83}, {2482, 1799}, {3124, 10097}, {6593, 1176}, {15449, 14977}, {23992, 4580}, {34452, 14908}, {40938, 671}, {48317, 58784}, {53981, 60863}, {53983, 5466}
X(64724) = X(i)-Ceva conjugate of X(j) for these {i, j}: {61207, 690}
X(64724) = pole of line {83, 5466} with respect to the polar circle
X(64724) = pole of line {26926, 32366} with respect to the Jerabek hyperbola
X(64724) = pole of line {1194, 44467} with respect to the Kiepert hyperbola
X(64724) = pole of line {32478, 46026} with respect to the Orthic inconic
X(64724) = pole of line {895, 1176} with respect to the Stammler hyperbola
X(64724) = pole of line {18311, 23285} with respect to the Steiner inellipse
X(64724) = pole of line {1368, 1799} with respect to the Wallace hyperbola
X(64724) = pole of line {4580, 34978} with respect to the dual conic of Wallace hyperbola
X(64724) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(41579)}}, {{A, B, C, X(39), X(29959)}}, {{A, B, C, X(141), X(524)}}, {{A, B, C, X(187), X(3313)}}, {{A, B, C, X(427), X(468)}}, {{A, B, C, X(690), X(6593)}}, {{A, B, C, X(1843), X(44102)}}, {{A, B, C, X(3266), X(8891)}}, {{A, B, C, X(3292), X(3917)}}, {{A, B, C, X(3867), X(60428)}}, {{A, B, C, X(5181), X(46165)}}, {{A, B, C, X(5642), X(14424)}}, {{A, B, C, X(5967), X(41586)}}, {{A, B, C, X(8024), X(51541)}}, {{A, B, C, X(15303), X(41583)}}, {{A, B, C, X(15471), X(27376)}}, {{A, B, C, X(16102), X(52094)}}, {{A, B, C, X(17171), X(21108)}}, {{A, B, C, X(21248), X(52898)}}, {{A, B, C, X(51371), X(51429)}}
X(64724) = barycentric product X(i)*X(j) for these (i, j): {4, 7813}, {39, 44146}, {141, 468}, {427, 524}, {1235, 187}, {1560, 46165}, {1843, 3266}, {3933, 60428}, {4235, 826}, {14210, 17442}, {14273, 4576}, {14417, 46151}, {14424, 648}, {16747, 21839}, {17171, 4062}, {20883, 896}, {21016, 6629}, {23285, 61207}, {27376, 6390}, {31068, 46026}, {31125, 5095}, {32459, 47730}, {34336, 46154}, {35325, 35522}, {37778, 3917}, {41676, 690}, {44102, 8024}, {57496, 9019}
X(64724) = barycentric quotient X(i)/X(j) for these (i, j): {39, 895}, {141, 30786}, {187, 1176}, {427, 671}, {468, 83}, {524, 1799}, {690, 4580}, {826, 14977}, {896, 34055}, {1235, 18023}, {1843, 111}, {1964, 36060}, {3005, 10097}, {3051, 14908}, {3292, 28724}, {3787, 6091}, {4235, 4577}, {5095, 52898}, {7813, 69}, {9019, 57481}, {14273, 58784}, {14424, 525}, {14567, 10547}, {17442, 897}, {20883, 46277}, {21108, 62626}, {27369, 32740}, {27376, 17983}, {35325, 691}, {37778, 46104}, {39691, 51258}, {41585, 52141}, {41676, 892}, {44102, 251}, {44146, 308}, {46154, 15398}, {58780, 22105}, {60428, 32085}, {61207, 827}, {61218, 32729}
X(64724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 16789, 3917}, {141, 41583, 51360}, {141, 41584, 1843}, {141, 41585, 427}, {343, 8263, 61667}, {427, 41584, 41585}, {468, 524, 44102}, {524, 44102, 5095}, {2393, 62376, 125}, {5181, 8262, 41586}, {8537, 14940, 25555}, {11405, 52292, 47352}, {21639, 61691, 62375}, {32113, 62376, 2393}, {61683, 63129, 184}

X(64725) = ORTHOLOGY CENTER OF THESE TRIANGLES: INNER-JOHNSON AND X(4)-CROSSPEDAL-OF-X(20)

Barycentrics    3*a^7-3*a^6*(b+c)+a^2*(b-c)^2*(b+c)^3-2*(b-c)^4*(b+c)^3+2*a*(b^2-c^2)^2*(b^2-3*b*c+c^2)-2*a^5*(2*b^2-5*b*c+2*c^2)+4*a^4*(b^3+c^3)-a^3*(b^4+4*b^3*c-2*b^2*c^2+4*b*c^3+c^4) : :
X(64725) = -3*X[4421]+4*X[18242], -4*X[6796]+3*X[34626], -2*X[10306]+3*X[11236], -4*X[12608]+3*X[56177]

X(64725) lies on these lines: {3, 3825}, {4, 1329}, {5, 35249}, {8, 37001}, {11, 20}, {12, 64078}, {30, 10525}, {55, 37437}, {72, 52860}, {165, 17619}, {355, 382}, {376, 10598}, {377, 7958}, {452, 25973}, {511, 39889}, {515, 10912}, {519, 40267}, {528, 12667}, {529, 40290}, {535, 8158}, {550, 26492}, {952, 16127}, {962, 10944}, {1001, 6850}, {1151, 13895}, {1152, 13952}, {1319, 40272}, {1479, 63991}, {1503, 12920}, {1657, 11928}, {1699, 17614}, {1709, 54290}, {1885, 11390}, {2777, 13213}, {2794, 12925}, {2801, 48664}, {2802, 52683}, {2829, 12513}, {3146, 3434}, {3436, 52836}, {3522, 10584}, {3529, 10785}, {3543, 34612}, {3583, 37022}, {3586, 9943}, {3627, 18516}, {3811, 22792}, {3813, 64120}, {3913, 6256}, {4297, 9668}, {4299, 10948}, {4301, 9655}, {4302, 10523}, {4413, 13729}, {4421, 18242}, {4423, 37163}, {5073, 18519}, {5101, 12173}, {5187, 59390}, {5217, 6932}, {5584, 11114}, {5587, 63266}, {5687, 41698}, {5691, 10914}, {5730, 34789}, {5731, 9670}, {5840, 11500}, {5904, 17661}, {5927, 45120}, {6253, 10522}, {6284, 6925}, {6459, 19024}, {6460, 19023}, {6796, 34626}, {6834, 24466}, {6838, 15338}, {6897, 8167}, {6898, 61158}, {6909, 10896}, {6923, 11496}, {6928, 64186}, {6938, 15908}, {6948, 7681}, {6960, 63756}, {6966, 7173}, {7080, 38757}, {7354, 10947}, {7580, 36152}, {7957, 17615}, {7988, 56997}, {7991, 52851}, {9579, 17625}, {9580, 17622}, {9581, 64128}, {9589, 37708}, {9669, 63983}, {10248, 59356}, {10306, 11236}, {10431, 52837}, {10728, 12245}, {10731, 52112}, {10786, 61153}, {10794, 12203}, {10826, 17613}, {10829, 39568}, {10949, 64079}, {11495, 31789}, {12182, 23698}, {12371, 12422}, {12433, 60896}, {12586, 29181}, {12608, 56177}, {12616, 28150}, {12635, 64119}, {12672, 41869}, {12679, 57287}, {12737, 48680}, {13294, 64509}, {15682, 34697}, {15726, 17649}, {15842, 50701}, {17556, 59326}, {17626, 58567}, {17647, 51118}, {17668, 52835}, {18236, 58637}, {25524, 26333}, {28164, 49600}, {28194, 34717}, {28236, 47746}, {35796, 42266}, {35797, 42267}, {42258, 44618}, {42259, 44619}, {43577, 43859}, {44669, 63962}, {50242, 59320}, {63324, 63386}

X(64725) = reflection of X(i) in X(j) for these {i,j}: {3811, 22792}, {3913, 6256}, {10912, 12700}, {12114, 10525}, {12635, 64119}, {13205, 12761}, {64074, 4}, {64076, 5}, {64120, 3813}
X(64725) = X(20)-of-inner-Johnson triangle
X(64725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11826, 1376}, {20, 10724, 12953}, {20, 7288, 38759}, {30, 10525, 12114}, {3146, 3434, 64000}, {5840, 12761, 13205}, {10525, 12114, 11235}, {10826, 64005, 17613}, {26333, 31775, 25524}

X(64726) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(4)-CROSSPEDAL-OF-X(20) AND ANTICEVIAN OF X(20)

Barycentrics    7*a^10-7*a^8*(b^2+c^2)+26*a^4*(b^2-c^2)^2*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)-5*a^2*(b^2-c^2)^2*(b^4+6*b^2*c^2+c^4)-2*a^6*(9*b^4-22*b^2*c^2+9*c^4) : :
X(64726) = -9*X[2]+8*X[5893], -13*X[3]+12*X[61606], -6*X[154]+7*X[50693], -3*X[376]+2*X[5878], -4*X[550]+3*X[5656], -5*X[631]+4*X[22802], -6*X[1853]+5*X[17578], -4*X[2883]+5*X[3522], -3*X[2979]+2*X[36982], -3*X[3060]+4*X[31978], -7*X[3090]+8*X[64027], -5*X[3091]+6*X[10606] and many others

X(64726) lies on these lines: {2, 5893}, {3, 61606}, {4, 74}, {20, 394}, {22, 46373}, {30, 11411}, {64, 3146}, {69, 31369}, {110, 27082}, {146, 38942}, {154, 50693}, {185, 32601}, {323, 46372}, {376, 5878}, {459, 33893}, {511, 30443}, {541, 12118}, {550, 5656}, {631, 22802}, {1073, 63640}, {1131, 8991}, {1132, 13980}, {1370, 22528}, {1503, 5059}, {1620, 62973}, {1657, 34781}, {1853, 17578}, {1885, 11433}, {2071, 64759}, {2781, 64025}, {2883, 3522}, {2979, 36982}, {3060, 31978}, {3090, 64027}, {3091, 10606}, {3183, 59424}, {3184, 59361}, {3524, 61749}, {3525, 11204}, {3529, 6000}, {3532, 47296}, {3543, 6247}, {3619, 63431}, {3627, 35450}, {3830, 61540}, {3832, 6696}, {3839, 40686}, {3854, 61735}, {3855, 23329}, {5056, 23328}, {5071, 25563}, {5562, 36983}, {6146, 49670}, {6616, 51892}, {6622, 21663}, {6640, 38790}, {6759, 17538}, {7401, 43577}, {7464, 32321}, {7691, 33522}, {8549, 40318}, {9306, 43813}, {9544, 46374}, {9778, 12779}, {9812, 12262}, {9833, 11001}, {9899, 28164}, {9914, 11413}, {9919, 37814}, {9961, 64039}, {10151, 58378}, {10182, 61787}, {10192, 21734}, {10193, 61867}, {10299, 61747}, {10304, 16252}, {11202, 62092}, {11999, 31726}, {12103, 32063}, {12220, 12279}, {12278, 32244}, {12315, 15704}, {13201, 22534}, {14216, 33703}, {14361, 36965}, {14862, 62096}, {15005, 52448}, {15105, 49135}, {15138, 37444}, {15316, 35512}, {15682, 18381}, {15683, 17845}, {15717, 64024}, {16386, 53050}, {17821, 62097}, {18383, 62021}, {18400, 49138}, {18405, 50691}, {18560, 18909}, {18913, 44438}, {18918, 35490}, {18925, 35481}, {20725, 35602}, {23291, 34469}, {23332, 50689}, {25406, 34117}, {27089, 33546}, {30552, 37669}, {32140, 34584}, {32602, 35259}, {32767, 41099}, {34170, 41425}, {34286, 58758}, {34785, 41470}, {34786, 62042}, {35864, 42276}, {35865, 42275}, {39874, 64029}, {41464, 41735}, {41715, 46850}, {43841, 55575}, {44762, 62149}, {45771, 51394}, {50692, 50709}, {51358, 58797}, {51538, 63420}, {53496, 63536}, {58434, 61804}, {58795, 62152}, {61138, 64063}, {61680, 61791}, {62120, 64714}, {62124, 64059}, {62155, 64033}, {63657, 63726}

X(64726) = reflection of X(i) in X(j) for these {i,j}: {4, 20427}, {20, 5925}, {3146, 64}, {5895, 5894}, {6225, 20}, {12250, 64758}, {12315, 15704}, {12324, 12250}, {33703, 14216}, {34781, 1657}, {36983, 5562}, {48672, 550}, {49135, 64037}, {51212, 61088}, {54211, 1498}, {64033, 62155}, {64034, 13093}, {64037, 15105}, {64187, 3}
X(64726) = anticomplement of X(5895)
X(64726) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34410, 2}
X(64726) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34410, 6327}
X(64726) = pole of line {6000, 6622} with respect to the Jerabek hyperbola
X(64726) = pole of line {107, 44060} with respect to the Kiepert parabola
X(64726) = pole of line {1498, 41427} with respect to the Stammler hyperbola
X(64726) = pole of line {20580, 58759} with respect to the Steiner circumellipse
X(64726) = pole of line {6527, 30552} with respect to the Wallace hyperbola
X(64726) = X(5894)-of-Gemini-111 triangle
X(64726) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1032), X(16080)}}, {{A, B, C, X(10152), X(15077)}}
X(64726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1204, 37643}, {4, 20427, 54050}, {20, 54211, 1498}, {20, 6225, 11206}, {30, 13093, 64034}, {30, 64758, 12250}, {64, 3146, 32064}, {550, 48672, 5656}, {1498, 15311, 54211}, {1498, 54211, 6225}, {2777, 20427, 4}, {2883, 3522, 35260}, {5893, 5894, 8567}, {5895, 8567, 5893}, {5925, 15311, 20}, {6696, 61721, 3832}, {10606, 51491, 3091}, {12250, 64034, 13093}, {13093, 64034, 12324}

X(64727) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND X(4)-CROSSPEDAL-OF-X(75)

Barycentrics    a*(2*b^2*c^2+a^3*(b+c)-a*b*c*(b+c)-a^2*(b^2+b*c+c^2)) : :

X(64727) lies on these lines: {1, 58583}, {2, 21926}, {3, 740}, {6, 1045}, {9, 58655}, {35, 49474}, {36, 49469}, {37, 1376}, {40, 518}, {55, 75}, {56, 49470}, {57, 64546}, {69, 4433}, {100, 192}, {239, 20992}, {284, 24264}, {480, 51052}, {519, 41430}, {527, 4097}, {536, 4421}, {573, 6007}, {726, 8715}, {742, 12329}, {874, 6374}, {940, 2667}, {956, 49459}, {958, 3696}, {966, 45705}, {984, 5687}, {991, 35104}, {993, 4709}, {999, 49471}, {1001, 3739}, {1011, 32860}, {1018, 60785}, {1486, 8301}, {1621, 4699}, {1716, 21857}, {1740, 21769}, {1742, 3169}, {2175, 54440}, {2223, 3875}, {2234, 28365}, {3286, 49486}, {3295, 24325}, {3685, 20923}, {3694, 18252}, {3728, 4414}, {3742, 64681}, {3747, 27623}, {3759, 36635}, {3797, 23868}, {3842, 9709}, {3871, 24349}, {3886, 37575}, {3923, 37502}, {3941, 4852}, {3980, 25124}, {3993, 25440}, {4000, 8299}, {4011, 25106}, {4022, 17595}, {4032, 37541}, {4068, 15668}, {4191, 32915}, {4199, 56953}, {4203, 4734}, {4360, 21010}, {4361, 8053}, {4363, 64169}, {4387, 18137}, {4413, 4687}, {4423, 4751}, {4427, 25277}, {4428, 4688}, {4447, 17314}, {4515, 58653}, {4557, 17262}, {4642, 49530}, {4686, 61153}, {4732, 9708}, {4764, 61154}, {4772, 61155}, {4812, 36559}, {4821, 61157}, {5132, 5695}, {5220, 22271}, {5432, 21927}, {6600, 24820}, {7075, 20995}, {7083, 17755}, {8167, 31238}, {8424, 36744}, {10267, 64728}, {10306, 29054}, {10310, 30273}, {11248, 29010}, {11322, 64161}, {11343, 27474}, {11358, 17592}, {11491, 63427}, {11496, 64088}, {11499, 20430}, {12513, 28581}, {12635, 20718}, {13476, 42871}, {13576, 27514}, {13587, 51054}, {14839, 64739}, {15569, 25524}, {16345, 27798}, {16370, 50086}, {16405, 46904}, {16417, 50111}, {16418, 50096}, {16684, 17119}, {17117, 23407}, {17156, 22060}, {17157, 32845}, {17318, 20990}, {17768, 48918}, {17788, 32117}, {19237, 31329}, {20367, 35892}, {20760, 21080}, {20794, 23363}, {20891, 32929}, {21495, 27480}, {21775, 21877}, {22316, 52139}, {24248, 53476}, {24357, 36528}, {25083, 40965}, {25269, 52923}, {25439, 49479}, {27471, 42843}, {27556, 46536}, {27639, 29982}, {28580, 31394}, {32921, 37590}, {33158, 50199}, {36740, 49531}, {37507, 49488}, {48696, 49448}, {56177, 63982}, {63304, 63398}

X(64727) = midpoint of X(i) and X(j) for these {i,j}: {1742, 3169}
X(64727) = reflection of X(i) in X(j) for these {i,j}: {64170, 15624}
X(64727) = pole of line {24560, 25925} with respect to the Steiner inellipse
X(64727) = pole of line {5208, 40874} with respect to the Wallace hyperbola
X(64727) = X(75)-of-anti-Mandart-incircle triangle
X(64727) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2665), X(8769)}}, {{A, B, C, X(8770), X(9082)}}
X(64727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 49474, 54410}, {100, 192, 34247}, {536, 15624, 64170}, {4421, 64170, 15624}

X(64728) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS AND X(4)-CROSSPEDAL-OF-X(75)

Barycentrics    2*a^4*b*c+a^5*(b+c)+b*c*(b^2-c^2)^2-3*a^2*b*c*(b^2+c^2)-a^3*(b^3+b^2*c+b*c^2+c^3) : :
X(64728) = -3*X[2]+X[20430], -X[4]+5*X[4699], X[20]+7*X[4772], -X[192]+5*X[631], X[550]+4*X[4739], -5*X[632]+4*X[4698], -X[984]+3*X[26446], X[1278]+7*X[3523], -5*X[1656]+7*X[4751], 3*X[3524]+X[4740], -11*X[3525]+7*X[27268], -7*X[3526]+5*X[4687] and many others

X(64728) lies on these lines: {2, 20430}, {3, 75}, {4, 4699}, {5, 3739}, {10, 24251}, {20, 4772}, {30, 4688}, {37, 140}, {182, 742}, {192, 631}, {228, 20879}, {376, 51040}, {381, 51044}, {496, 11997}, {511, 49481}, {517, 24325}, {518, 5690}, {536, 549}, {537, 50821}, {547, 51038}, {550, 4739}, {573, 29369}, {632, 4698}, {726, 6684}, {740, 1385}, {746, 13335}, {894, 37510}, {952, 3696}, {984, 26446}, {990, 36477}, {991, 29331}, {1009, 26538}, {1278, 3523}, {1483, 28581}, {1484, 2805}, {1656, 4751}, {1733, 37575}, {2782, 21443}, {3524, 4740}, {3525, 27268}, {3526, 4687}, {3530, 4686}, {3576, 49474}, {3579, 29054}, {3628, 31238}, {3644, 15720}, {3654, 31178}, {3655, 50086}, {3842, 11231}, {3993, 10165}, {4032, 37582}, {4192, 4359}, {4361, 37474}, {4664, 5054}, {4681, 14869}, {4704, 10303}, {4709, 5882}, {4718, 12108}, {4726, 15712}, {4755, 11539}, {4764, 61811}, {4788, 61820}, {4821, 15717}, {5050, 49496}, {5071, 51064}, {5446, 58499}, {5657, 24349}, {5844, 49478}, {5886, 40328}, {7201, 11374}, {8731, 17862}, {9588, 49532}, {9840, 20892}, {10164, 50117}, {10168, 50779}, {10246, 49470}, {10267, 64727}, {11171, 32453}, {11179, 51051}, {11362, 49479}, {11695, 58554}, {13373, 64546}, {13632, 37756}, {13731, 20891}, {14213, 22060}, {15026, 58485}, {15178, 49471}, {15310, 59620}, {15569, 38028}, {15681, 51065}, {15687, 51041}, {15692, 51043}, {15694, 51039}, {16058, 54284}, {16850, 24993}, {17225, 50983}, {19540, 19804}, {19546, 24589}, {20254, 27339}, {20881, 60723}, {21926, 26470}, {25124, 35631}, {27484, 36996}, {28204, 50096}, {29016, 48929}, {29028, 49131}, {29069, 48886}, {29073, 41430}, {29077, 49132}, {29327, 31394}, {30944, 48380}, {31317, 48875}, {31993, 37365}, {33813, 38612}, {34200, 51042}, {34718, 51055}, {36659, 64694}, {37727, 49459}, {38066, 50075}, {38068, 50777}, {38122, 51058}, {38127, 49510}, {38760, 51062}, {49450, 59503}, {49475, 61286}, {49483, 61524}, {49498, 63143}, {49523, 61614}, {49678, 61287}, {51052, 59381}, {63307, 63398}

X(64728) = midpoint of X(i) and X(j) for these {i,j}: {3, 75}, {376, 51040}, {381, 51044}, {549, 51048}, {3654, 31178}, {3655, 50086}, {4709, 5882}, {11179, 51051}, {11362, 49479}, {15681, 51065}, {20430, 63427}, {30271, 64088}, {34718, 51055}, {37727, 49459}
X(64728) = reflection of X(i) in X(j) for these {i,j}: {5, 3739}, {37, 140}, {549, 51049}, {5446, 58499}, {15687, 51041}, {20430, 61522}, {49471, 15178}, {49475, 61286}, {50779, 10168}, {51038, 547}, {51042, 34200}, {51045, 549}, {58554, 11695}, {64088, 61549}, {64546, 13373}
X(64728) = complement of X(20430)
X(64728) = anticomplement of X(61522)
X(64728) = pole of line {26640, 46383} with respect to the Steiner inellipse
X(64728) = X(75)-of-anti-X3-ABC-reflections triangle
X(64728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20430, 61522}, {2, 63427, 20430}, {3, 75, 29010}, {30, 61549, 64088}, {536, 51049, 549}, {4688, 64088, 61549}, {15694, 51039, 51488}, {30271, 64088, 30}, {51048, 51049, 51045}

X(64729) = ORTHOLOGY CENTER OF THESE TRIANGLES: MIDHEIGHT AND X(6)-CROSSPEDAL-OF-X(3)

Barycentrics    4*a^10-a^8*(b^2+c^2)+20*a^4*(b^2-c^2)^2*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)-2*a^6*(9*b^4-8*b^2*c^2+9*c^4) : :
X(64729) = -3*X[3]+X[41465], -3*X[4]+X[3426], -3*X[5]+2*X[4550], -3*X[5890]+X[10938], -2*X[31861]+3*X[38136]

X(64729) lies on these lines: {2, 54838}, {3, 41465}, {4, 3426}, {5, 4550}, {6, 30}, {51, 974}, {64, 16198}, {74, 427}, {113, 44212}, {140, 4549}, {143, 22530}, {185, 973}, {323, 38323}, {376, 53780}, {381, 37643}, {382, 11431}, {389, 3627}, {393, 38920}, {399, 38321}, {541, 1539}, {546, 9786}, {549, 18388}, {550, 10610}, {578, 8717}, {1192, 3628}, {1353, 17702}, {1368, 37470}, {1480, 15171}, {1495, 37458}, {1511, 59553}, {1514, 1596}, {1531, 37648}, {1595, 20303}, {1620, 12108}, {2777, 5480}, {2883, 7715}, {3146, 11432}, {3431, 10295}, {3529, 11426}, {3531, 35512}, {3534, 11427}, {3543, 44750}, {3564, 63646}, {3575, 11456}, {3581, 15760}, {3830, 11433}, {3853, 39571}, {3861, 15752}, {5066, 26958}, {5133, 34796}, {5663, 19161}, {5890, 10938}, {5895, 17822}, {6000, 9969}, {6102, 12235}, {6240, 12254}, {6247, 32393}, {6580, 18990}, {6800, 47340}, {6823, 37478}, {7378, 35450}, {7576, 12112}, {7699, 52293}, {7986, 11544}, {8703, 23292}, {10110, 31978}, {10293, 10721}, {10301, 32111}, {10564, 44241}, {11001, 63030}, {11002, 62288}, {11064, 44273}, {11245, 35480}, {11425, 12103}, {11566, 11744}, {11745, 22802}, {11801, 34802}, {12167, 39874}, {12173, 18914}, {12241, 62036}, {12244, 35484}, {13382, 41362}, {13403, 62041}, {13488, 18431}, {13754, 14913}, {14389, 44285}, {14763, 59399}, {14805, 44249}, {15018, 52069}, {15037, 18563}, {15051, 44268}, {15068, 31833}, {15080, 44239}, {15311, 23300}, {15435, 18358}, {15682, 63031}, {15687, 18390}, {15699, 44673}, {15873, 22968}, {18494, 26926}, {18533, 26864}, {18537, 62209}, {18570, 52019}, {18583, 49669}, {18911, 47339}, {19039, 23259}, {19040, 23249}, {22660, 43586}, {26879, 63662}, {31829, 37483}, {31860, 64471}, {31861, 38136}, {32423, 49011}, {34224, 43596}, {36852, 40112}, {37473, 44791}, {37505, 62162}, {37984, 61506}, {41447, 61680}, {42283, 44634}, {42284, 44633}, {43588, 50006}, {43903, 52295}, {44107, 61744}, {44280, 59771}, {44547, 50193}, {45019, 46030}, {45968, 64183}, {47003, 52743}, {47096, 48912}, {48876, 50008}, {55572, 61606}, {63659, 63727}

X(64729) = midpoint of X(i) and X(j) for these {i,j}: {4, 64094}, {376, 53780}, {3146, 11820}, {3543, 44750}, {4846, 40909}, {10293, 10721}, {33534, 43621}
X(64729) = reflection of X(i) in X(j) for these {i,j}: {5, 7706}, {4549, 140}, {11472, 546}, {15687, 51993}, {15704, 8717}, {34802, 11801}, {48876, 50008}, {49669, 18583}, {64097, 18358}
X(64729) = pole of line {1514, 32062} with respect to the Jerabek hyperbola
X(64729) = pole of line {381, 5158} with respect to the Kiepert hyperbola
X(64729) = pole of line {9209, 61656} with respect to the Orthic inconic
X(64729) = pole of line {15066, 54994} with respect to the Stammler hyperbola
X(64729) = pole of line {9007, 9209} with respect to the dual conic of DeLongchamps circle
X(64729) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3531), X(58082)}}, {{A, B, C, X(4846), X(56270)}}, {{A, B, C, X(34288), X(54838)}}
X(64729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1514, 34417, 1596}, {18420, 64097, 18358}, {33534, 43621, 30}

X(64730) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(2) AND X(6)-CROSSPEDAL-OF-X(51)

Barycentrics    2*a^6-12*a^2*b^2*c^2-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2) : :
X(64730) = 2*X[3]+X[16657], -4*X[5]+X[16654], X[51]+2*X[10691], -X[428]+4*X[6688], 5*X[631]+X[12022], -10*X[632]+X[12134], -10*X[1656]+X[16655], X[1885]+8*X[17704], -7*X[3090]+X[16658], 7*X[3523]+2*X[12241], -11*X[3525]+2*X[64035], 17*X[3533]+X[34224] and many others

X(64730) lies on these lines: {2, 154}, {3, 16657}, {4, 33534}, {5, 16654}, {6, 46336}, {20, 3066}, {30, 373}, {51, 10691}, {125, 128}, {141, 8546}, {182, 11064}, {235, 13347}, {323, 12007}, {343, 7484}, {376, 20192}, {382, 5544}, {394, 14912}, {427, 38317}, {428, 6688}, {468, 5092}, {511, 43957}, {524, 7998}, {542, 15082}, {549, 39242}, {550, 34417}, {631, 12022}, {632, 12134}, {858, 3589}, {1350, 63084}, {1368, 19131}, {1370, 17825}, {1656, 16655}, {1657, 62209}, {1885, 17704}, {1899, 16419}, {1995, 44882}, {2777, 16836}, {3090, 16658}, {3124, 63548}, {3523, 12241}, {3525, 64035}, {3533, 34224}, {3564, 5650}, {3575, 44862}, {3580, 7496}, {3631, 5888}, {3819, 5965}, {3853, 44300}, {3917, 7734}, {5012, 53415}, {5054, 44665}, {5056, 16621}, {5068, 16656}, {5480, 16063}, {5640, 29181}, {5646, 15069}, {5651, 48906}, {5656, 6804}, {5893, 13203}, {5943, 7667}, {5972, 20190}, {6090, 11179}, {6388, 37512}, {6676, 61691}, {6677, 22352}, {6815, 18405}, {7386, 10601}, {7399, 23325}, {7465, 26005}, {7485, 13567}, {7493, 53094}, {7495, 47296}, {7503, 23328}, {7605, 10989}, {7703, 51127}, {8550, 15066}, {9140, 20582}, {9820, 37471}, {9832, 32525}, {10168, 47097}, {10300, 18583}, {10301, 48898}, {10303, 12024}, {10541, 59767}, {10545, 37900}, {11284, 46264}, {11433, 62174}, {11451, 52397}, {11645, 12045}, {11745, 15028}, {12100, 32225}, {12108, 12370}, {13339, 14643}, {14516, 55864}, {14561, 31152}, {14810, 47582}, {15080, 15448}, {15126, 58450}, {15311, 20791}, {15431, 61914}, {15805, 45089}, {16659, 61886}, {17508, 44210}, {18928, 33586}, {19130, 46517}, {20725, 49669}, {21766, 37644}, {23061, 32455}, {25964, 37449}, {26929, 55438}, {26939, 55437}, {29012, 63632}, {31521, 61737}, {32216, 38064}, {32223, 55674}, {34799, 61848}, {35268, 44212}, {36990, 59777}, {37454, 58445}, {37515, 61747}, {37645, 53093}, {37899, 48892}, {41603, 58437}, {41673, 44479}, {43575, 61821}, {44076, 55863}, {44201, 54006}, {45731, 61852}, {45970, 61835}, {47095, 48895}, {47313, 50971}, {47314, 50959}, {52284, 63119}, {54013, 64080}, {55711, 63082}, {55858, 64036}, {59659, 61134}, {61773, 64060}

X(64730) = midpoint of X(i) and X(j) for these {i,j}: {3917, 61712}
X(64730) = reflection of X(i) in X(j) for these {i,j}: {35283, 2}, {61658, 61712}, {61712, 45298}
X(64730) = pole of line {231, 7735} with respect to the Kiepert hyperbola
X(64730) = pole of line {52742, 54259} with respect to the Orthic inconic
X(64730) = pole of line {1350, 54041} with respect to the Stammler hyperbola
X(64730) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3424), X(45088)}}, {{A, B, C, X(35140), X(35283)}}
X(64730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1503, 35283}, {2, 25406, 35259}, {2, 5085, 13394}, {2, 51737, 35266}, {2, 6800, 61507}, {3, 37648, 32269}, {3, 54012, 37648}, {1368, 38110, 61743}, {1368, 43650, 37649}, {3819, 11245, 64062}, {3917, 61712, 34380}, {7734, 45298, 3917}, {10300, 18583, 51360}, {34380, 45298, 61712}, {34380, 61712, 61658}, {43650, 61743, 38110}, {51737, 61507, 6800}

X(64731) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-AQUILA AND X(7)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a^6+6*a^4*b*c-3*a^5*(b+c)-3*a^2*(b^2-c^2)^2+2*(b^2-c^2)^2*(b^2-3*b*c+c^2)-a*(b-c)^2*(3*b^3+b^2*c+b*c^2+3*c^3)+a^3*(6*b^3-2*b^2*c-2*b*c^2+6*c^3)) : :
X(64731) = -3*X[16173]+X[64330], 3*X[59385]+X[64321]

X(64731) lies on these lines: {1, 227}, {3, 5883}, {4, 3649}, {5, 12635}, {7, 2829}, {8, 6991}, {10, 1482}, {11, 2099}, {20, 45084}, {30, 60896}, {40, 4004}, {55, 48363}, {56, 30538}, {65, 11496}, {104, 4860}, {200, 11525}, {355, 36867}, {381, 21635}, {382, 12267}, {392, 3646}, {405, 2949}, {496, 64266}, {515, 5542}, {517, 1001}, {758, 6913}, {938, 3427}, {942, 12114}, {946, 5722}, {952, 20330}, {958, 24474}, {993, 2095}, {999, 11715}, {1000, 1389}, {1012, 1768}, {1125, 64315}, {1158, 31794}, {1159, 2800}, {1320, 63168}, {1329, 5761}, {1376, 37533}, {1388, 45977}, {1490, 16616}, {1512, 17718}, {1532, 10051}, {1699, 5425}, {1837, 10894}, {2771, 16112}, {2802, 6600}, {3057, 64342}, {3091, 34195}, {3306, 50371}, {3309, 7986}, {3339, 64118}, {3340, 45776}, {3485, 5804}, {3487, 18242}, {3488, 5842}, {3560, 22936}, {3671, 64119}, {3742, 37611}, {3753, 37569}, {3754, 10306}, {3811, 10222}, {3812, 37531}, {3817, 62822}, {3924, 5706}, {3940, 10175}, {4049, 28292}, {4867, 7988}, {5221, 6906}, {5427, 6950}, {5439, 63391}, {5450, 5708}, {5535, 16370}, {5665, 56273}, {5728, 6001}, {5730, 8227}, {5777, 12559}, {5794, 55108}, {5806, 6261}, {5901, 10198}, {6147, 6256}, {6245, 17706}, {6260, 12563}, {6265, 10247}, {6825, 11281}, {6826, 44669}, {6832, 21677}, {6864, 22991}, {6911, 22935}, {6918, 22836}, {6930, 17768}, {6934, 10543}, {6938, 11246}, {7682, 64110}, {7962, 64346}, {7971, 11379}, {7989, 41696}, {8275, 31434}, {9803, 10883}, {9957, 12260}, {10044, 37468}, {10073, 18393}, {10107, 49163}, {10177, 43166}, {10202, 63991}, {10532, 10950}, {10573, 63257}, {10597, 10944}, {10679, 64745}, {10893, 12047}, {11009, 15079}, {11036, 12667}, {11108, 31806}, {11224, 36835}, {11248, 61541}, {11278, 58643}, {11518, 12675}, {11520, 14872}, {11522, 45035}, {11523, 58631}, {11729, 45701}, {11827, 55109}, {12116, 64327}, {12245, 19855}, {12332, 12736}, {12433, 48482}, {14110, 54392}, {14151, 38152}, {14497, 24297}, {15016, 37022}, {15173, 64329}, {15299, 18421}, {16173, 64330}, {16174, 48667}, {16417, 54192}, {17532, 54154}, {18221, 37434}, {18446, 44840}, {18761, 24475}, {19925, 62860}, {22770, 30147}, {25415, 41539}, {26332, 37730}, {26333, 39542}, {31786, 64675}, {33179, 64116}, {34231, 36127}, {34339, 64074}, {34588, 60744}, {37002, 52783}, {41711, 59388}, {56426, 64165}, {59385, 64321}, {59387, 63159}, {63986, 64332}, {64001, 64310}

X(64731) = midpoint of X(i) and X(j) for these {i,j}: {1, 3577}, {4, 64324}, {355, 36867}, {946, 14563}, {1482, 40587}, {11041, 64322}
X(64731) = reflection of X(i) in X(j) for these {i,j}: {3427, 63980}, {11500, 64328}, {12114, 64334}, {64109, 5901}, {64315, 1125}, {64316, 37837}, {64317, 18242}, {64325, 13374}, {64335, 5}, {64733, 64732}, {64735, 1}
X(64731) = inverse of X(2099) in Feuerbach hyperbola
X(64731) = pole of line {2099, 18446} with respect to the Feuerbach hyperbola
X(64731) = X(3577)-of-anti-Aquila triangle
X(64731) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7686, 11500}, {517, 64732, 64733}, {1482, 40587, 28234}, {1482, 5886, 5289}, {3340, 64669, 45776}, {3485, 5804, 7681}, {5603, 11041, 64322}, {5603, 18391, 7680}, {7982, 64673, 63976}

X(64732) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS AND X(7)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(2*a^3+3*b^3-7*b^2*c-7*b*c^2+3*c^3-3*a^2*(b+c)-2*a*(b^2+b*c+c^2)) : :
X(64732) = 3*X[2]+X[11041], -5*X[1698]+X[36922], X[3243]+3*X[9623], -X[5223]+3*X[9708], -5*X[5818]+X[64313], -X[12630]+9*X[15933], 3*X[38149]+X[64321], -3*X[57298]+X[64330]

X(64732) lies on these lines: {1, 3689}, {2, 11041}, {3, 3577}, {8, 36867}, {9, 1159}, {10, 5719}, {21, 4004}, {35, 3922}, {37, 4752}, {65, 191}, {72, 32635}, {100, 3753}, {140, 64315}, {142, 952}, {210, 5425}, {355, 3824}, {405, 50193}, {443, 37739}, {514, 4670}, {515, 31657}, {517, 1001}, {519, 3826}, {551, 3035}, {632, 1125}, {758, 15481}, {942, 956}, {958, 31794}, {971, 64320}, {997, 61158}, {1000, 1392}, {1126, 31503}, {1385, 3812}, {1698, 36922}, {2093, 16418}, {2320, 35271}, {2802, 42819}, {3243, 9623}, {3306, 5126}, {3340, 11108}, {3560, 64311}, {3579, 3754}, {3624, 11011}, {3636, 33895}, {3656, 26105}, {3679, 44840}, {3697, 34195}, {3740, 62822}, {3742, 51788}, {3816, 51709}, {3820, 64110}, {3822, 11698}, {3833, 22935}, {3838, 38140}, {3872, 5049}, {3918, 56176}, {3919, 4640}, {3983, 41696}, {3999, 16499}, {4002, 34772}, {4005, 16126}, {4018, 5260}, {4084, 5302}, {4323, 17559}, {4423, 25415}, {4649, 60353}, {4662, 62860}, {4663, 53114}, {4674, 4689}, {4682, 49682}, {4848, 6675}, {4867, 61686}, {4883, 49494}, {4930, 36835}, {5044, 64673}, {5048, 8275}, {5128, 17571}, {5223, 9708}, {5248, 10107}, {5426, 63211}, {5436, 12702}, {5437, 7966}, {5439, 24928}, {5440, 61156}, {5727, 17528}, {5775, 5791}, {5790, 25525}, {5795, 6147}, {5818, 64313}, {5836, 25439}, {5837, 50205}, {5853, 15935}, {5880, 28160}, {5886, 6978}, {5901, 9843}, {5919, 12653}, {6667, 11230}, {6690, 50821}, {6692, 38028}, {6736, 63282}, {6738, 31419}, {6911, 64312}, {7489, 10273}, {8162, 64203}, {8582, 37737}, {8728, 64163}, {9269, 14077}, {9345, 49487}, {9940, 64318}, {9956, 28628}, {9957, 54392}, {10156, 37611}, {10202, 12773}, {11260, 58565}, {11278, 14150}, {11551, 34606}, {11682, 16842}, {12436, 34773}, {12513, 50192}, {12609, 18480}, {12630, 15933}, {13384, 16417}, {13411, 44848}, {15178, 25524}, {15829, 16853}, {16137, 21075}, {16862, 56387}, {17527, 64160}, {17718, 51362}, {18421, 41712}, {18443, 64319}, {18491, 64328}, {19526, 63144}, {25466, 32213}, {26727, 29640}, {31197, 45763}, {31792, 64675}, {33697, 49113}, {33771, 56174}, {34339, 34862}, {37281, 64310}, {37313, 61155}, {37606, 64112}, {37623, 61541}, {38042, 58463}, {38149, 64321}, {40262, 64316}, {51787, 61159}, {54286, 61153}, {54391, 64664}, {57298, 64330}, {59337, 61154}, {63130, 63271}

X(64732) = midpoint of X(i) and X(j) for these {i,j}: {1, 40587}, {3, 3577}, {8, 36867}, {9, 1159}, {10, 14563}, {355, 64324}, {9623, 15934}, {9708, 11529}, {11041, 64734}, {64318, 64334}, {64320, 64326}, {64731, 64733}
X(64732) = reflection of X(i) in X(j) for these {i,j}: {64109, 1125}, {64315, 140}, {64316, 40262}, {64335, 9956}, {64735, 15178}
X(64732) = complement of X(64734)
X(64732) = X(3577)-of-anti-X3-ABC-reflections triangle
X(64732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11041, 64734}, {355, 28629, 3824}, {1125, 28234, 64109}, {64320, 64326, 971}, {64731, 64733, 517}

X(64733) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND X(7)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a^6-a^4*(b-c)^2-2*a^5*(b+c)+(b^2-c^2)^2*(b^2-4*b*c+c^2)-2*a*(b-c)^2*(b^3-2*b^2*c-2*b*c^2+c^3)+a^3*(4*b^3-6*b^2*c-6*b*c^2+4*c^3)-a^2*(b^4-2*b^3*c-14*b^2*c^2-2*b*c^3+c^4)) : :
X(64733) = -3*X[2]+X[64322], X[4900]+7*X[30389], X[24297]+3*X[34474], 3*X[59413]+X[64321]

X(64733) lies on circumconic {{A, B, C, X(3872), X(28234)}} and on these lines: {1, 631}, {2, 64322}, {3, 5836}, {8, 224}, {9, 2800}, {10, 5720}, {21, 40}, {55, 63132}, {56, 39779}, {78, 36922}, {100, 3576}, {140, 64109}, {165, 6950}, {200, 38127}, {355, 9710}, {484, 21165}, {515, 2550}, {516, 6930}, {517, 1001}, {519, 18443}, {549, 64742}, {936, 40257}, {946, 5084}, {958, 1158}, {993, 3359}, {997, 3035}, {1006, 5119}, {1376, 64312}, {1385, 3913}, {1482, 10179}, {1537, 4679}, {1621, 12703}, {1698, 6949}, {1699, 6965}, {1706, 6796}, {1750, 50796}, {2099, 64107}, {2551, 12608}, {2802, 52769}, {2951, 28172}, {2975, 59333}, {3149, 3698}, {3244, 12521}, {3340, 31806}, {3427, 12616}, {3428, 3753}, {3523, 4861}, {3579, 63754}, {3617, 17857}, {3626, 5534}, {3654, 28465}, {3679, 5531}, {3754, 5709}, {3811, 5690}, {3812, 22770}, {3870, 63143}, {3890, 7982}, {3895, 34486}, {4321, 38123}, {4666, 16200}, {4853, 5882}, {4900, 30389}, {5231, 10265}, {5234, 54156}, {5248, 49163}, {5258, 63399}, {5425, 15104}, {5450, 37560}, {5584, 37287}, {5587, 6932}, {5705, 64763}, {5759, 28194}, {5779, 6001}, {5789, 31494}, {5795, 6256}, {5818, 63988}, {5881, 10884}, {5884, 57279}, {5903, 55104}, {6260, 56273}, {6282, 38399}, {6326, 64141}, {6762, 12005}, {6875, 59316}, {6889, 10039}, {6897, 45287}, {6908, 64317}, {6937, 10827}, {6940, 37618}, {6947, 30384}, {6955, 21578}, {6963, 23708}, {6969, 10175}, {6986, 14923}, {7672, 11529}, {7962, 64676}, {7971, 20117}, {7987, 63752}, {8158, 13374}, {8666, 37534}, {9709, 37837}, {9746, 28292}, {9940, 12513}, {10156, 51788}, {10164, 37611}, {10393, 10573}, {10857, 51705}, {10902, 63130}, {11014, 17566}, {11108, 45776}, {11278, 64670}, {11496, 31798}, {12114, 31787}, {12514, 37562}, {12524, 26921}, {12565, 31673}, {12629, 13607}, {12635, 58643}, {12704, 64284}, {12736, 54408}, {13145, 24467}, {13205, 32613}, {13384, 54192}, {13528, 16370}, {13624, 63753}, {15016, 62874}, {16004, 64076}, {17502, 63751}, {17636, 34879}, {18250, 54198}, {18528, 38155}, {21231, 53996}, {22758, 64129}, {24297, 34474}, {25440, 64269}, {26066, 64279}, {28160, 43178}, {30147, 37531}, {31424, 40256}, {32633, 35242}, {34339, 62858}, {34489, 37407}, {36846, 64199}, {36867, 37615}, {37106, 63136}, {37569, 59417}, {37828, 52265}, {38460, 54445}, {41229, 64021}, {41859, 64291}, {48482, 64333}, {48667, 58666}, {50528, 59387}, {51077, 64667}, {57284, 64310}, {59413, 64321}, {62838, 64189}

X(64733) = midpoint of X(i) and X(j) for these {i,j}: {3, 40587}, {8, 64324}, {40, 3577}, {7966, 11525}, {9623, 30503}, {11362, 14563}, {64311, 64318}, {64319, 64320}
X(64733) = reflection of X(i) in X(j) for these {i,j}: {1158, 64311}, {3427, 12616}, {6261, 64328}, {48482, 64333}, {64109, 140}, {64315, 6684}, {64316, 6796}, {64325, 3812}, {64335, 10}, {64731, 64732}, {64735, 1385}
X(64733) = complement of X(64322)
X(64733) = X(4549)-of-1st-circumperp triangle
X(64733) = X(4550)-of-hexyl triangle
X(64733) = X(4846)-of-2nd-circumperp triangle
X(64733) = X(7706)-of-excentral triangle
X(64733) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 64732, 64731}, {958, 31788, 1158}, {3576, 11525, 7966}, {4853, 8726, 5882}, {6684, 28234, 64315}, {11014, 31423, 19861}, {11362, 14563, 28234}, {26446, 61146, 997}, {30147, 43174, 37531}, {64319, 64320, 515}

X(64734) = ORTHOLOGY CENTER OF THESE TRIANGLES: JOHNSON AND X(7)-CROSSPEDAL-OF-X(1)

Barycentrics    a^4+6*a^2*b*c-3*a^3*(b+c)-(b^2-c^2)^2+a*(3*b^3+b^2*c+b*c^2+3*c^3) : :
X(64734) = -3*X[2]+X[11041], -5*X[4668]+X[4900], -2*X[15935]+3*X[38316], -X[24297]+3*X[59415]

X(64734) lies on these lines: {1, 5791}, {2, 11041}, {3, 5837}, {5, 3577}, {8, 392}, {9, 952}, {10, 1482}, {11, 3679}, {72, 10941}, {80, 4679}, {142, 1159}, {149, 3419}, {210, 12647}, {355, 960}, {405, 37739}, {442, 11682}, {443, 50193}, {514, 4643}, {515, 5779}, {517, 2550}, {519, 1001}, {936, 5690}, {944, 31445}, {958, 16202}, {993, 3655}, {997, 3035}, {1125, 14563}, {1376, 3654}, {1385, 5770}, {1387, 5231}, {1478, 31165}, {1698, 15950}, {1836, 3899}, {2886, 3656}, {3295, 6737}, {3340, 8728}, {3427, 5787}, {3452, 5790}, {3576, 13226}, {3617, 7705}, {3625, 51572}, {3626, 21627}, {3632, 5506}, {3652, 12514}, {3678, 32049}, {3789, 14077}, {3822, 34647}, {3869, 14450}, {3872, 25416}, {3876, 64087}, {3878, 5794}, {3911, 35272}, {3925, 25415}, {3927, 10106}, {3940, 31397}, {4004, 37462}, {4533, 56879}, {4662, 49169}, {4668, 4900}, {4677, 30393}, {4752, 17281}, {4848, 16408}, {4853, 47746}, {4867, 17718}, {4930, 64110}, {5087, 61263}, {5119, 6154}, {5126, 5744}, {5128, 17563}, {5234, 61296}, {5251, 37740}, {5252, 5692}, {5258, 37738}, {5259, 37724}, {5273, 7967}, {5438, 61524}, {5698, 28160}, {5705, 5901}, {5720, 64319}, {5730, 11374}, {5745, 10246}, {5777, 64317}, {5795, 12645}, {5844, 9623}, {5855, 54318}, {5882, 18249}, {5887, 6259}, {6224, 62838}, {6734, 11373}, {7317, 56090}, {7373, 24391}, {7483, 56387}, {7971, 37424}, {7982, 31419}, {8158, 9709}, {8580, 63143}, {9945, 35445}, {10051, 44784}, {10176, 15863}, {10222, 19843}, {10573, 25917}, {10609, 35258}, {10742, 37822}, {10944, 41229}, {11011, 19854}, {11108, 64163}, {11729, 38112}, {12526, 18990}, {12572, 18525}, {12625, 15172}, {12667, 31821}, {12701, 47033}, {12702, 57284}, {14110, 64332}, {14647, 64659}, {15170, 64368}, {15178, 30478}, {15712, 45036}, {15935, 38316}, {16792, 49681}, {17532, 51423}, {18228, 59388}, {18250, 47745}, {18395, 24954}, {20103, 38127}, {21616, 61261}, {24297, 59415}, {24390, 64367}, {24474, 64325}, {24477, 51788}, {26066, 30144}, {26363, 61276}, {26727, 62711}, {27131, 59416}, {30827, 38042}, {30852, 38058}, {31424, 34773}, {31435, 37730}, {31446, 61286}, {31458, 61282}, {34606, 37708}, {36920, 61686}, {37611, 64320}, {38060, 38097}, {38067, 64154}, {45770, 64275}, {49168, 58679}, {50821, 59572}

X(64734) = midpoint of X(i) and X(j) for these {i,j}: {1, 36922}, {8, 1000}, {72, 39779}, {944, 64313}, {8275, 11525}, {14110, 64332}
X(64734) = reflection of X(i) in X(j) for these {i,j}: {1, 64109}, {3, 64315}, {355, 64335}, {1159, 142}, {3577, 5}, {5787, 3427}, {11041, 64732}, {14563, 1125}, {24474, 64325}, {36867, 1}, {37727, 64735}, {40587, 10}, {64324, 1385}
X(64734) = complement of X(11041)
X(64734) = anticomplement of X(64732)
X(64734) = X(3577)-of-Johnson triangle
X(64734) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11041, 64732}, {8, 392, 5722}, {10, 13464, 31493}, {10, 28234, 40587}, {10, 5289, 5886}, {3679, 8275, 11525}, {3878, 5794, 12699}, {5730, 24987, 11374}, {11362, 12447, 9709}, {36922, 64109, 36867}

X(64735) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND X(7)-CROSSPEDAL-OF-X(8)

Barycentrics    a*(a^6-a^5*(b+c)+2*b*c*(b^2-c^2)^2-2*a^4*(b^2+5*b*c+c^2)+a^2*(b-c)^2*(b^2+10*b*c+c^2)+2*a^3*(b^3+5*b^2*c+5*b*c^2+c^3)-a*(b-c)^2*(b^3+11*b^2*c+11*b*c^2+c^3)) : :
X(64735) = -X[4900]+9*X[30392]

X(64735) lies on these lines: {1, 227}, {3, 3244}, {4, 13865}, {12, 10806}, {35, 8275}, {36, 16236}, {55, 104}, {56, 11041}, {214, 1376}, {390, 2829}, {405, 61296}, {411, 20057}, {514, 24328}, {515, 6767}, {517, 11495}, {519, 6600}, {944, 3303}, {952, 1001}, {956, 34486}, {958, 16202}, {999, 14563}, {1056, 5842}, {1058, 18242}, {1319, 64341}, {1385, 3913}, {1480, 3309}, {1482, 16117}, {1483, 5428}, {1616, 37699}, {1621, 64313}, {1697, 12675}, {2095, 3892}, {2346, 3427}, {3058, 12115}, {3241, 3428}, {3295, 5882}, {3304, 11491}, {3488, 64317}, {3636, 6918}, {3655, 10679}, {3748, 64332}, {3880, 8730}, {3900, 37628}, {4326, 6001}, {4413, 38665}, {4421, 10269}, {4423, 59388}, {4428, 22758}, {4860, 48363}, {4900, 30392}, {5218, 20418}, {5251, 61294}, {5288, 61289}, {5434, 37000}, {5534, 58679}, {5541, 58595}, {5603, 8162}, {5657, 51463}, {5687, 11525}, {5709, 58609}, {5720, 10179}, {5790, 8167}, {5836, 64668}, {5919, 18446}, {6154, 6955}, {6244, 51705}, {6253, 10597}, {6256, 15172}, {6261, 31792}, {6284, 10805}, {6796, 7373}, {6913, 28236}, {6985, 33179}, {6986, 20050}, {7580, 16200}, {7971, 30337}, {7972, 15175}, {8166, 64148}, {8168, 26446}, {8273, 12245}, {10167, 12703}, {10222, 64077}, {10283, 18491}, {10680, 61284}, {10786, 37722}, {10894, 12116}, {10902, 61288}, {11108, 47745}, {11194, 32613}, {11227, 63132}, {11236, 32213}, {11238, 63270}, {11249, 61286}, {11362, 12333}, {11499, 37624}, {11510, 37734}, {11531, 37426}, {11715, 37606}, {12000, 18481}, {12001, 61282}, {12005, 12702}, {12520, 13600}, {12575, 64119}, {12735, 22775}, {12773, 61159}, {13405, 64333}, {15170, 26333}, {15178, 25524}, {15931, 51093}, {18518, 61276}, {24929, 64334}, {26487, 32214}, {28194, 43182}, {28466, 51087}, {34471, 64337}, {34474, 61154}, {34773, 37622}, {36746, 37588}, {37002, 63273}, {37525, 51767}, {37556, 45776}, {37740, 57278}, {38669, 61155}, {38693, 61157}, {39883, 49465}, {40257, 64326}, {43179, 64156}, {49163, 58567}, {50843, 52148}, {51779, 63992}, {53053, 64118}, {54342, 64145}

X(64735) = midpoint of X(i) and X(j) for these {i,j}: {1, 7966}, {944, 64322}, {1000, 64324}, {7972, 64330}, {37727, 64734}
X(64735) = reflection of X(i) in X(j) for these {i,j}: {11500, 64312}, {64319, 37837}, {64323, 13607}, {64326, 40257}, {64335, 64109}, {64731, 1}, {64732, 15178}, {64733, 1385}
X(64735) = X(1000)-of-anti-Mandart-incircle triangle
X(64735) = X(7966)-of-anti-Aquila triangle
X(64735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 64316, 64325}, {55, 64324, 64311}, {944, 3303, 11496}, {952, 64109, 64335}, {1000, 7967, 64324}, {3295, 5882, 12114}, {3655, 10679, 63991}, {12116, 15888, 10894}, {13607, 28234, 64323}, {16202, 37727, 958}, {34486, 61291, 956}, {34773, 37622, 64074}

X(64736) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(57) AND X(7)-CROSSPEDAL-OF-X(8)

Barycentrics    (a-2*(b+c))*(3*a-b-c)*(a+b-c)*(a-b+c) : :
X(64736) = -4*X[5289]+5*X[20196], -4*X[30305]+5*X[51791]

X(64736) lies on these lines: {1, 140}, {7, 31145}, {8, 226}, {11, 11224}, {12, 4668}, {36, 61291}, {46, 61296}, {56, 3633}, {57, 519}, {65, 3632}, {73, 50575}, {80, 31162}, {145, 1420}, {165, 37740}, {200, 5855}, {388, 3625}, {484, 50811}, {517, 1864}, {528, 61007}, {912, 4338}, {944, 5128}, {952, 2093}, {956, 3256}, {1000, 51779}, {1317, 13462}, {1319, 51093}, {1405, 4873}, {1445, 41558}, {1467, 64768}, {1482, 50443}, {1697, 3488}, {1698, 11011}, {1708, 3895}, {1737, 16200}, {1743, 4534}, {1788, 3244}, {1836, 37712}, {1837, 11531}, {2003, 60689}, {2099, 3679}, {2136, 41575}, {2171, 4034}, {3036, 34647}, {3057, 15104}, {3218, 34716}, {3241, 3911}, {3243, 12648}, {3339, 10944}, {3361, 37738}, {3474, 28236}, {3485, 3626}, {3585, 61250}, {3600, 20053}, {3601, 11362}, {3617, 64160}, {3621, 10106}, {3635, 7288}, {3654, 30282}, {3656, 11545}, {3671, 4701}, {3680, 12649}, {3880, 41539}, {3913, 37583}, {3947, 4746}, {4295, 47745}, {4297, 41348}, {4304, 50810}, {4308, 20014}, {4323, 4678}, {4654, 4677}, {4691, 10588}, {4816, 5290}, {5119, 54342}, {5176, 28609}, {5288, 11509}, {5289, 20196}, {5554, 15829}, {5587, 18393}, {5657, 13384}, {5697, 41538}, {5719, 50823}, {5731, 63207}, {5853, 12848}, {5854, 41556}, {5919, 8275}, {6604, 63574}, {6738, 37556}, {7175, 49680}, {7672, 60982}, {7962, 18391}, {7982, 9581}, {7987, 37734}, {7991, 10950}, {8148, 9614}, {8227, 11009}, {9588, 34471}, {9613, 12645}, {9624, 18395}, {9797, 61630}, {10826, 11280}, {10914, 14054}, {11041, 31397}, {11376, 16189}, {11526, 38200}, {11529, 12647}, {11682, 27131}, {12437, 63133}, {12531, 21139}, {12625, 14923}, {12701, 58245}, {12832, 26726}, {15228, 37706}, {15803, 37727}, {15844, 64200}, {15950, 19875}, {17151, 58800}, {20049, 64142}, {20050, 63987}, {24393, 60995}, {24471, 49690}, {24929, 34718}, {26481, 64370}, {30305, 51791}, {30827, 62826}, {31393, 50817}, {31425, 37616}, {31434, 50194}, {32003, 52563}, {34489, 64744}, {34641, 51782}, {34701, 63136}, {34772, 64204}, {35445, 59417}, {37618, 61288}, {37704, 63210}, {37711, 41869}, {37724, 53053}, {37730, 41864}, {37736, 64056}, {37739, 61763}, {38097, 61015}, {38455, 62823}, {41540, 41863}, {41549, 44669}, {41553, 64746}, {41711, 44784}, {48803, 56451}, {48831, 56453}, {50129, 62774}, {53056, 61294}

X(64736) = reflection of X(i) in X(j) for these {i,j}: {3057, 64157}, {7962, 18391}, {9580, 5727}
X(64736) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2163, 3680}, {2320, 3445}, {2364, 8056}, {5549, 58794}, {6557, 28607}, {16945, 56094}, {30608, 38266}
X(64736) = X(i)-Dao conjugate of X(j) for these {i, j}: {8, 56094}, {36911, 6557}, {40587, 3680}, {45036, 2320}
X(64736) = X(i)-Ceva conjugate of X(j) for these {i, j}: {62780, 5219}
X(64736) = pole of line {5587, 9669} with respect to the Feuerbach hyperbola
X(64736) = pole of line {28217, 51648} with respect to the Suppa-Cucoanes circle
X(64736) = intersection, other than A, B, C, of circumconics {{A, B, C, X(145), X(3679)}}, {{A, B, C, X(1420), X(2099)}}, {{A, B, C, X(1743), X(4867)}}, {{A, B, C, X(3158), X(3711)}}, {{A, B, C, X(3940), X(4792)}}, {{A, B, C, X(4653), X(40587)}}, {{A, B, C, X(4717), X(4856)}}, {{A, B, C, X(4873), X(12640)}}, {{A, B, C, X(5219), X(5435)}}, {{A, B, C, X(18743), X(27747)}}, {{A, B, C, X(27739), X(41629)}}, {{A, B, C, X(27752), X(31227)}}, {{A, B, C, X(36920), X(39126)}}, {{A, B, C, X(51362), X(51433)}}
X(64736) = barycentric product X(i)*X(j) for these (i, j): {145, 5219}, {1420, 4671}, {3161, 62780}, {3679, 5435}, {4814, 62532}, {4848, 5235}, {4873, 62787}, {18743, 2099}, {30719, 4767}, {31227, 36920}, {39126, 45}, {43052, 43290}
X(64736) = barycentric quotient X(i)/X(j) for these (i, j): {45, 3680}, {145, 30608}, {1405, 3445}, {1420, 89}, {1743, 2320}, {2099, 8056}, {3052, 2364}, {3161, 56094}, {3679, 6557}, {4752, 31343}, {4774, 27831}, {4848, 30588}, {4873, 6556}, {5219, 4373}, {5435, 39704}, {30719, 52620}, {39126, 20569}, {62780, 27818}
X(64736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40663, 31231}, {8, 3340, 9578}, {65, 3632, 37709}, {80, 31162, 51792}, {145, 4848, 1420}, {145, 51433, 3158}, {517, 5727, 9580}, {1788, 3244, 63208}, {2099, 36920, 3679}, {3654, 37728, 30282}, {3679, 16236, 2099}, {4654, 5252, 51789}, {4677, 18421, 5252}, {5252, 18421, 4654}, {5881, 5903, 9579}, {7982, 10573, 9581}, {12245, 64163, 1697}, {12645, 50193, 9613}, {13462, 34747, 1317}, {16236, 36920, 5219}, {18391, 28234, 7962}, {25415, 41684, 5587}, {50194, 59503, 31434}

X(64737) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(55) AND X(7)-CROSSPEDAL-OF-X(55)

Barycentrics    (a+b-c)*(a-b+c)*((b^2-c^2)^2+a^2*(b^2+c^2)-2*a*(b^3+b^2*c+b*c^2+c^3)) : :

X(64737) lies on these lines: {1, 5}, {2, 1617}, {7, 15346}, {10, 15844}, {30, 40292}, {46, 5771}, {55, 8727}, {56, 8728}, {57, 3925}, {63, 5857}, {65, 31419}, {85, 40615}, {140, 7742}, {142, 3660}, {149, 8543}, {226, 518}, {278, 427}, {347, 858}, {388, 442}, {390, 10883}, {497, 954}, {498, 6922}, {611, 26098}, {651, 33112}, {750, 43043}, {944, 33993}, {958, 47510}, {991, 51424}, {999, 6881}, {1001, 14022}, {1056, 6829}, {1058, 6990}, {1125, 50206}, {1214, 1368}, {1329, 5316}, {1441, 3006}, {1465, 29639}, {1478, 3428}, {1486, 33302}, {1532, 10590}, {1595, 1838}, {1621, 37358}, {1630, 56826}, {1699, 15298}, {1737, 61660}, {1836, 5762}, {1943, 33073}, {2256, 50036}, {2476, 5261}, {2550, 37363}, {2975, 47516}, {3085, 6831}, {3173, 3564}, {3256, 34612}, {3295, 6841}, {3361, 41859}, {3485, 24390}, {3600, 4197}, {3668, 23305}, {3703, 6358}, {3813, 64160}, {3817, 15845}, {3820, 61686}, {3822, 51782}, {3826, 3911}, {3841, 4298}, {3947, 25639}, {4187, 10588}, {4294, 37447}, {4848, 9710}, {5057, 29007}, {5083, 25557}, {5218, 37374}, {5226, 11680}, {5249, 17625}, {5290, 57285}, {5328, 11681}, {5432, 15931}, {5437, 25973}, {5572, 27869}, {5659, 11246}, {5713, 64069}, {5791, 37550}, {5805, 54408}, {5856, 8545}, {5880, 24465}, {6601, 8232}, {6675, 37579}, {6737, 12607}, {6830, 8164}, {6842, 9654}, {6882, 31479}, {6941, 8166}, {6991, 14986}, {7201, 21926}, {7288, 17529}, {7354, 37424}, {7680, 31397}, {7956, 17605}, {7965, 9580}, {8071, 37281}, {8581, 64115}, {9612, 15908}, {9655, 37401}, {10039, 14110}, {10106, 25466}, {10386, 16160}, {11230, 60769}, {11235, 42885}, {11501, 37356}, {12558, 12575}, {12588, 33137}, {12594, 34029}, {13411, 63980}, {13727, 27542}, {15185, 21617}, {15296, 24703}, {15909, 60919}, {16608, 26013}, {17080, 29664}, {17530, 34625}, {17660, 64345}, {18839, 20330}, {18990, 22759}, {20420, 26357}, {23304, 44411}, {24552, 28776}, {24953, 37583}, {25006, 41539}, {26942, 31330}, {30116, 51421}, {30275, 41555}, {30312, 64142}, {33136, 42289}, {34050, 64174}, {36482, 55010}, {37432, 37799}, {37468, 64280}, {38205, 41556}, {39542, 64041}, {41007, 45917}, {50195, 51755}, {50196, 55108}, {51784, 64346}, {52254, 60943}, {60909, 61716}, {61013, 64361}, {62843, 64408}

X(64737) = reflection of X(i) in X(j) for these {i,j}: {3428, 55300}
X(64737) = pole of line {900, 10006} with respect to the nine-point circle
X(64737) = pole of line {44428, 50347} with respect to the polar circle
X(64737) = pole of line {2245, 37541} with respect to the Kiepert hyperbola
X(64737) = pole of line {3911, 37597} with respect to the dual conic of Yff parabola
X(64737) = X(495)-of-1st-Johnson-Yff triangle
X(64737) = intersection, other than A, B, C, of circumconics {{A, B, C, X(80), X(60227)}}, {{A, B, C, X(1390), X(1807)}}
X(64737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37695, 15253}, {11, 12, 5219}, {12, 10957, 11375}, {12, 26481, 5}, {12, 5252, 495}, {226, 2886, 64127}, {226, 4847, 5173}, {495, 496, 5719}, {5726, 7951, 12}, {10957, 11375, 496}, {37363, 51416, 2550}

X(64738) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 110 AND X(7)-CROSSPEDAL-OF-X(100)

Barycentrics    (a-b-c)*(2*a^4-(b-c)^4-2*a^3*(b+c)+4*a*(b-c)^2*(b+c)+a^2*(-3*b^2+8*b*c-3*c^2)) : :
X(64738) = -X[1]+3*X[38060], 3*X[2]+X[1156], -X[3]+3*X[38131], -X[4]+3*X[38159], -X[6]+3*X[38195], -X[7]+5*X[31272], -X[12]+3*X[38218], -X[100]+5*X[18230], X[104]+3*X[5817], -X[119]+3*X[38108], -X[214]+3*X[38059], X[390]+3*X[59415] and many others

X(64738) lies on circumconic {{A, B, C, X(3254), X(60094)}} and on these lines: {1, 38060}, {2, 1156}, {3, 38131}, {4, 38159}, {5, 1158}, {6, 38195}, {7, 31272}, {8, 4578}, {9, 11}, {10, 528}, {12, 38218}, {100, 18230}, {104, 5817}, {119, 38108}, {142, 5851}, {214, 38059}, {390, 59415}, {405, 4305}, {516, 6702}, {518, 1387}, {522, 52873}, {527, 5087}, {900, 40551}, {908, 63254}, {952, 1001}, {960, 64205}, {971, 6713}, {1125, 2801}, {1145, 38057}, {1317, 38316}, {1320, 5686}, {1445, 24465}, {1484, 15296}, {1537, 38037}, {1698, 51768}, {1837, 47375}, {2478, 18231}, {2550, 34122}, {2829, 63970}, {3035, 6666}, {3036, 5853}, {3086, 5729}, {3622, 14151}, {3716, 59997}, {3816, 61004}, {3847, 18232}, {4069, 4853}, {5057, 37787}, {5083, 58564}, {5220, 45700}, {5223, 16173}, {5528, 6174}, {5542, 32557}, {5660, 64264}, {5698, 17556}, {5723, 62764}, {5732, 21154}, {5735, 38152}, {5759, 59391}, {5762, 60759}, {5779, 57298}, {5805, 23513}, {5840, 31658}, {5850, 33709}, {5854, 24393}, {5857, 8068}, {6172, 59377}, {6173, 59376}, {6675, 40539}, {6745, 15733}, {7678, 61026}, {8236, 12531}, {10177, 61015}, {10199, 25557}, {10525, 61524}, {10584, 60946}, {10589, 60940}, {10707, 61023}, {10724, 59418}, {10738, 59381}, {12735, 42819}, {14740, 58635}, {15185, 46685}, {15251, 24433}, {15863, 30331}, {19907, 38043}, {20119, 52653}, {21153, 24466}, {22799, 38139}, {23808, 25380}, {30424, 38207}, {31657, 34126}, {31672, 38761}, {33814, 38113}, {36868, 61028}, {36991, 38693}, {37736, 64674}, {38025, 50843}, {38026, 51099}, {38088, 51008}, {38090, 51002}, {38095, 60963}, {38097, 50842}, {38099, 51102}, {38104, 51100}, {38318, 58421}, {38319, 61595}, {38602, 60901}, {40659, 46694}, {41555, 60935}, {41556, 60995}, {46684, 63973}, {51090, 59419}, {52265, 58415}, {52835, 59390}, {52836, 59389}, {58608, 58683}, {58611, 58678}, {60905, 64155}, {62674, 62676}

X(64738) = midpoint of X(i) and X(j) for these {i,j}: {9, 11}, {1156, 10427}, {3254, 6068}, {15185, 46685}, {15863, 30331}, {31672, 38761}, {38211, 53055}, {38602, 60901}, {41555, 60935}, {46684, 63973}, {58608, 58683}, {58611, 58678}
X(64738) = reflection of X(i) in X(j) for these {i,j}: {142, 6667}, {3035, 6666}, {5083, 58564}, {12735, 42819}, {14740, 58635}, {40659, 46694}
X(64738) = inverse of X(6068) in Feuerbach hyperbola
X(64738) = complement of X(10427)
X(64738) = X(i)-complementary conjugate of X(j) for these {i, j}: {10426, 10}, {61230, 46415}
X(64738) = pole of line {6068, 15733} with respect to the Feuerbach hyperbola
X(64738) = pole of line {30565, 41798} with respect to the Steiner inellipse
X(64738) = X(1156)-of-Gemini-110 triangle
X(64738) = X(1177)-of-2nd-Zaniah triangle
X(64738) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {9, 11, 5514}
X(64738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1156, 10427}, {7, 31272, 38205}, {9, 3254, 6068}, {11, 6068, 3254}, {3254, 6068, 5856}, {5851, 6667, 142}

X(64739) = PERSPECTOR OF THESE TRIANGLES: X(8)-CROSSPEDAL-OF-X(1) AND UNARY COFACTOR TRIANGLE OF EXTANGENTS

Barycentrics    a^2*(a-b-c)*(-b^2+b*c-c^2+a*(b+c)) : :

X(64739) lies on these lines: {1, 142}, {2, 55340}, {3, 9052}, {6, 3939}, {7, 35338}, {8, 16713}, {9, 2293}, {31, 5037}, {37, 15733}, {40, 63395}, {42, 1449}, {43, 59584}, {48, 40910}, {55, 219}, {77, 3870}, {78, 3883}, {86, 59255}, {101, 1486}, {109, 23144}, {145, 37558}, {192, 522}, {200, 3686}, {218, 21002}, {241, 15185}, {332, 3996}, {344, 1026}, {386, 1386}, {480, 55432}, {517, 50656}, {518, 991}, {527, 1742}, {572, 12329}, {573, 674}, {579, 2223}, {581, 3811}, {612, 2900}, {664, 57792}, {672, 16688}, {995, 40499}, {1001, 56809}, {1002, 18164}, {1174, 7123}, {1212, 40659}, {1253, 2323}, {1376, 17049}, {1458, 3243}, {1621, 56813}, {1743, 4878}, {2141, 3730}, {2318, 4512}, {2324, 4326}, {2346, 37659}, {2667, 24394}, {2809, 18161}, {2810, 48908}, {3000, 60933}, {3056, 4266}, {3059, 40937}, {3066, 8694}, {3072, 8715}, {3161, 4069}, {3191, 4294}, {3193, 3871}, {3204, 16686}, {3207, 36641}, {3240, 61222}, {3247, 4343}, {3668, 41570}, {3720, 24392}, {3736, 3913}, {3745, 56178}, {3873, 17092}, {3880, 58583}, {3882, 25304}, {3912, 24388}, {3935, 17363}, {3941, 4253}, {3945, 7674}, {3957, 17391}, {3961, 25353}, {4105, 64343}, {4149, 4511}, {4254, 10387}, {4260, 37590}, {4300, 11523}, {4303, 41863}, {4318, 10571}, {4447, 35892}, {4551, 54425}, {5311, 56317}, {5856, 17365}, {6007, 64170}, {6510, 30621}, {6555, 55372}, {7671, 26669}, {7676, 62799}, {10177, 25067}, {10389, 25941}, {10679, 18451}, {12033, 17455}, {12625, 59305}, {13329, 45728}, {14839, 64727}, {16608, 50441}, {16670, 20978}, {17018, 54308}, {17059, 17234}, {17126, 53388}, {17245, 64443}, {17766, 22836}, {18162, 24309}, {19589, 41265}, {20195, 59217}, {20683, 20992}, {20990, 64751}, {21010, 52020}, {21346, 35293}, {21384, 22312}, {21746, 34247}, {22053, 62823}, {24386, 26102}, {24389, 29571}, {24635, 34784}, {24708, 60942}, {25716, 52980}, {26893, 54327}, {29696, 52923}, {29747, 62872}, {30116, 44669}, {30628, 57022}, {30682, 41353}, {37529, 64117}, {37699, 59722}, {37819, 56800}, {42079, 51058}, {42843, 64013}, {43924, 56314}, {52428, 58328}, {53391, 63498}, {54474, 61030}, {56808, 61155}, {60973, 64741}

X(64739) = reflection of X(i) in X(j) for these {i,j}: {573, 15624}, {3169, 4097}
X(64739) = perspector of circumconic {{A, B, C, X(5546), X(6078)}}
X(64739) = X(i)-isoconjugate-of-X(j) for these {i, j}: {57, 60075}
X(64739) = X(i)-Dao conjugate of X(j) for these {i, j}: {210, 10}, {5452, 60075}, {17059, 522}, {52594, 23989}
X(64739) = X(i)-Ceva conjugate of X(j) for these {i, j}: {86, 9}, {664, 47676}, {3873, 4253}, {32015, 8012}, {35160, 672}
X(64739) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2141, 329}
X(64739) = X(i)-cross conjugate of X(j) for these {i, j}: {40599, 25082}
X(64739) = pole of line {17642, 40937} with respect to the Feuerbach hyperbola
X(64739) = pole of line {7, 17127} with respect to the Stammler hyperbola
X(64739) = pole of line {672, 47676} with respect to the Steiner circumellipse
X(64739) = pole of line {6063, 55082} with respect to the Wallace hyperbola
X(64739) = X(3688)-of-anti-Mandart-incircle
X(64739) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(55), X(7241)}}, {{A, B, C, X(142), X(7123)}}, {{A, B, C, X(218), X(24181)}}, {{A, B, C, X(219), X(3970)}}, {{A, B, C, X(277), X(284)}}, {{A, B, C, X(1174), X(4000)}}, {{A, B, C, X(1252), X(47676)}}, {{A, B, C, X(2175), X(61038)}}, {{A, B, C, X(2191), X(2194)}}, {{A, B, C, X(2328), X(3873)}}, {{A, B, C, X(3913), X(4097)}}, {{A, B, C, X(3939), X(56314)}}, {{A, B, C, X(4648), X(38825)}}, {{A, B, C, X(5853), X(6600)}}
X(64739) = barycentric product X(i)*X(j) for these (i, j): {1, 25082}, {21, 3970}, {312, 3941}, {1252, 17059}, {3873, 9}, {3939, 47676}, {4253, 8}, {4905, 644}, {17092, 200}, {17234, 55}, {21946, 4570}, {22277, 333}, {23761, 59149}, {27827, 3158}, {28660, 61038}, {33933, 41}, {40599, 86}, {52594, 664}
X(64739) = barycentric quotient X(i)/X(j) for these (i, j): {55, 60075}, {3873, 85}, {3941, 57}, {3970, 1441}, {4253, 7}, {4905, 24002}, {17059, 23989}, {17092, 1088}, {17234, 6063}, {21946, 21207}, {22277, 226}, {23761, 23100}, {25082, 75}, {27827, 62528}, {33933, 20567}, {40599, 10}, {47676, 52621}, {52594, 522}, {61038, 1400}
X(64739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 60785, 4000}, {77, 3870, 8271}, {674, 15624, 573}, {2223, 3779, 579}, {2293, 2340, 9}, {3158, 3169, 4097}, {3939, 41457, 6600}, {3941, 22277, 4253}

X(64740) = ORTHOLOGY CENTER OF THESE TRIANGLES: HEXYL AND X(8)-CROSSPEDAL-OF-X(21)

Barycentrics    a*(a^6+a^3*b*c*(b+c)-a*b*(b-c)^2*c*(b+c)+a^4*(-3*b^2+7*b*c-3*c^2)+3*a^2*(b-c)^2*(b^2+b*c+c^2)-(b^2-c^2)^2*(b^2+4*b*c+c^2)) : :
X(64740) = X[1]+2*X[10308], -3*X[165]+4*X[3647], -8*X[1385]+9*X[5426], -3*X[2475]+4*X[19925], -3*X[3576]+4*X[31649], -2*X[4297]+3*X[15677], -3*X[5587]+4*X[22798], -6*X[6175]+7*X[7989], -8*X[6701]+9*X[7988], -5*X[8227]+4*X[49107], X[9589]+2*X[41691], -3*X[9812]+X[20084] and many others

X(64740) lies on these lines: {1, 10308}, {3, 5506}, {4, 1768}, {21, 3062}, {30, 40}, {56, 51768}, {57, 16141}, {63, 63280}, {79, 84}, {90, 64329}, {165, 3647}, {226, 41690}, {474, 61740}, {484, 31673}, {515, 4330}, {516, 3648}, {517, 11524}, {758, 7995}, {946, 16116}, {971, 37080}, {1012, 37571}, {1158, 1749}, {1385, 5426}, {1394, 15430}, {1454, 51790}, {1482, 2771}, {1484, 16159}, {1697, 16140}, {1698, 18540}, {1750, 3651}, {2136, 50871}, {2475, 19925}, {3146, 52126}, {3333, 11544}, {3337, 18483}, {3522, 60911}, {3576, 31649}, {3624, 7171}, {3627, 5535}, {3646, 15673}, {3649, 10085}, {3650, 57279}, {3667, 42740}, {3746, 63266}, {3817, 35010}, {4297, 15677}, {4857, 64352}, {5250, 15678}, {5441, 7966}, {5536, 10916}, {5538, 31803}, {5541, 18525}, {5587, 22798}, {5927, 59326}, {6001, 64281}, {6175, 7989}, {6326, 31828}, {6701, 7988}, {6763, 41869}, {6841, 37534}, {6845, 61703}, {6847, 14526}, {6909, 31871}, {6972, 15017}, {7284, 16005}, {7354, 64372}, {7991, 11684}, {7992, 64320}, {7997, 15064}, {8227, 49107}, {9275, 51748}, {9579, 18977}, {9580, 16142}, {9588, 10860}, {9589, 41691}, {9612, 10042}, {9614, 10050}, {9812, 20084}, {9841, 15670}, {9856, 20323}, {10122, 18219}, {10429, 15910}, {10543, 10864}, {11219, 61556}, {11240, 14450}, {11263, 64130}, {11919, 16154}, {11920, 16155}, {12114, 46816}, {12675, 36946}, {12679, 16160}, {13089, 64315}, {15071, 17637}, {15726, 59320}, {16006, 51816}, {16112, 37022}, {16117, 22936}, {16124, 29301}, {16125, 63399}, {16133, 24644}, {16150, 22793}, {17525, 31435}, {17728, 27197}, {17768, 63974}, {18243, 37701}, {19541, 41542}, {22792, 52850}, {26878, 63998}, {31424, 41860}, {31445, 41853}, {31938, 64197}, {33856, 37251}, {36991, 60912}, {37532, 52860}, {37712, 63142}, {37714, 63985}, {37731, 41543}, {39878, 63279}, {45632, 49177}, {48903, 63310}, {49169, 51897}, {50865, 62858}, {52836, 61553}, {61252, 63132}, {62874, 63285}

X(64740) = midpoint of X(i) and X(j) for these {i,j}: {10308, 21669}
X(64740) = reflection of X(i) in X(j) for these {i,j}: {1, 21669}, {3, 26202}, {40, 3652}, {79, 37447}, {191, 7701}, {1768, 3065}, {3746, 63266}, {7701, 16138}, {7991, 11684}, {15071, 17637}, {16116, 946}, {16117, 22936}, {16118, 4}, {16132, 13743}, {16143, 21}, {16150, 22793}, {33557, 3647}, {34628, 15678}, {39878, 63279}, {47032, 22798}, {49178, 6841}, {63267, 3}, {64005, 16113}, {64289, 49177}
X(64740) = pole of line {2533, 35057} with respect to the Conway circle
X(64740) = pole of line {35057, 39540} with respect to the incircle
X(64740) = pole of line {32636, 64131} with respect to the Feuerbach hyperbola
X(64740) = pole of line {21180, 35057} with respect to the Suppa-Cucoanes circle
X(64740) = X(3519)-of-hexyl triangle
X(64740) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 16113, 64005}, {30, 16138, 7701}, {30, 3652, 40}, {30, 7701, 191}, {40, 7701, 3652}, {79, 37447, 1699}, {3647, 33557, 165}, {10085, 11372, 11522}, {13743, 16132, 5426}, {22798, 47032, 5587}, {54370, 63984, 7987}

X(64741) = ORTHOLOGY CENTER OF THESE TRIANGLES: GARCIA-REFLECTION AND X(8)-CROSSPEDAL-OF-X(69)

Barycentrics    a*(a^4+4*a*(b-c)^2*(b+c)+a^2*(-4*b^2+6*b*c-4*c^2)-(b-c)^2*(b^2+4*b*c+c^2)) : :
X(64741) = -3*X[2]+2*X[59688], -2*X[990]+3*X[16475]

X(64741) lies on circumconic {{A, B, C, X(3062), X(14943)}} and on these lines: {1, 971}, {2, 59688}, {4, 50307}, {6, 1721}, {9, 1742}, {20, 54386}, {37, 16112}, {40, 1757}, {43, 10860}, {44, 11495}, {69, 21629}, {77, 2310}, {84, 256}, {87, 58034}, {165, 2348}, {170, 16572}, {171, 1750}, {193, 9801}, {238, 5732}, {241, 60910}, {511, 12717}, {513, 2961}, {516, 3751}, {517, 7996}, {518, 12652}, {519, 9950}, {614, 11220}, {651, 4319}, {975, 31871}, {978, 9841}, {982, 30304}, {984, 64197}, {986, 7992}, {990, 16475}, {991, 54370}, {1038, 1898}, {1044, 10396}, {1193, 63984}, {1445, 3000}, {1471, 8544}, {1490, 37552}, {1633, 2261}, {1697, 41680}, {1699, 4888}, {1707, 7580}, {1709, 17594}, {1722, 9943}, {1738, 63971}, {1743, 2951}, {1754, 41860}, {1766, 29353}, {1864, 60786}, {2082, 9309}, {2136, 2943}, {2263, 10394}, {2293, 8545}, {2340, 60966}, {2801, 16496}, {2808, 3056}, {3008, 43182}, {3073, 41854}, {3146, 54421}, {3551, 43747}, {3576, 8245}, {3664, 63973}, {3729, 28850}, {3731, 54474}, {3782, 41706}, {4307, 36991}, {4326, 9440}, {4383, 5918}, {4384, 59620}, {4675, 42356}, {4882, 8915}, {5228, 31391}, {5247, 12565}, {5255, 63981}, {5268, 5927}, {5272, 10167}, {5293, 35658}, {5438, 24265}, {5691, 29207}, {5851, 17276}, {5942, 23529}, {6223, 13161}, {6996, 43173}, {7271, 30330}, {7274, 9814}, {7982, 49498}, {7995, 37598}, {8069, 56824}, {9303, 17170}, {9812, 62819}, {9961, 54418}, {10178, 37679}, {10431, 41011}, {10436, 45305}, {10857, 17123}, {10868, 19861}, {12684, 37592}, {13329, 43178}, {15254, 50677}, {17668, 55432}, {23821, 24179}, {24210, 64130}, {24231, 36996}, {24728, 53602}, {25722, 28043}, {29571, 64699}, {31183, 64698}, {33144, 41561}, {34059, 56378}, {34852, 59600}, {35514, 49772}, {41351, 56310}, {43065, 56380}, {43166, 49490}, {48878, 50314}, {53014, 62997}, {53599, 60896}, {60973, 64739}

X(64741) = midpoint of X(i) and X(j) for these {i,j}: {193, 9801}
X(64741) = reflection of X(i) in X(j) for these {i,j}: {69, 21629}, {1721, 6}, {16496, 61086}
X(64741) = anticomplement of X(59688)
X(64741) = X(i)-Dao conjugate of X(j) for these {i, j}: {9312, 61413}, {41795, 30694}, {59688, 59688}
X(64741) = pole of line {4083, 9441} with respect to the Bevan circle
X(64741) = pole of line {3900, 17069} with respect to the incircle
X(64741) = pole of line {57, 64134} with respect to the Feuerbach hyperbola
X(64741) = pole of line {42309, 60992} with respect to the dual conic of Yff parabola
X(64741) = X(9308)-of-excentral triangle
X(64741) = barycentric product X(i)*X(j) for these (i, j): {41795, 7}
X(64741) = barycentric quotient X(i)/X(j) for these (i, j): {41795, 8}
X(64741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3062, 64134}, {6, 15726, 1721}, {193, 9801, 28849}, {1419, 4907, 1}, {1742, 9355, 9}, {1743, 2951, 9441}

X(64742) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a*(2*a^6-4*a^5*(b+c)-2*a^4*(b^2-8*b*c+c^2)+(b^2-c^2)^2*(2*b^2-5*b*c+2*c^2)-4*a*(b-c)^2*(b^3-2*b^2*c-2*b*c^2+c^3)+4*a^3*(2*b^3-3*b^2*c-3*b*c^2+2*c^3)-a^2*(2*b^4+11*b^3*c-28*b^2*c^2+11*b*c^3+2*c^4)) : :
X(64742) = -3*X[2]+X[64140], -X[8]+3*X[57298], -2*X[10]+3*X[34126], -X[100]+3*X[10246], -X[153]+5*X[10595], -2*X[546]+3*X[38038], -2*X[547]+3*X[38026], -5*X[631]+X[64743], X[1768]+3*X[16200], -2*X[3035]+3*X[38028], 3*X[3241]+X[12247], -7*X[3526]+5*X[64141] and many others

X(64742) lies on circumconic {{A, B, C, X(1392), X(56416)}} and on these lines: {1, 5}, {2, 64140}, {3, 1320}, {8, 57298}, {10, 34126}, {30, 64138}, {56, 38722}, {100, 10246}, {104, 1392}, {140, 1145}, {145, 6958}, {149, 6923}, {153, 10595}, {214, 5836}, {474, 12331}, {515, 22938}, {517, 4973}, {519, 12619}, {528, 31657}, {546, 38038}, {547, 38026}, {549, 64733}, {631, 64743}, {758, 33856}, {942, 41554}, {944, 10738}, {946, 22799}, {962, 38753}, {997, 59400}, {1012, 10247}, {1385, 2802}, {1388, 10090}, {1768, 16200}, {2098, 10058}, {2099, 10074}, {2771, 25485}, {2800, 3881}, {2801, 15570}, {2829, 22791}, {2932, 16203}, {3035, 38028}, {3036, 30144}, {3241, 12247}, {3244, 10265}, {3526, 64141}, {3576, 12653}, {3616, 38752}, {3623, 6833}, {3655, 12119}, {3656, 34789}, {3811, 11256}, {3833, 22935}, {3872, 38112}, {3937, 52478}, {4996, 37621}, {4999, 34352}, {5048, 12758}, {5054, 64746}, {5055, 50907}, {5083, 50194}, {5123, 15863}, {5603, 10742}, {5663, 31523}, {5690, 5854}, {5779, 53055}, {5790, 31272}, {5818, 32558}, {5840, 34773}, {5844, 25416}, {5882, 21630}, {6246, 22835}, {6361, 38754}, {6667, 38042}, {6702, 38177}, {6797, 25405}, {6955, 20095}, {7982, 12515}, {8148, 64189}, {9803, 20057}, {9945, 37615}, {9956, 32557}, {10031, 17532}, {10087, 34471}, {10267, 22560}, {10269, 13205}, {10707, 12747}, {10778, 12898}, {10912, 25438}, {11011, 11570}, {11014, 24466}, {11015, 18444}, {11849, 18861}, {12332, 37622}, {12611, 13464}, {12641, 47746}, {12645, 59415}, {12699, 64145}, {12702, 38693}, {12736, 24928}, {13226, 37533}, {13375, 20323}, {13607, 33281}, {13996, 38760}, {14217, 18481}, {16174, 18480}, {17100, 37535}, {17638, 33176}, {17652, 37562}, {17654, 23340}, {18240, 51788}, {18525, 59391}, {18526, 51517}, {18583, 38050}, {19916, 21343}, {20418, 46920}, {21154, 61524}, {21740, 61601}, {24927, 39776}, {26446, 64056}, {28174, 38761}, {28186, 64186}, {31649, 45065}, {33709, 38182}, {34122, 61510}, {34123, 51700}, {34339, 58595}, {34718, 50894}, {34748, 50890}, {35641, 48701}, {35642, 48700}, {35762, 48715}, {35763, 48714}, {35810, 35857}, {35811, 35856}, {36867, 64330}, {38055, 61509}, {38060, 61511}, {38069, 50842}, {38669, 48667}, {40273, 52836}, {45081, 61520}, {47745, 59419}, {50798, 59377}, {58504, 64663}, {58605, 62395}

X(64742) = midpoint of X(i) and X(j) for these {i,j}: {1, 12737}, {3, 1320}, {80, 37727}, {104, 1482}, {145, 19914}, {944, 10738}, {962, 38753}, {1317, 37726}, {1483, 1484}, {3244, 10265}, {3655, 50891}, {3811, 11256}, {5882, 21630}, {6264, 6265}, {7982, 12515}, {7993, 12738}, {8148, 64189}, {10698, 12773}, {10778, 12898}, {10912, 25438}, {11715, 64137}, {12641, 47746}, {12699, 64145}, {14217, 18481}, {17652, 37562}, {17654, 23340}, {19916, 21343}, {34718, 50894}, {34748, 50890}, {36867, 64330}, {38669, 48667}, {64138, 64191}
X(64742) = reflection of X(i) in X(j) for these {i,j}: {5, 1387}, {119, 5901}, {214, 15178}, {1145, 140}, {5690, 6713}, {11698, 11729}, {12611, 13464}, {18480, 16174}, {19907, 1}, {22799, 946}, {25485, 33179}, {33814, 1385}, {34339, 58595}, {38602, 11715}, {51525, 214}, {52836, 40273}, {61562, 51700}
X(64742) = complement of X(64140)
X(64742) = X(1320)-of-anti-X3-ABC-reflections triangle
X(64742) = X(1539)-of-2nd-circumperp triangle
X(64742) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1, 12737, 31523}, {3, 1320, 18342}, {100, 15343, 58123}, {3025, 6075, 44052}, {3244, 10265, 16338}, {11715, 11717, 64137}
X(64742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 12737, 952}, {1, 20586, 12735}, {1, 6264, 6265}, {1, 952, 19907}, {517, 11715, 38602}, {952, 11729, 11698}, {952, 1387, 5}, {952, 5901, 119}, {1145, 38032, 140}, {1385, 2802, 33814}, {1483, 10283, 32213}, {2771, 33179, 25485}, {5854, 6713, 5690}, {6265, 12737, 6264}, {10247, 12773, 10698}, {10283, 11698, 11729}, {11715, 64137, 517}, {16174, 18480, 38141}, {51700, 61562, 34123}, {64138, 64191, 30}

X(64743) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a^4+13*a^2*b*c-4*a^3*(b+c)-(b^2-c^2)^2+a*(4*b^3-7*b^2*c-7*b*c^2+4*c^3) : :
X(64743) = -3*X[8]+2*X[80], -4*X[11]+5*X[3617], -4*X[214]+3*X[3241], -5*X[631]+4*X[64742], -10*X[1698]+9*X[32558], -8*X[3035]+7*X[3622], -4*X[3036]+3*X[10707], -5*X[3091]+4*X[64138], -2*X[3244]+3*X[15015], -2*X[3254]+3*X[59413], -5*X[3522]+4*X[64191], -15*X[3616]+16*X[58453] and many others

X(64743) lies on these lines: {1, 13144}, {2, 1000}, {4, 64140}, {7, 12641}, {8, 80}, {10, 12653}, {11, 3617}, {20, 952}, {56, 100}, {104, 35238}, {144, 528}, {153, 517}, {214, 3241}, {484, 519}, {631, 64742}, {962, 12751}, {1445, 41558}, {1482, 6979}, {1484, 6963}, {1647, 13541}, {1698, 32558}, {1788, 20586}, {2475, 3909}, {2800, 6223}, {2805, 49450}, {2829, 20070}, {2894, 10914}, {2932, 54391}, {2975, 13205}, {3035, 3622}, {3036, 10707}, {3057, 37162}, {3091, 64138}, {3244, 15015}, {3254, 59413}, {3303, 63917}, {3522, 64191}, {3543, 50907}, {3616, 58453}, {3623, 25416}, {3625, 9897}, {3626, 37718}, {3632, 3648}, {3633, 33337}, {3679, 21041}, {3681, 17638}, {3698, 58611}, {3868, 64768}, {3870, 16236}, {3871, 37728}, {3877, 17652}, {3880, 36920}, {3885, 5722}, {3887, 63246}, {3911, 38460}, {3935, 6326}, {3957, 14563}, {4295, 12749}, {4430, 11570}, {4440, 19636}, {4661, 12532}, {4674, 24864}, {4678, 6919}, {4767, 52871}, {4792, 24222}, {4861, 37291}, {4996, 25438}, {5067, 38044}, {5068, 38038}, {5119, 15677}, {5176, 44784}, {5435, 41554}, {5601, 13230}, {5602, 13228}, {5657, 12737}, {5844, 6905}, {5853, 50573}, {6154, 20054}, {6174, 50894}, {6264, 11362}, {6366, 52164}, {6594, 8236}, {6667, 46932}, {6702, 50891}, {6827, 19914}, {6848, 10698}, {6970, 19907}, {7674, 12730}, {7967, 33814}, {7972, 20050}, {8148, 11698}, {8715, 14800}, {9778, 64145}, {9780, 16173}, {9945, 10031}, {10247, 61562}, {10265, 63143}, {10303, 38032}, {10595, 38752}, {10609, 20014}, {10711, 50872}, {10738, 59388}, {11045, 64745}, {11256, 24477}, {11531, 21635}, {12515, 50810}, {12640, 34772}, {12647, 33110}, {12690, 50890}, {12773, 37403}, {14217, 59387}, {14513, 53799}, {17460, 26727}, {17636, 45043}, {19875, 33709}, {19877, 32557}, {20013, 38665}, {20060, 49169}, {20067, 38455}, {25005, 37704}, {25439, 35204}, {28212, 38756}, {30331, 61012}, {31272, 46933}, {33108, 63270}, {33812, 51093}, {34711, 37299}, {37705, 48680}, {38314, 50841}, {39349, 39350}, {42696, 56433}, {51506, 61155}, {51517, 61510}, {52157, 56797}, {58591, 62854}, {59400, 61601}, {63135, 64372}

X(64743) = midpoint of X(i) and X(j) for these {i,j}: {3621, 20095}
X(64743) = reflection of X(i) in X(j) for these {i,j}: {2, 64746}, {4, 64140}, {8, 64056}, {20, 64136}, {100, 13996}, {145, 100}, {149, 8}, {962, 12751}, {1320, 1145}, {3543, 50907}, {3633, 33337}, {5176, 44784}, {6224, 5541}, {6264, 11362}, {8148, 11698}, {9802, 80}, {9897, 3625}, {9963, 12732}, {10707, 50842}, {11531, 21635}, {12248, 12702}, {12653, 10}, {20049, 10031}, {20050, 7972}, {20085, 12531}, {26726, 214}, {38460, 51433}, {48680, 37705}, {50872, 10711}, {50894, 6174}, {64009, 64189}
X(64743) = anticomplement of X(1320)
X(64743) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1, 5176}, {6, 908}, {7, 21282}, {44, 329}, {56, 519}, {57, 320}, {58, 62826}, {59, 17780}, {106, 12531}, {109, 900}, {222, 3007}, {519, 3436}, {604, 17495}, {651, 21297}, {900, 33650}, {902, 144}, {909, 34234}, {1014, 17145}, {1023, 4462}, {1317, 21290}, {1319, 8}, {1400, 63071}, {1404, 2}, {1407, 1266}, {1411, 80}, {1412, 17160}, {1415, 21222}, {1416, 24841}, {1431, 32844}, {1461, 4453}, {1462, 53381}, {1635, 37781}, {1877, 4}, {1960, 39351}, {2149, 2397}, {2251, 3177}, {2325, 54113}, {3285, 63}, {3911, 69}, {4358, 21286}, {4564, 61186}, {4565, 53333}, {4570, 23831}, {4573, 53368}, {5298, 2891}, {5440, 52366}, {7316, 53372}, {9459, 21218}, {14584, 5080}, {14628, 21277}, {16704, 20245}, {22356, 56943}, {23344, 4468}, {23703, 513}, {30572, 3448}, {30576, 21273}, {30606, 54109}, {30725, 150}, {32669, 2401}, {32674, 10015}, {32675, 60480}, {32735, 53361}, {36920, 21291}, {37790, 21270}, {38828, 4927}, {40151, 4887}, {40663, 1330}, {43924, 20042}, {51422, 151}, {52680, 3869}, {53528, 149}, {53529, 152}, {53530, 153}, {53531, 20344}, {53532, 34188}, {61047, 17487}, {61210, 514}, {62669, 20295}, {62789, 3434}
X(64743) = pole of line {1639, 3762} with respect to the Steiner circumellipse
X(64743) = pole of line {2397, 2403} with respect to the Yff parabola
X(64743) = X(1145)-of-Gemini-111 triangle
X(64743) = X(2935)-of-inner-Conway triangle
X(64743) = intersection, other than A, B, C, of circumconics {{A, B, C, X(80), X(8686)}}, {{A, B, C, X(1000), X(41529)}}, {{A, B, C, X(1120), X(36596)}}, {{A, B, C, X(3218), X(30578)}}, {{A, B, C, X(3880), X(22560)}}, {{A, B, C, X(8046), X(18359)}}
X(64743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 2802, 149}, {8, 9802, 80}, {80, 2802, 9802}, {80, 64139, 31018}, {100, 5854, 145}, {145, 63133, 4188}, {214, 26726, 3241}, {519, 5541, 6224}, {528, 12531, 20085}, {952, 12702, 12248}, {952, 12732, 9963}, {952, 64136, 20}, {952, 64189, 64009}, {1145, 1320, 2}, {1145, 1387, 64141}, {1320, 64141, 1387}, {1320, 64746, 1145}, {2802, 64056, 8}, {3621, 20095, 952}, {5854, 13996, 100}, {9963, 12732, 20095}, {12641, 39776, 12648}, {20085, 31145, 12531}

X(64744) = ORTHOLOGY CENTER OF THESE TRIANGLES: FUHRMANN AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    (a-b-c)*(a^3-2*a^2*(b+c)+(b-c)^2*(b+c)-2*a*(b^2-3*b*c+c^2)) : :
X(64744) = -3*X[2]+2*X[33895], -4*X[5]+3*X[34640], -X[20]+3*X[34711], -3*X[3158]+X[3633], -2*X[3244]+3*X[56177], -3*X[3576]+4*X[32157], -3*X[3679]+X[3680], -2*X[4301]+3*X[11236], -3*X[5587]+2*X[13463], -3*X[5657]+2*X[11260], -3*X[5790]+2*X[49600], -3*X[10247]+4*X[59719] and many others

X(64744) lies on these lines: {1, 1145}, {2, 33895}, {3, 519}, {4, 32537}, {5, 34640}, {8, 210}, {10, 10912}, {20, 34711}, {40, 38455}, {56, 51433}, {65, 10940}, {100, 34880}, {145, 1319}, {191, 2136}, {355, 2802}, {392, 10051}, {404, 64746}, {443, 5836}, {516, 52683}, {517, 6256}, {518, 12245}, {528, 5881}, {529, 7991}, {551, 31480}, {855, 12642}, {944, 13528}, {952, 1158}, {956, 8668}, {1000, 17559}, {1056, 10107}, {1155, 36977}, {1317, 4855}, {1320, 11376}, {1329, 7962}, {1482, 10915}, {1532, 7982}, {2098, 6735}, {2099, 51432}, {2475, 3909}, {3036, 9581}, {3039, 4936}, {3158, 3633}, {3169, 4271}, {3189, 3621}, {3241, 6921}, {3244, 56177}, {3303, 25875}, {3476, 37267}, {3576, 32157}, {3617, 64361}, {3625, 4133}, {3626, 21627}, {3679, 3680}, {3717, 34807}, {3811, 5844}, {3871, 37740}, {3872, 26066}, {3895, 10950}, {3951, 34689}, {4301, 11236}, {4534, 55337}, {4677, 11113}, {4848, 41426}, {4919, 46835}, {5048, 5552}, {5176, 12701}, {5183, 20076}, {5289, 6736}, {5450, 13205}, {5541, 37707}, {5554, 5919}, {5587, 13463}, {5657, 11260}, {5687, 10094}, {5697, 24703}, {5790, 49600}, {5794, 10914}, {5855, 6765}, {6264, 32198}, {6600, 42886}, {6601, 7317}, {6675, 63644}, {6737, 8168}, {6834, 34619}, {6872, 12632}, {6925, 44663}, {6959, 10222}, {6967, 34625}, {7741, 12653}, {8148, 21077}, {8275, 15829}, {9957, 58649}, {10093, 11508}, {10247, 59719}, {10528, 11011}, {10916, 59503}, {10944, 13996}, {11235, 64767}, {11510, 41575}, {12447, 45115}, {12629, 32426}, {12635, 28234}, {12649, 36920}, {15297, 37730}, {17563, 54286}, {17757, 30323}, {18395, 41702}, {18481, 35460}, {19860, 45081}, {20050, 37605}, {21272, 30617}, {22560, 25440}, {22837, 26446}, {24046, 24864}, {24390, 64203}, {24914, 38460}, {25438, 26285}, {25439, 37739}, {26476, 55016}, {28609, 58245}, {28628, 31397}, {31165, 56879}, {34489, 64736}, {34716, 63469}, {34791, 37566}, {35615, 35634}, {36846, 40663}, {37429, 54422}, {37516, 49688}, {37722, 50842}, {38496, 53618}, {40587, 50726}, {45287, 56998}, {48668, 61244}, {49168, 58643}, {51423, 63209}, {61296, 64191}

X(64744) = midpoint of X(i) and X(j) for these {i,j}: {2136, 3632}, {3189, 3621}, {5881, 64202}, {12641, 64056}
X(64744) = reflection of X(i) in X(j) for these {i,j}: {4, 32537}, {145, 56176}, {1482, 10915}, {3680, 3813}, {3913, 12640}, {6264, 32198}, {7982, 12607}, {8148, 21077}, {10912, 10}, {12513, 11362}, {21627, 3626}, {32049, 49169}, {37727, 8715}, {47746, 22837}
X(64744) = anticomplement of X(33895)
X(64744) = perspector of circumconic {{A, B, C, X(646), X(55996)}}
X(64744) = pole of line {2827, 15863} with respect to the Fuhrmann circle
X(64744) = pole of line {8, 58657} with respect to the Feuerbach hyperbola
X(64744) = pole of line {1408, 7419} with respect to the Stammler hyperbola
X(64744) = pole of line {20317, 30725} with respect to the Steiner inellipse
X(64744) = X(64)-of-Fuhrmann triangle
X(64744) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 60003, 61079}
X(64744) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(9353)}}, {{A, B, C, X(341), X(12641)}}, {{A, B, C, X(1000), X(42020)}}, {{A, B, C, X(3478), X(3885)}}, {{A, B, C, X(3880), X(57666)}}, {{A, B, C, X(5559), X(44720)}}
X(64744) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1145, 37828}, {1, 64204, 64123}, {8, 3885, 1837}, {517, 49169, 32049}, {519, 11362, 12513}, {519, 12640, 3913}, {519, 8715, 37727}, {2098, 6735, 25681}, {2136, 3632, 44669}, {3057, 44784, 8}, {3057, 46677, 960}, {3679, 3680, 3813}, {5697, 64087, 24703}, {5881, 64202, 528}, {7982, 12607, 34647}, {10914, 12647, 5794}, {10944, 13996, 63130}, {12641, 64056, 5854}, {26446, 47746, 22837}

X(64745) = ORTHOLOGY CENTER OF THESE TRIANGLES: INCIRCLE-CIRCLES AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a*(a^5*(b+c)-a^4*(b+c)^2-(b^2-c^2)^2*(b^2-3*b*c+c^2)+a^3*(-2*b^3+5*b^2*c+5*b*c^2-2*c^3)+a^2*(2*b^4-b^3*c-10*b^2*c^2-b*c^3+2*c^4)+a*(b^5-6*b^4*c+7*b^3*c^2+7*b^2*c^3-6*b*c^4+c^5)) : :
X(64745) = -3*X[2]+X[12758], -X[11]+3*X[3753], -3*X[354]+X[25416], -3*X[392]+5*X[31235], -X[3057]+3*X[34123], -5*X[3617]+X[12532], 3*X[3679]+X[11571], -5*X[3698]+X[17638], -X[3869]+5*X[64141], 5*X[4004]+X[13996], -5*X[5439]+X[17652], -X[5697]+5*X[64012]

X(64745) lies on circumconic {{A, B, C, X(519), X(13278)}} and on these lines: {1, 88}, {2, 12758}, {8, 10940}, {10, 119}, {11, 3753}, {40, 12775}, {65, 1145}, {80, 5554}, {104, 59333}, {354, 25416}, {377, 10057}, {392, 31235}, {474, 12740}, {517, 3035}, {519, 5083}, {528, 6797}, {758, 6735}, {936, 13253}, {942, 5854}, {952, 5836}, {958, 12515}, {993, 3359}, {997, 10698}, {1125, 15558}, {1317, 10914}, {1329, 12611}, {1376, 6265}, {1387, 3812}, {1519, 3814}, {1537, 21616}, {1706, 6326}, {1768, 9623}, {2077, 48363}, {2550, 2801}, {2771, 3036}, {2829, 31788}, {2886, 12619}, {2932, 22768}, {3057, 34123}, {3244, 46681}, {3296, 12641}, {3434, 10073}, {3617, 12532}, {3679, 11571}, {3698, 17638}, {3869, 64141}, {3872, 10074}, {3874, 49169}, {3878, 5657}, {3880, 12735}, {3884, 58453}, {3892, 11041}, {3898, 5218}, {3918, 6702}, {3919, 5542}, {3968, 33108}, {4004, 13996}, {4996, 59327}, {5123, 61580}, {5439, 17652}, {5552, 5903}, {5687, 12739}, {5694, 58674}, {5697, 64012}, {5722, 13271}, {5794, 19914}, {5902, 11046}, {6594, 42843}, {6684, 55296}, {8256, 10942}, {9709, 48667}, {9946, 57284}, {10058, 19860}, {10107, 16137}, {10176, 15017}, {10200, 32557}, {10202, 33337}, {10222, 58604}, {10269, 11715}, {10531, 14217}, {10609, 17636}, {10679, 64731}, {10916, 12832}, {10935, 11024}, {11045, 64743}, {11112, 18976}, {12514, 64189}, {12665, 64021}, {12703, 64136}, {12737, 16203}, {12755, 59413}, {12763, 64087}, {12773, 40587}, {13373, 64282}, {13747, 25414}, {14803, 17100}, {16209, 38693}, {17098, 45393}, {17646, 38156}, {17654, 37725}, {18398, 26726}, {18802, 64045}, {19907, 59691}, {20118, 24390}, {21077, 55016}, {22837, 41554}, {23340, 31870}, {24036, 61239}, {24473, 50842}, {25413, 37828}, {25466, 32198}, {25485, 30144}, {31787, 38759}, {34918, 49178}, {37561, 51111}, {37736, 63137}, {38213, 47320}, {38758, 58649}, {41558, 63146}, {44663, 58663}, {45701, 50841}, {51433, 53615}

X(64745) = midpoint of X(i) and X(j) for these {i,j}: {1, 39776}, {8, 11570}, {65, 1145}, {119, 37562}, {1317, 10914}, {5903, 64139}, {10609, 17636}, {11571, 46685}, {12665, 64021}, {17654, 37725}, {18802, 64045}, {24473, 50842}, {41558, 63146}, {51433, 53615}
X(64745) = reflection of X(i) in X(j) for these {i,j}: {1387, 3812}, {3244, 46681}, {3635, 58625}, {3884, 58453}, {5694, 58674}, {6702, 3918}, {10222, 58604}, {12735, 58591}, {12736, 3754}, {15528, 34339}, {15558, 1125}, {18254, 10}, {38759, 31787}, {64137, 18240}
X(64745) = complement of X(12758)
X(64745) = pole of line {2827, 10074} with respect to the incircle
X(64745) = pole of line {5048, 51409} with respect to the Feuerbach hyperbola
X(64745) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {1317, 6018, 10914}
X(64745) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 39776, 2802}, {1, 5541, 13278}, {10, 2800, 18254}, {119, 37562, 2800}, {952, 34339, 15528}, {1145, 10956, 10915}, {2802, 18240, 64137}, {2802, 3754, 12736}, {3359, 48695, 46684}, {3679, 11571, 46685}, {3880, 58591, 12735}, {5883, 64137, 18240}, {24982, 39692, 6702}

X(64746) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 107 AND X(8)-CROSSPEDAL-OF-X(100)

Barycentrics    a^4-6*a^3*(b+c)-2*(b^2-c^2)^2+a^2*(b^2+19*b*c+c^2)+a*(6*b^3-11*b^2*c-11*b*c^2+6*c^3) : :
X(64746) = -2*X[11]+3*X[53620], -4*X[3035]+3*X[38314], -4*X[3036]+X[9802], -3*X[3545]+2*X[64138], X[3621]+2*X[10609], -2*X[3655]+3*X[34474], -4*X[3828]+3*X[16173], -7*X[4678]+4*X[12019], -3*X[5054]+2*X[64742], -5*X[5734]+8*X[20400]

X(64746) lies on these lines: {1, 50841}, {2, 1000}, {8, 190}, {10, 30855}, {11, 53620}, {30, 50907}, {36, 100}, {63, 4677}, {80, 4669}, {88, 24864}, {104, 3654}, {145, 34753}, {214, 51093}, {376, 952}, {404, 64744}, {411, 38665}, {517, 10711}, {1317, 5435}, {1537, 50872}, {2094, 18802}, {2802, 3679}, {2804, 44553}, {2829, 34632}, {3035, 38314}, {3036, 9802}, {3241, 5854}, {3242, 51158}, {3244, 50844}, {3545, 64138}, {3621, 10609}, {3625, 50893}, {3626, 50889}, {3655, 34474}, {3828, 16173}, {3871, 37739}, {4421, 4996}, {4678, 12019}, {4745, 21630}, {4756, 50914}, {4997, 25030}, {5054, 64742}, {5734, 20400}, {5840, 34627}, {6224, 63212}, {6265, 50910}, {6326, 50817}, {6702, 51066}, {6942, 51525}, {9780, 59376}, {9884, 53729}, {10087, 62873}, {10265, 50827}, {10304, 64191}, {10728, 28198}, {10755, 47359}, {10827, 14923}, {10916, 56091}, {11015, 34639}, {11194, 17100}, {11274, 15015}, {11362, 38669}, {12640, 64199}, {12653, 19875}, {12730, 36920}, {12732, 20085}, {12737, 50821}, {12751, 28194}, {14217, 50796}, {15702, 38032}, {15703, 38044}, {19876, 32557}, {19907, 50805}, {19914, 28459}, {20050, 50846}, {20053, 62617}, {20119, 51102}, {25025, 31271}, {25055, 64137}, {26726, 51071}, {31140, 59416}, {31142, 64139}, {31164, 39776}, {31525, 50923}, {32041, 35168}, {33812, 51096}, {34605, 49169}, {34619, 62830}, {34620, 36972}, {34641, 63278}, {34789, 50906}, {36005, 44784}, {37375, 51379}, {38038, 61936}, {38050, 63109}, {38099, 51068}, {41553, 64736}, {50808, 64145}, {50810, 64189}, {50999, 51007}, {51000, 51157}, {51001, 51198}, {51008, 51192}, {51054, 51062}, {51103, 64012}, {51110, 58453}, {51147, 51199}, {51709, 64008}, {53055, 60986}

X(64746) = midpoint of X(i) and X(j) for these {i,j}: {2, 64743}, {4677, 5541}, {6326, 50817}, {13996, 50842}, {50907, 64136}
X(64746) = reflection of X(i) in X(j) for these {i,j}: {1, 50841}, {2, 1145}, {8, 50842}, {80, 4669}, {104, 3654}, {145, 50843}, {1320, 2}, {3241, 6174}, {3242, 51158}, {3244, 50844}, {3635, 50845}, {9884, 53729}, {10031, 100}, {10265, 50827}, {10707, 3679}, {10755, 47359}, {12531, 4677}, {12737, 50821}, {14217, 50796}, {19914, 50823}, {20050, 50846}, {20119, 51102}, {21630, 4745}, {26726, 51071}, {34747, 11274}, {34789, 50906}, {36005, 63136}, {50805, 19907}, {50872, 1537}, {50889, 3626}, {50890, 8}, {50891, 10}, {50892, 4691}, {50893, 3625}, {50894, 1}, {50907, 64140}, {50910, 6265}, {50923, 31525}, {50999, 51007}, {51000, 51157}, {51001, 51198}, {51054, 51062}, {51093, 214}, {51096, 33812}, {51147, 51199}, {51192, 51008}, {64145, 50808}, {64189, 50810}
X(64746) = pole of line {30565, 31171} with respect to the Steiner circumellipse
X(64746) = X(1320)-of-Gemini-107 triangle
X(64746) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1000), X(52746)}}, {{A, B, C, X(1121), X(37222)}}, {{A, B, C, X(1156), X(2718)}}
X(64746) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 34711, 11114}, {8, 528, 50890}, {10, 50891, 59377}, {30, 64140, 50907}, {100, 519, 10031}, {528, 50842, 8}, {1145, 1320, 64141}, {1145, 64743, 1320}, {2802, 3679, 10707}, {3679, 10707, 59415}, {5541, 12531, 9963}, {5854, 6174, 3241}, {13996, 50842, 528}, {15015, 34747, 11274}, {50907, 64136, 30}

X(64747) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(57) AND X(9)-CROSSPEDAL-OF-X(200)

Barycentrics    (a+b-c)*(a-b+c)*(a^4+2*a^2*(b-c)^2-2*a^3*(b+c)-2*a*(b-c)^2*(b+c)+(b^2-c^2)^2) : :

X(64747) lies on circumconic {{A, B, C, X(1096), X(40154)}} and on these lines: {1, 6865}, {2, 1617}, {4, 11}, {7, 3660}, {12, 17559}, {36, 6916}, {57, 497}, {65, 1058}, {145, 14594}, {149, 64142}, {196, 40959}, {226, 4321}, {241, 17721}, {244, 4331}, {278, 614}, {279, 40615}, {281, 46345}, {329, 17625}, {376, 1470}, {377, 5265}, {388, 1125}, {390, 37541}, {443, 3841}, {496, 6851}, {499, 6864}, {535, 5193}, {631, 37579}, {927, 56850}, {946, 1467}, {995, 56821}, {997, 3421}, {999, 6827}, {1014, 14956}, {1056, 1319}, {1088, 40154}, {1155, 35514}, {1254, 28074}, {1285, 1415}, {1388, 37703}, {1412, 17188}, {1445, 6601}, {1466, 4294}, {1471, 11269}, {1476, 20076}, {1478, 6939}, {1479, 3361}, {1708, 24477}, {1788, 5082}, {1836, 59386}, {1992, 14612}, {2078, 5218}, {2478, 3600}, {2550, 3911}, {2551, 5316}, {3256, 10385}, {3340, 4342}, {3434, 5435}, {3436, 4308}, {3485, 34489}, {3524, 5172}, {3677, 64708}, {3711, 10944}, {4295, 13374}, {4299, 13370}, {4311, 12667}, {4551, 63126}, {4554, 6604}, {4654, 51098}, {4679, 8581}, {4848, 64068}, {4860, 60883}, {5173, 10580}, {5252, 61686}, {5274, 10431}, {5298, 64086}, {5433, 17582}, {5563, 10629}, {5758, 50196}, {5759, 54408}, {5812, 58576}, {5856, 12848}, {6826, 15325}, {6836, 14986}, {6893, 18990}, {6903, 26437}, {6954, 41345}, {6988, 7742}, {7191, 57477}, {7290, 34050}, {7292, 37800}, {7365, 34036}, {8071, 59345}, {8732, 64443}, {9785, 13601}, {9799, 64131}, {10530, 37301}, {10596, 18838}, {10806, 64721}, {10832, 37441}, {10996, 56414}, {11678, 18228}, {12116, 37550}, {12447, 37709}, {14069, 28773}, {16020, 37695}, {18240, 60895}, {18391, 61660}, {22836, 33812}, {24703, 63994}, {25006, 62776}, {26040, 31231}, {28771, 32957}, {29668, 36482}, {29824, 56927}, {30353, 60992}, {32773, 56460}, {32942, 56367}, {33108, 61019}, {36059, 64177}, {36845, 41539}, {37374, 42884}, {37642, 55086}, {37787, 64153}, {38149, 61649}, {40718, 60076}, {41325, 56546}, {41563, 62235}, {41712, 51463}, {48482, 64124}, {63962, 64132}, {63995, 64130}

X(64747) = pole of line {1056, 6001} with respect to the Feuerbach hyperbola
X(64747) = pole of line {948, 34050} with respect to the dual conic of Yff parabola
X(64747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 56, 54366}, {3086, 4293, 22753}, {9785, 41824, 13601}

X(64748) = ORTHOLOGY CENTER OF THESE TRIANGLES: VIJAY POLAR EXCENTRAL AND X(10)-CROSSPEDAL-OF-X(72)

Barycentrics    a^3*b*(b-c)^2*c+2*a^6*(b+c)-a^2*b*(b-c)^2*c*(b+c)-b*(b-c)^2*c*(b+c)^3+a^5*(b^2+c^2)-a*(b^2-c^2)^2*(b^2+b*c+c^2)-2*a^4*(b^3+c^3) : :
X(64748) = -3*X[2]+X[10454], -5*X[3091]+4*X[64569], -5*X[3876]+3*X[54035]

X(64748) lies on these lines: {1, 9551}, {2, 10454}, {3, 10}, {4, 386}, {5, 48894}, {6, 64582}, {8, 1764}, {20, 391}, {21, 1746}, {30, 970}, {43, 5691}, {55, 9552}, {56, 9555}, {72, 29069}, {78, 22020}, {181, 7354}, {218, 5776}, {376, 48852}, {382, 9567}, {388, 64573}, {485, 9557}, {516, 59303}, {519, 10441}, {524, 31774}, {550, 35203}, {572, 1010}, {940, 10106}, {944, 30116}, {950, 19765}, {952, 37536}, {960, 24269}, {994, 64021}, {997, 35635}, {1012, 19763}, {1043, 6996}, {1478, 10408}, {1503, 4260}, {1614, 9563}, {1657, 9566}, {1682, 6284}, {1685, 6561}, {1686, 6560}, {1695, 64005}, {1730, 10463}, {1837, 64577}, {2050, 4255}, {2172, 2908}, {2777, 34453}, {2794, 34454}, {2829, 34456}, {3029, 23698}, {3031, 17702}, {3032, 5840}, {3033, 64502}, {3091, 64569}, {3146, 9535}, {3191, 40491}, {3216, 51558}, {3430, 37088}, {3436, 64567}, {3576, 19858}, {3597, 60172}, {3687, 5016}, {3876, 54035}, {4274, 64159}, {4276, 6906}, {4279, 12110}, {4301, 4780}, {4306, 24237}, {5217, 31496}, {5396, 46704}, {5482, 28204}, {5530, 10572}, {5721, 7683}, {5731, 19853}, {5767, 37530}, {5799, 48847}, {5816, 13725}, {5853, 43170}, {5882, 50317}, {5930, 21621}, {6048, 62320}, {6253, 10822}, {6685, 19925}, {6738, 35612}, {7387, 9571}, {7745, 9547}, {7747, 9561}, {7756, 9560}, {7823, 41832}, {7987, 59312}, {7989, 29825}, {8703, 62185}, {9546, 63548}, {9549, 41869}, {9550, 64054}, {9553, 12943}, {9554, 12953}, {9556, 42260}, {9562, 34148}, {9564, 57288}, {9565, 29207}, {9840, 48888}, {10434, 31339}, {10440, 28164}, {10446, 20018}, {10478, 19767}, {10882, 31330}, {10974, 37468}, {12203, 13727}, {12545, 29311}, {19513, 50605}, {26117, 64576}, {28236, 37521}, {28581, 31779}, {29057, 31803}, {29307, 64003}, {34455, 64507}, {34457, 64500}, {34459, 64501}, {36745, 56959}, {37331, 48937}, {37415, 48863}, {37469, 64384}, {37522, 45287}, {37523, 40687}, {37712, 59313}, {48899, 50588}, {49542, 52903}, {49641, 64525}, {50054, 64121}, {54586, 61129}

X(64748) = midpoint of X(i) and X(j) for these {i,j}: {8, 64568}, {5691, 64575}, {12545, 59302}
X(64748) = reflection of X(i) in X(j) for these {i,j}: {1, 64578}, {20, 64565}, {10454, 64566}, {44039, 10}, {64566, 64570}
X(64748) = inverse of X(50368) in excircles-radical circle
X(64748) = complement of X(10454)
X(64748) = anticomplement of X(64566)
X(64748) = pole of line {240, 522} with respect to the excircles-radical circle
X(64748) = pole of line {36, 238} with respect to the excentral-hexyl ellipse
X(64748) = pole of line {6332, 23799} with respect to the Steiner inellipse
X(64748) = pole of line {1400, 3772} with respect to the dual conic of Yff parabola
X(64748) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {8, 18340, 64568}
X(64748) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3192), X(52139)}}, {{A, B, C, X(10570), X(55035)}}
X(64748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10454, 64566}, {3, 5786, 13478}, {4, 386, 2051}, {8, 50702, 1764}, {10, 515, 44039}, {20, 9534, 573}, {43, 5691, 50037}, {376, 48852, 62189}, {573, 9534, 9568}, {12545, 59302, 29311}, {64566, 64570, 2}

X(64749) = ORTHOLOGY CENTER OF THESE TRIANGLES: ANTI-EULER AND X(10)-CROSSPEDAL-OF-X(99)

Barycentrics    a^8+2*a^6*b*c-a^7*(b+c)-2*b^2*c^2*(b^2-c^2)^2-a^4*b*c*(2*b^2+3*b*c+2*c^2)+2*a^5*(b^3+c^3)-a^2*(b+c)^2*(b^4-4*b^3*c+5*b^2*c^2-4*b*c^3+c^4)+a^3*(-2*b^5+b^3*c^2+b^2*c^3-2*c^5)+a*(b-c)^2*(b^5+b^4*c-b^3*c^2-b^2*c^3+b*c^4+c^5) : :
X(64749) = -2*X[10]+3*X[14651], -2*X[99]+3*X[3576], -4*X[114]+5*X[8227], -4*X[115]+3*X[5587], -3*X[165]+4*X[12042], -5*X[631]+4*X[51578], -5*X[1698]+6*X[38224], -3*X[1699]+2*X[6033], -3*X[3545]+2*X[50879], -7*X[3624]+6*X[15561], -3*X[5603]+2*X[21636]

X(64749) lies on these lines: {1, 2782}, {3, 13174}, {4, 2784}, {10, 14651}, {40, 98}, {57, 10069}, {99, 3576}, {114, 8227}, {115, 5587}, {147, 946}, {148, 515}, {165, 12042}, {376, 2796}, {516, 9862}, {517, 9860}, {519, 12243}, {542, 31162}, {543, 50811}, {551, 64090}, {631, 51578}, {690, 33535}, {962, 5984}, {1045, 2783}, {1281, 8235}, {1385, 13188}, {1420, 10089}, {1569, 9619}, {1697, 10053}, {1698, 38224}, {1699, 6033}, {1702, 49212}, {1703, 49213}, {1704, 47366}, {1705, 47365}, {2023, 9593}, {2077, 13173}, {2787, 6264}, {2792, 10446}, {2794, 41869}, {2795, 16132}, {2948, 18332}, {3029, 9548}, {3044, 9621}, {3333, 24472}, {3545, 50879}, {3586, 13183}, {3601, 10086}, {3624, 15561}, {3679, 11632}, {3923, 7709}, {4297, 13172}, {5250, 5985}, {5603, 21636}, {5691, 6321}, {5731, 20094}, {5881, 13178}, {5886, 51872}, {6036, 31423}, {6054, 12258}, {6055, 9881}, {6282, 52821}, {7970, 16200}, {7982, 7983}, {7987, 33813}, {7988, 61575}, {7989, 61576}, {7991, 51523}, {8591, 51705}, {8724, 25055}, {8726, 52822}, {9549, 34454}, {9583, 49266}, {9610, 39822}, {9611, 39851}, {9612, 12184}, {9613, 13182}, {9614, 12185}, {9622, 58058}, {9624, 11725}, {9625, 39857}, {9626, 39828}, {9875, 28204}, {9955, 38743}, {10476, 38481}, {11012, 22514}, {11014, 38498}, {11177, 28194}, {11522, 52090}, {11529, 59815}, {11646, 39885}, {11676, 50775}, {11705, 36776}, {11706, 61634}, {11711, 23235}, {11724, 61275}, {12177, 16475}, {12355, 28208}, {12368, 16278}, {12703, 49148}, {12704, 24469}, {13605, 18331}, {14061, 54447}, {14639, 18492}, {15092, 61264}, {15177, 39832}, {15452, 30282}, {15903, 60751}, {18480, 38732}, {18908, 58682}, {19875, 49102}, {19905, 50950}, {22566, 30308}, {22793, 38744}, {24727, 58036}, {24929, 51795}, {26446, 61560}, {28160, 38733}, {30389, 51524}, {31732, 39837}, {31738, 39807}, {34473, 35242}, {34627, 50884}, {34648, 50887}, {35774, 35825}, {35775, 35824}, {38034, 61599}, {38229, 61261}, {38531, 53260}, {38627, 58245}, {38741, 64005}, {41135, 50796}, {48657, 51709}, {50828, 52695}

X(64749) = midpoint of X(i) and X(j) for these {i,j}: {962, 5984}, {7983, 38664}
X(64749) = reflection of X(i) in X(j) for these {i,j}: {4, 11599}, {40, 98}, {99, 11710}, {147, 946}, {2948, 18332}, {3679, 11632}, {5691, 6321}, {5881, 13178}, {6054, 12258}, {7982, 7983}, {8591, 51705}, {9860, 12188}, {9864, 115}, {9881, 6055}, {11676, 50775}, {12368, 16278}, {13172, 4297}, {13174, 3}, {13188, 1385}, {14981, 11725}, {18331, 13605}, {23235, 11711}, {24469, 49147}, {31162, 50886}, {34627, 50884}, {34648, 50887}, {36776, 11705}, {38744, 22793}, {39807, 31738}, {39837, 31732}, {39885, 11646}, {48657, 51709}, {50950, 19905}, {61634, 11706}, {64005, 38741}, {64090, 551}, {64755, 1}
X(64749) = pole of line {804, 4707} with respect to the Conway circle
X(64749) = X(1298)-of-hexyl triangle
X(64749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2782, 64755}, {99, 11710, 3576}, {114, 38220, 8227}, {115, 9864, 5587}, {517, 12188, 9860}, {542, 50886, 31162}, {2784, 11599, 4}, {6054, 12258, 38021}

X(64750) = ORTHOLOGY CENTER OF THESE TRIANGLES: PEDAL OF X(77) AND X(33)-CROSSPEDAL-OF-X(1)

Barycentrics    a*(a^5-a*(b^2-c^2)^2-2*a^2*(b^3+c^3)+2*(b^5-b^3*c^2-b^2*c^3+c^5)) : :

X(64750) lies on these lines: {1, 6}, {2, 1897}, {3, 3100}, {4, 347}, {5, 1068}, {8, 25000}, {21, 55986}, {25, 21318}, {33, 1214}, {55, 11028}, {56, 32118}, {77, 971}, {154, 1726}, {198, 44661}, {222, 24430}, {223, 5927}, {240, 19329}, {241, 990}, {278, 8226}, {442, 7952}, {461, 56943}, {474, 17102}, {651, 5779}, {664, 48878}, {774, 5711}, {916, 45963}, {938, 5740}, {940, 62811}, {942, 7013}, {955, 1255}, {1011, 23171}, {1012, 1060}, {1020, 33536}, {1038, 37022}, {1074, 44217}, {1103, 3697}, {1172, 36017}, {1210, 3946}, {1376, 34977}, {1419, 64197}, {1442, 10394}, {1456, 54370}, {1465, 9817}, {1785, 17532}, {1824, 11347}, {1827, 37412}, {1837, 32594}, {1854, 37558}, {1861, 17073}, {1863, 37160}, {1864, 45126}, {1870, 6913}, {1872, 37413}, {1902, 37046}, {2915, 11399}, {3149, 37565}, {3157, 35194}, {3160, 36991}, {3219, 22117}, {3487, 5796}, {3560, 18447}, {3562, 3927}, {3677, 17626}, {3745, 62839}, {3826, 59458}, {4310, 38055}, {4329, 49132}, {4413, 24025}, {5018, 64134}, {5088, 51063}, {5256, 64157}, {5287, 11018}, {5691, 15832}, {5732, 59215}, {5751, 42447}, {5753, 15934}, {5777, 64347}, {5784, 53996}, {5805, 22464}, {5817, 54425}, {5824, 14986}, {6350, 33305}, {6360, 14004}, {6832, 38295}, {6883, 18455}, {6986, 9538}, {7069, 20277}, {7100, 8757}, {7411, 9539}, {7532, 41013}, {7688, 9611}, {7718, 13442}, {8727, 57477}, {9577, 15931}, {10004, 43736}, {10883, 37798}, {11019, 17599}, {11020, 17019}, {11113, 34231}, {11350, 20243}, {11363, 37052}, {11396, 13724}, {12664, 15836}, {12915, 62833}, {13615, 38288}, {15068, 23070}, {15430, 15726}, {15500, 37249}, {16370, 46974}, {17080, 19541}, {17086, 36652}, {17134, 49130}, {17463, 22769}, {18391, 64167}, {18593, 64152}, {18641, 56876}, {19544, 20254}, {20760, 38479}, {21333, 54326}, {23710, 37695}, {32047, 37234}, {36640, 59385}, {37320, 41340}, {37367, 51410}, {37426, 64054}, {37594, 62836}, {38052, 63625}, {40960, 64708}, {40971, 55875}, {41083, 56299}, {41344, 44706}, {43035, 63970}, {44692, 64673}, {45276, 56640}, {55400, 56294}, {57282, 62779}, {62333, 64339}, {64082, 64171}

X(64750) = X(i)-complementary conjugate of X(j) for these {i, j}: {56139, 1329}
X(64750) = pole of line {676, 17924} with respect to the polar circle
X(64750) = pole of line {55, 45126} with respect to the Feuerbach hyperbola
X(64750) = pole of line {17494, 39470} with respect to the Steiner circumellipse
X(64750) = pole of line {650, 39470} with respect to the Steiner inellipse
X(64750) = pole of line {3309, 58888} with respect to the Suppa-Cucoanes circle
X(64750) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(52781)}}, {{A, B, C, X(6), X(36122)}}, {{A, B, C, X(9), X(39531)}}, {{A, B, C, X(72), X(55986)}}, {{A, B, C, X(219), X(37741)}}, {{A, B, C, X(954), X(1255)}}, {{A, B, C, X(955), X(1100)}}, {{A, B, C, X(1530), X(7046)}}, {{A, B, C, X(3990), X(59144)}}
X(64750) = barycentric product X(i)*X(j) for these (i, j): {1530, 36101}, {39531, 63}
X(64750) = barycentric quotient X(i)/X(j) for these (i, j): {1530, 30807}, {39531, 92}
X(64750) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10398, 1449}, {1, 15299, 1386}, {1, 1736, 6}, {1, 37, 954}, {6, 1736, 5729}, {33, 1214, 7580}, {1442, 10394, 62183}, {7069, 20277, 34048}, {8727, 59611, 57477}, {37565, 37696, 3149}

X(64751) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(55)-CROSSPEDAL-OF-X(1) AND PEDAL OF X(7)

Barycentrics    a^2*(-((b-c)^2*(b+c))+a*(b^2+b*c+c^2)) : :
X(64751) = -3*X[3789]+4*X[4708], -5*X[4798]+6*X[28600]

X(64751) lies on these lines: {1, 674}, {2, 57024}, {6, 692}, {7, 13476}, {8, 44671}, {9, 22277}, {31, 5165}, {37, 3779}, {39, 4484}, {42, 2183}, {45, 20683}, {51, 4285}, {55, 2245}, {65, 4331}, {71, 4343}, {86, 64709}, {141, 35892}, {209, 968}, {269, 64206}, {284, 1631}, {291, 24696}, {320, 3873}, {346, 21865}, {354, 4675}, {386, 23383}, {513, 1002}, {516, 5751}, {518, 4643}, {572, 4497}, {573, 64169}, {579, 8053}, {583, 20992}, {584, 23868}, {869, 3122}, {941, 22301}, {942, 5880}, {966, 22271}, {995, 53307}, {1001, 4260}, {1045, 4446}, {1086, 64560}, {1100, 3056}, {1400, 15624}, {1429, 64551}, {1469, 49478}, {1633, 62797}, {1769, 2874}, {1964, 63497}, {2099, 2875}, {2176, 39688}, {2260, 2293}, {2276, 4735}, {2278, 17798}, {2309, 5069}, {2334, 16980}, {2345, 22279}, {2388, 30116}, {2389, 11529}, {2393, 3556}, {2810, 64165}, {2886, 35612}, {3672, 64553}, {3681, 17256}, {3688, 4890}, {3770, 21299}, {3778, 4261}, {3781, 15569}, {3789, 4708}, {3813, 35620}, {3868, 24723}, {3874, 4655}, {3888, 17378}, {3900, 11041}, {4000, 64524}, {4014, 62223}, {4026, 10477}, {4251, 4471}, {4272, 40954}, {4294, 51223}, {4361, 17049}, {4363, 6007}, {4364, 9054}, {4389, 62872}, {4393, 25048}, {4430, 4741}, {4553, 17316}, {4648, 58571}, {4649, 9018}, {4667, 29353}, {4798, 28600}, {4851, 17792}, {5135, 37576}, {5138, 20872}, {5208, 32773}, {5222, 64523}, {5296, 40607}, {5308, 64552}, {5320, 20988}, {5573, 58574}, {5728, 50861}, {5738, 11677}, {5752, 59301}, {5883, 24693}, {5902, 24715}, {5904, 24697}, {7064, 16675}, {7146, 17463}, {7174, 9049}, {9016, 49490}, {9320, 24457}, {9911, 36742}, {10580, 64548}, {11021, 24392}, {11495, 50658}, {11997, 21853}, {14523, 58562}, {14839, 17318}, {15185, 47595}, {15668, 64007}, {17065, 50584}, {17126, 61728}, {17257, 64581}, {17278, 61034}, {17301, 20358}, {17317, 25279}, {17321, 56537}, {17790, 24351}, {18165, 33137}, {18635, 23305}, {20456, 23634}, {20718, 64168}, {20961, 61358}, {20986, 37538}, {20990, 64739}, {21278, 25295}, {21889, 61704}, {22276, 37553}, {22312, 63978}, {24349, 24717}, {25291, 56249}, {26893, 37593}, {32784, 38485}, {37679, 53005}, {40910, 47373}, {44085, 61356}, {44094, 61398}

X(64751) = reflection of X(i) in X(j) for these {i,j}: {56542, 4364}
X(64751) = pole of line {665, 4893} with respect to the Brocard inellipse
X(64751) = pole of line {29830, 30941} with respect to the Stammler hyperbola
X(64751) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(513), X(60722)}}, {{A, B, C, X(692), X(1002)}}, {{A, B, C, X(1438), X(46018)}}, {{A, B, C, X(2175), X(13476)}}, {{A, B, C, X(33108), X(56853)}}, {{A, B, C, X(45966), X(64216)}}
X(64751) = barycentric product X(i)*X(j) for these (i, j): {101, 49300}, {33108, 6}
X(64751) = barycentric quotient X(i)/X(j) for these (i, j): {33108, 76}, {49300, 3261}
X(64751) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16686, 60722}, {6, 37580, 692}, {42, 23633, 3764}, {42, 3764, 4277}, {2260, 2293, 3941}, {3688, 4890, 16777}, {17792, 64546, 4851}, {21746, 52020, 6}

X(64752) = PERSPECTOR OF THESE TRIANGLES: X(65)-CROSSPEDAL-OF-X(1) AND ANTICEVIAN OF X(45)

Barycentrics    a^2*(-(a^2*b*c)+a^3*(b+c)-a*(b-c)^2*(b+c)-b*c*(b+c)^2) : :

X(64752) lies on these lines: {2, 23853}, {3, 8}, {6, 31}, {10, 13738}, {25, 281}, {35, 50581}, {36, 16499}, {38, 1403}, {40, 37195}, {56, 750}, {63, 37619}, {165, 22060}, {197, 199}, {200, 228}, {210, 3185}, {388, 47521}, {405, 26115}, {573, 51377}, {612, 1402}, {678, 23370}, {851, 2550}, {859, 5235}, {908, 31394}, {947, 43652}, {958, 28348}, {984, 5143}, {993, 996}, {999, 16374}, {1001, 16373}, {1331, 43146}, {1376, 4191}, {1486, 47523}, {1617, 7484}, {1621, 16058}, {1631, 20989}, {1995, 51621}, {2053, 6187}, {2187, 26885}, {2223, 16975}, {2551, 13724}, {3085, 37225}, {3145, 8193}, {3158, 54327}, {3240, 37502}, {3286, 37540}, {3293, 19763}, {3295, 16287}, {3304, 9345}, {3359, 63439}, {3421, 19262}, {3434, 4192}, {3436, 9840}, {3550, 59314}, {3588, 37499}, {3617, 4225}, {3681, 20760}, {3689, 15624}, {3711, 4557}, {3724, 3728}, {3730, 23988}, {3871, 16452}, {3872, 37620}, {3996, 19339}, {4088, 53262}, {4184, 16704}, {4413, 20470}, {4421, 19346}, {4423, 18613}, {4853, 10882}, {4882, 61124}, {5218, 30944}, {5220, 53280}, {5258, 15654}, {5260, 28383}, {5263, 16405}, {5264, 19762}, {5269, 40956}, {5291, 37586}, {5552, 13731}, {5584, 15622}, {5710, 54300}, {6048, 35206}, {6244, 7416}, {7080, 61109}, {8069, 52273}, {8715, 59302}, {9259, 62712}, {9342, 16409}, {9709, 16453}, {10527, 19513}, {11337, 38903}, {11344, 12410}, {11680, 19540}, {11688, 32937}, {12513, 32919}, {13588, 16738}, {13734, 64111}, {15066, 36942}, {15507, 31018}, {15625, 63756}, {15983, 50423}, {16064, 37577}, {16372, 37580}, {16506, 23832}, {16569, 27639}, {16788, 40910}, {16948, 17524}, {17126, 37507}, {17259, 23374}, {17784, 37400}, {18235, 33163}, {19543, 24390}, {19734, 59315}, {19843, 27622}, {21319, 25568}, {22344, 62824}, {22345, 57279}, {22837, 38484}, {23085, 62827}, {23207, 26901}, {23850, 37557}, {26227, 54410}, {27650, 29667}, {28349, 30478}, {28734, 30016}, {32911, 59300}, {32927, 64170}, {33104, 40109}, {33108, 47522}, {34868, 36152}, {35289, 46917}, {35448, 48917}, {37247, 37579}, {37684, 54391}, {43650, 55086}, {48875, 56878}, {49983, 61154}, {51380, 64125}, {53548, 56550}, {56162, 56853}

X(64752) = perspector of circumconic {{A, B, C, X(101), X(13136)}}
X(64752) = X(i)-Dao conjugate of X(j) for these {i, j}: {995, 4389}
X(64752) = X(i)-Ceva conjugate of X(j) for these {i, j}: {993, 45}, {996, 6}
X(64752) = pole of line {649, 900} with respect to the circumcircle
X(64752) = pole of line {3004, 39534} with respect to the polar circle
X(64752) = pole of line {86, 859} with respect to the Stammler hyperbola
X(64752) = pole of line {3904, 21225} with respect to the Steiner circumellipse
X(64752) = pole of line {46148, 62669} with respect to the Yff parabola
X(64752) = pole of line {2427, 52923} with respect to the Hutson-Moses hyperbola
X(64752) = pole of line {310, 17139} with respect to the Wallace hyperbola
X(64752) = pole of line {21207, 42759} with respect to the dual conic of Wallace hyperbola
X(64752) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(34234)}}, {{A, B, C, X(31), X(104)}}, {{A, B, C, X(42), X(38955)}}, {{A, B, C, X(55), X(24806)}}, {{A, B, C, X(71), X(14624)}}, {{A, B, C, X(212), X(1809)}}, {{A, B, C, X(281), X(2269)}}, {{A, B, C, X(672), X(56162)}}, {{A, B, C, X(902), X(36944)}}, {{A, B, C, X(2053), X(2361)}}, {{A, B, C, X(2177), X(36921)}}, {{A, B, C, X(2209), X(6187)}}, {{A, B, C, X(2267), X(23617)}}, {{A, B, C, X(3052), X(34429)}}
X(64752) = barycentric product X(i)*X(j) for these (i, j): {24806, 9}
X(64752) = barycentric quotient X(i)/X(j) for these (i, j): {24806, 85}
X(64752) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 902, 2209}, {55, 20992, 902}, {55, 52139, 1011}, {200, 10434, 228}, {902, 22343, 31}, {956, 5687, 5774}, {1376, 16678, 4191}, {15621, 52139, 55}

X(64753) = ORTHOLOGY CENTER OF THESE TRIANGLES: X(65)-CROSSPEDAL-OF-X(1) AND PEDAL OF X(21)

Barycentrics    a^2*(b+c)*(a^4+b*(b-c)^2*c+a^3*(b+c)-a^2*(b^2+b*c+c^2)-a*(b^3+b^2*c+b*c^2+c^3)) : :
X(64753) = -3*X[53035]+4*X[58392]

X(64753) lies on these lines: {1, 859}, {3, 758}, {6, 40978}, {10, 4557}, {12, 21319}, {21, 53280}, {35, 23845}, {40, 15624}, {48, 14529}, {55, 976}, {56, 2650}, {65, 228}, {72, 52139}, {73, 53321}, {100, 17164}, {191, 17524}, {198, 2294}, {497, 28098}, {501, 3733}, {513, 48897}, {520, 947}, {523, 64173}, {526, 53305}, {595, 5009}, {690, 53278}, {740, 3913}, {851, 3649}, {855, 10543}, {942, 20470}, {958, 20760}, {986, 5132}, {993, 22458}, {999, 63354}, {1001, 58386}, {1043, 11688}, {1046, 3286}, {1071, 53296}, {1104, 20967}, {1191, 3725}, {1284, 1834}, {1331, 55098}, {1376, 49598}, {1385, 53303}, {1403, 4255}, {1437, 53324}, {1482, 5496}, {1486, 3295}, {1631, 37547}, {1962, 3303}, {2098, 12081}, {2099, 31880}, {2183, 58493}, {2352, 54421}, {2390, 4300}, {2392, 48907}, {2646, 22345}, {2933, 11507}, {3191, 22299}, {3194, 53323}, {3207, 42669}, {3612, 23206}, {3714, 60723}, {3746, 20840}, {3811, 15621}, {3827, 37528}, {3868, 16678}, {3871, 32926}, {3901, 39578}, {3931, 52359}, {3958, 54322}, {4016, 36744}, {4065, 25439}, {4184, 11684}, {4191, 5221}, {4225, 34195}, {4245, 30143}, {4436, 63996}, {4491, 6089}, {4647, 5687}, {5267, 23169}, {5441, 13744}, {5692, 16287}, {5711, 20990}, {5883, 16414}, {5902, 16453}, {6370, 53277}, {6765, 44671}, {6767, 58380}, {6998, 53261}, {7416, 15071}, {7420, 37625}, {7421, 53252}, {7428, 37571}, {8053, 12514}, {8680, 24328}, {8731, 18253}, {9391, 53299}, {9840, 44669}, {9911, 10679}, {10176, 16286}, {10434, 11523}, {10834, 26358}, {11101, 63269}, {11281, 28258}, {11553, 58889}, {14547, 42450}, {15571, 35633}, {15622, 18446}, {16502, 40986}, {16679, 62805}, {16687, 57280}, {17768, 37425}, {18162, 37570}, {21677, 37225}, {21740, 53292}, {22344, 37600}, {22654, 25080}, {22769, 56839}, {23067, 37558}, {23167, 35628}, {31660, 37311}, {37154, 53566}, {37415, 42843}, {37503, 53037}, {37568, 54327}, {37619, 56176}, {38955, 56254}, {42666, 53308}, {53035, 58392}, {53249, 53262}, {53263, 53286}

X(64753) = midpoint of X(i) and X(j) for these {i,j}: {2292, 18673}
X(64753) = reflection of X(i) in X(j) for these {i,j}: {1, 42443}, {1482, 5496}, {42440, 3743}, {53286, 53263}
X(64753) = pole of line {656, 3737} with respect to the circumcircle
X(64753) = pole of line {523, 39541} with respect to the DeLongchamps ellipse
X(64753) = pole of line {2975, 11101} with respect to the Stammler hyperbola
X(64753) = X(2292)-of-anti-Mandart-incircle triangle
X(64753) = X(2650)-of-2nd-circumperp-tangential triangle
X(64753) = intersection, other than A, B, C, of circumconics {{A, B, C, X(859), X(56254)}}, {{A, B, C, X(947), X(53321)}}, {{A, B, C, X(8615), X(52150)}}, {{A, B, C, X(18165), X(60086)}}, {{A, B, C, X(18180), X(38955)}}, {{A, B, C, X(34434), X(59282)}}, {{A, B, C, X(53083), X(60135)}}
X(64753) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3185, 23383}, {1385, 55362, 53303}, {2650, 3724, 56}, {3295, 3743, 4068}, {3743, 44661, 42440}

X(64754) = ORTHOLOGY CENTER OF THESE TRIANGLES: EULER AND X(79)-CROSSPEDAL-OF-X(1)

Barycentrics    2*a^6*(b+c)-5*a^4*(b-c)^2*(b+c)-(b-c)^4*(b+c)^3-a*(b^2-c^2)^2*(b^2-6*b*c+c^2)+2*a^3*(b-c)^2*(b^2+4*b*c+c^2)-a^5*(b^2+10*b*c+c^2)+4*a^2*(b-c)^2*(b^3+c^3) : :
X(64754) = -3*X[5587]+2*X[64294], -4*X[5806]+X[13375], -4*X[12571]+X[15862], -X[34352]+3*X[38034], -3*X[59387]+X[64270]

X(64754) lies on these lines: {1, 5805}, {4, 1389}, {5, 17057}, {11, 7686}, {12, 946}, {30, 12600}, {40, 24953}, {55, 64280}, {56, 11023}, {65, 6245}, {72, 4301}, {354, 40249}, {355, 546}, {392, 7958}, {515, 3649}, {516, 57002}, {517, 6841}, {523, 42755}, {944, 64282}, {952, 15911}, {958, 962}, {1012, 64268}, {1319, 64001}, {1478, 52683}, {1482, 18517}, {1512, 3614}, {1519, 10955}, {1537, 6246}, {1836, 12676}, {1837, 3577}, {2346, 9785}, {2646, 64286}, {2800, 37447}, {3149, 15950}, {3303, 5603}, {3436, 64201}, {3485, 64298}, {3486, 36999}, {3656, 34699}, {3671, 12680}, {3679, 5763}, {3748, 13464}, {3753, 50031}, {3754, 37374}, {3839, 34700}, {3878, 8226}, {3925, 14110}, {4295, 12246}, {4299, 52682}, {5252, 5715}, {5258, 5762}, {5289, 6835}, {5559, 10827}, {5587, 64294}, {5659, 5791}, {5691, 37739}, {5722, 64292}, {5734, 59385}, {5804, 11238}, {5806, 13375}, {5812, 31162}, {5842, 10543}, {5901, 34486}, {5903, 8727}, {5919, 63256}, {6224, 59356}, {6284, 64279}, {6766, 41229}, {6831, 40663}, {6847, 37567}, {6894, 62826}, {7354, 7702}, {7681, 7704}, {7956, 10523}, {7965, 12672}, {8273, 28629}, {9778, 17574}, {10388, 12859}, {10404, 12650}, {10572, 52837}, {10894, 64322}, {10944, 26332}, {10954, 18393}, {11218, 11374}, {11246, 12114}, {11375, 64276}, {11510, 22753}, {11827, 12699}, {12047, 64271}, {12116, 64327}, {12513, 55109}, {12571, 15862}, {12611, 13600}, {12635, 13463}, {12667, 61716}, {12679, 64288}, {12688, 41562}, {12858, 63992}, {16139, 28212}, {16615, 59391}, {18357, 52850}, {18493, 26487}, {19925, 51409}, {21077, 64767}, {21627, 61030}, {24474, 51463}, {28174, 31649}, {28452, 46920}, {31157, 37623}, {34352, 38034}, {34471, 50701}, {34612, 37531}, {35250, 48661}, {36922, 37714}, {37711, 64766}, {37722, 64284}, {37724, 64261}, {37737, 44425}, {37740, 64287}, {59387, 64270}, {63989, 64332}, {64110, 64297}

X(64754) = midpoint of X(i) and X(j) for these {i,j}: {4, 1389}
X(64754) = reflection of X(i) in X(j) for these {i,j}: {944, 64282}, {45081, 63257}, {63257, 946}, {63287, 5603}, {64275, 5}, {64297, 64110}
X(64754) = inverse of X(7686) in Feuerbach hyperbola
X(64754) = pole of line {5173, 7686} with respect to the Feuerbach hyperbola
X(64754) = X(1389)-of-Euler triangle
X(64754) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {946, 63964, 38039}, {1532, 63257, 64273}

X(64755) = ORTHOLOGY CENTER OF THESE TRIANGLES: HEXYL AND X(98)-CROSSPEDAL-OF-X(1)

Barycentrics    a^8-a^7*(b+c)+a^6*(-4*b^2+2*b*c-4*c^2)+2*b^2*c^2*(b^2-c^2)^2+2*a^5*(b^3+c^3)+a^4*(4*b^4-2*b^3*c+5*b^2*c^2-2*b*c^3+4*c^4)+a^3*(-2*b^5+b^3*c^2+b^2*c^3-2*c^5)+a*(b-c)^2*(b^5+b^4*c-b^3*c^2-b^2*c^3+b*c^4+c^5)-a^2*(b^6-2*b^5*c+2*b^4*c^2+2*b^3*c^3+2*b^2*c^4-2*b*c^5+c^6) : :
X(64755) = -2*X[98]+3*X[3576], -4*X[114]+3*X[5587], -4*X[115]+5*X[8227], -3*X[165]+4*X[33813], -8*X[620]+7*X[31423], -2*X[671]+3*X[38021], -4*X[1125]+3*X[14651], -5*X[1698]+6*X[15561], -3*X[1699]+2*X[6321], -3*X[3545]+2*X[50884], -7*X[3624]+6*X[38224]

X(64755) lies on these lines: {1, 2782}, {3, 9860}, {4, 21636}, {40, 99}, {57, 10089}, {98, 3576}, {114, 5587}, {115, 8227}, {147, 515}, {148, 946}, {165, 33813}, {355, 51872}, {381, 9875}, {516, 13172}, {517, 13174}, {519, 64090}, {542, 33535}, {543, 31162}, {551, 12243}, {620, 31423}, {671, 38021}, {944, 2784}, {962, 20094}, {1125, 14651}, {1385, 12188}, {1420, 10069}, {1569, 9620}, {1697, 10086}, {1698, 15561}, {1699, 6321}, {1702, 49266}, {1703, 49267}, {2023, 9592}, {2077, 12178}, {2783, 6264}, {2787, 6326}, {3029, 9549}, {3044, 9622}, {3333, 59815}, {3545, 50884}, {3586, 12185}, {3601, 10053}, {3624, 38224}, {3679, 8724}, {3751, 12177}, {4297, 9862}, {5603, 11599}, {5613, 9901}, {5617, 9900}, {5657, 51578}, {5691, 6033}, {5731, 5984}, {5881, 9864}, {5969, 64084}, {6282, 52822}, {6770, 51115}, {6773, 51114}, {7970, 7982}, {7983, 16200}, {7987, 12042}, {7988, 61576}, {7989, 61575}, {7991, 51524}, {8591, 28194}, {8726, 52821}, {9548, 34454}, {9583, 49212}, {9610, 39851}, {9611, 39822}, {9612, 13182}, {9613, 12184}, {9614, 13183}, {9621, 58058}, {9624, 11724}, {9625, 39828}, {9626, 39857}, {9955, 38732}, {11005, 12407}, {11012, 22504}, {11014, 38499}, {11177, 51705}, {11529, 24472}, {11632, 25055}, {11710, 38664}, {11720, 22265}, {11725, 61275}, {12703, 49202}, {12704, 49201}, {15177, 39803}, {15452, 61763}, {18480, 38743}, {18908, 58681}, {21166, 35242}, {22793, 38733}, {23698, 41869}, {24929, 51796}, {26446, 61561}, {28160, 38744}, {28204, 48657}, {30389, 51523}, {31732, 39808}, {31738, 39836}, {34127, 34595}, {34627, 50879}, {34648, 50882}, {35774, 35879}, {35775, 35878}, {38034, 61600}, {38229, 61268}, {38628, 58245}, {38730, 64005}, {54447, 64089}

X(64755) = midpoint of X(i) and X(j) for these {i,j}: {962, 20094}, {7970, 23235}
X(64755) = reflection of X(i) in X(j) for these {i,j}: {4, 21636}, {40, 99}, {98, 11711}, {148, 946}, {355, 51872}, {3679, 8724}, {3751, 12177}, {5691, 6033}, {5881, 9864}, {6770, 51115}, {6773, 51114}, {7982, 7970}, {9860, 3}, {9862, 4297}, {9864, 14981}, {9875, 381}, {9900, 5617}, {9901, 5613}, {11177, 51705}, {12188, 1385}, {12243, 551}, {12407, 11005}, {13174, 13188}, {13178, 114}, {22265, 11720}, {31162, 50881}, {34627, 50879}, {34648, 50882}, {38664, 11710}, {38733, 22793}, {39808, 31732}, {39836, 31738}, {64005, 38730}, {64749, 1}
X(64755) = X(1303)-of-hexyl triangle
X(64755) = X(9860)-of-ABC-X3-reflections triangle
X(64755) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2782, 64749}, {98, 11711, 3576}, {114, 13178, 5587}, {517, 13188, 13174}, {543, 50881, 31162}, {11724, 38220, 9624}

X(64756) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 111 AND X(64)-CROSSPEDAL-OF-X(3)

Barycentrics    (a^2-b^2-c^2)*(5*a^8+3*(b^2-c^2)^4-10*a^6*(b^2+c^2)-6*a^2*(b^2-c^2)^2*(b^2+c^2)+8*a^4*(b^4+c^4)) : :
X(64756) = -10*X[1656]+9*X[64177], -7*X[3090]+6*X[3167], -5*X[3522]+4*X[12118], -7*X[3523]+8*X[12359], -3*X[3543]+4*X[12293], -9*X[3545]+8*X[61607], -5*X[3567]+6*X[61666], -5*X[3617]+4*X[9928], -7*X[3622]+8*X[12259], -5*X[3623]+4*X[9933], -7*X[3832]+8*X[9927], -9*X[3839]+8*X[22660] and many others

X(64756) lies on these lines: {2, 54}, {4, 193}, {5, 63030}, {8, 9896}, {20, 11411}, {22, 12309}, {23, 9908}, {69, 6146}, {155, 1994}, {254, 5962}, {275, 18855}, {287, 28425}, {323, 15316}, {343, 18925}, {390, 12428}, {393, 43995}, {511, 20079}, {524, 64037}, {542, 34621}, {912, 64047}, {1069, 5274}, {1092, 23291}, {1181, 41614}, {1199, 8548}, {1352, 10112}, {1587, 35836}, {1588, 35837}, {1594, 63092}, {1656, 64177}, {1899, 43652}, {1992, 45089}, {2071, 12301}, {2904, 32605}, {3088, 11442}, {3090, 3167}, {3146, 12282}, {3157, 5261}, {3522, 12118}, {3523, 12359}, {3542, 41615}, {3543, 12293}, {3545, 61607}, {3546, 25738}, {3549, 9704}, {3567, 61666}, {3600, 18970}, {3617, 9928}, {3620, 7509}, {3622, 12259}, {3623, 9933}, {3832, 9927}, {3839, 22660}, {3854, 5448}, {4232, 41587}, {5056, 14852}, {5059, 17702}, {5067, 59553}, {5068, 5654}, {5446, 7408}, {5562, 8681}, {5663, 54211}, {5889, 21651}, {6152, 15741}, {6515, 7487}, {6623, 11441}, {6642, 63081}, {6776, 7400}, {6803, 11245}, {6815, 45968}, {6823, 39899}, {6995, 12134}, {7378, 36747}, {7395, 19588}, {7399, 14912}, {7401, 13292}, {7486, 9820}, {7488, 9937}, {7494, 31804}, {7503, 12166}, {7544, 63012}, {7550, 9925}, {7585, 49224}, {7586, 49225}, {7689, 50693}, {8718, 52404}, {8909, 8972}, {9537, 12417}, {9538, 9931}, {9815, 11225}, {9932, 10298}, {10071, 14986}, {10303, 47391}, {10528, 49162}, {10529, 49161}, {10608, 50572}, {10996, 18914}, {11412, 20080}, {11414, 39874}, {11433, 64035}, {11898, 12362}, {12022, 63703}, {12038, 61820}, {12241, 15069}, {12318, 37444}, {12420, 14683}, {14788, 51171}, {14826, 39571}, {15022, 41597}, {15083, 50689}, {15692, 44158}, {15750, 25712}, {18356, 44441}, {18420, 32358}, {18537, 31831}, {18569, 50708}, {18909, 61113}, {18931, 63631}, {19061, 63016}, {19062, 63015}, {19597, 54004}, {20191, 61816}, {21734, 52104}, {23158, 26876}, {31304, 37779}, {32048, 37913}, {32064, 37498}, {32974, 56267}, {34608, 64033}, {34782, 64060}, {34986, 43841}, {35603, 37784}, {37460, 41724}, {40330, 52016}, {41171, 51170}, {41619, 43598}, {41819, 63353}, {49321, 62987}, {49322, 62986}, {51394, 58378}, {59346, 64717}, {59349, 63701}

X(64756) = midpoint of X(i) and X(j) for these {i,j}: {49052, 49053}
X(64756) = reflection of X(i) in X(j) for these {i,j}: {4, 12429}, {8, 9896}, {20, 11411}, {68, 63652}, {5889, 21651}, {6193, 68}, {9936, 9927}, {12271, 5562}
X(64756) = anticomplement of X(6193)
X(64756) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55031, 2}
X(64756) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34428, 8}, {41525, 5905}, {55031, 6327}
X(64756) = pole of line {44518, 53414} with respect to the Kiepert hyperbola
X(64756) = pole of line {2451, 2623} with respect to the MacBeath circumconic
X(64756) = pole of line {52, 3167} with respect to the Stammler hyperbola
X(64756) = pole of line {2501, 63829} with respect to the Steiner circumellipse
X(64756) = pole of line {14341, 63829} with respect to the Steiner inellipse
X(64756) = pole of line {6337, 7487} with respect to the Wallace hyperbola
X(64756) = X(68)-of-Gemini-111 triangle
X(64756) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(27364)}}, {{A, B, C, X(96), X(34208)}}, {{A, B, C, X(2996), X(57875)}}, {{A, B, C, X(14248), X(41271)}}
X(64756) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 539, 6193}, {68, 6193, 2}, {68, 63649, 5449}, {539, 63652, 68}, {3167, 61544, 3090}, {5562, 8681, 12271}, {6515, 14516, 7487}, {7401, 13292, 63031}, {9815, 11225, 11431}, {11411, 44665, 20}, {12134, 64048, 6995}, {13142, 18440, 4}, {49052, 49053, 3564}

X(64757) = ORTHOLOGY CENTER OF THESE TRIANGLES: EHRMANN-VERTEX AND X(54)-CROSSPEDAL-OF-X(4)

Barycentrics    a^10-2*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^6*(b^4-5*b^2*c^2+c^4)+2*a^2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)-a^4*(b^6-2*b^4*c^2-2*b^2*c^4+c^6) : :
X(64757) = -4*X[140]+3*X[6030], -5*X[3843]+2*X[44866], -5*X[5076]+2*X[34563], -5*X[11439]+X[15086], -4*X[12102]+X[44755], -3*X[13482]+2*X[36966], 3*X[15072]+X[15084], -X[15103]+3*X[15305], -4*X[32348]+3*X[34006], -2*X[53779]+5*X[62028]

X(64757) lies on circumconic {{A, B, C, X(15321), X(15424)}} and on these lines: {3, 2916}, {4, 3521}, {5, 8718}, {20, 64180}, {30, 6288}, {49, 16659}, {52, 32273}, {140, 6030}, {265, 3627}, {381, 15805}, {382, 9927}, {546, 5643}, {549, 54036}, {567, 1595}, {568, 14216}, {1176, 7403}, {1209, 47748}, {1503, 37472}, {1657, 35240}, {1885, 58789}, {2070, 20191}, {2072, 16621}, {2777, 6145}, {3146, 18387}, {3153, 32137}, {3518, 15061}, {3519, 13391}, {3581, 7553}, {3830, 5895}, {3843, 44866}, {3853, 25739}, {5073, 18474}, {5076, 34563}, {5189, 11591}, {5663, 15800}, {5944, 35482}, {6000, 32365}, {6102, 62967}, {6240, 20127}, {6243, 11411}, {6247, 7540}, {6368, 53320}, {6759, 61711}, {7391, 18436}, {7528, 40280}, {7566, 64098}, {7728, 11381}, {8549, 34780}, {9019, 11663}, {9820, 10540}, {10627, 60466}, {11439, 15086}, {11455, 18377}, {11572, 31726}, {12006, 37349}, {12086, 12121}, {12102, 44755}, {12134, 37477}, {12173, 18385}, {12290, 44288}, {12309, 47527}, {12688, 18480}, {13152, 20115}, {13163, 43584}, {13339, 50137}, {13340, 34938}, {13371, 14643}, {13445, 45971}, {13474, 18403}, {13482, 36966}, {14118, 61299}, {14130, 44407}, {14790, 18435}, {15038, 18128}, {15072, 15084}, {15103, 15305}, {15704, 41171}, {17712, 54006}, {18350, 23335}, {18378, 20299}, {18383, 63716}, {18390, 62008}, {18427, 50009}, {18430, 31725}, {18439, 22661}, {18859, 45286}, {23236, 37495}, {25563, 37922}, {30551, 40685}, {31133, 32139}, {32348, 34006}, {33332, 52525}, {34613, 63734}, {34826, 37925}, {36752, 38072}, {36753, 46026}, {40686, 51519}, {45622, 62961}, {45959, 46450}, {50435, 62026}, {51548, 54001}, {52163, 61984}, {53779, 62028}, {58922, 62036}, {62332, 64035}

X(64757) = midpoint of X(i) and X(j) for these {i,j}: {382, 33541}
X(64757) = reflection of X(i) in X(j) for these {i,j}: {3, 18488}, {20, 64180}, {1657, 35240}, {3521, 4}, {8718, 5}, {18442, 15062}, {47748, 1209}, {52100, 64179}, {52525, 33332}, {54036, 549}
X(64757) = pole of line {5305, 18367} with respect to the Kiepert hyperbola
X(64757) = pole of line {5944, 6636} with respect to the Stammler hyperbola
X(64757) = X(8718)-of-Johnson triangle
X(64757) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 15062, 18442}, {381, 52100, 64179}, {11381, 31724, 7728}, {18488, 29012, 3}, {37495, 64036, 23236}

X(64758) = ORTHOLOGY CENTER OF THESE TRIANGLES: EHRMANN-SIDE AND X(68)-CROSSPEDAL-OF-X(4)

Barycentrics    5*a^10-4*a^8*(b^2+c^2)+22*a^4*(b^2-c^2)^2*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)-4*a^6*(4*b^4-9*b^2*c^2+4*c^4)-a^2*(b^2-c^2)^2*(5*b^4+26*b^2*c^2+5*c^4) : :
X(64758) = -6*X[154]+7*X[62100], -6*X[376]+5*X[14530], -3*X[381]+4*X[3357], -4*X[548]+3*X[5656], -3*X[568]+4*X[31978], -2*X[1498]+3*X[3534], -5*X[1656]+6*X[10606], -6*X[1853]+5*X[5076], -7*X[3526]+8*X[64027], -3*X[3830]+4*X[6247], -5*X[3843]+4*X[51491], -7*X[3851]+8*X[6696] and many others

X(64758) lies on these lines: {3, 1661}, {4, 34469}, {5, 40920}, {20, 11820}, {24, 9919}, {30, 11411}, {64, 265}, {74, 37197}, {154, 62100}, {155, 541}, {376, 14530}, {381, 3357}, {548, 5656}, {550, 6225}, {568, 31978}, {1351, 61088}, {1498, 3534}, {1503, 17800}, {1593, 18431}, {1656, 10606}, {1657, 5925}, {1853, 5076}, {1885, 18916}, {3426, 3575}, {3526, 64027}, {3532, 44673}, {3830, 6247}, {3843, 51491}, {3851, 6696}, {5054, 8567}, {5055, 5893}, {5070, 23328}, {5072, 23329}, {5073, 14216}, {5876, 36983}, {6053, 45248}, {6759, 15696}, {9655, 10060}, {9668, 10076}, {9703, 46374}, {9833, 15681}, {9899, 28160}, {10182, 61793}, {10193, 61850}, {10282, 15688}, {10299, 61606}, {10539, 60746}, {11202, 62082}, {11204, 15720}, {11206, 12103}, {11432, 32601}, {11468, 37453}, {11472, 43577}, {11487, 31829}, {11598, 38789}, {11744, 15041}, {12084, 12412}, {12174, 35481}, {12233, 35501}, {12290, 37196}, {13203, 18377}, {13754, 30443}, {14862, 62074}, {15072, 44544}, {15585, 55624}, {15684, 41362}, {15704, 34781}, {15750, 32111}, {17821, 62085}, {17837, 37483}, {18383, 62016}, {18400, 49137}, {18438, 34146}, {18859, 32321}, {18931, 44226}, {20299, 61721}, {23039, 36982}, {23324, 62004}, {23325, 61990}, {23332, 61970}, {26944, 44438}, {31725, 34944}, {32064, 62036}, {32272, 36201}, {34782, 62131}, {34785, 58795}, {34786, 62040}, {35260, 46853}, {35864, 42264}, {35865, 42263}, {37984, 58378}, {41735, 55610}, {44762, 62142}, {44763, 45004}, {46372, 50461}, {49136, 64037}, {50709, 62053}, {55643, 61610}, {58434, 61815}, {61680, 61799}, {61735, 61946}, {61747, 61811}, {61803, 64063}, {62113, 64059}, {63671, 63726}

X(64758) = midpoint of X(i) and X(j) for these {i,j}: {12250, 64726}
X(64758) = reflection of X(i) in X(j) for these {i,j}: {3, 20427}, {382, 64}, {1351, 61088}, {1657, 5925}, {5073, 14216}, {5878, 5894}, {5895, 3357}, {6225, 550}, {9919, 12244}, {12315, 20}, {13093, 12250}, {14216, 15105}, {34780, 13093}, {34781, 15704}, {36983, 5876}, {48672, 3}, {49136, 64037}, {58795, 34785}, {64033, 1657}, {64187, 5}
X(64758) = pole of line {8057, 22089} with respect to the Stammler circle
X(64758) = pole of line {11413, 32063} with respect to the Stammler hyperbola
X(64758) = X(5895)-of-anti-Ehrmann-mid triangle
X(64758) = intersection, other than A, B, C, of circumconics {{A, B, C, X(265), X(51347)}}, {{A, B, C, X(39434), X(48672)}}
X(64758) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15311, 48672}, {30, 12250, 13093}, {30, 13093, 34780}, {64, 18405, 52102}, {64, 2777, 382}, {550, 6225, 32063}, {1657, 6000, 64033}, {3357, 5895, 381}, {5878, 20427, 5894}, {5894, 15311, 5878}, {5925, 6000, 1657}, {10606, 22802, 1656}, {12250, 64726, 30}, {15311, 20427, 3}, {20299, 61721, 61984}, {54050, 64187, 5}

X(64759) = ORTHOLOGY CENTER OF THESE TRIANGLES: TRINH AND X(68)-CROSSPEDAL-OF-X(4)

Barycentrics    a^2*(a^14-3*a^12*(b^2+c^2)+a^10*(b^4+6*b^2*c^2+c^4)-a^6*(b^2-c^2)^2*(5*b^4-2*b^2*c^2+5*c^4)-(b^2-c^2)^4*(b^6+b^4*c^2+b^2*c^4+c^6)-a^4*(b^2-c^2)^2*(b^6+11*b^4*c^2+11*b^2*c^4+c^6)+a^8*(5*b^6-7*b^4*c^2-7*b^2*c^4+5*c^6)+a^2*(b^2-c^2)^2*(3*b^8+4*b^6*c^2+18*b^4*c^4+4*b^2*c^6+3*c^8)) : :
X(64759) = -7*X[7999]+3*X[54038], -2*X[46374]+3*X[47391]

X(64759) lies on circumconic {{A, B, C, X(74), X(51347)}} and on these lines: {3, 1661}, {4, 20303}, {5, 44883}, {22, 1498}, {23, 12324}, {24, 64}, {25, 6247}, {26, 6000}, {30, 9938}, {68, 1503}, {154, 10323}, {155, 2781}, {161, 12088}, {186, 12250}, {378, 5895}, {382, 9919}, {1216, 3098}, {1350, 35219}, {1593, 51491}, {1598, 63420}, {1619, 11414}, {1658, 52019}, {1660, 15644}, {1853, 10594}, {1995, 40686}, {2070, 11999}, {2071, 64726}, {2777, 12084}, {2935, 45014}, {2937, 12315}, {3089, 61088}, {3146, 63422}, {3357, 6644}, {3515, 15105}, {3520, 64187}, {3542, 34944}, {4550, 64027}, {5064, 32351}, {5198, 23324}, {5621, 63695}, {5656, 7512}, {5663, 9932}, {5893, 9818}, {5899, 34780}, {5925, 11413}, {6001, 49553}, {6225, 7488}, {6293, 11456}, {6642, 6696}, {6689, 7526}, {7393, 15578}, {7505, 32125}, {7509, 64024}, {7514, 61749}, {7516, 32600}, {7517, 14216}, {7529, 23332}, {7530, 18381}, {7723, 9934}, {7999, 54038}, {8276, 8991}, {8277, 13980}, {9590, 9899}, {9609, 32445}, {9659, 12940}, {9672, 12950}, {9833, 12083}, {10249, 63737}, {10298, 54211}, {10605, 19353}, {10606, 15062}, {10984, 41580}, {11438, 31978}, {11440, 36983}, {11746, 19360}, {11793, 63431}, {12082, 17845}, {12106, 61540}, {12779, 15177}, {13171, 37197}, {13564, 32063}, {13754, 46372}, {13861, 20299}, {14790, 32123}, {15811, 63728}, {17814, 34778}, {17821, 43813}, {18439, 44259}, {18534, 41362}, {19347, 64031}, {19457, 64588}, {21213, 26883}, {21663, 30443}, {22467, 40914}, {32140, 33563}, {32316, 32337}, {32345, 35502}, {34117, 44479}, {35450, 45735}, {36982, 63425}, {37515, 45979}, {37777, 58378}, {37925, 64034}, {38444, 45839}, {41715, 52525}, {43809, 52055}, {43866, 61735}, {44544, 61752}, {44837, 64714}, {46374, 47391}, {50435, 64037}, {63682, 63726}

X(64759) = midpoint of X(i) and X(j) for these {i,j}: {3, 9914}, {20427, 43695}
X(64759) = X(i)-Dao conjugate of X(j) for these {i, j}: {51936, 56296}
X(64759) = pole of line {8057, 40494} with respect to the circumcircle
X(64759) = pole of line {11413, 34782} with respect to the Stammler hyperbola
X(64759) = X(6247)-of-Ara triangle
X(64759) = X(9914)-of-anti-X3-ABC-reflections triangle
X(64759) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64, 10117, 24}, {1619, 11414, 34782}, {12088, 34781, 161}, {20427, 43695, 15311}, {32345, 61721, 35502}

X(64760) = ORTHOLOGY CENTER OF THESE TRIANGLES: AQUILA AND X(102)-CROSSPEDAL-OF-X(4)

Barycentrics    a*(a^8+a^6*b*c-a^7*(b+c)+a^5*(b-c)^2*(b+c)-(b-c)^4*(b+c)^2*(b^2-b*c+c^2)+a^2*(b^2-c^2)^2*(4*b^2-5*b*c+4*c^2)-a^4*(b-c)^2*(4*b^2+7*b*c+4*c^2)+a^3*(b-c)^2*(b^3+7*b^2*c+7*b*c^2+c^3)-a*(b-c)^2*(b^5+5*b^4*c+2*b^3*c^2+2*b^2*c^3+5*b*c^4+c^5)) : :
X(64760) = -2*X[109]+3*X[165], -4*X[117]+5*X[1698], -4*X[124]+3*X[1699], -3*X[3576]+4*X[38600], -7*X[3624]+8*X[6711], -3*X[3679]+2*X[50899], -5*X[3697]+4*X[58685], -3*X[5587]+2*X[10740], -3*X[5886]+4*X[61564], -X[7982]+4*X[51527], -5*X[7987]+4*X[11700], -5*X[8227]+6*X[38776] and many others

X(64760) lies on the Bevan circle, circumconic {{A, B, C, X(972), X(3466)}}, and on these lines: {1, 102}, {3, 3464}, {4, 2816}, {9, 3042}, {10, 151}, {40, 1745}, {43, 34455}, {57, 1364}, {109, 165}, {117, 1698}, {124, 1699}, {226, 52167}, {515, 63417}, {516, 33650}, {517, 3465}, {573, 18599}, {653, 24030}, {851, 62340}, {928, 39156}, {1054, 2636}, {1282, 1763}, {1361, 1697}, {1394, 54083}, {1490, 2800}, {1695, 34459}, {1706, 3040}, {1750, 2184}, {1768, 3738}, {1795, 3345}, {2270, 20226}, {2629, 9355}, {2773, 9904}, {2779, 2939}, {2785, 9860}, {2792, 13174}, {2814, 5400}, {2835, 7994}, {2841, 16389}, {2853, 12408}, {3074, 5909}, {3075, 51490}, {3339, 12016}, {3576, 38600}, {3579, 38579}, {3624, 6711}, {3679, 50899}, {3697, 58685}, {5119, 52129}, {5538, 36001}, {5587, 10740}, {5691, 13532}, {5812, 34300}, {5886, 61564}, {7982, 51527}, {7987, 11700}, {8227, 38776}, {8677, 33811}, {9532, 13221}, {9586, 58051}, {9587, 58060}, {10703, 11531}, {10709, 19875}, {10716, 50865}, {10747, 41869}, {10771, 37718}, {11010, 38501}, {11727, 25055}, {14690, 38674}, {15015, 53740}, {15252, 53804}, {16192, 38697}, {16560, 34462}, {19872, 58419}, {20277, 37441}, {21228, 47605}, {22793, 38779}, {24031, 36100}, {28146, 38780}, {30392, 47115}, {31423, 57303}, {35242, 38607}, {37551, 52830}, {38042, 61603}, {50190, 58593}, {54081, 57281}, {54447, 61578}, {56824, 63468}, {64005, 64501}

X(64760) = reflection of X(i) in X(j) for these {i,j}: {1, 102}, {151, 10}, {1364, 52824}, {5691, 13532}, {10696, 11713}, {11531, 10703}, {38579, 3579}, {38674, 14690}, {41869, 10747}, {50865, 10716}, {64761, 40}
X(64760) = X(i)-Dao conjugate of X(j) for these {i, j}: {653, 18026}
X(64760) = X(i)-Ceva conjugate of X(j) for these {i, j}: {521, 1}
X(64760) = pole of line {8677, 33811} with respect to the Bevan circle
X(64760) = pole of line {2846, 14304} with respect to the polar circle
X(64760) = pole of line {2849, 12016} with respect to the Suppa-Cucoanes circle
X(64760) = X(102)-of-Aquila triangle
X(64760) = X(136)-of-6th-mixtilinear triangle
X(64760) = X(151)-of-outer-Garcia triangle
X(64760) = X(925)-of-excentral triangle
X(64760) = barycentric product X(i)*X(j) for these (i, j): {36100, 63792}, {39053, 521}
X(64760) = barycentric quotient X(i)/X(j) for these (i, j): {39053, 18026}, {63792, 64194}
X(64760) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 2818, 64761}, {40, 55311, 1745}, {102, 10696, 11713}, {102, 2817, 1}, {2817, 11713, 10696}, {11700, 38691, 7987}, {13532, 64507, 5691}

X(64761) = ORTHOLOGY CENTER OF THESE TRIANGLES: AQUILA AND X(102)-CROSSPEDAL-OF-X(4)

Barycentrics    a*(a^6+a^5*(b+c)+3*a^2*(b^2-c^2)^2-(b^2-c^2)^2*(b^2-b*c+c^2)-a^4*(3*b^2+b*c+3*c^2)+a*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)-2*a^3*(b^3-2*b^2*c-2*b*c^2+c^3)) : :
X(64761) = -2*X[102]+3*X[165], -4*X[117]+3*X[1699], -4*X[124]+5*X[1698], -3*X[3576]+4*X[38607], -7*X[3624]+8*X[6718], -3*X[3679]+2*X[13532], -3*X[5587]+2*X[10747], -3*X[5886]+4*X[61571], -3*X[5927]+4*X[58685], -X[7982]+4*X[51534], -5*X[7987]+4*X[11713], -5*X[8227]+6*X[57303] and many others

X(64761) lies on the Bevan circle and on these lines: {1, 104}, {9, 3040}, {10, 33650}, {19, 1743}, {36, 23205}, {40, 1745}, {43, 34459}, {46, 978}, {55, 53252}, {57, 1361}, {65, 3073}, {80, 9355}, {102, 165}, {117, 1699}, {124, 1698}, {151, 516}, {202, 51977}, {203, 51976}, {219, 1761}, {221, 3468}, {484, 6127}, {517, 38579}, {651, 24028}, {928, 1282}, {1046, 1710}, {1364, 1697}, {1409, 4424}, {1478, 2792}, {1537, 43043}, {1695, 34455}, {1706, 3042}, {1742, 2807}, {1836, 34300}, {1838, 52167}, {1935, 37562}, {2635, 48363}, {2773, 2948}, {2779, 9904}, {2785, 13174}, {2816, 6361}, {2817, 2956}, {2853, 13221}, {2943, 5697}, {3074, 31788}, {3075, 12672}, {3120, 4295}, {3339, 59816}, {3464, 53256}, {3465, 6001}, {3576, 38607}, {3579, 38573}, {3624, 6718}, {3679, 13532}, {3738, 5541}, {4559, 35046}, {5526, 52084}, {5587, 10747}, {5691, 50899}, {5886, 61571}, {5927, 58685}, {6326, 23703}, {7963, 15803}, {7971, 54083}, {7982, 51534}, {7987, 11713}, {8227, 57303}, {9532, 12408}, {9586, 58060}, {9587, 58051}, {9956, 38779}, {10571, 40256}, {10696, 11531}, {10709, 50865}, {10716, 19875}, {10740, 41869}, {10777, 37718}, {11734, 25055}, {12332, 51236}, {12515, 34586}, {12702, 64057}, {12736, 64013}, {15015, 53742}, {16128, 56416}, {16192, 38691}, {16560, 45022}, {16561, 22306}, {18480, 38780}, {19872, 58426}, {24410, 38955}, {25415, 32913}, {31423, 38776}, {31730, 63417}, {33645, 37815}, {35242, 38600}, {35281, 64139}, {36074, 38345}, {37551, 52824}, {38667, 63469}, {50190, 58600}, {51281, 64150}, {51842, 64309}, {51966, 52680}, {52659, 64193}, {54447, 61585}, {64005, 64507}

X(64761) = reflection of X(i) in X(j) for these {i,j}: {1, 109}, {102, 14690}, {1361, 52830}, {1795, 13539}, {5691, 50899}, {10703, 11700}, {11531, 10696}, {33650, 10}, {38573, 3579}, {38780, 18480}, {41869, 10740}, {50865, 10709}, {63417, 31730}, {64760, 40}
X(64761) = incircle-inverse of X(46681)
X(64761) = X(i)-Dao conjugate of X(j) for these {i, j}: {34234, 18816}
X(64761) = X(i)-Ceva conjugate of X(j) for these {i, j}: {517, 1}
X(64761) = pole of line {8677, 64761} with respect to the Bevan circle
X(64761) = pole of line {53305, 53535} with respect to the circumcircle
X(64761) = pole of line {3738, 46681} with respect to the incircle
X(64761) = pole of line {1319, 3465} with respect to the Feuerbach hyperbola
X(64761) = pole of line {3738, 4458} with respect to the Suppa-Cucoanes circle
X(64761) = X(109)-of-Aquila triangle
X(64761) = X(131)-of-6th-mixtilinear triangle
X(64761) = X(1300)-of-excentral triangle
X(64761) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(59998)}}, {{A, B, C, X(1795), X(2316)}}, {{A, B, C, X(3466), X(34051)}}, {{A, B, C, X(8752), X(34184)}}
X(64761) = barycentric product X(i)*X(j) for these (i, j): {59998, 651}
X(64761) = barycentric quotient X(i)/X(j) for these (i, j): {59998, 4391}
X(64761) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 2818, 64760}, {102, 14690, 165}, {104, 53530, 1}, {109, 10703, 11700}, {651, 64189, 24028}, {2800, 11700, 10703}, {2800, 13539, 1795}, {11713, 38697, 7987}, {50899, 64501, 5691}

X(64762) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND FUHRMANN AND X(79)-CROSSPEDAL-OF-X(5)

Barycentrics    -2*a^5*b*c+3*a^3*b*(b-c)^2*c+a^6*(b+c)-(b-c)^4*(b+c)^3-a*b*c*(b^2-c^2)^2+a^4*(-3*b^3+2*b^2*c+2*b*c^2-3*c^3)+a^2*(b-c)^2*(3*b^3+2*b^2*c+2*b*c^2+3*c^3) : :
X(64762) = -3*X[2]+X[40256], -3*X[3817]+X[12616], -X[5450]+3*X[5886], -9*X[7988]+X[54156], -X[8715]+3*X[37713], -3*X[9812]+X[40265], -3*X[11230]+X[64118], -X[12114]+5*X[18493], X[22792]+3*X[51709], 3*X[31162]+5*X[63966]

X(64762) lies on circumconic {{A, B, C, X(7952), X(10266)}} and on these lines: {1, 4}, {2, 40256}, {3, 11813}, {5, 2800}, {10, 6980}, {11, 5884}, {12, 1537}, {30, 26287}, {40, 5180}, {84, 10266}, {104, 37735}, {142, 6892}, {355, 21635}, {484, 6949}, {496, 12005}, {499, 1727}, {516, 26285}, {517, 63964}, {908, 11362}, {912, 24387}, {942, 22835}, {952, 32910}, {1071, 13751}, {1125, 6914}, {1158, 3306}, {1483, 52074}, {1538, 7686}, {2771, 20288}, {2801, 10943}, {2802, 10942}, {2829, 5901}, {2886, 20117}, {3065, 16116}, {3149, 14882}, {3576, 15680}, {3582, 26877}, {3814, 37562}, {3817, 12616}, {3825, 34339}, {3871, 14217}, {3878, 6842}, {4189, 10165}, {4292, 34880}, {5057, 11012}, {5080, 11014}, {5083, 10948}, {5087, 31788}, {5141, 10175}, {5253, 48695}, {5443, 6906}, {5450, 5886}, {5690, 40260}, {5693, 11680}, {5842, 40273}, {5885, 6001}, {5887, 25639}, {5903, 6941}, {6246, 10950}, {6326, 52367}, {6684, 6863}, {6692, 6862}, {6705, 10199}, {6796, 11849}, {6920, 64268}, {6923, 30144}, {6929, 30147}, {6933, 10172}, {6968, 10573}, {7491, 51717}, {7681, 31870}, {7704, 33593}, {7741, 10265}, {7743, 12675}, {7982, 31053}, {7988, 54156}, {8226, 64274}, {8715, 37713}, {8727, 40249}, {9624, 31019}, {9812, 40265}, {10284, 18242}, {10525, 22836}, {10698, 37710}, {10738, 37733}, {10944, 25485}, {10949, 12831}, {11230, 64118}, {11826, 54192}, {12114, 18493}, {12332, 45976}, {12672, 17605}, {12736, 26476}, {12747, 21630}, {15866, 64124}, {15908, 31806}, {16128, 26321}, {16160, 33592}, {17577, 50908}, {20085, 61296}, {21077, 28234}, {22792, 51709}, {22793, 37837}, {22799, 61148}, {23708, 63399}, {24390, 63967}, {24926, 52851}, {26470, 31803}, {26475, 41562}, {28160, 33657}, {28204, 32905}, {31162, 63966}, {31418, 64335}, {31419, 64693}, {31825, 56884}, {36002, 64269}, {37701, 64188}, {37702, 59391}, {37722, 38038}, {38028, 49107}, {38570, 51883}, {54154, 62830}, {59392, 64291}

X(64762) = midpoint of X(i) and X(j) for these {i,j}: {4, 40257}, {944, 40264}, {946, 12608}, {5450, 64119}, {6796, 12699}, {10525, 22836}, {12616, 54198}, {18242, 22791}, {22793, 37837}
X(64762) = reflection of X(i) in X(j) for these {i,j}: {5690, 40260}, {63963, 9955}, {63980, 40259}, {64763, 5}
X(64762) = complement of X(40256)
X(64762) = X(5448)-of-Fuhrmann triangle
X(64762) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {11, 124, 3326}, {1387, 11733, 39546}
X(64762) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 40257, 515}, {5, 2800, 64763}, {226, 946, 13464}, {946, 5882, 30384}, {1519, 12047, 946}, {3817, 54198, 12616}, {5443, 34789, 6906}, {6001, 9955, 63963}, {7681, 39542, 31870}, {7741, 64021, 10265}, {12005, 16174, 496}, {13743, 22775, 5450}, {15908, 51409, 31806}, {38034, 63980, 40259}

X(64763) = ORTHOLOGY CENTER OF THESE TRIANGLES: FUHRMANN AND X(80)-CROSSPEDAL-OF-X(5)

Barycentrics    a^6*(b+c)+(b-c)^4*(b+c)^3-2*a^5*(b^2+b*c+c^2)-a*(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)+a^3*(b-c)^2*(4*b^2+7*b*c+4*c^2)-a^4*(b^3-4*b^2*c-4*b*c^2+c^3)-a^2*(b-c)^2*(b^3+6*b^2*c+6*b*c^2+c^3) : :
X(64763) = -3*X[2]+X[40257], -X[1490]+9*X[19875], -5*X[1698]+X[6261], -5*X[5818]+X[6256], -X[7971]+9*X[54447], 7*X[7989]+X[54156], 7*X[9588]+X[64261], -3*X[11231]+X[37837], 5*X[37714]+3*X[52027], -11*X[46933]+3*X[64148], X[48695]+3*X[59415], -5*X[61261]+X[64119]

X(64763) lies on circumconic {{A, B, C, X(10570), X(64290)}} and on these lines: {1, 6952}, {2, 40257}, {3, 10}, {4, 484}, {5, 2800}, {8, 6972}, {12, 5884}, {40, 6840}, {79, 59392}, {80, 6906}, {84, 37163}, {104, 14800}, {119, 31803}, {495, 12005}, {517, 24387}, {519, 46920}, {944, 37616}, {946, 1737}, {952, 26287}, {1158, 2475}, {1210, 2099}, {1317, 17662}, {1329, 20117}, {1385, 58404}, {1484, 10284}, {1490, 19875}, {1512, 31673}, {1537, 7173}, {1698, 6261}, {1765, 21011}, {1788, 26332}, {1837, 14882}, {2077, 5086}, {2476, 7705}, {2801, 10942}, {2802, 10943}, {2829, 18357}, {3576, 37291}, {3814, 5887}, {3820, 64693}, {3822, 34339}, {3841, 6001}, {3871, 49176}, {3878, 6882}, {4855, 5881}, {5036, 10445}, {5123, 5777}, {5253, 48694}, {5270, 16763}, {5432, 64297}, {5445, 6905}, {5499, 18242}, {5657, 6903}, {5690, 63980}, {5693, 11681}, {5704, 64322}, {5705, 64733}, {5818, 6256}, {5842, 61524}, {5882, 10039}, {6259, 12919}, {6260, 6937}, {6326, 27529}, {6361, 40265}, {6734, 6943}, {6735, 47745}, {6831, 40663}, {6833, 10573}, {6862, 30147}, {6881, 64273}, {6958, 30144}, {6971, 11813}, {6986, 64269}, {7680, 12432}, {7951, 64021}, {7971, 54447}, {7989, 54156}, {7992, 7997}, {8582, 10172}, {8728, 40249}, {9588, 64261}, {9952, 37737}, {10165, 24987}, {10197, 37615}, {10225, 18480}, {10593, 16174}, {10698, 37735}, {10785, 12647}, {10827, 63399}, {10894, 36279}, {10916, 28234}, {10944, 11715}, {10948, 15558}, {11231, 37837}, {11491, 14799}, {11849, 62354}, {12332, 13743}, {12672, 17606}, {13607, 31397}, {13747, 38133}, {15178, 32905}, {15528, 26482}, {17579, 50796}, {17665, 34122}, {17757, 63967}, {18483, 37567}, {20118, 25485}, {21620, 30274}, {21635, 40266}, {22775, 45976}, {22791, 40259}, {25639, 37562}, {26333, 54361}, {26437, 64124}, {27385, 58744}, {28096, 32486}, {31837, 54288}, {33858, 59382}, {34030, 59285}, {37256, 40264}, {37714, 52027}, {38183, 49107}, {38755, 48668}, {46933, 64148}, {48695, 59415}, {56420, 64565}, {61261, 64119}

X(64763) = midpoint of X(i) and X(j) for these {i,j}: {4, 40256}, {10, 12616}, {355, 5450}, {5690, 63980}, {6361, 40265}, {18242, 33899}, {18480, 64118}
X(64763) = reflection of X(i) in X(j) for these {i,j}: {18242, 40260}, {22791, 40259}, {32905, 15178}, {63964, 9956}, {64762, 5}
X(64763) = complement of X(40257)
X(64763) = X(5449)-of-Fuhrmann triangle
X(64763) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 18339, 40256}
X(64763) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 2800, 64762}, {10, 12616, 515}, {5818, 14647, 6256}, {5903, 6830, 946}, {6001, 9956, 63964}, {6952, 12247, 1}, {18242, 38042, 40260}, {33899, 38042, 18242}

X(64764) = ORTHOLOGY CENTER OF THESE TRIANGLES: GEMINI 109 AND X(110)-CROSSPEDAL-OF-X(6)

Barycentrics    3*a^8-a^6*(b^2+c^2)+a^4*(-4*b^4+3*b^2*c^2-4*c^4)+(b^4-c^4)^2+a^2*(b^6+b^4*c^2+b^2*c^4+c^6) : :
X(64764) = -6*X[2]+X[67], 3*X[3]+2*X[32271], 3*X[6]+2*X[5181], 4*X[10]+X[32298], X[110]+4*X[3589], 2*X[113]+3*X[5085], 4*X[140]+X[9970], -6*X[141]+X[32244], 2*X[182]+3*X[14643], 4*X[206]+X[63716], -X[265]+6*X[38317], 4*X[468]+X[10510] and many others

X(64764) lies on these lines: {2, 67}, {3, 32271}, {5, 15133}, {6, 5181}, {10, 32298}, {110, 3589}, {113, 5085}, {125, 19125}, {140, 9970}, {141, 32244}, {182, 14643}, {184, 15128}, {206, 63716}, {265, 38317}, {373, 32227}, {468, 10510}, {511, 38794}, {524, 47458}, {542, 1656}, {569, 20301}, {575, 63700}, {590, 32253}, {597, 895}, {599, 5095}, {615, 32252}, {631, 2781}, {858, 18374}, {1125, 32278}, {1177, 15131}, {1350, 38793}, {1503, 64101}, {1511, 14561}, {2777, 53094}, {2836, 5439}, {2854, 3618}, {2930, 5642}, {3090, 32274}, {3313, 41671}, {3448, 63119}, {3525, 32247}, {3526, 45016}, {3619, 25321}, {3624, 32238}, {4413, 32256}, {5050, 64103}, {5054, 48679}, {5070, 32306}, {5092, 7728}, {5094, 32239}, {5432, 32290}, {5433, 32289}, {5449, 15069}, {5480, 15035}, {5621, 7395}, {5655, 10168}, {6034, 53735}, {6699, 51941}, {6723, 56565}, {7484, 32262}, {7493, 40949}, {7808, 32242}, {7914, 32268}, {8252, 49265}, {8253, 49264}, {8262, 22151}, {8550, 43836}, {9019, 37760}, {9140, 48310}, {10192, 38885}, {10272, 11579}, {10516, 12900}, {10706, 50983}, {11064, 47455}, {11178, 32272}, {11694, 38079}, {11720, 38047}, {12121, 19130}, {12584, 25555}, {13171, 31521}, {13202, 59411}, {13248, 58437}, {13595, 52363}, {13910, 19110}, {13972, 19111}, {14653, 34422}, {14853, 33851}, {14861, 34437}, {14984, 15026}, {15029, 64196}, {15036, 48881}, {15051, 29181}, {15059, 51126}, {15061, 19140}, {15116, 19153}, {15184, 32279}, {15303, 16176}, {16003, 37514}, {16010, 16534}, {16111, 55676}, {16163, 53023}, {16510, 63648}, {16511, 34470}, {17508, 20127}, {19510, 44102}, {19924, 37958}, {20126, 52098}, {20582, 41720}, {23042, 32743}, {24953, 32288}, {24981, 25330}, {25329, 34573}, {26363, 32310}, {26364, 32309}, {28708, 41673}, {31884, 48378}, {32245, 62375}, {32246, 40132}, {32255, 63109}, {32260, 61676}, {32273, 64182}, {32299, 40670}, {32303, 32785}, {32304, 32786}, {32740, 41939}, {34155, 40107}, {36201, 64024}, {36518, 36990}, {37853, 55673}, {37911, 62376}, {38723, 48901}, {38726, 48910}, {38788, 55674}, {38790, 55682}, {38791, 55684}, {46264, 61574}, {46686, 48905}, {47457, 62381}, {47549, 62382}, {48375, 55651}, {55856, 61543}, {63344, 63379}

X(64764) = reflection of X(i) in X(j) for these {i,j}: {15059, 51126}
X(64764) = pole of line {5159, 10317} with respect to the Kiepert hyperbola
X(64764) = pole of line {10510, 37784} with respect to the Stammler hyperbola
X(64764) = X(67)-of-Gemini-109 triangle
X(64764) = intersection, other than A, B, C, of circumconics {{A, B, C, X(316), X(6698)}}, {{A, B, C, X(10511), X(40347)}}
X(64764) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11061, 6698}, {2, 6593, 67}, {5, 15462, 32233}, {67, 6593, 34319}, {141, 41595, 32244}, {141, 52699, 64104}, {182, 14643, 14982}, {3526, 45016, 49116}, {5181, 32300, 6}, {5642, 15118, 2930}, {5972, 32300, 5181}, {6593, 6698, 11061}, {10272, 38110, 11579}, {15116, 19153, 32264}, {15303, 32257, 16176}, {19140, 58445, 15061}, {32244, 52699, 41595}, {47355, 52697, 125}

X(64765) = ORTHOLOGY CENTER OF THESE TRIANGLES: 2ND CIRCUMPERP AND X(80)-CROSSPEDAL-OF-X(7)

Barycentrics    a*(a^8-3*a^7*(b+c)-3*b*(b-c)^4*c*(b+c)^2+a^6*(b^2+11*b*c+c^2)+a^5*(5*b^3-7*b^2*c-7*b*c^2+5*c^3)+a^2*(b-c)^2*(3*b^4+7*b^3*c+12*b^2*c^2+7*b*c^3+3*c^4)-a^4*(5*b^4+9*b^3*c-16*b^2*c^2+9*b*c^3+5*c^4)-a^3*(b^5-7*b^4*c+2*b^3*c^2+2*b^2*c^3-7*b*c^4+c^5)-a*(b-c)^2*(b^5-b^4*c+12*b^3*c^2+12*b^2*c^3-b*c^4+c^5)) : :
X(64765) = -2*X[11]+3*X[38037], -X[2951]+3*X[15015], -5*X[3091]+3*X[45043], -4*X[3826]+5*X[64008], X[5531]+3*X[24644], -3*X[5817]+X[12247], -2*X[6246]+3*X[59389]

X(64765) lies on these lines: {1, 651}, {3, 1633}, {4, 528}, {7, 14878}, {9, 2800}, {11, 38037}, {21, 18645}, {40, 6594}, {80, 63970}, {100, 516}, {104, 1001}, {119, 2550}, {153, 390}, {214, 5732}, {411, 63752}, {518, 10698}, {527, 50908}, {946, 3254}, {952, 60901}, {954, 13257}, {971, 6265}, {1005, 50836}, {1537, 5856}, {1768, 11407}, {1776, 3660}, {2771, 10177}, {2802, 43166}, {2826, 62306}, {2829, 43161}, {2951, 15015}, {3091, 45043}, {3243, 25485}, {3358, 9946}, {3485, 38055}, {3560, 51529}, {3826, 64008}, {4312, 10090}, {4996, 63975}, {5223, 13253}, {5531, 24644}, {5735, 48713}, {5779, 48667}, {5805, 12611}, {5817, 12247}, {5853, 12751}, {5880, 6946}, {5887, 64198}, {6224, 36991}, {6246, 59389}, {6260, 64269}, {6326, 11372}, {6825, 38763}, {6905, 28534}, {6930, 47357}, {8581, 12740}, {9809, 52653}, {10306, 51525}, {10310, 63753}, {10384, 13227}, {10392, 41558}, {10707, 10883}, {11495, 34474}, {11570, 15299}, {11715, 38316}, {11729, 38053}, {12019, 38159}, {12047, 64155}, {12515, 31658}, {12560, 12736}, {12619, 38108}, {12739, 14100}, {12758, 15298}, {12775, 42843}, {12776, 42842}, {12831, 33925}, {13279, 60895}, {15017, 38052}, {15297, 64021}, {15726, 50371}, {15863, 38154}, {16133, 33593}, {20119, 30311}, {20418, 38060}, {21153, 46684}, {22767, 60956}, {28071, 61426}, {31937, 36868}, {37541, 60782}, {38031, 38602}, {38043, 61566}, {38139, 61553}, {38693, 52769}, {42356, 59391}, {43175, 64145}, {49177, 63989}, {51090, 51506}, {64199, 64291}

X(64765) = midpoint of X(i) and X(j) for these {i,j}: {153, 390}, {5223, 13253}, {5779, 48667}, {6224, 36991}, {6326, 11372}
X(64765) = reflection of X(i) in X(j) for these {i,j}: {40, 6594}, {80, 63970}, {104, 1001}, {1156, 54370}, {2550, 119}, {3243, 25485}, {3254, 946}, {5732, 214}, {5805, 12611}, {12515, 31658}, {36996, 25558}, {63971, 10427}, {64145, 43175}
X(64765) = pole of line {5537, 62756} with respect to the Stammler hyperbola
X(64765) = X(895)-of-2nd-circumperp triangle
X(64765) = X(5181)-of-hexyl triangle
X(64765) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {153, 390, 20344}
X(64765) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2801), X(6745)}}, {{A, B, C, X(4845), X(55966)}}, {{A, B, C, X(34894), X(60047)}}
X(64765) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1001, 5851, 104}, {1156, 14151, 10394}, {1156, 8543, 53055}, {2801, 54370, 1156}, {5851, 25558, 36996}

X(64766) = ORTHOLOGY CENTER OF THESE TRIANGLES: 5TH MIXTILINEAR AND X(79)-CROSSPEDAL-OF-X(8)

Barycentrics    3*a^4-5*a^3*(b+c)+5*a*(b-c)^2*(b+c)+a^2*(-2*b^2+7*b*c-2*c^2)-(b^2-c^2)^2 : :
X(64766) = -3*X[2]+2*X[15862], -5*X[4668]+6*X[61032]

X(64766) lies on these lines: {1, 140}, {2, 15862}, {8, 17057}, {10, 38410}, {36, 13607}, {46, 7966}, {65, 7972}, {79, 952}, {80, 946}, {100, 3244}, {145, 3881}, {390, 5697}, {484, 37734}, {517, 4330}, {519, 5178}, {523, 14812}, {758, 12535}, {944, 3474}, {1000, 56035}, {1317, 3337}, {1482, 11238}, {1483, 3336}, {2093, 7990}, {2099, 9654}, {2136, 3338}, {2346, 13606}, {2802, 47319}, {2886, 3632}, {3243, 3633}, {3245, 12512}, {3340, 7702}, {3582, 33179}, {3746, 28234}, {3871, 14804}, {4668, 61032}, {4857, 11278}, {5298, 61281}, {5442, 10246}, {5443, 9956}, {5557, 56091}, {5691, 7971}, {5734, 45035}, {7741, 63257}, {7967, 37524}, {8275, 63255}, {8422, 18409}, {10222, 16173}, {10483, 64697}, {10573, 10589}, {10950, 11280}, {11010, 37728}, {11041, 18398}, {11224, 37721}, {11246, 61295}, {11531, 11827}, {12047, 64270}, {12245, 37571}, {13869, 50148}, {15180, 56095}, {15909, 56152}, {16118, 28224}, {16126, 38455}, {16139, 37563}, {16200, 37720}, {18221, 50190}, {20050, 33110}, {21398, 64265}, {24470, 62617}, {30424, 45287}, {34612, 34747}, {34772, 64056}, {37618, 64282}, {37692, 64294}, {37705, 61703}, {37711, 64754}, {37731, 50194}, {43731, 61261}, {63210, 64163}

X(64766) = midpoint of X(i) and X(j) for these {i,j}: {3633, 11524}
X(64766) = reflection of X(i) in X(j) for these {i,j}: {3632, 64200}, {5559, 1}, {64199, 3244}, {64291, 1389}
X(64766) = anticomplement of X(15862)
X(64766) = pole of line {5443, 9957} with respect to the Feuerbach hyperbola
X(64766) = X(5559)-of-5th-mixtilinear triangle
X(64766) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 41687, 5445}, {1, 5844, 5559}, {10573, 10595, 15079}, {10595, 15079, 37735}, {11011, 41684, 5443}

X(64767) = ORTHOLOGY CENTER OF THESE TRIANGLES: EULER AND X(84)-CROSSPEDAL-OF-X(8)

Barycentrics    3*a^3*(b+c)-(b^2-c^2)^2+a^2*(b^2-14*b*c+c^2)+a*(-3*b^3+7*b^2*c+7*b*c^2-3*c^3) : :
X(64767) = -3*X[381]+X[64768], -X[2136]+3*X[5603], -7*X[3090]+5*X[64204], -3*X[3158]+5*X[10595], -X[3189]+3*X[16200], -X[3529]+3*X[34716], -6*X[3829]+5*X[31399], -2*X[5690]+3*X[24386], -5*X[5734]+X[12632], -4*X[5901]+3*X[59584], -X[7991]+3*X[34625], -3*X[11235]+X[64744]

X(64767) lies on these lines: {1, 6904}, {3, 64205}, {4, 519}, {5, 12640}, {8, 9614}, {10, 11}, {142, 31792}, {145, 9613}, {381, 64768}, {474, 551}, {515, 10912}, {516, 12650}, {517, 6245}, {528, 5882}, {758, 9949}, {946, 3880}, {952, 22792}, {962, 12629}, {1125, 1706}, {1210, 14923}, {1320, 57287}, {1376, 64703}, {1479, 64203}, {1482, 5805}, {1697, 6857}, {1953, 3950}, {2098, 63146}, {2099, 3244}, {2136, 5603}, {2476, 3885}, {2551, 11525}, {3090, 64204}, {3158, 10595}, {3189, 16200}, {3241, 37435}, {3529, 34716}, {3555, 17634}, {3621, 51423}, {3625, 4863}, {3635, 5542}, {3663, 50637}, {3679, 6919}, {3754, 21625}, {3813, 6922}, {3817, 7704}, {3829, 31399}, {3872, 6872}, {3878, 45120}, {3893, 21075}, {3895, 13411}, {3913, 6918}, {3947, 26482}, {4208, 7320}, {4292, 36846}, {4297, 22837}, {4304, 4861}, {4311, 37256}, {4669, 17556}, {4847, 5697}, {4853, 12572}, {5082, 7962}, {5129, 9623}, {5154, 6735}, {5493, 8666}, {5690, 24386}, {5734, 12632}, {5836, 9843}, {5844, 64272}, {5854, 6246}, {5901, 59584}, {6700, 63137}, {6736, 30384}, {6737, 30323}, {6765, 12541}, {6766, 28228}, {6841, 23340}, {6921, 44675}, {6926, 43174}, {6940, 34486}, {6964, 45701}, {7288, 63138}, {7991, 34625}, {8728, 9957}, {9819, 19843}, {10222, 12437}, {11112, 34699}, {11235, 64744}, {11260, 31730}, {11373, 63990}, {11522, 34619}, {11530, 17559}, {12245, 24392}, {12513, 28194}, {12635, 12858}, {12641, 59391}, {15955, 63969}, {16125, 44669}, {17460, 23675}, {17648, 63989}, {18483, 32049}, {18525, 47746}, {19860, 51724}, {19925, 49169}, {21077, 64754}, {22835, 63644}, {24297, 34918}, {24389, 31806}, {28236, 54227}, {30147, 30331}, {31673, 38455}, {32537, 50796}, {37001, 51118}, {37403, 50808}, {41702, 45287}, {45776, 63970}, {49627, 64721}, {56799, 62297}

X(64767) = midpoint of X(i) and X(j) for these {i,j}: {4, 3680}, {962, 12629}, {6765, 12541}, {7982, 64068}, {18525, 47746}
X(64767) = reflection of X(i) in X(j) for these {i,j}: {3, 64205}, {10, 49600}, {946, 13463}, {2136, 59722}, {3913, 13464}, {4297, 22837}, {5493, 8666}, {5882, 33895}, {11362, 3813}, {12437, 10222}, {12640, 5}, {31730, 11260}, {32049, 18483}, {49169, 19925}, {64117, 1}
X(64767) = complement of X(64202)
X(64767) = pole of line {329, 16610} with respect to the dual conic of Yff parabola
X(64767) = X(3680)-of-Euler triangle
X(64767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3680, 519}, {528, 33895, 5882}, {2136, 5603, 59722}, {3880, 13463, 946}, {3913, 34640, 13464}, {4853, 30305, 12572}, {5836, 63993, 9843}, {10914, 12053, 10}, {44675, 63130, 59675}

X(64768) = ORTHOLOGY CENTER OF THESE TRIANGLES: JOHNSON AND X(84)-CROSSPEDAL-OF-X(8)

Barycentrics    a^4+14*a^2*b*c-3*a^3*(b+c)-(b^2-c^2)^2+a*(3*b^3-7*b^2*c-7*b*c^2+3*c^3) : :
X(64768) = -4*X[140]+5*X[64204], -3*X[381]+2*X[64767], -4*X[548]+3*X[34716], -2*X[1483]+3*X[3158], -5*X[1656]+4*X[64205], -3*X[3656]+4*X[12607], -3*X[5790]+2*X[21627], -3*X[5886]+2*X[10912], -3*X[10247]+4*X[59722], -2*X[11278]+3*X[25568], -X[11519]+3*X[63143], -X[12541]+3*X[59388] and many others

X(64768) lies on these lines: {1, 47742}, {3, 519}, {5, 3680}, {8, 392}, {12, 64203}, {30, 64202}, {46, 13996}, {84, 952}, {140, 64204}, {145, 5440}, {355, 3880}, {377, 10914}, {381, 64767}, {404, 15179}, {452, 31145}, {517, 6259}, {548, 34716}, {1071, 12245}, {1145, 36846}, {1259, 37739}, {1317, 1420}, {1467, 64736}, {1482, 7682}, {1483, 3158}, {1656, 64205}, {1697, 3632}, {2802, 10742}, {3241, 17567}, {3244, 63990}, {3621, 17576}, {3625, 5795}, {3652, 44669}, {3656, 12607}, {3679, 17527}, {3811, 5854}, {3868, 64743}, {3872, 7483}, {3885, 5046}, {3893, 12647}, {4266, 17299}, {4677, 4866}, {4853, 5791}, {5126, 20050}, {5690, 12629}, {5779, 5853}, {5790, 21627}, {5844, 6765}, {5881, 34697}, {5886, 10912}, {6735, 11373}, {6849, 12856}, {6893, 64068}, {6944, 10222}, {7320, 17559}, {7982, 37725}, {7991, 34630}, {9623, 50205}, {10072, 37829}, {10247, 59722}, {10572, 36972}, {10573, 44784}, {11278, 25568}, {11376, 41702}, {11519, 63143}, {11525, 31419}, {12448, 58631}, {12541, 59388}, {12737, 55297}, {13600, 56089}, {14923, 57282}, {16126, 27197}, {17564, 51093}, {17566, 38460}, {18391, 20789}, {18481, 38455}, {18526, 64117}, {21290, 64563}, {24392, 61510}, {24927, 56176}, {25405, 59591}, {25416, 56387}, {26446, 32426}, {28234, 64326}, {33895, 45701}, {34717, 61248}, {37582, 63133}, {37624, 59584}, {37738, 48696}, {38067, 42842}, {49600, 61261}, {56091, 59416}, {56177, 61284}, {59719, 61277}

X(64768) = reflection of X(i) in X(j) for these {i,j}: {3, 12640}, {355, 49169}, {3680, 5}, {10912, 10915}, {12448, 58631}, {12629, 5690}, {12699, 32049}, {18526, 64117}, {37727, 3913}, {47746, 1}
X(64768) = X(3680)-of-Johnson triangle
X(64768) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 1000, 5044}, {519, 12640, 3}, {519, 3913, 37727}, {2802, 32049, 12699}, {3633, 64056, 41687}, {3880, 49169, 355}, {10912, 10915, 5886}, {33895, 45701, 61276}

X(64769) = X(399)X(1495)∩X(1990)X(3580)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - a^8*c^2 + 3*a^6*b^2*c^2 - 4*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - b^8*c^2 + 4*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 4*a^4*c^6 - 11*a^2*b^2*c^6 - 4*b^4*c^6 + 7*a^2*c^8 + 7*b^2*c^8 - 3*c^10)*(a^10 - a^8*b^2 - 4*a^4*b^6 + 7*a^2*b^8 - 3*b^10 - 3*a^8*c^2 + 3*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - 11*a^2*b^6*c^2 + 7*b^8*c^2 + 2*a^6*c^4 - 4*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 4*b^6*c^4 + 2*a^4*c^6 + 3*a^2*b^2*c^6 - 3*a^2*c^8 - b^2*c^8 + c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6653.

X(64769) lies on these lines: {6, 62606}, {323, 51545}, {399, 1495}, {1990, 3580}, {19457, 50464}, {34801, 35373}, {37638, 56399}

X(64769) = isotomic conjugate of the polar conjugate of X(35372)
X(64769) = X(i)-cross conjugate of X(j) for these (i,j): {21649, 69}, {50433, 3}
X(64769) = X(i)-isoconjugate of X(j) for these (i,j): {19, 12383}, {92, 52169}, {2173, 10421}, {24019, 38401}, {35201, 40389}
X(64769) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 12383}, {22391, 52169}, {35071, 38401}, {36896, 10421}
X(64769) = cevapoint of X(i) and X(j) for these (i,j): {6, 17835}, {520, 47414}
X(64769) = trilinear pole of line {9409, 14314}
X(64769) = barycentric product X(i)*X(j) for these {i,j}: {69, 35372}, {35373, 62338}
X(64769) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 12383}, {74, 10421}, {184, 52169}, {520, 38401}, {11079, 40389}, {35372, 4}, {35373, 1300}, {40390, 14165}

X(64770) = POINT FURUD 1

Barycentrics    cos 5A : cos 5B : cos 5C
Barycentrics    a^5*(a^2 - b^2 - c^2)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 7*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 + 6*a^4*c^4 - 2*a^2*b^2*c^4 + b^4*c^4 - 4*a^2*c^6 - b^2*c^6 + c^8) : :

X(64770) lies on these lines: {563, 63760}

X(64771) = POINT FURUD 2

Barycentrics    sin 5A : sin 5B : sin 5C
Barycentrics    a^5*(a^4 - 2*a^2*b^2 + b^4 + a^2*b*c - b^3*c - 2*a^2*c^2 + b^2*c^2 - b*c^3 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*b*c + b^3*c - 2*a^2*c^2 + b^2*c^2 + b*c^3 + c^4) : :

X(64771) lies on these lines: {560, 2964}

X(64771) = X(847)-isoconjugate of X(5964)
X(64771) = barycentric product X(63)*X(59279)
X(64771) = barycentric quotient X(i)/X(j) for these {i,j}: {563, 5964}, {5963, 57716}, {59279, 92}

X(64772) = POINT FURUD 3

Barycentrics    sin(3B-3C) : sin(3C-3A) : sin(3A-3B)
Barycentrics    b^3*(b - c)*c^3*(b + c)*(-(a^2*b^2) + b^4 - a^2*b*c - a^2*c^2 - 2*b^2*c^2 + c^4)*(-(a^2*b^2) + b^4 + a^2*b*c - a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(64772) lies on these lines: {1577, 14213}

X(64772) = barycentric product X(i)*X(j) for these {i,j}: {850, 9219}, {9220, 20948}
X(64772) = barycentric quotient X(i)/X(j) for these {i,j}: {9219, 110}, {9220, 163}

X(64773) = POINT FURUD 4

Barycentrics    sin(4B-4C) : sin(4C-4A) : sin(4A-4B)
Barycentrics    b^4*(b - c)*c^4*(b + c)*(-(a^2*b^2) + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4*b^4 - 2*a^2*b^6 + b^8 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(64773) lies on these lines: {6334, 14618}, {18314, 45793}

X(64773) = X(14586)-isoconjugate of X(57717)
X(64773) = X(338)-Dao conjugate of X(63766)
X(64773) = barycentric product X(i)*X(j) for these {i,j}: {1879, 15415}, {18314, 63763}
X(64773) = barycentric quotient X(i)/X(j) for these {i,j}: {564, 36134}, {1879, 14586}, {2618, 57717}, {5449, 15958}, {18314, 63766}, {63763, 18315}

X(64774) = X(74)X(16186)∩X(107)X(14220)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(a^8 + a^6*b^2 - 4*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 - 2*a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - b^2*c^6)*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 - 4*a^4*c^4 + 2*a^2*b^2*c^4 + 3*b^4*c^4 + a^2*c^6 - 3*b^2*c^6 + c^8) : :

See Peter Moses, euclid 6671.

X(64774) lies on the circumcircle and these lines: {74, 16186}, {107, 14220}, {108, 36117}, {112, 32712}, {399, 32418}, {476, 9033}, {477, 2777}, {526, 1304}, {1141, 46090}, {1294, 20127}, {1300, 10152}, {1302, 30528}, {2436, 23969}, {2693, 5663}, {9060, 44769}, {9161, 40352}, {13530, 57472}, {14385, 16169}, {14919, 53188}, {15396, 15468}, {16166, 36831}, {16170, 53233}, {32640, 32732}, {32650, 59091}, {32715, 53944}, {36034, 59828}, {51262, 53872}, {53235, 53881}, {53757, 53957}

X(64774) = isogonal conjugate of X(55141)
X(64774) = isotomic conjugate of the polar conjugate of X(32712)
X(64774) = Thomson isogonal conjugate of X(64510)
X(64774) = Collings transform of X(15468)
X(64774) = X(i)-cross conjugate of X(j) for these (i,j): {526, 15396}, {46585, 250}, {46616, 10419}
X(64774) = X(i)-isoconjugate of X(j) for these (i,j): {1, 55141}, {162, 13212}, {656, 11251}, {1109, 42742}, {5663, 36035}, {9033, 36063}
X(64774) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 55141}, {125, 13212}, {40596, 11251}
X(64774) = cevapoint of X(i) and X(j) for these (i,j): {526, 15468}, {14220, 39985}
X(64774) = trilinear pole of line {6, 32640}
X(64774) = barycentric product X(i)*X(j) for these {i,j}: {63, 36117}, {69, 32712}, {74, 30528}, {477, 44769}, {2411, 15395}, {16077, 32663}, {34210, 39290}, {36034, 36102}
. X(64774) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 55141}, {112, 11251}, {477, 41079}, {647, 13212}, {2420, 1553}, {2433, 6070}, {2436, 3258}, {15395, 2410}, {23357, 42742}, {30528, 3260}, {32640, 5663}, {32650, 14254}, {32663, 9033}, {32712, 4}, {32715, 47228}, {34210, 5664}, {36117, 92}, {36131, 36063}, {36151, 36035}, {44769, 35520}

X(64775) = X(67)X(98)∩X(74)X(3455)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 - b^4*c^2 + 2*a^2*c^4 + 2*b^2*c^4 - 2*c^6)*(a^6 - a^4*b^2 + 2*a^2*b^4 - 2*b^6 - a^4*c^2 + 2*b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :

See Peter Moses, euclid 6671.

X(64775) lies on the circumcircle and these lines: {67, 98}, {74, 3455}, {107, 14223}, {110, 35911}, {111, 10766}, {112, 35909}, {476, 2799}, {477, 2794}, {526, 2715}, {542, 2697}, {690, 935}, {691, 9517}, {842, 2781}, {1300, 11605}, {2367, 57452}, {2373, 36884}, {2421, 58979}, {2710, 5663}, {5649, 11636}, {9060, 51263}, {10097, 39413}, {14357, 53605}, {15342, 59098}, {20404, 53232}, {23350, 23969}, {44061, 53735}, {46157, 53945}, {58980, 61207}

X(64775) = isogonal conjugate of X(55142)
X(64775) = X(34291)-cross conjugate of X(10415)
X(64775) = X(i)-isoconjugate of X(j) for these (i,j): {1, 55142}, {897, 32313}, {1640, 16568}, {2247, 9979}, {6041, 20944}
X(64775) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 55142}, {6593, 32313}, {15900, 18312}
X(64775) = trilinear pole of line {6, 47415}
X(64775) = barycentric product X(i)*X(j) for these {i,j}: {67, 5649}, {842, 17708}, {3455, 6035}
X(64775) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 55142}, {67, 18312}, {187, 32313}, {842, 9979}, {935, 60502}, {3455, 1640}, {5649, 316}, {6035, 40074}, {23969, 52449}, {35909, 62563}, {52199, 33752}

X(64776) = X(74)X(61444)∩X(111)X(8681)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^2 + b^2 - 5*c^2)*(a^2 - 5*b^2 + c^2)*(a^4 - 4*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2)*(a^4 + a^2*b^2 - 4*a^2*c^2 + b^2*c^2 + c^4) : :

See Peter Moses, euclid 6671.

X(64776) lies on the circumcircle and these lines: {74, 61444}, {111, 8681}, {352, 53974}, {524, 2374}, {691, 2434}, {1296, 20186}, {1300, 38951}, {1499, 20187}, {6093, 34161}, {9084, 41909}, {14659, 21448}, {15406, 30247}, {40119, 55977}

X(64776) = isogonal conjugate of X(55140)
X(64776) = Thomson isogonal conjugate of X(64508)
X(64776) = X(524)-cross conjugate of X(15406)
X(64776) = X(i)-isoconjugate of X(j) for these (i,j): {1, 55140}, {2408, 17466}, {3291, 14207}, {9134, 36277}
X(64776) = X(3)-Dao conjugate of X(55140)
X(64776) = cevapoint of X(i) and X(j) for these (i,j): {3292, 8644}, {55977, 58754}
X(64776) = trilinear pole of line {6, 47412}
X(64776) = barycentric product X(i)*X(j) for these {i,j}: {1296, 41909}, {2418, 15387}, {2434, 44182}
X(64776) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 55140}, {1296, 47286}, {2434, 126}, {15387, 2408}, {21448, 9134}, {32648, 14263}, {57467, 55271}

X(64777) = X(74)X(34442)∩X(104)X(10693)

Barycentrics    a^2*(a - b)*(a - c)*(a^4 - 2*a^2*b^2 + b^4 + a^2*b*c + a*b^2*c - a*b*c^2 - c^4)*(a^4 - b^4 + a^2*b*c - a*b^2*c - 2*a^2*c^2 + a*b*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^5*c + 2*a^4*b*c - a^3*b^2*c - a^2*b^3*c + 2*a*b^4*c - b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 - 2*b^4*c^2 + 2*a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 + a^2*c^4 + b^2*c^4 - a*c^5 - b*c^5)*(a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 + 2*a^4*b*c - a^2*b^3*c - b^5*c - a^4*c^2 - a^3*b*c^2 + 2*a^2*b^2*c^2 - a*b^3*c^2 + b^4*c^2 - a^2*b*c^3 + 2*b^3*c^3 - a^2*c^4 + 2*a*b*c^4 - 2*b^2*c^4 - b*c^5 + c^6) : :

See Peter Moses, euclid 6671.

X(64777) lies on the circumcircle and these lines: {74, 34442}, {104, 10693}, {107, 14224}, {476, 2804}, {477, 2829}, {526, 2720}, {1290, 2850}, {1300, 39990}, {2687, 2778}, {2694, 2771}, {2745, 5663}, {2766, 8674}, {26700, 42768}

X(64777) = isogonal conjugate of X(55146)
X(64777) = X(i)-isoconjugate of X(j) for these (i,j): {1, 55146}, {2771, 21180}
X(64777) = X(3)-Dao conjugate of X(55146)
X(64777) = barycentric quotient X(6)/X(55146)

X(64778) = X(74)X(18876)∩X(111)X(46340)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(a^6 - a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 + c^6)*(a^10 - a^6*b^4 - a^4*b^6 + b^10 - 2*a^8*c^2 + 2*a^6*b^2*c^2 + 2*a^2*b^6*c^2 - 2*b^8*c^2 - a^4*b^2*c^4 - a^2*b^4*c^4 + 2*a^4*c^6 + 2*b^4*c^6 - a^2*c^8 - b^2*c^8)*(a^10 - 2*a^8*b^2 + 2*a^4*b^6 - a^2*b^8 + 2*a^6*b^2*c^2 - a^4*b^4*c^2 - b^8*c^2 - a^6*c^4 - a^2*b^4*c^4 + 2*b^6*c^4 - a^4*c^6 + 2*a^2*b^2*c^6 - 2*b^2*c^8 + c^10) : :

See Peter Moses, euclid 6671.

X(64778) lies on the circumcircle and these lines: {74, 18876}, {111, 46340}, {476, 55129}, {477, 64509}, {526, 46967}, {1177, 1297}, {1289, 60591}, {1300, 47110}, {2697, 36201}, {9517, 10423}, {13494, 56980}, {30247, 53760}, {58980, 61198}

X(64778) = barycentric quotient X(10423)/X(50188)

X(64779) = X(74)X(54086)∩X(110)X(57991)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(a^4*b^4 - a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 + 2*a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + b^4*c^4 + a^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 - a^4*b^2*c^2 - a^2*b^4*c^2 + a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 - a^2*c^6 - b^2*c^6) : :

See Peter Moses, euclid 6671.

X(64779) lies on the circumcircle and these lines: {74, 54086}, {98, 16069}, {110, 57991}, {111, 46806}, {112, 46040}, {290, 43654}, {804, 22456}, {805, 17932}, {842, 46142}, {878, 18858}, {2710, 5152}, {2715, 57562}, {2782, 48259}, {3563, 46039}, {40870, 59023}, {51229, 53700}

X(64779) = isogonal conjugate of X(55143)
X(64779) = X(1)-isoconjugate of X(55143)
X(64779) = X(3)-Dao conjugate of X(55143)
X(64779) = cevapoint of X(46039) and X(46040)
X(64779) = trilinear pole of line {6, 2966}
X(64779) = barycentric product X(i)*X(j) for these {i,j}: {2698, 43187}, {2966, 46142}, {16069, 39291}, {46039, 55266}, {46040, 57991}
X(64779) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 55143}, {2421, 6072}, {2422, 6071}, {2698, 3569}, {2966, 2782}, {41173, 48452}, {46039, 55267}, {46040, 868}, {46142, 2799}, {51229, 41167}

X(64780) = ISOGONAL CONJUGATE OF X(32726)

Barycentrics    2*Sec[A] - Sec[B] - Sec[C] : :
Barycentrics    a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 + a^4*c + a^2*b^2*c - 2*b^4*c - a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 + 2*b^2*c^3 + a*c^4 - 2*b*c^4 : :

X(64780) lies on these lines: {2, 92}, {30, 511}, {190, 40863}, {219, 45738}, {222, 20223}, {241, 4858}, {322, 3694}, {355, 24316}, {381, 39529}, {448, 648}, {664, 1944}, {671, 53191}, {857, 3007}, {1108, 17861}, {1121, 1952}, {1323, 44356}, {1375, 8756}, {1385, 24315}, {1494, 57862}, {1826, 41007}, {1943, 54107}, {2193, 56014}, {2223, 57031}, {3175, 22014}, {3262, 25083}, {3663, 42459}, {3668, 16608}, {3913, 15951}, {3928, 24310}, {3946, 59649}, {4081, 45281}, {4361, 60974}, {4363, 64053}, {4552, 30807}, {4659, 4853}, {4670, 30147}, {5777, 42456}, {5839, 60950}, {6354, 45206}, {7359, 26006}, {8609, 16732}, {9909, 20875}, {9956, 24317}, {9957, 24424}, {13624, 24684}, {14213, 18607}, {16578, 34852}, {17043, 40942}, {17079, 23603}, {17151, 60990}, {17262, 60973}, {17314, 61010}, {17318, 64054}, {17348, 60994}, {17950, 39351}, {18161, 64126}, {18480, 24682}, {18481, 24683}, {18593, 26011}, {18668, 48380}, {21084, 40659}, {21139, 52896}, {21933, 53596}, {22464, 26932}, {23583, 44336}, {23710, 33305}, {24400, 58330}, {24929, 56552}, {28610, 50106}, {32041, 53228}, {34744, 50083}, {36855, 44442}, {36949, 43035}, {40530, 59588}, {41804, 48381}, {41883, 64708}, {42044, 64143}, {52889, 62736}, {55076, 56718}, {55956, 59268}, {55998, 60965}, {58402, 59611}, {58457, 59646}

X(64780) = isogonal conjugate of X(32726)
X(64780) = polar conjugate of X(62742)
X(64780) = polar conjugate of the isogonal conjugate of X(62736)
X(64780) = trilinear pole of line {30691, 30692}
X(64780) = crossdifference of every pair of points on line {6, 1946}
X(64780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {92, 1214, 6708}, {92, 6360, 1214}, {190, 40863, 52978}, {281, 347, 17073}, {322, 25252, 3694}, {448, 648, 52949}, {664, 1944, 6510}, {1948, 44354, 44360}

X(64781) = ISOGONAL CONJUGATE OF X(26717)

Barycentrics    2*Tan[A]^2 - Tan[B]^2 - Tan[C]^2 : :
Barycentrics    2*Sec[A]^2 - Sec[B]^2 - Sec[C]^2 : :
Barycentrics    2*Csc[2*A] - Csc[2*B] - Csc[2*C] : :
Barycentrics    a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 + 2*a^4*b^2*c^2 - a^2*b^4*c^2 - 2*b^6*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 + 4*b^4*c^4 + a^2*c^6 - 2*b^2*c^6 : :

X(64781) lies on these lines: {2, 216}, {26, 7780}, {30, 511}, {53, 41005}, {99, 40888}, {141, 42459}, {187, 44375}, {297, 15526}, {316, 44363}, {338, 3003}, {340, 39352}, {376, 42329}, {381, 30258}, {389, 41481}, {401, 648}, {441, 1990}, {450, 34147}, {458, 5158}, {547, 10003}, {551, 57289}, {577, 9308}, {620, 44389}, {625, 44388}, {800, 41760}, {852, 52066}, {1316, 44102}, {1494, 1972}, {1495, 37926}, {1513, 62237}, {1632, 42671}, {1948, 35072}, {2450, 8754}, {2452, 21639}, {2453, 18374}, {3163, 40884}, {3199, 41009}, {3260, 14570}, {3292, 41202}, {3589, 59649}, {5032, 47740}, {5066, 42862}, {5112, 64724}, {5201, 60522}, {5446, 46977}, {5447, 6662}, {5462, 15912}, {5943, 42453}, {6638, 59660}, {6688, 59531}, {7387, 7751}, {7758, 34938}, {7759, 14790}, {7764, 23335}, {7781, 12085}, {7816, 19221}, {7843, 18569}, {8667, 9909}, {8716, 34808}, {9512, 52144}, {9766, 34609}, {9813, 35930}, {9822, 59566}, {10154, 13468}, {10282, 48581}, {11676, 38294}, {11793, 51888}, {13409, 42400}, {14023, 31305}, {14363, 38281}, {14581, 15013}, {15118, 16333}, {15694, 40329}, {16303, 62375}, {18026, 44354}, {18281, 50648}, {18324, 46893}, {18860, 48539}, {19568, 44442}, {19596, 37921}, {21356, 36889}, {22052, 46724}, {22151, 51372}, {24315, 48894}, {26870, 43999}, {32445, 59556}, {32456, 40879}, {32815, 53021}, {34003, 42556}, {34093, 44084}, {34351, 34506}, {34508, 46702}, {34509, 46703}, {34579, 34897}, {34622, 46776}, {34726, 63950}, {35073, 48316}, {36412, 45198}, {37067, 62196}, {38283, 59529}, {38297, 59527}, {39358, 44651}, {39568, 63933}, {39906, 40673}, {40074, 51373}, {40477, 44346}, {40484, 44334}, {41678, 60516}, {42368, 46394}, {44131, 63634}, {44135, 59197}, {44360, 52982}, {44560, 47233}, {44892, 47204}, {44894, 52604}, {45873, 58470}, {46788, 46808}, {47143, 60774}, {47322, 62376}, {51389, 62382}, {57529, 62261}, {58311, 58356}, {60524, 62338}

X(64781) = isogonal conjugate of X(26717)
X(64781) = isotomic conjugate of X(54973)
X(64781) = polar conjugate of X(57732)
X(64781) = isotomic conjugate of the isogonal conjugate of X(3331)
X(64781) = polar conjugate of the isogonal conjugate of X(852)
X(64781) = crossdifference of every pair of points on line {6, 39201}
X(64781) = barycentric product X(52491)*X(59572)
X(64781) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3164, 47383}, {2, 47383, 216}, {216, 264, 14767}, {216, 14767, 58454}, {264, 3164, 216}, {264, 47383, 2}, {324, 43988, 46832}, {393, 6527, 6389}, {401, 648, 3284}, {441, 1990, 23583}, {1494, 40885, 45312}, {2052, 46717, 6509}, {3164, 40896, 264}, {3260, 14570, 36212}, {9308, 20477, 577}, {15526, 52945, 297}, {18667, 31623, 18592}, {30258, 39530, 44924}, {39352, 40853, 340}, {45198, 56022, 36412}, {46106, 62308, 44436}, {46724, 56290, 22052}

X(64782) = ISOGONAL CONJUGATE OF X(59056)

Barycentrics    2*Sec[2*A] - Sec[2*B] - Sec[2*C] : :
Barycentrics    a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - 2*a^4*c^4 + a^2*b^2*c^4 + 4*b^4*c^4 + a^2*c^6 - 2*b^2*c^6 : :

X(64782) lies on these lines: {2, 311}, {30, 511}, {99, 44375}, {115, 44388}, {148, 44363}, {187, 44376}, {338, 36212}, {381, 41169}, {566, 59197}, {571, 56017}, {625, 53495}, {648, 44328}, {1879, 39113}, {3003, 14570}, {3613, 27364}, {5064, 9766}, {5485, 60130}, {6390, 44389}, {6823, 63923}, {7525, 7780}, {7526, 7781}, {8266, 8667}, {8716, 54994}, {8754, 45921}, {9967, 39910}, {11414, 63933}, {16310, 46184}, {18122, 32457}, {19161, 48716}, {23583, 44339}, {34990, 53474}, {37778, 41676}, {40888, 48540}, {41677, 44138}, {47113, 48974}, {51389, 62376}, {53416, 60524}, {59546, 63679}

X(64782) = isogonal conjugate of X(59056)
X(64782) = isotomic conjugate of the isogonal conjugate of X(45938)
X(64782) = crossdifference of every pair of points on line {6, 34952}
X(64782) = barycentric quotient X(44052)/X(28861)
X(64782) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {148, 44363, 53507}, {648, 44328, 52952}, {14570, 51481, 3003}

X(64783) = ISOGONAL CONJUGATE OF X(51222)

Barycentrics    2*Cot[2*A] - Cot[2*B] - Cot[2*C] : :
Barycentrics    2*a^8 - 4*a^6*b^2 + a^4*b^4 + 2*a^2*b^6 - b^8 - 4*a^6*c^2 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 2*b^6*c^2 + a^4*c^4 - 2*a^2*b^2*c^4 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8 : :

X(64783) lies on these lines: {2, 95}, {6, 10220}, {26, 7764}, {30, 511}, {99, 44363}, {115, 44375}, {216, 27377}, {297, 3284}, {316, 40888}, {340, 401}, {376, 26870}, {381, 42350}, {441, 40484}, {620, 44388}, {625, 44389}, {648, 40853}, {1316, 64724}, {1494, 44651}, {1634, 60522}, {1879, 63833}, {1991, 26875}, {3163, 36426}, {3629, 42459}, {4558, 60524}, {5112, 44102}, {6389, 32001}, {6748, 14767}, {7387, 7759}, {7751, 14790}, {7758, 31305}, {7780, 23335}, {8667, 34609}, {9380, 41679}, {9766, 9909}, {9813, 37242}, {11197, 35884}, {11416, 36163}, {12085, 63935}, {12242, 15780}, {14023, 34938}, {14461, 34147}, {18281, 34506}, {18569, 63924}, {18870, 51360}, {22052, 45198}, {22151, 51389}, {23200, 47200}, {31388, 35717}, {32002, 36412}, {32455, 59649}, {34505, 34725}, {34508, 46703}, {34509, 46702}, {34827, 46184}, {39568, 63932}, {40331, 61885}, {40477, 44216}, {40884, 45312}, {41202, 41586}, {47282, 51431}, {51372, 62382}, {53021, 64018}, {59531, 61677}, {60700, 62701}

X(64783) = isogonal conjugate of X(51222)
X(64783) = crossdifference of every pair of points on line {6, 15451}
X(64783) = X(10220)-line conjugate of X(6)
X(64783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {95, 233, 6709}, {95, 17035, 233}, {97, 34836, 58417}, {297, 3284, 23583}, {340, 401, 15526}, {648, 40853, 52945}, {6748, 41008, 14767}, {17035, 40897, 95}, {32002, 56290, 36412}, {44375, 53507, 115}

X(64784) = X(1)X(7335)∩X(3)X(318)

Barycentrics    a (a^2 b-b^3+a^2 c-2 a b c+b^2 c+b c^2-c^3) (a^6-a^5 b-a^4 b^2+2 a^3 b^3-a^2 b^4-a b^5+b^6+2 a^4 b c-2 a^3 b^2 c-2 a^2 b^3 c+2 a b^4 c-2 a^4 c^2+4 a^2 b^2 c^2-2 b^4 c^2-2 a^2 b c^3-2 a b^2 c^3+a^2 c^4+a b c^4+b^2 c^4) (a^6-2 a^4 b^2+a^2 b^4-a^5 c+2 a^4 b c-2 a^2 b^3 c+a b^4 c-a^4 c^2-2 a^3 b c^2+4 a^2 b^2 c^2-2 a b^3 c^2+b^4 c^2+2 a^3 c^3-2 a^2 b c^3-a^2 c^4+2 a b c^4-2 b^2 c^4-a c^5+c^6) : :

See Ivan Pavlov, Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6709.

X(64784) lies on these lines: {1, 7335}, {3,318}, {522, 23224}

X(64785) = X(10)X(1943)∩X(2321)X(7283)

Barycentrics    (a^5-a^3 b^2-a^2 b^3+b^5+2 a^4 c+a^3 b c-2 a^2 b^2 c+a b^3 c+2 b^4 c+a^3 c^2+b^3 c^2-a^2 c^3-3 a b c^3-b^2 c^3-2 a c^4-2 b c^4-c^5) (a^5+2 a^4 b+a^3 b^2-a^2 b^3-2 a b^4-b^5+a^3 b c-3 a b^3 c-2 b^4 c-a^3 c^2-2 a^2 b c^2-b^3 c^2-a^2 c^3+a b c^3+b^2 c^3+2 b c^4+c^5) : :

See Ivan Pavlov, Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6709.

X(64785) lies on these lines: {10, 1943}, {1947, 41013}, {2321, 7283}, {6757, 20320}, {15168, 20836}, {15628, 56974}

X(64786) = X(40)X(2784)∩X(515)X(9840)

Barycentrics    -2 a^7-5 a^6 b-3 a^5 b^2+3 a^4 b^3+4 a^3 b^4+a^2 b^5+a b^6+b^7-5 a^6 c-8 a^5 b c+2 a^4 b^2 c+6 a^3 b^3 c+a^2 b^4 c+2 a b^5 c+2 b^6 c-3 a^5 c^2+2 a^4 b c^2+4 a^3 b^2 c^2+2 a^2 b^3 c^2-a b^4 c^2+3 a^4 c^3+6 a^3 b c^3+2 a^2 b^2 c^3-4 a b^3 c^3-3 b^4 c^3+4 a^3 c^4+a^2 b c^4-a b^2 c^4-3 b^3 c^4+a^2 c^5+2 a b c^5+a c^6+2 b c^6+c^7 : :

See Ivan Pavlov, Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6709.

X(64786) lies on these lines: {3, 35099}, {10, 38856}, {40, 2784}, {515, 9840}, {516, 4065}, {2772, 5562}, {4221, 4297}, {13442, 58389}, {21628, 21669}, {28845, 37528}, {29040, 37425}, {29093, 48919}, {48941, 49564}

X(64787) = ORTHOPOINT OF X(64780)

Barycentrics    3*(Sec[B] - Sec[C])*Sin[A]^2 + (2*Sec[A] - Sec[B] - Sec[C])*(Sin[B]^2 - Sin[C]^2) : :

X(64787) lies on these lines: {3, 4885}, {4, 650}, {5, 31287}, {20, 693}, {30, 511}, {376, 45320}, {377, 24562}, {381, 44567}, {443, 25925}, {452, 25009}, {497, 30235}, {631, 31250}, {946, 23806}, {962, 47729}, {2475, 26641}, {3091, 31209}, {3146, 17494}, {3522, 26985}, {3529, 48125}, {3543, 31150}, {3832, 27115}, {4297, 48295}, {4301, 48285}, {4411, 30271}, {5059, 26824}, {5466, 54555}, {5706, 22383}, {6284, 11934}, {6847, 28834}, {6850, 28984}, {6872, 26546}, {6904, 26695}, {6938, 40166}, {7681, 15283}, {8641, 11496}, {15280, 63980}, {15683, 47869}, {15971, 28374}, {17578, 26777}, {21789, 39536}, {25902, 50408}, {25981, 26117}, {27417, 50700}, {34628, 50760}, {47664, 49135}, {47724, 64005}, {48284, 51118}

X(64787) = Thomson-isogonal conjugate of X(32726)
X(64787) = orthopoint of X(64780)
X(64787) = crossdifference of every pair of points on line {6, 62736}
X(64787) = barycentric product X(i)*X(j) for these {i,j}: {1034, 1847}, {1260, 1847}, {1265, 1847}, {48174, 51768}
X(64787) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 1847}, {845, 1847}, {1035, 1847}, {1119, 1847}, {1847, 1847}, {2057, 1847}, {2091, 1847}
X(64787) = {X(4885),X(8142)}-harmonic conjugate of X(3)

X(64788) = ORTHOPOINT OF X(64781)

Barycentrics    (Sin[B]^2 - Sin[C]^2)*(2*Tan[A]^2 - Tan[B]^2 - Tan[C]^2) + 3*Sin[A]^2*(Tan[B]^2 - Tan[C]^2) : :

X(64788) lies on these lines: {3, 30476}, {4, 647}, {20, 850}, {30, 511}, {186, 47255}, {376, 31174}, {381, 44560}, {382, 41300}, {403, 47251}, {468, 46991}, {578, 58310}, {631, 31277}, {2549, 7652}, {3146, 31296}, {3522, 31072}, {3543, 36900}, {5466, 60122}, {6587, 39533}, {7487, 28729}, {7687, 22264}, {9125, 37855}, {10295, 47004}, {10297, 46984}, {11799, 47442}, {14618, 42658}, {15683, 63786}, {16229, 39201}, {18312, 49669}, {34291, 53017}, {37242, 62688}, {37934, 47252}, {37952, 47264}, {37984, 47249}, {41038, 57122}, {41039, 57123}, {42660, 52737}, {43674, 54774}, {44280, 47259}, {44918, 63830}, {46985, 47248}, {46989, 47031}, {46990, 47308}, {46997, 47175}, {47001, 47310}, {47002, 47309}, {47254, 56369}, {47258, 62288}, {53275, 64711}

X(64788) = Thomson-isogonal conjugate of X(26717)
X(64788) = orthopoint of X(64781)
X(64788) = crossdifference of every pair of points on line {6, 852}
X(64788) = barycentric product X(i)*X(j) for these {i,j}: {1034, 1847}, {1260, 1847}, {1265, 1847}
X(64788) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 1847}, {845, 1847}, {1035, 1847}, {1119, 1847}, {1847, 1847}, {2057, 1847}, {2091, 1847}, {48340, 10073}
X(64788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16229, 39201, 52585}, {46991, 47003, 468}

X(64789) = ORTHOPOINT OF X(64782)

Barycentrics    3*(Sec[2*B] - Sec[2*C])*Sin[A]^2 + (2*Sec[2*A] - Sec[2*B] - Sec[2*C])*(Sin[B]^2 - Sin[C]^2) : :

X(64789) lies on these lines: {4, 6753}, {5, 8651}, {30, 511}, {5926, 30476}, {11615, 16040}, {16229, 58756}, {18313, 49671}, {43674, 54913}

X(64789) = Thomson-isogonal conjugate of X(59056)
X(64789) = orthopoint of X(64782)
X(64789) = barycentric product X(i)*X(j) for these {i,j}: {1034, 1847}, {1260, 1847}, {1265, 1847}
X(64789) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 1847}, {845, 1847}, {1035, 1847}, {1119, 1847}, {1709, 63871}, {1847, 1847}, {2057, 1847}, {2091, 1847}

X(64790) = ORTHOPOINT OF X(64783)

Barycentrics    3*(Cot[2*B] - Cot[2*C])*Sin[A]^2 + (2*Cot[2*A] - Cot[2*B] - Cot[2*C])*(Sin[B]^2 - Sin[C]^2) : :

X(64790) lies on these lines: {4, 12077}, {20, 41298}, {30, 511}, {381, 44568}, {1181, 2623}, {3543, 44554}, {5466, 60121}, {15451, 42731}

X(64790) = Thomson-isogonal conjugate of X(51222)
X(64790) = orthopoint of X(64783)
X(64790) = barycentric product X(i)*X(j) for these {i,j}: {1034, 1847}, {1260, 1847}, {1265, 1847}
X(64790) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 1847}, {845, 1847}, {1035, 1847}, {1119, 1847}, {1847, 1847}, {2057, 1847}, {2091, 1847}

X(64791) =  EULER LINE INTERCEPT OF X(515)X(51403)

Barycentrics    2 a^9 b+a^8 b^2-5 a^7 b^3-2 a^6 b^4+3 a^5 b^5+a^3 b^7+2 a^2 b^8-a b^9-b^10+2 a^9 c-2 a^8 b c-a^7 b^2 c+a^6 b^3 c-3 a^5 b^4 c+3 a^4 b^5 c+a^3 b^6 c-a^2 b^7 c+a b^8 c-b^9 c+a^8 c^2-a^7 b c^2+2 a^6 b^2 c^2+4 a^5 b^3 c^2-5 a^3 b^5 c^2-6 a^2 b^6 c^2+2 a b^7 c^2+3 b^8 c^2-5 a^7 c^3+a^6 b c^3+4 a^5 b^2 c^3-6 a^4 b^3 c^3+3 a^3 b^4 c^3+a^2 b^5 c^3-2 a b^6 c^3+4 b^7 c^3-2 a^6 c^4-3 a^5 b c^4+3 a^3 b^3 c^4+8 a^2 b^4 c^4-2 b^6 c^4+3 a^5 c^5+3 a^4 b c^5-5 a^3 b^2 c^5+a^2 b^3 c^5-6 b^5 c^5+a^3 b c^6-6 a^2 b^2 c^6-2 a b^3 c^6-2 b^4 c^6+a^3 c^7-a^2 b c^7+2 a b^2 c^7+4 b^3 c^7+2 a^2 c^8+a b c^8+3 b^2 c^8-a c^9-b c^9-c^10 : :
X(64791) = 2*X(403)-X(36195)

As a point on the Euler line, X(64791) has Shinagawa coefficients (3 r^2+8 r R+4 R^2-s^2,-r^2+8 r R+24 R^2-5 s^2).

See Tran Quang Hung and Ercole Suppa, euclid 6715.

X(64791) lies on these lines: {2, 3}, {515, 51403}

X(64791) = complement of the circumperp conjugate of X(37115)
X(64791) = reflection of X(186) in X(523)X(59998)
X(64791) = X(523)-vertex conjugate of-X(20838)
X(64791) = inverse in circumcircle of X(20838)
X(64791) = inverse in polar circle of X(412)
X(64791) = pole of the line X(523)X(20838) with respect to circumcircle
X(64791) = pole of the line X(412)X(523) with respect to polar circle

X(64792) =  X(1)X(399)∩X(3)X(142)

Barycentrics    a (a^6-a^5 (b+c)-a (b-c)^2 (b+c)^3+a^4 (-2 b^2+b c-2 c^2)-2 b c (b^2-c^2)^2+2 a^3 (b^3+b^2 c+b c^2+c^3)+a^2 (b^4+b^3 c-2 b^2 c^2+b c^3+c^4)) : :
X(64792) = 3*X(381)-2*X(18406), 2*X(5251)-3*X(7489), 3*X(10246)-2*X(18444)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6713.

X(64792) lies on these lines: {1, 399}, {2, 35000}, {3, 142}, {4, 37621}, {5, 100}, {21, 22791}, {30, 1621}, {31, 45923}, {35, 9955}, {36, 51709}, {55, 381}, {56, 11552}, {104, 10283}, {355, 25439}, {382, 10267}, {390, 34745}, {392, 35459}, {404, 61272}, {405, 12702}, {411, 40273}, {495, 10742}, {517, 3683}, {546, 11491}, {549, 5284}, {567, 692}, {595, 48903}, {601, 9345}, {943, 10386}, {952, 6912}, {956, 1482}, {958, 8148}, {993, 3656}, {999, 11551}, {1006, 28174}, {1012, 10246}, {1056, 34698},{1159, 57278}, {1260, 3419}, {1376, 5055}, {1532, 59382}, {1537, 5901}, {1617, 18541}, {1656, 4413}, {1699, 32613}, {1836, 41345}, {2070, 20988}, {2077, 11230}, {2346, 60901}, {2975, 3650}, {3059, 60885}, {3073, 4649}, {3090, 61156}, {3091, 32141}, {3243, 7330}, {3295, 5252}, {3303, 18526}, {3526, 10310}, {3579, 5259}, {3652, 3874}, {3746, 18480}, {3753, 35460}, {3830, 4428}, {3843, 11500}, {3851, 11499}, {3868, 13465}, {3871, 12690}, {3877, 35457}, {4294, 44229}, {4309, 18517}, {4421, 19709}, {4423, 5054}, {4512, 37584}, {5010, 38021}, {5047, 61524}, {5070, 61158}, {5072, 61154}, {5079, 61152}, {5172, 18393}, {5180, 5603}, {5223, 64369}, {5258, 11278}, {5396, 64013}, {5450, 61276}, {5537, 11231}, {5587, 12331}, {5690, 6920}, {5719, 8543}, {5883, 12515}, {6147, 16133}, {6199, 13887}, {6284, 37230}, {6395, 13940}, {6667, 55297}, {6763, 22936}, {6767, 18519}, {6841, 15171}, {6862, 10531}, {6887, 40333}, {6900, 20066}, {6905, 38034}, {6909, 38028}, {6946, 33814}, {6949, 61520}, {6974, 10596}, {6980, 26333}, {6985, 10129}, {7171, 38316}, {7411, 28178}, {7545, 20989}, {7688, 28198}, {7741, 14882}, {8167, 15694}, {8227, 26285}, {8273, 15696}, {8666, 28646}, {8715, 61261}, {9342, 15699}, {9624, 32612}, {9654, 11508}, {9655, 11510}, {9669, 11507}, {9670, 45630}, {9708, 34718}, {9856, 24299}, {10056, 18516}, {10058, 15950},{10247,22758}, {10284, 12653}, {10389, 18540}, {10540, 20986}, {10595, 32153}, {10902, 22793}, {11014, 26200}, {11108, 25011}, {11522, 26286}, {11729, 51636}, {12114, 37624}, {12611, 37701},{12645, 37622}, {12705, 37615}, {12743, 37710}, {12775, 57298}, {13369, 63266}, {13665, 44591}, {13785, 44590}, {14100, 40263}, {15931, 28146}, {16117, 41869}, {16160, 63269}, {16173, 35451}, {16408, 35251}, {16468, 37509}, {16617, 24390}, {17571, 35252}, {17577, 22938}, {17605, 32760}, {18445, 61398}, {18506, 62875}, {18510, 19000},{18512, 18999}, {18861, 38044}, {21669, 34773}, {22798, 63288}, {22937, 24468}, {25440, 61268}, {25466, 47032}, {26877, 58561}, {28160, 34486}, {28202, 41853}, {28443, 31162}, {28461, 54391}, {30308, 51817}, {31660, 46028}, {31937, 37080}, {33108, 34629}, {34474, 61270}, {35772, 42262}, {35773, 42265}, {37290, 63257}, {37533, 42012}, {38138, 38665}, {38669, 61283}, {38693, 61273}, {39877, 53091}, {41227, 44225}, {44846, 61840}, {51525, 61262}, {51529, 61280}, {58230, 63991}

X(64792) = crosssum of X(116) and X(63826)
X(64792) = pole of the line X(8674)X(21185) with respect to incircle
X(64792) = pole of the line X(35327)X(53283) with respect to Kiepert parabola

X(64793) =  X(517)X(3584)∩X(4717)X(6735)

Barycentrics    (a^4 b-2 a^2 b^3+b^5+2 a^4 c-4 a^3 b c-2 a^2 b^2 c+4 a b^3 c-2 a^3 c^2+3 a^2 b c^2-2 a b^2 c^2-2 b^3 c^2-2 a^2 c^3-4 a b c^3+2 a c^4+b c^4) (2 a^4 b-2 a^3 b^2-2 a^2 b^3+2 a b^4+a^4 c-4 a^3 b c+3 a^2 b^2 c-4 a b^3 c+b^4 c-2 a^2 b c^2-2 a b^2 c^2-2 a^2 c^3+4 a b c^3-2 b^2 c^3+c^5) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6713.

X(64793) lies on these lines: {517, 3584}, {4717, 6735}

X(64793) = intersection, other than A, B, C, of circumconics {A, B, C, X(1), X(318)} and {A, B, C, X(8), X(3584)}

X(64794) =  X(1)X(5)∩X(655)X(5903)

Barycentrics    (a^2-a b+b^2-c^2) (a^2-b^2-a c+c^2) (a^6-2 a^5 b-2 a^4 b^2+4 a^3 b^3+a^2 b^4-2 a b^5-2 a^5 c+4 a^4 b c-3 a^3 b^2 c-3 a^2 b^3 c+5 a b^4 c-b^5 c-2 a^4 c^2-3 a^3 b c^2+5 a^2 b^2 c^2-3 a b^3 c^2+4 a^3 c^3-3 a^2 b c^3-3 a b^2 c^3+2 b^3 c^3+a^2 c^4+5 a b c^4-2 a c^5-b c^5) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6713.

X(64794) lies on these lines: {1, 5}, {655, 5903}, {3585, 58739}, {4867, 51975}, {5902, 40437}, {14628, 63210}, {18393, 63750}

X(64795) =  (name pending)

Barycentrics    a^2*(a^7-b^7+2*a^5*b*c-b^6*c+b*c^6+c^7+a^6*(b+2*c)-a^4*c*(b^2+b*c+3*c^2)+a^3*c*(b^3+b^2*c-4*b*c^2-3*c^3)+a^2*b*c*(2*b^3+2*b^2*c+b*c^2-c^3)-a*(b+c)^2*(b^4-b^3*c-b^2*c^2+2*b*c^3-2*c^4))*(a^7+b^7+2*a^5*b*c+b^6*c-b*c^6-c^7+a^6*(2*b+c)-a^4*b*(3*b^2+b*c+c^2)+a^3*b*(-3*b^3-4*b^2*c+b*c^2+c^3)+a^2*b*c*(-b^3+b^2*c+2*b*c^2+2*c^3)+a*(b+c)^2*(2*b^4-2*b^3*c+b^2*c^2+b*c^3-c^4)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6713.

X(64795) lies on this line: {199, 4296}

X(64795) = intersection, other than A, B, C, of circumconics {A, B, C, X(21), X(199)} and {A, B, C, X(56), X(17798)}

X(64796) =  X(4)X(8143)∩X(546)X(2783)

Barycentrics    a^6 b+a^5 b^2+2 a^4 b^3+2 a^3 b^4-3 a^2 b^5-3 a b^6+a^6 c+4 a^5 b c+5 a^4 b^2 c+2 a^3 b^3 c-4 a^2 b^4 c-6 a b^5 c-2 b^6 c+a^5 c^2+5 a^4 b c^2+2 a^3 b^2 c^2+7 a^2 b^3 c^2+3 a b^4 c^2-2 b^5 c^2+2 a^4 c^3+2 a^3 b c^3+7 a^2 b^2 c^3+12 a b^3 c^3+4 b^4 c^3+2 a^3 c^4-4 a^2 b c^4+3 a b^2 c^4+4 b^3 c^4-3 a^2 c^5-6 a b c^5-2 b^2 c^5-3 a c^6-2 b c^6 : :
X(64796) = 3*X(1699)+X(5492), X(10036)+3*X(59390)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6713.

X(64796) lies on these lines: {4, 8143}, {30, 58392}, {517, 48887}, {546, 2783}, {946, 1484}, {1699, 5492}, {3652, 64400}, {9959, 22793}, {10036, 59390}, {10478, 31828}, {19922, 22938}, {32167, 58383}

X(64797) =  X(10)X(98)∩X(516)X(3743)

Barycentrics    2 a^7+3 a^6 b+a^5 b^2-3 a^4 b^3-4 a^3 b^4+a^2 b^5+a b^6-b^7+3 a^6 c+4 a^5 b c-4 a^4 b^2 c-6 a^3 b^3 c+a^2 b^4 c+2 a b^5 c+a^5 c^2-4 a^4 b c^2-4 a^3 b^2 c^2-6 a^2 b^3 c^2-a b^4 c^2+2 b^5 c^2-3 a^4 c^3-6 a^3 b c^3-6 a^2 b^2 c^3-4 a b^3 c^3-b^4 c^3-4 a^3 c^4+a^2 b c^4-a b^2 c^4-b^3 c^4+a^2 c^5+2 a b c^5+2 b^2 c^5+a c^6-c^7 : :
X(64797) = 3*X(1962)+X(48890), 3*X(10180)-X(13442), 3*X(11203)+X(46483)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6713.

X(64797) lies on these lines: {1, 37443}, {2, 35099}, {3, 59723}, {10, 98}, {30, 58381}, {511, 49564}, {515, 48894}, {516, 3743}, {1125, 37360}, {1330, 8245}, {1503, 58386}, {1962, 48890}, {2772, 5907}, {2792, 9959}, {3178, 4220}, {4297, 4653}, {4658, 54160}, {8235, 56949}, {8258, 37527}, {9840, 38456}, {10180, 13442}, {11203, 46483}, {15973, 29040}, {17748, 19544}, {29181, 58385}, {35016, 37447}, {39605, 43460}

X(64798) = CENTER OF 5th MIYAMOTO-MOSES-APOLLONIUS CIRCLE

Barycentrics    a*(a + b + c - (3*a + b + c)*Sin[A/2] + (a - b + c)*Sin[B/2] + (a + b - c)*Sin[C/2]) : :

Let ABC be a triangle, and I its incenter. Let A'B'C' be the circumcevian triangle of I. Let (Oa), (Ob), (Oc) be the circles with diameters IA', IB', IC', respectively. Then, there exists a circle (Oi) simultaneously tangent to the circumcircle, (Oa), (Ob) and (Oc). (Keita Miyamoto, Peter Moses, August 13, 2024)

Here, the circle (Oi) is named the 5th Miyamoto-Moses-Apollonius circle.

X(64798) lies on this line: {1, 164}

X(64798) = midpoint of X(1) and X(18291)

X(64799) = TOUCHPOINT OF CIRCUMCIRCLE AND 5th MIYAMOTO-MOSES-APOLLONIUS CIRCLE

Barycentrics    a*((5*a - b - c)*(a + b - c)*(a - b + c) - 2*a*(a^2 - b^2 + 6*b*c - c^2)*Sin[A/2] - 2*a*(a + b - 3*c)*(a - b + c)*Sin[B/2] - 2*a*(a + b - c)*(a - 3*b + c)*Sin[C/2]) : :

X(64799) lies on the circumcircle and these lines: {1, 3659}, {56, 12809}, {100, 7588}, {8077, 13385}, {8091, 10496}

X(64799) = midpoint of X(1) and X(20114)
X(64799) = crosssum of X(1) and X(60027)

X(64800) =  X(6)X(64)∩X(6587)X(8673)

Barycentrics    a^2 (a^18 b^2-5 a^16 b^4+8 a^14 b^6-14 a^10 b^10+14 a^8 b^12-8 a^4 b^16+5 a^2 b^18-b^20+a^18 c^2+12 a^16 b^2 c^2-14 a^14 b^4 c^2-54 a^12 b^6 c^2+84 a^10 b^8 c^2+10 a^8 b^10 c^2-66 a^6 b^12 c^2+30 a^4 b^14 c^2-5 a^2 b^16 c^2+2 b^18 c^2-5 a^16 c^4-14 a^14 b^2 c^4+116 a^12 b^4 c^4-70 a^10 b^6 c^4-134 a^8 b^8 c^4+102 a^6 b^10 c^4+20 a^4 b^12 c^4-18 a^2 b^14 c^4+3 b^16 c^4+8 a^14 c^6-54 a^12 b^2 c^6-70 a^10 b^4 c^6+220 a^8 b^6 c^6-36 a^6 b^8 c^6-94 a^4 b^10 c^6+34 a^2 b^12 c^6-8 b^14 c^6+84 a^10 b^2 c^8-134 a^8 b^4 c^8-36 a^6 b^6 c^8+104 a^4 b^8 c^8-16 a^2 b^10 c^8-2 b^12 c^8-14 a^10 c^10+10 a^8 b^2 c^10+102 a^6 b^4 c^10-94 a^4 b^6 c^10-16 a^2 b^8 c^10+12 b^10 c^10+14 a^8 c^12-66 a^6 b^2 c^12+20 a^4 b^4 c^12+34 a^2 b^6 c^12-2 b^8 c^12+30 a^4 b^2 c^14-18 a^2 b^4 c^14-8 b^6 c^14-8 a^4 c^16-5 a^2 b^2 c^16+3 b^4 c^16+5 a^2 c^18+2 b^2 c^18-c^20) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6726.

X(64800) lies on these lines: {6, 64}, {6587, 8673}

X(64800) = pole of the line X(25)X(13526) with respect to Jerabek hyperbola

X(64801) =  X(2)X(11643)∩X(184)X(8588)

Barycentrics    a^2 (2 a^4-5 a^2 b^2+2 b^4-2 c^4) (2 a^4-2 b^4-5 a^2 c^2+2 c^4) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64801) lies on these lines: {2, 11643}, {3, 15533}, {25, 15820}, {98, 35473}, {184, 8588}, {187, 37808}, {574, 14908}, {3425, 35472}, {5206, 10547}, {14002, 45103}, {15515, 40319}, {37457, 52153}

X(64801) = isogonal conjugate of the anticomplement of X(8589)
X(64801) = X(206)-Dao conjugate of-X(14002)
X(64801) = X(75)-isoconjugate of-X(14002)
X(64801) = X(32)-reciprocal conjugate of-X(14002)
X(64801) = X(i)-vertex conjugate of-X(j) for these {i, j}: {4, 54482}, {45103, 45103}, {54487, 54901}, {54805, 54903}
X(64801) = barycentric quotient X(32)/X(14002)
X(64801) = trilinear quotient X(31)/X(14002)
X(64801) = intersection, other than A, B, C, of circumconics {A, B, C, X(2), X(187)} and {A, B, C, X(3), X(25)}
X(64801) = trilinear pole of the line: {3049, 62412}

X(64802) =  X(13)X(44498)∩X(14)X(44497)

Barycentrics    4 a^6-7 a^4 b^2+5 a^2 b^4-2 b^6-7 a^4 c^2+2 b^4 c^2+5 a^2 c^4+2 b^2 c^4-2 c^6 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64802) lies on the cubic K936 and these lines: {13, 44498}, {14, 44497}, {76, 54805}, {114, 22329}, {115, 44496}, {125, 40112}, {147, 44367}, {184, 47596}, {230, 41672}, {287, 44575} and many others

X(64802) = isogonal conjugate of X(43656)
X(64802) = isotomic conjugate of the antitomic conjugate of X(2)
X(64802) = antigonal conjugate of the circumnormal-isogonal conjugate of X(33638)
X(64802) = circumnormal-isogonal conjugate of X(33638)
X(64802) = circumtangential-isogonal conjugate of X(43656)

X(64803) =  X(1212)X(25091)∩X(1898)X(3059)

Barycentrics    (a^4 b-2 a^3 b^2+2 a b^4-b^5-2 a^4 c-2 a^3 b c+2 a b^3 c+2 b^4 c+2 a^3 c^2+2 a^2 b c^2+2 a^2 c^3-2 a b c^3-2 b^2 c^3-2 a c^4+b c^4) (2 a^4 b-2 a^3 b^2-2 a^2 b^3+2 a b^4-a^4 c+2 a^3 b c-2 a^2 b^2 c+2 a b^3 c-b^4 c+2 a^3 c^2+2 b^3 c^2-2 a b c^3-2 a c^4-2 b c^4+c^5) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64803) lies on these lines: {1212, 25091}, {1898, 3059}, {3929, 35935}

X(64803) = intersection, other than A, B, C, of circumconics {A, B, C, X(4), X(1121)} and {A, B, C, X(9), X(85)}
X(64803) = trilinear pole of the line: {6608, 47800}

X(64804) =  X(3)X(9)∩X(5)X(515)

Barycentrics    a (2 a^6-3 a^5 b-3 a^4 b^2+6 a^3 b^3-3 a b^5+b^6-3 a^5 c-2 a^2 b^3 c+3 a b^4 c+2 b^5 c-3 a^4 c^2+4 a^2 b^2 c^2-b^4 c^2+6 a^3 c^3-2 a^2 b c^3-4 b^3 c^3+3 a b c^4-b^2 c^4-3 a c^5+2 b c^5+c^6) : :
X(64804) = 3*X(2)+X(64144), 3*X(3)-X(84), 5*X(3)-X(12684), 2*X(3)-X(34862), X(3)-3*X(52026), 5*X(3)-3*X(52027), X(4)+3*X(54051),X(20)+3*X(5658), X(84)+3*X(1490),5*X(84)-3*X(12684), 2*X(84)-3*X(34862), X(84)-6*X(40262), X(84)-9*X(52026), 5*X(84)-9*X(52027), 2*X(140)-X(6245), X(355)-3*X(64148), 3*X(376)+X(6223), 3*X(381)-5*X(63966), 3*X(381)-X(64261), 3*X(549)-2*X(6705), 5*X(631)-X(9799), X(1389)-3*X(64285), X(1389)+3*X(64298), 5*X(1490)+X(12684), 2*X(1490)+X(34862), X(1490)+2*X(40262), X(1490)+3*X(52026), 5*X(1490)+3*X(52027), 5*X(3522)-X(12246), 7*X(3528)-3*X(54052), 2*X(3530)-X(61556), 3*X(3534)+X(48664), 3*X(3579)-2*X(40256), 3*X(5658)-X(6259), 2*X(6260)-X(22792), 3*X(6796)-X(40256), 3*X(11230)-2*X(63980), 2*X(12684)-5*X(34862), X(12684)-10*X(40262), X(12684)-3*X(52027), 2*X(18242)-X(18480), X(34862)-4*X(40262), X(34862)-6*X(52026), 5*X(34862)-6*X(52027), 3*X(38140)-4*X(63964), 2*X(40262)-3*X(52026), 10*X(40262)-3*X(52027), 5*X(52026)-X(52027), X(52684)-3*X(64156), 5*X(63966)-X(64261)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64804) lies on these lines: {1, 5806}, {2, 5787}, {3, 9}, {4, 4313}, {5, 515}, {20, 5440}, {21, 5927}, {30, 6260}, {35, 12688}, {36, 12680}, {40, 3940}, {41, 44424}, {55, 9856}, {56, 64157}, {65, 44425}, {72, 411}, {78, 7580}, {140, 6245}, {153, 33598}, {210, 59320}, {214, 38757}, {226, 20420}, {227, 45272}, {355, 6825}, {376, 6223}, {378, 12136}, {381, 24299}, {382, 33596}, {404, 10167}, {405, 10157}, {474, 10884}, {516, 5763}, {517, 3811}, {549, 6705}, {581, 37594}, {631, 9799}, {912, 9942}, {916, 970}, {942, 3149}, {944, 5722}, {946, 5719}, {958, 9947}, {990, 4255}, {1071, 6905}, {1155, 15071}, {1158, 31663}, {1319, 9581}, {1376, 12520}, {1389, 17097}, {1420, 30283}, {1479, 1538}, {1656, 13151}, {1699, 9670}, {1709, 5217}, {1745, 46974}, {1750, 3601}, {1864, 37583}, {1868, 4219}, {1898, 5172}, {2646, 5219}, {2771, 64188}, {2800, 51525}, {2808, 15489}, {2829, 22935}, {2947, 37694}, {3256, 17634}, {3295, 63992}, {3357, 3579}, {3419, 6838}, {3428, 17857}, {3452, 4297}, {3465, 17102}, {3487, 5805}, {3522, 12246}, {3528, 54052}, {3530, 61556}, {3534, 48664}, {3543, 33595}, {3576, 11108}, {3646, 38031}, {3651, 64107}, {3682, 61161}, {3689, 7991}, {3748, 11522}, {3817, 51715}, {3824, 6826}, {3916, 12528}, {4188, 11220}, {4299, 12678}, {4302, 12679}, {4640, 31803}, {4855, 37022}, {4996, 17661}, {5045, 22753}, {5084, 5731}, {5122, 63399}, {5204, 10085}, {5302, 15064}, {5439, 6915}, {5450, 17502}, {5534, 22770}, {5687, 31798}, {5728, 57283}, {5761, 12699}, {5768, 6927}, {5791, 6988}, {5804, 7967}, {5811, 59345}, {5812, 6869}, {5817 ,17558}, {5842, 12608}, {5882, 7682}, {5886, 6849}, {5918, 16143}, {5930, 15252}, {6147, 64001}, {6200, 49234}, {6221, 19068}, {6244, 12565}, {6253, 12047}, {6256, 28160}, {6257, 35247}, {6258, 35246}, {6326, 14110}, {6396, 49235}, {6398, 19067}, {6684, 33899}, {6690, 12617}, {6700, 37364}, {6765, 8158}, {6827, 12667}, {6856, 59387}, {6858, 61261}, {6864, 61595}, {6868, 37822}, {6876, 9960}, {6883, 12114}, {6911, 9940}, {6918, 18443}, {6924, 13369}, {6942, 64358}, {6969, 7319}, {7162, 40292}, {7308, 7987}, {7681, 18527}, {7690, 48748}, {7692, 48749}, {7743, 12116}, {7956, 63999}, {7971, 12702}, {7992, 35242}, {7995,35445}, {8669, 28850}, {8726, 10156}, {8727, 13411}, {8987, 35255}, {9709, 30503}, {9779, 62870}, {9844, 62873}, {9845, 13462}, {9910, 35243}, {9943, 25440}, {9948, 10164}, {9955, 48482}, {9957, 63986}, {9961, 17613}, {10165, 38158}, {10202, 37251}, {10222, 40257}, {10246, 12650}, {10310, 50528}, {10393, 11018}, {10571, 20324}, {11012, 14872}, {11231, 12616}, {11260, 28236}, {11363, 37372}, {11491, 12672}, {11499, 31788}, {12054, 12196}, {12119, 33898}, {12330, 35238}, {12436, 31657}, {12456, 35244}, {12457, 35245}, {12496, 35248}, {12514, 31821}, {12668, 35241}, {12676, 35249}, {12677, 35250}, {12686, 35251}, {12687, 35252}, {12738, 64280}, {13257, 64002}, {13607, 15935}, {13974, 35256}, {14646, 54228}, {15171, 63989}, {15852, 30115}, {15931, 25917}, {16417, 37526}, {16761, 26086}, {16845, 38108}, {17552, 54445}, {17573, 21164}, {17580, 21151}, {17582, 38122}, {18237, 35239}, {18357, 64286}, {18491, 64328}, {18518, 61146}, {18524, 37562}, {19919, 22937}, {20323, 37723}, {21075, 31799}, {23512, 27399}, {24474, 62359}, {24475, 40249}, {26287, 28208}, {26333, 31795}, {27385, 37374}, {28146, 64119}, {28174, 54198}, {28204, 45700}, {28901, 62186}, {31053, 59355}, {31672, 37434}, {31730, 54227}, {31786, 45770}, {31828, 33862}, {31937, 32613}, {32905, 51087}, {34772, 36002}, {34789, 41541}, {37411, 37531}, {37424, 57284}, {37554, 62183}, {37561, 63432}, {37574, 64134}, {37579, 64131}, {40267, 50371}, {46839, 56809}, {50054, 59637}, {50701, 57282}, {51755, 52265}, {56824, 64057}, {59331, 61705}, {63307, 63445}, {63987, 64352}, {64316, 64326}

X(64804) = complement of X(5787)
X(64804) = pole of the line X(210)X(212) with respect to Stevanovic circle
X(64804) = pole of the line X(3340)X(30223) with respect to Feuerbach hyperbola

X(64805) =  X(23)X(1503)∩X(5972)X(9003)

Barycentrics    2 a^18-5 a^16 b^2+2 a^14 b^4-6 a^12 b^6+34 a^10 b^8-52 a^8 b^10+30 a^6 b^12-2 a^4 b^14-4 a^2 b^16+b^18-5 a^16 c^2+16 a^14 b^2 c^2-4 a^12 b^4 c^2-50 a^10 b^6 c^2+70 a^8 b^8 c^2-4 a^6 b^10 c^2-44 a^4 b^12 c^2+22 a^2 b^14 c^2-b^16 c^2+2 a^14 c^4-4 a^12 b^2 c^4+42 a^10 b^4 c^4-19 a^8 b^6 c^4-112 a^6 b^8 c^4+123 a^4 b^10 c^4-22 a^2 b^12 c^4-10 b^14 c^4-6 a^12 c^6-50 a^10 b^2 c^6-19 a^8 b^4 c^6+172 a^6 b^6 c^6-77 a^4 b^8 c^6-46 a^2 b^10 c^6+26 b^12 c^6+34 a^10 c^8+70 a^8 b^2 c^8-112 a^6 b^4 c^8-77 a^4 b^6 c^8+100 a^2 b^8 c^8-16 b^10 c^8-52 a^8 c^10-4 a^6 b^2 c^10+123 a^4 b^4 c^10-46 a^2 b^6 c^10-16 b^8 c^10+30 a^6 c^12-44 a^4 b^2 c^12-22 a^2 b^4 c^12+26 b^6 c^12-2 a^4 c^14+22 a^2 b^2 c^14-10 b^4 c^14-4 a^2 c^16-b^2 c^16+c^18 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64805) lies on these lines: {23, 1503}, {5972, 9003}

X(64805) = pole of the line X(146)X(14566) with respect to {circumcircle,ninepoint circle}-inverter (or orthoptic circle of Steiner inellipse)

X(64806) =  X(39)X(9469)∩X(620)X(690)

Barycentrics    a^14 b^2-2 a^12 b^4+6 a^10 b^6-6 a^8 b^8+2 a^6 b^10-2 a^4 b^12+a^2 b^14+a^14 c^2-6 a^12 b^2 c^2+4 a^10 b^4 c^2-2 a^8 b^6 c^2+4 a^4 b^10 c^2-a^2 b^12 c^2-2 a^12 c^4+4 a^10 b^2 c^4-4 a^8 b^4 c^4+3 a^6 b^6 c^4-2 a^4 b^8 c^4+2 a^2 b^10 c^4-2 b^12 c^4+6 a^10 c^6-2 a^8 b^2 c^6+3 a^6 b^4 c^6-2 a^4 b^6 c^6-2 a^2 b^8 c^6+2 b^10 c^6-6 a^8 c^8-2 a^4 b^4 c^8-2 a^2 b^6 c^8+2 a^6 c^10+4 a^4 b^2 c^10+2 a^2 b^4 c^10+2 b^6 c^10-2 a^4 c^12-a^2 b^2 c^12-2 b^4 c^12+a^2 c^14 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64806) lies on these lines: {39, 9469}, {148, 40236}, {620, 690}, {5152, 8784}, {6660,8178}

X(64806) = pole of the line X(147)X(62688) with respect to {circumcircle,ninepoint circle}-inverter (or orthoptic circle of Steiner inellipse)}

X(64807) =  X(147)X(32472)∩X(2793)X(6036)

Barycentrics    (b^2-c^2)(-a^12+5 a^10 b^2-13 a^8 b^4+9 a^6 b^6-5 a^4 b^8+a^2 b^10+5 a^10 c^2-2 a^8 b^2 c^2+7 a^6 b^4 c^2+8 a^4 b^6 c^2-a^2 b^8 c^2-13 a^8 c^4+7 a^6 b^2 c^4-19 a^4 b^4 c^4-a^2 b^6 c^4-2 b^8 c^4+9 a^6 c^6+8 a^4 b^2 c^6-a^2 b^4 c^6+6 b^6 c^6-5 a^4 c^8-a^2 b^2 c^8-2 b^4 c^8+a^2 c^10) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6730.

X(64807) lies on these lines: {147, 32472}, {2793, 6036}, {11616, 58752}

X(64807) = pole of the line X(148)X(11052) with respect to {circumcircle,ninepoint circle}-inverter (or orthoptic circle of Steiner inellipse)}

X(64808) =  X(5102)X(14848)∩X(31489)X(62977)

Barycentrics    (3 a^4-10 a^2 b^2+7 b^4-11 a^2 c^2-10 b^2 c^2+3 c^4) (3 a^4-11 a^2 b^2+3 b^4-10 a^2 c^2-10 b^2 c^2+7 c^4) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6735.

X(64808) lies on these lines: {5102, 14848}, {31489, 62977}

X(64808) = intersection, other than A, B, C, of circumconics {A, B, C, X(2), X(21358)} and {A, B, C, X(4), X(61887)}

X(64809) =  X(5)X(99)∩X(69)X(5071)

Barycentrics    a^4-10 a^2 b^2+9 b^4-10 a^2 c^2-17 b^2 c^2+9 c^4 : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6735.

X(64809) lies on these lines: {2, 54494}, {5, 99}, {69, 5071}, {76, 15022}, {183, 5079}, {316, 5055}, {325, 47478}, {597, 11161}, {1007, 61921}, {1078, 12812}, {3090, 7771}, {3544, 7782}, {3785, 5056}, {6033, 14159}, {6722, 16984}, {7603, 7827}, {7752, 61919}, {7768, 44904}, {7799, 61924}, {7802, 61905}, {7809, 61917}, {7832, 33010}, {7859, 32963}, {11057, 61913}, {11185, 61926}, {14907, 61912}, {31274, 33013}, {37688, 61916}, {39601, 51238}, {43459, 61900}, {48913, 61915}, {61914, 64018}

X(64809) = pole of the line X(5111)X(26613) with respect to Kiepert hyperbola
X(64809) = pole of the line X(5054)X(5965) with respect to Wallace hyperbola

X(64810) =  (name pending)

Barycentrics    a (2 a^3-2 a^2 b-2 a b^2+2 b^3+2 a b c-a c^2-b c^2-c^3) (2 a^3-a b^2-b^3-2 a^2 c+2 a b c-b^2 c-2 a c^2+2 c^3) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6735.

X(64810) lies on these lines: { }

X(64810) = intersection, other than A, B, C, of circumconics {A, B, C, X(1), X(15481)} and {A, B, C, X(9), X(60961)}

X(64811) =  X(1168)X(25440)∩X(1319)X(3869)

Barycentrics    a (2 a^3-2 a^2 b-2 a b^2+2 b^3+2 a b c-a c^2-b c^2+c^3) (2 a^3-a b^2+b^3-2 a^2 c+2 a b c-b^2 c-2 a c^2+2 c^3) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6735.

X(64811) lies on these lines: {1168, 25440}, {1319, 3869}, {1877, 17555}, {14584, 25005}

X(64811) = intersection, other than A, B, C, of circumconics {A, B, C, X(1), X(44)} and {A, B, C, X(21), X(318)}

X(64812) =  X(550)X(15466)∩X(3529)X(37669)

Barycentrics    (4 a^8+4 a^6 b^2-16 a^4 b^4+4 a^2 b^6+4 b^8-11 a^6 c^2+11 a^4 b^2 c^2+11 a^2 b^4 c^2-11 b^6 c^2+9 a^4 c^4-14 a^2 b^2 c^4+9 b^4 c^4-a^2 c^6-b^2 c^6-c^8) (4 a^8-11 a^6 b^2+9 a^4 b^4-a^2 b^6-b^8+4 a^6 c^2+11 a^4 b^2 c^2-14 a^2 b^4 c^2-b^6 c^2-16 a^4 c^4+11 a^2 b^2 c^4+9 b^4 c^4+4 a^2 c^6-11 b^2 c^6+4 c^8) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6735.

X(64812) lies on these lines: {550, 15466}, {3529, 37669}, {40170, 49135}

X(64812) = intersection, other than A, B, C, of circumconics {A, B, C, X(1), X(44)} and {A, B, C, X(21), X(318)}

X(64813) =  X(5)X(142)∩X(515)X(546)

Barycentrics    a^6 b+a^5 b^2-4 a^4 b^3-2 a^3 b^4+5 a^2 b^5+a b^6-2 b^7+a^6 c+4 a^5 b c-2 a^4 b^2 c+2 a^3 b^3 c-a^2 b^4 c-6 a b^5 c+2 b^6 c+a^5 c^2-2 a^4 b c^2-4 a^2 b^3 c^2-a b^4 c^2+6 b^5 c^2-4 a^4 c^3+2 a^3 b c^3-4 a^2 b^2 c^3+12 a b^3 c^3-6 b^4 c^3-2 a^3 c^4-a^2 b c^4-a b^2 c^4-6 b^3 c^4+5 a^2 c^5-6 a b c^5+6 b^2 c^5+a c^6+2 b c^6-2 c^7 : :
X(64813) = 3*X(1)+X(52683), 3*X(2)+X(6259), 9*X(2)-X(12246), X(3)-5*X(63966), 5*X(4)+3*X(54051), 3*X(5)-X(6245), X(84)-5*X(1656), 3*X(381)+X(1490), X(382)+3*X(52026),3*X(547)-X(61556), X(1158)-3*X(11231), 7*X(3090)+X(6223), 5*X(3091)+3*X(5658), 5*X(3091)-X(5787), X(3358)-3*X(38318), 11*X(3525)-3*X(54052), 7*X(3526)+X(48664), 7*X(3526)-3*X(52027), 9*X(3545)-X(9799), 3*X(3576)+X(40267), 2*X(3628)-X(6705), 7*X(3832)+X(64144), 5*X(3843)-X(64261), 9*X(5055)-X(12684), 3*X(5658)+X(5787), 3*X(5790)+X(7971), 3*X(5886)+X(12667), X(6245)+3*X(6260), 3*X(6259)+X(12246), 9*X(7988)-X(10864), X(7992)-9*X(54447), 5*X(9955)-4*X(40259),3*X(10175)-X(33899), 3*X(10175)+X(54227), 3*X(10202)+X(18239), 3*X(11230)-X(12114), X(12246)-3*X(34862), X(12650)-5*X(18493),X(12699)+3*X(64148), X(22792)+5*X(63966),3*X(26446)+X(63962), 3*X(38752)+X(46435), X(48664)+3*X(52027)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6735.

X(64813) lies on these lines: {1, 1538}, {2, 6259}, {3, 22792}, {4, 4313}, {5, 142}, {10, 31821}, {12,9856}, {30, 40262}, {72, 6932}, {84, 1656}, {119, 31788}, {226, 5806}, {355, 6982}, {381, 1490}, {382, 52026}, {442, 10157}, {495, 63989}, {498, 12679}, {499, 12678}, {515, 546}, {516, 64123}, {517, 10915}, {547, 61556}, {908, 31793}, {942, 1532}, {944, 7704}, {946,31792}, {952, 64205}, {960, 21635}, {1071, 6941}, {1158, 11231}, {1329, 31787}, {1385, 6256}, {1512, 50193}, {1519, 9957}, {1594, 12136}, {1699, 3303}, {2476, 5927}, {2646, 41698}, {2800, 4015}, {2829, 13624}, {2886, 9947}, {3090, 6223}, {3091, 5658}, {3358, 38318}, {3452, 37424}, {3525, 54052}, {3526, 48664}, {3545, 9799}, {3576, 40267}, {3579, 64119}, {3612, 37001}, {3616, 17618}, {3628, 6705}, {3634, 61511}, {3660, 26476}, {3814, 9943}, {3817, 51723}, {3825,58567}, {3832, 64144}, {3838, 19925}, {3841, 6001}, {3843, 64261}, {3916, 6960}, {4187, 11227}, {4193, 10167}, {4297, 5087}, {5044, 6907}, {5045, 7681}, {5055, 12684}, {5154, 11220}, {5217, 52860}, {5439, 6945}, {5440, 37437}, {5690, 54198}, {5691, 17605}, {5704, 36996}, {5705, 5779}, {5709, 60965}, {5714, 5805}, {5715, 18482}, {5777, 6842}, {5789, 64197}, {5790, 7971}, {5791, 5811}, {5882, 22835}, {5886, 12667}, {6147, 7682}, {6261, 18480}, {6684, 20400}, {6734, 13257}, {6745, 31777}, {6796, 28146}, {6825, 31445}, {6834, 37582}, {6838, 58798}, {6848, 57282}, {6874, 9960}, {6883, 56889}, {6908, 31658}, {6922, 31805}, {6980, 40263}, {7393, 9910}, {7741, 12680}, {7951, 12688}, {7956, 21620}, {7988, 10864}, {7992, 54447}, {8166, 11037}, {8976, 19068}, {9612, 19541}, {9654, 63992}, {9845, 50444}, {10105, 48931}, {10156, 17527}, {10175, 33899}, {10202, 18239}, {10525, 64116}, {10576, 49234}, {10577, 49235}, {10588, 64130}, {10884, 17556}, {10893, 18527}, {10895, 63988}, {11230, 12114}, {11500, 22793}, {12047, 64271}, {12115, 24928}, {12616, 18243}, {12650, 18493}, {12675, 58570}, {12699, 64148}, {12705, 31479}, {12761, 22935}, {13951, 19067}, {14882, 44425}, {15071, 17606}, {15845, 16215}, {15908, 34790}, {17559, 38122}, {17613, 27529}, {17757, 31798}, {18542, 61146}, {26087, 28204}, {26287, 28160}, {26446, 63962}, {30283, 50443}, {30852, 37022}, {31446, 51516}, {33858, 48697}, {33862, 64188}, {34789, 37568}, {38752, 46435}, {52684, 60953}, {57285, 64157}

X(64813) = complement of X(34862)

X(64814) =  X(40)X(572)∩X(329)X(405)

Barycentrics    a (a^3+3 a^2 b+3 a b^2+b^3+2 a b c-a c^2-b c^2) (a^3-a b^2+3 a^2 c+2 a b c-b^2 c+3 a c^2+c^3) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6753.

X(64814) lies on these lines: {6, 38856}, {40, 572}, {196, 54394}, {223, 1451}, {329, 405}, {943, 40956}, {1817, 17012}, {11108, 28626}

X(64814) = isogonal conjugate of X(5044)
X(64814) = X(3)-Dao conjugate of-X(5044)
X(64814) = X(54)-vertex conjugate of-X(44861)
X(64814) = crosssum of X(5044) and X(5044)
X(64814) = intersection, other than A, B, C, of circumconics {A, B, C, X(1), X(1014)} and {A, B, C, X(2), X(57748)}
X(64814) = trilinear pole of the line: {4790, 6129}

X(64815) =  X(20)X(578)∩X(1598)X(1629)

Barycentrics    (a^8+2 a^6 b^2-6 a^4 b^4+2 a^2 b^6+b^8-3 a^6 c^2-5 a^4 b^2 c^2-5 a^2 b^4 c^2-3 b^6 c^2+3 a^4 c^4+4 a^2 b^2 c^4+3 b^4 c^4-a^2 c^6-b^2 c^6) (a^8-3 a^6 b^2+3 a^4 b^4-a^2 b^6+2 a^6 c^2-5 a^4 b^2 c^2+4 a^2 b^4 c^2-b^6 c^2-6 a^4 c^4-5 a^2 b^2 c^4+3 b^4 c^4+2 a^2 c^6-3 b^2 c^6+c^8) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6753.

X(64815) lies on these lines: {20, 578}, {973, 11596}, {1078, 14615}, {1249, 10312}, {1294, 13568}, {1598, 1629}, {9786, 15318}, {10152, 13488}, {13567, 15319}, {37458, 38808}

X(64815) = isogonal conjugate of X(11793)
X(64815) = X(11745)-cross conjugate of-X(4)
X(64815) = X(3)-Dao conjugate of-X(11793)
X(64815) = X(54)-vertex conjugate of-X(45300)
X(64815) = crosssum of X(11793) and X(11793)
X(64815) = trilinear pole of the line: {3050, 6587}

X(64816) =  ISOGONAL CONJUGATE OF X(64817)

Barycentrics    a (a^9+a^8 b-4 a^7 b^2-4 a^6 b^3+6 a^5 b^4+6 a^4 b^5-4 a^3 b^6-4 a^2 b^7+a b^8+b^9+2 a^8 c-2 a^7 b c+4 a^6 b^2 c+2 a^5 b^3 c-12 a^4 b^4 c+2 a^3 b^5 c+4 a^2 b^6 c-2 a b^7 c+2 b^8 c-2 a^7 c^2-6 a^6 b c^2+6 a^5 b^2 c^2+2 a^4 b^3 c^2+2 a^3 b^4 c^2+6 a^2 b^5 c^2-6 a b^6 c^2-2 b^7 c^2-6 a^6 c^3+10 a^5 b c^3-10 a^4 b^2 c^3+12 a^3 b^3 c^3-10 a^2 b^4 c^3+10 a b^5 c^3-6 b^6 c^3+8 a^4 b c^4+8 a b^4 c^4+6 a^4 c^5-14 a^3 b c^5+8 a^2 b^2 c^5-14 a b^3 c^5+6 b^4 c^5+2 a^3 c^6-2 a^2 b c^6-2 a b^2 c^6+2 b^3 c^6-2 a^2 c^7+6 a b c^7-2 b^2 c^7-a c^8-b c^8) (a^9+2 a^8 b-2 a^7 b^2-6 a^6 b^3+6 a^4 b^5+2 a^3 b^6-2 a^2 b^7-a b^8+a^8 c-2 a^7 b c-6 a^6 b^2 c+10 a^5 b^3 c+8 a^4 b^4 c-14 a^3 b^5 c-2 a^2 b^6 c+6 a b^7 c-b^8 c-4 a^7 c^2+4 a^6 b c^2+6 a^5 b^2 c^2-10 a^4 b^3 c^2+8 a^2 b^5 c^2-2 a b^6 c^2-2 b^7 c^2-4 a^6 c^3+2 a^5 b c^3+2 a^4 b^2 c^3+12 a^3 b^3 c^3-14 a b^5 c^3+2 b^6 c^3+6 a^5 c^4-12 a^4 b c^4+2 a^3 b^2 c^4-10 a^2 b^3 c^4+8 a b^4 c^4+6 b^5 c^4+6 a^4 c^5+2 a^3 b c^5+6 a^2 b^2 c^5+10 a b^3 c^5-4 a^3 c^6+4 a^2 b c^6-6 a b^2 c^6-6 b^3 c^6-4 a^2 c^7-2 a b c^7-2 b^2 c^7+a c^8+2 b c^8+c^9) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6753.

X(64816) lies on the Feuerbach circumhyperbola and these lines: { }

X(64816) = isogonal conjugate of X(64817)

X(64817) =  X(1)X(3)∩X(2)X(5909)

Barycentrics    a (a^8 b+2 a^7 b^2-2 a^6 b^3-6 a^5 b^4+6 a^3 b^6+2 a^2 b^7-2 a b^8-b^9+a^8 c-6 a^7 b c+2 a^6 b^2 c+14 a^5 b^3 c-8 a^4 b^4 c-10 a^3 b^5 c+6 a^2 b^6 c+2 a b^7 c-b^8 c+2 a^7 c^2+2 a^6 b c^2-8 a^5 b^2 c^2+10 a^3 b^4 c^2-6 a^2 b^5 c^2-4 a b^6 c^2+4 b^7 c^2-2 a^6 c^3+14 a^5 b c^3-12 a^3 b^3 c^3-2 a^2 b^4 c^3-2 a b^5 c^3+4 b^6 c^3-6 a^5 c^4-8 a^4 b c^4+10 a^3 b^2 c^4-2 a^2 b^3 c^4+12 a b^4 c^4-6 b^5 c^4-10 a^3 b c^5-6 a^2 b^2 c^5-2 a b^3 c^5-6 b^4 c^5+6 a^3 c^6+6 a^2 b c^6-4 a b^2 c^6+4 b^3 c^6+2 a^2 c^7+2 a b c^7+4 b^2 c^7-2 a c^8-b c^8-c^9) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6753.

X(64817) lies on these lines: {1, 3}, {2, 5909}, {5, 20205}, {140, 58412}, {282, 6918}, {631, 52097}, {1490, 61671}, {2807, 58660}, {2817, 3812}, {5044, 11793}, {6684, 58460}, {6927, 14557}, {6935, 10373}, {9776, 56887}, {13614, 18180}, {14058, 44916}, {19904, 37696} ,{40953, 52027}

X(64817) = isogonal conjugate of X(64816)
X(64817) = complement of X(5909)

X(64818) =  X(5)X(10)∩X(1440)X(6926)

Barycentrics    a (a^8 b+2 a^7 b^2-2 a^6 b^3-6 a^5 b^4+6 a^3 b^6+2 a^2 b^7-2 a b^8-b^9+a^8 c+2 a^7 b c-6 a^6 b^2 c-6 a^5 b^3 c+12 a^4 b^4 c+6 a^3 b^5 c-10 a^2 b^6 c-2 a b^7 c+3 b^8 c+2 a^7 c^2-6 a^6 b c^2+8 a^5 b^2 c^2+4 a^4 b^3 c^2-14 a^3 b^4 c^2+2 a^2 b^5 c^2+4 a b^6 c^2-2 a^6 c^3-6 a^5 b c^3+4 a^4 b^2 c^3+4 a^3 b^3 c^3+6 a^2 b^4 c^3+2 a b^5 c^3-8 b^6 c^3-6 a^5 c^4+12 a^4 b c^4-14 a^3 b^2 c^4+6 a^2 b^3 c^4-4 a b^4 c^4+6 b^5 c^4+6 a^3 b c^5+2 a^2 b^2 c^5+2 a b^3 c^5+6 b^4 c^5+6 a^3 c^6-10 a^2 b c^6+4 a b^2 c^6-8 b^3 c^6+2 a^2 c^7-2 a b c^7-2 a c^8+3 b c^8-c^9) : :
X(64818) = 3*X(2)+X(52097), 5*X(631)-X(51490), X(1872)-3*X(10157), X(40953)-5*X(63966)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6753.

X(64818) lies on these lines: {2, 5908}, {3, 223}, {4, 51413}, {5, 10}, {140, 58412}, {389, 11018}, {631, 51490}, {1040, 19904}, {1440, 6926}, {1872, 10157}, {2818, 31787}, {3359, 34498}, {3827, 58660}, {6684, 20201}, {6705, 34371}, {6825, 31965}, {6844, 43213}, {6847, 14557}, {6848, 10373} ,{8679, 58588}, {9729, 9940}, {40953, 63966}

X(64818) = complement of X(5908)

X(64819) =  X(3)X(64)∩X(2060)X(5562)

Barycentrics    a^2 (a^18 b^2-9 a^16 b^4+36 a^14 b^6-84 a^12 b^8+126 a^10 b^10-126 a^8 b^12+84 a^6 b^14-36 a^4 b^16+9 a^2 b^18-b^20+a^18 c^2+16 a^16 b^2 c^2-48 a^14 b^4 c^2-36 a^12 b^6 c^2+266 a^10 b^8 c^2-356 a^8 b^10 c^2+184 a^6 b^12 c^2-12 a^4 b^14 c^2-19 a^2 b^16 c^2+4 b^18 c^2-9 a^16 c^4-48 a^14 b^2 c^4+272 a^12 b^4 c^4-392 a^10 b^6 c^4+126 a^8 b^8 c^4+160 a^6 b^10 c^4-136 a^4 b^12 c^4+24 a^2 b^14 c^4+3 b^16 c^4+36 a^14 c^6-36 a^12 b^2 c^6-392 a^10 b^4 c^6+712 a^8 b^6 c^6-428 a^6 b^8 c^6+204 a^4 b^10 c^6-48 a^2 b^12 c^6-48 b^14 c^6-84 a^12 c^8+266 a^10 b^2 c^8+126 a^8 b^4 c^8-428 a^6 b^6 c^8-40 a^4 b^8 c^8+34 a^2 b^10 c^8+126 b^12 c^8+126 a^10 c^10-356 a^8 b^2 c^10+160 a^6 b^4 c^10+204 a^4 b^6 c^10+34 a^2 b^8 c^10-168 b^10 c^10-126 a^8 c^12+184 a^6 b^2 c^12-136 a^4 b^4 c^12-48 a^2 b^6 c^12+126 b^8 c^12+84 a^6 c^14-12 a^4 b^2 c^14+24 a^2 b^4 c^14-48 b^6 c^14-36 a^4 c^16-19 a^2 b^2 c^16+3 b^4 c^16+9 a^2 c^18+4 b^2 c^18-c^20) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6753.

X(64819) lies on these lines: {3, 64}, {2060, 5562}, {3079, 15644}, {3344, 11695}

X(64820) =  X(4)X(51)∩X(25)X(394)

Barycentrics    a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^4 b^2-2 a^2 b^4+b^6+a^4 c^2+2 a^2 b^2 c^2+b^4 c^2-2 a^2 c^4+b^2 c^4+c^6) : :
X(64820) = 3*X(51)-X(1899), X(1619)-3*X(41580), 2*X(10110)-X(18390)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6765.

X(64820) lies on these lines: {2, 12058}, {4, 51}, {6, 1619}, {22, 1974}, {24, 15644}, {25, 394}, {34, 63513}, {52, 1598}, {154, 50649}, {193, 1843}, {232, 20859}, {235, 343}, {373, 8889}, {378, 16836}, {427, 5943}, {428, 542}, {468, 3819}, {568, 18535}, {674, 41611}, {1181, 46363}, {1194, 2211}, {1216, 21841}, {1351, 52077}, {1593, 9729}, {1595, 5462}, {1596, 13754}, {1597, 9730}, {1885, 46850}, {1916, 60125}, {1968, 42295}, {1993, 11470}, {2979, 4232}, {3089, 5562}, {3515, 13348}, {3516, 17704}, {3517, 10625}, {3541, 11695}, {3542, 11793}, {3575, 13598}, {3796, 19118}, {3867, 58471}, {3917, 6353}, {4260, 44086}, {5012, 44102}, {5020, 37511}, {5064, 58470}, {5090, 23841}, {5094, 6688}, {5198, 16625}, {5422, 19124}, {5446, 6756}, {5480, 15809}, {5640, 7378}, {5650, 38282}, {6403, 7714}, {6467, 11206}, {6623, 15030}, {6997, 9822}, {7408, 11002}, {7466, 44092}, {7487, 45186}, {7715, 10263}, {7716, 63180}, {7718, 16980}, {7998, 62973}, {9909, 9967}, {9969, 15255}, {10095, 16198}, {10151, 46847}, {10170, 37942}, {10219, 52298}, {11396, 58535}, {11402, 44495}, {11403, 15012}, {11451, 52284}, {11807, 15473}, {12147, 12237}, {12148, 12238}, {12167, 58555}, {12298, 55573}, {12299, 55569}, {12300, 44959}, {13417, 44106}, {13488, 40647}, {13567, 34146}, {13570, 18386}, {14642, 56364}, {15004, 39588}, {15060, 44957}, {15073, 34750}, {15082, 52297}, {15107, 44091}, {15818, 64052}, {15887, 58492}, {17810, 19161}, {18438, 20850}, {18440, 61666}, {19128, 22352}, {20299, 58482}, {21851, 34417}, {23292, 45979}, {31978, 52003}, {34986, 44080}, {35473, 55166}, {35501, 40280}, {35603, 64026}, {36426, 52280}, {36987, 37460}, {37183, 52545}, {37197, 44870}, {37920, 55631}, {37971, 45118}, {37981, 58481}, {40413, 56430}, {44077, 44479}, {44299, 53857}, {45173, 51394}, {52301, 62187}, {55446, 61349}, {62958, 63632}

X(64820) = complement of X(12058)
X(64820) = crosssum of X(3) and X(1368)
X(64820) = crosspoint of X(4) and X(57388)
X(64820) = pole of the line X(520)X(16230) with respect to incircle of orthic triangle
X(64820) = pole of the line X(520)X(30735) with respect to polar circle
X(64820) = pole of the line X(235)X(39569) with respect to Huygens hyperbola
X(64820) = pole of the line X(4)X(57388) with respect to Jerabek hyperbola
X(64820) = pole of the line X(53)X(36424) with respect to Kiepert hyperbola
X(64820) = pole of the line X(647)X(41336) with respect to orthic inconic
X(64820) = pole of the line X(1092)X(6776) with respect to Stammler hyperbola
X(64820) = pole of the line X(3964)X(62698) with respect to Wallace hyperbola
X(64820) = pole of the line X(5972)X(20190) with respect to Walsmith rectangular hyperbola

X(64821) =  90TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4 - (2*a^4 - 3*a^2*b^2 + b^4 - 3*a^2*c^2 - 2*b^2*c^2 + c^4)*J : :
X(64821) = 3 X[2] + X[1113], 5 X[2] - X[10719], 9 X[2] - X[14807], 7 X[2] + X[15158], 3 X[3] + X[10751], X[3] + 3 X[57322], X[4] + 3 X[38708], 3 X[140] - X[31682], 3 X[376] + X[10737], 3 X[549] - X[35232], 5 X[631] - X[1114], 5 X[631] + X[20408], 5 X[632] + X[30524], 5 X[1113] + 3 X[10719], 3 X[1113] + X[14807], 7 X[1113] - 3 X[15158], 3 X[1312] - X[10751], X[1312] - 3 X[57322], 5 X[1313] - 3 X[10719], 3 X[1313] - X[14807], 7 X[1313] + 3 X[15158], 5 X[1656] - X[10750], 5 X[1656] + 3 X[28447], 7 X[3090] + X[15160], 5 X[3091] - X[10736], 7 X[3523] + X[14808], 7 X[3523] - 3 X[38709], 3 X[3524] + X[10720], 9 X[3524] - X[15161], 11 X[3525] + X[15157], 7 X[3526] + X[15154], 7 X[3526] - X[20409], 7 X[3526] - 3 X[57323], 9 X[5054] - X[15155], 13 X[10303] - X[15156], 9 X[10719] - 5 X[14807], 7 X[10719] + 5 X[15158], 3 X[10720] + X[15161], X[10750] + 3 X[28447], X[10751] - 9 X[57322], 3 X[11539] - X[13627], 3 X[13626] + X[35232], 7 X[14807] + 9 X[15158], X[14808] + 3 X[38709], 7 X[14869] - X[30525], X[15154] + 3 X[57323], X[15159] - 9 X[15708], 11 X[15720] - 3 X[28448], X[20409] - 3 X[57323], 3 X[31681] + X[31682], X[2100] + 7 X[3624], X[2102] - 5 X[3616], X[2103] + 3 X[5657], X[2104] - 5 X[3618], X[2105] + 3 X[10519], X[10781] - 5 X[31272], X[10782] + 3 X[34474], X[14500] + 3 X[38727], X[15162] + 7 X[47355]

See Antreas Hatzipolakis and Peter Moses, euclid 6770.

X(64821) lies on the nine-point circle of the medial triangle and these lines: {2, 3}, {230, 15167}, {2100, 3624}, {2102, 3616}, {2103, 5657}, {2104, 3618}, {2105, 10519}, {2574, 5972}, {2575, 6699}, {3564, 13414}, {5432, 51874}, {5433, 51873}, {6390, 46813}, {8116, 34380}, {10781, 31272}, {10782, 34474}, {14374, 43839}, {14500, 38727}, {15162, 47355}, {15325, 34593}, {43395, 51425}

X(64821) = midpoint of X(i) and X(j) for these {i,j}: {3, 1312}, {5, 35231}, {140, 31681}, {549, 13626}, {1113, 1313}, {1114, 20408}, {13414, 62592}, {15154, 20409}
X(64821) = complement of X(1313)
X(64821) = orthoptic-circle-of-the-Steiner-inellipse inverse of X(14808)
X(64821) = complement of the isogonal conjugate of X(15461)
X(64821) = X(i)-complementary conjugate of X(j) for these (i,j): {1822, 1313}, {2576, 62593}, {15461, 10}, {41941, 226}, {44125, 24040}, {50944, 21253}, {52131, 8287}, {53384, 34846}
X(64821) = X(53153)-Ceva conjugate of X(2575)
X(64821) = crosssum of X(6) and X(44126)
X(64821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1113, 1313}, {2, 1312, 5159}, {2, 1344, 5}, {3, 57322, 1312}, {186, 46699, 45995}, {1656, 28447, 10750}, {2454, 2455, 44332}, {3523, 14808, 38709}, {3526, 15154, 57323}, {15154, 57323, 20409}

X(64822) =  91ST HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4 + (2*a^4 - 3*a^2*b^2 + b^4 - 3*a^2*c^2 - 2*b^2*c^2 + c^4)*J : :
X(64822) = 3 X[2] + X[1114], 5 X[2] - X[10720], 9 X[2] - X[14808], 7 X[2] + X[15159], 3 X[3] + X[10750], X[3] + 3 X[57323], X[4] + 3 X[38709], 3 X[140] - X[31681], 3 X[376] + X[10736], 3 X[549] - X[35231], 5 X[631] - X[1113], 5 X[631] + X[20409], 5 X[632] + X[30525], 5 X[1114] + 3 X[10720], 3 X[1114] + X[14808], 7 X[1114] - 3 X[15159], 5 X[1312] - 3 X[10720], 3 X[1312] - X[14808], 7 X[1312] + 3 X[15159], 3 X[1313] - X[10750], X[1313] - 3 X[57323], 5 X[1656] - X[10751], 5 X[1656] + 3 X[28448], 7 X[3090] + X[15161], 5 X[3091] - X[10737], 7 X[3523] + X[14807], 7 X[3523] - 3 X[38708], 3 X[3524] + X[10719], 9 X[3524] - X[15160], 11 X[3525] + X[15156], 7 X[3526] + X[15155], 7 X[3526] - X[20408], 7 X[3526] - 3 X[57322], 9 X[5054] - X[15154], 13 X[10303] - X[15157], 3 X[10719] + X[15160], 9 X[10720] - 5 X[14808], 7 X[10720] + 5 X[15159], X[10750] - 9 X[57323], X[10751] + 3 X[28448], 3 X[11539] - X[13626], 3 X[13627] + X[35231], X[14807] + 3 X[38708], 7 X[14808] + 9 X[15159], 7 X[14869] - X[30524], X[15155] + 3 X[57322], X[15158] - 9 X[15708], 11 X[15720] - 3 X[28447], X[20408] - 3 X[57322], X[31681] + 3 X[31682], X[2101] + 7 X[3624], X[2102] + 3 X[5657], X[2103] - 5 X[3616], X[2104] + 3 X[10519], X[2105] - 5 X[3618], X[10781] + 3 X[34474], X[10782] - 5 X[31272], X[14499] + 3 X[38727], X[15163] + 7 X[47355]

See Antreas Hatzipolakis and Peter Moses, euclid 6770.

X(64822) lies on the nine-point circle of the medial triangle and these lines: {2, 3}, {230, 15166}, {2101, 3624}, {2102, 5657}, {2103, 3616}, {2104, 10519}, {2105, 3618}, {2574, 6699}, {2575, 5972}, {3564, 13415}, {5432, 51873}, {5433, 51874}, {6390, 46810}, {8115, 34380}, {10781, 34474}, {10782, 31272}, {14375, 43839}, {14499, 38727}, {15163, 47355}, {15325, 34592}, {43396, 51425}

X(64822) = midpoint of X(i) and X(j) for these {i,j}: {3, 1313}, {5, 35232}, {140, 31682}, {549, 13627}, {1113, 20409}, {1114, 1312}, {13415, 62593}, {15155, 20408}
X(64822) = complement of X(1312)
X(64822) = orthoptic-circle-of-the-Steiner-inellipse inverse of X(14807)
X(64822) = complement of the isogonal conjugate of X(15460)
X(64822) = X(i)-complementary conjugate of X(j) for these (i,j): {1823, 1312}, {2577, 62592}, {15460, 10}, {41942, 226}, {44126, 24040}, {50945, 21253}, {52132, 8287}, {53385, 34846}
X(64822) = X(53154)-Ceva conjugate of X(2574)
X(64822) = crosssum of X(6) and X(44125)
X(64822) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1114, 1312}, {2, 1313, 5159}, {2, 1345, 5}, {3, 57323, 1313}, {186, 46698, 45994}, {1656, 28448, 10751}, {2454, 2455, 44333}, {3523, 14807, 38708}, {3526, 15155, 57322}, {15155, 57322, 20408}

X(64823) = ISOGONAL CONJUGATE OF X(58842)

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^3+2*b^3+2*b^2*c+b*c^2+c^3+a^2*(b+c)+a*(2*b^2+4*b*c+c^2))*(a^3+b^3+b^2*c+2*b*c^2+2*c^3+a^2*(b+c)+a*(b^2+4*b*c+2* c^2)) : :

Let IaIbIc be the cevian triangle of the incenter I. Denote by (cr) the circumconic with perspector I. Ray IaIb intersects (cr) at Ca. Ray IbIa intersects (cr) at Cb. Similarly define Ab, Ba, Bc, Ac. Let lines BaCa, AbCb, and AcBc form a triangle A'B'C'. Let lines BcCb, AcCa, and AbBa form a triangle A''B''C''. Both A'B'C' and A''B''C'' are perspective to the Montesdeoca-Hung triangle. X(64823) is the tripole of the line joining the two perspectors. (Ivan Pavlov, 17 Aug 2024).

X(64823) lies on these lines: {24624, 41809}, {37215, 55235}

X(64823) = isogonal conjugate of X(58842)
X(64823) = trilinear pole of line {1, 5974}
X(64823) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 58842}, {512, 6703}, {649, 27714}
X(64823) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 58842}, {5375, 27714}, {39054, 6703}
X(64823) = X(i)-cross conjugate of X(j) for these {i, j}: {2292, 24041}, {2363, 4600}, {58842, 1}
X(64823) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(88), X(100)}}, {{A, B, C, X(4585), X(41809)}}, {{A, B, C, X(4627), X(53633)}}, {{A, B, C, X(4629), X(36069)}}
X(64823) = barycentric quotient X(i)/X(j) for these (i, j): {6, 58842}, {100, 27714}, {662, 6703}

X(64824) = TRILINEAR POLE OF LINE {1, 26095}

Barycentrics    (a-b)*(a-c)*(a^3-a^2*b+b^3-a*(b-c)^2-b*c^2)*(-b^3+b*c^2+a*c*(-b+c)+a^2*(b+c))*(a*b*(b-c)+a^2*(b+c)+c*(b^2-c^2))*(a^3-a*(b-c)^2-a^2*c-b^2*c+c^3) : :

Let IaIbIc be the cevian triangle of the incenter I. Denote by (cr) the circumconic with perspector I. Ray IaIb intersects (cr) at Ca. Ray IbIa intersects (cr) at Cb. Similarly define Ab, Ba, Bc, Ac. Let lines BaCa, AbCb, and AcBc form a triangle A'B'C'. Let lines BcCb, AcCa, and AbBa form a triangle A''B''C''. Let T be the triangle formed by the Aubert (Steiner) lines of ABPC, BCPA, CAPB, where P=X(40). Both A'B'C' and A''B''C'' are perspective to T. X(64824) is the tripole of the line joining the two perspectors. (Ivan Pavlov, 17 Aug 2024).

X(64823) lies on these lines: {100, 53702}, {162, 1309}, {651, 17496}, {662, 13136}, {36037, 36098}

X(64824) = trilinear pole of line {1, 26095}
X(64824) = X(i)-isoconjugate-of-X(j) for these {i, j}: {572, 1769}, {2183, 21173}, {2975, 3310}, {10015, 20986}, {11998, 23981}, {14571, 23187}, {17074, 53549}, {22118, 39534}, {23706, 38344}
X(64824) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}}, {{A, B, C, X(1309), X(13136)}}, {{A, B, C, X(4560), X(17496)}} X(64824) = barycentric product X(i)*X(j) for these (i, j): {104, 56252}, {13136, 2051}, {18816, 56194}, {32641, 57905}, {34234, 56188}, {36037, 54121}, {53702, 75}, {57984, 59006}
X(64824) = barycentric quotient X(i)/X(j) for these (i, j): {104, 21173}, {1309, 11109}, {1795, 23187}, {2051, 10015}, {2401, 24237}, {13136, 14829}, {18816, 57244}, {20028, 23788}, {32641, 572}, {34234, 17496}, {34434, 1769}, {36037, 2975}, {37136, 17074}, {43728, 34589}, {51565, 57091}, {53702, 1}, {54121, 36038}, {56188, 908}, {56194, 517}, {56252, 3262}, {59006, 859}, {60817, 53549}, {61238, 11998}

X(64825) = ISOTOMIC CONJUGATE OF X(64824)

Barycentrics    (b-c)*(-a^3+b*c*(b+c)+a*(b^2-b*c+c^2))*(2*a*b*c-a^2*(b+c)+(b-c)^2*(b+c)) : :

X(64825) lies on these lines: {514, 661}, {2804, 39776}, {3310, 10015}, {3882, 4552}, {21385, 43991}, {24237, 40624}

X(64825) = perspector of circumconic {{A, B, C, X(75), X(17139)}}
X(64825) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 53702}, {909, 56194}, {2250, 59006}, {32641, 34434}, {34858, 56188}, {37136, 60817}
X(64825) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 53702}, {16586, 56188}, {23980, 56194}, {34589, 2250}, {46398, 2051}
X(64825) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4552, 16586}, {21272, 39776}, {24029, 908}, {35174, 52357}
X(64825) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {59073, 7}
X(64825) = pole of line {347, 62754} with respect to the DeLongchamps circle
X(64825) = pole of line {4467, 21273} with respect to the Kiepert parabola
X(64825) = pole of line {163, 32641} with respect to the Stammler hyperbola
X(64825) = pole of line {8, 4551} with respect to the Steiner circumellipse
X(64825) = pole of line {10, 34586} with respect to the Steiner inellipse
X(64825) = pole of line {522, 3869} with respect to the Yff parabola
X(64825) = pole of line {662, 13136} with respect to the Wallace hyperbola
X(64825) = pole of line {75, 56252} with respect to the dual conic of Hofstadter ellipse
X(64825) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(514), X(24237)}}, {{A, B, C, X(661), X(3310)}}, {{A, B, C, X(693), X(23788)}}, {{A, B, C, X(1577), X(10015)}}, {{A, B, C, X(3936), X(16586)}}, {{A, B, C, X(3948), X(51381)}}, {{A, B, C, X(4391), X(17496)}}
X(64825) = barycentric product X(i)*X(j) for these (i, j): {517, 57244}, {2397, 24237}, {2975, 36038}, {10015, 14829}, {17496, 908}, {17751, 23788}, {21173, 3262}, {22464, 57091}, {24029, 40624}
X(64825) = barycentric quotient X(i)/X(j) for these (i, j): {1, 53702}, {517, 56194}, {572, 32641}, {859, 59006}, {908, 56188}, {1769, 34434}, {2975, 36037}, {3262, 56252}, {10015, 2051}, {11109, 1309}, {11998, 61238}, {14829, 13136}, {17074, 37136}, {17496, 34234}, {21173, 104}, {23187, 1795}, {23788, 20028}, {24237, 2401}, {34589, 43728}, {36038, 54121}, {53549, 60817}, {57091, 51565}, {57244, 18816}

X(64826) = X(1)X(3689)∩X(165)X(748)

Barycentrics    a*(5*a^2-7*b^2+46*b*c-7*c^2-14*a*(b+c)) : :

X(64826) is the centroid of the tangential triangle of the X(1)-circumconcevian triangle (Ivan Pavlov, 17 Aug 2024).

X(64826) lies on these lines: {1, 3689}, {45, 36835}, {88, 5223}, {165, 748}, {4849, 10980}, {8056, 55935}, {9324, 60846}, {16676, 44798}, {17123, 52180}, {17595, 30393}, {30653, 64112}, {59207, 62711}

X(64827) = X(1)X(1350)∩X(7)X(21)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^2-2*b*c+a*(b+c)) : :

Let A' be the point, other than A, where the circle with diameter AI intersects the circumcircle, and define B' and C' cyclically. Then X(64827) is the symmedian point of A'B'C'. (Ivan Pavlov, 17 Aug 2024)

X(64827) lies on these lines: {1, 1350}, {2, 1696}, {3, 3663}, {6, 1423}, {7, 21}, {9, 25887}, {11, 21279}, {36, 4862}, {37, 57}, {45, 56547}, {55, 3598}, {65, 7190}, {69, 12513}, {75, 183}, {77, 1122}, {85, 28037}, {100, 4452}, {108, 1119}, {198, 4000}, {220, 27626}, {226, 4657}, {241, 28017}, {269, 1279}, {279, 51773}, {307, 30617}, {344, 5435}, {347, 7195}, {388, 4026}, {404, 31995}, {474, 25590}, {515, 24213}, {527, 5120}, {553, 41312}, {604, 6180}, {613, 1756}, {859, 17189}, {934, 7023}, {940, 61412}, {942, 46475}, {948, 28015}, {956, 17272}, {958, 4357}, {999, 3664}, {1086, 2178}, {1108, 7289}, {1259, 19850}, {1388, 1442}, {1400, 5228}, {1402, 40719}, {1407, 57037}, {1427, 28022}, {1439, 34489}, {1458, 40934}, {1461, 38855}, {1486, 1617}, {1616, 62791}, {1633, 21002}, {1788, 3932}, {2097, 18161}, {2099, 7269}, {2223, 11495}, {2352, 18655}, {3209, 5236}, {3212, 4360}, {3217, 4383}, {3295, 4021}, {3304, 3945}, {3306, 25099}, {3361, 7274}, {3554, 34371}, {3713, 25940}, {3729, 21477}, {3772, 15509}, {3875, 3913}, {3911, 17279}, {3946, 4254}, {4032, 24357}, {4188, 4373}, {4269, 37543}, {4298, 50290}, {4306, 37818}, {4346, 5204}, {4361, 16609}, {4419, 54322}, {4421, 50101}, {4428, 17320}, {4491, 43041}, {4497, 24405}, {4654, 41311}, {4687, 61018}, {4859, 37272}, {4888, 5563}, {4998, 57950}, {5022, 44421}, {5124, 49747}, {5219, 17384}, {5224, 56928}, {5687, 17151}, {6354, 28108}, {7011, 18589}, {7013, 37566}, {7053, 41426}, {7146, 16777}, {7179, 8167}, {7271, 13462}, {8666, 53598}, {8732, 16593}, {9310, 25878}, {10400, 16580}, {10436, 25524}, {10444, 64077}, {10446, 24203}, {10934, 63177}, {11194, 17274}, {11329, 48627}, {11343, 17304}, {11347, 23681}, {11499, 24209}, {11500, 17861}, {12114, 64122}, {12635, 55391}, {15668, 30097}, {16367, 17247}, {16412, 24199}, {16603, 17327}, {17132, 21539}, {17246, 54285}, {17276, 36743}, {17301, 36744}, {17355, 21526}, {17357, 31231}, {20470, 20876}, {20872, 22464}, {20905, 26267}, {21296, 54391}, {22753, 24179}, {24177, 37269}, {24796, 62779}, {24993, 26229}, {25440, 53594}, {26125, 41245}, {27623, 41526}, {27624, 62799}, {27659, 55405}, {27661, 55466}, {28083, 28113}, {28385, 63014}, {28402, 52134}, {28653, 61158}, {28739, 43053}, {28780, 31230}, {28978, 37789}, {31395, 36279}, {31643, 56129}, {34445, 56783}, {37499, 37555}, {37541, 52086}, {37583, 59247}, {37681, 61037}, {38859, 62783}, {40726, 50116}, {41004, 57278}, {44356, 55118}, {62781, 63574}, {62837, 62999}

X(64827) = reflection of X(i) in X(j) for these {i,j}: {59237, 3}
X(64827) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 39956}, {21, 56192}, {41, 40012}, {55, 34860}, {200, 56155}, {220, 42304}, {284, 56123}, {3158, 60789}, {3161, 60806}, {3169, 60807}, {4041, 8690}
X(64827) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 34860}, {478, 39956}, {3160, 40012}, {4394, 4534}, {6609, 56155}, {20317, 11}, {40590, 56123}, {40611, 56192}
X(64827) = X(i)-cross conjugate of X(j) for these {i, j}: {3214, 57}, {3915, 4383}
X(64827) = pole of line {3676, 4367} with respect to the circumcircle
X(64827) = pole of line {7178, 23729} with respect to the incircle
X(64827) = pole of line {10391, 17599} with respect to the Feuerbach hyperbola
X(64827) = pole of line {8, 3794} with respect to the Wallace hyperbola
X(64827) = pole of line {3664, 5711} with respect to the dual conic of Yff parabola
X(64827) = pole of line {6, 57} with respect to the dual conic of Moses-Feuerbach circumconic
X(64827) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(28387)}}, {{A, B, C, X(21), X(3217)}}, {{A, B, C, X(37), X(3214)}}, {{A, B, C, X(75), X(33947)}}, {{A, B, C, X(86), X(3875)}}, {{A, B, C, X(934), X(57950)}}, {{A, B, C, X(1001), X(35108)}}, {{A, B, C, X(1014), X(56358)}}, {{A, B, C, X(1444), X(15728)}}, {{A, B, C, X(3175), X(17321)}}, {{A, B, C, X(3286), X(16946)}}, {{A, B, C, X(3665), X(58008)}}, {{A, B, C, X(4106), X(17139)}}, {{A, B, C, X(4139), X(17768)}}, {{A, B, C, X(4389), X(56253)}}, {{A, B, C, X(4998), X(7023)}}, {{A, B, C, X(16705), X(18135)}}, {{A, B, C, X(17103), X(40438)}}, {{A, B, C, X(20992), X(56853)}}, {{A, B, C, X(52803), X(57858)}}
X(64827) = barycentric product X(i)*X(j) for these (i, j): {269, 30568}, {279, 3913}, {348, 4186}, {1014, 3175}, {1088, 3217}, {1412, 56253}, {1420, 27813}, {1434, 3214}, {3875, 57}, {3915, 85}, {4106, 651}, {4139, 4573}, {4383, 7}, {4498, 664}, {16946, 6063}, {18135, 56}, {20317, 934}, {21963, 4620}, {28387, 86}, {36838, 58334}, {42312, 658}, {57785, 61036}
X(64827) = barycentric quotient X(i)/X(j) for these (i, j): {7, 40012}, {56, 39956}, {57, 34860}, {65, 56123}, {269, 42304}, {1400, 56192}, {1407, 56155}, {3175, 3701}, {3214, 2321}, {3217, 200}, {3875, 312}, {3913, 346}, {3915, 9}, {4106, 4391}, {4139, 3700}, {4186, 281}, {4383, 8}, {4498, 522}, {4565, 8690}, {16945, 60806}, {16946, 55}, {17214, 17197}, {17477, 2170}, {18135, 3596}, {20317, 4397}, {21963, 21044}, {23777, 21132}, {28387, 10}, {30568, 341}, {40151, 60789}, {42312, 3239}, {56253, 30713}, {58334, 4130}, {61036, 210}
X(64827) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17321, 41003}, {56, 1284, 1001}, {604, 52896, 6180}, {934, 62787, 7023}, {1122, 1319, 77}, {1400, 7225, 5228}, {1423, 1429, 6}, {9310, 28351, 25878}

X(64828) = ISOGONAL CONJUGATE OF X(55259)

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(-2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

Let A1 be the intersection of the perpendicular bisector of BC and line AX39173 and similarly define B1 and C1. Then A1, B1, and C1 are collinear on a line with tripole X(64828). (Ivan Pavlov, 17 Aug 2024).

X(64828) lies on these lines: {2, 6}, {21, 24482}, {99, 32722}, {110, 9058}, {190, 14570}, {511, 7425}, {513, 4236}, {645, 648}, {651, 662}, {671, 54548}, {691, 2746}, {859, 63852}, {1331, 2617}, {2397, 2427}, {2398, 7253}, {2966, 35147}, {3110, 60698}, {3658, 53406}, {3737, 54353}, {4221, 59787}, {4560, 62669}, {4573, 62532}, {4833, 23344}, {10755, 56154}, {15418, 55256}, {17139, 51987}, {36280, 37019}, {52663, 57985}

X(64828) = isogonal conjugate of X(55259)
X(64828) = trilinear pole of line {859, 42746}
X(64828) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55259}, {10, 2423}, {42, 2401}, {65, 61238}, {71, 43933}, {104, 661}, {512, 34234}, {513, 2250}, {523, 909}, {647, 36123}, {649, 38955}, {798, 18816}, {810, 16082}, {1018, 15635}, {1400, 43728}, {1577, 34858}, {1795, 2501}, {1809, 55208}, {1880, 37628}, {1919, 57984}, {2342, 7178}, {2433, 52640}, {2720, 21044}, {3120, 32641}, {3122, 13136}, {3125, 36037}, {4017, 52663}, {4041, 34051}, {4120, 10428}, {4466, 14776}, {4516, 37136}, {7180, 51565}, {14578, 24006}, {15501, 55242}, {18785, 57468}, {21828, 40437}, {36110, 53560}, {36795, 51641}, {36819, 55261}, {36944, 55263}, {55255, 56638}
X(64828) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55259}, {908, 4707}, {1145, 3700}, {1769, 52341}, {2245, 53527}, {3259, 3125}, {5375, 38955}, {9296, 57984}, {16586, 1577}, {23980, 523}, {25640, 2501}, {31998, 18816}, {34961, 52663}, {36830, 104}, {38981, 21044}, {39004, 53560}, {39026, 2250}, {39052, 36123}, {39054, 34234}, {39062, 16082}, {40582, 43728}, {40592, 2401}, {40602, 61238}, {40613, 661}, {45247, 61179}, {46398, 16732}
X(64828) = pole of line {669, 16680} with respect to the circumcircle
X(64828) = pole of line {2501, 3125} with respect to the polar circle
X(64828) = pole of line {99, 104} with respect to the Kiepert parabola
X(64828) = pole of line {6, 650} with respect to the Stammler hyperbola
X(64828) = pole of line {523, 7477} with respect to the Steiner circumellipse
X(64828) = pole of line {523, 34977} with respect to the Steiner inellipse
X(64828) = pole of line {4427, 7283} with respect to the Yff parabola
X(64828) = pole of line {190, 321} with respect to the Hutson-Moses hyperbola
X(64828) = pole of line {2, 905} with respect to the Wallace hyperbola
X(64828) = pole of line {14570, 31623} with respect to the dual conic of Jerabek hyperbola
X(64828) = pole of line {3265, 53332} with respect to the dual conic of Orthic inconic
X(64828) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(651)}}, {{A, B, C, X(6), X(1415)}}, {{A, B, C, X(69), X(668)}}, {{A, B, C, X(81), X(648)}}, {{A, B, C, X(86), X(811)}}, {{A, B, C, X(100), X(1150)}}, {{A, B, C, X(110), X(26637)}}, {{A, B, C, X(190), X(14829)}}, {{A, B, C, X(230), X(14571)}}, {{A, B, C, X(325), X(3262)}}, {{A, B, C, X(333), X(662)}}, {{A, B, C, X(394), X(1332)}}, {{A, B, C, X(517), X(524)}}, {{A, B, C, X(645), X(1812)}}, {{A, B, C, X(859), X(52897)}}, {{A, B, C, X(908), X(3936)}}, {{A, B, C, X(940), X(23981)}}, {{A, B, C, X(1213), X(61170)}}, {{A, B, C, X(1310), X(56433)}}, {{A, B, C, X(1465), X(35466)}}, {{A, B, C, X(1993), X(46640)}}, {{A, B, C, X(2183), X(2238)}}, {{A, B, C, X(2287), X(5546)}}, {{A, B, C, X(2804), X(9034)}}, {{A, B, C, X(2966), X(19623)}}, {{A, B, C, X(4238), X(37142)}}, {{A, B, C, X(4585), X(9268)}}, {{A, B, C, X(4604), X(17277)}}, {{A, B, C, X(4606), X(5372)}}, {{A, B, C, X(5712), X(23706)}}, {{A, B, C, X(5739), X(53151)}}, {{A, B, C, X(10026), X(21801)}}, {{A, B, C, X(11064), X(42716)}}, {{A, B, C, X(17139), X(30941)}}, {{A, B, C, X(17757), X(44396)}}, {{A, B, C, X(32040), X(46922)}}, {{A, B, C, X(36099), X(37642)}}, {{A, B, C, X(36106), X(37136)}}, {{A, B, C, X(37783), X(44769)}}, {{A, B, C, X(40571), X(46639)}}, {{A, B, C, X(42757), X(45952)}}
X(64828) = barycentric product X(i)*X(j) for these (i, j): {100, 17139}, {110, 3262}, {517, 99}, {662, 908}, {668, 859}, {1145, 4622}, {1414, 6735}, {1444, 53151}, {1457, 7257}, {1465, 645}, {1769, 4600}, {1785, 4592}, {2183, 799}, {2397, 81}, {2427, 274}, {3310, 4601}, {4246, 69}, {4584, 51381}, {4596, 51409}, {4614, 51423}, {4616, 51380}, {4620, 46393}, {4623, 51377}, {10015, 4567}, {14260, 55243}, {14571, 4563}, {15507, 4589}, {16586, 47318}, {17757, 52935}, {21801, 4610}, {22350, 811}, {22464, 643}, {23706, 332}, {23788, 765}, {23981, 314}, {24029, 333}, {36038, 4570}, {36797, 62402}, {42746, 46141}, {51987, 55260}, {55258, 6}
X(64828) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55259}, {21, 43728}, {28, 43933}, {81, 2401}, {99, 18816}, {100, 38955}, {101, 2250}, {110, 104}, {162, 36123}, {163, 909}, {283, 37628}, {284, 61238}, {517, 523}, {643, 51565}, {645, 36795}, {648, 16082}, {662, 34234}, {668, 57984}, {859, 513}, {908, 1577}, {1333, 2423}, {1457, 4017}, {1465, 7178}, {1576, 34858}, {1769, 3120}, {1785, 24006}, {2183, 661}, {2397, 321}, {2427, 37}, {3262, 850}, {3286, 57468}, {3310, 3125}, {3658, 14266}, {3733, 15635}, {4236, 51832}, {4246, 4}, {4565, 34051}, {4567, 13136}, {4570, 36037}, {4575, 1795}, {5379, 1309}, {5546, 52663}, {6735, 4086}, {7435, 64635}, {7477, 38952}, {8677, 18210}, {10015, 16732}, {14010, 42455}, {14260, 55244}, {14571, 2501}, {15507, 4010}, {15632, 17757}, {16586, 4707}, {17139, 693}, {17757, 4036}, {21801, 4024}, {22350, 656}, {22464, 4077}, {23706, 225}, {23788, 1111}, {23981, 65}, {24029, 226}, {32661, 14578}, {34586, 53527}, {35049, 47317}, {36038, 21207}, {39173, 3657}, {42746, 2771}, {42757, 42759}, {46393, 21044}, {51377, 4705}, {51379, 52355}, {51409, 30591}, {51423, 4815}, {51433, 4404}, {51987, 55261}, {52031, 4049}, {52307, 53560}, {52378, 37136}, {53151, 41013}, {53530, 30572}, {53548, 53551}, {53549, 4516}, {54353, 36819}, {55258, 76}, {61672, 14431}, {62402, 17094}, {63852, 35353}

X(64829) = X(4)X(83)∩X(575)X(55005)

Barycentrics    a^2*(-2*a^6*b^2*c^2+2*a^8*(b^2+c^2)+b^2*c^2*(b^6-5*b^4*c^2-5*b^2*c^4+c^6)-2*a^4*(b^6+4*b^4*c^2+4*b^2*c^4+c^6)-a^2*(5*b^6*c^2+12*b^4*c^4+5*b^2*c^6)) : :
X(64829) = -3*X[597]+X[31869], -X[31989]+7*X[55708], -X[48262]+5*X[53093]

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6782.

X(64829) lies on the circumconic {{A, B, C, X(32581), X(55075)}} and these lines: {4, 83}, {575, 55005}, {576, 14134}, {597, 31869}, {1503, 64494}, {20190, 55075}, {31989, 55708}, {48262, 53093}

X(64829) = midpoint of X(576) and X(14134)

X(64830) = X(7)X(40)∩X(516)X(550)

Barycentrics    2*a^6-7*a^4*(b-c)^2+a^5*(b+c)+a*(b-c)^4*(b+c)-3*(b-c)^4*(b+c)^2-2*a^3*(b+c)^3+4*a^2*(b-c)^2*(2*b^2+b*c+2*c^2) : :
X(64830) = 3*X[7]+X[40], -X[9]+3*X[38123], -X[144]+3*X[38130], -X[355]+3*X[51100], -5*X[631]+X[60905], -X[946]+3*X[6173], -X[962]+9*X[59375], -X[1482]+3*X[5542], -3*X[2550]+X[47745], X[2951]+3*X[59386], -X[5698]+3*X[10165], -3*X[5759]+7*X[16192], -X[5779]+3*X[38204], 5*X[5818]+3*X[36996]

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6782.

X(64830) lies on these lines: {1, 60993}, {3, 30424}, {7, 40}, {9, 38123}, {30, 43181}, {46, 61021}, {142, 3358}, {144, 38130}, {165, 3982}, {355, 51100}, {515, 5880}, {516, 550}, {517, 43180}, {527, 6684}, {528, 13607}, {553, 5536}, {631, 60905}, {946, 6173}, {950, 64155}, {962, 59375}, {971, 3812}, {1482, 5542}, {2550, 47745}, {2801, 3918}, {2951, 59386}, {3336, 52819}, {3338, 60923}, {3485, 4312}, {3634, 64198}, {3671, 54178}, {4114, 41338}, {4297, 52682}, {5698, 10165}, {5714, 9814}, {5715, 45084}, {5735, 31730}, {5759, 16192}, {5762, 31663}, {5779, 38204}, {5784, 5884}, {5805, 43182}, {5818, 36996}, {5850, 12607}, {5851, 10172}, {6172, 31423}, {6260, 60987}, {6701, 61595}, {6850, 17706}, {6908, 60982}, {6940, 60885}, {7982, 30340}, {8227, 59374}, {8543, 37561}, {8545, 59333}, {8726, 30353}, {9940, 15726}, {10175, 64197}, {10394, 15016}, {10595, 38024}, {10902, 30295}, {11372, 62778}, {11531, 35514}, {12005, 15733}, {18230, 41705}, {18443, 28150}, {25681, 38122}, {26878, 61003}, {28194, 60895}, {28534, 50828}, {30275, 37526}, {30287, 62864}, {30331, 37624}, {30379, 64124}, {31672, 38151}, {33558, 58567}, {35010, 51768}, {37532, 60945}, {37560, 60953}, {38036, 64696}, {38054, 63983}, {38055, 64703}, {38107, 63973}, {38149, 64697}, {38158, 60884}, {38172, 60901}, {40273, 61509}, {49107, 60999}, {50371, 64110}, {58433, 60911}, {61028, 63967}

X(64830) = midpoint of X(i) and X(j) for these {i,j}: {3, 30424}, {142, 60896}, {946, 63971}, {4297, 52682}, {5735, 31730}, {5784, 5884}, {5805, 43182}, {5880, 43177}
X(64830) = reflection of X(i) in X(j) for these {i,j}: {6684, 64113}, {13464, 25557}, {60911, 58433}, {64198, 3634}, {64699, 61595}
X(64830) = pole of line {3554, 4328} with respect to the dual conic of the Yff parabola
X(64830) = X(5095)-of-K798i triangle
X(64830) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 25557, 13464}, {527, 64113, 6684}, {5880, 43177, 515}, {6173, 63971, 946}

X(64831) = X(2)X(2489)∩X(1499)X(3850)

Barycentrics    (b-c)*(b+c)*(-a^8+2*a^6*(b^2+c^2)+2*b^2*c^2*(b^4-3*b^2*c^2+c^4)+a^4*(6*b^4-19*b^2*c^2+6*c^4)-3*a^2*(b^6-2*b^4*c^2-2*b^2*c^4+c^6)) : :
X(64831) = -5*X[3522]+9*X[11633], -X[14135]+3*X[38237]

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6782.

X(64831) lies on these lines: {4, 2489}, {148, 64807}, {1499, 3850}, {3522, 11633}, {6658, 8644}, {14135, 38237}, {43674, 60209}

X(64831) = midpoint of X(148) and X(64807)
X(64831) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {148, 6719, 14090}

X(64832) = X(4)X(6591)∩X(3309)X(9955)

Barycentrics    (b-c)*(-a^6+a^5*(b+c)+a^4*(-2*b^2+7*b*c-2*c^2)+2*b*c*(b^2-c^2)^2+2*a^3*(b^3-4*b^2*c-4*b*c^2+c^3)+3*a^2*(b^4+b^3*c+b*c^3+c^4)-a*(3*b^5+b^4*c-2*b^3*c^2-2*b^2*c^3+b*c^4+3*c^5)) : :
X(64832) = 3*X[8027]+X[64527], -3*X[38238]+X[64531]

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6782.

X(64832) lies on these lines: {4, 6591}, {513, 24387}, {3309, 9955}, {8027, 64527}, {30234, 37256}, {38238, 64531}

X(64832) = midpoint of X(148) and X(64807)
X(64832) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {149, 6714, 14079}

X(64833) = 61st TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8-2*(b^2+c^2)*a^6+2*b^4*a^4-2*(b^6-c^6)*a^2+(b^4-c^4)*(b^2-c^2)^2)*(a^8-2*(b^2+c^2)*a^6+2*c^4*a^4+2*(b^6-c^6)*a^2-(b^4-c^4)*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung, problem 02/07/2024 (1).

X(64833) lies on these lines: {2, 20564}, {6, 70}, {111, 1288}, {115, 36416}, {251, 10550}, {1400, 2158}, {2165, 7505}, {2433, 55228}, {3767, 8882}, {5523, 59162}, {17907, 42354}, {28706, 42407}

X(64833) = polar conjugate of X(44128)
X(64833) = cevapoint of X(115) and X(6753)
X(64833) = X(44077)-cross conjugate of-X(4)
X(64833) = X(i)-Dao conjugate of-X(j) for these (i, j): (1249, 44128), (3162, 26), (5139, 55204), (15259, 8746)
X(64833) = X(i)-isoconjugate of-X(j) for these {i, j}: {26, 63}, {48, 44128}, {304, 44078}, {326, 8746}, {4592, 55204}, {24018, 52918}
X(64833) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 44128), (25, 26), (70, 69), (1288, 99), (1974, 44078), (2158, 63), (2207, 8746), (2489, 55204), (14581, 52953), (20564, 305), (32713, 52918), (44077, 34116), (55203, 52608), (55228, 525), (57415, 20563), (59162, 9723)
X(64833) = trilinear pole of the line {512, 55228} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64833) = pole of the the tripolar of X(44128) with respect to the polar circle
X(64833) = pole of the line {24, 70} with respect to the Kiepert circumhyperbola
X(64833) = barycentric product X(i)*X(j) for these {i, j}: {4, 70}, {24, 57415}, {25, 20564}, {92, 2158}, {523, 1288}, {648, 55228}, {847, 59162}, {2489, 55203}
X(64833) = trilinear product X(i)*X(j) for these {i, j}: {4, 2158}, {19, 70}, {162, 55228}, {661, 1288}, {1973, 20564}
X(64833) = trilinear quotient X(i)/X(j) for these (i, j): (19, 26), (70, 63), (92, 44128), (1096, 8746), (1288, 662), (1973, 44078), (2158, 3), (20564, 304), (24019, 52918), (55203, 55202), (55228, 656)

X(64834) = 62nd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2+b*a-c^2+b^2)*(a^2+c*a-b^2+c^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung, problem 02/07/2024 (1).

X(64834) lies on these lines: {19, 1990}, {28, 30602}, {33, 430}, {53, 11076}, {79, 1172}, {278, 18688}, {281, 451}, {1880, 1989}, {3064, 55236}, {6591, 43082}, {7129, 52372}, {17923, 20565}, {20624, 26700}

X(64834) = polar conjugate of X(319)
X(64834) = crosssum of X(219) and X(22136)
X(64834) = X(i)-cross conjugate of-X(j) for these (i, j): (1841, 19), (2355, 4), (6186, 79)
X(64834) = X(i)-Dao conjugate of-X(j) for these (i, j): (136, 7265), (1249, 319), (3162, 35), (5139, 55210), (5190, 4467), (5521, 14838), (6523, 52412), (7952, 42033), (14993, 52351), (15295, 52431), (20620, 57066), (32664, 52408), (36103, 3219), (39062, 55235), (40584, 52437), (40627, 22094), (40837, 17095), (47345, 40999), (53982, 42701), (55053, 23226), (56847, 306), (62602, 52421), (62605, 33939)
X(64834) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 52408}, {3, 3219}, {35, 63}, {48, 319}, {69, 2174}, {71, 56934}, {72, 40214}, {73, 56440}, {77, 52405}, {78, 2003}, {97, 35194}, {184, 33939}, {190, 23226}, {212, 17095}, {219, 1442}, {222, 4420}, {228, 34016}, {255, 52412}, {283, 16577}, {306, 17104}, {307, 35192}, {323, 1807}, {332, 21741}, {333, 22342}, {345, 1399}, {394, 6198}, {603, 42033}, {810, 55235}, {906, 4467}, {1214, 35193}, {1331, 14838}, {1332, 2605}, {1437, 3969}, {1790, 3678}, {1794, 16585}, {1796, 3647}, {1812, 2594}, {1813, 35057}, {1825, 6514}, {2161, 52437}, {2193, 40999}, {2289, 7282}, {3926, 14975}, {4558, 57099}, {4567, 22094}, {4575, 7265}, {4592, 55210}, {6149, 52351}, {6513, 56535}, {6516, 9404}
X(64834) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 319), (19, 3219), (25, 35), (27, 34016), (28, 56934), (31, 52408), (33, 4420), (34, 1442), (36, 52437), (79, 69), (92, 33939), (225, 40999), (273, 52421), (278, 17095), (281, 42033), (393, 52412), (607, 52405), (608, 2003), (648, 55235), (667, 23226), (1096, 6198), (1118, 7282), (1172, 56440), (1395, 1399), (1402, 22342), (1474, 40214), (1824, 3678), (1826, 3969), (1839, 3578), (1841, 16585), (1859, 31938), (1880, 16577), (1973, 2174), (1989, 52351), (2160, 63), (2181, 35194), (2203, 17104), (2204, 35192), (2299, 35193), (2355, 3647), (2489, 55210), (2501, 7265), (3064, 57066), (3122, 22094), (3615, 332), (4707, 45792), (6186, 3), (6344, 20566), (6591, 14838), (6742, 4561)
X(64834) = trilinear pole of the line {18344, 55236} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64834) = Zosma transform of X(16553)
X(64834) = pole of the line {4467, 7265} with respect to the polar circle
X(64834) = barycentric product X(i)*X(j) for these {i, j}: {4, 79}, {11, 34922}, {19, 30690}, {25, 20565}, {27, 8818}, {28, 6757}, {29, 52382}, {34, 52344}, {36, 6344}, {92, 2160}, {94, 52413}, {158, 7100}, {225, 3615}, {264, 6186}, {273, 7073}, {278, 7110}, {281, 52374}, {318, 52372}, {320, 18384}, {393, 52381}
X(64834) = trilinear product X(i)*X(j) for these {i, j}: {4, 2160}, {19, 79}, {25, 30690}, {28, 8818}, {33, 52374}, {34, 7110}, {92, 6186}, {162, 55236}, {278, 7073}, {281, 52372}, {393, 7100}, {608, 52344}, {1096, 52381}, {1172, 52382}, {1474, 6757}, {1824, 52393}, {1826, 52375}, {1839, 57419}, {1841, 57710}, {1870, 1989}
X(64834) = trilinear quotient X(i)/X(j) for these (i, j): (4, 3219), (6, 52408), (19, 35), (25, 2174), (27, 56934), (28, 40214), (29, 56440), (33, 52405), (34, 2003), (53, 35194), (79, 63), (92, 319), (158, 52412), (225, 16577), (264, 33939), (273, 17095), (278, 1442), (281, 4420), (286, 34016), (318, 42033)

X(64835) = 63rd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-b*a-c^2+b^2)*(a^2-c*a-b^2+c^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung, problem 02/07/2024 (1).

X(64835) lies on these lines: {19, 53}, {33, 7140}, {80, 1172}, {278, 2006}, {281, 15065}, {759, 59083}, {1411, 7129}, {1785, 8756}, {1877, 8755}, {1880, 1989}, {1990, 11069}, {2173, 38945}, {2222, 20624}, {2983, 21675}, {6335, 20566}, {7079, 56416}

X(64835) = polar conjugate of X(320)
X(64835) = isogonal conjugate of X(22128)
X(64835) = cevapoint of X(1826) and X(8756)
X(64835) = crosspoint of X(6336) and X(36123)
X(64835) = crosssum of X(i) and X(j) for these {i, j}: {219, 22141}, {22350, 22356}
X(64835) = X(281)-beth conjugate of-X(1783)
X(64835) = X(i)-cross conjugate of-X(j) for these (i, j): (6187, 80), (14571, 19), (47235, 1783)
X(64835) = X(i)-Dao conjugate of-X(j) for these (i, j): (136, 4707), (1249, 320), (3162, 36), (5139, 21828), (5190, 4453), (5521, 3960), (6523, 17923), (7952, 32851), (14993, 52381), (15259, 52413), (15898, 63), (20619, 51583), (20620, 3904), (25640, 16586), (32664, 52407), (36103, 3218), (36909, 345), (39062, 55237), (40837, 17078), (47345, 41804), (55053, 22379), (56416, 3977), (62576, 40075), (62605, 20924)
X(64835) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 52407}, {3, 3218}, {36, 63}, {48, 320}, {69, 7113}, {77, 2323}, {184, 20924}, {190, 22379}, {212, 17078}, {214, 1797}, {219, 1443}, {222, 4511}, {255, 17923}, {283, 18593}, {295, 27950}, {304, 52434}, {307, 4282}, {323, 7100}, {326, 52413}, {345, 52440}, {348, 2361}, {394, 1870}, {603, 32851}, {654, 6516}, {758, 1790}, {810, 55237}, {860, 18604}, {906, 4453}, {1227, 32659}, {1331, 3960}, {1332, 53314}, {1437, 3936}, {1444, 2245}, {1459, 4585}, {1464, 1812}, {1795, 16586}, {1796, 4973}, {1813, 3738}, {1835, 6514}, {1983, 4025}, {2160, 52437}, {2193, 41804}, {3724, 17206}, {3904, 36059}, {3977, 16944}, {4091, 4242}, {4558, 53527}, {4561, 21758}, {4575, 4707}, {4592, 21828}
X(64835) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 320), (19, 3218), (25, 36), (31, 52407), (33, 4511), (34, 1443), (35, 52437), (80, 69), (92, 20924), (225, 41804), (264, 40075), (278, 17078), (281, 32851), (393, 17923), (607, 2323), (648, 55237), (667, 22379), (759, 1444), (1096, 1870), (1395, 52440), (1411, 77), (1783, 4585), (1807, 326), (1824, 758), (1826, 3936), (1857, 5081), (1877, 41801), (1880, 18593), (1973, 7113), (1974, 52434), (1989, 52381), (2006, 348), (2161, 63), (2201, 27950), (2204, 4282), (2207, 52413), (2212, 2361), (2222, 6516), (2333, 2245), (2341, 1812), (2355, 4973), (2489, 21828), (2501, 4707), (2969, 4089), (3064, 3904), (6059, 52427), (6187, 3), (6344, 20565), (6591, 3960), (6740, 332)
X(64835) = trilinear pole of the line {1824, 18344} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64835) = Zosma transform of X(16554)
X(64835) = pole of the line {3904, 3960} with respect to the polar circle
X(64835) = barycentric product X(i)*X(j) for these {i, j}: {4, 80}, {19, 18359}, {25, 20566}, {28, 15065}, {29, 52383}, {33, 18815}, {34, 52409}, {35, 6344}, {92, 2161}, {108, 52356}, {158, 1807}, {225, 6740}, {264, 6187}, {273, 52371}, {278, 36910}, {281, 2006}, {286, 34857}, {318, 1411}, {319, 18384}, {393, 52351}
X(64835) = trilinear product X(i)*X(j) for these {i, j}: {4, 2161}, {19, 80}, {25, 18359}, {27, 34857}, {33, 2006}, {34, 36910}, {92, 6187}, {94, 14975}, {158, 52431}, {162, 55238}, {225, 2341}, {278, 52371}, {281, 1411}, {393, 1807}, {607, 18815}, {608, 52409}, {655, 18344}, {759, 1826}, {1096, 52351}, {1168, 8756}
X(64835) = trilinear quotient X(i)/X(j) for these (i, j): (4, 3218), (6, 52407), (19, 36), (25, 7113), (33, 2323), (80, 63), (92, 320), (158, 17923), (225, 18593), (242, 27950), (264, 20924), (273, 17078), (278, 1443), (281, 4511), (318, 32851), (393, 1870), (607, 2361), (608, 52440), (649, 22379), (655, 6516)

X(64836) = 64th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (5*a^2-2*b*a-5*c^2+5*b^2)*(5*a^2-2*c*a+5*c^2-5*b^2) : :
X(64836) = 13*X(19877)-8*X(63751)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 03/07/2024.

X(64836) lies on the Feuerbach hyperbola and these lines: {1, 3832}, {9, 53620}, {21, 4413}, {80, 9812}, {104, 19541}, {355, 7317}, {938, 5557}, {962, 43734}, {1000, 59387}, {1156, 41712}, {1320, 41711}, {1387, 50864}, {1479, 13606}, {1837, 5556}, {3241, 51792}, {3296, 5722}, {3436, 15998}, {3680, 20053}, {4678, 4866}, {4900, 31145}, {5080, 6601}, {5252, 7320}, {5559, 30305}, {5561, 18391}, {5809, 34917}, {6246, 64330}, {7319, 10248}, {9802, 12641}, {10307, 31672}, {10580, 18490}, {17613, 55918}, {18421, 61992}, {34919, 59412}, {35258, 46933}, {36926, 56076}

X(64836) = isotomic conjugate of the anticomplement of X(16670)
X(64836) = cevapoint of X(11) and X(6006)
X(64836) = X(16670)-cross conjugate of-X(2)
X(64836) = trilinear pole of the line {650, 28169} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64836) = perspector of the inconic with center X(16670)
X(64836) = trilinear quotient X(31145)/X(63913)

X(64837) = 65th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (-a^2+b^2+c^2)*(3*a^8-14*(b^2+c^2)*a^6-4*(2*b^4+13*b^2*c^2+2*c^4)*a^4+2*(b^2+c^2)*(3*b^4-14*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^2*(b^2-3*c^2)*(3*b^2-c^2)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/07/2024.

X(64837) lies on these lines: {3, 6340}, {1216, 3547}, {14853, 31360}

X(64838) = 66th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (-a^2+b^2+c^2)*(3*a^20-20*(b^2+c^2)*a^18+(53*b^4+94*b^2*c^2+53*c^4)*a^16-16*(b^2+c^2)*(4*b^4+9*b^2*c^2+4*c^4)*a^14+2*(7*b^8+7*c^8+2*(72*b^4+41*b^2*c^2+72*c^4)*b^2*c^2)*a^12+8*(b^2+c^2)*(7*b^8+7*c^8-2*(20*b^4-17*b^2*c^2+20*c^4)*b^2*c^2)*a^10-2*(b^2-c^2)^2*(35*b^8+35*c^8-2*(4*b^4+59*b^2*c^2+4*c^4)*b^2*c^2)*a^8+16*(b^4-c^4)*(b^2-c^2)^3*(2*b^4+3*b^2*c^2+2*c^4)*a^6-(b^2-c^2)^4*(b^4+6*b^2*c^2+c^4)*(b^4+14*b^2*c^2+c^4)*a^4-4*(b^2-c^2)^8*(b^2+c^2)*a^2+(b^2-c^2)^10) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/07/2024.

X(64838) lies on these lines: {3, 60114}, {20, 9308}, {185, 6193}

X(64839) = 67th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(2*a^3-(b+c)*a^2-2*(b^2-17*b*c+c^2)*a+(b^2-c^2)*(b-c)) : :
X(64839) = 7*X(1)+X(10980)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 10/07/2024.

X(64839) lies on these lines: {1, 3}, {1058, 33697}, {9655, 51791}, {9669, 51789}, {11019, 38176}, {11035, 31828}, {12127, 16863}, {38140, 51782}, {42819, 61000}, {61281, 64116}

X(64840) = 68th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*((2*b+c)*a^5-2*b*c*a^4-2*(2*b^3+c^3)*a^3+(b^4-c^4)*(2*b-c)*a+2*(b^2-c^2)^2*b*c)*((b+2*c)*a^5-2*b*c*a^4-2*(b^3+2*c^3)*a^3+(b^4-c^4)*(b-2*c)*a+2*(b^2-c^2)^2*b*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64840) lies on these lines: {1, 7524}, {3, 2654}, {77, 64053}, {78, 7532}, {283, 60691}, {284, 59223}, {1795, 41344}, {1936, 56336}, {3422, 10046}, {6198, 56104}, {7531, 23707}

X(64840) = isogonal conjugate of the Cundy-Parry-Psi-transform of X(2654)
X(64840) = Cundy-Parry-Phi-transform of X(2654)
X(64840) = X(64841)-reciprocal conjugate of-X(63)
X(64840) = barycentric product X(92)*X(64841)
X(64840) = trilinear product X(4)*X(64841)

X(64841) = 69th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(-a^2+b^2+c^2)*((2*b+c)*a^5-2*b*c*a^4-2*(2*b^3+c^3)*a^3+(b^4-c^4)*(2*b-c)*a+2*(b^2-c^2)^2*b*c)*((b+2*c)*a^5-2*b*c*a^4-2*(b^3+2*c^3)*a^3+(b^4-c^4)*(b-2*c)*a+2*(b^2-c^2)^2*b*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64841) lies on these lines: {3, 2654}, {21, 51282}, {255, 40946}, {6875, 56261}

X(64841) = X(64840)-reciprocal conjugate of-X(92)
X(64841) = barycentric product X(63)*X(64840)
X(64841) = trilinear product X(3)*X(64840)

X(64842) = 70th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(-a^2+b^2+c^2)*((2*b^2+c^2)*a^6-2*(2*b^4+b^2*c^2+c^4)*a^4+(b^4-c^4)*(2*b^2-c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2)*((b^2+2*c^2)*a^6-2*(b^4+b^2*c^2+2*c^4)*a^4+(b^4-c^4)*(b^2-2*c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64842) lies on these lines: {3, 14767}, {182, 19210}, {577, 43650}, {7485, 56337}, {37068, 56307}

X(64842) = isotomic conjugate of the polar conjugate of X(64846)
X(64842) = X(1147)-Dao conjugate of-X(26874)
X(64842) = X(158)-isoconjugate of-X(26874)
X(64842) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (577, 26874), (56341, 2052), (64846, 4)
X(64842) = barycentric product X(i)*X(j) for these {i, j}: {69, 64846}, {394, 56341}
X(64842) = trilinear product X(i)*X(j) for these {i, j}: {63, 64846}, {255, 56341}
X(64842) = trilinear quotient X(i)/X(j) for these (i, j): (255, 26874), (56341, 158)

X(64843) = 71st TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^3-(2*b+c)*a^2-2*(b^2+c^2)*a+(b^2-c^2)*(2*b-c))*(2*a^3-(b+2*c)*a^2-2*(b^2+c^2)*a+(b^2-c^2)*(b-2*c)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64843) lies on these lines: {4, 2646}, {29, 5705}, {158, 40950}, {273, 3664}, {281, 17275}, {318, 6737}, {7524, 56261}

X(64843) = polar conjugate of X(31266)
X(64843) = X(1249)-Dao conjugate of-X(31266)
X(64843) = X(48)-isoconjugate of-X(31266)
X(64843) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 31266), (56027, 63), (56062, 69), (56336, 394)
X(64843) = trilinear pole of the line {3064, 48277} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64843) = pole of the the tripolar of X(31266) with respect to the polar circle
X(64843) = barycentric product X(i)*X(j) for these {i, j}: {4, 56062}, {92, 56027}, {2052, 56336}
X(64843) = trilinear product X(i)*X(j) for these {i, j}: {4, 56027}, {19, 56062}, {158, 56336}
X(64843) = trilinear quotient X(i)/X(j) for these (i, j): (92, 31266), (56027, 3), (56062, 63), (56336, 255)

X(64844) = 72nd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^6-(2*b^2+3*c^2)*a^4-2*(b^2-5*c^2)*b^2*a^2+(2*b^2+c^2)*(b^2-c^2)^2)*(2*a^6-(3*b^2+2*c^2)*a^4+2*(5*b^2-c^2)*c^2*a^2+(b^2+2*c^2)*(b^2-c^2)^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64844) lies on these lines: {4, 56068}, {264, 13488}, {382, 32085}, {393, 7748}, {1093, 1885}, {1179, 35490}, {1597, 14860}, {8884, 44438}

X(64844) = Cundy-Parry-Phi-transform of the polar conjugate of X(53415)
X(64844) = X(56068)-reciprocal conjugate of-X(394)
X(64844) = trilinear pole of the line {2501, 33968} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64844) = barycentric product X(2052)*X(56068)
X(64844) = trilinear product X(158)*X(56068)
X(64844) = trilinear quotient X(56068)/X(255)

X(64845) = 73rd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*((2*b+c)*a+2*b*c)*((b+2*c)*a+2*b*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64845) lies on these lines: {1, 57397}, {6, 748}, {31, 2241}, {81, 4384}, {604, 56496}, {739, 6013}, {873, 3759}, {1206, 2162}, {1333, 2280}, {1449, 10458}, {1911, 61358}, {1914, 34819}, {2205, 9346}, {2214, 46772}, {2298, 17156}, {4289, 28607}, {9345, 21753}, {14621, 37685}, {18785, 62819}, {32864, 63066}

X(64845) = isogonal conjugate of X(4687)
X(64845) = cevapoint of X(1015) and X(4832)
X(64845) = cross-difference of every pair of points on the line X(6005)X(47666)
X(64845) = X(56208)-beth conjugate of-X(56208)
X(64845) = X(1185)-cross conjugate of-X(31)
X(64845) = X(i)-Dao conjugate of-X(j) for these (i, j): (1084, 48407), (8054, 47666), (32664, 17018), (38996, 50483), (55053, 6005)
X(64845) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 17018}, {100, 47666}, {190, 6005}, {312, 16878}, {321, 39673}, {662, 48407}, {799, 50483}, {1978, 8655}
X(64845) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (31, 17018), (512, 48407), (649, 47666), (667, 6005), (669, 50483), (1397, 16878), (1980, 8655), (2206, 39673), (6013, 668), (10013, 75), (17110, 34284), (46772, 313), (56051, 76), (56087, 3596), (56208, 312), (56236, 321), (56496, 7)
X(64845) = barycentric product X(i)*X(j) for these {i, j}: {1, 10013}, {6, 56051}, {8, 56496}, {56, 56087}, {57, 56208}, {58, 46772}, {81, 56236}, {513, 6013}, {941, 17110}
X(64845) = trilinear product X(i)*X(j) for these {i, j}: {6, 10013}, {9, 56496}, {31, 56051}, {56, 56208}, {58, 56236}, {604, 56087}, {649, 6013}, {1333, 46772}, {2258, 17110}
X(64845) = trilinear quotient X(i)/X(j) for these (i, j): (6, 17018), (513, 47666), (604, 16878), (649, 6005), (661, 48407), (798, 50483), (1333, 39673), (1919, 8655), (6013, 190), (10013, 2), (17110, 10436), (46772, 321), (56051, 75), (56087, 312), (56208, 8), (56236, 10), (56496, 57)
X(64845) = (X(10013), X(56208))-harmonic conjugate of X(56236)

X(64846) = 74th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*((2*b^2+c^2)*a^6-2*(2*b^4+b^2*c^2+c^4)*a^4+(b^4-c^4)*(2*b^2-c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2)*((b^2+2*c^2)*a^6-2*(b^4+b^2*c^2+2*c^4)*a^4+(b^4-c^4)*(b^2-2*c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/07/2024.

X(64846) lies on these lines: {6, 42400}, {394, 59197}, {577, 43650}, {10311, 14533}, {15004, 52177}

X(64846) = isogonal conjugate of the polar conjugate of X(56341)
X(64846) = polar conjugate of the isotomic conjugate of X(64842)
X(64846) = X(22391)-Dao conjugate of-X(26874)
X(64846) = X(92)-isoconjugate of-X(26874)
X(64846) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (184, 26874), (56341, 264), (64842, 69)
X(64846) = barycentric product X(i)*X(j) for these {i, j}: {3, 56341}, {4, 64842}
X(64846) = trilinear product X(i)*X(j) for these {i, j}: {19, 64842}, {48, 56341}
X(64846) = trilinear quotient X(i)/X(j) for these (i, j): (48, 26874), (56341, 92)

X(64847) = 75th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a+b-c)*(a-b+c)*(25*a-23*b-23*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 12/07/2024.

X(64847) lies on these lines: {1, 3}, {3982, 6049}, {7967, 51792}, {10595, 51790}, {11545, 61282}

X(64847) = pole of the line {513, 4770} with respect to the (circumcircle, incircle)-inverter)

X(64848) = 76th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a+b-c)*(a-b+c)*(8*a-7*b-7*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 12/07/2024.

X(64848) lies on these lines: {1, 3}, {499, 61284}, {551, 1317}, {1404, 39260}, {1442, 56049}, {1478, 61279}, {1483, 17606}, {1737, 61283}, {3241, 31188}, {3476, 4870}, {3622, 37738}, {3623, 24914}, {3625, 7294}, {3635, 5433}, {3636, 10944}, {3742, 64353}, {3983, 30144}, {4315, 51104}, {5252, 38314}, {5434, 39782}, {6049, 10404}, {7741, 32900}, {7972, 11230}, {10175, 62617}, {10283, 17605}, {10573, 61282}, {11545, 61286}, {14151, 29007}, {15570, 37787}, {15950, 51103}, {20057, 41687}, {20118, 31397}, {24798, 25723}, {24805, 25716}, {26877, 37518}, {30384, 50824}, {40663, 51071}, {42871, 60947}, {43179, 60993}, {45287, 61278}, {51714, 64337}, {51767, 64732}, {51786, 56177}

X(64848) = crosssum of X(1) and X(10247)
X(64848) = X(34641)-beth conjugate of-X(34641)
X(64848) = X(34641)-reciprocal conjugate of-X(312)
X(64848) = barycentric product X(57)*X(34641)
X(64848) = trilinear product X(56)*X(34641)
X(64848) = trilinear quotient X(34641)/X(8)
X(64848) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 25405, 354), (1, 64849, 56), (1319, 11011, 57), (3057, 13751, 65)

X(64849) = 77th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a+b-c)*(a-b+c)*(9*a-7*b-7*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 12/07/2024.

X(64849) lies on these lines: {1, 3}, {145, 31231}, {226, 6049}, {499, 61291}, {551, 9578}, {997, 4540}, {1317, 1698}, {1616, 2003}, {1737, 61288}, {1788, 51071}, {3247, 54377}, {3476, 3636}, {3485, 51103}, {3616, 37709}, {3622, 5219}, {3623, 3911}, {3624, 37738}, {3633, 5433}, {3635, 7288}, {3646, 12739}, {3655, 9614}, {3679, 38411}, {3890, 5083}, {3897, 41554}, {4308, 4654}, {4537, 57279}, {4848, 20057}, {4917, 38460}, {5727, 13607}, {5882, 50443}, {7330, 19907}, {7967, 9581}, {9579, 10595}, {9612, 10283}, {9613, 61276}, {10106, 38314}, {10895, 61274}, {10944, 25055}, {11373, 50824}, {11375, 51105}, {11530, 41553}, {12735, 38128}, {14923, 45036}, {15325, 61284}, {16489, 64020}, {17090, 25716}, {18990, 61279}, {19861, 37736}, {20014, 31188}, {20196, 24558}, {24914, 51093}, {37518, 64021}, {37707, 54447}, {38316, 51683}, {41864, 64703}, {45287, 61275}, {47444, 62705}, {63915, 64135}, {64041, 64260}

X(64849) = crosssum of X(1) and X(16189)
X(64849) = X(20052)-beth conjugate of-X(20052)
X(64849) = X(20052)-reciprocal conjugate of-X(312)
X(64849) = pole of the line {513, 50767} with respect to the (circumcircle, incircle)-inverter)
X(64849) = pole of the line {672, 17502} with respect to the Gheorghe circle
X(64849) = pole of the line {513, 24841} with respect to the Hatzipolakis-Lozada, circle
X(64849) = pole of the line {910, 17502} with respect to the Stevanovic circle
X(64849) = pole of the line {1, 60944} with respect to the Feuerbach circumhyperbola
X(64849) = barycentric product X(57)*X(20052)
X(64849) = trilinear product X(56)*X(20052)
X(64849) = trilinear quotient X(20052)/X(8)
X(64849) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 63208, 57), (56, 64848, 1), (25405, 37624, 1)

X(64850) = 78th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    3*a+4*b+4*c : :
X(64850) = X(1)-4*X(5550) = X(1)+4*X(46933) = 3*X(2)+X(46933) = X(8)+7*X(5550) = X(8)-7*X(46933) = 2*X(10)+3*X(5550) = 2*X(10)-3*X(46933) = 4*X(1125)-5*X(5550) = 4*X(1125)+5*X(46933)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 18/07/2024.

X(64850) lies on these lines: {1, 2}, {3, 7989}, {4, 10172}, {5, 165}, {9, 3336}, {11, 51559}, {12, 3361}, {20, 58441}, {35, 4413}, {36, 16408}, {37, 61313}, {40, 1656}, {46, 7308}, {55, 16853}, {56, 5726}, {57, 50726}, {58, 17124}, {72, 58451}, {75, 56061}, {79, 63276}, {80, 31235}, {100, 17534}, {115, 31421}, {140, 5587}, {141, 31312}, {169, 16546}, {191, 3305}, {210, 18398}, {226, 5586}, {274, 20943}, {312, 28611}, {355, 632}, {377, 18513}, {381, 35242}, {405, 5010}, {442, 16118}, {443, 3585}, {452, 4324}, {474, 5251}, {484, 5087}, {495, 50038}, {515, 3525}, {516, 5056}, {517, 5070}, {547, 12699}, {549, 61261}, {550, 61263}, {569, 9586}, {590, 13947}, {594, 62648}, {595, 17125}, {599, 36834}, {615, 13893}, {631, 5691}, {756, 24046}, {942, 4005}, {944, 31399}, {946, 5067}, {952, 55859}, {958, 16862}, {960, 4004}, {962, 10171}, {984, 31238}, {988, 56736}, {993, 17531}, {1001, 16854}, {1051, 41930}, {1054, 52785}, {1089, 19804}, {1126, 9345}, {1155, 50740}, {1203, 37679}, {1213, 1743}, {1224, 8056}, {1268, 3875}, {1282, 31273}, {1329, 5234}, {1376, 5259}, {1385, 37712}, {1478, 17582}, {1479, 17559}, {1482, 55860}, {1483, 41992}, {1621, 17546}, {1697, 50444}, {1699, 3090}, {1702, 10577}, {1703, 10576}, {1706, 37563}, {1707, 32781}, {1724, 17122}, {1750, 6889}, {1757, 3834}, {1768, 38133}, {1829, 52298}, {1837, 5326}, {1995, 9591}, {2049, 37603}, {2093, 5445}, {2476, 64112}, {2478, 18514}, {2550, 4857}, {2551, 5270}, {2886, 17575}, {2948, 15059}, {2951, 6838}, {2979, 58474}, {3035, 12690}, {3062, 38108}, {3091, 10164}, {3097, 3934}, {3099, 7914}, {3159, 64435}, {3306, 6763}, {3333, 31479}, {3337, 5437}, {3339, 3649}, {3340, 39782}, {3416, 51126}, {3454, 25961}, {3523, 19925}, {3524, 31673}, {3526, 3576}, {3533, 5818}, {3545, 31730}, {3555, 3848}, {3579, 5055}, {3583, 5084}, {3586, 16845}, {3601, 17606}, {3614, 9579}, {3620, 59408}, {3628, 7991}, {3646, 5119}, {3647, 9352}, {3648, 58449}, {3653, 37705}, {3654, 61272}, {3655, 47598}, {3656, 47599}, {3678, 3894}, {3681, 58565}, {3683, 37572}, {3697, 3742}, {3698, 5697}, {3715, 5708}, {3731, 17303}, {3739, 25503}, {3740, 4533}, {3746, 4423}, {3751, 3763}, {3754, 3899}, {3760, 60706}, {3767, 31428}, {3812, 4018}, {3814, 4197}, {3817, 7486}, {3820, 37719}, {3822, 55867}, {3824, 3929}, {3825, 33108}, {3826, 4187}, {3832, 12512}, {3833, 3868}, {3839, 50829}, {3841, 4193}, {3842, 4751}, {3844, 16475}, {3851, 31663}, {3855, 28150}, {3873, 4015}, {3874, 4547}, {3876, 3901}, {3877, 3918}, {3892, 4540}, {3911, 5290}, {3921, 34791}, {3922, 5903}, {3925, 7741}, {3931, 31318}, {3943, 16673}, {3947, 4355}, {3962, 5044}, {3968, 14923}, {3971, 64437}, {3973, 5750}, {3983, 5045}, {4002, 58679}, {4021, 5936}, {4040, 48196}, {4063, 31251}, {4065, 27812}, {4075, 17155}, {4297, 10303}, {4298, 64114}, {4299, 17580}, {4302, 5129}, {4312, 18230}, {4316, 6904}, {4333, 5177}, {4338, 61029}, {4357, 4902}, {4358, 28612}, {4383, 37559}, {4385, 6533}, {4389, 25590}, {4527, 17286}, {4640, 41872}, {4647, 18743}, {4654, 34502}, {4663, 21358}, {4687, 49474}, {4698, 49462}, {4699, 49445}, {4700, 63055}, {4731, 9957}, {4755, 49452}, {4757, 10176}, {4806, 47837}, {4855, 5426}, {4859, 26104}, {4892, 41812}, {4909, 28626}, {4995, 41864}, {5020, 37557}, {5047, 9342}, {5054, 18480}, {5068, 51118}, {5071, 18483}, {5072, 28146}, {5079, 22793}, {5090, 52297}, {5094, 7713}, {5128, 17605}, {5154, 35258}, {5184, 31275}, {5217, 16857}, {5220, 38093}, {5223, 20195}, {5248, 17536}, {5249, 31446}, {5252, 7294}, {5257, 54389}, {5258, 16864}, {5260, 17535}, {5261, 31188}, {5264, 17123}, {5265, 51782}, {5267, 17572}, {5284, 8715}, {5294, 16570}, {5296, 32857}, {5316, 12047}, {5328, 18249}, {5432, 9581}, {5433, 9578}, {5441, 6675}, {5442, 7951}, {5443, 24954}, {5444, 37711}, {5493, 9779}, {5506, 10129}, {5531, 38752}, {5541, 31272}, {5563, 9708}, {5603, 58245}, {5640, 31737}, {5657, 11522}, {5687, 8167}, {5690, 9624}, {5698, 6666}, {5715, 6877}, {5731, 61856}, {5734, 58241}, {5790, 55858}, {5791, 30393}, {5817, 64698}, {5847, 63119}, {5881, 16239}, {5882, 61873}, {5886, 11531}, {5901, 16189}, {6264, 34126}, {6282, 6861}, {6376, 52716}, {6459, 9584}, {6565, 9582}, {6668, 25525}, {6687, 31151}, {6690, 17590}, {6702, 15015}, {6707, 17296}, {6828, 21153}, {6842, 10270}, {6853, 63988}, {6863, 30503}, {6878, 64261}, {6882, 10268}, {6897, 41698}, {6913, 59326}, {6918, 59320}, {6949, 63992}, {6960, 12565}, {6989, 10857}, {7161, 15296}, {7173, 9580}, {7174, 25539}, {7226, 24167}, {7484, 8185}, {7509, 9590}, {7516, 9626}, {7585, 49619}, {7586, 49618}, {7746, 9593}, {7786, 9902}, {7808, 10789}, {7982, 11230}, {7992, 18243}, {7993, 57298}, {7999, 31760}, {8040, 36250}, {8148, 61882}, {8164, 64124}, {8252, 18992}, {8253, 18991}, {8270, 56469}, {8972, 49547}, {9306, 9587}, {9312, 41807}, {9350, 33771}, {9574, 13881}, {9575, 31489}, {9585, 35255}, {9592, 31455}, {9612, 53056}, {9616, 42262}, {9622, 13353}, {9778, 12571}, {9782, 26792}, {9812, 61914}, {9819, 50443}, {9860, 64089}, {9875, 64019}, {9896, 64181}, {9897, 34122}, {9899, 64024}, {9901, 36770}, {9903, 31268}, {9904, 64101}, {10124, 34773}, {10156, 12680}, {10246, 55866}, {10404, 50395}, {10436, 17250}, {10589, 51785}, {10591, 38059}, {10592, 44847}, {10595, 16191}, {10827, 24953}, {10882, 19549}, {10896, 35445}, {10980, 50394}, {11010, 31262}, {11015, 58404}, {11219, 20400}, {11263, 27131}, {11278, 38066}, {11362, 61881}, {11363, 52292}, {11372, 38318}, {11375, 18421}, {11451, 31757}, {11518, 61648}, {11530, 64203}, {11539, 18357}, {11681, 62824}, {11852, 15184}, {12407, 38794}, {12526, 30852}, {12560, 61017}, {12622, 55168}, {12645, 61289}, {12653, 32557}, {12702, 15703}, {12767, 15017}, {12782, 31239}, {13174, 14061}, {13178, 31274}, {13374, 15104}, {13624, 15694}, {13731, 61124}, {13883, 13942}, {13888, 13936}, {13911, 32790}, {13941, 49548}, {13973, 32789}, {13996, 16173}, {14005, 52680}, {14217, 38319}, {14269, 50812}, {14531, 58548}, {14869, 61259}, {15028, 31732}, {15043, 31752}, {15079, 59337}, {15082, 23841}, {15338, 51792}, {15689, 51088}, {15692, 38076}, {15699, 31162}, {15705, 50862}, {15706, 50820}, {15707, 58219}, {15708, 34648}, {15709, 50796}, {15712, 61262}, {15717, 28164}, {15720, 28160}, {15723, 28204}, {16143, 22798}, {16200, 61878}, {16209, 37438}, {16297, 52139}, {16414, 39578}, {16417, 59319}, {16418, 59325}, {16456, 37522}, {16468, 17259}, {16469, 17337}, {16472, 17825}, {16473, 17811}, {16667, 17398}, {16844, 37574}, {16859, 63752}, {16866, 63756}, {16975, 25614}, {17057, 17619}, {17151, 17322}, {17163, 58387}, {17210, 33947}, {17275, 61302}, {17277, 43997}, {17291, 26083}, {17293, 60688}, {17306, 33159}, {17371, 50314}, {17393, 32089}, {17502, 55863}, {17504, 50799}, {17552, 59572}, {17578, 59420}, {17592, 39564}, {17754, 46196}, {18140, 32092}, {18193, 32780}, {18493, 50821}, {18526, 61871}, {19249, 23361}, {19265, 23383}, {19280, 32916}, {19321, 37576}, {19705, 63754}, {19732, 37604}, {19873, 19932}, {19927, 19937}, {19933, 19972}, {19944, 46894}, {20182, 25431}, {20582, 51124}, {21356, 64073}, {21385, 30795}, {21735, 28172}, {23058, 52705}, {24003, 25529}, {24049, 59218}, {24176, 32925}, {24178, 63621}, {24183, 33115}, {24184, 33161}, {24325, 49501}, {24342, 28546}, {24392, 64123}, {24720, 47794}, {24821, 27191}, {24926, 51577}, {24957, 52068}, {25086, 44798}, {25264, 41836}, {25466, 31190}, {25507, 64072}, {26060, 37162}, {26066, 30827}, {28154, 61970}, {28158, 50689}, {28174, 61900}, {28186, 61837}, {28190, 61808}, {28194, 61895}, {28198, 61908}, {28202, 61925}, {28208, 61843}, {28604, 55998}, {28609, 28646}, {28618, 56018}, {28620, 64401}, {30337, 37704}, {30424, 61023}, {30598, 32025}, {30963, 32104}, {31160, 57005}, {31209, 47724}, {31237, 49500}, {31243, 49712}, {31260, 37710}, {31264, 56522}, {31289, 49709}, {31418, 59675}, {31419, 34501}, {31422, 39565}, {31445, 37524}, {31447, 48661}, {31657, 52665}, {32261, 64764}, {32771, 59666}, {33152, 39559}, {33535, 34128}, {34127, 64749}, {34573, 38047}, {34627, 61866}, {34632, 61897}, {34638, 61954}, {34790, 50190}, {34860, 56134}, {35018, 61265}, {36152, 50204}, {37244, 59334}, {37552, 56735}, {37608, 56767}, {37624, 38176}, {37633, 55103}, {37680, 62805}, {37727, 61876}, {38028, 55862}, {38034, 61894}, {38049, 63120}, {38057, 58433}, {38074, 61865}, {38075, 43178}, {38081, 61292}, {38089, 50952}, {38101, 43180}, {38112, 61276}, {38118, 39878}, {38122, 64697}, {38182, 38762}, {38282, 49542}, {38317, 64084}, {38763, 49176}, {39781, 64849}, {40273, 61266}, {40296, 61705}, {40328, 49448}, {40334, 51688}, {40335, 51690}, {40660, 61735}, {41861, 58634}, {41984, 50824}, {43174, 46935}, {43830, 43866}, {44314, 45684}, {44381, 50776}, {44401, 50250}, {45326, 49276}, {45829, 53002}, {46895, 53039}, {46916, 63999}, {47478, 50825}, {47683, 47829}, {47726, 47807}, {48037, 48573}, {48197, 48352}, {48205, 50346}, {48216, 48320}, {48218, 48282}, {48883, 50416}, {49483, 59582}, {49511, 63121}, {50050, 51590}, {50054, 51593}, {50393, 59491}, {50788, 63027}, {50802, 61906}, {50803, 62120}, {50807, 61917}, {50808, 61924}, {50813, 61959}, {50815, 61812}, {50816, 62032}, {50828, 61861}, {50866, 62130}, {50869, 61962}, {50871, 58231}, {50874, 61983}, {51078, 62029}, {51083, 58204}, {51586, 62322}, {51700, 61288}, {51705, 61859}, {51709, 61883}, {52027, 63964}, {52654, 56051}, {54357, 58405}, {54430, 60782}, {54445, 58229}, {54448, 61848}, {55169, 58712}, {55170, 58722}, {55864, 59387}, {56453, 60786}, {58213, 61788}, {58248, 61884}, {58453, 59415}, {59372, 60996}, {59382, 64668}, {59400, 61284}, {60905, 60986}, {61244, 61874}, {61258, 61853}, {61260, 61824}, {61275, 61877}, {61291, 61510}, {61294, 61875}, {61330, 63978}, {63310, 63344}, {64178, 64436}

X(64850) = midpoint of X(5550) and X(46933)
X(64850) = complement of X(5550)
X(64850) = X(28230)-complementary conjugate of-X(513)
X(64850) = X(39026)-Dao conjugate of-X(28200)
X(64850) = X(513)-isoconjugate of-X(28200)
X(64850) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (101, 28200), (28199, 514), (58181, 649)
X(64850) = pole of the line {4057, 28165} with respect to the circumcircle
X(64850) = pole of the line {28175, 44316} with respect to the nine-point circle
X(64850) = pole of the line {3667, 48106} with respect to the orthoptic circle of Steiner inellipse
X(64850) = pole of the line {962, 3667} with respect to the Spieker circle
X(64850) = pole of the line {2, 4007} with respect to the circumhyperbola dual of Yff parabola
X(64850) = pole of the line {3057, 34747} with respect to the Feuerbach circumhyperbola
X(64850) = pole of the line {1213, 1449} with respect to the Kiepert circumhyperbola
X(64850) = pole of the line {514, 4820} with respect to the Steiner inellipse
X(64850) = pole of the line {86, 34595} with respect to the Steiner-Wallace hyperbola
X(64850) = barycentric product X(i)*X(j) for these {i, j}: {190, 28199}, {1978, 58181}
X(64850) = trilinear product X(i)*X(j) for these {i, j}: {100, 28199}, {668, 58181}
X(64850) = trilinear quotient X(i)/X(j) for these (i, j): (100, 28200), (28199, 513), (58181, 667)
X(64850) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 1698, 1), (8, 25055, 1), (10, 3624, 1), (499, 31434, 1), (551, 3633, 1), (978, 56191, 1), (1125, 3679, 1), (3086, 51784, 1), (3244, 51105, 1), (3293, 26102, 1), (3616, 3632, 1), (3622, 51093, 1), (3634, 19872, 1), (4816, 15808, 1), (5313, 59305, 1), (6048, 25502, 1), (17284, 29633, 1), (19875, 34595, 1), (29598, 29674, 1), (49997, 59311, 1)

X(64851) = X(4)X(1216)∩X(52)X(428)

Barycentrics    a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^4-2 a^2 b^2+b^4-2 a^2 c^2-4 b^2 c^2+c^4) (a^4 b^2-2 a^2 b^4+b^6+a^4 c^2-8 a^2 b^2 c^2-b^4 c^2-2 a^2 c^4-b^2 c^4+c^6) : :
X(64851) = 2*X(1216)-3*X(11487), 3*X(3527)-4*X(10110)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6792.

X(64851) lies on these lines: {4, 1216}, {5, 46026}, {6, 1598}, {25, 13336}, {51, 34564}, {52, 428}, {113, 1906}, {143, 16624}, {155, 5198}, {185, 6756}, {193, 5446}, {1593, 33543}, {1596, 3574}, {1839, 1872}, {1843, 10263}, {1986, 46682}, {3518, 6030}, {3567, 6995}, {5422, 10594}, {5462, 7714}, {5895, 13474}, {6623, 44871}, {7576, 10575}, {7715, 12006}, {9730, 37122}, {10117, 19348}, {11576, 13431}, {12162, 40909}, {13202, 15738}, {13754, 15741}, {16194, 46027}, {26863, 52675}, {44079, 58531}, {45186, 64062}, {61664, 64759}

X(64851) = midpoint of X(4) and X(11387)
X(64851) = reflection of X(10625) in X(42021)
X(64851) = barycentric product X(1595)*X(5422)

X(64852) = 92ND HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^6 - 3*a^4*b^2 - 2*a^2*b^4 + 3*b^6 - 3*a^4*c^2 - 3*b^4*c^2 - 2*a^2*c^4 - 3*b^2*c^4 + 3*c^6 : :
X(64852) = 9 X[2] - X[22], 3 X[2] + X[427], 15 X[2] + X[7391], 33 X[2] - X[20062], 13 X[2] + 3 X[31105], 7 X[2] + X[31133], 3 X[2] + 5 X[31236], 5 X[2] - X[44210], 11 X[2] - 3 X[47596], 3 X[5] + X[18570], 5 X[5] - X[44263], X[22] + 3 X[427], X[22] - 3 X[6676], 5 X[22] + 3 X[7391], 11 X[22] - 3 X[20062], 13 X[22] + 27 X[31105], 7 X[22] + 9 X[31133], X[22] + 15 X[31236], 5 X[22] - 9 X[44210], 11 X[22] - 27 X[47596], X[378] + 7 X[3090], 3 X[381] + X[44249], 5 X[427] - X[7391], 11 X[427] + X[20062], 13 X[427] - 9 X[31105], 7 X[427] - 3 X[31133], X[427] - 5 X[31236], 5 X[427] + 3 X[44210], 11 X[427] + 9 X[47596], 3 X[547] + X[44236], 3 X[547] - X[46029], 3 X[549] + X[44288], 5 X[631] - X[44239], 5 X[632] - X[7502], 5 X[1656] - X[15760], 5 X[1656] + X[64474], 7 X[3523] + X[52842], 11 X[3525] - 3 X[44837], 7 X[3526] + X[31723], 17 X[3533] - X[44831], 9 X[3545] - X[35480], 3 X[3545] + X[44285], 3 X[5055] + X[44218], 33 X[5070] - X[44457], 15 X[5071] + X[35481], 5 X[6676] + X[7391], 11 X[6676] - X[20062], 13 X[6676] + 9 X[31105], 7 X[6676] + 3 X[31133], X[6676] + 5 X[31236], 5 X[6676] - 3 X[44210], 11 X[6676] - 9 X[47596], 11 X[7391] + 5 X[20062], 13 X[7391] - 45 X[31105], 7 X[7391] - 15 X[31133], X[7391] - 25 X[31236], X[7391] + 3 X[44210], 11 X[7391] + 45 X[47596], 17 X[7486] - X[44440], X[7555] - 7 X[55862], X[12082] - 25 X[60781], X[12083] - 17 X[55857], 5 X[15694] - X[44261], 3 X[15699] + X[44287], X[16618] - 7 X[55856], 5 X[18570] + 3 X[44263], X[18570] - 3 X[52262], 13 X[20062] + 99 X[31105], 7 X[20062] + 33 X[31133], X[20062] + 55 X[31236], 5 X[20062] - 33 X[44210], X[20062] - 9 X[47596], X[25337] - 5 X[48154], 21 X[31105] - 13 X[31133], 9 X[31105] - 65 X[31236], 15 X[31105] + 13 X[44210], 11 X[31105] + 13 X[47596], 3 X[31133] - 35 X[31236], 5 X[31133] + 7 X[44210], 11 X[31133] + 21 X[47596], 25 X[31236] + 3 X[44210], 55 X[31236] + 9 X[47596], X[35480] + 3 X[44285], 11 X[44210] - 15 X[47596], X[44262] - 5 X[61885], X[44263] + 5 X[52262], X[184] + 3 X[45303], X[343] + 3 X[61743], 9 X[373] - X[54384], 3 X[6688] - X[58480], 3 X[21243] + X[34986], 3 X[23292] - X[34986], 5 X[3763] - X[16789], 3 X[10175] + X[51707], X[11442] + 3 X[61690], X[11550] + 3 X[13394], X[19127] - 5 X[51126], 5 X[19862] - X[51692]

See Antreas Hatzipolakis and Peter Moses, euclid 6798.

X(64852) lies on these lines: {2, 3}, {10, 51718}, {125, 37649}, {141, 9813}, {154, 39884}, {182, 23332}, {184, 45303}, {343, 34380}, {373, 54384}, {394, 61545}, {578, 61544}, {614, 37729}, {1194, 47298}, {1196, 43291}, {1352, 59553}, {1353, 11427}, {1503, 58447}, {1853, 48906}, {2781, 6688}, {3054, 10314}, {3410, 61655}, {3564, 21243}, {3580, 53863}, {3589, 6697}, {3763, 16789}, {3818, 10192}, {5050, 23291}, {5268, 37697}, {5272, 37696}, {5480, 61646}, {5943, 21851}, {6329, 32068}, {6340, 32829}, {6515, 61624}, {6667, 58402}, {6668, 58403}, {7583, 8280}, {7584, 8281}, {7736, 59657}, {7746, 40326}, {8254, 43588}, {8770, 43620}, {8854, 18538}, {8855, 18762}, {9019, 9822}, {9306, 18358}, {9729, 32396}, {9826, 40685}, {10175, 51707}, {10516, 59543}, {10961, 32789}, {10963, 32790}, {11056, 45201}, {11245, 14389}, {11433, 59399}, {11442, 61690}, {11550, 13394}, {11574, 51994}, {11898, 63092}, {12164, 43841}, {13292, 34826}, {13567, 18583}, {14561, 26958}, {14767, 44377}, {15252, 24239}, {15880, 18907}, {17810, 38136}, {18289, 42215}, {18290, 42216}, {18553, 61681}, {18950, 53091}, {19127, 19137}, {19862, 51692}, {20204, 30794}, {21015, 56464}, {24206, 53415}, {26869, 52719}, {26933, 56462}, {30768, 59642}, {30792, 44815}, {32767, 64038}, {34481, 63534}, {34803, 50572}, {37638, 41588}, {38110, 61735}, {38397, 41628}, {39530, 53506}, {44817, 45689}, {46261, 61606}, {47256, 59742}, {47354, 59699}, {53022, 61737}, {56304, 63175}, {58408, 58464}, {64060, 64067}

X(64852) = midpoint of X(i) and X(j) for these {i,j}: {5, 52262}, {10, 51718}, {140, 39504}, {141, 51744}, {427, 6676}, {11574, 51994}, {15760, 64474}, {16196, 45179}, {21243, 23292}, {44236, 46029}
X(64852) = complement of X(6676)
X(64852) = X(54703)-complementary conjugate of X(20305)
X(64852) = crosssum of X(6) and X(21637)
X(64852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 6677}, {2, 427, 6676}, {2, 858, 7499}, {2, 1368, 140}, {2, 1995, 52297}, {2, 3091, 38282}, {2, 5094, 1368}, {2, 5133, 468}, {2, 6677, 37911}, {2, 6997, 37453}, {2, 7398, 52290}, {2, 8889, 3}, {2, 11548, 3628}, {2, 16051, 16419}, {2, 16419, 632}, {2, 30744, 30739}, {2, 31074, 7495}, {2, 31236, 427}, {2, 37454, 11548}, {2, 52284, 7494}, {2, 52299, 30771}, {2, 62958, 5159}, {5, 140, 9825}, {5, 547, 44912}, {5, 549, 18420}, {5, 632, 6642}, {5, 3628, 58465}, {5, 6677, 10128}, {5, 7526, 546}, {5, 9818, 44920}, {5, 44452, 10127}, {5, 63838, 11737}, {125, 37649, 45298}, {140, 546, 1658}, {140, 1368, 7734}, {140, 5094, 47629}, {140, 61736, 63860}, {427, 44210, 7391}, {547, 44236, 46029}, {547, 50142, 35018}, {632, 7516, 140}, {858, 7499, 10691}, {1656, 7404, 5}, {2454, 2455, 40889}, {3090, 11479, 5}, {3628, 11737, 15350}, {3628, 32144, 140}, {5000, 5001, 23047}, {5020, 7484, 6644}, {5055, 18537, 5}, {5094, 5159, 32144}, {5159, 11548, 2}, {5159, 37454, 3628}, {5169, 37897, 3861}, {5576, 7542, 6756}, {6639, 7403, 21841}, {6644, 23323, 31830}, {6756, 7542, 44277}, {6997, 37453, 44212}, {7378, 9909, 3627}, {7399, 37119, 16196}, {7494, 34609, 550}, {7494, 52284, 34609}, {7495, 31074, 7667}, {7495, 47315, 33923}, {7499, 10691, 3530}, {7539, 52298, 2}, {7569, 37119, 7399}, {7667, 31074, 47315}, {7734, 47629, 1368}, {10128, 37911, 6677}, {10565, 62975, 382}, {13361, 35018, 37439}, {14389, 23293, 11245}, {37439, 52293, 2}, {37454, 62958, 2}, {37649, 45298, 51732}, {44232, 50136, 23411}, {44920, 63679, 9818}, {47612, 47613, 12362}

X(64853) = 93RD HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^4 - 5*a^2*b^2 + 3*b^4 - 8*a^2*b*c - 8*a*b^2*c - 5*a^2*c^2 - 8*a*b*c^2 - 6*b^2*c^2 + 3*c^4 : :
X(64853) = 9 X[2] - X[21], 3 X[2] + X[442], 15 X[2] + X[2475], 7 X[2] + X[6175], 5 X[2] - X[15670], 11 X[2] - 3 X[15671], 19 X[2] - 3 X[15672], 7 X[2] - X[15673], 21 X[2] - 5 X[15674], 29 X[2] - 5 X[15675], 39 X[2] - 7 X[15676], 17 X[2] - X[15677], 25 X[2] - X[15678], 23 X[2] + X[15679], 33 X[2] - X[15680], 13 X[2] - X[17525], 3 X[2] + 5 X[31254], 21 X[2] - X[57002], 7 X[5] + X[31651], 5 X[5] - X[44258], X[21] + 3 X[442], 5 X[21] + 3 X[2475], 7 X[21] + 9 X[6175], X[21] - 3 X[6675], 5 X[21] - 9 X[15670], 11 X[21] - 27 X[15671], 19 X[21] - 27 X[15672], 7 X[21] - 9 X[15673], 7 X[21] - 15 X[15674], 29 X[21] - 45 X[15675], 13 X[21] - 21 X[15676], 17 X[21] - 9 X[15677], 25 X[21] - 9 X[15678], 23 X[21] + 9 X[15679], 11 X[21] - 3 X[15680], 13 X[21] - 9 X[17525], X[21] + 15 X[31254], 7 X[21] - 3 X[57002], 5 X[442] - X[2475], 7 X[442] - 3 X[6175], 5 X[442] + 3 X[15670], 11 X[442] + 9 X[15671], 19 X[442] + 9 X[15672], 7 X[442] + 3 X[15673], 7 X[442] + 5 X[15674], 29 X[442] + 15 X[15675], 13 X[442] + 7 X[15676], 17 X[442] + 3 X[15677], 25 X[442] + 3 X[15678], 23 X[442] - 3 X[15679], 11 X[442] + X[15680], 13 X[442] + 3 X[17525], X[442] - 5 X[31254], 7 X[442] + X[57002], 3 X[547] + X[11277], 3 X[547] - X[46028], 5 X[631] - X[44238], 5 X[632] - X[5428], 5 X[1656] - X[6841], 15 X[1656] + X[16117], 7 X[2475] - 15 X[6175], X[2475] + 5 X[6675], X[2475] + 3 X[15670], 11 X[2475] + 45 X[15671], 19 X[2475] + 45 X[15672], 7 X[2475] + 15 X[15673], 7 X[2475] + 25 X[15674], 29 X[2475] + 75 X[15675], 13 X[2475] + 35 X[15676], 17 X[2475] + 15 X[15677], 5 X[2475] + 3 X[15678], 23 X[2475] - 15 X[15679], 11 X[2475] + 5 X[15680], 13 X[2475] + 15 X[17525], X[2475] - 25 X[31254], 7 X[2475] + 5 X[57002], 7 X[3090] + X[3651], 7 X[3523] + X[52841], 11 X[3525] - 3 X[21161], 7 X[3526] - 3 X[28465], 7 X[3526] + X[37230], 11 X[5056] - 3 X[52269], 13 X[5067] - X[37447], 11 X[5070] + X[37401], X[5499] + 7 X[55856], 3 X[6175] + 7 X[6675], 5 X[6175] + 7 X[15670], 11 X[6175] + 21 X[15671], 19 X[6175] + 21 X[15672], 3 X[6175] + 5 X[15674], 29 X[6175] + 35 X[15675], 39 X[6175] + 49 X[15676], 17 X[6175] + 7 X[15677], 25 X[6175] + 7 X[15678], 23 X[6175] - 7 X[15679], 33 X[6175] + 7 X[15680], 13 X[6175] + 7 X[17525], 3 X[6175] - 35 X[31254], 3 X[6175] + X[57002], 5 X[6675] - 3 X[15670], 11 X[6675] - 9 X[15671], 19 X[6675] - 9 X[15672], 7 X[6675] - 3 X[15673], 7 X[6675] - 5 X[15674], 29 X[6675] - 15 X[15675], 13 X[6675] - 7 X[15676], 17 X[6675] - 3 X[15677], 25 X[6675] - 3 X[15678], 23 X[6675] + 3 X[15679], 11 X[6675] - X[15680], 13 X[6675] - 3 X[17525], X[6675] + 5 X[31254], 7 X[6675] - X[57002], 3 X[6841] + X[16117], 17 X[7486] - X[37433], X[10021] - 5 X[48154], X[12104] - 7 X[55862], X[13743] - 17 X[55857], 11 X[15670] - 15 X[15671], 19 X[15670] - 15 X[15672], 7 X[15670] - 5 X[15673], 21 X[15670] - 25 X[15674], 29 X[15670] - 25 X[15675], 39 X[15670] - 35 X[15676], 17 X[15670] - 5 X[15677], 5 X[15670] - X[15678], 23 X[15670] + 5 X[15679], 33 X[15670] - 5 X[15680], 13 X[15670] - 5 X[17525], 3 X[15670] + 25 X[31254], 21 X[15670] - 5 X[57002], 19 X[15671] - 11 X[15672], 21 X[15671] - 11 X[15673], 63 X[15671] - 55 X[15674], 87 X[15671] - 55 X[15675], 117 X[15671] - 77 X[15676], 51 X[15671] - 11 X[15677], 75 X[15671] - 11 X[15678], 69 X[15671] + 11 X[15679], 9 X[15671] - X[15680], 39 X[15671] - 11 X[17525], 9 X[15671] + 55 X[31254], 63 X[15671] - 11 X[57002], 21 X[15672] - 19 X[15673], 63 X[15672] - 95 X[15674], 87 X[15672] - 95 X[15675], 51 X[15672] - 19 X[15677], 75 X[15672] - 19 X[15678], 69 X[15672] + 19 X[15679], 99 X[15672] - 19 X[15680], 39 X[15672] - 19 X[17525], 9 X[15672] + 95 X[31254], 63 X[15672] - 19 X[57002], 3 X[15673] - 5 X[15674], 29 X[15673] - 35 X[15675], 39 X[15673] - 49 X[15676], 17 X[15673] - 7 X[15677], 25 X[15673] - 7 X[15678], 23 X[15673] + 7 X[15679], 33 X[15673] - 7 X[15680], 13 X[15673] - 7 X[17525], 3 X[15673] + 35 X[31254], 3 X[15673] - X[57002], 29 X[15674] - 21 X[15675], 65 X[15674] - 49 X[15676], 85 X[15674] - 21 X[15677], 125 X[15674] - 21 X[15678], 115 X[15674] + 21 X[15679], 55 X[15674] - 7 X[15680], 65 X[15674] - 21 X[17525], X[15674] + 7 X[31254], 5 X[15674] - X[57002], 85 X[15675] - 29 X[15677], 125 X[15675] - 29 X[15678], 115 X[15675] + 29 X[15679], 165 X[15675] - 29 X[15680], 65 X[15675] - 29 X[17525], 3 X[15675] + 29 X[31254], 105 X[15675] - 29 X[57002], 119 X[15676] - 39 X[15677], 175 X[15676] - 39 X[15678], 161 X[15676] + 39 X[15679], 77 X[15676] - 13 X[15680], 7 X[15676] - 3 X[17525], 7 X[15676] + 65 X[31254], 49 X[15676] - 13 X[57002], 25 X[15677] - 17 X[15678], 23 X[15677] + 17 X[15679], 33 X[15677] - 17 X[15680], 13 X[15677] - 17 X[17525], 3 X[15677] + 85 X[31254], 21 X[15677] - 17 X[57002], 23 X[15678] + 25 X[15679], 33 X[15678] - 25 X[15680], 13 X[15678] - 25 X[17525], 3 X[15678] + 125 X[31254], 21 X[15678] - 25 X[57002], 33 X[15679] + 23 X[15680], 13 X[15679] + 23 X[17525], 3 X[15679] - 115 X[31254], 21 X[15679] + 23 X[57002], 13 X[15680] - 33 X[17525], X[15680] + 55 X[31254], 7 X[15680] - 11 X[57002], 5 X[15694] - X[44255], 9 X[15699] - X[16160], X[16617] - 7 X[55856], 3 X[17525] + 65 X[31254], 21 X[17525] - 13 X[57002], X[21669] - 25 X[60781], 3 X[28443] - 19 X[55858], X[28460] - 9 X[61864], 3 X[28463] - 23 X[41992], 3 X[28465] + X[37230], 35 X[31254] + X[57002], X[31649] - 13 X[55861], 3 X[31650] - 11 X[55859], 5 X[31651] + 7 X[44258], X[33557] + 23 X[46936], X[44256] - 5 X[50207], X[44257] - 5 X[61885], X[47032] + 23 X[55860], X[191] - 17 X[19872], X[11544] + 17 X[19872], 3 X[58451] - X[58638], 15 X[1698] + X[16126], 5 X[1698] + X[16137], 5 X[1698] - X[21677], 5 X[1698] + 3 X[26725], X[16126] - 3 X[16137], X[16126] + 3 X[21677], X[16126] - 9 X[26725], X[16137] - 3 X[26725], X[21677] + 3 X[26725], X[11263] + 7 X[51073], X[18253] - 7 X[51073], 7 X[3624] - X[15174], 7 X[3624] + X[47033], 3 X[3848] - X[58568], 7 X[9780] + X[34195], 5 X[5439] - X[39772], X[6701] + 5 X[31253], 5 X[31253] - X[58449], 3 X[6688] - X[58479], X[10543] - 13 X[34595], 3 X[11231] + X[33592], 5 X[19862] - X[35016], 5 X[31235] - X[35204], 7 X[31423] + X[49177], 3 X[34122] + X[39778], 5 X[51126] - X[51729], 3 X[63276] + X[64289]

See Antreas Hatzipolakis and Peter Moses, euclid 6798.

X(64853) lies on these lines: {1, 64370}, {2, 3}, {10, 5719}, {79, 53056}, {141, 51747}, {142, 34753}, {191, 7308}, {495, 19854}, {496, 31245}, {758, 3634}, {942, 40661}, {1125, 12433}, {1213, 24937}, {1330, 31205}, {1698, 11374}, {2771, 6723}, {2795, 6722}, {2886, 15172}, {3339, 3649}, {3452, 11263}, {3454, 62689}, {3616, 15935}, {3624, 5722}, {3646, 61268}, {3743, 17070}, {3824, 5745}, {3826, 47742}, {3841, 6690}, {3848, 58568}, {3913, 10198}, {3936, 49718}, {3940, 9780}, {4423, 10593}, {4658, 17056}, {5427, 7294}, {5432, 41859}, {5437, 54302}, {5439, 39772}, {5720, 33858}, {5748, 11684}, {5763, 26446}, {5775, 19877}, {5785, 20195}, {5791, 6147}, {5818, 64321}, {5844, 24987}, {6362, 33528}, {6666, 6701}, {6667, 19878}, {6681, 33961}, {6688, 58479}, {6707, 17052}, {7173, 25542}, {8666, 25466}, {9342, 63269}, {9528, 58424}, {9581, 10543}, {9710, 10197}, {10122, 64157}, {10175, 64804}, {11231, 33592}, {11520, 41574}, {11533, 24161}, {13993, 31473}, {15901, 61035}, {16159, 38113}, {16589, 43291}, {17194, 48927}, {17245, 45939}, {18482, 38059}, {18990, 24953}, {19855, 31479}, {19860, 61510}, {19862, 35016}, {20106, 39564}, {24541, 51700}, {24883, 63344}, {24898, 64377}, {24902, 35466}, {24936, 64167}, {25441, 28618}, {25446, 41014}, {25666, 44314}, {25973, 38114}, {26131, 31204}, {26543, 34380}, {31235, 35204}, {31423, 49177}, {31435, 38034}, {31658, 38204}, {31837, 61541}, {33594, 64193}, {34122, 39778}, {36812, 44377}, {37532, 61509}, {37659, 45931}, {37700, 38042}, {38108, 63966}, {38123, 38318}, {51126, 51729}, {58433, 58619}, {61029, 61614}, {61624, 63070}, {63276, 64289}

X(64853) = midpoint of X(i) and X(j) for these {i,j}: {10, 11281}, {141, 51747}, {191, 11544}, {442, 6675}, {942, 40661}, {3850, 11276}, {5499, 16617}, {6175, 15673}, {6701, 58449}, {11263, 18253}, {11277, 46028}, {15174, 47033}, {16137, 21677}, {33594, 64193}, {58586, 58692}, {58619, 58658}
X(64853) = complement of X(6675)
X(64853) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 50205}, {2, 442, 6675}, {2, 1656, 51559}, {2, 3090, 16853}, {2, 4193, 17590}, {2, 4197, 7483}, {2, 6856, 11108}, {2, 6931, 16854}, {2, 6933, 16842}, {2, 7504, 17575}, {2, 8728, 140}, {2, 16408, 632}, {2, 17529, 52264}, {2, 17582, 3526}, {2, 31254, 442}, {2, 33026, 32954}, {2, 33033, 7819}, {2, 33199, 33027}, {2, 50393, 16862}, {2, 50727, 5054}, {2, 52264, 16239}, {3, 1656, 6855}, {3, 6858, 5}, {5, 632, 6883}, {442, 15670, 2475}, {442, 17527, 46028}, {442, 57002, 6175}, {547, 11277, 46028}, {632, 6924, 140}, {1656, 6825, 5}, {1698, 26725, 21677}, {3090, 19541, 5}, {3526, 37230, 28465}, {3628, 50394, 2}, {3634, 58463, 5044}, {3824, 5745, 24470}, {5055, 6849, 5}, {5177, 16418, 3627}, {5791, 25525, 6147}, {6175, 15674, 57002}, {6675, 15673, 15674}, {6856, 11108, 5}, {6857, 17528, 550}, {6910, 17563, 12100}, {6910, 44217, 17563}, {6931, 16854, 17527}, {8728, 17564, 37462}, {15674, 57002, 15673}, {16370, 50240, 12103}, {16408, 19520, 6924}, {17529, 25962, 8728}, {17532, 50241, 3853}, {17558, 50741, 382}, {21677, 26725, 16137}, {25446, 41878, 41014}, {37161, 50739, 1657}

X(64854) = X(2)X(389)∩X(3)X(51)

Barycentrics    a^2 (a^6 b^2-3 a^4 b^4+3 a^2 b^6-b^8+a^6 c^2+2 a^4 b^2 c^2-7 a^2 b^4 c^2+4 b^6 c^2-3 a^4 c^4-7 a^2 b^2 c^4-6 b^4 c^4+3 a^2 c^6+4 b^2 c^6-c^8) : : X(64854) = X[1] + 4 X[58487], 3 X[2] + 2 X[389], 6 X[2] - X[5562], 9 X[2] + X[5889], 3 X[2] - 8 X[11695], 9 X[2] - 4 X[11793], 4 X[2] + X[14831], 3 X[2] - 13 X[15028], 3 X[2] + 7 X[15043], 2 X[2] + 3 X[16226], 4 X[389] + X[5562], 6 X[389] - X[5889], 2 X[389] + X[11444], X[389] + 4 X[11695], 3 X[389] + 2 X[11793], 8 X[389] - 3 X[14831], 2 X[389] + 13 X[15028], 2 X[389] - 7 X[15043], 4 X[389] - 9 X[16226], and many others

Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6804.

X(64854) lies on these lines: {{1, 58487}, {2, 389}, {3, 51}, {4, 5943}, {5, 113}, {6, 1092}, {10, 64662}, {20, 5640}, {22, 37515}, {24, 182}, {25, 10984}, {26, 13336}, {30, 15026}, {39, 46094}, {40, 58469}, {49, 15037}, {52, 140}, {54, 575}, {74, 41671}, {83, 37124}, {98, 58503}, {99, 58502}, {100, 58508}, {101, 58507}, {102, 58513}, {103, 58505}, {104, 58504}, {109, 58506}, {110, 58498}, {127, 16225}, {143, 549}, {155, 5651}, {181, 602}, {184, 6642}, {186, 43651}, {193, 11431}, {216, 46736}, {235, 64179}, {264, 1075}, {375, 14872}, {376, 9781}, {378, 15010}, {381, 11381}, {382, 40280}, {394, 11432}, {417, 61378}, {511, 631}, {546, 10575}, {547, 5876}, {548, 58531}, {550, 10095}, {567, 2931}, {568, 1216}, {569, 6644}, {578, 5422}, {590, 12240}, {597, 40929}, {601, 3271}, {615, 12239}, {620, 39817}, {632, 1154}, {944, 23841}, {970, 1006}, {973, 9967}, {1071, 58497}, {1112, 38727}, {1147, 13366}, {1181, 5020}, {1192, 54994}, {1199, 34986}, {1204, 9818}, {1292, 58509}, {1293, 58510}, {1294, 58511}, {1295, 58512}, {1296, 58514}, {1297, 58515}, {1350, 31521}, {1352, 18916}, {1368, 45089}, {1385, 16980}, {1425, 37697}, {1482, 64663}, {1495, 7506}, {1498, 45979}, {1533, 1906}, {1568, 12233}, {1593, 37475}, {1598, 3066}, {1656, 13754}, {1658, 37513}, {1899, 7401}, {1986, 6723}, {1995, 6759}, {2070, 37471}, {2071, 58551}, {2393, 17821}, {2548, 50387}, {2781, 38729}, {2807, 8227}, {2883, 32184}, {2937, 13339}, {2979, 10303}, {3060, 3523}, {3088, 64820}, {3090, 5890}, {3091, 6000}, {3098, 58549}, {3146, 20791}, {3184, 58524}, {3270, 37696}, {3292, 12161}, {3313, 32191}, {3357, 63664}, {3398, 63556}, {3428, 58490}, {3515, 37476}, {3517, 3796}, {3518, 61134}, {3520, 43597}, {3521, 10293}, {3524, 13348}, {3525, 3819}, {3530, 10263}, {3533, 7999}, {3538, 51212}, {3541, 12294}, {3545, 6241}, {3547, 61506}, {3548, 61743}, {3549, 61645}, {3574, 11585}, {3575, 64038}, {3576, 58548}, {3589, 19161}, {3592, 62247}, {3594, 62248}, {3627, 13364}, {3628, 5891}, {3634, 31732}, {3651, 58479}, {3818, 11457}, {3830, 14641}, {3832, 13474}, {3839, 12279}, {3843, 14915}, {3845, 18874}, {3850, 13491}, {3851, 64029}, {3855, 12290}, {3857, 32137}, {3937, 37612}, {4297, 58474}, {5012, 10282}, {5050, 6467}, {5054, 5447}, {5055, 34783}, {5056, 12111}, {5067, 11459}, {5068, 15305}, {5070, 10170}, {5071, 15058}, {5072, 18439}, {5079, 18435}, {5085, 9715}, {5092, 7512}, {5133, 20299}, {5159, 16227}, {5188, 58486}, {5448, 50143}, {5449, 37347}, {5643, 7527}, {5732, 58473}, {5759, 58472}, {5972, 21649}, {6036, 39846}, {6146, 9825}, {6247, 41580}, {6293, 61735}, {6509, 42441}, {6524, 62897}, {6639, 61691}, {6643, 54012}, {6689, 12606}, {6699, 13417}, {6776, 9822}, {6803, 11433}, {6804, 21971}, {6815, 39571}, {6862, 61643}, {6875, 15489}, {6883, 22076}, {6902, 15488}, {6922, 18180}, {6928, 58889}, {6947, 10441}, {6967, 37521}, {6997, 14216}, {7387, 34417}, {7392, 18909}, {7393, 22112}, {7395, 9786}, {7398, 34781}, {7399, 13567}, {7404, 26937}, {7405, 12359}, {7464, 58481}, {7484, 17834}, {7485, 46728}, {7486, 15056}, {7503, 11438}, {7509, 46730}, {7516, 37478}, {7517, 44106}, {7526, 21663}, {7528, 11550}, {7529, 26883}, {7544, 18381}, {7556, 20190}, {7558, 61646}, {7576, 44829}, {7592, 9306}, {7691, 58489}, {7706, 18404}, {7745, 15575}, {7998, 15606}, {8541, 44503}, {8550, 29959}, {8718, 52294}, {8887, 46106}, {8954, 8963}, {9607, 61675}, {9714, 35268}, {9777, 37498}, {9827, 10619}, {9862, 58537}, {9940, 51413}, {9971, 10541}, {9973, 55703}, {10018, 58447}, {10112, 32068}, {10127, 12134}, {10160, 31739}, {10163, 31763}, {10164, 31757}, {10165, 31760}, {10202, 23154}, {10219, 61886}, {10267, 51377}, {10314, 39643}, {10323, 13347}, {10605, 11479}, {10606, 58544}, {10627, 14869}, {10628, 15059}, {11002, 15717}, {11179, 43130}, {11245, 64035}, {11257, 58500}, {11284, 17814}, {11413, 58482}, {11414, 17810}, {11426, 35602}, {11427, 46363}, {11430, 13434}, {11449, 27365}, {11455, 61964}, {11464, 41714}, {11477, 64599}, {11539, 32142}, {11554, 31848}, {11557, 15061}, {11591, 55856}, {11592, 13421}, {11692, 37955}, {11746, 16163}, {11750, 31830}, {11800, 15035}, {11802, 43581}, {11806, 14643}, {11807, 15055}, {11808, 46865}, {12002, 62100}, {12017, 16195}, {12045, 61881}, {12084, 37470}, {12088, 38848}, {12108, 14449}, {12118, 58496}, {12119, 58501}, {12160, 17811}, {12163, 58545}, {12228, 17701}, {12235, 47391}, {12236, 38793}, {12244, 58536}, {12245, 58535}, {12248, 58543}, {12251, 58556}, {12272, 33748}, {12282, 64177}, {12307, 58557}, {12824, 20417}, {13172, 58538}, {13199, 58539}, {13292, 61712}, {13321, 15720}, {13334, 37114}, {13340, 61811}, {13353, 18475}, {13376, 13619}, {13391, 15712}, {13403, 38323}, {13450, 59529}, {13451, 33923}, {13464, 64661}, {13470, 38322}, {13568, 34664}, {13595, 52525}, {14033, 55306}, {14110, 58493}, {14118, 15053}, {14128, 15699}, {14130, 43604}, {14538, 58477}, {14539, 58478}, {14689, 58528}, {14709, 24651}, {14710, 24650}, {14788, 21243}, {14853, 52520}, {14912, 14913}, {15004, 36747}, {15011, 33537}, {15022, 64025}, {15029, 54037}, {15032, 43598}, {15038, 37495}, {15060, 35018}, {15062, 43603}, {15067, 16239}, {15069, 61676}, {15082, 61867}, {15087, 41597}, {15133, 43821}, {15473, 18560}, {15559, 19130}, {15646, 48914}, {15686, 55286}, {15906, 35004}, {16042, 43605}, {16111, 58516}, {16196, 18583}, {16197, 32269}, {16224, 34841}, {16261, 61945}, {16657, 31829}, {16924, 40254}, {16981, 61816}, {16982, 54044}, {17504, 55320}, {17578, 52093}, {18128, 64036}, {18350, 43845}, {18446, 58491}, {18474, 18952}, {18860, 58552}, {19347, 35259}, {19467, 60774}, {21163, 27375}, {21312, 58483}, {21659, 31833}, {21661, 34838}, {21734, 55166}, {22115, 44111}, {22802, 30443}, {22829, 45248}, {23039, 46219}, {23308, 32050}, {23332, 41589}, {24466, 58475}, {24813, 58553}, {25555, 37118}, {26892, 37534}, {26913, 32767}, {27374, 37451}, {30264, 58476}, {30271, 58485}, {30273, 58499}, {31737, 58441}, {31752, 51073}, {32046, 51393}, {32136, 40111}, {32138, 58546}, {32233, 58495}, {32284, 53092}, {32348, 58445}, {32366, 55711}, {32829, 51386}, {32911, 37275}, {33884, 61842}, {34146, 40686}, {34148, 34545}, {34236, 46626}, {34339, 42448}, {34382, 53091}, {34565, 36749}, {35486, 44479}, {36754, 40952}, {36978, 42944}, {36980, 42945}, {36989, 58494}, {36996, 58534}, {37119, 52000}, {37120, 48886}, {37122, 46264}, {37301, 55303}, {37473, 47352}, {37732, 53391}, {37953, 55698}, {38737, 39835}, {38738, 58518}, {38748, 39806}, {38749, 58517}, {38761, 58522}, {38773, 58521}, {38785, 58526}, {38898, 40685}, {39530, 44732}, {40247, 46936}, {41171, 43808}, {41425, 52288}, {41614, 44489}, {41716, 63119}, {43394, 43898}, {43573, 44076}, {43608, 43896}, {43613, 43899}, {43816, 58922}, {44102, 44480}, {44299, 61863}, {44324, 61858}, {44495, 59373}, {44544, 63714}, {44682, 58533}, {44865, 64358}, {44871, 61990}, {44882, 58532}, {45177, 49109}, {45967, 58806}, {46852, 61953}, {47301, 51888}, {47413, 53844}, {51419, 56885}, {51491, 63737}, {51737, 63688}, {52262, 54384}, {52796, 64850}, {54041, 61814}, {54047, 61831}, {54048, 61850}, {58488, 63392}, {58519, 63403}, {58520, 63404}, {58523, 63406}, {58525, 63407}, {58527, 63408}, {58529, 63410}, {58530, 63411}, {58540, 63416}, {58541, 63417}, {58542, 63418}, {58547, 63420}, {58554, 63427}, {58555, 63428}, {58558, 63438}, {58559, 63441}, {58647, 61640}, {59399, 63709}, {61667, 63722}, {61820, 62187}, {61834, 62188}, {63128, 64585}

X(64854) = midpoint of X(i) and X(j) for these {i,j}: {631, 3567}, {1656, 37481}, {3091, 10574}, {17578, 52093}
X(64854) = reflection of X(5562) in X(11444)
X(64854) = complement of X(11444)
X(64854) = X(64854)-Dao conjugate of X(11444)
X(64854) = pole of line {30, 1181} with respect to the Jerabek circumhyperbola
X(64854) = pole of line {3289, 5065} with respect to the ABCGK
X(64854) = pole of line {44149, 64585} with respect to the Steiner / Wallace right hyperbola
X(64854) = pole of line {3091, 3292} with respect to the Jerabek circumhyperbola of the medial triangle
X(64854) = pole of line {578, 631} with respect to the Feuerbach circumhyperbola of the tangential triangle
X(64854) = pole of line {44149, 64585} with respect to the Kiepert circumhyperbola of the anticomplementary triangle
X(64854) = pole of line {41079, 41300} with respect to the Steiner inellipse
X(64854) = pole of line {1656, 11064} with respect to the Thomson-Gibert-Moses hyperbola
X(64854) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 389, 5562}, {2, 5889, 11793}, {2, 15028, 11695}, {2, 15043, 389}, {2, 16226, 14831}, {3, 51, 45186}, {3, 5462, 51}, {3, 15805, 43650}, {3, 45186, 36987}, {4, 9729, 64100}, {4, 15024, 5943}, {4, 15045, 9729}, {5, 185, 15030}, {5, 9730, 185}, {5, 12006, 9730}, {5, 13630, 12162}, {5, 45956, 45959}, {5, 45957, 45958}, {20, 5640, 10110}, {25, 37514, 10984}, {26, 13336, 22352}, {52, 140, 3917}, {125, 9826, 16223}, {140, 5946, 52}, {140, 16881, 6101}, {143, 549, 10625}, {143, 10625, 21969}, {185, 373, 5}, {373, 9730, 15030}, {375, 58617, 14872}, {376, 9781, 13598}, {381, 40647, 11381}, {381, 64030, 46849}, {389, 5562, 14831}, {389, 11695, 2}, {389, 11793, 5889}, {389, 15043, 16226}, {546, 10575, 32062}, {567, 43809, 12038}, {568, 1216, 14531}, {568, 3526, 1216}, {569, 6644, 13367}, {578, 17928, 51394}, {1147, 36753, 13366}, {1216, 3526, 5650}, {3060, 3523, 15644}, {3090, 5890, 5907}, {3090, 11465, 6688}, {3524, 64051, 13348}, {3525, 11412, 3819}, {3545, 6241, 44870}, {3628, 6102, 5891}, {3819, 16625, 11412}, {3832, 15072, 13474}, {3850, 13491, 16194}, {3855, 12290, 46847}, {3855, 61136, 12290}, {5012, 44802, 10282}, {5054, 6243, 5447}, {5070, 18436, 10170}, {5422, 17928, 578}, {5462, 5892, 3}, {5562, 16226, 389}, {5650, 14531, 1216}, {5889, 11793, 5562}, {5890, 11465, 3090}, {5891, 6102, 45187}, {5907, 6688, 3090}, {5907, 15012, 5890}, {5943, 9729, 4}, {5943, 15045, 64100}, {5946, 6101, 16881}, {5972, 46430, 21649}, {6101, 16881, 52}, {6642, 36752, 184}, {6688, 15012, 5907}, {6699, 16222, 13417}, {6815, 63084, 39571}, {7395, 9786, 63425}, {7506, 64049, 1495}, {7527, 43601, 64027}, {7544, 18911, 18381}, {7592, 9306, 43844}, {9730, 12162, 13630}, {9730, 13363, 373}, {9786, 17825, 7395}, {9825, 45298, 6146}, {10110, 16836, 20}, {10574, 11451, 3091}, {10575, 14845, 546}, {11002, 15717, 64050}, {11381, 27355, 381}, {11695, 15043, 5562}, {12006, 13363, 5}, {12006, 32205, 13630}, {12108, 14449, 54042}, {12162, 13630, 185}, {13321, 15720, 37484}, {13348, 21849, 64051}, {13353, 45735, 18475}, {13363, 13630, 32205}, {13434, 22467, 11430}, {13434, 43584, 22467}, {13598, 17704, 376}, {13598, 58470, 9781}, {13630, 32205, 5}, {13630, 45958, 45957}, {14641, 44863, 3830}, {14708, 23515, 21650}, {14788, 26879, 21243}, {15004, 43652, 36747}, {15018, 22467, 13434}, {15018, 43584, 11430}, {15024, 15045, 4}, {15028, 15043, 2}, {15037, 43586, 44109}, {15047, 43809, 567}, {16042, 43605, 43614}, {16270, 41670, 15063}, {17704, 58470, 13598}, {34148, 34545, 37505}, {40647, 46849, 64030}, {43598, 43600, 15032}, {45957, 45958, 12162}, {45979, 58492, 1498}, {46849, 64030, 11381}





leftri   Points on the line at infinity: X(64855) - X(64889)  rightri

Contributed by Clark Kimberling and Peter Moses, August 21, 2024

Suppose X = x:y:z is a point on the infinity line. Then the following points are also on the infinity line:

y sin B - z sin C : : y tan B - z tan C :: y sec B - z sec C : :

The appearance of (i,j) in the following list means that if X(i) = x:y:z, then X(j) = y sin B - z sin C : :

(511,64855), (512,714), (513,726), (514,536), (516,64856), (517,64857), (518,522), (519,4777), (521,64858), (522,518), (523,740), (524,64859), (525,8680), (527,28898), (528,64860), (536,514), (537,900), (545,64861), (690,64863), (696,64864), (698,64865), (700788), (712,64866), (714,512), (716,64867), (726,513), (740,523), (742,824), (744,826), (746,63814), (752,29370), (758,64868), (784,64869), (786,64870), (788,700), (802,64871), (812,9055), (814,64872), (824,742), (826,744), (834,64873), (891,64874), (900,537)

The appearance of (i,j) in the following list means that if X(i) = x:y:z, then X(j) = y tan B - z tan C : :

(30,9007), (511,520), (512,8681), (513,34381), (514,9028), (517,9051), (518,521), (519,9031), (520,511), (521,518), (522,64875), (523,3564), (524,525), (525,524), (526,14984), (538,64876), (539,64877), (542,9033), (674,64878), (688,64879), (690,64880), (698,64881), (804,64882), (664883), (900,64884), (912,9001)

The appearance of (i,j) in the following list means that if X(i) = x:y:z, then X(j) = y sec B - z sec C : :

(513,9028), (514,912), (515,64885), (518,64886), (520,8680), (521,527), (522,64887), (523,64888), (525,758), (527,521), (758,525), (812,64889), (912,514)

underbar



X(64855) = X(30)X(511)∩X(75)X(656)

Barycentrics    (b - c)*(-(a^4*b^2) + a^2*b^4 - a^4*b*c + a^2*b^3*c - a^4*c^2 + a^2*b^2*c^2 + b^4*c^2 + a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 + b^2*c^4) : :
Barycentrics    b y - c z : : , where x : y : z = X(511)

X(64855) lies on these lines: {30, 511}, {37, 4529}, {75, 656}, {192, 7253}, {647, 24353}, {850, 24718}, {984, 4086}, {4024, 45882}, {4411, 47843}, {4467, 14296}, {4664, 45686}, {4842, 24720}, {17899, 55230}, {21259, 52623}, {22316, 57207}, {23189, 54410}, {25380, 59721}, {45660, 50094}

X(64855) = crossdifference of every pair of points on line {6, 9417}
X(64855) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64855) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {19394, 4856}, {57326, 53578}

X(64856) = X(30)X(511)∩X(75)X(2400)

Barycentrics    (b - c)*(-a^3 - a*b^2 + 2*b^3 - 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2 + 2*c^3) : :
Barycentrics    b y - c z : : , where x : y : z = X(516)

X(64856) lies on these lines: {1, 49280}, {30, 511}, {37, 2509}, {75, 2400}, {649, 47700}, {650, 4088}, {659, 48088}, {676, 3239}, {905, 48272}, {984, 21189}, {1638, 47806}, {1639, 47800}, {2516, 2977}, {2517, 4411}, {2526, 16892}, {3004, 48039}, {3669, 48278}, {3700, 47123}, {3739, 21187}, {4010, 47131}, {4025, 50333}, {4106, 47691}, {4122, 7662}, {4142, 20317}, {4163, 55285}, {4382, 47705}, {4394, 48062}, {4408, 56124}, {4453, 47808}, {4458, 4522}, {4468, 50347}, {4474, 43052}, {4501, 43929}, {4724, 48087}, {4776, 48203}, {4790, 48106}, {4804, 4820}, {4808, 50501}, {4809, 47803}, {4813, 47702}, {4897, 48069}, {4944, 47832}, {4949, 48349}, {4951, 47833}, {7192, 47689}, {7658, 53573}, {7659, 47971}, {20295, 47692}, {21104, 49285}, {23684, 35519}, {23757, 49522}, {23770, 23813}, {23785, 49521}, {24349, 57091}, {25259, 47695}, {30565, 47798}, {40541, 59458}, {43067, 47690}, {44429, 47754}, {44567, 45344}, {45318, 45334}, {45320, 47887}, {46403, 49299}, {47653, 47940}, {47676, 47687}, {47685, 49302}, {47693, 49281}, {47694, 48271}, {47697, 49273}, {47698, 47962}, {47699, 47952}, {47701, 48026}, {47703, 48133}, {47704, 48125}, {47727, 49277}, {47729, 49274}, {47755, 48252}, {47758, 48232}, {47760, 47797}, {47761, 47809}, {47762, 48208}, {47765, 48179}, {47769, 48161}, {47770, 47804}, {47772, 48239}, {47802, 48227}, {47805, 48557}, {47810, 47880}, {47813, 47881}, {47821, 48223}, {47822, 48211}, {47823, 48200}, {47824, 48187}, {47870, 48237}, {47874, 48220}, {47886, 48193}, {47894, 48175}, {47919, 47943}, {47923, 48020}, {47924, 47950}, {47960, 48023}, {47972, 48082}, {48006, 48046}, {48029, 50340}, {48031, 50332}, {48032, 48117}, {48089, 48326}, {48095, 48118}, {48096, 50358}, {48102, 48124}, {48142, 48397}, {48164, 48422}, {48169, 48571}, {48174, 48558}, {48184, 58372}, {48188, 48219}, {48192, 48224}, {48266, 53558}, {48286, 49288}, {48300, 50517}, {48327, 49279}, {49272, 53343}, {50336, 50342}, {53551, 58335}

X(64856) = isogonal conjugate of X(59055)
X(64856) = crossdifference of every pair of points on line {6, 3220}
X(64856) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64856) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64856) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4458, 4522, 4885}, {4809, 48185, 47803}, {16892, 48077, 2526}, {44429, 48241, 47754}, {47804, 48171, 47770}

X(64857) = X(30)X(511)∩X(75)X(4025)

Barycentrics    (b - c)*(-(a^3*b) + a*b^3 - a^3*c + a^2*b*c - a*b^2*c + b^3*c - a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3) : :
Barycentrics    b y - c z : : , where x : y : z = X(517)

X(64857) lies on these lines: {30, 511}, {37, 3239}, {75, 4025}, {192, 23757}, {656, 4397}, {798, 47130}, {1459, 57091}, {1734, 4768}, {1769, 4391}, {2509, 4529}, {2517, 4017}, {3676, 4411}, {3739, 7658}, {3835, 48350}, {3993, 49288}, {4086, 20316}, {4688, 44551}, {4755, 45334}, {4828, 21183}, {6129, 8062}, {7253, 48303}, {7649, 46110}, {17072, 53527}, {20517, 21180}, {20907, 23785}, {21186, 21187}, {27485, 47757}, {28284, 47835}, {30572, 48278}, {47129, 57234}, {48325, 55969}, {55244, 59522}, {56125, 60574}, {59565, 59721}

X(64857) = crossdifference of every pair of points on line {6, 23531}
X(64857) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}, {15351, 49223}
X(64857) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2517, 4017, 47843}, {4086, 21189, 20316}

X(64858) = X(30)X(511)∩X(75)X(225)

Barycentrics    a^4*b^2 - a^3*b^3 - a^2*b^4 + a*b^5 + a^2*b^3*c - b^5*c + a^4*c^2 - a*b^3*c^2 - a^3*c^3 + a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 + a*c^5 - b*c^5 : :
Barycentrics    b y - c z : : , where x : y : z = X(521)

X(64858) lies on these lines: {3, 42456}, {30, 511}, {33, 20223}, {37, 216}, {73, 20222}, {75, 225}, {92, 24430}, {190, 23693}, {192, 3100}, {201, 23661}, {238, 24846}, {984, 10039}, {1278, 40896}, {1463, 23772}, {1736, 4858}, {1818, 4552}, {1897, 1936}, {2217, 23086}, {2635, 61185}, {3262, 44694}, {3739, 14767}, {3772, 24218}, {3826, 59621}, {3911, 44311}, {4318, 4861}, {4664, 47383}, {4698, 58454}, {5018, 24411}, {5136, 18477}, {5220, 21084}, {5745, 22027}, {6762, 64429}, {7004, 64194}, {10003, 61522}, {14547, 18662}, {17155, 24477}, {20430, 30258}, {20872, 23843}, {22465, 24325}, {24315, 46475}, {24474, 45131}, {24848, 32922}, {25568, 32925}, {27422, 28978}, {30271, 63433}, {30273, 42329}, {32921, 45728}, {32935, 45729}, {34822, 64708}, {34831, 41013}, {37565, 58411}, {39530, 64088}, {41541, 51062}, {45275, 49523}, {45281, 49493}, {58460, 59611}, {58463, 59638}

X(64858) = isogonal conjugate of X(59016)
X(64858) = isotomic conjugate of X(60046)
X(64858) = isotomic conjugate of the isogonal conjugate of X(45932)
X(64858) = crossdifference of every pair of points on line {6, 39199}
X(64858) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}, {43424, 53097}
X(64858) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {234, 2057}, {414, 2057}, {416, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {51612, 14940}
X(64858) = {X(41013),X(44706)}-harmonic conjugate of X(34831)

X(64859) = X(30)X(511)∩X(75)X(1577)

Barycentrics    (b - c)*(-a^2 + 2*b^2 + 3*b*c + 2*c^2) : :
Barycentrics    b y - c z : : , where x : y : z = X(524)

X(64859) lies on these lines: {2, 4931}, {30, 511}, {37, 14838}, {75, 1577}, {192, 4560}, {649, 47665}, {656, 24417}, {661, 17161}, {693, 4842}, {984, 4041}, {1635, 47870}, {3676, 48417}, {3700, 21196}, {3776, 48268}, {3835, 4820}, {4024, 4369}, {4025, 4500}, {4120, 45315}, {4122, 4913}, {4379, 48423}, {4380, 48436}, {4382, 47677}, {4411, 4823}, {4444, 4804}, {4453, 48416}, {4481, 21834}, {4486, 50341}, {4509, 4828}, {4529, 57066}, {4608, 48147}, {4664, 45671}, {4688, 45324}, {4728, 31094}, {4763, 27486}, {4786, 6590}, {4813, 47657}, {4838, 7192}, {4928, 47790}, {4932, 48397}, {4944, 47778}, {4951, 48225}, {4958, 47759}, {4976, 47884}, {4979, 47659}, {4984, 48567}, {4988, 44449}, {7201, 51664}, {16892, 47871}, {20295, 47673}, {20430, 39212}, {20908, 20954}, {21115, 47869}, {21183, 48419}, {21212, 45677}, {22043, 42327}, {23731, 47654}, {25259, 48000}, {26824, 47930}, {27483, 60042}, {30605, 48288}, {31148, 47792}, {31290, 47669}, {45313, 47881}, {45343, 45663}, {45675, 47785}, {45678, 47787}, {45679, 47767}, {45745, 48270}, {45746, 48049}, {47652, 48428}, {47653, 48114}, {47655, 48141}, {47656, 47971}, {47658, 50522}, {47660, 48429}, {47661, 48082}, {47664, 48117}, {47666, 50482}, {47667, 48076}, {47668, 47908}, {47762, 47873}, {47769, 47878}, {47923, 48435}, {47926, 49272}, {47932, 49273}, {47960, 49287}, {48008, 48271}, {48016, 49281}, {48101, 48438}, {48269, 48404}, {48398, 48427}, {48551, 57514}, {49286, 53580}, {49292, 50342}, {56130, 62619}

X(64859) = isogonal conjugate of X(59054)
X(64859) = isotomic conjugate of X(35180)
X(64859) = isotomic conjugate of the anticomplement of X(35134)
X(64859) = crossdifference of every pair of points on line {6, 922}
X(64859) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64859) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1653, 1038}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3700, 21196, 25666}, {3700, 47784, 45661}, {4024, 4467, 4369}, {4024, 4750, 4789}, {4120, 47782, 45315}, {4467, 4789, 4750}, {4750, 4789, 4369}, {4988, 44449, 47991}, {17161, 53339, 46915}, {21196, 45661, 47784}, {25259, 48277, 48000}, {27486, 47874, 4763}, {45343, 45669, 45663}, {45343, 45674, 47788}, {45661, 47784, 25666}, {45669, 47788, 45674}, {45674, 47788, 45663}, {45746, 48266, 48049}, {46915, 53339, 661}, {47656, 47971, 49291}, {47762, 48437, 47873}, {47785, 47879, 45675}, {47787, 47882, 45678}, {47790, 47886, 4928}, {47792, 53333, 31148}

X(64860) = X(30)X(511)∩X(75)X(4768)

Barycentrics    (b - c)*(-a^3 + a^2*b - 2*a*b^2 + 2*b^3 + a^2*c - 3*a*b*c + b^2*c - 2*a*c^2 + b*c^2 + 2*c^3) : :
Barycentrics    b y - c z : : , where x : y : z = X(528)

X(64860) lies on these lines: {30, 511}, {75, 4768}, {335, 60479}, {661, 48158}, {676, 45326}, {984, 1769}, {1491, 48224}, {1638, 4458}, {1639, 45337}, {2254, 48571}, {2977, 13246}, {3716, 4088}, {3835, 47131}, {3904, 30573}, {4369, 48235}, {4379, 48187}, {4453, 45328}, {4522, 47123}, {4763, 4809}, {4830, 48408}, {4874, 48201}, {4893, 48223}, {4895, 49274}, {4913, 27486}, {4951, 48189}, {6545, 31131}, {6546, 44433}, {10196, 26275}, {14315, 28601}, {20516, 21180}, {21204, 48182}, {23057, 53334}, {24623, 47689}, {25666, 48195}, {28602, 45675}, {30572, 43041}, {30792, 59755}, {31148, 48254}, {33888, 63251}, {36848, 58372}, {44902, 45668}, {45315, 48177}, {45323, 48212}, {45663, 48217}, {46403, 47705}, {47687, 47704}, {47688, 48020}, {47690, 49292}, {47691, 48050}, {47692, 48023}, {47693, 48153}, {47694, 47700}, {47697, 48118}, {47698, 47972}, {47701, 47992}, {47702, 47945}, {47709, 47912}, {47713, 47948}, {47717, 48086}, {47772, 53361}, {47778, 48211}, {47779, 48200}, {47798, 48562}, {47808, 47887}, {47810, 48203}, {47811, 48239}, {47812, 48169}, {47813, 48208}, {47924, 47940}, {47951, 48590}, {47961, 47985}, {48000, 50340}, {48039, 48554}, {48049, 48349}, {48056, 53580}, {48063, 48088}, {48069, 48574}, {48072, 48096}, {48188, 48234}, {48236, 48578}, {49490, 53532}

X(64860) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64860) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1617, 1709}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {18715, 64049}
X(64860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4088, 47695, 3716}, {4458, 50333, 25380}, {47691, 48077, 48050}, {47698, 47972, 48001}

X(64861) = X(30)X(511)∩X(75)X(661)

Barycentrics    (b - c)*(a^2*b^2 + 3*a^2*b*c + a^2*c^2 + b^2*c^2) : :
Barycentrics    b y - c z : : , where x : y : z = X(538)

X(64861) lies on these lines: {30, 511}, {37, 4369}, {75, 661}, {192, 7192}, {798, 17159}, {984, 4761}, {1278, 31290}, {3250, 4406}, {3261, 4502}, {3644, 48147}, {3709, 52602}, {3739, 25666}, {3835, 4411}, {4040, 24354}, {4077, 7201}, {4079, 4374}, {4363, 4833}, {4444, 24357}, {4664, 31148}, {4686, 47991}, {4687, 24924}, {4688, 45315}, {4728, 4828}, {4740, 47774}, {4750, 45882}, {4755, 45663}, {4764, 47903}, {4776, 27485}, {4789, 14296}, {4826, 17217}, {7199, 21834}, {14436, 47762}, {22316, 57077}, {25356, 50337}, {25384, 27929}, {36494, 56129}

X(64861) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64861) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64861) = {X(4079),X(4374)}-harmonic conjugate of X(42327)

X(64862) = X(30)X(511)∩X(75)X(3762)

Barycentrics    (b - c)*(-a^2 - 2*a*b + 2*b^2 - 2*a*c + b*c + 2*c^2) : :
Barycentrics    b y - c z : : , where x : y : z = X(545)

X(64862) lies on these lines: {30, 511}, {37, 3960}, {75, 3762}, {190, 1023}, {192, 21222}, {335, 4080}, {649, 48557}, {661, 47894}, {903, 23598}, {984, 2254}, {1086, 61073}, {1577, 4828}, {1635, 31349}, {1638, 37691}, {1639, 45674}, {3700, 47891}, {3716, 4809}, {3776, 48269}, {3835, 47754}, {3842, 18004}, {4010, 58372}, {4024, 49291}, {4025, 25666}, {4120, 4453}, {4369, 25259}, {4370, 35124}, {4379, 52620}, {4380, 48117}, {4411, 4791}, {4432, 30605}, {4440, 39364}, {4458, 50326}, {4467, 48000}, {4486, 36848}, {4500, 49296}, {4521, 59550}, {4707, 21131}, {4750, 4763}, {4813, 47677}, {4820, 48399}, {4830, 48083}, {4895, 49490}, {4897, 47767}, {4931, 47780}, {4932, 48271}, {4944, 47779}, {4958, 21115}, {4979, 49273}, {4984, 47892}, {6546, 14435}, {9318, 14191}, {14321, 21212}, {16892, 44449}, {17161, 47917}, {17494, 48112}, {19957, 25351}, {20295, 47930}, {20908, 21606}, {21196, 47876}, {23795, 49520}, {24349, 53343}, {24623, 48577}, {26853, 48130}, {27012, 47793}, {27074, 47796}, {27475, 52228}, {28779, 47795}, {30579, 33888}, {31147, 48422}, {31148, 47870}, {31290, 47673}, {45313, 47770}, {45315, 47769}, {45328, 50094}, {45663, 47758}, {45679, 47884}, {45746, 47991}, {47653, 48019}, {47657, 47908}, {47658, 48438}, {47659, 48147}, {47662, 50525}, {47665, 48141}, {47676, 48266}, {47778, 52593}, {47923, 48079}, {47939, 48435}, {47950, 48592}, {47960, 48041}, {47995, 48427}, {48008, 48087}, {48013, 48576}, {48016, 48095}, {48038, 48404}, {48071, 49281}, {48114, 49302}, {49274, 53536}, {49287, 49299}

X(64862) = isogonal conjugate of X(28875)
X(64862) = Thomson-isogonal conjugate of X(28876)
X(64862) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64862) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {46081, 20384}
X(64862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1638, 45661, 45678}, {1639, 45674, 45675}, {4025, 47765, 47882}, {4025, 48270, 25666}, {4120, 4453, 4928}, {4467, 48082, 48000}, {4750, 30565, 4763}, {4958, 21115, 21297}, {16892, 44449, 48049}, {25259, 47755, 47874}, {25259, 47971, 4369}, {45746, 48076, 47991}, {47676, 48266, 49289}, {47755, 47874, 4369}, {47758, 47879, 45663}, {47765, 47882, 25666}, {47769, 47886, 45315}, {47772, 53333, 1635}, {47874, 47971, 47755}, {47882, 48270, 47765}, {48571, 53339, 4728}

X(64863) = X(30)X(511)∩X(75)X(799)

Barycentrics    (b + c)*(-a^4 + 2*a^2*b^2 - 2*a^2*b*c + b^3*c + 2*a^2*c^2 - 3*b^2*c^2 + b*c^3) : :
Barycentrics    b y - c z : : , where x : y : z = X(690)

X(64863) lies on these lines: {6, 24292}, {30, 511}, {37, 16592}, {75, 799}, {99, 24345}, {115, 24348}, {148, 24711}, {190, 21254}, {192, 6758}, {903, 46912}, {984, 4736}, {2643, 4440}, {3739, 40546}, {3842, 4013}, {4128, 24722}, {8287, 21089}, {8591, 36224}, {17476, 17777}, {18159, 25138}

X(64863) = X(24292)-line conjugate of X(6)
X(64863) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64863) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 24345, 24714}, {148, 36223, 24711}, {190, 53559, 21254}

X(64864) = X(30)X(511)∩X(75)X(667)

Barycentrics    (b - c)*(-(a^4*b) - a^4*c - a*b^3*c - a*b^2*c^2 + b^3*c^2 - a*b*c^3 + b^2*c^3) : :
Barycentrics    b y - c z : : , where x : y : z = X(696)

X(64864) lies on these lines: {30, 511}, {37, 21260}, {75, 667}, {192, 21301}, {669, 20909}, {1278, 31291}, {3739, 31288}, {3797, 24601}, {4063, 49474}, {4411, 52601}, {4455, 20906}, {4664, 31149}, {4687, 31251}, {7234, 21438}, {8640, 20952}, {20891, 28255}, {21350, 44445}, {24325, 48330}, {24719, 49452}, {27485, 47839}, {28606, 30968}, {39227, 64728}, {48333, 49470}

X(64864) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64864) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64865) = X(30)X(511)∩X(75)X(798)

Barycentrics    (b - c)*(a^2 + b*c)*(-(a*b) - a*c + b*c) : :
Barycentrics    b y - c z : : , where x : y : z = X(698)

X(64865) lies on these lines: {30, 511}, {37, 22046}, {75, 798}, {192, 17217}, {649, 21438}, {661, 40849}, {669, 24356}, {894, 20981}, {3287, 4107}, {3709, 24782}, {3733, 4363}, {3768, 20949}, {3835, 25098}, {4017, 4444}, {4057, 24354}, {4357, 21099}, {4364, 31946}, {4369, 4374}, {4502, 48049}, {4504, 53553}, {4885, 21206}, {4897, 20508}, {5224, 21055}, {20295, 25271}, {20906, 20979}, {21191, 21348}, {24533, 30584}, {25258, 28372}, {25356, 44316}, {27469, 31296}, {27854, 49516}, {28960, 50458}, {51575, 58862}, {52615, 55184}

X(64865) = isogonal conjugate of X(58981)
X(64865) = crossdifference of every pair of points on line {6, 904}
X(64865) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64865) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {192, 17217, 21834}, {4374, 57234, 4369}, {14296, 45882, 4369}

X(64866) = X(30)X(511)∩X(75)X(649)

Barycentrics    (b - c)*(-(a^3*b) - a^3*c - a*b^2*c - a*b*c^2 + b^2*c^2) : :
Barycentrics    b y - c z : : , where x : y : z = X(712)

X(64866) lies on these lines: {2, 27485}, {30, 511}, {37, 3835}, {75, 649}, {192, 20295}, {667, 24354}, {798, 20906}, {1278, 26853}, {3261, 57234}, {3676, 4032}, {3739, 31286}, {4369, 4411}, {4375, 24357}, {4379, 4828}, {4664, 31147}, {4686, 48016}, {4687, 30835}, {4688, 45313}, {4699, 27013}, {4704, 26798}, {4751, 31207}, {4755, 45339}, {17217, 17458}, {20907, 52602}, {20949, 20979}, {21099, 21262}, {21260, 25356}, {21301, 24698}, {21348, 42327}, {22316, 50487}, {25381, 25384}, {27138, 27268}

X(64866) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64866) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64867) = X(30)X(511)∩X(75)X(3250)

Barycentrics    (b - c)*(a^2*b^2 + 2*a^2*b*c - a*b^2*c + a^2*c^2 - a*b*c^2 + b^2*c^2) : :
Barycentrics    b y - c z : : , where x : y : z = X(716)

X(64867) lies on these lines: {30, 511}, {75, 3250}, {321, 4079}, {350, 47874}, {663, 24354}, {889, 33946}, {1575, 47882}, {3063, 54282}, {3261, 4728}, {3666, 21348}, {3807, 31625}, {4374, 17458}, {4502, 20949}, {4688, 45658}, {4763, 6586}, {4817, 17318}, {4928, 45659}, {17072, 25356}, {17147, 17159}, {17759, 47894}, {18080, 62619}, {20907, 42327}, {20909, 42664}, {21113, 23794}, {21138, 39011}, {21225, 47776}, {21262, 21958}, {21433, 27485}, {24326, 36848}, {25368, 45666}, {41142, 47886}, {41144, 47879}, {47780, 50762}

X(64867) = crossdifference of every pair of points on line {6, 52892}
X(64867) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64867) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64868) = X(30)X(511)∩X(75)X(850)

Barycentrics    (b^2 - c^2)*(-a^3 + a*b^2 + b^2*c + a*c^2 + b*c^2) : :
Barycentrics    b y - c z : : , where x : y : z = X(758)

X(64868) lies on these lines: {30, 511}, {37, 647}, {75, 850}, {192, 31296}, {656, 4036}, {876, 56128}, {1577, 53527}, {1769, 48264}, {2394, 54679}, {2517, 50350}, {2530, 14288}, {2605, 7253}, {2667, 23757}, {3739, 17069}, {4010, 48350}, {4017, 30591}, {4025, 4411}, {4064, 62566}, {4086, 57099}, {4108, 44433}, {4122, 17989}, {4374, 57214}, {4391, 53574}, {4453, 4828}, {4477, 15624}, {4524, 22271}, {4560, 50349}, {4664, 36900}, {4681, 41300}, {4688, 31174}, {4699, 31072}, {4740, 63786}, {4755, 44560}, {4791, 23809}, {4833, 48288}, {5996, 31131}, {8062, 31947}, {14618, 44428}, {16229, 39534}, {17496, 53314}, {21180, 21192}, {21189, 50327}, {23301, 50335}, {23800, 50334}, {27485, 47886}, {28284, 47872}, {30572, 51641}, {31238, 31277}, {42027, 55244}, {42664, 48266}, {44918, 44929}, {48321, 55969}, {50329, 50330}, {50556, 53276}

X(64868) = crossdifference of every pair of points on line {6, 859}
X(64868) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1121, 1709}, {1260, 2057}, {1265, 2057}, {25836, 36038}
X(64868) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64869) = X(30)X(511)∩X(42)X(75)

Barycentrics    a^3*b^2 + 2*a^3*b*c - a*b^3*c + a^3*c^2 - b^3*c^2 - a*b*c^3 - b^2*c^3 : :
Barycentrics    b y - c z : : , where x : y : z = X(784)

X(64869) lies on these lines: {30, 511}, {37, 3741}, {42, 75}, {192, 7226}, {213, 24425}, {872, 20891}, {1278, 20011}, {2901, 49456}, {3009, 30939}, {3739, 6685}, {3783, 17790}, {3989, 4664}, {4022, 56185}, {4687, 31241}, {11364, 19623}, {15621, 64727}, {17144, 56129}, {21080, 64581}, {21878, 63570}, {22271, 59565}, {30273, 63389}, {41683, 50001}, {49491, 56125}, {49493, 64184}, {51063, 52856}, {58572, 58583}, {58644, 58655}, {61526, 61549}

X(64869) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}, {10113, 62513}
X(64869) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64870) = X(30)X(511)∩X(39)X(75)

Barycentrics    a^3*b^3 + a^3*b^2*c - a^2*b^3*c + a^3*b*c^2 + a^3*c^3 - a^2*b*c^3 - 2*b^3*c^3 : :
Barycentrics    b y - c z : : , where x : y : z = X(786)

X(64870) lies on these lines: {30, 511}, {37, 3934}, {39, 75}, {76, 192}, {194, 1278}, {350, 20688}, {1015, 19565}, {1574, 10009}, {1921, 21830}, {3739, 6683}, {3993, 12263}, {4363, 5145}, {4664, 9466}, {4686, 32450}, {4687, 31239}, {4688, 44562}, {4699, 7786}, {4704, 31276}, {4740, 7757}, {4788, 20081}, {5052, 49496}, {5188, 30273}, {6248, 20430}, {7751, 12338}, {7781, 22779}, {7976, 24349}, {8149, 49187}, {9902, 49445}, {11257, 63427}, {11272, 61549}, {12782, 49474}, {13334, 64728}, {14994, 49509}, {17486, 22199}, {17759, 20671}, {20889, 21814}, {21327, 28596}, {22012, 22036}, {25349, 60090}, {32035, 54101}, {33706, 51043}, {41622, 49533}, {44422, 51040}, {49111, 51046}, {49481, 64713}, {51063, 52854}, {56185, 56186}, {58486, 58499}, {58500, 58554}, {58584, 58620}, {58656, 58693}, {61550, 61623}

X(64870) = barycentric product X(i)*X(j) for these {i,j}: {554, 63871}, {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64870) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {6999, 64095}, {13158, 11015}
X(64870) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 21443, 3934}, {75, 32453, 39}, {1921, 21830, 27076}

X(64871) = X(30)X(511)∩X(75)X(3721)

Barycentrics    a^2*b^4 - a^3*b^2*c + a^2*b^3*c - a^3*b*c^2 - b^4*c^2 + a^2*b*c^3 + a^2*c^4 - b^2*c^4 : :
Barycentrics    b y - c z : : , where x : y : z = X(802)

X(64871) lies on these lines: {6, 25264}, {30, 511}, {75, 3721}, {141, 20888}, {192, 25270}, {335, 20432}, {3589, 25092}, {3726, 18157}, {3742, 59564}, {4022, 16720}, {6665, 58606}, {7781, 43149}, {15569, 59515}, {21138, 59526}, {21342, 62541}, {22285, 22316}, {33935, 49509}, {38047, 40774}

X(64871) = X(25264)-line conjugate of X(6)
X(64871) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64871) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64872) = X(30)X(511)∩X(75)X(2887)

Barycentrics    a*b^4 - 2*a^3*b*c + a*b^3*c - b^4*c + a*b*c^3 + a*c^4 - b*c^4 : :
Barycentrics    b y - c z : : , where x : y : z = X(814)

X(64872) lies on these lines: {3, 54220}, {4, 54165}, {20, 54221}, {30, 511}, {31, 192}, {37, 6679}, {75, 2887}, {209, 21080}, {1278, 6327}, {3993, 49480}, {4680, 49474}, {4699, 31237}, {4740, 31134}, {4788, 20064}, {17320, 33121}, {20575, 61623}, {23677, 25120}, {24325, 26728}, {24349, 49454}, {30269, 63427}, {49445, 49500}, {58390, 58400}

X(64872) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64872) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 18805, 6679}, {1278, 6327, 37003}

X(64873) = X(30)X(511)∩X(75)X(3670)

Barycentrics    a^3*b^3 + a^2*b^4 - b^4*c^2 + a^3*c^3 - 2*b^3*c^3 + a^2*c^4 - b^2*c^4 : :
Barycentrics    b y - c z : : , where x : y : z = X(834)

X(64873) lies on these lines: {30, 511}, {37, 10469}, {75, 3670}, {192, 19767}, {835, 5161}, {984, 4696}, {3159, 4681}, {3666, 22024}, {3706, 36862}, {3842, 59565}, {3931, 24068}, {4283, 17787}, {4686, 5295}, {4739, 24176}, {4980, 17155}, {5143, 32927}, {17157, 49493}, {17592, 32925}, {21080, 49456}, {24325, 27455}, {37598, 49517}

X(64873) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64873) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {234, 234}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {3327, 63947}, {33624, 46442}

X(64874) = X(30)X(511)∩X(75)X(244)

Barycentrics    a^2*b^3 - 2*a^2*b^2*c - 2*a^2*b*c^2 + 4*a*b^2*c^2 - b^3*c^2 + a^2*c^3 - b^2*c^3 : :
Barycentrics    b y - c z : : , where x : y : z = X(891)

X(64874) lies on these lines: {30, 511}, {37, 6377}, {75, 244}, {192, 872}, {668, 24338}, {984, 4738}, {1015, 25382}, {1086, 21100}, {1278, 17154}, {3123, 4033}, {3227, 35043}, {3248, 61183}, {3739, 40562}, {3807, 4664}, {3993, 34587}, {4674, 49474}, {4681, 52875}, {4686, 42027}, {4718, 4946}, {4764, 17157}, {4788, 20048}, {4868, 49456}, {4941, 30473}, {8683, 64727}, {9263, 24722}, {16495, 36798}, {17460, 49470}, {17793, 57023}, {21900, 40610}, {22313, 22316}, {39697, 50117}, {58396, 58401}

X(64874) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64874) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 1978, 52882}, {75, 41683, 244}, {192, 3952, 42083}, {9263, 36222, 24722}

X(64875) = X(30)X(511)∩X(69)X(73)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^4 - a^3*b - a^2*b^2 - a*b^3 + b^4 - a^3*c + 2*a^2*b*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(522)

X(64875) lies on these lines: {6, 7532}, {8, 28968}, {10, 3157}, {30, 511}, {68, 21077}, {69, 73}, {141, 6700}, {155, 10916}, {193, 5942}, {222, 34822}, {225, 5906}, {226, 5820}, {255, 34851}, {651, 1861}, {914, 1331}, {946, 12586}, {950, 37516}, {1001, 42460}, {1069, 45728}, {1352, 51759}, {1843, 14055}, {3100, 37781}, {3173, 4847}, {3416, 6736}, {3562, 46878}, {3751, 10573}, {3811, 11411}, {3911, 36059}, {3912, 23693}, {6193, 62858}, {6391, 15232}, {6510, 51366}, {6684, 47371}, {6776, 7289}, {7078, 34823}, {7352, 17647}, {10071, 21616}, {10072, 16475}, {10199, 38049}, {11019, 56294}, {12359, 59719}, {12513, 42461}, {12594, 31397}, {12832, 51198}, {14544, 23710}, {14913, 44548}, {18652, 21912}, {19588, 23361}, {20013, 20080}, {22769, 39870}, {23071, 60427}, {24477, 63174}, {30144, 49511}, {36643, 54420}, {36846, 51192}, {37836, 63612}, {39873, 64042}, {39889, 64119}, {41883, 58402}, {58462, 63840}, {58581, 58585}, {58653, 58657}, {61545, 61547}, {63357, 63450}

X(64875) = X(7532)-line conjugate of X(6)
X(64875) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64875) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {234, 234}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64876) = X(30)X(511)∩X(69)X(647)

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 + c^2)*(3*a^4 - a^2*b^2 - a^2*c^2 + 2*b^2*c^2) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(538)

X(64876) lies on these lines: {6, 30476}, {30, 511}, {69, 647}, {193, 850}, {599, 44560}, {1992, 31174}, {3049, 52598}, {3618, 31277}, {11160, 36900}, {19126, 58310}, {20080, 31296}, {22264, 32257}, {31072, 51170}, {32113, 47442}, {32220, 47004}, {40341, 41300}, {46989, 47541}, {47001, 47551}, {47255, 52238}

X(64876) = crossdifference of every pair of points on line {6, 46522}
X(64876) = X(30476)-line conjugate of X(6)
X(64876) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64876) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {12252, 36695}

X(64877) = X(30)X(511)∩X(69)X(41298)

Barycentrics    (b^2 - c^2)*(2*a^6 - 3*a^4*b^2 + b^6 - 3*a^4*c^2 - 2*a^2*b^2*c^2 - b^4*c^2 - b^2*c^4 + c^6) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(539)

X(64877) lies on these lines: {6, 2623}, {30, 511}, {69, 41298}, {141, 38429}, {597, 44568}, {1116, 10168}, {1176, 15328}, {1992, 44554}, {2394, 54879}, {2916, 30511}, {3005, 60342}, {3288, 47138}, {3818, 43083}, {5476, 15475}, {9131, 13318}, {9979, 13315}, {10412, 19130}, {13290, 41583}, {14220, 34437}, {14380, 15321}, {14610, 42651}, {15453, 18125}, {15543, 51737}, {19128, 50946}, {25565, 39494}, {32600, 46608}, {39481, 44809}, {46026, 50543}, {47193, 63830}

X(64877) = isogonal conjugate of X(58975)
X(64877) = Thomson-isogonal conjugate of X(64660)
X(64877) = crossdifference of every pair of points on line {6, 1154}
X(64877) = X(i)-line conjugate of X(j) for these (i,j): {30, 1154}, {2623, 6}
X(64877) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64877) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {32516, 46335}

X(64878) = X(3)X(4091)∩X(30)X(511)

Barycentrics    a^2*(b - c)*(a^2 - b^2 - c^2)*(a*b - b^2 + a*c - b*c - c^2) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(674)

X(64878) lies on these lines: {3, 4091}, {30, 511}, {72, 6332}, {101, 15378}, {386, 52595}, {650, 44410}, {652, 22160}, {663, 53554}, {905, 53550}, {942, 14837}, {1459, 17976}, {3157, 57223}, {3874, 20517}, {4163, 34790}, {4449, 53562}, {5045, 52596}, {5904, 48272}, {9404, 34975}, {10449, 52622}, {23090, 57129}, {23187, 57241}, {35100, 50504}, {39476, 44827}, {44408, 53249}, {48387, 53301}, {57042, 57133}, {57279, 58339}

X(64878) = isogonal conjugate of X(26705)
X(64878) = isotomic conjugate of the isogonal conjugate of X(22388)
X(64878) = isogonal conjugate of the isotomic conjugate of X(57054)
X(64878) = isotomic conjugate of the polar conjugate of X(6586)
X(64878) = isogonal conjugate of the polar conjugate of X(25259)
X(64878) = Thomson-isogonal conjugate of X(41905)
X(64878) = crossdifference of every pair of points on line {6, 1836}
X(64878) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}, {31524, 47025}
X(64878) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64878) = {X(4091),X(57108)}-harmonic conjugate of X(3)

X(64879) = X(30)X(511)∩X(69)X(4173)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4*b^4 + a^2*b^6 - a^2*b^4*c^2 + a^4*c^4 - a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(688)

X(64879) lies on these lines: {6, 19597}, {30, 511}, {69, 4173}, {193, 10340}, {263, 63174}, {695, 6391}, {1843, 7762}, {3499, 19588}, {3511, 52967}, {5039, 43977}, {7767, 11574}, {7893, 12220}, {17932, 34238}, {32451, 40951}, {34236, 59553}, {37890, 63612}, {47286, 52460}

X(64879) = X(19597)-line conjugate of X(6)
X(64879) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64879) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {414, 416}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}

X(64880) = X(30)X(511)∩X(69)X(125)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 - 2*a^4*b^2 - 3*a^2*b^4 + b^6 - 2*a^4*c^2 + 8*a^2*b^2*c^2 - b^4*c^2 - 3*a^2*c^4 - b^2*c^4 + c^6) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(690)

X(64880) lies on these lines: {6, 5181}, {30, 511}, {67, 6391}, {68, 5505}, {69, 125}, {74, 20187}, {110, 193}, {113, 1351}, {115, 36207}, {141, 6723}, {155, 19140}, {182, 5486}, {265, 11898}, {287, 46459}, {576, 5654}, {599, 45311}, {974, 52520}, {1147, 19138}, {1270, 13654}, {1271, 13774}, {1350, 37853}, {1352, 7687}, {1353, 1511}, {1495, 32220}, {1843, 40316}, {1992, 5642}, {2104, 14499}, {2105, 14500}, {2407, 47200}, {2452, 51389}, {2930, 6144}, {2931, 12584}, {3047, 19121}, {3167, 5648}, {3448, 20080}, {3580, 32127}, {3620, 15059}, {3629, 6593}, {3630, 25328}, {3631, 6698}, {3818, 63710}, {4590, 62348}, {5050, 38793}, {5085, 48375}, {5093, 14643}, {5102, 38792}, {5467, 41359}, {5477, 53735}, {5622, 10519}, {5655, 50962}, {5921, 10733}, {5987, 50248}, {6036, 40879}, {6053, 9970}, {6403, 15473}, {6467, 32285}, {6699, 48876}, {6721, 18122}, {6776, 16163}, {6791, 36696}, {7728, 44456}, {7890, 19597}, {8263, 61507}, {8541, 12827}, {8542, 12596}, {8548, 15115}, {8550, 33851}, {8584, 59553}, {9140, 11160}, {9813, 14561}, {9820, 22330}, {9822, 11746}, {9924, 32264}, {9925, 16510}, {9976, 49116}, {10117, 37491}, {10272, 61624}, {10516, 14914}, {10752, 15063}, {10754, 16278}, {10992, 48539}, {11008, 11061}, {11064, 47277}, {11178, 63650}, {11438, 63722}, {11477, 14982}, {11482, 38795}, {11574, 41673}, {11579, 20417}, {11720, 51196}, {11735, 49511}, {11800, 14913}, {12038, 33749}, {12039, 25555}, {12121, 39899}, {12164, 51941}, {12272, 32239}, {12294, 12825}, {12295, 18440}, {12302, 32305}, {12383, 32234}, {12900, 18583}, {12902, 32272}, {13169, 50992}, {13198, 19126}, {13202, 41737}, {13289, 37488}, {13417, 40228}, {13479, 35922}, {14852, 34507}, {14853, 36518}, {14912, 15035}, {15055, 62174}, {15061, 39562}, {15113, 23326}, {15526, 22143}, {16003, 37483}, {16111, 33878}, {16511, 58445}, {16534, 64067}, {19139, 25556}, {20127, 55584}, {20301, 23306}, {20304, 61545}, {20772, 41585}, {20806, 34470}, {21639, 62382}, {21850, 46686}, {22234, 64181}, {22660, 55718}, {22663, 44862}, {30714, 37489}, {32113, 32223}, {32269, 47279}, {32271, 37517}, {32661, 41672}, {34319, 45082}, {34417, 49125}, {34986, 41612}, {35266, 47541}, {35511, 39652}, {36891, 44556}, {37784, 64724}, {38726, 48906}, {38788, 55593}, {38794, 53091}, {39873, 46687}, {39897, 46683}, {40337, 40949}, {41583, 41615}, {41584, 41616}, {41586, 41617}, {41588, 41618}, {41614, 61644}, {41671, 58555}, {41720, 44082}, {44569, 47551}, {45237, 61667}, {47278, 47582}, {47280, 62381}, {51198, 53743}, {53351, 54395}, {58601, 58621}, {58671, 58694}, {58726, 64063}, {61665, 61666}, {63694, 63702}

X(64880) = isogonal conjugate of X(40119)
X(64880) = isotomic conjugate of the polar conjugate of X(10418)
X(64880) = Thomson-isogonal conjugate of X(53961)
X(64880) = X(5181)-line conjugate of X(6)
X(64880) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64880) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64880) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5181, 5972}, {6, 5972, 32300}, {69, 125, 32257}, {69, 895, 125}, {69, 4563, 52881}, {69, 64235, 4563}, {110, 193, 5095}, {141, 15118, 6723}, {193, 40317, 1974}, {265, 11898, 32275}, {1351, 63700, 113}, {2930, 6144, 64104}, {2930, 64104, 56565}, {3448, 20080, 32244}, {5095, 32114, 110}, {5622, 10519, 38727}, {5648, 15534, 15303}, {5921, 10733, 32250}, {11064, 53778, 47277}, {11800, 14913, 32246}, {12310, 19588, 2930}, {32113, 53777, 32223}, {41617, 41721, 41586}, {41737, 51212, 13202}

X(64881) = X(30)X(511)∩X(69)X(3049)

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 + c^2)*(2*a^4 - a^2*b^2 - a^2*c^2 + b^2*c^2) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(698)

X(64881) lies on these lines: {30, 511}, {69, 3049}, {193, 2451}, {1992, 55190}, {3050, 40341}, {3288, 20080}, {3629, 39520}, {4108, 13303}, {4590, 32661}, {7779, 32320}, {11160, 45335}, {13302, 36900}, {14023, 42660}, {14607, 61199}, {17731, 23145}, {52038, 63182}

X(64881) = isotomic conjugate of the polar conjugate of X(44451)
X(64881) = crossdifference of every pair of points on line {6, 30496}
X(64881) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64881) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {28134, 32792}

X(64882) = X(30)X(511)∩X(69)X(20819)

Barycentrics    (a^2 - b^2 - c^2)*(a^6*b^2 - 3*a^4*b^4 + a^6*c^2 + 2*a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 - 3*a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 + b^2*c^6) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(804)

X(64882) lies on these lines: {6, 59569}, {30, 511}, {69, 20819}, {193, 3186}, {287, 22143}, {290, 6391}, {648, 57258}, {800, 11672}, {1351, 43976}, {2421, 47211}, {2456, 40888}, {3167, 14614}, {3511, 19588}, {5306, 59553}, {6776, 30262}, {9307, 52091}, {32661, 41675}, {54998, 56268}, {56390, 57257}, {63065, 64177}, {63093, 63174}

X(64882) = crossdifference of every pair of points on line {6, 7656}
X(64882) = X(59569)-line conjugate of X(6)
X(64882) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64882) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64882) = {X(193),X(53350)}-harmonic conjugate of X(51335)

X(64883) = X(30)X(511)∩X(69)X(184)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 - a^2*b^4 + b^6 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(826)

X(64883) lies on these lines: {5, 12585}, {6, 8280}, {30, 511}, {68, 576}, {69, 184}, {98, 44363}, {110, 64724}, {114, 44375}, {125, 22151}, {141, 53022}, {155, 34507}, {161, 37491}, {193, 7378}, {575, 12359}, {578, 11411}, {597, 32068}, {599, 3167}, {895, 18125}, {1147, 40107}, {1351, 18474}, {1352, 9813}, {1843, 46442}, {1899, 11511}, {2916, 19588}, {3292, 32257}, {3448, 11416}, {3455, 7813}, {3521, 55977}, {3580, 44102}, {3630, 63612}, {5095, 12827}, {5181, 41615}, {5449, 25555}, {5476, 14852}, {5477, 58312}, {5486, 43689}, {5654, 11178}, {5972, 62376}, {5986, 7779}, {6030, 11160}, {6036, 44388}, {6144, 6391}, {6193, 46728}, {6593, 32317}, {6698, 32283}, {6776, 63425}, {7826, 19597}, {8538, 25738}, {8542, 15083}, {9306, 63129}, {9512, 60524}, {9822, 13562}, {9929, 44471}, {9930, 44472}, {10112, 50649}, {10116, 15074}, {11061, 27085}, {11255, 18356}, {11477, 12429}, {11574, 26926}, {11898, 18445}, {12118, 52987}, {12164, 15069}, {12310, 25336}, {13292, 44495}, {15054, 54216}, {15063, 54162}, {15136, 40919}, {15462, 44673}, {15526, 58356}, {16176, 64214}, {16511, 33749}, {16835, 56268}, {18374, 32223}, {18475, 48876}, {18488, 36747}, {18553, 22660}, {18951, 44489}, {19061, 44473}, {19062, 44474}, {19139, 24206}, {19153, 61646}, {19467, 35240}, {19596, 41583}, {20080, 41464}, {20190, 44158}, {20299, 44469}, {20417, 54215}, {21356, 64177}, {24981, 41721}, {25556, 46085}, {32154, 43839}, {32267, 45082}, {32275, 63720}, {32284, 32358}, {32300, 62375}, {32600, 32621}, {34787, 61751}, {34986, 54347}, {38303, 61199}, {40673, 45968}, {42007, 48999}, {43595, 64180}, {44475, 48738}, {44476, 48739}, {44501, 49225}, {44502, 49224}, {44654, 49321}, {44655, 49322}, {45016, 63735}, {47391, 50977}, {52144, 62338}, {53021, 64179}, {54036, 63118}, {59373, 61712}, {61544, 63702}, {61545, 61619}, {61677, 64599}

X(64883) = X(8280)-line conjugate of X(6)
X(64883) = barycentric product X(i)*X(j) for these {i,j}: {554, 1652}, {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64883) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64883) = {X(193),X(11442)}-harmonic conjugate of X(8541)

X(64884) = X(30)X(511)∩X(69)X(1565)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^4 - 2*a^3*b - a^2*b^2 - 2*a*b^3 + b^4 - 2*a^3*c + 4*a^2*b*c + 2*a*b^2*c - a^2*c^2 + 2*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 + c^4) : :
Barycentrics    y tan B - c tan C : : , where x : y : z = X(900)

X(64884) lies on these lines: {6, 59594}, {30, 511}, {69, 1565}, {193, 3732}, {613, 56294}, {1086, 36205}, {1146, 10756}, {2968, 22148}, {4551, 56848}, {6391, 38955}, {7289, 48906}, {17728, 59553}, {34586, 63612}, {42460, 42884}, {43146, 61524}, {51196, 51435}

X(64884) = X(59594)-line conjugate of X(6)
X(64884) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64884) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {24713, 25033}

X(64885) = X(30)X(511)∩X(63)X(57184)

Barycentrics    a*(b - c)*(a^2 - b^2 - c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 - c^3) : :
Barycentrics    y sec B - c sec C : : , where x : y : z = X(515)

X(64885) lies on these lines: {3, 58340}, {30, 511}, {63, 57184}, {69, 15416}, {222, 2431}, {651, 7128}, {652, 905}, {1019, 23090}, {1565, 52115}, {2095, 42772}, {3157, 34975}, {3669, 36054}, {4131, 6332}, {4391, 46400}, {7178, 46389}, {9810, 13302}, {9811, 13303}, {10397, 57233}, {11247, 28787}, {14298, 14837}, {14353, 51658}, {17094, 60494}, {17896, 59935}, {17924, 57166}, {21362, 52610}, {23727, 57243}, {24018, 57055}, {45709, 48971}, {45710, 49003}, {48107, 63245}, {48335, 57042}, {53833, 55063}

X(64885) = isogonal conjugate of X(40117)
X(64885) = isogonal conjugate of the anticomplement of X(53833)
X(64885) = isotomic conjugate of the polar conjugate of X(6129)
X(64885) = isogonal conjugate of the polar conjugate of X(17896)
X(64885) = trilinear pole of line {47432, 53557}
X(64885) = crossdifference of every pair of points on line {6, 33}
X(64885) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64885) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}
X(64885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {652, 51664, 905}, {4131, 20296, 6332}

X(64886) = X(30)X(511)∩X(63)X(652)

Barycentrics    (b - c)*(-a^2 + b^2 + c^2)*(-a^3 + a^2*b - a*b^2 + b^3 + a^2*c - 2*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3) : :
Barycentrics    y sec B - c sec C : : , where x : y : z = X(518)

X(64886) lies on these lines: {30, 511}, {63, 652}, {226, 3239}, {2509, 14837}, {2522, 21107}, {3064, 17896}, {3173, 57042}, {4391, 48070}, {5745, 7658}, {5905, 25259}, {6332, 15413}, {8611, 23727}, {8896, 55232}, {16612, 21174}, {17094, 57055}, {20315, 24459}, {22001, 57169}, {57243, 57245}

X(64886) = isogonal conjugate of X(58944)
X(64886) = isotomic conjugate of the polar conjugate of X(47123)
X(64886) = crossdifference of every pair of points on line {6, 2212}
X(64886) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64886) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {53212, 31074}

X(64887) = X(30)X(511)∩X(63)X(77)

Barycentrics    a*(a^2 - b^2 - c^2)*(a^4*b - 2*a^2*b^3 + b^5 + a^4*c - 2*a^3*b*c + 2*a^2*b^2*c - b^4*c + 2*a^2*b*c^2 - 2*a^2*c^3 - b*c^4 + c^5) : :
Barycentrics    y sec B - c sec C : : , where x : y : z = X(522)

X(64887) lies on these lines: {30, 511}, {63, 77}, {92, 1947}, {226, 6708}, {241, 52610}, {942, 56552}, {1439, 17073}, {1741, 4341}, {1763, 3684}, {1944, 1952}, {3157, 12514}, {3211, 60974}, {4566, 37805}, {4641, 22130}, {4643, 7352}, {5745, 53415}, {5887, 24316}, {6237, 63707}, {6360, 20078}, {6508, 40152}, {6511, 64455}, {9121, 54422}, {10605, 18446}, {14571, 45266}, {15836, 62858}, {16702, 32661}, {23075, 23853}, {24315, 34339}, {24682, 31937}, {24684, 40296}, {26932, 62402}, {34176, 59681}, {36949, 62326}, {37826, 39529}, {40843, 44360}, {44356, 59813}, {44916, 51755}, {56294, 62839}, {63447, 63448}

X(64887) = isogonal conjugate of X(20624)
X(64887) = isotomic conjugate of the polar conjugate of X(8758)
X(64887) = crossdifference of every pair of points on line {6, 18344}
X(64887) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}
X(64887) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {234, 234}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {42251, 44246}

X(64888) = X(30)X(511)∩X(48)X(63)

Barycentrics    a*(b + c)*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 + 3*a^2*b*c - b^3*c - 2*a^2*c^2 - b*c^3 + c^4) : :
Barycentrics    y sec B - c sec C : : , where x : y : z = X(523)

X(64888) lies on these lines: {30, 511}, {48, 63}, {226, 7363}, {2256, 3173}, {2294, 8545}, {3157, 3743}, {3167, 53035}, {3647, 41608}, {4068, 42460}, {5693, 24316}, {5745, 58406}, {5884, 24315}, {5905, 21270}, {6237, 63967}, {8896, 51367}, {9119, 40530}, {11411, 23555}, {12164, 42440}, {15071, 24683}, {18589, 52385}, {20074, 20078}, {20117, 24317}, {24682, 31803}, {25081, 61004}, {25255, 60946}, {31163, 31164}, {31265, 31266}, {47371, 58392}, {61531, 61539}

X(64888) = barycentric product X(i)*X(j) for these {i,j}: {554, 1652}, {1034, 2057}, {1260, 2057}, {1265, 2057}, {45938, 53925}
X(64888) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {53986, 37117}

X(64889) = X(30)X(511)∩X(63)X(295)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - a^2*b^2*c - b^4*c + a^3*c^2 - a^2*b*c^2 + 4*a*b^2*c^2 - a^2*c^3 - a*c^4 - b*c^4 + c^5) : :
Barycentrics    y sec B - c sec C : : , where x : y : z = X(812)

X(64889) lies on these lines: {30, 511}, {51, 31164}, {63, 295}, {101, 579}, {226, 5943}, {595, 3157}, {1362, 1397}, {1364, 22148}, {1851, 3060}, {3271, 36280}, {3433, 47391}, {4303, 22399}, {5185, 15906}, {5745, 64489}, {10219, 58463}, {10822, 34931}, {18389, 29957}, {18446, 64100}, {20078, 62188}, {20256, 59683}, {20760, 39796}, {23039, 52115}, {34928, 42463}, {46174, 61539}

X(64889) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2057}, {1260, 2057}, {1265, 2057}, {4373, 26390}
X(64889) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2057}, {845, 2057}, {1035, 2057}, {1119, 2057}, {1847, 2057}, {2057, 2057}, {2091, 2057}, {15372, 28688}

X(64890) = 13TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (3 a^6 - 4 a^4 b^2 - a^2 b^4 + 2 b^6 - 4 a^4 c^2 + 7 a^2 b^2 c^2 - 2 b^4 c^2 - a^2 c^4 - 2 b^2 c^4 + 2 c^6) : :

Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6813.

X(64890) lies on these lines: {2, 3}, {74, 13851}, {148, 56016}, {275, 19651}, {476, 23956}, {477, 33640}, {515, 31948}, {1154, 12292}, {1199, 13403}, {1300, 39371}, {1514, 15152}, {1531, 43574}, {1539, 3043}, {1699, 51701}, {1843, 48943}, {1986, 58789}, {2777, 13399}, {2914, 12112}, {3087, 47322}, {3357, 18394}, {5446, 43846}, {5890, 32411}, {5895, 16880}, {6000, 7722}, {6403, 48904}, {6746, 22948}, {6748, 47275}, {6759, 40242}, {7728, 30522}, {10098, 43663}, {10149, 12953}, {10152, 10421}, {10733, 13754}, {10735, 44972}, {11381, 48914}, {11456, 61721}, {11565, 43585}, {11649, 48884}, {11692, 14915}, {12133, 13391}, {12244, 15153}, {12289, 22802}, {12290, 34786}, {12294, 48942}, {12295, 50435}, {13376, 46850}, {14157, 15463}, {14537, 53026}, {14644, 21663}, {15081, 50709}, {16303, 40065}, {18848, 59278}, {19128, 29323}, {20774, 62490}, {21268, 32710}, {34224, 51491}, {36969, 56514}, {36970, 56515}, {40118, 58095}, {44872, 61691}, {44967, 44990}, {46045, 48364}, {51733, 53023}

X(64891) = 14TH HATZIPOLAKIS-GARCÍA CAPITÁN-EULER POINT

Barycentrics    4 a^10 - 5 a^8 b^2 - 6 a^6 b^4 + 8 a^4 b^6 + 2 a^2 b^8 - 3 b^10 - 5 a^8 c^2 + 22 a^6 b^2 c^2 - 10 a^4 b^4 c^2 - 16 a^2 b^6 c^2 + 9 b^8 c^2 - 6 a^6 c^4 - 10 a^4 b^2 c^4 + 28 a^2 b^4 c^4 - 6 b^6 c^4 + 8 a^4 c^6 - 16 a^2 b^2 c^6 - 6 b^4 c^6 + 2 a^2 c^8 + 9 b^2 c^8 - 3 c^10 : :

Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6813.

X(64891) lies on these lines: {2, 3}, {49, 5893}, {265, 15311}, {1514, 5504}, {3521, 12241}, {5895,25738}, {6000, 11800}, {7728, 44665}, {10721, 50435}, {12121, 51425}, {13202, 13754}, {15317, 46372}, {16163, 59648}, {16655, 52863}, {18481, 51713}, {22115, 51998}, {22337, 50472}, {22802, 44076}, {23515, 44872}, {28164, 51701}, {29323, 47455}, {30522, 32111}, {32113, 48904}, {34584, 63839}, {34783, 51491}, {38292, 47162}, {38956, 62501}, {43574, 58885}, {46264, 51742}, {46431, 53781}, {46686, 51394}, {46850, 58551}

X(64892) = X(526)X(12052)∩X(924)X(11746)

Barycentrics    a^2 (a^14 b^2 - 2 a^12 b^4 - 4 a^10 b^6 + 15 a^8 b^8 - 15 a^6 b^10 + 4 a^4 b^12 + 2 a^2 b^14 - b^16 + a^14 c^2 - 4 a^12 b^2 c^2 + 10 a^10 b^4 c^2 - 18 a^8 b^6 c^2 + 13 a^6 b^8 c^2 + 8 a^4 b^10 c^2 - 16 a^2 b^12 c^2 + 6 b^14 c^2 - 2 a^12 c^4 + 10 a^10 b^2 c^4 - 2 a^8 b^4 c^4 + 3 a^6 b^6 c^4 - 32 a^4 b^8 c^4 + 33 a^2 b^10 c^4 - 10 b^12 c^4 - 4 a^10 c^6 - 18 a^8 b^2 c^6 + 3 a^6 b^4 c^6 + 40 a^4 b^6 c^6 - 19 a^2 b^8 c^6 + 2 b^10 c^6 + 15 a^8 c^8 + 13 a^6 b^2 c^8 - 32 a^4 b^4 c^8 - 19 a^2 b^6 c^8 + 6 b^8 c^8 - 15 a^6 c^10 + 8 a^4 b^2 c^10 + 33 a^2 b^4 c^10 + 2 b^6 c^10 + 4 a^4 c^12 - 16 a^2 b^2 c^12 - 10 b^4 c^12 + 2 a^2 c^14 + 6 b^2 c^14 - c^16) : :

Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 6813.

X(64892) lies on these lines: {526, 12052}, {924, 11746}, {6000, 51998}, {11751, 45237}

X(64893) = 79th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(9*a^3-18*(b+c)*a^2-(9*b^2-40*b*c+9*c^2)*a+18*(b^2-c^2)*(b-c)) : :
X(64893) = 11*X(1)-9*X(64849) = 3*X(1)-X(64895)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 24/07/2024. (Aug 21, 2024)

X(64893) lies on these lines: {1, 3}, {4930, 20050}, {5330, 46931}, {5734, 10592}

X(64893) = reflection of X(64894) in X(1)

X(64894) = 80th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(9*a^2+4*b*c-9*b^2-9*c^2) : :
X(64894) = 7*X(1)-9*X(64849)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 24/07/2024. (Aug 21, 2024)

X(64894) lies on these lines: {1, 3}, {8, 19705}, {11, 15696}, {12, 61811}, {20, 10593}, {34, 55574}, {80, 38637}, {140, 5229}, {376, 9669}, {382, 7173}, {388, 15712}, {390, 62066}, {404, 46931}, {495, 15717}, {496, 3528}, {497, 33923}, {498, 15693}, {499, 3534}, {548, 7288}, {549, 9654}, {550, 5225}, {611, 55678}, {613, 55639}, {631, 9655}, {956, 37307}, {993, 17573}, {1056, 61791}, {1058, 62067}, {1124, 6451}, {1335, 6452}, {1398, 21844}, {1428, 55629}, {1469, 55682}, {1478, 15720}, {1479, 62100}, {1656, 15326}, {1657, 5433}, {2066, 6496}, {2067, 6456}, {3056, 55643}, {3058, 62070}, {3085, 12100}, {3086, 8703}, {3299, 6445}, {3301, 6446}, {3522, 15325}, {3523, 31479}, {3524, 18990}, {3526, 3614}, {3530, 4293}, {3582, 15695}, {3583, 62131}, {3584, 61797}, {3585, 46219}, {3600, 31480}, {3616, 19704}, {3617, 13587}, {3625, 11194}, {3634, 16417}, {3843, 4316}, {4188, 9708}, {4225, 27645}, {4294, 46853}, {4302, 62085}, {4317, 61793}, {4324, 62105}, {4325, 61818}, {4652, 35271}, {5020, 5370}, {5054, 7354}, {5055, 10483}, {5070, 12943}, {5072, 7294}, {5218, 44682}, {5261, 61807}, {5265, 21735}, {5267, 16408}, {5274, 62092}, {5281, 61787}, {5298, 14093}, {5303, 9780}, {5326, 61831}, {5414, 6497}, {5432, 61803}, {5434, 15706}, {5550, 16370}, {5552, 34740}, {6284, 15688}, {6407, 18995}, {6408, 18996}, {6455, 6502}, {6880, 40267}, {7286, 37955}, {7727, 38633}, {7741, 17800}, {7951, 55863}, {7972, 38636}, {8164, 61804}, {8540, 55595}, {8588, 16781}, {9341, 22332}, {9579, 28451}, {9670, 58192}, {9709, 19537}, {10056, 15716}, {10072, 62073}, {10304, 15171}, {10385, 15714}, {10386, 62064}, {10387, 55655}, {10529, 34707}, {10588, 12108}, {10589, 15704}, {10590, 14869}, {10591, 12103}, {10645, 54437}, {10646, 54438}, {10895, 15694}, {10896, 15681}, {11237, 15718}, {11238, 62088}, {11544, 21161}, {12019, 38693}, {12953, 62121}, {14986, 19708}, {15170, 15710}, {15172, 45759}, {15338, 62082}, {15655, 16502}, {15700, 52793}, {16402, 26115}, {16418, 19862}, {16431, 29579}, {17316, 21497}, {17549, 46934}, {18513, 61919}, {18514, 49139}, {19470, 38638}, {19706, 19854}, {21498, 26626}, {21539, 29596}, {31447, 37709}, {31461, 46846}, {35501, 54428}, {42115, 54403}, {42116, 54402}, {47743, 62097}

X(64894) = midpoint of X(1) and X(64895)
X(64894) = reflection of X(64893) in X(1)
X(64894) = pole of the line {21, 8163} with respect to the Stammler hyperbola
X(64894) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (5204, 5217, 36), (5204, 59319, 3)

X(64895) = 81st TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(9*a^3+9*(b+c)*a^2-(9*b^2+14*b*c+9*c^2)*a-9*(b^2-c^2)*(b-c)) : :
X(64895) = 8*X(1)-9*X(64849) = 3*X(1)-2*X(64893)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 24/07/2024. (Aug 21, 2024)

X(64895) lies on these lines: {1, 3}, {9, 61770}, {3614, 9588}, {3617, 3929}, {3621, 3928}, {3625, 63138}, {3626, 54290}, {5225, 5493}, {5229, 43174}, {7173, 9589}, {7308, 46931}, {11682, 63915}, {12512, 64736}, {12526, 63916}, {20070, 31231}, {31426, 46846}

X(64895) = reflection of X(1) in X(64894)
X(64895) = pole of the line {513, 58168} with respect to the Bevan circle
X(64895) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (40, 41348, 57), (46, 37556, 57)

X(64896) = 82nd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a^3-3*(b+c)*a^2-(b^2-7*b*c+c^2)*a+3*(b^2-c^2)*(b-c)) : :
X(64896) = 3*X(1)-2*X(36) = 7*X(1)-4*X(1155) = 5*X(1)-4*X(1319) = 5*X(1)-2*X(3245) = 3*X(1)-4*X(5048) = 13*X(1)-8*X(5122) = 11*X(1)-8*X(5126) = 5*X(1)-3*X(5131) = 9*X(1)-4*X(5183) = 9*X(1)-8*X(25405) = 4*X(36)-3*X(484) = 7*X(36)-6*X(1155) = 5*X(36)-6*X(1319) = 5*X(36)-3*X(3245) = 10*X(36)-9*X(5131) = 3*X(36)-2*X(5183) = 3*X(36)-4*X(25405) = X(36)-3*X(63210) = 7*X(484)-8*X(1155) = 5*X(484)-8*X(1319)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 24/07/2024. (Aug 21, 2024)

X(64896) lies on these lines: {1, 3}, {8, 11813}, {12, 5559}, {30, 7972}, {80, 5844}, {145, 5180}, {149, 519}, {191, 4861}, {497, 34631}, {498, 5734}, {513, 58167}, {515, 13253}, {518, 41702}, {529, 25416}, {535, 34611}, {758, 1320}, {912, 7993}, {1168, 34857}, {1317, 28174}, {1318, 4674}, {1389, 7161}, {1391, 56844}, {1392, 11279}, {2222, 28223}, {2308, 15955}, {2316, 21801}, {2392, 24681}, {2802, 45764}, {3241, 4302}, {3243, 28534}, {3244, 16126}, {3467, 21398}, {3577, 22835}, {3585, 4301}, {3625, 11524}, {3632, 5176}, {3633, 5057}, {3656, 7951}, {3678, 64201}, {3679, 3814}, {3680, 5560}, {3872, 3899}, {3880, 4867}, {3884, 5284}, {3901, 36846}, {3984, 4816}, {4293, 50872}, {4316, 28194}, {4324, 5882}, {4325, 63987}, {4345, 10072}, {4511, 5541}, {4668, 5087}, {4677, 11235}, {4695, 4792}, {4919, 5525}, {5123, 15829}, {5252, 61703}, {5274, 10573}, {5288, 33895}, {5326, 5901}, {5441, 37734}, {5444, 10283}, {5690, 37735}, {5730, 8168}, {5854, 51409}, {5881, 18514}, {5904, 10912}, {6264, 14988}, {6681, 25055}, {6763, 22837}, {6905, 25485}, {7727, 23153}, {7743, 36920}, {9037, 16496}, {9668, 50805}, {10483, 37738}, {10589, 12245}, {10590, 12647}, {10697, 34931}, {10698, 41689}, {11274, 36005}, {11523, 33956}, {12699, 37707}, {12701, 37706}, {12735, 15326}, {13391, 52524}, {13606, 16137}, {15015, 63136}, {15228, 28212}, {15338, 61286}, {15863, 37375}, {16118, 45287}, {16173, 40663}, {16548, 17455}, {17757, 64056}, {18513, 31162}, {19875, 31263}, {21578, 28228}, {22791, 37710}, {23708, 63143}, {26726, 38455}, {28186, 62617}, {28234, 30384}, {30294, 61709}, {31855, 61476}, {34743, 34747}, {37720, 41687}, {37730, 64766}, {37731, 45081}, {40109, 42042}, {40587, 58641}, {43731, 56152}, {43732, 56038}, {48293, 61637}, {52793, 61278}, {54154, 64138}, {54192, 64136}, {54391, 64137}, {56422, 56691}, {59311, 62352}, {61276, 61521}

X(64896) = midpoint of X(i) and X(j) for these (i, j): {145, 5180}, {5538, 11531}, {8148, 35457}
X(64896) = reflection of X(i) in X(j) for these (i, j): (1, 63210), (8, 11813), (36, 5048), (484, 1), (3245, 1319), (3632, 5176), (4677, 31160), (5183, 25405), (5541, 4511), (6905, 25485), (7991, 2077), (9897, 3583), (15326, 12735), (22765, 10222), (31855, 61476), (36005, 11274), (36920, 7743), (36975, 1317), (41347, 33179), (41684, 30384), (54154, 64138), (54391, 64137), (64056, 17757), (64136, 54192)
X(64896) = isogonal conjugate of the antigonal conjugate of X(17501)
X(64896) = cross-difference of every pair of points on the line X(650)X(16671)
X(64896) = X(24302)-Ceva conjugate of-X(1)
X(64896) = X(513)-vertex conjugate of-X(59319)
X(64896) = Gibert-Burek-Moses concurrent circles image of X(1482)
X(64896) = inverse of X(5563) in mixtilinear incircles radical circle
X(64896) = inverse of X(31792) in: incircle, de Longchamps ellipse
X(64896) = inverse of X(59319) in circumcircle
X(64896) = pole of the line {513, 59319} with respect to the circumcircle
X(64896) = pole of the line {513, 31792} with respect to the incircle
X(64896) = pole of the line {513, 5563} with respect to the mixtilinear incircles radical circle
X(64896) = pole of the line {513, 31792} with respect to the de Longchamps ellipse
X(64896) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (35, 10222, 1), (36, 5048, 1), (55, 62318, 36), (1482, 5697, 1), (2098, 5903, 1), (3057, 11009, 1), (3746, 11011, 1), (5119, 16200, 1), (5183, 25405, 36), (5425, 5919, 1), (5535, 13384, 36), (5902, 64897, 1), (7962, 25415, 1), (7982, 30323, 1), (10247, 37525, 1), (24926, 33179, 1)

X(64897) = 83rd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a^3-2*(b+c)*a^2-(b^2-8*b*c+c^2)*a+2*(b^2-c^2)*(b-c)) : :
X(64897) = 3*X(1)-X(57) = 5*X(1)-X(2093) = 4*X(1)-X(36279) = 3*X(1)-2*X(51788) = 2*X(57)-3*X(999) = 5*X(57)-3*X(2093) = X(57)+3*X(7962) = 4*X(57)-3*X(36279) = 5*X(999)-2*X(2093) = X(999)+2*X(7962) = 3*X(999)-4*X(51788)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 24/07/2024. (Aug 21, 2024)

X(64897) lies on these lines: {1, 3}, {2, 1000}, {4, 52683}, {7, 37429}, {8, 496}, {10, 10912}, {11, 5790}, {12, 18493}, {30, 3476}, {38, 47041}, {45, 2316}, {72, 36846}, {78, 51786}, {80, 11238}, {119, 15845}, {145, 1058}, {214, 4421}, {222, 1480}, {226, 3656}, {329, 3241}, {355, 9669}, {381, 5252}, {382, 12701}, {388, 22791}, {390, 6938}, {392, 3305}, {405, 3890}, {474, 14923}, {495, 1532}, {497, 952}, {498, 45081}, {514, 24352}, {515, 4342}, {519, 3452}, {527, 30331}, {551, 6692}, {855, 13097}, {936, 3680}, {943, 1392}, {944, 6223}, {946, 9654}, {950, 37727}, {956, 3219}, {957, 1255}, {958, 3884}, {962, 18990}, {997, 3880}, {1001, 3898}, {1056, 6925}, {1125, 37828}, {1168, 24864}, {1191, 15955}, {1317, 3058}, {1329, 49169}, {1376, 2802}, {1389, 5703}, {1476, 37403}, {1479, 10944}, {1483, 3486}, {1537, 12115}, {1656, 10039}, {1698, 37829}, {1737, 59503}, {1807, 3478}, {1837, 12645}, {1870, 37391}, {2094, 62863}, {2096, 4313}, {2264, 22147}, {2320, 56040}, {2346, 14497}, {2810, 3242}, {3085, 5901}, {3086, 5690}, {3090, 18220}, {3243, 63972}, {3244, 12635}, {3251, 48329}, {3297, 35641}, {3298, 35642}, {3445, 24046}, {3474, 28212}, {3485, 37406}, {3487, 5734}, {3534, 21578}, {3555, 11682}, {3582, 38066}, {3586, 28204}, {3616, 13747}, {3617, 47743}, {3622, 6921}, {3623, 6872}, {3648, 15174}, {3654, 3911}, {3655, 4304}, {3679, 20196}, {3698, 16863}, {3711, 4677}, {3816, 5854}, {3851, 10827}, {3878, 3927}, {3885, 5687}, {3891, 62401}, {3895, 5440}, {3913, 30144}, {3915, 52408}, {3920, 37366}, {3961, 13541}, {3968, 61158}, {4018, 62832}, {4186, 6198}, {4268, 16884}, {4271, 16777}, {4293, 28174}, {4294, 34773}, {4301, 57282}, {4305, 10386}, {4308, 6361}, {4314, 13607}, {4315, 28194}, {4323, 16137}, {4346, 56049}, {4383, 49494}, {4413, 6797}, {4847, 64734}, {4853, 5044}, {4857, 37707}, {4867, 31142}, {4879, 29126}, {5055, 23708}, {5176, 17556}, {5180, 34605}, {5218, 38028}, {5219, 51709}, {5229, 40273}, {5274, 12019}, {5434, 18541}, {5435, 50810}, {5438, 64202}, {5559, 18395}, {5587, 7743}, {5657, 15325}, {5726, 38021}, {5727, 18527}, {5779, 6264}, {5780, 9581}, {5794, 49600}, {5818, 10593}, {5836, 16408}, {5844, 18391}, {5881, 51785}, {5882, 12575}, {5886, 31397}, {6001, 30283}, {6224, 34611}, {6265, 41553}, {6326, 51767}, {6610, 8147}, {6700, 12640}, {6736, 64768}, {6834, 10595}, {6838, 63282}, {6914, 64742}, {6923, 64138}, {6967, 12245}, {6968, 38038}, {7052, 54435}, {7283, 64563}, {7288, 61524}, {7354, 48661}, {7682, 11374}, {7966, 64326}, {7969, 31474}, {8256, 10200}, {8257, 42819}, {8275, 63143}, {8580, 11525}, {8727, 64322}, {9538, 35998}, {9578, 9955}, {9580, 28160}, {9612, 51789}, {9613, 22793}, {9614, 18480}, {9619, 31461}, {9620, 62370}, {9623, 51780}, {9624, 51784}, {9655, 10106}, {9709, 10914}, {9780, 64201}, {9802, 49719}, {9856, 12650}, {9945, 34607}, {9956, 50443}, {9965, 63159}, {10043, 10949}, {10056, 15950}, {10057, 51517}, {10058, 18515}, {10072, 34718}, {10179, 54318}, {10385, 50824}, {10572, 18526}, {10573, 37722}, {10580, 11041}, {10582, 64732}, {10584, 34122}, {10588, 61272}, {10589, 38042}, {10590, 38034}, {10591, 18357}, {10609, 20075}, {10624, 18481}, {10702, 63770}, {10738, 10947}, {10866, 14872}, {10896, 37710}, {10915, 25681}, {10936, 63257}, {11019, 28234}, {11035, 12651}, {11108, 33895}, {11230, 31434}, {11235, 21630}, {11236, 11813}, {11237, 18393}, {11256, 18254}, {11260, 12514}, {11501, 37251}, {11502, 12331}, {12515, 41554}, {12559, 12710}, {12629, 15829}, {12648, 17757}, {12737, 15558}, {12747, 13274}, {12749, 38755}, {12758, 12773}, {12898, 46687}, {13405, 64731}, {13411, 31480}, {13606, 21398}, {13743, 16140}, {14260, 33151}, {14563, 51077}, {15175, 24302}, {15813, 25438}, {15952, 64421}, {16371, 63136}, {16417, 54286}, {16466, 61357}, {16483, 23112}, {16486, 30117}, {17054, 56804}, {17528, 34640}, {17564, 34711}, {17567, 63133}, {17614, 63130}, {17652, 52148}, {18519, 64041}, {18766, 43166}, {18976, 48680}, {20330, 30275}, {21454, 50872}, {21616, 32049}, {23135, 55432}, {23344, 49682}, {24558, 59591}, {24987, 31493}, {25417, 57664}, {25439, 56177}, {25485, 64735}, {26446, 44675}, {26910, 38512}, {28077, 36565}, {29815, 35996}, {30294, 61705}, {30827, 51362}, {31140, 50891}, {31231, 50821}, {32183, 55173}, {32554, 45635}, {32900, 41864}, {33535, 51794}, {33655, 54436}, {34040, 51654}, {34230, 49747}, {34371, 49465}, {35808, 44635}, {35809, 44636}, {37227, 64423}, {37503, 62239}, {37787, 42884}, {38314, 62773}, {39546, 61732}, {41012, 64087}, {41684, 61717}, {43135, 48805}, {47357, 60940}, {47623, 64176}, {48907, 64158}, {49557, 52524}, {50594, 50637}, {51795, 64755}, {51796, 64749}, {52541, 54319}, {52682, 60926}, {53055, 60944}, {54361, 61510}, {57284, 64767}, {61278, 61535}, {62207, 64449}, {62776, 64107}, {64530, 64538}

X(64897) = midpoint of X(i) and X(j) for these (i, j): {1, 7962}, {145, 3421}, {3476, 30305}, {6282, 7982}, {31142, 51093}, {37727, 37822}
X(64897) = reflection of X(i) in X(j) for these (i, j): (8, 3820), (40, 64659), (57, 51788), (999, 1), (3359, 1385), (3940, 5289), (5722, 63993), (5727, 18527), (6244, 37611), (7682, 13464), (8257, 42819), (12702, 35238), (18525, 18516), (36279, 999), (61535, 61278)
X(64897) = isogonal conjugate of the Cundy-Parry-Psi-transform of X(20323)
X(64897) = Cundy-Parry-Phi-transform of X(20323)
X(64897) = crosssum of X(35768) and X(35769)
X(64897) = pole of the line {1, 26742} with respect to the Feuerbach circumhyperbola
X(64897) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 3057, 3), (35, 34880, 3), (55, 22767, 3), (1319, 5119, 3), (3576, 13528, 3), (5048, 5919, 1), (6767, 10247, 1), (10222, 31792, 1), (10267, 40255, 3), (10966, 11508, 3), (33176, 37080, 1), (37568, 37618, 3), (37605, 59316, 3)

X(64898) = 84th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a^7-3*(b^2+c^2)*a^5+10*(b+c)*b*c*a^4+(3*b^4-46*b^2*c^2+3*c^4)*a^3-4*(b+c)*(3*b^2-8*b*c+3*c^2)*b*c*a^2-(b^2-4*b*c+c^2)*(b^2+6*b*c+c^2)*(b-c)^2*a+2*(b^2-c^2)*(b-c)^3*b*c) : :

See Tran Viet Hung, Ivan Pavlov and César Lozada, Tran Viet Hung problem 30/07/2024. (Aug 21, 2024)

X(64898) lies on these lines: {3, 527}, {999, 64017}, {7960, 51773}, {38902, 60998}

X(64899) = 85th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*((2*b-c)*(b-2*c)*a^5-(b+c)*(4*b^2-3*b*c+4*c^2)*a^4+28*(b^2-b*c+c^2)*b*c*a^3+4*(b+c)*(b^4+c^4-b*c*(7*b^2-11*b*c+7*c^2))*a^2-(2*b^2+7*b*c+2*c^2)*(b-c)^4*a+(b^2-c^2)*(b-c)^3*b*c) : :

See Tran Viet Hung, Ivan Pavlov and César Lozada, Tran Viet Hung problem 30/07/2024. (Aug 21, 2024)

X(64899) lies on these lines: {944, 15726}, {991, 995}, {3295, 48921}




leftri   Points on the line at infinity: X(64855) - X(64889)  rightri

Contributed by Clark Kimberling and Peter Moses, August 21, 2024

Suppose X = x:y:z is a point on the infinity line. Then the following points are also on the infinity line.

2 x sin A - y sin B – z sin C : : 2 x tan A - y tan B – z tan C : : 2x sec A - y sec B – z sec C : :

The appearance of (i,j) in the following list means that if X(i) = x:y:z, then X(j) = 2 x sin A - y sin B – z sin C : :

(30,64900), (512,64901), (513,4785), (514,513), (515,64902), (516,64903), (517,64904), (518,527), (519,4715), (520,64905), (522,4762), (523,28840), (524,28558), (527,28534), (528,64906), (529,64907), (536,519), (537,545), (545,64908), (698,64909), (700,716), (712,64910), (714,538), (716,64911), (726,536), (740,524), (742,752), (744,754), (746,33911), (758,64912), (812,64913), (824,64914), (900,812)

The appearance of (i,j) in the following list means that if X(i) = x:y:z, then X(j) = 2 x tan A - y tan B – z tan C : :

(30, 64915), (511,64781), (512, 64916), (513, 64917), (518,64780), (519, 64918), (520,23878), (521,4762), (523, 64919), (524,30), (525,523), (526, 64920), (538, 64921), (539, 64922), (542, 64923), (543, 64924), (690, 64925), (698, 64926), (732, 64927), (912, 64928)

The appearance of (i,j) in the following list means that if X(i) = x:y:z, then X(j) = 2 x secA - y sec B – z sec C : :

(514,64929), (515,64930), (517,64931), (518,64932), (519,64933), (521,522), (525,64934), (527,64780), (758,30), (912,519)

underbar



X(64900) = X(2)X(2173)∩X(30)X(511)

Barycentrics    4*a^5 + a^4*b - 2*a^3*b^2 + a^2*b^3 - 2*a*b^4 - 2*b^5 + a^4*c - 2*a^2*b^2*c + b^4*c - 2*a^3*c^2 - 2*a^2*b*c^2 + 4*a*b^2*c^2 + b^3*c^2 + a^2*c^3 + b^2*c^3 - 2*a*c^4 + b*c^4 - 2*c^5 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(30)

X(64900) lies on these lines: {2, 2173}, {3, 25362}, {27, 39704}, {30, 511}, {376, 24316}, {381, 24315}, {440, 16590}, {547, 25341}, {549, 24317}, {1762, 31153}, {3151, 17488}, {4644, 33094}, {6661, 25364}, {6678, 62682}, {7426, 25344}, {10989, 24322}, {14953, 53380}, {15670, 25359}, {24321, 31133}, {24452, 37098}, {24714, 24716}, {25343, 44210}, {25360, 44212}, {25363, 44217}, {31048, 61710}

X(64900) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64900) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64900) = {X(24682),X(24683)}-harmonic conjugate of X(24684)

X(64901) = X(2)X(798)∩X(30)X(511)

Barycentrics    (b - c)*(-2*a^3*b - a^2*b^2 - 2*a^3*c - a^2*b*c - a^2*c^2 + b^2*c^2) : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(512)

X(64901) lies on these lines: {2, 798}, {30, 511}, {3572, 17378}, {3768, 20295}, {4063, 24354}, {4380, 27469}, {4428, 23400}, {4481, 45671}, {4664, 21834}, {4832, 52602}, {4979, 29771}, {6586, 45658}, {7199, 31148}, {17330, 27854}, {18071, 48114}, {20979, 31147}, {20981, 46922}, {21191, 45313}, {24506, 26248}, {24698, 24716}

X(64901) = isogonal conjugate of X(59030)
X(64901) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64901) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64901) = {X(798),X(17217)}-harmonic conjugate of X(42327)

X(64902) = X(2)X(2182)∩X(30)X(511)

Barycentrics    4*a^5 - a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4 - 2*b^5 - a^4*c + 4*a^3*b*c - 3*a^2*b^2*c - 2*a*b^3*c + 2*b^4*c - 3*a^3*c^2 - 3*a^2*b*c^2 + 6*a*b^2*c^2 + 3*a^2*c^3 - 2*a*b*c^3 - a*c^4 + 2*b*c^4 - 2*c^5 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(515)

X(64902) lies on these lines: {2, 2182}, {30, 511}, {222, 4654}, {1012, 24328}, {1456, 63054}, {1763, 3929}, {1836, 4644}, {3220, 16370}, {3838, 4670}, {4640, 4643}, {4667, 39542}, {4708, 24684}, {5123, 24324}, {5325, 41883}, {36850, 41846}, {44447, 64015}

X(64902) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64902) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64903) = X(2)X(910)∩X(30)X(511)

Barycentrics    4*a^4 - a^3*b - a*b^3 - 2*b^4 - a^3*c - 2*a^2*b*c + a*b^2*c + 2*b^3*c + a*b*c^2 - a*c^3 + 2*b*c^3 - 2*c^4 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(516)

X(64903) lies on these lines: {2, 910}, {7, 1100}, {9, 17239}, {20, 42050}, {30, 511}, {144, 319}, {390, 50130}, {553, 34855}, {673, 51922}, {1155, 24712}, {1530, 10710}, {2201, 50063}, {3543, 42048}, {3775, 51090}, {3823, 24358}, {3834, 24699}, {4312, 4649}, {4419, 30332}, {4640, 24694}, {4643, 5698}, {4654, 58320}, {4667, 30424}, {4670, 5880}, {4690, 5220}, {4708, 15254}, {5011, 10708}, {5087, 24685}, {5195, 6603}, {5695, 60905}, {5829, 18650}, {6172, 17281}, {6173, 16503}, {9580, 24352}, {16590, 61023}, {17264, 20533}, {17294, 50995}, {17346, 60927}, {17392, 64702}, {24608, 59374}, {38093, 62682}, {39704, 55937}, {41312, 47357}, {48805, 50836}, {48821, 51100}, {49726, 51144}, {49747, 64695}, {50076, 50996}, {50082, 51053}, {50092, 51151}, {50097, 51191}, {50101, 60984}, {50114, 51150}, {50124, 51002}, {50127, 50997}

X(64903) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64903) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1653, 416}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64904) = X(2)X(2183)∩X(30)X(511)

Barycentrics    2*a^4*b + a^3*b^2 - 2*a^2*b^3 - a*b^4 + 2*a^4*c - 4*a^3*b*c + a^2*b^2*c + 2*a*b^3*c - b^4*c + a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + b^3*c^2 - 2*a^2*c^3 + 2*a*b*c^3 + b^2*c^3 - a*c^4 - b*c^4 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(517)

X(64904) lies on these lines: {2, 2183}, {30, 511}, {42, 3000}, {553, 1427}, {1458, 63054}, {3741, 4643}, {4271, 30097}, {4670, 6685}, {4748, 31241}, {17067, 52901}, {17135, 64015}, {17781, 18750}, {20470, 40726}, {24316, 63389}, {31164, 41846}

X(64904) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}, {52723, 61610}
X(64904) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {414, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64905) = X(2)X(656)∩X(30)X(511)

Barycentrics    (b - c)*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 - 2*a^3*c - a^2*b*c + 2*a*b^2*c + b^3*c - a^2*c^2 + 2*a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 + b*c^3) : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(520)

X(64905) lies on these lines: {2, 656}, {10, 45660}, {30, 511}, {1459, 44550}, {3679, 4086}, {3737, 45671}, {4529, 17281}, {4685, 57207}, {4913, 50349}, {7629, 45701}, {7655, 45320}, {14429, 57066}, {15419, 63110}, {16370, 23189}, {16590, 57046}, {17271, 18160}, {17378, 57214}, {17496, 53532}, {17549, 23226}, {20315, 45683}, {20316, 45664}, {20954, 36038}, {21102, 44553}, {21172, 44551}, {21187, 44409}, {24718, 26013}, {28958, 47785}, {31148, 47844}, {31149, 50331}, {31150, 46385}, {45315, 47842}, {45328, 50350}, {45667, 51648}, {50338, 57091}, {60074, 60079}

X(64905) = crossdifference of every pair of points on line {6, 42669}
X(64905) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64905) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7253, 45686}, {2, 45686, 8062}, {656, 7253, 8062}, {656, 45686, 2}

X(64906) = X(2)X(2246)∩X(30)X(511)

Barycentrics    4*a^4 - 3*a^3*b + a^2*b^2 - 2*b^4 - 3*a^3*c - 2*a^2*b*c + a*b^2*c + 3*b^3*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + 3*b*c^3 - 2*c^4 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(528)

X(64906) lies on these lines: {2, 2246}, {7, 63052}, {9, 17228}, {30, 511}, {190, 4873}, {335, 50133}, {673, 2364}, {903, 16834}, {1086, 4667}, {2161, 61004}, {2550, 24452}, {4366, 17254}, {4370, 29594}, {4432, 4643}, {4440, 50129}, {4644, 24715}, {4670, 25351}, {4758, 40480}, {4795, 5880}, {5698, 50316}, {6172, 17488}, {6174, 24318}, {9318, 10707}, {10031, 60692}, {16503, 27950}, {16590, 16593}, {17251, 24358}, {17346, 17755}, {17392, 36409}, {17487, 50079}, {24036, 55162}, {24333, 31140}, {25342, 45310}, {31349, 50074}, {32043, 40878}, {41845, 60984}, {41846, 61011}, {60999, 62682}

X(64906) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64906) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64907) = X(2)X(24700)∩X(30)X(511)

Barycentrics    4*a^5 + a^4*b - 2*a^3*b^2 + a^2*b^3 - 2*a*b^4 - 2*b^5 + a^4*c + 8*a^3*b*c - 4*a^2*b^2*c - 4*a*b^3*c + b^4*c - 2*a^3*c^2 - 4*a^2*b*c^2 + 8*a*b^2*c^2 + b^3*c^2 + a^2*c^3 - 4*a*b*c^3 + b^2*c^3 - 2*a*c^4 + b*c^4 - 2*c^5 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(529)

X(64907) lies on these lines: {2, 24700}, {30, 511}, {4363, 34739}, {4644, 33095}, {4654, 39704}, {5325, 16590}, {11113, 25371}, {17579, 24336}, {23512, 28609}, {24319, 31157}, {24334, 31141}, {24441, 34620}

X(64907) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64907) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {845, 2091}, {1035, 2091}, {1038, 414}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64908) = X(2)X(4432)∩X(30)X(511)

Barycentrics    4*a^3 - 3*a^2*b - 2*b^3 - 3*a^2*c + 3*b^2*c + 3*b*c^2 - 2*c^3 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(545)

X(64908) lies on these lines: {1, 903}, {2, 4432}, {8, 17487}, {10, 4370}, {30, 511}, {100, 4945}, {190, 3679}, {214, 19636}, {244, 42026}, {551, 1086}, {673, 50836}, {678, 4080}, {874, 43270}, {1125, 62682}, {1266, 49700}, {1644, 30566}, {2161, 60079}, {3058, 42053}, {3241, 4440}, {3656, 24833}, {3685, 31151}, {3722, 44006}, {3791, 42058}, {3821, 48810}, {3828, 4422}, {3842, 49725}, {3923, 48829}, {4085, 50115}, {4096, 34612}, {4437, 50781}, {4480, 49701}, {4535, 5695}, {4642, 17537}, {4655, 50316}, {4660, 17281}, {4672, 50287}, {4677, 24821}, {4693, 17310}, {4702, 24692}, {4709, 50082}, {4732, 17330}, {4745, 36522}, {4868, 39974}, {4974, 62392}, {4997, 9324}, {6154, 21093}, {9458, 31171}, {16561, 54286}, {16593, 51100}, {17274, 32941}, {17333, 49457}, {17378, 49471}, {17382, 49482}, {17399, 25055}, {17738, 50126}, {17755, 50096}, {19875, 41138}, {19883, 50290}, {24248, 49473}, {24325, 49746}, {24331, 31139}, {24441, 36480}, {24710, 31172}, {24813, 50811}, {24817, 50810}, {24828, 50796}, {24841, 51093}, {24844, 50798}, {30332, 36588}, {31134, 32929}, {31349, 50086}, {34611, 42055}, {36237, 50890}, {36525, 51103}, {38098, 50312}, {38314, 50293}, {41801, 60718}, {41842, 50303}, {42054, 49719}, {43677, 54564}, {49456, 50286}, {49459, 50074}, {49469, 50132}, {49472, 50101}, {49485, 50081}, {49489, 64016}, {49684, 50108}, {49720, 50094}, {50080, 50300}, {50091, 53600}, {50111, 50301}, {50295, 53620}, {51071, 53534}

X(64908) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64908) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {903, 43287, 39704}, {4432, 24715, 25351}

X(64909) = X(2)X(256)∩X(30)X(511)

Barycentrics    a^3*b^2 - 2*a^2*b^3 - 2*a^3*b*c + a^2*b^2*c + a*b^3*c + a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + b^3*c^2 - 2*a^2*c^3 + a*b*c^3 + b^2*c^3 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(698)

X(64909) lies on these lines: {2, 256}, {30, 511}, {75, 50613}, {190, 3507}, {314, 3551}, {386, 4672}, {1045, 42043}, {2092, 50115}, {3663, 50611}, {3729, 50576}, {3736, 4234}, {3821, 50609}, {3923, 50591}, {4096, 50093}, {4655, 10449}, {8845, 13586}, {17333, 42054}, {18830, 19567}, {20018, 24695}, {21746, 64545}, {24248, 50636}, {24325, 50616}, {24451, 46032}, {24688, 50605}, {27958, 58861}, {32921, 50635}, {32935, 50581}, {32941, 50612}, {39780, 42057}, {42027, 49537}, {42053, 50116}, {42055, 50128}, {49472, 50629}, {49473, 50615}, {49489, 50600}, {49598, 50618}, {50302, 50614}, {50303, 51678}, {50608, 63997}, {50627, 58399}

X(64909) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64909) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 234}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64910) = X(2)X(2228)∩X(30)X(511)

Barycentrics    a^3*b^2 - 2*a^2*b^3 - 2*a^3*b*c + a*b^3*c + a^3*c^2 + b^3*c^2 - 2*a^2*c^3 + a*b*c^3 + b^2*c^3 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(712)

X(64910) lies on these lines: {2, 2228}, {30, 511}, {42, 3758}, {751, 32931}, {3679, 4494}, {3741, 17237}, {4479, 17149}, {4741, 17135}, {16590, 42056}, {16606, 39974}, {22316, 64709}, {23633, 30939}

X(64910) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64910) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64911) = X(2)X(2230)∩X(30)X(511)

Barycentrics    2*a^3*b^2 - a^2*b^3 - 2*a^3*b*c + a^2*b^2*c + a*b^3*c + 2*a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - a^2*c^3 + a*b*c^3 - b^2*c^3 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(716)

X(64911) lies on these lines: {2, 2230}, {30, 511}, {350, 17378}, {871, 39704}, {1575, 17330}, {17346, 41142}, {17392, 30982}, {17759, 50074}, {17790, 50301}, {20530, 49738}, {24338, 49746}, {25382, 49725}, {35043, 40875}, {49740, 57037}, {50297, 57039}

X(64911) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64911) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}, {22859, 5037}

X(64912) = X(2)X(2245)∩X(30)X(511)

Barycentrics    2*a^4*b + a^3*b^2 - 2*a^2*b^3 - a*b^4 + 2*a^4*c - b^4*c + a^3*c^2 + b^3*c^2 - 2*a^2*c^3 + b^2*c^3 - a*c^4 - b*c^4 : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(758)

X(64912) lies on these lines: {2, 2245}, {6, 24296}, {30, 511}, {484, 24324}, {625, 50773}, {1284, 41312}, {1836, 4643}, {3286, 16370}, {3578, 42029}, {3663, 63359}, {3838, 4708}, {4363, 50160}, {4364, 39542}, {4419, 50184}, {4640, 4670}, {4644, 17018}, {4795, 49749}, {4887, 52901}, {5184, 24345}, {10022, 50163}, {11813, 25367}, {14636, 34647}, {15985, 17351}, {16383, 33844}, {17251, 17532}, {17276, 28369}, {17336, 30056}, {17781, 49724}, {21077, 48924}, {24441, 50179}, {25094, 37631}, {49721, 50159}, {49726, 50162}, {49741, 50173}, {49747, 50178}, {50259, 57006}

X(64912) = X(24296)-line conjugate of X(6)
X(64912) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64912) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {416, 234}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64913) = X(2)X(659)∩X(30)X(511)

Barycentrics    (b - c)*(-2*a^3 - a*b^2 + 2*a*b*c + b^2*c - a*c^2 + b*c^2) : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(812)

X(64913) lies on these lines: {2, 659}, {30, 511}, {190, 23354}, {549, 44805}, {551, 1960}, {553, 53539}, {650, 45323}, {665, 45657}, {667, 48406}, {693, 48234}, {876, 43262}, {903, 3226}, {1086, 3248}, {1491, 31150}, {1635, 36848}, {2526, 48190}, {2530, 45671}, {3058, 53523}, {3241, 21343}, {3679, 21385}, {3716, 45342}, {3768, 4370}, {3777, 44550}, {3828, 53571}, {3835, 45673}, {3928, 53403}, {4010, 48032}, {4040, 4992}, {4122, 48102}, {4380, 50359}, {4401, 23815}, {4448, 4728}, {4491, 53271}, {4724, 4806}, {4782, 24720}, {4800, 21297}, {4809, 6545}, {4810, 53343}, {4824, 48020}, {4830, 9508}, {4833, 17217}, {4874, 45320}, {4925, 49732}, {4927, 26275}, {4928, 45666}, {4948, 17494}, {4951, 48557}, {5434, 30725}, {6050, 44561}, {7212, 53528}, {7427, 53302}, {8689, 59522}, {10707, 13266}, {13246, 45668}, {14425, 30792}, {17487, 39354}, {18004, 48055}, {18160, 23794}, {21051, 31149}, {21146, 31148}, {21301, 48401}, {23789, 50512}, {24093, 34606}, {24097, 34605}, {24715, 24722}, {25380, 45691}, {25569, 38314}, {28602, 47884}, {31131, 47892}, {31291, 48323}, {39704, 59487}, {39982, 55261}, {39996, 52151}, {44429, 47829}, {44433, 47871}, {45315, 48050}, {45316, 48331}, {45337, 53580}, {45344, 48056}, {45664, 59521}, {45667, 48330}, {45669, 50348}, {45676, 48000}, {47652, 50340}, {47687, 48103}, {47689, 48140}, {47694, 47869}, {47697, 48120}, {47774, 47969}, {47776, 48244}, {47784, 48163}, {47788, 48247}, {47802, 48214}, {47803, 48198}, {47804, 48184}, {47805, 47833}, {47808, 47885}, {47811, 48180}, {47812, 48233}, {47822, 48572}, {47825, 48160}, {47827, 48164}, {47834, 48251}, {47928, 47940}, {47932, 50341}, {47933, 47946}, {47936, 48265}, {47964, 47985}, {47974, 48024}, {47977, 48267}, {48002, 48023}, {48008, 50335}, {48009, 48028}, {48010, 48593}, {48014, 49295}, {48030, 48042}, {48043, 48625}, {48063, 48090}, {48068, 49286}, {48072, 48394}, {48111, 48273}, {48150, 48279}, {48238, 48578}, {48289, 48335}, {48296, 51071}, {48324, 50760}, {48405, 49285}, {49301, 50342}, {50343, 58374}, {53572, 57605}

X(64913) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64913) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 659, 45314}, {2, 3837, 45340}, {2, 46403, 48167}, {2, 48167, 3837}, {659, 46403, 3837}, {659, 48167, 2}, {693, 50358, 48248}, {1635, 36848, 48229}, {3837, 45314, 2}, {4448, 4728, 48183}, {4724, 24719, 4806}, {4948, 50328, 48157}, {17494, 48157, 4948}, {44429, 48226, 47829}, {45314, 48167, 45340}, {47804, 48184, 48206}, {47805, 48170, 47833}, {47884, 48182, 28602}, {48164, 48240, 47827}

X(64914) = X(2)X(1491)∩X(30)X(511)

Barycentrics    (b - c)*(a^3 + 2*a*b^2 + 2*a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
Barycentrics    2 a x - b y - c z sin C : : , where x : y : z = X(824)

X(64914) lies on these lines: {2, 1491}, {30, 511}, {42, 4724}, {597, 36233}, {599, 35964}, {649, 50341}, {650, 45314}, {659, 4948}, {667, 45671}, {693, 48167}, {1577, 31149}, {1635, 48225}, {2254, 31148}, {2526, 3837}, {3241, 48298}, {3716, 45315}, {3741, 24720}, {3777, 17166}, {3835, 45342}, {4010, 31147}, {4122, 48077}, {4367, 44550}, {4369, 45328}, {4379, 36848}, {4380, 50339}, {4448, 4893}, {4728, 48189}, {4763, 48213}, {4776, 4800}, {4782, 4913}, {4784, 50356}, {4789, 31131}, {4804, 24719}, {4806, 48027}, {4809, 47886}, {4885, 45340}, {4927, 48163}, {4928, 48202}, {4951, 47870}, {4963, 47941}, {4992, 48092}, {7192, 50359}, {9508, 45313}, {14349, 48305}, {17072, 45332}, {17135, 48143}, {17494, 50358}, {18004, 48039}, {18821, 43099}, {18822, 43096}, {21051, 45664}, {21146, 31136}, {21212, 45668}, {21260, 45324}, {21301, 48392}, {24574, 47775}, {25380, 45663}, {25666, 45337}, {26275, 47784}, {28602, 47766}, {31286, 45691}, {39974, 55261}, {44429, 47833}, {44433, 47782}, {45341, 48290}, {45666, 47778}, {45673, 45676}, {45746, 50340}, {46403, 47869}, {47123, 48007}, {47131, 47960}, {47688, 47925}, {47691, 47968}, {47696, 48103}, {47698, 48083}, {47705, 47931}, {47760, 48183}, {47761, 48229}, {47762, 48244}, {47774, 47945}, {47788, 48182}, {47797, 47877}, {47802, 48206}, {47803, 47829}, {47804, 47827}, {47805, 47825}, {47810, 47822}, {47811, 48176}, {47812, 48238}, {47813, 47823}, {47814, 47872}, {47816, 47875}, {47818, 47888}, {47819, 47889}, {47820, 47893}, {47828, 48578}, {47834, 48164}, {47880, 48211}, {47881, 48200}, {47884, 48247}, {47885, 48250}, {47905, 48264}, {47909, 47946}, {47912, 48265}, {47928, 47969}, {47934, 48032}, {47940, 48080}, {47943, 53558}, {47948, 48267}, {47953, 47993}, {47956, 59590}, {47958, 48349}, {47964, 48001}, {47973, 48326}, {47982, 49295}, {47985, 48043}, {47992, 48028}, {47998, 53523}, {48002, 48029}, {48005, 59672}, {48015, 58375}, {48021, 48583}, {48042, 48394}, {48050, 48090}, {48066, 52601}, {48086, 48273}, {48098, 49292}, {48108, 58374}, {48122, 48279}, {48131, 48301}, {48158, 53361}, {48162, 48549}, {48194, 48562}, {48288, 48324}, {48289, 48327}, {48291, 48335}, {48351, 50449}, {48405, 50333}, {48422, 58372}

X(64914) = isogonal conjugate of X(59033)
X(64914) = crossdifference of every pair of points on line {6, 8624}
X(64914) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64914) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}, {61932, 38403}
X(64914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1491, 45323}, {2, 47694, 48234}, {2, 48157, 1491}, {2, 48234, 4874}, {659, 4948, 31150}, {1491, 47694, 4874}, {1491, 48234, 2}, {2526, 7662, 3837}, {4804, 48020, 24719}, {4874, 45323, 2}, {31150, 47975, 4948}, {44429, 47833, 48198}, {44429, 48237, 47833}, {47694, 48157, 2}, {47697, 47975, 659}, {47802, 48220, 48206}, {47803, 48193, 47829}, {47804, 47827, 48214}, {47804, 48175, 47827}, {47805, 47825, 48226}, {47827, 48251, 47804}, {47833, 48160, 44429}, {47834, 48164, 48184}, {47945, 53343, 48024}, {48039, 49286, 18004}, {48157, 48234, 45323}, {48160, 48237, 48198}, {48175, 48251, 48214}

X(64915) = X(2)X(1990)∩X(30)X(511)

Barycentrics    2*a^8 + a^6*b^2 - 9*a^4*b^4 + 7*a^2*b^6 - b^8 + a^6*c^2 + 14*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 8*b^6*c^2 - 9*a^4*c^4 - 7*a^2*b^2*c^4 + 18*b^4*c^4 + 7*a^2*c^6 - 8*b^2*c^6 - c^8 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(30)

X(64915) lies on these lines: {2, 1990}, {4, 42831}, {5, 42830}, {30, 511}, {230, 48540}, {297, 1494}, {401, 39358}, {441, 3163}, {546, 42853}, {648, 40884}, {1316, 15471}, {1495, 16312}, {3524, 41204}, {3545, 6530}, {3631, 42459}, {5066, 18552}, {5858, 40665}, {5859, 40666}, {6748, 40896}, {7780, 33591}, {7789, 19221}, {9308, 34828}, {9766, 45279}, {11184, 30775}, {13567, 34288}, {14023, 34726}, {14836, 23292}, {15448, 16334}, {15526, 18487}, {16303, 47296}, {23583, 44346}, {32459, 40879}, {34573, 59649}, {34608, 63951}, {34621, 63933}, {35266, 46869}, {35937, 57822}, {37765, 44576}, {39352, 40885}, {40477, 44335}, {40888, 59634}, {40996, 45312}, {41005, 58408}, {44569, 46808}, {47097, 47172}, {48539, 63440}

X(64915) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64915) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64915) = {X(15526),X(18487)}-harmonic conjugate of X(44216)

X(64916) = X(2)X(2489)∩X(30)X(511)

Barycentrics    (b^2 - c^2)*(-a^6 + a^2*b^4 - 8*a^2*b^2*c^2 + 2*b^4*c^2 + a^2*c^4 + 2*b^2*c^4) : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(512)

X(64916) lies on these lines: {2, 2489}, {30, 511}, {2485, 44560}, {3267, 31174}, {6131, 8651}, {6563, 14273}, {8644, 63250}, {9822, 54273}, {9909, 21006}, {18313, 47617}, {30476, 35522}, {36900, 47133}, {41300, 55974}, {50548, 57087}

X(64916) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64916) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64917) = X(2)X(7649)∩X(30)X(511)

Barycentrics    (b - c)*(-a^4 + 2*a^3*b - 2*a^2*b^2 - 2*a*b^3 + 3*b^4 + 2*a^3*c - 2*a^2*b*c - 2*a*b^2*c + 2*b^3*c - 2*a^2*c^2 - 2*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 + 2*b*c^3 + 3*c^4) : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(513)

X(64917) lies on these lines: {2, 7649}, {30, 511}, {381, 16231}, {4057, 9909}, {6332, 45686}, {8062, 45683}, {14070, 39225}, {21187, 44551}, {30775, 59969}, {39534, 44928}, {44409, 45341}, {44442, 44444}, {45664, 52355}

X(64917) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64917) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64917) = {X(7649),X(20294)}-harmonic conjugate of X(20315)

X(64918) = X(2)X(3007)∩X(30)X(511)

Barycentrics    2*a^5 - a^4*b + 2*a^3*b^2 + 2*a^2*b^3 - 4*a*b^4 - b^5 - a^4*c - 4*a^2*b^2*c + 5*b^4*c + 2*a^3*c^2 - 4*a^2*b*c^2 + 8*a*b^2*c^2 - 4*b^3*c^2 + 2*a^2*c^3 - 4*b^2*c^3 - 4*a*c^4 + 5*b*c^4 - c^5 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(519)

X(64918) lies on these lines: {2, 3007}, {10, 25362}, {19, 24608}, {30, 511}, {281, 30844}, {306, 36889}, {551, 24315}, {1266, 18735}, {1826, 31048}, {1839, 40903}, {3187, 18661}, {3679, 24316}, {3828, 24317}, {7289, 50101}, {7291, 41803}, {9909, 23854}, {16560, 41140}, {18161, 50116}, {24682, 50796}, {24683, 50811}, {24684, 50828}, {48381, 53380}

X(64918) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64918) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64919) = X(2)X(2501)∩X(30)X(511)

Barycentrics    (b^2 - c^2)*(a^4 - 4*a^2*b^2 + 3*b^4 - 4*a^2*c^2 - 2*b^2*c^2 + 3*c^4) : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(523)

X(64919) lies on these lines: {2, 2501}, {30, 511}, {381, 39533}, {647, 44552}, {669, 9909}, {850, 44554}, {2394, 41895}, {2485, 63830}, {2489, 44817}, {3265, 12077}, {3267, 18314}, {5466, 30775}, {5664, 11147}, {5915, 48540}, {5926, 14070}, {6334, 37350}, {6562, 50548}, {6587, 44560}, {7426, 47627}, {7631, 7663}, {8598, 44427}, {9209, 9979}, {10154, 45317}, {10279, 18281}, {14223, 60103}, {14273, 27088}, {14316, 45335}, {14618, 33228}, {14977, 36889}, {18311, 45681}, {18324, 46609}, {20577, 57069}, {24978, 61656}, {30451, 63094}, {30476, 44568}, {31176, 34609}, {32204, 34351}, {33294, 36900}, {33509, 50146}, {35297, 57065}, {39228, 53265}, {40727, 55271}, {41078, 52149}, {43665, 60095}, {43673, 60150}, {44010, 59927}, {44442, 44445}, {44565, 59652}, {46040, 54750}, {46995, 47216}, {50642, 54267}, {52459, 54659}, {54260, 56370}

X(64919) = crossdifference of every pair of points on line {6, 44200}
X(64919) = barycentric product X(i)*X(j) for these {i,j}: {554, 1653}, {1034, 2091}, {1039, 1709}, {1260, 2091}, {1265, 2091}, {46406, 62210}
X(64919) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64919) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2489, 52584, 44817}, {33294, 41298, 47122}

X(64920) = X(2)X(44817)∩X(30)X(511)

Barycentrics    (b^2 - c^2)*(-a^10 + 2*a^8*b^2 - 2*a^4*b^6 + a^2*b^8 + 2*a^8*c^2 - 3*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - 5*a^2*b^6*c^2 + 2*b^8*c^2 + 4*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 - 2*a^4*c^6 - 5*a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + 2*b^2*c^8) : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(526)

X(64920) lies on these lines: {2, 44817}, {30, 511}, {381, 17994}, {1989, 14592}, {2433, 46808}, {2492, 18312}, {3143, 8754}, {6334, 14273}, {8552, 35522}, {24978, 47138}, {43673, 54810}, {44212, 47206}

X(64920) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64920) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64920) = {X(35522),X(62307)}-harmonic conjugate of X(8552)

X(64921) = X(30)X(511)∩X(305)X(3260)

Barycentrics    a^6*b^2 + 4*a^4*b^4 - 5*a^2*b^6 + a^6*c^2 - 6*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + 4*b^6*c^2 + 4*a^4*c^4 + 3*a^2*b^2*c^4 - 8*b^4*c^4 - 5*a^2*c^6 + 4*b^2*c^6 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(538)

X(64921) lies on these lines: {30, 511}, {305, 3260}, {1196, 3003}, {3545, 44145}, {5201, 9909}, {5972, 16334}, {9813, 11286}, {10510, 47284}, {11064, 16312}, {11539, 45847}, {16303, 32223}, {16326, 47582}, {18114, 42830}, {18860, 36207}, {33228, 62237}, {41583, 47322}, {41626, 52144}, {47285, 51372}, {48540, 58849}, {53274, 58267}

X(64921) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}, {32513, 62352}
X(64921) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {414, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1652, 234}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64922) = X(2)X(231)∩X(30)X(511)

Barycentrics    2*a^8 - 2*a^6*b^2 - 3*a^4*b^4 + 4*a^2*b^6 - b^8 - 2*a^6*c^2 - 4*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 + 4*a^2*c^6 - 2*b^2*c^6 - c^8 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(539)

X(64922) lies on these lines: {2, 231}, {30, 511}, {343, 14836}, {1989, 60524}, {3589, 10220}, {5858, 40712}, {5859, 40711}, {6128, 51481}, {6515, 34288}, {7525, 63927}, {7764, 10414}, {7779, 48540}, {7799, 44375}, {7813, 40879}, {7855, 19221}, {9766, 45918}, {19570, 44363}, {36889, 57875}, {46184, 61656}, {46998, 47594}, {52952, 56021}

X(64922) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64922) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}, {7105, 32470}, {30180, 5035}

X(64923) = X(2)X(648)∩X(30)X(511)

Barycentrics    2*a^8 - 2*a^6*b^2 - 3*a^4*b^4 + 4*a^2*b^6 - b^8 - 2*a^6*c^2 + 8*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 - 4*a^2*b^2*c^4 + 6*b^4*c^4 + 4*a^2*c^6 - 2*b^2*c^6 - c^8 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(542)

X(64923) lies on these lines: {2, 648}, {6, 41145}, {26, 63927}, {30, 511}, {69, 51389}, {110, 46869}, {114, 36207}, {115, 48540}, {125, 2452}, {287, 1992}, {297, 18487}, {338, 6128}, {340, 40885}, {599, 15595}, {620, 40879}, {626, 19221}, {1272, 4558}, {1316, 5095}, {1561, 10752}, {1651, 47204}, {1972, 47383}, {1990, 40996}, {1993, 50433}, {2407, 35520}, {2453, 64104}, {2482, 40866}, {2930, 37921}, {3018, 62551}, {3284, 40884}, {3630, 42459}, {3631, 59649}, {5642, 46459}, {5858, 41889}, {6148, 14570}, {6330, 60874}, {6389, 56013}, {6722, 18122}, {7387, 63934}, {7764, 18281}, {7779, 62298}, {7780, 34351}, {7799, 40888}, {7809, 44363}, {9410, 39062}, {9740, 38918}, {9770, 30775}, {9909, 63951}, {11007, 32257}, {11050, 16075}, {11160, 40867}, {11178, 42830}, {12094, 15048}, {14070, 63952}, {14581, 44650}, {14836, 54347}, {15303, 50146}, {15351, 46270}, {15860, 52289}, {16077, 44653}, {16176, 47284}, {18552, 25561}, {23582, 31621}, {32224, 41583}, {32244, 36163}, {32300, 57588}, {32836, 53021}, {34288, 63129}, {34609, 60474}, {34725, 63932}, {34726, 63936}, {36426, 36430}, {37765, 44579}, {38738, 48539}, {38791, 47616}, {40506, 40512}, {40870, 44367}, {41092, 49932}, {41132, 49841}, {42831, 54131}, {44649, 52951}, {47285, 51431}, {49840, 49842}, {49931, 49971}, {50187, 51228}, {52149, 60524}, {54395, 62639}

X(64923) = isotomic conjugate of X(53201)
X(64923) = isotomic conjugate of the polar conjugate of X(47204)
X(64923) = trilinear pole of line {1651, 42733}
X(64923) = crossdifference of every pair of points on line {6, 9409}
X(64923) = X(41145)-line conjugate of X(6)
X(64923) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64923) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64923) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 648, 3163}, {2, 1494, 15526}, {2, 3163, 23583}, {2, 23583, 40477}, {2, 39352, 1494}, {2, 39358, 648}, {648, 1494, 2}, {648, 15526, 23583}, {648, 39352, 15526}, {1494, 39358, 3163}, {3163, 15526, 2}, {15526, 23583, 40484}, {18487, 45312, 297}, {39352, 39358, 2}, {40477, 40484, 2}

X(64924) = X(30)X(511)∩X(1007)X(9214)

Barycentrics    2*a^8 - 13*a^4*b^4 + 12*a^2*b^6 - b^8 + 20*a^4*b^2*c^2 - 10*a^2*b^4*c^2 - 12*b^6*c^2 - 13*a^4*c^4 - 10*a^2*b^2*c^4 + 26*b^4*c^4 + 12*a^2*c^6 - 12*b^2*c^6 - c^8 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(543)

X(64924) lies on these lines: {30, 511}, {1007, 9214}, {2453, 15303}, {2482, 36207}, {3018, 37637}, {5972, 50146}, {6055, 48540}, {6723, 50147}, {7665, 37667}, {7687, 16279}, {16312, 35266}, {23055, 47200}, {32223, 50150}, {32257, 36194}, {32300, 34094}, {34319, 47284}, {41720, 51431}, {45311, 50149}

X(64924) = barycentric product X(i)*X(j) for these {i,j}: {234, 554}, {1034, 2091}, {1260, 2091}, {1265, 2091}, {33428, 55327}
X(64924) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64925) = X(2)X(14273)∩X(30)X(511)

Barycentrics    (b^2 - c^2)*(4*a^6 - 3*a^4*b^2 - 4*a^2*b^4 + 3*b^6 - 3*a^4*c^2 + 14*a^2*b^2*c^2 - 5*b^4*c^2 - 4*a^2*c^4 - 5*b^2*c^4 + 3*c^6) : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(690)

X(64925) lies on these lines: {2, 14273}, {30, 511}, {1637, 14977}, {6334, 46067}, {7417, 36898}, {9909, 53272}, {10554, 14698}, {11616, 14070}, {13232, 45680}, {14694, 16230}, {39905, 53378}, {44427, 46069}, {45687, 55271}

X(64925) = barycentric product X(i)*X(j) for these {i,j}: {554, 1709}, {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64925) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64926) = X(2)X(59566)∩X(30)X(511)

Barycentrics    3*a^4*b^4 - 3*a^2*b^6 - 4*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + 3*b^6*c^2 + 3*a^4*c^4 + 2*a^2*b^2*c^4 - 6*b^4*c^4 - 3*a^2*c^6 + 3*b^2*c^6 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(698)

X(64926) lies on these lines: {2, 59566}, {3, 38294}, {5, 62237}, {30, 511}, {230, 59649}, {385, 9909}, {1990, 44347}, {7779, 44442}, {7840, 34609}, {8859, 42453}, {10154, 22329}, {15912, 33591}, {15993, 42459}, {18324, 44375}, {22151, 47285}, {32225, 47143}, {34478, 44386}, {34608, 44367}

X(64926) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64926) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 845}, {416, 234}, {845, 2091}, {899, 29692}, {1035, 2091}, {1119, 2091}, {1617, 1652}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64927) = X(2)X(3186)∩X(30)X(511)

Barycentrics    a^6*b^2 + a^4*b^4 - 2*a^2*b^6 + a^6*c^2 - 2*a^4*b^2*c^2 + a^2*b^4*c^2 + b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 - 2*a^2*c^6 + b^2*c^6 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(732)

X(64927) lies on these lines: {2, 3186}, {30, 511}, {376, 30262}, {381, 43976}, {648, 6660}, {800, 5306}, {1316, 11416}, {5999, 38294}, {6033, 44363}, {7788, 14615}, {9142, 44376}, {9307, 9909}, {11007, 64724}, {11574, 59566}, {12042, 44375}, {15526, 21536}, {15980, 62237}, {20975, 63736}, {22151, 51430}, {22515, 53507}, {23164, 35278}, {23583, 44347}, {34608, 63093}, {35002, 40888}, {37906, 44102}, {44388, 61575}, {50645, 59569}

X(64927) =barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}, {46196, 53646}
X(64927) =barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {414, 2091}, {416, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1709, 234}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64928) = X(2)X(3262)∩X(30)X(511)

Barycentrics    a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 + a^4*c + 3*a^2*b^2*c - 2*b^4*c - a^3*c^2 + 3*a^2*b*c^2 - 6*a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 + 2*b^2*c^3 + a*c^4 - 2*b*c^4 : :
Barycentrics    2 x tan A - y tan B - z tan C : : , where x : y : z = X(912)

X(64928) lies on these lines: {2, 3262}, {30, 511}, {1319, 24324}, {1445, 4361}, {3175, 4053}, {3870, 17318}, {3872, 4363}, {4364, 31397}, {4419, 12648}, {4643, 12647}, {4665, 4847}, {5123, 25367}, {5839, 41563}, {7263, 60992}, {8667, 57031}, {9766, 35552}, {10056, 41312}, {17151, 60968}, {17262, 60966}, {39765, 50106}

X(64928) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64928) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1164, 24682}, {1847, 2091}, {2057, 2091}, {2091, 2091}, {17941, 45587}, {49066, 6547}

X(64929) = X(2)X(17924)∩X(30)X(511)

Barycentrics    (b - c)*(-a^6 + a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - a^2*b^4 + a*b^5 + a^5*c - 2*a^3*b^2*c - 2*a^2*b^3*c + a*b^4*c + 2*b^5*c + 2*a^4*c^2 - 2*a^3*b*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 - 2*a^3*c^3 - 2*a^2*b*c^3 + 2*a*b^2*c^3 - 4*b^3*c^3 - a^2*c^4 + a*b*c^4 + a*c^5 + 2*b*c^5) : :
Barycentrics    2 x sec A - y sec B - z sec C : : , where x : y : z = X(514)

X(64929) lies on these lines: {2, 17924}, {30, 511}, {381, 39536}, {905, 36038}, {3679, 58333}, {4885, 63825}, {11113, 18344}, {17896, 44550}, {20317, 60074}, {24006, 52599}, {28454, 39227}, {31150, 56320}, {45664, 57055}

X(64929) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64929) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}, {13305, 35039}, {42784, 40613}

X(64930) = X(2)X(280)∩X(30)X(511)

Barycentrics    a^6*b + a^5*b^2 - 2*a^4*b^3 - 2*a^3*b^4 + a^2*b^5 + a*b^6 + a^6*c - 4*a^5*b*c + 2*a^4*b^2*c + 2*a^3*b^3*c - a^2*b^4*c + 2*a*b^5*c - 2*b^6*c + a^5*c^2 + 2*a^4*b*c^2 - a*b^4*c^2 - 2*b^5*c^2 - 2*a^4*c^3 + 2*a^3*b*c^3 - 4*a*b^3*c^3 + 4*b^4*c^3 - 2*a^3*c^4 - a^2*b*c^4 - a*b^2*c^4 + 4*b^3*c^4 + a^2*c^5 + 2*a*b*c^5 - 2*b^2*c^5 + a*c^6 - 2*b*c^6 : :
Barycentrics    2 x sec A - y sec B - z sec C : : , where x : y : z = X(515)

X(64930) lies on these lines: {2, 280}, {30, 511}, {376, 18283}, {942, 45131}, {1465, 38462}, {1785, 2968}, {1897, 10538}, {2321, 42459}, {3175, 3191}, {3811, 64054}, {7743, 31680}, {8144, 22836}, {9909, 39600}, {17355, 59649}, {18505, 24682}, {22837, 32047}, {31793, 42456}, {34050, 56939}, {34936, 44442}, {37045, 52954}, {37591, 42051}, {51359, 63770}, {52977, 53642}

X(64930) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64930) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64930) = {X(1897),X(10538)}-harmonic conjugate of X(46974)

X(64931) = X(2)X(1074)∩X(30)X(511)

Barycentrics    2*a^7 - 3*a^6*b - 4*a^5*b^2 + 5*a^4*b^3 + 2*a^3*b^4 - a^2*b^5 - b^7 - 3*a^6*c + 8*a^5*b*c - 3*a^4*b^2*c - 4*a^3*b^3*c + 3*a^2*b^4*c - 4*a*b^5*c + 3*b^6*c - 4*a^5*c^2 - 3*a^4*b*c^2 + 4*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + 5*b^5*c^2 + 5*a^4*c^3 - 4*a^3*b*c^3 - 2*a^2*b^2*c^3 + 8*a*b^3*c^3 - 7*b^4*c^3 + 2*a^3*c^4 + 3*a^2*b*c^4 - 7*b^3*c^4 - a^2*c^5 - 4*a*b*c^5 + 5*b^2*c^5 + 3*b*c^6 - c^7 : :
Barycentrics    2 x sec A - y sec B - z sec C : : , where x : y : z = X(517)

X(64931) lies on these lines: {2, 1074}, {30, 511}, {243, 11111}, {376, 45766}, {551, 51616}, {1125, 44901}, {1324, 9909}, {3679, 56825}, {4292, 45131}, {8808, 52121}, {14070, 54090}, {16869, 56862}, {16870, 47040}, {17355, 42459}, {22836, 64054}, {22837, 64053}, {23710, 37043}, {34609, 49554}, {34647, 56863}, {44442, 60448}, {49636, 62330}, {50366, 51889}

X(64931) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64931) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}

X(64932) = X(2)X(33)∩X(30)X(511)

Barycentrics    2*a^6 - 3*a^5*b + a^4*b^2 - 2*a^2*b^4 + 3*a*b^5 - b^6 - 3*a^5*c - 2*a^4*b*c + 2*a^3*b^2*c + 2*a^2*b^3*c + a*b^4*c + a^4*c^2 + 2*a^3*b*c^2 - 4*a*b^3*c^2 + b^4*c^2 + 2*a^2*b*c^3 - 4*a*b^2*c^3 - 2*a^2*c^4 + a*b*c^4 + b^2*c^4 + 3*a*c^5 - c^6 : :
Barycentrics    2 x sec A - y sec B - z sec C : : , where x : y : z = X(518)

X(64932) lies on these lines: {1, 45281}, {2, 33}, {10, 64054}, {30, 511}, {197, 4421}, {220, 17281}, {376, 36984}, {475, 9643}, {547, 61518}, {1062, 58403}, {1125, 8144}, {3241, 4318}, {3244, 64053}, {3543, 52848}, {3635, 32047}, {3679, 36985}, {3717, 54440}, {3829, 23304}, {3913, 34724}, {5695, 6737}, {6604, 22464}, {7387, 8715}, {8666, 12085}, {8756, 37009}, {9644, 34120}, {9645, 25440}, {10572, 15076}, {11194, 54992}, {11235, 34609}, {12513, 34723}, {15951, 24391}, {16548, 18596}, {17382, 21258}, {23335, 24387}, {34607, 34608}, {34619, 34621}, {34620, 34622}, {34639, 34642}, {34640, 34643}, {34654, 34658}, {34655, 34659}, {34671, 34675}, {34672, 34676}, {34687, 34691}, {34688, 34692}, {34700, 34713}, {34704, 34721}, {34705, 34722}, {34706, 34725}, {34707, 34726}, {34708, 34727}, {34709, 34728}, {34710, 34729}, {34711, 34730}, {34823, 56876}, {36844, 44442}, {36907, 60079}, {37045, 52949}, {45275, 48829}

X(64932) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64932) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64932) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33, 34822, 58402}, {33, 52365, 34822}, {4421, 34702, 9909}, {9909, 34703, 4421}

X(64933) = X(2)X(38462)∩X(30)X(511)

Barycentrics    a^6*b + a^5*b^2 - 2*a^4*b^3 - 2*a^3*b^4 + a^2*b^5 + a*b^6 + a^6*c - 8*a^5*b*c + 2*a^4*b^2*c + 4*a^3*b^3*c - a^2*b^4*c + 4*a*b^5*c - 2*b^6*c + a^5*c^2 + 2*a^4*b*c^2 - a*b^4*c^2 - 2*b^5*c^2 - 2*a^4*c^3 + 4*a^3*b*c^3 - 8*a*b^3*c^3 + 4*b^4*c^3 - 2*a^3*c^4 - a^2*b*c^4 - a*b^2*c^4 + 4*b^3*c^4 + a^2*c^5 + 4*a*b*c^5 - 2*b^2*c^5 + a*c^6 - 2*b*c^6 : :
Barycentrics    2 x sec A - y sec B - z sec C : : , where x : y : z = X(519)

X(64933) lies on these lines: {2, 38462}, {30, 511}, {78, 55917}, {3679, 24430}, {5044, 44040}, {8144, 30144}, {9371, 50104}, {10072, 50103}, {11240, 50102}, {13369, 45131}, {35652, 47040}, {36846, 64053}

X(64933) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64933) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {234, 2091}, {414, 2091}, {416, 2091}, {845, 2091}, {1035, 2091}, {1038, 234}, {1119, 2091}, {1616, 414}, {1847, 2091}, {2057, 2091}, {2091, 2091}, {63871, 234}

X(64934) = X(2)X(1577)∩X(30)X(511)

Barycentrics    (b - c)*(-a^3 + a*b^2 + a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :
Barycentrics    2 x sec A - y sec B - z sec C : : , where x : y : z = X(525)

X(64934) lies on these lines: {1, 4804}, {2, 1577}, {10, 4913}, {30, 511}, {381, 39212}, {650, 4791}, {661, 47683}, {667, 48234}, {693, 3960}, {905, 4823}, {1019, 31148}, {1022, 55953}, {1491, 31149}, {1734, 50764}, {2254, 47724}, {2530, 48167}, {3175, 57068}, {3578, 53045}, {3679, 4041}, {3716, 48284}, {3737, 45686}, {3762, 17494}, {4010, 48288}, {4024, 47682}, {4036, 45660}, {4040, 48264}, {4122, 50351}, {4129, 45315}, {4367, 48393}, {4378, 48120}, {4382, 27469}, {4391, 31150}, {4444, 60079}, {4449, 50760}, {4467, 4707}, {4654, 51664}, {4705, 4948}, {4730, 4774}, {4761, 50343}, {4820, 49280}, {4838, 47681}, {4885, 44561}, {4922, 48291}, {4931, 62634}, {4960, 48149}, {4976, 10015}, {4978, 17496}, {7178, 21192}, {8045, 45343}, {9508, 45332}, {13745, 21201}, {14349, 31147}, {14419, 47833}, {14431, 47827}, {16418, 21789}, {16892, 47680}, {17478, 48855}, {17925, 24006}, {19875, 21052}, {21120, 49724}, {21132, 49723}, {21188, 44551}, {21196, 50453}, {21222, 26824}, {21260, 45323}, {21301, 48157}, {21385, 29545}, {25666, 59737}, {29807, 47672}, {30234, 48220}, {30709, 47825}, {34914, 60043}, {37631, 48280}, {42029, 55184}, {45328, 50337}, {45667, 48295}, {45673, 59672}, {45676, 48005}, {47665, 47684}, {47687, 50171}, {47721, 50356}, {47727, 53558}, {47729, 48339}, {47774, 48612}, {48004, 48265}, {48012, 48190}, {48058, 48267}, {48065, 59590}, {48266, 49277}, {48273, 48348}, {48305, 48345}, {50155, 62635}, {50179, 62552}, {52374, 60044}

X(64934) = isogonal conjugate of X(59034)
X(64934) = crossdifference of every pair of points on line {6, 3724}
X(64934) = barycentric product X(i)*X(j) for these {i,j}: {1034, 2091}, {1260, 2091}, {1265, 2091}
X(64934) = barycentric quotient X(i)/X(j) for these {i,j}: {167, 2091}, {845, 2091}, {1035, 2091}, {1119, 2091}, {1653, 1038}, {1847, 2091}, {2057, 2091}, {2091, 2091}
X(64934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1577, 45324}, {2, 4560, 45671}, {2, 45671, 14838}, {693, 48321, 3960}, {1577, 4560, 14838}, {1577, 45671, 2}, {4774, 50339, 4730}, {14838, 45324, 2}, {47672, 53536, 48320}, {48325, 48394, 48295}

X(64935) = X(140)X(523)∩X(476)X(1291)

Barycentrics    (b^2 - c^2)*(-a^6 + 3*a^4*b^2 - 3*a^2*b^4 + b^6 + a^4*c^2 - a^2*b^2*c^2 - 3*b^4*c^2 + a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6) : :
X(64935) = 3 X[1116] - X[8562], 3 X[8029] + X[62173]

X(64935) lise on the X-parabola of ABC (see X(12065)), the cubic K130, and these lines: {140, 523}, {476, 1291}, {850, 1232}, {1117, 15543}, {1263, 10264}, {1510, 10095}, {2395, 14579}, {2501, 6748}, {4024, 21012}, {5466, 13582}, {5671, 15475}, {8029, 62173}, {12006, 20188}, {13597, 43657}, {14367, 44809}, {15047, 38539}, {15328, 43704}, {35055, 47054}, {55199, 57123}, {55201, 57122}

X(64935) = isogonal conjugate of X(47053)
X(64935) = X(1291)-Ceva conjugate of X(1263)
X(64935) = X(526)-cross conjugate of X(523)
X(64935) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47053}, {110, 1749}, {162, 50461}, {163, 37779}, {476, 51802}, {662, 11063}, {1101, 45147}, {1157, 2617}, {2914, 36061}, {4575, 37943}, {6140, 24041}, {10272, 36034}, {14570, 19306}, {32678, 40604}
X(64935) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 47053}, {115, 37779}, {125, 50461}, {136, 37943}, {244, 1749}, {523, 45147}, {1084, 11063}, {3005, 6140}, {3258, 10272}, {5664, 45790}, {16221, 2914}, {18334, 40604}, {38993, 5616}, {38994, 5612}, {60342, 8562}
X(64935) = cevapoint of X(i) and X(j) for these (i,j): {2088, 8029}, {2610, 12071}
X(64935) = crosssum of X(i) and X(j) for these (i,j): {523, 10277}, {6140, 11063}
X(64935) = trilinear pole of line {115, 55280}
X(64935) = crossdifference of every pair of points on line {5612, 5616}
X(64935) = barycentric product X(i)*X(j) for these {i,j}: {338, 1291}, {523, 13582}, {850, 14579}, {1263, 15412}, {1577, 51804}, {2394, 3471}, {3268, 11071}, {14618, 43704}, {15392, 44427}, {23870, 46072}, {23871, 46076}
X(64935) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 47053}, {115, 45147}, {512, 11063}, {523, 37779}, {526, 40604}, {647, 50461}, {661, 1749}, {1263, 14570}, {1291, 249}, {1637, 10272}, {2088, 8562}, {2394, 46751}, {2433, 3470}, {2501, 37943}, {2623, 1157}, {2624, 51802}, {3124, 6140}, {3471, 2407}, {6137, 5616}, {6138, 5612}, {8029, 10413}, {11071, 476}, {13582, 99}, {14579, 110}, {15392, 60053}, {15475, 56404}, {20578, 51267}, {20579, 51274}, {43704, 4558}, {46072, 23895}, {46076, 23896}, {47230, 2914}, {51804, 662}, {58900, 15766}, {58903, 15770}, {62551, 45790}

X(64936) = X(6)X(3200)∩X(140)X(523)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :

X(64936) lies on these lines: {6, 3200}, {140, 523}, {250, 3518}, {262, 7533}, {264, 1272}, {381, 45090}, {428, 60590}, {842, 1291}, {1263, 3613}, {2937, 3447}, {7953, 43657}

X(64936) = X(i)-isoconjugate of X(j) for these (i,j): {98, 1749}, {293, 37943}, {1821, 11063}, {1910, 37779}, {6140, 36036}, {19306, 53245}, {36084, 45147}, {36120, 50461}
X(64936) = X(i)-Dao conjugate of X(j) for these (i,j): {132, 37943}, {2679, 6140}, {11672, 37779}, {38987, 45147}, {40601, 11063}, {46094, 50461}, {55071, 8562}
X(64936) = crossdifference of every pair of points on line {11063, 45147}
X(64936) = barycentric product X(i)*X(j) for these {i,j}: {297, 43704}, {325, 14579}, {511, 13582}, {1291, 2799}, {1959, 51804}, {3471, 35910}, {11071, 51383}
X(64936) = barycentric quotient X(i)/X(j) for these {i,j}: {232, 37943}, {237, 11063}, {511, 37779}, {1263, 53245}, {1291, 2966}, {1755, 1749}, {2491, 6140}, {3289, 50461}, {3471, 60869}, {3569, 45147}, {13582, 290}, {14579, 98}, {14966, 47053}, {35910, 46751}, {41270, 1157}, {43704, 287}, {44114, 10413}, {51804, 1821}

X(64937) = X(140)X(523)∩X(512)X(13366)

Barycentrics    a^2*(b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :

X(64937) lies on the Lemoine asymptotic hyperbola and these lines: {140, 523}, {512, 13366}, {691, 1291}, {876, 51804}, {1263, 60037}, {6140, 15475}, {9178, 14579}, {13582, 60028}, {14367, 15567}, {22260, 57136}, {35364, 43704}

X(64937) = X(1291)-Ceva conjugate of X(14579)
X(64937) = X(14270)-cross conjugate of X(512)
X(64937) = X(i)-isoconjugate of X(j) for these (i,j): {75, 47053}, {99, 1749}, {662, 37779}, {799, 11063}, {811, 50461}, {4592, 37943}, {6140, 24037}, {24041, 45147}, {32680, 40604}, {35139, 51802}
X(64937) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 47053}, {512, 6140}, {1084, 37779}, {3005, 45147}, {5139, 37943}, {17423, 50461}, {38986, 1749}, {38996, 11063}, {60342, 45790}
X(64937) = crosspoint of X(i) and X(j) for these (i,j): {1291, 14579}, {1989, 53705}
X(64937) = crosssum of X(37779) and X(45147)
X(64937) = crossdifference of every pair of points on line {11063, 37779}
X(64937) = barycentric product X(i)*X(j) for these {i,j}: {115, 1291}, {512, 13582}, {523, 14579}, {526, 11071}, {661, 51804}, {1263, 2623}, {2433, 3471}, {2501, 43704}, {6137, 46072}, {6138, 46076}, {15392, 47230}, {43657, 55280}
X(64937) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 47053}, {512, 37779}, {669, 11063}, {798, 1749}, {1084, 6140}, {1291, 4590}, {2088, 45790}, {2433, 46751}, {2489, 37943}, {3049, 50461}, {3124, 45147}, {11071, 35139}, {13582, 670}, {14270, 40604}, {14398, 10272}, {14579, 99}, {22260, 10413}, {43657, 55279}, {43704, 4563}, {51804, 799}

X(64938) = X(2)X(39183)∩X(140)X(523)

Barycentrics    (b^2 - c^2)*(a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :

X(64937) lies on the orthic asymptotic hyperbola and these lines: {2, 39183}, {140, 523}, {525, 64062}, {879, 43704}, {935, 1291}, {1263, 60036}, {2394, 13582}, {5664, 15412}, {14367, 42731}, {14566, 14618}, {14579, 60040}

X(64938) = X(8552)-cross conjugate of X(525)
X(64938) = X(i)-isoconjugate of X(j) for these (i,j): {19, 47053}, {112, 1749}, {162, 11063}, {163, 37943}, {2914, 32678}, {3470, 56829}, {10272, 36131}, {19306, 35360}, {24019, 50461}, {32676, 37779}
X(64938) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 47053}, {115, 37943}, {125, 11063}, {647, 45147}, {15526, 37779}, {18334, 2914}, {34591, 1749}, {35071, 50461}, {39008, 10272}
X(64938) = barycentric product X(i)*X(j) for these {i,j}: {339, 1291}, {525, 13582}, {850, 43704}, {1263, 62428}, {3267, 14579}, {3268, 15392}, {3471, 34767}, {11071, 45792}, {14208, 51804}
X(64938) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 47053}, {125, 45147}, {520, 50461}, {523, 37943}, {525, 37779}, {526, 2914}, {647, 11063}, {656, 1749}, {1263, 35360}, {1291, 250}, {3471, 4240}, {8552, 40604}, {9033, 10272}, {13582, 648}, {14380, 3470}, {14579, 112}, {14582, 56404}, {15392, 476}, {16186, 8562}, {20975, 6140}, {23286, 1157}, {34767, 46751}, {43704, 110}, {46072, 36306}, {46076, 36309}, {51804, 162}, {60009, 5612}, {60010, 5616}

X(64939) = X(2)X(4048)∩X(83)X(51126)

Barycentrics    (2*a^2 + b^2 + c^2)*(a^4 + 5*a^2*b^2 + 3*b^4 + 5*a^2*c^2 + 7*b^2*c^2 + 3*c^4) : :
X(64939) = 9 X[2] - X[24273], X[83] - 5 X[51126], X[141] - 5 X[31268], X[2896] + 7 X[47355], 7 X[3589] - X[41623], 7 X[6292] + X[41623], X[20088] - 17 X[63120], X[31168] + 3 X[48310], X[32449] + 3 X[42006]

X(64939) lies on the cubic K1364 and these lines: {2, 4048}, {83, 51126}, {141, 7905}, {625, 6704}, {732, 6683}, {2896, 47355}, {3589, 5007}, {3628, 29012}, {5103, 16897}, {7769, 51128}, {17357, 49612}, {20088, 63120}, {31168, 48310}, {32449, 42006}

X(64939) = midpoint of X(3589) and X(6292)
X(64939) = reflection of X(6704) in X(51127)
X(64939) = barycentric product X(3589)*X(60728)
X(64939) = barycentric quotient X(60728)/X(10159)

X(64940) = X(2)X(353)∩X(512)X(61045)

Barycentrics    (4*a^2 + b^2 + c^2)*(a^4 - 4*a^2*b^2 - 2*b^4 - 4*a^2*c^2 - 7*b^2*c^2 - 2*c^4) : :
X(64940) = X[9731] + 2 X[15810], 3 X[5085] + X[10033], 3 X[47352] + X[55164]

X(64940) lies on the cubic K1364 and these lines: {2, 353}, {512, 61045}, {524, 10007}, {547, 11645}, {597, 5008}, {598, 60238}, {3589, 3849}, {5085, 10033}, {8355, 14762}, {12150, 47352}, {20582, 63647}, {24256, 52691}, {33184, 48310}

X(64940) = midpoint of X(i) and X(j) for these {i,j}: {597, 15810}, {24256, 52691}
X(64940) = reflection of X(9731) in X(597)
X(64940) = barycentric product X(31950)*X(35356)
X(64940) = barycentric quotient X(35357)/X(31951)

X(64941) = X(2)X(5477)∩X(193)X(26613)

Barycentrics    (5*a^2 - b^2 - c^2)*(11*a^4 - 8*a^2*b^2 + 5*b^4 - 8*a^2*c^2 - 14*b^2*c^2 + 5*c^4) : :
X(64941) = X[41895] - 5 X[63127]

X(64941) lies on the cubic K1364 and these lines: {2, 5477}, {193, 26613}, {381, 6776}, {524, 10008}, {597, 18584}, {598, 41895}, {1384, 1992}, {5032, 5052}, {7615, 39764}, {9300, 33692}, {9740, 51373}, {10011, 63107}, {11163, 60240}, {18800, 32815}, {33550, 51170}, {44839, 63022}, {60150, 60268}

X(64941) = midpoint of X(1992) and X(11147)
X(64941) = X(11147)-Dao conjugate of X(60240)
X(64941) = barycentric product X(1992)*X(23055)
X(64941) = barycentric quotient X(i)/X(j) for these {i,j}: {1992, 60240}, {23055, 5485}

X(64942) = X(2)X(5503)∩X(6)X(5215)

Barycentrics    (a^2 - 2*b^2 - 2*c^2)*(a^4 + 5*a^2*b^2 - 2*b^4 + 5*a^2*c^2 + 2*b^2*c^2 - 2*c^4) : :
X(64942) = 3 X[21358] - X[40727], 2 X[7775] + X[52987], 4 X[7843] + 5 X[55600], X[9741] + 3 X[21356], X[34511] + 2 X[40107], 2 X[50991] + X[51123], 5 X[50993] + X[51122], 7 X[55611] + 2 X[63931]

X(64942) lies on the cubic K1364 and these lines: {2, 5503}, {6, 5215}, {141, 52229}, {182, 524}, {184, 10554}, {511, 11184}, {538, 44774}, {542, 7618}, {543, 11178}, {574, 599}, {597, 13720}, {1352, 53142}, {2549, 19662}, {3094, 9466}, {3098, 3849}, {5028, 47352}, {5039, 63028}, {5476, 9771}, {5485, 7790}, {5969, 7617}, {7615, 24206}, {7619, 14645}, {7775, 52987}, {7843, 55600}, {7844, 16509}, {9741, 21356}, {9770, 54173}, {9888, 49788}, {10484, 42011}, {26613, 41412}, {34511, 40107}, {43461, 50967}, {50991, 51123}, {50993, 51122}, {54169, 63945}, {55611, 63931}, {60240, 62895}

X(64942) = midpoint of X(i) and X(j) for these {i,j}: {599, 11165}, {1352, 53142}, {9770, 54173}
X(64942) = reflection of X(i) in X(j) for these {i,j}: {182, 7622}, {597, 63647}, {5476, 9771}, {7615, 24206}, {16509, 20582}
X(64942) = X(11166)-isoconjugate of X(55927)
X(64942) = X(i)-Dao conjugate of X(j) for these (i,j): {8542, 11166}, {11165, 11167}
X(64942) = crossdifference of every pair of points on line {9135, 46001}
X(64942) = barycentric product X(i)*X(j) for these {i,j}: {599, 11163}, {8704, 9146}
X(64942) = barycentric quotient X(i)/X(j) for these {i,j}: {574, 11166}, {599, 11167}, {8704, 8599}, {9145, 6233}, {11163, 598}, {11186, 46001}, {58749, 14327}

X(64943) = X(2)X(187)∩X(230)X(9830)

Barycentrics    (a^4 + 5*a^2*b^2 - 2*b^4 + 5*a^2*c^2 + 2*b^2*c^2 - 2*c^4)*(4*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 4*b^2*c^2 + c^4) : :
X(64943) = X[598] + 3 X[26613], 3 X[5215] - X[15810], X[8592] + 3 X[8859], X[9774] + 3 X[38227]

X(64943) lies on the cubic K1364 and these lines: {2, 187}, {230, 9830}, {511, 63101}, {512, 9189}, {524, 51373}, {543, 2021}, {1513, 6055}, {1691, 7610}, {1692, 63065}, {2030, 18800}, {5017, 11184}, {5052, 63028}, {5104, 42849}, {8592, 8859}, {9300, 9731}, {9774, 25406}, {10033, 51537}, {11167, 23055}, {19661, 37451}, {21163, 52691}, {37455, 55801}, {37688, 38010}, {43535, 60103}

X(64943) = midpoint of X(22329) and X(62578)
X(64943) = X(62578)-Dao conjugate of X(11167)
X(64943) = crossdifference of every pair of points on line {17414, 62191}
X(64943) = barycentric product X(i)*X(j) for these {i,j}: {99, 14327}, {8704, 34245}, {11163, 22329}
X(64943) = barycentric quotient X(i)/X(j) for these {i,j}: {2030, 11166}, {8704, 34246}, {11163, 5503}, {14327, 523}, {22329, 11167}
X(64943) = {X(187),X(5215)}-harmonic conjugate of X(5569)

X(64944) = X(2)X(5471)∩X(15)X(5459)

Barycentrics    17*a^4 - 14*a^2*b^2 + 5*b^4 - 14*a^2*c^2 - 8*b^2*c^2 + 5*c^4 - 2*Sqrt[3]*(5*a^2 - b^2 - c^2)*S : :

X(64944) lies on the cubic K1364 and these lines: {2, 5471}, {15, 5459}, {396, 8598}, {524, 10617}, {530, 30560}, {598, 55951}, {3106, 13083}, {6772, 42062}, {6783, 45879}, {8594, 62198}, {8787, 33377}, {9123, 9194}, {9166, 51484}, {9763, 19781}, {26613, 37786}, {33517, 35931}, {36775, 41630}, {49862, 54618}

X(64944) = barycentric quotient X(37786)/X(55951)

X(64945) = X(2)X(5472)∩X(16)X(5460)

Barycentrics    17*a^4 - 14*a^2*b^2 + 5*b^4 - 14*a^2*c^2 - 8*b^2*c^2 + 5*c^4 + 2*Sqrt[3]*(5*a^2 - b^2 - c^2)*S : :

X(64945) lies on the cubic K1364 and these lines: {2, 5472}, {16, 5460}, {395, 8598}, {524, 10616}, {531, 30559}, {598, 55950}, {3107, 13084}, {6775, 42063}, {6782, 45880}, {8595, 62197}, {8787, 33376}, {9123, 9195}, {9166, 51485}, {9761, 19780}, {26613, 37785}, {33518, 35932}, {44219, 61514}, {49861, 54617}

X(64945) = barycentric quotient X(37785)/X(55950)

X(64946) = MIDPOINT OF X(1125) AND X(1213)

Barycentrics    (2*a + b + c)*(a^2 + 5*a*b + 3*b^2 + 5*a*c + 7*b*c + 3*c^2) : :
X(64946) = 15 X[2] + X[9791], 9 X[2] - X[24342], 3 X[2] + X[25354], 3 X[9791] + 5 X[24342], X[9791] - 5 X[25354], X[24342] + 3 X[25354], X[10] - 5 X[31248], X[86] - 5 X[19862], 3 X[551] + X[42334], 3 X[1125] - X[5625], 3 X[1213] + X[5625], X[1654] + 7 X[3624], 3 X[3817] + X[63402], 3 X[3828] - X[4733], X[3993] + 3 X[27483], 3 X[19883] + X[31144]

X(64946) lies on the cubic K1364 and these lines: {2, 846}, {10, 17315}, {86, 16477}, {551, 42334}, {740, 3634}, {1100, 1125}, {1654, 3624}, {3817, 63402}, {3828, 4733}, {3834, 6693}, {3993, 27483}, {6533, 27605}, {17263, 51073}, {17298, 34595}, {17357, 31253}, {17768, 58433}, {19883, 31144}, {29604, 31336}, {60688, 60710}

X(64946) = midpoint of X(1125) and X(1213)
X(64946) = reflection of X(6707) in X(19878)
X(64946) = X(i)-isoconjugate of X(j) for these (i,j): {28615, 60669}, {47947, 59080}
X(64946) = X(1213)-Dao conjugate of X(60669)
X(64946) = crosspoint of X(60708) and X(60710)
X(64946) = crossdifference of every pair of points on line {5029, 50344}
X(64946) = barycentric product X(i)*X(j) for these {i,j}: {1125, 60710}, {1213, 60708}, {4359, 60688}
X(64946) = barycentric quotient X(i)/X(j) for these {i,j}: {1125, 60669}, {35327, 59080}, {60688, 1255}, {60708, 32014}, {60710, 1268}

X(64947) = MIDPOINT OF X(385) AND X(8290)

Barycentrics    (a^2 - b*c)*(a^2 + b*c)*(a^4 + 2*a^2*b^2 + 2*a^2*c^2 + b^2*c^2) : :
X(64947) = X[11606] - 5 X[63047]

X(64947) lies on the cubic K1364 and these lines: {2, 32}, {3, 32476}, {69, 10334}, {98, 8784}, {114, 35376}, {182, 6194}, {183, 3407}, {187, 5152}, {230, 9478}, {385, 732}, {511, 39089}, {699, 53621}, {733, 59026}, {1184, 3866}, {1207, 34482}, {1447, 19572}, {1580, 7081}, {1692, 39097}, {1916, 2076}, {2080, 5999}, {2458, 36849}, {3329, 10007}, {3398, 37455}, {3406, 54155}, {5007, 51827}, {5025, 9990}, {5027, 9185}, {5038, 63038}, {5039, 62994}, {5171, 12122}, {5182, 44367}, {5970, 59047}, {5980, 36759}, {5981, 36760}, {6179, 41755}, {6249, 12110}, {6287, 10104}, {6671, 41632}, {6672, 41642}, {7754, 10131}, {7767, 10333}, {7777, 41749}, {7779, 10352}, {7780, 44772}, {7839, 12054}, {7893, 10349}, {8725, 14880}, {8789, 51983}, {10064, 10802}, {10080, 10801}, {10353, 50248}, {10519, 63017}, {10998, 35436}, {12191, 51224}, {12194, 12264}, {12252, 37182}, {13111, 13860}, {13196, 50251}, {13356, 33004}, {14614, 39560}, {16986, 42534}, {17004, 42535}, {18993, 19092}, {18994, 19091}, {19570, 53765}, {22329, 58765}, {22712, 39750}, {32134, 61555}, {35006, 39093}, {35540, 56979}, {39141, 63046}, {41295, 59249}, {41623, 63018}, {44586, 49255}, {44587, 49254}, {54539, 60128}, {59266, 60101}, {60181, 60184}

X(64947) = midpoint of X(385) and X(8290)
X(64947) = reflection of X(9478) in X(230)
X(64947) = complement of X(9866)
X(64947) = X(3407)-Ceva conjugate of X(4027)
X(64947) = X(i)-isoconjugate of X(j) for these (i,j): {694, 60664}, {1581, 60667}, {1934, 60672}, {1967, 42006}, {43763, 59262}
X(64947) = X(i)-Dao conjugate of X(j) for these (i,j): {8290, 42006}, {19576, 60667}, {36213, 59262}, {39043, 60664}
X(64947) = crosspoint of X(39685) and X(59249)
X(64947) = crosssum of X(i) and X(j) for these (i,j): {732, 24256}, {39684, 59273}
X(64947) = crossdifference of every pair of points on line {882, 3005}
X(64947) = barycentric product X(i)*X(j) for these {i,j}: {385, 3329}, {419, 60702}, {732, 60860}, {880, 14318}, {1580, 60683}, {1691, 60707}, {1966, 60686}, {3978, 12212}, {8623, 59249}, {10007, 56976}, {35540, 41295}, {36213, 39685}
X(64947) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 42006}, {1580, 60664}, {1691, 60667}, {3329, 1916}, {8623, 59262}, {10007, 56977}, {12212, 694}, {14318, 882}, {14602, 60672}, {41295, 733}, {51312, 43763}, {56915, 59273}, {56980, 43357}, {60683, 1934}, {60686, 1581}, {60702, 40708}, {60707, 18896}, {60860, 14970}
X(64947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 83, 12206}, {32, 8150, 83}, {83, 1078, 6292}, {83, 6308, 2896}, {183, 24273, 42006}, {183, 59232, 3407}, {385, 1691, 4027}, {1691, 51325, 56915}, {2896, 7793, 6308}, {7787, 7793, 3785}, {8623, 56976, 16985}

X(64948) = MIDPOINT OF X(193) AND X(51579)

Barycentrics    (3*a^2 - b^2 - c^2)*(13*a^4 - 10*a^2*b^2 + 9*b^4 - 10*a^2*c^2 - 14*b^2*c^2 + 9*c^4) : :
X(64948) = X[38259] - 5 X[51170]

X(64948) lies on the cubic K1364 and these lines: {2, 39764}, {4, 1353}, {6, 39143}, {193, 439}, {194, 63061}, {1570, 54097}, {7766, 40926}, {9734, 40925}, {9741, 35927}, {9742, 10011}, {20080, 32818}, {32988, 63123}

X(64948) = midpoint of X(193) and X(51579)
X(64948) = reflection of X(39143) in X(6)

X(64949) = MIDPOINT OF X(6390) and X(40727)

Barycentrics    (11*a^4 - 8*a^2*b^2 + 5*b^4 - 8*a^2*c^2 - 14*b^2*c^2 + 5*c^4)*(2*a^4 - 5*a^2*b^2 + 5*b^4 - 5*a^2*c^2 - 2*b^2*c^2 + 5*c^4) : :

X(64949) lies on the cubic K1364 and these lines: {2, 2418}, {182, 15597}, {524, 10011}, {2080, 63945}, {3564, 7610}, {5093, 9770}, {5107, 22110}, {9771, 38317}, {9877, 56370}, {11184, 18583}, {11898, 63029}, {16508, 37350}, {23055, 64941}

X(64949) = midpoint of X(i) and X(j) for these {i,j}: {6390, 40727}, {9877, 56370}, {16508, 37350}
X(64949) = barycentric product X(22110)*X(23055)
X(64949) = barycentric quotient X(i)/X(j) for these {i,j}: {22110, 60240}, {23055, 60103}

X(64950) = 86th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(5*a^2-5*b^2-5*c^2-6*b*c) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/08/2024. (Aug 23, 2024)

X(64950) lies on these lines: {1, 3}, {2, 9670}, {4, 4995}, {8, 17574}, {10, 19526}, {11, 3525}, {12, 3146}, {20, 11237}, {21, 4421}, {30, 9656}, {33, 55578}, {73, 43691}, {100, 16865}, {109, 28157}, {140, 4309}, {198, 16675}, {376, 15888}, {381, 4330}, {382, 3584}, {388, 50693}, {390, 5433}, {404, 4428}, {405, 3828}, {474, 19883}, {480, 15481}, {495, 12103}, {496, 12108}, {497, 10303}, {498, 546}, {499, 10386}, {519, 19535}, {528, 6910}, {550, 9657}, {551, 19537}, {611, 52987}, {612, 9628}, {613, 20190}, {631, 3058}, {632, 15171}, {902, 4255}, {943, 64152}, {958, 4678}, {993, 4701}, {1001, 17531}, {1030, 16674}, {1056, 62084}, {1058, 61807}, {1124, 6454}, {1193, 21000}, {1250, 22236}, {1253, 1399}, {1335, 6453}, {1376, 5047}, {1428, 55684}, {1469, 55614}, {1478, 15704}, {1479, 3628}, {1621, 17572}, {1656, 9671}, {1657, 37719}, {1698, 16860}, {2041, 36441}, {2042, 36459}, {2066, 3594}, {2177, 2334}, {2241, 31652}, {2256, 22357}, {2269, 38296}, {2330, 11477}, {2475, 34626}, {2975, 20014}, {3024, 15034}, {3028, 15021}, {3056, 53093}, {3085, 3529}, {3086, 61814}, {3090, 4294}, {3091, 5218}, {3522, 5434}, {3523, 10385}, {3526, 4857}, {3530, 10072}, {3534, 5270}, {3560, 61258}, {3582, 15720}, {3583, 5072}, {3585, 49136}, {3592, 5414}, {3600, 62078}, {3614, 61964}, {3627, 4302}, {3649, 9778}, {3679, 17571}, {3689, 31424}, {3711, 31445}, {3871, 20053}, {3912, 21510}, {3913, 4189}, {3916, 41711}, {3951, 4640}, {3984, 35258}, {4258, 41423}, {4293, 62092}, {4299, 44245}, {4313, 40663}, {4314, 24914}, {4316, 62119}, {4317, 8703}, {4324, 9654}, {4325, 62100}, {4413, 5248}, {4423, 16862}, {4669, 8715}, {4679, 59587}, {4691, 5687}, {4870, 9589}, {4999, 20075}, {5007, 31451}, {5013, 10987}, {5054, 37720}, {5076, 31479}, {5079, 9668}, {5084, 6174}, {5132, 8692}, {5141, 34706}, {5160, 37953}, {5198, 52427}, {5225, 15022}, {5229, 49140}, {5237, 54436}, {5238, 54435}, {5259, 16855}, {5261, 62152}, {5274, 7294}, {5297, 63676}, {5298, 15717}, {5302, 64135}, {5310, 11284}, {5326, 10591}, {5393, 21571}, {5405, 21576}, {5441, 5790}, {5445, 54342}, {5609, 10065}, {5657, 10543}, {5731, 45081}, {6154, 19843}, {6198, 35479}, {6419, 19037}, {6420, 19038}, {6425, 18996}, {6426, 18995}, {6448, 31474}, {6684, 61717}, {6857, 34612}, {6872, 31141}, {6914, 61249}, {6921, 49736}, {7031, 31461}, {7173, 46936}, {7288, 61804}, {7354, 17538}, {7483, 31140}, {7741, 55857}, {7772, 31448}, {7786, 22711}, {7951, 61984}, {8164, 11541}, {8167, 63753}, {8168, 63754}, {8567, 32065}, {9612, 52638}, {9629, 54401}, {9645, 12107}, {9655, 62134}, {9669, 55858}, {9711, 31156}, {9780, 17543}, {10053, 51524}, {10058, 51525}, {10086, 51523}, {10087, 51529}, {10088, 51522}, {10149, 37952}, {10197, 50239}, {10327, 59592}, {10387, 10541}, {10404, 12512}, {10483, 62143}, {10578, 52783}, {10588, 50689}, {10589, 61863}, {10590, 62028}, {10592, 12102}, {10593, 55862}, {10638, 22238}, {10786, 37001}, {10927, 45550}, {10928, 45551}, {10991, 12350}, {11001, 31410}, {11111, 21031}, {11189, 17821}, {11194, 17548}, {11236, 15680}, {11398, 35502}, {11399, 44879}, {11499, 61259}, {11500, 21669}, {11517, 51573}, {12185, 20399}, {12513, 17549}, {12588, 64196}, {12764, 20400}, {12896, 15027}, {12904, 20397}, {13116, 51536}, {13183, 20398}, {13897, 53513}, {13898, 31499}, {13954, 53516}, {14986, 61798}, {15170, 15712}, {15172, 61810}, {15175, 18491}, {15325, 61808}, {15326, 62097}, {15452, 23235}, {15837, 64197}, {16371, 51108}, {16417, 63752}, {16483, 41451}, {16502, 53096}, {16669, 37503}, {16814, 36744}, {16866, 19875}, {16885, 54285}, {17023, 21532}, {17539, 48832}, {17573, 25055}, {17576, 34606}, {17718, 31730}, {17783, 24851}, {17784, 24953}, {18513, 62024}, {18514, 61968}, {18990, 62104}, {19327, 26241}, {19704, 51091}, {19705, 51106}, {21518, 29574}, {22331, 31477}, {22356, 37504}, {22758, 61245}, {25524, 61155}, {26888, 58795}, {28628, 63145}, {31157, 64068}, {31436, 50811}, {31475, 41946}, {31649, 32141}, {32153, 61293}, {33557, 64074}, {34611, 37291}, {35007, 54416}, {37307, 40726}, {37701, 48661}, {37721, 50821}, {37724, 43174}, {38729, 46687}, {41869, 61648}, {45701, 57002}, {48829, 56778}, {50808, 63274}, {53095, 63493}, {59421, 63272}, {61716, 63259}

X(64950) = cross-difference of every pair of points on the line X(650)X(28191)
X(64950) = crosspoint of X(59) and X(28230)
X(64950) = crosssum of X(11) and X(28229)
X(64950) = X(643)-beth conjugate of-X(46933)
X(64950) = X(28155)-zayin conjugate of-X(513)
X(64950) = pole of the line {513, 58178} with respect to the circumcircle
X(64950) = pole of the line {20980, 58178} with respect to the Brocard inellipse
X(64950) = pole of the line {21, 40726} with respect to the Stammler hyperbola
X(64950) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 41348, 65), (3, 3303, 56), (55, 5217, 56), (55, 63756, 1), (3303, 5217, 3), (5010, 5563, 3)

X(64951) = 87th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(3*a^2-3*b^2-3*c^2-4*b*c) : :
X(64951) = X(1)-3*X(3601) = X(1)+3*X(61763) = 5*X(1)-3*X(64964)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/08/2024. (Aug 23, 2024)

X(64951) lies on these lines: {1, 3}, {2, 9669}, {4, 5281}, {5, 4294}, {6, 24047}, {7, 63282}, {8, 16370}, {10, 4421}, {11, 3526}, {12, 382}, {15, 54438}, {16, 54437}, {20, 495}, {21, 3617}, {24, 7071}, {25, 5297}, {30, 3085}, {32, 31477}, {33, 3517}, {34, 55571}, {44, 4254}, {45, 36744}, {72, 35258}, {73, 43719}, {100, 405}, {109, 28149}, {140, 497}, {145, 17549}, {182, 10387}, {197, 20831}, {198, 16676}, {200, 31445}, {202, 36843}, {203, 36836}, {218, 41423}, {220, 4262}, {221, 3357}, {355, 4304}, {372, 31474}, {376, 18990}, {381, 498}, {386, 3052}, {388, 550}, {390, 496}, {392, 4855}, {399, 10065}, {404, 46934}, {452, 3820}, {474, 1621}, {499, 3058}, {500, 22117}, {516, 11374}, {528, 26363}, {546, 10588}, {548, 4293}, {549, 3086}, {574, 16781}, {595, 4255}, {601, 1253}, {611, 33878}, {612, 7302}, {613, 12017}, {632, 10589}, {899, 16058}, {902, 16466}, {943, 5556}, {944, 33899}, {950, 26446}, {952, 4305}, {954, 3651}, {956, 3621}, {958, 3626}, {962, 37737}, {991, 5399}, {993, 3625}, {995, 19252}, {1001, 16408}, {1011, 3240}, {1012, 11491}, {1015, 15815}, {1030, 16672}, {1043, 5774}, {1056, 3522}, {1058, 3523}, {1124, 6398}, {1125, 4428}, {1151, 35809}, {1152, 35808}, {1191, 4256}, {1250, 11485}, {1260, 4420}, {1335, 6221}, {1351, 2330}, {1376, 3634}, {1384, 54416}, {1387, 9785}, {1398, 3520}, {1469, 55610}, {1478, 1657}, {1479, 1656}, {1500, 3053}, {1597, 11398}, {1598, 52427}, {1609, 62210}, {1616, 41451}, {1698, 16857}, {1770, 17718}, {1788, 12433}, {1836, 63259}, {1864, 58630}, {1870, 3516}, {1914, 9605}, {1918, 50598}, {2066, 3312}, {2067, 6449}, {2070, 5160}, {2192, 10282}, {2241, 5013}, {2242, 5023}, {2271, 17735}, {2276, 30435}, {2346, 5551}, {2476, 20066}, {2550, 6675}, {2551, 50241}, {2975, 19535}, {3024, 32609}, {3028, 15041}, {3056, 5050}, {3100, 9715}, {3146, 8164}, {3149, 15911}, {3158, 31424}, {3167, 6238}, {3241, 5303}, {3244, 11194}, {3270, 19357}, {3297, 6396}, {3298, 6200}, {3299, 6395}, {3301, 6199}, {3311, 5414}, {3421, 17576}, {3434, 7483}, {3436, 57002}, {3474, 6147}, {3475, 24470}, {3485, 28174}, {3486, 5690}, {3487, 9778}, {3515, 6198}, {3524, 14986}, {3525, 5274}, {3528, 3600}, {3529, 5261}, {3530, 7288}, {3534, 7354}, {3555, 4652}, {3560, 18357}, {3582, 15701}, {3583, 3851}, {3584, 3830}, {3585, 5073}, {3586, 9956}, {3616, 16371}, {3622, 13587}, {3624, 7743}, {3627, 10590}, {3628, 10591}, {3636, 40726}, {3647, 5220}, {3654, 64163}, {3689, 41229}, {3697, 64135}, {3730, 4258}, {3753, 62829}, {3811, 3927}, {3843, 4330}, {3870, 3916}, {3878, 56177}, {3912, 21509}, {3935, 20835}, {3940, 12514}, {3947, 28150}, {4018, 63144}, {4245, 19760}, {4251, 42316}, {4257, 41434}, {4278, 18185}, {4295, 5719}, {4299, 15696}, {4313, 5657}, {4314, 5722}, {4316, 9657}, {4317, 62085}, {4319, 37696}, {4324, 12943}, {4325, 62105}, {4326, 31658}, {4354, 9642}, {4366, 11285}, {4413, 5259}, {4423, 16863}, {4512, 5044}, {4646, 37817}, {4663, 12329}, {4781, 16406}, {4794, 48387}, {4816, 5258}, {4857, 46219}, {4930, 33595}, {4972, 56779}, {5020, 5310}, {5024, 10987}, {5047, 46931}, {5055, 10896}, {5070, 7741}, {5080, 50242}, {5084, 47742}, {5120, 16666}, {5132, 16286}, {5148, 38225}, {5219, 22793}, {5250, 5440}, {5251, 61154}, {5253, 19537}, {5260, 19526}, {5263, 19273}, {5265, 10299}, {5267, 12513}, {5270, 62131}, {5280, 21309}, {5284, 16862}, {5298, 15700}, {5302, 18247}, {5326, 55857}, {5393, 21558}, {5405, 21561}, {5433, 15720}, {5434, 15688}, {5441, 28453}, {5445, 61717}, {5450, 30283}, {5493, 64110}, {5552, 11113}, {5703, 6361}, {5745, 64117}, {5765, 48918}, {5779, 15837}, {5790, 10572}, {5791, 63146}, {5818, 7319}, {5840, 26487}, {5886, 10624}, {5901, 30305}, {6019, 52698}, {6154, 24953}, {6285, 32063}, {6286, 55039}, {6409, 35768}, {6410, 35769}, {6417, 19037}, {6418, 19038}, {6450, 6502}, {6645, 33235}, {6692, 51724}, {6763, 41711}, {6796, 11496}, {6831, 37000}, {6857, 17784}, {6872, 17757}, {6908, 31777}, {6910, 20075}, {6911, 61272}, {6913, 11499}, {6914, 37705}, {6917, 61533}, {6918, 61268}, {6927, 7956}, {6934, 63257}, {6937, 13199}, {6938, 40267}, {6950, 64173}, {7005, 22238}, {7006, 22236}, {7031, 43136}, {7074, 36742}, {7080, 11111}, {7085, 36277}, {7086, 22361}, {7160, 9841}, {7286, 18859}, {7292, 7484}, {7294, 61850}, {7298, 20850}, {7330, 64116}, {7355, 35450}, {7506, 10833}, {7701, 60884}, {7754, 32107}, {7866, 26629}, {8053, 37502}, {8068, 48680}, {8144, 14070}, {8252, 35803}, {8253, 35802}, {8275, 61288}, {8540, 53092}, {8572, 56804}, {8606, 56843}, {9342, 16854}, {9534, 16300}, {9538, 38444}, {9566, 58772}, {9578, 28160}, {9580, 9955}, {9581, 11231}, {9599, 31467}, {9612, 28146}, {9614, 11230}, {9637, 12160}, {9645, 16195}, {9646, 13665}, {9651, 44519}, {9656, 49134}, {9660, 44622}, {9664, 13881}, {9665, 31489}, {9671, 61905}, {9673, 13621}, {9707, 11461}, {9856, 52026}, {10037, 12083}, {10039, 18525}, {10053, 13188}, {10058, 12331}, {10060, 12315}, {10066, 12307}, {10072, 15693}, {10086, 12188}, {10087, 12773}, {10088, 10620}, {10091, 15040}, {10093, 48668}, {10149, 37955}, {10164, 63999}, {10165, 11373}, {10197, 34626}, {10198, 17528}, {10200, 49736}, {10303, 47743}, {10308, 55920}, {10483, 11237}, {10525, 31659}, {10527, 37298}, {10543, 10573}, {10638, 11486}, {10884, 17613}, {10912, 51111}, {10950, 59503}, {10956, 38753}, {11124, 11247}, {11174, 53680}, {11238, 15694}, {11239, 34740}, {11286, 27020}, {11329, 29595}, {11343, 29579}, {11350, 17021}, {11362, 37739}, {11399, 55572}, {11406, 14017}, {11426, 11436}, {11429, 11432}, {11495, 30424}, {11500, 31673}, {11517, 13615}, {11684, 31660}, {11898, 39900}, {12047, 48661}, {12245, 37728}, {12316, 47378}, {12332, 12333}, {12512, 21620}, {12572, 59584}, {12647, 18526}, {12669, 37287}, {12699, 13411}, {12701, 18493}, {12705, 64804}, {12710, 58637}, {12711, 31837}, {12735, 38693}, {12738, 41166}, {12896, 38724}, {12940, 64758}, {13075, 59384}, {13076, 59383}, {13115, 13311}, {13116, 13310}, {13405, 31730}, {13407, 18541}, {13735, 59299}, {13743, 18518}, {13903, 19030}, {13905, 18512}, {13961, 19029}, {13963, 18510}, {14100, 59381}, {14974, 18755}, {15061, 46687}, {15174, 21161}, {15175, 17501}, {15254, 58634}, {15326, 62100}, {15484, 31460}, {15624, 39600}, {15808, 17573}, {16059, 30950}, {16173, 38636}, {16367, 16816}, {16394, 26115}, {16395, 29822}, {16403, 26227}, {16412, 29578}, {16431, 26626}, {16436, 17316}, {16477, 20992}, {16670, 54322}, {16823, 19323}, {16830, 19322}, {16858, 46933}, {16861, 46932}, {16948, 17524}, {17018, 19346}, {17023, 21539}, {17527, 59572}, {17536, 61156}, {17542, 19877}, {17547, 46930}, {17548, 54391}, {17556, 27529}, {17564, 47357}, {17637, 41686}, {18391, 28466}, {18480, 31434}, {18481, 31397}, {18513, 62023}, {18514, 61970}, {18524, 37234}, {18527, 41864}, {18543, 34745}, {18907, 31402}, {18922, 31804}, {19247, 52352}, {19251, 30116}, {19313, 26241}, {19369, 55724}, {19524, 38901}, {19549, 21321}, {19705, 38314}, {19763, 57523}, {19843, 34607}, {19854, 34612}, {20818, 37504}, {20872, 39582}, {21153, 63972}, {21511, 29583}, {21514, 29596}, {22458, 49515}, {22758, 61244}, {24703, 59719}, {24850, 29670}, {25430, 61767}, {26029, 33309}, {26040, 50205}, {26060, 50207}, {26105, 52264}, {26590, 32954}, {28447, 51874}, {28448, 51873}, {28451, 50821}, {29585, 35276}, {30331, 64124}, {31410, 62155}, {31436, 37709}, {31447, 37723}, {31499, 44623}, {31799, 59345}, {31859, 32005}, {32153, 61292}, {32635, 55918}, {35272, 58679}, {35800, 42264}, {35801, 42263}, {36573, 63997}, {36740, 64070}, {36743, 62212}, {36750, 61397}, {37105, 62800}, {37289, 63965}, {37296, 56181}, {37499, 55100}, {37507, 64169}, {37509, 61398}, {37702, 54342}, {37706, 51515}, {37720, 55863}, {37722, 61811}, {37731, 61716}, {38723, 46683}, {39227, 58334}, {40262, 63992}, {40587, 63130}, {40998, 59587}, {41014, 63140}, {42115, 54436}, {42116, 54435}, {45410, 45471}, {45411, 45470}, {45701, 57288}, {48386, 58336}, {50587, 52139}, {52740, 53299}, {52783, 63287}, {54354, 60714}, {54992, 64053}, {59380, 60919}, {63266, 64156}, {63272, 64342}

X(64951) = midpoint of X(3601) and X(61763)
X(64951) = reflection of X(9654) in X(3085)
X(64951) = isogonal conjugate of X(43733)
X(64951) = cross-difference of every pair of points on the line X(650)X(28175)
X(64951) = crosspoint of X(59) and X(28196)
X(64951) = crosssum of X(i) and X(j) for these {i, j}: {11, 28195}, {1086, 49294}
X(64951) = X(643)-beth conjugate of-X(9780)
X(64951) = X(27789)-Ceva conjugate of-X(6)
X(64951) = X(4533)-reciprocal conjugate of-X(321)
X(64951) = X(28147)-zayin conjugate of-X(513)
X(64951) = perspector of the circumconic through X(651) and X(28176)
X(64951) = pole of the line {513, 47987} with respect to the circumcircle
X(64951) = pole of the line {20980, 58179} with respect to the Brocard inellipse
X(64951) = pole of the line {21, 11544} with respect to the Stammler hyperbola
X(64951) = pole of the line {314, 43733} with respect to the Steiner-Wallace hyperbola
X(64951) = barycentric product X(81)*X(4533)
X(64951) = trilinear product X(58)*X(4533)
X(64951) = trilinear quotient X(4533)/X(10)
X(64951) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 5217, 3), (35, 55, 3), (36, 63756, 3), (55, 5217, 1), (56, 5010, 3), (3428, 59331, 3), (3746, 59319, 1), (5204, 59325, 3), (8069, 37601, 3), (8273, 59326, 3), (10267, 26285, 3), (10269, 26086, 3), (10310, 10902, 3), (11248, 32613, 3), (11249, 33862, 3), (24929, 50193, 1), (37582, 63271, 1)

X(64952) = 88th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(7*a^3-5*(b+c)*a^2-(7*b^2-10*b*c+7*c^2)*a+5*(b^2-c^2)*(b-c)) : :
X(64952) = 5*X(1)+2*X(3) = 6*X(1)+X(40) = 3*X(1)+4*X(1385) = 9*X(1)-2*X(1482) = 4*X(1)+3*X(3576) = 8*X(1)-X(7982) = 11*X(1)-4*X(10222) = X(1)+6*X(10246) = 13*X(1)-6*X(10247) = X(1)-8*X(15178) = 3*X(1)+X(16192) = 10*X(1)-3*X(16200) = 15*X(1)-8*X(33179) = 3*X(1)-10*X(37624) = 12*X(3)-5*X(40) = 3*X(3)-10*X(1385) = 17*X(3)-10*X(3579) = 5*X(3)+2*X(11278) = 6*X(3)+X(11531) = 6*X(3)-5*X(16192)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/08/2024. (Aug 23, 2024)

X(64952) lies on these lines: {1, 3}, {2, 13607}, {4, 3636}, {8, 55864}, {9, 17438}, {10, 3533}, {30, 61277}, {104, 28192}, {140, 3632}, {145, 10165}, {191, 28463}, {214, 1706}, {355, 547}, {376, 51085}, {390, 64830}, {392, 19538}, {474, 64735}, {515, 3622}, {516, 62127}, {518, 55711}, {519, 15702}, {549, 50817}, {550, 61280}, {551, 944}, {581, 1149}, {631, 3244}, {632, 61292}, {946, 3543}, {952, 3624}, {962, 51705}, {1006, 62825}, {1064, 56804}, {1071, 10179}, {1125, 5067}, {1386, 5102}, {1483, 3679}, {1656, 37712}, {1698, 16239}, {1699, 3853}, {1702, 6437}, {1703, 6438}, {3083, 21552}, {3084, 21555}, {3090, 15808}, {3158, 22837}, {3241, 6684}, {3242, 55703}, {3243, 60912}, {3486, 37704}, {3523, 20057}, {3525, 3626}, {3526, 61289}, {3528, 28228}, {3582, 26487}, {3584, 26492}, {3616, 5056}, {3623, 11362}, {3628, 61244}, {3633, 26446}, {3635, 5657}, {3646, 17542}, {3652, 5426}, {3653, 5690}, {3654, 41983}, {3655, 3845}, {3656, 15686}, {3751, 39561}, {3828, 61868}, {3850, 5886}, {3851, 61271}, {3877, 12005}, {3889, 31806}, {3890, 5884}, {3897, 16858}, {3898, 64021}, {3899, 24475}, {4297, 10595}, {4301, 62113}, {4308, 64110}, {4313, 64703}, {4511, 63135}, {4512, 19539}, {4668, 11231}, {4677, 61847}, {4816, 38112}, {4861, 11525}, {4898, 59680}, {5054, 34747}, {5059, 5731}, {5071, 51082}, {5097, 16475}, {5288, 6883}, {5506, 37733}, {5603, 33703}, {5693, 58679}, {5734, 31730}, {5790, 32900}, {5844, 9588}, {5904, 31838}, {6264, 17535}, {6361, 62096}, {6431, 7968}, {6432, 7969}, {6433, 49226}, {6434, 49227}, {6480, 9615}, {6481, 35641}, {6484, 9616}, {6486, 35811}, {6487, 35810}, {6857, 64323}, {6940, 25439}, {7290, 7609}, {7701, 28461}, {7972, 38032}, {7988, 18525}, {7989, 28204}, {8583, 16854}, {9583, 44636}, {9589, 62123}, {9613, 15950}, {9617, 31439}, {9845, 51715}, {9864, 38746}, {9955, 61274}, {9956, 61887}, {10124, 50804}, {10175, 46934}, {10283, 11522}, {10303, 20050}, {10860, 62862}, {11230, 18526}, {11372, 42819}, {11523, 26878}, {11715, 64260}, {11735, 12407}, {11826, 15170}, {12245, 15719}, {12266, 55038}, {12368, 38792}, {12512, 62086}, {12571, 50868}, {12629, 56177}, {12645, 15723}, {12699, 61278}, {12751, 38758}, {12844, 55176}, {13178, 38735}, {13211, 38725}, {13532, 38782}, {15015, 64742}, {15570, 21153}, {15692, 51077}, {15694, 51087}, {15699, 61246}, {15701, 51094}, {15709, 34641}, {15715, 50814}, {15721, 50827}, {15839, 30117}, {16491, 37517}, {16496, 38029}, {16864, 64673}, {17536, 19861}, {18444, 63984}, {18480, 61946}, {18493, 61990}, {18991, 35762}, {18992, 35763}, {19862, 59388}, {19872, 41992}, {19883, 50818}, {20054, 61842}, {20070, 62081}, {21077, 34716}, {21151, 43179}, {21564, 56384}, {21569, 56427}, {21740, 38316}, {22791, 61279}, {22793, 34628}, {26726, 38760}, {28160, 62016}, {28174, 62106}, {28194, 62094}, {28198, 50820}, {28208, 61996}, {28224, 61268}, {28232, 50693}, {30264, 59372}, {30308, 61971}, {31425, 59417}, {31434, 37738}, {33858, 64740}, {34627, 51108}, {34631, 51107}, {34632, 62072}, {34648, 41150}, {34701, 49600}, {34718, 51097}, {34748, 51066}, {35018, 61257}, {35227, 54319}, {35401, 50806}, {37925, 51693}, {37940, 51701}, {38022, 61934}, {38024, 52682}, {38036, 43175}, {38074, 51109}, {38098, 61859}, {38176, 46219}, {38315, 55722}, {38335, 51709}, {38770, 50903}, {41722, 44878}, {45036, 54286}, {48661, 62140}, {48894, 48921}, {49176, 50843}, {49465, 55699}, {50796, 61927}, {50801, 61895}, {50812, 62089}, {50828, 61806}, {50830, 61839}, {50864, 61952}, {50865, 62158}, {51075, 62042}, {51080, 62161}, {51095, 61822}, {51104, 62077}, {51106, 62009}, {51781, 63915}, {54290, 62826}, {55582, 64084}, {56387, 57279}, {58609, 64107}, {59400, 61290}, {61245, 61890}, {61253, 61900}, {61259, 61917}, {61283, 61824}, {61294, 61875}, {63137, 64201}

X(64952) = midpoint of X(i) and X(j) for these (i, j): {1, 30389}, {3523, 20057}
X(64952) = reflection of X(i) in X(j) for these (i, j): (40, 16192), (3090, 15808), (9624, 3622), (10248, 946), (61256, 3090)
X(64952) = X(21)-beth conjugate of-X(64964)
X(64952) = pole of the line {21, 16200} with respect to the Stammler hyperbola
X(64952) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 1385, 40), (1, 21842, 57), (1, 30392, 3), (3, 11531, 40), (1385, 33179, 3), (1385, 37624, 1), (1482, 7987, 40), (2098, 64848, 1), (10246, 15178, 1), (11278, 31662, 3), (13384, 64849, 1)

X(64953) = 89th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(5*a^3-3*(b+c)*a^2-(5*b^2-6*b*c+5*c^2)*a+3*(b^2-c^2)*(b-c)) : :
X(64953) = 3*X(1)+2*X(3) = 4*X(1)+X(40) = 7*X(1)+3*X(165) = X(1)+4*X(1385) = 7*X(1)-2*X(1482) = 2*X(1)+3*X(3576) = 6*X(1)-X(7982) = 9*X(1)+X(7991) = 9*X(1)-4*X(10222) = X(1)-6*X(10246) = 11*X(1)-6*X(10247) = 13*X(1)-3*X(11224) = 11*X(1)-X(11531) = 3*X(1)-8*X(15178) = 3*X(1)-X(16189) = 8*X(1)-3*X(16200) = 3*X(1)+7*X(30389) = X(1)+9*X(30392) = 3*X(1)+4*X(31666) = 13*X(1)-8*X(33179)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/08/2024. (Aug 23, 2024)

X(64953) lies on these lines: {1, 3}, {2, 5881}, {4, 551}, {5, 3655}, {8, 10165}, {9, 2317}, {10, 3525}, {19, 22357}, {20, 13464}, {23, 51701}, {30, 11522}, {80, 38032}, {84, 2320}, {102, 47115}, {104, 5248}, {140, 3653}, {145, 6684}, {153, 26127}, {182, 16496}, {191, 12104}, {214, 5438}, {355, 3624}, {376, 4301}, {381, 51110}, {382, 34628}, {390, 64703}, {392, 5693}, {498, 37709}, {499, 5727}, {511, 16491}, {515, 3091}, {516, 10595}, {518, 53093}, {519, 631}, {546, 5691}, {547, 61258}, {549, 9588}, {550, 3656}, {572, 3247}, {575, 3751}, {576, 16475}, {581, 1201}, {601, 40091}, {632, 952}, {944, 1125}, {946, 3146}, {950, 37704}, {962, 26842}, {991, 35227}, {993, 15829}, {997, 51111}, {1001, 64197}, {1006, 8666}, {1071, 58679}, {1386, 11477}, {1387, 12119}, {1483, 3632}, {1572, 35007}, {1621, 5450}, {1656, 28204}, {1657, 50865}, {1699, 3627}, {1702, 6425}, {1703, 6426}, {1768, 19907}, {1829, 55578}, {2045, 36444}, {2046, 36462}, {2136, 22837}, {2650, 58392}, {2800, 3890}, {2975, 3951}, {3058, 31775}, {3083, 21553}, {3084, 21492}, {3085, 63987}, {3241, 3523}, {3242, 10541}, {3243, 52769}, {3244, 5657}, {3476, 13411}, {3485, 4311}, {3486, 44675}, {3487, 4315}, {3518, 7713}, {3522, 5734}, {3524, 31425}, {3526, 19875}, {3528, 5493}, {3529, 3636}, {3530, 3654}, {3533, 3828}, {3544, 15808}, {3545, 51108}, {3554, 37503}, {3582, 6863}, {3584, 6958}, {3586, 11376}, {3592, 7968}, {3594, 7969}, {3600, 64110}, {3617, 61848}, {3621, 38127}, {3623, 28234}, {3625, 58441}, {3626, 63915}, {3633, 5690}, {3634, 59388}, {3635, 10164}, {3640, 45551}, {3641, 45550}, {3646, 3897}, {3680, 6940}, {3720, 19647}, {3817, 61964}, {3843, 28208}, {3850, 38022}, {3855, 34648}, {3857, 61272}, {3869, 12005}, {3873, 31806}, {3877, 5884}, {3884, 64021}, {3915, 37469}, {3928, 6875}, {3984, 4511}, {4293, 64160}, {4305, 12053}, {4308, 21620}, {4309, 6948}, {4312, 38030}, {4313, 63993}, {4317, 4654}, {4355, 30264}, {4421, 33895}, {4652, 62826}, {4653, 64393}, {4666, 36002}, {4668, 61840}, {4669, 15702}, {4677, 5054}, {4745, 15709}, {4853, 5440}, {4855, 4861}, {4857, 6923}, {4870, 9657}, {4995, 31436}, {5007, 9575}, {5056, 50796}, {5067, 19883}, {5068, 50864}, {5070, 30315}, {5071, 51109}, {5072, 7988}, {5076, 18493}, {5079, 7989}, {5085, 49465}, {5198, 11363}, {5219, 45287}, {5223, 38031}, {5253, 6796}, {5258, 6883}, {5259, 22758}, {5270, 6928}, {5289, 31424}, {5290, 37737}, {5313, 37698}, {5315, 36742}, {5330, 35258}, {5426, 7701}, {5428, 16126}, {5432, 37738}, {5433, 37740}, {5434, 31789}, {5436, 6920}, {5437, 30147}, {5444, 37707}, {5453, 48883}, {5541, 64742}, {5550, 10175}, {5625, 39553}, {5687, 11525}, {5692, 31838}, {5730, 62824}, {5732, 42819}, {5735, 44238}, {5790, 55858}, {5794, 49176}, {5816, 62648}, {5818, 19862}, {5844, 61284}, {6173, 6934}, {6176, 21214}, {6261, 6912}, {6265, 7330}, {6361, 62092}, {6419, 18992}, {6420, 18991}, {6427, 19003}, {6428, 19004}, {6453, 9615}, {6454, 35774}, {6519, 9618}, {6713, 7972}, {6756, 34634}, {6762, 22836}, {6765, 11260}, {6825, 10072}, {6842, 37720}, {6878, 31458}, {6882, 37719}, {6889, 12625}, {6891, 10056}, {6897, 34701}, {6907, 37722}, {6915, 51683}, {6922, 15888}, {6936, 28609}, {6937, 24387}, {6946, 54318}, {6947, 34716}, {6949, 10199}, {6952, 10197}, {6961, 31452}, {6967, 45701}, {6978, 9578}, {6982, 10572}, {6984, 25525}, {6986, 62837}, {6987, 63274}, {6996, 29597}, {7091, 56027}, {7160, 63163}, {7162, 56036}, {7288, 64163}, {7308, 37700}, {7419, 54356}, {7483, 20418}, {7580, 64667}, {7772, 9619}, {7966, 17572}, {7984, 15020}, {7993, 22935}, {8129, 30411}, {8130, 30423}, {8550, 47358}, {8583, 16842}, {9538, 36984}, {9574, 31652}, {9579, 21578}, {9593, 22332}, {9612, 15950}, {9613, 11375}, {9616, 35642}, {9620, 53096}, {9623, 59691}, {9643, 37404}, {9708, 51577}, {9778, 62083}, {9780, 47745}, {9812, 49140}, {9856, 63432}, {9864, 20399}, {9897, 57298}, {9900, 20416}, {9901, 20415}, {9955, 61984}, {9956, 18526}, {10110, 64661}, {10129, 40259}, {10167, 45776}, {10179, 12672}, {10198, 10785}, {10200, 10786}, {10283, 12699}, {10299, 50810}, {10386, 24466}, {10444, 17394}, {10519, 49684}, {10573, 31231}, {10582, 12650}, {10860, 62856}, {10884, 58808}, {10888, 37869}, {10944, 31434}, {10990, 50878}, {10991, 50881}, {10992, 50886}, {10993, 50891}, {11001, 51106}, {11036, 63438}, {11191, 31791}, {11194, 54422}, {11231, 12645}, {11234, 31790}, {11240, 37112}, {11272, 22650}, {11372, 16132}, {11520, 37106}, {11539, 61297}, {11541, 51118}, {11682, 54290}, {11700, 38674}, {11709, 15054}, {11710, 38664}, {11711, 23235}, {11712, 38666}, {11713, 38667}, {11714, 38668}, {11716, 38670}, {11717, 38671}, {11718, 38672}, {11719, 38673}, {11720, 14094}, {11721, 38675}, {11722, 38676}, {11729, 64145}, {11826, 15172}, {12082, 51692}, {12102, 38034}, {12103, 22791}, {12114, 64260}, {12247, 33812}, {12265, 38689}, {12266, 15801}, {12407, 36253}, {12437, 34625}, {12512, 62084}, {12531, 38133}, {12577, 64004}, {12629, 56176}, {12653, 33814}, {12680, 61705}, {12735, 21154}, {12737, 15015}, {12751, 20400}, {12811, 61268}, {12812, 28224}, {12844, 55172}, {13178, 20398}, {13211, 20397}, {13253, 38602}, {13541, 38604}, {13747, 51112}, {14261, 47639}, {14872, 16860}, {14912, 49505}, {14986, 37797}, {15022, 46934}, {15069, 51003}, {15325, 37739}, {15682, 41150}, {15693, 31447}, {15694, 51066}, {15696, 28198}, {15698, 51107}, {15699, 61255}, {15707, 51094}, {15712, 50832}, {15719, 51091}, {15720, 34747}, {16113, 16137}, {16474, 36754}, {16483, 36746}, {16484, 37474}, {16486, 37501}, {16487, 62183}, {16625, 64662}, {16667, 64125}, {16673, 64121}, {16855, 35272}, {16862, 17614}, {16865, 31435}, {17170, 25723}, {17525, 41691}, {17527, 37725}, {17531, 19860}, {17543, 20117}, {18357, 61900}, {18483, 50688}, {19546, 26102}, {19708, 51104}, {19872, 38042}, {19876, 46219}, {19878, 38155}, {20049, 50827}, {20057, 59417}, {20070, 62078}, {20401, 50903}, {21151, 30331}, {21153, 42871}, {21165, 62822}, {21401, 51688}, {21402, 51690}, {21554, 48854}, {21565, 56384}, {21568, 56427}, {21734, 34632}, {21735, 50808}, {21740, 63430}, {22713, 61132}, {22793, 49136}, {23073, 40937}, {23155, 31825}, {24914, 37734}, {25440, 45036}, {25485, 38693}, {26066, 64283}, {26201, 40266}, {26487, 37711}, {26492, 37708}, {28146, 62143}, {28150, 62152}, {28164, 62028}, {28168, 62035}, {28174, 62104}, {28186, 61988}, {28202, 62131}, {28232, 58195}, {29580, 37416}, {29817, 35986}, {29826, 39572}, {30332, 64830}, {30714, 50921}, {31145, 38068}, {31673, 50689}, {31730, 62097}, {31870, 64149}, {33337, 64278}, {33520, 50898}, {33521, 50905}, {33538, 35193}, {33697, 62004}, {34474, 64137}, {34607, 64767}, {34631, 61138}, {34638, 62113}, {34641, 61836}, {34712, 34938}, {34718, 61811}, {34748, 55863}, {34772, 61122}, {34791, 64107}, {35479, 41722}, {35514, 43179}, {36846, 64199}, {36922, 64323}, {37438, 37726}, {37519, 54424}, {37699, 49997}, {37705, 55861}, {37710, 38033}, {37724, 52265}, {37733, 41229}, {37934, 47593}, {37946, 51693}, {38036, 43161}, {38053, 43175}, {38066, 51087}, {38074, 51082}, {38076, 61921}, {38083, 55860}, {38112, 61292}, {38140, 61935}, {38220, 38734}, {38315, 53097}, {38757, 64191}, {38760, 64056}, {40107, 50950}, {40273, 62044}, {40658, 58795}, {41705, 52653}, {41863, 54391}, {41989, 61266}, {41992, 61245}, {43177, 47357}, {44245, 61279}, {44811, 48337}, {46822, 62218}, {47495, 62344}, {48154, 61248}, {48661, 62134}, {48893, 52524}, {48894, 48897}, {49469, 64728}, {49532, 51046}, {50528, 64679}, {50799, 61940}, {50805, 61803}, {50806, 62023}, {50815, 62127}, {50819, 62147}, {50823, 61824}, {50829, 61817}, {50833, 61813}, {50871, 55856}, {50872, 62067}, {51068, 61846}, {51069, 61859}, {51072, 61844}, {51075, 62171}, {51077, 61791}, {51084, 61815}, {51092, 61812}, {51095, 61809}, {51096, 61822}, {51120, 62096}, {51713, 62288}, {51714, 64675}, {51715, 63992}, {53620, 55864}, {55873, 62874}, {59503, 61831}, {61254, 61892}, {61264, 61923}, {61271, 61955}, {61280, 62091}, {61281, 61802}, {61283, 61524}, {61290, 61837}, {61295, 61852}, {61510, 61858}, {61597, 61801}, {62870, 64150}, {64085, 64196}

X(64953) = midpoint of X(i) and X(j) for these (i, j): {1, 7987}, {3522, 5734}, {5882, 31399}, {16189, 63469}
X(64953) = reflection of X(i) in X(j) for these (i, j): (1, 37624), (3, 31666), (40, 35242), (5071, 51109), (5818, 19862), (7982, 16189), (8227, 3616), (11522, 61276), (18492, 8227), (35242, 7987), (37714, 1656), (51066, 15694), (61250, 5818), (63469, 3)
X(64953) = anticomplement of X(31399)
X(64953) = isogonal conjugate of the Cundy-Parry-Psi-transform of X(64964)
X(64953) = Cundy-Parry-Phi-transform of X(64964)
X(64953) = X(21)-beth conjugate of-X(3340)
X(64953) = X(31399)-Dao conjugate of-X(31399)
X(64953) = inverse of X(40) in Hung circle
X(64953) = pole of the line {672, 63214} with respect to the Gheorghe circle
X(64953) = pole of the line {40, 513} with respect to the Hung circle
X(64953) = pole of the line {910, 63214} with respect to the Stevanovic circle
X(64953) = pole of the line {21, 7982} with respect to the Stammler hyperbola
X(64953) = (2nd circumperp)-isogonal conjugate-of-X(63754)
X(64953) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 3576, 40), (1, 30389, 3), (3, 7982, 40), (3, 15178, 1), (1319, 34471, 1), (1385, 10246, 1), (1385, 15178, 3), (1388, 2646, 1), (1697, 59333, 40), (1697, 64849, 1), (3295, 25405, 1), (3340, 59331, 40), (3576, 7982, 3), (7962, 59332, 40), (7987, 63469, 3)

X(64954) = 90th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(11*a^3-5*(b+c)*a^2-(11*b^2-10*b*c+11*c^2)*a+5*(b^2-c^2)*(b-c)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 07/08/2024. (Aug 23, 2024)

X(64954) lies on these lines: {1, 3}, {2, 61256}, {4, 15808}, {8, 15708}, {10, 15702}, {20, 61275}, {104, 28156}, {140, 61244}, {145, 61806}, {355, 16239}, {376, 3636}, {392, 19539}, {515, 5056}, {516, 62113}, {518, 55699}, {519, 15719}, {547, 3624}, {548, 61277}, {549, 3632}, {551, 11001}, {572, 16676}, {631, 3626}, {632, 61253}, {944, 3533}, {946, 5059}, {952, 61837}, {962, 62102}, {1125, 3545}, {1386, 55582}, {1483, 9588}, {1571, 15602}, {1698, 3655}, {1699, 62036}, {1702, 6429}, {1703, 6430}, {3241, 61796}, {3244, 3524}, {3523, 13607}, {3525, 28236}, {3526, 37712}, {3530, 61287}, {3543, 3616}, {3617, 5882}, {3621, 6684}, {3622, 31162}, {3625, 7967}, {3633, 41983}, {3646, 16859}, {3647, 15829}, {3656, 62098}, {3679, 11812}, {3751, 50664}, {3832, 5731}, {3843, 61271}, {3845, 18481}, {3850, 5691}, {3853, 5886}, {3897, 17535}, {4297, 9624}, {4305, 37704}, {4663, 55711}, {4677, 32900}, {4678, 38068}, {4691, 50818}, {4816, 37727}, {5008, 9575}, {5067, 5587}, {5097, 38029}, {5438, 51111}, {5603, 62127}, {5657, 61288}, {5690, 61813}, {5881, 9780}, {5901, 62155}, {6361, 50812}, {6431, 9583}, {6433, 44636}, {6434, 44635}, {6437, 7968}, {6438, 7969}, {6484, 35775}, {6485, 35774}, {6486, 9616}, {7713, 47485}, {7988, 61946}, {7989, 61911}, {8583, 17542}, {9589, 10283}, {9615, 35762}, {9955, 34628}, {9956, 61875}, {10303, 47745}, {10308, 16132}, {10595, 62096}, {11230, 61937}, {11522, 51700}, {11684, 56387}, {12245, 31425}, {12699, 15686}, {13464, 62110}, {15690, 22791}, {15692, 20057}, {15693, 34747}, {15705, 51077}, {15707, 51087}, {15709, 51082}, {15717, 28234}, {15723, 28204}, {16475, 37517}, {16491, 55594}, {16496, 55691}, {16854, 17614}, {16858, 19861}, {18357, 54447}, {18480, 61920}, {18493, 51110}, {18519, 25542}, {18525, 34595}, {18526, 19875}, {19711, 51093}, {19860, 36006}, {19876, 61862}, {19878, 61884}, {19883, 61913}, {20054, 50827}, {21735, 28228}, {22793, 61274}, {26446, 61295}, {28160, 61990}, {28186, 41991}, {28194, 62081}, {28208, 61950}, {28232, 62097}, {28463, 33858}, {30308, 33697}, {31253, 38074}, {31445, 51577}, {31730, 38314}, {34627, 51073}, {34641, 61822}, {34716, 59719}, {34748, 51084}, {37714, 61878}, {37944, 51701}, {38022, 61999}, {38098, 61833}, {38127, 61820}, {38176, 55863}, {38315, 55607}, {38316, 43178}, {38758, 64191}, {44682, 61281}, {46333, 51075}, {46853, 61280}, {48154, 61257}, {50528, 64260}, {50796, 61897}, {50801, 61861}, {50804, 61827}, {50814, 61780}, {50819, 51119}, {50865, 62140}, {51080, 62017}, {51094, 61797}, {51103, 62077}, {51108, 62009}, {51109, 61961}, {51709, 62158}, {55591, 64084}, {55703, 64070}, {58808, 62829}, {61246, 61853}, {61276, 62123}, {61289, 61811}

X(64954) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 16200, 40), (1385, 31662, 3), (1482, 58223, 165), (3579, 10246, 1), (7987, 63468, 3), (8148, 15178, 1), (11278, 13624, 3), (24926, 37524, 1), (32636, 34471, 1)

X(64955) = 91st TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(a^4+2*b*a^3+(2*b^2+b*c-2*c^2)*a^2-b*(2*b+c)*(b-c)*a-(b^2-c^2)*(3*b^2+2*b*c+c^2))*(a^4+2*c*a^3-(2*b^2-b*c-2*c^2)*a^2+(b+2*c)*(b-c)*c*a+(b^2-c^2)*(b^2+2*b*c+3*c^2)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 09/08/2024. (Aug 23, 2024)

X(64955) lies on the cubics K680, K1056 and these lines: {35, 33669}, {42, 8614}, {55, 501}, {191, 210}, {1030, 1334}, {33670, 59140}

X(64955) = isogonal conjugate of X(3648)
X(64955) = crosssum of X(191) and X(63267)
X(64955) = X(6186)-cross conjugate of-X(6)
X(64955) = X(32664)-Dao conjugate of-X(16553)
X(64955) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 16553}, {1125, 33670}
X(64955) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (31, 16553), (28615, 33670)
X(64955) = X(35)-vertex conjugate of-X(35)
X(64955) = barycentric product X(19620)*X(57419)
X(64955) = trilinear quotient X(i)/X(j) for these (i, j): (6, 16553), (1126, 33670), (19620, 3578)

X(64956) = 92nd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(9*a^4+12*b*a^3+2*(9*b^2+2*b*c-9*c^2)*a^2-4*(3*b+c)*(b-c)*b*a-3*(b^2-c^2)*(9*b^2+4*b*c+3*c^2))*(9*a^4+12*c*a^3-2*(9*b^2-2*b*c-9*c^2)*a^2+4*(b+3*c)*(b-c)*c*a+3*(b^2-c^2)*(3*b^2+4*b*c+9*c^2)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 09/08/2024. (Aug 23, 2024)

X(64956) lies on these lines: {62218, 63469}

X(64956) = isogonal conjugate of the anticomplement of X(5556)
X(64956) = X(5217)-vertex conjugate of-X(5217)

X(64957) = 93rd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b+c)*(a^6+(b+c)*a^5-(b^2-b*c+c^2)*a^4-2*(b+c)*b^2*a^3-(b^4+2*b^3*c-c^4)*a^2+(b^4-c^4)*(b+c)*a+(b+c)*(b^2-c^2)*(b^3+c^3))*(a^6+(b+c)*a^5-(b^2-b*c+c^2)*a^4-2*(b+c)*c^2*a^3+(b^4-2*b*c^3-c^4)*a^2-(b^4-c^4)*(b+c)*a-(b+c)*(b^2-c^2)*(b^3+c^3)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/08/2024 (bottom). (Aug 24, 2024)

X(64957) lies on these lines: {10, 56295}, {1330, 56288}, {21076, 46676}

X(64957) = cevapoint of X(4064) and X(21710)
X(64957) = X(3)-cross conjugate of-X(10)
X(64957) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 1710), (40591, 56295)
X(64957) = X(i)-isoconjugate of-X(j) for these {i, j}: {28, 56295}, {58, 1710}
X(64957) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (37, 1710), (71, 56295)
X(64957) = trilinear quotient X(i)/X(j) for these (i, j): (10, 1710), (72, 56295)

X(64958) = 94th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b+c)*(a^6+(b+c)*a^5-(b^2-b*c-c^2)*a^4-2*(b+c)*(b^2-c^2)*a^3-(b^2-c^2)*(b^2+2*b*c-c^2)*a^2+(b^2-c^2)*(b+c)*(b^2+3*c^2)*a+(b^2-c^2)*(b+c)*(b^3+2*b*c^2+c^3))*(a^6+(b+c)*a^5+(b^2+b*c-c^2)*a^4+2*(b+c)*(b^2-c^2)*a^3-(b^2-c^2)*(b^2-2*b*c-c^2)*a^2-(b^2-c^2)*(b+c)*(3*b^2+c^2)*a+(b^2-c^2)*(b+c)*(-b^3-2*b^2*c-c^3)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/08/2024 (bottom). (Aug 24, 2024)

X(64958) lies on these lines: {10, 56300}, {306, 1330}, {3695, 21076}

X(64958) = X(i)-cross conjugate of-X(j) for these (i, j): (4, 10), (64959, 63885)
X(64958) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 2939), (37, 3151), (1214, 18631)
X(64958) = X(i)-isoconjugate of-X(j) for these {i, j}: {58, 2939}, {1333, 3151}, {1437, 56301}, {2194, 18631}
X(64958) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (10, 3151), (37, 2939), (226, 18631), (1826, 56301), (34440, 58)
X(64958) = barycentric product X(313)*X(34440)
X(64958) = trilinear product X(321)*X(34440)
X(64958) = trilinear quotient X(i)/X(j) for these (i, j): (10, 2939), (321, 3151), (1441, 18631), (34440, 1333), (41013, 56301)

X(64959) = 95th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b+c)*(a^4+(b+c)*a^3+b*c*a^2+(b+c)*(b^2-c^2)*a+(b+c)*(b^3-c^3))*(a^4+(b+c)*a^3+b*c*a^2-(b+c)*(b^2-c^2)*a-(b+c)*(b^3-c^3)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/08/2024 (bottom). (Aug 24, 2024)

X(64959) lies on these lines: {2, 15377}, {10, 199}, {27, 21046}, {42, 4213}, {71, 1654}, {306, 21587}, {2197, 16577}, {2359, 38822}, {3678, 3690}, {3949, 3969}, {6186, 15168}, {7560, 23899}, {21076, 28654}, {21092, 22000}

X(64959) = isogonal conjugate of X(40589)
X(64959) = cevapoint of X(i) and X(j) for these {i, j}: {6, 3437}, {523, 21046}, {661, 21054}, {3930, 20656}, {4024, 21710}, {4079, 21709}
X(64959) = crosspoint of X(63885) and X(64958)
X(64959) = X(6)-cross conjugate of-X(10)
X(64959) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 1761), (37, 1330), (115, 21187), (4075, 21076), (39026, 57062), (40586, 199), (40591, 22133), (40603, 20929)
X(64959) = X(i)-isoconjugate of-X(j) for these {i, j}: {28, 22133}, {58, 1761}, {81, 199}, {163, 21187}, {513, 57062}, {849, 21076}, {1330, 1333}, {2206, 20929}
X(64959) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (10, 1330), (37, 1761), (42, 199), (71, 22133), (101, 57062), (321, 20929), (523, 21187), (594, 21076), (3437, 58), (8044, 86), (40142, 593), (57778, 310)
X(64959) = trilinear pole of the line {23282, 53424} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(64959) = 1st Saragossa point of X(199)
X(64959) = barycentric product X(i)*X(j) for these {i, j}: {10, 8044}, {42, 57778}, {313, 3437}, {28654, 40142}
X(64959) = trilinear product X(i)*X(j) for these {i, j}: {37, 8044}, {213, 57778}, {321, 3437}, {1089, 40142}
X(64959) = trilinear quotient X(i)/X(j) for these (i, j): (10, 1761), (37, 199), (72, 22133), (100, 57062), (313, 20929), (321, 1330), (1089, 21076), (1577, 21187), (3437, 1333), (8044, 81), (40142, 849), (57778, 274)

X(64960) = 96th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b+c)*((b+c)*a^7+(3*b^2+2*b*c+3*c^2)*a^6+3*(b+c)*(b^2+c^2)*a^5+(b^4+c^4+2*(2*b^2-b*c+2*c^2)*b*c)*a^4-(b^3+c^3)*(b^2-3*b*c+c^2)*a^3-(b^3-c^3)*(b-c)*(3*b^2+7*b*c+3*c^2)*a^2-(b^2-c^2)*(b-c)*(3*b^4+3*c^4+2*(5*b^2+6*b*c+5*c^2)*b*c)*a-(b^4-c^4)*(b^2-c^2)*(b+c)^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/08/2024 (bottom). (Aug 24, 2024)

X(64960) lies on these lines: {10, 30447}, {12, 47057}

X(64961) = 97th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b+c)*((b+c)*a^5+(3*b^2+2*b*c+3*c^2)*a^4+(b+c)*(b^2+4*b*c+c^2)*a^3-(b^4+c^4-2*(2*b^2+b*c+2*c^2)*b*c)*a^2-(b+c)*(3*b^4-7*b^2*c^2+3*c^4)*a-(b^3-c^3)*(b-c)*(b^2+3*b*c+c^2)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 11/08/2024 (bottom). (Aug 25, 2024)

X(64961) lies on these lines: {10, 14873}, {12, 664}

X(64962) = 98th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b^2-c^2)^2*(a^3-2*(b+c)*a^2-(b^2+b*c+c^2)*a-b*c*(b+c)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 15/08/2024 (bottom). (Aug 25, 2024)

X(64962) lies on these lines: {10, 53332}, {115, 4705}, {3120, 21725}, {21043, 21961}, {21709, 21710}, {40608, 50487}

X(64962) = X(2051)-Ceva conjugate of-X(4079)
X(64962) = X(2533)-Dao conjugate of-X(17103)
X(64962) = X(25667)-reciprocal conjugate of-X(4623)
X(64962) = barycentric product X(4705)*X(25667)
X(64962) = trilinear product X(4079)*X(25667)
X(64962) = trilinear quotient X(25667)/X(4610)

X(64963) = 99th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a+b-c)*(a-b+c)*(a-4*b-4*c) : :
X(64963) = 4*X(1)-3*X(3303)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 16/08/2024. (Aug 25, 2024)

X(64963) lies on these lines: {1, 3}, {4, 16615}, {7, 10944}, {8, 3649}, {12, 3617}, {45, 2171}, {78, 10107}, {79, 18525}, {108, 28167}, {145, 5434}, {153, 5229}, {198, 62210}, {226, 3626}, {355, 9656}, {377, 5855}, {388, 3621}, {474, 3919}, {516, 37724}, {519, 10404}, {553, 3244}, {936, 3922}, {944, 11246}, {946, 61717}, {952, 9657}, {956, 4084}, {958, 11684}, {959, 40434}, {962, 9670}, {997, 4004}, {1317, 3600}, {1358, 62794}, {1376, 62830}, {1389, 12114}, {1400, 16672}, {1411, 4332}, {1468, 18360}, {1469, 9049}, {1478, 11544}, {1483, 4317}, {1698, 4870}, {1737, 61268}, {1770, 37739}, {1788, 4323}, {1836, 31673}, {1837, 18483}, {1887, 54446}, {2285, 16666}, {2334, 2650}, {3296, 34631}, {3475, 45081}, {3476, 52783}, {3485, 9780}, {3556, 56924}, {3577, 12688}, {3614, 6874}, {3622, 5298}, {3625, 3671}, {3632, 4654}, {3634, 4848}, {3647, 30147}, {3654, 63259}, {3754, 4413}, {3812, 11682}, {3869, 27065}, {3873, 10912}, {3878, 4423}, {3880, 11520}, {3885, 42871}, {3893, 41863}, {3899, 11108}, {3911, 15808}, {3913, 34195}, {3962, 9623}, {4292, 37740}, {4293, 37734}, {4295, 10950}, {4298, 37738}, {4299, 37728}, {4309, 28212}, {4338, 28160}, {4420, 12635}, {4430, 64201}, {4744, 8666}, {4816, 5290}, {4867, 9709}, {4955, 9312}, {5220, 7672}, {5247, 53115}, {5270, 12645}, {5302, 19860}, {5433, 46934}, {5554, 31141}, {5560, 14269}, {5586, 51093}, {5687, 62822}, {5692, 51572}, {5904, 40587}, {6147, 12647}, {6361, 10543}, {6738, 12701}, {7201, 49503}, {7319, 55924}, {9578, 36920}, {9612, 61256}, {9624, 61649}, {9654, 41684}, {9655, 11552}, {9671, 37702}, {10056, 16137}, {10573, 10895}, {10592, 64127}, {10624, 14563}, {10894, 12247}, {10896, 18391}, {10914, 12559}, {11238, 22791}, {11362, 17718}, {11553, 30116}, {12019, 38141}, {12047, 61261}, {12245, 15888}, {12560, 60909}, {12672, 61663}, {12953, 37730}, {13464, 17728}, {15254, 41712}, {15570, 60938}, {16236, 37709}, {17018, 63295}, {17097, 56203}, {17098, 31937}, {18761, 48668}, {18990, 61295}, {19037, 38235}, {19862, 24914}, {20070, 63273}, {21863, 54322}, {22759, 62235}, {22793, 37721}, {24297, 43733}, {24470, 61292}, {24982, 34647}, {25524, 62826}, {30332, 60883}, {31140, 49168}, {31145, 32634}, {31165, 64673}, {33895, 62832}, {34501, 45085}, {37106, 63272}, {37719, 59503}, {38513, 61696}, {39793, 50575}, {41436, 46190}, {57282, 61244}

X(64963) = isogonal conjugate of the Cundy-Parry-Psi-transform of X(13624)
X(64963) = Cundy-Parry-Phi-transform of X(13624)
X(64963) = isogonal conjugate of the Cundy-Parry-Phi-transform of X(16615)
X(64963) = Cundy-Parry-Psi-transform of X(16615)
X(64963) = X(1)-beth conjugate of-X(3339)
X(64963) = X(522)-isoconjugate of-X(28166)
X(64963) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1415, 28166), (16675, 8), (28165, 4391), (58165, 650), (64425, 314)
X(64963) = pole of the line {513, 30726} with respect to the incircle
X(64963) = pole of the line {513, 30726} with respect to the de Longchamps ellipse
X(64963) = pole of the line {1, 16616} with respect to the Feuerbach circumhyperbola
X(64963) = pole of the line {17496, 30724} with respect to the Steiner circumellipse
X(64963) = barycentric product X(i)*X(j) for these {i, j}: {7, 16675}, {65, 64425}, {651, 28165}, {4554, 58165}
X(64963) = trilinear product X(i)*X(j) for these {i, j}: {57, 16675}, {109, 28165}, {664, 58165}, {1400, 64425}
X(64963) = trilinear quotient X(i)/X(j) for these (i, j): (109, 28166), (16675, 9), (28165, 522), (58165, 663), (64425, 333)
X(64963) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 5221, 56), (1, 12702, 55), (57, 1388, 56), (65, 2099, 56), (65, 11011, 57), (942, 11278, 1), (1466, 18967, 56), (2099, 5221, 1), (3340, 18421, 65), (13624, 50194, 1)

X(64964) = 100th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(a+b-c)*(a-b+c)*(3*a-5*b-5*c) : :
X(64964) = 3*X(1)-X(61763)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 16/08/2024. (Aug 25, 2024)

X(64964) lies on these lines: {1, 3}, {2, 46872}, {7, 3623}, {8, 5219}, {9, 11526}, {10, 64736}, {12, 3632}, {34, 41434}, {84, 14497}, {145, 226}, {244, 15839}, {388, 3244}, {498, 63143}, {499, 61275}, {519, 3485}, {551, 1788}, {553, 4308}, {936, 4002}, {944, 9579}, {946, 5727}, {952, 9612}, {997, 3918}, {1191, 52423}, {1210, 10595}, {1317, 10404}, {1320, 5665}, {1389, 3577}, {1392, 7091}, {1405, 16676}, {1419, 7201}, {1421, 54418}, {1449, 2171}, {1450, 56804}, {1451, 40091}, {1478, 61296}, {1483, 57282}, {1616, 52424}, {1698, 15950}, {1699, 10950}, {1706, 4511}, {1737, 9624}, {1770, 50811}, {1836, 37734}, {1837, 11522}, {2003, 34040}, {2136, 4917}, {2263, 33633}, {3085, 28234}, {3158, 14923}, {3241, 4654}, {3243, 16133}, {3476, 3635}, {3486, 4301}, {3583, 18962}, {3584, 50817}, {3586, 22791}, {3600, 20057}, {3616, 4848}, {3621, 5226}, {3622, 3911}, {3624, 40663}, {3626, 10588}, {3633, 5252}, {3636, 7288}, {3649, 37738}, {3656, 9614}, {3679, 11375}, {3680, 3870}, {3697, 5730}, {3869, 3929}, {3872, 11523}, {3877, 5436}, {3890, 7672}, {3894, 45288}, {3898, 12432}, {3915, 55101}, {3928, 64047}, {4067, 57279}, {4292, 7967}, {4293, 13607}, {4295, 5882}, {4298, 51071}, {4305, 28194}, {4321, 15570}, {4327, 15600}, {4328, 4864}, {4338, 36975}, {4420, 51781}, {4662, 63916}, {4673, 6358}, {4677, 4870}, {4816, 39777}, {4853, 12635}, {4861, 6762}, {4930, 34790}, {5083, 62854}, {5229, 28236}, {5234, 31165}, {5261, 20050}, {5289, 64673}, {5290, 10944}, {5330, 54392}, {5434, 34719}, {5438, 56387}, {5443, 54447}, {5554, 30827}, {5603, 9581}, {5691, 37740}, {5726, 39782}, {5734, 12053}, {5795, 31142}, {5836, 46917}, {5844, 11374}, {5881, 12047}, {6049, 21454}, {6147, 61597}, {6692, 24558}, {7274, 19604}, {7308, 15829}, {7951, 64766}, {8000, 10698}, {8227, 10573}, {8236, 52819}, {8275, 45081}, {9613, 37727}, {9657, 61289}, {9848, 18979}, {10107, 64112}, {10572, 31162}, {10590, 47745}, {10826, 38021}, {10895, 37712}, {10956, 26726}, {11237, 34747}, {11260, 62823}, {11519, 41711}, {11520, 38460}, {11545, 61268}, {12245, 13411}, {12559, 22837}, {12560, 42871}, {12640, 63168}, {12653, 12739}, {12699, 37728}, {12709, 34791}, {12854, 45120}, {13253, 64372}, {13464, 18391}, {14563, 64703}, {15325, 61277}, {15888, 64127}, {16474, 64020}, {16616, 63992}, {16785, 56913}, {17090, 40719}, {17098, 21398}, {17474, 56546}, {17605, 37714}, {17606, 30286}, {17625, 58609}, {18393, 18492}, {18412, 64042}, {18990, 61287}, {19784, 56469}, {19836, 56467}, {20013, 21617}, {20076, 60933}, {22836, 63137}, {24392, 41575}, {24467, 61148}, {24470, 61283}, {24914, 25055}, {26742, 52541}, {30147, 31435}, {30305, 41864}, {30318, 60953}, {30332, 61021}, {31434, 37737}, {32098, 63578}, {35258, 51683}, {36845, 64205}, {37692, 41684}, {41539, 58679}, {41863, 62822}, {44635, 51841}, {44636, 51842}, {44663, 62824}, {45287, 61291}, {47057, 63333}, {50444, 61717}, {50575, 56198}, {51646, 53411}, {58816, 63574}, {59414, 60943}, {59584, 63133}, {61294, 61716}

X(64964) = midpoint of X(145) and X(5175)
X(64964) = reflection of X(i) in X(j) for these (i, j): (3601, 1), (9578, 3485)
X(64964) = isogonal conjugate of the Cundy-Parry-Psi-transform of X(64953)
X(64964) = Cundy-Parry-Phi-transform of X(64953)
X(64964) = crosssum of X(1) and X(30389)
X(64964) = X(4678)-beth conjugate of-X(4678)
X(64964) = X(522)-isoconjugate of-X(28192)
X(64964) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1415, 28192), (4678, 312), (58161, 650)
X(64964) = pole of the line {226, 4902} with respect to the circumhyperbola dual of Yff parabola
X(64964) = pole of the line {1, 40262} with respect to the Feuerbach circumhyperbola
X(64964) = pole of the line {905, 62575} with respect to the Steiner inellipse
X(64964) = barycentric product X(i)*X(j) for these {i, j}: {57, 4678}, {4554, 58161}
X(64964) = trilinear product X(i)*X(j) for these {i, j}: {56, 4678}, {664, 58161}
X(64964) = trilinear quotient X(i)/X(j) for these (i, j): (109, 28192), (4678, 8), (58161, 663)
X(64964) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 3340, 57), (1, 11531, 55), (1, 18421, 56), (1, 25415, 40), (65, 1420, 57), (942, 10247, 1), (999, 33179, 1), (1482, 50194, 1), (2099, 11011, 1), (3304, 33176, 1), (5173, 10389, 57)

X(64965) = MIDPOINT OF X(2492) AND X(5099)

Barycentrics    (b^2 - c^2)*(-a^4 + b^4 - b^2*c^2 + c^4)*(-a^12 + 2*a^10*b^2 - 3*a^8*b^4 + 4*a^4*b^8 - 2*a^2*b^10 + 2*a^10*c^2 + 2*a^6*b^4*c^2 - 6*a^4*b^6*c^2 + b^10*c^2 - 3*a^8*c^4 + 2*a^6*b^2*c^4 + 3*a^4*b^4*c^4 + 2*a^2*b^6*c^4 - 6*a^4*b^2*c^6 + 2*a^2*b^4*c^6 - 2*b^6*c^6 + 4*a^4*c^8 - 2*a^2*c^10 + b^2*c^10) : :

X(64965) lies on the cubic K869 and these lines: {468, 20403}, {523, 43291}, {804, 14120}, {2492, 5099}, {11176, 36168}, {16760, 62506}

X(64965) = midpoint of X(2492) and X(5099)

X(64966) = MIDPOINT OF X(230) AND X(5099)

Barycentrics    2*a^10 - 3*a^8*b^2 + 4*a^6*b^4 - 6*a^2*b^8 + 3*b^10 - 3*a^8*c^2 - 2*a^6*b^2*c^2 - a^4*b^4*c^2 + 17*a^2*b^6*c^2 - 7*b^8*c^2 + 4*a^6*c^4 - a^4*b^2*c^4 - 22*a^2*b^4*c^4 + 4*b^6*c^4 + 17*a^2*b^2*c^6 + 4*b^4*c^6 - 6*a^2*c^8 - 7*b^2*c^8 + 3*c^10 : :
X(64966) = 9 X[2] - X[57616], X[23] + 3 X[33228], 3 X[403] + X[36166], 3 X[468] - X[36180], X[7464] - 5 X[40336], X[8352] + 3 X[37907], X[11676] - 9 X[37943], 3 X[14041] + 5 X[37760], 3 X[14120] + X[36180], 3 X[35297] + X[36174], X[37459] - 3 X[44282], X[187] - 3 X[47243], X[842] + 3 X[39663], X[2682] + 3 X[61691], 3 X[47246] - X[47326], 3 X[47246] + X[53419], 3 X[47450] + X[53505], 5 X[47453] - X[53499]

X(64966) lies on these lines: {2, 3}, {115, 16320}, {187, 47243}, {230, 5099}, {523, 43291}, {597, 15539}, {842, 39663}, {1499, 47296}, {2453, 43620}, {2682, 61691}, {3564, 47550}, {5461, 62508}, {13881, 47284}, {15269, 34169}, {16316, 51258}, {16509, 50146}, {40544, 44381}, {46986, 52229}, {46998, 63945}, {46999, 47570}, {47246, 47326}, {47450, 53505}, {47453, 53499}, {47559, 47574}, {51733, 61755}

X(64966) = midpoint of X(i) and X(j) for these {i,j}: {115, 16320}, {230, 5099}, {468, 14120}, {7426, 37350}, {11799, 56370}, {16316, 51258}, {27088, 36196}, {46999, 47570}, {47326, 53419}, {47559, 47574}
X(64966) = reflection of X(40544) in X(44381)
X(64966) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 10151, 46619}, {468, 47097, 47349}, {47246, 53419, 47326}

X(64967) = X(2)X(2006)∩X(6)X(24159)

Barycentrics    b*c*(-(a^2*b^2) + b^4 + a^2*b*c - a^2*c^2 - 2*b^2*c^2 + c^4) : :
Barycentrics    (b c)(-(b^2 - c^2)^2 + a^2 (b^2 - b c + c^2) : :
Barycentrics    cos((3/2)(B-C)/cos((1/2)(B-C)) : :

X(64967) lies on these lines: {2, 2006}, {6, 24149}, {7, 2994}, {75, 3219}, {92, 3218}, {149, 17860}, {312, 20887}, {321, 5233}, {614, 17890}, {982, 1109}, {1029, 52442}, {1441, 27186}, {1479, 52344}, {1733, 17127}, {1993, 24148}, {2345, 56465}, {2475, 20320}, {3210, 62305}, {3262, 32858}, {3616, 23555}, {3782, 4957}, {3928, 14212}, {3995, 40564}, {4000, 56461}, {4671, 20237}, {5012, 24332}, {5271, 55872}, {5361, 20882}, {6757, 18398}, {7191, 17871}, {7741, 63804}, {14616, 40214}, {16732, 33146}, {17024, 17884}, {17118, 55438}, {17119, 55466}, {17861, 33150}, {17862, 31019}, {17874, 29814}, {19721, 28606}, {20223, 55873}, {20236, 28605}, {20883, 56448}, {23690, 33131}, {24209, 26723}, {24430, 60804}, {27003, 54284}, {31053, 48380}

X(64967) = barycentric product X(i)*X(j) for these {i,j}: {75, 7741}, {86, 63804}, {333, 63809}, {14616, 63803} X(64967) = barycentric quotient X(i)/X(j) for these {i,j}: {7741, 1}, {9219, 7951}, {63803, 758}, {63804, 10}, {63809, 226}
X(64967) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 24145, 20268}, {75, 20919, 32933}, {4858, 14213, 2}

X(64968) = X(94)X(20268)∩X(5392)X(24148)

Barycentrics    b^2*c^2*(a^4*b^4 - 2*a^2*b^6 + b^8 - a^4*b^3*c + a^2*b^5*c + a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 - a^4*b*c^3 - 2*a^2*b^3*c^3 + a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 + a^2*b*c^5 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :
Barycentrics    (b c)^2((b^2 - c^2)^4 - a^2 (b^2 - c^2)^2 (2 b^2 - b c + 2 c^2) + a^4 (b^4 - b^3 c + b^2 c^2 - b c^3 + c^4)) : :
Barycentrics    cos((5/2)(B-C)/cos((1/2)(B-C)) : :

X(64968) lies on these lines: {94, 20268}, {5392, 24148}

X(64969) = X(2)X(2006)∩X(8)X(79)

Barycentrics    b*c*(-(a^2*b^2) + b^4 - a^2*b*c - a^2*c^2 - 2*b^2*c^2 + c^4) : :
Barycentrics    (b c)^2(-(b^2 - c^2)^2 + a^2 (b^2 + b c + c^2)) : :
Barycentrics    sin((3/2)(B-C)/sin((1/2)(B-C)) : :

X(64969) lies on these lines: {2, 2006}, {6, 24148}, {8, 79}, {75, 1150}, {92, 3219}, {110, 24332}, {192, 62305}, {312, 20886}, {321, 3262}, {612, 17890}, {984, 1109}, {1441, 31019}, {1733, 17126}, {1993, 24149}, {2345, 56463}, {3006, 31084}, {3596, 61410}, {3920, 17871}, {3929, 14212}, {4000, 56459}, {4671, 20236}, {4980, 49722}, {5125, 41013}, {5143, 26227}, {5271, 55873}, {5372, 20882}, {11680, 45954}, {15065, 17057}, {16732, 33151}, {17018, 17874}, {17118, 22129}, {17119, 55437}, {17861, 33155}, {17862, 27186}, {17884, 29815}, {18668, 40903}, {20223, 55872}, {20883, 56449}, {20909, 47676}, {21028, 23293}, {23690, 33134}, {27065, 30854}, {31025, 40564}, {34772, 50558}

X(64969) = X(5397)-anticomplementary conjugate of X(69)
X(64969) = barycentric product X(i)*X(j) for these {i,j}: {75, 7951}, {190, 63825}, {15455, 63826}
X(64969) = barycentric quotient X(i)/X(j) for these {i,j}: {7951, 1}, {9219, 7741}, {18116, 2605}, {63825, 514}, {63826, 14838}
X(64969) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 20920, 1150}, {321, 3262, 33077}, {1441, 48380, 31019}, {6358, 14213, 2}



leftri

Basepoints of perspective triangles: X(64970)-X(65084)

rightri

This preamble and centers X(64970)-X(65084) were contributed by Ivan Pavlov on Aug 26, 2024.

Given two perspective, but non-homothetic central triangles P1P2P3 and Q1Q2Q3 with perpsector S, determine the numbers x1, x2, and x3 such that:
xi*S + (1-xi)*Qi = Pi for each i=1,2,3 where the sum and equality are barycentric operations.
If such numbers exist they are unique and (x1:x2:x3) is a triangle center which we call 1st basepoint of P1P2P3 wrt Q1Q2Q3.
Similarly, using the conditions (1-xi)*S + xi*Qi = Pi, we can define the 2nd basepoint.
It can be proven that if the 1st basepoint exists, then the 2nd basepoint also exists.

For more information and results see this Euclid thread.

X(64970) = 1ST BASEPOINT OF THE 1ST ALTINTAS-ISODYNAMIC TRIANGLE WRT ABC

Barycentrics    -((a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^8-3*b^8+5*b^6*c^2+4*b^4*c^4+5*b^2*c^6-3*c^8-4*a^6*(b^2+c^2)+2*a^2*(b^2+c^2)*(5*b^4+3*b^2*c^2+5*c^4)-a^4*(5*b^4+17*b^2*c^2+5*c^4)))+2*sqrt(3)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(4*a^4*(b^2+c^2)-(b^2+c^2)*(b^4+3*b^2*c^2+c^4)-a^2*(3*b^4+b^2*c^2+3*c^4))*S : :

X(64970) lies on these lines: {2, 3}, {298, 648}, {302, 17907}, {340, 37786}, {621, 44700}, {5463, 6111}, {6110, 50855}, {6117, 40334}, {6330, 36306}, {9308, 34540}, {15595, 51016}, {16080, 42035}, {32001, 63032}, {34389, 59156}, {36302, 52194}, {41000, 60516}, {43530, 62934}

X(64970) = polar conjugate of X(54569)
X(64970) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(14538)}}, {{A, B, C, X(30), X(42035)}}, {{A, B, C, X(381), X(62934)}}, {{A, B, C, X(441), X(40709)}}, {{A, B, C, X(470), X(6330)}}, {{A, B, C, X(2409), X(36306)}}, {{A, B, C, X(55950), X(60660)}}
X(64970) = barycentric product X(i)*X(j) for these (i, j): {14538, 264}
X(64970) = barycentric quotient X(i)/X(j) for these (i, j): {4, 54569}, {14538, 3}
X(64970) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 297, 470}

X(64971) = 1ST BASEPOINT OF THE 2ND ALTINTAS-ISODYNAMIC TRIANGLE WRT ABC

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^8-3*b^8+5*b^6*c^2+4*b^4*c^4+5*b^2*c^6-3*c^8-4*a^6*(b^2+c^2)+2*a^2*(b^2+c^2)*(5*b^4+3*b^2*c^2+5*c^4)-a^4*(5*b^4+17*b^2*c^2+5*c^4))+2*sqrt(3)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(4*a^4*(b^2+c^2)-(b^2+c^2)*(b^4+3*b^2*c^2+c^4)-a^2*(3*b^4+b^2*c^2+3*c^4))*S : :

X(64971) lies on these lines: {2, 3}, {299, 648}, {303, 17907}, {340, 37785}, {622, 44701}, {5464, 6110}, {6111, 50858}, {6116, 40335}, {6330, 36309}, {9308, 34541}, {15595, 51018}, {16080, 42036}, {32001, 63033}, {34390, 59156}, {36303, 52193}, {41001, 60516}, {43530, 62933}

X(64971) = polar conjugate of X(54570)
X(64971) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(14539)}}, {{A, B, C, X(30), X(42036)}}, {{A, B, C, X(381), X(62933)}}, {{A, B, C, X(441), X(40710)}}, {{A, B, C, X(471), X(6330)}}, {{A, B, C, X(2409), X(36309)}}, {{A, B, C, X(55951), X(60661)}}
X(64971) = barycentric product X(i)*X(j) for these (i, j): {14539, 264}
X(64971) = barycentric quotient X(i)/X(j) for these (i, j): {4, 54570}, {14539, 3}
X(64971) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 297, 471}

X(64972) = 2ND BASEPOINT OF THE ANDROMEDA TRIANGLE WRT ABC

Barycentrics    a*(a+b-c)*(a-b+c)*(a^3+a^2*(3*b-c)+(b+c)^3+a*(3*b^2-6*b*c-c^2))*(a^3-a^2*(b-3*c)+(b+c)^3-a*(b^2+6*b*c-3*c^2)) : :

X(64972) lies on these lines: {2, 738}, {9, 1407}, {56, 200}, {57, 346}, {63, 56200}, {281, 1435}, {282, 6612}, {1412, 2287}, {1416, 5269}, {1427, 56199}, {3928, 36916}, {19605, 61380}

X(64972) = trilinear pole of line {43924, 3900}
X(64972) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 9785}
X(64972) = X(i)-cross conjugate of X(j) for these {i, j}: {1696, 1}, {9850, 7}
X(64972) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6762)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(56), X(57)}}, {{A, B, C, X(63), X(5437)}}, {{A, B, C, X(84), X(5438)}}, {{A, B, C, X(85), X(25430)}}, {{A, B, C, X(189), X(3680)}}, {{A, B, C, X(241), X(5269)}}, {{A, B, C, X(1476), X(8051)}}, {{A, B, C, X(2994), X(31509)}}, {{A, B, C, X(2999), X(9309)}}, {{A, B, C, X(3305), X(51780)}}, {{A, B, C, X(3306), X(3928)}}, {{A, B, C, X(4564), X(39948)}}, {{A, B, C, X(5665), X(60076)}}, {{A, B, C, X(6598), X(60237)}}, {{A, B, C, X(7284), X(36603)}}, {{A, B, C, X(7285), X(39963)}}, {{A, B, C, X(10390), X(57658)}}, {{A, B, C, X(31190), X(56545)}}, {{A, B, C, X(33576), X(60107)}}, {{A, B, C, X(34546), X(34918)}}, {{A, B, C, X(39962), X(43730)}}, {{A, B, C, X(41790), X(56218)}}, {{A, B, C, X(56195), X(56226)}}
X(64972) = barycentric quotient X(i)/X(j) for these (i, j): {1, 9785}, {52013, 32559}

X(64973) = 2ND BASEPOINT OF THE ANTI-ARTZT TRIANGLE WRT ABC

Barycentrics    (2*a^2+2*b^2-c^2)*(2*a^2-b^2+2*c^2)*(a^4+5*a^2*(b^2+c^2)-2*(b^4-b^2*c^2+c^4)) : :

X(64973) lies on the K295 cubic and on these lines: {2, 187}, {263, 9214}, {599, 42365}, {1992, 35138}, {11002, 61439}, {63170, 63854}

X(64973) = trilinear pole of line {8704, 64943}
X(64973) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11166, 36263}
X(64973) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(11163)}}, {{A, B, C, X(4), X(3849)}}, {{A, B, C, X(187), X(263)}}, {{A, B, C, X(671), X(55164)}}, {{A, B, C, X(5485), X(15810)}}, {{A, B, C, X(5569), X(9302)}}, {{A, B, C, X(7771), X(54840)}}, {{A, B, C, X(8176), X(54724)}}, {{A, B, C, X(8182), X(54678)}}, {{A, B, C, X(9214), X(51372)}}, {{A, B, C, X(11057), X(17503)}}, {{A, B, C, X(14327), X(63853)}}, {{A, B, C, X(14537), X(60281)}}, {{A, B, C, X(14762), X(54616)}}, {{A, B, C, X(14976), X(54896)}}, {{A, B, C, X(19569), X(54642)}}, {{A, B, C, X(26613), X(54752)}}, {{A, B, C, X(34245), X(35138)}}, {{A, B, C, X(40344), X(54637)}}
X(64973) = barycentric product X(i)*X(j) for these (i, j): {11163, 598}, {35138, 8704}
X(64973) = barycentric quotient X(i)/X(j) for these (i, j): {598, 11167}, {1383, 11166}, {8704, 3906}, {11163, 599}, {11186, 17414}, {11636, 6233}

X(64974) = 1ST BASEPOINT OF THE 1ST ANTI-ORTHOSYMMEDIAL TRIANGLE WRT ABC

Barycentrics    (b^2+c^2)*(a^6-a^4*b^2+b^6+b^2*c^4-2*c^6+a^2*(-b^4+c^4))*(-a^6+2*b^6+a^4*c^2-b^4*c^2-c^6+a^2*(-b^4+c^4)) : :

X(64974) lies on these lines: {2, 44766}, {20, 99}, {1916, 43673}, {2419, 18019}, {3314, 26170}, {3933, 41676}, {4576, 46164}, {21458, 46967}, {28696, 32818}

X(64974) = isotomic conjugate of X(21458)
X(64974) = anticomplement of X(64648)
X(64974) = trilinear pole of line {141, 23881}
X(64974) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 21458}, {82, 42671}, {251, 2312}, {1503, 46289}, {34055, 51437}
X(64974) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 21458}, {39, 1503}, {141, 42671}, {40585, 2312}, {40938, 16318}, {64648, 64648}
X(64974) = X(i)-Ceva conjugate of X(j) for these {i, j}: {35140, 46164}
X(64974) = pole of line {6333, 46164} with respect to the Steiner circumellipse
X(64974) = pole of line {1503, 21458} with respect to the Wallace hyperbola
X(64974) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(315)}}, {{A, B, C, X(20), X(427)}}, {{A, B, C, X(39), X(30270)}}, {{A, B, C, X(66), X(31123)}}, {{A, B, C, X(99), X(1916)}}, {{A, B, C, X(141), X(37668)}}, {{A, B, C, X(147), X(20021)}}, {{A, B, C, X(253), X(39129)}}, {{A, B, C, X(826), X(2794)}}, {{A, B, C, X(1297), X(46164)}}, {{A, B, C, X(3313), X(56306)}}, {{A, B, C, X(3329), X(28675)}}, {{A, B, C, X(3424), X(27376)}}, {{A, B, C, X(3926), X(3933)}}, {{A, B, C, X(7796), X(60232)}}, {{A, B, C, X(7802), X(60190)}}, {{A, B, C, X(23285), X(46165)}}, {{A, B, C, X(32458), X(51371)}}, {{A, B, C, X(40824), X(52568)}}, {{A, B, C, X(40938), X(53851)}}, {{A, B, C, X(43537), X(47730)}}
X(64974) = barycentric product X(i)*X(j) for these (i, j): {141, 35140}, {1235, 64975}, {1297, 8024}, {2419, 41676}, {3933, 6330}, {43673, 4576}, {46164, 76}, {51371, 9476}
X(64974) = barycentric quotient X(i)/X(j) for these (i, j): {2, 21458}, {38, 2312}, {39, 42671}, {141, 1503}, {427, 16318}, {1235, 60516}, {1297, 251}, {1843, 51437}, {2419, 4580}, {3665, 43045}, {3917, 8779}, {3933, 441}, {4576, 34211}, {6330, 32085}, {7813, 35282}, {8024, 30737}, {9019, 28343}, {20021, 51963}, {23881, 55129}, {34212, 18105}, {35140, 83}, {35325, 2445}, {41676, 2409}, {43673, 58784}, {46151, 23977}, {46164, 6}, {46967, 58113}, {51343, 56975}, {51360, 6793}, {51371, 15595}, {64975, 1176}

X(64975) = 2ND BASEPOINT OF THE 1ST ANTI-ORTHOSYMMEDIAL TRIANGLE WRT ABC

Barycentrics    a^2*(a^2-b^2-c^2)*(a^6-a^4*b^2+b^6+b^2*c^4-2*c^6+a^2*(-b^4+c^4))*(a^6-2*b^6-a^4*c^2+b^4*c^2+c^6+a^2*(b^4-c^4)) : :

X(64975) lies on the MacBeath circumconic and on these lines: {2, 44766}, {6, 15394}, {22, 110}, {69, 648}, {141, 16039}, {193, 56570}, {206, 56306}, {287, 2419}, {323, 52513}, {511, 44770}, {524, 48373}, {651, 5279}, {895, 2435}, {1032, 14944}, {1993, 40358}, {2986, 43673}, {2987, 34212}, {3964, 4558}, {4176, 4563}, {9476, 43187}, {11064, 17708}, {13138, 41086}, {14919, 61215}, {15291, 22151}, {15407, 36212}, {15988, 46640}, {18315, 33629}, {34384, 42405}, {34403, 42287}, {39265, 40802}, {41614, 51937}, {60053, 62382}

X(64975) = reflection of X(i) in X(j) for these {i,j}: {46639, 6}
X(64975) = isogonal conjugate of X(16318)
X(64975) = isotomic conjugate of X(60516)
X(64975) = trilinear pole of line {3, 2435}
X(64975) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 16318}, {4, 2312}, {19, 1503}, {31, 60516}, {33, 43045}, {75, 51437}, {82, 51434}, {92, 42671}, {132, 1910}, {158, 8779}, {240, 51963}, {281, 51647}, {393, 8766}, {441, 1096}, {647, 24024}, {656, 23977}, {661, 2409}, {1577, 2445}, {1755, 52641}, {1973, 30737}, {2190, 51363}, {6793, 36119}, {8767, 23976}, {9475, 36120}, {17442, 21458}, {17875, 57260}, {24023, 43717}, {35282, 36128}, {36084, 55275}, {57490, 57653}
X(64975) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60516}, {3, 16318}, {5, 51363}, {6, 1503}, {141, 51434}, {206, 51437}, {1147, 8779}, {1511, 6793}, {6337, 30737}, {6503, 441}, {11672, 132}, {22391, 42671}, {36033, 2312}, {36830, 2409}, {36899, 52641}, {38987, 55275}, {39052, 24024}, {39071, 23976}, {39085, 51963}, {40596, 23977}, {41167, 57430}, {46094, 9475}, {55047, 55129}, {61505, 16230}, {62590, 15595}, {62606, 63856}
X(64975) = X(i)-Ceva conjugate of X(j) for these {i, j}: {35140, 1297}
X(64975) = X(i)-cross conjugate of X(j) for these {i, j}: {511, 69}, {8779, 3}, {10766, 895}, {17974, 43705}, {34137, 1176}, {44894, 1799}
X(64975) = pole of line {10766, 64975} with respect to the MacBeath circumconic
X(64975) = pole of line {132, 1503} with respect to the Stammler hyperbola
X(64975) = pole of line {1297, 34168} with respect to the Steiner circumellipse
X(64975) = pole of line {34841, 55129} with respect to the Steiner inellipse
X(64975) = pole of line {441, 9475} with respect to the Wallace hyperbola
X(64975) = pole of line {15595, 39473} with respect to the dual conic of polar circle
X(64975) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(22)}}, {{A, B, C, X(3), X(1350)}}, {{A, B, C, X(4), X(19149)}}, {{A, B, C, X(6), X(154)}}, {{A, B, C, X(54), X(14376)}}, {{A, B, C, X(63), X(5279)}}, {{A, B, C, X(67), X(17847)}}, {{A, B, C, X(69), X(394)}}, {{A, B, C, X(74), X(525)}}, {{A, B, C, X(76), X(28724)}}, {{A, B, C, X(97), X(2979)}}, {{A, B, C, X(98), X(19164)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(111), X(9157)}}, {{A, B, C, X(185), X(12294)}}, {{A, B, C, X(193), X(2063)}}, {{A, B, C, X(206), X(53851)}}, {{A, B, C, X(248), X(694)}}, {{A, B, C, X(263), X(60495)}}, {{A, B, C, X(265), X(56568)}}, {{A, B, C, X(275), X(40404)}}, {{A, B, C, X(323), X(45792)}}, {{A, B, C, X(459), X(34207)}}, {{A, B, C, X(511), X(15595)}}, {{A, B, C, X(647), X(1976)}}, {{A, B, C, X(1177), X(10117)}}, {{A, B, C, X(1296), X(48948)}}, {{A, B, C, X(1297), X(6330)}}, {{A, B, C, X(1503), X(15324)}}, {{A, B, C, X(1972), X(3267)}}, {{A, B, C, X(1993), X(28419)}}, {{A, B, C, X(2052), X(41715)}}, {{A, B, C, X(2139), X(3926)}}, {{A, B, C, X(2435), X(56601)}}, {{A, B, C, X(2715), X(10766)}}, {{A, B, C, X(3563), X(19165)}}, {{A, B, C, X(4580), X(16081)}}, {{A, B, C, X(5485), X(34801)}}, {{A, B, C, X(5504), X(34897)}}, {{A, B, C, X(5897), X(54975)}}, {{A, B, C, X(6333), X(36212)}}, {{A, B, C, X(6391), X(36609)}}, {{A, B, C, X(6464), X(15077)}}, {{A, B, C, X(6504), X(18124)}}, {{A, B, C, X(8552), X(34210)}}, {{A, B, C, X(9476), X(43717)}}, {{A, B, C, X(11064), X(16165)}}, {{A, B, C, X(11610), X(34137)}}, {{A, B, C, X(14380), X(33988)}}, {{A, B, C, X(18906), X(57008)}}, {{A, B, C, X(26881), X(30535)}}, {{A, B, C, X(33851), X(55981)}}, {{A, B, C, X(34802), X(51941)}}, {{A, B, C, X(34861), X(44073)}}, {{A, B, C, X(36823), X(53173)}}, {{A, B, C, X(40384), X(41511)}}, {{A, B, C, X(41081), X(56328)}}, {{A, B, C, X(41891), X(42330)}}, {{A, B, C, X(43216), X(44189)}}, {{A, B, C, X(46310), X(57845)}}, {{A, B, C, X(55033), X(62428)}}, {{A, B, C, X(56072), X(63154)}}, {{A, B, C, X(56179), X(64082)}}
X(64975) = barycentric product X(i)*X(j) for these (i, j): {3, 35140}, {110, 2419}, {326, 8767}, {394, 6330}, {511, 57761}, {1176, 64974}, {1297, 69}, {1799, 46164}, {2435, 99}, {3265, 44770}, {3569, 55274}, {3926, 43717}, {14944, 15394}, {15407, 325}, {32649, 52617}, {32687, 4143}, {34212, 4563}, {36212, 9476}, {39265, 6394}, {40708, 51343}, {43673, 4558}, {43705, 56687}, {46967, 57069}, {57549, 8779}
X(64975) = barycentric quotient X(i)/X(j) for these (i, j): {2, 60516}, {3, 1503}, {6, 16318}, {32, 51437}, {39, 51434}, {48, 2312}, {69, 30737}, {98, 52641}, {110, 2409}, {112, 23977}, {162, 24024}, {184, 42671}, {216, 51363}, {222, 43045}, {248, 51963}, {255, 8766}, {265, 43089}, {287, 57490}, {394, 441}, {511, 132}, {577, 8779}, {603, 51647}, {1176, 21458}, {1297, 4}, {1350, 1529}, {1576, 2445}, {2419, 850}, {2435, 523}, {3284, 6793}, {3289, 9475}, {3292, 35282}, {3569, 55275}, {4558, 34211}, {6330, 2052}, {8673, 55129}, {8766, 24023}, {8767, 158}, {8779, 23976}, {9476, 16081}, {10317, 28343}, {13754, 53568}, {14919, 63856}, {14941, 51960}, {14944, 14249}, {15394, 16096}, {15407, 98}, {17974, 34156}, {32649, 32713}, {32687, 6529}, {34137, 64648}, {34146, 50938}, {34212, 2501}, {35140, 264}, {36046, 24019}, {36092, 36126}, {36212, 15595}, {39265, 6530}, {41172, 57430}, {43673, 14618}, {43705, 56572}, {43717, 393}, {43754, 60506}, {44770, 107}, {46164, 427}, {46967, 1289}, {47409, 57296}, {51343, 419}, {51822, 34854}, {51937, 1990}, {52485, 52661}, {52613, 39473}, {55274, 43187}, {56601, 37778}, {56687, 44145}, {57761, 290}, {57799, 51257}, {61464, 36201}, {64974, 1235}

X(64976) = 1ST BASEPOINT OF THE ANTLIA TRIANGLE WRT ABC

Barycentrics    (3*a^2+(b-c)^2)*(a^3+(b-c)^3-a^2*(b+3*c)+a*(-b^2+6*b*c+3*c^2))*(a^3-(b-c)^3-a^2*(3*b+c)+a*(3*b^2+6*b*c-c^2)) : :

X(64976) lies on these lines: {1, 479}, {2, 728}, {3672, 28071}, {28057, 62697}

X(64976) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 32560}, {1190, 21446}, {4326, 52013}
X(64976) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 32560}
X(64976) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(390)}}, {{A, B, C, X(2), X(479)}}, {{A, B, C, X(7), X(30854)}}
X(64976) = barycentric quotient X(i)/X(j) for these (i, j): {1, 32560}, {5222, 10580}, {64977, 21450}

X(64977) = 2ND BASEPOINT OF THE ANTLIA TRIANGLE WRT ABC

Barycentrics    a*(a^2+(b-c)^2)*(a^3+(b-c)^3-a^2*(b+3*c)+a*(-b^2+6*b*c+3*c^2))*(a^3-(b-c)^3-a^2*(3*b+c)+a*(3*b^2+6*b*c-c^2)) : :

X(64977) lies on these lines: {2, 728}, {607, 1435}, {1462, 2999}, {2191, 3752}, {4000, 28070}, {28017, 30706}

X(64977) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1190, 8817}, {4326, 7131}, {7123, 10580}, {17410, 52778}
X(64977) = X(i)-Dao conjugate of X(j) for these {i, j}: {15487, 10580}
X(64977) = X(i)-cross conjugate of X(j) for these {i, j}: {12402, 7}
X(64977) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(614)}}, {{A, B, C, X(57), X(607)}}, {{A, B, C, X(1427), X(3914)}}, {{A, B, C, X(2051), X(41788)}}, {{A, B, C, X(3673), X(8056)}}, {{A, B, C, X(44733), X(51400)}}
X(64977) = barycentric product X(i)*X(j) for these (i, j): {21450, 64976}
X(64977) = barycentric quotient X(i)/X(j) for these (i, j): {614, 10580}, {7083, 4326}, {59031, 52778}

X(64978) = 1ST BASEPOINT OF THE APOLLONIUS TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^3+b^3+2*a^2*c-a*b*c+2*b^2*c-c^3)*(a^3+2*a^2*b-b^3-a*b*c+2*b*c^2+c^3) : :

X(64978) lies on these lines: {2, 18654}, {7, 24211}, {12, 86}, {27, 8736}, {75, 24914}, {310, 34388}, {1400, 6650}, {5252, 30598}, {10401, 39704}, {17720, 44733}, {20028, 54355}, {37634, 64984}

X(64978) = trilinear pole of line {23733, 514}
X(64978) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 26840}, {60, 42066}, {1333, 38408}, {2150, 34528}, {2185, 9560}, {2194, 56949}, {4612, 17411}
X(64978) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 38408}, {1214, 56949}, {3160, 26840}, {56325, 34528}
X(64978) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(14011)}}, {{A, B, C, X(12), X(8736)}}, {{A, B, C, X(59), X(1400)}}, {{A, B, C, X(80), X(54677)}}, {{A, B, C, X(264), X(7224)}}, {{A, B, C, X(393), X(56164)}}, {{A, B, C, X(959), X(24914)}}, {{A, B, C, X(1037), X(45988)}}, {{A, B, C, X(2006), X(31643)}}, {{A, B, C, X(3144), X(35991)}}, {{A, B, C, X(3596), X(13478)}}, {{A, B, C, X(3668), X(4998)}}, {{A, B, C, X(5561), X(54722)}}, {{A, B, C, X(7035), X(37759)}}, {{A, B, C, X(7261), X(24211)}}, {{A, B, C, X(8044), X(20566)}}, {{A, B, C, X(17751), X(54355)}}, {{A, B, C, X(18812), X(34527)}}, {{A, B, C, X(21277), X(37770)}}, {{A, B, C, X(26751), X(57788)}}, {{A, B, C, X(39970), X(56287)}}, {{A, B, C, X(54121), X(60615)}}, {{A, B, C, X(56046), X(58022)}}, {{A, B, C, X(58008), X(60085)}}
X(64978) = barycentric product X(i)*X(j) for these (i, j): {18812, 226}, {34527, 7}
X(64978) = barycentric quotient X(i)/X(j) for these (i, j): {7, 26840}, {10, 38408}, {12, 34528}, {181, 9560}, {226, 56949}, {2171, 42066}, {18812, 333}, {34527, 8}

X(64979) = 1ST BASEPOINT OF THE APUS TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+4*b*c+c^2))*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+4*b*c+c^2)) : :

X(64979) lies on these lines: {1, 7318}, {2, 7269}, {7, 46}, {75, 5552}, {77, 10056}, {86, 3193}, {273, 1068}, {498, 7190}, {673, 60943}, {1440, 1442}, {1804, 15888}, {3584, 4328}, {3598, 39723}, {3672, 18815}, {4293, 7279}, {6650, 26125}, {7179, 39732}, {8232, 55937}, {10527, 57883}, {14621, 28739}, {17321, 58028}, {27475, 61019}, {28780, 39716}, {42318, 61017}, {52412, 64988}, {56047, 56367}, {57497, 57809}

X(64979) = isogonal conjugate of X(61398)
X(64979) = isotomic conjugate of X(10527)
X(64979) = trilinear pole of line {46389, 514}
X(64979) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 61398}, {31, 10527}, {42, 64394}, {55, 3338}, {56, 42012}, {57, 32561}, {101, 13401}, {651, 17412}, {2194, 12609}
X(64979) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 42012}, {2, 10527}, {3, 61398}, {223, 3338}, {1015, 13401}, {1214, 12609}, {5452, 32561}, {38991, 17412}, {40592, 64394}
X(64979) = X(i)-cross conjugate of X(j) for these {i, j}: {498, 2}, {7190, 7}
X(64979) = pole of line {10527, 61398} with respect to the Wallace hyperbola
X(64979) = pole of line {498, 7190} with respect to the dual conic of Yff parabola
X(64979) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(46)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(13407)}}, {{A, B, C, X(8), X(1065)}}, {{A, B, C, X(9), X(15298)}}, {{A, B, C, X(29), X(37112)}}, {{A, B, C, X(37), X(1037)}}, {{A, B, C, X(59), X(941)}}, {{A, B, C, X(69), X(54121)}}, {{A, B, C, X(77), X(52351)}}, {{A, B, C, X(79), X(60164)}}, {{A, B, C, X(80), X(54758)}}, {{A, B, C, X(92), X(40417)}}, {{A, B, C, X(95), X(8048)}}, {{A, B, C, X(103), X(56232)}}, {{A, B, C, X(264), X(13577)}}, {{A, B, C, X(279), X(7269)}}, {{A, B, C, X(280), X(56104)}}, {{A, B, C, X(281), X(2346)}}, {{A, B, C, X(332), X(46880)}}, {{A, B, C, X(346), X(55920)}}, {{A, B, C, X(347), X(1442)}}, {{A, B, C, X(388), X(60321)}}, {{A, B, C, X(393), X(1002)}}, {{A, B, C, X(498), X(10044)}}, {{A, B, C, X(650), X(3477)}}, {{A, B, C, X(693), X(8797)}}, {{A, B, C, X(943), X(36626)}}, {{A, B, C, X(1000), X(6740)}}, {{A, B, C, X(1224), X(5665)}}, {{A, B, C, X(1441), X(8817)}}, {{A, B, C, X(1443), X(3672)}}, {{A, B, C, X(1937), X(17038)}}, {{A, B, C, X(2165), X(13476)}}, {{A, B, C, X(2298), X(57727)}}, {{A, B, C, X(2335), X(37741)}}, {{A, B, C, X(3086), X(27529)}}, {{A, B, C, X(3596), X(40419)}}, {{A, B, C, X(4998), X(58008)}}, {{A, B, C, X(5553), X(60162)}}, {{A, B, C, X(5555), X(43531)}}, {{A, B, C, X(5556), X(60157)}}, {{A, B, C, X(5561), X(54757)}}, {{A, B, C, X(7160), X(36629)}}, {{A, B, C, X(7179), X(28739)}}, {{A, B, C, X(7320), X(51565)}}, {{A, B, C, X(8047), X(57645)}}, {{A, B, C, X(8759), X(56225)}}, {{A, B, C, X(8829), X(25430)}}, {{A, B, C, X(9309), X(46952)}}, {{A, B, C, X(9436), X(60943)}}, {{A, B, C, X(10013), X(43947)}}, {{A, B, C, X(10309), X(60174)}}, {{A, B, C, X(11239), X(45701)}}, {{A, B, C, X(17097), X(56136)}}, {{A, B, C, X(17321), X(17740)}}, {{A, B, C, X(28742), X(41785)}}, {{A, B, C, X(31618), X(64240)}}, {{A, B, C, X(33298), X(57809)}}, {{A, B, C, X(39983), X(52013)}}, {{A, B, C, X(40412), X(58029)}}, {{A, B, C, X(40719), X(61019)}}, {{A, B, C, X(41527), X(41791)}}, {{A, B, C, X(42407), X(56129)}}, {{A, B, C, X(43733), X(60173)}}, {{A, B, C, X(43736), X(56217)}}, {{A, B, C, X(43740), X(54972)}}, {{A, B, C, X(50442), X(58009)}}, {{A, B, C, X(51351), X(61017)}}, {{A, B, C, X(52392), X(57832)}}, {{A, B, C, X(55076), X(56144)}}, {{A, B, C, X(56048), X(56218)}}, {{A, B, C, X(56356), X(63192)}}, {{A, B, C, X(57831), X(57882)}}, {{A, B, C, X(59255), X(59475)}}, {{A, B, C, X(60160), X(61105)}}
X(64979) = barycentric product X(i)*X(j) for these (i, j): {7162, 85}, {56231, 75}
X(64979) = barycentric quotient X(i)/X(j) for these (i, j): {2, 10527}, {6, 61398}, {9, 42012}, {55, 32561}, {57, 3338}, {81, 64394}, {226, 12609}, {513, 13401}, {663, 17412}, {7162, 9}, {56231, 1}

X(64980) = 1ST BASEPOINT OF THE ATIK TRIANGLE WRT ABC

Barycentrics    a*(a+b-c)*(a-b+c)*(a^2-2*a*b+b^2+2*a*c+2*b*c-3*c^2)*(a^2-3*b^2+2*a*(b-c)+2*b*c+c^2) : :

X(64980) lies on these lines: {1, 971}, {2, 3160}, {7, 56043}, {34, 36122}, {57, 7955}, {88, 43047}, {105, 1420}, {222, 39948}, {223, 25430}, {241, 8056}, {277, 1323}, {278, 62544}, {279, 60831}, {738, 2170}, {948, 56218}, {955, 11518}, {1002, 3340}, {1170, 62792}, {1219, 63165}, {1280, 36846}, {1390, 21147}, {1423, 61630}, {1465, 39963}, {2951, 45228}, {2982, 47848}, {3227, 53640}, {3680, 6168}, {4350, 34056}, {4853, 39959}, {5222, 44794}, {5228, 39980}, {5573, 60813}, {7982, 63203}, {18623, 40069}, {30710, 44186}, {30719, 62635}, {35348, 43049}, {36603, 51302}, {37551, 51498}, {37887, 43066}, {51223, 51969}, {51364, 63592}, {54425, 59610}, {56355, 60966}, {58320, 60666}

X(64980) = perspector of circumconic {{A, B, C, X(53640), X(61240)}}
X(64980) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 64083}, {8, 3207}, {9, 165}, {21, 21872}, {41, 16284}, {55, 144}, {59, 13609}, {109, 57064}, {200, 1419}, {219, 63965}, {220, 3160}, {281, 22117}, {284, 21060}, {480, 9533}, {651, 58835}, {728, 17106}, {1253, 31627}, {2332, 50563}, {3063, 62533}, {3939, 7658}, {4847, 33634}, {5546, 55285}, {6602, 50561}, {7071, 50559}, {14827, 50560}
X(64980) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 64083}, {11, 57064}, {223, 144}, {478, 165}, {3160, 16284}, {6609, 1419}, {6615, 13609}, {10001, 62533}, {17113, 31627}, {38991, 58835}, {40590, 21060}, {40611, 21872}, {40617, 7658}, {43182, 45203}
X(64980) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3062, 57}, {10405, 42872}, {36620, 3062}
X(64980) = X(i)-cross conjugate of X(j) for these {i, j}: {269, 57}, {2310, 3676}, {5573, 19604}, {11051, 3062}
X(64980) = pole of line {57, 8917} with respect to the Feuerbach hyperbola
X(64980) = pole of line {3062, 8166} with respect to the dual conic of Yff parabola
X(64980) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(11372)}}, {{A, B, C, X(7), X(31994)}}, {{A, B, C, X(8), X(10384)}}, {{A, B, C, X(9), X(9311)}}, {{A, B, C, X(19), X(23058)}}, {{A, B, C, X(21), X(44559)}}, {{A, B, C, X(33), X(10939)}}, {{A, B, C, X(34), X(738)}}, {{A, B, C, X(56), X(59215)}}, {{A, B, C, X(58), X(62183)}}, {{A, B, C, X(84), X(514)}}, {{A, B, C, X(85), X(7091)}}, {{A, B, C, X(92), X(9856)}}, {{A, B, C, X(104), X(41790)}}, {{A, B, C, X(189), X(10864)}}, {{A, B, C, X(220), X(2291)}}, {{A, B, C, X(241), X(1420)}}, {{A, B, C, X(269), X(1419)}}, {{A, B, C, X(294), X(4907)}}, {{A, B, C, X(312), X(10866)}}, {{A, B, C, X(479), X(2124)}}, {{A, B, C, X(650), X(2125)}}, {{A, B, C, X(673), X(3680)}}, {{A, B, C, X(1019), X(45818)}}, {{A, B, C, X(1121), X(33576)}}, {{A, B, C, X(1323), X(4350)}}, {{A, B, C, X(1396), X(18624)}}, {{A, B, C, X(1407), X(36636)}}, {{A, B, C, X(1411), X(17107)}}, {{A, B, C, X(1434), X(5665)}}, {{A, B, C, X(1436), X(2338)}}, {{A, B, C, X(1440), X(34060)}}, {{A, B, C, X(1476), X(21446)}}, {{A, B, C, X(2163), X(56005)}}, {{A, B, C, X(2217), X(9503)}}, {{A, B, C, X(3008), X(36846)}}, {{A, B, C, X(3062), X(10405)}}, {{A, B, C, X(3340), X(5228)}}, {{A, B, C, X(3577), X(14377)}}, {{A, B, C, X(3676), X(43064)}}, {{A, B, C, X(4560), X(44692)}}, {{A, B, C, X(4853), X(5222)}}, {{A, B, C, X(4900), X(60092)}}, {{A, B, C, X(5560), X(34529)}}, {{A, B, C, X(6180), X(7153)}}, {{A, B, C, X(7100), X(7177)}}, {{A, B, C, X(7129), X(58906)}}, {{A, B, C, X(7955), X(10307)}}, {{A, B, C, X(8809), X(34059)}}, {{A, B, C, X(8830), X(8835)}}, {{A, B, C, X(10389), X(45227)}}, {{A, B, C, X(10390), X(10509)}}, {{A, B, C, X(10429), X(55110)}}, {{A, B, C, X(11051), X(19605)}}, {{A, B, C, X(16572), X(43065)}}, {{A, B, C, X(18359), X(30294)}}, {{A, B, C, X(24644), X(55937)}}, {{A, B, C, X(30283), X(34234)}}, {{A, B, C, X(30290), X(30690)}}, {{A, B, C, X(30725), X(43047)}}, {{A, B, C, X(36621), X(43760)}}, {{A, B, C, X(56038), X(60075)}}, {{A, B, C, X(56042), X(63148)}}, {{A, B, C, X(57641), X(58322)}}
X(64980) = barycentric product X(i)*X(j) for these (i, j): {1, 36620}, {189, 42872}, {269, 63165}, {312, 61380}, {513, 53640}, {514, 61240}, {3062, 7}, {4017, 55284}, {10405, 57}, {11051, 85}, {19605, 279}, {44186, 56}, {53622, 693}, {56718, 56783}, {59170, 63192}, {60813, 9312}, {60831, 9}, {62544, 7131}
X(64980) = barycentric quotient X(i)/X(j) for these (i, j): {1, 64083}, {7, 16284}, {34, 63965}, {56, 165}, {57, 144}, {65, 21060}, {269, 3160}, {279, 31627}, {479, 50561}, {603, 22117}, {604, 3207}, {650, 57064}, {663, 58835}, {664, 62533}, {738, 9533}, {1088, 50560}, {1400, 21872}, {1407, 1419}, {1439, 50563}, {2170, 13609}, {3062, 8}, {3669, 7658}, {4017, 55285}, {5575, 63626}, {7023, 17106}, {7177, 50559}, {8581, 10324}, {10405, 312}, {11051, 9}, {19605, 346}, {20978, 45228}, {36620, 75}, {37566, 41561}, {40133, 45203}, {42872, 329}, {44186, 3596}, {53622, 100}, {53640, 668}, {55284, 7257}, {56718, 3717}, {60831, 85}, {61240, 190}, {61380, 57}, {63164, 44797}, {63165, 341}
X(64980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2124, 1419}, {1, 43064, 2124}, {40133, 62793, 57}, {43035, 59215, 36636}

X(64981) = 2ND BASEPOINT OF THE 3RD BROCARD TRIANGLE WRT ABC

Barycentrics    (a^2-a*b+b^2)*(a^2+a*b+b^2)*(a^2-b*c)*(a^2+b*c)*(a^2-a*c+c^2)*(a^2+a*c+c^2) : :

X(64981) lies on cubic K1285 and on these lines: {2, 1501}, {32, 11196}, {385, 18902}, {1976, 36897}, {3114, 33336}, {3978, 4027}, {7766, 19222}, {16609, 63237}, {23357, 34537}, {33514, 35146}, {38830, 44167}, {53704, 58111}

X(64981) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 42061}, {694, 51836}, {1581, 3094}, {1916, 3116}, {1934, 3117}, {1967, 3314}, {3862, 3865}, {3863, 3864}, {9468, 56784}, {36214, 46507}, {37134, 50549}
X(64981) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 42061}, {8290, 3314}, {19576, 3094}, {39031, 3116}, {39043, 51836}, {39044, 56784}
X(64981) = pole of line {3094, 19602} with respect to the Stammler hyperbola
X(64981) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(385)}}, {{A, B, C, X(251), X(1915)}}, {{A, B, C, X(699), X(1691)}}, {{A, B, C, X(707), X(5027)}}, {{A, B, C, X(1501), X(14602)}}, {{A, B, C, X(5207), X(8783)}}, {{A, B, C, X(8024), X(40379)}}, {{A, B, C, X(9865), X(51582)}}, {{A, B, C, X(39931), X(46807)}}, {{A, B, C, X(42534), X(56979)}}, {{A, B, C, X(43450), X(60105)}}, {{A, B, C, X(46809), X(51430)}}, {{A, B, C, X(47736), X(60177)}}
X(64981) = barycentric product X(i)*X(j) for these (i, j): {1580, 3113}, {1691, 3114}, {1933, 46281}, {3407, 385}, {14295, 58111}, {14617, 56976}, {17984, 43722}, {18898, 3978}, {33514, 804}, {40820, 8840}
X(64981) = barycentric quotient X(i)/X(j) for these (i, j): {32, 42061}, {385, 3314}, {419, 5117}, {1580, 51836}, {1691, 3094}, {1933, 3116}, {1966, 56784}, {3113, 1934}, {3114, 18896}, {3407, 1916}, {4027, 9865}, {5027, 50549}, {14602, 3117}, {14617, 56977}, {18898, 694}, {18902, 18899}, {33514, 18829}, {43722, 36214}, {44089, 56920}, {56828, 46507}, {56975, 62696}, {56976, 62699}, {58111, 805}, {63244, 63219}

X(64982) = 1ST BASEPOINT OF THE 4TH BROCARD TRIANGLE WRT ABC

Barycentrics    (a^2-b^2-c^2)*(2*a^2+2*b^2-c^2)*(2*a^2-b^2+2*c^2) : :

X(64982) lies on these lines: {2, 187}, {3, 30786}, {6, 10160}, {23, 21395}, {69, 3292}, {76, 7664}, {99, 47596}, {126, 33274}, {183, 1494}, {264, 468}, {287, 37638}, {305, 6390}, {325, 57822}, {328, 62698}, {599, 20380}, {647, 14977}, {842, 58043}, {1078, 2373}, {1992, 30516}, {3589, 30489}, {3796, 61382}, {5108, 20382}, {6340, 7494}, {6719, 7749}, {6800, 45018}, {7493, 11056}, {7495, 11059}, {7499, 59756}, {7610, 48540}, {7769, 56435}, {7782, 14360}, {7806, 9229}, {7844, 26257}, {7850, 26233}, {8030, 45796}, {8585, 17006}, {8599, 9168}, {8797, 40132}, {8860, 18818}, {10416, 22258}, {10418, 17004}, {10553, 34507}, {10603, 52290}, {11064, 42313}, {11176, 23287}, {11284, 40410}, {14165, 64983}, {18018, 40022}, {18024, 52145}, {20564, 64495}, {26255, 53127}, {34229, 36889}, {36948, 44128}, {37453, 40413}, {44451, 46001}, {45201, 65032}, {47597, 55958}

X(64982) = isogonal conjugate of X(8541)
X(64982) = isotomic conjugate of X(5094)
X(64982) = trilinear pole of line {30491, 525}
X(64982) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 8541}, {19, 574}, {25, 36263}, {31, 5094}, {162, 17414}, {599, 1973}, {1964, 32581}, {3906, 32676}, {17442, 58761}, {36128, 62657}
X(64982) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 264}
X(64982) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5094}, {3, 8541}, {6, 574}, {125, 17414}, {647, 8288}, {6337, 599}, {6505, 36263}, {15526, 3906}, {41884, 32581}, {52881, 39785}, {62569, 13857}, {62604, 9464}, {62607, 42008}
X(64982) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40826, 598}
X(64982) = X(i)-cross conjugate of X(j) for these {i, j}: {43697, 598}, {65006, 43697}
X(64982) = pole of line {8704, 13449} with respect to the orthoptic circle of the Steiner Inellipse
X(64982) = pole of line {574, 8541} with respect to the Stammler hyperbola
X(64982) = pole of line {599, 5094} with respect to the Wallace hyperbola
X(64982) = pole of line {3906, 4141} with respect to the dual conic of polar circle
X(64982) = pole of line {3268, 9209} with respect to the dual conic of anti-Artzt circle
X(64982) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(3), X(187)}}, {{A, B, C, X(6), X(60124)}}, {{A, B, C, X(23), X(52300)}}, {{A, B, C, X(25), X(6676)}}, {{A, B, C, X(68), X(7608)}}, {{A, B, C, X(76), X(316)}}, {{A, B, C, X(98), X(4846)}}, {{A, B, C, X(111), X(1176)}}, {{A, B, C, X(140), X(11284)}}, {{A, B, C, X(183), X(11064)}}, {{A, B, C, X(184), X(38279)}}, {{A, B, C, X(262), X(265)}}, {{A, B, C, X(290), X(43530)}}, {{A, B, C, X(325), X(37638)}}, {{A, B, C, X(394), X(37688)}}, {{A, B, C, X(525), X(3849)}}, {{A, B, C, X(549), X(47597)}}, {{A, B, C, X(598), X(10512)}}, {{A, B, C, X(625), X(36952)}}, {{A, B, C, X(631), X(40132)}}, {{A, B, C, X(895), X(39389)}}, {{A, B, C, X(1300), X(7612)}}, {{A, B, C, X(1368), X(37453)}}, {{A, B, C, X(1383), X(10511)}}, {{A, B, C, X(1485), X(8770)}}, {{A, B, C, X(1995), X(7495)}}, {{A, B, C, X(2165), X(2374)}}, {{A, B, C, X(2367), X(3972)}}, {{A, B, C, X(2501), X(60117)}}, {{A, B, C, X(3291), X(44451)}}, {{A, B, C, X(3519), X(60144)}}, {{A, B, C, X(3521), X(53100)}}, {{A, B, C, X(3763), X(45201)}}, {{A, B, C, X(4563), X(9170)}}, {{A, B, C, X(5020), X(7499)}}, {{A, B, C, X(5159), X(52292)}}, {{A, B, C, X(5485), X(23334)}}, {{A, B, C, X(6032), X(6325)}}, {{A, B, C, X(6353), X(7494)}}, {{A, B, C, X(6677), X(7484)}}, {{A, B, C, X(7386), X(38282)}}, {{A, B, C, X(7426), X(47596)}}, {{A, B, C, X(7603), X(11669)}}, {{A, B, C, X(7664), X(57481)}}, {{A, B, C, X(7761), X(51454)}}, {{A, B, C, X(7771), X(57799)}}, {{A, B, C, X(7804), X(53024)}}, {{A, B, C, X(7806), X(37894)}}, {{A, B, C, X(7898), X(42006)}}, {{A, B, C, X(7937), X(40050)}}, {{A, B, C, X(8176), X(42011)}}, {{A, B, C, X(8791), X(9307)}}, {{A, B, C, X(8858), X(60104)}}, {{A, B, C, X(9076), X(45835)}}, {{A, B, C, X(9080), X(60053)}}, {{A, B, C, X(9289), X(14712)}}, {{A, B, C, X(10153), X(37809)}}, {{A, B, C, X(10162), X(13377)}}, {{A, B, C, X(10185), X(42021)}}, {{A, B, C, X(10418), X(11176)}}, {{A, B, C, X(10604), X(11185)}}, {{A, B, C, X(13623), X(60175)}}, {{A, B, C, X(14376), X(60187)}}, {{A, B, C, X(14458), X(14537)}}, {{A, B, C, X(14484), X(43699)}}, {{A, B, C, X(14907), X(60101)}}, {{A, B, C, X(15077), X(53099)}}, {{A, B, C, X(15321), X(60141)}}, {{A, B, C, X(15464), X(55977)}}, {{A, B, C, X(15740), X(43537)}}, {{A, B, C, X(15749), X(60118)}}, {{A, B, C, X(15822), X(34816)}}, {{A, B, C, X(16051), X(52290)}}, {{A, B, C, X(16080), X(54124)}}, {{A, B, C, X(18022), X(34412)}}, {{A, B, C, X(18296), X(60328)}}, {{A, B, C, X(18401), X(40801)}}, {{A, B, C, X(18818), X(61345)}}, {{A, B, C, X(20573), X(60178)}}, {{A, B, C, X(21400), X(60329)}}, {{A, B, C, X(21843), X(53104)}}, {{A, B, C, X(26613), X(47389)}}, {{A, B, C, X(30516), X(43956)}}, {{A, B, C, X(30542), X(39602)}}, {{A, B, C, X(30771), X(52297)}}, {{A, B, C, X(31371), X(47586)}}, {{A, B, C, X(32533), X(60142)}}, {{A, B, C, X(32827), X(40824)}}, {{A, B, C, X(34205), X(35569)}}, {{A, B, C, X(34254), X(40022)}}, {{A, B, C, X(34405), X(60241)}}, {{A, B, C, X(34817), X(53864)}}, {{A, B, C, X(35142), X(60256)}}, {{A, B, C, X(37874), X(39287)}}, {{A, B, C, X(38263), X(39951)}}, {{A, B, C, X(40103), X(56072)}}, {{A, B, C, X(40118), X(60130)}}, {{A, B, C, X(40347), X(45838)}}, {{A, B, C, X(42410), X(44175)}}, {{A, B, C, X(43527), X(60855)}}, {{A, B, C, X(43528), X(43714)}}, {{A, B, C, X(43705), X(55982)}}, {{A, B, C, X(43722), X(52153)}}, {{A, B, C, X(43726), X(60125)}}, {{A, B, C, X(44182), X(57763)}}, {{A, B, C, X(44678), X(60181)}}, {{A, B, C, X(51224), X(60220)}}, {{A, B, C, X(52752), X(56399)}}, {{A, B, C, X(54774), X(57908)}}, {{A, B, C, X(60122), X(60590)}}
X(64982) = barycentric product X(i)*X(j) for these (i, j): {3, 40826}, {304, 55927}, {308, 65006}, {598, 69}, {1383, 305}, {1799, 23297}, {4563, 8599}, {10511, 37804}, {10512, 22151}, {11636, 3267}, {18818, 6390}, {30491, 670}, {30786, 51541}, {35138, 525}, {43697, 76}, {46001, 52608}, {52692, 57799}
X(64982) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5094}, {3, 574}, {6, 8541}, {63, 36263}, {69, 599}, {83, 32581}, {125, 8288}, {305, 9464}, {525, 3906}, {598, 4}, {647, 17414}, {895, 42007}, {1176, 58761}, {1332, 3908}, {1383, 25}, {1799, 10130}, {3292, 62657}, {3977, 4141}, {4558, 9145}, {4563, 9146}, {4846, 60588}, {6390, 39785}, {6393, 51397}, {8599, 2501}, {10511, 8791}, {10512, 46105}, {11064, 13857}, {11636, 112}, {13394, 30516}, {14977, 23288}, {18818, 17983}, {20380, 5095}, {22151, 10510}, {23287, 14273}, {23297, 427}, {30489, 1843}, {30491, 512}, {30786, 42008}, {35138, 648}, {40826, 264}, {41614, 8542}, {43697, 6}, {46001, 2489}, {51541, 468}, {52692, 232}, {55927, 19}, {60872, 63855}, {61345, 4232}, {62382, 19510}, {65006, 39}, {65007, 14580}
X(64982) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1383, 23297}, {2, 9829, 55164}, {598, 51541, 61345}, {1383, 23297, 598}, {23297, 51541, 1383}

X(64983) = 2ND BASEPOINT OF THE 9TH BROCARD TRIANGLE WRT ABC

Barycentrics    (a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(a^4+3*b^4-2*a^2*c^2+c^4)*(a^4-2*a^2*b^2+b^4+3*c^4) : :

X(64983) lies on these lines: {2, 6524}, {4, 287}, {69, 297}, {95, 17907}, {253, 43981}, {305, 2052}, {324, 18018}, {458, 10002}, {1007, 47739}, {1093, 14064}, {1217, 26155}, {1799, 11547}, {5921, 33971}, {11427, 40823}, {14165, 64982}, {15466, 59756}, {17500, 40404}, {18024, 18027}, {19174, 37192}, {21447, 40032}, {23582, 57991}, {36948, 37067}, {37344, 52439}, {37643, 57864}, {37765, 57822}, {37778, 57819}, {40803, 42313}, {41766, 41769}, {43710, 43727}, {51023, 52282}, {52288, 60872}

X(64983) = isotomic conjugate of X(37188)
X(64983) = trilinear pole of line {16229, 16230}
X(64983) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 37188}, {48, 6776}, {163, 47194}, {255, 7735}, {326, 40825}, {577, 4008}, {822, 35278}, {2148, 42353}, {4100, 43976}, {6507, 6620}, {9247, 62698}, {40814, 52430}
X(64983) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 37188}, {115, 47194}, {216, 42353}, {1249, 6776}, {6523, 7735}, {15259, 40825}, {62576, 62698}
X(64983) = X(i)-cross conjugate of X(j) for these {i, j}: {40801, 55972}, {52251, 2}, {54260, 53639}, {56370, 35142}, {64919, 648}
X(64983) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(4), X(297)}}, {{A, B, C, X(76), X(1217)}}, {{A, B, C, X(83), X(18855)}}, {{A, B, C, X(132), X(53015)}}, {{A, B, C, X(232), X(263)}}, {{A, B, C, X(254), X(43678)}}, {{A, B, C, X(275), X(8801)}}, {{A, B, C, X(276), X(18840)}}, {{A, B, C, X(308), X(60221)}}, {{A, B, C, X(324), X(17500)}}, {{A, B, C, X(393), X(2052)}}, {{A, B, C, X(427), X(37187)}}, {{A, B, C, X(458), X(52283)}}, {{A, B, C, X(459), X(9308)}}, {{A, B, C, X(467), X(37192)}}, {{A, B, C, X(671), X(18850)}}, {{A, B, C, X(847), X(52583)}}, {{A, B, C, X(1105), X(2996)}}, {{A, B, C, X(1502), X(53481)}}, {{A, B, C, X(2165), X(60527)}}, {{A, B, C, X(2987), X(56307)}}, {{A, B, C, X(3090), X(37067)}}, {{A, B, C, X(3346), X(9289)}}, {{A, B, C, X(3926), X(15318)}}, {{A, B, C, X(4846), X(34579)}}, {{A, B, C, X(5395), X(14860)}}, {{A, B, C, X(5485), X(18852)}}, {{A, B, C, X(6662), X(14376)}}, {{A, B, C, X(6820), X(52280)}}, {{A, B, C, X(8796), X(32085)}}, {{A, B, C, X(9214), X(46106)}}, {{A, B, C, X(9290), X(15740)}}, {{A, B, C, X(11331), X(52288)}}, {{A, B, C, X(11547), X(19174)}}, {{A, B, C, X(14064), X(37344)}}, {{A, B, C, X(14494), X(42300)}}, {{A, B, C, X(14593), X(39645)}}, {{A, B, C, X(15466), X(43981)}}, {{A, B, C, X(16080), X(42298)}}, {{A, B, C, X(17983), X(56270)}}, {{A, B, C, X(18841), X(18854)}}, {{A, B, C, X(18846), X(53105)}}, {{A, B, C, X(18847), X(32532)}}, {{A, B, C, X(18848), X(38259)}}, {{A, B, C, X(18851), X(60219)}}, {{A, B, C, X(34225), X(59169)}}, {{A, B, C, X(34403), X(54114)}}, {{A, B, C, X(36611), X(54710)}}, {{A, B, C, X(37188), X(52251)}}, {{A, B, C, X(37643), X(40888)}}, {{A, B, C, X(37765), X(52449)}}, {{A, B, C, X(40801), X(40802)}}, {{A, B, C, X(40815), X(44556)}}, {{A, B, C, X(42354), X(60256)}}, {{A, B, C, X(51228), X(52485)}}, {{A, B, C, X(52395), X(54797)}}, {{A, B, C, X(52441), X(56339)}}, {{A, B, C, X(52487), X(60133)}}, {{A, B, C, X(56067), X(60241)}}
X(64983) = barycentric product X(i)*X(j) for these (i, j): {4, 55972}, {264, 40801}, {393, 40824}, {2052, 40802}, {16230, 41074}, {18027, 40799}
X(64983) = barycentric quotient X(i)/X(j) for these (i, j): {2, 37188}, {4, 6776}, {5, 42353}, {107, 35278}, {158, 4008}, {264, 62698}, {393, 7735}, {523, 47194}, {1093, 43976}, {2052, 40814}, {2207, 40825}, {6524, 6620}, {6530, 1513}, {10002, 7710}, {18027, 40822}, {33971, 9755}, {40799, 577}, {40801, 3}, {40802, 394}, {40803, 54032}, {40823, 14585}, {40824, 3926}, {41074, 17932}, {55972, 69}

X(64984) = 2ND BASEPOINT OF THE 5TH CONWAY TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :

X(64984) lies on these lines: {1, 11233}, {2, 12}, {7, 940}, {27, 225}, {57, 75}, {65, 1999}, {73, 64997}, {81, 20028}, {85, 57923}, {86, 226}, {272, 1169}, {273, 1435}, {310, 349}, {312, 2285}, {333, 1400}, {335, 63994}, {553, 903}, {651, 40153}, {673, 1416}, {675, 8687}, {738, 1088}, {951, 3912}, {999, 2050}, {1014, 52358}, {1246, 37543}, {1268, 3911}, {1427, 7176}, {1429, 40418}, {1440, 6612}, {1460, 5263}, {1477, 8707}, {2006, 64457}, {2099, 58820}, {2171, 34064}, {2213, 34255}, {2296, 55082}, {2359, 60041}, {3361, 18229}, {3687, 10106}, {4031, 39710}, {4298, 6996}, {4315, 37617}, {4321, 17022}, {4373, 21454}, {4552, 39769}, {4581, 60479}, {4654, 39704}, {4911, 21621}, {5219, 30598}, {5226, 19701}, {5228, 39741}, {5244, 40765}, {5287, 37523}, {5435, 5936}, {5905, 26625}, {6384, 7153}, {6548, 30724}, {6650, 24836}, {7091, 30567}, {7130, 57884}, {7131, 57925}, {7318, 7363}, {7413, 37609}, {10401, 27184}, {10404, 50400}, {14621, 29841}, {16099, 55010}, {18044, 58019}, {18097, 52394}, {28650, 31231}, {33133, 40160}, {36147, 51567}, {36570, 58018}, {36620, 61380}, {37088, 37554}, {37265, 37583}, {37390, 62809}, {37634, 64978}, {39749, 52013}, {41260, 63013}, {56052, 60715}, {58027, 60085}

X(64984) = isogonal conjugate of X(2269)
X(64984) = isotomic conjugate of X(3687)
X(64984) = trilinear pole of line {4581, 5018}
X(64984) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2269}, {2, 20967}, {4, 22074}, {6, 960}, {8, 2300}, {9, 1193}, {21, 2092}, {31, 3687}, {33, 22097}, {37, 4267}, {41, 4357}, {42, 17185}, {48, 46878}, {55, 3666}, {56, 3965}, {58, 21033}, {60, 21810}, {63, 40976}, {65, 46889}, {78, 2354}, {81, 40966}, {100, 52326}, {101, 17420}, {200, 61412}, {210, 40153}, {212, 1848}, {219, 1829}, {220, 24471}, {281, 22345}, {284, 2292}, {333, 3725}, {429, 2193}, {521, 61205}, {644, 6371}, {646, 57157}, {649, 61223}, {650, 53280}, {652, 61226}, {663, 3882}, {692, 3910}, {849, 61377}, {893, 18235}, {1172, 22076}, {1211, 2194}, {1253, 3674}, {1333, 3704}, {1334, 54308}, {1400, 46877}, {1415, 57158}, {1682, 2298}, {1812, 44092}, {2150, 20653}, {2175, 20911}, {3063, 53332}, {3185, 19608}, {3737, 61168}, {3939, 48131}, {4612, 42661}, {4719, 34820}, {5546, 50330}, {7054, 52567}, {7058, 59174}, {7085, 56841}, {7252, 61172}, {18697, 57657}, {34434, 46879}, {34858, 51407}, {39167, 56905}, {40141, 41581}, {41609, 56269}, {45218, 56181}, {52425, 54314}, {54417, 56914}
X(64984) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 3965}, {2, 3687}, {3, 2269}, {9, 960}, {10, 21033}, {37, 3704}, {223, 3666}, {478, 1193}, {1015, 17420}, {1086, 3910}, {1146, 57158}, {1214, 1211}, {1249, 46878}, {3160, 4357}, {3162, 40976}, {4075, 61377}, {5375, 61223}, {6609, 61412}, {8054, 52326}, {10001, 53332}, {16586, 51407}, {17113, 3674}, {32664, 20967}, {36033, 22074}, {40582, 46877}, {40586, 40966}, {40589, 4267}, {40590, 2292}, {40592, 17185}, {40593, 20911}, {40597, 18235}, {40602, 46889}, {40611, 2092}, {40615, 3004}, {40617, 48131}, {40622, 21124}, {40837, 1848}, {47345, 429}, {52087, 1682}, {56325, 20653}, {59608, 41003}, {62570, 18697}, {62602, 54314}
X(64984) = X(i)-Ceva conjugate of X(j) for these {i, j}: {31643, 1220}
X(64984) = X(i)-cross conjugate of X(j) for these {i, j}: {1019, 651}, {1577, 653}, {2298, 1220}, {4017, 664}, {4298, 7}, {4369, 658}, {6002, 190}, {6996, 673}, {13161, 75}, {26146, 13149}, {29487, 37137}, {37607, 86}, {39595, 2}, {60086, 31643}, {62749, 36098}
X(64984) = pole of line {2269, 4267} with respect to the Stammler hyperbola
X(64984) = pole of line {2269, 3687} with respect to the Wallace hyperbola
X(64984) = pole of line {4298, 6996} with respect to the dual conic of Yff parabola
X(64984) = pole of line {65, 86} with respect to the dual conic of Moses-Feuerbach circumconic
X(64984) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(333)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(312)}}, {{A, B, C, X(8), X(60167)}}, {{A, B, C, X(12), X(225)}}, {{A, B, C, X(19), X(8770)}}, {{A, B, C, X(28), X(37092)}}, {{A, B, C, X(29), X(19645)}}, {{A, B, C, X(33), X(6559)}}, {{A, B, C, X(56), X(57)}}, {{A, B, C, X(58), X(54300)}}, {{A, B, C, X(59), X(1171)}}, {{A, B, C, X(63), X(40442)}}, {{A, B, C, X(65), X(43071)}}, {{A, B, C, X(77), X(57876)}}, {{A, B, C, X(79), X(1329)}}, {{A, B, C, X(80), X(4102)}}, {{A, B, C, X(81), X(1476)}}, {{A, B, C, X(83), X(32017)}}, {{A, B, C, X(84), X(2339)}}, {{A, B, C, X(85), X(278)}}, {{A, B, C, X(88), X(5253)}}, {{A, B, C, X(92), X(837)}}, {{A, B, C, X(104), X(2185)}}, {{A, B, C, X(106), X(53083)}}, {{A, B, C, X(171), X(37596)}}, {{A, B, C, X(189), X(9311)}}, {{A, B, C, X(190), X(47056)}}, {{A, B, C, X(279), X(3600)}}, {{A, B, C, X(284), X(34429)}}, {{A, B, C, X(286), X(58014)}}, {{A, B, C, X(306), X(52392)}}, {{A, B, C, X(514), X(529)}}, {{A, B, C, X(553), X(3911)}}, {{A, B, C, X(598), X(34523)}}, {{A, B, C, X(650), X(8605)}}, {{A, B, C, X(967), X(1037)}}, {{A, B, C, X(969), X(40417)}}, {{A, B, C, X(996), X(48832)}}, {{A, B, C, X(1000), X(42030)}}, {{A, B, C, X(1019), X(40153)}}, {{A, B, C, X(1029), X(18359)}}, {{A, B, C, X(1105), X(31623)}}, {{A, B, C, X(1120), X(2985)}}, {{A, B, C, X(1121), X(34606)}}, {{A, B, C, X(1211), X(34920)}}, {{A, B, C, X(1214), X(54339)}}, {{A, B, C, X(1220), X(14534)}}, {{A, B, C, X(1222), X(39694)}}, {{A, B, C, X(1255), X(5260)}}, {{A, B, C, X(1427), X(4032)}}, {{A, B, C, X(1432), X(28386)}}, {{A, B, C, X(1751), X(5665)}}, {{A, B, C, X(1791), X(2363)}}, {{A, B, C, X(1848), X(13161)}}, {{A, B, C, X(1937), X(56219)}}, {{A, B, C, X(1999), X(18812)}}, {{A, B, C, X(2222), X(53644)}}, {{A, B, C, X(2319), X(7050)}}, {{A, B, C, X(2346), X(56204)}}, {{A, B, C, X(2481), X(18021)}}, {{A, B, C, X(2982), X(4564)}}, {{A, B, C, X(2999), X(30567)}}, {{A, B, C, X(3296), X(30478)}}, {{A, B, C, X(3661), X(29841)}}, {{A, B, C, X(3666), X(37607)}}, {{A, B, C, X(3668), X(58005)}}, {{A, B, C, X(3674), X(4298)}}, {{A, B, C, X(3676), X(43053)}}, {{A, B, C, X(3687), X(39595)}}, {{A, B, C, X(3912), X(40940)}}, {{A, B, C, X(4313), X(20007)}}, {{A, B, C, X(4321), X(42309)}}, {{A, B, C, X(4384), X(17022)}}, {{A, B, C, X(4654), X(5219)}}, {{A, B, C, X(4999), X(5557)}}, {{A, B, C, X(5261), X(57826)}}, {{A, B, C, X(5265), X(44794)}}, {{A, B, C, X(5271), X(5287)}}, {{A, B, C, X(5434), X(52374)}}, {{A, B, C, X(5435), X(21454)}}, {{A, B, C, X(5555), X(60155)}}, {{A, B, C, X(5556), X(6557)}}, {{A, B, C, X(5558), X(56201)}}, {{A, B, C, X(5561), X(54586)}}, {{A, B, C, X(6336), X(20060)}}, {{A, B, C, X(6645), X(7176)}}, {{A, B, C, X(6654), X(27944)}}, {{A, B, C, X(6996), X(18155)}}, {{A, B, C, X(7017), X(54821)}}, {{A, B, C, X(7224), X(18025)}}, {{A, B, C, X(7284), X(42467)}}, {{A, B, C, X(7319), X(56086)}}, {{A, B, C, X(7320), X(30711)}}, {{A, B, C, X(7490), X(16054)}}, {{A, B, C, X(8056), X(14377)}}, {{A, B, C, X(8169), X(31507)}}, {{A, B, C, X(8748), X(40169)}}, {{A, B, C, X(10481), X(18087)}}, {{A, B, C, X(10509), X(21446)}}, {{A, B, C, X(11194), X(39980)}}, {{A, B, C, X(11236), X(60083)}}, {{A, B, C, X(11681), X(37203)}}, {{A, B, C, X(14554), X(42339)}}, {{A, B, C, X(15320), X(37865)}}, {{A, B, C, X(15474), X(60169)}}, {{A, B, C, X(17743), X(39703)}}, {{A, B, C, X(17758), X(25466)}}, {{A, B, C, X(18743), X(30699)}}, {{A, B, C, X(19607), X(51565)}}, {{A, B, C, X(19701), X(25507)}}, {{A, B, C, X(20076), X(56050)}}, {{A, B, C, X(23512), X(44734)}}, {{A, B, C, X(25417), X(63163)}}, {{A, B, C, X(31141), X(54928)}}, {{A, B, C, X(31359), X(60206)}}, {{A, B, C, X(32009), X(60235)}}, {{A, B, C, X(32020), X(40835)}}, {{A, B, C, X(34892), X(54553)}}, {{A, B, C, X(35058), X(55942)}}, {{A, B, C, X(36124), X(60617)}}, {{A, B, C, X(36603), X(40726)}}, {{A, B, C, X(36795), X(46103)}}, {{A, B, C, X(37129), X(57749)}}, {{A, B, C, X(37208), X(43736)}}, {{A, B, C, X(37520), X(37617)}}, {{A, B, C, X(37523), X(37543)}}, {{A, B, C, X(37660), X(42028)}}, {{A, B, C, X(37684), X(41629)}}, {{A, B, C, X(37870), X(62929)}}, {{A, B, C, X(39696), X(39702)}}, {{A, B, C, X(39698), X(40394)}}, {{A, B, C, X(40399), X(55938)}}, {{A, B, C, X(40414), X(52209)}}, {{A, B, C, X(40434), X(57721)}}, {{A, B, C, X(40444), X(50442)}}, {{A, B, C, X(40446), X(56224)}}, {{A, B, C, X(40843), X(52037)}}, {{A, B, C, X(41245), X(56783)}}, {{A, B, C, X(43733), X(45098)}}, {{A, B, C, X(51512), X(55962)}}, {{A, B, C, X(55922), X(56199)}}
X(64984) = barycentric product X(i)*X(j) for these (i, j): {1, 31643}, {75, 961}, {225, 57853}, {514, 6648}, {1169, 349}, {1220, 7}, {1240, 56}, {1254, 52550}, {1400, 40827}, {1412, 60264}, {1434, 14624}, {1441, 2363}, {1791, 273}, {1798, 57809}, {2298, 85}, {2359, 331}, {3261, 8687}, {3676, 8707}, {4554, 62749}, {4566, 57161}, {4581, 664}, {4625, 57162}, {6358, 64457}, {14534, 226}, {15420, 653}, {24002, 36147}, {30710, 57}, {32736, 52621}, {35519, 52928}, {36098, 693}, {60086, 86}
X(64984) = barycentric quotient X(i)/X(j) for these (i, j): {1, 960}, {2, 3687}, {4, 46878}, {6, 2269}, {7, 4357}, {9, 3965}, {10, 3704}, {12, 20653}, {21, 46877}, {25, 40976}, {31, 20967}, {34, 1829}, {37, 21033}, {42, 40966}, {48, 22074}, {56, 1193}, {57, 3666}, {58, 4267}, {65, 2292}, {73, 22076}, {81, 17185}, {85, 20911}, {100, 61223}, {108, 61226}, {109, 53280}, {171, 18235}, {222, 22097}, {225, 429}, {226, 1211}, {269, 24471}, {273, 54314}, {278, 1848}, {279, 3674}, {284, 46889}, {349, 1228}, {513, 17420}, {514, 3910}, {522, 57158}, {572, 46879}, {594, 61377}, {603, 22345}, {604, 2300}, {608, 2354}, {649, 52326}, {651, 3882}, {664, 53332}, {908, 51407}, {961, 1}, {1014, 54308}, {1169, 284}, {1193, 1682}, {1220, 8}, {1240, 3596}, {1254, 52567}, {1400, 2092}, {1402, 3725}, {1407, 61412}, {1412, 40153}, {1434, 16705}, {1441, 18697}, {1446, 45196}, {1791, 78}, {1798, 283}, {2171, 21810}, {2298, 9}, {2359, 219}, {2363, 21}, {3361, 4719}, {3668, 41003}, {3669, 48131}, {3676, 3004}, {4017, 50330}, {4032, 27697}, {4551, 61172}, {4559, 61168}, {4581, 522}, {4848, 4918}, {6648, 190}, {7153, 27455}, {7175, 28369}, {7176, 59509}, {7178, 21124}, {7249, 59191}, {8687, 101}, {8707, 3699}, {13478, 19608}, {14534, 333}, {14624, 2321}, {15420, 6332}, {18097, 27067}, {21147, 41600}, {24002, 4509}, {30710, 312}, {31643, 75}, {32674, 61205}, {32736, 3939}, {34036, 41581}, {34050, 51414}, {36098, 100}, {36147, 644}, {36570, 64654}, {40827, 28660}, {43924, 6371}, {52567, 6042}, {52928, 109}, {55323, 52087}, {57161, 7253}, {57162, 4041}, {57652, 44092}, {57785, 16739}, {57853, 332}, {58982, 4636}, {59159, 2330}, {60086, 10}, {60264, 30713}, {62749, 650}, {62761, 4009}, {64457, 2185}
X(64984) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {961, 60086, 1220}

X(64985) = 1ST BASEPOINT OF THE DAO TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(a^3+2*b^3-a^2*c+b^2*c+c^3+a*(b^2-c^2))*(a^3-a^2*b+b^3+b*c^2+2*c^3+a*(-b^2+c^2)) : :

X(64985) lies on these lines: {69, 7058}, {86, 2983}, {99, 18650}, {274, 1257}, {314, 1231}, {332, 951}, {1043, 3668}, {1509, 3926}, {2368, 29163}, {33297, 40445}, {44139, 57779}, {57825, 65015}

X(64985) = isogonal conjugate of X(40984)
X(64985) = isotomic conjugate of X(1834)
X(64985) = trilinear pole of line {3265, 7192}
X(64985) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 40984}, {6, 40977}, {19, 44093}, {25, 18673}, {31, 1834}, {42, 1104}, {213, 40940}, {228, 1842}, {440, 1973}, {512, 61221}, {798, 14543}, {950, 1402}, {1400, 2264}, {1918, 17863}, {2203, 21671}
X(64985) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 1834}, {3, 40984}, {6, 44093}, {9, 40977}, {6337, 440}, {6505, 18673}, {6626, 40940}, {31998, 14543}, {34021, 17863}, {36830, 53290}, {39054, 61221}, {40582, 2264}, {40592, 1104}, {40605, 950}, {40620, 29162}, {62564, 21671}
X(64985) = X(i)-cross conjugate of X(j) for these {i, j}: {4025, 99}, {46402, 670}
X(64985) = pole of line {40984, 44093} with respect to the Stammler hyperbola
X(64985) = pole of line {440, 950} with respect to the Wallace hyperbola
X(64985) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(3668)}}, {{A, B, C, X(7), X(14534)}}, {{A, B, C, X(67), X(40085)}}, {{A, B, C, X(69), X(76)}}, {{A, B, C, X(75), X(33116)}}, {{A, B, C, X(83), X(1246)}}, {{A, B, C, X(86), X(274)}}, {{A, B, C, X(95), X(57824)}}, {{A, B, C, X(98), X(42027)}}, {{A, B, C, X(249), X(57685)}}, {{A, B, C, X(253), X(60254)}}, {{A, B, C, X(261), X(310)}}, {{A, B, C, X(269), X(37128)}}, {{A, B, C, X(287), X(28786)}}, {{A, B, C, X(313), X(1494)}}, {{A, B, C, X(314), X(332)}}, {{A, B, C, X(321), X(54454)}}, {{A, B, C, X(671), X(8044)}}, {{A, B, C, X(811), X(6613)}}, {{A, B, C, X(951), X(1257)}}, {{A, B, C, X(1016), X(40422)}}, {{A, B, C, X(1175), X(56137)}}, {{A, B, C, X(1219), X(51512)}}, {{A, B, C, X(1441), X(60251)}}, {{A, B, C, X(2985), X(2997)}}, {{A, B, C, X(3596), X(57980)}}, {{A, B, C, X(4025), X(18650)}}, {{A, B, C, X(4373), X(24624)}}, {{A, B, C, X(4590), X(35150)}}, {{A, B, C, X(5224), X(17378)}}, {{A, B, C, X(7182), X(34399)}}, {{A, B, C, X(30701), X(58002)}}, {{A, B, C, X(30710), X(60041)}}, {{A, B, C, X(32017), X(40424)}}, {{A, B, C, X(34258), X(57818)}}, {{A, B, C, X(34282), X(44140)}}, {{A, B, C, X(35157), X(36036)}}, {{A, B, C, X(37142), X(56179)}}, {{A, B, C, X(37202), X(39749)}}, {{A, B, C, X(39695), X(40395)}}, {{A, B, C, X(40017), X(57792)}}, {{A, B, C, X(40408), X(56328)}}, {{A, B, C, X(40414), X(58005)}}, {{A, B, C, X(40802), X(57701)}}, {{A, B, C, X(45857), X(60090)}}, {{A, B, C, X(57858), X(62884)}}, {{A, B, C, X(57882), X(58027)}}
X(64985) = barycentric product X(i)*X(j) for these (i, j): {304, 40431}, {305, 57390}, {333, 58005}, {1257, 274}, {2983, 310}, {17206, 40445}, {28660, 951}, {29163, 52619}, {40414, 69}, {52396, 65015}
X(64985) = barycentric quotient X(i)/X(j) for these (i, j): {1, 40977}, {2, 1834}, {3, 44093}, {6, 40984}, {21, 2264}, {27, 1842}, {63, 18673}, {69, 440}, {81, 1104}, {86, 40940}, {99, 14543}, {110, 53290}, {274, 17863}, {306, 21671}, {333, 950}, {662, 61221}, {951, 1400}, {1043, 59646}, {1257, 37}, {2983, 42}, {4558, 61200}, {7192, 29162}, {17139, 51410}, {17206, 18650}, {29163, 4557}, {40414, 4}, {40431, 19}, {40445, 1826}, {52561, 3690}, {57390, 25}, {58005, 226}, {65015, 8747}

X(64986) = 1ST BASEPOINT OF THE 2ND EXCOSINE TRIANGLE WRT ABC

Barycentrics    (a^2-b^2-c^2)*(a^4+b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2-c^2))*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b^2-c^2))*(a^8+4*a^6*(b^2-c^2)+(b^2-c^2)^4+4*a^2*(b^2-c^2)*(b^2+c^2)^2+a^4*(-10*b^4+4*b^2*c^2+6*c^4))*(a^8-4*a^6*(b^2-c^2)+(b^2-c^2)^4-4*a^2*(b^2-c^2)*(b^2+c^2)^2+2*a^4*(3*b^4+2*b^2*c^2-5*c^4)) : :

X(64986) lies on these lines: {2, 1032}, {69, 46351}, {253, 3346}, {264, 34403}, {2373, 59077}, {28783, 42287}

X(64986) = isotomic conjugate of X(6616)
X(64986) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 6616}, {154, 1712}, {204, 1498}, {610, 1033}
X(64986) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6616}, {3343, 1498}, {3350, 3079}, {6587, 13613}, {14092, 1033}, {40839, 6523}
X(64986) = X(i)-cross conjugate of X(j) for these {i, j}: {459, 34403}, {3346, 1032}, {52559, 253}
X(64986) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(4), X(6247)}}, {{A, B, C, X(393), X(46347)}}, {{A, B, C, X(459), X(3343)}}, {{A, B, C, X(1249), X(15238)}}, {{A, B, C, X(3265), X(56594)}}, {{A, B, C, X(3344), X(3346)}}, {{A, B, C, X(6616), X(42465)}}, {{A, B, C, X(15394), X(34403)}}, {{A, B, C, X(51348), X(53050)}}
X(64986) = barycentric product X(i)*X(j) for these (i, j): {69, 64987}, {1032, 253}, {3267, 59077}, {3346, 34403}, {28783, 41530}, {47633, 52559}, {47849, 57921}
X(64986) = barycentric quotient X(i)/X(j) for these (i, j): {2, 6616}, {64, 1033}, {122, 13613}, {253, 14361}, {459, 6523}, {1032, 20}, {1073, 1498}, {2184, 1712}, {3344, 3079}, {3346, 1249}, {8805, 44695}, {8810, 44696}, {15394, 6617}, {28783, 154}, {34403, 6527}, {47633, 52578}, {47849, 610}, {52559, 3343}, {59077, 112}, {64987, 4}

X(64987) = 2ND BASEPOINT OF THE 2ND EXCOSINE TRIANGLE WRT ABC

Barycentrics    (a^4+b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2-c^2))*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b^2-c^2))*(a^8+4*a^6*(b^2-c^2)+(b^2-c^2)^4+4*a^2*(b^2-c^2)*(b^2+c^2)^2+a^4*(-10*b^4+4*b^2*c^2+6*c^4))*(a^8-4*a^6*(b^2-c^2)+(b^2-c^2)^4-4*a^2*(b^2-c^2)*(b^2+c^2)^2+2*a^4*(3*b^4+2*b^2*c^2-5*c^4)) : :

X(64987) lies on the Kiepert hyperbola and on these lines: {2, 1032}, {4, 1073}, {76, 47435}, {98, 59077}, {226, 8805}, {253, 2052}, {459, 52559}, {2184, 8808}, {3091, 46353}, {6504, 52514}, {13157, 54710}, {14572, 16080}, {15400, 38253}, {17811, 60618}, {28783, 56346}, {31363, 40813}, {57483, 60114}

X(64987) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 6616}, {204, 6617}, {610, 1498}, {1097, 47437}, {1712, 15905}
X(64987) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 6616}, {3343, 6617}, {3344, 2060}, {3350, 36413}, {14092, 1498}, {40839, 14361}
X(64987) = X(i)-Ceva conjugate of X(j) for these {i, j}: {64986, 3346}
X(64987) = X(i)-cross conjugate of X(j) for these {i, j}: {6526, 253}
X(64987) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(253), X(1073)}}, {{A, B, C, X(393), X(20265)}}, {{A, B, C, X(525), X(42468)}}, {{A, B, C, X(1032), X(3346)}}, {{A, B, C, X(3343), X(6526)}}, {{A, B, C, X(3344), X(47633)}}, {{A, B, C, X(6330), X(37669)}}, {{A, B, C, X(6524), X(46347)}}, {{A, B, C, X(14362), X(40839)}}, {{A, B, C, X(46065), X(58759)}}
X(64987) = barycentric product X(i)*X(j) for these (i, j): {4, 64986}, {253, 3346}, {1032, 459}, {14362, 31943}, {28783, 52581}, {46353, 52559}, {59077, 850}
X(64987) = barycentric quotient X(i)/X(j) for these (i, j): {4, 6616}, {64, 1498}, {253, 6527}, {459, 14361}, {1032, 37669}, {1073, 6617}, {1562, 13613}, {3344, 36413}, {3346, 20}, {3350, 2060}, {6526, 6523}, {8805, 27382}, {8810, 18623}, {28783, 15905}, {28785, 31944}, {31942, 41085}, {31943, 14365}, {41489, 1033}, {46353, 52578}, {52559, 46351}, {59077, 110}, {60803, 8886}, {64986, 69}
X(64987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1032, 3344}, {2, 14362, 3343}

X(64988) = 2ND BASEPOINT OF THE 3RD EXTOUCH TRIANGLE WRT ABC

Barycentrics    b*c*(-a^2+b^2-c^2)*(a^2+b^2-c^2)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)*(-a^3+a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2) : :

X(64988) lies on these lines: {2, 280}, {4, 11212}, {7, 92}, {27, 84}, {57, 63186}, {75, 7017}, {86, 309}, {108, 39451}, {158, 20320}, {264, 58001}, {271, 5271}, {273, 2052}, {278, 1440}, {282, 40447}, {285, 44734}, {312, 40424}, {321, 58002}, {331, 1088}, {653, 20223}, {673, 7008}, {675, 40117}, {1246, 1903}, {1422, 16082}, {1897, 56233}, {2989, 3187}, {3673, 60516}, {4385, 52283}, {5081, 6820}, {6617, 10538}, {6994, 55937}, {7149, 46355}, {7151, 14621}, {7282, 11433}, {7318, 17923}, {8059, 39429}, {18026, 20921}, {18750, 34402}, {18928, 55394}, {21620, 37448}, {31909, 64997}, {33116, 57884}, {37269, 45766}, {37276, 41013}, {37420, 39592}, {39695, 48380}, {39700, 48381}, {42361, 46108}, {44190, 57923}, {52346, 64082}, {52412, 64979}

X(64988) = isotomic conjugate of X(64082)
X(64988) = trilinear pole of line {16231, 44426}
X(64988) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 198}, {6, 7078}, {9, 7114}, {31, 64082}, {40, 48}, {41, 7013}, {55, 7011}, {56, 55111}, {63, 2187}, {71, 2360}, {78, 2199}, {109, 10397}, {184, 329}, {196, 6056}, {208, 2289}, {212, 223}, {219, 221}, {222, 7074}, {227, 2193}, {228, 1817}, {255, 2331}, {322, 9247}, {347, 52425}, {394, 3195}, {577, 7952}, {603, 2324}, {652, 57118}, {692, 64885}, {906, 6129}, {1259, 3209}, {1260, 6611}, {1262, 47432}, {1397, 55112}, {1400, 1819}, {1415, 57101}, {1437, 21871}, {2149, 53557}, {2188, 40212}, {2200, 8822}, {3194, 3990}, {4055, 41083}, {4100, 47372}, {4575, 55212}, {7053, 7368}, {7080, 52411}, {7115, 55044}, {7125, 40971}, {7335, 55116}, {7358, 23979}, {8058, 32660}, {8750, 57233}, {14298, 36059}, {14827, 57479}, {14837, 32656}, {15905, 41088}, {40701, 62257}, {52430, 64211}
X(64988) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 55111}, {2, 64082}, {9, 7078}, {11, 10397}, {136, 55212}, {223, 7011}, {281, 1103}, {478, 7114}, {650, 53557}, {1086, 64885}, {1146, 57101}, {1249, 40}, {1577, 16596}, {3160, 7013}, {3162, 2187}, {3341, 219}, {5190, 6129}, {6523, 2331}, {7129, 12335}, {7952, 2324}, {20620, 14298}, {23050, 7368}, {26932, 57233}, {36103, 198}, {40582, 1819}, {40624, 57245}, {40625, 57213}, {40628, 55044}, {40837, 223}, {40943, 52097}, {47345, 227}, {62576, 322}, {62585, 55112}, {62602, 347}, {62605, 329}
X(64988) = X(i)-cross conjugate of X(j) for these {i, j}: {84, 309}, {158, 273}, {278, 92}, {7003, 7020}, {7661, 36118}, {8808, 189}, {18634, 85}, {20320, 75}, {24026, 46107}, {26932, 57215}
X(64988) = pole of line {6129, 10397} with respect to the polar circle
X(64988) = pole of line {158, 20320} with respect to the dual conic of Yff parabola
X(64988) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(57), X(17102)}}, {{A, B, C, X(79), X(56216)}}, {{A, B, C, X(84), X(8808)}}, {{A, B, C, X(85), X(23661)}}, {{A, B, C, X(91), X(37887)}}, {{A, B, C, X(92), X(318)}}, {{A, B, C, X(158), X(196)}}, {{A, B, C, X(189), X(280)}}, {{A, B, C, X(226), X(57723)}}, {{A, B, C, X(312), X(17862)}}, {{A, B, C, X(345), X(26871)}}, {{A, B, C, X(522), X(2184)}}, {{A, B, C, X(1043), X(2994)}}, {{A, B, C, X(1435), X(7649)}}, {{A, B, C, X(1751), X(57724)}}, {{A, B, C, X(1838), X(39708)}}, {{A, B, C, X(1847), X(1895)}}, {{A, B, C, X(1937), X(56345)}}, {{A, B, C, X(2208), X(55242)}}, {{A, B, C, X(3187), X(48381)}}, {{A, B, C, X(3261), X(40015)}}, {{A, B, C, X(5931), X(8048)}}, {{A, B, C, X(6336), X(56270)}}, {{A, B, C, X(6521), X(46110)}}, {{A, B, C, X(7003), X(57492)}}, {{A, B, C, X(8809), X(64082)}}, {{A, B, C, X(14014), X(17555)}}, {{A, B, C, X(15149), X(37279)}}, {{A, B, C, X(30710), X(37874)}}, {{A, B, C, X(34860), X(40399)}}, {{A, B, C, X(40165), X(57215)}}, {{A, B, C, X(40430), X(56041)}}, {{A, B, C, X(40836), X(55110)}}, {{A, B, C, X(40940), X(53816)}}, {{A, B, C, X(46350), X(46355)}}, {{A, B, C, X(55105), X(60084)}}
X(64988) = barycentric product X(i)*X(j) for these (i, j): {7, 7020}, {19, 44190}, {34, 57793}, {189, 92}, {225, 57795}, {264, 84}, {273, 280}, {278, 34404}, {282, 331}, {285, 57809}, {286, 39130}, {309, 4}, {312, 55110}, {342, 46355}, {561, 7151}, {1088, 57492}, {1118, 57783}, {1422, 7017}, {1433, 57806}, {1436, 1969}, {1440, 318}, {1903, 44129}, {2052, 41081}, {2192, 57787}, {2357, 57796}, {2358, 28660}, {2501, 55211}, {3261, 40117}, {6063, 7008}, {7003, 85}, {7129, 76}, {13138, 46107}, {17924, 44327}, {18022, 2208}, {20567, 7154}, {31623, 8808}, {37141, 46110}, {40836, 75}, {44130, 52384}, {44426, 53642}, {47436, 7149}, {52938, 61040}, {55242, 6331}
X(64988) = barycentric quotient X(i)/X(j) for these (i, j): {1, 7078}, {2, 64082}, {4, 40}, {7, 7013}, {9, 55111}, {11, 53557}, {19, 198}, {21, 1819}, {25, 2187}, {27, 1817}, {28, 2360}, {33, 7074}, {34, 221}, {56, 7114}, {57, 7011}, {84, 3}, {92, 329}, {108, 57118}, {158, 7952}, {189, 63}, {196, 40212}, {225, 227}, {264, 322}, {268, 2289}, {271, 1259}, {273, 347}, {278, 223}, {280, 78}, {281, 2324}, {282, 219}, {285, 283}, {286, 8822}, {309, 69}, {312, 55112}, {318, 7080}, {331, 40702}, {342, 55015}, {393, 2331}, {514, 64885}, {522, 57101}, {608, 2199}, {650, 10397}, {905, 57233}, {946, 52097}, {1088, 57479}, {1093, 47372}, {1096, 3195}, {1118, 208}, {1256, 1433}, {1413, 603}, {1422, 222}, {1433, 255}, {1435, 6611}, {1436, 48}, {1440, 77}, {1826, 21871}, {1847, 14256}, {1857, 40971}, {1903, 71}, {2052, 64211}, {2188, 6056}, {2192, 212}, {2208, 184}, {2310, 47432}, {2357, 228}, {2358, 1400}, {2501, 55212}, {3064, 14298}, {4391, 57245}, {4560, 57213}, {4858, 16596}, {6331, 55241}, {6612, 7099}, {7003, 9}, {7004, 55044}, {7008, 55}, {7020, 8}, {7079, 7368}, {7118, 52425}, {7129, 6}, {7149, 3342}, {7151, 31}, {7154, 41}, {7367, 1802}, {7649, 6129}, {7952, 1103}, {8059, 36059}, {8747, 3194}, {8808, 1214}, {13138, 1331}, {13853, 37755}, {17924, 14837}, {24026, 7358}, {31623, 27398}, {32652, 32656}, {34400, 7183}, {34404, 345}, {36049, 906}, {36123, 15501}, {37141, 1813}, {39130, 72}, {40117, 101}, {40149, 64708}, {40836, 1}, {41013, 21075}, {41081, 394}, {41087, 3990}, {44189, 3719}, {44190, 304}, {44327, 1332}, {44426, 8058}, {46107, 17896}, {46355, 271}, {52037, 40152}, {52384, 73}, {52389, 3682}, {52571, 1071}, {53010, 52386}, {53013, 2318}, {53642, 6516}, {55110, 57}, {55117, 7125}, {55211, 4563}, {55242, 647}, {56939, 5440}, {56940, 4855}, {56944, 3998}, {56972, 1804}, {57492, 200}, {57783, 1264}, {57793, 3718}, {57795, 332}, {57809, 57810}, {60799, 14379}, {60803, 19614}, {61040, 57241}, {61229, 23067}
X(64988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 15466, 64211}, {75, 34404, 56944}, {2052, 54284, 273}, {7003, 55110, 189}

X(64989) = 1ST BASEPOINT OF THE 4TH EXTOUCH TRIANGLE WRT ABC

Barycentrics    b*c*(-a+b+c)*(a^2+2*a*b+b^2+c^2)*(a^2+b^2+2*a*c+c^2) : :

X(64989) lies on these lines: {2, 304}, {8, 3718}, {29, 314}, {69, 1829}, {75, 1220}, {76, 92}, {85, 17788}, {189, 56882}, {239, 2221}, {312, 57919}, {333, 2082}, {1008, 1245}, {1036, 52133}, {1121, 54982}, {1231, 1880}, {1310, 1311}, {1722, 1930}, {2994, 14258}, {3702, 56102}, {4673, 14942}, {5224, 31359}, {7020, 57793}, {14829, 57642}, {17016, 39731}, {18157, 65018}, {19607, 28916}, {20924, 64995}, {20925, 30690}, {20928, 57905}, {21615, 40011}, {33935, 56224}, {33939, 65029}, {34234, 37215}, {34284, 56044}

X(64989) = isotomic conjugate of X(2285)
X(64989) = trilinear pole of line {35518, 522}
X(64989) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1460}, {25, 2286}, {31, 2285}, {32, 388}, {41, 4320}, {56, 54416}, {109, 2484}, {213, 5323}, {604, 612}, {608, 7085}, {651, 8646}, {1037, 1184}, {1038, 1973}, {1395, 5227}, {1397, 2345}, {1400, 44119}, {1402, 2303}, {1409, 4206}, {1415, 8678}, {1919, 14594}, {1974, 56367}, {2175, 7365}, {2194, 8898}, {3974, 52410}, {4565, 50494}, {7102, 52411}, {7103, 52425}, {7197, 14827}
X(64989) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 54416}, {2, 2285}, {9, 1460}, {11, 2484}, {1146, 8678}, {1214, 8898}, {3160, 4320}, {3161, 612}, {6337, 1038}, {6376, 388}, {6505, 2286}, {6626, 5323}, {9296, 14594}, {38991, 8646}, {40582, 44119}, {40593, 7365}, {40605, 2303}, {40618, 51644}, {40624, 6590}, {40626, 2522}, {55064, 50494}, {59608, 10376}, {59619, 5286}, {62584, 5227}, {62585, 2345}, {62602, 7103}, {62647, 7085}
X(64989) = X(i)-cross conjugate of X(j) for these {i, j}: {11679, 75}, {30479, 57923}
X(64989) = pole of line {1038, 2285} with respect to the Wallace hyperbola
X(64989) = pole of line {2522, 51644} with respect to the dual conic of polar circle
X(64989) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(57), X(1829)}}, {{A, B, C, X(75), X(20911)}}, {{A, B, C, X(76), X(304)}}, {{A, B, C, X(274), X(3596)}}, {{A, B, C, X(318), X(52652)}}, {{A, B, C, X(429), X(60245)}}, {{A, B, C, X(960), X(39957)}}, {{A, B, C, X(961), X(9311)}}, {{A, B, C, X(1039), X(2339)}}, {{A, B, C, X(1880), X(2082)}}, {{A, B, C, X(2998), X(4451)}}, {{A, B, C, X(4110), X(52136)}}, {{A, B, C, X(4673), X(18157)}}, {{A, B, C, X(7058), X(52406)}}, {{A, B, C, X(7101), X(17788)}}, {{A, B, C, X(7131), X(42485)}}, {{A, B, C, X(11679), X(60084)}}, {{A, B, C, X(14829), X(20928)}}, {{A, B, C, X(20567), X(57921)}}, {{A, B, C, X(20570), X(57906)}}, {{A, B, C, X(20925), X(33939)}}, {{A, B, C, X(40014), X(57773)}}, {{A, B, C, X(40072), X(58013)}}, {{A, B, C, X(40827), X(57980)}}, {{A, B, C, X(45032), X(57725)}}, {{A, B, C, X(57783), X(57853)}}
X(64989) = barycentric product X(i)*X(j) for these (i, j): {333, 60197}, {522, 54982}, {1036, 561}, {1039, 305}, {1245, 40072}, {1310, 35519}, {1472, 40363}, {2082, 40831}, {2221, 28659}, {2339, 76}, {3596, 56328}, {28660, 56219}, {30479, 75}, {37215, 4391}, {57923, 8}
X(64989) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1460}, {2, 2285}, {7, 4320}, {8, 612}, {9, 54416}, {21, 44119}, {29, 4206}, {63, 2286}, {69, 1038}, {75, 388}, {78, 7085}, {85, 7365}, {86, 5323}, {226, 8898}, {253, 10375}, {273, 7103}, {304, 56367}, {312, 2345}, {314, 1010}, {318, 7102}, {333, 2303}, {341, 3974}, {345, 5227}, {522, 8678}, {650, 2484}, {663, 8646}, {668, 14594}, {1036, 31}, {1039, 25}, {1040, 19459}, {1088, 7197}, {1245, 1402}, {1310, 109}, {1472, 1397}, {2082, 1184}, {2221, 604}, {2339, 6}, {3596, 4385}, {3668, 10376}, {3718, 54433}, {4025, 51644}, {4041, 50494}, {4086, 48395}, {4329, 8900}, {4391, 6590}, {6332, 2522}, {11679, 34261}, {14258, 45126}, {17880, 26933}, {18155, 47844}, {30479, 1}, {35518, 23874}, {35519, 2517}, {36099, 32674}, {37215, 651}, {40072, 44154}, {41791, 40184}, {51686, 1395}, {54982, 664}, {56219, 1400}, {56328, 56}, {56841, 2354}, {57919, 19799}, {57923, 7}, {60197, 226}, {63195, 7131}

X(64990) = 1ST BASEPOINT OF THE FEUERBACH TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+3*b*c+c^2))*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+3*b*c+c^2)) : :

X(64990) lies on these lines: {2, 64991}, {7, 498}, {8, 57883}, {12, 7279}, {27, 37799}, {75, 27529}, {86, 40999}, {673, 7332}, {903, 55096}, {1442, 3584}, {1447, 39723}, {3085, 7318}, {5936, 26364}, {7179, 39728}, {10198, 28626}, {14621, 28780}, {26125, 39720}, {28741, 60873}, {55937, 60943}

X(64990) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 26842}, {55, 3337}, {2150, 5949}, {2194, 11263}, {3737, 21784}, {6186, 52126}
X(64990) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 3337}, {1214, 11263}, {3160, 26842}, {56325, 5949}
X(64990) = X(i)-cross conjugate of X(j) for these {i, j}: {7269, 7}, {31947, 651}, {44824, 100}
X(64990) = pole of line {7269, 64990} with respect to the dual conic of Yff parabola
X(64990) = pole of line {2895, 6358} with respect to the dual conic of Moses-Feuerbach circumconic
X(64990) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3336)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(498)}}, {{A, B, C, X(37), X(59)}}, {{A, B, C, X(79), X(60173)}}, {{A, B, C, X(95), X(54121)}}, {{A, B, C, X(281), X(55920)}}, {{A, B, C, X(451), X(37294)}}, {{A, B, C, X(693), X(40410)}}, {{A, B, C, X(1002), X(2165)}}, {{A, B, C, X(1037), X(39983)}}, {{A, B, C, X(1224), X(17097)}}, {{A, B, C, X(1441), X(4998)}}, {{A, B, C, X(1442), X(7045)}}, {{A, B, C, X(2346), X(7110)}}, {{A, B, C, X(2963), X(13476)}}, {{A, B, C, X(3085), X(5552)}}, {{A, B, C, X(3616), X(26364)}}, {{A, B, C, X(5397), X(11604)}}, {{A, B, C, X(5553), X(60163)}}, {{A, B, C, X(5556), X(60164)}}, {{A, B, C, X(5561), X(54727)}}, {{A, B, C, X(7179), X(28780)}}, {{A, B, C, X(7279), X(16577)}}, {{A, B, C, X(7319), X(60158)}}, {{A, B, C, X(8047), X(20565)}}, {{A, B, C, X(8048), X(36948)}}, {{A, B, C, X(8797), X(13577)}}, {{A, B, C, X(9436), X(61017)}}, {{A, B, C, X(9780), X(10198)}}, {{A, B, C, X(10309), X(60162)}}, {{A, B, C, X(20566), X(54454)}}, {{A, B, C, X(25430), X(56287)}}, {{A, B, C, X(34585), X(43947)}}, {{A, B, C, X(37741), X(56232)}}, {{A, B, C, X(39977), X(52377)}}, {{A, B, C, X(40216), X(57882)}}, {{A, B, C, X(40419), X(57830)}}, {{A, B, C, X(40999), X(60188)}}, {{A, B, C, X(43666), X(61105)}}, {{A, B, C, X(52392), X(57865)}}, {{A, B, C, X(56228), X(63192)}}, {{A, B, C, X(58007), X(63173)}}
X(64990) = barycentric product X(i)*X(j) for these (i, j): {4552, 7372}, {4998, 7332}, {7161, 85}, {64991, 75}
X(64990) = barycentric quotient X(i)/X(j) for these (i, j): {7, 26842}, {12, 5949}, {57, 3337}, {226, 11263}, {2594, 50657}, {3219, 52126}, {4552, 6758}, {4559, 21784}, {6354, 56849}, {6358, 42005}, {7161, 9}, {7332, 11}, {7372, 4560}, {21859, 21891}, {23067, 23084}, {55197, 12071}, {64991, 1}

X(64991) = 2ND BASEPOINT OF THE FEUERBACH TRIANGLE WRT ABC

Barycentrics    a*(a+b-c)*(a-b+c)*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+3*b*c+c^2))*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+3*b*c+c^2)) : :

X(64991) lies on these lines: {1, 7161}, {2, 64990}, {9, 56041}, {12, 5947}, {28, 1825}, {57, 21773}, {81, 16577}, {88, 26740}, {226, 21907}, {386, 51500}, {2003, 62210}, {2006, 7332}, {2171, 40143}, {2594, 30602}, {6354, 52374}, {7146, 52123}, {30144, 59760}

X(64991) = trilinear pole of line {42649, 513}
X(64991) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 3337}, {55, 26842}, {60, 5949}, {284, 11263}, {2150, 42005}, {2160, 52126}, {3615, 50657}, {4560, 21784}, {4636, 17422}, {6758, 7252}, {7054, 56849}
X(64991) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 26842}, {478, 3337}, {40590, 11263}, {56325, 42005}
X(64991) = X(i)-Ceva conjugate of X(j) for these {i, j}: {64990, 7161}
X(64991) = X(i)-cross conjugate of X(j) for these {i, j}: {52423, 57}, {55197, 4551}
X(64991) = pole of line {7161, 61105} with respect to the dual conic of Yff parabola
X(64991) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(6), X(7130)}}, {{A, B, C, X(42), X(2149)}}, {{A, B, C, X(58), X(37509)}}, {{A, B, C, X(189), X(14497)}}, {{A, B, C, X(226), X(4564)}}, {{A, B, C, X(312), X(6596)}}, {{A, B, C, X(998), X(39523)}}, {{A, B, C, X(1174), X(7073)}}, {{A, B, C, X(1262), X(2003)}}, {{A, B, C, X(1389), X(55987)}}, {{A, B, C, X(1825), X(6354)}}, {{A, B, C, X(2051), X(2167)}}, {{A, B, C, X(2185), X(14554)}}, {{A, B, C, X(2219), X(56232)}}, {{A, B, C, X(2320), X(60107)}}, {{A, B, C, X(2334), X(53995)}}, {{A, B, C, X(2994), X(21398)}}, {{A, B, C, X(3065), X(55027)}}, {{A, B, C, X(4567), X(34527)}}, {{A, B, C, X(5256), X(30144)}}, {{A, B, C, X(5287), X(30147)}}, {{A, B, C, X(6198), X(52062)}}, {{A, B, C, X(7161), X(34531)}}, {{A, B, C, X(15446), X(60155)}}, {{A, B, C, X(31629), X(37558)}}, {{A, B, C, X(41434), X(57418)}}, {{A, B, C, X(44178), X(56033)}}
X(64991) = barycentric product X(i)*X(j) for these (i, j): {1, 64990}, {7, 7161}, {4551, 7372}, {4564, 7332}
X(64991) = barycentric quotient X(i)/X(j) for these (i, j): {12, 42005}, {35, 52126}, {56, 3337}, {57, 26842}, {65, 11263}, {1254, 56849}, {2171, 5949}, {4551, 6758}, {7161, 8}, {7332, 4858}, {7372, 18155}, {14882, 13089}, {21741, 50657}, {57185, 17422}, {64990, 75}

X(64992) = 2ND BASEPOINT OF THE HATZIPOLAKIS-MOSES TRIANGLE WRT ABC

Barycentrics    (a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2))*(a^10-3*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+a^6*(2*b^4+b^2*c^2+2*c^4)-a^2*(b^2-c^2)^2*(3*b^4+b^2*c^2+3*c^4)+2*a^4*(b^6+c^6)) : :

X(64992) lies on these lines: {2, 95}, {54, 11225}, {94, 53028}, {252, 7512}, {343, 18315}, {1157, 7552}, {1658, 8884}, {6515, 63172}, {7488, 52677}, {10125, 19210}, {10298, 61440}, {19176, 37922}, {19179, 45735}, {38444, 59275}, {46724, 63763}

X(64992) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1953, 42059}
X(64992) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(58805)}}, {{A, B, C, X(13585), X(59492)}}, {{A, B, C, X(14918), X(42410)}}
X(64992) = barycentric product X(i)*X(j) for these (i, j): {58805, 95}
X(64992) = barycentric quotient X(i)/X(j) for these (i, j): {54, 42059}, {933, 6799}, {58805, 5}, {59492, 1263}

X(64993) = 1ST BASEPOINT OF THE 2ND HATZIPOLAKIS TRIANGLE WRT ABC

Barycentrics    b*(-a+b-c)^2*(a+b-c)^2*c*(-a^2+b^2-c^2)*(a^2+b^2-c^2)*(2*a^3+2*b^3+b^2*c+c^3+a^2*(-2*b+c)-2*a*b*(b+c))*(2*a^3+b^3+a^2*(b-2*c)+b*c^2+2*c^3-2*a*c*(b+c)) : :

X(64993) lies on these lines: {1119, 1265}

X(64993) = isotomic conjugate of X(42018)
X(64993) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42018}, {657, 35350}, {1802, 17054}, {1946, 35349}, {9581, 52425}
X(64993) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42018}, {39053, 35349}, {62602, 9581}
X(64993) = X(i)-cross conjugate of X(j) for these {i, j}: {4462, 18026}, {14743, 2}
X(64993) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1265)}}, {{A, B, C, X(85), X(264)}}, {{A, B, C, X(95), X(348)}}, {{A, B, C, X(276), X(20569)}}, {{A, B, C, X(277), X(1105)}}, {{A, B, C, X(279), X(55346)}}, {{A, B, C, X(673), X(18848)}}, {{A, B, C, X(14743), X(42018)}}, {{A, B, C, X(17054), X(29162)}}, {{A, B, C, X(20568), X(52581)}}, {{A, B, C, X(40411), X(40420)}}, {{A, B, C, X(40414), X(63164)}}, {{A, B, C, X(42326), X(56261)}}, {{A, B, C, X(42330), X(56044)}}
X(64993) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42018}, {273, 9581}, {653, 35349}, {934, 35350}, {1119, 17054}, {1847, 23681}

X(64994) = 2ND BASEPOINT OF THE HUTSON EXTOUCH TRIANGLE WRT ABC

Barycentrics    b*(-a+b-c)^2*(a+b-c)^2*c*(3*a^3+a*(b-c)^2-5*a^2*(b+c)+(b-c)^2*(b+c)) : :

X(64994) lies on these lines: {2, 85}, {7, 5918}, {57, 10509}, {269, 14828}, {553, 47374}, {3668, 62697}, {4350, 21453}, {5435, 53242}, {19804, 57792}, {21454, 50561}, {34018, 50392}, {56309, 62793}

X(64994) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 42015}, {220, 10579}, {657, 6575}, {6602, 63459}
X(64994) = X(i)-Dao conjugate of X(j) for these {i, j}: {3160, 42015}
X(64994) = X(i)-cross conjugate of X(j) for these {i, j}: {52817, 7}
X(64994) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10509)}}, {{A, B, C, X(57), X(1212)}}, {{A, B, C, X(189), X(30695)}}, {{A, B, C, X(8713), X(44664)}}, {{A, B, C, X(23062), X(59181)}}, {{A, B, C, X(31627), X(34521)}}
X(64994) = barycentric product X(i)*X(j) for these (i, j): {4569, 8713}, {10578, 1088}, {14282, 36838}, {14324, 4635}, {60939, 85}
X(64994) = barycentric quotient X(i)/X(j) for these (i, j): {7, 42015}, {269, 10579}, {479, 63459}, {934, 6575}, {8713, 3900}, {10578, 200}, {14282, 4130}, {14324, 4171}, {52817, 15853}, {60939, 9}
X(64994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1088, 17093, 85}

X(64995) = 1ST BASEPOINT OF THE INCIRCLE-CIRCLES TRIANGLE WRT ABC

Barycentrics    b*c*(a^2+4*a*b+b^2-c^2)*(-a^2+b^2-4*a*c-c^2) : :

X(64995) lies on these lines: {2, 17092}, {8, 443}, {29, 17194}, {57, 40435}, {63, 32008}, {75, 4102}, {92, 142}, {226, 65029}, {312, 1269}, {333, 3306}, {342, 40165}, {894, 55988}, {3911, 56062}, {4666, 14942}, {4674, 36596}, {4997, 31266}, {5437, 34234}, {6557, 27827}, {7020, 62605}, {10436, 56224}, {16352, 52133}, {17400, 52381}, {17862, 59374}, {18359, 27186}, {19804, 42030}, {20924, 64989}, {20925, 28660}, {24564, 31359}, {26627, 40394}, {28605, 56086}, {30807, 56054}, {30852, 42339}, {30854, 32015}, {40013, 46937}, {46938, 56075}, {56201, 62773}

X(64995) = isotomic conjugate of X(3305)
X(64995) = trilinear pole of line {4905, 4978}
X(64995) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3295}, {25, 55466}, {31, 3305}, {32, 42696}, {41, 7190}, {55, 52424}, {101, 48340}, {110, 58299}, {213, 63158}, {692, 47965}, {1333, 3697}, {1397, 42032}, {2174, 56843}, {2175, 52422}, {2193, 53861}, {4917, 38266}, {32739, 48268}, {34446, 63128}, {34819, 51572}
X(64995) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3305}, {9, 3295}, {37, 3697}, {223, 52424}, {244, 58299}, {1015, 48340}, {1086, 47965}, {3160, 7190}, {6376, 42696}, {6505, 55466}, {6626, 63158}, {40593, 52422}, {40619, 48268}, {47345, 53861}, {62585, 42032}, {62648, 51572}
X(64995) = X(i)-cross conjugate of X(j) for these {i, j}: {1698, 75}, {10980, 1088}, {21620, 7}
X(64995) = pole of line {3305, 63158} with respect to the Wallace hyperbola
X(64995) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3555)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(7), X(9776)}}, {{A, B, C, X(27), X(277)}}, {{A, B, C, X(57), X(942)}}, {{A, B, C, X(63), X(142)}}, {{A, B, C, X(75), X(873)}}, {{A, B, C, X(81), X(3873)}}, {{A, B, C, X(86), X(13577)}}, {{A, B, C, X(88), X(44733)}}, {{A, B, C, X(95), X(55106)}}, {{A, B, C, X(226), X(3306)}}, {{A, B, C, X(273), X(57831)}}, {{A, B, C, X(274), X(40012)}}, {{A, B, C, X(278), X(1056)}}, {{A, B, C, X(279), X(11037)}}, {{A, B, C, X(304), X(25526)}}, {{A, B, C, X(309), X(28626)}}, {{A, B, C, X(321), X(40014)}}, {{A, B, C, X(334), X(57923)}}, {{A, B, C, X(469), X(17581)}}, {{A, B, C, X(514), X(25430)}}, {{A, B, C, X(673), X(60156)}}, {{A, B, C, X(693), X(56074)}}, {{A, B, C, X(870), X(57925)}}, {{A, B, C, X(908), X(5437)}}, {{A, B, C, X(1088), X(40216)}}, {{A, B, C, X(1255), X(9311)}}, {{A, B, C, X(1441), X(58001)}}, {{A, B, C, X(1751), X(42326)}}, {{A, B, C, X(2051), X(39963)}}, {{A, B, C, X(2094), X(59374)}}, {{A, B, C, X(2167), X(7131)}}, {{A, B, C, X(2185), X(55985)}}, {{A, B, C, X(2186), X(65027)}}, {{A, B, C, X(2339), X(2349)}}, {{A, B, C, X(2985), X(32019)}}, {{A, B, C, X(3218), X(27186)}}, {{A, B, C, X(3305), X(4866)}}, {{A, B, C, X(3911), X(31266)}}, {{A, B, C, X(3912), X(4666)}}, {{A, B, C, X(4564), X(56041)}}, {{A, B, C, X(4935), X(18743)}}, {{A, B, C, X(5294), X(17282)}}, {{A, B, C, X(5936), X(41915)}}, {{A, B, C, X(6063), X(32021)}}, {{A, B, C, X(6336), X(56218)}}, {{A, B, C, X(6384), X(58013)}}, {{A, B, C, X(6692), X(30852)}}, {{A, B, C, X(7017), X(62927)}}, {{A, B, C, X(7101), X(7110)}}, {{A, B, C, X(7224), X(55967)}}, {{A, B, C, X(9258), X(65026)}}, {{A, B, C, X(10436), X(54311)}}, {{A, B, C, X(11024), X(57826)}}, {{A, B, C, X(11679), X(24564)}}, {{A, B, C, X(13478), X(64329)}}, {{A, B, C, X(15474), X(60169)}}, {{A, B, C, X(16352), X(31909)}}, {{A, B, C, X(17184), X(26627)}}, {{A, B, C, X(17923), X(20924)}}, {{A, B, C, X(18032), X(56212)}}, {{A, B, C, X(18140), X(46937)}}, {{A, B, C, X(19804), X(28605)}}, {{A, B, C, X(20568), X(34258)}}, {{A, B, C, X(20569), X(30710)}}, {{A, B, C, X(25525), X(59491)}}, {{A, B, C, X(26060), X(60258)}}, {{A, B, C, X(27003), X(31019)}}, {{A, B, C, X(27483), X(40025)}}, {{A, B, C, X(30598), X(40716)}}, {{A, B, C, X(30663), X(56329)}}, {{A, B, C, X(30829), X(46938)}}, {{A, B, C, X(31623), X(52147)}}, {{A, B, C, X(33078), X(37202)}}, {{A, B, C, X(34860), X(39747)}}, {{A, B, C, X(36124), X(60165)}}, {{A, B, C, X(37887), X(60085)}}, {{A, B, C, X(39700), X(39706)}}, {{A, B, C, X(39962), X(60071)}}, {{A, B, C, X(39981), X(45965)}}, {{A, B, C, X(40026), X(60097)}}, {{A, B, C, X(40027), X(51865)}}, {{A, B, C, X(40044), X(60082)}}, {{A, B, C, X(40843), X(63154)}}, {{A, B, C, X(41867), X(54357)}}, {{A, B, C, X(42318), X(60168)}}, {{A, B, C, X(56033), X(56230)}}, {{A, B, C, X(56051), X(60084)}}, {{A, B, C, X(57785), X(59255)}}, {{A, B, C, X(57792), X(59764)}}
X(64995) = barycentric product X(i)*X(j) for these (i, j): {312, 65028}, {561, 61375}, {3296, 75}, {20925, 52188}, {30679, 92}
X(64995) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3295}, {2, 3305}, {7, 7190}, {10, 3697}, {57, 52424}, {63, 55466}, {75, 42696}, {79, 56843}, {85, 52422}, {86, 63158}, {145, 4917}, {225, 53861}, {312, 42032}, {513, 48340}, {514, 47965}, {661, 58299}, {693, 48268}, {1698, 51572}, {3296, 1}, {3306, 63128}, {5119, 7086}, {7284, 6580}, {20925, 46951}, {30679, 63}, {61375, 31}, {65028, 57}

X(64996) = 1ST BASEPOINT OF THE JENKINS-CONTACT TRIANGLE WRT ABC

Barycentrics    b^2*c^2*(a^4-2*a^2*b^2+a^3*c-a*b*c^2+b^3*(b+c))*(-a^4-a^3*b+a*b^2*c+2*a^2*c^2-c^3*(b+c)) : :

X(64996) lies on these lines: {239, 30022}, {305, 1447}, {28660, 31905}

X(64996) = X(i)-cross conjugate of X(j) for these {i, j}: {24560, 799}
X(64996) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(239)}}, {{A, B, C, X(7), X(3210)}}, {{A, B, C, X(305), X(561)}}, {{A, B, C, X(310), X(30022)}}, {{A, B, C, X(757), X(18147)}}, {{A, B, C, X(7034), X(34384)}}
X(64996) = barycentric quotient X(i)/X(j) for these (i, j): {3596, 38406}, {28660, 14011}

X(64997) = 1ST BASEPOINT OF THE 1ST JENKINS TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(-(b^2*(b-c)*(b+c)^2)+a^3*(b^2+2*b*c+2*c^2)+a*b*(-b^3-2*b^2*c+b*c^2+2*c^3)+a^2*(b^3+b^2*c+2*b*c^2+2*c^3))*((b-c)*c^2*(b+c)^2+a^3*(2*b^2+2*b*c+c^2)+a*c*(2*b^3+b^2*c-2*b*c^2-c^3)+a^2*(2*b^3+2*b^2*c+b*c^2+c^3)) : :

X(64997) lies on these lines: {2, 970}, {27, 1193}, {73, 64984}, {86, 22097}, {306, 1240}, {675, 59066}, {1393, 44733}, {1817, 14621}, {4225, 56047}, {4417, 57824}, {31909, 64988}

X(64997) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 13323}
X(64997) = X(i)-Dao conjugate of X(j) for these {i, j}: {40589, 13323}
X(64997) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(57), X(10441)}}, {{A, B, C, X(58), X(970)}}, {{A, B, C, X(73), X(306)}}, {{A, B, C, X(81), X(28660)}}, {{A, B, C, X(92), X(959)}}, {{A, B, C, X(256), X(37865)}}, {{A, B, C, X(312), X(5331)}}, {{A, B, C, X(469), X(4225)}}, {{A, B, C, X(1393), X(17167)}}, {{A, B, C, X(1817), X(31909)}}, {{A, B, C, X(60172), X(62185)}}
X(64997) = barycentric product X(i)*X(j) for these (i, j): {3261, 59066}, {3597, 86}
X(64997) = barycentric quotient X(i)/X(j) for these (i, j): {58, 13323}, {3597, 10}, {59066, 101}

X(64998) = 1ST BASEPOINT OF THE LUCAS INNER TRIANGLE WRT ABC

Barycentrics    12*a^4-42*a^2*(b^2+c^2)+5*(2*b^4-9*b^2*c^2+2*c^4)-8*(4*a^2+5*(b^2+c^2))*S : :

X(64998) lies on the Kiepert hyperbola and on these lines: {1131, 6566}, {1151, 6568}, {51128, 64999}, {60315, 63121}

X(64998) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(1151)}}
X(64998) = barycentric quotient X(i)/X(j) for these (i, j): {1151, 32563}

X(64999) = 1ST BASEPOINT OF THE LUCAS(-1) INNER TRIANGLE WRT ABC

Barycentrics    12*a^4-42*a^2*(b^2+c^2)+5*(2*b^4-9*b^2*c^2+2*c^4)+8*(4*a^2+5*(b^2+c^2))*S : :

X(64999) lies on the Kiepert hyperbola and on these lines: {1132, 6567}, {1152, 6569}, {51128, 64998}, {60316, 63121}

X(64999) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(1152)}}
X(64999) = barycentric quotient X(i)/X(j) for these (i, j): {1152, 32570}

X(65000) = 2ND BASEPOINT OF THE MANDART-EXCIRCLES TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^4-2*a^2*(b-c)^2+(b^2-c^2)^2) : :

X(65000) lies on these lines: {1, 45655}, {2, 7}, {4, 10305}, {8, 18419}, {11, 64130}, {20, 34489}, {55, 21151}, {56, 4295}, {65, 1056}, {145, 10940}, {165, 60924}, {189, 4858}, {196, 37790}, {222, 4000}, {223, 24177}, {269, 34052}, {278, 1086}, {376, 1319}, {388, 3753}, {497, 3660}, {938, 37437}, {942, 6850}, {954, 15804}, {962, 1420}, {1119, 55110}, {1122, 46017}, {1408, 31900}, {1429, 7125}, {1462, 57494}, {1466, 3487}, {1467, 4292}, {1519, 3086}, {1565, 55117}, {1617, 3474}, {1767, 5236}, {1770, 18223}, {1788, 17757}, {1836, 59386}, {1851, 3937}, {1864, 36996}, {2003, 5222}, {2006, 65002}, {2078, 9778}, {2096, 57278}, {2550, 17625}, {3256, 10578}, {3339, 10039}, {3340, 11037}, {3475, 37541}, {3476, 11112}, {3488, 37430}, {3560, 24470}, {3600, 4861}, {3916, 7288}, {4310, 8270}, {4331, 61376}, {4644, 52424}, {4862, 64708}, {5083, 36845}, {5173, 10569}, {5265, 11415}, {5708, 6842}, {5714, 6975}, {5758, 15803}, {5766, 34881}, {5805, 64207}, {5880, 63994}, {6180, 40688}, {6223, 9581}, {6358, 31995}, {6875, 34880}, {6893, 57282}, {6941, 57285}, {6961, 37582}, {7055, 10030}, {7677, 44447}, {9364, 33144}, {9578, 11024}, {9580, 64696}, {9782, 41824}, {9785, 63208}, {9841, 12053}, {10309, 64658}, {10382, 43177}, {10580, 60925}, {10589, 17618}, {10711, 12832}, {10980, 60923}, {11019, 60896}, {12115, 18391}, {14450, 41547}, {15934, 28458}, {17074, 19785}, {17366, 62207}, {17604, 41706}, {17642, 35514}, {22464, 63584}, {22759, 52783}, {23681, 34050}, {24231, 60786}, {26871, 53994}, {26914, 31387}, {30623, 40154}, {33146, 57477}, {34855, 56873}, {37022, 41426}, {37583, 55109}, {37736, 64146}, {41777, 44708}, {44675, 52027}, {52635, 62693}, {56848, 62787}

X(65000) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 42019}, {55, 56354}, {200, 53995}, {220, 56287}, {1253, 34401}
X(65000) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 56354}, {478, 42019}, {3554, 2057}, {6609, 53995}, {17113, 34401}, {38015, 8}, {38357, 57049}, {40650, 13458}, {49171, 9}
X(65000) = X(i)-Ceva conjugate of X(j) for these {i, j}: {7, 63962}, {54240, 3669}
X(65000) = X(i)-cross conjugate of X(j) for these {i, j}: {3554, 3086}, {45639, 7}
X(65000) = pole of line {1058, 12675} with respect to the Feuerbach hyperbola
X(65000) = pole of line {241, 514} with respect to the dual conic of Mandart circle
X(65000) = pole of line {1, 10309} with respect to the dual conic of Yff parabola
X(65000) = pole of line {7, 15297} with respect to the dual conic of Moses-Feuerbach circumconic
X(65000) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3086)}}, {{A, B, C, X(9), X(3554)}}, {{A, B, C, X(63), X(10305)}}, {{A, B, C, X(189), X(56941)}}, {{A, B, C, X(269), X(56544)}}, {{A, B, C, X(278), X(908)}}, {{A, B, C, X(279), X(5905)}}, {{A, B, C, X(738), X(40212)}}, {{A, B, C, X(1119), X(7013)}}, {{A, B, C, X(1412), X(56549)}}, {{A, B, C, X(1422), X(49171)}}, {{A, B, C, X(2006), X(30827)}}, {{A, B, C, X(2982), X(55871)}}, {{A, B, C, X(3218), X(65002)}}, {{A, B, C, X(5257), X(24005)}}, {{A, B, C, X(13437), X(52419)}}, {{A, B, C, X(13459), X(52420)}}, {{A, B, C, X(23062), X(61010)}}, {{A, B, C, X(24029), X(32714)}}, {{A, B, C, X(28609), X(52374)}}, {{A, B, C, X(30852), X(45098)}}, {{A, B, C, X(33864), X(39732)}}, {{A, B, C, X(34401), X(45639)}}
X(65000) = barycentric product X(i)*X(j) for these (i, j): {273, 63399}, {279, 53994}, {1014, 17869}, {1088, 30223}, {1434, 24005}, {1440, 63962}, {3086, 7}, {3554, 85}, {13437, 40650}, {26871, 278}, {54284, 57}
X(65000) = barycentric quotient X(i)/X(j) for these (i, j): {56, 42019}, {57, 56354}, {269, 56287}, {279, 34401}, {1407, 53995}, {1440, 34413}, {1519, 6735}, {3086, 8}, {3554, 9}, {17869, 3701}, {19354, 1260}, {24005, 2321}, {26871, 345}, {26955, 3695}, {30223, 200}, {40650, 13425}, {45639, 26364}, {49171, 2057}, {53994, 346}, {54284, 312}, {63399, 78}, {63962, 7080}
X(65000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 5435, 5905}, {7, 9776, 226}, {1086, 1407, 278}, {1617, 24465, 3474}, {8732, 9965, 1708}, {24177, 62789, 223}, {26871, 54284, 53994}

X(65001) = 2ND BASEPOINT OF THE MCCAY TRIANGLE WRT ABC

Barycentrics    (2*a^4+2*b^4-3*b^2*c^2+c^4-a^2*(2*b^2+3*c^2))*(5*a^4+2*b^4-5*b^2*c^2+2*c^4-2*a^2*(b^2+c^2))*(2*a^4+b^4-3*b^2*c^2+2*c^4-a^2*(3*b^2+2*c^2)) : :

X(65001) lies on these lines: {2, 575}, {14567, 59007}, {22329, 35178}

X(65001) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8859)}}, {{A, B, C, X(98), X(64802)}}, {{A, B, C, X(1383), X(9716)}}, {{A, B, C, X(3292), X(38279)}}, {{A, B, C, X(7608), X(15850)}}, {{A, B, C, X(8787), X(37860)}}, {{A, B, C, X(10415), X(38397)}}, {{A, B, C, X(34507), X(52192)}}
X(65001) = barycentric product X(i)*X(j) for these (i, j): {7607, 8859}
X(65001) = barycentric quotient X(i)/X(j) for these (i, j): {7607, 42010}

X(65002) = 2ND BASEPOINT OF THE 3RD MIXTILINEAR TRIANGLE WRT ABC

Barycentrics    a*(a+b-c)^2*(a-b+c)^2*(2*a^2+2*b^2+b*c-c^2+a*(-4*b+c))*(2*a^2-b^2+a*(b-4*c)+b*c+2*c^2) : :

X(65002) lies on these lines: {1, 18419}, {2, 55989}, {56, 32075}, {88, 1407}, {241, 56355}, {269, 36603}, {1262, 5376}, {1427, 26745}, {2006, 65000}, {2990, 23958}, {3218, 56354}, {8056, 37789}, {18811, 30710}, {32017, 34523}

X(65002) = isogonal conjugate of X(34524)
X(65002) = trilinear pole of line {46004, 513}
X(65002) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 34524}, {9, 2098}, {55, 30827}, {220, 4862}, {341, 34543}, {346, 32577}, {480, 47444}, {2316, 44784}, {3699, 17424}
X(65002) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 34524}, {223, 30827}, {478, 2098}
X(65002) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65004, 63163}
X(65002) = X(i)-cross conjugate of X(j) for these {i, j}: {51656, 934}
X(65002) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(189), X(34529)}}, {{A, B, C, X(346), X(8602)}}, {{A, B, C, X(479), X(7045)}}, {{A, B, C, X(1262), X(1407)}}, {{A, B, C, X(4564), X(5435)}}, {{A, B, C, X(18419), X(42304)}}, {{A, B, C, X(43760), X(60831)}}
X(65002) = barycentric product X(i)*X(j) for these (i, j): {1, 65004}, {57, 63167}, {279, 55989}, {1407, 34523}, {18811, 56}, {46004, 6613}, {63163, 7}
X(65002) = barycentric quotient X(i)/X(j) for these (i, j): {6, 34524}, {56, 2098}, {57, 30827}, {269, 4862}, {738, 47444}, {1106, 32577}, {1319, 44784}, {18811, 3596}, {34523, 59761}, {41426, 15347}, {46004, 42337}, {52410, 34543}, {55989, 346}, {57181, 17424}, {63163, 8}, {63167, 312}, {65004, 75}

X(65003) = 2ND BASEPOINT OF THE 4TH MIXTILINEAR TRIANGLE WRT ABC

Barycentrics    a*(a+b-c)*(a-b+c)*(2*a^2+2*b^2-b*c-c^2-a*(4*b+c))*(2*a^2-b^2-b*c+2*c^2-a*(b+4*c)) : :

X(65003) lies on these lines: {1, 37787}, {2, 6603}, {6, 34056}, {7, 15730}, {55, 32076}, {57, 1055}, {88, 5228}, {89, 241}, {105, 2099}, {277, 30275}, {279, 4644}, {663, 35348}, {948, 21907}, {955, 24929}, {1002, 1319}, {1323, 60951}, {1388, 55087}, {1708, 39948}, {2006, 5222}, {3227, 60856}, {4511, 39959}, {5226, 37887}, {5526, 60944}, {5543, 42326}, {12848, 62705}, {18473, 40269}, {18810, 34018}, {34051, 62797}, {43052, 62635}, {45043, 53014}

X(65003) = isogonal conjugate of X(34522)
X(65003) = trilinear pole of line {6139, 43050}
X(65003) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 34522}, {6, 5231}, {7, 32578}, {9, 4860}, {55, 6173}, {57, 42014}, {220, 21314}, {664, 17425}, {2291, 44785}, {8012, 58809}
X(65003) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 34522}, {9, 5231}, {223, 6173}, {478, 4860}, {5452, 42014}, {39025, 17425}
X(65003) = X(i)-Ceva conjugate of X(j) for these {i, j}: {63166, 55920}
X(65003) = pole of line {55920, 61008} with respect to the dual conic of Yff parabola
X(65003) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(55986)}}, {{A, B, C, X(6), X(663)}}, {{A, B, C, X(7), X(4564)}}, {{A, B, C, X(9), X(60975)}}, {{A, B, C, X(21), X(60092)}}, {{A, B, C, X(63), X(45100)}}, {{A, B, C, X(104), X(55937)}}, {{A, B, C, X(241), X(2099)}}, {{A, B, C, X(294), X(4644)}}, {{A, B, C, X(514), X(14497)}}, {{A, B, C, X(598), X(5385)}}, {{A, B, C, X(673), X(2320)}}, {{A, B, C, X(997), X(17014)}}, {{A, B, C, X(1016), X(56314)}}, {{A, B, C, X(1126), X(56005)}}, {{A, B, C, X(1156), X(54622)}}, {{A, B, C, X(1171), X(53995)}}, {{A, B, C, X(1174), X(4845)}}, {{A, B, C, X(1319), X(5228)}}, {{A, B, C, X(1320), X(39273)}}, {{A, B, C, X(1389), X(10405)}}, {{A, B, C, X(1392), X(9311)}}, {{A, B, C, X(1411), X(42290)}}, {{A, B, C, X(1434), X(63163)}}, {{A, B, C, X(1445), X(30275)}}, {{A, B, C, X(2161), X(40779)}}, {{A, B, C, X(3512), X(41446)}}, {{A, B, C, X(3577), X(36101)}}, {{A, B, C, X(4511), X(5222)}}, {{A, B, C, X(4567), X(55989)}}, {{A, B, C, X(7131), X(17097)}}, {{A, B, C, X(7319), X(55965)}}, {{A, B, C, X(8545), X(12848)}}, {{A, B, C, X(10509), X(56028)}}, {{A, B, C, X(18421), X(59215)}}, {{A, B, C, X(20007), X(54369)}}, {{A, B, C, X(29624), X(54318)}}, {{A, B, C, X(36605), X(56152)}}, {{A, B, C, X(37131), X(55948)}}, {{A, B, C, X(42317), X(52663)}}, {{A, B, C, X(52896), X(60856)}}, {{A, B, C, X(55918), X(60094)}}, {{A, B, C, X(55920), X(55954)}}, {{A, B, C, X(55964), X(60155)}}, {{A, B, C, X(55985), X(60170)}}, {{A, B, C, X(55987), X(60167)}}, {{A, B, C, X(56027), X(60075)}}, {{A, B, C, X(56049), X(63150)}}, {{A, B, C, X(60944), X(60951)}}
X(65003) = barycentric product X(i)*X(j) for these (i, j): {1, 63166}, {220, 34521}, {18810, 55}, {46003, 6606}, {55920, 7}, {55954, 57}, {58105, 693}
X(65003) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5231}, {6, 34522}, {41, 32578}, {55, 42014}, {56, 4860}, {57, 6173}, {269, 21314}, {1155, 44785}, {3063, 17425}, {18810, 6063}, {34521, 57792}, {37541, 15346}, {46003, 6362}, {55920, 8}, {55954, 312}, {58105, 100}, {61373, 58809}, {63166, 75}

X(65004) = 1ST BASEPOINT OF THE 9TH MIXTILINEAR TRIANGLE WRT ABC

Barycentrics    (a+b-c)^2*(a-b+c)^2*(2*a^2+2*b^2+b*c-c^2+a*(-4*b+c))*(2*a^2-b^2+a*(b-4*c)+b*c+2*c^2) : :

X(65004) lies on these lines: {2, 55989}, {7, 20323}, {75, 18811}, {269, 903}, {279, 36606}, {479, 16078}, {3668, 39707}, {4373, 62787}, {4888, 21453}, {6548, 43932}, {7045, 62536}, {27475, 60961}, {62783, 65081}

X(65004) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 34524}, {41, 30827}, {55, 2098}, {200, 32577}, {346, 34543}, {644, 17424}, {1253, 4862}, {6602, 47444}
X(65004) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 34524}, {223, 2098}, {3160, 30827}, {6609, 32577}, {17113, 4862}, {52659, 44784}
X(65004) = X(i)-cross conjugate of X(j) for these {i, j}: {30719, 658}, {63163, 63167}
X(65004) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(20323)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(104), X(56094)}}, {{A, B, C, X(269), X(7045)}}, {{A, B, C, X(341), X(10309)}}, {{A, B, C, X(749), X(43947)}}, {{A, B, C, X(1041), X(46972)}}, {{A, B, C, X(1275), X(23062)}}, {{A, B, C, X(3664), X(7271)}}, {{A, B, C, X(4888), X(10481)}}, {{A, B, C, X(4998), X(39126)}}, {{A, B, C, X(10307), X(14942)}}, {{A, B, C, X(19604), X(56359)}}, {{A, B, C, X(39702), X(40446)}}, {{A, B, C, X(40719), X(60961)}}, {{A, B, C, X(52803), X(56783)}}, {{A, B, C, X(55989), X(63163)}}
X(65004) = barycentric product X(i)*X(j) for these (i, j): {269, 34523}, {1088, 55989}, {18811, 57}, {63163, 85}, {63167, 7}, {65002, 75}
X(65004) = barycentric quotient X(i)/X(j) for these (i, j): {1, 34524}, {7, 30827}, {57, 2098}, {279, 4862}, {479, 47444}, {1106, 34543}, {1407, 32577}, {3911, 44784}, {18811, 312}, {34523, 341}, {43924, 17424}, {55989, 200}, {62787, 63621}, {63163, 9}, {63167, 8}, {65002, 1}

X(65005) = 2ND BASEPOINT OF THE 2ND NEUBERG TRIANGLE WRT ABC

Barycentrics    (a^4+b^2*c^2+2*a^2*(b^2+c^2))*(-b^4+b^2*c^2+a^2*(b^2+2*c^2))*(c^2*(b^2-c^2)+a^2*(2*b^2+c^2)) : :

X(65005) lies on cubic K354 and on these lines: {2, 51}, {39, 3498}, {327, 7788}, {2186, 4876}, {3051, 26714}, {3117, 51997}, {7736, 51338}, {9300, 51543}, {14970, 36214}, {40820, 53865}, {42037, 42288}, {43718, 63024}

X(65005) = X(i)-isoconjugate-of-X(j) for these {i, j}: {182, 60664}, {3403, 60672}, {52134, 60667}
X(65005) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39968, 14252}
X(65005) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3329)}}, {{A, B, C, X(4), X(6194)}}, {{A, B, C, X(6), X(52658)}}, {{A, B, C, X(98), X(15819)}}, {{A, B, C, X(251), X(33873)}}, {{A, B, C, X(511), X(12212)}}, {{A, B, C, X(694), X(34236)}}, {{A, B, C, X(3060), X(41295)}}, {{A, B, C, X(3794), X(4876)}}, {{A, B, C, X(3917), X(21355)}}, {{A, B, C, X(10519), X(60702)}}, {{A, B, C, X(14318), X(47638)}}, {{A, B, C, X(14458), X(22712)}}, {{A, B, C, X(14484), X(44434)}}, {{A, B, C, X(33706), X(54582)}}, {{A, B, C, X(44422), X(54734)}}, {{A, B, C, X(54773), X(59249)}}
X(65005) = barycentric product X(i)*X(j) for these (i, j): {262, 3329}, {263, 60707}, {2186, 60683}, {10007, 42299}, {12212, 327}, {39685, 51543}
X(65005) = barycentric quotient X(i)/X(j) for these (i, j): {262, 42006}, {263, 60667}, {2186, 60664}, {3329, 183}, {10007, 14994}, {12212, 182}, {14318, 3288}, {26714, 43357}, {46319, 60672}, {51997, 60600}, {60683, 3403}, {60686, 52134}, {60707, 20023}

X(65006) = 1ST BASEPOINT OF THE 2ND ORTHOSYMMEDIAL TRIANGLE WRT ABC

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^2+2*b^2-c^2)*(b^2+c^2)*(2*a^2-b^2+2*c^2) : :

X(65006) lies on these lines: {2, 37808}, {3, 22087}, {22, 1383}, {30, 262}, {39, 9019}, {305, 6390}, {427, 23297}, {525, 13394}, {574, 9515}, {2781, 21163}, {3796, 54060}, {7495, 10511}, {11165, 47596}, {11636, 14675}, {14096, 46147}, {16509, 44420}, {20380, 47426}, {44210, 51541}

X(65006) = isogonal conjugate of X(32581)
X(65006) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 32581}, {19, 10130}, {82, 5094}, {92, 58761}, {3112, 8541}, {32085, 36263}
X(65006) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 32581}, {6, 10130}, {141, 5094}, {22391, 58761}, {34452, 8541}
X(65006) = X(i)-Ceva conjugate of X(j) for these {i, j}: {23297, 30489}
X(65006) = pole of line {5094, 10130} with respect to the Stammler hyperbola
X(65006) = pole of line {8541, 32581} with respect to the Wallace hyperbola
X(65006) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(39)}}, {{A, B, C, X(22), X(3796)}}, {{A, B, C, X(30), X(14096)}}, {{A, B, C, X(110), X(13394)}}, {{A, B, C, X(141), X(525)}}, {{A, B, C, X(184), X(41272)}}, {{A, B, C, X(3051), X(14908)}}, {{A, B, C, X(3521), X(27366)}}, {{A, B, C, X(4846), X(20021)}}, {{A, B, C, X(6390), X(20775)}}, {{A, B, C, X(6676), X(10547)}}, {{A, B, C, X(7767), X(11205)}}, {{A, B, C, X(14961), X(41328)}}, {{A, B, C, X(16102), X(43722)}}, {{A, B, C, X(16789), X(29959)}}, {{A, B, C, X(19127), X(42286)}}, {{A, B, C, X(27376), X(40441)}}, {{A, B, C, X(30489), X(43697)}}, {{A, B, C, X(36952), X(42551)}}
X(65006) = barycentric product X(i)*X(j) for these (i, j): {39, 64982}, {141, 43697}, {1383, 3933}, {3917, 598}, {11636, 2525}, {20775, 40826}, {23297, 3}, {30489, 69}, {30491, 4576}
X(65006) = barycentric quotient X(i)/X(j) for these (i, j): {3, 10130}, {6, 32581}, {39, 5094}, {184, 58761}, {598, 46104}, {1383, 32085}, {3051, 8541}, {3917, 599}, {3933, 9464}, {4020, 36263}, {11636, 42396}, {20775, 574}, {23297, 264}, {30489, 4}, {30491, 58784}, {43697, 83}, {64982, 308}, {65007, 21459}

X(65007) = 2ND BASEPOINT OF THE 2ND ORTHOSYMMEDIAL TRIANGLE WRT ABC

Barycentrics    a^2*(2*a^2+2*b^2-c^2)*(2*a^2-b^2+2*c^2)*(-2*a^2*b^2*c^2+a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)) : :

X(65007) lies on these lines: {2, 37808}, {6, 11226}, {23, 22258}, {25, 1383}, {111, 18374}, {351, 523}, {468, 10511}, {858, 47426}, {1995, 19153}, {2393, 64646}, {5133, 23297}, {9465, 9971}, {11580, 21419}, {11636, 53929}, {14580, 20410}, {18018, 40022}

X(65007) = X(i)-isoconjugate-of-X(j) for these {i, j}: {574, 37220}, {2373, 36263}
X(65007) = X(i)-Dao conjugate of X(j) for these {i, j}: {61067, 599}, {64646, 9464}
X(65007) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10512, 30489}
X(65007) = pole of line {5169, 55974} with respect to the nine-point circle
X(65007) = pole of line {8288, 45096} with respect to the Kiepert hyperbola
X(65007) = pole of line {598, 57082} with respect to the Lemoine inellipse
X(65007) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(21459)}}, {{A, B, C, X(25), X(523)}}, {{A, B, C, X(111), X(5523)}}, {{A, B, C, X(351), X(47426)}}, {{A, B, C, X(468), X(18374)}}, {{A, B, C, X(1304), X(7426)}}, {{A, B, C, X(2857), X(4108)}}, {{A, B, C, X(5354), X(62382)}}, {{A, B, C, X(14961), X(21309)}}, {{A, B, C, X(22329), X(61198)}}, {{A, B, C, X(36900), X(52672)}}, {{A, B, C, X(51541), X(58953)}}
X(65007) = barycentric product X(i)*X(j) for these (i, j): {1383, 858}, {2393, 598}, {10511, 64646}, {11636, 47138}, {14580, 64982}, {18669, 55927}, {18818, 47426}, {21459, 65006}, {30491, 61181}, {43697, 5523}, {51541, 57485}, {52672, 52692}, {61198, 8599}
X(65007) = barycentric quotient X(i)/X(j) for these (i, j): {598, 46140}, {858, 9464}, {1383, 2373}, {2393, 599}, {14580, 5094}, {30489, 46165}, {46001, 60040}, {47426, 39785}, {51962, 42007}, {55927, 37220}, {57485, 42008}, {61198, 9146}

X(65008) = 1ST BASEPOINT OF THE 3RD PARRY TRIANGLE WRT ABC

Barycentrics    b^2*(b-c)*c^2*(b+c)*(-2*a^2+b^2-2*c^2)*(2*a^2+2*b^2-c^2)*(-2*a^2+b^2+c^2) : :

X(65008) lies on these lines: {2, 11215}, {338, 1648}, {670, 5468}, {690, 850}, {1649, 14272}, {9979, 10512}, {14295, 34763}

X(65008) = isotomic conjugate of X(32583)
X(65008) = trilinear pole of line {23992, 52628}
X(65008) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 32583}, {163, 42007}, {574, 36142}, {923, 9145}, {23288, 23995}, {32729, 36263}
X(65008) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 32583}, {115, 42007}, {690, 62412}, {1648, 62657}, {1649, 17414}, {2482, 9145}, {18314, 23288}, {23992, 574}, {36901, 42008}, {48317, 8541}, {52628, 19510}, {62563, 10510}, {62577, 3906}
X(65008) = pole of line {8541, 42007} with respect to the polar circle
X(65008) = pole of line {5, 23297} with respect to the Lemoine inellipse
X(65008) = pole of line {5486, 11185} with respect to the Steiner circumellipse
X(65008) = pole of line {16511, 17430} with respect to the Steiner inellipse
X(65008) = pole of line {9145, 17414} with respect to the Wallace hyperbola
X(65008) = pole of line {16509, 26235} with respect to the dual conic of circumcircle
X(65008) = pole of line {598, 11059} with respect to the dual conic of Brocard inellipse
X(65008) = pole of line {599, 3906} with respect to the dual conic of Stammler hyperbola
X(65008) = pole of line {574, 17414} with respect to the dual conic of Wallace hyperbola
X(65008) = intersection, other than A, B, C, of circumconics {{A, B, C, X(94), X(44146)}}, {{A, B, C, X(290), X(3266)}}, {{A, B, C, X(338), X(670)}}, {{A, B, C, X(690), X(1648)}}, {{A, B, C, X(2501), X(22105)}}, {{A, B, C, X(8599), X(23287)}}, {{A, B, C, X(9134), X(53365)}}, {{A, B, C, X(11215), X(13241)}}, {{A, B, C, X(14272), X(14273)}}, {{A, B, C, X(14417), X(62428)}}, {{A, B, C, X(34289), X(52145)}}, {{A, B, C, X(44176), X(57496)}}, {{A, B, C, X(52094), X(58268)}}
X(65008) = barycentric product X(i)*X(j) for these (i, j): {3266, 8599}, {10512, 18311}, {18818, 52629}, {20380, 52632}, {20382, 53080}, {23287, 76}, {35138, 52628}, {35522, 598}, {40826, 690}, {51541, 850}
X(65008) = barycentric quotient X(i)/X(j) for these (i, j): {2, 32583}, {338, 23288}, {523, 42007}, {524, 9145}, {598, 691}, {690, 574}, {850, 42008}, {1383, 32729}, {1648, 17414}, {1649, 62657}, {3266, 9146}, {8599, 111}, {14273, 8541}, {18311, 10510}, {18818, 34574}, {20380, 5467}, {20382, 351}, {22105, 58761}, {23287, 6}, {23297, 36827}, {23992, 62412}, {30491, 14908}, {35522, 599}, {40826, 892}, {42713, 3908}, {46001, 32740}, {51541, 110}, {52628, 3906}, {52629, 39785}, {55135, 8542}, {55927, 36142}, {62577, 19510}, {65009, 21460}

X(65009) = 2ND BASEPOINT OF THE 3RD PARRY TRIANGLE WRT ABC

Barycentrics    (b-c)*(b+c)*(-2*a^2+b^2-2*c^2)*(2*a^2+2*b^2-c^2)*(a^6-3*a^4*(b^2+c^2)+b^2*c^2*(b^2+c^2)+a^2*(2*b^4-b^2*c^2+2*c^4)) : :

X(65009) lies on these lines: {2, 11215}, {351, 523}, {598, 46040}, {671, 11622}, {1992, 62412}, {2395, 18818}, {2407, 35138}, {39905, 41146}

X(65009) = X(i)-Dao conjugate of X(j) for these {i, j}: {39100, 9146}
X(65009) = pole of line {542, 598} with respect to the Lemoine inellipse
X(65009) = pole of line {1992, 17430} with respect to the Steiner circumellipse
X(65009) = pole of line {597, 17430} with respect to the Steiner inellipse
X(65009) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(21460)}}, {{A, B, C, X(351), X(2395)}}, {{A, B, C, X(523), X(46040)}}, {{A, B, C, X(2080), X(6094)}}, {{A, B, C, X(3228), X(22329)}}, {{A, B, C, X(9462), X(45146)}}, {{A, B, C, X(18818), X(52692)}}
X(65009) = barycentric product X(i)*X(j) for these (i, j): {21460, 65008}, {39099, 8599}, {59775, 598}
X(65009) = barycentric quotient X(i)/X(j) for these (i, j): {598, 53199}, {2080, 9145}, {8599, 43532}, {21460, 32583}, {39099, 9146}, {46001, 46316}, {59775, 599}

X(65010) = 1ST BASEPOINT OF THE 2ND SAVIN TRIANGLE WRT ABC

Barycentrics    (3*a+b+c)*(a+4*b+c)*(a+b+4*c) : :

X(65010) lies on these lines: {2, 3943}, {10, 41434}, {1434, 3911}, {3616, 4819}, {4700, 42028}, {5558, 19877}, {9105, 28210}, {24183, 31248}, {25529, 31238}, {34860, 56134}

X(65010) = isotomic conjugate of X(58859)
X(65010) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 58859}, {2334, 16666}, {4606, 58139}, {21747, 25430}, {28209, 34074}
X(65010) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 58859}, {51576, 16666}, {62608, 551}
X(65010) = pole of line {3707, 26860} with respect to the Wallace hyperbola
X(65010) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1434)}}, {{A, B, C, X(391), X(30608)}}, {{A, B, C, X(1449), X(16672)}}, {{A, B, C, X(3911), X(3943)}}, {{A, B, C, X(4673), X(4997)}}, {{A, B, C, X(4778), X(28309)}}, {{A, B, C, X(5342), X(32015)}}, {{A, B, C, X(17160), X(32016)}}
X(65010) = barycentric product X(i)*X(j) for these (i, j): {3616, 55955}, {4778, 58128}, {19804, 40434}, {27797, 42028}
X(65010) = barycentric quotient X(i)/X(j) for these (i, j): {2, 58859}, {391, 3707}, {1449, 16666}, {3616, 551}, {4673, 3902}, {4773, 14435}, {4778, 28209}, {19804, 24589}, {21454, 4031}, {27797, 60267}, {28210, 8694}, {30723, 30722}, {30728, 30727}, {37593, 21806}, {40434, 25430}, {41434, 2334}, {42028, 26860}, {55955, 5936}, {56115, 4866}, {56134, 56237}, {58128, 53658}, {58140, 58139}
X(65010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 65078, 40434}, {40434, 65078, 55955}

X(65011) = 2ND BASEPOINT OF THE 1ST SHARYGIN TRIANGLE WRT ABC

Barycentrics    a^2*(a+b-c)*(a-b+c)*(b+c)*(b^2+a*c)*(a*b+c^2) : :

X(65011) lies on cubic K972 and on these lines: {2, 257}, {6, 893}, {7, 54117}, {25, 904}, {31, 1976}, {37, 20684}, {42, 4531}, {43, 1581}, {55, 41532}, {56, 2248}, {57, 37128}, {65, 16606}, {92, 16081}, {111, 29055}, {251, 51947}, {256, 941}, {308, 17788}, {604, 1169}, {661, 2395}, {694, 1469}, {1215, 2171}, {1400, 16584}, {1401, 3572}, {1836, 19637}, {2998, 40849}, {3870, 3903}, {3930, 56258}, {4417, 7018}, {4603, 56439}, {5256, 40432}, {7015, 60038}, {9468, 23543}, {17493, 62998}, {18743, 27805}, {32911, 45986}, {39780, 45218}, {39798, 61704}, {39939, 56554}, {41346, 46286}, {45988, 51986}, {52136, 56358}

X(65011) = isogonal conjugate of X(27958)
X(65011) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 27958}, {9, 17103}, {21, 894}, {55, 8033}, {58, 17787}, {60, 3963}, {63, 14006}, {81, 7081}, {86, 2329}, {99, 3287}, {171, 333}, {172, 314}, {261, 2295}, {270, 4019}, {274, 2330}, {284, 1909}, {332, 7119}, {385, 56154}, {643, 4369}, {644, 17212}, {645, 4367}, {662, 3907}, {757, 4095}, {1021, 6649}, {1043, 7175}, {1098, 4032}, {1215, 2185}, {1237, 2150}, {1414, 4529}, {1580, 36800}, {1812, 7009}, {1920, 2194}, {1966, 2311}, {2287, 7176}, {2328, 7196}, {2344, 56696}, {2533, 4612}, {3699, 18200}, {3737, 18047}, {3786, 40745}, {3939, 16737}, {3955, 31623}, {4140, 52935}, {4374, 5546}, {4459, 4567}, {4477, 4573}, {4512, 65019}, {4560, 4579}, {4590, 40608}, {4631, 7234}, {5027, 36806}, {6064, 16592}, {7122, 28660}, {7257, 20981}, {13588, 39936}, {14534, 18235}, {20964, 52379}, {22061, 57779}, {27891, 57264}, {40415, 56558}, {40731, 52652}, {52133, 56441}, {56242, 62534}, {56982, 60577}
X(65011) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 27958}, {10, 17787}, {223, 8033}, {478, 17103}, {1084, 3907}, {1214, 1920}, {2887, 56558}, {3162, 14006}, {9467, 2311}, {15267, 4032}, {16591, 3978}, {36908, 7196}, {38986, 3287}, {39092, 36800}, {40586, 7081}, {40590, 1909}, {40600, 2329}, {40607, 4095}, {40608, 4529}, {40611, 894}, {40617, 16737}, {40627, 4459}, {55060, 4369}, {56325, 1237}, {59608, 7205}
X(65011) = X(i)-cross conjugate of X(j) for these {i, j}: {7180, 37137}, {39780, 65}
X(65011) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1215)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(31), X(92)}}, {{A, B, C, X(43), X(740)}}, {{A, B, C, X(56), X(17084)}}, {{A, B, C, X(57), X(181)}}, {{A, B, C, X(65), X(1403)}}, {{A, B, C, X(85), X(45208)}}, {{A, B, C, X(213), X(3061)}}, {{A, B, C, X(226), X(1402)}}, {{A, B, C, X(257), X(893)}}, {{A, B, C, X(306), X(1409)}}, {{A, B, C, X(312), X(3725)}}, {{A, B, C, X(512), X(9315)}}, {{A, B, C, X(604), X(2171)}}, {{A, B, C, X(647), X(41081)}}, {{A, B, C, X(756), X(65026)}}, {{A, B, C, X(872), X(22230)}}, {{A, B, C, X(904), X(7116)}}, {{A, B, C, X(1088), X(4017)}}, {{A, B, C, X(1178), X(59191)}}, {{A, B, C, X(1284), X(1469)}}, {{A, B, C, X(1333), X(8818)}}, {{A, B, C, X(1401), X(4551)}}, {{A, B, C, X(1423), X(4032)}}, {{A, B, C, X(1431), X(7249)}}, {{A, B, C, X(1824), X(56882)}}, {{A, B, C, X(2051), X(45785)}}, {{A, B, C, X(2162), X(52208)}}, {{A, B, C, X(2319), X(4095)}}, {{A, B, C, X(2339), X(44092)}}, {{A, B, C, X(3709), X(19605)}}, {{A, B, C, X(5665), X(7143)}}, {{A, B, C, X(17788), X(51947)}}, {{A, B, C, X(20284), X(52136)}}, {{A, B, C, X(20535), X(20674)}}, {{A, B, C, X(40873), X(41882)}}, {{A, B, C, X(43682), X(57185)}}, {{A, B, C, X(52373), X(57681)}}
X(65011) = barycentric product X(i)*X(j) for these (i, j): {6, 60245}, {10, 1431}, {42, 7249}, {181, 32010}, {225, 7015}, {226, 893}, {256, 65}, {349, 7104}, {1042, 4451}, {1178, 12}, {1284, 1581}, {1400, 257}, {1402, 7018}, {1432, 37}, {1441, 904}, {1874, 36214}, {2171, 40432}, {3669, 56257}, {3903, 4017}, {4032, 59480}, {4603, 57185}, {16609, 694}, {27805, 7180}, {29055, 523}, {37137, 661}, {40149, 7116}, {40729, 85}, {51641, 56241}, {52651, 57}, {53559, 55018}, {57652, 7019}
X(65011) = barycentric quotient X(i)/X(j) for these (i, j): {6, 27958}, {12, 1237}, {25, 14006}, {37, 17787}, {42, 7081}, {56, 17103}, {57, 8033}, {65, 1909}, {181, 1215}, {213, 2329}, {226, 1920}, {256, 314}, {257, 28660}, {512, 3907}, {694, 36800}, {798, 3287}, {882, 60577}, {893, 333}, {904, 21}, {1042, 7176}, {1178, 261}, {1284, 1966}, {1356, 4128}, {1400, 894}, {1402, 171}, {1427, 7196}, {1431, 86}, {1432, 274}, {1469, 56696}, {1500, 4095}, {1874, 17984}, {1918, 2330}, {1967, 56154}, {2171, 3963}, {2197, 4019}, {3122, 4459}, {3212, 27891}, {3668, 7205}, {3669, 16737}, {3709, 4529}, {3725, 18235}, {3903, 7257}, {4017, 4374}, {4079, 4140}, {4128, 3023}, {4559, 18047}, {4603, 4631}, {7015, 332}, {7018, 40072}, {7104, 284}, {7116, 1812}, {7180, 4369}, {7249, 310}, {9468, 2311}, {16584, 56558}, {16609, 3978}, {17970, 1808}, {27805, 62534}, {29055, 99}, {32010, 18021}, {36065, 36036}, {37134, 36806}, {37137, 799}, {39780, 51575}, {40432, 52379}, {40729, 9}, {43924, 17212}, {50491, 30584}, {51641, 4367}, {52651, 312}, {53321, 6649}, {56257, 646}, {56556, 56441}, {57181, 18200}, {57652, 7009}, {57663, 65019}, {60245, 76}, {61052, 53559}, {61059, 4154}, {61364, 20964}, {63461, 4477}

X(65012) = 2ND BASEPOINT OF THE INNER-SODDY TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3*(b+c)+a*(b-c)^2*(b+c)+(b-c)^2*(b^2+3*b*c+c^2)-a^2*(5*b^2+3*b*c+5*c^2))+2*(a+b-c)*(a-b+c)*(2*a^2+(b-c)^2-3*a*(b+c))*S : :

X(65012) lies on these lines: {176, 16213}, {482, 1088}, {658, 10134}, {13456, 52419}, {58816, 65013}

X(65012) = X(i)-Dao conjugate of X(j) for these {i, j}: {16662, 10134}
X(65012) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(13456)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(176)}}, {{A, B, C, X(7045), X(13389)}}, {{A, B, C, X(7056), X(56386)}}, {{A, B, C, X(7347), X(56359)}}, {{A, B, C, X(13387), X(55983)}}, {{A, B, C, X(13437), X(56783)}}, {{A, B, C, X(55346), X(60853)}}
X(65012) = barycentric quotient X(i)/X(j) for these (i, j): {16663, 10134}

X(65013) = 2ND BASEPOINT OF THE OUTER-SODDY TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(3*a^3*(b+c)+a*(b-c)^2*(b+c)+(b-c)^2*(b^2+3*b*c+c^2)-a^2*(5*b^2+3*b*c+5*c^2))-2*(a+b-c)*(a-b+c)*(2*a^2+(b-c)^2-3*a*(b+c))*S : :

X(65013) lies on these lines: {175, 16214}, {481, 1088}, {658, 10135}, {13427, 52420}, {58816, 65012}

X(65013) = X(i)-Dao conjugate of X(j) for these {i, j}: {16663, 10135}
X(65013) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(13427)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(8), X(175)}}, {{A, B, C, X(7045), X(13388)}}, {{A, B, C, X(7056), X(56385)}}, {{A, B, C, X(7348), X(56359)}}, {{A, B, C, X(13386), X(55983)}}, {{A, B, C, X(13459), X(56783)}}, {{A, B, C, X(55346), X(60854)}}
X(65013) = barycentric quotient X(i)/X(j) for these (i, j): {16662, 10135}

X(65014) = 1ST BASEPOINT OF THE VIJAY POLAR INCENTRAL TRIANGLE WRT ABC

Barycentrics    (a-b)^2*(a-c)^2*(a+b-c)*(a-b+c)*(-b^3+b*c^2+a*c*(-3*b+c)+a^2*(b+c))*(a*b*(b-3*c)+a^2*(b+c)+c*(b^2-c^2)) : :

X(65014) lies on these lines: {27, 46102}, {86, 4998}, {673, 14554}, {1025, 62619}, {50039, 60479}

X(65014) = trilinear pole of line {4552, 21362}
X(65014) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 52341}, {513, 53286}, {650, 21786}, {2170, 5053}, {3063, 21222}, {3271, 54391}, {7252, 21894}, {18344, 23087}
X(65014) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 52341}, {10001, 21222}, {39026, 53286}, {52659, 34590}
X(65014) = X(i)-cross conjugate of X(j) for these {i, j}: {517, 190}, {1739, 653}, {4674, 655}, {16610, 658}, {32486, 3257}, {49997, 651}
X(65014) = pole of line {52339, 52340} with respect to the dual conic of Wallace hyperbola
X(65014) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(899), X(1458)}}, {{A, B, C, X(1443), X(17160)}}, {{A, B, C, X(3264), X(22464)}}, {{A, B, C, X(3699), X(5377)}}, {{A, B, C, X(4998), X(35174)}}, {{A, B, C, X(5382), X(7035)}}
X(65014) = barycentric product X(i)*X(j) for these (i, j): {14554, 4998}, {50039, 664}
X(65014) = barycentric quotient X(i)/X(j) for these (i, j): {59, 5053}, {101, 53286}, {109, 21786}, {523, 52341}, {664, 21222}, {1813, 23087}, {3911, 34590}, {4551, 21894}, {4564, 54391}, {14554, 11}, {50039, 522}

X(65015) = 2ND BASEPOINT OF THE 7TH VIJAY TRIANGLE WRT ABC

Barycentrics    (a+b)^2*(a+c)^2*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(a^3+2*b^3-a^2*c+b^2*c+c^3+a*(b^2-c^2))*(a^3-a^2*b+b^3+b*c^2+2*c^3+a*(-b^2+c^2)) : :

X(65015) lies on these lines: {2, 36419}, {7, 46103}, {1246, 57390}, {16099, 52919}, {39700, 51354}, {57825, 64985}

X(65015) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 21671}, {71, 18673}, {72, 44093}, {228, 440}, {1104, 52386}, {1834, 3990}, {2264, 7066}, {3682, 40977}, {3998, 40984}, {7138, 59646}, {53290, 57109}, {55232, 61200}
X(65015) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 21671}
X(65015) = X(i)-cross conjugate of X(j) for these {i, j}: {27, 40414}, {17925, 52919}
X(65015) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(447), X(17925)}}, {{A, B, C, X(40395), X(53044)}}, {{A, B, C, X(46103), X(59482)}}
X(65015) = barycentric product X(i)*X(j) for these (i, j): {27, 40414}, {286, 40431}, {44129, 57390}, {64985, 8747}
X(65015) = barycentric quotient X(i)/X(j) for these (i, j): {4, 21671}, {27, 440}, {28, 18673}, {951, 7066}, {1257, 52387}, {1474, 44093}, {2983, 52386}, {5317, 40977}, {8747, 1834}, {36419, 40940}, {36421, 59646}, {40414, 306}, {40431, 72}, {40445, 3695}, {52919, 14543}, {52920, 61221}, {57390, 71}, {64985, 52396}

X(65016) = 1ST BASEPOINT OF THE 1ST MOSES-MIYAMOTO-APOLLONIUS TRIANGLE WRT ABC

Barycentrics    b*(-a+b-c)*(a+b-c)*c*((-a-b+c)*(a-b+c)+2*S) : :

X(65016) lies on these lines: {2, 85}, {7, 57270}, {75, 40699}, {6063, 60853}, {7056, 13387}, {7182, 56386}, {57785, 61401}

X(65016) = X(i)-isoconjugate-of-X(j) for these {i, j}: {33, 53065}, {41, 42013}, {55, 60852}, {220, 60849}, {607, 2066}, {657, 54016}, {1253, 16232}, {2175, 14121}, {2212, 30556}, {6502, 7071}, {6602, 61400}, {7079, 53064}, {9447, 60853}, {13390, 14827}, {13427, 53066}
X(65016) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 60852}, {3160, 42013}, {13389, 55}, {16662, 46379}, {17113, 16232}, {40593, 14121}, {64631, 220}
X(65016) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6063, 65017}
X(65016) = X(i)-cross conjugate of X(j) for these {i, j}: {7056, 65017}
X(65016) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(13387)}}, {{A, B, C, X(241), X(13388)}}, {{A, B, C, X(948), X(1659)}}, {{A, B, C, X(1212), X(30557)}}, {{A, B, C, X(1427), X(61401)}}, {{A, B, C, X(6554), X(7090)}}, {{A, B, C, X(7182), X(57785)}}, {{A, B, C, X(30807), X(60854)}}, {{A, B, C, X(44664), X(54017)}}
X(65016) = barycentric product X(i)*X(j) for these (i, j): {305, 61401}, {1088, 56386}, {1659, 7182}, {2362, 57918}, {4569, 54017}, {13387, 65017}, {13388, 6063}, {20567, 2067}, {30557, 57792}, {41283, 53063}, {60854, 7056}, {64230, 76}, {65082, 85}
X(65016) = barycentric quotient X(i)/X(j) for these (i, j): {7, 42013}, {57, 60852}, {77, 2066}, {85, 14121}, {222, 53065}, {269, 60849}, {279, 16232}, {348, 30556}, {479, 61400}, {934, 54016}, {1088, 13390}, {1659, 33}, {1847, 61393}, {2067, 41}, {2362, 607}, {5414, 1253}, {6063, 60853}, {7053, 53064}, {7056, 13389}, {7090, 7079}, {7133, 7071}, {7177, 6502}, {7182, 56385}, {13388, 55}, {13390, 13427}, {13436, 30557}, {16663, 46379}, {24002, 58838}, {30557, 220}, {30682, 64229}, {52420, 5414}, {53063, 2175}, {53066, 14827}, {54017, 3900}, {56386, 200}, {60850, 2212}, {60854, 7046}, {61401, 25}, {64229, 34125}, {64230, 6}, {65017, 13386}, {65082, 9}
X(65016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {85, 1088, 65017}

X(65017) = 1ST BASEPOINT OF THE 2ND MOSES-MIYAMOTO-APOLLONIUS TRIANGLE WRT ABC

Barycentrics    b*(-a+b-c)*(a+b-c)*c*((a+b-c)*(a-b+c)+2*S) : :

X(65017) lies on these lines: {2, 85}, {7, 57269}, {75, 40700}, {6063, 60854}, {7056, 13386}, {7182, 56385}, {57785, 61400}

X(65017) = X(i)-isoconjugate-of-X(j) for these {i, j}: {33, 53066}, {41, 7133}, {55, 60851}, {220, 60850}, {607, 5414}, {657, 54018}, {1253, 2362}, {1659, 14827}, {2067, 7071}, {2175, 7090}, {2212, 30557}, {6602, 61401}, {7079, 53063}, {9447, 60854}, {13456, 53065}
X(65017) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 60851}, {3160, 7133}, {13388, 55}, {16663, 46378}, {17113, 2362}, {40593, 7090}, {64632, 220}
X(65017) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6063, 65016}
X(65017) = X(i)-cross conjugate of X(j) for these {i, j}: {7056, 65016}
X(65017) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(13386)}}, {{A, B, C, X(241), X(13389)}}, {{A, B, C, X(948), X(13390)}}, {{A, B, C, X(1212), X(30556)}}, {{A, B, C, X(1427), X(61400)}}, {{A, B, C, X(6554), X(14121)}}, {{A, B, C, X(7182), X(57785)}}, {{A, B, C, X(30807), X(60853)}}, {{A, B, C, X(44664), X(54019)}}
X(65017) = barycentric product X(i)*X(j) for these (i, j): {305, 61400}, {1088, 56385}, {4569, 54019}, {13386, 65016}, {13389, 6063}, {13390, 7182}, {16232, 57918}, {20567, 6502}, {30556, 57792}, {41283, 53064}, {60853, 7056}, {64229, 76}
X(65017) = barycentric quotient X(i)/X(j) for these (i, j): {7, 7133}, {57, 60851}, {77, 5414}, {85, 7090}, {222, 53066}, {269, 60850}, {279, 2362}, {348, 30557}, {479, 61401}, {934, 54018}, {1088, 1659}, {1659, 13456}, {1847, 61392}, {2066, 1253}, {6063, 60854}, {6502, 41}, {7053, 53063}, {7056, 13388}, {7177, 2067}, {7182, 56386}, {13389, 55}, {13390, 33}, {13453, 30556}, {14121, 7079}, {16232, 607}, {16662, 46378}, {24002, 58840}, {30556, 220}, {30682, 64230}, {42013, 7071}, {52419, 2066}, {53064, 2175}, {53065, 14827}, {54019, 3900}, {56385, 200}, {60849, 2212}, {60853, 7046}, {61400, 25}, {64229, 6}, {64230, 34121}, {65016, 13387}
X(65017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {85, 1088, 65016}

X(65018) = 1ST BASEPOINT OF THE GEMINI 3 TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(a+3*b+c)*(a+b+3*c) : :

X(65018) lies on these lines: {2, 1434}, {8, 86}, {81, 30711}, {274, 312}, {333, 1509}, {873, 65058}, {1010, 4314}, {1311, 5545}, {2368, 8694}, {3691, 42302}, {4102, 29574}, {4518, 18827}, {4624, 18359}, {4633, 4997}, {4866, 14007}, {5333, 29624}, {5750, 32008}, {6557, 16705}, {10436, 12526}, {14828, 16458}, {17169, 17551}, {17206, 30608}, {17589, 56088}, {18157, 64989}, {18600, 56075}, {25508, 34820}, {27424, 51314}, {29605, 65025}, {33779, 40827}, {42028, 42030}, {52422, 63164}

X(65018) = isotomic conjugate of X(5257)
X(65018) = trilinear pole of line {7192, 47656}
X(65018) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37593}, {25, 4047}, {31, 5257}, {41, 3671}, {42, 1449}, {65, 4258}, {71, 5338}, {100, 4832}, {101, 4822}, {213, 3616}, {391, 1402}, {461, 1409}, {604, 4061}, {651, 8653}, {692, 4841}, {872, 42028}, {1018, 58140}, {1214, 44100}, {1334, 3361}, {1397, 42712}, {1400, 4512}, {1415, 4843}, {1911, 4771}, {1918, 19804}, {1973, 4101}, {2200, 5342}, {2223, 14625}, {2333, 4652}, {4557, 4790}, {4734, 21759}, {4815, 32739}, {4819, 9456}, {4827, 53321}, {4829, 18268}, {4839, 34067}, {30728, 51641}
X(65018) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5257}, {9, 37593}, {1015, 4822}, {1086, 4841}, {1146, 4843}, {3160, 3671}, {3161, 4061}, {4370, 4819}, {6337, 4101}, {6505, 4047}, {6626, 3616}, {6651, 4771}, {8054, 4832}, {34021, 19804}, {35068, 4829}, {35119, 4839}, {38991, 8653}, {40582, 4512}, {40592, 1449}, {40602, 4258}, {40605, 391}, {40619, 4815}, {40620, 4778}, {40625, 4765}, {55068, 4827}, {62585, 42712}, {62599, 14625}
X(65018) = X(i)-cross conjugate of X(j) for these {i, j}: {5333, 86}, {18228, 314}, {23880, 664}, {25430, 56048}, {47666, 190}, {47915, 53658}
X(65018) = pole of line {391, 1449} with respect to the Wallace hyperbola
X(65018) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16831)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(10), X(4733)}}, {{A, B, C, X(27), X(14005)}}, {{A, B, C, X(75), X(58012)}}, {{A, B, C, X(76), X(1268)}}, {{A, B, C, X(79), X(55949)}}, {{A, B, C, X(81), X(25507)}}, {{A, B, C, X(86), X(274)}}, {{A, B, C, X(142), X(5750)}}, {{A, B, C, X(279), X(28626)}}, {{A, B, C, X(284), X(5022)}}, {{A, B, C, X(304), X(57832)}}, {{A, B, C, X(332), X(348)}}, {{A, B, C, X(673), X(43531)}}, {{A, B, C, X(996), X(49680)}}, {{A, B, C, X(1010), X(15149)}}, {{A, B, C, X(1120), X(39738)}}, {{A, B, C, X(1125), X(29574)}}, {{A, B, C, X(1222), X(32009)}}, {{A, B, C, X(1224), X(17758)}}, {{A, B, C, X(2296), X(34284)}}, {{A, B, C, X(2334), X(25430)}}, {{A, B, C, X(3500), X(55919)}}, {{A, B, C, X(3616), X(29624)}}, {{A, B, C, X(3624), X(29605)}}, {{A, B, C, X(3691), X(59207)}}, {{A, B, C, X(5331), X(37128)}}, {{A, B, C, X(5333), X(42028)}}, {{A, B, C, X(5931), X(23618)}}, {{A, B, C, X(5936), X(40023)}}, {{A, B, C, X(6625), X(27483)}}, {{A, B, C, X(7110), X(38930)}}, {{A, B, C, X(7306), X(16709)}}, {{A, B, C, X(11546), X(44733)}}, {{A, B, C, X(14007), X(31926)}}, {{A, B, C, X(14621), X(39736)}}, {{A, B, C, X(17175), X(60735)}}, {{A, B, C, X(17206), X(57985)}}, {{A, B, C, X(17368), X(27147)}}, {{A, B, C, X(17377), X(20569)}}, {{A, B, C, X(19862), X(49761)}}, {{A, B, C, X(20568), X(56061)}}, {{A, B, C, X(27475), X(59760)}}, {{A, B, C, X(28650), X(40014)}}, {{A, B, C, X(32018), X(55955)}}, {{A, B, C, X(33296), X(51314)}}, {{A, B, C, X(39708), X(60083)}}, {{A, B, C, X(39740), X(56042)}}, {{A, B, C, X(40004), X(44129)}}, {{A, B, C, X(40017), X(56052)}}, {{A, B, C, X(40403), X(40430)}}, {{A, B, C, X(40417), X(57906)}}, {{A, B, C, X(40432), X(55971)}}, {{A, B, C, X(41506), X(60243)}}, {{A, B, C, X(44190), X(57831)}}, {{A, B, C, X(47915), X(56237)}}
X(65018) = barycentric product X(i)*X(j) for these (i, j): {29, 57873}, {257, 65019}, {333, 57826}, {1434, 56086}, {1509, 60267}, {2334, 310}, {3261, 4627}, {4560, 4624}, {4606, 7199}, {4614, 693}, {4633, 514}, {4866, 57785}, {5936, 86}, {25430, 274}, {28660, 57663}, {35519, 5545}, {40023, 81}, {44130, 57701}, {47915, 799}, {52619, 8694}, {53658, 7192}, {56048, 75}, {56204, 85}, {56237, 873}, {58860, 99}
X(65018) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37593}, {2, 5257}, {7, 3671}, {8, 4061}, {21, 4512}, {28, 5338}, {29, 461}, {63, 4047}, {69, 4101}, {81, 1449}, {86, 3616}, {239, 4771}, {274, 19804}, {284, 4258}, {286, 5342}, {312, 42712}, {314, 4673}, {333, 391}, {513, 4822}, {514, 4841}, {519, 4819}, {522, 4843}, {645, 30728}, {649, 4832}, {663, 8653}, {673, 14625}, {693, 4815}, {740, 4829}, {812, 4839}, {1014, 3361}, {1019, 4790}, {1021, 4827}, {1434, 21454}, {1444, 4652}, {1509, 42028}, {2299, 44100}, {2334, 42}, {3733, 58140}, {4560, 4765}, {4606, 1018}, {4614, 100}, {4624, 4552}, {4627, 101}, {4633, 190}, {4866, 210}, {5333, 62648}, {5545, 109}, {5936, 10}, {6629, 4831}, {7192, 4778}, {7199, 4801}, {8694, 4557}, {14626, 20683}, {16704, 4700}, {17096, 30723}, {17139, 51423}, {18155, 4811}, {23829, 50357}, {25430, 37}, {30939, 4742}, {30941, 4684}, {32010, 4835}, {33296, 4734}, {34820, 1334}, {40023, 321}, {47915, 661}, {48580, 53586}, {53658, 3952}, {54308, 4719}, {56048, 1}, {56086, 2321}, {56204, 9}, {56237, 756}, {57663, 1400}, {57701, 73}, {57826, 226}, {57873, 307}, {58860, 523}, {60267, 594}, {62755, 4706}, {65019, 894}

X(65019) = 2ND BASEPOINT OF THE GEMINI 3 TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(a+3*b+c)*(a+b+3*c)*(a^2+b*c) : :

X(65019) lies on these lines: {2, 1434}, {86, 25419}, {4633, 25430}, {5936, 40164}, {7081, 17103}, {7155, 51356}, {8033, 17787}, {17731, 56205}

X(65019) = trilinear pole of line {17212, 3907}
X(65019) = X(i)-isoconjugate-of-X(j) for these {i, j}: {213, 4835}, {893, 37593}, {904, 5257}, {1967, 4771}, {3616, 40729}, {3903, 4832}, {4512, 65011}, {8653, 37137}, {56257, 58140}
X(65019) = X(i)-Dao conjugate of X(j) for these {i, j}: {6626, 4835}, {8290, 4771}, {16592, 4841}, {40597, 37593}, {62650, 5257}
X(65019) = pole of line {391, 4734} with respect to the Wallace hyperbola
X(65019) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(894)}}, {{A, B, C, X(1434), X(8033)}}
X(65019) = barycentric product X(i)*X(j) for these (i, j): {1909, 56048}, {4369, 4633}, {4374, 4614}, {14006, 57873}, {16737, 4606}, {17103, 5936}, {17212, 53658}, {25430, 8033}, {27958, 57826}, {56204, 7196}, {65018, 894}
X(65019) = barycentric quotient X(i)/X(j) for these (i, j): {86, 4835}, {171, 37593}, {385, 4771}, {894, 5257}, {3907, 4843}, {4039, 4829}, {4107, 4839}, {4367, 4822}, {4369, 4841}, {4374, 4815}, {4434, 4819}, {4606, 56257}, {4614, 3903}, {4633, 27805}, {5545, 29055}, {7081, 4061}, {7176, 3671}, {8033, 19804}, {14006, 461}, {16737, 4801}, {17103, 3616}, {17212, 4778}, {17787, 42712}, {18200, 4790}, {20981, 4832}, {25430, 52651}, {27958, 391}, {56048, 256}, {57663, 65011}, {57826, 60245}, {65018, 257}

X(65020) = 1ST BASEPOINT OF THE GEMINI 10 TRIANGLE WRT ABC

Barycentrics    (2*a+2*b-3*c)*(a-b-c)*(2*a-3*b+2*c) : :

X(65020) lies on these lines: {2, 4912}, {8, 1392}, {92, 30829}, {226, 63167}, {257, 29613}, {333, 30827}, {345, 56075}, {1220, 3624}, {1311, 8697}, {2994, 37758}, {3452, 30608}, {3634, 31359}, {4417, 55956}, {4997, 30568}, {5219, 40420}, {5233, 42030}, {5328, 56201}, {5333, 55942}, {6557, 32851}, {17743, 29630}, {18134, 65045}, {18359, 18743}, {19804, 65029}, {20317, 60480}, {28808, 56086}, {30852, 34234}, {41878, 56947}

X(65020) = isotomic conjugate of X(31231)
X(65020) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1388}, {31, 31231}, {56, 16885}, {604, 3632}, {651, 58155}, {1402, 4921}, {1415, 4926}, {1461, 4959}
X(65020) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 16885}, {2, 31231}, {9, 1388}, {1146, 4926}, {3161, 3632}, {35508, 4959}, {38991, 58155}, {40605, 4921}
X(65020) = X(i)-cross conjugate of X(j) for these {i, j}: {1392, 39707}
X(65020) = pole of line {4921, 31231} with respect to the Wallace hyperbola
X(65020) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(16814)}}, {{A, B, C, X(27), X(6931)}}, {{A, B, C, X(57), X(5048)}}, {{A, B, C, X(75), X(7321)}}, {{A, B, C, X(142), X(20196)}}, {{A, B, C, X(226), X(30827)}}, {{A, B, C, X(309), X(57884)}}, {{A, B, C, X(314), X(28650)}}, {{A, B, C, X(345), X(30829)}}, {{A, B, C, X(522), X(4912)}}, {{A, B, C, X(650), X(36630)}}, {{A, B, C, X(673), X(10589)}}, {{A, B, C, X(908), X(30852)}}, {{A, B, C, X(1088), X(56365)}}, {{A, B, C, X(1320), X(39962)}}, {{A, B, C, X(1392), X(26745)}}, {{A, B, C, X(2006), X(11376)}}, {{A, B, C, X(2051), X(5123)}}, {{A, B, C, X(2185), X(25430)}}, {{A, B, C, X(3255), X(17276)}}, {{A, B, C, X(3452), X(5219)}}, {{A, B, C, X(3596), X(17249)}}, {{A, B, C, X(3624), X(3687)}}, {{A, B, C, X(3634), X(11679)}}, {{A, B, C, X(3699), X(62540)}}, {{A, B, C, X(3705), X(29630)}}, {{A, B, C, X(4998), X(44186)}}, {{A, B, C, X(5226), X(5328)}}, {{A, B, C, X(5233), X(5333)}}, {{A, B, C, X(5316), X(25525)}}, {{A, B, C, X(5557), X(25681)}}, {{A, B, C, X(7081), X(29613)}}, {{A, B, C, X(7308), X(58463)}}, {{A, B, C, X(7705), X(60087)}}, {{A, B, C, X(8797), X(40424)}}, {{A, B, C, X(13478), X(17501)}}, {{A, B, C, X(14554), X(17606)}}, {{A, B, C, X(17336), X(36796)}}, {{A, B, C, X(17351), X(36800)}}, {{A, B, C, X(18155), X(40027)}}, {{A, B, C, X(18490), X(56218)}}, {{A, B, C, X(18743), X(32851)}}, {{A, B, C, X(19804), X(28808)}}, {{A, B, C, X(20317), X(30568)}}, {{A, B, C, X(25417), X(30607)}}, {{A, B, C, X(28741), X(28826)}}, {{A, B, C, X(30588), X(30713)}}, {{A, B, C, X(31623), X(36805)}}, {{A, B, C, X(35519), X(57947)}}, {{A, B, C, X(43733), X(45098)}}, {{A, B, C, X(45100), X(61770)}}, {{A, B, C, X(51567), X(62528)}}
X(65020) = barycentric product X(i)*X(j) for these (i, j): {333, 65021}, {1392, 75}, {26745, 312}, {35519, 8697}, {39707, 8}
X(65020) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1388}, {2, 31231}, {8, 3632}, {9, 16885}, {333, 4921}, {522, 4926}, {663, 58155}, {1392, 1}, {3244, 39781}, {3900, 4959}, {8697, 109}, {26745, 57}, {39707, 7}, {56387, 51577}, {65021, 226}
X(65020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {26745, 65021, 39707}

X(65021) = 2ND BASEPOINT OF THE GEMINI 10 TRIANGLE WRT ABC

Barycentrics    (2*a+2*b-3*c)*(b+c)*(2*a-3*b+2*c) : :

X(65021) lies on the Kiepert hyperbola and on these lines: {2, 4912}, {4, 1392}, {10, 48646}, {76, 29577}, {98, 8697}, {1211, 65022}, {1751, 28609}, {3175, 4080}, {3622, 60077}, {3936, 4052}, {4054, 60267}, {4358, 40012}, {4359, 62884}, {4398, 31053}, {4415, 30588}, {4462, 60074}, {4654, 60085}, {4677, 60079}, {4685, 48645}, {4980, 34258}, {11346, 25055}, {13478, 31164}, {14534, 42025}, {17079, 57826}, {17310, 43676}, {17389, 53105}, {19722, 60082}, {19796, 62928}, {20942, 40021}, {24624, 41629}, {26580, 60203}, {29572, 60236}, {29584, 53109}, {31025, 56209}, {31179, 54586}, {33151, 62882}, {42044, 60261}, {42045, 60172}, {45100, 50071}, {50102, 60155}, {50105, 60254}, {51068, 54786}, {51103, 60078}, {55962, 64143}, {56559, 65044}, {60235, 64424}

X(65021) = isotomic conjugate of X(4921)
X(65021) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4921}, {58, 16885}, {163, 4926}, {284, 1388}, {662, 58155}, {1333, 3632}, {2194, 31231}, {4565, 4959}
X(65021) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4921}, {10, 16885}, {37, 3632}, {115, 4926}, {1084, 58155}, {1214, 31231}, {40590, 1388}, {55064, 4959}
X(65021) = pole of line {28321, 58155} with respect to the orthoptic circle of the Steiner Inellipse
X(65021) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(16814)}}, {{A, B, C, X(42), X(29577)}}, {{A, B, C, X(92), X(39702)}}, {{A, B, C, X(306), X(3241)}}, {{A, B, C, X(313), X(17249)}}, {{A, B, C, X(335), X(17351)}}, {{A, B, C, X(469), X(11346)}}, {{A, B, C, X(523), X(4912)}}, {{A, B, C, X(525), X(28204)}}, {{A, B, C, X(903), X(1441)}}, {{A, B, C, X(1211), X(42025)}}, {{A, B, C, X(1214), X(10222)}}, {{A, B, C, X(1427), X(30575)}}, {{A, B, C, X(1903), X(55992)}}, {{A, B, C, X(3175), X(4358)}}, {{A, B, C, X(3656), X(63171)}}, {{A, B, C, X(3936), X(4462)}}, {{A, B, C, X(4054), X(17079)}}, {{A, B, C, X(4415), X(4945)}}, {{A, B, C, X(4654), X(26580)}}, {{A, B, C, X(4685), X(29572)}}, {{A, B, C, X(4980), X(31993)}}, {{A, B, C, X(5734), X(56382)}}, {{A, B, C, X(8818), X(56123)}}, {{A, B, C, X(19722), X(32782)}}, {{A, B, C, X(25055), X(56810)}}, {{A, B, C, X(28609), X(56559)}}, {{A, B, C, X(30690), X(65059)}}, {{A, B, C, X(31143), X(37631)}}, {{A, B, C, X(39962), X(56174)}}, {{A, B, C, X(42715), X(50102)}}, {{A, B, C, X(48629), X(48646)}}
X(65021) = barycentric product X(i)*X(j) for these (i, j): {10, 39707}, {226, 65020}, {850, 8697}, {1392, 1441}, {26745, 321}
X(65021) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4921}, {10, 3632}, {37, 16885}, {65, 1388}, {226, 31231}, {512, 58155}, {523, 4926}, {1392, 21}, {4018, 51577}, {4041, 4959}, {4067, 63914}, {8697, 110}, {26745, 81}, {39707, 86}, {65020, 333}
X(65021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39707, 65020, 26745}

X(65022) = 2ND BASEPOINT OF THE GEMINI 11 TRIANGLE WRT ABC

Barycentrics    (b+c)*(2*a+3*b+2*c)*(2*a+2*b+3*c) : :

X(65022) lies on the Kiepert hyperbola and on these lines: {2, 3723}, {4, 3654}, {76, 4980}, {98, 28196}, {594, 60203}, {1211, 65021}, {3175, 6539}, {3617, 60077}, {3679, 19738}, {3995, 56209}, {4358, 62884}, {4359, 40012}, {4444, 47675}, {4745, 60078}, {4921, 14534}, {17251, 54775}, {19723, 60082}, {19797, 60258}, {19819, 60285}, {21020, 34475}, {29593, 60236}, {29615, 32014}, {30588, 56810}, {31144, 65051}, {41809, 60267}, {41816, 60139}, {42044, 56210}, {42045, 55949}, {50105, 60206}, {51066, 60079}, {51068, 54624}, {59772, 63060}

X(65022) = isotomic conjugate of X(42025)
X(65022) = trilinear pole of line {48551, 523}
X(65022) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42025}, {48, 31901}, {58, 16884}, {110, 50525}, {163, 28195}, {662, 58144}, {1333, 3624}, {1408, 4034}, {4556, 48053}, {17104, 43261}
X(65022) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42025}, {10, 16884}, {37, 3624}, {115, 28195}, {244, 50525}, {1084, 58144}, {1249, 31901}, {55065, 47669}, {56847, 43261}, {59577, 4034}
X(65022) = X(i)-cross conjugate of X(j) for these {i, j}: {50449, 4033}
X(65022) = pole of line {28332, 58144} with respect to the orthoptic circle of the Steiner Inellipse
X(65022) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(3723)}}, {{A, B, C, X(65), X(56213)}}, {{A, B, C, X(75), X(17393)}}, {{A, B, C, X(81), X(56174)}}, {{A, B, C, X(257), X(3175)}}, {{A, B, C, X(306), X(53620)}}, {{A, B, C, X(523), X(28329)}}, {{A, B, C, X(525), X(28198)}}, {{A, B, C, X(594), X(43260)}}, {{A, B, C, X(1211), X(4921)}}, {{A, B, C, X(1255), X(56237)}}, {{A, B, C, X(1441), X(5564)}}, {{A, B, C, X(3578), X(41816)}}, {{A, B, C, X(3679), X(56810)}}, {{A, B, C, X(3701), X(4102)}}, {{A, B, C, X(3948), X(47675)}}, {{A, B, C, X(4674), X(39948)}}, {{A, B, C, X(4685), X(29593)}}, {{A, B, C, X(4852), X(46772)}}, {{A, B, C, X(5224), X(19738)}}, {{A, B, C, X(8013), X(29615)}}, {{A, B, C, X(19723), X(32782)}}, {{A, B, C, X(21020), X(59212)}}, {{A, B, C, X(30713), X(42030)}}, {{A, B, C, X(31143), X(49724)}}, {{A, B, C, X(31144), X(42045)}}, {{A, B, C, X(39980), X(56135)}}, {{A, B, C, X(41809), X(42028)}}, {{A, B, C, X(56159), X(56219)}}
X(65022) = barycentric product X(i)*X(j) for these (i, j): {10, 28650}, {594, 65025}, {4033, 48587}, {27789, 321}, {28196, 850}
X(65022) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42025}, {4, 31901}, {10, 3624}, {37, 16884}, {512, 58144}, {523, 28195}, {661, 50525}, {1089, 42031}, {2321, 4034}, {4024, 47669}, {4705, 48053}, {8818, 43261}, {27789, 81}, {28196, 110}, {28650, 86}, {48587, 1019}, {65025, 1509}

X(65023) = 2ND BASEPOINT OF THE GEMINI 12 TRIANGLE WRT ABC

Barycentrics    (2*a+b+c)*(2*a+2*b+c)*(2*a+b+2*c) : :

X(65023) lies on these lines: {2, 319}, {86, 17190}, {551, 596}, {553, 41820}, {1125, 3578}, {1509, 30581}, {3296, 3616}, {3622, 50043}, {5905, 53854}, {7100, 56947}, {8652, 9108}, {14377, 56070}, {25055, 56343}, {45222, 65078}

X(65023) = isotomic conjugate of X(43260)
X(65023) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 43260}, {1126, 16777}, {1255, 61358}, {1698, 28615}, {4596, 4826}, {4629, 48005}, {4632, 58290}, {4658, 52555}, {4813, 8701}, {4834, 37212}, {5221, 33635}
X(65023) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43260}, {1213, 1698}, {3120, 4838}, {3647, 16777}, {16726, 4960}, {35076, 4802}, {56846, 4654}, {59592, 4007}, {62588, 28605}
X(65023) = pole of line {5333, 43260} with respect to the Wallace hyperbola
X(65023) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(553)}}, {{A, B, C, X(81), X(32636)}}, {{A, B, C, X(86), X(319)}}, {{A, B, C, X(321), X(3649)}}, {{A, B, C, X(348), X(4001)}}, {{A, B, C, X(551), X(45222)}}, {{A, B, C, X(1100), X(30581)}}, {{A, B, C, X(1213), X(42025)}}, {{A, B, C, X(1269), X(39704)}}, {{A, B, C, X(1962), X(21904)}}, {{A, B, C, X(2308), X(40746)}}, {{A, B, C, X(3616), X(62923)}}, {{A, B, C, X(3683), X(6605)}}, {{A, B, C, X(3702), X(4102)}}, {{A, B, C, X(4654), X(33935)}}, {{A, B, C, X(4725), X(4977)}}, {{A, B, C, X(4870), X(4945)}}, {{A, B, C, X(7100), X(56846)}}, {{A, B, C, X(16709), X(17394)}}, {{A, B, C, X(41818), X(42028)}}, {{A, B, C, X(41823), X(43268)}}
X(65023) = barycentric product X(i)*X(j) for these (i, j): {1125, 30598}, {1269, 56343}, {16709, 56221}, {25417, 4359}, {28625, 52572}, {32042, 4977}, {37211, 4978}, {42030, 553}, {60203, 8025}
X(65023) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43260}, {553, 4654}, {1100, 16777}, {1125, 1698}, {1269, 30596}, {2308, 61358}, {3683, 3715}, {3686, 4007}, {3916, 3927}, {4359, 28605}, {4427, 4756}, {4647, 4066}, {4856, 4898}, {4969, 4727}, {4973, 4880}, {4974, 4716}, {4976, 4820}, {4977, 4802}, {4978, 4823}, {4979, 4813}, {4983, 48005}, {4984, 4958}, {4988, 4838}, {8025, 5333}, {8652, 8701}, {25417, 1255}, {28625, 52555}, {30598, 1268}, {31900, 31902}, {32042, 6540}, {32636, 5221}, {34819, 28615}, {36075, 36074}, {37211, 37212}, {42030, 4102}, {48074, 47947}, {50512, 4834}, {56070, 1796}, {56203, 32635}, {56343, 1126}, {60203, 6539}
X(65023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 25417, 42030}, {2, 42030, 60203}, {30598, 42030, 2}

X(65024) = 2ND BASEPOINT OF THE GEMINI 14 TRIANGLE WRT ABC

Barycentrics    (2*a-b-c)*(a+4*b+c)*(a+b+4*c) : :

X(65024) lies on these lines: {2, 3943}, {514, 4120}, {903, 62227}, {996, 3241}, {1000, 15170}, {1016, 40891}, {2726, 28210}, {3679, 31035}, {4080, 54974}, {4370, 16704}, {4671, 20569}, {4908, 63233}, {6542, 35168}, {8046, 17487}, {18145, 39997}, {28602, 34764}, {30564, 36911}, {30578, 62413}, {36592, 42026}, {36915, 62620}, {36954, 41140}, {37168, 42070}, {40509, 41141}

X(65024) = isotomic conjugate of X(42026)
X(65024) = trilinear pole of line {36912, 50841}
X(65024) = perspector of circumconic {{A, B, C, X(55955), X(58128)}}
X(65024) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42026}, {88, 21747}, {106, 16666}, {551, 9456}, {1417, 3707}, {3257, 58139}, {22357, 36125}, {28209, 32665}
X(65024) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42026}, {214, 16666}, {1647, 14435}, {4370, 551}, {35092, 28209}, {36912, 16590}, {52659, 4031}, {52871, 3707}, {55055, 58139}, {62571, 24589}
X(65024) = pole of line {28312, 49631} with respect to the orthoptic circle of the Steiner Inellipse
X(65024) = pole of line {27081, 55955} with respect to the Kiepert hyperbola
X(65024) = pole of line {3679, 28209} with respect to the Steiner circumellipse
X(65024) = pole of line {3828, 28209} with respect to the Steiner inellipse
X(65024) = pole of line {26860, 42026} with respect to the Wallace hyperbola
X(65024) = pole of line {3828, 65078} with respect to the dual conic of Yff parabola
X(65024) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(60346)}}, {{A, B, C, X(2), X(514)}}, {{A, B, C, X(44), X(16672)}}, {{A, B, C, X(900), X(28309)}}, {{A, B, C, X(902), X(39967)}}, {{A, B, C, X(903), X(17160)}}, {{A, B, C, X(1255), X(52680)}}, {{A, B, C, X(1319), X(27789)}}, {{A, B, C, X(1644), X(6542)}}, {{A, B, C, X(1647), X(40891)}}, {{A, B, C, X(3264), X(51317)}}, {{A, B, C, X(3943), X(4080)}}, {{A, B, C, X(3992), X(6539)}}, {{A, B, C, X(4562), X(17310)}}, {{A, B, C, X(4665), X(48416)}}, {{A, B, C, X(4671), X(4908)}}, {{A, B, C, X(4723), X(56086)}}, {{A, B, C, X(4742), X(21454)}}, {{A, B, C, X(4975), X(8025)}}, {{A, B, C, X(17119), X(43264)}}, {{A, B, C, X(17318), X(31147)}}, {{A, B, C, X(17487), X(30578)}}, {{A, B, C, X(18359), X(46791)}}, {{A, B, C, X(20042), X(41140)}}, {{A, B, C, X(20058), X(41141)}}, {{A, B, C, X(30576), X(56037)}}, {{A, B, C, X(36872), X(47759)}}, {{A, B, C, X(47790), X(52746)}}, {{A, B, C, X(47792), X(52747)}}, {{A, B, C, X(47873), X(61321)}}
X(65024) = barycentric product X(i)*X(j) for these (i, j): {519, 55955}, {3264, 41434}, {16704, 27797}, {30939, 56134}, {31011, 65078}, {40434, 4358}, {58128, 900}
X(65024) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42026}, {44, 16666}, {519, 551}, {900, 28209}, {902, 21747}, {1960, 58139}, {2325, 3707}, {3911, 4031}, {3992, 4714}, {4358, 24589}, {4439, 4407}, {4723, 3902}, {4908, 16590}, {6544, 14435}, {16704, 26860}, {17780, 4781}, {21805, 21806}, {22356, 22357}, {27797, 4080}, {28210, 901}, {30725, 30722}, {30731, 30727}, {36920, 39782}, {40434, 88}, {41434, 106}, {55955, 903}, {56115, 1320}, {56134, 4674}, {58128, 4555}, {65078, 62732}
X(65024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 27797, 55955}, {2, 55955, 65078}, {40434, 55955, 2}

X(65025) = 1ST BASEPOINT OF THE GEMINI 25 TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(2*a+3*b+2*c)*(2*a+2*b+3*c) : :

X(65025) lies on these lines: {86, 1698}, {274, 27789}, {1434, 4654}, {1509, 5333}, {2368, 28196}, {17175, 55947}, {17394, 39708}, {28639, 32018}, {29605, 65018}, {29615, 32014}

X(65025) = trilinear pole of line {4802, 7192}
X(65025) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 42031}, {42, 16884}, {101, 48053}, {213, 3624}, {692, 47669}, {872, 42025}, {1018, 58144}, {1402, 4034}, {4557, 50525}
X(65025) = X(i)-Dao conjugate of X(j) for these {i, j}: {1015, 48053}, {1086, 47669}, {6376, 42031}, {6626, 3624}, {40592, 16884}, {40605, 4034}, {40620, 28195}
X(65025) = pole of line {3624, 4034} with respect to the Wallace hyperbola
X(65025) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29570)}}, {{A, B, C, X(2), X(79)}}, {{A, B, C, X(76), X(30598)}}, {{A, B, C, X(83), X(42335)}}, {{A, B, C, X(85), X(17360)}}, {{A, B, C, X(86), X(274)}}, {{A, B, C, X(257), X(1125)}}, {{A, B, C, X(1100), X(28639)}}, {{A, B, C, X(1255), X(39748)}}, {{A, B, C, X(3616), X(29605)}}, {{A, B, C, X(5839), X(28641)}}, {{A, B, C, X(6625), X(60669)}}, {{A, B, C, X(7261), X(17270)}}, {{A, B, C, X(15668), X(25508)}}, {{A, B, C, X(17275), X(28640)}}, {{A, B, C, X(17743), X(32009)}}, {{A, B, C, X(18140), X(31008)}}, {{A, B, C, X(25526), X(52137)}}, {{A, B, C, X(27483), X(43972)}}, {{A, B, C, X(27801), X(30588)}}, {{A, B, C, X(37595), X(37869)}}, {{A, B, C, X(37870), X(55942)}}, {{A, B, C, X(39949), X(56066)}}, {{A, B, C, X(56060), X(60239)}}
X(65025) = barycentric product X(i)*X(j) for these (i, j): {274, 27789}, {1509, 65022}, {28196, 52619}, {28650, 86}, {48587, 799}
X(65025) = barycentric quotient X(i)/X(j) for these (i, j): {75, 42031}, {81, 16884}, {86, 3624}, {333, 4034}, {513, 48053}, {514, 47669}, {1019, 50525}, {1509, 42025}, {3733, 58144}, {7192, 28195}, {27789, 37}, {28196, 4557}, {28650, 10}, {48587, 661}, {52393, 43261}, {65022, 594}

X(65026) = 1ST BASEPOINT OF THE GEMINI 31 TRIANGLE WRT ABC

Barycentrics    a^2*(2*b^2+a*c)*(a*b+2*c^2) : :

X(65026) lies on these lines: {2, 4495}, {31, 1908}, {45, 899}, {171, 30651}, {190, 56166}, {238, 30650}, {292, 750}, {748, 893}, {869, 2177}, {1405, 2225}, {2280, 4273}, {3121, 9345}, {4384, 4850}, {4664, 7035}, {8695, 28317}, {9284, 31134}, {9350, 21814}, {16584, 17124}, {17125, 30647}, {21352, 52655}, {26242, 29828}, {39044, 43095}, {40145, 51947}

X(65026) = isogonal conjugate of X(3758)
X(65026) = trilinear pole of line {3768, 4775}
X(65026) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3758}, {2, 17126}, {6, 64133}, {75, 609}, {81, 46897}, {86, 3997}, {100, 47762}, {238, 43262}, {651, 47729}, {662, 4761}, {739, 62627}, {765, 7208}, {2185, 7276}, {3809, 14621}, {4604, 4844}
X(65026) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3758}, {9, 64133}, {206, 609}, {513, 7208}, {1015, 4406}, {1084, 4761}, {8054, 47762}, {9470, 43262}, {32664, 17126}, {38991, 47729}, {40586, 46897}, {40600, 3997}, {40614, 62627}
X(65026) = X(i)-cross conjugate of X(j) for these {i, j}: {17125, 65027}, {30647, 31}
X(65026) = pole of line {609, 3758} with respect to the Stammler hyperbola
X(65026) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(649)}}, {{A, B, C, X(2), X(31)}}, {{A, B, C, X(6), X(45)}}, {{A, B, C, X(37), X(604)}}, {{A, B, C, X(38), X(57925)}}, {{A, B, C, X(39), X(7084)}}, {{A, B, C, X(41), X(650)}}, {{A, B, C, X(42), X(57)}}, {{A, B, C, X(43), X(3112)}}, {{A, B, C, X(48), X(52351)}}, {{A, B, C, X(55), X(39951)}}, {{A, B, C, X(56), X(21448)}}, {{A, B, C, X(81), X(37673)}}, {{A, B, C, X(85), X(661)}}, {{A, B, C, X(87), X(37132)}}, {{A, B, C, X(89), X(25426)}}, {{A, B, C, X(111), X(40746)}}, {{A, B, C, X(171), X(748)}}, {{A, B, C, X(213), X(56051)}}, {{A, B, C, X(238), X(750)}}, {{A, B, C, X(274), X(56162)}}, {{A, B, C, X(603), X(647)}}, {{A, B, C, X(665), X(43048)}}, {{A, B, C, X(739), X(40434)}}, {{A, B, C, X(751), X(3572)}}, {{A, B, C, X(756), X(65011)}}, {{A, B, C, X(873), X(3223)}}, {{A, B, C, X(941), X(38266)}}, {{A, B, C, X(1178), X(17038)}}, {{A, B, C, X(1193), X(29828)}}, {{A, B, C, X(1252), X(39389)}}, {{A, B, C, X(1255), X(2162)}}, {{A, B, C, X(1333), X(39983)}}, {{A, B, C, X(1402), X(56236)}}, {{A, B, C, X(1500), X(7180)}}, {{A, B, C, X(1581), X(1908)}}, {{A, B, C, X(1635), X(9319)}}, {{A, B, C, X(1646), X(3248)}}, {{A, B, C, X(1824), X(46331)}}, {{A, B, C, X(1921), X(61385)}}, {{A, B, C, X(2156), X(2339)}}, {{A, B, C, X(2157), X(55936)}}, {{A, B, C, X(2221), X(6186)}}, {{A, B, C, X(2258), X(2350)}}, {{A, B, C, X(2279), X(39963)}}, {{A, B, C, X(2296), X(9401)}}, {{A, B, C, X(3224), X(56066)}}, {{A, B, C, X(3666), X(26242)}}, {{A, B, C, X(3733), X(9348)}}, {{A, B, C, X(7077), X(11175)}}, {{A, B, C, X(8606), X(60495)}}, {{A, B, C, X(8632), X(27922)}}, {{A, B, C, X(9285), X(57947)}}, {{A, B, C, X(9315), X(25430)}}, {{A, B, C, X(9415), X(60716)}}, {{A, B, C, X(17124), X(17127)}}, {{A, B, C, X(17125), X(17126)}}, {{A, B, C, X(18140), X(57096)}}, {{A, B, C, X(26745), X(39961)}}, {{A, B, C, X(31008), X(62461)}}, {{A, B, C, X(32664), X(51947)}}, {{A, B, C, X(39962), X(39966)}}, {{A, B, C, X(39971), X(40735)}}, {{A, B, C, X(39981), X(60671)}}, {{A, B, C, X(40432), X(57129)}}, {{A, B, C, X(49979), X(57666)}}
X(65026) = barycentric product X(i)*X(j) for these (i, j): {1, 4492}, {32, 57920}, {4777, 8695}, {30635, 31}, {57725, 6}
X(65026) = barycentric quotient X(i)/X(j) for these (i, j): {1, 64133}, {6, 3758}, {31, 17126}, {32, 609}, {42, 46897}, {181, 7276}, {213, 3997}, {292, 43262}, {512, 4761}, {513, 4406}, {649, 47762}, {663, 47729}, {869, 3809}, {899, 62627}, {1015, 7208}, {4492, 75}, {4775, 4844}, {8695, 4597}, {30635, 561}, {57725, 76}, {57920, 1502}

X(65027) = 1ST BASEPOINT OF THE GEMINI 32 TRIANGLE WRT ABC

Barycentrics    a^2*(-2*b^2+a*c)*(a*b-2*c^2) : :

X(65027) lies on these lines: {2, 30630}, {171, 30650}, {238, 30651}, {292, 748}, {750, 893}, {869, 20963}, {872, 64845}, {873, 4687}, {2276, 3720}, {3121, 9350}, {5333, 16831}, {9345, 21814}, {16584, 17124}, {19554, 40145}, {26627, 28592}, {33589, 56556}

X(65027) = isogonal conjugate of X(3759)
X(65027) = trilinear pole of line {4834, 788}
X(65027) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3759}, {2, 17127}, {75, 7031}, {81, 3896}, {100, 4380}, {171, 43263}, {190, 4401}, {662, 4170}, {757, 4099}, {1434, 4097}, {4564, 4965}, {4961, 37211}, {7189, 17743}, {16948, 27823}
X(65027) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3759}, {206, 7031}, {1084, 4170}, {8054, 4380}, {32664, 17127}, {40586, 3896}, {40607, 4099}, {55053, 4401}
X(65027) = X(i)-cross conjugate of X(j) for these {i, j}: {17125, 65026}, {17477, 649}
X(65027) = pole of line {3759, 7031} with respect to the Stammler hyperbola
X(65027) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(873)}}, {{A, B, C, X(2), X(31)}}, {{A, B, C, X(6), X(1255)}}, {{A, B, C, X(9), X(3217)}}, {{A, B, C, X(38), X(57923)}}, {{A, B, C, X(39), X(1472)}}, {{A, B, C, X(41), X(25082)}}, {{A, B, C, X(42), X(2279)}}, {{A, B, C, X(43), X(37132)}}, {{A, B, C, X(48), X(52381)}}, {{A, B, C, X(55), X(21448)}}, {{A, B, C, X(56), X(1390)}}, {{A, B, C, X(57), X(40148)}}, {{A, B, C, X(81), X(39966)}}, {{A, B, C, X(87), X(3112)}}, {{A, B, C, X(88), X(2162)}}, {{A, B, C, X(101), X(62540)}}, {{A, B, C, X(171), X(750)}}, {{A, B, C, X(212), X(647)}}, {{A, B, C, X(213), X(56236)}}, {{A, B, C, X(238), X(748)}}, {{A, B, C, X(312), X(661)}}, {{A, B, C, X(561), X(30663)}}, {{A, B, C, X(593), X(39389)}}, {{A, B, C, X(604), X(18601)}}, {{A, B, C, X(649), X(8056)}}, {{A, B, C, X(739), X(39962)}}, {{A, B, C, X(741), X(52654)}}, {{A, B, C, X(872), X(4687)}}, {{A, B, C, X(1096), X(56230)}}, {{A, B, C, X(1280), X(3445)}}, {{A, B, C, X(1402), X(56158)}}, {{A, B, C, X(1431), X(11175)}}, {{A, B, C, X(1581), X(57947)}}, {{A, B, C, X(1911), X(39981)}}, {{A, B, C, X(2156), X(7131)}}, {{A, B, C, X(2157), X(55985)}}, {{A, B, C, X(2298), X(45988)}}, {{A, B, C, X(3009), X(17026)}}, {{A, B, C, X(3108), X(40746)}}, {{A, B, C, X(3223), X(7035)}}, {{A, B, C, X(6187), X(7123)}}, {{A, B, C, X(9285), X(57948)}}, {{A, B, C, X(9309), X(56239)}}, {{A, B, C, X(9315), X(39963)}}, {{A, B, C, X(9456), X(39960)}}, {{A, B, C, X(17124), X(17126)}}, {{A, B, C, X(17125), X(17127)}}, {{A, B, C, X(18098), X(40401)}}, {{A, B, C, X(19554), X(32664)}}, {{A, B, C, X(23493), X(39970)}}, {{A, B, C, X(25426), X(27789)}}, {{A, B, C, X(28615), X(39983)}}, {{A, B, C, X(30701), X(38252)}}, {{A, B, C, X(32017), X(56162)}}, {{A, B, C, X(37128), X(40735)}}, {{A, B, C, X(37129), X(55997)}}, {{A, B, C, X(38266), X(39694)}}, {{A, B, C, X(39748), X(56138)}}, {{A, B, C, X(39967), X(40434)}}, {{A, B, C, X(40737), X(56166)}}, {{A, B, C, X(51866), X(56165)}}
X(65027) = barycentric product X(i)*X(j) for these (i, j): {1, 7241}, {30636, 31}
X(65027) = barycentric quotient X(i)/X(j) for these (i, j): {6, 3759}, {31, 17127}, {32, 7031}, {42, 3896}, {512, 4170}, {649, 4380}, {667, 4401}, {893, 43263}, {1500, 4099}, {3271, 4965}, {4834, 4961}, {7032, 7189}, {7241, 75}, {30636, 561}
X(65027) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16584, 17124, 65026}

X(65028) = 2ND BASEPOINT OF THE GEMINI 35 TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^2+4*a*b+b^2-c^2)*(a^2-b^2+4*a*c+c^2) : :
Barycentrics    (-1+cos(A))*(2+cos(B))*(2+cos(C)) : :

X(65028) lies on these lines: {1, 376}, {2, 17092}, {7, 1255}, {81, 56846}, {105, 61375}, {222, 1170}, {241, 56217}, {274, 17079}, {278, 1418}, {527, 56230}, {948, 42326}, {957, 32065}, {1407, 2982}, {1427, 52188}, {1465, 44794}, {2006, 7365}, {2094, 40399}, {4000, 52374}, {4648, 4654}, {5435, 39962}, {19819, 55953}, {21454, 25417}, {26745, 63067}, {30701, 42033}, {41777, 43071}, {42047, 55952}, {50101, 65057}

X(65028) = isotomic conjugate of X(42032)
X(65028) = trilinear pole of line {30724, 513}
X(65028) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 3295}, {31, 42032}, {33, 55466}, {41, 42696}, {55, 3305}, {200, 52424}, {220, 7190}, {284, 3697}, {643, 58299}, {644, 48340}, {1253, 52422}, {1334, 63158}, {2327, 53861}, {3939, 47965}, {52405, 56843}, {52429, 63128}
X(65028) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42032}, {223, 3305}, {478, 3295}, {3160, 42696}, {6609, 52424}, {17113, 52422}, {40590, 3697}, {40615, 48268}, {40617, 47965}, {55060, 58299}
X(65028) = X(i)-cross conjugate of X(j) for these {i, j}: {4646, 19604}, {5069, 56155}, {5221, 7}, {62819, 40154}
X(65028) = pole of line {3296, 4654} with respect to the dual conic of Yff parabola
X(65028) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(6361)}}, {{A, B, C, X(7), X(552)}}, {{A, B, C, X(19), X(36916)}}, {{A, B, C, X(27), X(376)}}, {{A, B, C, X(40), X(54886)}}, {{A, B, C, X(92), X(54689)}}, {{A, B, C, X(189), X(14377)}}, {{A, B, C, X(196), X(54867)}}, {{A, B, C, X(222), X(1418)}}, {{A, B, C, X(226), X(27818)}}, {{A, B, C, X(281), X(2160)}}, {{A, B, C, X(514), X(28194)}}, {{A, B, C, X(673), X(10385)}}, {{A, B, C, X(937), X(54726)}}, {{A, B, C, X(1014), X(56356)}}, {{A, B, C, X(1121), X(54759)}}, {{A, B, C, X(1396), X(17107)}}, {{A, B, C, X(1412), X(17092)}}, {{A, B, C, X(1427), X(17079)}}, {{A, B, C, X(1434), X(42304)}}, {{A, B, C, X(1847), X(54831)}}, {{A, B, C, X(2221), X(54497)}}, {{A, B, C, X(2334), X(52424)}}, {{A, B, C, X(2994), X(54929)}}, {{A, B, C, X(3474), X(10509)}}, {{A, B, C, X(3669), X(57663)}}, {{A, B, C, X(4000), X(42033)}}, {{A, B, C, X(4102), X(9311)}}, {{A, B, C, X(4648), X(42028)}}, {{A, B, C, X(4654), X(5586)}}, {{A, B, C, X(4656), X(60267)}}, {{A, B, C, X(5221), X(52422)}}, {{A, B, C, X(6336), X(45098)}}, {{A, B, C, X(7365), X(17078)}}, {{A, B, C, X(8051), X(60085)}}, {{A, B, C, X(8747), X(54790)}}, {{A, B, C, X(14226), X(61392)}}, {{A, B, C, X(14241), X(61393)}}, {{A, B, C, X(17982), X(54885)}}, {{A, B, C, X(19796), X(42049)}}, {{A, B, C, X(23984), X(60120)}}, {{A, B, C, X(28610), X(60992)}}, {{A, B, C, X(36124), X(54690)}}, {{A, B, C, X(36623), X(57785)}}, {{A, B, C, X(36910), X(52223)}}, {{A, B, C, X(38825), X(39956)}}, {{A, B, C, X(40573), X(55956)}}, {{A, B, C, X(41790), X(54880)}}, {{A, B, C, X(42051), X(50101)}}, {{A, B, C, X(52382), X(56846)}}, {{A, B, C, X(54757), X(64814)}}, {{A, B, C, X(54788), X(55110)}}, {{A, B, C, X(54928), X(55948)}}
X(65028) = barycentric product X(i)*X(j) for these (i, j): {57, 64995}, {278, 30679}, {3296, 7}, {6063, 61375}, {17079, 52188}
X(65028) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42032}, {7, 42696}, {56, 3295}, {57, 3305}, {65, 3697}, {222, 55466}, {269, 7190}, {279, 52422}, {1014, 63158}, {1407, 52424}, {1420, 4917}, {1426, 53861}, {3296, 8}, {3669, 47965}, {3676, 48268}, {5221, 51572}, {7180, 58299}, {17079, 46951}, {30679, 345}, {43924, 48340}, {52188, 36916}, {52372, 56843}, {61375, 55}, {64995, 312}

X(65029) = 1ST BASEPOINT OF THE GEMINI 36 TRIANGLE WRT ABC

Barycentrics    b*c*(a^2-4*a*b+b^2-c^2)*(-a^2+b^2+4*a*c-c^2) : :
Barycentrics    (-2+cos(B))*(-2+cos(C)) : :

X(65029) lies on these lines: {2, 30673}, {8, 392}, {9, 34234}, {29, 936}, {63, 40420}, {75, 4997}, {85, 908}, {92, 3452}, {189, 18228}, {226, 64995}, {312, 3264}, {321, 6557}, {329, 63164}, {333, 3305}, {693, 60480}, {1121, 30854}, {1220, 19861}, {2863, 59068}, {3239, 52627}, {3661, 52517}, {3679, 36596}, {3912, 55984}, {4102, 20942}, {4359, 38255}, {4671, 56075}, {4737, 4767}, {5205, 34446}, {5328, 26591}, {7308, 40435}, {10405, 64194}, {14942, 51564}, {17342, 52351}, {17615, 56164}, {19804, 65020}, {20196, 54284}, {24589, 65080}, {24982, 31359}, {26015, 60668}, {26637, 55942}, {26688, 40394}, {27131, 30690}, {30608, 30829}, {30711, 46938}, {30807, 55948}, {33939, 64989}, {52156, 62704}, {59491, 63167}

X(65029) = isotomic conjugate of X(3306)
X(65029) = trilinear pole of line {3762, 4404}
X(65029) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 999}, {25, 22129}, {31, 3306}, {32, 42697}, {56, 55432}, {57, 52428}, {560, 20925}, {604, 3872}, {649, 35281}, {1333, 3753}, {1397, 28808}, {1409, 17519}, {2175, 17079}, {2206, 4054}, {7113, 56426}, {21183, 32739}, {28607, 40587}, {61375, 63128}
X(65029) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 55432}, {2, 3306}, {9, 999}, {37, 3753}, {3161, 3872}, {5375, 35281}, {5452, 52428}, {6374, 20925}, {6376, 42697}, {6505, 22129}, {36911, 40587}, {40593, 17079}, {40603, 4054}, {40619, 21183}, {62571, 62621}, {62585, 28808}
X(65029) = X(i)-cross conjugate of X(j) for these {i, j}: {3679, 75}, {5316, 2}, {63993, 7}
X(65029) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(392)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(908)}}, {{A, B, C, X(21), X(56234)}}, {{A, B, C, X(27), X(5084)}}, {{A, B, C, X(57), X(9957)}}, {{A, B, C, X(63), X(3452)}}, {{A, B, C, X(75), X(693)}}, {{A, B, C, X(76), X(36805)}}, {{A, B, C, X(80), X(60085)}}, {{A, B, C, X(81), X(3890)}}, {{A, B, C, X(84), X(2051)}}, {{A, B, C, X(88), X(9311)}}, {{A, B, C, X(226), X(3305)}}, {{A, B, C, X(273), X(40422)}}, {{A, B, C, X(277), X(6336)}}, {{A, B, C, X(278), X(1058)}}, {{A, B, C, X(304), X(52351)}}, {{A, B, C, X(306), X(936)}}, {{A, B, C, X(309), X(5936)}}, {{A, B, C, X(318), X(36795)}}, {{A, B, C, X(321), X(18743)}}, {{A, B, C, X(329), X(18228)}}, {{A, B, C, X(331), X(62927)}}, {{A, B, C, X(469), X(47512)}}, {{A, B, C, X(514), X(39963)}}, {{A, B, C, X(596), X(55952)}}, {{A, B, C, X(993), X(10176)}}, {{A, B, C, X(1156), X(27475)}}, {{A, B, C, X(1210), X(5271)}}, {{A, B, C, X(1255), X(1476)}}, {{A, B, C, X(1268), X(20570)}}, {{A, B, C, X(1847), X(2006)}}, {{A, B, C, X(2167), X(2339)}}, {{A, B, C, X(2185), X(56352)}}, {{A, B, C, X(2186), X(65026)}}, {{A, B, C, X(2267), X(21801)}}, {{A, B, C, X(2297), X(2321)}}, {{A, B, C, X(2349), X(7131)}}, {{A, B, C, X(2997), X(58001)}}, {{A, B, C, X(3219), X(27131)}}, {{A, B, C, X(3306), X(4900)}}, {{A, B, C, X(3661), X(5205)}}, {{A, B, C, X(3679), X(20925)}}, {{A, B, C, X(3687), X(19861)}}, {{A, B, C, X(3912), X(47787)}}, {{A, B, C, X(4080), X(56127)}}, {{A, B, C, X(4359), X(20942)}}, {{A, B, C, X(4384), X(26015)}}, {{A, B, C, X(4468), X(27819)}}, {{A, B, C, X(4564), X(55936)}}, {{A, B, C, X(4671), X(30829)}}, {{A, B, C, X(4737), X(33934)}}, {{A, B, C, X(5219), X(54357)}}, {{A, B, C, X(5233), X(26637)}}, {{A, B, C, X(5249), X(7308)}}, {{A, B, C, X(5273), X(5748)}}, {{A, B, C, X(5328), X(5744)}}, {{A, B, C, X(5555), X(60155)}}, {{A, B, C, X(5560), X(54768)}}, {{A, B, C, X(5745), X(30852)}}, {{A, B, C, X(7018), X(57925)}}, {{A, B, C, X(7033), X(57923)}}, {{A, B, C, X(7233), X(56163)}}, {{A, B, C, X(7249), X(56239)}}, {{A, B, C, X(9258), X(65027)}}, {{A, B, C, X(11679), X(24982)}}, {{A, B, C, X(13577), X(56026)}}, {{A, B, C, X(14555), X(24556)}}, {{A, B, C, X(17184), X(26688)}}, {{A, B, C, X(17279), X(42709)}}, {{A, B, C, X(17284), X(49991)}}, {{A, B, C, X(17335), X(30588)}}, {{A, B, C, X(17758), X(55931)}}, {{A, B, C, X(27065), X(31053)}}, {{A, B, C, X(27539), X(55910)}}, {{A, B, C, X(27789), X(56029)}}, {{A, B, C, X(28650), X(46750)}}, {{A, B, C, X(30565), X(30566)}}, {{A, B, C, X(30680), X(56107)}}, {{A, B, C, X(30693), X(56200)}}, {{A, B, C, X(30710), X(34523)}}, {{A, B, C, X(30827), X(59491)}}, {{A, B, C, X(30854), X(37780)}}, {{A, B, C, X(31002), X(40028)}}, {{A, B, C, X(31019), X(35595)}}, {{A, B, C, X(32009), X(62882)}}, {{A, B, C, X(32017), X(32018)}}, {{A, B, C, X(32019), X(60251)}}, {{A, B, C, X(32023), X(57815)}}, {{A, B, C, X(33939), X(52412)}}, {{A, B, C, X(34860), X(39698)}}, {{A, B, C, X(36807), X(60242)}}, {{A, B, C, X(39962), X(42304)}}, {{A, B, C, X(39994), X(40014)}}, {{A, B, C, X(40216), X(44186)}}, {{A, B, C, X(40410), X(55106)}}, {{A, B, C, X(40424), X(57818)}}, {{A, B, C, X(42029), X(46938)}}, {{A, B, C, X(51975), X(52627)}}, {{A, B, C, X(55964), X(56217)}}, {{A, B, C, X(55965), X(55995)}}, {{A, B, C, X(56212), X(58013)}}, {{A, B, C, X(57858), X(60041)}}, {{A, B, C, X(59761), X(59764)}}
X(65029) = barycentric product X(i)*X(j) for these (i, j): {1, 58029}, {1000, 75}, {1441, 56107}, {30680, 92}, {34446, 561}, {36916, 85}, {51564, 693}, {52429, 6063}
X(65029) = barycentric quotient X(i)/X(j) for these (i, j): {1, 999}, {2, 3306}, {8, 3872}, {9, 55432}, {10, 3753}, {29, 17519}, {55, 52428}, {63, 22129}, {75, 42697}, {76, 20925}, {80, 56426}, {85, 17079}, {100, 35281}, {312, 28808}, {321, 4054}, {693, 21183}, {997, 52148}, {1000, 1}, {3305, 63128}, {3679, 40587}, {4358, 62621}, {5119, 1480}, {7284, 1481}, {14556, 2999}, {30680, 63}, {31397, 39779}, {34446, 31}, {36596, 1320}, {36916, 9}, {51564, 100}, {52429, 55}, {56107, 21}, {58029, 75}, {59068, 32665}

X(65030) = 2ND BASEPOINT OF THE GEMINI 42 TRIANGLE WRT ABC

Barycentrics    (b^2+c^2)*(a^2+3*b^2+c^2)*(a^2+b^2+3*c^2) : :

X(65030) lies on these lines: {2, 3933}, {66, 599}, {141, 4175}, {427, 7794}, {428, 40189}, {907, 9076}, {5064, 8801}, {8362, 65031}, {10691, 14259}, {11168, 53864}, {17301, 23051}, {20775, 34285}, {34603, 59780}, {37671, 40416}, {40425, 41624}, {41513, 52397}, {43098, 54971}

X(65030) = isotomic conjugate of X(42037)
X(65030) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42037}, {82, 30435}, {251, 62834}, {3618, 46289}, {3800, 34072}, {3803, 4628}, {3804, 4599}, {39731, 46288}
X(65030) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42037}, {39, 3618}, {141, 30435}, {3124, 3804}, {6665, 8362}, {15449, 3800}, {40182, 251}, {40585, 62834}, {40938, 6995}
X(65030) = pole of line {3618, 42037} with respect to the Wallace hyperbola
X(65030) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(66)}}, {{A, B, C, X(39), X(9605)}}, {{A, B, C, X(76), X(7754)}}, {{A, B, C, X(428), X(42554)}}, {{A, B, C, X(1235), X(60143)}}, {{A, B, C, X(1930), X(34578)}}, {{A, B, C, X(3933), X(4175)}}, {{A, B, C, X(5064), X(8362)}}, {{A, B, C, X(5305), X(60181)}}, {{A, B, C, X(5485), X(27376)}}, {{A, B, C, X(5503), X(31406)}}, {{A, B, C, X(7839), X(42551)}}, {{A, B, C, X(7920), X(60214)}}, {{A, B, C, X(9924), X(40938)}}, {{A, B, C, X(10302), X(52568)}}, {{A, B, C, X(16893), X(37671)}}, {{A, B, C, X(21248), X(41584)}}, {{A, B, C, X(30489), X(34572)}}, {{A, B, C, X(46225), X(54540)}}
X(65030) = barycentric product X(i)*X(j) for these (i, j): {141, 18840}, {1235, 34817}, {1930, 23051}, {3933, 8801}, {23285, 907}, {39951, 8024}, {54971, 826}
X(65030) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42037}, {38, 62834}, {39, 30435}, {141, 3618}, {427, 6995}, {826, 3800}, {907, 827}, {1930, 39731}, {2528, 3806}, {2530, 3803}, {3005, 3804}, {3917, 3796}, {3933, 3785}, {7794, 8362}, {7813, 3793}, {8024, 40022}, {8801, 32085}, {16892, 48060}, {18840, 83}, {23051, 82}, {34817, 1176}, {39951, 251}, {40187, 26224}, {48084, 48109}, {54971, 4577}, {56207, 56245}

X(65031) = 1ST BASEPOINT OF THE GEMINI 43 TRIANGLE WRT ABC

Barycentrics    (b^2+c^2)*(2*a^2+2*b^2+c^2)*(2*a^2+b^2+2*c^2) : :

X(65031) lies on these lines: {2, 5007}, {39, 61418}, {66, 3619}, {141, 11205}, {251, 16988}, {1031, 60728}, {1502, 16986}, {3096, 37353}, {3266, 59758}, {3456, 6636}, {3613, 37990}, {6292, 8024}, {6995, 8801}, {7868, 45838}, {7954, 9076}, {8362, 65030}, {8891, 31125}, {17400, 29648}, {21248, 23297}, {31101, 45096}

X(65031) = isotomic conjugate of X(39668)
X(65031) = complement of X(41917)
X(65031) = trilinear pole of line {826, 57222}
X(65031) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 39668}, {82, 7772}, {3763, 46289}, {4599, 8665}, {7950, 34072}
X(65031) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 39668}, {39, 3763}, {141, 7772}, {3124, 8665}, {3589, 39784}, {15449, 7950}, {40938, 5064}
X(65031) = X(i)-cross conjugate of X(j) for these {i, j}: {3806, 4576}
X(65031) = pole of line {3763, 39668} with respect to the Wallace hyperbola
X(65031) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(66)}}, {{A, B, C, X(22), X(15080)}}, {{A, B, C, X(25), X(52554)}}, {{A, B, C, X(39), X(251)}}, {{A, B, C, X(76), X(7878)}}, {{A, B, C, X(1180), X(17042)}}, {{A, B, C, X(1235), X(7768)}}, {{A, B, C, X(1239), X(31360)}}, {{A, B, C, X(1843), X(3108)}}, {{A, B, C, X(3051), X(16986)}}, {{A, B, C, X(3266), X(8891)}}, {{A, B, C, X(3917), X(14919)}}, {{A, B, C, X(6179), X(47847)}}, {{A, B, C, X(6995), X(8362)}}, {{A, B, C, X(7858), X(60213)}}, {{A, B, C, X(8041), X(59213)}}, {{A, B, C, X(10130), X(21248)}}, {{A, B, C, X(16703), X(37870)}}, {{A, B, C, X(27366), X(60129)}}, {{A, B, C, X(27376), X(60285)}}, {{A, B, C, X(31107), X(37453)}}, {{A, B, C, X(37125), X(37990)}}, {{A, B, C, X(39951), X(46154)}}, {{A, B, C, X(52568), X(60278)}}
X(65031) = barycentric product X(i)*X(j) for these (i, j): {141, 43527}, {427, 65032}, {1235, 56072}, {1930, 56034}, {23285, 7954}, {39955, 8024}
X(65031) = barycentric quotient X(i)/X(j) for these (i, j): {2, 39668}, {39, 7772}, {141, 3763}, {427, 5064}, {826, 7950}, {3005, 8665}, {6292, 39784}, {7954, 827}, {16892, 47923}, {39955, 251}, {43527, 83}, {56034, 82}, {56072, 1176}, {65032, 1799}
X(65031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 39955, 43527}, {43527, 65032, 39955}

X(65032) = 2ND BASEPOINT OF THE GEMINI 43 TRIANGLE WRT ABC

Barycentrics    (a^2-b^2-c^2)*(2*a^2+2*b^2+c^2)*(2*a^2+b^2+2*c^2) : :

X(65032) lies on these lines: {2, 5007}, {3, 57852}, {69, 22352}, {76, 42052}, {95, 7788}, {183, 40410}, {264, 428}, {305, 7767}, {325, 63173}, {343, 60872}, {524, 31360}, {2373, 7954}, {7667, 65061}, {7811, 18018}, {16276, 57897}, {34608, 36889}, {40413, 62965}, {42313, 64062}, {44210, 65063}, {45201, 64982}

X(65032) = isotomic conjugate of X(5064)
X(65032) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 7772}, {31, 5064}, {162, 8665}, {1973, 3763}, {7950, 32676}
X(65032) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5064}, {6, 7772}, {125, 8665}, {6337, 3763}, {15526, 7950}, {40618, 47923}
X(65032) = X(i)-cross conjugate of X(j) for these {i, j}: {56072, 43527}
X(65032) = pole of line {3763, 5064} with respect to the Wallace hyperbola
X(65032) = pole of line {7950, 8665} with respect to the dual conic of polar circle
X(65032) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(3), X(428)}}, {{A, B, C, X(22), X(52397)}}, {{A, B, C, X(25), X(10691)}}, {{A, B, C, X(67), X(60141)}}, {{A, B, C, X(68), X(14492)}}, {{A, B, C, X(76), X(7768)}}, {{A, B, C, X(98), X(42021)}}, {{A, B, C, X(183), X(64062)}}, {{A, B, C, X(251), X(41435)}}, {{A, B, C, X(262), X(3519)}}, {{A, B, C, X(265), X(54582)}}, {{A, B, C, X(290), X(60120)}}, {{A, B, C, X(343), X(7788)}}, {{A, B, C, X(376), X(34608)}}, {{A, B, C, X(394), X(37671)}}, {{A, B, C, X(598), X(7878)}}, {{A, B, C, X(599), X(45201)}}, {{A, B, C, X(1176), X(34572)}}, {{A, B, C, X(1179), X(60150)}}, {{A, B, C, X(3504), X(3917)}}, {{A, B, C, X(3785), X(42037)}}, {{A, B, C, X(4590), X(40831)}}, {{A, B, C, X(4846), X(54477)}}, {{A, B, C, X(5486), X(60125)}}, {{A, B, C, X(5641), X(54636)}}, {{A, B, C, X(6179), X(57644)}}, {{A, B, C, X(7484), X(10128)}}, {{A, B, C, X(7667), X(9909)}}, {{A, B, C, X(7759), X(60180)}}, {{A, B, C, X(7780), X(11167)}}, {{A, B, C, X(7849), X(36952)}}, {{A, B, C, X(7854), X(34897)}}, {{A, B, C, X(7858), X(60095)}}, {{A, B, C, X(8858), X(43535)}}, {{A, B, C, X(9289), X(60214)}}, {{A, B, C, X(10154), X(31152)}}, {{A, B, C, X(14023), X(60181)}}, {{A, B, C, X(14489), X(43970)}}, {{A, B, C, X(14841), X(60329)}}, {{A, B, C, X(14861), X(60326)}}, {{A, B, C, X(15077), X(54520)}}, {{A, B, C, X(15740), X(54519)}}, {{A, B, C, X(26861), X(53100)}}, {{A, B, C, X(31371), X(54815)}}, {{A, B, C, X(31407), X(54523)}}, {{A, B, C, X(32533), X(54717)}}, {{A, B, C, X(34384), X(34412)}}, {{A, B, C, X(34386), X(60217)}}, {{A, B, C, X(34405), X(54911)}}, {{A, B, C, X(34483), X(60175)}}, {{A, B, C, X(34609), X(44210)}}, {{A, B, C, X(35142), X(54776)}}, {{A, B, C, X(36616), X(48911)}}, {{A, B, C, X(39284), X(54124)}}, {{A, B, C, X(39287), X(59256)}}, {{A, B, C, X(39955), X(56072)}}, {{A, B, C, X(40050), X(60277)}}, {{A, B, C, X(41008), X(52559)}}, {{A, B, C, X(42052), X(57480)}}, {{A, B, C, X(43714), X(54539)}}, {{A, B, C, X(44176), X(54907)}}, {{A, B, C, X(45838), X(47847)}}, {{A, B, C, X(46104), X(54910)}}, {{A, B, C, X(54171), X(54785)}}, {{A, B, C, X(54810), X(56068)}}
X(65032) = barycentric product X(i)*X(j) for these (i, j): {304, 56034}, {305, 39955}, {1799, 65031}, {3267, 7954}, {43527, 69}, {56072, 76}
X(65032) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5064}, {3, 7772}, {69, 3763}, {525, 7950}, {647, 8665}, {1799, 39668}, {4025, 47923}, {7767, 39784}, {7954, 112}, {39955, 25}, {43527, 4}, {56034, 19}, {56072, 6}, {65031, 427}
X(65032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39955, 65031, 43527}

X(65033) = 2ND BASEPOINT OF THE GEMINI 46 TRIANGLE WRT ABC

Barycentrics    (a-b-c)*(a^2+2*b^2+2*a*c+c^2)*(a^2+2*a*b+b^2+2*c^2) : :

X(65033) lies on these lines: {2, 64295}, {75, 7809}, {319, 519}, {596, 903}, {958, 65035}, {2325, 3687}, {2985, 3578}, {4023, 4076}, {11237, 58008}, {31141, 65067}, {33938, 51975}, {34606, 57887}, {38462, 54314}, {41804, 65034}

X(65033) = isotomic conjugate of X(5434)
X(65033) = trilinear pole of line {1639, 28831}
X(65033) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 5434}, {604, 17369}, {1397, 4692}
X(65033) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5434}, {3161, 17369}, {62585, 4692}
X(65033) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(54510)}}, {{A, B, C, X(2), X(261)}}, {{A, B, C, X(7), X(4021)}}, {{A, B, C, X(8), X(519)}}, {{A, B, C, X(11), X(4023)}}, {{A, B, C, X(75), X(319)}}, {{A, B, C, X(192), X(60214)}}, {{A, B, C, X(256), X(14492)}}, {{A, B, C, X(312), X(17320)}}, {{A, B, C, X(314), X(903)}}, {{A, B, C, X(333), X(17271)}}, {{A, B, C, X(529), X(34606)}}, {{A, B, C, X(958), X(11237)}}, {{A, B, C, X(1329), X(5298)}}, {{A, B, C, X(2321), X(43749)}}, {{A, B, C, X(2481), X(54692)}}, {{A, B, C, X(3718), X(57852)}}, {{A, B, C, X(4373), X(4464)}}, {{A, B, C, X(4451), X(33076)}}, {{A, B, C, X(4998), X(57822)}}, {{A, B, C, X(6063), X(36889)}}, {{A, B, C, X(7241), X(18361)}}, {{A, B, C, X(7261), X(54701)}}, {{A, B, C, X(11194), X(31141)}}, {{A, B, C, X(11609), X(39974)}}, {{A, B, C, X(20566), X(55958)}}, {{A, B, C, X(31643), X(56947)}}, {{A, B, C, X(34393), X(57815)}}, {{A, B, C, X(40419), X(54699)}}, {{A, B, C, X(44187), X(60202)}}
X(65033) = barycentric product X(i)*X(j) for these (i, j): {3596, 64295}, {41432, 76}
X(65033) = barycentric quotient X(i)/X(j) for these (i, j): {2, 5434}, {8, 17369}, {312, 4692}, {41432, 6}, {64295, 56}

X(65034) = 2ND BASEPOINT OF THE GEMINI 45 TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(a^2+2*b^2-2*a*c+c^2)*(a^2-2*a*b+b^2+2*c^2) : :

X(65034) lies on these lines: {319, 9436}, {553, 3912}, {1376, 65036}, {3263, 44139}, {4995, 40419}, {11238, 32023}, {18821, 34612}, {30941, 41431}, {31140, 65065}, {41804, 65033}

X(65034) = isotomic conjugate of X(3058)
X(65034) = trilinear pole of line {28779, 30724}
X(65034) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 3058}, {41, 17366}, {2175, 7264}
X(65034) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3058}, {3160, 17366}, {40593, 7264}
X(65034) = X(i)-cross conjugate of X(j) for these {i, j}: {17494, 4554}, {49732, 2}
X(65034) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(693)}}, {{A, B, C, X(7), X(552)}}, {{A, B, C, X(75), X(319)}}, {{A, B, C, X(85), X(32007)}}, {{A, B, C, X(261), X(57822)}}, {{A, B, C, X(286), X(903)}}, {{A, B, C, X(291), X(14492)}}, {{A, B, C, X(330), X(60214)}}, {{A, B, C, X(528), X(34612)}}, {{A, B, C, X(1376), X(11238)}}, {{A, B, C, X(2481), X(56947)}}, {{A, B, C, X(2550), X(10385)}}, {{A, B, C, X(2886), X(4995)}}, {{A, B, C, X(3058), X(49732)}}, {{A, B, C, X(3596), X(36889)}}, {{A, B, C, X(3826), X(4966)}}, {{A, B, C, X(3829), X(6174)}}, {{A, B, C, X(4102), X(18025)}}, {{A, B, C, X(4421), X(31140)}}, {{A, B, C, X(4492), X(18361)}}, {{A, B, C, X(4654), X(60717)}}, {{A, B, C, X(7182), X(57852)}}, {{A, B, C, X(7224), X(60172)}}, {{A, B, C, X(7233), X(52374)}}, {{A, B, C, X(7357), X(54929)}}, {{A, B, C, X(8049), X(60139)}}, {{A, B, C, X(18811), X(36588)}}, {{A, B, C, X(18895), X(60202)}}, {{A, B, C, X(20565), X(55958)}}, {{A, B, C, X(34399), X(39704)}}, {{A, B, C, X(35160), X(57785)}}, {{A, B, C, X(39741), X(54586)}}, {{A, B, C, X(43097), X(54686)}}, {{A, B, C, X(46395), X(62715)}}, {{A, B, C, X(54687), X(56164)}}
X(65034) = barycentric product X(i)*X(j) for these (i, j): {41431, 76}
X(65034) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3058}, {7, 17366}, {85, 7264}, {41431, 6}

X(65035) = 2ND BASEPOINT OF THE GEMINI 47 TRIANGLE WRT ABC

Barycentrics    (a-b-c)*(2*a^2+4*a*b+2*b^2+c^2)*(2*a^2+b^2+4*a*c+2*c^2) : :

X(65035) lies on these lines: {551, 4357}, {958, 65033}, {3687, 3707}, {5434, 58008}, {31157, 65068}, {34606, 65067}

X(65035) = isotomic conjugate of X(11237)
X(65035) = trilinear pole of line {28958, 3910}
X(65035) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 11237}, {604, 61321}, {1415, 47873}
X(65035) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 11237}, {1146, 47873}, {3161, 61321}
X(65035) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(54544)}}, {{A, B, C, X(2), X(261)}}, {{A, B, C, X(7), X(5325)}}, {{A, B, C, X(8), X(551)}}, {{A, B, C, X(9), X(7194)}}, {{A, B, C, X(75), X(17361)}}, {{A, B, C, X(86), X(4102)}}, {{A, B, C, X(256), X(14458)}}, {{A, B, C, X(314), X(17394)}}, {{A, B, C, X(333), X(903)}}, {{A, B, C, X(958), X(5434)}}, {{A, B, C, X(1494), X(6063)}}, {{A, B, C, X(2481), X(54729)}}, {{A, B, C, X(5641), X(57922)}}, {{A, B, C, X(11194), X(34606)}}, {{A, B, C, X(11236), X(31157)}}, {{A, B, C, X(20028), X(54929)}}, {{A, B, C, X(32635), X(56049)}}, {{A, B, C, X(36910), X(50296)}}, {{A, B, C, X(50040), X(54510)}}, {{A, B, C, X(55022), X(59255)}}, {{A, B, C, X(55958), X(57883)}}, {{A, B, C, X(57884), X(57895)}}
X(65035) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11237}, {8, 61321}, {522, 47873}

X(65036) = 2ND BASEPOINT OF THE GEMINI 48 TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(2*a^2-4*a*b+2*b^2+c^2)*(2*a^2+b^2-4*a*c+2*c^2) : :

X(65036) lies on these lines: {693, 49719}, {1376, 65034}, {3058, 32023}, {6063, 49732}, {6174, 65069}, {9436, 17361}, {34612, 65065}

X(65036) = isotomic conjugate of X(11238)
X(65036) = trilinear pole of line {29002, 30726}
X(65036) = X(i)-cross conjugate of X(j) for these {i, j}: {31209, 4554}
X(65036) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(693)}}, {{A, B, C, X(55), X(49732)}}, {{A, B, C, X(75), X(17361)}}, {{A, B, C, X(100), X(49719)}}, {{A, B, C, X(291), X(14458)}}, {{A, B, C, X(903), X(18811)}}, {{A, B, C, X(1376), X(3058)}}, {{A, B, C, X(1494), X(3596)}}, {{A, B, C, X(4102), X(34409)}}, {{A, B, C, X(4421), X(34612)}}, {{A, B, C, X(5641), X(57924)}}, {{A, B, C, X(6174), X(11235)}}, {{A, B, C, X(7224), X(54586)}}, {{A, B, C, X(34523), X(62536)}}, {{A, B, C, X(39741), X(60172)}}, {{A, B, C, X(42030), X(46137)}}, {{A, B, C, X(51567), X(56947)}}, {{A, B, C, X(52374), X(56358)}}, {{A, B, C, X(54517), X(56164)}}, {{A, B, C, X(55955), X(58005)}}, {{A, B, C, X(55958), X(57884)}}, {{A, B, C, X(57883), X(57895)}}

X(65037) = 1ST BASEPOINT OF THE GEMINI 55 TRIANGLE WRT ABC

Barycentrics    b*c*(b^2+4*a*c)*(4*a*b+c^2) : :

X(65037) lies on these lines: {334, 25960}, {2887, 65038}, {3846, 57947}, {17125, 40415}, {30957, 30966}

X(65037) = isotomic conjugate of X(17124)
X(65037) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 17124}, {32, 17118}, {1501, 30637}
X(65037) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17124}, {6376, 17118}
X(65037) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(334)}}, {{A, B, C, X(10), X(30957)}}, {{A, B, C, X(86), X(60087)}}, {{A, B, C, X(238), X(25960)}}, {{A, B, C, X(310), X(62884)}}, {{A, B, C, X(312), X(873)}}, {{A, B, C, X(321), X(40027)}}, {{A, B, C, X(693), X(56212)}}, {{A, B, C, X(748), X(3846)}}, {{A, B, C, X(2296), X(14554)}}, {{A, B, C, X(2339), X(24041)}}, {{A, B, C, X(2887), X(17125)}}, {{A, B, C, X(6063), X(56169)}}, {{A, B, C, X(6384), X(60097)}}, {{A, B, C, X(7035), X(57923)}}, {{A, B, C, X(17123), X(25760)}}, {{A, B, C, X(25885), X(26010)}}, {{A, B, C, X(31002), X(34258)}}, {{A, B, C, X(31237), X(31289)}}, {{A, B, C, X(31330), X(46843)}}, {{A, B, C, X(57916), X(63173)}}
X(65037) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17124}, {75, 17118}, {561, 30637}

X(65038) = 1ST BASEPOINT OF THE GEMINI 56 TRIANGLE WRT ABC

Barycentrics    b*c*(b^2-4*a*c)*(4*a*b-c^2) : :

X(65038) lies on these lines: {2887, 65037}, {3661, 24589}, {3836, 57948}, {7018, 25961}, {17124, 40415}, {48639, 56169}

X(65038) = isotomic conjugate of X(17125)
X(65038) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 17125}, {32, 17119}, {1501, 30638}
X(65038) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 17125}, {6376, 17119}
X(65038) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(334)}}, {{A, B, C, X(75), X(24589)}}, {{A, B, C, X(76), X(56169)}}, {{A, B, C, X(85), X(7035)}}, {{A, B, C, X(171), X(25961)}}, {{A, B, C, X(750), X(3836)}}, {{A, B, C, X(873), X(57925)}}, {{A, B, C, X(2887), X(17124)}}, {{A, B, C, X(4600), X(32019)}}, {{A, B, C, X(7131), X(24041)}}, {{A, B, C, X(17122), X(25957)}}, {{A, B, C, X(17758), X(56166)}}, {{A, B, C, X(25938), X(25970)}}, {{A, B, C, X(28650), X(40426)}}, {{A, B, C, X(30663), X(65026)}}, {{A, B, C, X(31002), X(59255)}}, {{A, B, C, X(31237), X(58443)}}, {{A, B, C, X(32011), X(57722)}}, {{A, B, C, X(40013), X(56212)}}, {{A, B, C, X(40021), X(60678)}}, {{A, B, C, X(40027), X(40216)}}, {{A, B, C, X(56163), X(60236)}}, {{A, B, C, X(57917), X(63173)}}
X(65038) = barycentric quotient X(i)/X(j) for these (i, j): {2, 17125}, {75, 17119}, {561, 30638}, {57948, 43264}

X(65039) = 2ND BASEPOINT OF THE GEMINI 57 TRIANGLE WRT ABC

Barycentrics    (a+b)^2*(a+c)^2*(b^2-b*c+c^2) : :

X(65039) lies on these lines: {2, 799}, {86, 65077}, {274, 65059}, {552, 553}, {2669, 4685}, {3175, 52137}, {7304, 41629}, {16711, 52379}, {18827, 42055}, {19723, 34016}, {32010, 65071}, {33947, 56805}, {40409, 46922}

X(65039) = isotomic conjugate of X(43265)
X(65039) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 43265}, {213, 56196}, {762, 38813}, {872, 17743}, {983, 1500}, {4621, 50487}, {7033, 7109}, {7064, 7132}, {8684, 46390}
X(65039) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43265}, {6626, 56196}, {16584, 6535}, {41771, 594}, {52657, 756}
X(65039) = pole of line {1334, 41333} with respect to the Stammler hyperbola
X(65039) = pole of line {2238, 2321} with respect to the Wallace hyperbola
X(65039) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(982)}}, {{A, B, C, X(553), X(3662)}}, {{A, B, C, X(1412), X(37128)}}, {{A, B, C, X(1434), X(33947)}}, {{A, B, C, X(3674), X(7185)}}, {{A, B, C, X(3794), X(60721)}}, {{A, B, C, X(3865), X(34914)}}, {{A, B, C, X(16592), X(18905)}}
X(65039) = barycentric product X(i)*X(j) for these (i, j): {261, 7185}, {873, 982}, {1509, 3662}, {2887, 6628}, {3705, 552}, {3721, 57949}, {3776, 4610}, {3777, 4623}, {3794, 57785}, {17206, 31917}, {18021, 7248}, {20234, 763}, {23473, 59148}, {33930, 757}, {33947, 86}, {41777, 52379}, {57992, 7032}
X(65039) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43265}, {86, 56196}, {261, 56180}, {552, 56358}, {757, 983}, {873, 7033}, {982, 756}, {1509, 17743}, {2275, 1500}, {2887, 6535}, {3056, 7064}, {3662, 594}, {3705, 6057}, {3721, 762}, {3776, 4024}, {3777, 4705}, {3784, 3690}, {3794, 210}, {3808, 4155}, {3888, 40521}, {4610, 4621}, {6628, 40415}, {7032, 872}, {7184, 21803}, {7185, 12}, {7187, 21021}, {7248, 181}, {23473, 21700}, {31917, 1826}, {33891, 4037}, {33930, 1089}, {33946, 4103}, {33947, 10}, {36066, 8684}, {41777, 2171}, {50514, 50487}, {57949, 38810}, {57992, 7034}
X(65039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61403, 61407, 873}

X(65040) = 2ND BASEPOINT OF THE GEMINI 58 TRIANGLE WRT ABC

Barycentrics    (a-b)^2*(a-c)^2*(b^2+b*c+c^2) : :

X(65040) lies on these lines: {2, 7035}, {190, 4785}, {238, 519}, {536, 1921}, {537, 30663}, {668, 4762}, {788, 3799}, {824, 3807}, {3773, 40793}, {3783, 4439}, {3790, 56854}, {4562, 28840}, {5378, 50313}, {6632, 50105}, {9285, 42054}, {9362, 45313}, {17281, 57950}, {40835, 43265}, {47774, 54099}

X(65040) = isotomic conjugate of X(43266)
X(65040) = trilinear pole of line {3799, 3807}
X(65040) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 43266}, {244, 40746}, {667, 4817}, {764, 825}, {789, 3249}, {870, 1977}, {875, 23597}, {985, 1015}, {1357, 2344}, {1492, 21143}, {3248, 14621}, {4586, 8027}, {6545, 34069}, {52652, 61048}
X(65040) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43266}, {3789, 1015}, {6631, 4817}, {19584, 244}, {27481, 1086}, {38995, 21143}, {55049, 8027}, {61065, 6545}
X(65040) = X(i)-cross conjugate of X(j) for these {i, j}: {2276, 3799}, {3661, 3807}, {3789, 668}, {3790, 4505}, {27481, 190}
X(65040) = pole of line {32094, 50023} with respect to the Yff parabola
X(65040) = pole of line {17205, 23597} with respect to the Wallace hyperbola
X(65040) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(238)}}, {{A, B, C, X(519), X(824)}}, {{A, B, C, X(536), X(788)}}, {{A, B, C, X(765), X(31625)}}, {{A, B, C, X(3227), X(52029)}}, {{A, B, C, X(3717), X(3790)}}, {{A, B, C, X(3773), X(6541)}}, {{A, B, C, X(3774), X(21897)}}, {{A, B, C, X(3789), X(4762)}}, {{A, B, C, X(3864), X(34892)}}, {{A, B, C, X(4785), X(14621)}}, {{A, B, C, X(7035), X(57566)}}, {{A, B, C, X(17264), X(33931)}}, {{A, B, C, X(18145), X(40091)}}, {{A, B, C, X(27474), X(39749)}}, {{A, B, C, X(30966), X(55955)}}, {{A, B, C, X(31909), X(33309)}}
X(65040) = barycentric product X(i)*X(j) for these (i, j): {100, 4505}, {190, 3807}, {1016, 3661}, {1491, 57950}, {2276, 31625}, {3773, 4600}, {3790, 4998}, {3799, 668}, {4076, 7179}, {4439, 62536}, {6632, 824}, {7035, 984}, {33931, 765}, {57731, 62415}
X(65040) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43266}, {190, 4817}, {765, 985}, {788, 8027}, {824, 6545}, {869, 3248}, {874, 63222}, {984, 244}, {1016, 14621}, {1252, 40746}, {1469, 1357}, {1491, 764}, {2276, 1015}, {3250, 21143}, {3570, 23597}, {3661, 1086}, {3773, 3120}, {3774, 3121}, {3781, 3937}, {3783, 27846}, {3786, 18191}, {3790, 11}, {3797, 27918}, {3799, 513}, {3807, 514}, {4076, 52133}, {4439, 1647}, {4481, 8042}, {4505, 693}, {4517, 3271}, {4522, 21132}, {6632, 4586}, {7035, 870}, {7146, 53538}, {7179, 1358}, {16603, 53545}, {30966, 17205}, {33931, 1111}, {40728, 1977}, {40773, 16726}, {40790, 53541}, {46386, 3249}, {52029, 43921}, {57731, 1492}, {57950, 789}, {59149, 825}
X(65040) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61402, 61406, 7035}

X(65041) = 2ND BASEPOINT OF THE GEMINI 59 TRIANGLE WRT ABC

Barycentrics    b*c*(3*b*c+a*(3*b+c))*(3*b*c+a*(b+3*c)) : :

X(65041) lies on these lines: {2, 32107}, {76, 56212}, {86, 4479}, {335, 42029}, {350, 28626}, {3679, 65075}, {3741, 65043}, {4441, 30712}, {4980, 27494}, {6384, 20888}, {17210, 56052}, {27475, 42034}, {37652, 60873}, {39704, 42057}, {40418, 42043}, {48107, 62638}

X(65041) = isotomic conjugate of X(42042)
X(65041) = trilinear pole of line {30020, 514}
X(65041) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42042}, {32, 27268}, {32739, 47996}
X(65041) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42042}, {6376, 27268}, {40619, 47996}
X(65041) = X(i)-cross conjugate of X(j) for these {i, j}: {17248, 85}
X(65041) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(321), X(4479)}}, {{A, B, C, X(330), X(32107)}}, {{A, B, C, X(350), X(42029)}}, {{A, B, C, X(3551), X(16606)}}, {{A, B, C, X(3679), X(42057)}}, {{A, B, C, X(3741), X(42043)}}, {{A, B, C, X(4441), X(42034)}}, {{A, B, C, X(4980), X(30963)}}, {{A, B, C, X(6063), X(60678)}}, {{A, B, C, X(6376), X(20888)}}, {{A, B, C, X(18032), X(58013)}}, {{A, B, C, X(18827), X(39948)}}, {{A, B, C, X(32010), X(39980)}}, {{A, B, C, X(34860), X(60110)}}, {{A, B, C, X(35159), X(62528)}}, {{A, B, C, X(36602), X(39711)}}, {{A, B, C, X(40028), X(51865)}}, {{A, B, C, X(54128), X(55947)}}, {{A, B, C, X(54657), X(57723)}}, {{A, B, C, X(54740), X(57724)}}, {{A, B, C, X(56125), X(56211)}}
X(65041) = barycentric product X(i)*X(j) for these (i, j): {39736, 75}
X(65041) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42042}, {75, 27268}, {693, 47996}, {39736, 1}

X(65042) = 1ST BASEPOINT OF THE GEMINI 60 TRIANGLE WRT ABC

Barycentrics    (a*(b-3*c)-3*b*c)*(-(b*c)+a*(b+c))*(3*a*b-a*c+3*b*c) : :

X(65042) lies on these lines: {2, 20943}, {43, 40598}, {87, 25502}, {256, 30998}, {940, 20332}, {1221, 27268}, {3223, 3720}, {4699, 17038}, {9082, 58117}, {25507, 55971}, {26974, 32129}, {60236, 60792}

X(65042) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2162, 42043}, {4704, 7121}
X(65042) = X(i)-Dao conjugate of X(j) for these {i, j}: {40598, 4704}
X(65042) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(32005)}}, {{A, B, C, X(2), X(43)}}, {{A, B, C, X(3835), X(57722)}}, {{A, B, C, X(3971), X(30588)}}, {{A, B, C, X(4699), X(56052)}}, {{A, B, C, X(4997), X(27538)}}, {{A, B, C, X(6376), X(20943)}}, {{A, B, C, X(6382), X(40013)}}, {{A, B, C, X(18197), X(25417)}}, {{A, B, C, X(20287), X(30571)}}, {{A, B, C, X(20979), X(39967)}}, {{A, B, C, X(25430), X(62421)}}, {{A, B, C, X(25502), X(53675)}}, {{A, B, C, X(30998), X(41318)}}, {{A, B, C, X(33296), X(39736)}}
X(65042) = barycentric product X(i)*X(j) for these (i, j): {43, 65043}, {192, 39740}, {20906, 58117}
X(65042) = barycentric quotient X(i)/X(j) for these (i, j): {43, 42043}, {192, 4704}, {39740, 330}, {58117, 932}, {65043, 6384}

X(65043) = 2ND BASEPOINT OF THE GEMINI 60 TRIANGLE WRT ABC

Barycentrics    b*c*(3*a*b-a*c+3*b*c)*(-(a*b)+3*a*c+3*b*c) : :

X(65043) lies on these lines: {2, 20943}, {7, 4479}, {75, 59505}, {76, 40027}, {335, 42034}, {350, 30712}, {675, 58117}, {3741, 65041}, {4441, 36606}, {20942, 27475}, {27494, 42029}, {28626, 30963}, {31137, 65077}, {32011, 36634}, {37683, 60873}, {40418, 42042}, {43040, 44733}, {43067, 62638}

X(65043) = isotomic conjugate of X(42043)
X(65043) = trilinear pole of line {30091, 514}
X(65043) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42043}, {32, 4704}
X(65043) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42043}, {6376, 4704}
X(65043) = X(i)-cross conjugate of X(j) for these {i, j}: {17236, 85}
X(65043) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(76), X(20943)}}, {{A, B, C, X(290), X(44186)}}, {{A, B, C, X(312), X(4479)}}, {{A, B, C, X(330), X(32005)}}, {{A, B, C, X(350), X(42034)}}, {{A, B, C, X(596), X(60792)}}, {{A, B, C, X(3741), X(39974)}}, {{A, B, C, X(3840), X(36634)}}, {{A, B, C, X(4441), X(20942)}}, {{A, B, C, X(4685), X(31137)}}, {{A, B, C, X(18155), X(41851)}}, {{A, B, C, X(18298), X(59505)}}, {{A, B, C, X(18827), X(39980)}}, {{A, B, C, X(18832), X(60276)}}, {{A, B, C, X(20615), X(52654)}}, {{A, B, C, X(30963), X(42029)}}, {{A, B, C, X(32010), X(39948)}}, {{A, B, C, X(32020), X(40023)}}, {{A, B, C, X(32023), X(60678)}}, {{A, B, C, X(34860), X(60090)}}, {{A, B, C, X(36603), X(55945)}}, {{A, B, C, X(36871), X(53679)}}, {{A, B, C, X(40026), X(40030)}}, {{A, B, C, X(41683), X(56211)}}, {{A, B, C, X(43040), X(43067)}}, {{A, B, C, X(54885), X(57723)}}
X(65043) = barycentric product X(i)*X(j) for these (i, j): {3261, 58117}, {6384, 65042}, {39740, 75}
X(65043) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42043}, {75, 4704}, {39740, 1}, {58117, 101}, {65042, 43}

X(65044) = 1ST BASEPOINT OF THE GEMINI 61 TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(2*a^3+2*b^3+b^2*c-2*b*c^2-c^3+a^2*(-2*b+c)-2*a*(b^2-b*c+c^2))*(2*a^3-b^3+a^2*(b-2*c)-2*b^2*c+b*c^2+2*c^3-2*a*(b^2-b*c+c^2)) : :

X(65044) lies on the Kiepert hyperbola and on these lines: {2, 65045}, {4, 5435}, {57, 54928}, {307, 4052}, {459, 17923}, {1445, 54586}, {1751, 31231}, {2051, 5740}, {3911, 54676}, {14986, 60158}, {21454, 60170}, {37797, 54499}, {56559, 65021}

X(65044) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 58786}, {284, 37567}, {2194, 28609}
X(65044) = X(i)-Dao conjugate of X(j) for these {i, j}: {1214, 28609}, {3160, 58786}, {40590, 37567}
X(65044) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(88), X(1214)}}, {{A, B, C, X(306), X(5704)}}, {{A, B, C, X(307), X(5435)}}, {{A, B, C, X(1441), X(40420)}}, {{A, B, C, X(3668), X(44794)}}, {{A, B, C, X(5740), X(14829)}}, {{A, B, C, X(31231), X(56559)}}, {{A, B, C, X(34862), X(52389)}}, {{A, B, C, X(54052), X(56944)}}
X(65044) = barycentric product X(i)*X(j) for these (i, j): {226, 65045}
X(65044) = barycentric quotient X(i)/X(j) for these (i, j): {7, 58786}, {65, 37567}, {226, 28609}, {65045, 333}

X(65045) = 2ND BASEPOINT OF THE GEMINI 61 TRIANGLE WRT ABC

Barycentrics    (2*a^3+2*b^3+b^2*c-2*b*c^2-c^3+a^2*(-2*b+c)-2*a*(b^2-b*c+c^2))*(2*a^3-b^3+a^2*(b-2*c)-2*b^2*c+b*c^2+2*c^3-2*a*(b^2-b*c+c^2)) : :

X(65045) lies on these lines: {2, 65044}, {8, 4640}, {29, 41629}, {69, 6557}, {92, 39126}, {312, 4416}, {527, 65047}, {1121, 3928}, {3929, 4102}, {4997, 30567}, {5325, 55954}, {14552, 56086}, {14942, 32853}, {17740, 30711}, {18134, 65020}, {18359, 18750}, {30690, 54284}, {37758, 38255}

X(65045) = isotomic conjugate of X(28609)
X(65045) = trilinear pole of line {522, 59980}
X(65045) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37567}, {31, 28609}, {213, 58786}
X(65045) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 28609}, {9, 37567}, {6626, 58786}
X(65045) = pole of line {28609, 58786} with respect to the Wallace hyperbola
X(65045) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(57), X(33576)}}, {{A, B, C, X(69), X(903)}}, {{A, B, C, X(75), X(57887)}}, {{A, B, C, X(81), X(55965)}}, {{A, B, C, X(278), X(43759)}}, {{A, B, C, X(286), X(34282)}}, {{A, B, C, X(519), X(30567)}}, {{A, B, C, X(527), X(3928)}}, {{A, B, C, X(553), X(3929)}}, {{A, B, C, X(673), X(34607)}}, {{A, B, C, X(1088), X(34409)}}, {{A, B, C, X(1434), X(60167)}}, {{A, B, C, X(1494), X(56596)}}, {{A, B, C, X(1751), X(42304)}}, {{A, B, C, X(3062), X(4416)}}, {{A, B, C, X(3345), X(54661)}}, {{A, B, C, X(4921), X(18134)}}, {{A, B, C, X(5325), X(6173)}}, {{A, B, C, X(7091), X(39948)}}, {{A, B, C, X(7319), X(44794)}}, {{A, B, C, X(8580), X(50095)}}, {{A, B, C, X(9311), X(13478)}}, {{A, B, C, X(11015), X(24624)}}, {{A, B, C, X(11019), X(17294)}}, {{A, B, C, X(14552), X(42028)}}, {{A, B, C, X(16704), X(39700)}}, {{A, B, C, X(17078), X(18750)}}, {{A, B, C, X(17740), X(42029)}}, {{A, B, C, X(18025), X(62528)}}, {{A, B, C, X(20942), X(37758)}}, {{A, B, C, X(26748), X(37222)}}, {{A, B, C, X(26750), X(60139)}}, {{A, B, C, X(29574), X(35613)}}, {{A, B, C, X(34863), X(54119)}}, {{A, B, C, X(35141), X(44186)}}, {{A, B, C, X(36588), X(58005)}}, {{A, B, C, X(36603), X(41790)}}, {{A, B, C, X(37131), X(39947)}}, {{A, B, C, X(40014), X(59759)}}, {{A, B, C, X(40419), X(55983)}}, {{A, B, C, X(42033), X(54284)}}, {{A, B, C, X(44733), X(54928)}}, {{A, B, C, X(54735), X(55938)}}
X(65045) = barycentric product X(i)*X(j) for these (i, j): {333, 65044}
X(65045) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37567}, {2, 28609}, {86, 58786}, {65044, 226}

X(65046) = 1ST BASEPOINT OF THE GEMINI 65 TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)*(3*a^2-2*a*b+3*b^2-3*c^2)*(3*a^2-3*b^2-2*a*c+3*c^2) : :

X(65046) lies on these lines: {1, 3091}, {2, 65047}, {7, 39980}, {57, 40968}, {81, 6180}, {226, 39948}, {274, 61413}, {277, 57477}, {279, 3772}, {346, 59759}, {347, 37887}, {948, 56043}, {1257, 55095}, {4000, 44794}, {5435, 36603}, {5723, 46873}, {8056, 36640}, {15474, 37798}, {25525, 62705}, {36871, 52358}, {37759, 39696}, {37787, 39947}, {37800, 56218}, {52374, 54366}

X(65046) = isogonal conjugate of X(62245)
X(65046) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 62245}, {9, 5204}, {33, 23140}, {41, 21296}, {55, 3928}, {212, 17917}, {284, 3962}, {2175, 21605}, {2194, 4035}
X(65046) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 62245}, {223, 3928}, {478, 5204}, {1214, 4035}, {3160, 21296}, {40590, 3962}, {40593, 21605}, {40837, 17917}
X(65046) = X(i)-cross conjugate of X(j) for these {i, j}: {1420, 7}, {41441, 7319}
X(65046) = pole of line {5435, 5691} with respect to the dual conic of Yff parabola
X(65046) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(19925)}}, {{A, B, C, X(7), X(5226)}}, {{A, B, C, X(19), X(51316)}}, {{A, B, C, X(27), X(3091)}}, {{A, B, C, X(92), X(59387)}}, {{A, B, C, X(189), X(6336)}}, {{A, B, C, X(196), X(16080)}}, {{A, B, C, X(226), X(3947)}}, {{A, B, C, X(281), X(46208)}}, {{A, B, C, X(312), X(1847)}}, {{A, B, C, X(346), X(393)}}, {{A, B, C, X(459), X(23984)}}, {{A, B, C, X(514), X(28236)}}, {{A, B, C, X(673), X(5274)}}, {{A, B, C, X(1086), X(31611)}}, {{A, B, C, X(1131), X(61392)}}, {{A, B, C, X(1132), X(61393)}}, {{A, B, C, X(1427), X(62207)}}, {{A, B, C, X(1440), X(56049)}}, {{A, B, C, X(1751), X(56086)}}, {{A, B, C, X(1945), X(30651)}}, {{A, B, C, X(2051), X(3817)}}, {{A, B, C, X(3219), X(54366)}}, {{A, B, C, X(4373), X(60254)}}, {{A, B, C, X(5261), X(57826)}}, {{A, B, C, X(5435), X(36621)}}, {{A, B, C, X(6180), X(40160)}}, {{A, B, C, X(9311), X(56201)}}, {{A, B, C, X(10405), X(13478)}}, {{A, B, C, X(10590), X(40573)}}, {{A, B, C, X(14377), X(45098)}}, {{A, B, C, X(18220), X(38255)}}, {{A, B, C, X(18359), X(60168)}}, {{A, B, C, X(23062), X(42318)}}, {{A, B, C, X(25525), X(34917)}}, {{A, B, C, X(27818), X(40420)}}, {{A, B, C, X(30699), X(37759)}}, {{A, B, C, X(30711), X(55962)}}, {{A, B, C, X(34529), X(55110)}}, {{A, B, C, X(36620), X(56783)}}, {{A, B, C, X(40154), X(56274)}}, {{A, B, C, X(43035), X(59612)}}, {{A, B, C, X(46873), X(60993)}}, {{A, B, C, X(51782), X(60076)}}, {{A, B, C, X(55938), X(56033)}}, {{A, B, C, X(56075), X(60107)}}, {{A, B, C, X(56264), X(56358)}}
X(65046) = barycentric product X(i)*X(j) for these (i, j): {7, 7319}, {57, 65047}, {41441, 85}
X(65046) = barycentric quotient X(i)/X(j) for these (i, j): {6, 62245}, {7, 21296}, {56, 5204}, {57, 3928}, {65, 3962}, {85, 21605}, {222, 23140}, {226, 4035}, {278, 17917}, {1420, 45036}, {7319, 8}, {41441, 9}, {63208, 63915}, {65047, 312}

X(65047) = 2ND BASEPOINT OF THE GEMINI 65 TRIANGLE WRT ABC

Barycentrics    b*c*(3*a^2-2*a*b+3*b^2-3*c^2)*(-3*a^2+3*b^2+2*a*c-3*c^2) : :

X(65047) lies on these lines: {2, 65046}, {8, 3967}, {75, 56201}, {321, 30711}, {333, 3729}, {527, 65045}, {1121, 28609}, {4102, 31142}, {4664, 46880}, {6557, 20942}, {17781, 55956}, {18359, 20921}, {18743, 38255}, {20223, 34234}, {30807, 36605}, {31164, 56947}, {42027, 60812}

X(65047) = isotomic conjugate of X(3928)
X(65047) = trilinear pole of line {21052, 23678}
X(65047) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 5204}, {25, 23140}, {31, 3928}, {32, 21296}, {56, 62245}, {184, 17917}, {560, 21605}, {1333, 3962}, {2206, 4035}, {38266, 45036}
X(65047) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 62245}, {2, 3928}, {9, 5204}, {37, 3962}, {6374, 21605}, {6376, 21296}, {6505, 23140}, {40603, 4035}, {62605, 17917}
X(65047) = X(i)-cross conjugate of X(j) for these {i, j}: {145, 75}
X(65047) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(27), X(54766)}}, {{A, B, C, X(75), X(42034)}}, {{A, B, C, X(145), X(21605)}}, {{A, B, C, X(226), X(3929)}}, {{A, B, C, X(278), X(5225)}}, {{A, B, C, X(309), X(903)}}, {{A, B, C, X(321), X(42029)}}, {{A, B, C, X(322), X(1494)}}, {{A, B, C, X(331), X(59761)}}, {{A, B, C, X(514), X(36603)}}, {{A, B, C, X(527), X(28609)}}, {{A, B, C, X(553), X(31142)}}, {{A, B, C, X(1222), X(60254)}}, {{A, B, C, X(1255), X(55965)}}, {{A, B, C, X(1434), X(45100)}}, {{A, B, C, X(1847), X(54622)}}, {{A, B, C, X(2051), X(9311)}}, {{A, B, C, X(2184), X(4564)}}, {{A, B, C, X(2185), X(56033)}}, {{A, B, C, X(2349), X(56352)}}, {{A, B, C, X(2481), X(44186)}}, {{A, B, C, X(3577), X(63194)}}, {{A, B, C, X(3729), X(3967)}}, {{A, B, C, X(6336), X(60155)}}, {{A, B, C, X(7319), X(65046)}}, {{A, B, C, X(12701), X(52374)}}, {{A, B, C, X(13405), X(17294)}}, {{A, B, C, X(14554), X(42304)}}, {{A, B, C, X(15909), X(24703)}}, {{A, B, C, X(17078), X(20921)}}, {{A, B, C, X(17781), X(31164)}}, {{A, B, C, X(18743), X(20942)}}, {{A, B, C, X(19804), X(60097)}}, {{A, B, C, X(20570), X(39704)}}, {{A, B, C, X(20923), X(35652)}}, {{A, B, C, X(30693), X(36910)}}, {{A, B, C, X(30710), X(40023)}}, {{A, B, C, X(31165), X(39948)}}, {{A, B, C, X(32017), X(40014)}}, {{A, B, C, X(32023), X(55983)}}, {{A, B, C, X(34535), X(54676)}}, {{A, B, C, X(34860), X(60261)}}, {{A, B, C, X(34863), X(60257)}}, {{A, B, C, X(36609), X(40843)}}, {{A, B, C, X(46277), X(57925)}}, {{A, B, C, X(54760), X(64984)}}, {{A, B, C, X(54788), X(56218)}}, {{A, B, C, X(56030), X(60071)}}, {{A, B, C, X(56127), X(60267)}}
X(65047) = barycentric product X(i)*X(j) for these (i, j): {312, 65046}, {7319, 75}, {41441, 76}
X(65047) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5204}, {2, 3928}, {9, 62245}, {10, 3962}, {63, 23140}, {75, 21296}, {76, 21605}, {92, 17917}, {145, 45036}, {321, 4035}, {3621, 63915}, {7319, 1}, {41441, 6}, {65046, 57}

X(65048) = 1ST BASEPOINT OF THE GEMINI 66 TRIANGLE WRT ABC

Barycentrics    a*(a+b)*(a+c)*(a+2*b+c)*(a+b+2*c)*(a^2+a*b+b^2-c^2)*(a^2-b^2+a*c+c^2) : :

X(65048) lies on these lines: {1, 2940}, {2, 8818}, {57, 1171}, {79, 6536}, {81, 2160}, {274, 30690}, {1929, 13486}, {4184, 6186}, {6539, 39722}, {25417, 40214}, {27186, 32014}, {35991, 56137}, {40143, 52558}

X(65048) = trilinear pole of line {14158, 513}
X(65048) = X(i)-isoconjugate-of-X(j) for these {i, j}: {10, 17454}, {35, 1213}, {37, 3647}, {42, 3578}, {319, 20970}, {756, 17190}, {1100, 3678}, {1962, 3219}, {2003, 4046}, {2174, 4647}, {2308, 3969}, {2594, 3686}, {2605, 4115}, {3649, 52405}, {3683, 16577}, {3702, 21741}, {3958, 6198}, {4427, 55210}, {7265, 35327}, {8013, 40214}, {8663, 55235}, {21816, 56934}, {22080, 52412}, {35057, 61170}, {35342, 57099}
X(65048) = X(i)-Dao conjugate of X(j) for these {i, j}: {40589, 3647}, {40592, 3578}
X(65048) = X(i)-cross conjugate of X(j) for these {i, j}: {58, 40438}, {2160, 57419}
X(65048) = pole of line {3647, 17454} with respect to the Stammler hyperbola
X(65048) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(27), X(37405)}}, {{A, B, C, X(58), X(40214)}}, {{A, B, C, X(267), X(2940)}}, {{A, B, C, X(2160), X(8818)}}, {{A, B, C, X(4184), X(31904)}}, {{A, B, C, X(14838), X(19620)}}, {{A, B, C, X(17190), X(32636)}}, {{A, B, C, X(52375), X(52393)}}, {{A, B, C, X(52380), X(56440)}}, {{A, B, C, X(57419), X(60139)}}
X(65048) = barycentric product X(i)*X(j) for these (i, j): {1171, 30690}, {1255, 52393}, {1268, 52375}, {2160, 32014}, {13486, 4608}, {40438, 79}, {52558, 6757}, {55236, 62535}, {57419, 86}, {60139, 81}
X(65048) = barycentric quotient X(i)/X(j) for these (i, j): {58, 3647}, {79, 4647}, {81, 3578}, {593, 17190}, {1126, 3678}, {1171, 3219}, {1255, 3969}, {1333, 17454}, {2160, 1213}, {3615, 3702}, {6186, 1962}, {6742, 61174}, {6757, 52576}, {7073, 4046}, {7100, 41014}, {13486, 4427}, {30690, 1230}, {32014, 33939}, {40438, 319}, {47947, 7265}, {50344, 57099}, {52372, 3649}, {52375, 1125}, {52393, 4359}, {52558, 56934}, {57419, 10}, {58301, 58304}, {59179, 8040}, {60139, 321}, {62535, 55235}

X(65049) = 1ST BASEPOINT OF THE GEMINI 68 TRIANGLE WRT ABC

Barycentrics    b*c*(b+c)*(a^2*(b-2*c)+b*c*(b+c)+a*(b^2+b*c-2*c^2))*(a^2*(-2*b+c)+b*c*(b+c)+a*(-2*b^2+b*c+c^2)) : :

X(65049) lies on the Kiepert hyperbola and on these lines: {2, 65050}, {3720, 60109}, {4035, 14554}, {17135, 56161}, {17751, 56172}, {18133, 57722}, {18743, 60071}, {19806, 54735}, {19810, 65051}, {20553, 60155}, {30588, 62588}, {46827, 60790}

X(65049) = isotomic conjugate of X(27643)
X(65049) = trilinear pole of line {523, 55184}
X(65049) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 27643}, {2206, 42044}
X(65049) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 27643}, {40603, 42044}
X(65049) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6383), X(25417)}}, {{A, B, C, X(15232), X(55990)}}, {{A, B, C, X(29687), X(41233)}}, {{A, B, C, X(36807), X(56246)}}, {{A, B, C, X(39747), X(42027)}}
X(65049) = barycentric product X(i)*X(j) for these (i, j): {321, 65050}
X(65049) = barycentric quotient X(i)/X(j) for these (i, j): {2, 27643}, {321, 42044}, {65050, 81}

X(65050) = 2ND BASEPOINT OF THE GEMINI 68 TRIANGLE WRT ABC

Barycentrics    (a^2*(2*b-c)-b*c*(b+c)+a*(2*b^2-b*c-c^2))*(a^2*(b-2*c)+b*c*(b+c)+a*(b^2+b*c-2*c^2)) : :

X(65050) lies on these lines: {1, 32933}, {2, 65049}, {89, 45222}, {1022, 29302}, {1150, 8056}, {1255, 17394}, {3227, 50106}, {4664, 56037}, {16834, 39950}, {17379, 27789}, {19684, 25430}, {26745, 37683}, {32009, 62803}, {39797, 62853}, {39970, 63060}, {42025, 56066}, {42029, 55953}, {42044, 65057}

X(65050) = isotomic conjugate of X(42044)
X(65050) = trilinear pole of line {47795, 47818}
X(65050) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42044}, {42, 27643}
X(65050) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42044}, {40592, 27643}
X(65050) = pole of line {27643, 42044} with respect to the Wallace hyperbola
X(65050) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(321), X(9311)}}, {{A, B, C, X(514), X(39700)}}, {{A, B, C, X(519), X(29302)}}, {{A, B, C, X(536), X(50106)}}, {{A, B, C, X(553), X(26223)}}, {{A, B, C, X(604), X(39982)}}, {{A, B, C, X(903), X(2995)}}, {{A, B, C, X(1121), X(54744)}}, {{A, B, C, X(1150), X(41629)}}, {{A, B, C, X(1222), X(62923)}}, {{A, B, C, X(1434), X(60082)}}, {{A, B, C, X(1751), X(46638)}}, {{A, B, C, X(3228), X(32936)}}, {{A, B, C, X(3679), X(45222)}}, {{A, B, C, X(3995), X(56135)}}, {{A, B, C, X(4359), X(31359)}}, {{A, B, C, X(4651), X(16834)}}, {{A, B, C, X(4921), X(37683)}}, {{A, B, C, X(6513), X(15419)}}, {{A, B, C, X(7093), X(18108)}}, {{A, B, C, X(14377), X(40394)}}, {{A, B, C, X(16709), X(17394)}}, {{A, B, C, X(16833), X(20011)}}, {{A, B, C, X(17379), X(42025)}}, {{A, B, C, X(19684), X(42028)}}, {{A, B, C, X(19796), X(50105)}}, {{A, B, C, X(26037), X(29584)}}, {{A, B, C, X(28630), X(60139)}}, {{A, B, C, X(32911), X(39969)}}, {{A, B, C, X(34860), X(40013)}}, {{A, B, C, X(35168), X(54686)}}, {{A, B, C, X(39994), X(42304)}}, {{A, B, C, X(40426), X(64984)}}, {{A, B, C, X(42030), X(52379)}}, {{A, B, C, X(42044), X(42051)}}, {{A, B, C, X(50043), X(50101)}}, {{A, B, C, X(52393), X(56046)}}, {{A, B, C, X(55026), X(55945)}}, {{A, B, C, X(55990), X(56145)}}
X(65050) = barycentric product X(i)*X(j) for these (i, j): {65049, 81}
X(65050) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42044}, {81, 27643}, {65049, 321}

X(65051) = 2ND BASEPOINT OF THE GEMINI 69 TRIANGLE WRT ABC

Barycentrics    (a^3+(b-2*c)*(b+c)^2-a*c*(2*b+3*c))*(a^3-(2*b-c)*(b+c)^2-a*b*(3*b+2*c)) : :

X(65051) lies on the Kiepert hyperbola and on these lines: {10, 32936}, {226, 50292}, {321, 32025}, {524, 60139}, {598, 63060}, {671, 3578}, {4052, 31143}, {4921, 60172}, {11599, 33075}, {17019, 30588}, {17346, 54744}, {19723, 54929}, {19810, 65049}, {23942, 40214}, {31144, 65022}, {32779, 60243}, {33133, 56226}, {37654, 54766}, {42025, 55949}, {50106, 60245}, {50796, 60634}

X(65051) = isotomic conjugate of X(42045)
X(65051) = trilinear pole of line {24959, 47839}
X(65051) = pole of line {49724, 65051} with respect to the Kiepert hyperbola
X(65051) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(50292)}}, {{A, B, C, X(75), X(57891)}}, {{A, B, C, X(81), X(41816)}}, {{A, B, C, X(257), X(52393)}}, {{A, B, C, X(524), X(3578)}}, {{A, B, C, X(525), X(57860)}}, {{A, B, C, X(897), X(40143)}}, {{A, B, C, X(903), X(32025)}}, {{A, B, C, X(1171), X(4674)}}, {{A, B, C, X(1494), X(36588)}}, {{A, B, C, X(1821), X(56947)}}, {{A, B, C, X(2987), X(40214)}}, {{A, B, C, X(3228), X(32936)}}, {{A, B, C, X(3679), X(17019)}}, {{A, B, C, X(4102), X(36590)}}, {{A, B, C, X(17787), X(50106)}}, {{A, B, C, X(19810), X(42044)}}, {{A, B, C, X(26665), X(50043)}}, {{A, B, C, X(31143), X(41629)}}, {{A, B, C, X(31144), X(42025)}}, {{A, B, C, X(32018), X(40394)}}, {{A, B, C, X(32779), X(42029)}}, {{A, B, C, X(33133), X(42034)}}, {{A, B, C, X(42045), X(49724)}}

X(65052) = 2ND BASEPOINT OF THE GEMINI 70 TRIANGLE WRT ABC

Barycentrics    (2*a^3-a^2*(2*b+c)+b*(2*b^2-b*c-3*c^2)-a*(2*b^2+b*c+3*c^2))*(2*a^3-a^2*(b+2*c)+c*(-3*b^2-b*c+2*c^2)-a*(3*b^2+b*c+2*c^2)) : :

X(65052) lies on these lines: {1150, 5219}, {3679, 32917}, {4384, 23598}, {25057, 35170}, {30608, 43757}

X(65052) = isotomic conjugate of X(26738)
X(65052) = trilinear pole of line {4702, 4777}
X(65052) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(80)}}, {{A, B, C, X(88), X(39952)}}, {{A, B, C, X(257), X(60247)}}, {{A, B, C, X(321), X(56062)}}, {{A, B, C, X(333), X(1150)}}, {{A, B, C, X(1016), X(62929)}}, {{A, B, C, X(2963), X(17275)}}, {{A, B, C, X(4358), X(55954)}}, {{A, B, C, X(4384), X(17780)}}, {{A, B, C, X(4391), X(30608)}}, {{A, B, C, X(4715), X(25057)}}, {{A, B, C, X(14621), X(24624)}}, {{A, B, C, X(16704), X(36818)}}, {{A, B, C, X(17335), X(24593)}}, {{A, B, C, X(25430), X(37633)}}, {{A, B, C, X(39706), X(56320)}}, {{A, B, C, X(42335), X(43759)}}, {{A, B, C, X(52500), X(58004)}}

X(65053) = 2ND BASEPOINT OF THE GEMINI 72 TRIANGLE WRT ABC

Barycentrics    (-3*a*b^4*c+2*b^3*c^3+a^3*(2*b^3-c^3))*(-2*b^3*c^3+3*a*b*c^4+a^3*(b^3-2*c^3)) : :

X(65053) lies on these lines: {238, 716}, {536, 3783}, {1921, 30875}, {3797, 6381}, {36816, 56854}

X(65053) = isotomic conjugate of X(42046)
X(65053) = trilinear pole of line {4728, 30665}
X(65053) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(238)}}, {{A, B, C, X(75), X(514)}}, {{A, B, C, X(561), X(716)}}, {{A, B, C, X(726), X(4762)}}, {{A, B, C, X(1581), X(43095)}}, {{A, B, C, X(21443), X(52049)}}, {{A, B, C, X(30028), X(42054)}}

X(65054) = 2ND BASEPOINT OF THE GEMINI 74 TRIANGLE WRT ABC

Barycentrics    a*(2*a^3*b-b^4-3*a^2*c^2+2*b*c^3)*(-3*a^2*b^2+2*a^3*c+2*b^3*c-c^4) : :

X(65054) lies on these lines: {44, 3783}, {238, 52957}, {519, 3797}, {751, 42084}, {752, 1921}, {1386, 40793}, {16468, 56854}, {18822, 64908}

X(65054) = isogonal conjugate of X(58863)
X(65054) = isotomic conjugate of X(43270)
X(65054) = trilinear pole of line {1635, 14402}
X(65054) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 58863}, {31, 43270}, {292, 27931}
X(65054) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 43270}, {3, 58863}, {19557, 27931}
X(65054) = pole of line {43270, 58863} with respect to the Wallace hyperbola
X(65054) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(44)}}, {{A, B, C, X(2), X(238)}}, {{A, B, C, X(31), X(752)}}, {{A, B, C, X(89), X(49712)}}, {{A, B, C, X(291), X(31349)}}, {{A, B, C, X(518), X(4785)}}, {{A, B, C, X(527), X(36276)}}, {{A, B, C, X(660), X(59043)}}, {{A, B, C, X(1386), X(1757)}}, {{A, B, C, X(1581), X(43097)}}, {{A, B, C, X(1929), X(37131)}}, {{A, B, C, X(2239), X(50300)}}, {{A, B, C, X(2382), X(3572)}}, {{A, B, C, X(3246), X(51297)}}, {{A, B, C, X(3257), X(8691)}}, {{A, B, C, X(4715), X(29350)}}, {{A, B, C, X(9073), X(36815)}}, {{A, B, C, X(12032), X(54619)}}, {{A, B, C, X(14665), X(35168)}}, {{A, B, C, X(17127), X(31151)}}, {{A, B, C, X(28288), X(42054)}}
X(65054) = barycentric quotient X(i)/X(j) for these (i, j): {2, 43270}, {6, 58863}, {238, 27931}

X(65055) = 2ND BASEPOINT OF THE GEMINI 76 TRIANGLE WRT ABC

Barycentrics    (a^3+b^3+a^2*(b-5*c)+b^2*c+b*c^2+c^3+a*(b^2+2*b*c-5*c^2))*(a^3+b^3+b^2*c+b*c^2+c^3+a^2*(-5*b+c)+a*(-5*b^2+2*b*c+c^2)) : :

X(65055) lies on these lines: {1, 59544}, {28, 41629}, {69, 8056}, {278, 19796}, {1255, 26065}, {3227, 42049}, {25101, 25430}, {42032, 55952}, {50043, 55953}

X(65055) = isotomic conjugate of X(42047)
X(65055) = trilinear pole of line {25923, 513}
X(65055) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42047}, {55, 28038}
X(65055) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42047}, {223, 28038}
X(65055) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(69), X(903)}}, {{A, B, C, X(345), X(19796)}}, {{A, B, C, X(536), X(42049)}}, {{A, B, C, X(553), X(26065)}}, {{A, B, C, X(2991), X(42467)}}, {{A, B, C, X(2994), X(54744)}}, {{A, B, C, X(7320), X(62884)}}, {{A, B, C, X(9311), X(60254)}}, {{A, B, C, X(14554), X(42360)}}, {{A, B, C, X(36916), X(56279)}}, {{A, B, C, X(39702), X(40420)}}, {{A, B, C, X(39732), X(51561)}}, {{A, B, C, X(39979), X(40151)}}, {{A, B, C, X(46638), X(60155)}}, {{A, B, C, X(55090), X(56044)}}, {{A, B, C, X(59544), X(60172)}}
X(65055) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42047}, {57, 28038}

X(65056) = 1ST BASEPOINT OF THE GEMINI 80 TRIANGLE WRT ABC

Barycentrics    b*c*(a^2*(b-2*c)+b*c*(b+c)+a*(b^2-2*b*c-2*c^2))*(a^2*(-2*b+c)+b*c*(b+c)+a*(-2*b^2-2*b*c+c^2)) : :

X(65056) lies on these lines: {2, 65057}, {7, 18140}, {75, 22220}, {86, 23579}, {335, 29982}, {350, 65075}, {1240, 46827}, {24524, 30598}, {30829, 44733}, {31002, 56253}

X(65056) = isotomic conjugate of X(27627)
X(65056) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 27627}, {32, 42051}
X(65056) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 27627}, {6376, 42051}
X(65056) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(264), X(57947)}}, {{A, B, C, X(286), X(7035)}}, {{A, B, C, X(334), X(57830)}}, {{A, B, C, X(350), X(29982)}}, {{A, B, C, X(561), X(57877)}}, {{A, B, C, X(1014), X(32016)}}, {{A, B, C, X(1193), X(46827)}}, {{A, B, C, X(1400), X(22220)}}, {{A, B, C, X(3831), X(59305)}}, {{A, B, C, X(4358), X(26734)}}, {{A, B, C, X(6381), X(56253)}}, {{A, B, C, X(18140), X(20568)}}, {{A, B, C, X(18812), X(55990)}}, {{A, B, C, X(31643), X(36805)}}, {{A, B, C, X(42285), X(56032)}}
X(65056) = barycentric product X(i)*X(j) for these (i, j): {65057, 75}
X(65056) = barycentric quotient X(i)/X(j) for these (i, j): {2, 27627}, {75, 42051}, {65057, 1}

X(65057) = 2ND BASEPOINT OF THE GEMINI 80 TRIANGLE WRT ABC

Barycentrics    (a^2*(2*b-c)-b*c*(b+c)+a*(2*b^2+2*b*c-c^2))*(a^2*(b-2*c)+b*c*(b+c)+a*(b^2-2*b*c-2*c^2)) : :

X(65057) lies on these lines: {1, 33309}, {2, 65056}, {57, 4360}, {81, 17319}, {88, 1999}, {89, 58820}, {239, 65074}, {291, 42057}, {314, 39747}, {536, 65059}, {959, 3241}, {1022, 6002}, {1258, 29584}, {3175, 3227}, {4139, 43928}, {4664, 39948}, {11679, 39963}, {16834, 39970}, {17350, 25417}, {19796, 34578}, {20942, 55952}, {29580, 56066}, {31036, 38247}, {36871, 42029}, {42044, 65050}, {48858, 51223}, {50101, 65028}

X(65057) = isotomic conjugate of X(42051)
X(65057) = trilinear pole of line {26078, 47793}
X(65057) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 27627}, {31, 42051}
X(65057) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42051}, {9, 27627}
X(65057) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(42360)}}, {{A, B, C, X(27), X(1016)}}, {{A, B, C, X(79), X(34527)}}, {{A, B, C, X(106), X(57749)}}, {{A, B, C, X(145), X(60167)}}, {{A, B, C, X(239), X(42057)}}, {{A, B, C, X(312), X(39702)}}, {{A, B, C, X(314), X(903)}}, {{A, B, C, X(335), X(42054)}}, {{A, B, C, X(519), X(1999)}}, {{A, B, C, X(536), X(3175)}}, {{A, B, C, X(1120), X(2985)}}, {{A, B, C, X(1221), X(42358)}}, {{A, B, C, X(1222), X(14534)}}, {{A, B, C, X(1389), X(54697)}}, {{A, B, C, X(1509), X(56224)}}, {{A, B, C, X(1751), X(56353)}}, {{A, B, C, X(3226), X(57785)}}, {{A, B, C, X(3241), X(11679)}}, {{A, B, C, X(3679), X(58820)}}, {{A, B, C, X(3741), X(29584)}}, {{A, B, C, X(3757), X(29574)}}, {{A, B, C, X(4362), X(17389)}}, {{A, B, C, X(4654), X(17350)}}, {{A, B, C, X(4664), X(42029)}}, {{A, B, C, X(5271), X(48858)}}, {{A, B, C, X(5557), X(62908)}}, {{A, B, C, X(5559), X(54119)}}, {{A, B, C, X(7320), X(60206)}}, {{A, B, C, X(9311), X(40012)}}, {{A, B, C, X(10453), X(16834)}}, {{A, B, C, X(14377), X(55988)}}, {{A, B, C, X(17264), X(19796)}}, {{A, B, C, X(17281), X(50068)}}, {{A, B, C, X(17319), X(42027)}}, {{A, B, C, X(18827), X(55997)}}, {{A, B, C, X(29580), X(43223)}}, {{A, B, C, X(34258), X(34860)}}, {{A, B, C, X(35168), X(56947)}}, {{A, B, C, X(35170), X(54775)}}, {{A, B, C, X(35652), X(42051)}}, {{A, B, C, X(38473), X(49543)}}, {{A, B, C, X(39594), X(50129)}}, {{A, B, C, X(39704), X(58021)}}, {{A, B, C, X(39739), X(58020)}}, {{A, B, C, X(41683), X(60264)}}, {{A, B, C, X(42032), X(50101)}}, {{A, B, C, X(43739), X(55992)}}, {{A, B, C, X(46638), X(60615)}}, {{A, B, C, X(52393), X(55990)}}, {{A, B, C, X(55945), X(56239)}}, {{A, B, C, X(56046), X(56145)}}
X(65057) = barycentric product X(i)*X(j) for these (i, j): {1, 65056}
X(65057) = barycentric quotient X(i)/X(j) for these (i, j): {1, 27627}, {2, 42051}, {65056, 75}

X(65058) = 1ST BASEPOINT OF THE GEMINI 81 TRIANGLE WRT ABC

Barycentrics    b*(a+b)*c*(a+c)*(-a+b+c)*(a*(b-2*c)+b*(b+c))*(a*(2*b-c)-c*(b+c)) : :

X(65058) lies on these lines: {2, 34283}, {8, 3794}, {38, 31359}, {81, 17743}, {85, 42304}, {92, 30035}, {257, 4359}, {314, 56086}, {873, 65018}, {1311, 8690}, {2064, 18359}, {4102, 17787}

X(65058) = isotomic conjugate of X(28387)
X(65058) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 28387}, {56, 61036}, {65, 16946}, {213, 64827}, {604, 3214}, {1042, 3217}, {1397, 3175}, {1400, 3915}, {1402, 4383}, {1409, 4186}, {1415, 4139}, {2149, 21963}, {52410, 59577}
X(65058) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 61036}, {2, 28387}, {650, 21963}, {1146, 4139}, {3161, 3214}, {6626, 64827}, {40582, 3915}, {40602, 16946}, {40605, 4383}, {40625, 4498}, {62585, 3175}
X(65058) = X(i)-cross conjugate of X(j) for these {i, j}: {341, 314}
X(65058) = pole of line {3217, 4383} with respect to the Wallace hyperbola
X(65058) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(63), X(30035)}}, {{A, B, C, X(81), X(3794)}}, {{A, B, C, X(314), X(873)}}, {{A, B, C, X(1432), X(10544)}}, {{A, B, C, X(2064), X(20924)}}, {{A, B, C, X(2350), X(4876)}}, {{A, B, C, X(3596), X(57947)}}, {{A, B, C, X(3975), X(27438)}}, {{A, B, C, X(4359), X(17787)}}, {{A, B, C, X(8042), X(17197)}}, {{A, B, C, X(20258), X(61412)}}, {{A, B, C, X(27391), X(30059)}}, {{A, B, C, X(39956), X(42304)}}, {{A, B, C, X(44130), X(44139)}}, {{A, B, C, X(55090), X(60320)}}
X(65058) = barycentric product X(i)*X(j) for these (i, j): {312, 65059}, {314, 34860}, {333, 40012}, {18021, 56192}, {28660, 39956}, {35519, 8690}, {52379, 56123}
X(65058) = barycentric quotient X(i)/X(j) for these (i, j): {2, 28387}, {8, 3214}, {9, 61036}, {11, 21963}, {21, 3915}, {29, 4186}, {86, 64827}, {284, 16946}, {312, 3175}, {314, 3875}, {333, 4383}, {341, 59577}, {522, 4139}, {1043, 3913}, {2287, 3217}, {3596, 56253}, {4560, 4498}, {7253, 42312}, {8690, 109}, {18155, 4106}, {18191, 17477}, {27424, 27432}, {28660, 18135}, {34860, 65}, {39956, 1400}, {40012, 226}, {42304, 1427}, {56123, 2171}, {56155, 1042}, {56192, 181}, {58329, 58334}, {65059, 57}

X(65059) = 2ND BASEPOINT OF THE GEMINI 81 TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(a*(b-2*c)+b*(b+c))*(a*(2*b-c)-c*(b+c)) : :

X(65059) lies on these lines: {1, 4234}, {2, 34283}, {57, 3759}, {81, 62300}, {86, 25430}, {88, 4921}, {105, 8690}, {274, 65039}, {279, 16711}, {291, 4685}, {314, 39694}, {333, 8056}, {536, 65057}, {553, 1432}, {894, 1255}, {959, 1401}, {1002, 35104}, {1224, 19870}, {1412, 7132}, {3227, 42051}, {4980, 55953}, {7192, 23834}, {8025, 27789}, {16696, 37870}, {16704, 26745}, {16726, 36805}, {18206, 39970}, {32009, 37596}, {34892, 42033}, {37756, 52374}, {38247, 62636}, {39703, 41834}, {39738, 40773}, {39962, 64424}, {40153, 60871}, {42034, 55952}, {50633, 51223}

X(65059) = isogonal conjugate of X(61036)
X(65059) = isotomic conjugate of X(3175)
X(65059) = trilinear pole of line {26144, 47796}
X(65059) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 61036}, {6, 3214}, {10, 16946}, {31, 3175}, {32, 56253}, {37, 3915}, {42, 4383}, {55, 28387}, {65, 3217}, {71, 4186}, {213, 3875}, {604, 59577}, {1020, 58334}, {1252, 21963}, {1334, 64827}, {1400, 3913}, {1402, 30568}, {1918, 18135}, {2209, 27432}, {4498, 4557}, {4559, 42312}
X(65059) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3175}, {3, 61036}, {9, 3214}, {223, 28387}, {661, 21963}, {1015, 4139}, {3161, 59577}, {6376, 56253}, {6626, 3875}, {34021, 18135}, {40582, 3913}, {40589, 3915}, {40592, 4383}, {40602, 3217}, {40605, 30568}, {40620, 4106}, {40625, 20317}, {55067, 42312}, {62574, 27432}
X(65059) = X(i)-cross conjugate of X(j) for these {i, j}: {8, 86}, {3794, 57785}, {18211, 7192}, {21342, 39734}
X(65059) = pole of line {3217, 3915} with respect to the Stammler hyperbola
X(65059) = pole of line {3175, 3875} with respect to the Wallace hyperbola
X(65059) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(30568)}}, {{A, B, C, X(27), X(4234)}}, {{A, B, C, X(86), X(552)}}, {{A, B, C, X(239), X(4685)}}, {{A, B, C, X(257), X(60267)}}, {{A, B, C, X(286), X(903)}}, {{A, B, C, X(335), X(42055)}}, {{A, B, C, X(514), X(4052)}}, {{A, B, C, X(536), X(42051)}}, {{A, B, C, X(553), X(894)}}, {{A, B, C, X(671), X(26735)}}, {{A, B, C, X(673), X(2985)}}, {{A, B, C, X(1121), X(54686)}}, {{A, B, C, X(1333), X(39982)}}, {{A, B, C, X(1401), X(16696)}}, {{A, B, C, X(1412), X(37128)}}, {{A, B, C, X(1434), X(14534)}}, {{A, B, C, X(1812), X(15419)}}, {{A, B, C, X(3175), X(56174)}}, {{A, B, C, X(3226), X(57815)}}, {{A, B, C, X(3759), X(42030)}}, {{A, B, C, X(4082), X(4765)}}, {{A, B, C, X(4610), X(32041)}}, {{A, B, C, X(4762), X(35104)}}, {{A, B, C, X(4921), X(16704)}}, {{A, B, C, X(7714), X(26643)}}, {{A, B, C, X(8025), X(42025)}}, {{A, B, C, X(9278), X(43265)}}, {{A, B, C, X(9311), X(34258)}}, {{A, B, C, X(14377), X(56046)}}, {{A, B, C, X(16755), X(37756)}}, {{A, B, C, X(16833), X(20012)}}, {{A, B, C, X(16834), X(59296)}}, {{A, B, C, X(17011), X(19870)}}, {{A, B, C, X(17301), X(50048)}}, {{A, B, C, X(17320), X(19797)}}, {{A, B, C, X(18821), X(57852)}}, {{A, B, C, X(18827), X(57785)}}, {{A, B, C, X(20568), X(39700)}}, {{A, B, C, X(21454), X(60077)}}, {{A, B, C, X(24850), X(60172)}}, {{A, B, C, X(25501), X(29580)}}, {{A, B, C, X(32010), X(55947)}}, {{A, B, C, X(34283), X(54549)}}, {{A, B, C, X(34860), X(40012)}}, {{A, B, C, X(35170), X(54744)}}, {{A, B, C, X(39956), X(60806)}}, {{A, B, C, X(46638), X(57721)}}, {{A, B, C, X(52393), X(55942)}}, {{A, B, C, X(54128), X(55945)}}, {{A, B, C, X(55090), X(58279)}}, {{A, B, C, X(55988), X(56145)}}
X(65059) = barycentric product X(i)*X(j) for these (i, j): {57, 65058}, {274, 39956}, {314, 56155}, {333, 42304}, {693, 8690}, {1509, 56123}, {34860, 86}, {40012, 81}, {56192, 873}
X(65059) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3214}, {2, 3175}, {6, 61036}, {8, 59577}, {21, 3913}, {28, 4186}, {57, 28387}, {58, 3915}, {75, 56253}, {81, 4383}, {86, 3875}, {244, 21963}, {274, 18135}, {284, 3217}, {330, 27432}, {333, 30568}, {513, 4139}, {1014, 64827}, {1019, 4498}, {1333, 16946}, {3737, 42312}, {4560, 20317}, {7192, 4106}, {8042, 23777}, {8690, 100}, {21789, 58334}, {34860, 10}, {39956, 37}, {40012, 321}, {42304, 226}, {56123, 594}, {56155, 65}, {56192, 756}, {60789, 56174}, {65058, 312}

X(65060) = 1ST BASEPOINT OF THE GEMINI 82 TRIANGLE WRT ABC

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*a^4-2*a^2*b^2+3*b^4-3*c^4)*(3*a^4-3*b^4-2*a^2*c^2+3*c^4) : :

X(65060) lies on these lines: {2, 65061}, {6, 8889}, {111, 62973}, {232, 51316}, {251, 1968}, {1368, 61301}, {1383, 7408}, {6103, 34570}, {6353, 36616}, {8770, 38282}, {21448, 52297}, {34212, 59652}, {34572, 52284}, {39951, 62958}

X(65060) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 32006}, {63, 9909}
X(65060) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 32006}, {3162, 9909}
X(65060) = X(i)-cross conjugate of X(j) for these {i, j}: {19118, 4}
X(65060) = pole of line {6353, 16774} with respect to the Kiepert hyperbola
X(65060) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(4), X(8889)}}, {{A, B, C, X(98), X(6340)}}, {{A, B, C, X(305), X(34285)}}, {{A, B, C, X(427), X(7378)}}, {{A, B, C, X(459), X(6531)}}, {{A, B, C, X(1093), X(7612)}}, {{A, B, C, X(1368), X(6623)}}, {{A, B, C, X(2052), X(47735)}}, {{A, B, C, X(3089), X(16419)}}, {{A, B, C, X(3424), X(17703)}}, {{A, B, C, X(3455), X(3926)}}, {{A, B, C, X(4232), X(52297)}}, {{A, B, C, X(5094), X(7408)}}, {{A, B, C, X(6353), X(36611)}}, {{A, B, C, X(6524), X(16080)}}, {{A, B, C, X(6776), X(57855)}}, {{A, B, C, X(7487), X(11548)}}, {{A, B, C, X(8753), X(52583)}}, {{A, B, C, X(8801), X(60125)}}, {{A, B, C, X(8884), X(14494)}}, {{A, B, C, X(10603), X(47847)}}, {{A, B, C, X(14572), X(16318)}}, {{A, B, C, X(14593), X(56270)}}, {{A, B, C, X(16263), X(60127)}}, {{A, B, C, X(17983), X(55023)}}, {{A, B, C, X(34208), X(40413)}}, {{A, B, C, X(36612), X(40120)}}, {{A, B, C, X(41932), X(53496)}}, {{A, B, C, X(52284), X(52285)}}, {{A, B, C, X(55972), X(62935)}}, {{A, B, C, X(57518), X(60073)}}
X(65060) = barycentric product X(i)*X(j) for these (i, j): {25, 65061}, {16774, 4}
X(65060) = barycentric quotient X(i)/X(j) for these (i, j): {4, 32006}, {25, 9909}, {16774, 69}, {65061, 305}

X(65061) = 2ND BASEPOINT OF THE GEMINI 82 TRIANGLE WRT ABC

Barycentrics    b^2*c^2*(3*a^4-2*a^2*b^2+3*b^4-3*c^4)*(-3*a^4+3*b^4+2*a^2*c^2-3*c^4) : :

X(65061) lies on these lines: {2, 65060}, {30, 65063}, {69, 16774}, {287, 37672}, {339, 21974}, {1494, 34609}, {1799, 1975}, {6340, 32818}, {7667, 65032}, {10691, 57822}, {13575, 62964}, {23292, 60872}, {30737, 35510}, {31152, 57852}, {36889, 62975}, {41009, 59756}

X(65061) = isotomic conjugate of X(9909)
X(65061) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 9909}, {560, 32006}
X(65061) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 9909}, {6374, 32006}
X(65061) = X(i)-cross conjugate of X(j) for these {i, j}: {193, 76}
X(65061) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(30), X(34609)}}, {{A, B, C, X(250), X(34427)}}, {{A, B, C, X(262), X(14528)}}, {{A, B, C, X(290), X(41530)}}, {{A, B, C, X(325), X(37672)}}, {{A, B, C, X(376), X(54707)}}, {{A, B, C, X(381), X(10691)}}, {{A, B, C, X(428), X(31152)}}, {{A, B, C, X(523), X(36616)}}, {{A, B, C, X(671), X(40009)}}, {{A, B, C, X(847), X(60185)}}, {{A, B, C, X(1093), X(60150)}}, {{A, B, C, X(1916), X(34861)}}, {{A, B, C, X(1975), X(42551)}}, {{A, B, C, X(3424), X(60822)}}, {{A, B, C, X(5064), X(7667)}}, {{A, B, C, X(5159), X(21974)}}, {{A, B, C, X(5641), X(54496)}}, {{A, B, C, X(6145), X(14458)}}, {{A, B, C, X(7788), X(23292)}}, {{A, B, C, X(9139), X(40144)}}, {{A, B, C, X(9909), X(38263)}}, {{A, B, C, X(14387), X(37874)}}, {{A, B, C, X(14492), X(14542)}}, {{A, B, C, X(18022), X(54636)}}, {{A, B, C, X(18848), X(54640)}}, {{A, B, C, X(31133), X(52397)}}, {{A, B, C, X(34168), X(54704)}}, {{A, B, C, X(34572), X(45096)}}, {{A, B, C, X(35142), X(54785)}}, {{A, B, C, X(40036), X(60277)}}, {{A, B, C, X(41009), X(62542)}}, {{A, B, C, X(44149), X(57902)}}, {{A, B, C, X(48374), X(54851)}}, {{A, B, C, X(52581), X(57799)}}, {{A, B, C, X(54973), X(60095)}}
X(65061) = barycentric product X(i)*X(j) for these (i, j): {305, 65060}, {16774, 76}
X(65061) = barycentric quotient X(i)/X(j) for these (i, j): {2, 9909}, {76, 32006}, {16774, 6}, {65060, 25}

X(65062) = 2ND BASEPOINT OF THE GEMINI 83 TRIANGLE WRT ABC

Barycentrics    (a^2+2*b^2+c^2)*(a^2+b^2+2*c^2)*(a^4+a^2*b^2+b^4-c^4)*(a^4-b^4+a^2*c^2+c^4) : :

X(65062) lies on these lines: {2, 14378}, {141, 15321}, {427, 3108}, {3456, 6636}, {5189, 61418}, {8024, 57852}, {41513, 57421}

X(65062) = isotomic conjugate of X(42052)
X(65062) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42052}, {6636, 17469}, {14247, 17457}, {18062, 37085}
X(65062) = X(i)-vertex conjugate of X(j) for these {i, j}: {6636, 65062}
X(65062) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 10159}
X(65062) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(66)}}, {{A, B, C, X(4), X(41366)}}, {{A, B, C, X(6), X(5064)}}, {{A, B, C, X(54), X(14492)}}, {{A, B, C, X(98), X(1487)}}, {{A, B, C, X(251), X(41464)}}, {{A, B, C, X(262), X(17711)}}, {{A, B, C, X(428), X(523)}}, {{A, B, C, X(847), X(14458)}}, {{A, B, C, X(930), X(41173)}}, {{A, B, C, X(1166), X(1297)}}, {{A, B, C, X(1494), X(34572)}}, {{A, B, C, X(3108), X(41435)}}, {{A, B, C, X(5627), X(54477)}}, {{A, B, C, X(10415), X(60125)}}, {{A, B, C, X(10422), X(53945)}}, {{A, B, C, X(14484), X(42021)}}, {{A, B, C, X(19307), X(54608)}}, {{A, B, C, X(34536), X(39284)}}, {{A, B, C, X(42052), X(46026)}}, {{A, B, C, X(43094), X(54540)}}
X(65062) = barycentric product X(i)*X(j) for these (i, j): {10159, 15321}, {14378, 40425}
X(65062) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42052}, {3108, 6636}, {3456, 5007}, {10159, 7768}, {14378, 6292}, {15321, 3589}, {31067, 57222}, {57421, 14247}

X(65063) = 2ND BASEPOINT OF THE GEMINI 84 TRIANGLE WRT ABC

Barycentrics    (2*a^6+2*b^6+b^4*c^2-2*b^2*c^4-c^6+a^4*(-2*b^2+c^2)-2*a^2*(b^4-b^2*c^2+c^4))*(2*a^6-b^6-2*b^4*c^2+b^2*c^4+2*c^6+a^4*(b^2-2*c^2)-2*a^2*(b^4-b^2*c^2+c^4)) : :

X(65063) lies on these lines: {30, 65061}, {287, 64060}, {305, 7667}, {315, 6340}, {1494, 9909}, {7714, 36889}, {7734, 59756}, {7788, 57800}, {13567, 60872}, {18018, 34603}, {37671, 40032}, {44210, 65032}

X(65063) = isotomic conjugate of X(34609)
X(65063) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(22), X(34603)}}, {{A, B, C, X(25), X(7667)}}, {{A, B, C, X(30), X(9909)}}, {{A, B, C, X(64), X(3425)}}, {{A, B, C, X(68), X(54709)}}, {{A, B, C, X(98), X(52441)}}, {{A, B, C, X(254), X(60185)}}, {{A, B, C, X(290), X(34412)}}, {{A, B, C, X(315), X(671)}}, {{A, B, C, X(376), X(7714)}}, {{A, B, C, X(1297), X(18848)}}, {{A, B, C, X(3504), X(60528)}}, {{A, B, C, X(5020), X(7734)}}, {{A, B, C, X(5064), X(44210)}}, {{A, B, C, X(5392), X(55032)}}, {{A, B, C, X(7788), X(13567)}}, {{A, B, C, X(8884), X(60150)}}, {{A, B, C, X(10154), X(34609)}}, {{A, B, C, X(13361), X(16419)}}, {{A, B, C, X(14457), X(14492)}}, {{A, B, C, X(15818), X(38321)}}, {{A, B, C, X(17811), X(37671)}}, {{A, B, C, X(22258), X(40119)}}, {{A, B, C, X(34285), X(55023)}}, {{A, B, C, X(34405), X(54922)}}, {{A, B, C, X(34861), X(54122)}}, {{A, B, C, X(35142), X(54930)}}, {{A, B, C, X(36616), X(41768)}}, {{A, B, C, X(40102), X(60141)}}, {{A, B, C, X(44175), X(54666)}}, {{A, B, C, X(46104), X(54798)}}, {{A, B, C, X(54124), X(54629)}}, {{A, B, C, X(54973), X(60218)}}

X(65064) = 1ST BASEPOINT OF THE GEMINI 85 TRIANGLE WRT ABC

Barycentrics    a*(a-b-c)*(a*(3*b-2*c)+3*b*(-b+c))*(a*(2*b-3*c)+3*c*(-b+c)) : :

X(65064) lies on these lines: {2, 42343}, {241, 16602}, {650, 10589}, {672, 3973}, {2340, 4050}, {3693, 4903}, {5089, 38282}, {40141, 60782}

X(65064) = trilinear pole of line {926, 54255}
X(65064) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 25716}, {56, 25728}, {57, 4421}, {109, 31287}, {604, 25278}
X(65064) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 25728}, {9, 25716}, {11, 31287}, {3161, 25278}, {5452, 4421}
X(65064) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(53056)}}, {{A, B, C, X(2), X(55)}}, {{A, B, C, X(8), X(4050)}}, {{A, B, C, X(9), X(3973)}}, {{A, B, C, X(21), X(16570)}}, {{A, B, C, X(33), X(88)}}, {{A, B, C, X(89), X(7073)}}, {{A, B, C, X(100), X(10589)}}, {{A, B, C, X(200), X(39963)}}, {{A, B, C, X(277), X(4845)}}, {{A, B, C, X(281), X(2316)}}, {{A, B, C, X(294), X(8056)}}, {{A, B, C, X(346), X(16602)}}, {{A, B, C, X(941), X(2364)}}, {{A, B, C, X(1376), X(5274)}}, {{A, B, C, X(1436), X(51316)}}, {{A, B, C, X(2165), X(19302)}}, {{A, B, C, X(2319), X(6557)}}, {{A, B, C, X(3434), X(60782)}}, {{A, B, C, X(4876), X(38255)}}, {{A, B, C, X(5218), X(5284)}}, {{A, B, C, X(5281), X(8167)}}, {{A, B, C, X(5326), X(61155)}}, {{A, B, C, X(5547), X(41791)}}, {{A, B, C, X(9375), X(57726)}}, {{A, B, C, X(9442), X(38254)}}, {{A, B, C, X(9445), X(56331)}}, {{A, B, C, X(11051), X(65046)}}, {{A, B, C, X(14943), X(42318)}}, {{A, B, C, X(27818), X(64458)}}, {{A, B, C, X(35348), X(40154)}}, {{A, B, C, X(36603), X(42317)}}, {{A, B, C, X(39962), X(41798)}}, {{A, B, C, X(39966), X(60817)}}, {{A, B, C, X(53055), X(59572)}}, {{A, B, C, X(56086), X(56116)}}, {{A, B, C, X(56783), X(60813)}}
X(65064) = barycentric product X(i)*X(j) for these (i, j): {55, 65065}, {41439, 8}, {42343, 650}
X(65064) = barycentric quotient X(i)/X(j) for these (i, j): {1, 25716}, {8, 25278}, {9, 25728}, {55, 4421}, {650, 31287}, {41439, 7}, {42343, 4554}, {65065, 6063}

X(65065) = 2ND BASEPOINT OF THE GEMINI 85 TRIANGLE WRT ABC

Barycentrics    b*c*(3*b*(b-c)+a*(-3*b+2*c))*(3*(b-c)*c+a*(-2*b+3*c)) : :

X(65065) lies on these lines: {2, 42343}, {528, 65069}, {3007, 65067}, {3912, 20942}, {4428, 40419}, {9436, 53594}, {11235, 18821}, {30941, 41439}, {31140, 65034}, {34612, 65036}, {59255, 59508}

X(65065) = isotomic conjugate of X(4421)
X(65065) = trilinear pole of line {26568, 918}
X(65065) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4421}, {32, 25728}, {560, 25278}, {2175, 25716}, {31287, 32739}
X(65065) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4421}, {6374, 25278}, {6376, 25728}, {40593, 25716}, {40619, 31287}
X(65065) = X(i)-cross conjugate of X(j) for these {i, j}: {3829, 2}, {48627, 76}
X(65065) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(693)}}, {{A, B, C, X(75), X(20942)}}, {{A, B, C, X(76), X(20943)}}, {{A, B, C, X(264), X(903)}}, {{A, B, C, X(528), X(11235)}}, {{A, B, C, X(2481), X(44186)}}, {{A, B, C, X(2886), X(4428)}}, {{A, B, C, X(3058), X(31140)}}, {{A, B, C, X(3227), X(60095)}}, {{A, B, C, X(3596), X(36588)}}, {{A, B, C, X(3829), X(4421)}}, {{A, B, C, X(4762), X(59508)}}, {{A, B, C, X(7233), X(36603)}}, {{A, B, C, X(7249), X(39980)}}, {{A, B, C, X(10707), X(49719)}}, {{A, B, C, X(11238), X(34612)}}, {{A, B, C, X(18836), X(34578)}}, {{A, B, C, X(20565), X(39704)}}, {{A, B, C, X(36889), X(57887)}}, {{A, B, C, X(40012), X(57995)}}, {{A, B, C, X(54128), X(58860)}}, {{A, B, C, X(55948), X(57880)}}, {{A, B, C, X(57796), X(65059)}}
X(65065) = barycentric product X(i)*X(j) for these (i, j): {6063, 65064}, {41439, 76}, {42343, 693}
X(65065) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4421}, {75, 25728}, {76, 25278}, {85, 25716}, {693, 31287}, {41439, 6}, {42343, 100}, {65064, 55}

X(65066) = 1ST BASEPOINT OF THE GEMINI 86 TRIANGLE WRT ABC

Barycentrics    a*(a+b-c)*(a-b+c)*(-3*b^3+3*b*c^2+2*a*c*(-2*b+c)+a^2*(3*b+2*c))*(2*a*b*(b-2*c)+a^2*(2*b+3*c)+3*c*(b^2-c^2)) : :

X(65066) lies on these lines: {2, 65067}, {1193, 3340}, {3666, 5226}

X(65066) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 11194}
X(65066) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 11194}
X(65066) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(56)}}, {{A, B, C, X(34), X(88)}}, {{A, B, C, X(57), X(3340)}}, {{A, B, C, X(89), X(1411)}}, {{A, B, C, X(269), X(5936)}}, {{A, B, C, X(1407), X(65046)}}, {{A, B, C, X(1427), X(44794)}}, {{A, B, C, X(1465), X(43049)}}, {{A, B, C, X(1875), X(56270)}}, {{A, B, C, X(4452), X(16610)}}, {{A, B, C, X(6336), X(59263)}}, {{A, B, C, X(8056), X(18840)}}, {{A, B, C, X(9309), X(30608)}}, {{A, B, C, X(34446), X(40779)}}, {{A, B, C, X(42753), X(60491)}}, {{A, B, C, X(45098), X(53083)}}, {{A, B, C, X(56166), X(56783)}}
X(65066) = barycentric product X(i)*X(j) for these (i, j): {56, 65067}, {41446, 7}
X(65066) = barycentric quotient X(i)/X(j) for these (i, j): {56, 11194}, {41446, 8}, {65067, 3596}

X(65067) = 2ND BASEPOINT OF THE GEMINI 86 TRIANGLE WRT ABC

Barycentrics    b*c*(2*a*(2*b-c)*c-a^2*(3*b+2*c)+3*b*(b^2-c^2))*(2*a*b*(b-2*c)+a^2*(2*b+3*c)+3*c*(b^2-c^2)) : :

X(65067) lies on these lines: {2, 65066}, {529, 65068}, {3007, 65065}, {3687, 42034}, {11236, 57887}, {31141, 65033}, {32087, 41446}, {34606, 65035}

X(65067) = isotomic conjugate of X(11194)
X(65067) = trilinear pole of line {47790, 3910}
X(65067) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(261)}}, {{A, B, C, X(75), X(42034)}}, {{A, B, C, X(264), X(903)}}, {{A, B, C, X(529), X(11236)}}, {{A, B, C, X(1121), X(55955)}}, {{A, B, C, X(1329), X(40726)}}, {{A, B, C, X(1441), X(32087)}}, {{A, B, C, X(3262), X(6604)}}, {{A, B, C, X(4518), X(55993)}}, {{A, B, C, X(5434), X(31141)}}, {{A, B, C, X(6063), X(36588)}}, {{A, B, C, X(11237), X(34606)}}, {{A, B, C, X(20566), X(32023)}}, {{A, B, C, X(36916), X(59260)}}, {{A, B, C, X(57822), X(57889)}}
X(65067) = barycentric product X(i)*X(j) for these (i, j): {3596, 65066}, {41446, 76}
X(65067) = barycentric quotient X(i)/X(j) for these (i, j): {2, 11194}, {41446, 6}, {65066, 56}

X(65068) = 2ND BASEPOINT OF THE GEMINI 87 TRIANGLE WRT ABC

Barycentrics    (2*a^4+2*b^4+2*a*b*(b-2*c)*c-b^2*c^2-c^4-a^2*(4*b^2-2*b*c+c^2))*(2*a^4-b^4-b^2*c^2+2*c^4+2*a*b*c*(-2*b+c)-a^2*(b^2-2*b*c+4*c^2)) : :

X(65068) lies on these lines: {529, 65067}, {3596, 34606}, {3687, 17346}, {11194, 57887}, {31157, 65035}, {34605, 54121}, {38468, 54314}

X(65068) = isotomic conjugate of X(11236)
X(65068) = trilinear pole of line {27486, 3910}
X(65068) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(261)}}, {{A, B, C, X(7), X(54768)}}, {{A, B, C, X(56), X(34606)}}, {{A, B, C, X(69), X(18821)}}, {{A, B, C, X(86), X(1121)}}, {{A, B, C, X(264), X(57889)}}, {{A, B, C, X(269), X(3512)}}, {{A, B, C, X(286), X(34282)}}, {{A, B, C, X(314), X(55956)}}, {{A, B, C, X(529), X(11194)}}, {{A, B, C, X(903), X(40417)}}, {{A, B, C, X(2975), X(34605)}}, {{A, B, C, X(5298), X(31141)}}, {{A, B, C, X(6063), X(55022)}}, {{A, B, C, X(11237), X(31157)}}, {{A, B, C, X(17378), X(29767)}}, {{A, B, C, X(20028), X(54735)}}, {{A, B, C, X(52376), X(55965)}}, {{A, B, C, X(54457), X(54745)}}, {{A, B, C, X(57881), X(59255)}}

X(65069) = 2ND BASEPOINT OF THE GEMINI 88 TRIANGLE WRT ABC

Barycentrics    (2*a^3+2*b^3-2*b^2*c+b*c^2-c^3-2*a^2*(b+c)+a*(-2*b^2+2*b*c+c^2))*(2*a^3-b^3+b^2*c-2*b*c^2+2*c^3-2*a^2*(b+c)+a*(b^2+2*b*c-2*c^2)) : :

X(65069) lies on these lines: {528, 65065}, {693, 34611}, {4421, 18821}, {6063, 34612}, {6174, 65036}, {32023, 49736}

X(65069) = isotomic conjugate of X(11235)
X(65069) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(693)}}, {{A, B, C, X(55), X(34612)}}, {{A, B, C, X(69), X(57887)}}, {{A, B, C, X(100), X(34611)}}, {{A, B, C, X(528), X(4421)}}, {{A, B, C, X(903), X(40417)}}, {{A, B, C, X(1376), X(49736)}}, {{A, B, C, X(3227), X(60218)}}, {{A, B, C, X(4428), X(49732)}}, {{A, B, C, X(4995), X(31140)}}, {{A, B, C, X(6174), X(11238)}}, {{A, B, C, X(7224), X(54928)}}, {{A, B, C, X(7350), X(14458)}}, {{A, B, C, X(31643), X(39704)}}, {{A, B, C, X(34409), X(51567)}}, {{A, B, C, X(39741), X(54676)}}, {{A, B, C, X(43948), X(54128)}}

X(65070) = 1ST BASEPOINT OF THE GEMINI 90 TRIANGLE WRT ABC

Barycentrics    a*(b+c)*(2*a*b-b^2-a*c+2*b*c)*(a*(b-2*c)+c*(-2*b+c)) : :

X(65070) lies on these lines: {2, 65071}, {756, 18905}, {982, 16592}, {1215, 43265}, {1743, 2238}, {3124, 9335}, {3948, 17056}, {3950, 4037}, {4849, 21868}

X(65070) = trilinear pole of line {4729, 4155}
X(65070) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 17261}, {81, 60714}, {110, 25666}, {593, 4096}, {662, 4879}, {1333, 25280}
X(65070) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 17261}, {37, 25280}, {244, 25666}, {1084, 4879}, {40586, 60714}
X(65070) = X(i)-cross conjugate of X(j) for these {i, j}: {21921, 37}, {22174, 10}
X(65070) = pole of line {3662, 3816} with respect to the Kiepert hyperbola
X(65070) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(41875)}}, {{A, B, C, X(2), X(661)}}, {{A, B, C, X(6), X(17056)}}, {{A, B, C, X(10), X(4135)}}, {{A, B, C, X(12), X(262)}}, {{A, B, C, X(37), X(1743)}}, {{A, B, C, X(42), X(17244)}}, {{A, B, C, X(57), X(52208)}}, {{A, B, C, X(85), X(43686)}}, {{A, B, C, X(181), X(39966)}}, {{A, B, C, X(226), X(16606)}}, {{A, B, C, X(292), X(65011)}}, {{A, B, C, X(321), X(56158)}}, {{A, B, C, X(512), X(20569)}}, {{A, B, C, X(523), X(32023)}}, {{A, B, C, X(594), X(62884)}}, {{A, B, C, X(870), X(982)}}, {{A, B, C, X(876), X(40737)}}, {{A, B, C, X(1213), X(37679)}}, {{A, B, C, X(1254), X(60077)}}, {{A, B, C, X(1427), X(40747)}}, {{A, B, C, X(2051), X(8818)}}, {{A, B, C, X(2162), X(7180)}}, {{A, B, C, X(2171), X(39956)}}, {{A, B, C, X(2295), X(56044)}}, {{A, B, C, X(6378), X(52660)}}, {{A, B, C, X(7148), X(60236)}}, {{A, B, C, X(8033), X(16592)}}, {{A, B, C, X(8056), X(9278)}}, {{A, B, C, X(9281), X(25430)}}, {{A, B, C, X(11599), X(52654)}}, {{A, B, C, X(21856), X(40593)}}, {{A, B, C, X(23493), X(41771)}}, {{A, B, C, X(27475), X(54980)}}, {{A, B, C, X(35353), X(40216)}}, {{A, B, C, X(40148), X(55263)}}, {{A, B, C, X(41501), X(43672)}}, {{A, B, C, X(54668), X(56174)}}, {{A, B, C, X(55926), X(60116)}}, {{A, B, C, X(56162), X(57722)}}
X(65070) = barycentric product X(i)*X(j) for these (i, j): {65071, 756}
X(65070) = barycentric quotient X(i)/X(j) for these (i, j): {10, 25280}, {37, 17261}, {42, 60714}, {512, 4879}, {661, 25666}, {756, 4096}, {4729, 4964}, {65071, 873}

X(65071) = 2ND BASEPOINT OF THE GEMINI 90 TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(2*a*b-b^2-a*c+2*b*c)*(a*(b-2*c)+c*(-2*b+c)) : :

X(65071) lies on these lines: {2, 65070}, {239, 41629}, {350, 3664}, {3794, 65077}, {7033, 8033}, {18822, 42053}, {18827, 41527}, {32010, 65039}, {42055, 65073}

X(65071) = isotomic conjugate of X(4096)
X(65071) = trilinear pole of line {26851, 812}
X(65071) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4096}, {42, 60714}, {213, 17261}, {1918, 25280}, {4557, 4879}
X(65071) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4096}, {6626, 17261}, {34021, 25280}, {40592, 60714}, {40620, 25666}
X(65071) = X(i)-cross conjugate of X(j) for these {i, j}: {21139, 7199}, {26806, 1509}
X(65071) = pole of line {4096, 17261} with respect to the Wallace hyperbola
X(65071) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(60792)}}, {{A, B, C, X(2), X(239)}}, {{A, B, C, X(269), X(757)}}, {{A, B, C, X(537), X(42053)}}, {{A, B, C, X(552), X(40164)}}, {{A, B, C, X(903), X(31643)}}, {{A, B, C, X(1929), X(60624)}}, {{A, B, C, X(3226), X(32021)}}, {{A, B, C, X(3676), X(51865)}}, {{A, B, C, X(4052), X(18032)}}, {{A, B, C, X(16709), X(17151)}}, {{A, B, C, X(17930), X(53226)}}, {{A, B, C, X(18827), X(57785)}}, {{A, B, C, X(28840), X(59622)}}, {{A, B, C, X(31161), X(42040)}}, {{A, B, C, X(36871), X(53679)}}, {{A, B, C, X(40737), X(43931)}}, {{A, B, C, X(52375), X(60078)}}
X(65071) = barycentric product X(i)*X(j) for these (i, j): {65070, 873}
X(65071) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4096}, {81, 60714}, {86, 17261}, {274, 25280}, {1019, 4879}, {7192, 25666}, {65070, 756}

X(65072) = 2ND BASEPOINT OF THE GEMINI 91 TRIANGLE WRT ABC

Barycentrics    (a^2*(b-2*c)+a*(b-c)^2+b*c*(-2*b+c))*(-(a*(b-c)^2)+a^2*(2*b-c)-b*(b-2*c)*c) : :

X(65072) lies on these lines: {239, 4641}, {350, 3879}, {537, 65073}, {732, 62625}, {1965, 7035}, {18822, 42055}, {27922, 29820}

X(65072) = isotomic conjugate of X(42054)
X(65072) = trilinear pole of line {27012, 47796}
X(65072) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(42057)}}, {{A, B, C, X(2), X(239)}}, {{A, B, C, X(38), X(60529)}}, {{A, B, C, X(75), X(42051)}}, {{A, B, C, X(86), X(2985)}}, {{A, B, C, X(286), X(903)}}, {{A, B, C, X(514), X(40038)}}, {{A, B, C, X(519), X(29820)}}, {{A, B, C, X(537), X(42055)}}, {{A, B, C, X(732), X(28840)}}, {{A, B, C, X(1965), X(43266)}}, {{A, B, C, X(3226), X(57785)}}, {{A, B, C, X(3879), X(4641)}}, {{A, B, C, X(14828), X(41629)}}, {{A, B, C, X(31161), X(42038)}}, {{A, B, C, X(32021), X(55997)}}, {{A, B, C, X(40415), X(56783)}}, {{A, B, C, X(42053), X(42054)}}, {{A, B, C, X(43097), X(56947)}}

X(65073) = 2ND BASEPOINT OF THE GEMINI 92 TRIANGLE WRT ABC

Barycentrics    (a^2*(b-2*c)+b*c*(-2*b+c)+a*(b+c)^2)*(a^2*(2*b-c)-b*(b-2*c)*c-a*(b+c)^2) : :

X(65073) lies on these lines: {239, 3175}, {350, 4685}, {536, 39937}, {537, 65072}, {873, 60683}, {1447, 4360}, {3875, 8616}, {3961, 27922}, {18822, 42054}, {42055, 65071}

X(65073) = isotomic conjugate of X(42055)
X(65073) = trilinear pole of line {27074, 47793}
X(65073) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4685)}}, {{A, B, C, X(2), X(239)}}, {{A, B, C, X(75), X(3175)}}, {{A, B, C, X(314), X(903)}}, {{A, B, C, X(519), X(3961)}}, {{A, B, C, X(537), X(42054)}}, {{A, B, C, X(740), X(43265)}}, {{A, B, C, X(2481), X(55997)}}, {{A, B, C, X(3226), X(57815)}}, {{A, B, C, X(3227), X(17143)}}, {{A, B, C, X(3680), X(56098)}}, {{A, B, C, X(4052), X(39714)}}, {{A, B, C, X(4096), X(42055)}}, {{A, B, C, X(31161), X(42039)}}, {{A, B, C, X(41629), X(56026)}}, {{A, B, C, X(42053), X(42056)}}, {{A, B, C, X(52651), X(60664)}}

X(65074) = 1ST BASEPOINT OF THE GEMINI 99 TRIANGLE WRT ABC

Barycentrics    a*(b*(b-2*c)*c+a^2*(b+c)+a*(b^2-2*b*c-2*c^2))*(b*c*(-2*b+c)+a^2*(b+c)+a*(-2*b^2-2*b*c+c^2)) : :

X(65074) lies on these lines: {2, 65075}, {45, 39736}, {239, 65057}, {274, 17260}, {291, 27627}, {330, 17277}, {3227, 16827}, {3729, 56051}, {8056, 62817}, {16815, 30710}, {16816, 39694}, {27644, 39950}, {28249, 39724}, {29578, 37870}, {29960, 34892}

X(65074) = isotomic conjugate of X(29982)
X(65074) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 42057}, {31, 29982}
X(65074) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 29982}, {9, 42057}
X(65074) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(83), X(55971)}}, {{A, B, C, X(239), X(27627)}}, {{A, B, C, X(899), X(16827)}}, {{A, B, C, X(978), X(16816)}}, {{A, B, C, X(1014), X(39717)}}, {{A, B, C, X(1126), X(32013)}}, {{A, B, C, X(1193), X(16815)}}, {{A, B, C, X(1400), X(17260)}}, {{A, B, C, X(3224), X(65027)}}, {{A, B, C, X(7292), X(29960)}}, {{A, B, C, X(13584), X(17501)}}, {{A, B, C, X(16833), X(27645)}}, {{A, B, C, X(17277), X(27644)}}, {{A, B, C, X(17743), X(39981)}}, {{A, B, C, X(18785), X(23617)}}, {{A, B, C, X(20036), X(54390)}}, {{A, B, C, X(20332), X(60075)}}, {{A, B, C, X(26736), X(55036)}}, {{A, B, C, X(28615), X(45988)}}, {{A, B, C, X(28660), X(56091)}}, {{A, B, C, X(29578), X(59305)}}, {{A, B, C, X(32008), X(37128)}}, {{A, B, C, X(32012), X(39748)}}, {{A, B, C, X(56174), X(60244)}}
X(65074) = barycentric product X(i)*X(j) for these (i, j): {1, 65075}
X(65074) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42057}, {2, 29982}, {65075, 75}

X(65075) = 2ND BASEPOINT OF THE GEMINI 99 TRIANGLE WRT ABC

Barycentrics    (b*(b-2*c)*c+a^2*(b+c)+a*(b^2-2*b*c-2*c^2))*(b*c*(-2*b+c)+a^2*(b+c)+a*(-2*b^2-2*b*c+c^2)) : :

X(65075) lies on these lines: {2, 65074}, {75, 42054}, {86, 3750}, {335, 42051}, {350, 65056}, {519, 65077}, {903, 4685}, {3679, 65041}, {4479, 58019}, {6384, 17143}, {32911, 60873}, {33296, 39734}, {39704, 42042}

X(65075) = isotomic conjugate of X(42057)
X(65075) = trilinear pole of line {27292, 514}
X(65075) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 42057}, {32, 29982}
X(65075) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 42057}, {6376, 29982}
X(65075) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(65), X(3750)}}, {{A, B, C, X(291), X(42054)}}, {{A, B, C, X(350), X(42051)}}, {{A, B, C, X(519), X(4685)}}, {{A, B, C, X(1126), X(28509)}}, {{A, B, C, X(1222), X(13576)}}, {{A, B, C, X(1434), X(40024)}}, {{A, B, C, X(3112), X(55947)}}, {{A, B, C, X(3210), X(4479)}}, {{A, B, C, X(3223), X(7241)}}, {{A, B, C, X(3227), X(17143)}}, {{A, B, C, X(3551), X(39966)}}, {{A, B, C, X(3679), X(42042)}}, {{A, B, C, X(7033), X(55945)}}, {{A, B, C, X(18822), X(65059)}}, {{A, B, C, X(18827), X(55997)}}, {{A, B, C, X(31137), X(36634)}}, {{A, B, C, X(34860), X(56161)}}, {{A, B, C, X(39711), X(60109)}}, {{A, B, C, X(39742), X(39967)}}, {{A, B, C, X(39744), X(39747)}}, {{A, B, C, X(43097), X(54686)}}
X(65075) = barycentric product X(i)*X(j) for these (i, j): {65074, 75}
X(65075) = barycentric quotient X(i)/X(j) for these (i, j): {2, 42057}, {75, 29982}, {65074, 1}

X(65076) = 1ST BASEPOINT OF THE GEMINI 100 TRIANGLE WRT ABC

Barycentrics    a*(a+b)*(a+c)*(-(b*c)+a*(b+c))*(b*(-2*b+c)+a*(b+c))*((b-2*c)*c+a*(b+c)) : :

X(65076) lies on these lines: {2, 4754}, {38, 17038}, {87, 748}, {256, 3720}

X(65076) = isotomic conjugate of X(27438)
X(65076) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 27438}, {2162, 4685}, {7121, 22016}, {8616, 16606}, {17144, 21759}, {17349, 23493}
X(65076) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 27438}, {3835, 22215}, {40598, 22016}
X(65076) = X(i)-cross conjugate of X(j) for these {i, j}: {53676, 33296}
X(65076) = pole of line {17349, 27438} with respect to the Wallace hyperbola
X(65076) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(43)}}, {{A, B, C, X(88), X(1403)}}, {{A, B, C, X(310), X(33947)}}, {{A, B, C, X(873), X(33296)}}, {{A, B, C, X(1255), X(52136)}}, {{A, B, C, X(2176), X(65027)}}, {{A, B, C, X(2350), X(51973)}}, {{A, B, C, X(3720), X(4754)}}, {{A, B, C, X(8042), X(16742)}}, {{A, B, C, X(30545), X(57722)}}, {{A, B, C, X(40013), X(40848)}}
X(65076) = barycentric product X(i)*X(j) for these (i, j): {43, 65077}, {27644, 60236}, {31008, 39966}, {33296, 39742}
X(65076) = barycentric quotient X(i)/X(j) for these (i, j): {2, 27438}, {43, 4685}, {192, 22016}, {6377, 22215}, {16695, 48331}, {17217, 23794}, {18197, 48008}, {27644, 17349}, {33296, 17144}, {38832, 8616}, {39742, 42027}, {39966, 16606}, {60236, 60244}, {65077, 6384}

X(65077) = 2ND BASEPOINT OF THE GEMINI 100 TRIANGLE WRT ABC

Barycentrics    (a+b)*(a+c)*(b*(-2*b+c)+a*(b+c))*((b-2*c)*c+a*(b+c)) : :

X(65077) lies on these lines: {2, 4754}, {75, 39742}, {81, 60873}, {86, 65039}, {274, 56212}, {335, 3175}, {519, 65075}, {673, 41629}, {903, 42057}, {1246, 17378}, {1434, 24801}, {3760, 6384}, {3794, 65071}, {4059, 7249}, {4373, 30941}, {4496, 27447}, {5936, 30966}, {14621, 42028}, {16711, 36854}, {16712, 24215}, {16887, 56052}, {31008, 40027}, {31137, 65043}, {33296, 39741}

X(65077) = isotomic conjugate of X(4685)
X(65077) = trilinear pole of line {27344, 514}
X(65077) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 4685}, {32, 22016}, {42, 8616}, {213, 17349}, {1252, 22215}, {1918, 17144}, {4557, 48331}, {27438, 62420}
X(65077) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4685}, {661, 22215}, {6376, 22016}, {6626, 17349}, {34021, 17144}, {40592, 8616}, {40620, 48008}, {62615, 27438}
X(65077) = X(i)-cross conjugate of X(j) for these {i, j}: {192, 274}
X(65077) = pole of line {4685, 8616} with respect to the Wallace hyperbola
X(65077) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(79), X(60624)}}, {{A, B, C, X(291), X(20615)}}, {{A, B, C, X(350), X(3175)}}, {{A, B, C, X(519), X(42057)}}, {{A, B, C, X(671), X(18299)}}, {{A, B, C, X(873), X(55947)}}, {{A, B, C, X(1002), X(60789)}}, {{A, B, C, X(1019), X(17179)}}, {{A, B, C, X(1222), X(60617)}}, {{A, B, C, X(1434), X(33947)}}, {{A, B, C, X(1909), X(4059)}}, {{A, B, C, X(2481), X(55997)}}, {{A, B, C, X(3551), X(39967)}}, {{A, B, C, X(3760), X(4496)}}, {{A, B, C, X(4052), X(7018)}}, {{A, B, C, X(4479), X(41839)}}, {{A, B, C, X(5557), X(60090)}}, {{A, B, C, X(16887), X(62541)}}, {{A, B, C, X(18827), X(57785)}}, {{A, B, C, X(30571), X(56237)}}, {{A, B, C, X(30941), X(41629)}}, {{A, B, C, X(30966), X(42028)}}, {{A, B, C, X(31137), X(42043)}}, {{A, B, C, X(34860), X(62921)}}, {{A, B, C, X(35153), X(56947)}}, {{A, B, C, X(39702), X(56164)}}, {{A, B, C, X(39742), X(39966)}}, {{A, B, C, X(43097), X(57784)}}, {{A, B, C, X(43732), X(60109)}}, {{A, B, C, X(60267), X(60678)}}
X(65077) = barycentric product X(i)*X(j) for these (i, j): {274, 39742}, {310, 39966}, {6384, 65076}, {60236, 86}
X(65077) = barycentric quotient X(i)/X(j) for these (i, j): {2, 4685}, {75, 22016}, {81, 8616}, {86, 17349}, {244, 22215}, {274, 17144}, {1019, 48331}, {6384, 27438}, {7192, 48008}, {7199, 23794}, {39742, 37}, {39966, 42}, {60236, 10}, {65076, 43}

X(65078) = 1ST BASEPOINT OF THE GEMINI 105 TRIANGLE WRT ABC

Barycentrics    (2*a+b+c)*(a+4*b+c)*(a+b+4*c) : :

X(65078) lies on these lines: {2, 3943}, {8, 41434}, {495, 3296}, {596, 1698}, {1125, 42437}, {1213, 62732}, {1509, 16704}, {4969, 8025}, {9108, 28210}, {14475, 46915}, {45222, 65023}, {58128, 60710}

X(65078) = X(i)-isoconjugate-of-X(j) for these {i, j}: {551, 28615}, {1126, 16666}, {1171, 21806}, {1255, 21747}, {37212, 58139}
X(65078) = X(i)-Dao conjugate of X(j) for these {i, j}: {1213, 551}, {3647, 16666}, {35076, 28209}, {56846, 4031}, {59592, 3707}, {62588, 24589}
X(65078) = pole of line {27081, 40434} with respect to the Kiepert hyperbola
X(65078) = pole of line {3828, 65024} with respect to the dual conic of Yff parabola
X(65078) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(553)}}, {{A, B, C, X(89), X(1100)}}, {{A, B, C, X(1213), X(3943)}}, {{A, B, C, X(1230), X(6539)}}, {{A, B, C, X(1268), X(7192)}}, {{A, B, C, X(1269), X(5936)}}, {{A, B, C, X(1698), X(18140)}}, {{A, B, C, X(2308), X(39966)}}, {{A, B, C, X(3702), X(56075)}}, {{A, B, C, X(4080), X(4647)}}, {{A, B, C, X(4977), X(28309)}}, {{A, B, C, X(27483), X(46896)}}, {{A, B, C, X(30581), X(39962)}}, {{A, B, C, X(30593), X(56061)}}, {{A, B, C, X(60873), X(61313)}}
X(65078) = barycentric product X(i)*X(j) for these (i, j): {1125, 55955}, {1269, 41434}, {4977, 58128}, {16709, 56134}, {27797, 8025}, {40434, 4359}, {62732, 65024}
X(65078) = barycentric quotient X(i)/X(j) for these (i, j): {553, 4031}, {1100, 16666}, {1125, 551}, {1962, 21806}, {2308, 21747}, {3686, 3707}, {3702, 3902}, {3775, 4407}, {4359, 24589}, {4427, 4781}, {4647, 4714}, {4717, 4793}, {4870, 39782}, {4977, 28209}, {4984, 14435}, {8025, 26860}, {22054, 22357}, {27797, 6539}, {28210, 8701}, {30724, 30722}, {30729, 30727}, {40434, 1255}, {41434, 1126}, {50512, 58139}, {55955, 1268}, {56115, 32635}, {58128, 6540}, {62732, 42026}, {65024, 31011}
X(65078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 27797, 40434}, {2, 55955, 65024}, {40434, 55955, 27797}, {40434, 65010, 2}

X(65079) = 1ST BASEPOINT OF THE GEMINI 106 TRIANGLE WRT ABC

Barycentrics    (2*a^2+b^2+c^2)*(a^2+4*b^2+c^2)*(a^2+b^2+4*c^2) : :

X(65079) lies on these lines: {2, 5355}, {3763, 6664}, {7693, 43726}, {7931, 45108}, {12074, 46226}, {42367, 60728}, {52395, 52898}

X(65079) = X(i)-Dao conjugate of X(j) for these {i, j}: {6292, 597}, {15527, 12073}
X(65079) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(428)}}, {{A, B, C, X(1383), X(5007)}}, {{A, B, C, X(6292), X(7813)}}, {{A, B, C, X(10159), X(52570)}}, {{A, B, C, X(10330), X(62672)}}, {{A, B, C, X(31125), X(42554)}}, {{A, B, C, X(40103), X(44091)}}, {{A, B, C, X(52787), X(54459)}}
X(65079) = barycentric product X(i)*X(j) for these (i, j): {10302, 3589}, {39389, 39998}, {42367, 7927}
X(65079) = barycentric quotient X(i)/X(j) for these (i, j): {428, 10301}, {3589, 597}, {5007, 5008}, {7927, 12073}, {10302, 10159}, {10330, 35356}, {12074, 7953}, {39389, 3108}, {39998, 26235}, {42367, 35137}, {61211, 35357}

X(65080) = 1ST BASEPOINT OF THE GEMINI 108 TRIANGLE WRT ABC

Barycentrics    (5*a+5*b-7*c)*(a-b-c)*(5*a-7*b+5*c) : :

X(65080) lies on these lines: {2, 4480}, {1121, 29627}, {2325, 6557}, {3161, 4997}, {3622, 63169}, {4521, 60480}, {5226, 63167}, {5328, 30608}, {6745, 56088}, {14942, 62710}, {24589, 65029}, {30827, 56201}, {46872, 46933}

X(65080) = isotomic conjugate of X(31188)
X(65080) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 31188}, {604, 31145}
X(65080) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 31188}, {3161, 31145}
X(65080) = X(i)-cross conjugate of X(j) for these {i, j}: {62706, 8}
X(65080) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(7), X(4887)}}, {{A, B, C, X(79), X(45098)}}, {{A, B, C, X(88), X(1392)}}, {{A, B, C, X(281), X(2325)}}, {{A, B, C, X(346), X(31722)}}, {{A, B, C, X(1320), X(39963)}}, {{A, B, C, X(2320), X(40434)}}, {{A, B, C, X(3254), X(42318)}}, {{A, B, C, X(4373), X(52714)}}, {{A, B, C, X(5219), X(5328)}}, {{A, B, C, X(5226), X(30827)}}, {{A, B, C, X(5748), X(30852)}}, {{A, B, C, X(6745), X(29627)}}, {{A, B, C, X(14475), X(53523)}}, {{A, B, C, X(24589), X(28808)}}, {{A, B, C, X(28626), X(56349)}}, {{A, B, C, X(33696), X(54587)}}, {{A, B, C, X(40410), X(58002)}}
X(65080) = barycentric product X(i)*X(j) for these (i, j): {65081, 8}
X(65080) = barycentric quotient X(i)/X(j) for these (i, j): {2, 31188}, {8, 31145}, {3680, 58793}, {65081, 7}

X(65081) = 2ND BASEPOINT OF THE GEMINI 108 TRIANGLE WRT ABC

Barycentrics    (5*a+5*b-7*c)*(5*a-7*b+5*c) : :

X(65081) lies on these lines: {2, 4480}, {75, 4487}, {145, 903}, {519, 4373}, {527, 42318}, {545, 36807}, {673, 60984}, {3667, 6548}, {4346, 39704}, {4862, 30712}, {5936, 17274}, {6084, 62623}, {7321, 28650}, {20347, 56163}, {27475, 59375}, {28626, 50116}, {31145, 36588}, {32093, 36606}, {39707, 50101}, {39716, 50128}, {42697, 55955}, {44724, 62536}, {45789, 53620}, {51351, 62723}, {62783, 65004}

X(65081) = isotomic conjugate of X(31145)
X(65081) = trilinear pole of line {14425, 44561}
X(65081) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 31145}, {41, 31188}, {3052, 58793}
X(65081) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 31145}, {3160, 31188}, {24151, 58793}
X(65081) = X(i)-cross conjugate of X(j) for these {i, j}: {3241, 2}, {51792, 189}
X(65081) = pole of line {3241, 65081} with respect to the dual conic of Yff parabola
X(65081) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(145)}}, {{A, B, C, X(8), X(31722)}}, {{A, B, C, X(79), X(54623)}}, {{A, B, C, X(279), X(4887)}}, {{A, B, C, X(527), X(51351)}}, {{A, B, C, X(545), X(6084)}}, {{A, B, C, X(596), X(54624)}}, {{A, B, C, X(1219), X(43733)}}, {{A, B, C, X(1280), X(55922)}}, {{A, B, C, X(1327), X(55154)}}, {{A, B, C, X(1328), X(55155)}}, {{A, B, C, X(2481), X(41895)}}, {{A, B, C, X(3062), X(55992)}}, {{A, B, C, X(3241), X(31145)}}, {{A, B, C, X(3254), X(36916)}}, {{A, B, C, X(3296), X(60079)}}, {{A, B, C, X(3617), X(38314)}}, {{A, B, C, X(3622), X(31359)}}, {{A, B, C, X(4346), X(4945)}}, {{A, B, C, X(4480), X(10405)}}, {{A, B, C, X(4492), X(51036)}}, {{A, B, C, X(5551), X(54786)}}, {{A, B, C, X(5553), X(54726)}}, {{A, B, C, X(5556), X(6553)}}, {{A, B, C, X(5557), X(43533)}}, {{A, B, C, X(5561), X(24858)}}, {{A, B, C, X(7319), X(35577)}}, {{A, B, C, X(9436), X(60984)}}, {{A, B, C, X(10305), X(54516)}}, {{A, B, C, X(10307), X(54687)}}, {{A, B, C, X(17274), X(21454)}}, {{A, B, C, X(18822), X(38247)}}, {{A, B, C, X(19604), X(36603)}}, {{A, B, C, X(19875), X(46934)}}, {{A, B, C, X(19883), X(46931)}}, {{A, B, C, X(23617), X(31507)}}, {{A, B, C, X(25055), X(39708)}}, {{A, B, C, X(26745), X(56049)}}, {{A, B, C, X(27818), X(52714)}}, {{A, B, C, X(35160), X(55948)}}, {{A, B, C, X(36889), X(46136)}}, {{A, B, C, X(39702), X(63169)}}, {{A, B, C, X(39742), X(39975)}}, {{A, B, C, X(40028), X(60635)}}, {{A, B, C, X(40719), X(59375)}}, {{A, B, C, X(42026), X(42697)}}, {{A, B, C, X(43732), X(60077)}}, {{A, B, C, X(54758), X(61105)}}, {{A, B, C, X(56258), X(60624)}}
X(65081) = barycentric product X(i)*X(j) for these (i, j): {7, 65080}
X(65081) = barycentric quotient X(i)/X(j) for these (i, j): {2, 31145}, {7, 31188}, {8056, 58793}, {65080, 8}

X(65082) = 1ST BASEPOINT OF THE AGUILERA TRIANGLE WRT ABC

Barycentrics    (a+b-c)*(a-b+c)-2*S : :

X(65082) lies on these lines: {1, 488}, {2, 7}, {3, 31550}, {4, 31549}, {8, 175}, {10, 481}, {40, 31551}, {69, 5391}, {72, 39795}, {75, 492}, {77, 3084}, {85, 7090}, {86, 1659}, {145, 17802}, {176, 3616}, {239, 62987}, {264, 55459}, {269, 65083}, {273, 1586}, {309, 60854}, {317, 55428}, {319, 32802}, {320, 491}, {326, 55456}, {347, 46422}, {348, 13436}, {482, 1125}, {519, 31539}, {551, 31538}, {590, 17365}, {591, 4361}, {615, 1086}, {664, 64314}, {942, 63810}, {946, 31552}, {1001, 31566}, {1119, 3536}, {1145, 58042}, {1267, 32805}, {1271, 21296}, {1371, 25055}, {1372, 3679}, {1373, 3624}, {1374, 1698}, {1441, 11090}, {1442, 56427}, {1585, 7282}, {1621, 8237}, {2047, 57282}, {2048, 64126}, {2067, 17206}, {2345, 5590}, {2550, 31565}, {3068, 4644}, {3069, 4000}, {3083, 7190}, {3593, 31995}, {3617, 31602}, {3622, 17805}, {3632, 17803}, {3663, 5405}, {3664, 5393}, {3673, 7388}, {3759, 45421}, {4329, 9789}, {4363, 45472}, {4416, 51841}, {4419, 6352}, {4648, 6351}, {4872, 64617}, {4911, 7389}, {5222, 7586}, {5228, 31473}, {5414, 31637}, {5439, 39794}, {5550, 21169}, {5839, 5860}, {6213, 17170}, {6348, 13386}, {6356, 55885}, {6604, 30556}, {7056, 64622}, {7222, 26361}, {7232, 45473}, {7269, 56384}, {7277, 32787}, {7321, 32791}, {7595, 8224}, {8233, 36698}, {8243, 13389}, {8253, 62223}, {9028, 19215}, {10481, 31595}, {10885, 16440}, {13360, 34855}, {13453, 52422}, {13757, 37756}, {14121, 31547}, {16663, 40653}, {17023, 51842}, {17361, 32809}, {17364, 62986}, {17366, 32788}, {17801, 53620}, {19862, 21171}, {21629, 57269}, {22464, 55877}, {28870, 52806}, {31540, 31562}, {31601, 46934}, {32099, 32814}, {32795, 32812}, {32796, 32806}, {32798, 32810}, {34495, 57279}, {40700, 63165}, {44129, 61392}, {45872, 48631}, {48900, 52805}, {55385, 55452}, {55386, 55423}, {55387, 55420}, {55388, 55451}, {55393, 55479}, {55394, 55474}, {55398, 56927}, {63152, 64229}

X(65082) = isogonal conjugate of X(60852)
X(65082) = isotomic conjugate of X(14121)
X(65082) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 60852}, {4, 53065}, {6, 42013}, {9, 60849}, {19, 2066}, {25, 30556}, {31, 14121}, {32, 60853}, {33, 6502}, {41, 13390}, {55, 16232}, {212, 61393}, {220, 61400}, {281, 53064}, {607, 13389}, {650, 54016}, {692, 58838}, {1336, 53066}, {1806, 1824}, {1973, 56385}, {2067, 13427}, {5414, 64210}, {6212, 60851}, {7071, 64229}, {7133, 34125}, {13426, 53063}, {30335, 46379}
X(65082) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14121}, {3, 60852}, {6, 2066}, {9, 42013}, {223, 16232}, {478, 60849}, {482, 32082}, {1086, 58838}, {3160, 13390}, {6337, 56385}, {6376, 60853}, {6505, 30556}, {13388, 6212}, {13389, 1}, {36033, 53065}, {40618, 54019}, {40837, 61393}, {64631, 9}
X(65082) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {15889, 3436}, {34215, 69}
X(65082) = X(i)-cross conjugate of X(j) for these {i, j}: {2067, 1659}, {30557, 56386}, {31534, 2}
X(65082) = pole of line {284, 2066} with respect to the Stammler hyperbola
X(65082) = pole of line {333, 14121} with respect to the Wallace hyperbola
X(65082) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6204)}}, {{A, B, C, X(2), X(13387)}}, {{A, B, C, X(9), X(7090)}}, {{A, B, C, X(57), X(13388)}}, {{A, B, C, X(63), X(3084)}}, {{A, B, C, X(69), X(85)}}, {{A, B, C, X(75), X(5490)}}, {{A, B, C, X(77), X(52419)}}, {{A, B, C, X(226), X(1659)}}, {{A, B, C, X(329), X(60854)}}, {{A, B, C, X(486), X(6203)}}, {{A, B, C, X(527), X(54017)}}, {{A, B, C, X(672), X(5414)}}, {{A, B, C, X(1400), X(2067)}}, {{A, B, C, X(1952), X(55021)}}, {{A, B, C, X(2285), X(2362)}}, {{A, B, C, X(5364), X(53066)}}, {{A, B, C, X(7133), X(40131)}}, {{A, B, C, X(11091), X(52381)}}, {{A, B, C, X(13386), X(30679)}}, {{A, B, C, X(53063), X(56556)}}
X(65082) = barycentric product X(i)*X(j) for these (i, j): {305, 60850}, {312, 64230}, {348, 7090}, {1659, 69}, {1805, 349}, {2067, 76}, {2362, 304}, {3718, 61401}, {3926, 61392}, {5414, 6063}, {7133, 7182}, {13388, 75}, {13389, 46745}, {13390, 5391}, {13436, 14121}, {20567, 53066}, {30557, 85}, {52420, 60853}, {53063, 561}, {54017, 664}, {56386, 7}, {57918, 60851}, {60854, 77}, {65016, 9}
X(65082) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42013}, {2, 14121}, {3, 2066}, {6, 60852}, {7, 13390}, {48, 53065}, {56, 60849}, {57, 16232}, {63, 30556}, {69, 56385}, {75, 60853}, {77, 13389}, {109, 54016}, {176, 64336}, {222, 6502}, {269, 61400}, {278, 61393}, {514, 58838}, {603, 53064}, {606, 53066}, {1335, 5414}, {1659, 4}, {1790, 1806}, {1805, 284}, {2067, 6}, {2362, 19}, {3084, 30557}, {4025, 54019}, {5391, 56386}, {5414, 55}, {6213, 7133}, {6502, 34125}, {7090, 281}, {7133, 33}, {7177, 64229}, {13387, 7090}, {13388, 1}, {13389, 6212}, {13390, 1336}, {13437, 61392}, {14121, 13426}, {16232, 64210}, {30557, 9}, {31548, 30412}, {34121, 60851}, {42013, 13427}, {46377, 30335}, {46421, 34910}, {46745, 60854}, {51842, 46379}, {52420, 13388}, {53063, 31}, {53066, 41}, {54017, 522}, {54018, 8750}, {56386, 8}, {58840, 3064}, {60850, 25}, {60851, 607}, {60854, 318}, {61392, 393}, {61400, 13460}, {61401, 34}, {64230, 57}, {64622, 15892}, {64626, 7347}, {65016, 85}
X(65082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 481, 57266}, {69, 5391, 56386}, {75, 492, 56385}, {320, 32792, 491}, {32805, 42697, 1267}

X(65083) = 1ST BASEPOINT OF THE AGUILERA-PAVLOV TRIANGLE WRT ABC

Barycentrics    2*a*b*c-a*S : :

X(65083) lies on these lines: {1, 2}, {6, 55441}, {9, 13388}, {11, 15235}, {12, 15236}, {33, 3535}, {34, 3536}, {35, 1583}, {36, 1584}, {40, 16433}, {55, 55579}, {56, 55577}, {57, 30557}, {81, 19004}, {142, 1659}, {165, 16441}, {175, 18228}, {210, 3640}, {223, 31534}, {269, 65082}, {278, 55454}, {281, 55455}, {326, 32792}, {329, 481}, {354, 3641}, {388, 3539}, {394, 3301}, {482, 9776}, {491, 55456}, {492, 55457}, {497, 3540}, {517, 21547}, {587, 2331}, {590, 3553}, {615, 3554}, {940, 18991}, {1038, 55885}, {1040, 55890}, {1124, 17825}, {1335, 17811}, {1336, 56230}, {1372, 31018}, {1374, 5905}, {1385, 21548}, {1449, 31473}, {1478, 6805}, {1479, 6806}, {1482, 21545}, {1585, 55482}, {1586, 55481}, {1591, 7951}, {1592, 7741}, {1599, 5010}, {1600, 7280}, {1750, 31563}, {2052, 55465}, {2551, 31532}, {3298, 55442}, {3299, 10601}, {3302, 56354}, {3305, 55398}, {3306, 55397}, {3452, 13390}, {3576, 16432}, {3579, 21558}, {3740, 45713}, {3742, 45714}, {3745, 11371}, {3817, 61095}, {4383, 18992}, {4682, 45398}, {5437, 13389}, {5589, 62819}, {5927, 60903}, {7308, 30556}, {7968, 37679}, {7969, 37674}, {7982, 21546}, {7987, 16440}, {7991, 21553}, {8125, 10236}, {8126, 10235}, {9817, 55887}, {10164, 61094}, {10246, 21550}, {10857, 31564}, {11398, 15211}, {11399, 15212}, {11531, 21552}, {11547, 55435}, {12702, 21557}, {13360, 64229}, {13624, 21561}, {14165, 55464}, {15200, 54428}, {15215, 52427}, {16192, 21566}, {16200, 21544}, {16667, 63072}, {17502, 21575}, {17784, 31567}, {17917, 55424}, {17923, 55389}, {19003, 32911}, {19372, 55892}, {21060, 31569}, {21446, 61401}, {21492, 30389}, {21555, 30392}, {21559, 35242}, {21564, 63468}, {21565, 63469}, {21567, 58221}, {21572, 31663}, {31594, 46421}, {32804, 44179}, {32805, 55392}, {32806, 55391}, {32807, 55427}, {37682, 44635}, {40998, 52808}, {52412, 55390}, {55475, 62957}, {55476, 62956}, {60877, 60972}

X(65083) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 63689}
X(65083) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 63689}
X(65083) = pole of line {3057, 3640} with respect to the Feuerbach hyperbola
X(65083) = pole of line {58, 19003} with respect to the Stammler hyperbola
X(65083) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3298)}}, {{A, B, C, X(8), X(15891)}}, {{A, B, C, X(1336), X(14986)}}, {{A, B, C, X(3083), X(55442)}}, {{A, B, C, X(3084), X(56230)}}, {{A, B, C, X(3085), X(3300)}}, {{A, B, C, X(3086), X(3302)}}, {{A, B, C, X(5222), X(61401)}}, {{A, B, C, X(21446), X(56385)}}, {{A, B, C, X(56354), X(56427)}}
X(65083) = barycentric product X(i)*X(j) for these (i, j): {1, 32794}, {3298, 75}
X(65083) = barycentric quotient X(i)/X(j) for these (i, j): {1, 63689}, {3298, 1}, {32794, 75}, {55442, 3083}
X(65083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3084, 1}, {2, 6347, 1698}, {10601, 55409, 3299}

X(65084) = 1ST BASEPOINT OF THE 11TH BROCARD TRIANGLE WRT ABC

Barycentrics    (4*a^6+(b^2-c^2)^2*(4*b^2+c^2)-a^4*(4*b^2+7*c^2)+2*a^2*(-2*b^4+9*b^2*c^2+c^4))*(4*a^6+(b^2-c^2)^2*(b^2+4*c^2)-a^4*(7*b^2+4*c^2)+2*a^2*(b^4+9*b^2*c^2-2*c^4)) : :

X(65084) lies on the Kiepert hyperbola and on these lines: {4, 13857}, {98, 32216}, {597, 62927}, {598, 11064}, {599, 16080}, {1555, 54941}, {1992, 62924}, {14458, 47311}, {15066, 58268}, {30734, 60142}, {34289, 40112}, {37669, 54771}, {53415, 54774}

X(65084) = isogonal conjugate of X(58265)
X(65084) = trilinear pole of line {523, 54995}
X(65084) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(15066)}}, {{A, B, C, X(297), X(32216)}}, {{A, B, C, X(599), X(11064)}}, {{A, B, C, X(10603), X(54171)}}, {{A, B, C, X(11331), X(47311)}}, {{A, B, C, X(18020), X(57822)}}, {{A, B, C, X(23582), X(52147)}}, {{A, B, C, X(40384), X(40802)}}, {{A, B, C, X(44569), X(59767)}}
X(65084) = barycentric quotient X(i)/X(j) for these (i, j): {6, 58265}, {376, 44750}

X(65085) = 94TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 9*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 6*a^4*b^2*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 3*a^2*b^2*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(65085) = 13 X[2] - 4 X[44266], 7 X[2] - 4 X[44282], 2 X[3] + X[3153], 4 X[3] - X[13619], X[3] + 2 X[37938], X[4] + 2 X[2071], X[4] - 4 X[2072], X[4] + 8 X[15122], 5 X[4] - 8 X[23323], X[4] - 10 X[30745], 7 X[4] - 4 X[64891], 5 X[5] - 2 X[11558], 2 X[5] + X[18859], 4 X[5] - X[52403], X[20] + 2 X[18403], X[20] - 4 X[34152], 2 X[23] - 11 X[3525], X[23] - 4 X[44452], 2 X[23] + X[60466], 4 X[140] - X[2070], 8 X[140] + X[5189], 2 X[186] - 5 X[631], X[186] + 2 X[858], X[186] - 4 X[10257], 2 X[186] + X[46450], X[376] + 8 X[47097], 4 X[403] - 7 X[3090], X[403] - 4 X[5159], 2 X[403] + X[7464], 5 X[403] - 8 X[44912], X[403] + 2 X[47090], 8 X[468] - 17 X[3533], 4 X[468] - X[37925], X[468] - 4 X[63860], 5 X[631] + 4 X[858], 5 X[631] - 8 X[10257], 5 X[631] + X[46450], 5 X[632] - 2 X[10096], 10 X[632] - X[37924], X[858] + 2 X[10257], 4 X[858] - X[46450], 5 X[1656] - 2 X[11563], 5 X[1656] + X[35452], 2 X[2070] + X[5189], X[2071] + 2 X[2072], X[2071] - 4 X[15122], 5 X[2071] + 4 X[23323], X[2071] + 5 X[30745], 7 X[2071] + 2 X[64891], X[2072] + 2 X[15122], 5 X[2072] - 2 X[23323], 2 X[2072] - 5 X[30745], 7 X[2072] - X[64891], 7 X[3090] - 16 X[5159], 7 X[3090] + 2 X[7464], 35 X[3090] - 32 X[44912], 7 X[3090] + 8 X[47090], 5 X[3091] - 2 X[31726], 5 X[3091] + 4 X[37950], 2 X[3153] + X[13619], X[3153] - 4 X[37938], 5 X[3522] + 4 X[18572], 7 X[3523] + 2 X[7574], 7 X[3523] - 4 X[15646], 3 X[3524] - X[35489], 3 X[3524] - 2 X[37941], 11 X[3525] - 8 X[44452], 11 X[3525] + X[60466], 7 X[3526] - X[5899], 14 X[3526] - 5 X[37760], 7 X[3526] - 4 X[44234], 7 X[3528] + 2 X[10296], 7 X[3528] - 4 X[44246], X[3529] + 8 X[10297], X[3529] - 4 X[16386], X[3529] + 2 X[64890], 17 X[3533] - 2 X[37925], 17 X[3533] - 32 X[63860], 17 X[3544] - 8 X[47336], 8 X[3628] + X[35001], 4 X[3628] - X[43893], 7 X[3832] - 4 X[44283], 11 X[3855] - 8 X[10151], 3 X[5054] - X[37922], 3 X[5054] + X[60462], 11 X[5056] - 2 X[18325], 11 X[5056] - 8 X[46031], 13 X[5067] - 4 X[11799], 13 X[5067] + 2 X[37944], 13 X[5068] - 4 X[44267], 11 X[5070] - 8 X[15350], 8 X[5159] + X[7464], 5 X[5159] - 2 X[44912], 2 X[5159] + X[47090], X[5189] + 4 X[16532], 2 X[5899] - 5 X[37760], X[5899] - 4 X[44234], 4 X[7426] - 13 X[61859], 5 X[7464] + 16 X[44912], X[7464] - 4 X[47090], 17 X[7486] - 8 X[44961], X[7574] + 2 X[15646], 4 X[7575] - 13 X[10303], 4 X[7575] + 5 X[60455], 4 X[10096] - X[37924], 8 X[10257] + X[46450], 4 X[10295] - 13 X[10299], X[10295] - 4 X[16976], X[10295] + 8 X[47629], X[10296] + 2 X[44246], 2 X[10297] + X[16386], 4 X[10297] - X[64890], 13 X[10299] - 16 X[16976], 13 X[10299] + 32 X[47629], 13 X[10303] + 5 X[60455], 2 X[10989] + 7 X[15702], X[10989] + 2 X[44214], 4 X[11539] - X[37909], 4 X[11558] + 5 X[18859], 8 X[11558] - 5 X[52403], 2 X[11563] + X[35452], 2 X[11799] + X[37944], 8 X[12105] - 35 X[61848], 8 X[13473] - 5 X[62028], X[13619] + 8 X[37938], 14 X[14869] - 5 X[37958], 5 X[15122] + X[23323], 4 X[15122] + 5 X[30745], 14 X[15122] + X[64891], 10 X[15694] - X[37901], 5 X[15694] - X[37956], 7 X[15698] - 4 X[44280], 7 X[15702] - 2 X[37940], 7 X[15702] - 4 X[44214], 9 X[15709] - 2 X[37939], 11 X[15717] - 8 X[37968], 2 X[16386] + X[64890], 16 X[16531] - 31 X[61836], 8 X[16619] - 35 X[61873], X[16976] + 2 X[47629], 5 X[17538] + 4 X[18323], X[18325] - 4 X[46031], X[18403] + 2 X[34152], 8 X[18571] - 17 X[61820], 8 X[18579] - 17 X[61833], 2 X[18859] + X[52403], X[20063] - 4 X[37936], X[20063] - 19 X[55864], 11 X[21735] - 2 X[56369], 8 X[22249] - 17 X[55863], 4 X[23323] - 25 X[30745], 14 X[23323] - 5 X[64891], 4 X[25338] - X[37949], 4 X[25338] - 13 X[46219], 35 X[30745] - 2 X[64891], X[31726] + 2 X[37950], X[33703] - 4 X[57584], X[35001] + 2 X[43893], 5 X[37760] - 8 X[44234], 2 X[37907] - 5 X[61861], 4 X[37911] - X[47093], 5 X[37923] - 23 X[61850], X[37925] - 16 X[63860], 8 X[37931] - 23 X[61807], 8 X[37935] - 5 X[37953], 2 X[37935] + X[46517], 4 X[37936] - 19 X[55864], 2 X[37942] + X[47091], 16 X[37942] - 31 X[61881], 4 X[37942] - X[62344], 13 X[37943] - 8 X[44266], 7 X[37943] - 8 X[44282], X[37943] + 2 X[44450], 3 X[37943] - 2 X[46451], 2 X[37945] - 23 X[61867], X[37945] + 2 X[62332], X[37946] - 4 X[37971], 2 X[37946] - 29 X[61870], 4 X[37947] - 25 X[61856], X[37948] + 4 X[47097], X[37949] - 13 X[46219], 5 X[37952] + 4 X[47341], 10 X[37952] - 19 X[61814], 5 X[37953] + 4 X[46517], X[37967] - 4 X[44900], 4 X[37967] - 31 X[61863], 8 X[37971] - 29 X[61870], 4 X[37985] - X[62345], 5 X[41099] + 4 X[54995], 4 X[44264] - 13 X[61853], 4 X[44265] - 13 X[61822], 7 X[44266] - 13 X[44282], 4 X[44266] + 13 X[44450], 12 X[44266] - 13 X[46451], 4 X[44282] + 7 X[44450], 12 X[44282] - 7 X[46451], 3 X[44450] + X[46451], 8 X[44452] + X[60466], 16 X[44900] - 31 X[61863], 4 X[44911] - X[47096], 16 X[44911] - 19 X[61886], 4 X[44912] + 5 X[47090], 8 X[47031] - 17 X[62055], 8 X[47091] + 31 X[61881], 2 X[47091] + X[62344], 4 X[47096] - 19 X[61886], 2 X[47114] + X[47339], 16 X[47114] - 19 X[62066], 8 X[47308] - 17 X[62084], 8 X[47310] - 17 X[61951], 8 X[47311] + 19 X[61838], 8 X[47332] - 17 X[61915], 8 X[47333] - 17 X[61809], 8 X[47334] - 17 X[61888], 8 X[47335] - 17 X[61138], 8 X[47339] + 19 X[62066], 8 X[47341] + 19 X[61814], 19 X[55858] - X[62290], 7 X[60456] + 29 X[61842], 23 X[61867] + 4 X[62332], 31 X[61881] - 4 X[62344], 13 X[61964] - 4 X[62288], 13 X[61964] - 16 X[63838], X[62288] - 4 X[63838], X[74] + 2 X[1568], X[110] - 4 X[14156], 2 X[113] + X[13445], 2 X[125] + X[43574], X[1291] + 2 X[16336], X[3448] + 2 X[22115], 4 X[5972] - X[14157], 2 X[6699] + X[51392], 8 X[6723] + X[43576], X[6761] - 4 X[16177], X[10264] + 2 X[46114], 2 X[10264] + X[50461], 4 X[46114] - X[50461], 4 X[10564] + 5 X[15081], 2 X[10564] + X[50435], 5 X[15081] - 2 X[50435], X[10625] + 2 X[11692], 8 X[11064] + X[12317], 17 X[11465] - 8 X[58481], X[12112] - 4 X[51425], X[12383] + 2 X[25739], X[12383] - 4 X[51394], X[25739] + 2 X[51394], 4 X[13376] - X[45186], 2 X[13399] + X[14094], X[14683] - 4 X[40111], 11 X[15024] - 8 X[58551], 5 X[15059] - 2 X[63735], 2 X[15644] + X[48914], 8 X[20397] + X[23061], X[37477] + 2 X[63839], X[37496] + 8 X[40685], 2 X[44673] + X[51360], 2 X[51403] - 5 X[64101], X[54216] + 8 X[61543]

See Antreas Hatzipolakis and Peter Moses, euclid 6840.

X(65085) lies on these lines: {2, 3}, {74, 1568}, {110, 14156}, {113, 13445}, {125, 43574}, {323, 18932}, {539, 5504}, {542, 43572}, {1092, 23294}, {1138, 37802}, {1154, 15061}, {1236, 7799}, {1273, 1494}, {1291, 16336}, {1614, 61681}, {1899, 64597}, {2888, 13561}, {2979, 61724}, {3086, 10149}, {3448, 22115}, {3574, 43597}, {5562, 43608}, {5972, 14157}, {6188, 14993}, {6699, 51392}, {6723, 43576}, {6761, 16177}, {7691, 20191}, {8718, 64063}, {9706, 18128}, {9730, 61715}, {10264, 46114}, {10564, 15081}, {10625, 11692}, {11064, 12317}, {11459, 23329}, {11465, 58481}, {12038, 12254}, {12112, 51425}, {12242, 43600}, {12325, 12359}, {12383, 25739}, {13346, 26917}, {13352, 26913}, {13376, 45186}, {13391, 34128}, {13399, 14094}, {13482, 43836}, {14683, 40111}, {14831, 32339}, {15024, 58551}, {15035, 18400}, {15045, 61743}, {15059, 63735}, {15392, 44028}, {15644, 48914}, {18488, 43614}, {20397, 23061}, {24206, 43579}, {26879, 61658}, {28408, 39874}, {34148, 43808}, {35265, 59648}, {37472, 43816}, {37477, 63839}, {37496, 40685}, {37497, 61701}, {38793, 44407}, {43666, 54769}, {43839, 52525}, {44673, 51360}, {51403, 64101}, {53415, 54434}, {54041, 61644}, {54216, 61543}, {57306, 57316}, {57317, 57344}, {57329, 57377}

X(65085) = midpoint of X(i) and X(j) for these {i,j}: {2, 44450}, {10989, 37940}, {37922, 60462}
X(65085) = reflection of X(i) in X(j) for these {i,j}: {376, 37948}, {2070, 16532}, {16532, 140}, {35265, 59648}, {35489, 37941}, {37901, 37956}, {37940, 44214}, {37943, 2}, {37955, 549}
X(65085) = complement of X(46451)
X(65085) = circumcircle inverse of X(12088)
X(65085) = polar circle inverse of X(21841)
X(65085) = orthoptic-circle-of-the-Steiner-inellipse inverse of X(7667)
X(65085) = first Droz-Farney circle inverse of X(140)
X(65085) = Stammler circles radical circle inverse of X(20)
X(65085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 10201}, {2, 376, 7552}, {2, 10201, 14940}, {2, 44441, 4}, {2, 58805, 34330}, {2, 61736, 6143}, {3, 3153, 13619}, {3, 10224, 34007}, {3, 30744, 7577}, {3, 37938, 3153}, {3, 61736, 2}, {5, 12086, 4}, {5, 18859, 52403}, {20, 6640, 14940}, {140, 48411, 2}, {186, 858, 46450}, {186, 10257, 631}, {403, 47090, 7464}, {427, 45173, 4}, {549, 13371, 38321}, {549, 38321, 22467}, {631, 46450, 186}, {858, 10257, 186}, {1113, 1114, 12088}, {1368, 37118, 35921}, {1656, 35452, 11563}, {2043, 2044, 50009}, {2071, 2072, 4}, {2071, 12086, 18859}, {2071, 30745, 2072}, {2072, 15122, 2071}, {3524, 30775, 3545}, {3524, 35489, 37941}, {3526, 5899, 44234}, {3546, 37119, 631}, {3548, 44441, 2}, {5054, 31152, 44837}, {5054, 60462, 37922}, {5159, 7464, 3090}, {5159, 47090, 403}, {5899, 44234, 37760}, {6640, 10201, 2}, {6644, 31074, 4}, {7396, 35486, 44831}, {7512, 7667, 376}, {10264, 46114, 50461}, {10297, 16386, 64890}, {10303, 60455, 7575}, {13371, 22467, 4}, {13626, 13627, 15759}, {15122, 30745, 4}, {15765, 18585, 43809}, {16386, 64890, 3529}, {18403, 34152, 20}, {18586, 18587, 44235}, {23335, 44211, 34603}, {23336, 37452, 14118}, {25739, 51394, 12383}, {34551, 34552, 34577}, {34603, 44211, 3518}, {37925, 63860, 3533}, {37942, 47091, 62344}, {57322, 57323, 549}

X(65086) = 95TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    a^16 - 2*a^14*b^2 - 5*a^12*b^4 + 19*a^10*b^6 - 20*a^8*b^8 + 4*a^6*b^10 + 7*a^4*b^12 - 5*a^2*b^14 + b^16 - 2*a^14*c^2 + 16*a^12*b^2*c^2 - 21*a^10*b^4*c^2 - 11*a^8*b^6*c^2 + 34*a^6*b^8*c^2 - 24*a^4*b^10*c^2 + 13*a^2*b^12*c^2 - 5*b^14*c^2 - 5*a^12*c^4 - 21*a^10*b^2*c^4 + 63*a^8*b^4*c^4 - 38*a^6*b^6*c^4 - 9*a^2*b^10*c^4 + 10*b^12*c^4 + 19*a^10*c^6 - 11*a^8*b^2*c^6 - 38*a^6*b^4*c^6 + 34*a^4*b^6*c^6 + a^2*b^8*c^6 - 11*b^10*c^6 - 20*a^8*c^8 + 34*a^6*b^2*c^8 + a^2*b^6*c^8 + 10*b^8*c^8 + 4*a^6*c^10 - 24*a^4*b^2*c^10 - 9*a^2*b^4*c^10 - 11*b^6*c^10 + 7*a^4*c^12 + 13*a^2*b^2*c^12 + 10*b^4*c^12 - 5*a^2*c^14 - 5*b^2*c^14 + c^16 : :
X(65086) = X[3] + 2 X[16340], 2 X[3] + X[17511], X[4] - 4 X[3154], X[4] + 2 X[36164], 4 X[5] - X[36172], X[20] + 2 X[36184], 4 X[140] - X[36193], X[550] + 3 X[20124], 5 X[631] - 2 X[7471], 7 X[3090] - 4 X[36169], 2 X[3154] + X[36164], 11 X[3525] - 8 X[12068], 2 X[3861] + X[13471], X[7464] + 2 X[47348], 4 X[15122] - X[36188], 4 X[16340] - X[17511], X[74] + 2 X[3258], X[74] - 4 X[55319], X[3258] + 2 X[55319], X[110] - 4 X[31379], 2 X[113] + X[14508], 2 X[125] + X[477], X[265] + 2 X[38610], X[476] - 4 X[6699], X[1138] + 2 X[40630], 2 X[1553] - 5 X[64101], X[3448] + 2 X[14934], 2 X[45694] - 3 X[57306], 4 X[7687] - X[14989], 2 X[12041] + X[20957], X[12112] - 4 X[16319], X[12244] + 2 X[46045], X[12308] - 4 X[33505], X[12317] + 2 X[14611], X[12383] - 4 X[47084], X[14094] - 4 X[55308], X[14480] + 2 X[16003], 3 X[14644] - X[57471], X[14731] + 2 X[46632], 3 X[14851] + X[14993], X[14993] - 3 X[15061], 7 X[15020] - X[31876], 5 X[15059] - 2 X[25641], 5 X[15081] - 2 X[34150], 2 X[16111] + X[44967], X[18319] - 4 X[40685], 5 X[20125] - 8 X[31945], 8 X[20397] + X[38678], 2 X[34209] + X[38581], 2 X[38609] - 5 X[38728], 5 X[38728] - X[51345], X[38677] - 10 X[38729], 4 X[47296] - X[47323]

See Antreas Hatzipolakis and Peter Moses, euclid 6840.

X(65086) lies on these lines: {2, 3}, {74, 3258}, {110, 31378}, {113, 14508}, {125, 477}, {265, 38610}, {476, 6699}, {523, 1138}, {1553, 64101}, {1989, 47414}, {3448, 14934}, {5663, 45694}, {5670, 40662}, {6128, 32640}, {7687, 14989}, {10264, 33855}, {12041, 20957}, {12112, 16319}, {12244, 46045}, {12308, 33505}, {12317, 14611}, {12383, 47084}, {14094, 55308}, {14480, 16003}, {14644, 57471}, {14731, 46632}, {14851, 14993}, {15020, 31876}, {15059, 25641}, {15081, 34150}, {15111, 23329}, {16111, 44967}, {17702, 38701}, {18319, 40685}, {20125, 31945}, {20397, 38678}, {34128, 57305}, {34209, 38581}, {38609, 38728}, {38677, 38729}, {38700, 38727}, {38793, 60605}, {47296, 47323}

X(65086) = midpoint of X(i) and X(j) for these {i,j}: {477, 5627}, {10264, 33855}, {14851, 15061}
X(65086) = reflection of X(i) in X(j) for these {i,j}: {110, 31378}, {5627, 125}, {31378, 31379}, {36193, 64652}, {38700, 38727}, {51345, 38609}, {57305, 34128}, {60605, 38793}, {64642, 3628}, {64652, 140}
X(65086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 16340, 17511}, {3154, 36164, 4}, {3258, 55319, 74}

X(65087) = 96TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    12*a^10 - 15*a^8*b^2 - 18*a^6*b^4 + 24*a^4*b^6 + 6*a^2*b^8 - 9*b^10 - 15*a^8*c^2 + 62*a^6*b^2*c^2 - 28*a^4*b^4*c^2 - 46*a^2*b^6*c^2 + 27*b^8*c^2 - 18*a^6*c^4 - 28*a^4*b^2*c^4 + 80*a^2*b^4*c^4 - 18*b^6*c^4 + 24*a^4*c^6 - 46*a^2*b^2*c^6 - 18*b^4*c^6 + 6*a^2*c^8 + 27*b^2*c^8 - 9*c^10 : :
X(65087) = 5 X[4] - 2 X[10257], 4 X[4] - X[16386], 3 X[4] - X[37948], 7 X[4] - 4 X[63838], X[186] + 5 X[62028], 2 X[382] + X[403], 11 X[382] + 4 X[16531], 3 X[382] + X[37955], 7 X[382] + 2 X[47335], 11 X[403] - 8 X[16531], 3 X[403] - 2 X[37955], 7 X[403] - 4 X[47335], 2 X[468] + 7 X[50690], X[858] - 4 X[13473], X[858] - 10 X[17578], X[2071] - 7 X[50688], X[2072] - 4 X[3853], X[3146] + 2 X[10151], 5 X[3153] - 2 X[47092], 5 X[3522] - 8 X[44912], X[3529] - 4 X[44911], 8 X[3543] + X[7426], 9 X[3543] + X[37940], 7 X[3543] + X[46451], 7 X[3543] + 2 X[47310], 10 X[3627] - X[18323], 4 X[3627] - X[57584], 8 X[3627] + X[62288], 2 X[3627] + X[64891], 10 X[3830] - X[54995], 7 X[3832] - 4 X[16976], X[5059] - 4 X[47114], X[5073] + 2 X[44452], 5 X[5076] - 2 X[23323], 9 X[7426] - 8 X[37940], 7 X[7426] - 8 X[46451], 7 X[7426] - 16 X[47310], 8 X[10096] - 5 X[10295], 2 X[10096] - 5 X[44283], X[10096] + 5 X[62026], 8 X[10257] - 5 X[16386], 6 X[10257] - 5 X[37948], 7 X[10257] - 10 X[63838], X[10295] - 4 X[44283], X[10295] + 8 X[62026], 4 X[12102] - X[34152], 2 X[13473] - 5 X[17578], X[15646] + 2 X[62034], 2 X[15682] + X[44280], 3 X[16386] - 4 X[37948], 7 X[16386] - 16 X[63838], 12 X[16531] - 11 X[37955], 14 X[16531] - 11 X[47335], 2 X[16619] - 5 X[31726], 6 X[16619] - 5 X[37956], 2 X[16619] + 25 X[62023], 2 X[18323] - 5 X[57584], 4 X[18323] + 5 X[62288], X[18323] + 5 X[64891], X[18403] - 7 X[62016], 3 X[31726] - X[37956], X[31726] + 5 X[62023], 2 X[35404] + X[44214], 5 X[37900] - 8 X[47094], 7 X[37900] - 16 X[47338], X[37900] - 4 X[52403], 8 X[37911] + X[50692], X[37922] + 7 X[62024], 7 X[37940] - 9 X[46451], 7 X[37940] - 18 X[47310], X[37943] + 3 X[62029], 7 X[37948] - 12 X[63838], 7 X[37955] - 6 X[47335], X[37956] + 15 X[62023], 2 X[37968] + X[62044], 4 X[37984] + 5 X[50691], X[44246] + 2 X[62036], X[44282] + 2 X[62031], X[44283] + 2 X[62026], 2 X[46031] + X[62041], 7 X[47094] - 10 X[47338], 2 X[47094] - 5 X[52403], X[47096] - 4 X[47309], X[47096] + 14 X[62021], X[47096] + 2 X[64890], 2 X[47309] + 7 X[62021], 2 X[47309] + X[64890], X[47314] - 28 X[62018], 2 X[47336] + 7 X[62024], 4 X[47338] - 7 X[52403], 2 X[57584] + X[62288], X[57584] + 2 X[64891], 7 X[62021] - X[64890], X[62288] - 4 X[64891], X[110] - 4 X[51998]

See Antreas Hatzipolakis and Peter Moses, euclid 6840.

X(65087) lies on these lines: {2, 3}, {110, 51998}, {45968, 61721}

X(65087) = midpoint of X(3146) and X(37941)
X(65087) = reflection of X(i) in X(j) for these {i,j}: {35489, 47332}, {37922, 47336}, {37941, 10151}, {46451, 47310}
X(65087) = orthoptic-circle-of-the-Steiner-inellipse-inverse of X(21974)
X(65087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {382, 3515, 3146}, {382, 3830, 18568}, {3515, 10151, 403}, {3543, 17578, 62964}, {3627, 64891, 57584}, {3830, 62966, 50687}, {6622, 35471, 3515}, {6995, 62964, 31133}, {47309, 64890, 47096}, {57584, 64891, 62288}

X(65088) =  X(30)X(24981)∩X(549)X(9214)

Barycentrics   (2 a^8-9 a^6 b^2+15 a^4 b^4-11 a^2 b^6+3 b^8+5 a^6 c^2+a^4 b^2 c^2+5 a^2 b^4 c^2-11 b^6 c^2-14 a^4 c^4+a^2 b^2 c^4+15 b^4 c^4+5 a^2 c^6-9 b^2 c^6+2 c^8) (2 a^8+5 a^6 b^2-14 a^4 b^4+5 a^2 b^6+2 b^8-9 a^6 c^2+a^4 b^2 c^2+a^2 b^4 c^2-9 b^6 c^2+15 a^4 c^4+5 a^2 b^2 c^4+15 b^4 c^4-11 a^2 c^6-11 b^2 c^6+3 c^8) : :
Barycentrics    (3*S^2-36*R^2*SB+13*SB^2+2*SA*SC)*(5*S^2-SC*(36*R^2-15*SC+2*SW)) : :
X(65088) = 2*X(3258)-X(46081)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65088) lies on the Euler hyperbola and these lines: {30, 24981}, {548, 15454}, {549, 9214}, {3258, 46081}, {3471, 61792}, {3628, 14254}, {35906, 63633}, {37942, 52661}

X(65088) = reflection of X(46081) in X(3258)
X(65088) = isogonal conjugate of the circumperp conjugate of X(15021)
X(65088) = antigonal conjugate of X(46081)
X(65088) = intersection, other than A, B, C, of Euler hyperbola and circumconic {{A, B, C, X(3), X(37942)}}
X(65088) = antipode in Euler hyperbola of X(46081)

X(65089) =  (name pending)

Barycentrics   (3 a^8-3 a^6 b^2-3 a^2 b^6+3 b^8-10 a^6 c^2-6 a^4 b^2 c^2-6 a^2 b^4 c^2-10 b^6 c^2+12 a^4 c^4+15 a^2 b^2 c^4+12 b^4 c^4-6 a^2 c^6-6 b^2 c^6+c^8) (3 a^8-10 a^6 b^2+12 a^4 b^4-6 a^2 b^6+b^8-3 a^6 c^2-6 a^4 b^2 c^2+15 a^2 b^4 c^2-6 b^6 c^2-6 a^2 b^2 c^4+12 b^4 c^4-3 a^2 c^6-10 b^2 c^6+3 c^8) : :
Barycentrics    (S^2-4*R^2*SB+9*SB^2-4*SA*SC)*(3*S^2+SC*(4*R^2-5*SC-4*SW)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65089) lies on this line: {3851, 19347}

X(65089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(19347)}} and {{A, B, C, X(4), X(3851)}}

X(65090) =  X(5)X(8884)∩X(54)X(5562)

Barycentrics    a^2 (a^4-2 a^2 b^2+b^4-a^2 c^2-b^2 c^2) (a^4-a^2 b^2-2 a^2 c^2-b^2 c^2+c^4) (a^6-3 a^2 b^4+2 b^6-a^4 c^2-3 b^4 c^2-a^2 c^4+c^6) (a^6-a^4 b^2-a^2 b^4+b^6-3 a^2 c^4-3 b^2 c^4+2 c^6) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65090) lies on these lines: {2, 59275}, {3, 57474}, {5, 8884}, {54, 5562}, {95, 52347}, {96, 60241}, {97, 31504}, {140, 34900}, {216, 7488}, {252, 631}, {275, 12225}, {933, 14118}, {3518, 63176}, {7503, 58079}, {10610, 50463}, {13160, 61440}, {13367, 18315}, {15958, 51033}, {18401, 42441}, {34148, 42487}, {34864, 44715}, {38444, 57489}, {38808, 41168}

X(65090) = isogonal conjugate of X(3574)
X(65090) = trilinear pole of the line: {2623, 10313}
X(65090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7488)}} and {{A, B, C, X(3), X(5)}}
X(65090) = barycentric product of X(i)*X(j) for these (i,j): (54, 60241), (95, 41891), (97, 14860)
X(65090) = barycentric quotient of X(i)/X(j) for these {i,j}: {54, 23292}, {95, 26166}, {97, 41008}, {577, 31388}, {2167, 17859}, {8882, 3575}
X(65090) = trilinear product of X(i)*X(j) for these (i,j): (2148, 60241), (2167, 41891), (2169, 14860)
X(65090) = trilinear quotient of X(i)/X(j) for these (i,j): (95, 17859), (255, 31388), (2167, 23292), (2169, 13367), (2190, 3575), (41891, 1953)

X(65091) =  X(25)X(38937)∩X(1495)X(2071)

Barycentrics    a^2 (a^10-3 a^8 b^2+2 a^6 b^4+2 a^4 b^6-3 a^2 b^8+b^10+5 a^8 c^2+6 a^6 b^2 c^2-22 a^4 b^4 c^2+6 a^2 b^6 c^2+5 b^8 c^2-15 a^6 c^4+19 a^4 b^2 c^4+19 a^2 b^4 c^4-15 b^6 c^4+5 a^4 c^6-32 a^2 b^2 c^6+5 b^4 c^6+10 a^2 c^8+10 b^2 c^8-6 c^10) (a^10+5 a^8 b^2-15 a^6 b^4+5 a^4 b^6+10 a^2 b^8-6 b^10-3 a^8 c^2+6 a^6 b^2 c^2+19 a^4 b^4 c^2-32 a^2 b^6 c^2+10 b^8 c^2+2 a^6 c^4-22 a^4 b^2 c^4+19 a^2 b^4 c^4+5 b^6 c^4+2 a^4 c^6+6 a^2 b^2 c^6-15 b^4 c^6-3 a^2 c^8+5 b^2 c^8+c^10) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65091) lies on these lines: {25, 38937}, {512, 57147}, {1495, 2071}, {3543, 14583}, {10419, 46431}, {13473, 34170}, {14581, 15262}

X(65091) = isogonal conjugate of X(37853)
X(65091) = trilinear pole of the line: {14398, 46425}
X(65091) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(13473)}} and {{A, B, C, X(4), X(2071)}}

X(65092) =  X(4)X(74)∩X(141)X(542)

Barycentrics    2 a^10-2 a^8 b^2-9 a^6 b^4+19 a^4 b^6-13 a^2 b^8+3 b^10-2 a^8 c^2+20 a^6 b^2 c^2-19 a^4 b^4 c^2+10 a^2 b^6 c^2-9 b^8 c^2-9 a^6 c^4-19 a^4 b^2 c^4+6 a^2 b^4 c^4+6 b^6 c^4+19 a^4 c^6+10 a^2 b^2 c^6+6 b^4 c^6-13 a^2 c^8-9 b^2 c^8+3 c^10 : :
Barycentrics    (5*S^2*(12*R^2-SA-2*SW)-3*SB*SC*(12*R^2-SW)) : :
X(65092) = 3*X(4)+5*X(74), X(4)-5*X(125), 3*X(4)-5*X(7687), 13*X(4)-5*X(10721), 9*X(4)-5*X(13202), X(4)+5*X(20417), X(5)-3*X(38725), X(74)+3*X(125), 7*X(74)-3*X(10990), 11*X(74)-3*X(12244), 3*X(74)+X(13202), 3*X(74)+5*X(15081), X(74)-3*X(20417), X(110)-5*X(38729), 5*X(113)-9*X(5055), X(113)+3*X(20126), X(113)-3*X(45311), 3*X(125)-X(7687),7*X(125)+X(10990), 9*X(125)-X(13202), 7*X(125)-3*X(14644), 9*X(125)-5*X(15081), 5*X(265)+3*X(3534), X(399)-3*X(5972), X(399)-9*X(15061), X(399)+3*X(16003), 9*X(549)-5*X(1511), 3*X(549)-5*X(6699), 3*X(549)+5*X(10264), 6*X(549)-5*X(48378), X(1511)-3*X(6699), X(1511)+3*X(10264), 2*X(1511)-3*X(48378), 3*X(3534)-5*X(37853), 3*X(5055)+5*X(20126), 3*X(5055)-5*X(45311), 2*X(6699)-X(48378), 13*X(7687)-3*X(10721), 7*X(7687)+3*X(10990), 3*X(7687)-X(13202), 7*X(7687)-9*X(14644), 3*X(7687)-5*X(15081), X(7687)+3*X(20417), 2*X(10264)+X(48378), 11*X(10990)-7*X(12244), X(10990)+3*X(14644), X(10990)-7*X(20417), X(13202)-5*X(15081), X(13202)+9*X(20417), 3*X(14644)+7*X(20417)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65092) lies on these lines: {2, 6053}, {3, 44787}, {4, 74}, {5, 38725}, {6, 19348}, {110, 10303}, {113, 5055}, {141, 542}, {146, 61936}, {265, 3534}, {389, 54376}, {399, 3526}, {541, 5066}, {548, 13470}, {631, 24981}, {974, 62958}, {1495, 44673}, {1503, 47451}, {1539, 23046}, {1656, 38792}, {1899, 10193}, {2771, 46694}, {2781, 58471}, {2914, 61659}, {2935, 35501}, {3258, 40630}, {3426, 26958}, {3448, 15051}, {3628, 5663}, {3856, 20396}, {3857, 46686}, {5072, 10620}, {5609, 61852}, {5621, 13289}, {5642, 12317}, {5655, 61883}, {5900, 57714}, {5965, 15122}, {6000, 15151}, {6143, 43596}, {6759, 58378}, {7486, 15059}, {7728, 61953}, {9140, 10304}, {9143, 61830}, {9934, 62973}, {9976, 49116}, {10113, 62041}, {10182, 26864}, {10272, 47598}, {10628, 16270}, {10657, 42955}, {10658, 42954}, {10706, 61926}, {10733, 15683}, {11202, 39874}, {11204, 23291}, {11410, 19457}, {11430, 25563}, {11456, 64063}, {11579, 32257}, {11801, 62034}, {11807, 12099}, {12041, 15704}, {12079,55319}, {12112, 13399}, {12121, 62082}, {12227, 15106}, {12295, 15027}, {12308, 38795}, {12383, 15698}, {12412, 32305}, {12902, 62107}, {13171, 55578}, {13293, 55575}, {13392, 14890}, {13403, 43607}, {14094, 61870}, {14643, 55860}, {14677, 33699}, {15021, 49140}, {15022, 15054}, {15032, 43608}, {15035, 61807}, {15042, 15706}, {15055, 50693}, {15526, 34842}, {15684, 20127}, {15738, 17855}, {16111, 17800}, {16534, 34128}, {17701, 34468}, {18381, 37487}, {18400, 37931}, {20125, 61865}, {21243, 37470}, {23332, 64729}, {25556, 32300}, {26879, 40240}, {29012, 47342}, {30714, 38728}, {32068, 44236}, {32423, 61792}, {32609, 61826}, {34153, 61785}, {35237, 61646}, {37118, 44109}, {37517, 44441}, {38626, 61598}, {38726, 62069}, {38788, 62142}, {38790, 61974}, {38793, 61832}, {38794, 61843}, {40640, 52171}, {44201, 55653}, {44904, 61574}, {50664, 52262}, {56567, 61872}, {61797, 64182}, {61895, 64101}, {61954, 64102}, {63735, 64624}

X(65092) = midpoint of X(i) and X(j) for these (i, j): {74, 7687}, {125, 20417}, {265, 37853}, {389, 54376}, {5972, 16003}, {6699, 10264}, {10620, 38791}, {11579, 32257}, {12041, 36253}, {12079, 55319}, {15738, 17855}, {20126, 45311}, {20379, 61548}, {38626, 61598}, {46686, 51522}
X(65092) = reflection of X(i) in X(j) for these (i, j): (6723, 20397), (12900, 40685), (48378, 6699)
X(65092) = complement of X(6053)
X(65092) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (74, 125, 7687), (74, 15081, 13202), (125, 10990, 14644), (125, 13202, 15081), (3448, 15057, 38727), (7687, 20417, 74), (10620, 23515, 38791), (12900, 20397, 40685), (12900, 40685, 6723), (13202, 15081, 7687), (15027, 15041, 12295), (15061, 16003, 5972), (30714, 38728, 48375)

X(65093) =  X(4)X(51)∩X(26)X(575)

Barycentrics    a^2 (3 a^6 b^2-9 a^4 b^4+9 a^2 b^6-3 b^8+3 a^6 c^2-4 a^4 b^2 c^2-9 a^2 b^4 c^2+10 b^6 c^2-9 a^4 c^4-9 a^2 b^2 c^4-14 b^4 c^4+9 a^2 c^6+10 b^2 c^6-3 c^8) : :
X(65093) = X(3)+3*X(21849), X(4)-9*X(51), 5*X(4)+3*X(185), X(4)+3*X(389), X(4)-3*X(10110), 11*X(4)-3*X(11381), 7*X(4)-3*X(13474), 17*X(4)-9*X(32062), 7*X(4)+X(64029), 2*X(5)-X(40247), X(5)-3*X(58470), X(20)-9*X(16226), 3*X(51)+X(389), 3*X(51)+5*X(3567), 7*X(51)+X(5890), 15*X(51)-7*X(9781), 3*X(51)-X(10110), 9*X(51)+X(13382), 3*X(52)+5*X(1656), X(52)+3*X(5943), X(52)-9*X(13321), 5*X(52)+3*X(23039), X(185)-5*X(389), 13*X(185)-5*X(6241), X(185)+7*X(9781), X(185)+5*X(10110), 5*X(185)+3*X(11455), 3*X(185)-5*X(13382), X(389)-5*X(3567), 7*X(389)-3*X(5890), 3*X(389)-X(13382), 7*X(389)+X(13474), 5*X(3567)+X(10110), 3*X(5890)+7*X(10110), 9*X(5890)-7*X(13382), 3*X(5890)+X(13474), 9*X(5890)-X(64029), 7*X(9781)-5*X(10110), 11*X(10110)-X(11381), 3*X(10110)+X(13382), 7*X(10110)-X(13474), 2*X(12002)+3*X(15012), X(12002)-6*X(58533), 7*X(13382)+3*X(13474), 7*X(13382)-X(64029), 3*X(13474)+X(64029), X(15012)+4*X(58533), 2*X(16625)+X(40247), X(16625)+3*X(58470), X(40247)-6*X(58470)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65093) lies on these lines: {2, 15606}, {3, 21849}, {4, 51}, {5, 16254}, {6, 3517}, {20, 16226}, {24, 15004}, {25, 50414}, {26,575}, {30,12002}, {52, 1656}, {54, 13433}, {140, 143}, {186, 1173}, {373, 11412}, {468, 973}, {550, 5446}, {568, 3851}, {576, 6642}, {578, 3515}, {631, 21969}, {1112, 20417}, {1147, 5097}, {1154, 12046}, {1199, 1495}, {1216, 6688}, {1614, 44106}, {1657, 9730}, {2810, 58575}, {2818, 58493}, {2979, 61856}, {3060, 3523}, {3066, 12160}, {3089, 15010}, {3090, 14531}, {3091, 14831}, {3098, 15805}, {3516, 10982}, {3518, 13366}, {3522, 11002}, {3527, 3532}, {3530, 16982}, {3533, 3917}, {3545, 45187}, {3546, 20423}, {3818, 18951}, {3819, 6243}, {3850, 10095}, {3854, 15030}, {3858, 6102}, {5056, 5562}, {5059, 64100}, {5068, 5889}, {5073, 37481}, {5480, 20299}, {5650, 11465}, {5663, 44863}, {5891, 61919}, {5892, 10263}, {6101, 55859}, {6146, 61657}, {6684, 58548}, {6746, 44084}, {6759, 11432}, {6995, 11431}, {7488, 15019}, {7506, 34986}, {7525, 20190}, {7555, 55704}, {7592, 34417}, {7687, 13148}, {7715, 8550}, {7730, 40632}, {8681, 12235}, {9052, 58647}, {9306, 37493}, {9815, 64048}, {9822, 34507}, {9833, 63031}, {10116, 13490}, {10170, 61907}, {10219, 32205}, {10299, 64051}, {10574, 49135}, {10575, 62023}, {10601, 46728}, {10619, 11808}, {10625, 15720}, {10628, 11746}, {10821, 34468}, {10990, 11807}, {11202, 11426}, {11225, 12134}, {11245, 13419}, {11423, 44110}, {11424, 35477}, {11425, 55574}, {11430, 32534}, {11451, 46935}, {11459, 27355}, {11591, 44904}, {11623, 39835}, {11645, 18128}, {11649, 47460}, {11745, 43174}, {31830, 58806}, {32140, 48889}, {33586, 37515}, {33591, 63124}, {34224, 61712}, {34566, 34567}, {34783, 46847}, {36153, 37936}, {36979, 42978}, {36981, 42979}, {36987, 62067}, {37484, 61832}, {37925, 43600}, {37944, 43603}, {37984, 63659}, {38005, 42021}, {39806, 58503}, {40280, 62107}, {40647, 62036}, {42457, 46866}, {43392, 43823}, {43586, 55715}, {43831, 44959}, {44495, 64599}, {44802, 53863}, {50476, 61299}, {55166, 62061}, {55860, 63632}, {58484, 64472}, {58555, 64067}, {61784, 63414}, {61791, 64050}, {63688, 63714}

X(65093) = midpoint of X(i) and X(j) for these (i, j): {4, 13382}, {5, 16625}, {52, 11793}, {143, 5462}, {389, 10110}, {973, 58489}, {1112, 58498}, {3530, 16982}, {5446, 9729}, {5447, 14449}, {6102, 44870}, {10095, 16881}, {10263, 13348}, {11806, 58536}, {12236, 41671}, {18583, 21852}, {31757, 58487}, {31760, 58469}, {31830, 58806}, {32191, 58471}, {32411, 58551}, {39806, 58503}, {39835, 58502}
X(65093) = reflection of X(i) in X(j) for these (i, j): (11695, 5462), (17704, 12006), (40247, 5)
X(65093) = complement of X(15606)
X(65093) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 389, 13382), (4, 5890, 64029), (4, 64029, 13474), (24, 15004, 37505), (25, 64026, 50414), (51, 185, 9781), (51, 389, 10110), (51, 3567, 389), (52, 5943, 11793), (143, 13363, 14449), (389, 13474, 5890), (1199, 38848, 1495), (1216, 15026, 6688), (5446, 5946, 9729), (5447, 5462, 13363), (5892, 10263, 13348), (7715, 8550, 45185), (10110, 13382, 4), (11002, 15043, 45186), (11432, 17810, 6759), (13363, 14449, 5447), (15043, 45186, 16836), (16625, 58470, 5)

X(65094) =  X(6)X(24)∩X(140)X(389)

Barycentrics    a^2 (a^12 b^2-4 a^10 b^4+5 a^8 b^6-5 a^4 b^10+4 a^2 b^12-b^14+a^12 c^2-10 a^8 b^4 c^2+16 a^6 b^6 c^2-3 a^4 b^8 c^2-8 a^2 b^10 c^2+4 b^12 c^2-4 a^10 c^4-10 a^8 b^2 c^4+16 a^6 b^4 c^4+8 a^4 b^6 c^4-4 a^2 b^8 c^4-6 b^10 c^4+5 a^8 c^6+16 a^6 b^2 c^6+8 a^4 b^4 c^6+16 a^2 b^6 c^6+3 b^8 c^6-3 a^4 b^2 c^8-4 a^2 b^4 c^8+3 b^6 c^8-5 a^4 c^10-8 a^2 b^2 c^10-6 b^4 c^10+4 a^2 c^12+4 b^2 c^12-c^14) : :
X(65094) = 3*X(51)+X(10619), 3*X(51)-X(11576), 3*X(54)+5*X(3567), 3*X(54)+X(6152), 5*X(54)+3*X(7730), 3*X(54)-X(11577), 9*X(54)-X(12291), 7*X(54)+X(13423), X(185)+3*X(3574), 3*X(568)+X(12606), 3*X(973)-5*X(3567), 3*X(973)-X(6152), 5*X(973)-3*X(7730), 3*X(973)+X(11577), 9*X(973)+X(12291), 7*X(973)-X(13423), X(1216)-3*X(6689), X(1216)+3*X(10115), X(1493)+3*X(5946), X(2914)+3*X(46430), 5*X(3567)-X(6152), 5*X(3567)+X(11577), 2*X(5462)-X(9827), 3*X(5890)+X(12300), 5*X(6152)-9*X(7730), 3*X(6152)+X(12291), 7*X(6152)-3*X(13423), 4*X(10110)-3*X(11743), X(10110)-3*X(58489), X(10263)+3*X(10610), 3*X(11245)-X(32377), 3*X(11577)-X(12291), 7*X(11577)+3*X(13423), X(11743)-4*X(58489), 7*X(15043)+X(15801), X(15089)+3*X(16222), X(15739)-3*X(61715), X(32352)+3*X(61659), 3*X(44056)+X(63414)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65094) lies on these lines: {6, 24}, {51, 10619}, {52, 12363}, {140, 389}, {143, 12107}, {185, 427}, {195, 11432}, {394, 15043}, {539, 5462}, {568, 12606}, {578, 7502}, {1147, 1493}, {1199, 52417}, {1209, 7405}, {2888, 11433}, {2914, 46430}, {5097, 63709}, {5890, 12300}, {5943, 61544}, {6288, 39571}, {6746, 13366}, {6756, 10110}, {6776, 32359}, {7485, 7691}, {8550, 51994}, {9729, 10691}, {9977, 44489}, {10095, 45286}, {10628, 16270}, {11245, 32377}, {11271, 11431}, {11425, 64050}, {11427, 41590}, {11430, 44056}, {11436, 13079}, {11548, 32396}, {11746, 32423}, {12266, 64722}, {12325, 63129}, {13142, 58480}, {13351, 26876}, {13474, 16198}, {13568, 58557}, {14542, 61116}, {15045, 61773}, {15089, 16222}, {15739, 37119}, {18388, 45959}, {18390, 22804}, {18916, 34118}, {18984, 19366}, {19161, 21167}, {19347, 32379}, {20424, 52003}, {22466, 38006}, {32352, 61659}, {37935, 46363}, {41578, 63031}, {41589, 45089}, {52540, 58468}, {58488, 58807}

X(65094) = midpoint of X(i) and X(j) for these (i, j): {52, 12363}, {54, 973}, {389, 12242}, {6152, 11577}, {6689, 10115}, {10619, 11576}
X(65094) = reflection of X(9827) in X(5462)
X(65094) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (51, 10619, 11576), (54, 3567, 6152), (54, 6152, 11577), (973, 11577, 6152), (3567, 6152, 973), (6689, 12242, 23292), (12241, 58550, 63659)

X(65095) =  X(5)X(113)∩X(110)X(1593)

Barycentrics    a^2 (a^12 b^2-4 a^10 b^4+5 a^8 b^6-5 a^4 b^10+4 a^2 b^12-b^14+a^12 c^2+8 a^8 b^4 c^2-30 a^6 b^6 c^2+27 a^4 b^8 c^2-2 a^2 b^10 c^2-4 b^12 c^2-4 a^10 c^4+8 a^8 b^2 c^4+24 a^6 b^4 c^4-14 a^4 b^6 c^4-32 a^2 b^8 c^4+18 b^10 c^4+5 a^8 c^6-30 a^6 b^2 c^6-14 a^4 b^4 c^6+60 a^2 b^6 c^6-13 b^8 c^6+27 a^4 b^2 c^8-32 a^2 b^4 c^8-13 b^6 c^8-5 a^4 c^10-2 a^2 b^2 c^10+18 b^4 c^10+4 a^2 c^12-4 b^2 c^12-c^14) : :
X(65095) = 2*X(5)-X(16270), 3*X(110)+5*X(11439), 5*X(113)-X(11562), 3*X(113)+X(12162), 3*X(113)-X(25711), X(185)-3*X(41670), 3*X(381)-2*X(15465), X(974)-3*X(36518),3*X(1112)-X(5889), 3*X(1539)+X(6101), 5*X(3091)-3*X(12099), 5*X(3091)+3*X(54037), 7*X(3832)-3*X(45237), X(5446)-3*X(46686), 3*X(5642)+X(11381), X(5889)+3*X(12825), 3*X(5972)-X(46850), 2*X(6723)-X(15151), X(7723)+3*X(38789), 3*X(9826)-2*X(13630), X(10575)-5*X(38795), 3*X(10706)+5*X(15058), 2*X(11017)-X(20396), 5*X(11439)-3*X(12133), 3*X(11455)+5*X(15034), 3*X(11562)+5*X(12162), 3*X(11562)-5*X(25711), 4*X(11793)-3*X(13416), X(12111)+3*X(12824), 3*X(12824)-X(13148), X(13630)-3*X(61574), 3*X(14643)-X(44573), 9*X(14643)-X(64030), 3*X(14708)-X(45957), 3*X(15030)+X(15063), 3*X(15030)-X(15738), 3*X(15035)+X(46431), 3*X(15113)-X(31978), 3*X(16194)+X(30714), 2*X(16881)-3*X(58516), X(17854)-5*X(64101), 3*X(44573)-X(64030)

See Antreas Hatzipolakis and Ercole Suppa, euclid 6851.

X(65095) lies on these lines: {3, 20772}, {4, 14984}, {5, 113}, {110, 1593}, {146, 6815}, {235, 12827}, {265, 45011}, {381, 15465}, {542, 12241}, {1112, 5889}, {1154, 47336}, {1498, 15462}, {1511, 12084}, {1539, 6101}, {1625, 44468}, {1986, 15751}, {2777, 11793}, {2781, 5893}, {2854, 46847}, {2883, 15116}, {3091, 12099}, {3541, 12292}, {3548, 5656}, {3832, 45237}, {5094, 15305}, {5159, 6000}, {5446, 44226}, {5562, 16105}, {5609, 18451}, {5621, 33537}, {5622, 11479}, {5642, 11381}, {5655, 43841}, {5972, 16196}, {6723, 15151}, {7592, 14094}, {7723, 38789}, {7728, 11487}, {8780, 11455}, {9820, 15115}, {9970, 32276}, {10539, 32137}, {10574, 15029}, {10575, 38795},{10706, 15058}, {11284, 15054}, {11746, 13487}, {12111, 12824}, {12362, 36201}, {13202, 41673}, {13391, 44267}, {13488, 17702}, {13491, 38398}, {13754, 37984}, {15035, 46431}, {15060, 50008}, {15113, 31978}, {15121, 62947}, {15122, 51425}, {15531, 16261}, {16165, 26883}, {16194, 30714}, {16881, 58516}, {17854, 64101}, {21243, 63695}, {32136, 38632}, {37950, 51393}, {60774, 63821}

X(65095) = midpoint of X(i) and X(j) for these (i, j): {110, 12133}, {146, 54376}, {1112, 12825}, {5562, 16105}, {5907, 38791}, {7728, 12358}, {12099, 54037}, {12111, 13148}, {12162, 25711}, {13202, 41673}, {15063, 15738}
X(65095) = reflection of X(i) in X(j) for these (i, j): (9826, 61574), (15151, 6723), (16270, 5), (20396, 11017), (60774, 63821)
X(65095) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (113, 12162, 25711), (12111, 12824, 13148), (15030, 15063, 15738), (15114, 61574, 5)





leftri   Sign-images: X(65096) - X(65106)  rightri

Contributed by Clark Kimberling and Peter Moses, August 28, 2024

Suppose that X = x(a,b,c) : : is a triangle center, and define

f(a,b,c) = x(a,-b,c) and g(a,b,c) = x(a,b,-c)
X'(a,b,c) = f(a,b,c) : f(b,c,a) : f(c,a,b)
X''(a,b,c) = g(a,b,c) : g(b,c,a) : g(c,a,b).

The point X' = X'(a,b,c) is here introduced as the sign-image of X. The set of triangle centers is partitioned by the sign-image operation into three subsets:

Type 1: self-sign-images X, for which X'=X;
Type 2: triangle centers X such that X' ≠ X and X' = X'';
Type 3: triangle centers X such that X' ≠ X''. In this case X' and X'' are a bicentric pair.

The appearance of k in the following list means that X(k) is self-sign-image:
1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 30, 31, 32, 38, 39, 47, 48, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 66, 67, 68, 69, 70, 74, 75, 76, 82, 83, 91, 92, 93, 94, 95, 96, 97, 98, 99, 107, 110, 111, 112, 113, 114, 115, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 143

The appearance of (h,k) in the following list means that X(k) is the sign-image of X(h) and X(k) is a triangle center:
(7,8), (10,514), (12,11), (34,33), (35,36), (36,35), (37,513), (42,649), (56,55), (57,9), (65,650), (71,1459), (72,905), (73,652), (77,78), (84,40), (85,312), (87,43), (90,46)

The appearance of k in the following list means that X'(k) and X''(k) are a bicentric pair:
8, 9, 11, 21, 27, 28, 29, 33, 40, 41, 43, 44, 45, 46, 55, 58, 59, 60, 78, 79, 80, 81, 86, 88, 89, 100, 101, 102, 103, 104, 105, 106, 108, 109, 116, 117, 118, 119, 120, 121, 123, 124, 142, 144, 145, 149, 150, 151, 152, 153

Regarding triangfle centers of Type 2, the appearance of {j,k} in the following list means that X(k) is the sign-image of X(j) and X(j) is the sign-image of X(k):
{10,514}, {35,36}, {37,513}, {42,649}, {71,1459}, {72,905}, {171,238}, {172,1914}, {202,7006}, {203,7005}, {213,667}, {228,22383}, {239,894}, {242,7009}, {244,756}, {259,266}, {306,4025}, {313,3261}, {319,320}, {321,693}, {350,1909}, {357,1134}, {358,1135}

underbar



X(65096) = SIGN-IMAGE OF X(816)

Barycentrics    (b + c)*(a^4 + b^3*c - b^2*c^2 + b*c^3) : :

X(65096) lies on these lines: {2, 4118}, {6, 18805}, {10, 16580}, {31, 20444}, {32, 4412}, {37, 19563}, {75, 2209}, {560, 4836}, {744, 1918}, {1215, 21231}, {2175, 4381}, {2887, 20713}, {4837, 17481}, {8053, 24255}, {16609, 21238}, {17763, 20932}, {20236, 24425}, {20964, 35550}, {22300, 49598}

X(65096) = midpoint of X(1918) and X(20234)
X(65096) = complement of X(4118)
X(65096) = complement of the isotomic conjugate of X(38847)
X(65096) = X(i)-complementary conjugate of X(j) for these (i,j): {711, 40876}, {38826, 2}, {38830, 626}, {38847, 2887}, {40416, 141}, {44163, 40380}, {44165, 40379}, {44167, 39}, {58114, 826}
X(65096) = crosspoint of X(2) and X(38847)
X(65096) = crosssum of X(6) and X(2085)
X(65096) = barycentric product X(321)*X(18209)
X(65096) = barycentric quotient X(18209)/X(81)
X(65096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 16580, 21235}, {1215, 21231, 28593}

X(65097) = SIGN-IMAGE OF X(851)

Barycentrics    a*(b - c)*(a^4 - a^2*b^2 - a^2*b*c + b^3*c - a^2*c^2 + 2*b^2*c^2 + b*c^3) : :
X(65097) = 3 X[14399] - 2 X[16612], 3 X[14399] - X[55232]

X(65097) lies on these lines: {1, 647}, {6, 3700}, {8, 21719}, {10, 24960}, {37, 9404}, {42, 4477}, {81, 4467}, {239, 24622}, {314, 21437}, {425, 2501}, {521, 6591}, {522, 22383}, {523, 7252}, {525, 17498}, {612, 4524}, {648, 23999}, {649, 4083}, {650, 2605}, {652, 21347}, {661, 38469}, {663, 50519}, {770, 58888}, {850, 3187}, {940, 17069}, {1734, 2523}, {2295, 46381}, {2451, 7253}, {2522, 3900}, {3063, 6590}, {3064, 36054}, {3287, 4024}, {4155, 56242}, {4501, 57181}, {4879, 42664}, {4897, 18199}, {5256, 24782}, {5269, 57067}, {5271, 30476}, {5287, 25084}, {5311, 58286}, {6587, 39540}, {11679, 30864}, {14399, 16612}, {16751, 62801}, {16826, 25594}, {17094, 37543}, {17478, 46382}, {17926, 32320}, {20980, 48269}, {21007, 48276}, {21761, 21831}, {25258, 58820}, {39548, 50511}, {43060, 48283}, {45745, 48288}, {47704, 50522}, {47874, 57164}, {48277, 58773}, {50492, 62749}, {51643, 55208}

X(65097) = reflection of X(i) in X(j) for these {i,j}: {46383, 22383}, {55232, 16612}
X(65097) = isogonal conjugate of the isotomic conjugate of X(17899)
X(65097) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {87, 13219}, {7121, 39352}, {15373, 34186}, {32676, 21219}, {34071, 52364}, {61206, 41840}
X(65097) = X(21831)-cross conjugate of X(8062)
X(65097) = X(i)-isoconjugate of X(j) for these (i,j): {109, 7108}, {651, 7105}, {653, 7016}, {664, 7106}, {1942, 1981}, {2713, 8680}, {7107, 18026}
X(65097) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 7108}, {8062, 525}, {16573, 75}, {38991, 7105}, {39025, 7106}
X(65097) = crosspoint of X(1) and X(648)
X(65097) = crosssum of X(i) and X(j) for these (i,j): {1, 647}, {512, 23543}
X(65097) = trilinear pole of line {16573, 35236}
X(65097) = X(65097) = crossdifference of every pair of points on line {43, 46}
X(65097) = barycentric product X(i)*X(j) for these {i,j}: {1, 8062}, {6, 17899}, {75, 21761}, {86, 21831}, {92, 22382}, {513, 7283}, {514, 54316}, {521, 1940}, {522, 1935}, {648, 16573}, {650, 1943}, {652, 1947}, {693, 26885}, {1950, 4391}, {2797, 37142}, {3064, 7364}, {3900, 6359}, {4025, 7076}, {6332, 7120}
X(65097) = barycentric quotient X(i)/X(j) for these {i,j}: {650, 7108}, {663, 7105}, {1935, 664}, {1940, 18026}, {1943, 4554}, {1946, 7016}, {1947, 46404}, {1950, 651}, {2797, 44150}, {3063, 7106}, {6359, 4569}, {7076, 1897}, {7120, 653}, {7283, 668}, {8062, 75}, {16573, 525}, {17899, 76}, {21761, 1}, {21831, 10}, {22382, 63}, {26885, 100}, {35236, 9391}, {40888, 15418}, {44096, 23353}, {54316, 190}
X(65097) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1021, 647}, {8, 26080, 21719}, {14399, 55232, 16612}

X(65098) = SIGN-IMAGE OF X(856)

Barycentrics    a*(b - c)*(a^2 - b^2 - c^2)*(a^6 - 2*a^4*b^2 + a^2*b^4 - 3*a^4*b*c + 2*a^2*b^3*c + b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^2*b*c^3 - 2*b^3*c^3 + a^2*c^4 + b*c^5) : :
X(65098) = 3 X[14395] - 2 X[14838]

X(65098) lies on these lines: {63, 52613}, {448, 525}, {514, 36054}, {520, 3737}, {521, 46385}, {651, 39053}, {652, 905}, {4063, 8677}, {4367, 9391}, {4705, 9253}, {5706, 14308}, {8057, 44409}, {14395, 14838}, {17925, 32320}, {39470, 57167}

X(65098) = isogonal conjugate of the polar conjugate of X(23683)
X(65098) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3362, 13219}, {7049, 21294}
X(65098) = X(16595)-Dao conjugate of X(92)
X(65098) = crosspoint of X(63) and X(648)
X(65098) = crosssum of X(i) and X(j) for these (i,j): {19, 647}, {650, 1841}
X(65098) = crossdifference of every pair of points on line {33, 11435}
X(65098) = barycentric product X(i)*X(j) for these {i,j}: {3, 23683}, {326, 54238}, {648, 16595}, {26888, 35518}
X(65098) = barycentric quotient X(i)/X(j) for these {i,j}: {16595, 525}, {23683, 264}, {26888, 108}, {54238, 158}
X(65098) = {X(63),X(57213)}-harmonic conjugate of X(52613)

X(65099) = SIGN-IMAGE OF X(857)

Barycentrics    (b - c)*(-a^4 + b^4 - a^2*b*c + b^3*c + b*c^3 + c^4) : :
X(65099) = X[7253] - 3 X[53352], 2 X[44409] - 3 X[53352], 3 X[4453] - 2 X[23800], 4 X[676] - 3 X[48173], 3 X[48173] - 2 X[57158], X[4064] - 3 X[11125], 2 X[4064] - 3 X[57066], 2 X[8062] - 3 X[11125], 4 X[8062] - 3 X[57066], 2 X[4397] - 3 X[23678], 4 X[21186] - 3 X[23678], 3 X[48243] - 2 X[50333], 3 X[47797] - 2 X[50330]

X(65099) lies on these lines: {1, 57081}, {2, 52355}, {75, 3267}, {145, 56092}, {447, 525}, {513, 3801}, {520, 3868}, {521, 43923}, {522, 693}, {523, 1325}, {648, 24000}, {656, 21187}, {676, 48173}, {905, 20294}, {1459, 3904}, {1476, 43737}, {2605, 6370}, {3810, 43924}, {3870, 57198}, {4064, 8062}, {4086, 21180}, {4142, 17420}, {4391, 7649}, {4397, 17899}, {4707, 6003}, {4811, 21185}, {4985, 21179}, {5214, 23879}, {6332, 21172}, {9013, 21121}, {10015, 20293}, {15413, 21178}, {15417, 57214}, {16612, 57197}, {17418, 23877}, {17498, 33294}, {18160, 21205}, {20517, 21189}, {21173, 23887}, {21437, 23557}, {28161, 47714}, {28423, 48243}, {41800, 53342}, {44550, 64917}, {47797, 50330}, {53522, 57091}

X(65099) = reflection of X(i) in X(j) for these {i,j}: {656, 21187}, {3904, 1459}, {4017, 4458}, {4064, 8062}, {4086, 21180}, {4391, 7649}, {4397, 21186}, {4811, 21185}, {4985, 21179}, {6332, 21172}, {7253, 44409}, {17420, 4142}, {20293, 10015}, {20294, 905}, {21189, 20517}, {53342, 41800}, {57066, 11125}, {57091, 53522}, {57158, 676}
X(65099) = anticomplement of X(52355)
X(65099) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {28, 33650}, {34, 3448}, {57, 13219}, {58, 34188}, {108, 1330}, {109, 52364}, {110, 52366}, {112, 329}, {162, 3436}, {163, 56943}, {278, 21294}, {603, 34186}, {604, 39352}, {608, 21221}, {648, 21286}, {653, 21287}, {1395, 148}, {1396, 150}, {1414, 1370}, {1415, 3151}, {1461, 2897}, {1474, 37781}, {2203, 39351}, {4565, 4329}, {32674, 2895}, {32676, 144}, {32713, 5942}, {32714, 2893}, {51651, 14721}, {61206, 3177}
X(65099) = X(i)-isoconjugate of X(j) for these (i,j): {100, 8615}, {692, 15314}
X(65099) = X(i)-Dao conjugate of X(j) for these (i,j): {1086, 15314}, {1104, 61221}, {8054, 8615}, {16612, 525}, {34846, 1}, {46878, 61226}
X(65099) = crosspoint of X(i) and X(j) for these (i,j): {75, 648}, {99, 59759}, {18026, 30710}
X(65099) = crosssum of X(i) and X(j) for these (i,j): {31, 647}, {1946, 2300}
X(65099) = trilinear pole of line {34846, 57606}
X(65099) = crossdifference of every pair of points on line {41, 2092}
X(65099) = barycentric product X(i)*X(j) for these {i,j}: {7, 57197}, {75, 16612}, {286, 57186}, {304, 54247}, {513, 2064}, {514, 7270}, {648, 34846}, {693, 5279}, {3261, 5285}, {4296, 4391}
X(65099) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 15314}, {649, 8615}, {2064, 668}, {2881, 39690}, {4296, 651}, {5279, 100}, {5285, 101}, {7270, 190}, {16612, 1}, {34846, 525}, {37202, 2867}, {48890, 14543}, {54247, 19}, {57186, 72}, {57197, 8}
X(65099) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {676, 57158, 48173}, {4064, 8062, 57066}, {4064, 11125, 8062}, {4397, 21186, 23678}, {7253, 53352, 44409}

X(65100) = SIGN-IMAGE OF X(860)

Barycentrics    (b - c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-a^2 + b^2 + b*c + c^2) : :
X(65100) = 3 X[14400] - X[57243]

X(65100) lies on these lines: {4, 28473}, {19, 1019}, {28, 4367}, {92, 14618}, {278, 7178}, {423, 2501}, {514, 3064}, {523, 2074}, {525, 17926}, {905, 57196}, {1848, 4129}, {2906, 50574}, {3904, 46110}, {4160, 54247}, {4467, 44427}, {4560, 57065}, {5142, 21051}, {6591, 47660}, {7265, 35057}, {7501, 44811}, {7649, 28147}, {8045, 55206}, {14077, 18344}, {14331, 60494}, {14400, 57243}, {16230, 48288}, {23882, 57043}, {24006, 50449}, {28537, 39536}, {30384, 44426}, {31902, 59629}, {45746, 57094}, {47235, 47782}, {50346, 57200}, {52584, 62857}

X(65100) = reflection of X(i) in X(j) for these {i,j}: {17924, 3064}, {60494, 14331}
X(65100) = polar conjugate of X(6742)
X(65100) = polar conjugate of the isotomic conjugate of X(4467)
X(65100) = polar conjugate of the isogonal conjugate of X(2605)
X(65100) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {90, 13219}, {7040, 21294}, {36082, 2897}
X(65100) = X(2605)-cross conjugate of X(4467)
X(65100) = X(i)-isoconjugate of X(j) for these (i,j): {48, 6742}, {71, 13486}, {79, 906}, {101, 7100}, {163, 52388}, {184, 15455}, {212, 38340}, {219, 26700}, {265, 1983}, {651, 8606}, {692, 52381}, {758, 32662}, {1331, 2160}, {1332, 6186}, {1789, 4559}, {1790, 56193}, {1813, 7073}, {2245, 36061}, {3724, 60053}, {3927, 58954}, {4242, 50433}, {4574, 52375}, {4575, 8818}, {4585, 52153}, {4587, 52372}, {5546, 52390}, {6757, 32661}, {7110, 36059}, {30690, 32656}, {32660, 52344}, {34922, 36054}, {56839, 59011}, {57691, 61220}
X(65100) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 52388}, {136, 8818}, {1015, 7100}, {1086, 52381}, {1249, 6742}, {3700, 52355}, {5190, 79}, {5521, 2160}, {8287, 63}, {14838, 525}, {16221, 2245}, {20620, 7110}, {20982, 23154}, {38991, 8606}, {40622, 63171}, {40837, 38340}, {55042, 219}, {55067, 1789}, {62605, 15455}
X(65100) = crosspoint of X(92) and X(648)
X(65100) = crosssum of X(i) and X(j) for these (i,j): {48, 647}, {520, 53847}, {652, 22054}, {3049, 23196}
X(65100) = trilinear pole of line {8287, 22094}
X(65100) = crossdifference of every pair of points on line {212, 8606}
X(65100) = barycentric product X(i)*X(j) for these {i,j}: {4, 4467}, {19, 18160}, {27, 7265}, {35, 46107}, {75, 54244}, {92, 14838}, {162, 17886}, {264, 2605}, {273, 35057}, {278, 57066}, {286, 57099}, {319, 7649}, {331, 9404}, {445, 56320}, {514, 52412}, {522, 7282}, {648, 8287}, {693, 6198}, {811, 2611}, {1442, 44426}, {1825, 18155}, {1826, 16755}, {2003, 46110}, {2501, 34016}, {3064, 17095}, {3219, 17924}, {3969, 17925}, {4077, 11107}, {6331, 20982}, {6335, 7202}, {6528, 22094}, {6591, 33939}, {14618, 40214}, {14975, 40495}, {16577, 57215}, {18026, 53524}, {18344, 52421}, {21824, 55231}, {23226, 57806}, {24006, 56934}, {24624, 44427}, {44129, 55210}, {44428, 63778}, {52414, 60074}
X(65100) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 6742}, {28, 13486}, {34, 26700}, {35, 1331}, {92, 15455}, {278, 38340}, {319, 4561}, {513, 7100}, {514, 52381}, {523, 52388}, {663, 8606}, {759, 36061}, {1399, 36059}, {1442, 6516}, {1824, 56193}, {1825, 4551}, {1844, 61220}, {2003, 1813}, {2174, 906}, {2501, 8818}, {2594, 23067}, {2605, 3}, {2611, 656}, {3064, 7110}, {3219, 1332}, {3737, 1789}, {3969, 52609}, {4017, 52390}, {4420, 4571}, {4467, 69}, {6198, 100}, {6591, 2160}, {6741, 52355}, {7178, 63171}, {7202, 905}, {7265, 306}, {7282, 664}, {7649, 79}, {8287, 525}, {9404, 219}, {11107, 643}, {14775, 57710}, {14838, 63}, {14975, 692}, {16755, 17206}, {17104, 4575}, {17886, 14208}, {17924, 30690}, {17925, 52393}, {18160, 304}, {18344, 7073}, {20982, 647}, {21054, 4064}, {21141, 4466}, {21824, 55232}, {22094, 520}, {23226, 255}, {24006, 6757}, {24624, 60053}, {34016, 4563}, {34079, 32662}, {35057, 78}, {35235, 6370}, {36127, 34922}, {40214, 4558}, {40570, 59011}, {41502, 5546}, {43923, 52372}, {44095, 61197}, {44129, 55209}, {44426, 52344}, {44427, 3936}, {44428, 63642}, {46107, 20565}, {46468, 14544}, {47230, 2245}, {50657, 23084}, {52405, 4587}, {52412, 190}, {52414, 4585}, {53524, 521}, {53542, 1459}, {53554, 1818}, {54244, 1}, {55210, 71}, {56320, 57860}, {56934, 4592}, {57066, 345}, {57099, 72}, {57200, 52375}, {58304, 3690}, {59837, 50462}, {62172, 6739}
X(65100) = {X(92),X(57215)}-harmonic conjugate of X(14618)

X(65101) = SIGN-IMAGE OF X(1237)

Barycentrics    b^2*(b - c)*c^2*(-a^2 + b*c) : :

X(65101) lies on these lines: {75, 2254}, {76, 3762}, {274, 3960}, {325, 523}, {334, 60577}, {350, 3716}, {514, 40495}, {659, 14296}, {661, 786}, {790, 21763}, {812, 46387}, {1086, 16727}, {1237, 18003}, {1978, 3807}, {3766, 4010}, {3777, 23807}, {3835, 21099}, {3887, 17143}, {4041, 57110}, {4374, 21146}, {4406, 48108}, {4408, 48090}, {4411, 48098}, {4441, 53343}, {4444, 18895}, {4458, 20518}, {4804, 20954}, {4895, 17144}, {4978, 52619}, {6376, 14430}, {7199, 18071}, {7212, 27951}, {14413, 31997}, {16992, 53308}, {17494, 27015}, {18031, 30997}, {18081, 48131}, {18277, 46390}, {20446, 20950}, {20907, 24720}, {20909, 50454}, {21222, 34284}, {21433, 36848}, {22384, 33295}, {25380, 60706}, {26824, 26855}, {46403, 53370}, {60719, 64862}

X(65101) = isotomic conjugate of X(813)
X(65101) = isotomic conjugate of the isogonal conjugate of X(812)
X(65101) = X(i)-Ceva conjugate of X(j) for these (i,j): {4602, 64222}, {6063, 64644}, {18036, 34387}, {27853, 1921}
X(65101) = X(20505)-cross conjugate of X(514)
X(65101) = X(i)-isoconjugate of X(j) for these (i,j): {6, 34067}, {31, 813}, {32, 660}, {100, 1922}, {101, 1911}, {109, 51858}, {190, 14598}, {291, 32739}, {292, 692}, {560, 4562}, {651, 18265}, {668, 18897}, {875, 1252}, {876, 23990}, {919, 40730}, {1110, 3572}, {1415, 7077}, {1501, 4583}, {1918, 4584}, {1919, 5378}, {1927, 18047}, {1978, 18893}, {2196, 8750}, {2205, 4589}, {2295, 17938}, {3051, 36081}, {3252, 32666}, {3570, 18267}, {3573, 51856}, {3862, 34069}, {4557, 18268}, {4579, 9468}, {7109, 36066}, {18900, 37207}, {30664, 40728}, {46288, 52922}, {51866, 54325}
X(65101) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 813}, {9, 34067}, {11, 51858}, {514, 3572}, {661, 875}, {812, 8632}, {1015, 1911}, {1086, 292}, {1146, 7077}, {1966, 3573}, {2238, 54325}, {3716, 46388}, {3912, 2284}, {6374, 4562}, {6376, 660}, {6377, 51973}, {6651, 101}, {8054, 1922}, {9296, 5378}, {16591, 4559}, {18277, 190}, {19557, 692}, {26932, 2196}, {27846, 21760}, {27918, 672}, {34021, 4584}, {35068, 4557}, {35078, 20964}, {35094, 3252}, {35119, 6}, {36901, 43534}, {38978, 7109}, {38980, 40730}, {38991, 18265}, {39028, 100}, {39029, 32739}, {39044, 4579}, {39786, 3747}, {40618, 295}, {40619, 291}, {40620, 741}, {40623, 31}, {40624, 4876}, {40625, 2311}, {55053, 14598}, {61065, 3862}, {62552, 649}, {62553, 1018}, {62558, 667}, {62610, 18047}, {64644, 38}
X(65101) = cevapoint of X(514) and X(20518)
X(65101) = crosspoint of X(i) and X(j) for these (i,j): {1921, 27853}, {1978, 18031}, {3112, 51560}
X(65101) = crosssum of X(1919) and X(9454)
X(65101) = crossdifference of every pair of points on line {32, 1922}
X(65101) = barycentric product X(i)*X(j) for these {i,j}: {75, 3766}, {76, 812}, {238, 40495}, {239, 3261}, {310, 4010}, {334, 27855}, {350, 693}, {513, 18891}, {514, 1921}, {522, 18033}, {561, 659}, {649, 44169}, {667, 44171}, {740, 52619}, {824, 63242}, {850, 33295}, {871, 30665}, {874, 1111}, {876, 64222}, {1086, 27853}, {1447, 35519}, {1502, 8632}, {1577, 30940}, {1978, 27918}, {3267, 31905}, {3570, 23989}, {3596, 43041}, {3676, 4087}, {3685, 52621}, {3716, 6063}, {3808, 7034}, {3948, 7199}, {3975, 24002}, {4025, 40717}, {4107, 44187}, {4124, 4572}, {4148, 57792}, {4155, 57992}, {4375, 18895}, {4391, 10030}, {4435, 20567}, {4444, 56660}, {4448, 57995}, {4602, 39786}, {5009, 44173}, {6385, 21832}, {6386, 27846}, {7018, 14296}, {7192, 35544}, {7212, 28660}, {14295, 32010}, {18022, 22384}, {18031, 62552}, {24459, 44129}, {27801, 50456}, {27951, 40845}, {33931, 63222}, {34856, 52617}, {40016, 46387}, {51560, 64644}, {52622, 62785}, {53556, 57796}, {62415, 63230}
X(65101) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 34067}, {2, 813}, {75, 660}, {76, 4562}, {238, 692}, {239, 101}, {242, 8750}, {244, 875}, {274, 4584}, {310, 4589}, {350, 100}, {513, 1911}, {514, 292}, {522, 7077}, {561, 4583}, {649, 1922}, {650, 51858}, {659, 31}, {663, 18265}, {667, 14598}, {668, 5378}, {693, 291}, {740, 4557}, {804, 20964}, {812, 6}, {824, 3862}, {850, 43534}, {870, 30664}, {871, 41072}, {873, 36066}, {874, 765}, {875, 18267}, {905, 2196}, {918, 3252}, {1019, 18268}, {1086, 3572}, {1111, 876}, {1178, 17938}, {1429, 1415}, {1447, 109}, {1914, 32739}, {1919, 18897}, {1921, 190}, {1930, 52922}, {1966, 4579}, {1980, 18893}, {2254, 40730}, {3112, 36081}, {3261, 335}, {3570, 1252}, {3572, 51856}, {3573, 1110}, {3596, 36801}, {3685, 3939}, {3716, 55}, {3766, 1}, {3808, 7032}, {3835, 51973}, {3837, 40155}, {3948, 1018}, {3975, 644}, {3978, 18047}, {4010, 42}, {4025, 295}, {4087, 3699}, {4107, 172}, {4124, 663}, {4148, 220}, {4155, 872}, {4164, 7122}, {4374, 18787}, {4375, 1914}, {4391, 4876}, {4432, 23344}, {4435, 41}, {4444, 52205}, {4448, 902}, {4455, 1918}, {4486, 2276}, {4508, 2242}, {4560, 2311}, {4800, 2177}, {4810, 61358}, {4974, 35327}, {5009, 1576}, {6385, 4639}, {6654, 919}, {7033, 8684}, {7192, 741}, {7193, 32656}, {7199, 37128}, {7212, 1400}, {8299, 54325}, {8632, 32}, {10030, 651}, {14295, 1215}, {14296, 171}, {14433, 3230}, {16609, 4559}, {17755, 2284}, {18033, 664}, {18155, 56154}, {18891, 668}, {20518, 9470}, {20769, 906}, {20906, 41531}, {20908, 52656}, {21207, 35352}, {21832, 213}, {22384, 184}, {23597, 40746}, {23989, 4444}, {24193, 8027}, {24284, 22061}, {24459, 71}, {27846, 667}, {27853, 1016}, {27854, 21788}, {27855, 238}, {27912, 41405}, {27918, 649}, {27922, 901}, {27929, 17735}, {27950, 1983}, {27951, 3509}, {30639, 40790}, {30665, 869}, {30870, 63228}, {30940, 662}, {31905, 112}, {32010, 805}, {33295, 110}, {34387, 60577}, {34856, 32713}, {35119, 8632}, {35519, 4518}, {35544, 3952}, {38348, 18266}, {39044, 3573}, {39775, 2283}, {39786, 798}, {39914, 34071}, {40495, 334}, {40717, 1897}, {40725, 2702}, {42767, 51377}, {43041, 56}, {44169, 1978}, {44171, 6386}, {46387, 3051}, {46390, 7109}, {47070, 2382}, {50456, 1333}, {51381, 2427}, {51435, 2426}, {52619, 18827}, {52621, 7233}, {53556, 228}, {53580, 3052}, {56660, 3570}, {58864, 18900}, {62415, 3864}, {62552, 672}, {62558, 21760}, {62625, 28841}, {62635, 51866}, {62637, 39420}, {62638, 63881}, {62785, 1461}, {63222, 985}, {63230, 1492}, {63237, 825}, {63242, 4586}, {64222, 874}, {64223, 1026}, {64644, 2254}
X(65101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 20906, 1491}, {14296, 27855, 659}

X(65102) = SIGN-IMAGE OF X(1410)

Barycentrics    a^3*(a - b - c)^2*(b - c)*(a^2 - b^2 - c^2) : :

X(65102) lies on these lines: {6, 6129}, {48, 23224}, {219, 521}, {220, 4130}, {513, 57237}, {520, 647}, {650, 15313}, {657, 663}, {798, 9245}, {905, 23146}, {1919, 8642}, {2287, 4397}, {2509, 2911}, {4017, 20980}, {4501, 42462}, {6591, 14298}, {6608, 46392}, {20818, 23187}, {22091, 22443}, {23090, 57055}, {24027, 36039}, {57134, 58340}

X(65102) = isogonal conjugate of X(13149)
X(65102) = isogonal conjugate of the isotomic conjugate of X(57055)
X(65102) = isotomic conjugate of the polar conjugate of X(8641)
X(65102) = isogonal conjugate of the polar conjugate of X(3900)
X(65102) = polar conjugate of the isotomic conjugate of X(58340)
X(65102) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 47432}, {48, 2638}, {101, 228}, {219, 3270}, {652, 1946}, {692, 1253}, {906, 212}, {1783, 55}, {1813, 22079}, {3900, 8641}, {7072, 3022}, {23090, 57108}, {57055, 58340}
X(65102) = X(39687)-cross conjugate of X(52425)
X(65102) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13149}, {2, 36118}, {4, 658}, {7, 653}, {19, 4569}, {25, 46406}, {27, 4566}, {33, 36838}, {34, 4554}, {56, 46404}, {57, 18026}, {75, 32714}, {77, 54240}, {85, 108}, {86, 52607}, {92, 934}, {100, 1847}, {107, 56382}, {109, 331}, {162, 1446}, {190, 1119}, {196, 53642}, {222, 52938}, {225, 4573}, {264, 1461}, {269, 6335}, {273, 651}, {278, 664}, {279, 1897}, {281, 4626}, {286, 1020}, {318, 4617}, {342, 37141}, {348, 36127}, {514, 55346}, {607, 52937}, {608, 4572}, {648, 3668}, {668, 1435}, {693, 7128}, {799, 1426}, {811, 1427}, {823, 1439}, {905, 24032}, {927, 5236}, {1042, 6331}, {1088, 1783}, {1254, 55231}, {1262, 46107}, {1275, 7649}, {1398, 1978}, {1410, 57973}, {1414, 40149}, {1415, 57787}, {1434, 61178}, {1459, 57538}, {1824, 4635}, {1826, 4616}, {1876, 34085}, {1880, 4625}, {2973, 4619}, {3064, 59457}, {3676, 46102}, {4025, 23984}, {4565, 57809}, {4637, 41013}, {5249, 58993}, {6063, 32674}, {6356, 52919}, {6528, 52373}, {6614, 7017}, {7012, 24002}, {7045, 17924}, {7103, 37215}, {7115, 52621}, {7143, 55233}, {7282, 38340}, {7339, 46110}, {8059, 40701}, {8750, 57792}, {15413, 24033}, {15466, 36079}, {15742, 58817}, {20618, 52921}, {23062, 56183}, {23710, 60487}, {23973, 52781}, {24015, 36122}, {26934, 54948}, {36908, 53639}, {37139, 38461}, {41353, 54235}, {44129, 53321}
X(65102) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 46404}, {3, 13149}, {6, 4569}, {11, 331}, {125, 1446}, {206, 32714}, {521, 15413}, {656, 3261}, {1146, 57787}, {2968, 1969}, {3239, 40495}, {3270, 26540}, {5452, 18026}, {6505, 46406}, {6600, 6335}, {6608, 46110}, {6741, 52575}, {7358, 76}, {8054, 1847}, {11517, 4554}, {14714, 92}, {17115, 17924}, {17423, 1427}, {22391, 934}, {26932, 57792}, {32664, 36118}, {34467, 279}, {35072, 6063}, {35508, 264}, {36033, 658}, {38966, 2052}, {38983, 85}, {38985, 56382}, {38991, 273}, {38996, 1426}, {39006, 1088}, {39025, 278}, {40600, 52607}, {40608, 40149}, {40626, 20567}, {40628, 52621}, {46095, 24015}, {55044, 40701}, {55053, 1119}, {55064, 57809}, {55066, 3668}, {55068, 44129}, {62647, 4572}
X(65102) = crosspoint of X(i) and X(j) for these (i,j): {6, 32652}, {48, 692}, {55, 1783}, {101, 2328}, {212, 906}, {651, 37741}, {652, 57108}, {1813, 47487}, {3900, 57055}, {23090, 57134}
X(65102) = crosssum of X(i) and X(j) for these (i,j): {2, 17896}, {7, 905}, {92, 693}, {273, 17924}, {279, 24002}, {514, 3668}, {523, 53422}, {650, 1836}, {653, 36118}, {934, 32714}, {1851, 6591}, {17094, 55010}
X(65102) = crossdifference of every pair of points on line {4, 7}
X(65102) = barycentric product X(i)*X(j) for these {i,j}: {1, 57108}, {3, 3900}, {4, 58340}, {6, 57055}, {8, 1946}, {9, 652}, {10, 57134}, {19, 57057}, {32, 15416}, {33, 57241}, {37, 23090}, {41, 6332}, {42, 57081}, {48, 3239}, {55, 521}, {63, 657}, {65, 58338}, {69, 8641}, {71, 1021}, {72, 21789}, {73, 58329}, {77, 4105}, {78, 663}, {100, 3270}, {101, 34591}, {184, 4397}, {200, 1459}, {210, 23189}, {212, 522}, {213, 15411}, {219, 650}, {220, 905}, {222, 4130}, {228, 7253}, {268, 14298}, {281, 36054}, {282, 10397}, {283, 4041}, {284, 8611}, {332, 63461}, {345, 3063}, {346, 22383}, {348, 57180}, {512, 1792}, {513, 1260}, {514, 1802}, {520, 4183}, {603, 4163}, {644, 7117}, {647, 2287}, {649, 3692}, {656, 2328}, {661, 2327}, {667, 1265}, {692, 2968}, {810, 1043}, {822, 2322}, {895, 58331}, {906, 1146}, {1098, 55230}, {1176, 58335}, {1253, 4025}, {1259, 18344}, {1331, 2310}, {1332, 14936}, {1364, 56183}, {1444, 4524}, {1783, 35072}, {1790, 4171}, {1793, 53562}, {1797, 14427}, {1807, 53285}, {1809, 53549}, {1812, 3709}, {1813, 3119}, {1814, 52614}, {1815, 46392}, {1897, 2638}, {1919, 52406}, {2155, 57045}, {2170, 4587}, {2175, 35518}, {2188, 8058}, {2192, 57101}, {2193, 3700}, {2194, 52355}, {2196, 4148}, {2212, 52616}, {2289, 3064}, {2316, 14418}, {2318, 3737}, {2332, 24018}, {2340, 23696}, {3022, 6516}, {3271, 4571}, {3694, 7252}, {3937, 4578}, {3939, 7004}, {3990, 17926}, {4081, 36059}, {4091, 7079}, {4131, 7071}, {4391, 52425}, {4477, 7015}, {4515, 7254}, {4528, 36058}, {4529, 7116}, {4558, 36197}, {4560, 52370}, {4575, 52335}, {4845, 14414}, {5546, 53560}, {6056, 44426}, {6335, 39687}, {6514, 55206}, {6607, 40443}, {6608, 47487}, {7046, 23224}, {7054, 55232}, {7072, 59973}, {7074, 61040}, {7118, 57245}, {7358, 32652}, {7367, 64885}, {8606, 35057}, {8750, 24031}, {9247, 52622}, {13138, 47432}, {14380, 58337}, {14392, 60047}, {14395, 15627}, {14827, 15413}, {15629, 46391}, {20752, 28132}, {22079, 62725}, {24026, 32656}, {28071, 53550}, {30681, 57181}, {34259, 58332}, {36039, 57292}, {44040, 57103}, {52222, 58325}, {52307, 52663}
X(65102) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 4569}, {6, 13149}, {9, 46404}, {31, 36118}, {32, 32714}, {33, 52938}, {41, 653}, {48, 658}, {55, 18026}, {63, 46406}, {77, 52937}, {78, 4572}, {184, 934}, {212, 664}, {213, 52607}, {219, 4554}, {220, 6335}, {222, 36838}, {228, 4566}, {283, 4625}, {332, 55213}, {521, 6063}, {522, 57787}, {603, 4626}, {607, 54240}, {647, 1446}, {649, 1847}, {650, 331}, {652, 85}, {657, 92}, {663, 273}, {667, 1119}, {669, 1426}, {692, 55346}, {810, 3668}, {822, 56382}, {905, 57792}, {906, 1275}, {1021, 44129}, {1043, 57968}, {1098, 55229}, {1253, 1897}, {1260, 668}, {1265, 6386}, {1437, 4616}, {1459, 1088}, {1783, 57538}, {1790, 4635}, {1792, 670}, {1802, 190}, {1919, 1435}, {1946, 7}, {1980, 1398}, {2175, 108}, {2188, 53642}, {2193, 4573}, {2200, 1020}, {2212, 36127}, {2287, 6331}, {2310, 46107}, {2322, 57973}, {2327, 799}, {2328, 811}, {2332, 823}, {2488, 53237}, {2638, 4025}, {2968, 40495}, {3022, 44426}, {3049, 1427}, {3063, 278}, {3119, 46110}, {3239, 1969}, {3270, 693}, {3692, 1978}, {3700, 52575}, {3709, 40149}, {3900, 264}, {3937, 59941}, {4041, 57809}, {4105, 318}, {4130, 7017}, {4183, 6528}, {4397, 18022}, {4524, 41013}, {6056, 6516}, {6139, 38461}, {6332, 20567}, {6514, 55205}, {7004, 52621}, {7054, 55231}, {7117, 24002}, {7253, 57796}, {8611, 349}, {8638, 1876}, {8641, 4}, {8646, 7103}, {8750, 24032}, {9247, 1461}, {9447, 32674}, {10397, 40702}, {14298, 40701}, {14427, 46109}, {14827, 1783}, {14936, 17924}, {15411, 6385}, {15416, 1502}, {20818, 62532}, {21789, 286}, {22079, 35312}, {22096, 43932}, {22383, 279}, {23090, 274}, {23189, 57785}, {23224, 7056}, {23225, 34855}, {32656, 7045}, {32739, 7128}, {34591, 3261}, {35072, 15413}, {35518, 41283}, {36054, 348}, {36059, 59457}, {36197, 14618}, {39201, 1439}, {39687, 905}, {46388, 5236}, {47432, 17896}, {52370, 4552}, {52411, 4617}, {52425, 651}, {52614, 46108}, {56305, 54948}, {57055, 76}, {57057, 304}, {57081, 310}, {57108, 75}, {57134, 86}, {57180, 281}, {57241, 7182}, {58310, 1410}, {58329, 44130}, {58331, 44146}, {58335, 1235}, {58338, 314}, {58340, 69}, {61050, 18344}, {62257, 36059}, {63461, 225}
X(65102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {652, 10397, 647}, {652, 36054, 22383}, {657, 663, 33525}, {657, 17412, 10581}, {3063, 57180, 657}

X(65103) = SIGN-IMAGE OF X(1426)

Barycentrics    a*(a - b - c)^2*(b - c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) : :

X(65103) lies on these lines: {19, 513}, {92, 20906}, {230, 231}, {281, 28132}, {607, 3063}, {608, 20980}, {652, 50338}, {657, 4041}, {905, 57196}, {1783, 7012}, {1824, 4079}, {1826, 16228}, {1848, 47760}, {1973, 48327}, {2522, 14331}, {4105, 4171}, {4397, 17926}, {7003, 61040}, {7297, 46389}, {7719, 21390}, {8735, 52946}, {14013, 17212}, {14298, 55232}, {17412, 58313}, {17442, 48332}, {17924, 47965}, {21127, 43923}, {39521, 52413}, {40117, 59058}, {40937, 59973}

X(65103) = polar conjugate of X(4569)
X(65103) = complement of the isotomic conjugate of X(46964)
X(65103) = polar conjugate of the isotomic conjugate of X(3900)
X(65103) = polar conjugate of the isogonal conjugate of X(8641)
X(65103) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 38966}, {46964, 2887}
X(65103) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 38966}, {19, 2310}, {281, 42069}, {459, 38388}, {653, 1827}, {1783, 33}, {1857, 3022}, {3064, 18344}, {6335, 1863}, {7003, 3270}, {13149, 4}, {40117, 25}, {56183, 7071}
X(65103) = X(i)-cross conjugate of X(j) for these (i,j): {3022, 1857}, {3709, 657}, {8641, 3900}, {14936, 607}
X(65103) = X(i)-isoconjugate of X(j) for these (i,j): {3, 658}, {7, 1813}, {48, 4569}, {57, 6516}, {63, 934}, {69, 1461}, {71, 4616}, {72, 4637}, {73, 4573}, {77, 651}, {78, 4617}, {85, 36059}, {86, 52610}, {99, 52373}, {100, 7177}, {101, 7056}, {108, 7183}, {109, 348}, {110, 56382}, {184, 46406}, {190, 7053}, {212, 36838}, {219, 4626}, {222, 664}, {228, 4635}, {255, 13149}, {269, 1332}, {278, 6517}, {279, 1331}, {307, 4565}, {326, 32714}, {345, 6614}, {394, 36118}, {479, 4587}, {603, 4554}, {652, 59457}, {653, 1804}, {662, 1439}, {668, 7099}, {738, 4571}, {799, 1410}, {905, 7045}, {906, 1088}, {1020, 1444}, {1042, 4563}, {1214, 1414}, {1262, 4025}, {1275, 1459}, {1402, 55205}, {1407, 4561}, {1409, 4625}, {1415, 7182}, {1425, 4610}, {1427, 4592}, {1434, 23067}, {1446, 4575}, {1565, 4619}, {1790, 4566}, {1803, 35312}, {1814, 41353}, {1815, 23973}, {3668, 4558}, {3676, 44717}, {3939, 30682}, {4091, 55346}, {4131, 7128}, {4556, 6356}, {4572, 52411}, {4636, 20618}, {6063, 32660}, {6332, 7339}, {7011, 53642}, {7013, 37141}, {7055, 32674}, {7125, 18026}, {7138, 55231}, {7289, 8269}, {7335, 46404}, {7340, 55234}, {15413, 24027}, {17094, 52378}, {17206, 53321}, {18607, 36048}, {23586, 57108}, {24013, 57055}, {24015, 36056}, {24016, 26006}, {26932, 59151}, {32656, 57792}, {34400, 57118}, {36049, 57479}, {36079, 37669}, {37136, 62402}, {37755, 52935}, {40443, 63203}, {47487, 61241}, {50559, 53622}, {52425, 52937}
X(65103) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 348}, {136, 1446}, {244, 56382}, {522, 15413}, {656, 30805}, {1015, 7056}, {1084, 1439}, {1146, 7182}, {1249, 4569}, {2968, 304}, {3162, 934}, {3900, 57055}, {5139, 1427}, {5190, 1088}, {5452, 6516}, {5514, 57479}, {5521, 279}, {6523, 13149}, {6600, 1332}, {6608, 6332}, {6741, 1231}, {7358, 3926}, {7952, 4554}, {8054, 7177}, {13999, 17078}, {14714, 63}, {14936, 17170}, {15259, 32714}, {15607, 18607}, {17115, 905}, {20620, 85}, {20622, 24015}, {23050, 190}, {24771, 4561}, {35072, 7055}, {35508, 69}, {36103, 658}, {38966, 2}, {38983, 7183}, {38986, 52373}, {38991, 77}, {38996, 1410}, {39025, 222}, {40600, 52610}, {40605, 55205}, {40608, 1214}, {40617, 30682}, {40624, 57918}, {40837, 36838}, {50930, 57455}, {53990, 17093}, {55053, 7053}, {55057, 23603}, {55064, 307}, {55068, 17206}, {62602, 52937}, {62605, 46406}
X(65103) = cevapoint of X(3709) and X(55206)
X(65103) = crosspoint of X(i) and X(j) for these (i,j): {2, 46964}, {4, 13149}, {33, 1783}, {281, 56183}, {40117, 57492}
X(65103) = crosssum of X(i) and X(j) for these (i,j): {63, 4131}, {77, 905}, {652, 22053}, {1459, 22088}, {1473, 22383}, {3668, 21188}, {36054, 53847}
X(65103) = trilinear pole of line {3022, 36197}
X(65103) = crossdifference of every pair of points on line {3, 77}
X(65103) = barycentric product X(i)*X(j) for these {i,j}: {4, 3900}, {8, 18344}, {9, 3064}, {11, 56183}, {19, 3239}, {25, 4397}, {27, 4171}, {29, 4041}, {33, 522}, {34, 4163}, {37, 17926}, {41, 46110}, {55, 44426}, {92, 657}, {100, 42069}, {108, 4081}, {158, 57108}, {162, 52335}, {200, 7649}, {220, 17924}, {225, 58329}, {264, 8641}, {273, 4105}, {278, 4130}, {281, 650}, {286, 4524}, {318, 663}, {331, 57180}, {333, 55206}, {346, 6591}, {393, 57055}, {513, 7046}, {514, 7079}, {521, 1857}, {523, 4183}, {607, 4391}, {644, 8735}, {648, 36197}, {649, 7101}, {653, 3119}, {661, 2322}, {692, 21666}, {693, 7071}, {1021, 1826}, {1093, 58340}, {1146, 1783}, {1172, 3700}, {1253, 46107}, {1334, 57215}, {1577, 2332}, {1792, 58757}, {1824, 7253}, {1827, 62725}, {1855, 62747}, {1897, 2310}, {1973, 52622}, {2207, 15416}, {2212, 35519}, {2287, 2501}, {2299, 4086}, {2326, 4024}, {2328, 24006}, {2969, 4578}, {3022, 18026}, {3063, 7017}, {3709, 31623}, {3737, 53008}, {4082, 57200}, {4092, 52914}, {4515, 17925}, {4516, 36797}, {4528, 36125}, {4705, 59482}, {5089, 28132}, {5423, 43923}, {5514, 40117}, {6059, 35518}, {6129, 57492}, {6335, 14936}, {6336, 14427}, {6520, 57057}, {7003, 14298}, {7007, 14302}, {7008, 8058}, {7012, 23615}, {7129, 57049}, {7367, 59935}, {8611, 8748}, {8750, 24026}, {13149, 35508}, {14775, 64171}, {17983, 58331}, {18808, 58337}, {21789, 41013}, {23893, 60431}, {23970, 32714}, {24010, 36118}, {30692, 62742}, {32085, 58335}, {33525, 40447}, {36421, 55232}, {38966, 46964}, {41339, 60583}, {41509, 57089}, {43933, 51380}, {44130, 63461}, {44428, 52371}, {46392, 52781}, {51361, 53152}, {51418, 53150}, {51762, 55145}, {52356, 52427}, {52409, 58313}, {52614, 54235}, {56146, 57092}
X(65103) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 4569}, {19, 658}, {25, 934}, {27, 4635}, {28, 4616}, {29, 4625}, {33, 664}, {34, 4626}, {41, 1813}, {55, 6516}, {92, 46406}, {108, 59457}, {200, 4561}, {212, 6517}, {213, 52610}, {220, 1332}, {273, 52937}, {278, 36838}, {281, 4554}, {318, 4572}, {333, 55205}, {393, 13149}, {480, 4571}, {512, 1439}, {513, 7056}, {521, 7055}, {522, 7182}, {607, 651}, {608, 4617}, {649, 7177}, {650, 348}, {652, 7183}, {657, 63}, {661, 56382}, {663, 77}, {667, 7053}, {669, 1410}, {798, 52373}, {1021, 17206}, {1043, 55202}, {1096, 36118}, {1146, 15413}, {1172, 4573}, {1253, 1331}, {1395, 6614}, {1474, 4637}, {1783, 1275}, {1824, 4566}, {1827, 35312}, {1857, 18026}, {1886, 24015}, {1919, 7099}, {1946, 1804}, {1973, 1461}, {2175, 36059}, {2204, 4565}, {2207, 32714}, {2212, 109}, {2287, 4563}, {2299, 1414}, {2310, 4025}, {2322, 799}, {2326, 4610}, {2328, 4592}, {2332, 662}, {2333, 1020}, {2356, 41353}, {2489, 1427}, {2501, 1446}, {2969, 59941}, {3022, 521}, {3063, 222}, {3064, 85}, {3119, 6332}, {3239, 304}, {3270, 4131}, {3669, 30682}, {3700, 1231}, {3709, 1214}, {3900, 69}, {4041, 307}, {4079, 37755}, {4081, 35518}, {4105, 78}, {4130, 345}, {4163, 3718}, {4171, 306}, {4183, 99}, {4391, 57918}, {4397, 305}, {4515, 52609}, {4516, 17094}, {4524, 72}, {4705, 6356}, {6059, 108}, {6129, 57479}, {6591, 279}, {6602, 4587}, {7008, 53642}, {7046, 668}, {7071, 100}, {7079, 190}, {7101, 1978}, {7154, 37141}, {7649, 1088}, {8611, 52565}, {8641, 3}, {8735, 24002}, {8750, 7045}, {9447, 32660}, {13149, 57581}, {14427, 3977}, {14827, 906}, {14936, 905}, {17115, 17170}, {17924, 57792}, {17926, 274}, {18344, 7}, {21666, 40495}, {21789, 1444}, {23615, 17880}, {23970, 15416}, {24012, 57108}, {32714, 23586}, {33525, 18607}, {34591, 30805}, {35508, 57055}, {36118, 24011}, {36197, 525}, {36421, 55231}, {40982, 62754}, {42067, 43932}, {42069, 693}, {43923, 479}, {44130, 55213}, {44426, 6063}, {46110, 20567}, {46392, 26006}, {50487, 1425}, {52335, 14208}, {52614, 25083}, {52622, 40364}, {52914, 7340}, {53549, 62402}, {55206, 226}, {56183, 4998}, {57055, 3926}, {57057, 1102}, {57108, 326}, {57180, 219}, {57185, 20618}, {58313, 1443}, {58329, 332}, {58331, 6390}, {58335, 3933}, {58340, 3964}, {58838, 65017}, {58840, 65016}, {59482, 4623}, {61050, 1946}, {63461, 73}
X(65103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3064, 6591}, {2501, 57094, 6591}

X(65104) = SIGN-IMAGE OF X(1825)

Barycentrics    a*(a - b - c)*(b - c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + b*c - c^2)*(a^2 - b^2 + c^2) : :

X(65104) lies on these lines: {4, 38324}, {11, 5190}, {19, 1635}, {25, 53287}, {101, 108}, {105, 9085}, {112, 53927}, {230, 231}, {278, 43050}, {608, 21786}, {652, 16612}, {654, 53527}, {661, 2616}, {663, 57092}, {667, 54247}, {770, 3063}, {812, 1848}, {909, 913}, {1435, 53544}, {1769, 46391}, {2600, 3738}, {2820, 4219}, {3737, 57212}, {5513, 20621}, {6197, 38327}, {11471, 38329}, {14837, 57230}, {14838, 17924}, {17420, 57200}, {21758, 46384}, {35348, 36122}, {44428, 53046}, {48297, 54244}, {48387, 58318}, {53285, 58313}

X(65104) = polar conjugate of X(35174)
X(65104) = polar conjugate of the isotomic conjugate of X(3738)
X(65104) = polar conjugate of the isogonal conjugate of X(8648)
X(65104) = X(31)-complementary conjugate of X(13999)
X(65104) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 13999}, {653, 1845}, {4242, 52427}, {36119, 2310}, {60584, 513}
X(65104) = X(i)-cross conjugate of X(j) for these (i,j): {8648, 3738}, {21828, 654}
X(65104) = X(i)-isoconjugate of X(j) for these (i,j): {3, 655}, {48, 35174}, {63, 2222}, {69, 32675}, {73, 47318}, {80, 1813}, {101, 52392}, {109, 52351}, {184, 46405}, {201, 37140}, {222, 51562}, {343, 36078}, {603, 36804}, {651, 1807}, {662, 52391}, {664, 52431}, {905, 52377}, {906, 18815}, {1020, 1793}, {1331, 2006}, {1332, 1411}, {1789, 63202}, {2161, 6516}, {2169, 62735}, {2594, 60053}, {4552, 57736}, {4558, 52383}, {4559, 57985}, {4575, 60091}, {6517, 64835}, {6740, 52610}, {16577, 36061}, {18359, 36059}, {20566, 32660}, {22342, 32680}, {22350, 53811}, {23067, 24624}, {26942, 36069}, {32662, 40999}, {32671, 57807}
X(65104) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 52351}, {136, 60091}, {860, 42718}, {1015, 52392}, {1084, 52391}, {1249, 35174}, {3162, 2222}, {5190, 18815}, {5521, 2006}, {7952, 36804}, {13999, 2}, {14363, 62735}, {16221, 16577}, {20620, 18359}, {35128, 69}, {35204, 1332}, {36103, 655}, {38966, 36910}, {38982, 26942}, {38984, 63}, {38991, 1807}, {39025, 52431}, {40584, 6516}, {53525, 914}, {53982, 4552}, {53985, 14628}, {55067, 57985}, {57434, 345}, {62605, 46405}
X(65104) = crosspoint of X(i) and X(j) for these (i,j): {278, 36110}, {653, 36123}, {1897, 37203}, {4242, 17923}
X(65104) = crosssum of X(i) and X(j) for these (i,j): {652, 22350}, {1459, 2252}
X(65104) = crossdifference of every pair of points on line {3, 201}
X(65104) = barycentric product X(i)*X(j) for these {i,j}: {1, 44428}, {4, 3738}, {11, 4242}, {19, 3904}, {29, 53527}, {33, 4453}, {36, 44426}, {75, 58313}, {92, 654}, {104, 53047}, {264, 8648}, {270, 6370}, {273, 53285}, {275, 2600}, {281, 3960}, {286, 53562}, {318, 53314}, {320, 18344}, {324, 62734}, {513, 5081}, {522, 1870}, {523, 17515}, {650, 17923}, {693, 52427}, {860, 3737}, {1172, 4707}, {1835, 7253}, {1845, 43728}, {1897, 53525}, {2190, 6369}, {2245, 57215}, {2323, 17924}, {2361, 46107}, {2610, 46103}, {3064, 3218}, {4089, 56183}, {4282, 14618}, {4391, 52413}, {4511, 7649}, {4585, 8735}, {6591, 32851}, {7017, 21758}, {7113, 46110}, {11700, 53152}, {16082, 53046}, {17926, 18593}, {18155, 44113}, {21828, 31623}, {36110, 57434}, {39534, 56757}, {42666, 57779}, {43933, 64139}, {46102, 46384}, {51663, 59482}, {54244, 63642}
X(65104) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 35174}, {19, 655}, {25, 2222}, {33, 51562}, {36, 6516}, {53, 62735}, {92, 46405}, {281, 36804}, {512, 52391}, {513, 52392}, {650, 52351}, {654, 63}, {663, 1807}, {1172, 47318}, {1835, 4566}, {1870, 664}, {1973, 32675}, {1983, 44717}, {2189, 37140}, {2323, 1332}, {2361, 1331}, {2501, 60091}, {2600, 343}, {2610, 26942}, {3063, 52431}, {3064, 18359}, {3724, 23067}, {3737, 57985}, {3738, 69}, {3904, 304}, {3960, 348}, {4242, 4998}, {4282, 4558}, {4453, 7182}, {4511, 4561}, {4707, 1231}, {5081, 668}, {6369, 18695}, {6370, 57807}, {6591, 2006}, {7113, 1813}, {7649, 18815}, {8648, 3}, {8735, 60074}, {8750, 52377}, {14270, 22342}, {17515, 99}, {17923, 4554}, {18344, 80}, {21758, 222}, {21789, 1793}, {21828, 1214}, {22379, 1804}, {42069, 52356}, {42666, 201}, {44113, 4551}, {44426, 20566}, {44428, 75}, {46384, 26932}, {47230, 16577}, {51663, 6356}, {52407, 6517}, {52413, 651}, {52426, 906}, {52427, 100}, {52434, 36059}, {53047, 3262}, {53285, 78}, {53314, 77}, {53525, 4025}, {53527, 307}, {53562, 72}, {54244, 63778}, {57174, 22128}, {58313, 1}, {58328, 4571}, {62268, 36078}, {62734, 97}
X(65104) = {X(650),X(6591)}-harmonic conjugate of X(3064)

X(65105) = SIGN-IMAGE OF X(1835)

Barycentrics    a*(a - b - c)*(b - c)*(a^2 + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + c^2) : :

X(65105) lies on these lines: {19, 661}, {28, 4160}, {112, 35056}, {230, 231}, {281, 17926}, {607, 7252}, {652, 1734}, {1848, 25666}, {4705, 54247}, {8611, 57198}, {9404, 54244}, {14400, 16612}, {17924, 48003}

X(65105) = polar conjugate of the isotomic conjugate of X(35057)
X(65105) = X(i)-Ceva conjugate of X(j) for these (i,j): {162, 33}, {653, 1844}, {2190, 2310}
X(65105) = X(55210)-cross conjugate of X(9404)
X(65105) = X(i)-isoconjugate of X(j) for these (i,j): {3, 38340}, {63, 26700}, {79, 1813}, {109, 52381}, {110, 63171}, {222, 6742}, {603, 15455}, {651, 7100}, {656, 35049}, {658, 8606}, {662, 52390}, {1020, 1789}, {1214, 13486}, {1331, 52374}, {1332, 52372}, {1464, 60053}, {2160, 6516}, {3615, 52610}, {4091, 34922}, {4558, 52382}, {4565, 52388}, {4575, 43682}, {6517, 64834}, {11064, 36064}, {18593, 36061}, {20565, 32660}, {22350, 47317}, {23067, 52393}, {30690, 36059}, {32662, 41804}
X(65105) = X(i)-Dao conjugate of X(j) for these (i,j): {11, 52381}, {136, 43682}, {244, 63171}, {1084, 52390}, {3162, 26700}, {3700, 14208}, {5521, 52374}, {7952, 15455}, {8287, 348}, {16221, 18593}, {20620, 30690}, {36103, 38340}, {38966, 7110}, {38991, 7100}, {40596, 35049}, {55042, 63}, {55064, 52388}, {56948, 4592}
X(65105) = crosssum of X(i) and X(j) for these (i,j): {222, 51664}, {652, 4303}
X(65105) = crossdifference of every pair of points on line {3, 7100}
X(65105) = barycentric product X(i)*X(j) for these {i,j}: {4, 35057}, {8, 54244}, {19, 57066}, {29, 57099}, {33, 4467}, {35, 44426}, {92, 9404}, {162, 6741}, {186, 52356}, {281, 14838}, {318, 2605}, {319, 18344}, {522, 6198}, {523, 11107}, {607, 18160}, {650, 52412}, {1172, 7265}, {1577, 41502}, {1825, 7253}, {1897, 53524}, {2174, 46110}, {2341, 44427}, {2501, 56440}, {2611, 36797}, {3064, 3219}, {3900, 7282}, {4420, 7649}, {6591, 42033}, {14618, 35192}, {14775, 31938}, {14975, 35519}, {16577, 17926}, {17924, 52405}, {21054, 52914}, {24006, 35193}, {31623, 55210}, {34016, 55206}, {44428, 56422}, {57779, 58304}
X(65105) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 38340}, {25, 26700}, {33, 6742}, {35, 6516}, {112, 35049}, {281, 15455}, {512, 52390}, {650, 52381}, {661, 63171}, {663, 7100}, {1825, 4566}, {2174, 1813}, {2299, 13486}, {2341, 60053}, {2501, 43682}, {2605, 77}, {2611, 17094}, {3064, 30690}, {4041, 52388}, {4420, 4561}, {4467, 7182}, {6198, 664}, {6591, 52374}, {6741, 14208}, {7265, 1231}, {7282, 4569}, {8641, 8606}, {9404, 63}, {11107, 99}, {14838, 348}, {14975, 109}, {18160, 57918}, {18344, 79}, {20982, 51664}, {21741, 52610}, {21789, 1789}, {21824, 57243}, {23226, 1804}, {31623, 55209}, {34016, 55205}, {35057, 69}, {35192, 4558}, {35193, 4592}, {41502, 662}, {42657, 50462}, {44426, 20565}, {47230, 18593}, {52356, 328}, {52405, 1332}, {52408, 6517}, {52412, 4554}, {53524, 4025}, {54244, 7}, {55206, 8818}, {55210, 1214}, {56440, 4563}, {57066, 304}, {57099, 307}, {58304, 201}, {58313, 56844}

X(65106) = SIGN-IMAGE OF X(1840)

Barycentrics    (b - c)*(-a^2 + b*c)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :

X(65106) lies on these lines: {4, 28521}, {25, 23866}, {230, 231}, {242, 53580}, {659, 7212}, {812, 22384}, {1086, 2969}, {1851, 48032}, {1897, 3699}, {3716, 53556}, {4010, 4435}, {7199, 57200}, {8062, 35519}, {13256, 33137}, {17924, 29051}, {17925, 28843}, {18070, 24006}, {43923, 43931}

X(65106) = polar conjugate of X(4562)
X(65106) = polar conjugate of the isotomic conjugate of X(812)
X(65106) = polar conjugate of the isogonal conjugate of X(8632)
X(65106) = X(17982)-Ceva conjugate of X(2969)
X(65106) = X(8632)-cross conjugate of X(812)
X(65106) = X(i)-isoconjugate of X(j) for these (i,j): {3, 660}, {48, 4562}, {63, 813}, {69, 34067}, {71, 4584}, {100, 295}, {184, 4583}, {190, 2196}, {228, 4589}, {291, 1331}, {292, 1332}, {334, 32656}, {335, 906}, {337, 692}, {603, 36801}, {1176, 52922}, {1459, 5378}, {1808, 4551}, {1813, 4876}, {1911, 4561}, {2200, 4639}, {3690, 36066}, {3781, 30664}, {3784, 8684}, {3917, 36081}, {4518, 36059}, {4557, 57738}, {4574, 37128}, {4575, 43534}, {4579, 36214}, {6516, 7077}, {18268, 52609}, {22061, 37134}, {22367, 41209}, {23067, 56154}
X(65106) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 43534}, {1086, 337}, {1249, 4562}, {3162, 813}, {5190, 335}, {5521, 291}, {6651, 4561}, {7952, 36801}, {8054, 295}, {8632, 23147}, {19557, 1332}, {20620, 4518}, {21261, 22444}, {35068, 52609}, {35078, 4019}, {35119, 69}, {36103, 660}, {38978, 3690}, {39029, 1331}, {40623, 63}, {55053, 2196}, {62552, 4025}, {62558, 905}, {62605, 4583}
X(65106) = crosspoint of X(1897) and X(36124)
X(65106) = crosssum of X(i) and X(j) for these (i,j): {3, 22384}, {1459, 1818}, {20777, 22383}
X(65106) = crossdifference of every pair of points on line {3, 295}
X(65106) = barycentric product X(i)*X(j) for these {i,j}: {4, 812}, {19, 3766}, {27, 4010}, {29, 7212}, {92, 659}, {238, 17924}, {239, 7649}, {242, 514}, {264, 8632}, {273, 4435}, {278, 3716}, {281, 43041}, {286, 21832}, {350, 6591}, {523, 31905}, {525, 34856}, {649, 40717}, {653, 4124}, {693, 2201}, {740, 17925}, {811, 39786}, {862, 7199}, {1119, 4148}, {1284, 57215}, {1428, 46110}, {1429, 44426}, {1447, 3064}, {1874, 4560}, {1897, 27918}, {1914, 46107}, {2052, 22384}, {2501, 33295}, {2969, 3570}, {3261, 57654}, {3948, 57200}, {3975, 43923}, {4448, 6336}, {4455, 44129}, {5009, 14618}, {6335, 27846}, {7178, 14024}, {8747, 24459}, {10030, 18344}, {17493, 54229}, {17982, 27929}, {27853, 42067}, {35544, 43925}, {36124, 62552}, {41013, 50456}, {43933, 51381}, {46104, 46387}, {51435, 53150}
X(65106) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 4562}, {19, 660}, {25, 813}, {27, 4589}, {28, 4584}, {92, 4583}, {238, 1332}, {239, 4561}, {242, 190}, {281, 36801}, {286, 4639}, {419, 18047}, {514, 337}, {649, 295}, {659, 63}, {667, 2196}, {740, 52609}, {804, 4019}, {812, 69}, {862, 1018}, {1019, 57738}, {1428, 1813}, {1429, 6516}, {1783, 5378}, {1874, 4552}, {1914, 1331}, {1973, 34067}, {2201, 100}, {2210, 906}, {2501, 43534}, {2969, 4444}, {3064, 4518}, {3684, 4571}, {3716, 345}, {3747, 4574}, {3766, 304}, {4010, 306}, {4124, 6332}, {4148, 1265}, {4155, 3949}, {4435, 78}, {4448, 3977}, {4455, 71}, {4839, 4101}, {5009, 4558}, {5027, 22061}, {6591, 291}, {7199, 57987}, {7212, 307}, {7252, 1808}, {7649, 335}, {8632, 3}, {8735, 60577}, {14024, 645}, {14599, 32656}, {17442, 52922}, {17922, 40093}, {17924, 334}, {17925, 18827}, {18344, 4876}, {21832, 72}, {22384, 394}, {24459, 52396}, {27846, 905}, {27918, 4025}, {30940, 55202}, {31905, 99}, {33295, 4563}, {34856, 648}, {38367, 20777}, {39786, 656}, {40717, 1978}, {42067, 3572}, {42767, 51367}, {43041, 348}, {43925, 741}, {46107, 18895}, {46387, 3917}, {46390, 3690}, {50456, 1444}, {53556, 3998}, {54229, 30669}, {56828, 4579}, {57200, 37128}, {57654, 101}, {57779, 36806}

X(65107) =  X(30)X(5667)∩X(74)X(186)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^16 - a^14*b^2 - 12*a^12*b^4 + 37*a^10*b^6 - 40*a^8*b^8 + 9*a^6*b^10 + 16*a^4*b^12 - 13*a^2*b^14 + 3*b^16 - a^14*c^2 + 16*a^12*b^2*c^2 - 24*a^10*b^4*c^2 - 40*a^8*b^6*c^2 + 115*a^6*b^8*c^2 - 84*a^4*b^10*c^2 + 14*a^2*b^12*c^2 + 4*b^14*c^2 - 12*a^12*c^4 - 24*a^10*b^2*c^4 + 135*a^8*b^4*c^4 - 120*a^6*b^6*c^4 - 30*a^4*b^8*c^4 + 72*a^2*b^10*c^4 - 21*b^12*c^4 + 37*a^10*c^6 - 40*a^8*b^2*c^6 - 120*a^6*b^4*c^6 + 196*a^4*b^6*c^6 - 73*a^2*b^8*c^6 - 40*a^8*c^8 + 115*a^6*b^2*c^8 - 30*a^4*b^4*c^8 - 73*a^2*b^6*c^8 + 28*b^8*c^8 + 9*a^6*c^10 - 84*a^4*b^2*c^10 + 72*a^2*b^4*c^10 + 16*a^4*c^12 + 14*a^2*b^2*c^12 - 21*b^4*c^12 - 13*a^2*c^14 + 4*b^2*c^14 + 3*c^16) : :
X(65107) = 3 X[186] - 2 X[1304], X[7464] - 4 X[34109], 2 X[6760] - 3 X[37941], 4 X[11589] - 3 X[37948], 5 X[30745] - 6 X[57344], 2 X[34147] - 3 X[38719], 5 X[37952] - 4 X[38625], 2 X[51939] + X[56369]

See Antreas Hatzipolakis and Peter Moses, euclid 6860.

X(65107) lies on these lines: {30, 5667}, {74, 186}, {112, 2693}, {378, 61508}, {1075, 36162}, {1515, 47152}, {2071, 11587}, {6760, 37941}, {7575, 38595}, {9862, 10295}, {11589, 37948}, {14165, 55319}, {14508, 46106}, {30745, 57344}, {31510, 48364}, {32111, 57587}, {34147, 38719}, {34170, 64890}, {36164, 41204}, {37952, 38625}, {44427, 55141}, {51939, 56369}

X(65107) = reflection of X(i) in X(j) for these {i,j}: {1515, 47152}, {2693, 34109}, {7464, 2693}, {38595, 7575}, {48364, 31510}, {64890, 34170}
X(65107) = crossdifference of every pair of points on line {14401, 62350}

X(65108) =  X(143)X(10224)∩X(526)X(32743)

Barycentrics    (a^10 - 2*a^8*b^2 + a^6*b^4 - a^4*b^6 + 2*a^2*b^8 - b^10 - 2*a^8*c^2 + a^6*b^2*c^2 + a^4*b^4*c^2 - 3*a^2*b^6*c^2 + 3*b^8*c^2 + a^6*c^4 + a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 2*b^6*c^4 - a^4*c^6 - 3*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10)*(a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - 3*a^2*b^10 + b^12 + a^10*c^2 - 4*a^8*b^2*c^2 + 4*a^6*b^4*c^2 - 3*a^4*b^6*c^2 + 5*a^2*b^8*c^2 - 3*b^10*c^2 - 3*a^8*c^4 + 4*a^6*b^2*c^4 - 2*a^4*b^4*c^4 - 2*a^2*b^6*c^4 + 3*b^8*c^4 + 2*a^6*c^6 - 3*a^4*b^2*c^6 - 2*a^2*b^4*c^6 - 2*b^6*c^6 + 2*a^4*c^8 + 5*a^2*b^2*c^8 + 3*b^4*c^8 - 3*a^2*c^10 - 3*b^2*c^10 + c^12)::

See Antreas Hatzipolakis and Peter Moses, euclid 6875.

X(65108) lies on these lines: {143, 10224}, {526, 32743}, {13371, 52534}

X(65108) = complement of the isogonal conjugate of X(25739)
X(65108) = medial isogonal conjugate of X(51393)
X(65108) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 51393}, {25739, 10}

X(65109) =  X(577)X(7502)∩X(1092)X(1511)

Barycentrics    a^2*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 2*a^8*c^2 + 3*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - 2*b^8*c^2 + a^6*c^4 - a^4*b^2*c^4 - a^2*b^4*c^4 + b^6*c^4 - a^4*c^6 - a^2*b^2*c^6 - b^4*c^6 + 2*a^2*c^8 + 2*b^2*c^8 - c^10)*(a^10 - 2*a^8*b^2 + a^6*b^4 - a^4*b^6 + 2*a^2*b^8 - b^10 - 3*a^8*c^2 + 3*a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + 2*b^8*c^2 + 2*a^6*c^4 - 2*a^4*b^2*c^4 - a^2*b^4*c^4 - b^6*c^4 + 2*a^4*c^6 + 3*a^2*b^2*c^6 + b^4*c^6 - 3*a^2*c^8 - 2*b^2*c^8 + c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6875.

X(65109) lies on these lines: {26, 16391}, {526, 13289}, {577, 7502}, {1092, 1511}, {2070, 14918}, {3964, 6148}, {5961, 24978}, {7488, 19210}, {7525, 64219}, {14379, 37814}, {15646, 40082}

X(65109) = isogonal conjugate of X(25739)
X(65109) = isogonal conjugate of the anticomplement of X(51393)
X(65109) = X(1)-isoconjugate of X(25739)
X(65109) = X(3)-Dao conjugate of X(25739)
X(65109) = cevapoint of X(i) and X(j) for these (i,j): {3, 2070}, {216, 1495}, {2088, 34952}
X(65109) = trilinear pole of line {32320, 52743}
X(65109) = barycentric quotient X(6)/X(25739)

X(65110) = (name pending)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 2*a^6*c^2 - a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + 2*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8)*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + a^8*c^2 - 4*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - b^8*c^2 - 4*a^6*c^4 + 4*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + 6*a^4*c^6 - 4*a^2*c^8 - b^2*c^8 + c^10) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6875.

X(65110) lies on this line: {1614, 13198}

X(65111) =  X(5)X(49)∩X(140)X(40640)

Barycentrics    4*a^16 - 17*a^14*b^2 + 23*a^12*b^4 - a^10*b^6 - 25*a^8*b^8 + 21*a^6*b^10 - 3*a^4*b^12 - 3*a^2*b^14 + b^16 - 17*a^14*c^2 + 42*a^12*b^2*c^2 - 29*a^10*b^4*c^2 + 8*a^8*b^6*c^2 - 11*a^6*b^8*c^2 + 2*a^4*b^10*c^2 + 9*a^2*b^12*c^2 - 4*b^14*c^2 + 23*a^12*c^4 - 29*a^10*b^2*c^4 + 6*a^8*b^4*c^4 + 5*a^6*b^6*c^4 - 9*a^2*b^10*c^4 + 4*b^12*c^4 - a^10*c^6 + 8*a^8*b^2*c^6 + 5*a^6*b^4*c^6 + 2*a^4*b^6*c^6 + 3*a^2*b^8*c^6 + 4*b^10*c^6 - 25*a^8*c^8 - 11*a^6*b^2*c^8 + 3*a^2*b^6*c^8 - 10*b^8*c^8 + 21*a^6*c^10 + 2*a^4*b^2*c^10 - 9*a^2*b^4*c^10 + 4*b^6*c^10 - 3*a^4*c^12 + 9*a^2*b^2*c^12 + 4*b^4*c^12 - 3*a^2*c^14 - 4*b^2*c^14 + c^16 : :
X(65111) = X[5] + 2 X[11597], X[54] + 2 X[10272], X[110] + 2 X[8254], X[265] - 4 X[64486], X[550] + 2 X[11805], 2 X[1511] + X[20424], 2 X[3574] + X[34153], 4 X[3628] - X[33565], 2 X[5972] + X[11702], 4 X[5972] - X[21230], 2 X[11702] + X[21230], 4 X[6689] - X[10264], 2 X[13392] + X[22051], X[14049] + 5 X[38795], 5 X[15034] + 4 X[30531], 5 X[22251] + X[54157], X[32196] - 4 X[41671], 5 X[38794] + X[43580]

See Antreas Hatzipolakis and Peter Moses, euclid 6876.

X(65111) lies on these lines: {5, 49}, {140, 40640}, {549, 10628}, {550, 11805}, {1154, 16223}, {1511, 20424}, {2914, 10018}, {3574, 34153}, {3628, 33565}, {5972, 11702}, {6689, 10264}, {11561, 14448}, {13392, 22051}, {14049, 38795}, {15034, 30531}, {21357, 34330}, {22251, 54157}, {30551, 32196}, {32609, 61715}, {38794, 43580}

X(65111) = midpoint of X(32609) and X(61715)
X(65111) = {X(5972),X(11702)}-harmonic conjugate of X(21230)





leftri   Double-sign-images: X(65112) - X(65118)  rightri

Contributed by Clark Kimberling and Peter Moses, August 31, 2024

Suppose that X = x(a,b,c) : : is a triangle center, and define

f(a,b,c) = x(a,-b,-c)
X*(a,b,c) = f(a,b,c) : f(b,c,a) : f(c,a,b)

The point X* = X*(a,b,c) is here introduced as the double-sign-image of X. The set of triangle centers is partitioned by the double-sign-image operation into two subsets:

(1) double-self-sign-images X, for which X*=X;
(2) triangle centers X such that X* ≠ X.

The appearance of (h,k) in the following list means that X(k) = X*(h): (8,2), (9,1), (11,1086), (21,100), (27,1897), (28,1783), (29,1897), (33,19), (40,1), (41,31), (43,1), (44,1100), (45,16777), (46,1), (55,6), (58,101), (59,7341), (60,1252), (78,63), (79,80), (80,79), (81,100), (86,190), (88,65112), (89,65113), (100,81), (101,58), (104,65115), (108,1396), (109,1412), (116,65116), (121,65117), (124,65118)

underbar



X(65112) = DOUBLE-SIGN-IMAGE OF X(88)

Barycentrics    a*(a + 2*b - c)*(a - b + 2*c) : :

X(65112) lies on these lines: {1, 9352}, {2, 3715}, {6, 9335}, {7, 37358}, {11, 26842}, {21, 3337}, {42, 88}, {56, 51683}, {57, 1621}, {81, 244}, {100, 354}, {165, 62862}, {171, 3315}, {200, 3306}, {226, 31272}, {404, 18398}, {518, 9342}, {553, 5057}, {750, 62814}, {942, 4511}, {982, 5311}, {1001, 23958}, {1054, 62867}, {1125, 4880}, {1155, 29817}, {1255, 46901}, {1320, 3919}, {1647, 33097}, {1817, 50378}, {1961, 42038}, {2093, 62835}, {2095, 54445}, {2346, 58607}, {2975, 3338}, {3218, 3683}, {3245, 51103}, {3296, 5552}, {3333, 3872}, {3339, 3890}, {3616, 5708}, {3622, 5221}, {3673, 62479}, {3677, 9347}, {3681, 5437}, {3720, 18201}, {3754, 64201}, {3756, 33107}, {3757, 24593}, {3816, 17483}, {3817, 13243}, {3834, 29872}, {3848, 27065}, {3871, 50190}, {3874, 17531}, {3920, 3999}, {4003, 17019}, {4392, 37674}, {4413, 4430}, {4557, 16057}, {4675, 29680}, {4871, 32940}, {4881, 44840}, {4915, 62832}, {5046, 52783}, {5049, 63136}, {5173, 37789}, {5178, 12436}, {5260, 5439}, {5268, 62868}, {5272, 62795}, {5297, 21342}, {5303, 32636}, {5333, 6682}, {5577, 37993}, {5883, 54391}, {5885, 45977}, {5902, 62826}, {5904, 17535}, {6532, 64072}, {6533, 64401}, {6583, 6940}, {6763, 17536}, {6915, 12005}, {7073, 53525}, {7191, 37520}, {9345, 17591}, {9350, 49498}, {9776, 33108}, {9782, 24390}, {10580, 34611}, {10582, 62838}, {10707, 11019}, {11246, 17051}, {12009, 33858}, {12702, 17504}, {14008, 53564}, {15803, 62870}, {16474, 24168}, {16569, 54352}, {17063, 32911}, {17122, 17449}, {17124, 62865}, {17290, 29864}, {17450, 17596}, {17595, 29814}, {17605, 59377}, {17728, 31019}, {17763, 42053}, {18141, 33089}, {18193, 28606}, {21453, 56543}, {21454, 60883}, {24594, 59296}, {25502, 36263}, {26102, 62796}, {27002, 46897}, {29688, 63343}, {29824, 64010}, {30090, 62482}, {30831, 49676}, {30852, 59372}, {30947, 32933}, {30950, 33761}, {30957, 41242}, {31164, 31249}, {32635, 51073}, {32912, 37687}, {32913, 37680}, {33142, 40688}, {33148, 37634}, {36279, 38314}, {37604, 62855}, {37621, 58605}, {40619, 57785}, {41700, 51098}, {41711, 61156}, {42014, 62778}, {51816, 64203}, {53056, 62856}, {56010, 62869}, {58626, 63917}, {62815, 64112}, {62823, 63961}

X(65112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 64149, 1621}, {100, 354, 62863}, {354, 27003, 100}, {942, 5253, 34195}, {1155, 58560, 29817}, {3218, 3742, 5284}, {3306, 10980, 3873}, {3337, 58565, 21}, {3919, 37602, 1320}, {9345, 17591, 62851}, {11019, 20292, 10707}

X(65113) = DOUBLE-SIGN-IMAGE OF X(89)

Barycentrics    a*(2*a + b - 2*c)*(2*a - 2*b + c) : :

X(65113) lies on these lines: {2, 1155}, {8, 4973}, {42, 89}, {46, 4188}, {57, 3957}, {63, 61156}, {65, 37307}, {88, 3052}, {100, 4430}, {145, 37582}, {149, 5435}, {165, 4666}, {200, 3218}, {244, 26745}, {354, 61157}, {902, 9335}, {1054, 17127}, {1159, 19705}, {1621, 63212}, {1707, 63096}, {1770, 5154}, {1788, 37256}, {2093, 4881}, {2320, 3919}, {3219, 30393}, {3306, 63207}, {3550, 29818}, {3579, 3622}, {3616, 37572}, {3623, 32636}, {3741, 24344}, {3752, 30652}, {3832, 64118}, {3871, 37545}, {3872, 15803}, {3873, 64343}, {3890, 63206}, {3916, 46933}, {4189, 54318}, {4427, 46938}, {4880, 25440}, {5059, 64128}, {5218, 26842}, {5311, 17596}, {5603, 10225}, {5657, 41347}, {6377, 30651}, {6594, 60971}, {7226, 56010}, {8012, 56350}, {9812, 46684}, {10164, 31019}, {13587, 36279}, {17024, 37540}, {17126, 29821}, {17484, 59572}, {17572, 56288}, {17595, 29815}, {17601, 29814}, {18391, 36004}, {19537, 62830}, {20075, 64142}, {24616, 59296}, {25417, 46904}, {25961, 59665}, {26910, 51377}, {29817, 35445}, {30578, 44446}, {30991, 33067}, {31445, 46931}, {36846, 53057}, {51073, 56203}, {61153, 62863}, {62856, 63214}, {63211, 64149}

X(65113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {46, 4188, 64047}, {100, 23958, 4430}, {165, 27003, 61155}, {1155, 9352, 2}

X(65114) = DOUBLE-SIGN-IMAGE OF X(104)

Barycentrics    a*(a^3 + a^2*b - a*b^2 - b^3 + 2*a*b*c - a*c^2 + b*c^2)*(a^3 - a*b^2 + a^2*c + 2*a*b*c + b^2*c - a*c^2 - c^3) : :

X(65114) lies on these lines: {4, 1407}, {28, 3937}, {81, 24470}, {104, 1042}, {225, 34051}, {269, 63399}, {443, 22129}, {601, 4334}, {631, 6180}, {651, 37582}, {943, 22053}, {1406, 4293}, {1427, 26877}, {1443, 37565}, {1870, 64132}, {2310, 10308}, {3073, 61376}, {4220, 64538}, {4303, 63291}, {4306, 6906}, {4320, 64021}, {5435, 8757}, {6198, 63995}, {6847, 62787}, {9316, 11491}, {11573, 63400}, {17074, 57282}, {17582, 55406}, {21454, 36742}, {26842, 64394}, {26910, 37231}, {26914, 37117}, {32911, 37545}, {52372, 53525}

X(65115) = DOUBLE-SIGN-IMAGE OF X(105)

Barycentrics    a*(a^2 + b^2 + a*c - b*c)*(a^2 + a*b - b*c + c^2) : :

X(65115) lies on these lines: {6, 144}, {7, 16502}, {75, 33854}, {81, 17302}, {86, 26807}, {100, 27633}, {105, 40934}, {142, 16488}, {192, 32911}, {278, 21148}, {346, 4383}, {390, 1191}, {614, 17872}, {651, 20228}, {1014, 1015}, {1104, 3100}, {1462, 3668}, {1616, 25878}, {1914, 28358}, {2298, 17023}, {2303, 17045}, {2999, 54359}, {3596, 17541}, {3663, 5299}, {3664, 16784}, {3744, 25887}, {3915, 27626}, {3945, 16781}, {3946, 16470}, {4000, 4329}, {4021, 5280}, {4223, 37819}, {4319, 7290}, {4366, 27644}, {4452, 63075}, {5276, 17321}, {7190, 16780}, {11349, 17053}, {16466, 64168}, {16997, 26143}, {17189, 17761}, {17280, 37680}, {17322, 37675}, {17358, 37687}, {17383, 37633}, {17481, 33146}, {17863, 40129}, {21769, 37659}, {26243, 26971}, {26267, 28023}, {26837, 33150}, {26959, 55094}, {28014, 62778}, {37666, 55909}

X(65116) = DOUBLE-SIGN-IMAGE OF X(116)

Barycentrics    (b - c)^2*(a*b + b^2 + a*c + b*c + c^2) : :

X(65116) lies on these lines: {2, 33952}, {10, 4920}, {11, 21208}, {21, 33870}, {31, 33866}, {58, 33865}, {115, 21138}, {116, 3125}, {214, 15903}, {325, 57029}, {386, 33949}, {595, 33867}, {712, 20541}, {812, 1015}, {993, 33869}, {1111, 3120}, {1358, 1365}, {1739, 33864}, {2643, 17886}, {2975, 33868}, {3290, 5074}, {3454, 17211}, {3674, 23537}, {3754, 24211}, {3924, 4056}, {4437, 22035}, {4568, 26582}, {4872, 30117}, {5195, 40091}, {5224, 33948}, {5883, 24241}, {6549, 58860}, {7247, 15955}, {7272, 49487}, {7743, 57033}, {16583, 40690}, {16732, 21429}, {17052, 18179}, {17170, 24159}, {17181, 24046}, {21272, 24222}, {24036, 53600}, {24172, 24387}, {24185, 58898}, {24254, 25345}, {26728, 64702}, {35080, 53167}

X(65116) = complement of X(33952)
X(65116) = circumcircle-of-outer-Napoleon-triangle-inverse of X(33967)
X(65116) = X(i)-Ceva conjugate of X(j) for these (i,j): {5224, 45746}, {33935, 23879}, {33949, 14349}
X(65116) = X(i)-isoconjugate of X(j) for these (i,j): {692, 835}, {1018, 58951}, {1110, 43531}, {1252, 2214}, {32739, 37218}
X(65116) = X(i)-Dao conjugate of X(j) for these (i,j): {514, 43531}, {661, 2214}, {1086, 835}, {6590, 2345}, {14349, 57280}, {39016, 101}, {40619, 37218}, {41849, 1016}, {47842, 612}, {62586, 765}
X(65116) = crosspoint of X(i) and X(j) for these (i,j): {5224, 45746}, {7199, 57923}
X(65116) = crosssum of X(7085) and X(32656)
X(65116) = crossdifference of every pair of points on line {4557, 32739}
X(65116) = barycentric product X(i)*X(j) for these {i,j}: {11, 33949}, {244, 33935}, {386, 23989}, {469, 1565}, {514, 45746}, {693, 14349}, {834, 3261}, {850, 52615}, {1086, 5224}, {1111, 28606}, {6545, 33948}, {7192, 23879}, {7199, 47842}, {16726, 42714}, {17205, 56810}, {21207, 61409}, {42664, 52619}
X(65116) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 2214}, {386, 1252}, {469, 15742}, {514, 835}, {693, 37218}, {834, 101}, {1086, 43531}, {1565, 57876}, {3261, 57977}, {3733, 58951}, {3937, 57704}, {5224, 1016}, {5515, 2345}, {6545, 43927}, {8637, 32739}, {14349, 100}, {17205, 56047}, {23282, 4103}, {23879, 3952}, {23989, 57824}, {28606, 765}, {33935, 7035}, {33948, 6632}, {33949, 4998}, {42664, 4557}, {45746, 190}, {47842, 1018}, {52615, 110}, {61409, 4570}
X(65116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1086, 1565, 17205}, {17211, 20911, 3454}

X(65117) = DOUBLE-SIGN-IMAGE OF X(121)

Barycentrics    (a*b + b^2 + a*c + c^2)*(a^2*b + b^3 + a^2*c + 2*a*b*c - b^2*c - b*c^2 + c^3) : :

X(65117) lies on these lines: {34, 50065}, {81, 26837}, {86, 1086}, {192, 4415}, {940, 4329}, {980, 41007}, {1211, 56914}, {1848, 3666}, {3100, 64158}, {3485, 19765}, {3662, 18156}, {3663, 16888}, {3672, 3782}, {3727, 26543}, {6354, 44733}, {11997, 24210}, {17365, 17481}, {17720, 54359}, {18697, 51571}, {21442, 26601}, {25245, 26611}, {26789, 37633}, {51422, 54292}

X(65117) = crosspoint of X(3674) and X(59191)
X(65117) = barycentric product X(i)*X(j) for these {i,j}: {4357, 24210}, {16739, 23668}, {20911, 41015}, {48400, 53332}
X(65117) = barycentric quotient X(i)/X(j) for these {i,j}: {16680, 32736}, {24210, 1220}, {41015, 2298}, {48400, 4581}

X(65118) = DOUBLE-SIGN-IMAGE OF X(124)

Barycentrics    (b - c)^2*(-(a^2*b) + b^3 - a^2*c - a*b*c + c^3) : :

X(65118) lies on these lines: {7, 1813}, {116, 16732}, {124, 53540}, {142, 16888}, {226, 16578}, {812, 1015}, {1111, 4466}, {1358, 1367}, {1731, 24781}, {1751, 15474}, {3675, 17059}, {3911, 21452}, {3942, 4089}, {4292, 51698}, {4858, 23989}, {16596, 40615}, {17058, 21138}, {24224, 58898}, {24235, 26933}, {40617, 46398}, {43040, 63844}

X(65118) = X(i)-Ceva conjugate of X(j) for these (i,j): {348, 3676}, {15474, 514}
X(65118) = X(i)-isoconjugate of X(j) for these (i,j): {1018, 58986}, {1110, 1751}, {1252, 2218}, {2149, 56146}, {2997, 23990}, {32739, 51566}
X(65118) = X(i)-Dao conjugate of X(j) for these (i,j): {514, 1751}, {650, 56146}, {661, 2218}, {4988, 41506}, {7649, 281}, {40615, 1305}, {40619, 51566}, {43060, 1724}
X(65118) = barycentric product X(i)*X(j) for these {i,j}: {57, 17878}, {348, 5190}, {579, 23989}, {693, 23800}, {1086, 18134}, {1111, 3868}, {1565, 5125}, {3261, 43060}, {3676, 20294}, {4306, 34387}, {8676, 52621}, {15413, 57173}, {16727, 22021}, {17094, 57072}, {17197, 56559}, {17205, 57808}, {18155, 51658}, {23100, 57217}, {58333, 59941}
X(65118) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 56146}, {244, 2218}, {579, 1252}, {693, 51566}, {1086, 1751}, {1111, 2997}, {2352, 1110}, {3120, 41506}, {3190, 6065}, {3676, 1305}, {3733, 58986}, {3868, 765}, {4306, 59}, {4466, 40161}, {5125, 15742}, {5190, 281}, {8676, 3939}, {17205, 272}, {17878, 312}, {18134, 1016}, {20294, 3699}, {21132, 23289}, {23800, 100}, {23989, 40011}, {43060, 101}, {51658, 4551}, {57072, 36797}, {57092, 56183}, {57173, 1783}, {57217, 59149}, {58333, 4578}
X(65118) = {X(1086),X(1565)}-harmonic conjugate of X(17197)

X(65119) =  X(1)X(3)∩X(90)X(200)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + 2*a^3*b*c + 2*a^2*b^2*c - 2*a*b^3*c - b^4*c - 2*a^3*c^2 + 2*a^2*b*c^2 - 4*a*b^2*c^2 + 2*b^3*c^2 + 2*a^2*c^3 - 2*a*b*c^3 + 2*b^2*c^3 + a*c^4 - b*c^4 - c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65119) lies on these lines: {1, 3}, {8, 10058}, {30, 26482}, {80, 5687}, {90, 200}, {100, 1479}, {119, 6284}, {378, 54194}, {474, 37735}, {498, 6941}, {944, 10087}, {956, 12641}, {1012, 37710}, {1259, 37711}, {1376, 7741}, {1478, 64076}, {1519, 6796}, {1621, 10200}, {1727, 5904}, {2057, 58328}, {2066, 35772}, {2164, 52405}, {2950, 15071}, {2964, 61397}, {2975, 13278}, {3085, 37437}, {3583, 11499}, {3585, 11501}, {3586, 11517}, {3632, 8668}, {3731, 11434}, {3871, 49169}, {3913, 37706}, {4187, 15813}, {4294, 5046}, {4302, 6256}, {4304, 10915}, {4305, 12648}, {4309, 6963}, {4421, 17556}, {4857, 11502}, {5218, 6949}, {5248, 24982}, {5281, 6960}, {5414, 35773}, {5533, 26492}, {6286, 12341}, {6735, 8715}, {6906, 12647}, {6932, 31452}, {6958, 10947}, {7676, 60896}, {7727, 13204}, {7951, 11496}, {7972, 12332}, {8068, 10525}, {10053, 38499}, {10056, 37430}, {10065, 38508}, {10086, 38498}, {10088, 38497}, {10483, 64074}, {10528, 15680}, {10956, 15338}, {10958, 63273}, {11114, 45701}, {11239, 37299}, {11500, 41698}, {12114, 37707}, {12189, 38556}, {12327, 19470}, {12381, 38555}, {12758, 30144}, {12953, 18524}, {13116, 38510}, {13118, 38571}, {13189, 38557}, {13217, 38566}, {13311, 38519}, {13313, 38567}, {15171, 26476}, {17516, 26378}, {18395, 62333}, {18491, 18514}, {22760, 41684}, {25440, 30384}, {26459, 44591}, {26465, 44590}, {36975, 37022}, {38506, 49207}, {41166, 63967}, {41389, 56176}, {58738, 64069}

X(65119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5010, 37561}, {1, 7280, 5193}, {1, 59316, 3359}, {3, 3295, 1388}, {3, 26358, 1}, {35, 3746, 3612}, {35, 5697, 3}, {40, 32760, 36152}, {55, 5217, 37621}, {55, 10310, 11508}, {55, 11248, 1}, {55, 11507, 3746}, {55, 14882, 3295}, {1470, 3295, 1}, {1479, 26364, 39692}, {2646, 23340, 1}, {3057, 26285, 14793}, {3295, 35251, 1470}, {3601, 12703, 1}, {3746, 59327, 1}, {5217, 10965, 10269}, {6244, 7742, 37572}, {8069, 10306, 5903}, {10269, 10965, 1}, {10310, 11508, 36}, {11491, 12775, 6256}, {11510, 35238, 7280}, {13528, 64045, 59330}, {14798, 59328, 165}, {18395, 63281, 62333}, {22768, 37622, 1}, {26437, 44455, 11280}, {35448, 37579, 484}, {40292, 64951, 35}

X(65120) =  X(1)X(3)∩X(80)X(956)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + 2*a^3*b*c - 2*a^2*b^2*c - 2*a*b^3*c + 3*b^4*c - 2*a^3*c^2 - 2*a^2*b*c^2 + 8*a*b^2*c^2 - 2*b^3*c^2 + 2*a^2*c^3 - 2*a*b*c^3 - 2*b^2*c^3 + a*c^4 + 3*b*c^4 - c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65120) lies on these lines: {1, 3}, {8, 48713}, {80, 956}, {90, 62824}, {104, 4302}, {405, 37735}, {499, 6963}, {944, 48694}, {958, 7741}, {993, 30384}, {1478, 6932}, {1479, 2975}, {2066, 35784}, {3149, 37710}, {3254, 15446}, {3583, 22758}, {3585, 22759}, {4193, 5260}, {4294, 11240}, {4299, 37430}, {4342, 17010}, {4857, 22760}, {5046, 10527}, {5231, 5258}, {5251, 23708}, {5261, 6960}, {5288, 37711}, {5414, 35785}, {5433, 38069}, {5657, 10090}, {5731, 10074}, {6284, 32153}, {6286, 22781}, {6902, 47743}, {6905, 12647}, {6941, 26332}, {6949, 10532}, {7580, 36975}, {7727, 22586}, {7951, 22753}, {7972, 22775}, {8070, 10526}, {8543, 60895}, {8666, 10572}, {10058, 30305}, {10198, 17566}, {10483, 64077}, {10529, 15680}, {10785, 64268}, {10948, 31789}, {11194, 57006}, {11491, 12776}, {11500, 37707}, {11502, 41684}, {12190, 38556}, {12382, 38555}, {12513, 37706}, {12953, 26321}, {13119, 38571}, {13190, 38557}, {13218, 38566}, {13314, 38567}, {15175, 34485}, {15868, 48482}, {17516, 26377}, {18514, 18761}, {19470, 22583}, {20846, 51111}, {29676, 52242}, {37437, 64079}, {37708, 44425}, {38497, 49151}, {38498, 49147}, {38499, 49201}, {38508, 49203}, {38510, 49205}, {38519, 49153}

X(65120) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5010, 34486}, {1, 5536, 5903}, {1, 7280, 2078}, {1, 11012, 36152}, {1, 14794, 10267}, {56, 35239, 7280}, {999, 40292, 37525}, {1385, 18839, 1}, {2078, 7280, 36152}, {2078, 11012, 7280}, {2975, 13279, 45700}, {3057, 26286, 59334}, {3428, 22767, 36}, {8071, 22770, 5903}, {10680, 26357, 1}, {10966, 11249, 1}, {16203, 37601, 37616}

X(65121) =  X(11)X(30)∩X(35)X(402)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - 3*a^2*b^10 + b^12 - a^10*b*c + a^8*b^3*c + 3*a^6*b^5*c - 5*a^4*b^7*c + 2*a^2*b^9*c + a^10*c^2 + 2*a^8*b^2*c^2 - a^6*b^4*c^2 - 9*a^4*b^6*c^2 + 8*a^2*b^8*c^2 - b^10*c^2 + a^8*b*c^3 - 7*a^6*b^3*c^3 + 5*a^4*b^5*c^3 + a^2*b^7*c^3 - 3*a^8*c^4 - a^6*b^2*c^4 + 14*a^4*b^4*c^4 - 5*a^2*b^6*c^4 - 5*b^8*c^4 + 3*a^6*b*c^5 + 5*a^4*b^3*c^5 - 6*a^2*b^5*c^5 + 2*a^6*c^6 - 9*a^4*b^2*c^6 - 5*a^2*b^4*c^6 + 10*b^6*c^6 - 5*a^4*b*c^7 + a^2*b^3*c^7 + 2*a^4*c^8 + 8*a^2*b^2*c^8 - 5*b^4*c^8 + 2*a^2*b*c^9 - 3*a^2*c^10 - b^2*c^10 + c^12) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65121) lies on these lines: {1, 11251}, {11, 30}, {35, 402}, {55, 11911}, {80, 11900}, {1479, 4240}, {1650, 7741}, {2066, 35790}, {3585, 11905}, {3746, 11912}, {4302, 11845}, {4857, 11906}, {5010, 26451}, {5119, 11852}, {5414, 35791}, {5697, 12438}, {5903, 12696}, {6284, 32162}, {6286, 12797}, {7280, 35241}, {7727, 13212}, {7951, 11897}, {7972, 12752}, {10572, 49585}, {10591, 45289}, {11831, 37525}, {11910, 63210}, {12369, 19470}, {12626, 37706}, {12953, 18508}, {18507, 18514}, {24926, 51712}

X(65121) = reflection of X(36) in X(11913)
X(65121) = {X(11251),X(11909)}-harmonic conjugate of X(1)

X(65122) =  X(1)X(7387)∩X(25)X(35)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 4*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + 4*b^6*c^2 + 4*a^2*b^3*c^3 + 2*a^2*b^2*c^4 - 6*b^4*c^4 + 2*a^2*c^6 + 4*b^2*c^6 - c^8) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65122) lies on these lines: {1, 7387}, {3, 3583}, {12, 7530}, {22, 1479}, {23, 4294}, {24, 4302}, {25, 35}, {26, 6284}, {36, 10046}, {55, 7517}, {56, 12083}, {80, 8193}, {90, 5285}, {382, 9659}, {388, 37925}, {497, 12088}, {498, 10594}, {499, 10323}, {1598, 7951}, {2066, 35776}, {2937, 9668}, {3295, 5899}, {3585, 10831}, {3586, 9591}, {3746, 10037}, {3760, 15574}, {4293, 12087}, {4299, 12082}, {4330, 9714}, {4857, 10832}, {5010, 6642}, {5119, 8185}, {5217, 7506}, {5218, 34484}, {5225, 7512}, {5414, 35777}, {5432, 13861}, {5697, 9798}, {5903, 9911}, {6238, 32048}, {6286, 9920}, {6636, 10591}, {6644, 15338}, {7173, 7516}, {7280, 35243}, {7727, 12310}, {7972, 9913}, {8192, 63210}, {9580, 9626}, {9655, 37924}, {9667, 16266}, {9669, 13564}, {9683, 44623}, {9712, 11113}, {9818, 18514}, {9919, 19470}, {10058, 11337}, {10117, 12896}, {10386, 37947}, {10483, 39568}, {10572, 49553}, {10588, 52294}, {10826, 37557}, {11365, 37525}, {12410, 37706}, {15171, 17714}, {18378, 64951}, {20831, 40292}, {37198, 59319}, {37546, 37711}

X(65122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2937, 9668, 9672}, {3295, 5899, 9658}, {7387, 10833, 1}, {10046, 11414, 36}, {10831, 18534, 3585}

X(65123) =  X(1)X(3)∩X(80)X(8197)

Barycentrics    a*((a^2*b - b^3 + a^2*c - 3*a*b*c + b^2*c + b*c^2 - c^3)*Sqrt[R*(r + 4*R)] + a*(a - b - c)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65123) lies on these lines: {1, 3}, {80, 8197}, {1479, 5601}, {2066, 35778}, {3583, 8200}, {3585, 11869}, {4302, 11843}, {4857, 11871}, {5414, 35781}, {5599, 7741}, {6284, 32146}, {6286, 12480}, {7727, 13208}, {7951, 8196}, {7972, 12462}, {9835, 37707}, {10572, 49555}, {11872, 41684}, {12365, 19470}, {12454, 37706}, {12953, 45379}, {18495, 18514}

X(65123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11252, 11873, 1}, {11822, 11879, 36}, {12458, 26393, 5903}

X(65124) =  X(1)X(3)∩X(80)X(8204)

Barycentrics    a*((a^2*b - b^3 + a^2*c - 3*a*b*c + b^2*c + b*c^2 - c^3)*Sqrt[R*(r + 4*R)] - a*(a - b - c)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65124) lies on these lines: {1, 3}, {80, 8204}, {1479, 5602}, {2066, 35780}, {3583, 8207}, {3585, 11870}, {4302, 11844}, {4857, 11872}, {5414, 35779}, {5600, 7741}, {6284, 32147}, {6286, 12481}, {7727, 13209}, {7951, 8203}, {7972, 12463}, {9834, 37707}, {10572, 49556}, {11871, 41684}, {12366, 19470}, {12455, 37706}, {12953, 45380}, {18497, 18514}

X(65124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11253, 11874, 1}, {11823, 11880, 36}, {12459, 26417, 5903}

X(65125) =  X(1)X(1161)∩X(6)X(35)

Barycentrics    a^2*(2*a^2*b^2 - 2*b^4 - a^2*b*c - b^3*c + 2*a^2*c^2 - b*c^3 - 2*c^4 - (a^2 - b^2 - b*c - c^2)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65125) lies on these lines: {1, 1161}, {6, 35}, {36, 10048}, {55, 11916}, {80, 5689}, {499, 10517}, {1271, 1479}, {2066, 35792}, {3056, 42858}, {3583, 6215}, {3585, 10923}, {3641, 5697}, {3746, 10040}, {4302, 10783}, {4857, 10925}, {5010, 26341}, {5119, 5589}, {5414, 35795}, {5591, 7741}, {5605, 63210}, {5875, 6284}, {5903, 12697}, {6202, 7951}, {6277, 6286}, {7280, 35246}, {7725, 19470}, {7727, 7732}, {7972, 12753}, {8540, 44483}, {10572, 49586}, {11370, 37525}, {12627, 37706}, {12953, 26336}, {18509, 18514}, {44471, 45571}, {45552, 59325}

X(65125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1161, 10927, 1}, {10048, 11824, 36}

X(65126) =  X(1)X(1160)∩X(6)X(35)

Barycentrics    a^2*(2*a^2*b^2 - 2*b^4 - a^2*b*c - b^3*c + 2*a^2*c^2 - b*c^3 - 2*c^4 + (a^2 - b^2 - b*c - c^2)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65126) lies on these lines: {1, 1160}, {6, 35}, {36, 10049}, {55, 11917}, {80, 5688}, {499, 10518}, {1270, 1479}, {2066, 35794}, {3056, 42859}, {3583, 6214}, {3585, 10924}, {3640, 5697}, {3746, 10041}, {4302, 10784}, {4857, 10926}, {5010, 26348}, {5119, 5588}, {5414, 35793}, {5590, 7741}, {5604, 63210}, {5874, 6284}, {5903, 12698}, {6201, 7951}, {6276, 6286}, {7280, 35247}, {7726, 19470}, {7727, 7733}, {7972, 12754}, {8540, 44484}, {10572, 49587}, {11371, 37525}, {12628, 37706}, {12953, 26346}, {18511, 18514}, {44472, 45570}, {45553, 59325}

X(65126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1160, 10928, 1}, {10049, 11825, 36}

X(65127) =  X(1)X(9821)∩X(32)X(35)

Barycentrics    a^2*(2*a^4*b^2 - a^2*b^4 - b^6 - a^4*b*c - a^2*b^3*c - b^5*c + 2*a^4*c^2 + a^2*b^2*c^2 - 2*b^4*c^2 - a^2*b*c^3 - b^3*c^3 - a^2*c^4 - 2*b^2*c^4 - b*c^5 - c^6) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65127) lies on these lines: {1, 9821}, {32, 35}, {36, 3056}, {55, 9301}, {80, 9857}, {350, 7811}, {499, 10357}, {1015, 46283}, {1479, 2896}, {2066, 35782}, {3096, 7741}, {3099, 5119}, {3583, 9996}, {3585, 10873}, {3746, 10038}, {4302, 9862}, {4857, 10874}, {5010, 26316}, {5414, 35783}, {5433, 42787}, {5697, 9941}, {5903, 12497}, {6284, 32151}, {6286, 9985}, {7280, 35248}, {7727, 13210}, {7951, 9993}, {7972, 12499}, {9984, 19470}, {9997, 63210}, {10572, 49561}, {11368, 37525}, {12495, 37706}, {12953, 18503}, {18500, 18514}

X(65127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3098, 10047, 36}, {9821, 10877, 1}

X(65128) =  X(1)X(4)∩X(25)X(35)

Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 - 4*b*c - c^2)*(a^2 - b^2 + c^2) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65128) lies on these lines: {1, 4}, {3, 9817}, {5, 1040}, {9, 54299}, {10, 4194}, {11, 1595}, {12, 1596}, {19, 3731}, {24, 5010}, {25, 35}, {27, 17022}, {28, 30282}, {29, 936}, {30, 1038}, {36, 1593}, {40, 1859}, {43, 4207}, {46, 1721}, {53, 3553}, {55, 1598}, {56, 1597}, {57, 1887}, {65, 3426}, {78, 7518}, {79, 1041}, {80, 1039}, {84, 3075}, {90, 1707}, {92, 6765}, {108, 3361}, {165, 1753}, {200, 318}, {208, 1844}, {235, 7951}, {264, 3760}, {269, 4056}, {273, 4328}, {282, 3362}, {286, 58788}, {378, 7280}, {381, 1062}, {382, 1060}, {389, 6285}, {406, 1698}, {412, 5732}, {427, 5272}, {429, 1717}, {451, 64850}, {461, 8580}, {469, 2999}, {475, 3624}, {484, 1452}, {498, 3089}, {499, 3088}, {546, 8144}, {578, 10535}, {607, 5526}, {609, 1968}, {612, 4294}, {614, 7378}, {663, 39532}, {971, 41344}, {975, 4198}, {990, 1210}, {1013, 31424}, {1061, 5560}, {1063, 5561}, {1069, 44413}, {1074, 6835}, {1076, 10431}, {1103, 39531}, {1112, 7727}, {1119, 7274}, {1125, 4200}, {1172, 1743}, {1203, 3195}, {1214, 37411}, {1425, 32062}, {1454, 53524}, {1500, 33842}, {1585, 55482}, {1586, 55476}, {1697, 1871}, {1709, 1771}, {1712, 10398}, {1724, 11323}, {1728, 1754}, {1770, 60786}, {1824, 4186}, {1826, 3293}, {1828, 30323}, {1829, 5697}, {1841, 3247}, {1845, 35665}, {1854, 7686}, {1864, 5706}, {1869, 56191}, {1875, 3340}, {1876, 18398}, {1878, 11396}, {1883, 23708}, {1885, 10483}, {1888, 11529}, {1890, 23050}, {1897, 5342}, {1902, 1905}, {1906, 37719}, {1907, 37720}, {1909, 58782}, {1935, 18540}, {1936, 7330}, {2000, 64002}, {2066, 35764}, {2093, 11471}, {2207, 5280}, {2275, 33843}, {2276, 3199}, {2324, 21073}, {2900, 3191}, {2956, 3062}, {3072, 30223}, {3074, 7070}, {3083, 55569}, {3084, 55573}, {3085, 4319}, {3091, 3100}, {3092, 3301}, {3093, 3299}, {3192, 5312}, {3295, 18535}, {3345, 3469}, {3515, 59325}, {3516, 59319}, {3517, 5217}, {3543, 4296}, {3554, 6748}, {3559, 17194}, {3601, 7497}, {3612, 4185}, {3614, 44960}, {3627, 37729}, {3679, 46878}, {3746, 5198}, {3761, 54412}, {3830, 18447}, {3832, 9539}, {3839, 9538}, {3843, 9644}, {3853, 32047}, {3920, 7408}, {3961, 52082}, {4183, 56831}, {4196, 26102}, {4212, 25502}, {4213, 16569}, {4214, 11363}, {4219, 15803}, {4292, 37104}, {4302, 7487}, {4324, 18533}, {4330, 37122}, {4354, 6623}, {4653, 54340}, {4656, 10624}, {4668, 56877}, {4853, 4894}, {4855, 17519}, {4882, 7046}, {5130, 37711}, {5155, 12135}, {5160, 37984}, {5174, 9623}, {5204, 55571}, {5219, 15763}, {5248, 62971}, {5259, 62972}, {5287, 6994}, {5293, 28076}, {5297, 52301}, {5338, 31508}, {5414, 35765}, {5432, 21841}, {5433, 64474}, {5438, 37393}, {5446, 6238}, {5534, 39529}, {5563, 11403}, {5587, 54295}, {5709, 24430}, {5720, 7524}, {5927, 7078}, {6000, 19366}, {6048, 40987}, {6212, 7133}, {6213, 42013}, {6284, 6756}, {6286, 11576}, {6289, 12911}, {6290, 12910}, {6759, 11429}, {6985, 54320}, {7031, 10311}, {7069, 55104}, {7074, 58631}, {7102, 50581}, {7129, 40065}, {7191, 7409}, {7296, 14581}, {7354, 13488}, {7355, 13474}, {7414, 58887}, {7466, 62871}, {7510, 37531}, {7687, 10118}, {7972, 12138}, {7987, 37305}, {7995, 64761}, {8270, 41869}, {8583, 11109}, {8750, 51768}, {9595, 53419}, {9628, 10896}, {9629, 10895}, {9631, 42277}, {9632, 22615}, {9635, 43457}, {9638, 15033}, {9642, 61984}, {9645, 9818}, {9786, 10060}, {9899, 40953}, {9931, 22660}, {10110, 11436}, {10594, 52427}, {10857, 37417}, {10982, 19354}, {11496, 51361}, {12133, 19470}, {12565, 37420}, {12888, 46686}, {12896, 46682}, {12953, 18494}, {15338, 37458}, {16192, 37441}, {16228, 48307}, {16231, 42312}, {17102, 19541}, {17151, 54314}, {17555, 64673}, {19504, 62316}, {20837, 59338}, {21628, 51375}, {25440, 35973}, {26686, 35920}, {29571, 37102}, {30145, 51783}, {30265, 37421}, {30267, 55875}, {31448, 59229}, {31902, 54407}, {34484, 51817}, {34595, 52252}, {35194, 37584}, {36118, 62793}, {36121, 62178}, {36660, 56098}, {37368, 37692}, {37387, 59337}, {37391, 37618}, {37523, 41854}, {37529, 42385}, {37558, 50528}, {37694, 44225}, {38336, 57277}, {38462, 54396}, {40263, 60691}, {40971, 53053}, {46467, 48897}, {54305, 56317}, {55392, 63155}, {55572, 63756}

X(65128) = reflection of X(1038) in X(37696)
X(65128) = polar conjugate of X(64995)
X(65128) = polar conjugate of the isotomic conjugate of X(3305)
X(65128) = X(i)-isoconjugate of X(j) for these (i,j): {3, 3296}, {6, 30679}, {48, 64995}, {69, 61375}, {219, 65028}, {22129, 52188}
X(65128) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 30679}, {1249, 64995}, {36103, 3296}
X(65128) = barycentric product X(i)*X(j) for these {i,j}: {4, 3305}, {19, 42696}, {27, 3697}, {33, 52422}, {34, 42032}, {92, 3295}, {158, 55466}, {281, 7190}, {318, 52424}, {333, 53861}, {811, 58299}, {1783, 48268}, {1826, 63158}, {1897, 47965}, {6335, 48340}, {18535, 65029}, {52412, 56843}
X(65128) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 30679}, {4, 64995}, {19, 3296}, {34, 65028}, {1973, 61375}, {3295, 63}, {3305, 69}, {3697, 306}, {7190, 348}, {18535, 3306}, {42032, 3718}, {42696, 304}, {47965, 4025}, {48268, 15413}, {48340, 905}, {52422, 7182}, {52424, 77}, {53861, 226}, {55466, 326}, {56843, 52381}, {58299, 656}, {63158, 17206}
X(65128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1750, 1745}, {1, 56824, 73}, {4, 33, 1}, {4, 6198, 34}, {4, 7952, 1838}, {4, 11392, 3585}, {5, 64054, 1040}, {33, 34, 6198}, {34, 6198, 1}, {318, 14004, 39585}, {381, 1062, 19372}, {406, 1861, 1698}, {546, 8144, 37697}, {1585, 55482, 65083}, {1593, 11399, 36}, {1753, 7412, 165}, {1824, 4186, 7713}, {1829, 17516, 54397}, {1862, 1904, 5090}, {1902, 1905, 5903}, {2654, 18446, 1}, {3627, 37729, 64053}, {5198, 7071, 11398}, {7071, 11398, 3746}, {46878, 56876, 3679}

X(65129) =  X(1)X(3)∩X(63)X(90)

Barycentrics    a*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 2*a^4*b*c + 2*b^5*c - 3*a^4*c^2 + 6*a^2*b^2*c^2 + b^4*c^2 - 4*b^3*c^3 + 3*a^2*c^4 + b^2*c^4 + 2*b*c^5 - c^6) : :
X(65129) = 8 X[16218] - 7 X[50190]

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65129) lies on these lines: {1, 3}, {9, 7741}, {10, 55870}, {11, 26921}, {63, 90}, {72, 52050}, {80, 57279}, {191, 9614}, {283, 5358}, {497, 920}, {498, 7162}, {499, 55104}, {1058, 7098}, {1071, 41685}, {1158, 12116}, {1512, 10827}, {1698, 50208}, {1709, 48482}, {1727, 26015}, {1768, 11920}, {1794, 39947}, {3218, 4294}, {3219, 10591}, {3583, 7330}, {3586, 6763}, {3719, 30171}, {3872, 56152}, {4299, 7284}, {4302, 63399}, {4324, 7171}, {4652, 10058}, {4857, 30223}, {5231, 37358}, {6284, 24467}, {6734, 10522}, {6762, 37706}, {7082, 9669}, {10039, 10532}, {10050, 54302}, {10393, 62859}, {10527, 12514}, {10529, 30305}, {10530, 11415}, {10572, 12649}, {10589, 26878}, {10624, 49627}, {10943, 12701}, {10957, 12699}, {11373, 16139}, {11570, 12520}, {12047, 55109}, {12758, 13279}, {13369, 41537}, {15298, 21617}, {15518, 60919}, {18514, 18540}, {23708, 26363}, {31435, 37735}, {37711, 49168}, {45287, 64079}, {48713, 64139}, {56418, 56535}, {60926, 61019}

X(65129) = reflection of X(1) in X(10966)
X(65129) = crosspoint of X(2994) and X(64979)
X(65129) = crosssum of X(2178) and X(61398)
X(65129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40, 59342}, {1, 165, 14798}, {1, 5709, 46}, {1, 11012, 37618}, {1, 37625, 25415}, {1, 58887, 37579}, {1, 59316, 10267}, {3, 64046, 1}, {40, 57, 58887}, {40, 5697, 5119}, {40, 12704, 11249}, {40, 37611, 59340}, {40, 59336, 37572}, {55, 37532, 17700}, {57, 18398, 3338}, {63, 1479, 90}, {1454, 3295, 17699}, {3057, 10680, 1}, {3338, 5119, 3612}, {5709, 54408, 1}, {9957, 18967, 1}, {10267, 18839, 1}, {11249, 64043, 1}, {24474, 26357, 1}

X(65130) =  X(1)X(6923)∩X(11)X(35)

Barycentrics    a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c + a^5*b*c + 2*a^4*b^2*c + a^3*b^3*c - 2*a^2*b^4*c - 2*a*b^5*c + b^6*c - a^5*c^2 + 2*a^4*b*c^2 - 6*a^3*b^2*c^2 + a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + a^4*c^3 + a^3*b*c^3 + a^2*b^2*c^3 + 4*a*b^3*c^3 - 3*b^4*c^3 - a^3*c^4 - 2*a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 + a^2*c^5 - 2*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65130) lies on these lines: {1, 6923}, {4, 30323}, {10, 1479}, {11, 35}, {30, 10949}, {36, 10948}, {55, 11928}, {79, 17625}, {80, 10914}, {149, 4861}, {355, 3583}, {496, 14803}, {497, 3612}, {498, 10598}, {1071, 12750}, {1376, 7741}, {1385, 13274}, {1709, 48482}, {1727, 10916}, {2066, 35796}, {3057, 10057}, {3585, 10944}, {3746, 10523}, {4302, 10785}, {5010, 26492}, {5086, 12758}, {5414, 35797}, {5533, 37561}, {5903, 12700}, {6284, 10943}, {6286, 12926}, {6922, 59328}, {6938, 15868}, {7280, 35249}, {7727, 13213}, {7951, 10893}, {7972, 12761}, {9670, 40292}, {10043, 30305}, {10058, 24387}, {10073, 37562}, {10087, 63964}, {10269, 41699}, {10483, 64725}, {10522, 37711}, {10531, 37692}, {10584, 20107}, {10827, 26333}, {10912, 37706}, {11235, 16370}, {11373, 37525}, {12371, 19470}, {12699, 45288}, {12953, 18519}, {14798, 15908}, {17614, 37735}, {17647, 30384}, {18514, 18516}, {22758, 40272}, {25542, 25973}, {25893, 41859}, {37707, 41698}, {37710, 45776}

X(65130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1479, 3434, 10826}, {10525, 10947, 1}, {10948, 11826, 36}

X(65131) =  X(1)X(6928)∩X(12)X(30)

Barycentrics    a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c + a^5*b*c - 2*a^4*b^2*c + a^3*b^3*c + 2*a^2*b^4*c - 2*a*b^5*c + b^6*c - a^5*c^2 - 2*a^4*b*c^2 + 6*a^3*b^2*c^2 - 3*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + a^4*c^3 + a^3*b*c^3 - 3*a^2*b^2*c^3 + 4*a*b^3*c^3 - 3*b^4*c^3 - a^3*c^4 + 2*a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 + a^2*c^5 - 2*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65131) lies on these lines: {1, 6928}, {4, 5119}, {12, 30}, {36, 6922}, {55, 11929}, {65, 16153}, {72, 80}, {355, 3583}, {498, 6934}, {519, 1479}, {958, 7741}, {1478, 3612}, {1727, 64002}, {1837, 41686}, {2066, 35798}, {2478, 23708}, {3149, 7951}, {3338, 10629}, {3579, 13273}, {3746, 10954}, {3822, 35979}, {4302, 10786}, {4325, 14800}, {4354, 51889}, {4857, 10950}, {4861, 5046}, {5010, 26487}, {5080, 10572}, {5270, 11374}, {5414, 35799}, {5812, 5903}, {6284, 10942}, {6286, 12936}, {6734, 10522}, {6827, 37618}, {6840, 45287}, {6903, 21578}, {6923, 59316}, {7280, 35250}, {7354, 14803}, {7491, 32760}, {7727, 13214}, {7972, 12762}, {8068, 11012}, {10073, 64046}, {10320, 59339}, {10483, 37022}, {10590, 50695}, {10742, 41541}, {10895, 40292}, {10955, 15171}, {11113, 15843}, {11500, 41698}, {11826, 59328}, {12372, 19470}, {12635, 37706}, {12953, 18518}, {14798, 31789}, {16139, 56790}, {17857, 37821}, {18395, 26921}, {18513, 61763}, {18514, 18517}, {18961, 58887}, {26332, 37692}, {31799, 59322}, {37708, 48482}, {47032, 63211}, {52383, 52408}

X(65131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1479, 3436, 37711}, {10523, 11827, 36}, {10526, 10953, 1}

X(65132) =  X(1)X(3)∩X(1727)X(3555)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c - a^3*b*c + 5*a^2*b^2*c + a*b^3*c - 4*b^4*c - 2*a^3*c^2 + 5*a^2*b*c^2 - 10*a*b^2*c^2 + 5*b^3*c^2 + 2*a^2*c^3 + a*b*c^3 + 5*b^2*c^3 + a*c^4 - 4*b*c^4 - c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65132) lies on these lines: {1, 3}, {80, 10915}, {497, 15867}, {498, 10596}, {946, 10087}, {1259, 64203}, {1479, 10528}, {1727, 3555}, {2066, 35816}, {3244, 10058}, {3299, 45642}, {3301, 45643}, {3583, 10942}, {3585, 10956}, {3871, 30384}, {3913, 10826}, {4302, 10805}, {4857, 10958}, {5259, 5554}, {5414, 35817}, {5552, 7741}, {5687, 23708}, {6284, 32213}, {6286, 13121}, {7727, 13217}, {7951, 10531}, {7972, 12775}, {10483, 64078}, {10572, 49626}, {10599, 26333}, {10955, 15171}, {11496, 37708}, {12381, 19470}, {12616, 12750}, {12648, 37706}, {12749, 64291}, {12758, 34772}, {12953, 18545}, {18514, 18542}, {21398, 56108}, {24982, 25542}, {25438, 27385}, {32537, 37711}, {34719, 45701}, {45393, 64056}, {49192, 51803}, {49204, 62316}

X(65132) = reflection of X(59322) in X(14798)
X(65132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5010, 16203}, {1, 11010, 34339}, {1, 11248, 36}, {1, 12703, 5903}, {1, 23340, 11009}, {1, 26358, 3746}, {1, 59327, 5563}, {35, 37602, 14800}, {55, 12000, 1}, {3295, 44455, 11510}, {3746, 5697, 35}, {10679, 10965, 1}, {26358, 37622, 1}

X(65133) =  X(1)X(3)∩X(80)X(5288)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + 3*a^3*b*c - 3*a^2*b^2*c - 3*a*b^3*c + 4*b^4*c - 2*a^3*c^2 - 3*a^2*b*c^2 + 10*a*b^2*c^2 - 3*b^3*c^2 + 2*a^2*c^3 - 3*a*b*c^3 - 3*b^2*c^3 + a*c^4 + 4*b*c^4 - c^5) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65133) lies on these lines: {1, 3}, {4, 15868}, {30, 10949}, {72, 22560}, {80, 5288}, {498, 10597}, {956, 10826}, {958, 23708}, {1479, 8666}, {1512, 37710}, {2066, 35818}, {2323, 3204}, {2975, 30384}, {3149, 37708}, {3299, 45640}, {3301, 45641}, {3583, 10943}, {3585, 10957}, {4297, 10074}, {4302, 10806}, {4324, 38761}, {4857, 10959}, {5187, 5258}, {5251, 37735}, {5414, 35819}, {6284, 32214}, {6286, 13122}, {6931, 26363}, {6968, 26332}, {7727, 13218}, {7951, 10532}, {7972, 12776}, {10090, 11362}, {10094, 63132}, {10483, 64079}, {10572, 49627}, {10827, 22753}, {10948, 11827}, {11920, 63430}, {12382, 19470}, {12513, 37711}, {12649, 37706}, {12701, 32153}, {12750, 48694}, {12758, 56288}, {12953, 18543}, {16132, 41537}, {16155, 46816}, {18514, 18544}, {22376, 34139}, {24541, 25542}, {26377, 54397}, {37707, 44425}, {48713, 64056}, {49191, 51803}, {49203, 62316}, {52050, 57279}

X(65133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5010, 16202}, {1, 7280, 11510}, {1, 11012, 14798}, {1, 11249, 36}, {1, 12704, 5903}, {1, 14794, 34486}, {1, 24474, 11009}, {1, 26357, 3746}, {35, 37602, 24926}, {36, 3746, 59334}, {36, 5697, 35}, {36, 59325, 59332}, {36, 59326, 59319}, {36, 59328, 3}, {55, 12001, 1}, {56, 5119, 14803}, {56, 58887, 36}, {2098, 26286, 32760}, {3428, 37618, 59321}, {5119, 14803, 35}, {5563, 59322, 36}, {7962, 59334, 3746}, {10680, 10966, 1}, {11012, 14798, 59319}, {11249, 35238, 35252}, {11510, 35252, 7280}, {14801, 14802, 10269}, {22767, 22770, 46}

X(65134) =  X(1)X(30)∩X(4)X(35)

Barycentrics    2*a^4 - a^2*b^2 - b^4 - a^2*b*c - a^2*c^2 + 2*b^2*c^2 - c^4 : :
X(65134) = 5 X[1] - 6 X[3058], 7 X[1] - 6 X[5434], 3 X[1] - 2 X[7354], 11 X[1] - 12 X[15170], 3 X[1] - 4 X[15171], 7 X[1] - 8 X[15172], 5 X[1] - 4 X[18990], 7 X[3058] - 5 X[5434], 3 X[3058] - 5 X[6284], 9 X[3058] - 5 X[7354], 12 X[3058] - 5 X[10483], 11 X[3058] - 10 X[15170], 9 X[3058] - 10 X[15171], 21 X[3058] - 20 X[15172], 3 X[3058] - 2 X[18990], 3 X[5434] - 7 X[6284], 9 X[5434] - 7 X[7354], 12 X[5434] - 7 X[10483], 11 X[5434] - 14 X[15170], 9 X[5434] - 14 X[15171], 3 X[5434] - 4 X[15172], 15 X[5434] - 14 X[18990], 3 X[6284] - X[7354], 4 X[6284] - X[10483], 11 X[6284] - 6 X[15170], 3 X[6284] - 2 X[15171], 7 X[6284] - 4 X[15172], 5 X[6284] - 2 X[18990], 4 X[7354] - 3 X[10483], 11 X[7354] - 18 X[15170], 7 X[7354] - 12 X[15172], 5 X[7354] - 6 X[18990], 11 X[10483] - 24 X[15170], 3 X[10483] - 8 X[15171], 7 X[10483] - 16 X[15172], 5 X[10483] - 8 X[18990], 9 X[15170] - 11 X[15171], 21 X[15170] - 22 X[15172], 15 X[15170] - 11 X[18990], 7 X[15171] - 6 X[15172], 5 X[15171] - 3 X[18990], 10 X[15172] - 7 X[18990], 2 X[10] - 3 X[11114], 2 X[145] - 3 X[34719], 3 X[165] - 2 X[11826], 3 X[165] - 4 X[31789], 3 X[354] - 4 X[31795], 3 X[5903] - 4 X[64163], 3 X[10572] - 2 X[64163], 4 X[950] - 3 X[5902], 5 X[950] - 4 X[17706], 2 X[1770] - 3 X[5902], 5 X[1770] - 8 X[17706], 15 X[5902] - 16 X[17706], 4 X[1125] - 3 X[17579], 5 X[1698] - 6 X[11113], 3 X[1699] - 2 X[37468], 2 X[3244] - 3 X[34611], 4 X[3244] - 3 X[34690], 7 X[3624] - 6 X[11112], 4 X[3626] - 3 X[49719], 4 X[3635] - 3 X[34605], 2 X[3635] - 3 X[34649], 3 X[3679] - 4 X[57288], 3 X[4292] - 4 X[6744], 4 X[4292] - 5 X[18398], 16 X[6744] - 15 X[18398], 5 X[4668] - 6 X[34606], 3 X[5587] - 4 X[37290], 3 X[5692] - 2 X[57287], 5 X[7987] - 4 X[31775], 9 X[7988] - 8 X[37281], 3 X[11246] - 4 X[12433], 5 X[17609] - 4 X[31776], 6 X[28459] - 5 X[35242], 4 X[31777] - 5 X[63469], 4 X[31799] - 3 X[63468], 4 X[32900] - 3 X[34698], 7 X[50190] - 8 X[63999]

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65134) lies on these lines: {1, 30}, {2, 7302}, {3, 3583}, {4, 35}, {5, 5010}, {8, 37006}, {9, 59341}, {10, 11114}, {11, 550}, {12, 3627}, {20, 36}, {33, 6240}, {34, 18560}, {40, 80}, {41, 5134}, {46, 2955}, {55, 382}, {56, 1657}, {57, 4333}, {65, 28146}, {145, 535}, {149, 8666}, {165, 5445}, {172, 9664}, {191, 3419}, {202, 43633}, {203, 43632}, {350, 7802}, {354, 31795}, {355, 11010}, {376, 499}, {377, 5259}, {381, 5217}, {388, 4309}, {390, 49135}, {405, 41859}, {411, 10058}, {427, 7298}, {428, 5268}, {442, 59338}, {443, 25542}, {484, 1837}, {495, 62036}, {496, 15326}, {497, 3529}, {515, 5697}, {516, 5903}, {517, 6243}, {528, 3632}, {529, 3633}, {546, 5432}, {548, 5433}, {549, 7173}, {611, 48910}, {612, 34603}, {613, 48905}, {614, 52397}, {920, 59324}, {942, 28154}, {944, 32905}, {946, 37525}, {950, 1770}, {958, 50242}, {962, 11009}, {968, 63319}, {993, 15680}, {999, 4325}, {1001, 50239}, {1003, 30103}, {1040, 12605}, {1056, 11541}, {1058, 4317}, {1062, 18563}, {1124, 42264}, {1125, 17579}, {1203, 48837}, {1210, 37524}, {1250, 19107}, {1335, 42263}, {1428, 48898}, {1469, 29317}, {1478, 3146}, {1490, 52860}, {1656, 63756}, {1698, 11113}, {1699, 3612}, {1709, 64261}, {1737, 31730}, {1870, 4354}, {1898, 37585}, {1914, 7748}, {1936, 58738}, {2066, 35820}, {2067, 42266}, {2077, 6928}, {2078, 18961}, {2093, 37721}, {2099, 48661}, {2275, 7756}, {2276, 7747}, {2307, 42157}, {2330, 48901}, {2475, 5248}, {2477, 37495}, {2549, 5299}, {2646, 18393}, {2654, 4337}, {2777, 7355}, {2829, 7971}, {2886, 57002}, {3028, 34584}, {3035, 63752}, {3056, 29012}, {3057, 28160}, {3062, 5559}, {3070, 9660}, {3085, 3543}, {3244, 34611}, {3245, 6361}, {3295, 5073}, {3299, 6560}, {3301, 6561}, {3303, 9655}, {3304, 49137}, {3336, 5722}, {3434, 5258}, {3436, 48696}, {3522, 10591}, {3528, 10589}, {3534, 3582}, {3576, 37735}, {3579, 18395}, {3584, 3830}, {3600, 49140}, {3601, 37701}, {3614, 3845}, {3624, 11112}, {3626, 49719}, {3635, 34605}, {3663, 29263}, {3679, 57288}, {3760, 7750}, {3761, 32819}, {3825, 4188}, {3841, 16865}, {3853, 51817}, {3884, 16120}, {3901, 17768}, {3925, 50241}, {4018, 28534}, {4026, 50391}, {4189, 25639}, {4292, 6744}, {4293, 5059}, {4295, 5425}, {4297, 21842}, {4304, 12047}, {4305, 9812}, {4311, 51783}, {4314, 13407}, {4338, 11529}, {4366, 33256}, {4396, 63935}, {4668, 34606}, {4680, 7283}, {4867, 11415}, {4880, 12649}, {4995, 10592}, {5046, 25440}, {5057, 11015}, {5076, 31479}, {5080, 8715}, {5119, 5691}, {5141, 58404}, {5187, 31263}, {5229, 10056}, {5251, 6872}, {5252, 37563}, {5254, 7031}, {5261, 50691}, {5267, 11680}, {5272, 7667}, {5280, 7737}, {5281, 50688}, {5297, 62963}, {5298, 15686}, {5310, 7391}, {5322, 20062}, {5332, 7765}, {5353, 42085}, {5357, 42086}, {5414, 35821}, {5426, 28628}, {5442, 37428}, {5444, 8227}, {5526, 17732}, {5533, 38761}, {5541, 64087}, {5552, 31160}, {5560, 61524}, {5561, 5719}, {5587, 37290}, {5603, 24926}, {5692, 57287}, {5841, 7982}, {5886, 37616}, {5904, 64002}, {5925, 10076}, {6198, 34797}, {6238, 7727}, {6253, 10827}, {6256, 37000}, {6261, 34789}, {6285, 6286}, {6449, 13898}, {6450, 13955}, {6502, 42267}, {6645, 19696}, {6681, 37307}, {6767, 9657}, {6827, 59326}, {6836, 59327}, {6842, 59331}, {6850, 15931}, {6868, 59320}, {6910, 31262}, {6914, 14794}, {6916, 35202}, {6922, 24466}, {6923, 10902}, {6925, 14798}, {6934, 14803}, {6938, 48482}, {6941, 24042}, {6950, 63963}, {6971, 26086}, {6980, 33862}, {6985, 59334}, {7005, 42431}, {7006, 42432}, {7051, 42099}, {7127, 16964}, {7171, 17437}, {7288, 17538}, {7294, 15712}, {7373, 49139}, {7576, 54401}, {7580, 36152}, {7743, 37605}, {7823, 25264}, {7833, 26959}, {7841, 30104}, {7987, 23708}, {7988, 37281}, {7991, 11827}, {8068, 37406}, {8069, 37411}, {8070, 37356}, {8164, 62021}, {8167, 56997}, {8703, 10593}, {8727, 52837}, {9541, 13904}, {9581, 58887}, {9589, 25415}, {9597, 16784}, {9612, 37731}, {9614, 16173}, {9629, 18447}, {9646, 42284}, {9648, 13925}, {9666, 61752}, {9671, 15696}, {9672, 12083}, {9817, 31833}, {9833, 12950}, {9955, 37600}, {9956, 63211}, {9957, 28168}, {10039, 31673}, {10046, 21312}, {10053, 10723}, {10060, 64037}, {10065, 10733}, {10072, 11001}, {10085, 12750}, {10086, 10722}, {10087, 10728}, {10088, 10721}, {10090, 37403}, {10106, 28172}, {10199, 36005}, {10385, 62042}, {10386, 15888}, {10525, 11012}, {10535, 34785}, {10590, 17578}, {10624, 28164}, {10638, 19106}, {10735, 13116}, {10738, 26286}, {10831, 47527}, {10833, 12085}, {10944, 28186}, {10950, 28174}, {11111, 19854}, {11237, 15684}, {11238, 15681}, {11246, 12433}, {11280, 37740}, {11355, 29633}, {11359, 19881}, {11361, 27020}, {11374, 61703}, {11398, 44438}, {11399, 37196}, {11436, 13403}, {11461, 40242}, {11500, 41698}, {11571, 12743}, {12053, 21578}, {12103, 15325}, {12121, 12374}, {12185, 38730}, {12254, 51803}, {12383, 62316}, {12512, 15079}, {12514, 47033}, {12515, 53616}, {12589, 48873}, {12702, 41684}, {12904, 20127}, {13183, 38741}, {13273, 63281}, {13274, 38753}, {13311, 44988}, {13735, 19846}, {13743, 18407}, {13744, 23361}, {13905, 23249}, {13963, 23259}, {14192, 44292}, {14450, 62860}, {14784, 14802}, {14785, 14801}, {14795, 37437}, {14927, 39901}, {14986, 15683}, {15015, 25681}, {15071, 41685}, {15452, 22505}, {15689, 64894}, {15800, 47378}, {15950, 40273}, {16113, 37584}, {16117, 56790}, {16128, 41689}, {16502, 44526}, {16785, 43618}, {16828, 48814}, {17501, 19875}, {17537, 26030}, {17571, 31245}, {17576, 31418}, {17606, 31663}, {17609, 31776}, {17647, 41866}, {17861, 20291}, {18406, 37234}, {18455, 18562}, {18480, 37568}, {18492, 35445}, {18499, 18761}, {18527, 32636}, {18533, 54428}, {19373, 42100}, {19687, 26590}, {19695, 26561}, {19784, 48817}, {19836, 48813}, {19858, 49735}, {19863, 37038}, {20060, 25439}, {20067, 62825}, {20095, 56880}, {20292, 30143}, {20420, 30282}, {22615, 44622}, {22644, 31472}, {22802, 26888}, {24248, 29050}, {24467, 49176}, {24914, 37718}, {25512, 48816}, {25524, 56998}, {26105, 57000}, {26363, 31159}, {26629, 33229}, {26686, 33250}, {26725, 62829}, {28178, 37730}, {28202, 50193}, {28444, 45630}, {28459, 35242}, {30286, 34618}, {30362, 48890}, {31015, 53591}, {31294, 51624}, {31423, 51792}, {31451, 62203}, {31460, 53418}, {31499, 42273}, {31777, 63469}, {31799, 63468}, {32900, 34698}, {32929, 36974}, {33134, 63292}, {33878, 39892}, {34706, 57006}, {35206, 37191}, {36250, 62802}, {36707, 37586}, {36999, 40292}, {37080, 54342}, {37163, 52769}, {37398, 54287}, {37425, 39578}, {37430, 45035}, {37482, 38474}, {37557, 56960}, {37574, 37693}, {37576, 49130}, {37587, 37722}, {37697, 52070}, {37727, 64896}, {39900, 51212}, {41227, 52845}, {41709, 54422}, {41853, 59321}, {41858, 44229}, {42096, 54435}, {42097, 54436}, {42154, 54403}, {42155, 54402}, {42260, 44623}, {42261, 44624}, {43178, 64155}, {44447, 49168}, {47743, 62127}, {50190, 63999}, {52129, 64507}, {54154, 59318}, {59330, 63985}, {62840, 63370}

X(65134) = reflection of X(i) in X(j) for these {i,j}: {1, 6284}, {40, 7491}, {1770, 950}, {5903, 10572}, {5904, 64002}, {7354, 15171}, {7991, 11827}, {10483, 1}, {11571, 12743}, {11826, 31789}, {19470, 12896}, {34605, 34649}, {34690, 34611}, {37707, 5697}, {45287, 10624}, {59355, 51118}
X(65134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16118, 57282}, {3, 3583, 7741}, {3, 12953, 3583}, {4, 35, 7951}, {4, 4302, 35}, {5, 15338, 5010}, {11, 550, 7280}, {12, 3627, 18513}, {20, 1479, 36}, {36, 1479, 37720}, {46, 3586, 37702}, {46, 64005, 15228}, {55, 382, 3585}, {55, 3585, 37719}, {56, 1657, 4316}, {56, 9668, 4857}, {165, 10826, 5445}, {376, 499, 59319}, {376, 5225, 499}, {382, 4330, 37719}, {496, 15704, 15326}, {497, 3529, 4299}, {497, 4299, 5563}, {950, 1770, 5902}, {1058, 4317, 37602}, {1478, 4294, 3746}, {1657, 9668, 56}, {1699, 3612, 5443}, {1737, 31730, 37572}, {2646, 22793, 18393}, {3058, 18990, 1}, {3146, 4294, 1478}, {3295, 5073, 12943}, {3295, 12943, 5270}, {3534, 9669, 5204}, {3583, 4324, 3}, {3585, 4330, 55}, {3586, 64005, 46}, {3830, 64951, 10895}, {4297, 30384, 21842}, {4304, 12047, 37571}, {4304, 51118, 12047}, {4316, 4857, 56}, {4324, 12953, 7741}, {5010, 18514, 5}, {5057, 11015, 22836}, {5080, 20066, 8715}, {5119, 5691, 37710}, {5204, 9669, 3582}, {5434, 15172, 1}, {6284, 7354, 15171}, {6361, 10573, 3245}, {7354, 15171, 1}, {7737, 9598, 5280}, {9612, 59337, 37731}, {9614, 37618, 16173}, {9670, 17800, 4325}, {10543, 39542, 1}, {10895, 64951, 3584}, {11826, 31789, 165}, {12701, 18481, 1}, {15228, 37702, 46}, {15680, 52367, 993}

X(65135) =  X(32)X(35)∩X(36)X(182)

Barycentrics    a^2*(a^6 - a^4*b^2 - a^2*b^3*c - a^4*c^2 - 3*a^2*b^2*c^2 - b^4*c^2 - a^2*b*c^3 - b^3*c^3 - b^2*c^4) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65135) lies on these lines: {1, 3398}, {32, 35}, {36, 182}, {55, 11842}, {80, 10791}, {83, 7741}, {98, 7951}, {499, 10359}, {609, 1691}, {1479, 7787}, {2066, 35766}, {2080, 5010}, {2307, 54298}, {2330, 39750}, {3583, 10796}, {3585, 10797}, {3746, 10801}, {4302, 10788}, {4857, 10798}, {5119, 10789}, {5171, 59325}, {5414, 35767}, {5697, 12194}, {5903, 12197}, {6284, 32134}, {6286, 12208}, {7095, 16549}, {7127, 36759}, {7280, 12054}, {7727, 13193}, {7972, 12199}, {10349, 30103}, {10483, 12203}, {10572, 49545}, {10800, 63210}, {11364, 37525}, {12192, 19470}, {12195, 37706}, {12837, 26316}, {12953, 18501}, {18502, 18514}, {34396, 40790}, {37479, 59319}

X(65135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 10802, 36}, {3398, 10799, 1}, {10797, 14880, 3585}

X(65136) =  X(1)X(8981)∩X(30)X(9648)

Barycentrics    2*a^4 - 3*a^2*b^2 + b^4 - a^2*b*c - 3*a^2*c^2 - 2*b^2*c^2 + c^4 - 4*a^2*S : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65136) lies on these lines: {1, 8981}, {30, 9648}, {35, 3068}, {36, 9540}, {55, 13903}, {80, 13893}, {371, 7951}, {550, 31500}, {590, 7741}, {1151, 10483}, {1479, 8972}, {1587, 59325}, {1702, 5443}, {2066, 35812}, {3299, 5418}, {3311, 13954}, {3582, 31474}, {3583, 8976}, {3584, 18996}, {3585, 6221}, {3627, 9662}, {3746, 13904}, {4299, 43509}, {4302, 13886}, {4316, 6449}, {4324, 13665}, {4857, 13898}, {5010, 7583}, {5119, 13888}, {5326, 19116}, {5414, 35815}, {5442, 51842}, {5444, 18992}, {5697, 8983}, {5903, 13912}, {6284, 13925}, {6286, 8995}, {6407, 12943}, {7280, 19028}, {7727, 8998}, {7972, 13913}, {8994, 19470}, {9582, 15228}, {9583, 37710}, {9615, 36975}, {9646, 31454}, {9660, 43879}, {9663, 18990}, {9689, 50239}, {10572, 49618}, {12953, 45384}, {13883, 37525}, {13902, 63210}, {13911, 37706}, {16173, 31432}, {18393, 31439}, {18512, 63756}, {18514, 18538}, {19037, 31487}, {19066, 24926}, {19117, 52793}, {31499, 32787}, {37731, 51841}

X(65136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6221, 13897, 3585}, {8981, 13901, 1}, {9540, 13905, 36}, {19028, 35255, 7280}

X(65137) =  X(35)X(3069)∩X(372)X(7951)

Barycentrics    2*a^4 - 3*a^2*b^2 + b^4 - a^2*b*c - 3*a^2*c^2 - 2*b^2*c^2 + c^4 + 4*a^2*S : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65137) lies on these lines: {1, 13958}, {35, 3069}, {36, 13935}, {55, 13961}, {80, 13947}, {372, 7951}, {615, 7741}, {1152, 10483}, {1479, 13941}, {1588, 59325}, {1703, 5443}, {2066, 35814}, {3301, 5420}, {3312, 13897}, {3583, 13951}, {3584, 18995}, {3585, 6398}, {3746, 13962}, {4299, 43510}, {4302, 13939}, {4316, 6450}, {4324, 13785}, {4857, 13955}, {5010, 7584}, {5119, 13942}, {5326, 19117}, {5414, 35813}, {5442, 51841}, {5444, 18991}, {5697, 13971}, {5903, 13975}, {6284, 13993}, {6286, 13986}, {6408, 12943}, {7280, 19027}, {7727, 13990}, {7972, 13977}, {9647, 52046}, {9649, 44682}, {9663, 12108}, {10572, 49619}, {12953, 45385}, {13936, 37525}, {13959, 63210}, {13969, 19470}, {13973, 37706}, {18510, 63756}, {18514, 18762}, {19065, 24926}, {19116, 52793}, {37731, 51842}

X(65137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6398, 13954, 3585}, {13935, 13963, 36}, {13958, 13966, 1}, {19027, 35256, 7280}

X(65138) =  X(6)X(35)∩X(36)X(372)

Barycentrics    a^2*(-a^2 + b^2 + b*c + c^2 - 4*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65138) lies on these lines: {1, 3312}, {6, 35}, {36, 372}, {55, 6418}, {56, 6395}, {80, 13936}, {371, 59325}, {498, 7581}, {1124, 6432}, {1152, 59319}, {1335, 3594}, {1479, 7586}, {1505, 5299}, {1587, 7951}, {1703, 5903}, {2066, 35770}, {2275, 62242}, {2362, 5425}, {3056, 42832}, {3069, 7741}, {3077, 58738}, {3086, 42523}, {3245, 49227}, {3298, 6471}, {3299, 3746}, {3311, 5010}, {3582, 18966}, {3583, 7584}, {3584, 19028}, {3585, 19027}, {3612, 19004}, {4294, 63016}, {4302, 7582}, {4324, 42215}, {4857, 19029}, {5062, 5280}, {5119, 19003}, {5217, 6417}, {5259, 63072}, {5326, 13925}, {5432, 19117}, {5444, 8983}, {5445, 13975}, {5697, 18992}, {6199, 63756}, {6284, 19116}, {6286, 19095}, {6398, 7280}, {6428, 19038}, {6460, 10483}, {6501, 64951}, {7173, 13993}, {7583, 13958}, {7727, 19110}, {7968, 63210}, {7969, 24926}, {7972, 19081}, {8540, 44481}, {9647, 41946}, {9649, 33923}, {9663, 15712}, {9688, 19704}, {10041, 45582}, {10572, 49547}, {10591, 63035}, {10881, 54428}, {11009, 35774}, {12953, 18510}, {13665, 13954}, {13785, 18514}, {13904, 13935}, {13942, 23708}, {13962, 37720}, {13966, 19030}, {13971, 37735}, {14803, 26465}, {18398, 51842}, {18965, 35256}, {18991, 37525}, {19059, 19470}, {19065, 37706}, {25542, 31473}, {37006, 49602}, {37524, 51841}, {44474, 45570}, {49257, 51803}, {49269, 62316}

X(65138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {372, 3301, 36}, {1587, 13963, 7951}, {3299, 5414, 3746}, {3312, 19037, 1}, {5414, 6420, 3299}, {6398, 18996, 7280}, {19027, 42216, 3585}

X(65139) =  X(6)X(35)∩X(36)X(371)

Barycentrics    a^2*(-a^2 + b^2 + b*c + c^2 + 4*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65139) lies on these lines: {1, 3311}, {6, 35}, {36, 371}, {55, 6417}, {56, 6199}, {80, 13883}, {372, 59325}, {484, 31439}, {498, 7582}, {548, 9662}, {549, 9648}, {1124, 3592}, {1151, 59319}, {1335, 6431}, {1479, 7585}, {1504, 5299}, {1588, 7951}, {1702, 5903}, {2066, 3301}, {2275, 62241}, {3056, 42833}, {3068, 7741}, {3076, 58738}, {3086, 42522}, {3245, 49226}, {3297, 6470}, {3312, 5010}, {3530, 31500}, {3582, 18965}, {3583, 7583}, {3584, 19027}, {3585, 19028}, {3612, 19003}, {4294, 63015}, {4302, 7581}, {4324, 42216}, {4857, 19030}, {5058, 5280}, {5119, 19004}, {5217, 6418}, {5326, 13993}, {5414, 35771}, {5425, 16232}, {5432, 19116}, {5444, 13971}, {5445, 13912}, {5697, 18991}, {6221, 7280}, {6284, 19117}, {6286, 19096}, {6395, 63756}, {6427, 19037}, {6459, 10483}, {6500, 64951}, {7173, 13925}, {7584, 13901}, {7727, 19111}, {7968, 24926}, {7969, 63210}, {7972, 19082}, {8540, 44482}, {8981, 19029}, {8983, 37735}, {9540, 13962}, {9583, 21842}, {9616, 37572}, {9689, 19537}, {9691, 64894}, {10040, 45583}, {10572, 49548}, {10591, 63023}, {10880, 54428}, {11009, 35775}, {12953, 18512}, {13665, 18514}, {13785, 13897}, {13888, 23708}, {13898, 31487}, {13904, 37720}, {14803, 26459}, {16785, 31471}, {18398, 51841}, {18966, 35255}, {18992, 37525}, {19060, 19470}, {19066, 37706}, {31499, 32788}, {37006, 49601}, {37524, 51842}, {44473, 45571}, {49256, 51803}, {49268, 62316}

X(65139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {371, 3299, 36}, {1588, 13905, 7951}, {2066, 3301, 3746}, {2066, 6419, 3301}, {3311, 19038, 1}, {3311, 31474, 18996}, {6221, 18995, 7280}, {18996, 19038, 31474}, {18996, 31474, 1}, {19028, 42215, 3585}

X(65140) =  X(2)X(35)∩X(11)X(30)

Barycentrics    a^4 + a^2*b^2 - 2*b^4 - 3*a^2*b*c + a^2*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(65140) = X[1] - 4 X[7743], 2 X[1] + X[37006], 8 X[7743] + X[37006], 4 X[11] - X[36], 2 X[11] + X[3583], 10 X[11] - X[4316], 3 X[11] - X[5298], 5 X[11] - 2 X[15325], 7 X[11] - X[15326], X[36] + 2 X[3583], 5 X[36] - 2 X[4316], 3 X[36] - 4 X[5298], 5 X[36] - 8 X[15325], 7 X[36] - 4 X[15326], 5 X[3582] - X[4316], 3 X[3582] - 2 X[5298], 5 X[3582] - 4 X[15325], 7 X[3582] - 2 X[15326], 5 X[3583] + X[4316], 3 X[3583] + 2 X[5298], 5 X[3583] + 4 X[15325], 7 X[3583] + 2 X[15326], 3 X[4316] - 10 X[5298], X[4316] - 4 X[15325], 7 X[4316] - 10 X[15326], 5 X[5298] - 6 X[15325], 7 X[5298] - 3 X[15326], 14 X[15325] - 5 X[15326], X[80] + 2 X[30384], 2 X[80] + X[63210], X[4867] - 4 X[11813], X[5176] + 2 X[21630], 2 X[5176] + X[41702], 2 X[10707] + X[31160], 4 X[21630] - X[41702], 4 X[30384] - X[63210], 2 X[100] - 5 X[31263], X[104] + 2 X[24042], 2 X[104] + X[52851], 4 X[24042] - X[52851], X[149] + 2 X[3814], 2 X[149] + X[48696], 4 X[3814] - X[48696], 4 X[1737] - X[3245], X[2077] + 2 X[10738], 4 X[3911] - X[15228], X[4880] + 2 X[5057], 2 X[5048] + X[9897], 4 X[5123] - X[5541], X[5537] - 4 X[6882], 4 X[6702] - X[63136], X[13587] - 3 X[59377], 4 X[12019] - X[41684], X[36975] - 4 X[44675]

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65140) lies on these lines: {1, 381}, {2, 35}, {3, 9671}, {4, 4317}, {5, 3058}, {11, 30}, {12, 5066}, {13, 5357}, {14, 5353}, {34, 62974}, {40, 11928}, {46, 50865}, {55, 5055}, {56, 3830}, {79, 553}, {80, 519}, {90, 3928}, {100, 31263}, {104, 24042}, {113, 6126}, {115, 16784}, {140, 4330}, {149, 3814}, {172, 14537}, {202, 42973}, {203, 42972}, {265, 7343}, {350, 7809}, {354, 61703}, {376, 499}, {388, 41099}, {390, 61924}, {484, 28198}, {495, 38071}, {496, 3585}, {497, 3545}, {498, 5071}, {515, 16173}, {517, 37718}, {528, 17533}, {539, 51803}, {542, 62316}, {546, 5270}, {547, 4995}, {549, 6284}, {551, 10572}, {611, 38072}, {613, 47353}, {614, 31133}, {946, 37702}, {950, 5443}, {960, 3679}, {999, 14269}, {1015, 39563}, {1056, 61967}, {1058, 41106}, {1125, 5441}, {1155, 28202}, {1203, 3017}, {1250, 37835}, {1319, 28208}, {1428, 11645}, {1478, 3839}, {1656, 9670}, {1699, 5902}, {1727, 28534}, {1737, 3245}, {1837, 3656}, {2043, 36461}, {2044, 36443}, {2077, 10738}, {2098, 50798}, {2241, 18362}, {2275, 11648}, {2307, 41108}, {3027, 22566}, {3056, 11178}, {3085, 61936}, {3086, 3543}, {3090, 4309}, {3091, 37719}, {3241, 37706}, {3295, 19709}, {3299, 35803}, {3301, 35802}, {3303, 3851}, {3304, 3843}, {3336, 22793}, {3524, 4302}, {3534, 7280}, {3586, 17532}, {3600, 61989}, {3612, 17528}, {3614, 11737}, {3624, 44217}, {3627, 4325}, {3628, 63273}, {3654, 12701}, {3655, 11376}, {3760, 7788}, {3817, 37701}, {3828, 10624}, {3829, 11113}, {3850, 15888}, {3911, 15228}, {3944, 36583}, {4187, 49732}, {4193, 49719}, {4293, 50687}, {4299, 15682}, {4304, 5444}, {4311, 50862}, {4324, 5433}, {4396, 63939}, {4654, 18398}, {4677, 30323}, {4880, 5057}, {4881, 32557}, {4999, 17525}, {5010, 5054}, {5046, 5258}, {5048, 9897}, {5056, 31452}, {5070, 64950}, {5119, 7308}, {5123, 5541}, {5131, 28146}, {5154, 8715}, {5193, 13273}, {5204, 15681}, {5217, 15694}, {5218, 61899}, {5229, 61980}, {5251, 11680}, {5253, 15679}, {5261, 61958}, {5265, 15640}, {5267, 15678}, {5272, 31152}, {5280, 7753}, {5281, 61906}, {5299, 5309}, {5313, 48842}, {5322, 62963}, {5326, 47599}, {5370, 37901}, {5425, 5722}, {5432, 15699}, {5442, 31730}, {5475, 16785}, {5537, 6882}, {5561, 18541}, {5603, 52850}, {5642, 12896}, {5655, 12904}, {5691, 10893}, {5903, 9581}, {5919, 38140}, {6054, 10070}, {6198, 62982}, {6321, 12351}, {6661, 30103}, {6702, 63136}, {6734, 16155}, {6767, 61948}, {6980, 34486}, {7005, 41121}, {7006, 41122}, {7051, 36970}, {7127, 16268}, {7288, 11001}, {7292, 10989}, {7294, 11812}, {7354, 15687}, {7373, 61974}, {7576, 54428}, {7704, 40257}, {7727, 9140}, {7739, 9599}, {7924, 26959}, {7972, 10711}, {7988, 59337}, {8227, 37571}, {8540, 64802}, {8724, 13183}, {9166, 10053}, {9612, 9844}, {9655, 61993}, {9656, 61970}, {9657, 61984}, {9660, 52045}, {9661, 41945}, {9672, 51519}, {9779, 15933}, {9817, 56965}, {9956, 37563}, {10046, 54994}, {10054, 14639}, {10058, 13587}, {10073, 50908}, {10077, 41043}, {10078, 41042}, {10086, 23234}, {10124, 52793}, {10199, 14800}, {10386, 61910}, {10523, 34746}, {10525, 59326}, {10543, 61272}, {10588, 61932}, {10590, 61954}, {10592, 61942}, {10598, 48482}, {10638, 37832}, {10706, 19470}, {10709, 52129}, {10827, 51785}, {10916, 17781}, {10948, 34697}, {11010, 17606}, {11112, 14803}, {11189, 23325}, {11236, 37711}, {11240, 34690}, {11269, 48870}, {11522, 37721}, {11632, 12185}, {12019, 41684}, {12047, 12563}, {12053, 37710}, {12100, 15338}, {12374, 20126}, {12571, 13407}, {12589, 20423}, {12647, 38074}, {12943, 37587}, {12951, 25164}, {12952, 25154}, {12956, 35197}, {14054, 28609}, {14793, 28444}, {14794, 28443}, {14893, 18990}, {14986, 61985}, {15031, 25303}, {15298, 38075}, {15701, 63756}, {15703, 64951}, {16118, 32636}, {16127, 18223}, {16371, 34706}, {16857, 40292}, {17530, 49736}, {17720, 48824}, {17721, 48819}, {17745, 24045}, {18455, 38458}, {18586, 36441}, {18587, 36459}, {18965, 52047}, {18966, 52048}, {18969, 22515}, {19373, 36969}, {19876, 61763}, {21620, 51074}, {21842, 50443}, {22461, 36250}, {24217, 48825}, {25524, 50397}, {26363, 31156}, {28224, 38141}, {28453, 37564}, {28459, 59320}, {28808, 48798}, {30171, 42033}, {30305, 53620}, {31181, 64054}, {31397, 38076}, {31479, 61933}, {31480, 61937}, {33106, 45897}, {33140, 46521}, {33176, 51087}, {34627, 37707}, {34628, 37618}, {34648, 45287}, {34719, 45701}, {36451, 36466}, {36975, 44675}, {37428, 59321}, {37524, 41869}, {37704, 51792}, {37731, 63999}, {37943, 52427}, {38073, 60923}, {39900, 59373}, {39901, 51023}, {41012, 47033}, {41496, 52374}, {45081, 61259}, {46028, 63288}, {50810, 54361}, {51817, 61887}, {54775, 65050}, {60759, 63281}, {62116, 64894}

X(65140) = midpoint of X(i) and X(j) for these {i,j}: {3582, 3583}, {10707, 37375}
X(65140) = reflection of X(i) in X(j) for these {i,j}: {36, 3582}, {3582, 11}, {4881, 32557}, {5131, 61649}, {31160, 37375}
X(65140) = crosspoint of X(903) and X(56947)
X(65140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5560, 18525}, {4, 37720, 5563}, {5, 3058, 3584}, {5, 4857, 3746}, {11, 3583, 36}, {80, 30384, 63210}, {104, 24042, 52851}, {149, 3814, 48696}, {381, 9669, 11238}, {381, 11238, 1}, {496, 3845, 5434}, {497, 3545, 10056}, {546, 37722, 5270}, {547, 15171, 4995}, {1479, 7741, 35}, {1479, 10591, 7741}, {3058, 3584, 3746}, {3545, 10056, 7951}, {3584, 4857, 3058}, {3586, 23708, 37525}, {3845, 5434, 3585}, {4316, 15325, 36}, {4995, 7173, 547}, {5046, 24387, 5258}, {5066, 15170, 12}, {5071, 10385, 498}, {5176, 21630, 41702}, {5722, 18393, 5425}, {9614, 10826, 5697}, {9669, 10896, 1}, {10572, 37735, 24926}, {10896, 11238, 381}, {11235, 17556, 3679}, {17605, 18527, 1}

X(65141) =  X(2)X(35)∩X(5)X(36)

Barycentrics    a^4 - 3*a^2*b^2 + 2*b^4 + a^2*b*c - 3*a^2*c^2 - 4*b^2*c^2 + 2*c^4 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65141) lies on these lines: {1, 1656}, {2, 35}, {3, 18514}, {4, 59319}, {5, 36}, {10, 5330}, {11, 3628}, {12, 547}, {30, 7294}, {33, 52296}, {46, 7988}, {55, 5070}, {56, 5055}, {79, 3911}, {80, 1125}, {90, 5437}, {125, 62316}, {140, 3583}, {172, 7603}, {191, 5087}, {381, 7280}, {388, 499}, {392, 1698}, {404, 20107}, {442, 6667}, {484, 9955}, {495, 61900}, {496, 3584}, {497, 61886}, {498, 1058}, {546, 4316}, {549, 4324}, {614, 7571}, {632, 6284}, {946, 3245}, {993, 5154}, {999, 61905}, {1203, 45939}, {1209, 51803}, {1210, 37701}, {1385, 37006}, {1478, 5056}, {1506, 5280}, {1594, 54428}, {1621, 20104}, {1699, 37572}, {1727, 3838}, {1737, 5443}, {1770, 5442}, {2307, 37835}, {2475, 6681}, {2476, 14800}, {2646, 37718}, {2975, 31160}, {3058, 61885}, {3085, 46936}, {3086, 7486}, {3091, 10483}, {3295, 15703}, {3299, 10576}, {3301, 10577}, {3303, 61892}, {3304, 61903}, {3336, 17605}, {3337, 61649}, {3525, 4302}, {3526, 5010}, {3533, 5225}, {3545, 4299}, {3600, 61912}, {3612, 34595}, {3614, 5270}, {3616, 37706}, {3624, 10826}, {3634, 30384}, {3646, 5119}, {3679, 34710}, {3814, 5258}, {3847, 7483}, {3850, 15326}, {3851, 5204}, {3918, 12758}, {4193, 5251}, {4293, 15022}, {4309, 61881}, {4330, 16239}, {4857, 5432}, {4995, 47599}, {4999, 17533}, {5054, 12953}, {5071, 7288}, {5072, 12943}, {5079, 10895}, {5122, 16118}, {5141, 15446}, {5217, 46219}, {5218, 60781}, {5219, 18398}, {5229, 61921}, {5261, 61906}, {5267, 37375}, {5272, 7539}, {5274, 31452}, {5288, 11681}, {5298, 10109}, {5299, 7746}, {5326, 15171}, {5353, 16967}, {5357, 16966}, {5370, 7533}, {5425, 11375}, {5434, 61910}, {5441, 19878}, {5444, 10572}, {5533, 58421}, {5587, 21842}, {5777, 15017}, {5818, 37707}, {5886, 11009}, {5901, 41684}, {5902, 12709}, {5903, 8227}, {5904, 30852}, {6126, 12900}, {6668, 45310}, {6691, 17530}, {6825, 35202}, {6829, 14804}, {6831, 59321}, {6855, 59323}, {6862, 59327}, {6863, 15931}, {6879, 59322}, {6881, 8070}, {6882, 59320}, {6918, 36152}, {6920, 10090}, {6931, 26363}, {6933, 10200}, {6949, 44425}, {6958, 59326}, {6959, 14798}, {6971, 11012}, {6979, 34890}, {6980, 37561}, {7031, 37637}, {7051, 42914}, {7127, 42489}, {7292, 7570}, {7295, 56468}, {7373, 61901}, {7489, 14792}, {7727, 15059}, {7743, 37563}, {7972, 64008}, {7989, 37618}, {8068, 38319}, {8976, 13955}, {9579, 61265}, {9581, 37571}, {9614, 19872}, {9654, 37587}, {9655, 61920}, {9661, 42583}, {9668, 55858}, {9669, 55857}, {9670, 51817}, {9671, 55866}, {9897, 15178}, {10021, 56790}, {10039, 10172}, {10056, 47743}, {10058, 17531}, {10072, 10588}, {10171, 12047}, {10175, 37710}, {10198, 10584}, {10535, 32767}, {10590, 61914}, {10592, 61907}, {10624, 31253}, {11010, 11231}, {11019, 36946}, {11237, 61908}, {11238, 61887}, {11280, 51709}, {12812, 18990}, {13751, 56762}, {13898, 13951}, {14940, 52427}, {15228, 18483}, {15694, 63756}, {16853, 40292}, {16922, 27020}, {17005, 25264}, {17057, 19861}, {17647, 64012}, {17717, 37559}, {18393, 24914}, {18538, 18966}, {18762, 18965}, {19373, 42915}, {19470, 64101}, {19540, 39578}, {19875, 30323}, {19925, 36975}, {24160, 28096}, {24387, 27529}, {25055, 37711}, {25431, 29657}, {26959, 32967}, {30103, 32992}, {30104, 33249}, {30282, 50726}, {31231, 37524}, {31283, 64054}, {33176, 38176}, {34466, 38474}, {37582, 61703}, {37605, 38140}, {37722, 61894}, {38066, 63209}, {38109, 61534}, {38458, 64339}, {39900, 63119}, {40259, 48363}, {40663, 61272}, {41694, 60988}, {41872, 55867}, {51700, 62616}, {54002, 56805}, {55860, 64951}, {61877, 63273}, {61970, 64894}

X(65141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3825, 5259}, {2, 7741, 35}, {5, 5433, 3585}, {10, 37735, 63210}, {80, 1125, 24926}, {140, 3583, 59325}, {140, 7173, 3583}, {498, 10589, 37720}, {499, 3090, 7951}, {499, 7951, 5563}, {946, 5445, 3245}, {1698, 23708, 5697}, {3086, 37719, 37602}, {3526, 10896, 5010}, {3585, 5433, 36}, {3614, 15325, 5270}, {3624, 10826, 37525}, {3851, 5204, 18513}, {5067, 10589, 498}, {5432, 10593, 4857}, {5886, 18395, 11009}, {6667, 52795, 442}, {6949, 63963, 44425}, {7504, 31272, 1125}, {10572, 19862, 5444}, {10593, 55856, 5432}, {11230, 17606, 1}, {15171, 48154, 5326}, {15325, 35018, 3614}, {24387, 27529, 48696}, {24914, 61268, 18393}, {31246, 31493, 19875}

X(65142) =  X(1)X(140)∩X(2)X(35)

Barycentrics    2*a^4 - 3*a^2*b^2 + b^4 - a^2*b*c - 3*a^2*c^2 - 2*b^2*c^2 + c^4 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65142) lies on these lines: {1, 140}, {2, 35}, {3, 3585}, {4, 59325}, {5, 5010}, {8, 24926}, {10, 3897}, {11, 632}, {12, 549}, {33, 10018}, {34, 37118}, {36, 388}, {40, 5443}, {46, 37701}, {55, 3526}, {56, 3584}, {57, 5442}, {79, 5219}, {80, 1698}, {90, 7308}, {165, 37692}, {172, 31501}, {215, 37471}, {226, 37524}, {355, 37616}, {381, 4324}, {390, 61863}, {484, 11375}, {495, 14869}, {496, 4995}, {497, 3533}, {499, 1058}, {550, 3614}, {609, 31460}, {615, 31499}, {950, 15079}, {993, 14800}, {999, 55863}, {1038, 10257}, {1040, 7542}, {1056, 61836}, {1125, 3890}, {1250, 33417}, {1329, 37298}, {1385, 37707}, {1478, 3523}, {1656, 3583}, {1697, 16173}, {1737, 37571}, {1788, 5425}, {1914, 31455}, {2077, 6863}, {2276, 7749}, {2307, 16241}, {2476, 20104}, {2478, 31263}, {2646, 11231}, {3056, 58445}, {3058, 10124}, {3074, 58738}, {3085, 5265}, {3086, 31452}, {3090, 4302}, {3147, 54428}, {3295, 3582}, {3299, 5420}, {3301, 5418}, {3303, 61850}, {3304, 61840}, {3305, 63286}, {3336, 11374}, {3337, 17718}, {3524, 4299}, {3530, 7354}, {3576, 31659}, {3579, 18393}, {3586, 19872}, {3600, 15721}, {3601, 37702}, {3616, 6681}, {3619, 39900}, {3624, 5119}, {3628, 6284}, {3632, 64123}, {3634, 10572}, {3647, 27131}, {3653, 37738}, {3654, 11280}, {3679, 4999}, {3760, 37688}, {3814, 4189}, {3815, 7031}, {3822, 4188}, {3911, 18398}, {4293, 61820}, {4304, 51073}, {4305, 19877}, {4309, 10589}, {4325, 9654}, {4330, 5070}, {4338, 63207}, {4848, 38068}, {4855, 47033}, {4857, 46219}, {5045, 52638}, {5047, 10058}, {5055, 12953}, {5131, 57282}, {5183, 31447}, {5204, 5270}, {5225, 61886}, {5229, 10299}, {5251, 6910}, {5253, 10197}, {5258, 5552}, {5261, 15708}, {5267, 11681}, {5268, 7499}, {5280, 31497}, {5281, 61856}, {5288, 45701}, {5298, 15713}, {5299, 31401}, {5312, 37646}, {5332, 9698}, {5353, 42092}, {5357, 42089}, {5434, 11812}, {5441, 6675}, {5498, 32047}, {5657, 11009}, {5660, 7330}, {5692, 27385}, {5818, 37006}, {5886, 11010}, {5902, 12563}, {5903, 6684}, {5904, 59491}, {5972, 7727}, {6174, 31260}, {6221, 13954}, {6238, 43839}, {6285, 64063}, {6286, 6689}, {6398, 13897}, {6668, 11112}, {6691, 25055}, {6699, 19470}, {6711, 52129}, {6713, 7972}, {6723, 12896}, {6767, 61849}, {6796, 6952}, {6825, 59326}, {6831, 59338}, {6833, 44425}, {6882, 59331}, {6883, 59334}, {6889, 59327}, {6891, 15931}, {6921, 10198}, {6922, 21155}, {6924, 14794}, {6926, 35202}, {6934, 52850}, {6950, 63964}, {6954, 59320}, {6958, 10902}, {6967, 14798}, {6971, 33862}, {6980, 26086}, {6989, 10320}, {7173, 55856}, {7288, 10056}, {7295, 56454}, {7298, 37439}, {7302, 62937}, {7352, 20191}, {7355, 25563}, {7356, 32348}, {7373, 61843}, {7907, 27020}, {7987, 10827}, {8068, 37438}, {8144, 10125}, {8227, 59316}, {8981, 13958}, {9352, 11263}, {9540, 13963}, {9588, 25415}, {9596, 21843}, {9624, 61533}, {9655, 15693}, {9656, 61799}, {9657, 61818}, {9660, 42583}, {9668, 55857}, {9669, 55858}, {9670, 55866}, {9671, 61878}, {9817, 16238}, {9897, 61562}, {9955, 63211}, {9956, 37600}, {10020, 64054}, {10039, 10165}, {10063, 61132}, {10072, 15709}, {10164, 12047}, {10385, 61861}, {10527, 48696}, {10578, 36946}, {10590, 15717}, {10592, 15326}, {10593, 55859}, {10624, 19878}, {10638, 33416}, {11011, 50821}, {11230, 37568}, {11237, 15701}, {11238, 61864}, {11277, 16118}, {11285, 30104}, {11376, 37563}, {11392, 35486}, {11540, 15170}, {12108, 18990}, {12758, 58453}, {13405, 50190}, {13901, 13966}, {13905, 13935}, {14782, 14801}, {14783, 14802}, {14986, 61848}, {15171, 16239}, {15172, 61858}, {15228, 35242}, {15452, 34127}, {15674, 46816}, {15888, 37587}, {15950, 61524}, {16408, 40292}, {16418, 31246}, {17004, 25264}, {17057, 17647}, {17527, 31235}, {17605, 31663}, {18968, 48378}, {19027, 35255}, {19028, 35256}, {19366, 44673}, {19369, 50977}, {19372, 52262}, {19547, 37557}, {19854, 59572}, {19861, 64012}, {19862, 30384}, {19875, 24953}, {20108, 50617}, {23329, 26888}, {23336, 64053}, {23708, 34595}, {24902, 24934}, {25669, 33174}, {26487, 37561}, {26492, 34486}, {26959, 33015}, {28198, 63213}, {29662, 33771}, {30103, 33233}, {30366, 56778}, {30389, 37708}, {31224, 64675}, {31434, 37618}, {31448, 37637}, {32612, 59382}, {34471, 41684}, {34577, 63676}, {36835, 38271}, {37119, 52427}, {37582, 61648}, {37602, 61842}, {37603, 37693}, {37696, 44452}, {37721, 53054}, {37722, 61853}, {37734, 38112}, {37737, 61614}, {41861, 61016}, {43238, 54403}, {43239, 54402}, {44535, 54416}, {47743, 61859}, {55297, 59333}, {55865, 65083}, {59372, 59476}, {61275, 61534}, {61276, 61521}, {61815, 64894}

X(65142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 31423, 5445}, {2, 35, 7741}, {3, 7951, 10483}, {3, 10895, 4316}, {5, 15338, 18514}, {5, 52793, 5010}, {10, 37525, 37706}, {12, 549, 7280}, {36, 498, 37719}, {140, 5432, 1}, {381, 63756, 4324}, {496, 11539, 7294}, {498, 631, 36}, {498, 4317, 8164}, {499, 5218, 3746}, {550, 3614, 18513}, {1478, 3523, 59319}, {1656, 5217, 3583}, {1698, 3612, 80}, {1698, 15015, 5794}, {2646, 11231, 18395}, {3035, 7483, 1698}, {3524, 10588, 4299}, {3525, 5218, 499}, {3624, 5119, 37735}, {3911, 63259, 18398}, {4995, 7294, 496}, {5010, 18514, 15338}, {5204, 31479, 5270}, {5219, 58887, 79}, {5251, 14803, 15446}, {5326, 52793, 5}, {5442, 37731, 57}, {6174, 31260, 31419}, {6690, 13747, 3624}, {6910, 26364, 5251}, {7987, 10827, 36975}, {10039, 10165, 21842}, {10164, 12047, 37572}, {10592, 15712, 15326}, {10826, 30282, 5441}, {15720, 31479, 5204}, {24953, 47742, 19875}, {27529, 37291, 993}, {30282, 64850, 10826}, {34595, 61763, 23708}, {59491, 59719, 5904}

X(65143) =  X(1)X(3)∩X(80)X(5258)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + a^3*b*c - a^2*b^2*c - a*b^3*c + 2*b^4*c - 2*a^3*c^2 - a^2*b*c^2 + 6*a*b^2*c^2 - b^3*c^2 + 2*a^2*c^3 - a*b*c^3 - b^2*c^3 + a*c^4 + 2*b*c^4 - c^5) : :
X(65143) = X[14882] - 3 X[37564]

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65143) lies on these lines: {1, 3}, {2, 64362}, {21, 16155}, {30, 10957}, {80, 5258}, {104, 12750}, {405, 23708}, {411, 45287}, {498, 6880}, {499, 6947}, {956, 37711}, {958, 10826}, {993, 1479}, {1387, 5428}, {1478, 6838}, {1727, 3916}, {2066, 45640}, {2174, 2323}, {2478, 5251}, {2975, 10572}, {3086, 6992}, {3149, 10827}, {3193, 4276}, {3476, 6876}, {3478, 56336}, {3583, 26470}, {3585, 26481}, {3651, 21578}, {3829, 11113}, {4189, 30305}, {4294, 10529}, {4302, 5450}, {4304, 49627}, {4313, 10936}, {4330, 37726}, {4857, 26475}, {4996, 12758}, {5218, 10597}, {5259, 24541}, {5267, 10058}, {5270, 64477}, {5288, 37706}, {5414, 45641}, {5441, 26015}, {5559, 64269}, {5836, 19524}, {6284, 10943}, {6286, 49191}, {6684, 10090}, {6796, 12647}, {6834, 7951}, {6905, 10039}, {6914, 12701}, {6921, 10198}, {6925, 10483}, {6936, 37720}, {6938, 48482}, {6962, 37719}, {6985, 22759}, {7727, 49203}, {7972, 48694}, {8068, 55296}, {8666, 12649}, {10053, 13190}, {10065, 13218}, {10086, 12190}, {10087, 12776}, {10088, 12382}, {10949, 15338}, {10959, 15171}, {11500, 37708}, {12575, 17010}, {12687, 59366}, {12749, 64188}, {12953, 18544}, {13116, 13314}, {13119, 13311}, {15446, 43740}, {18514, 45630}, {18515, 18543}, {19470, 49151}, {22345, 54081}, {22753, 37692}, {22775, 33597}, {23361, 45046}, {25542, 25875}, {29639, 35996}, {35206, 51629}, {37293, 63136}, {37308, 58679}, {37710, 44425}, {40950, 54428}, {41012, 51506}, {45230, 62859}, {46816, 57002}, {47033, 51432}, {51624, 51628}, {52769, 60926}, {62858, 64715}, {64268, 64292}

X(65143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3, 14798}, {1, 165, 59342}, {1, 484, 64721}, {1, 5010, 10267}, {1, 5709, 5903}, {1, 7280, 37579}, {1, 11012, 36}, {1, 14794, 10902}, {1, 37616, 24299}, {1, 37625, 11009}, {3, 3057, 32760}, {3, 5119, 35}, {3, 10966, 1}, {3, 22767, 37618}, {35, 36, 14803}, {35, 5563, 37525}, {35, 63210, 3746}, {36, 59320, 59321}, {40, 14793, 59327}, {46, 3428, 59322}, {55, 10680, 1}, {56, 40292, 3612}, {56, 51816, 5563}, {1385, 64046, 1}, {1470, 35239, 58887}, {2077, 11010, 59328}, {3057, 32760, 3746}, {3295, 18967, 1}, {3428, 8071, 46}, {3612, 5045, 24926}, {3612, 40292, 35}, {4302, 15868, 12116}, {5267, 10624, 10058}, {10222, 30323, 63210}, {10902, 14794, 59325}, {11010, 14792, 2077}, {11249, 26357, 1}, {11507, 22770, 25415}, {11510, 34880, 37583}, {14796, 14797, 59334}, {14801, 14802, 3576}, {18839, 24299, 1}, {22767, 37618, 5563}, {35252, 40295, 11249}

X(65144) =  X(1)X(3)∩X(80)X(6735)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + a^3*b*c + 3*a^2*b^2*c - a*b^3*c - 2*b^4*c - 2*a^3*c^2 + 3*a^2*b*c^2 - 6*a*b^2*c^2 + 3*b^3*c^2 + 2*a^2*c^3 - a*b*c^3 + 3*b^2*c^3 + a*c^4 - 2*b*c^4 - c^5) : :
X(65144) = X[36] - 4 X[55], 3 X[36] - 4 X[5172], 3 X[55] - X[5172], X[2077] + 2 X[10679], 2 X[5119] + X[63210], 2 X[5172] - 3 X[32760], 2 X[3814] + X[20075], 2 X[3434] - 5 X[31263], 2 X[37000] + X[52851]

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65144) lies on these lines: {1, 3}, {30, 10956}, {80, 6735}, {90, 8668}, {100, 30384}, {119, 3583}, {498, 10531}, {515, 10087}, {518, 1727}, {519, 10058}, {528, 17533}, {535, 11239}, {1012, 37708}, {1376, 23708}, {1478, 64078}, {1479, 3814}, {1519, 44425}, {1878, 11400}, {2066, 45642}, {2222, 16869}, {2342, 15381}, {2743, 53618}, {3434, 6931}, {3582, 38069}, {3585, 26482}, {3871, 5176}, {3913, 37711}, {4294, 5080}, {4302, 12115}, {4304, 49626}, {4309, 15867}, {4511, 12758}, {4857, 26476}, {5123, 5687}, {5218, 10596}, {5248, 5554}, {5259, 24982}, {5288, 15446}, {5414, 45643}, {5440, 13205}, {5533, 55297}, {5540, 60419}, {5842, 41698}, {6256, 37000}, {6284, 10942}, {6286, 49192}, {6968, 7951}, {6977, 15868}, {7727, 49204}, {7972, 48695}, {9037, 12594}, {10053, 13189}, {10065, 13217}, {10086, 12189}, {10088, 12381}, {10483, 64076}, {10624, 11813}, {10827, 11496}, {10955, 63273}, {10958, 15171}, {11491, 12608}, {12648, 25439}, {12701, 32141}, {12751, 37006}, {12953, 18542}, {13116, 13313}, {13118, 13311}, {15558, 54192}, {18499, 18514}, {19470, 49152}, {22835, 37692}, {28534, 42885}, {31160, 45701}, {35204, 39776}, {36976, 60896}, {37706, 49169}, {41684, 63281}, {44669, 46816}, {51433, 51506}, {63136, 64745}

X(65144) = reflection of X(i) in X(j) for these {i,j}: {36, 32760}, {32760, 55}
X(65144) = circumcircle inverse of X(58887)
X(65144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 35, 14803}, {1, 484, 18838}, {1, 2077, 36}, {1, 5010, 10269}, {1, 11010, 37562}, {1, 11248, 59327}, {1, 37616, 24927}, {1, 49163, 5903}, {1, 59316, 59333}, {3, 10965, 1}, {35, 63210, 36}, {40, 14798, 59321}, {55, 5119, 35}, {55, 10679, 1}, {484, 2078, 36}, {1381, 1382, 58887}, {3295, 11509, 1}, {3295, 35000, 1319}, {5048, 30323, 63210}, {5570, 13528, 46}, {5597, 26424, 1}, {5598, 26400, 1}, {6735, 25438, 48696}, {7991, 36152, 59322}, {8069, 25415, 5563}, {10087, 12775, 12749}, {10306, 11508, 46}, {10679, 11248, 12703}, {10679, 35251, 44455}, {11248, 26358, 1}, {11510, 35448, 58887}, {12000, 22768, 1}, {12000, 64951, 22768}, {14801, 14802, 59332}

X(65145) =  X(1)X(9739)∩X(35)X(372)

Barycentrics    a^2*(2*a^2*b^2 - 2*b^4 - a^2*b*c - b^3*c + 2*a^2*c^2 - b*c^3 - 2*c^4 + 2*(2*a^2 - 2*b^2 - b*c - 2*c^2)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65145) lies on these lines: {1, 9739}, {35, 372}, {36, 45498}, {55, 45578}, {80, 45546}, {182, 5010}, {499, 45522}, {641, 7741}, {1479, 45508}, {3583, 45554}, {3585, 45560}, {3746, 45580}, {4302, 45510}, {4857, 45562}, {5119, 45530}, {5217, 45410}, {5414, 45565}, {5697, 45715}, {5903, 48740}, {6284, 48772}, {6286, 48774}, {7280, 7690}, {7727, 48786}, {7951, 45544}, {7972, 48686}, {10572, 48764}, {10987, 62205}, {12953, 45377}, {18514, 45542}, {19470, 48730}, {37525, 45500}, {37706, 48746}, {45553, 59325}, {45572, 63210}

X(65145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9739, 45570, 1}, {45498, 45582, 36}

X(65146) =  X(1)X(9738)∩X(35)X(371)

Barycentrics    a^2*(2*a^2*b^2 - 2*b^4 - a^2*b*c - b^3*c + 2*a^2*c^2 - b*c^3 - 2*c^4 - 2*(2*a^2 - 2*b^2 - b*c - 2*c^2)*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65146) lies on these lines: {1, 9738}, {35, 371}, {36, 45499}, {55, 45579}, {80, 45547}, {182, 5010}, {499, 45523}, {642, 7741}, {1479, 45509}, {2066, 45564}, {3583, 45555}, {3585, 45561}, {3746, 45581}, {4302, 45511}, {4857, 45563}, {5119, 45531}, {5217, 45411}, {5697, 45716}, {5903, 48741}, {6284, 48773}, {6286, 48775}, {7280, 7692}, {7727, 48787}, {7951, 45545}, {7972, 48687}, {10572, 48765}, {10987, 62206}, {12953, 45378}, {18514, 45543}, {19470, 48731}, {37525, 45501}, {37706, 48747}, {45552, 59325}, {45573, 63210}

X(65146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9738, 45571, 1}, {45499, 45583, 36}

X(65147) =  X(1)X(371)∩X(6)X(35)

Barycentrics    a^2*(a^2 - b^2 - b*c - c^2 - 2*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65147) lies on these lines: {1, 371}, {3, 3299}, {4, 13905}, {5, 13901}, {6, 35}, {11, 8981}, {12, 42215}, {30, 19028}, {33, 10880}, {36, 1124}, {46, 9616}, {55, 3301}, {56, 6221}, {65, 31439}, {80, 13911}, {140, 19029}, {172, 9675}, {372, 5010}, {381, 13897}, {390, 42522}, {484, 2362}, {485, 3583}, {496, 18965}, {497, 13904}, {498, 1588}, {499, 9540}, {549, 18966}, {590, 7741}, {609, 12963}, {615, 31499}, {631, 13962}, {1040, 10897}, {1062, 18457}, {1152, 59325}, {1335, 3592}, {1378, 5251}, {1478, 6459}, {1479, 3068}, {1504, 1914}, {1587, 4302}, {1703, 59316}, {1737, 13912}, {2241, 62241}, {2275, 62206}, {2276, 5058}, {2307, 51728}, {2330, 45571}, {3070, 9660}, {3071, 7951}, {3083, 55566}, {3245, 38235}, {3295, 6199}, {3297, 5563}, {3304, 6447}, {3312, 5217}, {3364, 7127}, {3467, 7133}, {3526, 13955}, {3584, 44622}, {3585, 6561}, {3612, 18992}, {3679, 31453}, {4293, 43512}, {4294, 7585}, {4299, 9541}, {4304, 49548}, {4316, 42260}, {4324, 6560}, {4325, 9681}, {4857, 44623}, {5119, 18991}, {5204, 6449}, {5218, 7582}, {5225, 13886}, {5258, 9678}, {5265, 9542}, {5280, 6424}, {5299, 6422}, {5414, 6419}, {5415, 19004}, {5418, 44624}, {5432, 7584}, {5433, 9648}, {5434, 52047}, {5533, 13913}, {5697, 7969}, {5903, 49226}, {6200, 6502}, {6284, 7583}, {6286, 49256}, {6398, 63756}, {6409, 59319}, {6417, 19037}, {6427, 64950}, {6453, 35769}, {6564, 18514}, {7288, 43509}, {7296, 62219}, {7727, 49268}, {7968, 37525}, {7972, 48700}, {8375, 16785}, {8396, 10040}, {8540, 44656}, {8972, 10591}, {8976, 10896}, {8983, 30384}, {9582, 51842}, {9585, 13462}, {9614, 13888}, {9615, 37618}, {9647, 41945}, {9661, 31454}, {9662, 15326}, {9669, 13898}, {9670, 31487}, {9679, 31473}, {9688, 11194}, {9897, 35882}, {10053, 19109}, {10058, 19113}, {10065, 19111}, {10086, 19056}, {10087, 19082}, {10088, 19060}, {10483, 42258}, {10572, 13883}, {10588, 23273}, {10826, 13893}, {11010, 35774}, {11265, 64054}, {12896, 46688}, {12953, 13665}, {13116, 19115}, {13311, 19094}, {13389, 47057}, {13922, 39692}, {13954, 18510}, {13958, 19116}, {13966, 52793}, {14803, 19047}, {15171, 19030}, {15338, 42216}, {18513, 35821}, {19003, 30282}, {19470, 49216}, {24926, 44636}, {25440, 63072}, {26458, 44591}, {26465, 44590}, {31440, 37721}, {35771, 51817}, {35802, 35815}, {35803, 35812}, {37706, 49232}, {44635, 63210}

X(65147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 19038, 3299}, {55, 3311, 3301}, {371, 2066, 1}, {371, 35808, 2067}, {1124, 1151, 36}, {2066, 2067, 35808}, {2067, 35808, 1}, {3071, 9646, 7951}, {3295, 6199, 18996}, {5218, 7582, 13963}, {5433, 9648, 35255}, {6200, 6502, 7280}, {6221, 31474, 56}, {6417, 64951, 19037}, {6424, 31459, 5280}, {6561, 31472, 3585}, {9541, 31408, 4299}, {9582, 51842, 58887}, {9583, 31432, 1}, {9669, 13903, 13898}, {9675, 31471, 172}, {9681, 31475, 4325}

X(65148) =  X(1)X(372)∩X(6)X(35)

Barycentrics    a^2*(a^2 - b^2 - b*c - c^2 + 2*S) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6892.

X(65148) lies on these lines: {1, 372}, {3, 3301}, {4, 13963}, {5, 13958}, {6, 35}, {11, 13966}, {12, 42216}, {30, 19027}, {33, 10881}, {36, 1152}, {55, 3299}, {56, 6398}, {80, 13973}, {140, 19030}, {371, 5010}, {381, 13954}, {390, 42523}, {484, 16232}, {486, 3583}, {496, 18966}, {497, 13962}, {498, 1587}, {499, 13935}, {549, 18965}, {609, 12968}, {615, 7741}, {631, 13904}, {1040, 10898}, {1062, 18459}, {1124, 3594}, {1151, 59325}, {1377, 5251}, {1478, 6460}, {1479, 3069}, {1505, 1914}, {1588, 4302}, {1702, 59316}, {1737, 13975}, {2066, 6420}, {2067, 6396}, {2241, 62242}, {2275, 62205}, {2276, 5062}, {2330, 45570}, {3070, 7951}, {3084, 55567}, {3295, 6395}, {3298, 5563}, {3304, 6448}, {3311, 5217}, {3365, 7127}, {3467, 42013}, {3526, 13898}, {3584, 31472}, {3585, 6560}, {3612, 18991}, {4293, 43511}, {4294, 7586}, {4304, 49547}, {4316, 42261}, {4324, 6561}, {4857, 44624}, {5119, 18992}, {5204, 6450}, {5218, 7581}, {5225, 13939}, {5248, 63072}, {5259, 31473}, {5280, 6423}, {5299, 6421}, {5408, 65083}, {5416, 19003}, {5420, 44623}, {5432, 7583}, {5433, 35256}, {5434, 52048}, {5533, 13977}, {5697, 7968}, {5903, 49227}, {6221, 63756}, {6284, 7584}, {6286, 49257}, {6410, 59319}, {6418, 19038}, {6428, 64950}, {6454, 35768}, {6565, 18514}, {7288, 43510}, {7296, 62220}, {7727, 49269}, {7969, 37525}, {7972, 48701}, {8376, 16785}, {8416, 10041}, {8540, 44657}, {8981, 52793}, {9614, 13942}, {9669, 13955}, {9897, 35883}, {10053, 19108}, {10056, 31408}, {10058, 19112}, {10065, 19110}, {10086, 19055}, {10087, 19081}, {10088, 19059}, {10483, 42259}, {10572, 13936}, {10588, 23267}, {10591, 13941}, {10826, 13947}, {10896, 13951}, {11010, 35775}, {11266, 64054}, {12896, 46689}, {12953, 13785}, {13116, 19114}, {13311, 19093}, {13388, 47057}, {13897, 18512}, {13901, 19117}, {13971, 30384}, {13991, 39692}, {14803, 19048}, {15171, 19029}, {15338, 42215}, {18513, 35820}, {19004, 30282}, {19470, 49217}, {19854, 31413}, {24926, 44635}, {26459, 44591}, {26464, 44590}, {31411, 31497}, {31439, 63211}, {31499, 32787}, {35770, 51817}, {35802, 35813}, {35803, 35814}, {37706, 49233}, {44636, 63210}, {51841, 58887}

X(65148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 19037, 3301}, {55, 3312, 3299}, {372, 5414, 1}, {372, 35809, 6502}, {1152, 1335, 36}, {2067, 6396, 7280}, {3295, 6395, 18995}, {5218, 7581, 13905}, {5414, 6502, 35809}, {6418, 64951, 19038}, {6502, 35809, 1}, {6560, 44622, 3585}, {9669, 13961, 13955}

X(65149) =  X(3)X(161)∩X(4)X(567)

Barycentrics    2*a^10-4*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^4+c^4)+a^6*(b^4+3*b^2*c^2+c^4)+a^4*(b^6+c^6) : :
X(65149) = -3*X[2]+4*X[13470], -3*X[381]+2*X[61139], -3*X[568]+4*X[6146], -5*X[1656]+4*X[45286], -3*X[3060]+4*X[45970], -4*X[3575]+5*X[37481], -5*X[3843]+4*X[13419], -5*X[5076]+6*X[61744], -3*X[5946]+4*X[11565], -3*X[7540]+4*X[12241], -7*X[9781]+8*X[43575], -5*X[10574]+4*X[45971], -8*X[11745]+9*X[45967], -2*X[11819]+3*X[12022], -2*X[12162]+3*X[18564], -4*X[12605]+3*X[18435]

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6894.

X(65149) lies on these lines: {2, 13470}, {3, 161}, {4, 567}, {5, 26882}, {20, 30522}, {25, 43821}, {26, 265}, {30, 5889}, {49, 18569}, {54, 44288}, {113, 45185}, {156, 3153}, {184, 31724}, {381, 61139}, {382, 1181}, {550, 11454}, {568, 6146}, {1147, 7574}, {1154, 34799}, {1351, 5073}, {1498, 7728}, {1503, 18438}, {1593, 64757}, {1614, 18377}, {1656, 45286}, {1657, 10620}, {1658, 25739}, {2072, 34782}, {2883, 18323}, {2937, 9927}, {3060, 45970}, {3146, 61299}, {3521, 35480}, {3575, 37481}, {3581, 25738}, {3627, 11423}, {3830, 11426}, {3843, 13419}, {5076, 61744}, {5576, 14805}, {5944, 7577}, {5946, 11565}, {6000, 18562}, {6759, 18403}, {7502, 58922}, {7517, 18396}, {7540, 12241}, {7575, 26917}, {9781, 43575}, {9833, 10540}, {10018, 45622}, {10024, 18430}, {10224, 11464}, {10254, 18383}, {10255, 10282}, {10298, 13561}, {10574, 45971}, {10575, 18565}, {11412, 15100}, {11413, 12121}, {11422, 20424}, {11449, 37938}, {11456, 52843}, {11468, 15332}, {11550, 14130}, {11572, 18475}, {11576, 13630}, {11597, 32354}, {11645, 50649}, {11745, 45967}, {11819, 12022}, {12083, 12293}, {12118, 37477}, {12161, 15800}, {12162, 18564}, {12225, 18436}, {12290, 40241}, {12605, 18435}, {13406, 18394}, {13434, 63672}, {13491, 34797}, {14118, 34514}, {14516, 23039}, {14790, 37495}, {15043, 38322}, {15061, 32534}, {15331, 23294}, {15694, 44862}, {16013, 33282}, {16659, 52070}, {17712, 62100}, {17714, 50435}, {18350, 18531}, {18378, 18390}, {18392, 61750}, {18420, 37471}, {18445, 64717}, {18494, 36753}, {19357, 61711}, {19467, 31723}, {19506, 40276}, {22115, 37444}, {22658, 22808}, {31074, 43394}, {31833, 40280}, {32903, 43907}, {34350, 64624}, {35602, 64182}, {36201, 48672}, {37484, 44665}, {38444, 61702}, {43818, 62967}, {44263, 52525}, {50461, 61751}

X(65149) = midpoint of X(i) and X(j) for these (i, j): midpoint of X(i) and X(j) for these {i,j}: {12279, 40242}, {12289, 64718}, {12290, 40241}
X(65149) = reflection of X(i) in X(j) for these {i,j}: {3, 11750}, {382, 21659}, {5889, 45731}, {6243, 44076}, {12278, 550}, {16659, 52070}, {18436, 12225}, {18439, 18563}, {18565, 10575}, {34783, 34224}, {34797, 13491}, {64032, 5}, {64036, 12605}
X(65149) = pole of line {7488, 23039} with respect to the Stammler hyperbola
X(65149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 32140, 63392}, {30, 34224, 34783}, {30, 44076, 6243}, {30, 45731, 5889}, {1503, 18563, 18439}, {9833, 18404, 10540}, {10024, 41362, 18430}, {11750, 18400, 3}, {12279, 40242, 30}, {12605, 64036, 18435}, {18394, 26881, 13406}, {19467, 31723, 37472}, {21659, 44407, 382}, {25739, 41482, 1658}, {32345, 64037, 18381}

X(65150) =  X(2)X(187)∩X(8352)X(12505)

Barycentrics    32*a^8-22*b^8+56*b^6*c^2-60*b^4*c^4+56*b^2*c^6-22*c^8-79*a^6*(b^2+c^2)+a^4*(48*b^4-3*b^2*c^2+48*c^4)+a^2*(29*b^6+24*b^4*c^2+24*b^2*c^4+29*c^6) : :

See Antreas Hatzipolakis and Ivan Pavlov, euclid 6894.

X(65150) lies on the circumconic {{A, B, C, X(598), X(46672)}} and these lines: {2, 187}, {8352, 12505}, {11159, 46672}, {12506, 47061}, {31961, 35955}

X(65151) =  X(3)X(66)∩X(4)X(74)

Barycentrics    a^10-a^8 b^2-4 a^6 b^4+8 a^4 b^6-5 a^2 b^8+b^10-a^8 c^2+12 a^6 b^2 c^2-8 a^4 b^4 c^2-3 b^8 c^2-4 a^6 c^4-8 a^4 b^2 c^4+10 a^2 b^4 c^4+2 b^6 c^4+8 a^4 c^6+2 b^4 c^6-5 a^2 c^8-3 b^2 c^8+c^10 : :
X(65151) = X(3)+2*X(6247), X(3)-4*X(6696), 4*X(3)-X(9833), 2*X(3)+X(14216), 5*X(3)+X(34780), 5*X(3)-2*X(34782), 7*X(3)-X(64033), X(4)+2*X(3357), X(4)-4*X(20299), 2*X(4)+X(20427), 5*X(4)+X(64726), X(66)+2*X(44883), 2*X(66)+X(46264), X(1352)+2*X(63420), X(3357)+2*X(20299), 4*X(3357)-X(20427), 2*X(3357)-X(54050), 10*X(3357)-X(64726), X(5656)-6*X(23329), X(6247)+2*X(6696), 8*X(6247)+X(9833), 4*X(6247)-X(14216), 10*X(6247)-X(34780), 5*X(6247)+X(34782), 8*X(6696)+X(14216), 2*X(6696)-X(23328), 10*X(6696)-X(34782), X(9833)+2*X(14216), X(9833)-8*X(23328), 5*X(9833)+4*X(34780), 5*X(9833)-8*X(34782), 7*X(9833)-4*X(64033), X(12244)+2*X(19506), X(14216)+4*X(23328), 5*X(14216)-2*X(34780), 5*X(14216)+4*X(34782), 7*X(14216)+2*X(64033), 4*X(15578)-X(36989), 2*X(15579)+X(34118), 8*X(20299)+X(20427), 2*X(20299)-X(23325), 4*X(20299)+X(54050), X(20427)+4*X(23325), 5*X(20427)-2*X(64726), 2*X(23325)+X(54050), 5*X(23328)-X(34782), 3*X(23329)-X(61747), X(34780)+2*X(34782), 14*X(34782)-5*X(64033), 4*X(44883)-X(46264)

See Kadir Altintas and Ercole Suppa, euclid 6895.

X(65151) lies on these lines: {2, 5656}, {3, 66}, {4, 74}, {5, 64}, {6, 64474}, {11, 10060}, {12, 10076}, {20, 11454}, {24, 16658}, {25, 16654}, {30, 1853}, {52, 58492}, {68, 12084}, {69, 37480}, {113, 15113}, {140, 1498}, {146, 32743}, {154, 549}, {182, 41719}, {184, 13399}, {185, 3541}, {186, 31383}, {265, 11598}, {343, 21312}, {355, 12262}, {376, 11204}, {378, 1899}, {381, 15311}, {382, 5894}, {389, 3088}, {394, 47090}, {427, 10605}, {459, 36876}, {485, 49251}, {486, 49250}, {498, 7355}, {499, 6285}, {523, 62665}, {546, 5895}, {547, 64714}, {548, 17845}, {550, 8567}, {568, 2781}, {578, 14912}, {631, 5651}, {632, 58795}, {1176, 23042}, {1181, 61690}, {1192 ,6756}, {1350, 44683}, {1351, 23326}, {1370, 63425}, {1495, 35486}, {1593, 16657}, {1595, 9786}, {1596, 26958}, {1597, 13567}, {1656, 2883}, {1657, 41362}, {1971, 21843}, {1992, 10250}, {2071, 11442}, {2192, 15325}, {2393, 35704}, {2697, 2764}, {2892, 32305}, {2935, 10264}, {3089, 13474}, {3090, 6225}, {3091, 7703}, {3098, 36851}, {3146, 18383}, {3147, 26883}, {3311, 8991}, {3312, 13980}, {3426, 47296}, {3448, 13293}, {3515, 16655}, {3516, 6146}, {3517, 16621}, {3520, 11457}, {3522, 14864}, {3523, 10282}, {3524, 10193}, {3525, 64063}, {3526, 12315}, {3529, 34786}, {3530, 17821}, {3532, 44836}, {3533, 14862}, {3542, 11381}, {3543, 18376}, {3546, 5907}, {3547, 46850}, {3548, 12162}, {3549, 10575}, {3564, 37497}, {3566, 21733}, {3575, 43903}, {3581, 18382}, {3589, 64716}, {3618, 34779}, {3627, 5925}, {3628, 64024}, {3740, 6001}, {3818, 61088}, {3830, 23324}, {3832, 64187}, {3843, 51491}, {3845, 61721}, {3851, 5893}, {4549, 14791}, {5054, 10192}, {5068, 54211}, {5092, 5596}, {5418, 12964}, {5420, 12970}, {5621, 44274}, {5654, 5663}, {5892, 41580}, {5901, 7973}, {5965, 11411}, {6053, 62708}, {6145, 32210}, {6241, 37119}, {6293, 13630}, {6353, 44673}, {6639, 64030}, {6640, 14643}, {6662, 59496}, {6697, 37470}, {6699, 9934}, {6776, 11430}, {6961, 14925}, {7387, 44158}, {7394, 15053}, {7395, 64730}, {7403, 9815}, {7404, 9729}, {7505, 12290}, {7506, 64759}, {7507, 34469}, {7527, 18911}, {7528, 18488}, {7529, 9914}, {7544, 43601}, {7545, 9919}, {7583, 19087}, {7584, 19088}, {7689, 14790}, {7741, 12950}, {7951, 12940}, {8227, 9899}, {8549, 37483}, {8889, 18388}, {9708, 20307}, {9709, 20306}, {9730, 14561}, {9956, 12779}, {10056, 32065}, {10072, 11189}, {10104, 12202}, {10117, 12106}, {10249, 11179}, {10255, 38789}, {10257, 18451}, {10299 ,45185}, {10519, 61667}, {10539, 38793}, {10574, 41725}, {10576, 35865}, {10577, 35864}, {10620, 23315}, {10675, 42092}, {10676, 42089}, {10982, 61657}, {10984, 32379}, {11182, 20186}, {11250, 12118}, {11413, 54040}, {11424, 18916}, {11425, 18914}, {11440, 37444}, {11455, 62961}, {11456, 37118}, {11468, 35471}, {11539, 61606}, {11550, 18533}, {11579, 13352}, {11744, 20304}, {12006, 44544}, {12017, 34774}, {12024, 55575}, {12041, 34514}, {12085, 12359}, {12163, 23335}, {12220, 15644}, {12241, 26944}, {12317, 43578}, {12383, 25564}, {13339, 64061}, {13340, 44668}, {13371, 32123}, {13391, 34751}, {13445, 23293}, {13754, 44441}, {14059, 57329}, {14530, 15720}, {14787, 40280}, {14865, 18912}, {15024, 63697}, {15045, 41715}, {15068, 15122}, {15100, 64025}, {15138, 50008}, {15139, 18580}, {15583, 33878}, {15647, 38728}, {15684, 50709}, {15694, 58434}, {15708, 46265}, {15811, 21841}, {16196, 17814}, {16618, 35237}, {16659, 32534}, {17819, 35255}, {17820, 35256}, {17822, 34380}, {17846, 54201}, {17928, 32321}, {18390, 23291}, {18420, 34944}, {18430, 20127}, {18569, 32138}, {19153, 38064}, {20079, 34776}, {20376,48669}, {23048,54132}, {23049,23300}, {23336,32139}, {24206,41735}, {25739,35481}, {26879,35502}, {29317,34938}, {29323,31305}, {31401,32445}, {32062,61645}, {32110, 51756}, {32184, 37481}, {32247, 55293}, {32337, 32401}, {32903, 62097}, {34224, 35477}, {34350, 63710}, {35243, 44201}, {35503, 64032}, {36990, 37458}, {37201, 46349}, {37472, 46374}, {37478, 48873}, {37494, 62332}, {37514, 38110}, {37934, 47450}, {38323, 61700}, {38435, 45839}, {40664, 52448}, {41171, 41738}, {41372, 51358}, {41587, 47527}, {41744, 44493}, {43584, 62937}, {44076, 47524}, {44273, 47353}, {44276, 63839}, {44287, 45956}, {46034, 54961}, {46728, 52398}, {50414, 61820}, {53094, 64719}, {54149, 64724}, {61524, 64022}

X(65151) = midpoint of X(i) and X(j) for these (i, j): {4, 54050}, {376, 32064}, {381, 35450}, {1853, 10606}, {3357, 23325}, {6247, 23328}, {10182, 52102}, {23049, 34778}, {46034, 54961}, {61737, 63420}
X(65152) = reflection of X(i) in X(j) for these (i, j): (2, 23329), (3, 23328), (4, 23325), (113, 15113), (154, 549), (376, 11204), (381, 23332), (1351, 23326), (1352, 61737), (1992, 10250), (3543, 18376), (3830, 23324), (5654, 18281), (5656, 61747), (6759, 10182), (10182, 25563), (11179, 10249), (11202, 10193), (11206, 11202), (20423, 23327), (20427, 54050), (23049, 23300), (23325, 20299), (23328, 6696), (31670, 23049), (32063, 10192), (41580, 5892), (41719, 182), (54050, 3357), (54132, 23048), (61721, 3845)
X(65151) = complement of X(5656)
X(65151) = anticomplement of X(61747)
X(65151) = cross-difference of every pair of points on the line {1636, 2485}
X(65151) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 5656, 61747), (3, 6247, 14216), (3, 14216, 9833), (3, 34780, 34782), (4, 3357, 20427), (4, 18931, 11438), (5, 64, 5878), (5, 61540, 64), (64, 40686, 5), (66, 44883, 46264), (631, 12324, 6759), (631, 35260, 10182), (1593, 26869, 16657), (1656, 13093, 2883), (3088, 18913, 389), (3090, 6225, 61749), (3091, 12250, 22802), (3357, 20299, 4), (3520, 11457, 19467), (3522, 64034, 34785), (3523, 34781, 10282), (3524, 11206, 11202), (3526, 12315, 16252), (3843, 64758, 51491), (3851, 48672, 5893), (5054, 32063, 10192), (5893, 15105, 48672), (6247, 6696, 3), (6759, 10182, 35260), (6759, 25563, 631), (6759, 52102, 12324), (8567, 64037, 550), (10193, 11202, 3524), (10257, 18451, 59543), (10984, 44679, 32379), (11250, 32140, 12118), (11438, 20417, 18931), (11550, 21663, 18533), (12290, 43608, 7505), (13352, 16003, 18917), (13352, 18917, 63722), (13445, 23293, 44440), (14864, 34785, 64034), (16657, 26869, 39571), (18381, 64027, 20), (22802, 32767, 3091), (23300, 34778, 31670), (25563, 52102, 6759), (26944, 55571, 12241), (40686, 61540, 5878)

X(65152) = 101st TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (b^2-c^2)*((b^2+b*c+c^2)*a^2-b^2*c^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 18/08/2024 (top). (Aug 29, 2024)

X(65152) lies on these lines: {2, 7234}, {10, 3835}, {42, 24749}, {649, 25637}, {650, 30968}, {661, 2533}, {693, 4705}, {804, 55210}, {1491, 4036}, {2787, 16751}, {3837, 4824}, {4010, 31946}, {4129, 50497}, {4369, 50489}, {4455, 27045}, {4651, 27138}, {4685, 45339}, {4728, 21727}, {4885, 57077}, {9134, 55197}, {9148, 58289}, {14431, 58361}, {15523, 21720}, {19874, 27345}, {20906, 21350}, {21055, 21726}, {21146, 44316}, {21301, 26049}, {22318, 48136}, {22322, 59747}, {23655, 59305}, {23815, 47675}, {23818, 47666}, {24924, 25126}, {25128, 30023}, {25299, 27527}, {25666, 31003}, {27674, 57131}, {29487, 59312}, {30203, 31339}, {30476, 50494}, {42327, 50524}, {47917, 48401}

X(65152) = crosspoint of X(10) and X(6386)
X(65152) = crosssum of X(58) and X(1980)
X(65152) = X(42327)-Ceva conjugate of-X(21836)
X(65152) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 42328), (42327, 667), (50491, 8640)
X(65152) = X(163)-isoconjugate of-X(42328)
X(65152) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (523, 42328), (18106, 52394), (18196, 757), (21763, 58), (21836, 1), (22387, 1790), (25264, 99), (34022, 4623), (42327, 86), (50524, 81)
X(65152) = perspector of the circumconic through X(25264) and X(42027)
X(65152) = pole of the line {672, 1213} with respect to the nine-point circle
X(65152) = pole of the line {6381, 21024} with respect to the Steiner inellipse
X(65152) = barycentric product X(i)*X(j) for these {i, j}: {10, 42327}, {75, 21836}, {313, 21763}, {321, 50524}, {523, 25264}, {1089, 18196}, {4705, 34022}, {15523, 18106}
X(65152) = trilinear product X(i)*X(j) for these {i, j}: {2, 21836}, {10, 50524}, {37, 42327}, {321, 21763}, {594, 18196}, {661, 25264}, {3954, 18106}, {4079, 34022}, {22387, 41013}
X(65152) = trilinear quotient X(i)/X(j) for these (i, j): (1577, 42328), (18106, 52376), (18196, 593), (21763, 1333), (21836, 6), (22387, 1437), (25264, 662), (34022, 4610), (42327, 81), (50524, 58)
X(65152) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (10, 3835, 50487), (21051, 23301, 661), (21055, 21962, 21726), (27045, 44445, 4455)

X(65153) =  X(11)X(519)∩X(55)X(2718)

Barycentrics    (a - b - c)*(2*a^3 - 2*a^2*b - 3*a*b^2 + b^3 - 2*a^2*c + 8*a*b*c - b^2*c - 3*a*c^2 - b*c^2 + c^3)^2 : :

See Antreas Hatzipolakis and Peter Moses, euclid 6927.

X(65153) lies on the incircle and these lines: {1, 14026}, {11, 519}, {55, 2718}, {56, 2743}, {145, 16185}, {498, 57352}, {513, 6018}, {517, 1357}, {1317, 3667}, {1319, 37743}, {1320, 7336}, {1358, 4887}, {1365, 63210}, {2098, 3326}, {3025, 3057}, {3241, 60698}, {3244, 44046}, {3323, 38941}, {3328, 7962}, {4345, 19634}, {5577, 18839}, {5919, 47007}, {17460, 34194}, {23869, 33176}, {28234, 60058}

X(65153) = reflection of X(i) in X(j) for these {i,j}: {1319, 37743}, {14027, 1}
X(65153) = X(7)-Ceva conjugate of X(43055)
X(65153) = X(5854)-Dao conjugate of X(8)
X(65153) = crosspoint of X(7) and X(43055)
X(65153) = crosssum of X(43081) and X(56647)
X(65153) = barycentric product X(5854)*X(43055)

X(65154) =  97TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(6*a^8 - 7*a^6*b^2 - 5*a^4*b^4 + 7*a^2*b^6 - b^8 - 7*a^6*c^2 + 26*a^4*b^2*c^2 - 11*a^2*b^4*c^2 - 5*a^4*c^4 - 11*a^2*b^2*c^4 + 2*b^4*c^4 + 7*a^2*c^6 - c^8) : :
X(65154) = 3 X[403] + X[18533], X[403] + 3 X[37951], X[1596] + 3 X[44272], X[7426] + 3 X[26255], 3 X[7426] + X[37980], 3 X[10151] - X[44438], X[18533] - 9 X[37951], X[18534] + 3 X[44214], 9 X[26255] - X[37980], 3 X[37917] - X[37931], X[37934] + 2 X[64471], X[47097] - 3 X[47597], X[10602] - 3 X[47459]

See Antreas Hatzipolakis and Peter Moses, euclid 6933.

X(65154) lies on these lines: {2, 3}, {98, 47147}, {107, 16315}, {111, 16318}, {112, 16317}, {393, 47184}, {935, 47350}, {1289, 10102}, {1301, 2770}, {1304, 2374}, {2393, 11746}, {3233, 44099}, {3563, 47148}, {3564, 12828}, {7735, 47162}, {8263, 35259}, {8541, 20192}, {9060, 40120}, {9064, 40118}, {9084, 10423}, {9107, 53956}, {10192, 51742}, {10418, 60428}, {10602, 35260}, {10603, 32815}, {14984, 44084}, {15344, 53948}, {16303, 59229}, {17994, 47159}, {19128, 40114}, {19136, 41585}, {26864, 54218}, {30249, 53929}, {32269, 64724}, {35266, 44102}, {35904, 62382}, {36201, 47296}, {36898, 47172}, {40097, 53943}, {44662, 51725}, {47461, 64058}, {63181, 63646}

X(65154) = midpoint of X(25) and X(468)
X(65154) = reflection of X(i) in X(j) for these {i,j}: {1368, 37911}, {5159, 6677}
X(65154) = polar circle inverse of X(16051)
X(65154) = orthoptic-circle-of-the-Steiner-inellipse inverse of X(6623)
X(65154) = X(656)-isoconjugate of X(53961)
X(65154) = X(40596)-Dao conjugate of X(53961)
X(65154) = barycentric quotient X(112)/X(53961)
X(65154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 23, 16386}, {4, 186, 54995}, {25, 37917, 23}, {25, 47597, 4}, {25, 62966, 52301}, {403, 6353, 468}, {468, 10151, 2}, {468, 37904, 186}, {468, 37981, 37911}, {858, 6995, 13473}, {1596, 44241, 44438}, {1995, 7426, 16387}, {4232, 26255, 25}, {4232, 37962, 7426}, {6353, 37777, 403}, {7426, 37962, 468}, {37777, 37951, 25}, {37904, 47094, 23}, {44212, 44260, 6677}, {44212, 44272, 468}, {44212, 44273, 47597}

X(65155) =  X(2)X(15857)∩X(357)X(8065)

Barycentrics    3*Cot[A/3] - Tan[A/3] : :

See Antreas Hatzipolakis and Peter Moses, euclid 6964.

X(65155) lies on the Hatzipolakis-Moses-Morley hyperbola and these lines: {2, 15857}, {357, 8065}

X(65155) = isogonal conjugate of X(6120)
X(65155) = anticomplement of X(15857)
X(65155) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6120}, {3603, 5456}

X(65156) =  HATZIPOLAKIS-MOSES EQUILATERAL TRIANGLE CENTER

Barycentrics    (-Cos[B/3] + Cos[A/3]*Cos[C/3])*Sin[B] + (Cos[A/3]*Cos[B/3] - Cos[C/3])*Sin[C] : :

See Antreas Hatzipolakis and Peter Moses, euclid 6964.

X(65156) lies on this line: {2, 3276}

X(65156) = complement of X(3276)
X(65156) = complement of the isogonal conjugate of X(3606)
X(65156) = X(3606)-complementary conjugate of X(10)

X(65157) =  X(2)X(3276)∩X(5)X(3280)

Barycentrics    1 + (Cos[A/3] - Cos[B/3]*Cos[C/3])*(Cot[A] - Cot[w])*Csc[A] : :

See Antreas Hatzipolakis and Peter Moses, euclid 6968.

X(65157) lies on these lines: {2, 3276}, {5, 3280}, {140, 3281}, {3526, 8003}

X(65157) = perspector of the equilateral Hatzipolakis-Moses triangle with the Second Morley triangle

X(65158) =  X(357)X(5456)∩X(358)X(1136)

Barycentrics    Sin[A]*Tan[A/3]*((Cos[(2*A)/3] - Cos[(2*B)/3])*(Cos[C/3]*Sec[(A + 4*Pi)/3] - Cos[A/3]*Sec[(C + 4*Pi)/3])*Sin[C]*Tan[B/3] - (Cos[(2*A)/3] - Cos[(2*C)/3])*(Cos[B/3]*Sec[(A + 4*Pi)/3] - Cos[A/3]*Sec[(B + 4*Pi)/3])*Sin[B]*Tan[C/3]) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6970.

X(65158) lies on these lines: {357, 5456}, {358, 1136}, {1134, 3278}, {3602, 41111}, {5390, 5454}

X(65159) = TRILINEAR POLE OF LINE {40, 221}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3+a^2*(b+c)-(b-c)^2*(b+c)-a*(b+c)^2) : :

X(65159) lies on these lines: {7, 56233}, {40, 61493}, {56, 6068}, {57, 16578}, {100, 108}, {101, 651}, {109, 58991}, {144, 1804}, {190, 2406}, {198, 347}, {329, 7011}, {604, 23418}, {644, 56235}, {646, 4998}, {655, 65216}, {662, 65234}, {906, 32714}, {1014, 18645}, {1332, 4564}, {1445, 27396}, {1633, 2283}, {1696, 8232}, {1817, 64708}, {2324, 7013}, {2427, 52610}, {4606, 61240}, {5435, 17776}, {5546, 65232}, {7190, 47299}, {8732, 16593}, {11349, 22464}, {14733, 30237}, {21452, 37798}, {25737, 62669}, {26669, 62770}, {27508, 55119}, {27834, 37136}, {28739, 38869}, {30239, 65361}, {40212, 64082}, {55015, 55111}, {56549, 62798}

X(65159) = trilinear pole of line {40, 221}
X(65159) = perspector of circumconic {{A, B, C, X(7045), X(46102)}}
X(65159) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 36049}, {19, 61040}, {21, 55242}, {84, 650}, {189, 663}, {268, 7649}, {271, 6591}, {280, 649}, {282, 513}, {285, 661}, {309, 3063}, {514, 2192}, {521, 7129}, {522, 1436}, {652, 40836}, {657, 1440}, {667, 34404}, {693, 7118}, {798, 57795}, {905, 7008}, {1019, 53013}, {1021, 52384}, {1146, 8059}, {1256, 14298}, {1413, 3239}, {1422, 3900}, {1433, 3064}, {1459, 7003}, {1903, 3737}, {1919, 57793}, {1946, 64988}, {2170, 13138}, {2188, 17924}, {2208, 4391}, {2310, 37141}, {2357, 4560}, {2358, 57081}, {3270, 65330}, {3271, 44327}, {3676, 7367}, {4025, 7154}, {4163, 6612}, {4858, 32652}, {6332, 7151}, {7004, 40117}, {7020, 22383}, {7117, 65213}, {7252, 39130}, {8808, 21789}, {14331, 60803}, {14936, 53642}, {18344, 41081}, {35348, 56763}, {42069, 65179}, {55110, 57108}, {56972, 65103}
X(65159) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 61040}, {57, 514}, {281, 44426}, {5375, 280}, {5514, 11}, {6631, 34404}, {9296, 57793}, {10001, 309}, {16596, 4858}, {31998, 57795}, {36830, 285}, {39026, 282}, {39053, 64988}, {40611, 55242}, {55044, 1146}, {55063, 2968}, {61075, 24026}
X(65159) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 651}, {4564, 64082}, {4998, 7080}, {6516, 100}, {7045, 1103}
X(65159) = X(i)-cross conjugate of X(j) for these {i, j}: {1103, 7045}, {6129, 347}, {14298, 40}, {14837, 1817}, {55111, 59}, {57101, 7013}, {64885, 329}
X(65159) = pole of line {326, 3869} with respect to the Kiepert parabola
X(65159) = pole of line {1021, 23189} with respect to the Stammler hyperbola
X(65159) = pole of line {24025, 36949} with respect to the Steiner inellipse
X(65159) = pole of line {40, 329} with respect to the Yff parabola
X(65159) = pole of line {63, 77} with respect to the Hutson-Moses hyperbola
X(65159) = pole of line {651, 65160} with respect to the dual conic of incircle
X(65159) = pole of line {345, 17080} with respect to the dual conic of Feuerbach hyperbola
X(65159) = pole of line {59, 1155} with respect to the dual conic of Moses-Feuerbach circumconic
X(65159) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(40), X(23890)}}, {{A, B, C, X(100), X(1813)}}, {{A, B, C, X(101), X(56183)}}, {{A, B, C, X(108), X(1461)}}, {{A, B, C, X(329), X(24029)}}, {{A, B, C, X(347), X(41353)}}, {{A, B, C, X(646), X(7080)}}, {{A, B, C, X(651), X(1897)}}, {{A, B, C, X(653), X(934)}}, {{A, B, C, X(1020), X(61178)}}, {{A, B, C, X(1332), X(64082)}}, {{A, B, C, X(1817), X(4242)}}, {{A, B, C, X(2406), X(40212)}}, {{A, B, C, X(2804), X(16596)}}, {{A, B, C, X(3960), X(14837)}}, {{A, B, C, X(6129), X(53544)}}, {{A, B, C, X(6335), X(65296)}}, {{A, B, C, X(7011), X(23981)}}, {{A, B, C, X(30239), X(32714)}}
X(65159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {101, 1020, 651}, {108, 23067, 100}, {21362, 23890, 1461}

X(65160) = TRILINEAR POLE OF LINE {33, 200}

Barycentrics    (a-b)*(a-c)*(a-b-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65160) lies on these lines: {4, 10743}, {9, 7101}, {19, 16561}, {29, 4518}, {92, 30568}, {100, 40117}, {101, 1309}, {108, 6574}, {112, 9059}, {162, 65190}, {190, 653}, {243, 4009}, {278, 8055}, {281, 3161}, {318, 6559}, {346, 55116}, {412, 46937}, {522, 35349}, {644, 1783}, {648, 53658}, {664, 6332}, {1813, 44327}, {2322, 52409}, {2405, 4552}, {2415, 65337}, {2899, 5125}, {3064, 30720}, {3699, 4587}, {3732, 4391}, {4130, 21859}, {4578, 30730}, {4756, 61180}, {5081, 60431}, {5423, 44695}, {5546, 56112}, {6557, 17917}, {7046, 28120}, {8707, 58945}, {11109, 17916}, {14004, 64579}, {17923, 62297}, {17927, 46558}, {24036, 36123}, {25259, 26693}, {26003, 46108}, {26611, 52780}, {32704, 59095}, {34591, 51565}, {35341, 61236}, {36118, 65195}, {38462, 60355}, {41391, 45766}, {52412, 56078}, {56082, 64211}, {57168, 57220}, {65223, 65226}

X(65160) = trilinear pole of line {33, 200}
X(65160) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3669}, {7, 22383}, {27, 51640}, {34, 4091}, {48, 3676}, {56, 905}, {57, 1459}, {58, 51664}, {63, 43924}, {65, 7254}, {69, 57181}, {71, 7203}, {73, 1019}, {77, 649}, {109, 3942}, {184, 24002}, {212, 58817}, {219, 43932}, {222, 513}, {228, 17096}, {244, 1813}, {269, 652}, {278, 23224}, {279, 1946}, {283, 7216}, {307, 57129}, {348, 667}, {394, 43923}, {479, 65102}, {514, 603}, {520, 1396}, {521, 1407}, {522, 7099}, {525, 1408}, {604, 4025}, {608, 4131}, {647, 1014}, {650, 7053}, {651, 3937}, {656, 1412}, {663, 7177}, {693, 52411}, {738, 57108}, {757, 55234}, {764, 44717}, {810, 1434}, {849, 57243}, {906, 1358}, {934, 7117}, {1015, 6516}, {1086, 36059}, {1106, 6332}, {1111, 32660}, {1119, 36054}, {1214, 3733}, {1331, 53538}, {1332, 1357}, {1333, 17094}, {1364, 32714}, {1395, 30805}, {1397, 15413}, {1402, 15419}, {1409, 7192}, {1410, 4560}, {1413, 64885}, {1415, 1565}, {1427, 23189}, {1432, 22093}, {1435, 57241}, {1437, 7178}, {1439, 7252}, {1444, 7180}, {1461, 7004}, {1462, 53550}, {1790, 4017}, {1797, 53528}, {1803, 48151}, {1804, 6591}, {1812, 7250}, {1814, 53539}, {1919, 7182}, {1980, 57918}, {2006, 22379}, {2196, 43041}, {2221, 51644}, {2423, 62402}, {3049, 57785}, {3063, 7056}, {3248, 65164}, {3270, 4617}, {3271, 65296}, {3737, 52373}, {4554, 22096}, {4558, 53540}, {4565, 18210}, {4575, 53545}, {4790, 57701}, {6129, 55117}, {6611, 61040}, {6612, 57101}, {6614, 34591}, {7023, 57055}, {7125, 7649}, {7153, 22090}, {7335, 17924}, {7341, 55232}, {8641, 30682}, {8643, 27832}, {8677, 34051}, {9247, 52621}, {13149, 61054}, {14208, 16947}, {16726, 23067}, {17206, 51641}, {17925, 22341}, {18191, 52610}, {20615, 22154}, {20752, 43930}, {20780, 37626}, {21758, 52392}, {22086, 56049}, {22344, 60482}, {23086, 43051}, {23225, 34018}, {23226, 52374}, {30725, 36058}, {32658, 43042}, {35518, 52410}, {36057, 53544}, {40152, 57200}, {43925, 52385}, {52425, 59941}, {53542, 65300}, {57081, 62192}
X(65160) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 905}, {10, 51664}, {11, 3942}, {37, 17094}, {136, 53545}, {1146, 1565}, {1249, 3676}, {2968, 26932}, {3161, 4025}, {3162, 43924}, {4075, 57243}, {5190, 1358}, {5375, 77}, {5452, 1459}, {5521, 53538}, {6552, 6332}, {6600, 652}, {6631, 348}, {6741, 4466}, {7952, 514}, {9296, 7182}, {10001, 7056}, {11517, 4091}, {13999, 53546}, {14714, 7117}, {17073, 23727}, {20619, 30725}, {20620, 1086}, {20621, 53544}, {23050, 650}, {24771, 521}, {34961, 1790}, {35508, 7004}, {36103, 3669}, {38966, 2170}, {38991, 3937}, {39026, 222}, {39052, 1014}, {39053, 279}, {39060, 1088}, {39062, 1434}, {40181, 51644}, {40596, 1412}, {40599, 656}, {40602, 7254}, {40605, 15419}, {40607, 55234}, {40837, 58817}, {50441, 39470}, {55064, 18210}, {59577, 525}, {62576, 52621}, {62584, 30805}, {62585, 15413}, {62602, 59941}, {62605, 24002}, {62647, 4131}
X(65160) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6335, 1897}, {15742, 7046}, {36797, 56183}, {46102, 8}
X(65160) = X(i)-cross conjugate of X(j) for these {i, j}: {1018, 644}, {3064, 281}, {3239, 7101}, {3939, 3699}, {4163, 8}, {7046, 15742}, {18344, 29}, {40971, 7012}, {56183, 1897}, {57049, 346}
X(65160) = pole of line {1086, 1358} with respect to the polar circle
X(65160) = pole of line {3732, 61185} with respect to the Steiner circumellipse
X(65160) = pole of line {78, 280} with respect to the Yff parabola
X(65160) = pole of line {8, 7078} with respect to the Hutson-Moses hyperbola
X(65160) = pole of line {100, 108} with respect to the dual conic of incircle
X(65160) = pole of line {312, 27540} with respect to the dual conic of Feuerbach hyperbola
X(65160) = pole of line {16586, 24582} with respect to the dual conic of Suppa-Cucoanes circle
X(65160) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(664)}}, {{A, B, C, X(9), X(101)}}, {{A, B, C, X(162), X(9107)}}, {{A, B, C, X(190), X(644)}}, {{A, B, C, X(210), X(21859)}}, {{A, B, C, X(341), X(56252)}}, {{A, B, C, X(346), X(42718)}}, {{A, B, C, X(653), X(1783)}}, {{A, B, C, X(668), X(36802)}}, {{A, B, C, X(1000), X(53898)}}, {{A, B, C, X(1018), X(3939)}}, {{A, B, C, X(1309), X(1897)}}, {{A, B, C, X(2415), X(3161)}}, {{A, B, C, X(3064), X(8735)}}, {{A, B, C, X(3699), X(3952)}}, {{A, B, C, X(4163), X(6332)}}, {{A, B, C, X(4534), X(30725)}}, {{A, B, C, X(5548), X(59095)}}, {{A, B, C, X(5853), X(28915)}}, {{A, B, C, X(8750), X(58945)}}, {{A, B, C, X(12641), X(39444)}}, {{A, B, C, X(18086), X(33950)}}, {{A, B, C, X(23704), X(56536)}}, {{A, B, C, X(31624), X(36796)}}, {{A, B, C, X(32635), X(37138)}}, {{A, B, C, X(36118), X(65333)}}, {{A, B, C, X(53647), X(60488)}}
X(65160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 6335, 653}, {3699, 36797, 65193}

X(65161) = ANTICOMPLEMENT OF X(16726)

Barycentrics    (a-b)*b*(a-c)*c*(2*a+b+c) : :
X(65161) = -2*X[3122]+3*X[24517]

X(65161) lies on these lines: {2, 16723}, {6, 18046}, {9, 18040}, {10, 23823}, {37, 26799}, {44, 18073}, {63, 29508}, {69, 18137}, {75, 1654}, {76, 17346}, {99, 15322}, {100, 46961}, {190, 646}, {193, 18147}, {239, 39995}, {274, 31144}, {312, 2895}, {313, 4416}, {319, 4043}, {320, 3975}, {321, 4690}, {333, 27792}, {341, 1330}, {350, 62231}, {391, 44147}, {513, 53338}, {514, 65191}, {524, 3948}, {527, 3264}, {536, 25298}, {573, 29711}, {579, 29507}, {645, 4585}, {651, 37218}, {662, 799}, {666, 57975}, {670, 27853}, {894, 29388}, {1213, 16709}, {1227, 4858}, {1230, 3578}, {1269, 3686}, {1332, 42719}, {1655, 4664}, {1743, 18044}, {1909, 17256}, {1992, 18135}, {2475, 44720}, {2796, 4783}, {2893, 59201}, {3122, 24517}, {3248, 17793}, {3257, 65229}, {3596, 17347}, {3699, 61220}, {3718, 20444}, {3739, 26857}, {3758, 6376}, {3759, 29764}, {3909, 3952}, {3963, 17332}, {3973, 18065}, {4358, 17374}, {4359, 4410}, {4383, 18739}, {4427, 61174}, {4552, 46480}, {4586, 54957}, {4670, 59212}, {4687, 26110}, {4751, 26045}, {5224, 34283}, {6335, 65170}, {7199, 40529}, {8025, 62588}, {9359, 24487}, {14829, 29490}, {16574, 29395}, {16696, 26772}, {17144, 50077}, {17277, 18143}, {17330, 20913}, {17335, 20917}, {17336, 17786}, {17341, 41876}, {17344, 20891}, {17345, 20892}, {17348, 29756}, {17349, 18144}, {17350, 29423}, {17351, 29705}, {17361, 20923}, {17370, 27320}, {17371, 27270}, {17372, 22016}, {17376, 29982}, {17378, 30830}, {17387, 17778}, {17781, 30713}, {17790, 20072}, {17794, 25048}, {18136, 32911}, {18140, 46922}, {18164, 29559}, {20090, 25660}, {20956, 35550}, {21100, 60725}, {21278, 64581}, {21287, 46738}, {21591, 30807}, {23354, 40521}, {24625, 25534}, {24957, 25472}, {25278, 50107}, {26563, 30892}, {26764, 59715}, {28931, 44148}, {29477, 30882}, {30729, 61170}, {30829, 37635}, {30963, 40721}, {31060, 50074}, {35177, 35181}, {36269, 52044}, {44140, 63001}, {52609, 65195}, {54986, 65280}, {60736, 64712}

X(65161) = reflection of X(i) in X(j) for these {i,j}: {30939, 3948}
X(65161) = isotomic conjugate of X(47947)
X(65161) = anticomplement of X(16726)
X(65161) = trilinear pole of line {1125, 1962}
X(65161) = perspector of circumconic {{A, B, C, X(7035), X(24037)}}
X(65161) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 50344}, {31, 47947}, {32, 4608}, {58, 58294}, {81, 58301}, {513, 28615}, {649, 1126}, {667, 1255}, {669, 32014}, {798, 40438}, {1015, 8701}, {1268, 1919}, {1977, 6540}, {1980, 32018}, {2206, 31010}, {2489, 57685}, {3121, 4596}, {3122, 4629}, {3124, 6578}, {3248, 37212}, {3733, 52555}, {4079, 52558}, {5029, 53688}, {8054, 59014}, {32635, 57181}, {33635, 43924}, {57204, 57854}
X(65161) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 47947}, {9, 50344}, {10, 58294}, {1100, 2605}, {1125, 661}, {1213, 513}, {3120, 3125}, {3634, 48019}, {3647, 649}, {4359, 4129}, {5375, 1126}, {6376, 4608}, {6631, 1255}, {9296, 1268}, {16726, 16726}, {21709, 21833}, {31998, 40438}, {35076, 244}, {39026, 28615}, {39054, 1171}, {40586, 58301}, {40603, 31010}, {44307, 47918}, {56846, 3669}, {59592, 650}, {62588, 514}
X(65161) = X(i)-Ceva conjugate of X(j) for these {i, j}: {668, 61174}, {4601, 75}, {7035, 6533}
X(65161) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {42, 54102}, {59, 3875}, {101, 17154}, {765, 75}, {1016, 17135}, {1018, 149}, {1110, 17147}, {1252, 1}, {1334, 17036}, {3952, 150}, {4033, 21293}, {4069, 37781}, {4076, 20245}, {4103, 3448}, {4557, 4440}, {4559, 58371}, {4564, 3873}, {4567, 17140}, {4570, 4360}, {4600, 17143}, {4998, 20244}, {5376, 17145}, {5378, 30941}, {5385, 17146}, {6065, 63}, {6551, 53333}, {6632, 512}, {6635, 53368}, {7035, 17137}, {7045, 17158}, {9268, 17160}, {15742, 17220}, {23990, 17148}, {30730, 33650}, {31625, 17138}, {40521, 21221}, {57731, 7192}, {57950, 17217}, {59149, 523}, {61402, 1330}
X(65161) = X(i)-cross conjugate of X(j) for these {i, j}: {4115, 4427}, {4977, 16709}, {4978, 4359}, {4979, 1125}, {4985, 1269}, {6533, 7035}, {30591, 75}
X(65161) = pole of line {23947, 50319} with respect to the Kiepert hyperbola
X(65161) = pole of line {4360, 17103} with respect to the Kiepert parabola
X(65161) = pole of line {798, 33882} with respect to the Stammler hyperbola
X(65161) = pole of line {3952, 4010} with respect to the Steiner circumellipse
X(65161) = pole of line {4145, 21254} with respect to the Steiner inellipse
X(65161) = pole of line {1, 596} with respect to the Yff parabola
X(65161) = pole of line {75, 26223} with respect to the Hutson-Moses hyperbola
X(65161) = pole of line {661, 1019} with respect to the Wallace hyperbola
X(65161) = pole of line {3708, 3942} with respect to the dual conic of polar circle
X(65161) = pole of line {4033, 4552} with respect to the dual conic of DeLongchamps ellipse
X(65161) = pole of line {5219, 18044} with respect to the dual conic of Feuerbach hyperbola
X(65161) = pole of line {99, 100} with respect to the dual conic of Hofstadter ellipse
X(65161) = intersection, other than A, B, C, of circumconics {{A, B, C, X(190), X(4427)}}, {{A, B, C, X(646), X(4631)}}, {{A, B, C, X(662), X(1018)}}, {{A, B, C, X(668), X(4623)}}, {{A, B, C, X(799), X(4033)}}, {{A, B, C, X(812), X(4977)}}, {{A, B, C, X(874), X(16709)}}, {{A, B, C, X(1125), X(23891)}}, {{A, B, C, X(1213), X(3570)}}, {{A, B, C, X(1269), X(57975)}}, {{A, B, C, X(3257), X(3882)}}, {{A, B, C, X(3578), X(4585)}}, {{A, B, C, X(3762), X(4978)}}, {{A, B, C, X(3768), X(4979)}}, {{A, B, C, X(3952), X(37205)}}, {{A, B, C, X(4359), X(24004)}}, {{A, B, C, X(4440), X(35511)}}, {{A, B, C, X(4505), X(54957)}}, {{A, B, C, X(4647), X(24039)}}, {{A, B, C, X(6558), X(30729)}}, {{A, B, C, X(16726), X(21385)}}, {{A, B, C, X(16732), X(30591)}}, {{A, B, C, X(31900), X(46499)}}, {{A, B, C, X(35339), X(37212)}}
X(65161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 18133, 18046}, {9, 18040, 29396}, {190, 4033, 24004}, {190, 668, 4033}, {524, 3948, 30939}, {894, 56249, 29388}, {1654, 3770, 75}, {17277, 18143, 29446}, {17277, 44139, 18143}, {17336, 17786, 29712}, {17349, 18144, 29484}, {17350, 30473, 29423}

X(65162) = X(19)X(27)∩X(99)X(112)

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+b*c-c^2)*(a^2-b^2+c^2) : :
X(65162) = -3*X[2]+2*X[42761]

X(65162) lies on these lines: {2, 42761}, {4, 53792}, {19, 27}, {99, 112}, {190, 653}, {655, 65223}, {823, 65236}, {901, 1309}, {1281, 41499}, {1332, 32714}, {1783, 33951}, {1857, 44446}, {1897, 65166}, {2397, 31615}, {2399, 2406}, {3573, 5379}, {4427, 36797}, {4585, 53045}, {6012, 26706}, {7017, 32933}, {13149, 65164}, {20294, 53160}, {29163, 58993}, {30566, 37768}, {32674, 33946}, {46102, 62669}, {57456, 65336}, {65270, 65290}, {65331, 65344}

X(65162) = anticomplement of X(42761)
X(65162) = trilinear pole of line {860, 1870}
X(65162) = perspector of circumconic {{A, B, C, X(811), X(18020)}}
X(65162) = X(i)-isoconjugate-of-X(j) for these {i, j}: {80, 22383}, {125, 32671}, {184, 60074}, {513, 52431}, {647, 759}, {649, 1807}, {652, 1411}, {656, 34079}, {661, 57736}, {667, 52351}, {798, 57985}, {810, 24624}, {905, 6187}, {1168, 22086}, {1437, 55238}, {1459, 2161}, {1793, 7180}, {1946, 2006}, {1989, 23226}, {2222, 7117}, {2611, 32662}, {3049, 14616}, {3063, 52392}, {3271, 65299}, {3708, 36069}, {7004, 32675}, {7252, 52391}, {7254, 34857}, {14582, 17104}, {14838, 52153}, {20975, 37140}, {20982, 36061}, {22094, 32678}, {22096, 36804}, {23224, 64835}, {32655, 61039}, {32677, 61041}, {50433, 54244}, {52356, 52411}, {52380, 55234}, {61054, 65329}
X(65162) = X(i)-Dao conjugate of X(j) for these {i, j}: {44, 53532}, {2245, 8677}, {5375, 1807}, {6631, 52351}, {7359, 9033}, {10001, 52392}, {13999, 2170}, {16221, 20982}, {18334, 22094}, {23986, 61041}, {31998, 57985}, {34544, 23226}, {34586, 647}, {35069, 656}, {35128, 7004}, {35204, 652}, {36830, 57736}, {38982, 3708}, {38984, 7117}, {39026, 52431}, {39052, 759}, {39053, 2006}, {39060, 18815}, {39062, 24624}, {40584, 1459}, {40596, 34079}, {40612, 905}, {42761, 42761}, {46974, 46391}, {51583, 525}, {53982, 661}, {56847, 14582}, {57434, 34591}, {62605, 60074}
X(65162) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16077, 36797}, {65223, 6335}
X(65162) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1309, 21294}, {14776, 21221}, {36037, 13219}
X(65162) = pole of line {23864, 53273} with respect to the circumcircle
X(65162) = pole of line {115, 661} with respect to the polar circle
X(65162) = pole of line {69, 347} with respect to the Kiepert parabola
X(65162) = pole of line {48, 647} with respect to the Stammler hyperbola
X(65162) = pole of line {110, 1309} with respect to the Steiner circumellipse
X(65162) = pole of line {5972, 8062} with respect to the Steiner inellipse
X(65162) = pole of line {78, 1330} with respect to the Yff parabola
X(65162) = pole of line {63, 525} with respect to the Wallace hyperbola
X(65162) = pole of line {4552, 46102} with respect to the dual conic of incircle
X(65162) = pole of line {15526, 24018} with respect to the dual conic of polar circle
X(65162) = pole of line {312, 28754} with respect to the dual conic of Feuerbach hyperbola
X(65162) = pole of line {2, 6335} with respect to the dual conic of Jerabek hyperbola
X(65162) = pole of line {99, 36067} with respect to the dual conic of Orthic inconic
X(65162) = pole of line {664, 14208} with respect to the dual conic of Hofstadter ellipse
X(65162) = intersection, other than A, B, C, of circumconics {{A, B, C, X(19), X(112)}}, {{A, B, C, X(27), X(653)}}, {{A, B, C, X(63), X(4558)}}, {{A, B, C, X(75), X(99)}}, {{A, B, C, X(92), X(648)}}, {{A, B, C, X(190), X(333)}}, {{A, B, C, X(286), X(18026)}}, {{A, B, C, X(320), X(35157)}}, {{A, B, C, X(655), X(901)}}, {{A, B, C, X(666), X(20924)}}, {{A, B, C, X(758), X(8680)}}, {{A, B, C, X(860), X(4235)}}, {{A, B, C, X(877), X(40703)}}, {{A, B, C, X(1309), X(17923)}}, {{A, B, C, X(1748), X(41679)}}, {{A, B, C, X(1755), X(2245)}}, {{A, B, C, X(1760), X(4611)}}, {{A, B, C, X(1761), X(57062)}}, {{A, B, C, X(1762), X(57251)}}, {{A, B, C, X(1983), X(4269)}}, {{A, B, C, X(2397), X(2399)}}, {{A, B, C, X(2407), X(3936)}}, {{A, B, C, X(2799), X(6370)}}, {{A, B, C, X(4552), X(14213)}}, {{A, B, C, X(6335), X(31623)}}, {{A, B, C, X(13136), X(32851)}}, {{A, B, C, X(14590), X(52414)}}, {{A, B, C, X(16568), X(52630)}}, {{A, B, C, X(18593), X(60056)}}, {{A, B, C, X(18750), X(36841)}}, {{A, B, C, X(20883), X(41676)}}, {{A, B, C, X(29163), X(61233)}}, {{A, B, C, X(36100), X(64828)}}, {{A, B, C, X(51583), X(57456)}}
X(65162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 653, 6335}, {3573, 23353, 5379}, {4427, 61180, 36797}

X(65163) = ISOGONAL CONJUGATE OF X(17217)

Barycentrics    a^2*(a-b)*(a-c)*(b+c)*(a*(b-c)-b*c)*(a*(b-c)+b*c) : :

X(65163) lies on these lines: {55, 1911}, {87, 8053}, {99, 59094}, {100, 932}, {330, 23370}, {643, 23864}, {667, 61235}, {669, 3952}, {692, 34071}, {799, 16695}, {813, 58981}, {1283, 8843}, {2053, 6187}, {2177, 7121}, {2223, 40881}, {2319, 15621}, {4436, 18830}, {4557, 61164}, {5383, 23400}, {6384, 16678}, {7234, 7239}, {8616, 33784}, {8683, 43931}, {8709, 35572}, {16606, 21856}, {16681, 27424}, {20475, 34252}, {21759, 64169}, {23385, 24524}, {37619, 52211}, {40720, 61155}, {43077, 58958}

X(65163) = isogonal conjugate of X(17217)
X(65163) = trilinear pole of line {213, 6378}
X(65163) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 17217}, {2, 18197}, {27, 25098}, {43, 7192}, {57, 27527}, {58, 20906}, {63, 17921}, {75, 16695}, {76, 57074}, {81, 3835}, {86, 4083}, {92, 23092}, {99, 3123}, {100, 23824}, {190, 16742}, {192, 1019}, {244, 62530}, {274, 20979}, {286, 22090}, {310, 8640}, {333, 43051}, {513, 33296}, {514, 27644}, {649, 31008}, {662, 21138}, {670, 38986}, {693, 38832}, {757, 21051}, {799, 6377}, {873, 50491}, {1014, 4147}, {1015, 36860}, {1403, 18155}, {1423, 4560}, {1509, 21834}, {2176, 7199}, {2209, 52619}, {3208, 17096}, {3212, 3737}, {3676, 56181}, {3733, 6376}, {4481, 52136}, {4595, 16726}, {4602, 21762}, {4992, 40438}, {6382, 57129}, {7203, 27538}, {7252, 30545}, {7253, 62791}, {7255, 41886}, {16696, 18107}, {17205, 52923}, {17218, 20287}, {17925, 22370}, {18169, 63224}, {18200, 63486}, {21835, 52612}, {22386, 57968}, {24533, 32010}, {27346, 53083}, {40432, 64865}, {40848, 50456}, {48008, 65076}
X(65163) = X(i)-vertex conjugate of X(j) for these {i, j}: {190, 4598}, {799, 799}, {4573, 4633}, {4584, 4603}, {4610, 4632}, {18830, 65185}, {56053, 62530}, {61234, 65167}
X(65163) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 17217}, {10, 20906}, {206, 16695}, {1084, 21138}, {3162, 17921}, {5375, 31008}, {5452, 27527}, {8054, 23824}, {22391, 23092}, {32664, 18197}, {36830, 7304}, {38986, 3123}, {38996, 6377}, {39026, 33296}, {40586, 3835}, {40600, 4083}, {40607, 21051}, {55053, 16742}, {62574, 52619}, {63618, 693}
X(65163) = X(i)-Ceva conjugate of X(j) for these {i, j}: {932, 65167}, {59094, 4598}
X(65163) = X(i)-cross conjugate of X(j) for these {i, j}: {1018, 4557}, {1924, 6}, {9491, 1918}, {22229, 37}
X(65163) = pole of line {190, 4598} with respect to the circumcircle
X(65163) = pole of line {4992, 16695} with respect to the Stammler hyperbola
X(65163) = pole of line {2176, 23546} with respect to the Hutson-Moses hyperbola
X(65163) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(799)}}, {{A, B, C, X(25), X(46597)}}, {{A, B, C, X(31), X(34594)}}, {{A, B, C, X(42), X(3952)}}, {{A, B, C, X(55), X(643)}}, {{A, B, C, X(99), X(53268)}}, {{A, B, C, X(100), X(692)}}, {{A, B, C, X(803), X(4586)}}, {{A, B, C, X(813), X(4559)}}, {{A, B, C, X(835), X(32739)}}, {{A, B, C, X(1018), X(4595)}}, {{A, B, C, X(1924), X(16695)}}, {{A, B, C, X(2162), X(58981)}}, {{A, B, C, X(4598), X(34071)}}, {{A, B, C, X(8707), X(34067)}}, {{A, B, C, X(21051), X(22229)}}, {{A, B, C, X(23864), X(63461)}}, {{A, B, C, X(27805), X(39967)}}, {{A, B, C, X(52139), X(54325)}}
X(65163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 932, 4598}

X(65164) = ISOTOMIC CONJUGATE OF X(3064)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2-b^2-c^2) : :

X(65164) lies on these lines: {7, 30741}, {9, 30796}, {57, 17755}, {63, 7182}, {69, 2968}, {76, 56550}, {85, 55416}, {99, 109}, {100, 883}, {190, 658}, {222, 20742}, {226, 8781}, {296, 332}, {304, 7183}, {305, 56553}, {307, 30774}, {325, 16091}, {326, 62765}, {333, 52421}, {345, 7055}, {349, 40832}, {644, 4617}, {645, 44326}, {651, 37215}, {653, 799}, {668, 53642}, {813, 34083}, {934, 53332}, {1231, 17206}, {1331, 4025}, {1332, 52610}, {1813, 4563}, {2898, 44446}, {3218, 40704}, {3266, 56560}, {3699, 4998}, {3718, 7013}, {3952, 56543}, {4427, 35312}, {4561, 4571}, {4576, 65315}, {4598, 65237}, {4620, 55235}, {4631, 41206}, {4781, 61192}, {6063, 32939}, {6393, 51368}, {6649, 14594}, {7004, 31637}, {12215, 17975}, {13149, 65162}, {17336, 62704}, {20940, 34234}, {23691, 56383}, {30228, 38357}, {32933, 61413}, {33952, 63203}, {34085, 37206}, {40152, 57799}, {41353, 61223}, {52608, 55205}, {56549, 57518}

X(65164) = isotomic conjugate of X(3064)
X(65164) = trilinear pole of line {69, 73}
X(65164) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 3063}, {6, 18344}, {19, 663}, {21, 2489}, {25, 650}, {27, 63461}, {28, 3709}, {29, 798}, {31, 3064}, {32, 44426}, {33, 649}, {34, 657}, {41, 7649}, {55, 6591}, {56, 65103}, {58, 55206}, {108, 14936}, {112, 4516}, {210, 43925}, {220, 43923}, {270, 4079}, {278, 8641}, {281, 667}, {314, 57204}, {318, 1919}, {393, 1946}, {512, 1172}, {513, 607}, {514, 2212}, {521, 2207}, {522, 1973}, {523, 2204}, {560, 46110}, {608, 3900}, {644, 42067}, {652, 1096}, {661, 2299}, {669, 31623}, {692, 8735}, {810, 8748}, {884, 5089}, {905, 6059}, {926, 8751}, {1015, 56183}, {1021, 57652}, {1024, 2356}, {1039, 2484}, {1118, 65102}, {1119, 57180}, {1334, 57200}, {1395, 3239}, {1396, 4524}, {1398, 4130}, {1402, 17926}, {1415, 42069}, {1435, 4105}, {1474, 4041}, {1783, 3271}, {1824, 7252}, {1857, 22383}, {1880, 21789}, {1896, 3049}, {1918, 57215}, {1924, 44130}, {1974, 4391}, {1980, 7017}, {2161, 58313}, {2170, 8750}, {2175, 17924}, {2189, 4705}, {2193, 58757}, {2194, 2501}, {2203, 3700}, {2310, 32674}, {2322, 51641}, {2328, 55208}, {2332, 4017}, {2333, 3737}, {2971, 4612}, {3022, 32714}, {3121, 36797}, {3122, 65201}, {3124, 52914}, {3248, 65160}, {3669, 7071}, {4117, 55233}, {4183, 7180}, {4631, 42068}, {4895, 8752}, {5379, 63462}, {6129, 7154}, {6186, 65105}, {6187, 65104}, {6524, 36054}, {7046, 57181}, {7063, 55231}, {7079, 43924}, {7118, 54239}, {7151, 14298}, {7337, 57055}, {8638, 54235}, {8648, 64835}, {9447, 46107}, {13149, 61050}, {21044, 32676}, {24006, 57657}, {32713, 53560}, {35518, 36417}, {36124, 46388}, {37908, 55261}, {39109, 58888}, {40976, 62749}, {40982, 62748}, {40983, 62747}, {44100, 47915}, {46103, 50487}, {51858, 65106}, {53008, 57129}, {53581, 57779}
X(65164) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 65103}, {2, 3064}, {6, 663}, {9, 18344}, {10, 55206}, {63, 46389}, {223, 6591}, {226, 661}, {905, 42462}, {1086, 8735}, {1146, 42069}, {1214, 2501}, {3160, 7649}, {3239, 23615}, {5375, 33}, {6337, 522}, {6338, 6332}, {6374, 46110}, {6376, 44426}, {6503, 652}, {6505, 650}, {6631, 281}, {7358, 3119}, {9296, 318}, {9428, 44130}, {10001, 4}, {11517, 657}, {15526, 21044}, {26932, 2170}, {31998, 29}, {34021, 57215}, {34591, 4516}, {34961, 2332}, {35072, 2310}, {36033, 3063}, {36830, 2299}, {36908, 55208}, {38983, 14936}, {39006, 3271}, {39026, 607}, {39053, 393}, {39054, 1172}, {39060, 158}, {39062, 8748}, {40584, 58313}, {40591, 3709}, {40593, 17924}, {40605, 17926}, {40611, 2489}, {40612, 65104}, {40615, 2969}, {40618, 11}, {40626, 1146}, {47345, 58757}, {51574, 4041}, {52881, 14432}, {62564, 3700}, {62565, 523}, {62569, 14400}, {62570, 24006}, {62584, 3239}, {62604, 35519}, {62613, 52956}, {62614, 4086}, {62647, 3900}
X(65164) = X(i)-Ceva conjugate of X(j) for these {i, j}: {799, 4554}, {4572, 664}, {4620, 52565}
X(65164) = X(i)-cross conjugate of X(j) for these {i, j}: {345, 4998}, {1332, 4561}, {1813, 664}, {4025, 7182}, {6332, 69}, {15413, 17206}, {22443, 3}, {30805, 304}, {52565, 4620}, {52616, 7055}, {57242, 305}, {57243, 307}, {57245, 3718}, {65233, 6516}
X(65164) = pole of line {333, 24635} with respect to the Kiepert parabola
X(65164) = pole of line {663, 51726} with respect to the Stammler hyperbola
X(65164) = pole of line {200, 1742} with respect to the Yff parabola
X(65164) = pole of line {17257, 26658} with respect to the Hutson-Moses hyperbola
X(65164) = pole of line {243, 522} with respect to the Wallace hyperbola
X(65164) = pole of line {11, 1146} with respect to the dual conic of polar circle
X(65164) = pole of line {75, 7318} with respect to the dual conic of Feuerbach hyperbola
X(65164) = pole of line {1332, 52610} with respect to the dual conic of Orthic inconic
X(65164) = pole of line {4554, 18740} with respect to the dual conic of Hofstadter ellipse
X(65164) = pole of line {44717, 57750} with respect to the dual conic of Moses-Feuerbach circumconic
X(65164) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7462)}}, {{A, B, C, X(63), X(1025)}}, {{A, B, C, X(99), X(4554)}}, {{A, B, C, X(109), X(296)}}, {{A, B, C, X(190), X(643)}}, {{A, B, C, X(304), X(1978)}}, {{A, B, C, X(332), X(4631)}}, {{A, B, C, X(345), X(3699)}}, {{A, B, C, X(525), X(2785)}}, {{A, B, C, X(658), X(1414)}}, {{A, B, C, X(664), X(46404)}}, {{A, B, C, X(799), X(4592)}}, {{A, B, C, X(813), X(906)}}, {{A, B, C, X(2968), X(6332)}}, {{A, B, C, X(3926), X(55254)}}, {{A, B, C, X(4025), X(23829)}}, {{A, B, C, X(4235), X(30774)}}, {{A, B, C, X(4569), X(4573)}}, {{A, B, C, X(4587), X(35341)}}, {{A, B, C, X(4610), X(46406)}}, {{A, B, C, X(13149), X(54953)}}
X(65164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 883, 65199}, {190, 658, 4554}, {345, 50559, 7055}, {3699, 65165, 4998}

X(65165) = X(7)X(3035)∩X(100)X(658)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(3*a^2-(b-c)^2-2*a*(b+c)) : :

X(65165) lies on these lines: {7, 3035}, {85, 64112}, {100, 658}, {144, 13609}, {149, 62723}, {150, 13226}, {165, 31627}, {190, 53640}, {226, 21948}, {348, 64108}, {883, 43290}, {927, 1293}, {1025, 4763}, {1054, 56783}, {1331, 7045}, {3306, 55082}, {3699, 4998}, {3939, 4626}, {4025, 25724}, {4421, 31526}, {4554, 65166}, {5435, 16593}, {5744, 33298}, {6604, 51583}, {9352, 33765}, {18026, 58135}, {21453, 27003}, {22003, 24052}, {23703, 65188}, {25737, 53337}, {35258, 62704}, {35341, 42303}, {37139, 37206}, {41353, 61222}, {47374, 47375}, {50559, 64083}, {53642, 53658}, {53659, 54953}, {65222, 65242}

X(65165) = trilinear pole of line {144, 1419}
X(65165) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 19605}, {650, 11051}, {657, 64980}, {663, 3062}, {667, 63165}, {884, 56718}, {2310, 53622}, {3063, 10405}, {4130, 61380}, {8641, 36620}, {14936, 61240}, {57180, 60831}
X(65165) = X(i)-Dao conjugate of X(j) for these {i, j}: {7, 514}, {5375, 19605}, {6631, 63165}, {7658, 23615}, {10001, 10405}, {13609, 11}
X(65165) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 664}, {4998, 64083}
X(65165) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58108, 37781}
X(65165) = X(i)-cross conjugate of X(j) for these {i, j}: {7658, 31627}, {58877, 64083}
X(65165) = pole of line {144, 165} with respect to the Yff parabola
X(65165) = pole of line {220, 61006} with respect to the Hutson-Moses hyperbola
X(65165) = pole of line {346, 348} with respect to the dual conic of Feuerbach hyperbola
X(65165) = pole of line {527, 1275} with respect to the dual conic of Moses-Feuerbach circumconic
X(65165) = intersection, other than A, B, C, of circumconics {{A, B, C, X(144), X(37206)}}, {{A, B, C, X(165), X(1293)}}, {{A, B, C, X(658), X(53640)}}, {{A, B, C, X(664), X(30610)}}, {{A, B, C, X(934), X(61240)}}, {{A, B, C, X(2398), X(3699)}}, {{A, B, C, X(6366), X(13609)}}, {{A, B, C, X(6516), X(58135)}}, {{A, B, C, X(7658), X(43042)}}, {{A, B, C, X(16284), X(53659)}}, {{A, B, C, X(18006), X(55285)}}
X(65165) = barycentric product X(i)*X(j) for these (i, j): {57, 62533}, {100, 31627}, {101, 50560}, {144, 664}, {165, 4554}, {190, 3160}, {1419, 668}, {1897, 50559}, {3207, 4572}, {3699, 9533}, {4620, 55285}, {4998, 7658}, {16284, 651}, {17106, 646}, {21060, 4573}, {21872, 4625}, {22117, 46404}, {50561, 644}, {50562, 643}, {50563, 648}, {57064, 59457}, {63965, 65164}, {64083, 658}
X(65165) = barycentric quotient X(i)/X(j) for these (i, j): {100, 19605}, {109, 11051}, {144, 522}, {165, 650}, {190, 63165}, {651, 3062}, {658, 36620}, {664, 10405}, {934, 64980}, {1025, 56718}, {1262, 53622}, {1275, 53640}, {1419, 513}, {3160, 514}, {3207, 663}, {4554, 44186}, {4620, 55284}, {4626, 60831}, {6614, 61380}, {7045, 61240}, {7658, 11}, {9533, 3676}, {13609, 23615}, {16284, 4391}, {17106, 3669}, {21060, 3700}, {21872, 4041}, {22117, 652}, {31627, 693}, {50559, 4025}, {50560, 3261}, {50561, 24002}, {50562, 4077}, {50563, 525}, {55285, 21044}, {57064, 4081}, {58835, 3119}, {58877, 13609}, {62533, 312}, {63965, 3064}, {64083, 3239}, {65174, 59170}, {65188, 62544}
X(65165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 35312, 65194}, {100, 56543, 658}, {100, 658, 664}, {658, 65194, 35312}, {4998, 65164, 3699}

X(65166) = X(99)X(109)∩X(100)X(190)

Barycentrics    (a-b)*(a-c)*(3*a+b+c) : :

X(65166) lies on these lines: {2, 59580}, {8, 6154}, {35, 63996}, {55, 24349}, {63, 3996}, {65, 52352}, {75, 35258}, {99, 109}, {100, 190}, {110, 46961}, {149, 51583}, {165, 312}, {171, 3993}, {192, 37540}, {333, 3696}, {345, 9778}, {516, 32851}, {644, 35326}, {653, 36797}, {668, 58135}, {835, 901}, {846, 3842}, {874, 65185}, {883, 65194}, {894, 4689}, {902, 32845}, {903, 33148}, {931, 6013}, {1018, 28521}, {1043, 56288}, {1054, 4432}, {1155, 3685}, {1220, 24850}, {1279, 62300}, {1293, 8707}, {1420, 64563}, {1739, 33309}, {1897, 65162}, {1979, 17475}, {1999, 49461}, {2651, 30606}, {2796, 17719}, {3035, 4997}, {3052, 3210}, {3120, 25529}, {3474, 18134}, {3550, 32926}, {3579, 7283}, {3689, 62222}, {3712, 4645}, {3719, 10860}, {3722, 24841}, {3729, 35445}, {3756, 30577}, {3759, 36277}, {3888, 61172}, {3896, 41629}, {3914, 41806}, {3923, 17601}, {3977, 32850}, {3980, 40328}, {4000, 35261}, {4234, 4424}, {4360, 17126}, {4385, 59316}, {4387, 63212}, {4398, 26228}, {4414, 5263}, {4417, 44447}, {4421, 32937}, {4422, 26073}, {4440, 17724}, {4450, 33168}, {4512, 19804}, {4554, 65165}, {4597, 58133}, {4598, 65250}, {4650, 49678}, {4652, 4673}, {4773, 30728}, {4779, 64142}, {4819, 4831}, {4970, 41823}, {4975, 5131}, {5087, 59581}, {5195, 6390}, {5218, 24280}, {5233, 5698}, {5724, 51678}, {6014, 8706}, {6790, 9945}, {7081, 63211}, {7270, 31730}, {8720, 37588}, {9059, 28218}, {11246, 29839}, {14594, 23703}, {14829, 32929}, {15326, 60452}, {16706, 35263}, {17273, 33175}, {17277, 62838}, {17285, 33086}, {17593, 49482}, {17596, 32942}, {17764, 33140}, {20292, 41878}, {24542, 27191}, {24627, 49484}, {24723, 30832}, {25256, 25733}, {25568, 44446}, {25577, 61234}, {25728, 46917}, {25734, 64135}, {26139, 43055}, {26629, 41842}, {28530, 37759}, {28808, 64108}, {28956, 64154}, {29641, 59536}, {30567, 63207}, {30829, 64112}, {32025, 46918}, {32042, 35339}, {33068, 59692}, {33073, 59547}, {33118, 59544}, {33337, 41529}, {34594, 53637}, {35280, 53332}, {35338, 61223}, {35466, 62392}, {36086, 37215}, {37593, 42028}, {42033, 50808}, {42314, 51355}, {53534, 58371}, {53659, 58134}, {55095, 64010}, {61186, 65189}, {65225, 65230}

X(65166) = reflection of X(i) in X(j) for these {i,j}: {33140, 59665}
X(65166) = isotomic conjugate of X(58860)
X(65166) = anticomplement of X(62221)
X(65166) = trilinear pole of line {391, 1449}
X(65166) = perspector of circumconic {{A, B, C, X(1016), X(4620)}}
X(65166) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 47915}, {31, 58860}, {244, 8694}, {513, 2334}, {649, 25430}, {667, 5936}, {798, 65018}, {1015, 4606}, {1027, 14626}, {1086, 34074}, {1919, 40023}, {3063, 57826}, {3121, 4633}, {3122, 4614}, {3125, 4627}, {3248, 53658}, {3669, 34820}, {3733, 56237}, {4516, 5545}, {4866, 43924}, {7180, 56204}, {18344, 57701}, {56086, 57181}, {57129, 60267}
X(65166) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 58860}, {9, 47915}, {1698, 4802}, {3616, 28161}, {5257, 50457}, {5375, 25430}, {6631, 5936}, {9296, 40023}, {10001, 57826}, {31998, 65018}, {39026, 2334}, {39054, 56048}, {51576, 513}, {55056, 3120}, {62221, 62221}, {62608, 514}
X(65166) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32042, 190}
X(65166) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2149, 41913}, {28162, 149}, {58132, 21293}, {65259, 150}
X(65166) = X(i)-cross conjugate of X(j) for these {i, j}: {4765, 19804}, {4778, 3616}, {4790, 42028}, {58140, 1449}
X(65166) = pole of line {100, 23363} with respect to the circumcircle
X(65166) = pole of line {1, 333} with respect to the Kiepert parabola
X(65166) = pole of line {663, 3733} with respect to the Stammler hyperbola
X(65166) = pole of line {190, 17136} with respect to the Steiner circumellipse
X(65166) = pole of line {2, 1743} with respect to the Yff parabola
X(65166) = pole of line {6, 3622} with respect to the Hutson-Moses hyperbola
X(65166) = pole of line {522, 7192} with respect to the Wallace hyperbola
X(65166) = pole of line {344, 17095} with respect to the dual conic of Feuerbach hyperbola
X(65166) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(3699)}}, {{A, B, C, X(100), X(1414)}}, {{A, B, C, X(109), X(4557)}}, {{A, B, C, X(190), X(4573)}}, {{A, B, C, X(461), X(7462)}}, {{A, B, C, X(643), X(4578)}}, {{A, B, C, X(659), X(4790)}}, {{A, B, C, X(664), X(3952)}}, {{A, B, C, X(835), X(3616)}}, {{A, B, C, X(890), X(58140)}}, {{A, B, C, X(900), X(4773)}}, {{A, B, C, X(901), X(65313)}}, {{A, B, C, X(1293), X(53280)}}, {{A, B, C, X(1449), X(23343)}}, {{A, B, C, X(1897), X(4767)}}, {{A, B, C, X(2785), X(4843)}}, {{A, B, C, X(3361), X(23832)}}, {{A, B, C, X(3570), X(42028)}}, {{A, B, C, X(4436), X(37138)}}, {{A, B, C, X(4512), X(54353)}}, {{A, B, C, X(4571), X(4592)}}, {{A, B, C, X(4756), X(53658)}}, {{A, B, C, X(4765), X(23829)}}, {{A, B, C, X(4801), X(30565)}}, {{A, B, C, X(4822), X(17989)}}, {{A, B, C, X(4841), X(18004)}}, {{A, B, C, X(5342), X(56881)}}, {{A, B, C, X(6013), X(65225)}}, {{A, B, C, X(6014), X(23845)}}, {{A, B, C, X(8706), X(58134)}}, {{A, B, C, X(8707), X(43290)}}, {{A, B, C, X(13589), X(31903)}}, {{A, B, C, X(19804), X(37215)}}, {{A, B, C, X(21454), X(53337)}}, {{A, B, C, X(30723), X(47884)}}, {{A, B, C, X(47776), X(48580)}}, {{A, B, C, X(52923), X(65250)}}, {{A, B, C, X(58860), X(62221)}}
X(65166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 190, 3699}, {100, 3952, 43290}, {100, 4427, 190}, {100, 4756, 17780}, {100, 57151, 65186}, {109, 54440, 643}, {190, 43290, 3952}, {902, 32845, 32922}, {1054, 4432, 25531}, {3035, 17777, 4997}, {3550, 32934, 32926}, {3977, 63145, 32850}, {4427, 4781, 100}, {4640, 32932, 333}, {17764, 59665, 33140}

X(65167) = ISOGONAL CONJUGATE OF X(18197)

Barycentrics    a*(a-b)*(a-c)*(b+c)*(a*(b-c)-b*c)*(a*(b-c)+b*c) : :

X(65167) lies on these lines: {1, 9490}, {9, 87}, {37, 21759}, {44, 40881}, {45, 2162}, {101, 932}, {190, 4598}, {330, 16552}, {645, 4584}, {649, 61183}, {670, 18197}, {798, 4033}, {2161, 2319}, {3294, 23493}, {3494, 17744}, {4557, 61164}, {6383, 16574}, {8707, 58981}, {15966, 53676}, {17257, 27341}, {17336, 62419}, {17349, 32033}, {17742, 61427}, {18785, 21061}, {18793, 21835}, {20372, 39914}, {20375, 35032}, {29478, 34086}, {53338, 61235}, {53625, 58958}, {56257, 62753}, {60135, 60244}

X(65167) = isogonal conjugate of X(18197)
X(65167) = trilinear pole of line {42, 2229}
X(65167) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 18197}, {2, 16695}, {3, 17921}, {4, 23092}, {6, 17217}, {21, 43051}, {27, 22090}, {28, 25098}, {43, 1019}, {56, 27527}, {58, 3835}, {75, 57074}, {81, 4083}, {86, 20979}, {99, 6377}, {100, 16742}, {101, 23824}, {110, 21138}, {192, 3733}, {274, 8640}, {512, 7304}, {513, 27644}, {514, 38832}, {593, 21051}, {649, 33296}, {662, 3123}, {667, 31008}, {670, 21762}, {757, 21834}, {799, 38986}, {1015, 62530}, {1021, 62791}, {1171, 4992}, {1178, 64865}, {1333, 20906}, {1403, 4560}, {1412, 4147}, {1423, 3737}, {1509, 50491}, {2176, 7192}, {2209, 7199}, {3208, 7203}, {3212, 7252}, {3248, 36860}, {3669, 56181}, {4623, 21835}, {6331, 22386}, {6376, 57129}, {7255, 20284}, {16726, 52923}, {17187, 18107}, {17925, 20760}, {18155, 41526}, {18199, 20287}, {22370, 57200}, {24533, 40432}, {27346, 52150}, {40610, 56053}, {41531, 50456}, {48331, 65076}, {52619, 62420}
X(65167) = X(i)-vertex conjugate of X(j) for these {i, j}: {61234, 65163}
X(65167) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 27527}, {3, 18197}, {9, 17217}, {10, 3835}, {37, 20906}, {206, 57074}, {244, 21138}, {1015, 23824}, {1084, 3123}, {5375, 33296}, {6631, 31008}, {8054, 16742}, {16606, 23807}, {32664, 16695}, {36033, 23092}, {36103, 17921}, {38986, 6377}, {38996, 38986}, {39026, 27644}, {39054, 7304}, {40586, 4083}, {40591, 25098}, {40599, 4147}, {40600, 20979}, {40607, 21834}, {40611, 43051}, {52877, 14408}, {62574, 7199}, {62615, 52619}, {63618, 514}
X(65167) = X(i)-Ceva conjugate of X(j) for these {i, j}: {932, 65163}, {5383, 87}, {65163, 1018}
X(65167) = X(i)-cross conjugate of X(j) for these {i, j}: {669, 1}, {798, 21759}, {3952, 1018}, {22319, 291}, {23503, 213}, {62753, 4551}
X(65167) = pole of line {61234, 65163} with respect to the circumcircle
X(65167) = pole of line {18197, 57074} with respect to the Stammler hyperbola
X(65167) = pole of line {43, 213} with respect to the Yff parabola
X(65167) = pole of line {31, 87} with respect to the Hutson-Moses hyperbola
X(65167) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(670)}}, {{A, B, C, X(6), X(37205)}}, {{A, B, C, X(9), X(645)}}, {{A, B, C, X(37), X(4033)}}, {{A, B, C, X(87), X(56053)}}, {{A, B, C, X(101), X(190)}}, {{A, B, C, X(660), X(4551)}}, {{A, B, C, X(669), X(18197)}}, {{A, B, C, X(692), X(37218)}}, {{A, B, C, X(799), X(61234)}}, {{A, B, C, X(803), X(37133)}}, {{A, B, C, X(931), X(65250)}}, {{A, B, C, X(932), X(18830)}}, {{A, B, C, X(2284), X(21061)}}, {{A, B, C, X(3294), X(23343)}}, {{A, B, C, X(3709), X(21388)}}, {{A, B, C, X(3952), X(36863)}}, {{A, B, C, X(4594), X(53624)}}, {{A, B, C, X(4598), X(34071)}}, {{A, B, C, X(9282), X(9359)}}, {{A, B, C, X(17038), X(56241)}}
X(65167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 4598, 18830}

X(65168) = X(99)X(101)∩X(100)X(109)

Barycentrics    a*(a-b)*(a-c)*(a^2+2*b*c+a*(b+c)) : :

X(65168) lies on these lines: {9, 1958}, {37, 59693}, {41, 50127}, {48, 3729}, {75, 572}, {86, 55100}, {99, 101}, {100, 109}, {198, 29497}, {239, 5053}, {284, 894}, {321, 1790}, {326, 1766}, {332, 22008}, {527, 20769}, {536, 7113}, {581, 19845}, {604, 3875}, {646, 18047}, {664, 1461}, {692, 4436}, {785, 6013}, {851, 17977}, {909, 20881}, {940, 53543}, {1018, 1332}, {1020, 6516}, {1266, 1429}, {1310, 28477}, {1412, 1999}, {1438, 56851}, {1444, 21061}, {1630, 25252}, {1813, 2406}, {1897, 65232}, {1959, 16548}, {1978, 4610}, {1981, 6335}, {2173, 20602}, {2174, 17351}, {2182, 25083}, {2267, 4384}, {2268, 10436}, {2278, 4363}, {2298, 54308}, {2359, 18697}, {2360, 7283}, {3191, 14868}, {3257, 37211}, {3271, 8301}, {3430, 19842}, {3570, 65185}, {3673, 30885}, {3758, 4251}, {3879, 7175}, {4033, 4482}, {4149, 12530}, {4238, 8750}, {4268, 4361}, {4287, 17118}, {4416, 54316}, {4440, 27950}, {4557, 23363}, {4562, 62464}, {4565, 65203}, {4586, 18830}, {4604, 37212}, {4606, 65259}, {4659, 52134}, {4670, 60721}, {4855, 8545}, {5687, 43146}, {5764, 56984}, {5782, 11343}, {6007, 17798}, {6514, 22001}, {7364, 64708}, {8300, 9359}, {8694, 43350}, {8897, 56848}, {14543, 65195}, {16732, 24324}, {17274, 25940}, {18726, 27059}, {21272, 63782}, {21362, 35342}, {21937, 50093}, {22000, 31631}, {22311, 56193}, {24268, 24334}, {33952, 65298}, {36146, 36802}, {37793, 61410}, {60703, 60723}, {65170, 65201}

X(65168) = trilinear pole of line {940, 958}
X(65168) = perspector of circumconic {{A, B, C, X(4564), X(4600)}}
X(65168) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 32693}, {512, 37870}, {513, 941}, {514, 2258}, {649, 31359}, {650, 959}, {661, 5331}, {663, 44733}, {667, 34258}, {931, 3125}, {1980, 40828}, {2170, 65225}, {3063, 58008}, {3121, 65280}, {3122, 65230}, {3271, 32038}, {6591, 34259}, {7252, 60321}, {8678, 34260}
X(65168) = X(i)-Dao conjugate of X(j) for these {i, j}: {958, 6590}, {5257, 4815}, {5375, 31359}, {6631, 34258}, {10001, 58008}, {17417, 11}, {31993, 23879}, {34261, 522}, {34281, 6589}, {36830, 5331}, {39026, 941}, {39054, 37870}
X(65168) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4614, 100}
X(65168) = X(i)-cross conjugate of X(j) for these {i, j}: {17418, 10436}, {48144, 940}
X(65168) = pole of line {23845, 53268} with respect to the circumcircle
X(65168) = pole of line {86, 2975} with respect to the Kiepert parabola
X(65168) = pole of line {649, 3737} with respect to the Stammler hyperbola
X(65168) = pole of line {109, 835} with respect to the Steiner circumellipse
X(65168) = pole of line {6718, 16578} with respect to the Steiner inellipse
X(65168) = pole of line {10, 46} with respect to the Yff parabola
X(65168) = pole of line {9, 81} with respect to the Hutson-Moses hyperbola
X(65168) = pole of line {514, 18155} with respect to the Wallace hyperbola
X(65168) = pole of line {4466, 17880} with respect to the dual conic of polar circle
X(65168) = pole of line {28774, 33116} with respect to the dual conic of Feuerbach hyperbola
X(65168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(651)}}, {{A, B, C, X(100), X(645)}}, {{A, B, C, X(109), X(662)}}, {{A, B, C, X(190), X(4551)}}, {{A, B, C, X(664), X(3882)}}, {{A, B, C, X(785), X(4627)}}, {{A, B, C, X(940), X(23703)}}, {{A, B, C, X(1025), X(10436)}}, {{A, B, C, X(1461), X(4610)}}, {{A, B, C, X(1978), X(4605)}}, {{A, B, C, X(2254), X(17418)}}, {{A, B, C, X(2268), X(54325)}}, {{A, B, C, X(2786), X(8672)}}, {{A, B, C, X(3738), X(23880)}}, {{A, B, C, X(3939), X(7259)}}, {{A, B, C, X(4185), X(4237)}}, {{A, B, C, X(4604), X(61225)}}, {{A, B, C, X(5307), X(61231)}}, {{A, B, C, X(7451), X(44734)}}, {{A, B, C, X(33948), X(57977)}}, {{A, B, C, X(43050), X(43067)}}, {{A, B, C, X(48074), X(48144)}}, {{A, B, C, X(56188), X(61177)}}
X(65168) = barycentric product X(i)*X(j) for these (i, j): {7, 65190}, {100, 10436}, {101, 34284}, {190, 940}, {664, 958}, {1016, 48144}, {1332, 5307}, {1414, 3714}, {1461, 61414}, {1468, 668}, {1867, 4592}, {1978, 5019}, {2268, 4554}, {3713, 658}, {4185, 4561}, {4567, 50457}, {4600, 8672}, {11679, 651}, {17418, 4998}, {23880, 4564}, {31615, 53526}, {31993, 662}, {34261, 37215}, {34281, 57977}, {43067, 765}, {44734, 65233}, {53536, 5376}, {53543, 6632}, {54396, 6516}, {59305, 99}
X(65168) = barycentric quotient X(i)/X(j) for these (i, j): {59, 65225}, {100, 31359}, {101, 941}, {109, 959}, {110, 5331}, {190, 34258}, {651, 44733}, {662, 37870}, {664, 58008}, {692, 2258}, {835, 34265}, {940, 514}, {958, 522}, {1331, 34259}, {1468, 513}, {1867, 24006}, {1978, 40828}, {2149, 32693}, {2268, 650}, {3713, 3239}, {3714, 4086}, {4185, 7649}, {4551, 60321}, {4564, 32038}, {4567, 65230}, {4570, 931}, {4600, 65280}, {5019, 649}, {5307, 17924}, {8639, 3122}, {8672, 3120}, {10436, 693}, {11679, 4391}, {17418, 11}, {23880, 4858}, {31993, 1577}, {34261, 6590}, {34281, 834}, {34284, 3261}, {43067, 1111}, {44734, 57215}, {48144, 1086}, {50457, 16732}, {53526, 40166}, {53543, 6545}, {53561, 42462}, {54396, 44426}, {54417, 3737}, {57061, 34263}, {58332, 2310}, {59305, 523}, {61168, 56914}, {61414, 52622}, {65190, 8}, {65225, 50040}, {65298, 34260}
X(65168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 4579, 3939}, {100, 651, 3882}, {190, 4561, 65191}, {190, 662, 101}

X(65169) = ANTICOMPLEMENT OF X(16742)

Barycentrics    (a-b)*b*(a-c)*c*(b*c*(b+c)+a*(b^2+c^2)) : :
X(65169) = -3*X[2]+2*X[16742]

X(65169) lies on these lines: {2, 16742}, {75, 3125}, {190, 646}, {194, 18148}, {304, 20452}, {1086, 30026}, {1654, 4110}, {1655, 2276}, {1909, 26759}, {1978, 33946}, {3216, 29425}, {3570, 7257}, {3761, 17286}, {3770, 17281}, {3909, 23354}, {4087, 49755}, {4562, 65282}, {4568, 27808}, {4602, 55239}, {7260, 21604}, {16552, 29713}, {16709, 50160}, {17144, 27424}, {17149, 26767}, {17499, 24524}, {18050, 28659}, {20440, 21331}, {20453, 57015}, {20917, 29587}, {21138, 62553}, {24652, 31997}, {25264, 56250}, {26774, 52043}, {29388, 56191}, {29397, 29433}, {29423, 30114}, {30083, 36791}, {35342, 55243}, {35538, 46180}, {46132, 57965}, {65280, 65288}

X(65169) = anticomplement of X(16742)
X(65169) = trilinear pole of line {3728, 3741}
X(65169) = X(i)-isoconjugate-of-X(j) for these {i, j}: {110, 40525}, {649, 57399}, {667, 1258}, {669, 40409}, {1015, 59102}, {1221, 1980}, {1919, 40418}, {21762, 59094}
X(65169) = X(i)-Dao conjugate of X(j) for these {i, j}: {75, 63224}, {244, 40525}, {1107, 4367}, {3122, 3121}, {3741, 798}, {5375, 57399}, {6631, 1258}, {9296, 40418}, {16742, 16742}, {21024, 4083}, {21838, 513}, {51575, 649}, {59565, 661}
X(65169) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {765, 17149}, {1110, 36857}, {4600, 34086}, {5383, 17135}, {23493, 54102}, {34071, 17154}, {65163, 4440}, {65167, 149}
X(65169) = X(i)-cross conjugate of X(j) for these {i, j}: {61165, 53338}
X(65169) = pole of line {3952, 22319} with respect to the Steiner circumellipse
X(65169) = pole of line {1, 25295} with respect to the Yff parabola
X(65169) = pole of line {1019, 1924} with respect to the Wallace hyperbola
X(65169) = pole of line {3952, 4010} with respect to the dual conic of DeLongchamps ellipse
X(65169) = pole of line {18055, 18743} with respect to the dual conic of Feuerbach hyperbola
X(65169) = pole of line {668, 670} with respect to the dual conic of Hofstadter ellipse
X(65169) = intersection, other than A, B, C, of circumconics {{A, B, C, X(190), X(7260)}}, {{A, B, C, X(812), X(63812)}}, {{A, B, C, X(874), X(65282)}}, {{A, B, C, X(1018), X(4602)}}, {{A, B, C, X(1107), X(40782)}}, {{A, B, C, X(1978), X(4595)}}, {{A, B, C, X(3741), X(23891)}}, {{A, B, C, X(3882), X(4562)}}, {{A, B, C, X(20891), X(24004)}}, {{A, B, C, X(53268), X(57965)}}
X(65169) = barycentric product X(i)*X(j) for these (i, j): {190, 20891}, {274, 61165}, {1107, 1978}, {2309, 6386}, {3728, 670}, {3741, 668}, {4595, 61417}, {16738, 4033}, {18169, 27808}, {18830, 59565}, {21024, 799}, {21713, 4623}, {21838, 4602}, {22206, 52612}, {30097, 646}, {45208, 62534}, {51575, 56241}, {53268, 561}, {53338, 75}, {61234, 76}, {63812, 7035}
X(65169) = barycentric quotient X(i)/X(j) for these (i, j): {100, 57399}, {190, 1258}, {661, 40525}, {668, 40418}, {765, 59102}, {799, 40409}, {1107, 649}, {1197, 1919}, {1978, 1221}, {2309, 667}, {3728, 512}, {3741, 513}, {4033, 60230}, {4595, 63238}, {6376, 63224}, {16738, 1019}, {18091, 18108}, {18169, 3733}, {20891, 514}, {21024, 661}, {21700, 50487}, {21713, 4705}, {21838, 798}, {22065, 22383}, {22206, 4079}, {23473, 50514}, {27880, 7234}, {30097, 3669}, {36863, 63232}, {39780, 51641}, {40627, 3121}, {45208, 7180}, {45216, 8640}, {50510, 3248}, {51411, 1769}, {51575, 4367}, {53268, 31}, {53338, 1}, {56901, 62749}, {59565, 4083}, {61165, 37}, {61234, 6}, {63812, 244}
X(65169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {646, 668, 4595}

X(65170) = X(27)X(4641)∩X(162)X(190)

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(3*a^2-(b-c)^2+2*a*(b+c))*(a^2-b^2+c^2) : :

X(65170) lies on these lines: {27, 4641}, {44, 26003}, {72, 44698}, {101, 65232}, {144, 1249}, {162, 190}, {273, 1743}, {297, 20072}, {318, 50127}, {346, 56013}, {423, 27970}, {651, 653}, {894, 2322}, {1119, 37681}, {3172, 25242}, {3219, 41083}, {3758, 11109}, {4419, 40138}, {4644, 37448}, {4741, 11331}, {5702, 17014}, {6172, 7952}, {6335, 65161}, {6542, 56021}, {9308, 17350}, {16318, 56555}, {17347, 17907}, {17354, 44134}, {17555, 54280}, {18678, 64143}, {21362, 61236}, {22117, 56299}, {36048, 36049}, {36099, 37206}, {44765, 46639}, {52283, 64015}, {52288, 61330}, {62669, 65355}, {65168, 65201}

X(65170) = trilinear pole of line {1869, 3601}
X(65170) = X(i)-isoconjugate-of-X(j) for these {i, j}: {647, 63157}, {652, 5665}, {18210, 59079}, {22383, 43533}
X(65170) = X(i)-Dao conjugate of X(j) for these {i, j}: {39052, 63157}
X(65170) = pole of line {1146, 3120} with respect to the polar circle
X(65170) = pole of line {1043, 17134} with respect to the Kiepert parabola
X(65170) = pole of line {1459, 23090} with respect to the Stammler hyperbola
X(65170) = pole of line {1897, 14543} with respect to the Steiner circumellipse
X(65170) = pole of line {20, 306} with respect to the Yff parabola
X(65170) = pole of line {27, 329} with respect to the Hutson-Moses hyperbola
X(65170) = pole of line {4025, 15411} with respect to the Wallace hyperbola
X(65170) = pole of line {17216, 23983} with respect to the dual conic of polar circle
X(65170) = intersection, other than A, B, C, of circumconics {{A, B, C, X(162), X(32714)}}, {{A, B, C, X(190), X(4566)}}, {{A, B, C, X(643), X(651)}}, {{A, B, C, X(648), X(36118)}}, {{A, B, C, X(653), X(36797)}}, {{A, B, C, X(658), X(14543)}}, {{A, B, C, X(1331), X(52610)}}, {{A, B, C, X(1897), X(52607)}}, {{A, B, C, X(2406), X(5273)}}, {{A, B, C, X(3945), X(23973)}}, {{A, B, C, X(7490), X(46541)}}, {{A, B, C, X(36049), X(61197)}}
X(65170) = barycentric product X(i)*X(j) for these (i, j): {7, 65193}, {190, 7490}, {1869, 99}, {1897, 3945}, {5273, 653}, {18026, 3601}, {20007, 36118}, {62812, 6335}
X(65170) = barycentric quotient X(i)/X(j) for these (i, j): {108, 5665}, {162, 63157}, {1869, 523}, {1897, 43533}, {3601, 521}, {3945, 4025}, {4252, 1459}, {5273, 6332}, {7490, 514}, {62812, 905}, {65193, 8}
X(65170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 648, 1897}, {651, 653, 36118}

X(65171) = X(2)X(40347)∩X(99)X(112)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2-b^2-c^2)*((b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(65171) lies on these lines: {2, 40347}, {69, 3269}, {99, 112}, {194, 5976}, {339, 28438}, {385, 5866}, {974, 61113}, {1302, 58116}, {2396, 43188}, {2696, 53884}, {2966, 62522}, {3926, 28405}, {4563, 65311}, {4576, 61198}, {5913, 62310}, {8267, 31128}, {8716, 10607}, {9091, 34537}, {9723, 31859}, {10420, 53949}, {14420, 23181}, {34866, 40879}, {39127, 46712}, {39193, 47288}, {46721, 52067}, {48945, 64235}, {53273, 53350}, {60839, 63933}

X(65171) = trilinear pole of line {1368, 6467}
X(65171) = X(i)-isoconjugate-of-X(j) for these {i, j}: {683, 1924}, {798, 40413}
X(65171) = X(i)-Dao conjugate of X(j) for these {i, j}: {1196, 523}, {1368, 2489}, {5254, 16229}, {9428, 683}, {20975, 3124}, {22401, 3566}, {31998, 40413}, {36830, 57388}, {59561, 2501}, {63612, 647}
X(65171) = X(i)-Ceva conjugate of X(j) for these {i, j}: {99, 53273}, {23964, 28419}, {34537, 69}
X(65171) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1101, 19583}, {3565, 21294}, {65178, 21221}
X(65171) = X(i)-cross conjugate of X(j) for these {i, j}: {61199, 53350}
X(65171) = pole of line {69, 305} with respect to the Kiepert parabola
X(65171) = pole of line {647, 41336} with respect to the Stammler hyperbola
X(65171) = pole of line {110, 3565} with respect to the Steiner circumellipse
X(65171) = pole of line {525, 2451} with respect to the Wallace hyperbola
X(65171) = pole of line {110, 925} with respect to the dual conic of nine-point circle
X(65171) = pole of line {51389, 64920} with respect to the dual conic of orthoptic circle of the Steiner Inellipse
X(65171) = pole of line {1084, 6388} with respect to the dual conic of polar circle
X(65171) = pole of line {2, 1975} with respect to the dual conic of Jerabek hyperbola
X(65171) = pole of line {99, 670} with respect to the dual conic of Orthic inconic
X(65171) = intersection, other than A, B, C, of circumconics {{A, B, C, X(112), X(40347)}}, {{A, B, C, X(648), X(53350)}}, {{A, B, C, X(1368), X(4235)}}, {{A, B, C, X(2966), X(41678)}}, {{A, B, C, X(4580), X(14273)}}, {{A, B, C, X(14966), X(22401)}}, {{A, B, C, X(16237), X(53949)}}
X(65171) = barycentric product X(i)*X(j) for these (i, j): {305, 53273}, {1196, 52608}, {1368, 99}, {4563, 5254}, {4609, 682}, {6467, 670}, {12075, 47389}, {17872, 55202}, {18648, 190}, {18671, 799}, {21406, 662}, {22401, 6331}, {35136, 63612}, {45207, 55224}, {53350, 69}, {61199, 76}
X(65171) = barycentric quotient X(i)/X(j) for these (i, j): {99, 40413}, {110, 57388}, {670, 683}, {682, 669}, {1196, 2489}, {1368, 523}, {4563, 40405}, {4609, 57931}, {5254, 2501}, {6467, 512}, {12075, 8754}, {16716, 6591}, {18648, 514}, {18671, 661}, {21406, 1577}, {22401, 647}, {40326, 57071}, {53273, 25}, {53350, 4}, {59561, 16229}, {61199, 6}, {63612, 3566}
X(65171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 41676, 14570}, {99, 4611, 4235}

X(65172) = X(3)X(3224)∩X(99)X(3222)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(b^2+c^2)*(-(b^2*c^2)+a^2*(b^2-c^2))*(b^2*c^2+a^2*(b^2-c^2)) : :

X(65172) lies on these lines: {3, 3224}, {99, 3222}, {574, 51951}, {805, 59028}, {1576, 41337}, {2998, 8266}, {3455, 3504}, {19606, 41328}, {42551, 51869}

X(65172) = trilinear pole of line {3051, 19606}
X(65172) = X(i)-isoconjugate-of-X(j) for these {i, j}: {82, 23301}, {194, 55240}, {251, 20910}, {308, 23503}, {1577, 38834}, {1613, 18070}, {1740, 58784}, {2643, 62531}, {3112, 3221}, {4580, 51913}, {9491, 18833}, {10566, 21877}, {17149, 18105}, {18082, 50516}, {18098, 21191}, {18108, 21080}, {21056, 52376}, {23572, 56186}, {52618, 56836}
X(65172) = X(i)-vertex conjugate of X(j) for these {i, j}: {670, 53654}, {42371, 42371}
X(65172) = X(i)-Dao conjugate of X(j) for these {i, j}: {141, 23301}, {34452, 3221}, {40585, 20910}
X(65172) = X(i)-cross conjugate of X(j) for these {i, j}: {4576, 1634}
X(65172) = pole of line {9429, 32547} with respect to the 2nd Brocard circle
X(65172) = pole of line {670, 9429} with respect to the circumcircle
X(65172) = pole of line {1613, 41331} with respect to the Kiepert parabola
X(65172) = pole of line {9491, 23301} with respect to the Stammler hyperbola
X(65172) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(39681)}}, {{A, B, C, X(6), X(36881)}}, {{A, B, C, X(25), X(9062)}}, {{A, B, C, X(32), X(6573)}}, {{A, B, C, X(39), X(41337)}}, {{A, B, C, X(99), X(1576)}}, {{A, B, C, X(689), X(17965)}}, {{A, B, C, X(805), X(35325)}}, {{A, B, C, X(3224), X(59028)}}, {{A, B, C, X(4576), X(25424)}}, {{A, B, C, X(5118), X(41328)}}, {{A, B, C, X(6234), X(30254)}}, {{A, B, C, X(6572), X(14574)}}, {{A, B, C, X(9217), X(9431)}}, {{A, B, C, X(17938), X(35567)}}, {{A, B, C, X(27369), X(46598)}}, {{A, B, C, X(28469), X(35333)}}
X(65172) = barycentric product X(i)*X(j) for these (i, j): {110, 42551}, {1634, 2998}, {3051, 53654}, {3222, 39}, {3224, 4576}, {3504, 41676}, {4074, 59028}, {19606, 670}, {34248, 55239}, {35325, 43714}, {39927, 46161}
X(65172) = barycentric quotient X(i)/X(j) for these (i, j): {38, 20910}, {39, 23301}, {249, 62531}, {1576, 38834}, {1634, 194}, {1923, 23503}, {2998, 52618}, {3051, 3221}, {3222, 308}, {3223, 18070}, {3224, 58784}, {3504, 4580}, {4553, 22028}, {4576, 6374}, {16696, 23807}, {17187, 21191}, {19606, 512}, {20775, 2524}, {21035, 21056}, {21123, 21144}, {34248, 55240}, {35325, 3186}, {41331, 9491}, {41676, 51843}, {42551, 850}, {46148, 21080}, {51951, 18105}, {53654, 40016}, {55239, 18837}, {61218, 11325}

X(65173) = ISOGONAL CONJUGATE OF X(4162)

Barycentrics    a*(a-b)*(a+b-3*c)*(a-c)*(a+b-c)*(a-3*b+c)*(a-b+c) : :

X(65173) lies on these lines: {77, 19604}, {241, 51839}, {269, 47636}, {279, 56646}, {347, 4373}, {644, 3669}, {651, 23704}, {664, 31343}, {934, 1293}, {3160, 3445}, {3680, 9451}, {4318, 61438}, {6556, 34060}, {6557, 57477}, {8056, 17080}, {9312, 27813}, {16945, 60716}, {17074, 40151}, {26698, 43049}, {27829, 56309}, {34080, 36146}, {65330, 65337}

X(65173) = isogonal conjugate of X(4162)
X(65173) = trilinear pole of line {57, 1122}
X(65173) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4162}, {6, 4521}, {8, 8643}, {9, 4394}, {21, 4729}, {41, 4462}, {55, 3667}, {56, 4546}, {58, 44729}, {101, 4534}, {109, 4953}, {145, 663}, {200, 51656}, {220, 30719}, {284, 14321}, {512, 52352}, {513, 3158}, {522, 3052}, {649, 3161}, {650, 1743}, {657, 5435}, {667, 44720}, {692, 4939}, {884, 4899}, {1015, 30720}, {1420, 3900}, {1919, 44723}, {2170, 57192}, {2194, 4404}, {2195, 4925}, {2316, 14425}, {2325, 2441}, {3063, 18743}, {3064, 20818}, {3271, 43290}, {3445, 4943}, {3669, 4936}, {3700, 33628}, {3709, 41629}, {3737, 4849}, {3756, 3939}, {3950, 7252}, {4041, 16948}, {4069, 18211}, {4105, 62787}, {4848, 21789}, {4855, 18344}, {5546, 21950}, {6065, 23764}, {6555, 43924}, {7077, 53580}, {8641, 39126}, {14284, 51476}
X(65173) = X(i)-vertex conjugate of X(j) for these {i, j}: {56, 644}
X(65173) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4546}, {3, 4162}, {9, 4521}, {10, 44729}, {11, 4953}, {223, 3667}, {478, 4394}, {1015, 4534}, {1086, 4939}, {1214, 4404}, {3160, 4462}, {3452, 14284}, {5375, 3161}, {6609, 51656}, {6631, 44720}, {9296, 44723}, {10001, 18743}, {24151, 522}, {39026, 3158}, {39054, 52352}, {39063, 4925}, {40590, 14321}, {40611, 4729}, {40617, 3756}, {45036, 4943}, {62575, 4391}
X(65173) = X(i)-cross conjugate of X(j) for these {i, j}: {1, 5382}, {100, 651}, {1293, 27834}, {2827, 88}, {21362, 658}, {34039, 7128}, {43932, 7}, {48032, 43760}, {51656, 57}, {58794, 27818}, {63208, 4564}
X(65173) = pole of line {4488, 63130} with respect to the Yff parabola
X(65173) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(644)}}, {{A, B, C, X(7), X(668)}}, {{A, B, C, X(59), X(39443)}}, {{A, B, C, X(77), X(6516)}}, {{A, B, C, X(99), X(4606)}}, {{A, B, C, X(100), X(43290)}}, {{A, B, C, X(651), X(664)}}, {{A, B, C, X(655), X(53642)}}, {{A, B, C, X(927), X(6613)}}, {{A, B, C, X(932), X(1476)}}, {{A, B, C, X(1293), X(31343)}}, {{A, B, C, X(1305), X(54953)}}, {{A, B, C, X(1308), X(1783)}}, {{A, B, C, X(1310), X(4596)}}, {{A, B, C, X(1461), X(6571)}}, {{A, B, C, X(3160), X(41353)}}, {{A, B, C, X(3257), X(58131)}}, {{A, B, C, X(3445), X(34080)}}, {{A, B, C, X(4554), X(4617)}}, {{A, B, C, X(4624), X(4637)}}, {{A, B, C, X(5546), X(28291)}}, {{A, B, C, X(5548), X(53888)}}, {{A, B, C, X(6016), X(52013)}}, {{A, B, C, X(7091), X(65202)}}, {{A, B, C, X(9067), X(56358)}}, {{A, B, C, X(13138), X(13397)}}, {{A, B, C, X(27834), X(53647)}}, {{A, B, C, X(30237), X(60488)}}, {{A, B, C, X(37209), X(64984)}}, {{A, B, C, X(41431), X(59029)}}, {{A, B, C, X(52778), X(63163)}}, {{A, B, C, X(59125), X(65225)}}
X(65173) = barycentric product X(i)*X(j) for these (i, j): {100, 27818}, {101, 62528}, {109, 40014}, {190, 19604}, {279, 31343}, {664, 8056}, {1293, 85}, {1414, 4052}, {1897, 27832}, {2415, 56049}, {3445, 4554}, {3676, 5382}, {3680, 658}, {4373, 651}, {4573, 56174}, {4617, 6556}, {4998, 58794}, {6557, 934}, {10029, 36086}, {13397, 27815}, {16078, 57192}, {16945, 1978}, {27834, 7}, {27836, 52377}, {33963, 62532}, {34080, 6063}, {38266, 4572}, {38828, 75}, {40151, 668}, {45205, 8706}, {51656, 57578}, {53647, 57}, {65337, 77}
X(65173) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4521}, {6, 4162}, {7, 4462}, {9, 4546}, {37, 44729}, {56, 4394}, {57, 3667}, {59, 57192}, {65, 14321}, {100, 3161}, {101, 3158}, {109, 1743}, {190, 44720}, {226, 4404}, {241, 4925}, {269, 30719}, {513, 4534}, {514, 4939}, {604, 8643}, {644, 6555}, {650, 4953}, {651, 145}, {658, 39126}, {662, 52352}, {664, 18743}, {668, 44723}, {765, 30720}, {934, 5435}, {1020, 4848}, {1025, 4899}, {1293, 9}, {1319, 14425}, {1332, 44722}, {1400, 4729}, {1407, 51656}, {1414, 41629}, {1415, 3052}, {1417, 2441}, {1420, 31182}, {1429, 53580}, {1461, 1420}, {1813, 4855}, {2415, 4723}, {2429, 3689}, {3340, 14350}, {3445, 650}, {3669, 3756}, {3680, 3239}, {3752, 14284}, {3939, 4936}, {4017, 21950}, {4052, 4086}, {4373, 4391}, {4551, 3950}, {4552, 52353}, {4559, 4849}, {4564, 43290}, {4565, 16948}, {4617, 62787}, {5221, 4949}, {5382, 3699}, {6335, 44721}, {6557, 4397}, {7175, 4504}, {8056, 522}, {16079, 58794}, {16945, 649}, {19604, 514}, {21362, 12640}, {24029, 51433}, {27818, 693}, {27819, 44448}, {27829, 20907}, {27832, 4025}, {27833, 17860}, {27834, 8}, {31343, 346}, {31615, 44724}, {34080, 55}, {36042, 2316}, {36059, 20818}, {37141, 56940}, {38266, 663}, {38828, 1}, {40014, 35519}, {40151, 513}, {42717, 44728}, {43932, 40617}, {46367, 48334}, {51656, 40621}, {51839, 53523}, {53538, 23764}, {53647, 312}, {56049, 2403}, {56174, 3700}, {58794, 11}, {59095, 1261}, {59457, 62532}, {61225, 4856}, {62528, 3261}, {62669, 4487}, {62754, 45204}, {65232, 4248}, {65233, 52354}, {65337, 318}
X(65173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {27834, 38828, 651}

X(65174) = X(2)X(43047)∩X(7)X(2170)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(-2*a*(b-c)^2+a^2*(b+c)+(b-c)^2*(b+c)) : :

X(65174) lies on these lines: {2, 43047}, {7, 2170}, {109, 2398}, {190, 644}, {279, 41785}, {514, 4566}, {658, 57455}, {665, 30610}, {666, 6613}, {934, 3732}, {1025, 21272}, {1414, 4560}, {1422, 28951}, {1461, 14543}, {2124, 34059}, {2405, 57193}, {3160, 3177}, {3241, 53530}, {3872, 28968}, {4565, 36841}, {7176, 18785}, {7278, 60229}, {9312, 26653}, {15558, 60934}, {17079, 37800}, {18623, 28921}, {18624, 18663}, {24203, 34056}, {25237, 25716}, {25242, 25718}, {25244, 25719}, {25249, 25720}, {25257, 25726}, {25261, 25723}, {27340, 31994}, {30695, 34060}, {30719, 62754}, {30807, 43044}, {34488, 45738}, {36838, 61241}, {43064, 44664}, {43989, 56309}, {44351, 52160}, {56322, 60487}, {65330, 65355}

X(65174) = reflection of X(i) in X(j) for these {i,j}: {4566, 63203}
X(65174) = trilinear pole of line {10167, 11019}
X(65174) = X(i)-isoconjugate-of-X(j) for these {i, j}: {652, 14493}, {657, 63192}, {3063, 56026}, {8641, 23618}
X(65174) = X(i)-Dao conjugate of X(j) for these {i, j}: {2310, 3119}, {10001, 56026}, {11019, 4130}, {43182, 650}, {59573, 3239}
X(65174) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {24027, 31527}, {53622, 150}, {61240, 21293}
X(65174) = pole of line {100, 53622} with respect to the Steiner circumellipse
X(65174) = pole of line {8, 971} with respect to the Yff parabola
X(65174) = pole of line {2, 3160} with respect to the dual conic of Feuerbach hyperbola
X(65174) = intersection, other than A, B, C, of circumconics {{A, B, C, X(644), X(30610)}}, {{A, B, C, X(666), X(25268)}}, {{A, B, C, X(883), X(6613)}}, {{A, B, C, X(918), X(60482)}}, {{A, B, C, X(2284), X(40133)}}, {{A, B, C, X(2397), X(20905)}}, {{A, B, C, X(4585), X(26818)}}, {{A, B, C, X(60992), X(62669)}}
X(65174) = barycentric product X(i)*X(j) for these (i, j): {190, 60992}, {1200, 46406}, {10167, 18026}, {11019, 664}, {14100, 4569}, {20905, 651}, {20978, 4572}, {21049, 4573}, {22088, 46404}, {26818, 4552}, {40133, 4554}, {41006, 658}, {43182, 53640}, {45202, 62532}, {59170, 65165}
X(65174) = barycentric quotient X(i)/X(j) for these (i, j): {108, 14493}, {658, 23618}, {664, 56026}, {934, 63192}, {1200, 657}, {10167, 521}, {11019, 522}, {14100, 3900}, {20905, 4391}, {20978, 663}, {21049, 3700}, {22088, 652}, {26818, 4560}, {40133, 650}, {41006, 3239}, {45203, 57064}, {45228, 58835}, {60992, 514}
X(65174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 63203, 4566}, {664, 65195, 4552}

X(65175) = X(90)X(1745)∩X(223)X(2006)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(b+c)*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+c^2))*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+c^2)) : :

X(65175) lies on these lines: {90, 1745}, {108, 36082}, {223, 2006}, {651, 65216}, {1079, 55495}, {4554, 18740}, {32038, 65290}, {63827, 65233}

X(65175) = trilinear pole of line {65, 21318}
X(65175) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 46389}, {46, 1021}, {48, 57083}, {63, 57124}, {110, 6506}, {650, 3193}, {652, 3559}, {663, 31631}, {1068, 23090}, {1098, 55214}, {1172, 59973}, {1800, 3064}, {2178, 7253}, {2287, 51648}, {2328, 21188}, {3157, 17926}, {4560, 61397}, {5552, 7252}, {5905, 21789}, {52033, 57081}, {56848, 58329}
X(65175) = X(i)-Dao conjugate of X(j) for these {i, j}: {244, 6506}, {1249, 57083}, {3162, 57124}, {15267, 55214}, {36908, 21188}, {40611, 46389}
X(65175) = X(i)-cross conjugate of X(j) for these {i, j}: {2501, 1}, {52610, 1020}, {55214, 65}
X(65175) = pole of line {1158, 41013} with respect to the Yff parabola
X(65175) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4558)}}, {{A, B, C, X(108), X(651)}}, {{A, B, C, X(226), X(61231)}}, {{A, B, C, X(282), X(4069)}}, {{A, B, C, X(7097), X(65167)}}, {{A, B, C, X(9355), X(9394)}}, {{A, B, C, X(18740), X(36145)}}, {{A, B, C, X(37141), X(61178)}}
X(65175) = barycentric product X(i)*X(j) for these (i, j): {65, 65290}, {226, 65216}, {662, 7363}, {1020, 2994}, {1275, 55248}, {1441, 36082}, {4551, 7318}, {4566, 90}, {20570, 53321}, {52607, 6513}, {60249, 651}
X(65175) = barycentric quotient X(i)/X(j) for these (i, j): {4, 57083}, {25, 57124}, {73, 59973}, {90, 7253}, {108, 3559}, {109, 3193}, {651, 31631}, {661, 6506}, {1020, 5905}, {1042, 51648}, {1069, 57081}, {1275, 55247}, {1400, 46389}, {1427, 21188}, {2164, 1021}, {4551, 5552}, {4566, 20930}, {6513, 15411}, {7072, 58329}, {7318, 18155}, {7363, 1577}, {36059, 1800}, {36082, 21}, {52610, 6505}, {53321, 46}, {55248, 1146}, {60249, 4391}, {65216, 333}, {65290, 314}

X(65176) = TRILINEAR POLE OF LINE {25, 53}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(a^4-2*a^2*c^2+(b^2-c^2)^2) : :

X(65176) lies on these lines: {4, 56891}, {68, 41361}, {96, 56298}, {99, 32697}, {107, 32692}, {110, 39416}, {112, 925}, {393, 47731}, {648, 30450}, {847, 6531}, {1249, 2165}, {1300, 47421}, {1990, 62361}, {2501, 32661}, {3172, 46200}, {3542, 60778}, {5392, 56296}, {5523, 5962}, {5546, 32698}, {6524, 39111}, {6529, 61209}, {8744, 60519}, {8745, 60783}, {8753, 14593}, {14361, 52350}, {32674, 36145}, {32695, 57219}, {32696, 60504}, {32711, 41392}, {32713, 32734}, {36099, 65251}, {37802, 51358}, {41204, 46039}

X(65176) = isogonal conjugate of X(52584)
X(65176) = trilinear pole of line {25, 53}
X(65176) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52584}, {2, 63832}, {3, 63827}, {24, 24018}, {47, 525}, {48, 6563}, {63, 924}, {69, 55216}, {75, 30451}, {255, 57065}, {304, 34952}, {306, 34948}, {317, 822}, {326, 6753}, {520, 1748}, {563, 850}, {571, 14208}, {647, 44179}, {656, 1993}, {661, 9723}, {810, 7763}, {1147, 1577}, {1459, 42700}, {2169, 63829}, {2180, 62428}, {2616, 52032}, {2632, 41679}, {4064, 18605}, {4592, 47421}, {5961, 32679}, {15412, 63801}, {17879, 61208}, {17881, 32661}, {20948, 52435}, {20975, 55249}, {23286, 63808}, {52317, 62277}
X(65176) = X(i)-vertex conjugate of X(j) for these {i, j}: {648, 14586}, {6529, 32640}, {32661, 65176}, {61208, 65309}
X(65176) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52584}, {206, 30451}, {1249, 6563}, {3162, 924}, {5139, 47421}, {6523, 57065}, {14363, 63829}, {15259, 6753}, {32664, 63832}, {34853, 525}, {36103, 63827}, {36830, 9723}, {37864, 647}, {39052, 44179}, {39062, 7763}, {40596, 1993}
X(65176) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30450, 925}, {65348, 32734}
X(65176) = X(i)-cross conjugate of X(j) for these {i, j}: {1576, 107}, {1625, 112}, {8746, 23964}, {21731, 1300}, {32734, 925}, {55265, 62361}, {58757, 4}
X(65176) = pole of line {30451, 52584} with respect to the Stammler hyperbola
X(65176) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(99)}}, {{A, B, C, X(6), X(32661)}}, {{A, B, C, X(107), X(6344)}}, {{A, B, C, X(112), X(648)}}, {{A, B, C, X(275), X(59007)}}, {{A, B, C, X(685), X(1289)}}, {{A, B, C, X(925), X(46134)}}, {{A, B, C, X(935), X(53639)}}, {{A, B, C, X(1172), X(5546)}}, {{A, B, C, X(1249), X(57219)}}, {{A, B, C, X(1562), X(41077)}}, {{A, B, C, X(1576), X(1625)}}, {{A, B, C, X(1990), X(3018)}}, {{A, B, C, X(2501), X(47236)}}, {{A, B, C, X(2713), X(44828)}}, {{A, B, C, X(2715), X(44766)}}, {{A, B, C, X(3565), X(44768)}}, {{A, B, C, X(4558), X(58964)}}, {{A, B, C, X(4630), X(26714)}}, {{A, B, C, X(5523), X(35907)}}, {{A, B, C, X(6331), X(20031)}}, {{A, B, C, X(6570), X(14586)}}, {{A, B, C, X(8743), X(58070)}}, {{A, B, C, X(9160), X(38534)}}, {{A, B, C, X(14781), X(16080)}}, {{A, B, C, X(15388), X(34538)}}, {{A, B, C, X(18831), X(30247)}}, {{A, B, C, X(21731), X(47421)}}, {{A, B, C, X(23977), X(41361)}}, {{A, B, C, X(30450), X(39416)}}, {{A, B, C, X(32692), X(32734)}}, {{A, B, C, X(40402), X(59002)}}, {{A, B, C, X(52917), X(59004)}}, {{A, B, C, X(55189), X(62917)}}, {{A, B, C, X(55277), X(56891)}}, {{A, B, C, X(57065), X(58757)}}, {{A, B, C, X(58095), X(65279)}}, {{A, B, C, X(58973), X(65305)}}, {{A, B, C, X(59086), X(65181)}}, {{A, B, C, X(61203), X(61206)}}
X(65176) = barycentric product X(i)*X(j) for these (i, j): {4, 925}, {5, 65348}, {19, 65251}, {25, 46134}, {53, 65273}, {107, 68}, {110, 847}, {112, 5392}, {162, 91}, {163, 57716}, {264, 32734}, {324, 32692}, {393, 65309}, {476, 5962}, {1302, 51833}, {1576, 55553}, {1820, 823}, {1973, 55215}, {2165, 648}, {2351, 6528}, {3542, 63958}, {14593, 99}, {15352, 55549}, {20563, 32713}, {20571, 32676}, {27367, 689}, {30450, 6}, {32697, 60519}, {32708, 52504}, {34385, 52604}, {35360, 96}, {36145, 92}, {39416, 6515}, {41515, 54030}, {41516, 54031}, {51481, 58961}, {52350, 6529}, {52779, 61363}, {52918, 57415}, {56272, 933}, {57703, 65183}, {57763, 58757}, {57875, 61193}, {57904, 61206}, {60501, 6331}, {62361, 687}
X(65176) = barycentric quotient X(i)/X(j) for these (i, j): {4, 6563}, {6, 52584}, {19, 63827}, {25, 924}, {31, 63832}, {32, 30451}, {53, 63829}, {68, 3265}, {91, 14208}, {96, 62428}, {107, 317}, {110, 9723}, {112, 1993}, {162, 44179}, {393, 57065}, {460, 57154}, {648, 7763}, {685, 31635}, {847, 850}, {925, 69}, {1576, 1147}, {1625, 52032}, {1783, 42700}, {1820, 24018}, {1973, 55216}, {1974, 34952}, {2165, 525}, {2203, 34948}, {2207, 6753}, {2351, 520}, {2489, 47421}, {2715, 51776}, {3199, 52317}, {4230, 51439}, {5392, 3267}, {5962, 3268}, {6529, 11547}, {8745, 15423}, {14560, 5961}, {14574, 52435}, {14581, 14397}, {14593, 523}, {18384, 43088}, {20563, 52617}, {23347, 51393}, {23582, 55227}, {23964, 41679}, {24006, 17881}, {24019, 1748}, {27367, 3005}, {30450, 76}, {32676, 47}, {32692, 97}, {32708, 52505}, {32713, 24}, {32734, 3}, {34397, 44808}, {35360, 39113}, {36145, 63}, {37802, 45792}, {39383, 5409}, {39384, 5408}, {39416, 6504}, {40348, 9007}, {41271, 23286}, {41515, 54028}, {41516, 54029}, {41937, 61208}, {46134, 305}, {51833, 30474}, {52350, 4143}, {52604, 52}, {52917, 55551}, {53329, 45780}, {55215, 40364}, {55250, 20902}, {55253, 53576}, {55549, 52613}, {55553, 44173}, {57716, 20948}, {57875, 15414}, {58757, 136}, {58961, 2987}, {60501, 647}, {61193, 467}, {61206, 571}, {61208, 63835}, {62361, 6334}, {65251, 304}, {65273, 34386}, {65309, 3926}, {65348, 95}
X(65176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 30450, 65309}

X(65177) = X(4)X(6053)∩X(107)X(110)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*a^4+(b^2-c^2)^2-4*a^2*(b^2+c^2)) : :

X(65177) lies on these lines: {4, 6053}, {99, 933}, {107, 110}, {136, 20774}, {162, 65226}, {250, 14611}, {275, 34986}, {925, 58994}, {1105, 43605}, {1302, 33640}, {1304, 59038}, {1625, 2442}, {1629, 1993}, {1634, 65182}, {1994, 55084}, {2052, 3167}, {2434, 65353}, {3292, 41204}, {3448, 14920}, {3564, 14165}, {5562, 38808}, {5965, 41203}, {5972, 16080}, {6090, 52147}, {6331, 57216}, {6531, 20976}, {7473, 30221}, {8884, 56292}, {9705, 56303}, {10152, 15063}, {11064, 51939}, {11422, 36794}, {11547, 63174}, {12092, 30248}, {13739, 62825}, {14480, 30716}, {20123, 34153}, {23181, 36841}, {30506, 55038}, {32269, 56021}, {35260, 56013}, {35278, 41676}, {35602, 57517}, {37124, 44109}, {38664, 41253}, {38714, 40948}, {43462, 63722}, {43844, 51031}, {52772, 57487}, {57118, 65232}, {65309, 65348}

X(65177) = trilinear pole of line {631, 3087}
X(65177) = X(i)-isoconjugate-of-X(j) for these {i, j}: {647, 56033}, {656, 3527}, {661, 63154}, {810, 8797}, {822, 8796}, {2616, 63176}, {2632, 58950}, {24006, 64219}, {24018, 34818}
X(65177) = X(i)-Dao conjugate of X(j) for these {i, j}: {5522, 125}, {36830, 63154}, {39052, 56033}, {39062, 8797}, {40596, 3527}
X(65177) = pole of line {125, 41221} with respect to the polar circle
X(65177) = pole of line {52913, 61195} with respect to the Johnson circumconic
X(65177) = pole of line {20, 343} with respect to the Kiepert parabola
X(65177) = pole of line {107, 1625} with respect to the MacBeath circumconic
X(65177) = pole of line {520, 15451} with respect to the Stammler hyperbola
X(65177) = pole of line {3265, 6368} with respect to the Wallace hyperbola
X(65177) = pole of line {7769, 17907} with respect to the dual conic of Jerabek hyperbola
X(65177) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(35360)}}, {{A, B, C, X(107), X(18831)}}, {{A, B, C, X(631), X(4240)}}, {{A, B, C, X(933), X(32713)}}, {{A, B, C, X(16230), X(47122)}}, {{A, B, C, X(44149), X(61181)}}, {{A, B, C, X(52917), X(58994)}}
X(65177) = barycentric product X(i)*X(j) for these (i, j): {112, 44149}, {631, 648}, {3087, 99}, {4563, 61348}, {11402, 6331}, {18020, 47122}, {26907, 42405}, {36748, 6528}
X(65177) = barycentric quotient X(i)/X(j) for these (i, j): {107, 8796}, {110, 63154}, {112, 3527}, {162, 56033}, {631, 525}, {648, 8797}, {1625, 63176}, {3087, 523}, {6755, 12077}, {11402, 647}, {23964, 58950}, {26907, 17434}, {32661, 64219}, {32713, 34818}, {35318, 31505}, {36748, 520}, {44149, 3267}, {47122, 125}, {61348, 2501}
X(65177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 35311, 648}, {110, 35360, 52913}, {110, 648, 107}, {648, 52913, 35360}

X(65178) = X(154)X(1976)∩X(159)X(1177)

Barycentrics    a^4*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-3*c^2)*(a^2-3*b^2+c^2) : :

X(65178) lies on these lines: {110, 3565}, {154, 1976}, {159, 1177}, {184, 42068}, {206, 32740}, {685, 52913}, {925, 6562}, {1660, 2882}, {1974, 53068}, {2393, 32741}, {2872, 32734}, {2996, 64059}, {3566, 4563}, {4577, 35136}, {6340, 11206}, {8780, 64614}, {14248, 26864}, {15270, 40319}, {32713, 61213}, {52143, 64216}, {52454, 64058}

X(65178) = reflection of X(i) in X(j) for these {i,j}: {32740, 206}
X(65178) = trilinear pole of line {32, 11326}
X(65178) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 3566}, {99, 17876}, {193, 1577}, {304, 57071}, {321, 3798}, {523, 18156}, {561, 8651}, {656, 54412}, {661, 57518}, {693, 4028}, {799, 6388}, {850, 1707}, {1109, 57216}, {3053, 20948}, {3261, 21874}, {4086, 17081}, {4602, 47430}, {5139, 55202}, {6337, 24006}, {6353, 14208}, {20910, 47733}, {21447, 24018}
X(65178) = X(i)-vertex conjugate of X(j) for these {i, j}: {2966, 43188}, {4558, 65311}, {4563, 4563}, {4609, 31614}, {35136, 57216}, {44766, 65324}, {65307, 65321}
X(65178) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 3566}, {15261, 523}, {36830, 57518}, {38986, 17876}, {38996, 6388}, {40368, 8651}, {40596, 54412}, {64614, 850}
X(65178) = X(i)-cross conjugate of X(j) for these {i, j}: {32661, 1576}, {57204, 6}
X(65178) = pole of line {4558, 61199} with respect to the circumcircle
X(65178) = pole of line {25, 15591} with respect to the Kiepert parabola
X(65178) = pole of line {3566, 51374} with respect to the Stammler hyperbola
X(65178) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(4563)}}, {{A, B, C, X(25), X(925)}}, {{A, B, C, X(64), X(39639)}}, {{A, B, C, X(66), X(55034)}}, {{A, B, C, X(99), X(39644)}}, {{A, B, C, X(110), X(685)}}, {{A, B, C, X(154), X(52913)}}, {{A, B, C, X(184), X(61213)}}, {{A, B, C, X(206), X(61207)}}, {{A, B, C, X(669), X(42068)}}, {{A, B, C, X(924), X(2872)}}, {{A, B, C, X(1503), X(2882)}}, {{A, B, C, X(1660), X(2445)}}, {{A, B, C, X(2393), X(2854)}}, {{A, B, C, X(3566), X(57204)}}, {{A, B, C, X(6331), X(9091)}}, {{A, B, C, X(14586), X(59116)}}, {{A, B, C, X(32649), X(44060)}}, {{A, B, C, X(32666), X(59005)}}, {{A, B, C, X(32696), X(59039)}}
X(65178) = barycentric product X(i)*X(j) for these (i, j): {25, 65311}, {32, 35136}, {110, 8770}, {112, 6391}, {163, 8769}, {1576, 2996}, {3565, 6}, {14248, 4558}, {14586, 27364}, {32661, 34208}, {32713, 60839}, {38252, 662}, {40319, 648}, {53059, 99}, {61206, 6340}
X(65178) = barycentric quotient X(i)/X(j) for these (i, j): {32, 3566}, {110, 57518}, {112, 54412}, {163, 18156}, {669, 6388}, {798, 17876}, {1501, 8651}, {1576, 193}, {1974, 57071}, {2206, 3798}, {2996, 44173}, {3565, 76}, {6391, 3267}, {8769, 20948}, {8770, 850}, {9426, 47430}, {14248, 14618}, {14574, 3053}, {14966, 51374}, {23357, 57216}, {27364, 15415}, {32661, 6337}, {32713, 21447}, {32739, 4028}, {35136, 1502}, {38252, 1577}, {40319, 525}, {53059, 523}, {57204, 5139}, {60839, 52617}, {61194, 41588}, {61206, 6353}, {61218, 41584}, {62194, 58766}, {65311, 305}
X(65178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 3565, 65311}

X(65179) = TRILINEAR POLE OF LINE {3, 1433}

Barycentrics    a^2*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2-b^2-c^2)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2) : :

X(65179) lies on the MacBeath circumconic and on these lines: {84, 8759}, {109, 13138}, {110, 8059}, {189, 2988}, {268, 1815}, {271, 603}, {648, 1414}, {651, 36049}, {934, 8064}, {1332, 6517}, {1413, 60049}, {1422, 2990}, {1433, 60047}, {1436, 60025}, {1440, 2989}, {1461, 4091}, {1797, 55117}, {1814, 56972}, {2986, 8808}, {3561, 46881}, {4565, 46639}, {13136, 44327}, {41081, 65302}, {61229, 65303}

X(65179) = trilinear pole of line {3, 1433}
X(65179) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 14298}, {9, 54239}, {19, 8058}, {29, 55212}, {33, 14837}, {34, 57049}, {40, 3064}, {55, 59935}, {108, 5514}, {158, 10397}, {196, 3900}, {198, 44426}, {208, 3239}, {227, 17926}, {281, 6129}, {329, 18344}, {342, 657}, {347, 65103}, {393, 57101}, {513, 55116}, {514, 40971}, {522, 2331}, {607, 17896}, {644, 38362}, {650, 7952}, {652, 47372}, {663, 64211}, {1096, 57245}, {1783, 38357}, {1857, 64885}, {2187, 46110}, {2324, 7649}, {3194, 3700}, {3195, 4391}, {3209, 4397}, {3318, 40117}, {3737, 53009}, {4041, 41083}, {6591, 7080}, {7007, 8063}, {7074, 17924}, {8641, 40701}, {8822, 55206}, {42069, 65159}, {47432, 54240}
X(65179) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 8058}, {223, 59935}, {478, 54239}, {1147, 10397}, {6503, 57245}, {11517, 57049}, {36033, 14298}, {38983, 5514}, {39006, 38357}, {39026, 55116}
X(65179) = X(i)-Ceva conjugate of X(j) for these {i, j}: {53642, 8059}
X(65179) = X(i)-cross conjugate of X(j) for these {i, j}: {652, 271}, {10397, 3}, {22124, 59}, {46391, 1795}, {57241, 77}
X(65179) = pole of line {8058, 10397} with respect to the Stammler hyperbola
X(65179) = pole of line {41081, 56545} with respect to the Hutson-Moses hyperbola
X(65179) = intersection, other than A, B, C, of circumconics {{A, B, C, X(48), X(8750)}}, {{A, B, C, X(63), X(653)}}, {{A, B, C, X(77), X(4626)}}, {{A, B, C, X(101), X(61224)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(222), X(1461)}}, {{A, B, C, X(326), X(53643)}}, {{A, B, C, X(905), X(40527)}}, {{A, B, C, X(1414), X(6517)}}, {{A, B, C, X(7011), X(31511)}}, {{A, B, C, X(8059), X(65330)}}, {{A, B, C, X(8064), X(36049)}}, {{A, B, C, X(23144), X(56786)}}, {{A, B, C, X(41081), X(44327)}}, {{A, B, C, X(46964), X(65216)}}

X(65180) = X(101)X(108)∩X(107)X(109)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-2*b*c*(b+c)-a*(b+c)^2) : :

X(65180) lies on these lines: {29, 55101}, {57, 1957}, {58, 1940}, {92, 55086}, {101, 108}, {107, 109}, {158, 580}, {204, 8270}, {226, 7076}, {243, 13329}, {692, 53317}, {1096, 1708}, {1118, 1724}, {1331, 61180}, {1430, 3911}, {1451, 39585}, {1712, 54295}, {1754, 1857}, {1767, 8765}, {1813, 2617}, {1882, 56831}, {1897, 3939}, {2299, 40149}, {3194, 37558}, {6335, 65190}, {8750, 57218}, {13149, 65187}, {23067, 53323}, {32714, 61225}, {36797, 54440}, {52167, 64013}, {52921, 52938}

X(65180) = X(i)-isoconjugate-of-X(j) for these {i, j}: {521, 51223}, {905, 2335}, {1946, 57831}, {2194, 63220}, {2215, 6332}, {7004, 65227}, {7117, 54970}, {7252, 63235}, {26932, 36080}
X(65180) = X(i)-Dao conjugate of X(j) for these {i, j}: {1214, 63220}, {39053, 57831}
X(65180) = X(i)-cross conjugate of X(j) for these {i, j}: {46385, 39585}
X(65180) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(162)}}, {{A, B, C, X(107), X(1783)}}, {{A, B, C, X(108), X(65334)}}, {{A, B, C, X(405), X(7452)}}, {{A, B, C, X(653), X(4551)}}, {{A, B, C, X(1897), X(61236)}}, {{A, B, C, X(2812), X(23882)}}, {{A, B, C, X(3939), X(52921)}}, {{A, B, C, X(36050), X(54442)}}, {{A, B, C, X(46385), X(46393)}}
X(65180) = barycentric product X(i)*X(j) for these (i, j): {1, 65355}, {108, 5271}, {190, 54394}, {405, 653}, {1451, 6335}, {1882, 662}, {1897, 37543}, {4552, 56831}, {5295, 65232}, {23882, 7012}, {32674, 44140}, {39585, 651}, {46102, 46385}, {46404, 5320}
X(65180) = barycentric quotient X(i)/X(j) for these (i, j): {226, 63220}, {405, 6332}, {653, 57831}, {1451, 905}, {1882, 1577}, {4551, 63235}, {5271, 35518}, {5320, 652}, {7012, 54970}, {7115, 65227}, {8750, 2335}, {23882, 17880}, {32674, 51223}, {37543, 4025}, {39585, 4391}, {46385, 26932}, {54394, 514}, {56831, 4560}, {65355, 75}
X(65180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {108, 1783, 4551}, {162, 653, 109}

X(65181) = TRILINEAR POLE OF LINE {4, 64}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(a^4+b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2-c^2))*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b^2-c^2)) : :

X(65181) lies on these lines: {64, 57732}, {99, 59087}, {107, 1301}, {253, 393}, {459, 11547}, {525, 32646}, {648, 2404}, {653, 65224}, {685, 15384}, {823, 13149}, {1073, 2052}, {3343, 56296}, {6331, 44326}, {6335, 56235}, {6526, 17983}, {8764, 52158}, {9308, 15394}, {14249, 41085}, {14361, 40839}, {14362, 17037}, {14638, 57574}, {15459, 58759}, {15466, 57483}, {16081, 21447}, {20213, 64987}, {32687, 35571}, {44181, 65350}, {46065, 51358}, {46106, 52514}

X(65181) = isogonal conjugate of X(58796)
X(65181) = isotomic conjugate of X(20580)
X(65181) = trilinear pole of line {4, 64}
X(65181) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 58796}, {20, 822}, {31, 20580}, {48, 8057}, {63, 42658}, {122, 163}, {154, 24018}, {162, 47409}, {204, 52613}, {255, 6587}, {326, 62176}, {520, 610}, {577, 17898}, {656, 15905}, {810, 37669}, {1101, 55269}, {1410, 57045}, {1562, 4575}, {1895, 32320}, {3198, 4091}, {3990, 21172}, {5930, 36054}, {6507, 44705}, {7125, 14308}, {8804, 23224}, {14331, 22341}, {14345, 35200}, {18750, 39201}, {19614, 57201}, {27382, 51640}, {30456, 57241}, {36908, 58340}, {37754, 52913}, {40933, 57057}, {41086, 57233}, {52948, 62665}
X(65181) = X(i)-vertex conjugate of X(j) for these {i, j}: {32649, 65276}
X(65181) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 20580}, {3, 58796}, {4, 57201}, {115, 122}, {122, 39020}, {125, 47409}, {133, 14345}, {136, 1562}, {523, 55269}, {1249, 8057}, {3162, 42658}, {3343, 52613}, {6523, 6587}, {13567, 58763}, {14092, 520}, {15259, 62176}, {36830, 35602}, {39062, 37669}, {40596, 15905}, {40839, 525}
X(65181) = X(i)-Ceva conjugate of X(j) for these {i, j}: {23582, 14572}, {44181, 6526}, {53639, 107}, {55268, 44181}, {57574, 253}
X(65181) = X(i)-cross conjugate of X(j) for these {i, j}: {523, 253}, {525, 2052}, {1301, 53639}, {6526, 44181}, {6529, 107}, {6587, 4}, {6622, 18020}, {33630, 32230}, {41489, 15384}, {52585, 275}, {58759, 459}, {59932, 34407}
X(65181) = pole of line {122, 1562} with respect to the polar circle
X(65181) = pole of line {6225, 6527} with respect to the Kiepert parabola
X(65181) = pole of line {107, 46639} with respect to the Steiner circumellipse
X(65181) = pole of line {20580, 58796} with respect to the Wallace hyperbola
X(65181) = pole of line {14615, 46741} with respect to the dual conic of Jerabek hyperbola
X(65181) = pole of line {55269, 57296} with respect to the dual conic of Wallace hyperbola
X(65181) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(41678)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(253), X(35571)}}, {{A, B, C, X(393), X(23977)}}, {{A, B, C, X(523), X(14638)}}, {{A, B, C, X(525), X(55127)}}, {{A, B, C, X(645), X(41207)}}, {{A, B, C, X(847), X(30251)}}, {{A, B, C, X(1289), X(16039)}}, {{A, B, C, X(1301), X(44326)}}, {{A, B, C, X(1304), X(4558)}}, {{A, B, C, X(2052), X(2404)}}, {{A, B, C, X(4563), X(47269)}}, {{A, B, C, X(6526), X(55268)}}, {{A, B, C, X(6529), X(32646)}}, {{A, B, C, X(18315), X(33640)}}, {{A, B, C, X(22456), X(35136)}}, {{A, B, C, X(30249), X(36841)}}, {{A, B, C, X(32687), X(32713)}}, {{A, B, C, X(59086), X(65176)}}
X(65181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 53639, 46639}

X(65182) = X(3)X(3462)∩X(110)X(112)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6*(b^2+c^2)+3*a^2*(b^2-c^2)^2*(b^2+c^2)-3*a^4*(b^4+c^4)-(b^2-c^2)^2*(b^4+c^4)) : :

X(65182) lies on these lines: {3, 3462}, {4, 8901}, {22, 12384}, {107, 1624}, {110, 112}, {162, 23981}, {378, 12244}, {418, 56297}, {648, 23181}, {852, 51358}, {933, 46062}, {1301, 58950}, {1304, 39180}, {1576, 52917}, {1634, 65177}, {3574, 19172}, {6638, 56296}, {6750, 51887}, {6761, 62334}, {10594, 15960}, {11746, 47228}, {13417, 35908}, {15329, 35360}, {26895, 39575}, {35311, 50947}, {37937, 47248}, {41204, 44886}, {58070, 61194}

X(65182) = trilinear pole of line {389, 63634}
X(65182) = perspector of circumconic {{A, B, C, X(250), X(34538)}}
X(65182) = X(i)-isoconjugate-of-X(j) for these {i, j}: {656, 40448}, {810, 42333}, {20902, 59009}, {24018, 40402}
X(65182) = X(i)-Dao conjugate of X(j) for these {i, j}: {34836, 3265}, {39062, 42333}, {40596, 40448}
X(65182) = X(i)-Ceva conjugate of X(j) for these {i, j}: {14587, 24}
X(65182) = pole of line {107, 933} with respect to the circumcircle
X(65182) = pole of line {338, 2972} with respect to the polar circle
X(65182) = pole of line {22, 1498} with respect to the Kiepert parabola
X(65182) = pole of line {525, 15781} with respect to the Stammler hyperbola
X(65182) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 38577, 38585}, {1294, 18401, 38672}, {38605, 38616, 51532}
X(65182) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(32661)}}, {{A, B, C, X(110), X(15352)}}, {{A, B, C, X(389), X(2420)}}, {{A, B, C, X(933), X(1625)}}, {{A, B, C, X(1304), X(35324)}}, {{A, B, C, X(1636), X(39180)}}, {{A, B, C, X(4230), X(52280)}}, {{A, B, C, X(6750), X(53176)}}, {{A, B, C, X(14591), X(51887)}}, {{A, B, C, X(23181), X(52779)}}, {{A, B, C, X(45198), X(61198)}}, {{A, B, C, X(61207), X(63634)}}
X(65182) = barycentric product X(i)*X(j) for these (i, j): {107, 46832}, {110, 52280}, {112, 45198}, {162, 45224}, {275, 61195}, {389, 648}, {14570, 51887}, {16813, 42441}, {18315, 6750}, {19170, 35360}, {34836, 933}, {45225, 662}, {63634, 99}
X(65182) = barycentric quotient X(i)/X(j) for these (i, j): {112, 40448}, {389, 525}, {648, 42333}, {6750, 18314}, {19170, 62428}, {32713, 40402}, {42441, 60597}, {45198, 3267}, {45224, 14208}, {45225, 1577}, {46832, 3265}, {51887, 15412}, {52280, 850}, {57655, 59009}, {61195, 343}, {63634, 523}
X(65182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {107, 1624, 46587}, {1624, 52604, 107}

X(65183) = TRILINEAR POLE OF LINE {5, 324}

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(-(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(65183) lies on these lines: {5, 41219}, {53, 53245}, {94, 2052}, {107, 925}, {112, 39418}, {264, 1972}, {324, 62722}, {648, 1625}, {655, 823}, {11794, 41677}, {14570, 61193}, {14618, 41678}, {15466, 62583}, {16813, 23582}, {18315, 52779}, {23290, 52604}, {31610, 40684}, {35360, 61195}, {40853, 43752}, {46394, 47383}, {53205, 54950}, {56188, 65204}

X(65183) = isogonal conjugate of X(46088)
X(65183) = trilinear pole of line {5, 324}
X(65183) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46088}, {48, 23286}, {54, 822}, {63, 58308}, {97, 810}, {255, 2623}, {520, 2148}, {525, 62267}, {560, 15414}, {577, 2616}, {647, 2169}, {656, 14533}, {661, 19210}, {933, 37754}, {1577, 62256}, {2167, 39201}, {2190, 32320}, {2624, 50463}, {2631, 46090}, {2632, 14586}, {3049, 62277}, {3265, 62269}, {3269, 36134}, {3708, 15958}, {6507, 58756}, {9247, 62428}, {14208, 62270}, {15412, 52430}, {16813, 42080}, {24018, 54034}, {34980, 65221}, {52613, 62268}, {57703, 63832}, {58310, 62276}
X(65183) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46088}, {5, 32320}, {137, 3269}, {216, 520}, {338, 15526}, {1249, 23286}, {2972, 35071}, {3162, 58308}, {6374, 15414}, {6523, 2623}, {6663, 17434}, {14363, 647}, {14920, 8552}, {15450, 34980}, {36830, 19210}, {39019, 2972}, {39052, 2169}, {39062, 97}, {40588, 39201}, {40596, 14533}, {45249, 58796}, {52032, 52613}, {52869, 1636}, {62576, 62428}
X(65183) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6528, 35360}, {23582, 2052}, {57556, 264}
X(65183) = X(i)-cross conjugate of X(j) for these {i, j}: {525, 31610}, {6368, 264}, {14129, 23582}, {17434, 5}, {18314, 324}, {23290, 62275}
X(65183) = pole of line {3269, 38352} with respect to the polar circle
X(65183) = pole of line {11441, 20477} with respect to the Kiepert parabola
X(65183) = pole of line {32320, 46088} with respect to the Stammler hyperbola
X(65183) = pole of line {35360, 58071} with respect to the Steiner circumellipse
X(65183) = pole of line {46088, 52613} with respect to the Wallace hyperbola
X(65183) = pole of line {343, 15466} with respect to the dual conic of Jerabek hyperbola
X(65183) = intersection, other than A, B, C, of circumconics {{A, B, C, X(53), X(52604)}}, {{A, B, C, X(94), X(648)}}, {{A, B, C, X(264), X(54950)}}, {{A, B, C, X(467), X(15329)}}, {{A, B, C, X(1625), X(32662)}}, {{A, B, C, X(2052), X(16813)}}, {{A, B, C, X(4558), X(36831)}}, {{A, B, C, X(5392), X(16039)}}, {{A, B, C, X(6368), X(15526)}}, {{A, B, C, X(6528), X(18817)}}, {{A, B, C, X(6529), X(61193)}}, {{A, B, C, X(17434), X(41219)}}, {{A, B, C, X(18314), X(41079)}}, {{A, B, C, X(18315), X(23181)}}, {{A, B, C, X(38342), X(42405)}}
X(65183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6528, 15352, 648}

X(65184) = X(2)X(14652)∩X(107)X(112)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(2*a^8+a^4*(b^2-c^2)^2+(b^2-c^2)^4-3*a^6*(b^2+c^2)-a^2*(b^2-c^2)^2*(b^2+c^2)) : :

X(65184) lies on these lines: {2, 14652}, {4, 11587}, {20, 2917}, {107, 112}, {110, 925}, {476, 38861}, {512, 61195}, {523, 35311}, {930, 58975}, {933, 20626}, {1576, 35360}, {1601, 58805}, {1624, 4240}, {2407, 61182}, {2934, 7493}, {3432, 21451}, {4226, 23181}, {14586, 65348}, {14673, 37926}, {15139, 62308}, {17847, 44003}, {23315, 45289}, {41678, 52917}, {43768, 44668}, {56924, 62292}

X(65184) = X(i)-vertex conjugate of X(j) for these {i, j}: {14570, 23181}
X(65184) = X(i)-Dao conjugate of X(j) for these {i, j}: {10600, 523}
X(65184) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1101, 32354}, {16039, 21294}
X(65184) = pole of line {14570, 23181} with respect to the circumcircle
X(65184) = pole of line {128, 132} with respect to the orthoptic circle of the Steiner Inellipse
X(65184) = pole of line {136, 15526} with respect to the polar circle
X(65184) = pole of line {4, 54} with respect to the Kiepert parabola
X(65184) = pole of line {924, 52613} with respect to the Stammler hyperbola
X(65184) = pole of line {4558, 16039} with respect to the Steiner circumellipse
X(65184) = pole of line {4143, 6563} with respect to the Wallace hyperbola
X(65184) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(65309)}}, {{A, B, C, X(925), X(6529)}}, {{A, B, C, X(20626), X(61193)}}
X(65184) = barycentric product X(i)*X(j) for these (i, j): {6146, 648}, {10600, 16813}
X(65184) = barycentric quotient X(i)/X(j) for these (i, j): {6146, 525}, {10600, 60597}
X(65184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 925, 14570}

X(65185) = X(99)X(100)∩X(109)X(789)

Barycentrics    (a-b)*b*(a-c)*c*(2*a^2+b*c+a*(b+c)) : :

X(65185) lies on these lines: {31, 34020}, {99, 100}, {109, 789}, {171, 31008}, {190, 4598}, {274, 32917}, {692, 4623}, {750, 18140}, {785, 59093}, {874, 65166}, {902, 62234}, {932, 59094}, {1054, 39044}, {1150, 17143}, {1155, 1921}, {1920, 4640}, {1965, 17596}, {1978, 4427}, {3501, 24615}, {3550, 17149}, {3570, 65168}, {4432, 18149}, {4434, 52049}, {4589, 36806}, {4756, 7035}, {4781, 53363}, {6376, 56010}, {6377, 30667}, {6384, 8616}, {8709, 43350}, {17126, 30964}, {18037, 41163}, {18169, 40418}, {32042, 57977}, {53355, 61187}, {54982, 62464}

X(65185) = trilinear pole of line {17379, 31997}
X(65185) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 39967}, {667, 17038}, {669, 56052}, {798, 56066}, {1919, 56210}, {3122, 43359}
X(65185) = X(i)-vertex conjugate of X(j) for these {i, j}: {18830, 65163}
X(65185) = X(i)-Dao conjugate of X(j) for these {i, j}: {5224, 14349}, {5375, 39967}, {6631, 17038}, {9296, 56210}, {31998, 56066}
X(65185) = X(i)-Ceva conjugate of X(j) for these {i, j}: {37218, 668}
X(65185) = pole of line {4436, 18830} with respect to the circumcircle
X(65185) = pole of line {81, 34063} with respect to the Kiepert parabola
X(65185) = pole of line {667, 57074} with respect to the Stammler hyperbola
X(65185) = pole of line {53332, 61183} with respect to the Steiner circumellipse
X(65185) = pole of line {43, 894} with respect to the Yff parabola
X(65185) = pole of line {213, 17120} with respect to the Hutson-Moses hyperbola
X(65185) = pole of line {513, 18197} with respect to the Wallace hyperbola
X(65185) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(4598)}}, {{A, B, C, X(100), X(65167)}}, {{A, B, C, X(190), X(59094)}}, {{A, B, C, X(789), X(7257)}}, {{A, B, C, X(799), X(18830)}}, {{A, B, C, X(932), X(61234)}}, {{A, B, C, X(31997), X(55243)}}, {{A, B, C, X(43350), X(62841)}}
X(65185) = barycentric product X(i)*X(j) for these (i, j): {190, 31997}, {1978, 62841}, {4932, 7035}, {17379, 668}, {37218, 41849}, {43223, 799}
X(65185) = barycentric quotient X(i)/X(j) for these (i, j): {99, 56066}, {100, 39967}, {190, 17038}, {668, 56210}, {799, 56052}, {4567, 43359}, {4932, 244}, {17379, 513}, {28622, 50488}, {31997, 514}, {41849, 14349}, {43223, 661}, {62841, 649}
X(65185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 799, 668}, {190, 4598, 61234}

X(65186) = X(1)X(27666)∩X(100)X(190)

Barycentrics    a^2*(a-b)*(a-c)*(b^2+3*b*c+c^2+a*(b+c)) : :

X(65186) lies on these lines: {1, 27666}, {42, 63519}, {55, 9330}, {100, 190}, {101, 8701}, {109, 28210}, {110, 3939}, {210, 4184}, {354, 16057}, {835, 8708}, {901, 28226}, {931, 9059}, {1026, 65314}, {1897, 4250}, {1995, 6600}, {3240, 34247}, {3293, 27664}, {3681, 4210}, {3724, 5524}, {3732, 54118}, {3871, 31035}, {4191, 4661}, {4225, 4420}, {4246, 65193}, {4430, 16059}, {4551, 65315}, {4671, 5687}, {5640, 64739}, {7419, 56176}, {8652, 58125}, {8715, 64178}, {10545, 41457}, {14997, 37590}, {15507, 20095}, {15624, 63961}, {17136, 25310}, {17524, 32635}, {20470, 62236}, {27065, 54327}, {27812, 64753}, {28214, 28230}, {28218, 58110}, {28841, 29363}, {29199, 53625}, {35983, 46897}, {37138, 65256}, {37211, 40519}, {51377, 56808}

X(65186) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 46961}, {3737, 35576}
X(65186) = X(i)-Dao conjugate of X(j) for these {i, j}: {28651, 693}
X(65186) = pole of line {100, 28196} with respect to the circumcircle
X(65186) = pole of line {2969, 53564} with respect to the polar circle
X(65186) = pole of line {3733, 4401} with respect to the Stammler hyperbola
X(65186) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {104, 28197, 38665}
X(65186) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(101), X(4427)}}, {{A, B, C, X(109), X(4781)}}, {{A, B, C, X(190), X(4627)}}, {{A, B, C, X(835), X(4436)}}, {{A, B, C, X(3699), X(28210)}}, {{A, B, C, X(3952), X(8694)}}, {{A, B, C, X(4756), X(58125)}}, {{A, B, C, X(8708), X(65313)}}, {{A, B, C, X(17780), X(28226)}}, {{A, B, C, X(18004), X(58298)}}, {{A, B, C, X(30565), X(47959)}}, {{A, B, C, X(47656), X(50333)}}
X(65186) = barycentric product X(i)*X(j) for these (i, j): {1252, 47656}, {4600, 58298}, {28196, 28651}, {47959, 765}
X(65186) = barycentric quotient X(i)/X(j) for these (i, j): {1252, 46961}, {4559, 35576}, {47656, 23989}, {47959, 1111}, {58298, 3120}
X(65186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 4557, 65313}, {100, 4756, 4436}, {100, 52923, 4427}, {100, 57151, 65166}

X(65187) = X(101)X(651)∩X(109)X(658)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^2-2*b*c-a*(b+c)) : :

X(65187) lies on these lines: {7, 64013}, {77, 52769}, {101, 651}, {109, 658}, {212, 56309}, {238, 62786}, {479, 17127}, {664, 3939}, {1088, 55086}, {1331, 35312}, {1414, 4616}, {1471, 42309}, {1754, 2898}, {3246, 34855}, {4554, 65190}, {4566, 57250}, {6516, 35338}, {6649, 62532}, {7177, 52015}, {7290, 63150}, {13149, 65180}, {13329, 14189}, {23973, 61241}, {35281, 56543}, {61225, 65296}

X(65187) = trilinear pole of line {2280, 5228}
X(65187) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 59269}, {522, 60673}, {650, 40779}, {657, 27475}, {663, 60668}, {667, 59260}, {1002, 3900}, {1021, 60677}, {1146, 8693}, {2279, 3239}, {2310, 37138}, {4105, 62784}, {4130, 42290}, {4171, 42302}, {6608, 59193}, {8641, 59255}, {10581, 42310}, {14936, 32041}, {57180, 62946}
X(65187) = X(i)-Dao conjugate of X(j) for these {i, j}: {6631, 59260}, {39026, 59269}, {55059, 52335}, {61076, 24026}
X(65187) = X(i)-cross conjugate of X(j) for these {i, j}: {4724, 5228}
X(65187) = pole of line {1021, 4105} with respect to the Stammler hyperbola
X(65187) = pole of line {63, 6605} with respect to the Hutson-Moses hyperbola
X(65187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(1414)}}, {{A, B, C, X(109), X(1471)}}, {{A, B, C, X(651), X(927)}}, {{A, B, C, X(658), X(41353)}}, {{A, B, C, X(664), X(63203)}}, {{A, B, C, X(1020), X(4626)}}, {{A, B, C, X(3676), X(53544)}}, {{A, B, C, X(5228), X(23890)}}, {{A, B, C, X(24029), X(40719)}}
X(65187) = barycentric product X(i)*X(j) for these (i, j): {100, 42309}, {109, 60720}, {190, 59242}, {279, 54440}, {1001, 658}, {1275, 4724}, {1461, 4441}, {1471, 4554}, {2280, 4569}, {3696, 4637}, {3886, 4617}, {4384, 934}, {4565, 60734}, {4566, 60721}, {4616, 59207}, {4762, 7045}, {5228, 664}, {23151, 36118}, {28809, 6614}, {37658, 4626}, {40719, 651}, {41353, 63236}, {42289, 4573}, {45755, 59457}, {46406, 60722}, {53321, 60735}
X(65187) = barycentric quotient X(i)/X(j) for these (i, j): {101, 59269}, {109, 40779}, {190, 59260}, {651, 60668}, {658, 59255}, {934, 27475}, {1001, 3239}, {1262, 37138}, {1415, 60673}, {1461, 1002}, {1471, 650}, {2280, 3900}, {4384, 4397}, {4441, 52622}, {4617, 62784}, {4626, 62946}, {4724, 1146}, {4762, 24026}, {5228, 522}, {6614, 42290}, {7045, 32041}, {24027, 8693}, {37658, 4163}, {40719, 4391}, {40784, 4522}, {41353, 62622}, {42289, 3700}, {42309, 693}, {45755, 4081}, {53321, 60677}, {54440, 346}, {59242, 514}, {60720, 35519}, {60721, 7253}, {60722, 657}, {62786, 63223}
X(65187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {651, 934, 41353}

X(65188) = X(7)X(3315)∩X(109)X(658)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+(b-c)^2) : :

X(65188) lies on these lines: {7, 3315}, {57, 6169}, {108, 934}, {109, 658}, {222, 31526}, {223, 36905}, {278, 2898}, {279, 40615}, {347, 34188}, {651, 2428}, {664, 668}, {693, 1897}, {1088, 34036}, {1421, 56783}, {1465, 14189}, {3160, 5328}, {3660, 62785}, {4318, 37780}, {4573, 57216}, {4617, 23973}, {6545, 32739}, {6571, 8707}, {8270, 31627}, {9312, 26736}, {13149, 36127}, {16502, 28110}, {17671, 41786}, {18623, 31527}, {23703, 65165}, {29055, 34083}, {31599, 37800}, {38357, 45276}, {41353, 61227}, {45742, 47848}

X(65188) = trilinear pole of line {2082, 4000}
X(65188) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 48070}, {100, 14935}, {522, 7084}, {649, 56243}, {650, 7123}, {657, 7131}, {663, 56179}, {1037, 3900}, {1041, 57108}, {3022, 8269}, {3063, 30701}, {3271, 52778}, {3709, 40403}, {4105, 56359}, {7252, 56260}, {8611, 57386}, {8641, 8817}, {30705, 57180}
X(65188) = X(i)-Dao conjugate of X(j) for these {i, j}: {1565, 26932}, {3160, 48070}, {4000, 4163}, {5375, 56243}, {6554, 522}, {8054, 14935}, {10001, 30701}, {14936, 3119}, {15487, 650}, {16583, 52355}, {18589, 4041}, {59619, 4397}
X(65188) = X(i)-Ceva conjugate of X(j) for these {i, j}: {46102, 7}
X(65188) = X(i)-cross conjugate of X(j) for these {i, j}: {1633, 3732}
X(65188) = pole of line {3729, 17784} with respect to the Yff parabola
X(65188) = pole of line {7, 30616} with respect to the Hutson-Moses hyperbola
X(65188) = pole of line {85, 16706} with respect to the dual conic of Feuerbach hyperbola
X(65188) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(108), X(1633)}}, {{A, B, C, X(109), X(614)}}, {{A, B, C, X(668), X(927)}}, {{A, B, C, X(934), X(4561)}}, {{A, B, C, X(3676), X(48398)}}, {{A, B, C, X(4551), X(62752)}}, {{A, B, C, X(4625), X(14594)}}
X(65188) = barycentric product X(i)*X(j) for these (i, j): {190, 7195}, {274, 62752}, {497, 658}, {1040, 13149}, {1414, 53510}, {1473, 46404}, {1633, 85}, {1851, 65164}, {2082, 4569}, {3673, 651}, {3732, 7}, {3914, 4573}, {4000, 664}, {4554, 614}, {4561, 61411}, {4620, 48403}, {4626, 6554}, {16502, 4572}, {16583, 4625}, {16750, 4551}, {17170, 653}, {18026, 7289}, {20235, 65232}, {21750, 55213}, {27509, 36118}, {28017, 668}, {30706, 52937}, {36838, 4319}, {40576, 41788}, {40961, 799}, {40965, 4635}, {41786, 53643}, {46406, 7083}, {48398, 4998}, {51400, 927}, {57785, 61160}, {61241, 64438}, {62544, 65165}
X(65188) = barycentric quotient X(i)/X(j) for these (i, j): {7, 48070}, {100, 56243}, {109, 7123}, {497, 3239}, {614, 650}, {649, 14935}, {651, 56179}, {658, 8817}, {664, 30701}, {934, 7131}, {1040, 57055}, {1414, 40403}, {1415, 7084}, {1461, 1037}, {1473, 652}, {1633, 9}, {1851, 3064}, {2082, 3900}, {3673, 4391}, {3732, 8}, {3914, 3700}, {4000, 522}, {4319, 4130}, {4551, 56260}, {4554, 57925}, {4564, 52778}, {4617, 56359}, {4626, 30705}, {5324, 1021}, {6554, 4163}, {7083, 657}, {7124, 57108}, {7195, 514}, {7289, 521}, {16502, 663}, {16583, 4041}, {16750, 18155}, {17115, 3119}, {17170, 6332}, {17441, 8611}, {18589, 52355}, {21750, 63461}, {28017, 513}, {28110, 17072}, {30706, 4105}, {32714, 1041}, {40934, 3709}, {40961, 661}, {40965, 4171}, {40987, 65103}, {41785, 44448}, {48398, 11}, {48403, 21044}, {51400, 50333}, {53510, 4086}, {61160, 210}, {61411, 7649}, {62752, 37}
X(65188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 3676, 658}, {664, 4554, 14594}

X(65189) = X(190)X(2415)∩X(664)X(668)

Barycentrics    (a-b)*(a-c)*(a^2-b^2+6*b*c-c^2) : :

X(65189) lies on these lines: {99, 6014}, {190, 2415}, {279, 42020}, {664, 668}, {1222, 26563}, {1565, 21290}, {3732, 4482}, {4437, 39351}, {4534, 52157}, {4555, 33948}, {4572, 4626}, {6558, 65195}, {7181, 60367}, {9312, 44720}, {9369, 59507}, {17044, 27546}, {17136, 43290}, {21041, 25605}, {25718, 44722}, {31298, 32029}, {33780, 36846}, {58130, 58135}, {61186, 65166}

X(65189) = trilinear pole of line {5437, 31995}
X(65189) = X(i)-isoconjugate-of-X(j) for these {i, j}: {667, 7320}, {3063, 44794}, {56200, 57181}
X(65189) = X(i)-Dao conjugate of X(j) for these {i, j}: {6631, 7320}, {10001, 44794}, {22754, 663}
X(65189) = pole of line {3875, 32939} with respect to the Kiepert parabola
X(65189) = pole of line {3699, 21272} with respect to the Steiner circumellipse
X(65189) = pole of line {145, 3729} with respect to the Yff parabola
X(65189) = pole of line {4383, 24599} with respect to the Hutson-Moses hyperbola
X(65189) = pole of line {3737, 6006} with respect to the Wallace hyperbola
X(65189) = pole of line {85, 1997} with respect to the dual conic of Feuerbach hyperbola
X(65189) = intersection, other than A, B, C, of circumconics {{A, B, C, X(664), X(27834)}}, {{A, B, C, X(1026), X(4853)}}, {{A, B, C, X(2415), X(31995)}}, {{A, B, C, X(4551), X(6014)}}, {{A, B, C, X(4554), X(53647)}}, {{A, B, C, X(8706), X(30720)}}
X(65189) = barycentric product X(i)*X(j) for these (i, j): {190, 31995}, {646, 7271}, {1978, 3304}, {3698, 799}, {3699, 43983}, {4554, 4853}, {5437, 668}
X(65189) = barycentric quotient X(i)/X(j) for these (i, j): {190, 7320}, {664, 44794}, {3304, 649}, {3698, 661}, {3699, 56200}, {4853, 650}, {5437, 513}, {7271, 3669}, {31995, 514}, {43983, 3676}
X(65189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 53647, 21272}, {664, 668, 3699}

X(65190) = X(100)X(101)∩X(109)X(190)

Barycentrics    a*(a-b)*(a-c)*(a-b-c)*(a^2+2*b*c+a*(b+c)) : :

X(65190) lies on these lines: {31, 30568}, {58, 56311}, {100, 101}, {109, 190}, {124, 28829}, {162, 65160}, {171, 4078}, {238, 62297}, {283, 3701}, {573, 26264}, {580, 46937}, {595, 19582}, {643, 645}, {750, 59779}, {931, 8694}, {1083, 28353}, {1293, 53625}, {1331, 3952}, {1332, 4551}, {1357, 24826}, {1365, 24835}, {1724, 2899}, {1936, 3717}, {2222, 59104}, {2328, 7081}, {2361, 4009}, {3161, 17126}, {4069, 4571}, {4427, 25268}, {4553, 53279}, {4554, 65187}, {5205, 13329}, {6335, 65180}, {8055, 17127}, {9059, 59006}, {9347, 25082}, {17777, 64013}, {18743, 55086}, {23691, 44425}, {25968, 51390}, {65198, 65206}

X(65190) = trilinear pole of line {958, 2268}
X(65190) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 65225}, {667, 58008}, {931, 53540}, {941, 3669}, {1015, 32038}, {1086, 32693}, {2258, 3676}, {3733, 60321}, {4017, 5331}, {7180, 37870}, {18191, 52931}, {31359, 43924}, {34258, 57181}, {34259, 43923}
X(65190) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 44733}, {6631, 58008}, {17417, 1086}, {34261, 514}, {34961, 5331}, {39026, 959}
X(65190) = X(i)-cross conjugate of X(j) for these {i, j}: {17418, 958}
X(65190) = pole of line {1621, 52352} with respect to the Kiepert parabola
X(65190) = pole of line {1019, 43924} with respect to the Stammler hyperbola
X(65190) = pole of line {9, 345} with respect to the Yff parabola
X(65190) = pole of line {1, 59727} with respect to the Hutson-Moses hyperbola
X(65190) = pole of line {3676, 7199} with respect to the Wallace hyperbola
X(65190) = pole of line {101, 835} with respect to the dual conic of incircle
X(65190) = pole of line {17289, 25082} with respect to the dual conic of Feuerbach hyperbola
X(65190) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(645)}}, {{A, B, C, X(101), X(643)}}, {{A, B, C, X(190), X(61223)}}, {{A, B, C, X(644), X(7256)}}, {{A, B, C, X(958), X(1023)}}, {{A, B, C, X(1018), X(3699)}}, {{A, B, C, X(1026), X(11679)}}, {{A, B, C, X(1635), X(17418)}}, {{A, B, C, X(3887), X(23880)}}, {{A, B, C, X(7437), X(44734)}}, {{A, B, C, X(38325), X(53526)}}, {{A, B, C, X(53625), X(57192)}}, {{A, B, C, X(54396), X(61239)}}
X(65190) = barycentric product X(i)*X(j) for these (i, j): {100, 11679}, {109, 61414}, {190, 958}, {1016, 17418}, {1332, 54396}, {1468, 646}, {2268, 668}, {3699, 940}, {3713, 664}, {3714, 662}, {4033, 54417}, {4076, 48144}, {4571, 5307}, {10436, 644}, {23880, 765}, {31993, 643}, {34284, 3939}, {53526, 57731}, {59305, 645}, {65168, 8}
X(65190) = barycentric quotient X(i)/X(j) for these (i, j): {100, 44733}, {101, 959}, {190, 58008}, {643, 37870}, {644, 31359}, {765, 32038}, {940, 3676}, {958, 514}, {1018, 60321}, {1110, 32693}, {1252, 65225}, {1468, 3669}, {2268, 513}, {3699, 34258}, {3713, 522}, {3714, 1577}, {3939, 941}, {4587, 34259}, {5019, 43924}, {5546, 5331}, {8672, 53545}, {10436, 24002}, {11679, 693}, {17418, 1086}, {23880, 1111}, {31993, 4077}, {34284, 52621}, {48144, 1358}, {53561, 21132}, {54396, 17924}, {54417, 1019}, {58332, 2170}, {59305, 7178}, {61414, 35519}, {65168, 7}
X(65190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 644, 61223}, {643, 3699, 3939}

X(65191) = ANTICOMPLEMENT OF X(24195)

Barycentrics    (a-b)*(a-c)*(b+c)*(b^2+c^2+a*(b+c)) : :
X(65191) = -3*X[2]+2*X[24195]

X(65191) lies on these lines: {2, 24195}, {10, 2643}, {37, 3589}, {69, 24048}, {72, 2810}, {75, 24058}, {99, 101}, {141, 24090}, {142, 27705}, {192, 24067}, {306, 42710}, {321, 3452}, {514, 65161}, {522, 53338}, {523, 40529}, {594, 46826}, {646, 3807}, {668, 54986}, {908, 61410}, {1018, 52609}, {1026, 61169}, {1086, 24076}, {1227, 24237}, {1278, 24077}, {2321, 24086}, {3159, 42083}, {3662, 27727}, {3882, 53332}, {3912, 4053}, {3943, 24081}, {3952, 4069}, {3970, 42724}, {3977, 42701}, {3995, 17012}, {4009, 50747}, {4033, 4103}, {4357, 21810}, {4416, 21873}, {4606, 37210}, {4664, 46913}, {5295, 12019}, {5969, 17760}, {7035, 65229}, {14543, 30729}, {17234, 24050}, {17242, 27586}, {17464, 22021}, {17793, 21210}, {18134, 24066}, {18697, 21033}, {20336, 21078}, {24092, 36494}, {26700, 65372}, {27420, 45744}, {29456, 39765}, {30867, 31025}, {30895, 40586}, {31993, 37691}, {42363, 42720}, {42700, 62564}, {61223, 61226}

X(65191) = anticomplement of X(24195)
X(65191) = trilinear pole of line {1211, 2292}
X(65191) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 62749}, {512, 64457}, {593, 57162}, {604, 57161}, {649, 2363}, {667, 14534}, {961, 7252}, {1220, 57129}, {1333, 4581}, {1791, 43925}, {1798, 6591}, {1980, 40827}, {2203, 15420}, {2298, 3733}, {2359, 57200}, {3121, 65281}, {3122, 65255}, {3125, 58982}, {8687, 18191}, {16726, 32736}
X(65191) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 62749}, {37, 4581}, {960, 649}, {1211, 1019}, {2092, 3737}, {3125, 244}, {3161, 57161}, {3666, 514}, {4357, 17212}, {5375, 2363}, {6631, 14534}, {17419, 18191}, {24195, 24195}, {39026, 1169}, {39054, 64457}, {52087, 3733}, {56905, 7649}, {59509, 7192}, {62564, 15420}
X(65191) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 3882}, {4564, 306}, {7035, 10}, {24041, 21081}, {53332, 61172}
X(65191) = X(i)-cross conjugate of X(j) for these {i, j}: {3910, 321}, {21124, 1211}, {50330, 4357}
X(65191) = pole of line {86, 17164} with respect to the Kiepert parabola
X(65191) = pole of line {3882, 4427} with respect to the Steiner circumellipse
X(65191) = pole of line {10, 321} with respect to the Yff parabola
X(65191) = pole of line {81, 306} with respect to the Hutson-Moses hyperbola
X(65191) = pole of line {514, 18200} with respect to the Wallace hyperbola
X(65191) = pole of line {3882, 14543} with respect to the dual conic of incircle
X(65191) = pole of line {4466, 17219} with respect to the dual conic of polar circle
X(65191) = pole of line {1739, 3836} with respect to the dual conic of Yff parabola
X(65191) = pole of line {21131, 21132} with respect to the dual conic of Wallace hyperbola
X(65191) = intersection, other than A, B, C, of circumconics {{A, B, C, X(37), X(54328)}}, {{A, B, C, X(99), X(4552)}}, {{A, B, C, X(101), X(4103)}}, {{A, B, C, X(429), X(4237)}}, {{A, B, C, X(645), X(3952)}}, {{A, B, C, X(662), X(3882)}}, {{A, B, C, X(1978), X(4605)}}, {{A, B, C, X(3910), X(4858)}}, {{A, B, C, X(4069), X(7259)}}, {{A, B, C, X(4357), X(40529)}}, {{A, B, C, X(21124), X(30572)}}, {{A, B, C, X(48131), X(59737)}}, {{A, B, C, X(50330), X(50456)}}
X(65191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 4561, 65168}, {321, 24069, 30566}, {3912, 22047, 24062}, {3912, 4053, 22047}, {4053, 42713, 3912}, {4115, 22003, 190}, {20336, 21078, 22008}, {21810, 27697, 4357}

X(65192) = X(1026)X(8706)∩X(3699)X(3799)

Barycentrics    (a-b)*(a-c)*(a-b-c)*(b^2+a*c)*(a*b+c^2) : :

X(65192) lies on these lines: {668, 56241}, {1026, 8706}, {3699, 3799}, {4041, 7257}, {7256, 61223}, {23354, 65209}, {30670, 65369}, {36800, 40608}

X(65192) = trilinear pole of line {346, 3985}
X(65192) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 56242}, {34, 22093}, {56, 4367}, {57, 20981}, {109, 53541}, {171, 43924}, {172, 3669}, {603, 54229}, {604, 4369}, {649, 7175}, {667, 7176}, {894, 57181}, {1014, 7234}, {1106, 3907}, {1357, 4579}, {1397, 4374}, {1400, 18200}, {1402, 17212}, {1407, 3287}, {1408, 2533}, {1412, 57234}, {1414, 4128}, {1415, 7200}, {1416, 53553}, {1417, 4922}, {1919, 7196}, {1980, 7205}, {2330, 43932}, {3248, 6649}, {3676, 7122}, {3955, 43923}, {4032, 57129}, {4477, 7023}, {4504, 16945}, {4529, 7366}, {4565, 16592}, {4573, 21755}, {7203, 20964}, {7207, 29055}, {17103, 51641}
X(65192) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4367}, {8, 4504}, {11, 53541}, {1146, 7200}, {2968, 4459}, {3161, 4369}, {5375, 7175}, {5452, 20981}, {6552, 3907}, {6631, 7176}, {6741, 53559}, {7952, 54229}, {9296, 7196}, {11517, 22093}, {24771, 3287}, {40582, 18200}, {40599, 57234}, {40605, 17212}, {40608, 4128}, {40609, 53553}, {52871, 4922}, {55064, 16592}, {59577, 2533}, {62585, 4374}
X(65192) = X(i)-Ceva conjugate of X(j) for these {i, j}: {56241, 27805}
X(65192) = X(i)-cross conjugate of X(j) for these {i, j}: {4171, 312}
X(65192) = pole of line {14949, 17261} with respect to the Yff parabola
X(65192) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(7257)}}, {{A, B, C, X(312), X(4602)}}, {{A, B, C, X(341), X(7259)}}, {{A, B, C, X(643), X(1018)}}, {{A, B, C, X(644), X(3799)}}, {{A, B, C, X(646), X(4562)}}, {{A, B, C, X(668), X(3699)}}, {{A, B, C, X(1026), X(6736)}}, {{A, B, C, X(3700), X(9293)}}, {{A, B, C, X(6010), X(43073)}}

X(65193) = X(92)X(3158)∩X(100)X(108)

Barycentrics    (a-b)*(a-c)*(a-b-c)*(a^2+b^2-c^2)*(3*a^2-(b-c)^2+2*a*(b+c))*(a^2-b^2+c^2) : :

X(65193) lies on these lines: {27, 56316}, {29, 56176}, {92, 3158}, {100, 108}, {107, 8694}, {162, 3939}, {243, 3689}, {278, 64146}, {412, 3811}, {1013, 6600}, {2900, 37279}, {3189, 5125}, {3699, 4587}, {4246, 65186}, {5174, 12437}, {5281, 7046}, {5853, 17923}, {6154, 52167}, {6335, 43290}, {8707, 58944}, {13149, 65194}, {21077, 52846}, {41083, 56178}, {44695, 64083}, {52412, 59584}, {64135, 64211}, {65213, 65217}

X(65193) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1459, 5665}
X(65193) = pole of line {11, 53545} with respect to the polar circle
X(65193) = pole of line {65160, 65206} with respect to the dual conic of incircle
X(65193) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(7259)}}, {{A, B, C, X(108), X(65201)}}, {{A, B, C, X(653), X(36797)}}, {{A, B, C, X(3601), X(23981)}}, {{A, B, C, X(3699), X(4552)}}, {{A, B, C, X(4587), X(8694)}}
X(65193) = barycentric product X(i)*X(j) for these (i, j): {1869, 645}, {1897, 5273}, {3601, 6335}, {3699, 7490}, {3945, 65160}, {20007, 653}, {65170, 8}
X(65193) = barycentric quotient X(i)/X(j) for these (i, j): {1783, 5665}, {1869, 7178}, {3601, 905}, {5273, 4025}, {7490, 3676}, {20007, 6332}, {55346, 50392}, {65160, 43533}, {65170, 7}, {65201, 63157}
X(65193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 1897, 653}, {3699, 36797, 65160}

X(65194) = X(7)X(6154)∩X(100)X(658)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(3*a^2+(b-c)^2-4*a*(b+c)) : :

X(65194) lies on these lines: {7, 6154}, {100, 658}, {190, 6606}, {883, 65166}, {927, 4624}, {1088, 3158}, {3035, 62723}, {3689, 14189}, {3722, 56783}, {3870, 33765}, {4554, 43290}, {5853, 37757}, {13149, 65193}, {17093, 64146}, {25716, 64112}, {25718, 64108}, {31627, 64135}, {35338, 42301}, {46917, 62704}

X(65194) = X(i)-isoconjugate-of-X(j) for these {i, j}: {663, 10390}, {2310, 58103}, {3063, 56054}, {3900, 34821}, {8641, 56348}
X(65194) = X(i)-Dao conjugate of X(j) for these {i, j}: {10001, 56054}
X(65194) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58106, 37781}
X(65194) = pole of line {144, 4847} with respect to the Yff parabola
X(65194) = pole of line {348, 17263} with respect to the dual conic of Feuerbach hyperbola
X(65194) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(42301)}}, {{A, B, C, X(190), X(35312)}}, {{A, B, C, X(658), X(6606)}}, {{A, B, C, X(934), X(65222)}}, {{A, B, C, X(2283), X(8694)}}, {{A, B, C, X(18230), X(56543)}}, {{A, B, C, X(43042), X(58860)}}
X(65194) = barycentric product X(i)*X(j) for these (i, j): {10389, 4554}, {18230, 664}
X(65194) = barycentric quotient X(i)/X(j) for these (i, j): {651, 10390}, {658, 56348}, {664, 56054}, {1262, 58103}, {1461, 34821}, {10389, 650}, {18230, 522}
X(65194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 35312, 65165}, {100, 61192, 664}, {100, 664, 658}, {664, 65165, 35312}

X(65195) = ANTICOMPLEMENT OF X(1111)

Barycentrics    (a-b)*(a-c)*(-(b-c)^2+a*(b+c)) : :
X(65195) = -3*X[2]+2*X[1111], -3*X[14439]+X[21139], -4*X[17761]+3*X[53381]

X(65195) lies on these lines: {1, 25237}, {2, 1111}, {7, 26140}, {8, 3177}, {9, 9317}, {10, 25244}, {37, 7200}, {42, 25249}, {63, 5773}, {72, 48923}, {75, 31169}, {78, 30625}, {85, 25082}, {99, 666}, {100, 1292}, {101, 17136}, {142, 53240}, {144, 2801}, {145, 25256}, {162, 41676}, {190, 644}, {192, 537}, {194, 16476}, {200, 43989}, {239, 25257}, {279, 28740}, {321, 50154}, {344, 17079}, {348, 28734}, {513, 62753}, {514, 1018}, {573, 20248}, {668, 30730}, {672, 46180}, {765, 56322}, {835, 58967}, {894, 25255}, {944, 30616}, {1015, 24403}, {1016, 30732}, {1025, 4566}, {1026, 3952}, {1088, 64579}, {1125, 25261}, {1212, 20880}, {1233, 40606}, {1331, 2398}, {1358, 16593}, {1577, 26794}, {1655, 6625}, {1930, 26770}, {2795, 13576}, {3039, 26007}, {3160, 28967}, {3616, 27340}, {3665, 33839}, {3673, 26690}, {3693, 30806}, {3729, 3872}, {3877, 51052}, {3885, 9311}, {3891, 22253}, {3930, 35102}, {3995, 22035}, {4080, 63334}, {4253, 20247}, {4416, 45744}, {4511, 10025}, {4554, 36838}, {4561, 30729}, {4595, 61186}, {4723, 40883}, {4781, 17494}, {4824, 40501}, {4847, 62731}, {4919, 60692}, {5080, 56555}, {5179, 33864}, {5552, 30694}, {6005, 7287}, {6065, 60065}, {6558, 65189}, {6734, 43672}, {6758, 24074}, {7080, 30695}, {7187, 27097}, {7264, 26964}, {9312, 28961}, {9457, 55998}, {9780, 27288}, {9881, 17497}, {14439, 21139}, {14543, 65168}, {14740, 44005}, {14953, 20602}, {16600, 18600}, {16720, 27040}, {16834, 17147}, {17075, 28420}, {17077, 20927}, {17092, 20946}, {17095, 28761}, {17140, 40637}, {17166, 46369}, {17169, 21808}, {17350, 25241}, {17495, 41140}, {17496, 25267}, {17729, 21372}, {17760, 56024}, {17761, 53381}, {17781, 56187}, {18662, 32933}, {18668, 32849}, {20269, 27132}, {20331, 21138}, {20347, 57015}, {21044, 24318}, {21090, 31058}, {21226, 28598}, {21314, 30813}, {21362, 22003}, {23649, 24172}, {24635, 28797}, {25065, 27058}, {25066, 26563}, {25083, 30807}, {25243, 25728}, {25254, 41252}, {25264, 64071}, {25729, 57287}, {25918, 26094}, {27109, 33930}, {28090, 39956}, {30941, 49753}, {31087, 50286}, {32040, 58135}, {35312, 35341}, {35335, 48151}, {35338, 65198}, {36118, 65160}, {40534, 43057}, {41825, 41839}, {47666, 61177}, {52609, 65161}, {61185, 65196}

X(65195) = reflection of X(i) in X(j) for these {i,j}: {8, 4712}, {1111, 24036}, {20347, 57015}, {21139, 21232}, {21272, 1018}, {30806, 3693}
X(65195) = inverse of X(4560) in Wallace hyperbola
X(65195) = isotomic conjugate of X(56322)
X(65195) = anticomplement of X(1111)
X(65195) = trilinear pole of line {142, 354}
X(65195) = perspector of circumconic {{A, B, C, X(4998), X(35171)}}
X(65195) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 58322}, {31, 56322}, {56, 62747}, {513, 1174}, {604, 62725}, {649, 2346}, {657, 61373}, {663, 1170}, {667, 32008}, {1803, 18344}, {1919, 57815}, {2149, 56284}, {2170, 53243}, {3063, 21453}, {3121, 55281}, {3271, 65222}, {3669, 10482}, {3676, 59141}, {3733, 56255}, {6591, 47487}, {6605, 43924}, {8641, 10509}, {56118, 57181}, {56157, 57129}
X(65195) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 62747}, {2, 56322}, {9, 58322}, {142, 650}, {354, 6586}, {650, 56284}, {1111, 1111}, {1212, 514}, {3119, 2310}, {3161, 62725}, {5375, 2346}, {6631, 32008}, {9296, 57815}, {10001, 21453}, {39026, 1174}, {40606, 513}, {46196, 47970}
X(65195) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 35341}, {765, 2}, {4998, 6067}
X(65195) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32, 54102}, {59, 3434}, {100, 21293}, {101, 150}, {249, 17143}, {692, 149}, {765, 6327}, {1016, 315}, {1018, 21294}, {1101, 17140}, {1110, 8}, {1252, 69}, {1262, 6604}, {1576, 17154}, {2149, 7}, {2175, 17036}, {3939, 33650}, {4557, 3448}, {4564, 21285}, {4567, 17137}, {4570, 17135}, {4574, 13219}, {4590, 54112}, {4600, 17138}, {4619, 46402}, {4628, 25049}, {4998, 21280}, {5377, 20556}, {5379, 20242}, {6065, 3436}, {6066, 144}, {6632, 21304}, {7035, 21275}, {7109, 54104}, {7115, 56927}, {9268, 21282}, {15378, 17753}, {15742, 11442}, {23357, 4360}, {23963, 46720}, {23979, 4452}, {23990, 2}, {24027, 36845}, {31616, 3261}, {31625, 33796}, {32719, 20042}, {32739, 4440}, {40150, 44184}, {52378, 20244}, {52941, 674}, {57731, 21301}, {59101, 926}, {59149, 20295}
X(65195) = X(i)-cross conjugate of X(j) for these {i, j}: {6067, 4998}, {6362, 20880}, {21104, 142}, {35310, 35338}, {35338, 35312}, {35341, 65198}, {48151, 17169}
X(65195) = pole of line {75, 3873} with respect to the Kiepert parabola
X(65195) = pole of line {665, 7252} with respect to the Stammler hyperbola
X(65195) = pole of line {100, 101} with respect to the Steiner circumellipse
X(65195) = pole of line {3035, 3887} with respect to the Steiner inellipse
X(65195) = pole of line {7, 8} with respect to the Yff parabola
X(65195) = pole of line {2, 218} with respect to the Hutson-Moses hyperbola
X(65195) = pole of line {14408, 21320} with respect to the Hofstadter ellipse
X(65195) = pole of line {918, 4560} with respect to the Wallace hyperbola
X(65195) = pole of line {190, 658} with respect to the dual conic of incircle
X(65195) = pole of line {190, 46725} with respect to the dual conic of nine-point circle
X(65195) = pole of line {26932, 40618} with respect to the dual conic of polar circle
X(65195) = pole of line {42719, 43191} with respect to the dual conic of DeLongchamps ellipse
X(65195) = pole of line {1, 2} with respect to the dual conic of Feuerbach hyperbola
X(65195) = pole of line {6516, 40576} with respect to the dual conic of Orthic inconic
X(65195) = pole of line {4998, 6065} with respect to the dual conic of Moses-Feuerbach circumconic
X(65195) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(883)}}, {{A, B, C, X(142), X(62669)}}, {{A, B, C, X(190), X(46406)}}, {{A, B, C, X(644), X(4554)}}, {{A, B, C, X(651), X(1292)}}, {{A, B, C, X(664), X(35312)}}, {{A, B, C, X(666), X(4552)}}, {{A, B, C, X(918), X(4560)}}, {{A, B, C, X(919), X(4559)}}, {{A, B, C, X(1111), X(56322)}}, {{A, B, C, X(1212), X(2284)}}, {{A, B, C, X(1229), X(2397)}}, {{A, B, C, X(4585), X(16713)}}, {{A, B, C, X(6625), X(17169)}}, {{A, B, C, X(17494), X(47772)}}, {{A, B, C, X(21104), X(30725)}}, {{A, B, C, X(23599), X(60482)}}, {{A, B, C, X(30730), X(36803)}}, {{A, B, C, X(31624), X(54440)}}, {{A, B, C, X(60480), X(62306)}}
X(65195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {85, 25082, 28742}, {99, 32028, 33951}, {190, 33946, 53332}, {190, 4552, 25268}, {190, 664, 644}, {190, 65205, 4552}, {279, 56937, 28740}, {514, 1018, 21272}, {1111, 24036, 2}, {2398, 4427, 54440}, {3177, 25242, 8}, {3693, 44664, 30806}, {3952, 25272, 4568}, {4552, 65174, 664}, {9312, 55337, 28961}, {14439, 21139, 21232}, {17136, 53337, 101}, {17760, 56024, 56318}

X(65196) = ANTICOMPLEMENT OF X(24235)

Barycentrics    (a-b)*(a-c)*(b+c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :
X(65196) = -3*X[2]+2*X[24235]

X(65196) lies on these lines: {2, 24235}, {8, 39770}, {10, 1109}, {37, 17724}, {72, 952}, {100, 6011}, {101, 59097}, {162, 190}, {306, 57862}, {321, 4712}, {514, 3909}, {518, 50747}, {522, 4427}, {523, 61172}, {542, 17781}, {644, 4115}, {726, 50755}, {835, 58986}, {1365, 27692}, {1824, 29243}, {3159, 3244}, {3175, 9041}, {3710, 42456}, {3717, 61410}, {3751, 32925}, {3882, 53349}, {3952, 4069}, {3957, 3995}, {3977, 64858}, {4024, 61163}, {4082, 42710}, {4463, 22001}, {4861, 9369}, {4934, 27560}, {6590, 61234}, {6734, 45926}, {6745, 42701}, {14206, 44694}, {17776, 25664}, {21807, 22010}, {24225, 24542}, {25006, 42708}, {44311, 51583}, {53358, 61168}, {53794, 57287}, {61169, 61220}, {61178, 65233}, {61180, 61233}, {61185, 65195}

X(65196) = anticomplement of X(24235)
X(65196) = trilinear pole of line {442, 2294}
X(65196) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 1175}, {663, 63193}, {667, 40412}, {905, 40570}, {943, 3733}, {1019, 2259}, {1333, 56320}, {1437, 14775}, {1794, 57200}, {2203, 63245}, {2982, 7252}, {7202, 59011}, {15439, 18191}, {22383, 40395}, {40435, 57129}
X(65196) = X(i)-Dao conjugate of X(j) for these {i, j}: {37, 56320}, {442, 3737}, {942, 1459}, {6631, 40412}, {16585, 7192}, {16732, 1111}, {18591, 1019}, {24235, 24235}, {39026, 1175}, {40937, 514}, {52119, 3120}, {62564, 63245}
X(65196) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 61233}, {765, 10}, {65205, 61161}
X(65196) = X(i)-cross conjugate of X(j) for these {i, j}: {23752, 442}
X(65196) = pole of line {1043, 17164} with respect to the Kiepert parabola
X(65196) = pole of line {3882, 14543} with respect to the Steiner circumellipse
X(65196) = pole of line {226, 306} with respect to the Yff parabola
X(65196) = pole of line {10, 2287} with respect to the Hutson-Moses hyperbola
X(65196) = pole of line {4025, 16755} with respect to the Wallace hyperbola
X(65196) = pole of line {4427, 61233} with respect to the dual conic of incircle
X(65196) = pole of line {17216, 17219} with respect to the dual conic of polar circle
X(65196) = pole of line {21132, 21134} with respect to the dual conic of Wallace hyperbola
X(65196) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(162), X(4551)}}, {{A, B, C, X(442), X(46541)}}, {{A, B, C, X(643), X(61233)}}, {{A, B, C, X(648), X(4552)}}, {{A, B, C, X(3952), X(36797)}}, {{A, B, C, X(4033), X(57973)}}, {{A, B, C, X(8750), X(61169)}}, {{A, B, C, X(23752), X(30572)}}, {{A, B, C, X(58986), X(61197)}}
X(65196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65197, 65205, 61220}

X(65197) = X(8)X(11604)∩X(100)X(190)

Barycentrics    (a-b)*(a-c)*(a-b-c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :

X(65197) lies on these lines: {8, 11604}, {69, 20940}, {100, 190}, {312, 41228}, {329, 20445}, {522, 61223}, {643, 65206}, {645, 36797}, {668, 18026}, {1332, 1897}, {2550, 18037}, {3909, 53349}, {4103, 61239}, {4123, 28950}, {4397, 61174}, {4585, 14544}, {5218, 17611}, {7069, 27409}, {7259, 30729}, {12247, 21290}, {17165, 33108}, {23691, 64858}, {26704, 59104}, {31938, 51978}, {35519, 53363}, {53358, 62753}, {61169, 61220}

X(65197) = trilinear pole of line {6734, 40937}
X(65197) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 15439}, {512, 63193}, {603, 14775}, {604, 56320}, {649, 2982}, {667, 60041}, {943, 43924}, {1015, 65217}, {1175, 4017}, {1395, 63245}, {1794, 43923}, {2170, 32651}, {2259, 3669}, {3248, 54952}, {3271, 36048}, {22383, 40573}, {40412, 51641}, {40435, 57181}, {40570, 51664}, {57129, 60188}
X(65197) = X(i)-Dao conjugate of X(j) for these {i, j}: {442, 513}, {3161, 56320}, {5375, 2982}, {6631, 60041}, {6734, 6003}, {7952, 14775}, {15607, 3271}, {16585, 3676}, {18591, 3669}, {34961, 1175}, {39007, 3937}, {39054, 63193}, {40937, 7178}, {52119, 1365}, {62584, 63245}
X(65197) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {6011, 149}, {65236, 150}
X(65197) = X(i)-cross conjugate of X(j) for these {i, j}: {61233, 65205}
X(65197) = pole of line {1365, 2969} with respect to the polar circle
X(65197) = pole of line {3733, 57139} with respect to the Stammler hyperbola
X(65197) = pole of line {190, 65236} with respect to the Steiner circumellipse
X(65197) = pole of line {2, 17861} with respect to the Yff parabola
X(65197) = pole of line {6, 12649} with respect to the Hutson-Moses hyperbola
X(65197) = pole of line {7192, 17094} with respect to the Wallace hyperbola
X(65197) = pole of line {643, 644} with respect to the dual conic of incircle
X(65197) = pole of line {1364, 1367} with respect to the dual conic of polar circle
X(65197) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(11604)}}, {{A, B, C, X(190), X(46404)}}, {{A, B, C, X(645), X(52609)}}, {{A, B, C, X(650), X(53257)}}, {{A, B, C, X(655), X(14543)}}, {{A, B, C, X(668), X(4571)}}, {{A, B, C, X(942), X(23832)}}, {{A, B, C, X(3952), X(36797)}}, {{A, B, C, X(4427), X(60488)}}, {{A, B, C, X(4557), X(61169)}}, {{A, B, C, X(5249), X(53337)}}, {{A, B, C, X(6734), X(17780)}}, {{A, B, C, X(7253), X(53342)}}, {{A, B, C, X(23343), X(40937)}}, {{A, B, C, X(53280), X(61197)}}
X(65197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 3699, 4571}, {3952, 61185, 190}, {3952, 65198, 3699}, {61220, 65196, 65205}

X(65198) = X(8)X(3254)∩X(100)X(190)

Barycentrics    (a-b)*(a-c)*(a-b-c)*(-(b-c)^2+a*(b+c)) : :

X(65198) lies on these lines: {8, 3254}, {9, 38991}, {100, 190}, {210, 4459}, {346, 14943}, {522, 4069}, {645, 7253}, {653, 37223}, {668, 883}, {670, 53227}, {1026, 4552}, {1086, 40609}, {1227, 17165}, {1229, 3059}, {1332, 2398}, {3888, 53358}, {4033, 4397}, {4073, 27108}, {4103, 61237}, {4454, 6555}, {4553, 21272}, {4587, 30729}, {4738, 12736}, {4779, 19582}, {5281, 27538}, {9803, 21290}, {10005, 24349}, {16713, 21039}, {18151, 53382}, {20880, 61028}, {20946, 30628}, {25253, 44722}, {26651, 56179}, {30730, 61233}, {35338, 65195}, {44720, 49499}, {65190, 65206}

X(65198) = reflection of X(i) in X(j) for these {i,j}: {25268, 4069}
X(65198) = trilinear pole of line {1212, 4847}
X(65198) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 58322}, {244, 53243}, {604, 56322}, {663, 61373}, {667, 21453}, {1015, 65222}, {1106, 62725}, {1174, 3669}, {1407, 62747}, {1803, 6591}, {1919, 31618}, {2346, 43924}, {3063, 10509}, {3248, 6606}, {10482, 43932}, {24027, 56284}, {32008, 57181}, {43923, 47487}, {57129, 60229}, {58817, 59141}
X(65198) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 58322}, {142, 513}, {522, 56284}, {1212, 3676}, {3119, 2170}, {3161, 56322}, {4847, 3309}, {5375, 1170}, {6552, 62725}, {6631, 21453}, {9296, 31618}, {10001, 10509}, {24771, 62747}, {40606, 3669}
X(65198) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {59, 7674}, {100, 34547}, {1252, 56937}, {1292, 149}, {2428, 39353}, {15402, 20075}, {37206, 150}, {54987, 21293}, {57656, 54102}, {63906, 69}
X(65198) = X(i)-cross conjugate of X(j) for these {i, j}: {2488, 1212}, {6362, 4847}, {21127, 16713}, {35341, 65195}
X(65198) = pole of line {3733, 53539} with respect to the Stammler hyperbola
X(65198) = pole of line {190, 25736} with respect to the Steiner circumellipse
X(65198) = pole of line {2, 277} with respect to the Yff parabola
X(65198) = pole of line {6, 36845} with respect to the Hutson-Moses hyperbola
X(65198) = pole of line {7192, 21789} with respect to the Wallace hyperbola
X(65198) = pole of line {644, 3939} with respect to the dual conic of incircle
X(65198) = pole of line {1565, 3270} with respect to the dual conic of polar circle
X(65198) = pole of line {344, 61413} with respect to the dual conic of Feuerbach hyperbola
X(65198) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(3254)}}, {{A, B, C, X(142), X(53337)}}, {{A, B, C, X(190), X(46406)}}, {{A, B, C, X(354), X(23832)}}, {{A, B, C, X(522), X(53343)}}, {{A, B, C, X(644), X(54987)}}, {{A, B, C, X(645), X(1229)}}, {{A, B, C, X(650), X(53284)}}, {{A, B, C, X(653), X(61241)}}, {{A, B, C, X(659), X(21127)}}, {{A, B, C, X(668), X(4578)}}, {{A, B, C, X(883), X(3059)}}, {{A, B, C, X(890), X(2488)}}, {{A, B, C, X(900), X(6362)}}, {{A, B, C, X(1212), X(23343)}}, {{A, B, C, X(3570), X(16713)}}, {{A, B, C, X(3699), X(4572)}}, {{A, B, C, X(3952), X(36802)}}, {{A, B, C, X(4557), X(4566)}}, {{A, B, C, X(4571), X(37223)}}, {{A, B, C, X(4847), X(17780)}}, {{A, B, C, X(4858), X(30565)}}, {{A, B, C, X(6607), X(42341)}}, {{A, B, C, X(7253), X(50333)}}, {{A, B, C, X(21104), X(47884)}}, {{A, B, C, X(35326), X(53280)}}, {{A, B, C, X(53241), X(57018)}}
X(65198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 3699, 4578}, {190, 65200, 100}, {522, 4069, 25268}, {3699, 65197, 3952}

X(65199) = X(100)X(883)∩X(664)X(668)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2+c^2-2*a*(b+c)) : :

X(65199) lies on these lines: {100, 883}, {109, 35574}, {190, 6606}, {200, 7182}, {651, 42720}, {658, 4998}, {664, 668}, {1897, 46107}, {3870, 21609}, {3935, 40704}, {3952, 61192}, {4468, 65208}, {4569, 53653}, {4573, 7256}, {6604, 40615}, {17780, 35312}, {28808, 52659}, {30829, 56418}, {31638, 38375}, {32029, 43063}, {37757, 49698}

X(65199) = trilinear pole of line {344, 1445}
X(65199) = X(i)-isoconjugate-of-X(j) for these {i, j}: {277, 3063}, {650, 57656}, {657, 17107}, {663, 2191}, {667, 6601}, {884, 57469}, {1292, 3271}, {8641, 40154}, {8642, 55013}, {17435, 32644}
X(65199) = X(i)-Dao conjugate of X(j) for these {i, j}: {220, 657}, {1040, 17115}, {3676, 6545}, {4468, 23761}, {4847, 6608}, {4904, 2310}, {6631, 6601}, {10001, 277}
X(65199) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6632, 4998}, {46406, 190}
X(65199) = X(i)-cross conjugate of X(j) for these {i, j}: {4468, 21609}, {17093, 4998}, {31605, 6604}, {44448, 344}, {51652, 1445}
X(65199) = pole of line {24635, 32939} with respect to the Kiepert parabola
X(65199) = pole of line {3729, 4847} with respect to the Yff parabola
X(65199) = pole of line {85, 17263} with respect to the dual conic of Feuerbach hyperbola
X(65199) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(658), X(17093)}}, {{A, B, C, X(664), X(6183)}}, {{A, B, C, X(668), X(35574)}}, {{A, B, C, X(1026), X(1897)}}, {{A, B, C, X(3699), X(53653)}}, {{A, B, C, X(4468), X(46107)}}, {{A, B, C, X(4554), X(6606)}}, {{A, B, C, X(4561), X(51560)}}, {{A, B, C, X(21609), X(46404)}}, {{A, B, C, X(31605), X(40615)}}, {{A, B, C, X(43041), X(43049)}}
X(65199) = barycentric product X(i)*X(j) for these (i, j): {100, 21609}, {190, 6604}, {218, 4572}, {344, 664}, {1016, 31605}, {1275, 44448}, {1445, 668}, {1617, 1978}, {3870, 4554}, {3991, 4625}, {4350, 646}, {4468, 4998}, {4569, 55337}, {6063, 65208}, {17093, 3699}, {21945, 55194}, {31625, 51652}, {31638, 883}, {40615, 6632}, {41539, 799}, {43049, 7035}, {46406, 6600}, {63897, 65200}
X(65199) = barycentric quotient X(i)/X(j) for these (i, j): {109, 57656}, {190, 6601}, {218, 663}, {344, 522}, {651, 2191}, {658, 40154}, {664, 277}, {934, 17107}, {1025, 57469}, {1445, 513}, {1617, 649}, {3309, 2170}, {3870, 650}, {3991, 4041}, {4350, 3669}, {4468, 11}, {4564, 1292}, {4572, 57791}, {4878, 3709}, {4904, 21132}, {4998, 37206}, {6600, 657}, {6604, 514}, {7719, 18344}, {15185, 21127}, {17093, 3676}, {21059, 3063}, {21609, 693}, {21945, 55195}, {23144, 1459}, {23760, 7336}, {24562, 7004}, {31605, 1086}, {31638, 885}, {37206, 55013}, {40615, 6545}, {41539, 661}, {41610, 3737}, {43049, 244}, {44448, 1146}, {51378, 46393}, {51652, 1015}, {53653, 60832}, {55337, 3900}, {65208, 55}
X(65199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 883, 65164}, {658, 43290, 4998}, {664, 3699, 4554}

X(65200) = X(8)X(14151)∩X(100)X(190)

Barycentrics    (a-b)*(a-c)*(a^3-3*a^2*(b+c)-(b-c)^2*(b+c)+a*(3*b^2-2*b*c+3*c^2)) : :

X(65200) lies on these lines: {8, 14151}, {69, 28057}, {100, 190}, {653, 15742}, {664, 54987}, {3174, 20946}, {4569, 53653}, {36802, 44327}

X(65200) = trilinear pole of line {16572, 21096}
X(65200) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 53888}, {663, 64242}, {667, 42361}, {3248, 53653}, {42470, 43924}
X(65200) = X(i)-Dao conjugate of X(j) for these {i, j}: {200, 3900}, {6631, 42361}, {59979, 6545}
X(65200) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4569, 190}, {65199, 664}
X(65200) = pole of line {344, 1088} with respect to the dual conic of Feuerbach hyperbola
X(65200) = pole of line {765, 26015} with respect to the dual conic of Moses-Feuerbach circumconic
X(65200) = intersection, other than A, B, C, of circumconics {{A, B, C, X(653), X(8732)}}, {{A, B, C, X(3699), X(54987)}}, {{A, B, C, X(4578), X(53653)}}, {{A, B, C, X(16572), X(23343)}}, {{A, B, C, X(17780), X(36845)}}, {{A, B, C, X(20946), X(42720)}}
X(65200) = barycentric product X(i)*X(j) for these (i, j): {100, 20946}, {190, 36845}, {1978, 21002}, {3174, 4554}, {3699, 8732}, {16572, 668}, {21096, 99}, {24771, 4569}, {56937, 664}
X(65200) = barycentric quotient X(i)/X(j) for these (i, j): {190, 42361}, {644, 42470}, {651, 64242}, {1016, 53653}, {1252, 53888}, {3174, 650}, {8732, 3676}, {16572, 513}, {20946, 693}, {21002, 649}, {21096, 523}, {22153, 1459}, {24771, 3900}, {36845, 514}, {41573, 21104}, {56937, 522}, {59979, 2310}, {65199, 63897}
X(65200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 65198, 190}

X(65201) = TRILINEAR POLE OF LINE {9, 33}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a-b-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65201) lies on these lines: {9, 44693}, {27, 51567}, {28, 1280}, {29, 1855}, {41, 318}, {78, 7156}, {99, 58944}, {100, 112}, {101, 107}, {108, 59079}, {110, 13138}, {163, 1021}, {200, 56375}, {270, 607}, {281, 2326}, {284, 2322}, {518, 14192}, {643, 52914}, {644, 56183}, {648, 653}, {651, 46639}, {811, 51560}, {823, 65207}, {1120, 1474}, {1172, 1320}, {1625, 23090}, {2074, 60355}, {2202, 3684}, {2204, 8851}, {2907, 7119}, {3699, 4587}, {3870, 56374}, {3903, 61205}, {4183, 41798}, {4242, 35342}, {4251, 11109}, {4262, 37295}, {4552, 41678}, {4557, 52604}, {4559, 7012}, {4560, 41676}, {4566, 7128}, {6335, 51566}, {6742, 17914}, {7079, 11107}, {7719, 13739}, {14571, 56830}, {17926, 51562}, {18831, 39177}, {32676, 36147}, {35069, 47228}, {37305, 63087}, {40116, 53683}, {46541, 51564}, {53290, 53761}, {55185, 56829}, {65168, 65170}

X(65201) = isogonal conjugate of X(51664)
X(65201) = trilinear pole of line {9, 33}
X(65201) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 51664}, {3, 7178}, {6, 17094}, {7, 647}, {11, 52610}, {12, 7254}, {34, 24018}, {48, 4077}, {56, 525}, {57, 656}, {58, 57243}, {63, 4017}, {65, 905}, {69, 7180}, {71, 3676}, {72, 3669}, {73, 514}, {77, 661}, {78, 7216}, {85, 810}, {86, 55234}, {92, 51640}, {109, 4466}, {112, 1367}, {125, 4565}, {181, 15419}, {201, 1019}, {222, 523}, {225, 4091}, {226, 1459}, {228, 24002}, {241, 10099}, {244, 65233}, {269, 8611}, {273, 822}, {278, 520}, {295, 7212}, {304, 51641}, {306, 43924}, {307, 649}, {326, 55208}, {331, 39201}, {345, 7250}, {348, 512}, {513, 1214}, {521, 1427}, {522, 52373}, {603, 1577}, {604, 14208}, {608, 3265}, {648, 61058}, {650, 1439}, {651, 18210}, {652, 3668}, {663, 56382}, {667, 1231}, {669, 57918}, {693, 1409}, {798, 7182}, {850, 52411}, {879, 43034}, {934, 53560}, {1014, 55232}, {1020, 7004}, {1037, 21107}, {1042, 6332}, {1086, 23067}, {1118, 52613}, {1331, 53545}, {1332, 53540}, {1356, 52608}, {1357, 52609}, {1358, 4574}, {1363, 15352}, {1364, 52607}, {1365, 4558}, {1396, 57109}, {1397, 3267}, {1400, 4025}, {1401, 4580}, {1402, 15413}, {1407, 52355}, {1410, 4391}, {1412, 4064}, {1414, 3708}, {1425, 4560}, {1434, 55230}, {1441, 22383}, {1444, 57185}, {1446, 1946}, {1565, 4559}, {1797, 30572}, {1803, 55282}, {1804, 2501}, {1813, 3120}, {1814, 53551}, {1880, 4131}, {2197, 7192}, {2200, 52621}, {2318, 58817}, {2435, 43045}, {2489, 7055}, {2605, 63171}, {2611, 65300}, {2616, 44708}, {2632, 65232}, {2720, 42761}, {3049, 6063}, {3122, 65164}, {3125, 6516}, {3690, 17096}, {3694, 43932}, {3700, 7053}, {3709, 7056}, {3733, 26942}, {3737, 37755}, {3937, 4552}, {3942, 4551}, {3949, 7203}, {3960, 52391}, {3998, 43923}, {4041, 7177}, {4086, 7099}, {4143, 7337}, {4516, 65296}, {4524, 30682}, {4563, 61052}, {4566, 7117}, {4573, 20975}, {4729, 27832}, {4832, 57873}, {4841, 57701}, {6046, 23090}, {6129, 52037}, {6354, 23189}, {6356, 7252}, {6357, 14380}, {6591, 52385}, {7013, 55242}, {7066, 17925}, {7125, 24006}, {7138, 57215}, {7143, 15411}, {7147, 57081}, {7181, 10097}, {7316, 14417}, {7335, 14618}, {7649, 40152}, {14838, 52390}, {15412, 30493}, {16732, 36059}, {17216, 32674}, {17924, 22341}, {20336, 57181}, {20618, 21789}, {21134, 52378}, {21207, 32660}, {21828, 52392}, {22093, 60245}, {22094, 38340}, {22379, 60091}, {23224, 40149}, {23226, 43682}, {23755, 40442}, {26932, 53321}, {28786, 43060}, {30805, 57652}, {39791, 56320}, {51644, 56219}, {52306, 52560}, {52370, 59941}, {52384, 64885}, {55212, 56972}, {55259, 62402}, {57129, 57807}
X(65201) = X(i)-vertex conjugate of X(j) for these {i, j}: {653, 1415}
X(65201) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 525}, {3, 51664}, {9, 17094}, {10, 57243}, {11, 4466}, {1249, 4077}, {3161, 14208}, {3162, 4017}, {5375, 307}, {5452, 656}, {5521, 53545}, {6600, 8611}, {6631, 1231}, {6741, 20902}, {7952, 1577}, {11517, 24018}, {14714, 53560}, {15259, 55208}, {20620, 16732}, {22391, 51640}, {23050, 3700}, {24771, 52355}, {31998, 7182}, {34591, 1367}, {34961, 63}, {35072, 17216}, {36103, 7178}, {36830, 77}, {38966, 21044}, {38981, 42761}, {38991, 18210}, {39026, 1214}, {39052, 7}, {39053, 1446}, {39054, 348}, {39062, 85}, {40582, 4025}, {40596, 57}, {40599, 4064}, {40600, 55234}, {40602, 905}, {40605, 15413}, {40608, 3708}, {55064, 125}, {55066, 61058}, {55067, 1565}, {55068, 26932}, {62585, 3267}, {62647, 3265}
X(65201) = X(i)-Ceva conjugate of X(j) for these {i, j}: {648, 162}, {5379, 4183}, {24000, 56375}, {46254, 14006}, {65263, 4242}
X(65201) = X(i)-cross conjugate of X(j) for these {i, j}: {55, 7012}, {101, 5546}, {1021, 2322}, {3190, 765}, {4041, 318}, {4086, 56245}, {4183, 5379}, {8611, 9}, {17926, 2326}, {46393, 2341}, {55206, 33}, {56183, 36797}, {57198, 6605}, {58329, 21}, {65105, 281}, {65375, 643}
X(65201) = pole of line {4466, 8287} with respect to the polar circle
X(65201) = pole of line {4329, 8822} with respect to the Kiepert parabola
X(65201) = pole of line {652, 905} with respect to the Stammler hyperbola
X(65201) = pole of line {162, 14544} with respect to the Steiner circumellipse
X(65201) = pole of line {5279, 8804} with respect to the Yff parabola
X(65201) = pole of line {72, 4183} with respect to the Hutson-Moses hyperbola
X(65201) = pole of line {6332, 15413} with respect to the Wallace hyperbola
X(65201) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(4566)}}, {{A, B, C, X(9), X(14147)}}, {{A, B, C, X(21), X(1414)}}, {{A, B, C, X(29), X(811)}}, {{A, B, C, X(55), X(4559)}}, {{A, B, C, X(100), X(643)}}, {{A, B, C, X(101), X(906)}}, {{A, B, C, X(107), X(162)}}, {{A, B, C, X(112), X(24019)}}, {{A, B, C, X(163), X(284)}}, {{A, B, C, X(521), X(2811)}}, {{A, B, C, X(522), X(2806)}}, {{A, B, C, X(653), X(1783)}}, {{A, B, C, X(662), X(5546)}}, {{A, B, C, X(1018), X(61161)}}, {{A, B, C, X(1036), X(29055)}}, {{A, B, C, X(1305), X(36086)}}, {{A, B, C, X(3064), X(47235)}}, {{A, B, C, X(3555), X(23704)}}, {{A, B, C, X(4571), X(65227)}}, {{A, B, C, X(5548), X(29163)}}, {{A, B, C, X(17519), X(46541)}}, {{A, B, C, X(21789), X(39177)}}, {{A, B, C, X(32674), X(58944)}}, {{A, B, C, X(36049), X(37136)}}, {{A, B, C, X(36098), X(56112)}}, {{A, B, C, X(46964), X(53642)}}, {{A, B, C, X(58993), X(65333)}}
X(65201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {112, 1783, 162}, {163, 61237, 54442}, {281, 41502, 2326}, {648, 662, 65232}, {2202, 3684, 5081}, {35342, 61236, 4242}

X(65202) = ISOGONAL CONJUGATE OF X(4063)

Barycentrics    a*(a-b)*(a-c)*(a*(b-c)+b*(b+c))*(a*(b-c)-c*(b+c)) : :

X(65202) lies on these lines: {9, 36814}, {63, 40013}, {100, 59014}, {101, 34594}, {163, 4628}, {190, 37205}, {292, 3294}, {596, 5282}, {649, 4103}, {668, 4063}, {1018, 4427}, {1019, 4568}, {1020, 62669}, {1023, 4559}, {2161, 21061}, {3219, 39747}, {3730, 58073}, {4040, 52922}, {4557, 21003}, {4629, 52935}, {33946, 48320}, {40148, 62763}

X(65202) = isogonal conjugate of X(4063)
X(65202) = isotomic conjugate of X(20949)
X(65202) = trilinear pole of line {42, 1100}
X(65202) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4063}, {2, 4057}, {3, 17922}, {4, 22154}, {6, 20295}, {8, 57238}, {10, 57080}, {31, 20949}, {56, 47793}, {57, 48307}, {58, 4129}, {75, 57096}, {81, 4132}, {86, 58288}, {101, 21208}, {190, 8054}, {279, 58336}, {333, 51650}, {513, 32911}, {514, 595}, {649, 4360}, {667, 18140}, {693, 2220}, {905, 4222}, {1019, 3293}, {1919, 40087}, {3669, 3871}, {3733, 3995}, {8632, 40093}, {23355, 27044}, {45222, 50344}, {56249, 57129}
X(65202) = X(i)-vertex conjugate of X(j) for these {i, j}: {163, 36147}, {1018, 40519}
X(65202) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 47793}, {2, 20949}, {3, 4063}, {9, 20295}, {10, 4129}, {206, 57096}, {1015, 21208}, {5375, 4360}, {5452, 48307}, {6631, 18140}, {9296, 40087}, {32664, 4057}, {36033, 22154}, {36103, 17922}, {39026, 32911}, {40586, 4132}, {40600, 58288}, {55053, 8054}
X(65202) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34594, 40519}, {37205, 8050}, {59014, 1018}
X(65202) = X(i)-cross conjugate of X(j) for these {i, j}: {667, 1}, {4115, 1018}, {40521, 100}
X(65202) = pole of line {1018, 40519} with respect to the circumcircle
X(65202) = pole of line {16679, 17150} with respect to the Kiepert parabola
X(65202) = pole of line {4063, 57080} with respect to the Stammler hyperbola
X(65202) = pole of line {6, 3293} with respect to the Yff parabola
X(65202) = pole of line {58, 5253} with respect to the Hutson-Moses hyperbola
X(65202) = pole of line {4063, 20949} with respect to the Wallace hyperbola
X(65202) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(668)}}, {{A, B, C, X(9), X(644)}}, {{A, B, C, X(19), X(29149)}}, {{A, B, C, X(37), X(4103)}}, {{A, B, C, X(57), X(6016)}}, {{A, B, C, X(63), X(906)}}, {{A, B, C, X(84), X(1292)}}, {{A, B, C, X(90), X(52778)}}, {{A, B, C, X(99), X(660)}}, {{A, B, C, X(100), X(1929)}}, {{A, B, C, X(101), X(190)}}, {{A, B, C, X(163), X(799)}}, {{A, B, C, X(267), X(29151)}}, {{A, B, C, X(655), X(29127)}}, {{A, B, C, X(662), X(59085)}}, {{A, B, C, X(664), X(29351)}}, {{A, B, C, X(667), X(4063)}}, {{A, B, C, X(692), X(29303)}}, {{A, B, C, X(831), X(1414)}}, {{A, B, C, X(835), X(4551)}}, {{A, B, C, X(898), X(3903)}}, {{A, B, C, X(1019), X(21003)}}, {{A, B, C, X(1025), X(5282)}}, {{A, B, C, X(1026), X(16825)}}, {{A, B, C, X(1415), X(29014)}}, {{A, B, C, X(1783), X(6574)}}, {{A, B, C, X(2163), X(59029)}}, {{A, B, C, X(2170), X(3762)}}, {{A, B, C, X(2284), X(16552)}}, {{A, B, C, X(3257), X(36147)}}, {{A, B, C, X(3467), X(57731)}}, {{A, B, C, X(3952), X(53627)}}, {{A, B, C, X(4115), X(40521)}}, {{A, B, C, X(4568), X(54328)}}, {{A, B, C, X(4597), X(58117)}}, {{A, B, C, X(4598), X(43077)}}, {{A, B, C, X(6010), X(32665)}}, {{A, B, C, X(6013), X(37138)}}, {{A, B, C, X(7091), X(65173)}}, {{A, B, C, X(7284), X(46962)}}, {{A, B, C, X(8050), X(34594)}}, {{A, B, C, X(8707), X(56194)}}, {{A, B, C, X(8708), X(65250)}}, {{A, B, C, X(9067), X(39954)}}, {{A, B, C, X(15322), X(37212)}}, {{A, B, C, X(21390), X(25576)}}, {{A, B, C, X(28467), X(43739)}}, {{A, B, C, X(28480), X(32735)}}, {{A, B, C, X(29137), X(60055)}}, {{A, B, C, X(29163), X(32641)}}, {{A, B, C, X(29271), X(34073)}}, {{A, B, C, X(36049), X(37206)}}, {{A, B, C, X(37133), X(39797)}}, {{A, B, C, X(37205), X(40519)}}, {{A, B, C, X(39950), X(52612)}}
X(65202) = barycentric product X(i)*X(j) for these (i, j): {1, 8050}, {10, 34594}, {37, 37205}, {42, 65286}, {100, 596}, {101, 40013}, {190, 39798}, {1018, 39747}, {3952, 39949}, {4359, 59014}, {20615, 3699}, {40085, 662}, {40086, 765}, {40148, 668}, {40519, 75}, {57151, 60790}, {57915, 692}
X(65202) = barycentric quotient X(i)/X(j) for these (i, j): {1, 20295}, {2, 20949}, {6, 4063}, {9, 47793}, {19, 17922}, {31, 4057}, {32, 57096}, {37, 4129}, {42, 4132}, {48, 22154}, {55, 48307}, {100, 4360}, {101, 32911}, {190, 18140}, {213, 58288}, {513, 21208}, {596, 693}, {604, 57238}, {660, 40093}, {667, 8054}, {668, 40087}, {692, 595}, {1018, 3995}, {1253, 58336}, {1333, 57080}, {1402, 51650}, {3939, 3871}, {3952, 56249}, {4115, 62588}, {4557, 3293}, {8050, 75}, {8750, 4222}, {20615, 3676}, {21859, 56326}, {32739, 2220}, {34594, 86}, {35342, 45222}, {37205, 274}, {39747, 7199}, {39798, 514}, {39949, 7192}, {40013, 3261}, {40085, 1577}, {40086, 1111}, {40148, 513}, {40519, 1}, {40521, 4075}, {57915, 40495}, {59014, 1255}, {65286, 310}

X(65203) = X(32)X(145)∩X(101)X(110)

Barycentrics    a^2*(a-b)*(a-c)*(a^3-b*c*(b+c)-a*(b^2-b*c+c^2)) : :

X(65203) lies on these lines: {32, 145}, {50, 3943}, {100, 1415}, {101, 110}, {112, 835}, {172, 34772}, {190, 4558}, {251, 29840}, {346, 577}, {571, 17314}, {609, 3870}, {644, 906}, {901, 28467}, {919, 932}, {1018, 1983}, {1110, 57084}, {1262, 6516}, {1914, 38460}, {2965, 17388}, {2975, 11998}, {4565, 65168}, {4612, 56188}, {4996, 13006}, {5063, 54389}, {6078, 58947}, {6574, 58972}, {7031, 36846}, {7054, 38871}, {15440, 29163}, {22033, 57062}, {29018, 59120}, {33871, 61330}, {34075, 34080}, {39652, 54101}, {41679, 65204}, {52426, 56530}

X(65203) = trilinear pole of line {572, 9562}
X(65203) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 56188}, {513, 2051}, {514, 34434}, {523, 53083}, {649, 54121}, {661, 20028}, {667, 57905}, {1015, 56252}, {1019, 51870}, {1086, 56194}, {1577, 52150}, {3120, 65260}, {3125, 65275}, {4017, 46880}, {16732, 59006}, {21124, 40453}, {24002, 60817}, {42753, 64824}, {42754, 53702}
X(65203) = X(i)-Dao conjugate of X(j) for these {i, j}: {1193, 21124}, {5375, 54121}, {6631, 57905}, {34589, 16732}, {34961, 46880}, {36830, 20028}, {39026, 2051}
X(65203) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4612, 100}
X(65203) = pole of line {332, 4184} with respect to the Kiepert parabola
X(65203) = pole of line {514, 6589} with respect to the Stammler hyperbola
X(65203) = pole of line {71, 21076} with respect to the Yff parabola
X(65203) = pole of line {21, 60} with respect to the Hutson-Moses hyperbola
X(65203) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(44765)}}, {{A, B, C, X(110), X(36037)}}, {{A, B, C, X(163), X(8687)}}, {{A, B, C, X(572), X(28467)}}, {{A, B, C, X(835), X(1331)}}, {{A, B, C, X(906), X(22118)}}, {{A, B, C, X(932), X(2975)}}, {{A, B, C, X(1897), X(65313)}}, {{A, B, C, X(4243), X(11109)}}, {{A, B, C, X(5546), X(36147)}}, {{A, B, C, X(11998), X(17496)}}, {{A, B, C, X(20986), X(34080)}}, {{A, B, C, X(21061), X(65202)}}, {{A, B, C, X(21859), X(56188)}}, {{A, B, C, X(32653), X(32739)}}
X(65203) = barycentric product X(i)*X(j) for these (i, j): {100, 2975}, {101, 14829}, {110, 17751}, {190, 572}, {1110, 57244}, {1252, 17496}, {4612, 56325}, {4636, 52357}, {11109, 1331}, {11998, 31615}, {14973, 52935}, {15742, 23187}, {17074, 644}, {20986, 668}, {21061, 662}, {21173, 765}, {22118, 6335}, {24237, 59149}, {37558, 643}, {46879, 6648}, {52139, 99}, {52358, 5546}, {55323, 645}, {55362, 8706}, {57091, 59}, {57165, 86}, {58339, 7045}
X(65203) = barycentric quotient X(i)/X(j) for these (i, j): {100, 54121}, {101, 2051}, {110, 20028}, {163, 53083}, {190, 57905}, {572, 514}, {692, 34434}, {765, 56252}, {1110, 56194}, {1252, 56188}, {1576, 52150}, {2975, 693}, {4557, 51870}, {4570, 65275}, {5546, 46880}, {11109, 46107}, {11998, 40166}, {14829, 3261}, {14973, 4036}, {17074, 24002}, {17496, 23989}, {17751, 850}, {20986, 513}, {21061, 1577}, {21173, 1111}, {22118, 905}, {23187, 1565}, {24237, 23100}, {37558, 4077}, {46879, 3910}, {52087, 21124}, {52139, 523}, {55323, 7178}, {57091, 34387}, {57165, 10}, {58339, 24026}
X(65203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {644, 906, 1252}

X(65204) = X(162)X(190)∩X(192)X(264)

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^2+b*c+c^2+a*(b+c)) : :

X(65204) lies on these lines: {4, 29343}, {162, 190}, {192, 264}, {232, 33889}, {273, 3644}, {286, 56319}, {297, 3943}, {317, 17314}, {318, 4664}, {340, 6542}, {346, 17907}, {458, 17318}, {646, 2397}, {653, 37212}, {3807, 61226}, {3995, 31623}, {4360, 36794}, {4419, 44134}, {4552, 18026}, {7282, 17315}, {7952, 50107}, {9308, 17262}, {11331, 17269}, {17160, 26003}, {17305, 53025}, {17388, 27377}, {17395, 52289}, {18315, 44765}, {41679, 65203}, {50110, 56814}, {56188, 65183}

X(65204) = trilinear pole of line {469, 3876}
X(65204) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 43927}, {513, 57704}, {667, 57876}, {810, 56047}, {1459, 2214}, {18210, 58951}, {22096, 37218}, {22383, 43531}
X(65204) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 43927}, {6631, 57876}, {39016, 3937}, {39026, 57704}, {39062, 56047}, {41849, 4025}, {62586, 905}
X(65204) = X(i)-cross conjugate of X(j) for these {i, j}: {65313, 33948}
X(65204) = pole of line {1015, 3120} with respect to the polar circle
X(65204) = pole of line {4025, 7254} with respect to the Wallace hyperbola
X(65204) = pole of line {92, 16585} with respect to the dual conic of Jerabek hyperbola
X(65204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(162), X(6335)}}, {{A, B, C, X(190), X(27808)}}, {{A, B, C, X(469), X(46541)}}, {{A, B, C, X(643), X(646)}}, {{A, B, C, X(1331), X(52609)}}, {{A, B, C, X(2397), X(28606)}}
X(65204) = barycentric product X(i)*X(j) for these (i, j): {162, 42714}, {190, 469}, {264, 65313}, {1783, 33935}, {1897, 5224}, {1978, 44103}, {15742, 45746}, {18020, 23282}, {18026, 3876}, {28606, 6335}, {33948, 4}, {33949, 65160}, {56810, 648}, {56926, 6331}
X(65204) = barycentric quotient X(i)/X(j) for these (i, j): {4, 43927}, {101, 57704}, {190, 57876}, {386, 1459}, {469, 514}, {648, 56047}, {834, 3937}, {1783, 2214}, {1897, 43531}, {3876, 521}, {5224, 4025}, {8637, 22096}, {14349, 3942}, {15742, 835}, {23282, 125}, {23879, 4466}, {26911, 64878}, {28606, 905}, {33935, 15413}, {33948, 69}, {42714, 14208}, {44103, 649}, {45746, 1565}, {47842, 18210}, {56810, 525}, {56926, 647}, {61409, 7254}, {65313, 3}
X(65204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 1897, 648}

X(65205) = ANTICOMPLEMENT OF X(16732)

Barycentrics    (a-b)*(a-c)*(2*a*b*c+a^2*(b+c)-(b-c)^2*(b+c)) : :
X(65205) = -3*X[2]+2*X[16732], -4*X[2486]+3*X[53373]

X(65205) lies on these lines: {2, 16732}, {6, 25241}, {7, 18714}, {10, 23820}, {20, 2831}, {69, 25252}, {75, 16713}, {81, 25254}, {86, 25255}, {99, 112}, {100, 13397}, {110, 59097}, {190, 644}, {192, 4644}, {241, 37788}, {319, 45744}, {326, 45738}, {333, 39770}, {344, 948}, {345, 6360}, {346, 20932}, {347, 18721}, {514, 3882}, {523, 4436}, {536, 25257}, {643, 4427}, {653, 6516}, {662, 14543}, {668, 52609}, {1025, 4605}, {1234, 18591}, {1444, 11683}, {1760, 17134}, {1959, 8680}, {2396, 4623}, {2414, 32041}, {2486, 53373}, {2795, 4516}, {3177, 54280}, {3262, 25083}, {3729, 55392}, {3926, 21595}, {3936, 18668}, {3995, 24076}, {4033, 42720}, {4236, 53282}, {4329, 18720}, {4360, 62797}, {4391, 18740}, {4554, 6335}, {4557, 53358}, {4567, 56320}, {4608, 37143}, {4625, 15418}, {4664, 25237}, {8052, 65220}, {8299, 23772}, {14953, 16568}, {15455, 27133}, {17075, 28738}, {17147, 30579}, {17220, 18041}, {17221, 18042}, {17336, 25243}, {17351, 25245}, {17479, 32933}, {17762, 25242}, {18049, 18656}, {18206, 39765}, {18655, 18713}, {18657, 18715}, {18658, 18716}, {18659, 18717}, {18660, 18718}, {18661, 18722}, {18662, 32939}, {18666, 21287}, {20556, 35552}, {20927, 28748}, {20930, 27396}, {21138, 28283}, {21589, 28777}, {26738, 31035}, {27472, 56882}, {27514, 40903}, {28755, 41808}, {33066, 56187}, {35960, 39350}, {37796, 41804}, {46725, 63813}, {51978, 56839}, {53323, 61180}, {53367, 57115}, {56023, 56834}, {61169, 61220}

X(65205) = reflection of X(i) in X(j) for these {i,j}: {75, 16728}, {3262, 25083}, {3882, 22003}, {17139, 1959}, {20556, 35552}, {39765, 18206}
X(65205) = isotomic conjugate of X(56320)
X(65205) = anticomplement of X(16732)
X(65205) = trilinear pole of line {442, 942}
X(65205) = perspector of circumconic {{A, B, C, X(4998), X(18020)}}
X(65205) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 56320}, {48, 14775}, {513, 2259}, {649, 943}, {656, 40570}, {661, 1175}, {663, 2982}, {667, 40435}, {798, 40412}, {810, 40395}, {1794, 6591}, {1919, 40422}, {1946, 40573}, {1973, 63245}, {2170, 15439}, {2310, 32651}, {2611, 59011}, {3063, 60041}, {3271, 65217}, {3709, 63193}, {14936, 36048}, {54244, 57691}
X(65205) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 56320}, {442, 650}, {942, 647}, {1249, 14775}, {5249, 14838}, {5375, 943}, {6337, 63245}, {6631, 40435}, {9296, 40422}, {10001, 60041}, {15607, 14936}, {16585, 514}, {16732, 16732}, {18591, 513}, {31998, 40412}, {36830, 1175}, {39007, 7117}, {39026, 2259}, {39053, 40573}, {39062, 40395}, {40596, 40570}, {40937, 523}, {40952, 52589}, {52119, 115}
X(65205) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4567, 2}
X(65205) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {59, 2893}, {100, 21294}, {101, 3448}, {110, 150}, {163, 149}, {249, 17135}, {250, 17220}, {662, 21293}, {692, 21221}, {765, 21287}, {827, 25049}, {1101, 75}, {1110, 2895}, {1252, 1330}, {1331, 13219}, {1576, 4440}, {1918, 54104}, {2149, 2475}, {2206, 54102}, {4567, 6327}, {4570, 69}, {4590, 17138}, {4600, 315}, {4601, 21275}, {4620, 21280}, {4628, 25051}, {5379, 21270}, {5546, 33650}, {9274, 39765}, {14574, 21224}, {14587, 17221}, {23357, 1}, {23963, 17148}, {23990, 1654}, {23995, 17147}, {24041, 17137}, {32656, 39352}, {32739, 148}, {34072, 25048}, {44174, 18658}, {47390, 17134}, {52378, 3434}, {57655, 3187}, {57657, 17036}, {59152, 17159}, {65375, 37781}
X(65205) = X(i)-cross conjugate of X(j) for these {i, j}: {61161, 61220}, {61197, 61180}, {61233, 65197}
X(65205) = pole of line {4236, 53273} with respect to the circumcircle
X(65205) = pole of line {149, 2806} with respect to the DeLongchamps circle
X(65205) = pole of line {115, 5521} with respect to the polar circle
X(65205) = pole of line {7, 8} with respect to the Kiepert parabola
X(65205) = pole of line {647, 2605} with respect to the Stammler hyperbola
X(65205) = pole of line {100, 110} with respect to the Steiner circumellipse
X(65205) = pole of line {3035, 5972} with respect to the Steiner inellipse
X(65205) = pole of line {8, 79} with respect to the Yff parabola
X(65205) = pole of line {2, 2911} with respect to the Hutson-Moses hyperbola
X(65205) = pole of line {448, 525} with respect to the Wallace hyperbola
X(65205) = pole of line {190, 15455} with respect to the dual conic of incircle
X(65205) = pole of line {190, 14570} with respect to the dual conic of nine-point circle
X(65205) = pole of line {51389, 51390} with respect to the dual conic of orthoptic circle of the Steiner Inellipse
X(65205) = pole of line {15526, 16595} with respect to the dual conic of polar circle
X(65205) = pole of line {645, 648} with respect to the dual conic of DeLongchamps ellipse
X(65205) = pole of line {2, 6} with respect to the dual conic of Feuerbach hyperbola
X(65205) = pole of line {2, 37} with respect to the dual conic of Jerabek hyperbola
X(65205) = pole of line {99, 108} with respect to the dual conic of Orthic inconic
X(65205) = pole of line {3952, 4566} with respect to the dual conic of Hofstadter ellipse
X(65205) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 13199, 13200}
X(65205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(112), X(4559)}}, {{A, B, C, X(190), X(46404)}}, {{A, B, C, X(442), X(4235)}}, {{A, B, C, X(643), X(15455)}}, {{A, B, C, X(644), X(6335)}}, {{A, B, C, X(648), X(4552)}}, {{A, B, C, X(651), X(13149)}}, {{A, B, C, X(877), X(1234)}}, {{A, B, C, X(1332), X(4554)}}, {{A, B, C, X(2284), X(40937)}}, {{A, B, C, X(4560), X(49274)}}, {{A, B, C, X(5249), X(62669)}}, {{A, B, C, X(6331), X(52609)}}, {{A, B, C, X(6370), X(44427)}}, {{A, B, C, X(14590), X(16585)}}, {{A, B, C, X(14966), X(18591)}}, {{A, B, C, X(16732), X(56320)}}, {{A, B, C, X(37143), X(63782)}}, {{A, B, C, X(45273), X(45926)}}, {{A, B, C, X(60489), X(62306)}}
X(65205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 4552, 2397}, {190, 664, 1332}, {514, 22003, 3882}, {1959, 8680, 17139}, {4427, 14544, 643}, {4552, 65195, 190}, {14543, 17136, 662}, {25083, 64780, 3262}, {60476, 60477, 4585}

X(65206) = X(2)X(56317)∩X(100)X(108)

Barycentrics    (a-b)*(a-c)*(a-b-c)*(2*a^3+a^2*(b+c)+(b-c)^2*(b+c)) : :

X(65206) lies on these lines: {2, 56317}, {8, 27531}, {100, 108}, {145, 18467}, {321, 56178}, {521, 3909}, {522, 4427}, {643, 65197}, {644, 1639}, {664, 50392}, {919, 8707}, {1331, 61185}, {2000, 17077}, {2398, 4551}, {2900, 3187}, {3100, 7360}, {3158, 26267}, {3900, 61172}, {3939, 3952}, {4571, 25268}, {5494, 5657}, {5546, 36797}, {5853, 20045}, {6011, 44065}, {7070, 28950}, {7437, 53761}, {8694, 9057}, {13589, 53349}, {14543, 61221}, {14544, 61220}, {17780, 56248}, {24388, 26230}, {26139, 60368}, {28774, 52365}, {39766, 44669}, {50404, 61720}, {65190, 65198}

X(65206) = reflection of X(i) in X(j) for these {i,j}: {4427, 53388}
X(65206) = trilinear pole of line {950, 2264}
X(65206) = perspector of circumconic {{A, B, C, X(4076), X(46102)}}
X(65206) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 951}, {667, 58005}, {1257, 43924}, {2983, 3669}, {7004, 59090}, {29163, 53538}, {51641, 64985}, {51664, 57390}
X(65206) = X(i)-Dao conjugate of X(j) for these {i, j}: {440, 3676}, {950, 44409}, {1834, 522}, {6631, 58005}, {39026, 951}, {40940, 17094}, {59646, 7178}
X(65206) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {6011, 33650}
X(65206) = pole of line {23189, 57139} with respect to the Stammler hyperbola
X(65206) = pole of line {651, 65236} with respect to the Steiner circumellipse
X(65206) = pole of line {3039, 36949} with respect to the Steiner inellipse
X(65206) = pole of line {329, 440} with respect to the Yff parabola
X(65206) = pole of line {145, 219} with respect to the Hutson-Moses hyperbola
X(65206) = pole of line {17096, 31603} with respect to the Wallace hyperbola
X(65206) = pole of line {3699, 4587} with respect to the dual conic of incircle
X(65206) = pole of line {28739, 56937} with respect to the dual conic of Feuerbach hyperbola
X(65206) = intersection, other than A, B, C, of circumconics {{A, B, C, X(108), X(644)}}, {{A, B, C, X(643), X(44065)}}, {{A, B, C, X(653), X(3699)}}, {{A, B, C, X(919), X(53290)}}, {{A, B, C, X(950), X(30731)}}, {{A, B, C, X(1897), X(6558)}}, {{A, B, C, X(4552), X(36797)}}, {{A, B, C, X(5546), X(23067)}}, {{A, B, C, X(9057), X(30728)}}, {{A, B, C, X(14594), X(56112)}}, {{A, B, C, X(23981), X(61200)}}, {{A, B, C, X(30730), X(61178)}}, {{A, B, C, X(51562), X(61180)}}
X(65206) = barycentric product X(i)*X(j) for these (i, j): {190, 950}, {312, 61221}, {1104, 646}, {1834, 645}, {2264, 668}, {3596, 53290}, {3699, 40940}, {14543, 8}, {17863, 644}, {18650, 65160}, {29162, 4076}, {36797, 440}, {40977, 7257}, {40984, 62534}, {59646, 664}, {61200, 7017}
X(65206) = barycentric quotient X(i)/X(j) for these (i, j): {101, 951}, {190, 58005}, {440, 17094}, {644, 1257}, {645, 64985}, {950, 514}, {1104, 3669}, {1834, 7178}, {2264, 513}, {3939, 2983}, {6065, 29163}, {7115, 59090}, {14543, 7}, {17863, 24002}, {18673, 51664}, {21671, 57243}, {29162, 1358}, {36797, 40414}, {40940, 3676}, {40977, 4017}, {40984, 7180}, {52921, 65015}, {53290, 56}, {59646, 522}, {61200, 222}, {61221, 57}, {65160, 40445}, {65201, 40431}
X(65206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 1897, 4552}, {522, 53388, 4427}, {1331, 61185, 62669}, {14544, 61220, 63782}

X(65207) = TRILINEAR POLE OF LINE {10, 201}

Barycentrics    (a-b)*b*(a-c)*(a+b-c)*c*(a-b+c)*(b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65207) lies on these lines: {12, 318}, {59, 57083}, {75, 40626}, {92, 324}, {108, 835}, {190, 653}, {225, 41683}, {273, 335}, {278, 39698}, {307, 53009}, {342, 7101}, {648, 35174}, {651, 24035}, {811, 65232}, {823, 65201}, {1020, 1577}, {1441, 31043}, {1783, 65355}, {1826, 21091}, {1880, 27809}, {1897, 4551}, {1947, 52412}, {1978, 46404}, {3952, 61178}, {4080, 40149}, {4552, 52607}, {4624, 13149}, {17555, 52357}, {17763, 56822}, {17902, 28776}, {17906, 17924}, {17918, 28780}, {17985, 17987}, {18736, 56553}, {26942, 62605}, {53151, 61177}, {56881, 61180}

X(65207) = trilinear pole of line {10, 201}
X(65207) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 7252}, {6, 23189}, {11, 32661}, {21, 22383}, {28, 36054}, {48, 3737}, {55, 7254}, {56, 23090}, {57, 57134}, {58, 652}, {60, 647}, {78, 57129}, {81, 1946}, {110, 7117}, {112, 1364}, {163, 7004}, {184, 4560}, {212, 1019}, {219, 3733}, {222, 21789}, {261, 3049}, {270, 822}, {284, 1459}, {332, 1919}, {513, 2193}, {520, 2189}, {521, 1333}, {603, 1021}, {604, 57081}, {645, 22096}, {648, 61054}, {654, 57736}, {656, 2150}, {663, 1790}, {667, 1812}, {810, 2185}, {849, 8611}, {905, 2194}, {906, 18191}, {1014, 65102}, {1172, 23224}, {1175, 52306}, {1259, 43925}, {1396, 58340}, {1397, 15411}, {1407, 58338}, {1408, 57055}, {1412, 57108}, {1444, 3063}, {1474, 57241}, {1576, 26932}, {1792, 57181}, {1793, 21758}, {1798, 52326}, {1802, 7203}, {1808, 8632}, {2053, 23092}, {2170, 4575}, {2175, 15419}, {2204, 4131}, {2206, 6332}, {2208, 57213}, {2289, 57200}, {2299, 4091}, {2311, 22384}, {2326, 51640}, {2327, 43924}, {2341, 22379}, {2638, 65232}, {3270, 4565}, {3271, 4558}, {3289, 60568}, {3937, 5546}, {3942, 65375}, {4025, 57657}, {6056, 17925}, {7099, 58329}, {7192, 52425}, {7253, 52411}, {7335, 17926}, {9247, 18155}, {17197, 32656}, {17219, 32739}, {18344, 18604}, {38344, 59006}, {39177, 62266}, {39201, 46103}, {47390, 55195}, {47411, 59005}, {52430, 57215}
X(65207) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 23090}, {9, 23189}, {10, 652}, {37, 521}, {115, 7004}, {136, 2170}, {223, 7254}, {226, 4091}, {244, 7117}, {1214, 905}, {1249, 3737}, {3161, 57081}, {4075, 8611}, {4858, 26932}, {5190, 18191}, {5375, 283}, {5452, 57134}, {6631, 1812}, {6741, 34591}, {7952, 1021}, {9296, 332}, {10001, 1444}, {24771, 58338}, {34588, 47411}, {34589, 38344}, {34591, 1364}, {36103, 7252}, {36901, 17880}, {39026, 2193}, {39052, 60}, {39053, 81}, {39060, 86}, {39062, 2185}, {40586, 1946}, {40590, 1459}, {40591, 36054}, {40593, 15419}, {40596, 2150}, {40599, 57108}, {40603, 6332}, {40611, 22383}, {40619, 17219}, {40622, 3942}, {40626, 16731}, {40837, 1019}, {47345, 513}, {51574, 57241}, {52872, 14418}, {53982, 654}, {55064, 3270}, {55065, 53560}, {55066, 61054}, {56325, 656}, {56905, 17420}, {59577, 57055}, {62565, 4131}, {62570, 4025}, {62576, 18155}, {62585, 15411}, {62602, 7192}, {62605, 4560}, {62614, 52616}
X(65207) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6335, 4552}, {18026, 61178}, {46102, 92}
X(65207) = X(i)-cross conjugate of X(j) for these {i, j}: {2171, 7012}, {3700, 318}, {4086, 1441}, {4605, 4552}, {8611, 10}, {14618, 92}, {24006, 57809}, {35307, 4551}, {55208, 225}
X(65207) = pole of line {654, 2170} with respect to the polar circle
X(65207) = pole of line {61178, 61185} with respect to the Steiner circumellipse
X(65207) = pole of line {78, 56187} with respect to the Yff parabola
X(65207) = pole of line {92, 28950} with respect to the Hutson-Moses hyperbola
X(65207) = pole of line {4552, 24035} with respect to the dual conic of incircle
X(65207) = pole of line {312, 18736} with respect to the dual conic of Feuerbach hyperbola
X(65207) = intersection, other than A, B, C, of circumconics {{A, B, C, X(85), X(38340)}}, {{A, B, C, X(92), X(648)}}, {{A, B, C, X(190), X(335)}}, {{A, B, C, X(226), X(1020)}}, {{A, B, C, X(321), X(42718)}}, {{A, B, C, X(653), X(36127)}}, {{A, B, C, X(1018), X(61161)}}, {{A, B, C, X(3700), X(4081)}}, {{A, B, C, X(4241), X(31043)}}, {{A, B, C, X(4551), X(4605)}}, {{A, B, C, X(4565), X(44733)}}, {{A, B, C, X(6648), X(46405)}}, {{A, B, C, X(14618), X(57215)}}, {{A, B, C, X(15455), X(18740)}}, {{A, B, C, X(18026), X(54240)}}
X(65207) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6335, 18026, 653}

X(65208) = X(100)X(101)∩X(109)X(1252)

Barycentrics    a^2*(a-b)*(a-c)*(a^2+b^2+c^2-2*a*(b+c)) : :

X(65208) lies on these lines: {9, 37736}, {63, 6602}, {100, 101}, {109, 1252}, {220, 23988}, {658, 4564}, {664, 37206}, {1025, 1813}, {1174, 3957}, {1331, 2284}, {1897, 3064}, {1998, 60370}, {2329, 54357}, {3306, 9310}, {3870, 38375}, {4468, 65199}, {4551, 23704}, {4552, 46725}, {8701, 28879}, {14740, 28345}, {17615, 51418}, {28230, 28903}, {35281, 35326}, {43349, 54118}, {51949, 56507}

X(65208) = trilinear pole of line {218, 4878}
X(65208) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 37206}, {277, 513}, {514, 2191}, {522, 17107}, {667, 57791}, {693, 57656}, {764, 63906}, {1015, 54987}, {1086, 1292}, {2414, 43921}, {3669, 6601}, {3733, 60265}, {3937, 65339}, {32644, 62429}, {43049, 55013}, {57469, 62635}
X(65208) = X(i)-Dao conjugate of X(j) for these {i, j}: {220, 522}, {3309, 23760}, {4904, 4858}, {6631, 57791}, {39026, 277}
X(65208) = X(i)-Ceva conjugate of X(j) for these {i, j}: {664, 3939}, {4564, 1445}, {65222, 100}
X(65208) = X(i)-cross conjugate of X(j) for these {i, j}: {1617, 1252}
X(65208) = pole of line {1621, 20244} with respect to the Kiepert parabola
X(65208) = pole of line {3939, 65195} with respect to the Steiner circumellipse
X(65208) = pole of line {9, 3434} with respect to the Yff parabola
X(65208) = pole of line {1, 1170} with respect to the Hutson-Moses hyperbola
X(65208) = pole of line {25082, 28741} with respect to the dual conic of Feuerbach hyperbola
X(65208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(65333)}}, {{A, B, C, X(109), X(1617)}}, {{A, B, C, X(110), X(35280)}}, {{A, B, C, X(218), X(1023)}}, {{A, B, C, X(344), X(42723)}}, {{A, B, C, X(644), X(6078)}}, {{A, B, C, X(658), X(1445)}}, {{A, B, C, X(1026), X(1897)}}, {{A, B, C, X(3064), X(4468)}}, {{A, B, C, X(3309), X(3887)}}, {{A, B, C, X(3939), X(35341)}}, {{A, B, C, X(4233), X(7437)}}, {{A, B, C, X(7719), X(61239)}}, {{A, B, C, X(8632), X(8642)}}, {{A, B, C, X(28879), X(35342)}}
X(65208) = barycentric product X(i)*X(j) for these (i, j): {55, 65199}, {100, 3870}, {101, 344}, {190, 218}, {1018, 41610}, {1252, 4468}, {1332, 7719}, {1445, 644}, {1617, 3699}, {2284, 31638}, {3309, 765}, {3939, 6604}, {3991, 662}, {4076, 51652}, {4350, 4578}, {4878, 99}, {4904, 59149}, {6600, 664}, {7035, 8642}, {21059, 668}, {23144, 65160}, {27819, 57192}, {31605, 6065}, {31615, 38375}, {36037, 51378}, {41539, 643}, {44448, 59}, {55337, 651}
X(65208) = barycentric quotient X(i)/X(j) for these (i, j): {101, 277}, {109, 40154}, {190, 57791}, {218, 514}, {344, 3261}, {692, 2191}, {765, 54987}, {1018, 60265}, {1110, 1292}, {1252, 37206}, {1415, 17107}, {1445, 24002}, {1617, 3676}, {3309, 1111}, {3870, 693}, {3939, 6601}, {3991, 1577}, {4350, 59941}, {4468, 23989}, {4878, 523}, {4904, 23100}, {6600, 522}, {6604, 52621}, {7719, 17924}, {8642, 244}, {21059, 513}, {32739, 57656}, {38375, 40166}, {41539, 4077}, {41610, 7199}, {44448, 34387}, {51378, 36038}, {51652, 1358}, {54236, 26721}, {54325, 57469}, {55337, 4391}, {57250, 14268}, {59149, 63906}, {65199, 6063}

X(65209) = X(100)X(3903)∩X(244)X(1581)

Barycentrics    a*(a-b)*(a-c)*(b^2+a*c)*(a*b+c^2)*(b^2-b*c+c^2) : :

X(65209) lies on these lines: {100, 3903}, {110, 4603}, {149, 19637}, {244, 1581}, {256, 46901}, {257, 46909}, {649, 58981}, {799, 18829}, {893, 7191}, {1978, 56241}, {2611, 30942}, {3218, 41532}, {3873, 65011}, {3952, 27805}, {4451, 20892}, {5211, 17493}, {7226, 52651}, {8620, 51979}, {21341, 40729}, {23354, 65192}, {32010, 55026}, {56257, 61163}, {61180, 65332}

X(65209) = isotomic conjugate of X(63244)
X(65209) = trilinear pole of line {3061, 3094}
X(65209) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 63244}, {983, 4367}, {2533, 38813}, {3113, 58862}, {3287, 7132}, {3407, 45882}, {4459, 8685}, {7033, 56242}, {7234, 40415}, {7255, 20964}, {17743, 20981}, {30671, 64981}
X(65209) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 63244}, {2887, 7234}, {3061, 64865}, {19563, 804}, {19602, 3805}, {41771, 4374}, {41886, 3907}, {52657, 4369}, {52658, 58862}
X(65209) = X(i)-cross conjugate of X(j) for these {i, j}: {3808, 1581}
X(65209) = pole of line {256, 2329} with respect to the Hutson-Moses hyperbola
X(65209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(3888)}}, {{A, B, C, X(110), X(4609)}}, {{A, B, C, X(244), X(3808)}}, {{A, B, C, X(799), X(56982)}}, {{A, B, C, X(982), X(3952)}}, {{A, B, C, X(1978), X(33946)}}
X(65209) = barycentric product X(i)*X(j) for these (i, j): {190, 3865}, {256, 33946}, {257, 3888}, {2275, 56241}, {2887, 4603}, {3061, 65289}, {3662, 3903}, {3705, 37137}, {3721, 4594}, {3778, 7260}, {3863, 668}, {18829, 18904}, {27805, 982}, {30670, 3314}, {32010, 7239}, {33947, 56257}, {41777, 65192}
X(65209) = barycentric quotient X(i)/X(j) for these (i, j): {2, 63244}, {982, 4369}, {2275, 4367}, {3056, 3287}, {3061, 3907}, {3094, 3805}, {3116, 45882}, {3117, 58862}, {3662, 4374}, {3721, 2533}, {3777, 7200}, {3778, 57234}, {3863, 513}, {3865, 514}, {3888, 894}, {3903, 17743}, {4073, 4529}, {4594, 38810}, {4603, 40415}, {7032, 20981}, {7239, 1215}, {16584, 7234}, {18829, 40834}, {18904, 804}, {20284, 24533}, {27805, 7033}, {29055, 7132}, {30670, 3407}, {33891, 14296}, {33946, 1909}, {33947, 16737}, {37137, 56358}, {40432, 7255}, {40499, 2329}, {41886, 64865}, {56257, 56196}, {56805, 4107}, {62753, 2295}
X(65209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3903, 37137, 100}

X(65210) = X(100)X(649)∩X(110)X(8684)

Barycentrics    a*(a-b)*(a-c)*(-b^2+a*c)*(a*b-c^2)*(b^2+b*c+c^2) : :

X(65210) lies on these lines: {100, 649}, {110, 8684}, {149, 60844}, {291, 17449}, {335, 31348}, {693, 1978}, {876, 4562}, {899, 41531}, {1491, 3807}, {3218, 14200}, {3250, 3799}, {3797, 63234}, {3935, 7077}, {3952, 27805}, {4358, 4518}, {5378, 5386}, {8620, 51973}, {17230, 22116}, {17756, 52656}, {30664, 59120}, {61180, 65338}

X(65210) = isotomic conjugate of X(63222)
X(65210) = trilinear pole of line {984, 3094}
X(65210) = perspector of circumconic {{A, B, C, X(5378), X(57566)}}
X(65210) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 23597}, {31, 63222}, {649, 63237}, {659, 985}, {667, 63230}, {812, 40746}, {825, 27918}, {1492, 27846}, {1914, 4817}, {1919, 63242}, {4164, 40763}, {8632, 14621}, {40747, 50456}
X(65210) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 63222}, {9, 23597}, {3789, 659}, {5375, 63237}, {6631, 63230}, {9296, 63242}, {19584, 812}, {19602, 3808}, {27481, 3766}, {36906, 4817}, {38995, 27846}
X(65210) = X(i)-cross conjugate of X(j) for these {i, j}: {30665, 984}
X(65210) = pole of line {3808, 50456} with respect to the Stammler hyperbola
X(65210) = pole of line {672, 33888} with respect to the Yff parabola
X(65210) = pole of line {238, 4876} with respect to the Hutson-Moses hyperbola
X(65210) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(1978)}}, {{A, B, C, X(110), X(4609)}}, {{A, B, C, X(649), X(693)}}, {{A, B, C, X(813), X(4583)}}, {{A, B, C, X(824), X(37998)}}, {{A, B, C, X(3783), X(23354)}}, {{A, B, C, X(3797), X(42720)}}, {{A, B, C, X(3952), X(61164)}}, {{A, B, C, X(4505), X(59120)}}, {{A, B, C, X(46148), X(52922)}}
X(65210) = barycentric product X(i)*X(j) for these (i, j): {100, 63234}, {101, 63228}, {190, 3864}, {291, 3807}, {292, 4505}, {335, 3799}, {1252, 63219}, {2276, 4583}, {3314, 8684}, {3661, 660}, {3773, 4584}, {3862, 668}, {4562, 984}, {5378, 824}, {23596, 765}, {30665, 57566}, {30671, 7035}, {33931, 813}, {36801, 7146}, {63241, 692}, {65040, 876}
X(65210) = barycentric quotient X(i)/X(j) for these (i, j): {1, 23597}, {2, 63222}, {100, 63237}, {190, 63230}, {291, 4817}, {660, 14621}, {668, 63242}, {813, 985}, {869, 8632}, {876, 43266}, {984, 812}, {1491, 27918}, {2276, 659}, {3094, 3808}, {3250, 27846}, {3661, 3766}, {3736, 50456}, {3774, 4455}, {3783, 4375}, {3797, 27855}, {3799, 239}, {3807, 350}, {3862, 513}, {3864, 514}, {4505, 1921}, {4517, 4435}, {4562, 870}, {5378, 4586}, {7146, 43041}, {8684, 3407}, {23596, 1111}, {30665, 35119}, {30671, 244}, {33931, 65101}, {34067, 40746}, {36801, 52652}, {40790, 4107}, {57566, 41072}, {63219, 23989}, {63228, 3261}, {63234, 693}, {63241, 40495}, {65040, 874}

X(65211) = X(11)X(918)∩X(100)X(926)

Barycentrics    a*(b-c)*(-b^2-c^2+a*(b+c))*(b^3*(b-c)+a^3*c-2*a^2*c^2+a*(-b^3+b^2*c+c^3))*(a^3*b-2*a^2*b^2+c^3*(-b+c)+a*(b^3+b*c^2-c^3)) : :

X(65211) lies on these lines: {11, 918}, {100, 926}, {335, 47695}, {518, 650}, {693, 40704}, {4437, 50333}, {4712, 34905}, {60481, 62622}

X(65211) = trilinear pole of line {3126, 17435}
X(65211) = perspector of circumconic {{A, B, C, X(14947), X(60481)}}
X(65211) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 34906}, {101, 56896}, {919, 9318}, {1438, 40865}, {5091, 36086}
X(65211) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 34906}, {1015, 56896}, {6184, 40865}, {38980, 9318}, {38989, 5091}
X(65211) = intersection, other than A, B, C, of circumconics {{A, B, C, X(11), X(100)}}, {{A, B, C, X(110), X(665)}}, {{A, B, C, X(335), X(518)}}, {{A, B, C, X(926), X(52305)}}, {{A, B, C, X(2284), X(62429)}}, {{A, B, C, X(3126), X(63742)}}, {{A, B, C, X(3323), X(6078)}}, {{A, B, C, X(3675), X(6548)}}, {{A, B, C, X(3952), X(24290)}}, {{A, B, C, X(17435), X(62726)}}, {{A, B, C, X(34905), X(53607)}}
X(65211) = barycentric product X(i)*X(j) for these (i, j): {518, 60481}, {3126, 53214}, {14947, 918}, {34905, 75}, {59049, 62430}
X(65211) = barycentric quotient X(i)/X(j) for these (i, j): {1, 34906}, {513, 56896}, {518, 40865}, {665, 5091}, {2254, 9318}, {9319, 36086}, {14947, 666}, {34905, 1}, {60481, 2481}

X(65212) = X(1)X(88)∩X(11)X(4080)

Barycentrics    a*(a+b-2*c)*(a-2*b+c)*(2*b^3-b^2*c-b*c^2+2*c^3+a^2*(b+c)+a*(-3*b^2+2*b*c-3*c^2)) : :
X(65212) = X[80]+2*X[39697], -X[22306]+4*X[58587]

X(65212) lies on these lines: {1, 88}, {11, 4080}, {80, 39697}, {149, 19636}, {528, 42026}, {537, 4945}, {900, 903}, {1145, 24183}, {1168, 54391}, {1318, 62826}, {1387, 51583}, {1623, 53303}, {3218, 14190}, {3257, 62235}, {3681, 52140}, {3873, 52031}, {3952, 4997}, {4013, 59419}, {4392, 52900}, {6336, 61180}, {13266, 23345}, {13277, 55244}, {17449, 30575}, {20568, 40619}, {22306, 58587}, {26015, 60578}, {52925, 62236}, {61768, 62837}, {63851, 64151}

X(65212) = perspector of circumconic {{A, B, C, X(3257), X(54974)}}
X(65212) = pole of line {1623, 4491} with respect to the circumcircle
X(65212) = pole of line {2827, 37691} with respect to the incircle
X(65212) = pole of line {903, 21222} with respect to the Steiner circumellipse
X(65212) = pole of line {1023, 23838} with respect to the Hutson-Moses hyperbola
X(65212) = pole of line {908, 6549} with respect to the dual conic of Yff parabola
X(65212) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6548)}}, {{A, B, C, X(80), X(21297)}}, {{A, B, C, X(100), X(903)}}, {{A, B, C, X(214), X(4453)}}, {{A, B, C, X(678), X(900)}}, {{A, B, C, X(2177), X(23352)}}, {{A, B, C, X(4256), X(57707)}}, {{A, B, C, X(4927), X(17460)}}
X(65212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {88, 1320, 100}, {88, 3315, 106}, {149, 62732, 19636}, {244, 4674, 88}

X(65213) = TRILINEAR POLE OF LINE {1, 281}

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2) : :
X(65213) = -3*X[2]+2*X[55058]

X(65213) lies on these lines: {2, 55058}, {4, 280}, {20, 46350}, {27, 37202}, {29, 52389}, {33, 41081}, {84, 412}, {88, 5125}, {92, 11372}, {100, 40117}, {107, 65224}, {108, 37141}, {162, 36049}, {189, 36101}, {190, 65270}, {268, 1013}, {271, 318}, {282, 23707}, {309, 37214}, {522, 36127}, {651, 1897}, {653, 14304}, {658, 18026}, {662, 7452}, {673, 7008}, {1156, 7003}, {1309, 8059}, {1821, 2357}, {1895, 3341}, {1903, 37142}, {2349, 2816}, {3559, 24624}, {4238, 65244}, {4242, 65216}, {5779, 7046}, {6081, 26704}, {6223, 34162}, {7129, 37129}, {7151, 20332}, {7541, 56939}, {7952, 41084}, {14944, 56944}, {17923, 44901}, {18283, 60599}, {27834, 53151}, {38357, 52780}, {41083, 41086}, {43760, 55110}, {46541, 65254}, {61178, 65234}, {65193, 65217}

X(65213) = anticomplement of X(55058)
X(65213) = trilinear pole of line {1, 281}
X(65213) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 6129}, {6, 64885}, {19, 57233}, {40, 1459}, {48, 14837}, {56, 57101}, {57, 10397}, {108, 55044}, {109, 53557}, {184, 17896}, {196, 36054}, {198, 905}, {208, 57241}, {221, 521}, {222, 14298}, {223, 652}, {227, 23189}, {255, 54239}, {329, 22383}, {347, 1946}, {513, 7078}, {520, 3194}, {522, 7114}, {577, 59935}, {603, 8058}, {604, 57245}, {647, 1817}, {649, 64082}, {650, 7011}, {656, 2360}, {663, 7013}, {810, 8822}, {822, 41083}, {934, 47432}, {1400, 57213}, {1415, 16596}, {1790, 55212}, {1819, 4017}, {2187, 4025}, {2199, 6332}, {2331, 4091}, {3195, 4131}, {3669, 55111}, {6087, 36055}, {6611, 57055}, {7004, 57118}, {7099, 57049}, {7117, 65159}, {7254, 21871}, {7952, 23224}, {8641, 57479}, {8677, 15501}, {14256, 65102}, {36040, 57291}, {36059, 38357}, {41082, 42658}, {55112, 57181}
X(65213) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 36127}
X(65213) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 57101}, {6, 57233}, {9, 64885}, {11, 53557}, {1146, 16596}, {1249, 14837}, {2968, 7358}, {3161, 57245}, {3341, 521}, {5375, 64082}, {5452, 10397}, {6523, 54239}, {7952, 8058}, {10017, 57291}, {14714, 47432}, {20620, 38357}, {34961, 1819}, {36103, 6129}, {38983, 55044}, {39026, 7078}, {39052, 1817}, {39053, 347}, {39060, 40702}, {39062, 8822}, {40582, 57213}, {40596, 2360}, {51221, 6087}, {52389, 8057}, {55058, 55058}, {62605, 17896}
X(65213) = X(i)-Ceva conjugate of X(j) for these {i, j}: {53642, 653}
X(65213) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {65374, 34188}
X(65213) = X(i)-cross conjugate of X(j) for these {i, j}: {108, 1897}, {521, 29}, {522, 280}, {652, 41081}, {1728, 765}, {1741, 4564}, {1750, 24032}, {1753, 7012}, {2270, 7128}, {3239, 92}, {14302, 8}, {14331, 2}, {36049, 44327}, {40117, 65330}, {61229, 13138}
X(65213) = pole of line {3318, 6087} with respect to the polar circle
X(65213) = pole of line {27382, 56943} with respect to the Yff parabola
X(65213) = pole of line {7078, 27382} with respect to the Hutson-Moses hyperbola
X(65213) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(7452)}}, {{A, B, C, X(27), X(52920)}}, {{A, B, C, X(30), X(2816)}}, {{A, B, C, X(84), X(8059)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(107), X(10152)}}, {{A, B, C, X(108), X(36044)}}, {{A, B, C, X(412), X(4246)}}, {{A, B, C, X(522), X(2968)}}, {{A, B, C, X(643), X(43347)}}, {{A, B, C, X(664), X(14544)}}, {{A, B, C, X(1309), X(1897)}}, {{A, B, C, X(1414), X(43346)}}, {{A, B, C, X(2765), X(36050)}}, {{A, B, C, X(3559), X(4242)}}, {{A, B, C, X(3699), X(52938)}}, {{A, B, C, X(4238), X(37279)}}, {{A, B, C, X(4240), X(52846)}}, {{A, B, C, X(4571), X(36037)}}, {{A, B, C, X(5125), X(46541)}}, {{A, B, C, X(5704), X(17780)}}, {{A, B, C, X(7256), X(35157)}}, {{A, B, C, X(13138), X(53642)}}, {{A, B, C, X(14331), X(55058)}}, {{A, B, C, X(36049), X(61229)}}, {{A, B, C, X(36110), X(40097)}}

X(65214) = TRILINEAR POLE OF LINE {1, 185}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(-b^4+a^3*c+b^2*c^2+a^2*(b^2-2*c^2)+a*(-(b^2*c)+c^3))*(a^3*b+c^2*(b^2-c^2)+a^2*(-2*b^2+c^2)+a*(b^3-b*c^2)) : :

X(65214) lies on these lines: {100, 57108}, {162, 1624}, {190, 53211}, {241, 1952}, {243, 8758}, {296, 1155}, {647, 55346}, {650, 653}, {651, 652}, {658, 905}, {662, 7045}, {673, 1465}, {771, 1813}, {799, 15411}, {823, 17926}, {1156, 1937}, {1758, 2655}, {1936, 8763}, {9358, 65216}, {23981, 36086}, {36100, 40843}, {37130, 37757}, {37203, 56815}, {59041, 59090}

X(65214) = trilinear pole of line {1, 185}
X(65214) = X(i)-isoconjugate-of-X(j) for these {i, j}: {243, 652}, {513, 58325}, {521, 2202}, {522, 1951}, {647, 15146}, {649, 7360}, {650, 1936}, {657, 5088}, {663, 1944}, {851, 1021}, {1020, 1984}, {1430, 57055}, {1946, 1948}, {1981, 3270}, {2326, 9391}, {3239, 26884}, {6332, 51726}, {6518, 18344}, {7253, 42669}, {8680, 21789}, {23353, 34591}, {51645, 58329}
X(65214) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 7360}, {39026, 58325}, {39052, 15146}, {39053, 1948}, {39060, 57812}
X(65214) = X(i)-cross conjugate of X(j) for these {i, j}: {851, 55346}, {928, 7}, {1758, 7045}, {2655, 24032}, {3002, 59}, {52222, 37142}
X(65214) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(63), X(1309)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(108), X(65296)}}, {{A, B, C, X(109), X(13149)}}, {{A, B, C, X(241), X(1465)}}, {{A, B, C, X(243), X(929)}}, {{A, B, C, X(278), X(2720)}}, {{A, B, C, X(650), X(652)}}, {{A, B, C, X(1155), X(2635)}}, {{A, B, C, X(1301), X(1624)}}, {{A, B, C, X(1813), X(54240)}}, {{A, B, C, X(7045), X(7128)}}, {{A, B, C, X(9357), X(9394)}}, {{A, B, C, X(32651), X(52607)}}, {{A, B, C, X(56815), X(61231)}}
X(65214) = barycentric product X(i)*X(j) for these (i, j): {1, 53211}, {108, 57801}, {226, 41206}, {1020, 35145}, {1214, 41207}, {1937, 664}, {1945, 4554}, {1949, 46404}, {1952, 651}, {4569, 61427}, {18026, 296}, {37142, 4566}, {40843, 653}, {53321, 57980}, {59041, 6356}
X(65214) = barycentric quotient X(i)/X(j) for these (i, j): {100, 7360}, {101, 58325}, {108, 243}, {109, 1936}, {162, 15146}, {296, 521}, {651, 1944}, {653, 1948}, {934, 5088}, {1020, 8680}, {1275, 15418}, {1415, 1951}, {1425, 9391}, {1813, 6518}, {1937, 522}, {1945, 650}, {1949, 652}, {1952, 4391}, {2249, 1021}, {4566, 44150}, {7128, 1981}, {18026, 57812}, {21789, 1984}, {32674, 2202}, {37142, 7253}, {40843, 6332}, {41206, 333}, {41207, 31623}, {52222, 34591}, {53211, 75}, {53321, 851}, {57801, 35518}, {59041, 59482}, {61427, 3900}

X(65215) = TRILINEAR POLE OF LINE {1, 607}

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3+b^3-b^2*c+b*c^2-c^3-a^2*(b+c)+a*(-b^2-2*b*c+c^2))*(a^3-b^3+b^2*c-b*c^2+c^3-a^2*(b+c)+a*(b^2-2*b*c-c^2)) : :

X(65215) lies on these lines: {4, 673}, {19, 12718}, {21, 37202}, {88, 7466}, {100, 58944}, {108, 658}, {190, 56183}, {651, 8750}, {653, 1633}, {662, 4238}, {799, 36797}, {949, 23707}, {1005, 36100}, {1013, 3423}, {1783, 36086}, {1897, 37206}, {4242, 65242}, {7071, 51190}, {7437, 65216}, {10394, 36101}, {14776, 37136}, {18026, 34085}, {26706, 58989}, {37142, 62691}

X(65215) = trilinear pole of line {1, 607}
X(65215) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 47123}, {6, 64886}, {77, 6182}, {521, 2263}, {647, 16054}, {652, 948}, {657, 23603}, {905, 40131}, {1459, 2550}, {4025, 37580}
X(65215) = X(i)-vertex conjugate of X(j) for these {i, j}: {6516, 32674}
X(65215) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 64886}, {36103, 47123}, {39052, 16054}
X(65215) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(1783)}}, {{A, B, C, X(21), X(934)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(108), X(8750)}}, {{A, B, C, X(109), X(1633)}}, {{A, B, C, X(1005), X(7452)}}, {{A, B, C, X(1013), X(4246)}}, {{A, B, C, X(1026), X(41785)}}, {{A, B, C, X(1292), X(54952)}}, {{A, B, C, X(1415), X(57659)}}, {{A, B, C, X(3559), X(7437)}}, {{A, B, C, X(4628), X(58991)}}, {{A, B, C, X(5546), X(13395)}}, {{A, B, C, X(6516), X(36049)}}, {{A, B, C, X(7466), X(46541)}}, {{A, B, C, X(13138), X(53643)}}, {{A, B, C, X(32641), X(44059)}}, {{A, B, C, X(36118), X(65201)}}
X(65215) = barycentric product X(i)*X(j) for these (i, j): {108, 58004}, {281, 6183}, {1897, 39273}, {3423, 6335}, {18026, 949}, {46108, 58989}, {56098, 653}, {58944, 75}, {63150, 65160}
X(65215) = barycentric quotient X(i)/X(j) for these (i, j): {1, 64886}, {19, 47123}, {108, 948}, {162, 16054}, {607, 6182}, {934, 23603}, {949, 521}, {1783, 2550}, {3423, 905}, {6183, 348}, {8750, 40131}, {32674, 2263}, {39273, 4025}, {56098, 6332}, {58004, 35518}, {58944, 1}, {58989, 1814}

X(65216) = TRILINEAR POLE OF LINE {1, 90}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+c^2))*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+c^2)) : :

X(65216) lies on these lines: {2, 37203}, {3, 7040}, {88, 17080}, {90, 411}, {100, 13256}, {162, 3658}, {190, 65290}, {651, 65175}, {655, 65159}, {673, 2164}, {920, 55495}, {934, 38340}, {1069, 23707}, {1332, 65248}, {1816, 37142}, {1817, 24624}, {2994, 34234}, {4242, 65213}, {6512, 65246}, {6513, 36100}, {6516, 65247}, {7042, 58887}, {7437, 65215}, {9358, 65214}, {36101, 60974}, {55248, 65220}

X(65216) = isogonal conjugate of X(46389)
X(65216) = trilinear pole of line {1, 90}
X(65216) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46389}, {9, 51648}, {19, 59973}, {21, 55214}, {46, 650}, {55, 21188}, {109, 6506}, {453, 55248}, {512, 31631}, {514, 61397}, {521, 52033}, {522, 2178}, {647, 3559}, {649, 5552}, {652, 1068}, {654, 56417}, {661, 3193}, {663, 5905}, {1214, 57124}, {1406, 3239}, {1409, 57083}, {1800, 2501}, {3063, 20930}, {3064, 3157}, {3737, 21853}, {3900, 56848}, {6505, 18344}, {7252, 21077}, {39943, 57102}
X(65216) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46389}, {6, 59973}, {11, 6506}, {223, 21188}, {478, 51648}, {5375, 5552}, {10001, 20930}, {36830, 3193}, {39052, 3559}, {39054, 31631}, {40611, 55214}
X(65216) = X(i)-cross conjugate of X(j) for these {i, j}: {650, 7040}, {1813, 651}, {3064, 21}, {6985, 55346}, {15313, 7}, {36743, 59}, {46389, 1}, {48269, 1476}, {54420, 7012}, {58887, 7045}, {58888, 4}, {61228, 664}
X(65216) = pole of line {46389, 59973} with respect to the Stammler hyperbola
X(65216) = pole of line {1158, 5552} with respect to the Yff parabola
X(65216) = pole of line {1993, 56352} with respect to the Hutson-Moses hyperbola
X(65216) = pole of line {17776, 31600} with respect to the dual conic of Feuerbach hyperbola
X(65216) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1332)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(108), X(4565)}}, {{A, B, C, X(163), X(59083)}}, {{A, B, C, X(404), X(4237)}}, {{A, B, C, X(643), X(65330)}}, {{A, B, C, X(645), X(65331)}}, {{A, B, C, X(646), X(31628)}}, {{A, B, C, X(650), X(42069)}}, {{A, B, C, X(925), X(4558)}}, {{A, B, C, X(1025), X(61019)}}, {{A, B, C, X(1305), X(6516)}}, {{A, B, C, X(1461), X(2222)}}, {{A, B, C, X(1813), X(13397)}}, {{A, B, C, X(1816), X(1981)}}, {{A, B, C, X(1817), X(4242)}}, {{A, B, C, X(4236), X(11329)}}, {{A, B, C, X(4238), X(24580)}}, {{A, B, C, X(4573), X(65334)}}, {{A, B, C, X(4612), X(30610)}}, {{A, B, C, X(5546), X(40117)}}, {{A, B, C, X(6335), X(46640)}}, {{A, B, C, X(7437), X(16054)}}, {{A, B, C, X(9058), X(65298)}}, {{A, B, C, X(13256), X(24002)}}, {{A, B, C, X(36037), X(44327)}}, {{A, B, C, X(53952), X(65300)}}

X(65217) = TRILINEAR POLE OF LINE {1, 201}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3-a^2*b+b^3-b*c^2-a*(b+c)^2)*(a^3-a^2*c-b^2*c+c^3-a*(b+c)^2) : :

X(65217) lies on these lines: {88, 2982}, {100, 15439}, {101, 653}, {109, 65227}, {110, 65244}, {162, 4551}, {190, 4587}, {651, 906}, {655, 14543}, {658, 1813}, {662, 65233}, {664, 65247}, {673, 2259}, {823, 65201}, {943, 1156}, {1794, 23707}, {4552, 65236}, {4564, 65238}, {4565, 65256}, {4566, 38340}, {5745, 34234}, {7012, 61169}, {13395, 59060}, {24624, 60188}, {32680, 35174}, {36101, 61024}, {37128, 63193}, {37140, 65299}, {37143, 63782}, {37203, 40573}, {40412, 65264}, {65193, 65213}

X(65217) = trilinear pole of line {1, 201}
X(65217) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 52306}, {7, 33525}, {9, 50354}, {11, 61197}, {212, 23595}, {244, 61233}, {284, 23752}, {442, 7252}, {513, 40937}, {514, 14547}, {521, 1841}, {522, 2260}, {523, 46882}, {649, 6734}, {650, 942}, {652, 1838}, {654, 45926}, {656, 46884}, {657, 62779}, {661, 54356}, {663, 5249}, {905, 1859}, {1015, 65197}, {1019, 40967}, {1865, 23189}, {2170, 61220}, {2294, 3737}, {3064, 4303}, {3271, 65205}, {3669, 64171}, {4391, 40956}, {4560, 40952}, {7004, 61236}, {7117, 61180}, {7178, 8021}, {7180, 51978}, {8611, 46883}, {14597, 44426}, {17197, 61169}, {17924, 23207}, {17926, 39791}, {18155, 40978}, {18191, 61161}, {18344, 18607}, {21789, 55010}, {26932, 53323}, {37993, 56320}, {41214, 65334}, {46890, 52355}
X(65217) = X(i)-vertex conjugate of X(j) for these {i, j}: {653, 692}
X(65217) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 50354}, {5375, 6734}, {36033, 52306}, {36830, 54356}, {39026, 40937}, {40590, 23752}, {40596, 46884}, {40837, 23595}
X(65217) = X(i)-cross conjugate of X(j) for these {i, j}: {35, 7045}, {71, 7012}, {226, 4564}, {284, 59}, {3651, 55346}, {15439, 36048}
X(65217) = pole of line {2894, 2949} with respect to the Yff parabola
X(65217) = pole of line {2982, 40937} with respect to the Hutson-Moses hyperbola
X(65217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(71), X(61169)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(906)}}, {{A, B, C, X(109), X(65232)}}, {{A, B, C, X(648), X(36037)}}, {{A, B, C, X(664), X(13395)}}, {{A, B, C, X(666), X(4612)}}, {{A, B, C, X(1020), X(2222)}}, {{A, B, C, X(1025), X(21617)}}, {{A, B, C, X(1305), X(1414)}}, {{A, B, C, X(1332), X(1897)}}, {{A, B, C, X(2736), X(35338)}}, {{A, B, C, X(4551), X(4605)}}, {{A, B, C, X(4565), X(36146)}}, {{A, B, C, X(4566), X(35174)}}, {{A, B, C, X(4619), X(4629)}}, {{A, B, C, X(5745), X(24029)}}, {{A, B, C, X(6648), X(31615)}}, {{A, B, C, X(15439), X(32651)}}, {{A, B, C, X(24019), X(36080)}}, {{A, B, C, X(29163), X(36147)}}, {{A, B, C, X(36048), X(54952)}}, {{A, B, C, X(54240), X(54970)}}
X(65217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58993, 65334, 653}

X(65218) = TRILINEAR POLE OF LINE {1, 1783}

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a^2*b+b^3+b*c^2-2*c^3+a*(-b^2+c^2))*(a^3-2*b^3-a^2*c+b^2*c+c^3+a*(b^2-c^2)) : :

X(65218) lies on these lines: {4, 57435}, {88, 36122}, {100, 40116}, {103, 1309}, {108, 61240}, {162, 1021}, {190, 15742}, {521, 651}, {522, 653}, {655, 60583}, {658, 1897}, {662, 5379}, {673, 1861}, {971, 7291}, {1783, 65243}, {2338, 23707}, {3900, 7128}, {4242, 37139}, {8544, 37131}, {14953, 37202}, {18025, 37214}, {24624, 52891}, {34922, 38340}, {36002, 36100}, {37136, 37628}, {37141, 61040}, {37143, 53150}, {37215, 57928}, {43762, 56869}

X(65218) = trilinear pole of line {1, 1783}
X(65218) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 676}, {6, 39470}, {516, 1459}, {521, 1456}, {647, 14953}, {649, 26006}, {652, 43035}, {905, 910}, {927, 47422}, {1461, 57292}, {1565, 2426}, {1795, 42756}, {1886, 4091}, {2398, 3937}, {3270, 23973}, {3669, 51376}, {3733, 51366}, {7177, 46392}, {7254, 17747}, {15419, 51436}, {22086, 63851}, {22383, 30807}, {23696, 53547}, {32656, 58259}, {32657, 58280}, {53550, 56639}
X(65218) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 39470}, {5375, 26006}, {25640, 42756}, {35508, 57292}, {36103, 676}, {39052, 14953}
X(65218) = X(i)-cross conjugate of X(j) for these {i, j}: {910, 7128}, {1736, 765}, {8558, 4564}
X(65218) = pole of line {42756, 57439} with respect to the polar circle
X(65218) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(84), X(2728)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(516), X(971)}}, {{A, B, C, X(521), X(522)}}, {{A, B, C, X(664), X(46964)}}, {{A, B, C, X(1026), X(26001)}}, {{A, B, C, X(1309), X(5379)}}, {{A, B, C, X(1861), X(65338)}}, {{A, B, C, X(1897), X(56183)}}, {{A, B, C, X(2222), X(29374)}}, {{A, B, C, X(2766), X(36110)}}, {{A, B, C, X(3887), X(57435)}}, {{A, B, C, X(4238), X(26003)}}, {{A, B, C, X(4242), X(52891)}}, {{A, B, C, X(7291), X(14953)}}, {{A, B, C, X(7452), X(36002)}}, {{A, B, C, X(16077), X(40431)}}, {{A, B, C, X(18026), X(65201)}}, {{A, B, C, X(36118), X(40117)}}

X(65219) = TRILINEAR POLE OF LINE {1, 1828}

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-2*a*b+3*b^2+2*a*c-2*b*c+c^2)*(a^2+b^2+2*a*(b-c)-2*b*c+3*c^2) : :

X(65219) lies on these lines: {19, 88}, {100, 9088}, {190, 17906}, {1772, 51288}, {1783, 3257}, {3478, 23707}, {4000, 34234}

X(65219) = trilinear pole of line {1, 1828}
X(65219) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 47766}, {6, 9031}, {63, 48327}, {71, 47845}, {521, 54377}, {647, 4234}, {652, 3476}, {1459, 54389}, {4737, 22383}
X(65219) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 9031}, {3162, 48327}, {36103, 47766}, {39052, 4234}
X(65219) = X(i)-cross conjugate of X(j) for these {i, j}: {37391, 55346}, {48335, 92}, {62695, 7128}
X(65219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(19), X(1783)}}, {{A, B, C, X(75), X(934)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(108), X(65336)}}, {{A, B, C, X(2397), X(4000)}}, {{A, B, C, X(6335), X(17906)}}
X(65219) = barycentric product X(i)*X(j) for these (i, j): {75, 9088}, {18026, 3478}
X(65219) = barycentric quotient X(i)/X(j) for these (i, j): {1, 9031}, {19, 47766}, {25, 48327}, {28, 47845}, {108, 3476}, {162, 4234}, {1783, 54389}, {1897, 4737}, {3478, 521}, {9088, 1}, {32674, 54377}

X(65220) = X(100)X(2701)∩X(650)X(662)

Barycentrics    a*(a-b)*(a-c)*(a^3+b^3-2*b^2*c+c^3+a*b*(-2*b+c))*(a^3+b^3+a*(b-2*c)*c-2*b*c^2+c^3) : :

X(65220) lies on these lines: {100, 2701}, {162, 18344}, {190, 3700}, {650, 662}, {651, 661}, {653, 2501}, {655, 55238}, {658, 7178}, {673, 17963}, {799, 4391}, {896, 1156}, {897, 1155}, {1821, 64194}, {1931, 11608}, {1936, 2651}, {1959, 36100}, {2644, 4558}, {3257, 61179}, {8052, 65205}, {17931, 65230}, {17947, 34234}, {17973, 23707}, {24602, 37202}, {36098, 57162}, {37128, 37791}, {37131, 37520}, {37136, 55259}, {37141, 55242}, {37214, 37796}, {38340, 55236}, {39054, 65257}, {55248, 65216}

X(65220) = trilinear pole of line {1, 2648}
X(65220) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 5075}, {6, 2785}, {9, 51642}, {284, 18006}, {333, 17992}, {415, 647}, {512, 40882}, {522, 17966}, {523, 5060}, {652, 17985}, {661, 2651}, {663, 17950}, {2701, 35086}, {3064, 17975}, {17942, 21044}, {41499, 52222}
X(65220) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 2785}, {478, 51642}, {32664, 5075}, {36830, 2651}, {39052, 415}, {39054, 40882}, {40590, 18006}
X(65220) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(14202)}}, {{A, B, C, X(81), X(1290)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(241), X(35466)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(666), X(2222)}}, {{A, B, C, X(813), X(32641)}}, {{A, B, C, X(896), X(1155)}}, {{A, B, C, X(1020), X(4612)}}, {{A, B, C, X(1959), X(64194)}}, {{A, B, C, X(2651), X(41206)}}, {{A, B, C, X(3570), X(37791)}}, {{A, B, C, X(4238), X(46574)}}, {{A, B, C, X(4554), X(36050)}}, {{A, B, C, X(4573), X(6011)}}, {{A, B, C, X(4603), X(38470)}}, {{A, B, C, X(5549), X(8693)}}, {{A, B, C, X(7045), X(24041)}}, {{A, B, C, X(9357), X(9395)}}, {{A, B, C, X(33637), X(43190)}}
X(65220) = barycentric product X(i)*X(j) for these (i, j): {1, 35154}, {162, 57841}, {2648, 664}, {2652, 99}, {2701, 75}, {11608, 662}, {17931, 65}, {17947, 651}, {17963, 4554}, {17973, 18026}, {57675, 811}
X(65220) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2785}, {31, 5075}, {56, 51642}, {65, 18006}, {108, 17985}, {109, 1758}, {110, 2651}, {162, 415}, {163, 5060}, {651, 17950}, {662, 40882}, {1402, 17992}, {1415, 17966}, {2648, 522}, {2652, 523}, {2701, 1}, {11608, 1577}, {17931, 314}, {17947, 4391}, {17963, 650}, {17973, 521}, {18000, 4516}, {23353, 41499}, {35154, 75}, {36059, 17975}, {57675, 656}, {57841, 14208}

X(65221) = TRILINEAR POLE OF LINE {1, 1748}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(65221) lies on these lines: {54, 37142}, {95, 24581}, {100, 933}, {162, 36134}, {163, 823}, {190, 18831}, {275, 24624}, {276, 37219}, {563, 57806}, {648, 655}, {651, 18315}, {653, 16813}, {811, 65251}, {897, 2190}, {1821, 2148}, {2167, 2349}, {2616, 36084}, {4599, 62720}, {8882, 37128}, {15412, 60056}, {23707, 35196}, {32676, 65252}, {37132, 62268}, {37136, 39177}, {37220, 62276}, {52914, 65244}, {58756, 60057}

X(65221) = trilinear pole of line {1, 1748}
X(65221) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 15451}, {3, 12077}, {4, 17434}, {5, 647}, {6, 6368}, {25, 60597}, {48, 2618}, {51, 525}, {53, 520}, {54, 57195}, {68, 52317}, {69, 55219}, {71, 21102}, {74, 14391}, {112, 35442}, {115, 23181}, {125, 1625}, {184, 18314}, {216, 523}, {217, 850}, {233, 39180}, {264, 42293}, {265, 2081}, {275, 34983}, {311, 3049}, {324, 39201}, {339, 61194}, {343, 512}, {394, 51513}, {418, 14618}, {577, 23290}, {656, 1953}, {661, 44706}, {667, 42698}, {669, 28706}, {684, 60517}, {686, 60035}, {798, 18695}, {810, 14213}, {878, 60524}, {905, 21807}, {930, 47424}, {933, 39019}, {1154, 14582}, {1173, 35441}, {1393, 8611}, {1459, 21011}, {1568, 2433}, {1577, 62266}, {1637, 44715}, {2052, 58305}, {2179, 14208}, {2181, 24018}, {2351, 63829}, {2395, 44716}, {2435, 51363}, {2485, 41168}, {2489, 52347}, {2501, 5562}, {2600, 52391}, {2617, 3708}, {2963, 57135}, {2972, 61193}, {3078, 39181}, {3199, 3265}, {3267, 40981}, {3269, 35360}, {3289, 61196}, {3519, 57137}, {3569, 53174}, {3700, 30493}, {4024, 44709}, {4041, 44708}, {4558, 41221}, {4705, 16697}, {6137, 44713}, {6138, 44714}, {6587, 8798}, {7004, 35307}, {7069, 51664}, {7178, 44707}, {9409, 62722}, {10097, 41586}, {11062, 43083}, {11077, 55132}, {13157, 42658}, {13450, 32320}, {13754, 35361}, {14380, 52945}, {14569, 52613}, {14570, 20975}, {14575, 15415}, {15352, 41219}, {15412, 61378}, {15526, 52604}, {16813, 41212}, {17167, 55230}, {18180, 55232}, {18315, 24862}, {20577, 51477}, {20578, 44711}, {20579, 44712}, {23286, 36412}, {27371, 58353}, {27372, 33294}, {30451, 56272}, {32078, 39183}, {32692, 55073}, {34980, 65183}, {39469, 53245}, {41078, 52153}, {41222, 52932}, {42445, 50946}, {44710, 55195}, {45259, 57273}, {45793, 58308}, {46088, 60828}, {47122, 63176}, {52617, 61346}, {55250, 63801}, {57065, 61363}, {58310, 62274}, {61216, 63735}, {62260, 62428}
X(65221) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 6368}, {1249, 2618}, {6505, 60597}, {6631, 42698}, {31998, 18695}, {32664, 15451}, {34591, 35442}, {36033, 17434}, {36103, 12077}, {36830, 44706}, {39052, 5}, {39054, 343}, {39062, 14213}, {40596, 1953}, {62603, 14208}, {62605, 18314}
X(65221) = X(i)-cross conjugate of X(j) for these {i, j}: {47, 24041}, {48, 24000}, {163, 36134}, {2616, 40440}
X(65221) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}}, {{A, B, C, X(163), X(32660)}}, {{A, B, C, X(648), X(46103)}}, {{A, B, C, X(20883), X(62720)}}, {{A, B, C, X(32676), X(36104)}}, {{A, B, C, X(36105), X(57968)}}

X(65222) = ISOGONAL CONJUGATE OF X(21127)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b*(b-c)-a*(2*b+c))*(a^2+c*(-b+c)-a*(b+2*c)) : :

X(65222) lies on these lines: {88, 1170}, {100, 53243}, {101, 658}, {109, 37138}, {190, 6606}, {226, 673}, {655, 56322}, {662, 1025}, {664, 37206}, {799, 7259}, {1156, 2346}, {1414, 65256}, {1803, 32008}, {3219, 6605}, {4251, 59475}, {4551, 36086}, {4564, 35312}, {4571, 37223}, {6183, 53244}, {7045, 35326}, {10509, 41572}, {10572, 64438}, {17484, 62728}, {23707, 47487}, {24624, 60229}, {26722, 42311}, {31618, 37130}, {36039, 65245}, {37139, 62747}, {43760, 61373}, {53337, 65236}, {55281, 65230}, {56255, 65261}, {61185, 62725}, {65165, 65242}

X(65222) = isogonal conjugate of X(21127)
X(65222) = trilinear pole of line {1, 1170}
X(65222) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 21127}, {2, 2488}, {6, 6362}, {7, 10581}, {9, 48151}, {11, 35326}, {55, 21104}, {57, 6608}, {142, 663}, {244, 35341}, {279, 6607}, {284, 55282}, {354, 650}, {512, 16713}, {513, 1212}, {514, 2293}, {522, 1475}, {649, 4847}, {657, 10481}, {661, 17194}, {667, 1229}, {693, 20229}, {884, 51384}, {905, 1827}, {926, 53241}, {1015, 65198}, {1019, 21039}, {1174, 57252}, {1253, 23599}, {1418, 3900}, {1459, 1855}, {2170, 35338}, {2310, 63203}, {2423, 51416}, {2432, 51424}, {3022, 61241}, {3059, 3669}, {3063, 20880}, {3064, 22053}, {3239, 61376}, {3271, 65195}, {3676, 8012}, {3709, 17169}, {3737, 21808}, {3925, 7252}, {4041, 18164}, {4560, 52020}, {6139, 62731}, {6332, 40983}, {7192, 21795}, {8551, 59941}, {8641, 59181}, {10579, 14283}, {14827, 63218}, {14936, 35312}, {16708, 63461}, {17924, 22079}, {18191, 35310}, {21789, 52023}, {34522, 46003}, {43924, 51972}, {43932, 45791}, {53237, 65102}, {53242, 57180}
X(65222) = X(i)-vertex conjugate of X(j) for these {i, j}: {658, 692}
X(65222) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 21127}, {9, 6362}, {223, 21104}, {478, 48151}, {5375, 4847}, {5452, 6608}, {6631, 1229}, {10001, 20880}, {17113, 23599}, {32664, 2488}, {36830, 17194}, {39026, 1212}, {39054, 16713}, {40590, 55282}, {40606, 57252}
X(65222) = X(i)-cross conjugate of X(j) for these {i, j}: {7, 4564}, {55, 7045}, {218, 765}, {3730, 7012}, {4251, 59}, {7411, 55346}, {7676, 59457}, {21127, 1}, {42325, 7}, {58322, 21453}, {62747, 2346}
X(65222) = pole of line {4847, 60970} with respect to the Yff parabola
X(65222) = pole of line {1170, 1212} with respect to the Hutson-Moses hyperbola
X(65222) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(35312)}}, {{A, B, C, X(55), X(35326)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(7259)}}, {{A, B, C, X(109), X(4637)}}, {{A, B, C, X(110), X(4619)}}, {{A, B, C, X(226), X(1025)}}, {{A, B, C, X(514), X(42552)}}, {{A, B, C, X(643), X(666)}}, {{A, B, C, X(664), X(6183)}}, {{A, B, C, X(927), X(1414)}}, {{A, B, C, X(4571), X(65296)}}, {{A, B, C, X(4573), X(31615)}}, {{A, B, C, X(13138), X(32040)}}, {{A, B, C, X(13149), X(32041)}}, {{A, B, C, X(23599), X(42325)}}, {{A, B, C, X(24029), X(54357)}}, {{A, B, C, X(29007), X(56543)}}, {{A, B, C, X(36037), X(43190)}}, {{A, B, C, X(43191), X(55185)}}

X(65223) = TRILINEAR POLE OF LINE {1, 318}

Barycentrics    (a-b)*b*(a-c)*c*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a^2*b+b^3-a*(b-c)^2-b*c^2)*(a^3-a*(b-c)^2-a^2*c-b^2*c+c^3) : :

X(65223) lies on these lines: {88, 16082}, {92, 65249}, {100, 1309}, {162, 36037}, {190, 52622}, {281, 56753}, {648, 65260}, {651, 4391}, {653, 46110}, {655, 65162}, {658, 3261}, {660, 43933}, {673, 1948}, {823, 35321}, {1492, 14776}, {1821, 2250}, {17924, 46119}, {18026, 65234}, {18816, 36101}, {23707, 51565}, {34234, 46109}, {35516, 65246}, {36098, 36110}, {36100, 36795}, {36123, 37129}, {37136, 39294}, {37141, 54953}, {37142, 38955}, {37202, 57984}, {65160, 65226}

X(65223) = trilinear pole of line {1, 318}
X(65223) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 23220}, {3, 3310}, {6, 8677}, {48, 1769}, {56, 52307}, {184, 10015}, {222, 53549}, {248, 42751}, {517, 22383}, {577, 39534}, {603, 46393}, {647, 859}, {649, 22350}, {652, 1457}, {901, 47420}, {906, 42753}, {1415, 35014}, {1459, 2183}, {1465, 1946}, {1576, 42761}, {1875, 36054}, {1960, 57478}, {2200, 23788}, {2397, 22096}, {2427, 3937}, {2432, 56973}, {2804, 52411}, {3049, 17139}, {3063, 62402}, {4558, 42752}, {7117, 23981}, {7254, 51377}, {9247, 36038}, {10017, 32643}, {14260, 22086}, {14571, 23224}, {14578, 42757}, {14908, 42760}, {18877, 42750}, {23757, 32659}, {32641, 35012}, {32655, 42769}, {32656, 42754}, {32657, 42756}, {32658, 42758}, {32660, 35015}, {32661, 42759}, {41220, 65331}, {51379, 57181}, {51987, 53550}
X(65223) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 52307}, {9, 8677}, {1146, 35014}, {1249, 1769}, {4858, 42761}, {5190, 42753}, {5375, 22350}, {7952, 46393}, {10001, 62402}, {32664, 23220}, {36103, 3310}, {36944, 46391}, {38979, 47420}, {39039, 42751}, {39052, 859}, {39053, 1465}, {39060, 22464}, {57434, 38353}, {62576, 36038}, {62605, 10015}
X(65223) = X(i)-cross conjugate of X(j) for these {i, j}: {515, 24032}, {1737, 7035}, {3738, 40440}, {3762, 92}, {4242, 811}, {14304, 75}, {34234, 39294}, {35321, 36037}, {37420, 55346}
X(65223) = pole of line {10538, 22350} with respect to the Yff parabola
X(65223) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(53211)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(668), X(52938)}}, {{A, B, C, X(1309), X(65331)}}, {{A, B, C, X(3261), X(4391)}}, {{A, B, C, X(6335), X(46404)}}, {{A, B, C, X(8707), X(14546)}}, {{A, B, C, X(15742), X(39294)}}, {{A, B, C, X(24035), X(64194)}}, {{A, B, C, X(36141), X(43739)}}, {{A, B, C, X(46794), X(56753)}}, {{A, B, C, X(51560), X(58000)}}

X(65224) = TRILINEAR POLE OF LINE {1, 204}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2-c^2))*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b^2-c^2)) : :

X(65224) lies on these lines: {19, 19611}, {27, 65246}, {64, 37142}, {100, 1301}, {107, 65213}, {190, 53639}, {253, 24604}, {459, 24624}, {648, 658}, {651, 46639}, {653, 65181}, {656, 36092}, {1172, 41082}, {1748, 2184}, {1821, 2155}, {2633, 36084}, {23707, 52158}, {24001, 65251}, {37128, 41489}, {37141, 65232}, {37215, 44326}, {37219, 52581}, {37220, 57921}, {40117, 53886}, {58759, 60056}

X(65224) = trilinear pole of line {1, 204}
X(65224) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 42658}, {3, 6587}, {4, 58796}, {6, 8057}, {20, 647}, {25, 20580}, {30, 61215}, {48, 17898}, {64, 57201}, {69, 62176}, {71, 21172}, {73, 14331}, {74, 14345}, {107, 47409}, {110, 1562}, {112, 122}, {154, 525}, {204, 24018}, {222, 14308}, {250, 55269}, {305, 62175}, {394, 44705}, {512, 37669}, {520, 1249}, {521, 30456}, {523, 15905}, {610, 656}, {652, 5930}, {667, 42699}, {810, 18750}, {822, 1895}, {905, 3198}, {1042, 57045}, {1073, 58342}, {1301, 39020}, {1394, 8611}, {1459, 8804}, {1559, 2430}, {1636, 10152}, {2501, 35602}, {2525, 51508}, {2972, 57219}, {3049, 14615}, {3172, 3265}, {3269, 52913}, {4091, 53011}, {6368, 33629}, {6525, 52613}, {7070, 51664}, {8779, 61189}, {9033, 15291}, {10397, 52078}, {13613, 59077}, {14249, 32320}, {14343, 60674}, {15466, 39201}, {15526, 57153}, {17434, 38808}, {20975, 36841}, {22383, 52345}, {23286, 42459}, {36908, 57108}, {40384, 58352}, {40616, 53321}, {40933, 57055}, {41086, 64885}, {44770, 57296}, {55127, 59499}
X(65224) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 8057}, {244, 1562}, {1249, 17898}, {3343, 24018}, {6505, 20580}, {6631, 42699}, {14092, 656}, {32664, 42658}, {34591, 122}, {36033, 58796}, {36103, 6587}, {38985, 47409}, {39052, 20}, {39054, 37669}, {39062, 18750}, {40596, 610}, {40839, 1577}, {55068, 40616}
X(65224) = X(i)-cross conjugate of X(j) for these {i, j}: {656, 19611}, {11347, 7128}, {18594, 24000}, {24018, 92}, {24019, 162}, {32714, 648}, {40117, 107}, {57055, 40431}, {65374, 53886}
X(65224) = intersection, other than A, B, C, of circumconics {{A, B, C, X(27), X(7435)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(107), X(65232)}}, {{A, B, C, X(648), X(65201)}}, {{A, B, C, X(1748), X(24001)}}, {{A, B, C, X(1981), X(37258)}}, {{A, B, C, X(4592), X(53211)}}, {{A, B, C, X(15322), X(61236)}}, {{A, B, C, X(24019), X(32714)}}, {{A, B, C, X(32676), X(36046)}}, {{A, B, C, X(36126), X(65330)}}

X(65225) = ISOGONAL CONJUGATE OF X(17418)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(b*(b+c)+a*(b+2*c))*(c*(b+c)+a*(2*b+c)) : :

X(65225) lies on these lines: {1, 43759}, {88, 959}, {100, 4559}, {101, 36098}, {109, 662}, {110, 65253}, {162, 32674}, {190, 4551}, {386, 50040}, {651, 52931}, {653, 61226}, {664, 799}, {673, 2258}, {823, 36127}, {941, 1156}, {1411, 5331}, {1945, 37142}, {3699, 65229}, {3725, 64984}, {4604, 61225}, {4636, 65255}, {14594, 37218}, {19861, 31359}, {23703, 37211}, {34259, 36100}, {37130, 58008}, {37870, 65264}, {65166, 65230}, {65256, 65315}

X(65225) = isogonal conjugate of X(17418)
X(65225) = trilinear pole of line {1, 573}
X(65225) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 17418}, {6, 23880}, {7, 58332}, {9, 48144}, {21, 8672}, {55, 43067}, {101, 53526}, {244, 65190}, {284, 50457}, {314, 8639}, {513, 958}, {514, 2268}, {521, 4185}, {522, 1468}, {644, 53543}, {647, 44734}, {649, 11679}, {650, 940}, {651, 53561}, {652, 5307}, {663, 10436}, {1459, 54396}, {1867, 23189}, {2170, 65168}, {2316, 53536}, {3063, 34284}, {3669, 3713}, {3714, 3733}, {3737, 59305}, {4391, 5019}, {6588, 34279}, {7252, 31993}, {57181, 61414}
X(65225) = X(i)-vertex conjugate of X(j) for these {i, j}: {163, 36050}, {643, 1415}, {692, 36098}, {5546, 52928}
X(65225) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 17418}, {9, 23880}, {223, 43067}, {478, 48144}, {1015, 53526}, {5375, 11679}, {10001, 34284}, {38991, 53561}, {39026, 958}, {39052, 44734}, {40590, 50457}, {40611, 8672}
X(65225) = X(i)-cross conjugate of X(j) for these {i, j}: {386, 59}, {2285, 4564}, {6005, 7}, {12514, 7012}, {17418, 1}, {17594, 7045}, {37400, 55346}, {54386, 765}
X(65225) = pole of line {10437, 11679} with respect to the Yff parabola
X(65225) = pole of line {958, 959} with respect to the Hutson-Moses hyperbola
X(65225) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(28162)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(3699)}}, {{A, B, C, X(108), X(1414)}}, {{A, B, C, X(109), X(664)}}, {{A, B, C, X(110), X(1897)}}, {{A, B, C, X(643), X(1783)}}, {{A, B, C, X(931), X(65280)}}, {{A, B, C, X(1026), X(2999)}}, {{A, B, C, X(4561), X(29143)}}, {{A, B, C, X(4588), X(6742)}}, {{A, B, C, X(5221), X(23703)}}, {{A, B, C, X(6335), X(43188)}}, {{A, B, C, X(8652), X(51562)}}, {{A, B, C, X(8701), X(51564)}}, {{A, B, C, X(12560), X(41353)}}, {{A, B, C, X(13486), X(33637)}}, {{A, B, C, X(23981), X(37523)}}, {{A, B, C, X(30610), X(62534)}}, {{A, B, C, X(32675), X(59015)}}, {{A, B, C, X(36077), X(54240)}}, {{A, B, C, X(43350), X(58132)}}, {{A, B, C, X(59038), X(65333)}}, {{A, B, C, X(59125), X(65173)}}

X(65226) = TRILINEAR POLE OF LINE {1, 631}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2-4*a*b+b^2-c^2)*(a^2-b^2-4*a*c+c^2) : :

X(65226) lies on these lines: {7, 88}, {9, 34234}, {100, 51564}, {101, 37136}, {144, 30680}, {162, 65177}, {390, 952}, {527, 65249}, {528, 36596}, {651, 2427}, {653, 21362}, {655, 3732}, {658, 24029}, {664, 3257}, {673, 8545}, {1025, 65242}, {1445, 65241}, {2349, 60942}, {2406, 61240}, {4552, 27834}, {5732, 23707}, {6172, 36101}, {12848, 43760}, {14556, 60934}, {24624, 29007}, {37131, 50573}, {37142, 56107}, {37203, 60973}, {37222, 37787}, {42309, 43762}, {43757, 60944}, {60966, 65246}, {61227, 65227}, {65160, 65223}

X(65226) = reflection of X(i) in X(j) for these {i,j}: {7, 52659}, {34234, 9}
X(65226) = trilinear pole of line {1, 631}
X(65226) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 21183}, {513, 55432}, {514, 52428}, {647, 17519}, {649, 3872}, {650, 999}, {654, 56426}, {663, 3306}, {667, 28808}, {2170, 35281}, {3063, 42697}, {3753, 7252}, {8641, 17079}, {18344, 22129}
X(65226) = X(i)-vertex conjugate of X(j) for these {i, j}: {692, 37136}
X(65226) = X(i)-Dao conjugate of X(j) for these {i, j}: {3160, 21183}, {5375, 3872}, {6631, 28808}, {10001, 42697}, {39026, 55432}, {39052, 17519}
X(65226) = X(i)-cross conjugate of X(j) for these {i, j}: {376, 55346}, {3476, 4998}, {4266, 59}, {5119, 7045}, {6006, 7}, {56824, 24032}, {63126, 1016}
X(65226) = pole of line {3872, 5744} with respect to the Yff parabola
X(65226) = pole of line {5744, 55432} with respect to the Hutson-Moses hyperbola
X(65226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(664)}}, {{A, B, C, X(9), X(101)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(144), X(2406)}}, {{A, B, C, X(527), X(952)}}, {{A, B, C, X(1025), X(8545)}}, {{A, B, C, X(1813), X(21362)}}, {{A, B, C, X(1897), X(13136)}}, {{A, B, C, X(2737), X(32041)}}, {{A, B, C, X(3699), X(50039)}}, {{A, B, C, X(4582), X(30610)}}, {{A, B, C, X(10307), X(53898)}}, {{A, B, C, X(12848), X(53337)}}, {{A, B, C, X(24002), X(62623)}}, {{A, B, C, X(36118), X(54952)}}, {{A, B, C, X(43191), X(44765)}}, {{A, B, C, X(44327), X(55996)}}, {{A, B, C, X(54970), X(65330)}}
X(65226) = barycentric product X(i)*X(j) for these (i, j): {109, 58029}, {1000, 664}, {4566, 56107}, {4569, 52429}, {30680, 653}, {34446, 4572}, {36916, 658}, {51564, 7}, {65029, 651}
X(65226) = barycentric quotient X(i)/X(j) for these (i, j): {7, 21183}, {59, 35281}, {100, 3872}, {101, 55432}, {109, 999}, {162, 17519}, {190, 28808}, {651, 3306}, {658, 17079}, {664, 42697}, {692, 52428}, {1000, 522}, {1813, 22129}, {2222, 56426}, {4551, 3753}, {4552, 4054}, {4554, 20925}, {30680, 6332}, {34446, 663}, {36916, 3239}, {51564, 8}, {52429, 3900}, {56107, 7253}, {58029, 35519}, {59068, 2316}, {59129, 1481}, {62669, 62621}, {65029, 4391}

X(65227) = TRILINEAR POLE OF LINE {1, 71}

Barycentrics    a*(a-b)*(a-c)*(-b^3+b*c^2+2*a*c*(b+c)+a^2*(b+2*c))*(2*a*b*(b+c)+a^2*(2*b+c)+c*(b^2-c^2)) : :

X(65227) lies on these lines: {88, 5708}, {100, 4574}, {101, 162}, {109, 65217}, {110, 65254}, {190, 54970}, {295, 37128}, {651, 23067}, {653, 4551}, {662, 1331}, {673, 5256}, {799, 4561}, {823, 1897}, {936, 7572}, {1156, 2335}, {1807, 24624}, {2215, 37129}, {3699, 37218}, {5779, 33761}, {27834, 57151}, {37130, 57831}, {37202, 63235}, {43758, 45128}, {61227, 65226}

X(65227) = isogonal conjugate of X(46385)
X(65227) = trilinear pole of line {1, 71}
X(65227) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46385}, {6, 23882}, {27, 46382}, {213, 15417}, {405, 513}, {521, 54394}, {522, 1451}, {649, 5271}, {650, 37543}, {656, 56831}, {667, 44140}, {693, 5320}, {1459, 39585}, {1882, 23189}, {3733, 5295}, {4040, 14549}, {7004, 65180}, {7117, 65355}, {42706, 43925}
X(65227) = X(i)-vertex conjugate of X(j) for these {i, j}: {162, 692}
X(65227) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46385}, {9, 23882}, {5375, 5271}, {6626, 15417}, {6631, 44140}, {39026, 405}, {40596, 56831}
X(65227) = X(i)-cross conjugate of X(j) for these {i, j}: {581, 59}, {46382, 40435}, {46385, 1}, {50449, 40433}, {54405, 4564}, {55104, 7012}
X(65227) = pole of line {405, 51223} with respect to the Hutson-Moses hyperbola
X(65227) = pole of line {15417, 46385} with respect to the Wallace hyperbola
X(65227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(28148)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(295)}}, {{A, B, C, X(107), X(54952)}}, {{A, B, C, X(108), X(36048)}}, {{A, B, C, X(109), X(3466)}}, {{A, B, C, X(110), X(664)}}, {{A, B, C, X(668), X(931)}}, {{A, B, C, X(833), X(52935)}}, {{A, B, C, X(1026), X(5256)}}, {{A, B, C, X(1414), X(13397)}}, {{A, B, C, X(3699), X(5546)}}, {{A, B, C, X(4242), X(25516)}}, {{A, B, C, X(4246), X(7572)}}, {{A, B, C, X(4559), X(28624)}}, {{A, B, C, X(4571), X(65201)}}, {{A, B, C, X(4597), X(8690)}}, {{A, B, C, X(4627), X(44327)}}, {{A, B, C, X(5708), X(23703)}}, {{A, B, C, X(6606), X(59038)}}, {{A, B, C, X(6742), X(8652)}}, {{A, B, C, X(8694), X(36049)}}, {{A, B, C, X(15439), X(36127)}}, {{A, B, C, X(16415), X(46541)}}, {{A, B, C, X(28196), X(51562)}}, {{A, B, C, X(32656), X(61169)}}, {{A, B, C, X(34594), X(58132)}}, {{A, B, C, X(35281), X(61227)}}, {{A, B, C, X(36077), X(54970)}}, {{A, B, C, X(43290), X(57151)}}, {{A, B, C, X(43356), X(58135)}}, {{A, B, C, X(53649), X(59012)}}
X(65227) = barycentric product X(i)*X(j) for these (i, j): {1, 54970}, {101, 57831}, {162, 63235}, {190, 51223}, {306, 36077}, {2215, 668}, {2335, 664}, {36080, 75}, {51875, 65247}
X(65227) = barycentric quotient X(i)/X(j) for these (i, j): {1, 23882}, {6, 46385}, {86, 15417}, {100, 5271}, {101, 405}, {109, 37543}, {112, 56831}, {190, 44140}, {228, 46382}, {1018, 5295}, {1415, 1451}, {1783, 39585}, {2215, 513}, {2335, 522}, {7012, 65355}, {7115, 65180}, {32674, 54394}, {32739, 5320}, {36077, 27}, {36080, 1}, {51223, 514}, {54970, 75}, {57831, 3261}, {63235, 14208}

X(65228) = X(1)X(49)∩X(40)X(80)

Barycentrics    a*(a+b-c)*(a-b+c)*(a^2-a*b+b^2-c^2)*(a^2-b^2-b*c-c^2)*(a^2-b^2-a*c+c^2) : :

X(65228) lies on these lines: {1, 49}, {9, 52351}, {12, 57263}, {35, 35194}, {40, 80}, {46, 56419}, {57, 1020}, {63, 18359}, {94, 57645}, {267, 1710}, {484, 63750}, {655, 16548}, {759, 1175}, {1411, 3340}, {1708, 18815}, {1762, 21362}, {1768, 14204}, {1807, 3601}, {2003, 7202}, {2222, 28471}, {2595, 7741}, {2597, 3737}, {2599, 17104}, {2605, 62766}, {2608, 4551}, {3219, 41226}, {3460, 37732}, {3929, 36910}, {5536, 60845}, {5540, 56415}, {10260, 59331}, {11010, 58739}, {14628, 21367}, {16577, 40214}, {20602, 35174}, {35445, 52371}, {56417, 59335}, {56547, 64295}

X(65228) = trilinear pole of line {2594, 2605}
X(65228) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 63642}, {9, 56844}, {36, 7110}, {79, 2323}, {94, 215}, {654, 6742}, {1989, 4996}, {2160, 4511}, {2166, 34544}, {2245, 3615}, {2361, 30690}, {3218, 7073}, {4282, 6757}, {4551, 62746}, {6186, 32851}, {7113, 52344}, {8606, 17923}, {8648, 15455}, {20565, 52426}, {38340, 53285}, {52374, 58328}, {52381, 52427}
X(65228) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 63642}, {478, 56844}, {8287, 3904}, {11597, 34544}, {15898, 7110}, {34544, 4996}
X(65228) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57645, 1}, {63778, 56422}
X(65228) = X(i)-cross conjugate of X(j) for these {i, j}: {50, 1}, {2290, 17104}
X(65228) = pole of line {654, 55126} with respect to the Bevan circle
X(65228) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(94)}}, {{A, B, C, X(19), X(2174)}}, {{A, B, C, X(35), X(57)}}, {{A, B, C, X(50), X(215)}}, {{A, B, C, X(655), X(1020)}}, {{A, B, C, X(1086), X(3512)}}, {{A, B, C, X(1442), X(62780)}}, {{A, B, C, X(1825), X(6354)}}, {{A, B, C, X(2006), X(41226)}}, {{A, B, C, X(3772), X(42033)}}, {{A, B, C, X(4674), X(42701)}}, {{A, B, C, X(8557), X(41441)}}, {{A, B, C, X(14838), X(43043)}}, {{A, B, C, X(18785), X(55210)}}, {{A, B, C, X(26743), X(47054)}}, {{A, B, C, X(35194), X(60074)}}, {{A, B, C, X(37646), X(56440)}}, {{A, B, C, X(56848), X(65134)}}
X(65228) = barycentric product X(i)*X(j) for these (i, j): {1, 63778}, {323, 34535}, {1399, 20566}, {1411, 319}, {1442, 80}, {1807, 7282}, {1825, 57985}, {2006, 3219}, {2166, 7279}, {2222, 4467}, {2477, 63759}, {2599, 39277}, {2605, 35174}, {4560, 63202}, {14616, 2594}, {14838, 655}, {16577, 24624}, {17095, 2161}, {18160, 32675}, {18359, 2003}, {18815, 35}, {40214, 60091}, {40999, 759}, {41226, 57}, {47054, 64990}, {52383, 56934}, {52392, 6198}, {52421, 6187}, {56422, 7}, {57645, 6149}, {65100, 65299}
X(65228) = barycentric quotient X(i)/X(j) for these (i, j): {1, 63642}, {35, 4511}, {50, 34544}, {56, 56844}, {80, 52344}, {655, 15455}, {759, 3615}, {1399, 36}, {1411, 79}, {1442, 320}, {1825, 860}, {2003, 3218}, {2006, 30690}, {2161, 7110}, {2174, 2323}, {2222, 6742}, {2477, 6149}, {2594, 758}, {2605, 3738}, {3219, 32851}, {6149, 4996}, {6187, 7073}, {6198, 5081}, {7252, 62746}, {14838, 3904}, {14975, 52427}, {16577, 3936}, {17095, 20924}, {18815, 20565}, {21741, 2245}, {21794, 4053}, {34535, 94}, {40999, 35550}, {41226, 312}, {52383, 6757}, {52391, 52388}, {52421, 40075}, {53542, 53525}, {54244, 44428}, {56422, 8}, {57645, 63759}, {57736, 1789}, {63202, 4552}, {63750, 2166}, {63778, 75}
X(65228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {655, 24624, 60091}

X(65229) = TRILINEAR POLE OF LINE {1, 312}

Barycentrics    (a-b)*b*(a-c)*c*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :

X(65229) lies on these lines: {88, 4359}, {100, 646}, {190, 65282}, {604, 45242}, {645, 65260}, {651, 668}, {658, 4572}, {660, 4581}, {662, 4033}, {673, 1240}, {799, 35334}, {1018, 7258}, {1220, 37129}, {1492, 32736}, {1978, 37215}, {2298, 20332}, {3257, 65161}, {3596, 24612}, {3699, 65225}, {4552, 37137}, {4562, 37134}, {4607, 62749}, {6335, 36099}, {7035, 65191}, {8687, 65373}, {14624, 16738}, {19811, 34234}, {24004, 37212}, {24624, 60264}, {31643, 43760}, {36804, 37140}, {64984, 65241}

X(65229) = isotomic conjugate of X(48131)
X(65229) = trilinear pole of line {1, 312}
X(65229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 57157}, {6, 6371}, {31, 48131}, {32, 3004}, {56, 52326}, {513, 2300}, {560, 4509}, {593, 42661}, {604, 17420}, {649, 1193}, {663, 61412}, {667, 3666}, {669, 16705}, {798, 54308}, {960, 57181}, {1015, 53280}, {1019, 3725}, {1333, 50330}, {1397, 3910}, {1459, 2354}, {1829, 22383}, {1919, 4357}, {1924, 16739}, {1977, 53332}, {1980, 20911}, {2092, 3733}, {2206, 21124}, {2269, 43924}, {2292, 57129}, {3063, 24471}, {3248, 3882}, {3669, 20967}, {3768, 62769}, {3937, 61205}, {4267, 7180}, {6591, 22345}, {6648, 41224}, {7250, 46889}, {7254, 44092}, {8635, 17108}, {8640, 27455}, {8687, 61051}, {8707, 39015}, {14412, 38882}, {16695, 45218}, {17185, 51641}, {17939, 57462}, {22074, 43923}, {22076, 43925}, {35506, 52928}, {45197, 57074}, {52410, 57158}
X(65229) = X(i)-vertex conjugate of X(j) for these {i, j}: {40519, 65230}
X(65229) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 52326}, {2, 48131}, {9, 6371}, {37, 50330}, {3161, 17420}, {5375, 1193}, {6374, 4509}, {6376, 3004}, {6631, 3666}, {9296, 4357}, {9428, 16739}, {10001, 24471}, {17419, 61051}, {31998, 54308}, {32664, 57157}, {39026, 2300}, {39054, 40153}, {40603, 21124}, {62585, 3910}
X(65229) = X(i)-cross conjugate of X(j) for these {i, j}: {10, 7035}, {333, 1016}, {830, 3112}, {21061, 765}, {35334, 36147}, {57155, 86}, {62749, 1220}
X(65229) = pole of line {1193, 27064} with respect to the Yff parabola
X(65229) = pole of line {2300, 27064} with respect to the Hutson-Moses hyperbola
X(65229) = intersection, other than A, B, C, of circumconics {{A, B, C, X(75), X(57975)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(645), X(8706)}}, {{A, B, C, X(646), X(668)}}, {{A, B, C, X(666), X(52612)}}, {{A, B, C, X(670), X(51560)}}, {{A, B, C, X(789), X(4625)}}, {{A, B, C, X(811), X(839)}}, {{A, B, C, X(813), X(65167)}}, {{A, B, C, X(889), X(4623)}}, {{A, B, C, X(1978), X(6335)}}, {{A, B, C, X(2397), X(19811)}}, {{A, B, C, X(3570), X(16738)}}, {{A, B, C, X(3699), X(7258)}}, {{A, B, C, X(3952), X(65338)}}, {{A, B, C, X(4033), X(36804)}}, {{A, B, C, X(4359), X(24004)}}, {{A, B, C, X(4552), X(4562)}}, {{A, B, C, X(4584), X(59102)}}, {{A, B, C, X(4594), X(8709)}}, {{A, B, C, X(6010), X(32665)}}, {{A, B, C, X(6648), X(8707)}}, {{A, B, C, X(8050), X(54986)}}, {{A, B, C, X(9059), X(44765)}}, {{A, B, C, X(27805), X(56248)}}, {{A, B, C, X(29052), X(57960)}}, {{A, B, C, X(35009), X(65298)}}, {{A, B, C, X(35574), X(55281)}}, {{A, B, C, X(51563), X(57959)}}

X(65230) = TRILINEAR POLE OF LINE {1, 333}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(b*(b+c)+a*(b+2*c))*(c*(b+c)+a*(2*b+c)) : :

X(65230) lies on these lines: {88, 5333}, {99, 651}, {100, 645}, {163, 65255}, {190, 7257}, {314, 24633}, {333, 43759}, {643, 36098}, {653, 811}, {658, 4625}, {799, 3882}, {897, 31359}, {941, 17379}, {1018, 7258}, {2258, 37132}, {4594, 37137}, {4612, 65253}, {5278, 24624}, {5331, 37129}, {17931, 65220}, {34259, 37142}, {36860, 37133}, {37219, 40828}, {53338, 65250}, {55281, 65222}, {55284, 61240}, {65166, 65225}

X(65230) = isotomic conjugate of X(50457)
X(65230) = trilinear pole of line {1, 333}
X(65230) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 8639}, {6, 8672}, {31, 50457}, {42, 48144}, {213, 43067}, {512, 940}, {523, 5019}, {647, 4185}, {661, 1468}, {667, 31993}, {669, 34284}, {798, 10436}, {810, 5307}, {958, 7180}, {1400, 17418}, {1402, 23880}, {1427, 58332}, {1867, 22383}, {2268, 4017}, {3122, 65168}, {3713, 7250}, {3714, 57181}, {4557, 53543}, {11679, 51641}, {17110, 50483}, {53321, 53561}, {54417, 57185}
X(65230) = X(i)-vertex conjugate of X(j) for these {i, j}: {40519, 65229}
X(65230) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 50457}, {9, 8672}, {5375, 59305}, {6626, 43067}, {6631, 31993}, {31998, 10436}, {32664, 8639}, {34961, 2268}, {36830, 1468}, {39052, 4185}, {39054, 940}, {39062, 5307}, {40582, 17418}, {40592, 48144}, {40605, 23880}, {40625, 53526}, {55068, 53561}
X(65230) = X(i)-cross conjugate of X(j) for these {i, j}: {386, 7035}, {1010, 4600}, {6005, 40439}, {12514, 24041}, {65166, 99}
X(65230) = pole of line {23880, 43067} with respect to the Wallace hyperbola
X(65230) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(99), X(645)}}, {{A, B, C, X(163), X(1018)}}, {{A, B, C, X(643), X(7258)}}, {{A, B, C, X(648), X(4610)}}, {{A, B, C, X(670), X(51563)}}, {{A, B, C, X(1978), X(54970)}}, {{A, B, C, X(3570), X(17379)}}, {{A, B, C, X(3952), X(54986)}}, {{A, B, C, X(4552), X(27805)}}, {{A, B, C, X(4565), X(4603)}}, {{A, B, C, X(4584), X(4627)}}, {{A, B, C, X(4585), X(5278)}}, {{A, B, C, X(4602), X(32041)}}, {{A, B, C, X(28624), X(65298)}}, {{A, B, C, X(28841), X(65167)}}, {{A, B, C, X(35180), X(42362)}}, {{A, B, C, X(44765), X(46961)}}, {{A, B, C, X(51560), X(57959)}}
X(65230) = barycentric product X(i)*X(j) for these (i, j): {1, 65280}, {75, 931}, {163, 40828}, {190, 37870}, {314, 65225}, {799, 941}, {2258, 670}, {5331, 668}, {7257, 959}, {28660, 32693}, {31359, 99}, {32038, 333}, {34258, 662}, {34259, 811}, {44733, 645}, {58008, 643}
X(65230) = barycentric quotient X(i)/X(j) for these (i, j): {1, 8672}, {2, 50457}, {21, 17418}, {31, 8639}, {81, 48144}, {86, 43067}, {99, 10436}, {100, 59305}, {110, 1468}, {162, 4185}, {163, 5019}, {190, 31993}, {333, 23880}, {643, 958}, {645, 11679}, {648, 5307}, {662, 940}, {799, 34284}, {931, 1}, {941, 661}, {959, 4017}, {1019, 53543}, {1021, 53561}, {1897, 1867}, {2258, 512}, {2328, 58332}, {3699, 3714}, {4560, 53526}, {4567, 65168}, {4636, 54417}, {5331, 513}, {5546, 2268}, {7258, 61414}, {7259, 3713}, {16704, 53536}, {31359, 523}, {32038, 226}, {32693, 1400}, {34258, 1577}, {34259, 656}, {36797, 54396}, {37870, 514}, {40828, 20948}, {44733, 7178}, {52931, 1254}, {58008, 4077}, {65225, 65}, {65280, 75}

X(65231) = TRILINEAR POLE OF LINE {1, 3271}

Barycentrics    a*(a-b)*(a-c)*(a^2*c+b^2*(-b+c)+a*(b^2-3*b*c+c^2))*(a^2*b+(b-c)*c^2+a*(b^2-3*b*c+c^2)) : :

X(65231) lies on these lines: {100, 663}, {190, 650}, {239, 34234}, {241, 65241}, {649, 651}, {653, 6591}, {658, 3669}, {662, 7252}, {673, 16610}, {799, 4560}, {884, 23832}, {899, 1156}, {1155, 9432}, {1492, 35281}, {1821, 37759}, {2423, 37136}, {4598, 6631}, {4850, 37222}, {5205, 9371}, {7035, 25268}, {9358, 37141}, {17595, 24499}, {26273, 57037}, {28798, 37758}, {34085, 62635}, {37130, 37756}, {61214, 65248}

X(65231) = trilinear pole of line {1, 3271}
X(65231) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 56530}, {647, 15150}, {649, 5205}, {650, 9364}, {663, 40862}, {667, 40875}
X(65231) = X(i)-vertex conjugate of X(j) for these {i, j}: {31615, 32666}
X(65231) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 5205}, {6631, 40875}, {39026, 56530}, {39052, 15150}
X(65231) = X(i)-cross conjugate of X(j) for these {i, j}: {2821, 7}, {62371, 59}
X(65231) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(901)}}, {{A, B, C, X(57), X(666)}}, {{A, B, C, X(81), X(51562)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(109), X(30610)}}, {{A, B, C, X(241), X(16610)}}, {{A, B, C, X(646), X(1461)}}, {{A, B, C, X(649), X(650)}}, {{A, B, C, X(893), X(34067)}}, {{A, B, C, X(899), X(1155)}}, {{A, B, C, X(1293), X(4554)}}, {{A, B, C, X(2051), X(46405)}}, {{A, B, C, X(2222), X(31628)}}, {{A, B, C, X(2731), X(42467)}}, {{A, B, C, X(2737), X(5205)}}, {{A, B, C, X(2743), X(31615)}}, {{A, B, C, X(3903), X(35009)}}, {{A, B, C, X(4565), X(56248)}}, {{A, B, C, X(4573), X(56194)}}, {{A, B, C, X(4591), X(36804)}}, {{A, B, C, X(4617), X(31343)}}, {{A, B, C, X(5382), X(7035)}}, {{A, B, C, X(6014), X(32041)}}, {{A, B, C, X(9082), X(26273)}}, {{A, B, C, X(9357), X(9361)}}, {{A, B, C, X(14727), X(54128)}}, {{A, B, C, X(28218), X(54118)}}, {{A, B, C, X(30650), X(32718)}}, {{A, B, C, X(37756), X(42723)}}, {{A, B, C, X(37759), X(42717)}}, {{A, B, C, X(39741), X(46135)}}, {{A, B, C, X(42343), X(58124)}}
X(65231) = barycentric product X(i)*X(j) for these (i, j): {1, 53208}, {664, 9365}, {668, 9432}, {52517, 651}, {65367, 75}
X(65231) = barycentric quotient X(i)/X(j) for these (i, j): {100, 5205}, {101, 56530}, {109, 9364}, {162, 15150}, {190, 40875}, {651, 40862}, {9365, 522}, {9432, 513}, {52517, 4391}, {53208, 75}, {65367, 1}

X(65232) = ISOGONAL CONJUGATE OF X(8611)

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+b-c)*(a+c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65232) lies on these lines: {6, 57737}, {7, 2326}, {27, 1412}, {28, 34056}, {56, 270}, {77, 3213}, {99, 58945}, {101, 65170}, {107, 8059}, {108, 110}, {109, 36077}, {112, 934}, {163, 1020}, {196, 40214}, {241, 56830}, {273, 604}, {643, 65233}, {648, 653}, {811, 65207}, {823, 37136}, {1014, 1172}, {1326, 56909}, {1396, 56049}, {1414, 4556}, {1420, 13739}, {1461, 24019}, {1474, 56783}, {1625, 52610}, {1783, 4627}, {1790, 41083}, {1897, 65168}, {2073, 2078}, {2260, 63193}, {2360, 44698}, {2905, 7120}, {3733, 52604}, {3882, 4242}, {4552, 41676}, {4560, 41678}, {4610, 4625}, {4626, 4637}, {5053, 26003}, {5546, 65159}, {6610, 52955}, {7125, 44697}, {7128, 17925}, {8545, 11107}, {16754, 65253}, {16813, 39177}, {17094, 39052}, {17940, 43923}, {23353, 53323}, {32676, 36146}, {36119, 59818}, {37141, 65224}, {40862, 44330}, {44331, 56869}, {46151, 47844}, {52775, 59005}, {57118, 65177}, {58993, 59010}

X(65232) = isogonal conjugate of X(8611)
X(65232) = trilinear pole of line {28, 34}
X(65232) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 8611}, {3, 3700}, {6, 52355}, {8, 647}, {9, 656}, {10, 652}, {11, 4574}, {12, 23090}, {21, 55232}, {33, 24018}, {37, 521}, {41, 14208}, {42, 6332}, {48, 4086}, {55, 525}, {63, 4041}, {65, 57055}, {69, 3709}, {71, 522}, {72, 650}, {73, 3239}, {77, 4171}, {78, 661}, {100, 53560}, {112, 7068}, {125, 5546}, {181, 15411}, {200, 51664}, {201, 1021}, {210, 905}, {212, 1577}, {213, 35518}, {219, 523}, {220, 17094}, {225, 57057}, {226, 57108}, {228, 4391}, {271, 55212}, {281, 520}, {283, 4024}, {284, 4064}, {304, 63461}, {306, 663}, {307, 657}, {312, 810}, {318, 822}, {321, 1946}, {326, 55206}, {332, 4079}, {333, 55230}, {345, 512}, {348, 4524}, {513, 3694}, {514, 2318}, {594, 23189}, {607, 3265}, {643, 3708}, {644, 18210}, {645, 20975}, {649, 3710}, {669, 57919}, {684, 15628}, {686, 56103}, {693, 52370}, {798, 3718}, {850, 52425}, {879, 59734}, {1018, 7004}, {1043, 55234}, {1073, 14308}, {1146, 23067}, {1172, 57109}, {1214, 3900}, {1231, 8641}, {1259, 2501}, {1260, 7178}, {1264, 2489}, {1265, 7180}, {1331, 21044}, {1332, 4516}, {1334, 4025}, {1402, 15416}, {1409, 4397}, {1439, 4130}, {1441, 65102}, {1459, 2321}, {1792, 57185}, {1793, 2610}, {1802, 4077}, {1812, 4705}, {1813, 52335}, {1826, 57241}, {1857, 52613}, {1903, 57101}, {2171, 57081}, {2175, 3267}, {2193, 4036}, {2197, 7253}, {2200, 35519}, {2289, 24006}, {2310, 65233}, {2316, 14429}, {2328, 57243}, {2333, 52616}, {2357, 57245}, {2631, 44693}, {2632, 65201}, {2638, 65207}, {2968, 4559}, {3049, 3596}, {3063, 20336}, {3064, 3682}, {3120, 4587}, {3125, 4571}, {3269, 36797}, {3270, 4552}, {3271, 52609}, {3688, 4580}, {3690, 4560}, {3692, 4017}, {3693, 10099}, {3695, 7252}, {3701, 22383}, {3712, 10097}, {3737, 3949}, {3930, 23696}, {3937, 30730}, {3939, 4466}, {3942, 4069}, {3952, 7117}, {3990, 44426}, {3998, 18344}, {4055, 46110}, {4081, 52610}, {4091, 53008}, {4092, 4558}, {4105, 56382}, {4140, 7015}, {4143, 6059}, {4163, 52373}, {4551, 34591}, {4557, 26932}, {4636, 21046}, {4674, 14418}, {4876, 53556}, {5440, 61179}, {5547, 14417}, {6056, 14618}, {6057, 7254}, {6354, 58338}, {6358, 57134}, {6516, 36197}, {6730, 7591}, {7017, 39201}, {7063, 52608}, {7064, 15419}, {7065, 15352}, {7066, 17926}, {7077, 24459}, {7101, 51640}, {7250, 30681}, {7265, 8606}, {7359, 14380}, {8057, 30457}, {8058, 41087}, {8676, 40161}, {9033, 15627}, {9404, 52388}, {10397, 39130}, {10570, 52310}, {14298, 52389}, {14331, 53012}, {15412, 44707}, {15420, 40966}, {20902, 65375}, {21789, 26942}, {21801, 37628}, {21871, 61040}, {23289, 51574}, {35072, 61178}, {36054, 41013}, {37755, 58329}, {38955, 52307}, {40149, 58340}, {40628, 56259}, {51379, 55259}, {51641, 52406}, {52351, 53562}, {52385, 65103}, {52978, 55244}, {53013, 64885}
X(65232) = X(i)-vertex conjugate of X(j) for these {i, j}: {653, 32652}, {1020, 65375}, {1813, 8750}
X(65232) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 8611}, {9, 52355}, {223, 525}, {478, 656}, {1249, 4086}, {3160, 14208}, {3162, 4041}, {5375, 3710}, {5521, 21044}, {6609, 51664}, {6626, 35518}, {8054, 53560}, {10001, 20336}, {15259, 55206}, {31998, 3718}, {34591, 7068}, {34961, 3692}, {36103, 3700}, {36830, 78}, {36908, 57243}, {39026, 3694}, {39052, 8}, {39053, 321}, {39054, 345}, {39060, 313}, {39062, 312}, {40589, 521}, {40590, 4064}, {40592, 6332}, {40593, 3267}, {40596, 9}, {40602, 57055}, {40605, 15416}, {40611, 55232}, {40617, 4466}, {40620, 17880}, {40622, 20902}, {40837, 1577}, {47345, 4036}, {55060, 3708}, {55067, 2968}, {62602, 850}
X(65232) = X(i)-cross conjugate of X(j) for these {i, j}: {112, 162}, {278, 7128}, {608, 7012}, {1019, 27}, {1459, 63193}, {1461, 4565}, {3737, 1014}, {4017, 273}, {4306, 7045}, {7252, 270}, {51664, 57}, {55208, 34}, {56848, 35049}
X(65232) = pole of line {8822, 16049} with respect to the Kiepert parabola
X(65232) = pole of line {521, 652} with respect to the Stammler hyperbola
X(65232) = pole of line {3101, 64002} with respect to the Yff parabola
X(65232) = pole of line {6332, 8611} with respect to the Wallace hyperbola
X(65232) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(27), X(823)}}, {{A, B, C, X(108), X(653)}}, {{A, B, C, X(110), X(662)}}, {{A, B, C, X(112), X(24019)}}, {{A, B, C, X(162), X(648)}}, {{A, B, C, X(163), X(59010)}}, {{A, B, C, X(190), X(13397)}}, {{A, B, C, X(278), X(52607)}}, {{A, B, C, X(514), X(2850)}}, {{A, B, C, X(651), X(664)}}, {{A, B, C, X(1019), X(17197)}}, {{A, B, C, X(1020), X(26700)}}, {{A, B, C, X(1461), X(1813)}}, {{A, B, C, X(1474), X(32676)}}, {{A, B, C, X(1897), X(36099)}}, {{A, B, C, X(2720), X(32651)}}, {{A, B, C, X(3669), X(51643)}}, {{A, B, C, X(4617), X(37141)}}, {{A, B, C, X(7254), X(39177)}}, {{A, B, C, X(14543), X(44065)}}, {{A, B, C, X(17096), X(39179)}}, {{A, B, C, X(32674), X(58945)}}, {{A, B, C, X(36145), X(58987)}}, {{A, B, C, X(37140), X(55183)}}, {{A, B, C, X(52775), X(54240)}}, {{A, B, C, X(58992), X(65298)}}, {{A, B, C, X(59067), X(65375)}}
X(65232) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 662, 65201}

X(65233) = TRILINEAR POLE OF LINE {72, 73}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(b+c)*(a^2-b^2-c^2) : :

X(65233) lies on these lines: {7, 27514}, {9, 25000}, {12, 5880}, {57, 18139}, {63, 343}, {71, 307}, {77, 2197}, {78, 296}, {100, 109}, {101, 13395}, {190, 653}, {306, 40152}, {345, 56553}, {573, 28739}, {579, 56927}, {643, 65232}, {644, 56235}, {645, 4998}, {655, 65236}, {662, 65217}, {664, 54970}, {831, 53243}, {905, 23113}, {1018, 1020}, {1305, 29014}, {1332, 1813}, {1445, 16593}, {1730, 28776}, {1764, 28774}, {1765, 21270}, {2250, 21091}, {2252, 9028}, {2283, 4553}, {3682, 62765}, {3692, 7013}, {3694, 52385}, {3729, 34388}, {3952, 61229}, {4019, 57807}, {4558, 44717}, {4574, 52610}, {5249, 60188}, {14543, 21362}, {17740, 56550}, {17776, 56549}, {17975, 17977}, {21361, 28997}, {25083, 62402}, {25268, 57245}, {32849, 56560}, {40576, 54440}, {41342, 56559}, {44710, 57081}, {51367, 51368}, {53321, 61172}, {56826, 56886}, {61178, 65196}, {61236, 65355}, {63203, 63782}, {63827, 65175}, {65314, 65315}

X(65233) = isotomic conjugate of X(57215)
X(65233) = trilinear pole of line {72, 73}
X(65233) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 7252}, {8, 43925}, {9, 57200}, {11, 112}, {19, 3737}, {21, 6591}, {25, 4560}, {27, 663}, {28, 650}, {29, 649}, {31, 57215}, {33, 1019}, {34, 1021}, {55, 17925}, {56, 17926}, {58, 3064}, {60, 2501}, {81, 18344}, {107, 7117}, {110, 8735}, {162, 2170}, {232, 60568}, {244, 65201}, {250, 55195}, {261, 2489}, {270, 661}, {278, 21789}, {281, 3733}, {284, 7649}, {286, 3063}, {318, 57129}, {393, 23189}, {512, 46103}, {513, 1172}, {514, 2299}, {521, 5317}, {522, 1474}, {523, 2189}, {607, 7192}, {608, 7253}, {645, 42067}, {648, 3271}, {652, 8747}, {667, 31623}, {693, 2204}, {757, 55206}, {759, 65104}, {798, 57779}, {884, 15149}, {1014, 65103}, {1015, 36797}, {1024, 54407}, {1098, 55208}, {1118, 23090}, {1333, 44426}, {1364, 6529}, {1396, 3900}, {1435, 58329}, {1459, 8748}, {1783, 18191}, {1857, 7254}, {1896, 22383}, {1919, 44130}, {1973, 18155}, {2053, 17921}, {2150, 24006}, {2181, 39177}, {2194, 17924}, {2203, 4391}, {2206, 46110}, {2212, 7199}, {2287, 43923}, {2310, 65232}, {2311, 65106}, {2322, 43924}, {2326, 4017}, {2332, 3676}, {2354, 57161}, {2969, 5546}, {2971, 55196}, {3125, 52914}, {3572, 14024}, {3669, 4183}, {4565, 42069}, {4858, 32676}, {5190, 58986}, {6059, 15419}, {7004, 24019}, {7071, 17096}, {7079, 7203}, {7115, 56283}, {7180, 59482}, {7337, 15411}, {8676, 40574}, {8750, 17197}, {14010, 32702}, {14775, 46882}, {15352, 61054}, {16726, 56183}, {18020, 63462}, {18021, 57204}, {18101, 35325}, {24624, 58313}, {26932, 32713}, {33635, 46542}, {34079, 44428}, {34387, 61206}, {36420, 52355}, {37908, 62635}, {44113, 60571}, {46107, 57657}, {52375, 65105}, {52920, 53560}, {57212, 60816}
X(65233) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 17926}, {2, 57215}, {6, 3737}, {10, 3064}, {37, 44426}, {125, 2170}, {223, 17925}, {226, 514}, {244, 8735}, {478, 57200}, {905, 40213}, {1214, 17924}, {5375, 29}, {6337, 18155}, {6505, 4560}, {6631, 31623}, {9296, 44130}, {10001, 286}, {11517, 1021}, {15267, 55208}, {15526, 4858}, {26932, 17197}, {31998, 57779}, {34586, 65104}, {34591, 11}, {34961, 2326}, {35069, 44428}, {35071, 7004}, {36033, 7252}, {36830, 270}, {38985, 7117}, {39006, 18191}, {39019, 60804}, {39026, 1172}, {39054, 46103}, {40586, 18344}, {40590, 7649}, {40591, 650}, {40603, 46110}, {40607, 55206}, {40611, 6591}, {40628, 56283}, {51574, 522}, {55064, 42069}, {55066, 3271}, {56325, 24006}, {62564, 4391}, {62565, 693}, {62570, 46107}, {62573, 17880}, {62614, 35519}, {62647, 7253}
X(65233) = X(i)-Ceva conjugate of X(j) for these {i, j}: {190, 4552}, {4998, 78}, {6516, 23067}, {44717, 63}, {46102, 64082}, {65014, 22350}
X(65233) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2149, 52676}
X(65233) = X(i)-cross conjugate of X(j) for these {i, j}: {525, 63}, {656, 307}, {8611, 72}, {24018, 306}, {51664, 1214}
X(65233) = pole of line {14723, 23845} with respect to the circumcircle
X(65233) = pole of line {2975, 17221} with respect to the Kiepert parabola
X(65233) = pole of line {23113, 40518} with respect to the MacBeath circumconic
X(65233) = pole of line {3737, 57212} with respect to the Stammler hyperbola
X(65233) = pole of line {4552, 61185} with respect to the Steiner circumellipse
X(65233) = pole of line {3, 63} with respect to the Yff parabola
X(65233) = pole of line {9, 16577} with respect to the Hutson-Moses hyperbola
X(65233) = pole of line {18155, 57215} with respect to the Wallace hyperbola
X(65233) = pole of line {2170, 3904} with respect to the dual conic of polar circle
X(65233) = pole of line {312, 52358} with respect to the dual conic of Feuerbach hyperbola
X(65233) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7451)}}, {{A, B, C, X(63), X(4558)}}, {{A, B, C, X(71), X(54325)}}, {{A, B, C, X(78), X(645)}}, {{A, B, C, X(100), X(1332)}}, {{A, B, C, X(109), X(296)}}, {{A, B, C, X(190), X(1331)}}, {{A, B, C, X(226), X(61231)}}, {{A, B, C, X(306), X(4033)}}, {{A, B, C, X(307), X(1025)}}, {{A, B, C, X(343), X(4585)}}, {{A, B, C, X(525), X(3738)}}, {{A, B, C, X(651), X(4566)}}, {{A, B, C, X(656), X(2254)}}, {{A, B, C, X(662), X(61220)}}, {{A, B, C, X(831), X(35338)}}, {{A, B, C, X(906), X(29014)}}, {{A, B, C, X(1018), X(3939)}}, {{A, B, C, X(1214), X(23703)}}, {{A, B, C, X(3694), X(4069)}}, {{A, B, C, X(3882), X(4592)}}, {{A, B, C, X(3998), X(42718)}}, {{A, B, C, X(4551), X(4605)}}, {{A, B, C, X(4571), X(4606)}}, {{A, B, C, X(8611), X(14392)}}, {{A, B, C, X(17094), X(43050)}}, {{A, B, C, X(22003), X(53388)}}, {{A, B, C, X(24029), X(40152)}}, {{A, B, C, X(37136), X(61227)}}, {{A, B, C, X(37205), X(57876)}}, {{A, B, C, X(51664), X(53528)}}, {{A, B, C, X(61225), X(65300)}}
X(65233) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1018, 1020, 4552}, {1025, 3882, 651}, {1332, 6516, 1813}, {21362, 61237, 14543}

X(65234) = TRILINEAR POLE OF LINE {1, 227}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3+3*b^3-a*(b-c)^2-b^2*c-3*b*c^2+c^3-a^2*(3*b+c))*(a^3+b^3-a*(b-c)^2-3*b^2*c-b*c^2+3*c^3-a^2*(b+3*c)) : :

X(65234) lies on these lines: {7, 34234}, {9, 36100}, {88, 1445}, {100, 24029}, {144, 65246}, {658, 2406}, {662, 65159}, {673, 12848}, {934, 37136}, {1020, 37141}, {1156, 2800}, {1813, 65259}, {2349, 29007}, {8545, 36101}, {8732, 65241}, {18026, 65223}, {24624, 41572}, {30379, 37222}, {37131, 60363}, {37203, 41563}, {37206, 62669}, {37787, 65249}, {61178, 65213}

X(65234) = reflection of X(i) in X(j) for these {i,j}: {36100, 9}
X(65234) = trilinear pole of line {1, 227}
X(65234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {650, 3576}, {652, 34231}, {663, 5744}
X(65234) = X(i)-cross conjugate of X(j) for these {i, j}: {1012, 55346}, {2093, 7045}
X(65234) = pole of line {54051, 64316} with respect to the Yff parabola
X(65234) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(934)}}, {{A, B, C, X(9), X(1783)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(514), X(46041)}}, {{A, B, C, X(527), X(2800)}}, {{A, B, C, X(1020), X(61178)}}, {{A, B, C, X(1025), X(12848)}}, {{A, B, C, X(1445), X(62669)}}, {{A, B, C, X(2346), X(53811)}}, {{A, B, C, X(4571), X(65299)}}, {{A, B, C, X(6183), X(35157)}}, {{A, B, C, X(43190), X(65331)}}, {{A, B, C, X(44765), X(56235)}}, {{A, B, C, X(54240), X(56188)}}
X(65234) = barycentric product X(i)*X(j) for these (i, j): {3577, 664}, {4552, 55938}, {50442, 651}
X(65234) = barycentric quotient X(i)/X(j) for these (i, j): {108, 34231}, {109, 3576}, {651, 5744}, {3577, 522}, {36925, 4768}, {44730, 4985}, {50442, 4391}, {55938, 4560}

X(65235) = REFLECTION OF X(88) IN X(9)

Barycentrics    a*(a-b)*(a+b-5*c)*(a-c)*(a-5*b+c) : :
X(65235) = -4*X[142]+5*X[31271], -5*X[18230]+4*X[58413], -X[20092]+5*X[61006]

X(65235) lies on these lines: {7, 16594}, {9, 88}, {100, 6014}, {142, 31271}, {144, 30578}, {190, 6009}, {527, 31171}, {528, 36924}, {545, 673}, {644, 3257}, {651, 1023}, {658, 62669}, {897, 15481}, {1001, 37129}, {1156, 2802}, {4606, 21362}, {4767, 6006}, {8545, 43760}, {18230, 58413}, {20092, 61006}, {23343, 37138}, {24029, 61240}, {24624, 60942}, {25737, 65236}, {36100, 60966}, {36101, 36973}, {37130, 40029}, {37131, 56551}, {53337, 65242}, {60935, 65249}

X(65235) = midpoint of X(i) and X(j) for these {i,j}: {144, 30578}
X(65235) = reflection of X(i) in X(j) for these {i,j}: {7, 16594}, {88, 9}
X(65235) = trilinear pole of line {1, 3689}
X(65235) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 8656}, {6, 6006}, {513, 16670}, {649, 3241}, {650, 13462}, {663, 64142}, {667, 30829}, {1019, 21870}, {2163, 52593}, {3733, 4029}, {4982, 50344}, {7649, 23073}, {43924, 62706}
X(65235) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 6006}, {5375, 3241}, {6631, 30829}, {32664, 8656}, {39026, 16670}, {40587, 52593}
X(65235) = X(i)-cross conjugate of X(j) for these {i, j}: {4752, 100}, {63468, 7045}
X(65235) = pole of line {4767, 51564} with respect to the Steiner circumellipse
X(65235) = pole of line {3241, 3306} with respect to the Yff parabola
X(65235) = pole of line {89, 3306} with respect to the Hutson-Moses hyperbola
X(65235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(6016)}}, {{A, B, C, X(7), X(668)}}, {{A, B, C, X(9), X(644)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(144), X(24029)}}, {{A, B, C, X(513), X(6009)}}, {{A, B, C, X(518), X(545)}}, {{A, B, C, X(527), X(2802)}}, {{A, B, C, X(646), X(42343)}}, {{A, B, C, X(666), X(29351)}}, {{A, B, C, X(932), X(2346)}}, {{A, B, C, X(934), X(53658)}}, {{A, B, C, X(1001), X(23343)}}, {{A, B, C, X(1025), X(6172)}}, {{A, B, C, X(1292), X(3062)}}, {{A, B, C, X(1461), X(58124)}}, {{A, B, C, X(2406), X(60966)}}, {{A, B, C, X(4554), X(50039)}}, {{A, B, C, X(4565), X(8699)}}, {{A, B, C, X(4582), X(31343)}}, {{A, B, C, X(4591), X(58123)}}, {{A, B, C, X(4627), X(28230)}}, {{A, B, C, X(4638), X(58126)}}, {{A, B, C, X(4767), X(40434)}}, {{A, B, C, X(6540), X(13396)}}, {{A, B, C, X(8545), X(53337)}}, {{A, B, C, X(9067), X(55967)}}, {{A, B, C, X(14074), X(43751)}}, {{A, B, C, X(28184), X(65298)}}, {{A, B, C, X(31171), X(46779)}}, {{A, B, C, X(32041), X(46480)}}
X(65235) = barycentric product X(i)*X(j) for these (i, j): {1, 53659}, {100, 36588}, {101, 40029}, {190, 39963}, {3257, 36915}, {4900, 664}, {6014, 75}, {36924, 4618}, {41436, 668}, {56075, 651}, {56159, 99}
X(65235) = barycentric quotient X(i)/X(j) for these (i, j): {1, 6006}, {31, 8656}, {45, 52593}, {100, 3241}, {101, 16670}, {109, 13462}, {190, 30829}, {644, 62706}, {651, 64142}, {906, 23073}, {1018, 4029}, {4557, 21870}, {4752, 36911}, {4900, 522}, {6014, 1}, {35342, 4982}, {36588, 693}, {36915, 3762}, {39963, 514}, {40029, 3261}, {41436, 513}, {52925, 36593}, {53659, 75}, {56075, 4391}, {56159, 523}

X(65236) = TRILINEAR POLE OF LINE {1, 442}

Barycentrics    (a-b)*(a-c)*(a^3-a^2*b-a*b*(b+c)+(b-c)^2*(b+c))*(a^3-a^2*c+(b-c)^2*(b+c)-a*c*(b+c)) : :
X(65236) = -3*X[2]+2*X[40622]

X(65236) lies on these lines: {2, 40622}, {10, 41495}, {63, 24624}, {88, 24175}, {100, 6011}, {142, 43760}, {144, 21221}, {162, 61180}, {329, 2349}, {655, 65233}, {662, 14543}, {673, 11683}, {823, 65162}, {897, 41501}, {1156, 6598}, {3869, 37142}, {4552, 65217}, {4558, 37140}, {24635, 37128}, {25737, 65235}, {26563, 43762}, {27003, 65241}, {36086, 61184}, {36101, 60979}, {37202, 45738}, {53337, 65222}

X(65236) = anticomplement of X(40622)
X(65236) = trilinear pole of line {1, 442}
X(65236) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 6003}, {9, 57139}, {41, 31603}, {163, 8286}, {284, 57107}, {512, 56439}, {647, 13739}, {649, 34772}, {650, 37583}, {661, 56840}, {667, 33116}, {3733, 59733}, {4017, 56948}, {5174, 22383}, {7180, 56946}, {7252, 15556}, {40622, 65375}, {41503, 51664}
X(65236) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 6003}, {115, 8286}, {478, 57139}, {3160, 31603}, {4988, 23775}, {5375, 34772}, {6631, 33116}, {34961, 56948}, {36830, 56840}, {39052, 13739}, {39054, 56439}, {40590, 57107}, {40622, 40622}, {55065, 21961}
X(65236) = X(i)-cross conjugate of X(j) for these {i, j}: {5546, 6742}, {5755, 59}, {7178, 2}, {53388, 664}, {61233, 100}
X(65236) = pole of line {7, 34195} with respect to the Kiepert parabola
X(65236) = pole of line {643, 65197} with respect to the Steiner circumellipse
X(65236) = pole of line {226, 2475} with respect to the Yff parabola
X(65236) = pole of line {226, 2982} with respect to the Hutson-Moses hyperbola
X(65236) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(645)}}, {{A, B, C, X(63), X(4558)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(92), X(4033)}}, {{A, B, C, X(99), X(4566)}}, {{A, B, C, X(107), X(3952)}}, {{A, B, C, X(110), X(1020)}}, {{A, B, C, X(142), X(53337)}}, {{A, B, C, X(648), X(4552)}}, {{A, B, C, X(666), X(56188)}}, {{A, B, C, X(668), X(1305)}}, {{A, B, C, X(670), X(2995)}}, {{A, B, C, X(901), X(32651)}}, {{A, B, C, X(1018), X(59079)}}, {{A, B, C, X(1025), X(60970)}}, {{A, B, C, X(1290), X(65232)}}, {{A, B, C, X(2415), X(24175)}}, {{A, B, C, X(3573), X(24635)}}, {{A, B, C, X(3903), X(53683)}}, {{A, B, C, X(4554), X(44765)}}, {{A, B, C, X(4569), X(43349)}}, {{A, B, C, X(4572), X(51568)}}, {{A, B, C, X(4625), X(35154)}}, {{A, B, C, X(5546), X(61233)}}, {{A, B, C, X(6335), X(51562)}}, {{A, B, C, X(6648), X(54118)}}, {{A, B, C, X(7178), X(40622)}}, {{A, B, C, X(10405), X(35177)}}, {{A, B, C, X(13397), X(32714)}}, {{A, B, C, X(15455), X(47318)}}, {{A, B, C, X(23831), X(62795)}}, {{A, B, C, X(24004), X(26724)}}, {{A, B, C, X(25268), X(26563)}}, {{A, B, C, X(29163), X(32641)}}, {{A, B, C, X(32038), X(43190)}}, {{A, B, C, X(54121), X(56241)}}, {{A, B, C, X(54458), X(54979)}}, {{A, B, C, X(56248), X(65336)}}, {{A, B, C, X(59491), X(62669)}}
X(65236) = barycentric product X(i)*X(j) for these (i, j): {190, 37887}, {6011, 75}, {6598, 664}, {41501, 99}, {43683, 662}, {43708, 811}
X(65236) = barycentric quotient X(i)/X(j) for these (i, j): {1, 6003}, {7, 31603}, {56, 57139}, {65, 57107}, {100, 34772}, {109, 37583}, {110, 56840}, {162, 13739}, {190, 33116}, {523, 8286}, {643, 56946}, {662, 56439}, {1018, 59733}, {1897, 5174}, {3120, 23775}, {4024, 21961}, {4551, 15556}, {5546, 56948}, {6011, 1}, {6598, 522}, {7178, 40622}, {37887, 514}, {41501, 523}, {43683, 1577}, {43708, 656}, {56183, 56316}, {61220, 39772}, {61225, 41547}

X(65237) = TRILINEAR POLE OF LINE {1, 147}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3+b^3-a*b*c-c^3)*(a^3-b^3-a*b*c+c^3) : :

X(65237) lies on these lines: {100, 4467}, {190, 4529}, {241, 37128}, {650, 37137}, {651, 3287}, {658, 4369}, {662, 16755}, {664, 1492}, {673, 3512}, {1155, 7061}, {1156, 7261}, {1447, 63875}, {1821, 10030}, {4573, 65257}, {4598, 65164}, {7045, 36098}, {24002, 38340}, {34234, 40845}, {37135, 57460}, {37202, 40704}, {43761, 56413}

X(65237) = trilinear pole of line {1, 147}
X(65237) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 4458}, {522, 19554}, {650, 17798}, {657, 5018}, {663, 3509}, {926, 40754}, {3063, 4645}, {3287, 41532}, {3907, 41882}, {4391, 18262}, {7252, 20715}, {18038, 60577}, {18265, 27951}, {18344, 20741}, {40724, 46388}
X(65237) = X(i)-Dao conjugate of X(j) for these {i, j}: {3160, 4458}, {10001, 4645}
X(65237) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65293, 51614}
X(65237) = X(i)-cross conjugate of X(j) for these {i, j}: {514, 63875}, {2786, 7}, {6999, 55346}, {24287, 64984}, {24290, 21453}, {53344, 99}, {53600, 39293}
X(65237) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(53224)}}, {{A, B, C, X(76), X(35169)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(241), X(16609)}}, {{A, B, C, X(650), X(3287)}}, {{A, B, C, X(666), X(36801)}}, {{A, B, C, X(1305), X(46406)}}, {{A, B, C, X(2690), X(17758)}}, {{A, B, C, X(2701), X(3497)}}, {{A, B, C, X(2702), X(41532)}}, {{A, B, C, X(2966), X(65351)}}, {{A, B, C, X(4467), X(16755)}}, {{A, B, C, X(4615), X(46143)}}
X(65237) = barycentric product X(i)*X(j) for these (i, j): {1, 65293}, {109, 18036}, {664, 7261}, {3512, 4554}, {4569, 7281}, {4572, 8852}, {34085, 40781}, {37137, 40846}, {40845, 651}, {51614, 7}, {65289, 7061}
X(65237) = barycentric quotient X(i)/X(j) for these (i, j): {7, 4458}, {109, 17798}, {651, 3509}, {664, 4645}, {927, 40724}, {934, 5018}, {1415, 19554}, {1813, 20741}, {3512, 650}, {4551, 20715}, {4552, 4071}, {4554, 17789}, {7061, 3907}, {7261, 522}, {7281, 3900}, {8852, 663}, {8926, 54271}, {10030, 27951}, {18036, 35519}, {29055, 41532}, {36146, 40754}, {37137, 40873}, {40845, 4391}, {41534, 3287}, {51614, 8}, {63782, 4987}, {63875, 60577}, {65289, 52135}, {65293, 75}

X(65238) = TRILINEAR POLE OF LINE {1, 149}

Barycentrics    (a-b)*(a-c)*(a^3+a^2*(b-c)+(b-c)^2*(b+c)+a*(b^2-b*c-c^2))*(a^3+a^2*(-b+c)+(b-c)^2*(b+c)-a*(b^2+b*c-c^2)) : :

X(65238) lies on these lines: {63, 65240}, {88, 21907}, {100, 523}, {142, 37131}, {162, 7649}, {190, 1577}, {514, 662}, {527, 31175}, {651, 7178}, {660, 35352}, {673, 16568}, {799, 3261}, {897, 1738}, {908, 2349}, {1156, 11604}, {2607, 5883}, {3218, 24624}, {3257, 4049}, {3732, 4604}, {4564, 65217}, {4570, 23752}, {4599, 10566}, {4707, 47318}, {14206, 34234}, {18014, 37135}, {20332, 30930}, {22003, 31010}, {27003, 37222}, {36085, 62626}, {36101, 37796}, {37203, 52414}, {59491, 65249}

X(65238) = reflection of X(i) in X(j) for these {i,j}: {56935, 3218}
X(65238) = trilinear pole of line {1, 149}
X(65238) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 42670}, {3, 47235}, {6, 8674}, {9, 51646}, {37, 42741}, {513, 17796}, {523, 19622}, {647, 2074}, {650, 5172}, {661, 5127}, {667, 32849}, {1290, 35090}, {1946, 37799}, {2433, 16164}, {22383, 56877}, {47227, 51470}
X(65238) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 8674}, {478, 51646}, {6631, 32849}, {32664, 42670}, {36103, 47235}, {36830, 5127}, {39026, 17796}, {39052, 2074}, {39053, 37799}, {39054, 37783}, {40589, 42741}
X(65238) = X(i)-cross conjugate of X(j) for these {i, j}: {5535, 7045}, {6840, 55346}, {21180, 75}, {53527, 86}
X(65238) = pole of line {758, 56935} with respect to the Kiepert parabola
X(65238) = pole of line {13146, 17484} with respect to the Yff parabola
X(65238) = pole of line {17484, 17796} with respect to the Hutson-Moses hyperbola
X(65238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(47318)}}, {{A, B, C, X(27), X(36167)}}, {{A, B, C, X(57), X(4591)}}, {{A, B, C, X(86), X(35154)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(514), X(523)}}, {{A, B, C, X(527), X(17768)}}, {{A, B, C, X(648), X(15455)}}, {{A, B, C, X(666), X(36804)}}, {{A, B, C, X(908), X(14206)}}, {{A, B, C, X(927), X(35171)}}, {{A, B, C, X(1020), X(4556)}}, {{A, B, C, X(1025), X(60989)}}, {{A, B, C, X(1268), X(51614)}}, {{A, B, C, X(2160), X(2702)}}, {{A, B, C, X(3911), X(35466)}}, {{A, B, C, X(4552), X(6758)}}, {{A, B, C, X(4584), X(39137)}}, {{A, B, C, X(4615), X(8046)}}, {{A, B, C, X(4622), X(56935)}}, {{A, B, C, X(17930), X(35147)}}
X(65238) = barycentric product X(i)*X(j) for these (i, j): {1, 35156}, {190, 21907}, {1290, 75}, {5620, 99}, {11604, 664}
X(65238) = barycentric quotient X(i)/X(j) for these (i, j): {1, 8674}, {19, 47235}, {31, 42670}, {56, 51646}, {58, 42741}, {101, 17796}, {109, 5172}, {110, 5127}, {162, 2074}, {163, 19622}, {190, 32849}, {653, 37799}, {662, 37783}, {1290, 1}, {1897, 56877}, {5620, 523}, {11125, 57447}, {11604, 522}, {13589, 5497}, {21180, 5520}, {21907, 514}, {23703, 41541}, {35156, 75}, {53527, 38982}, {58076, 21180}, {61225, 41542}

X(65239) = TRILINEAR POLE OF LINE {1, 3122}

Barycentrics    a*(a-b)*(a-c)*(-b^3-a*b*c+a*c*(a+c))*(a^2*b+a*b*(b-c)-c^3) : :

X(65239) lies on these lines: {88, 17946}, {100, 512}, {190, 661}, {239, 11611}, {514, 799}, {649, 662}, {651, 7180}, {653, 55208}, {655, 60484}, {658, 7216}, {896, 17954}, {897, 899}, {908, 1821}, {1156, 6007}, {1959, 34234}, {3218, 37128}, {3257, 55263}, {3571, 46904}, {4564, 36098}, {4584, 21828}, {7035, 65191}, {17961, 20332}, {18001, 18015}, {24041, 65255}, {24504, 62796}, {24627, 37222}, {30997, 37130}, {37131, 56509}, {37142, 57680}, {37202, 57847}, {37212, 58294}, {55237, 65258}

X(65239) = trilinear pole of line {1, 3122}
X(65239) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 5040}, {6, 2787}, {81, 17989}, {422, 647}, {512, 19623}, {513, 5291}, {523, 5006}, {649, 17763}, {650, 5061}, {667, 17790}, {798, 5209}, {1333, 18003}, {2703, 35079}, {3121, 17935}, {3125, 17944}, {6591, 17977}, {17987, 22383}
X(65239) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 2787}, {37, 18003}, {5375, 17763}, {6631, 17790}, {31998, 5209}, {32664, 5040}, {39026, 5291}, {39052, 422}, {39054, 19623}, {40586, 17989}
X(65239) = X(i)-Ceva conjugate of X(j) for these {i, j}: {17929, 2703}
X(65239) = pole of line {5291, 17946} with respect to the Hutson-Moses hyperbola
X(65239) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4584)}}, {{A, B, C, X(57), X(4615)}}, {{A, B, C, X(81), X(35148)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(109), X(1978)}}, {{A, B, C, X(110), X(27805)}}, {{A, B, C, X(239), X(3218)}}, {{A, B, C, X(512), X(514)}}, {{A, B, C, X(527), X(6007)}}, {{A, B, C, X(668), X(35009)}}, {{A, B, C, X(896), X(899)}}, {{A, B, C, X(901), X(4562)}}, {{A, B, C, X(908), X(1959)}}, {{A, B, C, X(3911), X(55262)}}, {{A, B, C, X(3952), X(4603)}}, {{A, B, C, X(4033), X(4556)}}, {{A, B, C, X(4551), X(4610)}}, {{A, B, C, X(4559), X(7260)}}, {{A, B, C, X(4564), X(7035)}}, {{A, B, C, X(4565), X(54986)}}, {{A, B, C, X(5386), X(59096)}}, {{A, B, C, X(7315), X(9361)}}, {{A, B, C, X(8046), X(9510)}}, {{A, B, C, X(17012), X(56811)}}, {{A, B, C, X(17929), X(35147)}}
X(65239) = barycentric product X(i)*X(j) for these (i, j): {1, 35147}, {10, 17929}, {162, 57847}, {2703, 75}, {4564, 60484}, {11609, 664}, {11611, 662}, {17939, 313}, {17946, 190}, {17954, 668}, {17961, 1978}, {17981, 4561}, {18015, 4600}, {57680, 811}
X(65239) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2787}, {10, 18003}, {31, 5040}, {42, 17989}, {99, 5209}, {100, 17763}, {101, 5291}, {109, 5061}, {162, 422}, {163, 5006}, {190, 17790}, {662, 19623}, {1331, 17977}, {1897, 17987}, {2703, 1}, {4570, 17944}, {4600, 17935}, {11609, 522}, {11611, 1577}, {17929, 86}, {17939, 58}, {17946, 514}, {17954, 513}, {17961, 649}, {17971, 1459}, {17981, 7649}, {18002, 3122}, {18015, 3120}, {35147, 75}, {53689, 62749}, {57680, 656}, {57847, 14208}, {60484, 4858}

X(65240) = X(30)X(100)∩X(323)X(651)

Barycentrics    (a^6-a^5*c+b*(b-c)^3*(b+c)^2-a^4*(b^2-2*b*c+2*c^2)+a^3*(-(b^2*c)+2*c^3)-a^2*(b^4+b^3*c-2*b^2*c^2+b*c^3-c^4)+a*(2*b^4*c-b^2*c^3-c^5))*(a^6-a^5*b-(b-c)^3*c*(b+c)^2-a^4*(2*b^2-2*b*c+c^2)+a^3*(2*b^3-b*c^2)+a^2*(b^4-b^3*c+2*b^2*c^2-b*c^3-c^4)-a*(b^5+b^3*c^2-2*b*c^4)) : :

X(65240) lies on these lines: {27, 65263}, {30, 100}, {63, 65238}, {88, 41800}, {162, 1785}, {190, 14206}, {226, 37136}, {323, 651}, {333, 32680}, {514, 2349}, {653, 52414}, {655, 3219}, {662, 908}, {1156, 14224}, {1577, 34234}, {3218, 38340}, {3257, 17781}, {15776, 65244}, {37139, 54357}, {37141, 37797}

X(65240) = trilinear pole of line {1, 11125}
X(65240) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 2771}, {647, 37966}, {8609, 61463}, {42746, 55259}
X(65240) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 2771}, {4988, 57423}, {39052, 37966}
X(65240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(17484)}}, {{A, B, C, X(27), X(30)}}, {{A, B, C, X(57), X(35000)}}, {{A, B, C, X(63), X(5127)}}, {{A, B, C, X(81), X(48698)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(92), X(1029)}}, {{A, B, C, X(226), X(908)}}, {{A, B, C, X(323), X(333)}}, {{A, B, C, X(329), X(37797)}}, {{A, B, C, X(527), X(54357)}}, {{A, B, C, X(1751), X(7164)}}, {{A, B, C, X(2006), X(11698)}}, {{A, B, C, X(2861), X(35164)}}, {{A, B, C, X(3911), X(17781)}}, {{A, B, C, X(4391), X(17923)}}, {{A, B, C, X(4564), X(40435)}}, {{A, B, C, X(6336), X(10742)}}, {{A, B, C, X(13478), X(18524)}}, {{A, B, C, X(13582), X(18359)}}, {{A, B, C, X(15776), X(37279)}}, {{A, B, C, X(60139), X(64984)}}
X(65240) = barycentric product X(i)*X(j) for these (i, j): {1, 46141}, {2687, 75}, {14224, 664}
X(65240) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2771}, {162, 37966}, {2687, 1}, {3120, 57423}, {14224, 522}, {21180, 55146}, {34234, 52499}, {36052, 61463}, {39991, 1737}, {46141, 75}

X(65241) = X(56)X(100)∩X(57)X(190)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+a*(-4*b+c)+b*(b+c))*(a^2+a*(b-4*c)+c*(b+c)) : :

X(65241) lies on these lines: {7, 16594}, {56, 100}, {57, 190}, {88, 2403}, {162, 4248}, {241, 65231}, {651, 1407}, {653, 1435}, {655, 37789}, {658, 738}, {662, 1412}, {799, 1434}, {1156, 23836}, {1416, 9364}, {1445, 65226}, {1477, 6079}, {3257, 3911}, {3306, 17107}, {3732, 46116}, {4598, 7153}, {4606, 57663}, {6612, 37141}, {8056, 42304}, {8732, 65234}, {9311, 62695}, {24618, 43759}, {24627, 25917}, {27003, 65236}, {37129, 37627}, {37209, 41245}, {37223, 52013}, {42338, 61412}, {43043, 46119}, {43760, 47884}, {56081, 59779}, {61240, 61380}, {64984, 65229}

X(65241) = isotomic conjugate of X(62297)
X(65241) = trilinear pole of line {1, 23836}
X(65241) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3880}, {9, 1149}, {31, 62297}, {41, 1266}, {44, 45247}, {55, 16610}, {219, 1878}, {281, 23205}, {284, 4695}, {644, 6085}, {646, 8660}, {649, 23705}, {902, 52140}, {1320, 20972}, {2316, 17460}, {2325, 17109}, {3063, 61186}, {3689, 52206}, {6018, 40400}, {7252, 61176}, {9456, 52871}
X(65241) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 62297}, {9, 3880}, {223, 16610}, {478, 1149}, {3160, 1266}, {3669, 62559}, {4370, 52871}, {5375, 23705}, {10001, 61186}, {40590, 4695}, {40594, 52140}, {40595, 45247}, {40615, 4927}, {52659, 16594}
X(65241) = X(i)-cross conjugate of X(j) for these {i, j}: {519, 7}, {24216, 1088}, {26727, 903}, {40400, 1120}, {53528, 664}, {56009, 21453}
X(65241) = pole of line {1120, 30725} with respect to the Steiner circumellipse
X(65241) = pole of line {60374, 61483} with respect to the dual conic of Yff parabola
X(65241) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(145)}}, {{A, B, C, X(7), X(64142)}}, {{A, B, C, X(27), X(4188)}}, {{A, B, C, X(56), X(57)}}, {{A, B, C, X(80), X(26748)}}, {{A, B, C, X(81), X(62837)}}, {{A, B, C, X(85), X(62919)}}, {{A, B, C, X(86), X(37684)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(189), X(63133)}}, {{A, B, C, X(241), X(9364)}}, {{A, B, C, X(277), X(30608)}}, {{A, B, C, X(278), X(63167)}}, {{A, B, C, X(333), X(979)}}, {{A, B, C, X(514), X(4997)}}, {{A, B, C, X(519), X(16594)}}, {{A, B, C, X(650), X(6559)}}, {{A, B, C, X(903), X(30577)}}, {{A, B, C, X(908), X(18802)}}, {{A, B, C, X(1120), X(36805)}}, {{A, B, C, X(1121), X(13996)}}, {{A, B, C, X(1317), X(2006)}}, {{A, B, C, X(1445), X(3306)}}, {{A, B, C, X(3008), X(47884)}}, {{A, B, C, X(3218), X(37789)}}, {{A, B, C, X(3676), X(35160)}}, {{A, B, C, X(3729), X(62695)}}, {{A, B, C, X(4564), X(34051)}}, {{A, B, C, X(4859), X(59779)}}, {{A, B, C, X(4998), X(56783)}}, {{A, B, C, X(5744), X(8732)}}, {{A, B, C, X(7192), X(51567)}}, {{A, B, C, X(7233), X(62723)}}, {{A, B, C, X(8046), X(18359)}}, {{A, B, C, X(9082), X(51845)}}, {{A, B, C, X(13478), X(36602)}}, {{A, B, C, X(17595), X(51301)}}, {{A, B, C, X(24002), X(39994)}}, {{A, B, C, X(24175), X(56078)}}, {{A, B, C, X(25430), X(56031)}}, {{A, B, C, X(26727), X(62582)}}, {{A, B, C, X(27475), X(64151)}}, {{A, B, C, X(32008), X(39963)}}, {{A, B, C, X(36807), X(58371)}}, {{A, B, C, X(37540), X(51302)}}, {{A, B, C, X(39126), X(52803)}}, {{A, B, C, X(39698), X(60482)}}, {{A, B, C, X(39962), X(40435)}}, {{A, B, C, X(40617), X(61079)}}, {{A, B, C, X(44733), X(44794)}}, {{A, B, C, X(47892), X(63233)}}, {{A, B, C, X(54128), X(56026)}}, {{A, B, C, X(56201), X(56202)}}, {{A, B, C, X(56947), X(60087)}}, {{A, B, C, X(60107), X(65045)}}
X(65241) = barycentric product X(i)*X(j) for these (i, j): {75, 8686}, {1120, 7}, {1811, 273}, {3676, 6079}, {23836, 664}, {36805, 57}, {37627, 668}, {40400, 85}, {56642, 903}
X(65241) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3880}, {2, 62297}, {7, 1266}, {34, 1878}, {56, 1149}, {57, 16610}, {65, 4695}, {88, 52140}, {100, 23705}, {106, 45247}, {109, 23832}, {519, 52871}, {603, 23205}, {664, 61186}, {1120, 8}, {1149, 6018}, {1317, 62666}, {1319, 17460}, {1404, 20972}, {1417, 17109}, {1434, 16711}, {1811, 78}, {1877, 5151}, {3676, 4927}, {3911, 16594}, {4551, 61176}, {6079, 3699}, {8686, 1}, {23836, 522}, {30725, 21129}, {36805, 312}, {37627, 513}, {40400, 9}, {40617, 62559}, {40663, 21041}, {43081, 61484}, {43924, 6085}, {52556, 2325}, {56642, 519}, {61483, 5854}

X(65242) = TRILINEAR POLE OF LINE {1, 4419}

Barycentrics    (a-b)*(a-c)*(a^2+a*(4*b-2*c)+(b-c)^2)*(a^2-2*a*(b-2*c)+(b-c)^2) : :

X(65242) lies on these lines: {2, 1156}, {57, 43762}, {88, 5222}, {100, 14074}, {651, 56543}, {664, 37139}, {673, 3306}, {897, 52764}, {1025, 65226}, {3732, 37143}, {4242, 65215}, {4384, 34234}, {5744, 24582}, {14829, 37213}, {16054, 24624}, {17780, 37223}, {24580, 36100}, {35281, 36086}, {35312, 61240}, {37141, 63782}, {37203, 37389}, {43760, 64142}, {53337, 65235}, {54357, 65261}, {65165, 65222}

X(65242) = isotomic conjugate of X(47787)
X(65242) = trilinear pole of line {1, 4419}
X(65242) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 14077}, {31, 47787}, {41, 30181}, {657, 62792}, {663, 8545}, {667, 50107}, {1996, 8641}, {6139, 46644}, {47386, 57180}
X(65242) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 47787}, {9, 14077}, {3160, 30181}, {6631, 50107}
X(65242) = X(i)-cross conjugate of X(j) for these {i, j}: {8257, 4564}, {28292, 7}, {46919, 2}, {56380, 24011}
X(65242) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(664)}}, {{A, B, C, X(27), X(52935)}}, {{A, B, C, X(57), X(101)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(666), X(51564)}}, {{A, B, C, X(927), X(4597)}}, {{A, B, C, X(1025), X(3306)}}, {{A, B, C, X(1897), X(4573)}}, {{A, B, C, X(3658), X(37389)}}, {{A, B, C, X(3699), X(43190)}}, {{A, B, C, X(3911), X(43057)}}, {{A, B, C, X(4242), X(16054)}}, {{A, B, C, X(4617), X(58991)}}, {{A, B, C, X(4817), X(45695)}}, {{A, B, C, X(5222), X(17780)}}, {{A, B, C, X(7452), X(24580)}}, {{A, B, C, X(9058), X(36146)}}, {{A, B, C, X(10566), X(47762)}}, {{A, B, C, X(18087), X(27003)}}, {{A, B, C, X(32040), X(51562)}}, {{A, B, C, X(43349), X(58133)}}, {{A, B, C, X(46406), X(64995)}}, {{A, B, C, X(46919), X(47787)}}, {{A, B, C, X(52620), X(62623)}}, {{A, B, C, X(53337), X(64142)}}, {{A, B, C, X(59031), X(63203)}}
X(65242) = barycentric product X(i)*X(j) for these (i, j): {14074, 75}, {34919, 664}, {55984, 651}
X(65242) = barycentric quotient X(i)/X(j) for these (i, j): {1, 14077}, {2, 47787}, {7, 30181}, {109, 37541}, {190, 50107}, {651, 8545}, {658, 1996}, {934, 62792}, {4626, 47386}, {14074, 1}, {34919, 522}, {35338, 61028}, {37139, 46644}, {55984, 4391}

X(65243) = TRILINEAR POLE OF LINE {1, 910}

Barycentrics    a*(a-b)*(a-c)*(3*a^2+3*b^2+2*a*(b-c)-2*b*c-c^2)*(3*a^2-2*a*b-b^2+2*a*c-2*b*c+3*c^2) : :

X(65243) lies on these lines: {1, 36101}, {88, 36277}, {100, 26716}, {109, 61240}, {190, 2398}, {238, 56716}, {658, 23973}, {660, 57192}, {673, 55937}, {934, 65245}, {1156, 16670}, {1783, 65218}, {2114, 43760}, {3246, 37131}, {3573, 27834}, {3939, 4606}, {4663, 65261}, {16948, 37128}, {24624, 54668}, {36089, 36136}, {36100, 62838}, {37130, 55983}

X(65243) = trilinear pole of line {1, 910}
X(65243) = X(i)-isoconjugate-of-X(j) for these {i, j}: {101, 61673}, {513, 5223}, {514, 42316}, {657, 10004}, {3063, 59200}
X(65243) = X(i)-vertex conjugate of X(j) for these {i, j}: {677, 1461}
X(65243) = X(i)-Dao conjugate of X(j) for these {i, j}: {1015, 61673}, {5375, 29616}, {10001, 59200}, {39026, 5223}
X(65243) = X(i)-cross conjugate of X(j) for these {i, j}: {11372, 7012}, {35280, 100}, {45755, 81}, {54250, 57}
X(65243) = pole of line {5223, 37658} with respect to the Hutson-Moses hyperbola
X(65243) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(934)}}, {{A, B, C, X(58), X(32722)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(109), X(677)}}, {{A, B, C, X(110), X(3939)}}, {{A, B, C, X(644), X(1414)}}, {{A, B, C, X(1897), X(4626)}}, {{A, B, C, X(3246), X(52985)}}, {{A, B, C, X(3573), X(16948)}}, {{A, B, C, X(4616), X(9057)}}, {{A, B, C, X(5556), X(18026)}}, {{A, B, C, X(8750), X(32735)}}, {{A, B, C, X(10308), X(26706)}}, {{A, B, C, X(13138), X(59125)}}, {{A, B, C, X(13486), X(58991)}}, {{A, B, C, X(30244), X(64013)}}, {{A, B, C, X(32641), X(58105)}}, {{A, B, C, X(36049), X(53243)}}
X(65243) = barycentric product X(i)*X(j) for these (i, j): {1, 32040}, {100, 55937}, {101, 55983}, {26716, 75}, {35517, 36136}, {42317, 664}, {54668, 662}, {59259, 692}
X(65243) = barycentric quotient X(i)/X(j) for these (i, j): {100, 29616}, {101, 5223}, {109, 59215}, {513, 61673}, {664, 59200}, {692, 42316}, {934, 10004}, {26716, 1}, {32040, 75}, {32721, 911}, {36136, 103}, {42317, 522}, {54668, 1577}, {55937, 693}, {55983, 3261}, {59259, 40495}

X(65244) = X(21)X(37203)∩X(162)X(7437)

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^3*(b-c)*c+a^4*(b+c)-a*(b-c)*c*(b+c)^2+b*(b^2-c^2)^2-a^2*(2*b^3+b^2*c+c^3))*(a^3*b*(-b+c)+a^4*(b+c)+a*b*(b-c)*(b+c)^2+c*(b^2-c^2)^2-a^2*(b^3+b*c^2+2*c^3)) : :

X(65244) lies on these lines: {21, 37203}, {100, 59010}, {110, 65217}, {162, 7437}, {411, 24624}, {651, 2617}, {653, 3658}, {673, 1817}, {823, 7451}, {1156, 43729}, {1816, 34234}, {4238, 65213}, {4575, 65254}, {13614, 65246}, {15776, 65240}, {35981, 43764}, {37219, 57910}, {41509, 65261}, {52914, 65221}

X(65244) = trilinear pole of line {1, 15656}
X(65244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {73, 57089}, {307, 58318}, {513, 3191}, {647, 37279}, {650, 41342}, {656, 41227}, {661, 62798}, {663, 52673}, {3737, 15443}
X(65244) = X(i)-Dao conjugate of X(j) for these {i, j}: {36830, 62798}, {39026, 3191}, {39052, 37279}, {40596, 41227}
X(65244) = X(i)-cross conjugate of X(j) for these {i, j}: {23067, 110}
X(65244) = pole of line {3191, 56000} with respect to the Hutson-Moses hyperbola
X(65244) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7437)}}, {{A, B, C, X(3), X(7451)}}, {{A, B, C, X(21), X(925)}}, {{A, B, C, X(28), X(58986)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(107), X(5546)}}, {{A, B, C, X(108), X(163)}}, {{A, B, C, X(404), X(13589)}}, {{A, B, C, X(411), X(4242)}}, {{A, B, C, X(644), X(36126)}}, {{A, B, C, X(811), X(13138)}}, {{A, B, C, X(1290), X(36134)}}, {{A, B, C, X(1305), X(1331)}}, {{A, B, C, X(1816), X(4246)}}, {{A, B, C, X(1817), X(4238)}}, {{A, B, C, X(2617), X(35360)}}, {{A, B, C, X(4203), X(46597)}}, {{A, B, C, X(4236), X(13588)}}, {{A, B, C, X(4565), X(36077)}}, {{A, B, C, X(4566), X(61220)}}, {{A, B, C, X(4575), X(6516)}}, {{A, B, C, X(7411), X(53160)}}, {{A, B, C, X(7435), X(13614)}}, {{A, B, C, X(7450), X(35995)}}, {{A, B, C, X(15776), X(37966)}}, {{A, B, C, X(35977), X(57600)}}
X(65244) = barycentric product X(i)*X(j) for these (i, j): {163, 57910}, {41509, 4573}, {43729, 664}, {57719, 662}, {59010, 75}
X(65244) = barycentric quotient X(i)/X(j) for these (i, j): {101, 3191}, {109, 41342}, {110, 62798}, {112, 41227}, {162, 37279}, {163, 580}, {651, 52673}, {1172, 57089}, {2204, 58318}, {4559, 15443}, {41509, 3700}, {43729, 522}, {57719, 1577}, {57910, 20948}, {59010, 1}, {61197, 45038}

X(65245) = TRILINEAR POLE OF LINE {1, 103}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^3-a^2*b+b^3+b*c^2-2*c^3+a*(-b^2+c^2))*(a^3-2*b^3-a^2*c+b^2*c+c^3+a*(b^2-c^2)) : :

X(65245) lies on these lines: {100, 677}, {162, 4637}, {190, 1275}, {241, 36101}, {650, 4617}, {653, 4626}, {655, 60581}, {658, 7658}, {662, 32668}, {673, 9503}, {823, 7199}, {905, 24013}, {934, 65243}, {1156, 1443}, {2400, 23973}, {24015, 34085}, {34234, 37757}, {36039, 65222}, {36086, 41353}, {38340, 61241}

X(65245) = isogonal conjugate of X(46392)
X(65245) = trilinear pole of line {1, 103}
X(65245) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46392}, {220, 676}, {513, 51418}, {516, 657}, {650, 41339}, {663, 40869}, {885, 56785}, {910, 3900}, {926, 56900}, {1146, 2426}, {1456, 4130}, {1566, 52927}, {1886, 57108}, {2398, 14936}, {3270, 41321}, {4105, 43035}, {4524, 14953}, {7071, 39470}, {7253, 51436}, {8641, 30807}, {8750, 57292}, {17747, 21789}, {18344, 51376}, {23973, 35508}, {24012, 24015}, {52614, 56639}
X(65245) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46392}, {26932, 57292}, {39026, 51418}
X(65245) = X(i)-cross conjugate of X(j) for these {i, j}: {241, 7045}, {11349, 55346}, {46392, 1}
X(65245) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}}, {{A, B, C, X(241), X(24015)}}, {{A, B, C, X(650), X(7658)}}, {{A, B, C, X(677), X(9503)}}, {{A, B, C, X(1275), X(7045)}}, {{A, B, C, X(1414), X(36838)}}, {{A, B, C, X(2728), X(41790)}}, {{A, B, C, X(4131), X(7199)}}, {{A, B, C, X(4626), X(4637)}}, {{A, B, C, X(41353), X(62786)}}

X(65246) = X(20)X(100)∩X(63)X(653)

Barycentrics    (a^6-a^5*c+b*(b-c)^3*(b+c)^2-a^4*(b^2-3*b*c+2*c^2)+a^3*(-2*b^2*c+2*c^3)+a^2*(-b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)+a*(3*b^4*c-2*b^2*c^3-c^5))*(a^6-a^5*b-(b-c)^3*c*(b+c)^2-a^4*(2*b^2-3*b*c+c^2)+2*a^3*(b^3-b*c^2)+a^2*(b^4-2*b^3*c+4*b^2*c^2-2*b*c^3-c^4)-a*(b^5+2*b^3*c^2-3*b*c^4)) : :

X(65246) lies on these lines: {2, 37141}, {20, 100}, {27, 65224}, {57, 63876}, {63, 653}, {144, 65234}, {162, 283}, {189, 23983}, {190, 3719}, {271, 318}, {329, 394}, {333, 823}, {658, 7183}, {662, 6514}, {908, 37136}, {1156, 43737}, {2417, 36100}, {5744, 61240}, {6512, 65216}, {13614, 65244}, {23695, 36084}, {35516, 65223}, {36044, 36093}, {37139, 37774}, {60966, 65226}

X(65246) = trilinear pole of line {1, 8058}
X(65246) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 6001}, {9, 51660}, {48, 51359}, {55, 43058}, {104, 47434}, {219, 51399}, {521, 2443}, {647, 7435}, {1415, 14312}, {1946, 2405}, {2182, 56634}, {2194, 51365}, {14571, 39175}, {14578, 25640}, {32647, 58264}
X(65246) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 6001}, {223, 43058}, {281, 1528}, {478, 51660}, {1146, 14312}, {1214, 51365}, {1249, 51359}, {39052, 7435}, {39053, 2405}, {40613, 47434}
X(65246) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {15629, 34550}
X(65246) = X(i)-cross conjugate of X(j) for these {i, j}: {1785, 75}, {15629, 51565}, {34050, 2}
X(65246) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(318)}}, {{A, B, C, X(4), X(64111)}}, {{A, B, C, X(7), X(56596)}}, {{A, B, C, X(20), X(27)}}, {{A, B, C, X(57), X(1767)}}, {{A, B, C, X(63), X(271)}}, {{A, B, C, X(77), X(8822)}}, {{A, B, C, X(85), X(55963)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(92), X(837)}}, {{A, B, C, X(144), X(5744)}}, {{A, B, C, X(153), X(6336)}}, {{A, B, C, X(253), X(63186)}}, {{A, B, C, X(273), X(55024)}}, {{A, B, C, X(278), X(12667)}}, {{A, B, C, X(312), X(60114)}}, {{A, B, C, X(514), X(2829)}}, {{A, B, C, X(908), X(4997)}}, {{A, B, C, X(1751), X(3347)}}, {{A, B, C, X(1959), X(23695)}}, {{A, B, C, X(2006), X(37725)}}, {{A, B, C, X(2184), X(11500)}}, {{A, B, C, X(2988), X(51565)}}, {{A, B, C, X(3306), X(60966)}}, {{A, B, C, X(4391), X(52780)}}, {{A, B, C, X(7097), X(8748)}}, {{A, B, C, X(13614), X(37279)}}, {{A, B, C, X(17781), X(59491)}}, {{A, B, C, X(22464), X(34393)}}, {{A, B, C, X(36795), X(46102)}}, {{A, B, C, X(37774), X(37780)}}, {{A, B, C, X(40435), X(55987)}}, {{A, B, C, X(46137), X(55346)}}, {{A, B, C, X(50442), X(57826)}}, {{A, B, C, X(54357), X(60979)}}
X(65246) = barycentric product X(i)*X(j) for these (i, j): {63, 65342}, {1295, 75}, {2417, 653}, {2431, 46404}, {35518, 36044}, {43737, 664}
X(65246) = barycentric quotient X(i)/X(j) for these (i, j): {1, 6001}, {4, 51359}, {34, 51399}, {56, 51660}, {57, 43058}, {102, 56634}, {162, 7435}, {226, 51365}, {522, 14312}, {653, 2405}, {1295, 1}, {1785, 25640}, {1795, 39175}, {2183, 47434}, {2417, 6332}, {2431, 652}, {7952, 1528}, {15405, 1795}, {21186, 55139}, {32647, 32674}, {32674, 2443}, {34234, 57495}, {35015, 57445}, {36044, 108}, {36123, 64635}, {43737, 522}, {54241, 1785}, {57291, 35580}, {65342, 92}

X(65247) = TRILINEAR POLE OF LINE {1, 224}

Barycentrics    (a-b)*(a-c)*(a^3+a^2*(b-c)+(b-c)^2*(b+c)+a*(b^2-2*b*c-c^2))*(a^3+a^2*(-b+c)+(b-c)^2*(b+c)+a*(-b^2-2*b*c+c^2)) : :

X(65247) lies on these lines: {63, 37203}, {75, 46886}, {88, 15474}, {100, 13397}, {514, 65248}, {662, 3732}, {664, 65217}, {673, 1760}, {897, 23604}, {1156, 5225}, {4558, 65254}, {6516, 65216}, {18151, 18750}, {18747, 36101}, {20332, 28090}, {20914, 37214}, {24624, 43675}, {28787, 37142}, {37131, 37774}, {40702, 43762}, {43760, 61019}

X(65247) = trilinear pole of line {1, 224}
X(65247) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 57094}, {6, 15313}, {48, 57044}, {212, 57230}, {228, 57073}, {512, 40571}, {513, 2911}, {523, 41332}, {647, 30733}, {649, 3811}, {650, 37579}, {657, 4341}, {661, 1780}, {663, 1708}, {667, 17776}, {906, 5521}, {2164, 57102}, {2353, 26217}, {2501, 41608}, {3063, 56927}, {3064, 3215}, {3173, 18344}, {6591, 11517}, {7252, 41538}, {17877, 32739}, {22383, 56876}, {47235, 61453}
X(65247) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 15313}, {1249, 57044}, {5190, 5521}, {5375, 3811}, {6631, 17776}, {10001, 56927}, {36103, 57094}, {36830, 1780}, {39026, 2911}, {39052, 30733}, {39054, 40571}, {40619, 17877}, {40837, 57230}, {51473, 649}
X(65247) = X(i)-cross conjugate of X(j) for these {i, j}: {1331, 664}, {5709, 7045}, {6836, 55346}, {7649, 75}, {21188, 2}, {23797, 310}, {23800, 86}, {53599, 39293}
X(65247) = pole of line {1770, 3811} with respect to the Yff parabola
X(65247) = pole of line {2911, 5905} with respect to the Hutson-Moses hyperbola
X(65247) = pole of line {278, 28753} with respect to the dual conic of Feuerbach hyperbola
X(65247) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(514), X(55126)}}, {{A, B, C, X(646), X(65336)}}, {{A, B, C, X(648), X(4554)}}, {{A, B, C, X(666), X(6335)}}, {{A, B, C, X(927), X(54987)}}, {{A, B, C, X(1020), X(65298)}}, {{A, B, C, X(1025), X(60974)}}, {{A, B, C, X(1305), X(53652)}}, {{A, B, C, X(1897), X(15455)}}, {{A, B, C, X(1978), X(52919)}}, {{A, B, C, X(3732), X(4033)}}, {{A, B, C, X(4552), X(43190)}}, {{A, B, C, X(4572), X(53643)}}, {{A, B, C, X(4573), X(54970)}}, {{A, B, C, X(10566), X(48408)}}, {{A, B, C, X(17930), X(57969)}}, {{A, B, C, X(40015), X(62540)}}, {{A, B, C, X(44327), X(47318)}}, {{A, B, C, X(53337), X(61019)}}, {{A, B, C, X(53653), X(56596)}}, {{A, B, C, X(53906), X(55105)}}

X(65248) = TRILINEAR POLE OF LINE {1, 1331}

Barycentrics    a*(a-b)*(a-c)*(a^4-a^3*c+b*(b-c)^2*(b+c)+a*c*(b^2+c^2)-a^2*(2*b^2-b*c+c^2))*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b*(b^2+c^2)-a^2*(b^2-b*c+2*c^2)) : :

X(65248) lies on these lines: {88, 2990}, {100, 1618}, {162, 4570}, {514, 65247}, {651, 44717}, {653, 4564}, {655, 2397}, {765, 61043}, {908, 37203}, {914, 32851}, {915, 29241}, {1156, 45393}, {1332, 65216}, {3657, 37135}, {4585, 37136}, {20332, 32655}, {32698, 36099}, {36052, 37129}, {37131, 60974}, {43760, 63190}, {61214, 65231}

X(65248) = trilinear pole of line {1, 1331}
X(65248) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 55126}, {119, 2423}, {244, 61239}, {513, 8609}, {649, 1737}, {650, 18838}, {663, 64115}, {665, 52456}, {667, 48380}, {912, 6591}, {1015, 56881}, {2170, 61231}, {2252, 7649}, {3064, 51649}, {3125, 3658}, {3310, 14266}, {8735, 56410}, {10015, 51824}, {43933, 47408}, {52413, 61039}
X(65248) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 55126}, {5375, 1737}, {6631, 48380}, {39026, 8609}
X(65248) = X(i)-cross conjugate of X(j) for these {i, j}: {908, 4564}, {909, 9268}, {2077, 7045}, {2323, 765}, {65104, 40436}
X(65248) = pole of line {1737, 41699} with respect to the Yff parabola
X(65248) = pole of line {2990, 8609} with respect to the Hutson-Moses hyperbola
X(65248) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}}, {{A, B, C, X(514), X(15313)}}, {{A, B, C, X(908), X(914)}}, {{A, B, C, X(929), X(4584)}}, {{A, B, C, X(1618), X(2742)}}, {{A, B, C, X(2397), X(4585)}}, {{A, B, C, X(4556), X(15439)}}, {{A, B, C, X(4564), X(4570)}}, {{A, B, C, X(4589), X(58000)}}, {{A, B, C, X(4592), X(51566)}}, {{A, B, C, X(6516), X(53652)}}, {{A, B, C, X(13136), X(31615)}}, {{A, B, C, X(29014), X(36145)}}, {{A, B, C, X(29127), X(36147)}}, {{A, B, C, X(31628), X(65336)}}, {{A, B, C, X(36037), X(47318)}}
X(65248) = barycentric product X(i)*X(j) for these (i, j): {63, 65344}, {190, 2990}, {304, 32698}, {1331, 46133}, {1332, 37203}, {1978, 32655}, {3657, 4600}, {3699, 63190}, {4561, 915}, {6099, 75}, {36052, 668}, {36106, 69}, {45393, 664}
X(65248) = barycentric quotient X(i)/X(j) for these (i, j): {1, 55126}, {59, 61231}, {100, 1737}, {101, 8609}, {109, 18838}, {190, 48380}, {651, 64115}, {765, 56881}, {906, 2252}, {913, 6591}, {915, 7649}, {1252, 61239}, {1331, 912}, {1332, 914}, {1807, 61039}, {2990, 514}, {3657, 3120}, {4570, 3658}, {6099, 1}, {22350, 42769}, {23703, 12832}, {32655, 649}, {32698, 19}, {36037, 14266}, {36052, 513}, {36059, 51649}, {36086, 52456}, {36106, 4}, {37203, 17924}, {39173, 1769}, {45393, 522}, {46133, 46107}, {61043, 53525}, {61214, 2170}, {61228, 41552}, {63190, 3676}, {65344, 92}

X(65249) = ISOGONAL CONJUGATE OF X(2265)

Barycentrics    a*(a^4+b^4-2*a^3*c-2*b^3*c+2*a*(b-c)^2*c+b^2*c^2+2*b*c^3-2*c^4+a^2*(-2*b^2+2*b*c+c^2))*(a^4-2*a^3*b-2*b^4+2*a*b*(b-c)^2+2*b^3*c+b^2*c^2-2*b*c^3+c^4+a^2*(b^2+2*b*c-2*c^2)) : :

X(65249) lies on these lines: {2, 655}, {57, 37136}, {63, 3257}, {88, 905}, {92, 65223}, {100, 517}, {162, 17515}, {190, 908}, {514, 34234}, {527, 65226}, {651, 1465}, {653, 3911}, {658, 17078}, {673, 47785}, {998, 36090}, {1156, 46041}, {2051, 64824}, {2185, 37140}, {2320, 60687}, {2717, 35011}, {3306, 37139}, {4560, 24624}, {4564, 16586}, {4833, 37142}, {4850, 36087}, {4858, 34535}, {5744, 37143}, {7541, 56939}, {16610, 46119}, {35258, 36086}, {37141, 37789}, {37222, 50943}, {37787, 65234}, {59491, 65238}, {60935, 65235}

X(65249) = isogonal conjugate of X(2265)
X(65249) = trilinear pole of line {1, 1769}
X(65249) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2265}, {6, 952}, {44, 52478}, {55, 43043}, {953, 61066}, {1252, 6075}, {1960, 57456}, {2183, 61481}, {6073, 41933}, {32641, 35013}
X(65249) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 2265}, {9, 952}, {223, 43043}, {661, 6075}, {40595, 52478}
X(65249) = X(i)-cross conjugate of X(j) for these {i, j}: {1772, 75}, {2265, 1}, {2800, 7}, {35050, 1414}, {43048, 2}
X(65249) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2167)}}, {{A, B, C, X(4), X(48363)}}, {{A, B, C, X(27), X(6905)}}, {{A, B, C, X(57), X(92)}}, {{A, B, C, X(63), X(905)}}, {{A, B, C, X(81), X(62826)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(89), X(44559)}}, {{A, B, C, X(189), X(8046)}}, {{A, B, C, X(329), X(8051)}}, {{A, B, C, X(527), X(3306)}}, {{A, B, C, X(693), X(7045)}}, {{A, B, C, X(757), X(54121)}}, {{A, B, C, X(1443), X(36917)}}, {{A, B, C, X(1577), X(18593)}}, {{A, B, C, X(1817), X(7541)}}, {{A, B, C, X(2006), X(6265)}}, {{A, B, C, X(2184), X(36603)}}, {{A, B, C, X(2339), X(56062)}}, {{A, B, C, X(2725), X(35348)}}, {{A, B, C, X(2990), X(4997)}}, {{A, B, C, X(3752), X(42709)}}, {{A, B, C, X(4358), X(5382)}}, {{A, B, C, X(4858), X(16586)}}, {{A, B, C, X(5744), X(37787)}}, {{A, B, C, X(6336), X(10698)}}, {{A, B, C, X(12032), X(35365)}}, {{A, B, C, X(14838), X(52414)}}, {{A, B, C, X(17080), X(57716)}}, {{A, B, C, X(17484), X(27003)}}, {{A, B, C, X(30608), X(55936)}}, {{A, B, C, X(34393), X(63190)}}, {{A, B, C, X(35355), X(53181)}}, {{A, B, C, X(39962), X(55987)}}, {{A, B, C, X(39980), X(56033)}}, {{A, B, C, X(43363), X(62723)}}, {{A, B, C, X(46102), X(59196)}}, {{A, B, C, X(54357), X(60989)}}, {{A, B, C, X(55985), X(63167)}}, {{A, B, C, X(56352), X(65020)}}, {{A, B, C, X(60935), X(64142)}}
X(65249) = barycentric product X(i)*X(j) for these (i, j): {1, 46136}, {63, 65345}, {75, 953}, {3257, 50943}, {4564, 60582}, {18816, 61482}, {35011, 36038}, {37629, 54953}, {46041, 664}, {52479, 903}
X(65249) = barycentric quotient X(i)/X(j) for these (i, j): {1, 952}, {6, 2265}, {57, 43043}, {104, 61481}, {106, 52478}, {244, 6075}, {953, 1}, {1769, 35013}, {1772, 31841}, {2265, 61066}, {2718, 56644}, {3257, 57456}, {24028, 6073}, {35011, 36037}, {37629, 2804}, {41343, 39758}, {46041, 522}, {46136, 75}, {50943, 3762}, {52479, 519}, {59018, 2222}, {60582, 4858}, {61482, 517}, {65345, 92}

X(65250) = ISOGONAL CONJUGATE OF X(4784)

Barycentrics    a*(a-b)*(a-c)*(a*(2*b+c)+b*(b+2*c))*(c*(2*b+c)+a*(b+2*c)) : :
X(65250) = -3*X[2]+2*X[55059]

X(65250) lies on these lines: {1, 4094}, {2, 55059}, {45, 897}, {88, 17593}, {99, 65258}, {100, 24052}, {110, 62535}, {190, 65288}, {643, 65257}, {660, 1018}, {662, 3573}, {673, 6651}, {799, 874}, {894, 56703}, {1156, 60675}, {1492, 54440}, {3240, 37132}, {3799, 37138}, {3903, 37134}, {4557, 37212}, {4598, 65166}, {4606, 52923}, {4607, 4781}, {4613, 37207}, {5220, 65261}, {11684, 36101}, {16477, 20332}, {16666, 25426}, {17029, 62625}, {23831, 37216}, {24592, 56658}, {24624, 36815}, {37130, 60678}, {53338, 65230}

X(65250) = isogonal conjugate of X(4784)
X(65250) = anticomplement of X(55059)
X(65250) = trilinear pole of line {1, 1573}
X(65250) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4784}, {6, 28840}, {56, 4913}, {58, 4824}, {512, 51356}, {513, 4649}, {514, 60697}, {523, 59243}, {647, 31904}, {649, 16826}, {650, 60715}, {663, 60717}, {667, 60706}, {798, 51314}, {1019, 60724}, {1459, 60699}, {1919, 60719}, {2163, 4948}, {2382, 45657}, {3063, 60732}, {3572, 20142}, {3669, 60711}, {3676, 60713}, {3733, 3842}, {4753, 23345}, {4963, 56343}, {5625, 50344}, {6591, 60701}, {7649, 60703}, {43924, 60731}, {57129, 60736}, {57181, 60730}
X(65250) = X(i)-vertex conjugate of X(j) for these {i, j}: {163, 4596}, {660, 40519}
X(65250) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4913}, {3, 4784}, {9, 28840}, {10, 4824}, {5375, 16826}, {6631, 60706}, {9296, 60719}, {10001, 60732}, {31998, 51314}, {36830, 51311}, {39026, 4649}, {39052, 31904}, {39054, 51356}, {40587, 4948}, {51572, 4963}, {55059, 55059}
X(65250) = X(i)-cross conjugate of X(j) for these {i, j}: {4784, 1}, {9279, 37}, {24512, 1016}, {48886, 59}
X(65250) = pole of line {1001, 4393} with respect to the Kiepert parabola
X(65250) = pole of line {16826, 25427} with respect to the Yff parabola
X(65250) = pole of line {4649, 30571} with respect to the Hutson-Moses hyperbola
X(65250) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(99)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(32042)}}, {{A, B, C, X(110), X(2054)}}, {{A, B, C, X(163), X(29151)}}, {{A, B, C, X(668), X(6013)}}, {{A, B, C, X(670), X(3952)}}, {{A, B, C, X(692), X(29329)}}, {{A, B, C, X(931), X(65167)}}, {{A, B, C, X(932), X(58135)}}, {{A, B, C, X(1023), X(60690)}}, {{A, B, C, X(1026), X(16815)}}, {{A, B, C, X(1415), X(29171)}}, {{A, B, C, X(2284), X(15254)}}, {{A, B, C, X(3799), X(32041)}}, {{A, B, C, X(4551), X(24052)}}, {{A, B, C, X(4559), X(43359)}}, {{A, B, C, X(4622), X(8691)}}, {{A, B, C, X(4639), X(27805)}}, {{A, B, C, X(4781), X(16666)}}, {{A, B, C, X(5546), X(56203)}}, {{A, B, C, X(6742), X(46193)}}, {{A, B, C, X(8708), X(65202)}}, {{A, B, C, X(15322), X(52935)}}, {{A, B, C, X(17593), X(23703)}}, {{A, B, C, X(17780), X(30950)}}, {{A, B, C, X(23831), X(36277)}}, {{A, B, C, X(29121), X(32653)}}, {{A, B, C, X(29127), X(55918)}}, {{A, B, C, X(29351), X(58134)}}, {{A, B, C, X(36803), X(54118)}}, {{A, B, C, X(46961), X(57959)}}, {{A, B, C, X(53606), X(55929)}}
X(65250) = barycentric product X(i)*X(j) for these (i, j): {1, 65288}, {100, 27483}, {101, 60678}, {190, 30571}, {1978, 60671}, {3807, 40748}, {3952, 60680}, {25426, 668}, {28841, 75}, {37138, 56658}, {59194, 61174}, {59261, 662}, {59272, 799}, {60675, 664}, {60676, 99}, {62625, 660}
X(65250) = barycentric quotient X(i)/X(j) for these (i, j): {1, 28840}, {6, 4784}, {9, 4913}, {37, 4824}, {45, 4948}, {99, 51314}, {100, 16826}, {101, 4649}, {109, 60715}, {110, 51311}, {162, 31904}, {163, 59243}, {190, 60706}, {644, 60731}, {651, 60717}, {662, 51356}, {664, 60732}, {668, 60719}, {692, 60697}, {906, 60703}, {1018, 3842}, {1023, 4753}, {1331, 60701}, {1332, 60729}, {1783, 60699}, {3573, 20142}, {3699, 60730}, {3799, 27495}, {3939, 60711}, {3952, 60736}, {4557, 60724}, {16777, 4963}, {20331, 45657}, {25426, 513}, {27483, 693}, {28841, 1}, {30571, 514}, {35342, 5625}, {40748, 4817}, {59261, 1577}, {59272, 661}, {60671, 649}, {60675, 522}, {60676, 523}, {60678, 3261}, {60680, 7192}, {61163, 59219}, {61174, 59203}, {62625, 3766}, {65288, 75}

X(65251) = TRILINEAR POLE OF LINE {1, 91}

Barycentrics    (a-b)*b*(a+b)*(a-c)*c*(a+c)*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(a^4-2*a^2*c^2+(b^2-c^2)^2) : :

X(65251) lies on these lines: {63, 57716}, {68, 37142}, {91, 897}, {100, 925}, {190, 46134}, {333, 37203}, {651, 65309}, {653, 30450}, {662, 18740}, {799, 55215}, {811, 65221}, {1492, 32734}, {1577, 65262}, {1760, 1820}, {2165, 37128}, {2349, 18750}, {5392, 24624}, {20563, 37202}, {24001, 65224}, {35174, 65273}, {36085, 55250}, {36099, 65176}, {37219, 57904}

X(65251) = isogonal conjugate of X(55216)
X(65251) = isotomic conjugate of X(63827)
X(65251) = trilinear pole of line {1, 91}
X(65251) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55216}, {2, 34952}, {3, 6753}, {4, 30451}, {6, 924}, {19, 63832}, {24, 647}, {25, 52584}, {31, 63827}, {32, 6563}, {37, 34948}, {47, 661}, {50, 43088}, {52, 2623}, {54, 52317}, {68, 58760}, {74, 14397}, {110, 47421}, {125, 61208}, {136, 32661}, {184, 57065}, {317, 3049}, {467, 58308}, {512, 1993}, {520, 8745}, {523, 571}, {525, 44077}, {563, 24006}, {667, 42700}, {669, 7763}, {798, 44179}, {810, 1748}, {850, 52436}, {925, 39013}, {1147, 2501}, {1989, 44808}, {2180, 2616}, {2351, 15423}, {2422, 51439}, {2433, 51393}, {2489, 9723}, {2491, 31635}, {3133, 55253}, {3269, 52917}, {4705, 18605}, {5961, 47230}, {6754, 65309}, {8911, 58867}, {11547, 39201}, {14270, 18883}, {14380, 52952}, {14576, 23286}, {14582, 52416}, {14618, 52435}, {17994, 51776}, {20975, 41679}, {21731, 52505}, {26920, 58865}, {32654, 57154}, {32692, 55072}, {34116, 55228}, {41213, 65273}, {47390, 55278}, {52000, 61216}, {52032, 58756}, {54034, 63829}, {55204, 59162}, {60775, 63959}
X(65251) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 63827}, {3, 55216}, {6, 63832}, {9, 924}, {244, 47421}, {6376, 6563}, {6505, 52584}, {6631, 42700}, {31998, 44179}, {32664, 34952}, {34544, 44808}, {34853, 661}, {36033, 30451}, {36103, 6753}, {36830, 47}, {36901, 17881}, {37864, 798}, {39052, 24}, {39054, 1993}, {39062, 1748}, {40589, 34948}, {62605, 57065}
X(65251) = X(i)-cross conjugate of X(j) for these {i, j}: {1577, 57716}, {4575, 811}, {18595, 24000}, {24006, 75}, {55216, 1}, {55250, 91}
X(65251) = pole of line {34948, 55216} with respect to the Stammler hyperbola
X(65251) = pole of line {55216, 63827} with respect to the Wallace hyperbola
X(65251) = intersection, other than A, B, C, of circumconics {{A, B, C, X(75), X(55202)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(811), X(35174)}}, {{A, B, C, X(1760), X(62720)}}, {{A, B, C, X(15455), X(18740)}}, {{A, B, C, X(18750), X(24001)}}, {{A, B, C, X(36036), X(57968)}}, {{A, B, C, X(52609), X(60206)}}
X(65251) = barycentric product X(i)*X(j) for these (i, j): {1, 46134}, {68, 811}, {75, 925}, {91, 99}, {110, 20571}, {162, 20563}, {163, 57904}, {304, 65176}, {1820, 6331}, {2165, 799}, {2351, 57968}, {2617, 34385}, {4558, 57716}, {4575, 55553}, {4590, 55250}, {4592, 847}, {4602, 60501}, {5392, 662}, {14213, 65273}, {14593, 55202}, {18695, 65348}, {24006, 57763}, {30450, 63}, {32661, 57898}, {32680, 37802}, {32692, 62272}, {32734, 561}, {33808, 63958}, {36145, 76}, {52350, 823}, {52504, 65262}, {55215, 6}, {55549, 57973}, {65309, 92}
X(65251) = barycentric quotient X(i)/X(j) for these (i, j): {1, 924}, {2, 63827}, {3, 63832}, {6, 55216}, {19, 6753}, {31, 34952}, {48, 30451}, {58, 34948}, {63, 52584}, {68, 656}, {75, 6563}, {91, 523}, {92, 57065}, {96, 2616}, {99, 44179}, {110, 47}, {162, 24}, {163, 571}, {190, 42700}, {648, 1748}, {661, 47421}, {662, 1993}, {799, 7763}, {811, 317}, {823, 11547}, {847, 24006}, {850, 17881}, {920, 63959}, {925, 1}, {1625, 2180}, {1733, 57154}, {1748, 15423}, {1820, 647}, {1953, 52317}, {2165, 661}, {2166, 43088}, {2168, 2623}, {2173, 14397}, {2351, 810}, {2617, 52}, {4556, 18605}, {4575, 1147}, {4590, 55249}, {4592, 9723}, {5392, 1577}, {6149, 44808}, {14213, 63829}, {14570, 63808}, {20563, 14208}, {20571, 850}, {23181, 63801}, {24000, 52917}, {24006, 136}, {24019, 8745}, {30450, 92}, {32661, 563}, {32676, 44077}, {32680, 18883}, {32692, 2148}, {32734, 31}, {36036, 31635}, {36061, 5961}, {36129, 52415}, {36145, 6}, {37802, 32679}, {44174, 4575}, {46134, 75}, {46254, 55227}, {52350, 24018}, {54030, 55398}, {54031, 55397}, {55215, 76}, {55216, 39013}, {55250, 115}, {55277, 62719}, {55549, 822}, {56272, 2618}, {56829, 52952}, {57716, 14618}, {57763, 4592}, {57904, 20948}, {60501, 798}, {63958, 921}, {65176, 19}, {65262, 52505}, {65273, 2167}, {65309, 63}, {65348, 2190}

X(65252) = TRILINEAR POLE OF LINE {1, 1755}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(-b^4+b^2*c^2+a^2*(b^2+2*c^2))*(c^2*(b^2-c^2)+a^2*(2*b^2+c^2)) : :

X(65252) lies on these lines: {1, 1821}, {100, 26714}, {163, 36084}, {190, 65271}, {262, 24624}, {263, 37128}, {327, 37219}, {651, 65310}, {653, 46153}, {662, 23997}, {673, 60679}, {799, 2617}, {897, 2186}, {1967, 56681}, {2227, 56678}, {2349, 36263}, {3402, 36277}, {4575, 4599}, {6037, 29055}, {16948, 20332}, {32676, 65221}, {37137, 63741}, {37142, 43718}, {37202, 42313}, {37204, 55202}, {52631, 60057}

X(65252) = trilinear pole of line {1, 1755}
X(65252) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 3288}, {6, 23878}, {99, 6784}, {182, 523}, {183, 512}, {237, 63746}, {290, 9420}, {385, 39680}, {458, 647}, {513, 60723}, {514, 60726}, {520, 33971}, {525, 10311}, {526, 56401}, {649, 60737}, {656, 60685}, {661, 52134}, {667, 42711}, {669, 20023}, {798, 3403}, {822, 51315}, {842, 45321}, {850, 34396}, {2422, 51373}, {2433, 51372}, {2623, 59197}, {2799, 51542}, {3049, 44144}, {3569, 46806}, {4041, 60716}, {5027, 8842}, {6037, 62596}, {6130, 39683}, {14096, 58784}, {14994, 18105}, {15412, 59208}, {23286, 39530}, {31296, 60497}, {33569, 34536}, {59804, 65271}
X(65252) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 23878}, {5375, 60737}, {6631, 42711}, {31998, 3403}, {32664, 3288}, {36830, 52134}, {38986, 6784}, {39026, 60723}, {39052, 458}, {39054, 183}, {40596, 60685}
X(65252) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(163)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(2617), X(32676)}}, {{A, B, C, X(4575), X(46153)}}, {{A, B, C, X(24039), X(36289)}}, {{A, B, C, X(25424), X(51563)}}, {{A, B, C, X(43531), X(59034)}}
X(65252) = barycentric product X(i)*X(j) for these (i, j): {1, 65271}, {63, 65349}, {100, 60679}, {162, 42313}, {163, 327}, {262, 662}, {263, 799}, {325, 36132}, {1581, 39681}, {1755, 53196}, {1821, 63741}, {1959, 6037}, {2186, 99}, {2617, 42300}, {3402, 670}, {4602, 46319}, {24019, 59257}, {24037, 52631}, {26714, 75}, {32680, 57268}, {32716, 46238}, {36036, 51543}, {36084, 46807}, {42288, 55239}, {43718, 811}, {52926, 62276}, {54032, 823}, {65310, 92}
X(65252) = barycentric quotient X(i)/X(j) for these (i, j): {1, 23878}, {31, 3288}, {99, 3403}, {100, 60737}, {101, 60723}, {107, 51315}, {110, 52134}, {112, 60685}, {162, 458}, {163, 182}, {190, 42711}, {262, 1577}, {263, 661}, {327, 20948}, {662, 183}, {692, 60726}, {798, 6784}, {799, 20023}, {811, 44144}, {1821, 63746}, {1967, 39680}, {2186, 523}, {2247, 45321}, {2617, 59197}, {3402, 512}, {4565, 60716}, {6037, 1821}, {9417, 9420}, {24019, 33971}, {26714, 1}, {32676, 10311}, {32678, 56401}, {32716, 1910}, {36084, 46806}, {36132, 98}, {37134, 8842}, {39681, 1966}, {42075, 33569}, {42288, 55240}, {42299, 18070}, {42313, 14208}, {43718, 656}, {46319, 798}, {51997, 54252}, {52631, 2643}, {52926, 1953}, {53196, 46273}, {54032, 24018}, {57268, 32679}, {60679, 693}, {63741, 1959}, {65271, 75}, {65310, 63}, {65349, 92}
X(65252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39342, 42075, 1821}

X(65253) = TRILINEAR POLE OF LINE {1, 1437}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^3+b^3+a*(b-c)*c-b*c^2)*(a^3-b^2*c+c^3+a*b*(-b+c)) : :

X(65253) lies on these lines: {81, 36100}, {100, 4575}, {110, 65225}, {162, 46588}, {163, 65260}, {190, 4558}, {653, 4565}, {897, 2217}, {1156, 16948}, {1821, 2995}, {2349, 62795}, {3737, 36094}, {4612, 65230}, {13478, 24624}, {15232, 57682}, {16754, 65232}, {19607, 34234}, {26540, 37202}, {26704, 59130}, {32641, 64824}, {36101, 56834}, {37142, 56840}, {37219, 57906}

X(65253) = trilinear pole of line {1, 1437}
X(65253) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 52310}, {10, 6589}, {37, 21189}, {71, 59915}, {124, 4559}, {512, 4417}, {513, 21078}, {514, 22276}, {522, 40590}, {523, 573}, {525, 3192}, {647, 17555}, {652, 56827}, {661, 3869}, {756, 16754}, {1577, 3185}, {1824, 57184}, {1880, 57111}, {2333, 57242}, {2489, 51612}, {3700, 10571}, {4024, 4225}, {4041, 17080}, {4551, 38345}, {22134, 24006}, {47411, 61178}, {47842, 53081}
X(65253) = X(i)-Dao conjugate of X(j) for these {i, j}: {36033, 52310}, {36830, 3869}, {39026, 21078}, {39052, 17555}, {39054, 4417}, {40589, 21189}, {55067, 124}
X(65253) = X(i)-cross conjugate of X(j) for these {i, j}: {1415, 110}, {30212, 7}, {32653, 59005}, {36050, 54951}, {53279, 99}
X(65253) = pole of line {6589, 21189} with respect to the Stammler hyperbola
X(65253) = pole of line {1812, 21078} with respect to the Hutson-Moses hyperbola
X(65253) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(46588)}}, {{A, B, C, X(81), X(65232)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(108), X(46640)}}, {{A, B, C, X(110), X(4612)}}, {{A, B, C, X(163), X(8687)}}, {{A, B, C, X(934), X(4592)}}, {{A, B, C, X(1169), X(32676)}}, {{A, B, C, X(1783), X(36145)}}, {{A, B, C, X(2222), X(56188)}}, {{A, B, C, X(3882), X(9070)}}, {{A, B, C, X(4558), X(4565)}}, {{A, B, C, X(32038), X(33637)}}, {{A, B, C, X(36050), X(44765)}}, {{A, B, C, X(51568), X(55202)}}
X(65253) = barycentric product X(i)*X(j) for these (i, j): {1, 54951}, {110, 2995}, {163, 57906}, {274, 32653}, {1014, 56112}, {1444, 26704}, {2217, 99}, {3737, 57757}, {10570, 1414}, {13478, 662}, {15232, 52935}, {15386, 18155}, {19607, 651}, {36050, 86}, {40160, 4612}, {42550, 65281}, {44765, 81}, {59005, 75}
X(65253) = barycentric quotient X(i)/X(j) for these (i, j): {28, 59915}, {48, 52310}, {58, 21189}, {101, 21078}, {108, 56827}, {110, 3869}, {162, 17555}, {163, 573}, {283, 57111}, {593, 16754}, {662, 4417}, {692, 22276}, {1333, 6589}, {1415, 40590}, {1444, 57242}, {1576, 3185}, {1790, 57184}, {2217, 523}, {2995, 850}, {3737, 124}, {4565, 17080}, {4592, 51612}, {7252, 38345}, {10570, 4086}, {13478, 1577}, {15232, 4036}, {15386, 4551}, {19607, 4391}, {23189, 34588}, {26704, 41013}, {32653, 37}, {32661, 22134}, {32676, 3192}, {36050, 10}, {44765, 321}, {53082, 23879}, {54951, 75}, {56112, 3701}, {57906, 20948}, {58951, 53081}, {58982, 40452}, {59005, 1}

X(65254) = TRILINEAR POLE OF LINE {1, 1762}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^3+b^3-b*c^2-a*c*(b+c))*(a^3-b^2*c+c^3-a*b*(b+c)) : :

X(65254) lies on these lines: {88, 1817}, {100, 58986}, {110, 65227}, {112, 653}, {162, 13589}, {163, 651}, {190, 5546}, {272, 673}, {658, 4565}, {799, 4612}, {897, 2218}, {1751, 24624}, {1821, 2997}, {4558, 65247}, {4575, 65244}, {7054, 37086}, {7437, 32676}, {27418, 37202}, {37203, 40574}, {37218, 51566}, {37219, 40011}, {46541, 65213}

X(65254) = trilinear pole of line {1, 1762}
X(65254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 51658}, {10, 43060}, {37, 23800}, {72, 57173}, {73, 57043}, {209, 514}, {226, 8676}, {512, 18134}, {513, 22021}, {523, 579}, {647, 5125}, {649, 57808}, {661, 3868}, {663, 56559}, {693, 2198}, {1214, 57092}, {1400, 20294}, {1427, 58333}, {1577, 2352}, {2197, 57072}, {3120, 57217}, {3190, 7178}, {3700, 4306}, {4017, 27396}, {4557, 65118}, {5190, 23067}, {7649, 51574}, {17094, 41320}, {21044, 65315}, {23752, 40572}
X(65254) = X(i)-vertex conjugate of X(j) for these {i, j}: {4552, 32676}
X(65254) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 51658}, {5375, 57808}, {34961, 27396}, {36830, 3868}, {39026, 22021}, {39052, 5125}, {39054, 18134}, {40582, 20294}, {40589, 23800}, {40625, 17878}
X(65254) = X(i)-cross conjugate of X(j) for these {i, j}: {906, 110}, {54354, 24041}
X(65254) = pole of line {23800, 43060} with respect to the Stammler hyperbola
X(65254) = pole of line {1782, 57808} with respect to the Yff parabola
X(65254) = pole of line {22021, 40571} with respect to the Hutson-Moses hyperbola
X(65254) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(13589)}}, {{A, B, C, X(21), X(4237)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(112), X(163)}}, {{A, B, C, X(404), X(46499)}}, {{A, B, C, X(643), X(65232)}}, {{A, B, C, X(644), X(24019)}}, {{A, B, C, X(811), X(35169)}}, {{A, B, C, X(919), X(32676)}}, {{A, B, C, X(1332), X(13397)}}, {{A, B, C, X(1817), X(46541)}}, {{A, B, C, X(2222), X(56248)}}, {{A, B, C, X(4236), X(16050)}}, {{A, B, C, X(4238), X(24606)}}, {{A, B, C, X(4552), X(6011)}}, {{A, B, C, X(4556), X(59112)}}, {{A, B, C, X(6335), X(33637)}}, {{A, B, C, X(7437), X(37086)}}, {{A, B, C, X(11320), X(46597)}}, {{A, B, C, X(29014), X(57217)}}, {{A, B, C, X(31015), X(53160)}}
X(65254) = barycentric product X(i)*X(j) for these (i, j): {1, 65274}, {100, 272}, {110, 2997}, {163, 40011}, {1305, 21}, {1332, 40574}, {1414, 56146}, {1751, 662}, {2218, 99}, {15467, 65375}, {28786, 52914}, {41506, 52935}, {51566, 58}, {57784, 692}, {58986, 75}
X(65254) = barycentric quotient X(i)/X(j) for these (i, j): {21, 20294}, {56, 51658}, {58, 23800}, {100, 57808}, {101, 22021}, {110, 3868}, {162, 5125}, {163, 579}, {270, 57072}, {272, 693}, {651, 56559}, {662, 18134}, {692, 209}, {906, 51574}, {1019, 65118}, {1172, 57043}, {1305, 1441}, {1333, 43060}, {1474, 57173}, {1576, 2352}, {1751, 1577}, {2194, 8676}, {2218, 523}, {2299, 57092}, {2328, 58333}, {2997, 850}, {4560, 17878}, {5546, 27396}, {32739, 2198}, {40011, 20948}, {40574, 17924}, {41506, 4036}, {51566, 313}, {56146, 4086}, {57784, 40495}, {58986, 1}, {65274, 75}, {65375, 3190}

X(65255) = TRILINEAR POLE OF LINE {1, 849}

Barycentrics    a*(a-b)*(a+b)^2*(a-c)*(a+c)^2*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :

X(65255) lies on these lines: {88, 30581}, {100, 4612}, {163, 65230}, {190, 4556}, {261, 24583}, {651, 52935}, {655, 6648}, {660, 32736}, {897, 2363}, {1169, 37128}, {1798, 37142}, {3882, 64823}, {4565, 37137}, {4581, 60055}, {4610, 37215}, {4636, 65225}, {8687, 43069}, {14534, 24624}, {15420, 60056}, {24041, 65239}, {36085, 62749}, {36147, 37212}, {37202, 57853}, {37219, 40827}

X(65255) = trilinear pole of line {1, 849}
X(65255) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 42661}, {12, 52326}, {37, 50330}, {42, 21124}, {115, 53280}, {125, 61205}, {181, 3910}, {429, 647}, {512, 1211}, {513, 21810}, {523, 2092}, {525, 44092}, {594, 6371}, {661, 2292}, {669, 1228}, {756, 48131}, {798, 18697}, {872, 4509}, {960, 57185}, {1193, 4024}, {1500, 3004}, {1577, 3725}, {1829, 55232}, {1848, 55230}, {2171, 17420}, {2300, 4036}, {2354, 4064}, {2501, 22076}, {2643, 3882}, {3005, 27067}, {3120, 61168}, {3122, 65191}, {3124, 53332}, {3125, 61172}, {3666, 4705}, {3704, 7180}, {3708, 61226}, {3709, 41003}, {4017, 21033}, {4079, 4357}, {4267, 55197}, {4391, 59174}, {6042, 62749}, {7178, 40966}, {8672, 56914}, {14394, 38882}, {16705, 58289}, {20911, 50487}, {21051, 45218}, {21834, 45197}, {28654, 57157}, {40976, 57243}, {43924, 61377}, {45196, 63461}, {46878, 55234}
X(65255) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 20653}, {31998, 18697}, {32664, 42661}, {34961, 21033}, {36830, 2292}, {39026, 21810}, {39052, 429}, {39054, 1211}, {40589, 50330}, {40592, 21124}
X(65255) = X(i)-cross conjugate of X(j) for these {i, j}: {58, 24041}, {62749, 2363}
X(65255) = pole of line {21810, 64457} with respect to the Hutson-Moses hyperbola
X(65255) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}}, {{A, B, C, X(1169), X(32736)}}, {{A, B, C, X(4565), X(53628)}}, {{A, B, C, X(4612), X(52935)}}, {{A, B, C, X(4628), X(36142)}}, {{A, B, C, X(6648), X(14534)}}, {{A, B, C, X(9070), X(54986)}}
X(65255) = barycentric product X(i)*X(j) for these (i, j): {1, 65281}, {109, 52550}, {162, 57853}, {163, 40827}, {190, 64457}, {261, 36098}, {593, 65229}, {757, 8707}, {1169, 799}, {1220, 52935}, {1509, 36147}, {1798, 811}, {2185, 6648}, {2298, 4610}, {2359, 55231}, {2363, 99}, {4590, 62749}, {4612, 64984}, {14534, 662}, {24041, 4581}, {30710, 4556}, {31643, 4636}, {32736, 873}, {40452, 54951}, {52379, 8687}, {58982, 75}, {65282, 849}
X(65255) = barycentric quotient X(i)/X(j) for these (i, j): {31, 42661}, {58, 50330}, {60, 17420}, {81, 21124}, {99, 18697}, {100, 20653}, {101, 21810}, {109, 52567}, {110, 2292}, {162, 429}, {163, 2092}, {249, 3882}, {250, 61226}, {593, 48131}, {643, 3704}, {644, 61377}, {662, 1211}, {757, 3004}, {799, 1228}, {849, 6371}, {1098, 57158}, {1101, 53280}, {1169, 661}, {1220, 4036}, {1414, 41003}, {1509, 4509}, {1576, 3725}, {1791, 4064}, {1798, 656}, {2150, 52326}, {2185, 3910}, {2298, 4024}, {2359, 55232}, {2363, 523}, {4556, 3666}, {4567, 65191}, {4570, 61172}, {4573, 45196}, {4575, 22076}, {4581, 1109}, {4599, 27067}, {4610, 20911}, {4612, 3687}, {4636, 960}, {5546, 21033}, {6648, 6358}, {8687, 2171}, {8707, 1089}, {14534, 1577}, {15420, 20902}, {24041, 53332}, {30710, 52623}, {32676, 44092}, {32736, 756}, {36098, 12}, {36147, 594}, {40827, 20948}, {52550, 35519}, {52914, 46878}, {52928, 1254}, {52935, 4357}, {53280, 6042}, {57162, 21043}, {57853, 14208}, {58982, 1}, {59005, 42550}, {62749, 115}, {64457, 514}, {65229, 28654}, {65281, 75}, {65375, 40966}

X(65256) = TRILINEAR POLE OF LINE {1, 3286}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(b*(-b+c)+a*(b+c))*((b-c)*c+a*(b+c)) : :

X(65256) lies on these lines: {2, 65264}, {6, 61403}, {81, 673}, {86, 27190}, {88, 39950}, {100, 43076}, {110, 36086}, {162, 4250}, {190, 4576}, {660, 63918}, {897, 13476}, {1414, 65222}, {1821, 40216}, {2287, 37214}, {2350, 32911}, {3570, 37205}, {4551, 16751}, {4565, 65217}, {4573, 34085}, {4599, 52935}, {4604, 64828}, {4607, 62530}, {5235, 34234}, {7192, 35326}, {17758, 24624}, {27644, 27666}, {37130, 40004}, {37138, 65186}, {37142, 37659}, {39046, 53707}, {65225, 65315}

X(65256) = isotomic conjugate of X(58361)
X(65256) = trilinear pole of line {1, 3286}
X(65256) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4151}, {10, 21007}, {31, 58361}, {37, 4040}, {42, 17494}, {81, 21727}, {210, 58324}, {213, 20954}, {512, 17277}, {513, 3294}, {514, 64169}, {647, 14004}, {649, 4651}, {661, 1621}, {667, 4043}, {669, 18152}, {756, 57148}, {798, 17143}, {1018, 64523}, {1019, 40607}, {1334, 57167}, {1826, 22160}, {1924, 40088}, {3700, 55086}, {3709, 55082}, {3737, 20616}, {3952, 38346}, {3996, 7180}, {4171, 38859}, {4524, 33765}, {4551, 38347}, {4552, 38365}, {4557, 17761}, {43915, 62747}, {50520, 62646}, {55240, 56537}
X(65256) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 58361}, {9, 4151}, {1015, 2486}, {5375, 4651}, {6626, 20954}, {6631, 4043}, {9428, 40088}, {31998, 17143}, {36830, 1621}, {39026, 3294}, {39052, 14004}, {39054, 17277}, {40586, 21727}, {40589, 4040}, {40592, 17494}, {40620, 40619}
X(65256) = X(i)-cross conjugate of X(j) for these {i, j}: {2350, 63918}, {4557, 99}, {7192, 81}, {24948, 1255}, {32913, 24041}, {35326, 110}, {46148, 34594}, {47970, 40438}
X(65256) = pole of line {4040, 21007} with respect to the Stammler hyperbola
X(65256) = pole of line {86, 3294} with respect to the Hutson-Moses hyperbola
X(65256) = pole of line {17494, 20954} with respect to the Wallace hyperbola
X(65256) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4250)}}, {{A, B, C, X(81), X(110)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(43190)}}, {{A, B, C, X(163), X(8693)}}, {{A, B, C, X(274), X(11794)}}, {{A, B, C, X(648), X(4627)}}, {{A, B, C, X(666), X(8701)}}, {{A, B, C, X(813), X(39276)}}, {{A, B, C, X(1019), X(61403)}}, {{A, B, C, X(1255), X(6742)}}, {{A, B, C, X(1414), X(51563)}}, {{A, B, C, X(3570), X(32911)}}, {{A, B, C, X(4565), X(59012)}}, {{A, B, C, X(4575), X(65296)}}, {{A, B, C, X(4576), X(4589)}}, {{A, B, C, X(4584), X(4610)}}, {{A, B, C, X(4585), X(37633)}}, {{A, B, C, X(4586), X(53627)}}, {{A, B, C, X(4593), X(53624)}}, {{A, B, C, X(4603), X(4615)}}, {{A, B, C, X(4633), X(43356)}}, {{A, B, C, X(5235), X(64828)}}, {{A, B, C, X(7192), X(57148)}}, {{A, B, C, X(9090), X(36148)}}, {{A, B, C, X(16751), X(18155)}}, {{A, B, C, X(27644), X(62530)}}, {{A, B, C, X(35312), X(41353)}}, {{A, B, C, X(35326), X(54325)}}, {{A, B, C, X(36797), X(56204)}}, {{A, B, C, X(56053), X(59093)}}, {{A, B, C, X(63784), X(65059)}}
X(65256) = barycentric product X(i)*X(j) for these (i, j): {1, 53649}, {100, 39734}, {101, 40004}, {110, 40216}, {190, 39950}, {1414, 55076}, {2350, 799}, {13476, 99}, {17758, 662}, {43076, 75}, {54118, 81}, {63918, 7192}
X(65256) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4151}, {2, 58361}, {42, 21727}, {58, 4040}, {81, 17494}, {86, 20954}, {99, 17143}, {100, 4651}, {101, 3294}, {110, 1621}, {162, 14004}, {163, 4251}, {190, 4043}, {513, 2486}, {593, 57148}, {643, 3996}, {662, 17277}, {670, 40088}, {692, 64169}, {799, 18152}, {1014, 57167}, {1019, 17761}, {1333, 21007}, {1412, 58324}, {1414, 55082}, {1434, 57247}, {1437, 22160}, {1634, 56537}, {2350, 661}, {3733, 64523}, {4557, 40607}, {4559, 20616}, {4589, 40094}, {4637, 33765}, {7192, 40619}, {7252, 38347}, {13476, 523}, {17758, 1577}, {18191, 42454}, {39734, 693}, {39950, 514}, {40004, 3261}, {40216, 850}, {43076, 1}, {53649, 75}, {54118, 321}, {55076, 4086}, {57129, 38346}, {57148, 26846}, {63918, 3952}

X(65257) = TRILINEAR POLE OF LINE {1, 1326}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2+b*c-c^2+a*(b+c))*(a^2-b^2+b*c+c^2+a*(b+c)) : :

X(65257) lies on these lines: {81, 21833}, {100, 17943}, {110, 2644}, {190, 22033}, {643, 65250}, {662, 21383}, {673, 40164}, {757, 16592}, {799, 21604}, {897, 13610}, {1414, 37137}, {1821, 51865}, {2248, 37128}, {4573, 65237}, {6625, 24624}, {14985, 60055}, {18757, 37132}, {36066, 37134}, {39054, 65220}, {39276, 43763}

X(65257) = trilinear pole of line {1, 1326}
X(65257) = X(i)-isoconjugate-of-X(j) for these {i, j}: {42, 21196}, {110, 6627}, {213, 50451}, {512, 1654}, {513, 21879}, {523, 18755}, {647, 4213}, {649, 21085}, {661, 846}, {663, 27691}, {667, 27569}, {669, 51857}, {798, 17762}, {893, 24381}, {2501, 22139}, {2905, 55230}, {3124, 57060}, {3709, 17084}, {4079, 6626}, {4155, 45783}, {4556, 21709}, {4705, 38814}, {4988, 38836}, {14844, 55210}, {17990, 39921}, {18004, 51332}, {46390, 52207}, {53581, 64224}, {57234, 63627}
X(65257) = X(i)-Dao conjugate of X(j) for these {i, j}: {244, 6627}, {5375, 21085}, {6626, 50451}, {6631, 27569}, {31998, 17762}, {36830, 846}, {39026, 21879}, {39052, 4213}, {39054, 1654}, {40592, 21196}, {40597, 24381}
X(65257) = X(i)-cross conjugate of X(j) for these {i, j}: {661, 52208}, {4705, 40438}, {37527, 7045}, {52935, 662}, {57234, 2363}
X(65257) = pole of line {21196, 50451} with respect to the Wallace hyperbola
X(65257) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}}, {{A, B, C, X(110), X(1171)}}, {{A, B, C, X(661), X(21833)}}, {{A, B, C, X(1414), X(36066)}}, {{A, B, C, X(4103), X(21383)}}, {{A, B, C, X(4573), X(14534)}}, {{A, B, C, X(4603), X(17930)}}, {{A, B, C, X(4610), X(13486)}}, {{A, B, C, X(26700), X(35180)}}, {{A, B, C, X(35148), X(38470)}}
X(65257) = barycentric product X(i)*X(j) for these (i, j): {1, 53655}, {100, 40164}, {110, 51865}, {662, 6625}, {2248, 799}, {4610, 52208}, {13610, 99}, {15377, 55231}, {18757, 670}, {52935, 63885}, {53628, 75}
X(65257) = barycentric quotient X(i)/X(j) for these (i, j): {81, 21196}, {86, 50451}, {99, 17762}, {100, 21085}, {101, 21879}, {110, 846}, {162, 4213}, {163, 18755}, {171, 24381}, {190, 27569}, {651, 27691}, {661, 6627}, {662, 1654}, {799, 51857}, {1414, 17084}, {2248, 661}, {4556, 38814}, {4575, 22139}, {4623, 64224}, {4705, 21709}, {6625, 1577}, {13486, 14844}, {13610, 523}, {15377, 55232}, {18757, 512}, {24041, 57060}, {36066, 52207}, {40164, 693}, {40777, 4122}, {51865, 850}, {52208, 4024}, {52935, 6626}, {53628, 1}, {53655, 75}, {63885, 4036}

X(65258) = TRILINEAR POLE OF LINE {1, 99}

Barycentrics    (a-b)*(a+b)^2*(a-c)*(a+c)^2*(-b^2+a*c)*(a*b-c^2) : :

X(65258) lies on these lines: {88, 4615}, {99, 65250}, {100, 4589}, {162, 18020}, {190, 4584}, {651, 4620}, {660, 17934}, {662, 4590}, {741, 9150}, {799, 4369}, {805, 53631}, {876, 60057}, {892, 897}, {1019, 24037}, {1492, 52935}, {1821, 43187}, {3572, 37134}, {4367, 9425}, {4444, 36085}, {4562, 37212}, {4573, 7180}, {4598, 4631}, {18829, 53655}, {20142, 37128}, {24624, 40017}, {36084, 57991}, {36800, 65261}, {37133, 52612}, {37142, 57738}, {37202, 57987}, {40459, 47376}, {41209, 43763}, {55237, 65239}, {65352, 65354}

X(65258) = isogonal conjugate of X(46390)
X(65258) = trilinear pole of line {1, 99}
X(65258) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46390}, {6, 4155}, {37, 4455}, {42, 21832}, {181, 4435}, {213, 4010}, {238, 4079}, {239, 50487}, {350, 53581}, {512, 2238}, {523, 41333}, {647, 862}, {659, 1500}, {661, 3747}, {667, 4037}, {669, 3948}, {740, 798}, {756, 8632}, {804, 40729}, {812, 872}, {874, 1084}, {875, 35068}, {1284, 3709}, {1914, 4705}, {1924, 35544}, {2086, 3903}, {2201, 55230}, {2210, 4024}, {2333, 53556}, {2422, 50440}, {3063, 7235}, {3124, 3573}, {3572, 4094}, {3766, 7109}, {3985, 51641}, {4036, 14599}, {4093, 55240}, {4117, 27853}, {4433, 7180}, {4557, 39786}, {5027, 52651}, {16609, 63461}, {18892, 52623}, {55232, 57654}
X(65258) = X(i)-vertex conjugate of X(j) for these {i, j}: {213, 36133}
X(65258) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46390}, {9, 4155}, {6626, 4010}, {6631, 4037}, {9428, 35544}, {9470, 4079}, {10001, 7235}, {31998, 740}, {36830, 3747}, {36906, 4705}, {39052, 862}, {39054, 2238}, {40589, 4455}, {40592, 21832}, {62557, 4024}
X(65258) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39292, 37128}
X(65258) = X(i)-cross conjugate of X(j) for these {i, j}: {3570, 99}, {4444, 18827}, {4584, 36066}, {4589, 65285}, {18206, 24041}, {33295, 24037}, {46390, 1}
X(65258) = pole of line {1931, 2669} with respect to the Kiepert parabola
X(65258) = pole of line {4455, 46390} with respect to the Stammler hyperbola
X(65258) = pole of line {4010, 4839} with respect to the Wallace hyperbola
X(65258) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(51225)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(892), X(4590)}}, {{A, B, C, X(898), X(36133)}}, {{A, B, C, X(3570), X(20142)}}, {{A, B, C, X(3572), X(4369)}}, {{A, B, C, X(4555), X(32014)}}, {{A, B, C, X(4562), X(63896)}}, {{A, B, C, X(4573), X(53631)}}, {{A, B, C, X(4589), X(4639)}}, {{A, B, C, X(4610), X(4623)}}, {{A, B, C, X(16609), X(27853)}}, {{A, B, C, X(17930), X(17934)}}, {{A, B, C, X(52612), X(52935)}}
X(65258) = barycentric product X(i)*X(j) for these (i, j): {1, 65285}, {162, 57987}, {274, 4584}, {291, 4623}, {292, 52612}, {295, 55229}, {334, 52935}, {335, 4610}, {660, 873}, {670, 741}, {1509, 4562}, {3570, 57554}, {4444, 4590}, {4563, 65352}, {4583, 757}, {4589, 86}, {4625, 56154}, {4639, 81}, {17103, 18829}, {18268, 4602}, {18827, 99}, {18895, 4556}, {24037, 876}, {34067, 57992}, {34537, 3572}, {36066, 75}, {36800, 4573}, {36801, 552}, {36806, 57}, {37128, 799}, {37134, 8033}, {39276, 55239}, {39292, 4369}, {40017, 662}, {46159, 689}, {52207, 53655}, {57738, 811}, {60577, 7340}
X(65258) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4155}, {6, 46390}, {58, 4455}, {81, 21832}, {86, 4010}, {99, 740}, {110, 3747}, {162, 862}, {163, 41333}, {190, 4037}, {261, 3716}, {291, 4705}, {292, 4079}, {295, 55230}, {334, 4036}, {335, 4024}, {337, 4064}, {552, 43041}, {593, 8632}, {643, 4433}, {645, 3985}, {660, 756}, {662, 2238}, {664, 7235}, {670, 35544}, {741, 512}, {757, 659}, {763, 50456}, {799, 3948}, {813, 1500}, {873, 3766}, {876, 2643}, {1019, 39786}, {1414, 1284}, {1434, 7212}, {1444, 53556}, {1509, 812}, {1634, 4093}, {1911, 50487}, {1922, 53581}, {2185, 4435}, {2311, 3709}, {3570, 35068}, {3572, 3124}, {3573, 4094}, {4444, 115}, {4556, 1914}, {4562, 594}, {4573, 16609}, {4583, 1089}, {4584, 37}, {4589, 10}, {4590, 3570}, {4610, 239}, {4612, 3684}, {4623, 350}, {4631, 3975}, {4639, 321}, {5378, 40521}, {7058, 4148}, {17103, 804}, {17139, 42767}, {17206, 24459}, {17941, 4154}, {18268, 798}, {18827, 523}, {18895, 52623}, {20981, 2086}, {24037, 874}, {24041, 3573}, {34067, 872}, {34537, 27853}, {35352, 21043}, {36066, 1}, {36800, 3700}, {36801, 6057}, {36806, 312}, {37128, 661}, {37134, 52651}, {39276, 55240}, {39292, 27805}, {40017, 1577}, {40095, 21714}, {42028, 4839}, {46159, 3005}, {52612, 1921}, {52935, 238}, {53631, 39926}, {55229, 40717}, {55243, 4783}, {56154, 4041}, {56934, 53563}, {57554, 4444}, {57738, 656}, {57987, 14208}, {60577, 4092}, {65166, 4829}, {65283, 36815}, {65285, 75}, {65338, 7140}, {65352, 2501}
X(65258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {36806, 65285, 4639}

X(65259) = TRILINEAR POLE OF LINE {1, 3052}

Barycentrics    a*(a-b)*(a-c)*(3*a+3*b-c)*(3*a-b+3*c) : :

X(65259) lies on these lines: {2, 43759}, {11, 19641}, {88, 2999}, {100, 13245}, {101, 27834}, {190, 17136}, {653, 63782}, {673, 17379}, {897, 17016}, {1156, 19861}, {1332, 37212}, {1813, 65234}, {4579, 37223}, {4585, 37211}, {4606, 65168}, {5278, 34234}, {5333, 18645}, {28283, 37129}

X(65259) = trilinear pole of line {1, 3052}
X(65259) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 48338}, {6, 28161}, {513, 3731}, {649, 3617}, {650, 3340}, {657, 62783}, {661, 64415}, {663, 5226}, {667, 42034}, {3445, 14350}, {3669, 62218}, {3733, 4058}, {3984, 6591}, {4394, 10563}
X(65259) = X(i)-vertex conjugate of X(j) for these {i, j}: {692, 27834}
X(65259) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 28161}, {1015, 62221}, {5375, 3617}, {6631, 42034}, {32664, 48338}, {36830, 64415}, {39026, 3731}, {45036, 14350}
X(65259) = X(i)-cross conjugate of X(j) for these {i, j}: {5437, 4564}, {7987, 7045}, {47915, 25417}, {48144, 81}
X(65259) = pole of line {3617, 3929} with respect to the Yff parabola
X(65259) = pole of line {940, 3731} with respect to the Hutson-Moses hyperbola
X(65259) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(32038)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(101), X(38828)}}, {{A, B, C, X(110), X(1461)}}, {{A, B, C, X(645), X(43190)}}, {{A, B, C, X(666), X(29199)}}, {{A, B, C, X(934), X(4597)}}, {{A, B, C, X(1025), X(62778)}}, {{A, B, C, X(1310), X(4555)}}, {{A, B, C, X(1332), X(63782)}}, {{A, B, C, X(1414), X(58133)}}, {{A, B, C, X(2999), X(17780)}}, {{A, B, C, X(4556), X(28166)}}, {{A, B, C, X(4565), X(4588)}}, {{A, B, C, X(4573), X(44765)}}, {{A, B, C, X(4584), X(58117)}}, {{A, B, C, X(4585), X(5333)}}, {{A, B, C, X(4586), X(29227)}}, {{A, B, C, X(4591), X(28206)}}, {{A, B, C, X(4596), X(58134)}}, {{A, B, C, X(4616), X(43349)}}, {{A, B, C, X(4627), X(8652)}}, {{A, B, C, X(4629), X(28152)}}, {{A, B, C, X(4817), X(13245)}}, {{A, B, C, X(5278), X(64828)}}, {{A, B, C, X(6335), X(46480)}}, {{A, B, C, X(6606), X(9086)}}, {{A, B, C, X(6648), X(55996)}}, {{A, B, C, X(6742), X(44327)}}, {{A, B, C, X(8693), X(34071)}}, {{A, B, C, X(30555), X(32736)}}, {{A, B, C, X(30610), X(56188)}}, {{A, B, C, X(36049), X(59079)}}, {{A, B, C, X(36147), X(53630)}}
X(65259) = barycentric product X(i)*X(j) for these (i, j): {1, 58132}, {100, 30712}, {190, 39980}, {28162, 75}, {31503, 99}, {56201, 651}, {56226, 662}
X(65259) = barycentric quotient X(i)/X(j) for these (i, j): {1, 28161}, {31, 48338}, {100, 3617}, {101, 3731}, {109, 3340}, {110, 64415}, {190, 42034}, {513, 62221}, {651, 5226}, {934, 62783}, {1018, 4058}, {1293, 10563}, {1331, 3984}, {1743, 14350}, {3939, 62218}, {28162, 1}, {30712, 693}, {31503, 523}, {35338, 61031}, {39980, 514}, {56201, 4391}, {56226, 1577}, {58132, 75}

X(65260) = TRILINEAR POLE OF LINE {1, 859}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(-b^3+b*c^2+a*c*(-b+c)+a^2*(b+c))*(a*b*(b-c)+a^2*(b+c)+c*(b^2-c^2)) : :

X(65260) lies on these lines: {6, 26856}, {81, 34234}, {88, 53083}, {100, 2617}, {110, 36098}, {162, 7461}, {163, 65253}, {190, 14570}, {645, 65229}, {648, 65223}, {653, 57220}, {673, 20028}, {897, 34434}, {1020, 16754}, {1332, 37218}, {1746, 2051}, {1821, 54121}, {2349, 62796}, {4560, 64824}, {4565, 37136}, {4585, 37205}, {7253, 61202}, {16749, 37130}, {16948, 37129}, {36087, 57148}, {36101, 40773}, {37133, 55256}, {37202, 37659}, {37219, 57905}

X(65260) = trilinear pole of line {1, 859}
X(65260) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 51662}, {37, 21173}, {42, 17496}, {54, 52322}, {101, 53566}, {213, 57244}, {512, 14829}, {513, 21061}, {514, 52139}, {522, 55323}, {523, 572}, {647, 11109}, {649, 17751}, {650, 37558}, {661, 2975}, {663, 52358}, {1019, 14973}, {1021, 20617}, {1086, 57165}, {1400, 57091}, {1427, 58339}, {1577, 20986}, {1826, 23187}, {2171, 57125}, {3120, 65203}, {3737, 56325}, {4041, 17074}, {4551, 11998}, {4557, 24237}, {4559, 34589}, {4581, 52087}, {7252, 52357}, {22118, 24006}, {23493, 27346}, {38344, 61178}
X(65260) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 51662}, {1015, 53566}, {5375, 17751}, {6626, 57244}, {36830, 2975}, {39026, 21061}, {39052, 11109}, {39054, 14829}, {40582, 57091}, {40589, 21173}, {40592, 17496}, {40625, 40624}, {55067, 34589}
X(65260) = X(i)-cross conjugate of X(j) for these {i, j}: {4559, 110}, {4560, 81}, {23845, 99}, {25667, 1258}, {56194, 65275}
X(65260) = pole of line {333, 21061} with respect to the Hutson-Moses hyperbola
X(65260) = pole of line {17496, 27346} with respect to the Wallace hyperbola
X(65260) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1020)}}, {{A, B, C, X(81), X(648)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(109), X(44765)}}, {{A, B, C, X(110), X(645)}}, {{A, B, C, X(163), X(1783)}}, {{A, B, C, X(249), X(23592)}}, {{A, B, C, X(666), X(59102)}}, {{A, B, C, X(811), X(934)}}, {{A, B, C, X(901), X(6648)}}, {{A, B, C, X(1332), X(4575)}}, {{A, B, C, X(1414), X(7257)}}, {{A, B, C, X(1461), X(28624)}}, {{A, B, C, X(2617), X(14570)}}, {{A, B, C, X(3737), X(26856)}}, {{A, B, C, X(3882), X(3952)}}, {{A, B, C, X(4556), X(47318)}}, {{A, B, C, X(4577), X(17929)}}, {{A, B, C, X(4585), X(32911)}}, {{A, B, C, X(23997), X(62813)}}, {{A, B, C, X(38828), X(59113)}}, {{A, B, C, X(40773), X(55256)}}, {{A, B, C, X(52931), X(61226)}}, {{A, B, C, X(56188), X(56194)}}

X(65261) = X(9)X(662)∩X(33)X(162)

Barycentrics    a*(a^3-a*b^2+b^3+b^2*c-2*c^3+a^2*(-b+c))*(a^3-2*b^3+a^2*(b-c)-a*c^2+b*c^2+c^3) : :
X(65261) = -4*X[142]+5*X[31278], -5*X[18230]+4*X[40539], -X[31297]+5*X[61006]

X(65261) lies on these lines: {7, 8287}, {9, 662}, {33, 162}, {37, 651}, {88, 61179}, {100, 210}, {142, 31278}, {144, 21221}, {190, 319}, {226, 658}, {312, 799}, {518, 37135}, {527, 31175}, {653, 1826}, {655, 63778}, {673, 2786}, {897, 35347}, {1156, 8674}, {1757, 36086}, {1903, 37141}, {2250, 37136}, {2341, 37140}, {4599, 56245}, {4663, 65243}, {5220, 65250}, {6007, 60057}, {9034, 36101}, {14616, 32680}, {17484, 31058}, {17740, 37210}, {17768, 60055}, {17781, 37206}, {18230, 40539}, {24619, 44449}, {24624, 53339}, {27834, 43216}, {31297, 61006}, {36800, 65258}, {37137, 52651}, {37212, 59140}, {41509, 65244}, {54357, 65242}, {56255, 65222}

X(65261) = midpoint of X(i) and X(j) for these {i,j}: {144, 21221}
X(65261) = reflection of X(i) in X(j) for these {i,j}: {7, 8287}, {662, 9}
X(65261) = trilinear pole of line {1, 4041}
X(65261) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17768}, {55, 43066}, {28471, 35066}
X(65261) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 17768}, {223, 43066}
X(65261) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15481)}}, {{A, B, C, X(2), X(29007)}}, {{A, B, C, X(4), X(55965)}}, {{A, B, C, X(7), X(319)}}, {{A, B, C, X(9), X(33)}}, {{A, B, C, X(27), X(35989)}}, {{A, B, C, X(57), X(60942)}}, {{A, B, C, X(63), X(41572)}}, {{A, B, C, X(74), X(52378)}}, {{A, B, C, X(76), X(55991)}}, {{A, B, C, X(80), X(4564)}}, {{A, B, C, X(84), X(9311)}}, {{A, B, C, X(85), X(90)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(103), X(60025)}}, {{A, B, C, X(104), X(1121)}}, {{A, B, C, X(335), X(765)}}, {{A, B, C, X(513), X(3512)}}, {{A, B, C, X(514), X(3065)}}, {{A, B, C, X(516), X(9034)}}, {{A, B, C, X(518), X(1757)}}, {{A, B, C, X(527), X(8674)}}, {{A, B, C, X(671), X(4567)}}, {{A, B, C, X(759), X(47947)}}, {{A, B, C, X(903), X(2991)}}, {{A, B, C, X(1262), X(15337)}}, {{A, B, C, X(1434), X(10308)}}, {{A, B, C, X(1445), X(17781)}}, {{A, B, C, X(1910), X(24479)}}, {{A, B, C, X(2185), X(3255)}}, {{A, B, C, X(2346), X(56037)}}, {{A, B, C, X(2987), X(4570)}}, {{A, B, C, X(2996), X(40436)}}, {{A, B, C, X(3062), X(4416)}}, {{A, B, C, X(3467), X(17758)}}, {{A, B, C, X(3497), X(57666)}}, {{A, B, C, X(4649), X(5220)}}, {{A, B, C, X(4663), X(5223)}}, {{A, B, C, X(5325), X(60937)}}, {{A, B, C, X(6043), X(57690)}}, {{A, B, C, X(6625), X(40430)}}, {{A, B, C, X(7131), X(38271)}}, {{A, B, C, X(7313), X(48074)}}, {{A, B, C, X(7319), X(55986)}}, {{A, B, C, X(8545), X(54357)}}, {{A, B, C, X(8773), X(35162)}}, {{A, B, C, X(9282), X(39979)}}, {{A, B, C, X(9442), X(9503)}}, {{A, B, C, X(9505), X(43751)}}, {{A, B, C, X(10390), X(46971)}}, {{A, B, C, X(10394), X(41228)}}, {{A, B, C, X(10693), X(11608)}}, {{A, B, C, X(15175), X(60083)}}, {{A, B, C, X(15227), X(40076)}}, {{A, B, C, X(15254), X(51294)}}, {{A, B, C, X(17484), X(37787)}}, {{A, B, C, X(21446), X(63167)}}, {{A, B, C, X(26750), X(34919)}}, {{A, B, C, X(32635), X(63191)}}, {{A, B, C, X(36128), X(53686)}}, {{A, B, C, X(36599), X(44178)}}, {{A, B, C, X(36605), X(63163)}}, {{A, B, C, X(37797), X(60935)}}, {{A, B, C, X(39749), X(55989)}}, {{A, B, C, X(40023), X(56220)}}, {{A, B, C, X(43730), X(64980)}}, {{A, B, C, X(54497), X(56320)}}, {{A, B, C, X(55920), X(56039)}}, {{A, B, C, X(55922), X(55925)}}, {{A, B, C, X(56203), X(57826)}}, {{A, B, C, X(56204), X(63384)}}, {{A, B, C, X(64836), X(65003)}}
X(65261) = barycentric product X(i)*X(j) for these (i, j): {1, 35141}, {28471, 75}, {35347, 99}
X(65261) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17768}, {57, 43066}, {28471, 1}, {35141, 75}, {35347, 523}

X(65262) = TRILINEAR POLE OF LINE {1, 4575}

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^6-a^4*(b^2+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4+2*b^2*c^2+c^4))*(a^6-a^4*(2*b^2+c^2)+(-(b^2*c)+c^3)^2+a^2*(b^4+2*b^2*c^2-c^4)) : :

X(65262) lies on these lines: {100, 10420}, {162, 1101}, {190, 18878}, {651, 43755}, {653, 687}, {662, 63827}, {799, 62719}, {897, 36053}, {1577, 65251}, {1821, 20884}, {2986, 24624}, {5504, 37142}, {14910, 37128}, {15328, 60055}, {15421, 60056}, {18750, 36102}, {18879, 37140}, {32708, 36099}, {36095, 62720}, {37202, 57829}, {37219, 40832}, {37220, 46238}

X(65262) = trilinear pole of line {1, 4575}
X(65262) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 21731}, {3, 47236}, {4, 686}, {6, 55121}, {25, 6334}, {74, 55265}, {113, 2433}, {115, 15329}, {125, 61209}, {403, 647}, {512, 3580}, {523, 3003}, {525, 44084}, {526, 56403}, {661, 1725}, {690, 60498}, {924, 62361}, {1637, 14264}, {1986, 14582}, {1989, 60342}, {2088, 41512}, {2315, 24006}, {2489, 62338}, {2501, 13754}, {2623, 63735}, {3049, 44138}, {3124, 61188}, {3569, 52451}, {4705, 18609}, {10097, 12828}, {10420, 39021}, {14270, 57486}, {15475, 34834}, {16221, 32662}, {16237, 20975}, {18314, 61372}, {18781, 58900}, {18808, 47405}, {34212, 53568}, {34952, 52504}, {39170, 47230}, {41079, 51821}
X(65262) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 55121}, {6505, 6334}, {32664, 21731}, {34544, 60342}, {36033, 686}, {36103, 47236}, {36830, 1725}, {39052, 403}, {39054, 3580}
X(65262) = X(i)-cross conjugate of X(j) for these {i, j}: {6149, 24041}
X(65262) = intersection, other than A, B, C, of circumconics {{A, B, C, X(75), X(36105)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(1101), X(52378)}}, {{A, B, C, X(1577), X(2616)}}, {{A, B, C, X(14206), X(36061)}}, {{A, B, C, X(20884), X(46238)}}, {{A, B, C, X(36104), X(36142)}}
X(65262) = barycentric product X(i)*X(j) for these (i, j): {1, 18878}, {48, 57932}, {63, 687}, {162, 57829}, {163, 40832}, {304, 32708}, {1300, 4592}, {1414, 56103}, {1577, 18879}, {2173, 55264}, {2986, 662}, {4575, 65267}, {5504, 811}, {10420, 75}, {14910, 799}, {15328, 24041}, {36034, 52552}, {36053, 99}, {36114, 69}, {43755, 92}, {46254, 61216}, {52505, 65251}
X(65262) = barycentric quotient X(i)/X(j) for these (i, j): {1, 55121}, {19, 47236}, {31, 21731}, {48, 686}, {63, 6334}, {110, 1725}, {162, 403}, {163, 3003}, {662, 3580}, {687, 92}, {811, 44138}, {1101, 15329}, {1300, 24006}, {2173, 55265}, {2617, 63735}, {2986, 1577}, {4556, 18609}, {4575, 13754}, {4592, 62338}, {5504, 656}, {6149, 60342}, {10420, 1}, {14910, 661}, {15328, 1109}, {15421, 20902}, {15454, 36035}, {18878, 75}, {18879, 662}, {24041, 61188}, {32661, 2315}, {32676, 44084}, {32678, 56403}, {32680, 57486}, {32708, 19}, {36034, 14264}, {36053, 523}, {36061, 39170}, {36084, 52451}, {36114, 4}, {36142, 60498}, {36145, 62361}, {40832, 20948}, {43755, 63}, {52505, 63827}, {52557, 2624}, {55264, 33805}, {56103, 4086}, {57829, 14208}, {57932, 1969}, {60035, 2618}, {61216, 3708}, {65251, 52504}

X(65263) = ISOGONAL CONJUGATE OF X(2631)

Barycentrics    a*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4+b^2*c^2-2*c^4+a^2*(-2*b^2+c^2))*(a^4-2*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2)) : :

X(65263) lies on these lines: {27, 65240}, {74, 37142}, {88, 56830}, {92, 36102}, {100, 1304}, {162, 656}, {190, 16077}, {240, 897}, {648, 38340}, {651, 44769}, {653, 15459}, {662, 24018}, {799, 46254}, {823, 1577}, {1156, 14192}, {1492, 32715}, {1494, 37202}, {1821, 2159}, {1955, 35200}, {2173, 2349}, {2394, 60056}, {2642, 36104}, {8749, 37128}, {16080, 24624}, {18808, 60055}, {23692, 23707}, {24001, 32680}, {32695, 36099}, {33805, 37220}, {36085, 62720}, {36097, 36117}

X(65263) = isogonal conjugate of X(2631)
X(65263) = trilinear pole of line {1, 162}
X(65263) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2631}, {2, 9409}, {3, 1637}, {4, 1636}, {6, 9033}, {25, 41077}, {30, 647}, {48, 36035}, {54, 14391}, {64, 14345}, {65, 14395}, {66, 14396}, {68, 14397}, {69, 14398}, {71, 11125}, {72, 14399}, {73, 14400}, {74, 14401}, {112, 1650}, {113, 61216}, {125, 2420}, {133, 2430}, {184, 41079}, {186, 18558}, {265, 52743}, {476, 47414}, {512, 11064}, {520, 1990}, {523, 3284}, {525, 1495}, {526, 56399}, {656, 2173}, {684, 35906}, {686, 15454}, {810, 14206}, {822, 1784}, {878, 51389}, {1304, 39008}, {1511, 14582}, {1568, 2623}, {2081, 64228}, {2407, 20975}, {2433, 16163}, {2435, 6793}, {2501, 51394}, {2632, 56829}, {2682, 65321}, {3049, 3260}, {3163, 14380}, {3258, 32662}, {3265, 14581}, {3267, 9407}, {3269, 4240}, {3569, 35912}, {5504, 55265}, {5642, 10097}, {5664, 52153}, {6587, 11589}, {8552, 14583}, {8611, 51654}, {9406, 14208}, {9408, 34767}, {9411, 60872}, {9517, 60496}, {13857, 30491}, {14270, 57482}, {14499, 52131}, {14500, 52132}, {14919, 58346}, {15328, 47405}, {15451, 43768}, {15526, 23347}, {16080, 58345}, {16186, 41392}, {16240, 62665}, {18557, 34397}, {18653, 55230}, {18877, 58263}, {20123, 58900}, {23286, 52945}, {32320, 52661}, {32661, 58261}, {32663, 55141}, {34570, 57295}, {35071, 58071}, {36298, 60009}, {36299, 60010}, {38956, 61215}, {39176, 43083}, {39201, 46106}, {39469, 60869}, {40352, 52624}, {42293, 43752}, {43701, 47433}, {46425, 51346}, {47228, 53235}, {47230, 51254}, {50433, 62172}, {51382, 55234}, {51420, 55232}, {52955, 57109}
X(65263) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 2631}, {9, 9033}, {1249, 36035}, {6505, 41077}, {9410, 14208}, {32664, 9409}, {34591, 1650}, {36033, 1636}, {36103, 1637}, {36896, 656}, {39052, 30}, {39054, 11064}, {39062, 14206}, {40596, 2173}, {40602, 14395}, {62605, 41079}, {62606, 24018}
X(65263) = X(i)-cross conjugate of X(j) for these {i, j}: {1725, 24041}, {2173, 24000}, {2631, 1}, {32678, 36114}, {32679, 92}, {56829, 162}
X(65263) = pole of line {2631, 14395} with respect to the Stammler hyperbola
X(65263) = intersection, other than A, B, C, of circumconics {{A, B, C, X(19), X(36104)}}, {{A, B, C, X(27), X(37966)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(240), X(62720)}}, {{A, B, C, X(656), X(1577)}}, {{A, B, C, X(2173), X(32678)}}, {{A, B, C, X(5379), X(24000)}}, {{A, B, C, X(24001), X(36114)}}, {{A, B, C, X(35342), X(61236)}}, {{A, B, C, X(36046), X(36142)}}, {{A, B, C, X(40116), X(57390)}}, {{A, B, C, X(40395), X(65331)}}
X(65263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {656, 2633, 24000}

X(65264) = TRILINEAR POLE OF LINE {1, 4560}

Barycentrics    (a+b)*(a+c)*(-2*a^2*b^2+a^3*(b+c)+b*c*(b^2-c^2)+a*(b^3-c^3))*(-(b^3*c)-2*a^2*c^2+b*c^3+a^3*(b+c)+a*(-b^3+c^3)) : :

X(65264) lies on these lines: {2, 65256}, {6, 26856}, {86, 651}, {100, 333}, {162, 14004}, {190, 314}, {261, 572}, {286, 653}, {655, 14616}, {658, 57785}, {660, 36800}, {799, 14829}, {897, 60574}, {2250, 64824}, {11998, 65275}, {14534, 36098}, {29437, 29490}, {32010, 37137}, {37870, 65225}, {40412, 65217}

X(65264) = trilinear pole of line {1, 4560}
X(65264) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 20718}, {37, 20470}, {42, 20367}, {213, 20347}, {647, 4250}, {1824, 20744}, {1918, 20448}, {18785, 39046}
X(65264) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 20718}, {6626, 20347}, {34021, 20448}, {39052, 4250}, {40589, 20470}, {40592, 20367}, {40620, 20520}
X(65264) = X(i)-cross conjugate of X(j) for these {i, j}: {3286, 86}, {13576, 18827}, {53343, 99}
X(65264) = pole of line {20470, 39046} with respect to the Stammler hyperbola
X(65264) = pole of line {20347, 20367} with respect to the Wallace hyperbola
X(65264) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4043)}}, {{A, B, C, X(6), X(572)}}, {{A, B, C, X(27), X(1171)}}, {{A, B, C, X(81), X(29767)}}, {{A, B, C, X(86), X(261)}}, {{A, B, C, X(88), X(100)}}, {{A, B, C, X(1029), X(56246)}}, {{A, B, C, X(1150), X(46922)}}, {{A, B, C, X(1222), X(40827)}}, {{A, B, C, X(1246), X(60167)}}, {{A, B, C, X(1434), X(40408)}}, {{A, B, C, X(1751), X(39981)}}, {{A, B, C, X(2051), X(45108)}}, {{A, B, C, X(2669), X(14195)}}, {{A, B, C, X(3512), X(10566)}}, {{A, B, C, X(4251), X(16552)}}, {{A, B, C, X(15232), X(60320)}}, {{A, B, C, X(15320), X(60172)}}, {{A, B, C, X(17206), X(57668)}}, {{A, B, C, X(29437), X(32911)}}, {{A, B, C, X(31618), X(35144)}}, {{A, B, C, X(32008), X(32014)}}, {{A, B, C, X(36807), X(40017)}}, {{A, B, C, X(38955), X(54497)}}, {{A, B, C, X(39971), X(60615)}}, {{A, B, C, X(40433), X(64984)}}, {{A, B, C, X(40435), X(42335)}}, {{A, B, C, X(47947), X(60135)}}, {{A, B, C, X(56853), X(62749)}}, {{A, B, C, X(57536), X(57554)}}, {{A, B, C, X(57719), X(57905)}}, {{A, B, C, X(57980), X(62723)}}
X(65264) = barycentric product X(i)*X(j) for these (i, j): {4560, 53644}, {53707, 75}, {60574, 99}
X(65264) = barycentric quotient X(i)/X(j) for these (i, j): {1, 20718}, {58, 20470}, {81, 20367}, {86, 20347}, {162, 4250}, {274, 20448}, {1790, 20744}, {3286, 39046}, {7192, 20520}, {53644, 4552}, {53707, 1}, {60574, 523}

X(65265) = TRILINEAR POLE OF LINE {2, 107}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(a^6-a^4*b^2+b^6+b^2*c^4-2*c^6+a^2*(-b^4+c^4))*(a^6-2*b^6-a^4*c^2+b^4*c^2+c^6+a^2*(b^4-c^4)) : :

X(65265) lies on the Steiner circumellipse and on these lines: {30, 14944}, {99, 20580}, {107, 44552}, {190, 36092}, {232, 57761}, {290, 9476}, {297, 35140}, {393, 35088}, {525, 6529}, {648, 8057}, {671, 34170}, {1249, 46097}, {1297, 54973}, {1494, 6330}, {2404, 2419}, {2409, 2966}, {2416, 32646}, {2435, 53205}, {3543, 52485}, {5641, 56601}, {6528, 34538}, {6587, 44181}, {8767, 35145}, {14638, 57574}, {15352, 65266}, {16077, 43673}, {16096, 44334}, {23590, 33294}, {37200, 39265}, {54988, 64975}

X(65265) = reflection of X(i) in X(j) for these {i,j}: {16096, 44334}
X(65265) = isotomic conjugate of X(39473)
X(65265) = trilinear pole of line {2, 107}
X(65265) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 39473}, {441, 810}, {520, 2312}, {647, 8766}, {656, 8779}, {822, 1503}, {2409, 37754}, {24018, 42671}, {24024, 35071}
X(65265) = X(i)-vertex conjugate of X(j) for these {i, j}: {394, 32725}
X(65265) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 39473}, {107, 63791}, {122, 57296}, {23976, 60341}, {36901, 58258}, {39052, 8766}, {39062, 441}, {40596, 8779}
X(65265) = X(i)-cross conjugate of X(j) for these {i, j}: {297, 23582}, {520, 57761}, {1503, 44181}, {23977, 107}, {33294, 57549}, {39473, 2}, {43673, 6330}, {61189, 35140}
X(65265) = pole of line {61189, 65265} with respect to the Steiner circumellipse
X(65265) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(297), X(685)}}, {{A, B, C, X(394), X(6080)}}, {{A, B, C, X(459), X(22239)}}, {{A, B, C, X(525), X(2416)}}, {{A, B, C, X(2867), X(16096)}}, {{A, B, C, X(4240), X(44216)}}, {{A, B, C, X(6529), X(32646)}}, {{A, B, C, X(7473), X(62955)}}, {{A, B, C, X(9476), X(44770)}}, {{A, B, C, X(15459), X(23582)}}, {{A, B, C, X(16230), X(35088)}}, {{A, B, C, X(32649), X(43717)}}, {{A, B, C, X(32725), X(56364)}}, {{A, B, C, X(47105), X(56601)}}

X(65266) = ISOTOMIC CONJUGATE OF X(8673)

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-c^4)*(a^4-b^4+c^4) : :
X(65266) = -3*X[2]+2*X[55047]

X(65266) lies on the Steiner circumellipse and on these lines: {2, 55047}, {4, 40421}, {30, 16097}, {66, 290}, {69, 56599}, {76, 58075}, {99, 1289}, {112, 53657}, {264, 35140}, {315, 59432}, {427, 46241}, {648, 44766}, {670, 61181}, {671, 43678}, {850, 32713}, {877, 46134}, {1494, 18018}, {2966, 41679}, {3228, 13854}, {4577, 6331}, {5641, 44138}, {14376, 54973}, {15352, 65265}, {17984, 34138}, {41677, 65271}, {44134, 54988}, {51843, 60495}, {54976, 55560}

X(65266) = isotomic conjugate of X(8673)
X(65266) = anticomplement of X(55047)
X(65266) = trilinear pole of line {2, 1235}
X(65266) = X(i)-isoconjugate-of-X(j) for these {i, j}: {22, 810}, {31, 8673}, {48, 2485}, {72, 21122}, {163, 38356}, {206, 656}, {525, 17453}, {560, 57069}, {647, 2172}, {798, 20806}, {822, 8743}, {905, 21034}, {1577, 22075}, {1760, 3049}, {1924, 34254}, {1973, 58359}, {2156, 57202}, {2159, 14396}, {2200, 16757}, {4456, 22383}, {4548, 51664}, {7251, 8611}, {9247, 33294}, {14208, 20968}, {17186, 55232}, {17409, 24018}, {18187, 32739}, {23995, 55273}, {32676, 47413}, {52430, 59932}
X(65266) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 8673}, {115, 38356}, {1249, 2485}, {3163, 14396}, {6337, 58359}, {6374, 57069}, {9428, 34254}, {15526, 47413}, {18314, 55273}, {31998, 20806}, {36830, 10316}, {36901, 127}, {39052, 2172}, {39062, 22}, {40596, 206}, {40619, 18187}, {55047, 55047}, {62576, 33294}
X(65266) = X(i)-cross conjugate of X(j) for these {i, j}: {66, 44183}, {112, 6331}, {850, 40421}, {1632, 30450}, {3267, 264}, {7391, 23582}, {8673, 2}, {18656, 55346}, {46151, 648}, {51884, 44181}, {64023, 250}
X(65266) = pole of line {46151, 65266} with respect to the Steiner circumellipse
X(65266) = pole of line {8673, 58359} with respect to the Wallace hyperbola
X(65266) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(32713)}}, {{A, B, C, X(69), X(46639)}}, {{A, B, C, X(95), X(30441)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(18125)}}, {{A, B, C, X(112), X(11605)}}, {{A, B, C, X(264), X(15352)}}, {{A, B, C, X(317), X(877)}}, {{A, B, C, X(933), X(44770)}}, {{A, B, C, X(2867), X(16039)}}, {{A, B, C, X(4240), X(31133)}}, {{A, B, C, X(8673), X(55047)}}, {{A, B, C, X(22456), X(30450)}}, {{A, B, C, X(35360), X(59100)}}, {{A, B, C, X(47138), X(53569)}}

X(65267) = ISOTOMIC CONJUGATE OF X(13754)

Barycentrics    b^2*c^2*(-a^2+b^2-c^2)*(a^2+b^2-c^2)*(a^6-a^4*(b^2+2*c^2)+(b^3-b*c^2)^2+a^2*(-b^4+2*b^2*c^2+c^4))*(a^6-a^4*(2*b^2+c^2)+(-(b^2*c)+c^3)^2+a^2*(b^4+2*b^2*c^2-c^4)) : :

X(65267) lies on the Steiner circumellipse and on these lines: {4, 65284}, {69, 46134}, {76, 58081}, {97, 52505}, {99, 264}, {290, 15328}, {315, 56684}, {317, 6528}, {340, 18817}, {648, 1993}, {664, 57809}, {670, 18022}, {687, 2966}, {892, 46111}, {2970, 36207}, {3260, 18878}, {4577, 46104}, {5408, 54030}, {5409, 54031}, {5504, 8795}, {6331, 53192}, {8749, 46106}, {14615, 46746}, {15421, 54973}, {15454, 54100}, {16077, 40423}, {20572, 46139}, {35136, 44133}, {40074, 65277}, {40427, 54959}, {46927, 47269}, {54952, 56103}

X(65267) = isotomic conjugate of X(13754)
X(65267) = trilinear pole of line {2, 14618}
X(65267) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 2315}, {31, 13754}, {48, 3003}, {163, 686}, {184, 1725}, {255, 44084}, {403, 52430}, {560, 62338}, {563, 62361}, {810, 15329}, {822, 61209}, {2159, 47405}, {2200, 18609}, {3580, 9247}, {4575, 21731}, {44706, 61372}, {62267, 63735}
X(65267) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 13754}, {9, 2315}, {115, 686}, {136, 21731}, {1249, 3003}, {3163, 47405}, {6374, 62338}, {6523, 44084}, {34834, 34333}, {36901, 6334}, {39062, 15329}, {62576, 3580}, {62605, 1725}, {62606, 53785}
X(65267) = X(i)-cross conjugate of X(j) for these {i, j}: {69, 57760}, {323, 276}, {2986, 40832}, {3260, 264}, {13754, 2}, {15328, 687}, {15454, 40427}, {18808, 46456}, {44427, 6331}, {55121, 30450}, {56577, 40423}, {60035, 2986}
X(65267) = pole of line {686, 21731} with respect to the polar circle
X(65267) = pole of line {13754, 34333} with respect to the Wallace hyperbola
X(65267) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(378)}}, {{A, B, C, X(69), X(97)}}, {{A, B, C, X(74), X(39985)}}, {{A, B, C, X(94), X(3260)}}, {{A, B, C, X(95), X(801)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(250), X(57732)}}, {{A, B, C, X(253), X(55031)}}, {{A, B, C, X(264), X(2052)}}, {{A, B, C, X(265), X(8431)}}, {{A, B, C, X(297), X(46239)}}, {{A, B, C, X(325), X(44375)}}, {{A, B, C, X(328), X(850)}}, {{A, B, C, X(895), X(35098)}}, {{A, B, C, X(1989), X(15928)}}, {{A, B, C, X(2986), X(40423)}}, {{A, B, C, X(5392), X(57819)}}, {{A, B, C, X(5504), X(60035)}}, {{A, B, C, X(5890), X(11459)}}, {{A, B, C, X(5891), X(9730)}}, {{A, B, C, X(5892), X(10170)}}, {{A, B, C, X(6063), X(57885)}}, {{A, B, C, X(13582), X(57766)}}, {{A, B, C, X(14910), X(15328)}}, {{A, B, C, X(14919), X(43767)}}, {{A, B, C, X(15454), X(58942)}}, {{A, B, C, X(16080), X(58016)}}, {{A, B, C, X(18848), X(57677)}}, {{A, B, C, X(34384), X(54774)}}, {{A, B, C, X(36889), X(44176)}}, {{A, B, C, X(43710), X(56307)}}, {{A, B, C, X(44133), X(54412)}}, {{A, B, C, X(55560), X(55562)}}, {{A, B, C, X(57765), X(57894)}}, {{A, B, C, X(57817), X(65084)}}

X(65268) = TRILINEAR POLE OF LINE {2, 112}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6-a^4*b^2+b^6-b^2*c^4-a^2*(b^2-c^2)^2)*(a^6-a^4*c^2-b^4*c^2+c^6-a^2*(b^2-c^2)^2) : :

X(65268) lies on the Steiner circumellipse and on these lines: {99, 250}, {190, 36095}, {290, 685}, {316, 61489}, {317, 5641}, {340, 35140}, {648, 23964}, {668, 5379}, {670, 18020}, {671, 5523}, {850, 32713}, {877, 18878}, {892, 61181}, {1304, 1494}, {2419, 32649}, {2485, 44183}, {2966, 16237}, {3267, 40596}, {4580, 53657}, {6528, 32230}, {10313, 52513}, {15384, 53639}, {18823, 51823}, {18876, 54973}, {32715, 53331}, {35179, 52913}, {36823, 53200}, {44146, 46140}, {52916, 65269}, {54412, 58078}

X(65268) = isogonal conjugate of X(42665)
X(65268) = trilinear pole of line {2, 112}
X(65268) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42665}, {48, 47138}, {228, 21109}, {647, 18669}, {656, 2393}, {798, 62382}, {810, 858}, {822, 5523}, {2631, 60499}, {2632, 46592}, {3049, 20884}, {3708, 61198}, {14580, 24018}, {21017, 22383}
X(65268) = X(i)-vertex conjugate of X(j) for these {i, j}: {69, 32715}
X(65268) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 42665}, {1249, 47138}, {31998, 62382}, {36830, 14961}, {39052, 18669}, {39062, 858}, {40596, 2393}, {62597, 38971}
X(65268) = X(i)-cross conjugate of X(j) for these {i, j}: {23, 23582}, {935, 65350}, {2393, 44183}, {37784, 4590}, {44146, 18020}
X(65268) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(46619)}}, {{A, B, C, X(69), X(2867)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(250), X(685)}}, {{A, B, C, X(264), X(15459)}}, {{A, B, C, X(687), X(22456)}}, {{A, B, C, X(850), X(2419)}}, {{A, B, C, X(877), X(16237)}}, {{A, B, C, X(935), X(5523)}}, {{A, B, C, X(1990), X(47150)}}, {{A, B, C, X(4235), X(37855)}}, {{A, B, C, X(4240), X(7426)}}, {{A, B, C, X(10603), X(53944)}}, {{A, B, C, X(17932), X(44769)}}, {{A, B, C, X(20031), X(32085)}}, {{A, B, C, X(32649), X(32713)}}, {{A, B, C, X(32715), X(57388)}}, {{A, B, C, X(41511), X(65306)}}, {{A, B, C, X(43187), X(54108)}}, {{A, B, C, X(51862), X(58070)}}, {{A, B, C, X(53708), X(56307)}}

X(65269) = TRILINEAR POLE OF LINE {2, 339}

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-a^2*b^2+b^4-c^4)*(a^4-b^4-a^2*c^2+c^4) : :
X(65269) = -3*X[2]+2*X[55048]

X(65269) lies on the Steiner circumellipse and on these lines: {2, 55048}, {67, 290}, {76, 39269}, {99, 935}, {250, 23285}, {264, 5641}, {316, 11605}, {648, 850}, {671, 44146}, {877, 35139}, {1494, 10989}, {2966, 14590}, {3228, 8791}, {3260, 35140}, {4577, 18020}, {6331, 35138}, {14221, 46134}, {14970, 65351}, {16083, 53229}, {18823, 57496}, {22456, 64775}, {34897, 54973}, {35142, 44138}, {44155, 53200}, {44183, 53657}, {52916, 65268}

X(65269) = isogonal conjugate of X(42659)
X(65269) = isotomic conjugate of X(9517)
X(65269) = anticomplement of X(55048)
X(65269) = trilinear pole of line {2, 339}
X(65269) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42659}, {23, 810}, {31, 9517}, {48, 2492}, {656, 18374}, {661, 10317}, {798, 22151}, {822, 8744}, {1924, 37804}, {2157, 57203}, {3049, 16568}, {9247, 9979}, {36142, 47415}
X(65269) = X(i)-vertex conjugate of X(j) for these {i, j}: {1485, 46456}
X(65269) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 9517}, {3, 42659}, {1249, 2492}, {9428, 37804}, {14357, 42665}, {15900, 647}, {23992, 47415}, {31998, 22151}, {36830, 10317}, {36901, 62563}, {39062, 23}, {40583, 57203}, {40596, 18374}, {55048, 55048}, {62576, 9979}, {62595, 33752}, {62613, 16165}
X(65269) = X(i)-cross conjugate of X(j) for these {i, j}: {935, 65356}, {4235, 6331}, {5189, 23582}, {9019, 250}, {9517, 2}, {18657, 55346}, {19577, 44168}, {35522, 264}, {61181, 648}
X(65269) = pole of line {61181, 65269} with respect to the Steiner circumellipse
X(65269) = pole of line {9517, 16165} with respect to the Wallace hyperbola
X(65269) = pole of line {57426, 62594} with respect to the dual conic of Stammler hyperbola
X(65269) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(7482)}}, {{A, B, C, X(66), X(2715)}}, {{A, B, C, X(67), X(36884)}}, {{A, B, C, X(69), X(44769)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(36828)}}, {{A, B, C, X(264), X(22456)}}, {{A, B, C, X(316), X(691)}}, {{A, B, C, X(317), X(14221)}}, {{A, B, C, X(340), X(877)}}, {{A, B, C, X(685), X(30716)}}, {{A, B, C, X(850), X(3267)}}, {{A, B, C, X(2867), X(60053)}}, {{A, B, C, X(3260), X(30737)}}, {{A, B, C, X(4240), X(10989)}}, {{A, B, C, X(9060), X(41896)}}, {{A, B, C, X(9517), X(55048)}}, {{A, B, C, X(10420), X(13485)}}, {{A, B, C, X(14560), X(15321)}}, {{A, B, C, X(16083), X(44155)}}, {{A, B, C, X(18020), X(44183)}}, {{A, B, C, X(39193), X(44768)}}, {{A, B, C, X(40423), X(57761)}}, {{A, B, C, X(44146), X(59762)}}, {{A, B, C, X(56473), X(65321)}}
X(65269) = barycentric product X(i)*X(j) for these (i, j): {69, 65356}, {76, 935}, {670, 8791}, {2157, 57968}, {6331, 67}, {14357, 59762}, {17708, 264}, {18019, 648}, {18023, 60503}, {34897, 6528}, {46105, 99}, {46140, 60507}, {57476, 65268}, {57496, 892}
X(65269) = barycentric quotient X(i)/X(j) for these (i, j): {2, 9517}, {4, 2492}, {6, 42659}, {23, 57203}, {67, 647}, {99, 22151}, {107, 8744}, {110, 10317}, {112, 18374}, {264, 9979}, {297, 33752}, {648, 23}, {670, 37804}, {690, 47415}, {811, 16568}, {850, 62563}, {892, 57481}, {935, 6}, {2157, 810}, {2407, 16165}, {2409, 28343}, {3455, 3049}, {4235, 6593}, {4240, 52951}, {4558, 58357}, {6331, 316}, {6528, 37765}, {8791, 512}, {9517, 55048}, {10415, 10097}, {10511, 30491}, {11605, 2485}, {16081, 52076}, {16237, 12824}, {17708, 3}, {17983, 10561}, {18019, 525}, {18020, 52630}, {23582, 52916}, {34897, 520}, {35522, 62594}, {39269, 47138}, {41676, 9019}, {44129, 21205}, {44146, 18311}, {44766, 54060}, {46105, 523}, {46456, 52449}, {52916, 36415}, {57496, 690}, {57968, 20944}, {58980, 57655}, {59762, 52551}, {60496, 9409}, {60502, 55142}, {60503, 187}, {60507, 2393}, {61181, 64646}, {65266, 37801}, {65268, 60002}, {65350, 14246}, {65356, 4}

X(65270) = TRILINEAR POLE OF LINE {2, 280}

Barycentrics    (a-b)*b*(a-c)*c*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2) : :

X(65270) lies on the Steiner circumellipse and on these lines: {92, 34393}, {99, 40117}, {189, 18816}, {190, 65213}, {264, 46137}, {271, 54966}, {282, 60046}, {290, 1903}, {309, 18025}, {648, 13138}, {653, 53642}, {664, 6335}, {823, 53639}, {903, 64988}, {1121, 7020}, {2358, 35159}, {2481, 7003}, {2966, 32652}, {3226, 7129}, {3227, 40836}, {4391, 54240}, {4569, 46404}, {7008, 60014}, {7017, 44189}, {7151, 18825}, {31623, 56944}, {35145, 39130}, {37141, 54953}, {40717, 53228}, {52389, 54973}, {54989, 57783}, {65162, 65290}

X(65270) = isotomic conjugate of X(64885)
X(65270) = trilinear pole of line {2, 280}
X(65270) = X(i)-isoconjugate-of-X(j) for these {i, j}: {25, 57233}, {31, 64885}, {40, 22383}, {48, 6129}, {56, 10397}, {184, 14837}, {198, 1459}, {208, 36054}, {221, 652}, {223, 1946}, {521, 2199}, {577, 54239}, {603, 14298}, {604, 57101}, {647, 2360}, {649, 7078}, {650, 7114}, {663, 7011}, {667, 64082}, {810, 1817}, {822, 3194}, {905, 2187}, {1397, 57245}, {1402, 57213}, {1415, 53557}, {1437, 55212}, {1461, 47432}, {1819, 7180}, {2331, 23224}, {3049, 8822}, {3063, 7013}, {3195, 4091}, {3209, 57241}, {6611, 57108}, {7117, 57118}, {8058, 52411}, {9247, 17896}, {32643, 57291}, {32660, 38357}, {32674, 55044}, {39201, 41083}, {43924, 55111}, {52430, 59935}
X(65270) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 10397}, {2, 64885}, {1146, 53557}, {1249, 6129}, {3161, 57101}, {3341, 652}, {5375, 7078}, {6505, 57233}, {6631, 64082}, {7952, 14298}, {10001, 7013}, {35072, 55044}, {35508, 47432}, {39052, 2360}, {39053, 223}, {39060, 347}, {39062, 1817}, {40605, 57213}, {40624, 16596}, {62576, 17896}, {62585, 57245}, {62605, 14837}
X(65270) = X(i)-cross conjugate of X(j) for these {i, j}: {653, 6335}, {962, 55346}, {4391, 34404}, {4397, 264}, {6332, 31623}, {64885, 2}
X(65270) = pole of line {57213, 64885} with respect to the Wallace hyperbola
X(65270) = pole of line {18750, 56595} with respect to the dual conic of Feuerbach hyperbola
X(65270) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(32714)}}, {{A, B, C, X(8), X(56235)}}, {{A, B, C, X(92), X(24035)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(189), X(37141)}}, {{A, B, C, X(286), X(52919)}}, {{A, B, C, X(651), X(43346)}}, {{A, B, C, X(823), X(13149)}}, {{A, B, C, X(1903), X(32652)}}, {{A, B, C, X(2994), X(46640)}}, {{A, B, C, X(6335), X(46404)}}

X(65271) = ISOGONAL CONJUGATE OF X(3288)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(-b^4+b^2*c^2+a^2*(b^2+2*c^2))*(c^2*(b^2-c^2)+a^2*(2*b^2+c^2)) : :

X(65271) lies on the Steiner circumellipse and on these lines: {2, 290}, {6, 43664}, {30, 39682}, {76, 14252}, {99, 1625}, {110, 2966}, {112, 18831}, {190, 65252}, {193, 51338}, {194, 51997}, {262, 381}, {263, 1992}, {376, 54032}, {519, 53194}, {523, 53199}, {524, 46142}, {536, 53198}, {538, 53197}, {542, 9513}, {574, 48992}, {599, 1494}, {648, 1634}, {662, 65291}, {668, 42717}, {670, 2396}, {850, 36886}, {903, 60679}, {1975, 60601}, {1987, 35937}, {1989, 42300}, {2186, 18827}, {2407, 35138}, {3225, 3511}, {3226, 41629}, {3227, 24473}, {3402, 18826}, {4226, 35178}, {4558, 4577}, {5118, 48961}, {5641, 7840}, {5649, 40866}, {6331, 31174}, {6528, 41676}, {6776, 40803}, {7788, 35140}, {9766, 35142}, {10706, 53201}, {11054, 38889}, {11794, 63786}, {12177, 53865}, {12215, 57259}, {14559, 54959}, {14568, 63711}, {14607, 46144}, {14970, 36214}, {15352, 54950}, {16712, 43093}, {18829, 52631}, {22329, 35146}, {23342, 35179}, {23878, 53196}, {31296, 63784}, {32734, 65273}, {32833, 46140}, {34384, 40588}, {35136, 57150}, {35165, 37792}, {35935, 60046}, {35941, 54976}, {37785, 60015}, {37786, 60016}, {39291, 45329}, {41677, 65266}, {42371, 52608}, {43188, 44560}, {51224, 57268}, {51880, 54033}, {52926, 63741}, {54975, 64714}

X(65271) = midpoint of X(i) and X(j) for these {i,j}: {2, 39355}
X(65271) = reflection of X(i) in X(j) for these {i,j}: {2, 11672}, {290, 2}
X(65271) = isogonal conjugate of X(3288)
X(65271) = isotomic conjugate of X(23878)
X(65271) = trilinear pole of line {2, 51}
X(65271) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3288}, {31, 23878}, {182, 661}, {183, 798}, {458, 810}, {512, 52134}, {513, 60726}, {647, 60685}, {649, 60723}, {656, 10311}, {662, 6784}, {667, 60737}, {669, 3403}, {822, 33971}, {1577, 34396}, {1580, 39680}, {1821, 9420}, {1919, 42711}, {1924, 20023}, {2616, 59208}, {2624, 56401}, {3709, 60716}, {9417, 63746}, {14096, 55240}, {36132, 62596}, {39201, 51315}, {59804, 65252}
X(65271) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 2966}, {18315, 32696}, {35278, 65310}
X(65271) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 23878}, {3, 3288}, {511, 33569}, {1084, 6784}, {5375, 60723}, {6631, 60737}, {9296, 42711}, {9428, 20023}, {23967, 45321}, {31998, 183}, {36830, 182}, {38997, 59804}, {39009, 62596}, {39026, 60726}, {39052, 60685}, {39054, 52134}, {39058, 63746}, {39062, 458}, {39092, 39680}, {40596, 10311}, {40601, 9420}, {62596, 39009}, {62613, 51372}
X(65271) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6037, 39681}, {53196, 63741}
X(65271) = X(i)-cross conjugate of X(j) for these {i, j}: {647, 40803}, {1352, 18020}, {7774, 4590}, {22240, 250}, {23878, 2}, {26714, 65349}, {32451, 34537}, {33569, 511}, {45907, 6}, {52631, 42299}, {54257, 3}, {63741, 53196}
X(65271) = pole of line {35278, 39681} with respect to the circumcircle
X(65271) = pole of line {183, 1350} with respect to the Kiepert parabola
X(65271) = pole of line {52926, 63741} with respect to the Steiner circumellipse
X(65271) = pole of line {45319, 45336} with respect to the Steiner inellipse
X(65271) = pole of line {3288, 23878} with respect to the Wallace hyperbola
X(65271) = pole of line {1007, 47738} with respect to the dual conic of Jerabek hyperbola
X(65271) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(110)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(112), X(1625)}}, {{A, B, C, X(308), X(39632)}}, {{A, B, C, X(381), X(4235)}}, {{A, B, C, X(523), X(46040)}}, {{A, B, C, X(524), X(2782)}}, {{A, B, C, X(538), X(34383)}}, {{A, B, C, X(542), X(40866)}}, {{A, B, C, X(599), X(2407)}}, {{A, B, C, X(647), X(31174)}}, {{A, B, C, X(687), X(59098)}}, {{A, B, C, X(691), X(18818)}}, {{A, B, C, X(827), X(30450)}}, {{A, B, C, X(850), X(36900)}}, {{A, B, C, X(907), X(1634)}}, {{A, B, C, X(925), X(42396)}}, {{A, B, C, X(1289), X(16813)}}, {{A, B, C, X(1296), X(6094)}}, {{A, B, C, X(1992), X(23342)}}, {{A, B, C, X(2574), X(50945)}}, {{A, B, C, X(2575), X(50944)}}, {{A, B, C, X(2799), X(46245)}}, {{A, B, C, X(3565), X(13578)}}, {{A, B, C, X(4226), X(52282)}}, {{A, B, C, X(4554), X(8690)}}, {{A, B, C, X(4573), X(65059)}}, {{A, B, C, X(4603), X(62534)}}, {{A, B, C, X(4609), X(58118)}}, {{A, B, C, X(4611), X(41677)}}, {{A, B, C, X(5467), X(32447)}}, {{A, B, C, X(5468), X(11163)}}, {{A, B, C, X(7473), X(40885)}}, {{A, B, C, X(7788), X(34211)}}, {{A, B, C, X(7840), X(14999)}}, {{A, B, C, X(7953), X(18315)}}, {{A, B, C, X(7954), X(38342)}}, {{A, B, C, X(9069), X(9133)}}, {{A, B, C, X(9087), X(32729)}}, {{A, B, C, X(9100), X(62672)}}, {{A, B, C, X(11058), X(63466)}}, {{A, B, C, X(11636), X(46456)}}, {{A, B, C, X(12074), X(44769)}}, {{A, B, C, X(14607), X(22329)}}, {{A, B, C, X(15459), X(30247)}}, {{A, B, C, X(16081), X(53937)}}, {{A, B, C, X(18800), X(48947)}}, {{A, B, C, X(26714), X(32716)}}, {{A, B, C, X(30476), X(44560)}}, {{A, B, C, X(31296), X(63786)}}, {{A, B, C, X(34898), X(58090)}}, {{A, B, C, X(36885), X(46807)}}, {{A, B, C, X(39681), X(42299)}}, {{A, B, C, X(43351), X(44766)}}, {{A, B, C, X(43535), X(53603)}}, {{A, B, C, X(44061), X(54899)}}, {{A, B, C, X(46639), X(58116)}}, {{A, B, C, X(52917), X(55252)}}, {{A, B, C, X(56008), X(59100)}}, {{A, B, C, X(58975), X(65306)}}
X(65271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 26714, 39681}, {11672, 39355, 290}

X(65272) = ISOTOMIC CONJUGATE OF X(39469)

Barycentrics    (a-b)*b^4*(a+b)*(a-c)*c^4*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-a^2*c^2-b^2*c^2)*(a^4-a^2*b^2-b^2*c^2+c^4) : :

X(65272) lies on the Steiner circumellipse and on these lines: {4, 53197}, {76, 53200}, {99, 22089}, {264, 46142}, {286, 53198}, {648, 2451}, {671, 59762}, {685, 4577}, {877, 35362}, {886, 53149}, {1494, 18024}, {1502, 46145}, {2966, 41174}, {3225, 6531}, {3228, 16081}, {5641, 18022}, {6331, 31174}, {6394, 54976}, {6528, 16229}, {12833, 46134}, {14618, 53230}, {17932, 18831}, {18826, 36120}, {32696, 33514}, {35145, 46273}, {35151, 57796}, {39266, 46140}, {43665, 53202}, {44129, 53194}, {44132, 53229}, {54973, 57799}, {57968, 65289}

X(65272) = isotomic conjugate of X(39469)
X(65272) = trilinear pole of line {2, 6331}
X(65272) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 39469}, {48, 2491}, {237, 810}, {240, 58310}, {560, 684}, {647, 9417}, {656, 9418}, {798, 3289}, {822, 2211}, {878, 42075}, {1755, 3049}, {1917, 6333}, {1919, 42702}, {1924, 36212}, {3569, 9247}, {4575, 58260}, {17994, 52430}, {34859, 37754}, {39201, 57653}
X(65272) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 39469}, {136, 58260}, {1249, 2491}, {6374, 684}, {9296, 42702}, {9428, 36212}, {31998, 3289}, {35078, 47418}, {36899, 3049}, {36901, 41172}, {39052, 9417}, {39058, 647}, {39062, 237}, {39085, 58310}, {40596, 9418}, {62576, 3569}, {62595, 58262}
X(65272) = X(i)-cross conjugate of X(j) for these {i, j}: {290, 41174}, {850, 57541}, {877, 6331}, {11442, 57562}, {14295, 264}, {14957, 23582}, {30737, 57556}, {39469, 2}, {51481, 44168}, {53149, 16081}, {53331, 276}, {53345, 308}, {53371, 30450}
X(65272) = pole of line {3978, 16089} with respect to the dual conic of Jerabek hyperbola
X(65272) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(317), X(12833)}}, {{A, B, C, X(476), X(44176)}}, {{A, B, C, X(689), X(42405)}}, {{A, B, C, X(805), X(52446)}}, {{A, B, C, X(879), X(2451)}}, {{A, B, C, X(4576), X(35319)}}, {{A, B, C, X(10425), X(41208)}}, {{A, B, C, X(14295), X(16230)}}, {{A, B, C, X(31174), X(63746)}}, {{A, B, C, X(32729), X(55028)}}, {{A, B, C, X(39266), X(61181)}}, {{A, B, C, X(41174), X(59762)}}, {{A, B, C, X(41209), X(44770)}}

X(65273) = TRILINEAR POLE OF LINE {2, 54}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(a^4-2*a^2*c^2+(b^2-c^2)^2)*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(65273) lies on the Steiner circumellipse and on these lines: {2, 57890}, {95, 35142}, {96, 671}, {97, 52505}, {99, 18315}, {290, 34385}, {577, 55553}, {648, 925}, {892, 55253}, {1494, 57875}, {2165, 60034}, {2168, 18827}, {2623, 57763}, {3228, 41271}, {4558, 46134}, {5392, 46138}, {6528, 16813}, {14570, 14586}, {15412, 18878}, {15958, 52932}, {18831, 41677}, {21449, 55560}, {32734, 65271}, {35139, 64516}, {35174, 65251}, {39116, 57489}, {52968, 64782}, {52975, 64783}

X(65273) = reflection of X(i) in X(j) for these {i,j}: {57890, 2}
X(65273) = isogonal conjugate of X(52317)
X(65273) = isotomic conjugate of X(63829)
X(65273) = trilinear pole of line {2, 54}
X(65273) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52317}, {5, 55216}, {31, 63829}, {47, 12077}, {51, 63827}, {52, 661}, {53, 63832}, {467, 810}, {512, 63808}, {523, 2180}, {563, 23290}, {571, 2618}, {656, 14576}, {798, 39113}, {924, 1953}, {1748, 15451}, {2179, 6563}, {2181, 52584}, {2290, 43088}, {2501, 63801}, {2617, 47421}, {3133, 55250}, {6753, 44706}, {14213, 34952}, {17881, 61194}, {21011, 34948}, {36145, 55072}, {41213, 65251}, {44179, 55219}, {57065, 62266}
X(65273) = X(i)-vertex conjugate of X(j) for these {i, j}: {32734, 41679}
X(65273) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 63829}, {3, 52317}, {31998, 39113}, {34853, 12077}, {36830, 52}, {37864, 55219}, {39013, 55072}, {39019, 55073}, {39054, 63808}, {39062, 467}, {40596, 14576}, {62603, 6563}
X(65273) = X(i)-Ceva conjugate of X(j) for these {i, j}: {57573, 55552}
X(65273) = X(i)-cross conjugate of X(j) for these {i, j}: {3, 57763}, {4558, 18315}, {6334, 65326}, {6368, 55553}, {11412, 18020}, {15958, 18831}, {32692, 65348}, {55253, 96}, {63829, 2}
X(65273) = pole of line {14516, 39113} with respect to the Kiepert parabola
X(65273) = pole of line {15958, 52932} with respect to the Steiner circumellipse
X(65273) = pole of line {52317, 63829} with respect to the Wallace hyperbola
X(65273) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(52760)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(687), X(4558)}}, {{A, B, C, X(925), X(30450)}}, {{A, B, C, X(930), X(14570)}}, {{A, B, C, X(933), X(16813)}}, {{A, B, C, X(4226), X(41237)}}, {{A, B, C, X(4590), X(57639)}}, {{A, B, C, X(14590), X(57474)}}

X(65274) = TRILINEAR POLE OF LINE {2, 272}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^3+b^3-b*c^2-a*c*(b+c))*(a^3-b^2*c+c^3-a*b*(b+c)) : :

X(65274) lies on the Steiner circumellipse and on these lines: {99, 4636}, {110, 664}, {162, 18026}, {190, 5546}, {272, 903}, {283, 57997}, {290, 40011}, {333, 40574}, {349, 40602}, {643, 668}, {662, 54970}, {671, 1751}, {799, 57976}, {1414, 4569}, {2218, 18827}, {2997, 14616}, {6528, 52921}, {13486, 65292}, {23289, 35154}, {35141, 56146}, {35162, 41506}, {43093, 57784}

X(65274) = trilinear pole of line {2, 272}
X(65274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 43060}, {42, 23800}, {55, 51658}, {65, 8676}, {71, 57173}, {73, 57092}, {209, 513}, {512, 3868}, {514, 2198}, {523, 2352}, {579, 661}, {649, 22021}, {667, 57808}, {798, 18134}, {810, 5125}, {1042, 58333}, {1402, 20294}, {1409, 57043}, {3063, 56559}, {3125, 57217}, {3190, 4017}, {4041, 4306}, {4516, 65315}, {6591, 51574}, {7180, 27396}, {41320, 51664}, {56000, 57185}
X(65274) = X(i)-vertex conjugate of X(j) for these {i, j}: {664, 1576}
X(65274) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 51658}, {5375, 22021}, {6631, 57808}, {10001, 56559}, {31998, 18134}, {34961, 3190}, {36830, 579}, {39026, 209}, {39054, 3868}, {39062, 5125}, {40589, 43060}, {40592, 23800}, {40602, 8676}, {40605, 20294}, {40620, 65118}
X(65274) = X(i)-cross conjugate of X(j) for these {i, j}: {1331, 662}, {7538, 23582}, {37652, 4590}
X(65274) = pole of line {27, 18134} with respect to the Kiepert parabola
X(65274) = pole of line {8676, 43060} with respect to the Stammler hyperbola
X(65274) = pole of line {20294, 23800} with respect to the Wallace hyperbola
X(65274) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(190)}}, {{A, B, C, X(107), X(3699)}}, {{A, B, C, X(110), X(162)}}, {{A, B, C, X(112), X(36086)}}, {{A, B, C, X(644), X(53683)}}, {{A, B, C, X(811), X(47318)}}, {{A, B, C, X(1305), X(51566)}}, {{A, B, C, X(1897), X(59097)}}, {{A, B, C, X(2363), X(3565)}}, {{A, B, C, X(4614), X(55281)}}, {{A, B, C, X(6331), X(51614)}}, {{A, B, C, X(13138), X(34594)}}, {{A, B, C, X(23999), X(57757)}}, {{A, B, C, X(37206), X(44766)}}
X(65274) = barycentric product X(i)*X(j) for these (i, j): {101, 57784}, {110, 40011}, {190, 272}, {1305, 333}, {1751, 99}, {2218, 799}, {2997, 662}, {4573, 56146}, {15467, 5546}, {23289, 4620}, {40574, 4561}, {41506, 4610}, {51566, 81}, {58986, 76}, {65254, 75}
X(65274) = barycentric quotient X(i)/X(j) for these (i, j): {28, 57173}, {29, 57043}, {57, 51658}, {58, 43060}, {81, 23800}, {99, 18134}, {100, 22021}, {101, 209}, {110, 579}, {163, 2352}, {190, 57808}, {272, 514}, {284, 8676}, {333, 20294}, {643, 27396}, {648, 5125}, {662, 3868}, {664, 56559}, {692, 2198}, {1172, 57092}, {1305, 226}, {1331, 51574}, {1751, 523}, {2218, 661}, {2287, 58333}, {2997, 1577}, {4565, 4306}, {4570, 57217}, {4636, 56000}, {5546, 3190}, {7192, 65118}, {18155, 17878}, {23289, 21044}, {28786, 57243}, {40011, 850}, {40161, 4064}, {40574, 7649}, {41506, 4024}, {46103, 57072}, {51566, 321}, {52378, 65315}, {56146, 3700}, {57784, 3261}, {58986, 6}, {65254, 1}

X(65275) = TRILINEAR POLE OF LINE {2, 573}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(-b^3+b*c^2+a*c*(-b+c)+a^2*(b+c))*(a*b*(b-c)+a^2*(b+c)+c*(b^2-c^2)) : :

X(65275) lies on the Steiner circumellipse and on these lines: {86, 18816}, {99, 59006}, {110, 54951}, {190, 14570}, {290, 37678}, {662, 6648}, {668, 56194}, {671, 2051}, {903, 20028}, {1121, 46880}, {1414, 54953}, {1494, 17271}, {2481, 33296}, {3226, 52150}, {3227, 41629}, {4360, 14616}, {4417, 34267}, {4559, 4560}, {4561, 57977}, {4573, 6613}, {7199, 62754}, {7257, 65282}, {11998, 65264}, {17136, 53649}, {17731, 35151}, {18025, 30966}, {18827, 34063}, {35155, 37792}, {35162, 51870}

X(65275) = trilinear pole of line {2, 573}
X(65275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {42, 21173}, {55, 51662}, {181, 57125}, {213, 17496}, {244, 57165}, {512, 2975}, {513, 52139}, {523, 20986}, {572, 661}, {649, 21061}, {650, 55323}, {663, 37558}, {667, 17751}, {692, 53566}, {798, 14829}, {810, 11109}, {1042, 58339}, {1402, 57091}, {1824, 23187}, {1918, 57244}, {2148, 52322}, {2501, 22118}, {3063, 52358}, {3125, 65203}, {3709, 17074}, {3733, 14973}, {4559, 11998}, {7252, 56325}, {20617, 21789}, {21759, 27346}, {52087, 62749}
X(65275) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 54951}
X(65275) = X(i)-Dao conjugate of X(j) for these {i, j}: {216, 52322}, {223, 51662}, {1086, 53566}, {5375, 21061}, {6626, 17496}, {6631, 17751}, {10001, 52358}, {31998, 14829}, {34021, 57244}, {36830, 572}, {39026, 52139}, {39054, 2975}, {39062, 11109}, {40592, 21173}, {40605, 57091}, {40620, 24237}, {40625, 34589}, {55067, 11998}
X(65275) = X(i)-cross conjugate of X(j) for these {i, j}: {4551, 662}, {18155, 86}, {20040, 1016}, {21362, 799}, {53280, 190}, {56194, 65260}, {62998, 4590}
X(65275) = pole of line {314, 1764} with respect to the Kiepert parabola
X(65275) = pole of line {53280, 65275} with respect to the Steiner circumellipse
X(65275) = pole of line {17496, 21173} with respect to the Wallace hyperbola
X(65275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4559)}}, {{A, B, C, X(75), X(4566)}}, {{A, B, C, X(86), X(811)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(1897)}}, {{A, B, C, X(163), X(5331)}}, {{A, B, C, X(658), X(6331)}}, {{A, B, C, X(662), X(7257)}}, {{A, B, C, X(874), X(34063)}}, {{A, B, C, X(931), X(3699)}}, {{A, B, C, X(1043), X(65201)}}, {{A, B, C, X(1310), X(51566)}}, {{A, B, C, X(2407), X(17271)}}, {{A, B, C, X(2421), X(37678)}}, {{A, B, C, X(4033), X(53332)}}, {{A, B, C, X(4551), X(53280)}}, {{A, B, C, X(4558), X(4561)}}, {{A, B, C, X(4573), X(62534)}}, {{A, B, C, X(6742), X(34594)}}, {{A, B, C, X(11794), X(43190)}}, {{A, B, C, X(37138), X(43359)}}, {{A, B, C, X(40430), X(53683)}}, {{A, B, C, X(56188), X(56252)}}, {{A, B, C, X(56194), X(59006)}}

X(65276) = TRILINEAR POLE OF LINE {2, 154}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(3*a^4+3*b^4-2*b^2*c^2-c^4+2*a^2*(b^2-c^2))*(3*a^4-b^4-2*b^2*c^2+3*c^4-2*a^2*(b^2-c^2)) : :

X(65276) lies on the Steiner circumellipse and on these lines: {2, 20232}, {99, 34211}, {107, 44552}, {112, 35571}, {290, 14614}, {376, 54975}, {524, 46145}, {648, 2409}, {670, 36841}, {671, 2794}, {1494, 1992}, {2407, 35179}, {2966, 60506}, {4558, 54971}, {5641, 22329}, {6179, 37200}, {6528, 57219}, {7757, 54973}, {12150, 46140}, {14999, 46144}, {17941, 35136}, {18025, 41629}, {18026, 57193}, {18829, 57216}, {32833, 54958}, {35142, 62955}, {35150, 37792}, {51224, 53201}

X(65276) = reflection of X(i) in X(j) for these {i,j}: {2, 23976}, {35140, 2}
X(65276) = trilinear pole of line {2, 154}
X(65276) = X(i)-isoconjugate-of-X(j) for these {i, j}: {512, 51304}, {647, 23052}, {656, 45141}, {661, 1350}, {798, 37668}, {810, 52283}, {822, 10002}, {2155, 14343}, {12037, 32676}
X(65276) = X(i)-vertex conjugate of X(j) for these {i, j}: {32649, 65181}, {44326, 61206}
X(65276) = X(i)-Dao conjugate of X(j) for these {i, j}: {15526, 12037}, {31998, 37668}, {36830, 1350}, {39052, 23052}, {39054, 51304}, {39062, 52283}, {40596, 45141}, {45245, 14343}
X(65276) = X(i)-cross conjugate of X(j) for these {i, j}: {35278, 99}, {51212, 18020}, {54259, 4}, {54267, 98}, {63042, 4590}
X(65276) = pole of line {14927, 37668} with respect to the Kiepert parabola
X(65276) = pole of line {26714, 35571} with respect to the MacBeath circumconic
X(65276) = pole of line {35278, 65276} with respect to the Steiner circumellipse
X(65276) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(107)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(112), X(1461)}}, {{A, B, C, X(523), X(52459)}}, {{A, B, C, X(524), X(2794)}}, {{A, B, C, X(691), X(65322)}}, {{A, B, C, X(827), X(4558)}}, {{A, B, C, X(925), X(36886)}}, {{A, B, C, X(933), X(56008)}}, {{A, B, C, X(1289), X(16039)}}, {{A, B, C, X(1302), X(17708)}}, {{A, B, C, X(1992), X(2407)}}, {{A, B, C, X(2421), X(14614)}}, {{A, B, C, X(2987), X(53937)}}, {{A, B, C, X(3265), X(44552)}}, {{A, B, C, X(3543), X(4235)}}, {{A, B, C, X(4226), X(62955)}}, {{A, B, C, X(4563), X(42396)}}, {{A, B, C, X(5503), X(53692)}}, {{A, B, C, X(7473), X(44216)}}, {{A, B, C, X(7954), X(18315)}}, {{A, B, C, X(11636), X(44769)}}, {{A, B, C, X(11794), X(53862)}}, {{A, B, C, X(14999), X(22329)}}, {{A, B, C, X(17941), X(57216)}}, {{A, B, C, X(30247), X(48373)}}, {{A, B, C, X(32697), X(58098)}}, {{A, B, C, X(34572), X(58966)}}, {{A, B, C, X(58994), X(65306)}}, {{A, B, C, X(59098), X(60053)}}, {{A, B, C, X(59136), X(62900)}}
X(65276) = barycentric product X(i)*X(j) for these (i, j): {20, 35571}, {110, 59256}, {3424, 99}, {42287, 648}, {58963, 76}, {60674, 6331}
X(65276) = barycentric quotient X(i)/X(j) for these (i, j): {20, 14343}, {99, 37668}, {107, 10002}, {110, 1350}, {112, 45141}, {162, 23052}, {525, 12037}, {648, 52283}, {662, 51304}, {685, 45031}, {2409, 1529}, {3424, 523}, {35278, 7710}, {35571, 253}, {41173, 47382}, {42287, 525}, {46639, 40813}, {58963, 6}, {59256, 850}, {60674, 647}

X(65277) = ISOGONAL CONJUGATE OF X(42663)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4+2*b^4-b^2*c^2+c^4-a^2*(b^2+2*c^2))*(a^4+b^4-b^2*c^2+2*c^4-a^2*(2*b^2+c^2)) : :
X(65277) = -3*X[2]+2*X[55152]

X(65277) lies on the Steiner circumellipse and on these lines: {2, 55152}, {76, 14253}, {99, 3566}, {290, 19599}, {325, 35142}, {523, 35136}, {648, 4590}, {670, 33799}, {671, 7799}, {880, 53196}, {892, 62645}, {1494, 57872}, {1975, 47736}, {2396, 2966}, {2858, 9131}, {2987, 3228}, {3225, 32654}, {3926, 35088}, {5641, 36891}, {7757, 64618}, {8667, 35146}, {8773, 18827}, {9487, 23055}, {11160, 18823}, {17731, 53646}, {18826, 36051}, {18829, 35364}, {34157, 53197}, {40074, 65267}, {46134, 52608}, {46142, 52091}, {46145, 56572}

X(65277) = isogonal conjugate of X(42663)
X(65277) = isotomic conjugate of X(55122)
X(65277) = anticomplement of X(55152)
X(65277) = trilinear pole of line {2, 2987}
X(65277) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42663}, {31, 55122}, {230, 798}, {460, 810}, {512, 8772}, {656, 44099}, {661, 1692}, {669, 1733}, {1924, 51481}, {2422, 17462}, {2643, 61213}
X(65277) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55122}, {3, 42663}, {5976, 55267}, {6388, 51610}, {9428, 51481}, {15525, 51613}, {31998, 230}, {36830, 1692}, {39054, 8772}, {39062, 460}, {40596, 44099}, {55152, 55152}, {62613, 51431}
X(65277) = X(i)-cross conjugate of X(j) for these {i, j}: {98, 39292}, {99, 55266}, {325, 4590}, {6563, 57553}, {10425, 65354}, {16230, 42407}, {54103, 57991}, {55122, 2}, {62645, 8781}
X(65277) = pole of line {230, 46236} with respect to the Kiepert parabola
X(65277) = pole of line {5477, 42663} with respect to the Wallace hyperbola
X(65277) = pole of line {41181, 51610} with respect to the dual conic of polar circle
X(65277) = pole of line {2395, 55266} with respect to the dual conic of Orthic inconic
X(65277) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2858)}}, {{A, B, C, X(98), X(36898)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(325), X(17932)}}, {{A, B, C, X(523), X(3566)}}, {{A, B, C, X(685), X(46606)}}, {{A, B, C, X(689), X(55279)}}, {{A, B, C, X(691), X(33799)}}, {{A, B, C, X(805), X(32716)}}, {{A, B, C, X(930), X(55034)}}, {{A, B, C, X(1138), X(2696)}}, {{A, B, C, X(3565), X(9132)}}, {{A, B, C, X(4226), X(44768)}}, {{A, B, C, X(4235), X(33228)}}, {{A, B, C, X(4576), X(20189)}}, {{A, B, C, X(4590), X(47389)}}, {{A, B, C, X(5468), X(22110)}}, {{A, B, C, X(6037), X(41209)}}, {{A, B, C, X(6082), X(62672)}}, {{A, B, C, X(6331), X(42297)}}, {{A, B, C, X(6333), X(35088)}}, {{A, B, C, X(8667), X(14607)}}, {{A, B, C, X(9069), X(63784)}}, {{A, B, C, X(9124), X(58091)}}, {{A, B, C, X(9134), X(45687)}}, {{A, B, C, X(9182), X(11160)}}, {{A, B, C, X(10425), X(32697)}}, {{A, B, C, X(13575), X(53953)}}, {{A, B, C, X(23055), X(56429)}}, {{A, B, C, X(31614), X(53080)}}, {{A, B, C, X(32717), X(53893)}}, {{A, B, C, X(35511), X(42398)}}, {{A, B, C, X(55122), X(55152)}}

X(65278) = ISOGONAL CONJUGATE OF X(5113)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4+b^4-b^2*c^2-c^4+a^2*(b^2-c^2))*(a^4-b^4-b^2*c^2+c^4+a^2*(-b^2+c^2)) : :

X(65278) lies on the Steiner circumellipse and on these lines: {99, 826}, {290, 39093}, {385, 9477}, {523, 4577}, {524, 17949}, {597, 18823}, {670, 23285}, {671, 754}, {827, 62452}, {1494, 57845}, {3225, 16985}, {3228, 46286}, {4563, 65287}, {4590, 31067}, {5641, 37671}, {7779, 15573}, {9182, 42367}, {17957, 57945}, {18829, 53379}, {35140, 40876}, {35146, 63038}, {39941, 53229}, {42371, 44173}

X(65278) = reflection of X(i) in X(j) for these {i,j}: {7779, 15573}, {40850, 385}
X(65278) = isogonal conjugate of X(5113)
X(65278) = isotomic conjugate of X(9479)
X(65278) = trilinear pole of line {2, 4048}
X(65278) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 5113}, {31, 9479}, {38, 17997}, {420, 810}, {512, 17799}, {656, 44090}, {798, 7779}, {1964, 18010}, {2084, 40850}, {3005, 34054}, {8061, 46228}
X(65278) = X(i)-vertex conjugate of X(j) for these {i, j}: {32729, 37880}
X(65278) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 9479}, {3, 5113}, {31998, 7779}, {36830, 2076}, {39054, 17799}, {39062, 420}, {39079, 24973}, {40596, 44090}, {41884, 18010}, {62452, 40850}
X(65278) = X(i)-cross conjugate of X(j) for these {i, j}: {523, 9477}, {9479, 2}, {14316, 76}, {17941, 99}, {41209, 53621}, {50248, 4590}, {50542, 10159}
X(65278) = pole of line {17941, 65278} with respect to the Steiner circumellipse
X(65278) = pole of line {5113, 9479} with respect to the Wallace hyperbola
X(65278) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(98), X(53379)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(251), X(36827)}}, {{A, B, C, X(385), X(46294)}}, {{A, B, C, X(476), X(53080)}}, {{A, B, C, X(523), X(826)}}, {{A, B, C, X(524), X(754)}}, {{A, B, C, X(597), X(9182)}}, {{A, B, C, X(691), X(9218)}}, {{A, B, C, X(2421), X(39093)}}, {{A, B, C, X(3222), X(44766)}}, {{A, B, C, X(4563), X(58119)}}, {{A, B, C, X(4576), X(52936)}}, {{A, B, C, X(4590), X(57545)}}, {{A, B, C, X(5468), X(44367)}}, {{A, B, C, X(6037), X(44768)}}, {{A, B, C, X(9132), X(58121)}}, {{A, B, C, X(9150), X(17708)}}, {{A, B, C, X(9186), X(11636)}}, {{A, B, C, X(14420), X(14424)}}, {{A, B, C, X(14607), X(63038)}}, {{A, B, C, X(14999), X(37671)}}, {{A, B, C, X(16095), X(52630)}}, {{A, B, C, X(17930), X(36036)}}, {{A, B, C, X(17941), X(40850)}}, {{A, B, C, X(35511), X(62451)}}, {{A, B, C, X(36517), X(56980)}}
X(65278) = barycentric product X(i)*X(j) for these (i, j): {11606, 99}, {17941, 9477}, {17949, 4577}, {17957, 4593}, {46286, 670}, {46970, 76}, {57678, 6331}, {57845, 648}
X(65278) = barycentric quotient X(i)/X(j) for these (i, j): {2, 9479}, {6, 5113}, {83, 18010}, {99, 7779}, {110, 2076}, {112, 44090}, {251, 17997}, {648, 420}, {662, 17799}, {827, 46228}, {4226, 12830}, {4577, 40850}, {4599, 34054}, {5113, 24973}, {11606, 523}, {14316, 46669}, {17941, 8290}, {17949, 826}, {17957, 8061}, {46286, 512}, {46970, 6}, {57678, 647}, {57845, 525}

X(65279) = ISOGONAL CONJUGATE OF X(6140)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^6+(b^2-c^2)^3-a^4*(b^2+3*c^2)+a^2*(-b^4+b^2*c^2+3*c^4))*(a^6-(b^2-c^2)^3-a^4*(3*b^2+c^2)+a^2*(3*b^4+b^2*c^2-c^4)) : :

X(65279) lies on the Steiner circumellipse and on these lines: {76, 38539}, {99, 1291}, {290, 43704}, {316, 1263}, {340, 14106}, {532, 11118}, {533, 11117}, {671, 13582}, {850, 46139}, {892, 64935}, {1273, 1494}, {2966, 64938}, {3228, 14579}, {3260, 46138}, {3471, 5641}, {4577, 14221}, {7809, 15392}, {18020, 33513}, {18827, 51804}, {18829, 64937}, {23872, 32037}, {23873, 32036}, {31998, 53192}, {46142, 64936}

X(65279) = isogonal conjugate of X(6140)
X(65279) = isotomic conjugate of X(45147)
X(65279) = trilinear pole of line {2, 13582}
X(65279) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6140}, {31, 45147}, {163, 10413}, {512, 1749}, {661, 11063}, {798, 37779}, {810, 37943}, {2624, 56404}, {2643, 47053}, {12077, 19306}, {15475, 51802}
X(65279) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 45147}, {3, 6140}, {115, 10413}, {31998, 37779}, {36830, 11063}, {39054, 1749}, {39062, 37943}, {40604, 8562}, {62613, 10272}
X(65279) = X(i)-cross conjugate of X(j) for these {i, j}: {10264, 39295}, {10411, 99}, {10412, 2986}, {24978, 76}, {44450, 23582}, {45147, 2}, {53495, 52940}, {64935, 13582}
X(65279) = pole of line {10411, 65279} with respect to the Steiner circumellipse
X(65279) = pole of line {6140, 6592} with respect to the Wallace hyperbola
X(65279) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(190)}}, {{A, B, C, X(249), X(57803)}}, {{A, B, C, X(532), X(533)}}, {{A, B, C, X(691), X(44768)}}, {{A, B, C, X(850), X(23872)}}, {{A, B, C, X(1235), X(14221)}}, {{A, B, C, X(1273), X(3260)}}, {{A, B, C, X(4240), X(65085)}}, {{A, B, C, X(10425), X(17708)}}, {{A, B, C, X(18020), X(57764)}}, {{A, B, C, X(40423), X(57758)}}, {{A, B, C, X(40705), X(64516)}}, {{A, B, C, X(58095), X(65176)}}
X(65279) = barycentric product X(i)*X(j) for these (i, j): {1291, 76}, {4590, 64935}, {13582, 99}, {14579, 670}, {18020, 64938}, {34537, 64937}, {43187, 64936}, {43704, 6331}, {51804, 799}
X(65279) = barycentric quotient X(i)/X(j) for these (i, j): {2, 45147}, {6, 6140}, {99, 37779}, {110, 11063}, {249, 47053}, {323, 8562}, {476, 56404}, {523, 10413}, {648, 37943}, {662, 1749}, {1263, 12077}, {1291, 6}, {2407, 10272}, {3471, 1637}, {4558, 50461}, {7799, 45790}, {10411, 40604}, {11071, 15475}, {13582, 523}, {14367, 58903}, {14579, 512}, {14590, 2914}, {15392, 14582}, {17402, 5616}, {17403, 5612}, {18315, 1157}, {23895, 51267}, {23896, 51274}, {24978, 46439}, {36134, 19306}, {41078, 43958}, {43704, 647}, {44769, 3470}, {46072, 20578}, {46076, 20579}, {51804, 661}, {64935, 115}, {64936, 3569}, {64937, 3124}, {64938, 125}

X(65280) = ISOGONAL CONJUGATE OF X(8639)

Barycentrics    (a-b)*b*(a+b)*(a-c)*c*(a+c)*(b*(b+c)+a*(b+2*c))*(c*(b+c)+a*(2*b+c)) : :

X(65280) lies on the Steiner circumellipse and on these lines: {99, 931}, {110, 65281}, {190, 7257}, {290, 34259}, {314, 31165}, {645, 4559}, {648, 61205}, {664, 799}, {668, 61172}, {670, 53332}, {671, 34258}, {941, 3228}, {959, 35159}, {960, 40827}, {2258, 18826}, {3226, 5331}, {3227, 37870}, {3952, 65282}, {6331, 18026}, {6540, 55245}, {7260, 65289}, {18827, 31359}, {32042, 55243}, {33948, 57977}, {35176, 44733}, {53642, 55211}, {54986, 65161}, {55209, 65292}, {65169, 65288}

X(65280) = isogonal conjugate of X(8639)
X(65280) = isotomic conjugate of X(8672)
X(65280) = trilinear pole of line {2, 314}
X(65280) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 8639}, {31, 8672}, {32, 50457}, {213, 48144}, {512, 1468}, {661, 5019}, {667, 59305}, {669, 10436}, {798, 940}, {810, 4185}, {958, 51641}, {1042, 58332}, {1402, 17418}, {1918, 43067}, {1919, 31993}, {1924, 34284}, {2268, 7180}, {3049, 5307}, {3121, 65168}
X(65280) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 65281}
X(65280) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 8672}, {3, 8639}, {6376, 50457}, {6626, 48144}, {6631, 59305}, {9296, 31993}, {9428, 34284}, {31998, 940}, {34021, 43067}, {36830, 5019}, {39054, 1468}, {39062, 4185}, {40605, 17418}, {40620, 53543}
X(65280) = X(i)-cross conjugate of X(j) for these {i, j}: {5739, 4590}, {8672, 2}, {23880, 40827}, {28606, 31625}, {34283, 34537}
X(65280) = pole of line {8639, 8672} with respect to the Wallace hyperbola
X(65280) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(3903)}}, {{A, B, C, X(660), X(43359)}}, {{A, B, C, X(789), X(51566)}}, {{A, B, C, X(799), X(4631)}}, {{A, B, C, X(811), X(4623)}}, {{A, B, C, X(874), X(31997)}}, {{A, B, C, X(931), X(65225)}}, {{A, B, C, X(1414), X(4594)}}, {{A, B, C, X(4566), X(42363)}}, {{A, B, C, X(4589), X(4614)}}, {{A, B, C, X(8050), X(43356)}}, {{A, B, C, X(27805), X(43188)}}, {{A, B, C, X(51560), X(59093)}}

X(65281) = TRILINEAR POLE OF LINE {2, 261}

Barycentrics    (a-b)*(a+b)^2*(a-c)*(a+c)^2*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :

X(65281) lies on the Steiner circumellipse and on these lines: {99, 55196}, {110, 65280}, {190, 4556}, {261, 31157}, {290, 1798}, {662, 54986}, {664, 4610}, {668, 4631}, {671, 14534}, {892, 4581}, {903, 30593}, {1169, 3228}, {1220, 35162}, {1414, 65289}, {1415, 4612}, {1494, 57853}, {2363, 18827}, {2966, 15420}, {3227, 64457}, {4562, 36147}, {4590, 35147}, {4623, 54982}, {4999, 31620}, {6540, 6578}, {7340, 65293}, {14970, 39276}, {17935, 65282}, {18026, 55231}, {18816, 52550}, {18829, 36066}, {35154, 57161}

X(65281) = isogonal conjugate of X(42661)
X(65281) = trilinear pole of line {2, 261}
X(65281) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42661}, {42, 50330}, {181, 17420}, {213, 21124}, {429, 810}, {512, 2292}, {522, 59174}, {523, 3725}, {649, 21810}, {656, 44092}, {661, 2092}, {663, 52567}, {667, 20653}, {669, 18697}, {756, 6371}, {798, 1211}, {872, 3004}, {1089, 57157}, {1193, 4705}, {1228, 1924}, {1500, 48131}, {1829, 55230}, {2084, 27067}, {2171, 52326}, {2269, 57185}, {2300, 4024}, {2354, 55232}, {2643, 53280}, {3121, 65191}, {3122, 61172}, {3124, 3882}, {3125, 61168}, {3666, 4079}, {3704, 51641}, {3708, 61205}, {4017, 40966}, {4357, 50487}, {4509, 7109}, {7180, 21033}, {20911, 53581}, {20975, 61226}, {21834, 45218}, {41003, 63461}, {45197, 50491}, {54308, 58289}, {57181, 61377}, {61052, 61223}
X(65281) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 65280}
X(65281) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 42661}, {5375, 21810}, {6626, 21124}, {6631, 20653}, {9428, 1228}, {31998, 1211}, {34961, 40966}, {36830, 2092}, {39054, 2292}, {39062, 429}, {40592, 50330}, {40596, 44092}, {62452, 27067}
X(65281) = X(i)-cross conjugate of X(j) for these {i, j}: {81, 4590}, {314, 18020}, {3910, 31620}, {4581, 14534}, {15420, 40827}, {16049, 23582}, {26843, 57545}
X(65281) = pole of line {21124, 42661} with respect to the Wallace hyperbola
X(65281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(81), X(17935)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(1415)}}, {{A, B, C, X(1414), X(36066)}}, {{A, B, C, X(1492), X(53628)}}, {{A, B, C, X(2363), X(36147)}}, {{A, B, C, X(4556), X(6578)}}, {{A, B, C, X(4610), X(4631)}}, {{A, B, C, X(6516), X(17932)}}

X(65282) = ISOTOMIC CONJUGATE OF X(6371)

Barycentrics    (a-b)*b^2*(a-c)*c^2*(a^2+a*c+b*(b+c))*(a^2+a*b+c*(b+c)) : :
X(65282) = -3*X[2]+2*X[39015]

X(65282) lies on the Steiner circumellipse and on these lines: {2, 39015}, {99, 8707}, {190, 65229}, {646, 21859}, {664, 1978}, {671, 60264}, {889, 4581}, {903, 1240}, {1220, 3226}, {2298, 18825}, {3227, 30710}, {3228, 14624}, {3596, 31141}, {3952, 65280}, {4033, 54986}, {4505, 57969}, {4562, 65169}, {4577, 32736}, {4583, 18829}, {4586, 36147}, {6386, 54982}, {7257, 65275}, {17935, 65281}, {18827, 40827}, {31625, 35147}, {35159, 60086}, {35334, 57960}, {53216, 57162}

X(65282) = isogonal conjugate of X(57157)
X(65282) = isotomic conjugate of X(6371)
X(65282) = anticomplement of X(39015)
X(65282) = trilinear pole of line {2, 1240}
X(65282) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 57157}, {31, 6371}, {32, 48131}, {560, 3004}, {604, 52326}, {649, 2300}, {667, 1193}, {669, 54308}, {798, 40153}, {849, 42661}, {890, 62769}, {1397, 17420}, {1501, 4509}, {1919, 3666}, {1924, 16705}, {1977, 3882}, {1980, 4357}, {2092, 57129}, {2206, 50330}, {2269, 57181}, {2354, 22383}, {3063, 61412}, {3248, 53280}, {3725, 3733}, {4267, 51641}, {9426, 16739}, {20967, 43924}, {22096, 61226}, {36098, 41224}, {36147, 39015}, {45218, 57074}, {61048, 61223}
X(65282) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6371}, {3, 57157}, {3161, 52326}, {4075, 42661}, {5375, 2300}, {6374, 3004}, {6376, 48131}, {6631, 1193}, {9296, 3666}, {9428, 16705}, {10001, 61412}, {31998, 40153}, {38992, 41224}, {39015, 39015}, {40603, 50330}, {62585, 17420}
X(65282) = X(i)-cross conjugate of X(j) for these {i, j}: {314, 7035}, {321, 31625}, {4581, 30710}, {6371, 2}, {17751, 1016}, {47660, 308}
X(65282) = pole of line {6371, 57157} with respect to the Wallace hyperbola
X(65282) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(28480)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(115), X(18003)}}, {{A, B, C, X(321), X(17935)}}, {{A, B, C, X(660), X(4559)}}, {{A, B, C, X(901), X(8050)}}, {{A, B, C, X(1310), X(35008)}}, {{A, B, C, X(1978), X(62534)}}, {{A, B, C, X(3952), X(21859)}}, {{A, B, C, X(4602), X(36803)}}, {{A, B, C, X(6371), X(39015)}}, {{A, B, C, X(17929), X(29233)}}, {{A, B, C, X(29279), X(54458)}}

X(65283) = ISOTOMIC CONJUGATE OF X(6370)

Barycentrics    (a-b)*(a+b)^2*(a-c)*(a+c)^2*(a^2-a*b+b^2-c^2)*(a^2-b^2-a*c+c^2) : :

X(65283) lies on the Steiner circumellipse and on these lines: {80, 35162}, {99, 4467}, {110, 48288}, {190, 4567}, {249, 4560}, {261, 46136}, {290, 36036}, {476, 4608}, {648, 65100}, {655, 6648}, {659, 17939}, {662, 45671}, {664, 52935}, {666, 60571}, {668, 4600}, {670, 24037}, {671, 24624}, {691, 50343}, {757, 35175}, {759, 18827}, {903, 4622}, {1098, 35164}, {1414, 4077}, {1494, 57985}, {1509, 18821}, {1577, 39054}, {1931, 46800}, {2341, 35144}, {2481, 52380}, {2605, 53192}, {2966, 9273}, {3228, 34079}, {4586, 32671}, {4597, 4610}, {5641, 34016}, {6528, 23999}, {6540, 51562}, {6626, 52639}, {6740, 35141}, {17731, 61479}, {32004, 35153}, {35142, 36105}, {39277, 46138}, {40214, 60013}, {46160, 57945}, {50351, 53379}, {56320, 60053}

X(65283) = isogonal conjugate of X(42666)
X(65283) = isotomic conjugate of X(6370)
X(65283) = trilinear pole of line {2, 662}
X(65283) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42666}, {6, 2610}, {12, 8648}, {31, 6370}, {36, 4705}, {37, 21828}, {42, 53527}, {55, 51663}, {65, 53562}, {115, 1983}, {181, 3738}, {201, 58313}, {213, 4707}, {320, 50487}, {512, 758}, {523, 3724}, {594, 21758}, {649, 4053}, {654, 2171}, {656, 44113}, {661, 2245}, {669, 35550}, {756, 53314}, {798, 3936}, {810, 860}, {872, 4453}, {1254, 53285}, {1464, 4041}, {1500, 3960}, {1870, 55230}, {1919, 61410}, {2197, 65104}, {2323, 57185}, {2624, 8818}, {3124, 4585}, {3218, 4079}, {3709, 18593}, {4024, 7113}, {4036, 52434}, {4242, 20975}, {4282, 55197}, {6757, 14270}, {7140, 22379}, {20924, 53581}, {39149, 42653}, {40988, 55263}, {41804, 63461}, {52356, 61060}, {52413, 55232}, {56844, 58304}
X(65283) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6370}, {3, 42666}, {9, 2610}, {223, 51663}, {5375, 4053}, {6626, 4707}, {9296, 61410}, {15898, 4705}, {31998, 3936}, {36830, 2245}, {39054, 758}, {39062, 860}, {40589, 21828}, {40592, 53527}, {40596, 44113}, {40602, 53562}, {62613, 6739}
X(65283) = X(i)-cross conjugate of X(j) for these {i, j}: {2407, 4573}, {4560, 57555}, {6370, 2}, {6740, 39295}, {16704, 4590}, {17139, 18020}, {17161, 57788}, {18662, 57568}, {39765, 4998}, {39766, 1016}, {39767, 1275}, {49274, 32014}, {57736, 9273}
X(65283) = pole of line {21828, 42666} with respect to the Stammler hyperbola
X(65283) = pole of line {37783, 46800} with respect to the Hutson-Moses hyperbola
X(65283) = pole of line {4707, 4736} with respect to the Wallace hyperbola
X(65283) = intersection, other than A, B, C, of circumconics {{A, B, C, X(10), X(60055)}}, {{A, B, C, X(58), X(17939)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(32641)}}, {{A, B, C, X(162), X(58982)}}, {{A, B, C, X(476), X(51562)}}, {{A, B, C, X(691), X(2363)}}, {{A, B, C, X(1414), X(6578)}}, {{A, B, C, X(4077), X(4467)}}, {{A, B, C, X(4567), X(4600)}}, {{A, B, C, X(4596), X(64823)}}, {{A, B, C, X(4612), X(52935)}}, {{A, B, C, X(6083), X(36037)}}, {{A, B, C, X(6742), X(43354)}}, {{A, B, C, X(17708), X(37143)}}

X(65284) = ISOTOMIC CONJUGATE OF X(8675)

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^4+a^2*(4*b^2-2*c^2)+(b^2-c^2)^2)*(a^4-2*a^2*(b^2-2*c^2)+(b^2-c^2)^2) : :

X(65284) lies on the Steiner circumellipse and on these lines: {4, 65267}, {69, 56598}, {76, 1494}, {99, 1302}, {110, 18878}, {113, 40832}, {290, 4846}, {315, 54988}, {316, 39985}, {648, 61209}, {670, 61188}, {671, 34289}, {3228, 34288}, {3260, 10706}, {3978, 53221}, {4577, 32738}, {4586, 36149}, {6331, 16077}, {7799, 56709}, {20023, 46140}, {35139, 41512}, {35142, 58782}, {46142, 56925}

X(65284) = isogonal conjugate of X(42660)
X(65284) = isotomic conjugate of X(8675)
X(65284) = trilinear pole of line {2, 3003}
X(65284) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42660}, {31, 8675}, {378, 810}, {560, 30474}, {656, 44080}, {661, 5063}, {798, 15066}, {1577, 52438}, {1919, 42704}, {1924, 32833}
X(65284) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 18878}
X(65284) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 8675}, {3, 42660}, {6374, 30474}, {9296, 42704}, {9428, 32833}, {31998, 15066}, {36830, 5063}, {39062, 378}, {40596, 44080}, {62613, 10564}
X(65284) = X(i)-cross conjugate of X(j) for these {i, j}: {5890, 249}, {8675, 2}, {37644, 4590}, {44440, 23582}, {46229, 40832}
X(65284) = pole of line {8675, 10564} with respect to the Wallace hyperbola
X(65284) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(110)}}, {{A, B, C, X(76), X(6331)}}, {{A, B, C, X(83), X(43188)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(685), X(59098)}}, {{A, B, C, X(827), X(32695)}}, {{A, B, C, X(877), X(11185)}}, {{A, B, C, X(1302), X(60119)}}, {{A, B, C, X(2996), X(11794)}}, {{A, B, C, X(5485), X(36886)}}, {{A, B, C, X(9066), X(54733)}}, {{A, B, C, X(9069), X(54899)}}, {{A, B, C, X(9100), X(54819)}}, {{A, B, C, X(41895), X(63784)}}, {{A, B, C, X(43532), X(53603)}}
X(65284) = barycentric product X(i)*X(j) for these (i, j): {264, 65323}, {1302, 76}, {1502, 32738}, {4846, 6331}, {34288, 670}, {34289, 99}, {36083, 46234}, {36149, 561}, {43187, 56925}, {57819, 648}
X(65284) = barycentric quotient X(i)/X(j) for these (i, j): {2, 8675}, {6, 42660}, {76, 30474}, {99, 15066}, {110, 5063}, {112, 44080}, {648, 378}, {668, 42704}, {670, 32833}, {1302, 6}, {1576, 52438}, {2407, 10564}, {2966, 11653}, {3260, 46229}, {4846, 647}, {6331, 44134}, {9064, 47649}, {14570, 5891}, {30450, 51833}, {32681, 40352}, {32738, 32}, {34288, 512}, {34289, 523}, {36083, 2159}, {36149, 31}, {39263, 9209}, {52933, 40353}, {56925, 3569}, {57819, 525}, {60119, 2433}, {60588, 17414}, {65323, 3}

X(65285) = ISOTOMIC CONJUGATE OF X(4155)

Barycentrics    (a-b)*b*(a+b)^2*(a-c)*c*(a+c)^2*(-b^2+a*c)*(a*b-c^2) : :

X(65285) lies on the Steiner circumellipse and on these lines: {86, 35166}, {99, 4367}, {190, 4584}, {274, 35173}, {290, 57738}, {334, 35162}, {648, 46254}, {668, 2533}, {670, 4374}, {671, 40017}, {741, 18826}, {799, 31148}, {873, 18822}, {875, 886}, {876, 18829}, {903, 4634}, {1494, 57987}, {1509, 35172}, {3225, 18268}, {3228, 37128}, {4017, 4625}, {4583, 6540}, {4586, 4610}, {7192, 34537}, {8033, 35146}, {18021, 53218}, {30940, 57554}, {35144, 36800}, {35167, 52379}, {46159, 57938}, {52935, 62468}, {54986, 55202}

X(65285) = isotomic conjugate of X(4155)
X(65285) = trilinear pole of line {2, 799}
X(65285) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 46390}, {31, 4155}, {42, 4455}, {213, 21832}, {238, 50487}, {239, 53581}, {512, 3747}, {659, 872}, {661, 41333}, {669, 740}, {798, 2238}, {810, 862}, {812, 7109}, {874, 4117}, {875, 4094}, {881, 4154}, {1084, 3570}, {1284, 63461}, {1500, 8632}, {1914, 4079}, {1918, 4010}, {1919, 4037}, {1924, 3948}, {2210, 4705}, {3716, 61364}, {4024, 14599}, {4036, 18892}, {4093, 18105}, {4433, 51641}, {5009, 58289}, {9426, 35544}, {9427, 27853}, {18894, 52623}, {55230, 57654}
X(65285) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4155}, {9, 46390}, {6626, 21832}, {9296, 4037}, {9428, 3948}, {9470, 50487}, {31998, 2238}, {34021, 4010}, {36830, 41333}, {36906, 4079}, {39054, 3747}, {39062, 862}, {40592, 4455}, {40620, 39786}, {62557, 4705}
X(65285) = X(i)-cross conjugate of X(j) for these {i, j}: {874, 799}, {875, 37128}, {4155, 2}, {4589, 65258}, {7192, 57554}, {17140, 57566}, {17166, 52209}, {30940, 34537}, {30941, 4590}, {56154, 39292}, {62636, 44168}
X(65285) = pole of line {2238, 2669} with respect to the Kiepert parabola
X(65285) = pole of line {4094, 4155} with respect to the Wallace hyperbola
X(65285) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(513), X(9422)}}, {{A, B, C, X(660), X(63874)}}, {{A, B, C, X(805), X(34067)}}, {{A, B, C, X(876), X(2533)}}, {{A, B, C, X(4427), X(53363)}}, {{A, B, C, X(4576), X(52922)}}, {{A, B, C, X(4584), X(4589)}}, {{A, B, C, X(4598), X(53631)}}, {{A, B, C, X(4601), X(4634)}}, {{A, B, C, X(4607), X(9150)}}, {{A, B, C, X(4623), X(52612)}}
X(65285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4639, 65258, 36806}

X(65286) = ISOTOMIC CONJUGATE OF X(4132)

Barycentrics    (a-b)*b*(a+b)*(a-c)*c*(a+c)*(a*(b-c)+b*(b+c))*(a*(b-c)-c*(b+c)) : :

X(65286) lies on the Steiner circumellipse and on these lines: {76, 58073}, {86, 53650}, {99, 34594}, {190, 37205}, {274, 3226}, {314, 903}, {596, 17143}, {664, 55243}, {668, 4576}, {671, 40013}, {799, 6540}, {874, 53649}, {3227, 39747}, {3228, 39798}, {4555, 7257}, {4577, 52935}, {4602, 54985}, {7192, 27808}, {14616, 57915}, {18826, 40148}, {20615, 35159}, {35147, 40086}, {35166, 52137}, {40519, 57959}, {55245, 58130}

X(65286) = isotomic conjugate of X(4132)
X(65286) = trilinear pole of line {2, 3770}
X(65286) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 58288}, {31, 4132}, {32, 4129}, {37, 57096}, {42, 4057}, {55, 51650}, {213, 4063}, {512, 595}, {661, 2220}, {667, 3293}, {669, 4360}, {798, 32911}, {810, 4222}, {1042, 58336}, {1334, 57238}, {1402, 48307}, {1500, 57080}, {1918, 20295}, {1919, 3995}, {1924, 18140}, {1980, 56249}, {2200, 17922}, {2205, 20949}, {2333, 22154}, {3871, 51641}, {4557, 8054}, {9426, 40087}
X(65286) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4132}, {9, 58288}, {223, 51650}, {6376, 4129}, {6626, 4063}, {6631, 3293}, {9296, 3995}, {9428, 18140}, {31998, 32911}, {34021, 20295}, {36830, 2220}, {39054, 595}, {39062, 4222}, {40589, 57096}, {40592, 4057}, {40605, 48307}
X(65286) = X(i)-cross conjugate of X(j) for these {i, j}: {1019, 274}, {4033, 799}, {4132, 2}, {8050, 37205}, {20950, 40017}, {32863, 4590}, {44444, 14534}, {48293, 32017}
X(65286) = pole of line {4057, 4063} with respect to the Wallace hyperbola
X(65286) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(75), X(27808)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(274), X(4602)}}, {{A, B, C, X(314), X(7257)}}, {{A, B, C, X(660), X(43076)}}, {{A, B, C, X(874), X(17143)}}, {{A, B, C, X(4576), X(4589)}}, {{A, B, C, X(4594), X(4596)}}, {{A, B, C, X(4639), X(52612)}}, {{A, B, C, X(8050), X(34594)}}

X(65287) = ISOTOMIC CONJUGATE OF X(25423)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2*(b^2-c^2)+b^2*(2*b^2+c^2))*(a^2*(b^2-c^2)-c^2*(b^2+2*c^2)) : :

X(65287) lies on the Steiner circumellipse and on these lines: {2, 3225}, {69, 43664}, {99, 25424}, {290, 7788}, {524, 53231}, {599, 3228}, {671, 7818}, {3222, 45317}, {4563, 65278}, {4577, 57150}, {4609, 31176}, {7809, 53197}, {7840, 35146}, {7883, 57935}, {16712, 53641}, {18827, 51844}, {23342, 35138}, {31168, 43094}

X(65287) = reflection of X(i) in X(j) for these {i,j}: {3225, 2}
X(65287) = isotomic conjugate of X(25423)
X(65287) = trilinear pole of line {2, 10335}
X(65287) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 25423}, {512, 51291}, {669, 52138}, {798, 7766}, {923, 45680}, {1924, 41259}
X(65287) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 25423}, {2482, 45680}, {9428, 41259}, {31998, 7766}, {36830, 59232}, {39054, 51291}
X(65287) = X(i)-cross conjugate of X(j) for these {i, j}: {14318, 10159}, {25423, 2}, {54262, 76}
X(65287) = pole of line {25423, 45680} with respect to the Wallace hyperbola
X(65287) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3222)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(599), X(23342)}}, {{A, B, C, X(669), X(31176)}}, {{A, B, C, X(689), X(36886)}}, {{A, B, C, X(1634), X(58121)}}, {{A, B, C, X(2421), X(7788)}}, {{A, B, C, X(4563), X(57852)}}, {{A, B, C, X(4576), X(63784)}}, {{A, B, C, X(7840), X(14607)}}, {{A, B, C, X(9066), X(53080)}}, {{A, B, C, X(11058), X(33638)}}, {{A, B, C, X(11163), X(34203)}}, {{A, B, C, X(14492), X(39639)}}, {{A, B, C, X(23301), X(45317)}}
X(65287) = barycentric product X(i)*X(j) for these (i, j): {110, 59258}, {25424, 76}, {43688, 99}, {51844, 799}, {52660, 670}
X(65287) = barycentric quotient X(i)/X(j) for these (i, j): {2, 25423}, {99, 7766}, {110, 59232}, {524, 45680}, {662, 51291}, {670, 41259}, {799, 52138}, {4576, 32449}, {4609, 10010}, {25424, 6}, {43688, 523}, {51450, 18105}, {51844, 661}, {52660, 512}, {59258, 850}

X(65288) = TRILINEAR POLE OF LINE {2, 1962}

Barycentrics    (a-b)*(a-c)*(a*(2*b+c)+b*(b+2*c))*(c*(2*b+c)+a*(b+2*c)) : :

X(65288) lies on the Steiner circumellipse and on these lines: {2, 18827}, {37, 56703}, {99, 3570}, {190, 65250}, {519, 35173}, {536, 35166}, {551, 3227}, {645, 53655}, {664, 61170}, {668, 4115}, {670, 27853}, {671, 3679}, {799, 31148}, {903, 4688}, {1018, 6540}, {1121, 31165}, {1494, 31158}, {2481, 50095}, {3226, 25426}, {3228, 4664}, {3799, 53648}, {3807, 32041}, {3952, 4562}, {4595, 53658}, {14616, 17346}, {14970, 42054}, {17264, 35152}, {17294, 20538}, {17310, 35153}, {18822, 40891}, {18825, 60671}, {18829, 27805}, {20529, 29575}, {23891, 58128}, {24074, 32042}, {29615, 35162}, {31143, 43097}, {31167, 43098}, {35143, 50127}, {35144, 50107}, {35180, 62644}, {46922, 60680}, {65169, 65280}

X(65288) = midpoint of X(i) and X(j) for these {i,j}: {2, 39367}
X(65288) = reflection of X(i) in X(j) for these {i,j}: {2, 35068}, {18827, 2}
X(65288) = isotomic conjugate of X(28840)
X(65288) = trilinear pole of line {2, 1962}
X(65288) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4784}, {31, 28840}, {513, 60697}, {604, 4913}, {649, 4649}, {661, 59243}, {663, 60715}, {667, 16826}, {669, 51314}, {798, 51356}, {810, 31904}, {875, 20142}, {1333, 4824}, {1919, 60706}, {1980, 60719}, {3063, 60717}, {3669, 60713}, {3733, 60724}, {3842, 57129}, {4948, 28607}, {4963, 34819}, {6591, 60703}, {22383, 60699}, {43924, 60711}, {57181, 60731}
X(65288) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 28840}, {9, 4784}, {37, 4824}, {3161, 4913}, {5375, 4649}, {6631, 16826}, {9296, 60706}, {10001, 60717}, {31998, 51356}, {35123, 45657}, {36830, 59243}, {36911, 4948}, {39026, 60697}, {39054, 51311}, {39062, 31904}, {62648, 4963}
X(65288) = X(i)-cross conjugate of X(j) for these {i, j}: {4804, 75}, {24325, 7035}, {28840, 2}, {42334, 4600}, {54256, 10}, {54258, 37}
X(65288) = pole of line {3993, 16826} with respect to the Yff parabola
X(65288) = pole of line {20142, 28840} with respect to the Wallace hyperbola
X(65288) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(799)}}, {{A, B, C, X(42), X(59030)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(551), X(23891)}}, {{A, B, C, X(643), X(42030)}}, {{A, B, C, X(661), X(31148)}}, {{A, B, C, X(662), X(1018)}}, {{A, B, C, X(812), X(43266)}}, {{A, B, C, X(1026), X(50095)}}, {{A, B, C, X(3257), X(8691)}}, {{A, B, C, X(3903), X(4584)}}, {{A, B, C, X(4033), X(4602)}}, {{A, B, C, X(4369), X(45315)}}, {{A, B, C, X(4585), X(17346)}}, {{A, B, C, X(4615), X(37210)}}, {{A, B, C, X(4632), X(6742)}}, {{A, B, C, X(4688), X(24004)}}, {{A, B, C, X(5388), X(65040)}}, {{A, B, C, X(6011), X(60172)}}, {{A, B, C, X(7192), X(47774)}}, {{A, B, C, X(9070), X(36085)}}, {{A, B, C, X(17254), X(62669)}}, {{A, B, C, X(23354), X(29584)}}, {{A, B, C, X(25666), X(45663)}}, {{A, B, C, X(27929), X(45665)}}, {{A, B, C, X(29615), X(62644)}}, {{A, B, C, X(35068), X(40529)}}, {{A, B, C, X(40891), X(56811)}}, {{A, B, C, X(55213), X(65041)}}
X(65288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35068, 39367, 18827}

X(65289) = ISOTOMIC CONJUGATE OF X(3907)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(b^2+a*c)*(a*b+c^2) : :
X(65289) =

X(65289) lies on the Steiner circumellipse and on these lines: {7, 18827}, {57, 35143}, {75, 290}, {85, 53559}, {99, 4594}, {100, 65291}, {109, 62464}, {190, 27805}, {256, 2481}, {257, 1121}, {320, 35151}, {350, 53198}, {522, 65293}, {527, 40873}, {648, 4603}, {651, 4586}, {662, 2966}, {664, 3888}, {666, 21362}, {668, 56241}, {671, 60245}, {893, 60014}, {903, 7249}, {1020, 6648}, {1414, 65281}, {1423, 3225}, {1431, 3226}, {1432, 3227}, {1447, 35165}, {1581, 39775}, {1821, 39040}, {1916, 4440}, {1967, 3123}, {3228, 65011}, {4014, 61421}, {4017, 4625}, {4357, 40846}, {4389, 14616}, {4419, 35144}, {4451, 18025}, {4458, 4569}, {4552, 4562}, {4554, 18830}, {4572, 46132}, {4573, 53655}, {6604, 35176}, {6613, 41353}, {6646, 40099}, {7015, 60046}, {7018, 18816}, {7019, 34393}, {7260, 65280}, {10030, 53222}, {16591, 36800}, {16609, 35146}, {17272, 35141}, {17493, 35167}, {22003, 32041}, {23996, 35044}, {28391, 39917}, {33940, 43093}, {35150, 52135}, {35159, 39126}, {35180, 63782}, {39919, 64909}, {40432, 55082}, {57887, 59191}, {57968, 65272}

X(65289) = reflection of X(i) in X(j) for these {i,j}: {40846, 4357}
X(65289) = isotomic conjugate of X(3907)
X(65289) = trilinear pole of line {2, 257}
X(65289) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3287}, {8, 56242}, {9, 20981}, {21, 7234}, {31, 3907}, {33, 22093}, {41, 4369}, {55, 4367}, {56, 4477}, {110, 40608}, {171, 663}, {172, 650}, {212, 54229}, {284, 57234}, {513, 2330}, {522, 7122}, {604, 4529}, {643, 4128}, {645, 21755}, {649, 2329}, {652, 7119}, {657, 7175}, {667, 7081}, {692, 4459}, {798, 27958}, {810, 14006}, {884, 4447}, {894, 3063}, {1333, 4140}, {1334, 18200}, {1919, 17787}, {1933, 60577}, {1946, 7009}, {2053, 24533}, {2175, 4374}, {2194, 2533}, {2195, 53553}, {2295, 7252}, {2344, 45882}, {3271, 4579}, {3737, 20964}, {3903, 61053}, {3939, 53541}, {3955, 18344}, {4095, 57129}, {4107, 51858}, {4164, 7077}, {4612, 21823}, {4636, 21725}, {5027, 56154}, {5546, 16592}, {7121, 30584}, {7176, 8641}, {14296, 18265}, {17103, 63461}, {17420, 59159}, {18111, 40972}, {22373, 36797}, {52133, 58862}, {53559, 65375}, {57264, 64865}
X(65289) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4477}, {2, 3907}, {9, 3287}, {37, 4140}, {223, 4367}, {244, 40608}, {478, 20981}, {1086, 4459}, {1214, 2533}, {3160, 4369}, {3161, 4529}, {5375, 2329}, {6631, 7081}, {9296, 17787}, {10001, 894}, {16591, 804}, {16592, 3023}, {31998, 27958}, {37137, 9860}, {39026, 2330}, {39053, 7009}, {39062, 14006}, {39063, 53553}, {40590, 57234}, {40593, 4374}, {40598, 30584}, {40611, 7234}, {40615, 7200}, {40617, 53541}, {40622, 53559}, {40837, 54229}, {52659, 4922}, {55060, 4128}, {59507, 28006}, {62575, 27831}
X(65289) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {55018, 329}
X(65289) = X(i)-cross conjugate of X(j) for these {i, j}: {38, 4564}, {661, 85}, {2254, 1581}, {3903, 27805}, {3907, 2}, {4388, 46102}, {6646, 1275}, {29055, 65332}, {29840, 1016}, {56928, 4998}
X(65289) = pole of line {11683, 27958} with respect to the Kiepert parabola
X(65289) = pole of line {65209, 65289} with respect to the Steiner circumellipse
X(65289) = pole of line {7081, 17739} with respect to the Yff parabola
X(65289) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(4552)}}, {{A, B, C, X(10), X(8691)}}, {{A, B, C, X(75), X(662)}}, {{A, B, C, X(86), X(15455)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(100), X(3888)}}, {{A, B, C, X(307), X(65300)}}, {{A, B, C, X(522), X(4458)}}, {{A, B, C, X(645), X(51614)}}, {{A, B, C, X(651), X(4572)}}, {{A, B, C, X(661), X(53559)}}, {{A, B, C, X(799), X(6649)}}, {{A, B, C, X(1020), X(1414)}}, {{A, B, C, X(1492), X(65338)}}, {{A, B, C, X(2701), X(8750)}}, {{A, B, C, X(3123), X(8632)}}, {{A, B, C, X(3663), X(21362)}}, {{A, B, C, X(4017), X(61052)}}, {{A, B, C, X(4373), X(51563)}}, {{A, B, C, X(4492), X(4557)}}, {{A, B, C, X(4551), X(55213)}}, {{A, B, C, X(4594), X(27805)}}, {{A, B, C, X(4628), X(29095)}}, {{A, B, C, X(6011), X(36086)}}, {{A, B, C, X(6386), X(35008)}}, {{A, B, C, X(17254), X(56543)}}, {{A, B, C, X(27853), X(36860)}}, {{A, B, C, X(36099), X(52938)}}, {{A, B, C, X(51560), X(56188)}}

X(65290) = TRILINEAR POLE OF LINE {2, 914}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^3+a^2*(-b+c)+(b-c)*(b+c)^2-a*(b^2+c^2))*(a^3+a^2*(b-c)-(b-c)*(b+c)^2-a*(b^2+c^2)) : :

X(65290) lies on the Steiner circumellipse and on these lines: {75, 46133}, {90, 2481}, {99, 36082}, {190, 65216}, {522, 6517}, {658, 65292}, {671, 60249}, {903, 7318}, {1069, 60046}, {1121, 2994}, {2164, 60014}, {6512, 54966}, {7040, 33298}, {8822, 14616}, {10001, 53211}, {18025, 36626}, {18816, 20570}, {32038, 65175}, {65162, 65270}

X(65290) = trilinear pole of line {2, 914}
X(65290) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 46389}, {25, 59973}, {41, 21188}, {46, 663}, {55, 51648}, {73, 57124}, {284, 55214}, {512, 3193}, {513, 61397}, {650, 2178}, {652, 52033}, {657, 56848}, {667, 5552}, {798, 31631}, {810, 3559}, {1068, 1946}, {1406, 3900}, {1415, 6506}, {3063, 5905}, {3157, 18344}, {7252, 21853}, {8648, 56417}
X(65290) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 46389}, {223, 51648}, {1146, 6506}, {3160, 21188}, {6505, 59973}, {6631, 5552}, {10001, 5905}, {31998, 31631}, {39026, 61397}, {39053, 1068}, {39054, 3193}, {39062, 3559}, {40590, 55214}
X(65290) = X(i)-cross conjugate of X(j) for these {i, j}: {6516, 664}, {10529, 1016}, {11415, 46102}, {20078, 1275}, {44426, 333}, {62858, 4564}
X(65290) = pole of line {92, 31631} with respect to the Kiepert parabola
X(65290) = pole of line {6516, 65290} with respect to the Steiner circumellipse
X(65290) = pole of line {5552, 5942} with respect to the Yff parabola
X(65290) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(1305)}}, {{A, B, C, X(63), X(6517)}}, {{A, B, C, X(75), X(4561)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(643), X(43347)}}, {{A, B, C, X(653), X(1414)}}, {{A, B, C, X(655), X(934)}}, {{A, B, C, X(1309), X(3699)}}, {{A, B, C, X(4592), X(65251)}}, {{A, B, C, X(4626), X(58993)}}, {{A, B, C, X(26706), X(36086)}}
X(65290) = barycentric product X(i)*X(j) for these (i, j): {190, 7318}, {314, 65175}, {1069, 46404}, {2164, 4572}, {2994, 664}, {4554, 90}, {18026, 6513}, {20570, 651}, {36082, 76}, {36626, 658}, {46406, 7072}, {52938, 6512}, {55247, 57696}, {60249, 99}, {65164, 7040}, {65216, 75}
X(65290) = barycentric quotient X(i)/X(j) for these (i, j): {1, 46389}, {7, 21188}, {57, 51648}, {63, 59973}, {65, 55214}, {90, 650}, {99, 31631}, {101, 61397}, {108, 52033}, {109, 2178}, {190, 5552}, {522, 6506}, {648, 3559}, {651, 46}, {653, 1068}, {655, 56417}, {662, 3193}, {664, 5905}, {934, 56848}, {1069, 652}, {1172, 57124}, {1461, 1406}, {1708, 57102}, {1813, 3157}, {2164, 663}, {2994, 522}, {4551, 21853}, {4552, 21077}, {4554, 20930}, {4558, 1800}, {6512, 57241}, {6513, 521}, {6516, 6505}, {6517, 6511}, {7040, 3064}, {7072, 657}, {7318, 514}, {20570, 4391}, {31623, 57083}, {36082, 6}, {36626, 3239}, {55248, 4516}, {57696, 55248}, {60249, 523}, {60794, 36054}, {65175, 65}, {65216, 1}

X(65291) = ISOTOMIC CONJUGATE OF X(3810)

Barycentrics    (a-b)*(a^2-a*b+b^2)*(a-c)*(a+b-c)*(a-b+c)*(a^2-a*c+c^2) : :

X(65291) lies on the Steiner circumellipse and on these lines: {99, 8685}, {100, 65289}, {109, 18830}, {190, 4621}, {651, 4562}, {662, 65271}, {664, 4579}, {903, 56358}, {983, 2481}, {1014, 18827}, {1121, 17743}, {1633, 53208}, {3227, 7132}, {4551, 57969}, {4552, 4586}, {4559, 57965}, {4569, 6649}, {7033, 18816}, {8684, 52923}, {14616, 40415}, {14727, 36086}, {18025, 56180}, {35141, 56196}, {36036, 53196}

X(65291) = isotomic conjugate of X(3810)
X(65291) = trilinear pole of line {2, 1429}
X(65291) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 50514}, {31, 3810}, {41, 3776}, {55, 3777}, {244, 40499}, {512, 3794}, {513, 3056}, {514, 20665}, {522, 7032}, {649, 3061}, {650, 2275}, {657, 41777}, {663, 982}, {667, 3705}, {1019, 20684}, {2194, 3801}, {3063, 3662}, {3271, 3888}, {3287, 3863}, {3721, 7252}, {3737, 3778}, {3784, 18344}, {3808, 7077}, {3900, 7248}, {4073, 43924}, {4136, 57129}, {4531, 7192}, {4560, 16584}, {7185, 8641}, {7649, 20753}, {18155, 40935}, {18191, 62753}, {33947, 63461}
X(65291) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3810}, {223, 3777}, {1214, 3801}, {3160, 3776}, {5375, 3061}, {6631, 3705}, {10001, 3662}, {39026, 3056}, {39054, 3794}, {52659, 53533}
X(65291) = X(i)-cross conjugate of X(j) for these {i, j}: {31, 4564}, {3212, 4998}, {3810, 2}, {3905, 7035}, {17350, 1275}, {25304, 57750}, {32937, 46102}, {48094, 85}
X(65291) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(100), X(4579)}}, {{A, B, C, X(646), X(51614)}}, {{A, B, C, X(651), X(1014)}}, {{A, B, C, X(655), X(4572)}}, {{A, B, C, X(662), X(36036)}}, {{A, B, C, X(1293), X(34071)}}, {{A, B, C, X(1897), X(36801)}}, {{A, B, C, X(3573), X(52923)}}, {{A, B, C, X(4606), X(55281)}}, {{A, B, C, X(8750), X(34067)}}, {{A, B, C, X(9086), X(55996)}}, {{A, B, C, X(44765), X(51560)}}
X(65291) = barycentric product X(i)*X(j) for these (i, j): {76, 8685}, {190, 56358}, {651, 7033}, {668, 7132}, {1415, 7034}, {4554, 983}, {4573, 56196}, {4621, 7}, {10030, 8684}, {16603, 33514}, {17743, 664}, {38810, 4551}, {40415, 4552}, {56180, 658}
X(65291) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3810}, {7, 3776}, {57, 3777}, {100, 3061}, {101, 3056}, {109, 2275}, {190, 3705}, {226, 3801}, {604, 50514}, {644, 4073}, {651, 982}, {658, 7185}, {662, 3794}, {664, 3662}, {692, 20665}, {906, 20753}, {934, 41777}, {983, 650}, {1252, 40499}, {1415, 7032}, {1429, 3808}, {1461, 7248}, {1813, 3784}, {3776, 3020}, {3911, 53533}, {3952, 4136}, {4551, 3721}, {4552, 2887}, {4554, 33930}, {4557, 20684}, {4559, 3778}, {4564, 3888}, {4566, 16888}, {4573, 33947}, {4579, 56558}, {4621, 8}, {4998, 33946}, {6649, 7187}, {7033, 4391}, {7132, 513}, {7255, 17197}, {8684, 4876}, {8685, 6}, {17743, 522}, {21859, 7237}, {23067, 20727}, {29055, 3863}, {37137, 3865}, {38810, 18155}, {38813, 7252}, {40415, 4560}, {56180, 3239}, {56196, 3700}, {56358, 514}

X(65292) = ISOTOMIC CONJUGATE OF X(35057)

Barycentrics    (a-b)*b*(a-c)*(a+b-c)*c*(a-b+c)*(a^2+a*b+b^2-c^2)*(a^2-b^2+a*c+c^2) : :

X(65292) lies on the Steiner circumellipse and on these lines: {7, 14616}, {75, 1494}, {79, 2481}, {85, 6757}, {99, 26700}, {150, 265}, {190, 15455}, {290, 52390}, {320, 46141}, {350, 53215}, {648, 24001}, {658, 65290}, {664, 6742}, {671, 43682}, {811, 16077}, {1111, 2166}, {1121, 17862}, {1414, 4077}, {1565, 52200}, {2160, 60014}, {2966, 35049}, {3226, 52372}, {3227, 19796}, {3615, 55082}, {4554, 32042}, {4566, 35174}, {4572, 54957}, {4872, 51883}, {7100, 60046}, {7321, 18816}, {8818, 35144}, {10030, 35152}, {13486, 65274}, {17078, 50148}, {17181, 58740}, {17753, 56845}, {18025, 20880}, {18593, 60013}, {18827, 52382}, {23674, 33298}, {35145, 63171}, {35164, 63642}, {51663, 53192}, {52621, 65293}, {52938, 54968}, {55209, 65280}

X(65292) = isotomic conjugate of X(35057)
X(65292) = trilinear pole of line {2, 7110}
X(65292) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 9404}, {31, 35057}, {32, 57066}, {33, 23226}, {35, 663}, {41, 14838}, {48, 65105}, {55, 2605}, {60, 58304}, {212, 54244}, {284, 55210}, {512, 35193}, {521, 14975}, {647, 41502}, {649, 52405}, {650, 2174}, {657, 2003}, {661, 35192}, {667, 4420}, {692, 53524}, {798, 56440}, {810, 11107}, {1021, 21741}, {1399, 3900}, {1442, 8641}, {1576, 6741}, {1825, 57134}, {1919, 42033}, {1946, 6198}, {2175, 4467}, {2194, 57099}, {2195, 53554}, {2341, 2624}, {2594, 21789}, {2611, 65375}, {3063, 3219}, {3709, 40214}, {3939, 53542}, {4041, 17104}, {5546, 20982}, {6740, 14270}, {7265, 57657}, {7343, 42657}, {8648, 56422}, {9447, 18160}, {18344, 52408}, {52425, 65100}, {56934, 63461}
X(65292) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 35057}, {9, 9404}, {223, 2605}, {1086, 53524}, {1214, 57099}, {1249, 65105}, {3160, 14838}, {4858, 6741}, {5375, 52405}, {6376, 57066}, {6631, 4420}, {8287, 3024}, {9296, 42033}, {10001, 3219}, {16591, 53563}, {31998, 56440}, {36830, 35192}, {38340, 9904}, {39052, 41502}, {39053, 6198}, {39054, 35193}, {39060, 52412}, {39062, 11107}, {39063, 53554}, {40590, 55210}, {40593, 4467}, {40615, 7202}, {40617, 53542}, {40622, 2611}, {40837, 54244}, {56847, 4041}, {62570, 7265}, {62602, 65100}
X(65292) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {55017, 329}
X(65292) = X(i)-cross conjugate of X(j) for these {i, j}: {1577, 85}, {3874, 4564}, {6742, 15455}, {17483, 1275}, {21276, 57757}, {35057, 2}, {36038, 63759}, {52367, 46102}, {52390, 35049}, {55186, 75}, {63782, 4554}
X(65292) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(55181)}}, {{A, B, C, X(7), X(1414)}}, {{A, B, C, X(65), X(29055)}}, {{A, B, C, X(75), X(811)}}, {{A, B, C, X(85), X(4635)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(883), X(32007)}}, {{A, B, C, X(1577), X(17886)}}, {{A, B, C, X(1783), X(2691)}}, {{A, B, C, X(2864), X(52937)}}, {{A, B, C, X(19796), X(41314)}}, {{A, B, C, X(30257), X(36086)}}, {{A, B, C, X(43740), X(65201)}}
X(65292) = barycentric product X(i)*X(j) for these (i, j): {264, 65300}, {1978, 52372}, {2160, 4572}, {3262, 47317}, {4554, 79}, {4569, 7110}, {4573, 6757}, {4625, 8818}, {6742, 85}, {13486, 349}, {15413, 34922}, {15455, 7}, {18026, 52381}, {18160, 55017}, {18593, 35139}, {20565, 651}, {26700, 76}, {30690, 664}, {32680, 41804}, {35049, 850}, {36064, 46234}, {38340, 75}, {43682, 99}, {46404, 7100}, {46405, 56844}, {46406, 7073}, {52344, 658}, {52374, 668}, {52382, 799}, {52390, 6331}, {55209, 65}, {63171, 811}
X(65292) = barycentric quotient X(i)/X(j) for these (i, j): {1, 9404}, {2, 35057}, {4, 65105}, {7, 14838}, {57, 2605}, {65, 55210}, {75, 57066}, {79, 650}, {85, 4467}, {94, 52356}, {99, 56440}, {100, 52405}, {109, 2174}, {110, 35192}, {162, 41502}, {190, 4420}, {222, 23226}, {226, 57099}, {241, 53554}, {273, 65100}, {278, 54244}, {476, 2341}, {514, 53524}, {648, 11107}, {651, 35}, {653, 6198}, {655, 56422}, {658, 1442}, {662, 35193}, {664, 3219}, {668, 42033}, {934, 2003}, {1020, 2594}, {1414, 40214}, {1441, 7265}, {1461, 1399}, {1464, 2624}, {1577, 6741}, {1789, 23090}, {1813, 52408}, {1835, 47230}, {2160, 663}, {2171, 58304}, {3615, 1021}, {3669, 53542}, {3676, 7202}, {4017, 20982}, {4077, 8287}, {4552, 3678}, {4554, 319}, {4565, 17104}, {4566, 16577}, {4569, 17095}, {4572, 33939}, {4573, 56934}, {4625, 34016}, {6063, 18160}, {6186, 3063}, {6742, 9}, {6757, 3700}, {7073, 657}, {7100, 652}, {7110, 3900}, {7178, 2611}, {8606, 65102}, {8818, 4041}, {10404, 30600}, {11076, 42657}, {13149, 7282}, {13486, 284}, {14838, 3024}, {15455, 8}, {16609, 53563}, {18026, 52412}, {18593, 526}, {20565, 4391}, {26700, 6}, {30690, 522}, {32674, 14975}, {32680, 6740}, {34922, 1783}, {35049, 110}, {35174, 41226}, {36064, 2159}, {38340, 1}, {41804, 32679}, {43682, 523}, {46406, 52421}, {47317, 104}, {51663, 2088}, {51664, 22094}, {52344, 3239}, {52372, 649}, {52374, 513}, {52375, 7252}, {52381, 521}, {52382, 661}, {52388, 8611}, {52390, 647}, {52393, 3737}, {52569, 4976}, {52607, 1825}, {52610, 22342}, {53321, 21741}, {55209, 314}, {55236, 4516}, {56193, 1334}, {56844, 654}, {57785, 16755}, {60053, 1793}, {61225, 17454}, {63171, 656}, {63782, 3647}, {64834, 18344}, {65205, 31938}, {65300, 3}

X(65293) = X(190)X(4529)∩X(664)X(3907)

Barycentrics    (a-b)*b*(a-c)*(a+b-c)*c*(a-b+c)*(a^3+b^3-a*b*c-c^3)*(a^3-b^3-a*b*c+c^3) : :

X(65293) lies on the Steiner circumellipse and on these lines: {75, 35150}, {85, 35163}, {190, 4529}, {290, 18033}, {522, 65289}, {527, 40846}, {664, 3907}, {1121, 40845}, {1275, 6648}, {2481, 7261}, {3225, 39930}, {3226, 39919}, {3512, 60014}, {4374, 4569}, {4554, 4586}, {4625, 53655}, {7340, 65281}, {9436, 18827}, {10030, 63895}, {17254, 53212}, {18036, 18816}, {35143, 40862}, {35167, 64231}, {52621, 65292}

X(65293) = trilinear pole of line {2, 20940}
X(65293) = X(i)-isoconjugate-of-X(j) for these {i, j}: {522, 18262}, {650, 19554}, {663, 17798}, {2175, 4458}, {3063, 3509}, {3287, 41882}, {5018, 8641}, {8638, 40724}, {40754, 46388}
X(65293) = X(i)-Dao conjugate of X(j) for these {i, j}: {10001, 3509}, {40593, 4458}
X(65293) = X(i)-cross conjugate of X(j) for these {i, j}: {693, 63895}, {4088, 31618}
X(65293) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(190)}}, {{A, B, C, X(522), X(3907)}}, {{A, B, C, X(1275), X(7340)}}, {{A, B, C, X(18160), X(52621)}}, {{A, B, C, X(34083), X(46404)}}, {{A, B, C, X(37135), X(40873)}}
X(65293) = barycentric product X(i)*X(j) for these (i, j): {3512, 4572}, {4554, 7261}, {18036, 651}, {40781, 46135}, {40845, 664}, {40846, 65289}, {46406, 7281}, {51614, 85}, {65237, 75}
X(65293) = barycentric quotient X(i)/X(j) for these (i, j): {85, 4458}, {109, 19554}, {651, 17798}, {658, 5018}, {664, 3509}, {927, 40754}, {1415, 18262}, {3512, 663}, {4552, 20715}, {4554, 4645}, {4572, 17789}, {6516, 20741}, {7061, 3287}, {7261, 650}, {7281, 657}, {8852, 3063}, {18033, 27951}, {18036, 4391}, {29055, 41882}, {34085, 40724}, {37137, 41532}, {40781, 926}, {40845, 522}, {40846, 3907}, {51614, 9}, {63895, 60577}, {64231, 3716}, {65237, 1}, {65289, 40873}

X(65294) = TRILINEAR POLE OF LINE {2, 658}

Barycentrics    (a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^3-a^2*b+b^3+b*c^2-2*c^3+a*(-b^2+c^2))*(a^3-2*b^3-a^2*c+b^2*c+c^3+a*(b^2-c^2)) : :

X(65294) lies on the Steiner circumellipse and on these lines: {99, 24016}, {190, 1275}, {269, 53217}, {279, 35094}, {522, 4626}, {648, 4616}, {658, 32040}, {664, 59457}, {666, 60581}, {668, 57928}, {677, 6606}, {1088, 35164}, {1121, 17078}, {2400, 35157}, {2424, 14727}, {2481, 43736}, {3668, 35150}, {4025, 23586}, {4569, 24011}, {4586, 32668}, {6528, 52619}, {9436, 18025}, {18026, 36838}, {53212, 60984}, {53228, 57792}

X(65294) = trilinear pole of line {2, 658}
X(65294) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 46392}, {516, 8641}, {649, 51418}, {657, 910}, {663, 41339}, {676, 1253}, {1021, 51436}, {1024, 56785}, {1456, 4105}, {1886, 65102}, {2310, 2426}, {3063, 40869}, {23973, 24012}, {43035, 57180}, {46388, 56900}
X(65294) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 46392}, {658, 63790}, {5375, 51418}, {10001, 40869}, {17113, 676}, {40618, 57292}, {45250, 52614}
X(65294) = X(i)-cross conjugate of X(j) for these {i, j}: {2400, 52156}, {4025, 57548}, {9436, 1275}, {23973, 658}, {43042, 56668}, {46402, 57752}, {50333, 30705}, {57455, 36838}
X(65294) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(190)}}, {{A, B, C, X(522), X(57064)}}, {{A, B, C, X(927), X(9436)}}, {{A, B, C, X(1275), X(24011)}}, {{A, B, C, X(1309), X(13577)}}, {{A, B, C, X(4573), X(52937)}}, {{A, B, C, X(4616), X(36838)}}, {{A, B, C, X(15419), X(30805)}}, {{A, B, C, X(35094), X(43042)}}, {{A, B, C, X(46964), X(56183)}}
X(65294) = barycentric product X(i)*X(j) for these (i, j): {103, 46406}, {279, 57928}, {1275, 2400}, {2338, 52937}, {4998, 60581}, {18025, 658}, {23973, 57548}, {24016, 76}, {32668, 561}, {36101, 4569}, {43736, 4554}, {46135, 52213}, {52156, 664}, {56668, 927}, {57792, 677}, {57996, 934}, {65245, 75}
X(65294) = barycentric quotient X(i)/X(j) for these (i, j): {1, 46392}, {100, 51418}, {103, 657}, {279, 676}, {651, 41339}, {658, 516}, {664, 40869}, {677, 220}, {911, 8641}, {927, 56900}, {934, 910}, {1262, 2426}, {1275, 2398}, {1815, 57108}, {2283, 56785}, {2338, 4105}, {2400, 1146}, {2424, 14936}, {4025, 57292}, {4566, 17747}, {4569, 30807}, {4616, 14953}, {4617, 1456}, {4626, 43035}, {6516, 51376}, {7056, 39470}, {15634, 42462}, {18025, 3239}, {23586, 23973}, {23973, 23972}, {24011, 24015}, {24015, 24014}, {24016, 6}, {32642, 14827}, {32668, 31}, {36039, 1253}, {36056, 65102}, {36101, 3900}, {36118, 1886}, {36122, 65103}, {40116, 7071}, {41353, 9502}, {43042, 1566}, {43736, 650}, {46406, 35517}, {52156, 522}, {52213, 926}, {53150, 42069}, {53321, 51436}, {55346, 41321}, {56668, 50333}, {57928, 346}, {57996, 4397}, {60581, 11}, {65218, 7079}, {65245, 1}

X(65295) = TRILINEAR POLE OF LINE {2, 196}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-a^3*c-b^3*c+a*(b-c)^2*c+b^2*c^2+b*c^3-2*c^4+a^2*(-2*b^2+b*c+c^2))*(a^4-a^3*b-2*b^4+a*b*(b-c)^2+b^3*c+b^2*c^2-b*c^3+c^4+a^2*(b^2+b*c-2*c^2)) : :

X(65295) lies on the Steiner circumellipse and on these lines: {4, 56666}, {99, 36067}, {102, 60046}, {190, 46102}, {225, 35149}, {317, 46136}, {648, 65297}, {664, 55346}, {666, 60584}, {903, 56869}, {1121, 52780}, {2481, 36121}, {2966, 32643}, {4025, 36118}, {4391, 54240}, {4586, 32667}, {5081, 22464}, {6332, 39053}, {17896, 18026}, {35145, 41207}, {35157, 53152}, {40701, 56634}, {53218, 54412}

X(65295) = isotomic conjugate of X(39471)
X(65295) = trilinear pole of line {2, 196}
X(65295) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 46391}, {31, 39471}, {184, 14304}, {212, 53522}, {515, 1946}, {652, 2182}, {663, 46974}, {1455, 57108}, {1459, 51361}, {2188, 6087}, {2361, 61041}, {2425, 34591}, {2638, 23987}, {8755, 36054}, {24035, 39687}, {32652, 57291}, {34050, 65102}, {51421, 57134}
X(65295) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 39471}, {9, 46391}, {653, 63792}, {16596, 57291}, {39053, 515}, {39060, 64194}, {40837, 53522}, {46398, 10017}, {62605, 14304}
X(65295) = X(i)-cross conjugate of X(j) for these {i, j}: {1309, 65336}, {2405, 13149}, {5081, 46102}, {10015, 56666}, {22464, 55346}, {23987, 653}, {39471, 2}, {46400, 57751}, {53152, 52780}
X(65295) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(190)}}, {{A, B, C, X(1309), X(5081)}}, {{A, B, C, X(4025), X(4391)}}, {{A, B, C, X(16230), X(18006)}}, {{A, B, C, X(24032), X(41207)}}, {{A, B, C, X(36118), X(54240)}}
X(65295) = barycentric product X(i)*X(j) for these (i, j): {102, 46404}, {264, 65297}, {1275, 53152}, {1309, 56666}, {1969, 36040}, {2399, 55346}, {4998, 60584}, {18022, 32643}, {18026, 36100}, {23987, 57551}, {32667, 561}, {34393, 653}, {36067, 76}, {36121, 4554}, {40701, 6081}, {52780, 664}
X(65295) = barycentric quotient X(i)/X(j) for these (i, j): {1, 46391}, {2, 39471}, {92, 14304}, {102, 652}, {108, 2182}, {196, 6087}, {278, 53522}, {651, 46974}, {653, 515}, {1783, 51361}, {2006, 61041}, {2399, 2968}, {2406, 38554}, {2432, 3270}, {4566, 51368}, {6081, 268}, {10015, 10017}, {14837, 57291}, {15629, 57108}, {18026, 64194}, {23984, 23987}, {23987, 23986}, {24032, 24035}, {24035, 24034}, {32643, 184}, {32667, 31}, {32677, 1946}, {32714, 1455}, {34393, 6332}, {36040, 48}, {36055, 36054}, {36067, 6}, {36100, 521}, {36118, 34050}, {36121, 650}, {36127, 8755}, {39053, 63792}, {46404, 35516}, {52607, 51421}, {52780, 522}, {53152, 1146}, {55346, 2406}, {60000, 8677}, {60584, 11}, {65297, 3}, {65329, 59283}, {65331, 56638}, {65335, 63857}

X(65296) == TRILINEAR POLE OF LINE {3, 77}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^2-b^2-c^2) : :

X(65296) lies on the MacBeath circumconic and on these lines: {6, 23587}, {7, 8759}, {57, 60025}, {63, 1815}, {69, 7358}, {77, 7004}, {85, 2988}, {100, 677}, {109, 6183}, {110, 934}, {222, 1814}, {269, 60049}, {279, 2990}, {348, 22129}, {394, 50559}, {648, 4569}, {651, 658}, {662, 46639}, {664, 13138}, {895, 1439}, {905, 65304}, {1088, 2989}, {1275, 4554}, {1331, 6516}, {1332, 52610}, {1407, 2991}, {1427, 2987}, {1446, 2986}, {1461, 65298}, {1797, 7177}, {1936, 56383}, {1993, 57498}, {1996, 6180}, {4563, 55205}, {4566, 65303}, {13243, 43736}, {22053, 40443}, {23144, 30682}, {23973, 35312}, {24015, 43190}, {34028, 50561}, {43358, 53632}, {61225, 65187}

X(65296) = isogonal conjugate of X(65103)
X(65296) = trilinear pole of line {3, 77}
X(65296) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 65103}, {4, 657}, {9, 18344}, {19, 3900}, {21, 55206}, {25, 3239}, {27, 4524}, {28, 4171}, {29, 3709}, {33, 650}, {34, 4130}, {41, 44426}, {42, 17926}, {55, 3064}, {92, 8641}, {101, 42069}, {108, 3119}, {112, 52335}, {158, 65102}, {162, 36197}, {200, 6591}, {220, 7649}, {273, 57180}, {278, 4105}, {281, 663}, {318, 3063}, {393, 57108}, {512, 2322}, {513, 7079}, {514, 7071}, {522, 607}, {523, 2332}, {608, 4163}, {649, 7046}, {652, 1857}, {653, 3022}, {661, 4183}, {667, 7101}, {728, 43923}, {1021, 1824}, {1043, 2489}, {1096, 57055}, {1146, 8750}, {1172, 4041}, {1253, 17924}, {1783, 2310}, {1826, 21789}, {1827, 62747}, {1880, 58329}, {1897, 14936}, {1973, 4397}, {1974, 52622}, {2170, 56183}, {2175, 46110}, {2204, 4086}, {2212, 4391}, {2299, 3700}, {2326, 4705}, {2327, 58757}, {2328, 2501}, {2333, 7253}, {2356, 28132}, {3271, 65160}, {3939, 8735}, {4079, 59482}, {4081, 32674}, {4082, 43925}, {4515, 57200}, {4516, 65201}, {4528, 8752}, {6059, 6332}, {6520, 58340}, {6524, 57057}, {6558, 42067}, {7008, 14298}, {7063, 55233}, {7073, 65105}, {7115, 23615}, {7151, 57049}, {7154, 8058}, {7252, 53008}, {7367, 54239}, {13149, 24012}, {14427, 36125}, {14827, 46107}, {21666, 32739}, {23289, 41320}, {23351, 60431}, {24010, 32714}, {31623, 63461}, {35508, 36118}, {36122, 46392}, {36124, 52614}, {36128, 58331}, {36421, 55230}, {36910, 58313}, {46404, 61050}, {52371, 65104}, {53285, 64835}, {55208, 56182}, {57045, 61349}
X(65296) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 65103}, {6, 3900}, {125, 36197}, {223, 3064}, {226, 3700}, {478, 18344}, {1015, 42069}, {1147, 65102}, {3160, 44426}, {5375, 7046}, {6337, 4397}, {6338, 15416}, {6503, 57055}, {6505, 3239}, {6609, 6591}, {6631, 7101}, {7358, 23970}, {10001, 318}, {11517, 4130}, {17113, 17924}, {22391, 8641}, {26932, 1146}, {34467, 14936}, {34591, 52335}, {35072, 4081}, {36033, 657}, {36830, 4183}, {36908, 2501}, {37867, 58340}, {38983, 3119}, {39006, 2310}, {39026, 7079}, {39054, 2322}, {40591, 4171}, {40592, 17926}, {40593, 46110}, {40611, 55206}, {40617, 8735}, {40618, 24026}, {40619, 21666}, {40628, 23615}, {46095, 46392}, {59608, 24006}, {62565, 4086}, {62647, 4163}
X(65296) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1275, 348}, {4569, 934}, {4573, 658}, {23586, 57479}, {59457, 1804}
X(65296) = X(i)-cross conjugate of X(j) for these {i, j}: {63, 7045}, {652, 40443}, {905, 77}, {1804, 59457}, {1813, 6516}, {4091, 1444}, {7011, 55346}, {22131, 59}, {23144, 44717}, {64885, 69}, {65102, 3}
X(65296) = pole of line {1817, 18750} with respect to the Kiepert parabola
X(65296) = pole of line {3900, 65102} with respect to the Stammler hyperbola
X(65296) = pole of line {934, 46964} with respect to the Steiner circumellipse
X(65296) = pole of line {40555, 55145} with respect to the Steiner inellipse
X(65296) = pole of line {144, 348} with respect to the Hutson-Moses hyperbola
X(65296) = pole of line {4397, 17926} with respect to the Wallace hyperbola
X(65296) = pole of line {1146, 7358} with respect to the dual conic of polar circle
X(65296) = pole of line {347, 3262} with respect to the dual conic of Feuerbach hyperbola
X(65296) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(63), X(100)}}, {{A, B, C, X(101), X(23601)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(222), X(36059)}}, {{A, B, C, X(345), X(30610)}}, {{A, B, C, X(348), X(4554)}}, {{A, B, C, X(658), X(1414)}}, {{A, B, C, X(905), X(1638)}}, {{A, B, C, X(906), X(35326)}}, {{A, B, C, X(934), X(13149)}}, {{A, B, C, X(1444), X(4610)}}, {{A, B, C, X(1812), X(4636)}}, {{A, B, C, X(4571), X(65222)}}, {{A, B, C, X(4573), X(6517)}}, {{A, B, C, X(4617), X(24016)}}, {{A, B, C, X(4626), X(4637)}}, {{A, B, C, X(7358), X(15416)}}, {{A, B, C, X(23603), X(41353)}}, {{A, B, C, X(30679), X(54118)}}, {{A, B, C, X(32714), X(52610)}}, {{A, B, C, X(51642), X(51664)}}, {{A, B, C, X(57055), X(58835)}}, {{A, B, C, X(57455), X(57479)}}
X(65296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {651, 4617, 658}

X(65297) = TRILINEAR POLE OF LINE {3, 102}

Barycentrics    a^2*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^4+b^4-a^3*c-b^3*c+a*(b-c)^2*c+b^2*c^2+b*c^3-2*c^4+a^2*(-2*b^2+b*c+c^2))*(a^4-a^3*b-2*b^4+a*b*(b-c)^2+b^3*c+b^2*c^2-b*c^3+c^4+a^2*(b^2+b*c-2*c^2)) : :

X(65297) lies on the MacBeath circumconic and on these lines: {59, 1331}, {102, 14733}, {108, 521}, {110, 36067}, {287, 17950}, {518, 14203}, {648, 65295}, {651, 7128}, {653, 44765}, {1262, 1813}, {1332, 4564}, {1461, 4091}, {1814, 32677}, {1815, 15629}, {1993, 60000}, {2399, 2406}, {2432, 65304}, {2988, 52780}, {3218, 36100}, {4558, 32643}, {4563, 4620}, {8677, 14776}, {8759, 36121}, {14919, 56560}, {17942, 43754}, {24029, 65299}, {32667, 65298}, {62402, 63068}, {65303, 65312}

X(65297) = trilinear pole of line {3, 102}
X(65297) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 46391}, {6, 14304}, {9, 53522}, {19, 39471}, {282, 6087}, {514, 51361}, {515, 650}, {521, 8755}, {522, 2182}, {654, 59283}, {663, 64194}, {1021, 51421}, {1455, 3239}, {2310, 2406}, {2399, 42076}, {2425, 24026}, {2432, 24034}, {3063, 35516}, {3064, 46974}, {3270, 24035}, {3271, 42718}, {3900, 34050}, {7452, 53560}, {23893, 51408}, {23987, 34591}, {40117, 57291}, {42755, 52663}, {46393, 56638}, {51424, 62747}
X(65297) = X(i)-vertex conjugate of X(j) for these {i, j}: {14776, 65297}
X(65297) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 39471}, {9, 14304}, {478, 53522}, {10001, 35516}, {36033, 46391}
X(65297) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65295, 36067}
X(65297) = X(i)-cross conjugate of X(j) for these {i, j}: {2323, 59}, {2425, 109}, {2432, 102}, {32641, 901}, {32643, 36067}
X(65297) = pole of line {1309, 2405} with respect to the Steiner circumellipse
X(65297) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(14776)}}, {{A, B, C, X(7), X(24016)}}, {{A, B, C, X(59), X(1262)}}, {{A, B, C, X(81), X(65331)}}, {{A, B, C, X(108), X(1461)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(284), X(40116)}}, {{A, B, C, X(518), X(34371)}}, {{A, B, C, X(521), X(4091)}}, {{A, B, C, X(653), X(4565)}}, {{A, B, C, X(655), X(901)}}, {{A, B, C, X(2323), X(32641)}}, {{A, B, C, X(3257), X(4619)}}, {{A, B, C, X(4591), X(37139)}}, {{A, B, C, X(13404), X(35184)}}, {{A, B, C, X(17942), X(17950)}}, {{A, B, C, X(33637), X(65216)}}, {{A, B, C, X(36082), X(38828)}}

X(65298) = TRILINEAR POLE OF LINE {3, 31}

Barycentrics    a^2*(a-b)*(a-c)*(a^2+2*a*b+b^2+c^2)*(a^2+b^2+2*a*c+c^2) : :

X(65298) lies on the MacBeath circumconic and on these lines: {101, 1310}, {110, 32676}, {163, 4558}, {190, 36147}, {287, 1910}, {648, 3732}, {651, 32674}, {662, 4563}, {692, 1331}, {895, 923}, {909, 2339}, {911, 1815}, {913, 2990}, {1036, 34068}, {1039, 8759}, {1415, 1813}, {1438, 1449}, {1461, 65296}, {1472, 62769}, {1797, 2221}, {1974, 23075}, {2159, 14919}, {2224, 16783}, {2281, 18268}, {2284, 34074}, {2576, 8115}, {2577, 8116}, {4251, 30878}, {4586, 54982}, {14543, 44765}, {32667, 65297}, {32675, 65299}, {32678, 60053}, {33952, 65168}, {34072, 65307}, {34079, 56219}, {36131, 44769}, {36141, 65304}, {36142, 65321}, {36145, 65309}, {36146, 65301}, {36149, 65323}, {36151, 65325}, {51686, 60049}, {60134, 60197}

X(65298) = isogonal conjugate of X(6590)
X(65298) = trilinear pole of line {3, 31}
X(65298) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6590}, {2, 8678}, {4, 2522}, {6, 2517}, {19, 23874}, {37, 47844}, {75, 2484}, {76, 8646}, {81, 48395}, {274, 50494}, {281, 51644}, {388, 650}, {513, 2345}, {514, 612}, {522, 2285}, {523, 2303}, {525, 4206}, {649, 4385}, {661, 1010}, {693, 54416}, {798, 44154}, {905, 7102}, {1038, 3064}, {1460, 4391}, {1577, 44119}, {1783, 26933}, {2170, 14594}, {2286, 44426}, {3239, 4320}, {3610, 57200}, {3669, 3974}, {3700, 5323}, {3900, 7365}, {4130, 7197}, {5227, 7649}, {5517, 65303}, {6591, 54433}, {7085, 17924}, {7103, 57055}, {7253, 8898}, {8816, 17115}, {10375, 14331}, {17421, 59083}, {18344, 56367}, {54982, 55046}
X(65298) = X(i)-vertex conjugate of X(j) for these {i, j}: {651, 32736}, {662, 8750}
X(65298) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 6590}, {6, 23874}, {9, 2517}, {206, 2484}, {5375, 4385}, {31998, 44154}, {32664, 8678}, {36033, 2522}, {36830, 1010}, {39006, 26933}, {39016, 5515}, {39026, 2345}, {40586, 48395}, {40589, 47844}
X(65298) = X(i)-cross conjugate of X(j) for these {i, j}: {1496, 7045}, {30435, 1252}
X(65298) = pole of line {2484, 6590} with respect to the Stammler hyperbola
X(65298) = pole of line {835, 32691} with respect to the Steiner circumellipse
X(65298) = pole of line {2339, 28606} with respect to the Hutson-Moses hyperbola
X(65298) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(100), X(4565)}}, {{A, B, C, X(101), X(163)}}, {{A, B, C, X(109), X(190)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(666), X(785)}}, {{A, B, C, X(825), X(8750)}}, {{A, B, C, X(901), X(4606)}}, {{A, B, C, X(1293), X(37212)}}, {{A, B, C, X(1449), X(2284)}}, {{A, B, C, X(1459), X(48070)}}, {{A, B, C, X(2421), X(25898)}}, {{A, B, C, X(3257), X(28162)}}, {{A, B, C, X(3732), X(52610)}}, {{A, B, C, X(3939), X(4628)}}, {{A, B, C, X(4557), X(28847)}}, {{A, B, C, X(4584), X(59135)}}, {{A, B, C, X(4588), X(27834)}}, {{A, B, C, X(4591), X(8694)}}, {{A, B, C, X(4604), X(4629)}}, {{A, B, C, X(4627), X(8652)}}, {{A, B, C, X(6335), X(37137)}}, {{A, B, C, X(9058), X(65216)}}, {{A, B, C, X(28895), X(32736)}}, {{A, B, C, X(29063), X(33952)}}, {{A, B, C, X(32691), X(37215)}}, {{A, B, C, X(37141), X(58991)}}, {{A, B, C, X(58992), X(65232)}}
X(65298) = barycentric product X(i)*X(j) for these (i, j): {1, 1310}, {31, 54982}, {48, 65341}, {100, 56328}, {109, 30479}, {163, 60197}, {190, 2221}, {1036, 664}, {1039, 6516}, {1245, 99}, {1415, 64989}, {1472, 668}, {2281, 799}, {2339, 651}, {4561, 51686}, {32691, 69}, {34260, 65168}, {36099, 63}, {37215, 6}, {56219, 662}, {57923, 692}
X(65298) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2517}, {3, 23874}, {6, 6590}, {31, 8678}, {32, 2484}, {42, 48395}, {48, 2522}, {58, 47844}, {59, 14594}, {99, 44154}, {100, 4385}, {101, 2345}, {109, 388}, {110, 1010}, {163, 2303}, {560, 8646}, {603, 51644}, {692, 612}, {834, 5515}, {906, 5227}, {1036, 522}, {1039, 44426}, {1245, 523}, {1310, 75}, {1331, 54433}, {1332, 19799}, {1415, 2285}, {1459, 26933}, {1461, 7365}, {1472, 513}, {1576, 44119}, {1813, 56367}, {1918, 50494}, {2221, 514}, {2281, 661}, {2339, 4391}, {3939, 3974}, {4574, 3610}, {6614, 7197}, {8750, 7102}, {30479, 35519}, {32656, 7085}, {32660, 2286}, {32676, 4206}, {32691, 4}, {32739, 54416}, {36059, 1038}, {36099, 92}, {37215, 76}, {51686, 7649}, {54982, 561}, {56219, 1577}, {56328, 693}, {57923, 40495}, {60197, 20948}, {65341, 1969}

X(65299) = TRILINEAR POLE OF LINE {3, 201}

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2-b^2-c^2)*(a^2-a*b+b^2-c^2)*(a^2-b^2-a*c+c^2) : :

X(65299) lies on the MacBeath circumconic and on these lines: {6, 23593}, {59, 110}, {80, 8759}, {514, 651}, {518, 1411}, {521, 1331}, {648, 35174}, {662, 18315}, {677, 52377}, {895, 52391}, {905, 1813}, {908, 2006}, {914, 22128}, {1332, 6332}, {1797, 62402}, {1807, 60047}, {1814, 9028}, {1815, 6510}, {1944, 2989}, {2161, 60025}, {2341, 63778}, {2986, 60091}, {2988, 18359}, {2991, 49783}, {4558, 44717}, {4585, 13136}, {13138, 51562}, {16577, 60022}, {22123, 23120}, {23189, 44710}, {24029, 65297}, {32675, 65298}, {34048, 52212}, {37140, 65217}, {42405, 57973}, {43756, 56540}, {52610, 65300}

X(65299) = isogonal conjugate of X(65104)
X(65299) = trilinear pole of line {3, 201}
X(65299) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 65104}, {2, 58313}, {4, 654}, {6, 44428}, {19, 3738}, {25, 3904}, {27, 53562}, {29, 21828}, {33, 3960}, {36, 3064}, {92, 8648}, {270, 2610}, {278, 53285}, {281, 53314}, {318, 21758}, {514, 52427}, {522, 52413}, {607, 4453}, {649, 5081}, {650, 1870}, {661, 17515}, {663, 17923}, {860, 7252}, {909, 53047}, {1021, 1835}, {1172, 53527}, {1443, 65103}, {1464, 17926}, {1783, 53525}, {1825, 62746}, {1830, 62750}, {1845, 61238}, {2170, 4242}, {2189, 6370}, {2190, 2600}, {2299, 4707}, {2323, 7649}, {2326, 51663}, {2361, 17924}, {3218, 18344}, {3271, 65162}, {3615, 47230}, {3724, 57215}, {4282, 24006}, {4511, 6591}, {4560, 44113}, {6369, 8882}, {7012, 46384}, {7113, 44426}, {8755, 61042}, {14776, 46398}, {32702, 57434}, {36123, 53046}, {42666, 46103}, {46107, 52426}, {46110, 52434}, {53546, 56183}, {56844, 65105}
X(65299) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 65104}, {5, 2600}, {6, 3738}, {9, 44428}, {226, 4707}, {5375, 5081}, {6505, 3904}, {15898, 3064}, {22391, 8648}, {23980, 53047}, {32664, 58313}, {36033, 654}, {36830, 17515}, {39006, 53525}
X(65299) = X(i)-Ceva conjugate of X(j) for these {i, j}: {35174, 2222}, {47318, 655}
X(65299) = X(i)-cross conjugate of X(j) for these {i, j}: {22123, 59}, {46391, 78}, {53532, 77}
X(65299) = pole of line {2600, 3738} with respect to the Stammler hyperbola
X(65299) = pole of line {515, 21368} with respect to the Yff parabola
X(65299) = pole of line {655, 908} with respect to the Hutson-Moses hyperbola
X(65299) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(59), X(44717)}}, {{A, B, C, X(63), X(3257)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(345), X(50039)}}, {{A, B, C, X(514), X(521)}}, {{A, B, C, X(518), X(9028)}}, {{A, B, C, X(653), X(36050)}}, {{A, B, C, X(662), X(2617)}}, {{A, B, C, X(771), X(4554)}}, {{A, B, C, X(813), X(2359)}}, {{A, B, C, X(908), X(914)}}, {{A, B, C, X(1783), X(4587)}}, {{A, B, C, X(2335), X(36107)}}, {{A, B, C, X(4551), X(4605)}}, {{A, B, C, X(4585), X(22128)}}, {{A, B, C, X(24029), X(42718)}}, {{A, B, C, X(36061), X(37140)}}, {{A, B, C, X(36804), X(52351)}}
X(65299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35174, 65329, 62735}

X(65300) = ISOGONAL CONJUGATE OF X(65105)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2-b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2+a*c+c^2) : :

X(65300) lies on the MacBeath circumconic and on these lines: {63, 14919}, {79, 8759}, {110, 9811}, {222, 63171}, {648, 24001}, {651, 38340}, {662, 35049}, {677, 35338}, {895, 52390}, {1071, 7100}, {2160, 60025}, {2986, 43682}, {2988, 30690}, {2990, 52374}, {6180, 8818}, {6742, 13138}, {13136, 15455}, {18593, 60022}, {22145, 50433}, {43756, 56848}, {52372, 60049}, {52381, 65302}, {52610, 65299}

X(65300) = isogonal conjugate of X(65105)
X(65300) = trilinear pole of line {3, 7100}
X(65300) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 65105}, {4, 9404}, {9, 54244}, {19, 35057}, {25, 57066}, {29, 55210}, {33, 14838}, {35, 3064}, {55, 65100}, {112, 6741}, {281, 2605}, {523, 41502}, {607, 4467}, {650, 6198}, {657, 7282}, {661, 11107}, {663, 52412}, {1021, 1825}, {1172, 57099}, {1442, 65103}, {1783, 53524}, {2174, 44426}, {2212, 18160}, {2299, 7265}, {2501, 35193}, {2594, 17926}, {2611, 65201}, {3219, 18344}, {4391, 14975}, {4420, 6591}, {6740, 47230}, {7202, 56183}, {7649, 52405}, {20982, 36797}, {21824, 52914}, {24006, 35192}, {41226, 58313}, {46103, 58304}, {53542, 65160}, {55206, 56934}, {56422, 65104}
X(65300) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 65105}, {6, 35057}, {223, 65100}, {226, 7265}, {478, 54244}, {6505, 57066}, {34591, 6741}, {36033, 9404}, {36830, 11107}, {39006, 53524}
X(65300) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65292, 26700}
X(65300) = X(i)-cross conjugate of X(j) for these {i, j}: {656, 77}, {22122, 59}, {44706, 7045}, {51664, 63171}
X(65300) = pole of line {35057, 65105} with respect to the Stammler hyperbola
X(65300) = pole of line {17781, 52381} with respect to the Hutson-Moses hyperbola
X(65300) = intersection, other than A, B, C, of circumconics {{A, B, C, X(63), X(662)}}, {{A, B, C, X(72), X(8691)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(222), X(52610)}}, {{A, B, C, X(348), X(4552)}}, {{A, B, C, X(525), X(35053)}}, {{A, B, C, X(653), X(53206)}}, {{A, B, C, X(905), X(35055)}}, {{A, B, C, X(4025), X(45756)}}, {{A, B, C, X(13486), X(38340)}}, {{A, B, C, X(14592), X(35050)}}, {{A, B, C, X(15455), X(52381)}}, {{A, B, C, X(37141), X(44063)}}, {{A, B, C, X(51663), X(51664)}}, {{A, B, C, X(53952), X(65216)}}, {{A, B, C, X(56269), X(65375)}}
X(65300) = barycentric product X(i)*X(j) for these (i, j): {3, 65292}, {664, 7100}, {1332, 52374}, {1409, 55209}, {1414, 52388}, {1789, 4566}, {1813, 30690}, {2160, 65164}, {4561, 52372}, {4569, 8606}, {4592, 52382}, {6516, 79}, {6742, 77}, {13486, 307}, {15455, 222}, {18593, 60053}, {20565, 36059}, {26700, 69}, {34922, 4131}, {35049, 525}, {36061, 41804}, {38340, 63}, {43682, 4558}, {52381, 651}, {52390, 99}, {52393, 65233}, {63171, 662}, {65296, 7110}
X(65300) = barycentric quotient X(i)/X(j) for these (i, j): {3, 35057}, {6, 65105}, {48, 9404}, {56, 54244}, {57, 65100}, {63, 57066}, {73, 57099}, {77, 4467}, {79, 44426}, {109, 6198}, {110, 11107}, {163, 41502}, {222, 14838}, {265, 52356}, {348, 18160}, {603, 2605}, {651, 52412}, {656, 6741}, {906, 52405}, {934, 7282}, {1214, 7265}, {1331, 4420}, {1332, 42033}, {1409, 55210}, {1459, 53524}, {1789, 7253}, {1813, 3219}, {2160, 3064}, {4558, 56440}, {4575, 35193}, {6186, 18344}, {6516, 319}, {6742, 318}, {7100, 522}, {7335, 23226}, {8606, 3900}, {13486, 29}, {15455, 7017}, {17094, 17886}, {18593, 44427}, {23067, 3678}, {23226, 3024}, {26700, 4}, {30690, 46110}, {32660, 2174}, {32661, 35192}, {32662, 2341}, {35049, 648}, {36059, 35}, {36061, 6740}, {36064, 36119}, {38340, 92}, {43682, 14618}, {47317, 16082}, {51640, 22094}, {51663, 35235}, {51664, 8287}, {52372, 7649}, {52374, 17924}, {52381, 4391}, {52382, 24006}, {52388, 4086}, {52390, 523}, {52393, 57215}, {52610, 16577}, {53321, 1825}, {55234, 21824}, {56193, 53008}, {56844, 44428}, {63171, 1577}, {65164, 33939}, {65233, 3969}, {65292, 264}, {65296, 17095}, {65299, 41226}

X(65301) = TRILINEAR POLE OF LINE {3, 348}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b*(b-c)-a*c)*(a^2-b^2-c^2)*(a^2-a*b+c*(-b+c)) : :

X(65301) lies on the MacBeath circumconic and on these lines: {110, 927}, {239, 1462}, {320, 56783}, {648, 46135}, {651, 666}, {664, 36086}, {673, 60025}, {677, 883}, {1331, 4025}, {1332, 15413}, {1815, 26006}, {2481, 8759}, {2988, 18031}, {2990, 34018}, {4554, 26692}, {4558, 15419}, {13136, 15418}, {13138, 51560}, {31637, 60047}, {36146, 65298}

X(65301) = trilinear pole of line {3, 348}
X(65301) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 46388}, {19, 926}, {33, 665}, {34, 52614}, {92, 8638}, {607, 2254}, {650, 2356}, {657, 1876}, {661, 37908}, {663, 5089}, {672, 18344}, {918, 2212}, {1024, 42071}, {1458, 65103}, {1861, 3063}, {1973, 50333}, {2204, 4088}, {2223, 3064}, {2299, 24290}, {2332, 53551}, {2340, 6591}, {3286, 55206}, {3709, 54407}, {5236, 8641}, {7071, 53544}, {7079, 53539}, {8735, 54325}, {8750, 17435}, {9454, 44426}, {9455, 46110}, {15149, 63461}
X(65301) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 926}, {226, 24290}, {6337, 50333}, {10001, 1861}, {11517, 52614}, {22391, 8638}, {26932, 17435}, {33675, 44426}, {36033, 46388}, {36830, 37908}, {62554, 18344}, {62565, 4088}, {62599, 3064}
X(65301) = X(i)-Ceva conjugate of X(j) for these {i, j}: {46135, 927}
X(65301) = X(i)-cross conjugate of X(j) for these {i, j}: {20811, 59}, {39470, 69}
X(65301) = pole of line {10025, 40704} with respect to the Hutson-Moses hyperbola
X(65301) = intersection, other than A, B, C, of circumconics {{A, B, C, X(63), X(660)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(304), X(4555)}}, {{A, B, C, X(658), X(53643)}}, {{A, B, C, X(898), X(34055)}}, {{A, B, C, X(2398), X(26006)}}, {{A, B, C, X(2400), X(4025)}}, {{A, B, C, X(4569), X(4573)}}, {{A, B, C, X(57853), X(65258)}}

X(65302) = ISOGONAL CONJUGATE OF X(14571)

Barycentrics    a*(a^2-b^2-c^2)*(a^3-a^2*b+b^3-a*(b-c)^2-b*c^2)*(a^3-a*(b-c)^2-a^2*c-b^2*c+c^3) : :

X(65302) lies on the MacBeath circumconic and on these lines: {2, 222}, {7, 55963}, {21, 104}, {63, 1813}, {78, 255}, {81, 648}, {100, 1364}, {145, 280}, {219, 30680}, {323, 52499}, {345, 394}, {348, 22129}, {416, 65305}, {677, 3935}, {909, 2339}, {914, 22128}, {938, 36123}, {1812, 4558}, {1993, 23122}, {2342, 36819}, {2401, 2990}, {2423, 2991}, {2720, 26703}, {2975, 7335}, {2987, 55259}, {3218, 36100}, {3219, 55987}, {4358, 13136}, {4422, 17811}, {5253, 30493}, {5554, 24537}, {6001, 15405}, {7361, 62798}, {8759, 43728}, {9965, 41514}, {10759, 59788}, {15066, 56753}, {15524, 38460}, {16594, 25934}, {18359, 53811}, {20744, 21940}, {25954, 60025}, {26884, 62971}, {26892, 35973}, {37628, 60047}, {37783, 44769}, {40457, 61492}, {40571, 46639}, {41081, 65179}, {41610, 65322}, {52381, 65300}, {54953, 62799}, {65331, 65342}

X(65302) = isogonal conjugate of X(14571)
X(65302) = trilinear pole of line {3, 23187}
X(65302) = perspector of circumconic {{A, B, C, X(54953), X(57753)}}
X(65302) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14571}, {4, 2183}, {6, 1785}, {9, 1875}, {19, 517}, {25, 908}, {27, 51377}, {28, 21801}, {33, 1465}, {101, 39534}, {108, 46393}, {119, 913}, {281, 1457}, {393, 22350}, {607, 22464}, {608, 6735}, {649, 53151}, {653, 53549}, {859, 1826}, {909, 21664}, {1145, 8752}, {1435, 51380}, {1474, 17757}, {1769, 1783}, {1845, 2161}, {1846, 2316}, {1861, 51987}, {1897, 3310}, {1973, 3262}, {2333, 17139}, {2427, 7649}, {2804, 32674}, {3064, 23981}, {5089, 54364}, {7115, 35015}, {8750, 10015}, {8756, 14260}, {16082, 42078}, {18344, 24029}, {23980, 36123}, {32675, 53047}, {34234, 42072}, {34586, 64835}, {36110, 60339}, {36127, 52307}, {40116, 42756}, {52212, 52427}, {52413, 56416}
X(65302) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14571}, {6, 517}, {9, 1785}, {478, 1875}, {1015, 39534}, {5375, 53151}, {6337, 3262}, {6505, 908}, {14578, 54064}, {23980, 21664}, {26932, 10015}, {34467, 3310}, {35072, 2804}, {35128, 53047}, {36033, 2183}, {36830, 4246}, {38983, 46393}, {39004, 60339}, {39006, 1769}, {39175, 8609}, {40584, 1845}, {40591, 21801}, {40618, 36038}, {40628, 35015}, {51574, 17757}, {60339, 3326}, {62647, 6735}
X(65302) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18816, 104}, {57753, 53786}
X(65302) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {909, 34550}, {15405, 4329}
X(65302) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 15405}, {912, 69}, {2431, 6081}, {14578, 104}, {46974, 77}, {52307, 100}, {52407, 1444}, {53786, 57753}
X(65302) = pole of line {517, 14571} with respect to the Stammler hyperbola
X(65302) = pole of line {104, 1295} with respect to the Steiner circumellipse
X(65302) = pole of line {2804, 6713} with respect to the Steiner inellipse
X(65302) = pole of line {13136, 62669} with respect to the Hutson-Moses hyperbola
X(65302) = pole of line {3262, 14571} with respect to the Wallace hyperbola
X(65302) = pole of line {10015, 26611} with respect to the dual conic of polar circle
X(65302) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(7), X(326)}}, {{A, B, C, X(48), X(2298)}}, {{A, B, C, X(69), X(26637)}}, {{A, B, C, X(72), X(392)}}, {{A, B, C, X(77), X(30712)}}, {{A, B, C, X(81), X(222)}}, {{A, B, C, X(86), X(62277)}}, {{A, B, C, X(88), X(905)}}, {{A, B, C, X(89), X(7177)}}, {{A, B, C, X(97), X(1790)}}, {{A, B, C, X(104), X(16082)}}, {{A, B, C, X(105), X(293)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(145), X(64082)}}, {{A, B, C, X(189), X(3719)}}, {{A, B, C, X(219), X(22129)}}, {{A, B, C, X(226), X(21740)}}, {{A, B, C, X(268), X(2287)}}, {{A, B, C, X(275), X(829)}}, {{A, B, C, X(283), X(55942)}}, {{A, B, C, X(285), X(1259)}}, {{A, B, C, X(294), X(652)}}, {{A, B, C, X(296), X(9372)}}, {{A, B, C, X(304), X(18465)}}, {{A, B, C, X(321), X(5887)}}, {{A, B, C, X(401), X(416)}}, {{A, B, C, X(525), X(2771)}}, {{A, B, C, X(693), X(57801)}}, {{A, B, C, X(739), X(32658)}}, {{A, B, C, X(850), X(57850)}}, {{A, B, C, X(914), X(3904)}}, {{A, B, C, X(1071), X(3998)}}, {{A, B, C, X(1073), X(34048)}}, {{A, B, C, X(1214), X(1385)}}, {{A, B, C, X(1264), X(8048)}}, {{A, B, C, X(1462), X(22145)}}, {{A, B, C, X(1795), X(34051)}}, {{A, B, C, X(1796), X(31626)}}, {{A, B, C, X(1807), X(4358)}}, {{A, B, C, X(1809), X(34234)}}, {{A, B, C, X(2349), X(52780)}}, {{A, B, C, X(2481), X(63245)}}, {{A, B, C, X(2994), X(44189)}}, {{A, B, C, X(3083), X(13388)}}, {{A, B, C, X(3084), X(13389)}}, {{A, B, C, X(3692), X(55989)}}, {{A, B, C, X(3935), X(26006)}}, {{A, B, C, X(4373), X(19611)}}, {{A, B, C, X(6332), X(18359)}}, {{A, B, C, X(6514), X(19607)}}, {{A, B, C, X(7055), X(13577)}}, {{A, B, C, X(11064), X(16164)}}, {{A, B, C, X(14578), X(34858)}}, {{A, B, C, X(16731), X(23983)}}, {{A, B, C, X(17191), X(41801)}}, {{A, B, C, X(18444), X(56382)}}, {{A, B, C, X(21739), X(37781)}}, {{A, B, C, X(23135), X(40400)}}, {{A, B, C, X(24537), X(27174)}}, {{A, B, C, X(33858), X(63171)}}, {{A, B, C, X(36055), X(63068)}}, {{A, B, C, X(36607), X(36609)}}, {{A, B, C, X(36918), X(52392)}}, {{A, B, C, X(37669), X(40571)}}, {{A, B, C, X(40715), X(41804)}}, {{A, B, C, X(41798), X(57055)}}, {{A, B, C, X(45127), X(60082)}}, {{A, B, C, X(55400), X(56046)}}, {{A, B, C, X(55979), X(56266)}}, {{A, B, C, X(56003), X(56269)}}, {{A, B, C, X(56070), X(56338)}}, {{A, B, C, X(58012), X(64393)}}, {{A, B, C, X(63154), X(64841)}}
X(65302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34051, 52663, 34234}

X(65303) = TRILINEAR POLE OF LINE {3, 37}

Barycentrics    a*(a-b)*(a-c)*(a^3+a^2*(b+c)+(b-c)*(b+c)^2+a*(b^2+2*b*c-c^2))*(a^3+a^2*(b+c)-(b-c)*(b+c)^2+a*(-b^2+2*b*c+c^2)) : :
X(65303) = -3*X[2]+2*X[17421]

X(65303) lies on the MacBeath circumconic and on these lines: {2, 17421}, {100, 4558}, {110, 1783}, {651, 53349}, {668, 4563}, {1018, 1331}, {1332, 3952}, {1449, 56225}, {1797, 4674}, {1813, 4551}, {1814, 5800}, {1830, 60025}, {1897, 46640}, {2994, 44105}, {4566, 65296}, {5380, 65321}, {5554, 24537}, {14919, 25909}, {61229, 65179}, {65297, 65312}

X(65303) = anticomplement of X(17421)
X(65303) = trilinear pole of line {3, 37}
X(65303) = X(i)-isoconjugate-of-X(j) for these {i, j}: {406, 1459}, {513, 12514}, {514, 36744}, {521, 1452}, {522, 64020}, {649, 5739}, {2484, 14258}, {4025, 44086}, {5517, 65298}, {17421, 32691}, {42707, 57129}
X(65303) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 5739}, {17421, 17421}, {36830, 27174}, {39026, 12514}, {55046, 5517}
X(65303) = X(i)-cross conjugate of X(j) for these {i, j}: {2522, 2}, {48395, 2298}
X(65303) = pole of line {1310, 59083} with respect to the Steiner circumellipse
X(65303) = pole of line {2345, 3876} with respect to the Hutson-Moses hyperbola
X(65303) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(80), X(100)}}, {{A, B, C, X(108), X(6742)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(162), X(664)}}, {{A, B, C, X(643), X(65227)}}, {{A, B, C, X(644), X(8701)}}, {{A, B, C, X(833), X(4555)}}, {{A, B, C, X(883), X(5800)}}, {{A, B, C, X(934), X(13486)}}, {{A, B, C, X(1897), X(9058)}}, {{A, B, C, X(2522), X(17421)}}, {{A, B, C, X(4240), X(25909)}}, {{A, B, C, X(4246), X(24537)}}, {{A, B, C, X(36037), X(65225)}}, {{A, B, C, X(36049), X(58992)}}, {{A, B, C, X(37135), X(43350)}}, {{A, B, C, X(52914), X(53349)}}
X(65303) = barycentric product X(i)*X(j) for these (i, j): {100, 60156}, {321, 59130}, {1783, 57832}, {46010, 668}, {56225, 664}, {57667, 6335}, {59083, 69}
X(65303) = barycentric quotient X(i)/X(j) for these (i, j): {100, 5739}, {101, 12514}, {109, 45126}, {110, 27174}, {692, 36744}, {1310, 14258}, {1415, 64020}, {1783, 406}, {2522, 17421}, {3952, 42707}, {8678, 5517}, {32674, 1452}, {46010, 513}, {56225, 522}, {57667, 905}, {57832, 15413}, {59083, 4}, {59130, 81}, {60156, 693}

X(65304) = X(650)X(651)∩X(652)X(1813)

Barycentrics    a^2*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2+b*c-2*c^2+a*(-2*b+c))*(a^2-b^2-c^2)*(a^2-2*b^2+a*(b-2*c)+b*c+c^2) : :

X(65304) lies on the MacBeath circumconic and on these lines: {110, 14733}, {648, 17926}, {650, 651}, {652, 1813}, {895, 17975}, {905, 65296}, {1121, 2988}, {1156, 8759}, {1331, 44717}, {1332, 57055}, {1815, 22128}, {2291, 60025}, {2432, 65297}, {2989, 62723}, {2990, 34056}, {4558, 23090}, {4563, 15411}, {35340, 61231}, {36141, 65298}, {40116, 59105}, {44765, 57757}, {56320, 60487}, {62756, 62764}

X(65304) = trilinear pole of line {3, 1813}
X(65304) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 6366}, {33, 1638}, {92, 6139}, {108, 33573}, {278, 14392}, {281, 14413}, {393, 14414}, {513, 60431}, {527, 18344}, {650, 23710}, {657, 38461}, {661, 52891}, {663, 37805}, {1055, 44426}, {1155, 3064}, {1172, 30574}, {1323, 65103}, {2501, 62756}, {6591, 6745}, {6603, 7649}, {7012, 52334}, {23890, 42069}, {54239, 56763}
X(65304) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 6366}, {22391, 6139}, {36830, 52891}, {38983, 33573}, {39026, 60431}
X(65304) = X(i)-Ceva conjugate of X(j) for these {i, j}: {35157, 14733}
X(65304) = intersection, other than A, B, C, of circumconics {{A, B, C, X(63), X(37143)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(650), X(652)}}, {{A, B, C, X(666), X(1812)}}, {{A, B, C, X(901), X(1790)}}, {{A, B, C, X(6513), X(51562)}}, {{A, B, C, X(7045), X(44717)}}, {{A, B, C, X(35187), X(40407)}}, {{A, B, C, X(36085), X(57668)}}
X(65304) = barycentric product X(i)*X(j) for these (i, j): {3, 35157}, {219, 60487}, {304, 36141}, {305, 32728}, {394, 65335}, {1121, 1813}, {1156, 6516}, {1331, 62723}, {1332, 34056}, {2291, 65164}, {2968, 59105}, {4592, 62764}, {6517, 65340}, {14733, 69}, {37139, 63}, {41798, 65296}, {44717, 60479}, {60047, 664}
X(65304) = barycentric quotient X(i)/X(j) for these (i, j): {3, 6366}, {73, 30574}, {101, 60431}, {109, 23710}, {110, 52891}, {184, 6139}, {212, 14392}, {222, 1638}, {255, 14414}, {603, 14413}, {651, 37805}, {652, 33573}, {906, 6603}, {934, 38461}, {1121, 46110}, {1156, 44426}, {1331, 6745}, {1813, 527}, {2291, 3064}, {4575, 62756}, {6516, 30806}, {7117, 52334}, {14733, 4}, {18889, 65103}, {23351, 42069}, {32660, 1055}, {32728, 25}, {34056, 17924}, {34068, 18344}, {35157, 264}, {36059, 1155}, {36141, 19}, {37139, 92}, {56410, 12831}, {59105, 55346}, {60047, 522}, {60487, 331}, {61493, 59935}, {62723, 46107}, {62764, 24006}, {63748, 21666}, {65296, 37780}, {65335, 2052}

X(65305) = X(287)X(401)∩X(520)X(648)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^6*c^2+b^4*(b^2-c^2)^2+a^4*(b^4-2*c^4)+a^2*(-2*b^6+b^4*c^2+c^6))*(a^6*b^2+c^4*(b^2-c^2)^2+a^4*(-2*b^4+c^4)+a^2*(b^6+b^2*c^4-2*c^6)) : :

X(65305) lies on the MacBeath circumconic and on these lines: {110, 32320}, {250, 18315}, {287, 401}, {416, 65302}, {450, 2986}, {476, 1298}, {520, 648}, {576, 40804}, {685, 39469}, {852, 14919}, {877, 43187}, {895, 1987}, {1993, 57500}, {2987, 15143}, {3580, 14510}, {4563, 15631}, {5640, 65325}, {14966, 43754}, {15329, 53175}, {23582, 58305}, {34211, 63741}, {35360, 41208}, {44768, 62519}, {60036, 60053}

X(65305) = isogonal conjugate of X(6130)
X(65305) = trilinear pole of line {3, 1625}
X(65305) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6130}, {523, 1955}, {656, 41204}, {798, 44137}, {810, 16089}, {1577, 1971}, {2313, 15412}, {2616, 32428}, {14208, 58311}
X(65305) = X(i)-vertex conjugate of X(j) for these {i, j}: {685, 65305}, {6529, 44828}
X(65305) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 6130}, {31998, 44137}, {36830, 401}, {39062, 16089}, {40596, 41204}
X(65305) = X(i)-Ceva conjugate of X(j) for these {i, j}: {41208, 53205}, {53205, 53708}
X(65305) = X(i)-cross conjugate of X(j) for these {i, j}: {2966, 805}, {4230, 110}, {60036, 1298}
X(65305) = pole of line {4230, 65305} with respect to the MacBeath circumconic
X(65305) = pole of line {6130, 52128} with respect to the Stammler hyperbola
X(65305) = pole of line {22456, 53173} with respect to the Steiner circumellipse
X(65305) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(16077)}}, {{A, B, C, X(4), X(2713)}}, {{A, B, C, X(6), X(685)}}, {{A, B, C, X(54), X(935)}}, {{A, B, C, X(99), X(44828)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(250), X(476)}}, {{A, B, C, X(340), X(19167)}}, {{A, B, C, X(401), X(2966)}}, {{A, B, C, X(416), X(4246)}}, {{A, B, C, X(450), X(15329)}}, {{A, B, C, X(511), X(805)}}, {{A, B, C, X(520), X(6080)}}, {{A, B, C, X(576), X(53155)}}, {{A, B, C, X(852), X(3284)}}, {{A, B, C, X(1304), X(46426)}}, {{A, B, C, X(1625), X(33513)}}, {{A, B, C, X(2867), X(15407)}}, {{A, B, C, X(4226), X(15143)}}, {{A, B, C, X(5504), X(13494)}}, {{A, B, C, X(6528), X(32661)}}, {{A, B, C, X(10422), X(53944)}}, {{A, B, C, X(14483), X(32732)}}, {{A, B, C, X(15958), X(54950)}}, {{A, B, C, X(23061), X(51263)}}, {{A, B, C, X(36885), X(63472)}}, {{A, B, C, X(39099), X(61198)}}, {{A, B, C, X(58973), X(65176)}}
X(65305) = barycentric product X(i)*X(j) for these (i, j): {3, 53205}, {110, 1972}, {216, 41208}, {249, 60036}, {394, 65358}, {1298, 14570}, {1956, 662}, {1987, 99}, {2966, 40804}, {14941, 648}, {18829, 32542}, {39683, 65271}, {41210, 5562}, {43187, 57500}, {52177, 6331}, {53708, 69}
X(65305) = barycentric quotient X(i)/X(j) for these (i, j): {6, 6130}, {99, 44137}, {110, 401}, {112, 41204}, {163, 1955}, {648, 16089}, {1298, 15412}, {1576, 1971}, {1625, 32428}, {1956, 1577}, {1972, 850}, {1987, 523}, {2715, 32545}, {4230, 62595}, {14941, 525}, {14966, 52128}, {26714, 39682}, {32542, 804}, {39469, 38974}, {39683, 23878}, {40804, 2799}, {41208, 276}, {41210, 8795}, {47390, 62523}, {52177, 647}, {53175, 3269}, {53205, 264}, {53708, 4}, {57500, 3569}, {60036, 338}, {61206, 58311}, {62519, 2970}, {65358, 2052}

X(65306) = X(23)X(895)∩X(287)X(2373)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^6-a^4*b^2+b^6-b^2*c^4-a^2*(b^2-c^2)^2)*(a^6-a^4*c^2-b^4*c^2+c^6-a^2*(b^2-c^2)^2) : :

X(65306) lies on the MacBeath circumconic and on these lines: {23, 895}, {110, 8673}, {249, 4563}, {287, 2373}, {297, 2986}, {323, 52513}, {525, 15388}, {648, 23964}, {651, 36095}, {1304, 64778}, {1993, 36823}, {2421, 43755}, {4235, 17708}, {4558, 23357}, {6515, 51823}, {14919, 18876}, {14999, 65309}, {15329, 43754}, {16039, 41678}, {32661, 65324}, {32985, 53784}, {34211, 60040}, {37645, 65325}, {43187, 60179}, {44770, 53176}, {46165, 52898}, {52630, 61198}

X(65306) = isogonal conjugate of X(47138)
X(65306) = trilinear pole of line {3, 1177}
X(65306) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 47138}, {37, 21109}, {92, 42665}, {513, 21017}, {523, 18669}, {656, 5523}, {661, 858}, {798, 1236}, {923, 62577}, {1109, 61198}, {1577, 2393}, {2642, 59422}, {3708, 61181}, {4705, 17172}, {5181, 23894}, {14208, 14580}, {14961, 24006}, {20902, 46592}, {36035, 60499}
X(65306) = X(i)-vertex conjugate of X(j) for these {i, j}: {2, 32696}, {32729, 65321}, {32734, 65324}
X(65306) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 47138}, {2482, 62577}, {22391, 42665}, {31998, 1236}, {36830, 858}, {39026, 21017}, {39054, 20884}, {40589, 21109}, {40596, 5523}, {55048, 38971}
X(65306) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65268, 10423}
X(65306) = X(i)-cross conjugate of X(j) for these {i, j}: {524, 249}, {10317, 250}, {61207, 110}
X(65306) = pole of line {61207, 65306} with respect to the MacBeath circumconic
X(65306) = pole of line {5181, 21109} with respect to the Stammler hyperbola
X(65306) = pole of line {935, 10423} with respect to the Steiner circumellipse
X(65306) = pole of line {47138, 62577} with respect to the Wallace hyperbola
X(65306) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1304)}}, {{A, B, C, X(23), X(691)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(249), X(2715)}}, {{A, B, C, X(251), X(32696)}}, {{A, B, C, X(297), X(2421)}}, {{A, B, C, X(323), X(34211)}}, {{A, B, C, X(476), X(32697)}}, {{A, B, C, X(524), X(2393)}}, {{A, B, C, X(525), X(8673)}}, {{A, B, C, X(671), X(64775)}}, {{A, B, C, X(935), X(19330)}}, {{A, B, C, X(1289), X(4611)}}, {{A, B, C, X(1993), X(14999)}}, {{A, B, C, X(2966), X(10420)}}, {{A, B, C, X(5392), X(53205)}}, {{A, B, C, X(5467), X(53777)}}, {{A, B, C, X(5468), X(37784)}}, {{A, B, C, X(5649), X(9060)}}, {{A, B, C, X(7953), X(63784)}}, {{A, B, C, X(10422), X(10423)}}, {{A, B, C, X(10425), X(13485)}}, {{A, B, C, X(17932), X(54108)}}, {{A, B, C, X(18876), X(64778)}}, {{A, B, C, X(33640), X(44326)}}, {{A, B, C, X(41511), X(65268)}}, {{A, B, C, X(42396), X(59004)}}, {{A, B, C, X(58113), X(61206)}}, {{A, B, C, X(58975), X(65271)}}
X(65306) = barycentric product X(i)*X(j) for these (i, j): {3, 65268}, {110, 2373}, {163, 37220}, {249, 60040}, {1177, 99}, {1576, 46140}, {2966, 36823}, {4558, 60133}, {10422, 5468}, {10423, 69}, {17708, 60002}, {18876, 648}, {36095, 63}, {41511, 4235}, {43754, 52486}, {44766, 52513}, {46165, 827}, {51823, 65321}
X(65306) = barycentric quotient X(i)/X(j) for these (i, j): {6, 47138}, {58, 21109}, {99, 1236}, {101, 21017}, {110, 858}, {112, 5523}, {163, 18669}, {184, 42665}, {250, 61181}, {524, 62577}, {662, 20884}, {691, 59422}, {935, 39269}, {1177, 523}, {1576, 2393}, {1624, 41603}, {2373, 850}, {2715, 52672}, {4556, 17172}, {4558, 62382}, {5467, 5181}, {9145, 19510}, {9517, 38971}, {10422, 5466}, {10423, 4}, {15329, 12827}, {17708, 57476}, {18876, 525}, {19153, 55151}, {23357, 61198}, {32640, 60499}, {32661, 14961}, {32729, 57485}, {36095, 92}, {36823, 2799}, {37220, 20948}, {41511, 14977}, {44766, 52512}, {46140, 44173}, {46165, 23285}, {52513, 33294}, {53784, 45807}, {57655, 46592}, {60002, 9979}, {60040, 338}, {60133, 14618}, {61206, 14580}, {61207, 1560}, {64778, 2697}, {65268, 264}

X(65307) = X(110)X(827)∩X(287)X(343)

Barycentrics    a^2*(a-b)*(a+b)*(a^2+b^2)*(a-c)*(a+c)*(a^2-b^2-c^2)*(a^2+c^2) : :

X(65307) lies on the MacBeath circumconic and on these lines: {83, 2986}, {99, 44766}, {110, 827}, {249, 4576}, {251, 1994}, {287, 343}, {305, 22075}, {394, 57480}, {511, 56917}, {648, 4577}, {651, 4599}, {689, 2715}, {895, 1176}, {1501, 32451}, {1691, 51459}, {2421, 18315}, {2989, 52394}, {2990, 52376}, {3448, 9076}, {3629, 41909}, {4563, 32661}, {4580, 60053}, {6800, 14247}, {14919, 28724}, {16039, 34211}, {18105, 60054}, {23181, 43754}, {33632, 56007}, {34072, 65298}, {35316, 60052}, {35317, 60051}, {37779, 52898}, {37804, 46243}, {41628, 56006}, {43357, 59076}, {44768, 58784}, {53885, 58112}, {57216, 65324}, {61199, 65321}

X(65307) = trilinear pole of line {3, 1176}
X(65307) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 8061}, {19, 826}, {25, 62418}, {37, 21108}, {38, 2501}, {39, 24006}, {92, 3005}, {162, 39691}, {264, 2084}, {427, 661}, {512, 20883}, {513, 21016}, {523, 17442}, {656, 27376}, {688, 1969}, {798, 1235}, {1096, 2525}, {1109, 35325}, {1577, 1843}, {1824, 16892}, {1826, 2530}, {1880, 48278}, {1930, 2489}, {1964, 14618}, {1973, 23285}, {2333, 48084}, {2616, 27371}, {2643, 41676}, {2969, 35309}, {2971, 55239}, {3404, 16230}, {3665, 55206}, {3703, 55208}, {3708, 46151}, {3954, 7649}, {4079, 16747}, {4705, 17171}, {6591, 15523}, {14424, 36128}, {17924, 21035}, {20948, 27369}, {21044, 46152}, {21123, 41013}, {21814, 46107}, {23894, 64724}, {23994, 61218}
X(65307) = X(i)-vertex conjugate of X(j) for these {i, j}: {4563, 32734}, {6331, 32696}, {65178, 65321}
X(65307) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 826}, {125, 39691}, {6337, 23285}, {6503, 2525}, {6505, 62418}, {22391, 3005}, {31998, 1235}, {36033, 8061}, {36830, 427}, {39026, 21016}, {39054, 20883}, {40589, 21108}, {40596, 27376}, {41884, 14618}, {62452, 264}
X(65307) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4577, 827}
X(65307) = X(i)-cross conjugate of X(j) for these {i, j}: {69, 249}, {10316, 250}, {58353, 1799}
X(65307) = pole of line {1369, 6636} with respect to the Kiepert parabola
X(65307) = pole of line {826, 21108} with respect to the Stammler hyperbola
X(65307) = pole of line {827, 53949} with respect to the Steiner circumellipse
X(65307) = pole of line {2525, 23285} with respect to the Wallace hyperbola
X(65307) = pole of line {39691, 62417} with respect to the dual conic of polar circle
X(65307) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(46543)}}, {{A, B, C, X(69), X(4576)}}, {{A, B, C, X(99), X(4611)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(343), X(2421)}}, {{A, B, C, X(525), X(60352)}}, {{A, B, C, X(647), X(5113)}}, {{A, B, C, X(689), X(1799)}}, {{A, B, C, X(827), X(42396)}}, {{A, B, C, X(925), X(32697)}}, {{A, B, C, X(930), X(40173)}}, {{A, B, C, X(933), X(2966)}}, {{A, B, C, X(1304), X(43188)}}, {{A, B, C, X(2715), X(14574)}}, {{A, B, C, X(4630), X(58113)}}, {{A, B, C, X(5052), X(56389)}}, {{A, B, C, X(6467), X(61199)}}, {{A, B, C, X(7953), X(52608)}}, {{A, B, C, X(8858), X(59047)}}, {{A, B, C, X(10425), X(46134)}}, {{A, B, C, X(11794), X(58975)}}, {{A, B, C, X(47443), X(59039)}}
X(65307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 4630, 827}

X(65308) = X(6)X(5649)∩X(23)X(110)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^6+b^6-b^4*c^2+2*b^2*c^4-2*c^6-a^4*(b^2+c^2)-a^2*(b^4-2*c^4))*(a^6-2*b^6+2*b^4*c^2-b^2*c^4+c^6-a^4*(b^2+c^2)+a^2*(2*b^4-c^4)) : :
X(65308) = -3*X[250]+4*X[6593]

X(65308) lies on the MacBeath circumconic and on these lines: {2, 17708}, {3, 43754}, {6, 5649}, {23, 110}, {69, 56399}, {76, 6035}, {193, 48373}, {249, 36790}, {250, 6593}, {287, 525}, {297, 340}, {394, 57481}, {520, 895}, {576, 40804}, {647, 10766}, {1993, 36823}, {2710, 53691}, {2986, 10754}, {2987, 14998}, {3284, 4558}, {3580, 34138}, {4563, 6393}, {11477, 39265}, {19778, 60052}, {19779, 60051}, {20806, 43755}, {34174, 50641}, {37784, 46639}, {38413, 44718}, {38414, 44719}, {40112, 50639}, {41617, 48453}, {42313, 63464}, {44767, 57504}, {44768, 59436}, {50942, 62307}, {53929, 64775}, {54554, 60255}, {62382, 65309}, {62428, 65326}

X(65308) = reflection of X(i) in X(j) for these {i,j}: {44769, 6}
X(65308) = isogonal conjugate of X(6103)
X(65308) = isotomic conjugate of X(60502)
X(65308) = trilinear pole of line {3, 684}
X(65308) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6103}, {4, 2247}, {19, 542}, {31, 60502}, {92, 5191}, {162, 1640}, {240, 34369}, {656, 35907}, {661, 7473}, {811, 6041}, {1755, 52491}, {1784, 48451}, {1910, 54380}, {2173, 17986}, {2312, 47105}, {2642, 53155}, {18312, 32676}, {36128, 45662}, {46786, 57653}
X(65308) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 60502}, {3, 6103}, {6, 542}, {125, 1640}, {11672, 54380}, {15526, 18312}, {17423, 6041}, {22391, 5191}, {23967, 38552}, {36033, 2247}, {36830, 7473}, {36896, 17986}, {36899, 52491}, {39085, 34369}, {40596, 35907}, {51472, 2493}, {55048, 55142}, {62606, 51227}
X(65308) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5641, 842}, {5649, 35911}
X(65308) = X(i)-cross conjugate of X(j) for these {i, j}: {14984, 69}, {35911, 5649}
X(65308) = pole of line {542, 6103} with respect to the Stammler hyperbola
X(65308) = pole of line {842, 2697} with respect to the Steiner circumellipse
X(65308) = pole of line {16760, 47214} with respect to the Steiner inellipse
X(65308) = pole of line {6103, 60502} with respect to the Wallace hyperbola
X(65308) = pole of line {1640, 18312} with respect to the dual conic of polar circle
X(65308) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(23)}}, {{A, B, C, X(3), X(76)}}, {{A, B, C, X(6), X(647)}}, {{A, B, C, X(30), X(48871)}}, {{A, B, C, X(69), X(323)}}, {{A, B, C, X(74), X(10752)}}, {{A, B, C, X(97), X(23061)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(112), X(10766)}}, {{A, B, C, X(263), X(43706)}}, {{A, B, C, X(265), X(19140)}}, {{A, B, C, X(394), X(520)}}, {{A, B, C, X(523), X(47213)}}, {{A, B, C, X(671), X(9970)}}, {{A, B, C, X(694), X(52153)}}, {{A, B, C, X(843), X(10097)}}, {{A, B, C, X(1173), X(62911)}}, {{A, B, C, X(1176), X(15107)}}, {{A, B, C, X(1177), X(16080)}}, {{A, B, C, X(1993), X(62382)}}, {{A, B, C, X(2394), X(32710)}}, {{A, B, C, X(2693), X(53201)}}, {{A, B, C, X(3580), X(20806)}}, {{A, B, C, X(3926), X(55976)}}, {{A, B, C, X(5649), X(51263)}}, {{A, B, C, X(6391), X(56021)}}, {{A, B, C, X(6504), X(56473)}}, {{A, B, C, X(6593), X(62594)}}, {{A, B, C, X(9381), X(13417)}}, {{A, B, C, X(9513), X(63473)}}, {{A, B, C, X(10159), X(40441)}}, {{A, B, C, X(10630), X(30491)}}, {{A, B, C, X(12584), X(34897)}}, {{A, B, C, X(13472), X(62916)}}, {{A, B, C, X(13582), X(18125)}}, {{A, B, C, X(14376), X(55980)}}, {{A, B, C, X(15077), X(54453)}}, {{A, B, C, X(15421), X(60013)}}, {{A, B, C, X(15470), X(57487)}}, {{A, B, C, X(25322), X(61679)}}, {{A, B, C, X(28724), X(54513)}}, {{A, B, C, X(34403), X(55999)}}, {{A, B, C, X(35265), X(42287)}}, {{A, B, C, X(35911), X(51228)}}, {{A, B, C, X(37669), X(37784)}}, {{A, B, C, X(40112), X(41614)}}, {{A, B, C, X(43676), X(43689)}}, {{A, B, C, X(44549), X(52518)}}, {{A, B, C, X(45788), X(60209)}}, {{A, B, C, X(50712), X(51258)}}, {{A, B, C, X(55957), X(57271)}}

X(65309) = TRILINEAR POLE OF LINE {3, 68}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2-b^2-c^2)*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(a^4-2*a^2*c^2+(b^2-c^2)^2) : :
X(65309) =

X(65309) lies on the MacBeath circumconic and on these lines: {2, 43756}, {6, 56006}, {68, 895}, {69, 2165}, {96, 5562}, {99, 18315}, {110, 925}, {155, 40698}, {193, 47731}, {287, 20563}, {323, 52504}, {328, 57875}, {338, 394}, {343, 57647}, {524, 62361}, {525, 43755}, {648, 30450}, {651, 65251}, {1812, 2990}, {1992, 56007}, {1993, 39116}, {2407, 46639}, {2421, 44766}, {4558, 6334}, {6193, 8906}, {10916, 60049}, {11064, 37802}, {11411, 32132}, {14593, 14826}, {14919, 37669}, {14999, 65306}, {17197, 60025}, {28419, 64975}, {34211, 56008}, {36145, 65298}, {36841, 44769}, {39111, 63174}, {40330, 56892}, {41614, 41909}, {41679, 61188}, {42405, 55227}, {43187, 55225}, {43754, 44174}, {46640, 64828}, {56017, 59155}, {57763, 65321}, {62382, 65308}, {65177, 65348}

X(65309) = reflection of X(i) in X(j) for these {i,j}: {56006, 6}
X(65309) = isogonal conjugate of X(6753)
X(65309) = isotomic conjugate of X(57065)
X(65309) = trilinear pole of line {3, 68}
X(65309) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6753}, {4, 55216}, {19, 924}, {24, 661}, {25, 63827}, {31, 57065}, {47, 2501}, {91, 58760}, {92, 34952}, {136, 163}, {158, 30451}, {162, 47421}, {317, 798}, {393, 63832}, {512, 1748}, {571, 24006}, {656, 8745}, {810, 11547}, {1096, 52584}, {1101, 55278}, {1109, 61208}, {1577, 44077}, {1826, 34948}, {1973, 6563}, {2190, 52317}, {2489, 44179}, {2616, 14576}, {2624, 52415}, {2643, 41679}, {2971, 55249}, {3708, 52917}, {6754, 65251}, {14397, 36119}, {15422, 63801}, {17881, 61206}, {34338, 36145}, {52432, 55250}, {58756, 63808}, {62268, 63829}
X(65309) = X(i)-vertex conjugate of X(j) for these {i, j}: {61208, 65176}
X(65309) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 57065}, {3, 6753}, {5, 52317}, {6, 924}, {115, 136}, {125, 47421}, {523, 55278}, {1147, 30451}, {1511, 14397}, {6337, 6563}, {6503, 52584}, {6505, 63827}, {22391, 34952}, {24245, 58865}, {24246, 58867}, {31998, 317}, {34116, 58760}, {34853, 2501}, {35067, 57154}, {36033, 55216}, {36830, 24}, {37864, 2489}, {39013, 34338}, {39054, 1748}, {39062, 11547}, {40596, 8745}, {47421, 55072}, {52032, 63829}
X(65309) = X(i)-Ceva conjugate of X(j) for these {i, j}: {46134, 925}, {55277, 57763}, {57763, 68}, {65273, 4558}
X(65309) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {57638, 4329}, {63958, 21294}
X(65309) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 57638}, {68, 57763}, {523, 69}, {525, 5392}, {647, 96}, {17431, 486}, {17432, 485}, {30451, 3}, {40494, 57800}, {52742, 265}, {55549, 44174}
X(65309) = pole of line {136, 47421} with respect to the polar circle
X(65309) = pole of line {4, 8905} with respect to the Kiepert parabola
X(65309) = pole of line {924, 6753} with respect to the Stammler hyperbola
X(65309) = pole of line {925, 4558} with respect to the Steiner circumellipse
X(65309) = pole of line {34843, 34844} with respect to the Steiner inellipse
X(65309) = pole of line {6563, 6753} with respect to the Wallace hyperbola
X(65309) = pole of line {2052, 42376} with respect to the dual conic of Jerabek hyperbola
X(65309) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(30512)}}, {{A, B, C, X(68), X(55277)}}, {{A, B, C, X(69), X(35136)}}, {{A, B, C, X(99), X(328)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(338), X(525)}}, {{A, B, C, X(523), X(57154)}}, {{A, B, C, X(670), X(17932)}}, {{A, B, C, X(925), X(30450)}}, {{A, B, C, X(1289), X(2966)}}, {{A, B, C, X(2407), X(36841)}}, {{A, B, C, X(2421), X(20806)}}, {{A, B, C, X(4561), X(54951)}}, {{A, B, C, X(5467), X(8538)}}, {{A, B, C, X(10420), X(41679)}}, {{A, B, C, X(14999), X(62382)}}, {{A, B, C, X(15419), X(17197)}}, {{A, B, C, X(15459), X(47269)}}, {{A, B, C, X(15740), X(20187)}}, {{A, B, C, X(16813), X(43188)}}, {{A, B, C, X(28419), X(34211)}}, {{A, B, C, X(32661), X(58949)}}, {{A, B, C, X(32692), X(32734)}}, {{A, B, C, X(35178), X(48539)}}, {{A, B, C, X(45792), X(62624)}}
X(65309) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 30450, 65176}, {54030, 54031, 925}

X(65310) = TRILINEAR POLE OF LINE {3, 217}

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2-b^2-c^2)*(-b^4+b^2*c^2+a^2*(b^2+2*c^2))*(c^2*(b^2-c^2)+a^2*(2*b^2+c^2)) : :

X(65310) lies on the MacBeath circumconic and on these lines: {3, 287}, {23, 46807}, {99, 6037}, {107, 42405}, {110, 14966}, {237, 10753}, {262, 1995}, {263, 576}, {648, 1634}, {651, 65252}, {895, 5158}, {1576, 18315}, {2989, 7419}, {4243, 55996}, {4563, 23181}, {9145, 44769}, {11672, 63472}, {12177, 32599}, {14919, 54032}, {15329, 65324}, {17708, 36829}, {32661, 43754}, {35278, 39681}, {41909, 46319}, {44766, 50947}, {51444, 52153}, {52631, 60054}, {57268, 60022}

X(65310) = trilinear pole of line {3, 217}
X(65310) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 23878}, {92, 3288}, {182, 24006}, {458, 661}, {523, 60685}, {647, 51315}, {656, 33971}, {798, 44144}, {811, 6784}, {1577, 10311}, {2489, 3403}, {2501, 52134}, {2616, 39530}, {6591, 60737}, {7649, 60723}, {17924, 60726}, {57653, 63746}
X(65310) = X(i)-vertex conjugate of X(j) for these {i, j}: {648, 685}, {6529, 18831}, {32734, 43754}, {35278, 65271}
X(65310) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 23878}, {17423, 6784}, {22391, 3288}, {31998, 44144}, {36830, 458}, {39052, 51315}, {40596, 33971}
X(65310) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65271, 26714}
X(65310) = X(i)-cross conjugate of X(j) for these {i, j}: {19139, 44174}
X(65310) = pole of line {35278, 65271} with respect to the circumcircle
X(65310) = pole of line {1350, 37184} with respect to the Kiepert parabola
X(65310) = pole of line {9420, 23878} with respect to the Stammler hyperbola
X(65310) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(99)}}, {{A, B, C, X(107), X(1576)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(248), X(53937)}}, {{A, B, C, X(576), X(52035)}}, {{A, B, C, X(1173), X(65176)}}, {{A, B, C, X(1289), X(14586)}}, {{A, B, C, X(1995), X(15329)}}, {{A, B, C, X(4226), X(37465)}}, {{A, B, C, X(4243), X(7419)}}, {{A, B, C, X(5158), X(5467)}}, {{A, B, C, X(6528), X(6570)}}, {{A, B, C, X(6529), X(58973)}}, {{A, B, C, X(7468), X(35298)}}, {{A, B, C, X(8690), X(36059)}}, {{A, B, C, X(9160), X(34802)}}, {{A, B, C, X(11636), X(32662)}}, {{A, B, C, X(15958), X(43351)}}, {{A, B, C, X(26714), X(53196)}}, {{A, B, C, X(30247), X(32640)}}, {{A, B, C, X(41173), X(43706)}}, {{A, B, C, X(42313), X(63741)}}
X(65310) = barycentric product X(i)*X(j) for these (i, j): {3, 65271}, {63, 65252}, {110, 42313}, {112, 59257}, {262, 4558}, {263, 4563}, {287, 63741}, {394, 65349}, {1331, 60679}, {2186, 4592}, {3289, 53196}, {3402, 55202}, {14570, 51444}, {17932, 51543}, {23181, 42300}, {26714, 69}, {32661, 327}, {32716, 6393}, {34386, 52926}, {36212, 6037}, {36214, 39681}, {36885, 65308}, {43718, 99}, {43754, 46807}, {46319, 52608}, {47389, 52631}, {54032, 648}, {57268, 60053}
X(65310) = barycentric quotient X(i)/X(j) for these (i, j): {3, 23878}, {99, 44144}, {110, 458}, {112, 33971}, {162, 51315}, {163, 60685}, {184, 3288}, {262, 14618}, {263, 2501}, {287, 63746}, {906, 60723}, {1331, 60737}, {1332, 42711}, {1576, 10311}, {1625, 39530}, {2186, 24006}, {3049, 6784}, {4558, 183}, {4563, 20023}, {4575, 52134}, {4592, 3403}, {6037, 16081}, {17970, 39680}, {23181, 59197}, {26714, 4}, {32656, 60726}, {32661, 182}, {32662, 56401}, {32716, 6531}, {36132, 36120}, {36885, 60502}, {39681, 17984}, {42313, 850}, {43718, 523}, {43754, 46806}, {46319, 2489}, {51444, 15412}, {51543, 16230}, {52631, 8754}, {52926, 53}, {53196, 60199}, {54032, 525}, {57268, 44427}, {59257, 3267}, {60679, 46107}, {63741, 297}, {65252, 92}, {65271, 264}, {65327, 8842}, {65349, 2052}
X(65310) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 63741, 26714}

X(65311) = X(2)X(56006)∩X(6)X(56007)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-3*c^2)*(a^2-b^2-c^2)*(a^2-3*b^2+c^2) : :

X(65311) lies on the MacBeath circumconic and on these lines: {2, 56006}, {6, 56007}, {69, 6387}, {110, 3565}, {287, 6340}, {394, 2987}, {648, 35136}, {895, 6391}, {1812, 2991}, {1995, 41385}, {2063, 64975}, {2421, 46639}, {2986, 2996}, {3167, 64614}, {4558, 61199}, {4563, 65171}, {4576, 65324}, {5468, 44766}, {6090, 14248}, {9129, 41673}, {14919, 60839}, {14999, 48373}, {15066, 43756}, {43187, 55224}, {52016, 53068}, {56008, 61198}

X(65311) = reflection of X(i) in X(j) for these {i,j}: {56007, 6}
X(65311) = isogonal conjugate of X(57071)
X(65311) = anticomplement of X(63614)
X(65311) = trilinear pole of line {3, 6391}
X(65311) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 57071}, {19, 3566}, {92, 8651}, {112, 17876}, {162, 6388}, {661, 6353}, {662, 5139}, {798, 54412}, {810, 21447}, {811, 47430}, {1577, 19118}, {1707, 2501}, {1824, 3798}, {2489, 18156}, {3053, 24006}, {4028, 6591}, {7649, 21874}, {17081, 55206}, {36105, 51613}, {41584, 55240}
X(65311) = X(i)-vertex conjugate of X(j) for these {i, j}: {4558, 65178}, {32729, 56008}
X(65311) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 57071}, {6, 3566}, {125, 6388}, {1084, 5139}, {8770, 58882}, {15261, 2489}, {17423, 47430}, {22391, 8651}, {31998, 54412}, {34591, 17876}, {36830, 6353}, {39001, 51613}, {39062, 21447}, {63614, 63614}, {64614, 2501}
X(65311) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3565, 4558}, {35136, 3565}
X(65311) = X(i)-cross conjugate of X(j) for these {i, j}: {512, 69}, {647, 8770}, {2451, 57648}, {2519, 6}
X(65311) = pole of line {4558, 65178} with respect to the circumcircle
X(65311) = pole of line {25, 19583} with respect to the Kiepert parabola
X(65311) = pole of line {3566, 57071} with respect to the Stammler hyperbola
X(65311) = pole of line {3565, 65171} with respect to the Steiner circumellipse
X(65311) = pole of line {6388, 63614} with respect to the dual conic of polar circle
X(65311) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(13398)}}, {{A, B, C, X(69), X(53367)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(112), X(40347)}}, {{A, B, C, X(512), X(6388)}}, {{A, B, C, X(647), X(3124)}}, {{A, B, C, X(1301), X(2966)}}, {{A, B, C, X(2063), X(34211)}}, {{A, B, C, X(2421), X(37669)}}, {{A, B, C, X(4559), X(16680)}}, {{A, B, C, X(4561), X(59065)}}, {{A, B, C, X(4584), X(55207)}}, {{A, B, C, X(4603), X(55205)}}, {{A, B, C, X(5468), X(20806)}}, {{A, B, C, X(10425), X(57216)}}, {{A, B, C, X(14417), X(60352)}}, {{A, B, C, X(17932), X(35575)}}, {{A, B, C, X(28419), X(61198)}}, {{A, B, C, X(32661), X(59115)}}, {{A, B, C, X(44326), X(59039)}}, {{A, B, C, X(60834), X(62542)}}
X(65311) = barycentric product X(i)*X(j) for these (i, j): {3, 35136}, {110, 6340}, {305, 65178}, {2996, 4558}, {3565, 69}, {4563, 8770}, {4592, 8769}, {6391, 99}, {38252, 55202}, {40319, 670}, {52608, 53059}, {53068, 54956}, {60839, 648}
X(65311) = barycentric quotient X(i)/X(j) for these (i, j): {3, 3566}, {6, 57071}, {99, 54412}, {110, 6353}, {184, 8651}, {512, 5139}, {647, 6388}, {648, 21447}, {656, 17876}, {906, 21874}, {1331, 4028}, {1576, 19118}, {1634, 41584}, {1790, 3798}, {2996, 14618}, {3049, 47430}, {3167, 58766}, {3565, 4}, {4558, 193}, {4563, 57518}, {4575, 1707}, {4592, 18156}, {6340, 850}, {6391, 523}, {8681, 57087}, {8769, 24006}, {8770, 2501}, {10425, 63613}, {14248, 58757}, {23181, 41588}, {27364, 23290}, {32661, 3053}, {35136, 264}, {40319, 512}, {53059, 2489}, {60839, 525}, {61199, 40326}, {64614, 58882}, {65178, 25}
X(65311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 3565, 65178}

X(65312) = X(4)X(19367)∩X(108)X(110)

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(a*b*c*(b+c)-(b^2-c^2)^2+a^2*(b^2+b*c+c^2)) : :

X(65312) lies on these lines: {4, 19367}, {20, 52830}, {22, 34032}, {23, 56910}, {108, 110}, {109, 13589}, {149, 53548}, {196, 11445}, {225, 41723}, {226, 14008}, {278, 3060}, {323, 41349}, {511, 37798}, {664, 3909}, {851, 56560}, {858, 51365}, {942, 7548}, {1020, 61220}, {1068, 5889}, {1415, 57194}, {1425, 2475}, {1426, 64715}, {2617, 4243}, {2979, 57477}, {3028, 10778}, {4551, 24029}, {4552, 65314}, {4554, 4576}, {4566, 18026}, {5640, 37800}, {6888, 34956}, {6923, 19368}, {6960, 40644}, {7952, 12111}, {11446, 63965}, {31019, 45963}, {32038, 52931}, {34035, 35996}, {35360, 54240}, {45122, 59415}, {52827, 64142}, {65297, 65303}

X(65312) = X(i)-isoconjugate-of-X(j) for these {i, j}: {652, 62879}
X(65312) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {65225, 34188}
X(65312) = pole of line {18026, 32038} with respect to the Steiner circumellipse
X(65312) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(18026)}}, {{A, B, C, X(162), X(33637)}}, {{A, B, C, X(2476), X(4246)}}, {{A, B, C, X(4566), X(36059)}}, {{A, B, C, X(35174), X(65313)}}
X(65312) = barycentric product X(i)*X(j) for these (i, j): {2476, 651}, {56908, 99}
X(65312) = barycentric quotient X(i)/X(j) for these (i, j): {108, 62879}, {2476, 4391}, {56908, 523}
X(65312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {108, 651, 110}, {1020, 61220, 65315}

X(65313) = X(100)X(190)∩X(101)X(110)

Barycentrics    a^2*(a-b)*(a-c)*(b^2+b*c+c^2+a*(b+c)) : :

X(65313) lies on these lines: {2, 20256}, {3, 13243}, {22, 1260}, {55, 33761}, {63, 4210}, {72, 4225}, {100, 190}, {101, 110}, {109, 8701}, {144, 35980}, {149, 15507}, {228, 3219}, {244, 27666}, {323, 17976}, {404, 22458}, {511, 56808}, {651, 23067}, {835, 931}, {851, 17484}, {858, 51366}, {894, 35983}, {901, 8694}, {1255, 18185}, {1284, 33139}, {1293, 28210}, {1305, 54952}, {1310, 65372}, {1757, 3724}, {1897, 4246}, {1977, 52127}, {1978, 62530}, {2979, 56813}, {3060, 3190}, {3185, 3681}, {3191, 41723}, {3315, 54333}, {3732, 46725}, {3882, 65314}, {3920, 20967}, {3927, 16451}, {3940, 4216}, {3995, 56181}, {4188, 20805}, {4191, 22149}, {4192, 26792}, {4245, 63159}, {4551, 24029}, {4552, 53349}, {4561, 4576}, {4588, 28196}, {4651, 11688}, {4661, 23853}, {5132, 62796}, {5143, 21805}, {5260, 64753}, {6646, 35984}, {7419, 34772}, {7998, 56809}, {8697, 58125}, {8698, 58110}, {8708, 46961}, {9070, 65370}, {9963, 13744}, {11003, 23095}, {11322, 17350}, {13587, 23169}, {15624, 62838}, {15934, 19291}, {16056, 17483}, {16057, 27003}, {16059, 23958}, {16371, 23170}, {17126, 34247}, {19308, 20796}, {20013, 28376}, {20078, 37262}, {20470, 62235}, {21320, 27628}, {21362, 61220}, {23085, 37307}, {23089, 37309}, {23161, 50947}, {28148, 28176}, {28152, 28200}, {28162, 28214}, {28184, 28230}, {28218, 28226}, {28624, 43359}, {28841, 29329}, {29199, 43350}, {30653, 37590}, {37301, 42461}, {37405, 38856}, {46923, 52020}, {53302, 63917}, {56538, 64401}, {58992, 65361}

X(65313) = isogonal conjugate of X(43927)
X(65313) = trilinear pole of line {386, 28622}
X(65313) = perspector of circumconic {{A, B, C, X(1016), X(4570)}}
X(65313) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 43927}, {244, 835}, {513, 43531}, {514, 2214}, {661, 56047}, {667, 57824}, {1015, 37218}, {3248, 57977}, {6591, 57876}, {16732, 58951}, {17924, 57704}
X(65313) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 43927}, {386, 28623}, {6631, 57824}, {36830, 56047}, {39016, 1086}, {39026, 43531}, {41849, 3261}, {62586, 693}
X(65313) = X(i)-Ceva conjugate of X(j) for these {i, j}: {931, 100}
X(65313) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {28624, 149}
X(65313) = X(i)-cross conjugate of X(j) for these {i, j}: {834, 386}
X(65313) = pole of line {100, 8652} with respect to the circumcircle
X(65313) = pole of line {2969, 53566} with respect to the polar circle
X(65313) = pole of line {1, 4184} with respect to the Kiepert parabola
X(65313) = pole of line {514, 3733} with respect to the Stammler hyperbola
X(65313) = pole of line {190, 4574} with respect to the Steiner circumellipse
X(65313) = pole of line {2, 71} with respect to the Yff parabola
X(65313) = pole of line {6, 21} with respect to the Hutson-Moses hyperbola
X(65313) = pole of line {3261, 7192} with respect to the Wallace hyperbola
X(65313) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {104, 28145, 38665}
X(65313) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(163)}}, {{A, B, C, X(101), X(3952)}}, {{A, B, C, X(109), X(4427)}}, {{A, B, C, X(110), X(190)}}, {{A, B, C, X(386), X(8694)}}, {{A, B, C, X(469), X(4243)}}, {{A, B, C, X(833), X(13589)}}, {{A, B, C, X(834), X(900)}}, {{A, B, C, X(890), X(8637)}}, {{A, B, C, X(1293), X(4781)}}, {{A, B, C, X(1331), X(52609)}}, {{A, B, C, X(2774), X(23879)}}, {{A, B, C, X(3570), X(61409)}}, {{A, B, C, X(3699), X(5546)}}, {{A, B, C, X(4436), X(46961)}}, {{A, B, C, X(4557), X(32739)}}, {{A, B, C, X(4756), X(8652)}}, {{A, B, C, X(4767), X(28196)}}, {{A, B, C, X(5029), X(18004)}}, {{A, B, C, X(8050), X(53338)}}, {{A, B, C, X(9070), X(53279)}}, {{A, B, C, X(14349), X(30565)}}, {{A, B, C, X(15343), X(53606)}}, {{A, B, C, X(17989), X(50488)}}, {{A, B, C, X(28210), X(43290)}}, {{A, B, C, X(28606), X(42720)}}, {{A, B, C, X(32042), X(59012)}}, {{A, B, C, X(45746), X(50333)}}, {{A, B, C, X(47776), X(52615)}}, {{A, B, C, X(54952), X(65315)}}, {{A, B, C, X(58992), X(61185)}}
X(65313) = barycentric product X(i)*X(j) for these (i, j): {3, 65204}, {100, 28606}, {101, 5224}, {110, 56810}, {163, 42714}, {190, 386}, {1016, 834}, {1252, 45746}, {1331, 469}, {3876, 651}, {3952, 61409}, {4567, 47842}, {4601, 50488}, {14349, 765}, {23282, 249}, {23879, 4570}, {26911, 43190}, {31625, 8637}, {33935, 692}, {33948, 6}, {33949, 3939}, {42664, 4600}, {44103, 4561}, {56926, 99}, {59149, 65116}, {62586, 8652}
X(65313) = barycentric quotient X(i)/X(j) for these (i, j): {6, 43927}, {101, 43531}, {110, 56047}, {190, 57824}, {386, 514}, {469, 46107}, {692, 2214}, {765, 37218}, {834, 1086}, {1016, 57977}, {1252, 835}, {1331, 57876}, {3876, 4391}, {5224, 3261}, {8637, 1015}, {14349, 1111}, {23282, 338}, {23879, 21207}, {26911, 25259}, {28606, 693}, {32656, 57704}, {33935, 40495}, {33948, 76}, {33949, 52621}, {34281, 48144}, {42664, 3120}, {42714, 20948}, {43359, 28621}, {44103, 7649}, {45746, 23989}, {47842, 16732}, {50488, 3125}, {52615, 17205}, {56810, 850}, {56926, 523}, {61409, 7192}, {65116, 23100}, {65204, 264}
X(65313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 4557, 65186}, {100, 52923, 3952}, {100, 57151, 190}, {101, 1331, 110}, {228, 3219, 4184}, {651, 23067, 65315}, {4551, 24029, 65312}, {4557, 53280, 100}

X(65314) = X(10)X(35636)∩X(100)X(110)

Barycentrics    a*(a-b)*(a-c)*(b^3+b^2*c+b*c^2+c^3+a*(b^2+b*c+c^2)) : :

X(65314) lies on these lines: {10, 35636}, {23, 56529}, {100, 110}, {190, 3909}, {306, 38480}, {323, 17977}, {344, 5640}, {345, 2979}, {511, 32849}, {644, 61173}, {668, 891}, {815, 835}, {858, 51367}, {906, 57119}, {1018, 57217}, {1026, 65186}, {1310, 8701}, {1370, 55112}, {2895, 3690}, {3060, 17776}, {3688, 33175}, {3699, 61177}, {3781, 33077}, {3792, 32848}, {3882, 65313}, {3888, 4427}, {3917, 33168}, {3932, 56878}, {4158, 52364}, {4552, 65312}, {4756, 40521}, {4767, 61166}, {5739, 26911}, {6335, 35360}, {7998, 17740}, {13397, 29163}, {14839, 33148}, {17390, 61728}, {21334, 29872}, {22276, 33078}, {22306, 59415}, {24542, 25048}, {25308, 32929}, {26893, 32858}, {29026, 43348}, {32025, 63961}, {32851, 33852}, {33083, 40966}, {33139, 35104}, {33170, 64006}, {33637, 59104}, {36080, 43356}, {41723, 57808}, {46918, 64007}, {51377, 60459}, {65233, 65315}

X(65314) = trilinear pole of line {4261, 56541}
X(65314) = perspector of circumconic {{A, B, C, X(4567), X(31625)}}
X(65314) = X(i)-isoconjugate-of-X(j) for these {i, j}: {839, 3248}, {3120, 59112}
X(65314) = X(i)-Dao conjugate of X(j) for these {i, j}: {4261, 23882}, {5375, 60082}, {32782, 48107}, {39026, 54336}
X(65314) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2215, 54102}, {36080, 4440}, {54970, 150}, {65227, 149}
X(65314) = X(i)-cross conjugate of X(j) for these {i, j}: {838, 4261}
X(65314) = pole of line {21, 17147} with respect to the Kiepert parabola
X(65314) = pole of line {668, 52609} with respect to the Steiner circumellipse
X(65314) = pole of line {192, 3187} with respect to the Yff parabola
X(65314) = pole of line {37, 5047} with respect to the Hutson-Moses hyperbola
X(65314) = pole of line {693, 3733} with respect to the Wallace hyperbola
X(65314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(27808)}}, {{A, B, C, X(110), X(668)}}, {{A, B, C, X(662), X(1978)}}, {{A, B, C, X(692), X(3952)}}, {{A, B, C, X(815), X(33948)}}, {{A, B, C, X(838), X(891)}}, {{A, B, C, X(3658), X(5142)}}, {{A, B, C, X(4261), X(41314)}}, {{A, B, C, X(5040), X(18003)}}, {{A, B, C, X(42717), X(56564)}}, {{A, B, C, X(43356), X(54970)}}, {{A, B, C, X(53363), X(54458)}}
X(65314) = barycentric product X(i)*X(j) for these (i, j): {100, 32782}, {110, 56564}, {1332, 5142}, {4261, 668}, {31625, 838}, {56541, 99}
X(65314) = barycentric quotient X(i)/X(j) for these (i, j): {100, 60082}, {101, 54336}, {838, 1015}, {1016, 839}, {4261, 513}, {5142, 17924}, {31625, 57979}, {32782, 693}, {56541, 523}, {56564, 850}
X(65314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 1332, 110}, {3952, 21272, 53349}, {4553, 61172, 100}

X(65315) = X(100)X(658)∩X(109)X(110)

Barycentrics    a^2*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(-b^3+a*b*c-c^3+a^2*(b+c)) : :

X(65315) lies on these lines: {20, 20764}, {22, 7011}, {56, 3315}, {100, 658}, {108, 13397}, {109, 110}, {162, 4243}, {323, 17975}, {347, 35980}, {511, 56560}, {651, 23067}, {653, 3658}, {851, 37798}, {858, 51368}, {901, 8059}, {1020, 61220}, {1214, 4184}, {1262, 36030}, {1305, 36077}, {1331, 1461}, {1398, 37301}, {1410, 34772}, {1441, 35983}, {1633, 53322}, {1897, 7451}, {2979, 56553}, {3060, 56549}, {3100, 62736}, {3724, 5018}, {4210, 17080}, {4225, 4296}, {4551, 65186}, {4576, 65164}, {7411, 23171}, {7421, 18447}, {7998, 56550}, {9538, 38284}, {17086, 35984}, {23890, 61221}, {24029, 61227}, {32047, 37115}, {35987, 38288}, {65225, 65256}, {65233, 65314}

X(65315) = isogonal conjugate of X(23289)
X(65315) = trilinear pole of line {579, 4306}
X(65315) = perspector of circumconic {{A, B, C, X(1275), X(52378)}}
X(65315) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 23289}, {272, 4041}, {513, 56146}, {522, 2218}, {650, 1751}, {663, 2997}, {1305, 2310}, {3063, 40011}, {3271, 51566}, {3737, 41506}, {4516, 65274}, {8611, 40574}, {8641, 15467}, {21044, 65254}, {57784, 63461}, {58074, 65102}
X(65315) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 23289}, {72, 52355}, {10001, 40011}, {39026, 56146}
X(65315) = X(i)-cross conjugate of X(j) for these {i, j}: {8676, 579}
X(65315) = pole of line {1633, 53324} with respect to the circumcircle
X(65315) = pole of line {34969, 42069} with respect to the polar circle
X(65315) = pole of line {63, 4225} with respect to the Kiepert parabola
X(65315) = pole of line {522, 21789} with respect to the Stammler hyperbola
X(65315) = pole of line {664, 52610} with respect to the Steiner circumellipse
X(65315) = pole of line {7253, 23289} with respect to the Wallace hyperbola
X(65315) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(65375)}}, {{A, B, C, X(109), X(4566)}}, {{A, B, C, X(110), X(664)}}, {{A, B, C, X(579), X(56543)}}, {{A, B, C, X(658), X(4565)}}, {{A, B, C, X(906), X(44065)}}, {{A, B, C, X(1305), X(23067)}}, {{A, B, C, X(2283), X(2352)}}, {{A, B, C, X(2398), X(3190)}}, {{A, B, C, X(4306), X(8059)}}, {{A, B, C, X(4453), X(23800)}}, {{A, B, C, X(4569), X(59012)}}, {{A, B, C, X(4575), X(6516)}}, {{A, B, C, X(5075), X(18006)}}, {{A, B, C, X(5125), X(7450)}}, {{A, B, C, X(6366), X(8676)}}, {{A, B, C, X(17136), X(58992)}}, {{A, B, C, X(43042), X(43060)}}, {{A, B, C, X(51646), X(51658)}}, {{A, B, C, X(54952), X(65313)}}
X(65315) = barycentric product X(i)*X(j) for these (i, j): {109, 18134}, {110, 56559}, {190, 4306}, {209, 4573}, {579, 664}, {1262, 20294}, {1275, 8676}, {1414, 22021}, {1813, 5125}, {2198, 4625}, {2352, 4554}, {3190, 658}, {3868, 651}, {4565, 57808}, {4566, 56000}, {4567, 51658}, {19367, 44765}, {23800, 4564}, {27396, 934}, {43060, 4998}, {57217, 7}
X(65315) = barycentric quotient X(i)/X(j) for these (i, j): {6, 23289}, {101, 56146}, {109, 1751}, {209, 3700}, {579, 522}, {651, 2997}, {658, 15467}, {664, 40011}, {1262, 1305}, {1415, 2218}, {2198, 4041}, {2352, 650}, {3190, 3239}, {3868, 4391}, {4306, 514}, {4559, 41506}, {4564, 51566}, {4565, 272}, {4573, 57784}, {5125, 46110}, {8676, 1146}, {18134, 35519}, {20294, 23978}, {22021, 4086}, {23067, 40161}, {23800, 4858}, {27396, 4397}, {36118, 58074}, {43060, 11}, {51574, 52355}, {51658, 16732}, {52378, 65274}, {52610, 28786}, {56000, 7253}, {56559, 850}, {57043, 21666}, {57217, 8}, {57501, 57108}
X(65315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {109, 1813, 110}, {651, 23067, 65313}, {1020, 61220, 65312}, {2283, 53321, 100}, {4296, 22341, 4225}

X(65316) = X(23)X(74)∩X(110)X(250)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^4+b^4+b^2*c^2-2*c^4+a^2*(-2*b^2+c^2))*(a^4-2*(b^2-c^2)^2+a^2*(b^2+c^2))*(a^4-2*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2)) : :

X(65316) lies on these lines: {22, 57488}, {23, 74}, {52, 3470}, {110, 250}, {511, 14919}, {852, 37477}, {1351, 9717}, {1494, 15360}, {1495, 62606}, {1995, 35910}, {2070, 50464}, {2394, 57627}, {2420, 2433}, {3060, 57487}, {3580, 17986}, {4240, 16077}, {5627, 63735}, {7426, 51227}, {7488, 38933}, {7493, 63856}, {8675, 32738}, {9139, 65320}, {10296, 57472}, {10421, 50435}, {11454, 38937}, {12295, 14989}, {13352, 14385}, {14264, 37489}, {15107, 40384}, {15459, 35360}, {26255, 36890}, {32223, 53768}, {32225, 46808}, {32583, 63741}, {32681, 53958}, {34150, 47348}, {39290, 65317}, {40353, 46233}, {46261, 53785}, {47596, 60870}

X(65316) = trilinear pole of line {4550, 5158}
X(65316) = perspector of circumconic {{A, B, C, X(15395), X(57570)}}
X(65316) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 46809}, {1577, 51545}, {2631, 43530}, {3431, 36035}
X(65316) = X(i)-Dao conjugate of X(j) for these {i, j}: {4550, 9033}, {5158, 46229}, {36830, 46809}
X(65316) = X(i)-cross conjugate of X(j) for these {i, j}: {14314, 381}
X(65316) = pole of line {5502, 14560} with respect to the circumcircle
X(65316) = pole of line {5664, 9033} with respect to the Stammler hyperbola
X(65316) = pole of line {16077, 16237} with respect to the Steiner circumellipse
X(65316) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(16077)}}, {{A, B, C, X(250), X(9060)}}, {{A, B, C, X(381), X(2437)}}, {{A, B, C, X(476), X(2420)}}, {{A, B, C, X(520), X(34767)}}, {{A, B, C, X(5158), X(65305)}}, {{A, B, C, X(9064), X(32738)}}, {{A, B, C, X(32225), X(63741)}}, {{A, B, C, X(53958), X(65322)}}
X(65316) = barycentric product X(i)*X(j) for these (i, j): {110, 46808}, {381, 44769}, {1304, 37638}, {1531, 34568}, {3581, 39290}, {15459, 63425}, {16077, 5158}, {18477, 65263}, {32640, 44135}, {36831, 4993}, {51544, 99}
X(65316) = barycentric quotient X(i)/X(j) for these (i, j): {110, 46809}, {381, 41079}, {1304, 43530}, {1531, 52624}, {1576, 51545}, {3581, 5664}, {4550, 46229}, {5158, 9033}, {15395, 54959}, {18478, 18557}, {18479, 18558}, {18487, 58263}, {32640, 3431}, {32695, 16263}, {34416, 14398}, {34417, 1637}, {44769, 57822}, {46808, 850}, {51544, 523}, {63425, 41077}
X(65316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 46788, 74}, {110, 36831, 44769}, {1304, 44769, 110}

X(65317) = X(94)X(511)∩X(110)X(476)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(2*b^4+b^2*c^2+2*c^4)) : :

X(65317) lies on these lines: {23, 56397}, {94, 511}, {110, 476}, {265, 11564}, {1352, 52449}, {1531, 18300}, {1989, 15360}, {2979, 57482}, {3060, 57486}, {3580, 51847}, {5640, 43084}, {5889, 58725}, {11412, 58723}, {11459, 14254}, {14595, 37779}, {15107, 53768}, {15958, 64516}, {18436, 59274}, {32662, 47053}, {35139, 35316}, {35360, 46456}, {39290, 65316}, {41171, 58733}, {53693, 58983}, {56292, 58925}, {56400, 64105}

X(65317) = trilinear pole of line {566, 56408}
X(65317) = perspector of circumconic {{A, B, C, X(39295), X(57546)}}
X(65317) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2624, 7578}
X(65317) = pole of line {30, 18301} with respect to the Kiepert parabola
X(65317) = pole of line {526, 57136} with respect to the Stammler hyperbola
X(65317) = pole of line {2407, 35139} with respect to the Steiner circumellipse
X(65317) = pole of line {3268, 62173} with respect to the Wallace hyperbola
X(65317) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(11564)}}, {{A, B, C, X(935), X(14480)}}, {{A, B, C, X(3233), X(51391)}}, {{A, B, C, X(7471), X(7577)}}, {{A, B, C, X(14559), X(56408)}}, {{A, B, C, X(16167), X(60605)}}, {{A, B, C, X(53693), X(54959)}}
X(65317) = barycentric product X(i)*X(j) for these (i, j): {23039, 46456}, {35139, 566}, {36829, 94}, {39290, 51391}, {56408, 99}, {60053, 7577}
X(65317) = barycentric quotient X(i)/X(j) for these (i, j): {476, 7578}, {566, 526}, {7577, 44427}, {18117, 2088}, {23039, 8552}, {35139, 57899}, {36829, 323}, {51391, 5664}, {56408, 523}
X(65317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {476, 60053, 110}, {35316, 35317, 35139}, {41512, 46155, 476}

X(65318) = X(2)X(51)∩X(110)X(1114)

Barycentrics    a^6-4*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+a^2*(2*b^4+3*b^2*c^2+2*c^4)+a^2*(b^4+3*b^2*c^2+c^4-a^2*(b^2+c^2))*J : :

X(65318) lies on these lines: {2, 51}, {23, 13414}, {110, 1114}, {323, 13415}, {468, 24650}, {850, 15165}, {858, 25407}, {1113, 15107}, {1154, 57323}, {1313, 3580}, {1345, 15066}, {2574, 9140}, {3564, 20406}, {4576, 46810}, {8115, 23061}, {10113, 10750}, {11064, 25408}, {12824, 64481}, {13391, 57322}, {15156, 43396}, {18911, 41518}, {20409, 32617}, {35360, 46812}, {36830, 57025}, {41724, 44126}, {47582, 64821}

X(65318) = reflection of X(i) in X(j) for these {i,j}: {65319, 2}
X(65318) = perspector of circumconic {{A, B, C, X(39299), X(57544)}}
X(65318) = pole of line {39241, 44125} with respect to the polar circle
X(65318) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(15165)}}, {{A, B, C, X(262), X(1114)}}, {{A, B, C, X(263), X(44124)}}, {{A, B, C, X(850), X(2575)}}, {{A, B, C, X(8116), X(42313)}}, {{A, B, C, X(15460), X(27867)}}
X(65318) = barycentric product X(i)*X(j) for these (i, j): {1347, 8116}
X(65318) = barycentric quotient X(i)/X(j) for these (i, j): {1347, 2593}
X(65318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1114, 8116, 110}, {11002, 32225, 65319}

X(65319) = X(2)X(51)∩X(110)X(1113)

Barycentrics    a^6-4*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+a^2*(2*b^4+3*b^2*c^2+2*c^4)-a^2*(b^4+3*b^2*c^2+c^4-a^2*(b^2+c^2))*J : :

X(65319) lies on these lines: {2, 51}, {23, 13415}, {110, 1113}, {323, 13414}, {468, 24651}, {850, 15164}, {858, 25408}, {1114, 15107}, {1154, 57322}, {1312, 3580}, {1344, 15066}, {2575, 9140}, {3564, 20405}, {4576, 46813}, {8116, 23061}, {10113, 10751}, {11064, 25407}, {12824, 64480}, {13391, 57323}, {15157, 43395}, {18911, 41519}, {20408, 32616}, {35360, 46815}, {36830, 57026}, {41724, 44125}, {47582, 64822}

X(65319) = reflection of X(i) in X(j) for these {i,j}: {65318, 2}
X(65319) = inverse of X(2574) in Stammler hyperbola
X(65319) = perspector of circumconic {{A, B, C, X(39298), X(57543)}}
X(65319) = pole of line {39240, 44126} with respect to the polar circle
X(65319) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(15164)}}, {{A, B, C, X(262), X(1113)}}, {{A, B, C, X(263), X(44123)}}, {{A, B, C, X(850), X(2574)}}, {{A, B, C, X(8115), X(42313)}}, {{A, B, C, X(15461), X(27867)}}
X(65319) = barycentric product X(i)*X(j) for these (i, j): {1346, 8115}
X(65319) = barycentric quotient X(i)/X(j) for these (i, j): {1346, 2592}
X(65319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 8115, 110}, {11002, 32225, 65318}

X(65320) = X(6)X(110)∩X(671)X(690)

Barycentrics    a^2*(a^2+b^2-2*c^2)*(a^2-2*b^2+c^2)*(2*b^6-b^4*c^2-b^2*c^4+2*c^6+a^4*(b^2+c^2)+a^2*(-3*b^4+2*b^2*c^2-3*c^4)) : :
X(65320) = X[67]+2*X[25322], 2*X[125]+X[25047], -2*X[4576]+5*X[15059]

X(65320) lies on these lines: {6, 110}, {67, 25322}, {74, 53687}, {125, 25047}, {262, 9759}, {511, 36827}, {526, 17993}, {576, 10560}, {671, 690}, {691, 15107}, {3060, 57485}, {3580, 51258}, {4576, 15059}, {5012, 57481}, {5969, 42008}, {7664, 15118}, {7998, 52152}, {8705, 52197}, {9138, 9178}, {9139, 65316}, {9155, 12099}, {10558, 53863}, {11002, 51980}, {13192, 17964}, {14263, 38523}, {15360, 16092}, {15398, 23061}, {17983, 35360}, {18023, 36901}, {20975, 40283}, {40915, 64880}, {41724, 51405}

X(65320) = reflection of X(i) in X(j) for these {i,j}: {110, 46131}, {36827, 46783}, {46131, 3124}
X(65320) = perspector of circumconic {{A, B, C, X(691), X(57539)}}
X(65320) = X(i)-isoconjugate-of-X(j) for these {i, j}: {39450, 42081}
X(65320) = pole of line {6055, 19912} with respect to the orthoptic circle of the Steiner Inellipse
X(65320) = pole of line {858, 64258} with respect to the Kiepert hyperbola
X(65320) = pole of line {11634, 44010} with respect to the Kiepert parabola
X(65320) = pole of line {2492, 5461} with respect to the Steiner inellipse
X(65320) = pole of line {1649, 52628} with respect to the dual conic of Wallace hyperbola
X(65320) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(5466)}}, {{A, B, C, X(67), X(53365)}}, {{A, B, C, X(110), X(671)}}, {{A, B, C, X(690), X(39689)}}, {{A, B, C, X(2502), X(18007)}}, {{A, B, C, X(2987), X(52699)}}, {{A, B, C, X(3124), X(15359)}}, {{A, B, C, X(6593), X(9979)}}
X(65320) = barycentric product X(i)*X(j) for these (i, j): {46127, 671}
X(65320) = barycentric quotient X(i)/X(j) for these (i, j): {10630, 39450}, {15359, 52628}, {46127, 524}
X(65320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 39024, 32740}, {111, 895, 110}, {511, 46783, 36827}, {2854, 3124, 46131}, {3124, 46154, 111}, {5968, 60498, 5640}

X(65321) = ISOGONAL CONJUGATE OF X(14273)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-2*c^2)*(a^2-b^2-c^2)*(a^2-2*b^2+c^2) : :

X(65321) lies on the MacBeath circumconic and on these lines: {2, 52668}, {23, 53770}, {69, 62594}, {99, 35188}, {110, 249}, {111, 323}, {287, 11064}, {394, 57481}, {524, 9225}, {525, 4563}, {647, 4558}, {648, 892}, {651, 36085}, {671, 2986}, {878, 43754}, {895, 3292}, {1331, 55230}, {1332, 55232}, {1813, 55234}, {1993, 57491}, {2421, 2433}, {2434, 34574}, {2502, 52198}, {2623, 18315}, {2709, 53690}, {2715, 45773}, {2991, 37783}, {3229, 19626}, {3291, 37784}, {3580, 56006}, {5380, 65303}, {5466, 44768}, {5468, 17708}, {5651, 21460}, {5968, 6090}, {6091, 52144}, {9143, 34320}, {9178, 60054}, {9190, 23348}, {9306, 10559}, {10420, 35191}, {13857, 14833}, {14582, 14977}, {14919, 36212}, {15066, 60022}, {28419, 56569}, {30491, 32661}, {32697, 47230}, {34211, 48373}, {36142, 65298}, {36894, 37669}, {37804, 41511}, {40814, 60863}, {42405, 59762}, {43187, 43665}, {43755, 61216}, {44718, 60024}, {44719, 60023}, {44766, 57216}, {44767, 61190}, {52630, 61198}, {53202, 64460}, {57763, 65309}, {61199, 65307}

X(65321) = isogonal conjugate of X(14273)
X(65321) = trilinear pole of line {3, 895}
X(65321) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14273}, {4, 2642}, {19, 690}, {92, 351}, {162, 1648}, {187, 24006}, {240, 52038}, {468, 661}, {656, 60428}, {798, 44146}, {810, 37778}, {811, 21906}, {896, 2501}, {897, 58780}, {922, 14618}, {1096, 14417}, {1109, 61207}, {1577, 44102}, {1649, 36128}, {1824, 4750}, {1826, 14419}, {1880, 14432}, {1973, 35522}, {2173, 52475}, {2247, 53156}, {2489, 14210}, {2643, 4235}, {2682, 65263}, {2971, 24039}, {3712, 55208}, {4062, 6591}, {5095, 23894}, {7181, 55206}, {7649, 21839}, {8754, 23889}, {17442, 22105}, {32676, 52628}, {36104, 51429}, {45775, 55270}, {55240, 64724}
X(65321) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 32697}, {4235, 32709}, {32696, 47443}, {32729, 65306}, {32734, 65328}, {65178, 65307}
X(65321) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14273}, {6, 690}, {125, 1648}, {6337, 35522}, {6338, 45807}, {6503, 14417}, {6593, 58780}, {15477, 2489}, {15526, 52628}, {15899, 2501}, {17423, 21906}, {22391, 351}, {31998, 44146}, {36033, 2642}, {36830, 468}, {36896, 52475}, {39000, 51429}, {39061, 14618}, {39062, 37778}, {39085, 52038}, {39169, 2492}, {40596, 60428}, {52881, 52629}, {55048, 5099}, {62607, 850}
X(65321) = X(i)-Ceva conjugate of X(j) for these {i, j}: {892, 691}, {34539, 57481}, {52940, 30786}
X(65321) = X(i)-cross conjugate of X(j) for these {i, j}: {525, 41511}, {647, 15398}, {9517, 69}, {10097, 895}, {10766, 57742}, {14961, 250}, {22151, 249}, {42665, 305}
X(65321) = pole of line {23, 5866} with respect to the Kiepert parabola
X(65321) = pole of line {10097, 65321} with respect to the MacBeath circumconic
X(65321) = pole of line {690, 5095} with respect to the Stammler hyperbola
X(65321) = pole of line {691, 53351} with respect to the Steiner circumellipse
X(65321) = pole of line {37742, 40544} with respect to the Steiner inellipse
X(65321) = pole of line {126, 1560} with respect to the Wallace hyperbola
X(65321) = pole of line {1648, 52628} with respect to the dual conic of polar circle
X(65321) = pole of line {858, 3566} with respect to the dual conic of Yff hyperbola
X(65321) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7468)}}, {{A, B, C, X(3), X(2709)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(249), X(10425)}}, {{A, B, C, X(305), X(18829)}}, {{A, B, C, X(394), X(14999)}}, {{A, B, C, X(512), X(525)}}, {{A, B, C, X(524), X(8681)}}, {{A, B, C, X(671), X(35191)}}, {{A, B, C, X(691), X(15398)}}, {{A, B, C, X(801), X(57932)}}, {{A, B, C, X(805), X(9218)}}, {{A, B, C, X(827), X(52608)}}, {{A, B, C, X(933), X(43188)}}, {{A, B, C, X(1304), X(2966)}}, {{A, B, C, X(1799), X(9150)}}, {{A, B, C, X(2421), X(11064)}}, {{A, B, C, X(2434), X(3292)}}, {{A, B, C, X(4561), X(6578)}}, {{A, B, C, X(5107), X(56389)}}, {{A, B, C, X(5468), X(22151)}}, {{A, B, C, X(5653), X(35909)}}, {{A, B, C, X(6331), X(59039)}}, {{A, B, C, X(9091), X(32696)}}, {{A, B, C, X(9124), X(55977)}}, {{A, B, C, X(9213), X(14977)}}, {{A, B, C, X(9476), X(40384)}}, {{A, B, C, X(9517), X(45807)}}, {{A, B, C, X(15387), X(32729)}}, {{A, B, C, X(18876), X(64775)}}, {{A, B, C, X(21639), X(61207)}}, {{A, B, C, X(30786), X(45773)}}, {{A, B, C, X(32661), X(59008)}}, {{A, B, C, X(34470), X(60503)}}, {{A, B, C, X(35325), X(61199)}}, {{A, B, C, X(37804), X(52630)}}, {{A, B, C, X(50941), X(57481)}}, {{A, B, C, X(56473), X(65269)}}, {{A, B, C, X(61198), X(62382)}}
X(65321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 32583, 691}, {110, 36827, 32729}, {11064, 51405, 30786}, {32583, 32729, 36827}

X(65322) = ISOGONAL CONJUGATE OF X(9209)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^4+b^4+4*b^2*c^2-5*c^4-2*a^2*(b^2-2*c^2))*(a^4-5*b^4+4*b^2*c^2+c^4+a^2*(4*b^2-2*c^2)) : :
X(65322) =

X(65322) lies on the MacBeath circumconic and on these lines: {6, 14919}, {69, 62583}, {110, 9064}, {112, 44769}, {193, 2986}, {287, 1992}, {323, 40386}, {524, 65325}, {895, 1351}, {2407, 4563}, {2420, 4558}, {3629, 65326}, {5921, 52452}, {8675, 32738}, {14927, 64505}, {18554, 64802}, {32110, 61448}, {34211, 65324}, {37489, 52168}, {37784, 60022}, {40318, 43756}, {41392, 60053}, {41610, 65302}, {41614, 51937}, {41617, 48453}, {46229, 65323}

X(65322) = reflection of X(i) in X(j) for these {i,j}: {69, 62583}, {14919, 6}
X(65322) = isogonal conjugate of X(9209)
X(65322) = trilinear pole of line {3, 1495}
X(65322) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 9209}, {19, 9007}, {376, 661}, {656, 40138}, {798, 44133}, {810, 52147}, {822, 47392}, {1577, 26864}, {36149, 53832}, {40348, 63827}
X(65322) = X(i)-vertex conjugate of X(j) for these {i, j}: {4558, 14560}, {32713, 44769}, {32738, 65322}
X(65322) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 9209}, {6, 9007}, {31998, 44133}, {36830, 376}, {39062, 52147}, {40596, 40138}
X(65322) = pole of line {9007, 9209} with respect to the Stammler hyperbola
X(65322) = pole of line {1302, 9064} with respect to the Steiner circumellipse
X(65322) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(112)}}, {{A, B, C, X(69), X(6528)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(511), X(64923)}}, {{A, B, C, X(524), X(5663)}}, {{A, B, C, X(892), X(35575)}}, {{A, B, C, X(1176), X(44828)}}, {{A, B, C, X(1296), X(2966)}}, {{A, B, C, X(1301), X(15459)}}, {{A, B, C, X(1351), X(5467)}}, {{A, B, C, X(1992), X(2421)}}, {{A, B, C, X(5505), X(53187)}}, {{A, B, C, X(8675), X(46229)}}, {{A, B, C, X(9033), X(35911)}}, {{A, B, C, X(14570), X(47269)}}, {{A, B, C, X(14999), X(41617)}}, {{A, B, C, X(30528), X(30535)}}, {{A, B, C, X(32697), X(58099)}}, {{A, B, C, X(32713), X(59136)}}, {{A, B, C, X(33513), X(43352)}}, {{A, B, C, X(34211), X(41614)}}, {{A, B, C, X(34898), X(58090)}}, {{A, B, C, X(41610), X(64828)}}
X(65322) = barycentric product X(i)*X(j) for these (i, j): {69, 9064}, {110, 36889}, {3426, 99}, {4558, 56270}, {51990, 6331}
X(65322) = barycentric quotient X(i)/X(j) for these (i, j): {3, 9007}, {6, 9209}, {99, 44133}, {107, 47392}, {110, 376}, {112, 40138}, {648, 52147}, {1301, 58758}, {1302, 39263}, {1576, 26864}, {3426, 523}, {8675, 53832}, {9060, 52447}, {9064, 4}, {32681, 40385}, {32734, 40348}, {36889, 850}, {46587, 1515}, {51990, 647}, {53958, 59430}, {56270, 14618}, {61448, 9003}

X(65323) = X(6)X(2986)∩X(110)X(1302)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2-b^2-c^2)*(a^4+a^2*(4*b^2-2*c^2)+(b^2-c^2)^2)*(a^4-2*a^2*(b^2-2*c^2)+(b^2-c^2)^2) : :
X(65323) =

X(65323) lies on the MacBeath circumconic and on these lines: {6, 2986}, {69, 14919}, {99, 32681}, {110, 1302}, {193, 43756}, {287, 41614}, {524, 60022}, {542, 54925}, {648, 61209}, {895, 4846}, {1992, 2987}, {2421, 65324}, {2990, 41610}, {3629, 57647}, {5656, 59429}, {6148, 40385}, {9190, 48960}, {10330, 56008}, {10753, 32220}, {11456, 39263}, {12383, 40387}, {14570, 46639}, {18315, 36841}, {22151, 65325}, {32111, 47103}, {32451, 41909}, {32661, 43755}, {36149, 65298}, {46229, 65322}, {47405, 57829}, {51196, 60049}

X(65323) = reflection of X(i) in X(j) for these {i,j}: {69, 62569}, {2986, 6}
X(65323) = trilinear pole of line {3, 4549}
X(65323) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 8675}, {92, 42660}, {378, 661}, {798, 44134}, {1577, 44080}, {1973, 30474}, {5063, 24006}, {51833, 55216}
X(65323) = X(i)-vertex conjugate of X(j) for these {i, j}: {648, 32715}, {32734, 43755}
X(65323) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 8675}, {6337, 30474}, {22391, 42660}, {31998, 44134}, {36830, 378}, {51471, 9209}, {62569, 46229}, {62613, 62628}
X(65323) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65284, 1302}
X(65323) = X(i)-cross conjugate of X(j) for these {i, j}: {9007, 69}, {63649, 57763}
X(65323) = pole of line {1302, 53958} with respect to the Steiner circumellipse
X(65323) = pole of line {30474, 46229} with respect to the Wallace hyperbola
X(65323) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(57627)}}, {{A, B, C, X(6), X(32661)}}, {{A, B, C, X(69), X(99)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(524), X(17702)}}, {{A, B, C, X(525), X(9003)}}, {{A, B, C, X(687), X(925)}}, {{A, B, C, X(1992), X(52035)}}, {{A, B, C, X(2421), X(41614)}}, {{A, B, C, X(2966), X(30247)}}, {{A, B, C, X(3267), X(62624)}}, {{A, B, C, X(9007), X(46229)}}, {{A, B, C, X(14570), X(36841)}}, {{A, B, C, X(15352), X(30249)}}, {{A, B, C, X(15396), X(41511)}}, {{A, B, C, X(15459), X(43188)}}, {{A, B, C, X(16813), X(47269)}}, {{A, B, C, X(17932), X(35138)}}, {{A, B, C, X(30528), X(42313)}}, {{A, B, C, X(32681), X(32738)}}, {{A, B, C, X(34568), X(40404)}}, {{A, B, C, X(36789), X(62569)}}, {{A, B, C, X(39290), X(60872)}}
X(65323) = barycentric product X(i)*X(j) for these (i, j): {3, 65284}, {110, 57819}, {304, 36149}, {305, 32738}, {1302, 69}, {4846, 99}, {17932, 56925}, {34288, 4563}, {34289, 4558}
X(65323) = barycentric quotient X(i)/X(j) for these (i, j): {3, 8675}, {69, 30474}, {99, 44134}, {110, 378}, {184, 42660}, {925, 51833}, {1302, 4}, {1332, 42704}, {1576, 44080}, {2407, 62628}, {4558, 15066}, {4563, 32833}, {4846, 523}, {9007, 53832}, {11064, 46229}, {23181, 5891}, {32661, 5063}, {32681, 8749}, {32738, 25}, {34288, 2501}, {34289, 14618}, {36083, 36119}, {36149, 19}, {43754, 11653}, {53958, 58081}, {56925, 16230}, {57819, 850}, {60119, 18808}, {65284, 264}

X(65324) = X(2)X(895)∩X(110)X(4235)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^4-4*a^2*b^2+b^4-c^4)*(a^4-b^4-4*a^2*c^2+c^4) : :

X(65324) lies on the MacBeath circumconic and on these lines: {2, 895}, {99, 35188}, {110, 4235}, {287, 15066}, {323, 52501}, {394, 36792}, {458, 2986}, {648, 61198}, {651, 37217}, {1332, 42721}, {1499, 15406}, {1797, 52759}, {1814, 26637}, {1993, 41909}, {2418, 9146}, {2421, 65323}, {2987, 37645}, {4558, 5468}, {4576, 65311}, {6515, 56007}, {8593, 37860}, {8600, 38343}, {11064, 57466}, {13608, 32985}, {14514, 58768}, {14608, 52275}, {14919, 36890}, {15304, 32133}, {15329, 65310}, {26645, 60047}, {32583, 48539}, {32661, 65306}, {34211, 65322}, {40112, 50639}, {44766, 61199}, {51831, 52283}, {55847, 62382}, {57216, 65307}

X(65324) = trilinear pole of line {3, 5486}
X(65324) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 30209}, {25, 14209}, {661, 1995}, {798, 11185}, {923, 55135}, {1577, 19136}, {2159, 44203}, {14207, 52174}, {23894, 53777}, {29959, 55240}
X(65324) = X(i)-vertex conjugate of X(j) for these {i, j}: {648, 32729}, {32734, 65306}, {44766, 65178}
X(65324) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 30209}, {2482, 55135}, {3163, 44203}, {6505, 14209}, {31998, 11185}, {35133, 5512}, {36830, 1995}
X(65324) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {15406, 4329}
X(65324) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 15406}, {2434, 6082}, {9145, 99}
X(65324) = pole of line {30209, 53777} with respect to the Stammler hyperbola
X(65324) = pole of line {1296, 30247} with respect to the Steiner circumellipse
X(65324) = pole of line {40556, 44813} with respect to the Steiner inellipse
X(65324) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(99)}}, {{A, B, C, X(83), X(6233)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(275), X(59007)}}, {{A, B, C, X(323), X(51478)}}, {{A, B, C, X(394), X(32661)}}, {{A, B, C, X(458), X(15329)}}, {{A, B, C, X(850), X(39905)}}, {{A, B, C, X(925), X(35178)}}, {{A, B, C, X(1302), X(2966)}}, {{A, B, C, X(2421), X(15066)}}, {{A, B, C, X(2434), X(8542)}}, {{A, B, C, X(4240), X(37188)}}, {{A, B, C, X(4576), X(57216)}}, {{A, B, C, X(5181), X(36792)}}, {{A, B, C, X(5546), X(56045)}}, {{A, B, C, X(6082), X(9146)}}, {{A, B, C, X(6331), X(43351)}}, {{A, B, C, X(8600), X(32583)}}, {{A, B, C, X(11794), X(44326)}}, {{A, B, C, X(14999), X(40112)}}, {{A, B, C, X(15118), X(41498)}}, {{A, B, C, X(16511), X(42286)}}, {{A, B, C, X(20404), X(58268)}}, {{A, B, C, X(26714), X(32640)}}, {{A, B, C, X(30247), X(60317)}}, {{A, B, C, X(32901), X(39639)}}, {{A, B, C, X(52231), X(56429)}}, {{A, B, C, X(52235), X(61486)}}, {{A, B, C, X(63179), X(63646)}}
X(65324) = barycentric product X(i)*X(j) for these (i, j): {3266, 35188}, {4558, 60266}, {5468, 60317}, {5486, 99}, {13608, 35179}, {30247, 69}, {37217, 63}, {39157, 6082}, {46144, 53764}
X(65324) = barycentric quotient X(i)/X(j) for these (i, j): {3, 30209}, {30, 44203}, {63, 14209}, {99, 11185}, {110, 1995}, {524, 55135}, {1296, 14262}, {1499, 5512}, {1576, 19136}, {1634, 29959}, {2709, 34241}, {4235, 37855}, {4558, 41614}, {5467, 53777}, {5486, 523}, {6082, 34166}, {9145, 8542}, {13608, 1499}, {15406, 1296}, {30247, 4}, {32709, 8753}, {35188, 111}, {36115, 36128}, {37217, 92}, {44061, 38331}, {51239, 6088}, {51831, 59932}, {53764, 2793}, {57466, 47138}, {60266, 14618}, {60317, 5466}, {61443, 2780}

X(65325) = X(2)X(30528)∩X(30)X(110)

Barycentrics    (a^2-b^2-c^2)*(a^8+a^6*(b^2-3*c^2)+b^2*(b^2-c^2)^3+a^4*(-4*b^4+2*b^2*c^2+3*c^4)+a^2*(b^6+2*b^4*c^2-2*b^2*c^4-c^6))*(a^8+a^6*(-3*b^2+c^2)+c^2*(-b^2+c^2)^3+a^4*(3*b^4+2*b^2*c^2-4*c^4)+a^2*(-b^6-2*b^4*c^2+2*b^2*c^4+c^6)) : :

X(65325) lies on the MacBeath circumconic and on these lines: {2, 30528}, {30, 110}, {323, 648}, {394, 57482}, {524, 65322}, {525, 14919}, {651, 36102}, {895, 9007}, {1331, 36062}, {1993, 48373}, {2411, 60022}, {2697, 64774}, {3580, 46639}, {4558, 11064}, {5640, 65305}, {14920, 23582}, {15066, 17708}, {18315, 43768}, {22151, 65323}, {35912, 43754}, {36151, 65298}, {37645, 65306}, {37669, 43755}, {44770, 52485}, {47071, 53235}

X(65325) = isogonal conjugate of X(47228)
X(65325) = trilinear pole of line {3, 9033}
X(65325) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 47228}, {6, 36063}, {19, 5663}, {661, 7480}, {1973, 35520}, {2159, 11251}, {2173, 52493}, {36131, 55141}
X(65325) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 47228}, {6, 5663}, {9, 36063}, {647, 6070}, {3163, 11251}, {6337, 35520}, {14401, 13212}, {36830, 7480}, {36896, 52493}, {39008, 55141}, {51475, 3018}, {62606, 46788}
X(65325) = X(i)-cross conjugate of X(j) for these {i, j}: {17702, 69}, {32663, 477}
X(65325) = pole of line {5663, 47228} with respect to the Stammler hyperbola
X(65325) = pole of line {477, 2693} with respect to the Steiner circumellipse
X(65325) = pole of line {31379, 45681} with respect to the Steiner inellipse
X(65325) = pole of line {35520, 47228} with respect to the Wallace hyperbola
X(65325) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(30)}}, {{A, B, C, X(3), X(37477)}}, {{A, B, C, X(4), X(32111)}}, {{A, B, C, X(6), X(40114)}}, {{A, B, C, X(69), X(9141)}}, {{A, B, C, X(94), X(7728)}}, {{A, B, C, X(97), X(249)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(265), X(5655)}}, {{A, B, C, X(275), X(14157)}}, {{A, B, C, X(323), X(394)}}, {{A, B, C, X(523), X(47148)}}, {{A, B, C, X(524), X(9007)}}, {{A, B, C, X(671), X(10706)}}, {{A, B, C, X(879), X(2770)}}, {{A, B, C, X(1073), X(10540)}}, {{A, B, C, X(2394), X(46045)}}, {{A, B, C, X(3265), X(13485)}}, {{A, B, C, X(3519), X(40113)}}, {{A, B, C, X(3580), X(6504)}}, {{A, B, C, X(4993), X(42330)}}, {{A, B, C, X(5641), X(34767)}}, {{A, B, C, X(10721), X(16080)}}, {{A, B, C, X(12121), X(56063)}}, {{A, B, C, X(14918), X(60597)}}, {{A, B, C, X(14920), X(15526)}}, {{A, B, C, X(14934), X(15421)}}, {{A, B, C, X(15066), X(22151)}}, {{A, B, C, X(18020), X(62428)}}, {{A, B, C, X(18550), X(54807)}}, {{A, B, C, X(30535), X(41511)}}, {{A, B, C, X(32730), X(61216)}}, {{A, B, C, X(34897), X(64182)}}, {{A, B, C, X(37645), X(62382)}}, {{A, B, C, X(38005), X(60193)}}, {{A, B, C, X(43572), X(57875)}}, {{A, B, C, X(43576), X(55982)}}, {{A, B, C, X(43670), X(54453)}}, {{A, B, C, X(44549), X(60161)}}, {{A, B, C, X(51228), X(62624)}}, {{A, B, C, X(51405), X(54607)}}, {{A, B, C, X(54803), X(60872)}}

X(65326) = X(5)X(49)∩X(94)X(275)

Barycentrics    (a^2-b^2-c^2)*(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(65326) lies on the MacBeath circumconic and on these lines: {2, 18315}, {5, 49}, {94, 275}, {97, 343}, {125, 15958}, {288, 30529}, {328, 57875}, {476, 1298}, {651, 24149}, {858, 54062}, {933, 3448}, {1332, 42698}, {1813, 52381}, {1993, 16039}, {2413, 57647}, {3484, 50435}, {3580, 46064}, {3629, 65322}, {4563, 28706}, {5449, 46089}, {5889, 34304}, {8884, 18300}, {13157, 41628}, {14920, 18831}, {15412, 60022}, {18027, 42405}, {18576, 58785}, {19180, 57482}, {19188, 63160}, {20574, 44516}, {25044, 25738}, {34799, 58079}, {37779, 43768}, {38413, 44714}, {38414, 44713}, {39295, 43766}, {43754, 53174}, {44766, 60515}, {51444, 52153}, {59771, 63172}, {60053, 62360}, {62428, 65308}

X(65326) = isogonal conjugate of X(11062)
X(65326) = isotomic conjugate of X(14918)
X(65326) = trilinear pole of line {3, 6368}
X(65326) = perspector of circumconic {{A, B, C, X(57758), X(64516)}}
X(65326) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 11062}, {4, 2290}, {6, 51801}, {19, 1154}, {31, 14918}, {51, 52414}, {53, 6149}, {162, 2081}, {186, 1953}, {323, 2181}, {340, 2179}, {1273, 1973}, {2151, 6116}, {2152, 6117}, {2180, 5962}, {2617, 47230}, {2618, 14591}, {2624, 35360}, {14165, 62266}, {14213, 34397}, {19627, 62273}, {32676, 41078}, {32679, 52604}, {35194, 52413}, {44706, 52418}
X(65326) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14918}, {3, 11062}, {6, 1154}, {9, 51801}, {125, 2081}, {6337, 1273}, {11077, 54067}, {14993, 53}, {15295, 3199}, {15526, 41078}, {36033, 2290}, {39019, 55132}, {39170, 52945}, {40578, 6116}, {40579, 6117}, {56399, 63735}, {62603, 340}
X(65326) = X(i)-Ceva conjugate of X(j) for these {i, j}: {46138, 1141}
X(65326) = X(i)-cross conjugate of X(j) for these {i, j}: {265, 46138}, {539, 69}, {577, 12028}, {6334, 65273}, {9033, 18831}, {11077, 1141}, {14592, 60053}, {50433, 50463}
X(65326) = pole of line {14592, 65326} with respect to the MacBeath circumconic
X(65326) = pole of line {1154, 11062} with respect to the Stammler hyperbola
X(65326) = pole of line {1141, 18401} with respect to the Steiner circumellipse
X(65326) = pole of line {24978, 34837} with respect to the Steiner inellipse
X(65326) = pole of line {1273, 11062} with respect to the Wallace hyperbola
X(65326) = pole of line {2081, 41078} with respect to the dual conic of polar circle
X(65326) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5)}}, {{A, B, C, X(3), X(567)}}, {{A, B, C, X(4), X(12022)}}, {{A, B, C, X(49), X(394)}}, {{A, B, C, X(54), X(97)}}, {{A, B, C, X(63), X(24149)}}, {{A, B, C, X(69), X(14389)}}, {{A, B, C, X(76), X(41171)}}, {{A, B, C, X(83), X(55978)}}, {{A, B, C, X(94), X(265)}}, {{A, B, C, X(95), X(4993)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(248), X(57407)}}, {{A, B, C, X(276), X(19176)}}, {{A, B, C, X(323), X(11597)}}, {{A, B, C, X(328), X(18883)}}, {{A, B, C, X(401), X(41202)}}, {{A, B, C, X(458), X(54375)}}, {{A, B, C, X(525), X(13582)}}, {{A, B, C, X(801), X(43598)}}, {{A, B, C, X(1073), X(18350)}}, {{A, B, C, X(2052), X(16000)}}, {{A, B, C, X(3519), X(62951)}}, {{A, B, C, X(3521), X(54663)}}, {{A, B, C, X(3615), X(30690)}}, {{A, B, C, X(5392), X(58922)}}, {{A, B, C, X(5486), X(56267)}}, {{A, B, C, X(5504), X(12228)}}, {{A, B, C, X(6288), X(11140)}}, {{A, B, C, X(6504), X(14516)}}, {{A, B, C, X(8796), X(38443)}}, {{A, B, C, X(8836), X(40710)}}, {{A, B, C, X(8838), X(40709)}}, {{A, B, C, X(8901), X(43766)}}, {{A, B, C, X(9033), X(14920)}}, {{A, B, C, X(9289), X(54913)}}, {{A, B, C, X(10272), X(11064)}}, {{A, B, C, X(11538), X(43575)}}, {{A, B, C, X(11564), X(14644)}}, {{A, B, C, X(11801), X(18366)}}, {{A, B, C, X(13434), X(31626)}}, {{A, B, C, X(13579), X(44076)}}, {{A, B, C, X(13585), X(45970)}}, {{A, B, C, X(14376), X(60255)}}, {{A, B, C, X(14542), X(60161)}}, {{A, B, C, X(14643), X(56063)}}, {{A, B, C, X(15077), X(60256)}}, {{A, B, C, X(15740), X(54792)}}, {{A, B, C, X(15749), X(54778)}}, {{A, B, C, X(21400), X(54927)}}, {{A, B, C, X(23236), X(34897)}}, {{A, B, C, X(36296), X(41907)}}, {{A, B, C, X(36297), X(41908)}}, {{A, B, C, X(37669), X(41628)}}, {{A, B, C, X(42313), X(62899)}}, {{A, B, C, X(44877), X(64101)}}, {{A, B, C, X(47388), X(60111)}}, {{A, B, C, X(52668), X(61216)}}, {{A, B, C, X(55980), X(56266)}}, {{A, B, C, X(56071), X(56338)}}, {{A, B, C, X(59763), X(60872)}}, {{A, B, C, X(60034), X(62724)}}
X(65326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {265, 50463, 1141}, {46138, 65360, 94}

X(65327) = X(110)X(669)∩X(648)X(2489)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(-b^2+a*c)*(b^2+a*c)*(a*b-c^2)*(a^2-b^2-c^2)*(a*b+c^2) : :

X(65327) lies on the MacBeath circumconic and on these lines: {110, 669}, {287, 12215}, {647, 4563}, {648, 2489}, {651, 4584}, {694, 2987}, {733, 2858}, {880, 2395}, {882, 60054}, {895, 36214}, {1916, 2986}, {3049, 4558}, {3292, 17970}, {9225, 47642}, {9468, 39099}, {15422, 42405}, {32526, 56442}

X(65327) = trilinear pole of line {3, 1808}
X(65327) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 804}, {92, 5027}, {242, 57234}, {419, 661}, {523, 56828}, {659, 1840}, {798, 17984}, {811, 2086}, {862, 4369}, {1096, 24284}, {1577, 44089}, {1580, 2501}, {1691, 24006}, {1824, 4107}, {1826, 4164}, {1874, 3287}, {1926, 57204}, {1933, 14618}, {1966, 2489}, {1973, 14295}, {2201, 2533}, {2238, 54229}, {2295, 65106}, {2333, 14296}, {2395, 56679}, {4010, 7119}, {4039, 6591}, {7009, 21832}, {8754, 56982}, {11183, 36128}, {56788, 62720}
X(65327) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 804}, {6337, 14295}, {6503, 24284}, {9467, 2489}, {17423, 2086}, {22391, 5027}, {31998, 17984}, {36830, 419}, {39092, 2501}, {47648, 16230}
X(65327) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18829, 805}, {39292, 40708}
X(65327) = X(i)-cross conjugate of X(j) for these {i, j}: {647, 15391}, {878, 43705}, {39469, 69}
X(65327) = pole of line {237, 19599} with respect to the Kiepert parabola
X(65327) = pole of line {804, 12829} with respect to the Stammler hyperbola
X(65327) = pole of line {14295, 24284} with respect to the Wallace hyperbola
X(65327) = pole of line {232, 46236} with respect to the dual conic of Jerabek hyperbola
X(65327) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(53893)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(647), X(669)}}, {{A, B, C, X(805), X(65351)}}, {{A, B, C, X(880), X(12215)}}, {{A, B, C, X(886), X(43714)}}, {{A, B, C, X(1576), X(43188)}}, {{A, B, C, X(2396), X(36212)}}, {{A, B, C, X(2713), X(53202)}}, {{A, B, C, X(5111), X(56389)}}, {{A, B, C, X(14586), X(55189)}}, {{A, B, C, X(15391), X(17938)}}, {{A, B, C, X(18878), X(56004)}}, {{A, B, C, X(19599), X(65277)}}, {{A, B, C, X(30530), X(60610)}}, {{A, B, C, X(32661), X(52608)}}
X(65327) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17938, 46161, 805}

X(65328) = X(110)X(9208)∩X(184)X(895)

Barycentrics    a^2*(a-b)*(a+b)*(a-c)*(a+c)*(a^2-b^2-c^2)*(2*a^2+2*b^2-c^2)*(2*a^2-b^2+2*c^2) : :

X(65328) lies on the MacBeath circumconic and on these lines: {99, 17708}, {110, 9208}, {184, 895}, {287, 37638}, {598, 2986}, {648, 35138}, {1383, 2987}, {1915, 30489}, {5986, 10511}, {7812, 64973}, {8593, 14567}, {8599, 44768}, {15534, 20380}, {30491, 32661}, {44555, 51541}, {46001, 60054}

X(65328) = trilinear pole of line {3, 22087}
X(65328) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 3906}, {92, 17414}, {162, 8288}, {574, 24006}, {661, 5094}, {1577, 8541}, {2501, 36263}, {8061, 32581}
X(65328) = X(i)-vertex conjugate of X(j) for these {i, j}: {32734, 65321}
X(65328) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 3906}, {125, 8288}, {22391, 17414}, {36830, 5094}
X(65328) = X(i)-Ceva conjugate of X(j) for these {i, j}: {35138, 11636}
X(65328) = X(i)-cross conjugate of X(j) for these {i, j}: {30491, 43697}, {41614, 249}
X(65328) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(6233)}}, {{A, B, C, X(99), X(1799)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(184), X(32661)}}, {{A, B, C, X(647), X(9208)}}, {{A, B, C, X(2421), X(37638)}}, {{A, B, C, X(2966), X(58994)}}, {{A, B, C, X(9145), X(55977)}}, {{A, B, C, X(26714), X(32662)}}, {{A, B, C, X(32697), X(53958)}}, {{A, B, C, X(33640), X(43188)}}, {{A, B, C, X(44116), X(61213)}}, {{A, B, C, X(52153), X(59136)}}, {{A, B, C, X(52608), X(58121)}}
X(65328) = barycentric product X(i)*X(j) for these (i, j): {3, 35138}, {110, 64982}, {1383, 4563}, {4558, 598}, {4577, 65006}, {4592, 55927}, {11636, 69}, {17932, 52692}, {23297, 65307}, {30491, 4590}, {32661, 40826}, {37804, 58953}, {43697, 99}, {46001, 47389}, {51541, 65321}
X(65328) = barycentric quotient X(i)/X(j) for these (i, j): {3, 3906}, {110, 5094}, {184, 17414}, {598, 14618}, {647, 8288}, {827, 32581}, {895, 23288}, {1383, 2501}, {1576, 8541}, {4558, 599}, {4563, 9464}, {4575, 36263}, {8599, 2970}, {11636, 4}, {23200, 62412}, {30491, 115}, {32661, 574}, {35138, 264}, {43697, 523}, {46001, 8754}, {47390, 9145}, {52692, 16230}, {55927, 24006}, {58953, 8791}, {64982, 850}, {65006, 826}, {65307, 10130}, {65321, 42008}

X(65329) = TRILINEAR POLE OF LINE {4, 80}

Barycentrics    (a-b)*b*(a-c)*(a+b-c)*c*(a-b+c)*(a^2+b^2-c^2)*(a^2-a*b+b^2-c^2)*(a^2-b^2+c^2)*(a^2-b^2-a*c+c^2) : :

X(65329) lies on these lines: {80, 62742}, {92, 14628}, {107, 2222}, {243, 14204}, {648, 35174}, {653, 655}, {823, 16813}, {1807, 8764}, {1895, 59283}, {1897, 44426}, {2006, 16082}, {6335, 36804}, {6336, 37790}, {7012, 24006}, {16080, 60091}, {16577, 65359}, {18359, 52780}, {18815, 37805}, {24035, 53811}, {37770, 37799}, {46405, 65341}, {52167, 60845}, {52351, 65342}, {52391, 57732}, {54235, 64835}, {55238, 65343}

X(65329) = trilinear pole of line {4, 80}
X(65329) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 654}, {9, 22379}, {36, 652}, {48, 3738}, {63, 8648}, {78, 21758}, {184, 3904}, {212, 3960}, {219, 53314}, {222, 53285}, {255, 65104}, {283, 21828}, {394, 58313}, {521, 7113}, {577, 44428}, {650, 52407}, {656, 4282}, {663, 22128}, {822, 17515}, {905, 2361}, {906, 53525}, {1443, 65102}, {1459, 2323}, {1464, 23090}, {1789, 2624}, {1790, 53562}, {1795, 53046}, {1807, 57174}, {1870, 36054}, {1946, 3218}, {1983, 7004}, {2169, 2600}, {2193, 53527}, {2245, 23189}, {2252, 61043}, {2720, 38353}, {4025, 52426}, {4091, 52427}, {4453, 52425}, {4511, 22383}, {6332, 52434}, {6369, 14533}, {14418, 16944}, {18593, 57134}, {22086, 62703}, {22342, 62746}, {22346, 62750}, {44706, 62734}, {46391, 58741}, {52413, 57241}, {52440, 57055}, {61054, 65162}
X(65329) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 22379}, {1249, 3738}, {3162, 8648}, {5190, 53525}, {6523, 65104}, {13999, 35128}, {14363, 2600}, {15898, 652}, {25640, 53046}, {36103, 654}, {36909, 57055}, {38981, 38353}, {39053, 3218}, {39060, 320}, {40596, 4282}, {40837, 3960}, {47345, 53527}, {56416, 14418}, {62602, 4453}, {62605, 3904}
X(65329) = X(i)-cross conjugate of X(j) for these {i, j}: {1784, 24032}, {2222, 35174}, {37799, 46102}, {52356, 18815}, {65104, 4}
X(65329) = pole of line {35128, 53046} with respect to the polar circle
X(65329) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(37136)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(643), X(56248)}}, {{A, B, C, X(651), X(15455)}}, {{A, B, C, X(655), X(36804)}}, {{A, B, C, X(2222), X(65299)}}, {{A, B, C, X(17924), X(44426)}}, {{A, B, C, X(35174), X(57645)}}, {{A, B, C, X(36039), X(56232)}}, {{A, B, C, X(53211), X(60041)}}
X(65329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {62735, 65299, 35174}

X(65330) = TRILINEAR POLE OF LINE {4, 57}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2) : :

X(65330) lies on these lines: {19, 56972}, {27, 52037}, {34, 7020}, {84, 62742}, {92, 41081}, {107, 8059}, {108, 58990}, {189, 278}, {243, 52007}, {273, 282}, {648, 1414}, {651, 1897}, {653, 934}, {664, 6335}, {1422, 16082}, {1433, 8764}, {1440, 7003}, {1903, 57737}, {2262, 63186}, {2358, 65352}, {4625, 6331}, {4626, 13149}, {6336, 55110}, {7129, 54235}, {8808, 16080}, {34056, 40836}, {36048, 36049}, {36118, 54240}, {36146, 65333}, {41906, 58984}, {55242, 65343}, {58995, 65362}, {65173, 65337}, {65174, 65355}

X(65330) = isogonal conjugate of X(10397)
X(65330) = isotomic conjugate of X(57245)
X(65330) = trilinear pole of line {4, 57}
X(65330) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 10397}, {3, 14298}, {6, 57101}, {31, 57245}, {33, 57233}, {40, 652}, {42, 57213}, {48, 8058}, {55, 64885}, {196, 58340}, {198, 521}, {208, 57057}, {212, 14837}, {219, 6129}, {221, 57055}, {223, 57108}, {227, 23090}, {283, 55212}, {329, 1946}, {347, 65102}, {513, 55111}, {603, 57049}, {650, 7078}, {651, 47432}, {657, 7013}, {661, 1819}, {663, 64082}, {667, 55112}, {692, 16596}, {810, 27398}, {905, 7074}, {906, 38357}, {1415, 7358}, {1459, 2324}, {1783, 55044}, {2187, 6332}, {2289, 54239}, {2331, 57241}, {2360, 8611}, {3239, 7114}, {3270, 65159}, {3900, 7011}, {4091, 40971}, {5514, 36059}, {6056, 59935}, {7080, 22383}, {7952, 36054}, {15501, 52307}, {17896, 52425}, {21871, 23189}, {23224, 55116}, {34591, 57118}, {57134, 64708}, {57180, 57479}
X(65330) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 57245}, {3, 10397}, {9, 57101}, {223, 64885}, {278, 8063}, {1015, 53557}, {1086, 16596}, {1146, 7358}, {1249, 8058}, {3341, 57055}, {5190, 38357}, {6631, 55112}, {7952, 57049}, {20620, 5514}, {36103, 14298}, {36830, 1819}, {38991, 47432}, {39006, 55044}, {39026, 55111}, {39053, 329}, {39060, 322}, {39062, 27398}, {40592, 57213}, {40616, 55058}, {40837, 14837}, {55058, 55063}, {62602, 17896}
X(65330) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65270, 653}
X(65330) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {8064, 34188}
X(65330) = X(i)-cross conjugate of X(j) for these {i, j}: {514, 189}, {522, 273}, {905, 27}, {1459, 56972}, {3064, 7020}, {6129, 63186}, {8059, 53642}, {21172, 7}, {32714, 653}, {36127, 36118}, {40117, 65213}
X(65330) = pole of line {5514, 13612} with respect to the polar circle
X(65330) = pole of line {653, 13138} with respect to the Steiner circumellipse
X(65330) = pole of line {6223, 56943} with respect to the Yff parabola
X(65330) = pole of line {10397, 57213} with respect to the Wallace hyperbola
X(65330) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(92), X(2405)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(190), X(41906)}}, {{A, B, C, X(278), X(23987)}}, {{A, B, C, X(514), X(26932)}}, {{A, B, C, X(522), X(55144)}}, {{A, B, C, X(643), X(65216)}}, {{A, B, C, X(645), X(60487)}}, {{A, B, C, X(651), X(664)}}, {{A, B, C, X(658), X(14544)}}, {{A, B, C, X(662), X(43346)}}, {{A, B, C, X(1332), X(37136)}}, {{A, B, C, X(13138), X(37141)}}, {{A, B, C, X(32714), X(36127)}}, {{A, B, C, X(38340), X(50392)}}, {{A, B, C, X(57215), X(60482)}}

X(65331) = TRILINEAR POLE OF LINE {4, 11}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a^2*b+b^3-a*(b-c)^2-b*c^2)*(a^3-a*(b-c)^2-a^2*c-b^2*c+c^3) : :

X(65331) lies on the Moses-Feuerbach circumconic and on these lines: {104, 62742}, {107, 2720}, {109, 522}, {278, 40218}, {514, 653}, {648, 4560}, {651, 4391}, {685, 60568}, {885, 14776}, {929, 59103}, {1462, 54235}, {1795, 8764}, {2401, 2405}, {4573, 6331}, {4581, 52928}, {4617, 13149}, {6336, 60578}, {7316, 17983}, {16080, 37799}, {16082, 34051}, {17923, 34050}, {17924, 23984}, {24035, 53811}, {32641, 32651}, {36123, 60579}, {37805, 52663}, {38828, 65337}, {39294, 60480}, {40577, 44699}, {43728, 60583}, {44356, 52781}, {54368, 62745}, {55259, 65343}, {60479, 65335}, {60577, 65338}, {65162, 65344}, {65302, 65342}

X(65331) = isogonal conjugate of X(52307)
X(65331) = trilinear pole of line {4, 11}
X(65331) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52307}, {3, 46393}, {9, 8677}, {48, 2804}, {63, 53549}, {78, 3310}, {101, 35014}, {212, 10015}, {219, 1769}, {312, 23220}, {517, 652}, {521, 2183}, {649, 51379}, {650, 22350}, {657, 62402}, {859, 8611}, {906, 35015}, {908, 1946}, {1457, 57055}, {1465, 57108}, {1785, 36054}, {1795, 60339}, {1807, 53046}, {1875, 57057}, {2222, 38353}, {2289, 39534}, {2427, 7004}, {3270, 24029}, {4587, 42753}, {4895, 57478}, {6735, 22383}, {14260, 14418}, {14571, 57241}, {21801, 23189}, {22464, 65102}, {23706, 35072}, {23788, 52370}, {23980, 37628}, {23981, 34591}, {36038, 52425}, {37136, 41215}, {41220, 65223}, {42761, 65375}
X(65331) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52307}, {478, 8677}, {1015, 35014}, {1249, 2804}, {3162, 53549}, {5190, 35015}, {5375, 51379}, {25640, 60339}, {36103, 46393}, {38984, 38353}, {39053, 908}, {39060, 3262}, {40622, 42761}, {40837, 10015}, {62602, 36038}
X(65331) = X(i)-cross conjugate of X(j) for these {i, j}: {1870, 55346}, {2401, 16082}, {2405, 54240}, {2720, 54953}, {18838, 4998}, {21786, 28}, {23987, 36118}, {30725, 278}, {37790, 46102}, {44428, 273}, {53522, 7}
X(65331) = pole of line {35015, 55153} with respect to the polar circle
X(65331) = pole of line {2406, 43737} with respect to the Steiner circumellipse
X(65331) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(109), X(651)}}, {{A, B, C, X(514), X(522)}}, {{A, B, C, X(645), X(65216)}}, {{A, B, C, X(1172), X(40116)}}, {{A, B, C, X(1783), X(59084)}}, {{A, B, C, X(7012), X(7128)}}, {{A, B, C, X(13136), X(36037)}}, {{A, B, C, X(14546), X(36098)}}, {{A, B, C, X(17923), X(24035)}}, {{A, B, C, X(23353), X(54407)}}, {{A, B, C, X(37139), X(47318)}}, {{A, B, C, X(37141), X(44765)}}, {{A, B, C, X(40395), X(65263)}}

X(65332) = TRILINEAR POLE OF LINE {4, 240}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(b^2+a*c)*(a^2+b^2-c^2)*(a*b+c^2)*(a^2-b^2+c^2) : :

X(65332) lies on these lines: {92, 16081}, {107, 29055}, {108, 30670}, {162, 685}, {243, 41532}, {256, 62742}, {257, 52780}, {278, 17082}, {648, 4603}, {653, 37137}, {1432, 16082}, {1897, 3903}, {6331, 7260}, {6335, 27805}, {7015, 8764}, {7249, 52781}, {16080, 60245}, {19637, 52167}, {61178, 65338}, {61180, 65209}

X(65332) = trilinear pole of line {4, 240}
X(65332) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3287}, {9, 22093}, {48, 3907}, {78, 20981}, {171, 652}, {172, 521}, {212, 4369}, {219, 4367}, {222, 4477}, {283, 57234}, {345, 56242}, {603, 4529}, {645, 22373}, {650, 3955}, {810, 27958}, {822, 14006}, {894, 1946}, {905, 2330}, {906, 4459}, {1437, 4140}, {1459, 2329}, {1812, 7234}, {2193, 2533}, {2289, 54229}, {2295, 23189}, {2318, 18200}, {3737, 22061}, {4032, 57134}, {4374, 52425}, {4558, 40608}, {4579, 7117}, {4587, 53541}, {6332, 7122}, {7009, 36054}, {7081, 22383}, {7119, 57241}, {7175, 57108}, {7176, 65102}, {15373, 30584}, {17212, 52370}
X(65332) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 22093}, {1249, 3907}, {5190, 4459}, {7952, 4529}, {16591, 24284}, {36103, 3287}, {39053, 894}, {39060, 1909}, {39062, 27958}, {40837, 4369}, {47345, 2533}, {62602, 4374}
X(65332) = X(i)-cross conjugate of X(j) for these {i, j}: {17442, 7012}, {29055, 65289}
X(65332) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55211)}}, {{A, B, C, X(92), X(162)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(108), X(46404)}}, {{A, B, C, X(226), X(26700)}}, {{A, B, C, X(278), X(61178)}}, {{A, B, C, X(651), X(1978)}}, {{A, B, C, X(658), X(35148)}}, {{A, B, C, X(3903), X(4603)}}, {{A, B, C, X(4637), X(44733)}}

X(65333) = TRILINEAR POLE OF LINE {4, 218}

Barycentrics    (a-b)*(a-c)*(a^2+b*(b-c)-a*c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-a*b+c*(-b+c)) : :

X(65333) lies on these lines: {4, 56850}, {33, 6654}, {100, 25009}, {105, 243}, {107, 919}, {108, 927}, {242, 52480}, {294, 62742}, {297, 56855}, {458, 60857}, {648, 666}, {653, 7012}, {673, 1861}, {885, 14776}, {1897, 3064}, {5236, 54234}, {5377, 65344}, {6331, 36797}, {6335, 15742}, {6336, 23710}, {8756, 65340}, {13576, 16080}, {14775, 52927}, {14942, 52780}, {16081, 56853}, {18026, 34085}, {18344, 46102}, {26704, 65371}, {31905, 52209}, {36146, 65330}, {46163, 65349}, {51560, 65341}, {53151, 63745}

X(65333) = isogonal conjugate of X(53550)
X(65333) = trilinear pole of line {4, 218}
X(65333) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 53550}, {3, 2254}, {48, 918}, {63, 665}, {75, 23225}, {77, 926}, {78, 53539}, {212, 43042}, {219, 53544}, {228, 23829}, {241, 652}, {283, 53551}, {348, 46388}, {513, 1818}, {514, 20752}, {518, 1459}, {520, 54407}, {521, 1458}, {603, 50333}, {647, 18206}, {656, 3286}, {672, 905}, {810, 30941}, {822, 15149}, {876, 20778}, {1025, 7117}, {1026, 3937}, {1331, 3675}, {1362, 23696}, {1437, 4088}, {1565, 54325}, {1790, 24290}, {1795, 42758}, {1807, 53555}, {1813, 17435}, {1861, 23224}, {1876, 57241}, {1946, 9436}, {2196, 62552}, {2223, 4025}, {2283, 7004}, {2284, 3942}, {2356, 4131}, {3049, 18157}, {3126, 36057}, {3270, 41353}, {3912, 22383}, {3930, 7254}, {4091, 5089}, {5236, 36054}, {6332, 52635}, {7015, 53553}, {7100, 53554}, {7177, 52614}, {7182, 8638}, {8677, 36819}, {9454, 15413}, {15419, 39258}, {18210, 54353}, {20749, 35355}, {22116, 22384}, {22350, 57468}, {32656, 62429}, {32658, 53583}, {34230, 53532}, {34855, 57108}, {37628, 53548}, {62786, 65102}
X(65333) = X(i)-vertex conjugate of X(j) for these {i, j}: {28, 32641}, {56, 54953}, {4238, 32644}
X(65333) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 53550}, {206, 23225}, {1249, 918}, {3162, 665}, {5375, 25083}, {5521, 3675}, {7952, 50333}, {20621, 3126}, {25640, 42758}, {33675, 15413}, {36103, 2254}, {39026, 1818}, {39052, 18206}, {39053, 9436}, {39060, 40704}, {39062, 30941}, {40596, 3286}, {40837, 43042}, {62554, 905}, {62599, 4025}
X(65333) = X(i)-cross conjugate of X(j) for these {i, j}: {242, 15742}, {919, 666}, {4250, 162}, {5089, 46102}, {28132, 673}, {41321, 653}
X(65333) = pole of line {3126, 3675} with respect to the polar circle
X(65333) = pole of line {20778, 23225} with respect to the Stammler hyperbola
X(65333) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(929)}}, {{A, B, C, X(21), X(14733)}}, {{A, B, C, X(101), X(54952)}}, {{A, B, C, X(105), X(32735)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(108), X(8750)}}, {{A, B, C, X(242), X(54407)}}, {{A, B, C, X(243), X(23353)}}, {{A, B, C, X(644), X(1305)}}, {{A, B, C, X(651), X(9057)}}, {{A, B, C, X(666), X(36803)}}, {{A, B, C, X(673), X(56786)}}, {{A, B, C, X(677), X(2346)}}, {{A, B, C, X(835), X(4606)}}, {{A, B, C, X(927), X(36086)}}, {{A, B, C, X(943), X(32641)}}, {{A, B, C, X(1309), X(5379)}}, {{A, B, C, X(1783), X(26705)}}, {{A, B, C, X(1861), X(41321)}}, {{A, B, C, X(2218), X(32675)}}, {{A, B, C, X(2222), X(39026)}}, {{A, B, C, X(2398), X(26001)}}, {{A, B, C, X(2402), X(25009)}}, {{A, B, C, X(3064), X(7649)}}, {{A, B, C, X(4241), X(26003)}}, {{A, B, C, X(4246), X(62971)}}, {{A, B, C, X(6606), X(37138)}}, {{A, B, C, X(8708), X(55181)}}, {{A, B, C, X(8756), X(23710)}}, {{A, B, C, X(9311), X(60487)}}, {{A, B, C, X(36084), X(40412)}}, {{A, B, C, X(56850), X(63745)}}, {{A, B, C, X(58993), X(65201)}}, {{A, B, C, X(59038), X(65225)}}

X(65334) = TRILINEAR POLE OF LINE {4, 12}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-a^2*b+b^3-b*c^2-a*(b+c)^2)*(a^3-a^2*c-b^2*c+c^3-a*(b+c)^2) : :

X(65334) lies on these lines: {101, 653}, {107, 15439}, {294, 54235}, {644, 6335}, {645, 6331}, {648, 4552}, {651, 13149}, {943, 62742}, {1783, 54240}, {1794, 8764}, {1897, 3939}, {2311, 65352}, {2316, 6336}, {2338, 40942}, {2341, 40395}, {2982, 16082}, {4845, 65340}, {5547, 17983}, {5548, 65336}, {14775, 52927}, {15627, 16080}, {15628, 16081}, {15629, 40435}, {32641, 32651}, {36048, 36049}

X(65334) = isogonal conjugate of X(52306)
X(65334) = trilinear pole of line {4, 12}
X(65334) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52306}, {77, 33525}, {219, 50354}, {514, 23207}, {520, 46884}, {521, 2260}, {522, 14597}, {647, 54356}, {650, 4303}, {652, 942}, {656, 46882}, {663, 18607}, {905, 14547}, {1021, 39791}, {1364, 61236}, {1459, 40937}, {1838, 36054}, {1841, 57241}, {1859, 4091}, {1946, 5249}, {2193, 23752}, {2294, 23189}, {3737, 18591}, {3937, 61233}, {6056, 23595}, {6332, 40956}, {6734, 22383}, {7004, 61197}, {7117, 61220}, {7252, 56839}, {7254, 40967}, {8021, 51664}, {41214, 65217}, {55010, 57134}, {62779, 65102}
X(65334) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52306}, {39052, 54356}, {39053, 5249}, {40596, 46882}, {47345, 23752}
X(65334) = X(i)-cross conjugate of X(j) for these {i, j}: {1172, 7012}, {6198, 55346}, {15439, 54952}, {40149, 46102}, {41538, 4998}, {56320, 40447}
X(65334) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(294)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(655), X(4552)}}, {{A, B, C, X(823), X(1309)}}, {{A, B, C, X(2982), X(32651)}}, {{A, B, C, X(4573), X(65216)}}, {{A, B, C, X(37141), X(43190)}}, {{A, B, C, X(44765), X(56235)}}
X(65334) = barycentric product X(i)*X(j) for these (i, j): {4, 54952}, {108, 40422}, {190, 40573}, {318, 36048}, {1794, 52938}, {1897, 60041}, {2259, 46404}, {2982, 6335}, {14775, 4998}, {15439, 264}, {18026, 943}, {32651, 7017}, {35320, 40440}, {36797, 52560}, {40395, 4552}, {40412, 61178}, {40435, 653}, {40447, 651}, {46102, 56320}, {58993, 8}, {60188, 648}, {65217, 92}
X(65334) = barycentric quotient X(i)/X(j) for these (i, j): {6, 52306}, {34, 50354}, {108, 942}, {109, 4303}, {112, 46882}, {162, 54356}, {225, 23752}, {607, 33525}, {651, 18607}, {653, 5249}, {692, 23207}, {943, 521}, {1175, 23189}, {1415, 14597}, {1783, 40937}, {1794, 57241}, {1897, 6734}, {2259, 652}, {2982, 905}, {4551, 56839}, {4559, 18591}, {7012, 61220}, {7115, 61197}, {8750, 14547}, {14775, 11}, {15439, 3}, {15742, 65197}, {24019, 46884}, {32651, 222}, {32674, 2260}, {35320, 44706}, {36048, 77}, {36118, 62779}, {36127, 1838}, {36797, 51978}, {40395, 4560}, {40422, 35518}, {40435, 6332}, {40447, 4391}, {40570, 7252}, {40573, 514}, {46102, 65205}, {52560, 17094}, {52607, 55010}, {53321, 39791}, {53323, 37993}, {54952, 69}, {56183, 64171}, {56320, 26932}, {58993, 7}, {59060, 56269}, {60041, 4025}, {60188, 525}, {61178, 442}, {65217, 63}
X(65334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {653, 65217, 58993}

X(65335) = TRILINEAR POLE OF LINE {4, 653}

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2+b*c-2*c^2+a*(-2*b+c))*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-2*b^2+a*(b-2*c)+b*c+c^2) : :

X(65335) lies on these lines: {107, 14733}, {243, 1156}, {648, 17926}, {653, 3064}, {685, 32728}, {1121, 52780}, {1897, 46102}, {5236, 6336}, {8764, 60047}, {13149, 17924}, {16082, 34056}, {17923, 52781}, {17983, 17985}, {23710, 37769}, {24032, 54240}, {37790, 54235}, {37805, 46644}, {41207, 62757}, {60479, 65331}

X(65335) = trilinear pole of line {4, 653}
X(65335) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 14414}, {48, 6366}, {63, 6139}, {212, 1638}, {219, 14413}, {222, 14392}, {521, 1055}, {527, 1946}, {647, 62756}, {652, 1155}, {663, 6510}, {822, 52891}, {1323, 65102}, {1459, 6603}, {2193, 30574}, {3270, 23890}, {6610, 57108}, {6745, 22383}, {23224, 60431}, {23346, 34591}, {23710, 36054}, {33573, 36059}
X(65335) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 14414}, {1249, 6366}, {3162, 6139}, {20620, 33573}, {39052, 62756}, {39053, 527}, {39060, 30806}, {40837, 1638}, {47345, 30574}
X(65335) = X(i)-cross conjugate of X(j) for these {i, j}: {14733, 35157}, {23710, 55346}, {63748, 62723}
X(65335) = pole of line {33573, 35091} with respect to the polar circle
X(65335) = intersection, other than A, B, C, of circumconics {{A, B, C, X(92), X(1309)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(243), X(62757)}}, {{A, B, C, X(658), X(42343)}}, {{A, B, C, X(3064), X(17924)}}, {{A, B, C, X(4624), X(32038)}}, {{A, B, C, X(5236), X(37790)}}, {{A, B, C, X(24032), X(41207)}}, {{A, B, C, X(36129), X(40395)}}, {{A, B, C, X(37139), X(60487)}}
X(65335) = barycentric product X(i)*X(j) for these (i, j): {281, 60487}, {664, 65340}, {1121, 653}, {1156, 18026}, {1897, 62723}, {1969, 36141}, {2052, 65304}, {2291, 46404}, {13149, 41798}, {14733, 264}, {18022, 32728}, {21666, 59105}, {34056, 6335}, {35157, 4}, {37139, 92}, {46102, 60479}, {52938, 60047}, {55346, 63748}, {61493, 65270}, {62764, 811}, {63857, 65295}
X(65335) = barycentric quotient X(i)/X(j) for these (i, j): {1, 14414}, {4, 6366}, {25, 6139}, {33, 14392}, {34, 14413}, {107, 52891}, {108, 1155}, {162, 62756}, {225, 30574}, {278, 1638}, {651, 6510}, {653, 527}, {1121, 6332}, {1156, 521}, {1783, 6603}, {1877, 30573}, {1897, 6745}, {2291, 652}, {3064, 33573}, {4845, 57108}, {7128, 23890}, {8735, 52334}, {13149, 37780}, {14733, 3}, {18026, 30806}, {18889, 65102}, {23351, 3270}, {23710, 62579}, {23893, 34591}, {23987, 51408}, {32674, 1055}, {32714, 6610}, {32728, 184}, {34056, 905}, {34068, 1946}, {35157, 69}, {35348, 7004}, {36118, 1323}, {36127, 23710}, {36141, 48}, {37139, 63}, {40117, 56763}, {41798, 57055}, {54240, 37805}, {55346, 56543}, {60047, 57241}, {60479, 26932}, {60487, 348}, {61493, 64885}, {62723, 4025}, {62764, 656}, {63748, 2968}, {63857, 39471}, {65304, 394}, {65340, 522}

X(65336) = TRILINEAR POLE OF LINE {4, 145}

Barycentrics    (a-b)*(a+b-2*c)*(a-c)*(a-2*b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65336) lies on these lines: {2, 65345}, {88, 16082}, {107, 901}, {190, 65337}, {242, 36125}, {243, 14193}, {648, 4555}, {653, 3257}, {685, 32719}, {903, 52781}, {1320, 62742}, {1861, 65340}, {1897, 7649}, {1981, 23598}, {4080, 16080}, {4582, 6335}, {4997, 52780}, {5376, 65344}, {5548, 65334}, {6336, 8756}, {10015, 13136}, {13149, 62532}, {15466, 57478}, {17927, 17983}, {19634, 52167}, {37805, 54235}, {39294, 60480}, {46162, 65349}, {52925, 61180}, {57456, 65162}, {61179, 65343}

X(65336) = isogonal conjugate of X(22086)
X(65336) = trilinear pole of line {4, 145}
X(65336) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 22086}, {3, 1635}, {6, 53532}, {44, 1459}, {48, 900}, {56, 14418}, {63, 1960}, {184, 3762}, {212, 30725}, {219, 53528}, {222, 4895}, {513, 22356}, {514, 23202}, {519, 22383}, {521, 1404}, {603, 1639}, {647, 52680}, {649, 5440}, {652, 1319}, {656, 3285}, {667, 3977}, {810, 16704}, {822, 37168}, {902, 905}, {906, 1647}, {1022, 22371}, {1023, 3937}, {1331, 2087}, {1333, 14429}, {1437, 4120}, {1444, 14407}, {1790, 4730}, {1797, 3251}, {1877, 36054}, {1946, 3911}, {2193, 30572}, {2196, 4448}, {2251, 4025}, {3049, 30939}, {3942, 23344}, {4528, 7099}, {4530, 36059}, {4768, 52411}, {4922, 7116}, {6544, 36058}, {7004, 61210}, {7053, 14427}, {7117, 23703}, {7254, 21805}, {8756, 23224}, {9459, 15413}, {14408, 23086}, {14578, 23757}, {22096, 24004}, {30576, 55230}, {36037, 47420}, {38266, 39472}, {43924, 52978}, {52431, 53535}, {62789, 65102}
X(65336) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 14418}, {3, 22086}, {9, 53532}, {37, 14429}, {1249, 900}, {3162, 1960}, {3259, 47420}, {5190, 1647}, {5375, 5440}, {5521, 2087}, {6631, 3977}, {7952, 1639}, {9460, 4025}, {20619, 6544}, {20620, 4530}, {23050, 14427}, {36103, 1635}, {39026, 22356}, {39052, 52680}, {39053, 3911}, {39062, 16704}, {40594, 905}, {40595, 1459}, {40596, 3285}, {40837, 30725}, {45247, 52307}, {47345, 30572}, {53985, 35092}, {62582, 6332}, {62605, 3762}
X(65336) = X(i)-cross conjugate of X(j) for these {i, j}: {901, 4555}, {1309, 65295}, {1785, 55346}, {8756, 15742}, {17923, 46102}, {23678, 75}, {35013, 46136}, {39534, 264}, {43933, 46133}, {53151, 18026}, {65162, 648}
X(65336) = pole of line {1647, 2087} with respect to the polar circle
X(65336) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(655)}}, {{A, B, C, X(75), X(927)}}, {{A, B, C, X(86), X(35157)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(190), X(8706)}}, {{A, B, C, X(666), X(36804)}}, {{A, B, C, X(1268), X(57928)}}, {{A, B, C, X(1309), X(17923)}}, {{A, B, C, X(1861), X(37805)}}, {{A, B, C, X(3257), X(4582)}}, {{A, B, C, X(4555), X(57788)}}, {{A, B, C, X(5936), X(51568)}}, {{A, B, C, X(6648), X(15455)}}, {{A, B, C, X(7649), X(17924)}}, {{A, B, C, X(8709), X(54979)}}, {{A, B, C, X(14534), X(32680)}}, {{A, B, C, X(15742), X(39294)}}, {{A, B, C, X(17906), X(52607)}}, {{A, B, C, X(31643), X(58000)}}, {{A, B, C, X(37140), X(60235)}}, {{A, B, C, X(37143), X(50039)}}, {{A, B, C, X(38340), X(56188)}}, {{A, B, C, X(53225), X(55955)}}

X(65337) = X(2)X(6336)∩X(4)X(31316)

Barycentrics    (a-b)*(a+b-3*c)*(a-c)*(a-3*b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65337) lies on these lines: {2, 6336}, {4, 31316}, {107, 1293}, {190, 65336}, {281, 27817}, {297, 17951}, {450, 17978}, {458, 60865}, {468, 17988}, {648, 53647}, {653, 27834}, {1897, 17780}, {2415, 65160}, {3680, 62742}, {4052, 16080}, {4373, 52283}, {5382, 65344}, {6331, 55262}, {6335, 24004}, {6557, 52780}, {8056, 16082}, {11109, 36872}, {17555, 52746}, {17983, 52747}, {26003, 46797}, {27819, 54235}, {27833, 54240}, {38828, 65331}, {65173, 65330}

X(65337) = trilinear pole of line {4, 3680}
X(65337) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 4394}, {48, 3667}, {63, 8643}, {145, 22383}, {184, 4462}, {212, 30719}, {219, 51656}, {222, 4162}, {513, 20818}, {603, 4521}, {647, 16948}, {649, 4855}, {652, 1420}, {656, 33628}, {810, 41629}, {822, 4248}, {905, 3052}, {906, 3756}, {1437, 14321}, {1459, 1743}, {1790, 4729}, {1946, 5435}, {2196, 53580}, {2403, 23202}, {2441, 5440}, {3937, 57192}, {4504, 7116}, {4534, 36059}, {4546, 7099}, {4574, 18211}, {4575, 21950}, {4849, 7254}, {4925, 32658}, {4939, 32660}, {9456, 39472}, {14425, 36058}, {44722, 57181}, {52354, 57129}, {62787, 65102}
X(65337) = X(i)-Dao conjugate of X(j) for these {i, j}: {136, 21950}, {1249, 3667}, {3162, 8643}, {4370, 39472}, {5190, 3756}, {5375, 4855}, {7952, 4521}, {20619, 14425}, {20620, 4534}, {24151, 905}, {36103, 4394}, {39026, 20818}, {39052, 16948}, {39053, 5435}, {39060, 39126}, {39062, 41629}, {40596, 33628}, {40837, 30719}, {62575, 4025}, {62605, 4462}
X(65337) = X(i)-cross conjugate of X(j) for these {i, j}: {1293, 53647}, {17917, 46102}, {21129, 46109}, {55134, 903}, {65160, 1897}
X(65337) = pole of line {3756, 4534} with respect to the polar circle
X(65337) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(190)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(525), X(9524)}}, {{A, B, C, X(646), X(37206)}}, {{A, B, C, X(655), X(44327)}}, {{A, B, C, X(658), X(56188)}}, {{A, B, C, X(4241), X(52283)}}, {{A, B, C, X(8056), X(38828)}}, {{A, B, C, X(17906), X(36118)}}, {{A, B, C, X(27834), X(31316)}}, {{A, B, C, X(36037), X(56235)}}, {{A, B, C, X(37139), X(46640)}}, {{A, B, C, X(42343), X(42408)}}

X(65338) = X(107)X(813)∩X(653)X(660)

Barycentrics    (a-b)*(a-c)*(-b^2+a*c)*(a*b-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65338) lies on these lines: {107, 813}, {108, 8684}, {162, 42396}, {243, 14200}, {291, 16082}, {335, 52781}, {648, 4562}, {653, 660}, {1861, 33676}, {1897, 6591}, {4518, 52780}, {4583, 65341}, {4876, 62742}, {5378, 65344}, {6335, 7649}, {15149, 17927}, {16080, 43534}, {52167, 60844}, {60577, 65331}, {61178, 65332}, {61180, 65210}

X(65338) = isogonal conjugate of X(22384)
X(65338) = trilinear pole of line {4, 1840}
X(65338) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 22384}, {3, 659}, {48, 812}, {58, 53556}, {63, 8632}, {71, 50456}, {184, 3766}, {212, 43041}, {222, 4435}, {238, 1459}, {239, 22383}, {242, 23224}, {255, 65106}, {513, 7193}, {521, 1428}, {603, 3716}, {649, 20769}, {652, 1429}, {656, 5009}, {810, 33295}, {822, 31905}, {874, 22096}, {905, 1914}, {906, 27918}, {1027, 20778}, {1284, 23189}, {1331, 27846}, {1333, 24459}, {1437, 4010}, {1444, 4455}, {1447, 1946}, {1790, 21832}, {2193, 7212}, {2196, 4375}, {2201, 4091}, {2210, 4025}, {2238, 7254}, {3049, 30940}, {3573, 3937}, {4107, 7116}, {4124, 36059}, {4131, 57654}, {4148, 7099}, {4164, 7015}, {4448, 36058}, {4558, 39786}, {9247, 65101}, {14024, 51640}, {14599, 15413}, {15419, 41333}, {17972, 38348}, {18786, 22093}, {22090, 34252}, {22379, 36815}, {23696, 51329}, {25098, 51321}, {32658, 62552}, {34055, 46387}, {62785, 65102}
X(65338) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 22384}, {10, 53556}, {37, 24459}, {1249, 812}, {3162, 8632}, {5190, 27918}, {5375, 20769}, {5521, 27846}, {6523, 65106}, {7952, 3716}, {9470, 1459}, {16587, 24284}, {20619, 4448}, {20620, 4124}, {36103, 659}, {36906, 905}, {39026, 7193}, {39053, 1447}, {39060, 10030}, {39062, 33295}, {40596, 5009}, {40837, 43041}, {47345, 7212}, {62557, 4025}, {62576, 65101}, {62605, 3766}
X(65338) = X(i)-cross conjugate of X(j) for these {i, j}: {240, 7012}, {813, 4562}, {17927, 15742}, {65106, 4}
X(65338) = pole of line {4124, 4448} with respect to the polar circle
X(65338) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34085)}}, {{A, B, C, X(75), X(36086)}}, {{A, B, C, X(100), X(4572)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(162), X(46152)}}, {{A, B, C, X(596), X(1308)}}, {{A, B, C, X(660), X(8684)}}, {{A, B, C, X(1220), X(35174)}}, {{A, B, C, X(2730), X(57719)}}, {{A, B, C, X(4562), X(40098)}}, {{A, B, C, X(6591), X(7649)}}, {{A, B, C, X(27805), X(37133)}}, {{A, B, C, X(36093), X(36106)}}, {{A, B, C, X(37135), X(53208)}}

X(65339) = ISOTOMIC CONJUGATE OF X(24562)

Barycentrics    (a-b)*b*(a-c)*c*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-2*a*b+(b-c)^2)*(a^2+(b-c)^2-2*a*c) : :

X(65339) lies on these lines: {2, 54235}, {100, 25009}, {107, 1292}, {277, 16082}, {648, 54987}, {653, 1025}, {1026, 1897}, {2052, 57499}, {6331, 55260}, {6335, 42720}, {6601, 62742}, {16080, 60265}, {46106, 52502}, {52781, 64211}, {61180, 63743}, {63906, 65344}

X(65339) = isotomic conjugate of X(24562)
X(65339) = trilinear pole of line {4, 6601}
X(65339) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 24562}, {48, 3309}, {63, 8642}, {184, 4468}, {212, 43049}, {218, 1459}, {219, 51652}, {652, 1617}, {663, 23144}, {810, 41610}, {822, 4233}, {905, 21059}, {1445, 1946}, {1818, 2440}, {3870, 22383}, {3937, 65208}, {4350, 65102}, {4878, 7254}, {4904, 32656}, {7719, 23224}, {21945, 32661}, {23225, 31638}, {31605, 52425}, {36059, 38375}, {44448, 52411}
X(65339) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 24562}, {1249, 3309}, {3162, 8642}, {20620, 38375}, {39053, 1445}, {39060, 6604}, {39062, 41610}, {40837, 43049}, {62602, 31605}, {62605, 4468}
X(65339) = X(i)-cross conjugate of X(j) for these {i, j}: {1292, 54987}, {55133, 2481}, {56183, 18026}
X(65339) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(100)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(525), X(9520)}}, {{A, B, C, X(693), X(25009)}}, {{A, B, C, X(1305), X(51568)}}, {{A, B, C, X(4624), X(15455)}}, {{A, B, C, X(11794), X(53683)}}, {{A, B, C, X(36838), X(43190)}}

X(65340) = X(4)X(653)∩X(29)X(648)

Barycentrics    (a^2+b^2+b*c-2*c^2+a*(-2*b+c))*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-2*b^2+a*(b-2*c)+b*c+c^2) : :

X(65340) lies on these lines: {4, 653}, {29, 648}, {107, 2291}, {158, 54240}, {273, 13149}, {281, 1897}, {318, 6335}, {415, 65350}, {1861, 65336}, {3542, 36610}, {4845, 65334}, {6331, 44130}, {8756, 65333}, {14733, 32706}, {16080, 47210}, {16082, 35348}, {17555, 52746}, {23710, 37769}, {23893, 62742}, {34056, 40836}, {36123, 60579}, {37139, 43764}, {44428, 52781}, {52780, 53152}

X(65340) = trilinear pole of line {4, 3064}
X(65340) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 1155}, {6, 6510}, {48, 527}, {63, 1055}, {73, 62756}, {109, 14414}, {184, 30806}, {212, 1323}, {219, 6610}, {222, 6603}, {255, 23710}, {521, 23346}, {577, 37805}, {603, 6745}, {652, 23890}, {906, 1638}, {1331, 14413}, {1946, 56543}, {2196, 24685}, {4575, 30574}, {6056, 38461}, {6139, 6516}, {6174, 36058}, {6366, 36059}, {6647, 7116}, {7011, 56763}, {7125, 60431}, {22341, 52891}, {23202, 36887}, {35293, 36057}, {36055, 51408}, {37780, 52425}, {42082, 60047}
X(65340) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 6510}, {11, 14414}, {136, 30574}, {1249, 527}, {3162, 1055}, {5190, 1638}, {5521, 14413}, {6523, 23710}, {7952, 6745}, {20619, 6174}, {20620, 6366}, {20621, 35293}, {36103, 1155}, {38966, 14392}, {39053, 56543}, {40837, 1323}, {51221, 51408}, {53985, 30573}, {62602, 37780}, {62605, 30806}
X(65340) = X(i)-cross conjugate of X(j) for these {i, j}: {2291, 1121}, {23710, 4}, {37769, 40446}, {62764, 1156}
X(65340) = pole of line {1638, 6174} with respect to the polar circle
X(65340) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(36279)}}, {{A, B, C, X(2), X(12848)}}, {{A, B, C, X(4), X(29)}}, {{A, B, C, X(9), X(5729)}}, {{A, B, C, X(80), X(12019)}}, {{A, B, C, X(91), X(1067)}}, {{A, B, C, X(104), X(44693)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(406), X(31903)}}, {{A, B, C, X(415), X(468)}}, {{A, B, C, X(650), X(1937)}}, {{A, B, C, X(897), X(8759)}}, {{A, B, C, X(903), X(40450)}}, {{A, B, C, X(915), X(36119)}}, {{A, B, C, X(917), X(34922)}}, {{A, B, C, X(1120), X(1219)}}, {{A, B, C, X(1156), X(41798)}}, {{A, B, C, X(1268), X(2346)}}, {{A, B, C, X(1311), X(34393)}}, {{A, B, C, X(1440), X(56263)}}, {{A, B, C, X(1861), X(8756)}}, {{A, B, C, X(1990), X(47210)}}, {{A, B, C, X(2291), X(60047)}}, {{A, B, C, X(3477), X(17038)}}, {{A, B, C, X(4248), X(17555)}}, {{A, B, C, X(5559), X(55076)}}, {{A, B, C, X(7012), X(36122)}}, {{A, B, C, X(7110), X(34917)}}, {{A, B, C, X(7649), X(36124)}}, {{A, B, C, X(14942), X(18815)}}, {{A, B, C, X(34056), X(61493)}}, {{A, B, C, X(36624), X(62948)}}, {{A, B, C, X(36798), X(56365)}}, {{A, B, C, X(36910), X(43672)}}, {{A, B, C, X(36916), X(45097)}}, {{A, B, C, X(51565), X(64330)}}, {{A, B, C, X(52156), X(56322)}}, {{A, B, C, X(63748), X(63857)}}

X(65341) = TRILINEAR POLE OF LINE {4, 75}

Barycentrics    (a-b)*b*(a-c)*c*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2+2*a*b+b^2+c^2)*(a^2+b^2+2*a*c+c^2) : :

X(65341) lies on these lines: {107, 811}, {305, 17903}, {648, 799}, {653, 4554}, {668, 1897}, {685, 36036}, {789, 32691}, {1978, 6335}, {4583, 65338}, {4593, 42396}, {4602, 6331}, {6336, 20568}, {13149, 46406}, {15352, 57973}, {16080, 33805}, {16081, 46273}, {17983, 46277}, {18031, 54235}, {30450, 55215}, {30479, 62742}, {40017, 65352}, {46404, 54240}, {46405, 65329}, {51560, 65333}, {52780, 64989}, {52781, 57923}

X(65341) = isotomic conjugate of X(2522)
X(65341) = trilinear pole of line {4, 75}
X(65341) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 2484}, {31, 2522}, {32, 23874}, {41, 51644}, {48, 8678}, {63, 8646}, {184, 6590}, {612, 22383}, {647, 44119}, {649, 7085}, {652, 1460}, {663, 2286}, {667, 5227}, {810, 2303}, {822, 4206}, {1010, 3049}, {1038, 3063}, {1459, 54416}, {1790, 50494}, {1919, 54433}, {1946, 2285}, {1980, 19799}, {2200, 47844}, {2517, 9247}, {4320, 65102}, {8898, 57134}, {26933, 32739}
X(65341) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 2522}, {1249, 8678}, {3160, 51644}, {3162, 8646}, {5375, 7085}, {6376, 23874}, {6631, 5227}, {9296, 54433}, {10001, 1038}, {36103, 2484}, {39052, 44119}, {39053, 2285}, {39060, 388}, {39062, 2303}, {40619, 26933}, {62576, 2517}, {62605, 6590}
X(65341) = X(i)-cross conjugate of X(j) for these {i, j}: {1310, 54982}
X(65341) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(668), X(789)}}, {{A, B, C, X(18026), X(55231)}}
X(65341) = barycentric product X(i)*X(j) for these (i, j): {4, 54982}, {1039, 4572}, {1245, 57968}, {1310, 264}, {1897, 57923}, {1969, 65298}, {2339, 46404}, {18026, 30479}, {32691, 561}, {36099, 76}, {37215, 92}, {51686, 6386}, {56219, 6331}, {60197, 648}, {64989, 653}
X(65341) = barycentric quotient X(i)/X(j) for these (i, j): {2, 2522}, {4, 8678}, {7, 51644}, {19, 2484}, {25, 8646}, {75, 23874}, {92, 6590}, {100, 7085}, {107, 4206}, {108, 1460}, {162, 44119}, {190, 5227}, {264, 2517}, {286, 47844}, {648, 2303}, {651, 2286}, {653, 2285}, {664, 1038}, {668, 54433}, {693, 26933}, {811, 1010}, {1036, 1946}, {1039, 663}, {1245, 810}, {1310, 3}, {1633, 19459}, {1783, 54416}, {1824, 50494}, {1897, 612}, {1978, 19799}, {2221, 22383}, {2281, 3049}, {2339, 652}, {4033, 3610}, {4554, 56367}, {6335, 2345}, {13149, 7365}, {18026, 388}, {30479, 521}, {32691, 31}, {36099, 6}, {36118, 4320}, {37215, 63}, {41013, 48395}, {51686, 667}, {52607, 8898}, {54982, 69}, {56219, 647}, {56328, 1459}, {56841, 52326}, {57923, 4025}, {57968, 44154}, {60197, 525}, {64989, 6332}, {65298, 48}

X(65342) = X(21)X(107)∩X(63)X(653)

Barycentrics    b*c*(-a^2+b^2-c^2)*(a^2+b^2-c^2)*(a^6-a^5*c+b*(b-c)^3*(b+c)^2-a^4*(b^2-3*b*c+2*c^2)+a^3*(-2*b^2*c+2*c^3)+a^2*(-b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)+a*(3*b^4*c-2*b^2*c^3-c^5))*(-a^6+a^5*b+(b-c)^3*c*(b+c)^2+a^4*(2*b^2-3*b*c+c^2)-2*a^3*(b^3-b*c^2)+a^2*(-b^4+2*b^3*c-4*b^2*c^2+2*b*c^3+c^4)+a*(b^5+2*b^3*c^2-3*b*c^4)) : :

X(65342) lies on these lines: {2, 54240}, {21, 107}, {63, 653}, {78, 1895}, {92, 41081}, {297, 65343}, {345, 6335}, {348, 13149}, {425, 685}, {648, 1812}, {2052, 34277}, {15352, 31623}, {36038, 52780}, {43737, 53353}, {46106, 52500}, {52351, 65329}, {65302, 65331}

X(65342) = trilinear pole of line {4, 43737}
X(65342) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 6001}, {212, 43058}, {219, 51660}, {577, 51359}, {822, 7435}, {1795, 47434}, {2183, 39175}, {2289, 51399}, {2443, 57241}, {14312, 32660}
X(65342) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 6001}, {25640, 47434}, {40837, 43058}
X(65342) = X(i)-cross conjugate of X(j) for these {i, j}: {104, 46133}, {2804, 18026}
X(65342) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(21)}}, {{A, B, C, X(92), X(40701)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(264), X(57827)}}, {{A, B, C, X(278), X(1767)}}, {{A, B, C, X(297), X(425)}}, {{A, B, C, X(525), X(9528)}}, {{A, B, C, X(1847), X(1895)}}, {{A, B, C, X(2988), X(6740)}}, {{A, B, C, X(18815), X(36038)}}, {{A, B, C, X(18816), X(57983)}}, {{A, B, C, X(30710), X(57974)}}, {{A, B, C, X(51567), X(55346)}}
X(65342) = barycentric product X(i)*X(j) for these (i, j): {1295, 264}, {2417, 54240}, {18026, 43737}, {18816, 54241}, {35519, 36044}, {65246, 92}
X(65342) = barycentric quotient X(i)/X(j) for these (i, j): {4, 6001}, {34, 51660}, {104, 39175}, {107, 7435}, {158, 51359}, {278, 43058}, {1118, 51399}, {1295, 3}, {2431, 36054}, {14312, 58264}, {14571, 47434}, {16082, 57495}, {32647, 1415}, {36044, 109}, {36121, 56634}, {40149, 51365}, {43737, 521}, {44426, 14312}, {47372, 1528}, {54240, 2405}, {54241, 517}, {65246, 63}

X(65343) = X(107)X(2714)∩X(648)X(650)

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^5*c-b^3*(b-c)^2*(b+c)-a^3*(b^3-2*b*c^2+2*c^3)+a^2*b*(b^3-b^2*c-2*b*c^2+2*c^3)+a*(b^5-b^4*c-b^3*c^2+c^5))*(a^5*b-(b-c)^2*c^3*(b+c)-a^3*(2*b^3-2*b^2*c+c^3)+a^2*c*(2*b^3-2*b^2*c-b*c^2+c^3)+a*(b^5-b^2*c^3-b*c^4+c^5)) : :

X(65343) lies on these lines: {107, 2714}, {297, 65342}, {468, 43746}, {648, 650}, {653, 661}, {685, 7435}, {1897, 4041}, {2501, 54240}, {3700, 6335}, {4391, 6331}, {6330, 57850}, {7178, 13149}, {55238, 65329}, {55242, 65330}, {55259, 65331}, {57683, 57732}, {61179, 65336}

X(65343) = trilinear pole of line {4, 4516}
X(65343) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 2798}, {425, 822}, {647, 23695}, {652, 41349}, {36054, 56822}
X(65343) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 2798}, {39052, 23695}
X(65343) = X(i)-cross conjugate of X(j) for these {i, j}: {2714, 53191}
X(65343) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(158), X(41207)}}, {{A, B, C, X(297), X(7435)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(2766), X(40149)}}
X(65343) = barycentric product X(i)*X(j) for these (i, j): {4, 53191}, {107, 57850}, {264, 2714}, {18026, 43746}, {57683, 6528}
X(65343) = barycentric quotient X(i)/X(j) for these (i, j): {4, 2798}, {107, 425}, {108, 41349}, {162, 23695}, {2714, 3}, {36127, 56822}, {43746, 521}, {53191, 69}, {57683, 520}, {57850, 3265}

X(65344) = TRILINEAR POLE OF LINE {4, 100}

Barycentrics    (a-b)*(a-c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-a^3*c+b*(b-c)^2*(b+c)+a*c*(b^2+c^2)-a^2*(2*b^2-b*c+c^2))*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b*(b^2+c^2)-a^2*(b^2-b*c+2*c^2)) : :

X(65344) lies on the Hutson-Moses hyperbola and on these lines: {107, 5379}, {645, 30450}, {648, 4567}, {653, 4564}, {666, 46133}, {765, 1897}, {898, 915}, {1016, 6335}, {1275, 13149}, {1332, 17924}, {2990, 13136}, {3257, 6336}, {3657, 57740}, {4584, 65352}, {4601, 6331}, {5376, 65336}, {5377, 65333}, {5378, 65338}, {5380, 17983}, {5382, 65337}, {14776, 53151}, {45393, 62742}, {46102, 54240}, {63906, 65339}, {65162, 65331}

X(65344) = trilinear pole of line {4, 100}
X(65344) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 55126}, {513, 2252}, {649, 912}, {650, 51649}, {652, 18838}, {667, 914}, {909, 42769}, {1459, 8609}, {1737, 22383}, {1946, 64115}, {2170, 56410}, {3937, 61239}, {7113, 61039}, {7117, 61231}
X(65344) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 55126}, {5375, 912}, {6631, 914}, {23980, 42769}, {39026, 2252}, {39053, 64115}
X(65344) = X(i)-cross conjugate of X(j) for these {i, j}: {2397, 6335}, {15500, 55346}
X(65344) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(655), X(2397)}}, {{A, B, C, X(666), X(765)}}, {{A, B, C, X(1783), X(14776)}}, {{A, B, C, X(4582), X(7017)}}, {{A, B, C, X(14775), X(17924)}}
X(65344) = barycentric product X(i)*X(j) for these (i, j): {100, 46133}, {190, 37203}, {264, 6099}, {668, 915}, {1978, 913}, {2990, 6335}, {18026, 45393}, {32698, 76}, {36106, 75}, {53151, 57753}, {65248, 92}
X(65344) = barycentric quotient X(i)/X(j) for these (i, j): {4, 55126}, {59, 56410}, {80, 61039}, {100, 912}, {101, 2252}, {108, 18838}, {109, 51649}, {190, 914}, {517, 42769}, {653, 64115}, {913, 649}, {915, 513}, {1309, 14266}, {1783, 8609}, {1897, 1737}, {2427, 47408}, {2990, 905}, {3657, 18210}, {4242, 11570}, {5379, 3658}, {6099, 3}, {6335, 48380}, {7012, 61231}, {14776, 51824}, {15742, 56881}, {32655, 22383}, {32698, 6}, {36052, 1459}, {36106, 1}, {37203, 514}, {39173, 8677}, {45393, 521}, {46133, 693}, {53151, 119}, {56881, 34332}, {61214, 7117}, {65248, 63}, {65333, 52456}

X(65345) = POLAR CONJUGATE OF X(952)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-2*a^3*c-2*b^3*c+2*a*(b-c)^2*c+b^2*c^2+2*b*c^3-2*c^4+a^2*(-2*b^2+2*b*c+c^2))*(a^4-2*a^3*b-2*b^4+2*a*b*(b-c)^2+2*b^3*c+b^2*c^2-2*b*c^3+c^4+a^2*(b^2+2*b*c-2*c^2)) : :

X(65345) lies on these lines: {2, 65336}, {92, 14628}, {107, 953}, {278, 40218}, {514, 6336}, {519, 1785}, {648, 16704}, {653, 3911}, {1016, 26611}, {1086, 59196}, {4358, 6335}, {16082, 17924}, {34764, 53157}, {37790, 54240}, {46041, 62742}

X(65345) = trilinear pole of line {4, 18341}
X(65345) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 2265}, {48, 952}, {212, 43043}, {22356, 52478}
X(65345) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 952}, {36103, 2265}, {39535, 61066}, {40837, 43043}
X(65345) = X(i)-cross conjugate of X(j) for these {i, j}: {953, 46136}
X(65345) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(514)}}, {{A, B, C, X(27), X(39284)}}, {{A, B, C, X(92), X(275)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(278), X(1785)}}, {{A, B, C, X(1086), X(26611)}}, {{A, B, C, X(2990), X(60251)}}, {{A, B, C, X(14165), X(65100)}}, {{A, B, C, X(34050), X(65046)}}, {{A, B, C, X(46107), X(55346)}}
X(65345) = barycentric product X(i)*X(j) for these (i, j): {4, 46136}, {264, 953}, {4555, 53157}, {18026, 46041}, {46102, 60582}, {50943, 65336}, {65249, 92}
X(65345) = barycentric quotient X(i)/X(j) for these (i, j): {4, 952}, {19, 2265}, {278, 43043}, {953, 3}, {2969, 6075}, {21664, 6073}, {36123, 61481}, {36125, 52478}, {39534, 35013}, {46041, 521}, {46136, 69}, {52479, 5440}, {53157, 900}, {60582, 26932}, {61482, 22350}, {65249, 63}, {65336, 57456}

X(65346) = TRILINEAR POLE OF LINE {4, 15}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+2*(b^2-c^2)^2-a^2*(3*b^2+3*c^2+2*sqrt(3)*S)) : :

X(65346) lies on these lines: {17, 16080}, {62, 51268}, {107, 16806}, {110, 36306}, {112, 930}, {470, 36304}, {648, 17402}, {685, 55199}, {1990, 40667}, {2970, 56515}, {6110, 8172}, {6111, 11600}, {6330, 40712}, {6331, 55220}, {8174, 44701}, {8741, 17983}, {11139, 58911}, {16081, 16249}, {23896, 46456}, {32585, 57732}, {35360, 36309}

X(65346) = trilinear pole of line {4, 15}
X(65346) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 23872}, {61, 656}, {63, 55221}, {302, 810}, {473, 822}, {661, 52348}, {3376, 60009}, {3708, 52605}, {10642, 24018}, {55201, 63760}
X(65346) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 65347}
X(65346) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 23872}, {3162, 55221}, {10639, 63830}, {36830, 52348}, {39062, 302}, {40596, 61}
X(65346) = X(i)-cross conjugate of X(j) for these {i, j}: {16806, 32036}, {35311, 65347}, {35443, 470}, {64468, 250}
X(65346) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(110), X(6151)}}, {{A, B, C, X(925), X(23895)}}, {{A, B, C, X(930), X(32036)}}, {{A, B, C, X(32037), X(43351)}}, {{A, B, C, X(36840), X(53957)}}
X(65346) = barycentric product X(i)*X(j) for these (i, j): {17, 648}, {25, 55220}, {107, 40712}, {112, 34389}, {470, 60051}, {472, 930}, {8741, 99}, {10641, 46139}, {11144, 65347}, {16806, 264}, {18020, 55199}, {18831, 36300}, {19779, 36309}, {21461, 6331}, {32036, 4}, {32585, 6528}, {38342, 62}, {52606, 93}
X(65346) = barycentric quotient X(i)/X(j) for these (i, j): {4, 23872}, {17, 525}, {25, 55221}, {62, 63830}, {107, 473}, {110, 52348}, {112, 61}, {250, 52605}, {472, 41298}, {648, 302}, {930, 40711}, {5995, 50468}, {8603, 60010}, {8741, 523}, {10641, 1510}, {10642, 57142}, {16806, 3}, {18020, 55198}, {21461, 647}, {32036, 69}, {32585, 520}, {32713, 10642}, {32737, 32586}, {34389, 3267}, {36300, 6368}, {36306, 8838}, {36309, 16771}, {38342, 34390}, {40712, 3265}, {51890, 60009}, {52606, 44180}, {52670, 20577}, {52930, 52349}, {55199, 125}, {55220, 305}, {58869, 20975}, {60051, 40709}, {61193, 52671}, {65347, 11143}

X(65347) = TRILINEAR POLE OF LINE {4, 16}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+2*(b^2-c^2)^2-a^2*(3*b^2+3*c^2-2*sqrt(3)*S)) : :

X(65347) lies on these lines: {18, 16080}, {61, 51275}, {107, 16807}, {110, 36309}, {112, 930}, {471, 36305}, {648, 17403}, {685, 55201}, {1990, 40668}, {2970, 56514}, {6110, 11601}, {6111, 8173}, {6330, 40711}, {6331, 55222}, {8175, 44700}, {8742, 17983}, {11138, 58910}, {16081, 16250}, {23895, 46456}, {32586, 57732}, {35360, 36306}

X(65347) = trilinear pole of line {4, 16}
X(65347) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 23873}, {62, 656}, {63, 55223}, {303, 810}, {472, 822}, {661, 52349}, {3383, 60010}, {3708, 52606}, {10641, 24018}, {55199, 63760}
X(65347) = X(i)-vertex conjugate of X(j) for these {i, j}: {1576, 65346}
X(65347) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 23873}, {3162, 55223}, {10640, 63830}, {36830, 52349}, {39062, 303}, {40596, 62}
X(65347) = X(i)-cross conjugate of X(j) for these {i, j}: {16807, 32037}, {35311, 65346}, {35444, 471}, {64469, 250}
X(65347) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(110), X(2981)}}, {{A, B, C, X(925), X(23896)}}, {{A, B, C, X(930), X(32037)}}, {{A, B, C, X(32036), X(43351)}}, {{A, B, C, X(36839), X(53957)}}
X(65347) = barycentric product X(i)*X(j) for these (i, j): {18, 648}, {25, 55222}, {107, 40711}, {112, 34390}, {471, 60052}, {473, 930}, {8742, 99}, {10642, 46139}, {11143, 65346}, {16807, 264}, {18020, 55201}, {18831, 36301}, {19778, 36306}, {21462, 6331}, {32037, 4}, {32586, 6528}, {38342, 61}, {52605, 93}
X(65347) = barycentric quotient X(i)/X(j) for these (i, j): {4, 23873}, {18, 525}, {25, 55223}, {61, 63830}, {107, 472}, {110, 52349}, {112, 62}, {250, 52606}, {473, 41298}, {648, 303}, {930, 40712}, {5994, 50469}, {8604, 60009}, {8742, 523}, {10641, 57143}, {10642, 1510}, {16807, 3}, {18020, 55200}, {21462, 647}, {32037, 69}, {32586, 520}, {32713, 10641}, {32737, 32585}, {34390, 3267}, {36301, 6368}, {36306, 16770}, {36309, 8836}, {38342, 34389}, {40711, 3265}, {51891, 60010}, {52605, 44180}, {52671, 20577}, {52929, 52348}, {55201, 125}, {55222, 305}, {58870, 20975}, {60052, 40710}, {61193, 52670}, {65346, 11144}

X(65348) = TRILINEAR POLE OF LINE {4, 96}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-2*a^2*b^2+(b^2-c^2)^2)*(a^4-2*a^2*c^2+(b^2-c^2)^2)*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2)) : :

X(65348) lies on these lines: {96, 10018}, {107, 32692}, {110, 30450}, {648, 925}, {685, 55253}, {687, 15958}, {847, 58079}, {5962, 14106}, {6330, 57875}, {6331, 18831}, {11547, 39111}, {14586, 65184}, {15352, 32734}, {16081, 41271}, {18315, 63958}, {23181, 58756}, {37802, 51939}, {57703, 57732}, {65177, 65309}

X(65348) = trilinear pole of line {4, 96}
X(65348) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 63832}, {47, 6368}, {48, 63829}, {52, 656}, {63, 52317}, {216, 63827}, {343, 55216}, {467, 822}, {523, 63801}, {525, 2180}, {563, 18314}, {647, 63808}, {661, 52032}, {810, 39113}, {924, 44706}, {1147, 2618}, {1748, 17434}, {1953, 52584}, {6563, 62266}, {14213, 30451}, {14576, 24018}, {15451, 44179}, {18695, 34952}, {36134, 55073}
X(65348) = X(i)-vertex conjugate of X(j) for these {i, j}: {4, 15958}, {14586, 35360}, {23181, 65348}
X(65348) = X(i)-Dao conjugate of X(j) for these {i, j}: {135, 55072}, {137, 55073}, {1249, 63829}, {3162, 52317}, {34853, 6368}, {36830, 52032}, {37864, 15451}, {39052, 63808}, {39062, 39113}, {40596, 52}
X(65348) = X(i)-cross conjugate of X(j) for these {i, j}: {110, 933}, {1632, 52779}, {14586, 16813}, {15422, 275}, {32692, 65273}, {32734, 32692}, {55121, 1141}, {57154, 23233}, {65184, 107}
X(65348) = pole of line {55072, 55073} with respect to the polar circle
X(65348) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(930)}}, {{A, B, C, X(6), X(23181)}}, {{A, B, C, X(54), X(15958)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(110), X(14586)}}, {{A, B, C, X(925), X(46134)}}, {{A, B, C, X(933), X(18831)}}, {{A, B, C, X(1990), X(47201)}}, {{A, B, C, X(4240), X(10018)}}, {{A, B, C, X(6037), X(53657)}}, {{A, B, C, X(13398), X(18878)}}, {{A, B, C, X(15395), X(32230)}}, {{A, B, C, X(20626), X(35360)}}, {{A, B, C, X(32692), X(52932)}}, {{A, B, C, X(32708), X(59004)}}, {{A, B, C, X(53176), X(58079)}}

X(65349) = TRILINEAR POLE OF LINE {4, 39}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-b^4+b^2*c^2+a^2*(b^2+2*c^2))*(c^2*(b^2-c^2)+a^2*(2*b^2+c^2)) : :

X(65349) lies on these lines: {4, 263}, {67, 42299}, {107, 26714}, {110, 42396}, {112, 685}, {262, 5094}, {276, 15897}, {290, 63472}, {327, 44134}, {393, 51338}, {427, 65005}, {648, 1634}, {653, 46153}, {877, 4576}, {1897, 46148}, {1990, 51543}, {3172, 60601}, {3498, 12143}, {4232, 46156}, {4553, 6335}, {6330, 11331}, {6336, 46150}, {6528, 53196}, {15352, 46151}, {16813, 32713}, {17983, 46154}, {18384, 65360}, {31916, 52781}, {35278, 54267}, {36827, 36885}, {40138, 43718}, {42300, 42873}, {46149, 54235}, {46152, 54240}, {46155, 46456}, {46157, 52492}, {46159, 65352}, {46161, 65351}, {46162, 65336}, {46163, 65333}, {46166, 46815}, {46167, 46812}, {46359, 52780}, {54032, 56605}, {57268, 65359}

X(65349) = trilinear pole of line {4, 39}
X(65349) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 23878}, {63, 3288}, {182, 656}, {183, 810}, {336, 9420}, {458, 822}, {520, 60685}, {647, 52134}, {905, 60726}, {1459, 60723}, {3049, 3403}, {4592, 6784}, {10311, 24018}, {14208, 34396}, {22383, 60737}, {32320, 51315}
X(65349) = X(i)-vertex conjugate of X(j) for these {i, j}: {685, 1576}
X(65349) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 23878}, {3162, 3288}, {5139, 6784}, {39052, 52134}, {39062, 183}, {40596, 182}, {42426, 45321}
X(65349) = X(i)-cross conjugate of X(j) for these {i, j}: {6403, 250}, {26714, 65271}, {41371, 32230}, {52926, 26714}, {54269, 6}, {54273, 25}
X(65349) = pole of line {6784, 45321} with respect to the polar circle
X(65349) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(63859)}}, {{A, B, C, X(4), X(112)}}, {{A, B, C, X(67), X(110)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(263), X(63741)}}, {{A, B, C, X(290), X(53937)}}, {{A, B, C, X(476), X(35138)}}, {{A, B, C, X(691), X(65284)}}, {{A, B, C, X(827), X(46134)}}, {{A, B, C, X(892), X(1302)}}, {{A, B, C, X(925), X(4577)}}, {{A, B, C, X(933), X(44770)}}, {{A, B, C, X(1289), X(18831)}}, {{A, B, C, X(1576), X(65305)}}, {{A, B, C, X(1625), X(58973)}}, {{A, B, C, X(1990), X(47202)}}, {{A, B, C, X(2409), X(11331)}}, {{A, B, C, X(4240), X(5094)}}, {{A, B, C, X(4241), X(31916)}}, {{A, B, C, X(6035), X(41173)}}, {{A, B, C, X(6037), X(65271)}}, {{A, B, C, X(7954), X(46139)}}, {{A, B, C, X(8105), X(53153)}}, {{A, B, C, X(8106), X(53154)}}, {{A, B, C, X(10293), X(53972)}}, {{A, B, C, X(11636), X(35139)}}, {{A, B, C, X(14528), X(44828)}}, {{A, B, C, X(14574), X(27374)}}, {{A, B, C, X(15274), X(23977)}}, {{A, B, C, X(16077), X(30247)}}, {{A, B, C, X(18384), X(32713)}}, {{A, B, C, X(18878), X(59098)}}, {{A, B, C, X(26714), X(53196)}}, {{A, B, C, X(32738), X(38005)}}, {{A, B, C, X(33513), X(65176)}}, {{A, B, C, X(35136), X(59038)}}, {{A, B, C, X(35137), X(43351)}}, {{A, B, C, X(43187), X(43188)}}, {{A, B, C, X(44134), X(61181)}}, {{A, B, C, X(44768), X(53957)}}, {{A, B, C, X(58994), X(65269)}}

X(65350) = ISOTOMIC CONJUGATE OF X(14417)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-2*c^2)*(a^2+b^2-c^2)*(a^2-2*b^2+c^2)*(a^2-b^2+c^2) : :

X(65350) lies on these lines: {4, 63853}, {99, 65353}, {107, 691}, {111, 16081}, {297, 671}, {415, 65340}, {419, 8753}, {423, 6336}, {425, 62742}, {450, 895}, {458, 60863}, {468, 10416}, {648, 892}, {653, 36085}, {685, 4240}, {877, 34760}, {1637, 2966}, {1990, 17948}, {2052, 57491}, {3168, 10559}, {4235, 50941}, {5641, 62594}, {6330, 30786}, {6331, 14618}, {9979, 17708}, {10097, 65357}, {14977, 15459}, {15422, 16813}, {15466, 57481}, {17907, 52551}, {32583, 35360}, {34574, 61181}, {36128, 65352}, {36827, 36885}, {37174, 52450}, {37778, 44182}, {38342, 55251}, {44181, 65181}, {46989, 47288}, {51358, 51405}, {52147, 65359}, {52632, 65356}, {52940, 60338}

X(65350) = isotomic conjugate of X(14417)
X(65350) = trilinear pole of line {4, 576}
X(65350) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 2642}, {31, 14417}, {48, 690}, {63, 351}, {71, 14419}, {187, 656}, {228, 4750}, {255, 14273}, {468, 822}, {524, 810}, {525, 922}, {560, 45807}, {647, 896}, {661, 3292}, {798, 6390}, {1409, 14432}, {1459, 21839}, {1577, 23200}, {1648, 4575}, {1649, 36060}, {2631, 9717}, {2632, 61207}, {3049, 14210}, {3708, 5467}, {4020, 22105}, {4062, 22383}, {4592, 21906}, {9247, 35522}, {10097, 42081}, {14208, 14567}, {16702, 55230}, {20975, 23889}, {24018, 44102}, {52373, 58331}
X(65350) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 2966}, {4235, 32648}
X(65350) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 14417}, {136, 1648}, {1249, 690}, {1560, 1649}, {3162, 351}, {5099, 47415}, {5139, 21906}, {6374, 45807}, {6523, 14273}, {15477, 3049}, {15899, 647}, {23967, 39474}, {31998, 6390}, {36103, 2642}, {36830, 3292}, {38970, 51429}, {39052, 896}, {39061, 525}, {39062, 524}, {40596, 187}, {40938, 14424}, {48317, 23992}, {62576, 35522}, {62597, 62594}, {62607, 3265}
X(65350) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59762, 892}
X(65350) = X(i)-cross conjugate of X(j) for these {i, j}: {468, 18020}, {691, 892}, {935, 65268}, {4235, 648}, {5466, 46111}, {5523, 32230}, {8430, 9154}, {14273, 4}, {14977, 671}, {37765, 23582}, {44564, 2}, {55142, 5641}, {57491, 34539}, {61181, 6528}
X(65350) = pole of line {1648, 1649} with respect to the polar circle
X(65350) = pole of line {39474, 53155} with respect to the Steiner circumellipse
X(65350) = pole of line {11054, 37765} with respect to the dual conic of Jerabek hyperbola
X(65350) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(476)}}, {{A, B, C, X(99), X(52141)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(110), X(55279)}}, {{A, B, C, X(111), X(32729)}}, {{A, B, C, X(297), X(4240)}}, {{A, B, C, X(420), X(46543)}}, {{A, B, C, X(423), X(46541)}}, {{A, B, C, X(468), X(935)}}, {{A, B, C, X(523), X(41357)}}, {{A, B, C, X(689), X(35137)}}, {{A, B, C, X(691), X(15398)}}, {{A, B, C, X(805), X(14565)}}, {{A, B, C, X(892), X(53080)}}, {{A, B, C, X(925), X(35178)}}, {{A, B, C, X(1302), X(65271)}}, {{A, B, C, X(1304), X(32697)}}, {{A, B, C, X(1637), X(2799)}}, {{A, B, C, X(1916), X(14734)}}, {{A, B, C, X(2374), X(36898)}}, {{A, B, C, X(2407), X(44569)}}, {{A, B, C, X(2501), X(14618)}}, {{A, B, C, X(5466), X(62629)}}, {{A, B, C, X(5649), X(9060)}}, {{A, B, C, X(6083), X(31628)}}, {{A, B, C, X(8587), X(20404)}}, {{A, B, C, X(8770), X(9091)}}, {{A, B, C, X(9066), X(54990)}}, {{A, B, C, X(9080), X(9133)}}, {{A, B, C, X(9150), X(65277)}}, {{A, B, C, X(11794), X(53957)}}, {{A, B, C, X(14417), X(44564)}}, {{A, B, C, X(16077), X(18020)}}, {{A, B, C, X(16166), X(40173)}}, {{A, B, C, X(32694), X(60128)}}, {{A, B, C, X(34760), X(63853)}}, {{A, B, C, X(37139), X(40430)}}, {{A, B, C, X(37765), X(65268)}}, {{A, B, C, X(37778), X(62237)}}, {{A, B, C, X(55142), X(62594)}}
X(65350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4240, 5466, 53155}

X(65351) = TRILINEAR POLE OF LINE {4, 147}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(-b^2+a*c)*(b^2+a*c)*(a*b-c^2)*(a^2+b^2-c^2)*(a*b+c^2)*(a^2-b^2+c^2) : :

X(65351) lies on these lines: {107, 805}, {297, 694}, {419, 9467}, {450, 17970}, {468, 17980}, {648, 2489}, {653, 37134}, {685, 4230}, {882, 61181}, {1916, 16080}, {2501, 6331}, {3569, 43187}, {6330, 40708}, {14970, 65269}, {17907, 40810}, {18020, 35325}, {36214, 57732}, {39292, 65354}, {43188, 44451}, {45336, 53199}, {46161, 65349}, {56981, 65356}

X(65351) = isotomic conjugate of X(24284)
X(65351) = trilinear pole of line {4, 147}
X(65351) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 24284}, {48, 804}, {63, 5027}, {71, 4164}, {172, 53556}, {228, 4107}, {385, 810}, {419, 822}, {520, 56828}, {525, 1933}, {647, 1580}, {656, 1691}, {659, 22061}, {798, 12215}, {1966, 3049}, {2086, 4592}, {2200, 14296}, {2238, 22093}, {2295, 22384}, {3570, 22373}, {3708, 56980}, {3955, 21832}, {4039, 22383}, {7122, 24459}, {7193, 57234}, {7234, 20769}, {9247, 14295}, {11183, 36060}, {14208, 14602}, {20975, 56982}, {24018, 44089}, {36036, 47418}
X(65351) = X(i)-vertex conjugate of X(j) for these {i, j}: {2353, 53202}
X(65351) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 24284}, {1249, 804}, {1560, 11183}, {2679, 47418}, {3162, 5027}, {5139, 2086}, {9467, 3049}, {31998, 12215}, {39052, 1580}, {39062, 385}, {39092, 647}, {40596, 1691}, {47648, 684}, {62576, 14295}
X(65351) = X(i)-cross conjugate of X(j) for these {i, j}: {420, 18020}, {805, 18829}, {877, 648}, {17994, 264}, {22456, 53205}, {53149, 35142}, {53347, 671}, {53371, 99}, {55143, 46142}, {56981, 14970}
X(65351) = pole of line {2086, 11183} with respect to the polar circle
X(65351) = pole of line {232, 17984} with respect to the dual conic of Jerabek hyperbola
X(65351) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(43187)}}, {{A, B, C, X(4), X(59762)}}, {{A, B, C, X(76), X(691)}}, {{A, B, C, X(83), X(35139)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(297), X(4230)}}, {{A, B, C, X(476), X(6035)}}, {{A, B, C, X(670), X(3222)}}, {{A, B, C, X(694), X(17938)}}, {{A, B, C, X(877), X(17984)}}, {{A, B, C, X(892), X(31998)}}, {{A, B, C, X(935), X(55270)}}, {{A, B, C, X(2396), X(6037)}}, {{A, B, C, X(2489), X(2501)}}, {{A, B, C, X(2715), X(34138)}}, {{A, B, C, X(7473), X(11331)}}, {{A, B, C, X(9186), X(42286)}}, {{A, B, C, X(9192), X(25322)}}, {{A, B, C, X(18020), X(44183)}}, {{A, B, C, X(18829), X(39291)}}, {{A, B, C, X(32662), X(36952)}}, {{A, B, C, X(32708), X(43678)}}, {{A, B, C, X(39058), X(53196)}}, {{A, B, C, X(40423), X(44182)}}, {{A, B, C, X(42313), X(43754)}}, {{A, B, C, X(43665), X(44823)}}, {{A, B, C, X(45336), X(59775)}}, {{A, B, C, X(53876), X(54749)}}, {{A, B, C, X(55189), X(55218)}}

X(65352) = X(19)X(648)∩X(27)X(295)

Barycentrics    (a+b)*(a+c)*(-b^2+a*c)*(a*b-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

X(65352) lies on these lines: {19, 648}, {27, 295}, {92, 6331}, {107, 741}, {242, 423}, {243, 14196}, {278, 17082}, {286, 334}, {297, 51225}, {653, 1880}, {813, 39438}, {1870, 15147}, {2311, 65334}, {2358, 65330}, {3572, 16081}, {4444, 16080}, {4584, 65344}, {5307, 52207}, {6520, 15352}, {15149, 17927}, {18787, 46883}, {19635, 52167}, {31905, 52209}, {36128, 65350}, {40017, 65341}, {46159, 65349}, {65258, 65354}

X(65352) = trilinear pole of line {4, 4444}
X(65352) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 2238}, {37, 7193}, {42, 20769}, {48, 740}, {63, 3747}, {69, 41333}, {71, 238}, {72, 1914}, {73, 3684}, {101, 53556}, {184, 3948}, {212, 16609}, {219, 1284}, {222, 4433}, {228, 239}, {242, 3990}, {248, 50440}, {306, 2210}, {350, 2200}, {394, 862}, {603, 3985}, {647, 3573}, {659, 4574}, {692, 24459}, {810, 3570}, {874, 3049}, {906, 4010}, {1018, 22384}, {1331, 21832}, {1332, 4455}, {1409, 3685}, {1428, 3694}, {1429, 2318}, {1437, 4037}, {1447, 52370}, {1874, 2289}, {2193, 7235}, {2196, 4368}, {2201, 3682}, {3949, 5009}, {3998, 57654}, {4019, 61385}, {4039, 7116}, {4093, 34055}, {4155, 4558}, {4435, 23067}, {4592, 46390}, {4783, 32659}, {8298, 57681}, {9247, 35544}, {12215, 40729}, {14599, 20336}, {18785, 20778}, {18786, 22061}, {18793, 20750}, {18892, 40071}, {52373, 58327}
X(65352) = X(i)-vertex conjugate of X(j) for these {i, j}: {34179, 35145}
X(65352) = X(i)-Dao conjugate of X(j) for these {i, j}: {1015, 53556}, {1086, 24459}, {1249, 740}, {3162, 3747}, {5139, 46390}, {5190, 4010}, {5521, 21832}, {7952, 3985}, {9470, 71}, {16592, 24284}, {36103, 2238}, {36906, 72}, {39039, 50440}, {39052, 3573}, {39062, 3570}, {40589, 7193}, {40592, 20769}, {40837, 16609}, {45162, 47416}, {47345, 7235}, {62557, 306}, {62576, 35544}, {62605, 3948}
X(65352) = X(i)-cross conjugate of X(j) for these {i, j}: {240, 273}, {741, 18827}, {15149, 27}, {65106, 811}
X(65352) = pole of line {4010, 4839} with respect to the polar circle
X(65352) = pole of line {7193, 20778} with respect to the Stammler hyperbola
X(65352) = pole of line {20750, 20769} with respect to the Wallace hyperbola
X(65352) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(62853)}}, {{A, B, C, X(2), X(1999)}}, {{A, B, C, X(4), X(31904)}}, {{A, B, C, X(19), X(92)}}, {{A, B, C, X(27), X(286)}}, {{A, B, C, X(28), X(31909)}}, {{A, B, C, X(29), X(14013)}}, {{A, B, C, X(57), X(29967)}}, {{A, B, C, X(75), X(19791)}}, {{A, B, C, X(81), X(5208)}}, {{A, B, C, X(85), X(2363)}}, {{A, B, C, X(105), X(38479)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(226), X(13610)}}, {{A, B, C, X(239), X(27321)}}, {{A, B, C, X(242), X(17927)}}, {{A, B, C, X(278), X(7009)}}, {{A, B, C, X(295), X(741)}}, {{A, B, C, X(314), X(55968)}}, {{A, B, C, X(334), X(335)}}, {{A, B, C, X(514), X(759)}}, {{A, B, C, X(673), X(14616)}}, {{A, B, C, X(1014), X(60679)}}, {{A, B, C, X(1396), X(31917)}}, {{A, B, C, X(1821), X(4581)}}, {{A, B, C, X(1847), X(40431)}}, {{A, B, C, X(8747), X(40411)}}, {{A, B, C, X(9311), X(40430)}}, {{A, B, C, X(9499), X(26702)}}, {{A, B, C, X(13739), X(37448)}}, {{A, B, C, X(15149), X(31905)}}, {{A, B, C, X(16465), X(39273)}}, {{A, B, C, X(19642), X(24624)}}, {{A, B, C, X(27475), X(40438)}}, {{A, B, C, X(31908), X(31925)}}, {{A, B, C, X(31912), X(31916)}}, {{A, B, C, X(36101), X(53707)}}, {{A, B, C, X(36800), X(37128)}}, {{A, B, C, X(40515), X(57419)}}, {{A, B, C, X(58074), X(63187)}}

X(65353) = X(2)X(17983)∩X(107)X(1296)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-5*c^2)*(a^2+b^2-c^2)*(a^2-5*b^2+c^2)*(a^2-b^2+c^2) : :

X(65353) lies on these lines: {2, 17983}, {4, 63854}, {99, 65350}, {107, 1296}, {297, 17952}, {450, 17979}, {458, 14608}, {468, 37860}, {648, 5468}, {653, 37216}, {2434, 65177}, {5485, 16080}, {6335, 42721}, {6336, 52759}, {13492, 44146}, {16081, 21448}, {37863, 52288}, {46106, 52496}, {55977, 57732}

X(65353) = trilinear pole of line {4, 5485}
X(65353) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 1499}, {63, 8644}, {71, 30234}, {184, 14207}, {228, 4786}, {647, 36277}, {656, 1384}, {810, 1992}, {822, 4232}, {4575, 6791}, {9125, 36060}
X(65353) = X(i)-Dao conjugate of X(j) for these {i, j}: {136, 6791}, {1249, 1499}, {1560, 9125}, {3162, 8644}, {39052, 36277}, {39062, 1992}, {40596, 1384}, {53992, 35133}, {62605, 14207}
X(65353) = X(i)-cross conjugate of X(j) for these {i, j}: {1296, 35179}, {48539, 99}, {52290, 18020}, {55135, 671}
X(65353) = pole of line {6791, 9125} with respect to the polar circle
X(65353) = pole of line {11054, 58782} with respect to the dual conic of Jerabek hyperbola
X(65353) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(99)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(459), X(65176)}}, {{A, B, C, X(525), X(9529)}}, {{A, B, C, X(925), X(17708)}}, {{A, B, C, X(1302), X(36886)}}, {{A, B, C, X(4240), X(52283)}}, {{A, B, C, X(4563), X(35178)}}, {{A, B, C, X(6233), X(60187)}}, {{A, B, C, X(11794), X(59038)}}, {{A, B, C, X(15466), X(57219)}}, {{A, B, C, X(32697), X(58994)}}, {{A, B, C, X(35136), X(53080)}}
X(65353) = barycentric product X(i)*X(j) for these (i, j): {1296, 264}, {2434, 46111}, {5485, 648}, {17983, 2418}, {21448, 6331}, {35179, 4}, {37216, 92}, {52477, 892}, {55923, 811}, {55977, 6528}, {57467, 59762}
X(65353) = barycentric quotient X(i)/X(j) for these (i, j): {4, 1499}, {25, 8644}, {27, 4786}, {28, 30234}, {92, 14207}, {107, 4232}, {112, 1384}, {162, 36277}, {186, 9126}, {468, 9125}, {648, 1992}, {877, 51438}, {1296, 3}, {2418, 6390}, {2434, 3292}, {2501, 6791}, {4235, 27088}, {4240, 35266}, {5094, 62568}, {5485, 525}, {6331, 11059}, {6335, 42724}, {6528, 58782}, {8753, 2444}, {10098, 61452}, {14262, 30209}, {17983, 2408}, {21448, 647}, {30247, 13608}, {32648, 14908}, {34336, 58284}, {35179, 69}, {36045, 36060}, {37216, 63}, {39238, 3049}, {39533, 14856}, {46151, 41585}, {52477, 690}, {53351, 53778}, {55923, 656}, {55977, 520}, {62237, 55140}, {65350, 52141}
X(65353) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {297, 17952, 52477}

X(65354) = TRILINEAR POLE OF LINE {4, 99}

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4+2*b^4-b^2*c^2+c^4-a^2*(b^2+2*c^2))*(a^4+b^4-b^2*c^2+2*c^4-a^2*(2*b^2+c^2)) : :

X(65354) lies on these lines: {107, 10425}, {297, 57553}, {340, 892}, {468, 63613}, {648, 4590}, {653, 4620}, {670, 30450}, {685, 877}, {687, 55226}, {1897, 4600}, {2501, 4563}, {2987, 16081}, {3563, 9150}, {4601, 6335}, {4615, 6336}, {6330, 57872}, {6331, 34537}, {8781, 16080}, {9170, 52290}, {35364, 57739}, {39292, 65351}, {42297, 58961}, {43705, 57732}, {47389, 57065}, {52940, 60338}, {65258, 65352}

X(65354) = trilinear pole of line {4, 99}
X(65354) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 55122}, {63, 42663}, {230, 810}, {460, 822}, {647, 8772}, {656, 1692}, {661, 52144}, {798, 3564}, {878, 17462}, {1733, 3049}, {2643, 56389}, {3708, 61213}, {24018, 44099}
X(65354) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 55122}, {3162, 42663}, {15525, 51610}, {31998, 3564}, {35088, 41181}, {36830, 52144}, {39052, 8772}, {39062, 230}, {40596, 1692}, {62595, 55267}
X(65354) = X(i)-cross conjugate of X(j) for these {i, j}: {297, 18020}, {2396, 6331}, {10425, 65277}, {60338, 35142}
X(65354) = pole of line {51613, 55152} with respect to the polar circle
X(65354) = pole of line {40867, 51374} with respect to the Kiepert parabola
X(65354) = pole of line {17932, 53149} with respect to the Steiner circumellipse
X(65354) = pole of line {35067, 47406} with respect to the Wallace hyperbola
X(65354) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(44768)}}, {{A, B, C, X(76), X(14221)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(297), X(2396)}}, {{A, B, C, X(670), X(42297)}}, {{A, B, C, X(683), X(886)}}, {{A, B, C, X(877), X(41074)}}, {{A, B, C, X(892), X(4590)}}, {{A, B, C, X(2421), X(65305)}}, {{A, B, C, X(2501), X(57071)}}, {{A, B, C, X(2855), X(40824)}}, {{A, B, C, X(2996), X(53895)}}, {{A, B, C, X(4235), X(52477)}}, {{A, B, C, X(4563), X(35136)}}, {{A, B, C, X(4577), X(55279)}}, {{A, B, C, X(5468), X(44369)}}, {{A, B, C, X(16077), X(55270)}}, {{A, B, C, X(44770), X(47443)}}, {{A, B, C, X(46144), X(55972)}}, {{A, B, C, X(52035), X(60073)}}, {{A, B, C, X(52476), X(60338)}}, {{A, B, C, X(55266), X(65277)}}

X(65355) = X(7)X(9308)∩X(100)X(108)

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-2*b*c*(b+c)-a*(b+c)^2) : :

X(65355) lies on these lines: {7, 9308}, {81, 1947}, {100, 108}, {329, 56296}, {393, 56927}, {644, 6335}, {648, 651}, {1172, 57809}, {1249, 28739}, {1783, 65207}, {1948, 62799}, {2052, 62798}, {2323, 52982}, {6516, 14570}, {7282, 56014}, {8748, 52673}, {13395, 58965}, {14361, 27540}, {28951, 64988}, {36118, 63782}, {41083, 52358}, {56300, 57810}, {61236, 65233}, {62669, 65170}, {65174, 65330}

X(65355) = trilinear pole of line {405, 1882}
X(65355) = X(i)-isoconjugate-of-X(j) for these {i, j}: {521, 2215}, {652, 51223}, {1459, 2335}, {7004, 36080}, {7117, 65227}, {57657, 63220}
X(65355) = X(i)-Dao conjugate of X(j) for these {i, j}: {38967, 53560}, {39060, 57831}, {62570, 63220}
X(65355) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {58965, 33650}
X(65355) = pole of line {11, 31653} with respect to the polar circle
X(65355) = pole of line {23189, 36054} with respect to the Stammler hyperbola
X(65355) = pole of line {651, 36127} with respect to the Steiner circumellipse
X(65355) = pole of line {92, 219} with respect to the Hutson-Moses hyperbola
X(65355) = intersection, other than A, B, C, of circumconics {{A, B, C, X(100), X(648)}}, {{A, B, C, X(108), X(65334)}}, {{A, B, C, X(651), X(23067)}}, {{A, B, C, X(681), X(65181)}}, {{A, B, C, X(823), X(1897)}}, {{A, B, C, X(2804), X(23882)}}, {{A, B, C, X(4552), X(18026)}}, {{A, B, C, X(6335), X(61180)}}, {{A, B, C, X(23981), X(37543)}}, {{A, B, C, X(54240), X(61178)}}
X(65355) = barycentric product X(i)*X(j) for these (i, j): {108, 44140}, {1882, 99}, {5271, 653}, {18026, 405}, {23882, 46102}, {37543, 6335}, {39585, 664}, {54394, 668}, {65180, 75}
X(65355) = barycentric quotient X(i)/X(j) for these (i, j): {108, 51223}, {405, 521}, {1441, 63220}, {1451, 1459}, {1783, 2335}, {1882, 523}, {4552, 63235}, {5271, 6332}, {5295, 52355}, {5320, 1946}, {7012, 65227}, {7115, 36080}, {18026, 57831}, {23882, 26932}, {32674, 2215}, {37543, 905}, {39585, 522}, {44140, 35518}, {46102, 54970}, {46385, 7004}, {54394, 513}, {56831, 3737}, {65180, 1}
X(65355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 18026, 651}, {653, 1897, 4552}

X(65356) = TRILINEAR POLE OF LINE {4, 67}

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(a^4-a^2*b^2+b^4-c^4)*(a^4-b^4-a^2*c^2+c^4) : :

X(65356) lies on these lines: {67, 51939}, {107, 935}, {648, 850}, {685, 43665}, {1897, 52623}, {2052, 57496}, {6330, 18019}, {6331, 44173}, {8791, 14165}, {10415, 17983}, {15466, 57476}, {16080, 46105}, {22456, 58980}, {23582, 42396}, {39269, 51260}, {52632, 65350}, {56981, 65351}

X(65356) = trilinear pole of line {4, 67}
X(65356) = X(i)-isoconjugate-of-X(j) for these {i, j}: {23, 822}, {48, 9517}, {63, 42659}, {255, 2492}, {656, 10317}, {661, 58357}, {810, 22151}, {9979, 52430}, {16568, 39201}, {18374, 24018}, {20944, 58310}, {37754, 52916}
X(65356) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 9517}, {3162, 42659}, {5099, 55048}, {6523, 2492}, {15900, 520}, {36830, 58357}, {39062, 22151}, {40596, 10317}, {48317, 47415}
X(65356) = X(i)-cross conjugate of X(j) for these {i, j}: {935, 65269}, {2492, 4}, {60040, 671}
X(65356) = pole of line {47415, 55048} with respect to the polar circle
X(65356) = pole of line {316, 34163} with respect to the dual conic of Jerabek hyperbola
X(65356) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1304)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(112), X(36828)}}, {{A, B, C, X(275), X(53205)}}, {{A, B, C, X(523), X(47004)}}, {{A, B, C, X(850), X(14618)}}, {{A, B, C, X(933), X(11794)}}, {{A, B, C, X(935), X(10415)}}, {{A, B, C, X(8791), X(58980)}}, {{A, B, C, X(10423), X(37801)}}, {{A, B, C, X(13854), X(32696)}}, {{A, B, C, X(14165), X(53176)}}, {{A, B, C, X(21459), X(37765)}}, {{A, B, C, X(30248), X(55279)}}, {{A, B, C, X(32687), X(32708)}}, {{A, B, C, X(32697), X(53923)}}, {{A, B, C, X(33640), X(43188)}}, {{A, B, C, X(39413), X(60507)}}, {{A, B, C, X(40173), X(53962)}}, {{A, B, C, X(46106), X(58071)}}, {{A, B, C, X(58994), X(65271)}}
X(65356) = barycentric product X(i)*X(j) for these (i, j): {4, 65269}, {107, 18019}, {264, 935}, {2157, 57973}, {6331, 8791}, {6528, 67}, {11605, 65266}, {15352, 34897}, {17708, 2052}, {23962, 58980}, {39269, 65268}, {46105, 648}, {46111, 60503}, {57496, 65350}
X(65356) = barycentric quotient X(i)/X(j) for these (i, j): {4, 9517}, {25, 42659}, {67, 520}, {107, 23}, {110, 58357}, {112, 10317}, {393, 2492}, {648, 22151}, {823, 16568}, {935, 3}, {1289, 54060}, {2052, 9979}, {2157, 822}, {2492, 55048}, {3455, 39201}, {4240, 16165}, {6331, 37804}, {6528, 316}, {6529, 8744}, {6530, 33752}, {8744, 57203}, {8791, 647}, {9076, 58353}, {11605, 8673}, {14273, 47415}, {14618, 62563}, {15352, 37765}, {17708, 394}, {18019, 3265}, {23582, 52630}, {23977, 28343}, {32230, 52916}, {32713, 18374}, {34897, 52613}, {37778, 18311}, {46105, 525}, {46151, 9019}, {57496, 14417}, {57973, 20944}, {58980, 23357}, {60496, 1636}, {60503, 3292}, {60507, 14961}, {65269, 69}, {65350, 57481}

X(65357) = X(107)X(512)∩X(647)X(648)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(b^4+a^3*c-b^2*c^2-a^2*(b^2-2*c^2)+a*(-(b^2*c)+c^3))*(-b^4+a^3*c+b^2*c^2+a^2*(b^2-2*c^2)+a*(-(b^2*c)+c^3))*(a^3*b+c^2*(b^2-c^2)+a^2*(-2*b^2+c^2)+a*(b^3-b*c^2))*(a^3*b-b^2*c^2+c^4+a^2*(2*b^2-c^2)+a*(b^3-b*c^2)) : :

X(65357) lies on these lines: {107, 512}, {415, 8764}, {450, 52463}, {468, 1942}, {525, 6331}, {647, 648}, {653, 55234}, {685, 878}, {686, 53205}, {687, 61216}, {1897, 55230}, {2433, 15459}, {2501, 15352}, {2623, 16813}, {6330, 57864}, {6335, 55232}, {10097, 65350}, {14582, 46456}, {16081, 51358}, {43462, 65359}, {54240, 57185}

X(65357) = trilinear pole of line {4, 1942}
X(65357) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 2797}, {450, 822}, {662, 35236}, {810, 40888}, {851, 22382}, {24018, 44096}, {32320, 41497}
X(65357) = X(i)-vertex conjugate of X(j) for these {i, j}: {2351, 53205}
X(65357) = X(i)-Dao conjugate of X(j) for these {i, j}: {1084, 35236}, {1249, 2797}, {39062, 40888}
X(65357) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(297), X(46587)}}, {{A, B, C, X(512), X(525)}}, {{A, B, C, X(1304), X(2052)}}, {{A, B, C, X(34289), X(65306)}}
X(65357) = barycentric product X(i)*X(j) for these (i, j): {107, 57864}, {264, 2713}, {1942, 6528}, {41207, 7108}
X(65357) = barycentric quotient X(i)/X(j) for these (i, j): {4, 2797}, {107, 450}, {512, 35236}, {648, 40888}, {1942, 520}, {2249, 22382}, {2713, 3}, {6529, 41368}, {32713, 44096}, {36126, 41497}, {41206, 7364}, {41207, 1943}, {57864, 3265}

X(65358) = X(107)X(647)∩X(520)X(648)

Barycentrics    (a-b)*(a+b)*(a-c)*(a+c)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2*(a^6*c^2+b^4*(b^2-c^2)^2+a^4*(b^4-2*c^4)+a^2*(-2*b^6+b^4*c^2+c^6))*(a^6*b^2+c^4*(b^2-c^2)^2+a^4*(-2*b^4+c^4)+a^2*(b^6+b^2*c^4-2*c^6)) : :

X(65358) lies on these lines: {107, 647}, {520, 648}, {523, 15352}, {685, 58070}, {1972, 6330}, {1987, 1990}, {2052, 57500}, {3265, 6331}, {6335, 57109}, {6530, 16081}, {14380, 15459}, {15274, 51960}, {15451, 34538}, {16813, 23286}, {41204, 52177}, {42396, 58353}, {43083, 46456}, {53175, 58071}

X(65358) = trilinear pole of line {4, 1987}
X(65358) = X(i)-isoconjugate-of-X(j) for these {i, j}: {255, 6130}, {401, 822}, {520, 1955}, {1971, 24018}, {3708, 62523}
X(65358) = X(i)-vertex conjugate of X(j) for these {i, j}: {32649, 41173}
X(65358) = X(i)-Dao conjugate of X(j) for these {i, j}: {6523, 6130}
X(65358) = X(i)-Ceva conjugate of X(j) for these {i, j}: {41210, 53708}
X(65358) = X(i)-cross conjugate of X(j) for these {i, j}: {3569, 2052}, {6130, 4}, {53175, 1987}, {53708, 53205}
X(65358) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(648)}}, {{A, B, C, X(264), X(44770)}}, {{A, B, C, X(520), X(523)}}, {{A, B, C, X(847), X(10423)}}, {{A, B, C, X(935), X(14536)}}, {{A, B, C, X(1093), X(32695)}}, {{A, B, C, X(1990), X(58071)}}, {{A, B, C, X(2764), X(15318)}}, {{A, B, C, X(6530), X(32687)}}, {{A, B, C, X(10415), X(53944)}}, {{A, B, C, X(14560), X(52604)}}, {{A, B, C, X(31510), X(57526)}}, {{A, B, C, X(41210), X(53205)}}, {{A, B, C, X(53708), X(65305)}}
X(65358) = barycentric product X(i)*X(j) for these (i, j): {4, 53205}, {107, 1972}, {264, 53708}, {1298, 65183}, {1956, 823}, {1987, 6528}, {2052, 65305}, {14941, 15352}, {18020, 62519}, {23582, 60036}, {41208, 53}, {41210, 5}, {51960, 65265}, {53175, 57556}
X(65358) = barycentric quotient X(i)/X(j) for these (i, j): {107, 401}, {250, 62523}, {393, 6130}, {1956, 24018}, {1972, 3265}, {1987, 520}, {6528, 44137}, {6529, 41204}, {14941, 52613}, {15352, 16089}, {17994, 38974}, {20031, 32545}, {24019, 1955}, {32713, 1971}, {41208, 34386}, {41210, 95}, {51960, 39473}, {52177, 32320}, {53175, 35071}, {53205, 69}, {53708, 3}, {58070, 52128}, {60036, 15526}, {61193, 32428}, {62519, 125}, {65305, 394}

X(65359) = X(2)X(46456)∩X(107)X(186)

Barycentrics    b^2*c^2*(-a^2+b^2-c^2)*(a^2+b^2-c^2)*(a^8+a^6*(b^2-3*c^2)+b^2*(b^2-c^2)^3+a^4*(-4*b^4+2*b^2*c^2+3*c^4)+a^2*(b^6+2*b^4*c^2-2*b^2*c^4-c^6))*(-a^8+c^2*(b^2-c^2)^3+a^6*(3*b^2-c^2)+a^4*(-3*b^4-2*b^2*c^2+4*c^4)+a^2*(b^6+2*b^4*c^2-2*b^2*c^4-c^6)) : :

X(65359) lies on these lines: {2, 46456}, {15, 36309}, {16, 36306}, {107, 186}, {249, 36789}, {323, 648}, {338, 40384}, {653, 36102}, {685, 14355}, {687, 15466}, {1897, 36130}, {2052, 15459}, {3431, 43707}, {6331, 7799}, {6335, 42701}, {9213, 17983}, {14165, 15352}, {14220, 57732}, {14618, 16080}, {15412, 65360}, {16577, 65329}, {16813, 32663}, {30450, 37802}, {43462, 65357}, {52147, 65350}, {57268, 65349}

X(65359) = trilinear pole of line {4, 14220}
X(65359) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 5663}, {255, 47228}, {577, 36063}, {822, 7480}, {2315, 39986}, {2631, 53233}, {9247, 35520}
X(65359) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 5663}, {6523, 47228}, {62576, 35520}
X(65359) = X(i)-cross conjugate of X(j) for these {i, j}: {47228, 4}, {55130, 35139}
X(65359) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(15)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(275), X(23582)}}, {{A, B, C, X(276), X(60138)}}, {{A, B, C, X(338), X(36789)}}, {{A, B, C, X(477), X(65325)}}, {{A, B, C, X(525), X(62501)}}, {{A, B, C, X(2052), X(14618)}}, {{A, B, C, X(34990), X(58416)}}, {{A, B, C, X(37778), X(42298)}}, {{A, B, C, X(46789), X(52494)}}, {{A, B, C, X(53201), X(54837)}}
X(65359) = barycentric product X(i)*X(j) for these (i, j): {264, 477}, {340, 43707}, {1494, 52494}, {1969, 36151}, {2052, 65325}, {2411, 46456}, {14220, 6528}, {14618, 30528}, {16077, 53178}, {16080, 46789}, {18027, 32663}, {18817, 34210}, {35139, 53158}, {36062, 57806}, {36102, 92}, {36130, 75}, {39985, 65267}
X(65359) = barycentric quotient X(i)/X(j) for these (i, j): {4, 5663}, {107, 7480}, {158, 36063}, {264, 35520}, {393, 47228}, {477, 3}, {1300, 39986}, {1304, 53233}, {2411, 8552}, {2970, 6070}, {4240, 42742}, {6344, 34209}, {14220, 520}, {16080, 46788}, {30528, 4558}, {32650, 32662}, {32663, 577}, {32712, 32640}, {34210, 22115}, {34334, 1553}, {36047, 36061}, {36062, 255}, {36102, 63}, {36117, 36034}, {36130, 1}, {36151, 48}, {39985, 13754}, {43707, 265}, {46456, 2410}, {46789, 11064}, {52494, 30}, {52661, 11251}, {53158, 526}, {53178, 9033}, {58086, 17702}, {58261, 13212}, {65267, 39988}, {65325, 394}

X(65360) = X(2)X(38342)∩X(94)X(275)

Barycentrics    b^2*c^2*(-a^2+b^2-c^2)*(a^2+b^2-c^2)*(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(-a^2+b^2-a*c-c^2)*(-a^2+b^2+a*c-c^2)*(a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(-a^4+c^2*(b^2-c^2)+a^2*(b^2+2*c^2)) : :

X(65360) lies on these lines: {2, 38342}, {54, 58943}, {61, 51275}, {62, 51268}, {94, 275}, {107, 1141}, {276, 6331}, {476, 39452}, {687, 40427}, {847, 58079}, {933, 2970}, {1989, 8794}, {2052, 11077}, {11079, 15459}, {15412, 65359}, {18384, 65349}, {18817, 18883}, {30529, 37766}, {51887, 56407}

X(65360) = trilinear pole of line {4, 10412}
X(65360) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 2290}, {48, 1154}, {50, 44706}, {216, 6149}, {255, 11062}, {323, 62266}, {418, 52414}, {577, 51801}, {1273, 9247}, {1953, 22115}, {2081, 4575}, {2151, 44712}, {2152, 44711}, {2179, 52437}, {2624, 23181}, {14918, 52430}, {18695, 19627}
X(65360) = X(i)-Dao conjugate of X(j) for these {i, j}: {128, 47423}, {136, 2081}, {1249, 1154}, {6523, 11062}, {14993, 216}, {15295, 217}, {36103, 2290}, {40578, 44712}, {40579, 44711}, {62576, 1273}, {62603, 52437}
X(65360) = X(i)-cross conjugate of X(j) for these {i, j}: {1141, 46138}, {1989, 1141}, {11062, 4}, {37943, 39286}, {43088, 35139}, {47230, 933}, {55150, 46139}
X(65360) = pole of line {2081, 47423} with respect to the polar circle
X(65360) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(61)}}, {{A, B, C, X(94), X(6344)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(275), X(276)}}, {{A, B, C, X(324), X(847)}}, {{A, B, C, X(1141), X(65326)}}, {{A, B, C, X(1989), X(11077)}}, {{A, B, C, X(3580), X(41665)}}, {{A, B, C, X(7578), X(59278)}}, {{A, B, C, X(9381), X(14618)}}, {{A, B, C, X(11547), X(58079)}}, {{A, B, C, X(14165), X(37766)}}, {{A, B, C, X(14592), X(58704)}}, {{A, B, C, X(14860), X(39284)}}, {{A, B, C, X(15412), X(43766)}}, {{A, B, C, X(21449), X(43462)}}, {{A, B, C, X(36612), X(60256)}}, {{A, B, C, X(39183), X(62722)}}, {{A, B, C, X(51222), X(60517)}}, {{A, B, C, X(56067), X(62927)}}, {{A, B, C, X(57899), X(62926)}}
X(65360) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {94, 65326, 46138}

X(65361) = X(72)X(104)∩X(106)X(1167)

Barycentrics    a^2*(a-b)*(a-c)*(a^4-a^3*c+b*(b-c)^2*(b+c)+a*c*(b+c)^2-a^2*(2*b^2-b*c+c^2))*(a^4-a^3*b+(b-c)^2*c*(b+c)+a*b*(b+c)^2-a^2*(b^2-b*c+2*c^2)) : :

X(65361) lies on the circumcircle and on these lines: {72, 104}, {105, 17642}, {106, 1167}, {107, 53151}, {112, 2427}, {190, 41906}, {644, 40117}, {675, 40424}, {692, 58991}, {759, 56259}, {917, 40444}, {1290, 34151}, {1309, 3952}, {1331, 8059}, {2222, 61222}, {2291, 52405}, {2376, 40397}, {2720, 23067}, {2726, 56529}, {2730, 6065}, {4571, 43347}, {5546, 59010}, {15728, 63185}, {30239, 65159}, {43078, 51632}, {58992, 65313}

X(65361) = trilinear pole of line {6, 1167}
X(65361) = X(i)-isoconjugate-of-X(j) for these {i, j}: {11, 61227}, {244, 61185}, {278, 40628}, {513, 1210}, {514, 1108}, {522, 37566}, {649, 17862}, {667, 1226}, {693, 40958}, {1019, 21933}, {1071, 7649}, {1086, 61237}, {1111, 53288}, {1864, 3676}, {3737, 57285}, {4858, 61212}, {6129, 52571}, {7178, 40979}, {23204, 46107}
X(65361) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 17862}, {6631, 1226}, {39026, 1210}
X(65361) = X(i)-cross conjugate of X(j) for these {i, j}: {40, 59}, {212, 1252}, {38857, 7012}
X(65361) = intersection, other than A, B, C, of circumconics {{A, B, C, X(72), X(2427)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(644), X(1331)}}, {{A, B, C, X(1897), X(5548)}}, {{A, B, C, X(2283), X(17642)}}, {{A, B, C, X(5546), X(36106)}}, {{A, B, C, X(34151), X(56877)}}, {{A, B, C, X(56280), X(61222)}}
X(65361) = barycentric product X(i)*X(j) for these (i, j): {100, 40399}, {101, 40424}, {1167, 190}, {1331, 40444}, {40397, 4571}, {55112, 58984}, {56259, 662}, {63185, 644}
X(65361) = barycentric quotient X(i)/X(j) for these (i, j): {100, 17862}, {101, 1210}, {190, 1226}, {212, 40628}, {692, 1108}, {906, 1071}, {1110, 61237}, {1167, 514}, {1252, 61185}, {1415, 37566}, {2149, 61227}, {2427, 1532}, {4557, 21933}, {4559, 57285}, {23990, 53288}, {32739, 40958}, {36049, 52571}, {40399, 693}, {40424, 3261}, {40444, 46107}, {56259, 1577}, {58984, 55110}, {63185, 24002}, {65375, 40979}

X(65362) = ANTICOMPLEMENT OF X(13612)

Barycentrics    a*(a-b)*(a-c)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)^2*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2)^2 : :
X(65362) = -3*X[2]+2*X[13612]

X(65362) lies on the circumcircle and on these lines: {2, 13612}, {84, 102}, {104, 46355}, {106, 1256}, {108, 37141}, {109, 13138}, {189, 972}, {271, 52027}, {280, 1295}, {285, 26701}, {934, 53642}, {2357, 29056}, {2716, 56939}, {6245, 48358}, {14312, 30239}, {32652, 58972}, {36049, 58946}, {36067, 61040}, {44327, 58991}, {58995, 65330}

X(65362) = reflection of X(i) in X(j) for these {i,j}: {48358, 6245}
X(65362) = anticomplement of X(13612)
X(65362) = trilinear pole of line {6, 282}
X(65362) = X(i)-isoconjugate-of-X(j) for these {i, j}: {40, 6129}, {109, 3318}, {196, 10397}, {198, 14837}, {208, 57101}, {221, 8058}, {223, 14298}, {513, 1103}, {650, 40212}, {663, 55015}, {1461, 61075}, {1817, 55212}, {2187, 17896}, {2331, 64885}, {3209, 57245}, {6611, 57049}, {7078, 54239}, {8063, 57454}, {38357, 57118}
X(65362) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 3318}, {282, 8063}, {3341, 8058}, {13612, 13612}, {35508, 61075}, {39026, 1103}
X(65362) = X(i)-cross conjugate of X(j) for these {i, j}: {1622, 59}, {3900, 282}, {8059, 13138}, {23224, 1433}, {40117, 37141}
X(65362) = pole of line {3318, 13612} with respect to the polar circle
X(65362) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31511)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(668), X(61185)}}, {{A, B, C, X(693), X(2968)}}, {{A, B, C, X(4397), X(14312)}}, {{A, B, C, X(4571), X(54953)}}, {{A, B, C, X(13138), X(53642)}}

X(65363) = X(105)X(4518)∩X(106)X(291)

Barycentrics    a*(a-b)^3*(a-c)^3*(-b^2+a*c)*(a*b-c^2) : :

X(65363) lies on the circumcircle and on these lines: {100, 6632}, {101, 57731}, {105, 4518}, {106, 291}, {109, 31615}, {292, 59035}, {660, 901}, {739, 1922}, {765, 2382}, {789, 57950}, {825, 59149}, {898, 34067}, {927, 4583}, {1016, 8299}, {1252, 9111}, {1308, 4562}, {2222, 36801}, {2726, 4076}, {4557, 59043}, {6635, 23343}, {7035, 9073}, {9081, 31073}

X(65363) = trilinear pole of line {6, 765}
X(65363) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 24193}, {238, 764}, {239, 21143}, {244, 659}, {350, 8027}, {513, 27846}, {649, 27918}, {812, 1015}, {1019, 39786}, {1027, 38989}, {1086, 8632}, {1357, 3716}, {1428, 21132}, {1914, 6545}, {1921, 3249}, {1977, 65101}, {2238, 8042}, {2969, 22384}, {3125, 50456}, {3248, 3766}, {3271, 43041}, {3572, 35119}, {3937, 65106}, {4124, 43924}, {4435, 53538}, {4448, 43922}, {4455, 17205}, {8034, 33295}, {8661, 27922}, {14599, 23100}, {16726, 21832}, {46051, 52205}, {46387, 61404}, {46390, 61403}, {60577, 61061}
X(65363) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 27918}, {8054, 24193}, {9470, 764}, {36906, 6545}, {39026, 27846}
X(65363) = X(i)-cross conjugate of X(j) for these {i, j}: {660, 5378}, {2284, 1016}, {3573, 765}, {54328, 4567}
X(65363) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(98)}}, {{A, B, C, X(291), X(660)}}, {{A, B, C, X(662), X(39276)}}, {{A, B, C, X(765), X(6635)}}, {{A, B, C, X(874), X(2284)}}, {{A, B, C, X(1280), X(4555)}}, {{A, B, C, X(1922), X(34067)}}, {{A, B, C, X(3573), X(8300)}}, {{A, B, C, X(4518), X(4583)}}, {{A, B, C, X(5376), X(6632)}}, {{A, B, C, X(5548), X(8851)}}, {{A, B, C, X(23343), X(23344)}}, {{A, B, C, X(36802), X(56111)}}, {{A, B, C, X(57950), X(59149)}}

X(65364) = X(1)X(28485)∩X(81)X(745)

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2+a*(b-c)-b*c+c^2)*(a^2+b^2-b*c+c^2+a*(-b+c)) : :

X(65364) lies on the circumcircle and on these lines: {1, 28485}, {37, 25433}, {81, 745}, {98, 8857}, {100, 33946}, {101, 3888}, {104, 37331}, {105, 5253}, {106, 7194}, {190, 65369}, {292, 733}, {644, 28883}, {651, 8685}, {675, 40038}, {727, 3502}, {932, 1633}, {1332, 29026}, {4562, 8684}, {4579, 28486}, {4599, 59076}, {28856, 35342}, {29055, 46153}, {52778, 52923}

X(65364) = trilinear pole of line {6, 982}
X(65364) = X(i)-isoconjugate-of-X(j) for these {i, j}: {213, 18077}, {512, 33954}, {513, 3961}, {522, 41346}, {649, 17280}, {650, 56547}, {663, 56928}, {667, 33938}, {3494, 4083}, {3835, 34249}
X(65364) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 17280}, {6626, 18077}, {6631, 33938}, {39026, 3961}, {39054, 33954}
X(65364) = X(i)-cross conjugate of X(j) for these {i, j}: {21123, 81}
X(65364) = pole of line {38, 1582} with respect to the Kiepert parabola
X(65364) = pole of line {3496, 6646} with respect to the Yff parabola
X(65364) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(292), X(46153)}}, {{A, B, C, X(651), X(3888)}}, {{A, B, C, X(660), X(1414)}}, {{A, B, C, X(664), X(1220)}}, {{A, B, C, X(668), X(37135)}}, {{A, B, C, X(1015), X(18108)}}, {{A, B, C, X(1633), X(52923)}}, {{A, B, C, X(3903), X(36086)}}, {{A, B, C, X(4246), X(37331)}}, {{A, B, C, X(4622), X(65202)}}, {{A, B, C, X(8050), X(13486)}}, {{A, B, C, X(39949), X(52935)}}
X(65364) = barycentric product X(i)*X(j) for these (i, j): {100, 39724}, {101, 40038}, {190, 7194}, {3502, 4598}, {43749, 651}
X(65364) = barycentric quotient X(i)/X(j) for these (i, j): {86, 18077}, {100, 17280}, {101, 3961}, {109, 56547}, {190, 33938}, {651, 56928}, {662, 33954}, {1415, 41346}, {3502, 3835}, {4579, 17741}, {7194, 514}, {21123, 55043}, {34071, 3494}, {39724, 693}, {40038, 3261}, {43749, 4391}

X(65365) = X(1)X(2712)∩X(100)X(4367)

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2+3*a*(b-c)-3*b*c+c^2)*(a^2-3*a*b+b^2+3*a*c-3*b*c+c^2) : :

X(65365) lies on the circumcircle and on these lines: {1, 2712}, {21, 59827}, {99, 17212}, {100, 4367}, {101, 6163}, {106, 7312}, {111, 7292}, {551, 2718}, {741, 1149}, {1284, 8686}, {1621, 2721}, {2382, 54310}, {2726, 16823}, {2752, 2975}, {2758, 54335}, {3257, 53682}, {5380, 14419}, {20459, 35106}, {28471, 38460}, {28482, 60353}, {29055, 43924}, {39445, 47626}

X(65365) = trilinear pole of line {6, 1054}
X(65365) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 45661}, {37, 53412}, {513, 5524}
X(65365) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 45661}, {39026, 5524}, {40589, 53412}
X(65365) = pole of line {896, 39339} with respect to the Kiepert parabola
X(65365) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4622)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(651), X(35180)}}, {{A, B, C, X(1149), X(1284)}}, {{A, B, C, X(3257), X(6163)}}, {{A, B, C, X(4367), X(17212)}}, {{A, B, C, X(4618), X(9505)}}, {{A, B, C, X(5557), X(35156)}}, {{A, B, C, X(27834), X(35177)}}, {{A, B, C, X(60353), X(62644)}}
X(65365) = barycentric product X(i)*X(j) for these (i, j): {190, 7312}
X(65365) = barycentric quotient X(i)/X(j) for these (i, j): {1, 45661}, {58, 53412}, {101, 5524}, {7312, 514}

X(65366) = X(1)X(53688)∩X(111)X(3920)

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2+b*c+c^2+a*(3*b+c))*(a^2+b^2+b*c+c^2+a*(b+3*c)) : :

X(65366) lies on the circumcircle and on these lines: {1, 53688}, {100, 23861}, {104, 14636}, {105, 19318}, {106, 9277}, {111, 3920}, {662, 53628}, {741, 1193}, {813, 61168}, {2375, 2670}, {2702, 35342}, {2712, 5529}, {3799, 8694}, {4115, 59085}, {4557, 65369}, {4596, 4983}, {5293, 28482}, {9108, 16823}, {38470, 62644}

X(65366) = trilinear pole of line {6, 846}
X(65366) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 1961}, {649, 28604}
X(65366) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 28604}, {36830, 1963}, {39026, 1961}
X(65366) = pole of line {1962, 1963} with respect to the Kiepert parabola
X(65366) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4596)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(662), X(3903)}}, {{A, B, C, X(1018), X(37135)}}, {{A, B, C, X(1193), X(61168)}}, {{A, B, C, X(1414), X(65250)}}, {{A, B, C, X(4238), X(19318)}}, {{A, B, C, X(4246), X(14636)}}, {{A, B, C, X(4557), X(23861)}}, {{A, B, C, X(5293), X(62644)}}, {{A, B, C, X(17940), X(34076)}}
X(65366) = barycentric product X(i)*X(j) for these (i, j): {190, 9277}, {9281, 99}, {17934, 6158}
X(65366) = barycentric quotient X(i)/X(j) for these (i, j): {100, 28604}, {101, 1961}, {110, 1963}, {6158, 18014}, {9277, 514}, {9281, 523}, {17943, 6157}

X(65367) = X(1)X(2726)∩X(104)X(238)

Barycentrics    a^2*(a-b)*(a-c)*(a^2*c+b^2*(-b+c)+a*(b^2-3*b*c+c^2))*(a^2*b+(b-c)*c^2+a*(b^2-3*b*c+c^2)) : :

X(65367) lies on the circumcircle and on these lines: {1, 2726}, {98, 60353}, {99, 3737}, {100, 663}, {101, 3063}, {104, 238}, {105, 1149}, {106, 9432}, {109, 667}, {675, 7292}, {739, 1055}, {741, 859}, {813, 2427}, {901, 46597}, {927, 1027}, {932, 6163}, {934, 43924}, {995, 2718}, {997, 2757}, {1016, 8706}, {1026, 6079}, {1083, 2751}, {1262, 59123}, {1311, 38460}, {1458, 8686}, {1951, 59131}, {2291, 3230}, {2370, 3100}, {2382, 16483}, {2716, 49128}, {2724, 12652}, {2758, 30115}, {3109, 53920}, {6905, 15323}, {7290, 14665}, {9082, 33849}, {9266, 53625}, {19554, 35105}, {21788, 35106}, {32666, 59101}, {39445, 45763}, {40499, 52778}, {43655, 61432}, {52092, 53703}

X(65367) = trilinear pole of line {6, 9432}
X(65367) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 5205}, {514, 56530}, {522, 9364}, {649, 40875}, {650, 40862}, {656, 15150}
X(65367) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 40875}, {39026, 5205}, {40596, 15150}
X(65367) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(32665)}}, {{A, B, C, X(56), X(36086)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(238), X(859)}}, {{A, B, C, X(663), X(667)}}, {{A, B, C, X(664), X(34080)}}, {{A, B, C, X(1016), X(1262)}}, {{A, B, C, X(1026), X(1149)}}, {{A, B, C, X(1055), X(3230)}}, {{A, B, C, X(1178), X(17939)}}, {{A, B, C, X(5548), X(32735)}}, {{A, B, C, X(34085), X(39970)}}, {{A, B, C, X(34434), X(35174)}}, {{A, B, C, X(37168), X(46597)}}, {{A, B, C, X(40437), X(63881)}}
X(65367) = barycentric product X(i)*X(j) for these (i, j): {1, 65231}, {109, 52517}, {190, 9432}, {651, 9365}, {53208, 6}
X(65367) = barycentric quotient X(i)/X(j) for these (i, j): {100, 40875}, {101, 5205}, {109, 40862}, {112, 15150}, {692, 56530}, {1415, 9364}, {9365, 4391}, {9432, 514}, {52517, 35519}, {53208, 76}, {65231, 75}

X(65368) = X(40)X(915)∩X(212)X(2376)

Barycentrics    a^2*(a-b)*(a-c)*(a^4-2*a^2*b^2-2*a^3*c+(b-c)^3*(b+c)+2*a*c^2*(b+c))*(a^4-2*a^3*b-2*a^2*c^2+2*a*b^2*(b+c)-(b-c)^3*(b+c)) : :

X(65368) lies on the circumcircle and on these lines: {40, 915}, {99, 53652}, {103, 64889}, {104, 56278}, {105, 39947}, {106, 11249}, {212, 2376}, {573, 9085}, {675, 39695}, {759, 37585}, {917, 5759}, {1331, 13397}, {1477, 37578}, {1766, 20624}, {2077, 43078}, {3939, 6011}, {5657, 40101}, {8059, 56410}, {8686, 37618}, {9058, 61221}, {23067, 36082}, {32691, 57218}, {32706, 64111}, {40117, 61239}

X(65368) = trilinear pole of line {6, 34430}
X(65368) = X(i)-isoconjugate-of-X(j) for these {i, j}: {224, 7649}, {513, 12649}, {514, 1723}, {522, 34489}, {2900, 3676}, {3211, 17924}
X(65368) = X(i)-Dao conjugate of X(j) for these {i, j}: {39026, 12649}
X(65368) = X(i)-cross conjugate of X(j) for these {i, j}: {43923, 1167}
X(65368) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(40), X(56410)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(516), X(64889)}}, {{A, B, C, X(1331), X(36106)}}, {{A, B, C, X(2283), X(41338)}}, {{A, B, C, X(5759), X(56742)}}, {{A, B, C, X(11249), X(23703)}}, {{A, B, C, X(23832), X(37618)}}, {{A, B, C, X(23981), X(63391)}}
X(65368) = barycentric product X(i)*X(j) for these (i, j): {100, 39947}, {101, 39695}, {190, 34430}, {1332, 41505}, {53652, 6}, {56278, 651}, {57794, 906}
X(65368) = barycentric quotient X(i)/X(j) for these (i, j): {101, 12649}, {692, 1723}, {906, 224}, {1415, 34489}, {2427, 51432}, {32656, 3211}, {34430, 514}, {39695, 3261}, {39947, 693}, {41505, 17924}, {53652, 76}, {56278, 4391}

X(65369) = X(109)X(3799)∩X(644)X(825)

Barycentrics    a*(a-b)*(a-c)*(a^2+b^2+a*(b-c)+b*c+c^2)*(a^2+b^2+b*c+c^2+a*(-b+c)) : :

X(65369) lies on the circumcircle and on these lines: {105, 5260}, {106, 39977}, {109, 3799}, {190, 65364}, {644, 825}, {675, 40033}, {741, 40794}, {1018, 2702}, {1308, 39185}, {1310, 52923}, {1332, 29075}, {3952, 38470}, {4557, 65366}, {13396, 33948}, {28895, 57192}, {30664, 36801}, {30670, 65192}, {40521, 53628}

X(65369) = trilinear pole of line {6, 3961}
X(65369) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 29821}, {649, 17302}, {667, 33944}, {3733, 4425}, {16726, 21383}, {17205, 23861}
X(65369) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 17302}, {6631, 33944}, {39026, 29821}
X(65369) = X(i)-cross conjugate of X(j) for these {i, j}: {846, 765}
X(65369) = pole of line {17469, 39244} with respect to the Hutson-Moses hyperbola
X(65369) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(98)}}, {{A, B, C, X(644), X(3799)}}, {{A, B, C, X(660), X(36147)}}, {{A, B, C, X(1018), X(40794)}}, {{A, B, C, X(37135), X(65202)}}, {{A, B, C, X(37212), X(55179)}}
X(65369) = barycentric product X(i)*X(j) for these (i, j): {100, 39722}, {101, 40033}, {190, 39977}
X(65369) = barycentric quotient X(i)/X(j) for these (i, j): {100, 17302}, {101, 29821}, {190, 33944}, {1018, 4425}, {39722, 693}, {39977, 514}, {40033, 3261}

X(65370) = X(105)X(3705)∩X(106)X(3976)

Barycentrics    a*(a-b)*(a-c)*(a^3-a^2*b-a*b^2+b^3+c^3)*(a^3+b^3-a^2*c-a*c^2+c^3) : :

X(65370) lies on the circumcircle and on these lines: {105, 3705}, {106, 3976}, {107, 7256}, {108, 4571}, {190, 6011}, {643, 58986}, {646, 26704}, {668, 1305}, {739, 56003}, {759, 1043}, {833, 53280}, {915, 34406}, {1026, 8685}, {1978, 2864}, {2222, 3699}, {2731, 4076}, {2743, 30721}, {3573, 29083}, {3952, 33637}, {6012, 23845}, {8707, 42380}, {9070, 65313}, {9085, 55994}, {15344, 56305}, {15728, 34399}, {53388, 58947}

X(65370) = trilinear pole of line {6, 26690}
X(65370) = X(i)-isoconjugate-of-X(j) for these {i, j}: {244, 53279}, {512, 17189}, {513, 3924}, {649, 3772}, {667, 17861}, {798, 16749}, {1837, 43924}, {3669, 40968}, {3733, 21935}, {4017, 40980}, {6591, 26934}, {62749, 64654}
X(65370) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 3772}, {6631, 17861}, {31998, 16749}, {34961, 40980}, {39026, 3924}, {39054, 17189}
X(65370) = X(i)-cross conjugate of X(j) for these {i, j}: {219, 1016}, {3869, 765}, {5279, 4567}, {38875, 46102}
X(65370) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(98)}}, {{A, B, C, X(643), X(668)}}, {{A, B, C, X(660), X(36050)}}, {{A, B, C, X(1026), X(3705)}}, {{A, B, C, X(1043), X(3699)}}, {{A, B, C, X(3976), X(23703)}}, {{A, B, C, X(4555), X(13138)}}, {{A, B, C, X(4571), X(7256)}}, {{A, B, C, X(17780), X(30144)}}
X(65370) = barycentric product X(i)*X(j) for these (i, j): {100, 59759}, {190, 40436}, {1332, 34406}, {4561, 55994}, {34399, 644}, {42380, 56}, {56003, 668}
X(65370) = barycentric quotient X(i)/X(j) for these (i, j): {99, 16749}, {100, 3772}, {101, 3924}, {109, 36570}, {190, 17861}, {644, 1837}, {662, 17189}, {1018, 21935}, {1252, 53279}, {1331, 26934}, {1332, 41004}, {3939, 40968}, {5546, 40980}, {34399, 24002}, {34406, 17924}, {40436, 514}, {42380, 3596}, {53280, 64654}, {55994, 7649}, {56003, 513}, {56305, 6591}, {59759, 693}

X(65371) = ISOGONAL CONJUGATE OF X(42341)

Barycentrics    a*(a-b)*(a-c)*(a^2+b*(b-c)-a*c)*(a*(b-2*c)+b*(-b+c))*(a^2-a*b+c*(-b+c))*(2*a*b-a*c-b*c+c^2) : :

X(65371) lies on the circumcircle and on these lines: {99, 14727}, {100, 8641}, {101, 48294}, {103, 238}, {106, 51845}, {666, 932}, {667, 934}, {673, 29352}, {840, 9309}, {884, 927}, {1016, 52778}, {1293, 36086}, {1477, 58320}, {2291, 6169}, {2371, 56530}, {2382, 16487}, {2725, 9311}, {2726, 42884}, {2862, 32023}, {7128, 59128}, {8685, 32666}, {8706, 36802}, {9067, 51560}, {9266, 53630}, {9439, 12032}, {26704, 65333}, {32728, 59105}, {32735, 59123}, {36146, 53622}

X(65371) = isogonal conjugate of X(42341)
X(65371) = trilinear pole of line {6, 1633}
X(65371) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42341}, {513, 56714}, {518, 4449}, {649, 40883}, {665, 3729}, {672, 4885}, {918, 9310}, {926, 9312}, {1026, 4014}, {1376, 2254}, {1861, 22091}, {2223, 20907}, {2284, 21139}, {3286, 21052}, {3900, 41355}, {3912, 20980}, {3930, 18199}, {4513, 53544}, {9316, 50333}, {17218, 20683}, {46388, 61413}
X(65371) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 42341}, {5375, 40883}, {39026, 56714}, {45252, 50333}, {62554, 4885}, {62599, 20907}
X(65371) = X(i)-cross conjugate of X(j) for these {i, j}: {3063, 6185}, {4879, 52030}
X(65371) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(57928)}}, {{A, B, C, X(19), X(35157)}}, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(82), X(13136)}}, {{A, B, C, X(660), X(9452)}}, {{A, B, C, X(667), X(884)}}, {{A, B, C, X(1016), X(7128)}}, {{A, B, C, X(4616), X(8750)}}, {{A, B, C, X(31209), X(48294)}}, {{A, B, C, X(32719), X(34443)}}, {{A, B, C, X(32735), X(36802)}}, {{A, B, C, X(36142), X(40412)}}
X(65371) = barycentric product X(i)*X(j) for these (i, j): {105, 30610}, {190, 51845}, {666, 9309}, {6169, 664}, {14727, 6}, {32023, 919}, {34085, 9439}, {36086, 9311}, {51560, 9315}
X(65371) = barycentric quotient X(i)/X(j) for these (i, j): {6, 42341}, {100, 40883}, {101, 56714}, {105, 4885}, {109, 6168}, {673, 20907}, {919, 1376}, {927, 61413}, {1027, 21139}, {1438, 4449}, {1461, 41355}, {6169, 522}, {9309, 918}, {9315, 2254}, {14727, 76}, {18785, 21052}, {30610, 3263}, {32658, 22091}, {32666, 9310}, {32735, 6180}, {36086, 3729}, {36146, 9312}, {43929, 4014}, {51845, 514}, {52927, 4513}, {59101, 61415}, {64216, 20980}

X(65372) = X(108)X(3952)∩X(112)X(644)

Barycentrics    a*(a-b)*(a-c)*(a^3+b^3+a^2*(b-c)+b^2*c+b*c^2+c^3+a*(b^2-c^2))*(a^3+b^3+b^2*c+b*c^2+c^3+a^2*(-b+c)+a*(-b^2+c^2)) : :

X(65372) lies on the circumcircle and on these lines: {105, 5278}, {106, 19861}, {108, 3952}, {110, 4571}, {112, 644}, {190, 13397}, {741, 56045}, {1252, 59134}, {1290, 4756}, {1292, 4427}, {1310, 65313}, {1331, 58967}, {1633, 43348}, {3699, 9058}, {4578, 58991}, {4767, 26711}, {9088, 61226}, {26700, 65191}, {38470, 52923}

X(65372) = trilinear pole of line {6, 3694}
X(65372) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 19785}, {2478, 43924}, {41340, 57200}
X(65372) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 19785}
X(65372) = X(i)-cross conjugate of X(j) for these {i, j}: {7085, 1252}, {8193, 59}, {12514, 765}
X(65372) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(98)}}, {{A, B, C, X(644), X(3952)}}, {{A, B, C, X(1897), X(53652)}}, {{A, B, C, X(8050), X(13138)}}, {{A, B, C, X(17780), X(19861)}}, {{A, B, C, X(36147), X(65227)}}, {{A, B, C, X(53647), X(55185)}}
X(65372) = barycentric product X(i)*X(j) for these (i, j): {190, 56220}, {3952, 56045}
X(65372) = barycentric quotient X(i)/X(j) for these (i, j): {100, 19785}, {644, 2478}, {4574, 41340}, {56045, 7192}, {56220, 514}

X(65373) = TRILINEAR POLE OF LINE {6, 312}

Barycentrics    (a-b)*b*(a-c)*c*(a^3+a^2*c+a*b*c+b^2*(b+c))*(a^3+a^2*b+a*b*c+c^2*(b+c)) : :

X(65373) lies on the circumcircle and on these lines: {101, 646}, {105, 56202}, {106, 58021}, {109, 668}, {110, 7257}, {190, 6010}, {645, 59066}, {727, 987}, {739, 56046}, {741, 1010}, {815, 53338}, {835, 46597}, {874, 1310}, {934, 4572}, {1978, 38470}, {2703, 33948}, {3596, 49128}, {4505, 29143}, {4561, 29055}, {8687, 65229}, {9078, 17522}, {9082, 59353}

X(65373) = trilinear pole of line {6, 312}
X(65373) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 2277}, {667, 986}, {1919, 27184}
X(65373) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 2277}, {6631, 986}, {9296, 27184}
X(65373) = X(i)-cross conjugate of X(j) for these {i, j}: {958, 1016}, {6133, 2}
X(65373) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(98)}}, {{A, B, C, X(75), X(57976)}}, {{A, B, C, X(646), X(668)}}, {{A, B, C, X(670), X(51566)}}, {{A, B, C, X(811), X(18830)}}, {{A, B, C, X(874), X(1010)}}, {{A, B, C, X(4614), X(57959)}}, {{A, B, C, X(4623), X(58135)}}, {{A, B, C, X(37218), X(65280)}}, {{A, B, C, X(53332), X(56248)}}, {{A, B, C, X(53658), X(57950)}}
X(65373) = barycentric product X(i)*X(j) for these (i, j): {190, 58021}, {1978, 987}, {4554, 56202}, {28659, 59015}, {56046, 668}
X(65373) = barycentric quotient X(i)/X(j) for these (i, j): {100, 2277}, {190, 986}, {668, 27184}, {987, 649}, {56046, 513}, {56202, 650}, {58021, 514}, {59015, 604}

X(65374) = X(64)X(102)∩X(84)X(1295)

Barycentrics    a^2*(a-b)*(a-c)*(a^3-a*(b-c)^2+a^2*(-b+c)+(b-c)*(b+c)^2)*(a^3+a^2*(b-c)-a*(b-c)^2-(b-c)*(b+c)^2)*(a^4+b^4+2*b^2*c^2-3*c^4-2*a^2*(b^2-c^2))*(a^4-3*b^4+2*b^2*c^2+c^4+2*a^2*(b^2-c^2)) : :

X(65374) lies on the circumcircle and on these lines: {64, 102}, {84, 1295}, {104, 60799}, {106, 60803}, {107, 65213}, {108, 61229}, {112, 36049}, {189, 41905}, {280, 41904}, {934, 13138}, {972, 2184}, {1073, 2192}, {1294, 39130}, {1297, 2357}, {1433, 41088}, {2370, 56940}, {2732, 11589}, {2734, 56939}, {26701, 52158}, {34168, 56944}, {44327, 59038}, {56235, 58991}

X(65374) = trilinear pole of line {6, 7367}
X(65374) = X(i)-isoconjugate-of-X(j) for these {i, j}: {20, 6129}, {40, 21172}, {108, 55058}, {154, 17896}, {223, 14331}, {610, 14837}, {1249, 64885}, {1394, 8058}, {1817, 6587}, {2360, 17898}, {3194, 8057}, {3213, 57245}, {10397, 44697}, {14298, 18623}, {15905, 59935}, {16596, 57193}, {32714, 55063}, {41082, 58342}, {44696, 57101}
X(65374) = X(i)-Dao conjugate of X(j) for these {i, j}: {14092, 14837}, {14390, 57233}, {38983, 55058}
X(65374) = X(i)-Ceva conjugate of X(j) for these {i, j}: {65224, 40117}
X(65374) = X(i)-cross conjugate of X(j) for these {i, j}: {652, 1073}, {57108, 282}
X(65374) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(98)}}, {{A, B, C, X(522), X(24031)}}, {{A, B, C, X(652), X(55044)}}, {{A, B, C, X(36049), X(61229)}}
X(65374) = barycentric product X(i)*X(j) for these (i, j): {190, 60803}, {253, 36049}, {1073, 65213}, {1301, 56944}, {2357, 44326}, {13138, 2184}, {19611, 40117}, {19614, 65270}, {30457, 53642}, {32652, 57921}, {37141, 44692}, {39130, 46639}, {41087, 53639}, {44327, 64}, {52389, 65224}, {56235, 84}, {60799, 6335}
X(65374) = barycentric quotient X(i)/X(j) for these (i, j): {64, 14837}, {652, 55058}, {1301, 41083}, {1436, 21172}, {1903, 17898}, {2155, 6129}, {2184, 17896}, {2192, 14331}, {2357, 6587}, {8059, 18623}, {13138, 18750}, {14379, 57233}, {19614, 64885}, {30457, 8058}, {32652, 610}, {36049, 20}, {36079, 14256}, {37141, 33673}, {40117, 1895}, {41087, 8057}, {41489, 54239}, {44327, 14615}, {46639, 8822}, {56235, 322}, {57108, 55063}, {60799, 905}, {60803, 514}, {65213, 15466}

X(65375) = ISOGONAL CONJUGATE OF X(4077)

Barycentrics    a^3*(a-b)*(a+b)*(a-c)*(a-b-c)*(a+c) : :

X(65375) lies on these lines: {1, 16599}, {31, 21756}, {35, 40602}, {58, 1066}, {99, 58947}, {100, 58986}, {101, 112}, {109, 110}, {162, 4551}, {163, 692}, {284, 2195}, {516, 23692}, {601, 17104}, {643, 4612}, {662, 3737}, {827, 29052}, {1110, 4557}, {1253, 35192}, {1414, 41353}, {1624, 23067}, {1625, 61202}, {1634, 23189}, {2150, 2175}, {2310, 2341}, {2328, 2342}, {3190, 41503}, {3939, 4587}, {4069, 7259}, {4558, 54353}, {4965, 8300}, {16686, 34079}, {19622, 19624}, {21784, 23861}, {23703, 54442}, {24027, 52610}, {32652, 32661}, {36080, 58951}, {41339, 52949}, {43076, 58974}, {51361, 58337}, {53280, 61200}, {56948, 64739}, {59061, 59079}, {59063, 59067}

X(65375) = isogonal conjugate of X(4077)
X(65375) = trilinear pole of line {41, 212}
X(65375) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4077}, {2, 7178}, {4, 17094}, {7, 523}, {10, 3676}, {11, 4566}, {12, 7192}, {27, 57243}, {34, 14208}, {37, 24002}, {42, 52621}, {56, 850}, {57, 1577}, {65, 693}, {73, 46107}, {75, 4017}, {76, 7180}, {77, 24006}, {85, 661}, {92, 51664}, {99, 1365}, {107, 1367}, {109, 21207}, {115, 4573}, {181, 52619}, {190, 53545}, {210, 59941}, {222, 14618}, {225, 4025}, {226, 514}, {269, 4086}, {273, 656}, {274, 57185}, {278, 525}, {279, 3700}, {304, 55208}, {307, 7649}, {312, 7216}, {313, 43924}, {321, 3669}, {331, 647}, {335, 7212}, {338, 4565}, {348, 2501}, {349, 649}, {512, 6063}, {513, 1441}, {522, 3668}, {553, 31010}, {561, 51641}, {594, 17096}, {604, 20948}, {608, 3267}, {650, 1446}, {651, 16732}, {653, 4466}, {658, 21044}, {664, 3120}, {668, 53540}, {669, 41283}, {670, 61052}, {798, 20567}, {810, 57787}, {903, 30572}, {905, 40149}, {1014, 4036}, {1019, 6358}, {1020, 4858}, {1042, 35519}, {1086, 4552}, {1088, 4041}, {1089, 7203}, {1109, 1414}, {1111, 4551}, {1118, 3265}, {1119, 52355}, {1214, 17924}, {1231, 6591}, {1254, 18155}, {1275, 55195}, {1356, 4609}, {1357, 27808}, {1358, 3952}, {1397, 44173}, {1400, 3261}, {1401, 52618}, {1402, 40495}, {1412, 52623}, {1426, 35518}, {1427, 4391}, {1434, 4024}, {1439, 44426}, {1447, 35352}, {1459, 57809}, {1509, 55197}, {1565, 61178}, {1847, 8611}, {1880, 15413}, {2006, 4707}, {2171, 7199}, {2321, 58817}, {2394, 6357}, {2481, 53551}, {2489, 57918}, {2528, 41284}, {2533, 7249}, {2611, 65292}, {2643, 4625}, {2973, 23067}, {2997, 51658}, {3004, 60086}, {3064, 56382}, {3122, 4572}, {3125, 4554}, {3596, 7250}, {3649, 4608}, {3665, 58784}, {3671, 58860}, {3701, 43932}, {3709, 57792}, {3733, 34388}, {3801, 56358}, {3911, 4049}, {3932, 43930}, {3942, 65207}, {3960, 60091}, {4010, 7233}, {4033, 53538}, {4052, 30719}, {4080, 30725}, {4088, 56783}, {4092, 4616}, {4171, 23062}, {4369, 60245}, {4404, 19604}, {4415, 60482}, {4444, 16609}, {4453, 52383}, {4467, 52382}, {4516, 4569}, {4524, 57880}, {4559, 23989}, {4560, 6354}, {4581, 41003}, {4605, 17197}, {4620, 21131}, {4626, 52335}, {4705, 57785}, {4729, 62528}, {4804, 62784}, {4817, 16603}, {4841, 57826}, {5466, 7181}, {6046, 7253}, {6528, 61058}, {6539, 30724}, {6548, 40663}, {7055, 58757}, {7198, 31065}, {7209, 21834}, {7265, 52374}, {7316, 35522}, {7337, 52617}, {7340, 8029}, {7372, 56849}, {8287, 38340}, {8672, 58008}, {8736, 15419}, {8808, 14837}, {8809, 17898}, {8817, 48403}, {9293, 17085}, {9426, 41287}, {13149, 53560}, {13576, 43042}, {14321, 27818}, {14616, 51663}, {14838, 43682}, {16727, 21859}, {16892, 18097}, {17078, 55238}, {17095, 55236}, {17216, 36127}, {17747, 60581}, {17886, 26700}, {17896, 52384}, {17925, 26942}, {17926, 20618}, {18026, 18210}, {18593, 60074}, {18623, 58759}, {18815, 53527}, {20336, 43923}, {20902, 65232}, {21104, 60229}, {21124, 64984}, {21188, 60249}, {21453, 55282}, {22383, 52575}, {23599, 56255}, {23752, 60041}, {24290, 34018}, {26932, 52607}, {27797, 30722}, {27801, 57181}, {30574, 62723}, {30588, 43052}, {30723, 60267}, {31603, 41501}, {31643, 50330}, {34387, 53321}, {35160, 53558}, {35353, 43037}, {35576, 47656}, {36197, 36838}, {36620, 55285}, {36621, 59589}, {37755, 57215}, {40622, 65236}, {40702, 55242}, {40704, 55261}, {42759, 54953}, {42761, 65331}, {43034, 43665}, {43041, 43534}, {43045, 43673}, {43049, 60265}, {43051, 60244}, {43067, 60321}, {44129, 55234}, {44733, 50457}, {45196, 62749}, {46110, 52373}, {48402, 60076}, {50453, 60085}, {51368, 60584}, {51640, 57806}, {51650, 57915}, {51659, 58026}, {51662, 54121}, {52023, 56322}, {52037, 59935}, {52622, 62192}, {53559, 65289}, {54394, 63220}, {55010, 56320}, {57200, 57807}, {63171, 65100}
X(65375) = X(i)-vertex conjugate of X(j) for these {i, j}: {163, 61197}, {651, 32714}, {1020, 65232}
X(65375) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 850}, {3, 4077}, {11, 21207}, {206, 4017}, {3161, 20948}, {5375, 349}, {5452, 1577}, {6600, 4086}, {6741, 23994}, {11517, 14208}, {22391, 51664}, {31998, 20567}, {32664, 7178}, {34961, 75}, {36033, 17094}, {36830, 85}, {38985, 1367}, {38986, 1365}, {38991, 16732}, {39025, 3120}, {39026, 1441}, {39052, 331}, {39054, 6063}, {39062, 57787}, {40368, 51641}, {40582, 3261}, {40589, 24002}, {40592, 52621}, {40596, 273}, {40599, 52623}, {40602, 693}, {40605, 40495}, {40608, 1109}, {55042, 17886}, {55053, 53545}, {55064, 338}, {55067, 23989}, {55068, 34387}, {56948, 18160}, {62585, 44173}, {62647, 3267}
X(65375) = X(i)-Ceva conjugate of X(j) for these {i, j}: {110, 163}, {1101, 35192}, {4570, 284}, {4636, 5546}, {36034, 1983}
X(65375) = X(i)-cross conjugate of X(j) for these {i, j}: {55, 1110}, {46388, 2311}, {52425, 2149}, {57134, 2328}, {63461, 41}
X(65375) = pole of line {163, 53290} with respect to the circumcircle
X(65375) = pole of line {1631, 4225} with respect to the Kiepert parabola
X(65375) = pole of line {522, 693} with respect to the Stammler hyperbola
X(65375) = pole of line {4456, 20602} with respect to the Yff parabola
X(65375) = pole of line {4077, 23877} with respect to the Wallace hyperbola
X(65375) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(36516)}}, {{A, B, C, X(21), X(4249)}}, {{A, B, C, X(55), X(4557)}}, {{A, B, C, X(100), X(65315)}}, {{A, B, C, X(101), X(906)}}, {{A, B, C, X(109), X(643)}}, {{A, B, C, X(112), X(163)}}, {{A, B, C, X(219), X(52610)}}, {{A, B, C, X(284), X(662)}}, {{A, B, C, X(521), X(9518)}}, {{A, B, C, X(522), X(2878)}}, {{A, B, C, X(644), X(36080)}}, {{A, B, C, X(651), X(36039)}}, {{A, B, C, X(663), X(42670)}}, {{A, B, C, X(919), X(32651)}}, {{A, B, C, X(1036), X(8691)}}, {{A, B, C, X(1415), X(59061)}}, {{A, B, C, X(1576), X(4636)}}, {{A, B, C, X(1946), X(42662)}}, {{A, B, C, X(2293), X(35338)}}, {{A, B, C, X(2335), X(4552)}}, {{A, B, C, X(2773), X(3900)}}, {{A, B, C, X(4041), X(42666)}}, {{A, B, C, X(4069), X(61223)}}, {{A, B, C, X(4183), X(7450)}}, {{A, B, C, X(4551), X(61169)}}, {{A, B, C, X(4569), X(43358)}}, {{A, B, C, X(4614), X(6575)}}, {{A, B, C, X(5075), X(8641)}}, {{A, B, C, X(5549), X(32665)}}, {{A, B, C, X(7257), X(29052)}}, {{A, B, C, X(15455), X(56232)}}, {{A, B, C, X(24019), X(59010)}}, {{A, B, C, X(32666), X(58947)}}, {{A, B, C, X(32714), X(36141)}}, {{A, B, C, X(52927), X(58974)}}, {{A, B, C, X(56269), X(65300)}}, {{A, B, C, X(57134), X(58329)}}, {{A, B, C, X(59067), X(65232)}}
X(65375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {692, 1576, 163}, {35327, 53325, 61197}

X(65376) = X(2)X(3)∩X(52)X(1353)

Barycentrics    4 a^10 - 7 a^8 b^2 - 2 a^6 b^4 + 8 a^4 b^6 - 2 a^2 b^8 - b^10 - 7 a^8 c^2 + 4 a^2 b^6 c^2 + 3 b^8 c^2 - 2 a^6 c^4 - 4 a^2 b^4 c^4 - 2 b^6 c^4 + 8 a^4 c^6 + 4 a^2 b^2 c^6 - 2 b^4 c^6 - 2 a^2 c^8 + 3 b^2 c^8 - c^10 : :

See Kadir Altintas and Francisco Javier García Capitán, euclid 6975.

X(65376) lies on these lines: {2, 3}, {32, 42459}, {52, 1353}, {154, 61607}, {182, 11745}, {184, 31802}, {206, 13346}, {343, 61139}, {389, 21852}, {511, 34774}, {524, 61751}, {569, 19154}, {578, 21850}, {1154, 34750}, {1192, 48905}, {1350, 13562}, {1351, 18925}, {1503, 46730}, {2165, 5023}, {3564, 9833}, {3574, 13394}, {4319, 8144}, {4320, 32047}, {5085, 9815}, {5878, 32602}, {6146, 41588}, {6193, 34380}, {6247, 29012}, {6465, 32177}, {6466, 32178}, {6696, 51756}, {7991, 34712}, {8550, 16625}, {9019, 41589}, {9645, 15171}, {9729, 9969}, {9786, 46264}, {10263, 43595}, {10282, 59553}, {10283, 51696}, {10316, 59657}, {10619, 21969}, {11206, 12164}, {11265, 19117}, {11266, 19116}, {11411, 64033}, {11425, 31670}, {11750, 41587}, {12134, 37478}, {12359, 44407}, {13142, 19467}, {13348, 48881}, {13419, 39884}, {13567, 44829}, {13598, 58550}, {14576, 22401}, {14927, 18913}, {15107, 41482}, {15644, 48874}, {16105, 16163}, {16655, 63425}, {17704, 48892}, {18583, 37476}, {18914, 37489}, {19125, 51212}, {19139, 37498}, {23328, 29323}, {27364, 34449}, {30435, 59649}, {32062, 35240}, {34286, 41766}, {40348, 46200}, {41719, 63702}, {43136, 52223}, {46728, 48876}, {61544, 64037}

X(65377) = CENTER OF HATZIPOLAKIS-MOSES-MORLEY HYPERBOLA

Barycentrics    (Cos[B]*Cos[C/3] - Cos[B/3]*Cos[C])*(Cos[A/3]*(Cot[B] - Cot[C]) + Cos[C/3]*Csc[B] - Cos[B/3]*Csc[C]) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6982.

X(65377) lies on the nine-point circle and these lines: { }

X(65377) = complement of X(65380)

X(65378) = PERSPECTOR OF HATZIPOLAKIS-MOSES-MORLEY HYPERBOLA

Barycentrics    Cos[B/3]*Cot[C]*Csc[B] - Cos[C/3]*Cot[B]*Csc[C] : :

See Antreas Hatzipolakis and Peter Moses, euclid 6982.

X(65378) lies on this line: {230, 231}

X(65378) = crossdifference of every pair of points on line {3, 358}

X(65379) = X(357)X(1136)∩X(10632)X(16871)

Barycentrics    Sin[2*(A - Pi)/3]*Tan[A] : :

See Antreas Hatzipolakis and Peter Moses, euclid 6982.

X(65379) lies on Hatzipolakis-Moses-Morley hyperbola and these lines: {357, 1136}, {10632, 16871}

X(65379) = isogonal conjugate of X(16840)
X(65379) = polar conjugate of the isotomic conjugate of X(7309)
X(65379) = barycentric product X(4)*X(7309)
X(65379) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16840}, {7309, 69}

X(65380) = ANTICOMPLEMENT OF X(65377)

Barycentrics    Sin[A]/(Csc[(B - 2*Pi)/3]*Sin[C] - Csc[(C - 2*Pi)/3]*Sin[B]) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6987.

X(65380) lies on the circumcircle and this line: {2, 65377}

X(65380) = anticomplement of X(65377)
X(65380) = isotomic conjugate of the anticomplement of X(65378)
X(65380) = Collings transform of X(15857)
X(65380) = X(65378)-cross conjugate of X(2)
X(65380) = trilinear pole of line {6, 3604}
X(65380) = barycentric quotient X(65378)/X(65377)

X(65381) = 98TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    (Cot[A] - Cot[B])*(Cot[A] - Cot[C])*(Cos[B/3]*Cot[C]*Csc[B] - Cos[C/3]*Cot[B]*Csc[C]) : :

See Antreas Hatzipolakis and Peter Moses, euclid 6987.

X(65381) lies on the Hatzipolakis-Moses-Morley hyperbola and these lines: {2, 3}, {357, 52522}, {7309, 65379}

X(65382) = TRILINEAR POLE OF LINE {6, 65378}

Barycentrics    1/(Cos[A/3]*(Cot[B]*(-Cot[B] + Cot[w]) + Cot[C]*(-Cot[C] + Cot[w]))*Csc[A] - Cot[A]*(Cos[B/3]*(-Cot[B] + Cot[w])*Csc[B] + Cos[C/3]*(-Cot[C] + Cot[w])*Csc[C])) : :
Barycentrics    a*(b*SB*(a*cos(A/3)+c*cos(C/3))-(S^2+SA*SC)*cos(B/3))*(c*SC*(a*cos(A/3)+b*cos(B/3))-(S^2+SA*SB)*cos(C/3)) : : (César Lozada, Sep 21, 2024)

See Antreas Hatzipolakis and Peter Moses, euclid 6987.

X(65382) lies on the circumcircle, the Hatzipolakis-Moses-Morley hyperbola and this line: {4, 65377}

X(65382) = reflection of X(4) in X(65377)
X(65382) = Collings transform of X(65377)
X(65382) = trilinear pole of line {6, 65378}

X(65383) = 102nd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a+b-c)*(a-b+c)*(5*a+b+c)*(a+3*b+3*c) : :
X(65383) = 2*X(1)-3*X(5558) = X(1)-3*X(18217)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 19/09/2024. (Sep 21, 2024)

X(65383) lies on these lines: {1, 3522}, {2, 3649}, {4, 16006}, {7, 3617}, {8, 5586}, {56, 32633}, {57, 46934}, {65, 3621}, {79, 61985}, {145, 553}, {226, 46931}, {388, 34502}, {1071, 31794}, {1159, 6934}, {1317, 3600}, {1406, 63039}, {1537, 5708}, {3091, 11544}, {3146, 5902}, {3336, 61820}, {3339, 3947}, {3579, 11036}, {3622, 65384}, {3623, 39781}, {3625, 4355}, {3671, 5550}, {3812, 28647}, {3832, 9809}, {4031, 4323}, {4190, 39783}, {4298, 16236}, {4452, 39773}, {4654, 46933}, {4678, 10404}, {5059, 11246}, {5068, 15079}, {5229, 45043}, {5434, 20014}, {5441, 62145}, {5556, 62180}, {7995, 11379}, {9948, 18483}, {10543, 62129}, {11035, 39779}, {12019, 43733}, {12649, 64262}, {15174, 15697}, {15692, 16137}, {15717, 37524}, {16118, 62030}, {16133, 17570}, {18419, 41537}, {24987, 59375}, {30332, 60945}, {30340, 37567}, {30424, 36991}, {31295, 33667}, {32636, 39782}, {36279, 37112}, {37267, 39778}, {37435, 39772}, {39774, 62999}, {39777, 52783}, {39780, 63580}

X(65383) = reflection of X(5558) in X(18217)
X(65383) = crosspoint of X(7) and X(65384)
X(65383) = X(9780)-Dao conjugate of-X(8)
X(65383) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3622, 30711), (65384, 28626)
X(65383) = pole of the the tripolar of X(65384) with respect to the incircle
X(65383) = X(52518)-of-intouch triangle
X(65383) = barycentric product X(9780)*X(65384)
X(65383) = trilinear product X(i)*X(j) for these {i, j}: {3247, 65384}, {3339, 3622}
X(65383) = (X(11246), X(18221))-harmonic conjugate of X(5059)

X(65384) = 103rd TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a+b-c)*(a-b+c)*(5*a+b+c) : :
X(65384) = X(7)+2*X(60939) = X(7)-4*X(60955)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 19/09/2024. (Sep 21, 2024)

X(65384) lies on these lines: {1, 10304}, {2, 7}, {8, 5221}, {30, 938}, {46, 11037}, {56, 4323}, {65, 3241}, {81, 56846}, {89, 52374}, {165, 11038}, {189, 56947}, {241, 5543}, {279, 39980}, {354, 8236}, {376, 942}, {381, 24470}, {388, 26060}, {390, 10980}, {479, 33765}, {519, 3339}, {549, 3487}, {551, 3361}, {950, 15683}, {959, 17114}, {962, 3338}, {982, 4344}, {999, 4345}, {1014, 42028}, {1056, 3654}, {1058, 28198}, {1125, 5586}, {1155, 10578}, {1159, 50824}, {1210, 3839}, {1418, 17080}, {1434, 16711}, {1443, 5256}, {1458, 42042}, {1466, 13587}, {1788, 11237}, {1876, 7714}, {1892, 62975}, {1992, 24471}, {3008, 62794}, {3058, 3474}, {3160, 5228}, {3210, 4460}, {3296, 3579}, {3303, 5558}, {3333, 9785}, {3336, 10056}, {3337, 4295}, {3340, 6049}, {3475, 4995}, {3485, 5298}, {3488, 3534}, {3522, 11518}, {3524, 5703}, {3543, 4292}, {3545, 5704}, {3586, 15640}, {3601, 62063}, {3616, 4640}, {3622, 65383}, {3649, 5550}, {3655, 31794}, {3666, 17092}, {3671, 5265}, {3679, 4298}, {3742, 52653}, {3772, 63576}, {3828, 5290}, {3845, 18541}, {3873, 64146}, {3916, 17561}, {3947, 19876}, {4000, 18625}, {4032, 4740}, {4102, 63164}, {4190, 12536}, {4297, 18221}, {4304, 15697}, {4307, 18193}, {4312, 5274}, {4315, 51093}, {4328, 44303}, {4334, 42043}, {4346, 39595}, {4355, 5261}, {4402, 37683}, {4421, 51099}, {4423, 16133}, {4454, 30567}, {4488, 18743}, {4650, 16020}, {4676, 26112}, {4754, 49730}, {4771, 17490}, {4870, 7288}, {4888, 33795}, {4955, 31225}, {5054, 6147}, {5055, 5714}, {5059, 37723}, {5122, 15698}, {5222, 24608}, {5252, 51072}, {5281, 5542}, {5393, 21169}, {5556, 10896}, {5557, 31452}, {5563, 5734}, {5719, 15693}, {5722, 15682}, {5726, 51069}, {5731, 5902}, {5758, 37612}, {5766, 11575}, {5791, 50727}, {5918, 7671}, {6361, 15170}, {6738, 34628}, {6744, 34638}, {7011, 21503}, {7175, 63108}, {7176, 16834}, {7198, 32098}, {7268, 49543}, {7319, 34648}, {7320, 7991}, {7672, 63994}, {8591, 59815}, {8703, 15934}, {9143, 59817}, {9352, 63168}, {9533, 42309}, {9579, 50687}, {9581, 61985}, {9612, 61936}, {9779, 17728}, {9780, 10404}, {9812, 11238}, {10032, 41549}, {10106, 31145}, {10156, 21168}, {10164, 59372}, {10707, 24465}, {11019, 50865}, {11024, 62858}, {11036, 15692}, {11111, 64664}, {11177, 24472}, {11227, 59418}, {11374, 15702}, {11520, 37267}, {11529, 51705}, {11679, 52709}, {12433, 15681}, {12436, 54398}, {12541, 62832}, {12630, 17784}, {13388, 17805}, {13389, 17802}, {13405, 30340}, {13411, 15708}, {13462, 51103}, {14450, 26129}, {14829, 31995}, {14986, 31162}, {15672, 41547}, {15690, 15935}, {15717, 63274}, {16192, 18217}, {16236, 51096}, {16371, 57283}, {17012, 56848}, {17013, 47057}, {17294, 32003}, {17301, 36640}, {17580, 54422}, {17595, 37631}, {18141, 42033}, {18391, 37006}, {18421, 51071}, {18990, 34627}, {19708, 24929}, {20057, 64963}, {22345, 27654}, {24046, 48870}, {24175, 37681}, {24177, 37666}, {24391, 56999}, {24473, 37544}, {24477, 59412}, {25718, 50129}, {26105, 63975}, {29611, 50052}, {29627, 32007}, {30282, 62059}, {30286, 50801}, {30424, 50802}, {30947, 44446}, {31994, 50095}, {32079, 55937}, {32087, 37655}, {32939, 42032}, {34255, 50043}, {34605, 41824}, {34631, 50193}, {36279, 50810}, {36588, 64984}, {36603, 44794}, {36845, 49719}, {37520, 50068}, {37749, 59819}, {38021, 64124}, {39126, 42034}, {40663, 51068}, {40891, 43040}, {41777, 63052}, {43180, 50829}, {44447, 65112}, {47357, 58560}, {50626, 56155}, {51066, 51782}, {51790, 62002}, {51841, 63059}, {51842, 63058}, {55010, 64592}, {55948, 65045}, {60076, 65022}, {62208, 63583}, {62240, 62695}, {62300, 63057}, {62782, 62812}

X(65384) = X(i)-cross conjugate of-X(j) for these (i, j): (16667, 3622), (65383, 7)
X(65384) = X(650)-isoconjugate of-X(28226)
X(65384) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (109, 28226), (3622, 8), (3986, 2321), (14351, 4521), (16667, 9), (28225, 522), (58138, 663), (65383, 9780)
X(65384) = X(47921)-zayin conjugate of-X(657)
X(65384) = pole of the line {1, 3543} with respect to the circumhyperbola dual of Yff parabola
X(65384) = pole of the line {333, 3161} with respect to the Steiner-Wallace hyperbola
X(65384) = barycentric product X(i)*X(j) for these {i, j}: {7, 3622}, {85, 16667}, {664, 28225}, {1434, 3986}, {4572, 58138}, {28626, 65383}
X(65384) = trilinear product X(i)*X(j) for these {i, j}: {7, 16667}, {57, 3622}, {651, 28225}, {1014, 3986}, {4554, 58138}, {14351, 65173}, {39948, 65383}
X(65384) = trilinear quotient X(i)/X(j) for these (i, j): (651, 28226), (3622, 9), (3986, 210), (14351, 4162), (16667, 55), (28225, 650), (58138, 3063)
X(65384) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 553, 7), (2, 2094, 28610), (2, 3929, 61023), (2, 9965, 17781), (7, 57, 5435), (7, 5435, 5226), (57, 63, 60948), (57, 226, 64142), (57, 553, 2), (57, 4031, 21454), (354, 9778, 8236), (376, 942, 15933), (376, 15933, 4313), (3218, 9776, 5273), (3306, 9965, 18228), (3474, 4860, 10580), (3474, 10580, 30332), (5226, 5435, 31188), (5273, 9776, 60996), (5542, 53056, 5281)

X(65385) = 104th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    (a+b-c)*(a-b+c)*(4*a+b+c)*(2*a+5*b+5*c) : :
X(65385) = 9*X(53620)-7*X(56115)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 19/09/2024. (Sep 21, 2024)

X(65385) lies on these lines: {1, 548}, {7, 11237}, {145, 52783}, {551, 4031}, {553, 1317}, {3626, 34502}, {3649, 3911}, {3982, 51069}, {4114, 4669}, {4298, 39777}, {4315, 39781}, {5183, 63258}, {5252, 5586}, {5265, 15950}, {5434, 16236}, {7178, 39771}, {11552, 40273}, {16006, 16125}

X(65385) = crosspoint of X(7) and X(4031)
X(65385) = X(664)-Ceva conjugate of-X(30722)
X(65385) = X(3828)-Dao conjugate of-X(8)
X(65385) = pole of the line {28209, 30722} with respect to the incircle
X(65385) = intouch-isogonal conjugate-of-X(5049)
X(65385) = X(14483)-of-intouch triangle
X(65385) = barycentric product X(3828)*X(4031)
X(65385) = trilinear quotient X(3828)/X(56115)





leftri  Pairs of triangles with a common inconic: X(65386) - X(65524)  rightri

This preamble and centers X(65386)-X(65524) were contributed by César Eliud Lozada, September 24, 2024.

The following proposition is proved in Macaulay, F.S., Geometrical conics, Cambridge, 1895, pp 241:
Prop. 77: If two triangles are circumscribed to a conic, they are also inscribed to a conic; and conversely.

In the preamble just before X(14713), there were described a set of conics circumscribing some selected pairs of triangles. Then, according to the reciprocal of the previous proposition, all pairs of triangles having a common circumconic also have a common inconic.

Let T=ABC, T'=A'B'C' be two triangles. The cross-triangle of T and T' is defined as the triangle A*B*C*, with A*=BC'∩B'C, B*=CA'∩C'A and C*=AB'∩A'B. Then, by Brianchon theorem, the points A, B, C, A", B", C" lie on a conic if A*, B*, C* are collinear or coincident points, i.e., if A*B*C* is a degenerate triangle. This is the required condition for T and T' to be inscribed in a common conic and, consequently, to be circumscribed to another common conic.

An extensive list of centers of inconics of pairs of triangles can be seen here. For definitions of all triangles listed here, check the Index of triangles referenced in ETC.

underbar

X(65386) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC AND ARIES

Barycentrics    (b^2-c^2)*(3*a^4-2*(b^2+c^2)*a^2+b^4+c^4) : :
X(65386) = X(647)-3*X(45687) = 3*X(647)-X(47126) = X(669)+3*X(11123) = X(6563)-3*X(11123) = 9*X(9168)-X(44445) = 3*X(10190)-X(23301)

X(65386) lies on these lines: {22, 669}, {25, 65393}, {230, 231}, {351, 33294}, {525, 5027}, {550, 1499}, {804, 3265}, {826, 41300}, {850, 9131}, {1368, 10190}, {1632, 18020}, {1649, 31279}, {1658, 5926}, {2799, 8651}, {3566, 6333}, {3800, 50549}, {4108, 41298}, {7667, 25423}, {8644, 50548}, {9009, 17710}, {9134, 31277}, {9168, 16063}, {10154, 45317}, {10278, 14341}, {15647, 36739}, {30476, 55122}, {31296, 50552}, {36900, 50545}, {39533, 44960}, {44267, 62507}, {45689, 58882}

X(65386) = midpoint of X(i) and X(j) for these (i, j): {647, 50553}, {669, 6563}, {3265, 6562}, {5926, 8151}, {31296, 50552}, {46953, 57154}, {47128, 55280}
X(65386) = reflection of X(i) in X(j) for these (i, j): (2501, 44451), (6587, 58766)
X(65386) = complement of the isotomic conjugate of X(42297)
X(65386) = cross-difference of every pair of points on the line X(3)X(3981)
X(65386) = crosspoint of X(i) and X(j) for these {i, j}: {2, 42297}, {99, 9307}
X(65386) = crosssum of X(512) and X(9306)
X(65386) = X(i)-complementary conjugate of-X(j) for these (i, j): (42297, 2887), (42407, 21253), (56004, 8287)
X(65386) = X(16925)-reciprocal conjugate of-X(99)
X(65386) = center of the inconic with perspector X(42297)
X(65386) = perspector of the circumconic through X(4) and X(16925)
X(65386) = inverse of X(6587) in Kiepert parabola
X(65386) = pole of the line {7840, 44442} with respect to the anticomplementary circle
X(65386) = pole of the line {25, 317} with respect to the circumcircle
X(65386) = pole of the line {36207, 44438} with respect to the 2nd Droz-Farny circle
X(65386) = pole of the line {427, 44377} with respect to the nine-point circle
X(65386) = pole of the line {4, 7891} with respect to the orthoptic circle of Steiner inellipse
X(65386) = pole of the line {7396, 7779} with respect to the power circles radical circle
X(65386) = pole of the line {2450, 3566} with respect to the Kiepert parabola
X(65386) = pole of the line {155, 1613} with respect to the MacBeath circumconic
X(65386) = pole of the line {193, 3552} with respect to the Steiner circumellipse
X(65386) = pole of the line {6, 6393} with respect to the Steiner inellipse
X(65386) = pole of the line {4563, 53371} with respect to the Steiner-Wallace hyperbola
X(65386) = barycentric product X(523)*X(16925)
X(65386) = trilinear product X(661)*X(16925)
X(65386) = trilinear quotient X(16925)/X(662)
X(65386) = X(65393)-of-Ara triangle
X(65386) = (X(669), X(11123))-harmonic conjugate of X(6563)

X(65387) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC AND 1st SCHIFFLER

Barycentrics    2*a^6-5*(b+c)*a^5+10*b*c*a^4+(b+c)*(8*b^2-13*b*c+8*c^2)*a^3-4*(b^2+3*b*c+c^2)*(b-c)^2*a^2-(b^2-c^2)*(b-c)*(3*b^2-5*b*c+3*c^2)*a+2*(b^2-c^2)^2*(b-c)^2 : :

X(65387) lies on these lines: {1, 7504}, {2, 18412}, {11, 3748}, {498, 10176}, {1621, 30852}, {3085, 3884}, {3295, 40259}, {3452, 6690}, {3742, 65388}, {3814, 13411}, {3878, 15865}, {5330, 51784}, {5703, 37702}, {6853, 12432}, {8070, 63259}, {10039, 15862}, {10175, 37730}, {10954, 51111}, {11374, 31870}, {18977, 52793}

X(65387) = complement of the isotomic conjugate of X(42321)
X(65387) = crosspoint of X(2) and X(42321)
X(65387) = X(42321)-complementary conjugate of-X(2887)
X(65387) = center of the inconic with perspector X(42321)
X(65387) = pole of the the tripolar of X(42321) with respect to the Steiner inellipse

X(65388) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC AND 2nd SCHIFFLER

Barycentrics    2*a^6-3*(b+c)*a^5-2*(2*b^2-7*b*c+2*c^2)*a^4+(b+c)*(8*b^2-17*b*c+8*c^2)*a^3-16*(b-c)^2*b*c*a^2-(b^2-c^2)*(b-c)*(5*b^2-13*b*c+5*c^2)*a+2*(b^2-c^2)^2*(b-c)^2 : :

X(65388) lies on these lines: {1, 58453}, {2, 14740}, {11, 516}, {63, 31272}, {80, 5704}, {100, 31224}, {119, 64124}, {214, 1210}, {499, 3878}, {938, 64012}, {1387, 11362}, {1737, 15863}, {2802, 3086}, {3035, 11019}, {3333, 64008}, {3452, 6667}, {3742, 65387}, {3817, 24465}, {5083, 17728}, {5265, 64145}, {5435, 34789}, {6702, 8666}, {6738, 34123}, {10072, 50841}, {10090, 35976}, {11715, 15325}, {12611, 34753}, {12915, 58663}, {13405, 31235}, {14217, 47743}, {15558, 24914}, {16174, 40256}, {21620, 58421}, {31837, 34126}, {37704, 64136}, {38205, 61002}, {38752, 46681}, {38760, 63999}, {44675, 64137}, {58591, 64157}, {63975, 64155}

X(65388) = complement of the isotomic conjugate of X(42324)
X(65388) = crosspoint of X(2) and X(42324)
X(65388) = X(42324)-complementary conjugate of-X(2887)
X(65388) = center of the inconic with perspector X(42324)
X(65388) = pole of the the tripolar of X(42324) with respect to the Steiner inellipse
X(65388) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (11, 3911, 46684), (499, 12736, 32557)

X(65389) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND CIRCUMMEDIAL

Barycentrics    (b^2-c^2)*(5*a^8-11*(b^2+c^2)*a^6+(7*b^4+12*b^2*c^2+7*c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2-2*(b^2-c^2)^2*b^2*c^2) : :

X(65389) lies on these lines: {2, 65434}, {3, 23878}, {4, 647}, {5, 44560}, {20, 36900}, {30, 47247}, {140, 30476}, {186, 47254}, {389, 54269}, {523, 37934}, {550, 30209}, {631, 31174}, {850, 3523}, {3522, 31296}, {3533, 31277}, {8550, 8675}, {8704, 65419}, {10295, 47250}, {11623, 62489}, {15412, 42658}, {15644, 54272}, {15717, 63786}, {16619, 47442}, {18925, 54268}, {31072, 61834}, {39469, 65425}, {46983, 47339}, {47003, 47248}, {47122, 64790}, {47261, 47338}, {52585, 65403}

X(65389) = midpoint of X(i) and X(j) for these (i, j): {10295, 47250}, {15412, 42658}, {47003, 47248}
X(65389) = anticomplement of X(65434)
X(65389) = cross-difference of every pair of points on the line X(852)X(52703)
X(65389) = X(65434)-Dao conjugate of-X(65434)
X(65389) = perspector of the circumconic through X(57732) and X(60193)
X(65389) = pole of the line {232, 15302} with respect to the orthoptic circle of Steiner inellipse
X(65389) = pole of the line {3545, 64781} with respect to the polar circle

X(65390) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND CIRCUMSYMMEDIAL

Barycentrics    a^2*(b^2-c^2)*(3*a^6-5*(b^2+c^2)*a^4+(b^4+c^4)*a^2+(b^2+c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(65390) = 3*X(647)-4*X(65418) = 3*X(5926)-2*X(65418) = 3*X(8644)-2*X(11615) = 3*X(8644)-4*X(65422)

X(65390) lies on these lines: {3, 512}, {4, 4108}, {39, 65425}, {523, 62438}, {631, 5996}, {647, 5926}, {669, 30209}, {850, 64789}, {1499, 3265}, {2485, 39214}, {2799, 65419}, {3800, 42658}, {5188, 8704}, {6756, 16229}, {7404, 44918}, {7405, 34964}, {7487, 14618}, {8644, 11615}, {14417, 65436}, {23285, 32472}, {31277, 39511}

X(65390) = reflection of X(i) in X(j) for these (i, j): (647, 5926), (2485, 39214), (11615, 65422)
X(65390) = cross-difference of every pair of points on the line X(230)X(40126)
X(65390) = perspector of the circumconic through X(2987) and X(62926)
X(65390) = pole of the line {511, 9813} with respect to the circumcircle
X(65390) = (X(11615), X(65422))-harmonic conjugate of X(8644)

X(65391) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND 3rd MIXTILINEAR

Barycentrics    a*(b-c)*(3*a^5-3*(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2-(b^4+c^4-2*b*c*(b^2-3*b*c+c^2))*a+(b^2-c^2)*(b-c)^3) : :

X(65391) lies on these lines: {4, 47815}, {5, 48561}, {35, 59977}, {36, 3669}, {40, 3309}, {517, 48329}, {631, 47819}, {667, 11249}, {905, 44805}, {1385, 48346}, {1842, 39536}, {2526, 44824}, {2814, 4401}, {3803, 28473}, {4162, 5697}, {4905, 58887}, {6362, 65392}, {28537, 50517}, {38327, 48018}, {39225, 51648}

X(65391) = midpoint of X(40) and X(48111)
X(65391) = reflection of X(i) in X(j) for these (i, j): (905, 44805), (2526, 44824), (3669, 39227), (48018, 38327), (48346, 1385), (51648, 39225)
X(65391) = pole of the line {518, 3149} with respect to the Bevan circle
X(65391) = pole of the line {8279, 11248} with respect to the circumcircle

X(65392) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND 4th MIXTILINEAR

Barycentrics    a*(b-c)*(3*a^5-3*(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+2*(b+c)^3*a^2-(b^4+c^4+6*b*c*(b^2+b*c+c^2))*a+(b^2-c^2)^2*(b+c)) : :

X(65392) lies on these lines: {3, 6182}, {35, 650}, {40, 14077}, {1938, 37585}, {6362, 65391}, {8760, 11248}, {9366, 37562}, {9373, 35448}, {32195, 54255}

X(65392) = X(65436)-of-excentral triangle, when ABC is acute
X(65392) = X(65419)-of-1st circumperp triangle, when ABC is acute

X(65393) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ANTI-ARA AND 2nd HYACINTH

Barycentrics    (b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6+(b^2+c^2)*a^4-3*(b^4+c^4)*a^2+(b^2+c^2)*(b^4+c^4)) : :

X(65393) lies on these lines: {25, 65386}, {427, 2501}, {523, 65394}, {546, 39533}, {1499, 13488}, {1995, 6563}, {2489, 50548}, {3265, 47206}, {3566, 13400}, {5159, 14341}, {12077, 16229}, {13487, 44931}, {17994, 33294}, {47217, 65154}

X(65393) = cross-difference of every pair of points on the line X(23115)X(52077)
X(65393) = pole of the line {25, 317} with respect to the incircle-of-orthic triangle
X(65393) = pole of the line {3542, 21445} with respect to the orthoptic circle of Steiner inellipse
X(65393) = pole of the line {385, 1370} with respect to the polar circle
X(65393) = pole of the line {297, 315} with respect to the orthic inconic
X(65393) = X(65386)-of-anti-Ara triangle

X(65394) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ANTI-ARA AND ORTHIC AXES

Barycentrics    (b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6-(b^2+c^2)*a^4+b^2*c^2*a^2+b^2*c^2*(b^2+c^2)) : :

X(65394) lies on these lines: {4, 3005}, {523, 65393}, {647, 16229}, {669, 14618}, {804, 2501}, {850, 47206}, {2797, 3265}, {5064, 45333}, {6995, 58784}, {17994, 31296}, {23290, 53263}, {47217, 62489}, {50545, 59932}

X(65394) = reflection of X(65455) in X(16229)
X(65394) = cross-difference of every pair of points on the line X(6638)X(23115)
X(65394) = perspector of the circumconic through X(43710) and X(52583)
X(65394) = pole of the line {25, 183} with respect to the incircle-of-orthic triangle
X(65394) = pole of the line {1370, 3164} with respect to the polar circle
X(65394) = pole of the line {83, 458} with respect to the orthic inconic

X(65395) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ANTI-ARA AND PELLETIER

Barycentrics    (b-c)*(2*a^9-(b+c)*a^8-4*(b^2-c^2)^2*a^5+2*(b^2-c^2)^2*(b+c)*a^4-4*(b^2-c^2)*(b-c)*b^2*c^2*a^2+2*(b^4-c^4)^2*a-(b^4-c^4)^2*(b+c)) : :

X(65395) lies on these lines: {11, 244}, {523, 65393}

X(65395) = cross-difference of every pair of points on the line X(101)X(23115)
X(65395) = perspector of the circumconic through X(514) and X(52583)
X(65395) = pole of the line {25, 2968} with respect to the incircle-of-orthic triangle
X(65395) = pole of the line {1370, 1897} with respect to the polar circle
X(65395) = pole of the line {1146, 2207} with respect to the orthic inconic

X(65396) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ANTI-ARA AND SCHRÖETER

Barycentrics    (b^2-c^2)*(a^12-(2*b^4-3*b^2*c^2+2*c^4)*a^8+(b^4+c^4)*(b^2-c^2)^2*a^4-(b^4-c^4)^2*b^2*c^2) : :

X(65396) lies on these lines: {115, 804}, {523, 65393}, {59900, 65403}

X(65396) = cross-difference of every pair of points on the line X(1634)X(23115)
X(65396) = X(54080)-reciprocal conjugate of-X(4558)
X(65396) = perspector of the circumconic through X(52583) and X(58784)
X(65396) = pole of the line {25, 339} with respect to the incircle-of-orthic triangle
X(65396) = pole of the line {1370, 41676} with respect to the polar circle
X(65396) = pole of the line {338, 2207} with respect to the orthic inconic
X(65396) = barycentric product X(14618)*X(54080)
X(65396) = trilinear product X(24006)*X(54080)
X(65396) = trilinear quotient X(54080)/X(4575)

X(65397) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL AND MIDARC

Barycentrics    -(b-c)*(-a+b+c)*(a-3*b-3*c)*((b+c)*a-(b-c)^2)*sin(A/2)-(a-b+c)*(c*a^3+(3*b^2-5*c^2)*a^2-(b-c)*(4*b^2+7*b*c+7*c^2)*a+(b^2-c^2)*(b-c)*(b-3*c))*sin(B/2)+(a+b-c)*(b*a^3-(5*b^2-3*c^2)*a^2+(b-c)*(7*b^2+7*b*c+4*c^2)*a+(b^2-c^2)*(b-c)*(-3*b+c))*sin(C/2)-(b-c)*(a-3*b-3*c)*(a+b-c)*(a-b+c)*(-a+b+c) : :

As a conic with center in the infinity, it is a parabola.

X(65397) lies on these lines: {30, 511}, {13301, 47695}

X(65398) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL AND 2nd MIDARC

Barycentrics    (-a+b+c)*(2*a^4-(b^2-10*b*c+c^2)*a^2-(b^2-c^2)^2)*sin(A/2)+(2*a^3+(2*b-3*c)*a^2+(b+2*c)*(b+c)*a+(b+c)*(b^2-c^2))*(a-b+c)^2*sin(B/2)+(2*a^3-(3*b-2*c)*a^2+(b+c)*(2*b+c)*a-(b+c)*(b^2-c^2))*(a+b-c)^2*sin(C/2) : :
X(65398) = 3*X(1)-X(31769) = 3*X(5434)+X(8422) = 3*X(5434)-X(31735) = X(7354)+3*X(11234) = 3*X(11234)-X(31770) = 3*X(31734)+X(31769) = 2*X(31734)+X(65476) = 2*X(31769)-3*X(65476)

X(65398) lies on these lines: {1, 31734}, {388, 12614}, {516, 65454}, {999, 12622}, {1056, 12523}, {3487, 55176}, {3600, 12518}, {4292, 31767}, {4355, 11528}, {5434, 8422}, {5571, 10106}, {7354, 11234}, {12577, 58616}, {18990, 32183}, {21620, 55172}

X(65398) = midpoint of X(i) and X(j) for these (i, j): {1, 31734}, {4292, 31767}, {5571, 10106}, {7354, 31770}, {8422, 31735}, {18990, 32183}
X(65398) = reflection of X(i) in X(j) for these (i, j): (58616, 12577), (65476, 1)
X(65398) = X(31728)-of-incircle-circles triangle, when ABC is acute
X(65398) = X(31734)-of-anti-Aquila triangle
X(65398) = X(65399)-of-Hutson intouch triangle, when ABC is acute
X(65398) = X(65423)-of-intouch triangle, when ABC is acute
X(65398) = X(65435)-of-Ursa-minor triangle, when ABC is acute
X(65398) = X(65476)-of-5th mixtilinear triangle
X(65398) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (5434, 8422, 31735), (7354, 11234, 31770)

X(65399) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP AND 2nd CIRCUMPERP

Barycentrics    a^2*((b^2+c^2)*a^3+(b+c)*(b^2+c^2)*a^2-(b^2+c^2)^2*a-(b^3+c^3)*(b^2+b*c+c^2)) : :
X(65399) = X(1)+3*X(2979) = 3*X(3)-X(31728) = X(10)-3*X(3917) = 3*X(10)-X(16980) = 3*X(1125)-2*X(58469) = 3*X(2979)-X(31737) = 3*X(3576)+X(11412) = 3*X(3576)-X(31732) = 9*X(3917)-X(16980) = X(31728)+3*X(31738) = 2*X(31728)-3*X(65423) = 2*X(31738)+X(65423) = 3*X(31757)-4*X(58469)

X(65399) lies on these lines: {1, 2979}, {2, 58474}, {3, 31728}, {4, 65435}, {8, 33884}, {10, 3917}, {30, 31751}, {51, 19862}, {52, 10165}, {58, 3792}, {72, 23156}, {140, 31760}, {404, 62352}, {511, 1125}, {515, 1216}, {516, 15644}, {517, 10627}, {518, 23157}, {519, 64573}, {535, 22299}, {595, 7186}, {674, 3881}, {758, 11573}, {942, 63370}, {946, 10625}, {960, 2392}, {978, 50593}, {1071, 31817}, {1154, 13624}, {1350, 49553}, {1385, 6101}, {1469, 30142}, {1698, 7998}, {1699, 64050}, {2475, 38474}, {2807, 12512}, {3056, 30148}, {3060, 3624}, {3313, 49511}, {3576, 11412}, {3579, 54042}, {3616, 62188}, {3634, 3819}, {3650, 58893}, {3678, 8679}, {3817, 45186}, {3822, 37536}, {3828, 23841}, {3833, 58493}, {3840, 50601}, {3916, 56894}, {4067, 23154}, {4297, 5562}, {5044, 9037}, {5045, 9047}, {5248, 37482}, {5267, 22076}, {5447, 6684}, {5482, 58404}, {5550, 62187}, {5587, 7999}, {5640, 34595}, {5650, 51073}, {5691, 11444}, {5886, 37484}, {5889, 7987}, {5891, 31673}, {5904, 23155}, {5907, 28164}, {5943, 19878}, {6102, 17502}, {6681, 34466}, {7485, 16473}, {8185, 15066}, {8227, 64051}, {9587, 15080}, {9798, 62217}, {9955, 13391}, {9956, 32142}, {10110, 10171}, {10263, 11230}, {10574, 58221}, {11365, 33878}, {11574, 34379}, {11591, 28160}, {11793, 19925}, {12571, 13598}, {12699, 13340}, {12702, 54047}, {14963, 22065}, {15049, 25917}, {15060, 33697}, {15067, 18480}, {18357, 44324}, {18481, 23039}, {19872, 44299}, {19883, 21969}, {20470, 48928}, {20718, 64538}, {21334, 36250}, {22060, 35468}, {25639, 50362}, {28146, 63414}, {28168, 45959}, {30116, 50630}, {31819, 33574}, {35242, 54041}, {37607, 41329}, {50597, 59301}, {50625, 64709}, {51103, 58535}, {58441, 58487}

X(65399) = midpoint of X(i) and X(j) for these (i, j): {1, 31737}, {3, 31738}, {72, 23156}, {946, 10625}, {1071, 31817}, {1385, 6101}, {3313, 49511}, {4067, 23154}, {4297, 5562}, {11412, 31732}
X(65399) = reflection of X(i) in X(j) for these (i, j): (4, 65435), (6684, 5447), (9956, 32142), (12512, 13348), (13598, 12571), (19925, 11793), (31752, 1216), (31757, 1125), (31760, 140), (65423, 3)
X(65399) = anticomplement of X(58474)
X(65399) = X(58474)-Dao conjugate of-X(58474)
X(65399) = pole of the line {14008, 29631} with respect to the Stammler hyperbola
X(65399) = X(31737)-of-anti-Aquila triangle
X(65399) = X(31738)-of-anti-X3-ABC reflections triangle
X(65399) = X(65398)-of-anti-Hutson intouch triangle
X(65399) = X(65423)-of-ABC-X3 reflections triangle
X(65399) = X(65435)-of-anti-Euler triangle
X(65399) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 2979, 31737), (3576, 11412, 31732), (50597, 64006, 59301)

X(65400) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP AND CIRCUMSYMMEDIAL

Barycentrics    a^2*(2*(b^4+c^4)*a^4-(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^2-2*b^4*c^4) : :

X(65400) lies on these lines: {538, 4173}, {2387, 3934}, {3491, 7849}, {5167, 7861}, {5876, 17710}, {6310, 32457}, {6683, 40951}, {7780, 63554}, {7843, 41262}, {9292, 47101}, {13207, 15031}, {14962, 63569}, {31239, 61727}, {32450, 55005}, {40344, 52042}

X(65400) = reflection of X(40951) in X(6683)

X(65401) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP AND INNER-CONWAY

Barycentrics    a*(b-c)*(a^4-(b+c)*a^3+2*b*c*a^2-(b+c)*(b^2+c^2)*a+b^4+c^4) : :
X(65401) = 3*X(2)-4*X(65410)

X(65401) lies on these lines: {2, 2520}, {512, 6333}, {513, 4468}, {1734, 46383}, {2473, 44435}, {3888, 54110}, {4131, 6182}, {6139, 26641}, {9256, 50505}

X(65401) = reflection of X(2520) in X(65410)
X(65401) = anticomplement of X(2520)
X(65401) = cross-difference of every pair of points on the line X(16502)X(42295)
X(65401) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (34409, 33650), (37741, 39351), (54968, 5906), (55965, 37781), (56005, 4440)
X(65401) = X(2520)-Dao conjugate of-X(2520)
X(65401) = perspector of the circumconic through X(30701) and X(42407)
X(65401) = pole of the line {1851, 41762} with respect to the polar circle
X(65401) = pole of the line {346, 3926} with respect to the Steiner circumellipse
X(65401) = pole of the line {3788, 17279} with respect to the Steiner inellipse
X(65401) = (X(2520), X(65410))-harmonic conjugate of X(2)

X(65402) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd ANTI-CONWAY AND MIDHEIGHT

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6+6*(b^2+c^2)*b^2*c^2*a^4+2*(b^4-3*b^2*c^2+c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(65402) = 3*X(51)+X(1899) = 3*X(51)-X(64820) = 3*X(3060)+X(12058) = 3*X(5943)-X(9306)

X(65402) lies on these lines: {4, 51}, {5, 46363}, {6, 1196}, {154, 21313}, {343, 11793}, {373, 11427}, {511, 1368}, {542, 11746}, {578, 10601}, {800, 6638}, {1503, 58483}, {1619, 17810}, {3060, 7396}, {3819, 26958}, {3917, 37643}, {4232, 34750}, {5462, 9825}, {5640, 7398}, {5644, 11426}, {6353, 6467}, {6677, 34382}, {6688, 23292}, {6776, 44079}, {6803, 45011}, {8550, 45979}, {9729, 12241}, {9786, 13598}, {9969, 15583}, {10192, 32366}, {11245, 44084}, {11430, 43650}, {11432, 18451}, {11438, 21312}, {11451, 63030}, {12283, 62979}, {12294, 23291}, {13346, 45045}, {13754, 44920}, {15606, 41586}, {15887, 41589}, {16836, 61113}, {19161, 21849}, {21971, 51170}, {23158, 59707}, {23841, 44547}, {32068, 58480}, {32284, 59553}, {43130, 44489}, {44479, 61646}, {46737, 58471}

X(65402) = midpoint of X(i) and X(j) for these (i, j): {389, 18390}, {1899, 64820}
X(65402) = cross-difference of every pair of points on the line X(3566)X(32320)
X(65402) = crosssum of X(3) and X(6677)
X(65402) = perspector of the circumconic through X(3565) and X(15352)
X(65402) = pole of the line {53, 1368} with respect to the Kiepert circumhyperbola
X(65402) = pole of the line {193, 1092} with respect to the Stammler hyperbola
X(65402) = pole of the line {2489, 52585} with respect to the Steiner inellipse
X(65402) = pole of the line {3964, 57518} with respect to the Steiner-Wallace hyperbola
X(65402) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (51, 1899, 64820), (51, 11433, 389), (5020, 52077, 9306), (5020, 61666, 14913), (5943, 14913, 5020), (6688, 44495, 23292), (11746, 58550, 58470), (26958, 50649, 3819)

X(65403) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd ANTI-CONWAY AND ORTHIC AXES

Barycentrics    (b^2-c^2)*(a^8-2*(b^2+c^2)*a^6+(b^4+3*b^2*c^2+c^4)*a^4-(b^2-c^2)^2*b^2*c^2) : :

As a conic with center in the infinity, it is a parabola. Its focus is X(65500).

X(65403) lies on these lines: {3, 18314}, {4, 15412}, {5, 27363}, {30, 511}, {74, 32439}, {134, 48318}, {578, 58308}, {647, 16229}, {850, 22089}, {2394, 54664}, {6130, 14618}, {14592, 18570}, {15543, 35885}, {23286, 23290}, {39228, 44818}, {42405, 57635}, {45259, 51513}, {52585, 65389}, {54003, 61196}, {59900, 65396}

X(65403) = isogonal conjugate of X(1303)
X(65403) = cross-difference of every pair of points on the line X(6)X(6638)
X(65403) = crosspoint of X(i) and X(j) for these {i, j}: {4, 52779}, {99, 40448}, {107, 57408}
X(65403) = crosssum of X(i) and X(j) for these {i, j}: {3, 58305}, {389, 512}, {520, 3819}, {525, 34850}, {6368, 21243}, {39469, 52128}
X(65403) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1303, 8), (9251, 3448), (9290, 21294)
X(65403) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4, 130), (42405, 6)
X(65403) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 130), (1303, 10), (9251, 125), (9290, 21253), (57686, 34846)
X(65403) = X(130)-cross conjugate of-X(27359)
X(65403) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 9290), (125, 57686), (244, 9251), (15526, 57855), (42293, 17434)
X(65403) = X(53175)-hirst inverse of-X(60036)
X(65403) = X(i)-isoconjugate of-X(j) for these {i, j}: {110, 9251}, {162, 57686}, {163, 9290}, {32676, 57855}
X(65403) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (130, 17434), (436, 648), (523, 9290), (525, 57855), (647, 57686), (661, 9251), (1954, 662), (1970, 110), (8754, 62520), (9252, 811), (9291, 6331), (16813, 57635), (21449, 18831), (27359, 35360), (42331, 76), (42405, 57759), (56290, 99), (62521, 2052)
X(65403) = X(i)-vertex conjugate of-X(j) for these {i, j}: {3, 32428}, {57635, 57635}
X(65403) = ideal of tripolar of X(i) for these i: {436, 21449, 43710, 56290}
X(65403) = pedal antipodal perspector of X(1303)
X(65403) = perspector of the circumconic through X(2) and X(436)
X(65403) = barycentric product X(i)*X(j) for these {i, j}: {6, 42331}, {130, 42405}, {394, 62521}, {436, 525}, {523, 56290}, {647, 9291}, {656, 9252}, {850, 1970}, {1577, 1954}, {2970, 62522}, {6368, 21449}, {27359, 62428}
X(65403) = trilinear product X(i)*X(j) for these {i, j}: {31, 42331}, {255, 62521}, {436, 656}, {523, 1954}, {647, 9252}, {661, 56290}, {810, 9291}, {1577, 1970}
X(65403) = trilinear quotient X(i)/X(j) for these (i, j): (436, 162), (523, 9251), (656, 57686), (1577, 9290), (1954, 110), (1970, 163), (9252, 648), (9291, 811), (14208, 57855), (21449, 65221), (42331, 75), (56290, 662), (62521, 158)

X(65404) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ANTI-HUTSON INTOUCH AND HEXYL

Barycentrics    a*(2*a^6-3*(b+c)*a^5-3*(b^2+c^2)*a^4+2*(b+c)*(3*b^2-4*b*c+3*c^2)*a^3+8*b^2*c^2*a^2-(b^2-c^2)*(b-c)*(3*b^2-2*b*c+3*c^2)*a+(b^4-c^4)*(b^2-c^2)) : :
X(65404) = X(1012)-3*X(3576) = X(1709)-5*X(7987) = X(1709)-3*X(16370) = 3*X(3576)+X(50528) = 3*X(5731)+X(6925) = 5*X(7987)-3*X(16370)

X(65404) lies on these lines: {1, 1427}, {3, 960}, {4, 3838}, {10, 64804}, {20, 1836}, {21, 12688}, {30, 551}, {36, 10167}, {40, 4421}, {55, 64150}, {56, 10391}, {65, 411}, {72, 59320}, {78, 5584}, {103, 8691}, {104, 63432}, {165, 5440}, {214, 38759}, {354, 18444}, {376, 28534}, {392, 15931}, {405, 63988}, {497, 1319}, {515, 2886}, {516, 8255}, {517, 25439}, {518, 3428}, {944, 11260}, {950, 64127}, {953, 2691}, {958, 1490}, {962, 10385}, {971, 993}, {999, 5572}, {1001, 1012}, {1006, 15254}, {1064, 1386}, {1071, 11012}, {1125, 8727}, {1214, 45272}, {1376, 30503}, {1420, 64679}, {1709, 7987}, {1727, 59319}, {1768, 33598}, {1837, 6838}, {1854, 54320}, {1859, 37258}, {2287, 59079}, {2550, 54051}, {2883, 37836}, {2951, 53054}, {2975, 12680}, {3149, 3812}, {3486, 37421}, {3522, 44447}, {3579, 14988}, {3601, 12565}, {3612, 37022}, {3616, 10431}, {3649, 64003}, {3651, 14110}, {3683, 37106}, {3689, 59417}, {3740, 5720}, {3742, 18443}, {3753, 44425}, {3916, 15071}, {4189, 9961}, {4300, 37539}, {4325, 16152}, {4511, 7411}, {4662, 17857}, {4679, 6992}, {4881, 54348}, {4999, 6245}, {5010, 17613}, {5087, 6827}, {5217, 63985}, {5248, 9856}, {5251, 5927}, {5267, 34862}, {5302, 5777}, {5327, 7415}, {5536, 24473}, {5538, 41853}, {5603, 42819}, {5691, 17532}, {5730, 59340}, {5787, 26363}, {5794, 6908}, {5806, 30143}, {5836, 11500}, {5880, 50701}, {5884, 37623}, {5886, 13151}, {5918, 6909}, {6260, 57288}, {6282, 11495}, {6326, 7688}, {6675, 12617}, {6796, 15813}, {6831, 31936}, {6836, 11375}, {6840, 17605}, {6865, 25681}, {6868, 64119}, {6872, 12679}, {6876, 64021}, {6914, 13624}, {6923, 18481}, {6924, 40296}, {6960, 17606}, {6962, 24914}, {6974, 54445}, {6985, 7686}, {6986, 25917}, {6987, 24703}, {6988, 26066}, {7508, 17502}, {7957, 34772}, {7971, 10268}, {8071, 64132}, {8273, 19861}, {8715, 31798}, {8726, 25524}, {9614, 21842}, {9799, 30478}, {9960, 15823}, {10165, 64705}, {10176, 31658}, {10267, 45776}, {10404, 64079}, {10860, 30282}, {10902, 12672}, {11014, 33895}, {11111, 64130}, {11194, 63430}, {11235, 50811}, {11249, 12675}, {11362, 64116}, {12114, 41854}, {12511, 22836}, {12608, 31789}, {12609, 20420}, {12616, 52265}, {12699, 24299}, {12711, 37583}, {13369, 26286}, {13374, 37615}, {14100, 62873}, {14828, 62385}, {15569, 30265}, {16209, 19537}, {16418, 54370}, {16788, 44424}, {17044, 18589}, {17647, 37424}, {17768, 63438}, {19541, 54318}, {19843, 64144}, {21077, 31799}, {22770, 34791}, {22935, 46684}, {24036, 64121}, {24316, 64902}, {24474, 33858}, {24541, 64707}, {24806, 51361}, {24928, 63999}, {25440, 31787}, {26446, 64335}, {27385, 50031}, {28629, 50700}, {30271, 63423}, {30389, 41860}, {31445, 31803}, {31786, 40257}, {32214, 34773}, {35239, 37700}, {37420, 60681}, {37426, 63391}, {37564, 64704}, {37571, 64005}, {37585, 37733}, {37606, 43178}, {37620, 53292}, {37979, 41722}, {41003, 64700}, {41541, 64189}, {43175, 63993}, {44547, 59317}, {50242, 52860}, {53252, 63439}, {57282, 64075}, {58679, 63986}, {59345, 63962}, {59421, 63211}

X(65404) = midpoint of X(i) and X(j) for these (i, j): {1, 7580}, {20, 1836}, {55, 64150}, {1012, 50528}, {3428, 18446}, {6923, 18481}
X(65404) = reflection of X(i) in X(j) for these (i, j): (4, 3838), (4640, 3), (6914, 13624), (8727, 1125), (10391, 58567)
X(65404) = X(21)-beth conjugate of-X(1427)
X(65404) = pole of the line {22760, 62864} with respect to the Feuerbach circumhyperbola
X(65404) = X(343)-of-2nd circumperp triangle, when ABC is acute
X(65404) = X(3838)-of-anti-Euler triangle
X(65404) = X(4640)-of-ABC-X3 reflections triangle
X(65404) = X(7580)-of-anti-Aquila triangle
X(65404) = X(10391)-of-2nd circumperp tangential triangle
X(65404) = X(23292)-of-hexyl triangle, when ABC is acute
X(65404) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 6261, 960), (3, 9943, 64128), (3, 12520, 9943), (3, 37837, 59691), (40, 33597, 56176), (56, 10884, 58567), (78, 5584, 58637), (946, 1385, 51715), (1709, 7987, 16370), (3576, 5732, 63991), (3576, 50528, 1012), (3576, 63992, 1001), (3601, 12565, 64074), (3651, 21740, 14110), (4297, 51717, 1385), (5918, 37600, 6909), (11012, 16132, 1071), (18443, 22753, 3742), (30503, 52026, 1376), (51695, 51721, 51715)

X(65405) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND EXCENTRAL

Barycentrics    a*(2*a^4-5*(b+c)*a^3+(3*b^2+4*b*c+3*c^2)*a^2+(b^2-c^2)*(b-c)*a-(b^2+c^2)*(b-c)^2) : :
X(65405) = X(7)-9*X(64108) = X(9)+3*X(165) = 3*X(9)+X(2951) = 5*X(9)-X(3062) = 3*X(9)-X(16112) = X(20)+3*X(38057) = X(40)+3*X(21153) = 3*X(40)+X(43166) = 9*X(165)-X(2951) = 3*X(165)-X(11495) = 9*X(165)+X(16112) = 5*X(2951)+3*X(3062) = X(2951)-3*X(11495) = 11*X(2951)-3*X(58834) = X(3062)+5*X(11495) = 3*X(3062)-5*X(16112) = 2*X(3579)+X(15254) = 3*X(11231)-X(18482) = 3*X(11495)+X(16112) = 11*X(11495)-X(58834)

X(65405) lies on these lines: {2, 7964}, {3, 518}, {5, 516}, {7, 1155}, {9, 165}, {10, 63413}, {11, 61016}, {20, 5302}, {35, 5728}, {37, 9441}, {40, 1001}, {44, 1742}, {45, 1721}, {46, 954}, {55, 1445}, {57, 58563}, {63, 480}, {71, 56715}, {100, 3059}, {142, 6690}, {210, 7411}, {220, 56380}, {226, 59476}, {241, 1253}, {354, 2346}, {390, 1788}, {497, 62775}, {517, 42819}, {527, 43151}, {528, 10265}, {549, 20330}, {692, 65416}, {958, 37551}, {960, 5584}, {971, 6796}, {991, 4663}, {1100, 54474}, {1158, 64156}, {1212, 5527}, {1385, 15570}, {1386, 13329}, {1389, 14110}, {1418, 9440}, {1698, 52835}, {1754, 4682}, {1836, 60943}, {2283, 22079}, {2550, 6836}, {2646, 7672}, {2801, 33814}, {2938, 50198}, {3057, 7677}, {3174, 4421}, {3219, 5918}, {3243, 7987}, {3246, 61086}, {3358, 11500}, {3359, 42843}, {3474, 8232}, {3522, 5686}, {3523, 38053}, {3555, 35202}, {3576, 42871}, {3651, 58638}, {3683, 9778}, {3689, 34784}, {3742, 41338}, {3748, 11025}, {3751, 50677}, {3817, 61001}, {3916, 5223}, {4297, 24393}, {4312, 37572}, {4326, 35445}, {4335, 17601}, {4343, 4689}, {4413, 60958}, {4422, 21629}, {4428, 7994}, {4698, 48900}, {4995, 60932}, {5010, 18412}, {5044, 12511}, {5119, 42884}, {5128, 12560}, {5217, 7675}, {5220, 5732}, {5281, 60939}, {5432, 21617}, {5493, 38059}, {5537, 10177}, {5542, 37582}, {5657, 43161}, {5698, 6838}, {5735, 31425}, {5759, 5880}, {5762, 64113}, {5779, 43178}, {5836, 59340}, {5851, 6594}, {5852, 43177}, {5853, 43174}, {6067, 59491}, {6173, 63268}, {6211, 30271}, {6244, 8257}, {6326, 7688}, {6361, 38037}, {6745, 61003}, {6870, 40333}, {6947, 13528}, {6986, 7957}, {7674, 24477}, {7676, 14100}, {7991, 38316}, {8255, 52819}, {8273, 34791}, {8543, 63206}, {8544, 60909}, {8545, 63212}, {9352, 62778}, {9355, 15492}, {9446, 10509}, {9588, 38200}, {9943, 55104}, {10434, 35892}, {11038, 15717}, {11246, 41857}, {11362, 43175}, {11526, 34471}, {12512, 31445}, {12616, 61524}, {12669, 37105}, {12702, 38031}, {12755, 41541}, {13405, 60945}, {15185, 15931}, {15298, 58887}, {15299, 59316}, {15692, 51099}, {15733, 60994}, {16503, 18788}, {16814, 64134}, {16842, 63469}, {16885, 64741}, {17243, 28849}, {17332, 59688}, {17348, 28850}, {17351, 59620}, {17605, 61017}, {17706, 43179}, {18481, 38126}, {19541, 58451}, {20195, 63974}, {21168, 63971}, {21734, 62827}, {22277, 50658}, {22937, 64198}, {24309, 64125}, {24929, 30329}, {25557, 37623}, {26062, 52653}, {29007, 30295}, {29181, 35203}, {30284, 37600}, {30330, 31508}, {30379, 60919}, {30503, 44663}, {31423, 38150}, {31730, 38130}, {31786, 33895}, {34628, 38097}, {34632, 38025}, {34638, 38101}, {35986, 63961}, {36002, 61686}, {36706, 38047}, {36976, 61019}, {37364, 64443}, {37524, 59372}, {38122, 60895}, {40659, 58651}, {41430, 64121}, {42885, 59333}, {47375, 60990}, {50808, 60986}, {50829, 60999}, {50835, 62063}, {51090, 59675}, {53056, 60955}, {54370, 59381}, {56288, 64723}, {58433, 58441}, {58678, 61005}, {59320, 59691}, {59389, 64005}, {60910, 60947}, {60933, 64698}, {60937, 63207}, {60979, 61035}, {61013, 61648}, {61122, 64077}, {64154, 64189}

X(65405) = midpoint of X(i) and X(j) for these (i, j): {9, 11495}, {10, 63413}, {40, 1001}, {1158, 64156}, {2951, 16112}, {3358, 11500}, {3579, 31658}, {4297, 24393}, {5220, 5732}, {5759, 5880}, {5779, 43178}, {6244, 8257}, {6594, 46684}, {6600, 60974}, {11362, 43175}, {31730, 63970}, {43182, 60942}, {50808, 60986}
X(65405) = reflection of X(i) in X(j) for these (i, j): (3826, 6684), (15254, 31658), (15481, 60912), (15570, 1385), (42356, 6666), (42819, 52769), (60999, 50829), (65426, 3), (65452, 58433), (65466, 58634)
X(65405) = X(i)-zayin conjugate of-X(j) for these (i, j): (6608, 513), (58635, 40)
X(65405) = pole of the line {7671, 29007} with respect to the Feuerbach circumhyperbola
X(65405) = pole of the line {4130, 24562} with respect to the Steiner inellipse
X(65405) = X(141)-of-1st circumperp triangle, when ABC is acute
X(65405) = X(3589)-of-excentral triangle, when ABC is acute
X(65405) = X(5572)-of-anti-Mandart-incircle triangle
X(65405) = X(34573)-of-6th mixtilinear triangle, when ABC is acute
X(65405) = X(44882)-of-2nd circumperp triangle, when ABC is acute
X(65405) = X(64195)-of-2nd Zaniah triangle, when ABC is acute
X(65405) = X(65426)-of-ABC-X3 reflections triangle
X(65405) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 58637, 56176), (9, 165, 11495), (9, 1376, 58634), (9, 2951, 16112), (40, 21153, 1001), (55, 1445, 5572), (100, 60970, 3059), (241, 1253, 30621), (1155, 15837, 7), (2346, 60948, 354), (5217, 41712, 7675), (6986, 7957, 51715), (7676, 37787, 14100), (7688, 64107, 65404), (11495, 16112, 2951), (14100, 63211, 7676), (29007, 30295, 31391), (31730, 38130, 63970), (58441, 65452, 58433)

X(65406) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND MIDHEIGHT

Barycentrics    a^2*(b^2-c^2)*(a^8-2*(b^2+c^2)*a^6+2*(b^4+4*b^2*c^2+c^4)*a^4-2*(b^2+c^2)^3*a^2+b^8+6*b^4*c^4+c^8) : :

X(65406) lies on these lines: {512, 65407}, {520, 6587}, {647, 2422}, {924, 44451}, {21243, 30476}

X(65406) = complement of the complementary conjugate of X(53569)
X(65406) = cross-difference of every pair of points on the line X(1498)X(1513)
X(65406) = X(i)-complementary conjugate of-X(j) for these (i, j): (34405, 34846), (56004, 16595), (56307, 16573), (56364, 16592)
X(65406) = perspector of the circumconic through X(3346) and X(6339)
X(65406) = pole of the line {393, 3926} with respect to the Steiner inellipse

X(65407) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND MOSES-SODDY

Barycentrics    (b-c)*(2*a^5-(b+c)*a^4-4*(b^2+c^2)*a^3+2*(b+c)*(3*b^2-4*b*c+3*c^2)*a^2+2*(b^2+c^2)^2*a-(b+c)*(b^2+c^2)^2) : :

X(65407) lies on these lines: {2, 65486}, {11, 244}, {512, 65406}

X(65407) = complement of X(65486)
X(65407) = cross-difference of every pair of points on the line X(101)X(1611)
X(65407) = perspector of the circumconic through X(514) and X(6339)
X(65407) = pole of the line {20999, 37491} with respect to the circumcircle
X(65407) = pole of the line {1086, 3926} with respect to the Steiner inellipse

X(65408) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND SCHRÖETER

Barycentrics    (b^2-c^2)*(2*a^6-5*(b^2+c^2)*a^4+8*(b^4+c^4)*a^2-(b^2+c^2)^3) : :
X(65408) = X(6333)+3*X(34290)

X(65408) lies on these lines: {2, 65484}, {115, 125}, {512, 65406}, {3566, 14341}, {3620, 57087}, {6333, 34290}, {14417, 63733}

X(65408) = complement of X(65484)
X(65408) = cross-difference of every pair of points on the line X(110)X(1611)
X(65408) = X(i)-complementary conjugate of-X(j) for these (i, j): (8769, 36472), (8773, 5139), (36051, 15525), (36105, 63612), (38252, 55152)
X(65408) = perspector of the circumconic through X(523) and X(6339)
X(65408) = pole of the line {7669, 37491} with respect to the circumcircle
X(65408) = pole of the line {98, 20080} with respect to the orthoptic circle of Steiner inellipse
X(65408) = pole of the line {523, 15525} with respect to the Kiepert circumhyperbola
X(65408) = pole of the line {148, 54097} with respect to the Steiner circumellipse
X(65408) = pole of the line {115, 2996} with respect to the Steiner inellipse
X(65408) = X(58882)-of-1st Brocard triangle

X(65409) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND 1st ZANIAH

Barycentrics    a*(b-c)*(a^5-2*(b+c)*a^4+(b^2+6*b*c+c^2)*a^3+(b^2-c^2)*(b-c)*a^2-2*(b^4+c^4+2*b*c*(b^2+c^2))*a+(b+c)*(b^2+c^2)^2) : :

X(65409) lies on these lines: {2, 65445}, {512, 65406}, {514, 12447}, {663, 3126}, {3452, 59903}, {3741, 17072}, {3900, 7658}

X(65409) = complement of X(65445)
X(65409) = cross-difference of every pair of points on the line X(1611)X(1615)
X(65409) = X(i)-complementary conjugate of-X(j) for these (i, j): (34399, 124), (40436, 5514), (52775, 24005), (54948, 63840), (56003, 13609)
X(65409) = perspector of the circumconic through X(6339) and X(42483)
X(65409) = pole of the line {279, 3926} with respect to the Steiner inellipse

X(65410) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND 2nd ZANIAH

Barycentrics    a*(b-c)*(a^4-(b+c)*a^3+4*b*c*a^2-(b+c)^3*a+(b^2+c^2)^2) : :
X(65410) = 3*X(2)+X(65401)

X(65410) lies on these lines: {2, 2520}, {512, 65406}, {513, 2490}, {514, 2473}, {649, 3126}, {4131, 4524}, {4932, 17072}, {6139, 24562}, {8641, 25900}, {15584, 46396}

X(65410) = midpoint of X(i) and X(j) for these (i, j): {2520, 65401}, {4131, 4524}
X(65410) = complement of X(2520)
X(65410) = cross-difference of every pair of points on the line X(1611)X(1616)
X(65410) = X(i)-complementary conjugate of-X(j) for these (i, j): (34409, 124), (37741, 1146), (52776, 24005), (54968, 63840), (55965, 26932), (56005, 1086)
X(65410) = perspector of the circumconic through X(6339) and X(6553)
X(65410) = pole of the line {346, 3926} with respect to the Steiner inellipse
X(65410) = (X(2), X(65401))-harmonic conjugate of X(2520)

X(65411) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: BCE-INCENTERS AND TANGENTIAL-MIDARC

Barycentrics    a*(-2*(-a+b+c)*(b-c)*(a+b-c)*(a-b+c)+(-a+b+c)*(b-c)*(a^2-4*(b+c)*a+3*b^2-2*b*c+3*c^2)*sin(A/2)+(a-b+c)*((3*b-2*c)*a^2-2*(2*b^2+b*c-2*c^2)*a+(b-c)*(b^2-b*c+2*c^2))*sin(B/2)+(a+b-c)*((2*b-3*c)*a^2-2*(2*b^2-b*c-2*c^2)*a+(b-c)*(2*b^2-b*c+c^2))*sin(C/2)) : :

As a conic with center in the infinity, it is a parabola. Its focus is X(10215).

X(65411) lies on these lines: {30, 511}, {505, 45087}, {2254, 13301}, {8076, 10231}, {10496, 55363}

X(65411) = isogonal conjugate of X(10496)
X(65411) = circumtangential-isogonal conjugate of X(10496)
X(65411) = circumnormal-isogonal conjugate of the isogonal conjugate of X(55174)
X(65411) = cross-difference of every pair of points on the line X(6)X(7707)
X(65411) = crosspoint of X(7) and X(45875)
X(65411) = crosssum of X(55) and X(45877)
X(65411) = X(7025)-aleph conjugate of-X(20114)
X(65411) = X(10496)-anticomplementary conjugate of-X(8)
X(65411) = X(55363)-Ceva conjugate of-X(1)
X(65411) = X(10496)-complementary conjugate of-X(10)
X(65411) = X(3)-vertex conjugate of-X(55174)
X(65411) = X(i)-zayin conjugate of-X(j) for these (i, j): (6728, 8075), (10495, 164), (45878, 503)
X(65411) = pedal antipodal perspector of X(10496)

X(65412) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND MOSES-SODDY

Barycentrics    (b-c)*(3*a^3+(b+c)*a^2-(3*b^2-2*b*c+3*c^2)*a-(b^2-c^2)*(b-c)) : :
X(65412) = X(650)+3*X(30724) = 3*X(1638)+X(3669) = 3*X(1638)-X(14837) = 9*X(1638)-X(21120) = 3*X(3669)+X(21120) = X(3960)+2*X(59612)

X(65412) lies on these lines: {241, 514}, {522, 14353}, {1519, 1769}, {2487, 8712}, {3239, 47795}, {3309, 52596}, {3737, 28225}, {4025, 47796}, {4091, 58817}, {4453, 6332}, {4560, 21183}, {4765, 4978}, {4801, 47785}, {4962, 44409}, {8058, 51648}, {20317, 44902}, {28161, 59750}, {28529, 44314}, {43932, 64885}, {47757, 48144}, {47758, 48131}, {47800, 48151}, {47820, 48015}, {47981, 48580}, {47995, 48570}, {48121, 48574}, {48136, 48245}, {48149, 48554}

X(65412) = midpoint of X(i) and X(j) for these (i, j): {905, 3676}, {3669, 14837}, {3960, 21188}, {4765, 4978}, {7658, 30723}, {10015, 30719}, {21172, 23800}
X(65412) = reflection of X(21188) in X(59612)
X(65412) = crosspoint of X(658) and X(1440)
X(65412) = crosssum of X(657) and X(7074)
X(65412) = X(i)-Dao conjugate of-X(j) for these (i, j): (11, 36629), (1015, 38271), (1146, 36624)
X(65412) = X(i)-isoconjugate of-X(j) for these {i, j}: {101, 38271}, {109, 36629}, {1415, 36624}
X(65412) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (513, 38271), (522, 36624), (650, 36629), (9965, 190), (15803, 100), (21866, 1018), (23072, 1331), (27383, 3699), (37519, 101), (65414, 10)
X(65412) = X(65159)-zayin conjugate of-X(657)
X(65412) = perspector of the circumconic through X(7) and X(9965)
X(65412) = pole of the line {7, 1210} with respect to the incircle
X(65412) = pole of the line {614, 44431} with respect to the orthoptic circle of Steiner inellipse
X(65412) = pole of the line {281, 3950} with respect to the polar circle
X(65412) = pole of the line {9709, 17355} with respect to the Spieker circle
X(65412) = pole of the line {11, 3942} with respect to the circumhyperbola dual of Yff parabola
X(65412) = pole of the line {145, 4292} with respect to the Steiner circumellipse
X(65412) = pole of the line {1, 6904} with respect to the Steiner inellipse
X(65412) = barycentric product X(i)*X(j) for these {i, j}: {86, 65414}, {514, 9965}, {693, 15803}, {3261, 37519}, {3676, 27383}, {7199, 21866}, {23072, 46107}
X(65412) = trilinear product X(i)*X(j) for these {i, j}: {81, 65414}, {513, 9965}, {514, 15803}, {693, 37519}, {3669, 27383}, {7192, 21866}, {17924, 23072}
X(65412) = trilinear quotient X(i)/X(j) for these (i, j): (514, 38271), (522, 36629), (4391, 36624), (9965, 100), (15803, 101), (21866, 4557), (23072, 906), (27383, 644), (37519, 692)
X(65412) = (X(1638), X(3669))-harmonic conjugate of X(14837)

X(65413) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND PELLETIER

Barycentrics    a*(b-c)*(a^4-2*(b^2+3*b*c+c^2)*a^2+4*(b+c)*b*c*a+(b^2+4*b*c+c^2)*(b-c)^2) : :

X(65413) lies on these lines: {513, 2473}, {514, 40137}, {521, 4885}, {650, 58324}, {661, 905}, {1538, 3309}, {1638, 46389}, {2526, 21189}, {2999, 23792}, {3063, 28042}, {3676, 14298}, {3798, 30198}, {3887, 59752}, {4524, 14077}, {4940, 23806}, {10015, 48398}, {14300, 46919}, {14353, 53551}, {21188, 64885}, {21195, 48049}, {25924, 57055}, {27417, 57167}, {41800, 48554}, {43049, 46393}, {43932, 59612}

X(65413) = midpoint of X(3676) and X(14298)
X(65413) = reflection of X(43932) in X(59612)
X(65413) = X(60107)-complementary conjugate of-X(124)
X(65413) = perspector of the circumconic through X(969) and X(56043)
X(65413) = pole of the line {7274, 10980} with respect to the incircle
X(65413) = pole of the line {1441, 3672} with respect to the Steiner inellipse

X(65414) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND SCHRÖETER

Barycentrics    (b^2-c^2)*(3*a^3+(b+c)*a^2-(3*b^2-2*b*c+3*c^2)*a-(b^2-c^2)*(b-c)) : :
X(65414) = X(656)+3*X(2457) = 3*X(656)+X(23752) = 3*X(2457)-X(7178) = 9*X(2457)-X(23752) = X(4017)+3*X(30574) = 3*X(7178)-X(23752) = X(53527)+2*X(65494)

X(65414) lies on these lines: {513, 14837}, {521, 21188}, {523, 656}, {650, 2523}, {676, 15313}, {900, 7649}, {918, 20316}, {1459, 1638}, {1769, 14284}, {2487, 3733}, {2773, 59875}, {3737, 41800}, {3910, 47843}, {4453, 20293}, {4707, 52355}, {4843, 30591}, {5957, 59974}, {6362, 50350}, {6366, 51648}, {6587, 14321}, {8674, 39540}, {10015, 23800}, {21120, 50354}, {25009, 50357}, {28209, 46385}, {30724, 48342}, {34958, 35057}, {48283, 57108}

X(65414) = midpoint of X(i) and X(j) for these (i, j): {656, 7178}, {4707, 52355}, {7649, 7655}, {10015, 23800}, {21120, 50354}
X(65414) = reflection of X(i) in X(j) for these (i, j): (3733, 2487), (14321, 31946), (21121, 7657)
X(65414) = cross-difference of every pair of points on the line X(284)X(2256)
X(65414) = crosspoint of X(4566) and X(8808)
X(65414) = X(i)-Dao conjugate of-X(j) for these (i, j): (244, 38271), (6741, 36624), (55064, 36629)
X(65414) = X(i)-isoconjugate of-X(j) for these {i, j}: {110, 38271}, {4565, 36629}
X(65414) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (661, 38271), (3700, 36624), (4041, 36629), (9965, 99), (15803, 662), (21866, 100), (23072, 4558), (27383, 645), (37519, 110), (65412, 86)
X(65414) = perspector of the circumconic through X(226) and X(3296)
X(65414) = pole of the line {3333, 3649} with respect to the incircle
X(65414) = pole of the line {3142, 5230} with respect to the nine-point circle
X(65414) = pole of the line {29, 145} with respect to the polar circle
X(65414) = pole of the line {18210, 21044} with respect to the Kiepert circumhyperbola
X(65414) = pole of the line {281, 1901} with respect to the orthic inconic
X(65414) = pole of the line {16777, 17056} with respect to the Steiner inellipse
X(65414) = barycentric product X(i)*X(j) for these {i, j}: {10, 65412}, {523, 9965}, {693, 21866}, {850, 37519}, {1577, 15803}, {7178, 27383}, {14618, 23072}
X(65414) = trilinear product X(i)*X(j) for these {i, j}: {37, 65412}, {514, 21866}, {523, 15803}, {661, 9965}, {1577, 37519}, {4017, 27383}, {23072, 24006}
X(65414) = trilinear quotient X(i)/X(j) for these (i, j): (523, 38271), (3700, 36629), (4086, 36624), (9965, 662), (15803, 110), (21866, 101), (23072, 4575), (27383, 643), (37519, 163)
X(65414) = (X(656), X(2457))-harmonic conjugate of X(7178)

X(65415) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND SODDY

Barycentrics    (a+b-c)*(a-b+c)*(4*a^3-(b+c)*a^2-2*(b^2+c^2)*a-(b^2-c^2)*(b-c)) : :

X(65415) lies on these lines: {1, 15006}, {6, 1323}, {7, 33633}, {9, 2124}, {71, 63203}, {77, 142}, {223, 3452}, {226, 1029}, {269, 3946}, {279, 1449}, {282, 32446}, {307, 63782}, {347, 527}, {348, 3686}, {514, 59644}, {579, 34497}, {604, 52563}, {610, 2391}, {651, 52405}, {664, 2321}, {1100, 10481}, {1214, 5325}, {1418, 50114}, {1443, 60992}, {2323, 34028}, {3247, 62705}, {3663, 6610}, {3668, 4667}, {3669, 40590}, {3755, 5018}, {4007, 25718}, {4296, 12437}, {5745, 18623}, {5750, 9312}, {5837, 15832}, {5882, 32047}, {6666, 54425}, {6692, 36636}, {7177, 54420}, {10164, 59613}, {16668, 43186}, {16884, 58816}, {17014, 60955}, {17086, 50092}, {18163, 62192}, {18624, 25525}, {22464, 60962}, {25723, 26125}, {28015, 63208}, {28079, 47444}, {34059, 40942}, {36640, 60933}, {39126, 50109}, {40869, 56309}, {40937, 43064}, {43182, 59458}, {53994, 62388}, {59611, 59687}, {60982, 62997}

X(65415) = midpoint of X(347) and X(1419)
X(65415) = cevapoint of X(2124) and X(47057)
X(65415) = pole of the line {3337, 15299} with respect to the circumhyperbola dual of Yff parabola
X(65415) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (77, 43035, 142), (269, 3946, 61022), (279, 1449, 60945), (54425, 59215, 6666)

X(65416) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND TANGENTIAL

Barycentrics    a*(2*a^4+(b+c)*a^3-3*(b^2+c^2)*a^2-(b^2-c^2)*(b-c)*a+(b^2+c^2)*(b-c)^2) : :

X(65416) lies on these lines: {1, 37273}, {2, 54008}, {3, 12335}, {48, 241}, {57, 37519}, {77, 198}, {141, 37836}, {142, 1385}, {214, 21255}, {223, 11212}, {269, 24328}, {515, 21239}, {573, 6510}, {610, 59215}, {692, 65405}, {910, 18161}, {1214, 1630}, {1229, 17136}, {1319, 4000}, {1386, 16679}, {1418, 18162}, {1442, 2262}, {2178, 24471}, {2267, 25067}, {2347, 51653}, {2646, 4648}, {3207, 7289}, {3946, 24928}, {4361, 11260}, {4640, 9306}, {4851, 56176}, {4859, 21842}, {5440, 17296}, {5942, 61693}, {6505, 11350}, {6706, 25523}, {7011, 46330}, {9259, 28022}, {11712, 41430}, {12610, 17043}, {14557, 47057}, {15624, 30621}, {16453, 64722}, {16578, 64121}, {16608, 51775}, {17044, 18589}, {17073, 37837}, {17221, 20905}, {17306, 17614}, {18261, 25405}, {18634, 33597}, {20206, 40555}, {20818, 60974}, {23585, 40590}, {25930, 54322}, {28639, 34830}, {36016, 52385}, {37269, 45126}, {42819, 62383}

X(65416) = midpoint of X(77) and X(198)
X(65416) = reflection of X(21239) in X(58412)
X(65416) = complement of X(54008)
X(65416) = crosspoint of X(2) and X(34411)
X(65416) = X(34411)-complementary conjugate of-X(2887)
X(65416) = center of the inconic with perspector X(34411)
X(65416) = pole of the the tripolar of X(34411) with respect to the Steiner inellipse
X(65416) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (141, 59693, 59691), (1442, 11349, 2262)

X(65417) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd BROCARD AND 7th BROCARD

Barycentrics    2*a^6-2*(b^2+c^2)*a^4-(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2) : :

X(65417) lies on these lines: {2, 60280}, {4, 5034}, {6, 382}, {30, 5052}, {32, 46264}, {39, 1503}, {69, 7781}, {110, 59768}, {115, 182}, {141, 7863}, {187, 44882}, {193, 7802}, {511, 7756}, {542, 1569}, {543, 18906}, {574, 1352}, {597, 39563}, {611, 9651}, {613, 9664}, {626, 12215}, {732, 7826}, {754, 32451}, {1351, 44526}, {1353, 5107}, {1506, 3818}, {1570, 8550}, {1571, 39885}, {1691, 7755}, {1692, 5254}, {2076, 48892}, {2458, 12203}, {2549, 2794}, {3070, 48742}, {3071, 48743}, {3410, 38862}, {3564, 32152}, {3589, 39565}, {3618, 7902}, {3767, 5033}, {3787, 7667}, {3815, 39884}, {4045, 43449}, {4048, 7820}, {5007, 64196}, {5013, 18440}, {5017, 6781}, {5024, 48662}, {5026, 51848}, {5038, 19130}, {5050, 44518}, {5085, 7746}, {5092, 7749}, {5097, 53505}, {5104, 48885}, {5116, 11646}, {5207, 7764}, {5309, 40825}, {5355, 53499}, {5475, 36990}, {5965, 44453}, {6388, 18911}, {7737, 14927}, {7738, 9873}, {7739, 64014}, {7753, 11645}, {7790, 39141}, {7810, 14994}, {7890, 41622}, {9597, 39900}, {9598, 39901}, {9830, 10007}, {10329, 21243}, {10516, 31455}, {11173, 48872}, {11179, 11648}, {12017, 13881}, {12588, 31451}, {13330, 29317}, {14810, 15993}, {14901, 32233}, {18362, 38064}, {18583, 53419}, {19124, 27371}, {20977, 61712}, {29323, 44500}, {31415, 51537}, {31448, 39891}, {33878, 44519}, {35301, 37803}, {35387, 38738}, {35902, 61755}, {37648, 40350}, {38110, 63534}, {43457, 48889}, {43619, 51212}, {44535, 55682}, {44541, 55629}, {48873, 63043}

X(65417) = midpoint of X(i) and X(j) for these (i, j): {193, 7802}, {9873, 39874}
X(65417) = reflection of X(i) in X(j) for these (i, j): (69, 7830), (7747, 6), (7890, 41622)
X(65417) = pole of the line {525, 52591} with respect to the Moses circle
X(65417) = pole of the line {632, 13334} with respect to the Evans conic
X(65417) = pole of the line {546, 50774} with respect to the Kiepert circumhyperbola
X(65417) = pole of the line {19687, 50771} with respect to the Steiner-Wallace hyperbola
X(65417) = X(7750)-of-1st Brocard triangle
X(65417) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2549, 6776, 5028), (3094, 32429, 1569), (3767, 25406, 5033), (3818, 50659, 1506), (5017, 48898, 6781), (5028, 6776, 5477), (5092, 53475, 7749), (5116, 11646, 24206), (5254, 48906, 1692), (48889, 53484, 43457)

X(65418) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMMEDIAL AND CIRCUMNORMAL

Barycentrics    a^2*(b^2-c^2)*(3*a^6-7*(b^2+c^2)*a^4+(5*b^4+3*b^2*c^2+5*c^4)*a^2-b^6-c^6) : :
X(65418) = X(3)+3*X(351) = X(3)-3*X(9126) = 7*X(3)-3*X(61776) = 3*X(351)-X(11615) = 7*X(351)+X(61776) = 5*X(631)+3*X(9147) = 5*X(631)-3*X(16235) = 5*X(631)-X(62433) = 3*X(647)+X(65390) = 3*X(5926)-X(65390) = X(8151)-3*X(45687) = 3*X(9126)+X(11615) = 7*X(9126)-X(61776) = 3*X(9147)+X(62433) = 7*X(11615)+3*X(61776) = 3*X(16235)-X(62433) = 3*X(45687)+X(62438)

X(65418) lies on these lines: {3, 351}, {5, 11176}, {20, 19912}, {24, 47230}, {140, 804}, {512, 65422}, {575, 9023}, {576, 9188}, {631, 9147}, {632, 45689}, {647, 5926}, {686, 19357}, {1499, 8651}, {2492, 11616}, {2793, 44820}, {2799, 32204}, {2869, 14271}, {3517, 17994}, {3525, 53365}, {3526, 9148}, {3566, 45856}, {4155, 58382}, {6088, 11621}, {6132, 9517}, {6140, 39477}, {6642, 44817}, {7907, 13306}, {8151, 45687}, {8552, 53263}, {8644, 32231}, {8704, 65420}, {9123, 16220}, {9125, 32228}, {9138, 15034}, {9213, 37953}, {10279, 55122}, {10280, 44564}, {11620, 62506}, {12105, 20403}, {14094, 19902}, {19901, 38675}, {21731, 44810}, {22105, 44813}, {23236, 36255}, {24978, 57154}, {34351, 64920}, {34952, 63830}, {38327, 58380}, {39227, 42653}, {39501, 44814}, {39511, 64789}, {47442, 62507}, {61138, 62177}

X(65418) = midpoint of X(i) and X(j) for these (i, j): {3, 11615}, {351, 9126}, {647, 5926}, {2492, 11616}, {6132, 14270}, {6140, 39477}, {8151, 62438}, {8552, 53263}, {8644, 32231}, {9147, 16235}, {21731, 44810}, {22105, 44813}, {24978, 57154}, {34952, 63830}, {38327, 58380}, {39227, 42653}
X(65418) = cross-difference of every pair of points on the line X(10418)X(44529)
X(65418) = pole of the line {2854, 5093} with respect to the circumcircle
X(65418) = X(11615)-of-anti-X3-ABC reflections triangle
X(65418) = X(65418)-of-circumsymmedial triangle
X(65418) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 351, 11615), (631, 9147, 62433), (631, 62433, 16235), (9126, 11615, 3), (45687, 62438, 8151)

X(65419) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMMEDIAL AND CIRCUMORTHIC

Barycentrics    (b^2-c^2)*(3*a^8-4*(b^2+c^2)*a^6-2*(b^2+c^2)^2*a^4+2*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(b^4+c^4)*(b^2-c^2)^2) : :
X(65419) = 3*X(5926)-2*X(32204) = 3*X(6563)-4*X(32204)

X(65419) lies on these lines: {2, 65436}, {4, 1499}, {26, 669}, {512, 62438}, {2485, 32473}, {2799, 65390}, {3566, 18314}, {5576, 23301}, {5926, 6563}, {7540, 25423}, {7556, 8151}, {7565, 10280}, {8704, 65389}, {10024, 59740}, {12077, 64789}, {15099, 31279}, {30209, 50548}, {32379, 65440}, {50946, 59744}, {52300, 59927}

X(65419) = reflection of X(i) in X(j) for these (i, j): (6563, 5926), (8151, 65422)
X(65419) = anticomplement of X(65436)
X(65419) = X(65436)-Dao conjugate of-X(65436)
X(65419) = perspector of the circumconic through X(17983) and X(62899)
X(65419) = pole of the line {7514, 44388} with respect to the circumcircle
X(65419) = pole of the line {41231, 47286} with respect to the Steiner circumellipse

X(65420) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMMEDIAL AND CIRCUMSYMMEDIAL

Barycentrics    a^4*(b^2-c^2)*(6*(b^2+c^2)*a^2-2*b^4+b^2*c^2-2*c^4) : :

X(65420) lies on these lines: {39, 8644}, {76, 15724}, {3202, 9426}, {3221, 58486}, {3906, 8651}, {6683, 32472}, {8704, 65418}, {9489, 23099}

X(65420) = cross-difference of every pair of points on the line X(9870)X(15271)

X(65421) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMMEDIAL AND CIRCUMTANGENTIAL

Barycentrics    a^2*(3*(b^2+c^2)*a^4-4*(b^4+c^4)*a^2+(b^2+c^2)*(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2)) : :

X(65421) lies on these lines: {3, 2854}, {32, 32154}, {524, 13334}, {3001, 22062}, {3934, 11594}, {5188, 9019}, {7998, 18573}, {8266, 41579}, {8362, 20113}, {9027, 65429}, {13335, 37283}, {50991, 59707}

X(65421) = pole of the line {2780, 12308} with respect to the 2nd Brocard circle

X(65422) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMNORMAL AND CIRCUMSYMMEDIAL

Barycentrics    a^2*(b^2-c^2)*(4*a^6-8*(b^2+c^2)*a^4+(4*b^4-3*b^2*c^2+4*c^4)*a^2-b^2*c^2*(b^2+c^2)) : :
X(65422) = X(3)+3*X(669) = X(3)-3*X(5926) = 4*X(3628)-3*X(39511) = 2*X(3628)-3*X(44451) = 3*X(8644)-X(11615) = 3*X(8644)+X(65390)

X(65422) lies on these lines: {3, 669}, {5, 45317}, {26, 64919}, {140, 25423}, {512, 65418}, {523, 12105}, {575, 9009}, {632, 23301}, {2501, 3518}, {3053, 59928}, {3525, 44445}, {3526, 31176}, {3628, 39511}, {3800, 34952}, {6563, 38435}, {7555, 32204}, {7556, 8151}, {8644, 11615}, {10279, 12106}, {10303, 31299}, {10594, 39533}, {14002, 59927}, {15562, 62510}, {31279, 55858}, {37967, 62507}, {64789, 65434}

X(65422) = midpoint of X(i) and X(j) for these (i, j): {669, 5926}, {8151, 65419}, {11615, 65390}
X(65422) = reflection of X(39511) in X(44451)
X(65422) = pole of the line {524, 5055} with respect to the circumcircle
X(65422) = pole of the line {524, 62033} with respect to the Nguyen-Moses circle
X(65422) = pole of the line {524, 62027} with respect to the Stammler circle
X(65422) = (X(8644), X(65390))-harmonic conjugate of X(11615)

X(65423) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMORTHIC AND 1st CIRCUMPERP

Barycentrics    a^2*((b^2+c^2)*a^6-(3*b^4-2*b^2*c^2+3*c^4)*a^4+(b+c)*b^2*c^2*a^3+(3*b^4+3*c^4-b*c*(6*b^2-5*b*c+6*c^2))*(b+c)^2*a^2-(b^2-c^2)*(b-c)*b^2*c^2*a-(b^6-c^6)*(b^2-c^2)) : :
X(65423) = 3*X(3)-X(31738) = X(40)+3*X(5890) = 3*X(165)+X(5889) = 3*X(165)-X(31737) = 3*X(5890)-X(31732) = 3*X(31728)+X(31738) = 2*X(31728)+X(65399) = 2*X(31738)-3*X(65399)

X(65423) lies on these lines: {1, 10574}, {2, 65435}, {3, 31728}, {4, 58474}, {10, 185}, {30, 31760}, {40, 5890}, {51, 51118}, {52, 31730}, {140, 31751}, {143, 28146}, {165, 5889}, {389, 516}, {411, 62352}, {511, 12512}, {515, 40647}, {517, 13630}, {916, 3678}, {944, 61136}, {946, 9730}, {1125, 2807}, {1154, 31663}, {1698, 12111}, {1699, 15043}, {1742, 50593}, {2392, 9943}, {2772, 5777}, {2779, 34339}, {2979, 16192}, {3060, 64005}, {3567, 41869}, {3579, 6102}, {3634, 5907}, {3817, 64854}, {3881, 58617}, {4297, 64100}, {4301, 64662}, {4347, 11436}, {5446, 28150}, {5462, 18483}, {5562, 10164}, {5587, 6241}, {5663, 9956}, {5690, 45956}, {5691, 15072}, {5752, 12511}, {5876, 11231}, {5943, 12571}, {5946, 22793}, {6000, 19925}, {6684, 13754}, {7729, 12779}, {7987, 20791}, {7988, 15028}, {7989, 15305}, {8227, 15045}, {9037, 31805}, {9047, 31819}, {9441, 41329}, {9587, 11449}, {9590, 52525}, {9780, 64025}, {9786, 49553}, {9899, 41715}, {9955, 12006}, {10167, 23156}, {10171, 11695}, {10175, 12162}, {10575, 31673}, {11412, 35242}, {11413, 16473}, {11459, 31423}, {11793, 58441}, {12290, 18492}, {12294, 59408}, {12688, 15049}, {12699, 37481}, {13382, 43174}, {13491, 18480}, {13598, 28158}, {14641, 28172}, {14831, 50808}, {15012, 58469}, {15056, 64850}, {15058, 54447}, {16881, 28178}, {18439, 61261}, {21969, 34638}, {23157, 58567}, {25639, 34462}, {26446, 34783}, {28164, 46850}, {31817, 64107}, {31834, 61614}, {31871, 58497}, {34379, 52520}, {38042, 45957}, {44547, 52003}

X(65423) = midpoint of X(i) and X(j) for these (i, j): {3, 31728}, {10, 185}, {40, 31732}, {52, 31730}, {3579, 6102}, {5889, 31737}, {10575, 31673}, {13491, 18480}, {14831, 50808}, {21969, 34638}
X(65423) = reflection of X(i) in X(j) for these (i, j): (4, 58474), (1125, 9729), (3678, 58690), (3881, 58617), (5907, 3634), (9955, 12006), (18483, 5462), (19925, 58487), (23157, 58567), (31751, 140), (31752, 6684), (31757, 389), (31871, 58497), (58469, 15012), (65399, 3)
X(65423) = anticomplement of X(65435)
X(65423) = X(65435)-Dao conjugate of-X(65435)
X(65423) = X(31728)-of-anti-X3-ABC reflections triangle
X(65423) = X(58474)-of-anti-Euler triangle
X(65423) = X(65399)-of-ABC-X3 reflections triangle
X(65423) = X(65476)-of-anti-Hutson intouch triangle
X(65423) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (40, 5890, 31732), (165, 5889, 31737)

X(65424) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMORTHIC AND 2nd CIRCUMPERP

Barycentrics    a^2*(b-c)*((b+c)*a^3-(b+c)^2*a^2-(b^2-c^2)*(b-c)*a+b^4-b^2*c^2+c^4) : :

As a conic with center in the infinity, it is a parabola. Its focus is X(65501).

X(65424) lies on these lines: {30, 511}, {663, 52726}, {1734, 53562}, {4091, 48338}, {39476, 53300}, {44410, 48294}, {48287, 53550}, {48386, 53285}

X(65424) = isogonal conjugate of the circumperp conjugate of X(65501)
X(65424) = cross-difference of every pair of points on the line X(6)X(13898)

X(65425) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMORTHIC AND CIRCUMSYMMEDIAL

Barycentrics    a^2*(b^2-c^2)*(2*(b^2+c^2)*a^10-(8*b^4+7*b^2*c^2+8*c^4)*a^8+(b^2+c^2)*(12*b^4-7*b^2*c^2+12*c^4)*a^6-(8*b^8+8*c^8-b^2*c^2*(3*b^4+4*b^2*c^2+3*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(2*b^4-b^2*c^2+2*c^4)*a^2-2*b^4*c^4*(b^2-c^2)^2) : :

X(65425) lies on these lines: {39, 65390}, {389, 512}, {8704, 31745}, {39469, 65389}

X(65426) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL AND HEXYL

Barycentrics    a*(2*a^5-5*(b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*(2*b^2-b*c+2*c^2)*a^2-2*(2*b^2+b*c+2*c^2)*(b-c)^2*a+(b^4-c^4)*(b-c)) : :
X(65426) = X(9)-5*X(7987) = 7*X(9)-3*X(52665) = 3*X(9)+X(64697) = X(20)+3*X(38053) = 5*X(142)-3*X(38151) = 3*X(165)+X(3243) = X(1001)-3*X(3576) = 3*X(1001)-X(11372) = X(2951)+7*X(30389) = X(2951)+3*X(38316) = 3*X(3576)+X(5732) = 9*X(3576)-X(11372) = 5*X(4297)+3*X(38151) = 3*X(5732)+X(11372) = 4*X(13624)-X(15254) = 6*X(13624)-X(60911) = 3*X(15254)-2*X(60911) = X(15481)-6*X(17502) = 3*X(17502)-X(31658) = X(43175)-3*X(51705)

X(65426) lies on these lines: {1, 1418}, {3, 518}, {7, 2646}, {9, 3207}, {20, 38053}, {36, 5728}, {40, 42871}, {55, 10178}, {56, 5572}, {65, 30284}, {72, 35202}, {104, 20219}, {142, 4297}, {165, 3243}, {214, 5851}, {354, 7411}, {390, 1319}, {480, 4855}, {515, 3826}, {516, 550}, {517, 15570}, {527, 43176}, {528, 11715}, {954, 3612}, {958, 58634}, {960, 8273}, {971, 5450}, {990, 15569}, {991, 1386}, {1001, 1012}, {1006, 63432}, {1125, 42356}, {1155, 7672}, {1279, 1742}, {1376, 10857}, {1420, 4326}, {1445, 5204}, {1458, 30621}, {1621, 5918}, {1750, 8167}, {1768, 4640}, {1837, 61019}, {2550, 5731}, {2801, 15481}, {2951, 30389}, {2975, 3059}, {3057, 7676}, {3174, 12513}, {3486, 8732}, {3522, 11038}, {3523, 38057}, {3579, 12005}, {3601, 4321}, {3624, 59389}, {3651, 58568}, {3683, 11220}, {3689, 64108}, {3742, 7580}, {3748, 9778}, {3812, 8726}, {3848, 19541}, {3873, 7964}, {3880, 7966}, {3897, 59412}, {4312, 37525}, {4428, 10860}, {4511, 64723}, {4663, 13329}, {5045, 12511}, {5048, 7673}, {5126, 63972}, {5220, 21153}, {5223, 5440}, {5248, 31805}, {5302, 6986}, {5303, 60970}, {5542, 24929}, {5584, 34791}, {5686, 15717}, {5691, 20195}, {5759, 50371}, {5805, 13151}, {5809, 7288}, {5853, 11260}, {5880, 6934}, {6067, 57287}, {6210, 63390}, {6666, 64804}, {6690, 64705}, {6796, 58588}, {6992, 12678}, {7280, 18412}, {7354, 21617}, {7677, 14100}, {8236, 20323}, {8255, 12573}, {8543, 31391}, {8581, 18450}, {9441, 49478}, {9588, 59414}, {10164, 13226}, {10165, 63970}, {10179, 64150}, {10304, 51099}, {10391, 37578}, {10882, 35892}, {10902, 64128}, {11227, 58578}, {11526, 37567}, {12114, 65466}, {12520, 58679}, {12560, 13384}, {12635, 60990}, {12669, 37106}, {14151, 63211}, {15185, 59320}, {15705, 50835}, {16112, 17614}, {17768, 43177}, {18443, 64731}, {18481, 38122}, {19925, 58433}, {24299, 38030}, {24928, 30331}, {25466, 64706}, {27475, 37416}, {28160, 61595}, {28534, 60896}, {29181, 48893}, {30318, 63756}, {30329, 37582}, {31423, 38154}, {31649, 31666}, {34628, 38093}, {35016, 38054}, {35986, 64149}, {36698, 38186}, {36991, 54445}, {37424, 64443}, {37499, 51194}, {37571, 59372}, {37618, 42884}, {38031, 54370}, {38052, 56997}, {38073, 50819}, {38082, 50833}, {38158, 61001}, {43179, 51788}, {43182, 51717}, {47357, 64696}, {49484, 59620}, {50693, 62870}, {59340, 60968}

X(65426) = midpoint of X(i) and X(j) for these (i, j): {1, 11495}, {40, 42871}, {142, 4297}, {550, 20330}, {1001, 5732}, {3174, 12513}, {5542, 63413}, {5880, 43161}, {12635, 60990}
X(65426) = reflection of X(i) in X(j) for these (i, j): (15254, 52769), (15481, 31658), (19925, 58433), (42356, 1125), (42819, 1385), (52769, 13624), (65405, 3)
X(65426) = X(21)-beth conjugate of-X(1418)
X(65426) = pole of the line {4228, 7964} with respect to the Stammler hyperbola
X(65426) = X(141)-of-2nd circumperp triangle, when ABC is acute
X(65426) = X(3589)-of-hexyl triangle, when ABC is acute
X(65426) = X(5572)-of-2nd circumperp tangential triangle
X(65426) = X(11495)-of-anti-Aquila triangle
X(65426) = X(44882)-of-1st circumperp triangle, when ABC is acute
X(65426) = X(65405)-of-ABC-X3 reflections triangle
X(65426) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (56, 7675, 5572), (2951, 30389, 38316), (3576, 5732, 1001), (6986, 12680, 5302), (8273, 10884, 960), (10167, 15931, 4640), (14100, 37605, 7677), (21151, 43161, 5880)

X(65427) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st CIRCUMPERP AND 4th MIXTILINEAR

Barycentrics    a*(4*(b+c)*a^5-10*(b^2+b*c+c^2)*a^4+(b+c)*(6*b^2+b*c+6*c^2)*a^3+(2*b^2+3*b*c+2*c^2)*(b-c)^2*a^2-(b^2-c^2)*(b-c)*(2*b^2+b*c+2*c^2)*a-b*c*(b-c)^4) : :
X(65427) = 9*X(165)-X(170) = 3*X(165)+X(3730) = X(170)+3*X(3730) = 5*X(170)+3*X(41680) = 5*X(3730)-X(41680)

X(65427) lies on these lines: {5, 516}, {165, 170}, {1155, 58816}, {2140, 10164}, {2808, 31663}, {17753, 64108}, {34848, 50808}, {39789, 63211}, {52155, 63469}

X(65427) = perspector of the circumconic through X(42301) and X(43191)
X(65427) = X(6683)-of-excentral triangle, when ABC is acute
X(65427) = X(3934)-of-1st circumperp triangle, when ABC is acute

X(65428) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd CIRCUMPERP AND 3rd MIXTILINEAR

Barycentrics    a*(b-c)*(2*a-b)*(2*a-c) : :
X(65428) = 3*X(1)+X(4498) = X(1)+3*X(8643) = X(659)-5*X(58152) = 3*X(663)+X(1019) = 5*X(663)-X(48352) = 3*X(667)+X(4879) = X(667)+3*X(25569) = 3*X(667)-X(48011) = 5*X(1019)+3*X(48352) = 3*X(1960)+X(48328) = 3*X(1960)-X(48331) = 5*X(1960)+X(48344) = 3*X(4401)-X(4498) = X(4401)-3*X(8643) = X(4498)-9*X(8643) = X(48287)+5*X(58152) = X(48328)-3*X(48330) = 5*X(48328)-3*X(48344) = 3*X(48330)+X(48331) = 5*X(48330)-X(48344)

X(65428) lies on these lines: {1, 4401}, {513, 58156}, {514, 1960}, {659, 48287}, {663, 1019}, {667, 4879}, {905, 48345}, {1125, 28470}, {1319, 30719}, {1420, 51652}, {2832, 58794}, {3249, 57050}, {3251, 50355}, {3803, 48348}, {3960, 48329}, {4040, 48341}, {4063, 8656}, {4083, 58150}, {4129, 45316}, {4162, 30234}, {4367, 4794}, {4378, 48065}, {4449, 58153}, {4504, 59672}, {4775, 48064}, {4782, 48347}, {4784, 58159}, {4943, 56176}, {4983, 48587}, {6161, 48075}, {14413, 48111}, {14419, 48018}, {14838, 48327}, {16483, 57238}, {29358, 48299}, {47729, 47818}, {47915, 48058}, {48012, 48322}, {48045, 48582}, {48066, 48324}, {48091, 50517}, {48099, 48612}, {48303, 53411}, {48323, 48623}, {48333, 58151}, {48336, 58157}, {48337, 58140}, {48595, 50523}

X(65428) = midpoint of X(i) and X(j) for these (i, j): {1, 4401}, {659, 48287}, {667, 48294}, {905, 48345}, {1960, 48330}, {3803, 48348}, {3960, 48329}, {4040, 48343}, {4367, 4794}, {4378, 48065}, {4504, 59672}, {4775, 48064}, {4782, 48347}, {4879, 48011}, {6161, 48075}, {14838, 48327}, {48012, 48322}, {48066, 48324}, {48323, 48623}, {48328, 48331}
X(65428) = X(21)-beth conjugate of-X(4498)
X(65428) = perspector of the circumconic through X(42302) and X(60873)
X(65428) = X(4401)-of-anti-Aquila triangle
X(65428) = X(52585)-of-2nd circumperp triangle, when ABC is acute
X(65428) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 8643, 4401), (667, 4879, 48011), (667, 25569, 48294), (1960, 48328, 48331), (4367, 58155, 4794), (48011, 48294, 4879), (48330, 48331, 48328), (48347, 58149, 4782)

X(65429) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMSYMMEDIAL AND CIRCUMTANGENTIAL

Barycentrics    a^2*(4*(b^2+c^2)*a^4-2*(b^2+2*c^2)*(2*b^2+c^2)*a^2-b^2*c^2*(b^2+c^2)) : :

X(65429) lies on these lines: {3, 524}, {23, 9300}, {39, 8705}, {160, 6329}, {237, 63124}, {523, 32516}, {597, 37465}, {1634, 20582}, {2854, 13334}, {3589, 20775}, {3631, 41328}, {5013, 8547}, {5201, 32455}, {7492, 41624}, {8584, 37184}, {9027, 65421}, {9145, 12054}, {9149, 58446}, {13357, 46337}, {14002, 63101}, {14096, 50991}, {15826, 41335}, {20190, 34383}, {33980, 63028}, {34990, 44323}, {36182, 63548}, {37283, 37479}

X(65429) = pole of the line {1499, 3830} with respect to the 2nd Brocard circle
X(65429) = pole of the line {1995, 8556} with respect to the Stammler hyperbola

X(65430) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMSYMMEDIAL AND 2nd EHRMANN

Barycentrics    a^2*(16*a^6-14*(b^2+c^2)*a^4-2*(8*b^4+b^2*c^2+8*c^4)*a^2+(b^2+c^2)*(14*b^4-23*b^2*c^2+14*c^4)) : :
X(65430) = 3*X(6)+X(9716)

X(65430) lies on these lines: {6, 9716}, {547, 25555}, {576, 7575}, {597, 38397}, {1176, 10510}, {3431, 11477}, {8584, 47458}, {10541, 41398}, {11232, 36253}, {11482, 11935}, {22151, 38402}, {32455, 58450}, {35921, 53093}, {53092, 58891}

X(65430) = pole of the line {15534, 38397} with respect to the Stammler hyperbola

X(65431) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: CIRCUMTANGENTIAL AND 3rd MIXTILINEAR

Barycentrics    a*(4*(b+c)*a^5+2*(2*b^2-11*b*c+2*c^2)*a^4-4*(b^2-c^2)*(b-c)*a^3-(4*b^2-5*b*c+4*c^2)*(b^2-4*b*c+c^2)*a^2-2*(b+c)*(4*b^2-7*b*c+4*c^2)*b*c*a+(b^2-c^2)^2*b*c) : :

X(65431) lies on these lines: {3, 32426}, {9026, 13624}

X(65432) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND EXTOUCH

Barycentrics    (b-c)*(-a+b+c)^4*(2*a^2+(b+c)*a-(b-c)^2) : :

X(65432) lies on these lines: {3239, 3900}, {21302, 50333}, {29278, 58333}, {65433, 65503}

X(65432) = X(17056)-Dao conjugate of-X(4626)
X(65432) = X(6614)-isoconjugate of-X(17097)
X(65432) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2646, 4617), (4130, 17097), (5745, 4626), (6737, 658), (17136, 23586), (21748, 6614), (23970, 56321), (53324, 23971), (58329, 63194)
X(65432) = perspector of the circumconic through X(346) and X(60254)
X(65432) = barycentric product X(i)*X(j) for these {i, j}: {3239, 6737}, {4163, 5745}, {17136, 23970}
X(65432) = trilinear product X(i)*X(j) for these {i, j}: {2646, 4163}, {3900, 6737}, {4081, 53388}, {4130, 5745}, {17136, 24010}, {21677, 58329}, {56182, 62566}
X(65432) = trilinear quotient X(i)/X(j) for these (i, j): (2646, 6614), (4163, 17097), (5745, 4617), (6737, 934), (17136, 24013), (53388, 7339)

X(65433) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND YFF CONTACT

Barycentrics    a*(b-c)*(-a+b+c)^4*(-a^2+b^2+c^2)*(a^4-(b^2-b*c+c^2)*a^2-b*c*(b-c)^2) : :

X(65433) lies on these lines: {100, 190}, {57055, 57108}, {65432, 65503}

X(65433) = cross-difference of every pair of points on the line X(1015)X(1435)
X(65433) = X(i)-isoconjugate of-X(j) for these {i, j}: {1398, 53211}, {1435, 65214}, {41207, 62192}
X(65433) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1260, 65214), (1984, 17925), (3692, 53211), (6518, 4626), (7360, 13149), (56182, 41207), (58325, 36118)
X(65433) = perspector of the circumconic through X(1016) and X(3692)
X(65433) = barycentric product X(i)*X(j) for these {i, j}: {1984, 52609}, {4163, 6518}, {7360, 57055}
X(65433) = trilinear product X(i)*X(j) for these {i, j}: {4130, 6518}, {7360, 57108}, {57055, 58325}
X(65433) = trilinear quotient X(i)/X(j) for these (i, j): (1265, 53211), (1984, 57200), (3692, 65214), (6518, 4617), (7360, 36118), (58325, 32714)

X(65434) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EULER AND 5th EULER

Barycentrics    (b^2-c^2)*(a^8+(b^2+c^2)*a^6-5*(b^4+c^4)*a^4+(b^2+c^2)*(3*b^4+2*b^2*c^2+3*c^4)*a^2-6*(b^2-c^2)^2*b^2*c^2) : :

X(65434) lies on these lines: {2, 65389}, {3, 30476}, {4, 31174}, {5, 23878}, {546, 30209}, {576, 64876}, {647, 3090}, {850, 3091}, {1656, 44560}, {3146, 31072}, {3525, 31277}, {5056, 36900}, {5068, 63786}, {5079, 41300}, {8675, 59741}, {8704, 65436}, {10110, 54272}, {11793, 54269}, {15022, 31296}, {20186, 59568}, {20399, 62489}, {37953, 47255}, {37957, 47264}, {46989, 47339}, {64789, 65422}

X(65434) = complement of X(65389)
X(65434) = pole of the line {10245, 64781} with respect to the circumcircle

X(65435) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd EULER AND 3rd EULER

Barycentrics    a^2*((b^2+c^2)*a^6-(3*b^4+2*b^2*c^2+3*c^4)*a^4+(b+c)*b^2*c^2*a^3+(b^2+b*c+c^2)*(3*b^4+3*c^4-b*c*(3*b^2-4*b*c+3*c^2))*a^2-(b^2-c^2)*(b-c)*b^2*c^2*a-(b^4+5*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(65435) = 3*X(5)-X(31760) = X(946)+3*X(5891) = 3*X(1699)+5*X(11444) = 3*X(1699)+X(31737) = 3*X(3817)+X(5562) = 3*X(3817)-X(31757) = 3*X(5891)-X(31752) = 5*X(8227)+3*X(11459) = 5*X(8227)-X(31732) = 5*X(11444)-X(31737) = 3*X(11459)+X(31732) = 3*X(31751)+X(31760) = 2*X(31751)+X(58474) = 2*X(31760)-3*X(58474)

X(65435) lies on these lines: {1, 15056}, {2, 65423}, {4, 65399}, {5, 31751}, {185, 19862}, {381, 31738}, {389, 10171}, {511, 12571}, {516, 11793}, {517, 14128}, {916, 58565}, {946, 5891}, {1125, 5907}, {1216, 18483}, {1385, 15060}, {1656, 31728}, {1699, 11444}, {2772, 9940}, {2807, 3634}, {2842, 31821}, {3576, 15058}, {3624, 12111}, {3817, 5562}, {3819, 12512}, {3917, 51118}, {4297, 15030}, {5447, 28150}, {5876, 11230}, {5889, 7988}, {5927, 23156}, {6684, 10170}, {6894, 38474}, {6915, 62352}, {7987, 15305}, {7998, 64005}, {7999, 41869}, {8227, 11459}, {9590, 43614}, {9729, 19878}, {9955, 11591}, {10165, 12162}, {10248, 33884}, {10574, 34595}, {11573, 31871}, {12279, 58221}, {12558, 37536}, {13348, 28158}, {13624, 45959}, {15067, 22793}, {16881, 61267}, {18436, 61268}, {28146, 32142}, {28160, 45958}, {28164, 44870}, {28172, 46849}, {31834, 61269}, {43174, 52796}, {45305, 50610}

X(65435) = midpoint of X(i) and X(j) for these (i, j): {4, 65399}, {5, 31751}, {946, 31752}, {1125, 5907}, {1216, 18483}, {5562, 31757}, {9955, 11591}, {11573, 31871}, {13624, 45959}
X(65435) = reflection of X(i) in X(j) for these (i, j): (9729, 19878), (58474, 5)
X(65435) = complement of X(65423)
X(65435) = X(58474)-of-Johnson triangle
X(65435) = X(65398)-of-anti-Ursa minor triangle
X(65435) = X(65399)-of-Euler triangle
X(65435) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (946, 5891, 31752), (1699, 11444, 31737), (3817, 5562, 31757), (8227, 11459, 31732)

X(65436) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd EULER AND 5th EULER

Barycentrics    (b^2-c^2)*(a^8+2*(b^2+c^2)*a^6-2*(4*b^4+5*b^2*c^2+4*c^4)*a^4+6*(b^6+c^6)*a^2-(b^4-c^4)^2) : :
X(65436) = X(669)+3*X(15099) = 3*X(2501)-4*X(10280) = 2*X(10280)-3*X(39511)

X(65436) lies on these lines: {2, 65419}, {3, 669}, {523, 47341}, {1594, 2501}, {3566, 11615}, {6563, 37444}, {7507, 39533}, {7568, 44451}, {8151, 14791}, {8704, 65434}, {13371, 23301}, {14417, 65390}, {18117, 59744}, {44445, 47528}

X(65436) = reflection of X(2501) in X(39511)
X(65436) = complement of X(65419)
X(65436) = pole of the line {44376, 62237} with respect to the polar circle

X(65437) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 3rd EULER AND FEUERBACH

Barycentrics    (b-c)*((2*b^2-b*c+2*c^2)*a^4-(b+c)*(2*b^2-b*c+2*c^2)*a^3-(2*b^2+3*b*c+2*c^2)*(b^2-3*b*c+c^2)*a^2+(b^2-c^2)*(b-c)*(2*b^2+3*b*c+2*c^2)*a-2*(b^2-c^2)^2*b*c) : :

X(65437) lies on these lines: {5, 514}, {4449, 37718}, {5047, 48218}, {37162, 47795}, {37701, 48294}, {37702, 48287}, {48386, 62359}, {65438, 65449}

X(65437) = pole of the line {516, 22936} with respect to the nine-point circle

X(65438) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 4th EULER AND FEUERBACH

Barycentrics    2*b*c*a^5-(b+c)*(2*b^2-b*c+2*c^2)*a^4-(2*b^4+2*c^4+3*b*c*(3*b^2+4*b*c+3*c^2))*a^3+(b+c)*(2*b^4+2*c^4-b*c*(3*b^2+11*b*c+3*c^2))*a^2+(2*b^2+7*b*c+2*c^2)*(b^2-c^2)^2*a+2*(b^2-c^2)^2*(b+c)*b*c : :

X(65438) lies on these lines: {5, 516}, {10, 61699}, {1125, 25444}, {1698, 35468}, {3136, 58449}, {25648, 31253}, {65437, 65449}

X(65438) = X(52540)-of-4th Euler triangle, when ABC is acute

X(65439) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXCENTRAL AND X-PARABOLA-TANGENTIAL

Barycentrics    2*a^5-2*(b^2+c^2)*a^3-(b^4-4*b^2*c^2+c^4)*a+(b^2-c^2)^2*(b+c) : :

X(65439) lies on these lines: {2, 4934}, {10, 542}, {115, 2640}, {523, 40539}, {543, 21089}, {662, 4092}, {897, 24957}, {2643, 11725}, {8043, 34990}, {17058, 24345}, {59671, 64007}

X(65439) = midpoint of X(662) and X(4092)
X(65439) = complement of X(4934)
X(65439) = pole of the line {620, 690} with respect to the Spieker circle
X(65439) = X(18315)-of-2nd Zaniah triangle, when ABC is acute

X(65440) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st EXCOSINE AND STEINER

Barycentrics    a^2*(b^2-c^2)*(2*a^8-4*(b^2+c^2)*a^6+(2*b^4+7*b^2*c^2+2*c^4)*a^4-2*(b^2+c^2)*b^2*c^2*a^2-(b^2-c^2)^2*b^2*c^2) : :

X(65440) lies on these lines: {25, 30451}, {110, 6563}, {154, 669}, {159, 9009}, {182, 14341}, {184, 2501}, {206, 57128}, {512, 46005}, {578, 39533}, {924, 6132}, {1499, 6759}, {1503, 23301}, {1853, 31279}, {3566, 5027}, {5926, 10282}, {6587, 58310}, {10192, 44451}, {11206, 44445}, {14529, 56242}, {18381, 39511}, {21646, 44110}, {30442, 53318}, {31299, 64059}, {32379, 65419}

X(65440) = reflection of X(i) in X(j) for these (i, j): (5926, 10282), (18381, 39511)
X(65440) = cross-difference of every pair of points on the line X(13881)X(26958)
X(65440) = crosssum of X(523) and X(41005)
X(65440) = perspector of the circumconic through X(41894) and X(55999)
X(65440) = pole of the line {3167, 3289} with respect to the circumcircle
X(65440) = pole of the line {297, 44451} with respect to the Kiepert parabola

X(65441) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd EXCOSINE AND EXTANGENTS

Barycentrics    a*(a^8-4*(b+c)*a^7+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^5-2*(b^2-c^2)^2*a^4-4*(b^4-c^4)*(b-c)*a^3+4*(b^2-c^2)^2*(b+c)*b*c*a+(b^2-c^2)^4) : :

X(65441) lies on these lines: {19, 31}, {33, 2357}, {40, 197}, {55, 8602}, {65, 1035}, {196, 2385}, {207, 8803}, {380, 20986}, {610, 10537}, {3197, 3198}, {7070, 60784}, {11124, 50501}, {18673, 19614}, {26377, 37550}, {30503, 52139}

X(65441) = isogonal conjugate of the isotomic conjugate of X(64583)
X(65441) = X(64583)-reciprocal conjugate of-X(76)
X(65441) = pole of the line {14298, 57101} with respect to the circumcircle
X(65441) = barycentric product X(6)*X(64583)
X(65441) = trilinear product X(31)*X(64583)
X(65441) = trilinear quotient X(64583)/X(75)
X(65441) = X(17832)-of-anti-Mandart-incircle triangle

X(65442) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND INCENTRAL

Barycentrics    a^2*(b-c)*(-a+b+c)^2*((b-c)^2+(b+c)*a) : :
X(65442) = X(2488)+2*X(53549)

X(65442) lies on these lines: {187, 237}, {513, 30719}, {520, 48302}, {810, 40984}, {905, 2821}, {926, 4162}, {928, 39541}, {2328, 21789}, {2520, 8678}, {2605, 53305}, {3057, 21120}, {3239, 3900}, {4041, 40966}, {6129, 7250}, {6363, 6615}, {15283, 17072}, {53285, 58336}, {57108, 58334}

X(65442) = midpoint of X(i) and X(j) for these (i, j): {663, 53549}, {3057, 21120}
X(65442) = reflection of X(i) in X(j) for these (i, j): (2488, 663), (7250, 6129), (39541, 48294), (65445, 17115)
X(65442) = isogonal conjugate of X(6613)
X(65442) = Gibert-circumtangential conjugate of X(59123)
X(65442) = cross-difference of every pair of points on the line X(2)X(1407)
X(65442) = crosspoint of X(i) and X(j) for these {i, j}: {6, 59123}, {9, 61222}, {663, 3900}, {2347, 23845}
X(65442) = crosssum of X(i) and X(j) for these {i, j}: {2, 42337}, {522, 6692}, {664, 934}, {1476, 60482}, {40420, 56323}
X(65442) = X(i)-Ceva conjugate of-X(j) for these (i, j): (9, 14936), (23845, 2347), (59123, 6)
X(65442) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 59123), (2170, 85), (3452, 4569), (3752, 4572), (6600, 8706), (12640, 668), (14714, 1222), (17115, 56323), (35508, 32017), (38991, 40420), (39025, 1476), (40608, 56173), (59507, 46406)
X(65442) = X(i)-isoconjugate of-X(j) for these {i, j}: {75, 59123}, {269, 8706}, {651, 40420}, {658, 23617}, {664, 1476}, {934, 1222}, {1261, 4626}, {1275, 62748}, {1414, 56173}, {1461, 32017}, {3451, 4554}, {4564, 60482}, {4569, 51476}, {4616, 56190}, {4617, 52549}, {4637, 56258}, {6516, 40446}, {7045, 56323}, {59478, 62754}
X(65442) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (32, 59123), (220, 8706), (657, 1222), (663, 40420), (1122, 36838), (1201, 658), (1828, 13149), (2347, 664), (3057, 4554), (3063, 1476), (3271, 60482), (3452, 4572), (3663, 46406), (3709, 56173), (3752, 4569), (3900, 32017), (4105, 52549), (4524, 56258), (6363, 279), (6615, 85), (6736, 1978), (8641, 23617), (14936, 56323), (18163, 4625), (20228, 934), (21120, 6063), (21796, 4566), (22072, 65164), (22344, 65296), (23845, 1275), (28006, 7205), (40982, 653), (42336, 738), (42337, 76), (45219, 62532), (48334, 1088), (52563, 52937), (57180, 1261), (59173, 4626)
X(65442) = perspector of the circumconic through X(6) and X(346)
X(65442) = pole of the line {6, 1604} with respect to the circumcircle
X(65442) = pole of the line {3340, 4907} with respect to the incircle
X(65442) = pole of the line {264, 1119} with respect to the polar circle
X(65442) = pole of the line {6, 1604} with respect to the Brocard inellipse
X(65442) = pole of the line {3340, 13476} with respect to the de Longchamps ellipse
X(65442) = pole of the line {4534, 11998} with respect to the Feuerbach circumhyperbola
X(65442) = pole of the line {200, 3056} with respect to the Mandart inellipse
X(65442) = pole of the line {99, 6613} with respect to the Stammler hyperbola
X(65442) = pole of the line {194, 30695} with respect to the Steiner circumellipse
X(65442) = pole of the line {39, 6554} with respect to the Steiner inellipse
X(65442) = pole of the line {670, 4616} with respect to the Steiner-Wallace hyperbola
X(65442) = pole of the line {20979, 57064} with respect to the Yff parabola
X(65442) = barycentric product X(i)*X(j) for these {i, j}: {6, 42337}, {9, 6615}, {55, 21120}, {200, 48334}, {346, 6363}, {522, 2347}, {649, 6736}, {650, 3057}, {657, 3663}, {663, 3452}, {1021, 4642}, {1122, 4130}, {1146, 23845}, {1201, 3239}, {1828, 57055}, {2170, 61222}, {2310, 21362}, {3063, 20895}, {3064, 22072}, {3119, 62754}
X(65442) = trilinear product X(i)*X(j) for these {i, j}: {31, 42337}, {41, 21120}, {55, 6615}, {200, 6363}, {220, 48334}, {521, 40982}, {650, 2347}, {657, 3752}, {663, 3057}, {667, 6736}, {1021, 21796}, {1122, 4105}, {1201, 3900}, {1828, 57108}, {2310, 23845}, {3022, 62754}, {3063, 3452}, {3239, 20228}, {3271, 61222}, {3663, 8641}
X(65442) = trilinear quotient X(i)/X(j) for these (i, j): (31, 59123), (200, 8706), (650, 40420), (657, 23617), (663, 1476), (1122, 4626), (1201, 934), (1828, 36118), (2170, 60482), (2310, 56323), (2347, 651), (3057, 664), (3063, 3451), (3239, 32017), (3452, 4554), (3663, 4569), (3752, 658), (3900, 1222), (4041, 56173), (4105, 1261)
X(65442) = X(65455)-of-excentral triangle, when ABC is acute
X(65442) = (X(663), X(1946))-harmonic conjugate of X(1960)

X(65443) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND LEMOINE

Barycentrics    (b-c)*(-a+b+c)^2*(4*a^2+3*(b+c)*a+b^2+c^2)*(4*a^3+(b^2+c^2)*a+3*(b^2-c^2)*(b-c)) : :

X(65443) lies on these lines: {3239, 3900}, {8599, 12073}

X(65444) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND MACBEATH

Barycentrics    (b-c)*(-a+b+c)^3*((b+c)*a^2+2*b*c*a-(b^2-c^2)*(b-c))*((b^2+c^2)*a^3-(b^2-c^2)*(b-c)*a^2-(b^2-c^2)^2*a+(b^4-c^4)*(b-c)) : :

X(65444) lies on these lines: {850, 6368}, {3239, 3900}

X(65444) = cross-difference of every pair of points on the line X(1407)X(14585)
X(65444) = X(42447)-reciprocal conjugate of-X(32651)
X(65444) = perspector of the circumconic through X(346) and X(18027)
X(65444) = pole of the line {1604, 35225} with respect to the circumcircle
X(65444) = pole of the line {184, 1119} with respect to the polar circle
X(65444) = pole of the line {317, 30695} with respect to the Steiner circumellipse

X(65445) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND ORTHIC

Barycentrics    a*(b-c)*(-a+b+c)^2*(a^3+(b+c)*(b-c)^2) : :

X(65445) lies on these lines: {2, 65409}, {42, 663}, {226, 59903}, {460, 512}, {514, 6738}, {885, 21302}, {1946, 50504}, {2488, 8678}, {3063, 55206}, {3239, 3900}, {4036, 23289}, {4041, 8641}, {6139, 50501}

X(65445) = reflection of X(i) in X(j) for these (i, j): (2520, 18344), (65442, 17115)
X(65445) = anticomplement of X(65409)
X(65445) = cross-difference of every pair of points on the line X(394)X(1407)
X(65445) = crosspoint of X(i) and X(j) for these {i, j}: {3900, 18344}, {40968, 53279}
X(65445) = crosssum of X(934) and X(6516)
X(65445) = X(i)-Ceva conjugate of-X(j) for these (i, j): (281, 14936), (53279, 40968)
X(65445) = X(i)-Dao conjugate of-X(j) for these (i, j): (11, 34399), (6523, 54948), (6600, 65370), (7117, 348), (14714, 40436), (15259, 52775), (35508, 59759), (38966, 34406), (65409, 65409)
X(65445) = X(i)-isoconjugate of-X(j) for these {i, j}: {109, 34399}, {255, 54948}, {269, 65370}, {326, 52775}, {658, 56003}, {934, 40436}, {1461, 59759}, {6507, 42381}, {7366, 42380}, {55994, 65296}
X(65445) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (220, 65370), (393, 54948), (650, 34399), (657, 40436), (1837, 4554), (2207, 52775), (3772, 4569), (3900, 59759), (3924, 658), (5423, 42380), (6524, 42381), (8641, 56003), (17189, 4635), (17861, 46406), (36570, 4626), (40968, 664), (40980, 4573), (53279, 1275), (65103, 34406)
X(65445) = perspector of the circumconic through X(346) and X(393)
X(65445) = pole of the line {1604, 1609} with respect to the circumcircle
X(65445) = pole of the line {1420, 4907} with respect to the incircle
X(65445) = pole of the line {800, 2183} with respect to the 1st Lozada, circle
X(65445) = pole of the line {69, 1119} with respect to the polar circle
X(65445) = pole of the line {800, 2183} with respect to the Brocard inellipse
X(65445) = pole of the line {6392, 30695} with respect to the Steiner circumellipse
X(65445) = pole of the line {3767, 6554} with respect to the Steiner inellipse
X(65445) = barycentric product X(i)*X(j) for these {i, j}: {522, 40968}, {650, 1837}, {657, 17861}, {1021, 21935}, {1146, 53279}, {3239, 3924}, {3700, 40980}, {3772, 3900}, {4163, 36570}, {4171, 17189}, {4524, 16749}, {41004, 65103}
X(65445) = trilinear product X(i)*X(j) for these {i, j}: {650, 40968}, {657, 3772}, {663, 1837}, {2310, 53279}, {3900, 3924}, {4041, 40980}, {4130, 36570}, {4524, 17189}, {8641, 17861}, {21789, 21935}, {26934, 65103}
X(65445) = trilinear quotient X(i)/X(j) for these (i, j): (158, 54948), (200, 65370), (522, 34399), (657, 56003), (1096, 52775), (1837, 664), (3239, 59759), (3772, 658), (3900, 40436), (3924, 934), (6520, 42381), (16749, 4635), (17189, 4616), (17861, 4569), (21935, 4566), (26934, 65296), (30693, 42380), (36570, 4617), (40968, 651), (40980, 1414)

X(65446) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND STEINER

Barycentrics    (b-c)*(-a+b+c)^2*(2*a^2-(b+c)*a-b^2-c^2)*(2*a^3-(b^2+c^2)*a-(b^2-c^2)*(b-c)) : :

X(65446) lies on these lines: {2, 65495}, {99, 110}, {3239, 3900}

X(65446) = anticomplement of X(65495)
X(65446) = cross-difference of every pair of points on the line X(1407)X(3124)
X(65446) = X(65495)-Dao conjugate of-X(65495)
X(65446) = perspector of the circumconic through X(346) and X(4590)
X(65446) = pole of the line {1604, 1634} with respect to the circumcircle
X(65446) = pole of the line {1119, 8754} with respect to the polar circle
X(65446) = pole of the line {99, 30695} with respect to the Steiner circumellipse
X(65446) = pole of the line {620, 6554} with respect to the Steiner inellipse
X(65446) = pole of the line {523, 4616} with respect to the Steiner-Wallace hyperbola
X(65446) = pole of the line {1654, 57064} with respect to the Yff parabola

X(65447) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND SYMMEDIAL

Barycentrics    a^4*(b-c)*(-a+b+c)^2*((b+c)*a+b^2+c^2)*((b^2+c^2)*a+(b+c)*(b-c)^2) : :

X(65447) lies on these lines: {669, 688}, {3239, 3900}

X(65447) = cross-difference of every pair of points on the line X(76)X(1407)
X(65447) = X(61051)-Dao conjugate of-X(6063)
X(65447) = perspector of the circumconic through X(32) and X(346)
X(65447) = pole of the line {1604, 1613} with respect to the circumcircle
X(65447) = pole of the line {1119, 18022} with respect to the polar circle
X(65447) = pole of the line {8264, 30695} with respect to the Steiner circumellipse
X(65447) = pole of the line {6554, 8265} with respect to the Steiner inellipse
X(65447) = pole of the line {4609, 4616} with respect to the Steiner-Wallace hyperbola
X(65447) = barycentric product X(23638)*X(52326)

X(65448) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: EXTOUCH AND YFF CONTACT

Barycentrics    (b-c)*(-a+b+c)^3*(2*a^2-(b+c)*a-(b-c)^2) : :

X(65448) lies on these lines: {2, 65483}, {100, 190}, {3059, 30692}, {3119, 4081}, {3239, 3900}, {6366, 38376}, {21060, 39470}, {57049, 58835}

X(65448) = anticomplement of X(65483)
X(65448) = cross-difference of every pair of points on the line X(1015)X(1407)
X(65448) = X(i)-Dao conjugate of-X(j) for these (i, j): (2968, 62723), (3161, 60487), (3900, 23351), (6552, 35157), (6594, 934), (6600, 14733), (6608, 35348), (24771, 37139), (35091, 279), (35110, 4626), (35508, 34056), (40629, 479), (62579, 3676), (65483, 65483)
X(65448) = X(i)-isoconjugate of-X(j) for these {i, j}: {244, 59105}, {269, 14733}, {279, 36141}, {604, 60487}, {1088, 32728}, {1106, 35157}, {1156, 6614}, {1407, 37139}, {1435, 65304}, {1461, 34056}, {2291, 4617}, {4626, 34068}, {7099, 65335}, {7339, 35348}, {23351, 24013}, {23893, 23971}
X(65448) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (8, 60487), (200, 37139), (220, 14733), (346, 35157), (527, 4626), (1055, 6614), (1155, 4617), (1252, 59105), (1253, 36141), (1260, 65304), (1638, 479), (3119, 35348), (3239, 62723), (3900, 34056), (4081, 60479), (4105, 2291), (4130, 1156), (4163, 1121), (4171, 62764), (6139, 1407), (6366, 279), (6603, 934), (6745, 658), (7046, 65335), (14392, 57), (14413, 738), (14414, 7177), (14827, 32728), (23346, 23971), (23890, 24013), (23970, 63748), (24010, 23893), (30806, 36838), (33573, 3676), (35508, 23351), (38376, 37757), (52334, 1358), (56543, 23586), (57180, 34068), (60431, 36118), (61035, 61241), (62756, 4637)
X(65448) = perspector of the circumconic through X(346) and X(1016)
X(65448) = pole of the line {100, 1604} with respect to the circumcircle
X(65448) = pole of the line {1119, 2969} with respect to the polar circle
X(65448) = pole of the line {190, 5528} with respect to the Steiner circumellipse
X(65448) = pole of the line {4422, 6554} with respect to the Steiner inellipse
X(65448) = pole of the line {4616, 7192} with respect to the Steiner-Wallace hyperbola
X(65448) = pole of the line {2, 57064} with respect to the Yff parabola
X(65448) = barycentric product X(i)*X(j) for these {i, j}: {312, 14392}, {346, 6366}, {527, 4163}, {1638, 5423}, {3239, 6745}, {3699, 33573}, {4076, 52334}, {4130, 30806}, {4397, 6603}, {6139, 59761}, {7101, 14414}, {14413, 30693}, {23970, 56543}
X(65448) = trilinear product X(i)*X(j) for these {i, j}: {8, 14392}, {200, 6366}, {341, 6139}, {527, 4130}, {644, 33573}, {728, 1638}, {1155, 4163}, {3239, 6603}, {3900, 6745}, {4105, 30806}, {5423, 14413}, {7046, 14414}, {23890, 23970}, {24010, 56543}, {30574, 56182}, {38376, 42064}, {56763, 57049}, {57055, 60431}
X(65448) = trilinear quotient X(i)/X(j) for these (i, j): (200, 14733), (220, 36141), (312, 60487), (341, 35157), (346, 37139), (527, 4617), (765, 59105), (1155, 6614), (1253, 32728), (1638, 738), (3239, 34056), (3692, 65304), (4081, 35348), (4105, 34068), (4130, 2291), (4163, 1156), (4397, 62723), (6139, 1106), (6366, 269), (6603, 1461)

X(65449) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: FEUERBACH AND MEDIAL

Barycentrics    (b-c)*(a^3-(2*b^2+3*b*c+2*c^2)*a+b*c*(b+c)) : :
X(65449) = 3*X(2)+X(4705) = 9*X(2)-X(17166) = X(667)-5*X(31209) = X(667)+3*X(47814) = 3*X(4705)+X(17166) = X(4874)-3*X(48196) = X(14838)-3*X(47829) = X(17072)+3*X(47778) = X(17166)-3*X(52601) = X(21051)+3*X(47829) = X(23815)-3*X(47802) = 5*X(31209)+3*X(47814) = 3*X(47778)-X(50507) = 3*X(47802)+X(47965) = X(48012)+3*X(48196)

X(65449) lies on these lines: {2, 4705}, {5, 44824}, {10, 29298}, {512, 25666}, {514, 3634}, {650, 21260}, {659, 47816}, {661, 47837}, {663, 899}, {667, 31209}, {693, 31251}, {838, 25142}, {1491, 47794}, {1577, 47827}, {1698, 2533}, {1734, 47822}, {2254, 48553}, {2526, 48561}, {2530, 47793}, {2787, 14838}, {2977, 29098}, {3035, 40544}, {3762, 47893}, {3831, 4147}, {3835, 50504}, {3837, 48003}, {3960, 48401}, {4041, 47839}, {4129, 9508}, {4369, 48005}, {4391, 47888}, {4401, 48214}, {4490, 47795}, {4522, 29194}, {4560, 14431}, {4730, 47840}, {4763, 50512}, {4776, 4834}, {4784, 48551}, {4808, 47797}, {4824, 64850}, {4874, 48012}, {4893, 50352}, {4978, 30795}, {4983, 47836}, {5958, 65450}, {6050, 44567}, {6372, 25380}, {8043, 31946}, {8678, 31287}, {9422, 40533}, {10278, 12071}, {14349, 47835}, {17069, 29090}, {17072, 29188}, {18004, 21192}, {21052, 48288}, {21212, 29354}, {21301, 27115}, {23815, 47802}, {24948, 65152}, {28602, 29128}, {29051, 53571}, {29142, 53573}, {29154, 50453}, {30835, 48273}, {31207, 47912}, {36848, 47970}, {41800, 48047}, {45315, 48053}, {45323, 48066}, {47760, 50501}, {47761, 47956}, {47784, 48395}, {47807, 48402}, {47817, 50328}, {47823, 47959}, {47824, 47949}, {47825, 48393}, {47828, 48267}, {47833, 48407}, {47838, 50355}, {47842, 48205}, {47872, 48409}, {47875, 47975}, {47918, 48569}, {47967, 48216}, {48024, 48573}, {48049, 58179}, {48058, 48180}, {48079, 58181}, {48092, 48559}, {48165, 50345}, {48204, 50330}, {50335, 59672}, {51073, 54265}, {59521, 64934}, {65437, 65438}

X(65449) = midpoint of X(i) and X(j) for these (i, j): {5, 44824}, {650, 21260}, {3835, 50504}, {3837, 48003}, {3960, 48401}, {4129, 9508}, {4369, 48005}, {4705, 52601}, {4874, 48012}, {8043, 31946}, {14838, 21051}, {17072, 50507}, {18004, 21192}, {23815, 47965}, {48049, 58179}, {50335, 59672}
X(65449) = reflection of X(31288) in X(31287)
X(65449) = complement of X(52601)
X(65449) = pole of the line {9569, 29301} with respect to the excircles radical circle
X(65449) = pole of the line {502, 11795} with respect to the nine-point circle
X(65449) = pole of the line {3647, 29301} with respect to the Spieker circle
X(65449) = pole of the line {57461, 64523} with respect to the Kiepert circumhyperbola
X(65449) = pole of the line {1655, 2895} with respect to the Steiner inellipse
X(65449) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 4705, 52601), (17072, 47778, 50507), (21051, 47829, 14838), (31209, 47814, 667), (47802, 47965, 23815), (48012, 48196, 4874)

X(65450) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: FEUERBACH AND ORTHIC

Barycentrics    a*(b-c)*(a^4-(2*b^2+3*b*c+2*c^2)*a^2+(b+c)*b*c*a+(b^2-c^2)^2) : :

X(65450) lies on these lines: {6, 57185}, {44, 513}, {197, 16874}, {1621, 42319}, {2262, 21353}, {2605, 55212}, {2681, 38390}, {3185, 7234}, {3309, 4949}, {3700, 8674}, {4024, 8702}, {4132, 12077}, {4369, 9034}, {4521, 63978}, {5958, 65449}, {6003, 14321}, {8774, 17069}, {12572, 28292}, {30203, 34434}, {40589, 57182}, {55214, 59837}

X(65450) = reflection of X(13401) in X(2516)
X(65450) = cross-difference of every pair of points on the line X(1)X(6597)
X(65450) = crosspoint of X(i) and X(j) for these {i, j}: {57, 5606}, {100, 64991}
X(65450) = crosssum of X(i) and X(j) for these {i, j}: {9, 8702}, {650, 37564}
X(65450) = X(30238)-Ceva conjugate of-X(55)
X(65450) = X(i)-Dao conjugate of-X(j) for these (i, j): (32664, 39633), (38991, 6597)
X(65450) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 39633}, {651, 6597}
X(65450) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (31, 39633), (663, 6597)
X(65450) = X(i)-zayin conjugate of-X(j) for these (i, j): (9, 39633), (650, 6597), (30200, 57)
X(65450) = perspector of the circumconic through X(1) and X(39164)
X(65450) = pole of the line {92, 32859} with respect to the polar circle
X(65450) = pole of the line {908, 1211} with respect to the Spieker circle
X(65450) = pole of the line {2310, 21043} with respect to the Feuerbach circumhyperbola
X(65450) = pole of the line {65, 11363} with respect to the orthic inconic
X(65450) = trilinear quotient X(i)/X(j) for these (i, j): (6, 39633), (650, 6597), (41550, 65205), (41551, 63782)
X(65450) = X(57195)-of-2nd Zaniah triangle, when ABC is acute

X(65451) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: GARCIA-REFLECTION AND 1st SCHIFFLER

Barycentrics    2*(b+c)*a^5-(5*b^2+2*b*c+5*c^2)*a^4+2*(b^2-c^2)*(b-c)*a^3+4*(b-c)^4*a^2-4*(b^2-c^2)*(b-c)*(b^2-4*b*c+c^2)*a+(b^2-c^2)^2*(b-c)^2 : :

X(65451) lies on these lines: {11, 5173}, {354, 41561}, {1519, 3649}, {1699, 41706}, {3817, 51463}, {5433, 64669}, {5603, 40663}, {5804, 10944}, {7965, 11019}, {7988, 38175}, {9812, 17051}, {13464, 45081}

X(65452) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: GARCIA-REFLECTION AND WASAT

Barycentrics    2*a^5-3*(b+c)*a^4-2*(b^2-c^2)*(b-c)*a^2+2*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a-3*(b^2-c^2)*(b-c)^3 : :
X(65452) = X(4)+3*X(38036) = X(7)+3*X(1699) = 3*X(7)+X(3062) = X(9)-3*X(3817) = 3*X(142)-X(11495) = X(144)-9*X(9779) = 5*X(946)+X(52682) = 3*X(1125)-2*X(52769) = 9*X(1699)-X(3062) = 3*X(1699)-X(63973) = 5*X(2346)-9*X(11218) = X(2346)+3*X(15909) = X(3062)-3*X(63973) = X(5542)-3*X(38036) = 5*X(5805)-X(52682) = 3*X(5886)+X(31671) = 2*X(11495)-3*X(43151) = 2*X(18483)+X(43180) = 2*X(42356)-3*X(50802) = 3*X(50802)-X(64699)

X(65452) lies on these lines: {1, 59385}, {2, 63974}, {3, 142}, {4, 5542}, {5, 38179}, {7, 1699}, {9, 3817}, {10, 38150}, {11, 52819}, {40, 38204}, {144, 5231}, {165, 60996}, {382, 38030}, {390, 11522}, {515, 15935}, {517, 58634}, {518, 5806}, {519, 3577}, {527, 3829}, {551, 43161}, {553, 7965}, {962, 38052}, {971, 12005}, {997, 43166}, {1537, 38152}, {1656, 38130}, {1709, 60938}, {1721, 63589}, {1750, 64672}, {1836, 60992}, {2346, 11218}, {2550, 4301}, {2807, 58472}, {2951, 9812}, {3086, 4312}, {3091, 5223}, {3174, 22836}, {3254, 21635}, {3543, 38024}, {3579, 38171}, {3624, 59418}, {3626, 7686}, {3627, 38041}, {3636, 43175}, {3826, 43174}, {3828, 7680}, {4297, 38053}, {4326, 30275}, {4887, 64134}, {4896, 64741}, {5071, 38101}, {5536, 61024}, {5572, 58626}, {5603, 30331}, {5686, 7989}, {5691, 11038}, {5715, 5811}, {5732, 38054}, {5735, 26363}, {5759, 8227}, {5762, 9955}, {5785, 31418}, {5818, 38210}, {5853, 13463}, {6067, 8226}, {6172, 30308}, {6173, 43182}, {6666, 10171}, {6684, 50394}, {6743, 6835}, {7678, 41572}, {7982, 38149}, {7988, 18230}, {7991, 40333}, {8255, 15006}, {8583, 59412}, {8727, 60945}, {9950, 42697}, {10164, 20195}, {10392, 10896}, {10398, 10591}, {10481, 30682}, {11372, 30424}, {11531, 59413}, {11680, 60979}, {12577, 30283}, {12630, 16189}, {12669, 18398}, {13159, 37447}, {13253, 45043}, {13464, 43179}, {15726, 58564}, {15911, 63972}, {16112, 60962}, {17605, 60919}, {17768, 20288}, {19862, 21153}, {21151, 41869}, {22791, 38137}, {22793, 31657}, {24644, 53057}, {25557, 43176}, {26333, 51098}, {28236, 42871}, {29668, 43173}, {30311, 60936}, {30340, 64697}, {31162, 35514}, {31391, 60993}, {31399, 38126}, {33558, 58608}, {34627, 51101}, {34648, 51099}, {36971, 61014}, {36990, 38046}, {36991, 59372}, {38055, 52836}, {38056, 52837}, {38075, 50834}, {38093, 50808}, {38143, 64085}, {38205, 46684}, {40273, 61509}, {41338, 60958}, {41573, 61011}, {45305, 53598}, {50865, 59374}, {54370, 60990}, {58433, 58441}, {59381, 61268}, {60910, 61021}, {60911, 61005}, {60961, 63275}, {61030, 65466}, {63258, 64162}

X(65452) = midpoint of X(i) and X(j) for these (i, j): {4, 5542}, {7, 63973}, {946, 5805}, {2550, 4301}, {3254, 21635}, {4297, 52835}, {5732, 51118}, {5735, 51090}, {11372, 30424}, {13159, 37447}, {16112, 60962}, {18482, 20330}, {22793, 31657}, {31162, 51100}, {34627, 51101}, {34648, 51099}, {40273, 61509}, {60895, 63970}
X(65452) = reflection of X(i) in X(j) for these (i, j): (6684, 61595), (20116, 13374), (43151, 142), (43174, 3826), (43175, 3636), (43176, 25557), (43179, 13464), (43181, 31657), (63970, 12571), (64699, 42356), (64830, 61509), (65405, 58433)
X(65452) = crosspoint of X(10405) and X(21453)
X(65452) = crosssum of X(2293) and X(3207)
X(65452) = pole of the line {7658, 21185} with respect to the incircle
X(65452) = pole of the line {6, 279} with respect to the circumhyperbola dual of Yff parabola
X(65452) = pole of the line {31391, 61021} with respect to the Feuerbach circumhyperbola
X(65452) = X(1843)-of-3rd Euler triangle, when ABC is acute
X(65452) = X(5542)-of-Euler triangle
X(65452) = X(11574)-of-Wasat triangle, when ABC is acute
X(65452) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 38036, 5542), (7, 1699, 63973), (7, 5274, 30330), (3091, 5223, 38158), (4301, 38151, 2550), (5735, 38037, 51090), (5759, 8227, 38059), (9812, 62778, 2951), (11372, 59386, 30424), (31162, 38073, 51100), (38053, 52835, 4297), (38054, 51118, 5732), (50802, 64699, 42356), (58433, 65405, 58441)

X(65453) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: HUTSON INTOUCH AND MIDARC

Barycentrics    a*(-4*(-a+b+c)*(b-c)*(a+b-c)*(a-b+c)+(-a+b+c)*(b-c)*(a^2-4*(b+c)*a+(3*b-c)*(b-3*c))*sin(A/2)+(a-b+c)*((3*b-4*c)*a^2-2*(2*b^2+b*c-4*c^2)*a+(b-c)*(b^2-7*b*c+4*c^2))*sin(B/2)+(a+b-c)*((4*b-3*c)*a^2-2*(4*b^2-b*c-2*c^2)*a+(b-c)*(4*b^2-7*b*c+c^2))*sin(C/2)) : :

As a conic with center in the infinity, it is a parabola. Its focus is X(65502).

X(65453) lies on these lines: {30, 511}, {1130, 45878}, {13301, 48032}

X(65453) = isogonal conjugate of the circumperp conjugate of X(10497)
X(65453) = crosspoint of X(7) and X(43192)
X(65453) = crosssum of X(55) and X(10495)
X(65453) = X(i)-zayin conjugate of-X(j) for these (i, j): (6730, 8108), (45877, 363)

X(65454) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: HUTSON INTOUCH AND 2nd MIDARC

Barycentrics    a*((-a+b+c)*((b+c)*a^2-12*b*c*a-(b^2-c^2)*(b-c))*sin(A/2)+(a-b+c)*((b+2*c)*a^2-10*b*c*a-(b^2-c^2)*(b-2*c))*sin(B/2)+(a+b-c)*((2*b+c)*a^2-10*b*c*a-(b^2-c^2)*(2*b-c))*sin(C/2)) : :
X(65454) = 3*X(1)-X(31768) = X(3057)+3*X(11234) = X(5571)-3*X(11234) = 3*X(5919)+X(8422) = 3*X(5919)-X(31766) = 3*X(31767)+X(31768) = 2*X(31767)+X(58616) = 2*X(31768)-3*X(58616)

X(65454) lies on these lines: {1, 168}, {164, 30337}, {516, 65398}, {3057, 5571}, {3295, 55172}, {5919, 8422}, {9957, 32183}, {10106, 31770}, {10624, 31734}, {12523, 31393}, {12622, 63993}, {13600, 31791}, {31792, 53007}, {58679, 58689}

X(65454) = midpoint of X(i) and X(j) for these (i, j): {1, 31767}, {3057, 5571}, {8422, 31766}, {9957, 32183}, {10106, 31770}, {10624, 31734}, {13600, 31791}
X(65454) = reflection of X(i) in X(j) for these (i, j): (58616, 1), (58689, 58679)
X(65454) = X(1125)-of-Hutson intouch triangle, when ABC is acute
X(65454) = X(12512)-of-intouch triangle, when ABC is acute
X(65454) = X(12571)-of-Ursa-minor triangle, when ABC is acute
X(65454) = X(31730)-of-incircle-circles triangle, when ABC is acute
X(65454) = X(31767)-of-anti-Aquila triangle
X(65454) = X(51118)-of-inverse-in-incircle triangle, when ABC is acute
X(65454) = X(58616)-of-5th mixtilinear triangle
X(65454) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3057, 11234, 5571), (5919, 8422, 31766)

X(65455) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd HYACINTH AND ORTHIC AXES

Barycentrics    (b^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^10-3*(b^2+c^2)*a^8+(3*b^4+11*b^2*c^2+3*c^4)*a^6-(b^4+7*b^2*c^2+c^4)*(b^2+c^2)*a^4-(b^4-10*b^2*c^2+c^4)*b^2*c^2*a^2+(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :

X(65455) lies on these lines: {647, 16229}, {804, 57071}, {2797, 20580}, {3566, 13400}, {22089, 47206}

X(65455) = reflection of X(65394) in X(16229)
X(65455) = cross-difference of every pair of points on the line X(6638)X(52077)
X(65455) = pole of the line {3164, 37201} with respect to the polar circle
X(65455) = pole of the line {394, 801} with respect to the orthic inconic

X(65456) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd HYACINTH AND PELLETIER

Barycentrics    (b-c)*(2*a^11-(b+c)*a^10-6*(b^2+c^2)*a^9+3*(b+c)*(b^2+c^2)*a^8+4*(b^4+4*b^2*c^2+c^4)*a^7-2*(b+c)*(b^4+4*b^2*c^2+c^4)*a^6+4*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^5-2*(b+c)*(b^6+c^6+3*b^2*c^2*(b^2-4*b*c+c^2))*a^4-6*(b^2-c^2)^4*a^3+(b^2-c^2)*(b-c)*(3*b^6+3*c^6+(6*b^4+6*c^4+b*c*(b^2-12*b*c+c^2))*b*c)*a^2+2*(b^4-c^4)*(b^2-c^2)^3*a-(b^4-c^4)*(b^2-c^2)^3*(b+c)) : :

X(65456) lies on these lines: {11, 244}, {3566, 13400}

X(65456) = cross-difference of every pair of points on the line X(101)X(52077)
X(65456) = pole of the line {394, 1146} with respect to the orthic inconic

X(65457) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd HYACINTH AND SCHRÖETER

Barycentrics    (b^2-c^2)*(a^14-3*(b^2+c^2)*a^12+(2*b^4+7*b^2*c^2+2*c^4)*a^10+(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^8-(3*b^8+3*c^8+2*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^6+(b^2+c^2)*(b^8+c^8-2*(b^4-3*b^2*c^2+c^4)*b^2*c^2)*a^4+3*(b^2-c^2)^4*b^2*c^2*a^2-(b^4-c^4)*(b^2-c^2)^3*b^2*c^2) : :

X(65457) lies on these lines: {115, 804}, {3566, 13400}

X(65457) = cross-difference of every pair of points on the line X(1634)X(52077)
X(65457) = pole of the line {5139, 35588} with respect to the Jerabek circumhyperbola
X(65457) = pole of the line {512, 6754} with respect to the Kiepert circumhyperbola
X(65457) = pole of the line {338, 394} with respect to the orthic inconic

X(65458) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INCENTRAL AND LEMOINE

Barycentrics    a^2*(b^2-c^2)*((2*a^2-b^2-c^2)^2-9*b^2*c^2) : :
X(65458) = 3*X(3288)-X(17414) = 4*X(3288)-X(50549)

X(65458) lies on these lines: {187, 237}, {523, 8584}, {3050, 9178}, {8599, 12073}, {11182, 45335}

X(65458) = reflection of X(11182) in X(45335)
X(65458) = cross-difference of every pair of points on the line X(2)X(8586)
X(65458) = X(1084)-Dao conjugate of-X(10484)
X(65458) = X(662)-isoconjugate of-X(10484)
X(65458) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (512, 10484), (10485, 99)
X(65458) = perspector of the circumconic through X(6) and X(8587)
X(65458) = pole of the line {574, 5640} with respect to the 1st Brocard circle
X(65458) = pole of the line {262, 10484} with respect to the orthoptic circle of Steiner inellipse
X(65458) = pole of the line {194, 7618} with respect to the Steiner circumellipse
X(65458) = pole of the line {39, 7619} with respect to the Steiner inellipse
X(65458) = barycentric product X(523)*X(10485)
X(65458) = trilinear product X(661)*X(10485)
X(65458) = trilinear quotient X(i)/X(j) for these (i, j): (661, 10484), (10485, 662)

X(65459) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INCENTRAL AND MACBEATH

Barycentrics    a^2*(b^2-c^2)*((b^2+b*c+c^2)*a^2-(b+c)^2*(b^2-b*c+c^2))*((b^2-b*c+c^2)*a^2-(b-c)^2*(b^2+b*c+c^2)) : :

X(65459) lies on these lines: {187, 237}, {850, 6368}, {3265, 41167}, {6587, 15508}, {16040, 58310}, {17434, 17994}, {34983, 58757}

X(65459) = reflection of X(58310) in X(16040)
X(65459) = cross-difference of every pair of points on the line X(2)X(14585)
X(65459) = perspector of the circumconic through X(6) and X(18027)
X(65459) = pole of the line {6, 35225} with respect to the circumcircle
X(65459) = pole of the line {3613, 23292} with respect to the nine-point circle
X(65459) = pole of the line {262, 578} with respect to the orthoptic circle of Steiner inellipse
X(65459) = pole of the line {184, 264} with respect to the polar circle
X(65459) = pole of the line {6, 35225} with respect to the Brocard inellipse
X(65459) = pole of the line {324, 23635} with respect to the MacBeath inconic
X(65459) = pole of the line {194, 317} with respect to the Steiner circumellipse
X(65459) = pole of the line {39, 53477} with respect to the Steiner inellipse
X(65459) = barycentric product X(21117)*X(26893)

X(65460) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INCIRCLE-CIRCLES AND 1st SAVIN

Barycentrics    2*a^4+8*(b+c)*a^3+(7*b^2+16*b*c+7*c^2)*a^2+8*(b+c)*b*c*a-(b^2-c^2)^2 : :
X(65460) = X(1)+3*X(37631) = 7*X(1)-3*X(49739) = 5*X(1)+3*X(49744) = 3*X(1)+X(49745) = 5*X(1)-X(64158) = X(3244)+3*X(50226) = 5*X(3616)+3*X(42045) = 5*X(3616)-X(49716) = 3*X(42045)+X(49716) = X(49734)-3*X(50226)

X(65460) lies on these lines: {1, 30}, {2, 49718}, {3, 1014}, {5, 5712}, {6, 50205}, {21, 41819}, {57, 48924}, {58, 63401}, {69, 50409}, {81, 6675}, {86, 41014}, {140, 940}, {145, 50169}, {193, 16844}, {325, 33770}, {386, 17392}, {442, 37635}, {468, 2906}, {511, 5045}, {524, 1125}, {540, 3636}, {548, 19765}, {550, 4340}, {551, 49728}, {613, 28369}, {999, 48930}, {1056, 46704}, {1154, 16193}, {1211, 28619}, {1213, 28620}, {1434, 41810}, {1509, 6390}, {2303, 52259}, {2895, 17514}, {3244, 49734}, {3333, 48882}, {3487, 18631}, {3530, 37522}, {3564, 5719}, {3578, 5550}, {3616, 42045}, {3622, 13745}, {3623, 50171}, {3624, 49724}, {3628, 5718}, {3631, 52782}, {3664, 24470}, {3745, 63282}, {3746, 15447}, {3946, 52495}, {4046, 41812}, {4205, 17778}, {4307, 10386}, {4349, 48893}, {4658, 17056}, {4667, 31445}, {4869, 56736}, {4909, 34937}, {5049, 49557}, {5625, 56949}, {5703, 15936}, {5708, 48917}, {5716, 15935}, {5717, 12433}, {6000, 16201}, {6767, 37425}, {6841, 63338}, {7373, 9840}, {7483, 14996}, {7819, 20132}, {10580, 48877}, {11018, 13754}, {11019, 48887}, {11037, 48941}, {11108, 63007}, {11110, 20090}, {11359, 19783}, {11374, 59613}, {13728, 63056}, {14552, 16457}, {15673, 16948}, {15808, 49729}, {15934, 48909}, {16020, 50261}, {16239, 37634}, {16617, 64420}, {16845, 62997}, {16884, 24159}, {17300, 56734}, {17316, 50153}, {17379, 17698}, {17527, 63008}, {17557, 20086}, {17590, 63074}, {17768, 58380}, {19273, 63057}, {19334, 31303}, {19684, 50318}, {19766, 48815}, {19862, 49730}, {21620, 48931}, {21677, 63310}, {24883, 63343}, {25650, 42028}, {26109, 56018}, {26131, 64167}, {26860, 56778}, {28212, 37548}, {29585, 50168}, {31393, 48915}, {35018, 37693}, {37633, 52264}, {44238, 63297}, {44669, 63370}, {45931, 52265}, {46467, 63965}, {46934, 50256}, {48847, 50238}, {48861, 50395}, {48894, 51788}, {50125, 50606}, {50262, 52229}, {50264, 63940}, {50266, 63945}, {50299, 50590}, {51559, 63089}, {56993, 63009}, {58469, 58571}

X(65460) = midpoint of X(i) and X(j) for these (i, j): {1, 49743}, {3244, 49734}, {5045, 10108}
X(65460) = complement of X(49718)
X(65460) = pole of the line {523, 4960} with respect to the incircle
X(65460) = pole of the line {8818, 37500} with respect to the Kiepert circumhyperbola
X(65460) = pole of the line {13615, 35193} with respect to the Stammler hyperbola
X(65460) = pole of the line {41800, 46915} with respect to the Steiner inellipse
X(65460) = X(6675)-of-2nd Pavlov triangle
X(65460) = X(35719)-of-inverse-in-incircle triangle, when ABC is acute
X(65460) = X(46025)-of-incircle-circles triangle, when ABC is acute
X(65460) = X(49743)-of-anti-Aquila triangle
X(65460) = X(58468)-of-intouch triangle, when ABC is acute
X(65460) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 37631, 49743), (3244, 50226, 49734), (3616, 42045, 49716), (37635, 64377, 442)

X(65461) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INTOUCH AND LEMOINE

Barycentrics    (b-c)*(4*a^2-3*(b+c)*a+b^2+c^2)*(4*a^3+(b^2+c^2)*a-3*(b^2-c^2)*(b-c)) : :

X(65461) lies on these lines: {513, 676}, {8599, 12073}

X(65462) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INTOUCH AND MACBEATH

Barycentrics    (b-c)*((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))*((b^2+c^2)*a^3+(b^2-c^2)*(b-c)*a^2-(b^2-c^2)^2*a-(b^4-c^4)*(b-c)) : :

X(65462) lies on these lines: {513, 676}, {850, 6368}

X(65462) = cross-difference of every pair of points on the line X(220)X(14585)
X(65462) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (41007, 13136), (42448, 32641)
X(65462) = perspector of the circumconic through X(279) and X(18027)
X(65462) = pole of the line {1617, 35225} with respect to the circumcircle
X(65462) = pole of the line {184, 7046} with respect to the polar circle
X(65462) = pole of the line {317, 4452} with respect to the Steiner circumellipse
X(65462) = barycentric product X(10015)*X(41007)
X(65462) = trilinear product X(i)*X(j) for these {i, j}: {1769, 41007}, {36038, 42448}
X(65462) = trilinear quotient X(41007)/X(36037)

X(65463) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INTOUCH AND STEINER

Barycentrics    (b-c)*(2*a^2+(b+c)*a-b^2-c^2)*(2*a^3-(b^2+c^2)*a+(b^2-c^2)*(b-c)) : :

X(65463) lies on these lines: {2, 65496}, {99, 110}, {513, 676}

X(65463) = anticomplement of X(65496)
X(65463) = cross-difference of every pair of points on the line X(220)X(3124)
X(65463) = X(65496)-Dao conjugate of-X(65496)
X(65463) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4897, 60251), (17476, 35354)
X(65463) = perspector of the circumconic through X(279) and X(4590)
X(65463) = pole of the line {1617, 1634} with respect to the circumcircle
X(65463) = pole of the line {7046, 8754} with respect to the polar circle
X(65463) = pole of the line {2, 57088} with respect to the Kiepert parabola
X(65463) = pole of the line {99, 4452} with respect to the Steiner circumellipse
X(65463) = pole of the line {620, 4000} with respect to the Steiner inellipse
X(65463) = pole of the line {523, 7256} with respect to the Steiner-Wallace hyperbola
X(65463) = barycentric product X(4897)*X(35466)
X(65463) = trilinear quotient X(17058)/X(35354)

X(65464) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INTOUCH AND SYMMEDIAL

Barycentrics    a^4*(b-c)*((b+c)*a-b^2-c^2)*((b^2+c^2)*a-(b+c)*(b-c)^2) : :

X(65464) lies on these lines: {513, 676}, {669, 688}

X(65464) = cross-difference of every pair of points on the line X(76)X(220)
X(65464) = crosssum of X(36802) and X(36803)
X(65464) = X(40419)-isoconjugate of-X(51560)
X(65464) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (9449, 36802), (21746, 36803)
X(65464) = perspector of the circumconic through X(32) and X(279)
X(65464) = pole of the line {1613, 1617} with respect to the circumcircle
X(65464) = pole of the line {7046, 18022} with respect to the polar circle
X(65464) = pole of the line {3051, 23653} with respect to the Brocard inellipse
X(65464) = pole of the line {4452, 8264} with respect to the Steiner circumellipse
X(65464) = pole of the line {4000, 8265} with respect to the Steiner inellipse
X(65464) = pole of the line {4609, 7256} with respect to the Steiner-Wallace hyperbola
X(65464) = barycentric product X(i)*X(j) for these {i, j}: {665, 21746}, {9449, 43042}, {9454, 21118}, {16588, 53539}
X(65464) = trilinear product X(i)*X(j) for these {i, j}: {9449, 53544}, {9455, 21118}
X(65464) = trilinear quotient X(i)/X(j) for these (i, j): (17451, 36803), (21746, 51560)

X(65465) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND 1st ZANIAH

Barycentrics    a*((b+c)*a^4-2*(b^2+b*c+c^2)*a^3+6*(b+c)*b*c*a^2+2*(b^2-3*b*c+c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)*(b^2-4*b*c+c^2)) : :
X(65465) = 3*X(354)+X(497) = 3*X(354)-X(63994) = 9*X(354)-X(63995) = 3*X(497)+X(63995) = X(1376)-3*X(3742) = X(3476)-5*X(17609) = 5*X(5439)-X(63137) = 3*X(11019)-X(64157) = 3*X(12915)+X(64157)

X(65465) lies on these lines: {1, 474}, {7, 354}, {56, 63141}, {390, 10178}, {515, 5045}, {516, 58577}, {518, 3452}, {528, 11018}, {614, 30621}, {938, 34791}, {942, 4301}, {960, 14986}, {1058, 9943}, {1210, 4662}, {1699, 10569}, {1750, 30350}, {3057, 5435}, {3333, 63991}, {3476, 17609}, {3586, 50190}, {3660, 64162}, {3848, 13405}, {4640, 42884}, {4847, 58634}, {5049, 37728}, {5274, 8581}, {5281, 5919}, {5728, 28609}, {5745, 58679}, {5853, 58623}, {6259, 12675}, {6738, 16215}, {6767, 63132}, {7373, 7686}, {9025, 57033}, {9940, 40270}, {9957, 10164}, {10156, 31792}, {10453, 63151}, {10860, 10980}, {11035, 19925}, {11227, 30331}, {12564, 50192}, {14760, 58612}, {15172, 58573}, {15587, 24392}, {16201, 58565}, {16216, 58561}, {17658, 31249}, {17784, 64149}, {18389, 50196}, {30343, 62178}, {36973, 62823}, {39595, 59812}, {46681, 58613}, {58567, 58576}, {58637, 64124}, {64127, 64352}

X(65465) = midpoint of X(i) and X(j) for these (i, j): {497, 63994}, {942, 63993}, {11019, 12915}, {12675, 26333}
X(65465) = reflection of X(18227) in X(3816)
X(65465) = cross-difference of every pair of points on the line X(4394)X(57180)
X(65465) = crosssum of X(55) and X(20323)
X(65465) = perspector of the circumconic through X(27834) and X(36838)
X(65465) = pole of the line {650, 30198} with respect to the incircle
X(65465) = pole of the line {3452, 10481} with respect to the circumhyperbola dual of Yff parabola
X(65465) = pole of the line {7, 2098} with respect to the Feuerbach circumhyperbola
X(65465) = X(13567)-of-inverse-in-incircle triangle, when ABC is acute
X(65465) = X(53415)-of-intouch triangle, when ABC is acute
X(65465) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 17626, 3742), (354, 497, 63994), (354, 10580, 5572), (3742, 5836, 5437), (5045, 5806, 12577), (6738, 16215, 58609), (11018, 18240, 58560), (58576, 63999, 58567)

X(65466) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: INNER-JOHNSON AND URSA MAJOR

Barycentrics    a*((b+c)*a^6-2*(2*b^2+b*c+2*c^2)*a^5+(b+c)*(5*b^2-2*b*c+5*c^2)*a^4-6*(b^2+c^2)*b*c*a^3-5*(b^4-c^4)*(b-c)*a^2+4*(b^4+c^4+b*c*(2*b^2+b*c+2*c^2))*(b-c)^2*a-(b^2-c^2)*(b-c)^3*(b^2+4*b*c+c^2)) : :
X(65466) = 3*X(5927)-X(16112) = 3*X(5927)+X(17668) = X(11495)-3*X(61028) = 3*X(15064)-X(60942)

X(65466) lies on these lines: {7, 61663}, {9, 165}, {11, 5572}, {142, 58578}, {355, 518}, {516, 20117}, {908, 7965}, {960, 6253}, {971, 3826}, {1001, 33597}, {1071, 3812}, {1898, 60925}, {2801, 60980}, {3059, 3434}, {5660, 36868}, {5696, 59389}, {5720, 11496}, {5728, 10826}, {5777, 17768}, {6690, 10157}, {6796, 60911}, {8226, 41548}, {10178, 54357}, {11246, 41572}, {12114, 65426}, {14100, 60943}, {15064, 58651}, {15481, 18491}, {15733, 42356}, {17615, 60979}, {17616, 25973}, {17625, 58563}, {17857, 42885}, {31391, 41563}, {38454, 40659}, {40263, 60896}, {40269, 54448}, {41566, 61011}, {61030, 65452}

X(65466) = midpoint of X(i) and X(j) for these (i, j): {16112, 17668}, {40263, 60896}
X(65466) = reflection of X(i) in X(j) for these (i, j): (15481, 58631), (65405, 58634)
X(65466) = pole of the line {38454, 41563} with respect to the Feuerbach circumhyperbola
X(65466) = X(3589)-of-Ursa-major triangle, when ABC is acute
X(65466) = X(5572)-of-inner-Johnson triangle
X(65466) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (11, 17620, 5572), (5927, 17668, 16112), (11495, 16112, 1709), (15587, 41871, 17668)

X(65467) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: LEMOINE AND MACBEATH

Barycentrics    (b^2-c^2)*(a^4-b^4+b^2*c^2-c^4)*((b^2+c^2)*a^4+b^2*c^2*a^2-(b^4-c^4)*(b^2-c^2)) : :

X(65467) lies on these lines: {850, 6368}, {8599, 12073}, {9517, 9979}

X(65467) = X(5099)-Dao conjugate of-X(19151)
X(65467) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2492, 19151), (5169, 17708)
X(65467) = perspector of the circumconic through X(18027) and X(37765)
X(65467) = pole of the line {67, 184} with respect to the polar circle
X(65467) = barycentric product X(5169)*X(9979)

X(65468) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: LEMOINE AND ORTHIC

Barycentrics    (b^2-c^2)*(4*a^4+(b^2+c^2)*a^2-3*(b^2-c^2)^2) : :
X(65468) = 4*X(2501)-X(12075)

X(65468) lies on these lines: {351, 12077}, {460, 512}, {647, 59849}, {804, 44568}, {826, 9208}, {1637, 17414}, {5466, 45103}, {8599, 12073}, {8644, 55122}, {9134, 32478}, {9188, 64877}, {10278, 32473}, {50548, 53365}

X(65468) = midpoint of X(i) and X(j) for these (i, j): {351, 12077}, {50548, 53365}
X(65468) = cross-difference of every pair of points on the line X(394)X(53095)
X(65468) = crosspoint of X(2501) and X(8599)
X(65468) = crosssum of X(4558) and X(9145)
X(65468) = X(i)-Dao conjugate of-X(j) for these (i, j): (6523, 54949), (15259, 52777)
X(65468) = X(i)-isoconjugate of-X(j) for these {i, j}: {255, 54949}, {326, 52777}, {6507, 42393}
X(65468) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (393, 54949), (2207, 52777), (6524, 42393), (53418, 99)
X(65468) = perspector of the circumconic through X(393) and X(53101)
X(65468) = pole of the line {3839, 9752} with respect to the orthoptic circle of Steiner inellipse
X(65468) = pole of the line {69, 62960} with respect to the polar circle
X(65468) = pole of the line {25, 18429} with respect to the orthic inconic
X(65468) = pole of the line {6392, 7620} with respect to the Steiner circumellipse
X(65468) = pole of the line {3767, 7617} with respect to the Steiner inellipse
X(65468) = barycentric product X(523)*X(53418)
X(65468) = trilinear product X(661)*X(53418)
X(65468) = trilinear quotient X(i)/X(j) for these (i, j): (158, 54949), (1096, 52777), (6520, 42393), (53418, 662)

X(65469) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: LEMOINE AND STEINER

Barycentrics    (b^2-c^2)*(5*a^2-b^2-c^2)*(4*a^4-(b^2+c^2)*a^2+b^4-4*b^2*c^2+c^4) : :
X(65469) = X(6333)+2*X(39904)

X(65469) lies on these lines: {99, 110}, {512, 9189}, {523, 47545}, {1499, 4786}, {2793, 9135}, {6791, 35234}, {8371, 42663}, {8599, 12073}, {15724, 45680}, {55122, 64941}

X(65469) = midpoint of X(i) and X(j) for these (i, j): {8371, 42663}, {9168, 39904}
X(65469) = reflection of X(6333) in X(9168)
X(65469) = cross-difference of every pair of points on the line X(3124)X(21448)
X(65469) = crosspoint of X(17937) and X(22329)
X(65469) = crosssum of X(17999) and X(21448)
X(65469) = X(17937)-Ceva conjugate of-X(22329)
X(65469) = X(i)-Dao conjugate of-X(j) for these (i, j): (2793, 18012), (11147, 46144), (35133, 5503), (61071, 5485), (62568, 34246), (62578, 35179)
X(65469) = X(27088)-hirst inverse of-X(37745)
X(65469) = X(2709)-isoconjugate of-X(55923)
X(65469) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1384, 2709), (1499, 5503), (1992, 46144), (2030, 1296), (2793, 5485), (6791, 34246), (9135, 21448), (17937, 57569), (18800, 2418), (22329, 35179), (61071, 18012)
X(65469) = perspector of the circumconic through X(1992) and X(4590)
X(65469) = pole of the line {114, 9770} with respect to the orthoptic circle of Steiner inellipse
X(65469) = pole of the line {512, 1296} with respect to the Stammler hyperbola
X(65469) = pole of the line {99, 11148} with respect to the Steiner circumellipse
X(65469) = pole of the line {620, 11165} with respect to the Steiner inellipse
X(65469) = pole of the line {523, 35179} with respect to the Steiner-Wallace hyperbola
X(65469) = barycentric product X(i)*X(j) for these {i, j}: {1499, 22329}, {1992, 2793}, {2408, 18800}, {6791, 34245}, {9125, 63853}, {9135, 11059}, {17937, 35133}
X(65469) = trilinear product X(i)*X(j) for these {i, j}: {2030, 14207}, {2793, 36277}
X(65469) = trilinear quotient X(i)/X(j) for these (i, j): (2793, 55923), (14207, 5503), (22329, 37216), (36277, 2709)
X(65469) = X(45327)-of-anti-McCay triangle
X(65469) = X(18800)-of-1st Parry triangle
X(65469) = X(1637)-of-anti-Artzt triangle

X(65470) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: LEMOINE AND SYMMEDIAL

Barycentrics    a^4*(b^2-c^2)*(2*a^2-b^2-c^2)*(2*(b^2+c^2)*a^2-b^4+4*b^2*c^2-c^4) : :

X(65470) lies on these lines: {669, 688}, {8599, 12073}

X(65470) = X(13410)-reciprocal conjugate of-X(53080)
X(65470) = barycentric product X(351)*X(13410)

X(65471) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: LEMOINE AND YFF CONTACT

Barycentrics    (b-c)*(2*a^2+3*(b+c)*a-b^2-3*b*c-c^2)*(4*a^3-2*(b+c)*a^2+(b^2+c^2)*a+(b+c)*(b^2-3*b*c+c^2)) : :

X(65471) lies on these lines: {100, 190}, {8599, 12073}

X(65471) = perspector of the circumconic through X(1016) and X(50121)

X(65472) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MACBEATH AND ORTHIC

Barycentrics    (b^4-c^4)*(a^2+b^2-c^2)^2*(a^2-b^2+c^2)^2 : :

X(65472) lies on these lines: {4, 50548}, {107, 46970}, {460, 512}, {850, 6368}, {6753, 55122}, {12077, 17994}, {14618, 47126}, {15422, 53149}, {16229, 33294}, {36827, 46151}, {47128, 59932}, {52317, 53386}

X(65472) = cross-difference of every pair of points on the line X(394)X(14585)
X(65472) = crosspoint of X(27376) and X(46151)
X(65472) = crosssum of X(28724) and X(58353)
X(65472) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2207, 8754), (46151, 27376)
X(65472) = X(i)-Dao conjugate of-X(j) for these (i, j): (136, 1799), (1084, 28724), (3005, 58353), (3124, 394), (3162, 65307), (5139, 1176), (6523, 4577), (15259, 827), (15449, 3926), (40938, 4563), (53983, 69), (55043, 326), (55050, 577)
X(65472) = X(i)-isoconjugate of-X(j) for these {i, j}: {63, 65307}, {255, 4577}, {326, 827}, {394, 4599}, {577, 4593}, {662, 28724}, {689, 52430}, {1176, 4592}, {1799, 4575}, {3926, 34072}, {4558, 34055}, {6507, 42396}, {10547, 55202}, {14585, 37204}, {24041, 58353}
X(65472) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (25, 65307), (158, 4593), (393, 4577), (427, 4563), (512, 28724), (688, 577), (826, 3926), (1096, 4599), (1235, 52608), (1843, 4558), (2052, 689), (2084, 255), (2207, 827), (2489, 1176), (2501, 1799), (2525, 4176), (3005, 394), (3124, 58353), (6524, 42396), (8061, 326), (8754, 4580), (9494, 14585), (15422, 39287), (17442, 4592), (18027, 42371), (20883, 55202), (21016, 4561), (21108, 17206), (27369, 32661), (27373, 4611), (27376, 99), (36417, 4630), (39691, 3265), (41375, 55225), (41676, 47389), (46151, 4590), (50521, 18604), (57204, 10547), (57806, 37204), (58757, 83), (61218, 47390)
X(65472) = perspector of the circumconic through X(393) and X(18027)
X(65472) = pole of the line {1609, 35225} with respect to the circumcircle
X(65472) = pole of the line {1843, 46442} with respect to the incircle-of-orthic triangle
X(65472) = pole of the line {7487, 9752} with respect to the orthoptic circle of Steiner inellipse
X(65472) = pole of the line {69, 184} with respect to the polar circle
X(65472) = pole of the line {324, 15809} with respect to the MacBeath inconic
X(65472) = pole of the line {25, 13881} with respect to the orthic inconic
X(65472) = pole of the line {317, 6392} with respect to the Steiner circumellipse
X(65472) = barycentric product X(i)*X(j) for these {i, j}: {107, 39691}, {115, 46151}, {141, 58757}, {158, 8061}, {393, 826}, {427, 2501}, {523, 27376}, {688, 18027}, {1096, 62418}, {1235, 2489}, {1826, 21108}, {1843, 14618}, {2052, 3005}, {2084, 57806}, {2207, 23285}, {2525, 6524}, {2970, 35325}, {7649, 21016}, {8754, 41676}, {12077, 19174}
X(65472) = trilinear product X(i)*X(j) for these {i, j}: {38, 58757}, {158, 3005}, {393, 8061}, {661, 27376}, {688, 57806}, {826, 1096}, {1824, 21108}, {1843, 24006}, {2052, 2084}, {2207, 62418}, {2489, 20883}, {2501, 17442}, {2643, 46151}, {6591, 21016}, {24019, 39691}
X(65472) = trilinear quotient X(i)/X(j) for these (i, j): (19, 65307), (158, 4577), (393, 4599), (427, 4592), (661, 28724), (688, 52430), (826, 326), (1096, 827), (1235, 55202), (1843, 4575), (2052, 4593), (2084, 577), (2207, 34072), (2501, 34055), (2525, 1102), (2643, 58353), (3005, 255), (6520, 42396), (8061, 394), (17442, 4558)
X(65472) = (X(12075), X(51513))-harmonic conjugate of X(2501)

X(65473) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MACBEATH AND STEINER

Barycentrics    (b^2-c^2)*(a^4-2*(b^2+c^2)*a^2+b^4+c^4)*((b^2+c^2)*a^4-2*(b^4-b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :

X(65473) lies on these lines: {99, 110}, {525, 15423}, {850, 6368}, {924, 6563}, {2081, 2799}, {3265, 6132}, {3580, 47236}, {6334, 34834}, {9134, 23293}, {11442, 55122}, {12827, 55121}

X(65473) = cross-difference of every pair of points on the line X(3124)X(14585)
X(65473) = crosspoint of X(44138) and X(61188)
X(65473) = crosssum of X(1576) and X(53329)
X(65473) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1299, 21221), (46969, 18664)
X(65473) = X(16077)-Ceva conjugate of-X(317)
X(65473) = X(i)-Dao conjugate of-X(j) for these (i, j): (113, 32734), (16178, 14593), (34834, 925), (35588, 184), (39005, 2351), (39013, 14910), (39021, 2165), (52584, 15328)
X(65473) = X(i)-isoconjugate of-X(j) for these {i, j}: {1820, 32708}, {2351, 36114}, {14910, 36145}, {32734, 36053}, {60501, 65262}
X(65473) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (24, 32708), (317, 687), (403, 65176), (686, 2351), (924, 14910), (1725, 36145), (1748, 36114), (1993, 10420), (3003, 32734), (3580, 925), (6334, 68), (6563, 2986), (7763, 18878), (9723, 43755), (16172, 39416), (21731, 60501), (44138, 30450), (44179, 65262), (44808, 52557), (47236, 14593), (52000, 112), (52584, 5504), (55121, 2165), (57065, 1300), (62338, 65309), (63827, 36053), (63829, 60035)
X(65473) = perspector of the circumconic through X(4590) and X(7763)
X(65473) = pole of the line {1634, 35225} with respect to the circumcircle
X(65473) = pole of the line {184, 8754} with respect to the polar circle
X(65473) = pole of the line {2, 38380} with respect to the Kiepert parabola
X(65473) = pole of the line {512, 32734} with respect to the Stammler hyperbola
X(65473) = pole of the line {99, 317} with respect to the Steiner circumellipse
X(65473) = pole of the line {620, 6644} with respect to the Steiner inellipse
X(65473) = pole of the line {523, 925} with respect to the Steiner-Wallace hyperbola
X(65473) = barycentric product X(i)*X(j) for these {i, j}: {317, 6334}, {3267, 52000}, {3580, 6563}, {7763, 55121}, {44138, 52584}, {57065, 62338}
X(65473) = trilinear product X(i)*X(j) for these {i, j}: {1725, 6563}, {1748, 6334}, {3580, 63827}, {14208, 52000}, {15329, 17881}, {44138, 63832}, {44179, 55121}
X(65473) = trilinear quotient X(i)/X(j) for these (i, j): (317, 36114), (1725, 32734), (1748, 32708), (3580, 36145), (6334, 1820), (6563, 36053), (7763, 65262), (17881, 15328), (44179, 10420), (52000, 32676), (55249, 18879), (63827, 14910)

X(65474) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MACBEATH AND SYMMEDIAL

Barycentrics    a^4*(b^2-c^2)*((b^2+c^2)*a^2-b^4-c^4)*((b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2)) : :

X(65474) lies on these lines: {669, 688}, {850, 6368}, {39691, 41221}

X(65474) = cross-difference of every pair of points on the line X(76)X(14585)
X(65474) = crosspoint of X(2491) and X(16230)
X(65474) = crosssum of X(43187) and X(43754)
X(65474) = X(21243)-Dao conjugate of-X(17932)
X(65474) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (23635, 43187), (40951, 2966)
X(65474) = perspector of the circumconic through X(32) and X(18027)
X(65474) = pole of the line {1613, 35225} with respect to the circumcircle
X(65474) = pole of the line {184, 18022} with respect to the polar circle
X(65474) = pole of the line {317, 8264} with respect to the Steiner circumellipse
X(65474) = barycentric product X(i)*X(j) for these {i, j}: {2491, 21243}, {2799, 40951}, {3569, 23635}, {17994, 22416}, {44114, 45215}
X(65474) = trilinear quotient X(i)/X(j) for these (i, j): (23635, 36036), (40951, 36084)

X(65475) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MACBEATH AND YFF CONTACT

Barycentrics    (b-c)*(-a+b+c)*((b+c)*a^2+b*c*a-b^3-c^3)*((b^2+c^2)*a^3-(b^3+c^3)*a^2-(b^2-c^2)^2*a+(b^2-c^2)*(b^3-c^3)) : :

X(65475) lies on these lines: {100, 190}, {850, 6368}

X(65475) = cross-difference of every pair of points on the line X(1015)X(14585)
X(65475) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3190, 35182), (20294, 2989), (41320, 32699), (48381, 1305), (57043, 917)
X(65475) = perspector of the circumconic through X(1016) and X(18027)
X(65475) = pole of the line {100, 35225} with respect to the circumcircle
X(65475) = pole of the line {184, 2969} with respect to the polar circle
X(65475) = pole of the line {190, 317} with respect to the Steiner circumellipse
X(65475) = pole of the line {2, 57043} with respect to the Yff parabola
X(65475) = barycentric product X(20294)*X(48381)
X(65475) = trilinear product X(i)*X(j) for these {i, j}: {1736, 20294}, {17878, 56742}, {27396, 55125}
X(65475) = trilinear quotient X(27396)/X(35182)

X(65476) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MANDART-INCIRCLE AND MIDARC

Barycentrics    -(2*a^2+(b-c)^2)*(-a+b+c)^2*sin(A/2)+(a-b+c)*(2*a^3-(2*b+3*c)*a^2+(b-c)*(b-2*c)*a-(b^2-c^2)*(b-c))*sin(B/2)+(a+b-c)*(2*a^3-(3*b+2*c)*a^2+(2*b-c)*(b-c)*a-(b^2-c^2)*(b-c))*sin(C/2) : :
X(65476) = 3*X(1)-X(31734) = X(177)+3*X(3058) = 3*X(3058)-X(31770) = X(6284)+3*X(11191) = 3*X(11191)-X(31735) = X(31734)+3*X(31769) = 2*X(31734)-3*X(65398) = 2*X(31769)+X(65398)

X(65476) lies on these lines: {1, 31734}, {177, 3058}, {390, 12518}, {497, 12614}, {516, 58616}, {528, 58444}, {950, 31766}, {1058, 12523}, {3295, 12622}, {3488, 55173}, {5571, 64162}, {5853, 58689}, {6284, 11191}, {10624, 31768}, {12908, 15171}, {15170, 32183}, {18258, 49736}, {21633, 30331}, {55172, 63993}, {55174, 63999}

X(65476) = midpoint of X(i) and X(j) for these (i, j): {1, 31769}, {177, 31770}, {950, 31766}, {6284, 31735}, {10624, 31768}, {12908, 15171}
X(65476) = reflection of X(65398) in X(1)
X(65476) = X(31738)-of-incircle-circles triangle, when ABC is acute
X(65476) = X(31769)-of-anti-Aquila triangle
X(65476) = X(58474)-of-Ursa-minor triangle, when ABC is acute
X(65476) = X(65398)-of-5th mixtilinear triangle
X(65476) = X(65399)-of-intouch triangle, when ABC is acute
X(65476) = X(65423)-of-Hutson intouch triangle, when ABC is acute
X(65476) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (177, 3058, 31770), (6284, 11191, 31735)

X(65477) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MIDHEIGHT AND MOSES-SODDY

Barycentrics    (b-c)*(2*a^9-(b+c)*a^8-4*(b^2-c^2)*(b-c)*a^6-4*(b^2-c^2)^2*a^5+2*(b^2-c^2)*(b-c)*(5*b^2+2*b*c+5*c^2)*a^4-4*(b^4-c^4)*(b^2+c^2)*(b-c)*a^2+2*(b^2-c^2)^4*a-(b^2-c^2)^4*(b+c)) : :

X(65477) lies on these lines: {11, 244}, {520, 6587}, {23982, 24030}

X(65477) = cross-difference of every pair of points on the line X(101)X(1498)
X(65477) = X(32668)-complementary conjugate of-X(6389)
X(65477) = perspector of the circumconic through X(514) and X(3346)
X(65477) = pole of the line {1897, 14361} with respect to the polar circle
X(65477) = pole of the line {514, 40616} with respect to the circumhyperbola dual of Yff parabola
X(65477) = pole of the line {122, 661} with respect to the Kiepert circumhyperbola
X(65477) = pole of the line {64, 1146} with respect to the orthic inconic
X(65477) = pole of the line {393, 1086} with respect to the Steiner inellipse

X(65478) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MIDHEIGHT AND SCHRÖETER

Barycentrics    (b^2-c^2)*(2*a^10-(b^2+c^2)*a^8-8*(b^2-c^2)^2*a^6+10*(b^4-c^4)*(b^2-c^2)*a^4-2*(b^2-c^2)^2*(b^4+6*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(65478) = X(686)+3*X(1637)

X(65478) lies on these lines: {6, 14345}, {115, 125}, {520, 6587}, {2433, 47236}, {9033, 46425}, {9209, 62176}, {13567, 39473}

X(65478) = cross-difference of every pair of points on the line X(110)X(1498)
X(65478) = crosspoint of X(18808) and X(58759)
X(65478) = X(43701)-Ceva conjugate of-X(512)
X(65478) = X(i)-complementary conjugate of-X(j) for these (i, j): (1096, 16177), (24022, 57128), (32695, 18589), (36119, 55069), (36131, 6389), (40354, 16595)
X(65478) = X(i)-Dao conjugate of-X(j) for these (i, j): (1084, 5897), (3184, 36841)
X(65478) = X(662)-isoconjugate of-X(5897)
X(65478) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (512, 5897), (15311, 99), (46065, 44326), (62346, 36841)
X(65478) = center of the circumconic through X(43701) and X(57290)
X(65478) = perspector of the circumconic through X(523) and X(3346)
X(65478) = pole of the line {648, 14361} with respect to the polar circle
X(65478) = pole of the line {20975, 44079} with respect to the Brocard inellipse
X(65478) = pole of the line {122, 523} with respect to the Kiepert circumhyperbola
X(65478) = pole of the line {2777, 17838} with respect to the MacBeath circumconic
X(65478) = pole of the line {64, 125} with respect to the orthic inconic
X(65478) = pole of the line {115, 393} with respect to the Steiner inellipse
X(65478) = barycentric product X(i)*X(j) for these {i, j}: {523, 15311}, {3184, 18808}, {6587, 46065}, {43701, 50937}, {58759, 62346}
X(65478) = trilinear product X(661)*X(15311)
X(65478) = trilinear quotient X(i)/X(j) for these (i, j): (661, 5897), (15311, 662)

X(65479) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MIDHEIGHT AND 1st ZANIAH

Barycentrics    a*(b-c)*(a^10-3*(b+c)*a^9+(b+c)^2*a^8+4*(b^3+c^3)*a^7-2*(b^2-c^2)^2*a^6-2*(b+c)*(b^4+c^4-6*b*c*(b-c)^2)*a^5-2*(b^2-c^2)^2*(b+c)^2*a^4+4*(b^3+c^3)*(b-c)^2*(b^2+c^2)*a^3+(b^2-c^2)^4*a^2-(b^2-c^2)*(b-c)^3*(3*b^2+2*b*c+c^2)*(b^2+2*b*c+3*c^2)*a+(b^2-c^2)^4*(b+c)^2) : :

X(65479) lies on these lines: {520, 6587}, {3900, 7658}

X(65479) = cross-difference of every pair of points on the line X(1498)X(1615)
X(65479) = perspector of the circumconic through X(3346) and X(42483)
X(65479) = pole of the line {279, 393} with respect to the Steiner inellipse

X(65480) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MIDHEIGHT AND 2nd ZANIAH

Barycentrics    a*(b-c)*(a^7-2*(b+c)^2*a^5+(b+c)*(b^2+6*b*c+c^2)*a^4+(b^2-c^2)^2*a^3-2*(b+c)*(b^4+c^4+2*b*c*(b^2+c^2))*a^2+4*(b^3+c^3)*(b+c)*b*c*a+(b^2-c^2)^3*(b-c)) : :

X(65480) lies on these lines: {513, 2490}, {520, 6587}, {652, 60339}

X(65480) = cross-difference of every pair of points on the line X(1498)X(1616)
X(65480) = X(i)-complementary conjugate of-X(j) for these (i, j): (52775, 11019), (56305, 2968)
X(65480) = perspector of the circumconic through X(3346) and X(6553)
X(65480) = pole of the line {346, 393} with respect to the Steiner inellipse

X(65481) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 3rd MIXTILINEAR AND 4th MIXTILINEAR

Barycentrics    a*(b-c)*(11*a^5-11*(b+c)*a^4-2*(5*b^2+3*b*c+5*c^2)*a^3+2*(b+c)*(5*b^2+b*c+5*c^2)*a^2-(b^4+c^4+2*b*c*(5*b^2-3*b*c+5*c^2))*a+(b^4-c^4)*(b-c)) : :

X(65481) lies on these lines: {4394, 16192}, {7280, 30234}, {59859, 62437}

X(65482) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MOSES-SODDY AND 1st SAVIN

Barycentrics    (b-c)*(a^3-(b+c)*a^2-(2*b^2-3*b*c+2*c^2)*a+b*c*(b+c)) : :
X(65482) = 3*X(1022)+X(3762) = 3*X(3669)+X(4106) = X(3762)-3*X(4928) = 3*X(4801)+X(47926) = 3*X(4927)+X(30725) = 3*X(4978)+X(47683) = X(7192)+3*X(48131) = 5*X(24924)-9*X(47796) = 5*X(24924)+3*X(48334) = 3*X(47796)+X(48334)

X(65482) lies on these lines: {1, 28521}, {514, 4521}, {676, 44315}, {764, 3716}, {812, 1015}, {891, 19947}, {905, 48008}, {1022, 3762}, {1125, 2832}, {1387, 2827}, {2530, 48291}, {3616, 48032}, {3667, 39540}, {3669, 4106}, {3676, 28468}, {3887, 23814}, {3904, 6545}, {3907, 23815}, {4369, 48335}, {4378, 48050}, {4382, 44550}, {4444, 4876}, {4449, 47819}, {4504, 28519}, {4728, 21222}, {4730, 45328}, {4763, 21385}, {4801, 30061}, {4830, 14419}, {4897, 30722}, {4922, 48167}, {4927, 30725}, {4978, 18071}, {6084, 40480}, {6366, 44314}, {7178, 28497}, {7192, 26854}, {10015, 21204}, {14349, 47991}, {14413, 46403}, {14432, 49301}, {17072, 48346}, {21115, 49274}, {21297, 53536}, {21343, 36848}, {23738, 47840}, {23765, 47841}, {23789, 48348}, {24720, 48332}, {24924, 27014}, {28478, 30723}, {28487, 34958}, {28490, 30719}, {28501, 30724}, {29051, 48289}, {32212, 53573}, {45667, 48327}, {45675, 58413}, {47812, 48298}, {48049, 48320}, {48079, 48144}, {48089, 48325}, {48091, 48588}, {48279, 50339}, {48282, 48556}, {48321, 49289}

X(65482) = midpoint of X(i) and X(j) for these (i, j): {764, 3716}, {1022, 4928}, {4369, 48335}, {4378, 48050}, {17072, 48346}, {20317, 58794}, {23789, 48348}, {24720, 48332}, {48049, 48320}, {48089, 48325}, {48321, 49289}
X(65482) = reflection of X(i) in X(j) for these (i, j): (676, 44315), (25380, 19947), (32212, 53573), (53580, 1125)
X(65482) = cross-difference of every pair of points on the line X(3052)X(4557)
X(65482) = X(661)-Dao conjugate of-X(23835)
X(65482) = X(1252)-isoconjugate of-X(23835)
X(65482) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (244, 23835), (23831, 765), (45142, 813), (62300, 190)
X(65482) = perspector of the circumconic through X(4373) and X(7192)
X(65482) = pole of the line {23392, 36641} with respect to the circumcircle
X(65482) = pole of the line {75, 537} with respect to the incircle
X(65482) = pole of the line {513, 1357} with respect to the circumhyperbola dual of Yff parabola
X(65482) = pole of the line {4129, 17058} with respect to the Kiepert circumhyperbola
X(65482) = pole of the line {4965, 24392} with respect to the Mandart inellipse
X(65482) = pole of the line {3621, 17154} with respect to the Steiner circumellipse
X(65482) = pole of the line {8, 244} with respect to the Steiner inellipse
X(65482) = barycentric product X(i)*X(j) for these {i, j}: {514, 62300}, {1111, 23831}, {45142, 65101}
X(65482) = trilinear product X(i)*X(j) for these {i, j}: {513, 62300}, {1086, 23831}, {3766, 45142}
X(65482) = trilinear quotient X(i)/X(j) for these (i, j): (1086, 23835), (23831, 1252), (45142, 34067), (62300, 100)

X(65483) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: MOSES-SODDY AND 1st ZANIAH

Barycentrics    (b-c)*(2*a^5-(b+c)*a^4-8*(b-c)^2*a^3+10*(b^2-c^2)*(b-c)*a^2-2*(b^2+6*b*c+c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)^3) : :

X(65483) lies on these lines: {2, 65448}, {11, 244}, {3900, 7658}, {23587, 59458}

X(65483) = complement of X(65448)
X(65483) = cross-difference of every pair of points on the line X(101)X(1615)
X(65483) = X(i)-complementary conjugate of-X(j) for these (i, j): (269, 46415), (1106, 35091), (4617, 31844), (6614, 10427), (36141, 6554), (59105, 24003), (60487, 21244)
X(65483) = X(56741)-reciprocal conjugate of-X(644)
X(65483) = perspector of the circumconic through X(514) and X(10307)
X(65483) = pole of the line {11, 3062} with respect to the incircle
X(65483) = pole of the line {514, 13609} with respect to the circumhyperbola dual of Yff parabola
X(65483) = pole of the line {1146, 64130} with respect to the orthic inconic
X(65483) = pole of the line {279, 1086} with respect to the Steiner inellipse
X(65483) = barycentric product X(i)*X(j) for these {i, j}: {24002, 56741}, {60479, 63777}
X(65483) = trilinear product X(i)*X(j) for these {i, j}: {3676, 56741}, {35348, 63777}
X(65483) = trilinear quotient X(56741)/X(3939)

X(65484) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ORTHIC AND STEINER

Barycentrics    (b^2-c^2)*(3*a^2-b^2-c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(65484) = 3*X(5652)-X(6333)

X(65484) lies on these lines: {2, 65408}, {99, 110}, {113, 21905}, {193, 57087}, {460, 512}, {1499, 10011}, {1637, 63733}, {3566, 3798}, {5139, 6388}, {5477, 42663}, {6562, 50644}, {32478, 50550}, {38359, 57154}

X(65484) = midpoint of X(i) and X(j) for these (i, j): {193, 57087}, {6562, 50644}, {38359, 57154}
X(65484) = anticomplement of X(65408)
X(65484) = cross-difference of every pair of points on the line X(394)X(2987)
X(65484) = crosspoint of X(i) and X(j) for these {i, j}: {460, 4226}, {648, 63613}, {685, 51820}
X(65484) = crosssum of X(i) and X(j) for these {i, j}: {684, 52091}, {35364, 43705}
X(65484) = X(i)-Ceva conjugate of-X(j) for these (i, j): (685, 6353), (63613, 15525)
X(65484) = X(3566)-daleth conjugate of-X(8651)
X(65484) = X(i)-Dao conjugate of-X(j) for these (i, j): (114, 35136), (2489, 60338), (6388, 57872), (15525, 8781), (39001, 6391), (39072, 3565), (51579, 65277), (55152, 2996), (65408, 65408)
X(65484) = X(3566)-hirst inverse of-X(58766)
X(65484) = X(i)-isoconjugate of-X(j) for these {i, j}: {3565, 8773}, {6391, 36105}, {8769, 10425}, {35136, 36051}, {38252, 65277}
X(65484) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (193, 65277), (230, 35136), (1692, 3565), (3053, 10425), (3566, 8781), (5139, 60338), (6353, 65354), (6388, 62645), (8651, 2987), (19118, 32697), (42663, 8770), (47430, 35364), (51610, 525), (51613, 523), (52144, 65311), (55122, 2996), (57071, 35142)
X(65484) = trilinear pole of the line {51610, 51613} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65484) = perspector of the circumconic through X(193) and X(230)
X(65484) = pole of the line {1609, 1634} with respect to the circumcircle
X(65484) = pole of the line {800, 47406} with respect to the 1st Lozada, circle
X(65484) = pole of the line {114, 193} with respect to the orthoptic circle of Steiner inellipse
X(65484) = pole of the line {69, 8754} with respect to the polar circle
X(65484) = pole of the line {800, 47406} with respect to the Brocard inellipse
X(65484) = pole of the line {2, 6562} with respect to the Kiepert parabola
X(65484) = pole of the line {1611, 52077} with respect to the MacBeath circumconic
X(65484) = pole of the line {512, 3565} with respect to the Stammler hyperbola
X(65484) = pole of the line {99, 439} with respect to the Steiner circumellipse
X(65484) = pole of the line {620, 3767} with respect to the Steiner inellipse
X(65484) = pole of the line {523, 35136} with respect to the Steiner-Wallace hyperbola
X(65484) = barycentric product X(i)*X(j) for these {i, j}: {99, 51613}, {193, 55122}, {230, 3566}, {648, 51610}, {3564, 57071}, {4226, 6388}, {8651, 51481}, {42663, 57518}, {56891, 57154}
X(65484) = trilinear product X(i)*X(j) for these {i, j}: {162, 51610}, {662, 51613}, {1707, 55122}, {1733, 8651}, {3566, 8772}, {17876, 61213}, {18156, 42663}
X(65484) = trilinear quotient X(i)/X(j) for these (i, j): (1707, 10425), (1733, 35136), (3566, 8773), (6353, 36105), (8651, 36051), (8772, 3565), (17876, 62645), (18156, 65277), (42663, 38252), (51610, 656), (51613, 661), (55122, 8769)
X(65484) = X(6562)-of-1st Brocard triangle

X(65485) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ORTHIC AND SYMMEDIAL

Barycentrics    a^4*(b^2-c^2)*(-a^2+b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2) : :

X(65485) lies on these lines: {25, 2623}, {51, 12077}, {389, 64790}, {460, 512}, {647, 39469}, {669, 688}, {879, 42299}, {1510, 45259}, {1637, 21646}, {3060, 41298}, {3221, 6562}, {3265, 54272}, {9969, 64877}, {9979, 11450}, {15451, 17434}, {16040, 42651}, {37085, 58317}, {44568, 58470}, {47122, 54269}

X(65485) = reflection of X(44568) in X(58470)
X(65485) = isogonal conjugate of the isotomic conjugate of X(15451)
X(65485) = polar conjugate of the isotomic conjugate of X(42293)
X(65485) = isogonal conjugate of the polar conjugate of X(55219)
X(65485) = cross-difference of every pair of points on the line X(76)X(275)
X(65485) = crosspoint of X(i) and X(j) for these {i, j}: {51, 61194}, {512, 3049}, {15451, 55219}
X(65485) = crosssum of X(i) and X(j) for these {i, j}: {69, 15414}, {99, 6331}, {275, 58756}, {523, 53477}, {850, 26166}, {1232, 3267}
X(65485) = X(i)-Ceva conjugate of-X(j) for these (i, j): (512, 55219), (15451, 42293), (27375, 20975), (60501, 1084)
X(65485) = X(3049)-daleth conjugate of-X(2491)
X(65485) = X(i)-Dao conjugate of-X(j) for these (i, j): (5, 670), (6, 55218), (115, 57790), (125, 34384), (130, 69), (136, 57844), (137, 18022), (206, 18831), (338, 44161), (1084, 276), (2972, 305), (3162, 42405), (5139, 8795), (6523, 54950), (15259, 52779), (15450, 76), (17423, 95), (38986, 40440), (38996, 275), (39019, 1502), (40368, 933), (40588, 6331), (52032, 4609), (52878, 877), (55066, 62276), (63463, 264)
X(65485) = X(i)-isoconjugate of-X(j) for these {i, j}: {19, 55218}, {54, 57968}, {63, 42405}, {75, 18831}, {76, 65221}, {95, 811}, {97, 57973}, {99, 40440}, {162, 34384}, {163, 57790}, {255, 54950}, {275, 799}, {276, 662}, {304, 16813}, {326, 52779}, {561, 933}, {648, 62276}, {670, 2190}, {823, 34386}, {1969, 18315}, {2167, 6331}, {4100, 42369}, {4575, 57844}, {4592, 8795}, {4602, 8882}, {4609, 62268}, {6507, 42401}, {6528, 62277}, {8884, 55202}, {14213, 52939}, {15412, 46254}, {18022, 36134}, {23999, 62428}, {55229, 56254}, {55231, 56246}
X(65485) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3, 55218), (25, 42405), (32, 18831), (51, 6331), (216, 670), (217, 99), (343, 4609), (393, 54950), (418, 4563), (512, 276), (523, 57790), (560, 65221), (647, 34384), (669, 275), (798, 40440), (810, 62276), (1093, 42369), (1501, 933), (1924, 2190), (1953, 57968), (1974, 16813), (2179, 811), (2181, 57973), (2207, 52779), (2489, 8795), (2501, 57844), (3049, 95), (3199, 6528), (5562, 52608), (6368, 1502), (6524, 42401), (9426, 8882), (9427, 58756), (12077, 18022), (14398, 43752), (14575, 18315), (15451, 76), (17434, 305), (18314, 44161), (23181, 34537), (23216, 2623), (24862, 15415), (27374, 41676), (34980, 15414), (34983, 28706), (39201, 34386), (40373, 14586), (40981, 648), (41219, 4143), (42068, 15422)
X(65485) = perspector of the circumconic through X(32) and X(216)
X(65485) = pole of the line {1609, 1613} with respect to the circumcircle
X(65485) = pole of the line {800, 3051} with respect to the 1st Lozada, circle
X(65485) = pole of the line {69, 8795} with respect to the polar circle
X(65485) = pole of the line {61658, 64783} with respect to the Taylor circle
X(65485) = pole of the line {800, 3051} with respect to the Brocard inellipse
X(65485) = pole of the line {216, 343} with respect to the Johnson circumconic
X(65485) = pole of the line {6562, 9491} with respect to the Kiepert parabola
X(65485) = pole of the line {19597, 52077} with respect to the MacBeath circumconic
X(65485) = pole of the line {25, 32445} with respect to the orthic inconic
X(65485) = pole of the line {670, 18831} with respect to the Stammler hyperbola
X(65485) = pole of the line {6392, 8264} with respect to the Steiner circumellipse
X(65485) = pole of the line {3767, 8265} with respect to the Steiner inellipse
X(65485) = barycentric product X(i)*X(j) for these {i, j}: {3, 55219}, {4, 42293}, {5, 3049}, {6, 15451}, {25, 17434}, {32, 6368}, {51, 647}, {53, 39201}, {125, 61194}, {184, 12077}, {216, 512}, {217, 523}, {324, 58310}, {343, 669}, {393, 58305}, {418, 2501}, {520, 3199}, {525, 40981}, {577, 51513}, {656, 2179}
X(65485) = trilinear product X(i)*X(j) for these {i, j}: {19, 42293}, {31, 15451}, {48, 55219}, {51, 810}, {216, 798}, {217, 661}, {343, 1924}, {512, 62266}, {560, 6368}, {647, 2179}, {656, 40981}, {669, 44706}, {822, 3199}, {1096, 58305}, {1953, 3049}, {1973, 17434}, {2181, 39201}, {2618, 14575}, {3708, 61194}, {9247, 12077}
X(65485) = trilinear quotient X(i)/X(j) for these (i, j): (5, 57968), (19, 42405), (31, 18831), (32, 65221), (51, 811), (53, 57973), (63, 55218), (158, 54950), (216, 799), (217, 662), (343, 4602), (418, 4592), (512, 40440), (560, 933), (647, 62276), (656, 34384), (661, 276), (669, 2190), (798, 275), (810, 95)
X(65485) = (X(669), X(3049))-harmonic conjugate of X(58310)

X(65486) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ORTHIC AND YFF CONTACT

Barycentrics    (b-c)*(a^2+2*(b+c)*a-(b+c)^2)*(2*a^3-(b+c)*a^2+(b^2-c^2)*(b-c)) : :

X(65486) lies on these lines: {2, 65407}, {100, 190}, {460, 512}, {48269, 50501}

X(65486) = anticomplement of X(65407)
X(65486) = cross-difference of every pair of points on the line X(394)X(1015)
X(65486) = X(65407)-Dao conjugate of-X(65407)
X(65486) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (14974, 29241), (17314, 54979)
X(65486) = perspector of the circumconic through X(393) and X(1016)
X(65486) = pole of the line {100, 1609} with respect to the circumcircle
X(65486) = pole of the line {69, 2969} with respect to the polar circle
X(65486) = pole of the line {1, 6562} with respect to the Kiepert parabola
X(65486) = pole of the line {190, 6392} with respect to the Steiner circumellipse
X(65486) = pole of the line {3767, 4422} with respect to the Steiner inellipse
X(65486) = barycentric product X(i)*X(j) for these {i, j}: {3011, 48269}, {17314, 29240}
X(65486) = trilinear product X(3011)*X(50501)
X(65486) = trilinear quotient X(i)/X(j) for these (i, j): (46937, 54979), (50501, 60049)

X(65487) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ORTHIC AXES AND PELLETIER

Barycentrics    (b-c)*((b^2-c^2)*(b-c)*a^8-2*(b^4-b^2*c^2+c^4)*a^7-(b^3+c^3)*(b^2-3*b*c+c^2)*a^6+4*(b^4-c^4)*(b^2-c^2)*a^5-(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(4*b^2+b*c+4*c^2))*a^4-2*(b^6-c^6)*(b^2-c^2)*a^3+(b^6-c^6)*(b^2-c^2)*(b+c)*a^2-(b^2-c^2)^3*(b-c)*b^2*c^2) : :

X(65487) lies on these lines: {11, 244}, {647, 16229}

X(65487) = cross-difference of every pair of points on the line X(101)X(6638)
X(65487) = perspector of the circumconic through X(514) and X(43710)
X(65487) = pole of the line {11, 53} with respect to the nine-point circle
X(65487) = pole of the line {1897, 3164} with respect to the polar circle
X(65487) = pole of the line {661, 34980} with respect to the Kiepert circumhyperbola
X(65487) = pole of the line {1146, 2052} with respect to the orthic inconic

X(65488) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: ORTHIC AXES AND SCHRÖETER

Barycentrics    (b^2-c^2)*(a^8-(3*b^4-5*b^2*c^2+3*c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*a^2-3*(b^2-c^2)^2*b^2*c^2) : :
X(65488) = 3*X(4)+X(9409) = X(647)+3*X(16229) = X(647)-3*X(59745) = 3*X(6130)-X(9409) = X(6140)-3*X(39509) = X(24978)+3*X(39491) = X(24978)-3*X(44204) = 3*X(45689)-X(53247)

X(65488) lies on these lines: {4, 6130}, {5, 2797}, {30, 44818}, {115, 804}, {133, 6086}, {381, 41079}, {403, 47214}, {523, 16231}, {526, 7687}, {546, 9517}, {647, 16229}, {684, 3091}, {690, 45259}, {3545, 45319}, {3566, 59652}, {3627, 44810}, {3832, 53345}, {5907, 64439}, {6140, 39509}, {6334, 44203}, {14639, 31953}, {24978, 39491}, {41254, 45689}, {42733, 44427}

X(65488) = midpoint of X(i) and X(j) for these (i, j): {4, 6130}, {3627, 44810}, {5907, 64439}, {16229, 59745}, {39491, 44204}
X(65488) = complement of the circumperp conjugate of X(53723)
X(65488) = cross-difference of every pair of points on the line X(1634)X(6638)
X(65488) = perspector of the circumconic through X(43710) and X(56270)
X(65488) = pole of the line {53, 115} with respect to the nine-point circle
X(65488) = pole of the line {4232, 47202} with respect to the orthoptic circle of Steiner inellipse
X(65488) = pole of the line {376, 3164} with respect to the polar circle
X(65488) = pole of the line {512, 34980} with respect to the Kiepert circumhyperbola
X(65488) = pole of the line {338, 2052} with respect to the orthic inconic
X(65488) = pole of the line {3124, 37643} with respect to the Steiner inellipse
X(65488) = X(6130)-of-Euler triangle

X(65489) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd PARRY AND 3rd PARRY

Barycentrics    a^2*(b^2-c^2)*(a^6-4*(b^2+c^2)*a^4+(2*b^4-3*b^2*c^2+2*c^4)*a^2+(b^4+b^2*c^2+c^4)*(b^2+c^2)) : :
X(65489) = X(9979)-3*X(22734) = X(13306)+3*X(22734)

X(65489) lies on these lines: {111, 53890}, {187, 237}, {251, 14998}, {526, 2491}, {804, 1637}, {2081, 10329}, {2433, 46286}, {6030, 13318}, {6041, 53263}, {8675, 45907}, {9138, 14660}, {9147, 13309}, {9185, 13307}, {9209, 25423}, {9979, 13306}, {14417, 59775}, {58900, 63787}

X(65489) = midpoint of X(9979) and X(13306)
X(65489) = reflection of X(10567) in X(2491)
X(65489) = cross-difference of every pair of points on the line X(2)X(7711)
X(65489) = X(1084)-Dao conjugate of-X(9302)
X(65489) = X(662)-isoconjugate of-X(9302)
X(65489) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (512, 9302), (9301, 99)
X(65489) = perspector of the circumconic through X(6) and X(9301)
X(65489) = pole of the line {44423, 52693} with respect to the Gallatly circle
X(65489) = pole of the line {6, 12308} with respect to the Moses circle
X(65489) = pole of the line {262, 5309} with respect to the orthoptic circle of Steiner inellipse
X(65489) = pole of the line {264, 63018} with respect to the polar circle
X(65489) = pole of the line {7668, 51428} with respect to the Kiepert circumhyperbola
X(65489) = pole of the line {51, 41254} with respect to the orthic inconic
X(65489) = pole of the line {194, 20423} with respect to the Steiner circumellipse
X(65489) = pole of the line {39, 6034} with respect to the Steiner inellipse
X(65489) = barycentric product X(523)*X(9301)
X(65489) = trilinear product X(661)*X(9301)
X(65489) = trilinear quotient X(i)/X(j) for these (i, j): (661, 9302), (9301, 662)
X(65489) = X(39)-of-{these triangles}: {2nd Parry, 3rd Parry}
X(65489) = X(5188)-of-1st Parry triangle
X(65489) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (6137, 6138, 5113), (13306, 22734, 9979)

X(65490) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: PELLETIER AND 1st SAVIN

Barycentrics    (b-c)*(-a+b+c)*((b^2-b*c+c^2)*a^4-2*(b+c)*b*c*a^3-(b^4+c^4-b*c*(b^2+3*b*c+c^2))*a^2+b^2*c^2*(b-c)^2) : :

X(65490) lies on these lines: {11, 116}, {3669, 4106}, {3835, 4162}, {4107, 58369}, {24354, 54359}, {42312, 42327}

X(65490) = pole of the line {75, 2310} with respect to the incircle
X(65490) = pole of the line {650, 1357} with respect to the circumhyperbola dual of Yff parabola
X(65490) = pole of the line {1111, 24174} with respect to the Steiner inellipse

X(65491) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: PELLETIER AND SODDY

Barycentrics    (b-c)*(3*a^4-5*(b+c)*a^3+(b^2+4*b*c+c^2)*a^2+(b^2-c^2)*(b-c)*a+2*b*c*(b-c)^2) : :

X(65491) lies on these lines: {513, 21195}, {521, 4885}, {650, 57167}, {693, 4827}, {905, 50449}, {4130, 53357}, {4778, 7658}, {10015, 28590}, {21188, 39470}, {33562, 40554}, {53579, 59612}

X(65491) = midpoint of X(i) and X(j) for these (i, j): {650, 57167}, {693, 4827}, {4130, 53357}
X(65491) = X(60092)-complementary conjugate of-X(124)
X(65491) = pole of the line {1441, 10578} with respect to the Steiner inellipse

X(65492) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: PELLETIER AND X-PARABOLA-TANGENTIAL

Barycentrics    (b-c)*(a^6-(b+c)*a^5-(b^2+c^2)*a^4+(b+c)*(b^2+c^2)*a^3+b^2*c^2*a^2-(b+c)*b^2*c^2*a+(b^2-c^2)^2*b*c) : :

X(65492) lies on these lines: {513, 11263}, {514, 1125}, {523, 6675}, {2787, 47203}, {3309, 16160}, {21201, 50757}, {21203, 50574}, {29150, 37369}, {37047, 47799}, {44824, 61520}

X(65492) = pole of the line {239, 37783} with respect to the Steiner inellipse

X(65493) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st SCHIFFLER AND 2nd SCHIFFLER

Barycentrics    a^9-3*(b+c)*a^8+12*b*c*a^7+(b+c)*(8*b^2-21*b*c+8*c^2)*a^6-3*(2*b^4+2*c^4+5*b*c*(b^2-3*b*c+c^2))*a^5-2*(b^2-c^2)*(b-c)*(3*b^2-17*b*c+3*c^2)*a^4+(8*b^4+8*c^4+b*c*(2*b^2-45*b*c+2*c^2))*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(21*b^2-44*b*c+21*c^2)*b*c*a^2-(b^2-c^2)^2*(b-c)^2*(3*b^2-11*b*c+3*c^2)*a+(b^2-c^2)^3*(b-c)^3 : :

X(65493) lies on these lines: {11, 2078}, {1768, 5435}, {3582, 6246}, {5428, 60759}, {5531, 31146}, {5541, 6944}, {6960, 33709}, {6979, 21630}, {17483, 21635}, {34126, 61792}

X(65494) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: SCHRÖETER AND SODDY

Barycentrics    (b^2-c^2)*(5*a^2-2*(b+c)*a-3*(b-c)^2) : :
X(65494) = 3*X(676)-X(4162) = 5*X(676)-3*X(59980) = X(4041)+3*X(7178) = X(4041)-9*X(30574) = 5*X(4041)+3*X(55282) = X(4041)-3*X(55285) = 5*X(4162)-9*X(59980) = X(7178)+3*X(30574) = 5*X(7178)-X(55282) = X(7657)+2*X(59743) = 3*X(30574)-X(55285) = X(53527)-3*X(65414) = X(55282)+5*X(55285)

X(65494) lies on these lines: {523, 656}, {676, 4162}, {2490, 29082}, {4905, 10015}, {6362, 48018}, {6366, 21188}, {21120, 23738}, {21952, 44729}, {24290, 59521}, {28213, 47921}, {34959, 59629}, {44566, 59672}

X(65494) = midpoint of X(7178) and X(55285)
X(65494) = reflection of X(59589) in X(59521)
X(65494) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 36605), (6741, 36625), (40611, 58108), (40622, 38254), (55064, 36627)
X(65494) = X(i)-isoconjugate of-X(j) for these {i, j}: {21, 58108}, {163, 36605}, {4565, 36627}, {38254, 65375}
X(65494) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (523, 36605), (1400, 58108), (3700, 36625), (4041, 36627), (7178, 38254), (20059, 99), (33633, 1414), (38293, 5546), (53056, 662), (59612, 86)
X(65494) = perspector of the circumconic through X(226) and X(20059)
X(65494) = pole of the line {29, 20008} with respect to the polar circle
X(65494) = pole of the line {4934, 21044} with respect to the Kiepert circumhyperbola
X(65494) = pole of the line {17056, 23903} with respect to the Steiner inellipse
X(65494) = barycentric product X(i)*X(j) for these {i, j}: {10, 59612}, {523, 20059}, {1577, 53056}, {4086, 33633}
X(65494) = trilinear product X(i)*X(j) for these {i, j}: {37, 59612}, {523, 53056}, {661, 20059}, {3700, 33633}, {4077, 38293}
X(65494) = trilinear quotient X(i)/X(j) for these (i, j): (65, 58108), (1577, 36605), (3700, 36627), (4077, 38254), (4086, 36625), (20059, 662), (33633, 4565), (38293, 65375), (53056, 110), (59612, 81)
X(65494) = (X(7178), X(30574))-harmonic conjugate of X(55285)

X(65495) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: SCHRÖETER AND 1st ZANIAH

Barycentrics    (b^2-c^2)*(2*a^6-(5*b^2-8*b*c+5*c^2)*a^4-4*(b^2-c^2)*(b-c)*a^3+12*(b^3-c^3)*(b-c)*a^2-4*(b^2-c^2)^2*(b+c)*a-(b-c)^4*(b^2+c^2)) : :

X(65495) lies on these lines: {2, 65446}, {115, 125}, {3900, 7658}

X(65495) = complement of X(65446)
X(65495) = cross-difference of every pair of points on the line X(110)X(1615)
X(65495) = perspector of the circumconic through X(523) and X(42483)
X(65495) = pole of the line {3062, 4934} with respect to the incircle
X(65495) = pole of the line {13609, 21196} with respect to the circumhyperbola dual of Yff parabola
X(65495) = pole of the line {115, 279} with respect to the Steiner inellipse

X(65496) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: SCHRÖETER AND 2nd ZANIAH

Barycentrics    (b^2-c^2)*(2*a^4-4*(b+c)*a^3+(b^2+4*b*c+c^2)*a^2+2*(b+c)*(3*b^2-4*b*c+3*c^2)*a-(b^2+c^2)*(b+c)^2) : :
X(65496) = 5*X(2610)+3*X(4120)

X(65496) lies on these lines: {2, 65463}, {115, 125}, {513, 2490}

X(65496) = complement of X(65463)
X(65496) = cross-difference of every pair of points on the line X(110)X(1616)
X(65496) = perspector of the circumconic through X(523) and X(6553)
X(65496) = pole of the line {115, 346} with respect to the Steiner inellipse

X(65497) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: STEINER AND SYMMEDIAL

Barycentrics    a^6*(b^2-c^2)*((b^2+c^2)*a^2-2*b^2*c^2) : :

X(65497) lies on these lines: {99, 110}, {669, 688}, {699, 6380}, {887, 14406}, {888, 38366}, {3051, 9429}, {9427, 23216}, {39689, 59802}, {53354, 58784}

X(65497) = isogonal conjugate of X(57993)
X(65497) = cross-difference of every pair of points on the line X(76)X(3124)
X(65497) = crosspoint of X(i) and X(j) for these {i, j}: {32, 32717}, {4577, 6579}, {5118, 33875}
X(65497) = crosssum of X(i) and X(j) for these {i, j}: {76, 9148}, {523, 30736}, {34087, 60028}
X(65497) = X(i)-Ceva conjugate of-X(j) for these (i, j): (5118, 33875), (32717, 32)
X(65497) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 886), (38996, 34087), (38998, 4609), (39010, 1502), (40368, 9150), (40369, 32717), (62611, 850)
X(65497) = X(i)-isoconjugate of-X(j) for these {i, j}: {75, 886}, {561, 9150}, {799, 34087}, {1502, 36133}, {1928, 32717}, {3228, 4602}, {4609, 37132}
X(65497) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (32, 886), (669, 34087), (887, 76), (888, 1502), (1501, 9150), (1645, 850), (1917, 36133), (3231, 4609), (5118, 44168), (9148, 40362), (9233, 32717), (9426, 3228), (9427, 60028), (14406, 8024), (32717, 57571), (33875, 670), (33918, 115), (41294, 892), (52625, 44173)
X(65497) = perspector of the circumconic through X(32) and X(4590)
X(65497) = pole of the line {2, 30495} with respect to the 1st Brocard circle
X(65497) = pole of the line {1613, 1634} with respect to the circumcircle
X(65497) = pole of the line {8754, 18022} with respect to the polar circle
X(65497) = pole of the line {3051, 38998} with respect to the Brocard inellipse
X(65497) = pole of the line {2, 9491} with respect to the Kiepert parabola
X(65497) = pole of the line {19597, 61199} with respect to the MacBeath circumconic
X(65497) = pole of the line {512, 670} with respect to the Stammler hyperbola
X(65497) = pole of the line {99, 8264} with respect to the Steiner circumellipse
X(65497) = pole of the line {620, 8265} with respect to the Steiner inellipse
X(65497) = pole of the line {523, 4609} with respect to the Steiner-Wallace hyperbola
X(65497) = barycentric product X(i)*X(j) for these {i, j}: {6, 887}, {32, 888}, {110, 1645}, {251, 14406}, {512, 33875}, {538, 9426}, {669, 3231}, {690, 41294}, {1084, 5118}, {1501, 9148}, {1576, 52625}, {1919, 52894}, {1924, 2234}, {1980, 52893}, {3049, 46522}, {4590, 33918}, {9427, 23342}, {32717, 39010}
X(65497) = trilinear product X(i)*X(j) for these {i, j}: {31, 887}, {163, 1645}, {560, 888}, {798, 33875}, {1917, 9148}, {1924, 3231}, {1980, 52894}, {2234, 9426}, {2642, 41294}, {4117, 5118}, {14406, 46289}, {24041, 33918}
X(65497) = trilinear quotient X(i)/X(j) for these (i, j): (31, 886), (560, 9150), (798, 34087), (887, 75), (888, 561), (1501, 36133), (1645, 1577), (1917, 32717), (1924, 3228), (2234, 4609), (3231, 4602), (4117, 60028), (9148, 1928), (9426, 37132), (14406, 1930), (33875, 799), (33918, 2643), (36133, 57571), (41294, 36085), (46522, 57968)

X(65498) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: SYMMEDIAL AND YFF CONTACT

Barycentrics    a^4*(b-c)*((b+c)*a-b*c)*((b^2+c^2)*a-b*c*(b+c)) : :

X(65498) lies on these lines: {100, 190}, {669, 688}, {8640, 20979}

X(65498) = cross-difference of every pair of points on the line X(76)X(330)
X(65498) = X(34067)-Ceva conjugate of-X(2209)
X(65498) = X(i)-isoconjugate of-X(j) for these {i, j}: {87, 54985}, {3226, 18830}, {4598, 32020}, {6384, 8709}, {32039, 40844}
X(65498) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2176, 54985), (6373, 6383), (8640, 32020), (21760, 18830), (21762, 62638), (57050, 64226), (62420, 8709)
X(65498) = perspector of the circumconic through X(32) and X(1016)
X(65498) = pole of the line {100, 1613} with respect to the circumcircle
X(65498) = pole of the line {2969, 18022} with respect to the polar circle
X(65498) = pole of the line {43, 3051} with respect to the Brocard inellipse
X(65498) = pole of the line {1, 9491} with respect to the Kiepert parabola
X(65498) = pole of the line {670, 3733} with respect to the Stammler hyperbola
X(65498) = pole of the line {190, 8264} with respect to the Steiner circumellipse
X(65498) = pole of the line {4422, 8265} with respect to the Steiner inellipse
X(65498) = pole of the line {4609, 7192} with respect to the Steiner-Wallace hyperbola
X(65498) = barycentric product X(i)*X(j) for these {i, j}: {1575, 8640}, {2176, 6373}, {3009, 20979}, {3837, 62420}, {4083, 21760}, {16695, 21830}, {21762, 23354}, {25142, 51864}, {38367, 41531}
X(65498) = trilinear product X(i)*X(j) for these {i, j}: {2209, 6373}, {3009, 8640}, {20979, 21760}, {21830, 57074}, {38367, 51973}, {51864, 57050}
X(65498) = trilinear quotient X(i)/X(j) for these (i, j): (43, 54985), (2209, 8709), (3009, 18830), (6373, 6384), (8640, 3226), (20979, 32020), (21760, 4598), (25142, 64226), (38367, 39914), (38986, 62638), (51864, 32039), (57050, 40844)

X(65499) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 1st ZANIAH AND 2nd ZANIAH

Barycentrics    a*(b-c)*(a^4-2*(b+c)*a^3+2*(b^2+4*b*c+c^2)*a^2-2*(b+c)^3*a+b^4+6*b^2*c^2+c^4) : :

X(65499) lies on these lines: {2, 17115}, {10, 9373}, {513, 2490}, {521, 24675}, {650, 1027}, {905, 4477}, {1376, 28984}, {2550, 29005}, {2886, 4885}, {3309, 31286}, {3900, 7658}, {4369, 8678}, {8641, 25925}, {8760, 9956}, {9511, 57055}, {10855, 54271}, {11934, 31250}, {14077, 21212}, {42341, 43932}

X(65499) = complementary conjugate of the complement of X(8269)
X(65499) = complement of X(17115)
X(65499) = cross-difference of every pair of points on the line X(1615)X(1616)
X(65499) = X(i)-complementary conjugate of-X(j) for these (i, j): (1037, 1146), (1041, 6506), (7045, 17115), (7084, 35508), (7123, 13609), (7131, 26932), (8269, 10), (8817, 124), (30705, 116), (56179, 5514), (56359, 11), (59128, 6), (59133, 40869), (62538, 5510), (63178, 4904)
X(65499) = X(6167)-reciprocal conjugate of-X(664)
X(65499) = perspector of the circumconic through X(6167) and X(6553)
X(65499) = pole of the line {3452, 18252} with respect to the Spieker circle
X(65499) = pole of the line {279, 304} with respect to the Steiner inellipse
X(65499) = barycentric product X(522)*X(6167)
X(65499) = trilinear product X(650)*X(6167)
X(65499) = trilinear quotient X(6167)/X(651)
X(65499) = X(65393)-of-Wasat triangle, when ABC is acute
X(65499) = X(65386)-of-2nd Zaniah triangle, when ABC is acute

X(65500) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 2nd ANTI-CONWAY AND ORTHIC AXES

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^12-4*(b^2+c^2)*a^10+(5*b^4+12*b^2*c^2+5*c^4)*a^8-12*(b^2+c^2)*b^2*c^2*a^6-(5*b^8+5*c^8-(5*b^4+9*b^2*c^2+5*c^4)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*(2*b^4+b^2*c^2+2*c^4)*a^2-(b^2-c^2)^2*(b^4+c^4+(b^2+b*c+c^2)*b*c)*(b^4+c^4-(b^2-b*c+c^2)*b*c)) : :
X(65500) = 3*X(51)-X(130) = 3*X(51)+X(21661)

X(65500) lies on these lines: {4, 13527}, {51, 130}, {52, 129}, {53, 1263}, {112, 47424}, {143, 27359}, {511, 34839}, {1154, 61588}, {1298, 3567}, {1303, 3060}, {1994, 58065}, {3284, 7575}, {3518, 58069}, {5462, 34838}, {5890, 44989}, {6243, 57335}, {6748, 10214}, {10095, 61589}, {11432, 22551}, {12236, 32438}, {13321, 38594}, {16625, 38734}, {17810, 22552}, {32411, 59533}, {39019, 53808}

X(65500) = midpoint of X(i) and X(j) for these (i, j): {52, 129}, {130, 21661}, {20411, 20412}
X(65500) = reflection of X(i) in X(j) for these (i, j): (34838, 5462), (61589, 10095)
X(65500) = crosssum of X(3) and X(39019)
X(65500) = orthoassociate of X(13527)
X(65500) = inverse of X(13527) in polar circle
X(65500) = pole of the line {933, 46062} with respect to the orthic inconic
X(65500) = X(99)-of-2nd anti-Conway triangle
X(65500) = X(115)-of-orthic triangle
X(65500) = X(620)-of-anti-Wasat triangle
X(65500) = X(38738)-of-2nd Euler triangle
X(65500) = (X(51), X(21661))-harmonic conjugate of X(130)

X(65501) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: CIRCUMORTHIC AND 2nd CIRCUMPERP

Barycentrics    (a^7-(b+c)*a^6+2*(b-c)*c*a^5-(b^2-2*c^2)*c*a^4+(b-c)^2*c^2*a^3-(b^3-c^3)*(b-c)*c*a^2-(b^2-c^2)*(b-c)^2*b^2*a+(b^2-c^2)^2*(b-c)*b^2)*(a^7-(b+c)*a^6-2*(b-c)*b*a^5+(2*b^2-c^2)*b*a^4+(b-c)^2*b^2*a^3-(b^3-c^3)*(b-c)*b*a^2+(b^2-c^2)*(b-c)^2*c^2*a-(b^2-c^2)^2*(b-c)*c^2) : :

X(65501) lies on the circumcircle and these lines: {100, 17860}, {101, 355}, {109, 1836}, {110, 14008}, {158, 52776}, {929, 54090}, {5057, 43355}, {14719, 31732}, {59016, 64013}

X(65501) = circumperp conjugate of the isogonal conjugate of X(65424)
X(65501) = areal center of cevian and pedal triangles of X(65424)
X(65501) = V-transform of X(65424)
X(65501) = X(65520)-of-anti-Euler triangle
X(65501) = X(65514)-of-ABC-X3 reflections triangle
X(65501) = X(21662)-of-hexyl triangle, when ABC is acute
X(65501) = X(14720)-of-1st circumperp triangle, when ABC is acute
X(65501) = X(14719)-of-2nd circumperp triangle, when ABC is acute

X(65502) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: HUTSON INTOUCH AND MIDARC

Barycentrics    (-a+b+c)*(-4*b*c*(a-b+c)*(a+b-c)*sin(A/2)+8*a^2*(a+b-c)*c*sin(B/2)+8*a^2*(a-b+c)*b*sin(C/2)+4*a^4-5*(b+c)*a^3+3*(b-c)^2*a^2-3*(b^2-c^2)*(b-c)*a+(b-c)^4) : :

X(65502) lies on the incircle and these lines: {1, 10491}, {55, 10497}, {174, 10504}, {1358, 10499}, {3022, 31766}, {10489, 12646}, {10501, 11234}, {52999, 55342}

X(65502) = reflection of X(10491) in X(1)
X(65502) = infinity-incircle transform of X(65453)
X(65502) = antipode of X(10491) in incircle
X(65502) = X(38574)-of-incircle-circles triangle, when ABC is acute
X(65502) = X(10497)-of-Mandart-incircle triangle
X(65502) = X(10491)-of-5th mixtilinear triangle
X(65502) = X(5185)-of-excenters-reflections triangle, when ABC is acute
X(65502) = X(152)-of-inverse-in-incircle triangle, when ABC is acute
X(65502) = X(118)-of-Ursa-minor triangle, when ABC is acute
X(65502) = X(103)-of-intouch triangle, when ABC is acute
X(65502) = X(101)-of-Hutson intouch triangle, when ABC is acute

X(65503) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND INCENTRAL

Barycentrics    a^3*(b-c)*(-a+b+c)^4*((b+c)*a^3+2*(b^2-b*c+c^2)*a^2+(b^2-c^2)*(b-c)*a+2*b*c*(b-c)^2) : :

X(65503) lies on these lines: {187, 237}, {65432, 65433}

X(65503) = perspector of the circumconic through X(6) and X(51539)

X(65504) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND INTOUCH

Barycentrics    (b-c)*(-a+b+c)^4*(5*a^3+3*(b+c)*a^2-(b-c)^2*a+(b^2-c^2)*(b-c))*(2*a^4+(b+c)*a^3+3*(b-c)^2*a^2+3*(b^2-c^2)*(b-c)*a-(b-c)^4) : :

X(65504) lies on these lines: {513, 676}, {65432, 65433}

X(65505) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND LEMOINE

Barycentrics    (b-c)*(-a+b+c)^4*(6*a^4+7*(b+c)*a^3+(b^2+7*b*c+c^2)*a^2+(b+c)*(b^2+c^2)*a+(b^2+3*b*c+c^2)*(b-c)^2)*(4*a^5+2*(b+c)*a^4+(b^2+c^2)*a^3+(b+c)*(7*b^2-13*b*c+7*c^2)*a^2+3*(b^2-c^2)^2*a-(b^2-c^2)*(b-c)*(b^2-3*b*c+c^2)) : :

X(65505) lies on these lines: {8599, 12073}, {65432, 65433}

X(65506) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND MACBEATH

Barycentrics    (b-c)*(-a+b+c)^4*((b+c)*a^5-(b^2-b*c+c^2)*a^4-2*(b+c)*(b^2+c^2)*a^3+2*(b^4+c^4-b*c*(b+c)^2)*a^2+(b^2-c^2)^2*(b+c)*a-(b^2-c^2)*(b-c)*(b^3+c^3))*((b^2+c^2)*a^5-(b+c)*(b^2-3*b*c+c^2)*a^4-2*(b^2-c^2)^2*a^3+2*(b^3+c^3)*(b-c)^2*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)*(b-c)^2*(b^3-c^3)) : :

X(65506) lies on these lines: {850, 6368}, {65432, 65433}

X(65507) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND MEDIAL

Barycentrics    (b-c)*(-a+b+c)^4*(3*a^2+2*(b+c)*a-(b-c)^2)*(2*a^3+(b+c)*a^2+(b^2-c^2)*(b-c)) : :

As a conic with center in the infinity, it is a parabola. Its focus is X(65513).

X(65507) lies on these lines: {30, 511}, {65432, 65433}

X(65507) = X(950)-reciprocal conjugate of-X(50392)
X(65507) = ideal of tripolar of X(59646)
X(65507) = perspector of the circumconic through X(2) and X(59646)

X(65508) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND ORTHIC

Barycentrics    (b-c)*(-a+b+c)^4*(3*a^3+(b+c)*a^2-(b-c)^2*a+(b^2-c^2)*(b-c))*(2*a^5+(b+c)*a^4+4*(b^2-c^2)*(b-c)*a^2+2*(b^2-c^2)^2*a-(b^2-c^2)*(b-c)^3) : :

X(65508) lies on these lines: {460, 512}, {65432, 65433}

X(65509) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND STEINER

Barycentrics    (b-c)*(a+b)^2*(a+c)^2*(-a+b+c)^4*(3*a^2-2*(b+c)*a-(b-c)^2)*(2*a^3-(b+c)*a^2-(b^2-c^2)*(b-c)) : :

X(65509) lies on these lines: {99, 110}, {65432, 65433}

X(65510) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: DAO AND SYMMEDIAL

Barycentrics    a^4*(b-c)*(-a+b+c)^4*((b+c)*a^3+(2*b^2+b*c+2*c^2)*a^2+(b+c)*(b^2+c^2)*a+b*c*(b-c)^2)*((b^2+c^2)*a^3+(b+c)*(2*b^2-3*b*c+2*c^2)*a^2+(b^2-c^2)^2*a+(b^2-c^2)*(b-c)*b*c) : :

X(65510) lies on these lines: {669, 688}, {65432, 65433}

X(65511) = CENTER OF THE COMMON INCONIC OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND MEDIAL

Barycentrics    a*(b-c)*(2*a^3+(b+c)*a^2+(b^2-c^2)*(b-c))*(a^3+(b-c)^2*a+2*(b^2-c^2)*(b-c)) : :

As a conic with center in the infinity, it is a parabola. Its focus is X(65512).

X(65511) lies on these lines: {30, 511}

X(65511) = isogonal conjugate of the anticomplement of X(65512)
X(65511) = complementary conjugate of X(65512)
X(65511) = X(4)-Ceva conjugate of-X(65512)
X(65511) = X(1)-complementary conjugate of-X(65512)
X(65511) = X(38351)-Dao conjugate of-X(1265)
X(65511) = ideal of tripolar of X(17054)
X(65511) = perspector of the circumconic through X(2) and X(17054)
X(65511) = barycentric product X(17054)*X(29162)

X(65512) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND MEDIAL

Barycentrics    (b-c)^2*(2*a^3+(b+c)*a^2+(b^2-c^2)*(b-c))*(a^3+(b-c)^2*a+2*(b^2-c^2)*(b-c))*(2*a^7-6*(b+c)*a^6+2*(b-c)^2*a^5+(b+c)*(10*b^2-b*c+10*c^2)*a^4-2*(5*b^2-4*b*c+5*c^2)*(b+c)^2*a^3-2*(b+c)*(b^4+c^4+b*c*(3*b^2-4*b*c+3*c^2))*a^2+2*(b^2+c^2)*(3*b^2-2*b*c+3*c^2)*(b+c)^2*a-(2*b^2-b*c+c^2)*(b^2-b*c+2*c^2)*(b+c)^3) : :

X(65512) lies on the nine-point circle and these lines: {}

X(65512) = complement of the isogonal conjugate of X(65511)
X(65512) = complementary conjugate of X(65511)
X(65512) = X(4)-Ceva conjugate of-X(65511)
X(65512) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 65511), (65511, 10)

X(65513) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: DAO AND MEDIAL

Barycentrics    (b-c)^2*(-a+b+c)^4*(3*a^2+2*(b+c)*a-(b-c)^2)*(2*a^3+(b+c)*a^2+(b^2-c^2)*(b-c))*((b+c)*a^10-6*b*c*a^9-(b+c)*(5*b^2+2*b*c+5*c^2)*a^8+8*(2*b^2+3*b*c+2*c^2)*b*c*a^7+2*(b+c)*(5*b^4-2*b^2*c^2+5*c^4)*a^6-4*(3*b^2+4*b*c+3*c^2)*(b+c)^2*b*c*a^5-2*(b^2-c^2)^2*(b+c)*(5*b^2-6*b*c+5*c^2)*a^4+8*(b+c)^4*b^2*c^2*a^3+(b^2-c^2)^3*(b-c)*(5*b^2-6*b*c+5*c^2)*a^2+2*(b^2-c^2)^2*(b+c)^4*b*c*a-(b^2-c^2)^3*(b-c)^5) : :

X(65513) lies on the nine-point circle and these lines: {}

X(65513) = complement of the isogonal conjugate of X(65507)
X(65513) = complementary conjugate of X(65507)
X(65513) = X(4)-Ceva conjugate of-X(65507)
X(65513) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 65507), (65507, 10)

X(65514) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP AND 1st CIRCUMPERP

Barycentrics    (a-b)*(a-c)*(a^4-b*a^3-(b^2-b*c+c^2)*a^2+(b-c)^2*b*a+(b^2-c^2)*(b-c)*c)*(a^4-c*a^3-(b^2-b*c+c^2)*a^2+(b-c)^2*c*a+(b^2-c^2)*(b-c)*b) : :

X(65514) lies on the circumcircle and these lines: {2, 65520}, {3, 65501}, {4, 65519}, {103, 18481}, {109, 23737}, {993, 14987}, {14720, 31737}

X(65514) = reflection of X(i) in X(j) for these (i, j): (4, 65519), (65501, 3)
X(65514) = isogonal conjugate of X(65424)
X(65514) = circumtangential-isogonal conjugate of X(65424)
X(65514) = circumnormal-isogonal conjugate of the isogonal conjugate of X(65501)
X(65514) = circumperp conjugate of X(65501)
X(65514) = circumnormal-isogonal conjugate of the complementary conjugate of X(65519)
X(65514) = anticomplement of X(65520)
X(65514) = X(65520)-Dao conjugate of-X(65520)
X(65514) = trilinear pole of the line {6, 13898} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65514) = Collings transform of X(65519)
X(65514) = V-transform of X(65501)
X(65514) = X(65519)-of-anti-Euler triangle
X(65514) = X(65501)-of-ABC-X3 reflections triangle
X(65514) = X(21662)-of-excentral triangle, when ABC is acute
X(65514) = X(14720)-of-2nd circumperp triangle, when ABC is acute
X(65514) = X(14719)-of-1st circumperp triangle, when ABC is acute

X(65515) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 2nd ANTI-CONWAY AND 2nd HYACINTH

Barycentrics    a^2*((b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10+(b^2+c^2)*(5*b^4+3*b^2*c^2+5*c^4)*a^8-2*(7*b^4-2*b^2*c^2+7*c^4)*b^2*c^2*a^6-(b^2+c^2)*(5*b^8+5*c^8-2*b^2*c^2*(12*b^4-17*b^2*c^2+12*c^4))*a^4+2*(b^2-c^2)^2*(2*b^8+2*c^8-3*b^2*c^2*(b^4+c^4))*a^2-(b^6+c^6)*(b^2-c^2)^4) : :
X(65515) = X(3563)-5*X(3567)

X(65515) lies on these lines: {6, 1511}, {51, 5139}, {52, 31842}, {143, 7737}, {389, 23698}, {578, 51460}, {1112, 47236}, {3053, 63709}, {3060, 3565}, {3563, 3567}, {6243, 57357}, {6746, 10311}, {9721, 13754}, {11433, 65518}, {16270, 34866}, {39835, 55122}

X(65515) = midpoint of X(52) and X(31842)
X(65515) = pole of the line {110, 13398} with respect to the orthic inconic
X(65515) = X(9721)-of-orthocentroidal triangle

X(65516) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 2nd ANTI-CONWAY AND PELLETIER

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b+c)*(b^2+c^2)*a^7-2*(b^4+c^4-4*b*c*(b^2+c^2))*a^6+2*(b+c)*(3*b^4+3*c^4-b*c*(5*b^2-2*b*c+5*c^2))*a^5-(14*b^4+14*c^4-b*c*(13*b^2+4*b*c+13*c^2))*b*c*a^4-2*(b^2-c^2)*(b-c)*(3*b^4+3*c^4-b*c*(4*b^2+3*b*c+4*c^2))*a^3+2*(b^6+c^6+b*c*(4*b^2+7*b*c+4*c^2)*(b-c)^2)*(b-c)^2*a^2+2*(b^2-c^2)*(b-c)*(b^2-3*b*c+c^2)*(b^4-b^2*c^2+c^4)*a-(b^2-c^2)^2*(b-c)^2*(b^4-b^2*c^2+c^4)) : :
X(65516) = X(953)-5*X(3567) = X(3025)-3*X(61696)

X(65516) lies on these lines: {6, 10016}, {51, 3259}, {52, 31841}, {57, 3025}, {59, 14667}, {143, 5903}, {511, 22102}, {513, 15914}, {568, 38954}, {578, 39479}, {901, 3060}, {953, 3567}, {1112, 1830}, {1168, 51896}, {1866, 6746}, {5890, 44979}, {5905, 64688}, {5946, 38617}, {6243, 57313}, {7982, 13756}, {10263, 38614}, {11028, 18839}, {12006, 14800}, {12236, 53615}, {13321, 38586}, {15043, 38707}, {15381, 54064}, {15632, 34372}, {31760, 64721}, {38705, 64051}, {39806, 53792}, {55314, 58508}, {55317, 58504}

X(65516) = midpoint of X(i) and X(j) for these (i, j): {52, 31841}, {10263, 38614}
X(65516) = reflection of X(i) in X(j) for these (i, j): (55314, 58508), (55317, 58504)
X(65516) = pole of the line {32698, 32702} with respect to the orthic inconic

X(65517) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 2nd ANTI-CONWAY AND SCHRÖETER

Barycentrics    a^2*((b^2+c^2)*a^10-(3*b^4+2*b^2*c^2+3*c^4)*a^8+2*(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^6-2*(2*b^8+2*c^8-(b^2-c^2)^2*b^2*c^2)*a^4+(b^2+c^2)*(3*b^8+3*c^8-(7*b^4-9*b^2*c^2+7*c^4)*b^2*c^2)*a^2-(b^2-c^2)^2*(b^8+c^8-(b^4-3*b^2*c^2+c^4)*b^2*c^2)) : :
X(65517) = 3*X(51)-X(2679) = X(805)+3*X(3060) = 3*X(3060)-X(16979)

X(65517) lies on these lines: {6, 842}, {51, 2679}, {52, 33330}, {143, 53797}, {230, 511}, {249, 2079}, {512, 12076}, {805, 3060}, {1112, 2501}, {1351, 5941}, {2065, 19165}, {2698, 3567}, {2871, 15630}, {3815, 61733}, {6071, 39846}, {6072, 39817}, {6243, 57310}, {6792, 11002}, {12829, 13137}, {15544, 18907}, {16188, 21850}, {20403, 58900}, {36830, 39024}, {38703, 64051}, {55312, 58503}

X(65517) = midpoint of X(i) and X(j) for these (i, j): {52, 33330}, {805, 16979}, {6071, 39846}, {6072, 39817}
X(65517) = reflection of X(i) in X(j) for these (i, j): (55312, 58503), (55313, 58502)
X(65517) = crosssum of X(3) and X(41181)
X(65517) = perspector of the circumconic through X(46606) and X(53691)
X(65517) = inverse of X(1112) in Dou circles radical circle
X(65517) = pole of the line {460, 1112} with respect to the Dou circles radical circle
X(65517) = pole of the line {114, 58909} with respect to the Kiepert circumhyperbola
X(65517) = pole of the line {4230, 32696} with respect to the orthic inconic
X(65517) = (X(805), X(3060))-harmonic conjugate of X(16979)

X(65518) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: ANTI-INVERSE-IN-INCIRCLE AND STEINER

Barycentrics    (-a^2+b^2+c^2)*(a^8-(2*b^4-b^2*c^2+2*c^4)*a^4+(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^4) : :

X(65518) lies on the Steiner 2nd circle and these lines: {2, 2079}, {4, 99}, {30, 5866}, {69, 265}, {115, 4558}, {127, 28725}, {148, 65171}, {316, 46450}, {325, 3153}, {376, 21395}, {381, 9723}, {631, 51460}, {1272, 39118}, {1368, 34883}, {1370, 2373}, {3265, 24974}, {3926, 18404}, {5099, 39193}, {5189, 5971}, {6031, 16063}, {6091, 7386}, {6390, 18403}, {6516, 13273}, {6643, 31842}, {6997, 7664}, {7391, 14360}, {7401, 15565}, {7528, 57356}, {7574, 62338}, {8797, 18537}, {10297, 52437}, {11433, 65515}, {13203, 53331}, {13219, 32006}, {13512, 31723}, {13851, 51386}, {14790, 53796}, {14791, 64018}, {15760, 44180}, {18019, 40123}, {18420, 34803}, {18568, 32837}, {18569, 32816}, {19598, 39842}, {20477, 44402}, {22555, 57008}, {28437, 62563}, {28438, 35923}, {32255, 64235}, {36163, 53570}, {36851, 39127}, {50435, 51439}

X(65518) = anticomplement of X(2079)
X(65518) = isotomic conjugate of the isogonal conjugate of X(12310)
X(65518) = anticomplementary conjugate of the anticomplement of X(54453)
X(65518) = X(54453)-anticomplementary conjugate of-X(8)
X(65518) = X(13485)-Ceva conjugate of-X(69)
X(65518) = X(2079)-Dao conjugate of-X(2079)
X(65518) = X(12310)-reciprocal conjugate of-X(6)
X(65518) = inverse of X(99) in anticomplementary circle
X(65518) = pole of the line {99, 3565} with respect to the anticomplementary circle
X(65518) = pole of the line {18313, 55122} with respect to the Johnson triangle circumcircle
X(65518) = pole of the line {34397, 52144} with respect to the Stammler hyperbola
X(65518) = pole of the line {186, 3564} with respect to the Steiner-Wallace hyperbola
X(65518) = barycentric product X(76)*X(12310)
X(65518) = trilinear product X(75)*X(12310)
X(65518) = trilinear quotient X(12310)/X(31)
X(65518) = X(934)-of-anti-inverse-in-incircle triangle

X(65519) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 2nd EULER AND 4th EULER

Barycentrics    ((b^2+c^2)*a^5-(b+c)*(b^2+c^2)*a^4-2*(b^3-c^3)*(b-c)*a^3+(b+c)*(2*b^4+2*c^4-b*c*(2*b^2-b*c+2*c^2))*a^2+(b^4+c^4)*(b-c)^2*a+(b^6-c^6)*(c-b))*(2*a^7-2*(b+c)*a^6-2*(b-c)^2*a^5+(b+c)*(2*b^2-3*b*c+2*c^2)*a^4+(b^2+c^2)*(b-c)^2*a^3-(b^3-c^3)*(b^2-c^2)*a^2-(b^2-c^2)^2*(b-c)^2*a+(b^2-c^2)^3*(b-c)) : :

X(65519) lies on the nine-point circle and these lines: {2, 65501}, {4, 65514}, {5, 65520}, {116, 1385}, {124, 4640}, {1155, 13141}, {21662, 31752}

X(65519) = midpoint of X(4) and X(65514)
X(65519) = reflection of X(65520) in X(5)
X(65519) = complement of X(65501)
X(65519) = complementary conjugate of the circumnormal-isogonal conjugate of X(65514)
X(65519) = Poncelet point of X(65514)
X(65519) = center of the circumconic through X(4) and X(65514)
X(65519) = X(65520)-of-Johnson triangle
X(65519) = X(65514)-of-Euler triangle
X(65519) = X(14720)-of-3rd Euler triangle, when ABC is acute
X(65519) = X(14719)-of-4th Euler triangle, when ABC is acute

X(65520) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 3rd EULER AND ORTHIC

Barycentrics    (b-c)^2*(b*a-b^2+c^2)*(c*a+b^2-c^2)*((b+c)*a^3-(b+c)^2*a^2-(b^2-c^2)*(b-c)*a+b^4-b^2*c^2+c^4) : :

X(65520) lies on the nine-point circle and these lines: {2, 65514}, {4, 65501}, {5, 65519}, {118, 18480}

X(65520) = midpoint of X(4) and X(65501)
X(65520) = reflection of X(65519) in X(5)
X(65520) = complementary conjugate of X(65424)
X(65520) = complement of X(65514)
X(65520) = X(4)-Ceva conjugate of-X(65424)
X(65520) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 65424), (65424, 10)
X(65520) = Poncelet point of X(i) for these i: {12614, 14008, 65501}
X(65520) = center of the circumconic through X(4) and X(12614)
X(65520) = X(65519)-of-Johnson triangle
X(65520) = X(65501)-of-Euler triangle
X(65520) = X(21662)-of-Wasat triangle, when ABC is acute
X(65520) = X(14720)-of-4th Euler triangle, when ABC is acute
X(65520) = X(14719)-of-3rd Euler triangle, when ABC is acute

X(65521) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND MOSES-SODDY

Barycentrics    (a+b-c)*(a-b+c)*((b+c)*a^5-(3*b^2+2*b*c+3*c^2)*a^4+3*(b+c)*(b^2+c^2)*a^3-2*(b^2+c^2)^2*a^2+(b+c)*(b^2-b*c+c^2)^2*a-b^2*c^2*(b-c)^2) : :
X(65521) = 3*X(354)-X(15615) = 3*X(354)-2*X(40458)

X(65521) lies on these lines: {1, 927}, {57, 813}, {226, 27942}, {354, 15615}, {1054, 4998}, {3676, 5083}, {3911, 31380}, {5988, 9436}, {7178, 40459}, {9320, 59813}

X(65521) = reflection of X(15615) in X(40458)
X(65521) = inverse of X(927) in incircle
X(65521) = pole of the line {813, 927} with respect to the incircle
X(65521) = X(22456)-of-inverse-in-incircle triangle, when ABC is acute
X(65521) = X(38974)-of-intouch triangle, when ABC is acute
X(65521) = (X(354), X(15615))-harmonic conjugate of X(40458)

X(65522) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND PELLETIER

Barycentrics    a*(a+b-c)*(a-b+c)*((b+c)*a^6-(3*b^2+2*b*c+3*c^2)*a^5+3*(b+c)*(b^2+c^2)*a^4-2*(b^2+c^2)^2*a^3+(b+c)*(3*b^4+3*c^4-5*b*c*(2*b^2-3*b*c+2*c^2))*a^2-(3*b^4-5*b^2*c^2+3*c^4)*(b-c)^2*a+(b^2-c^2)^3*(b-c)) : :

X(65522) lies on these lines: {1, 2717}, {36, 47621}, {57, 1308}, {59, 5540}, {65, 3322}, {354, 3328}, {513, 59813}, {514, 5083}, {516, 12736}, {517, 11028}, {942, 53801}, {1319, 5144}, {1323, 3660}, {2078, 5011}, {2801, 60579}, {5199, 17615}, {5902, 33645}, {7178, 59817}, {10015, 43914}

X(65522) = midpoint of X(65) and X(3322)
X(65522) = reflection of X(i) in X(j) for these (i, j): (1323, 3660), (17615, 5199)
X(65522) = inverse of X(14733) in incircle
X(65522) = pole of the line {1308, 4394} with respect to the incircle
X(65522) = pole of the line {4862, 12831} with respect to the Feuerbach circumhyperbola
X(65522) = X(40544)-of-Ursa-minor triangle, when ABC is acute
X(65522) = X(5099)-of-intouch triangle, when ABC is acute
X(65522) = X(691)-of-inverse-in-incircle triangle, when ABC is acute

X(65523) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND 1st SAVIN

Barycentrics    (b+c)*a^6-2*(b^2+c^2)*a^5-2*(b+c)*(2*b^2-3*b*c+2*c^2)*a^4+(b^4+6*b^2*c^2+c^4)*a^3+(b+c)*(b^2-b*c+c^2)^2*a^2-(b^6+c^6-(2*b^4+2*c^4-b*c*(b^2+4*b*c+c^2))*b*c)*a+(b^2-c^2)*(b-c)*b^2*c^2 : :
X(65523) = 3*X(354)-X(1356)

X(65523) lies on these lines: {1, 99}, {57, 6010}, {226, 44950}, {354, 1356}, {518, 3037}, {1210, 45162}, {3586, 44940}, {5530, 49650}, {9579, 45152}, {11374, 57308}

X(65523) = inverse of X(99) in incircle
X(65523) = pole of the line {99, 3882} with respect to the incircle
X(65523) = X(52779)-of-inverse-in-incircle triangle, when ABC is acute
X(65523) = X(38976)-of-intouch triangle, when ABC is acute

X(65524) = FOCUS OF THE COMMON INPARABOLA OF THESE TRIANGLES: 1st PAVLOV AND 2nd PAVLOV

Barycentrics    a*(2*a^5-(b+c)*a^4-2*(b^2-b*c+c^2)*a^3+(b+c)*b*c*a^2-(b-c)^2*b*c*a+(b^4-c^4)*(b-c)) : :
X(65524) = 3*X(354)-2*X(15904)

X(65524) lies on these lines: {1, 399}, {6, 47231}, {55, 9904}, {58, 16164}, {65, 5504}, {74, 63291}, {77, 34879}, {81, 105}, {100, 40612}, {113, 63318}, {125, 17056}, {215, 942}, {265, 56417}, {323, 518}, {511, 63451}, {517, 37477}, {526, 53550}, {541, 63449}, {542, 3745}, {895, 63385}, {1054, 53743}, {1100, 38347}, {1112, 63293}, {1155, 18593}, {1319, 61638}, {1362, 2772}, {1364, 2646}, {1456, 6357}, {1511, 32636}, {1836, 18625}, {2254, 3722}, {2777, 63386}, {2778, 3057}, {2781, 63349}, {2842, 11717}, {2854, 63359}, {2948, 63310}, {3242, 17847}, {3338, 32609}, {3448, 9347}, {3475, 14683}, {3579, 46819}, {3683, 16585}, {3756, 5642}, {4414, 20277}, {4658, 56405}, {4682, 9140}, {4870, 12261}, {5121, 5972}, {5453, 5663}, {5902, 11935}, {6149, 41542}, {7702, 59653}, {7732, 63321}, {7733, 63322}, {7984, 63333}, {8998, 63336}, {9033, 53522}, {9143, 62807}, {9627, 34043}, {10035, 63282}, {10081, 37600}, {10091, 17609}, {10113, 63317}, {10264, 63259}, {10404, 12383}, {10620, 59337}, {10693, 57667}, {10700, 31523}, {11237, 12407}, {12080, 45147}, {12310, 63311}, {12373, 64055}, {12375, 63330}, {12376, 63331}, {12826, 18178}, {12902, 63296}, {12903, 63326}, {12904, 17605}, {13193, 63294}, {13204, 63304}, {13208, 63312}, {13209, 63313}, {13210, 63315}, {13211, 63319}, {13212, 63320}, {13213, 63324}, {13214, 63325}, {13217, 63341}, {13218, 63342}, {13407, 32423}, {13408, 17702}, {13990, 63337}, {14984, 63452}, {15059, 63344}, {15888, 63370}, {16272, 17768}, {18210, 53324}, {19110, 63298}, {19111, 63299}, {19470, 24929}, {22586, 63316}, {24981, 63401}, {32167, 63288}, {33649, 41541}, {38458, 58587}, {41339, 43066}, {44782, 52362}, {45946, 63334}, {47484, 63354}, {48535, 64354}, {48536, 64355}, {48786, 63302}, {48787, 63303}, {49098, 63305}, {49099, 63306}, {49203, 63308}, {49204, 63309}, {49268, 63328}, {49269, 63329}, {49369, 63300}, {49370, 63301}, {63396, 64339}

X(65524) = midpoint of X(1) and X(6126)
X(65524) = reflection of X(i) in X(j) for these (i, j): (1155, 51881), (13408, 63455), (63348, 5453), (63352, 63374)
X(65524) = cross-difference of every pair of points on the line X(2775)X(5540)
X(65524) = crosssum of X(1) and X(53524)
X(65524) = X(55)-line conjugate of-X(9904)
X(65524) = inverse of X(17660) in incircle
X(65524) = pole of the line {8674, 11670} with respect to the incircle
X(65524) = pole of the line {36, 2071} with respect to the Feuerbach circumhyperbola
X(65524) = pole of the line {4236, 53283} with respect to the Kiepert parabola
X(65524) = pole of the line {14395, 24290} with respect to the MacBeath circumconic
X(65524) = X(110)-of-2nd Pavlov triangle
X(65524) = X(354)-of-anti-orthocentroidal triangle
X(65524) = X(6126)-of-anti-Aquila triangle
X(65524) = X(14652)-of-intouch triangle, when ABC is acute
X(65524) = X(14769)-of-Ursa-minor triangle, when ABC is acute
X(65524) = X(35718)-of-Fuhrmann triangle, when ABC is acute
X(65524) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 8614, 17637), (1, 61225, 53524), (63295, 63446, 2646), (63339, 63388, 65)





leftri  Centers of common circumconics of two triangles (2): X(65525) - X(65562)  rightri

This preamble and centers X(65525)-X(65562) were contributed by César Eliud Lozada, September 27, 2024.

This section continues the Centers of common circumconics: X(14713)-X(14781) (See preamble just before X(14713)).

For definitions of all triangles listed here, check the Index of triangles referenced in ETC.

underbar

X(65525) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ABC AND URSA MINOR

Barycentrics    a*(b-c)^2*(-a+b+c)^2*((b+c)*a-(b-c)^2)*(a^4-2*(b+c)*a^3+(b^2+3*b*c+c^2)*a^2-(b-c)^2*b*c) : :

X(65525) lies on these lines: {11, 65548}, {55, 14722}, {56, 65541}, {1086, 3022}, {2310, 21127}, {4014, 40615}, {8255, 39789}, {15587, 16593}, {39063, 63258}, {39790, 52870}, {40622, 65546}

X(65525) = crosspoint of X(7) and X(21127)
X(65525) = crosssum of X(55) and X(65222)
X(65525) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 10581), (43750, 21104)
X(65525) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 10581), (9440, 513), (9446, 17072)
X(65525) = X(10581)-Dao conjugate of-X(2)
X(65525) = center of the circumconic with perspector X(10581)
X(65525) = perspector of the circumconic with center X(10581)
X(65525) = pole of the the tripolar of X(21127) with respect to the incircle

X(65526) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ANTI-ARA AND ORTHIC AXES

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*(b^2+c^2)*a^6-3*(b^2+c^2)^2*a^4+((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2) : :

X(65526) lies on these lines: {4, 55028}, {25, 34452}, {232, 428}, {3867, 14715}, {40684, 44146}

X(65527) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 3rd ANTI-EULER AND STAMMLER

Barycentrics    a^2*(a^2-b^2)*(a^2-c^2)*(b^2*a^10-(4*b^4+2*b^2*c^2+c^4)*a^8+(6*b^6+4*c^6+b^2*c^2*(2*b^2+c^2))*a^6-(4*b^8+6*c^8-b^2*c^2*(2*b^4+b^2*c^2+4*c^4))*a^4+(b^2-c^2)^2*(b^6+4*c^6)*a^2-(b^2-c^2)^4*c^4)*(c^2*a^10-(b^4+2*b^2*c^2+4*c^4)*a^8+(4*b^6+6*c^6+b^2*c^2*(b^2+2*c^2))*a^6-(6*b^8+4*c^8-b^2*c^2*(4*b^4+b^2*c^2+2*c^4))*a^4+(4*b^6+c^6)*(b^2-c^2)^2*a^2-(b^2-c^2)^4*b^4) : :

X(65527) lies on the circumcircle and these lines: {1141, 6102}, {1300, 6242}

X(65528) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ANTI-HUTSON INTOUCH AND ANTI-MANDART-INCIRCLE

Barycentrics    a^2*((b+c)^2*a^9+(b^2-c^2)*(b-c)*a^8-(3*b^2-2*b*c+3*c^2)*(b+c)^2*a^7-(b+c)*(3*b^4+3*c^4-2*b*c*(3*b^2-b*c+3*c^2))*a^6+(3*b^6+3*c^6+2*b^2*c^2*(b+2*c)*(2*b+c))*a^5+(b+c)*(3*b^6+3*c^6-2*b*c*(3*b^2+b*c+3*c^2)*(b^2-b*c+c^2))*a^4-(b^2-c^2)^2*(b^4+c^4-4*b*c*(b^2-b*c+c^2))*a^3-(b^2-c^2)*(b-c)^3*(b^4+c^4+2*b*c*(b+c)^2)*a^2-(b^2-c^2)^2*(2*b^4+2*c^4+b*c*(b^2+6*b*c+c^2))*b*c*a-(b^2-c^2)^2*(b+c)^3*b^2*c^2) : :

X(65528) lies on these lines: {3, 40496}, {55, 40611}, {56, 14753}, {100, 55036}, {7421, 11491}

X(65528) = reflection of X(40496) in X(3)

X(65529) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ANTI-HUTSON INTOUCH AND 2nd CIRCUMPERP TANGENTIAL

Barycentrics    a^2*((b-c)^2*a^10-2*(b^2-c^2)*(b-c)*a^9-2*(b^4+c^4-4*b*c*(b^2-b*c+c^2))*a^8+2*(b+c)*(b^2+c^2)*(3*b^2-7*b*c+3*c^2)*a^7-(12*b^4+12*c^4-b*c*(23*b^2-18*b*c+23*c^2))*b*c*a^6-2*(b^2-c^2)*(b-c)*(3*b^4+3*c^4-b*c*(3*b^2-7*b*c+3*c^2))*a^5+(2*b^6+2*c^6+(12*b^4+12*c^4+b*c*(b+3*c)*(3*b+c))*b*c)*(b-c)^2*a^4+2*(b^3-c^3)*(b^2-c^2)*(b^4+c^4-2*b*c*(2*b-c)*(b-2*c))*a^3-(b^2-c^2)^2*(b^6+c^6+2*(b^4+c^4-b*c*(b^2-7*b*c+c^2))*b*c)*a^2+2*(b^2-c^2)^2*(b-c)^2*b*c*(b^3+c^3)*a-(b^2-c^2)^2*(b-c)^4*b^2*c^2) : :

X(65529) lies on these lines: {3, 14723}, {55, 65533}, {56, 14714}, {103, 44408}, {104, 7440}

X(65529) = reflection of X(14723) in X(3)
X(65529) = circumnormal-isogonal conjugate of X(48387)

X(65530) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND MOSES-SODDY

Barycentrics    (3*b^2-2*b*c+3*c^2)*a^4-(b+c)^3*a^3-(5*b^4+5*c^4-b*c*(7*b^2-8*b*c+7*c^2))*a^2-(b+c)*(b^2+c^2)*(b^2-6*b*c+c^2)*a+b*c*(b^2-4*b*c+c^2)*(b+c)^2 : :

X(65530) lies on these lines: {2, 14774}, {8, 596}, {5272, 8054}, {36951, 62673}

X(65530) = complement of X(14774)

X(65531) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND 1st ZANIAH

Barycentrics    (b+c)*a^7-3*(b^2+c^2)*a^6+(b^2-c^2)*(b-c)*a^5+(4*b^4+4*c^4-3*b*c*(b-c)^2)*a^4-(b^2-c^2)*(b-c)*(5*b^2+b*c+5*c^2)*a^3+(b^4+c^4+b*c*(b-c)^2)*(b-c)^2*a^2+(b^3+c^3)*(b-c)^2*(3*b^2+2*b*c+3*c^2)*a-2*(b^2-c^2)^2*(b^2-b*c+c^2)^2 : :

X(65531) lies on these lines: {2, 14737}

X(65531) = complement of X(14737)

X(65532) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR AND 2nd ZANIAH

Barycentrics    (b+c)*a^5+(b^2+c^2)*a^4-2*(b+c)*(b^2+c^2)*a^3-(b^3-c^3)*(b-c)*a^2-(b^3-c^3)*(b^2-c^2)*a+2*(b^2+b*c+c^2)^2*(b-c)^2 : :
X(65532) = 3*X(2)+X(14716)

X(65532) lies on these lines: {2, 14716}, {3740, 17239}

X(65532) = midpoint of X(14716) and X(14756)
X(65532) = complement of X(14756)
X(65532) = (X(2), X(14716))-harmonic conjugate of X(14756)

X(65533) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC AND 5th MIXTILINEAR

Barycentrics    a*(a+b-c)*(a-b+c)*((b-c)^2*a^6-2*(b^2-c^2)*(b-c)*a^5+(5*b^2-2*b*c+5*c^2)*b*c*a^4+(b+c)*(2*b^4+2*c^4-b*c*(7*b^2-2*b*c+7*c^2))*a^3-(b+c)^2*(b^4+c^4+b*c*(b^2-6*b*c+c^2))*a^2+3*(b^2-c^2)^2*(b+c)*b*c*a-2*(b^2-c^2)^2*b^2*c^2) : :

X(65533) lies on these lines: {1, 4566}, {55, 65529}, {56, 14723}, {1362, 4449}, {17460, 53547}, {42289, 50194}

X(65533) = reflection of X(14714) in X(1)

X(65534) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ARA AND 1st EXCOSINE

Barycentrics    a^2*(a^20-4*(b^2+c^2)*a^18+2*(2*b^4+7*b^2*c^2+2*c^4)*a^16+2*(b^2+c^2)*(b^4-8*b^2*c^2+c^4)*a^14+(b^8+c^8-b^2*c^2*(6*b^4-19*b^2*c^2+6*c^4))*a^12-2*(b^4-c^4)*(b^2-c^2)*(10*b^4-3*b^2*c^2+10*c^4)*a^10+(29*b^8+29*c^8+b^2*c^2*(32*b^4+19*b^2*c^2+32*c^4))*(b^2-c^2)^2*a^8-2*(b^4-c^4)*(b^2-c^2)*(7*b^8+7*c^8+2*b^2*c^2*(2*b^4-b^2*c^2+2*c^4))*a^6-(b^2-c^2)^4*(2*b^8+2*c^8-b^2*c^2*(6*b^4+11*b^2*c^2+6*c^4))*a^4+2*(b^4-c^4)*(b^2-c^2)^3*(2*b^8+2*c^8-(b^2-c^2)^2*b^2*c^2)*a^2-(b^2-c^2)^6*(b^2+b*c+c^2)^2*(b^2-b*c+c^2)^2) : :

X(65534) lies on the tangential circle and these lines: {3, 129}, {6, 65500}, {22, 1303}, {24, 1298}, {25, 130}, {154, 22552}, {184, 21661}, {378, 44989}, {577, 3165}, {1993, 58065}, {2070, 38594}, {2081, 13558}, {2917, 19165}, {2931, 32438}, {5683, 8471}, {6642, 34838}, {6794, 61217}, {7506, 57333}, {7514, 61588}, {9707, 58069}, {10311, 34131}, {13861, 61589}, {39828, 46730}, {41373, 54067}

X(65534) = midpoint of X(3) and X(22551)
X(65534) = isogonal conjugate of the cyclocevian conjugate of X(35360)
X(65534) = X(17434)-Ceva conjugate of-X(6)
X(65534) = X(16813)-Dao conjugate of-X(42405)
X(65534) = inverse of X(38976) in circumcircle
X(65534) = pole of the line {130, 38976} with respect to the circumcircle

X(65535) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: BCE-INCENTERS AND TANGENTIAL-MIDARC

Barycentrics    (-a+b+c)*(4*a*b*c*(b-c)*(5*a^2-4*(b+c)*a-(b-c)^2)*sin(A/2)+2*a*(a-b+c)*(a^4-(2*b-c)*a^3+(b-c)*c*a^2+(b^2-c^2)*(2*b+c)*a-(b^2-c^2)*(b-c)*b)*sin(B/2)-2*a*(a+b-c)*(a^4+(b-2*c)*a^3-(b-c)*b*a^2-(b^2-c^2)*(b+2*c)*a-(b^2-c^2)*(b-c)*c)*sin(C/2)+(b-c)*(a+b-c)*(a-b+c)*(a^3-(b+c)*a^2-(b+c)^2*a+(b^2-c^2)*(b-c))) : :

X(65535) lies on these lines: {9, 173}, {166, 8089}

X(65536) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND HEXYL

Barycentrics    a*(a^12-2*(b+c)^2*a^10-(b^4+c^4-2*b*c*(4*b^2-3*b*c+4*c^2))*a^8+4*(b^4+c^4+b*c*(2*b^2+7*b*c+2*c^2))*(b-c)^2*a^6-(b^2+c^2)*(b^2+6*b*c+c^2)*(b^2+4*b*c+c^2)*(b-c)^2*a^4-2*(b^2-c^2)^2*(b^6+c^6-(2*b^4+2*c^4-b*c*(b^2-8*b*c+c^2))*b*c)*a^2+(b^4-c^4)^2*(b^2-c^2)^2) : :

X(65536) lies on these lines: {1, 7169}, {58, 4227}, {84, 3073}, {109, 54295}, {991, 64347}, {1040, 1394}, {10571, 10884}

X(65537) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND MOSES-SODDY

Barycentrics    (a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^3-b*a^2-(b-c)^2*a+(b^2-c^2)*b)*(a^3-c*a^2-(b-c)^2*a-c*(b^2-c^2)) : :

X(65537) lies on these lines: {104, 38461}, {514, 653}, {693, 934}, {927, 59103}, {2401, 53150}, {2720, 58993}, {3669, 23984}, {3676, 6614}, {4453, 65295}, {4616, 52619}, {14776, 65540}, {15634, 36123}, {32702, 62635}, {39053, 65412}

X(65537) = cevapoint of X(i) and X(j) for these {i, j}: {278, 39534}, {513, 43058}, {1875, 3669}, {2401, 36123}
X(65537) = X(i)-cross conjugate of-X(j) for these (i, j): (1875, 23984), (36110, 65331), (39534, 278)
X(65537) = X(i)-Dao conjugate of-X(j) for these (i, j): (478, 52307), (3259, 41215), (6609, 8677), (39053, 6735), (40617, 35014), (40837, 2804)
X(65537) = X(i)-isoconjugate of-X(j) for these {i, j}: {9, 52307}, {78, 53549}, {200, 8677}, {212, 2804}, {219, 46393}, {341, 23220}, {517, 57108}, {663, 51379}, {908, 65102}, {1260, 1769}, {1459, 51380}, {1785, 58340}, {1802, 10015}, {1946, 6735}, {2183, 57055}, {2427, 34591}, {2638, 53151}, {3310, 3692}, {3900, 22350}, {3939, 35014}, {4105, 62402}, {14427, 57478}, {14571, 57057}, {17757, 57134}, {21801, 23090}, {36037, 41215}, {51377, 57081}
X(65537) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (34, 46393), (56, 52307), (104, 57055), (278, 2804), (608, 53549), (651, 51379), (653, 6735), (909, 57108), (1119, 10015), (1309, 346), (1398, 3310), (1407, 8677), (1435, 1769), (1461, 22350), (1783, 51380), (1795, 57057), (1847, 36038), (1875, 60339), (2401, 2968), (2423, 3270), (2720, 219), (2969, 52316), (3310, 41215), (3669, 35014), (4566, 51367), (4617, 62402), (13136, 1265), (13149, 3262), (14578, 58340), (14776, 220), (16082, 4397), (17925, 14010), (18816, 15416), (23984, 53151), (32641, 1260), (32669, 212), (32702, 55), (32714, 517), (34051, 521), (34858, 65102), (36037, 3692), (36110, 9), (36118, 908), (36123, 3239), (37136, 78), (39294, 3699), (39534, 55153), (43933, 1146), (52410, 23220), (52607, 17757)
X(65537) = X(2947)-zayin conjugate of-X(46393)
X(65537) = trilinear pole of the line {278, 1086} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65537) = perspector of the central inconic through X(39534) and X(43933)
X(65537) = barycentric product X(i)*X(j) for these {i, j}: {7, 65331}, {85, 36110}, {104, 13149}, {269, 65223}, {273, 37136}, {278, 54953}, {279, 1309}, {331, 2720}, {658, 36123}, {934, 16082}, {1119, 13136}, {1275, 43933}, {1847, 36037}, {2401, 55346}, {3676, 39294}, {6063, 32702}, {7282, 47317}, {14776, 57792}, {18026, 34051}, {18816, 32714}
X(65537) = trilinear product X(i)*X(j) for these {i, j}: {7, 36110}, {34, 54953}, {57, 65331}, {85, 32702}, {104, 36118}, {269, 1309}, {273, 2720}, {278, 37136}, {331, 32669}, {653, 34051}, {909, 13149}, {934, 36123}, {1088, 14776}, {1111, 59103}, {1119, 36037}, {1407, 65223}, {1435, 13136}, {1461, 16082}, {1847, 32641}, {2401, 7128}
X(65537) = trilinear quotient X(i)/X(j) for these (i, j): (34, 53549), (57, 52307), (104, 57108), (269, 8677), (273, 2804), (278, 46393), (664, 51379), (909, 65102), (934, 22350), (1106, 23220), (1119, 1769), (1309, 200), (1435, 3310), (1769, 41215), (1795, 58340), (1847, 10015), (1897, 51380), (2401, 34591), (2720, 212), (3676, 35014)

X(65538) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND PELLETIER

Barycentrics    (a-b)*(a-c)*a^2*(a+b-c)^2*(a-b+c)^2*(a^2+2*(b-c)*a-(3*b+c)*(b-c))*(a^2-2*(b-c)*a+(b+3*c)*(b-c))*(a^3-b*a^2-(b^2-c^2)*a+(b-c)*(b^2+b*c+2*c^2))*(a^3-c*a^2+(b^2-c^2)*a-(b-c)*(2*b^2+b*c+c^2)) : :

X(65538) lies on these lines: {657, 1461}, {663, 6614}, {934, 3900}, {4616, 7253}

X(65538) = X(24016)-hirst inverse of-X(53622)
X(65538) = X(i)-isoconjugate of-X(j) for these {i, j}: {144, 46392}, {516, 58835}, {910, 57064}, {1254, 65509}, {7658, 51418}
X(65538) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (103, 57064), (911, 58835), (2424, 13609), (7054, 65509), (24016, 144), (32668, 165), (53622, 40869), (61380, 676), (65245, 16284)
X(65538) = X(45721)-zayin conjugate of-X(46392)
X(65538) = trilinear pole of the line {1407, 11051} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65538) = barycentric product X(i)*X(j) for these {i, j}: {677, 60831}, {3062, 65245}, {10405, 24016}, {11051, 65294}, {32668, 44186}, {43736, 61240}, {52156, 53622}, {57928, 61380}
X(65538) = trilinear product X(i)*X(j) for these {i, j}: {3062, 24016}, {10405, 32668}, {11051, 65245}, {36039, 60831}, {43736, 53622}
X(65538) = trilinear quotient X(i)/X(j) for these (i, j): (103, 58835), (1098, 65509), (11051, 46392), (24016, 165), (32668, 3207), (36101, 57064), (53622, 41339), (61240, 40869), (65245, 144), (65294, 16284)

X(65539) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND SCHRÖETER

Barycentrics    (a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^3+b*a^2-(b-c)*b*a-(b+c)*(b^2-c^2))*(a^3+c*a^2+(b-c)*c*a+(b+c)*(b^2-c^2))*(a^4+(b-c)*a^3-b^2*a^2-(b-c)*(b^2-b*c-c^2)*a-(b^2-c^2)*(b+c)*c)*(a^4-(b-c)*a^3-c^2*a^2-(b-c)*(b^2+b*c-c^2)*a+(b^2-c^2)*(b+c)*b) : :

X(65539) lies on these lines: {850, 4616}, {934, 4036}, {1461, 4024}

X(65539) = trilinear pole of the line {115, 1407} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line

X(65540) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: BEVAN ANTIPODAL AND TANGENTIAL

Barycentrics    (a-b)*(a-c)*a^2*(a+b-c)^3*(a-b+c)^3*(a^2-(2*b+c)*a+b*(b-c))*(a^2-(b+2*c)*a-c*(b-c)) : :

X(65540) lies on these lines: {110, 4616}, {692, 934}, {1461, 32739}, {6606, 6613}, {14776, 65537}, {34858, 61373}

X(65540) = isogonal conjugate of the isotomic conjugate of X(65545)
X(65540) = X(i)-cross conjugate of-X(j) for these (i, j): (604, 23971), (738, 7339)
X(65540) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 6607), (6609, 6362)
X(65540) = X(i)-isoconjugate of-X(j) for these {i, j}: {8, 6608}, {75, 6607}, {142, 4130}, {200, 6362}, {312, 10581}, {341, 2488}, {346, 21127}, {354, 4163}, {514, 45791}, {522, 3059}, {650, 51972}, {657, 1229}, {728, 21104}, {1146, 35341}, {1212, 3239}, {1233, 57180}, {1855, 57055}, {2293, 4397}, {2310, 65198}, {3119, 65195}, {3261, 8551}, {3900, 4847}, {3925, 58329}, {4081, 35338}, {4105, 20880}, {4171, 16713}, {4391, 8012}, {5423, 48151}, {7253, 21039}, {20229, 52622}, {23970, 63203}, {24010, 35312}, {55282, 56182}
X(65540) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (32, 6607), (109, 51972), (604, 6608), (692, 45791), (934, 1229), (1106, 21127), (1170, 4397), (1174, 4163), (1262, 65198), (1397, 10581), (1407, 6362), (1415, 3059), (1461, 4847), (4617, 20880), (4626, 1233), (6606, 59761), (6614, 142), (7023, 21104), (7339, 65195), (7366, 48151), (10509, 35519), (21453, 52622), (23971, 35312), (24027, 35341), (40443, 15416), (52410, 2488), (53243, 346), (61373, 4391), (62192, 55282), (65222, 341), (65545, 76), (65552, 23978)
X(65540) = X(10860)-zayin conjugate of-X(21127)
X(65540) = trilinear pole of the line {32, 1407} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65540) = barycentric product X(i)*X(j) for these {i, j}: {6, 65545}, {109, 10509}, {269, 65222}, {279, 53243}, {651, 61373}, {934, 1170}, {1174, 4626}, {1262, 65552}, {1407, 6606}, {1415, 42311}, {1461, 21453}, {1803, 36118}, {2346, 4617}, {6614, 32008}, {7339, 56322}, {23971, 62725}, {24013, 62747}, {32714, 40443}, {55281, 62192}
X(65540) = trilinear product X(i)*X(j) for these {i, j}: {31, 65545}, {109, 61373}, {269, 53243}, {1106, 6606}, {1170, 1461}, {1174, 4617}, {1407, 65222}, {1415, 10509}, {1803, 32714}, {2346, 6614}, {7339, 58322}, {23971, 62747}, {24027, 65552}
X(65540) = trilinear quotient X(i)/X(j) for these (i, j): (31, 6607), (56, 6608), (101, 45791), (109, 3059), (269, 6362), (604, 10581), (651, 51972), (658, 1229), (738, 21104), (934, 4847), (1106, 2488), (1170, 3239), (1174, 4130), (1262, 35341), (1407, 21127), (1415, 8012), (1461, 1212), (1803, 57055), (2346, 4163), (4617, 142)

X(65541) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL AND HEXYL

Barycentrics    a*(a^11-4*(b+c)*a^10+2*(2*b^2+7*b*c+2*c^2)*a^9+3*(b+c)*(b^2-6*b*c+c^2)*a^8-(5*b^4+5*c^4+b*c*(2*b^2-23*b*c+2*c^2))*a^7-(b^2-c^2)*(b-c)*(5*b^2-17*b*c+5*c^2)*a^6+(9*b^4+9*c^4-b*c*(3*b+4*c)*(4*b+3*c))*(b-c)^2*a^5+(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(17*b^2+16*b*c+17*c^2))*a^4-(2*b^2+b*c+2*c^2)*(4*b^4+4*c^4+b*c*(b^2+6*b*c+c^2))*(b-c)^2*a^3+(b^2-c^2)*(b-c)^3*(5*b^4+5*c^4-3*b*c*(b^2-4*b*c+c^2))*a^2-(b^6+c^6-2*(2*b^4+2*c^4+b*c*(2*b^2+b*c+2*c^2))*b*c)*(b-c)^4*a-(b^2-c^2)^3*(b-c)^3*b*c) : :

X(65541) lies on these lines: {3, 14722}, {56, 65525}, {103, 53302}, {6608, 38451}, {12114, 65548}

X(65541) = reflection of X(14722) in X(3)

X(65542) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: DAO AND EXTOUCH

Barycentrics    (-a+b+c)^2*(2*a^6-2*(b+c)*a^5-2*(2*b^2+b*c+2*c^2)*a^4+(b+c)*(3*b^2-8*b*c+3*c^2)*a^3+(b^3-c^3)*(b-c)*a^2-(b^2-c^2)*(b-c)^3*a+(b^2-c^2)*(b-c)*(b^3+c^3)) : :

X(65542) lies on these lines: {2321, 42378}, {2328, 7046}

X(65543) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: DAO AND MEDIAL

Barycentrics    2*a^4-(b^2+c^2)*a^2+2*(b+c)*(b^2+c^2)*a+(b^2+c^2)*(b+c)^2 : :
X(65543) = X(1)+3*X(33160) = 3*X(2)+X(1043) = X(1330)+3*X(4234) = X(3704)-3*X(33160) = 3*X(4234)-X(64159) = 3*X(15670)-X(54399)

X(65543) lies on these lines: {1, 3704}, {2, 1043}, {3, 66}, {5, 48863}, {6, 37176}, {8, 35466}, {10, 6675}, {12, 29846}, {21, 1211}, {30, 3454}, {35, 44419}, {56, 33171}, {58, 524}, {69, 4252}, {72, 44416}, {78, 32777}, {140, 6176}, {183, 56733}, {226, 50054}, {230, 21024}, {306, 37539}, {325, 33954}, {377, 30811}, {386, 3589}, {404, 5347}, {405, 5743}, {442, 25645}, {519, 6693}, {525, 21203}, {536, 34937}, {550, 48835}, {620, 2784}, {740, 1125}, {846, 59592}, {899, 25992}, {936, 17279}, {946, 49484}, {958, 8731}, {960, 34851}, {964, 5718}, {966, 4258}, {975, 17243}, {976, 3703}, {997, 1062}, {1009, 54300}, {1010, 17056}, {1046, 59574}, {1104, 3687}, {1150, 56781}, {1213, 11110}, {1329, 37370}, {1330, 4234}, {1375, 5438}, {1376, 28258}, {1714, 56779}, {1792, 26543}, {2245, 10461}, {2292, 3712}, {2345, 5703}, {2475, 24946}, {2895, 16948}, {2975, 33175}, {3002, 25066}, {3035, 3831}, {3085, 5793}, {3416, 37552}, {3430, 29181}, {3487, 4363}, {3616, 20182}, {3619, 37339}, {3624, 33135}, {3631, 4257}, {3649, 4418}, {3685, 65117}, {3695, 30115}, {3710, 50104}, {3741, 4999}, {3763, 56737}, {3771, 25466}, {3773, 8669}, {3811, 49524}, {3813, 32941}, {3834, 12436}, {3840, 6691}, {3915, 28273}, {3932, 5293}, {3936, 11115}, {4026, 37573}, {4046, 27368}, {4101, 4641}, {4104, 5302}, {4188, 33172}, {4189, 32782}, {4195, 4417}, {4205, 4653}, {4217, 27739}, {4256, 34573}, {4267, 15985}, {4304, 50050}, {4364, 62871}, {4383, 17526}, {4415, 7283}, {4422, 5044}, {4643, 31424}, {4720, 24883}, {4851, 37554}, {4966, 37607}, {4968, 17724}, {5047, 5241}, {5051, 64158}, {5178, 29872}, {5192, 37663}, {5217, 26034}, {5224, 56769}, {5233, 17697}, {5235, 15674}, {5253, 33173}, {5254, 56765}, {5263, 41877}, {5266, 5846}, {5433, 30942}, {5719, 7227}, {5737, 6857}, {5741, 11319}, {5814, 37817}, {5955, 54318}, {6147, 7228}, {6284, 25760}, {6390, 16887}, {6678, 20106}, {6679, 59303}, {6700, 52260}, {6910, 37660}, {7238, 24470}, {7263, 24159}, {7419, 32269}, {7483, 10479}, {7745, 37100}, {8062, 42337}, {10449, 37646}, {11281, 49598}, {12514, 59580}, {12618, 64804}, {13411, 44417}, {13567, 37248}, {13740, 37662}, {13741, 51415}, {13742, 37679}, {14005, 24936}, {15447, 35978}, {15670, 49730}, {15673, 49729}, {16061, 54365}, {16617, 48887}, {16845, 17259}, {17206, 59538}, {17234, 56768}, {17245, 56766}, {17251, 50739}, {17265, 17582}, {17332, 31445}, {17390, 37594}, {17539, 31037}, {17580, 53665}, {17588, 41809}, {17740, 37549}, {17768, 24850}, {18139, 19284}, {18235, 64753}, {19512, 64570}, {19528, 36740}, {19721, 25519}, {19879, 60714}, {20083, 48847}, {21081, 63292}, {21258, 24384}, {24327, 44387}, {24935, 53417}, {24953, 31330}, {25079, 44910}, {25441, 64167}, {25663, 26051}, {25914, 29637}, {26117, 30832}, {26131, 51669}, {26582, 30175}, {26686, 31027}, {26942, 37583}, {26989, 27096}, {27385, 30818}, {28530, 63997}, {28628, 50314}, {30828, 50408}, {32779, 34772}, {32784, 37574}, {32918, 52793}, {32943, 37722}, {32947, 63273}, {33069, 52783}, {33077, 62802}, {33087, 37608}, {33089, 36565}, {34822, 59691}, {37836, 59701}, {41818, 46934}, {43531, 50059}, {44379, 49560}, {44898, 51693}, {47040, 50058}, {47595, 51609}, {49473, 49613}, {49716, 52680}, {49768, 58628}, {50750, 63282}, {51126, 56735}, {51128, 56736}, {56018, 61661}, {56986, 63089}, {56987, 63126}, {58386, 59723}

X(65543) = midpoint of X(i) and X(j) for these (i, j): {1, 3704}, {58, 41014}, {1043, 1834}, {1330, 64159}, {21081, 63292}, {24850, 56949}
X(65543) = complement of X(1834)
X(65543) = crosspoint of X(2) and X(64985)
X(65543) = crosssum of X(6) and X(40984)
X(65543) = X(i)-complementary conjugate of-X(j) for these (i, j): (951, 442), (1257, 3454), (2983, 1211), (29163, 4129), (40414, 20305), (40431, 5), (57390, 226), (64985, 2887)
X(65543) = center of the inconic with perspector X(64985)
X(65543) = pole of the line {966, 3767} with respect to the Kiepert circumhyperbola
X(65543) = pole of the line {22, 4252} with respect to the Stammler hyperbola
X(65543) = pole of the line {3265, 7192} with respect to the Steiner inellipse
X(65543) = pole of the line {315, 3945} with respect to the Steiner-Wallace hyperbola
X(65543) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 33160, 3704), (2, 1043, 1834), (8, 56778, 35466), (10, 6675, 62689), (21, 1211, 49728), (386, 17698, 3589), (1010, 25650, 17056), (1330, 4234, 64159), (2475, 24946, 30831), (3936, 11115, 49745), (4653, 24931, 4205), (25663, 26051, 41878), (29846, 54331, 12), (30832, 52352, 26117)

X(65544) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: DAO AND YFF CONTACT

Barycentrics    (-a+b+c)^2*(a^10-(b+c)*a^9-2*(b-c)^2*a^8+3*(b^3+c^3)*a^7-(3*b^2-b*c+3*c^2)*b*c*a^6-(b^3+c^3)*(3*b^2-4*b*c+3*c^2)*a^5+(2*b^6+2*c^6-5*(b^3-c^3)*(b-c)*b*c)*a^4+(b-c)^4*(b^3+c^3)*a^3-(b-c)^2*(b^6+c^6-(b^4+c^4+2*b*c*(b+c)^2)*b*c)*a^2+(b^4-c^4)*(b-c)^3*b*c*a+(b^2-c^2)*(b-c)^3*b*c*(b^3+c^3)) : :

X(65544) lies on these lines: {242, 7360}, {6736, 7283}

X(65545) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: EXCENTRAL AND SODDY

Barycentrics    (a-b)*(a-c)*(a+b-c)^3*(a-b+c)^3*(a^2-(2*b+c)*a+b*(b-c))*(a^2-(b+2*c)*a-(b-c)*c) : :

X(65545) lies on the circumcircle and these lines: {2, 38973}, {7, 38451}, {100, 4569}, {101, 658}, {103, 5542}, {104, 42311}, {105, 61373}, {109, 4626}, {110, 4616}, {664, 6575}, {972, 40443}, {1292, 36838}, {1308, 59457}, {2291, 10509}, {2346, 15731}, {2371, 32008}, {4617, 8693}, {4637, 59067}, {6614, 59135}, {7056, 53910}, {14733, 65552}, {23586, 58322}, {35312, 43344}, {43349, 52937}, {59031, 65165}, {59064, 65296}

X(65545) = isogonal conjugate of X(6607)
X(65545) = circumtangential-isogonal conjugate of X(6607)
X(65545) = anticomplement of X(38973)
X(65545) = isotomic conjugate of the isogonal conjugate of X(65540)
X(65545) = cevapoint of X(i) and X(j) for these {i, j}: {57, 58322}, {513, 45227}, {514, 65452}, {934, 4626}, {2488, 23653}, {10509, 65552}
X(65545) = X(i)-cross conjugate of-X(j) for these (i, j): (57, 23586), (4350, 1275), (23062, 59457), (65552, 10509)
X(65545) = X(i)-Dao conjugate of-X(j) for these (i, j): (223, 6608), (478, 10581), (5375, 45791), (6609, 2488), (10001, 51972), (17113, 6362), (38973, 38973)
X(65545) = X(i)-isoconjugate of-X(j) for these {i, j}: {9, 10581}, {55, 6608}, {142, 57180}, {200, 2488}, {220, 21127}, {354, 4105}, {480, 48151}, {514, 8551}, {649, 45791}, {650, 8012}, {657, 1212}, {663, 3059}, {1021, 21795}, {1253, 6362}, {1475, 4130}, {1827, 57108}, {1855, 65102}, {2293, 3900}, {3022, 35338}, {3063, 51972}, {3119, 35326}, {3239, 20229}, {4524, 17194}, {4847, 8641}, {6602, 21104}, {14936, 35341}, {21039, 21789}, {24012, 35312}, {35508, 63203}, {52020, 58329}, {52064, 61241}
X(65545) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (56, 10581), (57, 6608), (100, 45791), (109, 8012), (269, 21127), (279, 6362), (479, 21104), (651, 3059), (658, 4847), (664, 51972), (692, 8551), (738, 48151), (934, 1212), (1020, 21039), (1170, 3900), (1174, 4105), (1275, 65198), (1407, 2488), (1461, 2293), (1803, 57108), (2346, 4130), (4569, 1229), (4616, 16713), (4617, 354), (4626, 142), (4637, 17194), (6606, 346), (6614, 1475), (7045, 35341), (7339, 35326), (10509, 522), (21453, 3239), (23586, 35312), (24013, 63203), (31618, 4397), (32008, 4163), (32714, 1827), (36118, 1855), (36838, 20880), (40443, 57055), (42311, 4391), (52937, 1233), (53243, 220), (53321, 21795), (56322, 4081), (58322, 3119), (59457, 65195), (61241, 6067), (61373, 650), (62725, 23970)
X(65545) = X(170)-zayin conjugate of-X(21127)
X(65545) = trilinear pole of the line {6, 279} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65545) = Collings transform of X(i) for these i: {17113, 45227, 65452}
X(65545) = barycentric product X(i)*X(j) for these {i, j}: {76, 65540}, {279, 6606}, {651, 42311}, {658, 21453}, {664, 10509}, {934, 31618}, {1088, 65222}, {1170, 4569}, {1174, 52937}, {1275, 65552}, {2346, 36838}, {4554, 61373}, {4616, 60229}, {4617, 57815}, {4626, 32008}, {13149, 40443}, {23586, 62725}, {24011, 62747}, {53243, 57792}, {56322, 59457}
X(65545) = trilinear product X(i)*X(j) for these {i, j}: {75, 65540}, {109, 42311}, {269, 6606}, {279, 65222}, {651, 10509}, {658, 1170}, {664, 61373}, {934, 21453}, {1088, 53243}, {1174, 36838}, {1461, 31618}, {1803, 13149}, {2346, 4626}, {4617, 32008}, {4637, 60229}, {6614, 57815}, {7045, 65552}, {23586, 62747}, {24013, 62725}, {36118, 40443}
X(65545) = trilinear quotient X(i)/X(j) for these (i, j): (7, 6608), (57, 10581), (101, 8551), (190, 45791), (269, 2488), (279, 21127), (479, 48151), (651, 8012), (658, 1212), (664, 3059), (934, 2293), (1020, 21795), (1088, 6362), (1170, 657), (1174, 57180), (1275, 35341), (1461, 20229), (1803, 65102), (2346, 4105), (4554, 51972)

X(65546) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: GARCIA-REFLECTION AND URSA MINOR

Barycentrics    a*(b-c)*(b^2-c^2)*(a^3-(b+c)*a^2+b*c*a+b*c*(b+c)) : :

X(65546) lies on these lines: {4, 36120}, {7, 4635}, {11, 1356}, {30, 63822}, {115, 512}, {148, 3903}, {758, 51464}, {1111, 4170}, {1357, 31890}, {1365, 3022}, {1367, 31892}, {1537, 39780}, {1565, 4014}, {2170, 4822}, {2310, 61052}, {2782, 61421}, {3023, 6002}, {3027, 28850}, {3110, 11725}, {4128, 16613}, {4804, 21139}, {4890, 5049}, {4983, 20982}, {16591, 58034}, {17761, 38989}, {21746, 39542}, {27008, 47840}, {40622, 65525}

X(65546) = midpoint of X(148) and X(3903)
X(65546) = reflection of X(i) in X(j) for these (i, j): (3110, 11725), (40608, 115)
X(65546) = crosspoint of X(7) and X(661)
X(65546) = crosssum of X(55) and X(662)
X(65546) = X(i)-Ceva conjugate of-X(j) for these (i, j): (1440, 7180), (43750, 7178)
X(65546) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (21960, 668), (23774, 274), (24622, 670), (32932, 4601)
X(65546) = orthojoin of X(3287)
X(65546) = orthopole of tripolar of X(37137)
X(65546) = perspector of the circumconic through X(2395) and X(21960)
X(65546) = pole of the line {2642, 2643} with respect to the incircle
X(65546) = pole of the line {4897, 6002} with respect to the Feuerbach circumhyperbola
X(65546) = barycentric product X(i)*X(j) for these {i, j}: {37, 23774}, {512, 24622}, {513, 21960}, {3125, 32932}
X(65546) = trilinear product X(i)*X(j) for these {i, j}: {42, 23774}, {649, 21960}, {798, 24622}, {3122, 32932}
X(65546) = trilinear quotient X(i)/X(j) for these (i, j): (21960, 190), (23774, 86), (24622, 799), (32932, 4600)

X(65547) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 2nd HYACINTH AND ORTHIC AXES

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*(b^2+c^2)*a^14-(11*b^4+6*b^2*c^2+11*c^4)*a^12+(b^2+c^2)*(5*b^2-8*b*c+5*c^2)*(5*b^2+8*b*c+5*c^2)*a^10-(30*b^8+30*c^8+b^2*c^2*(15*b^4-26*b^2*c^2+15*c^4))*a^8+4*(b^4-c^4)*(b^2-c^2)*(5*b^4+7*b^2*c^2+5*c^4)*a^6-(b^2-c^2)^2*(b^4+c^4)*(7*b^4+10*b^2*c^2+7*c^4)*a^4+(b^2+c^2)*(b^2-c^2)^6*a^2+(b^2-c^2)^6*b^2*c^2) : :

X(65547) lies on these lines: {4, 55345}, {11245, 53420}

X(65548) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: INNER-JOHNSON AND URSA MAJOR

Barycentrics    a*(b-c)^2*((b+c)*a^7-(5*b^2+4*b*c+5*c^2)*a^6+(b+c)*(10*b^2-b*c+10*c^2)*a^5-(10*b^4+10*c^4+b*c*(15*b^2+2*b*c+15*c^2))*a^4+(b+c)*(5*b^4+5*c^4+12*b*c*(b^2-b*c+c^2))*a^3-(b^6+c^6+(12*b^4+12*c^4+b*c*(3*b-c)*(b-3*c))*b*c)*a^2+(b^2-c^2)*(b-c)*(5*b^2+4*b*c+5*c^2)*b*c*a-b*(b-c)^2*c*(b^4+c^4)) : :

X(65548) lies on these lines: {11, 65525}, {1376, 14722}, {12114, 65541}

X(65549) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MIDHEIGHT AND MOSES-SODDY

Barycentrics    (a+b-c)*(a-b+c)*((b+c)^2*a^6-(b+c)^3*a^5-(2*b^4+2*c^4-b*c*(3*b^2+2*b*c+3*c^2))*a^4+2*(b^3-c^3)*(b^2-c^2)*a^3+(b^2-6*b*c+c^2)*(b^2-c^2)^2*a^2-(b^2-c^2)^2*(b+c)*(b^2-4*b*c+c^2)*a+(b^2-c^2)^2*(b-c)^2*b*c) : :

X(65549) lies on these lines: {7, 21208}, {57, 39006}, {1111, 1210}, {3668, 7682}, {4566, 5400}, {5723, 40940}, {18026, 44311}, {34852, 40483}

X(65549) = pole of the line {3007, 37374} with respect to the circumhyperbola dual of Yff parabola

X(65550) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MIDHEIGHT AND 2nd ZANIAH

Barycentrics    (b+c)*a^9-(b^2+c^2)*a^8+(3*b^4+3*c^4-b*c*(b^2+c^2))*a^6-(b+c)*(4*b^4+4*c^4-b*c*(b+c)^2)*a^5-(b^2-c^2)^2*(b-c)^2*a^4+2*(b^2-c^2)*(b-c)*(2*b^4+2*c^4+3*b*c*(b^2+b*c+c^2))*a^3-(b^2-c^2)*(b-c)*(b^3+c^3)*(3*b^2+4*b*c+3*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^3+c^3)*a+2*(b^2-c^2)^2*(b^3+c^3)^2 : :

X(65550) lies on these lines: {942, 63840}, {29307, 63978}

X(65551) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: 6th MIXTILINEAR AND YFF CONTACT

Barycentrics    a*((b^2-b*c+c^2)^2*a^10-2*(b^3+c^3)*(3*b^2-5*b*c+3*c^2)*a^9+3*(5*b^6+5*c^6-(6*b^4+6*c^4+b*c*(b^2-6*b*c+c^2))*b*c)*a^8-2*(b+c)*(10*b^6+10*c^6-(15*b^4+15*c^4-b*c*(2*b^2+7*b*c+2*c^2))*b*c)*a^7+(15*b^8+15*c^8+(10*b^6+10*c^6-(48*b^4+48*c^4-b*c*(32*b^2-17*b*c+32*c^2))*b*c)*b*c)*a^6-2*(b^2-c^2)*(b-c)*(3*b^6+3*c^6+(12*b^4+12*c^4-5*b*c*(2*b-c)*(b-2*c))*b*c)*a^5+(b^8+c^8+(12*b^6+12*c^6-(12*b^4+12*c^4-b*c*(14*b^2+39*b*c+14*c^2))*b*c)*b*c)*(b-c)^2*a^4-2*(b^2-c^2)*(b-c)*(b^6+c^6-2*(4*b^4+4*c^4-3*b*c*(b^2+b*c+c^2))*b*c)*b*c*a^3-(5*b^4+5*c^4+b*c*(22*b^2+15*b*c+22*c^2))*(b-c)^4*b^2*c^2*a^2+2*(b^2-c^2)*(b-c)^3*(3*b^2-2*b*c+3*c^2)*b^3*c^3*a-b^4*c^4*(b-c)^6) : :

X(65551) lies on these lines: {514, 58034}, {4063, 39156}, {9355, 21390}

X(65552) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MOSES-SODDY AND PELLETIER

Barycentrics    (b-c)*(a+b-c)*(a-b+c)*(a^2-(2*b+c)*a+b*(b-c))*(a^2-(b+2*c)*a-c*(b-c)) : :
X(65552) = 4*X(3676)-X(59925)

X(65552) lies on these lines: {7, 23599}, {279, 48151}, {512, 43930}, {513, 50360}, {514, 657}, {663, 3676}, {693, 3900}, {885, 42311}, {927, 4566}, {1170, 7178}, {2346, 28473}, {3309, 24002}, {4444, 17084}, {4555, 6606}, {4564, 35312}, {6548, 21453}, {7192, 21789}, {7253, 52619}, {10509, 23351}, {14733, 65545}, {14776, 65537}, {18344, 30804}, {46006, 59930}, {52621, 53343}, {53150, 65100}

X(65552) = midpoint of X(57090) and X(57167)
X(65552) = reflection of X(i) in X(j) for these (i, j): (7, 23599), (56322, 62747)
X(65552) = isotomic conjugate of X(65198)
X(65552) = cevapoint of X(i) and X(j) for these {i, j}: {513, 3676}, {514, 3309}
X(65552) = cross-difference of every pair of points on the line X(2293)X(8012)
X(65552) = crosspoint of X(i) and X(j) for these {i, j}: {6606, 21453}, {10509, 65545}
X(65552) = crosssum of X(i) and X(j) for these {i, j}: {2293, 2488}, {6607, 8012}, {6608, 21039}, {8642, 61399}
X(65552) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1170, 34547), (53243, 56937), (53244, 144)
X(65552) = X(i)-Ceva conjugate of-X(j) for these (i, j): (6606, 21453), (65222, 7), (65545, 10509)
X(65552) = X(i)-cross conjugate of-X(j) for these (i, j): (513, 58322), (2170, 279), (17463, 278), (58322, 56322), (64523, 57)
X(65552) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 65198), (9, 35341), (11, 3059), (223, 35338), (244, 21039), (478, 35326), (513, 2488), (514, 6362), (661, 21127), (1015, 1212), (1084, 21795), (1086, 4847), (1146, 51972), (3160, 65195), (5190, 1855), (5521, 1827), (6615, 6608), (8054, 2293), (17113, 35312), (17115, 6607), (34467, 22079), (35508, 45791), (38991, 8012), (40590, 35310), (40615, 142), (40617, 354), (40619, 1229), (40620, 16713), (40622, 3925), (40629, 61035), (46398, 51416), (55053, 20229), (55060, 52020)
X(65552) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 35341}, {9, 35326}, {31, 65198}, {41, 65195}, {55, 35338}, {59, 6608}, {100, 2293}, {101, 1212}, {109, 3059}, {110, 21039}, {190, 20229}, {220, 63203}, {284, 35310}, {354, 3939}, {643, 52020}, {644, 1475}, {651, 8012}, {658, 8551}, {662, 21795}, {692, 4847}, {765, 2488}, {906, 1855}, {1110, 6362}, {1229, 32739}, {1252, 21127}, {1253, 35312}, {1331, 1827}, {1415, 51972}, {1461, 45791}, {1897, 22079}, {3925, 65375}, {4557, 17194}, {4564, 10581}, {4571, 40983}, {4578, 61376}, {5546, 21808}, {6065, 48151}, {6602, 61241}, {6607, 7045}, {22053, 56183}
X(65552) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1, 35341), (2, 65198), (7, 65195), (56, 35326), (57, 35338), (65, 35310), (244, 21127), (269, 63203), (279, 35312), (479, 61241), (512, 21795), (513, 1212), (514, 4847), (522, 51972), (649, 2293), (650, 3059), (661, 21039), (663, 8012), (667, 20229), (693, 1229), (1015, 2488), (1019, 17194), (1086, 6362), (1170, 100), (1174, 3939), (1358, 21104), (1638, 61035), (1803, 1331), (2170, 6608), (2346, 644), (3271, 10581), (3669, 354), (3676, 142), (3900, 45791), (4017, 21808), (6591, 1827), (6605, 4578), (6606, 1016), (7178, 3925), (7180, 52020), (7192, 16713), (7203, 18164), (7649, 1855), (8641, 8551), (10015, 51416), (10509, 664), (14936, 6607), (17096, 17169), (21104, 6067), (21453, 190)
X(65552) = X(35338)-zayin conjugate of-X(21127)
X(65552) = trilinear pole of the line {1086, 14936} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65552) = perspector of the circumconic through X(10509) and X(21453)
X(65552) = pole of the line {7, 3730} with respect to the Adams circle
X(65552) = pole of the line {10509, 38859} with respect to the circumcircle
X(65552) = pole of the line {16601, 45227} with respect to the incircle
X(65552) = pole of the line {1827, 1855} with respect to the polar circle
X(65552) = pole of the line {85, 3870} with respect to the Steiner circumellipse
X(65552) = pole of the line {6706, 13405} with respect to the Steiner inellipse
X(65552) = barycentric product X(i)*X(j) for these {i, j}: {7, 56322}, {85, 58322}, {279, 62725}, {513, 31618}, {514, 21453}, {522, 10509}, {650, 42311}, {693, 1170}, {1086, 6606}, {1088, 62747}, {1111, 65222}, {1146, 65545}, {1174, 52621}, {1275, 56284}, {1803, 46107}, {2346, 24002}, {3669, 57815}, {3676, 32008}, {4391, 61373}, {6605, 59941}
X(65552) = trilinear product X(i)*X(j) for these {i, j}: {7, 58322}, {57, 56322}, {244, 6606}, {269, 62725}, {279, 62747}, {513, 21453}, {514, 1170}, {522, 61373}, {649, 31618}, {650, 10509}, {663, 42311}, {1019, 60229}, {1086, 65222}, {1111, 53243}, {1174, 24002}, {1803, 17924}, {2310, 65545}, {2346, 3676}, {3669, 32008}, {6605, 58817}
X(65552) = trilinear quotient X(i)/X(j) for these (i, j): (2, 35341), (7, 35338), (11, 6608), (57, 35326), (75, 65198), (85, 65195), (226, 35310), (244, 2488), (279, 63203), (513, 2293), (514, 1212), (522, 3059), (523, 21039), (649, 20229), (650, 8012), (657, 8551), (661, 21795), (693, 4847), (1086, 21127), (1088, 35312)

X(65553) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MOSES-SODDY AND SODDY

Barycentrics    (a-b)*(a-c)*(a+b-c)^3*(a-b+c)^3*(a^2+(b-2*c)*a-(2*b+c)*(b-c))*(a^2-(2*b-c)*a+(b+2*c)*(b-c)) : :

X(65553) lies on these lines: {514, 658}, {693, 4569}, {927, 59105}, {3676, 4626}, {4453, 65294}, {4616, 7192}, {14733, 65545}, {15634, 62723}, {23351, 65558}, {32728, 65562}, {53150, 65335}

X(65553) = isotomic conjugate of X(65448)
X(65553) = cevapoint of X(i) and X(j) for these {i, j}: {513, 43064}, {23351, 34056}
X(65553) = X(i)-cross conjugate of-X(j) for these (i, j): (23351, 34056), (65483, 2)
X(65553) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 65448), (223, 14392), (6609, 6139), (17113, 6366), (40615, 33573)
X(65553) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 65448}, {55, 14392}, {200, 6139}, {480, 14413}, {527, 57180}, {657, 6603}, {1055, 4130}, {1155, 4105}, {1253, 6366}, {1638, 6602}, {4524, 62756}, {6745, 8641}, {7071, 14414}, {23346, 24010}, {23890, 35508}, {24012, 56543}, {60431, 65102}
X(65553) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 65448), (57, 14392), (279, 6366), (479, 1638), (658, 6745), (738, 14413), (934, 6603), (1121, 4163), (1156, 4130), (1358, 52334), (1407, 6139), (2291, 4105), (3676, 33573), (4617, 1155), (4626, 527), (4637, 62756), (6614, 1055), (7177, 14414), (14733, 220), (23351, 35508), (23586, 56543), (23893, 24010), (23971, 23346), (24013, 23890), (32728, 14827), (34056, 3900), (34068, 57180), (35157, 346), (35348, 3119), (36118, 60431), (36141, 1253), (36838, 30806), (37139, 200), (37757, 38376), (59105, 1252), (60479, 4081), (60487, 8), (61241, 61035), (62723, 3239), (62764, 4171), (63748, 23970), (65304, 1260), (65335, 7046), (65545, 62728)
X(65553) = trilinear pole of the line {279, 1086} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65553) = perspector of the inconic with center X(65483)
X(65553) = barycentric product X(i)*X(j) for these {i, j}: {7, 60487}, {279, 35157}, {658, 62723}, {1088, 37139}, {1121, 4626}, {1156, 36838}, {2291, 52937}, {4569, 34056}, {4635, 62764}, {7056, 65335}, {14733, 57792}, {23351, 57581}, {23586, 63748}, {23893, 24011}, {23989, 59105}, {59457, 60479}, {62731, 65545}
X(65553) = trilinear product X(i)*X(j) for these {i, j}: {57, 60487}, {269, 35157}, {279, 37139}, {658, 34056}, {934, 62723}, {1088, 14733}, {1111, 59105}, {1121, 4617}, {1156, 4626}, {1847, 65304}, {2291, 36838}, {4616, 62764}, {7177, 65335}, {23351, 24011}, {23586, 23893}, {24013, 63748}, {34068, 52937}, {35348, 59457}, {36141, 57792}
X(65553) = trilinear quotient X(i)/X(j) for these (i, j): (7, 14392), (75, 65448), (269, 6139), (479, 14413), (658, 6603), (1088, 6366), (1121, 4130), (1156, 4105), (2291, 57180), (4569, 6745), (4616, 62756), (4617, 1055), (4626, 1155), (7056, 14414), (13149, 60431), (14733, 1253), (23062, 1638), (23351, 24012), (23586, 23890), (23893, 35508)

X(65554) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MOSES-SODDY AND TANGENTIAL

Barycentrics    (a-b)*(a-c)*(a^2+(b-c)*a+b*(b-c))*(a^2-(b-c)*a-c*(b-c))*(a^3-b*a^2-c^2*(b-c))*(a^3-c*a^2+b^2*(b-c)) : :

X(65554) lies on these lines: {110, 52619}, {514, 15378}, {675, 15634}, {692, 693}, {1576, 7192}, {6548, 32719}, {17925, 61206}, {26705, 35190}

X(65554) = X(i)-isoconjugate of-X(j) for these {i, j}: {674, 1734}, {2225, 25259}, {6586, 57015}, {15624, 23887}, {20974, 42723}
X(65554) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (675, 25259), (2224, 1734), (14377, 23887), (32682, 3730), (36087, 3681), (43190, 3006)
X(65554) = X(8049)-vertex conjugate of-X(32642)
X(65554) = trilinear pole of the line {32, 1086} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65554) = barycentric product X(675)*X(43190)
X(65554) = trilinear product X(i)*X(j) for these {i, j}: {2224, 43190}, {14377, 36087}
X(65554) = trilinear quotient X(i)/X(j) for these (i, j): (675, 1734), (2224, 6586), (32682, 15624), (36087, 3730), (37130, 25259), (43190, 57015), (57750, 42723), (60573, 38358)

X(65555) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MOSES-SODDY AND X-PARABOLA-TANGENTIAL

Barycentrics    (b-c)*(a^2+(b+c)*a+b^2+b*c-c^2)*(a^2+(b+c)*a-b^2+b*c+c^2)*(a^3+b*a^2-b^2*a-2*b^3+c^3-b*c*(b-c))*(a^3+c*a^2-c^2*a+b^3-2*c^3+b*c*(b-c)) : :

X(65555) lies on these lines: {514, 6625}, {693, 51865}, {7192, 8029}, {23105, 52619}

X(65555) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (6625, 62644), (60042, 1654), (60050, 18755)
X(65555) = trilinear pole of the line {1086, 61339} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65555) = barycentric product X(6625)*X(60042)
X(65555) = trilinear product X(i)*X(j) for these {i, j}: {13610, 60042}, {51865, 60050}
X(65555) = trilinear quotient X(i)/X(j) for these (i, j): (51865, 62644), (60042, 846)

X(65556) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: MOSES-SODDY AND 2nd ZANIAH

Barycentrics    (b+c)*a^3-(b^2+6*b*c+c^2)*a^2-(b+c)*(2*b^2-9*b*c+2*c^2)*a+b*c*(b^2-6*b*c+c^2) : :

X(65556) lies on these lines: {2, 14759}, {10, 1565}, {75, 537}, {519, 57033}, {1015, 16602}, {1054, 65189}, {17090, 63577}, {21272, 24003}, {58467, 61186}

X(65556) = complement of X(14759)
X(65556) = crosspoint of X(4373) and X(32016)
X(65556) = pole of the line {1266, 57033} with respect to the circumhyperbola dual of Yff parabola
X(65556) = pole of the line {4928, 53364} with respect to the Steiner inellipse

X(65557) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: ORTHIC AXES AND SCHRÖETER

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^12-5*(b^2+c^2)*a^10+2*(b^4+5*b^2*c^2+c^4)*a^8+(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^6+(5*b^4+b^2*c^2+5*c^4)*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)*(8*b^4-7*b^2*c^2+8*c^4)*a^2+(3*b^4+5*b^2*c^2+3*c^4)*(b^2-c^2)^4) : :

X(65557) lies on these lines: {4, 61217}, {53, 6529}, {115, 6748}, {10628, 65500}, {18383, 27358}

X(65557) = pole of the line {18400, 41204} with respect to the Kiepert circumhyperbola

X(65558) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: PELLETIER AND SODDY

Barycentrics    (a-b)*(a-c)*(a+b-c)^4*(a-b+c)^4*((2*b-c)*a^3-(4*b^2-b*c-2*c^2)*a^2+(b^2-c^2)*(2*b+c)*a-b*c*(b-c)^2)*((b-2*c)*a^3-(2*b^2+b*c-4*c^2)*a^2+(b^2-c^2)*(b+2*c)*a+b*c*(b-c)^2)/a : :

X(65558) lies on these lines: {657, 658}, {663, 4626}, {3900, 4569}, {4616, 21789}, {23351, 65553}

X(65558) = X(i)-isoconjugate of-X(j) for these {i, j}: {4105, 62738}, {52888, 57180}
X(65558) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4617, 62738), (4626, 52888), (62744, 4130)
X(65558) = trilinear pole of the line {279, 14936} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65558) = barycentric product X(36838)*X(62744)
X(65558) = trilinear product X(4626)*X(62744)
X(65558) = trilinear quotient X(i)/X(j) for these (i, j): (4626, 62738), (36838, 52888), (62744, 4105)

X(65559) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: SCHRÖETER AND SODDY

Barycentrics    (a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^2+b*a-(2*b+c)*(b-c))*(a^2+c*a+(b+2*c)*(b-c))*(a^3+(b-c)*a^2-c^2*a-(b-c)*(2*b^2+2*b*c+c^2))*(a^3-(b-c)*a^2-b^2*a+(b-c)*(b^2+2*b*c+2*c^2)) : :

X(65559) lies on these lines: {523, 4616}, {658, 4024}, {4036, 4569}

X(65559) = isotomic conjugate of X(65446)
X(65559) = X(65495)-cross conjugate of-X(2)
X(65559) = X(2)-Dao conjugate of-X(65446)
X(65559) = X(31)-isoconjugate of-X(65446)
X(65559) = X(2)-reciprocal conjugate of-X(65446)
X(65559) = trilinear pole of the line {115, 279} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65559) = perspector of the inconic with center X(65495)
X(65559) = trilinear quotient X(75)/X(65446)

X(65560) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: SCHRÖETER AND 1st ZANIAH

Barycentrics    2*(b+c)*a^7-2*(b-c)^2*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5+4*(b^2-b*c+c^2)*(b-c)^2*a^4-(b+c)*(b^2+c^2)*(4*b^2-9*b*c+4*c^2)*a^3+(6*b^4+6*c^4+b*c*(11*b^2-8*b*c+11*c^2))*(b-c)^2*a^2-(b^2-c^2)*(b-c)*(3*b^4+3*c^4+b*c*(b^2-14*b*c+c^2))*a+b*c*(b^2+4*b*c+c^2)*(b-c)^4 : :

X(65560) lies on these lines: {2, 14738}, {1086, 23903}

X(65560) = complement of X(14738)

X(65561) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: SCHRÖETER AND 2nd ZANIAH

Barycentrics    (b+c)*(2*a^5-2*(b+c)*a^4-(b+c)^2*a^3+4*(b+c)*b*c*a^2-(3*b^4+3*c^4-b*c*(b^2+6*b*c+c^2))*a+b*c*(b+c)*(b^2-4*b*c+c^2)) : :

X(65561) lies on these lines: {2, 14757}, {594, 3952}, {17476, 58413}

X(65561) = complement of X(14757)

X(65562) = CENTER OF THE COMMON CIRCUMCONIC OF THESE TRIANGLES: SODDY AND TANGENTIAL

Barycentrics    (a-b)*(a-c)*(a+b-c)^2*(a-b+c)^2*(a^2-b*a-c*(b-c))*(a^2-c*a+b*(b-c))*(a^3-(b+c)*a^2-b^2*a+b^2*(b-c))*(a^3-(b+c)*a^2-c^2*a-c^2*(b-c)) : :

X(65562) lies on these lines: {658, 32739}, {692, 4569}, {1576, 4616}, {32728, 65553}, {51150, 63148}

X(65562) = X(i)-isoconjugate of-X(j) for these {i, j}: {341, 65464}, {2254, 52562}, {17451, 52614}, {40997, 46388}
X(65562) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (919, 52562), (927, 40997), (3449, 52614), (32735, 16588), (52410, 65464), (63148, 50333)
X(65562) = trilinear pole of the line {32, 279} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65562) = barycentric product X(i)*X(j) for these {i, j}: {927, 63148}, {34085, 63188}
X(65562) = trilinear product X(i)*X(j) for these {i, j}: {927, 63188}, {36146, 63148}
X(65562) = trilinear quotient X(i)/X(j) for these (i, j): (1106, 65464), (34085, 40997), (36086, 52562), (36146, 16588), (63188, 926)

X(65563) = X(2)X(74)∩X(20)X(155)

Barycentrics    (5*a^4 - 4*a^2*b^2 - b^4 - 4*a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6 + a^4*b^2 - 5*a^2*b^4 + 3*b^6 + a^4*c^2 + 10*a^2*b^2*c^2 - 3*b^4*c^2 - 5*a^2*c^4 - 3*b^2*c^4 + 3*c^6) : :
X(65563) = 9 X[2] - 8 X[4550], 3 X[2] - 4 X[4846], 2 X[4550] - 3 X[4846], 3 X[4] - 2 X[3426], 3 X[4] - 4 X[64729], X[3426] - 3 X[64094], 3 X[64094] - 2 X[64729], 3 X[20] - 4 X[35237], 3 X[20] - 2 X[41465], 8 X[8717] - 7 X[50693], 5 X[3091] - 4 X[11472], 5 X[3522] - 4 X[4549], 3 X[3543] - 4 X[40909], 5 X[3620] - 4 X[64097], 7 X[3832] - 8 X[7706], 13 X[10303] - 12 X[32620], 9 X[10304] - 8 X[35254], X[11008] + 3 X[40196], 2 X[33878] - 3 X[35513], 5 X[51170] - 4 X[64096], 8 X[51993] - 7 X[62005], 4 X[56966] - 5 X[63127]

See Peter Moses, euclid 7009.

X(65563) lies on the Feuerbach circumhyperbola of the orthic triangle and these lines: {2, 74}, {3, 32601}, {4, 3426}, {5, 15751}, {6, 15311}, {20, 155}, {30, 193}, {52, 3146}, {185, 64187}, {376, 26864}, {382, 15741}, {390, 1480}, {525, 16251}, {648, 18850}, {1181, 64726}, {1249, 38920}, {1495, 5656}, {1499, 53016}, {1514, 6623}, {1614, 8717}, {1839, 53994}, {1843, 6000}, {1899, 13202}, {1986, 10938}, {2777, 5095}, {2883, 37487}, {2904, 15032}, {2914, 35481}, {3088, 3574}, {3089, 5878}, {3090, 34469}, {3091, 11472}, {3431, 10293}, {3522, 4549}, {3529, 11820}, {3541, 18431}, {3543, 37644}, {3566, 62172}, {3600, 6580}, {3620, 64097}, {3832, 7706}, {3854, 23294}, {4232, 32111}, {4295, 40950}, {5059, 13431}, {5067, 43903}, {5654, 58871}, {5663, 5921}, {5893, 43592}, {5895, 18909}, {5925, 18925}, {6225, 7487}, {7401, 11469}, {7408, 11455}, {7486, 43607}, {7500, 34796}, {7687, 23291}, {8889, 35450}, {9707, 62097}, {10295, 41450}, {10298, 52019}, {10303, 32620}, {10304, 35254}, {11008, 40196}, {11430, 20427}, {11457, 17578}, {11468, 61820}, {11738, 61116}, {12112, 18533}, {12289, 50692}, {12290, 64851}, {13403, 16624}, {13754, 20080}, {14054, 64047}, {15066, 61113}, {15107, 34621}, {15448, 41447}, {16111, 41467}, {16253, 40138}, {16879, 18945}, {18913, 22802}, {18918, 61721}, {18931, 47296}, {19041, 23273}, {19042, 23267}, {23249, 44637}, {23259, 44638}, {25739, 50687}, {32603, 53091}, {33878, 35513}, {34224, 49135}, {35483, 61690}, {37478, 52404}, {37645, 50434}, {39263, 59430}, {41424, 64714}, {43608, 61914}, {43713, 61680}, {47392, 58758}, {49138, 64717}, {50644, 58780}, {51170, 64096}, {51993, 62005}, {53780, 62042}, {56966, 63127}, {64025, 64756}, {64029, 64034}

X(65563) = reflection of X(i) in X(j) for these {i,j}: {4, 64094}, {376, 44750}, {3426, 64729}, {3529, 11820}, {12244, 10293}, {41465, 35237}, {49670, 6776}, {62042, 53780}
X(65563) = orthic isogonal conjugate of X(6623)
X(65563) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 6623}, {648, 9209}
X(65563) = X(i)-Dao conjugate of X(j) for these (i,j): {16253, 18850}, {37643, 69}
X(65563) = crosspoint of X(4) and X(376)
X(65563) = crosssum of X(3) and X(3426)
X(65563) = barycentric product X(i)*X(j) for these {i,j}: {376, 37643}, {10605, 52147}
X(65563) = barycentric quotient X(i)/X(j) for these {i,j}: {6623, 56270}, {37643, 36889}, {40138, 18850}
X(65563) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1514, 10605, 37643}, {1514, 37643, 6623}, {3426, 64094, 64729}, {3426, 64729, 4}, {35237, 41465, 20}

X(65564) = X(5)X(182)∩X(184)X(460)

Barycentrics    a^2*(a^8 - a^6*b^2 + a^4*b^4 - a^2*b^6 - a^6*c^2 + b^6*c^2 + a^4*c^4 - 2*b^4*c^4 - a^2*c^6 + b^2*c^6) : :

See Peter Moses, euclid 7009.

X(65564) lies on these lines: {3, 39072}, {5, 182}, {76, 50732}, {110, 1975}, {154, 3148}, {156, 2782}, {184, 460}, {685, 62576}, {1181, 45030}, {1614, 39646}, {1625, 20968}, {1971, 15270}, {1976, 13881}, {2001, 59635}, {2393, 44499}, {2871, 23128}, {3224, 14601}, {5012, 7851}, {5167, 40373}, {5876, 40121}, {6721, 64063}, {7789, 9306}, {8406, 12964}, {8414, 12970}, {9292, 41336}, {14585, 61213}, {16385, 42826}, {18451, 20993}, {19153, 32734}, {21177, 52436}, {32716, 60601}, {44127, 63554}

X(65564) = midpoint of X(30427) and X(30428)
X(65564) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 2909, 19156}, {30390, 30391, 64061}

X(65565) = X(5)X(182)∩X(22)X(110)

Barycentrics    a^2*(a^10 - 2*a^8*b^2 + 2*a^4*b^6 - a^2*b^8 - 2*a^8*c^2 - 4*a^6*b^2*c^2 + 3*a^4*b^4*c^2 + 2*a^2*b^6*c^2 + b^8*c^2 + 3*a^4*b^2*c^4 - 2*a^2*b^4*c^4 - b^6*c^4 + 2*a^4*c^6 + 2*a^2*b^2*c^6 - b^4*c^6 - a^2*c^8 + b^2*c^8) : :
X(65565) = X[182] - 3 X[206], X[182] + 3 X[6759], 5 X[182] - 9 X[23042], 2 X[182] - 3 X[64061], 5 X[206] - 3 X[23042], 5 X[6759] + 3 X[23042], 2 X[6759] + X[64061], 6 X[23042] - 5 X[64061], X[39884] + 3 X[64719], X[51756] - 3 X[61747], 9 X[154] - X[1350], 3 X[154] - X[15577], 3 X[154] + X[19149], X[1350] - 3 X[15577], X[1350] + 3 X[19149], 3 X[64] - 11 X[55671], X[15582] - 4 X[50414], 3 X[159] + X[1351], X[159] - 5 X[14530], X[1351] + 15 X[14530], X[1351] - 3 X[34117], 5 X[14530] + X[34117], X[1352] + 3 X[31166], X[1498] + 3 X[23041], 3 X[1498] + 5 X[53094], 3 X[23041] - X[44883], 9 X[23041] - 5 X[53094], 3 X[44883] - 5 X[53094], 2 X[5097] + 3 X[15580], 3 X[3357] - 7 X[55669], 3 X[10282] - X[14810], 2 X[14810] - 3 X[35228], 3 X[5596] + 5 X[40330], 3 X[34118] - 5 X[40330], 3 X[15578] - 4 X[55674], 3 X[34782] + X[51163], X[34775] - 5 X[64024], X[8549] - 5 X[19132], 3 X[8549] - 7 X[55711], 15 X[19132] - 7 X[55711], 9 X[11202] - 5 X[55655], 3 X[11202] - X[63431], 5 X[55655] - 3 X[63431], X[14216] - 5 X[31267], 3 X[32063] + X[63420], 2 X[15516] - 3 X[41593], 5 X[17821] - X[34778], 15 X[17821] - 7 X[55651], 3 X[34778] - 7 X[55651], 3 X[19153] + X[39879], 9 X[19153] - 5 X[53091], 3 X[39879] + 5 X[53091], X[61545] - 3 X[61610], 3 X[34779] + X[55587], 3 X[34787] + X[55722], X[55584] + 3 X[64031], 5 X[55629] + 3 X[64716], 5 X[55666] - 3 X[64027], 7 X[55676] + X[58795], X[61542] - 3 X[61606]

See Peter Moses, euclid 7009.

X(65565) lies on these lines: {5, 182}, {6, 1173}, {22, 110}, {25, 32191}, {49, 31670}, {54, 53023}, {64, 55671}, {69, 59351}, {141, 10539}, {156, 511}, {159, 195}, {160, 61748}, {184, 428}, {524, 64052}, {542, 19154}, {567, 9833}, {1092, 48881}, {1147, 29181}, {1176, 10516}, {1352, 10540}, {1469, 9667}, {1495, 19161}, {1498, 7509}, {1853, 7571}, {1971, 12212}, {1974, 8550}, {2080, 15270}, {2393, 5097}, {3056, 9652}, {3098, 9968}, {3357, 55669}, {3564, 64472}, {3763, 43598}, {3827, 6583}, {4577, 8920}, {5085, 52525}, {5092, 15579}, {5447, 7525}, {5448, 14862}, {5596, 7558}, {5651, 7499}, {6000, 15578}, {6403, 19596}, {6697, 64063}, {6776, 18374}, {7387, 64195}, {7394, 11003}, {7519, 63082}, {7553, 13352}, {7566, 32395}, {7699, 14157}, {8549, 19132}, {8717, 15311}, {8718, 59411}, {9019, 19139}, {9544, 51212}, {9545, 51538}, {9967, 35707}, {10984, 44762}, {11202, 55655}, {11842, 15257}, {12007, 19136}, {12017, 43811}, {12294, 44110}, {13336, 51126}, {13339, 14216}, {13861, 58532}, {14560, 43089}, {14912, 56918}, {14926, 32063}, {14927, 28708}, {15069, 19121}, {15139, 35260}, {15321, 52295}, {15516, 41593}, {15576, 32713}, {16187, 58434}, {17821, 34778}, {18358, 44491}, {19128, 64080}, {19130, 32046}, {19153, 39879}, {20299, 58450}, {22112, 23332}, {22115, 48873}, {25337, 61545}, {31723, 36989}, {32139, 63740}, {32217, 37971}, {32344, 51797}, {32445, 59232}, {33801, 44716}, {34148, 48910}, {34779, 55587}, {34787, 55722}, {37480, 46374}, {37489, 41589}, {37495, 43621}, {37813, 42671}, {37947, 55720}, {38851, 41450}, {40111, 48874}, {41579, 44480}, {43574, 48872}, {45014, 48905}, {47355, 61134}, {47474, 51733}, {55584, 64031}, {55629, 64716}, {55666, 64027}, {55676, 58795}, {58471, 64026}, {61542, 61606}

X(65565) = midpoint of X(i) and X(j) for these {i,j}: {6, 15581}, {159, 34117}, {206, 6759}, {1498, 44883}, {3098, 9968}, {5596, 34118}, {7387, 64195}, {9833, 18382}, {15577, 19149}, {19130, 45185}
X(65565) = reflection of X(i) in X(j) for these {i,j}: {6697, 64063}, {15579, 5092}, {20299, 58450}, {35228, 10282}, {64061, 206}
X(65565) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {154, 19149, 15577}, {1498, 23041, 44883}, {6776, 18374, 51730}, {63658, 63663, 63688}

X(65566) = X(3)X(15619)∩X(53)X(232)

Barycentrics    4*a^10*(b^2+c^2)-a^4*(b^2-c^2)^2*(b^4-b^2*c^2+c^4)-(b^2-c^2)^4*(2*b^4+5*b^2*c^2+2*c^4)-a^8*(9*b^4+14*b^2*c^2+9*c^4)+a^6*(5*b^6+7*b^4*c^2+7*b^2*c^4+5*c^6)+3*a^2*(b^10-b^8*c^2-b^2*c^8+c^10) : :

See Ivan Pavlov, euclid 7012.

X(65566) lies on these lines: {3, 15619}, {53, 232}, {550, 20299}, {1853, 35885}, {15557, 31868}, {18381, 35728}, {21243, 38429}, {33992, 61743}

X(65566) = pole of line {233, 647} with respect to the nine-point circle

X(65567) = X(33)X(6750)∩X(6198)X(8884)

Barycentrics    a*(a^12-a^10*(3*b^2+2*b*c+3*c^2)+(b^2-c^2)^4*(b^4+b^3*c+b^2*c^2+b*c^3+c^4)+a^4*(b^2-c^2)^2*(3*b^4-b^3*c+2*b^2*c^2-b*c^3+3*c^4)+a^8*(3*b^4+4*b^3*c+7*b^2*c^2+4*b*c^3+3*c^4)-a^6*(2*b^6+b^5*c+4*b^4*c^2+4*b^3*c^3+4*b^2*c^4+b*c^5+2*c^6)-a^2*(b^2-c^2)^2*(3*b^6+b^5*c-b^4*c^2-b^2*c^4+b*c^5+3*c^6)) : :

See Ivan Pavlov, euclid 7012.

X(65567) lies on these lines: {1, 18400}, {33, 6750}, {55, 58735}, {1062, 10600}, {6198, 8884}, {8144, 32428}, {18455, 36245}, {37729, 37846}, {37733, 45272}

X(65568) = X(6)-DAO CONJUGATE OF X(12)

Barycentrics    a^2*(a + b)^2*(a - b - c)*(a + c)^2*(a^2 - b^2 - c^2) : :

X(65568) lies on these lines: {3, 1798}, {60, 4267}, {63, 4558}, {81, 593}, {110, 3185}, {212, 1808}, {261, 2189}, {283, 6514}, {285, 1098}, {333, 19607}, {343, 57985}, {348, 1509}, {1414, 34035}, {1790, 4288}, {1804, 7341}, {1812, 2193}, {1993, 36744}, {4282, 17185}, {4565, 17080}, {4612, 7058}, {4636, 6061}, {5546, 56440}, {18021, 55196}, {29206, 58982}, {56934, 62857}, {57685, 57704}

X(65568) = isogonal conjugate of X(8736)
X(65568) = isotomic conjugate of the polar conjugate of X(60)
X(65568) = isogonal conjugate of the polar conjugate of X(261)
X(65568) = X(261)-Ceva conjugate of X(60)
X(65568) = X(i)-cross conjugate of X(j) for these (i,j): {1790, 2185}, {7117, 23189}, {22056, 3}
X(65568) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8736}, {4, 2171}, {6, 56285}, {10, 1880}, {12, 19}, {25, 6358}, {33, 6354}, {34, 594}, {37, 225}, {42, 40149}, {57, 7140}, {65, 1826}, {92, 181}, {108, 4024}, {115, 7012}, {158, 2197}, {162, 55197}, {201, 393}, {213, 57809}, {226, 1824}, {273, 1500}, {278, 756}, {281, 1254}, {321, 57652}, {331, 872}, {512, 65207}, {604, 7141}, {608, 1089}, {653, 4705}, {661, 61178}, {1091, 2189}, {1096, 26942}, {1109, 7115}, {1118, 3949}, {1395, 28654}, {1396, 6535}, {1400, 41013}, {1426, 2321}, {1427, 53008}, {1435, 6057}, {1441, 2333}, {1825, 8818}, {1847, 7064}, {1857, 37755}, {1893, 60677}, {1897, 57185}, {1918, 52575}, {1969, 61364}, {1973, 34388}, {2149, 2970}, {2207, 57807}, {2326, 7314}, {2358, 21075}, {2501, 4551}, {2643, 46102}, {3952, 55208}, {4036, 32674}, {4041, 52607}, {4079, 18026}, {4092, 7128}, {4103, 43923}, {4559, 24006}, {4564, 8754}, {4566, 55206}, {4605, 18344}, {6046, 7079}, {6520, 7066}, {7046, 7147}, {7101, 7143}, {7109, 57787}, {7337, 52369}, {7649, 21859}, {13853, 40971}, {21824, 34922}, {36127, 55232}, {42666, 65329}, {44113, 60091}, {46404, 50487}, {52384, 53009}, {54240, 55230}, {58757, 65233}
X(65568) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 8736}, {6, 12}, {9, 56285}, {125, 55197}, {650, 2970}, {905, 338}, {1147, 2197}, {3161, 7141}, {5452, 7140}, {6337, 34388}, {6503, 26942}, {6505, 6358}, {6626, 57809}, {11517, 594}, {22391, 181}, {34021, 52575}, {34467, 57185}, {35072, 4036}, {36033, 2171}, {36830, 61178}, {37867, 7066}, {38983, 4024}, {39054, 65207}, {40582, 41013}, {40589, 225}, {40592, 40149}, {40602, 1826}, {40625, 14618}, {40626, 52623}, {40628, 1109}, {55067, 24006}, {62584, 28654}, {62647, 1089}
X(65568) = cevapoint of X(i) and X(j) for these (i,j): {3, 22118}, {283, 2193}, {1790, 18604}, {7117, 23189}
X(65568) = crosspoint of X(249) and X(4612)
X(65568) = crosssum of X(115) and X(57185)
X(65568) = crossdifference of every pair of points on line {4705, 55197}
X(65568) = barycentric product X(i)*X(j) for these {i,j}: {3, 261}, {21, 1444}, {27, 6514}, {48, 52379}, {58, 332}, {60, 69}, {63, 2185}, {77, 1098}, {78, 757}, {81, 1812}, {86, 283}, {99, 23189}, {184, 18021}, {212, 873}, {219, 1509}, {222, 7058}, {249, 26932}, {255, 57779}, {270, 326}, {274, 2193}, {284, 17206}, {304, 2150}, {314, 1437}, {333, 1790}, {345, 593}, {348, 7054}, {394, 46103}, {521, 52935}, {552, 1260}, {645, 7254}, {647, 55196}, {652, 4610}, {763, 3694}, {849, 3718}, {905, 4612}, {1014, 1792}, {1101, 17880}, {1265, 7341}, {1364, 18020}, {1414, 57081}, {1434, 2327}, {1789, 56934}, {1797, 30606}, {1804, 59482}, {1808, 33295}, {1946, 4623}, {2170, 62719}, {2189, 3926}, {2318, 6628}, {2326, 7183}, {3270, 7340}, {3271, 47389}, {3737, 4592}, {3937, 6064}, {4025, 4636}, {4131, 52914}, {4267, 57853}, {4556, 6332}, {4558, 4560}, {4563, 7252}, {4565, 15411}, {4570, 17219}, {4573, 23090}, {4575, 18155}, {4590, 7117}, {4616, 58338}, {4625, 57134}, {4631, 22383}, {5546, 15419}, {6061, 7056}, {7004, 24041}, {18604, 31623}, {22056, 31620}, {22345, 52550}, {26856, 44717}, {34387, 47390}, {36054, 55231}, {52370, 57949}, {55207, 57129}
X(65568) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 56285}, {3, 12}, {6, 8736}, {8, 7141}, {11, 2970}, {21, 41013}, {48, 2171}, {55, 7140}, {58, 225}, {60, 4}, {63, 6358}, {69, 34388}, {78, 1089}, {81, 40149}, {86, 57809}, {110, 61178}, {184, 181}, {201, 1091}, {212, 756}, {219, 594}, {222, 6354}, {249, 46102}, {255, 201}, {261, 264}, {270, 158}, {274, 52575}, {283, 10}, {284, 1826}, {326, 57807}, {332, 313}, {345, 28654}, {394, 26942}, {521, 4036}, {577, 2197}, {593, 278}, {603, 1254}, {647, 55197}, {652, 4024}, {662, 65207}, {757, 273}, {849, 34}, {873, 57787}, {906, 21859}, {1092, 7066}, {1098, 318}, {1101, 7012}, {1259, 3695}, {1260, 6057}, {1333, 1880}, {1364, 125}, {1408, 1426}, {1425, 7314}, {1437, 65}, {1444, 1441}, {1509, 331}, {1789, 6757}, {1790, 226}, {1792, 3701}, {1793, 15065}, {1798, 60086}, {1800, 21077}, {1804, 6356}, {1808, 43534}, {1812, 321}, {1813, 4605}, {1819, 21075}, {1946, 4705}, {2150, 19}, {2185, 92}, {2189, 393}, {2193, 37}, {2194, 1824}, {2206, 57652}, {2289, 3949}, {2318, 6535}, {2327, 2321}, {2328, 53008}, {3270, 4092}, {3271, 8754}, {3561, 56327}, {3690, 6058}, {3719, 52369}, {3737, 24006}, {3937, 1365}, {3955, 7211}, {4091, 57243}, {4225, 56827}, {4267, 429}, {4556, 653}, {4558, 4552}, {4560, 14618}, {4565, 52607}, {4575, 4551}, {4587, 4103}, {4610, 46404}, {4612, 6335}, {4636, 1897}, {5009, 1874}, {6056, 3690}, {6061, 7046}, {6332, 52623}, {6514, 306}, {7004, 1109}, {7053, 6046}, {7054, 281}, {7058, 7017}, {7099, 7147}, {7117, 115}, {7125, 37755}, {7193, 7235}, {7215, 1367}, {7252, 2501}, {7254, 7178}, {7335, 1425}, {7341, 1119}, {7342, 1398}, {14575, 61364}, {17104, 1825}, {17206, 349}, {17219, 21207}, {17880, 23994}, {18021, 18022}, {18604, 1214}, {20753, 7237}, {20803, 51879}, {22074, 21810}, {22096, 61052}, {22118, 56325}, {22345, 52567}, {22361, 21674}, {22379, 51663}, {22383, 57185}, {23090, 3700}, {23145, 21958}, {23189, 523}, {23357, 7115}, {23609, 4183}, {26932, 338}, {30576, 37790}, {30606, 46109}, {32661, 4559}, {36054, 55232}, {37140, 65329}, {41608, 41538}, {46103, 2052}, {46882, 1865}, {47390, 59}, {52370, 762}, {52379, 1969}, {52425, 1500}, {52935, 18026}, {54417, 1867}, {55117, 13853}, {55196, 6331}, {56269, 41508}, {57042, 21721}, {57081, 4086}, {57129, 55208}, {57134, 4041}, {57241, 4064}, {57657, 2333}, {57736, 52383}, {57779, 57806}, {61054, 20975}
X(65568) = {X(593),X(7054)}-harmonic conjugate of X(2185)

X(65569) = X(9)-DAO CONJUGATE OF X(13)

Barycentrics    a*(Sqrt[3]*(a^2 - b^2 - c^2) - 2*S) : :

X(65569) lies on these lines: {1, 21}, {2, 1081}, {9, 5362}, {15, 42701}, {48, 19299}, {75, 2154}, {100, 51688}, {533, 3578}, {618, 39150}, {1082, 2307}, {1094, 51806}, {1653, 5367}, {2153, 18722}, {2173, 15772}, {3180, 19551}, {3218, 5240}, {3639, 54357}, {4467, 23870}, {7026, 21739}, {10651, 33108}, {14206, 51805}, {17402, 56934}, {17484, 51271}, {17494, 54023}, {17781, 53588}, {19772, 36929}, {33529, 40999}, {37833, 64153}, {39153, 54378}, {41804, 41887}, {54402, 55399}, {54403, 55400}, {54437, 55405}, {54438, 55406}

X(65569) = isogonal conjugate of X(2153)
X(65569) = isotomic conjugate of the isogonal conjugate of X(2151)
X(65569) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7026, 21287}, {19551, 1330}, {33655, 2893}, {34079, 36928}
X(65569) = X(11073)-complementary conjugate of X(25639)
X(65569) = X(298)-Ceva conjugate of X(44688)
X(65569) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2153}, {2, 3457}, {3, 8737}, {4, 36296}, {6, 13}, {14, 11081}, {15, 11080}, {16, 1989}, {17, 11083}, {18, 11142}, {25, 40709}, {32, 300}, {51, 51275}, {61, 11139}, {62, 11082}, {74, 36299}, {94, 34395}, {110, 20578}, {111, 52039}, {187, 36307}, {249, 30452}, {265, 8740}, {299, 11060}, {395, 2381}, {396, 16459}, {463, 47481}, {471, 52153}, {476, 6138}, {512, 23895}, {523, 5995}, {532, 11084}, {604, 44690}, {619, 11089}, {647, 36306}, {690, 9206}, {1251, 33655}, {1495, 36308}, {1990, 39377}, {2152, 2166}, {2154, 51805}, {2160, 46073}, {2161, 39153}, {2306, 19551}, {2378, 11537}, {2379, 18777}, {2501, 38414}, {2981, 8014}, {3438, 51270}, {3440, 40578}, {3441, 41889}, {3458, 11078}, {3489, 51276}, {5318, 41892}, {5612, 11071}, {5618, 57122}, {5994, 23283}, {6104, 11087}, {6110, 39380}, {6111, 11079}, {6116, 11077}, {6137, 36839}, {6151, 61370}, {6344, 46113}, {8603, 11581}, {8738, 50465}, {8739, 10217}, {8741, 50468}, {8838, 21461}, {8882, 44713}, {10630, 30454}, {10641, 52204}, {11063, 46072}, {11072, 39151}, {11073, 42677}, {11075, 46071}, {11085, 36208}, {11086, 36211}, {11088, 11601}, {14358, 42623}, {14373, 40581}, {14560, 23871}, {14579, 51267}, {14642, 44702}, {15475, 17403}, {16770, 21462}, {18384, 44719}, {19780, 53029}, {23588, 52342}, {23964, 41997}, {32586, 46925}, {34537, 41993}, {40355, 41888}, {40384, 41995}, {51446, 59209}, {55221, 60051}
X(65569) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 2153}, {9, 13}, {244, 20578}, {3161, 44690}, {6376, 300}, {6505, 40709}, {10639, 3383}, {11597, 2152}, {30471, 75}, {32664, 3457}, {34544, 16}, {35443, 1109}, {36033, 36296}, {36103, 8737}, {38993, 661}, {39052, 36306}, {39054, 23895}, {40579, 2166}, {40580, 1}, {40581, 51805}, {40584, 39153}, {41888, 14206}, {43961, 1577}, {47898, 24006}
X(65569) = cevapoint of X(1) and X(19298)
X(65569) = crosssum of X(6) and X(42623)
X(65569) = trilinear pole of line {32679, 54027}
X(65569) = barycentric product X(i)*X(j) for these {i,j}: {1, 298}, {7, 44688}, {15, 75}, {63, 470}, {76, 2151}, {92, 44718}, {299, 51806}, {300, 1094}, {301, 6149}, {303, 3384}, {304, 8739}, {319, 39152}, {320, 46077}, {561, 34394}, {662, 23870}, {799, 6137}, {811, 60010}, {1577, 17402}, {1969, 46112}, {2153, 11129}, {2154, 7799}, {2167, 33529}, {2349, 41887}, {3179, 46175}, {6117, 62277}, {6782, 8773}, {9204, 36085}, {19604, 44725}, {19611, 44700}, {23896, 32679}, {24041, 30465}, {34390, 35198}, {37773, 40713}, {40440, 44711}, {40710, 52414}
X(65569) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 13}, {6, 2153}, {8, 44690}, {14, 2166}, {15, 1}, {16, 51805}, {19, 8737}, {31, 3457}, {35, 46073}, {36, 39153}, {48, 36296}, {50, 2152}, {62, 3383}, {63, 40709}, {75, 300}, {162, 36306}, {163, 5995}, {202, 3179}, {298, 75}, {301, 63759}, {470, 92}, {661, 20578}, {662, 23895}, {896, 52039}, {897, 36307}, {1094, 15}, {1095, 36208}, {1250, 19551}, {1749, 51267}, {1895, 44702}, {2151, 6}, {2152, 11081}, {2153, 11080}, {2154, 1989}, {2167, 51275}, {2173, 36299}, {2307, 33655}, {2349, 36308}, {2624, 6138}, {2632, 41997}, {2643, 30452}, {3200, 35198}, {3384, 18}, {4117, 41993}, {4575, 38414}, {5239, 36933}, {5353, 39151}, {5357, 42677}, {5616, 1749}, {5994, 32678}, {6110, 1784}, {6126, 46071}, {6137, 661}, {6149, 16}, {6782, 1733}, {8739, 19}, {11086, 2154}, {17402, 662}, {19298, 40578}, {19299, 41889}, {19373, 2306}, {23870, 1577}, {23896, 32680}, {30465, 1109}, {32679, 23871}, {33529, 14213}, {34394, 31}, {35198, 62}, {35199, 6104}, {35200, 39377}, {35201, 6111}, {36072, 54026}, {36142, 9206}, {36209, 51806}, {36309, 36129}, {37773, 1081}, {38413, 36061}, {39152, 79}, {41887, 14206}, {42074, 41995}, {42081, 30454}, {44688, 8}, {44700, 1895}, {44706, 44713}, {44711, 44706}, {44718, 63}, {44725, 44720}, {46075, 50148}, {46077, 80}, {46112, 48}, {51801, 6116}, {51802, 5612}, {51804, 46072}, {51805, 36211}, {51806, 14}, {52414, 471}, {54027, 54015}, {60010, 656}
X(65569) = {X(9),X(51976)}-harmonic conjugate of X(5362)

X(65570) = X(9)-DAO CONJUGATE OF X(14)

Barycentrics    a*(Sqrt[3]*(a^2 - b^2 - c^2) + 2*S) : :

X(65570) lies on these lines: {1, 21}, {2, 554}, {9, 5367}, {16, 42701}, {48, 19298}, {75, 2153}, {100, 51690}, {532, 3578}, {559, 3219}, {619, 39151}, {1095, 51805}, {1652, 5362}, {2154, 18722}, {2173, 15771}, {3181, 7126}, {3218, 5239}, {3638, 54357}, {4467, 23871}, {7043, 21739}, {10652, 33108}, {14206, 51806}, {17403, 56934}, {17484, 51264}, {17494, 54021}, {17781, 53589}, {19773, 36928}, {33530, 40999}, {37830, 64153}, {39152, 54379}, {41804, 41888}, {54402, 55400}, {54403, 55399}, {54437, 55406}, {54438, 55405}

X(65570) = isogonal conjugate of X(2154)
X(65570) = complement of the isogonal conjugate of X(42624)
X(65570) = isotomic conjugate of the isogonal conjugate of X(2152)
X(65570) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7043, 21287}, {7052, 2893}, {7126, 1330}, {34079, 36929}
X(65570) = X(i)-complementary conjugate of X(j) for these (i,j): {7150, 141}, {11072, 25639}, {42624, 10}
X(65570) = X(299)-Ceva conjugate of X(44689)
X(65570) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2154}, {2, 3458}, {3, 8738}, {4, 36297}, {6, 14}, {13, 11086}, {15, 1989}, {16, 11085}, {17, 11141}, {18, 11088}, {25, 40710}, {32, 301}, {51, 51268}, {61, 11087}, {62, 11138}, {74, 36298}, {94, 34394}, {110, 20579}, {111, 52040}, {187, 36310}, {249, 30453}, {265, 8739}, {298, 11060}, {395, 16460}, {396, 2380}, {462, 47482}, {470, 52153}, {476, 6137}, {512, 23896}, {523, 5994}, {533, 11089}, {604, 44691}, {618, 11084}, {647, 36309}, {690, 9207}, {1495, 36311}, {1990, 39378}, {2151, 2166}, {2153, 51806}, {2160, 46077}, {2161, 39152}, {2378, 18776}, {2379, 11549}, {2501, 38413}, {2981, 61371}, {3439, 51277}, {3441, 40579}, {3457, 11092}, {3490, 51269}, {5321, 41893}, {5616, 11071}, {5619, 57123}, {5995, 23284}, {6105, 11082}, {6110, 11079}, {6111, 39381}, {6117, 11077}, {6138, 36840}, {6151, 8015}, {6344, 46112}, {7052, 33653}, {7126, 33654}, {8604, 11582}, {8737, 50466}, {8740, 10218}, {8742, 50469}, {8836, 21462}, {8882, 44714}, {10630, 30455}, {10642, 52203}, {11063, 46076}, {11072, 42680}, {11073, 39150}, {11075, 46075}, {11080, 36209}, {11081, 36210}, {11083, 11600}, {14372, 40580}, {14560, 23870}, {14579, 51274}, {14642, 44703}, {15475, 17402}, {16771, 21461}, {18384, 44718}, {19781, 53030}, {23588, 52343}, {23964, 41998}, {32585, 46926}, {34537, 41994}, {40355, 41887}, {40384, 41996}, {51447, 59210}, {55223, 60052}
X(65570) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 2154}, {9, 14}, {244, 20579}, {3161, 44691}, {6376, 301}, {6505, 40710}, {10640, 3376}, {11597, 2151}, {30472, 75}, {32664, 3458}, {34544, 15}, {35444, 1109}, {36033, 36297}, {36103, 8738}, {38994, 661}, {39052, 36309}, {39054, 23896}, {40578, 2166}, {40580, 51806}, {40581, 1}, {40584, 39152}, {41887, 14206}, {43962, 1577}, {47899, 24006}
X(65570) = cevapoint of X(1) and X(19299)
X(65570) = trilinear pole of line {32679, 54025}
X(65570) = barycentric product X(i)*X(j) for these {i,j}: {1, 299}, {7, 44689}, {16, 75}, {63, 471}, {76, 2152}, {92, 44719}, {298, 51805}, {300, 6149}, {301, 1095}, {302, 3375}, {304, 8740}, {319, 39153}, {320, 46073}, {561, 34395}, {662, 23871}, {799, 6138}, {811, 60009}, {1577, 17403}, {1969, 46113}, {2153, 7799}, {2154, 11128}, {2167, 33530}, {2349, 41888}, {6116, 62277}, {6783, 8773}, {9205, 36085}, {19604, 44726}, {19611, 44701}, {23895, 32679}, {24041, 30468}, {34389, 35199}, {37772, 40714}, {40440, 44712}, {40709, 52414}, {41225, 46176}
X(65570) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14}, {6, 2154}, {8, 44691}, {13, 2166}, {15, 51806}, {16, 1}, {19, 8738}, {31, 3458}, {35, 46077}, {36, 39152}, {48, 36297}, {50, 2151}, {61, 3376}, {63, 40710}, {75, 301}, {162, 36309}, {163, 5994}, {203, 41225}, {299, 75}, {300, 63759}, {471, 92}, {661, 20579}, {662, 23896}, {896, 52040}, {897, 36310}, {1094, 36209}, {1095, 16}, {1749, 51274}, {1895, 44703}, {2151, 11086}, {2152, 6}, {2153, 1989}, {2154, 11085}, {2167, 51268}, {2173, 36298}, {2349, 36311}, {2624, 6137}, {2632, 41998}, {2643, 30453}, {3201, 35199}, {3375, 17}, {4117, 41994}, {4575, 38413}, {5240, 36932}, {5353, 42680}, {5357, 39150}, {5612, 1749}, {5995, 32678}, {6111, 1784}, {6126, 46075}, {6138, 661}, {6149, 15}, {6783, 1733}, {7005, 7150}, {7051, 33654}, {7127, 33653}, {7150, 14359}, {8740, 19}, {10638, 7126}, {11081, 2153}, {17403, 662}, {19299, 40579}, {23871, 1577}, {23895, 32680}, {30468, 1109}, {32679, 23870}, {33530, 14213}, {34395, 31}, {35198, 6105}, {35199, 61}, {35200, 39378}, {35201, 6110}, {36073, 54024}, {36142, 9207}, {36208, 51805}, {36306, 36129}, {37772, 554}, {38414, 36061}, {39153, 79}, {41888, 14206}, {42074, 41996}, {42081, 30455}, {44689, 8}, {44701, 1895}, {44706, 44714}, {44712, 44706}, {44719, 63}, {44726, 44720}, {46071, 50148}, {46073, 80}, {46113, 48}, {51801, 6117}, {51802, 5616}, {51804, 46076}, {51805, 13}, {51806, 36210}, {52414, 470}, {54025, 54014}, {60009, 656}
X(65570) = {X(9),X(51977)}-harmonic conjugate of X(5367)

X(65571) = X(9)-DAO CONJUGATE OF X(17)

Barycentrics    a*(a^2 - b^2 - c^2 - 2*Sqrt[3]*S) : :

X(65571) lies on these lines: {1, 21}, {2, 1082}, {554, 17483}, {559, 3218}, {662, 2154}, {908, 53588}, {1081, 31019}, {2152, 16568}, {3181, 33653}, {3219, 5239}, {3376, 63760}, {3434, 37833}, {3639, 5249}, {5057, 51749}, {5353, 54444}, {10651, 20292}, {11680, 51750}, {23958, 37773}, {25722, 30356}, {27003, 37772}, {30338, 36845}, {33393, 42678}, {33395, 42681}, {37795, 62998}, {37830, 44447}, {37831, 40713}, {53589, 59491}, {54435, 55400}, {54436, 55399}

X(65571) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {33653, 1330}, {33654, 2893}
X(65571) = X(i)-isoconjugate of X(j) for these (i,j): {2, 21461}, {3, 8741}, {4, 32585}, {6, 17}, {13, 8603}, {14, 51890}, {15, 11139}, {16, 11087}, {18, 51547}, {25, 40712}, {32, 34389}, {54, 36300}, {62, 2963}, {99, 58869}, {110, 55199}, {396, 34321}, {472, 51477}, {512, 32036}, {523, 16806}, {647, 65346}, {669, 55220}, {930, 55223}, {2154, 3375}, {2380, 40667}, {2981, 36304}, {3458, 19779}, {3519, 10641}, {6137, 60051}, {8740, 52203}, {10677, 11082}, {11080, 37848}, {11081, 11600}, {11144, 21462}, {23302, 57384}, {23873, 32737}, {52930, 55201}
X(65571) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 17}, {244, 55199}, {600, 42676}, {5507, 42679}, {6376, 34389}, {6505, 40712}, {10640, 1}, {32664, 21461}, {36033, 32585}, {36103, 8741}, {38986, 58869}, {39052, 65346}, {39054, 32036}, {40581, 3375}, {62600, 75}
X(65571) = barycentric product X(i)*X(j) for these {i,j}: {1, 302}, {61, 75}, {63, 473}, {92, 52348}, {299, 3376}, {301, 35199}, {304, 10642}, {661, 55198}, {662, 23872}, {799, 55221}, {1577, 52605}, {2154, 11132}, {2964, 34390}, {32791, 42681}, {32792, 42678}, {51806, 52220}, {52671, 62277}
X(65571) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17}, {16, 3375}, {18, 2962}, {19, 8741}, {31, 21461}, {48, 32585}, {61, 1}, {63, 40712}, {75, 34389}, {162, 65346}, {163, 16806}, {302, 75}, {473, 92}, {661, 55199}, {662, 32036}, {798, 58869}, {799, 55220}, {1094, 37848}, {1953, 36300}, {2151, 8603}, {2152, 51890}, {2153, 11139}, {2154, 11087}, {2964, 62}, {3201, 1095}, {3299, 42676}, {3301, 42679}, {3376, 14}, {6104, 51805}, {10642, 19}, {11083, 2153}, {11135, 2152}, {11137, 2151}, {11141, 2154}, {16807, 36148}, {23872, 1577}, {35198, 10677}, {35199, 16}, {42678, 3302}, {42681, 3300}, {51806, 11600}, {52348, 63}, {52605, 662}, {55198, 799}, {55221, 661}, {63760, 52349}
X(65571) = {X(1082),X(5240)}-harmonic conjugate of X(2)

X(65572) = X(9)-DAO CONJUGATE OF X(18)

Barycentrics    a*(a^2 - b^2 - c^2 + 2*Sqrt[3]*S) : :

X(65572) lies on these lines: {1, 21}, {2, 559}, {554, 31019}, {662, 2153}, {908, 53589}, {1081, 17483}, {1082, 3218}, {1251, 3180}, {2151, 16568}, {3219, 5240}, {3383, 63760}, {3434, 37830}, {3638, 5249}, {5057, 51750}, {5357, 54444}, {10652, 20292}, {11680, 51749}, {23958, 37772}, {25722, 30357}, {27003, 37773}, {30339, 36845}, {33392, 42679}, {33394, 42676}, {37794, 62998}, {37833, 44447}, {37834, 40714}, {53588, 59491}, {54435, 55399}, {54436, 55400}

X(65572) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1251, 1330}, {2306, 2893}
X(65572) = X(i)-isoconjugate of X(j) for these (i,j): {2, 21462}, {3, 8742}, {4, 32586}, {6, 18}, {13, 51891}, {14, 8604}, {15, 11082}, {16, 11138}, {17, 51546}, {25, 40711}, {32, 34390}, {54, 36301}, {61, 2963}, {99, 58870}, {110, 55201}, {395, 34322}, {473, 51477}, {512, 32037}, {523, 16807}, {647, 65347}, {669, 55222}, {930, 55221}, {2153, 3384}, {2381, 40668}, {3457, 19778}, {3519, 10642}, {6138, 60052}, {6151, 36305}, {8739, 52204}, {10678, 11087}, {11085, 37850}, {11086, 11601}, {11143, 21461}, {23303, 57385}, {23872, 32737}, {52929, 55199}
X(65572) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 18}, {244, 55201}, {600, 42678}, {5507, 42681}, {6376, 34390}, {6505, 40711}, {10639, 1}, {32664, 21462}, {36033, 32586}, {36103, 8742}, {38986, 58870}, {39052, 65347}, {39054, 32037}, {40580, 3384}, {62601, 75}
X(65572) = barycentric product X(i)*X(j) for these {i,j}: {1, 303}, {62, 75}, {63, 472}, {92, 52349}, {298, 3383}, {300, 35198}, {304, 10641}, {661, 55200}, {662, 23873}, {799, 55223}, {1577, 52606}, {2153, 11133}, {2964, 34389}, {32791, 42679}, {32792, 42676}, {51805, 52221}, {52670, 62277}
X(65572) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18}, {15, 3384}, {17, 2962}, {19, 8742}, {31, 21462}, {48, 32586}, {62, 1}, {63, 40711}, {75, 34390}, {162, 65347}, {163, 16807}, {303, 75}, {472, 92}, {661, 55201}, {662, 32037}, {798, 58870}, {799, 55222}, {1095, 37850}, {1953, 36301}, {2151, 51891}, {2152, 8604}, {2153, 11082}, {2154, 11138}, {2964, 61}, {3200, 1094}, {3299, 42678}, {3301, 42681}, {3383, 13}, {6105, 51806}, {10641, 19}, {11088, 2154}, {11134, 2152}, {11136, 2151}, {11142, 2153}, {16806, 36148}, {23873, 1577}, {35198, 15}, {35199, 10678}, {42676, 3302}, {42679, 3300}, {51805, 11601}, {52349, 63}, {52606, 662}, {55200, 799}, {55223, 661}, {63760, 52348}
X(65572) = {X(559),X(5239)}-harmonic conjugate of X(2)

X(65573) = X(10)-DAO CONJUGATE OF X(11)

Barycentrics    a*(a - b)^2*(a - c)^2*(a + b - c)*(a - b + c)*(b + c) : :

X(65573) lies on these lines: {21, 4570}, {59, 518}, {100, 522}, {101, 21390}, {109, 53685}, {190, 53644}, {523, 4552}, {651, 660}, {664, 57167}, {860, 17757}, {934, 2748}, {960, 57141}, {1014, 4620}, {1018, 4171}, {1026, 24029}, {1110, 1736}, {1252, 5089}, {1284, 3932}, {1431, 5378}, {1447, 3263}, {1897, 57089}, {2283, 23343}, {2346, 5377}, {2752, 59101}, {3952, 23067}, {4017, 4551}, {4069, 65233}, {4578, 65159}, {4581, 50039}, {5260, 55091}, {5692, 62741}, {6516, 57054}, {6986, 14887}, {7451, 56881}, {8543, 62721}, {12081, 22220}, {14594, 65313}, {17780, 23981}, {47318, 57093}, {51506, 63755}, {62235, 63918}

X(65573) = isogonal conjugate of X(18191)
X(65573) = isogonal conjugate of the complement of X(3909)
X(65573) = X(31615)-Ceva conjugate of X(21859)
X(65573) = X(i)-cross conjugate of X(j) for these (i,j): {10, 100}, {37, 4552}, {65, 4551}, {72, 3952}, {209, 1783}, {210, 1018}, {1400, 651}, {1402, 4559}, {2318, 644}, {3191, 1897}, {3694, 65233}, {21061, 190}, {21078, 4033}, {21859, 31615}, {22021, 65207}, {22275, 668}, {24053, 4632}, {41538, 61178}, {41539, 4566}, {56538, 835}, {60723, 4613}
X(65573) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18191}, {6, 17197}, {9, 16726}, {11, 58}, {21, 244}, {25, 17219}, {27, 7117}, {28, 7004}, {29, 3937}, {41, 16727}, {55, 17205}, {60, 3120}, {81, 2170}, {86, 3271}, {109, 56283}, {110, 21132}, {163, 40166}, {261, 3122}, {270, 18210}, {283, 2969}, {284, 1086}, {314, 3248}, {332, 42067}, {333, 1015}, {513, 3737}, {514, 7252}, {521, 57200}, {522, 3733}, {593, 21044}, {643, 764}, {644, 8042}, {645, 21143}, {649, 4560}, {650, 1019}, {652, 17925}, {657, 17096}, {663, 7192}, {667, 18155}, {741, 4124}, {757, 4516}, {759, 53525}, {884, 23829}, {1014, 2310}, {1021, 3669}, {1043, 1357}, {1098, 53540}, {1111, 2194}, {1146, 1412}, {1172, 3942}, {1178, 4459}, {1333, 4858}, {1334, 61403}, {1358, 2328}, {1364, 8747}, {1396, 34591}, {1400, 26856}, {1408, 24026}, {1415, 40213}, {1434, 14936}, {1474, 26932}, {1565, 2299}, {1790, 8735}, {1977, 28660}, {2053, 23824}, {2150, 16732}, {2185, 3125}, {2189, 4466}, {2203, 17880}, {2206, 34387}, {2287, 53538}, {2311, 27918}, {2319, 16742}, {2341, 53546}, {3063, 7199}, {3064, 7254}, {3121, 52379}, {3249, 62534}, {3285, 60578}, {3615, 53542}, {3676, 21789}, {3680, 18211}, {3900, 7203}, {4391, 57129}, {4556, 55195}, {4565, 42462}, {4570, 7336}, {4591, 52338}, {4610, 63462}, {5546, 6545}, {6332, 43925}, {6371, 57161}, {7054, 53545}, {7253, 43924}, {7257, 8027}, {7303, 40608}, {7341, 52335}, {7649, 23189}, {9315, 16759}, {11998, 53083}, {14432, 43926}, {16947, 23978}, {17187, 18101}, {21828, 60571}, {22096, 44130}, {22383, 57215}, {23989, 57657}, {27846, 56154}, {34589, 52150}, {38347, 39950}, {38365, 39734}, {42454, 43076}, {43923, 57081}, {43932, 58329}, {52375, 53524}, {52378, 64445}, {53521, 60568}
X(65573) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 18191}, {9, 17197}, {10, 11}, {11, 56283}, {12, 53566}, {37, 4858}, {115, 40166}, {223, 17205}, {226, 1565}, {244, 21132}, {478, 16726}, {1145, 14010}, {1146, 40213}, {1214, 1111}, {3160, 16727}, {5375, 4560}, {6505, 17219}, {6631, 18155}, {6741, 42455}, {8299, 4124}, {10001, 7199}, {15267, 53540}, {17761, 42454}, {34586, 53525}, {36908, 1358}, {39026, 3737}, {40582, 26856}, {40586, 2170}, {40590, 1086}, {40591, 7004}, {40599, 1146}, {40600, 3271}, {40603, 34387}, {40607, 4516}, {40611, 244}, {50330, 7336}, {51574, 26932}, {55060, 764}, {55064, 42462}, {56325, 16732}, {59577, 24026}, {62564, 17880}, {62566, 1090}, {62570, 23989}
X(65573) = cevapoint of X(i) and X(j) for these (i,j): {1, 53280}, {37, 4557}, {56, 61225}, {65, 4551}, {72, 23067}, {100, 5260}, {210, 1018}, {1402, 4559}, {3694, 4069}, {3952, 17751}
X(65573) = crosspoint of X(i) and X(j) for these (i,j): {765, 15742}, {4564, 4998}
X(65573) = crosssum of X(i) and X(j) for these (i,j): {244, 3937}, {2170, 3271}
X(65573) = trilinear pole of line {1018, 4551}
X(65573) = barycentric product X(i)*X(j) for these {i,j}: {10, 4564}, {12, 4567}, {37, 4998}, {59, 321}, {65, 1016}, {72, 46102}, {99, 21859}, {100, 4552}, {108, 52609}, {109, 4033}, {181, 4601}, {190, 4551}, {210, 1275}, {226, 765}, {306, 7012}, {313, 2149}, {349, 1110}, {523, 31615}, {643, 4605}, {644, 4566}, {646, 53321}, {651, 3952}, {658, 4069}, {664, 1018}, {668, 4559}, {756, 4620}, {762, 7340}, {934, 30730}, {1014, 61402}, {1020, 3699}, {1089, 52378}, {1214, 15742}, {1252, 1441}, {1262, 3701}, {1331, 65207}, {1332, 61178}, {1400, 7035}, {1402, 31625}, {1414, 4103}, {1415, 27808}, {1427, 4076}, {1446, 6065}, {1897, 65233}, {2171, 4600}, {2321, 7045}, {3694, 55346}, {3710, 7128}, {3930, 39293}, {3936, 52377}, {4017, 6632}, {4077, 59149}, {4086, 4619}, {4515, 59457}, {4554, 4557}, {4555, 61171}, {4570, 6358}, {4571, 52607}, {4573, 40521}, {4574, 18026}, {4705, 55194}, {4848, 5382}, {5376, 40663}, {5378, 16609}, {5379, 26942}, {5384, 16603}, {6335, 23067}, {6540, 61170}, {6606, 35310}, {6648, 61172}, {6649, 56257}, {7115, 20336}, {7178, 57731}, {7180, 57950}, {7206, 35049}, {7212, 65363}, {7239, 65291}, {21078, 57757}, {24027, 30713}, {36098, 65191}, {41013, 44717}, {41539, 63906}, {54952, 61161}, {61164, 65289}, {65196, 65217}
X(65573) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17197}, {6, 18191}, {7, 16727}, {10, 4858}, {12, 16732}, {21, 26856}, {37, 11}, {42, 2170}, {56, 16726}, {57, 17205}, {59, 81}, {63, 17219}, {65, 1086}, {71, 7004}, {72, 26932}, {73, 3942}, {100, 4560}, {101, 3737}, {108, 17925}, {109, 1019}, {181, 3125}, {190, 18155}, {201, 4466}, {210, 1146}, {213, 3271}, {226, 1111}, {228, 7117}, {306, 17880}, {321, 34387}, {522, 40213}, {523, 40166}, {644, 7253}, {650, 56283}, {651, 7192}, {661, 21132}, {664, 7199}, {692, 7252}, {756, 21044}, {762, 4092}, {765, 333}, {906, 23189}, {934, 17096}, {1014, 61403}, {1016, 314}, {1018, 522}, {1020, 3676}, {1025, 23829}, {1042, 53538}, {1110, 284}, {1214, 1565}, {1252, 21}, {1254, 53545}, {1259, 16731}, {1262, 1014}, {1275, 57785}, {1284, 27918}, {1334, 2310}, {1376, 16759}, {1400, 244}, {1402, 1015}, {1403, 16742}, {1409, 3937}, {1415, 3733}, {1423, 23824}, {1427, 1358}, {1441, 23989}, {1461, 7203}, {1464, 53546}, {1500, 4516}, {1824, 8735}, {1880, 2969}, {1897, 57215}, {2149, 58}, {2171, 3120}, {2197, 18210}, {2238, 4124}, {2245, 53525}, {2295, 4459}, {2318, 34591}, {2321, 24026}, {2594, 7202}, {3125, 7336}, {3690, 53560}, {3694, 2968}, {3700, 42455}, {3701, 23978}, {3939, 1021}, {3950, 4939}, {3952, 4391}, {3970, 17059}, {3990, 1364}, {4017, 6545}, {4033, 35519}, {4041, 42462}, {4069, 3239}, {4077, 23100}, {4103, 4086}, {4115, 4985}, {4169, 4768}, {4171, 23615}, {4515, 4081}, {4516, 64445}, {4551, 514}, {4552, 693}, {4554, 52619}, {4557, 650}, {4559, 513}, {4564, 86}, {4566, 24002}, {4567, 261}, {4570, 2185}, {4571, 15411}, {4574, 521}, {4587, 57081}, {4600, 52379}, {4601, 18021}, {4605, 4077}, {4619, 1414}, {4620, 873}, {4674, 60578}, {4705, 55195}, {4730, 52338}, {4849, 4534}, {4878, 38375}, {4998, 274}, {5260, 40625}, {5378, 36800}, {5379, 46103}, {6065, 2287}, {6358, 21207}, {6516, 15419}, {6632, 7257}, {6649, 16737}, {7012, 27}, {7035, 28660}, {7045, 1434}, {7064, 36197}, {7115, 28}, {7180, 764}, {7239, 3810}, {7340, 57949}, {15742, 31623}, {17751, 40624}, {18098, 18101}, {18593, 4089}, {20616, 2486}, {20683, 17435}, {21011, 60804}, {21044, 1090}, {21061, 34589}, {21078, 124}, {21741, 53542}, {21794, 2611}, {21797, 55335}, {21801, 35015}, {21805, 4530}, {21821, 4542}, {21859, 523}, {21871, 38357}, {22276, 38345}, {23067, 905}, {23979, 1408}, {23990, 2194}, {24027, 1412}, {24029, 23788}, {24290, 52305}, {30730, 4397}, {31615, 99}, {31625, 40072}, {32674, 57200}, {35307, 21102}, {35309, 48278}, {35310, 6362}, {36059, 7254}, {36074, 4840}, {36147, 57161}, {36197, 5532}, {37558, 24237}, {40149, 2973}, {40521, 3700}, {40988, 51402}, {41539, 4904}, {43924, 8042}, {44710, 16697}, {44717, 1444}, {46102, 286}, {50487, 63462}, {51641, 21143}, {52139, 11998}, {52370, 3270}, {52377, 24624}, {52378, 757}, {52609, 35518}, {52923, 27527}, {53321, 3669}, {53562, 46384}, {55100, 64416}, {55194, 4623}, {56183, 17926}, {56325, 53566}, {57731, 645}, {57808, 17878}, {57950, 62534}, {59149, 643}, {59151, 4637}, {59305, 53526}, {61163, 48264}, {61164, 3907}, {61166, 21120}, {61168, 17420}, {61170, 4977}, {61171, 900}, {61172, 3910}, {61178, 17924}, {61364, 3121}, {61402, 3701}, {62752, 48398}, {64169, 38347}, {65203, 57125}, {65207, 46107}, {65233, 4025}
X(65573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {765, 4564, 59}, {2283, 23343, 62669}

X(65574) = X(10)-DAO CONJUGATE OF X(20)

Barycentrics    a*(b + c)*(a^4 - 2*a^2*b^2 + b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 3*c^4)*(a^4 + 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4) : :

X(65574) lies on these lines: {10, 6356}, {12, 53008}, {37, 2331}, {40, 64}, {65, 53013}, {100, 5896}, {201, 210}, {253, 322}, {459, 1148}, {1073, 9708}, {1301, 43659}, {1807, 52158}, {1824, 31942}, {2968, 16388}, {3695, 4082}, {3949, 4515}, {3998, 57414}, {4866, 8282}, {5295, 52566}, {6526, 41013}, {19614, 20280}, {40933, 52389}

X(65574) = reflection of X(40933X(65574) = ) in X(52389)
X(65574) = X(44692)-Ceva conjugate of X(53012)
X(65574) = X(i)-cross conjugate of X(j) for these (i,j): {1254, 10}, {1824, 37}
X(65574) = X(i)-isoconjugate of X(j) for these (i,j): {3, 44698}, {20, 58}, {21, 1394}, {27, 15905}, {60, 5930}, {81, 610}, {86, 154}, {110, 21172}, {204, 1444}, {283, 44696}, {284, 18623}, {593, 8804}, {649, 36841}, {757, 3198}, {849, 52345}, {1014, 7070}, {1098, 40933}, {1249, 1790}, {1333, 18750}, {1408, 52346}, {1412, 27382}, {1437, 1895}, {1459, 52913}, {1474, 37669}, {1812, 3213}, {1919, 55224}, {2185, 30456}, {2193, 44697}, {2194, 33673}, {2206, 14615}, {2360, 41084}, {3172, 17206}, {4025, 57153}, {4091, 57219}, {4556, 6587}, {4565, 14331}, {4610, 62176}, {7054, 36908}, {7338, 52158}, {8747, 35602}, {15291, 18653}, {16887, 51508}, {17167, 33629}, {38808, 44709}, {52612, 62175}, {52919, 58796}
X(65574) = X(i)-Dao conjugate of X(j) for these (i,j): {10, 20}, {37, 18750}, {244, 21172}, {1214, 33673}, {3343, 1444}, {4075, 52345}, {5375, 36841}, {9296, 55224}, {14092, 81}, {14390, 18604}, {15267, 40933}, {36103, 44698}, {40586, 610}, {40590, 18623}, {40599, 27382}, {40600, 154}, {40603, 14615}, {40607, 3198}, {40611, 1394}, {40839, 286}, {47345, 44697}, {51574, 37669}, {55064, 14331}, {55065, 17898}, {59577, 52346}
X(65574) = crosspoint of X(i) and X(j) for these (i,j): {253, 2184}, {8806, 39130}
X(65574) = crosssum of X(154) and X(610)
X(65574) = trilinear pole of line {4171, 55212}
X(65574) = barycentric product X(i)*X(j) for these {i,j}: {10, 2184}, {37, 253}, {42, 57921}, {64, 321}, {72, 459}, {92, 53012}, {100, 58759}, {213, 41530}, {226, 44692}, {228, 52581}, {313, 2155}, {523, 56235}, {1073, 41013}, {1441, 30457}, {1824, 34403}, {1826, 19611}, {2171, 5931}, {2321, 8809}, {2333, 57780}, {3998, 6526}, {4036, 46639}, {4064, 65224}, {4705, 44326}, {6358, 52158}, {13157, 56254}, {20336, 41489}, {27801, 33581}, {31942, 42699}, {53639, 55232}, {57109, 65181}
X(65574) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 18750}, {19, 44698}, {37, 20}, {42, 610}, {64, 81}, {65, 18623}, {72, 37669}, {100, 36841}, {181, 30456}, {210, 27382}, {213, 154}, {225, 44697}, {226, 33673}, {228, 15905}, {253, 274}, {321, 14615}, {459, 286}, {594, 52345}, {661, 21172}, {668, 55224}, {756, 8804}, {1073, 1444}, {1254, 36908}, {1334, 7070}, {1400, 1394}, {1500, 3198}, {1783, 52913}, {1824, 1249}, {1826, 1895}, {1880, 44696}, {1903, 41084}, {2155, 58}, {2171, 5930}, {2184, 86}, {2321, 52346}, {2333, 204}, {3198, 36413}, {3695, 42699}, {3990, 35602}, {4024, 17898}, {4041, 14331}, {4705, 6587}, {5931, 52379}, {8798, 16697}, {8804, 1097}, {8809, 1434}, {14379, 18604}, {14642, 1437}, {19611, 17206}, {19614, 1790}, {21807, 42459}, {30456, 7338}, {30457, 21}, {33581, 1333}, {36079, 4637}, {41013, 15466}, {41088, 1817}, {41489, 28}, {41530, 6385}, {44326, 4623}, {44692, 333}, {46639, 52935}, {50487, 62176}, {52158, 2185}, {52566, 18603}, {52581, 57796}, {53012, 63}, {53639, 55231}, {55232, 8057}, {56235, 99}, {57109, 20580}, {57652, 3213}, {57921, 310}, {58759, 693}, {61349, 5317}
X(65574) = {X(2184),X(44692)}-harmonic conjugate of X(64)

X(65575) = X(11)-DAO CONJUGATE OF X(12)

Barycentrics    a*(a + b)^2*(a - b - c)^2*(b - c)*(a + c)^2 : :

X(65575) lies on these lines: {21, 522}, {28, 59915}, {58, 21173}, {81, 1459}, {86, 46402}, {100, 4570}, {250, 37966}, {333, 20293}, {514, 57246}, {523, 42741}, {657, 2287}, {659, 3004}, {934, 59041}, {1010, 48243}, {1021, 57081}, {1325, 62495}, {1444, 16755}, {1817, 47785}, {2303, 6586}, {3737, 3738}, {4036, 5260}, {4184, 48242}, {4225, 39199}, {4228, 47798}, {4397, 58332}, {4560, 14024}, {4990, 7253}, {5235, 20316}, {5253, 31947}, {9000, 41610}, {11110, 48173}, {13588, 47828}, {14005, 48228}, {16158, 38469}, {16754, 57200}, {17557, 48186}, {27174, 27486}, {32475, 64720}, {32676, 65253}, {36068, 65362}, {39210, 45671}, {46041, 52380}, {46385, 57189}, {48303, 64415}, {54239, 54340}, {56000, 57237}, {57227, 57241}

X(65575) = midpoint of X(21) and X(57093)
X(65575) = X(i)-Ceva conjugate of X(j) for these (i,j): {261, 26856}, {4612, 7054}, {4636, 21}, {52914, 60}, {52935, 2185}
X(65575) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4605}, {10, 53321}, {12, 109}, {37, 1020}, {42, 4566}, {57, 21859}, {65, 4551}, {71, 52607}, {73, 61178}, {100, 1254}, {101, 6354}, {108, 201}, {115, 4619}, {181, 664}, {225, 23067}, {226, 4559}, {227, 61229}, {269, 40521}, {594, 1461}, {644, 7147}, {651, 2171}, {653, 2197}, {658, 1500}, {756, 934}, {762, 4637}, {872, 4569}, {1018, 1427}, {1042, 3952}, {1262, 4024}, {1275, 4079}, {1400, 4552}, {1407, 4103}, {1409, 65207}, {1415, 6358}, {1425, 1897}, {1783, 37755}, {1813, 8736}, {1826, 52610}, {1880, 65233}, {3668, 4557}, {3690, 36118}, {3699, 7143}, {3939, 6046}, {3949, 32714}, {4036, 24027}, {4092, 59151}, {4564, 57185}, {4572, 61364}, {4626, 7064}, {4636, 7314}, {4705, 7045}, {6057, 6614}, {6356, 8750}, {7066, 36127}, {7109, 46406}, {7115, 57243}, {7128, 55232}, {7211, 29055}, {20617, 56194}, {20653, 52928}, {21015, 59128}, {21671, 59090}, {21675, 32651}, {21794, 38340}, {21853, 65175}, {23979, 52623}, {24033, 57109}, {26942, 32674}, {30730, 62192}, {36059, 56285}, {36098, 52567}, {46102, 55234}, {51663, 52377}, {52378, 55197}, {52560, 61169}, {52931, 59305}, {55230, 55346}
X(65575) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 4605}, {11, 12}, {521, 57109}, {522, 4036}, {656, 4064}, {1015, 6354}, {1146, 6358}, {2968, 1089}, {5452, 21859}, {6600, 40521}, {7358, 3695}, {8054, 1254}, {14714, 756}, {17115, 4705}, {17197, 41003}, {20620, 56285}, {24771, 4103}, {26932, 6356}, {34467, 1425}, {35072, 26942}, {35508, 594}, {38966, 7140}, {38983, 201}, {38991, 2171}, {38992, 52567}, {39006, 37755}, {39007, 41393}, {39025, 181}, {40582, 4552}, {40589, 1020}, {40592, 4566}, {40602, 4551}, {40617, 6046}, {40620, 1446}, {40624, 34388}, {40625, 1441}, {40626, 57807}, {40628, 57243}, {55065, 1091}, {55067, 226}, {55068, 10}
X(65575) = cevapoint of X(i) and X(j) for these (i,j): {1, 34462}, {1021, 21789}, {3737, 23189}
X(65575) = crosspoint of X(i) and X(j) for these (i,j): {261, 4612}, {662, 40412}, {2185, 52935}, {52914, 59482}
X(65575) = crosssum of X(i) and X(j) for these (i,j): {181, 57185}, {512, 40977}, {661, 40952}, {756, 55232}, {2171, 4705}, {21813, 50487}
X(65575) = crossdifference of every pair of points on line {1254, 1500}
X(65575) = barycentric product X(i)*X(j) for these {i,j}: {11, 4612}, {21, 4560}, {27, 57081}, {28, 15411}, {60, 4391}, {81, 7253}, {86, 1021}, {100, 26856}, {107, 16731}, {249, 42455}, {261, 650}, {270, 6332}, {274, 21789}, {283, 57215}, {284, 18155}, {286, 23090}, {314, 7252}, {333, 3737}, {513, 7058}, {514, 1098}, {521, 46103}, {522, 2185}, {552, 4130}, {593, 4397}, {643, 17197}, {645, 18191}, {652, 57779}, {657, 873}, {663, 52379}, {693, 7054}, {757, 3239}, {849, 52622}, {905, 59482}, {1019, 1043}, {1146, 52935}, {1434, 58329}, {1444, 17926}, {1509, 3900}, {1792, 17925}, {2150, 35519}, {2189, 35518}, {2287, 7192}, {2310, 4610}, {2326, 4025}, {2328, 7199}, {3063, 18021}, {3270, 55231}, {3271, 4631}, {3904, 52380}, {4131, 36421}, {4171, 6628}, {4183, 15419}, {4511, 60571}, {4516, 55196}, {4524, 57949}, {4529, 7303}, {4556, 24026}, {4567, 56283}, {4570, 40213}, {4578, 61403}, {4623, 14936}, {4636, 4858}, {6061, 24002}, {7256, 16726}, {7259, 17205}, {17096, 56182}, {17185, 57161}, {17219, 65201}, {23189, 31623}, {23838, 30606}, {23983, 52920}, {24031, 52919}, {24041, 42462}, {26932, 52914}, {44129, 57134}, {46880, 57125}, {52326, 52550}, {57158, 64457}
X(65575) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4605}, {21, 4552}, {28, 52607}, {29, 65207}, {55, 21859}, {58, 1020}, {60, 651}, {81, 4566}, {200, 4103}, {220, 40521}, {261, 4554}, {270, 653}, {283, 65233}, {284, 4551}, {513, 6354}, {521, 26942}, {522, 6358}, {552, 36838}, {593, 934}, {649, 1254}, {650, 12}, {652, 201}, {657, 756}, {663, 2171}, {757, 658}, {763, 4616}, {849, 1461}, {873, 46406}, {905, 6356}, {1019, 3668}, {1021, 10}, {1043, 4033}, {1098, 190}, {1101, 4619}, {1146, 4036}, {1172, 61178}, {1333, 53321}, {1437, 52610}, {1459, 37755}, {1509, 4569}, {1792, 52609}, {1946, 2197}, {2150, 109}, {2185, 664}, {2189, 108}, {2193, 23067}, {2194, 4559}, {2287, 3952}, {2310, 4024}, {2326, 1897}, {2328, 1018}, {3063, 181}, {3064, 56285}, {3239, 1089}, {3270, 55232}, {3271, 57185}, {3287, 7211}, {3669, 6046}, {3733, 1427}, {3737, 226}, {3900, 594}, {4024, 1091}, {4130, 6057}, {4171, 6535}, {4391, 34388}, {4397, 28654}, {4435, 7235}, {4477, 21021}, {4516, 55197}, {4524, 762}, {4556, 7045}, {4560, 1441}, {4578, 61402}, {4612, 4998}, {4636, 4564}, {6061, 644}, {6332, 57807}, {6628, 4635}, {7004, 57243}, {7054, 100}, {7058, 668}, {7192, 1446}, {7252, 65}, {7253, 321}, {7254, 1439}, {7341, 4617}, {8021, 61161}, {8641, 1500}, {14936, 4705}, {15411, 20336}, {16731, 3265}, {17197, 4077}, {17926, 41013}, {18155, 349}, {18191, 7178}, {18344, 8736}, {21789, 37}, {22383, 1425}, {23090, 72}, {23189, 1214}, {23609, 5546}, {24026, 52623}, {26856, 693}, {34591, 4064}, {35072, 57109}, {36054, 7066}, {40213, 21207}, {42455, 338}, {42462, 1109}, {43924, 7147}, {43925, 1426}, {46103, 18026}, {46877, 65191}, {46889, 61172}, {48307, 56326}, {52306, 41393}, {52326, 52567}, {52379, 4572}, {52380, 655}, {52914, 46102}, {52919, 24032}, {52920, 23984}, {52935, 1275}, {53285, 4053}, {56182, 30730}, {56283, 16732}, {57055, 3695}, {57057, 52387}, {57081, 306}, {57108, 3949}, {57125, 52358}, {57129, 1042}, {57134, 71}, {57174, 3028}, {57180, 7064}, {57181, 7143}, {57185, 7314}, {57215, 57809}, {57779, 46404}, {58329, 2321}, {58338, 3694}, {58340, 52386}, {59482, 6335}, {60571, 18815}, {61403, 59941}, {65102, 3690}, {65103, 7140}

X(65576) = X(12)-DAO CONJUGATE OF X(4)

Barycentrics    a*(a + b - c)*(a - b + c)*(b + c)^2*(a^2 - b^2 - c^2)*(a^3 - a*b^2 + a*b*c - b^2*c - a*c^2 - b*c^2) : :

X(65576) lies on these lines: {12, 34829}, {65, 4647}, {72, 73}, {78, 23067}, {518, 4032}, {758, 15443}, {912, 1216}, {960, 16577}, {1425, 26942}, {2171, 12709}, {3695, 7066}, {3869, 4552}, {3970, 20616}, {4559, 17742}, {5440, 22342}, {5717, 44547}, {5814, 19366}, {10454, 64580}, {14829, 56412}, {14973, 20617}, {16788, 20739}, {21061, 37558}, {22001, 22299}, {52385, 57807}

X(65576) = isotomic conjugate of the polar conjugate of X(56325)
X(65576) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 26942}, {17751, 52357}
X(65576) = X(i)-isoconjugate of X(j) for these (i,j): {29, 52150}, {270, 34434}, {1172, 53083}, {1474, 46880}, {2051, 2189}, {2299, 20028}
X(65576) = X(i)-Dao conjugate of X(j) for these (i,j): {12, 4}, {226, 20028}, {51574, 46880}
X(65576) = barycentric product X(i)*X(j) for these {i,j}: {63, 52357}, {69, 56325}, {72, 52358}, {201, 14829}, {306, 37558}, {307, 21061}, {345, 20617}, {348, 14973}, {572, 57807}, {1214, 17751}, {1231, 52139}, {2975, 26942}, {3695, 17074}, {20336, 55323}, {22118, 34388}, {51662, 52609}
X(65576) = barycentric quotient X(i)/X(j) for these {i,j}: {72, 46880}, {73, 53083}, {201, 2051}, {572, 270}, {1214, 20028}, {1409, 52150}, {2197, 34434}, {2975, 46103}, {14829, 57779}, {14973, 281}, {17751, 31623}, {20617, 278}, {20986, 2189}, {21061, 29}, {22118, 60}, {23067, 65260}, {26942, 54121}, {37558, 27}, {51662, 17925}, {52139, 1172}, {52357, 92}, {52358, 286}, {55323, 28}, {56325, 4}, {57165, 65201}, {57807, 57905}, {65203, 52914}, {65233, 65275}
X(65576) = {X(14973),X(20617)}-harmonic conjugate of X(52357)

X(65577) = X(12)-DAO CONJUGATE OF X(6)

Barycentrics    b*(-a + b - c)*(a + b - c)*c*(b + c)^2*(-a^3 + a*b^2 - a*b*c + b^2*c + a*c^2 + b*c^2) : :

X(65577) lies on these lines: {7, 46331}, {201, 3701}, {226, 306}, {312, 4552}, {1089, 1254}, {1457, 3702}, {4032, 20891}, {4358, 16577}, {4359, 26740}, {4559, 28997}, {4696, 15556}, {6354, 34388}, {14829, 40624}, {15443, 56318}, {17184, 37636}, {17862, 54311}, {19807, 28774}, {21021, 42708}, {26942, 28654}, {40013, 60091}, {52358, 56325}

X(65577) = isotomic conjugate of the isogonal conjugate of X(56325)
X(65577) = X(76)-Ceva conjugate of X(34388)
X(65577) = X(i)-isoconjugate of X(j) for these (i,j): {284, 52150}, {593, 60817}, {2150, 34434}, {2194, 53083}, {2206, 46880}, {7252, 59006}, {20028, 57657}
X(65577) = X(i)-Dao conjugate of X(j) for these (i,j): {12, 6}, {1214, 53083}, {4391, 26856}, {34589, 7252}, {40590, 52150}, {40603, 46880}, {56325, 34434}, {62570, 20028}
X(65577) = barycentric product X(i)*X(j) for these {i,j}: {75, 52357}, {76, 56325}, {313, 37558}, {321, 52358}, {349, 21061}, {1441, 17751}, {2975, 34388}, {3596, 20617}, {6063, 14973}, {6358, 14829}, {11109, 57807}, {17074, 28654}, {27801, 55323}, {27808, 51662}
X(65577) = barycentric quotient X(i)/X(j) for these {i,j}: {12, 34434}, {65, 52150}, {226, 53083}, {321, 46880}, {572, 2150}, {756, 60817}, {1441, 20028}, {2975, 60}, {4551, 59006}, {4552, 65260}, {6358, 2051}, {11109, 270}, {14829, 2185}, {14973, 55}, {17074, 593}, {17751, 21}, {20617, 56}, {21061, 284}, {34388, 54121}, {37558, 58}, {40624, 26856}, {51662, 3733}, {52139, 2194}, {52357, 1}, {52358, 81}, {53566, 18191}, {55323, 1333}, {56325, 6}, {57165, 65375}, {60086, 40453}

X(65578) = X(12)-DAO CONJUGATE OF X(9)

Barycentrics    (a + b - c)^2*(a - b + c)^2*(b + c)^2*(a^3 - a*b^2 + a*b*c - b^2*c - a*c^2 - b*c^2) : :

X(65578) lies on these lines: {2, 1020}, {7, 1764}, {10, 1425}, {12, 7143}, {37, 226}, {307, 22020}, {347, 10478}, {1254, 10408}, {1398, 43531}, {1439, 31993}, {1446, 56214}, {2051, 17080}, {4605, 6358}, {5249, 64194}, {14110, 21620}, {14973, 20617}, {17074, 24237}, {17167, 37798}, {21061, 52358}, {24220, 57477}, {41393, 56327}

X(65578) = X(56325)-cross conjugate of X(52357)
X(65578) = X(i)-isoconjugate of X(j) for these (i,j): {1021, 59006}, {2185, 60817}, {2194, 46880}, {2287, 52150}, {2328, 53083}, {7054, 34434}, {21789, 65260}, {40453, 46889}
X(65578) = X(i)-Dao conjugate of X(j) for these (i,j): {12, 9}, {1193, 46889}, {1214, 46880}, {34589, 1021}, {36908, 53083}, {59608, 20028}
X(65578) = cevapoint of X(20617) and X(56325)
X(65578) = crosssum of X(41) and X(60817)
X(65578) = barycentric product X(i)*X(j) for these {i,j}: {7, 52357}, {75, 20617}, {85, 56325}, {226, 52358}, {349, 55323}, {1088, 14973}, {1441, 37558}, {1446, 21061}, {3668, 17751}, {4605, 17496}, {6354, 14829}, {6356, 11109}, {6358, 17074}
X(65578) = barycentric quotient X(i)/X(j) for these {i,j}: {181, 60817}, {226, 46880}, {572, 7054}, {1020, 65260}, {1042, 52150}, {1254, 34434}, {1427, 53083}, {2975, 1098}, {3668, 20028}, {4566, 65275}, {4605, 56188}, {6354, 2051}, {11109, 59482}, {14829, 7058}, {14973, 200}, {17074, 2185}, {17751, 1043}, {20617, 1}, {21061, 2287}, {24237, 26856}, {37558, 21}, {51662, 3737}, {52087, 46889}, {52139, 2328}, {52357, 8}, {52358, 333}, {53321, 59006}, {55323, 284}, {56325, 9}
X(65578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {226, 64708, 22000}, {6358, 37755, 4605}

X(65579) = X(15)-DAO CONJUGATE OF X(3)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(Sqrt[3]*(a^2 - b^2 - c^2) - 2*S)*(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 2*(a^2 - b^2 - c^2)*S) : :

X(65579) lies on the cubic K859b and these lines: {2, 19774}, {4, 3181}, {13, 648}, {14, 264}, {112, 11300}, {298, 11094}, {303, 44714}, {324, 472}, {381, 9308}, {458, 42975}, {470, 11092}, {473, 1993}, {533, 6117}, {618, 6110}, {621, 11093}, {1080, 2967}, {1235, 11304}, {1249, 37170}, {8743, 11303}, {11117, 18831}, {32000, 37171}, {33960, 51220}, {34508, 58732}, {37765, 50855}, {41016, 44704}

X(65579) = polar conjugate of the isogonal conjugate of X(40580)
X(65579) = X(i)-Ceva conjugate of X(j) for these (i,j): {14, 11094}, {264, 470}
X(65579) = X(2153)-isoconjugate of X(64246)
X(65579) = X(i)-Dao conjugate of X(j) for these (i,j): {15, 3}, {40580, 64246}
X(65579) = barycentric product X(i)*X(j) for these {i,j}: {264, 40580}, {301, 64250}, {470, 621}, {11092, 11093}
X(65579) = barycentric quotient X(i)/X(j) for these {i,j}: {15, 64246}, {470, 2992}, {621, 40709}, {3129, 36296}, {8738, 14372}, {8739, 3438}, {11093, 11078}, {14368, 44719}, {23715, 3480}, {39262, 47481}, {40580, 3}, {51270, 10217}, {56514, 40156}, {64250, 16}

X(65580) = X(16)-DAO CONJUGATE OF X(3)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(Sqrt[3]*(a^2 - b^2 - c^2) + 2*S)*(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 2*(a^2 - b^2 - c^2)*S) : :

X(65580) lies on the cubic K859a and these lines: {2, 19775}, {4, 3180}, {13, 264}, {14, 648}, {112, 11299}, {299, 11093}, {302, 44713}, {324, 473}, {381, 9308}, {383, 2967}, {458, 42974}, {471, 11078}, {472, 1993}, {532, 6116}, {619, 6111}, {622, 11094}, {1235, 11303}, {1249, 37171}, {8743, 11304}, {11118, 18831}, {32000, 37170}, {33959, 51219}, {34509, 58732}, {36794, 61719}, {37765, 50858}, {41017, 44704}

X(65580) = polar conjugate of the isogonal conjugate of X(40581)
X(65580) = X(i)-Ceva conjugate of X(j) for these (i,j): {13, 11093}, {264, 471}
X(65580) = X(2154)-isoconjugate of X(64245)
X(65580) = X(i)-Dao conjugate of X(j) for these (i,j): {16, 3}, {40581, 64245}
X(65580) = barycentric product X(i)*X(j) for these {i,j}: {264, 40581}, {300, 64251}, {471, 622}, {11078, 11094}
X(65580) = barycentric quotient X(i)/X(j) for these {i,j}: {16, 64245}, {471, 2993}, {622, 40710}, {3130, 36297}, {8737, 14373}, {8740, 3439}, {11094, 11092}, {14369, 44718}, {23714, 3479}, {39261, 47482}, {40581, 3}, {51277, 10218}, {56515, 40157}, {64251, 15}

X(65581) = X(19)-DAO CONJUGATE OF X(6)

Barycentrics    b*c*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-a^5 - a^4*b + a*b^4 + b^5 - a^4*c + 2*a^2*b^2*c - b^4*c + 2*a^2*b*c^2 - 2*a*b^2*c^2 + a*c^4 - b*c^4 + c^5) : :

X(65581) lies on these lines: {4, 7}, {75, 17555}, {92, 393}, {108, 17134}, {158, 57809}, {208, 18655}, {297, 20171}, {307, 51359}, {318, 5051}, {321, 459}, {322, 1897}, {653, 1766}, {1229, 52283}, {1249, 30807}, {1441, 7952}, {1785, 17861}, {2997, 36121}, {3176, 57810}, {3672, 4194}, {6335, 46738}, {7108, 53417}, {7120, 24268}, {14004, 62697}, {17903, 27540}, {17907, 20927}, {19645, 44697}, {19788, 37279}, {20914, 36103}, {26267, 38860}, {26563, 32000}, {33673, 36118}, {44695, 50698}

X(65581) = polar conjugate of X(7097)
X(65581) = isotomic conjugate of the isogonal conjugate of X(36103)
X(65581) = polar conjugate of the isotomic conjugate of X(20914)
X(65581) = polar conjugate of the isogonal conjugate of X(1763)
X(65581) = X(76)-Ceva conjugate of X(92)
X(65581) = X(1763)-cross conjugate of X(20914)
X(65581) = X(i)-isoconjugate of X(j) for these (i,j): {3, 7169}, {48, 7097}, {184, 7219}, {255, 40169}, {2194, 47344}, {9247, 40015}
X(65581) = X(i)-Dao conjugate of X(j) for these (i,j): {19, 6}, {1214, 47344}, {1249, 7097}, {6523, 40169}, {36103, 7169}, {62576, 40015}, {62605, 7219}
X(65581) = cevapoint of X(1763) and X(36103)
X(65581) = barycentric product X(i)*X(j) for these {i,j}: {4, 20914}, {75, 17903}, {76, 36103}, {92, 4329}, {264, 1763}, {273, 27540}, {286, 21062}, {331, 54295}, {561, 21148}, {1969, 3556}, {6335, 21174}, {22119, 57806}, {44129, 52359}
X(65581) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 7097}, {19, 7169}, {92, 7219}, {226, 47344}, {264, 40015}, {393, 40169}, {1763, 3}, {1863, 40176}, {3556, 48}, {4329, 63}, {8900, 2286}, {17903, 1}, {20914, 69}, {21062, 72}, {21148, 31}, {21174, 905}, {22119, 255}, {27540, 78}, {36103, 6}, {52359, 71}, {54295, 219}
X(65581) = {X(393),X(53510)}-harmonic conjugate of X(92)

X(65582) = X(19)-DAO CONJUGATE OF X(9)

Barycentrics    (a + b - c)*(a - b + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^5 + a^4*b - a*b^4 - b^5 + a^4*c - 2*a^2*b^2*c + b^4*c - 2*a^2*b*c^2 + 2*a*b^2*c^2 - a*c^4 + b*c^4 - c^5) : :

X(65582) lies on these lines: {4, 15314}, {7, 8048}, {34, 269}, {108, 347}, {196, 226}, {208, 3668}, {273, 39732}, {278, 55463}, {342, 14257}, {406, 41003}, {478, 32714}, {653, 28739}, {1439, 51399}, {1441, 13575}, {1763, 17903}, {1905, 24471}, {3213, 43035}, {3596, 18026}, {6046, 6059}, {11398, 64827}, {34937, 56887}, {41010, 51359}, {57807, 61178}

X(65582) = X(85)-Ceva conjugate of X(278)
X(65582) = X(36103)-cross conjugate of X(17903)
X(65582) = X(i)-isoconjugate of X(j) for these (i,j): {78, 7169}, {212, 7219}, {219, 7097}, {1259, 40169}, {2328, 47344}, {40015, 52425}
X(65582) = X(i)-Dao conjugate of X(j) for these (i,j): {19, 9}, {36908, 47344}, {40180, 1038}, {40837, 7219}, {62602, 40015}
X(65582) = barycentric product X(i)*X(j) for these {i,j}: {7, 17903}, {34, 20914}, {85, 36103}, {273, 1763}, {278, 4329}, {331, 3556}, {653, 21174}, {1119, 27540}, {1847, 54295}, {6063, 21148}
X(65582) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 7097}, {273, 40015}, {278, 7219}, {608, 7169}, {1427, 47344}, {1763, 78}, {3556, 219}, {4329, 345}, {8900, 5227}, {17903, 8}, {20914, 3718}, {21062, 3710}, {21148, 55}, {21174, 6332}, {22119, 1259}, {27540, 1265}, {36103, 9}, {40183, 1038}, {40987, 40176}, {52359, 3694}, {54295, 3692}

X(65583) = X(19)-DAO CONJUGATE OF X(10)

Barycentrics    a*(a + b)*(a + c)*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^5 + a^4*b - a*b^4 - b^5 + a^4*c - 2*a^2*b^2*c + b^4*c - 2*a^2*b*c^2 + 2*a*b^2*c^2 - a*c^4 + b*c^4 - c^5) : :

X(65583) lies on these lines: {1, 204}, {2, 2138}, {27, 39732}, {28, 614}, {81, 8048}, {112, 1817}, {269, 1396}, {278, 5317}, {306, 1783}, {475, 19724}, {857, 18686}, {1172, 1848}, {1763, 36103}, {2207, 37388}, {2299, 7290}, {2332, 2999}, {3172, 11347}, {4219, 54426}, {4329, 17903}, {7490, 45786}, {14954, 19993}, {18642, 18687}, {21483, 45141}, {32714, 36908}, {37185, 41361}, {41083, 41364}

X(65583) = X(86)-Ceva conjugate of X(28)
X(65583) = X(i)-isoconjugate of X(j) for these (i,j): {9, 47344}, {71, 7219}, {72, 7097}, {228, 40015}, {306, 7169}, {3998, 40169}
X(65583) = X(i)-Dao conjugate of X(j) for these (i,j): {19, 10}, {478, 47344}
X(65583) = cevapoint of X(i) and X(j) for these (i,j): {204, 3162}, {21148, 36103}
X(65583) = barycentric product X(i)*X(j) for these {i,j}: {27, 1763}, {28, 4329}, {81, 17903}, {86, 36103}, {162, 21174}, {274, 21148}, {286, 3556}, {1396, 27540}, {1474, 20914}
X(65583) = barycentric quotient X(i)/X(j) for these {i,j}: {27, 40015}, {28, 7219}, {56, 47344}, {1474, 7097}, {1763, 306}, {2203, 7169}, {3556, 72}, {4329, 20336}, {17903, 321}, {20914, 40071}, {21062, 52369}, {21148, 37}, {21174, 14208}, {22119, 3998}, {36103, 10}, {52359, 3695}, {54295, 3710}

X(65584) = X(515)-DAO CONJUGATE OF X(3)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^4 + a^3*b + a^2*b^2 - a*b^3 + b^4 + a^3*c - 2*a^2*b*c + a*b^2*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4)^2 : :

X(65584) lies on the MacBeath inconic and these lines: {3, 26704}, {4, 151}, {25, 9056}, {117, 14304}, {273, 2973}, {355, 7141}, {407, 2970}, {2968, 6831}, {2969, 37368}, {2972, 3142}, {23978, 60758}, {23987, 56973}, {25640, 44426}, {38554, 59205}

X(65584) = polar conjugate of the isotomic conjugate of X(59205)
X(65584) = polar conjugate of the isogonal conjugate of X(23986)
X(65584) = X(23986)-cross conjugate of X(59205)
X(65584) = X(i)-isoconjugate of X(j) for these (i,j): {102, 36055}, {9247, 57551}
X(65584) = X(i)-Dao conjugate of X(j) for these (i,j): {515, 3}, {51221, 102}, {57291, 57241}, {62576, 57551}
X(65584) = barycentric product X(i)*X(j) for these {i,j}: {4, 59205}, {92, 24034}, {264, 23986}, {1359, 7017}, {1969, 42076}, {2052, 38554}, {8755, 35516}, {14304, 24035}
X(65584) = barycentric quotient X(i)/X(j) for these {i,j}: {264, 57551}, {1359, 222}, {2182, 36055}, {8755, 102}, {23986, 3}, {23987, 65297}, {24034, 63}, {38554, 394}, {42076, 48}, {59205, 69}

X(65585) = X(519)-DAO CONJUGATE OF X(3)

Barycentrics    b^2*c^2*(-2*a + b + c)^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2) : :

X(65585) lies on the MacBeath inconic and these lines: {3, 2370}, {4, 10744}, {25, 9059}, {119, 4397}, {121, 4768}, {264, 2973}, {318, 7141}, {339, 16052}, {1000, 7046}, {1145, 4723}, {1883, 2969}, {2968, 4187}, {2970, 44143}, {36791, 42070}

X(65585) = polar conjugate of X(2226)
X(65585) = isotomic conjugate of the isogonal conjugate of X(42070)
X(65585) = polar conjugate of the isotomic conjugate of X(36791)
X(65585) = polar conjugate of the isogonal conjugate of X(4370)
X(65585) = X(264)-Ceva conjugate of X(46109)
X(65585) = X(4370)-cross conjugate of X(36791)
X(65585) = X(i)-isoconjugate of X(j) for these (i,j): {48, 2226}, {63, 41935}, {88, 32659}, {106, 36058}, {184, 679}, {603, 1318}, {1797, 9456}, {4638, 22383}, {9247, 54974}, {14575, 57929}, {23202, 59150}
X(65585) = X(i)-Dao conjugate of X(j) for these (i,j): {214, 36058}, {519, 3}, {900, 3937}, {1249, 2226}, {1647, 1459}, {3162, 41935}, {4370, 1797}, {7952, 1318}, {20619, 106}, {53985, 23345}, {62576, 54974}, {62605, 679}
X(65585) = cevapoint of X(i) and X(j) for these (i,j): {4370, 42070}, {23644, 47425}
X(65585) = crosspoint of X(264) and X(46109)
X(65585) = crosssum of X(184) and X(32659)
X(65585) = barycentric product X(i)*X(j) for these {i,j}: {4, 36791}, {76, 42070}, {92, 4738}, {264, 4370}, {331, 4152}, {519, 46109}, {678, 1969}, {1017, 18022}, {1317, 7017}, {1897, 52627}, {3264, 8756}, {4358, 38462}, {4543, 46404}, {4723, 37790}, {6336, 58254}, {16729, 41013}, {18027, 22371}, {21821, 57796}, {46107, 53582}
X(65585) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 2226}, {25, 41935}, {44, 36058}, {92, 679}, {264, 54974}, {281, 1318}, {519, 1797}, {678, 48}, {902, 32659}, {1017, 184}, {1145, 57478}, {1317, 222}, {1897, 4638}, {1969, 57929}, {3251, 22383}, {4152, 219}, {4370, 3}, {4542, 7117}, {4543, 652}, {4738, 63}, {5151, 52206}, {6335, 4618}, {6336, 59150}, {6544, 1459}, {8028, 22356}, {8756, 106}, {16729, 1444}, {21821, 228}, {22371, 577}, {33922, 22086}, {35092, 3937}, {36791, 69}, {37790, 56049}, {38462, 88}, {41013, 30575}, {42070, 6}, {46109, 903}, {46541, 4591}, {52627, 4025}, {53582, 1331}, {58254, 3977}, {61047, 52411}, {65336, 39414}

X(65586) = X(526)-DAO CONJUGATE OF X(3)

Barycentrics    a^2*(b - c)^2*(b + c)^2*(a^2 + b^2 - c^2)*(a^2 - b^2 - b*c - c^2)^2*(a^2 - b^2 + b*c - c^2)^2*(a^2 - b^2 + c^2) : :

X(65586) lies on the MacBeath inconic and these lines: {3, 10420}, {4, 14670}, {25, 842}, {30, 16933}, {110, 10689}, {136, 46439}, {186, 323}, {250, 19504}, {325, 34336}, {339, 6563}, {403, 34334}, {427, 38552}, {468, 2967}, {523, 2970}, {858, 2974}, {1112, 7480}, {2972, 3154}, {3258, 16186}, {5099, 16178}, {10419, 35372}, {12052, 44889}, {12079, 20975}, {12133, 52493}, {13409, 36178}, {15329, 16978}, {17847, 30715}, {18114, 22104}, {21664, 37982}, {30447, 34332}, {33329, 34335}, {44084, 47215}, {46199, 48376}

X(65586) = reflection of X(2970) in the Euler line
X(65586) = polar conjugate of the isogonal conjugate of X(18334)
X(65586) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 44427}, {38936, 526}, {57487, 47230}
X(65586) = X(i)-isoconjugate of X(j) for these (i,j): {63, 23588}, {304, 23966}, {476, 36061}, {9247, 57546}, {14595, 24041}, {32662, 32680}, {32678, 60053}
X(65586) = X(i)-Dao conjugate of X(j) for these (i,j): {526, 3}, {1637, 57482}, {3005, 14595}, {3162, 23588}, {5664, 328}, {16221, 476}, {18334, 60053}, {47230, 57486}, {60342, 265}, {62576, 57546}, {63837, 47390}
X(65586) = crosspoint of X(264) and X(44427)
X(65586) = crosssum of X(i) and X(j) for these (i,j): {110, 10733}, {184, 32662}, {14560, 56403}
X(65586) = crossdifference of every pair of points on line {14582, 32662}
X(65586) = barycentric product X(i)*X(j) for these {i,j}: {25, 23965}, {186, 62551}, {264, 18334}, {323, 35235}, {338, 3043}, {339, 36423}, {340, 2088}, {470, 52342}, {471, 52343}, {526, 44427}, {3258, 57487}, {3268, 47230}, {14165, 16186}, {14618, 62173}, {14920, 56792}, {23108, 46456}, {43961, 56515}, {43962, 56514}
X(65586) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 23588}, {186, 39295}, {264, 57546}, {526, 60053}, {1974, 23966}, {2088, 265}, {2624, 36061}, {3043, 249}, {3124, 14595}, {3258, 57482}, {14270, 32662}, {14591, 58979}, {16221, 57486}, {18334, 3}, {23108, 8552}, {23965, 305}, {35235, 94}, {36423, 250}, {44427, 35139}, {47230, 476}, {47414, 51254}, {52342, 40709}, {52343, 40710}, {56514, 57580}, {56515, 57579}, {57136, 32661}, {62173, 4558}, {62551, 328}, {63834, 47390}
X(65586) = {X(3258),X(16221)}-harmonic conjugate of X(35235)

X(65587) = X(527)-DAO CONJUGATE OF X(3)

Barycentrics    b^2*c^2*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(-2*a^2 + a*b + b^2 + a*c - 2*b*c + c^2)^2 : :

X(65587) lies on the MacBeath inconic and these lines:{25, 9086}, {92, 2973}, {264, 21666}, {1441, 2968}, {7046, 18026}, {30806, 38461}, {31844, 42762}

X(65587) = polar conjugate of the isogonal conjugate of X(35110)
X(65587) = X(i)-isoconjugate of X(j) for these (i,j): {9247, 57565}, {34068, 60047}
X(65587) = X(i)-Dao conjugate of X(j) for these (i,j): {527, 3}, {6366, 3270}, {33573, 652}, {35110, 60047}, {62576, 57565}
X(65587) = barycentric product X(i)*X(j) for these {i,j}: {264, 35110}, {331, 6068}, {1969, 42082}, {3321, 7017}, {18022, 59798}, {30806, 37805}, {46404, 62579}
X(65587) = barycentric quotient X(i)/X(j) for these {i,j}: {264, 57565}, {527, 60047}, {3321, 222}, {3328, 7117}, {6068, 219}, {23710, 2291}, {35091, 3270}, {35110, 3}, {37805, 1156}, {38461, 34056}, {42082, 48}, {56543, 65304}, {59798, 184}, {60431, 4845}, {62579, 652}

X(65588) = X(6)X(10204)∩X(511)X(11820)

Barycentrics    a^2 (3 a^8 - 28 a^6 b^2 + 98 a^4 b^4 - 92 a^2 b^6 + 19 b^8 - 28 a^6 c^2 - 4 a^4 b^2 c^2 + 68 a^2 b^4 c^2 - 4 b^6 c^2 + 98 a^4 c^4 + 68 a^2 b^2 c^4 - 94 b^4 c^4 - 92 a^2 c^6 - 4 b^2 c^6 + 19 c^8) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 7018.

X(65588) lies on these lines: {6, 10204}, {511, 11820}, {33962, 55722}

X(65589) = 105th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a*(4*a^3+4*(b+c)*a^2-(4*b^2+7*b*c+4*c^2)*a-4*(b^2-c^2)*(b-c)) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 02/10/2024. (Oct 2, 2024)

X(65589) lies on these lines: {1, 3}, {3218, 34747}, {3654, 15228}, {3679, 16558}, {4316, 59417}, {4668, 56288}, {4677, 63136}, {4744, 61157}, {5493, 18395}, {5657, 18513}, {5726, 16140}, {6361, 18514}, {9778, 41684}, {11545, 65134}, {12515, 34628}, {19875, 27065}, {31188, 34632}, {51066, 54286}, {51768, 60947}

X(65589) = midpoint of X(12702) and X(65590)
X(65589) = pole of the line {4604, 21362} with respect to the Yff parabola

X(65590) = 106th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(4*a^5-4*(b+c)*a^4-(8*b^2-9*b*c+8*c^2)*a^3+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^2+(4*b^4+4*c^4-b*c*(9*b^2-16*b*c+9*c^2))*a-4*(b^3+c^3)*(b-c)^2) : :

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 02/10/2024. (Oct 2, 2024)

X(65590) lies on these lines: {1, 3}, {993, 5055}, {1656, 59392}, {3534, 10707}, {3830, 18515}, {4588, 28203}, {5073, 5450}, {5251, 15703}, {5267, 18493}, {6942, 12645}, {11194, 18524}, {12104, 46934}, {12511, 62093}, {34748, 54391}, {41853, 62109}, {62121, 63983}

X(65590) = reflection of X(12702) in X(65589)
X(65590) = pole of the line {513, 50767} with respect to the Stammler circle

X(65591) = 107th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(9*a^5-9*(b+c)*a^4-2*(9*b^2-11*b*c+9*c^2)*a^3+6*(b+c)*(3*b^2-5*b*c+3*c^2)*a^2+(9*b^4+9*c^4-2*b*c*(11*b^2-21*b*c+11*c^2))*a+(b^2-c^2)*(b-c)*(-9*c^2+12*b*c-9*b^2)) : :
X(65591) = 2*X(3)-3*X(64894)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 02/10/2024. (Oct 2, 2024)

X(65591) lies on these lines: {1, 3}, {5734, 19704}, {6834, 34740}, {14217, 38637}, {28162, 28235}

X(65591) = reflection of X(65592) in X(3)
X(65591) = X(65592)-of-ABC-X3 reflections triangle

X(65592) = 108th TRAN VIET HUNG-LOZADA CENTER

Barycentrics    a^2*(9*a^5-9*(b+c)*a^4-2*(9*b^2-11*b*c+9*c^2)*a^3+6*(b+c)*(3*b^2-b*c+3*c^2)*a^2+(9*b^4+9*c^4-2*b*c*(11*b^2+3*b*c+11*c^2))*a+(b^2-c^2)*(b-c)*(-9*c^2-12*b*c-9*b^2)) : :
X(65592) = 4*X(3)-3*X(64894)

See Tran Viet Hung and César Lozada, Tran Viet Hung problem 02/10/2024. (Oct 2, 2024)

X(65592) lies on these lines: {1, 3}, {6890, 34707}, {8699, 28163}, {28451, 31447}, {38031, 61814}, {51118, 63753}

X(65592) = reflection of X(65591) in X(3)
X(65592) = X(65591)-of-ABC-X3 reflections triangle

X(65593) = (name pending)

Barycentrics    (3*a^6 - 7*a^4*b^2 - 7*a^2*b^4 + 3*b^6 - 3*a^4*c^2 - 4*a^2*b^2*c^2 - 3*b^4*c^2 - 5*a^2*c^4 - 5*b^2*c^4 + c^6)*(3*a^6 - 3*a^4*b^2 - 5*a^2*b^4 + b^6 - 7*a^4*c^2 - 4*a^2*b^2*c^2 - 5*b^4*c^2 - 7*a^2*c^4 - 3*b^2*c^4 + 3*c^6) : :

See Peter Moses, euclid 7034.

X(65593) lies on these lines: { }

X(65593) = perspector of the Steiner inellipse of the circumedial triangle

X(65594) = X(2)X(20382)∩X(115)X(3849)

Barycentrics    4*a^14 - 13*a^12*b^2 + 21*a^10*b^4 + 8*a^8*b^6 - 20*a^6*b^8 + 3*a^4*b^10 - 5*a^2*b^12 + 2*b^14 - 13*a^12*c^2 - 6*a^8*b^4*c^2 + 4*a^6*b^6*c^2 + 21*a^2*b^10*c^2 - 10*b^12*c^2 + 21*a^10*c^4 - 6*a^8*b^2*c^4 - 24*a^6*b^4*c^4 + 12*a^4*b^6*c^4 - 6*a^2*b^8*c^4 + 12*b^10*c^4 + 8*a^8*c^6 + 4*a^6*b^2*c^6 + 12*a^4*b^4*c^6 - 10*a^2*b^6*c^6 - 8*b^8*c^6 - 20*a^6*c^8 - 6*a^2*b^4*c^8 - 8*b^6*c^8 + 3*a^4*c^10 + 21*a^2*b^2*c^10 + 12*b^4*c^10 - 5*a^2*c^12 - 10*b^2*c^12 + 2*c^14 : :
X(65594) = 3 X[9829] - X[9831]

See Peter Moses, euclid 7034.

X(65594) lies on the Steiner inellipse of the circumedial triangle and these lines: {2, 20382}, {115, 3849}, {5939, 32424}, {5976, 8704}, {6031, 14731}, {9080, 9829}, {12505, 13241}

X(65594) = midpoint of X(12505) and X(13241)

X(65595) = X(2)X(34227)∩X(69)X(5648)

Barycentrics    4*a^10 - 9*a^8*b^2 + 5*a^6*b^4 + 7*a^4*b^6 - 9*a^2*b^8 + 2*b^10 - 9*a^8*c^2 - 8*a^6*b^2*c^2 + 6*a^4*b^4*c^2 + 9*a^2*b^6*c^2 - 2*b^8*c^2 + 5*a^6*c^4 + 6*a^4*b^2*c^4 - 6*a^2*b^4*c^4 - 4*b^6*c^4 + 7*a^4*c^6 + 9*a^2*b^2*c^6 - 4*b^4*c^6 - 9*a^2*c^8 - 2*b^2*c^8 + 2*c^10 : :

See Peter Moses, euclid 7034.

X(65595) lies on the Steiner inellipse of the circumedial triangle and these lines: {2, 34227}, {69, 5648}, {76, 31744}, {99, 32424}, {183, 6322}, {325, 2482}, {1975, 12505}, {5976, 8704}, {6232, 51580}, {7664, 9123}, {7750, 31729}, {7769, 32156}, {7788, 47075}, {10162, 37647}, {10163, 10418}, {11594, 16320}, {14653, 14907}, {14866, 32819}, {31606, 59635}, {37671, 47074}

X(65596) = X(2)X(67)∩X(115)X(3849)

Barycentrics    20*a^10 - 17*a^8*b^2 - 7*a^6*b^4 + 11*a^4*b^6 - 17*a^2*b^8 + 2*b^10 - 17*a^8*c^2 + 4*a^6*b^2*c^2 + 6*a^4*b^4*c^2 + 13*a^2*b^6*c^2 - 26*b^8*c^2 - 7*a^6*c^4 + 6*a^4*b^2*c^4 + 6*a^2*b^4*c^4 + 20*b^6*c^4 + 11*a^4*c^6 + 13*a^2*b^2*c^6 + 20*b^4*c^6 - 17*a^2*c^8 - 26*b^2*c^8 + 2*c^10 : :

See Peter Moses, euclid 7034.

X(65596) lies on the Steiner inellipse of the circumedial triangle and these lines: {2, 67}, {98, 32424}, {115, 3849}, {183, 6322}, {6031, 63029}, {7792, 10162}

X(65597) = X(2)X(353)∩X(183)X(1494)

Barycentrics    4*a^8 - a^6*b^2 - 3*a^4*b^4 - 2*a^2*b^6 + 2*b^8 - a^6*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 3*a^4*c^4 + 3*a^2*b^2*c^4 - 2*a^2*c^6 - b^2*c^6 + 2*c^8 : :

See Peter Moses, euclid 7034.

X(65597) lies on the Steiner inellipse of the circumedial triangle and these lines: {2, 353}, {183, 1494}, {316, 51430}, {325, 5642}, {1649, 3268}, {5989, 30786}, {7792, 10418}, {7868, 35279}, {9100, 11628}, {17416, 61064}, {22329, 23992}, {30516, 63101}, {37688, 47200}, {38650, 50550}, {40884, 51389}

X(65598) = ISOGONAL CONJUGATE OF X(20993)

Barycentrics    (a^8 - 2*a^4*b^4 + b^8 + 2*a^4*c^4 + 2*b^4*c^4 - 3*c^8)*(a^8 + 2*a^4*b^4 - 3*b^8 - 2*a^4*c^4 + 2*b^4*c^4 + c^8) : :

X(65598) lies on the cubic K1365 and these lines: {2, 19615}, {69, 19595}, {315, 5596}, {1235, 58075}, {1370, 3926}, {6394, 28406}

X(65598) = isogonal conjugate of X(20993)
X(65598) = isotomic conjugate of X(5596)
X(65598) = polar conjugate of X(8879)
X(65598) = anticomplement of the isogonal conjugate of X(19613)
X(65598) = isotomic conjugate of the anticomplement of X(66)
X(65598) = isotomic conjugate of the complement of X(20079)
X(65598) = isotomic conjugate of the isogonal conjugate of X(34427)
X(65598) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19613, 8}, {19615, 192}, {19616, 2}, {34427, 17481}
X(65598) = X(i)-cross conjugate of X(j) for these (i,j): {66, 2}, {27376, 76}, {39129, 18018}
X(65598) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20993}, {6, 16544}, {19, 22135}, {31, 5596}, {32, 20931}, {48, 8879}, {692, 21190}, {1333, 21079}, {1973, 28696}, {18596, 46769}
X(65598) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 5596}, {3, 20993}, {6, 22135}, {9, 16544}, {37, 21079}, {1086, 21190}, {1249, 8879}, {6337, 28696}, {6376, 20931}, {40938, 19595}
X(65598) = cevapoint of X(i) and X(j) for these (i,j): {2, 20079}, {523, 62573}, {525, 53822}, {19615, 22262}
X(65598) = trilinear pole of line {3265, 23881}
X(65598) = barycentric product X(i)*X(j) for these {i,j}: {76, 34427}, {1502, 22262}, {18018, 19613}, {19615, 40421}, {19616, 46244}
X(65598) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16544}, {2, 5596}, {3, 22135}, {4, 8879}, {6, 20993}, {10, 21079}, {69, 28696}, {75, 20931}, {427, 19595}, {514, 21190}, {19613, 22}, {19615, 206}, {19616, 2172}, {22262, 32}, {34207, 46769}, {34427, 6}

X(65599) = X(315)-CEVA CONJUGATE OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^12 - 2*a^10*b^2 - a^8*b^4 + 4*a^6*b^6 - a^4*b^8 - 2*a^2*b^10 + b^12 - 2*a^10*c^2 - 2*a^8*b^2*c^2 + 2*a^2*b^8*c^2 + 2*b^10*c^2 - a^8*c^4 + 2*a^4*b^4*c^4 - b^8*c^4 + 4*a^6*c^6 - 4*b^6*c^6 - a^4*c^8 + 2*a^2*b^2*c^8 - b^4*c^8 - 2*a^2*c^10 + 2*b^2*c^10 + c^12) : :

X(65599) lies on the cubic K1365 and these lines: {2, 2138}, {4, 66}, {69, 19595}, {92, 4911}, {112, 28696}, {459, 62911}, {1370, 59165}, {1895, 5015}, {5523, 6392}, {6515, 60516}, {7762, 51358}, {7879, 56296}, {12384, 37444}, {14376, 51509}, {20806, 46741}, {27376, 63129}, {32006, 34163}

X(65599) = anticomplement of X(52041)
X(65599) = anticomplement of the isogonal conjugate of X(41361)
X(65599) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 7500}, {75, 13575}, {92, 36851}, {159, 6360}, {162, 57069}, {811, 52617}, {1370, 4329}, {3162, 192}, {17407, 17481}, {18596, 20}, {18629, 52365}, {21582, 1370}, {33584, 18663}, {41361, 8}, {41766, 5905}, {57086, 4560}, {58075, 17492}
X(65599) = X(315)-Ceva conjugate of X(4)
X(65599) = X(13854)-Dao conjugate of X(66)
X(65599) = {X(66),X(27373)}-harmonic conjugate of X(4)

X(65600) = ANTICOMPLEMENT OF X(1676)

Barycentrics    a^6 - a^4*b^2 + a^2*b^4 - b^6 - a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6 - 2*a^2*(a^2 - b^2 - c^2)*Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2] : :

X(65600) lies on the Kiepert circumhyperbola of the anticomplementary triangle, the cubic K1365 and these lines: {2, 1343}, {3, 66}, {4, 1670}, {69, 1671}, {315, 10999}, {1342, 6776}, {1899, 15247}, {3410, 15250}, {3818, 8160}, {5207, 38721}, {8161, 34507}, {11442, 15245}
X(65600) = anticomplement of X(1676)
X(65600) = anticomplement of the isogonal conjugate of X(1671)
X(65600) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1671, 8}, {16246, 21270}, {41378, 192}
X(65600) = X(10999)-Ceva conjugate of X(1671)

X(65601) = ANTICOMPLEMENT OF X(1677)

Barycentrics    a^6 - a^4*b^2 + a^2*b^4 - b^6 - a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6 + 2*a^2*(a^2 - b^2 - c^2)*Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2] : :

X(65601) lies on the Kiepert circumhyperbola of the anticomplementary triangle, the cubic K1365 and these lines: {2, 1342}, {3, 66}, {4, 1671}, {69, 1670}, {315, 11000}, {1343, 6776}, {1899, 15248}, {3410, 15249}, {3818, 8161}, {5207, 38720}, {8160, 34507}, {11442, 15244}, {11547, 16246}

X(65601) = anticomplement of X(1677)
X(65601) = anticomplement of the isogonal conjugate of X(1670)
X(65601) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1670, 8}, {41379, 192}
X(65601) = X(11000)-Ceva conjugate of X(1670)

X(65602) = ANTICOMPLEMENT OF X(41378)

Barycentrics    (a^4 + a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 + a^2*c^2 - b^2*c^2 + c^4)*(a^2*b^2 + b^4 + a^2*c^2 + 3*b^2*c^2 + c^4 - 2*(b^2 + c^2)*Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2]) : :

X(65602) lies on the cubics K267 and K1365 and these lines: {2, 1343}, {160, 15244}, {315, 2387}

X(65602) = anticomplement of X(41378)
X(65602) = isotomic conjugate of the anticomplement of X(41379)
X(65602) = X(1676)-anticomplementary conjugate of X(192)
X(65602) = X(41379)-cross conjugate of X(2)
X(65602) = barycentric quotient X(i)/X(j) for these {i,j}: {1670, 1671}, {1676, 1677}, {41379, 41378}

X(65603) = ANTICOMPLEMENT OF X(41379)

Barycentrics    (a^4 + a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 + a^2*c^2 - b^2*c^2 + c^4)*(a^2*b^2 + b^4 + a^2*c^2 + 3*b^2*c^2 + c^4 + 2*(b^2 + c^2)*Sqrt[a^2*b^2 + a^2*c^2 + b^2*c^2]) : :

X(65603) lies on the cubics K267 and K1365 and these lines: {2, 1342}, {160, 15245}, {315, 2387}

X(65603) = anticomplement of X(41379)
X(65603) = isotomic conjugate of the anticomplement of X(41378)
X(65603) = X(1677)-anticomplementary conjugate of X(192)
X(65603) = X(41378)-cross conjugate of X(2)
X(65603) = barycentric quotient X(i)/X(j) for these {i,j}: {1671, 1670}, {1677, 1676}, {41378, 41379}

X(65604) = X(2)X(4723)∩X(497)X(517)

Barycentrics    b*c*(3*a^5 - 3*a^4*b + 4*a^3*b^2 + 6*a^2*b^3 - 3*a*b^4 + b^5 - 3*a^4*c + 4*a^3*b*c - 6*a^2*b^2*c + b^4*c + 4*a^3*c^2 - 6*a^2*b*c^2 + 6*a*b^2*c^2 - 2*b^3*c^2 + 6*a^2*c^3 - 2*b^2*c^3 - 3*a*c^4 + b*c^4 + c^5) : :

X(65604) lies on these lines: {2, 4723}, {497, 517}, {982, 1737}, {1111, 5587}, {3673, 4346}, {37715, 62697}, {54318, 59511}

X(65605) = X(1)X(7225)∩X(3)X(902)

Barycentrics    a^2*(a^5 + 2*a^2*b^3 - a*b^4 - 2*b^5 - 2*a^2*b^2*c + 2*b^4*c - 2*a^2*b*c^2 + 6*a*b^2*c^2 - 4*b^3*c^2 + 2*a^2*c^3 - 4*b^2*c^3 - a*c^4 + 2*b*c^4 - 2*c^5) : :

X(65605) lies on these lines: {1, 7225}, {3, 902}, {40, 78}, {65, 36509}, {515, 5014}, {517, 3938}, {573, 3217}, {840, 28520}, {916, 42461}, {1037, 1042}, {1457, 37577}, {1473, 3428}, {3430, 7991}, {3576, 62806}, {3877, 35975}, {3913, 33587}, {4300, 37474}, {5247, 9309}, {5255, 36510}, {5731, 49704}, {9778, 63423}, {31435, 35667}

X(65606) = X(4)X(17869)∩X(3556)X(40097)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + 2*a^2*b*c + 2*a*b^2*c - 2*a*b*c^2 - c^4)*(a^4 - b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a^2*c^2 + 2*a*b*c^2 + c^4)*(a^8 - 2*a^7*b + 2*a^5*b^3 - 2*a^4*b^4 + 2*a^3*b^5 - 2*a*b^7 + b^8 - 2*a^7*c - 4*a^5*b^2*c + 2*a^4*b^3*c + 6*a^3*b^4*c - 4*a^2*b^5*c + 2*b^7*c - 4*a^5*b*c^2 + 8*a^4*b^2*c^2 - 8*a^3*b^3*c^2 + 4*a*b^5*c^2 + 2*a^5*c^3 + 2*a^4*b*c^3 - 8*a^3*b^2*c^3 + 8*a^2*b^3*c^3 - 2*a*b^4*c^3 - 2*b^5*c^3 - 2*a^4*c^4 + 6*a^3*b*c^4 - 2*a*b^3*c^4 - 2*b^4*c^4 + 2*a^3*c^5 - 4*a^2*b*c^5 + 4*a*b^2*c^5 - 2*b^3*c^5 - 2*a*c^7 + 2*b*c^7 + c^8) : :

X(65606) lies on the cubic K1366 and these lines: {4, 17869}, {3556, 40097}

X(65606) = X(75)-Ceva conjugate of X(34277)

X(65607) = X(8)X(1943)∩X(63)X(1619)

Barycentrics    a*(a^2 - b^2 - c^2)*(a^5 - a^4*b - a*b^4 + b^5 + a^4*c - 2*a^2*b^2*c + b^4*c + 2*a^2*b*c^2 + 2*a*b^2*c^2 - a*c^4 - b*c^4 - c^5)*(a^5 + a^4*b - a*b^4 - b^5 - a^4*c + 2*a^2*b^2*c - b^4*c - 2*a^2*b*c^2 + 2*a*b^2*c^2 - a*c^4 + b*c^4 + c^5) : :

X(65607) lies on the cubic K1366 and these lines: {8, 1943}, {63, 1619}, {78, 7111}, {1106, 24031}, {1265, 37669}, {1792, 1801}, {2000, 40015}, {2287, 7097}, {3692, 22132}, {5749, 41084}, {7177, 19611}

X(65607) = isogonal conjugate of X(36103)
X(65607) = isotomic conjugate of X(65581)
X(65607) = isogonal conjugate of the complement of X(7219)
X(65607) = isotomic conjugate of the polar conjugate of X(7097)
X(65607) = isogonal conjugate of the polar conjugate of X(40015)
X(65607) = X(40015)-Ceva conjugate of X(7097)
X(65607) = X(i)-cross conjugate of X(j) for these (i,j): {6, 63}, {20280, 1}, {47344, 7219}
X(65607) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36103}, {2, 21148}, {4, 3556}, {6, 17903}, {19, 1763}, {25, 4329}, {28, 52359}, {31, 65581}, {34, 54295}, {37, 65583}, {55, 65582}, {393, 22119}, {608, 27540}, {1039, 8900}, {1474, 21062}, {1973, 20914}, {8750, 21174}
X(65607) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 65581}, {3, 36103}, {6, 1763}, {9, 17903}, {223, 65582}, {6337, 20914}, {6505, 4329}, {11517, 54295}, {26932, 21174}, {32664, 21148}, {36033, 3556}, {40589, 65583}, {40591, 52359}, {51574, 21062}, {62647, 27540}
X(65607) = cevapoint of X(i) and X(j) for these (i,j): {6, 7169}, {1459, 24031}
X(65607) = barycentric product X(i)*X(j) for these {i,j}: {3, 40015}, {63, 7219}, {69, 7097}, {304, 7169}, {333, 47344}, {3926, 40169}
X(65607) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17903}, {2, 65581}, {3, 1763}, {6, 36103}, {31, 21148}, {48, 3556}, {57, 65582}, {58, 65583}, {63, 4329}, {69, 20914}, {71, 52359}, {72, 21062}, {78, 27540}, {219, 54295}, {255, 22119}, {905, 21174}, {2286, 8900}, {7097, 4}, {7169, 19}, {7219, 92}, {40015, 264}, {40169, 393}, {40176, 1863}, {47344, 226}

X(65608) = X(115)X(525)∩X(125)X(523)

Barycentrics    (b^2 - c^2)^2*(-a^6 + 4*a^4*b^2 - 5*a^2*b^4 + 2*b^6 + 4*a^4*c^2 - 3*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 + 2*c^6) : :
X(65608) = X[323] - 5 X[7925], X[15993] - 3 X[62376], X[40112] - 3 X[41133], 3 X[125] - X[51428], X[51428] + 3 X[51429], 5 X[15059] - X[53379], 3 X[15061] - X[46633], 2 X[15448] - 3 X[47246], X[15545] + 3 X[57311], X[38730] - 3 X[54248], 2 X[47239] - 3 X[61691]

X(65608) lies on the cubic K1367 and these lines: {2, 6}, {30, 53710}, {115, 525}, {125, 523}, {265, 46634}, {338, 850}, {511, 36170}, {542, 16760}, {690, 14120}, {826, 34953}, {842, 1550}, {1495, 47171}, {1499, 5099}, {1503, 11005}, {2623, 53576}, {2682, 3566}, {2777, 46988}, {2854, 47557}, {3124, 62572}, {3564, 53725}, {3800, 35605}, {3906, 15359}, {5641, 41254}, {6388, 23991}, {6587, 6791}, {6699, 46981}, {7471, 32269}, {7687, 46982}, {9140, 53136}, {11006, 36196}, {11645, 46992}, {14915, 46993}, {15059, 53379}, {15061, 46633}, {15448, 47246}, {15526, 23992}, {15545, 57311}, {17702, 46987}, {29181, 36173}, {31644, 39691}, {35909, 36189}, {38393, 44114}, {38730, 54248}, {44526, 60704}, {45311, 46980}, {47239, 61691}, {47565, 64880}, {47616, 63534}, {58907, 59549}

X(65608) = midpoint of X(i) and X(j) for these {i,j}: {125, 51429}, {265, 46634}, {325, 3580}, {842, 1550}, {5099, 15357}, {5641, 51227}, {9140, 53136}, {11005, 36166}, {11006, 36196}, {43961, 43962}
X(65608) = reflection of X(i) in X(j) for these {i,j}: {230, 47296}, {1495, 47171}, {11064, 44377}, {46980, 45311}, {46981, 6699}, {46982, 7687}, {51258, 15359}
X(65608) = complement of X(14999)
X(65608) = complement of the isogonal conjugate of X(14998)
X(65608) = complement of the isotomic conjugate of X(14223)
X(65608) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 16188}, {798, 23967}, {842, 4369}, {1973, 60510}, {2159, 60340}, {5641, 42327}, {5649, 21254}, {14223, 2887}, {14998, 10}, {35909, 18589}
X(65608) = X(5641)-Ceva conjugate of X(523)
X(65608) = X(i)-Dao conjugate of X(j) for these (i,j): {1640, 542}, {57465, 3233}
X(65608) = crosspoint of X(2) and X(14223)
X(65608) = crossdifference of every pair of points on line {512, 2420}
X(65608) = barycentric product X(i)*X(j) for these {i,j}: {338, 54439}, {850, 34291}
X(65608) = barycentric quotient X(i)/X(j) for these {i,j}: {12079, 54495}, {34291, 110}, {54439, 249}, {60509, 7473}
X(65608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 62639}, {39022, 39023, 62551}

X(65609) = X(4)X(1499)∩X(111)X(2697)

Barycentrics    (a^2 + b^2 - 2*c^2)*(b^2 - c^2)*(-a^2 + 2*b^2 - c^2)*(-(a^4*b^2) + b^6 - a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - b^2*c^4 + c^6) : :

X(65609) lies on the cubic K1367 and these lines: {4, 1499}, {111, 2697}, {338, 850}, {523, 10415}, {525, 14364}, {671, 33294}, {858, 47138}, {3265, 42008}, {6563, 14977}, {8430, 12077}, {9213, 47122}, {9979, 53419}, {10630, 41254}, {23301, 45096}, {52672, 57485}

X(65609) = X(i)-Ceva conjugate of X(j) for these (i,j): {2052, 10555}, {10630, 64258}
X(65609) = X(i)-isoconjugate of X(j) for these (i,j): {896, 65306}, {1177, 23889}, {3292, 36095}, {4575, 51823}, {32676, 53784}
X(65609) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 51823}, {15526, 53784}, {15899, 65306}, {38971, 524}, {52628, 36792}, {61067, 5467}, {64646, 5468}
X(65609) = barycentric product X(i)*X(j) for these {i,j}: {523, 59422}, {671, 47138}, {850, 57485}, {858, 5466}, {1236, 9178}, {2393, 52632}, {3267, 64619}, {5523, 14977}, {10561, 57476}, {10630, 62577}, {20884, 23894}, {21017, 62626}, {42665, 46111}, {44173, 51962}, {51258, 61181}, {52672, 62629}
X(65609) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 65306}, {525, 53784}, {858, 5468}, {2393, 5467}, {2501, 51823}, {5466, 2373}, {5523, 4235}, {8430, 36823}, {8753, 10423}, {9178, 1177}, {10097, 18876}, {10561, 60002}, {14580, 61207}, {14618, 58078}, {17983, 65268}, {18669, 23889}, {20884, 24039}, {21109, 6629}, {34158, 32661}, {36128, 36095}, {42665, 3292}, {47138, 524}, {51962, 1576}, {52632, 46140}, {57485, 110}, {59422, 99}, {62577, 36792}, {64258, 60040}, {64619, 112}
X(65609) = {X(5466),X(10561)}-harmonic conjugate of X(2501)

X(65610) = X(2)X(523)∩X(125)X(136)

Barycentrics    (b^2 - c^2)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8) : :
X(65610) = 2 X[35364] + X[38359], 2 X[15328] + X[62172], 4 X[1116] - X[18556], X[5489] - 4 X[59741], X[5664] + 2 X[15475], 2 X[15543] + X[58346], 4 X[45259] - X[53263]

X(65610) lies on the cubic K1367 and these lines: {2, 523}, {4, 3566}, {6, 2501}, {51, 924}, {125, 136}, {311, 850}, {512, 9730}, {520, 61666}, {525, 14852}, {526, 9979}, {690, 9880}, {804, 42738}, {826, 1209}, {1007, 62645}, {1116, 18556}, {1499, 53017}, {1637, 6041}, {3800, 10279}, {3815, 55267}, {4240, 61213}, {5467, 30512}, {5489, 59741}, {5664, 15475}, {6055, 55122}, {6132, 9131}, {7468, 60511}, {8675, 61667}, {9033, 9171}, {9175, 55142}, {11184, 64919}, {12075, 22260}, {12106, 34952}, {14223, 34368}, {14355, 52076}, {14424, 53567}, {15543, 58346}, {16188, 55131}, {18039, 30735}, {18808, 34208}, {18867, 45147}, {32193, 45259}, {34175, 38939}, {35912, 53149}, {37930, 44823}, {41254, 51480}, {45331, 55130}, {53418, 58780}, {54274, 65468}, {58784, 64935}, {58882, 63551}

X(65610) = midpoint of X(9134) and X(16230)
X(65610) = reflection of X(i) in X(j) for these {i,j}: {9131, 6132}, {14424, 53567}, {32193, 45259}, {53263, 32193}, {53266, 10278}
X(65610) = X(14221)-Ceva conjugate of X(54395)
X(65610) = X(i)-isoconjugate of X(j) for these (i,j): {896, 35191}, {1101, 51480}, {4575, 40118}, {36034, 51457}, {36084, 40083}
X(65610) = X(i)-Dao conjugate of X(j) for these (i,j): {136, 40118}, {523, 51480}, {2493, 14999}, {3258, 51457}, {15899, 35191}, {16188, 110}, {36189, 15462}, {38987, 40083}
X(65610) = crosspoint of X(i) and X(j) for these (i,j): {850, 14223}, {14221, 54395}
X(65610) = crosssum of X(3) and X(34291)
X(65610) = crossdifference of every pair of points on line {187, 13754}
X(65610) = barycentric product X(i)*X(j) for these {i,j}: {115, 14221}, {338, 7468}, {523, 54395}, {671, 55131}, {850, 2493}, {2799, 34175}, {14223, 16188}, {14618, 14984}, {18312, 38939}, {44427, 51847}
X(65610) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 35191}, {115, 51480}, {1637, 51457}, {1640, 51474}, {2493, 110}, {2501, 40118}, {3569, 40083}, {7468, 249}, {14221, 4590}, {14984, 4558}, {16188, 14999}, {34175, 2966}, {38939, 5649}, {51847, 60053}, {52515, 10425}, {54395, 99}, {55131, 524}

X(65611) = X(6)X(525)∩X(125)X(512)

Barycentrics    (b^2 - c^2)*(-2*a^2 + b^2 + c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(-a^6 + a^2*b^4 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 - c^6) : :

X(65611) lies on the cubic K1367 and these lines: {6, 525}, {125, 512}, {187, 14417}, {249, 4563}, {523, 64218}, {524, 45807}, {598, 57082}, {690, 44102}, {843, 2373}, {1177, 3566}, {1499, 5621}, {1649, 39201}, {2482, 52613}, {5181, 8673}, {9517, 62376}, {10630, 41254}, {14223, 57065}, {15387, 41511}, {35146, 46140}, {39062, 65268}, {51999, 53784}

X(65611) = X(i)-complementary conjugate of X(j) for these (i,j): {24019, 52533}, {59175, 16595}, {60503, 18589}, {65356, 21256}
X(65611) = X(65306)-Ceva conjugate of X(524)
X(65611) = X(i)-cross conjugate of X(j) for these (i,j): {3269, 14357}, {47415, 468}, {58780, 690}
X(65611) = X(i)-isoconjugate of X(j) for these (i,j): {163, 59422}, {662, 57485}, {691, 18669}, {799, 51962}, {811, 34158}, {858, 36142}, {897, 61198}, {2393, 36085}, {4592, 64619}, {20884, 32729}, {24019, 51253}, {36060, 61181}
X(65611) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 59422}, {1084, 57485}, {1560, 61181}, {1648, 5181}, {1649, 47138}, {5139, 64619}, {6593, 61198}, {17423, 34158}, {23992, 858}, {35071, 51253}, {38988, 2393}, {38996, 51962}, {48317, 5523}, {62594, 62382}
X(65611) = crossdifference of every pair of points on line {2393, 51962}
X(65611) = barycentric product X(i)*X(j) for these {i,j}: {351, 46140}, {524, 60040}, {525, 51823}, {647, 58078}, {690, 2373}, {1177, 35522}, {2501, 53784}, {2642, 37220}, {10422, 52629}, {14417, 60133}, {22105, 46165}, {52628, 65306}
X(65611) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 61198}, {351, 2393}, {468, 61181}, {512, 57485}, {520, 51253}, {523, 59422}, {669, 51962}, {690, 858}, {1177, 691}, {1648, 47138}, {1649, 5181}, {2373, 892}, {2489, 64619}, {2642, 18669}, {3049, 34158}, {4750, 17172}, {10422, 34574}, {14273, 5523}, {14417, 62382}, {18876, 65321}, {35522, 1236}, {44102, 46592}, {46140, 53080}, {51823, 648}, {52038, 52672}, {53784, 4563}, {54274, 47426}, {58078, 6331}, {58780, 1560}, {60040, 671}, {60133, 65350}

X(65612) = X(4)X(523)∩X(6)X(525)

Barycentrics    (b^2 - c^2)*(-(a^8*b^2) + 2*a^6*b^4 - 2*a^2*b^8 + b^10 - a^8*c^2 - a^4*b^4*c^2 + 2*a^2*b^6*c^2 + 2*a^6*c^4 - a^4*b^2*c^4 - b^6*c^4 + 2*a^2*b^2*c^6 - b^4*c^6 - 2*a^2*c^8 + c^10) : :
X(65612) = 3 X[18311] - 2 X[62307]

X(65612) lies on the cubic K1367 and these lines: {2, 2419}, {4, 523}, {6, 525}, {24, 46614}, {25, 47216}, {39, 2485}, {115, 127}, {253, 14977}, {378, 46615}, {427, 55273}, {520, 50649}, {1640, 50942}, {1649, 47249}, {1975, 57069}, {2492, 44427}, {3268, 46425}, {3566, 61088}, {4580, 10548}, {6130, 42738}, {8029, 59742}, {8057, 15069}, {9479, 44821}, {13567, 23616}, {13881, 14566}, {14537, 23878}, {14592, 60515}, {15421, 52041}, {23881, 52624}, {26958, 38240}, {34767, 37643}, {37930, 46609}, {37937, 60512}, {42854, 44705}, {47296, 52720}, {59900, 59932}, {60597, 62577}

X(65612) = reflection of X(i) in X(j) for these {i,j}: {35522, 6334}, {44427, 2492}, {59932, 59900}
X(65612) = X(i)-isoconjugate of X(j) for these (i,j): {163, 2697}, {18669, 64778}
X(65612) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 2697}, {647, 60591}, {5099, 46340}, {6103, 7473}, {35594, 10317}, {38970, 47110}
X(65612) = crosspoint of X(14223) and X(14618)
X(65612) = crossdifference of every pair of points on line {1576, 2393}
X(65612) = barycentric product X(i)*X(j) for these {i,j}: {339, 37937}, {525, 50188}, {850, 2781}, {3268, 43090}
X(65612) = barycentric quotient X(i)/X(j) for these {i,j}: {125, 60591}, {523, 2697}, {1177, 64778}, {2492, 46340}, {2781, 110}, {8749, 59108}, {16230, 47110}, {37937, 250}, {40079, 43754}, {42426, 7473}, {43090, 476}, {50188, 648}
X(65612) = {X(41172),X(52628)}-harmonic conjugate of X(62551)

X(65613) = X(4)X(6)∩X(115)X(523)

Barycentrics    (b^2 - c^2)^2*(a^8 + a^6*b^2 - 3*a^4*b^4 - a^2*b^6 + 2*b^8 + a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 - 3*a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :
X(65613) = 3 X[6034] - X[34369]

X(65613) lies on the cubic K1367 and these lines: {4, 6}, {115, 523}, {125, 2501}, {230, 36166}, {338, 14618}, {842, 34366}, {1637, 3154}, {2549, 56967}, {3258, 9209}, {3269, 38361}, {3566, 53569}, {6034, 34175}, {6103, 52464}, {8754, 44705}, {14998, 36189}, {34370, 43090}, {34981, 59900}, {37987, 60510}, {51404, 52076}

X(65613) = midpoint of X(1990) and X(53419)
X(65613) = polar conjugate of the isotomic conjugate of X(37987)
X(65613) = X(i)-Dao conjugate of X(j) for these (i,j): {37987, 14999}, {60510, 69}
X(65613) = crosspoint of X(4) and X(14223)
X(65613) = crossdifference of every pair of points on line {520, 5467}
X(65613) = barycentric product X(i)*X(j) for these {i,j}: {4, 37987}, {14223, 60510}
X(65613) = barycentric quotient X(i)/X(j) for these {i,j}: {37987, 69}, {60510, 14999}
X(65613) = {X(5523),X(6530)}-harmonic conjugate of X(1990)

X(65614) = X(2)X(525)∩X(74)X(3566)

Barycentrics    (b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :
X(65614) = X[74] + 2 X[52475], X[3580] + 2 X[6334], X[44427] - 4 X[47296]

X(65614) lies on the cubic K1367 and these lines: {2, 525}, {74, 3566}, {338, 14618}, {403, 55121}, {523, 5627}, {826, 32112}, {3580, 6334}, {9007, 57147}, {12079, 34953}, {14264, 52451}, {16080, 57065}, {18312, 18557}, {18808, 52487}, {36189, 56792}, {36841, 44769}, {40384, 41254}, {44427, 47296}

X(65614) = X(55264)-Ceva conjugate of X(1494)
X(65614) = X(i)-cross conjugate of X(j) for these (i,j): {6334, 2394}, {55265, 55121}
X(65614) = X(i)-isoconjugate of X(j) for these (i,j): {163, 15454}, {1495, 65262}, {2173, 10420}, {2420, 36053}, {3284, 36114}, {4575, 51965}, {5504, 56829}, {9406, 18878}, {32678, 39371}
X(65614) = X(i)-Dao conjugate of X(j) for these (i,j): {113, 2420}, {115, 15454}, {136, 51965}, {2088, 1511}, {3003, 3233}, {6334, 5664}, {9410, 18878}, {16178, 1990}, {18334, 39371}, {34834, 2407}, {36896, 10420}, {36901, 52552}, {39005, 3284}, {39021, 30}, {39174, 32661}, {47230, 62172}, {55121, 55265}, {56792, 6}, {62606, 43755}
X(65614) = cevapoint of X(i) and X(j) for these (i,j): {686, 60342}, {55121, 55265}
X(65614) = crosspoint of X(i) and X(j) for these (i,j): {1494, 55264}, {16080, 39290}
X(65614) = crosssum of X(3284) and X(52743)
X(65614) = barycentric product X(i)*X(j) for these {i,j}: {403, 34767}, {850, 14264}, {1494, 55121}, {2394, 3580}, {6334, 16080}, {12079, 61188}, {14380, 44138}, {18808, 62338}, {31621, 55265}, {39021, 55264}, {44173, 51821}
X(65614) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 10420}, {113, 3233}, {403, 4240}, {523, 15454}, {526, 39371}, {686, 3284}, {850, 52552}, {1494, 18878}, {2349, 65262}, {2394, 2986}, {2433, 14910}, {2501, 51965}, {3003, 2420}, {3580, 2407}, {6334, 11064}, {8749, 32708}, {10412, 39375}, {12079, 15328}, {14264, 110}, {14380, 5504}, {14919, 43755}, {16080, 687}, {16221, 62172}, {18808, 1300}, {21731, 1495}, {31621, 55264}, {34767, 57829}, {36119, 36114}, {39021, 55265}, {44084, 23347}, {44769, 18879}, {47236, 1990}, {51821, 1576}, {55121, 30}, {55265, 3163}, {56403, 41392}, {56792, 15470}, {60342, 1511}

X(65615) = X(6)X(2501)∩X(115)X(647)

Barycentrics    (b^2 - c^2)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^4*c^2 + 2*a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - 2*b^2*c^4 + c^6) : :

X(65615) lies on the cubic K1367 and these lines: {6, 2501}, {115, 647}, {523, 11079}, {525, 64769}, {669, 58346}, {1637, 3284}, {1990, 14397}, {2986, 10754}, {3233, 41392}, {6529, 23964}, {6587, 14910}, {9209, 15470}, {11064, 41079}, {14566, 15421}, {40384, 41254}, {47230, 53416}, {52743, 56399}

X(65615) = X(32708)-Ceva conjugate of X(1990)
X(65615) = X(i)-cross conjugate of X(j) for these (i,j): {3124, 14583}, {14401, 1637}
X(65615) = X(i)-isoconjugate of X(j) for these (i,j): {662, 14264}, {799, 51821}, {823, 53785}, {1725, 44769}, {2159, 61188}, {2315, 16077}, {2349, 15329}, {3580, 36034}, {13754, 65263}, {16237, 35200}, {36131, 62338}
X(65615) = X(i)-Dao conjugate of X(j) for these (i,j): {133, 16237}, {1084, 14264}, {1650, 62569}, {3163, 61188}, {3258, 3580}, {38996, 51821}, {39008, 62338}, {57295, 6334}
X(65615) = cevapoint of X(i) and X(j) for these (i,j): {1637, 52743}, {14398, 58346}
X(65615) = crosssum of X(3003) and X(60342)
X(65615) = crossdifference of every pair of points on line {13754, 14264}
X(65615) = barycentric product X(i)*X(j) for these {i,j}: {30, 15328}, {512, 52552}, {523, 15454}, {525, 51965}, {526, 39375}, {1300, 9033}, {1637, 2986}, {1990, 15421}, {9409, 65267}, {10412, 39371}, {10419, 58263}, {10420, 58261}, {12028, 62172}, {14222, 51254}, {14254, 15470}, {14398, 40832}, {14910, 41079}, {35361, 43768}, {36035, 36053}, {39986, 53178}, {40388, 52624}, {40423, 58346}, {40427, 52743}, {46106, 61216}
X(65615) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 61188}, {512, 14264}, {669, 51821}, {1300, 16077}, {1495, 15329}, {1637, 3580}, {1990, 16237}, {9033, 62338}, {9409, 13754}, {14398, 3003}, {14399, 18609}, {14401, 62569}, {14581, 61209}, {14583, 41512}, {14910, 44769}, {15328, 1494}, {15454, 99}, {35361, 62722}, {39201, 53785}, {39371, 10411}, {39375, 35139}, {40388, 34568}, {51965, 648}, {52552, 670}, {52743, 34834}, {58346, 113}, {61216, 14919}

X(65616) = X(2)X(98)∩X(523)X(2065)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(2*a^10 - 5*a^8*b^2 + 7*a^6*b^4 - 7*a^4*b^6 + 3*a^2*b^8 - 5*a^8*c^2 + 4*a^6*b^2*c^2 - 4*a^2*b^6*c^2 + b^8*c^2 + 7*a^6*c^4 + 6*a^2*b^4*c^4 - b^6*c^4 - 7*a^4*c^6 - 4*a^2*b^2*c^6 - b^4*c^6 + 3*a^2*c^8 + b^2*c^8) : :
X(65616) = X[98] + 2 X[5967], 2 X[34369] + X[53866]

X(65616) lies on the cubic K1367 and these lines: {2, 98}, {6, 60504}, {249, 34473}, {338, 14265}, {523, 2065}, {1576, 10753}, {6034, 34175}, {11596, 32545}, {14356, 52081}, {14639, 58907}, {34810, 56788}, {34953, 38224}, {51963, 52472}

X(65616) = X(47082)-cross conjugate of X(98)
X(65616) = X(47082)-Dao conjugate of X(114)
X(65616) = barycentric product X(34536)*X(47079)
X(65616) = barycentric quotient X(i)/X(j) for these {i,j}: {2715, 53695}, {47079, 36790}
X(65616) = {X(6055),X(51820)}-harmonic conjugate of X(98)

X(65617) = X(6)X(13)∩X(125)X(14583)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(2*a^10 - 3*a^8*b^2 + a^6*b^4 - 5*a^4*b^6 + 9*a^2*b^8 - 4*b^10 - 3*a^8*c^2 + 4*a^6*b^2*c^2 + 4*a^4*b^4*c^2 - 8*a^2*b^6*c^2 + 3*b^8*c^2 + a^6*c^4 + 4*a^4*b^2*c^4 - 2*a^2*b^4*c^4 + b^6*c^4 - 5*a^4*c^6 - 8*a^2*b^2*c^6 + b^4*c^6 + 9*a^2*c^8 + 3*b^2*c^8 - 4*c^10) : :
X(65617) = X[265] + 2 X[14356], 2 X[265] + X[14559], 4 X[14356] - X[14559], 2 X[10113] + X[52772], 5 X[15081] + X[52472]

X(65617) lies on the cubic K1367 and these lines: {6, 13}, {125, 14583}, {338, 14254}, {523, 5627}, {5622, 14560}, {9140, 41512}, {9214, 59428}, {10113, 52772}, {14223, 34368}, {15061, 51345}, {15081, 52472}, {20126, 58733}, {36189, 43090}, {39295, 54501}, {44889, 52153}, {52056, 55319}

X(65617) = X(6149)-isoconjugate of X(54527)
X(65617) = X(14993)-Dao conjugate of X(54527)
X(65617) = crosspoint of X(5627) and X(54554)
X(65617) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 54527}, {52464, 14920}
X(65617) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 14, 41392}, {265, 14356, 14559}

X(65618) = X(115)X(232)∩X(125)X(511)

Barycentrics    (a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 - a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + 2*b^8*c^2 - a^6*c^4 + 4*a^4*b^2*c^4 - a^2*b^4*c^4 - a^4*c^6 - a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + b^2*c^8)*(a^8*b^2 - a^6*b^4 - a^4*b^6 + a^2*b^8 + a^8*c^2 - a^6*b^2*c^2 + 4*a^4*b^4*c^2 - a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 - a^4*b^2*c^4 - a^2*b^4*c^4 - 2*b^6*c^4 - a^2*b^2*c^6 + 2*a^2*c^8 + 2*b^2*c^8 - c^10) : :

X(65618) lies on the cubic K1367 and these lines: {5, 5968}, {6, 36183}, {30, 51862}, {98, 250}, {115, 232}, {125, 511}, {325, 339}, {427, 12079}, {468, 8901}, {826, 32112}, {842, 34175}, {1316, 3425}, {1485, 37930}, {1594, 39269}, {2697, 5622}, {2970, 6530}, {3447, 36166}, {5133, 14356}, {8430, 12077}, {9139, 11596}, {11799, 52692}, {16083, 46142}, {20975, 38552}, {21017, 21046}, {34370, 43090}, {37990, 64936}, {40801, 57583}, {46982, 53570}, {60502, 60590}

X(65618) = isogonal conjugate of X(15462)
X(65618) = polar conjugate of X(41253)
X(65618) = X(i)-cross conjugate of X(j) for these (i,j): {54380, 98}, {60500, 14223}
X(65618) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15462}, {48, 41253}, {163, 62307}, {1101, 36189}, {6149, 53768}
X(65618) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 15462}, {115, 62307}, {523, 36189}, {1249, 41253}, {14993, 53768}
X(65618) = cevapoint of X(i) and X(j) for these (i,j): {1640, 20975}, {53132, 60342}
X(65618) = trilinear pole of line {3569, 32312}
X(65618) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 41253}, {6, 15462}, {115, 36189}, {523, 62307}, {1989, 53768}

X(65619) = X(2)X(1637)∩X(6)X(14273)

Barycentrics    (b^2 - c^2)*(-4*a^12*b^2 + 11*a^10*b^4 - 8*a^8*b^6 - 4*a^6*b^8 + 10*a^4*b^10 - 7*a^2*b^12 + 2*b^14 - 4*a^12*c^2 + 10*a^10*b^2*c^2 - 16*a^8*b^4*c^2 + 11*a^6*b^6*c^2 - 11*a^4*b^8*c^2 + 15*a^2*b^10*c^2 - 5*b^12*c^2 + 11*a^10*c^4 - 16*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 3*a^4*b^6*c^4 - 17*a^2*b^8*c^4 + 3*b^10*c^4 - 8*a^8*c^6 + 11*a^6*b^2*c^6 - 3*a^4*b^4*c^6 + 18*a^2*b^6*c^6 - 4*a^6*c^8 - 11*a^4*b^2*c^8 - 17*a^2*b^4*c^8 + 10*a^4*c^10 + 15*a^2*b^2*c^10 + 3*b^4*c^10 - 7*a^2*c^12 - 5*b^2*c^12 + 2*c^14) : :

X(65619) lies on the cubic K1367 and these lines: {2, 1637}, {6, 14273}, {115, 55267}, {125, 55265}, {427, 9134}, {523, 6128}, {570, 2492}, {1194, 47230}, {8430, 12077}, {9722, 47138}, {36189, 55131}, {55122, 57598}

X(65619) = X(41254)-Ceva conjugate of X(125)
X(65619) = crossdifference of every pair of points on line {5191, 14984}
X(65619) = {X(14998),X(60510)}-harmonic conjugate of X(1637)

X(65620) = X(30)X(115)∩X(98)X(523)

Barycentrics    4*a^14 - 8*a^12*b^2 + 5*a^10*b^4 - 2*a^8*b^6 - 4*a^6*b^8 + 10*a^4*b^10 - 5*a^2*b^12 - 8*a^12*c^2 + 14*a^10*b^2*c^2 - 6*a^8*b^4*c^2 + 9*a^6*b^6*c^2 - 19*a^4*b^8*c^2 + 13*a^2*b^10*c^2 - 3*b^12*c^2 + 5*a^10*c^4 - 6*a^8*b^2*c^4 - 6*a^6*b^4*c^4 + 9*a^4*b^6*c^4 - 19*a^2*b^8*c^4 + 9*b^10*c^4 - 2*a^8*c^6 + 9*a^6*b^2*c^6 + 9*a^4*b^4*c^6 + 22*a^2*b^6*c^6 - 6*b^8*c^6 - 4*a^6*c^8 - 19*a^4*b^2*c^8 - 19*a^2*b^4*c^8 - 6*b^6*c^8 + 10*a^4*c^10 + 13*a^2*b^2*c^10 + 9*b^4*c^10 - 5*a^2*c^12 - 3*b^2*c^12 : :
X(65620) = 3 X[6055] - X[16188], 3 X[12042] - X[38611], 2 X[16188] - 3 X[46980], 2 X[38611] - 3 X[46981], 3 X[46998] - 2 X[47584], 3 X[98] + X[842], 3 X[98] - X[60508], X[842] - 3 X[36166], 3 X[36166] + X[60508], 3 X[186] + X[61102], 4 X[16760] - 3 X[46986], X[7472] - 3 X[34473], X[13202] - 3 X[58907], 3 X[36196] - X[44969], 3 X[38227] - 4 X[47241], X[38582] - 3 X[46633], X[38664] + 3 X[38704], 3 X[38704] - X[47293], X[43460] - 4 X[47244]

X(65620) lies on the cubic K1367 and these lines: {2, 3233}, {6, 35912}, {23, 8902}, {30, 115}, {74, 3566}, {98, 523}, {111, 2697}, {125, 468}, {157, 37930}, {186, 60514}, {338, 38552}, {403, 53570}, {542, 16760}, {669, 47252}, {858, 53577}, {1316, 9756}, {1499, 47502}, {1513, 47239}, {2782, 46987}, {2794, 14120}, {3154, 47200}, {3288, 47505}, {3564, 47570}, {5099, 10991}, {5159, 13611}, {5191, 36189}, {5318, 57585}, {5321, 57593}, {5912, 48981}, {6036, 36170}, {6103, 52464}, {7417, 8371}, {7418, 44821}, {7422, 42733}, {7472, 34473}, {7473, 41254}, {9007, 48984}, {9418, 51733}, {10151, 44099}, {11177, 53136}, {11623, 51258}, {12079, 47220}, {12188, 46634}, {13202, 58907}, {14659, 53931}, {16315, 62509}, {30549, 47285}, {34845, 36183}, {36176, 45030}, {36196, 44969}, {37987, 47085}, {38227, 47241}, {38582, 46633}, {38613, 51523}, {38664, 38704}, {38680, 47292}, {39201, 47003}, {39874, 52473}, {43460, 47244}, {47152, 65154}, {53726, 62507}, {53890, 53935}

X(65620) = midpoint of X(i) and X(j) for these {i,j}: {98, 36166}, {842, 60508}, {5099, 10991}, {11177, 53136}, {12188, 46634}, {38613, 51523}, {38664, 47293}, {38680, 47292}
X(65620) = reflection of X(i) in X(j) for these {i,j}: {1513, 47239}, {36170, 6036}, {46980, 6055}, {46981, 12042}, {46982, 115}, {46988, 14120}, {51258, 11623}
X(65620) = X(i)-Ceva conjugate of X(j) for these (i,j): {7473, 523}, {41254, 6}
X(65620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 842, 60508}, {36166, 60508, 842}, {38664, 38704, 47293}

X(65621) = X(2)X(94)∩X(6)X(41512)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^12*b^2 - 3*a^10*b^4 + 2*a^8*b^6 + 2*a^6*b^8 - 3*a^4*b^10 + a^2*b^12 + a^12*c^2 - 4*a^10*b^2*c^2 + 7*a^8*b^4*c^2 - 4*a^6*b^6*c^2 - 3*a^4*b^8*c^2 + 4*a^2*b^10*c^2 - b^12*c^2 - 3*a^10*c^4 + 7*a^8*b^2*c^4 - 10*a^6*b^4*c^4 + 8*a^4*b^6*c^4 - 9*a^2*b^8*c^4 + 3*b^10*c^4 + 2*a^8*c^6 - 4*a^6*b^2*c^6 + 8*a^4*b^4*c^6 + 8*a^2*b^6*c^6 - 2*b^8*c^6 + 2*a^6*c^8 - 3*a^4*b^2*c^8 - 9*a^2*b^4*c^8 - 2*b^6*c^8 - 3*a^4*c^10 + 4*a^2*b^2*c^10 + 3*b^4*c^10 + a^2*c^12 - b^2*c^12) : :

X(65621) lies on the cubic K1367 and these lines: {2, 94}, {6, 41512}, {115, 39170}, {125, 56403}, {523, 11079}, {541, 56395}, {1640, 51480}, {6128, 14583}, {14254, 44468}, {34370, 43090}, {41392, 52010}

X(65621) = crosspoint of X(40427) and X(54554)

X(65622) = X(125)X(511)∩X(523)X(895)

Barycentrics    2*a^14*b^2 - 7*a^12*b^4 + 7*a^10*b^6 + 2*a^8*b^8 - 8*a^6*b^10 + 5*a^4*b^12 - a^2*b^14 + 2*a^14*c^2 - 10*a^12*b^2*c^2 + 21*a^10*b^4*c^2 - 23*a^8*b^6*c^2 + 20*a^6*b^8*c^2 - 16*a^4*b^10*c^2 + 5*a^2*b^12*c^2 + b^14*c^2 - 7*a^12*c^4 + 21*a^10*b^2*c^4 - 22*a^8*b^4*c^4 + 6*a^6*b^6*c^4 + 19*a^4*b^8*c^4 - 7*a^2*b^10*c^4 - 2*b^12*c^4 + 7*a^10*c^6 - 23*a^8*b^2*c^6 + 6*a^6*b^4*c^6 - 24*a^4*b^6*c^6 + 3*a^2*b^8*c^6 - b^10*c^6 + 2*a^8*c^8 + 20*a^6*b^2*c^8 + 19*a^4*b^4*c^8 + 3*a^2*b^6*c^8 + 4*b^8*c^8 - 8*a^6*c^10 - 16*a^4*b^2*c^10 - 7*a^2*b^4*c^10 - b^6*c^10 + 5*a^4*c^12 + 5*a^2*b^2*c^12 - 2*b^4*c^12 - a^2*c^14 + b^2*c^14 : :

X(65622) lies on the cubic K1367 and these lines: {2, 60498}, {6, 60511}, {125, 511}, {338, 524}, {401, 37784}, {523, 895}, {1995, 46124}, {2986, 10754}, {3124, 11064}, {10752, 41512}, {14221, 41254}, {14984, 36189}, {22486, 34289}, {40112, 62311}

X(65622) = anticomplement of the isotomic conjugate of X(41254)
X(65622) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {5622, 4329}, {41254, 6327}
X(65622) = X(i)-Ceva conjugate of X(j) for these (i,j): {14221, 523}, {41254, 2}

X(65623) = X(4)X(690)∩X(6)X(9033)

Barycentrics    (b^2 - c^2)*(4*a^14*b^2 - 9*a^12*b^4 + a^10*b^6 + 8*a^8*b^8 - 2*a^6*b^10 - a^4*b^12 - 3*a^2*b^14 + 2*b^16 + 4*a^14*c^2 - 14*a^12*b^2*c^2 + 23*a^10*b^4*c^2 - 21*a^8*b^6*c^2 + 10*a^6*b^8*c^2 - 8*a^4*b^10*c^2 + 11*a^2*b^12*c^2 - 5*b^14*c^2 - 9*a^12*c^4 + 23*a^10*b^2*c^4 - 6*a^8*b^4*c^4 - 4*a^6*b^6*c^4 - 3*a^4*b^8*c^4 - 3*a^2*b^10*c^4 + 2*b^12*c^4 + a^10*c^6 - 21*a^8*b^2*c^6 - 4*a^6*b^4*c^6 + 24*a^4*b^6*c^6 - 5*a^2*b^8*c^6 + 5*b^10*c^6 + 8*a^8*c^8 + 10*a^6*b^2*c^8 - 3*a^4*b^4*c^8 - 5*a^2*b^6*c^8 - 8*b^8*c^8 - 2*a^6*c^10 - 8*a^4*b^2*c^10 - 3*a^2*b^4*c^10 + 5*b^6*c^10 - a^4*c^12 + 11*a^2*b^2*c^12 + 2*b^4*c^12 - 3*a^2*c^14 - 5*b^2*c^14 + 2*c^16) : :

X(65623) lies on the cubic K1367 and these lines: {4, 690}, {6, 9033}, {115, 60500}, {338, 58263}, {389, 9517}, {512, 974}, {520, 32246}, {523, 15118}, {525, 7687}, {526, 9969}, {826, 32112}, {7927, 10821}, {8673, 12236}, {23300, 55121}

X(65623) = midpoint of X(35909) and X(60509)
X(65623) = X(41254)-Ceva conjugate of X(115)

X(65624) = X(115)X(232)∩X(523)X(8749)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^18*b^2 - 5*a^16*b^4 - a^14*b^6 + 11*a^12*b^8 - 5*a^10*b^10 - 7*a^8*b^12 + 5*a^6*b^14 + a^4*b^16 - a^2*b^18 + 2*a^18*c^2 - 6*a^16*b^2*c^2 + 13*a^14*b^4*c^2 - 13*a^12*b^6*c^2 - 5*a^10*b^8*c^2 + 13*a^8*b^10*c^2 - 5*a^6*b^12*c^2 + 5*a^4*b^14*c^2 - 5*a^2*b^16*c^2 + b^18*c^2 - 5*a^16*c^4 + 13*a^14*b^2*c^4 - 12*a^12*b^4*c^4 + 12*a^10*b^6*c^4 - 17*a^8*b^8*c^4 + 21*a^6*b^10*c^4 - 26*a^4*b^12*c^4 + 18*a^2*b^14*c^4 - 4*b^16*c^4 - a^14*c^6 - 13*a^12*b^2*c^6 + 12*a^10*b^4*c^6 + 22*a^8*b^6*c^6 - 21*a^6*b^8*c^6 + 11*a^4*b^10*c^6 - 14*a^2*b^12*c^6 + 4*b^14*c^6 + 11*a^12*c^8 - 5*a^10*b^2*c^8 - 17*a^8*b^4*c^8 - 21*a^6*b^6*c^8 + 18*a^4*b^8*c^8 + 2*a^2*b^10*c^8 + 4*b^12*c^8 - 5*a^10*c^10 + 13*a^8*b^2*c^10 + 21*a^6*b^4*c^10 + 11*a^4*b^6*c^10 + 2*a^2*b^8*c^10 - 10*b^10*c^10 - 7*a^8*c^12 - 5*a^6*b^2*c^12 - 26*a^4*b^4*c^12 - 14*a^2*b^6*c^12 + 4*b^8*c^12 + 5*a^6*c^14 + 5*a^4*b^2*c^14 + 18*a^2*b^4*c^14 + 4*b^6*c^14 + a^4*c^16 - 5*a^2*b^2*c^16 - 4*b^4*c^16 - a^2*c^18 + b^2*c^18) : :

X(65624) lies on the cubic K1367 and these lines: {4, 60499}, {6, 60512}, {115, 232}, {338, 1990}, {419, 15262}, {468, 47427}, {523, 8749}, {3269, 15311}, {5622, 35907}, {14223, 57065}, {43717, 51480}

X(65624) = X(41254)-Ceva conjugate of X(4)

X(65625) = X(13)X(15)∩X(524)X(11119)

Barycentrics    (8*a^6-5*(b^2+c^2)*a^4-(11*b^4+48*b^2*c^2+11*c^4)*a^2+2*(4*a^4-11*(b^2+c^2)*a^2+2*b^4-10*b^2*c^2+2*c^4)*sqrt(3)*S+8*(b^4-c^4)*(b^2-c^2))*(2*S+(a^2+b^2-c^2)*sqrt(3))*(2*S+(a^2-b^2+c^2)*sqrt(3)) : :

See Sriram Panchapakesan and César Lozada, euclid 7054.

X(65625) lies on these lines: {13, 15}, {524, 11119}, {8014, 23302}, {8838, 44383}, {11555, 16772}

X(65625) = X(13)-daleth conjugate of-X(46078)
X(65625) = inverse of X(46078) in 1st Simmons inconic
X(65625) = pole of the line {13, 41472} with respect to the Kiepert circumhyperbola
X(65625) = pole of the line {523, 16530} with respect to the 1st Simmons inconic
X(65625) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (13, 396, 34325), (396, 34325, 11537), (396, 48255, 13)

X(65626) = X(14)X(16)∩X(524)X(11120)

Barycentrics    (8*a^6-5*(b^2+c^2)*a^4-(11*b^4+48*b^2*c^2+11*c^4)*a^2-2*(4*a^4-11*(b^2+c^2)*a^2+2*b^4-10*b^2*c^2+2*c^4)*sqrt(3)*S+8*(b^4-c^4)*(b^2-c^2))*(-2*S+(a^2+b^2-c^2)*sqrt(3))*(-2*S+(a^2-b^2+c^2)*sqrt(3)) : :

See Sriram Panchapakesan and César Lozada, euclid 7054.

X(65626) lies on these lines: {14, 16}, {524, 11120}, {8015, 23303}, {8836, 44382}, {11556, 16773}

X(65626) = X(14)-daleth conjugate of-X(46074)
X(65626) = inverse of X(46074) in 2nd Simmons inconic
X(65626) = pole of the line {14, 41473} with respect to the Kiepert circumhyperbola
X(65626) = pole of the line {523, 16529} with respect to the 2nd Simmons inconic
X(65626) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (14, 395, 34326), (395, 34326, 11549), (395, 48256, 14)

X(65627) = X(6)X(39164)∩X(39022)X(39165)

Barycentrics    2*(sqrt(-3*S^2+SW^2)*a^2-2*S^2-SA^2+SB*SC+SW^2)*sqrt(-2*OH^2*sqrt(-3*S^2+SW^2)-3*S^2-18*SW*R^2+5*SW^2)-(6*SA+SW)*S^2-3*(SA^2-SB*SC-SW^2)*SA+(S^2-3*SB*SC)*sqrt(-3*S^2+SW^2) : :

See Sriram Panchapakesan and César Lozada, euclid 7054.

X(65627) lies on the cubic K002 and these lines: {6, 39164}, {39022, 39165}

X(65627) = complement of the isotomic conjugate of X(39161)
X(65627) = Dao image of X(39164)
X(65627) = barycentric product X(i)*X(j) for these {i, j}: {39160, 60612}, {39161, 39164}

X(65628) = X(6)X(39165)∩X(39022)X(39164)

Barycentrics    -2*(sqrt(-3*S^2+SW^2)*a^2-2*S^2-SA^2+SB*SC+SW^2)*sqrt(-2*OH^2*sqrt(-3*S^2+SW^2)-3*S^2-18*SW*R^2+5*SW^2)-(6*SA+SW)*S^2-3*(SA^2-SB*SC-SW^2)*SA+(S^2-3*SB*SC)*sqrt(-3*S^2+SW^2) : :

See Sriram Panchapakesan and César Lozada, euclid 7054.

X(65628) lies on the cubic K002 and these lines: {6, 39165}, {39022, 39164}

X(65628) = complement of the isotomic conjugate of X(39160)
X(65628) = Dao image of X(39165)
X(65628) = barycentric product X(i)*X(j) for these {i,j}: {39160, 39165}, {39161, 60613}

X(65629) = X(546)X(6346)∩X(14857)X(33332)

Barycentrics    4 a^18 b^4 - 27 a^16 b^6 + 76 a^14 b^8 - 112 a^12 b^10 + 84 a^10 b^12 - 14 a^8 b^14 - 28 a^6 b^16 + 24 a^4 b^18 - 8 a^2 b^20 + b^22 - 13 a^16 b^4 c^2 + 40 a^14 b^6 c^2 - 12 a^12 b^8 c^2 - 75 a^10 b^10 c^2 + 65 a^8 b^12 c^2 + 58 a^6 b^14 c^2 - 110 a^4 b^16 c^2 + 57 a^2 b^18 c^2 - 10 b^20 c^2 + 4 a^18 c^4 - 13 a^16 b^2 c^4 + 24 a^14 b^4 c^4 + 4 a^12 b^6 c^4 - 28 a^10 b^8 c^4 - 36 a^8 b^10 c^4 - 5 a^6 b^12 c^4 + 167 a^4 b^14 c^4 - 159 a^2 b^16 c^4 + 42 b^18 c^4 - 27 a^16 c^6 + 40 a^14 b^2 c^6 + 4 a^12 b^4 c^6 - 34 a^10 b^6 c^6 - 15 a^8 b^8 c^6 - 6 a^6 b^10 c^6 - 81 a^4 b^12 c^6 + 214 a^2 b^14 c^6 - 95 b^16 c^6 + 76 a^14 c^8 - 12 a^12 b^2 c^8 - 28 a^10 b^4 c^8 - 15 a^8 b^6 c^8 - 38 a^6 b^8 c^8 - 137 a^2 b^12 c^8 + 118 b^14 c^8 - 112 a^12 c^10 - 75 a^10 b^2 c^10 - 36 a^8 b^4 c^10 - 6 a^6 b^6 c^10 + 66 a^2 b^10 c^10 - 56 b^12 c^10 + 84 a^10 c^12 + 65 a^8 b^2 c^12 - 5 a^6 b^4 c^12 - 81 a^4 b^6 c^12 - 137 a^2 b^8 c^12 - 56 b^10 c^12 - 14 a^8 c^14 + 58 a^6 b^2 c^14 + 167 a^4 b^4 c^14 + 214 a^2 b^6 c^14 + 118 b^8 c^14 - 28 a^6 c^16 - 110 a^4 b^2 c^16 - 159 a^2 b^4 c^16 - 95 b^6 c^16 + 24 a^4 c^18 + 57 a^2 b^2 c^18 + 42 b^4 c^18 - 8 a^2 c^20 - 10 b^2 c^20 + c^22 : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 7059.

X(65629) lies on these lines: {546, 6346}, {14857, 33332}




leftri  In-Exsimilicenters of Hatzipolakis-Suppa Circle and some circles: X(65630) - X(65633)  rightri

This preamble and centers X(65330)-X(65533) were contributed by Ercole Suppa, October 8, 2024.

X(m,n) = (insimilicenter, exsimilicenter) of circles
Hatzipolakis-Suppa circle, anticomplementary circle X(3543, 3146)
Hatzipolakis-Suppa circle, circumcircle X (4, 30)
Hatzipolakis-Suppa circle, 2nd Lemoine circle (or cosine circle) X(35820, 35821)
Hatzipolakis-Suppa circle, half-Moses circle X(65630, 44526)
Hatzipolakis-Suppa circle, incircle X(12943,12953)
Hatzipolakis-Suppa circle, Johnson triangle circumcircle X(3627, 30)
Hatzipolakis-Suppa circle, 1st Johnson-Yff circle X(65631 ,6284)
Hatzipolakis-Suppa circle, 2nd Johnson-Yff circle X(7354,65532)
Hatzipolakis-Suppa circle, Moses circle X(62203, 65633)
Hatzipolakis-Suppa circle, nine-point circle X(4, 20)
Hatzipolakis-Suppa circle, sine triple angle circle X(6759, 13352)
Hatzipolakis-Suppa circle, Stammler circle X(3830, 5073)
Hatzipolakis-Suppa circle, Steiner circle X(17578, 33703)
Hatzipolakis-Suppa circle, incircle of orthic triangle X(44438, 12173)
Hatzipolakis-Suppa circle, Lucas inner circle X(8981, 9541)
Hatzipolakis-Suppa circle, Lucas radical circle X(6564, 42266)
Hatzipolakis-Suppa circle, Lucas(-1) inner circle X(?, 13966)
Hatzipolakis-Suppa circle, Lucas(-1) circles radical circle X(42267, 6565)

For definitions of circles listed here, check the Extended glossary.

underbar

X(65630) = INSIMILICENTER OF HATZIPOLAKIS-SUPPA CIRCLE AND HALF-MOSES CIRCLE

Barycentrics    3 a^4+a^2 b^2-2 b^4+a^2 c^2+4 b^2 c^2-2 c^4 : :
Barycentrics    4 SB SC+SB SW+SC SW : :
X(65630) = 2*X(2548)-X(5013) = 3*X(2548)-2*X(31406) = 4*X(2548)-X(44519) = 2*X(3785)-3*X(8556) = X(3785)-3*X(32983) = 3*X(5013)-4*X(31406) = 2*X(5013)-X(44519) = 8*X(31406)-3*X(44519)

X(65630) lies on these lines: {2, 5023}, {3, 1506}, {4, 6}, {5, 3053}, {20, 3815}, {24, 44538}, {25, 44523}, {30, 2548}, {32, 381}, {39, 382}, {51, 63544}, {69, 32979}, {76, 40341}, {83, 598}, {112, 7547}, {114, 44532}, {115, 3843}, {140, 5210}, {141, 32006}, {148, 7921}, {172, 10896}, {183, 7823}, {187, 1656}, {193, 63923}, {194, 14042}, {230, 3091}, {232, 12173}, {262, 54873}, {315, 599}, {316, 2076}, {325, 14035}, {376, 31404}, {378, 9608}, {384, 7773}, {385, 33018}, {439, 34803}, {458, 26958}, {460, 17810}, {546, 3767}, {548, 31417}, {550, 31401}, {574, 1657}, {625, 32954}, {626, 11286}, {671, 7894}, {999, 9665}, {1003, 7752}, {1007, 32981}, {1015, 9655}, {1030, 37415}, {1078, 44543}, {1184, 7394}, {1194, 62976}, {1285, 3855}, {1327, 19105}, {1328, 19102}, {1384, 3851}, {1478, 16781}, {1500, 9668}, {1569, 38733}, {1571, 28146}, {1572, 18480}, {1593, 34866}, {1597, 44528}, {1598, 44524}, {1609, 11479}, {1611, 6997}, {1613, 62949}, {1691, 10358}, {1870, 9595}, {1914, 10895}, {1915, 57533}, {1968, 7507}, {1971, 64024}, {1975, 7785}, {1992, 2996}, {2023, 10722}, {2079, 7506}, {2241, 9654}, {2242, 9669}, {2275, 12943}, {2276, 12953}, {2549, 3627}, {2794, 44531}, {3054, 5056}, {3055, 3523}, {3094, 48910}, {3146, 7736}, {3172, 18386}, {3199, 18494}, {3295, 9650}, {3311, 35831}, {3312, 35830}, {3329, 33019}, {3399, 54482}, {3522, 62993}, {3526, 5206}, {3529, 31400}, {3534, 31467}, {3543, 7738}, {3544, 46453}, {3560, 44520}, {3575, 59229}, {3583, 54416}, {3585, 16502}, {3589, 32974}, {3592, 39660}, {3594, 39661}, {3618, 5395}, {3628, 21843}, {3629, 6392}, {3673, 62223}, {3734, 7776}, {3785, 8556}, {3830, 7748}, {3832, 7735}, {3839, 5306}, {3845, 5305}, {3849, 7815}, {3850, 43620}, {3853, 15048}, {3854, 37689}, {3858, 43291}, {3861, 5319}, {3934, 63931}, {3972, 7887}, {4258, 36654}, {4302, 31460}, {4385, 62224}, {5007, 61984}, {5008, 61975}, {5017, 10516}, {5024, 5073}, {5025, 10583}, {5038, 43273}, {5039, 48889}, {5041, 11648}, {5046, 5275}, {5052, 18440}, {5054, 15513}, {5055, 7749}, {5058, 13665}, {5062, 13785}, {5068, 62992}, {5072, 35007}, {5076, 7772}, {5085, 53484}, {5093, 35832}, {5116, 59411}, {5277, 17556}, {5280, 18514}, {5299, 18513}, {5304, 50689}, {5309, 14269}, {5355, 61991}, {5359, 37349}, {5477, 11482}, {5899, 9700}, {5943, 15575}, {6144, 7762}, {6179, 15031}, {6221, 31481}, {6248, 13330}, {6284, 9596}, {6410, 21737}, {6421, 35820}, {6422, 35821}, {6423, 6565}, {6424, 6564}, {6655, 11174}, {6656, 47355}, {6658, 7777}, {6680, 11318}, {6759, 9604}, {6823, 36748}, {6872, 37661}, {6913, 44517}, {6918, 44542}, {6995, 15437}, {7354, 9599}, {7387, 44521}, {7388, 8253}, {7389, 8252}, {7395, 8553}, {7398, 40326}, {7406, 37662}, {7517, 44525}, {7530, 44522}, {7578, 54683}, {7610, 7793}, {7697, 46321}, {7739, 15687}, {7750, 15271}, {7754, 7812}, {7755, 18424}, {7763, 19687}, {7765, 62008}, {7769, 33235}, {7774, 14068}, {7775, 7816}, {7783, 11163}, {7786, 33234}, {7787, 7851}, {7788, 7900}, {7789, 14033}, {7792, 14063}, {7797, 14062}, {7798, 63922}, {7800, 44678}, {7802, 11285}, {7803, 33229}, {7804, 7825}, {7805, 18546}, {7806, 32993}, {7808, 7842}, {7809, 7881}, {7833, 42849}, {7836, 14034}, {7838, 22253}, {7845, 17130}, {7846, 33219}, {7852, 33241}, {7858, 31859}, {7860, 7879}, {7862, 11288}, {7867, 31173}, {7868, 7885}, {7874, 33242}, {7883, 51186}, {7891, 19686}, {7899, 33220}, {7904, 33020}, {7911, 60855}, {7932, 14045}, {7934, 33217}, {7941, 32821}, {8352, 51185}, {8375, 8960}, {8376, 58866}, {8588, 15720}, {8589, 62100}, {8667, 20065}, {8976, 9675}, {8981, 9602}, {9112, 42991}, {9113, 42990}, {9541, 9601}, {9600, 42266}, {9603, 13352}, {9606, 33703}, {9607, 17578}, {9613, 62370}, {9619, 28160}, {9620, 22793}, {9657, 63493}, {9698, 17800}, {9745, 14002}, {9756, 36998}, {9771, 35287}, {9969, 40325}, {10296, 16308}, {10311, 37197}, {10312, 35488}, {10314, 40320}, {10323, 15109}, {10542, 53505}, {10983, 23698}, {11173, 34507}, {11184, 33007}, {11289, 43028}, {11290, 43029}, {11303, 16645}, {11304, 16644}, {12082, 50660}, {12102, 63633}, {12110, 42535}, {12362, 36751}, {12601, 35840}, {12602, 35841}, {12829, 14639}, {12902, 46301}, {12963, 42265}, {12968, 42262}, {13108, 46313}, {13111, 43183}, {13161, 16884}, {13240, 63556}, {13357, 22682}, {13567, 62950}, {14001, 32827}, {14023, 64093}, {14614, 20088}, {14712, 16921}, {14901, 38789}, {14907, 32992}, {15171, 31409}, {15338, 31497}, {15491, 32990}, {15515, 15696}, {15603, 61855}, {15655, 46219}, {16318, 63662}, {16932, 31076}, {16989, 32996}, {17004, 33024}, {17005, 33014}, {17006, 33010}, {17008, 32995}, {17129, 63951}, {17131, 63936}, {17500, 56428}, {17683, 26145}, {18840, 50993}, {18841, 18844}, {18842, 18843}, {19130, 40825}, {19780, 42095}, {19781, 42098}, {21358, 23334}, {22505, 44536}, {22728, 32452}, {23292, 37174}, {28150, 31396}, {28154, 31430}, {30496, 42299}, {31407, 49138}, {31411, 42215}, {31441, 31663}, {31443, 64005}, {31448, 65134}, {31450, 62155}, {31457, 62121}, {31463, 42258}, {31470, 62170}, {31476, 64951}, {31490, 57288}, {31652, 49137}, {32459, 32829}, {32828, 63928}, {32830, 50771}, {32962, 37688}, {32964, 37647}, {32968, 64018}, {32973, 44377}, {32987, 58446}, {32988, 44381}, {32991, 34229}, {33023, 63041}, {33192, 63101}, {33201, 37690}, {33244, 63083}, {34482, 63538}, {35480, 39575}, {35930, 44539}, {37446, 39656}, {38259, 63122}, {39563, 61993}, {39593, 62000}, {39601, 61946}, {41408, 42918}, {41409, 42919}, {41895, 63062}, {42147, 61332}, {42148, 61331}, {42157, 63199}, {42158, 63198}, {42268, 49221}, {42269, 49220}, {42270, 62202}, {42273, 62201}, {42431, 63200}, {42432, 63201}, {43619, 62036}, {44537, 63665}, {45103, 53105}, {46951, 63944}, {47322, 47339}, {48884, 64713}, {48905, 50659}, {49136, 53096}, {50687, 63024}, {51171, 54097}, {52250, 63104}, {52454, 57688}, {53093, 53499}, {53102, 60146}, {54714, 54858}, {54868, 60619}, {56395, 58733}, {59546, 62988}, {60644, 62944}, {61985, 63006}, {63004, 63537}, {63005, 63536}

X(65630) = reflection of X(i) in X(j) for these (i, j): (5013, 2548), (8556, 32983), (44519, 5013)
X(65630) = insimilicenter of Hatzipolakis-Suppa circle and half-Moses circle
X(65630) = inverse in orthosymmedial circle of X(44518)
X(65630) = pole of the tripolar of X(5395) wrt the orthic inconic
X(65630) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 7745, 6), (5, 3053, 37637), (5, 7737, 3053), (20, 3815, 15815), (20, 15815, 44541), (32, 381, 13881), (32, 39590, 381), (39, 382, 44526), (39, 62203, 382), (76, 63932, 40341), (183, 7823, 63938), (187, 1656, 44535), (316, 7770, 7784), (382, 15484, 39), (384, 7773, 7778), (546, 18907, 3767), (550, 31401, 53095), (1007, 32981, 59545), (1384, 3851, 7746), (1975, 7785, 9766), (3146, 7736, 63548), (3534, 31467, 37512), (3734, 7843, 7776), (3815, 15815, 31492), (3830, 9605, 7748), (3832, 7735, 63534), (3843, 30435, 115), (5024, 5073, 7756), (5206, 7603, 3526), (5304, 50689, 63533), (5359, 37349, 63541), (5395, 32982, 3618), (5475, 7747, 3), (6781, 31455, 3), (7736, 63548, 22332), (7745, 53418, 4), (7746, 43457, 3851), (7748, 7753, 9605), (7770, 7784, 3763), (7785, 11361, 1975), (7823, 16044, 183), (7921, 14066, 148), (14537, 39590, 32), (15484, 62203, 44526), (18584, 44535, 1656), (31401, 43618, 550), (31492, 44541, 15815), (32006, 32971, 141), (35832, 35833, 5093), (42645, 42646, 5480)

X(65631) = INSIMILICENTER OF HATZIPOLAKIS-SUPPA CIRCLE AND 1st JOHNSON-YFF CIRCLE

Barycentrics    4 a^4-a^2 b^2-3 b^4+2 a^2 b c-a^2 c^2+6 b^2 c^2-3 c^4 : :
Barycentrics    S^2-a^2*b*c-7*SB*SC : :
X(65631) = 3*X(12)-2*X(35) = 7*X(12)-6*X(3584) = 5*X(12)-2*X(4324) = 4*X(12)-3*X(4995) = 2*X(12)-X(15338) = 7*X(35)-9*X(3584) = X(35)-3*X(3585) = 5*X(35)-3*X(4324) = 8*X(35)-9*X(4995) = 4*X(35)-3*X(15338) = X(2975)-3*X(62969) = 3*X(3584)-7*X(3585) = 15*X(3584)-7*X(4324) = 8*X(3584)-7*X(4995) = 12*X(3584)-7*X(15338) = 5*X(3585)-X(4324) = 8*X(3585)-3*X(4995) = 4*X(3585)-X(15338) = 4*X(4324)-5*X(15338) = 3*X(4995)-2*X(15338) = 2*X(4999)-3*X(17577) = 2*X(5267)-3*X(17530) = 4*X(5267)-5*X(31260) = 4*X(6668)-3*X(17549) = 2*X(6842)-X(30264) = 4*X(11011)-3*X(37734) = 6*X(17530)-5*X(31260) = 4*X(25639)-3*X(31157) = 2*X(37737)-3*X(61703)

X(65631) lies on these lines: {1, 3627}, {3, 3614}, {4, 11}, {5, 7280}, {10, 63206}, {12, 30}, {20, 5432}, {36, 546}, {55, 3146}, {65, 16006}, {79, 37730}, {80, 16118}, {115, 9341}, {140, 4316}, {172, 53419}, {226, 10543}, {378, 9658}, {381, 4299}, {382, 1478}, {388, 3058}, {390, 50690}, {484, 3652}, {495, 62036}, {496, 15687}, {497, 9657}, {498, 1657}, {499, 3843}, {515, 11011}, {528, 20060}, {529, 52367}, {535, 24390}, {550, 7951}, {952, 11280}, {962, 63209}, {999, 5076}, {1056, 9670}, {1058, 62017}, {1060, 63676}, {1124, 22615}, {1155, 19925}, {1250, 42109}, {1254, 53524}, {1317, 22791}, {1319, 18483}, {1329, 17579}, {1335, 22644}, {1358, 4056}, {1376, 31295}, {1479, 3830}, {1482, 62617}, {1503, 19369}, {1539, 18968}, {1597, 18954}, {1698, 50240}, {1699, 63208}, {1727, 16138}, {1770, 18480}, {1836, 3340}, {1837, 3339}, {1870, 9628}, {2066, 42271}, {2067, 42284}, {2078, 7965}, {2098, 9812}, {2275, 53418}, {2307, 5318}, {2475, 3925}, {2477, 14157}, {2594, 52524}, {2646, 28164}, {2975, 62969}, {3023, 39838}, {3024, 13202}, {3027, 39809}, {3028, 12295}, {3035, 37256}, {3056, 51163}, {3057, 51118}, {3085, 9656}, {3091, 5204}, {3245, 61510}, {3303, 62028}, {3304, 5225}, {3336, 12019}, {3361, 51792}, {3436, 34612}, {3486, 61716}, {3529, 5217}, {3582, 14893}, {3583, 3853}, {3586, 10404}, {3600, 11238}, {3628, 59319}, {3649, 10572}, {3650, 54288}, {3671, 50862}, {3746, 62034}, {3817, 37605}, {3822, 57002}, {3839, 7288}, {3845, 5298}, {3861, 4325}, {3874, 12690}, {4188, 31235}, {4209, 31192}, {4294, 11237}, {4297, 17605}, {4302, 5073}, {4314, 63287}, {4317, 9669}, {4330, 62038}, {4333, 26446}, {4400, 63941}, {4413, 37435}, {4848, 34648}, {4857, 62013}, {4999, 17577}, {5010, 10592}, {5059, 5218}, {5066, 65141}, {5079, 64894}, {5080, 21031}, {5082, 34689}, {5086, 17768}, {5160, 9627}, {5172, 21669}, {5252, 41869}, {5254, 7296}, {5265, 61985}, {5267, 17530}, {5270, 15171}, {5281, 50692}, {5290, 37703}, {5322, 52285}, {5353, 42137}, {5357, 42136}, {5370, 37454}, {5414, 42272}, {5425, 11544}, {5441, 5719}, {5445, 61259}, {5561, 37728}, {5563, 12102}, {5657, 63215}, {5722, 44286}, {5724, 24851}, {5841, 15908}, {5893, 10535}, {5901, 36975}, {5903, 62616}, {6046, 7282}, {6057, 7270}, {6154, 12607}, {6174, 11681}, {6198, 57584}, {6253, 6256}, {6285, 51491}, {6502, 42283}, {6560, 19027}, {6561, 19028}, {6564, 9647}, {6565, 18966}, {6658, 26629}, {6668, 17549}, {6690, 15680}, {6691, 37375}, {6759, 9653}, {6767, 62024}, {6842, 30264}, {6923, 11827}, {6938, 10894}, {6971, 21154}, {6972, 38759}, {7005, 19107}, {7006, 19106}, {7051, 42102}, {7127, 42165}, {7158, 38956}, {7286, 18323}, {7355, 41362}, {7756, 31460}, {8164, 11541}, {8703, 65142}, {8976, 9663}, {8981, 9649}, {9541, 9648}, {9580, 30337}, {9596, 44526}, {9613, 12701}, {9646, 42266}, {9651, 62203}, {9652, 13352}, {9660, 35800}, {9661, 35786}, {9662, 13901}, {9667, 26883}, {9668, 62023}, {9671, 14986}, {9672, 35502}, {9780, 63212}, {9955, 21578}, {10037, 47527}, {10039, 28146}, {10056, 15684}, {10072, 38335}, {10149, 64891}, {10198, 50242}, {10385, 62032}, {10386, 35404}, {10406, 64748}, {10431, 10953}, {10526, 11826}, {10589, 50689}, {10593, 61988}, {10638, 42108}, {10721, 12903}, {10722, 13182}, {10723, 12184}, {10724, 12763}, {10733, 12373}, {10735, 12945}, {10832, 11403}, {10944, 12699}, {10957, 65120}, {10958, 20420}, {11009, 28224}, {11010, 28178}, {11114, 25466}, {11235, 20076}, {11361, 26561}, {11392, 44438}, {12047, 28160}, {12101, 65140}, {12103, 59325}, {12588, 48910}, {12647, 48661}, {12667, 36999}, {12678, 64261}, {12940, 64037}, {12950, 61721}, {13077, 52854}, {13296, 44988}, {13411, 28172}, {13851, 26955}, {13958, 42259}, {14041, 26686}, {15170, 62022}, {15228, 61524}, {15932, 16141}, {15933, 50867}, {15950, 18481}, {16616, 18838}, {17532, 24953}, {17678, 25992}, {17800, 31479}, {18393, 34773}, {18492, 24914}, {18517, 34697}, {18984, 32340}, {18995, 23259}, {18996, 23249}, {19029, 23261}, {19030, 23251}, {19297, 53421}, {19373, 42101}, {19695, 27020}, {21677, 64002}, {21842, 38034}, {21935, 64159}, {22793, 45287}, {24470, 37702}, {25639, 31157}, {26040, 50725}, {26364, 56998}, {26590, 33019}, {28150, 37568}, {28174, 37710}, {28190, 37737}, {31160, 47742}, {31162, 37738}, {31408, 52666}, {31448, 43619}, {31452, 49134}, {31472, 42263}, {31497, 44519}, {31670, 39897}, {31672, 60883}, {31730, 63213}, {31775, 50031}, {34434, 38389}, {34706, 34749}, {34753, 37718}, {36002, 37564}, {36990, 39873}, {37567, 59387}, {37572, 38042}, {37709, 50865}, {37719, 62041}, {37720, 62006}, {39891, 51212}, {40267, 40271}, {42104, 54436}, {42105, 54435}, {42160, 54402}, {42161, 54403}, {42225, 65147}, {42226, 65148}, {42264, 44622}, {44226, 54428}, {49136, 64951}, {50038, 50239}, {52835, 60919}, {58887, 61261}, {61598, 62316}

X(65631) = reflection of X(i) in X(j) for these (i, j): (12, 3585), (15338, 12), (30264, 6842)
X(65631) = insimilicenter of Hatzipolakis-Suppa circle and 1st Johnson-Yff circle
X(65631) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 3614, 5326), (4, 4293, 10896), (4, 7354, 11), (4, 7681, 59390), (4, 12943, 7354), (5, 7280, 7294), (5, 10483, 15326), (12, 15338, 4995), (20, 10588, 63756), (20, 10895, 5432), (36, 546, 7173), (56, 10896, 47743), (381, 4299, 5433), (382, 1478, 6284), (388, 3543, 12953), (388, 12953, 3058), (495, 62036, 65134), (495, 65134, 63273), (496, 15687, 18514), (550, 7951, 52793), (1478, 6284, 15888), (1479, 9655, 5434), (1770, 18480, 40663), (1836, 5691, 10950), (1837, 9579, 11246), (2475, 57288, 3925), (3146, 5229, 55), (3529, 10590, 5217), (3583, 18990, 37722), (3830, 9655, 1479), (3853, 18990, 3583), (4293, 47743, 56), (5073, 9654, 4302), (5267, 17530, 31260), (6564, 9647, 18965), (7294, 15326, 7280), (9541, 13897, 9648), (10483, 18513, 5), (10588, 63756, 5432), (10592, 15704, 5010), (10895, 63756, 10588), (13901, 42258, 9662)

X(65632) = EXSIMILICENTER OF HATZIPOLAKIS-SUPPA CIRCLE AND 2nd JOHNSON-YFF CIRCLE

Barycentrics    4 a^4 - a^2 b^2 - 3 b^4 - 2 a^2 b c - a^2 c^2 + 6 b^2 c^2 - 3 c^4 : :
Barycentrics    S^2+a^2*b*c-7*SB*SC : :
X(65632) = 3*X(11)-2*X(36) = 7*X(11)-6*X(3582) = 5*X(11)-2*X(4316) = 4*X(11)-3*X(5298) = 5*X(11)-4*X(15325) = 2*X(11)-X(15326) = 5*X(11)-6*X(65140) = 7*X(36)-9*X(3582) = X(36)-3*X(3583) = 5*X(36)-3*X(4316) = 8*X(36)-9*X(5298) = 5*X(36)-6*X(15325) = 4*X(36)-3*X(15326) = 5*X(36)-9*X(65140) = 3*X(1317)-4*X(5048) = 2*X(1387)-X(36975) = 2*X(1532)-3*X(59390) = 2*X(3035)-3*X(37375) = 3*X(3582)-7*X(3583) = 15*X(3582)-7*X(4316) = 8*X(3582)-7*X(5298) = 12*X(3582)-7*X(15326) = 5*X(3582)-7*X(65140) = 5*X(3583)-X(4316) = 8*X(3583)-3*X(5298) = 5*X(3583)-2*X(15325) = 4*X(3583)-X(15326) = 5*X(3583)-3*X(65140) = 4*X(3814)-3*X(6174) = 4*X(4316)-5*X(15326) = X(4316)-3*X(65140) = 2*X(5123)-X(63145) = 2*X(5176)-X(13996) = 2*X(5183)-3*X(40663) = 3*X(5298)-2*X(15326) = 5*X(5298)-8*X(65140) = 4*X(6667)-3*X(13587) = 8*X(6681)-9*X(59376) = 2*X(6882)-X(24466) = 2*X(7743)-X(21578) = 3*X(10707)-X(20067) = 3*X(10738)-X(62318) = X(15228)-3*X(37718) = 8*X(15325)-5*X(15326) = 2*X(15325)-3*X(65140) = 6*X(17533)-5*X(31235) = 4*X(24042)-3*X(59390) = 2*X(25405)-3*X(30384) = 5*X(31272)-3*X(36004)

X(65632) lies on these lines: {1, 3627}, {3, 7173}, {4, 12}, {5, 5010}, {8, 4942}, {11, 30}, {20, 5433}, {35, 546}, {56, 3146}, {65, 9844}, {79, 12433}, {80, 28174}, {140, 4324}, {149, 529}, {165, 51792}, {202, 19106}, {203, 19107}, {215, 14157}, {377, 8167}, {378, 9673}, {381, 4302}, {382, 999}, {388, 8162}, {390, 11237}, {484, 12019}, {495, 15687}, {496, 10483}, {497, 3543}, {498, 3843}, {499, 1657}, {515, 1317}, {516, 5183}, {517, 33519}, {528, 5080}, {550, 7741}, {553, 50869}, {590, 31500}, {758, 12690}, {942, 34502}, {950, 3649}, {952, 64896}, {1056, 62017}, {1058, 9657}, {1062, 63669}, {1124, 22644}, {1155, 28150}, {1250, 42101}, {1319, 28164}, {1335, 22615}, {1358, 4872}, {1376, 44847}, {1387, 28190}, {1469, 51163}, {1478, 3058}, {1503, 8540}, {1532, 24042}, {1539, 12896}, {1597, 10833}, {1621, 62969}, {1698, 63214}, {1699, 13384}, {1737, 28146}, {1834, 2308}, {1836, 3586}, {1837, 2093}, {1845, 43911}, {1870, 9629}, {1878, 44670}, {1914, 53419}, {2066, 42284}, {2067, 42271}, {2099, 9812}, {2276, 53418}, {2307, 42164}, {2475, 5284}, {2646, 18483}, {2654, 63295}, {2886, 11114}, {3023, 39809}, {3024, 12295}, {3027, 39838}, {3028, 13202}, {3035, 37375}, {3057, 31673}, {3086, 9671}, {3090, 63756}, {3091, 5217}, {3245, 11545}, {3295, 5076}, {3303, 5229}, {3304, 62028}, {3324, 38956}, {3421, 34720}, {3434, 34606}, {3436, 8168}, {3474, 61717}, {3485, 10248}, {3488, 61716}, {3529, 5204}, {3530, 65141}, {3584, 14893}, {3585, 3853}, {3600, 50690}, {3624, 50240}, {3628, 59325}, {3746, 12102}, {3814, 6174}, {3816, 17579}, {3817, 37600}, {3839, 5218}, {3845, 4995}, {3847, 4188}, {3861, 4330}, {3911, 28158}, {3925, 11113}, {4038, 49745}, {4081, 5081}, {4189, 31260}, {4293, 11238}, {4299, 5073}, {4304, 17605}, {4309, 9654}, {4325, 62038}, {4342, 50862}, {4396, 63941}, {4680, 6057}, {4845, 10725}, {4857, 18990}, {4972, 17537}, {4999, 15680}, {5057, 44669}, {5059, 7288}, {5123, 63145}, {5160, 18323}, {5172, 36002}, {5176, 13996}, {5180, 5855}, {5252, 9580}, {5254, 5332}, {5265, 50692}, {5270, 15172}, {5281, 61985}, {5310, 52285}, {5321, 7127}, {5353, 42136}, {5357, 42137}, {5414, 42283}, {5441, 37737}, {5444, 61269}, {5561, 15935}, {5563, 62034}, {5691, 7962}, {5719, 61703}, {5722, 11246}, {5724, 33095}, {5727, 50865}, {5787, 52860}, {5840, 35000}, {5841, 10738}, {5844, 37006}, {5893, 26888}, {5919, 51783}, {6154, 17757}, {6285, 41362}, {6502, 42272}, {6560, 19029}, {6561, 19030}, {6564, 9660}, {6565, 13958}, {6658, 26686}, {6667, 13587}, {6681, 59376}, {6690, 17577}, {6691, 37256}, {6759, 9666}, {6836, 64725}, {6840, 10724}, {6872, 24953}, {6882, 24466}, {6917, 7958}, {6928, 11826}, {6934, 10893}, {6980, 21155}, {7051, 42108}, {7280, 10593}, {7286, 62288}, {7302, 37454}, {7355, 51491}, {7373, 62024}, {7491, 15908}, {7526, 65122}, {7688, 31789}, {7743, 21578}, {8976, 9648}, {8981, 9662}, {9541, 9663}, {9578, 53052}, {9579, 10980}, {9581, 53056}, {9589, 41687}, {9599, 44526}, {9646, 35786}, {9647, 35802}, {9649, 18965}, {9652, 26883}, {9655, 62023}, {9659, 35502}, {9661, 42266}, {9664, 62203}, {9667, 13352}, {9802, 32426}, {10046, 47527}, {10056, 38335}, {10058, 62359}, {10072, 15684}, {10151, 52427}, {10175, 63211}, {10200, 56998}, {10385, 62007}, {10386, 37719}, {10404, 44841}, {10525, 11827}, {10526, 44455}, {10543, 12047}, {10572, 22793}, {10573, 48661}, {10588, 50689}, {10592, 61988}, {10609, 11813}, {10624, 45081}, {10638, 42102}, {10707, 20067}, {10721, 12904}, {10722, 13183}, {10723, 12185}, {10728, 13274}, {10733, 12374}, {10735, 12955}, {10741, 34931}, {10831, 11403}, {10949, 48482}, {10950, 12699}, {10956, 41698}, {11010, 18357}, {11111, 31245}, {11236, 20075}, {11361, 26590}, {11374, 44286}, {11375, 53054}, {11393, 44438}, {11541, 47743}, {11680, 31157}, {12103, 59319}, {12589, 48910}, {12679, 64261}, {12688, 45288}, {12940, 61721}, {12950, 64037}, {13079, 32340}, {13273, 53055}, {13297, 44988}, {13407, 31795}, {13851, 26956}, {14041, 26629}, {14269, 31479}, {14794, 31649}, {14986, 50691}, {15170, 62015}, {15228, 28182}, {15726, 18838}, {16118, 24470}, {17533, 31235}, {17606, 31730}, {17784, 31141}, {18499, 18516}, {18782, 28459}, {18966, 42259}, {18982, 52854}, {19027, 23261}, {19028, 23251}, {19037, 23259}, {19038, 23249}, {19373, 42109}, {19695, 26959}, {19925, 37568}, {20066, 64123}, {21669, 37564}, {22791, 37734}, {24914, 63207}, {25405, 28160}, {25524, 31295}, {25542, 50238}, {25639, 57002}, {26363, 50242}, {26561, 33019}, {27639, 37191}, {28172, 44675}, {28212, 41684}, {28224, 62617}, {28228, 36920}, {31162, 37740}, {31221, 37416}, {31272, 36004}, {31452, 61990}, {31460, 39590}, {31670, 39873}, {31672, 60919}, {33697, 45287}, {34699, 34739}, {36005, 45310}, {36990, 39897}, {37291, 52795}, {37411, 62333}, {37525, 38034}, {37616, 61272}, {37720, 62041}, {38950, 39148}, {39751, 62493}, {39892, 51212}, {42104, 54435}, {42105, 54436}, {42160, 54403}, {42161, 54402}, {42263, 44623}, {42264, 44624}, {51421, 53529}, {52367, 57288}, {52835, 60883}, {59316, 61261}, {61984, 64951}, {62143, 64894}, {63676, 64349}, {64337, 64804}

X(65632) = midpoint of X(6840) and X(10724)
X(65632) = reflection of X(i) in X(j) for these (i, j): (11, 3583), (484, 12019), (1532, 24042), (3245, 11545), (4316, 15325), (6154, 17757), (10609, 11813), (13996, 5176), (15326, 11), (21578, 7743), (24466, 6882), (36005, 45310), (36975, 1387), (62617, 63210), (63145, 5123)
X(65632) = exsimilicenter of Hatzipolakis-Suppa circle and 2nd Johnson-Yff circle
X(65632) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3, 7173, 7294), (4, 4294, 10895), (4, 6284, 12), (4, 12953, 6284), (5, 5010, 5326), (5, 15338, 52793), (5, 65134, 15338), (11, 15326, 5298), (12, 6284, 63273), (20, 10896, 5433), (35, 546, 3614), (55, 10895, 8164), (381, 4302, 5432), (382, 1479, 7354), (495, 15687, 18513), (496, 62036, 10483), (497, 3543, 12943), (497, 12943, 5434), (1478, 9668, 3058), (1479, 7354, 37722), (1532, 24042, 59390), (1870, 9629, 10149), (3146, 5225, 56), (3529, 10591, 5204), (3583, 4316, 65140), (3585, 15171, 15888), (3830, 9668, 1478), (3853, 15171, 3585), (4294, 8164, 55), (4316, 65140, 15325), (5010, 5326, 52793), (5073, 9669, 4299), (5326, 15338, 5010), (5691, 12701, 10944), (6564, 9660, 13901), (6928, 11826, 50031), (9541, 13898, 9663), (10593, 15704, 7280), (15325, 65140, 11), (18499, 18516, 34746), (18514, 65134, 5), (18965, 42258, 9649)

X(65633) = EXSIMILICENTER OF HATZIPOLAKIS-SUPPA CIRCLE AND MOSES CIRCLE

Barycentrics    3 a^4 - 2 a^2 b^2 - 2 b^4 - 2 a^2 c^2 + 4 b^2 c^2 - 2 c^4 : :
Barycentrics    4*S^2+SB^2-10*SB*SC+SC^2 : :
X(65633) = 3*X(32)-4*X(5254) = 7*X(32)-8*X(5305) = 5*X(32)-6*X(5309) = 9*X(32)-10*X(5346) = 2*X(32)-3*X(11648) = X(315)-3*X(33192) = 2*X(626)-3*X(33017) = 3*X(1003)-4*X(7861) = 2*X(1975)-3*X(7818) = 3*X(1975)-4*X(7895) = 7*X(5254)-6*X(5305) = 11*X(5254)-9*X(5306) = 10*X(5254)-9*X(5309) = 6*X(5254)-5*X(5346) = 2*X(5254)-3*X(7748) = 8*X(5254)-9*X(11648) = 4*X(5305)-7*X(7748) = 3*X(5309)-5*X(7748) = 4*X(5309)-5*X(11648) = 5*X(5346)-9*X(7748) = 4*X(6680)-3*X(33007) = 4*X(7748)-3*X(11648) = 2*X(7816)-3*X(7841) = 4*X(7816)-5*X(7867) = 10*X(7816)-9*X(11164) = 3*X(7818)-4*X(7842) = 9*X(7818)-8*X(7895) = 6*X(7841)-5*X(7867) = 5*X(7841)-3*X(11164) = 3*X(7842)-2*X(7895) = 2*X(20065)-3*X(41748)

X(65633) lies on these lines: {2, 55808}, {3, 39565}, {4, 574}, {5, 15515}, {6, 5073}, {20, 115}, {30, 32}, {39, 382}, {76, 33256}, {83, 54737}, {99, 7825}, {140, 18424}, {148, 7751}, {183, 63922}, {187, 1657}, {194, 63931}, {230, 15704}, {232, 35490}, {315, 543}, {316, 7781}, {376, 7749}, {378, 9700}, {381, 37512}, {384, 7872}, {546, 31455}, {548, 63534}, {550, 7746}, {577, 18563}, {620, 14063}, {626, 33017}, {671, 7793}, {1003, 7861}, {1015, 12953}, {1078, 18546}, {1370, 34481}, {1384, 49139}, {1500, 12943}, {1504, 35820}, {1505, 35821}, {1569, 10722}, {1656, 8589}, {1691, 48896}, {1692, 48905}, {1870, 9635}, {1975, 7818}, {2076, 48879}, {2241, 65134}, {2242, 10483}, {2548, 3543}, {2549, 3146}, {2937, 34866}, {3053, 17800}, {3054, 33923}, {3055, 3858}, {3070, 62241}, {3071, 62242}, {3094, 48884}, {3096, 3734}, {3199, 44438}, {3522, 43620}, {3526, 39601}, {3529, 3767}, {3534, 13881}, {3552, 7844}, {3585, 31451}, {3627, 5475}, {3788, 33229}, {3815, 3853}, {3830, 5013}, {3843, 7603}, {3849, 7754}, {3851, 53095}, {3861, 31457}, {3934, 33234}, {3972, 7902}, {4045, 14035}, {5007, 49136}, {5008, 49133}, {5023, 15681}, {5024, 62023}, {5028, 29012}, {5033, 48898}, {5034, 48901}, {5041, 62040}, {5052, 48910}, {5058, 42263}, {5059, 7755}, {5062, 42264}, {5076, 31652}, {5107, 64080}, {5171, 6321}, {5210, 62131}, {5286, 43618}, {5319, 50692}, {5355, 11541}, {5461, 33208}, {5471, 42160}, {5472, 42161}, {5585, 62107}, {6284, 9651}, {6292, 32986}, {6564, 9674}, {6658, 7790}, {6680, 33007}, {6722, 32964}, {6759, 9696}, {7354, 9664}, {7519, 59768}, {7735, 49138}, {7736, 62028}, {7737, 7765}, {7738, 7753}, {7739, 62042}, {7745, 62036}, {7750, 17131}, {7761, 17130}, {7763, 33279}, {7769, 14062}, {7771, 33267}, {7775, 7783}, {7782, 7862}, {7786, 14042}, {7794, 32815}, {7795, 33238}, {7796, 20094}, {7798, 7823}, {7800, 32826}, {7803, 33280}, {7808, 7847}, {7812, 40246}, {7813, 32006}, {7815, 7833}, {7816, 7841}, {7820, 32974}, {7822, 8357}, {7826, 64018}, {7828, 33257}, {7830, 11185}, {7834, 19687}, {7843, 31859}, {7846, 19686}, {7857, 33265}, {7859, 14034}, {7860, 7916}, {7865, 7910}, {7869, 7911}, {7885, 7908}, {7886, 33235}, {7887, 32456}, {7889, 14033}, {7896, 7898}, {7914, 7924}, {7940, 14045}, {8352, 34504}, {8353, 59635}, {8721, 39838}, {8981, 9684}, {9300, 35404}, {9541, 9685}, {9601, 45384}, {9605, 14537}, {9607, 62038}, {9675, 42266}, {9697, 13352}, {9698, 17578}, {9821, 38733}, {10311, 34797}, {10316, 18562}, {10721, 41367}, {11057, 17129}, {11614, 61832}, {11646, 52987}, {11742, 44535}, {12083, 44528}, {12173, 33843}, {12815, 21735}, {13509, 40242}, {14061, 33014}, {14075, 62047}, {14130, 44521}, {14907, 33271}, {14971, 35287}, {15031, 33004}, {15048, 62041}, {15301, 32821}, {15482, 16044}, {15602, 18584}, {15655, 62142}, {15686, 63543}, {15696, 37637}, {16589, 50239}, {17538, 21843}, {18492, 31422}, {18503, 46283}, {18581, 36958}, {18582, 36959}, {18859, 44523}, {18907, 62044}, {20065, 41748}, {21312, 44527}, {21659, 39913}, {22332, 62024}, {23004, 47066}, {23005, 47068}, {23251, 62206}, {23261, 62205}, {23698, 30270}, {28080, 35076}, {30435, 49134}, {31152, 40350}, {31274, 32972}, {31400, 50688}, {31404, 50687}, {31411, 52667}, {31467, 38335}, {31481, 42284}, {31489, 61984}, {32452, 36997}, {32832, 33253}, {33227, 44381}, {35007, 49137}, {35955, 47617}, {36523, 52943}, {38741, 62356}, {39575, 64890}, {39593, 43136}, {39764, 46264}, {41134, 45017}, {42429, 62199}, {42430, 62200}, {42433, 62197}, {42434, 62198}, {42988, 63196}, {42989, 63197}, {43291, 62144}, {44938, 63908}, {47286, 63935}, {48880, 53475}, {48895, 50659}, {48943, 64713}, {53418, 62026}, {62127, 62992}

X(65633) = reflection of X(i) in X(j) for these (i, j): (32, 7748), (1975, 7842)
X(65633) = exsimilicenter of Hatzipolakis-Suppa circle and Moses circle
X(65633) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 7756, 574), (4, 31401, 43457), (4, 43619, 7756), (20, 115, 5206), (32, 7748, 11648), (39, 382, 62203), (99, 7825, 7888), (99, 33019, 7825), (148, 7802, 7751), (148, 19691, 7802), (316, 7781, 7903), (381, 44519, 37512), (382, 44526, 39), (384, 7872, 7913), (550, 7746, 8588), (550, 53419, 7746), (1657, 44518, 187), (1975, 7842, 7818), (2549, 3146, 7747), (2549, 7747, 7772), (3529, 3767, 6781), (3534, 13881, 15513), (3627, 63548, 5475), (3734, 6655, 7935), (3830, 5013, 39590), (3843, 15815, 7603), (5286, 49135, 43618), (5475, 63548, 53096), (7761, 32819, 17130), (7782, 14041, 7862), (7816, 7841, 7867), (7847, 11361, 7808), (7910, 17128, 7865), (11185, 32997, 7830), (11742, 44535, 62100), (15513, 39563, 13881), (17538, 63533, 21843), (19695, 32819, 7761), (32826, 33272, 7800)

X(65634) = (name pending)

Barycentrics    (b^2 - c^2)*(-a^2 + 2*b^2 + 2*c^2)*(17*a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 - 6*b^2*c^2 + c^4) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 7075.

X(65634) lies on these lines: { }

X(65634) = crosspoint of X(9146) and X(43956) [Peter Moses]




leftri   P-antipodes of points on the circumcircle: X(65635) - X(63650)  rightri

Contributed by Clark Kimberling and Peter Moses, October, 2024.

Suppose that P is a point on the circumcircle of a triangle ABC, and that U is the isogonal conjugate of P, so that U is on the line at infinity. The U-antipode of P is the point, other than P, in which the line PU meets the circumcircle. If P = p : q : r (on the circumcircle), then a 1st barycentric for the U-antipode of P is given by:

a^2*q*r/(a^2*q*(q - r)*r - p*(q + r)*(c^2*q - b^2*r)) : : .

this being the Collings transform of the isogonal conjugate of P.

The appearance of (i,j,k) in the following list means that X(k) = X(j)-antipode of X(i) and k < 65000 :

(74,30,476), (98,511,805), (99,512,805), (100,513,901), (101,514,927), (102,515,1309), (103,516,927), (104,517,901), (105,518,6078), (106,519,6079), (107,520,6080), (108,521,6081), (109,522,1309), (110,523,476), (111,524,6082), (112,525,2867), (476,526,16170), (477,5663,16170), (691,690,20404), (759,758,6083), (842,542,20404), (930,1510,54049), (1113,2574,110), (1114,2575,110), (1141,1154,54049), (1292,3309,6078), (1293,3667,6079), (1294,6000,6080), (1295,6001,6081), (1296,1499,6082), (1297,1503,2867), (1304,9033,53881), (1379,3413,99), (1380,3414,99), (1381,3307,100), (1382,3308,100), (2222,3738,35011), (2693,2777,53881), (2716,2800,35011), (6011,6003,6083)

The appearance of (i,j,k) in the following list means that X(k) = X(j)-antipode of X(i) and k > 65000 :

(741,740,65635), (813,812,65636), (840,528,65637), (843,543,65638), (901,900,65639), (925, 924, 65640), (929,928,65641), (934,3900,65642), (935,9517,65643), (1290,8674,65644), (1291,45147,65645), (1308,3887,65646), (2700,2784,65647), (2710,2794,65648), (2718,2802,65649), (8686,3880,65650)

underbar



X(65635) = TRILINEAR POLE OF X(6)X(645)

Barycentrics    (a^2 - b^2)*b*(a^2 - c^2)*c*(-2*a^2*b^2 + a^3*c - a^2*b*c - a*b^2*c + b^3*c + a^2*c^2 + b^2*c^2)*(a^3*b + a^2*b^2 - a^2*b*c - 2*a^2*c^2 - a*b*c^2 + b^2*c^2 + b*c^3) : :

X(65635) lies on the circumcircle and these lines: {105, 14195}, {106, 5209}, {109, 4600}, {110, 6064}, {668, 29151}, {719, 34996}, {740, 741}, {874, 36066}, {901, 17935}, {2703, 55243}, {6002, 6010}

X(65635) = Collings transform of X(i) for these i: {740, 6002}
X(65635) = X(2238)-cross conjugate of X(34537)
X(65635) = X(35104)-isoconjugate of X(51641)
X(65635) = cevapoint of X(i) and X(j) for these (i,j): {99, 874}, {740, 6002}
X(65635) = trilinear pole of line {6, 645}
X(65635) = barycentric product X(i)*X(j) for these {i,j}: {645, 35159}, {35108, 62534}
X(65635) = barycentric quotient X(i)/X(j) for these {i,j}: {645, 35104}, {874, 46842}, {35108, 7180}, {35159, 7178}

X(65636) = TRILINEAR POLE OF X(6)X(666)

Barycentrics    (a - b)*b*(a - c)*c*(a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(-2*a^2*b^2 + a^3*c + a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 - b^2*c^2)*(a^3*b - a^2*b^2 + a^2*b*c - 2*a^2*c^2 + a*b*c^2 - b^2*c^2 + b*c^3) : :

X(65636) lies on the circumcircle and these lines: {100, 27855}, {101, 4375}, {109, 39293}, {739, 63236}, {812, 813}, {840, 53219}, {874, 65363}, {919, 57536}, {12032, 28850}, {30664, 63222}, {46802, 59049}

X(65636) = Collings transform of X(i) for these i: {812, 28850}
X(65636) = X(43063)-isoconjugate of X(46388)
X(65636) = cevapoint of X(812) and X(28850)
X(65636) = trilinear pole of line {6, 666}
X(65636) = barycentric product X(i)*X(j) for these {i,j}: {666, 53219}, {14665, 36803}
X(65636) = barycentric quotient X(i)/X(j) for these {i,j}: {666, 14839}, {927, 43063}, {14665, 665}, {46802, 3126}, {53219, 918}

X(65637) = TRILINEAR POLE OF X(6)X(35113)

Barycentrics    (a - b)*(a - c)*(a^2 + a*b + b^2 - 2*a*c - 2*b*c + c^2)*(a^2 - 2*a*b + b^2 + a*c - 2*b*c + c^2)*(a^4 - 3*a^3*b + 4*a^2*b^2 - 3*a*b^3 + b^4 - a^3*c + 2*a^2*b*c + 2*a*b^2*c - b^3*c - a^2*c^2 - 2*a*b*c^2 - b^2*c^2 + a*c^3 + b*c^3)*(a^4 - a^3*b - a^2*b^2 + a*b^3 - 3*a^3*c + 2*a^2*b*c - 2*a*b^2*c + b^3*c + 4*a^2*c^2 + 2*a*b*c^2 - b^2*c^2 - 3*a*c^3 - b*c^3 + c^4) : :

X(65637) lies on the circumcircle and these lines: {2, 35585}, {106, 34578}, {528, 840}, {900, 6078}, {901, 6084}, {952, 28914}, {953, 28915}, {1477, 3254}, {2742, 2826}, {6551, 53337}, {59021, 63745}

X(65637) = anticomplement of X(35585)
X(65637) = Collings transform of X(i) for these i: {528, 2826}
X(65637) = cevapoint of X(528) and X(2826)
X(65637) = trilinear pole of line {6, 35113}

X(65638) = TRILINEAR POLE OF X(6)X(35087)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + 3*a^3*b + 5*a^2*b^2 + 3*a*b^3 + b^4 - 4*a^2*c^2 - 6*a*b*c^2 - 4*b^2*c^2 + c^4)*(a^4 - 3*a^3*b + 5*a^2*b^2 - 3*a*b^3 + b^4 - 4*a^2*c^2 + 6*a*b*c^2 - 4*b^2*c^2 + c^4)*(a^4 - 4*a^2*b^2 + b^4 - 3*a^3*c + 6*a*b^2*c + 5*a^2*c^2 - 4*b^2*c^2 - 3*a*c^3 + c^4)*(a^4 - 4*a^2*b^2 + b^4 + 3*a^3*c - 6*a*b^2*c + 5*a^2*c^2 - 4*b^2*c^2 + 3*a*c^3 + c^4) : :

X(65638) lies on the circumcircle and these lines: {2, 35586}, {543, 843}, {804, 6082}, {805, 6088}, {2698, 33962}, {2709, 2793}, {2782, 6093}, {34760, 53690}, {53882, 62508}

X(65638) = anticomplement of X(35586)
X(65638) = Thomson-isogonal conjugate of X(53798)
X(65638) = Collings transform of X(i) for these i: {543, 2793}
X(65638) = cevapoint of X(543) and X(2793)
X(65638) = trilinear pole of line {6, 35087}

X(65639) = TRILINEAR POLE OF X(6)X(34232)

Barycentrics    (a - b)*(a - c)*(a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^3 - 2*a^2*b - 2*a*b^2 + b^3 + 4*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - 2*a^2*c + 4*a*b*c - b^2*c - 2*a*c^2 + c^3) : :

X(65639) lies on the circumcircle and these lines: {2, 35587}, {55, 44052}, {74, 56756}, {80, 106}, {101, 6544}, {105, 14204}, {109, 15343}, {840, 37222}, {900, 901}, {952, 953}, {2222, 46649}, {2757, 17100}, {6548, 39414}, {6551, 17780}, {56416, 56644}

X(65639) = anticomplement of X(35587)
X(65639) = reflection of X(51562) in line X(1)X(5)
X(65639) = Thomson-isogonal conjugate of X(53800)
X(65639) = Collings transform of X(i) for these i: {900, 952, 56416}
X(65639) = X(i)-cross conjugate of X(j) for these (i,j): {2265, 23592}, {35013, 56644}
X(65639) = X(i)-isoconjugate of X(j) for these (i,j): {36, 24457}, {654, 43048}, {1769, 56751}, {2802, 53314}, {3025, 37630}, {21758, 30566}, {53535, 61476}
X(65639) = X(15898)-Dao conjugate of X(24457)
X(65639) = cevapoint of X(i) and X(j) for these (i,j): {900, 952}, {35013, 56416}
X(65639) = trilinear pole of line {6, 34232}
X(65639) = barycentric product X(i)*X(j) for these {i,j}: {2718, 36804}, {37222, 51562}
X(65639) = barycentric quotient X(i)/X(j) for these {i,j}: {2161, 24457}, {2222, 43048}, {2718, 3960}, {32641, 56751}, {37222, 4453}, {51562, 30566}

X(65640) = TRILINEAR POLE OF X(6)X(39013)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(-(a^4*b^2) + 2*a^2*b^4 - b^6 + a^5*c - a*b^4*c + 2*b^4*c^2 - 2*a^3*c^3 - b^2*c^4 + a*c^5)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^5*c - a*b^4*c - 2*b^4*c^2 - 2*a^3*c^3 + b^2*c^4 + a*c^5)*(a^5*b - 2*a^3*b^3 + a*b^5 - a^4*c^2 - b^4*c^2 + 2*a^2*c^4 - a*b*c^4 + 2*b^2*c^4 - c^6)*(a^5*b - 2*a^3*b^3 + a*b^5 + a^4*c^2 + b^4*c^2 - 2*a^2*c^4 - a*b*c^4 - 2*b^2*c^4 + c^6) : :

X(65640) lies on the circumcircle and these lines: {2, 35588}, {112, 58760}, {477, 11412}, {924, 925}, {1300, 13754}, {7689, 32710}, {12111, 53924}, {19167, 23233}

X(65640) = anticomplement of X(35588)
X(65640) = Thomson-isogonal conjugate of X(53802)
X(65640) = Collings transform of X(i) for these i: {924, 5449, 13754, 62335, 64689}
X(65640) = X(13557)-isoconjugate of X(24006)
X(65640) = cevapoint of X(i) and X(j) for these (i,j): {512, 62335}, {520, 64689}, {924, 13754}, {5449, 55121}
X(65640) = trilinear pole of line {6, 39013}
X(65640) = barycentric quotient X(32661)/X(13557)

X(65641) = TRILINEAR POLE OF X(6)X(39017)

Barycentrics    a^2*(a - b)*(a - c)*(a + b - c)*(a - b + c)*(a^2*b^2 - b^4 + a^3*c - a*b^2*c - 2*a^2*c^2 + b^2*c^2 + a*c^3)*(a^3*b - 2*a^2*b^2 + a*b^3 + a^2*c^2 - a*b*c^2 + b^2*c^2 - c^4)*(-(a^4*b^2) + a^3*b^3 + a^2*b^4 - a*b^5 + a^5*c - a^4*b*c + a^3*b^2*c - 2*a^2*b^3*c + 2*a*b^4*c - b^5*c + a^3*b*c^2 - 2*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + a^2*b*c^3 + a*b^2*c^3 + b^3*c^3 - a*b*c^4 - b^2*c^4 + a*c^5)*(a^5*b - 2*a^3*b^3 + a*b^5 - a^4*b*c + a^3*b^2*c + a^2*b^3*c - a*b^4*c - a^4*c^2 + a^3*b*c^2 + a*b^3*c^2 - b^4*c^2 + a^3*c^3 - 2*a^2*b*c^3 - 2*a*b^2*c^3 + b^3*c^3 + a^2*c^4 + 2*a*b*c^4 + b^2*c^4 - a*c^5 - b*c^5) : :

X(65641) lies on the circumcircle and these lines: {2, 35590}, {104, 61427}, {105, 296}, {926, 1309}, {927, 8677}, {928, 929}, {2720, 23225}, {2723, 2807}, {2724, 2818}, {2734, 2808}

X(65641) = anticomplement of X(35590)
X(65641) = Collings transform of X(i) for these i: {928, 2807}
X(65641) = cevapoint of X(928) and X(2807)
X(65641) = trilinear pole of line {6, 39017}

X(65642) = TRILINEAR POLE OF X(6)X(2338)

Barycentrics    a^2*(a - b)*(a - c)*(a^2 - 2*a*b + b^2 + 2*a*c + 2*b*c - 3*c^2)*(a^2 + 2*a*b - 3*b^2 - 2*a*c + 2*b*c + c^2)*(a^3 - a^2*b - a*b^2 + b^3 + a*c^2 + b*c^2 - 2*c^3)*(a^3 + a*b^2 - 2*b^3 - a^2*c + b^2*c - a*c^2 + c^3) : :

X(65642) lies on the circumcircle and these lines: {2, 35593}, {105, 56718}, {108, 61240}, {109, 677}, {934, 3900}, {971, 972}, {2371, 32625}, {2717, 3062}, {2723, 63165}, {2724, 10405}, {11051, 43079}, {15731, 36101}, {26716, 36039}, {62725, 65545}

X(65642) = anticomplement of X(35593)
X(65642) = Thomson-isogonal conjugate of X(53804)
X(65642) = Collings transform of X(i) for these i: {971, 3900}
X(65642) = X(657)-cross conjugate of X(59195)
X(65642) = X(i)-isoconjugate of X(j) for these (i,j): {165, 676}, {910, 7658}, {9533, 46392}
X(65642) = cevapoint of X(971) and X(3900)
X(65642) = trilinear pole of line {6, 2338}
X(65642) = barycentric product X(i)*X(j) for these {i,j}: {346, 65538}, {677, 10405}, {2338, 53640}, {11051, 57928}, {36039, 44186}
X(65642) = barycentric quotient X(i)/X(j) for these {i,j}: {103, 7658}, {677, 144}, {11051, 676}, {24016, 9533}, {32642, 3207}, {32668, 17106}, {36039, 165}, {40116, 63965}, {53622, 43035}, {65245, 50561}, {65538, 279}

X(65643) = TRILINEAR POLE OF X(6)X(55048)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(-(a^6*b^2) + a^4*b^4 + a^2*b^6 - b^8 + a^7*c - a^3*b^4*c - a^2*b^4*c^2 + b^6*c^2 - a^5*c^3 + 2*a^3*b^2*c^3 - a*b^4*c^3 + b^4*c^4 - a^3*c^5 - b^2*c^6 + a*c^7)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^7*c - a^3*b^4*c + a^2*b^4*c^2 - b^6*c^2 - a^5*c^3 + 2*a^3*b^2*c^3 - a*b^4*c^3 - b^4*c^4 - a^3*c^5 + b^2*c^6 + a*c^7)*(a^7*b - a^5*b^3 - a^3*b^5 + a*b^7 - a^6*c^2 + 2*a^3*b^3*c^2 - b^6*c^2 + a^4*c^4 - a^3*b*c^4 - a^2*b^2*c^4 - a*b^3*c^4 + b^4*c^4 + a^2*c^6 + b^2*c^6 - c^8)*(a^7*b - a^5*b^3 - a^3*b^5 + a*b^7 + a^6*c^2 + 2*a^3*b^3*c^2 + b^6*c^2 - a^4*c^4 - a^3*b*c^4 + a^2*b^2*c^4 - a*b^3*c^4 - b^4*c^4 - a^2*c^6 - b^2*c^6 + c^8) : :

X(65643) lies on the circumcircle and these lines: {2, 35594}, {112, 57203}, {476, 2881}, {477, 53795}, {526, 2867}, {935, 9517}, {2697, 2781}, {5663, 53912}

X(65643) = anticomplement of X(35594)
X(65643) = Collings transform of X(i) for these i: {2781, 9517}
X(65643) = cevapoint of X(2781) and X(9517)
X(65643) = trilinear pole of line {6, 55048}

X(65644) = TRILINEAR POLE OF X(6)X(35090)

Barycentrics    a^2*(a - b)*(a - c)*(a^3 - a^2*b - a*b^2 + b^3 + a^2*c + a*b*c + b^2*c - a*c^2 - b*c^2 - c^3)*(a^3 + a^2*b - a*b^2 - b^3 - a^2*c + a*b*c - b^2*c - a*c^2 + b*c^2 + c^3)*(a^4 - 2*a^2*b^2 + b^4 - a^3*c - b^3*c + a^2*c^2 + b^2*c^2 + a*c^3 + b*c^3 - 2*c^4)*(a^4 - a^3*b + a^2*b^2 + a*b^3 - 2*b^4 + b^3*c - 2*a^2*c^2 + b^2*c^2 - b*c^3 + c^4) : :

X(65644) lies on the circumcircle and these lines: {55, 44054}, {106, 7343}, {476, 900}, {477, 952}, {526, 901}, {759, 3065}, {953, 5663}, {1290, 8674}, {2687, 2771}, {5951, 12515}

X(65644) = Thomson-isogonal conjugate of X(53809)
X(65644) = Collings transform of X(i) for these i: {2771, 8674}
X(65644) = cevapoint of X(2771) and X(8674)
X(65644) = trilinear pole of line {6, 35090}

X(65645) = X(265)X(33643)∩X(476)X(25149)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^6 + 2*a^5*b - a^4*b^2 - 4*a^3*b^3 - a^2*b^4 + 2*a*b^5 + b^6 - a^4*c^2 - 2*a^3*b*c^2 - a^2*b^2*c^2 - 2*a*b^3*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - a^4*c^2 + 2*a^3*b*c^2 - a^2*b^2*c^2 + 2*a*b^3*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^5*c + 2*a^3*b^2*c - a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 + 4*a^3*c^3 + 2*a*b^2*c^3 - a^2*c^4 - b^2*c^4 - 2*a*c^5 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^5*c - 2*a^3*b^2*c - a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 - 4*a^3*c^3 - 2*a*b^2*c^3 - a^2*c^4 - b^2*c^4 + 2*a*c^5 + c^6) : :

X(65645) lies on the circumcircle and these lines: {265, 33643}, {476, 25149}, {477, 25150}, {526, 54049}, {1291, 43965}, {5663, 15907}, {5966, 34308}, {14979, 32423}

X(65645) = Collings transform of X(i) for these i: {32423, 45147}
X(65645) = cevapoint of X(32423) and X(45147)

X(65646) = TRILINEAR POLE OF X(6)X(35116)

Barycentrics    a^2*(a - b)*(a - c)*(a^2 - 2*a*b + b^2 + a*c + b*c - 2*c^2)*(a^2 + a*b - 2*b^2 - 2*a*c + b*c + c^2)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - b^2*c + 2*a*c^2 + 2*b*c^2 - 2*c^3)*(a^3 - a^2*b + 2*a*b^2 - 2*b^3 - a^2*c + 2*b^2*c - a*c^2 - b*c^2 + c^3) : :

X(65646) lies on the circumcircle and these lines: {105, 1156}, {106, 4845}, {900, 927}, {901, 926}, {952, 2724}, {953, 2808}, {1308, 3887}, {2222, 37139}, {2717, 2801}, {9057, 15343}, {18821, 53183}, {23344, 59101}, {37131, 53181}

X(65646) = Thomson-isogonal conjugate of X(53801)
X(65646) = Collings transform of X(i) for these i: {2801, 3887}
X(65646) = X(i)-isoconjugate of X(j) for these (i,j): {527, 1643}, {528, 14413}, {1638, 2246}, {14190, 30573}, {23890, 52946}
X(65646) = cevapoint of X(2801) and X(3887)
X(65646) = trilinear pole of line {6, 35116}
X(65646) = barycentric quotient X(i)/X(j) for these {i,j}: {840, 1638}, {14733, 5723}, {23351, 52946}, {34068, 1643}

X(65647) = TRILINEAR POLE OF X(6)X(35080)

Barycentrics    (a - b)*(a - c)*(a^3 + b^3 - a*b*c - c^3)*(a^3 - b^3 - a*b*c + c^3)*(a^4 - a^3*b - 2*a^2*b^2 - a*b^3 + b^4 + a^2*b*c + a*b^2*c + 2*a*b*c^2 - a*c^3 - b*c^3)*(a^4 - a*b^3 - a^3*c + a^2*b*c + 2*a*b^2*c - b^3*c - 2*a^2*c^2 + a*b*c^2 - a*c^3 + c^4) : :

X(65647) lies on the circumcircle and these lines: {105, 7061}, {741, 7281}, {804, 927}, {805, 926}, {2698, 2808}, {2700, 2784}, {2702, 2786}, {2724, 2782}

X(65647) = Collings transform of X(i) for these i: {2784, 2786}
X(65647) = cevapoint of X(2784) and X(2786)
X(65647) = trilinear pole of line {6, 35080}

X(65648) = TRILINEAR POLE OF X(6)X(35088)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^6 + a^5*b + a*b^5 + b^6 - a^4*c^2 - a^3*b*c^2 - a^2*b^2*c^2 - a*b^3*c^2 - b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^6 - a^5*b - a*b^5 + b^6 - a^4*c^2 + a^3*b*c^2 - a^2*b^2*c^2 + a*b^3*c^2 - b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^6 - a^4*b^2 + a^2*b^4 - b^6 - a^5*c + a^3*b^2*c - a^2*b^2*c^2 + b^4*c^2 + a*b^2*c^3 - b^2*c^4 - a*c^5 + c^6)*(a^6 - a^4*b^2 + a^2*b^4 - b^6 + a^5*c - a^3*b^2*c - a^2*b^2*c^2 + b^4*c^2 - a*b^2*c^3 - b^2*c^4 + a*c^5 + c^6) : :

X(65648) lies on the circumcircle and these lines: {2, 46413}, {98, 62431}, {110, 62555}, {804, 2867}, {805, 2881}, {2698, 53795}, {2710, 2794}, {2715, 2799}, {2782, 53912}, {18858, 56981}, {34765, 53691}

X(65648) = anticomplement of X(46413)
X(65648) = Collings transform of X(i) for these i: {2794, 2799}
X(65648) = cevapoint of X(2794) and X(2799)
X(65648) = trilinear pole of line {6, 35088}

X(65649) = TRILINEAR POLE OF X(6)X(5548)

Barycentrics    a^2*(a - b)*(a + b - 2*c)*(a - c)*(a - 2*b + c)*(a^3 - 3*a^2*b - 2*a*b^2 + 2*b^3 - a^2*c + 8*a*b*c - 2*b^2*c - a*c^2 - 3*b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - 3*a^2*c + 8*a*b*c - 3*b^2*c - 2*a*c^2 - 2*b*c^2 + 2*c^3) : :

X(65649) lies on the circumcircle and these lines: {105, 14193}, {106, 61484}, {109, 9268}, {900, 6079}, {901, 6085}, {952, 44873}, {953, 53790}, {1320, 8686}, {2718, 2802}, {2743, 2827}, {6551, 23832}, {17100, 43081}, {56647, 62703}

X(65649) = Thomson-isogonal conjugate of X(53799)
X(65649) = Collings transform of X(i) for these i: {2802, 2827, 62703}
X(65649) = X(i)-isoconjugate of X(j) for these (i,j): {1635, 43055}, {5854, 53528}
X(65649) = cevapoint of X(2802) and X(2827)
X(65649) = trilinear pole of line {6, 5548}
X(65649) = barycentric product X(4582)*X(43081)
X(65649) = barycentric quotient X(i)/X(j) for these {i,j}: {901, 43055}, {5548, 5854}, {43081, 30725}, {61484, 21129}

X(65650) = TRILINEAR POLE OF X(6)X(56795)

Barycentrics    a^2*(a - b)*(a + b - 3*c)*(a - c)*(a - 3*b + c)*(a^3 - 4*a^2*b - 3*a*b^2 + 2*b^3 - a^2*c + 12*a*b*c - 3*b^2*c - a*c^2 - 4*b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - 4*a^2*c + 12*a*b*c - 4*b^2*c - 3*a*c^2 - 3*b*c^2 + 2*c^3) : :

X(65650) lies on the circumcircle and these lines: {104, 1339}, {2415, 6079}, {2718, 12629}, {3445, 56635}, {3880, 8686}, {4394, 53630}, {8668, 43081}, {30198, 30236}

X(65650) = Collings transform of X(i) for these i: {3445, 3880, 30198}
X(65650) = X(6085)-cross conjugate of X(56635)
X(65650) = X(513)-isoconjugate of X(37743)
X(65650) = X(39026)-Dao conjugate of X(37743)
X(65650) = cevapoint of X(i) and X(j) for these (i,j): {2429, 3939}, {3445, 6085}, {3880, 30198}
X(65650) = trilinear pole of line {6, 56795}
X(65650) = barycentric quotient X(101)/X(37743)





leftri  Crosshexagon points and lines: X(65651) - X(65709)  rightri

This preamble and centers X(65651)-X(65709) were contributed by César Eliud Lozada, October 13, 2024.

Let T' = A'B'C' and T" = A"B"C" be two triangles circumscribed by a conic. Let Ab = B'C'∩A"C" and Ac = B'C'∩A"B", and denote Bc, Ca and Ba, Cb cyclically. Let Pa = AbBc∩AcCb, and define Pb, Pc cyclically. Then:

  1. Lines BcCb, CaAc, AbBa concur in a point 𝒳.
  2. Points Pa, Pb, Pc lie on a line ℒ.

The hexagon with vertices {Ab, Ac, Bc, Ba, Ca, Cb} is named here the crosshexagon of T' and T", and 𝒳 and ℒ will be referred here as the crosshexagon point and crosshexagon line, respectively, of T' and T".

Lists of calculated and not calculated crosshexagon points are available here. For definitions of all triangles referred here, check the Index of triangles referenced in ETC.

underbar

X(65651) = CROSSHEXAGON POINT OF THESE TRIANGLES: ABC AND 2nd TANGENTIAL-MIDARC

Barycentrics    a*((-a+b+c)*(b-c)*(a+b-c)*(a-b+c)+4*b*(-a+b+c)*(b-c)*c*sin(A/2)+c*(a-b+c)*(a^2-2*c*a+(3*b-c)*(b-c))*sin(B/2)-b*(a+b-c)*(a^2-2*b*a+(b-c)*(b-3*c))*sin(C/2)) : :

X(65651) lies on these lines: {30, 511}, {659, 13301}, {3659, 55342}, {6728, 10492}, {21618, 45304}

X(65651) = isogonal conjugate of X(3659)
X(65651) = isotomic conjugate of the anticomplement of X(61072)
X(65651) = cevapoint of X(i) and X(j) for these {i, j}: {1, 20114}, {513, 6728}, {10495, 65696}
X(65651) = cross-difference of every pair of points on the line X(6)X(259)
X(65651) = crosspoint of X(i) and X(j) for these {i, j}: {7, 55328}, {1488, 55331}, {7057, 55342}
X(65651) = crosssum of X(i) and X(j) for these {i, j}: {513, 10500}, {10495, 15997}
X(65651) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (101, 556), (3659, 8), (16011, 149), (16015, 150), (42017, 33650), (45874, 7057), (55331, 69)
X(65651) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 61072), (4, 45304), (7, 21623), (2089, 6732), (7057, 10504), (43192, 177), (45876, 16015), (55328, 173), (55331, 236), (55342, 1)
X(65651) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 45304), (6, 21623), (31, 61072), (2091, 17059), (3659, 10), (16011, 11), (16015, 116), (42017, 124), (45874, 178), (55331, 141)
X(65651) = X(i)-cross conjugate of-X(j) for these (i, j): (513, 65661), (6732, 2089), (45877, 10492), (61072, 2)
X(65651) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 55331), (11, 42017), (236, 55332), (1015, 16015), (8054, 16011), (10494, 7028), (10504, 53122), (13443, 55342), (15495, 45876), (21623, 7048), (40617, 2091), (61072, 2)
X(65651) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 55331}, {100, 16011}, {101, 16015}, {109, 42017}, {188, 45874}, {259, 45875}, {266, 55363}, {2091, 3939}, {6733, 15997}, {7028, 58968}, {43192, 53119}, {45876, 60539}, {55342, 60554}
X(65651) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1, 55331), (173, 55342), (174, 45876), (188, 55332), (259, 55363), (266, 45875), (513, 16015), (649, 16011), (650, 42017), (2089, 55341), (3669, 2091), (6728, 2090), (6729, 15997), (10492, 7048), (10495, 7028), (45877, 188), (45878, 259), (55331, 59443), (65661, 174), (65696, 39121)
X(65651) = X(i)-zayin conjugate of-X(j) for these (i, j): (522, 52797), (13443, 43192)
X(65651) = trilinear pole of the line {6732, 61072} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65651) = center of the circumconic with perspector X(61072)
X(65651) = perspector of: the circumconic with center X(61072), the inconic with center X(61072)
X(65651) = barycentric product X(i)*X(j) for these {i, j}: {556, 65661}, {4146, 45877}, {6732, 55341}, {7057, 10492}, {10504, 55331}, {21623, 55342}
X(65651) = trilinear product X(i)*X(j) for these {i, j}: {173, 10492}, {174, 45877}, {188, 65661}, {2089, 10495}, {3659, 10504}, {4146, 45878}, {6732, 43192}, {55331, 61072}
X(65651) = trilinear quotient X(i)/X(j) for these (i, j): (2, 55331), (174, 45875), (188, 55363), (266, 45874), (513, 16011), (514, 16015), (522, 42017), (556, 55332), (2089, 43192), (3676, 2091), (4146, 45876), (6728, 15997), (6732, 10495), (7057, 55342), (10492, 258), (10495, 53119), (10504, 65651), (18886, 55328), (21623, 10492), (45877, 259)
X(65651) = (2nd midarc)-isotomic conjugate-of-X(10491)
X(65651) = (midarc)-isotomic conjugate-of-X(65502)
X(65651) = (medial)-isotomic conjugate-of-X(61072)

X(65652) = CROSSHEXAGON POINT OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND CIRCUMMEDIAL

Barycentrics    3*a^8+30*(b^2+c^2)*a^6-8*(5*b^4-4*b^2*c^2+5*c^4)*a^4+2*(b^2+c^2)*(5*b^4-34*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^2*(3*b^2+c^2)*(b^2+3*c^2) : :

X(65652) lies on these lines: {2, 39453}, {524, 10304}, {3003, 7736}, {7426, 42850}

X(65652) = anticomplement of X(65676)
X(65652) = X(65676)-Dao conjugate of-X(65676)

X(65653) = CROSSHEXAGON POINT OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND CIRCUMSYMMEDIAL

Barycentrics    a^2*(a^8-18*(b^2+c^2)*a^6+4*(2*b^4-7*b^2*c^2+2*c^4)*a^4+2*(b^2+c^2)*(b^4+30*b^2*c^2+c^4)*a^2+(7*b^4+30*b^2*c^2+7*c^4)*(b^2-c^2)^2) : :

X(65653) lies on these lines: {511, 53019}, {1495, 5024}

X(65654) = CROSSHEXAGON POINT OF THESE TRIANGLES: ANTI-ARA AND 2nd HYACINTH

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^4-2*(b^4+c^4)*a^2+(b^2+c^2)*(b^4+c^4)) : :
X(65654) = 3*X(51)-2*X(13567) = 3*X(3060)-X(6515) = 3*X(3917)-4*X(53415)

X(65654) lies on these lines: {2, 37511}, {4, 52}, {6, 17409}, {22, 9967}, {24, 10625}, {25, 394}, {51, 125}, {143, 1595}, {154, 44439}, {184, 11470}, {185, 1885}, {235, 5562}, {373, 15010}, {378, 5422}, {389, 1593}, {403, 5891}, {428, 524}, {468, 3917}, {541, 1986}, {568, 1597}, {1154, 1596}, {1196, 35325}, {1205, 41616}, {1216, 3542}, {1235, 33798}, {1368, 12058}, {1598, 6243}, {1853, 60774}, {1899, 34146}, {1906, 14531}, {1907, 6746}, {1974, 3313}, {1993, 40914}, {2211, 20859}, {2393, 31383}, {2979, 6353}, {3088, 3567}, {3089, 11412}, {3147, 5447}, {3515, 15644}, {3516, 9729}, {3517, 37484}, {3541, 5462}, {3575, 45186}, {3796, 44479}, {3819, 37453}, {3981, 14580}, {4232, 62188}, {4259, 44086}, {4260, 44097}, {4563, 40413}, {5028, 36417}, {5064, 21849}, {5094, 5943}, {5186, 39846}, {5640, 8889}, {5650, 52297}, {5876, 44226}, {5890, 63031}, {5894, 52003}, {5907, 37197}, {5946, 64474}, {6000, 18396}, {6101, 21841}, {6102, 13488}, {6152, 64851}, {6241, 54211}, {6403, 6995}, {6467, 34774}, {6622, 11444}, {6623, 11459}, {6636, 19128}, {6688, 52298}, {6756, 10263}, {6776, 41715}, {7378, 11002}, {7408, 16981}, {7484, 52520}, {7487, 64051}, {7507, 10110}, {7577, 14845}, {7998, 38282}, {9047, 41611}, {9909, 18438}, {9969, 63129}, {10116, 46443}, {10151, 15030}, {10539, 32048}, {10575, 18560}, {11206, 15073}, {11381, 21652}, {11403, 16625}, {11410, 16836}, {11451, 52299}, {11473, 12239}, {11474, 12240}, {11550, 18382}, {11557, 12901}, {11574, 19118}, {11591, 44960}, {11743, 32352}, {12052, 28144}, {12131, 39817}, {12133, 21649}, {12135, 16980}, {12173, 13598}, {12220, 34608}, {12300, 41578}, {13340, 55572}, {13348, 15750}, {13391, 37458}, {13403, 41725}, {13473, 32062}, {14831, 62962}, {14855, 35481}, {14865, 15019}, {15004, 19124}, {15060, 37984}, {15067, 37942}, {15473, 38321}, {15809, 21850}, {17810, 37473}, {18914, 44544}, {19127, 22352}, {19504, 34986}, {20302, 63683}, {20791, 60765}, {21243, 37981}, {21525, 30214}, {26869, 65402}, {26879, 43896}, {27365, 46682}, {32110, 44269}, {33884, 62973}, {34336, 59535}, {34751, 36990}, {34854, 57533}, {35603, 64049}, {35908, 51821}, {36987, 37931}, {37481, 55571}, {37516, 44105}, {37920, 55606}, {37935, 54042}, {37951, 43586}, {40316, 40337}, {43574, 45173}, {44162, 46546}, {44889, 46831}, {45179, 63735}, {45780, 46261}, {53023, 61739}, {54003, 61378}, {57388, 63069}, {58470, 62980}, {58483, 61506}

X(65654) = midpoint of X(6243) and X(58891)
X(65654) = reflection of X(i) in X(j) for these (i, j): (25, 64820), (10605, 389), (12058, 1368), (12828, 1112), (63129, 9969)
X(65654) = cross-difference of every pair of points on the line X(22159)X(30451)
X(65654) = crosspoint of X(4) and X(56307)
X(65654) = crosssum of X(3) and X(1899)
X(65654) = perspector of the circumconic through X(30450) and X(39417)
X(65654) = inverse of X(19161) in Hatzipolakis-Lozada, hyperbola
X(65654) = inverse of X(44899) in incircle-of-orthic triangle
X(65654) = pole of the line {924, 2501} with respect to the incircle-of-orthic triangle
X(65654) = pole of the line {924, 30735} with respect to the polar circle
X(65654) = pole of the line {185, 1503} with respect to the Hatzipolakis-Lozada, hyperbola
X(65654) = pole of the line {235, 1503} with respect to the Jerabek circumhyperbola
X(65654) = pole of the line {15578, 50649} with respect to the Moses-Jerabek conic
X(65654) = pole of the line {3569, 6753} with respect to the orthic inconic
X(65654) = pole of the line {1147, 3546} with respect to the Stammler hyperbola
X(65654) = pole of the line {9723, 62698} with respect to the Steiner-Wallace hyperbola
X(65654) = X(394)-of-anti-Ara triangle
X(65654) = X(1370)-of-1st orthosymmedial triangle
X(65654) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (4, 3060, 47328), (51, 12294, 427), (51, 13417, 54384), (51, 54384, 19161), (378, 52000, 9730), (427, 1112, 51), (1593, 45010, 10982), (2211, 20859, 40938), (3917, 44079, 468), (6995, 62187, 6403), (12162, 61666, 11442), (41580, 50649, 184)

X(65655) = CROSSHEXAGON POINT OF THESE TRIANGLES: 1st ANTI-CIRCUMPERP AND 1st CIRCUMPERP

Barycentrics    a^11-2*(b+c)*a^10-(b^2-3*b*c+c^2)*a^9+(b+c)*(2*b^2-b*c+2*c^2)*a^8+(2*b^4+2*c^4-b*c*(b^2+b*c+c^2))*a^7+(b+c)*(b^4+c^4-2*b*c*(3*b^2-4*b*c+3*c^2))*a^6-(5*b^4+5*c^4+b*c*(b^2-10*b*c+c^2))*(b^2-b*c+c^2)*a^5+(b^2-c^2)*(b-c)*(5*b^2-8*b*c+5*c^2)*b*c*a^4+(3*b^6+3*c^6-(b^4+c^4+b*c*(b^2-8*b*c+c^2))*b*c)*(b-c)^2*a^3-(b^3+c^3)*(b-c)^4*(b^2+3*b*c+c^2)*a^2+(b^2-c^2)^2*(b-c)^4*b*c*a+(b^2-c^2)^3*(b-c)*b^2*c^2 : :

X(65655) lies on these lines: {2, 65679}, {3, 65668}, {4, 65677}, {20, 34935}, {102, 65514}

X(65655) = reflection of X(i) in X(j) for these (i, j): (4, 65677), (65668, 3)
X(65655) = anticomplement of X(65679)
X(65655) = X(65679)-Dao conjugate of-X(65679)
X(65655) = X(65677)-of-anti-Euler triangle
X(65655) = X(65668)-of-ABC-X3 reflections triangle

X(65656) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd ANTI-CONWAY AND MIDHEIGHT

Barycentrics    a^2*(b^2-c^2)*(a^8-4*(b^2+c^2)*a^6+2*(3*b^4+b^2*c^2+3*c^4)*a^4-4*(b^6+c^6)*a^2+(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(65656) = X(647)-9*X(58900) = X(14346)+2*X(58895)

X(65656) lies on these lines: {6, 647}, {389, 30209}, {512, 54259}, {520, 6587}, {526, 59652}, {686, 6753}, {850, 11433}, {924, 2501}, {2485, 17434}, {2506, 3569}, {12241, 64788}, {13400, 65694}, {13567, 30476}, {16040, 62176}, {17810, 54268}, {26958, 31277}, {30211, 46425}, {31072, 63081}, {31296, 63031}, {50647, 55265}

X(65656) = midpoint of X(6587) and X(14346)
X(65656) = reflection of X(6587) in X(58895)
X(65656) = cross-difference of every pair of points on the line X(30)X(155)
X(65656) = crosspoint of X(4) and X(46639)
X(65656) = crosssum of X(3) and X(6587)
X(65656) = X(i)-complementary conjugate of-X(j) for these (i, j): (91, 55069), (1096, 136), (14593, 34846), (36145, 6389), (60501, 16595), (65176, 18589)
X(65656) = X(1084)-Dao conjugate of-X(59496)
X(65656) = X(662)-isoconjugate of-X(59496)
X(65656) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (512, 59496), (11441, 99)
X(65656) = perspector of the circumconic through X(74) and X(254)
X(65656) = pole of the line {13754, 44705} with respect to the Dou circles radical circle
X(65656) = pole of the line {6515, 6820} with respect to the polar circle
X(65656) = pole of the line {122, 136} with respect to the Kiepert circumhyperbola
X(65656) = pole of the line {64, 12085} with respect to the MacBeath circumconic
X(65656) = pole of the line {3, 64} with respect to the orthic inconic
X(65656) = pole of the line {393, 847} with respect to the Steiner inellipse
X(65656) = barycentric product X(523)*X(11441)
X(65656) = trilinear product X(661)*X(11441)
X(65656) = trilinear quotient X(i)/X(j) for these (i, j): (661, 59496), (11441, 662)
X(65656) = (X(17434), X(30442))-harmonic conjugate of X(2485)

X(65657) = CROSSHEXAGON POINT OF THESE TRIANGLES: 3rd ANTI-EULER AND EXCENTRAL

Barycentrics    a*(b-c)*(a^6-(b^2+b*c+c^2)*a^4+2*(b+c)*b*c*a^3-(b^4-3*b^2*c^2+c^4)*a^2-2*(b+c)*(b^2+c^2)*b*c*a+(b^4+c^4-b*c*(b^2-b*c+c^2))*(b+c)^2) : :

X(65657) lies on these lines: {2, 65663}, {3, 65658}, {522, 1770}, {17220, 46402}

X(65657) = reflection of X(65658) in X(3)
X(65657) = anticomplement of X(65663)
X(65657) = X(65663)-Dao conjugate of-X(65663)
X(65657) = X(65658)-of-ABC-X3 reflections triangle

X(65658) = CROSSHEXAGON POINT OF THESE TRIANGLES: 4th ANTI-EULER AND HEXYL

Barycentrics    a*(b-c)*(a^9-(b+c)*a^8-(2*b^2+b*c+2*c^2)*a^7+(b+c)*(2*b^2+b*c+2*c^2)*a^6+(b^2+b*c+c^2)*b*c*a^5-(b+c)*(3*b^2+b*c+3*c^2)*b*c*a^4+(2*b^2-3*b*c+2*c^2)*(b^2+c^2)*(b+c)^2*a^3-(b^2-c^2)*(b-c)*(2*b^4+2*c^4+b*c*(b^2+c^2))*a^2-(b^2-c^2)^2*(b^4+c^4+b*c*(b^2+b*c+c^2))*a+(b^2-c^2)^2*(b+c)*(b^4+c^4-(b^2-b*c+c^2)*b*c)) : :

X(65658) lies on these lines: {3, 65657}, {4, 65663}, {6003, 48080}

X(65658) = reflection of X(i) in X(j) for these (i, j): (4, 65663), (65657, 3)
X(65658) = X(65663)-of-anti-Euler triangle
X(65658) = X(65657)-of-ABC-X3 reflections triangle

X(65659) = CROSSHEXAGON POINT OF THESE TRIANGLES: ANTI-HUTSON INTOUCH AND HEXYL

Barycentrics    a^2*(b-c)*(a^4-2*(b+c)*a^3+2*b*c*a^2+2*(b+c)*(b^2+c^2)*a-b^4-c^4-2*(b^2-b*c+c^2)*b*c) : :
X(65659) = 3*X(4091)-2*X(53301) = 3*X(44408)-X(53301) = 4*X(44827)-3*X(57108)

X(65659) lies on these lines: {1, 3676}, {3, 649}, {4, 3835}, {5, 30835}, {20, 20295}, {30, 31147}, {40, 15599}, {56, 65697}, {74, 2700}, {78, 4468}, {101, 61106}, {102, 28838}, {103, 953}, {104, 12032}, {106, 28914}, {140, 31207}, {376, 4785}, {405, 25924}, {474, 25955}, {512, 684}, {513, 50371}, {514, 44827}, {631, 31286}, {650, 30199}, {661, 8760}, {663, 905}, {788, 63389}, {936, 4521}, {991, 14812}, {1064, 14205}, {1292, 40499}, {1293, 28293}, {1296, 2705}, {1350, 9002}, {1459, 3960}, {1565, 14714}, {2646, 44319}, {2742, 3939}, {2814, 48335}, {2821, 4775}, {2826, 4724}, {3064, 57276}, {3091, 27138}, {3146, 26798}, {3522, 26853}, {3523, 27013}, {3524, 45313}, {3528, 48016}, {3545, 45339}, {3601, 58324}, {3667, 3737}, {4025, 62436}, {4091, 8676}, {4105, 14077}, {4106, 64787}, {4375, 36489}, {4449, 28473}, {4905, 51652}, {5720, 47765}, {5732, 6006}, {6008, 8142}, {6261, 28589}, {6545, 37533}, {7380, 30764}, {7513, 46107}, {9000, 53249}, {9313, 30269}, {9840, 28398}, {10884, 48013}, {10984, 58315}, {17697, 26694}, {18200, 64393}, {18443, 47758}, {18444, 47755}, {18446, 28846}, {21172, 48307}, {23100, 59362}, {25381, 36543}, {26117, 26596}, {27485, 64088}, {27673, 61109}, {28159, 28876}, {28203, 28892}, {28474, 28520}, {29066, 62432}, {29241, 53906}, {30209, 42664}, {30273, 64866}, {34772, 47676}, {37531, 48398}, {37700, 48082}, {39227, 58140}, {41854, 49284}, {42312, 44409}, {48294, 65412}

X(65659) = midpoint of X(20) and X(20295)
X(65659) = reflection of X(i) in X(j) for these (i, j): (4, 3835), (40, 15599), (649, 3), (4091, 44408), (62436, 4025)
X(65659) = circumperp conjugate of X(46407)
X(65659) = cross-difference of every pair of points on the line X(3011)X(7735)
X(65659) = X(21)-beth conjugate of-X(3676)
X(65659) = X(78)-gimel conjugate of-X(15599)
X(65659) = perspector of the circumconic through X(39273) and X(40802)
X(65659) = pole of the line {674, 1350} with respect to the circumcircle
X(65659) = pole of the line {376, 527} with respect to the hexyl circle
X(65659) = pole of the line {527, 5728} with respect to the incircle
X(65659) = pole of the line {674, 55582} with respect to the Nguyen-Moses circle
X(65659) = pole of the line {29639, 51400} with respect to the orthoptic circle of Steiner inellipse
X(65659) = pole of the line {902, 2030} with respect to the Schoute circle
X(65659) = pole of the line {674, 55584} with respect to the Stammler circle
X(65659) = pole of the line {990, 5757} with respect to the excentral-hexyl ellipse
X(65659) = pole of the line {47845, 53326} with respect to the Kiepert parabola
X(65659) = pole of the line {4237, 35278} with respect to the Stammler hyperbola
X(65659) = pole of the line {25939, 37597} with respect to the Steiner inellipse
X(65659) = (ABC-X3 reflections)-isogonal conjugate-of-X(24813)
X(65659) = (2nd circumperp)-isogonal conjugate-of-X(53302)
X(65659) = X(65697)-of-2nd circumperp tangential triangle
X(65659) = X(62432)-of-anti-inner-Garcia triangle
X(65659) = X(3835)-of-anti-Euler triangle
X(65659) = X(850)-of-2nd circumperp triangle
X(65659) = X(649)-of-ABC-X3 reflections triangle
X(65659) = X(647)-of-hexyl triangle

X(65660) = CROSSHEXAGON POINT OF THESE TRIANGLES: ANTI-INVERSE-IN-INCIRCLE AND YFF CONTACT

Barycentrics    (b-c)*((b+c)*a^4-2*(b^2+b*c+c^2)*a^3+(b+c)*(b^2+c^2)*a^2-2*b^2*c^2*a+b^2*c^2*(b+c)) : :

X(65660) lies on these lines: {2, 24462}, {42, 20525}, {100, 190}, {316, 512}, {918, 17165}, {926, 17135}, {2340, 8714}, {4453, 17140}, {6327, 46401}, {17146, 30704}, {24349, 48571}, {32937, 47772}, {48169, 57091}, {48269, 58288}, {49273, 63812}, {49276, 56318}

X(65660) = isotomic conjugate of the anticomplement of X(38990)
X(65660) = anticomplement of X(65703)
X(65660) = cross-difference of every pair of points on the line X(1015)X(3051)
X(65660) = crosspoint of X(190) and X(43093)
X(65660) = crosssum of X(i) and X(j) for these {i, j}: {39, 65703}, {649, 8618}
X(65660) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (675, 149), (2224, 4440), (32682, 192), (36087, 2), (37130, 150), (43093, 21293), (52941, 17494), (60135, 21221), (65554, 4430)
X(65660) = X(38990)-cross conjugate of-X(2)
X(65660) = X(65703)-Dao conjugate of-X(65703)
X(65660) = X(38990)-reciprocal conjugate of-X(65703)
X(65660) = perspector of: the circumconic through X(308) and X(1016), the inconic with center X(38990)
X(65660) = pole of the line {100, 8266} with respect to the circumcircle
X(65660) = pole of the line {100, 573} with respect to the incircle of anticomplementary triangle
X(65660) = pole of the line {1843, 2969} with respect to the polar circle
X(65660) = pole of the line {1, 31296} with respect to the Kiepert parabola
X(65660) = pole of the line {76, 190} with respect to the Steiner circumellipse
X(65660) = pole of the line {3934, 4422} with respect to the Steiner inellipse
X(65660) = pole of the line {1634, 7192} with respect to the Steiner-Wallace hyperbola
X(65660) = pole of the line {2, 2412} with respect to the Yff parabola

X(65661) = CROSSHEXAGON POINT OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC AND TANGENTIAL-MIDARC

Barycentrics    a*(a+b-c)*(a-b+c)*(-2*(-a+b+c)*(b-c)-2*(-a+b+c)*(b-c)*sin(A/2)+(a^2-2*b*a+(b-c)*(b-3*c))*sin(B/2)-(a^2-2*c*a+(3*b-c)*(b-c))*sin(C/2)) : :

X(65661) lies on these lines: {1, 65411}, {513, 663}, {6728, 10492}, {8077, 65453}, {43192, 45874}

X(65661) = reflection of X(65696) in X(1)
X(65661) = isogonal conjugate of X(55363)
X(65661) = cross-difference of every pair of points on the line X(9)X(259)
X(65661) = crosspoint of X(i) and X(j) for these {i, j}: {1, 10496}, {174, 45876}, {2089, 43192}
X(65661) = crosssum of X(i) and X(j) for these {i, j}: {1, 65411}, {259, 45878}, {10495, 53119}
X(65661) = X(21)-beth conjugate of-X(65411)
X(65661) = X(i)-Ceva conjugate of-X(j) for these (i, j): (57, 61072), (13444, 10490), (43192, 266), (45875, 173), (45876, 174), (55342, 65662)
X(65661) = X(i)-cross conjugate of-X(j) for these (i, j): (513, 65651), (45878, 45877), (61072, 57)
X(65661) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 55332), (223, 45876), (478, 45875), (1015, 2090), (8054, 15997), (21623, 53123), (61072, 556)
X(65661) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 55332}, {8, 45874}, {9, 45875}, {55, 45876}, {100, 15997}, {101, 2090}, {188, 3659}, {259, 55331}, {644, 41799}, {6733, 42017}, {45878, 59443}, {53119, 55342}
X(65661) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1, 55332), (56, 45875), (57, 45876), (266, 55331), (513, 2090), (604, 45874), (649, 15997), (6729, 42017), (10492, 53123), (43924, 41799), (45875, 59443), (45877, 8), (45878, 9), (65651, 556)
X(65661) = X(3659)-zayin conjugate of-X(10495)
X(65661) = perspector of the circumconic through X(57) and X(174)
X(65661) = pole of the line {52510, 55174} with respect to the Adams circle
X(65661) = pole of the line {56, 10490} with respect to the circumcircle
X(65661) = pole of the line {12435, 12554} with respect to the Conway circle
X(65661) = pole of the line {6769, 55174} with respect to the hexyl circle
X(65661) = pole of the line {65, 177} with respect to the incircle
X(65661) = pole of the line {21623, 24237} with respect to the circumhyperbola dual of Yff parabola
X(65661) = pole of the line {7004, 10501} with respect to the Feuerbach circumhyperbola
X(65661) = pole of the line {643, 55363} with respect to the Stammler hyperbola
X(65661) = pole of the line {174, 3210} with respect to the Steiner circumellipse
X(65661) = pole of the line {3752, 16015} with respect to the Steiner inellipse
X(65661) = pole of the line {7257, 55363} with respect to the Steiner-Wallace hyperbola
X(65661) = barycentric product X(i)*X(j) for these {i, j}: {7, 45877}, {85, 45878}, {174, 65651}, {2089, 10492}, {6732, 55328}, {10495, 18886}, {10504, 45875}, {12809, 55332}, {21623, 43192}, {45876, 61072}
X(65661) = trilinear product X(i)*X(j) for these {i, j}: {7, 45878}, {57, 45877}, {266, 65651}, {6732, 13444}, {10504, 45874}, {12809, 55363}, {21623, 58968}, {45875, 61072}
X(65661) = trilinear quotient X(i)/X(j) for these (i, j): (2, 55332), (7, 45876), (56, 45874), (57, 45875), (174, 55331), (266, 3659), (513, 15997), (514, 2090), (2089, 55342), (3669, 41799), (6728, 42017), (10492, 7028), (12809, 65661), (18886, 55341), (45876, 59443), (45877, 9), (45878, 55), (61072, 45877)
X(65661) = X(65696)-of-5th mixtilinear triangle
X(65661) = X(59915)-of-2nd circumperp triangle
X(65661) = X(54239)-of-excentral triangle
X(65661) = X(39199)-of-intouch triangle

X(65662) = CROSSHEXAGON POINT OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC AND 2nd TANGENTIAL-MIDARC

Barycentrics    a*(-2*b*c*(b-c)*(-a+b+c)*(3*a-b-c)*sin(A/2)+2*c*a*(a-b+c)*((3*b+c)*a-b^2-4*b*c+c^2)*sin(B/2)-2*b*a*(a+b-c)*((b+3*c)*a+b^2-4*b*c-c^2)*sin(C/2)+a*(b-c)*(a+b-c)*(a-b+c)*(a+b+c)) : :

X(65662) lies on these lines: {1, 164}, {57, 61635}, {65, 10490}, {145, 174}, {390, 8242}, {944, 8092}, {5441, 16147}, {7590, 8000}, {7707, 60533}, {7966, 8082}, {7971, 8096}, {7972, 8098}, {7990, 8090}, {8351, 11041}, {10698, 12772}, {10890, 11895}, {11924, 18221}, {13100, 13125}, {18456, 64173}, {30408, 64766}, {45087, 64697}

X(65662) = reflection of X(15997) in X(1)
X(65662) = crosssum of X(1) and X(12523)
X(65662) = X(i)-beth conjugate of-X(j) for these (i, j): (1, 10490), (21, 55172)
X(65662) = X(55342)-Ceva conjugate of-X(65661)
X(65662) = trilinear quotient X(21622)/X(178)
X(65662) = X(40950)-of-excenters-reflections triangle
X(65662) = X(23361)-of-Hutson intouch triangle
X(65662) = X(15997)-of-5th mixtilinear triangle
X(65662) = X(15622)-of-intouch triangle

X(65663) = CROSSHEXAGON POINT OF THESE TRIANGLES: ANTI-WASAT AND WASAT

Barycentrics    a*(b-c)*(a^6-(b+c)^2*a^4+(b+c)*b*c*a^3-(b^2-3*b*c+c^2)*(b+c)^2*a^2-(b+c)*(b^2+c^2)*b*c*a+(b+c)*(b^2-c^2)*(b^3-c^3)) : :

X(65663) lies on these lines: {2, 65657}, {4, 65658}, {71, 657}, {513, 5570}, {3064, 15313}, {35604, 38357}

X(65663) = midpoint of X(4) and X(65658)
X(65663) = complement of X(65657)
X(65663) = cross-difference of every pair of points on the line X(2911)X(3157)
X(65663) = crosssum of X(3) and X(50350)
X(65663) = X(1479)-Ceva conjugate of-X(11)
X(65663) = perspector of the circumconic through X(7040) and X(15474)
X(65663) = pole of the line {3, 4354} with respect to the incircle
X(65663) = pole of the line {5905, 56876} with respect to the polar circle
X(65663) = pole of the line {1, 584} with respect to the orthic inconic
X(65663) = X(65658)-of-Euler triangle

X(65664) = CROSSHEXAGON POINT OF THESE TRIANGLES: BEVAN ANTIPODAL AND PELLETIER

Barycentrics    a*(b-c)*(-a+b+c)*(2*a^3-(b+c)*a^2-(b^2-c^2)*(b-c)) : :
X(65664) = X(4895)+2*X(65680) = 3*X(14413)-2*X(53544)

X(65664) lies on these lines: {55, 14392}, {103, 105}, {513, 663}, {516, 39077}, {649, 17115}, {652, 6608}, {654, 11193}, {657, 4041}, {661, 2520}, {676, 1360}, {812, 885}, {926, 2170}, {934, 53622}, {1024, 2195}, {1635, 6139}, {1946, 21127}, {2161, 23351}, {2488, 4979}, {3683, 14418}, {3738, 53055}, {3887, 51768}, {3900, 54255}, {4105, 14298}, {4455, 8638}, {4729, 65445}, {6084, 21132}, {8648, 16686}, {15283, 24924}, {17410, 58140}, {22108, 42657}, {25900, 65401}, {46392, 56785}, {48322, 65442}

X(65664) = reflection of X(4041) in X(657)
X(65664) = cross-difference of every pair of points on the line X(9)X(77)
X(65664) = crosspoint of X(i) and X(j) for these {i, j}: {9, 36086}, {513, 1024}, {673, 4626}, {2195, 8750}, {43736, 61240}
X(65664) = crosssum of X(i) and X(j) for these {i, j}: {7, 53357}, {57, 2254}, {100, 1025}, {522, 26001}, {672, 4105}, {4025, 9436}
X(65664) = X(105)-Ceva conjugate of-X(2170)
X(65664) = X(513)-daleth conjugate of-X(663)
X(65664) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 57928), (11, 18025), (223, 65294), (478, 65245), (661, 60581), (1015, 52156), (1146, 57996), (1566, 85), (6615, 2400), (8054, 43736), (20622, 18026), (23972, 4554), (38980, 56668), (38991, 36101), (39025, 103), (39077, 883), (46095, 6516), (50441, 668)
X(65664) = X(61240)-he conjugate of-X(3900)
X(65664) = X(i)-isoconjugate of-X(j) for these {i, j}: {7, 677}, {8, 24016}, {9, 65245}, {55, 65294}, {56, 57928}, {59, 2400}, {77, 65218}, {85, 36039}, {100, 43736}, {101, 52156}, {103, 664}, {109, 18025}, {312, 32668}, {348, 40116}, {651, 36101}, {653, 1815}, {658, 2338}, {666, 52213}, {911, 4554}, {919, 56668}, {1025, 9503}, {1252, 60581}, {1415, 57996}, {1813, 52781}, {2424, 4998}, {4620, 55257}, {6063, 32642}, {6516, 36122}, {18026, 36056}, {32657, 46404}, {33298, 35184}, {36136, 59200}, {44717, 53150}, {64083, 65538}
X(65664) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (9, 57928), (41, 677), (56, 65245), (57, 65294), (244, 60581), (513, 52156), (516, 4554), (522, 57996), (604, 24016), (607, 65218), (649, 43736), (650, 18025), (663, 36101), (676, 85), (884, 9503), (910, 664), (1360, 24015), (1397, 32668), (1456, 658), (1886, 18026), (1946, 1815), (2170, 2400), (2175, 36039), (2212, 40116), (2254, 56668), (2426, 4564), (3063, 103), (8641, 2338), (9447, 32642), (9502, 883), (14953, 4625), (18344, 52781), (30807, 4572), (39470, 7182), (40869, 668), (41339, 190), (43035, 4569), (46392, 8), (51376, 4561), (51418, 3699), (51436, 4551), (56639, 34085), (56785, 1026), (56900, 51560), (57292, 35518)
X(65664) = X(36146)-zayin conjugate of-X(2254)
X(65664) = perspector of the circumconic through X(33) and X(57)
X(65664) = pole of the line {56, 2170} with respect to the circumcircle
X(65664) = pole of the line {12435, 38479} with respect to the Conway circle
X(65664) = pole of the line {65, 1360} with respect to the incircle
X(65664) = pole of the line {85, 318} with respect to the polar circle
X(65664) = pole of the line {1410, 1475} with respect to the Brocard inellipse
X(65664) = pole of the line {21195, 24237} with respect to the circumhyperbola dual of Yff parabola
X(65664) = pole of the line {650, 3119} with respect to the Feuerbach circumhyperbola
X(65664) = pole of the line {3271, 14100} with respect to the Mandart inellipse
X(65664) = pole of the line {1827, 2262} with respect to the orthic inconic
X(65664) = pole of the line {3752, 20310} with respect to the Steiner inellipse
X(65664) = pole of the line {7257, 55205} with respect to the Steiner-Wallace hyperbola
X(65664) = barycentric product X(i)*X(j) for these {i, j}: {7, 46392}, {9, 676}, {33, 39470}, {108, 57292}, {513, 40869}, {514, 41339}, {516, 650}, {521, 1886}, {522, 910}, {663, 30807}, {885, 9502}, {1024, 50441}, {1456, 3239}, {1566, 36086}, {2170, 2398}, {2254, 56900}, {2426, 4858}, {3022, 24015}, {3063, 35517}, {3119, 23973}
X(65664) = trilinear product X(i)*X(j) for these {i, j}: {11, 2426}, {55, 676}, {57, 46392}, {513, 41339}, {516, 663}, {607, 39470}, {649, 40869}, {650, 910}, {652, 1886}, {657, 43035}, {665, 56900}, {884, 50441}, {919, 1566}, {926, 56639}, {1024, 9502}, {1456, 3900}, {2342, 42756}, {2398, 3271}, {3022, 23973}, {3063, 30807}
X(65664) = trilinear quotient X(i)/X(j) for these (i, j): (7, 65294), (8, 57928), (11, 2400), (33, 65218), (41, 36039), (55, 677), (56, 24016), (57, 65245), (513, 43736), (514, 52156), (516, 664), (522, 18025), (604, 32668), (607, 40116), (650, 36101), (652, 1815), (657, 2338), (663, 103), (665, 52213), (676, 7)
X(65664) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (55, 46393, 14392), (652, 11934, 6608), (2520, 8641, 661)

X(65665) = CROSSHEXAGON POINT OF THESE TRIANGLES: BEVAN ANTIPODAL AND SCHRÖETER

Barycentrics    a*(b^2-c^2)*((b+c)*a^3+(b-c)^2*a^2-(b^3+c^3)*a-(b^3-c^3)*(b-c)) : :

X(65665) lies on these lines: {115, 125}, {513, 663}, {676, 3649}, {3743, 32679}, {4854, 6366}, {10015, 63997}, {30691, 39793}

X(65665) = cross-difference of every pair of points on the line X(9)X(110)
X(65665) = perspector of the circumconic through X(57) and X(523)
X(65665) = pole of the line {56, 7669} with respect to the circumcircle
X(65665) = pole of the line {65, 4934} with respect to the incircle
X(65665) = pole of the line {318, 648} with respect to the polar circle
X(65665) = pole of the line {1475, 20975} with respect to the Brocard inellipse
X(65665) = pole of the line {21196, 24237} with respect to the circumhyperbola dual of Yff parabola
X(65665) = pole of the line {125, 2262} with respect to the orthic inconic
X(65665) = pole of the line {249, 643} with respect to the Stammler hyperbola
X(65665) = pole of the line {148, 3210} with respect to the Steiner circumellipse
X(65665) = pole of the line {115, 3752} with respect to the Steiner inellipse
X(65665) = pole of the line {4590, 7257} with respect to the Steiner-Wallace hyperbola

X(65666) = CROSSHEXAGON POINT OF THESE TRIANGLES: BEVAN ANTIPODAL AND X-PARABOLA-TANGENTIAL

Barycentrics    a*(b-c)*(b^2-c^2)^2*(a^5+(b+c)*a^4-2*(b^2+b*c+c^2)*a^3-2*(b^3+c^3)*a^2+(b^4+c^4+b*c*(b^2+b*c+c^2))*a+(b+c)*(b^4+c^4-b*c*(b^2-b*c+c^2))) : :

X(65666) lies on these lines: {513, 663}, {1648, 8029}

X(65666) = cross-difference of every pair of points on the line X(9)X(249)
X(65666) = perspector of the circumconic through X(57) and X(115)
X(65666) = pole of the line {318, 18020} with respect to the polar circle
X(65666) = pole of the line {1475, 55384} with respect to the Brocard inellipse
X(65666) = pole of the line {2262, 58907} with respect to the orthic inconic
X(65666) = pole of the line {643, 59152} with respect to the Stammler hyperbola
X(65666) = pole of the line {3210, 54104} with respect to the Steiner circumellipse
X(65666) = pole of the line {3752, 23991} with respect to the Steiner inellipse
X(65666) = pole of the line {7257, 31614} with respect to the Steiner-Wallace hyperbola

X(65667) = CROSSHEXAGON POINT OF THESE TRIANGLES: CIRCUMMEDIAL AND CIRCUMORTHIC

Barycentrics    a^20-3*(b^2+c^2)*a^18+2*(b^4+5*b^2*c^2+c^4)*a^16+2*((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^14-4*(b^8+c^8+2*b^2*c^2*(b^4+c^4))*a^12+4*(b^2+c^2)*(b^8+c^8+2*b^2*c^2*(2*b^4-b^2*c^2+2*c^4))*a^10-2*(b^12+c^12-b^4*c^4*(b^4+24*b^2*c^2+c^4))*a^8-2*(b^8-c^8)*a^6*(b^2-c^2)*(b^4+8*b^2*c^2+c^4)+(b^2-c^2)^2*(b^6-3*c^6+3*b^2*c^2*(b^2+c^2))*(3*b^6-c^6-3*b^2*c^2*(b^2+c^2))*a^4-(b^4-c^4)*(b^2-c^2)^3*(b^8+c^8-2*b^2*c^2*(2*b^4+b^2*c^2+2*c^4))*a^2-2*(b^2-c^2)^6*b^2*c^2*(b^2+c^2)^2 : :

X(65667) lies on these lines: {2, 65678}, {3260, 15574}, {18420, 44375}

X(65667) = anticomplement of X(65678)
X(65667) = X(65678)-Dao conjugate of-X(65678)

X(65668) = CROSSHEXAGON POINT OF THESE TRIANGLES: CIRCUMORTHIC AND 2nd CIRCUMPERP

Barycentrics    a^15-2*(b+c)*a^14-(b^2-7*b*c+c^2)*a^13+(b+c)*(6*b^2-11*b*c+6*c^2)*a^12-(5*b^4+5*c^4+(11*b^2-21*b*c+11*c^2)*b*c)*a^11-(b+c)*(5*b^4+5*c^4-2*(13*b^2-20*b*c+13*c^2)*b*c)*a^10+(10*b^6+10*c^6-(5*b^4+5*c^4+(23*b^2-42*b*c+23*c^2)*b*c)*b*c)*a^9-16*(b^3+c^3)*(b-c)^2*b*c*a^8-(5*b^6+5*c^6-2*(b^4+c^4+3*(b-c)^2*b*c)*b*c)*(b-c)^2*a^7+(b^2-c^2)*(b-c)*(2*b^4+2*c^4-(7*b^2-6*b*c+7*c^2)*b*c)*b*c*a^6-(b^2-c^2)^2*(b^6+c^6+(b^2+4*b*c+c^2)*(b-c)^2*b*c)*a^5+(b^2-c^2)*(b-c)^3*(2*b^6+2*c^6+(3*b^4+3*c^4+b*c*(7*b^2+16*b*c+7*c^2))*b*c)*a^4+(b^2-c^2)^2*(b-c)^2*(b^6+c^6+(b^4+c^4+b*c*(5*b^2-8*b*c+5*c^2))*b*c)*a^3-(b^2-c^2)^3*(b-c)^3*(b^4+5*b^2*c^2+c^4)*a^2-(b^2-c^2)^4*(b-c)^4*b*c*a-(b^2-c^2)^5*(b-c)*b^2*c^2 : :

X(65668) lies on these lines: {2, 65677}, {3, 65655}, {4, 14529}, {109, 1836}

X(65668) = reflection of X(i) in X(j) for these (i, j): (4, 65679), (65655, 3)
X(65668) = anticomplement of X(65677)
X(65668) = X(65677)-Dao conjugate of-X(65677)
X(65668) = X(65679)-of-anti-Euler triangle
X(65668) = X(65655)-of-ABC-X3 reflections triangle

X(65669) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd CONWAY AND STEINER

Barycentrics    (a+b)*(a+c)*(b-c)*(a^3-(b+c)*a^2-(b^2+b*c+c^2)*a+(b+c)*(b^2+c^2)) : :

X(65669) lies on these lines: {2, 2610}, {58, 49276}, {63, 42744}, {81, 918}, {86, 4453}, {99, 110}, {320, 350}, {333, 30565}, {1638, 5333}, {1639, 5235}, {3310, 25060}, {3738, 55022}, {3762, 21739}, {3910, 57189}, {4467, 7372}, {4560, 23876}, {4608, 56321}, {6546, 53412}, {8025, 48571}, {9511, 35983}, {16704, 47772}, {17212, 47755}, {18200, 47971}, {21222, 57076}, {25526, 62435}, {30992, 30995}, {35623, 65703}, {38477, 38480}, {45326, 64425}

X(65669) = reflection of X(21222) in X(57076)
X(65669) = anticomplement of X(2610)
X(65669) = anticomplementary conjugate of the anticomplement of X(37140)
X(65669) = isotomic conjugate of the anticomplement of X(38982)
X(65669) = isotomic conjugate of the isogonal conjugate of X(42741)
X(65669) = cross-difference of every pair of points on the line X(213)X(3124)
X(65669) = crosspoint of X(i) and X(j) for these {i, j}: {86, 65283}, {99, 14616}
X(65669) = crosssum of X(i) and X(j) for these {i, j}: {42, 42666}, {512, 3724}, {8648, 20959}
X(65669) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (759, 21221), (4556, 6224), (9273, 523), (9274, 4560), (14616, 21294), (24624, 3448), (32671, 192), (32675, 56291), (34079, 148), (36069, 2), (37140, 8), (40214, 14731), (47318, 1330), (52380, 37781), (57736, 39352), (57985, 13219), (58979, 662), (65283, 69)
X(65669) = X(55237)-Ceva conjugate of-X(16704)
X(65669) = X(38982)-cross conjugate of-X(2)
X(65669) = X(i)-Dao conjugate of-X(j) for these (i, j): (1086, 5620), (2610, 2610), (6626, 65238), (34021, 35156), (35090, 37), (40592, 1290), (40620, 21907), (40625, 11604), (53988, 1824)
X(65669) = X(i)-isoconjugate of-X(j) for these {i, j}: {42, 1290}, {213, 65238}, {692, 5620}, {1918, 35156}
X(65669) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (81, 1290), (86, 65238), (274, 35156), (514, 5620), (2074, 1783), (4560, 11604), (5127, 101), (5172, 4559), (7192, 21907), (8674, 37), (17796, 4557), (19622, 692), (32849, 3952), (37783, 100), (37799, 61178), (38982, 2610), (41541, 61171), (41542, 61170), (42670, 213), (42741, 6), (47235, 1824), (51646, 1400), (57447, 1637)
X(65669) = perspector of: the circumconic through X(274) and X(4590), the inconic with center X(38982)
X(65669) = pole of the line {1634, 16678} with respect to the circumcircle
X(65669) = pole of the line {1764, 32863} with respect to the Conway circle
X(65669) = pole of the line {1824, 8754} with respect to the polar circle
X(65669) = pole of the line {6360, 39352} with respect to the power circles radical circle
X(65669) = pole of the line {2, 1577} with respect to the Kiepert parabola
X(65669) = pole of the line {512, 692} with respect to the Stammler hyperbola
X(65669) = pole of the line {75, 99} with respect to the Steiner circumellipse
X(65669) = pole of the line {620, 3739} with respect to the Steiner inellipse
X(65669) = pole of the line {100, 523} with respect to the Steiner-Wallace hyperbola
X(65669) = pole of the line {1654, 17494} with respect to the Yff parabola
X(65669) = barycentric product X(i)*X(j) for these {i, j}: {76, 42741}, {274, 8674}, {693, 37783}, {2074, 15413}, {3261, 5127}, {6385, 42670}, {7192, 32849}, {15419, 56877}, {17796, 52619}, {19622, 40495}, {28660, 51646}
X(65669) = trilinear product X(i)*X(j) for these {i, j}: {75, 42741}, {86, 8674}, {310, 42670}, {314, 51646}, {514, 37783}, {693, 5127}, {1019, 32849}, {2074, 4025}, {3261, 19622}, {5172, 18155}, {7199, 17796}, {17206, 47235}, {38982, 65283}
X(65669) = trilinear quotient X(i)/X(j) for these (i, j): (86, 1290), (274, 65238), (310, 35156), (693, 5620), (2074, 8750), (5127, 692), (7199, 21907), (8674, 42), (18155, 11604), (19622, 32739), (32849, 1018), (37783, 101), (38982, 42666), (42670, 1918), (42741, 31), (47235, 2333), (51646, 1402)

X(65670) = CROSSHEXAGON POINT OF THESE TRIANGLES: DAO AND INCENTRAL

Barycentrics    a*(-a+b+c)^2*((b+c)*a^3+2*(b^2-b*c+c^2)*a^2+(b^2-c^2)*(b-c)*a+2*(b-c)^2*b*c) : :

X(65670) lies on these lines: {1, 7}, {11, 28352}, {38, 3057}, {42, 3486}, {55, 10448}, {78, 2899}, {200, 6552}, {212, 22760}, {497, 1201}, {774, 14110}, {851, 2646}, {899, 1837}, {950, 1193}, {958, 1253}, {960, 2310}, {976, 28104}, {1040, 3924}, {1066, 18481}, {1106, 63991}, {1107, 2269}, {1149, 12053}, {1457, 6284}, {1496, 12114}, {2098, 38496}, {2340, 12437}, {2650, 10391}, {3214, 5727}, {3270, 10544}, {3601, 27621}, {3616, 26050}, {3691, 53561}, {4186, 52092}, {4642, 9371}, {4849, 17632}, {4907, 15829}, {5274, 21214}, {5281, 59311}, {6737, 65671}, {7004, 64043}, {9316, 37022}, {9581, 27627}, {9819, 50637}, {10543, 14547}, {10572, 22350}, {10866, 45219}, {14714, 17793}, {17449, 64046}, {17452, 18671}, {37570, 62873}, {49487, 54295}, {52524, 64110}

X(65670) = crosspoint of X(1) and X(1043)
X(65670) = crosssum of X(1) and X(1042)
X(65670) = X(799)-Ceva conjugate of-X(657)
X(65670) = X(65503)-reciprocal conjugate of-X(657)
X(65670) = pole of the line {17418, 44408} with respect to the circumcircle
X(65670) = pole of the line {514, 40467} with respect to the incircle
X(65670) = pole of the line {354, 1201} with respect to the Feuerbach circumhyperbola
X(65670) = pole of the line {1042, 1043} with respect to the Steiner-Wallace hyperbola
X(65670) = barycentric product X(46406)*X(65503)
X(65670) = trilinear product X(4569)*X(65503)
X(65670) = trilinear quotient X(65503)/X(8641)
X(65670) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 20, 1042), (1, 4297, 1458), (1, 4304, 4300), (1, 4313, 2293), (20, 1042, 3000), (1837, 22072, 899), (2646, 2654, 3720), (6737, 65671, 65673)

X(65671) = CROSSHEXAGON POINT OF THESE TRIANGLES: DAO AND INTOUCH

Barycentrics    (-a+b+c)^2*(2*a^4+(b+c)*a^3+3*(b-c)^2*a^2+3*(b^2-c^2)*(b-c)*a-(b-c)^4) : :

X(65671) lies on these lines: {1, 9799}, {7, 45742}, {33, 39595}, {222, 51617}, {269, 10430}, {354, 39789}, {390, 62818}, {497, 3663}, {516, 62811}, {950, 3666}, {990, 11019}, {1040, 3008}, {2310, 40998}, {2999, 5809}, {3022, 5579}, {3100, 40940}, {3486, 37553}, {3664, 10391}, {3668, 10431}, {3914, 45275}, {4314, 62871}, {4319, 4847}, {4328, 10580}, {4383, 10392}, {5274, 23681}, {5324, 58326}, {6737, 65670}, {9812, 62780}, {10383, 29571}, {10473, 63601}, {10521, 40959}, {10624, 44706}, {11220, 62789}, {12053, 17597}

X(65671) = crosspoint of X(7) and X(1043)
X(65671) = crosssum of X(55) and X(1042)
X(65671) = pole of the line {657, 1021} with respect to the incircle
X(65671) = pole of the line {1122, 10481} with respect to the Feuerbach circumhyperbola
X(65671) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (10391, 40960, 3664), (65670, 65673, 6737)

X(65672) = CROSSHEXAGON POINT OF THESE TRIANGLES: DAO AND MACBEATH

Barycentrics    (-a+b+c)^2*((b^2+c^2)*a^5-(b+c)*(b^2-3*b*c+c^2)*a^4-2*(b^2-c^2)^2*a^3+2*(b-c)^2*(b^3+c^3)*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)*(b-c)^2*(b^3-c^3)) : :

X(65672) lies on these lines: {8, 90}, {92, 10883}, {318, 64564}, {1441, 65684}, {23661, 44256}, {50696, 56943}

X(65672) = crosspoint of X(264) and X(1043)
X(65672) = crosssum of X(184) and X(1042)
X(65672) = pole of the line {657, 1021} with respect to the MacBeath inconic

X(65673) = CROSSHEXAGON POINT OF THESE TRIANGLES: DAO AND ORTHIC

Barycentrics    (-a+b+c)^2*(2*a^5+(b+c)*a^4+4*(b^2-c^2)*(b-c)*a^2+2*(b^2-c^2)^2*a-(b^2-c^2)*(b-c)^3) : :

X(65673) lies on these lines: {1, 6837}, {8, 4319}, {10, 27521}, {65, 1827}, {515, 774}, {950, 2292}, {968, 3486}, {1254, 63998}, {1837, 1853}, {1858, 40950}, {1877, 1898}, {2650, 40960}, {3012, 5930}, {4320, 9799}, {4331, 5691}, {4332, 21628}, {4907, 12625}, {6737, 65670}, {6738, 42289}, {9316, 9948}, {12053, 49454}, {16870, 21935}, {18391, 65128}

X(65673) = crosspoint of X(4) and X(1043)
X(65673) = crosssum of X(3) and X(1042)
X(65673) = pole of the line {407, 1828} with respect to the Feuerbach circumhyperbola
X(65673) = pole of the line {657, 1021} with respect to the orthic inconic
X(65673) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1837, 1854, 3914), (1858, 40950, 41011), (6737, 65671, 65670)

X(65674) = CROSSHEXAGON POINT OF THESE TRIANGLES: DAO AND STEINER

Barycentrics    (a+b)*(a+c)*(b-c)*(-a+b+c)^2*(3*a^2-2*(b+c)*a-(b-c)^2) : :

X(65674) lies on these lines: {20, 24018}, {21, 58338}, {99, 24016}, {522, 663}, {1043, 15411}, {4367, 53269}, {4467, 65685}

X(65674) = cevapoint of X(57064) and X(58835)
X(65674) = crosspoint of X(i) and X(j) for these {i, j}: {99, 1043}, {333, 55284}
X(65674) = crosssum of X(512) and X(1042)
X(65674) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4573, 2287), (55284, 333)
X(65674) = X(i)-Dao conjugate of-X(j) for these (i, j): (4130, 3700), (7658, 523), (13609, 3668), (40582, 61240), (40602, 53622), (40605, 53640), (40620, 60831), (40625, 36620), (55067, 64980), (55068, 3062)
X(65674) = X(i)-isoconjugate of-X(j) for these {i, j}: {65, 53622}, {1018, 61380}, {1020, 11051}, {1400, 61240}, {1402, 53640}, {3062, 53321}, {4559, 64980}
X(65674) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (21, 61240), (144, 4566), (165, 1020), (284, 53622), (333, 53640), (1021, 3062), (3207, 53321), (3733, 61380), (3737, 64980), (4560, 36620), (7058, 55284), (7192, 60831), (7253, 10405), (7658, 3668), (13609, 523), (21060, 4605), (21789, 11051), (22117, 52610), (55285, 6354), (57064, 10), (58329, 19605), (58835, 37), (63965, 52607), (64083, 4552)
X(65674) = pole of the line {657, 1021} with respect to the Kiepert parabola
X(65674) = pole of the line {109, 53622} with respect to the Stammler hyperbola
X(65674) = pole of the line {664, 23973} with respect to the Steiner-Wallace hyperbola
X(65674) = barycentric product X(i)*X(j) for these {i, j}: {86, 57064}, {99, 13609}, {144, 7253}, {274, 58835}, {1021, 16284}, {1043, 7658}, {4560, 64083}, {7058, 55285}, {15411, 63965}, {31627, 58329}
X(65674) = trilinear product X(i)*X(j) for these {i, j}: {81, 57064}, {86, 58835}, {144, 1021}, {165, 7253}, {662, 13609}, {1098, 55285}, {2287, 7658}, {3160, 58329}, {3737, 64083}, {16284, 21789}, {21060, 65575}, {57081, 63965}
X(65674) = trilinear quotient X(i)/X(j) for these (i, j): (21, 53622), (144, 1020), (165, 53321), (314, 53640), (333, 61240), (1019, 61380), (1021, 11051), (4560, 64980), (7199, 60831), (7253, 3062), (7658, 1427), (13609, 661), (16284, 4566), (18155, 36620), (55285, 1254), (57064, 37), (58835, 42), (64083, 4551)
X(65674) = (X(4560), X(58329))-harmonic conjugate of X(7253)

X(65675) = CROSSHEXAGON POINT OF THESE TRIANGLES: DAO AND SYMMEDIAL

Barycentrics    a^2*(-a+b+c)^2*((b^2+c^2)*a^3+(b+c)*(2*b^2-3*b*c+2*c^2)*a^2+(b^2-c^2)^2*a+(b^2-c^2)*(b-c)*b*c) : :

X(65675) lies on these lines: {6, 45739}, {25, 41}, {1042, 11347}, {1183, 1193}, {1185, 1200}, {2264, 3725}, {2309, 20967}, {3009, 40962}, {3010, 3198}, {3778, 23638}, {14936, 40966}, {23632, 23640}

X(65675) = crosspoint of X(6) and X(1043)
X(65675) = crosssum of X(i) and X(j) for these {i, j}: {2, 1042}, {269, 6359}
X(65675) = X(65163)-Ceva conjugate of-X(8641)
X(65675) = pole of the line {657, 1021} with respect to the Brocard inellipse

X(65676) = CROSSHEXAGON POINT OF THESE TRIANGLES: EULER AND 5th EULER

Barycentrics    3*a^8-3*(b^2+c^2)*a^6+(13*b^4+58*b^2*c^2+13*c^4)*a^4-13*(b^4-c^4)*(b^2-c^2)*a^2-20*(b^2-c^2)^2*b^2*c^2 : :

X(65676) lies on these lines: {2, 39453}, {524, 3545}, {1990, 7736}, {5201, 11284}, {42849, 47097}

X(65676) = complement of X(65652)
X(65676) = X(43956)-of-Artzt triangle

X(65677) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd EULER AND 4th EULER

Barycentrics    2*(b^2+b*c+c^2)*a^13-(b+2*c)*(2*b+c)*(b+c)*a^12-(7*b^4+7*c^4-b*c*(b+3*c)*(3*b+c))*a^11+3*(b+c)*(2*b^4+2*c^4+3*b*c*(b-c)^2)*a^10+(10*b^6+10*c^6-(16*b^4+16*c^4+b*c*(7*b^2-30*b*c+7*c^2))*b*c)*a^9-(b+c)*(5*b^6+5*c^6+(5*b^4+5*c^4-12*b*c*(3*b^2-5*b*c+3*c^2))*b*c)*a^8-(10*b^8+10*c^8-(16*b^6+16*c^6-(13*b^4+13*c^4+6*b*c*(4*b^2-9*b*c+4*c^2))*b*c)*b*c)*a^7+(b^2-c^2)*(b-c)*(8*b^4+8*c^4-b*c*(11*b^2-30*b*c+11*c^2))*b*c*a^6+(10*b^8+10*c^8+(8*b^6+8*c^6+(5*b^4+5*c^4+2*b*c*(4*b^2-3*b*c+4*c^2))*b*c)*b*c)*(b-c)^2*a^5-3*(b^2-c^2)*(b-c)^3*(3*b^4+3*c^4+b*c*(3*b^2+4*b*c+3*c^2))*b*c*a^4-(b^2-c^2)^2*(b-c)^2*(7*b^6+7*c^6+(b^4+c^4+2*b*c*(b+c)^2)*b*c)*a^3+(b^2-c^2)^3*(b-c)*(2*b^6+2*c^6+b*c*(3*b^2-b*c+3*c^2)*(b-c)^2)*a^2+2*(b^2-c^2)^2*(b-c)^3*(b^3+c^3)*(b^4-c^4)*a-(b^2-c^2)^5*(b-c)*(b^2+c^2)*(b^2-b*c+c^2) : :

X(65677) lies on these lines: {2, 65668}, {4, 65655}, {5, 65679}, {124, 4640}

X(65677) = midpoint of X(4) and X(65655)
X(65677) = reflection of X(65679) in X(5)
X(65677) = complement of X(65668)
X(65677) = X(65679)-of-Johnson triangle
X(65677) = X(65655)-of-Euler triangle

X(65678) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd EULER AND 5th EULER

Barycentrics    3*(b^2+c^2)*a^18-(11*b^4+14*b^2*c^2+11*c^4)*a^16+2*(b^2+c^2)*(5*b^4+b^2*c^2+5*c^4)*a^14+2*(5*b^8+5*c^8+b^2*c^2*(5*b^4+12*b^2*c^2+5*c^4))*a^12-2*(b^2+c^2)*(12*b^8+12*c^8-b^2*c^2*(11*b^4-10*b^2*c^2+11*c^4))*a^10+2*(6*b^12+6*c^12-(11*b^8+11*c^8+2*b^2*c^2*(13*b^4+b^2*c^2+13*c^4))*b^2*c^2)*a^8+2*(b^2+c^2)*(3*b^12+3*c^12-(b^8+c^8-5*(-4*b^2*c^2+(b^2-c^2)^2)*b^2*c^2)*b^2*c^2)*a^6-2*(b^4-c^4)^2*(5*b^8+5*c^8-b^2*c^2*(11*b^4-4*b^2*c^2+11*c^4))*a^4+(b^2-c^2)^6*(b^2+c^2)*(5*b^4+8*b^2*c^2+5*c^4)*a^2-(b^4+c^4)*(b^2+c^2)^2*(b^2-c^2)^6 : :

X(65678) lies on these lines: {2, 65667}, {7514, 44388}

X(65678) = complement of X(65667)

X(65679) = CROSSHEXAGON POINT OF THESE TRIANGLES: 3rd EULER AND ORTHIC

Barycentrics    (b*a-b^2+c^2)*(c*a+b^2-c^2)*(2*a^7-(b+c)*a^6-(3*b^2-4*b*c+3*c^2)*a^5+(b^2-c^2)*(b-c)*a^4-3*(b-c)^2*b*c*a^3+(b^3-c^3)*(b^2-c^2)*a^2+(b^2-c^2)*(b-c)*(b^3+c^3)*a-(b^2-c^2)*(b-c)^2*(b^3-c^3)) : :

X(65679) lies on these lines: {2, 65655}, {4, 14529}, {5, 65677}, {117, 65520}

X(65679) = midpoint of X(4) and X(65668)
X(65679) = reflection of X(65677) in X(5)
X(65679) = complement of X(65655)
X(65679) = X(65677)-of-Johnson triangle
X(65679) = X(65668)-of-Euler triangle

X(65680) = CROSSHEXAGON POINT OF THESE TRIANGLES: EXCENTRAL AND PELLETIER

Barycentrics    a*(b-c)*(-a+b+c)*(2*a^2-(b+c)*a-(b-c)^2) : :
X(65680) = 2*X(650)-3*X(657) = 4*X(650)-3*X(21127) = 3*X(1635)-4*X(22108) = 4*X(3960)-3*X(53544) = X(4895)-3*X(65664)

X(65680) lies on these lines: {6, 1769}, {9, 3738}, {37, 53532}, {44, 513}, {101, 651}, {144, 53357}, {198, 53305}, {284, 35055}, {294, 1024}, {391, 4148}, {514, 50573}, {521, 4171}, {526, 2294}, {665, 53528}, {900, 42462}, {926, 2170}, {1156, 3887}, {1638, 3321}, {1757, 13259}, {1937, 52222}, {2178, 22379}, {2291, 15731}, {2520, 6608}, {2820, 5540}, {3063, 6615}, {3064, 48266}, {3569, 40977}, {3686, 4768}, {3958, 6370}, {4017, 20980}, {4131, 25924}, {4529, 20293}, {4728, 24712}, {4814, 6182}, {4822, 58332}, {4932, 27417}, {4958, 14400}, {6006, 14330}, {6068, 6366}, {6084, 40520}, {6139, 14392}, {7216, 64885}, {9029, 48322}, {9502, 53535}, {14282, 28225}, {14331, 48269}, {14413, 42082}, {17412, 48340}, {17439, 21320}, {17455, 42768}, {21828, 52307}, {22383, 55212}, {23730, 43042}, {23819, 49287}, {24792, 63589}, {26017, 46400}, {26985, 46402}, {36054, 55214}, {48151, 57180}, {50354, 57237}, {52306, 55210}, {53277, 54322}, {53286, 58370}, {58817, 59612}

X(65680) = midpoint of X(144) and X(53357)
X(65680) = reflection of X(i) in X(j) for these (i, j): (21127, 657), (23730, 43042)
X(65680) = polar conjugate of the isotomic conjugate of X(14414)
X(65680) = isogonal conjugate of X(37139)
X(65680) = cross-difference of every pair of points on the line X(1)X(651)
X(65680) = crosspoint of X(i) and X(j) for these {i, j}: {1, 37139}, {650, 23893}, {651, 1156}, {1155, 23890}, {1638, 6366}
X(65680) = crosssum of X(i) and X(j) for these {i, j}: {57, 43050}, {514, 30379}, {650, 1155}, {651, 23890}, {1156, 23893}, {2291, 35348}
X(65680) = X(i)-Ceva conjugate of-X(j) for these (i, j): (651, 42082), (1156, 2310), (1308, 55), (1638, 14413), (6366, 14392), (23890, 1155), (23893, 650), (37139, 1), (60094, 11), (60431, 33573), (61230, 663), (65222, 15730)
X(65680) = X(6139)-cross conjugate of-X(14413)
X(65680) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 35157), (11, 1121), (206, 36141), (223, 60487), (1015, 62723), (1084, 62764), (6594, 190), (6615, 60479), (8054, 34056), (14714, 41798), (17115, 23893), (32664, 14733), (33573, 30806), (35091, 75), (35110, 4554), (36033, 65304), (36103, 65335), (38991, 1156), (39025, 2291), (40629, 85), (52870, 4569), (52879, 658), (52880, 65164), (62579, 4391)
X(65680) = X(4895)-hirst inverse of-X(17435)
X(65680) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 14733}, {3, 65335}, {4, 65304}, {6, 35157}, {55, 60487}, {59, 60479}, {75, 36141}, {76, 32728}, {100, 34056}, {101, 62723}, {109, 1121}, {220, 65553}, {651, 1156}, {653, 60047}, {658, 4845}, {662, 62764}, {664, 2291}, {934, 41798}, {1146, 59105}, {1262, 63748}, {1275, 23351}, {1813, 65340}, {4554, 34068}, {4564, 35348}, {4569, 18889}, {4619, 60579}, {6139, 57563}, {7045, 23893}, {13138, 61493}, {14074, 46644}, {23346, 57565}, {53243, 62731}, {63857, 65297}
X(65680) = X(i)-line conjugate of-X(j) for these (i, j): (101, 651), (926, 2310), (2820, 9355), (3887, 1156), (14413, 42082)
X(65680) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1, 35157), (19, 65335), (31, 14733), (32, 36141), (48, 65304), (57, 60487), (269, 65553), (512, 62764), (513, 62723), (527, 4554), (560, 32728), (649, 34056), (650, 1121), (657, 41798), (663, 1156), (1055, 651), (1155, 664), (1323, 4569), (1638, 85), (1946, 60047), (2170, 60479), (2310, 63748), (3063, 2291), (3271, 35348), (4895, 52746), (6139, 1), (6366, 75), (6510, 65164), (6603, 190), (6610, 658), (6745, 668), (8641, 4845), (14392, 8), (14413, 7), (14414, 69), (14936, 23893), (18344, 65340), (20958, 35340), (21127, 62731), (23346, 7045), (23710, 18026), (23890, 1275), (23893, 57565), (24027, 59105), (30574, 1441), (30806, 4572), (33573, 4391), (35293, 883), (37139, 57563), (37780, 46406)
X(65680) = X(i)-zayin conjugate of-X(j) for these (i, j): (9, 14733), (43, 35157), (46, 65304), (63, 36141), (101, 35348), (170, 65553), (513, 34056), (514, 2291), (521, 61493), (650, 1156), (651, 23893), (652, 60047), (657, 4845), (661, 62764), (905, 41798), (1155, 651), (1156, 23890), (1308, 43050), (1742, 60487), (1745, 65335), (1759, 32728), (1776, 1813), (2170, 35340), (2958, 59105), (3887, 57), (4040, 62723), (4551, 60479), (5011, 109), (5030, 4551), (15726, 934), (21173, 1121), (21390, 34068), (23890, 650), (23893, 1155), (30295, 63203), (35348, 37787), (36002, 1020), (37787, 101), (43065, 100), (56741, 61240), (60479, 5030), (60782, 24029), (61224, 63748), (61230, 30379)
X(65680) = perspector of the circumconic through X(1) and X(650)
X(65680) = pole of the line {52508, 52509} with respect to the Adams circle
X(65680) = pole of the line {57, 934} with respect to the Bevan circle
X(65680) = pole of the line {55, 17439} with respect to the circumcircle
X(65680) = pole of the line {354, 3022} with respect to the incircle
X(65680) = pole of the line {92, 1121} with respect to the polar circle
X(65680) = pole of the line {517, 14392} with respect to the Stevanovic circle
X(65680) = pole of the line {42, 7117} with respect to the Brocard inellipse
X(65680) = pole of the line {17761, 21195} with respect to the circumhyperbola dual of Yff parabola
X(65680) = pole of the line {354, 38530} with respect to the de Longchamps ellipse
X(65680) = pole of the line {5435, 13478} with respect to the excentral-hexyl ellipse
X(65680) = pole of the line {650, 2310} with respect to the Feuerbach circumhyperbola
X(65680) = pole of the line {661, 3270} with respect to the Jerabek circumhyperbola
X(65680) = pole of the line {1254, 3157} with respect to the MacBeath circumconic
X(65680) = pole of the line {3057, 3271} with respect to the Mandart inellipse
X(65680) = pole of the line {65, 3270} with respect to the orthic inconic
X(65680) = pole of the line {662, 1021} with respect to the Stammler hyperbola
X(65680) = pole of the line {192, 63168} with respect to the Steiner circumellipse
X(65680) = pole of the line {37, 24025} with respect to the Steiner inellipse
X(65680) = pole of the line {799, 37139} with respect to the Steiner-Wallace hyperbola
X(65680) = pole of the line {40, 649} with respect to the Yff parabola
X(65680) = barycentric product X(i)*X(j) for these {i, j}: {1, 6366}, {4, 14414}, {7, 14392}, {8, 14413}, {9, 1638}, {21, 30574}, {75, 6139}, {269, 65448}, {513, 6745}, {514, 6603}, {521, 23710}, {522, 1155}, {523, 62756}, {527, 650}, {651, 33573}, {652, 37805}, {656, 52891}, {657, 37780}, {663, 30806}, {885, 35293}
X(65680) = trilinear product X(i)*X(j) for these {i, j}: {2, 6139}, {6, 6366}, {9, 14413}, {19, 14414}, {55, 1638}, {57, 14392}, {59, 52334}, {109, 33573}, {284, 30574}, {513, 6603}, {522, 1055}, {527, 663}, {647, 52891}, {649, 6745}, {650, 1155}, {652, 23710}, {657, 1323}, {661, 62756}, {1024, 35293}, {1146, 23346}
X(65680) = trilinear quotient X(i)/X(j) for these (i, j): (2, 35157), (3, 65304), (4, 65335), (6, 14733), (7, 60487), (11, 60479), (31, 36141), (32, 32728), (279, 65553), (513, 34056), (514, 62723), (522, 1121), (527, 664), (650, 1156), (652, 60047), (657, 4845), (661, 62764), (663, 2291), (1055, 109), (1146, 63748)
X(65680) = (1st circumperp)-isotomic conjugate-of-X(14733)
X(65680) = X(5027)-of-Honsberger triangle
X(65680) = X(14273)-of-excentral triangle
X(65680) = X(40890)-of-2nd Sharygin triangle
X(65680) = X(53272)-of-intouch triangle
X(65680) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2246, 2254, 1635), (2590, 2591, 657)

X(65681) = CROSSHEXAGON POINT OF THESE TRIANGLES: EXCENTRAL AND X-PARABOLA-TANGENTIAL

Barycentrics    a*(b-c)*(b^2-c^2)^2*(a^4-2*(b^2+b*c+c^2)*a^2+b^4+c^4+b*c*(b^2+b*c+c^2)) : :

X(65681) lies on these lines: {44, 513}, {1648, 8029}

X(65681) = cross-difference of every pair of points on the line X(1)X(249)
X(65681) = X(35347)-Ceva conjugate of-X(2643)
X(65681) = X(3005)-Dao conjugate of-X(59088)
X(65681) = X(i)-isoconjugate of-X(j) for these {i, j}: {249, 60055}, {24041, 59088}
X(65681) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2643, 60055), (3124, 59088)
X(65681) = X(662)-zayin conjugate of-X(59088)
X(65681) = perspector of the circumconic through X(1) and X(115)
X(65681) = pole of the line {92, 18020} with respect to the polar circle
X(65681) = pole of the line {42, 55384} with respect to the Brocard inellipse
X(65681) = pole of the line {11, 10278} with respect to the Kiepert circumhyperbola
X(65681) = pole of the line {65, 58907} with respect to the orthic inconic
X(65681) = pole of the line {662, 59152} with respect to the Stammler hyperbola
X(65681) = pole of the line {192, 54104} with respect to the Steiner circumellipse
X(65681) = pole of the line {37, 23991} with respect to the Steiner inellipse
X(65681) = pole of the line {799, 31614} with respect to the Steiner-Wallace hyperbola
X(65681) = trilinear quotient X(i)/X(j) for these (i, j): (115, 60055), (2643, 59088)

X(65682) = CROSSHEXAGON POINT OF THESE TRIANGLES: EXTOUCH AND 2nd HATZIPOLAKIS

Barycentrics    (-a+b+c)*(a^5+3*(b-c)^2*a^3+3*(b^2-c^2)*(b-c)*a^2+(b^2-c^2)*(b-c)^3) : :

X(65682) lies on these lines: {497, 30620}, {1836, 3271}, {1837, 40962}, {1851, 65687}, {4847, 52528}

X(65682) = crosspoint of X(8) and X(1119)
X(65682) = crosssum of X(56) and X(1260)
X(65682) = pole of the line {3669, 6591} with respect to the Mandart inellipse
X(65682) = (X(1851), X(65687))-harmonic conjugate of X(65688)

X(65683) = CROSSHEXAGON POINT OF THESE TRIANGLES: EXTOUCH AND LEMOINE

Barycentrics    (-a+b+c)*(4*a^3+(b^2+c^2)*a+3*(b^2-c^2)*(b-c)) : :

X(65683) lies on these lines: {9, 1837}, {30, 6205}, {80, 56532}, {4262, 34122}, {5525, 37702}, {6284, 41322}, {12019, 16788}, {16783, 18357}, {40663, 41319}, {53418, 65695}

X(65683) = crosspoint of X(8) and X(598)
X(65683) = crosssum of X(56) and X(574)
X(65683) = pole of the line {41501, 55927} with respect to the Kiepert circumhyperbola
X(65683) = pole of the line {522, 650} with respect to the Lemoine inellipse
X(65683) = pole of the line {351, 523} with respect to the Mandart inellipse
X(65683) = (X(53418), X(65695))-harmonic conjugate of X(65698)

X(65684) = CROSSHEXAGON POINT OF THESE TRIANGLES: EXTOUCH AND MACBEATH

Barycentrics    (-a+b+c)*((b^2+c^2)*a^3-(b^2-c^2)*(b-c)*a^2-(b^2-c^2)^2*a+(b^4-c^4)*(b-c)) : :

X(65684) lies on these lines: {1, 23292}, {2, 1897}, {3, 52365}, {4, 56943}, {5, 41013}, {8, 405}, {9, 45802}, {10, 25091}, {33, 33305}, {92, 8226}, {200, 3932}, {226, 59575}, {280, 443}, {306, 64171}, {318, 442}, {347, 57534}, {427, 21318}, {1006, 56877}, {1074, 64930}, {1214, 1861}, {1441, 65672}, {1503, 1726}, {1736, 13567}, {1809, 19525}, {1824, 19542}, {1864, 45206}, {1985, 7140}, {2321, 3693}, {2886, 6358}, {3101, 49132}, {3416, 42012}, {3717, 17658}, {3925, 4081}, {3998, 5295}, {4126, 14740}, {4939, 15845}, {5081, 11113}, {5090, 13442}, {5662, 22410}, {5729, 11433}, {5805, 20223}, {6198, 7515}, {6350, 7580}, {6708, 53008}, {6907, 38462}, {6923, 34332}, {7069, 41883}, {7123, 33163}, {7360, 33116}, {7718, 37052}, {8727, 64194}, {8728, 23661}, {10538, 11112}, {12135, 13733}, {14544, 59613}, {16608, 21911}, {20277, 36949}, {20588, 30620}, {21666, 34335}, {23528, 31419}, {23542, 50067}, {24430, 26932}, {25973, 52112}, {26061, 28125}, {29641, 51416}, {32858, 41228}, {39591, 43213}, {40688, 44311}

X(65684) = isotomic conjugate of the isogonal conjugate of X(42447)
X(65684) = crosspoint of X(8) and X(264)
X(65684) = crosssum of X(56) and X(184)
X(65684) = X(23581)-Ceva conjugate of-X(16608)
X(65684) = X(16608)-Dao conjugate of-X(3)
X(65684) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (16608, 7), (21911, 226), (23581, 85), (23726, 3676), (39796, 222), (42447, 6)
X(65684) = pole of the line {676, 39199} with respect to the polar circle
X(65684) = pole of the line {3688, 40944} with respect to the Feuerbach circumhyperbola
X(65684) = pole of the line {522, 650} with respect to the MacBeath inconic
X(65684) = pole of the line {297, 525} with respect to the Mandart inellipse
X(65684) = pole of the line {14344, 39470} with respect to the Steiner inellipse
X(65684) = barycentric product X(i)*X(j) for these {i, j}: {8, 16608}, {9, 23581}, {76, 42447}, {333, 21911}, {3699, 23726}, {7017, 39796}
X(65684) = trilinear product X(i)*X(j) for these {i, j}: {9, 16608}, {21, 21911}, {55, 23581}, {75, 42447}, {318, 39796}, {644, 23726}, {36048, 65444}
X(65684) = trilinear quotient X(i)/X(j) for these (i, j): (16608, 57), (21911, 65), (23581, 7), (23726, 3669), (39796, 603), (42447, 31)
X(65684) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (8, 17776, 1260), (427, 21318, 41007), (3925, 4081, 17860)

X(65685) = CROSSHEXAGON POINT OF THESE TRIANGLES: EXTOUCH AND STEINER

Barycentrics    (b-c)*(-a+b+c)*(2*a^2-(b+c)*a-b^2-c^2) : :
X(65685) = 3*X(6332)-X(44448) = 2*X(44448)-3*X(50333)

X(65685) lies on these lines: {1, 525}, {2, 55285}, {8, 57066}, {99, 7340}, {512, 48290}, {514, 50508}, {521, 14312}, {522, 4162}, {523, 4833}, {643, 39054}, {663, 3910}, {690, 48328}, {826, 48347}, {918, 4449}, {1019, 1499}, {1125, 41800}, {1577, 28473}, {1639, 4147}, {1697, 57121}, {2533, 47788}, {2605, 57081}, {2785, 7178}, {2786, 4504}, {2804, 56324}, {3004, 48136}, {3566, 4367}, {3669, 50357}, {3700, 3907}, {3716, 21120}, {3800, 47682}, {3810, 53523}, {3900, 6332}, {3904, 6362}, {4041, 14432}, {4083, 47890}, {4086, 56092}, {4170, 29126}, {4391, 4990}, {4467, 65674}, {4560, 4843}, {4707, 34958}, {4775, 29142}, {4811, 4977}, {4895, 48278}, {9508, 57088}, {16678, 22089}, {23770, 29082}, {23875, 48287}, {23876, 48294}, {28478, 50517}, {28481, 48324}, {29051, 48280}, {29062, 48285}, {29094, 48403}, {29162, 47728}, {29168, 58163}, {29200, 48344}, {29226, 48055}, {29240, 48273}, {29278, 47729}, {29284, 48330}, {29288, 48333}, {29298, 48395}, {29304, 48295}, {29312, 58160}, {29324, 50326}, {29354, 48296}, {29366, 48396}, {35057, 52355}, {39540, 65099}, {42337, 57091}, {47972, 58161}, {47988, 48123}, {47989, 48129}, {48166, 48401}, {48206, 59743}, {48209, 65414}, {48282, 49276}, {50342, 59549}, {53356, 65494}

X(65685) = midpoint of X(i) and X(j) for these (i, j): {4895, 48278}, {47682, 48337}, {48282, 49276}, {48333, 49279}
X(65685) = reflection of X(i) in X(j) for these (i, j): (3004, 48136), (4391, 4990), (4707, 34958), (4897, 4367), (21120, 3716), (47890, 48299), (47988, 48123), (47989, 48129), (48395, 49290), (50333, 6332), (50347, 663), (50357, 3669), (65099, 39540)
X(65685) = anticomplement of X(55285)
X(65685) = cross-difference of every pair of points on the line X(478)X(39690)
X(65685) = crosspoint of X(8) and X(99)
X(65685) = crosssum of X(i) and X(j) for these {i, j}: {56, 512}, {523, 23304}
X(65685) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (3062, 3448), (4565, 31527), (10405, 21294), (11051, 21221), (53622, 2475), (55284, 6327), (61240, 2893)
X(65685) = X(1043)-beth conjugate of-X(57066)
X(65685) = X(i)-Ceva conjugate of-X(j) for these (i, j): (53655, 333), (55284, 2)
X(65685) = X(i)-Dao conjugate of-X(j) for these (i, j): (17069, 523), (55285, 55285)
X(65685) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4416, 664), (4640, 651), (4934, 7178), (17069, 7)
X(65685) = perspector of the circumconic through X(4416) and X(34277)
X(65685) = pole of the line {1444, 3435} with respect to the circumcircle
X(65685) = pole of the line {1503, 1854} with respect to the incircle
X(65685) = pole of the line {11684, 64696} with respect to the incircle of anticomplementary triangle
X(65685) = pole of the line {407, 14257} with respect to the polar circle
X(65685) = pole of the line {3152, 20216} with respect to the power circles radical circle
X(65685) = pole of the line {2968, 40608} with respect to the Feuerbach circumhyperbola
X(65685) = pole of the line {522, 650} with respect to the Kiepert parabola
X(65685) = pole of the line {2, 6} with respect to the Mandart inellipse
X(65685) = pole of the line {16680, 53324} with respect to the Stammler hyperbola
X(65685) = pole of the line {333, 5792} with respect to the Steiner circumellipse
X(65685) = pole of the line {1375, 16832} with respect to the Steiner inellipse
X(65685) = barycentric product X(i)*X(j) for these {i, j}: {8, 17069}, {522, 4416}, {645, 4934}, {4391, 4640}
X(65685) = trilinear product X(i)*X(j) for these {i, j}: {9, 17069}, {522, 4640}, {643, 4934}, {650, 4416}
X(65685) = trilinear quotient X(i)/X(j) for these (i, j): (4416, 651), (4640, 109), (4934, 4017), (17069, 57)

X(65686) = CROSSHEXAGON POINT OF THESE TRIANGLES: FEUERBACH AND LEMOINE

Barycentrics    (b+c)*(4*a^5+8*(b+c)*a^4-(b^2-12*b*c+c^2)*a^3-(b+c)*(5*b^2-12*b*c+5*c^2)*a^2-(5*b^4+5*c^4-b*c*(3*b^2+8*b*c+3*c^2))*a-(b+c)*(4*b^4+4*c^4-b*c*(3*b^2+b*c+3*c^2))) : :

X(65686) lies on these lines: {9, 46}, {597, 598}

X(65686) = pole of the line {1, 598} with respect to the Kiepert circumhyperbola

X(65687) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND INCENTRAL

Barycentrics    a*((b+c)*a^4-2*(b-c)^2*a^3+2*(b^2-c^2)^2*a-(b^2-c^2)*(b-c)^3) : :

X(65687) lies on these lines: {1, 939}, {6, 354}, {31, 65}, {34, 1407}, {38, 1212}, {73, 52541}, {204, 1876}, {210, 3011}, {212, 1279}, {223, 3660}, {244, 1427}, {269, 64207}, {517, 16485}, {938, 1097}, {942, 1453}, {948, 63994}, {971, 23681}, {1086, 63995}, {1122, 26892}, {1201, 17609}, {1428, 44087}, {1851, 65682}, {1864, 3772}, {2262, 40959}, {2299, 18191}, {2999, 11018}, {3271, 40961}, {3742, 5712}, {3752, 14547}, {3812, 5716}, {3914, 14100}, {4000, 10391}, {4847, 14523}, {5173, 7290}, {5222, 11020}, {5439, 5717}, {5728, 40940}, {5784, 24789}, {9850, 23675}, {10167, 24177}, {10202, 51340}, {10394, 62208}, {11227, 62695}, {12680, 23536}, {15852, 24443}, {16465, 26723}, {16572, 62823}, {16583, 20229}, {16700, 54411}, {16968, 20358}, {17194, 37597}, {17435, 20311}, {17612, 24175}, {20227, 30456}, {20264, 64658}, {26934, 40970}, {32636, 54431}, {37646, 61660}, {63007, 64149}

X(65687) = crosspoint of X(i) and X(j) for these {i, j}: {1, 1119}, {1422, 40154}
X(65687) = crosssum of X(i) and X(j) for these {i, j}: {1, 1260}, {2324, 6600}
X(65687) = X(36049)-Ceva conjugate of-X(513)
X(65687) = pole of the line {34847, 40677} with respect to the circumhyperbola dual of Yff parabola
X(65687) = pole of the line {4394, 51648} with respect to the de Longchamps ellipse
X(65687) = pole of the line {2385, 4319} with respect to the Feuerbach circumhyperbola
X(65687) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 10900, 1260), (244, 40958, 1427), (65682, 65688, 1851)

X(65688) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND INTOUCH

Barycentrics    (a+b-c)*(a-b+c)*(a^3+(b^2-c^2)*(b-c)) : :

X(65688) lies on these lines: {7, 8}, {11, 41010}, {19, 1086}, {37, 28081}, {40, 4862}, {55, 3663}, {56, 2218}, {57, 1723}, {71, 17276}, {196, 37790}, {226, 17355}, {269, 1358}, {273, 16099}, {307, 24914}, {347, 1319}, {355, 17885}, {604, 53545}, {1111, 64122}, {1118, 1119}, {1439, 18838}, {1836, 12723}, {1837, 17861}, {1842, 17054}, {1851, 65682}, {1875, 65582}, {2093, 4902}, {2264, 4000}, {2285, 52023}, {2294, 4675}, {2995, 23989}, {3101, 33146}, {3189, 4452}, {3598, 62783}, {3662, 11683}, {3664, 52563}, {3665, 10436}, {3666, 28108}, {3672, 37080}, {3674, 24549}, {3752, 28107}, {3772, 26934}, {3782, 10319}, {3925, 25590}, {3945, 44840}, {4329, 12701}, {4346, 37568}, {4373, 17784}, {4415, 28038}, {4419, 28015}, {4654, 50048}, {4887, 37567}, {4888, 11529}, {5435, 31232}, {5575, 40617}, {6047, 54422}, {6173, 54424}, {7179, 55096}, {7225, 17301}, {7243, 10447}, {7271, 63574}, {7702, 10400}, {11375, 41003}, {11376, 24179}, {16732, 54008}, {17189, 40980}, {17272, 21677}, {17278, 54324}, {17728, 53596}, {17863, 28109}, {17895, 21270}, {18634, 40535}, {20872, 22464}, {23536, 64022}, {24779, 59681}, {28023, 28112}, {37550, 62780}, {41245, 63588}, {53594, 63146}

X(65688) = cevapoint of X(3924) and X(36570)
X(65688) = crosspoint of X(7) and X(1119)
X(65688) = crosssum of X(55) and X(1260)
X(65688) = X(i)-beth conjugate of-X(j) for these (i, j): (2, 30811), (17861, 17861)
X(65688) = X(i)-Ceva conjugate of-X(j) for these (i, j): (7, 41004), (13149, 3669)
X(65688) = X(i)-cross conjugate of-X(j) for these (i, j): (3924, 3772), (64654, 16749)
X(65688) = X(i)-Dao conjugate of-X(j) for these (i, j): (223, 40436), (478, 56003), (3160, 59759), (3772, 1265), (7117, 57055), (9296, 42380), (17113, 34399), (40837, 34406)
X(65688) = X(i)-isoconjugate of-X(j) for these {i, j}: {9, 56003}, {41, 59759}, {55, 40436}, {78, 56305}, {212, 34406}, {219, 55994}, {663, 65370}, {1253, 34399}, {1919, 42380}
X(65688) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (7, 59759), (34, 55994), (56, 56003), (57, 40436), (278, 34406), (279, 34399), (608, 56305), (651, 65370), (668, 42380), (1837, 346), (3772, 8), (3924, 9), (16749, 314), (17189, 333), (17861, 312), (21935, 2321), (26934, 78), (36570, 1), (40968, 200), (40980, 2287), (41004, 345), (53279, 644), (64654, 960), (65445, 4130)
X(65688) = pole of the line {3669, 6591} with respect to the incircle
X(65688) = pole of the line {950, 3663} with respect to the circumhyperbola dual of Yff parabola
X(65688) = pole of the line {497, 14523} with respect to the Feuerbach circumhyperbola
X(65688) = pole of the line {2194, 56948} with respect to the Stammler hyperbola
X(65688) = pole of the line {4885, 28590} with respect to the Steiner inellipse
X(65688) = barycentric product X(i)*X(j) for these {i, j}: {7, 3772}, {57, 17861}, {65, 16749}, {75, 36570}, {85, 3924}, {226, 17189}, {273, 26934}, {278, 41004}, {279, 1837}, {1088, 40968}, {1434, 21935}, {1446, 40980}, {24002, 53279}, {31643, 64654}, {36838, 65445}
X(65688) = trilinear product X(i)*X(j) for these {i, j}: {2, 36570}, {7, 3924}, {34, 41004}, {56, 17861}, {57, 3772}, {65, 17189}, {269, 1837}, {278, 26934}, {279, 40968}, {1014, 21935}, {1400, 16749}, {3668, 40980}, {3676, 53279}, {4626, 65445}, {64654, 64984}
X(65688) = trilinear quotient X(i)/X(j) for these (i, j): (7, 40436), (34, 56305), (57, 56003), (85, 59759), (273, 34406), (278, 55994), (664, 65370), (1088, 34399), (1837, 200), (1978, 42380), (3772, 9), (3924, 55), (16749, 333), (17189, 21), (17861, 8), (21935, 210), (26934, 219), (36570, 6), (40968, 220), (40980, 2328)
X(65688) = X(8745)-of-intouch triangle
X(65688) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (7, 75, 30617), (7, 85, 10401), (7, 7195, 1122), (56, 63575, 3668), (1851, 65687, 65682), (17861, 41004, 1837), (24179, 41007, 11376)

X(65689) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND MACBEATH

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2+2*(b^2-c^2)*(b-c)*a+(b^2+c^2)*(b-c)^2) : :

X(65689) lies on these lines: {4, 4452}, {273, 2969}, {347, 37366}, {427, 3263}, {1441, 37439}, {1862, 3875}, {1878, 3663}, {3672, 17516}, {12138, 64122}

X(65689) = crosspoint of X(264) and X(1119)
X(65689) = crosssum of X(184) and X(1260)
X(65689) = pole of the line {3669, 6591} with respect to the MacBeath inconic

X(65690) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND STEINER

Barycentrics    (b-c)*(4*a^5+3*(b+c)*a^4-2*(b^2+c^2)*a^3+2*(b+c)*(b^2-3*b*c+c^2)*a^2+2*(b^2-c^2)^2*a-(b^4-c^4)*(b-c)) : :

X(65690) lies on these lines: {21184, 29240}, {48013, 48039}

X(65690) = crosspoint of X(99) and X(1119)
X(65690) = crosssum of X(512) and X(1260)
X(65690) = pole of the line {3669, 6591} with respect to the Kiepert parabola

X(65691) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND SYMMEDIAL

Barycentrics    a^2*((b^2+c^2)*a^4-2*(b^2-c^2)*(b-c)*a^3-2*(b-c)^2*b*c*a^2+2*(b^4-c^4)*(b-c)*a-(b^2-c^2)^2*(b-c)^2) : :

X(65691) lies on these lines: {6, 10934}, {31, 52020}, {51, 1400}, {184, 7083}, {511, 27624}, {604, 3271}, {1108, 42447}, {1475, 20978}, {3270, 3554}, {3917, 27626}, {3937, 28017}, {4000, 22440}, {5222, 50658}, {37993, 54321}

X(65691) = crosspoint of X(6) and X(1119)
X(65691) = crosssum of X(2) and X(1260)
X(65691) = pole of the line {3669, 6591} with respect to the Brocard inellipse

X(65692) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HATZIPOLAKIS AND YFF CONTACT

Barycentrics    (b-c)*(5*a^4-4*b*c*a^2+4*(b^2-c^2)*(b-c)*a-(b^2-c^2)^2) : :

X(65692) lies on these lines: {513, 21120}, {522, 47700}, {3667, 4498}, {4017, 47801}

X(65692) = crosspoint of X(190) and X(1119)
X(65692) = crosssum of X(649) and X(1260)
X(65692) = pole of the line {2136, 41575} with respect to the Bevan circle
X(65692) = pole of the line {1, 26065} with respect to the incircle of anticomplementary triangle
X(65692) = pole of the line {26685, 30568} with respect to the Steiner circumellipse
X(65692) = pole of the line {3669, 6591} with respect to the Yff parabola

X(65693) = CROSSHEXAGON POINT OF THESE TRIANGLES: HUTSON INTOUCH AND MIDARC

Barycentrics    2*(-a+b+c)*(b-c)*(a^4+(b+c)*a^3-(b-c)^2*a^2-(b+c)*(b^2-6*b*c+c^2)*a+4*b*c*(b-c)^2)*sin(A/2)+2*(-a+b+c)*a*((b-9*c)*a^3+(b^2-10*b*c+17*c^2)*a^2-(b^2-c^2)*(b-3*c)*a+(b^2-c^2)*(b-c)*(-b+3*c))*sin(B/2)+2*(-a+b+c)*a*((9*b-c)*a^3-(17*b^2-10*b*c+c^2)*a^2+(b^2-c^2)*(3*b-c)*a+(b^2-c^2)*(b-c)*(-3*b+c))*sin(C/2)-(-a+b+c)*(b-c)*(21*a^4-26*(b+c)*a^3+4*(3*b^2+b*c+3*c^2)*a^2-6*(b^2-c^2)*(b-c)*a-(b^2-6*b*c+c^2)*(b-c)^2) : :

X(65693) lies on these lines: {1, 166}, {9, 12646}, {168, 1697}, {177, 3057}, {390, 8084}, {8083, 11191}, {10501, 11234}

X(65693) = reflection of X(i) in X(j) for these (i, j): (8422, 10968), (65699, 1)
X(65693) = (midarc)-isogonal conjugate-of-X(58868)
X(65693) = X(65699)-of-5th mixtilinear triangle
X(65693) = X(63970)-of-Ursa-minor triangle
X(65693) = X(36991)-of-inverse-in-incircle triangle
X(65693) = X(5732)-of-intouch triangle
X(65693) = X(9)-of-Hutson intouch triangle

X(65694) = CROSSHEXAGON POINT OF THESE TRIANGLES: 2nd HYACINTH AND SCHRÖETER

Barycentrics    (b^2-c^2)*(a^6-3*(b^2+c^2)*a^4+(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2-c^2)) : :

X(65694) lies on these lines: {4, 43709}, {6, 38359}, {30, 511}, {64, 15328}, {66, 35364}, {74, 40048}, {110, 53953}, {125, 16178}, {351, 13223}, {686, 2501}, {879, 34207}, {925, 46969}, {1177, 51480}, {1853, 65610}, {2883, 60342}, {2935, 15470}, {3265, 46953}, {3569, 47125}, {3657, 43703}, {4143, 35522}, {5466, 54778}, {5489, 9914}, {5894, 38401}, {5895, 62172}, {6132, 59706}, {6562, 57154}, {6563, 57275}, {6759, 61756}, {9142, 48989}, {9145, 48958}, {10117, 30715}, {10264, 57512}, {10279, 10412}, {11744, 15453}, {12250, 18808}, {13400, 65656}, {14380, 43695}, {15139, 47627}, {16172, 57065}, {23300, 56739}, {23301, 65459}, {27087, 44816}, {30735, 33294}, {34952, 54061}, {34963, 39510}, {34967, 39511}, {41362, 43088}, {45261, 59568}, {46608, 64759}, {47194, 53263}, {53331, 57069}, {57638, 65309}, {58757, 58892}, {58812, 58888}, {58882, 65472}, {59652, 65478}

X(65694) = isogonal conjugate of X(13398)
X(65694) = cross-difference of every pair of points on the line X(6)X(1147)
X(65694) = crosspoint of X(i) and X(j) for these {i, j}: {4, 925}, {99, 2052}, {110, 57387}
X(65694) = crosssum of X(i) and X(j) for these {i, j}: {3, 924}, {512, 577}, {523, 11585}
X(65694) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (921, 3448), (6504, 21294), (13398, 8), (60775, 21221)
X(65694) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4, 135), (99, 6503), (925, 34853), (44064, 3), (57065, 2501), (65309, 6)
X(65694) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 135), (163, 6503), (921, 125), (4575, 34853), (6504, 21253), (13398, 10), (15316, 34846), (39416, 63843), (57998, 53575), (60775, 8287), (63958, 34825)
X(65694) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 6504), (125, 15316), (135, 34756), (136, 254), (137, 8800), (139, 39114), (244, 921), (1084, 60775), (2165, 65309), (4858, 57998), (5139, 39109), (6753, 57065), (16178, 16172), (34853, 63958), (39013, 57484), (46093, 60835)
X(65694) = X(i)-isoconjugate of-X(j) for these {i, j}: {47, 63958}, {110, 921}, {162, 15316}, {163, 6504}, {254, 4575}, {662, 60775}, {1576, 57998}, {4592, 39109}, {8800, 36134}, {36126, 60835}, {36145, 57484}
X(65694) = X(i)-line conjugate of-X(j) for these (i, j): (30, 34382), (38359, 6)
X(65694) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (135, 57065), (155, 4558), (512, 60775), (523, 6504), (647, 15316), (661, 921), (920, 662), (924, 57484), (1577, 57998), (1609, 110), (2165, 63958), (2489, 39109), (2501, 254), (3542, 648), (6515, 99), (6753, 34756), (8883, 18315), (12077, 8800), (14593, 39416), (14618, 46746), (15478, 43755), (32320, 60835), (33808, 799), (34853, 65309), (35603, 41679), (39116, 46134), (40697, 4563), (41587, 14570), (44816, 323), (47236, 16172), (47731, 925), (51425, 2407), (51513, 41536), (52317, 40678), (55265, 59497), (57070, 317), (58792, 59155), (58812, 3542), (58888, 21), (63959, 1993), (64455, 4592)
X(65694) = X(i)-vertex conjugate of-X(j) for these {i, j}: {3, 44665}, {68, 54061}, {57638, 57638}
X(65694) = center of the circumconic through X(58812) and X(65694)
X(65694) = perspector of the circumconic through X(2) and X(847)
X(65694) = barycentric product X(i)*X(j) for these {i, j}: {68, 57070}, {94, 44816}, {135, 65309}, {155, 14618}, {523, 6515}, {525, 3542}, {661, 33808}, {850, 1609}, {920, 1577}, {924, 39116}, {1441, 58888}, {2394, 51425}, {2501, 40697}, {5392, 63959}, {6563, 47731}, {8883, 18314}, {15412, 41587}, {24006, 64455}, {34853, 57065}, {52582, 58792}
X(65694) = trilinear product X(i)*X(j) for these {i, j}: {91, 63959}, {155, 24006}, {226, 58888}, {512, 33808}, {523, 920}, {656, 3542}, {661, 6515}, {1577, 1609}, {1820, 57070}, {2166, 44816}, {2501, 64455}, {2616, 41587}, {2618, 8883}, {39116, 55216}, {47731, 63827}
X(65694) = trilinear quotient X(i)/X(j) for these (i, j): (91, 63958), (155, 4575), (523, 921), (656, 15316), (661, 60775), (850, 57998), (920, 110), (1577, 6504), (1609, 163), (2618, 8800), (3542, 162), (6515, 662), (8883, 36134), (24006, 254), (33808, 99), (39116, 65251), (40697, 4592), (41587, 2617), (44816, 6149), (47731, 36145)

X(65695) = CROSSHEXAGON POINT OF THESE TRIANGLES: INCENTRAL AND LEMOINE

Barycentrics    a*(b+c)*(2*a^2-b^2+3*b*c-c^2) : :

X(65695) lies on these lines: {1, 574}, {10, 21057}, {37, 65}, {42, 4128}, {213, 3754}, {517, 24512}, {672, 21332}, {762, 4067}, {1449, 5114}, {1743, 54382}, {2238, 3753}, {2243, 16788}, {2650, 20691}, {2802, 16971}, {3125, 3919}, {3230, 5883}, {3340, 54317}, {3698, 21874}, {3726, 5902}, {3727, 5903}, {3780, 5836}, {3922, 16605}, {3954, 4084}, {3987, 20970}, {4004, 16583}, {4674, 40747}, {4695, 21904}, {4699, 21281}, {4757, 28594}, {5228, 37789}, {5710, 16884}, {9259, 27003}, {9346, 49494}, {9620, 63099}, {10107, 41015}, {17365, 30806}, {17450, 20358}, {53418, 65683}, {60353, 60697}

X(65695) = cross-difference of every pair of points on the line X(3737)X(48226)
X(65695) = crosspoint of X(1) and X(598)
X(65695) = crosssum of X(1) and X(574)
X(65695) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (50128, 274), (65458, 48226)
X(65695) = pole of the line {44, 513} with respect to the Lemoine inellipse
X(65695) = barycentric product X(i)*X(j) for these {i, j}: {37, 50128}, {27777, 53114}
X(65695) = trilinear product X(i)*X(j) for these {i, j}: {42, 50128}, {27777, 28658}
X(65695) = trilinear quotient X(i)/X(j) for these (i, j): (27777, 5235), (50128, 86)
X(65695) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 6205, 574), (65, 2295, 3721), (213, 3754, 21951), (3125, 3997, 46907), (3919, 3997, 3125), (5903, 17750, 3727), (65683, 65698, 53418)

X(65696) = CROSSHEXAGON POINT OF THESE TRIANGLES: INTANGENTS AND 2nd TANGENTIAL-MIDARC

Barycentrics    a*(4*(-a+b+c)*(b-c)*(a^2-2*(b+c)*a+b^2+c^2)*sin(A/2)+(-a+b+c)*(a-b+c)*(a^2-2*(3*b-2*c)*a+b^2-c^2)*sin(B/2)-(-a+b+c)*(a+b-c)*(a^2+2*(2*b-3*c)*a-b^2+c^2)*sin(C/2)-2*(-a+b+c)*(b-c)*(a+b-c)*(a-b+c)) : :

X(65696) lies on these lines: {1, 65411}, {513, 4162}, {6728, 6729}

X(65696) = reflection of X(65661) in X(1)
X(65696) = cevapoint of X(4162) and X(6729)
X(65696) = cross-difference of every pair of points on the line X(173)X(266)
X(65696) = crosspoint of X(i) and X(j) for these {i, j}: {1, 55363}, {1488, 55332}
X(65696) = crosssum of X(i) and X(j) for these {i, j}: {1, 65661}, {8422, 65651}
X(65696) = X(65651)-Ceva conjugate of-X(10495)
X(65696) = X(i)-isoconjugate of-X(j) for these {i, j}: {12644, 13444}, {24242, 43192}
X(65696) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (8078, 55341), (61635, 55328)
X(65696) = perspector of the circumconic through X(188) and X(258)
X(65696) = pole of the line {3057, 8422} with respect to the incircle
X(65696) = pole of the line {16019, 17490} with respect to the Steiner circumellipse
X(65696) = pole of the line {16016, 16602} with respect to the Steiner inellipse
X(65696) = barycentric product X(i)*X(j) for these {i, j}: {10492, 12646}, {39121, 65651}
X(65696) = trilinear product X(8078)*X(10495)
X(65696) = trilinear quotient X(i)/X(j) for these (i, j): (8078, 43192), (10495, 24242), (12646, 55342), (39121, 55331), (61635, 13444)
X(65696) = X(65661)-of-5th mixtilinear triangle
X(65696) = X(54239)-of-excenters-reflections triangle
X(65696) = X(39199)-of-Hutson intouch triangle

X(65697) = CROSSHEXAGON POINT OF THESE TRIANGLES: INTANGENTS AND URSA MINOR

Barycentrics    a^2*(b-c)*(-a+b+c)*((b+c)*a-b^2+b*c-c^2) : :
X(65697) = 3*X(354)-2*X(3676) = 3*X(354)-X(44319) = 3*X(650)-2*X(4524) = 3*X(663)-X(53562) = 3*X(2488)-X(4524) = 3*X(3873)-X(47676)

X(65697) lies on these lines: {1, 58324}, {11, 3835}, {55, 649}, {56, 65659}, {65, 28292}, {101, 6066}, {210, 4521}, {354, 3676}, {390, 26853}, {497, 20295}, {512, 4162}, {513, 11934}, {518, 4468}, {521, 50347}, {522, 50518}, {523, 50519}, {650, 926}, {652, 663}, {654, 8641}, {661, 9029}, {788, 50503}, {1155, 15599}, {1357, 44045}, {1859, 3064}, {2499, 48026}, {2520, 11193}, {2774, 4794}, {3022, 3025}, {3056, 9002}, {3057, 29350}, {3058, 4785}, {3309, 4897}, {3667, 51662}, {3669, 39541}, {3700, 54271}, {3741, 59673}, {3873, 23761}, {3900, 4976}, {4040, 64878}, {4375, 36488}, {4413, 25955}, {4423, 25924}, {4429, 26571}, {4435, 9437}, {4449, 23740}, {4724, 9000}, {4775, 58369}, {4834, 58334}, {4840, 42312}, {4995, 45313}, {5218, 27013}, {5263, 26652}, {5274, 26798}, {5432, 31286}, {5577, 5582}, {5580, 59807}, {6006, 14100}, {6018, 6024}, {6182, 13401}, {6589, 65703}, {9010, 50490}, {9313, 50521}, {10391, 48013}, {10589, 27138}, {11238, 31147}, {17115, 46389}, {21321, 27673}, {42319, 42322}, {42341, 48087}, {47883, 57232}, {50506, 50510}

X(65697) = midpoint of X(4724) and X(53554)
X(65697) = reflection of X(i) in X(j) for these (i, j): (650, 2488), (3669, 39541), (44319, 3676), (46389, 17115), (48026, 2499), (50506, 50510), (50513, 50514)
X(65697) = cross-difference of every pair of points on the line X(218)X(226)
X(65697) = crosspoint of X(i) and X(j) for these {i, j}: {7, 101}, {1172, 26706}
X(65697) = crosssum of X(i) and X(j) for these {i, j}: {1, 58324}, {55, 514}, {65, 43049}, {3676, 24796}, {16593, 55133}
X(65697) = X(200)-beth conjugate of-X(4521)
X(65697) = X(7192)-Ceva conjugate of-X(650)
X(65697) = X(i)-Dao conjugate of-X(j) for these (i, j): (210, 3952), (17059, 8), (38991, 60075), (52594, 3261)
X(65697) = X(651)-isoconjugate of-X(60075)
X(65697) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (663, 60075), (3873, 4554), (3941, 651), (4253, 664), (4905, 85), (17059, 3261), (17092, 4569), (17234, 4572), (21946, 850), (22277, 4552), (23761, 23989), (25082, 668), (40599, 3952), (47676, 6063), (52594, 8), (61038, 4559), (64739, 190)
X(65697) = perspector of the circumconic through X(277) and X(284)
X(65697) = pole of the line {48, 672} with respect to the circumcircle
X(65697) = pole of the line {3, 41} with respect to the (circumcircle, incircle)-inverter)
X(65697) = pole of the line {674, 2900} with respect to the Conway circle
X(65697) = pole of the line {6, 31} with respect to the incircle
X(65697) = pole of the line {55, 64553} with respect to the de Longchamps ellipse
X(65697) = pole of the line {812, 1015} with respect to the Feuerbach circumhyperbola
X(65697) = pole of the line {3691, 3715} with respect to the Mandart inellipse
X(65697) = pole of the line {17278, 20269} with respect to the Steiner inellipse
X(65697) = barycentric product X(i)*X(j) for these {i, j}: {7, 52594}, {9, 4905}, {55, 47676}, {101, 17059}, {110, 21946}, {513, 25082}, {514, 64739}, {522, 4253}, {650, 3873}, {663, 17234}, {1252, 23761}, {3063, 33933}, {3737, 3970}, {3900, 17092}, {3941, 4391}, {4162, 27827}, {4560, 22277}, {7192, 40599}
X(65697) = trilinear product X(i)*X(j) for these {i, j}: {41, 47676}, {55, 4905}, {57, 52594}, {163, 21946}, {513, 64739}, {522, 3941}, {649, 25082}, {650, 4253}, {657, 17092}, {663, 3873}, {692, 17059}, {1019, 40599}, {1110, 23761}, {3063, 17234}, {3737, 22277}, {3970, 7252}, {18155, 61038}
X(65697) = trilinear quotient X(i)/X(j) for these (i, j): (650, 60075), (3873, 664), (3941, 109), (3970, 4552), (4253, 651), (4905, 7), (17059, 693), (17092, 658), (17234, 4554), (21946, 1577), (22277, 4551), (23761, 1111), (25082, 190), (33933, 4572), (40599, 1018), (47676, 85), (52594, 9), (64739, 100)
X(65697) = (intouch)-isogonal conjugate-of-X(1086)
X(65697) = (Mandart-incircle)-isogonal conjugate-of-X(24840)
X(65697) = X(647)-of-Ursa-minor triangle
X(65697) = X(649)-of-Mandart-incircle triangle
X(65697) = X(850)-of-intouch triangle
X(65697) = X(31296)-of-inverse-in-incircle triangle
X(65697) = X(65659)-of-2nd anti-circumperp-tangential triangle
X(65697) = (X(354), X(44319))-harmonic conjugate of X(3676)

X(65698) = CROSSHEXAGON POINT OF THESE TRIANGLES: INTOUCH AND LEMOINE

Barycentrics    4*a^3+(b^2+c^2)*a-3*(b^2-c^2)*(b-c) : :

X(65698) lies on these lines: {1, 30}, {7, 31599}, {31, 17070}, {55, 17775}, {65, 53614}, {149, 17365}, {516, 4689}, {528, 24725}, {545, 29832}, {553, 51615}, {896, 2886}, {940, 9812}, {1699, 37634}, {1770, 37599}, {3434, 64070}, {3999, 30424}, {4054, 28566}, {4312, 17721}, {4364, 24724}, {4663, 41011}, {4883, 51783}, {5057, 5297}, {5524, 33096}, {7292, 20292}, {9756, 37540}, {11112, 45763}, {11246, 18201}, {12047, 37589}, {15447, 31394}, {17126, 62221}, {17724, 61716}, {17726, 24248}, {17768, 33104}, {17779, 24715}, {21242, 28508}, {21282, 49524}, {24330, 50278}, {24695, 31140}, {25385, 28494}, {28512, 48641}, {28530, 33070}, {28534, 29639}, {29823, 49741}, {31079, 49726}, {31091, 49721}, {32939, 60446}, {35466, 36277}, {37522, 40273}, {53418, 65683}

X(65698) = crosspoint of X(7) and X(598)
X(65698) = crosssum of X(55) and X(574)
X(65698) = X(65461)-reciprocal conjugate of-X(47884)
X(65698) = pole of the line {351, 523} with respect to the incircle
X(65698) = pole of the line {241, 514} with respect to the Lemoine inellipse
X(65698) = (X(53418), X(65695))-harmonic conjugate of X(65683)

X(65699) = CROSSHEXAGON POINT OF THESE TRIANGLES: INTOUCH AND 2nd MIDARC

Barycentrics    (a+b-c)*(a-b+c)*(2*(b-c)*(a^2-(b+c)*a-2*b*c)*sin(A/2)*(-a+b+c)+2*(a-b+c)*((b+3*c)*a-b^2-3*c^2)*sin(B/2)*a-2*(a+b-c)*((3*b+c)*a-3*b^2-c^2)*sin(C/2)*a+(-a+b+c)*(b-c)*(a+b-c)*(a-b+c)) : :
X(65699) = 2*X(10968)-3*X(11234)

X(65699) lies on these lines: {1, 166}, {7, 177}, {57, 168}, {65, 2091}, {173, 45707}, {188, 3243}, {7371, 13385}, {8113, 44841}, {8388, 55328}, {10491, 10506}, {10968, 11033}, {21465, 30419}

X(65699) = reflection of X(i) in X(j) for these (i, j): (177, 8083), (65693, 1)
X(65699) = crosspoint of X(7) and X(1488)
X(65699) = crosssum of X(55) and X(53118)
X(65699) = X(10503)-reciprocal conjugate of-X(16016)
X(65699) = pole of the line {10492, 45877} with respect to the incircle
X(65699) = trilinear quotient X(10503)/X(16012)
X(65699) = (inverse-in-incircle)-isotomic conjugate-of-X(177)
X(65699) = (2nd midarc)-isotomic conjugate-of-X(8422)
X(65699) = X(65693)-of-5th mixtilinear triangle
X(65699) = X(5779)-of-incircle-circles triangle
X(65699) = X(5732)-of-Hutson intouch triangle
X(65699) = X(142)-of-Ursa-minor triangle
X(65699) = X(9)-of-intouch triangle
X(65699) = X(7)-of-inverse-in-incircle triangle

X(65700) = CROSSHEXAGON POINT OF THESE TRIANGLES: INVERSE-IN-INCIRCLE AND 1st ZANIAH

Barycentrics    a*(b-c)*(a^4-4*(b+c)*a^3+2*(3*b^2+b*c+3*c^2)*a^2-4*(b^3+c^3)*a+(b^2+4*b*c+c^2)*(b-c)^2) : :

X(65700) lies on these lines: {1, 650}, {354, 11934}, {513, 54261}, {521, 676}, {693, 10580}, {905, 6608}, {926, 65413}, {2254, 14353}, {2499, 39541}, {2820, 43932}, {3309, 3676}, {3887, 59612}, {3900, 7658}, {4314, 8142}, {4666, 24562}, {4885, 11019}, {5045, 8760}, {6182, 11018}, {6744, 29066}, {9373, 16215}, {10578, 31209}, {10582, 25925}, {10980, 54255}, {12915, 17115}, {13405, 31287}, {21104, 21185}, {21625, 48295}, {24201, 59814}, {25009, 36845}, {26641, 29817}, {30198, 53523}, {32195, 50196}, {44409, 47123}, {63999, 64787}

X(65700) = reflection of X(7658) in X(17427)
X(65700) = cross-difference of every pair of points on the line X(1155)X(1615)
X(65700) = X(i)-complementary conjugate of-X(j) for these (i, j): (269, 5511), (1407, 40615), (2191, 5514), (6614, 6600), (17107, 26932), (40154, 124), (57656, 13609)
X(65700) = perspector of the circumconic through X(1156) and X(42483)
X(65700) = pole of the line {9, 165} with respect to the incircle
X(65700) = pole of the line {13609, 40615} with respect to the circumhyperbola dual of Yff parabola
X(65700) = pole of the line {165, 18725} with respect to the de Longchamps ellipse
X(65700) = pole of the line {277, 279} with respect to the Steiner inellipse
X(65700) = X(14341)-of-Ursa-minor triangle
X(65700) = X(2501)-of-inverse-in-incircle triangle

X(65701) = CROSSHEXAGON POINT OF THESE TRIANGLES: LEMOINE AND YFF CONTACT

Barycentrics    (b-c)*(2*a^2+3*(b+c)*a-b^2-3*b*c-c^2) : :
X(65701) = X(4024)+2*X(48041) = X(4786)-3*X(47786) = 2*X(4789)-3*X(47790) = 4*X(4789)-3*X(47791) = 2*X(4813)+X(47656) = 2*X(20295)+X(25259) = X(20295)+2*X(48269) = 5*X(20295)+X(49273) = 5*X(20295)-2*X(49294) = 4*X(20295)-X(49298) = X(25259)-4*X(48269) = 5*X(25259)-2*X(49273) = 5*X(25259)+4*X(49294) = 2*X(25259)+X(49298) = X(26824)+2*X(48038) = 2*X(31290)+X(47674) = X(31290)+2*X(48268) = X(47650)+2*X(48082) = X(47650)-4*X(49287) = 4*X(48547)-3*X(59912)

X(65701) lies on these lines: {2, 3667}, {513, 4789}, {514, 4024}, {522, 46915}, {649, 45661}, {812, 47769}, {824, 4958}, {900, 1491}, {1499, 8352}, {1994, 39525}, {2786, 31147}, {3151, 20294}, {3239, 26853}, {3700, 48079}, {3798, 27138}, {3835, 4750}, {4025, 26798}, {4106, 4949}, {4120, 4785}, {4380, 14321}, {4440, 30190}, {4467, 4940}, {4500, 48019}, {4728, 28867}, {4778, 47792}, {4810, 47698}, {4897, 45677}, {4926, 47782}, {4931, 28859}, {4944, 48567}, {4962, 47783}, {4977, 48423}, {4984, 47778}, {6002, 9810}, {6006, 47763}, {6008, 30565}, {6545, 28906}, {7192, 49284}, {7381, 44444}, {17011, 42312}, {17019, 43924}, {21297, 28846}, {23729, 49272}, {26985, 48013}, {27013, 59751}, {28209, 50326}, {28217, 47762}, {28220, 49275}, {28332, 30234}, {28840, 51317}, {28878, 47869}, {28898, 48550}, {30605, 47728}, {39386, 47788}, {45746, 48049}, {47663, 48114}, {47665, 47988}, {47667, 48026}, {47757, 53333}, {47764, 47775}, {47765, 47776}, {47894, 48554}, {47939, 48274}, {48076, 49289}, {48147, 48417}, {48271, 49297}, {48592, 50522}, {56810, 59839}

X(65701) = midpoint of X(i) and X(j) for these (i, j): {20295, 53339}, {44449, 47871}
X(65701) = reflection of X(i) in X(j) for these (i, j): (2, 47786), (649, 45661), (4380, 47884), (4440, 30190), (4467, 47880), (4750, 3835), (4897, 45677), (4984, 47778), (25259, 53339), (27486, 4776), (44435, 31147), (47676, 47871), (47728, 30605), (47755, 4728), (47763, 47787), (47771, 4120), (47775, 47764), (47776, 47765), (47781, 47759), (47791, 47790), (47871, 4106), (47880, 4940), (47884, 14321), (47894, 48554), (48567, 4944), (53333, 47757), (53339, 48269)
X(65701) = anticomplement of X(4786)
X(65701) = cross-difference of every pair of points on the line X(2242)X(2308)
X(65701) = crosspoint of X(i) and X(j) for these {i, j}: {190, 598}, {32014, 35179}
X(65701) = crosssum of X(i) and X(j) for these {i, j}: {574, 649}, {8644, 20970}
X(65701) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (692, 11148), (1296, 75), (5485, 21293), (21448, 149), (35179, 17137), (36045, 17162), (37216, 17135), (39238, 9263), (55923, 150), (65353, 20242)
X(65701) = X(4786)-Dao conjugate of-X(4786)
X(65701) = X(50121)-reciprocal conjugate of-X(190)
X(65701) = X(3908)-zayin conjugate of-X(649)
X(65701) = perspector of the circumconic through X(1268) and X(50121)
X(65701) = pole of the line {4021, 51615} with respect to the incircle
X(65701) = pole of the line {519, 7610} with respect to the orthoptic circle of Steiner inellipse
X(65701) = pole of the line {17134, 17162} with respect to the power circles radical circle
X(65701) = pole of the line {1, 2} with respect to the Lemoine inellipse
X(65701) = pole of the line {10, 4419} with respect to the Steiner circumellipse
X(65701) = pole of the line {3634, 4364} with respect to the Steiner inellipse
X(65701) = pole of the line {351, 523} with respect to the Yff parabola
X(65701) = barycentric product X(514)*X(50121)
X(65701) = trilinear product X(513)*X(50121)
X(65701) = trilinear quotient X(50121)/X(100)
X(65701) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (3700, 48079, 49282), (4106, 4949, 44449), (4106, 44449, 47676), (20295, 25259, 49298), (20295, 48269, 25259), (20295, 49273, 49294), (31290, 48268, 47674), (48049, 48266, 45746), (48082, 49287, 47650), (48114, 48270, 47663)

X(65702) = CROSSHEXAGON POINT OF THESE TRIANGLES: MIDHEIGHT AND 1st ZANIAH

Barycentrics    a*(2*a^5-(b+c)*a^4-2*(b^2-b*c+c^2)*a^3-2*(b-c)^2*b*c*a+(b^2-c^2)^2*(b+c)) : :

X(65702) lies on these lines: {1, 3}, {4, 18623}, {5, 59613}, {6, 20310}, {7, 63965}, {9, 22117}, {10, 53415}, {33, 222}, {34, 5806}, {37, 8558}, {63, 64750}, {72, 3562}, {73, 64804}, {77, 7580}, {81, 162}, {109, 57418}, {142, 59645}, {154, 21370}, {189, 461}, {212, 31658}, {221, 9856}, {223, 19541}, {226, 15252}, {255, 31445}, {278, 5805}, {282, 1449}, {394, 2000}, {495, 51375}, {603, 34862}, {650, 14756}, {651, 5927}, {912, 37729}, {938, 7498}, {954, 5287}, {990, 1407}, {1071, 6198}, {1103, 9709}, {1210, 52260}, {1364, 20122}, {1376, 53996}, {1386, 11019}, {1419, 1750}, {1433, 7008}, {1439, 4219}, {1456, 1699}, {1465, 20277}, {1503, 21621}, {1538, 34029}, {1736, 4641}, {1818, 56178}, {1824, 26884}, {1864, 2003}, {1870, 37380}, {1872, 40396}, {1887, 7335}, {1898, 8614}, {1961, 9440}, {2906, 57392}, {3100, 10167}, {3149, 64347}, {3157, 5777}, {3220, 61671}, {3332, 7365}, {3955, 64121}, {4336, 9316}, {4682, 13405}, {4906, 18240}, {5020, 42460}, {5044, 7078}, {5399, 64116}, {5712, 5803}, {5722, 15524}, {5762, 59611}, {5784, 56317}, {5930, 20420}, {6245, 40658}, {6357, 18482}, {7009, 64126}, {7069, 64198}, {7191, 17626}, {7330, 23072}, {7412, 51490}, {7686, 59285}, {7952, 57282}, {8144, 13369}, {8727, 34050}, {9306, 59681}, {9347, 10578}, {9370, 9947}, {9539, 11220}, {9817, 10157}, {10382, 62183}, {10580, 62807}, {11020, 14996}, {11022, 20831}, {11372, 34033}, {11429, 36059}, {12688, 34043}, {12904, 17605}, {13614, 64377}, {14058, 51699}, {14557, 33849}, {16058, 20793}, {16465, 37782}, {17019, 62800}, {18624, 59385}, {23070, 40263}, {26885, 61662}, {34790, 64069}, {34822, 58460}, {37366, 51413}, {38336, 64704}, {39542, 51616}, {39595, 51617}, {40942, 59657}, {41883, 58402}, {42019, 58645}, {42884, 62834}, {44225, 56814}, {52423, 61660}, {55108, 59647}, {56848, 64152}, {57278, 64166}, {64020, 64131}, {64057, 65128}

X(65702) = midpoint of X(i) and X(j) for these (i, j): {33, 222}, {1060, 60691}
X(65702) = reflection of X(i) in X(j) for these (i, j): (34822, 58460), (41883, 58402), (64708, 59611)
X(65702) = complement of the isotomic conjugate of X(34398)
X(65702) = crosspoint of X(2) and X(34398)
X(65702) = X(i)-complementary conjugate of-X(j) for these (i, j): (34398, 2887), (37741, 34823), (52776, 20316), (56005, 18589), (63187, 141)
X(65702) = center of the inconic with perspector X(34398)
X(65702) = perspector of the circumconic through X(651) and X(46964)
X(65702) = pole of the line {910, 12688} with respect to the Stevanovic circle
X(65702) = pole of the line {3900, 36054} with respect to the MacBeath circumconic
X(65702) = pole of the line {905, 57196} with respect to the Steiner inellipse
X(65702) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 940, 11018), (1, 3075, 17102), (394, 2000, 64171), (3100, 17074, 10167), (3157, 37696, 5777), (4682, 30621, 13405), (5805, 59606, 278), (9817, 34048, 10157), (34050, 40960, 8727)

X(65703) = CROSSHEXAGON POINT OF THESE TRIANGLES: MOSES-SODDY AND TANGENTIAL

Barycentrics    a^2*(b-c)*((b^2+c^2)*a-b^3-c^3) : :

X(65703) lies on these lines: {2, 24462}, {11, 244}, {31, 654}, {38, 918}, {42, 926}, {58, 42744}, {187, 237}, {650, 58286}, {756, 1639}, {982, 4453}, {984, 30565}, {1734, 27486}, {2308, 22086}, {2426, 32656}, {2499, 58300}, {2610, 20966}, {3670, 62435}, {3741, 20525}, {3801, 16892}, {4025, 8714}, {4079, 14436}, {4392, 48571}, {4905, 47755}, {6373, 8034}, {6589, 65697}, {7226, 47772}, {9032, 55263}, {17449, 30704}, {17989, 34857}, {21189, 47798}, {23740, 47672}, {26098, 46401}, {30671, 62446}, {33105, 46397}, {35365, 53326}, {35623, 65669}, {40471, 48276}, {42078, 42079}

X(65703) = reflection of X(42) in X(3310)
X(65703) = isogonal conjugate of the isotomic conjugate of X(23887)
X(65703) = Gibert-circumtangential conjugate of X(32682)
X(65703) = complement of X(65660)
X(65703) = cross-difference of every pair of points on the line X(2)X(101)
X(65703) = crosspoint of X(i) and X(j) for these {i, j}: {6, 32682}, {101, 60049}, {675, 43190}
X(65703) = crosssum of X(i) and X(j) for these {i, j}: {2, 23887}, {514, 3011}, {674, 6586}
X(65703) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 38990), (675, 20974), (32682, 6), (35365, 649)
X(65703) = X(31)-complementary conjugate of-X(38990)
X(65703) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 32682), (1015, 37130), (1084, 60135), (1086, 43093), (8054, 675), (32664, 36087), (38990, 2), (53980, 1897), (55053, 2224)
X(65703) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 36087}, {75, 32682}, {100, 675}, {101, 37130}, {190, 2224}, {662, 60135}, {692, 43093}, {693, 52941}, {3681, 65554}, {4564, 60573}
X(65703) = X(24462)-line conjugate of-X(2)
X(65703) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (31, 36087), (32, 32682), (512, 60135), (513, 37130), (514, 43093), (649, 675), (667, 2224), (674, 190), (2225, 100), (3006, 1978), (3271, 60573), (8618, 101), (14964, 99), (21123, 46158), (23887, 76), (32739, 52941), (38990, 65660), (42723, 7035), (43039, 664), (51657, 651), (57015, 668), (64611, 4555)
X(65703) = center of the circumconic with perspector X(38990)
X(65703) = perspector of the circumconic with center X(38990)
X(65703) = pole of the line {6, 20974} with respect to the circumcircle
X(65703) = pole of the line {11, 21746} with respect to the incircle
X(65703) = pole of the line {11, 3613} with respect to the nine-point circle
X(65703) = pole of the line {262, 995} with respect to the orthoptic circle of Steiner inellipse
X(65703) = pole of the line {264, 1897} with respect to the polar circle
X(65703) = pole of the line {6, 20974} with respect to the Brocard inellipse
X(65703) = pole of the line {514, 20974} with respect to the circumhyperbola dual of Yff parabola
X(65703) = pole of the line {513, 11998} with respect to the Feuerbach circumhyperbola
X(65703) = pole of the line {661, 7668} with respect to the Kiepert circumhyperbola
X(65703) = pole of the line {669, 16681} with respect to the Kiepert parabola
X(65703) = pole of the line {4534, 23638} with respect to the Mandart inellipse
X(65703) = pole of the line {51, 1146} with respect to the orthic inconic
X(65703) = pole of the line {99, 4570} with respect to the Stammler hyperbola
X(65703) = pole of the line {194, 4440} with respect to the Steiner circumellipse
X(65703) = pole of the line {39, 1086} with respect to the Steiner inellipse
X(65703) = pole of the line {670, 4600} with respect to the Steiner-Wallace hyperbola
X(65703) = pole of the line {6546, 20979} with respect to the Yff parabola
X(65703) = barycentric product X(i)*X(j) for these {i, j}: {6, 23887}, {244, 42723}, {513, 57015}, {514, 674}, {522, 43039}, {523, 14964}, {649, 3006}, {693, 2225}, {900, 64611}, {3261, 8618}, {4249, 4466}, {4391, 51657}, {5513, 35365}
X(65703) = trilinear product X(i)*X(j) for these {i, j}: {31, 23887}, {513, 674}, {514, 2225}, {522, 51657}, {649, 57015}, {650, 43039}, {661, 14964}, {667, 3006}, {693, 8618}, {1015, 42723}, {1635, 64611}, {4249, 18210}
X(65703) = trilinear quotient X(i)/X(j) for these (i, j): (6, 36087), (31, 32682), (513, 675), (514, 37130), (649, 2224), (661, 60135), (674, 100), (692, 52941), (693, 43093), (2170, 60573), (2225, 101), (2530, 46158), (3006, 668), (4249, 5379), (8618, 692), (14964, 662), (23887, 75), (42723, 1016), (43039, 651), (51657, 109)
X(65703) = (medial)-isotomic conjugate-of-X(38990)
X(65703) = (X(663), X(5075))-harmonic conjugate of X(8645)

X(65704) = CROSSHEXAGON POINT OF THESE TRIANGLES: MOSES-SODDY AND X-PARABOLA-TANGENTIAL

Barycentrics    (b^2-c^2)^2*(2*a^3+(b+c)*a^2-(b^2+c^2)*a-b^3-c^3) : :

X(65704) lies on these lines: {11, 244}, {86, 4425}, {1648, 8029}, {6627, 21043}, {21135, 23763}

X(65704) = cross-difference of every pair of points on the line X(101)X(249)
X(65704) = crosspoint of X(i) and X(j) for these {i, j}: {4024, 11599}, {6625, 60042}
X(65704) = crosssum of X(1326) and X(4556)
X(65704) = X(i)-Ceva conjugate of-X(j) for these (i, j): (3120, 41180), (18014, 21131)
X(65704) = X(i)-Dao conjugate of-X(j) for these (i, j): (523, 35162), (3005, 28482), (35114, 4590), (41180, 4610), (51578, 4600)
X(65704) = X(i)-isoconjugate of-X(j) for these {i, j}: {1101, 35162}, {24041, 28482}
X(65704) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (115, 35162), (3124, 28482), (10026, 4600), (17770, 4590), (20666, 4570), (20685, 765), (21131, 60042), (41180, 17731)
X(65704) = perspector of the circumconic through X(115) and X(514)
X(65704) = pole of the line {1897, 18020} with respect to the polar circle
X(65704) = pole of the line {20974, 55384} with respect to the Brocard inellipse
X(65704) = pole of the line {514, 1509} with respect to the circumhyperbola dual of Yff parabola
X(65704) = pole of the line {661, 10278} with respect to the Kiepert circumhyperbola
X(65704) = pole of the line {1146, 58907} with respect to the orthic inconic
X(65704) = pole of the line {4570, 59152} with respect to the Stammler hyperbola
X(65704) = pole of the line {4440, 54104} with respect to the Steiner circumellipse
X(65704) = pole of the line {1086, 23991} with respect to the Steiner inellipse
X(65704) = pole of the line {4600, 21085} with respect to the Steiner-Wallace hyperbola
X(65704) = barycentric product X(i)*X(j) for these {i, j}: {115, 17770}, {1111, 20685}, {3120, 10026}, {11599, 41180}, {20666, 21207}, {21131, 62644}
X(65704) = trilinear product X(i)*X(j) for these {i, j}: {1086, 20685}, {2643, 17770}, {3125, 10026}, {9278, 41180}, {16732, 20666}
X(65704) = trilinear quotient X(i)/X(j) for these (i, j): (1109, 35162), (2643, 28482), (10026, 4567), (17770, 24041), (20685, 1252), (41180, 1931)

X(65705) = CROSSHEXAGON POINT OF THESE TRIANGLES: PELLETIER AND SODDY

Barycentrics    a*(b-c)*(-a+b+c)*((b+c)*a^3-2*(b^2-b*c+c^2)*a^2+(b^2-c^2)*(b-c)*a-2*b*c*(b-c)^2) : :
X(65705) = 2*X(650)-3*X(10581)

X(65705) lies on these lines: {241, 514}, {676, 40133}, {891, 46388}, {926, 2170}, {1212, 6366}, {1475, 30691}, {3762, 28143}, {4449, 57180}, {4724, 17425}, {4875, 50333}, {5011, 52730}, {9442, 23893}, {14413, 46392}, {17451, 53550}, {21222, 28132}, {34522, 53285}, {36838, 61241}

X(65705) = reflection of X(52614) in X(1212)
X(65705) = cross-difference of every pair of points on the line X(55)X(651)
X(65705) = crosspoint of X(36838) and X(62744)
X(65705) = crosssum of X(57180) and X(62738)
X(65705) = X(62744)-Ceva conjugate of-X(3022)
X(65705) = X(1015)-Dao conjugate of-X(62744)
X(65705) = X(i)-isoconjugate of-X(j) for these {i, j}: {101, 62744}, {6602, 65558}
X(65705) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (479, 65558), (513, 62744), (3000, 664), (44664, 4554), (52888, 190), (52980, 46406), (62738, 100)
X(65705) = perspector of the circumconic through X(7) and X(650)
X(65705) = pole of the line {7, 3022} with respect to the incircle
X(65705) = pole of the line {281, 18026} with respect to the polar circle
X(65705) = pole of the line {7117, 21746} with respect to the Brocard inellipse
X(65705) = pole of the line {11, 21195} with respect to the circumhyperbola dual of Yff parabola
X(65705) = pole of the line {650, 3022} with respect to the Feuerbach circumhyperbola
X(65705) = pole of the line {497, 3271} with respect to the Mandart inellipse
X(65705) = pole of the line {1836, 3270} with respect to the orthic inconic
X(65705) = barycentric product X(i)*X(j) for these {i, j}: {514, 52888}, {522, 3000}, {650, 44664}, {657, 52980}, {693, 62738}, {6608, 62759}
X(65705) = trilinear product X(i)*X(j) for these {i, j}: {513, 52888}, {514, 62738}, {650, 3000}, {663, 44664}, {8641, 52980}, {10581, 62759}
X(65705) = trilinear quotient X(i)/X(j) for these (i, j): (514, 62744), (3000, 651), (10581, 62767), (23062, 65558), (44664, 664), (52888, 100), (52980, 4569), (62738, 101)
X(65705) = X(887)-of-intouch triangle

X(65706) = CROSSHEXAGON POINT OF THESE TRIANGLES: PELLETIER AND X-PARABOLA-TANGENTIAL

Barycentrics    a*(-a+b+c)*(b^2-c^2)^2*((b+c)*a^4+2*b*c*a^3-(b+c)*(2*b^2-3*b*c+2*c^2)*a^2-(b^2+c^2)*b*c*a+(b^4-c^4)*(b-c)) : :

X(65706) lies on these lines: {926, 2170}, {1648, 8029}

X(65706) = cross-difference of every pair of points on the line X(249)X(651)
X(65706) = perspector of the circumconic through X(115) and X(650)
X(65706) = pole of the line {18020, 18026} with respect to the polar circle
X(65706) = pole of the line {7117, 55384} with respect to the Brocard inellipse
X(65706) = pole of the line {650, 7054} with respect to the Feuerbach circumhyperbola
X(65706) = pole of the line {3270, 58907} with respect to the orthic inconic
X(65706) = barycentric product X(37982)*X(53560)

X(65707) = CROSSHEXAGON POINT OF THESE TRIANGLES: SCHRÖETER AND SODDY

Barycentrics    (b^2-c^2)*(2*a^3-(b^2+c^2)*a-(b^2-c^2)*(b-c)) : :
X(65707) = X(4838)-5*X(54256)

X(65707) lies on these lines: {115, 125}, {241, 514}, {649, 29136}, {918, 62675}, {1213, 6370}, {2642, 6089}, {4041, 4838}, {8674, 47234}, {9278, 18014}, {17422, 55282}, {24617, 24619}, {34959, 59629}, {53527, 55195}

X(65707) = midpoint of X(2642) and X(21131)
X(65707) = complement of the isotomic conjugate of X(60055)
X(65707) = cross-difference of every pair of points on the line X(55)X(110)
X(65707) = crosspoint of X(2) and X(60055)
X(65707) = X(i)-complementary conjugate of-X(j) for these (i, j): (59088, 141), (60055, 2887)
X(65707) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 35141), (244, 65261), (1084, 28471), (35066, 99)
X(65707) = X(i)-isoconjugate of-X(j) for these {i, j}: {110, 65261}, {163, 35141}, {249, 35347}, {662, 28471}
X(65707) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (512, 28471), (523, 35141), (661, 65261), (2643, 35347), (17768, 99), (43066, 4573)
X(65707) = center of the inconic with perspector X(60055)
X(65707) = perspector of the circumconic through X(7) and X(523)
X(65707) = pole of the line {1486, 7669} with respect to the circumcircle
X(65707) = pole of the line {7, 4616} with respect to the incircle
X(65707) = pole of the line {7668, 44412} with respect to the nine-point circle
X(65707) = pole of the line {98, 44431} with respect to the orthoptic circle of Steiner inellipse
X(65707) = pole of the line {281, 648} with respect to the polar circle
X(65707) = pole of the line {20975, 21746} with respect to the Brocard inellipse
X(65707) = pole of the line {11, 21196} with respect to the circumhyperbola dual of Yff parabola
X(65707) = pole of the line {523, 4092} with respect to the Kiepert circumhyperbola
X(65707) = pole of the line {4897, 11123} with respect to the Kiepert parabola
X(65707) = pole of the line {8288, 65698} with respect to the Lemoine inellipse
X(65707) = pole of the line {125, 1836} with respect to the orthic inconic
X(65707) = pole of the line {249, 5546} with respect to the Stammler hyperbola
X(65707) = pole of the line {145, 148} with respect to the Steiner circumellipse
X(65707) = pole of the line {1, 115} with respect to the Steiner inellipse
X(65707) = pole of the line {645, 4590} with respect to the Steiner-Wallace hyperbola
X(65707) = barycentric product X(i)*X(j) for these {i, j}: {523, 17768}, {3700, 43066}
X(65707) = trilinear product X(i)*X(j) for these {i, j}: {661, 17768}, {4041, 43066}, {35066, 35347}
X(65707) = trilinear quotient X(i)/X(j) for these (i, j): (115, 35347), (523, 65261), (661, 28471), (1577, 35141), (17768, 662), (43066, 1414)

X(65708) = CROSSHEXAGON POINT OF THESE TRIANGLES: SODDY AND X-PARABOLA-TANGENTIAL

Barycentrics    (b-c)*(b^2-c^2)^2*(2*a^4-2*(b+c)*a^3-2*(b^2+c^2)*a^2+(b+c)*(b^2+c^2)*a+b^4+c^4) : :

X(65708) lies on these lines: {241, 514}, {1648, 8029}

X(65708) = cross-difference of every pair of points on the line X(55)X(249)
X(65708) = perspector of the circumconic through X(7) and X(115)
X(65708) = pole of the line {281, 18020} with respect to the polar circle
X(65708) = pole of the line {21746, 55384} with respect to the Brocard inellipse
X(65708) = pole of the line {8287, 10278} with respect to the Kiepert circumhyperbola
X(65708) = pole of the line {1836, 58907} with respect to the orthic inconic
X(65708) = pole of the line {5546, 59152} with respect to the Stammler hyperbola
X(65708) = pole of the line {145, 54104} with respect to the Steiner circumellipse
X(65708) = pole of the line {1, 23991} with respect to the Steiner inellipse
X(65708) = pole of the line {645, 31614} with respect to the Steiner-Wallace hyperbola

X(65709) = CROSSHEXAGON POINT OF THESE TRIANGLES: TANGENTIAL AND X-PARABOLA-TANGENTIAL

Barycentrics    a^2*(b^2-c^2)^3*((-a^2+b^2+c^2)^2-b^2*c^2) : :
X(65709) = X(323)-3*X(9213) = 3*X(351)-2*X(1495) = 2*X(3580)-3*X(36255)

X(65709) lies on these lines: {187, 237}, {323, 526}, {520, 30219}, {523, 3580}, {690, 51360}, {1648, 8029}, {1649, 41167}, {2433, 40355}, {2780, 64624}, {3258, 53132}, {6370, 51465}, {9138, 15107}, {13290, 55142}, {13291, 16188}, {16186, 55071}, {17994, 44084}, {19912, 51548}, {34397, 47230}, {58871, 61776}, {61198, 61213}

X(65709) = Gibert-circumtangential conjugate of X(58979)
X(65709) = cross-difference of every pair of points on the line X(2)X(249)
X(65709) = crosspoint of X(i) and X(j) for these {i, j}: {6, 58979}, {115, 10412}, {125, 61216}, {526, 2088}, {2433, 56792}, {35235, 47230}
X(65709) = crosssum of X(i) and X(j) for these {i, j}: {249, 52603}, {250, 16237}, {476, 39295}, {523, 24975}, {526, 34990}, {6370, 40539}
X(65709) = X(i)-Ceva conjugate of-X(j) for these (i, j): (476, 55384), (526, 2088), (2433, 3124), (10412, 115), (15470, 47414), (43709, 3269), (58979, 6)
X(65709) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 58979), (512, 14560), (523, 35139), (526, 10411), (1084, 39295), (3005, 476), (5664, 670), (11597, 59152), (16221, 18020), (18334, 4590), (21905, 14559), (40604, 31614), (60342, 99), (62572, 34537)
X(65709) = X(i)-isoconjugate of-X(j) for these {i, j}: {75, 58979}, {249, 32680}, {476, 24041}, {662, 39295}, {1101, 35139}, {2166, 59152}, {4590, 32678}, {9273, 15455}, {14560, 24037}, {18020, 36061}, {32662, 46254}
X(65709) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (32, 58979), (50, 59152), (115, 35139), (186, 55270), (323, 31614), (512, 39295), (526, 4590), (1084, 14560), (2088, 99), (2624, 24041), (2643, 32680), (3124, 476), (3268, 34537), (8029, 94), (8552, 47389), (8754, 46456), (9213, 52940), (10412, 57546), (14270, 249), (16186, 4563), (18334, 10411), (20975, 60053), (20982, 65283), (21906, 14559), (22260, 1989), (23099, 11060), (23105, 20573), (32679, 24037), (33919, 43084), (34397, 47443), (35235, 6331), (42344, 51479), (47230, 18020), (52668, 45773), (60777, 57991), (61339, 10412), (62551, 670)
X(65709) = perspector of the circumconic through X(6) and X(115)
X(65709) = pole of the line {6, 23357} with respect to the circumcircle
X(65709) = pole of the line {3613, 27867} with respect to the nine-point circle
X(65709) = pole of the line {262, 39295} with respect to the orthoptic circle of Steiner inellipse
X(65709) = pole of the line {264, 18020} with respect to the polar circle
X(65709) = pole of the line {6, 23357} with respect to the Brocard inellipse
X(65709) = pole of the line {7668, 10278} with respect to the Kiepert circumhyperbola
X(65709) = pole of the line {669, 39857} with respect to the Kiepert parabola
X(65709) = pole of the line {51, 58907} with respect to the orthic inconic
X(65709) = pole of the line {99, 14559} with respect to the Stammler hyperbola
X(65709) = pole of the line {194, 54104} with respect to the Steiner circumellipse
X(65709) = pole of the line {39, 18122} with respect to the Steiner inellipse
X(65709) = pole of the line {670, 31614} with respect to the Steiner-Wallace hyperbola
X(65709) = barycentric product X(i)*X(j) for these {i, j}: {50, 23105}, {115, 526}, {125, 47230}, {323, 8029}, {338, 14270}, {512, 62551}, {523, 2088}, {647, 35235}, {868, 60777}, {1109, 2624}, {1637, 56792}, {1648, 9213}, {2081, 8901}, {2433, 3258}, {2436, 6070}, {2501, 16186}, {2610, 2611}, {2643, 32679}, {2971, 45792}, {3124, 3268}
X(65709) = trilinear product X(i)*X(j) for these {i, j}: {115, 2624}, {526, 2643}, {661, 2088}, {798, 62551}, {810, 35235}, {1109, 14270}, {2610, 20982}, {2611, 42666}, {3124, 32679}, {3708, 47230}, {6149, 8029}, {21824, 21828}
X(65709) = trilinear quotient X(i)/X(j) for these (i, j): (31, 58979), (115, 32680), (526, 24041), (661, 39295), (1109, 35139), (2088, 662), (2611, 65283), (2624, 249), (2643, 476), (3124, 32678), (3268, 24037), (3708, 60053), (6149, 59152), (8029, 2166), (8552, 62719), (8754, 36129), (14270, 1101), (16186, 4592), (20975, 36061), (20982, 37140)
X(65709) = X(13291)-of-anti-orthocentroidal triangle

X(65710) = X(2)X(525)∩X(99)X(110)

Barycentrics    (b^2 - c^2)*(-a^6 + 4*a^4*b^2 - 5*a^2*b^4 + 2*b^6 + 4*a^4*c^2 - 3*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 + 2*c^6) : :
X(65710) = 5 X[2] - 4 X[45327], 5 X[1640] - 6 X[45327], 4 X[1640] - 3 X[53374], 8 X[45327] - 5 X[53374], X[69] + 8 X[64690], 4 X[45808] - X[53378], X[45808] + 4 X[64690], X[53378] + 16 X[64690], 2 X[62555] + X[62642], 4 X[62555] - X[62645], 2 X[62642] + X[62645], 3 X[5466] - 4 X[11182], 2 X[5652] - 3 X[9168], 4 X[6333] - X[53331], 7 X[3619] - 4 X[45801], X[44445] - 4 X[50551]

X(65710) lies on the cubic K1368 and these lines: {2, 525}, {20, 1499}, {54, 62428}, {69, 523}, {76, 850}, {99, 110}, {320, 62397}, {512, 2979}, {520, 15531}, {599, 14977}, {826, 34290}, {1649, 3265}, {1992, 18311}, {2710, 2857}, {2780, 54037}, {2793, 50641}, {2799, 39905}, {3566, 11123}, {3619, 45801}, {5641, 34765}, {7664, 14932}, {10190, 59549}, {11459, 30209}, {12073, 41298}, {13306, 59775}, {14223, 54395}, {18808, 44134}, {20186, 54039}, {32478, 54036}, {44445, 50551}, {45693, 59773}, {45792, 53369}, {46616, 52437}, {50942, 62307}, {53186, 53929}

X(65710) = reflection of X(i) in X(j) for these {i,j}: {69, 45808}, {1992, 18311}, {3268, 6333}, {14977, 599}, {39904, 45687}, {53331, 3268}, {53369, 45792}, {53374, 2}, {53378, 69}, {62663, 34290}
X(65710) = anticomplement of X(1640)
X(65710) = anticomplement of the isogonal conjugate of X(5649)
X(65710) = anticomplement of the isotomic conjugate of X(6035)
X(65710) = isotomic conjugate of the isogonal conjugate of X(34291)
X(65710) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {842, 21221}, {5641, 21294}, {5649, 8}, {6035, 6327}, {36096, 37779}, {64775, 17482}
X(65710) = X(6035)-Ceva conjugate of X(2)
X(65710) = X(i)-Dao conjugate of X(j) for these (i,j): {57465, 3163}, {65608, 542}
X(65710) = crosspoint of X(99) and X(5641)
X(65710) = crosssum of X(512) and X(5191)
X(65710) = trilinear pole of line {57465, 65608}
X(65710) = crossdifference of every pair of points on line {1495, 1692}
X(65710) = barycentric product X(i)*X(j) for these {i,j}: {76, 34291}, {99, 65608}, {850, 54439}
X(65710) = barycentric quotient X(i)/X(j) for these {i,j}: {2394, 54495}, {34291, 6}, {54439, 110}, {60509, 6103}, {65608, 523}
X(65710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2396, 61188, 5468}, {30508, 30509, 3268}, {62555, 62642, 62645}, {62631, 62632, 62663}

X(65711) = X(20)X(99)∩X(69)X(110)

Barycentrics    a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + a^4*b^4*c^2 - 2*a^2*b^6*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 + b^6*c^4 - 2*a^2*b^2*c^6 + b^4*c^6 + 2*a^2*c^8 - c^10 : :

X(65711) lies on the cubic K1368 and these lines: {2, 648}, {5, 339}, {20, 99}, {22, 1634}, {23, 340}, {69, 110}, {95, 54459}, {125, 53348}, {127, 41676}, {253, 30769}, {264, 5169}, {305, 51967}, {316, 10296}, {317, 7519}, {325, 523}, {328, 18018}, {401, 7840}, {468, 40996}, {541, 36890}, {542, 52094}, {868, 56390}, {1007, 30789}, {1272, 1370}, {2071, 7799}, {2493, 62551}, {2847, 6527}, {2972, 30739}, {3153, 7809}, {3164, 7897}, {3314, 11672}, {4611, 28726}, {7417, 41360}, {7488, 7768}, {7763, 51884}, {7774, 31636}, {7778, 19221}, {7779, 10313}, {7811, 10298}, {10718, 35923}, {11413, 32821}, {11799, 44146}, {12037, 15595}, {13575, 57829}, {15589, 52711}, {16386, 59634}, {17974, 63722}, {32820, 52071}, {32833, 44440}, {34897, 40856}, {35911, 62307}, {37929, 52437}, {37980, 52149}, {38448, 54071}, {38553, 51872}, {40107, 52128}, {46787, 54395}

X(65711) = isotomic conjugate of X(2697)
X(65711) = anticomplement of X(6103)
X(65711) = anticomplement of the isogonal conjugate of X(65308)
X(65711) = isotomic conjugate of the anticomplement of X(42426)
X(65711) = isotomic conjugate of the isogonal conjugate of X(2781)
X(65711) = isotomic conjugate of the polar conjugate of X(50188)
X(65711) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {842, 5905}, {5641, 21270}, {5649, 7253}, {6035, 21300}, {35909, 21221}, {36096, 41079}, {65308, 8}
X(65711) = X(i)-cross conjugate of X(j) for these (i,j): {2781, 50188}, {42426, 2}
X(65711) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2697}, {2157, 46340}, {2631, 59108}, {32676, 60591}
X(65711) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2697}, {15526, 60591}, {35594, 42659}, {40583, 46340}, {62595, 47110}, {65612, 37987}
X(65711) = crosspoint of X(264) and X(5641)
X(65711) = crosssum of X(184) and X(5191)
X(65711) = crossdifference of every pair of points on line {32, 9409}
X(65711) = barycentric product X(i)*X(j) for these {i,j}: {69, 50188}, {76, 2781}, {99, 65612}, {3267, 37937}, {7799, 43090}, {40079, 44132}
X(65711) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2697}, {23, 46340}, {297, 47110}, {525, 60591}, {1304, 59108}, {1554, 6793}, {2781, 6}, {37937, 112}, {40079, 248}, {42426, 6103}, {43090, 1989}, {47427, 5191}, {50188, 4}, {60502, 58087}, {60512, 35907}, {65306, 64778}, {65612, 523}
X(65711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {325, 62338, 3266}, {684, 35522, 3268}, {22339, 22340, 30737}

X(65712) = X(6)X(525)∩X(69)X(110)

Barycentrics    (2*a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - a^2*c^4 - b^2*c^4)*(a^6 - a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 + c^6) : :

X(65712) lies on the cubics K260, K1315, K1368 and these lines: {2, 41511}, {4, 14364}, {6, 525}, {69, 110}, {193, 65306}, {317, 5641}, {524, 51823}, {577, 2482}, {1249, 5485}, {1992, 60002}, {2434, 62664}, {5467, 6390}, {6593, 34336}, {9233, 23992}, {10422, 63646}, {10423, 53186}, {11185, 34574}, {14559, 41612}, {15303, 36890}, {33769, 35138}, {34319, 36884}, {44146, 53777}, {47389, 59152}

X(65712) = reflection of X(60503) in X(6593)
X(65712) = isogonal conjugate of X(57485)
X(65712) = isotomic conjugate of X(59422)
X(65712) = complement of X(56569)
X(65712) = anticomplement of the isogonal conjugate of X(60002)
X(65712) = isotomic conjugate of the anticomplement of X(14357)
X(65712) = isotomic conjugate of the polar conjugate of X(51823)
X(65712) = isogonal conjugate of the polar conjugate of X(58078)
X(65712) = polar conjugate of the isotomic conjugate of X(53784)
X(65712) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1177, 17482}, {2373, 21274}, {16568, 2892}, {36095, 9517}, {60002, 8}
X(65712) = X(58078)-Ceva conjugate of X(51823)
X(65712) = X(i)-cross conjugate of X(j) for these (i,j): {184, 34161}, {3292, 18876}, {5095, 524}, {14357, 2}, {52629, 5468}
X(65712) = X(i)-isoconjugate of X(j) for these (i,j): {1, 57485}, {31, 59422}, {63, 64619}, {75, 51962}, {92, 34158}, {111, 18669}, {163, 65609}, {858, 923}, {897, 2393}, {1096, 51253}, {5523, 36060}, {14961, 36128}, {20884, 32740}, {23894, 61198}, {36142, 47138}
X(65712) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 59422}, {3, 57485}, {115, 65609}, {187, 64646}, {206, 51962}, {524, 5181}, {1560, 5523}, {2482, 858}, {3162, 64619}, {6503, 51253}, {6593, 2393}, {14417, 38971}, {18876, 19330}, {22391, 34158}, {23992, 47138}, {52881, 62382}
X(65712) = cevapoint of X(i) and X(j) for these (i,j): {524, 6593}, {690, 62594}, {2482, 3292}
X(65712) = crosssum of X(i) and X(j) for these (i,j): {2393, 47426}, {34158, 51962}
X(65712) = trilinear pole of line {187, 14417}
X(65712) = barycentric product X(i)*X(j) for these {i,j}: {3, 58078}, {4, 53784}, {69, 51823}, {99, 65611}, {187, 46140}, {524, 2373}, {896, 37220}, {1177, 3266}, {5468, 60040}, {6390, 60133}, {10422, 36792}, {10423, 45807}, {14417, 65268}, {18876, 44146}, {34161, 56685}, {34336, 41511}, {35522, 65306}, {36823, 52145}, {46165, 52898}
X(65712) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 59422}, {6, 57485}, {25, 64619}, {32, 51962}, {184, 34158}, {187, 2393}, {394, 51253}, {468, 5523}, {523, 65609}, {524, 858}, {690, 47138}, {896, 18669}, {1177, 111}, {2373, 671}, {2482, 5181}, {3266, 1236}, {3292, 14961}, {4062, 21017}, {4235, 61181}, {4750, 21109}, {5095, 1560}, {5467, 61198}, {5967, 52672}, {6390, 62382}, {6593, 64646}, {6629, 17172}, {9717, 60499}, {10422, 10630}, {14210, 20884}, {18876, 895}, {34161, 56579}, {36823, 5968}, {37220, 46277}, {39689, 47426}, {39785, 19510}, {41511, 15398}, {44102, 14580}, {46140, 18023}, {46165, 31125}, {51823, 4}, {52629, 62577}, {53784, 69}, {57496, 39269}, {58078, 264}, {60002, 14246}, {60040, 5466}, {60133, 17983}, {60503, 60507}, {61207, 46592}, {62594, 38971}, {65268, 65350}, {65306, 691}, {65611, 523}

X(65713) = X(99)X(523)∩X(110)X(685)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 3*b^6*c^2 - a^4*c^4 - a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 3*b^2*c^6) : :
X(65713) = 4 X[182] - 3 X[47388], 3 X[671] - 4 X[65613], 3 X[5182] - 2 X[34369]

X(65713) lies on the cubic K1368 and these lines: {99, 523}, {110, 685}, {182, 14382}, {250, 47256}, {290, 11579}, {316, 1503}, {340, 3564}, {525, 648}, {542, 5641}, {670, 18878}, {671, 65613}, {877, 53351}, {1990, 47286}, {2966, 23878}, {3260, 12215}, {3265, 30221}, {3268, 14480}, {4577, 14560}, {5182, 34369}, {5649, 62307}, {5921, 56572}, {6528, 32230}, {11185, 34574}, {14611, 30474}, {15454, 40423}, {18831, 65269}, {35137, 65279}, {38613, 54089}, {39462, 48947}, {41204, 44146}, {55226, 61188}, {57804, 65354}, {57991, 62642}

X(65713) = reflection of X(i) in X(j) for these {i,j}: {2966, 40866}, {47286, 1990}
X(65713) = X(i)-isoconjugate of X(j) for these (i,j): {163, 60500}, {810, 60590}
X(65713) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 60500}, {39062, 60590}
X(65713) = cevapoint of X(542) and X(62307)
X(65713) = crosssum of X(647) and X(10567)
X(65713) = barycentric product X(i)*X(j) for these {i,j}: {99, 41254}, {5622, 6331}, {6035, 60508}, {7418, 43187}
X(65713) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 60500}, {648, 60590}, {5622, 647}, {7418, 3569}, {41254, 523}, {60508, 1640}
X(65713) = {X(850),X(54108)}-harmonic conjugate of X(18020)

X(65714) = X(2)X(523)∩X(4)X(525)

Barycentrics    (b^2 - c^2)*(a^8 + a^6*b^2 - 3*a^4*b^4 - a^2*b^6 + 2*b^8 + a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 - 3*a^4*c^4 + 3*a^2*b^2*c^4 + 2*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :
X(65714) = 3 X[5466] - 4 X[65610], 3 X[9168] - 4 X[34291], 4 X[16230] - X[53345], X[18808] - 4 X[58263], 5 X[3091] - 2 X[5489], 3 X[3524] - 2 X[18556], 3 X[3524] - 4 X[45681], 2 X[58346] + X[63248], 3 X[3839] - 2 X[42733], 5 X[5071] - 4 X[14566], 4 X[39491] - 5 X[41099]

X(65714) lies on the cubic K1368 and these lines: {2, 523}, {4, 525}, {107, 110}, {193, 9007}, {264, 850}, {376, 5664}, {381, 2394}, {512, 15072}, {520, 3060}, {542, 14223}, {647, 15355}, {842, 2697}, {879, 46512}, {924, 41715}, {1176, 15328}, {1249, 2501}, {2071, 53330}, {2395, 47737}, {2799, 6054}, {3091, 5489}, {3265, 63098}, {3524, 18556}, {3543, 58346}, {3800, 16220}, {3839, 42733}, {5071, 14566}, {5641, 34765}, {6587, 37689}, {7736, 62384}, {7927, 8723}, {7950, 23105}, {8057, 63174}, {8675, 11188}, {9003, 41720}, {9529, 41077}, {10033, 23878}, {10412, 31065}, {11050, 34312}, {11177, 42738}, {14618, 51260}, {15412, 19176}, {23870, 41042}, {23871, 41043}, {33928, 63464}, {35912, 52076}, {37668, 62555}, {39474, 53156}, {39491, 41099}, {41254, 65623}, {41761, 44445}, {44891, 47175}, {45289, 53320}, {47071, 53159}, {53365, 55121}

X(65714) = midpoint of X(3543) and X(63248)
X(65714) = reflection of X(i) in X(j) for these {i,j}: {376, 5664}, {2394, 381}, {3543, 58346}, {9979, 16230}, {11177, 42738}, {18556, 45681}, {53345, 9979}, {53383, 2}
X(65714) = reflection of X(53383) in the Euler line
X(65714) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {5649, 4329}, {36096, 3153}
X(65714) = X(53155)-Ceva conjugate of X(53161)
X(65714) = X(i)-Dao conjugate of X(j) for these (i,j): {37987, 542}, {60510, 525}
X(65714) = cevapoint of X(523) and X(65623)
X(65714) = crosspoint of X(648) and X(5641)
X(65714) = crosssum of X(647) and X(5191)
X(65714) = trilinear pole of line {37987, 60510}
X(65714) = crossdifference of every pair of points on line {187, 3269}
X(65714) = barycentric product X(i)*X(j) for these {i,j}: {99, 65613}, {648, 37987}, {5641, 60510}
X(65714) = barycentric quotient X(i)/X(j) for these {i,j}: {37987, 525}, {60510, 542}, {65613, 523}
X(65714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4240, 53351, 34211}, {9214, 62629, 5466}, {18556, 45681, 3524}, {53153, 53154, 53345}

X(65715) = X(2)X(39290)∩X(69)X(74)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(65715) lies on the cubics K1315 and K1368 and these lines: {2, 39290}, {6, 51227}, {69, 74}, {141, 35910}, {193, 44769}, {264, 850}, {317, 16077}, {1138, 36889}, {3164, 18301}, {3580, 16237}, {3589, 60870}, {3618, 63856}, {4846, 31621}, {6389, 14919}, {6795, 40630}, {14264, 61188}, {15454, 40423}, {16080, 17907}, {17986, 18440}, {19776, 19777}, {21850, 35908}, {37644, 62606}, {37645, 57487}, {37648, 57488}, {45198, 52766}, {51346, 56576}, {56580, 57762}

X(65715) = isotomic conjugate of X(15454)
X(65715) = anticomplement of X(56399)
X(65715) = polar conjugate of X(51965)
X(65715) = anticomplement of the isogonal conjugate of X(57487)
X(65715) = isotomic conjugate of the anticomplement of X(39170)
X(65715) = isotomic conjugate of the complement of X(56686)
X(65715) = isotomic conjugate of the isogonal conjugate of X(14264)
X(65715) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {92, 59428}, {2349, 3153}, {14385, 6360}, {16080, 63642}, {36119, 37779}, {52414, 146}, {57487, 8}, {65263, 526}
X(65715) = X(i)-cross conjugate of X(j) for these (i,j): {113, 3580}, {39170, 2}, {62338, 1494}, {65473, 16077}
X(65715) = X(i)-isoconjugate of X(j) for these (i,j): {31, 15454}, {48, 51965}, {163, 65615}, {560, 52552}, {1495, 36053}, {2173, 14910}, {2631, 32708}, {2986, 9406}, {9409, 36114}, {10419, 42074}, {14398, 65262}, {56829, 61216}
X(65715) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 15454}, {113, 1495}, {115, 65615}, {1249, 51965}, {2088, 52743}, {3003, 3163}, {3580, 1511}, {6334, 3258}, {6374, 52552}, {9410, 2986}, {11064, 16163}, {34834, 30}, {36896, 14910}, {39005, 9409}, {39021, 1637}, {39174, 184}, {40604, 39371}, {56792, 512}, {62606, 5504}
X(65715) = cevapoint of X(i) and X(j) for these (i,j): {2, 56686}, {113, 3580}, {525, 56792}, {13754, 34834}
X(65715) = crosssum of X(9407) and X(9408)
X(65715) = trilinear pole of line {3580, 6334}
X(65715) = barycentric product X(i)*X(j) for these {i,j}: {76, 14264}, {99, 65614}, {113, 31621}, {1494, 3580}, {1502, 51821}, {1725, 33805}, {2394, 61188}, {6334, 16077}, {14919, 44138}, {16080, 62338}, {16237, 34767}, {18027, 53785}
X(65715) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 15454}, {4, 51965}, {74, 14910}, {76, 52552}, {94, 39375}, {113, 3163}, {323, 39371}, {403, 1990}, {523, 65615}, {686, 9409}, {1304, 32708}, {1494, 2986}, {1725, 2173}, {1986, 39176}, {2349, 36053}, {2394, 15328}, {3003, 1495}, {3580, 30}, {6334, 9033}, {12824, 52951}, {13754, 3284}, {14264, 6}, {14380, 61216}, {14385, 52557}, {14919, 5504}, {15329, 2420}, {16077, 687}, {16080, 1300}, {16237, 4240}, {18609, 51420}, {18781, 11070}, {21731, 14398}, {31621, 40423}, {34333, 47405}, {34767, 15421}, {34834, 1511}, {39170, 56399}, {40384, 10419}, {41512, 41392}, {44084, 14581}, {44138, 46106}, {44769, 10420}, {46788, 39986}, {46808, 58942}, {51227, 51456}, {51821, 32}, {52000, 52952}, {52451, 35906}, {53568, 6793}, {53785, 577}, {55121, 1637}, {55265, 58346}, {56403, 14583}, {57486, 14254}, {57487, 38936}, {57488, 51895}, {58940, 51545}, {60342, 52743}, {61188, 2407}, {61209, 23347}, {62338, 11064}, {62569, 16163}, {62722, 60035}, {63735, 52945}, {65263, 36114}, {65614, 523}

X(65716) = X(2)X(9717)∩X(6)X(9214)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(2*a^6 + a^4*b^2 + a^2*b^4 + 2*b^6 - 5*a^4*c^2 - 3*a^2*b^2*c^2 - 5*b^4*c^2 + 4*a^2*c^4 + 4*b^2*c^4 - c^6)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 + a^4*c^2 - 3*a^2*b^2*c^2 + 4*b^4*c^2 + a^2*c^4 - 5*b^2*c^4 + 2*c^6) : :

X(65716) lies on the X-parabola [see X(12065], the cubics K1353 and K1368, and these lines: {2, 9717}, {6, 9214}, {99, 62645}, {110, 5466}, {476, 62663}, {523, 2407}, {542, 34174}, {575, 5967}, {648, 18808}, {850, 5468}, {892, 59152}, {1649, 30221}, {2395, 60504}, {2501, 4240}, {3233, 8029}, {4036, 42716}, {7417, 44420}, {9168, 14480}, {10412, 14559}, {10418, 48450}, {15069, 56687}, {15328, 53350}, {15543, 62613}, {21732, 34246}, {35311, 60503}, {35314, 62632}, {35315, 62631}, {41309, 52752}, {50187, 52234}, {52472, 60696}, {53232, 62307}

X(65716) = isogonal conjugate of X(34291)
X(65716) = isotomic conjugate of the anticomplement of X(1640)
X(65716) = X(i)-cross conjugate of X(j) for these (i,j): {1640, 2}, {64607, 476}, {65610, 4}
X(65716) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34291}, {163, 65608}, {661, 54439}
X(65716) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 34291}, {115, 65608}, {36830, 54439}, {42426, 60509}
X(65716) = cevapoint of X(i) and X(j) for these (i,j): {512, 2493}, {523, 542}, {690, 46986}, {6593, 55142}
X(65716) = trilinear pole of line {30, 115}
X(65716) = barycentric product X(2407)*X(54495)
X(65716) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34291}, {110, 54439}, {523, 65608}, {6103, 60509}, {54495, 2394}

X(65717) = X(110)X(61191)∩X(113)X(525)

Barycentrics    (b^2 - c^2)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + 3*a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 6*a^4*c^4 - a^2*b^2*c^4 - b^4*c^4 + 3*a^2*c^6 + b^2*c^6)*(3*a^6*b^2 - 6*a^4*b^4 + 3*a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - a^4*c^4 + 3*a^2*b^2*c^4 - b^4*c^4 - a^2*c^6 - b^2*c^6 + c^8) : :
X(65717) = 3 X[34291] - X[51480]

X(65717) lies on the cubic K1368 and these lines: {110, 61191}, {113, 525}, {115, 60500}, {125, 41167}, {512, 16163}, {520, 5095}, {523, 5181}, {526, 22105}, {542, 35909}, {647, 5642}, {684, 690}, {826, 18557}, {850, 12827}, {879, 5972}, {1634, 14559}, {3569, 9033}, {6103, 60591}, {6333, 35522}, {8754, 58263}, {9003, 23287}, {9517, 14900}, {16230, 41079}, {20772, 47261}, {24981, 60352}, {34156, 34157}, {34291, 51480}

X(65717) = reflection of X(i) in X(j) for these {i,j}: {125, 41167}, {879, 5972}
X(65717) = X(i)-isoconjugate of X(j) for these (i,j): {162, 5622}, {163, 41254}, {7418, 36084}
X(65717) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 41254}, {125, 5622}, {38987, 7418}
X(65717) = cevapoint of X(i) and X(j) for these (i,j): {542, 5972}, {1649, 39474}, {57464, 65709}
X(65717) = crosssum of X(2781) and X(34291)
X(65717) = trilinear pole of line {1648, 1650}
X(65717) = crossdifference of every pair of points on line {5622, 7418}
X(65717) = barycentric product X(i)*X(j) for these {i,j}: {99, 60500}, {525, 60590}
X(65717) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 41254}, {647, 5622}, {1640, 60508}, {3569, 7418}, {60500, 523}, {60590, 648}

X(65718) = X(30)X(99)∩X(110)X(468)

Barycentrics    4*a^12*b^2 - 11*a^10*b^4 + 8*a^8*b^6 + 4*a^6*b^8 - 10*a^4*b^10 + 7*a^2*b^12 - 2*b^14 + 4*a^12*c^2 - 10*a^10*b^2*c^2 + 16*a^8*b^4*c^2 - 11*a^6*b^6*c^2 + 11*a^4*b^8*c^2 - 15*a^2*b^10*c^2 + 5*b^12*c^2 - 11*a^10*c^4 + 16*a^8*b^2*c^4 - 18*a^6*b^4*c^4 + 3*a^4*b^6*c^4 + 17*a^2*b^8*c^4 - 3*b^10*c^4 + 8*a^8*c^6 - 11*a^6*b^2*c^6 + 3*a^4*b^4*c^6 - 18*a^2*b^6*c^6 + 4*a^6*c^8 + 11*a^4*b^2*c^8 + 17*a^2*b^4*c^8 - 10*a^4*c^10 - 15*a^2*b^2*c^10 - 3*b^4*c^10 + 7*a^2*c^12 + 5*b^2*c^12 - 2*c^14 : :
X(65718) = 3 X[99] + X[44969], X[842] + 3 X[6054], X[842] - 3 X[53136], 3 X[114] - X[16188], 2 X[16188] - 3 X[36170], 3 X[403] - X[47286], 2 X[16760] - 3 X[46986], 3 X[46986] - X[65620], 3 X[15561] - X[46633], X[16092] - 3 X[23234], X[20127] - 3 X[54248], 4 X[20304] - 3 X[34953], X[52090] + 3 X[57311]

X(65718) lies on the cubic K1368 and these lines: {2, 9717}, {4, 47293}, {5, 5968}, {23, 50947}, {25, 16933}, {30, 99}, {110, 468}, {113, 525}, {114, 523}, {141, 47049}, {147, 36166}, {403, 41676}, {524, 47584}, {538, 46999}, {542, 16760}, {620, 46981}, {698, 47579}, {850, 34336}, {858, 62308}, {1352, 33928}, {1503, 47570}, {2452, 37071}, {2782, 14120}, {2794, 46987}, {3233, 47220}, {5099, 14981}, {6795, 7778}, {7777, 36183}, {7897, 15915}, {9168, 57607}, {9742, 36181}, {9744, 36177}, {9766, 60696}, {10011, 16315}, {10257, 46637}, {10297, 10748}, {14653, 47333}, {15561, 46633}, {16092, 23234}, {18440, 56572}, {20127, 54248}, {20304, 34953}, {20399, 40544}, {23698, 46988}, {30739, 33927}, {32459, 53737}, {33988, 59767}, {34291, 62307}, {34312, 47311}, {36196, 64090}, {46998, 64802}, {47332, 52229}, {52090, 57311}

X(65718) = midpoint of X(i) and X(j) for these {i,j}: {4, 47293}, {147, 36166}, {5099, 14981}, {6033, 46634}, {6054, 53136}, {36196, 64090}
X(65718) = reflection of X(i) in X(j) for these {i,j}: {16315, 10011}, {36170, 114}, {40544, 20399}, {46981, 620}, {51258, 5}, {65620, 16760}
X(65718) = complement of X(60508)
X(65718) = X(54439)-anticomplementary conjugate of X(4329)
X(65718) = X(17986)-Ceva conjugate of X(30)
X(65718) = barycentric product X(99)*X(65619)
X(65718) = barycentric quotient X(65619)/X(523)
X(65718) = {X(46986),X(65620)}-harmonic conjugate of X(16760)

X(65719) = X(2)X(36894)∩X(110)X(858)

Barycentrics    4*a^14*b^2 - 9*a^12*b^4 + a^10*b^6 + 8*a^8*b^8 - 2*a^6*b^10 - a^4*b^12 - 3*a^2*b^14 + 2*b^16 + 4*a^14*c^2 - 14*a^12*b^2*c^2 + 23*a^10*b^4*c^2 - 21*a^8*b^6*c^2 + 10*a^6*b^8*c^2 - 8*a^4*b^10*c^2 + 11*a^2*b^12*c^2 - 5*b^14*c^2 - 9*a^12*c^4 + 23*a^10*b^2*c^4 - 6*a^8*b^4*c^4 - 4*a^6*b^6*c^4 - 3*a^4*b^8*c^4 - 3*a^2*b^10*c^4 + 2*b^12*c^4 + a^10*c^6 - 21*a^8*b^2*c^6 - 4*a^6*b^4*c^6 + 24*a^4*b^6*c^6 - 5*a^2*b^8*c^6 + 5*b^10*c^6 + 8*a^8*c^8 + 10*a^6*b^2*c^8 - 3*a^4*b^4*c^8 - 5*a^2*b^6*c^8 - 8*b^8*c^8 - 2*a^6*c^10 - 8*a^4*b^2*c^10 - 3*a^2*b^4*c^10 + 5*b^6*c^10 - a^4*c^12 + 11*a^2*b^2*c^12 + 2*b^4*c^12 - 3*a^2*c^14 - 5*b^2*c^14 + 2*c^16 : :

X(65719) lies on the cubic K1368 and these lines: {2, 36894}, {110, 858}, {141, 35910}, {297, 340}, {523, 5181}, {525, 15595}, {542, 37987}, {850, 36789}, {2493, 65608}, {5254, 47616}, {6587, 62583}, {14570, 62382}, {15069, 56687}, {44569, 62311}, {47296, 53475}, {54395, 65613}

X(65719) = X(51405)-Ceva conjugate of X(524)
X(65719) = barycentric product X(99)*X(65623)
X(65719) = barycentric quotient X(65623)/X(523)

X(65720) = X(74)X(525)∩X(110)X(879)

Barycentrics    (b^2 - c^2)*(a^16 - 3*a^14*b^2 + 4*a^12*b^4 - 4*a^10*b^6 + a^8*b^8 + 5*a^6*b^10 - 6*a^4*b^12 + 2*a^2*b^14 - 3*a^14*c^2 + 14*a^12*b^2*c^2 - 20*a^10*b^4*c^2 + 18*a^8*b^6*c^2 - 19*a^6*b^8*c^2 + 14*a^4*b^10*c^2 - 6*a^2*b^12*c^2 + 2*b^14*c^2 + 4*a^12*c^4 - 20*a^10*b^2*c^4 + 19*a^8*b^4*c^4 - 3*a^6*b^6*c^4 - 3*a^4*b^8*c^4 + 7*a^2*b^10*c^4 - 4*b^12*c^4 - 4*a^10*c^6 + 18*a^8*b^2*c^6 - 3*a^6*b^4*c^6 - 2*a^4*b^6*c^6 - 3*a^2*b^8*c^6 - 2*b^10*c^6 + a^8*c^8 - 19*a^6*b^2*c^8 - 3*a^4*b^4*c^8 - 3*a^2*b^6*c^8 + 8*b^8*c^8 + 5*a^6*c^10 + 14*a^4*b^2*c^10 + 7*a^2*b^4*c^10 - 2*b^6*c^10 - 6*a^4*c^12 - 6*a^2*b^2*c^12 - 4*b^4*c^12 + 2*a^2*c^14 + 2*b^2*c^14) : :
X(65720) = 3 X[9140] - 2 X[35909], 3 X[53374] - 2 X[60509], 3 X[5622] - 2 X[62307], 5 X[15059] - 4 X[41167]

X(65720) lies on the cubic K1368 and these lines: {74, 525}, {99, 53383}, {110, 879}, {290, 850}, {512, 10733}, {520, 32244}, {523, 895}, {648, 18808}, {690, 15054}, {5622, 62307}, {9033, 53331}, {11005, 56687}, {15059, 41167}, {41254, 65623}, {56571, 56572}

X(65720) = reflection of X(110) in X(879)
X(65720) = X(41254)-anticomplementary conjugate of X(21294)

X(65721) = X(99)X(1236)∩X(290)X(54108)

Barycentrics    b^2*c^2*(-(a^16*b^4) + 3*a^14*b^6 - a^12*b^8 - 5*a^10*b^10 + 5*a^8*b^12 + a^6*b^14 - 3*a^4*b^16 + a^2*b^18 - 6*a^16*b^2*c^2 + 13*a^14*b^4*c^2 - 7*a^12*b^6*c^2 + a^10*b^8*c^2 + a^8*b^10*c^2 - 9*a^6*b^12*c^2 + 11*a^4*b^14*c^2 - 5*a^2*b^16*c^2 + b^18*c^2 - a^16*c^4 + 13*a^14*b^2*c^4 - 32*a^12*b^4*c^4 + 20*a^10*b^6*c^4 - 11*a^8*b^8*c^4 + 19*a^6*b^10*c^4 - 16*a^4*b^12*c^4 + 12*a^2*b^14*c^4 - 4*b^16*c^4 + 3*a^14*c^6 - 7*a^12*b^2*c^6 + 20*a^10*b^4*c^6 + 2*a^8*b^6*c^6 - 11*a^6*b^8*c^6 + 5*a^4*b^10*c^6 - 16*a^2*b^12*c^6 + 4*b^14*c^6 - a^12*c^8 + a^10*b^2*c^8 - 11*a^8*b^4*c^8 - 11*a^6*b^6*c^8 + 6*a^4*b^8*c^8 + 8*a^2*b^10*c^8 + 4*b^12*c^8 - 5*a^10*c^10 + a^8*b^2*c^10 + 19*a^6*b^4*c^10 + 5*a^4*b^6*c^10 + 8*a^2*b^8*c^10 - 10*b^10*c^10 + 5*a^8*c^12 - 9*a^6*b^2*c^12 - 16*a^4*b^4*c^12 - 16*a^2*b^6*c^12 + 4*b^8*c^12 + a^6*c^14 + 11*a^4*b^2*c^14 + 12*a^2*b^4*c^14 + 4*b^6*c^14 - 3*a^4*c^16 - 5*a^2*b^2*c^16 - 4*b^4*c^16 + a^2*c^18 + b^2*c^18) : :

X(65721) lies on the cubic K1368 and these lines: {99, 1236}, {290, 54108}, {525, 60513}, {648, 37778}, {850, 12827}, {1235, 15454}, {2393, 3260}, {13754, 44146}, {39099, 41743}, {60502, 65624}

X(65721) = anticomplement of the isogonal conjugate of X(41253)
X(65721) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {15462, 6360}, {41253, 8}

X(65722) = X(2)X(99)∩X(3)X(125)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) : :
X(65722) = X[5191] - 3 X[45662]

X(65722) lies on the cubic K1369 and these lines: {2, 99}, {3, 125}, {30, 47220}, {32, 37644}, {39, 14389}, {69, 248}, {110, 14981}, {114, 1316}, {147, 35278}, {187, 3580}, {231, 53474}, {237, 32223}, {316, 401}, {323, 7813}, {325, 40884}, {338, 46184}, {394, 4175}, {441, 525}, {511, 47526}, {524, 58267}, {542, 5191}, {570, 3589}, {858, 18860}, {868, 23698}, {1272, 3163}, {1370, 63410}, {1531, 44231}, {1576, 56565}, {2080, 41586}, {2407, 35520}, {2782, 47200}, {2794, 4226}, {2854, 41359}, {3014, 53274}, {3018, 24975}, {3148, 3818}, {3154, 46987}, {3258, 46634}, {3284, 62338}, {3448, 10991}, {3788, 41238}, {3926, 4563}, {4235, 50188}, {5181, 9145}, {5642, 8724}, {5972, 9155}, {6033, 51431}, {6070, 46633}, {6103, 60502}, {6128, 18122}, {6292, 40604}, {6337, 62708}, {6781, 35933}, {7473, 42426}, {7495, 21163}, {7799, 44575}, {7801, 14901}, {7806, 40814}, {8369, 37648}, {8429, 14928}, {8749, 44402}, {9737, 14003}, {10607, 20208}, {11007, 33813}, {11623, 53346}, {11842, 61712}, {12079, 46981}, {14357, 33927}, {14570, 23583}, {14982, 53568}, {14999, 23967}, {15093, 61659}, {15118, 46127}, {15367, 58429}, {16235, 62507}, {16280, 53725}, {16760, 36189}, {18876, 52350}, {20399, 46512}, {21166, 35922}, {21243, 37457}, {21731, 32121}, {23200, 64883}, {24981, 52090}, {26958, 35302}, {27088, 44569}, {29012, 37916}, {30789, 36163}, {31127, 38747}, {32225, 37461}, {32459, 47296}, {32985, 37643}, {33237, 63128}, {34291, 51480}, {34511, 37645}, {35002, 51360}, {36181, 39838}, {36841, 39352}, {37340, 46833}, {37341, 46834}, {37688, 59197}, {39785, 40112}, {40708, 60872}, {40867, 45018}, {41145, 50567}, {41275, 61646}, {42671, 46818}, {44578, 59634}, {44887, 59707}, {46546, 48892}, {47326, 47348}, {51430, 51872}, {57588, 61561}
X(65722) = midpoint of X(i) and X(j) for these {i,j}: {2407, 35520}, {3014, 53274}
X(65722) = reflection of X(3018) in X(24975)
X(65722) = complement of X(54395)
X(65722) = isotomic conjugate of the polar conjugate of X(542)
X(65722) = psi-transform of X(56438)
X(65722) = X(i)-complementary conjugate of X(j) for these (i,j): {40118, 20305}, {51480, 21253}
X(65722) = X(i)-isoconjugate of X(j) for these (i,j): {19, 842}, {162, 14998}, {1096, 65308}, {1910, 52492}, {1973, 5641}, {14223, 32676}, {23350, 36104}, {24019, 35909}, {36096, 47230}, {36119, 48453}, {36120, 52199}, {36142, 53156}
X(65722) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 842}, {125, 14998}, {542, 6103}, {1511, 48453}, {6337, 5641}, {6503, 65308}, {11672, 52492}, {15526, 14223}, {23967, 4}, {23992, 53156}, {35067, 34174}, {35071, 35909}, {35582, 14273}, {39000, 23350}, {42426, 393}, {46094, 52199}, {52881, 52094}, {55048, 53177}, {62569, 51228}, {62590, 46787}, {62594, 50942}
X(65722) = crosssum of X(6) and X(2493)
X(65722) = crossdifference of every pair of points on line {25, 351}
X(65722) = barycentric product X(i)*X(j) for these {i,j}: {69, 542}, {304, 2247}, {305, 5191}, {394, 60502}, {524, 51405}, {525, 14999}, {892, 39474}, {1640, 4563}, {3265, 7473}, {3926, 6103}, {4143, 35907}, {4558, 18312}, {6041, 52608}, {6333, 34761}, {6390, 16092}, {6393, 34369}, {6394, 54380}, {11064, 51227}, {14417, 50941}, {23968, 45792}, {30786, 45662}, {34767, 64607}, {36212, 46786}, {43087, 52437}, {47389, 51428}, {51386, 52491}, {51456, 62338}
X(65722) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 842}, {69, 5641}, {265, 54554}, {394, 65308}, {511, 52492}, {520, 35909}, {525, 14223}, {542, 4}, {647, 14998}, {684, 23350}, {690, 53156}, {1640, 2501}, {2247, 19}, {3284, 48453}, {3289, 52199}, {3564, 34174}, {3917, 46157}, {4558, 5649}, {4563, 6035}, {5191, 25}, {6041, 2489}, {6103, 393}, {6333, 34765}, {6390, 52094}, {7473, 107}, {9517, 53177}, {11064, 51228}, {12215, 57452}, {14417, 50942}, {14984, 38939}, {14999, 648}, {16092, 17983}, {18312, 14618}, {22115, 52179}, {23967, 6103}, {32662, 23969}, {34369, 6531}, {34761, 685}, {35907, 6529}, {35912, 53866}, {36061, 36096}, {36212, 46787}, {36885, 65349}, {39474, 690}, {42743, 4230}, {43087, 6344}, {43754, 53691}, {45662, 468}, {46786, 16081}, {48451, 8749}, {50941, 65350}, {51227, 16080}, {51262, 1304}, {51405, 671}, {51428, 8754}, {51456, 1300}, {51474, 40118}, {52613, 35911}, {53132, 35235}, {53232, 935}, {54380, 6530}, {58252, 38552}, {58348, 16240}, {60502, 2052}, {60505, 35907}, {61446, 3563}, {64607, 4240}, {64880, 56603}
X(65722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 99, 51389}, {325, 40884, 51372}, {441, 6390, 11064}, {441, 54075, 44436}, {6390, 11064, 36212}, {8552, 24284, 14417}, {9155, 15000, 5972}, {14417, 41077, 6333}, {14981, 35282, 110}, {28437, 28725, 115}, {28438, 28726, 620}, {40709, 40710, 125}, {45662, 53132, 47082}, {46811, 46814, 36212}

X(65723) = X(2)X(523)∩X(3)X(525)

Barycentrics    (b - c)*(b + c)*(-a^2 + b^2 + c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :
X(65723) = 3 X[1649] - 2 X[34291], 3 X[8371] - 2 X[65610], 3 X[53383] + X[65714], 2 X[3] + X[5489], X[47194] + 2 X[54260], 2 X[18556] + X[42733], X[14380] + 2 X[38401], 4 X[14566] - X[58346], 3 X[5054] - 2 X[45681], 2 X[6334] + X[9409], 5 X[15692] - X[63248], X[44427] - 4 X[44818]

X(65723) lies on the cubic K1369 and these lines: {2, 523}, {3, 525}, {30, 18556}, {69, 3265}, {122, 125}, {157, 669}, {183, 62555}, {216, 647}, {230, 62384}, {351, 13290}, {376, 2394}, {381, 14566}, {512, 15030}, {520, 3917}, {526, 14424}, {549, 5664}, {690, 61776}, {826, 44814}, {1640, 6041}, {1651, 47219}, {2525, 22078}, {2528, 41328}, {2799, 6055}, {3005, 60342}, {3566, 54050}, {3830, 39491}, {3906, 21163}, {5054, 45681}, {5191, 32313}, {5467, 34211}, {6103, 60510}, {6130, 9979}, {6334, 9409}, {6368, 32078}, {6563, 53347}, {6587, 62992}, {7473, 51262}, {7927, 34347}, {8057, 38240}, {9818, 53330}, {14652, 14809}, {14685, 47216}, {14999, 34761}, {15000, 40550}, {15329, 53371}, {15692, 63248}, {16188, 18312}, {16230, 44564}, {17008, 33294}, {18114, 58262}, {18808, 47217}, {20208, 40920}, {22240, 47233}, {23055, 44552}, {31521, 50552}, {40913, 46616}, {43537, 43673}, {44427, 44818}, {47229, 55267}, {51474, 61446}, {53232, 60505}, {54439, 65720}, {65612, 65620}

X(65723) = midpoint of X(i) and X(j) for these {i,j}: {2, 53383}, {376, 2394}
X(65723) = reflection of X(i) in X(j) for these {i,j}: {381, 14566}, {684, 14417}, {1640, 45321}, {3830, 39491}, {5664, 549}, {8029, 53266}, {9979, 6130}, {16230, 44564}, {42738, 6055}, {45662, 60340}, {58346, 381}
X(65723) = complement of X(65714)
X(65723) = isotomic conjugate of the polar conjugate of X(1640)
X(65723) = isogonal conjugate of the polar conjugate of X(18312)
X(65723) = tripolar centroid for these (i,j): {287, 51227}
X(65723) = X(i)-Ceva conjugate of X(j) for these (i,j): {7473, 542}, {18312, 1640}, {51456, 53132}, {53232, 45662}, {60591, 520}
X(65723) = X(i)-isoconjugate of X(j) for these (i,j): {19, 5649}, {162, 842}, {186, 36096}, {240, 53691}, {1973, 6035}, {5641, 32676}, {23969, 52414}, {24000, 35909}, {24019, 65308}, {36084, 52492}, {36092, 40080}, {36104, 46787}, {36119, 51263}, {36129, 52179}, {36131, 51228}, {48453, 65263}
X(65723) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 5649}, {125, 842}, {542, 7473}, {647, 14223}, {1511, 51263}, {1649, 53156}, {6337, 6035}, {15526, 5641}, {17434, 35911}, {23967, 648}, {35071, 65308}, {35582, 468}, {38987, 52492}, {39000, 46787}, {39008, 51228}, {39085, 53691}, {41167, 23350}, {42426, 107}, {60340, 62172}, {62594, 52094}
X(65723) = crosspoint of X(i) and X(j) for these (i,j): {523, 51480}, {542, 7473}
X(65723) = crosssum of X(i) and X(j) for these (i,j): {110, 7468}, {842, 35909}
X(65723) = crossdifference of every pair of points on line {112, 186}
X(65723) = barycentric product X(i)*X(j) for these {i,j}: {3, 18312}, {69, 1640}, {125, 14999}, {305, 6041}, {520, 60502}, {525, 542}, {671, 39474}, {684, 46786}, {690, 51405}, {2247, 14208}, {3265, 6103}, {3267, 5191}, {4563, 51428}, {6333, 34369}, {6334, 51456}, {7473, 15526}, {8552, 43087}, {9033, 51227}, {14417, 16092}, {14977, 45662}, {17986, 41077}, {34897, 55142}, {35911, 38552}, {39473, 47105}, {42313, 45321}, {53132, 60053}, {53173, 54380}, {53232, 62563}
X(65723) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 5649}, {69, 6035}, {125, 14223}, {248, 53691}, {520, 65308}, {525, 5641}, {542, 648}, {647, 842}, {684, 46787}, {1640, 4}, {1648, 53156}, {2247, 162}, {2972, 35911}, {3269, 35909}, {3284, 51263}, {3569, 52492}, {5191, 112}, {6041, 25}, {6103, 107}, {7473, 23582}, {9033, 51228}, {9409, 48453}, {14417, 52094}, {14582, 54554}, {14999, 18020}, {16092, 65350}, {17986, 15459}, {18312, 264}, {20975, 14998}, {23967, 7473}, {24284, 57452}, {34369, 685}, {34761, 60179}, {35907, 32230}, {39469, 52199}, {39474, 524}, {41172, 23350}, {43087, 46456}, {45321, 458}, {45662, 4235}, {46048, 60505}, {46786, 22456}, {47105, 65265}, {47427, 37937}, {48451, 1304}, {51227, 16077}, {51405, 892}, {51428, 2501}, {51456, 687}, {52153, 23969}, {53132, 44427}, {55142, 37765}, {57464, 62172}, {60502, 6528}, {61446, 32697}

X(65724) = X(115)X(523)∩X(125)X(647)

Barycentrics    (b - c)^2*(b + c)^2*(-a^2 + b^2 + c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) : :
X(65724) = 3 X[115] - 2 X[65613], 3 X[34366] - X[35907], X[6776] - 3 X[47388]

X(65724) lies on the cubic K1369 and these lines: {2, 65713}, {115, 523}, {125, 647}, {187, 1503}, {525, 15526}, {542, 23967}, {574, 14357}, {1084, 39021}, {1637, 6070}, {1640, 57464}, {1990, 12003}, {3003, 52967}, {3284, 3564}, {5158, 10217}, {5489, 21134}, {5661, 24206}, {6103, 17986}, {6776, 34156}, {9209, 12079}, {9243, 43589}, {14683, 23357}, {15449, 18334}, {15451, 20975}, {18121, 39565}, {23878, 35088}, {36166, 36204}, {39019, 55048}, {42306, 61215}, {51428, 57465}

X(65724) = midpoint of X(17986) and X(60508)
X(65724) = reflection of X(1990) in X(43291)
X(65724) = complement of X(65713)
X(65724) = complement of the isotomic conjugate of X(65717)
X(65724) = isotomic conjugate of the polar conjugate of X(51428)
X(65724) = X(i)-complementary conjugate of X(j) for these (i,j): {60500, 21253}, {60590, 21259}, {65717, 2887}
X(65724) = X(i)-Ceva conjugate of X(j) for these (i,j): {6103, 1640}, {51405, 39474}
X(65724) = X(i)-isoconjugate of X(j) for these (i,j): {162, 5649}, {6035, 32676}, {14590, 36096}, {24000, 65308}, {51263, 65263}, {53691, 62720}
X(65724) = X(i)-Dao conjugate of X(j) for these (i,j): {125, 5649}, {647, 5641}, {15526, 6035}, {23967, 18020}, {35582, 4235}, {41167, 46787}, {42426, 23582}, {57295, 51228}, {60340, 14920}
X(65724) = crosspoint of X(i) and X(j) for these (i,j): {2, 65717}, {542, 18312}, {1640, 6103}
X(65724) = crosssum of X(i) and X(j) for these (i,j): {648, 41253}, {5649, 65308}
X(65724) = crossdifference of every pair of points on line {250, 4230}
X(65724) = barycentric product X(i)*X(j) for these {i,j}: {69, 51428}, {125, 542}, {265, 53132}, {339, 5191}, {525, 1640}, {647, 18312}, {1648, 51405}, {1650, 17986}, {2247, 20902}, {3267, 6041}, {3269, 60502}, {5466, 39474}, {5489, 7473}, {6103, 15526}, {16186, 43087}, {23616, 35907}, {41172, 46786}, {45662, 51258}
X(65724) = barycentric quotient X(i)/X(j) for these {i,j}: {125, 5641}, {525, 6035}, {542, 18020}, {647, 5649}, {878, 53691}, {1640, 648}, {3269, 65308}, {5191, 250}, {6041, 112}, {6103, 23582}, {9409, 51263}, {14999, 55270}, {17986, 42308}, {18312, 6331}, {20975, 842}, {33919, 53156}, {34369, 60179}, {39474, 5468}, {41172, 46787}, {44114, 52492}, {46786, 41174}, {51405, 52940}, {51428, 4}, {53132, 340}, {57464, 14920}
X(65724) = {X(34366),X(60508)}-harmonic conjugate of X(6103)

X(65725) = X(6)X(67)∩X(141)X(525)

Barycentrics    (a^4 - a^2*b^2 + b^4 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4)*(a^4*b^2 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :
X(65725) = 3 X[2] + X[56569]

X(65725) lies on the cubics K260, K284, K1369 and these lines: {2, 41511}, {3, 15900}, {6, 67}, {66, 15388}, {69, 17708}, {127, 36884}, {141, 525}, {157, 3455}, {159, 34190}, {574, 14357}, {577, 23967}, {935, 35902}, {5486, 10415}, {5523, 39269}, {8589, 52974}, {11165, 20208}, {14961, 19510}, {17416, 59994}, {18019, 64620}, {40380, 40553}, {41760, 46105}, {41939, 59175}, {54347, 57496}, {57476, 62382}, {60499, 60507}

X(65725) = midpoint of X(i) and X(j) for these {i,j}: {67, 60503}, {56569, 65712}
X(65725) = isogonal conjugate of X(60002)
X(65725) = complement of X(65712)
X(65725) = complement of the isogonal conjugate of X(57485)
X(65725) = complement of the isotomic conjugate of X(59422)
X(65725) = isogonal conjugate of the isotomic conjugate of X(57476)
X(65725) = isogonal conjugate of the polar conjugate of X(39269)
X(65725) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 14357}, {897, 2393}, {923, 468}, {2393, 16597}, {18669, 126}, {34158, 1214}, {36060, 54075}, {51962, 37}, {57485, 10}, {59422, 2887}, {64619, 226}, {65609, 21253}
X(65725) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 14357}, {67, 2393}
X(65725) = X(47426)-cross conjugate of X(858)
X(65725) = X(i)-isoconjugate of X(j) for these (i,j): {1, 60002}, {1177, 16568}, {9517, 36095}, {18374, 37220}
X(65725) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 60002}, {5181, 22151}, {14357, 2}, {14961, 7664}, {15900, 2373}, {38971, 9979}, {61067, 23}, {64646, 316}
X(65725) = crosspoint of X(i) and X(j) for these (i,j): {2, 59422}, {10415, 46105}, {39269, 57476}
X(65725) = crosssum of X(i) and X(j) for these (i,j): {23, 36415}, {6593, 10317}
X(65725) = crossdifference of every pair of points on line {9517, 18374}
X(65725) = barycentric product X(i)*X(j) for these {i,j}: {3, 39269}, {6, 57476}, {67, 858}, {525, 60507}, {1236, 3455}, {2157, 20884}, {2393, 18019}, {5181, 10415}, {5523, 34897}, {8791, 62382}, {10511, 19510}, {14357, 59422}, {14961, 46105}, {17708, 47138}, {42665, 65269}
X(65725) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 60002}, {67, 2373}, {858, 316}, {935, 65268}, {1236, 40074}, {2393, 23}, {3455, 1177}, {5181, 7664}, {5523, 37765}, {8791, 60133}, {14357, 65712}, {14580, 8744}, {14961, 22151}, {18019, 46140}, {18669, 16568}, {20884, 20944}, {21017, 21094}, {21109, 21205}, {39269, 264}, {42665, 9517}, {46592, 52916}, {47138, 9979}, {47426, 6593}, {51962, 52142}, {57476, 76}, {57485, 14246}, {57496, 58078}, {59422, 52551}, {60507, 648}, {61198, 52630}, {62382, 37804}, {64218, 10422}
X(65725) = {X(2),X(56569)}-harmonic conjugate of X(65712)

X(65726) = X(6)X(523)∩X(69)X(248)

Barycentrics    (a^2 - b^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(65726) lies on the cubics K260 and K1369 and these lines: {2, 40428}, {4, 46237}, {6, 523}, {69, 248}, {98, 5033}, {115, 65616}, {193, 2966}, {206, 1976}, {230, 51820}, {393, 685}, {1249, 6531}, {1692, 14265}, {2065, 14384}, {2715, 36472}, {3564, 53783}, {3618, 52081}, {3767, 39085}, {5477, 36875}, {6037, 51338}, {6103, 60506}, {6776, 34156}, {7735, 36899}, {7736, 47737}, {7738, 8861}, {8553, 47635}, {14355, 52672}, {14382, 39141}, {14600, 53174}, {14912, 32545}, {15391, 43718}, {17008, 46806}, {17974, 31842}, {20021, 45838}, {35912, 48906}, {39078, 62562}, {41181, 52473}

X(65726) = isogonal conjugate of X(57493)
X(65726) = complement of X(56572)
X(65726) = complement of the isotomic conjugate of X(56687)
X(65726) = isotomic conjugate of the polar conjugate of X(51820)
X(65726) = isogonal conjugate of the polar conjugate of X(14265)
X(65726) = polar conjugate of the isotomic conjugate of X(53783)
X(65726) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 34156}, {8772, 132}, {56687, 2887}
X(65726) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 34156}, {287, 3564}, {685, 55122}, {14265, 51820}, {41932, 248}
X(65726) = X(i)-isoconjugate of X(j) for these (i,j): {1, 57493}, {19, 52091}, {92, 34157}, {232, 8773}, {240, 2987}, {297, 36051}, {1755, 35142}, {1959, 3563}, {3569, 36105}, {8781, 57653}, {23997, 60338}, {32654, 40703}, {35364, 62720}, {39374, 52414}
X(65726) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 57493}, {6, 52091}, {114, 297}, {3564, 62590}, {22391, 34157}, {34156, 2}, {35067, 325}, {36212, 32458}, {36899, 35142}, {39001, 3569}, {39069, 240}, {39072, 232}, {39085, 2987}, {41181, 6333}, {51610, 55267}, {55152, 16230}, {56788, 2501}, {62562, 60338}
X(65726) = crosspoint of X(i) and X(j) for these (i,j): {2, 56687}, {287, 47388}, {685, 57562}
X(65726) = crosssum of X(i) and X(j) for these (i,j): {232, 2967}, {511, 47406}, {684, 59805}
X(65726) = crossdifference of every pair of points on line {511, 17994}
X(65726) = barycentric product X(i)*X(j) for these {i,j}: {3, 14265}, {4, 53783}, {69, 51820}, {98, 3564}, {114, 47388}, {230, 287}, {248, 51481}, {290, 52144}, {293, 1733}, {336, 8772}, {460, 6394}, {525, 60504}, {879, 4226}, {1692, 57799}, {2065, 2974}, {17932, 55122}, {17974, 44145}, {34156, 56687}, {34536, 47406}, {35912, 36875}, {41181, 57562}, {41932, 62590}, {43665, 56389}, {51776, 60519}
X(65726) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 52091}, {6, 57493}, {98, 35142}, {184, 34157}, {230, 297}, {248, 2987}, {287, 8781}, {293, 8773}, {460, 6530}, {878, 35364}, {879, 62645}, {1692, 232}, {1733, 40703}, {1976, 3563}, {2395, 60338}, {2715, 32697}, {2966, 65354}, {3564, 325}, {4226, 877}, {6394, 57872}, {8772, 240}, {12829, 39931}, {14265, 264}, {14600, 32654}, {17932, 65277}, {17974, 43705}, {34156, 56572}, {35067, 62590}, {35912, 36891}, {36084, 36105}, {40820, 47736}, {41181, 35088}, {42663, 17994}, {43754, 10425}, {44099, 34854}, {47388, 40428}, {47406, 36790}, {51335, 2967}, {51481, 44132}, {51820, 4}, {52144, 511}, {52153, 39374}, {53783, 69}, {55122, 16230}, {56389, 2421}, {60504, 648}, {61213, 4230}, {62590, 32458}
X(65726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 34369, 51963}, {6, 51963, 35906}, {5967, 34369, 35906}, {5967, 51963, 6}, {6776, 47388, 34156}, {36899, 40820, 7735}, {52081, 60862, 3618}

X(65727) = X(2)X(2966)∩X(4)X(842)

Barycentrics    (b - c)^2*(b + c)^2*(-a^2 + b^2 + c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 - b^4*c^2 + 2*a^2*c^4 + 2*b^2*c^4 - 2*c^6)*(-a^6 + a^4*b^2 - 2*a^2*b^4 + 2*b^6 + a^4*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) : :

X(65727) lies on the cubic K1369 and these lines: {2, 2966}, {4, 842}, {69, 56399}, {115, 2394}, {125, 879}, {127, 15421}, {325, 60511}, {339, 14592}, {393, 15459}, {523, 868}, {525, 62563}, {543, 52094}, {1316, 36825}, {1640, 65608}, {2794, 7422}, {5489, 51258}, {6103, 48453}, {14120, 42733}, {14618, 52628}, {14977, 15526}, {14998, 60040}, {32528, 57452}, {34765, 46245}, {46787, 54395}, {50187, 51228}, {65612, 65613}

X(65727) = midpoint of X(54395) and X(65711)
X(65727) = on the orthic-asymptotic hyperbola
X(65727) = X(5641)-Ceva conjugate of X(35909)
X(65727) = X(i)-isoconjugate of X(j) for these (i,j): {163, 7473}, {250, 2247}, {1101, 6103}, {4575, 35907}, {14999, 32676}, {23995, 60502}, {36104, 42743}, {36131, 64607}, {51262, 56829}
X(65727) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 7473}, {136, 35907}, {523, 6103}, {647, 542}, {15526, 14999}, {18314, 60502}, {39000, 42743}, {39008, 64607}, {55267, 54380}
X(65727) = barycentric product X(i)*X(j) for these {i,j}: {125, 5641}, {338, 65308}, {339, 842}, {525, 14223}, {850, 35909}, {879, 34765}, {3267, 14998}, {14618, 35911}, {14977, 50942}, {51258, 52094}
X(65727) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 6103}, {125, 542}, {338, 60502}, {523, 7473}, {525, 14999}, {684, 42743}, {842, 250}, {868, 54380}, {879, 34761}, {1640, 60505}, {2501, 35907}, {3708, 2247}, {5466, 53155}, {5641, 18020}, {5649, 47443}, {6035, 55270}, {9033, 64607}, {12079, 17986}, {14223, 648}, {14380, 51262}, {14582, 23968}, {14977, 50941}, {14998, 112}, {20975, 5191}, {23350, 4230}, {34765, 877}, {35909, 110}, {35911, 4558}, {50942, 4235}, {51258, 16092}, {51404, 34369}, {53177, 52916}, {65308, 249}

X(65728) = X(2)X(9717)∩X(115)X(55267)

Barycentrics    (b - c)^2*(b + c)^2*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(-a^6 + 4*a^4*b^2 - 5*a^2*b^4 + 2*b^6 + 4*a^4*c^2 - 3*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 + 2*c^6) : :

X(65728) lies on the cubic K1369 and these lines: {2, 9717}, {115, 55267}, {125, 1649}, {141, 47047}, {512, 55071}, {523, 868}, {542, 5191}, {647, 1648}, {1494, 6035}, {1640, 57464}, {3005, 16186}, {3154, 9168}, {3258, 11123}, {5967, 8550}, {6070, 8371}, {9140, 60611}, {14995, 18122}, {15526, 65717}, {20975, 60342}, {30465, 35444}, {30468, 35443}, {34291, 65608}, {37637, 39078}, {53166, 57607}

X(65728) = complement of X(65716)
X(65728) = complement of the isogonal conjugate of X(34291)
X(65728) = complement of the isotomic conjugate of X(65710)
X(65728) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1640}, {34291, 10}, {54439, 4369}, {65608, 21253}, {65710, 2887}
X(65728) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 1640}, {12079, 53132}
X(65728) = X(i)-Dao conjugate of X(j) for these (i,j): {1640, 2}, {65608, 99}
X(65728) = crosspoint of X(i) and X(j) for these (i,j): {2, 65710}, {523, 542}
X(65728) = crosssum of X(110) and X(842)
X(65728) = crossdifference of every pair of points on line {7468, 14998}
X(65728) = barycentric product X(i)*X(j) for these {i,j}: {525, 60509}, {542, 65608}, {1494, 57465}, {1640, 65710}, {18312, 34291}
X(65728) = barycentric quotient X(i)/X(j) for these {i,j}: {1640, 65716}, {34291, 5649}, {57465, 30}, {60509, 648}, {65608, 5641}, {65710, 6035}

X(65729) = X(2)X(9717)∩X(30)X(115)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 + a^4*b^2 + a^2*b^4 + 2*b^6 - 5*a^4*c^2 - 3*a^2*b^2*c^2 - 5*b^4*c^2 + 4*a^2*c^4 + 4*b^2*c^4 - c^6)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 + a^4*c^2 - 3*a^2*b^2*c^2 + 4*b^4*c^2 + a^2*c^4 - 5*b^2*c^4 + 2*c^6) : :
X(65729) = 3 X[2] + X[60508], 3 X[230] - X[47584], 3 X[6055] + X[16188], 3 X[6055] - X[65620], X[16188] - 3 X[46980], X[38611] + 3 X[49102], 3 X[46980] + X[65620], X[265] - 3 X[34953], X[6390] - 3 X[10257], 3 X[6036] - X[16760], 5 X[631] - X[47293], X[842] + 3 X[16092], X[2697] + 3 X[34366], X[5099] - 5 X[38740], 3 X[5622] + X[51405], X[7472] + 3 X[14651], 9 X[9166] - X[44969], X[14120] - 3 X[38224], 3 X[38224] + X[46633], 3 X[23514] - X[46988], 3 X[38737] - X[46987], 5 X[38739] - X[46634]

X(65729) lies on the cubic K1369 and these lines: {2, 9717}, {3, 51258}, {23, 62727}, {30, 115}, {98, 36170}, {125, 3292}, {140, 14357}, {265, 34953}, {339, 6390}, {468, 2970}, {511, 47238}, {523, 6036}, {525, 6699}, {631, 47293}, {842, 16092}, {858, 8901}, {1499, 33511}, {2697, 34366}, {5099, 38740}, {5622, 51405}, {6103, 60590}, {6676, 57482}, {6719, 14341}, {6795, 37637}, {7472, 14651}, {7612, 36163}, {7806, 36183}, {8371, 47159}, {9166, 44969}, {9175, 18312}, {11623, 40544}, {12068, 47200}, {14120, 38224}, {16315, 56370}, {19163, 63838}, {23514, 46988}, {35912, 48906}, {37688, 52145}, {38737, 46987}, {38739, 46634}, {39899, 52473}, {40118, 47108}, {41939, 50979}, {44529, 51456}, {46809, 47097}, {47173, 47262}, {47239, 62490}, {47242, 47570}

X(65729) = midpoint of X(i) and X(j) for these {i,j}: {3, 51258}, {98, 36170}, {115, 46981}, {6055, 46980}, {11623, 40544}, {14120, 46633}, {16188, 65620}, {16315, 56370}, {38749, 46982}, {47242, 47570}, {60508, 65718}
X(65729) = complement of X(65718)
X(65729) = X(i)-isoconjugate of X(j) for these (i,j): {19, 54439}, {162, 34291}, {32676, 65710}
X(65729) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 54439}, {125, 34291}, {647, 65608}, {15526, 65710}
X(65729) = cevapoint of X(3) and X(39562)
X(65729) = barycentric product X(i)*X(j) for these {i,j}: {525, 65716}, {11064, 54495}
X(65729) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 54439}, {125, 65608}, {525, 65710}, {647, 34291}, {1640, 60509}, {54495, 16080}, {65716, 648}
X(65729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 60508, 65718}, {6055, 16188, 65620}, {38224, 46633, 14120}, {46980, 65620, 16188}

X(65730) = X(2)X(52668)∩X(69)X(56399)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8) : :
X(65730) = X[62338] - 3 X[62382]

X(65730) lies on the cubic K1369 and these lines: {2, 52668}, {69, 56399}, {115, 65622}, {125, 3292}, {247, 511}, {249, 40867}, {343, 62594}, {523, 5181}, {524, 16310}, {525, 62590}, {542, 51456}, {647, 62569}, {1640, 18312}, {3291, 3580}, {6103, 14999}, {14221, 54395}, {14341, 62583}, {14984, 51847}, {15526, 36212}, {31655, 51938}, {34156, 43754}, {47296, 63614}

X(65730) = midpoint of X(69) and X(60053)
X(65730) = complement of the isogonal conjugate of X(2493)
X(65730) = complement of the isotomic conjugate of X(54395)
X(65730) = isotomic conjugate of the polar conjugate of X(16188)
X(65730) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 14984}, {661, 36189}, {1755, 47079}, {2493, 10}, {7468, 4369}, {14221, 42327}, {14984, 18589}, {36142, 55131}, {54395, 2887}, {65610, 21253}
X(65730) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 14984}, {892, 55131}
X(65730) = X(i)-Dao conjugate of X(j) for these (i,j): {2493, 4}, {23967, 40118}
X(65730) = crosspoint of X(2) and X(54395)
X(65730) = barycentric product X(i)*X(j) for these {i,j}: {69, 16188}, {525, 60511}
X(65730) = barycentric quotient X(i)/X(j) for these {i,j}: {542, 40118}, {14984, 842}, {16188, 4}, {51847, 54554}, {55131, 53156}, {60511, 648}

X(65731) = X(2)X(65717)∩X(115)X(10097)

Barycentrics    (b - c)*(b + c)*(-a^2 + b^2 + c^2)*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 3*b^6*c^2 - a^4*c^4 - a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 3*b^2*c^6) : :
X(65731) = 3 X[2] + X[65720], X[51480] + 3 X[53266], 3 X[125] - X[35909], 3 X[879] + X[35909], 3 X[1640] - X[60509]

X(65731) lies on the cubic K1369 and these lines: {2, 65717}, {115, 10097}, {125, 879}, {512, 7687}, {520, 32257}, {523, 15118}, {525, 6699}, {542, 18312}, {690, 6130}, {1640, 6103}, {2492, 45801}, {5972, 40550}, {6723, 41167}, {8552, 15115}, {9033, 24284}, {9517, 36253}, {12099, 47175}, {14380, 15526}, {23583, 45327}, {30476, 45311}, {59741, 65488}

X(65731) = midpoint of X(i) and X(j) for these {i,j}: {125, 879}, {65717, 65720}
X(65731) = reflection of X(i) in X(j) for these {i,j}: {5972, 40550}, {41167, 6723}
X(65731) = complement of X(65717)
X(65731) = complement of the isotomic conjugate of X(65713)
X(65731) = X(i)-complementary conjugate of X(j) for these (i,j): {1101, 34291}, {5622, 34846}, {41254, 21253}, {65713, 2887}
X(65731) = crosspoint of X(i) and X(j) for these (i,j): {2, 65713}, {34761, 47388}
X(65731) = crosssum of X(2967) and X(23350)
X(65731) = barycentric product X(i)*X(j) for these {i,j}: {525, 60508}, {5622, 18312}
X(65731) = barycentric quotient X(i)/X(j) for these {i,j}: {1640, 60590}, {5622, 5649}, {60508, 648}
X(65731) = {X(2),X(65720)}-harmonic conjugate of X(65717)

X(65732) = X(2)X(65721)∩X(125)X(41167)

Barycentrics    b^2*(b - c)^2*c^2*(b + c)^2*(-2*a^6 + 2*a^4*b^2 - a^2*b^4 + b^6 + 2*a^4*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)*(-a^10 + 2*a^8*b^2 - 2*a^4*b^6 + a^2*b^8 + 2*a^8*c^2 - a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + b^8*c^2 - a^4*b^2*c^4 + 4*a^2*b^4*c^4 - b^6*c^4 - 2*a^4*c^6 - a^2*b^2*c^6 - b^4*c^6 + a^2*c^8 + b^2*c^8) : :

X(65732) lies on the cubic K1369 and these lines: {2, 65721}, {125, 41167}, {140, 14357}, {290, 5649}, {338, 18311}, {339, 5664}, {523, 3150}, {525, 2088}, {3589, 43084}, {6103, 60502}, {15526, 62577}, {18314, 62563}, {23285, 62551}

X(65732) = complement of the isotomic conjugate of X(62307)
X(65732) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 18312}, {15462, 4369}, {36189, 21253}, {41253, 21259}, {62307, 2887}
X(65732) = X(2)-Ceva conjugate of X(18312)
X(65732) = X(18312)-Dao conjugate of X(2)
X(65732) = crosspoint of X(2) and X(62307)
X(65732) = barycentric product X(i)*X(j) for these {i,j}: {525, 60513}, {18312, 62307}
X(65732) = barycentric quotient X(i)/X(j) for these {i,j}: {36189, 842}, {60513, 648}, {62307, 5649}

X(65733) = X(2)X(52668)∩X(32)X(23967)

Barycentrics    (b - c)^2*(b + c)^2*(a^8 - 3*a^6*b^2 + 4*a^4*b^4 - 3*a^2*b^6 + b^8 - a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - b^6*c^2 - a^4*c^4 - 2*a^2*b^2*c^4 - b^4*c^4 + a^2*c^6 + b^2*c^6)*(a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - 3*a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + b^6*c^2 + 4*a^4*c^4 + 2*a^2*b^2*c^4 - b^4*c^4 - 3*a^2*c^6 - b^2*c^6 + c^8) : :

X(65733) lies on the cubic K1369 and these lines: {2, 52668}, {32, 23967}, {115, 10097}, {125, 61216}, {525, 2088}, {542, 51457}, {647, 1648}, {1692, 60505}, {2433, 6388}, {2715, 36472}, {3124, 14582}, {41181, 47049}

X(65733) = X(i)-isoconjugate of X(j) for these (i,j): {163, 14221}, {662, 7468}, {1101, 54395}, {2493, 24041}
X(65733) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 14221}, {523, 54395}, {1084, 7468}, {3005, 2493}
X(65733) = cevapoint of X(3124) and X(51428)
X(65733) = crosssum of X(2493) and X(7468)
X(65733) = trilinear pole of line {20975, 33919}
X(65733) = barycentric product X(i)*X(j) for these {i,j}: {125, 40118}, {523, 51480}, {12079, 51457}
X(65733) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 54395}, {512, 7468}, {523, 14221}, {1640, 60511}, {3124, 2493}, {8029, 65610}, {20975, 14984}, {33919, 55131}, {35191, 45773}, {40118, 18020}, {51428, 16188}, {51441, 34175}, {51480, 99}

X(65734) = X(2)X(36894)∩X(125)X(468)

Barycentrics    (2*a^8 - 3*a^6*b^2 + 2*a^4*b^4 - 3*a^2*b^6 + 2*b^8 - a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - b^6*c^2 - 3*a^4*c^4 - a^2*b^2*c^4 - 3*b^4*c^4 + a^2*c^6 + b^2*c^6 + c^8)*(2*a^8 - a^6*b^2 - 3*a^4*b^4 + a^2*b^6 + b^8 - 3*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 + 2*a^4*c^4 + 3*a^2*b^2*c^4 - 3*b^4*c^4 - 3*a^2*c^6 - b^2*c^6 + 2*c^8) : :
X(65734) = X[1990] - 3 X[62375], 3 X[5622] + X[17986], 3 X[51227] + X[65308]

X(65734) lies on the cubics K1367 and K1369 and these lines: {2, 36894}, {6, 63856}, {125, 468}, {237, 14634}, {323, 31068}, {338, 1990}, {441, 524}, {523, 15118}, {1640, 50942}, {2770, 51938}, {3266, 11064}, {3580, 52898}, {3589, 43084}, {5621, 37937}, {5622, 17986}, {5967, 8550}, {11623, 40542}, {13567, 51823}, {16080, 23964}, {23292, 57496}, {34369, 65608}, {36189, 43090}, {41254, 65613}, {41997, 52039}, {41998, 52040}, {44569, 51541}, {44891, 51737}, {51227, 65308}, {51257, 52289}, {53576, 62376}

X(65734) = midpoint of X(34369) and X(65608)
X(65734) = complement of X(65719)
X(65734) = X(60500)-cross conjugate of X(51480)
X(65734) = X(i)-isoconjugate of X(j) for these (i,j): {163, 65714}, {1101, 65613}
X(65734) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 65714}, {523, 65613}, {647, 37987}
X(65734) = cevapoint of X(i) and X(j) for these (i,j): {6, 5621}, {125, 1640}, {52743, 53132}
X(65734) = trilinear pole of line {690, 5489}
X(65734) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 65613}, {125, 37987}, {523, 65714}, {1640, 60510}

X(65735) = X(2)X(1304)∩X(115)X(34212)

Barycentrics    (b - c)^2*(b + c)^2*(-a^2 + b^2 + c^2)^2*(a^10 - a^6*b^4 - a^4*b^6 + b^10 - 2*a^8*c^2 + 2*a^6*b^2*c^2 + 2*a^2*b^6*c^2 - 2*b^8*c^2 - a^4*b^2*c^4 - a^2*b^4*c^4 + 2*a^4*c^6 + 2*b^4*c^6 - a^2*c^8 - b^2*c^8)*(-a^10 + 2*a^8*b^2 - 2*a^4*b^6 + a^2*b^8 - 2*a^6*b^2*c^2 + a^4*b^4*c^2 + b^8*c^2 + a^6*c^4 + a^2*b^4*c^4 - 2*b^6*c^4 + a^4*c^6 - 2*a^2*b^2*c^6 + 2*b^2*c^8 - c^10) : :

X(65735) lies on the cubic K1369 and these lines: {2, 1304}, {115, 34212}, {523, 3150}, {577, 23967}, {647, 1650}, {3265, 58258}, {9530, 47110}, {14380, 15526}, {34156, 43754}, {43083, 47413}

X(65735) = X(2697)-Ceva conjugate of X(60591)
X(65735) = X(i)-isoconjugate of X(j) for these (i,j): {162, 37937}, {2781, 24000}
X(65735) = X(i)-Dao conjugate of X(j) for these (i,j): {125, 37937}, {525, 65711}, {647, 50188}
X(65735) = crosspoint of X(2697) and X(60591)
X(65735) = crosssum of X(2781) and X(37937)
X(65735) = barycentric product X(i)*X(j) for these {i,j}: {525, 60591}, {2697, 15526}
X(65735) = barycentric quotient X(i)/X(j) for these {i,j}: {125, 50188}, {647, 37937}, {1640, 60512}, {2697, 23582}, {3269, 2781}, {5489, 65612}, {15526, 65711}, {60591, 648}

X(65736) = X(2)X(65721)∩X(115)X(232)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 - a^6*b^2*c^2 - a^4*b^4*c^2 - a^2*b^6*c^2 + 2*b^8*c^2 - a^6*c^4 + 4*a^4*b^2*c^4 - a^2*b^4*c^4 - a^4*c^6 - a^2*b^2*c^6 - 2*b^4*c^6 + a^2*c^8 + b^2*c^8)*(a^8*b^2 - a^6*b^4 - a^4*b^6 + a^2*b^8 + a^8*c^2 - a^6*b^2*c^2 + 4*a^4*b^4*c^2 - a^2*b^6*c^2 + b^8*c^2 - 2*a^6*c^4 - a^4*b^2*c^4 - a^2*b^4*c^4 - 2*b^6*c^4 - a^2*b^2*c^6 + 2*a^2*c^8 + 2*b^2*c^8 - c^10) : :

X(65736) lies on the cubic K1369 and these lines: {2, 65721}, {39, 14264}, {115, 232}, {187, 41270}, {237, 2393}, {248, 23357}, {3269, 3289}, {5622, 40079}, {5661, 40799}, {11672, 12827}, {15526, 36212}, {15993, 57466}, {48452, 59023}

X(65736) = isogonal conjugate of X(41253)
X(65736) = complement of X(65721)
X(65736) = isogonal conjugate of the polar conjugate of X(65618)
X(65736) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41253}, {92, 15462}, {162, 62307}, {52414, 53768}
X(65736) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 41253}, {125, 62307}, {22391, 15462}
X(65736) = trilinear pole of line {686, 39469}
X(65736) = barycentric product X(3)*X(65618)
X(65736) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 41253}, {184, 15462}, {647, 62307}, {1640, 60513}, {20975, 36189}, {52153, 53768}, {65618, 264}

X(65737) = X(1576)X(34845)∩X(3049)X(7668)

Barycentrics    (b - c)^2*(b + c)^2*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - a^4*c^4 - b^4*c^4)*(-(a^6*b^2) + a^4*b^4 - a^6*c^2 + a^4*b^2*c^2 + 2*a^4*c^4 + a^2*b^2*c^4 + b^4*c^4 - a^2*c^6 - b^2*c^6) : :

See Peter Moses, euclid 7087.

X(65737) lies on these lines: {1576, 34845}, {2491, 34981}, {3049, 7668}, {39469, 53575}

X(65737) = X(i)-isoconjugate of X(j) for these (i,j): {163, 46726}, {1101, 34845}
X(65737) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 46726}, {523, 34845}
X(65737) = barycentric product X(850)*X(36198)
X(65737) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 34845}, {523, 46726}, {23105, 36199}, {36198, 110}

X(65738) = INTERNAL SAVIN POINT

Barycentrics    a^2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 2*a^3*c + 4*a^2*b*c + 2*a*b^2*c + 2*a*b*c^2 + b^2*c^2 - 2*a*c^3 - c^4) : :
X(65738) = 3*r*R^2*X[2] - 4*(R - r)*s^2*X[56]

In the plane of a triangle ABC, let
OA = circle through A tangent to line BC and to the circumcircle
AB = OA∩AB, and define BC and CA cyclically
AC = Oa∩AC, and define BA and CB cyclically
The circles OA, OB, OC and points AB, BC, CA, AC, BA, CB are defined in X(593); see X(65738)x1. Let
A' =ACBA∩CAAB, and define B' and C' cyclically; see X(65738)x2.
The lines AA', BB', CC' concur in X(65738). (Andrey Savin, October 13, 2024). See also X(65739).

Barycentrics associated with the construction of X(65738) follow:
OA = -2*a^2*b*c : b^2*(-a^2 + b^2 - c^2) : c^2*(-a^2 - b^2 + c^2)
radius = 2*R*(1 + Cos[A]) / (2 + Cos[A] + Cot[w]*Sin[A])
AB = a^2 : -((a - b - c)*(a + b + c)) :
(Peter Moses, October 13, 2024) The point X(65738) is here named the internal Savin point.

X(65738) lies on these lines: {2, 12}, {23, 40956}, {36, 17011}, {593, 47479}, {604, 1994}, {1014, 26842}, {1400, 34545}, {1402, 65739}, {2178, 63074}, {5124, 62851}, {5287, 37587}, {5563, 17019}, {11340, 17013}, {15246, 37609}, {17045, 40592}, {19308, 45222}, {21773, 32911}, {41820, 56934}, {50378, 59477}

X(65738) = crosssum of X(594) and X(17362)

X(65739) = EXTERNAL SAVIN POINT

Barycentrics    a^2*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 - 2*a^3*c + 4*a^2*b*c - 2*a*b^2*c - 2*a*b*c^2 + b^2*c^2 + 2*a*c^3 - c^4) : :
X(65739) = 3*(2*r + R)*X[2] - 4*r*X[11]

Continuing from X(65738), the external Savin point is the point given by
OA = 2*a^2*b*c : b^2*(-a^2 + b^2 - c^2) : c^2*(-a^2 - b^2 + c^2)
AB = -a^2 : (a + b - c)*(a - b + c) : 0
(Peter Moses, October 14, 2024)

X(65739) lies on these lines: {1, 4996}, {2, 11}, {3, 5330}, {8, 10087}, {10, 53616}, {20, 12775}, {21, 952}, {23, 9978}, {31, 1994}, {35, 214}, {42, 34545}, {63, 37736}, {80, 5248}, {104, 4189}, {110, 53873}, {119, 5046}, {145, 11508}, {153, 6872}, {323, 902}, {377, 13199}, {392, 22935}, {394, 21000}, {404, 5901}, {405, 12331}, {411, 1537}, {474, 38044}, {517, 27086}, {529, 48698}, {900, 16158}, {958, 12531}, {960, 41541}, {993, 7972}, {1005, 13257}, {1145, 3871}, {1155, 58591}, {1156, 61025}, {1252, 23988}, {1259, 3621}, {1317, 2975}, {1320, 3295}, {1385, 17654}, {1402, 65738}, {1484, 7483}, {1617, 23958}, {1768, 35258}, {1862, 62971}, {1993, 3052}, {2077, 4881}, {2078, 3218}, {2177, 15018}, {2223, 35296}, {2346, 5856}, {2475, 5840}, {2476, 10738}, {2783, 5985}, {2800, 10902}, {2801, 64297}, {2802, 3746}, {2829, 15680}, {2932, 64951}, {2950, 10884}, {3036, 5260}, {3045, 20986}, {3219, 41553}, {3256, 27003}, {3303, 22560}, {3337, 58625}, {3616, 10090}, {3622, 11507}, {3689, 58663}, {3724, 58397}, {3869, 12739}, {3877, 6265}, {3878, 14795}, {3890, 12740}, {3897, 12737}, {3935, 14740}, {3957, 62852}, {4187, 61562}, {4188, 11248}, {4193, 32141}, {4305, 6224}, {4511, 32760}, {4512, 5531}, {4640, 17660}, {5047, 34122}, {5086, 12743}, {5141, 59391}, {5154, 11499}, {5172, 62826}, {5250, 6326}, {5251, 15863}, {5253, 14882}, {5258, 15862}, {5259, 6702}, {5267, 33812}, {5541, 19860}, {5554, 25438}, {5687, 64141}, {5731, 48695}, {5857, 17484}, {6594, 61012}, {6600, 61026}, {6713, 37291}, {6905, 11729}, {6986, 64193}, {7489, 59416}, {7504, 60759}, {7676, 10427}, {8070, 27529}, {8715, 25005}, {9024, 15988}, {9963, 37228}, {10031, 12773}, {10306, 37301}, {10310, 37307}, {10528, 45393}, {10679, 37300}, {10724, 11496}, {10742, 11114}, {10956, 20060}, {11012, 25485}, {11113, 11698}, {11570, 14798}, {11715, 34486}, {12332, 17548}, {12514, 12532}, {12735, 54391}, {13243, 20835}, {13278, 64743}, {13587, 35000}, {15015, 19861}, {15246, 37619}, {15253, 24145}, {15914, 17494}, {15931, 46684}, {16418, 50890}, {16865, 38665}, {17532, 48680}, {17543, 38629}, {17549, 38602}, {17566, 38762}, {17573, 38636}, {17574, 51529}, {17576, 64009}, {17577, 22938}, {18240, 29817}, {18524, 37375}, {19112, 44590}, {19113, 44591}, {19525, 64742}, {21630, 24541}, {21842, 34758}, {23858, 65186}, {24465, 26842}, {24466, 37256}, {24987, 63281}, {25439, 64056}, {25440, 37735}, {26639, 40910}, {27065, 46694}, {30305, 65119}, {30323, 64362}, {34772, 64139}, {37298, 61566}, {37299, 38761}, {37579, 64047}, {38058, 61553}, {38756, 50242}, {41701, 62838}, {48715, 63072}, {51377, 58504}, {62856, 64676}, {62969, 64186}, {63136, 64745}, {63269, 63270}

X(65739) = midpoint of X(3746) and X(35204)
X(65739) = crosssum of X(1086) and X(17365)
X(65739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 214, 17100}, {100, 1621, 11}, {100, 63917, 3035}, {405, 12331, 59415}, {10087, 51506, 8}, {24646, 24647, 11680}, {33814, 34123, 404}

X(65740) = X(100)X(961)∩X(105)X(5211)

Barycentrics    (a^3 - 2 a^2 b - 2 a b^2 + b^3 + a b c + c^3) (a^3 + b^3 - 2 a^2 c + a b c - 2 a c^2 + c^3) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 7092.

X(65740) lies on the circumconic {{A,B,C,X(1),X(2)}} and these lines: {1, 8258}, {28, 2907}, {57, 3882}, {81, 40605}, {88, 3936}, {89, 20090}, {100, 961}, {105, 5211}, {277, 24620}, {278, 3210}, {330, 17740}, {345, 39694}, {646, 30710}, {1022, 4707}, {1054, 17748}, {2006, 37759}, {4612, 64457}, {4850, 39724}, {7052, 37794}, {7132, 37684}, {15474, 17490}, {17282, 39963}, {17495, 21907}, {17776, 39703}, {20882, 37887}, {24183, 30831}, {25430, 56519}, {30699, 65046}, {32779, 39722}, {32849, 39698}, {33116, 56184}, {33168, 35058}, {33655, 37795}, {41839, 56218}

X(65740) = isotomic conjugate of X(37759)
X(65740) = isotomic conjugate of the anticomplement of X(32851)
X(65740) = X(36935)-anticomplementary conjugate of X(21286)
X(65740) = X(32851)-cross conjugate of X(2)
X(65740) = X(i)-isoconjugate of X(j) for these (i,j): {6, 60353}, {31, 37759}, {42, 37791}, {604, 36926}, {902, 47056}
X(65740) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 37759}, {9, 60353}, {3161, 36926}, {40592, 37791}, {40594, 47056}
X(65740) = cevapoint of X(i) and X(j) for these (i,j): {758, 2092}, {1015, 3738}
X(65740) = trilinear pole of line {513, 960}
X(65740) = pole of line {37759, 37791} with respect to the Kiepert circumhyperbola of the anticomplementary triangle
X(65740) = pole of line {30572, 51643} with respect to the Steiner circumellipse
X(65740) = barycentric product X(i)*X(j) for these {i,j}: {86, 34895}, {320, 36935}
X(65740) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 60353}, {2, 37759}, {8, 36926}, {81, 37791}, {88, 47056}, {320, 41873}, {34895, 10}, {36935, 80}

X(65741) = ISOGONAL CONJUGATE OF X(65740)

Barycentrics    a^2*(a^3 + b^3 + a*b*c - 2*b^2*c - 2*b*c^2 + c^3) : :

X(65741) lies on these lines: {1, 6}, {31, 47523}, {48, 62214}, {55, 3764}, {81, 20072}, {182, 37819}, {284, 21796}, {320, 940}, {404, 28249}, {415, 56830}, {478, 1463}, {513, 5061}, {572, 17053}, {595, 4274}, {608, 4186}, {692, 39688}, {752, 5711}, {859, 3285}, {995, 5114}, {1015, 5053}, {1086, 6996}, {1149, 1404}, {1400, 1950}, {1405, 3915}, {1407, 28039}, {1429, 57037}, {1611, 20995}, {1731, 49758}, {1914, 2183}, {1995, 38904}, {2092, 33771}, {2161, 56911}, {2182, 3290}, {2241, 4266}, {2245, 17735}, {2267, 2275}, {2268, 2277}, {2278, 21008}, {2298, 4645}, {2330, 40934}, {3122, 17798}, {3125, 16548}, {3782, 50400}, {3834, 25527}, {3836, 34261}, {4286, 16287}, {4363, 41236}, {4370, 33309}, {4383, 33116}, {4700, 50028}, {5211, 33854}, {5710, 49709}, {5783, 31289}, {6180, 28014}, {6687, 37679}, {7113, 8610}, {7122, 22172}, {8614, 55323}, {9456, 40595}, {13740, 17369}, {14020, 57280}, {16047, 27644}, {16611, 60361}, {17054, 37415}, {17697, 54389}, {17811, 25894}, {19729, 26223}, {20227, 64121}, {20331, 35992}, {21495, 28283}, {21892, 54316}, {25496, 40401}, {25536, 52897}, {28011, 54377}, {28078, 28739}, {31243, 37682}, {37501, 63390}, {37759, 37791}, {40091, 45955}, {41772, 55406}, {49710, 62805}

X(65741) = isogonal conjugate of X(65740)
X(65741) = isogonal conjugate of the isotomic conjugate of X(37759)
X(65741) = X(37791)-Ceva conjugate of X(60353)
X(65741) = X(i)-isoconjugate of X(j) for these (i,j): {81, 34895}, {3218, 36935}
X(65741) = X(40586)-Dao conjugate of X(34895)
X(65741) = crosspoint of X(i) and X(j) for these (i,j): {759, 14534}, {1016, 2222}
X(65741) = crosssum of X(i) and X(j) for these (i,j): {758, 2092}, {1015, 3738}
X(65741) = crossdifference of every pair of points on line {513, 960}
X(65741) = X(i)-line conjugate of X(j) for these (i,j): {1, 960}, {5061, 513}
X(65741) = pole of line {442, 1220} with respect to the Kiepert circumhyperbola
X(65741) = pole of line {101, 2092} with respect to the ABCGK
X(65741) = pole of line {1, 38903} with respect to the ABCGI
X(65741) = pole of line {42, 23858} with respect to the ABCIK
X(65741) = pole of line {1376, 24445} with respect to the Feuerbach circumhyperbola of the medial triangle
X(65741) = pole of line {81, 40605} with respect to the Feuerbach circumhyperbola of the tangential triangle
X(65741) = pole of line {1, 8258} with respect to the Kiepert circumhyperbola of the excentral triangle
X(65741) = pole of line {15313, 44545} with respect to the Orthic inconic
X(65741) = pole of line {513, 5247} with respect to the Mandart circumellipse, CC9
X(65741) = pole of line {100, 30721} with respect to the Hutson-Moses hyperbola
X(65741) = pole of line {667, 1402} with respect to the circumcircle
X(65741) = barycentric product X(i)*X(j) for these {i,j}: {1, 60353}, {6, 37759}, {37, 37791}, {44, 47056}, {56, 36926}, {6187, 41873}
X(65741) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 34895}, {6187, 36935}, {36926, 3596}, {37759, 76}, {37791, 274}, {41873, 40075}, {47056, 20568}, {60353, 75}
X(65741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2268, 2277, 5110}, {3246, 16796, 1191}, {7113, 8610, 9259}, {16502, 55432, 6}





leftri   D-maps: X(65742) - X(65752)  rightri

Contributed by Clark Kimberling and Peter Moses, October 17, 2024.

Suppose that U and V are given by normalized barycentrics U = (u,v,w) and U' = (u',v',w'). The D-map of U and V is here introduced as the point u'' : v'' : w'' given by

u'' = SA(u - u')2, v'' = SB(v - v')2, w'' = SC(w - w')2.

The name D-map corresponds to the fact that |UU'|2 = u''+v''+w''. If U and U' lie on a line L, then every pair of points on L have the same D-map. If U and U' are triangle centers, then the D-map of U and U' are triangle centers.

The appearance of (i,j,k) in the following list means that the D-map of X(i) and X(j) is X(k), where k < 60000.

(1, 4, 38554)
(2, 3, 16163) (Euler line)
(3, 10, 38554)
(8, 20, 38554)
(13, 15, 16163)
(14, 16, 16163)
(44, 513, 3937) (anti-orthic axis)
(230, 231, 125) (orthic axis)
(241, 514, 1565) (Gergonne line)
(325, 523, 125) (de Longchamps axis)
(522, 650, 2968) (Garcia-Reznik line)
(513, 663, 3937) (Helman line)

The appearance of (i,j,k) in the following list means that the D-map of X(i) and X(j) is X(k), where k > 60000.

(1, 2, 65742)
(1, 3, 65743)
(1, 6, 65744)
(1, 7, 65745)
(1, 21, 65746)
(2, 6, 65747)
(3,6, 65748)
(4, 6, 65749)
(6, 13, 65750)
(187, 237, 65751)
(650, 663, 65752)

underbar



X(65742) = D-MAP OF X(1) AND X(2)

Barycentrics    (2*a - b - c)^2*(a^2 - b^2 - c^2) : :
X(65742) = 2 X[121] - 3 X[12035], 3 X[3699] - X[21290], 3 X[6790] + X[21290], 3 X[3756] - 4 X[6715], 2 X[6715] - 3 X[6789], 2 X[15522] - 3 X[38384]

X(65742) lies on these lines: {3, 1811}, {8, 1387}, {11, 49998}, {69, 1565}, {72, 3937}, {78, 1062}, {104, 4578}, {106, 9041}, {121, 519}, {125, 41014}, {190, 9945}, {952, 3699}, {997, 49688}, {1017, 4370}, {1026, 34586}, {1145, 17780}, {1260, 1809}, {1317, 4152}, {1332, 22141}, {1483, 44720}, {3589, 30115}, {3756, 6715}, {3952, 10609}, {3977, 5440}, {4126, 37525}, {4415, 48836}, {4767, 6224}, {4899, 5126}, {5846, 56807}, {6555, 7967}, {9053, 45763}, {9963, 30578}, {12690, 30566}, {14429, 39472}, {15522, 38384}, {15935, 30829}, {17527, 50624}, {21282, 51409}, {22147, 30681}, {24203, 32087}, {24929, 25101}, {27549, 37606}, {31853, 64504}, {34587, 53534}, {36791, 42070}

X(65742) = midpoint of X(3699) and X(6790)
X(65742) = reflection of X(3756) in X(6789)
X(65742) = isotomic conjugate of the isogonal conjugate of X(22371)
X(65742) = isotomic conjugate of the polar conjugate of X(4370)
X(65742) = isogonal conjugate of the polar conjugate of X(36791)
X(65742) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 3977}, {36791, 4370}
X(65742) = X(22371)-cross conjugate of X(4370)
X(65742) = X(i)-isoconjugate of X(j) for these (i,j): {19, 2226}, {25, 679}, {34, 1318}, {88, 8752}, {92, 41935}, {106, 36125}, {1474, 30575}, {1973, 54974}, {1974, 57929}, {4638, 6591}, {6336, 9456}
X(65742) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 2226}, {214, 36125}, {519, 4}, {900, 2969}, {1647, 7649}, {4370, 6336}, {6337, 54974}, {6505, 679}, {11517, 1318}, {22391, 41935}, {51574, 30575}
X(65742) = crosspoint of X(i) and X(j) for these (i,j): {69, 3977}, {519, 57506}
X(65742) = crosssum of X(i) and X(j) for these (i,j): {25, 8752}, {106, 39264}
X(65742) = crossdifference of every pair of points on line {2441, 8752}
X(65742) = barycentric product X(i)*X(j) for these {i,j}: {3, 36791}, {63, 4738}, {69, 4370}, {72, 16729}, {76, 22371}, {304, 678}, {305, 1017}, {345, 1317}, {348, 4152}, {394, 65585}, {519, 3977}, {1331, 52627}, {1797, 58254}, {2415, 39472}, {3264, 22356}, {3926, 42070}, {4025, 53582}, {4358, 5440}, {4543, 65164}, {4561, 6544}, {24004, 53532}, {57919, 61047}
X(65742) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 2226}, {44, 36125}, {63, 679}, {69, 54974}, {72, 30575}, {184, 41935}, {219, 1318}, {304, 57929}, {519, 6336}, {678, 19}, {902, 8752}, {1017, 25}, {1317, 278}, {1331, 4638}, {1332, 4618}, {1797, 59150}, {3251, 6591}, {3977, 903}, {4152, 281}, {4370, 4}, {4542, 8735}, {4543, 3064}, {4738, 92}, {5440, 88}, {6544, 7649}, {8028, 8756}, {14418, 23838}, {14429, 4049}, {16729, 286}, {17780, 65336}, {21821, 1824}, {22082, 52206}, {22086, 23345}, {22356, 106}, {22371, 6}, {22428, 39264}, {23202, 9456}, {35092, 2969}, {36791, 264}, {39472, 2403}, {42070, 393}, {52627, 46107}, {52978, 1320}, {53532, 1022}, {53582, 1897}, {58254, 46109}, {61047, 608}, {65585, 2052}
X(65742) = {X(1317),X(4152)}-harmonic conjugate of X(4738)

X(65743) = D-MAP OF X(1) AND X(3)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3)^2 : :
X(65743) = 2 X[119] - 3 X[61672], 3 X[549] - 2 X[46174], 5 X[631] - 4 X[64489], 4 X[6713] - 3 X[61674], X[10724] - 3 X[61729], 3 X[61731] - 5 X[64008]

X(65743) lies on these lines: {1, 58487}, {3, 1331}, {40, 2841}, {51, 37533}, {72, 2968}, {73, 22346}, {78, 5562}, {100, 2818}, {102, 3939}, {104, 2810}, {119, 517}, {125, 21530}, {185, 37700}, {307, 1565}, {389, 34772}, {513, 24466}, {549, 46174}, {631, 64489}, {651, 52830}, {915, 42067}, {952, 34462}, {953, 6551}, {970, 4158}, {1092, 7078}, {1265, 12245}, {1361, 23101}, {1807, 3270}, {2390, 13528}, {2807, 6326}, {2842, 46684}, {2850, 16163}, {3035, 31849}, {3428, 53294}, {5720, 15030}, {5840, 31847}, {6282, 36987}, {6516, 7215}, {6713, 61674}, {6906, 29958}, {8677, 42769}, {8679, 50371}, {10724, 61729}, {11248, 42448}, {13199, 29349}, {16836, 18444}, {18446, 64100}, {21362, 33810}, {21664, 26611}, {21669, 44865}, {22758, 61640}, {23980, 59800}, {32486, 53391}, {33814, 61638}, {34586, 53548}, {35281, 38579}, {37531, 45186}, {37725, 61166}, {38513, 53790}, {45022, 52659}, {46044, 55317}, {61731, 64008}, {63425, 63436}

X(65743) = midpoint of X(38513) and X(64136)
X(65743) = reflection of X(i) in X(j) for these {i,j}: {3937, 3}, {6073, 15632}, {31849, 3035}, {37725, 61166}, {38389, 31847}, {46044, 55317}
X(65743) = isotomic conjugate of the polar conjugate of X(23980)
X(65743) = isogonal conjugate of the polar conjugate of X(26611)
X(65743) = X(26611)-Ceva conjugate of X(23980)
X(65743) = X(i)-isoconjugate of X(j) for these (i,j): {19, 59196}, {92, 41933}, {104, 36123}, {909, 16082}, {1973, 57550}, {2423, 65223}, {36037, 43933}, {36110, 43728}, {61238, 65331}
X(65743) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 59196}, {517, 4}, {2804, 21666}, {3259, 43933}, {6337, 57550}, {8677, 3937}, {22391, 41933}, {23980, 16082}, {35014, 44426}, {39004, 43728}, {40613, 36123}, {57293, 513}
X(65743) = crosspoint of X(i) and X(j) for these (i,j): {517, 39173}, {57478, 62402}
X(65743) = crosssum of X(i) and X(j) for these (i,j): {104, 14266}, {2423, 22096}
X(65743) = barycentric product X(i)*X(j) for these {i,j}: {3, 26611}, {63, 24028}, {69, 23980}, {222, 55016}, {304, 42078}, {305, 59800}, {345, 1361}, {394, 21664}, {859, 51367}, {905, 15632}, {908, 22350}, {1016, 35012}, {1145, 57478}, {1275, 41215}, {1332, 42757}, {1465, 51379}, {2397, 8677}, {3326, 44717}, {3926, 42072}, {6516, 60339}, {23101, 65302}, {57919, 61057}
X(65743) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 59196}, {69, 57550}, {184, 41933}, {517, 16082}, {1361, 278}, {2183, 36123}, {2427, 1309}, {3310, 43933}, {8677, 2401}, {15632, 6335}, {21664, 2052}, {22350, 34234}, {23220, 2423}, {23980, 4}, {23981, 65331}, {24028, 92}, {26611, 264}, {35012, 1086}, {41215, 1146}, {41220, 7117}, {42072, 393}, {42078, 19}, {42757, 17924}, {47408, 14266}, {47420, 56761}, {47434, 64635}, {51367, 57984}, {51379, 36795}, {52307, 43728}, {55016, 7017}, {55153, 21666}, {59800, 25}, {60339, 44426}, {61057, 608}

X(65744) = D-MAP OF X(1) AND X(6)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a*b - b^2 + a*c - c^2)^2 : :

X(65744) lies on these lines: {3, 1810}, {63, 295}, {72, 1565}, {100, 52823}, {120, 518}, {219, 36057}, {306, 2968}, {394, 1260}, {644, 2808}, {1332, 3270}, {1350, 38876}, {1362, 4712}, {1818, 20749}, {2875, 3908}, {3292, 22371}, {3873, 4260}, {4437, 34337}, {6184, 39686}, {9317, 14839}, {14520, 25082}, {14826, 17784}, {20683, 56714}, {22148, 62217}, {22352, 60703}, {25006, 38055}, {29653, 62852}, {31865, 64503}, {35341, 58035}

X(65744) = isotomic conjugate of the isogonal conjugate of X(20776)
X(65744) = isotomic conjugate of the polar conjugate of X(6184)
X(65744) = isogonal conjugate of the polar conjugate of X(4437)
X(65744) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 25083}, {4437, 6184}
X(65744) = X(20776)-cross conjugate of X(6184)
X(65744) = X(i)-isoconjugate of X(j) for these (i,j): {4, 51838}, {19, 6185}, {34, 62715}, {92, 41934}, {105, 36124}, {673, 8751}, {1027, 65333}, {1438, 54235}, {1973, 57537}
X(65744) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 6185}, {518, 4}, {918, 2973}, {6184, 54235}, {6337, 57537}, {11517, 62715}, {17435, 17924}, {22391, 41934}, {36033, 51838}, {39046, 36124}
X(65744) = crosspoint of X(i) and X(j) for these (i,j): {69, 25083}, {518, 34159}
X(65744) = crosssum of X(i) and X(j) for these (i,j): {25, 8751}, {105, 14267}
X(65744) = crossdifference of every pair of points on line {2440, 8751}
X(65744) = barycentric product X(i)*X(j) for these {i,j}: {3, 4437}, {63, 4712}, {69, 6184}, {72, 16728}, {76, 20776}, {304, 42079}, {305, 39686}, {345, 1362}, {394, 34337}, {518, 25083}, {906, 62430}, {1331, 53583}, {1332, 3126}, {1814, 23102}, {1818, 3912}, {3263, 20752}, {3926, 42071}, {20778, 40217}, {42720, 53550}, {57919, 61055}
X(65744) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 6185}, {48, 51838}, {69, 57537}, {184, 41934}, {219, 62715}, {518, 54235}, {672, 36124}, {1362, 278}, {1818, 673}, {2223, 8751}, {2284, 65333}, {3126, 17924}, {4437, 264}, {4712, 92}, {6184, 4}, {16728, 286}, {20728, 14267}, {20749, 52210}, {20752, 105}, {20776, 6}, {20778, 6654}, {23102, 46108}, {23225, 43929}, {23612, 5089}, {25083, 2481}, {34337, 2052}, {35094, 2973}, {35505, 2969}, {39686, 25}, {42071, 393}, {42079, 19}, {53550, 62635}, {53583, 46107}, {61055, 608}
X(65744) = {X(1818),X(20778)}-harmonic conjugate of X(20749)

X(65745) = D-MAP OF X(1) AND X(7)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^3 - a^2*b - b^3 - a^2*c + b^2*c + b*c^2 - c^3)^2 : :
X(65745) = 2 X[118] - 3 X[51406], 4 X[6712] - 3 X[61673], X[10725] - 3 X[61730], 2 X[17044] - 3 X[38690]

X(65745) lies on these lines: {3, 348}, {4, 27541}, {20, 3732}, {40, 728}, {63, 2968}, {100, 329}, {103, 5845}, {105, 30242}, {118, 516}, {125, 440}, {514, 63403}, {664, 53804}, {917, 2969}, {952, 63416}, {1146, 31852}, {1360, 24014}, {1427, 24025}, {1763, 10860}, {2724, 59101}, {2826, 24466}, {3198, 22001}, {3937, 10167}, {4512, 25968}, {4566, 15725}, {5762, 16091}, {6361, 37412}, {6710, 31851}, {6712, 61673}, {6776, 64884}, {7046, 17784}, {10725, 61730}, {17044, 38690}, {20344, 35514}, {21665, 42073}, {23972, 59799}

X(65745) = midpoint of X(20) and X(3732)
X(65745) = reflection of X(i) in X(j) for these {i,j}: {1146, 31852}, {1530, 40869}, {1536, 910}, {1541, 53579}, {1565, 3}, {6074, 3234}, {31851, 6710}
X(65745) = isotomic conjugate of the polar conjugate of X(23972)
X(65745) = isogonal conjugate of the polar conjugate of X(59206)
X(65745) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 26006}, {15742, 2398}, {59206, 23972}
X(65745) = X(i)-isoconjugate of X(j) for these (i,j): {19, 59195}, {103, 36122}, {911, 52781}, {1973, 57548}, {2424, 65218}, {36039, 53150}
X(65745) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 59195}, {516, 4}, {1566, 53150}, {6337, 57548}, {23972, 52781}, {39470, 1565}, {46095, 103}, {57292, 514}, {62591, 18025}
X(65745) = crosspoint of X(i) and X(j) for these (i,j): {69, 26006}, {516, 54233}, {2398, 15742}
X(65745) = crosssum of X(i) and X(j) for these (i,j): {103, 54232}, {2424, 3937}
X(65745) = barycentric product X(i)*X(j) for these {i,j}: {3, 59206}, {63, 24014}, {69, 23972}, {222, 55019}, {304, 42077}, {305, 59799}, {345, 1360}, {394, 21665}, {516, 26006}, {1331, 58280}, {2398, 39470}, {3234, 4025}, {3926, 42073}, {14953, 51366}, {54233, 62591}
X(65745) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 59195}, {69, 57548}, {516, 52781}, {676, 53150}, {910, 36122}, {1360, 278}, {2426, 40116}, {3234, 1897}, {21665, 2052}, {23972, 4}, {24014, 92}, {26006, 18025}, {39470, 2400}, {42073, 393}, {42077, 19}, {47407, 54232}, {47422, 56787}, {55019, 7017}, {56785, 60001}, {58280, 46107}, {59206, 264}, {59799, 25}

X(65746) = D-MAP OF X(1) AND X(21)

Barycentrics    a^2*(b + c)^2*(a^2 - b^2 - c^2)*(a^2 - b^2 + b*c - c^2)^2 : :

X(65746) lies on these lines: {72, 125}, {643, 5663}, {662, 52831}, {758, 31845}, {2968, 41014}, {3028, 4736}, {3269, 4574}, {3695, 7066}, {3916, 3937}, {6739, 64139}, {8287, 18254}, {22128, 52407}, {37346, 64041}

X(65746) = isotomic conjugate of the polar conjugate of X(35069)
X(65746) = X(4592)-Ceva conjugate of X(8552)
X(65746) = X(i)-isoconjugate of X(j) for these (i,j): {34, 62713}, {270, 63750}, {1973, 57555}, {2189, 34535}
X(65746) = X(i)-Dao conjugate of X(j) for these (i,j): {758, 4}, {6149, 270}, {6337, 57555}, {6370, 2970}, {11517, 62713}
X(65746) = crosspoint of X(758) and X(39166)
X(65746) = crosssum of X(759) and X(38938)
X(65746) = barycentric product X(i)*X(j) for these {i,j}: {63, 4736}, {69, 35069}, {345, 3028}, {4996, 26942}, {34544, 57807}, {52407, 61410}, {57919, 61060}
X(65746) = barycentric quotient X(i)/X(j) for these {i,j}: {69, 57555}, {201, 34535}, {215, 2189}, {219, 62713}, {2197, 63750}, {3028, 278}, {4736, 92}, {4996, 46103}, {26942, 57645}, {34544, 270}, {35069, 4}, {47417, 38938}, {61060, 608}

X(65747) = D-MAP OF X(2) AND X(6)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^2 - b^2 - c^2)^2 : :
X(65747) = X[111] - 3 X[14916], 2 X[126] - 3 X[12036], 3 X[9146] - X[14360], X[14360] + 3 X[38940], 3 X[5108] - 2 X[6719], 4 X[6719] - 3 X[6791], 3 X[9169] - 4 X[58427], 3 X[14856] - 2 X[22338]

X(65747) lies on these lines: {69, 125}, {99, 10553}, {111, 14916}, {126, 524}, {394, 4175}, {542, 9146}, {576, 56435}, {877, 16240}, {1092, 53784}, {1366, 7067}, {1499, 38805}, {1565, 4001}, {2482, 8030}, {3292, 6390}, {4576, 14928}, {5095, 34336}, {5108, 6719}, {5181, 10417}, {5468, 5642}, {5477, 45672}, {6333, 16163}, {7665, 50639}, {7813, 62657}, {9169, 58427}, {10552, 18800}, {11064, 62590}, {14856, 22338}, {15098, 64508}, {36739, 64690}, {40112, 51397}, {54274, 58284}, {62299, 64802}

X(65747) = midpoint of X(9146) and X(38940)
X(65747) = reflection of X(6791) in X(5108)
X(65747) = isotomic conjugate of the polar conjugate of X(2482)
X(65747) = isogonal conjugate of the polar conjugate of X(36792)
X(65747) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 6390}, {4563, 14417}, {36792, 2482}
X(65747) = X(i)-isoconjugate of X(j) for these (i,j): {19, 10630}, {92, 41936}, {111, 36128}, {897, 8753}, {923, 17983}, {1096, 15398}, {1973, 57539}
X(65747) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 10630}, {524, 4}, {690, 8754}, {1648, 2501}, {2482, 17983}, {6337, 57539}, {6503, 15398}, {6593, 8753}, {14417, 10555}, {22391, 41936}, {52881, 671}, {62594, 5466}
X(65747) = crosspoint of X(i) and X(j) for these (i,j): {69, 6390}, {524, 34161}
X(65747) = crosssum of X(i) and X(j) for these (i,j): {25, 8753}, {111, 14263}
X(65747) = crossdifference of every pair of points on line {2444, 8753}
X(65747) = barycentric product X(i)*X(j) for these {i,j}: {3, 36792}, {63, 24038}, {69, 2482}, {72, 16733}, {304, 42081}, {305, 39689}, {345, 1366}, {348, 7067}, {394, 34336}, {524, 6390}, {895, 23106}, {1649, 4563}, {3266, 3292}, {3926, 5095}, {4558, 52629}, {5181, 53784}, {5467, 45807}, {5468, 14417}, {8030, 30786}, {17206, 52068}, {23992, 47389}, {34161, 52881}, {34897, 62661}, {52608, 54274}
X(65747) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 10630}, {69, 57539}, {184, 41936}, {187, 8753}, {394, 15398}, {524, 17983}, {896, 36128}, {1366, 278}, {1649, 2501}, {2482, 4}, {3266, 46111}, {3292, 111}, {4558, 34574}, {5095, 393}, {5468, 65350}, {6390, 671}, {7067, 281}, {8030, 468}, {9177, 52490}, {14417, 5466}, {16733, 286}, {23106, 44146}, {23200, 32740}, {23992, 8754}, {24038, 92}, {30454, 8737}, {30455, 8738}, {33915, 14273}, {34336, 2052}, {36792, 264}, {39689, 25}, {42081, 19}, {45807, 52632}, {47389, 57552}, {47412, 14263}, {47426, 64619}, {52068, 1826}, {52629, 14618}, {54274, 2489}, {58780, 58757}, {59801, 2971}, {62594, 10555}, {62656, 62237}, {62661, 37765}
X(65747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1366, 7067, 24038}, {5468, 50567, 5642}, {10552, 31128, 18800}, {45672, 62658, 5477}

X(65748) = D-MAP OF X(3) AND X(6)

Barycentrics    a^4*(a^2 - b^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)^2 : :
X(65748) = 2 X[114] - 3 X[6786], 3 X[549] - 2 X[46172], 5 X[631] - 4 X[64490], 4 X[6036] - 3 X[6784], 3 X[6785] - 5 X[64089], 3 X[6787] - X[10723], 5 X[38750] - 3 X[41330], 2 X[39806] - 3 X[61733], X[39807] + 3 X[61734]

X(65748) lies on these lines: {3, 1808}, {69, 53174}, {98, 34383}, {114, 325}, {125, 343}, {127, 30214}, {184, 23217}, {394, 6638}, {512, 38738}, {549, 46172}, {577, 14600}, {620, 31850}, {631, 64490}, {684, 39469}, {1092, 10316}, {1147, 40373}, {1350, 2882}, {1355, 7062}, {1565, 11573}, {2387, 18860}, {2421, 52128}, {2698, 47389}, {2967, 23611}, {3095, 27374}, {3289, 46094}, {3563, 42068}, {3933, 5562}, {3937, 18607}, {4176, 63428}, {4558, 17974}, {5889, 7906}, {5999, 61101}, {6036, 6784}, {6752, 9723}, {6785, 64089}, {6787, 10723}, {9419, 11672}, {9517, 14689}, {9737, 40951}, {10607, 63531}, {11674, 55005}, {12251, 40050}, {13137, 22103}, {15630, 61485}, {18321, 38730}, {23698, 31848}, {31127, 33884}, {31406, 64854}, {31859, 40254}, {33548, 49111}, {38750, 41330}, {39806, 61733}, {39807, 61734}, {46046, 55312}

X(65748) = midpoint of X(i) and X(j) for these {i,j}: {5999, 61101}, {18321, 38730}
X(65748) = reflection of X(i) in X(j) for these {i,j}: {1513, 51427}, {6072, 15631}, {13137, 22103}, {15630, 61485}, {31850, 620}, {46046, 55312}
X(65748) = isotomic conjugate of the polar conjugate of X(11672)
X(65748) = isogonal conjugate of the polar conjugate of X(36790)
X(65748) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 36212}, {36790, 11672}
X(65748) = X(i)-isoconjugate of X(j) for these (i,j): {19, 34536}, {92, 41932}, {98, 36120}, {158, 47388}, {1821, 6531}, {1910, 16081}, {1973, 57541}, {2190, 60594}, {24006, 41173}, {36036, 53149}, {36104, 43665}, {46273, 57260}
X(65748) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 60594}, {6, 34536}, {511, 4}, {1147, 47388}, {2679, 53149}, {5976, 60199}, {6337, 57541}, {11672, 16081}, {22391, 41932}, {39000, 43665}, {39073, 52641}, {40601, 6531}, {41172, 14618}, {46094, 98}, {57294, 512}, {62590, 290}
X(65748) = crosspoint of X(i) and X(j) for these (i,j): {69, 36212}, {511, 34157}
X(65748) = crosssum of X(i) and X(j) for these (i,j): {25, 6531}, {98, 14265}, {2422, 23216}, {2501, 51441}
X(65748) = crossdifference of every pair of points on line {2422, 6531}
X(65748) = barycentric product X(i)*X(j) for these {i,j}: {3, 36790}, {63, 23996}, {69, 11672}, {72, 16725}, {184, 32458}, {232, 51386}, {237, 6393}, {287, 23098}, {304, 42075}, {305, 9419}, {325, 3289}, {345, 1355}, {348, 7062}, {394, 2967}, {511, 36212}, {647, 15631}, {684, 2421}, {1092, 36426}, {2396, 39469}, {3964, 51334}, {4558, 41167}, {4563, 58262}, {6333, 14966}, {23611, 57799}, {32661, 62555}, {34157, 62590}, {35088, 47390}, {36214, 46888}, {36425, 40050}, {42702, 51369}, {47406, 52091}
X(65748) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 34536}, {69, 57541}, {184, 41932}, {216, 60594}, {237, 6531}, {325, 60199}, {511, 16081}, {577, 47388}, {684, 43665}, {1355, 278}, {1755, 36120}, {2396, 65272}, {2421, 22456}, {2491, 53149}, {2967, 2052}, {3289, 98}, {6393, 18024}, {7062, 281}, {9418, 57260}, {9419, 25}, {9475, 52641}, {11672, 4}, {14966, 685}, {15631, 6331}, {16725, 286}, {23098, 297}, {23611, 232}, {23996, 92}, {32458, 18022}, {32661, 41173}, {36212, 290}, {36425, 1974}, {36790, 264}, {39469, 2395}, {41167, 14618}, {42075, 19}, {44716, 53245}, {46888, 17984}, {47390, 57562}, {47406, 14265}, {47418, 56788}, {51334, 1093}, {51386, 57799}, {58262, 2501}, {59805, 2970}
X(65748) = {X(1355),X(7062)}-harmonic conjugate of X(23996)

X(65749) = D-MAP OF X(4) AND X(6)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6)^2 : :
X(65749) = 2 X[132] - 3 X[6793], 3 X[6794] - X[10735], 3 X[12037] - 4 X[34841], X[18337] - 3 X[38699]

X(65749) lies on these lines: {2, 98}, {4, 57219}, {5, 46173}, {107, 3079}, {132, 1503}, {159, 34131}, {525, 14689}, {648, 14944}, {1181, 22146}, {1498, 2138}, {1562, 2794}, {2445, 50938}, {2777, 13200}, {3269, 10991}, {6103, 64080}, {6524, 31383}, {6720, 43389}, {6794, 10735}, {12037, 34841}, {16240, 43952}, {18337, 38699}, {18400, 41377}, {21659, 39646}, {33971, 62261}, {38747, 60704}, {46097, 47105}, {53912, 57655}

X(65749) = reflection of X(i) in X(j) for these {i,j}: {5, 46173}, {1562, 18338}, {43389, 6720}, {47105, 46097}
X(65749) = isotomic conjugate of the polar conjugate of X(23976)
X(65749) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 441}, {32230, 2409}
X(65749) = X(i)-isoconjugate of X(j) for these (i,j): {1297, 8767}, {1973, 57549}, {2435, 36092}, {36046, 43673}
X(65749) = X(i)-Dao conjugate of X(j) for these (i,j): {1503, 4}, {6337, 57549}, {15595, 35140}, {23976, 6330}, {33504, 43673}, {39071, 1297}, {39073, 39265}, {57296, 525}, {65726, 9476}
X(65749) = crosspoint of X(i) and X(j) for these (i,j): {69, 441}, {1503, 34156}, {2409, 32230}
X(65749) = crosssum of X(i) and X(j) for these (i,j): {25, 43717}, {1297, 39265}, {2435, 2972}
X(65749) = crossdifference of every pair of points on line {2435, 3569}
X(65749) = barycentric product X(i)*X(j) for these {i,j}: {63, 24023}, {69, 23976}, {441, 1503}, {648, 60341}, {2409, 39473}, {3265, 15639}, {8779, 30737}, {15595, 34156}, {35282, 36894}, {58256, 64975}
X(65749) = barycentric quotient X(i)/X(j) for these {i,j}: {69, 57549}, {441, 35140}, {1503, 6330}, {2312, 8767}, {2409, 65265}, {2445, 32687}, {6793, 52485}, {8779, 1297}, {9475, 39265}, {15639, 107}, {23976, 4}, {24023, 92}, {34156, 9476}, {35282, 56601}, {39473, 2419}, {42671, 43717}, {58256, 60516}, {60341, 525}
X(65749) = {X(1899),X(47200)}-harmonic conjugate of X(125)

X(65750) = D-MAP OF X(6) AND X(13)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)^2 : :
X(65750) = 3 X[125] - 4 X[65729], 3 X[5642] - 2 X[65718], 2 X[6390] - 3 X[51394], 3 X[9144] - X[44969], 4 X[16760] - 3 X[51429], 2 X[16760] - 3 X[53725]

X(65750) lies on these lines: {69, 17932}, {125, 3292}, {325, 6055}, {524, 65620}, {525, 16163}, {542, 1550}, {2682, 18332}, {5095, 60590}, {5642, 65718}, {6390, 51394}, {9144, 44969}, {10553, 18020}, {16760, 51429}, {39474, 65723}

X(65750) = reflection of X(i) in X(j) for these {i,j}: {2682, 18332}, {51429, 53725}, {57431, 14999}
X(65750) = isotomic conjugate of the polar conjugate of X(23967)
X(65750) = X(69)-Ceva conjugate of X(65722)
X(65750) = X(1973)-isoconjugate of X(57547)
X(65750) = X(i)-Dao conjugate of X(j) for these (i,j): {542, 4}, {6337, 57547}, {35582, 53156}, {57464, 44427}, {65730, 5641}
X(65750) = crosspoint of X(i) and X(j) for these (i,j): {69, 65722}, {542, 51474}
X(65750) = crosssum of X(842) and X(38939)
X(65750) = barycentric product X(i)*X(j) for these {i,j}: {69, 23967}, {394, 38552}, {542, 65722}, {3265, 60505}, {14999, 65723}, {39474, 50941}, {45662, 51405}, {51474, 65730}, {58252, 65308}, {60053, 60340}
X(65750) = barycentric quotient X(i)/X(j) for these {i,j}: {69, 57547}, {23967, 4}, {38552, 2052}, {39474, 50942}, {46048, 6103}, {58252, 60502}, {60340, 44427}, {60505, 107}, {65722, 5641}, {65723, 14223}

X(65751) = D-MAP OF X(187) AND X(237)

Barycentrics    a^4*(b - c)^2*(b + c)^2*(a^2 - b^2 - c^2) : :
X(65751) = 3 X[2] - 4 X[64490], 2 X[115] - 3 X[6784], X[148] - 3 X[46303], 2 X[620] - 3 X[3111], 4 X[620] - 3 X[6786], X[6033] - 3 X[41330], 3 X[6785] - X[10722], 3 X[6787] - 5 X[14061], X[11674] - 3 X[21445], 3 X[13586] - X[61101], 3 X[15544] - 2 X[39835], X[18321] - 3 X[38224], 3 X[35297] - 2 X[51427]

X(65751) lies on these lines: {2, 64490}, {3, 1808}, {4, 9292}, {5, 46172}, {6, 2882}, {20, 63559}, {25, 61204}, {30, 63560}, {32, 2909}, {51, 15510}, {69, 52608}, {99, 34383}, {112, 1976}, {115, 512}, {125, 127}, {140, 63569}, {148, 46303}, {184, 14908}, {187, 2387}, {211, 35007}, {217, 682}, {230, 5167}, {249, 3044}, {263, 1285}, {325, 35060}, {385, 55005}, {511, 38642}, {620, 3111}, {688, 59801}, {694, 9431}, {754, 14962}, {766, 5164}, {810, 22373}, {827, 13193}, {887, 1084}, {974, 6467}, {1092, 40319}, {1181, 52170}, {1356, 7063}, {1691, 3852}, {1916, 38527}, {1974, 40354}, {2084, 15615}, {2386, 50387}, {2393, 53499}, {2698, 12176}, {2794, 31850}, {2871, 39846}, {2971, 3124}, {3269, 9409}, {3491, 7807}, {3564, 48445}, {3972, 61727}, {4531, 9560}, {5025, 32547}, {5943, 53489}, {6033, 41330}, {6036, 31848}, {6752, 40947}, {6754, 8754}, {6785, 10722}, {6787, 14061}, {7754, 58212}, {7777, 61745}, {7783, 58211}, {9755, 40254}, {10568, 44468}, {10605, 63531}, {11672, 21444}, {11674, 21445}, {12215, 64879}, {12833, 22103}, {13586, 61101}, {14444, 62412}, {15544, 39835}, {16068, 53797}, {17423, 39201}, {18321, 38224}, {20982, 50488}, {32761, 39834}, {35297, 51427}, {40050, 43714}, {40847, 59028}, {41262, 63935}, {42295, 62546}, {44114, 47421}, {47211, 59698}

X(65751) = midpoint of X(i) and X(j) for these {i,j}: {1916, 38527}, {17970, 63554}
X(65751) = reflection of X(i) in X(j) for these {i,j}: {5, 46172}, {325, 35060}, {2679, 14113}, {5167, 230}, {6071, 15630}, {6786, 3111}, {12833, 22103}, {31848, 6036}
X(65751) = reflection of X(2679) in the Brocard axis
X(65751) = isotomic conjugate of the isogonal conjugate of X(23216)
X(65751) = isogonal conjugate of the isotomic conjugate of X(20975)
X(65751) = isotomic conjugate of the polar conjugate of X(1084)
X(65751) = isogonal conjugate of the polar conjugate of X(3124)
X(65751) = X(62935)-complementary conjugate of X(8062)
X(65751) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 647}, {184, 3049}, {1501, 688}, {1974, 669}, {1976, 2491}, {2351, 42293}, {3124, 1084}, {6524, 2489}, {9292, 512}, {14575, 65485}, {17970, 39469}, {34238, 878}, {40146, 9426}, {40319, 39201}, {43714, 525}
X(65751) = X(23216)-cross conjugate of X(1084)
X(65751) = X(i)-isoconjugate of X(j) for these (i,j): {2, 46254}, {4, 24037}, {19, 34537}, {27, 4601}, {69, 23999}, {75, 18020}, {92, 4590}, {99, 811}, {100, 55229}, {107, 55202}, {110, 57968}, {112, 4602}, {158, 47389}, {162, 670}, {190, 55231}, {249, 1969}, {250, 561}, {264, 24041}, {273, 6064}, {286, 4600}, {304, 23582}, {305, 24000}, {310, 5379}, {318, 7340}, {648, 799}, {651, 55233}, {653, 4631}, {662, 6331}, {823, 4563}, {873, 15742}, {877, 36036}, {1101, 18022}, {1102, 34538}, {1577, 55270}, {1783, 52612}, {1897, 4623}, {1928, 57655}, {1959, 41174}, {1973, 44168}, {2052, 62719}, {4176, 24021}, {4558, 57973}, {4567, 44129}, {4570, 57796}, {4572, 52914}, {4592, 6528}, {4593, 41676}, {4609, 32676}, {4610, 6335}, {4612, 46404}, {4620, 31623}, {4625, 36797}, {4634, 46541}, {4998, 57779}, {6507, 57556}, {7012, 18021}, {20641, 44183}, {20948, 47443}, {23889, 59762}, {23964, 40364}, {23995, 44161}, {23997, 65272}, {24006, 31614}, {24019, 52608}, {24039, 65350}, {30450, 55249}, {35325, 37204}, {40703, 57991}, {41679, 55215}, {42396, 55239}, {43187, 62720}, {46102, 52379}, {46238, 60179}, {55194, 57215}, {55196, 65207}, {55224, 65224}, {55227, 65251}, {62534, 65232}
X(65751) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 34537}, {125, 670}, {206, 18020}, {244, 57968}, {512, 4}, {520, 4176}, {523, 18022}, {525, 40050}, {647, 1502}, {1084, 6331}, {1147, 47389}, {2679, 877}, {3005, 264}, {5139, 6528}, {6337, 44168}, {8054, 55229}, {9494, 11325}, {15526, 4609}, {17423, 99}, {18314, 44161}, {21905, 44146}, {22391, 4590}, {23285, 40362}, {23301, 3186}, {32664, 46254}, {34467, 4623}, {34591, 4602}, {35071, 52608}, {36033, 24037}, {38985, 55202}, {38986, 811}, {38991, 55233}, {38996, 648}, {39006, 52612}, {40368, 250}, {40369, 57655}, {40627, 44129}, {50330, 57796}, {50497, 286}, {55050, 41676}, {55053, 55231}, {55066, 799}, {57294, 15631}, {62562, 65272}, {62649, 17984}
X(65751) = crosspoint of X(i) and X(j) for these (i,j): {32, 512}, {69, 647}, {184, 3049}, {669, 1974}, {879, 15391}, {881, 34238}, {2207, 58756}, {2489, 6524}, {3124, 20975}, {50487, 61364}
X(65751) = crosssum of X(i) and X(j) for these (i,j): {2, 53350}, {4, 41676}, {25, 648}, {76, 99}, {107, 21447}, {264, 6331}, {305, 670}, {317, 55252}, {880, 5976}, {1634, 4074}, {3964, 4563}, {4230, 39931}, {4590, 18020}, {4623, 18021}, {15164, 46810}, {15165, 46813}, {55227, 55551}
X(65751) = crossdifference of every pair of points on line {648, 670}
X(65751) = barycentric product X(i)*X(j) for these {i,j}: {3, 3124}, {6, 20975}, {25, 3269}, {31, 3708}, {32, 125}, {48, 2643}, {69, 1084}, {71, 3122}, {72, 3121}, {76, 23216}, {115, 184}, {127, 40146}, {181, 7117}, {213, 18210}, {217, 8901}, {219, 61052}, {228, 3125}, {237, 51404}, {248, 44114}, {287, 58260}, {304, 4117}, {305, 9427}, {338, 14575}, {339, 1501}, {345, 1356}, {348, 7063}, {351, 10097}, {393, 34980}, {394, 2971}, {512, 647}, {520, 2489}, {523, 3049}, {525, 669}, {560, 20902}, {577, 8754}, {594, 22096}, {607, 61058}, {649, 55230}, {656, 798}, {661, 810}, {663, 55234}, {667, 55232}, {684, 2422}, {688, 4580}, {868, 14600}, {872, 3942}, {878, 3569}, {879, 2491}, {881, 24284}, {895, 21906}, {905, 50487}, {1015, 3690}, {1096, 37754}, {1109, 9247}, {1365, 52425}, {1402, 53560}, {1409, 4516}, {1410, 36197}, {1425, 14936}, {1437, 21833}, {1459, 4079}, {1500, 3937}, {1562, 33581}, {1565, 7109}, {1648, 14908}, {1650, 40354}, {1918, 4466}, {1919, 4064}, {1924, 14208}, {1946, 57185}, {1973, 2632}, {1974, 15526}, {1976, 41172}, {1977, 3695}, {2086, 36214}, {2088, 52153}, {2197, 3271}, {2200, 3120}, {2206, 21046}, {2207, 2972}, {2351, 47421}, {2353, 38356}, {2395, 39469}, {2433, 9409}, {2501, 39201}, {2623, 15451}, {2679, 15391}, {2970, 14585}, {3248, 3949}, {3265, 57204}, {3267, 9426}, {3289, 51441}, {3917, 51906}, {3926, 42068}, {4025, 53581}, {4092, 52411}, {4558, 22260}, {4563, 23099}, {4574, 8034}, {4705, 22383}, {5489, 61206}, {6041, 35909}, {6388, 40319}, {6391, 47430}, {6520, 42080}, {6524, 35071}, {6784, 43718}, {7015, 21823}, {7116, 21725}, {7254, 58289}, {8029, 32661}, {8574, 60352}, {8611, 51641}, {8736, 61054}, {10547, 39691}, {11060, 16186}, {12077, 58308}, {14270, 14582}, {14380, 14398}, {14533, 41221}, {14567, 51258}, {14595, 18334}, {14618, 58310}, {15166, 44125}, {15167, 44126}, {15398, 59801}, {15412, 65485}, {15422, 58305}, {15630, 36212}, {17414, 30491}, {17434, 58756}, {19610, 22143}, {20618, 61050}, {20775, 34294}, {21131, 32656}, {21134, 32739}, {21731, 61216}, {22373, 52651}, {23067, 63462}, {23200, 64258}, {23286, 55219}, {23610, 52608}, {23962, 40373}, {26932, 61364}, {27375, 38352}, {30452, 46112}, {30453, 46113}, {32320, 58757}, {32662, 65709}, {35442, 62271}, {36793, 44162}, {36897, 47418}, {40355, 47414}, {40981, 53576}, {42067, 52386}, {46088, 51513}, {47390, 61339}, {47409, 61349}, {47415, 64218}, {51640, 55206}, {51664, 63461}, {52370, 53540}
X(65751) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 34537}, {31, 46254}, {32, 18020}, {48, 24037}, {69, 44168}, {115, 18022}, {125, 1502}, {184, 4590}, {228, 4601}, {338, 44161}, {339, 40362}, {512, 6331}, {520, 52608}, {525, 4609}, {577, 47389}, {647, 670}, {649, 55229}, {656, 4602}, {661, 57968}, {663, 55233}, {667, 55231}, {669, 648}, {688, 41676}, {798, 811}, {810, 799}, {822, 55202}, {878, 43187}, {881, 65351}, {1084, 4}, {1356, 278}, {1459, 52612}, {1501, 250}, {1576, 55270}, {1924, 162}, {1946, 4631}, {1973, 23999}, {1974, 23582}, {1976, 41174}, {2086, 17984}, {2200, 4600}, {2205, 5379}, {2395, 65272}, {2422, 22456}, {2489, 6528}, {2491, 877}, {2632, 40364}, {2643, 1969}, {2971, 2052}, {3049, 99}, {3121, 286}, {3122, 44129}, {3124, 264}, {3125, 57796}, {3269, 305}, {3690, 31625}, {3708, 561}, {3942, 57992}, {4117, 19}, {4580, 42371}, {6524, 57556}, {6784, 44144}, {7063, 281}, {7109, 15742}, {7117, 18021}, {8754, 18027}, {8901, 57790}, {9178, 59762}, {9233, 57655}, {9247, 24041}, {9426, 112}, {9427, 25}, {9494, 35325}, {10097, 53080}, {14574, 47443}, {14575, 249}, {14595, 57546}, {14600, 57991}, {14601, 60179}, {14908, 52940}, {15422, 54950}, {15526, 40050}, {15630, 16081}, {17970, 39292}, {18210, 6385}, {20902, 1928}, {20975, 76}, {21906, 44146}, {22096, 1509}, {22143, 61497}, {22260, 14618}, {22373, 8033}, {22383, 4623}, {22386, 7304}, {23099, 2501}, {23216, 6}, {23286, 55218}, {23610, 2489}, {32661, 31614}, {34952, 55227}, {34980, 3926}, {35071, 4176}, {36417, 32230}, {36793, 40360}, {38352, 33769}, {38356, 40073}, {39201, 4563}, {39469, 2396}, {40146, 44183}, {40354, 42308}, {40373, 23357}, {41221, 62274}, {41993, 8737}, {41994, 8738}, {42068, 393}, {42080, 1102}, {42658, 55224}, {42659, 55226}, {44114, 44132}, {44125, 57543}, {44126, 57544}, {44162, 23964}, {47418, 5976}, {47430, 54412}, {50487, 6335}, {51404, 18024}, {51441, 60199}, {51640, 55205}, {51664, 55213}, {51906, 46104}, {52065, 1824}, {52411, 7340}, {52425, 6064}, {52430, 62719}, {52439, 34538}, {52618, 42395}, {53560, 40072}, {53581, 1897}, {55230, 1978}, {55232, 6386}, {55234, 4572}, {57204, 107}, {58260, 297}, {58310, 4558}, {58756, 42405}, {59801, 34336}, {61052, 331}, {61058, 57918}, {61361, 47390}, {61364, 46102}, {62175, 52913}, {65485, 14570}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 63554, 4173}, {32, 40951, 27374}, {9292, 63555, 4}

X(65752) = D-MAP OF X(650) AND X(663)

Barycentrics    a^2*(a - b - c)^4*(b - c)^2*(a^2 - b^2 - c^2) : :

X(65752) lies on these lines: {125, 7358}, {200, 1018}, {650, 11918}, {1260, 4587}, {3022, 3119}, {3270, 34591}, {3900, 5514}, {3937, 24031}, {7215, 64878}, {11381, 44692}, {35072, 57108}, {36101, 52825}, {38554, 64107}

X(65752) = reflection of X(38388) in X(5514)
X(65752) = isotomic conjugate of the polar conjugate of X(35508)
X(65752) = isogonal conjugate of the polar conjugate of X(23970)
X(65752) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 57055}, {7046, 4130}, {19611, 647}, {23970, 35508}
X(65752) = X(i)-isoconjugate of X(j) for these (i,j): {4, 24013}, {19, 23586}, {25, 24011}, {34, 59457}, {92, 23971}, {108, 4626}, {269, 55346}, {273, 7339}, {279, 7128}, {479, 7012}, {653, 4617}, {658, 32714}, {738, 46102}, {934, 36118}, {1119, 7045}, {1262, 1847}, {1275, 1435}, {1461, 13149}, {1973, 57581}, {4637, 52607}, {6614, 18026}, {7053, 24032}, {7056, 24033}, {7099, 57538}, {7115, 23062}, {7177, 23984}, {32674, 36838}
X(65752) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 23586}, {521, 7056}, {656, 1088}, {905, 57880}, {3239, 57792}, {3900, 4}, {6337, 57581}, {6505, 24011}, {6600, 55346}, {6608, 273}, {7358, 4569}, {11517, 59457}, {14714, 36118}, {17115, 1119}, {22391, 23971}, {23050, 24032}, {35072, 36838}, {35508, 13149}, {36033, 24013}, {38983, 4626}, {40626, 52937}, {40628, 23062}, {58776, 14615}
X(65752) = crosspoint of X(i) and X(j) for these (i,j): {69, 57055}, {220, 57108}, {3900, 7367}, {4130, 7046}
X(65752) = crosssum of X(i) and X(j) for these (i,j): {20, 3732}, {25, 32714}, {279, 36118}, {934, 14256}, {4617, 7053}
X(65752) = crossdifference of every pair of points on line {4617, 32714}
X(65752) = barycentric product X(i)*X(j) for these {i,j}: {3, 23970}, {63, 24010}, {69, 35508}, {78, 3119}, {200, 34591}, {219, 4081}, {220, 2968}, {304, 24012}, {345, 3022}, {346, 3270}, {480, 26932}, {521, 4130}, {652, 4163}, {728, 7004}, {1146, 1260}, {1265, 14936}, {1792, 36197}, {1802, 24026}, {2310, 3692}, {2327, 52335}, {2638, 7101}, {3239, 57108}, {3271, 30681}, {3700, 58338}, {3900, 57055}, {4105, 6332}, {4171, 57081}, {4397, 65102}, {4524, 15411}, {4587, 23615}, {5423, 7117}, {6602, 17880}, {7046, 35072}, {7071, 23983}, {7079, 24031}, {7182, 52064}, {7358, 7367}, {8611, 58329}, {8641, 15416}, {35518, 57180}, {53560, 56182}, {57919, 61050}
X(65752) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 23586}, {48, 24013}, {63, 24011}, {69, 57581}, {184, 23971}, {219, 59457}, {220, 55346}, {480, 46102}, {521, 36838}, {652, 4626}, {657, 36118}, {1253, 7128}, {1260, 1275}, {1364, 30682}, {1802, 7045}, {1946, 4617}, {2310, 1847}, {2638, 7177}, {2968, 57792}, {3022, 278}, {3119, 273}, {3270, 279}, {3900, 13149}, {4081, 331}, {4105, 653}, {4130, 18026}, {4163, 46404}, {4524, 52607}, {6332, 52937}, {6602, 7012}, {7004, 23062}, {7046, 57538}, {7071, 23984}, {7079, 24032}, {7117, 479}, {8641, 32714}, {14936, 1119}, {23090, 4616}, {23970, 264}, {24010, 92}, {24012, 19}, {26932, 57880}, {34591, 1088}, {35072, 7056}, {35508, 4}, {39687, 7053}, {47432, 14256}, {52064, 33}, {52425, 7339}, {57055, 4569}, {57081, 4635}, {57108, 658}, {57134, 4637}, {57180, 108}, {58338, 4573}, {58340, 65296}, {61050, 608}, {65102, 934}, {65433, 15418}

X(65753) = X(2)X(216)∩X(3)X(2453)

Barycentrics    b^2*(b - c)^2*c^2*(b + c)^2*(-a^2 + b^2 + c^2)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(65753) lies on the cubic K1370 and these lines: {2, 216}, {3, 2453}, {67, 10749}, {94, 14919}, {115, 127}, {122, 2970}, {401, 14590}, {441, 24975}, {523, 3150}, {577, 40879}, {1632, 34217}, {1650, 3258}, {2072, 14356}, {2407, 3260}, {3267, 65727}, {3818, 16194}, {5664, 62598}, {7422, 44145}, {7761, 35923}, {8749, 51967}, {8754, 55069}, {10718, 18866}, {11064, 56399}, {16186, 43083}, {18023, 57799}, {18122, 41005}, {34828, 44386}, {35088, 62577}, {37987, 38393}, {40996, 53474}, {44146, 45312}, {51481, 62639}, {60502, 64923}

X(65753) = complement of X(16237)
X(65753) = complement of the isogonal conjugate of X(61216)
X(65753) = complement of the isotomic conjugate of X(15421)
X(65753) = isotomic conjugate of the polar conjugate of X(58261)
X(65753) = polar conjugate of the isogonal conjugate of X(1650)
X(65753) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 60342}, {661, 46085}, {810, 62569}, {822, 131}, {2986, 21259}, {3708, 16221}, {5504, 4369}, {14910, 8062}, {15328, 20305}, {15421, 2887}, {32708, 23998}, {36053, 30476}, {36114, 59698}, {43755, 21254}, {57829, 42327}, {61216, 10}
X(65753) = X(i)-Ceva conjugate of X(j) for these (i,j): {94, 525}, {264, 58263}, {3260, 9033}, {46106, 41079}, {51967, 523}, {57482, 52624}, {65267, 520}
X(65753) = X(i)-isoconjugate of X(j) for these (i,j): {110, 36131}, {112, 36034}, {162, 32640}, {163, 1304}, {250, 2159}, {662, 32715}, {1101, 8749}, {1576, 65263}, {2349, 57655}, {4575, 32695}, {9247, 42308}, {16080, 23995}, {18877, 24000}, {23357, 36119}, {23964, 35200}, {24037, 40351}, {24041, 40354}, {32676, 44769}
X(65753) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 1304}, {125, 32640}, {133, 23964}, {136, 32695}, {244, 36131}, {512, 40351}, {523, 8749}, {525, 14919}, {647, 74}, {1084, 32715}, {1511, 23357}, {1637, 186}, {1650, 2420}, {3005, 40354}, {3163, 250}, {3258, 112}, {4858, 65263}, {5664, 57487}, {8552, 323}, {9033, 3284}, {14401, 3}, {15526, 44769}, {18314, 16080}, {23285, 1494}, {34591, 36034}, {35441, 44715}, {36901, 16077}, {38999, 32661}, {39008, 110}, {39019, 36831}, {42306, 54057}, {46425, 2071}, {55267, 35908}, {57295, 6}, {62551, 14590}, {62569, 249}, {62576, 42308}, {62598, 648}, {62613, 47443}, {65478, 12096}, {65731, 48451}
X(65753) = crosspoint of X(i) and X(j) for these (i,j): {2, 15421}, {328, 3267}, {14592, 57482}, {41079, 46106}
X(65753) = crosssum of X(i) and X(j) for these (i,j): {6, 61209}, {18877, 32640}, {32715, 40354}, {34397, 61206}
X(65753) = trilinear pole of line {13212, 57424}
X(65753) = crossdifference of every pair of points on line {1576, 32640}
X(65753) = barycentric product X(i)*X(j) for these {i,j}: {30, 339}, {69, 58261}, {125, 3260}, {264, 1650}, {328, 3258}, {338, 11064}, {525, 41079}, {850, 9033}, {1637, 3267}, {1784, 17879}, {1990, 36793}, {2394, 52624}, {2631, 20948}, {3284, 23962}, {3708, 46234}, {5664, 14592}, {9409, 44173}, {14206, 20902}, {14208, 36035}, {14618, 41077}, {15526, 46106}, {16177, 51967}, {18557, 44427}, {20573, 47414}, {34767, 58263}, {35442, 43752}, {35912, 62431}, {52485, 58258}, {54988, 57424}, {57482, 62551}
X(65753) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 250}, {115, 8749}, {125, 74}, {264, 42308}, {265, 15395}, {338, 16080}, {339, 1494}, {402, 54057}, {512, 32715}, {523, 1304}, {525, 44769}, {647, 32640}, {656, 36034}, {661, 36131}, {850, 16077}, {868, 35908}, {1084, 40351}, {1109, 36119}, {1495, 57655}, {1562, 15291}, {1577, 65263}, {1636, 32661}, {1637, 112}, {1650, 3}, {1784, 24000}, {1990, 23964}, {2394, 34568}, {2407, 47443}, {2501, 32695}, {2631, 163}, {2632, 35200}, {2682, 44102}, {3124, 40354}, {3258, 186}, {3260, 18020}, {3269, 18877}, {3284, 23357}, {3708, 2159}, {5489, 14380}, {5664, 14590}, {6070, 52493}, {6368, 36831}, {9033, 110}, {9409, 1576}, {11064, 249}, {13212, 5663}, {14220, 64774}, {14391, 1625}, {14397, 61208}, {14398, 61206}, {14401, 2420}, {14499, 15460}, {14500, 15461}, {14581, 41937}, {14592, 39290}, {14618, 15459}, {15526, 14919}, {16177, 2071}, {16186, 14385}, {18557, 60053}, {18558, 32662}, {20902, 2349}, {20975, 40352}, {23105, 18808}, {23616, 62665}, {35442, 44715}, {35912, 57742}, {36035, 162}, {39008, 3284}, {41077, 4558}, {41079, 648}, {41997, 39377}, {41998, 39378}, {46106, 23582}, {46234, 46254}, {47414, 50}, {51258, 9139}, {51394, 47390}, {52624, 2407}, {52661, 32230}, {52743, 14591}, {55141, 7480}, {55265, 61209}, {55269, 61215}, {55276, 2442}, {57295, 5502}, {57424, 6000}, {57482, 39295}, {58261, 4}, {58263, 4240}, {58346, 23347}, {60869, 60179}, {62172, 53176}, {62551, 57487}, {65615, 32708}, {65723, 51262}, {65724, 48451}
X(65753) = {X(18312),X(62431)}-harmonic conjugate of X(52628)

X(65754) = X(2)X(523)∩X(3)X(45681)

Barycentrics    (b - c)*(b + c)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(65754) = 3 X[8371] - 2 X[53266], X[53383] + 3 X[65714], 2 X[53383] - 3 X[65723], 2 X[65714] + X[65723], 4 X[5] - X[5489], 2 X[5664] + X[58346], X[684] + 2 X[16230], 2 X[65623] + X[65717], X[22089] + 2 X[59932], 3 X[381] - 2 X[39491], 4 X[39491] - 3 X[42733], X[2394] - 3 X[3545], 2 X[57128] + X[62172], 3 X[3839] + X[63248], 3 X[5055] - 2 X[14566], 2 X[20126] - 3 X[42739], 4 X[45259] - X[53345]

X(65754) lies on the cubic K1370 and these lines: {2, 523}, {3, 45681}, {5, 5489}, {30, 5664}, {51, 520}, {114, 132}, {115, 60500}, {232, 55275}, {325, 23350}, {378, 22089}, {381, 525}, {402, 31945}, {512, 64100}, {526, 12824}, {542, 42738}, {549, 18556}, {826, 39494}, {868, 35088}, {879, 45327}, {924, 41580}, {1007, 3265}, {1116, 7927}, {1499, 44750}, {1636, 1637}, {1640, 57618}, {1650, 3258}, {1992, 9007}, {2394, 3545}, {2407, 3233}, {2452, 62350}, {2501, 45141}, {3167, 8057}, {3268, 45319}, {3815, 62384}, {3839, 63248}, {3906, 39482}, {5055, 14566}, {6033, 35909}, {6054, 14223}, {6368, 11197}, {6587, 7735}, {6644, 39201}, {7774, 33294}, {8675, 29959}, {9003, 14697}, {9148, 55121}, {9209, 47597}, {9409, 44202}, {9517, 42731}, {14356, 32112}, {14484, 43673}, {14489, 53173}, {15355, 47233}, {15928, 62307}, {20126, 42739}, {21525, 38354}, {24974, 62173}, {31174, 52720}, {34810, 35912}, {35906, 51937}, {35908, 56605}, {36207, 63464}, {36876, 58757}, {41079, 44204}, {44203, 46229}, {44438, 44705}, {44891, 47004}, {45259, 53345}, {48778, 54029}, {48779, 54028}, {59745, 62947}

X(65754) = midpoint of X(i) and X(j) for these {i,j}: {2, 65714}, {6054, 14223}
X(65754) = reflection of X(i) in X(j) for these {i,j}: {3, 45681}, {879, 45327}, {3268, 45319}, {8029, 65610}, {9409, 44202}, {11123, 34291}, {18556, 549}, {41079, 44204}, {42733, 381}, {65723, 2}
X(65754) = complement of X(53383)
X(65754) = reflection of X(65723) in the Euler line
X(65754) = tripolar centroid for these (i,j): {297, 51228}
X(65754) = X(i)-Ceva conjugate of X(j) for these (i,j): {2799, 58351}, {14356, 868}
X(65754) = X(58351)-cross conjugate of X(2799)
X(65754) = X(i)-isoconjugate of X(j) for these (i,j): {74, 36084}, {98, 36034}, {248, 65263}, {287, 36131}, {293, 1304}, {336, 32715}, {685, 35200}, {1821, 32640}, {1910, 44769}, {2159, 2966}, {2349, 2715}, {11653, 36083}, {14919, 36104}, {36036, 40352}, {36119, 43754}
X(65754) = X(i)-Dao conjugate of X(j) for these (i,j): {132, 1304}, {133, 685}, {868, 36875}, {1511, 43754}, {1650, 35912}, {2679, 40352}, {3163, 2966}, {3258, 98}, {11672, 44769}, {14401, 53173}, {35088, 1494}, {38970, 16080}, {38987, 74}, {38999, 17974}, {39000, 14919}, {39008, 287}, {39039, 65263}, {40601, 32640}, {41167, 14380}, {41172, 35910}, {55071, 14385}, {55267, 2394}, {57295, 879}, {62569, 17932}, {62595, 16077}, {62598, 290}, {62613, 57991}
X(65754) = crosspoint of X(i) and X(j) for these (i,j): {2407, 36891}, {4240, 52485}
X(65754) = crosssum of X(i) and X(j) for these (i,j): {74, 32112}, {879, 52451}, {1976, 60777}
X(65754) = crossdifference of every pair of points on line {74, 187}
X(65754) = barycentric product X(i)*X(j) for these {i,j}: {30, 2799}, {297, 9033}, {325, 1637}, {511, 41079}, {523, 51389}, {684, 46106}, {868, 2407}, {1494, 58351}, {1959, 36035}, {1990, 6333}, {2420, 62431}, {2421, 58261}, {2631, 40703}, {3260, 3569}, {5642, 62629}, {5664, 14356}, {6530, 41077}, {9409, 44132}, {11064, 16230}, {14223, 57431}, {14399, 42703}, {32112, 36789}, {35906, 62555}, {35908, 52624}, {35910, 58263}, {36891, 55267}, {41167, 60869}, {46229, 56925}
X(65754) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 2966}, {232, 1304}, {237, 32640}, {240, 65263}, {297, 16077}, {511, 44769}, {684, 14919}, {868, 2394}, {1495, 2715}, {1636, 17974}, {1637, 98}, {1650, 53173}, {1755, 36034}, {1990, 685}, {2173, 36084}, {2211, 32715}, {2407, 57991}, {2420, 57742}, {2491, 40352}, {2631, 293}, {2682, 52038}, {2799, 1494}, {3260, 43187}, {3284, 43754}, {3569, 74}, {4240, 60179}, {6530, 15459}, {6793, 60506}, {8430, 9139}, {9033, 287}, {9409, 248}, {11064, 17932}, {14206, 36036}, {14356, 39290}, {14391, 53174}, {14398, 1976}, {14401, 35912}, {14581, 32696}, {16230, 16080}, {17994, 8749}, {32112, 40384}, {34854, 32695}, {35906, 41173}, {35908, 34568}, {36035, 1821}, {36891, 55266}, {39469, 18877}, {41077, 6394}, {41079, 290}, {41167, 35910}, {41172, 14380}, {44114, 2433}, {46106, 22456}, {48453, 53691}, {51389, 99}, {51431, 60504}, {52743, 14355}, {55265, 52451}, {55267, 36875}, {57431, 14999}, {57653, 36131}, {58261, 43665}, {58263, 60869}, {58343, 2420}, {58346, 35906}, {58351, 30}, {59805, 32112}
{X(18311),X(46986)}-harmonic conjugate of X(1649)

X(65755) = X(2)X(65350)∩X(115)X(523)

Barycentrics    (b - c)^2*(b + c)^2*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(65755) = 4 X[65613] - X[65724], X[1513] - 3 X[6530]

X(65770) lies on the cubic K1370 and these lines: {2, 65350}, {4, 54808}, {30, 1990}, {39, 18121}, {115, 523}, {132, 232}, {148, 65713}, {187, 62509}, {868, 41172}, {1503, 1570}, {1637, 3258}, {2501, 3154}, {2682, 57464}, {2799, 35088}, {3269, 55219}, {6070, 12077}, {6103, 36166}, {8029, 60500}, {11648, 51980}, {14356, 34370}, {14583, 60496}, {14731, 23589}, {15526, 64919}, {17994, 38368}, {35906, 52472}, {36204, 60508}, {37350, 64915}, {41181, 51429}, {46988, 53419}

X(65755) = midpoint of X(i) and X(j) for these {i,j}: {148, 65713}, {52472, 53866}
X(65755) = reflection of X(i) in X(j) for these {i,j}: {115, 65613}, {65724, 115}
X(65755) = X(35906)-Ceva conjugate of X(1637)
X(65755) = X(i)-isoconjugate of X(j) for these (i,j): {2159, 57991}, {2349, 57742}, {2966, 36034}, {17932, 36131}, {32640, 36036}, {35200, 60179}, {36084, 44769}, {43754, 65263}
X(65755) = X(i)-Dao conjugate of X(j) for these (i,j): {133, 60179}, {2679, 32640}, {3163, 57991}, {3258, 2966}, {14401, 6394}, {38970, 16077}, {38987, 44769}, {39008, 17932}, {41167, 14919}, {55267, 1494}, {57295, 287}, {62598, 43187}
X(65755) = crosspoint of X(i) and X(j) for these (i,j): {1637, 35906}, {2799, 14356}
X(65755) = crosssum of X(i) and X(j) for these (i,j): {2715, 14355}, {35910, 44769}
X(65755) = crossdifference of every pair of points on line {5467, 14380}
X(65755) = barycentric product X(i)*X(j) for these {i,j}: {30, 868}, {115, 51389}, {511, 58261}, {1495, 62431}, {1637, 2799}, {1650, 6530}, {2394, 58351}, {3258, 14356}, {3260, 44114}, {3569, 41079}, {9033, 16230}, {9214, 51429}, {32112, 58263}, {35088, 35906}, {41172, 46106}, {56605, 57424}, {59805, 60869}
X(65755) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 57991}, {868, 1494}, {1495, 57742}, {1637, 2966}, {1650, 6394}, {1990, 60179}, {2491, 32640}, {2682, 5967}, {3569, 44769}, {6530, 42308}, {9033, 17932}, {9409, 43754}, {14398, 2715}, {16230, 16077}, {17994, 1304}, {35906, 57562}, {36035, 36036}, {41079, 43187}, {41172, 14919}, {44114, 74}, {46106, 41174}, {51389, 4590}, {51429, 36890}, {57424, 36893}, {57430, 63856}, {58260, 40352}, {58261, 290}, {58351, 2407}, {59805, 35910}
X(65755) = {X(57430),X(59805)}-harmonic conjugate of X(41181)

X(65756) = X(2)X(648)∩X(125)X(523)

Barycentrics    (b - c)^2*(b + c)^2*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4) : :

X(65756) lies on the cubic K1370 and these lines: {2, 648}, {30, 52469}, {74, 2794}, {98, 36875}, {115, 2394}, {125, 523}, {132, 35908}, {543, 36890}, {868, 16230}, {1637, 62551}, {9717, 47200}, {14120, 52475}, {17986, 36166}, {35088, 62629}, {35906, 63856}, {35910, 51389}

X(65756) = X(i)-isoconjugate of X(j) for these (i,j): {1101, 35906}, {2173, 57742}, {2420, 36084}, {9406, 57991}, {23995, 60869}, {43754, 56829}
X(65756) = X(i)-Dao conjugate of X(j) for these (i,j): {523, 35906}, {647, 35912}, {2799, 51389}, {9410, 57991}, {18314, 60869}, {35088, 2407}, {36896, 57742}, {38970, 4240}, {38987, 2420}, {41167, 3284}, {55267, 30}
X(65756) = crossdifference of every pair of points on line {2420, 9409}
X(65756) = barycentric product X(i)*X(j) for these {i,j}: {74, 62431}, {325, 12079}, {338, 35910}, {339, 35908}, {850, 32112}, {868, 1494}, {2394, 2799}, {6333, 18808}, {16230, 34767}
X(65756) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 57742}, {115, 35906}, {125, 35912}, {338, 60869}, {868, 30}, {1494, 57991}, {2394, 2966}, {2433, 2715}, {2799, 2407}, {3569, 2420}, {12079, 98}, {14380, 43754}, {16080, 60179}, {16230, 4240}, {17994, 23347}, {18808, 685}, {23350, 51263}, {32112, 110}, {34767, 17932}, {35088, 51389}, {35908, 250}, {35910, 249}, {41172, 3284}, {44114, 1495}, {51429, 5642}, {56792, 14355}, {57430, 6793}, {58260, 9407}, {62431, 3260}

X(65757) = X(5)X(523)∩X(131)X(132)

Barycentrics    b^2*(b - c)*c^2*(b + c)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(65757) lies on the cubic K1370 and these lines: {2, 14618}, {3, 46371}, {5, 523}, {115, 65732}, {131, 132}, {525, 13567}, {850, 2394}, {868, 16221}, {1637, 5664}, {2485, 3767}, {2797, 33813}, {2799, 62577}, {6334, 47236}, {6644, 62489}, {7706, 30209}, {9818, 53266}, {12228, 57136}, {18314, 34836}, {18557, 52743}, {20207, 45681}, {23285, 65612}, {30476, 52600}, {35088, 39021}, {41167, 46085}, {44452, 44814}, {52585, 63847}, {57486, 65614}, {62551, 62598}

X(65757) = midpoint of X(6334) and X(47236)
X(65757) = complement of X(15421)
X(65757) = complement of the isogonal conjugate of X(61209)
X(65757) = complement of the isotomic conjugate of X(16237)
X(65757) = isotomic conjugate of the isogonal conjugate of X(55265)
X(65757) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 3134}, {163, 10257}, {403, 21253}, {1725, 127}, {1973, 2088}, {2315, 122}, {3003, 34846}, {15329, 18589}, {16237, 2887}, {24019, 13754}, {32676, 11064}, {32678, 12358}, {36131, 6699}, {36145, 64689}, {44084, 8287}, {56829, 52010}, {61209, 10}
X(65757) = X(i)-Ceva conjugate of X(j) for these (i,j): {850, 55121}, {6528, 13754}, {14618, 41079}, {30450, 46106}
X(65757) = X(i)-isoconjugate of X(j) for these (i,j): {163, 10419}, {560, 55264}, {2159, 10420}, {4575, 40388}, {5504, 36131}, {14910, 36034}, {18877, 36114}, {32640, 36053}, {32708, 35200}, {40352, 65262}
X(65757) = X(i)-Dao conjugate of X(j) for these (i,j): {113, 32640}, {115, 10419}, {133, 32708}, {136, 40388}, {1637, 15470}, {2088, 14385}, {3003, 110}, {3163, 10420}, {3258, 14910}, {6374, 55264}, {11064, 4558}, {16178, 8749}, {34834, 44769}, {36901, 40423}, {39005, 18877}, {39008, 5504}, {39021, 74}, {56792, 40353}, {57295, 61216}, {62569, 43755}, {62598, 2986}, {62613, 18879}
X(65757) = crosspoint of X(i) and X(j) for these (i,j): {2, 16237}, {30450, 52504}
X(65757) = crosssum of X(6) and X(61216)
X(65757) = crossdifference of every pair of points on line {50, 40352}
X(65757) = barycentric product X(i)*X(j) for these {i,j}: {76, 55265}, {113, 850}, {3260, 55121}, {3580, 41079}, {5664, 57486}, {6334, 46106}, {9033, 44138}, {14618, 62569}, {36789, 65614}, {40427, 58790}, {58261, 61188}, {58263, 65715}
X(65757) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 10420}, {76, 55264}, {113, 110}, {403, 1304}, {523, 10419}, {686, 18877}, {850, 40423}, {1637, 14910}, {1725, 36034}, {1784, 36114}, {1990, 32708}, {2407, 18879}, {2501, 40388}, {3003, 32640}, {3258, 15470}, {3260, 18878}, {3580, 44769}, {6334, 14919}, {9033, 5504}, {11064, 43755}, {14206, 65262}, {15328, 39379}, {16319, 53776}, {21731, 40352}, {34104, 15329}, {36035, 36053}, {39985, 64774}, {41079, 2986}, {41512, 15395}, {44084, 32715}, {44138, 16077}, {46106, 687}, {47236, 8749}, {47405, 32661}, {52743, 52557}, {55121, 74}, {55141, 39986}, {55265, 6}, {57486, 39290}, {58261, 15328}, {58263, 15454}, {58790, 34834}, {59497, 13398}, {60342, 14385}, {62172, 38936}, {62569, 4558}, {63735, 36831}, {65614, 40384}
X(65757) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5664, 41079, 52624}, {14566, 14592, 18312}

X(65758) = X(2)X(2501)∩X(115)X(525)

Barycentrics    (b - c)*(b + c)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - a^2*b^2 + 2*b^4 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + 2*c^4) : :
X(65758) = 3 X[33228] + X[44427]

X(65758) lies on the cubic K1370 and these lines: {2, 2501}, {115, 525}, {132, 36170}, {232, 44817}, {523, 6036}, {1499, 4846}, {1637, 11064}, {2697, 3563}, {2799, 44377}, {2987, 65325}, {5664, 36891}, {6529, 23582}, {6720, 46115}, {8057, 42065}, {8781, 14223}, {10425, 14999}, {12068, 41357}, {16230, 56370}, {33228, 44427}, {34810, 35912}, {35142, 53201}, {40428, 62629}, {46981, 61446}

X(65758) = midpoint of X(16230) and X(56370)
X(65758) = X(i)-isoconjugate of X(j) for these (i,j): {163, 36875}, {230, 36034}, {1733, 32640}, {2159, 4226}, {2349, 61213}, {3564, 36131}, {8772, 44769}, {36119, 56389}, {52144, 65263}
X(65758) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 36875}, {1511, 56389}, {3163, 4226}, {3258, 230}, {39008, 3564}, {62598, 51481}
X(65758) = crossdifference of every pair of points on line {52144, 61213}
X(65758) = barycentric product X(i)*X(j) for these {i,j}: {30, 62645}, {523, 36891}, {1637, 8781}, {2987, 41079}, {3260, 35364}, {8773, 36035}, {9033, 35142}, {10425, 58261}, {11064, 60338}
X(65758) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 4226}, {523, 36875}, {1495, 61213}, {1637, 230}, {2987, 44769}, {3284, 56389}, {3563, 1304}, {9033, 3564}, {9214, 52035}, {9409, 52144}, {14398, 1692}, {32654, 32640}, {35142, 16077}, {35364, 74}, {35906, 60504}, {36035, 1733}, {36051, 36034}, {36891, 99}, {41079, 51481}, {58346, 51431}, {60338, 16080}, {61446, 51262}, {62645, 1494}

X(65759) = X(2)X(107)∩X(115)X(34212)

Barycentrics    (b - c)^2*(b + c)^2*(-a^2 + b^2 + c^2)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + a^2*c^4 + b^2*c^4 - 2*c^6)*(-a^6 - a^2*b^4 + 2*b^6 + a^4*c^2 - b^4*c^2 + a^2*c^4 - c^6) : :

X(65759) lies on the cubic K1370 and these lines: {2, 107}, {115, 34212}, {125, 23616}, {523, 15526}, {1637, 1650}, {2435, 14220}, {2799, 57606}, {3163, 51937}, {56601, 64923}, {60510, 61505}

X(65759) = X(i)-isoconjugate of X(j) for these (i,j): {2409, 36034}, {34211, 36131}
X(65759) = X(i)-Dao conjugate of X(j) for these (i,j): {647, 63856}, {3258, 2409}, {14401, 441}, {39008, 34211}, {57295, 1503}
X(65759) = barycentric product X(i)*X(j) for these {i,j}: {339, 51937}, {1637, 2419}, {1650, 6330}, {2435, 41079}, {9033, 43673}, {15526, 52485}, {58261, 64975}
X(65759) = barycentric quotient X(i)/X(j) for these {i,j}: {125, 63856}, {1637, 2409}, {1650, 441}, {2435, 44769}, {6330, 42308}, {9033, 34211}, {14398, 2445}, {34212, 1304}, {43673, 16077}, {51937, 250}, {52485, 23582}, {58261, 60516}

X(65760) = X(2)X(14221)∩X(115)X(65622)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 - c^4)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 - 4*b^4*c^4 + 2*b^2*c^6) : :

X(65760) lies on the cubic K1370 and these lines: {2, 14221}, {115, 65622}, {511, 868}, {523, 65722}, {524, 6128}, {1637, 11064}, {2407, 3260}, {2799, 36212}, {3003, 24975}, {3258, 62569}, {3291, 23589}, {5159, 47207}, {31998, 41254}, {35088, 62590}

X(65760) = midpoint of X(2407) and X(3260)
X(65760) = reflection of X(3003) in X(24975)
X(65760) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 51389}, {53266, 21253}
X(65760) = X(2)-Ceva conjugate of X(51389)
X(65760) = X(51389)-Dao conjugate of X(2)
X(65760) = barycentric product X(i)*X(j) for these {i,j}: {325, 34810}, {3260, 47049}
X(65760) = barycentric quotient X(i)/X(j) for these {i,j}: {34810, 98}, {47049, 74}, {55071, 56792}

X(65761) = X(2)X(10555)∩X(30)X(114)

Barycentrics    (2*a^2 - b^2 - c^2)*(2*a^6 - a^4*b^2 - a^2*b^4 + 2*b^6 - 3*a^4*c^2 - a^2*b^2*c^2 - 3*b^4*c^2 + 4*a^2*c^4 + 4*b^2*c^4 - 3*c^6)*(2*a^6 - 3*a^4*b^2 + 4*a^2*b^4 - 3*b^6 - a^4*c^2 - a^2*b^2*c^2 + 4*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + 2*c^6) : :

X(65761) lies on the cubic K1370 and these lines: {2, 10555}, {30, 114}, {98, 36875}, {115, 14357}, {620, 34161}, {1637, 1649}, {5181, 51457}, {5477, 51429}, {5642, 8030}, {6721, 14356}, {7664, 32458}, {31274, 40517}

X(65761) = X(36142)-isoconjugate of X(53374)
X(65761) = X(23992)-Dao conjugate of X(53374)
X(65761) = cevapoint of X(1649) and X(51429)
X(65761) = barycentric quotient X(690)/X(53374)

X(65762) = X(115)X(647)∩X(184)X(512)

Barycentrics    a^2*(b - c)*(b + c)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^4*c^2 + 2*a^2*b^2*c^2 - 2*b^4*c^2 + a^2*c^4 + b^2*c^4)*(a^6 - 2*a^4*b^2 + a^2*b^4 - a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - 2*b^2*c^4 + c^6) : :

X(65762) lies on the cubic K1370 and these lines: {2, 14618}, {30, 47230}, {112, 6753}, {115, 647}, {184, 512}, {237, 17994}, {523, 65736}, {1300, 59023}, {2485, 14910}, {2489, 3163}, {2491, 58351}, {2799, 36212}, {2986, 46040}, {3003, 55130}, {3289, 3569}, {8430, 47079}, {9213, 10419}, {15328, 43718}, {18878, 53230}

X(65762) = X(i)-isoconjugate of X(j) for these (i,j): {293, 16237}, {336, 61209}, {662, 52451}, {1725, 2966}, {1821, 15329}, {1910, 61188}, {2315, 22456}, {3003, 36036}, {3580, 36084}, {36104, 62338}
X(65762) = X(i)-Dao conjugate of X(j) for these (i,j): {132, 16237}, {1084, 52451}, {2679, 3003}, {11672, 61188}, {38970, 44138}, {38987, 3580}, {39000, 62338}, {40601, 15329}, {41167, 6334}, {55071, 34834}
X(65762) = crosssum of X(35912) and X(60777)
X(65762) = trilinear pole of line {39469, 44114}
X(65762) = crossdifference of every pair of points on line {3580, 15329}
X(65762) = barycentric product X(i)*X(j) for these {i,j}: {232, 15421}, {297, 61216}, {511, 15328}, {684, 1300}, {687, 41172}, {868, 10420}, {2491, 40832}, {2799, 14910}, {2986, 3569}, {5504, 16230}, {14356, 15470}, {15454, 32112}, {17994, 57829}, {18878, 44114}, {23350, 51456}, {35910, 65615}, {39469, 65267}
X(65762) = barycentric quotient X(i)/X(j) for these {i,j}: {232, 16237}, {237, 15329}, {511, 61188}, {512, 52451}, {684, 62338}, {687, 41174}, {1300, 22456}, {2211, 61209}, {2491, 3003}, {2986, 43187}, {3569, 3580}, {5504, 17932}, {10420, 57991}, {14910, 2966}, {15328, 290}, {15421, 57799}, {16230, 44138}, {17994, 403}, {32112, 65715}, {32708, 60179}, {35361, 53245}, {36053, 36036}, {39469, 13754}, {41172, 6334}, {44114, 55121}, {58260, 21731}, {61216, 287}, {65267, 65272}, {65615, 60869}

X(65763) = X(115)X(65610)∩X(690)X(7687)

Barycentrics    (b - c)*(b + c)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(a^8 - a^6*b^2 + a^4*b^4 - 3*a^2*b^6 + 2*b^8 - a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 5*b^6*c^2 + a^4*c^4 + 3*a^2*b^2*c^4 + 6*b^4*c^4 - 3*a^2*c^6 - 5*b^2*c^6 + 2*c^8) : :

X(65763) lies on the cubic K1370 and these lines: {115, 65610}, {690, 7687}, {868, 16230}, {1637, 35906}, {2799, 14356}, {3163, 62172}, {10278, 65731}, {22104, 44564}, {34840, 34841}, {38393, 55121}, {56967, 62651}

X(65763) = midpoint of X(868) and X(16230)
X(65763) = crosspoint of X(4240) and X(6530)
X(65763) = crosssum of X(14380) and X(17974)
X(65763) = barycentric product X(2799)*X(52472)
X(65763) = barycentric quotient X(52472)/X(2966)

X(65764) = X(2)X(14221)∩X(30)X(2088)

Barycentrics    (b - c)^2*(b + c)^2*(a^4*b^4 - 2*a^2*b^6 + b^8 + 2*a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 2*b^6*c^2 - 4*a^4*c^4 - a^2*b^2*c^4 + b^4*c^4 + 2*a^2*c^6)*(2*a^6*b^2 - 4*a^4*b^4 + 2*a^2*b^6 - a^4*b^2*c^2 - a^2*b^4*c^2 + a^4*c^4 + 3*a^2*b^2*c^4 + b^4*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :

X(65764) lies on the cubic K1370 and these lines: {2, 14221}, {30, 2088}, {115, 65610}, {523, 65733}, {1648, 3258}, {3163, 21906}, {14113, 61733}, {35088, 39021}, {35235, 47236}, {44114, 55122}

X(65764) = barycentric quotient X(i)/X(j) for these {i,j}: {8029, 53266}, {44114, 47049}

X(65765) = X(2)X(65613)∩X(115)X(65734)

Barycentrics    (2*a^8 - 3*a^6*b^2 + 3*a^4*b^4 - 5*a^2*b^6 + 3*b^8 - a^6*c^2 + a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 5*b^6*c^2 - 2*a^4*c^4 + a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + 2*c^8)*(2*a^8 - a^6*b^2 - 2*a^4*b^4 - a^2*b^6 + 2*b^8 - 3*a^6*c^2 + a^4*b^2*c^2 + a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 + 5*a^2*b^2*c^4 + 3*b^4*c^4 - 5*a^2*c^6 - 5*b^2*c^6 + 3*c^8) : :
X(65765) = 3 X[44576] + X[51228]

X(65765) lies on the cubic K1370 and these lines: {2, 65613}, {115, 65734}, {132, 468}, {524, 3163}, {868, 1503}, {1637, 47296}, {1990, 62551}, {2799, 44334}, {3266, 36789}, {41995, 52039}, {41996, 52040}, {44576, 51228}, {50942, 55267}

X(65765) = midpoint of X(1990) and X(62551)
X(65765) = X(6793)-cross conjugate of X(4)
X(65765) = X(163)-isoconjugate of X(53383)
X(65765) = X(115)-Dao conjugate of X(53383)
X(65765) = cevapoint of X(i) and X(j) for these (i,j): {868, 1637}, {3569, 16186}, {10151, 16318}
X(65765) = trilinear pole of line {690, 13202}
X(65765) = barycentric quotient X(523)/X(53383)

X(65766) = X(30)X(6334)∩X(131)X(132)

Barycentrics    (b - c)*(b + c)*(2*a^8 - 5*a^6*b^2 + 6*a^4*b^4 - 5*a^2*b^6 + 2*b^8 - 3*a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 + b^4*c^4 - a^2*c^6 - b^2*c^6 + c^8)*(2*a^8 - 3*a^6*b^2 + a^4*b^4 - a^2*b^6 + b^8 - 5*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + 6*a^4*c^4 + 3*a^2*b^2*c^4 + b^4*c^4 - 5*a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :

X(65766) lies on the cubisc K1370 and K1371 and these lines: {30, 6334}, {115, 65723}, {131, 132}, {523, 65722}, {690, 16163}, {1637, 60340}, {2799, 40080}, {3163, 9475}, {3258, 14417}, {6394, 62645}, {8779, 52038}, {9033, 53132}, {11123, 65717}, {14559, 53274}

X(65766) = reflection of X(1637) in X(60340)
X(65766) = on the Euler-line-asymptotic hyperbola (see X(1650))
X(65766) = X(36034)-isoconjugate of X(52472)
X(65766) = X(i)-Dao conjugate of X(j) for these (i,j): {3258, 52472}, {65728, 1550}
X(65766) = cevapoint of X(41172) and X(65709)
X(65766) = trilinear pole of line {1648, 14401}
X(65766) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 52472}, {1640, 1550}

X(65767) = X(2)X(99)∩X(30)X(74)

Barycentrics    a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 - 4*b^4*c^4 + 2*b^2*c^6 : :
X(65767) = 3 X[110] - 4 X[51430], 3 X[1316] - 2 X[51430], 3 X[5622] - 2 X[6795], 4 X[11007] - 5 X[15059], 3 X[15035] - 4 X[36177]

X(65767) lies on the cubic K1371 and these lines: {2, 99}, {6, 41625}, {30, 74}, {50, 53474}, {94, 23588}, {98, 4226}, {110, 1316}, {112, 60502}, {125, 23698}, {146, 1561}, {182, 30540}, {187, 35933}, {193, 64923}, {248, 290}, {251, 18372}, {287, 2395}, {323, 538}, {328, 14910}, {338, 4558}, {458, 31859}, {523, 895}, {542, 51431}, {754, 37779}, {868, 6321}, {1272, 6128}, {1494, 62639}, {1632, 25051}, {1916, 39291}, {1975, 41238}, {1976, 46648}, {1989, 24975}, {1993, 22146}, {1995, 9775}, {2394, 2986}, {2407, 48540}, {2453, 2854}, {2592, 44333}, {2593, 44332}, {2794, 3448}, {3849, 44555}, {3972, 40814}, {4590, 18023}, {5012, 39906}, {5063, 44135}, {5191, 12188}, {5622, 6795}, {5640, 35930}, {5986, 9157}, {6033, 57598}, {6248, 37335}, {7391, 44988}, {7668, 14060}, {7737, 37644}, {7739, 63036}, {7798, 11004}, {7804, 15018}, {7998, 64653}, {8288, 37638}, {8724, 57618}, {8749, 16237}, {9142, 53274}, {9146, 15066}, {9148, 53247}, {9155, 13188}, {9609, 15271}, {10723, 31127}, {10752, 60696}, {10796, 15019}, {11007, 15059}, {11174, 41231}, {11579, 62490}, {11632, 45662}, {11657, 14834}, {12066, 16080}, {12177, 46124}, {13172, 35922}, {14033, 63084}, {14389, 15048}, {14559, 48988}, {14712, 44651}, {14918, 40889}, {14999, 48721}, {15014, 46106}, {15035, 36177}, {15093, 55038}, {15988, 17351}, {16280, 17702}, {16770, 22513}, {16771, 22512}, {20021, 38873}, {22151, 64782}, {23061, 32515}, {23235, 46512}, {25155, 60858}, {25165, 60859}, {30465, 40709}, {30468, 40710}, {32121, 55122}, {32456, 35296}, {34834, 44468}, {35278, 38664}, {35345, 49006}, {36189, 46634}, {36212, 46571}, {36822, 46303}, {37183, 58849}, {37784, 64781}, {40112, 52229}, {40870, 40871}, {40884, 47286}, {41253, 41676}, {41626, 58267}, {43705, 44377}, {43756, 65326}, {44328, 60516}, {46718, 54104}, {54651, 58268}, {62950, 62988}

X(65767) = midpoint of X(3448) and X(36181)
X(65767) = reflection of X(i) in X(j) for these {i,j}: {110, 1316}, {146, 1561}, {323, 51372}, {10752, 60696}, {14999, 48721}, {36163, 125}
X(65767) = anticomplement of X(51389)
X(i)-anticomplementary conjugate of X(j) for these (i,j): {1910, 146}, {2159, 147}, {36034, 62642}
X(65767) = X(i)-Dao conjugate of X(j) for these (i,j): {34810, 230}, {47049, 3003}
X(65767) = crosspoint of X(i) and X(j) for these (i,j): {290, 40832}, {1494, 8781}, {2966, 39295}, {16077, 41174}
X(65767) = crosssum of X(i) and X(j) for these (i,j): {1495, 1692}, {2088, 3569}
X(65767) = trilinear pole of line {34810, 47049}
X(65767) = crossdifference of every pair of points on line {351, 51335}
X(65767) = barycentric product X(i)*X(j) for these {i,j}: {99, 53266}, {290, 47049}, {1494, 34810}
X(65767) = barycentric quotient X(i)/X(j) for these {i,j}: {34810, 30}, {47049, 511}, {53266, 523}
X(65767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 99, 54439}, {2, 148, 54395}, {99, 671, 48982}, {99, 41254, 2}, {115, 65722, 2}, {265, 53132, 9140}, {671, 50941, 111}, {4226, 53346, 98}, {11078, 11092, 9140}, {24975, 53495, 1989}, {40854, 40855, 110}

X(65768) = X(30)X(340)∩X(99)X(523)

Barycentrics    (a - b)*(a + b)*(a - c)*(a + c)*(a^8 - a^6*b^2 + a^4*b^4 - 3*a^2*b^6 + 2*b^8 - a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 5*b^6*c^2 + a^4*c^4 + 3*a^2*b^2*c^4 + 6*b^4*c^4 - 3*a^2*c^6 - 5*b^2*c^6 + 2*c^8) : :
X(65768) = 2 X[1990] - 3 X[35297], 3 X[6530] - 4 X[10011], 5 X[14061] - 4 X[65613]

X(65768) lies on the cubic K1371 and these lines: {2, 65350}, {30, 340}, {99, 523}, {148, 65724}, {316, 62509}, {476, 3268}, {648, 64919}, {685, 877}, {687, 15421}, {1297, 5999}, {1503, 51438}, {1990, 35297}, {2799, 2966}, {6530, 10011}, {6563, 7471}, {7769, 18121}, {8598, 64915}, {10411, 14560}, {10754, 34369}, {14061, 65613}, {14480, 41298}, {14587, 18831}, {17932, 53379}, {36173, 65711}

X(65768) = reflection of X(i) in X(j) for these {i,j}: {148, 65724}, {10754, 34369}, {65713, 99}
X(65768) = X(36034)-anticomplementary conjugate of X(39359)
X(65768) = barycentric product X(i)*X(j) for these {i,j}: {1550, 6035}, {52473, 65354}
X(65768) = barycentric quotient X(i)/X(j) for these {i,j}: {1550, 1640}, {52472, 1637}
X(65768) = {X(99),X(14221)}-harmonic conjugate of X(4590)

X(65769) = X(2)X(10555)∩X(30)X(98)

Barycentrics    (a^2 + b^2 - 2*c^2)*(a^2 - 2*b^2 + c^2)*(2*a^10 - 5*a^8*b^2 + 7*a^6*b^4 - 5*a^4*b^6 + 3*a^2*b^8 - 2*b^10 - 5*a^8*c^2 + 4*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 3*b^8*c^2 + 7*a^6*c^4 - 2*a^4*b^2*c^4 - 2*a^2*b^4*c^4 - b^6*c^4 - 5*a^4*c^6 - b^4*c^6 + 3*a^2*c^8 + 3*b^2*c^8 - 2*c^10) : :

X(65769) lies on the cubic K1371 and these lines: {2, 10555}, {30, 98}, {99, 59422}, {114, 9214}, {115, 59423}, {147, 52035}, {476, 10416}, {892, 54103}, {895, 39819}, {3268, 5466}, {5968, 64089}, {6054, 51926}, {10556, 47200}, {10557, 52141}, {16237, 17983}, {31125, 36849}, {31127, 42008}, {44534, 64258}, {52632, 57799}

X(65770) = X(2)X(476)∩X(3)X(523)

Barycentrics    2*a^12 - 5*a^10*b^2 + 6*a^8*b^4 - 8*a^6*b^6 + 8*a^4*b^8 - 3*a^2*b^10 - 5*a^10*c^2 + 6*a^8*b^2*c^2 + a^6*b^4*c^2 - 5*a^4*b^6*c^2 + 2*a^2*b^8*c^2 + b^10*c^2 + 6*a^8*c^4 + a^6*b^2*c^4 - 2*a^4*b^4*c^4 + a^2*b^6*c^4 - 4*b^8*c^4 - 8*a^6*c^6 - 5*a^4*b^2*c^6 + a^2*b^4*c^6 + 6*b^6*c^6 + 8*a^4*c^8 + 2*a^2*b^2*c^8 - 4*b^4*c^8 - 3*a^2*c^10 + b^2*c^10 : :
X(65770) = 3 X[3] - X[34810], 2 X[34810] - 3 X[52772], 3 X[376] + X[36875], 3 X[3524] - X[9214], X[10754] - 3 X[65616], 4 X[20304] - 3 X[65617]

X(65770) lies on the cubic K1371 and these lines: {2, 476}, {3, 523}, {4, 14884}, {20, 14508}, {30, 53274}, {69, 74}, {127, 131}, {186, 16237}, {511, 4226}, {549, 14995}, {631, 30717}, {1138, 3524}, {1316, 14687}, {1511, 14559}, {1553, 52488}, {2799, 40080}, {3018, 21843}, {3164, 10298}, {3233, 9717}, {3431, 54959}, {4240, 47215}, {6194, 7492}, {7422, 62490}, {7471, 33927}, {7473, 35908}, {7493, 47200}, {7502, 8266}, {9168, 63767}, {9970, 35278}, {10754, 65616}, {14694, 47170}, {15928, 47285}, {16186, 30512}, {20304, 65617}, {30737, 52145}, {35912, 53383}, {36177, 46127}, {47047, 47079}, {47150, 54380}, {47327, 57627}, {47570, 57607}, {51254, 56686}, {53793, 57612}, {57603, 62509}, {61446, 62645}

X(65770) = reflection of X(i) in X(j) for these {i,j}: {14559, 1511}, {14995, 549}, {52472, 14356}, {52772, 3}
X(65770) = complement of X(52472)
X(65770) = anticomplement of X(14356)
X(65770) = reflection of X(52772) in the Euler line
X(65770) = anticomplement of the isogonal conjugate of X(14355)
X(65770) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {98, 63642}, {293, 3153}, {1910, 37779}, {2624, 39359}, {6149, 147}, {14355, 8}, {36084, 526}, {36104, 41079}, {60777, 21221}
X(65770) = X(53866)-Ceva conjugate of X(542)
X(65770) = crosspoint of X(290) and X(40427)
X(65770) = crossdifference of every pair of points on line {3003, 14398}
X(65770) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 52472, 14356}, {3, 46632, 47050}, {46632, 47050, 59291}, {51898, 51899, 18331}

X(65771) = X(20)X(99)∩X(69)X(523)

Barycentrics    2*a^12 - 5*a^10*b^2 + 6*a^8*b^4 - 6*a^6*b^6 + 2*a^4*b^8 + 3*a^2*b^10 - 2*b^12 - 5*a^10*c^2 + 6*a^8*b^2*c^2 - a^6*b^4*c^2 - a^4*b^6*c^2 - 2*a^2*b^8*c^2 + 3*b^10*c^2 + 6*a^8*c^4 - a^6*b^2*c^4 + 2*a^4*b^4*c^4 - a^2*b^6*c^4 - 6*b^8*c^4 - 6*a^6*c^6 - a^4*b^2*c^6 - a^2*b^4*c^6 + 10*b^6*c^6 + 2*a^4*c^8 - 2*a^2*b^2*c^8 - 6*b^4*c^8 + 3*a^2*c^10 + 3*b^2*c^10 - 2*c^12 : :

X(65771) lies on the cubic K1371 and these lines: {2, 2966}, {20, 99}, {30, 36890}, {69, 523}, {316, 57611}, {325, 4226}, {340, 16237}, {2857, 55972}, {6036, 53783}, {6103, 37667}, {6394, 30789}, {9473, 15589}, {11160, 40867}, {32815, 34193}, {36822, 63768}

X(65771) = anticomplement of X(35906)
X(65771) = anticomplement of the isogonal conjugate of X(35910)
X(65771) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1755, 39358}, {1959, 146}, {2159, 385}, {2349, 511}, {3405, 25045}, {23997, 63248}, {32112, 21221}, {33805, 14957}, {35200, 401}, {35908, 5905}, {35910, 8}, {36034, 2799}, {36119, 51481}, {65263, 53345}
X(65771) = crosspoint of X(1494) and X(40428)
X(65771) = crosssum of X(1495) and X(51335)

X(65772) = X(2)X(2501)∩X(30)X(6334)

Barycentrics    (b - c)*(b + c)*(2*a^12 - 9*a^10*b^2 + 16*a^8*b^4 - 16*a^6*b^6 + 12*a^4*b^8 - 7*a^2*b^10 + 2*b^12 - 9*a^10*c^2 + 18*a^8*b^2*c^2 - 15*a^6*b^4*c^2 + 5*a^4*b^6*c^2 + 4*a^2*b^8*c^2 - 3*b^10*c^2 + 16*a^8*c^4 - 15*a^6*b^2*c^4 + 2*a^4*b^4*c^4 - a^2*b^6*c^4 + 2*b^8*c^4 - 16*a^6*c^6 + 5*a^4*b^2*c^6 - a^2*b^4*c^6 - 2*b^6*c^6 + 12*a^4*c^8 + 4*a^2*b^2*c^8 + 2*b^4*c^8 - 7*a^2*c^10 - 3*b^2*c^10 + 2*c^12) : :
X(65772) = 3 X[35297] - X[44427]

X(65772) lies on the cubic K1371 and these lines: {2, 2501}, {30, 6334}, {99, 249}, {114, 523}, {127, 38970}, {230, 2799}, {1297, 36166}, {1499, 18556}, {1550, 36875}, {3268, 3580}, {3566, 38749}, {7471, 47627}, {10011, 16230}, {14223, 60073}, {35297, 44427}

X(65772) = reflection of X(16230) in X(10011)
X(65772) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {36034, 325}, {36131, 3564}, {36875, 21294}
X(65772) = crosspoint of X(i) and X(j) for these (i,j): {1494, 55266}, {16077, 57553}
X(65772) = crossdifference of every pair of points on line {44114, 52144}

X(65773) = X(2)X(648)∩X(110)X(476)

Barycentrics    (a - b)*(a + b)*(a - c)*(a + c)*(2*a^12 - 3*a^10*b^2 - a^8*b^4 + 3*a^6*b^6 - 3*a^4*b^8 + 4*a^2*b^10 - 2*b^12 - 3*a^10*c^2 + 8*a^8*b^2*c^2 - 4*a^6*b^4*c^2 + 2*a^4*b^6*c^2 - 9*a^2*b^8*c^2 + 6*b^10*c^2 - a^8*c^4 - 4*a^6*b^2*c^4 + 2*a^4*b^4*c^4 + 5*a^2*b^6*c^4 - 6*b^8*c^4 + 3*a^6*c^6 + 2*a^4*b^2*c^6 + 5*a^2*b^4*c^6 + 4*b^6*c^6 - 3*a^4*c^8 - 9*a^2*b^2*c^8 - 6*b^4*c^8 + 4*a^2*c^10 + 6*b^2*c^10 - 2*c^12) : :

X(65773) lies on the cubic K1371 and these lines: {2, 648}, {99, 63248}, {110, 476}, {146, 2794}, {147, 52035}, {385, 46787}, {2407, 3268}, {2799, 34211}, {12228, 36177}, {14566, 41392}, {15421, 41676}, {23588, 39290}, {32661, 63249}

X(65773) = crosspoint of X(2966) and X(39290)
X(65773) = crosssum of X(3569) and X(52743)
X(65773) = crossdifference of every pair of points on line {2088, 9409}

X(65774) = X(2)X(65613)∩X(287)X(524)

Barycentrics    4*a^16 - 12*a^14*b^2 + 15*a^12*b^4 - 19*a^10*b^6 + 28*a^8*b^8 - 26*a^6*b^10 + 15*a^4*b^12 - 7*a^2*b^14 + 2*b^16 - 12*a^14*c^2 + 26*a^12*b^2*c^2 - 13*a^10*b^4*c^2 - a^8*b^6*c^2 + 2*a^6*b^8*c^2 - 8*a^4*b^10*c^2 + 7*a^2*b^12*c^2 - b^14*c^2 + 15*a^12*c^4 - 13*a^10*b^2*c^4 - 18*a^8*b^4*c^4 + 20*a^6*b^6*c^4 - 3*a^4*b^8*c^4 + 9*a^2*b^10*c^4 - 10*b^12*c^4 - 19*a^10*c^6 - a^8*b^2*c^6 + 20*a^6*b^4*c^6 - 8*a^4*b^6*c^6 - 9*a^2*b^8*c^6 + 17*b^10*c^6 + 28*a^8*c^8 + 2*a^6*b^2*c^8 - 3*a^4*b^4*c^8 - 9*a^2*b^6*c^8 - 16*b^8*c^8 - 26*a^6*c^10 - 8*a^4*b^2*c^10 + 9*a^2*b^4*c^10 + 17*b^6*c^10 + 15*a^4*c^12 + 7*a^2*b^2*c^12 - 10*b^4*c^12 - 7*a^2*c^14 - b^2*c^14 + 2*c^16 : :
X(65774) = 3 X[44578] - X[51228]

X(65774) lies on the cubic K1371 and these lines: {2, 65613}, {99, 65719}, {287, 524}, {441, 2799}, {476, 858}, {523, 65722}, {1503, 4226}, {1990, 16237}, {3268, 11064}, {15421, 54075}, {44436, 46425}, {44578, 51228}, {45331, 64915}, {65622, 65734}

X(65774) = reflection of X(1990) in X(24975)
X(65774) = X(53383)-anticomplementary conjugate of X(21294)

X(65775) = X(30)X(44427)∩X(99)X(65714)

Barycentrics    (b - c)*(b + c)*(2*a^16 - 7*a^14*b^2 + 12*a^12*b^4 - 15*a^10*b^6 + 12*a^8*b^8 - 5*a^6*b^10 + 4*a^4*b^12 - 5*a^2*b^14 + 2*b^16 - 7*a^14*c^2 + 20*a^12*b^2*c^2 - 23*a^10*b^4*c^2 + 17*a^8*b^6*c^2 - 13*a^6*b^8*c^2 + 2*a^4*b^10*c^2 + 11*a^2*b^12*c^2 - 7*b^14*c^2 + 12*a^12*c^4 - 23*a^10*b^2*c^4 + 16*a^8*b^4*c^4 - a^6*b^6*c^4 - 9*a^4*b^8*c^4 - 8*a^2*b^10*c^4 + 13*b^12*c^4 - 15*a^10*c^6 + 17*a^8*b^2*c^6 - a^6*b^4*c^6 + 14*a^4*b^6*c^6 + 2*a^2*b^8*c^6 - 21*b^10*c^6 + 12*a^8*c^8 - 13*a^6*b^2*c^8 - 9*a^4*b^4*c^8 + 2*a^2*b^6*c^8 + 26*b^8*c^8 - 5*a^6*c^10 + 2*a^4*b^2*c^10 - 8*a^2*b^4*c^10 - 21*b^6*c^10 + 4*a^4*c^12 + 11*a^2*b^2*c^12 + 13*b^4*c^12 - 5*a^2*c^14 - 7*b^2*c^14 + 2*c^16) : :

X(65775) lies on the cubic K1371 and these lines: {30, 44427}, {99, 65714}, {476, 2966}, {523, 54395}, {690, 10723}, {1297, 1300}, {1494, 18808}, {2799, 34174}, {4226, 16230}, {62663, 65720}

X(65775) = reflection of X(4226) in X(16230)

X(65776) = X(2)X(98)∩X(250)X(523)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(65776) lies on the cubic K1372 and these lines: {2, 98}, {30, 51228}, {99, 6035}, {250, 523}, {1302, 2715}, {1494, 51262}, {1637, 4240}, {2395, 60504}, {2407, 9033}, {2799, 4226}, {3014, 31636}, {3018, 6531}, {3163, 9214}, {4230, 53265}, {5502, 11176}, {6037, 11636}, {6394, 35520}, {7471, 52076}, {9211, 43187}, {14220, 30528}, {14559, 15395}, {22456, 58994}, {34810, 51430}, {36084, 38340}, {41173, 52035}, {51389, 65759}, {51431, 52472}, {53383, 65773}, {53701, 58948}, {58978, 59098}

X(65776) = reflection of X(i) in X(j) for these {i,j}: {287, 5967}, {9214, 3163}
X(65776) = isogonal conjugate of X(32112)
X(65776) = antitomic image of X(9214)
X(65776) = X(65754)-cross conjugate of X(30)
X(65776) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32112}, {163, 65756}, {240, 14380}, {656, 35908}, {661, 35910}, {684, 36119}, {868, 36034}, {1755, 2394}, {1959, 2433}, {2159, 2799}, {2349, 3569}, {2491, 33805}, {12079, 23997}, {16230, 35200}, {34767, 57653}, {41172, 65263}
X(65776) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 32112}, {30, 65754}, {115, 65756}, {133, 16230}, {1511, 684}, {3163, 2799}, {3258, 868}, {36830, 35910}, {36899, 2394}, {39085, 14380}, {40596, 35908}, {62562, 12079}, {62569, 6333}, {62598, 62431}, {62613, 325}, {65760, 62555}
X(65776) = cevapoint of X(i) and X(j) for these (i,j): {30, 65754}, {1637, 51431}
X(65776) = trilinear pole of line {30, 2420}
X(65776) = crossdifference of every pair of points on line {3569, 41172}
X(65776) = barycentric product X(i)*X(j) for these {i,j}: {30, 2966}, {98, 2407}, {99, 35906}, {110, 60869}, {287, 4240}, {290, 2420}, {293, 24001}, {336, 56829}, {648, 35912}, {685, 11064}, {1495, 43187}, {1637, 57991}, {1990, 17932}, {2173, 36036}, {2715, 3260}, {3284, 22456}, {6037, 51372}, {9033, 60179}, {9409, 41174}, {14206, 36084}, {14999, 53866}, {23347, 57799}, {34761, 51228}, {36891, 60504}, {39291, 51430}, {41079, 57742}, {41173, 51389}, {43754, 46106}, {46786, 51263}, {51431, 55266}, {57562, 65754}
X(65776) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 32112}, {30, 2799}, {98, 2394}, {110, 35910}, {112, 35908}, {248, 14380}, {287, 34767}, {523, 65756}, {685, 16080}, {1495, 3569}, {1637, 868}, {1976, 2433}, {1990, 16230}, {2395, 12079}, {2407, 325}, {2420, 511}, {2715, 74}, {2966, 1494}, {3081, 58351}, {3163, 65754}, {3233, 51389}, {3284, 684}, {4240, 297}, {6531, 18808}, {9214, 62629}, {9407, 2491}, {9409, 41172}, {11064, 6333}, {14398, 44114}, {14581, 17994}, {17974, 62665}, {23347, 232}, {24001, 40703}, {32696, 8749}, {34761, 51227}, {35906, 523}, {35912, 525}, {36036, 33805}, {36084, 2349}, {36104, 36119}, {41079, 62431}, {41392, 14356}, {42716, 42703}, {43754, 14919}, {48453, 23350}, {51228, 34765}, {51263, 46787}, {51389, 62555}, {51431, 55267}, {52451, 65614}, {52951, 33752}, {53866, 14223}, {56829, 240}, {57742, 44769}, {58346, 65755}, {60179, 16077}, {60504, 36875}, {60506, 63856}, {60777, 56792}, {60869, 850}, {65754, 35088}
X(65776) = {X(1976),X(5967)}-harmonic conjugate of X(65616)

X(65777) = X(2)X(9141)∩X(30)X(2420)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)^2*(a^4 - a^2*b^2 - b^2*c^2 + c^4) : :

X(65777) lies on the cubic K1372 and these lines: {2, 9141}, {30, 2420}, {98, 54527}, {230, 54380}, {287, 46808}, {476, 2395}, {523, 60505}, {1637, 4240}, {1692, 65764}, {2394, 2966}, {2799, 34211}, {3233, 14401}, {5967, 11657}, {10313, 14966}, {14910, 57260}

X(65777) = X(60179)-Ceva conjugate of X(35912)
X(65777) = X(58351)-cross conjugate of X(3163)
X(65777) = X(i)-isoconjugate of X(j) for these (i,j): {2349, 32112}, {36034, 65756}
X(65777) = X(i)-Dao conjugate of X(j) for these (i,j): {30, 2799}, {3258, 65756}
X(65777) = cevapoint of X(3163) and X(58351)
X(65777) = crosssum of X(3569) and X(32112)
X(65777) = trilinear pole of line {3163, 58348}
X(65777) = barycentric product X(i)*X(j) for these {i,j}: {98, 3233}, {685, 16163}, {1099, 36084}, {2407, 35906}, {2420, 60869}, {2715, 36789}, {2966, 3163}, {4240, 35912}, {9408, 43187}, {14401, 60179}, {16240, 17932}, {34334, 43754}, {36036, 42074}, {53866, 64607}, {57562, 58351}, {57742, 58263}, {57991, 58346}
X(65777) = barycentric quotient X(i)/X(j) for these {i,j}: {1495, 32112}, {1637, 65756}, {2420, 35910}, {2715, 40384}, {2966, 31621}, {3081, 65754}, {3163, 2799}, {3233, 325}, {9408, 3569}, {16163, 6333}, {16240, 16230}, {23347, 35908}, {35906, 2394}, {35912, 34767}, {36435, 58351}, {58263, 62431}, {58343, 41167}, {58344, 44114}, {58346, 868}, {58349, 51429}, {58351, 35088}

X(65778) = X(2)X(647)∩X(30)X(9409)

Barycentrics    b^2*(b - c)*c^2*(b + c)*(-a^2 + b^2 + c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :

X(65778) lies on the cubic K1372 and these lines: {2, 647}, {30, 9409}, {98, 2697}, {112, 2966}, {148, 15351}, {287, 65325}, {290, 53201}, {339, 525}, {520, 53174}, {523, 2967}, {879, 4846}, {1636, 11064}, {1637, 46106}, {2799, 30737}, {3267, 35911}, {7480, 47004}, {12042, 39201}, {12384, 52076}, {18314, 46115}, {18558, 57482}, {18850, 64788}, {23105, 53783}, {28438, 52613}, {35906, 65757}, {36893, 63247}, {47256, 65729}, {52472, 52485}

X(65778) = X(i)-isoconjugate of X(j) for these (i,j): {163, 35908}, {232, 36034}, {237, 65263}, {240, 32640}, {511, 36131}, {1304, 1755}, {1959, 32715}, {2159, 4230}, {8749, 23997}, {9417, 16077}, {14966, 36119}, {32676, 35910}, {35200, 58070}, {40352, 62720}, {44769, 57653}
X(65778) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 35908}, {133, 58070}, {647, 32112}, {1511, 14966}, {3163, 4230}, {3258, 232}, {14401, 684}, {15526, 35910}, {36899, 1304}, {38999, 3289}, {39008, 511}, {39058, 16077}, {39085, 32640}, {57295, 3569}, {62562, 8749}, {62569, 2421}, {62598, 297}, {65757, 2799}
X(65778) = trilinear pole of line {9033, 65753}
X(65778) = barycentric product X(i)*X(j) for these {i,j}: {287, 41079}, {290, 9033}, {336, 36035}, {525, 60869}, {850, 35912}, {879, 3260}, {1636, 60199}, {1637, 57799}, {1650, 22456}, {2631, 46273}, {2966, 65753}, {3267, 35906}, {9409, 18024}, {11064, 43665}, {16081, 41077}, {17932, 58261}, {46106, 53173}
X(65778) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 4230}, {98, 1304}, {125, 32112}, {248, 32640}, {287, 44769}, {290, 16077}, {293, 36034}, {523, 35908}, {525, 35910}, {878, 40352}, {879, 74}, {1636, 3289}, {1637, 232}, {1650, 684}, {1821, 65263}, {1910, 36131}, {1976, 32715}, {1990, 58070}, {2395, 8749}, {2422, 40354}, {2631, 1755}, {3260, 877}, {3284, 14966}, {6531, 32695}, {9033, 511}, {9409, 237}, {11064, 2421}, {14206, 62720}, {14398, 2211}, {14581, 34859}, {16081, 15459}, {22456, 42308}, {35906, 112}, {35912, 110}, {36035, 240}, {41077, 36212}, {41079, 297}, {43665, 16080}, {51404, 2433}, {52624, 51389}, {53173, 14919}, {53174, 36831}, {58261, 16230}, {60869, 648}, {65753, 2799}, {65754, 2967}, {65758, 57493}
X(65778) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16083, 37858, 46786}, {43665, 52145, 18312}

X(65779) = X(2)X(35909)∩X(74)X(98)

Barycentrics    (b - c)*(b + c)*(-a^2 + b^2 - b*c + c^2)*(-a^2 + b^2 + b*c + c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(65779) = 3 X[9979] - X[65775], 3 X[1637] - 2 X[65763]

X(65779) lies on the cubic K1372 and these lines: {2, 35909}, {30, 9409}, {74, 98}, {186, 14270}, {230, 3569}, {248, 2395}, {476, 2966}, {523, 5191}, {526, 53132}, {868, 6130}, {1511, 5664}, {1637, 35906}, {2407, 9033}, {2409, 16230}, {2411, 14355}, {2799, 40080}, {3268, 60340}, {4226, 53345}, {5967, 9003}, {9185, 58349}, {9517, 57603}, {11081, 23283}, {11086, 23284}, {12042, 65723}, {15469, 35912}, {18316, 43665}, {21525, 53263}, {34156, 59291}, {39176, 62172}, {46608, 51869}, {51430, 65754}, {52763, 60869}, {53783, 62438}

X(65779) = midpoint of X(4226) and X(53345)
X(65779) = reflection of X(i) in X(j) for these {i,j}: {868, 6130}, {3268, 60340}
X(65779) = X(i)-Ceva conjugate of X(j) for these (i,j): {685, 14355}, {2966, 35906}
X(65779) = X(i)-isoconjugate of X(j) for these (i,j): {1755, 39290}, {5627, 23997}, {11079, 62720}, {14356, 36034}, {32678, 35910}, {35908, 36061}
X(65779) = X(i)-Dao conjugate of X(j) for these (i,j): {1637, 2799}, {3258, 14356}, {3284, 2421}, {8552, 6333}, {14918, 877}, {16221, 35908}, {18334, 35910}, {36899, 39290}, {60342, 32112}, {62551, 325}, {62562, 5627}
X(65779) = crosssum of X(511) and X(32112)
X(65779) = trilinear pole of line {3258, 52743}
X(65779) = barycentric product X(i)*X(j) for these {i,j}: {98, 5664}, {287, 62172}, {290, 52743}, {526, 60869}, {879, 14920}, {1511, 43665}, {2395, 6148}, {2966, 3258}, {3260, 60777}, {3268, 35906}, {14355, 41079}, {22456, 47414}, {35912, 44427}
X(65779) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 39290}, {526, 35910}, {878, 11079}, {1511, 2421}, {1637, 14356}, {2088, 32112}, {2395, 5627}, {2422, 40355}, {2715, 15395}, {3258, 2799}, {5664, 325}, {6148, 2396}, {14355, 44769}, {14920, 877}, {35201, 62720}, {35906, 476}, {35912, 60053}, {39176, 4230}, {47230, 35908}, {47414, 684}, {52743, 511}, {60777, 74}, {60869, 35139}, {62172, 297}

X(65780) = X(23)X(94)∩X(287)X(37784)

Barycentrics    b^2*c^2*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(-a^4 + a^2*b^2 + b^2*c^2 - c^4)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(65780) lies on the cubic K1372 and these lines: {23, 94}, {287, 37784}, {523, 60502}, {686, 3580}, {687, 2966}, {1637, 46106}, {2394, 44146}, {2407, 3260}, {2409, 44145}, {2799, 51481}, {3003, 16237}, {53245, 64781}

X(65780) = reflection of X(i) in X(j) for these {i,j}: {3260, 65753}, {16237, 3003}
X(65780) = X(i)-Ceva conjugate of X(j) for these (i,j): {290, 52451}, {16081, 60869}
X(65780) = X(i)-isoconjugate of X(j) for these (i,j): {1755, 10419}, {9417, 40423}, {36034, 65762}
X(65780) = X(i)-Dao conjugate of X(j) for these (i,j): {3003, 511}, {3258, 65762}, {11064, 36212}, {34834, 35910}, {36899, 10419}, {39021, 32112}, {39058, 40423}, {65753, 2799}
X(65780) = trilinear pole of line {113, 65757}
X(65780) = barycentric product X(i)*X(j) for these {i,j}: {113, 290}, {2966, 65757}, {3260, 52451}, {3580, 60869}, {16081, 62569}, {35912, 44138}, {43187, 55265}, {47405, 60199}
X(65780) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 10419}, {113, 511}, {290, 40423}, {403, 35908}, {1637, 65762}, {3580, 35910}, {6531, 40388}, {35906, 14910}, {35912, 5504}, {43187, 55264}, {47405, 3289}, {52451, 74}, {55121, 32112}, {55265, 3569}, {60869, 2986}, {62569, 36212}, {65757, 2799}

X(65781) = X(230)X(297)∩X(287)X(2395)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(a^4 - a^2*b^2 + 2*b^4 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + 2*c^4) : :

X(65781) lies on the cubic K1372 and these lines: {230, 297}, {287, 2395}, {476, 39374}, {2065, 56925}, {2409, 3563}, {8781, 55266}, {10723, 41173}, {35906, 36891}, {36181, 60506}, {39809, 51820}, {41253, 57493}, {51431, 52472}, {52081, 52091}, {54395, 60504}

X(65781) = X(i)-cross conjugate of X(j) for these (i,j): {30, 36891}, {11064, 60869}
X(65781) = X(i)-isoconjugate of X(j) for these (i,j): {74, 17462}, {114, 2159}, {1755, 36875}, {2349, 51335}, {8772, 35910}, {36034, 55267}, {36119, 47406}
X(65781) = X(i)-Dao conjugate of X(j) for these (i,j): {1511, 47406}, {3163, 114}, {3258, 55267}, {36899, 36875}, {57295, 41181}, {62569, 62590}
X(65781) = cevapoint of X(30) and X(35906)
X(65781) = trilinear pole of line {34810, 35912}
X(65781) = barycentric product X(i)*X(j) for these {i,j}: {30, 40428}, {98, 36891}, {1637, 55266}, {2065, 3260}, {2966, 65758}, {2987, 60869}, {8781, 35906}, {35142, 35912}
X(65781) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 114}, {98, 36875}, {1495, 51335}, {1637, 55267}, {2065, 74}, {2173, 17462}, {2987, 35910}, {3284, 47406}, {3563, 35908}, {11064, 62590}, {35364, 32112}, {35906, 230}, {35912, 3564}, {36891, 325}, {40428, 1494}, {53866, 34174}, {60869, 51481}, {65758, 2799}

X(65782) = X(2)X(525)∩X(30)X(1637)

Barycentrics    (b^2 - c^2)*(-2*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4)*(3*a^8 - 5*a^6*b^2 + 3*a^4*b^4 - 3*a^2*b^6 + 2*b^8 - 5*a^6*c^2 + 5*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + 3*a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 - b^2*c^6 + 2*c^8) : :
X(65782) = 3 X[1637] - X[58351], X[3268] - 3 X[44578]

X(65782) lies on the cubic K1372 and these lines: {2, 525}, {30, 1637}, {112, 476}, {113, 38975}, {115, 6587}, {441, 2799}, {523, 3163}, {647, 31945}, {1990, 55141}, {2395, 34810}, {2966, 62629}, {3268, 44578}, {5915, 50642}, {9979, 40884}, {14417, 44346}, {14910, 47125}, {35906, 51937}, {36899, 52038}, {44216, 44564}, {45801, 56399}, {47085, 62612}

X(65782) = midpoint of X(i) and X(j) for these {i,j}: {2966, 62629}, {9979, 40884}
X(65782) = reflection of X(i) in X(j) for these {i,j}: {14417, 44346}, {44216, 44564}
X(65782) = X(i)-complementary conjugate of X(j) for these (i,j): {2173, 36471}, {9406, 35088}, {35906, 21253}
X(65782) = X(i)-Ceva conjugate of X(j) for these (i,j): {2966, 30}, {43673, 9033}
X(65782) = X(36034)-isoconjugate of X(65765)
X(65782) = X(i)-Dao conjugate of X(j) for these (i,j): {3258, 65765}, {65754, 2799}
X(65782) = crosspoint of X(648) and X(52485)
X(65782) = crosssum of X(6) and X(32112)
X(65782) = crossdifference of every pair of points on line {1495, 5502}
X(65782) = barycentric product X(30)*X(53383)
X(65782) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 65765}, {53383, 1494}

X(65783) = X(69)X(65616)∩X(230)X(54380)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(2*a^8 - 5*a^6*b^2 + 6*a^4*b^4 - 5*a^2*b^6 + 2*b^8 - 3*a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 + b^4*c^4 - a^2*c^6 - b^2*c^6 + c^8)*(2*a^8 - 3*a^6*b^2 + a^4*b^4 - a^2*b^6 + b^8 - 5*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 - b^6*c^2 + 6*a^4*c^4 + 3*a^2*b^2*c^4 + b^4*c^4 - 5*a^2*c^6 - 3*b^2*c^6 + 2*c^8) : :

X(65783) lies on the cubic K1372 and these lines: {69, 65616}, {230, 54380}, {523, 53783}, {542, 65726}, {2395, 34810}, {2409, 44145}, {2799, 40080}, {2966, 52472}, {3564, 5967}, {14356, 35906}, {18312, 34156}

X(65783) = X(i)-cross conjugate of X(j) for these (i,j): {1637, 2966}, {60340, 34761}
X(65783) = X(36034)-isoconjugate of X(65763)
X(65783) = X(i)-Dao conjugate of X(j) for these (i,j): {3258, 65763}, {34156, 52473}
X(65783) = cevapoint of X(35912) and X(53783)
X(65783) = trilinear pole of line {8779, 52038}
X(65783) = barycentric product X(2966)*X(65766)
X(65783) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 65763}, {2966, 65768}, {34369, 1550}, {35906, 52472}, {65726, 52473}, {65766, 2799}





leftri  Bicevian-, bianticevian-, bipedal- and biantipedal- inconics: X(65784) - X(65852)  rightri

This preamble and centers X(65784)-X(65852) were contributed by César Eliud Lozada, October 19, 2024.

Let ABC be a triangle and P', P" two distinct points. The following facts are widely known:

  1. The circumcevian triangles T', T" of P', P", respectively, are inscribed in the circumcircle of ABC.
  2. The circumanticevian triangles T', T" of P', P", respectively, are inscribed in the circumcircle of ABC.
  3. The cevian triangles T', T" of P', P", respectively, are circumscribed by a conic, named the bicevian conic of P' and P".
  4. The anticevian triangles T', T" of P', P", respectively, are circumscribed by a conic, named the bianticevian conic of P' and P".
  5. If P', P" are isogonal conjugates, the pedal triangles T', T" of P', P", respectively, are circumscribed by a circle, named the pedal circle of P' or P".
  6. If P', P" are isogonal conjugates, the antipedal triangles T', T" of P', P", respectively, are circumscribed by a conic, named the antipedal conic of P' or P", or the apedal conic of P' or P" (see preamble before X(8268)).

In all the previous cases, there are two triangles inscribed in a conic. Therefore, by the proposition if two triangles are circumscribed to a conic, they are also inscribed to a conic; and conversely, used in the preamble before X(65386), every pair of those of triangles are tangent to a common conic, here accordingly named, the bicircumcevian-, bicircumanticevian-, bicevian-, bianticevian-, bipedal- and biantipedal- inconic of T' and T".

This section includes the centers and perspectors of these inconics for P'=X(i) and P"=X(j), with 1≤{i, j}≤11. A list of already known centers and perspectors can be seen here.

As a remarkable note, for any P' and P", ABC is autopolar with respect to the bicevian inconic of P' and P".

underbar

X(65784) = CENTER OF THE BICEVIAN INCONIC OF X(1) AND X(5)

Barycentrics    a^2*(b^2-c^2)*((-a^2+b^2+c^2)^2-b^2*c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2 : :

X(65784) lies on these lines: {187, 237}, {526, 2914}, {690, 3574}, {1510, 12060}, {6750, 16230}, {24862, 41221}, {32737, 61203}, {34983, 57195}

X(65784) = midpoint of X(15451) and X(42650)
X(65784) = Gibert-circumtangential conjugate of X(46966)
X(65784) = isogonal conjugate of the isotomic conjugate of X(55132)
X(65784) = cross-difference of every pair of points on the line X(2)X(18315)
X(65784) = crosspoint of X(i) and X(j) for these {i, j}: {6, 46966}, {1154, 2439}, {10412, 12077}, {11062, 53176}
X(65784) = crosssum of X(i) and X(j) for these {i, j}: {2, 55132}, {1141, 2413}, {1154, 63830}, {18315, 52603}, {43083, 65326}
X(65784) = X(i)-Ceva conjugate of-X(j) for these (i, j): (1141, 47424), (10412, 12077), (46966, 6), (53176, 11062)
X(65784) = X(i)-Dao conjugate of-X(j) for these (i, j): (130, 50463), (137, 46138), (206, 46966), (1154, 10411), (6663, 35139), (15450, 65326), (17433, 95), (18402, 18831), (35591, 63172), (40588, 64516), (61504, 46139), (63463, 1141)
X(65784) = X(i)-isoconjugate of-X(j) for these {i, j}: {75, 46966}, {2167, 64516}, {36134, 46138}, {65221, 65326}
X(65784) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (32, 46966), (51, 64516), (186, 52939), (1273, 55218), (2081, 95), (2439, 57764), (11062, 18831), (12077, 46138), (15451, 65326), (24862, 14592), (36412, 35139), (41078, 34384), (42293, 50463), (51513, 65360), (53176, 57573), (55132, 76), (55219, 1141), (57195, 328), (61378, 60053), (62259, 32680), (62260, 476), (62261, 46456), (65485, 11077)
X(65784) = perspector of the circumconic through X(6) and X(11062)
X(65784) = pole of the line {6, 11077} with respect to the circumcircle
X(65784) = pole of the line {1141, 3613} with respect to the nine-point circle
X(65784) = pole of the line {264, 18831} with respect to the polar circle
X(65784) = pole of the line {6, 11077} with respect to the Brocard inellipse
X(65784) = pole of the line {3269, 58903} with respect to the Jerabek circumhyperbola
X(65784) = pole of the line {669, 2934} with respect to the Kiepert parabola
X(65784) = pole of the line {51, 24862} with respect to the orthic inconic
X(65784) = pole of the line {99, 46966} with respect to the Stammler hyperbola
X(65784) = barycentric product X(i)*X(j) for these {i, j}: {5, 2081}, {6, 55132}, {51, 41078}, {137, 2439}, {186, 57195}, {526, 36412}, {1087, 2624}, {1154, 12077}, {1273, 55219}, {2290, 2618}, {2599, 2600}, {3268, 62260}, {6368, 11062}, {8552, 62261}, {14165, 34983}, {14270, 45793}, {14590, 24862}, {14918, 15451}, {32679, 62259}, {34520, 46002}
X(65784) = trilinear product X(i)*X(j) for these {i, j}: {31, 55132}, {526, 62259}, {1087, 14270}, {1953, 2081}, {2179, 41078}, {2290, 12077}, {2624, 36412}, {15451, 51801}, {32679, 62260}
X(65784) = trilinear quotient X(i)/X(j) for these (i, j): (31, 46966), (1087, 35139), (1953, 64516), (2081, 2167), (2290, 18315), (2618, 46138), (11062, 65221), (36412, 32680), (41078, 62276), (51801, 18831), (52414, 52939), (55132, 75), (61378, 36061), (62259, 476), (62260, 32678), (62261, 36129)

X(65785) = CENTER OF THE BICEVIAN INPARABOLA OF X(2) AND X(5)

Barycentrics    (b^2-c^2)*(-a^2+b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :

X(65785) lies on these lines: {30, 511}, {17434, 42650}, {34983, 57195}

X(65785) = isogonal conjugate of the anticomplement of X(65786)
X(65785) = complementary conjugate of X(65786)
X(65785) = cross-difference of every pair of points on the line X(6)X(288)
X(65785) = crosspoint of X(i) and X(j) for these {i, j}: {5, 35318}, {233, 35311}, {6368, 57195}
X(65785) = crosssum of X(i) and X(j) for these {i, j}: {54, 39181}, {288, 39180}
X(65785) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4, 65786), (5, 39019), (6368, 35441), (23607, 41212), (35311, 233)
X(65785) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 65786), (59143, 34846)
X(65785) = X(i)-Dao conjugate of-X(j) for these (i, j): (125, 59143), (130, 20574), (137, 39286), (140, 18831), (233, 52939), (6368, 62724), (6663, 33513), (15450, 288), (35442, 95), (39019, 31617)
X(65785) = X(i)-isoconjugate of-X(j) for these {i, j}: {162, 59143}, {288, 65221}, {36134, 39286}
X(65785) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (140, 52939), (233, 18831), (647, 59143), (3078, 648), (6368, 31617), (12077, 39286), (14978, 42405), (15451, 288), (24862, 39183), (32078, 18315), (34983, 31626), (35311, 57573), (35441, 95), (36412, 33513), (39019, 62724), (42293, 20574), (53386, 16813), (57195, 40410), (59164, 6331)
X(65785) = center of the central inconic through X(62724) and X(65785)
X(65785) = perspector of the circumconic through X(2) and X(233)
X(65785) = barycentric product X(i)*X(j) for these {i, j}: {5, 35441}, {140, 57195}, {233, 6368}, {525, 3078}, {647, 59164}, {14978, 17434}, {15451, 57811}, {18314, 32078}, {34983, 40684}, {35311, 39019}, {35318, 35442}, {53386, 60597}
X(65785) = trilinear product X(i)*X(j) for these {i, j}: {656, 3078}, {810, 59164}, {1953, 35441}, {2618, 32078}, {17438, 57195}
X(65785) = trilinear quotient X(i)/X(j) for these (i, j): (233, 65221), (656, 59143), (1087, 33513), (2618, 39286), (3078, 162), (20879, 52939), (32078, 36134), (35441, 2167), (59164, 811)

X(65786) = FOCUS OF THE BICEVIAN INPARABOLA OF X(2) AND X(5)

Barycentrics    (b^2-c^2)^2*(-a^2+b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2)*(a^16-6*(b^2+c^2)*a^14+2*(7*b^4+11*b^2*c^2+7*c^4)*a^12-2*(b^2+c^2)*(7*b^4+5*b^2*c^2+7*c^4)*a^10+b^2*c^2*(b^4+3*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(7*b^8+7*c^8-2*b^2*c^2*(2*b^4-3*b^2*c^2+2*c^4))*a^6-2*(b^2-c^2)^2*(7*b^8+7*c^8+b^2*c^2*(8*b^4+9*b^2*c^2+8*c^4))*a^4+2*(b^2-c^2)^3*(b^4-c^4)*(3*b^4+b^2*c^2+3*c^4)*a^2-(b^2-c^2)^4*(b^8+c^8-(b^4+b^2*c^2+c^4)*b^2*c^2)) : :

X(65786) lies on the nine-point circle and these lines: {137, 39019}, {14635, 18402}, {35441, 35592}

X(65786) = complement of the isogonal conjugate of X(65785)
X(65786) = complementary conjugate of X(65785)
X(65786) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4, 65785), (54449, 6368)
X(65786) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 65785), (810, 52540), (2618, 10184), (3078, 8062), (35441, 21231), (59164, 21259), (65785, 10)
X(65786) = center of the circumconic through X(4) and X(54449)

X(65787) = FOCUS OF THE BICEVIAN INPARABOLA OF X(2) AND X(10)

Barycentrics    (b+c)*(2*a+b+c)*(b^2-c^2)^2*(a^4+2*(b+c)*a^3+2*b*c*a^2-2*(b+c)*(b^2+c^2)*a-b^4-c^4-b*c*(2*b^2+b*c+2*c^2)) : :

X(65787) lies on the nine-point circle and these lines: {2, 6578}, {114, 51586}, {3258, 4988}, {6627, 38960}, {15611, 35076}, {23064, 46660}

X(65787) = complementary conjugate of X(6367)
X(65787) = complement of X(6578)
X(65787) = X(4)-Ceva conjugate of-X(6367)
X(65787) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 6367), (42, 8043), (430, 8062), (512, 3743), (523, 27798), (594, 48049), (661, 6707), (756, 4977), (1100, 21196), (1125, 52601), (1213, 4369), (1230, 42327), (1500, 48003), (1962, 523), (2308, 31947), (2355, 21187), (2643, 3120), (3124, 16726), (3125, 24185), (4024, 17239), (4041, 18253), (4079, 44307), (4359, 52602), (4427, 21254), (4647, 512), (4705, 3634), (4976, 21233), (4979, 17045), (4983, 1125), (4988, 3739), (6367, 10), (8013, 513), (8663, 37), (20970, 14838), (21816, 514), (30591, 3741), (35327, 16598), (35342, 620), (44143, 21259), (52576, 21260)
X(65787) = center of the circumconic through X(4) and X(35468)
X(65787) = pole of the line {6367, 8043} with respect to the Kiepert circumhyperbola

X(65788) = CENTER OF THE BICEVIAN INCONIC OF X(3) AND X(4)

Barycentrics    a^4*(b^2-c^2)*(-a^2+b^2+c^2)^2*((b^2+c^2)*a^4-2*(b^2-c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)) : :

X(65788) lies on these lines: {460, 512}, {520, 20580}, {2524, 39469}, {2713, 23582}, {3049, 62175}, {32320, 39201}, {54034, 58308}

X(65788) = cross-difference of every pair of points on the line X(394)X(801)
X(65788) = crosspoint of X(i) and X(j) for these {i, j}: {6, 1624}, {512, 39201}, {16035, 61204}
X(65788) = crosssum of X(99) and X(6528)
X(65788) = X(i)-Dao conjugate of-X(j) for these (i, j): (125, 57775), (136, 57843), (244, 57972), (2883, 6528), (3269, 76), (5139, 57677), (13567, 670), (17423, 1105), (35071, 40830), (38985, 57955), (38986, 821), (46093, 57800)
X(65788) = X(i)-isoconjugate of-X(j) for these {i, j}: {99, 821}, {107, 57955}, {110, 57972}, {162, 57775}, {775, 6528}, {801, 823}, {811, 1105}, {4575, 57843}, {4592, 57677}, {24019, 40830}, {36126, 57800}, {41890, 57973}, {57806, 59039}
X(65788) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (185, 6331), (417, 4563), (520, 40830), (647, 57775), (661, 57972), (774, 57973), (798, 821), (800, 6528), (820, 799), (822, 57955), (2489, 57677), (2501, 57843), (3049, 1105), (6508, 57968), (6509, 670), (14585, 59039), (16035, 42405), (32320, 57800), (39201, 801), (44079, 15352), (58310, 41890), (61374, 648)
X(65788) = perspector of the circumconic through X(393) and X(577)
X(65788) = pole of the line {1609, 9244} with respect to the circumcircle
X(65788) = pole of the line {185, 800} with respect to the 1st Lozada, circle
X(65788) = pole of the line {69, 57677} with respect to the polar circle
X(65788) = pole of the line {185, 800} with respect to the Brocard inellipse
X(65788) = pole of the line {6638, 52077} with respect to the MacBeath circumconic
X(65788) = pole of the line {25, 63531} with respect to the orthic inconic
X(65788) = pole of the line {6528, 55224} with respect to the Stammler hyperbola
X(65788) = barycentric product X(i)*X(j) for these {i, j}: {185, 647}, {235, 32320}, {417, 2501}, {512, 6509}, {520, 800}, {525, 61374}, {661, 820}, {774, 822}, {810, 6508}, {1624, 3269}, {2972, 61204}, {3049, 41005}, {13567, 39201}, {15451, 19180}, {16035, 17434}, {19166, 42293}, {34980, 41678}, {44079, 52613}, {52566, 58796}, {58763, 61349}
X(65788) = trilinear product X(i)*X(j) for these {i, j}: {185, 810}, {512, 820}, {656, 61374}, {774, 39201}, {798, 6509}, {800, 822}, {3049, 6508}, {17858, 58310}, {37754, 61204}
X(65788) = trilinear quotient X(i)/X(j) for these (i, j): (185, 811), (417, 4592), (512, 821), (520, 57955), (523, 57972), (656, 57775), (774, 6528), (800, 823), (810, 1105), (820, 99), (822, 801), (1624, 23999), (6508, 6331), (6509, 799), (13567, 57973), (24006, 57843), (24018, 40830), (39201, 775), (41005, 57968), (44079, 36126)

X(65789) = CENTER OF THE BICEVIAN INCONIC OF X(3) AND X(5)

Barycentrics    a^4*(b^2-c^2)*(-a^2+b^2+c^2)^3*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*((b^2+c^2)*a^6-3*(b^4+c^4)*a^4+3*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+c^4)*(b^2-c^2)^2) : :

X(65789) lies on these lines: {6368, 14618}, {32320, 39201}, {34983, 57195}

X(65789) = cross-difference of every pair of points on the line X(2052)X(21449)
X(65789) = crosspoint of X(i) and X(j) for these {i, j}: {216, 61195}, {34983, 58305}
X(65789) = X(i)-Dao conjugate of-X(j) for these (i, j): (389, 18831), (46832, 54950)
X(65789) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (6750, 42401), (34836, 54950), (42441, 42405)
X(65789) = perspector of the circumconic through X(577) and X(34836)
X(65789) = barycentric product X(i)*X(j) for these {i, j}: {17434, 42441}, {34836, 58305}, {34983, 46832}

X(65790) = CENTER OF THE BICEVIAN INCONIC OF X(3) AND X(7)

Barycentrics    a^4*(b-c)*(-a+b+c)*(-a^2+b^2+c^2)^2*((b+c)*a^2+2*b*c*a-(b^2-c^2)*(b-c))*((b^2+c^2)*a^3-(b^2-c^2)*(b-c)*a^2-(b^2-c^2)^2*a+(b^4-c^4)*(b-c)) : :

X(65790) lies on these lines: {513, 676}, {32320, 39201}

X(65790) = cross-difference of every pair of points on the line X(220)X(2052)
X(65790) = perspector of the circumconic through X(279) and X(577)
X(65790) = pole of the line {1617, 41373} with respect to the circumcircle
X(65790) = barycentric product X(39796)*X(52306)

X(65791) = CENTER OF THE BICEVIAN INCONIC OF X(3) AND X(8)

Barycentrics    a^4*(b-c)*(-a+b+c)^2*(-a^2+b^2+c^2)^2*((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))*((b^2+c^2)*a^3+(b^2-c^2)*(b-c)*a^2-(b^2-c^2)^2*a-(b^4-c^4)*(b-c)) : :

X(65791) lies on these lines: {3239, 3900}, {32320, 39201}

X(65791) = cross-difference of every pair of points on the line X(1407)X(2052)
X(65791) = perspector of the circumconic through X(346) and X(577)
X(65791) = pole of the line {1604, 41373} with respect to the circumcircle
X(65791) = barycentric product X(40944)*X(52307)

X(65792) = CENTER OF THE BICEVIAN INCONIC OF X(3) AND X(9)

Barycentrics    a^4*(b-c)*(-a+b+c)^2*(-a^2+b^2+c^2)^2*(a^3+(b+c)*a^2-(b+c)^2*a-(b^2-c^2)*(b-c))*((b+c)*a^3+(b-c)^2*a^2-(b^2-c^2)*(b-c)*a-(b^2-c^2)^2) : :

X(65792) lies on these lines: {657, 4105}, {32320, 39201}

X(65792) = cross-difference of every pair of points on the line X(279)X(2052)
X(65792) = perspector of the circumconic through X(220) and X(577)
X(65792) = pole of the line {1615, 41373} with respect to the circumcircle
X(65792) = pole of the line {4616, 6528} with respect to the Stammler hyperbola
X(65792) = barycentric product X(i)*X(j) for these {i, j}: {10397, 40945}, {40943, 58340}, {52097, 65102}

X(65793) = CENTER OF THE BICEVIAN INCONIC OF X(3) AND X(10)

Barycentrics    a^4*(b+c)*(b^2-c^2)*(-a^2+b^2+c^2)^2*((b+c)*a^2-b*c*a-b^3-c^3)*((b^2+c^2)*a^3+(b^3+c^3)*a^2-(b^2-c^2)^2*a-(b^2-c^2)*(b^3-c^3)) : :

X(65793) lies on these lines: {4024, 4705}, {32320, 39201}

X(65793) = cross-difference of every pair of points on the line X(593)X(2052)
X(65793) = perspector of the circumconic through X(577) and X(594)
X(65793) = pole of the line {35212, 41373} with respect to the circumcircle
X(65793) = barycentric product X(52310)*X(55351)

X(65794) = CENTER OF THE BICEVIAN INCONIC OF X(4) AND X(5)

Barycentrics    (b^2-c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(2*a^6-3*(b^2+c^2)*a^4+(b^4-c^4)*(b^2-c^2)) : :

X(65794) lies on these lines: {460, 512}, {34983, 57195}

X(65794) = X(63463)-Dao conjugate of-X(65090)
X(65794) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (3575, 52939), (55219, 65090)
X(65794) = perspector of the circumconic through X(393) and X(36412)
X(65794) = pole of the line {25, 63552} with respect to the orthic inconic
X(65794) = barycentric product X(i)*X(j) for these {i, j}: {3574, 12077}, {3575, 57195}

X(65795) = CENTER OF THE BICEVIAN INCONIC OF X(4) AND X(9)

Barycentrics    a^2*(b-c)*(-a+b+c)^2*((b+c)*a^3-(b-c)^2*a^2-(b^2-c^2)*(b-c)*a+(b^2-c^2)^2) : :

X(65795) lies on these lines: {460, 512}, {657, 4105}, {661, 2488}, {663, 58299}, {926, 14298}, {3900, 57049}, {4895, 65442}, {8638, 58303}

X(65795) = cross-difference of every pair of points on the line X(279)X(394)
X(65795) = crosspoint of X(657) and X(18344)
X(65795) = crosssum of X(658) and X(6516)
X(65795) = X(33)-Ceva conjugate of-X(14936)
X(65795) = X(i)-Dao conjugate of-X(j) for these (i, j): (6260, 4569), (7004, 7182), (14714, 40424), (39025, 63185)
X(65795) = X(i)-isoconjugate of-X(j) for these {i, j}: {658, 40399}, {664, 63185}, {934, 40424}, {1088, 65361}, {1167, 4569}, {4616, 56259}, {40397, 65164}, {40444, 65296}
X(65795) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (657, 40424), (1108, 4569), (1210, 46406), (1864, 4554), (3063, 63185), (8641, 40399), (14827, 65361), (23204, 65296), (37566, 36838), (40628, 7182), (40958, 658), (40979, 4625), (53288, 1275), (61212, 59457)
X(65795) = perspector of the circumconic through X(220) and X(393)
X(65795) = pole of the line {1609, 1615} with respect to the circumcircle
X(65795) = pole of the line {198, 800} with respect to the 1st Lozada, circle
X(65795) = pole of the line {198, 800} with respect to the Brocard inellipse
X(65795) = pole of the line {6392, 46706} with respect to the Steiner circumellipse
X(65795) = barycentric product X(i)*X(j) for these {i, j}: {33, 40628}, {650, 1864}, {657, 1210}, {1071, 65103}, {1108, 3900}, {1146, 53288}, {2310, 61237}, {3119, 61227}, {3239, 40958}, {3611, 17926}, {4041, 40979}, {4081, 61212}, {4130, 37566}, {8641, 17862}, {14936, 61185}, {21789, 21933}
X(65795) = trilinear product X(i)*X(j) for these {i, j}: {607, 40628}, {657, 1108}, {663, 1864}, {1210, 8641}, {2310, 53288}, {3022, 61227}, {3119, 61212}, {3709, 40979}, {3900, 40958}, {4105, 37566}, {14936, 61237}
X(65795) = trilinear quotient X(i)/X(j) for these (i, j): (657, 40399), (663, 63185), (1108, 658), (1210, 4569), (1253, 65361), (1864, 664), (3900, 40424), (4524, 56259), (8641, 1167), (17862, 46406), (37566, 4626), (40628, 348), (40958, 934), (40979, 4573), (53288, 7045), (61227, 59457), (61237, 1275), (65103, 40444)
X(65795) = (X(4524), X(65804))-harmonic conjugate of X(8641)

X(65796) = CENTER OF THE BICEVIAN INCONIC OF X(4) AND X(10)

Barycentrics    (b+c)*(b^2-c^2)*(2*a^3+(b+c)*a^2+(b^2-c^2)*(b-c)) : :

X(65796) lies on these lines: {460, 512}, {523, 3239}, {649, 1637}, {650, 6089}, {690, 48269}, {2799, 3835}, {3268, 27138}, {3700, 21099}, {4024, 4705}, {4079, 55197}, {4155, 4524}, {6370, 14321}, {8029, 8663}, {8672, 47124}, {9979, 20295}, {12077, 42664}, {14417, 30835}, {16230, 57043}, {18004, 57199}, {31286, 44564}, {42666, 55212}

X(65796) = midpoint of X(12077) and X(42664)
X(65796) = cross-difference of every pair of points on the line X(394)X(593)
X(65796) = crosspoint of X(i) and X(j) for these {i, j}: {1834, 14543}, {2501, 4024}
X(65796) = crosssum of X(4556) and X(4558)
X(65796) = X(i)-Ceva conjugate of-X(j) for these (i, j): (1826, 115), (14543, 1834)
X(65796) = X(i)-Dao conjugate of-X(j) for these (i, j): (115, 64985), (136, 40414), (440, 4610), (4466, 17206), (5139, 57390), (40607, 29163), (40940, 4563), (59646, 99)
X(65796) = X(i)-isoconjugate of-X(j) for these {i, j}: {163, 64985}, {757, 29163}, {951, 4612}, {1257, 4556}, {2983, 52935}, {4558, 40431}, {4575, 40414}, {4592, 57390}
X(65796) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (440, 4563), (523, 64985), (1104, 52935), (1500, 29163), (1834, 99), (2264, 4612), (2489, 57390), (2501, 40414), (4079, 2983), (4705, 1257), (14543, 4590), (17863, 4623), (18673, 4592), (21671, 4561), (29162, 1509), (40940, 4610), (40977, 662), (40984, 110), (44093, 4558), (53290, 249), (61221, 24041), (65206, 6064)
X(65796) = perspector of the circumconic through X(393) and X(594)
X(65796) = pole of the line {1609, 35212} with respect to the circumcircle
X(65796) = pole of the line {7390, 9752} with respect to the orthoptic circle of Steiner inellipse
X(65796) = pole of the line {69, 7058} with respect to the polar circle
X(65796) = pole of the line {6392, 46707} with respect to the Steiner circumellipse
X(65796) = pole of the line {966, 3767} with respect to the Steiner inellipse
X(65796) = barycentric product X(i)*X(j) for these {i, j}: {115, 14543}, {338, 53290}, {440, 2501}, {523, 1834}, {594, 29162}, {850, 40984}, {1104, 4036}, {1109, 61221}, {1365, 65206}, {1577, 40977}, {1842, 4064}, {2970, 61200}, {4024, 40940}, {4705, 17863}, {7649, 21671}, {14618, 44093}, {18673, 24006}
X(65796) = trilinear product X(i)*X(j) for these {i, j}: {115, 61221}, {523, 40977}, {661, 1834}, {756, 29162}, {950, 57185}, {1104, 4024}, {1109, 53290}, {1577, 40984}, {1842, 55232}, {2501, 18673}, {2643, 14543}, {4079, 17863}, {4705, 40940}, {6591, 21671}, {24006, 44093}
X(65796) = trilinear quotient X(i)/X(j) for these (i, j): (440, 4592), (756, 29163), (950, 4612), (1104, 4556), (1577, 64985), (1834, 662), (2264, 4636), (2501, 40431), (4024, 1257), (4705, 2983), (14543, 24041), (17863, 4610), (18673, 4558), (21671, 1332), (24006, 40414), (29162, 757), (40940, 52935), (40977, 110), (40984, 163), (44093, 4575)

X(65797) = CENTER OF THE BICEVIAN INCONIC OF X(5) AND X(6)

Barycentrics    a^4*(b^2-c^2)*(a^4-2*(b^2+c^2)*a^2+b^4+c^4)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*((b^2+c^2)*a^4-2*(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :

X(65797) lies on these lines: {669, 688}, {34983, 57195}

X(65797) = X(55072)-Dao conjugate of-X(34384)
X(65797) = perspector of the circumconic through X(32) and X(36412)

X(65798) = CENTER OF THE BICEVIAN INCONIC OF X(5) AND X(7)

Barycentrics    (b-c)*(-a+b+c)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(2*a^3+(b+c)*a^2-2*(b^2-b*c+c^2)*a-(b^2-c^2)*(b-c))*(2*a^5-3*(b^2+c^2)*a^3-(b^2-c^2)*(b-c)*a^2+(b^2-c^2)^2*a+(b^4-c^4)*(b-c)) : :

X(65798) lies on these lines: {513, 676}, {34983, 57195}

X(65798) = perspector of the circumconic through X(279) and X(36412)

X(65799) = CENTER OF THE BICEVIAN INCONIC OF X(5) AND X(8)

Barycentrics    (b-c)*(-a+b+c)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(2*a^3-(b+c)*a^2-2*(b^2-b*c+c^2)*a+(b^2-c^2)*(b-c))*(2*a^5-3*(b^2+c^2)*a^3+(b^2-c^2)*(b-c)*a^2+(b^2-c^2)^2*a-(b^4-c^4)*(b-c)) : :

X(65799) lies on these lines: {3239, 3900}, {34983, 57195}

X(65799) = perspector of the circumconic through X(346) and X(36412)

X(65800) = CENTER OF THE BICEVIAN INCONIC OF X(5) AND X(9)

Barycentrics    a^2*(b-c)*(-a+b+c)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(a^5-(b+c)*a^4-(2*b^2+b*c+2*c^2)*a^3+(b+c)*(2*b^2-b*c+2*c^2)*a^2+(b^3+c^3)*(b+c)*a-(b^2-c^2)*(b^3-c^3))*((b+c)*a^5-(b-c)^2*a^4-(b+c)*(2*b^2-b*c+2*c^2)*a^3+(2*b^2+b*c+2*c^2)*(b-c)^2*a^2+(b^3-c^3)*(b^2-c^2)*a-(b^2-c^2)*(b-c)*(b^3+c^3)) : :

X(65800) lies on these lines: {657, 4105}, {34983, 57195}

X(65800) = perspector of the circumconic through X(220) and X(36412)

X(65801) = CENTER OF THE BICEVIAN INCONIC OF X(5) AND X(10)

Barycentrics    (b+c)*(b^2-c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2*(a^3-(b^2-b*c+c^2)*a-b*c*(b+c))*(2*a^5+(b+c)*a^4-3*(b^2+c^2)*a^3-(b+c)*(b^2+b*c+c^2)*a^2+(b^2-c^2)^2*a+(b^2-c^2)*(b-c)*b*c) : :

X(65801) lies on these lines: {4024, 4705}, {34983, 57195}

X(65801) = perspector of the circumconic through X(594) and X(36412)

X(65802) = CENTER OF THE BICEVIAN INCONIC OF X(6) AND X(9)

Barycentrics    a^4*(b-c)*(-a+b+c)^2*((b+c)*a+(b-c)^2) : :

X(65802) lies on these lines: {657, 4105}, {669, 688}

X(65802) = isogonal conjugate of the isotomic conjugate of X(65442)
X(65802) = cross-difference of every pair of points on the line X(76)X(279)
X(65802) = crosssum of X(i) and X(j) for these {i, j}: {4569, 4572}, {4885, 5836}
X(65802) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 6613), (2170, 20567), (12640, 6386), (40368, 59123)
X(65802) = X(i)-isoconjugate of-X(j) for these {i, j}: {75, 6613}, {561, 59123}, {658, 32017}, {1088, 8706}, {1222, 4569}, {1261, 52937}, {1476, 4572}, {4554, 40420}, {4625, 56173}, {4635, 56258}, {23617, 46406}, {36838, 52549}
X(65802) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (32, 6613), (1201, 46406), (1501, 59123), (2347, 4572), (6363, 57792), (6615, 20567), (8641, 32017), (14827, 8706), (18163, 55213), (20228, 4569), (21120, 41283), (40982, 46404), (42336, 23062), (42337, 1502), (59173, 52937), (65442, 76)
X(65802) = perspector of the circumconic through X(32) and X(220)
X(65802) = pole of the line {1613, 1615} with respect to the circumcircle
X(65802) = pole of the line {3051, 30706} with respect to the Brocard inellipse
X(65802) = pole of the line {670, 4616} with respect to the Stammler hyperbola
X(65802) = pole of the line {8264, 46706} with respect to the Steiner circumellipse
X(65802) = barycentric product X(i)*X(j) for these {i, j}: {6, 65442}, {32, 42337}, {41, 6615}, {220, 6363}, {652, 40982}, {657, 1201}, {663, 2347}, {728, 42336}, {1122, 57180}, {1253, 48334}, {1828, 65102}, {1919, 6736}, {2175, 21120}, {3057, 3063}, {3752, 8641}, {3900, 20228}, {4105, 59173}, {14936, 23845}, {18163, 63461}, {21789, 21796}
X(65802) = trilinear product X(i)*X(j) for these {i, j}: {31, 65442}, {480, 42336}, {560, 42337}, {657, 20228}, {1201, 8641}, {1253, 6363}, {1946, 40982}, {1980, 6736}, {2175, 6615}, {2347, 3063}, {9447, 21120}, {14827, 48334}, {57180, 59173}, {61050, 62754}
X(65802) = trilinear quotient X(i)/X(j) for these (i, j): (31, 6613), (560, 59123), (657, 32017), (1122, 52937), (1201, 4569), (1253, 8706), (2347, 4554), (3057, 4572), (3063, 40420), (3752, 46406), (6363, 1088), (6615, 6063), (6736, 6386), (8641, 1222), (17183, 55213), (20228, 658), (21120, 20567), (40982, 18026), (42336, 479), (42337, 561)

X(65803) = CENTER OF THE BICEVIAN INCONIC OF X(6) AND X(10)

Barycentrics    a^4*(b+c)*(b^2-c^2)*((b+c)*a+b^2+b*c+c^2)*((b^2+c^2)*a+b^3+c^3) : :

X(65803) lies on these lines: {669, 688}, {4024, 4705}

X(65803) = cross-difference of every pair of points on the line X(76)X(593)
X(65803) = perspector of the circumconic through X(32) and X(594)
X(65803) = pole of the line {1613, 35212} with respect to the circumcircle
X(65803) = pole of the line {8264, 46707} with respect to the Steiner circumellipse
X(65803) = pole of the line {6537, 8265} with respect to the Steiner inellipse
X(65803) = barycentric product X(i)*X(j) for these {i, j}: {4016, 50488}, {8637, 20654}, {20966, 42664}, {40986, 47842}
X(65803) = trilinear product X(i)*X(j) for these {i, j}: {20966, 50488}, {40986, 42664}

X(65804) = CENTER OF THE BICEVIAN INCONIC OF X(7) AND X(9)

Barycentrics    a^2*(b-c)*(-a+b+c)^2*((b+c)*a^2-2*(b-c)^2*a+(b^2-c^2)*(b-c)) : :

X(65804) lies on these lines: {512, 65664}, {513, 676}, {657, 4105}, {663, 20980}, {926, 4162}, {1174, 23351}, {3900, 57064}, {6182, 65445}, {8653, 62176}, {15283, 46399}

X(65804) = reflection of X(4524) in X(657)
X(65804) = cross-difference of every pair of points on the line X(144)X(220)
X(65804) = crosspoint of X(513) and X(657)
X(65804) = crosssum of X(100) and X(658)
X(65804) = X(1)-Ceva conjugate of-X(14936)
X(65804) = X(i)-Dao conjugate of-X(j) for these (i, j): (2310, 75), (11019, 668), (14714, 56026), (38991, 23618), (39025, 63192), (43182, 4569), (59573, 4572)
X(65804) = X(i)-isoconjugate of-X(j) for these {i, j}: {651, 23618}, {664, 63192}, {934, 56026}
X(65804) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (657, 56026), (663, 23618), (1200, 664), (3063, 63192), (11019, 46406), (14100, 4554), (20978, 658), (40133, 4569), (41006, 4572), (60992, 52937)
X(65804) = perspector of the circumconic through X(220) and X(279)
X(65804) = pole of the line {1615, 1617} with respect to the circumcircle
X(65804) = pole of the line {57, 63601} with respect to the incircle
X(65804) = pole of the line {56, 23653} with respect to the Brocard inellipse
X(65804) = pole of the line {3056, 52562} with respect to the Mandart inellipse
X(65804) = pole of the line {4452, 46706} with respect to the Steiner circumellipse
X(65804) = barycentric product X(i)*X(j) for these {i, j}: {522, 1200}, {650, 14100}, {657, 11019}, {663, 41006}, {3022, 65174}, {3239, 20978}, {3900, 40133}, {4105, 60992}, {4162, 45202}, {4521, 45229}, {4524, 26818}, {8641, 20905}, {10167, 65103}, {21049, 21789}
X(65804) = trilinear product X(i)*X(j) for these {i, j}: {650, 1200}, {657, 40133}, {663, 14100}, {3063, 41006}, {3900, 20978}, {4162, 45229}, {8641, 11019}, {22088, 65103}, {57180, 60992}
X(65804) = trilinear quotient X(i)/X(j) for these (i, j): (650, 23618), (663, 63192), (1200, 651), (3900, 56026), (11019, 4569), (14100, 664), (20905, 46406), (20978, 934), (22088, 65296), (26818, 4635), (40133, 658), (41006, 4554), (45228, 65165), (45229, 65173), (60992, 36838)
X(65804) = (X(8641), X(65795))-harmonic conjugate of X(4524)

X(65805) = CENTER OF THE BICEVIAN INCONIC OF X(7) AND X(10)

Barycentrics    (b+c)*(3*a+b+c)*(b^2-c^2)*(2*a^2+(b+c)*a+(b-c)^2) : :

X(65805) lies on these lines: {513, 676}, {4024, 4705}

X(65805) = cross-difference of every pair of points on the line X(220)X(593)
X(65805) = X(4854)-reciprocal conjugate of-X(4633)
X(65805) = perspector of the circumconic through X(279) and X(594)
X(65805) = pole of the line {1617, 35212} with respect to the circumcircle
X(65805) = pole of the line {4452, 46707} with respect to the Steiner circumellipse
X(65805) = pole of the line {4000, 6537} with respect to the Steiner inellipse
X(65805) = barycentric product X(i)*X(j) for these {i, j}: {4841, 4854}, {21673, 30723}
X(65805) = trilinear product X(4822)*X(4854)
X(65805) = trilinear quotient X(4854)/X(4614)

X(65806) = CENTER OF THE BICEVIAN INCONIC OF X(8) AND X(10)

Barycentrics    (b+c)*(b^2-c^2)*(-a+b+c)^2*(2*a^2+(b+c)*a-(b-c)^2) : :

X(65806) lies on these lines: {3239, 3900}, {4024, 4705}

X(65806) = cross-difference of every pair of points on the line X(593)X(1407)
X(65806) = X(i)-Dao conjugate of-X(j) for these (i, j): (5745, 4616), (21044, 1434), (55064, 63194)
X(65806) = X(4565)-isoconjugate of-X(63194)
X(65806) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2650, 4637), (4041, 63194), (4171, 40430), (6737, 4610), (17056, 4616), (18698, 4635), (21674, 658), (21677, 4573), (21811, 1414), (42708, 4569), (62566, 1434), (65432, 7058)
X(65806) = perspector of the circumconic through X(346) and X(594)
X(65806) = pole of the line {1604, 35212} with respect to the circumcircle
X(65806) = pole of the line {200, 23902} with respect to the Mandart inellipse
X(65806) = pole of the line {30695, 46707} with respect to the Steiner circumellipse
X(65806) = pole of the line {6537, 6554} with respect to the Steiner inellipse
X(65806) = barycentric product X(i)*X(j) for these {i, j}: {2321, 62566}, {3239, 21674}, {3700, 21677}, {3900, 42708}, {4024, 6737}, {4082, 23755}, {4086, 21811}, {4171, 18698}, {6354, 65432}, {22003, 52335}
X(65806) = trilinear product X(i)*X(j) for these {i, j}: {210, 62566}, {657, 42708}, {1254, 65432}, {3700, 21811}, {3900, 21674}, {4041, 21677}, {4092, 53388}, {4171, 17056}, {4515, 23755}, {4524, 18698}, {4705, 6737}, {22003, 36197}
X(65806) = trilinear quotient X(i)/X(j) for these (i, j): (3700, 63194), (6737, 52935), (17056, 4637), (18698, 4616), (21674, 934), (21677, 1414), (21811, 4565), (42708, 658), (62566, 1014), (65432, 1098)

X(65807) = CENTER OF THE BICEVIAN INCONIC OF X(9) AND X(10)

Barycentrics    a^2*(b+c)*(b^2-c^2)*(-a+b+c)^2*(-a^2+b^2+c^2)*((b+c)*a^2+2*b*c*a-(b^2-c^2)*(b-c)) : :

X(65807) lies on these lines: {657, 4105}, {4024, 4705}

X(65807) = cross-difference of every pair of points on the line X(279)X(593)
X(65807) = X(i)-Dao conjugate of-X(j) for these (i, j): (942, 4616), (39007, 552), (40607, 58993)
X(65807) = X(i)-isoconjugate of-X(j) for these {i, j}: {757, 58993}, {4635, 40570}, {4637, 40395}
X(65807) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1500, 58993), (4524, 40395), (7064, 65334), (18591, 4616), (41393, 36838), (52306, 552), (56839, 4635), (59177, 65296), (64171, 55231)
X(65807) = perspector of the circumconic through X(220) and X(594)
X(65807) = pole of the line {1615, 35212} with respect to the circumcircle
X(65807) = pole of the line {46706, 46707} with respect to the Steiner circumellipse
X(65807) = barycentric product X(i)*X(j) for these {i, j}: {3695, 33525}, {4130, 41393}, {4171, 56839}, {6057, 52306}, {8611, 40967}, {21675, 57108}, {55232, 64171}, {59163, 65103}
X(65807) = trilinear product X(i)*X(j) for these {i, j}: {3949, 33525}, {4105, 41393}, {4171, 18591}, {4524, 56839}, {21675, 65102}, {55230, 64171}
X(65807) = trilinear quotient X(i)/X(j) for these (i, j): (756, 58993), (3690, 36048), (4171, 40395), (18591, 4637), (21675, 13149), (41393, 4626), (56839, 4616)

X(65808) = CENTER OF THE BIANTICEVIAN INCONIC OF X(1) AND X(11)

Barycentrics    2*a^4-2*(b+c)*a^3+(b^2+c^2)*a^2-2*(b^2-c^2)*(b-c)*a+(b^2-c^2)^2 : :
X(65808) = 3*X(2)+X(3732) = X(101)-3*X(51406) = X(101)+3*X(61730) = X(1146)+3*X(51406) = X(1146)-3*X(61730)

X(65808) lies on these lines: {1, 4534}, {2, 1565}, {3, 6554}, {4, 27541}, {5, 169}, {6, 59594}, {8, 57192}, {9, 119}, {10, 30618}, {11, 5540}, {19, 1596}, {30, 910}, {37, 59588}, {41, 37730}, {101, 952}, {116, 5845}, {118, 31852}, {140, 1212}, {150, 31640}, {220, 5690}, {230, 49758}, {242, 51366}, {355, 23058}, {381, 5819}, {404, 26793}, {442, 27068}, {495, 40131}, {496, 2082}, {514, 6710}, {515, 5199}, {517, 8074}, {519, 44897}, {528, 21090}, {644, 1145}, {650, 13006}, {812, 4422}, {948, 31184}, {956, 26258}, {999, 40127}, {1060, 46344}, {1111, 26007}, {1213, 62652}, {1358, 31192}, {1368, 15487}, {1375, 30807}, {1385, 41006}, {1387, 2170}, {1503, 31897}, {1566, 34805}, {1737, 2348}, {2183, 7359}, {2246, 12019}, {2550, 10743}, {2792, 63978}, {2809, 62674}, {2826, 3035}, {2973, 59206}, {3109, 5546}, {3207, 34773}, {3234, 44012}, {3730, 61524}, {3752, 63633}, {4187, 33950}, {4251, 12433}, {4253, 34753}, {4530, 12735}, {4904, 9318}, {5011, 17747}, {5134, 28178}, {5305, 16583}, {5526, 40663}, {5552, 56536}, {5813, 30808}, {5839, 22147}, {5844, 6603}, {5856, 24346}, {6001, 31896}, {6700, 52528}, {6706, 58442}, {6735, 41391}, {6883, 15288}, {7819, 25994}, {9945, 35342}, {13226, 58036}, {13747, 26690}, {14985, 16562}, {15252, 65813}, {15325, 43065}, {17170, 17675}, {17451, 37737}, {17744, 21031}, {17757, 60355}, {18328, 38690}, {19512, 34852}, {20262, 51755}, {20818, 53994}, {21139, 43057}, {21232, 40534}, {21808, 63282}, {22758, 38902}, {23972, 36205}, {24025, 65814}, {24045, 40273}, {24582, 65195}, {24828, 45282}, {25066, 47742}, {26074, 34122}, {28118, 35273}, {28346, 28850}, {28915, 50441}, {31273, 61673}, {34522, 38028}, {34586, 61224}, {36949, 39470}, {37727, 63592}, {38015, 42018}, {38042, 56746}, {38764, 53804}, {40560, 63793}, {40943, 59649}, {44664, 51775}, {49997, 57019}, {56937, 59591}, {58418, 58898}, {59543, 59613}, {59644, 64121}, {59646, 64125}

X(65808) = midpoint of X(i) and X(j) for these (i, j): {10, 51435}, {101, 1146}, {118, 31852}, {242, 51366}, {910, 5179}, {1565, 3732}, {1566, 34805}, {3234, 44012}, {5011, 17747}, {5199, 53579}, {8074, 40869}, {51406, 61730}
X(65808) = reflection of X(i) in X(j) for these (i, j): (116, 40483), (17044, 6710), (58898, 58418)
X(65808) = complement of X(1565)
X(65808) = crosspoint of X(2) and X(15742)
X(65808) = crosssum of X(6) and X(3937)
X(65808) = X(i)-complementary conjugate of-X(j) for these (i, j): (33, 46100), (59, 34822), (108, 17059), (112, 17761), (162, 53564), (692, 2968), (765, 1368), (1018, 127), (1110, 3), (1252, 18589), (1783, 116), (1897, 21252), (1973, 6547), (2149, 17073), (2212, 46101), (3939, 123), (4557, 34846), (4564, 18639), (5379, 3741), (6065, 34823), (7012, 2886), (7115, 142), (7128, 21258), (8750, 11), (15742, 2887), (23990, 1214), (32656, 55044), (32674, 4904), (32676, 244), (46102, 17046), (56183, 124), (65375, 34588)
X(65808) = center of the inconic with perspector X(15742)
X(65808) = pole of the line {918, 3960} with respect to the Spieker circle
X(65808) = pole of the line {6547, 18455} with respect to the Kiepert circumhyperbola
X(65808) = pole of the line {644, 1783} with respect to the Steiner inellipse
X(65808) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 3732, 1565), (9, 59671, 59680), (101, 61730, 1146), (169, 46835, 5), (650, 13006, 65818), (1111, 26007, 52826), (1146, 51406, 101), (3035, 3039, 24036), (4251, 21049, 12433)

X(65809) = CENTER OF THE BIANTICEVIAN INCONIC OF X(3) AND X(5)

Barycentrics    2*a^8-3*(b^2+c^2)*a^6+(b^4+6*b^2*c^2+c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4 : :
X(65809) = 3*X(2)+X(9308) = 7*X(53)-9*X(36430)

X(65809) lies on these lines: {2, 253}, {3, 393}, {4, 15905}, {5, 6}, {30, 53}, {32, 9825}, {37, 15252}, {39, 63679}, {69, 52251}, {95, 37765}, {115, 44920}, {132, 46700}, {140, 216}, {141, 44334}, {230, 800}, {232, 6676}, {233, 547}, {264, 441}, {297, 41008}, {381, 3087}, {382, 61301}, {401, 56022}, {428, 10313}, {468, 15355}, {523, 58436}, {524, 58408}, {546, 3284}, {548, 22052}, {549, 36751}, {550, 36748}, {570, 3018}, {571, 31833}, {631, 33630}, {632, 52703}, {648, 45198}, {1172, 6831}, {1368, 55415}, {1595, 23115}, {1609, 6644}, {1625, 43917}, {1630, 51421}, {1656, 15851}, {1657, 62195}, {1713, 35466}, {1865, 20420}, {1885, 41890}, {1950, 8735}, {1951, 8736}, {1968, 31829}, {2193, 31789}, {2207, 6823}, {2257, 37695}, {2965, 61656}, {3003, 16238}, {3054, 16306}, {3068, 55887}, {3069, 55892}, {3091, 36413}, {3172, 6815}, {3197, 34030}, {3530, 10979}, {3553, 37696}, {3554, 37697}, {3589, 14767}, {3613, 51744}, {3627, 61315}, {3628, 5158}, {3815, 64852}, {3843, 33636}, {3850, 6749}, {3851, 62213}, {5007, 40136}, {5020, 7735}, {5056, 5702}, {5065, 5254}, {5133, 52058}, {5286, 11479}, {5304, 7392}, {5306, 10128}, {5523, 34664}, {6641, 14569}, {6642, 8573}, {6678, 37646}, {6708, 39595}, {6720, 8368}, {6756, 10316}, {6793, 35283}, {7395, 41361}, {7399, 8743}, {7401, 30435}, {7403, 22120}, {7404, 9605}, {7499, 22240}, {7522, 37642}, {7549, 18685}, {7585, 55881}, {7586, 55882}, {7746, 46432}, {8553, 37814}, {8745, 15760}, {8755, 40937}, {8791, 37454}, {8797, 59373}, {8882, 10317}, {8969, 13567}, {9220, 23323}, {9512, 26926}, {9818, 15048}, {10020, 11062}, {10024, 52418}, {10127, 13345}, {10154, 59229}, {10257, 47162}, {10984, 56866}, {11245, 34965}, {11547, 26906}, {12100, 18487}, {12103, 61314}, {12108, 62196}, {12362, 27376}, {12812, 15860}, {13383, 14576}, {13630, 50671}, {14152, 40402}, {14269, 36427}, {14390, 20265}, {14571, 59671}, {14577, 64472}, {14743, 17278}, {14961, 64474}, {15030, 15341}, {15646, 47322}, {16303, 44452}, {16328, 44234}, {18420, 18907}, {18424, 63821}, {21448, 37689}, {21841, 63634}, {23607, 61355}, {26868, 42215}, {26953, 41516}, {27377, 52247}, {30258, 59661}, {33537, 46829}, {33885, 47093}, {34828, 64781}, {34836, 61658}, {35937, 43980}, {36422, 61810}, {36431, 61858}, {37188, 43981}, {37649, 63175}, {40799, 44156}, {40885, 40897}, {40888, 53481}, {41758, 45735}, {44338, 46115}, {44911, 47168}, {45800, 57529}, {46184, 59702}, {48154, 62701}, {50666, 56370}, {52070, 53416}, {52704, 61894}, {57528, 60106}, {58446, 58464}, {58447, 59662}, {59681, 65813}, {61312, 61790}

X(65809) = midpoint of X(i) and X(j) for these (i, j): {53, 577}, {9308, 41005}
X(65809) = complement of X(41005)
X(65809) = cross-difference of every pair of points on the line X(924)X(42658)
X(65809) = crosspoint of X(2) and X(1105)
X(65809) = crosssum of X(6) and X(185)
X(65809) = X(i)-complementary conjugate of-X(j) for these (i, j): (775, 1368), (821, 21243), (1105, 2887), (41890, 18589), (57414, 20309), (57775, 21235)
X(65809) = center of the inconic with perspector X(1105)
X(65809) = perspector of the circumconic through X(925) and X(53639)
X(65809) = pole of the line {6587, 57065} with respect to the polar circle
X(65809) = pole of the line {3, 47296} with respect to the Evans conic
X(65809) = pole of the line {3, 2929} with respect to the Kiepert circumhyperbola
X(65809) = pole of the line {1993, 15905} with respect to the Stammler hyperbola
X(65809) = pole of the line {450, 2451} with respect to the Steiner inellipse
X(65809) = pole of the line {7763, 37669} with respect to the Steiner-Wallace hyperbola
X(65809) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (2, 9308, 41005), (2, 32000, 20208), (3, 393, 42459), (140, 59649, 216), (216, 1990, 59649), (297, 56290, 41008), (381, 38292, 3087), (1656, 59655, 15851), (3091, 36413, 40065), (3284, 36412, 6748), (6748, 36412, 546), (6749, 61327, 3850), (14767, 23583, 3589), (15252, 59483, 37), (15851, 59655, 40138)

X(65810) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(3) AND X(7)

Barycentrics    (a+b-c)*(a-b+c)*(a^5-(b+c)*a^4-b^2*a^3+b*(b^2+b*c+2*c^2)*a^2+(b^2-c^2)*c^2*a+(b^2-c^2)*(b-c)*c^2)*(a^5-(b+c)*a^4-c^2*a^3+c*(2*b^2+b*c+c^2)*a^2-(b^2-c^2)*b^2*a+(b^2-c^2)*(b-c)*b^2) : :

X(65810) lies on these lines: {7, 6056}, {5249, 26006}, {7411, 23207}, {33765, 62779}

X(65810) = isogonal conjugate of X(42447)
X(65810) = isotomic conjugate of X(65684)
X(65810) = cevapoint of X(i) and X(j) for these {i, j}: {3, 7}, {1086, 44408}
X(65810) = X(i)-cross conjugate of-X(j) for these (i, j): (22160, 651), (65816, 2)
X(65810) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 65684), (1214, 21911), (3160, 16608), (40593, 23581), (40615, 23726)
X(65810) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 65684}, {33, 39796}, {41, 16608}, {2175, 23581}, {2194, 21911}
X(65810) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 65684), (7, 16608), (85, 23581), (222, 39796), (226, 21911), (3676, 23726)
X(65810) = trilinear pole of the line {39470, 57167} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65810) = perspector of the inconic with center X(65816)
X(65810) = pole of the line {42447, 65684} with respect to the Steiner-Wallace hyperbola
X(65810) = trilinear quotient X(i)/X(j) for these (i, j): (75, 65684), (77, 39796), (85, 16608), (1441, 21911), (6063, 23581), (24002, 23726)

X(65811) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(3) AND X(8)

Barycentrics    (a^5+(b-c)*a^4-b^2*a^3-b*(b^2-b*c+2*c^2)*a^2+(b^2-c^2)*c^2*a-(b^2-c^2)*(b+c)*c^2)*(a^5-(b-c)*a^4-c^2*a^3-c*(2*b^2-b*c+c^2)*a^2-(b^2-c^2)*b^2*a+(b^2-c^2)*(b+c)*b^2) : :

X(65811) lies on these lines: {8, 7335}, {404, 23661}, {2975, 4397}, {6735, 7270}, {13136, 40944}

X(65811) = isotomic conjugate of X(41007)
X(65811) = isogonal conjugate of X(42448)
X(65811) = cevapoint of X(i) and X(j) for these {i, j}: {3, 8}, {2968, 57091}
X(65811) = X(i)-cross conjugate of-X(j) for these (i, j): (52307, 13136), (59671, 2)
X(65811) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 41007), (3161, 41883), (11517, 40944), (46398, 65462)
X(65811) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 41007}, {34, 40944}, {604, 41883}
X(65811) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 41007), (8, 41883), (219, 40944), (10015, 65462)
X(65811) = trilinear pole of the line {57042, 57156} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65811) = perspector of the inconic with center X(59671)
X(65811) = pole of the line {41007, 42448} with respect to the Steiner-Wallace hyperbola
X(65811) = trilinear quotient X(i)/X(j) for these (i, j): (75, 41007), (78, 40944), (312, 41883), (36038, 65462)

X(65812) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(3) AND X(10)

Barycentrics    (a^5+b*a^4-(b^2+c^2)*a^3-(b^3+2*b*c^2+c^3)*a^2-(b^2-c^2)*(b+c)*c^2)*(a^5+c*a^4-(b^2+c^2)*a^3-(b^3+2*b^2*c+c^3)*a^2+(b^2-c^2)*(b+c)*b^2) : :

X(65812) lies on these lines: {3, 7141}, {304, 55094}, {5552, 56367}, {7465, 19799}, {44765, 55351}

X(65812) = isogonal conjugate of X(42450)
X(65812) = cevapoint of X(i) and X(j) for these {i, j}: {3, 10}, {20654, 55364}
X(65812) = X(52310)-cross conjugate of-X(44765)
X(65812) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 42440), (4075, 21670), (40591, 55351)
X(65812) = X(i)-isoconjugate of-X(j) for these {i, j}: {28, 55351}, {58, 42440}, {849, 21670}
X(65812) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (37, 42440), (71, 55351), (594, 21670)
X(65812) = trilinear pole of the line {23874, 57042} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65812) = trilinear quotient X(i)/X(j) for these (i, j): (10, 42440), (72, 55351), (1089, 21670)

X(65813) = CENTER OF THE BIANTICEVIAN INCONIC OF X(3) AND X(11)

Barycentrics    2*a^7-2*(b+c)*a^6-(b^2+c^2)*a^5+(b+c)^3*a^4-2*b*c*(b^2+c^2)*a^3-(b^2-c^2)^2*(b-c)^2*a+(b^2-c^2)^3*(b-c) : :

X(65813) lies on these lines: {11, 22144}, {119, 1783}, {906, 5840}, {1146, 1807}, {1951, 5841}, {2006, 5540}, {3035, 65814}, {6713, 7117}, {11499, 17905}, {15252, 65808}, {16869, 31896}, {23583, 36949}, {27076, 40534}, {37696, 46835}, {59681, 65809}

X(65813) = midpoint of X(906) and X(8735)
X(65813) = X(8750)-complementary conjugate of-X(5521)
X(65813) = pole of the line {1783, 53358} with respect to the Steiner inellipse
X(65813) = (X(3035), X(65814))-harmonic conjugate of X(65818)

X(65814) = CENTER OF THE BIANTICEVIAN INCONIC OF X(4) AND X(11)

Barycentrics    2*a^7-2*(b+c)*a^6+(3*b^2-4*b*c+3*c^2)*a^5-3*(b^2-c^2)*(b-c)*a^4-4*(b^3-c^3)*(b-c)*a^3+4*(b^3-c^3)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*a+(b^2-c^2)^3*(b-c) : :

X(65814) lies on these lines: {528, 22144}, {1249, 40117}, {1783, 2829}, {2272, 45929}, {3035, 65813}, {7117, 20418}, {14838, 40555}, {17905, 63980}, {23882, 40561}, {24025, 65808}, {24036, 65824}, {56890, 65104}, {59644, 59649}

X(65814) = (X(65813), X(65818))-harmonic conjugate of X(3035)

X(65815) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(4) AND X(11)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^5-(b+c)*a^4+b^2*a^3-b*(b+2*c)*(b-c)*a^2-(b-c)*(2*b^3-c^3-b*c*(2*b+c))*a+(b^2-c^2)*(b-c)*(2*b^2+c^2))*(a^5-(b+c)*a^4+c^2*a^3+c*(2*b+c)*(b-c)*a^2-(b-c)*(b^3-2*c^3+b*c*(b+2*c))*a+(b^2-c^2)*(b-c)*(b^2+2*c^2)) : :

X(65815) lies on these lines: {1785, 7541}, {55359, 65331}

X(65815) = polar conjugate of X(36949)
X(65815) = cevapoint of X(4) and X(11)
X(65815) = X(52316)-cross conjugate of-X(65331)
X(65815) = X(i)-Dao conjugate of-X(j) for these (i, j): (1249, 36949), (62605, 18689)
X(65815) = X(i)-isoconjugate of-X(j) for these {i, j}: {48, 36949}, {184, 18689}
X(65815) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 36949), (92, 18689), (8735, 55359)
X(65815) = pole of the the tripolar of X(36949) with respect to the polar circle
X(65815) = trilinear quotient X(i)/X(j) for these (i, j): (92, 36949), (264, 18689)

X(65816) = CENTER OF THE BIANTICEVIAN INCONIC OF X(5) AND X(9)

Barycentrics    2*a^6-2*(b+c)*a^5-(b^2+c^2)*a^4+2*(b+c)*(b^2+c^2)*a^3-2*(b^3-c^3)*(b-c)*a^2+(b^2-c^2)^2*(b-c)^2 : :

X(65816) lies on these lines: {1, 3925}, {2, 1897}, {3, 278}, {5, 33}, {7, 22117}, {12, 33178}, {30, 1074}, {34, 37424}, {55, 15253}, {140, 23710}, {142, 59645}, {212, 5762}, {222, 31657}, {255, 24470}, {497, 15251}, {954, 19785}, {1040, 8727}, {1215, 24980}, {1376, 65824}, {1503, 40677}, {1626, 2834}, {1886, 40937}, {2969, 16064}, {3008, 64157}, {3100, 8226}, {3946, 13405}, {4224, 51410}, {4995, 60359}, {5089, 6676}, {5432, 45946}, {5719, 22350}, {5728, 26723}, {5805, 7070}, {6147, 7078}, {6354, 13329}, {6357, 22053}, {6675, 17102}, {6690, 16579}, {6881, 18455}, {6907, 37697}, {6914, 60757}, {6991, 9538}, {7069, 61511}, {7580, 37800}, {7952, 11108}, {9440, 33147}, {10157, 16870}, {11018, 40940}, {11227, 34050}, {16056, 23171}, {17528, 34231}, {18623, 21151}, {20834, 36124}, {31658, 64708}, {31805, 53592}, {32047, 44222}, {33150, 62800}, {37271, 38288}, {38122, 59606}, {49743, 64722}

X(65816) = complement of X(65684)
X(65816) = crosspoint of X(2) and X(65810)
X(65816) = crosssum of X(6) and X(42447)
X(65816) = X(65810)-complementary conjugate of-X(2887)
X(65816) = center of the inconic with perspector X(65810)
X(65816) = pole of the line {39470, 57167} with respect to the Steiner inellipse
X(65816) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (142, 59645, 65702), (1040, 37695, 8727), (31657, 59613, 222)

X(65817) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(5) AND X(9)

Barycentrics    (a^6-(b+c)*a^5-(2*b^2+c^2)*a^4+(2*b^3+2*c^3+b*c*(3*b+c))*a^3+(b-c)*(b^3+2*b^2*c+c^3)*a^2-(b^2-c^2)*(b+c)*(b^2+b*c-c^2)*a-(b^2-c^2)^2*(b-c)*c)*(a^6-(b+c)*a^5-(b^2+2*c^2)*a^4+(2*b^3+2*c^3+b*c*(b+3*c))*a^3-(b-c)*(b^3+2*b*c^2+c^3)*a^2-(b^2-c^2)*(b+c)*(b^2-b*c-c^2)*a+(b^2-c^2)^2*(b-c)*b) : :

X(65817) lies on these lines: {5, 62265}, {5178, 6735}

X(65817) = cevapoint of X(5) and X(9)
X(65817) = X(9)-Dao conjugate of-X(12005)
X(65817) = X(6)-isoconjugate of-X(12005)
X(65817) = X(1)-reciprocal conjugate of-X(12005)
X(65817) = trilinear pole of the line {2804, 57198} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65817) = trilinear quotient X(2)/X(12005)

X(65818) = CENTER OF THE BIANTICEVIAN INCONIC OF X(5) AND X(11)

Barycentrics    a*(2*(b^2-b*c+c^2)*a^4-2*(b^3+c^3)*a^3-(2*b^4+2*c^4-3*b*c*(b^2+c^2))*a^2+2*(b^3-c^3)*(b^2-c^2)*a-(b^2-c^2)^2*b*c) : :

X(65818) lies on these lines: {3, 1783}, {5, 8735}, {100, 22144}, {216, 59671}, {523, 23993}, {607, 6924}, {650, 13006}, {906, 33814}, {952, 7117}, {1565, 24499}, {3035, 65813}, {6958, 17905}, {7124, 32141}, {7359, 22059}, {8608, 15325}, {9945, 61161}, {14838, 17044}, {14936, 34460}, {15252, 65104}, {16573, 36155}, {22070, 61524}, {34586, 61237}, {43063, 52826}

X(65818) = crosssum of X(6) and X(38389)
X(65818) = pole of the line {2427, 57151} with respect to the Steiner inellipse
X(65818) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (650, 13006, 65808), (3035, 65814, 65813)

X(65819) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(6) AND X(11)

Barycentrics    (a^5-(b+c)*a^4+c*(2*b-c)*a^3-c^2*(b-c)*a^2-b^2*(b-c)^2*a+(b^2-c^2)*(b-c)*b^2)*(a^5-(b+c)*a^4-b*(b-2*c)*a^3+b^2*(b-c)*a^2-c^2*(b-c)^2*a+(b^2-c^2)*(b-c)*c^2) : :

X(65819) lies on these lines: {11, 57410}, {238, 1737}, {239, 48380}, {929, 55366}, {1429, 64115}, {52456, 61426}

X(65819) = isogonal conjugate of X(13006)
X(65819) = cevapoint of X(i) and X(j) for these {i, j}: {6, 11}, {650, 34949}
X(65819) = X(i)-cross conjugate of-X(j) for these (i, j): (6, 57410), (52331, 929)
X(65819) = X(i)-Dao conjugate of-X(j) for these (i, j): (650, 46100), (22391, 23198), (40592, 16701)
X(65819) = X(i)-isoconjugate of-X(j) for these {i, j}: {42, 16701}, {92, 23198}, {2149, 46100}, {4564, 55366}
X(65819) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (11, 46100), (81, 16701), (184, 23198), (3271, 55366), (57410, 59)
X(65819) = trilinear pole of the line {659, 14667} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65819) = pole of the line {13006, 16701} with respect to the Steiner-Wallace hyperbola
X(65819) = barycentric product X(34387)*X(57410)
X(65819) = trilinear product X(4858)*X(57410)
X(65819) = trilinear quotient X(i)/X(j) for these (i, j): (48, 23198), (86, 16701), (2170, 55366), (4858, 46100), (57410, 2149)

X(65820) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(7) AND X(10)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+(b-2*c)*a+2*b^2+b*c+c^2)*(a^2-(2*b-c)*a+b^2+b*c+2*c^2) : :

X(65820) lies on these lines: {7, 6057}, {319, 4061}, {1434, 33078}, {3969, 6604}, {4624, 4854}, {17093, 40999}

X(65820) = isotomic conjugate of X(40998)
X(65820) = cevapoint of X(i) and X(j) for these {i, j}: {7, 10}, {3219, 3870}
X(65820) = X(4841)-cross conjugate of-X(4624)
X(65820) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 40998), (10, 42446), (37, 38930), (1214, 4854), (3160, 3946), (4075, 21673), (17113, 10521), (40615, 23729)
X(65820) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 40998}, {41, 3946}, {58, 42446}, {849, 21673}, {1253, 10521}, {1333, 38930}, {2194, 4854}
X(65820) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 40998), (7, 3946), (10, 38930), (37, 42446), (226, 4854), (279, 10521), (594, 21673), (3676, 23729), (38811, 58), (38825, 55), (63191, 1)
X(65820) = trilinear pole of the line {7265, 22042} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65820) = barycentric product X(i)*X(j) for these {i, j}: {75, 63191}, {313, 38811}, {6063, 38825}
X(65820) = trilinear product X(i)*X(j) for these {i, j}: {2, 63191}, {85, 38825}, {321, 38811}
X(65820) = trilinear quotient X(i)/X(j) for these (i, j): (10, 42446), (75, 40998), (85, 3946), (321, 38930), (1088, 10521), (1089, 21673), (1441, 4854), (24002, 23729), (38811, 1333), (38825, 41), (63191, 6)

X(65821) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(7) AND X(11)

Barycentrics    (a+b-c)*(a-b+c)*(a^4-2*b*a^3+(2*b^2-c^2)*a^2-2*(b-c)*(b^2+b*c-c^2)*a+(b^2+2*b*c+2*c^2)*(b-c)^2)*(a^4-2*c*a^3-(b^2-2*c^2)*a^2-2*(b-c)*(b^2-b*c-c^2)*a+(2*b^2+2*b*c+c^2)*(b-c)^2) : :

X(65821) lies on these lines: {7, 5532}, {11, 59457}, {527, 10001}, {18810, 61716}, {55370, 60487}

X(65821) = cevapoint of X(7) and X(11)
X(65821) = X(52334)-cross conjugate of-X(60487)
X(65821) = X(i)-Dao conjugate of-X(j) for these (i, j): (514, 55370), (1214, 21914), (3160, 17044), (40615, 23730)
X(65821) = X(i)-isoconjugate of-X(j) for these {i, j}: {41, 17044}, {1110, 55370}, {2194, 21914}
X(65821) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (7, 17044), (226, 21914), (1086, 55370), (3676, 23730)
X(65821) = trilinear pole of the line {1638, 37771} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65821) = trilinear quotient X(i)/X(j) for these (i, j): (85, 17044), (1111, 55370), (1441, 21914), (24002, 23730)

X(65822) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(8) AND X(10)

Barycentrics    (a^2-(2*b+c)*a+(b+c)*(b-2*c))*(a^2-(b+2*c)*a-(b+c)*(2*b-c)) : :

X(65822) lies on these lines: {1, 56094}, {8, 12}, {10, 1043}, {45, 346}, {75, 62780}, {86, 57833}, {190, 21677}, {313, 25280}, {318, 56285}, {333, 5086}, {341, 1089}, {1222, 4847}, {1268, 27714}, {1826, 2322}, {1837, 17277}, {2550, 56205}, {3626, 4013}, {3696, 4451}, {4651, 14008}, {4678, 6556}, {4691, 6538}, {5229, 17347}, {5260, 56946}, {5794, 14829}, {5827, 48850}, {6734, 40442}, {6736, 56118}, {7270, 63194}, {9578, 49450}, {12447, 37758}, {17272, 40014}, {23352, 28183}, {25446, 37730}, {30606, 37152}, {32087, 56349}, {47033, 56133}, {54288, 63996}, {58132, 59602}

X(65822) = midpoint of X(8) and X(30543)
X(65822) = isotomic conjugate of X(3664)
X(65822) = cevapoint of X(i) and X(j) for these {i, j}: {1, 56288}, {2, 4416}, {8, 10}, {42, 573}, {4061, 62608}
X(65822) = X(i)-cross conjugate of-X(j) for these (i, j): (3700, 190), (63978, 2)
X(65822) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 2646), (2, 3664), (10, 2650), (37, 17056), (115, 23755), (3161, 5745), (4075, 21674), (5452, 21748), (6552, 6737), (6631, 17136), (6741, 62566), (7952, 40950), (11517, 22361), (36103, 40985), (39026, 53324), (40599, 21811), (40603, 18698), (59577, 21677)
X(65822) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 40985}, {31, 3664}, {34, 22361}, {56, 2646}, {57, 21748}, {58, 2650}, {163, 23755}, {407, 1437}, {513, 53324}, {603, 40950}, {604, 5745}, {667, 17136}, {849, 21674}, {1106, 6737}, {1333, 17056}, {1408, 21677}, {1412, 21811}, {2206, 18698}, {2217, 37836}, {22003, 57129}, {43924, 53388}
X(65822) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 3664), (8, 5745), (9, 2646), (10, 17056), (19, 40985), (37, 2650), (55, 21748), (101, 53324), (190, 17136), (210, 21811), (219, 22361), (281, 40950), (321, 18698), (346, 6737), (523, 23755), (573, 37836), (594, 21674), (644, 53388), (1089, 42708), (1826, 407), (2321, 21677), (3700, 62566), (3952, 22003), (4416, 59602), (4931, 30604), (17097, 57), (40430, 81), (40442, 222), (56321, 514), (57668, 1790), (57833, 17206), (60235, 86), (63194, 1014)
X(65822) = trilinear pole of the line {3239, 4024} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65822) = perspector of the inconic with center X(63978)
X(65822) = barycentric product X(i)*X(j) for these {i, j}: {10, 60235}, {190, 56321}, {312, 17097}, {321, 40430}, {1826, 57833}, {3701, 63194}, {7017, 40442}
X(65822) = trilinear product X(i)*X(j) for these {i, j}: {8, 17097}, {10, 40430}, {37, 60235}, {100, 56321}, {318, 40442}, {1824, 57833}, {2321, 63194}, {41013, 57668}
X(65822) = trilinear quotient X(i)/X(j) for these (i, j): (4, 40985), (8, 2646), (9, 21748), (10, 2650), (75, 3664), (78, 22361), (100, 53324), (312, 5745), (313, 18698), (318, 40950), (321, 17056), (341, 6737), (668, 17136), (1089, 21674), (1577, 23755), (2321, 21811), (3699, 53388), (3701, 21677), (3869, 37836), (4033, 22003)

X(65823) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(8) AND X(11)

Barycentrics    (-a+b+c)*(a^2-2*b*a+2*b^2-2*b*c+c^2)*(a^2-2*c*a+b^2-2*b*c+2*c^2) : :

X(65823) lies on these lines: {8, 7336}, {11, 4076}, {519, 1738}, {4385, 51975}, {4582, 55376}, {4723, 59415}, {5082, 21306}, {6079, 26073}, {52746, 62540}

X(65823) = cevapoint of X(i) and X(j) for these {i, j}: {8, 11}, {4543, 54270}
X(65823) = X(i)-cross conjugate of-X(j) for these (i, j): (30731, 4997), (52338, 4582)
X(65823) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 3722), (11, 6161), (522, 55376), (650, 6547), (1146, 6546), (3161, 4422), (7952, 1862), (51402, 33905), (62585, 4986)
X(65823) = X(i)-isoconjugate of-X(j) for these {i, j}: {56, 3722}, {109, 6161}, {603, 1862}, {604, 4422}, {1397, 4986}, {1415, 6546}, {2149, 6547}, {24027, 55376}, {32094, 57181}, {43924, 46973}
X(65823) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (8, 4422), (9, 3722), (11, 6547), (281, 1862), (312, 4986), (522, 6546), (644, 46973), (650, 6161), (1146, 55376), (1639, 33905), (3699, 32094), (46972, 57), (58373, 3669), (62540, 664)
X(65823) = pole of the line {190, 24795} with respect to the circumhyperbola dual of Yff parabola
X(65823) = barycentric product X(i)*X(j) for these {i, j}: {312, 46972}, {522, 62540}, {646, 58373}
X(65823) = trilinear product X(i)*X(j) for these {i, j}: {8, 46972}, {650, 62540}, {3699, 58373}
X(65823) = trilinear quotient X(i)/X(j) for these (i, j): (8, 3722), (312, 4422), (318, 1862), (522, 6161), (646, 32094), (3596, 4986), (3699, 46973), (4391, 6546), (4768, 33905), (4858, 6547), (24026, 55376), (46972, 56), (58373, 43924), (62540, 651)

X(65824) = CENTER OF THE BIANTICEVIAN INCONIC OF X(9) AND X(11)

Barycentrics    (-a+b+c)*(2*a^4-2*(b+c)*a^3+(b^2+c^2)*a^2-(b-c)^4) : :

X(65824) lies on these lines: {3, 2834}, {100, 15253}, {142, 30621}, {522, 4422}, {528, 15251}, {651, 10427}, {676, 2804}, {1086, 3939}, {1331, 24465}, {1376, 65816}, {1633, 51419}, {2310, 64738}, {2323, 61035}, {3008, 15733}, {4000, 6600}, {5723, 35338}, {5834, 47042}, {5857, 13329}, {6174, 45946}, {17059, 40480}, {17061, 59584}, {17278, 64443}, {17356, 24388}, {17366, 64739}, {17724, 61222}, {19512, 44670}, {24036, 65814}, {24980, 36949}, {24988, 65206}, {31657, 45729}, {33814, 60757}, {40560, 63793}

X(65824) = midpoint of X(1086) and X(3939)
X(65824) = reflection of X(17059) in X(40480)
X(65824) = X(i)-complementary conjugate of-X(j) for these (i, j): (109, 5511), (1292, 124), (1415, 40615), (2191, 46100), (24027, 6600), (63906, 21244)
X(65824) = center of the central inconic through X(1617) and X(6601)
X(65824) = pole of the line {9521, 19915} with respect to the circumcircle
X(65824) = pole of the line {651, 2428} with respect to the Steiner inellipse
X(65824) = (X(3035), X(59458))-harmonic conjugate of X(16578)

X(65825) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(9) AND X(11)

Barycentrics    (-a+b+c)*(a^3-2*b*a^2+b^2*a+c*(b-c)^2)*(a^3-2*c*a^2+c^2*a+b*(b-c)^2) : :

X(65825) lies on these lines: {11, 6065}, {908, 3008}, {5853, 6735}, {26003, 60355}, {55380, 60488}

X(65825) = cevapoint of X(9) and X(11)
X(65825) = X(23704)-cross conjugate of-X(14942)
X(65825) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 24036), (9, 5083)
X(65825) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 5083}, {56, 24036}, {1262, 55380}
X(65825) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1, 5083), (9, 24036), (2310, 55380)
X(65825) = trilinear pole of the line {2804, 15914} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65825) = trilinear quotient X(i)/X(j) for these (i, j): (2, 5083), (8, 24036), (1146, 55380)

X(65826) = PERSPECTOR OF THE BIANTICEVIAN INCONIC OF X(10) AND X(11)

Barycentrics    ((b+c)*a^3-2*(b^2+c^2)*a^2+(b^3+2*b*c^2-c^3)*a+(b^2-c^2)*c*(b-2*c))*((b+c)*a^3-2*(b^2+c^2)*a^2-(b^3-2*b^2*c-c^3)*a+(b^2-c^2)*b*(2*b-c)) : :

X(65826) lies on these lines: {1737, 24231}, {5818, 14266}, {26074, 44184}, {50039, 55382}

X(65826) = cevapoint of X(10) and X(11)
X(65826) = X(52341)-cross conjugate of-X(50039)
X(65826) = X(i)-Dao conjugate of-X(j) for these (i, j): (4075, 21676), (62566, 55382)
X(65826) = X(849)-isoconjugate of-X(21676)
X(65826) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (594, 21676), (21044, 55382)
X(65826) = trilinear pole of the line {22035, 23887} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65826) = trilinear quotient X(1089)/X(21676)

X(65827) = PERSPECTOR OF THE BIPEDAL INCONIC OF X(13) OR X(15)

Barycentrics    -2*(9*(b^2+c^2)*a^4-(4*b^2-c^2)*(b^2-4*c^2)*a^2-(b^4-c^4)*(b^2-c^2))*sqrt(3)*S+6*a^8-9*(b^2+c^2)*a^6-7*(b^4+7*b^2*c^2+c^4)*a^4+(b^2+c^2)*(13*b^4-29*b^2*c^2+13*c^4)*a^2-(3*b^4-8*b^2*c^2+3*c^4)*(b^2-c^2)^2 : :

X(65827) lies on these lines: {530, 16267}, {11537, 37640}

X(65827) = trilinear pole of the line {9123, 9200} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line

X(65828) = PERSPECTOR OF THE BIPEDAL INCONIC OF X(14) OR X(16)

Barycentrics    2*(9*(b^2+c^2)*a^4-(4*b^2-c^2)*(b^2-4*c^2)*a^2-(b^4-c^4)*(b^2-c^2))*sqrt(3)*S+6*a^8-9*(b^2+c^2)*a^6-7*(b^4+7*b^2*c^2+c^4)*a^4+(b^2+c^2)*(13*b^4-29*b^2*c^2+13*c^4)*a^2-(3*b^4-8*b^2*c^2+3*c^4)*(b^2-c^2)^2 : :

X(65828) lies on these lines: {531, 16268}, {11549, 37641}

X(65828) = trilinear pole of the line {9123, 9201} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line

X(65829) = CENTER OF THE BIPEDAL INCONIC OF X(20) OR X(64)

Barycentrics    (b^2-c^2)*(-a^2+b^2+c^2)^2*(a^6-3*(b^2-c^2)^2*a^2+2*(b^4-c^4)*(b^2-c^2)) : :
X(65829) = X(647)+3*X(23616) = X(850)-9*X(34767)

X(65829) lies on these lines: {264, 850}, {520, 3265}, {525, 7658}, {647, 23616}, {14417, 58796}, {30209, 44870}, {30476, 38240}, {31277, 52720}

X(65829) = crosssum of X(32713) and X(57153)
X(65829) = X(34403)-Ceva conjugate of-X(15526)
X(65829) = X(i)-Dao conjugate of-X(j) for these (i, j): (1562, 1249), (15526, 18848), (26958, 52913), (35071, 41894)
X(65829) = X(i)-isoconjugate of-X(j) for these {i, j}: {18848, 32676}, {24000, 46005}, {24019, 41894}
X(65829) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (520, 41894), (525, 18848), (1204, 112), (3269, 46005), (5895, 57219), (14638, 34410), (18691, 823), (26958, 107), (37197, 6529), (40995, 648), (46432, 32713)
X(65829) = perspector of the circumconic through X(3926) and X(35510)
X(65829) = pole of the line {1495, 3079} with respect to the polar circle
X(65829) = pole of the line {340, 5059} with respect to the Steiner circumellipse
X(65829) = pole of the line {20, 6389} with respect to the Steiner inellipse
X(65829) = barycentric product X(i)*X(j) for these {i, j}: {525, 40995}, {1204, 3267}, {3265, 26958}, {4143, 37197}, {5895, 14638}, {18691, 24018}, {46432, 52617}
X(65829) = trilinear product X(i)*X(j) for these {i, j}: {520, 18691}, {656, 40995}, {1204, 14208}, {24018, 26958}
X(65829) = trilinear quotient X(i)/X(j) for these (i, j): (1204, 32676), (2632, 46005), (14208, 18848), (18691, 107), (24018, 41894), (26958, 24019), (40995, 162)

X(65830) = CENTER OF THE BIANTIPEDAL INCONIC OF X(2) OR X(6)

Barycentrics    (a^2-3*b^2-c^2)*(a^2-b^2-3*c^2)*(12*a^6+15*(b^2+c^2)*a^4-2*(5*b^4-16*b^2*c^2+5*c^4)*a^2-(b^4-c^4)*(b^2-c^2)) : :

X(65830) lies on these lines: {2, 43956}, {30, 10516}

X(65830) = complement of X(43956)

X(65831) = CENTER OF THE BICIRCUMCEVIAN INCONIC OF X(1) AND X(6)

Barycentrics    a^2*(b-c)*(4*(b+c)*a^3+2*(b^2+3*b*c+c^2)*a^2-2*(b+c)*(b^2+c^2)*a-b^2*c^2) : :

X(65831) lies on these lines: {386, 8643}, {1125, 28470}, {1960, 48030}, {4401, 59301}

X(65832) = PERSPECTOR OF THE BICIRCUMCEVIAN INCONIC OF X(1) AND X(6)

Barycentrics    a^2*(a-b)*(a-c)*(2*b*a+c^2)*(2*c*a+b^2) : :

X(65832) lies on these lines: {6, 30650}, {649, 4604}, {17277, 57948}

X(65832) = isogonal conjugate of X(4379)
X(65832) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 4411), (5375, 3761), (5452, 4474), (8054, 4403), (32664, 4378), (39026, 4363), (39029, 4508)
X(65832) = X(i)-isoconjugate of-X(j) for these {i, j}: {2, 4378}, {6, 4411}, {57, 4474}, {100, 4403}, {244, 4482}, {291, 4508}, {513, 4363}, {514, 750}, {649, 3761}, {650, 7223}, {659, 7245}, {693, 2242}, {876, 4396}, {1022, 62659}, {1635, 4510}, {3572, 4495}, {3676, 4390}, {3733, 4377}, {4410, 50344}, {4494, 43924}, {4503, 4581}, {4506, 23345}, {23352, 29908}
X(65832) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (1, 4411), (31, 4378), (55, 4474), (100, 3761), (101, 4363), (109, 7223), (644, 4494), (649, 4403), (692, 750), (751, 693), (813, 7245), (901, 4510), (1018, 4377), (1023, 4506), (1252, 4482), (1914, 4508), (3573, 4495), (23344, 62659), (30650, 514), (32739, 2242), (35342, 4410), (57948, 40495)
X(65832) = X(6)-vertex conjugate of-X(4604)
X(65832) = trilinear pole of the line {869, 902} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65832) = pole of the line {4379, 4396} with respect to the Stammler hyperbola
X(65832) = barycentric product X(i)*X(j) for these {i, j}: {100, 751}, {190, 30650}, {692, 57948}
X(65832) = trilinear product X(i)*X(j) for these {i, j}: {100, 30650}, {101, 751}, {32739, 57948}
X(65832) = trilinear quotient X(i)/X(j) for these (i, j): (2, 4411), (6, 4378), (9, 4474), (100, 4363), (101, 750), (190, 3761), (238, 4508), (513, 4403), (651, 7223), (660, 7245), (692, 2242), (751, 514), (765, 4482), (1023, 62659), (3257, 4510), (3570, 4495), (3573, 4396), (3699, 4494), (3939, 4390), (3952, 4377)

X(65833) = CENTER OF THE BICIRCUMCEVIAN INCONIC OF X(1) AND X(8)

Barycentrics    a^2*(b-c)*((b+c)*a^3-(b^2+8*b*c+c^2)*a^2-(b+c)*(b^2-8*b*c+c^2)*a+b^4+c^4-b*c*(2*b^2+3*b*c+2*c^2)) : :

X(65833) lies on these lines: {2821, 65428}, {3309, 58679}, {3884, 28576}

X(65834) = CENTER OF THE BICIRCUMCEVIAN INCONIC OF X(1) AND X(9)

Barycentrics    a*(b-c)*(5*a^5-5*(b+c)*a^4-4*(b+c)^2*a^3+4*(b+c)*(b^2+b*c+c^2)*a^2-(b^2+c^2)*(b^2+4*b*c+c^2)*a+(b^2-c^2)^2*(b+c)) : :

X(65834) lies on these lines: {3, 59835}, {3309, 5248}, {4162, 62871}, {53287, 65392}

X(65835) = PERSPECTOR OF THE BICIRCUMCEVIAN INCONIC OF X(2) AND X(3)

Barycentrics    (a^2-b^2)*(a^2-c^2)*((2*b^2+c^2)*a^6-(b^2-c^2)*(4*b^2-3*c^2)*a^4+(b^2-c^2)*(2*b^4+9*b^2*c^2-3*c^4)*a^2+(b^2-c^2)^3*c^2)*((b^2+2*c^2)*a^6-(b^2-c^2)*(3*b^2-4*c^2)*a^4+(b^2-c^2)*(3*b^4-9*b^2*c^2-2*c^4)*a^2-(b^2-c^2)^3*b^2) : :

X(65835) lies on the Steiner circumellipse and these lines: {2, 54988}, {648, 46587}, {671, 2790}, {1494, 57488}, {1992, 54973}, {2404, 6528}, {47383, 54975}

X(65835) = reflection of X(54988) in X(2)
X(65835) = X(36830)-Dao conjugate of-X(37480)
X(65835) = X(i)-isoconjugate of-X(j) for these {i, j}: {661, 37480}, {822, 41372}
X(65835) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (107, 41372), (110, 37480)
X(65835) = trilinear pole of the line {2, 5656} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65835) = pole of the the tripolar of X(37480) with respect to the Stammler hyperbola
X(65835) = trilinear quotient X(i)/X(j) for these (i, j): (662, 37480), (823, 41372)

X(65836) = PERSPECTOR OF THE BICIRCUMCEVIAN INCONIC OF X(2) AND X(6)

Barycentrics    a^2*(a^2-b^2)*(a^2-c^2)*(2*b^2*a^2+c^4)*(2*c^2*a^2+b^4) : :

X(65836) lies on these lines: {6, 44557}, {512, 35138}, {5468, 62412}

X(65836) = cevapoint of X(512) and X(5640)
X(65836) = X(36830)-Dao conjugate of-X(3734)
X(65836) = X(661)-isoconjugate of-X(3734)
X(65836) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (110, 3734), (44557, 523)
X(65836) = X(6)-vertex conjugate of-X(35138)
X(65836) = trilinear pole of the line {187, 353} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65836) = pole of the the tripolar of X(3734) with respect to the Stammler hyperbola
X(65836) = barycentric product X(99)*X(44557)
X(65836) = trilinear product X(662)*X(44557)
X(65836) = trilinear quotient X(i)/X(j) for these (i, j): (662, 3734), (44557, 661)

X(65837) = PERSPECTOR OF THE BICIRCUMCEVIAN INCONIC OF X(3) AND X(4)

Barycentrics    (a^2-b^2)*(a^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((2*b^2-c^2)*a^2-(b^2-c^2)*c^2)*((b^2-2*c^2)*a^2-(b^2-c^2)*b^2) : :

X(65837) lies on these lines: {4, 9292}, {512, 6528}, {877, 39469}, {1624, 4230}, {2790, 5186}, {5895, 9289}, {57219, 58070}

X(65837) = isogonal conjugate of X(22089)
X(65837) = polar conjugate of X(30476)
X(65837) = isotomic conjugate of the anticomplement of X(62176)
X(65837) = cevapoint of X(i) and X(j) for these {i, j}: {4, 512}, {523, 23332}, {1368, 8057}, {2883, 58342}
X(65837) = crosssum of X(2524) and X(42658)
X(65837) = X(i)-cross conjugate of-X(j) for these (i, j): (512, 9292), (2491, 16081), (3221, 25), (8651, 393), (41678, 107), (62176, 2)
X(65837) = X(i)-Dao conjugate of-X(j) for these (i, j): (1015, 16758), (1249, 30476), (2679, 57294), (3162, 2451), (5190, 21137), (6523, 16229), (14091, 17773), (36103, 17478), (39052, 1958), (39062, 1975), (40596, 9306), (62605, 17893)
X(65837) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 17478}, {48, 30476}, {63, 2451}, {101, 16758}, {184, 17893}, {228, 17215}, {255, 16229}, {520, 1957}, {647, 1958}, {656, 9306}, {810, 1975}, {822, 9308}, {906, 21137}, {1437, 21050}, {1968, 24018}, {36036, 57294}
X(65837) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (4, 30476), (19, 17478), (25, 2451), (27, 17215), (92, 17893), (107, 9308), (112, 9306), (162, 1958), (235, 17773), (393, 16229), (513, 16758), (648, 1975), (1826, 21050), (2491, 57294), (4230, 56437), (7649, 21137), (9255, 24018), (9258, 656), (9289, 3265), (9292, 647), (9307, 525), (24019, 1957), (32713, 1968), (41678, 59527), (43188, 69), (51336, 520), (58070, 15143)
X(65837) = X(i)-vertex conjugate of-X(j) for these {i, j}: {3, 6528}, {18831, 32661}, {44828, 44828}
X(65837) = trilinear pole of the line {232, 800} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65837) = perspector of the inconic with center X(62176)
X(65837) = pole of the line {21137, 57294} with respect to the polar circle
X(65837) = pole of the line {154, 3164} with respect to the Kiepert parabola
X(65837) = barycentric product X(i)*X(j) for these {i, j}: {4, 43188}, {107, 9289}, {648, 9307}, {811, 9258}, {823, 9255}, {6331, 9292}, {6528, 51336}
X(65837) = trilinear product X(i)*X(j) for these {i, j}: {19, 43188}, {107, 9255}, {162, 9307}, {648, 9258}, {811, 9292}, {823, 51336}, {9289, 24019}
X(65837) = trilinear quotient X(i)/X(j) for these (i, j): (4, 17478), (19, 2451), (92, 30476), (107, 1957), (158, 16229), (162, 9306), (264, 17893), (286, 17215), (514, 16758), (648, 1958), (811, 1975), (823, 9308), (9255, 520), (9258, 647), (9289, 24018), (9292, 810), (9307, 656), (17924, 21137), (24019, 1968), (41013, 21050)

X(65838) = CENTER OF THE BICIRCUMCEVIAN INCONIC OF X(3) AND X(5)

Barycentrics    (b^2-c^2)*(2*a^8-5*(b^2+c^2)*a^6+2*(2*b^4+3*b^2*c^2+2*c^4)*a^4-(b^6+c^6)*a^2-(b^2-c^2)^2*b^2*c^2) : :

X(65838) lies on these lines: {3, 15412}, {5, 27363}, {30, 15451}, {140, 18314}, {523, 15646}, {826, 10610}, {1510, 30481}, {8673, 65389}, {13349, 23873}, {13350, 23872}, {20577, 42731}, {38613, 38618}

X(65838) = midpoint of X(3) and X(15412)
X(65838) = reflection of X(i) in X(j) for these (i, j): (5, 63830), (18314, 140)
X(65838) = pole of the line {10224, 32428} with respect to the nine-point circle

X(65839) = PERSPECTOR OF THE BICIRCUMCEVIAN INCONIC OF X(3) AND X(6)

Barycentrics    a^2*(a^2-b^2)*(a^2-c^2)*(a^4+2*(3*b^2-2*c^2)*a^2+(b^2-c^2)*(b^2-3*c^2))*(a^4-2*(2*b^2-3*c^2)*a^2+(b^2-c^2)*(3*b^2-c^2)) : :

X(65839) lies on these lines: {647, 65322}, {2847, 35906}, {51937, 52699}

X(65839) = X(36830)-Dao conjugate of-X(32817)
X(65839) = X(i)-isoconjugate of-X(j) for these {i, j}: {661, 32817}, {1577, 6090}
X(65839) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (110, 32817), (1576, 6090), (23347, 15144), (44556, 850)
X(65839) = X(6)-vertex conjugate of-X(65322)
X(65839) = trilinear pole of the line {1384, 1495} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65839) = pole of the the tripolar of X(32817) with respect to the Stammler hyperbola
X(65839) = barycentric product X(110)*X(44556)
X(65839) = trilinear product X(163)*X(44556)
X(65839) = trilinear quotient X(i)/X(j) for these (i, j): (163, 6090), (662, 32817), (44556, 1577), (56829, 15144)

X(65840) = CENTER OF THE BICIRCUMCEVIAN INCONIC OF X(3) AND X(8)

Barycentrics    a*(b-c)*((b+c)*a^7-2*(b^2+6*b*c+c^2)*a^6-(b+c)*(b^2-20*b*c+c^2)*a^5+2*(2*b^4-19*b^2*c^2+2*c^4)*a^4-(b+c)*(b^4+c^4+2*b*c*(8*b^2-19*b*c+8*c^2))*a^3-2*(b-c)^2*(b^4+c^4-4*b*c*(b^2+3*b*c+c^2))*a^2+(b^2-c^2)*(b-c)*(b^4+c^4-2*b*c*(b^2+5*b*c+c^2))*a+2*(b^2-c^2)^2*b^2*c^2) : :

X(65840) lies on these lines: {928, 5882}, {944, 53549}, {3309, 30719}, {5836, 44819}, {7967, 53550}

X(65840) = midpoint of X(944) and X(53549)
X(65840) = reflection of X(5836) in X(44819)

X(65841) = CENTER OF THE BICIRCUMCEVIAN INCONIC OF X(4) AND X(5)

Barycentrics    (b^2-c^2)*(2*a^8-3*(b^2+c^2)*a^6-(b^4+c^4)*a^4+(b^2+c^2)*(3*b^4-5*b^2*c^2+3*c^4)*a^2-(b^4+c^4)*(b^2-c^2)^2) : :
X(65841) = 3*X(1116)-2*X(39512)

X(65841) lies on these lines: {4, 18335}, {512, 24978}, {690, 18314}, {826, 53345}, {1116, 39504}, {1658, 39481}, {7927, 62438}, {10254, 18308}, {34964, 42732}, {50548, 53365}

X(65841) = pole of the line {54, 32152} with respect to the 1st Brocard circle
X(65841) = pole of the line {5965, 8537} with respect to the polar circle

X(65842) = CENTER OF THE BICIRCUMANTICEVIAN INCONIC OF X(1) AND X(9)

Barycentrics    a*(b-c)*(3*a^5-3*(b+c)*a^4-4*(b^2+c^2)*a^3+4*(b+c)*(b^2+b*c+c^2)*a^2+(b^4+c^4-2*b*c*(2*b^2+3*b*c+2*c^2))*a-(b^2-c^2)^2*(b+c)) : :

X(65842) lies on these lines: {35, 18344}, {3309, 6796}, {3887, 6050}, {3900, 52739}, {4040, 7634}, {4091, 14392}, {5218, 17924}, {8678, 48386}, {9373, 39476}, {20317, 50366}

X(65842) = midpoint of X(4040) and X(7634)

X(65843) = CENTER OF THE BICIRCUMANTICEVIAN INCONIC OF X(2) AND X(4)

Barycentrics    (b^2-c^2)*(5*a^8-8*(b^2+c^2)*a^6+2*(b^4+6*b^2*c^2+c^4)*a^4-2*b^2*c^2*(b^2+c^2)*a^2+(b^4+c^4)*(b^2-c^2)^2) : :

X(65843) lies on these lines: {20, 525}, {26, 39201}, {186, 39228}, {512, 57154}, {523, 44246}, {2848, 52584}, {3542, 44705}, {11799, 59745}, {18531, 18556}, {39510, 44958}, {44810, 57065}

X(65843) = reflection of X(i) in X(j) for these (i, j): (57065, 44810), (59932, 39228)

X(65844) = CENTER OF THE BICIRCUMANTICEVIAN INCONIC OF X(5) AND X(6)

Barycentrics    (b^2-c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^10-4*(b^2+c^2)*a^8+(6*b^4+7*b^2*c^2+6*c^4)*a^6-(b^2+c^2)*(2*b^2-3*b*c+2*c^2)*(2*b^2+3*b*c+2*c^2)*a^4+(b^6+c^6)*(b^2+c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2) : :

X(65844) lies on these lines: {68, 58756}, {129, 33330}, {297, 525}, {343, 63829}, {36472, 46655}, {41587, 51513}

X(65844) = complement of the isotomic conjugate of X(65845)
X(65844) = crosspoint of X(2) and X(65845)
X(65844) = X(i)-complementary conjugate of-X(j) for these (i, j): (925, 21231), (1087, 46655), (1820, 2972), (1953, 136), (2179, 39013), (32734, 16577), (36145, 140), (56272, 21253), (61363, 16595), (65251, 3819), (65845, 2887)
X(65844) = center of the inconic with perspector X(65845)
X(65844) = pole of the line {5, 45793} with respect to the Steiner inellipse

X(65845) = PERSPECTOR OF THE BICIRCUMANTICEVIAN INCONIC OF X(5) AND X(6)

Barycentrics    (a^4-2*b^2*a^2+(b^2-c^2)^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^4-2*c^2*a^2+(b^2-c^2)^2)*(a^2-c^2)*(a^2-b^2)/a^2 : :

X(65845) lies on these lines: {5, 41213}, {68, 25051}, {94, 5392}, {648, 30450}, {655, 65251}, {847, 8754}, {925, 23181}, {1972, 20563}, {35139, 64516}

X(65845) = isotomic conjugate of the anticomplement of X(65844)
X(65845) = cevapoint of X(i) and X(j) for these {i, j}: {5, 52317}, {343, 18314}
X(65845) = X(30450)-Ceva conjugate of-X(14570)
X(65845) = X(i)-cross conjugate of-X(j) for these (i, j): (12077, 847), (23290, 311), (52317, 5), (65844, 2)
X(65845) = X(i)-Dao conjugate of-X(j) for these (i, j): (5, 30451), (137, 47421), (139, 34338), (216, 924), (6663, 52317), (14363, 6753), (34853, 2623), (40588, 34952), (52032, 52584), (52869, 14397)
X(65845) = X(i)-isoconjugate of-X(j) for these {i, j}: {47, 2623}, {54, 55216}, {571, 2616}, {924, 2148}, {1748, 58308}, {2167, 34952}, {2169, 6753}, {2190, 30451}, {6563, 62269}, {8882, 63832}, {36134, 47421}, {52584, 62268}, {54034, 63827}, {57065, 62267}
X(65845) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (5, 924), (51, 34952), (53, 6753), (68, 23286), (91, 2616), (216, 30451), (311, 6563), (324, 57065), (343, 52584), (467, 15423), (925, 54), (1154, 44808), (1625, 571), (1953, 55216), (2165, 2623), (2351, 58308), (2617, 47), (5392, 15412), (12077, 47421), (14213, 63827), (14570, 1993), (14576, 58760), (14593, 58756), (18180, 34948), (20563, 62428), (23181, 1147), (23290, 136), (30450, 275), (32734, 54034), (35360, 24), (36145, 2148), (36412, 52317), (41587, 63959), (44174, 15958), (44706, 63832), (45793, 63829), (46134, 95), (52317, 39013), (52604, 44077), (52945, 14397), (55215, 62276), (55549, 46088), (56272, 523), (61193, 8745), (61194, 52436), (61363, 39201), (65176, 8882), (65183, 11547), (65251, 2167), (65309, 97)
X(65845) = trilinear pole of the line {5, 45793} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65845) = perspector of the inconic with center X(65844)
X(65845) = pole of the line {34338, 47421} with respect to the polar circle
X(65845) = barycentric product X(i)*X(j) for these {i, j}: {5, 46134}, {99, 56272}, {311, 925}, {324, 65309}, {343, 30450}, {1625, 57904}, {1953, 55215}, {2617, 20571}, {5392, 14570}, {14213, 65251}, {20563, 35360}, {23181, 55553}, {23290, 57763}, {28706, 65176}, {32734, 62278}, {36145, 62272}, {45793, 65273}, {52350, 65183}
X(65845) = trilinear product X(i)*X(j) for these {i, j}: {5, 65251}, {51, 55215}, {91, 14570}, {311, 36145}, {662, 56272}, {925, 14213}, {1087, 65273}, {1625, 20571}, {1953, 46134}, {2617, 5392}, {18695, 65176}, {23181, 57716}, {30450, 44706}, {32734, 62272}, {57973, 61363}
X(65845) = trilinear quotient X(i)/X(j) for these (i, j): (5, 55216), (91, 2623), (311, 63827), (343, 63832), (925, 2148), (1087, 52317), (1820, 58308), (1953, 34952), (2617, 571), (2618, 47421), (5392, 2616), (14213, 924), (14570, 47), (15415, 17881), (17167, 34948), (18695, 52584), (20571, 15412), (23181, 563), (30450, 2190), (32734, 62269)
X(65845) = (X(30450), X(46134))-harmonic conjugate of X(65309)

X(65846) = CENTER OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(7)

Barycentrics    (b-c)*((b+c)*a^5-(3*b^2+2*b*c+3*c^2)*a^4+(b+c)*(3*b^2-2*b*c+3*c^2)*a^3-(b^4+c^4)*a^2+2*b^2*c^2*(b-c)^2) : :

X(65846) lies on these lines: {2, 52614}, {85, 65705}, {522, 676}, {665, 60490}, {928, 2140}, {3716, 24285}, {3739, 53573}, {6366, 6706}, {6607, 46399}, {10015, 24774}, {10581, 52621}, {14377, 52730}, {21195, 24720}, {24775, 24792}, {24782, 24793}, {30949, 53550}, {31250, 54266}, {52739, 55161}, {53300, 62383}

X(65846) = midpoint of X(i) and X(j) for these (i, j): {85, 65705}, {10581, 52621}
X(65846) = complement of X(52614)
X(65846) = cross-difference of every pair of points on the line X(3207)X(35215)
X(65846) = crosspoint of X(2) and X(65847)
X(65846) = X(i)-complementary conjugate of-X(j) for these (i, j): (57, 1566), (105, 13609), (269, 35094), (604, 39014), (658, 120), (673, 5514), (927, 3452), (934, 16593), (1438, 35508), (1461, 6184), (1462, 1146), (1814, 40616), (4569, 20540), (4617, 50441), (4626, 17060), (4637, 8299), (7045, 62552), (9503, 57292), (32735, 1212), (34018, 124), (34085, 1329), (36086, 6554), (36146, 9), (39293, 20317), (46135, 21244), (53538, 35509), (56783, 26932), (65301, 34823), (65847, 2887)
X(65846) = center of the inconic with perspector X(65847)
X(65846) = pole of the line {1146, 4147} with respect to the circumhyperbola dual of Yff parabola
X(65846) = pole of the line {7, 2481} with respect to the Steiner inellipse

X(65847) = PERSPECTOR OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(7)

Barycentrics    (a-b)*(a-c)*(a^2-c*a+b*(b-c))*(a^2-b*a-c*(b-c))*(a+b-c)^2*(a-b+c)^2/a^2 : :

X(65847) lies on these lines: {7, 15615}, {658, 34085}, {664, 4449}, {2481, 62744}, {4554, 4885}, {4569, 53227}, {4573, 18199}, {18031, 52156}, {34018, 57537}, {36838, 57581}, {56667, 57880}

X(65847) = isotomic conjugate of X(52614)
X(65847) = cevapoint of X(i) and X(j) for these {i, j}: {7, 665}, {2481, 28132}
X(65847) = X(i)-cross conjugate of-X(j) for these (i, j): (665, 7), (28132, 2481), (34085, 46135), (45902, 52030), (65846, 2)
X(65847) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 52614), (223, 46388), (478, 8638), (3160, 926), (10001, 2340), (17113, 665), (33675, 3900), (38989, 39014), (62554, 8641), (62599, 657)
X(65847) = X(46135)-hirst inverse of-X(46406)
X(65847) = X(i)-isoconjugate of-X(j) for these {i, j}: {9, 8638}, {31, 52614}, {41, 926}, {55, 46388}, {657, 2223}, {665, 1253}, {672, 8641}, {1025, 61050}, {1458, 57180}, {2254, 14827}, {2340, 3063}, {2356, 65102}, {3239, 9455}, {3900, 9454}, {4105, 52635}, {6602, 53539}, {7079, 23225}, {9447, 50333}, {14936, 54325}, {21789, 39258}, {36086, 39014}
X(65847) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 52614), (7, 926), (56, 8638), (57, 46388), (105, 8641), (279, 665), (294, 57180), (479, 53539), (658, 672), (664, 2340), (665, 39014), (666, 220), (673, 657), (884, 61050), (885, 3022), (919, 14827), (927, 55), (934, 2223), (1020, 39258), (1088, 2254), (1275, 2284), (1446, 24290), (1461, 9454), (1462, 3063), (1814, 65102), (2481, 3900), (4554, 3693), (4566, 20683), (4569, 518), (4572, 3717), (4616, 3286), (4617, 52635), (4626, 1458), (4635, 18206), (5723, 14411), (6063, 50333), (7045, 54325), (7053, 23225), (7056, 53550), (13149, 5089), (13576, 4524), (14942, 4105), (18031, 3239), (23062, 53544), (24002, 17435), (24011, 41353), (24015, 9502), (28132, 35508), (31637, 57108), (32735, 2175)
X(65847) = X(1742)-zayin conjugate of-X(46388)
X(65847) = trilinear pole of the line {7, 2481} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65847) = perspector of the inconic with center X(65846)
X(65847) = barycentric product X(i)*X(j) for these {i, j}: {7, 46135}, {85, 34085}, {279, 36803}, {331, 65301}, {658, 18031}, {666, 57792}, {673, 46406}, {927, 6063}, {1088, 51560}, {2481, 4569}, {4554, 34018}, {4572, 56783}, {14942, 52937}, {20567, 36146}, {28132, 57581}, {32735, 41283}, {36796, 36838}, {36802, 57880}, {39293, 52621}
X(65847) = trilinear product X(i)*X(j) for these {i, j}: {7, 34085}, {57, 46135}, {85, 927}, {105, 46406}, {269, 36803}, {273, 65301}, {279, 51560}, {294, 52937}, {658, 2481}, {664, 34018}, {666, 1088}, {673, 4569}, {934, 18031}, {1462, 4572}, {4554, 56783}, {4626, 36796}, {4635, 13576}, {6063, 36146}, {13149, 31637}, {14942, 36838}
X(65847) = trilinear quotient X(i)/X(j) for these (i, j): (7, 46388), (57, 8638), (75, 52614), (85, 926), (658, 2223), (666, 1253), (673, 8641), (927, 41), (934, 9454), (1024, 61050), (1088, 665), (1275, 54325), (1461, 9455), (2254, 39014), (2481, 657), (4554, 2340), (4566, 39258), (4569, 672), (4572, 3693), (4626, 52635)

X(65848) = CENTER OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(8)

Barycentrics    (b-c)*(-a+b+c)*((b+c)*a^4+2*(b^2+c^2)*a^3+(b^2-c^2)*(b-c)*a^2+2*b^2*c^2*a-2*b^2*c^2*(b+c)) : :

X(65848) lies on these lines: {514, 4521}, {6363, 21260}, {24782, 47794}

X(65848) = complement of the isotomic conjugate of X(65849)
X(65848) = crosspoint of X(2) and X(65849)
X(65848) = X(i)-complementary conjugate of-X(j) for these (i, j): (9, 15611), (41, 39015), (1220, 4904), (2298, 3756), (3699, 51571), (6648, 11019), (8687, 52541), (8707, 142), (14624, 8286), (30710, 17059), (32736, 3752), (35334, 17055), (36098, 4000), (36147, 1), (56245, 55054), (65229, 2886), (65255, 59477), (65282, 17046), (65849, 2887)
X(65848) = center of the inconic with perspector X(65849)
X(65848) = pole of the line {9, 39} with respect to the Spieker circle
X(65848) = pole of the line {8, 23638} with respect to the Steiner inellipse

X(65849) = PERSPECTOR OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(8)

Barycentrics    (a-b)*(a-c)*(-a+b+c)*(a^2+b*a+c*(b+c))*(a^2+c*a+b*(b+c))/a^2 : :

X(65849) lies on these lines: {8, 41224}, {190, 65229}, {1240, 36807}, {3596, 30826}, {4033, 27805}, {4554, 6386}, {25534, 28358}, {30710, 36805}, {60251, 60264}

X(65849) = isotomic conjugate of the anticomplement of X(65848)
X(65849) = cevapoint of X(8) and X(52326)
X(65849) = X(i)-cross conjugate of-X(j) for these (i, j): (52326, 8), (65848, 2)
X(65849) = X(i)-Dao conjugate of-X(j) for these (i, j): (3161, 6371), (5452, 57157), (6552, 52326), (6631, 61412), (9296, 24471), (38992, 39015), (62585, 48131)
X(65849) = X(i)-isoconjugate of-X(j) for these {i, j}: {57, 57157}, {604, 6371}, {667, 61412}, {1106, 52326}, {1193, 57181}, {1397, 48131}, {1919, 24471}, {1980, 3674}, {2300, 43924}, {3882, 61048}, {4509, 41280}, {16947, 50330}, {17420, 52410}, {36098, 39015}, {40153, 51641}
X(65849) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (8, 6371), (55, 57157), (190, 61412), (312, 48131), (341, 17420), (346, 52326), (644, 2300), (645, 40153), (646, 3666), (668, 24471), (1220, 43924), (1240, 3676), (1978, 3674), (2298, 57181), (3596, 3004), (3699, 1193), (3701, 50330), (4069, 3725), (4076, 53280), (4571, 22345), (4578, 20967), (4581, 1357), (6057, 42661), (6558, 2269), (6648, 1407), (7256, 4267), (7257, 54308), (7258, 17185), (8687, 52410), (8707, 56), (14624, 7180), (27808, 41003), (28659, 4509), (30710, 3669), (30713, 21124), (30730, 2092), (31643, 43932), (32736, 1397), (36098, 1106), (36147, 604), (40521, 59174), (40827, 17096), (52326, 39015), (57158, 61051), (58982, 7342), (59761, 3910), (60086, 7250), (60264, 7178), (62534, 16705), (65160, 2354)
X(65849) = trilinear pole of the line {8, 23638} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65849) = perspector of the inconic with center X(65848)
X(65849) = barycentric product X(i)*X(j) for these {i, j}: {8, 65282}, {312, 65229}, {645, 60264}, {646, 30710}, {1240, 3699}, {3596, 8707}, {6648, 59761}, {14624, 62534}, {28659, 36147}, {30730, 40827}, {32736, 40363}
X(65849) = trilinear product X(i)*X(j) for these {i, j}: {8, 65229}, {9, 65282}, {312, 8707}, {341, 6648}, {643, 60264}, {644, 1240}, {646, 1220}, {3596, 36147}, {3699, 30710}, {4069, 40827}, {4103, 52550}, {6558, 31643}, {7257, 14624}, {7258, 60086}, {28659, 32736}, {35334, 62539}, {36098, 59761}
X(65849) = trilinear quotient X(i)/X(j) for these (i, j): (9, 57157), (312, 6371), (341, 52326), (646, 1193), (668, 61412), (1220, 57181), (1240, 3669), (1978, 24471), (3596, 48131), (3699, 2300), (4103, 59174), (6386, 3674), (6558, 20967), (6648, 1106), (7257, 40153), (7258, 4267), (8707, 604), (14624, 51641), (17420, 39015), (28659, 3004)

X(65850) = PERSPECTOR OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(10)

Barycentrics    (a-b)*(a-c)*(b+c)*(a^2+(b+c)*a+(b+c)*c)*(a^2+(b+c)*a+b*(b+c))/a^2 : :

X(65850) lies on these lines: {10, 52328}, {190, 27808}, {335, 57824}, {1089, 37842}, {4033, 61167}, {4632, 62534}, {20654, 59138}, {52609, 56188}

X(65850) = isotomic conjugate of X(52615)
X(65850) = cevapoint of X(i) and X(j) for these {i, j}: {10, 42664}, {20654, 23282}
X(65850) = X(i)-cross conjugate of-X(j) for these (i, j): (661, 34265), (23282, 59138), (42664, 10), (52586, 2)
X(65850) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 52615), (37, 834), (4075, 42664), (6631, 61409), (36901, 65116), (40586, 8637), (40603, 14349)
X(65850) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 52615}, {81, 8637}, {386, 57129}, {593, 50488}, {667, 61409}, {834, 1333}, {849, 42664}, {2206, 14349}
X(65850) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (2, 52615), (10, 834), (42, 8637), (190, 61409), (313, 45746), (321, 14349), (594, 42664), (756, 50488), (835, 58), (850, 65116), (1089, 47842), (2214, 57129), (3952, 386), (4033, 28606), (4103, 56926), (27808, 5224), (28654, 23879), (37218, 81), (42664, 39016), (43531, 3733), (57824, 7192), (57876, 7254), (57977, 86)
X(65850) = trilinear pole of the line {10, 20966} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65850) = perspector of the inconic with center X(52586)
X(65850) = barycentric product X(i)*X(j) for these {i, j}: {10, 57977}, {313, 835}, {321, 37218}, {3952, 57824}, {27808, 43531}
X(65850) = trilinear product X(i)*X(j) for these {i, j}: {10, 37218}, {37, 57977}, {321, 835}, {1018, 57824}, {2214, 27808}, {4033, 43531}
X(65850) = trilinear quotient X(i)/X(j) for these (i, j): (37, 8637), (75, 52615), (313, 14349), (321, 834), (594, 50488), (668, 61409), (835, 1333), (1089, 42664), (4033, 386), (20948, 65116), (27801, 45746), (27808, 28606), (28654, 47842), (37218, 58), (43531, 57129), (47842, 39016), (57824, 1019), (57977, 81)

X(65851) = CENTER OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(11)

Barycentrics    (b-c)^2*(-a+b+c)^2*((b+c)*a^5-(b+c)*(2*b^2-3*b*c+2*c^2)*a^3-b*c*(b-c)^2*a^2+(b^3+c^3)*(b-c)^2*a+b*c*(b^2+c^2)*(b-c)^2) : :

X(65851) lies on these lines: {213, 37646}, {918, 1086}, {5249, 13567}

X(65851) = complement of the isotomic conjugate of X(65852)
X(65851) = crosspoint of X(2) and X(65852)
X(65851) = X(i)-complementary conjugate of-X(j) for these (i, j): (929, 21232), (2170, 15612), (65852, 2887)
X(65851) = center of the inconic with perspector X(65852)
X(65851) = pole of the line {11, 47394} with respect to the Steiner inellipse

X(65852) = PERSPECTOR OF THE BICIRCUMANTICEVIAN INCONIC OF X(6) AND X(11)

Barycentrics    (b-c)*(-a+b+c)*(a^4-b*a^3-b*(b-c)*a^2+b*(b-c)^2*a+(b^2-c^2)*(b-c)*c)*(a^4-c*a^3+c*(b-c)*a^2+c*(b-c)^2*a+(b^2-c^2)*(b-c)*b)/a^2 : :

X(65852) lies on these lines: {11, 52330}, {514, 18161}, {522, 17860}, {666, 58000}

X(65852) = isotomic conjugate of the anticomplement of X(65851)
X(65852) = cevapoint of X(11) and X(52331)
X(65852) = X(i)-cross conjugate of-X(j) for these (i, j): (47137, 44426), (52331, 11), (65851, 2)
X(65852) = X(i)-Dao conjugate of-X(j) for these (i, j): (650, 928), (64440, 52331)
X(65852) = X(928)-isoconjugate of-X(2149)
X(65852) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (11, 928), (929, 59), (52331, 39017), (58000, 4998), (64445, 52331)
X(65852) = trilinear pole of the line {11, 47394} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65852) = perspector of the inconic with center X(65851)
X(65852) = barycentric product X(i)*X(j) for these {i, j}: {11, 58000}, {929, 34387}
X(65852) = trilinear product X(i)*X(j) for these {i, j}: {929, 4858}, {2170, 58000}
X(65852) = trilinear quotient X(i)/X(j) for these (i, j): (929, 2149), (1090, 52331), (4858, 928), (58000, 4564)

X(65853) = ISOGONAL CONJUGATE OF X(65638)

Barycentrics    a^2*(b^2 - c^2)*(a^4 - 4*a^2*b^2 + b^4 + 6*a^2*b*c - 3*b^3*c - 4*a^2*c^2 + 5*b^2*c^2 - 3*b*c^3 + c^4)*(a^4 - 4*a^2*b^2 + b^4 - 6*a^2*b*c + 3*b^3*c - 4*a^2*c^2 + 5*b^2*c^2 + 3*b*c^3 + c^4) : :

X(65853) lies on these lines: {30, 511}, {351, 352}, {805, 6082}, {843, 64220}, {2679, 31654}, {2698, 6093}, {5104, 9135}, {6092, 33330}, {9127, 11176}, {9178, 52198}, {9184, 53882}, {44042, 44048}, {57310, 57361}, {57347, 57362}

X(65853) = isogonal conjugate of X(65638)
X(65853) = isogonal conjugate of the anticomplement of X(35586)
X(65853) = crossdifference of every pair of points on line {6, 35087}
X(65853) = {X(352),X(9212)}-harmonic conjugate of X(351)

X(65854) = ISOGONAL CONJUGATE OF X(65639)

Barycentrics    a^2*(b - c)*(a^2 - b^2 + b*c - c^2)*(a^2*b - b^3 + a^2*c - 4*a*b*c + 2*b^2*c + 2*b*c^2 - c^3) : :

X(65854) lies on these lines: {30, 511}, {36, 39478}, {901, 4638}, {3025, 53525}, {3259, 56893}, {3814, 53574}, {5570, 59956}, {13756, 24457}, {22765, 39200}, {23152, 42763}, {23153, 23838}, {34464, 53401}, {38614, 52732}, {38617, 45949}, {56881, 64688}

X(65854) = isogonal conjugate of X(65639)
X(65854) = isogonal conjugate of the anticomplement of X(35587)
X(65854) = crossdifference of every pair of points on line {6, 34232}
X(65854) = barycentric quotient X(23964)/X(25701)

X(65855) = X(8)X(19917)∩X(30)X(511)

Barycentrics    (b - c)*(2*a^2 - a*b - a*c + b*c)*(-(a*b^2) + b^2*c - a*c^2 + b*c^2) : :

X(65855) lies on these lines: {8, 19917}, {30, 511}, {190, 932}, {659, 11689}, {890, 17165}, {1086, 5518}, {3709, 40464}, {3837, 20366}, {14426, 24165}, {15323, 24813}, {20375, 21391}, {21349, 49447}, {24828, 50936}, {48330, 57235}

X(65855) = crossdifference of every pair of points on line {6, 40610}
X(65855) = barycentric quotient X(42700)/X(5559)

X(65856) = ISOGONAL CONJUGATE OF X(65644)

Barycentrics    (b - c)*(-a^3 - a^2*b + a*b^2 + b^3 - a^2*c + a*b*c - b^2*c + a*c^2 - b*c^2 + c^3)*(-2*a^4 + a^3*b + a^2*b^2 - a*b^3 + b^4 + a^3*c + a^2*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :

X(65856) lies on these lines: {3, 39493}, {23, 26275}, {30, 511}, {186, 39534}, {476, 901}, {477, 953}, {484, 35055}, {858, 30792}, {867, 5520}, {1290, 13589}, {1325, 42741}, {2070, 39478}, {2687, 14127}, {3025, 33965}, {3258, 3259}, {5189, 31131}, {5899, 39200}, {7477, 42746}, {10989, 48182}, {13619, 44428}, {13756, 33964}, {14989, 44979}, {15646, 44815}, {20957, 40100}, {22102, 22104}, {24201, 59823}, {25641, 31841}, {33645, 59825}, {37311, 48384}, {37901, 44433}, {38580, 38584}, {38581, 38586}, {38609, 38614}, {38610, 38617}, {38678, 38682}, {38700, 38705}, {38701, 38707}, {39751, 51663}, {44967, 44973}, {46487, 47788}, {47270, 51631}, {57305, 57313}, {57306, 57320}

X(65856) = isogonal conjugate of X(65644)
X(65856) = crossdifference of every pair of points on line {6, 35090}
X(65856) = barycentric product X(3346)*X(27446)

X(65857) = ISOGONAL CONJUGATE OF X(53881)

Barycentrics    a^2*(b^2 - c^2)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*b*c + 3*a^4*b^3*c - b^7*c - 2*a^6*c^2 + 7*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - b^6*c^2 + 3*a^4*b*c^3 - 4*a^2*b^3*c^3 + b^5*c^3 - 4*a^2*b^2*c^4 + 4*b^4*c^4 + b^3*c^5 + 2*a^2*c^6 - b^2*c^6 - b*c^7 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 + 2*a^6*b*c - 3*a^4*b^3*c + b^7*c - 2*a^6*c^2 + 7*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - b^6*c^2 - 3*a^4*b*c^3 + 4*a^2*b^3*c^3 - b^5*c^3 - 4*a^2*b^2*c^4 + 4*b^4*c^4 - b^3*c^5 + 2*a^2*c^6 - b^2*c^6 + b*c^7 - c^8) : :

X(65857) lies on these lines: {30, 511}, {476, 6080}, {477, 44874}, {1304, 5502}, {2693, 46613}, {3258, 35579}, {7740, 38625}, {9409, 65107}, {10151, 57516}, {15262, 15292}, {16177, 57128}, {18577, 58263}, {44992, 53320}

X(65857) = isogonal conjugate of X(53881)
X(65857) = crossdifference of every pair of points on line {6, 39008}
X(65857) = barycentric product X(9502)*X(49883)

X(65858) = ISOGONAL CONJUGATE OF X(65646)

Barycentrics    (b - c)*(-2*a^2 + a*b + b^2 + a*c - 2*b*c + c^2)*(-2*a^3 + 2*a^2*b - a*b^2 + b^3 + 2*a^2*c - b^2*c - a*c^2 - b*c^2 + c^3) : :

X(65858) lies on these lines: {30, 511}, {901, 927}, {953, 2724}, {1155, 1638}, {1566, 3259}, {3025, 44043}, {3322, 42763}, {3328, 30573}, {5011, 22108}, {5057, 30565}, {5087, 45326}, {5179, 28603}, {7112, 21433}, {13756, 59808}, {14190, 61477}, {14475, 14477}, {14732, 44009}, {22102, 40554}, {31841, 33331}, {44973, 44975}, {52334, 65680}, {57313, 57315}, {57320, 57353}

X(65858) = isogonal conjugate of X(65646)
X(65858) = crossdifference of every pair of points on line {6, 35116}
X(65858) = barycentric quotient X(i)/X(j) for these {i,j}: {53945, 42546}, {63152, 2682}
X(65858) = {X(1155),X(41162)}-harmonic conjugate of X(6139)

X(65859) = X(15)X(351)∩X(30)X(511)

Barycentrics    a^2*(b^2 - c^2)*(Sqrt[3]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 9*a^2*b^2*c^2 - 4*b^4*c^2 - a^2*c^4 - 4*b^2*c^4 + c^6) - 2*(a^4 - 4*a^2*b^2 + b^4 - 4*a^2*c^2 + 5*b^2*c^2 + c^4)*S) : :

X(65859) lies on these lines: {15, 351}, {30, 511}, {621, 53365}, {623, 45689}, {9126, 13350}, {9147, 51484}, {9148, 50855}, {9171, 11617}, {9208, 11618}, {11176, 45879}, {14538, 61776}, {21401, 65418}

X(65859) = Thomson-isogonal conjugate of X(44875)
X(65859) = crossdifference of every pair of points on line {6, 61068}
X(65859) = {X(15),X(9162)}-harmonic conjugate of X(351)

X(65860) = X(16)X(351)∩X(30)X(511)

Barycentrics    a^2*(b^2 - c^2)*(Sqrt[3]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 9*a^2*b^2*c^2 - 4*b^4*c^2 - a^2*c^4 - 4*b^2*c^4 + c^6) + 2*(a^4 - 4*a^2*b^2 + b^4 - 4*a^2*c^2 + 5*b^2*c^2 + c^4)*S) : :

X(65860) lies on these lines: {16, 351}, {30, 511}, {622, 53365}, {624, 45689}, {2698, 44875}, {9126, 13349}, {9147, 51485}, {9148, 50858}, {9171, 11618}, {9208, 11617}, {11176, 45880}, {14539, 61776}, {21402, 65418}

X(65860) = crossdifference of every pair of points on line {6, 61069}
X(65860) = barycentric quotient X(56561)/X(60699)
X(65860) = {X(16),X(9163)}-harmonic conjugate of X(351)

X(65861) = X(30)X(511)∩X(476)X(927)

Barycentrics    (b - c)*(a^5 - a^4*b - a^3*b^2 + a^2*b^3 - a^4*c - a^3*b*c + a^2*b^2*c + b^4*c - a^3*c^2 + a^2*b*c^2 - b^3*c^2 + a^2*c^3 - b^2*c^3 + b*c^4)*(-(a^5*b) + a^4*b^2 + a^3*b^3 - a^2*b^4 - a^5*c + b^5*c + a^4*c^2 + a^3*c^3 - 2*b^3*c^3 - a^2*c^4 + b*c^5) : :

X(65861) lies on these lines: {30, 511}, {476, 927}, {477, 2724}, {1566, 3258}, {2688, 46596}, {2690, 46595}, {5196, 42744}, {7479, 42745}, {14731, 14732}, {22104, 40554}, {25641, 33331}, {33964, 59808}, {33965, 44043}, {44967, 44975}, {57305, 57315}, {57306, 57353}

X(65862) = X(30)X(511)∩X(476)X(6078)

Barycentrics    (b - c)*(-a^3 + a^2*b - a*b^2 + b^3 + a^2*c - 3*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3)*(2*a^5 - a^4*b - 2*a*b^4 + b^5 - a^4*c - 2*a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c + a^2*b*c^2 + 2*a*b^2*c^2 + a*b*c^3 - 2*a*c^4 - b*c^4 + c^5) : :

X(65862) lies on these lines: {23, 47884}, {30, 511}, {476, 6078}, {477, 28914}, {858, 45677}, {2691, 46593}, {2752, 46586}, {3258, 5519}, {4789, 24585}, {4927, 10989}, {5189, 47871}, {7426, 14425}, {7475, 42747}, {33965, 44045}, {37901, 47892}

X(65863) = X(30)X(511)∩X(476)X(6082)

Barycentrics    (b^2 - c^2)*(a^6 - a^2*b^4 - 2*a^4*b*c - a^2*b^3*c + b^5*c + 5*a^2*b^2*c^2 - 2*b^4*c^2 - a^2*b*c^3 + 2*b^3*c^3 - a^2*c^4 - 2*b^2*c^4 + b*c^5)*(-a^6 + a^2*b^4 - 2*a^4*b*c - a^2*b^3*c + b^5*c - 5*a^2*b^2*c^2 + 2*b^4*c^2 - a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 + 2*b^2*c^4 + b*c^5) : :

X(65863) lies on these lines: {30, 511}, {476, 6082}, {477, 6093}, {2492, 5913}, {2770, 46589}, {3258, 31654}, {5971, 35522}, {6092, 25641}, {9178, 34320}, {9213, 62294}, {33965, 44048}, {53604, 53882}, {57305, 57361}, {57306, 57362}

X(65864) = X(30)X(511)∩X(805)X(901)

Barycentrics    a^2*(b - c)*(a^3*b - a*b^3 + a^3*c - a^2*b*c + a*b^2*c + a*b*c^2 - b^2*c^2 - a*c^3)*(a^3*b^2 - a*b^4 - a^2*b^2*c + a^3*c^2 - a^2*b*c^2 + b^3*c^2 + b^2*c^3 - a*c^4) : :

X(65864) lies on these lines: {30, 511}, {805, 901}, {953, 2698}, {2511, 5164}, {2679, 3259}, {2703, 18002}, {3025, 44042}, {17989, 56878}, {22102, 22103}, {31841, 33330}, {38703, 38705}, {44971, 44973}, {57310, 57313}, {57320, 57347}, {65516, 65517}

X(65864) = crossdifference of every pair of points on line {6, 35079}

X(65865) = ISOGONAL CONJUGATE OF X(65647)

Barycentrics    a^2*(b - c)*(a^3 - b^3 + a*b*c - c^3)*(a^3*b - b^4 + a^3*c - 2*a^2*b*c - a*b^2*c + b^3*c - a*b*c^2 + 2*b^2*c^2 + b*c^3 - c^4) : :

X(65865) lies on these lines: {30, 511}, {805, 927}, {1566, 2679}, {2698, 2724}, {2702, 18001}, {14196, 61434}, {17990, 41323}, {22103, 40554}, {33330, 33331}, {44042, 44043}, {44971, 44975}, {57310, 57315}, {57347, 57353}

X(65865) = isogonal conjugate of X(65647)
X(65865) = crossdifference of every pair of points on line {6, 35080}

X(65866) = ISOGONAL CONJUGATE OF X(65649)

Barycentrics    (2*a - b - c)*(b - c)*(2*a^3 - 2*a^2*b - 3*a*b^2 + b^3 - 2*a^2*c + 8*a*b*c - b^2*c - 3*a*c^2 - b*c^2 + c^3) : :

X(65866) lies on these lines: {30, 511}, {901, 6079}, {953, 44873}, {1647, 3259}, {3025, 44046}, {5121, 26275}, {5205, 31131}, {7336, 24131}, {22102, 59997}, {24188, 43909}, {25996, 60409}, {30792, 50535}, {44433, 50533}, {47622, 53314}, {47786, 62621}, {59957, 60374}

X(65866) = isogonal conjugate of X(65649)
X(65866) = crossdifference of every pair of points on line {6, 5548}
X(65866) = barycentric quotient X(1602)/X(5215)

X(65867) = ISOTOMIC CONJUGATE OF X(901)

Barycentrics    b^2*(b - c)*c^2*(-2*a + b + c) : :

X(65867) lies on these lines: {2, 3310}, {69, 46401}, {75, 4453}, {99, 53611}, {312, 30565}, {314, 65669}, {321, 918}, {325, 523}, {654, 1150}, {668, 891}, {900, 1227}, {926, 17135}, {1111, 3120}, {1577, 48416}, {1638, 4359}, {1639, 4358}, {3676, 17894}, {3741, 20525}, {3762, 4120}, {3776, 20909}, {3904, 18359}, {3936, 46397}, {4374, 47780}, {4391, 47790}, {4462, 47769}, {4467, 57244}, {4647, 62435}, {4671, 47772}, {4768, 20900}, {4928, 59736}, {4978, 52623}, {6063, 63742}, {6371, 20295}, {6545, 20908}, {6548, 21433}, {7192, 56323}, {8034, 20512}, {16704, 22086}, {17140, 30704}, {17165, 42341}, {17899, 47796}, {18031, 63748}, {18071, 47660}, {20907, 21183}, {20937, 21606}, {20949, 48550}, {20950, 47871}, {20952, 29739}, {21438, 47676}, {24462, 31330}, {24589, 44902}, {24622, 26985}, {25667, 47661}, {27114, 52326}, {28605, 48571}, {29312, 62415}, {57995, 63216}, {58286, 59721}, {59522, 59713}

X(65867) = midpoint of X(17135) and X(65660)
X(65867) = reflection of X(65703) in X(3741)
X(65867) = isogonal conjugate of X(32719)
X(65867) = isotomic conjugate of X(901)
X(65867) = anticomplement of X(3310)
X(65867) = anticomplement of the isogonal conjugate of X(13136)
X(65867) = isotomic conjugate of the anticomplement of X(3259)
X(65867) = isotomic conjugate of the isogonal conjugate of X(900)
X(65867) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {104, 4440}, {190, 153}, {664, 36918}, {909, 9263}, {1309, 5905}, {2250, 148}, {2720, 3210}, {13136, 8}, {14776, 21216}, {18816, 150}, {32641, 192}, {34051, 58371}, {34234, 149}, {34858, 21224}, {35321, 17035}, {36037, 2}, {36110, 30699}, {36795, 33650}, {36819, 39353}, {37136, 145}, {38955, 21221}, {39294, 521}, {51565, 37781}, {52663, 39351}, {53702, 62998}, {54953, 7}, {57984, 21294}, {61238, 17036}, {64824, 20060}, {65223, 4}, {65331, 12649}
X(65867) = X(i)-Ceva conjugate of X(j) for these (i,j): {1978, 36791}, {3261, 52627}, {20566, 34387}, {57995, 23989}
X(65867) = X(i)-cross conjugate of X(j) for these (i,j): {3259, 2}, {52627, 3261}
X(65867) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32719}, {6, 32665}, {31, 901}, {32, 3257}, {88, 32739}, {101, 9456}, {106, 692}, {213, 4591}, {560, 4555}, {604, 5548}, {667, 9268}, {906, 8752}, {1022, 23990}, {1023, 41935}, {1110, 23345}, {1415, 2316}, {1417, 3939}, {1576, 4674}, {1743, 32645}, {1783, 32659}, {1918, 4622}, {1919, 5376}, {1980, 62536}, {2205, 4615}, {2251, 4638}, {3052, 36042}, {3248, 6551}, {4618, 9459}, {8750, 36058}, {9247, 65336}, {32656, 36125}, {32666, 34230}, {46162, 46289}
X(65867) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 901}, {3, 32719}, {9, 32665}, {39, 46162}, {44, 1983}, {214, 692}, {514, 23345}, {519, 23344}, {900, 1960}, {1015, 9456}, {1086, 106}, {1146, 2316}, {1577, 23838}, {1639, 654}, {1647, 902}, {3161, 5548}, {3911, 23981}, {3960, 53314}, {4370, 101}, {4521, 2441}, {4858, 4674}, {4988, 55263}, {5190, 8752}, {5516, 3052}, {6374, 4555}, {6376, 3257}, {6544, 649}, {6626, 4591}, {6631, 9268}, {9296, 5376}, {9460, 4638}, {16610, 23832}, {20619, 8750}, {21894, 21786}, {24151, 36042}, {26932, 36058}, {34021, 4622}, {35092, 6}, {35094, 34230}, {36901, 4080}, {38979, 31}, {39006, 32659}, {40617, 1417}, {40618, 1797}, {40619, 88}, {40624, 1320}, {46398, 14260}, {51402, 55}, {52659, 109}, {52871, 3939}, {52872, 4557}, {53985, 25}, {55055, 32}, {59737, 4491}, {62559, 1149}, {62571, 100}, {62576, 65336}
X(65867) = cevapoint of X(3762) and X(4768)
X(65867) = crosspoint of X(i) and X(j) for these (i,j): {668, 18816}, {1978, 57995}, {6063, 46405}
X(65867) = crosssum of X(i) and X(j) for these (i,j): {184, 23220}, {1919, 9459}, {23638, 53549}
X(65867) = crossdifference of every pair of points on line {32, 1977}
X(65867) = barycentric product X(i)*X(j) for these {i,j}: {44, 40495}, {75, 3762}, {76, 900}, {85, 4768}, {310, 4120}, {514, 3264}, {519, 3261}, {561, 1635}, {693, 4358}, {850, 16704}, {903, 52627}, {1111, 24004}, {1227, 60074}, {1502, 1960}, {1577, 30939}, {1639, 6063}, {1647, 1978}, {1969, 53532}, {2087, 6386}, {2325, 52621}, {3120, 55262}, {3267, 37168}, {3285, 44173}, {3596, 30725}, {3911, 35519}, {3943, 52619}, {3977, 46107}, {3992, 7199}, {4025, 46109}, {4448, 18895}, {4528, 57792}, {4530, 4572}, {4671, 63217}, {4723, 24002}, {4730, 6385}, {4777, 63240}, {4791, 63226}, {4895, 20567}, {4922, 44187}, {6544, 57995}, {6548, 36791}, {6550, 31625}, {14418, 57787}, {14429, 44129}, {15413, 38462}, {16732, 55243}, {17780, 23989}, {18022, 22086}, {20948, 52680}, {23888, 58027}, {28659, 53528}, {28660, 30572}, {34387, 62669}, {35518, 37790}, {46405, 51402}, {52622, 62789}
X(65867) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 32665}, {2, 901}, {6, 32719}, {8, 5548}, {44, 692}, {75, 3257}, {76, 4555}, {86, 4591}, {141, 46162}, {190, 9268}, {214, 1983}, {264, 65336}, {274, 4622}, {310, 4615}, {513, 9456}, {514, 106}, {519, 101}, {522, 2316}, {668, 5376}, {693, 88}, {850, 4080}, {900, 6}, {902, 32739}, {903, 4638}, {905, 36058}, {918, 34230}, {996, 32686}, {1000, 59068}, {1016, 6551}, {1023, 1110}, {1086, 23345}, {1111, 1022}, {1145, 2427}, {1227, 4585}, {1317, 61210}, {1319, 1415}, {1459, 32659}, {1577, 4674}, {1635, 31}, {1639, 55}, {1647, 649}, {1877, 32674}, {1960, 32}, {1978, 62536}, {2087, 667}, {2325, 3939}, {2401, 10428}, {3120, 55263}, {3251, 2251}, {3259, 3310}, {3261, 903}, {3264, 190}, {3285, 1576}, {3445, 32645}, {3596, 4582}, {3669, 1417}, {3756, 2441}, {3762, 1}, {3904, 62703}, {3911, 109}, {3943, 4557}, {3960, 16944}, {3977, 1331}, {3992, 1018}, {4025, 1797}, {4120, 42}, {4358, 100}, {4370, 23344}, {4391, 1320}, {4448, 1914}, {4453, 40215}, {4487, 57192}, {4528, 220}, {4530, 663}, {4671, 52925}, {4723, 644}, {4730, 213}, {4738, 1023}, {4768, 9}, {4791, 4792}, {4858, 23838}, {4895, 41}, {4922, 172}, {4927, 52206}, {4957, 23352}, {4958, 61358}, {4969, 35327}, {4975, 35342}, {4984, 2308}, {5298, 36075}, {5440, 906}, {6385, 4634}, {6544, 902}, {6545, 43922}, {6548, 2226}, {6550, 1015}, {6630, 53682}, {7649, 8752}, {8056, 36042}, {8661, 1977}, {8756, 8750}, {10015, 14260}, {14407, 1918}, {14408, 2209}, {14418, 212}, {14425, 3052}, {14427, 1253}, {14429, 71}, {14435, 21747}, {14436, 18900}, {14439, 54325}, {14584, 32675}, {14628, 2222}, {16594, 23832}, {16704, 110}, {16732, 55244}, {16892, 46150}, {17780, 1252}, {17924, 36125}, {20568, 4618}, {20908, 36814}, {21129, 1149}, {21198, 39148}, {21207, 4049}, {22086, 184}, {22356, 32656}, {23100, 6549}, {23344, 23990}, {23345, 41935}, {23703, 2149}, {23757, 2183}, {23887, 64611}, {23888, 995}, {23989, 6548}, {24002, 56049}, {24004, 765}, {24188, 21143}, {28602, 17735}, {30572, 1400}, {30573, 1055}, {30583, 3230}, {30606, 4636}, {30725, 56}, {30731, 6065}, {30939, 662}, {31011, 8701}, {31059, 17943}, {31625, 6635}, {33920, 8649}, {33922, 1017}, {34387, 60480}, {34590, 21786}, {34764, 2384}, {35092, 1960}, {35519, 4997}, {36038, 52031}, {36791, 17780}, {36872, 34075}, {36915, 6014}, {36944, 32641}, {37168, 112}, {37790, 108}, {38462, 1783}, {39472, 20818}, {39771, 1404}, {40218, 2720}, {40495, 20568}, {40663, 4559}, {45144, 32642}, {45314, 21793}, {45677, 45140}, {46107, 6336}, {46109, 1897}, {46781, 2718}, {47420, 23220}, {50943, 953}, {51402, 654}, {51406, 2426}, {51415, 23845}, {51422, 2425}, {51463, 35326}, {52338, 3271}, {52623, 4013}, {52627, 519}, {52659, 23981}, {52680, 163}, {53528, 604}, {53532, 48}, {53533, 2275}, {53535, 7113}, {53536, 1468}, {54974, 39414}, {55243, 4567}, {55262, 4600}, {56761, 2423}, {56939, 36049}, {57051, 33882}, {58254, 53582}, {58282, 31182}, {60074, 1168}, {60480, 1318}, {62413, 53634}, {62621, 35281}, {62630, 41405}, {62669, 59}, {62789, 1461}, {63217, 89}, {63226, 4604}, {63233, 4588}, {63240, 4597}, {65024, 28210}, {65101, 27922}
X(65867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 20906, 44435}, {693, 35519, 850}, {693, 47656, 50557}, {20952, 29739, 47652}

X(65868) = ISOTOMIC CONJUGATE OF X(1308)

Barycentrics    (b - c)*(-a^2 + b^2 + c^2)*(-(a^2*b) + b^3 - a^2*c + 2*a*b*c - b^2*c - b*c^2 + c^3) : :

X(65868) lies on these lines: {63, 39470}, {99, 53612}, {100, 658}, {325, 523}, {521, 4025}, {525, 57184}, {676, 53353}, {900, 46401}, {918, 23737}, {1565, 2968}, {2417, 36100}, {2804, 36038}, {3310, 10015}, {4467, 46400}, {4791, 18118}, {4847, 55123}, {6084, 43991}, {20296, 57245}, {21107, 25098}, {22464, 45945}, {39471, 52392}, {39534, 42751}, {46402, 47894}

X(65868) = isogonal conjugate of X(14776)
X(65868) = isotomic conjugate of X(1309)
X(65868) = anticomplement of the isogonal conjugate of X(65297)
X(65868) = isotomic conjugate of the anticomplement of X(10017)
X(65868) = isotomic conjugate of the isogonal conjugate of X(8677)
X(65868) = isotomic conjugate of the polar conjugate of X(10015)
X(65868) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {102, 37781}, {651, 151}, {6081, 189}, {32643, 192}, {32667, 193}, {32677, 39351}, {36040, 2}, {36067, 5905}, {36100, 33650}, {65295, 21270}, {65297, 8}
X(65868) = X(i)-Ceva conjugate of X(j) for these (i,j): {4554, 26611}, {4555, 69}, {46405, 343}
X(65868) = X(i)-cross conjugate of X(j) for these (i,j): {8677, 10015}, {10017, 2}, {35012, 57478}, {42769, 905}
X(65868) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14776}, {9, 32702}, {19, 32641}, {25, 36037}, {31, 1309}, {32, 65223}, {33, 2720}, {41, 65331}, {55, 36110}, {104, 8750}, {108, 2342}, {112, 2250}, {281, 32669}, {607, 37136}, {692, 36123}, {909, 1783}, {1110, 43933}, {1253, 65537}, {1897, 34858}, {1973, 13136}, {2212, 54953}, {2310, 59103}, {3063, 39294}, {7115, 61238}, {8882, 35321}, {11383, 36090}, {16082, 32739}, {32674, 52663}, {32676, 38955}, {36106, 51824}
X(65868) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 1309}, {3, 14776}, {6, 32641}, {223, 36110}, {478, 32702}, {514, 43933}, {905, 43728}, {908, 4242}, {1086, 36123}, {1145, 56183}, {1465, 23987}, {3160, 65331}, {3259, 25}, {6337, 13136}, {6376, 65223}, {6505, 36037}, {8677, 23220}, {10001, 39294}, {10015, 44428}, {15526, 38955}, {16586, 1897}, {17113, 65537}, {23980, 1783}, {26932, 104}, {34467, 34858}, {34591, 2250}, {35072, 52663}, {38981, 33}, {38983, 2342}, {39002, 51824}, {39004, 55}, {39006, 909}, {40613, 8750}, {40618, 34234}, {40619, 16082}, {40626, 51565}, {40628, 61238}, {42761, 860}, {46398, 4}, {55153, 281}, {60339, 650}
X(65868) = crosspoint of X(i) and X(j) for these (i,j): {99, 57985}, {264, 65295}, {664, 34393}
X(65868) = crosssum of X(i) and X(j) for these (i,j): {25, 58313}, {512, 44113}
X(65868) = crossdifference of every pair of points on line {32, 607}
X(65868) = barycentric product X(i)*X(j) for these {i,j}: {63, 36038}, {69, 10015}, {76, 8677}, {99, 42761}, {304, 1769}, {305, 3310}, {306, 23788}, {348, 2804}, {517, 15413}, {525, 17139}, {859, 3267}, {905, 3262}, {908, 4025}, {1465, 35518}, {1502, 23220}, {1565, 2397}, {1785, 30805}, {3261, 22350}, {3926, 39534}, {4391, 62402}, {4554, 35014}, {4561, 42754}, {4563, 42759}, {6063, 52307}, {6332, 22464}, {7182, 46393}, {7192, 51367}, {15419, 17757}, {17880, 24029}, {18210, 55258}, {24002, 51379}, {30786, 42760}, {35015, 65164}, {39471, 56666}, {42751, 57799}, {42752, 52608}, {52392, 53045}, {53549, 57918}
X(65868) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1309}, {3, 32641}, {6, 14776}, {7, 65331}, {56, 32702}, {57, 36110}, {63, 36037}, {69, 13136}, {75, 65223}, {77, 37136}, {222, 2720}, {279, 65537}, {348, 54953}, {514, 36123}, {517, 1783}, {521, 52663}, {525, 38955}, {603, 32669}, {652, 2342}, {656, 2250}, {664, 39294}, {693, 16082}, {859, 112}, {905, 104}, {908, 1897}, {1086, 43933}, {1262, 59103}, {1457, 32674}, {1459, 909}, {1465, 108}, {1565, 2401}, {1769, 19}, {2183, 8750}, {2397, 15742}, {2804, 281}, {3262, 6335}, {3267, 57984}, {3310, 25}, {3937, 2423}, {4025, 34234}, {4091, 1795}, {4131, 65302}, {6332, 51565}, {6735, 65160}, {7004, 61238}, {8677, 6}, {10015, 4}, {14010, 17926}, {15413, 18816}, {16586, 4242}, {17139, 648}, {18210, 55259}, {22350, 101}, {22383, 34858}, {22464, 653}, {23220, 32}, {23224, 14578}, {23757, 8756}, {23788, 27}, {23981, 7115}, {24029, 7012}, {26611, 53151}, {26932, 43728}, {35012, 3310}, {35014, 650}, {35015, 3064}, {35518, 36795}, {36038, 92}, {38353, 53285}, {39173, 32698}, {39534, 393}, {42750, 1990}, {42751, 232}, {42752, 2489}, {42753, 6591}, {42754, 7649}, {42755, 8755}, {42756, 1886}, {42757, 14571}, {42758, 5089}, {42759, 2501}, {42760, 468}, {42761, 523}, {42762, 23710}, {42769, 8609}, {44706, 35321}, {45928, 23711}, {46393, 33}, {46398, 44428}, {47420, 1960}, {49280, 36921}, {51367, 3952}, {51379, 644}, {52307, 55}, {52316, 42069}, {52392, 53811}, {53045, 5081}, {53046, 52427}, {53549, 607}, {56666, 65295}, {56973, 2425}, {57478, 901}, {60000, 36067}, {62402, 651}, {64825, 11109}, {64828, 5379}, {64885, 15501}, {65743, 2427}
X(65868) = {X(35518),X(57242)}-harmonic conjugate of X(3265)

X(65869) = ISOTOMIC CONJUGATE OF X(6078)

Barycentrics    b^2*(b - c)*c^2*(2*a^2 - a*b + b^2 - a*c - 2*b*c + c^2) : :

X(65869) lies on these lines: {325, 523}, {885, 2481}, {1978, 41315}, {2821, 20244}, {2826, 20880}, {3239, 59713}, {3762, 23100}, {4462, 52621}, {4468, 20335}, {4509, 27712}, {4858, 23989}, {18151, 20940}, {20908, 53583}, {24002, 26546}, {54987, 65198}

X(65869) = isotomic conjugate of X(6078)
X(65869) = isotomic conjugate of the anticomplement of X(5519)
X(65869) = isotomic conjugate of the isogonal conjugate of X(6084)
X(65869) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {673, 34547}, {1292, 20533}, {2191, 39353}, {32644, 192}, {36041, 2}, {36086, 56937}, {36146, 7674}, {37206, 20344}, {54987, 20552}
X(65869) = X(18031)-Ceva conjugate of X(23989)
X(65869) = X(5519)-cross conjugate of X(2)
X(65869) = X(i)-isoconjugate of X(j) for these (i,j): {31, 6078}, {1280, 32739}, {6066, 37626}, {9454, 39272}, {23990, 35355}
X(65869) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6078}, {3008, 2284}, {6084, 8659}, {16593, 101}, {33675, 39272}, {35111, 3939}, {39048, 692}, {40615, 1477}, {40618, 1810}, {40619, 1280}, {56900, 52927}, {61074, 6}
X(65869) = crosspoint of X(i) and X(j) for these (i,j): {2481, 54987}, {46135, 57792}
X(65869) = crosssum of X(i) and X(j) for these (i,j): {2223, 8642}, {8638, 14827}
X(65869) = crossdifference of every pair of points on line {32, 39686}
X(65869) = barycentric product X(i)*X(j) for these {i,j}: {76, 6084}, {310, 53558}, {561, 48032}, {918, 56667}, {1279, 40495}, {1502, 8659}, {3008, 3261}, {5853, 52621}, {6063, 53523}, {23989, 53337}
X(65869) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6078}, {693, 1280}, {1111, 35355}, {1279, 692}, {2481, 39272}, {2976, 3052}, {3008, 101}, {3261, 36807}, {3676, 1477}, {4025, 1810}, {5853, 3939}, {6084, 6}, {8659, 32}, {16593, 2284}, {20780, 32656}, {24002, 43760}, {34387, 60576}, {43042, 56643}, {48032, 31}, {51419, 2427}, {51839, 34080}, {52210, 919}, {52621, 35160}, {53337, 1252}, {53523, 55}, {53534, 23344}, {53552, 54325}, {53558, 42}, {54234, 8750}, {56667, 666}, {56793, 2440}, {56796, 2428}, {61074, 8659}
X(65869) = {X(53370),X(63221)}-harmonic conjugate of X(53343)

X(65870) = ISOTOMIC CONJUGATE OF X(6082)

Barycentrics    (b^2 - c^2)*(a^2 + b^2 - 3*b*c + c^2)*(a^2 + b^2 + 3*b*c + c^2) : :
X(65870) = 3 X[9123] - 4 X[9125], 3 X[9123] - 2 X[9485], X[850] + 8 X[58882], X[3268] - 4 X[9148], 4 X[9134] - X[9979], 2 X[9134] + X[53365], X[9979] + 2 X[53365], X[9131] - 4 X[45689], X[9147] - 4 X[45688]

X(65870) lies on these lines: {2, 2793}, {125, 41125}, {325, 523}, {351, 62662}, {671, 690}, {804, 8371}, {888, 7998}, {1499, 8352}, {1649, 9131}, {1995, 34519}, {2408, 42008}, {2789, 9810}, {5468, 52035}, {6088, 12093}, {6089, 27812}, {7496, 11616}, {8288, 38361}, {9146, 18012}, {9147, 9189}, {9168, 55122}, {14223, 62671}, {14273, 52284}, {14417, 44010}, {16220, 32228}, {18911, 39904}, {19912, 39492}, {32472, 47587}, {33915, 41724}, {34174, 63768}, {40916, 53272}, {46336, 47139}, {57813, 60028}, {65467, 65610}

X(65870) = midpoint of X(5466) and X(53365)
X(65870) = reflection of X(i) in X(j) for these {i,j}: {351, 62662}, {1649, 45689}, {3268, 9191}, {5466, 9134}, {9123, 2}, {9131, 1649}, {9147, 9189}, {9185, 8371}, {9189, 45688}, {9191, 9148}, {9485, 9125}, {9979, 5466}, {19912, 39492}, {44010, 14417}
X(65870) = isotomic conjugate of X(6082)
X(65870) = complement of X(9485)
X(65870) = anticomplement of X(9125)
X(65870) = isotomic conjugate of the anticomplement of X(31654)
X(65870) = isotomic conjugate of the isogonal conjugate of X(6088)
X(65870) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {32648, 192}, {36045, 2}, {36142, 11148}, {37216, 14360}
X(65870) = X(65008)-Ceva conjugate of X(9979)
X(65870) = X(31654)-cross conjugate of X(2)
X(65870) = X(i)-isoconjugate of X(j) for these (i,j): {31, 6082}, {163, 34898}, {922, 39296}
X(65870) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6082}, {115, 34898}, {5512, 13493}, {16597, 8691}, {35133, 34581}, {39061, 39296}, {61071, 18775}
X(65870) = crosspoint of X(i) and X(j) for these (i,j): {598, 892}, {671, 35179}
X(65870) = crosssum of X(i) and X(j) for these (i,j): {187, 8644}, {351, 574}, {5467, 35357}
X(65870) = crossdifference of every pair of points on line {32, 9486}
X(65870) = barycentric product X(i)*X(j) for these {i,j}: {76, 6088}, {523, 11054}, {850, 11580}, {4442, 4789}, {8599, 62309}, {12093, 43665}
X(65870) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6082}, {523, 34898}, {671, 39296}, {1499, 34581}, {2793, 18775}, {4442, 37210}, {4789, 51561}, {6088, 6}, {9872, 9145}, {10354, 2434}, {11054, 99}, {11580, 110}, {12093, 2421}, {13492, 1296}, {16611, 8691}, {31654, 9125}, {39157, 65324}, {62309, 9146}
X(65870) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9485, 9125}, {9125, 9485, 9123}, {9134, 53365, 9979}

X(65871) = ISOTOMIC CONJUGATE OF X(2867)

Barycentrics    (b^2 - c^2)*(-a^4 + b^4 + a^2*b*c - b^3*c - b*c^3 + c^4)*(-a^4 + b^4 - a^2*b*c + b^3*c + b*c^3 + c^4) : :
X(65871) = 3 X[9979] - 4 X[16230], 3 X[9979] - 2 X[53345], 2 X[16230] - 3 X[65714], X[53345] - 3 X[65714], 4 X[684] - 3 X[3268], 3 X[2394] - 4 X[44921], 3 X[5664] - 2 X[44810], 2 X[6130] - 3 X[65754]

X(65871) lies on these lines: {20, 2848}, {107, 110}, {147, 2799}, {325, 523}, {525, 51940}, {879, 31636}, {1297, 34168}, {1636, 2501}, {2071, 52737}, {2394, 44921}, {5466, 44877}, {5664, 44810}, {6130, 65754}, {6333, 35140}, {8057, 33294}, {9003, 11061}, {9517, 44427}, {13114, 14273}, {13203, 55121}, {14944, 39473}, {25644, 54071}, {30789, 53383}, {34186, 55127}, {46512, 65623}

X(65871) = reflection of X(i) in X(j) for these {i,j}: {20, 41077}, {3265, 14343}, {9979, 65714}, {53345, 16230}
X(65871) = isotomic conjugate of X(2867)
X(65871) = anticomplement of the isogonal conjugate of X(44770)
X(65871) = isotomic conjugate of the anticomplement of X(33504)
X(65871) = isotomic conjugate of the isogonal conjugate of X(2881)
X(65871) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {162, 12384}, {6330, 21294}, {8767, 3448}, {32649, 192}, {32687, 5905}, {36046, 2}, {36092, 4}, {43717, 21221}, {44770, 8}, {65265, 21270}
X(65871) = X(33504)-cross conjugate of X(2)
X(65871) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2867}, {810, 39297}
X(65871) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2867}, {13611, 48448}, {34846, 26702}, {35968, 10229}, {39062, 39297}, {57606, 1503}, {62612, 525}
X(65871) = crosspoint of X(i) and X(j) for these (i,j): {264, 65265}, {648, 35140}
X(65871) = crosssum of X(647) and X(42671)
X(65871) = trilinear pole of line {57606, 62612}
X(65871) = crossdifference of every pair of points on line {32, 1204}
X(65871) = barycentric product X(i)*X(j) for these {i,j}: {76, 2881}, {648, 57606}, {850, 52058}, {857, 65099}, {3260, 15292}, {35140, 62612}
X(65871) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2867}, {648, 39297}, {2881, 6}, {15292, 74}, {16612, 26702}, {52058, 110}, {56794, 2445}, {57606, 525}, {61505, 2435}, {62612, 1503}, {65099, 37202}
X(65871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16230, 53345, 9979}, {53345, 65714, 16230}

X(65872) = ISOTOMIC CONJUGATE OF X(20404)

Barycentrics    (b^2 - c^2)*(-a^4 + b^4 + 2*a^2*b*c - b^3*c - b^2*c^2 - b*c^3 + c^4)*(-a^4 + b^4 - 2*a^2*b*c + b^3*c - b^2*c^2 + b*c^3 + c^4) : :
X(65872) = 3 X[8859] - 4 X[44564]

X(65872) lies on these lines: {316, 690}, {325, 523}, {340, 16230}, {385, 1637}, {524, 9141}, {525, 8352}, {892, 5466}, {2501, 56021}, {2793, 5999}, {2799, 7840}, {3906, 39266}, {5641, 34765}, {7471, 9182}, {8859, 44564}, {9003, 39099}, {9185, 26276}, {14221, 14607}, {15475, 18829}, {33919, 53365}, {34205, 62651}, {39359, 63248}, {52094, 55142}

X(65872) = reflection of X(i) in X(j) for these {i,j}: {385, 1637}, {3268, 325}, {9979, 62629}
X(65872) = isotomic conjugate of X(20404)
X(65872) = isotomic conjugate of the anticomplement of X(35582)
X(65872) = isotomic conjugate of the isogonal conjugate of X(20403)
X(65872) = X(35582)-cross conjugate of X(2)
X(65872) = X(31)-isoconjugate of X(20404)
X(65872) = X(2)-Dao conjugate of X(20404)
X(65872) = crosspoint of X(892) and X(5641)
X(65872) = crosssum of X(i) and X(j) for these (i,j): {187, 10567}, {351, 5191}
X(65872) = crossdifference of every pair of points on line {32, 59801}
X(65872) = barycentric product X(i)*X(j) for these {i,j}: {76, 20403}, {523, 22254}
X(65872) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 20404}, {20403, 6}, {22254, 99}
X(65872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {850, 3260, 14295}, {5466, 53378, 53347}

X(65873) = ISOTOMIC CONJUGATE OF X(65635)

Barycentrics    a*(b^2 - c^2)*(a^2*b^2 + a*b^3 - a*b^2*c + a^2*c^2 - a*b*c^2 - 2*b^2*c^2 + a*c^3) : :
X(65873) = 4 X[3837] - 3 X[9148], 3 X[351] - 2 X[659], 3 X[1962] - X[48032], 3 X[10180] - 2 X[53580]

X(65873) lies on these lines: {325, 523}, {351, 659}, {512, 4378}, {513, 8663}, {514, 42661}, {690, 764}, {804, 5992}, {876, 18009}, {891, 42666}, {1365, 2611}, {1962, 48032}, {2254, 4155}, {2530, 6367}, {2832, 3743}, {4010, 8034}, {4502, 4526}, {4824, 58289}, {4988, 50330}, {6085, 14752}, {6370, 48326}, {9279, 48023}, {10180, 53580}, {18015, 55244}, {21349, 48408}, {23765, 59629}, {23768, 48080}, {42758, 55122}, {48047, 58360}, {49598, 65482}

X(65873) = reflection of X(i) in X(j) for these {i,j}: {49598, 65482}, {50538, 1491}
X(65873) = isotomic conjugate of X(65635)
X(65873) = X(40017)-Ceva conjugate of X(3124)
X(65873) = X(i)-isoconjugate of X(j) for these (i,j): {31, 65635}, {643, 35108}, {35159, 65375}
X(65873) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 65635}, {35095, 645}, {40622, 35159}, {46842, 99}, {55060, 35108}
X(65873) = crosspoint of X(i) and X(j) for these (i,j): {523, 876}, {18827, 54986}
X(65873) = crosssum of X(110) and X(3573)
X(65873) = crossdifference of every pair of points on line {32, 5546}
X(65873) = barycentric product X(i)*X(j) for these {i,j}: {876, 46842}, {7178, 35104}
X(65873) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 65635}, {7178, 35159}, {7180, 35108}, {35104, 645}, {46842, 874}

X(65874) = ISOTOMIC CONJUGATE OF X(65636)

Barycentrics    a*(b - c)*(a*b - b^2 + a*c - c^2)*(a^2*b^2 - a*b^3 - a*b^2*c + a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3) : :

X(65874) lies on these lines: {325, 523}, {513, 3693}, {522, 20335}, {764, 23102}, {876, 4562}, {899, 3310}, {2254, 3930}, {3126, 3675}, {3783, 24462}, {4724, 52614}, {6168, 53539}, {33891, 47695}, {46403, 56555}

X(65874) = midpoint of X(2254) and X(3930)
X(65874) = isotomic conjugate of X(65636)
X(65874) = X(i)-isoconjugate of X(j) for these (i,j): {31, 65636}, {14665, 36086}, {32666, 53219}
X(65874) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 65636}, {17435, 46802}, {35094, 53219}, {38989, 14665}
X(65874) = crosspoint of X(4562) and X(53210)
X(65874) = crossdifference of every pair of points on line {32, 919}
X(65874) = barycentric product X(i)*X(j) for these {i,j}: {918, 14839}, {3126, 46798}, {43063, 50333}
X(65874) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 65636}, {665, 14665}, {918, 53219}, {3126, 46802}, {14839, 666}, {43063, 927}

X(65875) = X(1)X(1290)∩X(36)X(110)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - a^3*c - b^3*c + a^2*c^2 + b^2*c^2 + a*c^3 + b*c^3 - 2*c^4)*(a^4 - a^3*b + a^2*b^2 + a*b^3 - 2*b^4 + b^3*c - 2*a^2*c^2 + b^2*c^2 - b*c^3 + c^4) : :

X(65875) lies on the circumcircle and these lines: {1, 1290}, {35, 901}, {36, 110}, {56, 34921}, {58, 36069}, {65, 2222}, {79, 476}, {99, 320}, {100, 484}, {101, 2245}, {104, 6003}, {106, 2605}, {108, 1835}, {109, 1464}, {112, 52413}, {513, 759}, {517, 6011}, {1293, 35000}, {1308, 24929}, {1309, 5174}, {1319, 26700}, {2392, 53633}, {2689, 7354}, {2690, 39542}, {2692, 34773}, {2720, 37583}, {2742, 7688}, {2743, 3579}, {2758, 62323}, {3025, 13868}, {5563, 6584}, {9059, 60459}, {13273, 34172}, {22765, 39633}, {28658, 58955}, {33858, 53936}, {36975, 53611}, {50344, 53254}

X(65875) = reflection of X(5127) in X(36)
X(65875) = reflection of X(759) in the X(1)X(3) line
X(65875) = X(758)-isoconjugate of X(61479)
X(65875) = trilinear pole of line {6, 21828}
X(65875) = barycentric quotient X(34079)/X(61479)

X(65876) = X(1)X(2701)∩X(100)X(851)

Barycentrics    a*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - a^4*c - b^4*c + a^2*b*c^2 + a*b^2*c^2 + a^2*c^3 + b^2*c^3 - a*c^4 - b*c^4)*(a^5 - a^4*b + a^2*b^3 - a*b^4 + a^2*b^2*c - b^4*c - a^3*c^2 + a*b^2*c^2 + b^3*c^2 - a^2*c^3 - b*c^4 + c^5) : :

X(65876) lies on the circumcircle and these lines: {1, 2701}, {28, 59041}, {71, 813}, {81, 36069}, {99, 5088}, {100, 851}, {101, 758}, {103, 6003}, {104, 4367}, {105, 47797}, {107, 242}, {108, 1284}, {109, 1758}, {110, 2651}, {112, 1870}, {226, 2222}, {476, 30690}, {514, 759}, {516, 6011}, {649, 2249}, {741, 1459}, {805, 7015}, {919, 40754}, {1290, 1621}, {1309, 7009}, {1444, 36066}, {1457, 29055}, {2736, 41430}, {5127, 43076}, {5144, 8691}, {5994, 39152}, {5995, 39153}, {13397, 62314}, {38470, 51621}, {53114, 58955}

X(65876) = trilinear pole of line {6, 53527}

X(65877) = X(10)X(2222)∩X(100)X(1324)

Barycentrics    a*(a^6 - a^5*b - a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - a*b^5 + b^6 + a^4*b*c - a^3*b^2*c - a^2*b^3*c + a*b^4*c - a^4*c^2 - a^3*b*c^2 + 2*a^2*b^2*c^2 - a*b^3*c^2 - b^4*c^2 + a^3*c^3 + b^3*c^3 + 2*a*b*c^4 - a*c^5 - b*c^5)*(a^6 - a^4*b^2 + a^3*b^3 - a*b^5 - a^5*c + a^4*b*c - a^3*b^2*c + 2*a*b^4*c - b^5*c - a^4*c^2 - a^3*b*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 + b^3*c^3 - a^2*c^4 + a*b*c^4 - b^2*c^4 - a*c^5 + c^6) : :

X(65877) lies on the circumcircle and these lines: {10, 2222}, {21, 36069}, {100, 1324}, {102, 6003}, {108, 860}, {109, 758}, {110, 4511}, {112, 56830}, {476, 52344}, {515, 6011}, {522, 759}, {901, 56288}, {925, 10538}, {934, 41804}, {993, 2701}, {1283, 36935}, {1290, 2975}, {2690, 54335}, {3006, 9070}, {5127, 59006}, {5251, 34309}, {20294, 39435}, {26709, 60358}, {30115, 32682}, {36078, 56254}, {44184, 54081}, {45272, 58986}, {59097, 62342}

X(65878) = X(518)X(1293)∩X(519)X(1292)

Barycentrics    a*(a^5 - 4*a^4*b + 3*a^3*b^2 + 3*a^2*b^3 - 4*a*b^4 + b^5 + 2*a^3*b*c + 2*a*b^3*c - 5*a^2*b*c^2 - 5*a*b^2*c^2 + 8*a*b*c^3 - a*c^4 - b*c^4)*(a^5 - a*b^4 - 4*a^4*c + 2*a^3*b*c - 5*a^2*b^2*c + 8*a*b^3*c - b^4*c + 3*a^3*c^2 - 5*a*b^2*c^2 + 3*a^2*c^3 + 2*a*b*c^3 - 4*a*c^4 + c^5) : :

X(65878) lies on the circumcircle and these lines: {1, 59117}, {3, 2748}, {100, 4899}, {105, 3667}, {106, 3309}, {518, 1293}, {519, 1292}, {901, 3870}, {919, 1743}, {927, 39126}, {2743, 4421}, {9097, 14126}, {53296, 53896}, {53897, 64129}

X(65878) = reflection of X(2748) in X(3)
X(65878) = isogonal conjugate of X(9519)
X(65878) = isogonal conjugate of the anticomplement of X(9519)
X(65878) = isogonal conjugate of the complement of X(9519)
X(65878) = Thomson-isogonal conjugate of X(2832)
X(65878) = X(1)-isoconjugate of X(9519)
X(65878) = X(3)-Dao conjugate of X(9519)
X(65878) = barycentric quotient X(6)/X(9519)

X(65879) = X(72)X(2222)∩X(107)X(5081)

Barycentrics    a^2*(a^7 - a^6*b - 3*a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 - 3*a^2*b^5 - a*b^6 + b^7 + a^5*b*c - 2*a^3*b^3*c + a*b^5*c + a^5*c^2 - 2*a^4*b*c^2 + a^3*b^2*c^2 + a^2*b^3*c^2 - 2*a*b^4*c^2 + b^5*c^2 + a^3*b*c^3 - 2*a^2*b^2*c^3 + a*b^3*c^3 - 3*a^3*c^4 + 2*a^2*b*c^4 + 2*a*b^2*c^4 - 3*b^3*c^4 + 2*a^2*c^5 - 2*a*b*c^5 + 2*b^2*c^5 + a*c^6 + b*c^6 - 2*c^7)*(a^7 + a^5*b^2 - 3*a^3*b^4 + 2*a^2*b^5 + a*b^6 - 2*b^7 - a^6*c + a^5*b*c - 2*a^4*b^2*c + a^3*b^3*c + 2*a^2*b^4*c - 2*a*b^5*c + b^6*c - 3*a^5*c^2 + a^3*b^2*c^2 - 2*a^2*b^3*c^2 + 2*a*b^4*c^2 + 2*b^5*c^2 + 3*a^4*c^3 - 2*a^3*b*c^3 + a^2*b^2*c^3 + a*b^3*c^3 - 3*b^4*c^3 + 3*a^3*c^4 - 2*a*b^2*c^4 - 3*a^2*c^5 + a*b*c^5 + b^2*c^5 - a*c^6 + c^7) : :

X(65879) lies on the circumcircle and these lines: {72, 2222}, {107, 5081}, {108, 758}, {112, 2323}, {283, 36069}, {521, 759}, {1290, 3869}, {1295, 6003}, {5127, 59005}, {6001, 6011}, {26704, 56877}, {52405, 59062}

X(65880) = X(98)X(758)∩X(99)X(6003)

Barycentrics    a^2*(a - b)*(a - c)*(-(a^3*b^3) + a^2*b^4 + a*b^5 - b^6 + a^5*c - a^4*b*c + a^2*b^3*c + b^5*c - a^2*b^2*c^2 + a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 - b^3*c^3 - a*b*c^4 + a*c^5)*(a^5*b - 2*a^3*b^3 + a*b^5 - a^4*b*c - a*b^4*c - a^2*b^2*c^2 - a^3*c^3 + a^2*b*c^3 + a*b^2*c^3 - b^3*c^3 + a^2*c^4 + b^2*c^4 + a*c^5 + b*c^5 - c^6) : :

X(65880) lies on the circumcircle and these lines: {3, 53970}, {98, 758}, {99, 6003}, {511, 759}, {512, 6011}, {991, 12031}, {1983, 2715}, {2687, 63400}, {2708, 3430}, {23997, 36069}, {37508, 53179}

X(65880) = reflection of X(53970) in X(3)
X(65880) = reflection of X(6011) in the Brocard axis

X(65881) = X(74)X(2077)∩X(100)X(6003)

Barycentrics    a^2*(a - b)*(a - c)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^3*c + a^2*b*c + a*b^2*c - 2*b^3*c - a*b*c^2 + 2*a*c^3 + 2*b*c^3 - c^4)*(a^4 - 2*a^3*b + 2*a*b^3 - b^4 + a^2*b*c - a*b^2*c + 2*b^3*c - 2*a^2*c^2 + a*b*c^2 - 2*b*c^3 + c^4) : :

X(65881) lies on the circumcircle and these lines: {40, 2687}, {74, 2077}, {100, 6003}, {104, 758}, {105, 5536}, {106, 22765}, {109, 57139}, {477, 16113}, {513, 6011}, {517, 759}, {840, 15931}, {953, 11012}, {1331, 33637}, {1385, 2718}, {1477, 41341}, {2651, 53707}, {2695, 11827}, {2716, 14110}, {2758, 5690}, {5537, 28471}, {5563, 43081}, {12030, 16139}, {19628, 39136}, {39630, 53280}

X(65881) = reflection of X(22765) in X(49118)
X(65881) = reflection of X(6011) in the OI line
X(65881) = X(51646)-cross conjugate of X(1)
X(65881) = X(i)-isoconjugate of X(j) for these (i,j): {650, 37797}, {23838, 41558}
X(65881) = cevapoint of X(649) and X(2361)
X(65881) = barycentric product X(651)*X(6596)
X(65881) = barycentric quotient X(i)/X(j) for these {i,j}: {109, 37797}, {1983, 39778}, {6596, 4391}, {61197, 41557}, {61210, 41558}

X(65882) = X(40)X(2708)∩X(101)X(6003)

Barycentrics    a*(a - b)*(a - c)*(a^5 - 2*a^4*b + a^3*b^2 + a^2*b^3 - 2*a*b^4 + b^5 - a^3*b*c + 3*a*b^3*c - 2*b^4*c - a^3*c^2 + 2*a^2*b*c^2 + b^3*c^2 - a^2*c^3 - a*b*c^3 + b^2*c^3 - 2*b*c^4 + c^5)*(a^5 - a^3*b^2 - a^2*b^3 + b^5 - 2*a^4*c - a^3*b*c + 2*a^2*b^2*c - a*b^3*c - 2*b^4*c + a^3*c^2 + b^3*c^2 + a^2*c^3 + 3*a*b*c^3 + b^2*c^3 - 2*a*c^4 - 2*b*c^4 + c^5) : :

X(65882) lies on the circumcircle and these lines: {40, 2708}, {101, 6003}, {103, 758}, {514, 6011}, {516, 759}, {840, 18444}, {2249, 2651}, {2716, 63438}, {5127, 59074}, {12032, 63395}, {36516, 65659}

X(65882) = Collings transform of X(1936)
X(65882) = X(51642)-cross conjugate of X(1)
X(65882) = cevapoint of X(513) and X(1936)
X(65882) = trilinear pole of line {6, 39032}

X(65883) = X(102)X(758)∩X(109)X(6003)

Barycentrics    a*(a - b)*(a - c)*(a^6 - a^5*b - a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - a*b^5 + b^6 - a^5*c + a^4*b*c - 2*a^3*b^2*c - 2*a^2*b^3*c + a*b^4*c - b^5*c - a^4*c^2 + 4*a^2*b^2*c^2 - b^4*c^2 + 2*a^3*c^3 + 2*b^3*c^3 - a^2*c^4 + a*b*c^4 - b^2*c^4 - a*c^5 - b*c^5 + c^6)*(a^6 - a^5*b - a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - a*b^5 + b^6 - a^5*c + a^4*b*c + a*b^4*c - b^5*c - a^4*c^2 - 2*a^3*b*c^2 + 4*a^2*b^2*c^2 - b^4*c^2 + 2*a^3*c^3 - 2*a^2*b*c^3 + 2*b^3*c^3 - a^2*c^4 + a*b*c^4 - b^2*c^4 - a*c^5 - b*c^5 + c^6) : :

X(65883) lies on the circumcircle and these lines: {102, 758}, {105, 8229}, {109, 6003}, {515, 759}, {522, 6011}, {934, 31603}, {953, 21740}, {1300, 45766}, {2687, 11491}, {2716, 4297}, {34309, 44425}

X(65883) = X(51643)-cross conjugate of X(1)

X(65884) = X(111)X(1503)∩X(112)X(1499)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^8 - 5*a^6*b^2 - 5*a^2*b^6 + b^8 + 6*a^4*b^2*c^2 + 6*a^2*b^4*c^2 - 2*a^4*c^4 - a^2*b^2*c^4 - 2*b^4*c^4 + c^8)*(a^8 - 2*a^4*b^4 + b^8 - 5*a^6*c^2 + 6*a^4*b^2*c^2 - a^2*b^4*c^2 + 6*a^2*b^2*c^4 - 2*b^4*c^4 - 5*a^2*c^6 + c^8) : :

X(65884) lies on the circumcircle and these lines: {3, 53186}, {111, 1503}, {112, 1499}, {352, 26717}, {524, 1297}, {525, 1296}, {691, 34211}, {842, 6776}, {1300, 41377}, {2763, 14916}, {3565, 53379}, {9136, 37689}, {10102, 37643}, {40119, 63768}, {53929, 64014}

X(65884) = reflection of X(53186) in X(3)
X(65884) = isogonal conjugate of X(62506)
X(65884) = isogonal conjugate of the anticomplement of X(62506)
X(65884) = isogonal conjugate of the complement of X(62506)
X(65884) = X(1)-isoconjugate of X(62506)
X(65884) = X(3)-Dao conjugate of X(62506)
X(65884) = trilinear pole of line {6, 35282}
X(65884) = barycentric quotient X(6)/X(62506)

X(65885) = X(105)X(758)∩X(111)X(5526)

Barycentrics    a^2*(a - b)*(a - c)*(a^3 - a^2*b + a*b^2 + b^3 - a^2*c - a*b*c + b^2*c - a*c^2 - b*c^2 + c^3)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - a*b*c - b^2*c + a*c^2 + b*c^2 + c^3) : :

X(65885) lies on the circumcircle and these lines: {105, 758}, {111, 5526}, {518, 759}, {741, 5127}, {1290, 3573}, {1292, 6003}, {3309, 6011}, {5315, 9097}, {5525, 53686}, {6065, 8701}, {36069, 54353}

X(65885) = X(513)-isoconjugate of X(33139)
X(65885) = X(39026)-Dao conjugate of X(33139)
X(65885) = trilinear pole of line {6, 64710}
X(65885) = barycentric quotient X(101)/X(33139)

X(65886) = X(98)X(5205)∩X(100)X(30721)

Barycentrics    a*(a - b)*(a - c)*(a^3 - 2*a^2*b - 2*a*b^2 + b^3 + a*b*c + c^3)*(a^3 + b^3 - 2*a^2*c + a*b*c - 2*a*c^2 + c^3) : :

X(65886) lies on the circumcircle and these lines: {98, 5205}, {100, 30721}, {104, 47624}, {105, 5211}, {106, 758}, {519, 759}, {643, 53633}, {644, 28467}, {649, 6010}, {741, 2651}, {1201, 12029}, {1252, 8687}, {1293, 6003}, {2701, 3573}, {3667, 6011}, {4076, 8707}, {4571, 53625}, {4578, 9104}, {5127, 59072}, {5524, 28482}, {5529, 38453}, {7191, 9097}, {9058, 52923}, {26711, 57151}, {28485, 34997}, {38470, 53280}, {57192, 59109}, {61223, 64519}, {62644, 65365}

X(65886) = X(i)-isoconjugate of X(j) for these (i,j): {513, 60353}, {514, 65741}, {649, 37759}, {661, 37791}, {1635, 47056}, {36926, 43924}
X(65886) = X(i)-Dao conjugate of X(j) for these (i,j): {5375, 37759}, {36830, 37791}, {39026, 60353}
X(65886) = cevapoint of X(i) and X(j) for these (i,j): {9, 4730}, {667, 2323}
X(65886) = trilinear pole of line {6, 5429}
X(65886) = barycentric product X(i)*X(j) for these {i,j}: {100, 65740}, {662, 34895}, {4585, 36935}
X(65886) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 37759}, {101, 60353}, {110, 37791}, {644, 36926}, {692, 65741}, {901, 47056}, {4585, 41873}, {34895, 1577}, {36935, 60074}, {65740, 693}





leftri   W-maps: X(65887) - X(65947)  rightri

Contributed by Clark Kimberling and Peter Moses, October 22, 2024.

Suppose that distinct points U and U' are given by normalized barycentrics U = (u,v,w) and U' = (u',v',w'). The W-map of U and U' is here introduced as the point W(U,U') given by

W = W(U,U') = (u - u')2 : (v - v')2 : (w - w')2.

As a barycentric square, the point W lies on the Steiner inellipse, and the point W* = u-u' : v-v' : w-w' lies on the line at infinity. Let g(W*) = isogonal conjugate of W*, so that g(W*) lies on the circumcircle. Then W = crosspoint(X(2) and W*) = crosssum(X(6) and g(W*)).

The W-map is related to the D-map introduced in the preamble just before X(65742). If U and U' lie on a line L, then every pair of points on L have the same W-map. Thus, W(U,U') can be regarded as a mapping from the line L = UU' to W(U,U'), for which we write W(L), as well as W(U,U'). If U and U' are triangle centers, then W(U,U') is a triangle center.

W(Euler line) = W(X(2),X(3)) = X(3163) = crosssum of X(6) and X(74)
W(Brocard axis) = W(X(3),X(6)) = X(11672) = crosssum of X(6) and X(98)
W(IO line) = W(X(1),X(3)) = X(23980) = crosssum of X(6) and X(104)
W(orthic axis) = W(X(230),X(231)) = X(115) = crosssum of X(6) and X(110)
W(anti-orthic axis) = W(X(44),X(513)) = X(1015) = crosssum of X(6) and X(100)
W(Lemoine axis) = W(X(187),X(237)) = X(1084) = crosssum of X(6) and X(99)
W(de Longchamps axis) = W(X(325),X(523)) = X(115) = crosssum of X(6) and X(110)
W(Gergonne line) = W(X(241),X(514)) = X(1086) = crosssum of X(6) and X(101)
W(Soddy line) = W(X(1),X(7)) = X(23972) = crosssum of X(6) and X(103)
W(Nagel line) = W(X(1),X(2)) = X(4370) = crosssum of X(6) and X(106)
W(Fermat line) = W(X(6),X(13)) = X(23967) = crosssum of X(6) and X(842)
W(Napoleon axis) = W(X(6),X(17)) = X(65917) = crosssum of X(6) and X(5966)
W(van Aubel line) = W(X(4),X(6)) = X(23976) = crosssum of X(6) and X(1297)
W(GK line) = W(X(2),X(6)) = X(2482) = crosssum of X(6) and X(111)
W(IN line) = W(X(1),X(5)) = X(61066)
W(IK line) = W(X(1),X(6)) = X(6184)
W(Hatzipolakis axis) = W(X(5),X(523)) = X(115) = crosssum of X(6) and X(110)
W(Koiller line) = W(X(650),X(663)) = X(35508) = crosssum of X(6) and X(934)
W(Garcia-Reznick line) = W(X(522),X(650)) = X(1146) = crosssum of X(6) and X(109)
W(Helman line) = W(X(513),X(663)) = X(1015) = crosssum of X(6) and X(100)
W(Steiner minor axis) = W(X(2),X(1340)) = X(39022) = crosssum of X(6) and X(1380)
W(Steiner major axis) = W(X(2),X(1341)) = X(39023) = crosssum of X(6) and X(1279)

The appearance of (i,j,k) in the following list means that W(X(i),X(j)) = X(k), where k < 65887. (1,2,4370), (1,3,23980), (1,4,23986), (1,5,61066), (1,6,6184), (1,7,23972), (1,21,35069), (1,79,3163), (1,75,35068), (1,87,20532), (1,88,35129), (1,142,35111), (1,147,35082), (1,190,35123), (2,3,3163), (2,6,2482), (2,7,35110), (2,11,35113), (2,13,61068), (2,14,61069), (2,32,61064), (2,37,13466), (2,38,35123), (2,39,35073), (2,44,35124), (2,45,35121), (2,51,11672), (2,98,23967), (2,99,35087), (2,165,23972), (3,6,11672), (3,8,61066), (3,10,23986), (3,66,23976), (3,67,23967), (3,69,35067), (3,76,61070), (3,142,23972), (4,6,23976), (4,8,23980), (4,9,23972), (4,69,11672), (4,145,61066), (4,147,61070), (5,6,35067), (5,10,23980), (5,39,61070), (5,141,11672), (5,182,23976), (6,7,35093), (6,13,23967), (6,25,61067), (6,76,61063), (6,99,35077), (6,190,35126), (7,8,6184), (7,21,35066), (7,80,35116), (7,192,35120), (8,9,35111), (8,20,23986), (8,79,35069), (8,80,35129), (8,144,23972), (8,190,35113), (8,192,35068), (9,46,35066), (9,48,35116), (9,75,35120), (9,80,35113), (10,11,35129), (10,12,35069), (10,37,35068), (10,75,20532), (10,98,35082), (10,140,61066), (10,141,6184), (10,190,35085), (11,36,3163), (11,118,35116), (12,35,3163), (13,15,3163), (14,16,3163), (19,27,35075), (20,64,23976), (20,145,23980), (20,185,11672), (21,99,35084), (22,161,23976), (22,184,11672), (23,110,11672), (40,191,3163), (52,185,3163), (53,577,3163), (55,495,3163), (56,496,3163), (61,397,3163), (62,398,3163), (64,68,3163), (74,265,3163), (80,484,3163), (98,671,3163), (99,316,3163), (110,477,3163), (115,187,3163), (143,389,3163), (146,323,3163), (148,385,3163), (182,597,3163), (36,80,23986), (36,100,4370), (37,39,20532), (37,86,35127), (38,42,6184), (39,141,61063), (44,190,13466), (46,78,35069), (55,63,6184), (56,78,6184), (57,85,35074), (57,200,6184), (58,86,35114), (58,99,35117), (59,100,35072), (63,100,35116), (66,68,11672), (67,74,23976), (69,74,23967), (69,144,35093), (69,194,61063), (74,98,23992), (75,141,35126), (81,99,35089), (86,99,35085), (86,142,35115), (98,100,35083), (98,109,35081), (99,100,35079), (99,101,35080), (99,102,35081), (99,104,35083), (99,109,35086), (99,110,23992), (99,112,35088), (99,187,35073), (100,101,35125), (100,108,55153), (100,109,35128), (100,110,35090), (100,190,35092), (101,109,39017), (102,103,39017), (107,110,39008), (113,114,23992), (114,132,35088), (115,120,35084), (115,125,23992), (115,127,35088), (116,119,35116), (116,124,39017), (117,118,39017), (122,125,39008), (125,136,39021), (140,141,35067), (140,143,11672), (144,145,6184), (146,147,23992), (146,148,23967), (151,152,39017), (155,159,11672), (162,190,35122), (171,181,11672)

The appearance of (i,j,k) in the following list means that W(X(i),X(j)) = X(k), where k > 65886.

(1,19,65887), (1,39,65888), (1,41,65889), (1,76,65890), (1,84,65891), (1,85,65892), (1,90,65893), (1,99,65894), (1,104,65895), (2,12,65896), (2,17,65897), (2,18, 65898), (2,31,65899), (2,85,65900), (2,92,65901), (2,94,65902), (2,187,65903), (3,9,65904), (3,49, 65905), (3, 54,65906), (3,64,65907), (3,74,65908), (3,95,65909), (3,101,65910), (3,101,65910), (3,113,65911), (3,114,65912), (3,110,65913), (4,67,65914), (4,99,65915), (4,195,65916), (6,17,65917), (6,22,65918), (6,31,65919), (6,67,65920), (6,75,65921), (6,101,65922), (6,110, 65923), (6,169,65924), (6,194,65925), (7,104,65926), (8,21,65927), (8,193,65928), (9,43,65929), (9,55,65930), (9,165,65931), (10,21,65932), (10,86,65933), (11,113,65934), (19,25,65935), (19,57,65936), (22,98,65937), (32,99, 65938), (37,101,65939), (38,75,65940), (42,81,65941), (63,194,65942), (75,77,65943), (75,99,65944), (81,105,65945), (99,108,65946), (104,105,65947)

underbar



X(65887) = CROSSSUM OF X(6) AND X(26702)

Barycentrics    a^2*(b + c)^2*(a^4 - b^4 - a^2*b*c + b^3*c + b*c^3 - c^4)^2 : :

X(65887) lies on the Steiner inellipse and these lines: {37, 15526}, {115, 16583}, {1015, 1104}, {1086, 1901}, {1146, 1834}, {2092, 35508}, {6354, 21813}, {9475, 21789}, {33504, 53982}, {38930, 61075}

X(65887) = complement of the isotomic conjugate of X(44661)
X(65887) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 44661}, {32, 1375}, {857, 626}, {1402, 1861}, {1918, 910}, {3220, 3741}, {7291, 21240}, {39690, 141}, {44661, 2887}
X(65887) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 44661}, {162, 2881}
X(65887) = X(26702)-isoconjugate of X(37202)
X(65887) = X(44661)-Dao conjugate of X(2)
X(65887) = crosspoint of X(2) and X(44661)
X(65887) = crosssum of X(6) and X(26702)
X(65887) = barycentric product X(i)*X(j) for these {i,j}: {8, 3320}, {857, 39690}, {44661, 44661}
X(65887) = barycentric quotient X(i)/X(j) for these {i,j}: {3320, 7}, {39690, 37202}

X(65888) = CROSSSUM OF X(6) AND X(14665)

Barycentrics    a^2*(a^2*b^2 - a*b^3 - a*b^2*c + a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3)^2 : :

X(65888) lies on the Steiner inellipse and these lines: {2, 53219}, {9, 39014}, {37, 35119}, {141, 35094}, {513, 6184}, {518, 1015}, {536, 61076}, {1084, 2238}, {1086, 1575}, {1146, 3932}, {1573, 5701}, {2276, 24338}, {3508, 39015}, {3789, 35026}, {4370, 45673}, {4762, 13466}, {25382, 44798}, {35509, 46100}, {52656, 52922}

X(65888) = complement of X(53219)
X(65888) = complement of the isotomic conjugate of X(14839)
X(65888) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 14839}, {14839, 2887}, {43063, 17046}
X(65888) = X(2)-Ceva conjugate of X(14839)
X(65888) = X(14839)-Dao conjugate of X(2)
X(65888) = crosspoint of X(2) and X(14839)
X(65888) = crosssum of X(6) and X(14665)
X(65888) = barycentric product X(14839)*X(14839)
X(65888) = barycentric quotient X(14839)/X(53219)

X(65889) = CROSSSUM OF X(6) AND X(2725)

Barycentrics    a^2*(a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c - 2*a^2*b*c + b^3*c - a^2*c^2 + a*c^3 + b*c^3 - c^4)^2 : :

X(65889) lies on the Steiner inellipse and these lines: {6, 52927}, {37, 35094}, {1015, 1279}, {1086, 3290}, {1633, 62554}, {2276, 35125}, {6184, 6586}, {16686, 41934}, {17366, 35119}, {20672, 23990}, {35072, 51418}

X(65889) = complement of the isotomic conjugate of X(2809)
X(65889) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2809}, {32, 26007}, {2809, 2887}
X(65889) = X(2)-Ceva conjugate of X(2809)
X(65889) = X(2809)-Dao conjugate of X(2)
X(65889) = crosspoint of X(2) and X(2809)
X(65889) = crosssum of X(6) and X(2725)
X(65889) = barycentric product X(2809)*X(2809)

X(65890) = CROSSSUM OF X(6) AND X(731)

Barycentrics    (a^3*b^2 + a^3*c^2 - b^3*c^2 - b^2*c^3)^2 : :

X(65890) lies on the Steiner inellipse and these lines: {2, 43096}, {37, 55049}, {141, 61065}, {742, 35119}, {1015, 24325}, {1086, 21264}, {2235, 35539}, {35123, 64914}, {35964, 43099}, {36256, 37133}

X(65890) = complement of X(43096)
X(65890) = complement of the isogonal conjugate of X(8622)
X(65890) = complement of the isotomic conjugate of X(730)
X(65890) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 730}, {730, 2887}, {1492, 62446}, {2235, 141}, {8622, 10}, {35539, 21235}, {62446, 55061}
X(65890) = X(2)-Ceva conjugate of X(730)
X(65890) = X(730)-Dao conjugate of X(2)
X(65890) = crosspoint of X(2) and X(730)
X(65890) = crosssum of X(6) and X(731)
X(65890) = barycentric product X(i)*X(j) for these {i,j}: {730, 730}, {8622, 35539}
X(65890) = barycentric quotient X(i)/X(j) for these {i,j}: {730, 43096}, {8622, 731}

X(65891) = CROSSSUM OF X(6) AND X(1295)

Barycentrics    a^2*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c + 2*a^3*b^2*c - 3*a*b^4*c - a^4*c^2 + 2*a^3*b*c^2 - 4*a^2*b^2*c^2 + 2*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + 2*a*b^2*c^3 + 2*a^2*c^4 - 3*a*b*c^4 + b^2*c^4 + a*c^5 - c^6)^2 : :

X(65891) lies on the Steiner inellipse and these lines: {6, 268}, {32, 14578}, {37, 61075}, {115, 1865}, {800, 1015}, {1086, 1427}, {1108, 1146}, {2092, 35071}, {6184, 47408}, {8557, 35508}, {8609, 55153}, {18591, 39020}, {35090, 40135}

X(65891) = complement of the isotomic conjugate of X(6001)
X(65891) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 6001}, {32, 34050}, {560, 14571}, {1397, 51616}, {1918, 3330}, {2443, 46396}, {6001, 2887}, {7435, 21259}, {43058, 17046}, {51359, 21243}, {51660, 2886}
X(65891) = X(2)-Ceva conjugate of X(6001)
X(65891) = X(i)-isoconjugate of X(j) for these (i,j): {1295, 65246}, {2417, 36044}
X(65891) = X(i)-Dao conjugate of X(j) for these (i,j): {6001, 2}, {35580, 2417}, {53991, 65342}
X(65891) = crosspoint of X(i) and X(j) for these (i,j): {2, 6001}, {43058, 56634}
X(65891) = crosssum of X(6) and X(1295)
X(65891) = crossdifference of every pair of points on line {1295, 6087}
X(65891) = barycentric product X(i)*X(j) for these {i,j}: {108, 58264}, {6001, 6001}, {25640, 39175}, {47434, 57495}
X(65891) = barycentric quotient X(58264)/X(35518)

X(65892) = CROSSSUM OF X(6) AND X(12032)

Barycentrics    (a^4*b - 2*a^3*b^2 + a^2*b^3 + a^4*c - b^4*c - 2*a^3*c^2 + b^3*c^2 + a^2*c^3 + b^2*c^3 - b*c^4)^2 : :

X(65892) lies on the Steiner inellipse and these lines: {2, 53210}, {6, 666}, {37, 39014}, {142, 35094}, {518, 1146}, {522, 6184}, {527, 61076}, {1086, 9436}, {4762, 35110}, {5701, 35128}, {17754, 24411}, {35508, 40869}, {36219, 39012}, {48315, 59573}

X(65892) = complement of X(53210)
X(65892) = complement of the isotomic conjugate of X(28850)
X(65892) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 28850}, {32, 43063}, {14197, 20544}, {28850, 2887}
X(65892) = X(2)-Ceva conjugate of X(28850)
X(65892) = X(28850)-Dao conjugate of X(2)
X(65892) = crosspoint of X(2) and X(28850)
X(65892) = crosssum of X(6) and X(12032)
X(65892) = barycentric product X(i)*X(j) for these {i,j}: {8, 59808}, {28850, 28850}
X(65892) = barycentric quotient X(i)/X(j) for these {i,j}: {28850, 53210}, {59808, 7}

X(65893) = CROSSSUM OF X(6) AND X(915)

Barycentrics    a^2*(a^2 - b^2 - c^2)^2*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4)^2 : :

X(65893) lies on the Steiner inellipse and these lines: {2, 46133}, {115, 18591}, {216, 1015}, {219, 577}, {1086, 1214}, {2092, 39013}, {3163, 47235}, {3284, 35090}, {35128, 46974}, {55153, 63849}

X(65893) = complement of X(46133)
X(65893) = complement of the isotomic conjugate of X(912)
X(65893) = isogonal conjugate of the polar conjugate of X(34332)
X(65893) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 912}, {810, 3139}, {912, 2887}, {914, 626}, {1737, 21243}, {1918, 45886}, {2252, 141}, {3658, 21259}, {8609, 20305}, {32656, 55126}, {51649, 2886}, {56410, 17072}
X(65893) = X(2)-Ceva conjugate of X(912)
X(65893) = X(i)-isoconjugate of X(j) for these (i,j): {913, 46133}, {915, 37203}
X(65893) = X(912)-Dao conjugate of X(2)
X(65893) = crosspoint of X(2) and X(912)
X(65893) = crosssum of X(6) and X(915)
X(65893) = crossdifference of every pair of points on line {915, 39534}
X(65893) = barycentric product X(i)*X(j) for these {i,j}: {3, 34332}, {119, 53786}, {912, 912}, {914, 2252}
X(65893) = barycentric quotient X(i)/X(j) for these {i,j}: {912, 46133}, {2252, 37203}, {34332, 264}, {53786, 57753}

X(65894) = CROSSSUM OF X(6) AND X(12031)

Barycentrics    (b + c)^2*(-a^4 + a^2*b^2 + a*b^3 - a*b^2*c + a^2*c^2 - a*b*c^2 - b^2*c^2 + a*c^3)^2 : :

X(65894) lies on the Steiner inellipse and these lines: {115, 740}, {523, 35068}, {1015, 4974}, {1086, 10026}, {1213, 35080}, {2482, 28840}, {4370, 45676}, {4590, 9509}, {6543, 61339}, {17045, 35119}, {23992, 24348}, {34528, 35088}, {35078, 36227}, {44396, 61065}

X(65894) = complement of the isogonal conjugate of X(5147)
X(65894) = X(5147)-complementary conjugate of X(10)
X(65894) = crosssum of X(6) and X(12031)
X(65894) = barycentric quotient X(5147)/X(12031)

X(65895) = CROSSSUM OF X(6) AND X(2716)

Barycentrics    a^2*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c - 2*a^4*b*c + 3*a^3*b^2*c + a^2*b^3*c - 4*a*b^4*c + b^5*c - a^4*c^2 + 3*a^3*b*c^2 - 6*a^2*b^2*c^2 + 3*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + a^2*b*c^3 + 3*a*b^2*c^3 - 2*b^3*c^3 + 2*a^2*c^4 - 4*a*b*c^4 + b^2*c^4 + a*c^5 + b*c^5 - c^6)^2 : :

X(65895) lies on the Steiner inellipse and these lines: {6, 32641}, {37, 55153}, {44, 35072}, {650, 23986}, {1015, 8607}, {1086, 1465}, {1108, 35092}, {1146, 8609}, {4370, 47408}, {6589, 23980}, {8557, 35125}

X(65895) = complement of the isotomic conjugate of X(2800)
X(65895) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2800}, {32, 43043}, {2800, 2887}
X(65895) = X(2)-Ceva conjugate of X(2800)
X(65895) = X(2800)-Dao conjugate of X(2)
X(65895) = crosspoint of X(2) and X(2800)
X(65895) = crosssum of X(6) and X(2716)
X(65895) = crossdifference of every pair of points on line {2716, 35013}
X(65895) = barycentric product X(2800)*X(2800)

X(65896) = CROSSSUM OF X(6) AND X(38882)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 + 4*a^2*b*c - 2*a*b^2*c - a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 - c^4)^2 : :
X(65896) = 3 X[6648] + X[57887]

X(65896) lies on the Steiner inellipse and these lines: {2, 6648}, {478, 31141}, {529, 52970}, {1086, 39595}, {1146, 5750}, {3509, 35091}, {14394, 14412}, {17053, 39015}, {31157, 56325}, {35092, 60353}, {55153, 56906}

X(65896) = midpoint of X(2) and X(6648)
X(65896) = complement of X(57887)
X(65896) = complement of the isotomic conjugate of X(529)
X(65896) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 529}, {529, 2887}, {43036, 17046}, {52970, 142}
X(65896) = X(2)-Ceva conjugate of X(529)
X(65896) = X(529)-Dao conjugate of X(2)
X(65896) = crosspoint of X(2) and X(529)
X(65896) = crosssum of X(6) and X(38882)
X(65896) = barycentric product X(529)*X(529)
X(65896) = barycentric quotient X(529)/X(57887)

X(65897) = CROSSSUM OF X(6) AND X(2380)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4 + 2*Sqrt[3]*(2*a^2 - b^2 - c^2)*S)^2 : :
X(65897) = X[11117] + 3 X[32036]

X(65897) lies on the Steiner inellipse and these lines: {2, 11087}, {30, 33500}, {115, 619}, {299, 6148}, {465, 15526}, {531, 15609}, {532, 18803}, {1084, 40696}, {5642, 45147}, {35443, 61069}, {41888, 43961}

X(65897) = midpoint of X(2) and X(32036)
X(65897) = complement of X(11117)
X(65897) = complement of the isotomic conjugate of X(532)
X(65897) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 532}, {532, 2887}, {2152, 44383}, {8014, 63803}, {14446, 21253}, {23714, 20305}, {52750, 21256}
X(65897) = X(2)-Ceva conjugate of X(532)
X(65897) = X(532)-Dao conjugate of X(2)
X(65897) = crosspoint of X(2) and X(532)
X(65897) = crosssum of X(6) and X(2380)
X(65897) = barycentric product X(i)*X(j) for these {i,j}: {298, 42003}, {299, 30462}, {532, 532}
X(65897) = barycentric quotient X(i)/X(j) for these {i,j}: {532, 11117}, {30462, 14}, {42003, 13}

X(65898) = CROSSSUM OF X(6) AND X(2381)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4 - 2*Sqrt[3]*(2*a^2 - b^2 - c^2)*S)^2 : :
X(65898) = X[11118] + 3 X[32037]

X(65898) lies on the Steiner inellipse and these lines: {2, 11082}, {30, 33498}, {115, 618}, {298, 6148}, {466, 15526}, {530, 15610}, {533, 18804}, {1084, 40695}, {5642, 45147}, {35444, 61068}, {41887, 43962}

X(65898) = midpoint of X(2) and X(32037)
X(65898) = complement of X(11118)
X(65898) = complement of the isotomic conjugate of X(533)
X(65898) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 533}, {533, 2887}, {2151, 44382}, {8015, 63803}, {14447, 21253}, {23715, 20305}, {52751, 21256}
X(65898) = X(2)-Ceva conjugate of X(533)
X(65898) = X(533)-Dao conjugate of X(2)
X(65898) = crosspoint of X(2) and X(533)
X(65898) = crosssum of X(6) and X(2381)
X(65898) = barycentric product X(i)*X(j) for these {i,j}: {298, 30459}, {299, 42004}, {533, 533}
X(65898) = barycentric quotient X(i)/X(j) for these {i,j}: {533, 11118}, {30459, 13}, {42004, 14}

X(65899) = CROSSSUM OF X(6) AND X(753)

Barycentrics    (2*a^3 - b^3 - c^3)^2 : :
X(65899) = 5 X[2] - X[39345], 5 X[4586] + X[39345], 3 X[4586] + X[43097], 2 X[4586] + X[61065], 3 X[39345] - 5 X[43097], 2 X[39345] - 5 X[61065], 2 X[43097] - 3 X[61065]

X(65899) lies on the Steiner inellipse and these lines: {2, 4586}, {115, 41193}, {752, 52957}, {1086, 4670}, {1146, 50305}, {1501, 42058}, {4809, 14402}, {6174, 35123}, {16584, 55049}, {19557, 31151}, {31134, 32664}, {35092, 50023}

X(65899) = midpoint of X(2) and X(4586)
X(65899) = reflection of X(61065) in X(2)
X(65899) = complement of X(43097)
X(65899) = complement of the isogonal conjugate of X(8626)
X(65899) = complement of the isotomic conjugate of X(752)
X(65899) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 752}, {752, 2887}, {2243, 141}, {4070, 21244}, {4144, 21245}, {4809, 21252}, {8626, 10}, {14402, 61065}, {14438, 116}, {30874, 40379}, {34069, 33904}, {35548, 21235}, {52957, 2}, {62448, 55061}
X(65899) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 752}, {752, 8032}, {4586, 33904}
X(65899) = X(8032)-cross conjugate of X(752)
X(65899) = X(i)-Dao conjugate of X(j) for these (i,j): {752, 2}, {33904, 61065}
X(65899) = crosspoint of X(2) and X(752)
X(65899) = crosssum of X(6) and X(753)
X(65899) = trilinear pole of line {8032, 33568}
X(65899) = crossdifference of every pair of points on line {753, 62448}
X(65899) = barycentric product X(i)*X(j) for these {i,j}: {752, 752}, {4586, 33568}, {8032, 43097}, {8626, 35548}, {30874, 52957}
X(65899) = barycentric quotient X(i)/X(j) for these {i,j}: {752, 43097}, {8032, 752}, {8626, 753}, {33568, 824}

X(65900) = CROSSPOINT OF X(2) AND X(44664)

Barycentrics    (a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c + 2*a^2*b*c - a*b^2*c - 2*b^3*c - 2*a^2*c^2 - a*b*c^2 + 4*b^2*c^2 + a*c^3 - 2*b*c^3)^2 : :
X(65900) = 2 X[4569] + X[35508], X[14943] - 3 X[38093]

X(65900) lies on the Steiner inellipse and these lines: {2, 4569}, {115, 18635}, {142, 1146}, {536, 48315}, {1015, 4000}, {1086, 11019}, {6173, 61076}, {9436, 35091}, {13466, 42341}, {14943, 38093}, {17073, 35072}, {20206, 61075}, {31169, 40593}, {35094, 41555}, {39011, 57033}, {44664, 52980}

X(65900) = midpoint of X(2) and X(4569)
X(65900) = reflection of X(35508) in X(2)
X(65900) = complement of the isotomic conjugate of X(44664)
X(65900) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 44664}, {3000, 141}, {44664, 2887}, {52888, 1329}, {52980, 17047}, {62738, 3452}, {65705, 124}
X(65900) = X(2)-Ceva conjugate of X(44664)
X(65900) = X(44664)-Dao conjugate of X(2)
X(65900) = crosspoint of X(2) and X(44664)
X(65900) = barycentric product X(i)*X(j) for these {i,j}: {44664, 44664}, {52888, 52980}

X(65901) = CROSSSUM OF X(6) AND X(32726)

Barycentrics    (a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 + a^4*c + a^2*b^2*c - 2*b^4*c - a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 + 2*b^3*c^2 - a^2*c^3 + 2*b^2*c^3 + a*c^4 - 2*b*c^4)^2 : :
X(65901) = 5 X[2] - 4 X[40482], 2 X[18026] + X[35072], 5 X[18026] + 4 X[40482], 5 X[35072] - 8 X[40482]

X(65901) lies on the Steiner inellipse and these lines: {2, 18026}, {226, 1146}, {381, 2808}, {442, 15526}, {1015, 3772}, {1086, 1210}, {2482, 2798}, {18592, 35071}, {30691, 30692}, {35508, 46835}, {39036, 64781}, {52982, 64780}

X(65901) = midpoint of X(2) and X(18026)
X(65901) = reflection of X(35072) in X(2)
X(65901) = complement of the isotomic conjugate of X(64780)
X(65901) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 64780}, {2635, 141}, {2637, 123}, {30691, 116}, {52889, 21246}, {52982, 21243}, {62736, 18589}, {64780, 2887}
X(65901) = X(2)-Ceva conjugate of X(64780)
X(65901) = X(i)-isoconjugate of X(j) for these (i,j): {23707, 32726}, {36140, 63744}
X(65901) = X(i)-Dao conjugate of X(j) for these (i,j): {33572, 521}, {64780, 2}
X(65901) = crosspoint of X(2) and X(64780)
X(65901) = crosssum of X(6) and X(32726)
X(65901) = barycentric product X(64780)*X(64780)
X(65901) = barycentric quotient X(2635)/X(23707)

X(65902) = CROSSSUM OF X(6) AND X(32730)

Barycentrics    (a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 - 2*b^6*c^2 - 2*a^4*c^4 + 4*b^4*c^4 + a^2*c^6 - 2*b^2*c^6)^2 : :
X(65902) = 5 X[2] - 4 X[40485], X[18334] + 2 X[35139], 5 X[18334] - 8 X[40485], 3 X[18334] - 2 X[60013], 5 X[35139] + 4 X[40485], 3 X[35139] + X[60013], 12 X[40485] - 5 X[60013]

X(65902) lies on the Steiner inellipse and these lines: {2, 18334}, {115, 3580}, {623, 43962}, {624, 43961}, {2072, 15526}, {2482, 31174}, {7603, 13162}, {7753, 35078}, {7810, 16535}, {9466, 35088}, {16188, 34209}

X(65902) = midpoint of X(2) and X(35139)
X(65902) = reflection of X(18334) in X(2)
X(65902) = complement of X(60013)
X(65902) = complement of the isogonal conjugate of X(3016)
X(65902) = X(i)-complementary conjugate of X(j) for these (i,j): {3016, 10}, {32678, 64461}
X(65902) = X(35139)-Ceva conjugate of X(64461)
X(65902) = X(64461)-Dao conjugate of X(18334)
X(65902) = crosssum of X(6) and X(32730)
X(65902) = barycentric quotient X(3016)/X(32730)

X(65903) = CROSSSUM OF X(6) AND X(6323)

Barycentrics    (4*a^4 - a^2*b^2 - 2*b^4 - a^2*c^2 + 2*b^2*c^2 - 2*c^4)^2 : :
X(65903) = X[17416] + 2 X[35138]

X(65903) lies on the Steiner inellipse and these lines: {2, 17416}, {115, 597}, {1084, 9465}, {1641, 35073}, {5306, 35133}, {5642, 35087}, {6593, 31173}, {11168, 15526}, {11672, 45331}, {15303, 35088}, {22329, 23992}, {35077, 44397}

X(65903) = midpoint of X(2) and X(35138)
X(65903) = reflection of X(17416) in X(2)
X(65903) = complement of the isotomic conjugate of X(3849)
X(65903) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3849}, {3849, 2887}, {60867, 21256}
X(65903) = X(2)-Ceva conjugate of X(3849)
X(65903) = X(3849)-Dao conjugate of X(2)
X(65903) = crosspoint of X(2) and X(3849)
X(65903) = crosssum of X(6) and X(6323)
X(65903) = barycentric product X(3849)*X(3849)

X(65904) = CROSSSUM OF X(6) AND X(972)

Barycentrics    a^2*(a^4*b - 2*a^3*b^2 + 2*a*b^4 - b^5 + a^4*c + 2*a^3*b*c - 2*a*b^3*c - b^4*c - 2*a^3*c^2 + 2*b^3*c^2 - 2*a*b*c^3 + 2*b^2*c^3 + 2*a*c^4 - b*c^4 - c^5)^2 : :

X(65904) lies on the Steiner inellipse and these lines: {1, 35072}, {2, 46137}, {6, 2338}, {115, 44993}, {216, 59215}, {220, 36049}, {577, 32652}, {1015, 17054}, {1086, 1108}, {1146, 1210}, {1212, 20264}, {8609, 35091}, {9502, 23980}, {15526, 18635}, {43065, 55153}

X(65904) = complement of X(46137)
X(65904) = complement of the isotomic conjugate of X(971)
X(65904) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 971}, {32, 43035}, {971, 2887}, {2272, 141}, {43044, 17046}, {51364, 17047}
X(65904) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 971}, {45250, 2272}
X(65904) = X(971)-Dao conjugate of X(2)
X(65904) = crosspoint of X(i) and X(j) for these (i,j): {2, 971}, {43044, 56640}
X(65904) = crosssum of X(6) and X(972)
X(65904) = barycentric product X(971)*X(971)
X(65904) = barycentric quotient X(971)/X(46137)

X(65905) = CROSSSUM OF X(6) AND X(1300)

Barycentrics    a^4*(a^2 - b^2 - c^2)^2*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6)^2 : :

X(65905) lies on the Steiner inellipse and these lines: {2, 65267}, {6, 39013}, {115, 131}, {343, 6509}, {577, 18877}, {686, 47405}, {1084, 5158}, {3003, 39021}, {3163, 47230}, {3284, 18334}, {8571, 39170}, {11672, 60342}, {35088, 44388}, {39019, 46085}

X(65905) = complement of X(65267)
X(65905) = complement of the isotomic conjugate of X(13754)
X(65905) = isogonal conjugate of the polar conjugate of X(34333)
X(65905) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 13754}, {560, 16310}, {686, 21253}, {810, 3134}, {1725, 21243}, {2315, 141}, {3003, 20305}, {9247, 11064}, {13754, 2887}, {15329, 21259}, {44084, 63840}, {52430, 10257}, {62267, 14156}, {62338, 21235}
X(65905) = X(2)-Ceva conjugate of X(13754)
X(65905) = X(13754)-Dao conjugate of X(2)
X(65905) = crosspoint of X(2) and X(13754)
X(65905) = crosssum of X(6) and X(1300)
X(65905) = barycentric product X(i)*X(j) for these {i,j}: {3, 34333}, {113, 53785}, {13754, 13754}
X(65905) = barycentric quotient X(i)/X(j) for these {i,j}: {13754, 65267}, {34333, 264}, {53785, 40423}

X(65906) = CROSSSUM OF X(6) AND X(1141)

Barycentrics    a^4*(a^2 - b^2 - b*c - c^2)^2*(a^2 - b^2 + b*c - c^2)^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)^2 : :

X(65906) lies on the Steiner inellipse and these lines: {2, 46138}, {6, 39018}, {50, 18334}, {115, 128}, {216, 34520}, {577, 14586}, {1511, 22052}, {2081, 47423}, {15526, 34834}, {17434, 47405}, {39013, 63845}

X(65906) = complement of X(46138)
X(65906) = complement of the isotomic conjugate of X(1154)
X(65906) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1154}, {50, 21231}, {51, 63803}, {560, 231}, {1154, 2887}, {1273, 21235}, {1953, 34827}, {2081, 21253}, {2179, 3580}, {2181, 63839}, {2290, 141}, {6149, 3819}, {11062, 20305}, {19627, 16577}, {51801, 21243}, {52414, 34850}, {62266, 2072}
X(65906) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 1154}, {14570, 55132}
X(65906) = X(2167)-isoconjugate of X(14859)
X(65906) = X(i)-Dao conjugate of X(j) for these (i,j): {1154, 2}, {18402, 65360}, {35591, 2413}, {40588, 14859}
X(65906) = crosspoint of X(2) and X(1154)
X(65906) = crosssum of X(6) and X(1141)
X(65906) = crossdifference of every pair of points on line {1141, 10412}
X(65906) = barycentric product X(i)*X(j) for these {i,j}: {1154, 1154}, {10411, 65784}, {45793, 63834}, {52603, 55132}
X(65906) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 14859}, {1154, 46138}, {11062, 65360}, {65784, 10412}

X(65907) = CROSSSUM OF X(6) AND X(1294)

Barycentrics    a^4*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 4*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 - 3*a^2*b^2*c^4 + 6*b^4*c^4 + 3*a^2*c^6 - 2*b^2*c^6 - c^8)^2 : :
X(65907) = X[54988] + 3 X[65835]

X(65907) lies on the Steiner inellipse and these lines: {2, 54988}, {6, 35071}, {32, 18877}, {53, 115}, {216, 20265}, {577, 14390}, {3003, 39008}, {3163, 46425}, {5158, 53851}, {9119, 35072}, {11672, 47405}, {13567, 15526}, {18334, 40135}, {39013, 46432}

X(65907) = midpoint of X(2) and X(65835)
X(65907) = complement of X(54988)
X(65907) = complement of the isotomic conjugate of X(6000)
X(65907) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 6000}, {560, 1990}, {6000, 2887}, {46587, 21259}
X(65907) = X(2)-Ceva conjugate of X(6000)
X(65907) = X(2416)-isoconjugate of X(36043)
X(65907) = X(i)-Dao conjugate of X(j) for these (i,j): {6000, 2}, {35579, 2416}
X(65907) = crosspoint of X(2) and X(6000)
X(65907) = crosssum of X(6) and X(1294)
X(65907) = crossdifference of every pair of points on line {1294, 6086}
X(65907) = barycentric product X(i)*X(j) for these {i,j}: {133, 39174}, {6000, 6000}, {40948, 52646}, {47433, 57488}, {51964, 62583}
X(65907) = barycentric quotient X(i)/X(j) for these {i,j}: {6000, 54988}, {39174, 57762}

X(65908) = CROSSSUM OF X(6) AND X(477)

Barycentrics    a^4*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 - 3*a^4*c^4 - 2*a^2*b^2*c^4 + 4*b^4*c^4 + 3*a^2*c^6 - b^2*c^6 - c^8)^2 : :

X(65908) lies on the Steiner inellipse and these lines: {6, 18334}, {115, 3003}, {187, 39987}, {216, 39008}, {577, 32640}, {647, 3163}, {800, 39021}, {3284, 35071}, {3580, 15526}, {5158, 55048}, {17434, 47405}, {18122, 35088}, {34209, 47228}, {39013, 40135}

X(65908) = complement of the isotomic conjugate of X(5663)
X(65908) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 5663}, {560, 3018}, {810, 37985}, {5663, 2887}, {7480, 21259}, {23995, 55308}, {35520, 21235}, {36063, 21243}, {47228, 20305}
X(65908) = X(2)-Ceva conjugate of X(5663)
X(65908) = X(i)-isoconjugate of X(j) for these (i,j): {477, 36102}, {2411, 36047}, {36062, 65359}, {36130, 65325}
X(65908) = X(i)-Dao conjugate of X(j) for these (i,j): {5663, 2}, {18809, 65359}, {35581, 2411}
X(65908) = crosspoint of X(2) and X(5663)
X(65908) = crosssum of X(6) and X(477)
X(65908) = crossdifference of every pair of points on line {477, 16171}
X(65908) = barycentric product X(i)*X(j) for these {i,j}: {5663, 5663}, {53233, 55141}
X(65908) = barycentric quotient X(47228)/X(65359)

X(65909) = CROSSSUM OF X(6) AND X(1298)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)^2*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 + a^4*c^4 - 2*b^4*c^4 + b^2*c^6)^2 : :

X(65909) lies on the Steiner inellipse and these lines: {5, 35318}, {115, 129}, {140, 35071}, {233, 14767}, {401, 16089}, {577, 16813}, {6663, 46394}, {7755, 39018}, {11672, 45259}, {24862, 36412}, {36422, 55074}

X(65909) = complement of the isotomic conjugate of X(32428)
X(65909) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 32428}, {1955, 3819}, {1971, 21231}, {2179, 297}, {2313, 141}, {32428, 2887}
X(65909) = X(2)-Ceva conjugate of X(32428)
X(65909) = X(32428)-Dao conjugate of X(2)
X(65909) = crosspoint of X(2) and X(32428)
X(65909) = crosssum of X(6) and X(1298)
X(65909) = crossdifference of every pair of points on line {1298, 53175}
X(65909) = barycentric product X(32428)*X(32428)

X(65910) = CROSSSUM OF X(6) AND X(2724)

Barycentrics    a^4*(a^4*b^2 - 2*a^3*b^3 + 2*a*b^5 - b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - 2*a*b^3*c^2 - b^4*c^2 - 2*a^3*c^3 - 2*a*b^2*c^3 + 4*b^3*c^3 - b^2*c^4 + 2*a*c^5 - c^6)^2 : :

X(65910) lies on the Steiner inellipse and these lines: {2, 53228}, {6, 39014}, {115, 33331}, {518, 35072}, {521, 6184}, {577, 32642}, {1086, 8608}, {1108, 35119}, {5701, 55153}, {6586, 23972}, {16608, 35094}, {61076, 64780}

X(65910) = complement of X(53228)
X(65910) = complement of the isotomic conjugate of X(2808)
X(65910) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2808}, {2808, 2887}, {23694, 20544}
X(65910) = X(2)-Ceva conjugate of X(2808)
X(65910) = X(2808)-Dao conjugate of X(2)
X(65910) = crosspoint of X(2) and X(2808)
X(65910) = crosssum of X(6) and X(2724)
X(65910) = barycentric product X(2808)*X(2808)
X(65910) = barycentric quotient X(2808)/X(53228)

X(65911) = CROSSSUM OF X(6) AND X(2693)

Barycentrics    (2*a^10 - 2*a^8*b^2 - 5*a^6*b^4 + 7*a^4*b^6 - a^2*b^8 - b^10 - 2*a^8*c^2 + 12*a^6*b^2*c^2 - 7*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 5*a^6*c^4 - 7*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 + 7*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 - a^2*c^8 + 3*b^2*c^8 - c^10)^2 : :

X(65911) lies on the Steiner inellipse and these lines: {6, 39008}, {32, 32663}, {115, 1990}, {187, 47087}, {800, 18334}, {3003, 35071}, {3163, 6587}, {3284, 39020}, {15526, 47296}, {39021, 46432}, {44909, 46211}

X(65911) = complement of the isotomic conjugate of X(2777)
X(65911) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2777}, {560, 47228}, {2777, 2887}, {31510, 21259}
X(65911) = X(2)-Ceva conjugate of X(2777)
X(65911) = X(2777)-Dao conjugate of X(2)
X(65911) = crosspoint of X(2) and X(2777)
X(65911) = crosssum of X(6) and X(2693)
X(65911) = crossdifference of every pair of points on line {2693, 46613}
X(65911) = barycentric product X(i)*X(j) for these {i,j}: {1552, 12113}, {2777, 2777}, {18809, 51475}, {31510, 62350}

X(65912) = CROSSSUM OF X(6) AND X(2710)

Barycentrics    (2*a^8 - 2*a^6*b^2 + a^4*b^4 - b^8 - 2*a^6*c^2 + 2*b^6*c^2 + a^4*c^4 - 2*b^4*c^4 + 2*b^2*c^6 - c^8)^2 : :

X(65912) lies on the Steiner inellipse and these lines: {2, 46145}, {6, 35088}, {115, 1503}, {230, 15526}, {232, 1084}, {523, 23976}, {2485, 11672}, {2549, 39008}, {6531, 61339}, {7735, 23992}, {15449, 39095}, {16320, 35133}, {23967, 62384}, {39020, 63440}, {55152, 65726}

X(65912) = complement of X(46145)
X(65912) = complement of the isotomic conjugate of X(2794)
X(65912) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2794}, {2794, 2887}
X(65912) = X(2)-Ceva conjugate of X(2794)
X(65912) = X(2794)-Dao conjugate of X(2)
X(65912) = crosspoint of X(2) and X(2794)
X(65912) = crosssum of X(6) and X(2710)
X(65912) = barycentric product X(2794)*X(2794)
X(65912) = barycentric quotient X(2794)/X(46145)

X(65913) = CROSSSUM OF X(6) AND X(2745)

Barycentrics    (2*a^7 - 2*a^6*b - 3*a^5*b^2 + 3*a^4*b^3 + a*b^6 - b^7 - 2*a^6*c + 8*a^5*b*c - 3*a^4*b^2*c - 4*a^3*b^3*c + 4*a^2*b^4*c - 4*a*b^5*c + b^6*c - 3*a^5*c^2 - 3*a^4*b*c^2 + 8*a^3*b^2*c^2 - 4*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + 3*a^4*c^3 - 4*a^3*b*c^3 - 4*a^2*b^2*c^3 + 8*a*b^3*c^3 - 3*b^4*c^3 + 4*a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 - 4*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7)^2 : :

X(65913) lies on the Steiner inellipse and these lines: {6, 55153}, {44, 61075}, {115, 3330}, {1015, 14571}, {1086, 34050}, {1108, 35128}, {3554, 35092}, {4370, 57049}, {6588, 23980}, {8557, 35091}, {8609, 35072}

X(65913) = complement of the isotomic conjugate of X(2829)
X(65913) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2829}, {2829, 2887}
X(65913) = X(2)-Ceva conjugate of X(2829)
X(65913) = X(2829)-Dao conjugate of X(2)
X(65913) = crosspoint of X(2) and X(2829)
X(65913) = crosssum of X(6) and X(2745)
X(65913) = barycentric product X(2829)*X(2829)

X(65914) = CROSSSUM OF X(6) AND X(2697)

Barycentrics    a^4*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + a^4*b^4*c^2 - 2*a^2*b^6*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 + b^6*c^4 - 2*a^2*b^2*c^6 + b^4*c^6 + 2*a^2*c^8 - c^10)^2 : :

X(65914) lies on the Steiner inellipse and these lines: {6, 55048}, {32, 14385}, {39, 39008}, {115, 232}, {187, 12096}, {647, 23976}, {800, 23992}, {1084, 40135}, {2482, 52613}, {2485, 3163}, {3003, 15526}, {3284, 55047}, {14961, 39020}, {52590, 61067}

X(65914) = complement of the isotomic conjugate of X(2781)
X(65914) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2781}, {560, 6103}, {2781, 2887}, {37937, 21259}, {65711, 21235}
X(65914) = X(2)-Ceva conjugate of X(2781)
X(65914) = X(2781)-Dao conjugate of X(2)
X(65914) = crosspoint of X(2) and X(2781)
X(65914) = crosssum of X(6) and X(2697)
X(65914) = crossdifference of every pair of points on line {2697, 46594}
X(65914) = barycentric product X(i)*X(j) for these {i,j}: {2781, 2781}, {42426, 51472}

X(65915) = CROSSSUM OF X(6) AND X(23700)

Barycentrics    (2*a^8 - 4*a^6*b^2 + 3*a^4*b^4 - b^8 - 4*a^6*c^2 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 4*b^6*c^2 + 3*a^4*c^4 - 2*a^2*b^2*c^4 - 6*b^4*c^4 + 4*b^2*c^6 - c^8)^2 : :

X(65915) lies on the Steiner inellipse and these lines: {6, 55152}, {69, 35088}, {115, 1570}, {230, 15525}, {523, 35067}, {2482, 64919}, {2489, 11672}, {15526, 44377}, {23992, 36207}, {34810, 39008}

X(65915) = complement of the isotomic conjugate of X(23698)
X(65915) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 23698}, {23698, 2887}
X(65915) = X(2)-Ceva conjugate of X(23698)
X(65915) = X(23698)-Dao conjugate of X(2)
X(65915) = crosspoint of X(2) and X(23698)
X(65915) = crosssum of X(6) and X(23700)
X(65915) = barycentric product X(23698)*X(23698)

X(65916) = CROSSSUM OF X(6) AND X(14979)

Barycentrics    (2*a^10 - 5*a^8*b^2 + 4*a^6*b^4 - 2*a^4*b^6 + 2*a^2*b^8 - b^10 - 5*a^8*c^2 + 6*a^6*b^2*c^2 - a^4*b^4*c^2 - 3*a^2*b^6*c^2 + 3*b^8*c^2 + 4*a^6*c^4 - a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 2*b^6*c^4 - 2*a^4*c^6 - 3*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10)^2 : :

X(65916) lies on the Steiner inellipse and these lines: {50, 115}, {323, 15526}, {570, 18334}, {3003, 39018}, {3163, 12077}, {3284, 39019}, {22052, 39008}, {32662, 36412}, {35088, 44386}, {36422, 47414}

X(65916) = complement of the isotomic conjugate of X(32423)
X(65916) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 32423}, {560, 47226}, {32423, 2887}
X(65916) = X(2)-Ceva conjugate of X(32423)
X(65916) = X(32423)-Dao conjugate of X(2)
X(65916) = crosspoint of X(2) and X(32423)
X(65916) = crosssum of X(6) and X(14979)
X(65916) = barycentric product X(32423)*X(32423)

X(65917) = CROSSSUM OF X(6) AND X(5966)

Barycentrics    (2*a^6 - 4*a^4*b^2 + 3*a^2*b^4 - b^6 - 4*a^4*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6)^2 : :

X(65917) lies on the Steiner inellipse and these lines: {2, 60034}, {3, 39019}, {32, 39171}, {39, 15345}, {50, 23992}, {115, 140}, {187, 6592}, {401, 7925}, {570, 1084}, {3631, 15526}, {15109, 15449}, {23967, 47406}, {36422, 59739}

X(65917) = complement of X(60034)
X(65917) = complement of the isotomic conjugate of X(5965)
X(65917) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 5965}, {5965, 2887}
X(65917) = X(2)-Ceva conjugate of X(5965)
X(65917) = X(5965)-Dao conjugate of X(2)
X(65917) = crosspoint of X(2) and X(5965)
X(65917) = crosssum of X(6) and X(5966)
X(65917) = barycentric product X(5965)*X(5965)
X(65917) = barycentric quotient X(5965)/X(60034)

X(65918) = CROSSSUM OF X(6) AND X(9076)

Barycentrics    a^4*(b^2 + c^2)^2*(a^4 - b^4 + b^2*c^2 - c^4)^2 : :

X(65918) lies on the Steiner inellipse and these lines: {39, 15449}, {115, 1194}, {1084, 5007}, {3005, 47426}, {6292, 15526}, {8623, 18334}, {10317, 18374}, {23967, 52591}, {35088, 64647}, {40377, 55050}

X(65918) = complement of the isotomic conjugate of X(9019)
X(65918) = X(i)-complementary conjugate of X(j) for these (i,j): {23, 21238}, {31, 9019}, {39, 21234}, {1923, 187}, {1964, 858}, {3051, 16581}, {9019, 2887}, {18374, 1215}, {18715, 626}
X(65918) = X(2)-Ceva conjugate of X(9019)
X(65918) = X(9076)-isoconjugate of X(37221)
X(65918) = X(9019)-Dao conjugate of X(2)
X(65918) = crosspoint of X(2) and X(9019)
X(65918) = crosssum of X(6) and X(9076)
X(65918) = barycentric product X(i)*X(j) for these {i,j}: {23, 60463}, {7794, 36415}, {9019, 9019}
X(65918) = barycentric quotient X(i)/X(j) for these {i,j}: {36415, 52395}, {60463, 18019}

X(65919) = CROSSSUM OF X(6) AND X(675)

Barycentrics    a^4*(a*b^2 - b^3 + a*c^2 - c^3)^2 : :

X(65919) lies on the Steiner inellipse and these lines: {2, 43093}, {32, 32656}, {39, 1086}, {115, 3136}, {354, 1015}, {1084, 20970}, {1146, 1573}, {23988, 36230}, {35119, 49758}, {39014, 52963}, {51406, 52592}

X(65919) = complement of X(43093)
X(65919) = complement of the isogonal conjugate of X(8618)
X(65919) = complement of the isotomic conjugate of X(674)
X(65919) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 674}, {560, 3011}, {674, 2887}, {2225, 141}, {3006, 21235}, {4249, 21259}, {8618, 10}, {14964, 21240}, {42723, 21262}, {43039, 17046}, {51657, 2886}, {57015, 626}, {65703, 21252}
X(65919) = X(2)-Ceva conjugate of X(674)
X(65919) = X(i)-isoconjugate of X(j) for these (i,j): {675, 37130}, {2224, 43093}
X(65919) = X(674)-Dao conjugate of X(2)
X(65919) = crosspoint of X(2) and X(674)
X(65919) = crosssum of X(6) and X(675)
X(65919) = crossdifference of every pair of points on line {675, 53276}
X(65919) = barycentric product X(i)*X(j) for these {i,j}: {674, 674}, {2225, 57015}, {3006, 8618}, {32739, 62556}
X(65919) = barycentric quotient X(i)/X(j) for these {i,j}: {674, 43093}, {2225, 37130}, {8618, 675}

X(65920) = CROSSSUM OF X(6) AND X(53929)

Barycentrics    (2*a^8 - 2*a^6*b^2 - a^4*b^4 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - a^4*c^4 - 2*a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*c^6 - c^8)^2 : :

X(65920) lies on the Steiner inellipse and these lines: {32, 14357}, {39, 55048}, {115, 468}, {187, 15526}, {574, 39008}, {647, 61067}, {2482, 3265}, {5475, 35088}, {14961, 55047}, {35133, 40135}

X(65920) = X(i)-complementary conjugate of X(j) for these (i,j): {560, 44467}, {46619, 21259}
X(65920) = crosssum of X(6) and X(53929)

X(65921) = CROSSSUM OF X(6) AND X(743)

Barycentrics    (a^3*b + a^3*c - b^3*c - b*c^3)^2 : :

X(65921) lies on the Steiner inellipse and these lines: {2, 57944}, {10, 61065}, {39, 55049}, {115, 5977}, {668, 29945}, {730, 35119}, {760, 35094}, {1015, 17023}, {1086, 3821}, {1146, 30847}, {50305, 61076}

X(65921) = complement of X(57944)
X(65921) = complement of the isogonal conjugate of X(8624)
X(65921) = complement of the isotomic conjugate of X(742)
X(65921) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 742}, {742, 2887}, {2239, 141}, {8624, 10}, {35545, 21235}
X(65921) = X(2)-Ceva conjugate of X(742)
X(65921) = X(742)-Dao conjugate of X(2)
X(65921) = crosspoint of X(2) and X(742)
X(65921) = crosssum of X(6) and X(743)
X(65921) = barycentric product X(i)*X(j) for these {i,j}: {742, 742}, {8624, 35545}
X(65921) = barycentric quotient X(i)/X(j) for these {i,j}: {742, 57944}, {8624, 743}

X(65922) = CROSSSUM OF X(6) AND X(2726)

Barycentrics    a^4*(a^2*b^2 - b^4 - 2*a*b^2*c + 2*b^3*c + a^2*c^2 - 2*a*b*c^2 + 2*b*c^3 - c^4)^2 : :

X(65922) lies on the Steiner inellipse and these lines: {2, 53218}, {39, 35092}, {513, 23980}, {517, 1015}, {1084, 2245}, {1086, 8610}, {1146, 1575}, {1329, 55153}, {3752, 35119}, {4370, 6586}, {5662, 35094}, {8608, 40621}, {17735, 39015}, {24289, 39011}

X(65922) = complement of X(53218)
X(65922) = complement of the isotomic conjugate of X(2810)
X(65922) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2810}, {2810, 2887}
X(65922) = X(2)-Ceva conjugate of X(2810)
X(65922) = X(2810)-Dao conjugate of X(2)
X(65922) = crosspoint of X(2) and X(2810)
X(65922) = crosssum of X(6) and X(2726)
X(65922) = barycentric product X(2810)*X(2810)
X(65922) = barycentric quotient X(2810)/X(53218)

X(65923) = CROSSSUM OF X(6) AND X(2770)

Barycentrics    a^4*(a^4*b^2 - b^6 + a^4*c^2 - 4*a^2*b^2*c^2 + 2*b^4*c^2 + 2*b^2*c^4 - c^6)^2 : :

X(65923) lies on the Steiner inellipse and these lines: {3, 55048}, {32, 39169}, {39, 23992}, {115, 858}, {187, 1084}, {574, 18334}, {647, 2482}, {1576, 15477}, {3003, 35133}, {3005, 47426}, {5355, 35078}, {7813, 14961}, {7820, 61077}, {7853, 35088}, {17416, 52961}, {17964, 61503}, {40349, 55047}

X(65923) = complement of the isotomic conjugate of X(2854)
X(65923) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2854}, {560, 10418}, {2854, 2887}, {7482, 21259}, {44467, 20305}, {46783, 21256}, {52197, 4892}
X(65923) = X(2)-Ceva conjugate of X(2854)
X(65923) = X(2854)-Dao conjugate of X(2)
X(65923) = crosspoint of X(2) and X(2854)
X(65923) = crosssum of X(6) and X(2770)
X(65923) = crossdifference of every pair of points on line {2770, 46589}
X(65923) = barycentric product X(i)*X(j) for these {i,j}: {2854, 2854}, {9177, 46783}
X(65923) = barycentric quotient X(9177)/X(52501)

X(65924) = CROSSSUM OF X(6) AND X(15344)

Barycentrics    a^2*(a^2 - b^2 - c^2)^2*(a^2*b + b^3 + a^2*c - 2*a*b*c - b^2*c - b*c^2 + c^3)^2 : :

X(65924) lies on the Steiner inellipse and these lines: {3, 1015}, {32, 51473}, {115, 21530}, {577, 32658}, {1084, 18591}, {1086, 18589}, {1146, 16605}, {2092, 15525}, {14961, 35090}, {22401, 35072}, {23980, 42769}, {35508, 42018}

X(65924) = complement of the isotomic conjugate of X(34381)
X(65924) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 34381}, {810, 3140}, {1738, 21243}, {3290, 20305}, {4236, 21259}, {9247, 25083}, {20728, 20540}, {32656, 2977}, {34381, 2887}
X(65924) = X(2)-Ceva conjugate of X(34381)
X(65924) = X(34381)-Dao conjugate of X(2)
X(65924) = crosspoint of X(2) and X(34381)
X(65924) = crosssum of X(6) and X(15344)
X(65924) = crossdifference of every pair of points on line {2977, 15344}
X(65924) = barycentric product X(34381)*X(34381)
X(65924) = barycentric quotient X(20728)/X(57499)

X(65925) = CROSSSUM OF X(6) AND X(699)

Barycentrics    (a^2*b^4 - b^4*c^2 + a^2*c^4 - b^2*c^4)^2 : :
X(65925) = X[3225] + 3 X[65287]

X(65925) lies on the Steiner inellipse and these lines: {2, 3225}, {76, 115}, {141, 1084}, {325, 35078}, {887, 2482}, {1015, 21240}, {4357, 40610}, {6292, 55050}, {6786, 61063}, {7813, 39010}, {15526, 50666}

X(65925) = midpoint of X(2) and X(65287)
X(65925) = complement of X(3225)
X(65925) = complement of the isogonal conjugate of X(3229)
X(65925) = complement of the isotomic conjugate of X(698)
X(65925) = isotomic conjugate of the isogonal conjugate of X(59802)
X(65925) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 698}, {698, 2887}, {798, 2086}, {799, 9429}, {1755, 40810}, {1964, 35540}, {2227, 141}, {3229, 10}, {9429, 16592}, {32540, 16609}, {32748, 37}, {35524, 21235}, {36821, 4892}, {41337, 4369}, {51322, 19563}, {51907, 2}, {51912, 39080}, {52460, 226}
X(65925) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 698}, {55034, 9429}
X(65925) = X(699)-isoconjugate of X(43761)
X(65925) = X(i)-Dao conjugate of X(j) for these (i,j): {698, 2}, {3229, 32544}, {39080, 699}, {40810, 51992}
X(65925) = crosspoint of X(2) and X(698)
X(65925) = crosssum of X(6) and X(699)
X(65925) = barycentric product X(i)*X(j) for these {i,j}: {76, 59802}, {698, 698}, {3229, 35524}
X(65925) = barycentric quotient X(i)/X(j) for these {i,j}: {698, 3225}, {2227, 43761}, {3229, 699}, {39080, 32544}, {47648, 51992}, {59567, 8858}, {59802, 6}

X(65926) = CROSSSUM OF X(6) AND X(53911)

Barycentrics    (2*a^6 - 2*a^5*b - 3*a^4*b^2 + 2*a^3*b^3 + 2*a^2*b^4 - b^6 - 2*a^5*c + 8*a^4*b*c - 2*a^3*b^2*c - 2*a^2*b^3*c - 4*a*b^4*c + 2*b^5*c - 3*a^4*c^2 - 2*a^3*b*c^2 + 4*a*b^3*c^2 + b^4*c^2 + 2*a^3*c^3 - 2*a^2*b*c^3 + 4*a*b^2*c^3 - 4*b^3*c^3 + 2*a^2*c^4 - 4*a*b*c^4 + b^2*c^4 + 2*b*c^5 - c^6)^2 : :

X(65926) lies on the Steiner inellipse and these lines: {1, 55153}, {6, 35091}, {115, 50940}, {1086, 6610}, {1108, 35125}, {1146, 44675}, {4370, 57064}, {6129, 23980}, {6603, 61075}, {8609, 35508}, {14837, 35110}, {35072, 43065}, {35128, 40133}

X(65926) = X(32)-complementary conjugate of X(43047)
X(65926) = crosssum of X(6) and X(53911)

X(65927) = CROSSPOINT OF X(2) AND X(44669)

Barycentrics    (a - b - c)^2*(2*a^3 - a*b^2 + b^3 - b^2*c - a*c^2 - b*c^2 + c^3)^2 : :

X(65927) lies on the Steiner inellipse and these lines: {9, 115}, {220, 2341}, {1015, 40937}, {1084, 16588}, {1086, 5745}, {1100, 40621}, {1146, 3686}, {1944, 35094}, {2323, 35092}, {35080, 49776}, {35086, 40869}

X(65927) = complement of the isotomic conjugate of X(44669)
X(65927) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 44669}, {35466, 17046}, {44669, 2887}, {65375, 6089}
X(65927) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 44669}, {65236, 6089}
X(65927) = X(44669)-Dao conjugate of X(2)
X(65927) = crosspoint of X(2) and X(44669)
X(65927) = barycentric product X(i)*X(j) for these {i,j}: {8, 34194}, {44669, 44669}
X(65927) = barycentric quotient X(34194)/X(7)

X(65928) = CROSSSUM OF X(6) AND X(28476)

Barycentrics    (2*a^3 + a^2*b - b^3 + a^2*c - b^2*c - b*c^2 - c^3)^2 : :

X(65928) lies on the Steiner inellipse and these lines: {37, 55046}, {39, 39016}, {115, 4205}, {594, 37586}, {958, 1146}, {1015, 37592}, {1086, 4657}, {35068, 51406}, {35069, 47431}, {35080, 50252}, {35092, 50020}, {59515, 59545}

X(65928) = complement of the isotomic conjugate of X(5847)
X(65928) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 5847}, {5847, 2887}, {43054, 17046}
X(65928) = X(2)-Ceva conjugate of X(5847)
X(65928) = X(5847)-Dao conjugate of X(2)
X(65928) = crosspoint of X(2) and X(5847)
X(65928) = crosssum of X(6) and X(28476)
X(65928) = barycentric product X(5847)*X(5847)

X(65929) = CROSSSUM OF X(6) AND X(6015)

Barycentrics    a^2*(a^2*b^2 - a*b^3 + a*b^2*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3)^2 : :

X(65929) lies on the Steiner inellipse and these lines: {1, 1084}, {115, 1573}, {960, 35508}, {1015, 3742}, {1086, 1107}, {1146, 3741}, {6786, 40627}, {8299, 39014}, {15526, 18639}, {30109, 35094}, {35079, 43065}, {35119, 50014}

X(65929) = complement of the isotomic conjugate of X(6007)
X(65929) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 6007}, {6007, 2887}, {43059, 17046}
X(65929) = X(2)-Ceva conjugate of X(6007)
X(65929) = X(6007)-Dao conjugate of X(2)
X(65929) = crosspoint of X(2) and X(6007)
X(65929) = crosssum of X(6) and X(6015)
X(65929) = barycentric product X(6007)*X(6007)

X(65930) = CROSSSUM OF X(6) AND X(15728)

Barycentrics    a^2*(a - b - c)^2*(a^2*b - 2*a*b^2 + b^3 + a^2*c + 2*a*b*c - b^2*c - 2*a*c^2 - b*c^2 + c^3)^2 : :

X(65930) lies on the Steiner inellipse and these lines: {220, 3939}, {1015, 16588}, {1040, 34526}, {1086, 1212}, {1146, 4847}, {1642, 23980}, {6603, 35125}, {14936, 42064}, {26698, 62705}, {35091, 60419}, {35110, 43050}, {41555, 43065}, {49758, 61074}

X(65930) = complement of the isotomic conjugate of X(15733)
X(65930) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 15733}, {2175, 6745}, {15733, 2887}, {26015, 17047}, {43065, 17046}
X(65930) = X(2)-Ceva conjugate of X(15733)
X(65930) = X(15728)-isoconjugate of X(43762)
X(65930) = X(15733)-Dao conjugate of X(2)
X(65930) = crosspoint of X(i) and X(j) for these (i,j): {2, 15733}, {43065, 56636}
X(65930) = crosssum of X(6) and X(15728)
X(65930) = barycentric product X(i)*X(j) for these {i,j}: {8, 5580}, {15733, 15733}
X(65930) = barycentric quotient X(5580)/X(7)

X(65931) = CROSSSUM OF X(6) AND X(15731)

Barycentrics    a^2*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4 + a^3*c + 4*a^2*b*c - 3*a*b^2*c - 2*b^3*c - 3*a^2*c^2 - 3*a*b*c^2 + 6*b^2*c^2 + 3*a*c^3 - 2*b*c^3 - c^4)^2 : :

X(65931) lies on the Steiner inellipse and these lines: {1, 35508}, {6, 4845}, {650, 63777}, {1015, 5573}, {1086, 10481}, {1146, 11019}, {14936, 34056}, {34522, 35072}, {35091, 43065}, {42048, 61076}

X(65931) = complement of the isotomic conjugate of X(15726)
X(65931) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 15726}, {32, 1323}, {15726, 2887}, {43064, 17046}
X(65931) = X(2)-Ceva conjugate of X(15726)
X(65931) = X(15726)-Dao conjugate of X(2)
X(65931) = crosspoint of X(i) and X(j) for these (i,j): {2, 15726}, {43064, 56637}
X(65931) = crosssum of X(6) and X(15731)
X(65931) = barycentric product X(15726)*X(15726)

X(65932) = CROSSSUM OF X(6) AND X(65875)

Barycentrics    (2*a^4 - a^3*b - a^2*b^2 + a*b^3 - b^4 - a^3*c - a^2*c^2 + 2*b^2*c^2 + a*c^3 - c^4)^2 : :

X(65932) lies on the Steiner inellipse and these lines: {37, 35090}, {44, 115}, {594, 35122}, {650, 35069}, {1015, 56531}, {1086, 3218}, {1100, 35092}, {1146, 2323}, {3700, 4370}, {35128, 40937}, {40621, 62211}

X(65932) = X(65238)-Ceva conjugate of X(65856)
X(65932) = crosssum of X(6) and X(65875)
X(65932) = barycentric product X(8)*X(31524)
X(65932) = barycentric quotient X(31524)/X(7)

X(65933) = CROSSSUM OF X(6) AND X(53688)

Barycentrics    (2*a + b + c)^2*(a^2 + a*b - b^2 + a*c - b*c - c^2)^2 : :

X(65933) lies on the Steiner inellipse and these lines: {115, 3634}, {594, 37212}, {1015, 3743}, {1086, 6651}, {1125, 35076}, {1146, 18253}, {1931, 6157}, {4370, 39256}, {4988, 35085}, {17398, 39340}

X(65933) = X(i)-complementary conjugate of X(j) for these (i,j): {1326, 27798}, {1962, 20546}, {2308, 49676}, {17735, 17239}, {18266, 3634}, {20970, 20337}, {64215, 6707}
X(65933) = X(57461)-Dao conjugate of X(4608)
X(65933) = crosssum of X(6) and X(53688)
X(65933) = crossdifference of every pair of points on line {18001, 53688}

X(65934) = CROSSSUM OF X(6) AND X(2687)

Barycentrics    a^2*(a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c + a^3*b^2*c - 2*a*b^4*c - a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 + a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + a*b^2*c^3 + 2*a^2*c^4 - 2*a*b*c^4 + b^2*c^4 + a*c^5 - c^6)^2 : :

X(65934) lies on the Steiner inellipse and these lines: {2, 46141}, {6, 35090}, {115, 8609}, {187, 47086}, {647, 23980}, {650, 3163}, {1015, 3003}, {1086, 18593}, {1100, 35128}, {1146, 56531}, {2092, 18334}, {2323, 3284}, {18591, 39008}, {40937, 55153}

X(65934) = complement of X(46141)
X(65934) = complement of the isotomic conjugate of X(2771)
X(65934) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2771}, {1918, 3013}, {2771, 2887}, {37966, 21259}
X(65934) = X(2)-Ceva conjugate of X(2771)
X(65934) = X(2687)-isoconjugate of X(65240)
X(65934) = X(2771)-Dao conjugate of X(2)
X(65934) = crosspoint of X(2) and X(2771)
X(65934) = crosssum of X(6) and X(2687)
X(65934) = crossdifference of every pair of points on line {2687, 14127}
X(65934) = barycentric product X(2771)*X(2771)
X(65934) = barycentric quotient X(2771)/X(46141)

X(65935) = CROSSSUM OF X(6) AND X(43363)

Barycentrics    a^2*(a^3*b - a^2*b^2 + a*b^3 - b^4 + a^3*c - a*b^2*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 + a*c^3 - c^4)^2 : :

X(65935) lies on the Steiner inellipse and these lines: {115, 20623}, {614, 1015}, {1084, 53387}, {1086, 16583}, {1146, 20310}, {1500, 7079}, {5309, 61076}, {14581, 59799}, {15526, 16589}, {16588, 35072}, {35094, 49758}

X(65935) = complement of the isotomic conjugate of X(44670)
X(65935) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 44670}, {32, 51775}, {560, 8758}, {1918, 851}, {2175, 50366}, {5179, 626}, {44670, 2887}
X(65935) = X(2)-Ceva conjugate of X(44670)
X(65935) = X(37214)-isoconjugate of X(43363)
X(65935) = X(44670)-Dao conjugate of X(2)
X(65935) = crosspoint of X(2) and X(44670)
X(65935) = crosssum of X(6) and X(43363)
X(65935) = barycentric product X(44670)*X(44670)

X(65936) = X(4)X(1086)∩X(440)X(39020)

Barycentrics    (2*a^5 - a^4*b + 2*a^2*b^3 - 2*a*b^4 - b^5 - a^4*c - 2*a^2*b^2*c + 3*b^4*c - 2*a^2*b*c^2 + 4*a*b^2*c^2 - 2*b^3*c^2 + 2*a^2*c^3 - 2*b^2*c^3 - 2*a*c^4 + 3*b*c^4 - c^5)^2 : :

X(65936) lies on the Steiner inellipse and these lines: {4, 1086}, {440, 39020}, {1015, 1427}, {1146, 3772}, {1834, 15526}, {3752, 35072}, {4415, 61075}, {6554, 23982}, {16583, 35508}, {35122, 44334}

X(65936) = X(16870)-complementary conjugate of X(21244)

X(65937) = CROSSSUM OF X(6) AND X(59025)

Barycentrics    (a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8 + a^10*c^2 - 2*a^8*b^2*c^2 + 2*a^6*b^4*c^2 - a^4*b^6*c^2 + a^2*b^8*c^2 - b^10*c^2 - 3*a^8*c^4 + 2*a^6*b^2*c^4 - a^2*b^6*c^4 + 4*b^8*c^4 + 3*a^6*c^6 - a^4*b^2*c^6 - a^2*b^4*c^6 - 6*b^6*c^6 - a^4*c^8 + a^2*b^2*c^8 + 4*b^4*c^8 - b^2*c^10)^2 : :

X(65937) lies on the Steiner inellipse and these lines: {5, 39021}, {115, 13754}, {230, 39013}, {343, 35088}, {1084, 16310}, {2501, 11672}, {7749, 18334}, {10257, 35071}, {15526, 44388}, {39008, 52010}

X(65937) = crosssum of X(6) and X(59025)

X(65938) = CROSSSUM OF X(6) AND X(53966)

Barycentrics    (-(a^2*b^6) + 2*a^4*b^2*c^2 - a^2*b^4*c^2 + b^6*c^2 - a^2*b^2*c^4 - a^2*c^6 + b^2*c^6)^2 : :

X(65938) lies on the Steiner inellipse and these lines: {2, 53231}, {115, 698}, {141, 35078}, {325, 1084}, {2482, 25423}, {3314, 23992}, {4045, 39010}, {15449, 35540}, {18896, 61339}, {35088, 40810}

X(65938) = complement of X(53231)
X(65938) = crosssum of X(6) and X(53966)

X(65939) = CROSSSUM OF X(6) AND X(65876)

Barycentrics    a^2*(a^4*b - a^3*b^2 + a*b^4 - b^5 + a^4*c - a^2*b^2*c - a^3*c^2 - a^2*b*c^2 + b^3*c^2 + b^2*c^3 + a*c^4 - c^5)^2 : :

X(65939) lies on the Steiner inellipse and these lines: {10, 35122}, {37, 35086}, {115, 5179}, {514, 35075}, {1015, 3002}, {1086, 8680}, {1146, 50014}, {1500, 35090}, {3239, 35068}, {3709, 23980}, {3912, 15526}, {4370, 64905}, {5060, 17735}, {6586, 35069}, {35072, 58325}, {35119, 40940}

X(65939) = crosssum of X(6) and X(65876)

X(65940) = CROSSSUM OF X(6) AND X(715)

Barycentrics    (b + c)^2*(-(a^2*b^2) + a^2*b*c - a^2*c^2 + b^2*c^2)^2 : :

X(65940) lies on the Steiner inellipse and these lines: {2, 18826}, {10, 1084}, {115, 2887}, {1015, 3741}, {1086, 20888}, {3124, 60288}, {16587, 55050}, {16589, 40610}, {20548, 35080}, {30109, 35119}, {30229, 62534}

X(65940) = complement of X(18826)
X(65940) = complement of the isotomic conjugate of X(714)
X(65940) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 714}, {213, 6381}, {714, 2887}, {2229, 141}, {4557, 14426}, {35532, 21235}, {53366, 23301}
X(65940) = X(2)-Ceva conjugate of X(714)
X(65940) = X(714)-Dao conjugate of X(2)
X(65940) = crosspoint of X(2) and X(714)
X(65940) = crosssum of X(6) and X(715)
X(65940) = barycentric product X(714)*X(714)
X(65940) = barycentric quotient X(714)/X(18826)

X(65941) = X(37)X(35079)∩X(44)X(1084)

Barycentrics    a^2*(a^3*b^2 - a*b^4 - a^2*b^2*c + a^3*c^2 - a^2*b*c^2 + b^3*c^2 + b^2*c^3 - a*c^4)^2 : :

X(65941) lies on the Steiner inellipse and these lines: {37, 35079}, {44, 1084}, {115, 1575}, {513, 35069}, {650, 35068}, {758, 1015}, {960, 35128}, {1086, 57039}, {1107, 35092}, {1146, 59734}, {3647, 18334}, {3666, 35119}, {3709, 4370}, {13466, 64934}, {21879, 35090}

X(65941) = X(61433)-complementary conjugate of X(21241)
X(65941) = X(65239)-Ceva conjugate of X(65864)

X(65942) = CROSSSUM OF X(6) AND X(59020)

Barycentrics    (a^2*b^2 - a*b^3 + b^3*c + a^2*c^2 - 2*b^2*c^2 - a*c^3 + b*c^3)^2 : :

X(65942) lies on the Steiner inellipse and these lines: {2, 60014}, {115, 17052}, {141, 1146}, {142, 1015}, {325, 35086}, {982, 1086}, {1084, 17056}, {3452, 35508}, {9025, 35119}, {9443, 35120}, {16593, 39014}, {18589, 35072}, {20528, 40610}, {20935, 30631}, {31844, 35091}, {50092, 61076}

X(65942) = complement of X(60014)
X(65942) = complement of the isotomic conjugate of X(46180)
X(65942) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 46180}, {46180, 2887}
X(65942) = X(2)-Ceva conjugate of X(46180)
X(65942) = X(46180)-Dao conjugate of X(2)
X(65942) = crosspoint of X(2) and X(46180)
X(65942) = crosssum of X(6) and X(59020)
X(65942) = barycentric product X(46180)*X(46180)
X(65942) = barycentric quotient X(46180)/X(60014)

X(65943) = X(2)X(53209)∩X(10)X(55153)

Barycentrics    (a^5*b - a^4*b^2 - a^3*b^3 + a^2*b^4 + a^5*c - 2*a^4*b*c + 2*a^3*b^2*c - a^2*b^3*c + a*b^4*c - b^5*c - a^4*c^2 + 2*a^3*b*c^2 - a*b^3*c^2 - a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 + a^2*c^4 + a*b*c^4 - b*c^5)^2 : :

X(65943) lies on the Steiner inellipse and these lines: {2, 53209}, {10, 55153}, {37, 39017}, {226, 35094}, {517, 1146}, {522, 23980}, {1015, 44675}, {1577, 35075}, {3239, 6184}, {20310, 39014}, {35072, 40869}

X(65943) = complement of X(53209)
X(65943) = X(52480)-complementary conjugate of X(20544)

X(65944) = CROSSSUM OF X(6) AND X(53970)

Barycentrics    (b + c)^2*(-a^5 + a^3*b^2 + b^4*c + a^3*c^2 - a*b^2*c^2 - b^3*c^2 - b^2*c^3 + b*c^4)^2 : :

X(65944) lies on the Steiner inellipse and these lines: {115, 758}, {523, 35069}, {1015, 50757}, {1146, 10026}, {1213, 35086}, {2482, 64934}, {4999, 35128}, {16589, 35090}, {17056, 35080}, {21024, 35122}, {23992, 36227}

X(65944) = complement of the isogonal conjugate of X(5202)
X(65944) = X(5202)-complementary conjugate of X(10)
X(65944) = crosssum of X(6) and X(53970)
X(65944) = barycentric quotient X(5202)/X(53970)

X(65945) = CROSSSUM OF X(6) AND X(2752)

Barycentrics    a^2*(a^4*b - b^5 + a^4*c - 2*a^3*b*c - a^2*b^2*c + a*b^3*c + b^4*c - a^2*b*c^2 + a*b*c^3 + b*c^4 - c^5)^2 : :

X(65945) lies on the Steiner inellipse and these lines: {36, 187}, {39, 35090}, {115, 3290}, {241, 35131}, {647, 6184}, {905, 2482}, {1086, 16581}, {1146, 16611}, {2092, 23992}, {3666, 35094}, {14961, 35072}, {18591, 55048}, {25062, 35122}, {35092, 41015}, {35128, 37599}

X(65945) = complement of the isotomic conjugate of X(2836)
X(65945) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2836}, {560, 47231}, {1918, 2503}, {2836, 2887}, {7476, 21259}, {47232, 20305}
X(65945) = X(2)-Ceva conjugate of X(2836)
X(65945) = X(2836)-Dao conjugate of X(2)
X(65945) = crosspoint of X(2) and X(2836)
X(65945) = crosssum of X(6) and X(2752)
X(65945) = crossdifference of every pair of points on line {2752, 46586}
X(65945) = barycentric product X(2836)*X(2836)

X(65946) = CROSSSUM OF X(6) AND X(2714)

Barycentrics    (b - c)^2*(-a^6 + a^5*b + a^4*b^2 - a^3*b^3 + a^5*c - a^4*b*c - a^3*b^2*c + b^5*c + a^4*c^2 - a^3*b*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 - a^3*c^3 + 2*a*b^2*c^3 - 2*b^3*c^3 + b*c^5)^2 : :

X(65946) lies on the Steiner inellipse and these lines: {2, 53191}, {115, 521}, {523, 35072}, {1084, 6588}, {1146, 8062}, {2482, 64780}, {4885, 15526}, {6510, 35075}, {11672, 14571}, {35071, 59973}, {35081, 36227}, {35084, 36207}, {39008, 57095}

X(65946) = complement of X(53191)
X(65946) = complement of the isotomic conjugate of X(2798)
X(65946) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2798}, {425, 21259}, {2798, 2887}, {23695, 512}, {41349, 17072}
X(65946) = X(2)-Ceva conjugate of X(2798)
X(65946) = X(2798)-Dao conjugate of X(2)
X(65946) = crosspoint of X(2) and X(2798)
X(65946) = crosssum of X(6) and X(2714)
X(65946) = barycentric product X(2798)*X(2798)
X(65946) = barycentric quotient X(2798)/X(53191)

X(65947) = CROSSSUM OF X(6) AND X(2742)

Barycentrics    (b - c)^2*(a^2*b - 2*a*b^2 + b^3 + a^2*c + 2*a*b*c - b^2*c - 2*a*c^2 - b*c^2 + c^3)^2 : :

X(65947) lies on the Steiner inellipse and these lines: {6, 35113}, {44, 35111}, {1015, 52946}, {1086, 3676}, {1108, 35116}, {3290, 23980}, {6184, 8609}, {8557, 61066}, {17435, 55153}, {35066, 62211}, {35508, 46101}, {41555, 43065}

X(65947) = complement of the isotomic conjugate of X(2826)
X(65947) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2826}, {32, 43050}, {667, 6745}, {2826, 2887}, {3660, 17072}, {15733, 59971}, {26015, 21260}, {37788, 21262}, {43065, 3835}, {43924, 15733}
X(65947) = X(2)-Ceva conjugate of X(2826)
X(65947) = X(2826)-Dao conjugate of X(2)
X(65947) = crosspoint of X(2) and X(2826)
X(65947) = crosssum of X(6) and X(2742)
X(65947) = barycentric product X(2826)*X(2826)
X(65947) = barycentric quotient X(5580)/X(6065)

X(65948) = X(3)X(3847)∩X(4)X(11)

Barycentrics    (b - c)^2*(-a + b + c)*(2*a^2*b^2 - 2*b^4 + 2*a^2*c^2 + 4*b^2*c^2 - 2*c^4) + (a - b)^2*(a + b - c)*(a^4 - b^4 + 2*b^2*c^2 - c^4) + (-a + c)^2*(a - b + c)*(a^4 - b^4 + 2*b^2*c^2 - c^4) : :
X(65948) = X[1] - 3 X[38038], 3 X[2] + X[10724], X[2] - 3 X[38077], X[10724] + 9 X[38077], X[24466] - 9 X[38077], X[3] - 3 X[23513], 2 X[6667] - 3 X[23513], 2 X[6667] + X[64186], 3 X[23513] + X[64186], 3 X[4] + X[104], 5 X[4] - X[10728], 7 X[4] + X[12248], 2 X[4] + X[20418], 3 X[4] - X[52836], X[4] - 3 X[59390], X[4] + 3 X[59391], 3 X[11] - X[104], and many others

See Van Khea and Peter Moses, euclid 7119.

X(65948) lies on these lines: {1, 38038}, {2, 10724}, {3, 3847}, {4, 11}, {5, 3035}, {6, 38147}, {7, 38152}, {8, 38156}, {9, 38159}, {10, 38161}, {12, 38163}, {20, 21154}, {30, 6713}, {40, 34122}, {55, 6968}, {80, 1537}, {100, 3091}, {119, 381}, {140, 38319}, {149, 3832}, {153, 3839}, {214, 3817}, {355, 5854}, {376, 59376}, {382, 38761}, {389, 58475}, {497, 64735}, {515, 1387}, {516, 6702}, {517, 3036}, {546, 946}, {550, 34126}, {962, 59415}, {971, 15528}, {1001, 6982}, {1012, 10090}, {1145, 5587}, {1156, 38306}, {1210, 24465}, {1317, 5603}, {1320, 38307}, {1329, 10525}, {1376, 6973}, {1479, 18242}, {1484, 3845}, {1532, 3583}, {1598, 54065}, {1656, 38760}, {1836, 12832}, {1862, 23047}, {2077, 17533}, {2771, 5806}, {2800, 6797}, {2801, 65452}, {2802, 19925}, {2804, 44929}, {2807, 58501}, {2818, 38390}, {2886, 6929}, {2950, 11372}, {3062, 46435}, {3090, 31235}, {3146, 38693}, {3149, 10058}, {3254, 38308}, {3309, 52873}, {3434, 55016}, {3534, 38069}, {3543, 59377}, {3545, 6174}, {3579, 38182}, {3582, 52851}, {3585, 5533}, {3627, 38602}, {3813, 11928}, {3816, 6923}, {3825, 31775}, {3829, 22758}, {3830, 38753}, {3843, 10742}, {3850, 38758}, {3851, 10993}, {3853, 61566}, {3854, 20095}, {3855, 6154}, {3857, 51525}, {3858, 11698}, {3925, 6965}, {4193, 11826}, {4297, 32557}, {4301, 15863}, {4996, 6912}, {4999, 37290}, {5046, 15908}, {5055, 38762}, {5066, 61562}, {5072, 38763}, {5073, 38754}, {5083, 13374}, {5187, 10310}, {5225, 11500}, {5450, 10593}, {5480, 5848}, {5691, 16173}, {5715, 13257}, {5732, 38205}, {5805, 5851}, {5817, 6068}, {5818, 64136}, {5856, 63970}, {5881, 25416}, {5927, 12665}, {6000, 58508}, {6001, 12736}, {6224, 9779}, {6256, 9669}, {6284, 6941}, {6326, 12690}, {6560, 13977}, {6561, 13913}, {6690, 6980}, {6714, 57605}, {6827, 11495}, {6831, 39692}, {6834, 12953}, {6843, 64154}, {6844, 12332}, {6891, 64725}, {6905, 65632}, {6906, 7173}, {6907, 52769}, {6913, 51506}, {6915, 17100}, {6949, 15338}, {6971, 55297}, {6976, 31245}, {7682, 10265}, {7687, 8674}, {7972, 11522}, {7988, 64012}, {7995, 12767}, {8227, 12119}, {8703, 38084}, {8735, 65814}, {9373, 42863}, {9581, 64119}, {9656, 10597}, {9670, 10786}, {9671, 12116}, {9812, 64189}, {9913, 18535}, {9946, 58613}, {9955, 11729}, {10006, 64787}, {10151, 12138}, {10171, 58453}, {10276, 31764}, {10427, 38150}, {10516, 51007}, {10531, 10895}, {10532, 12763}, {10596, 11237}, {10698, 62616}, {10711, 41099}, {10767, 14644}, {10768, 14639}, {11238, 12115}, {11479, 13222}, {11604, 52269}, {11715, 31673}, {12295, 53753}, {12619, 22793}, {12675, 18240}, {12702, 38128}, {12735, 13464}, {12743, 17605}, {12751, 18492}, {12773, 61984}, {13143, 64291}, {13202, 53715}, {13226, 64001}, {13570, 58543}, {13922, 42265}, {13991, 42262}, {14054, 15094}, {14269, 38756}, {14496, 64290}, {14497, 23959}, {14647, 52116}, {14740, 58631}, {14853, 51198}, {15033, 58056}, {15171, 63964}, {18481, 38032}, {18514, 37468}, {18861, 21669}, {19081, 23249}, {19082, 23259}, {19112, 42561}, {19113, 31412}, {19541, 64188}, {19907, 38034}, {23514, 53720}, {23515, 53711}, {24302, 37707}, {26726, 37712}, {28164, 33709}, {30308, 64011}, {31730, 38133}, {31849, 38389}, {34773, 38044}, {35514, 38202}, {36518, 53743}, {36519, 53729}, {37447, 56790}, {37714, 64056}, {37730, 64762}, {37736, 64669}, {38021, 50843}, {38026, 50811}, {38060, 43161}, {38072, 51008}, {38074, 50842}, {38076, 50841}, {38090, 43273}, {38099, 50810}, {38104, 50808}, {38109, 64792}, {38119, 46264}, {38168, 48906}, {38207, 43182}, {38636, 61923}, {38637, 62024}, {38665, 61964}, {38669, 50689}, {38755, 61970}, {39809, 53733}, {39838, 53722}, {40273, 61553}, {41698, 65140}, {42270, 48715}, {42273, 48714}, {42283, 48700}, {42284, 48701}, {44870, 58539}, {46684, 51118}, {46694, 63976}, {50908, 64278}, {51409, 54154}, {51529, 61988}, {51702, 61519}, {51718, 61518}, {51792, 63992}, {54448, 64743}, {55359, 64512}, {61985, 64009}

X(65948) = midpoint of X(i) and X(j) for these {i,j}: {3, 64186}, {4, 11}, {5, 22938}, {80, 1537}, {104, 52836}, {119, 10738}, {149, 37725}, {355, 64138}, {382, 38761}, {946, 6246}, {1145, 14217}, {1484, 22799}, {1532, 3583}, {3627, 38602}, {3853, 61566}, {4301, 15863}, {5691, 64191}, {5881, 25416}, {6326, 12690}, {6797, 9856}, {6905, 65632}, {10698, 62616}, {10724, 24466}, {10742, 37726}, {10993, 48680}, {11715, 31673}, {12295, 53753}, {12619, 22793}, {13202, 53715}, {13257, 49176}, {14054, 15094}, {31849, 38389}, {37447, 56790}, {39809, 53733}, {39838, 53722}, {40273, 61553}, {44870, 58539}, {46684, 51118}, {51409, 54154}, {59390, 59391}
X(65948) = reflection of X(i) in X(j) for these {i,j}: {3, 6667}, {100, 20400}, {389, 58475}, {1387, 16174}, {3035, 5}, {5083, 13374}, {6713, 60759}, {9946, 58613}, {10993, 35023}, {11729, 9955}, {12675, 18240}, {12735, 13464}, {14740, 58631}, {15528, 58587}, {20418, 11}, {31764, 10276}, {33814, 58421}, {38759, 6713}, {61580, 3850}, {63976, 46694}, {64192, 946}, {64193, 6702}
X(65948) = complement of X(24466)
X(65948) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10724, 24466}, {3, 23513, 6667}, {4, 104, 52836}, {4, 10591, 12114}, {4, 10598, 56}, {4, 10785, 37001}, {4, 10893, 7681}, {4, 10896, 63980}, {4, 59391, 11}, {5, 33814, 58421}, {11, 52836, 104}, {11, 59390, 4}, {20, 31272, 21154}, {80, 1699, 1537}, {381, 10738, 119}, {381, 26333, 7680}, {382, 57298, 38761}, {1484, 3845, 22799}, {3090, 34474, 31235}, {3545, 13199, 64008}, {3843, 51517, 10742}, {3851, 48680, 38752}, {5587, 14217, 1145}, {5691, 16173, 64191}, {6713, 60759, 45310}, {8227, 12119, 34123}, {10742, 51517, 37726}, {10895, 13274, 10956}, {10896, 13273, 11}, {10993, 38752, 35023}, {11928, 37821, 3813}, {13199, 64008, 6174}, {22938, 38141, 5}, {23513, 64186, 3}, {33814, 58421, 3035}, {38752, 48680, 10993}, {38759, 45310, 6713}, {51118, 59419, 46684}

X(65949) = X(4)X(12)∩X(5)X(993)

Barycentrics    (a + b - c)*(a - b + c)*(b + c)^2*(2*a^2*b^2 - 2*b^4 + 2*a^2*c^2 + 4*b^2*c^2 - 2*c^4) + (a + b - c)*(a + c)^2*(-a + b + c)*(a^4 - b^4 + 2*b^2*c^2 - c^4) + (a + b)^2*(a - b + c)*(-a + b + c)*(a^4 - b^4 + 2*b^2*c^2 - c^4) : :
X(65949) = X[1] - 3 X[38039], X[2] - 3 X[38078], X[30264] - 9 X[38078], X[3] - 3 X[38109], 2 X[6668] - 3 X[38109], 3 X[4] + X[11491], 3 X[4] - X[52837], X[4] + 3 X[59392], 3 X[12] - X[11491], 3 X[12] + X[52837], X[12] - 3 X[59392], X[11491] - 9 X[59392], X[52837] + 9 X[59392], X[5] - 3 X[38142], and many others

See Van Khea and Peter Moses, euclid 7119.

X(65949) lies on these lines: {1, 38039}, {2, 30264}, {3, 6668}, {4, 12}, {5, 993}, {6, 38148}, {7, 38153}, {8, 38157}, {9, 38160}, {10, 38162}, {11, 38163}, {20, 21155}, {30, 31659}, {40, 38058}, {65, 12691}, {119, 12615}, {355, 5855}, {381, 529}, {382, 59382}, {389, 58476}, {515, 37737}, {546, 946}, {550, 38114}, {758, 5777}, {958, 6867}, {962, 59416}, {1329, 6917}, {1387, 40259}, {1389, 62616}, {1478, 63980}, {1532, 65143}, {1537, 64291}, {1699, 30323}, {2476, 11827}, {2829, 3585}, {2886, 10526}, {2975, 3091}, {3090, 31260}, {3146, 59421}, {3428, 6871}, {3534, 38070}, {3545, 31157}, {3579, 38183}, {3583, 63257}, {3614, 6905}, {3814, 37281}, {3817, 51111}, {3822, 31789}, {3832, 10893}, {3843, 12000}, {3858, 7956}, {3861, 24042}, {4134, 61510}, {4297, 38062}, {4996, 6915}, {5080, 7548}, {5204, 6879}, {5229, 6844}, {5480, 5849}, {5587, 12526}, {5603, 37734}, {5691, 37701}, {5694, 15064}, {5715, 18492}, {5732, 38206}, {5775, 38306}, {5805, 5852}, {5857, 63970}, {6690, 7491}, {6691, 6971}, {6796, 10592}, {6830, 7354}, {6833, 12943}, {6841, 33961}, {6845, 64000}, {6874, 24953}, {6906, 65631}, {6907, 12511}, {6928, 25466}, {6951, 50031}, {6952, 15326}, {6965, 7958}, {6980, 55296}, {6982, 64077}, {7951, 37468}, {7995, 64119}, {8703, 38085}, {9654, 48482}, {9656, 12115}, {9657, 10785}, {9671, 10596}, {9956, 18253}, {10175, 31445}, {10265, 24470}, {10516, 51009}, {10532, 10896}, {10597, 11238}, {10942, 18407}, {11012, 17530}, {11237, 12116}, {11929, 12607}, {12019, 31870}, {12571, 22835}, {12675, 58566}, {12702, 38129}, {15908, 17577}, {16125, 31750}, {16160, 22799}, {18481, 38033}, {18483, 44685}, {18990, 20418}, {20420, 63964}, {21669, 52836}, {31673, 64804}, {31730, 38134}, {34773, 38045}, {35514, 38203}, {37447, 41698}, {38021, 51112}, {38027, 50811}, {38034, 61148}, {38061, 43161}, {38063, 64191}, {38076, 51113}, {38091, 43273}, {38100, 50810}, {38105, 50808}, {38120, 46264}, {38135, 38761}, {38158, 64198}, {38169, 48906}, {38184, 38602}, {38208, 43182}, {38219, 46684}, {45310, 61534}, {51702, 61518}, {51718, 61519}, {51792, 64669}, {58636, 63976}, {59387, 62830}, {64110, 64282}

X(65949) = midpoint of X(i) and X(j) for these {i,j}: {4, 12}, {3585, 6831}, {6906, 65631}, {11491, 52837}
X(65949) = reflection of X(i) in X(j) for these {i,j}: {3, 6668}, {389, 58476}, {4999, 5}, {12675, 58566}, {31659, 61512}, {63976, 58636}
X(65949) = complement of X(30264)
X(65949) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 38109, 6668}, {4, 10590, 11500}, {4, 10599, 55}, {4, 10786, 36999}, {4, 10894, 7680}, {4, 10895, 18242}, {4, 11491, 52837}, {4, 59392, 12}, {12, 52837, 11491}, {381, 26332, 7681}, {3585, 52850, 6831}, {5229, 6844, 12114}, {11929, 37820, 12607}, {18990, 63963, 20418}

X(65950) = X(4)X(9)∩X(27)X(103)

Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^2*b^2 - 2*b^4 + 2*a^2*c^2 + 4*b^2*c^2 - 2*c^4) + b*(a^2 + b^2 - c^2)*(-a^2 + b^2 + c^2)*(a^4 - b^4 + 2*b^2*c^2 - c^4) + c*(a^2 - b^2 + c^2)*(-a^2 + b^2 + c^2)*(a^4 - b^4 + 2*b^2*c^2 - c^4) : :
X(65950) = 3 X[4] - X[52840], 3 X[19] + X[52840], 3 X[5587] - X[50861], X[20] - 3 X[21160], 7 X[3090] - 5 X[31261], 5 X[3091] - X[4329], 3 X[3545] - X[31158], 7 X[3832] + X[20061], 3 X[14853] - X[51210]

See Van Khea and Peter Moses, euclid 7119.

X(65950) lies on these lines: {2, 30265}, {3, 40530}, {4, 9}, {5, 18589}, {20, 21160}, {25, 39475}, {27, 103}, {28, 4297}, {30, 61517}, {33, 13405}, {34, 6738}, {92, 4847}, {118, 1824}, {124, 50930}, {132, 42425}, {158, 273}, {165, 37104}, {226, 1859}, {235, 39579}, {240, 3663}, {278, 11019}, {381, 534}, {515, 7497}, {946, 1871}, {950, 54394}, {971, 16608}, {1096, 40940}, {1125, 57276}, {1486, 1598}, {1595, 23305}, {1596, 7680}, {1784, 23689}, {1848, 3817}, {1876, 30329}, {1882, 10395}, {1888, 4848}, {1893, 42069}, {1900, 1906}, {2181, 3914}, {2263, 18391}, {3085, 4319}, {3089, 10198}, {3090, 31261}, {3091, 4329}, {3545, 31158}, {3755, 14571}, {3827, 5480}, {3832, 20061}, {4198, 5691}, {4200, 64673}, {4219, 10164}, {4231, 6011}, {4233, 15931}, {4304, 54368}, {4314, 41227}, {4353, 23052}, {5125, 8582}, {5174, 6736}, {5236, 5542}, {5732, 37102}, {5927, 26942}, {6245, 6523}, {6248, 46181}, {6708, 8727}, {6734, 45738}, {6743, 56876}, {7466, 44425}, {7490, 64705}, {7511, 31673}, {7518, 24987}, {7537, 19862}, {7682, 10002}, {8680, 15762}, {12688, 58890}, {14119, 62493}, {14853, 51210}, {14954, 35263}, {15942, 28164}, {20420, 34823}, {21620, 64543}, {24248, 51288}, {25935, 63395}, {25993, 38204}, {30687, 37371}, {37245, 63983}, {37377, 63998}, {37381, 37805}, {37387, 49542}, {40149, 43672}, {40998, 55472}, {44178, 55105}, {60685, 63969}

X(65950) = midpoint of X(i) and X(j) for these {i,j}: {4, 19}, {15942, 37395}
X(65950) = reflection of X(i) in X(j) for these {i,j}: {3, 40530}, {18589, 5}
X(65950) = complement of X(30265)
X(65950) = polar conjugate of the isotomic conjugate of X(25935)
X(65950) = X(905)-isoconjugate of X(59063)
X(65950) = barycentric product X(i)*X(j) for these {i,j}: {4, 25935}, {92, 5728}, {1536, 52781}, {2052, 63395}
X(65950) = barycentric quotient X(i)/X(j) for these {i,j}: {1536, 26006}, {5728, 63}, {8750, 59063}, {25935, 69}, {63395, 394}
X(65950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 63970, 51758}, {281, 1861, 10}, {1848, 37372, 3817}, {1871, 15763, 946}

X(65951) = (name pending)

Barycentrics    (a*(a - b - c) - x)*(a^2 - a*b - 2*a*c - b*c + c^2 - y)*(a^2 - 2*a*b + b^2 - a*c - b*c - z)*(b*(a + b - c)*c*(a - b + c)*(a^5 - 3*a^4*b + 3*a^2*b^3 + a*b^4 - 2*b^5 - 3*a^4*c - 4*a^3*b*c - 3*a^2*b^2*c + 4*a*b^3*c + 6*b^4*c - 3*a^2*b*c^2 - 10*a*b^2*c^2 - 4*b^3*c^2 + 3*a^2*c^3 + 4*a*b*c^3 - 4*b^2*c^3 + a*c^4 + 6*b*c^4 - 2*c^5) - b*(a + b - c)*c*(a - b + c)*(2*a^3 + a^2*b - a*b^2 - 2*b^3 + a^2*c + 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2 - 2*c^3)*x + (a + b - c)*c*(a^5 - 2*a^4*b - 2*a^3*b^2 + 5*a^2*b^3 - a*b^4 - b^5 - 2*a^4*c - 2*a^3*b*c - 5*a^2*b^2*c + 6*a*b^3*c + 3*b^4*c - a^2*b*c^2 - 8*a*b^2*c^2 - 2*b^3*c^2 + a^2*c^3 + 2*a*b*c^3 - 2*b^2*c^3 + a*c^4 + 3*b*c^4 - c^5)*y - (a + b - c)*c*(a^3 + 2*a^2*b - 2*a*b^2 - b^3 + 2*a*b*c + b^2*c + b*c^2 - c^3)*x*y + b*(a - b + c)*(a^5 - 2*a^4*b + a^2*b^3 + a*b^4 - b^5 - 2*a^4*c - 2*a^3*b*c - a^2*b^2*c + 2*a*b^3*c + 3*b^4*c - 2*a^3*c^2 - 5*a^2*b*c^2 - 8*a*b^2*c^2 - 2*b^3*c^2 + 5*a^2*c^3 + 6*a*b*c^3 - 2*b^2*c^3 - a*c^4 + 3*b*c^4 - c^5)*z - b*(a - b + c)*(a^3 - b^3 + 2*a^2*c + 2*a*b*c + b^2*c - 2*a*c^2 + b*c^2 - c^3)*x*z + a*(a^4 - a^3*b - 2*a^2*b^2 + 3*a*b^3 - b^4 - a^3*c - 3*a*b^2*c + 4*b^3*c - 2*a^2*c^2 - 3*a*b*c^2 - 6*b^2*c^2 + 3*a*c^3 + 4*b*c^3 - c^4)*y*z - a*(a*b - b^2 + a*c + 2*b*c - c^2)*x*y*z) : : where x, y, z = cyclic[Sqrt[-(a*(a - b - c)*(a^2 + a*b - 2*b^2 + a*c + 4*b*c - 2*c^2))]]

Let A'B'C' be the cevian triangle of X(7) and Iab, Iac the X(1) of ABA', ACA', respectively. Define Ibc, Iba and Ica, Icb cyclically. Let A*B*C* be the triangle bounded by IabIac, IbcIba, IcaIcb. The triangles ABC, A*B*C* are orthologic. The orthologic center (ABC, A*B*C*) is X(7) and the reciprocal is X(65951)

See Antreas Hatzipolakis and Peter Moses, euclid 7126.

X(65951) lies on these lines: { }

X(65952) = ISOGONAL CONJUGATE OF X(9316)

Barycentrics    (a - b - c)*(a*b - b^2 - 2*a*c + b*c)*(2*a*b - a*c - b*c + c^2) : :

X(65952) lies on the cubic K1373 and these lines: {2, 56718}, {8, 63624}, {9, 6169}, {11, 48627}, {55, 17261}, {75, 2310}, {85, 64134}, {144, 145}, {190, 4319}, {239, 60910}, {312, 60812}, {335, 24840}, {497, 41794}, {664, 64741}, {765, 1253}, {982, 3663}, {1120, 7962}, {1278, 63600}, {1837, 62392}, {1861, 4429}, {2293, 4664}, {2751, 65371}, {3062, 9312}, {3100, 4676}, {3161, 3693}, {3675, 63586}, {3717, 4073}, {3729, 4907}, {3758, 4336}, {4373, 5274}, {4862, 35160}, {9439, 52352}, {10384, 49446}, {10866, 17480}, {10939, 27340}, {12053, 34860}, {13727, 15430}, {14727, 53210}, {17350, 41339}, {17353, 45275}, {17490, 17604}, {20359, 39703}, {24003, 30610}, {24538, 56940}, {25243, 25722}, {28058, 34524}, {31225, 59620}, {39250, 39924}, {44040, 46937}

X(65952) = isogonal conjugate of X(9316)
X(65952) = isotomic conjugate of X(9312)
X(65952) = anticomplement of X(59573)
X(65952) = isotomic conjugate of the anticomplement of X(41006)
X(65952) = isotomic conjugate of the isogonal conjugate of X(9439)
X(65952) = X(32023)-Ceva conjugate of X(9311)
X(65952) = X(i)-cross conjugate of X(j) for these (i,j): {3061, 312}, {3452, 8}, {3912, 14942}, {30854, 60668}, {41006, 2}, {45206, 29}
X(65952) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9316}, {6, 6180}, {31, 9312}, {32, 61413}, {56, 1376}, {57, 9310}, {59, 4014}, {108, 22091}, {109, 4449}, {279, 16283}, {604, 3729}, {651, 20980}, {1015, 61415}, {1407, 4513}, {1408, 3967}, {1409, 56014}, {1415, 4885}, {1416, 56714}, {1438, 6168}, {2149, 21139}, {2195, 41355}, {4559, 18199}, {32735, 42341}
X(65952) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 1376}, {2, 9312}, {3, 9316}, {9, 6180}, {11, 4449}, {650, 21139}, {1146, 4885}, {3161, 3729}, {3752, 59507}, {5452, 9310}, {6184, 6168}, {6376, 61413}, {6615, 4014}, {6741, 21052}, {24771, 4513}, {38983, 22091}, {38991, 20980}, {39063, 41355}, {40609, 56714}, {40624, 20907}, {40625, 17218}, {45252, 1}, {55062, 24749}, {55067, 18199}, {59577, 3967}, {62575, 27829}
X(65952) = cevapoint of X(i) and X(j) for these (i,j): {1, 64129}, {9, 4319}, {514, 24775}, {522, 2310}
X(65952) = crosspoint of X(i) and X(j) for these (i,j): {4373, 56265}, {7155, 63165}
X(65952) = crosssum of X(3052) and X(20995)
X(65952) = trilinear pole of line {4147, 4521}
X(65952) = barycentric product X(i)*X(j) for these {i,j}: {8, 9311}, {9, 32023}, {76, 9439}, {192, 60812}, {312, 9309}, {522, 30610}, {3263, 6169}, {3596, 9315}, {20287, 27424}, {27498, 27538}
X(65952) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6180}, {2, 9312}, {6, 9316}, {8, 3729}, {9, 1376}, {11, 21139}, {29, 56014}, {55, 9310}, {75, 61413}, {200, 4513}, {241, 41355}, {518, 6168}, {522, 4885}, {650, 4449}, {652, 22091}, {663, 20980}, {765, 61415}, {1253, 16283}, {2170, 4014}, {2321, 3967}, {3452, 59507}, {3693, 56714}, {3700, 21052}, {3717, 40883}, {3737, 18199}, {4007, 4942}, {4373, 27829}, {4391, 20907}, {4560, 17218}, {6169, 105}, {9309, 57}, {9311, 7}, {9315, 56}, {9439, 6}, {14727, 34085}, {20287, 1423}, {30610, 664}, {32023, 85}, {41006, 59573}, {51845, 1462}, {60812, 330}, {60813, 64980}, {65371, 36146}
X(65952) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 2310, 63597}, {3729, 4907, 14942}

X(65953) = ISOTOMIC CONJUGATE OF X(43750)

Barycentrics    (a - b - c)*(a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c + a^2*b*c - a*b^2*c - b^3*c - 2*a^2*c^2 - a*b*c^2 + 2*b^2*c^2 + a*c^3 - b*c^3) : :

X(65953) lies on the cubic K1373 and these lines: {1, 59621}, {2, 9445}, {7, 8}, {9, 28058}, {78, 3685}, {144, 28057}, {190, 480}, {192, 2340}, {193, 28124}, {200, 1721}, {294, 7155}, {318, 1827}, {329, 9801}, {346, 14943}, {894, 28043}, {1282, 24728}, {1654, 28118}, {1742, 3177}, {2398, 63088}, {2951, 30625}, {3161, 3693}, {3198, 9778}, {3570, 8844}, {3661, 23529}, {3705, 51400}, {3713, 24351}, {3886, 52507}, {3912, 63598}, {4073, 17755}, {4081, 17233}, {4847, 24199}, {4899, 6736}, {5281, 21811}, {5696, 48878}, {6745, 25101}, {7080, 27544}, {7081, 21387}, {9950, 21060}, {14100, 30854}, {17234, 61035}, {17277, 42014}, {17294, 63594}, {17379, 28125}, {18252, 30946}, {20905, 30628}, {20935, 31526}, {21039, 26059}, {24341, 26125}, {24799, 31183}, {25722, 30807}, {28072, 52888}, {28131, 63001}, {28795, 52157}, {34019, 56310}, {34852, 63597}, {52562, 64007}, {56882, 64709}, {59296, 64171}

X(65953) = reflection of X(39126) in X(59573)
X(65953) = isotomic conjugate of X(43750)
X(65953) = X(i)-Ceva conjugate of X(j) for these (i,j): {200, 8}, {3729, 3161}, {20935, 3177}, {32932, 56313}, {32937, 19582}
X(65953) = X(20935)-cross conjugate of X(8)
X(65953) = X(i)-isoconjugate of X(j) for these (i,j): {31, 43750}, {604, 56265}, {663, 53632}, {1407, 64458}, {2175, 60811}
X(65953) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 43750}, {85, 1088}, {3161, 56265}, {21195, 4014}, {24771, 64458}, {40593, 60811}
X(65953) = crosssum of X(649) and X(61050)
X(65953) = barycentric product X(i)*X(j) for these {i,j}: {8, 3177}, {9, 20935}, {200, 40593}, {312, 1742}, {314, 21856}, {333, 21084}, {341, 34497}, {346, 31526}, {3596, 20995}, {3699, 21195}, {3717, 51846}, {7017, 20793}
X(65953) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43750}, {8, 56265}, {85, 60811}, {200, 64458}, {651, 53632}, {1742, 57}, {3177, 7}, {20793, 222}, {20935, 85}, {20995, 56}, {21084, 226}, {21195, 3676}, {21856, 65}, {31526, 279}, {34497, 269}, {40593, 1088}, {51846, 56783}
X(65953) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 4012, 8}, {75, 3059, 8}, {1742, 21084, 3177}

X(65954) = X(7)X(192)∩X(9)X(33676)

Barycentrics    (a - b - c)*(-b^2 + a*c)*(a*b - c^2)*(2*a^3 - a^2*b - b^3 - a^2*c + b^2*c + b*c^2 - c^3) : :

X(65954) lies on the cubic K1373 and these lines: {7, 192}, {9, 33676}, {190, 56897}, {522, 2321}, {660, 12530}, {813, 1766}, {2311, 40979}, {3161, 4518}, {3729, 40217}, {12723, 40730}, {17738, 56895}, {24280, 52085}, {25269, 63234}, {40968, 51858}, {43534, 56144}, {52209, 64695}

X(65954) = X(i)-isoconjugate of X(j) for these (i,j): {103, 1429}, {911, 1447}, {1428, 36101}, {1914, 43736}, {2210, 52156}, {3716, 32668}, {4435, 24016}, {9503, 51329}, {36039, 43041}
X(65954) = X(i)-Dao conjugate of X(j) for these (i,j): {1566, 43041}, {23972, 1447}, {36906, 43736}, {39077, 34253}, {40869, 39775}, {50441, 239}, {62557, 52156}
X(65954) = crosspoint of X(335) and X(33676)
X(65954) = crosssum of X(1914) and X(51329)
X(65954) = barycentric product X(i)*X(j) for these {i,j}: {334, 41339}, {335, 40869}, {516, 4518}, {676, 36801}, {2398, 60577}, {4583, 65664}, {4876, 30807}, {7077, 35517}, {17747, 36800}, {33676, 50441}, {40217, 56900}
X(65954) = barycentric quotient X(i)/X(j) for these {i,j}: {291, 43736}, {335, 52156}, {516, 1447}, {676, 43041}, {910, 1429}, {3252, 52213}, {4444, 60581}, {4518, 18025}, {4876, 36101}, {7077, 103}, {9502, 34253}, {17747, 16609}, {30807, 10030}, {35517, 18033}, {36801, 57928}, {40217, 56668}, {40869, 239}, {41339, 238}, {43035, 62785}, {46392, 4435}, {50441, 39775}, {51376, 20769}, {51418, 3684}, {51858, 911}, {56900, 6654}, {60577, 2400}, {65664, 659}

X(65955) = X(7)X(56668)∩X(69)X(144)

Barycentrics    (a^2 - b*c)*(a^3 - a^2*b - a*b^2 + b^3 + a*c^2 + b*c^2 - 2*c^3)*(a^3 + a*b^2 - 2*b^3 - a^2*c + b^2*c - a*c^2 + c^3) : :

X(65955) lies on the cubic K1373 and these lines: {7, 56668}, {69, 144}, {86, 2400}, {103, 789}, {269, 53217}, {3570, 27945}, {3729, 40217}, {7155, 43736}, {26651, 59195}, {52156, 56102}

X(65955) = X(i)-cross conjugate of X(j) for these (i,j): {39775, 350}, {51435, 239}
X(65955) = X(i)-isoconjugate of X(j) for these (i,j): {292, 910}, {516, 1911}, {676, 34067}, {875, 2398}, {876, 2426}, {1456, 7077}, {1886, 2196}, {1922, 30807}, {9502, 51866}, {14598, 35517}, {17747, 18268}, {37128, 51436}, {40730, 56639}, {43035, 51858}
X(65955) = X(i)-Dao conjugate of X(j) for these (i,j): {239, 28346}, {2238, 9502}, {3912, 50441}, {6651, 516}, {18277, 35517}, {19557, 910}, {35068, 17747}, {35119, 676}, {39028, 30807}, {45250, 3252}
X(65955) = cevapoint of X(i) and X(j) for these (i,j): {239, 51435}, {3685, 17755}
X(65955) = trilinear pole of line {239, 4148}
X(65955) = barycentric product X(i)*X(j) for these {i,j}: {103, 1921}, {238, 57996}, {239, 18025}, {350, 36101}, {677, 65101}, {812, 57928}, {911, 18891}, {1815, 40717}, {2338, 18033}, {2400, 3570}, {2424, 27853}, {3685, 52156}, {3975, 43736}, {4148, 65294}, {9503, 64223}, {51435, 57548}
X(65955) = barycentric quotient X(i)/X(j) for these {i,j}: {103, 292}, {238, 910}, {239, 516}, {242, 1886}, {350, 30807}, {677, 813}, {740, 17747}, {812, 676}, {874, 42719}, {911, 1911}, {1429, 1456}, {1447, 43035}, {1815, 295}, {1921, 35517}, {2338, 7077}, {2400, 4444}, {2424, 3572}, {3570, 2398}, {3684, 41339}, {3685, 40869}, {3747, 51436}, {4366, 51435}, {4432, 51406}, {4435, 65664}, {6651, 28346}, {6654, 56639}, {8299, 9502}, {9503, 52030}, {17755, 50441}, {18025, 335}, {27922, 63851}, {33295, 14953}, {34253, 53547}, {36039, 34067}, {36056, 2196}, {36101, 291}, {39775, 39063}, {51435, 23972}, {52156, 7233}, {57928, 4562}, {57996, 334}, {58327, 51418}

X(65956) = X(2)X(56897)∩X(144)X(673)

Barycentrics    (a - b - c)*(a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(a^3 - a^2*b + 2*a*b^2 - a^2*c - a*b*c - b^2*c + 2*a*c^2 - b*c^2) : :

X(65956) lies on the cubic K1373 and these lines: {2, 56897}, {6, 33674}, {9, 33676}, {105, 38869}, {144, 673}, {192, 6654}, {294, 7155}, {346, 14942}, {666, 1743}, {894, 56895}, {1278, 63236}, {3287, 23617}, {3729, 6185}, {4452, 52210}, {5749, 40724}, {26685, 62599}, {59579, 61477}

X(65956) = X(6185)-Ceva conjugate of X(14942)
X(65956) = X(3717)-Dao conjugate of X(4437)
X(65956) = barycentric product X(2481)*X(19589)
X(65956) = barycentric quotient X(i)/X(j) for these {i,j}: {19589, 518}, {27830, 10029}

X(65957) = X(2)X(63624)∩X(7)X(145)

Barycentrics    (a - b - c)*(3*a^4 - 3*a^3*b + 5*a^2*b^2 - 5*a*b^3 - 3*a^3*c - 6*a^2*b*c + 5*a*b^2*c + 4*b^3*c + 5*a^2*c^2 + 5*a*b*c^2 - 8*b^2*c^2 - 5*a*c^3 + 4*b*c^3) : :

X(65957) lies on the cubic K1373 and these lines: {1, 59573}, {2, 63624}, {7, 145}, {9, 6169}, {192, 3158}, {200, 14522}, {346, 19605}, {2136, 49446}, {4000, 5573}, {4012, 4901}, {5845, 39878}, {7155, 42317}, {25243, 46917}, {25722, 25725}, {35445, 65206}, {50441, 63625}

X(65957) = complement of X(63624)
X(65957) = X(3729)-Ceva conjugate of X(9)
X(65957) = barycentric product X(3729)*X(45252)
X(65957) = barycentric quotient X(45252)/X(9311)

X(65958) = X(8)X(765)∩X(59)X(1016)

Barycentrics    (b+c)^4*(a-b+c)*(a+b-c)*(a^2-b^2)^2*(a^2-c^2)^2 : :

See Antreas Hatzipolakis and César Lozada, euclid 7129.

X(65958) lies on these lines: {8, 765}, {10, 55382}, {11, 65826}, {59, 1016}, {345, 44710}, {1284, 3932}, {3952, 4086}, {4017, 4552}, {4036, 40521}, {4551, 51650}, {6065, 15742}, {17420, 50039}, {23354, 62669}

X(65958) = cevapoint of X(i) and X(j) for these {i, j}: {10, 61172}, {181, 21859}, {594, 40521}, {4103, 6057}
X(65958) = X(i)-cross conjugate of-X(j) for these (i, j): (181, 21859), (1089, 3952), (2171, 4552), (6057, 4103), (21676, 10)
X(65958) = X(i)-Dao conjugate of-X(j) for these (i, j): (10, 18191), (37, 17197), (523, 7336), (758, 3025), (1214, 17205), (1500, 38347), (3160, 61403), (3161, 26856), (4075, 11), (6741, 56283), (15267, 1357), (40590, 16726), (40607, 3271), (55065, 21132), (56325, 1086), (62564, 17219), (62570, 16727)
X(65958) = X(i)-isoconjugate of-X(j) for these {i, j}: {11, 849}, {41, 61403}, {58, 18191}, {60, 244}, {261, 3248}, {270, 3937}, {284, 16726}, {593, 2170}, {604, 26856}, {757, 3271}, {764, 4636}, {1015, 2185}, {1019, 7252}, {1086, 2150}, {1098, 1357}, {1101, 7336}, {1333, 17197}, {1977, 52379}, {2189, 3942}, {2194, 17205}, {2203, 17219}, {2310, 7341}, {3249, 4631}, {3733, 3737}, {4560, 57129}, {4612, 21143}, {5546, 8042}, {7054, 53538}, {7203, 21789}, {7342, 24026}, {16727, 57657}, {21758, 60571}, {22096, 57779}, {23189, 57200}, {43924, 65575}
X(65958) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (7, 61403), (8, 26856), (10, 17197), (12, 1086), (37, 18191), (59, 593), (65, 16726), (115, 7336), (181, 1015), (201, 3942), (226, 17205), (306, 17219), (594, 11), (644, 65575), (756, 2170), (762, 4516), (765, 2185), (1016, 261), (1018, 3737), (1020, 7203), (1089, 4858), (1110, 2150), (1252, 60), (1254, 53538), (1262, 7341), (1275, 552), (1441, 16727), (1500, 3271), (2149, 849), (2171, 244), (2197, 3937), (3027, 35119), (3690, 7117), (3695, 26932), (3700, 56283), (3949, 7004), (3952, 4560), (3967, 16759), (4013, 60578), (4017, 8042), (4024, 21132), (4033, 18155), (4036, 40166), (4037, 4124), (4053, 53525), (4069, 1021), (4076, 7058), (4086, 40213), (4092, 64445), (4099, 4965)
X(65958) = X(34460)-zayin conjugate of-X(649)
X(65958) = trilinear pole of the line {4103, 21859} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65958) = perspector of the central inconic through X(12) and X(181)
X(65958) = barycentric product X(i)*X(j) for these {i,j}: {7, 61402}, {12, 1016}, {59, 28654}, {181, 31625}, {321, 65573}, {594, 4998}, {664, 4103}, {668, 21859}, {765, 6358}, {1089, 4564}, {1252, 34388}, {1275, 6057}, {2171, 7035}, {3027, 57566}, {3695, 46102}, {3699, 4605}, {3952, 4552}, {4033, 4551}, {4036, 31615}, {4076, 6354}
X(65958) = trilinear product X(i)*X(j) for these {i,j}: {10, 65573}, {12, 765}, {57, 61402}, {59, 1089}, {181, 7035}, {190, 21859}, {201, 15742}, {594, 4564}, {644, 4605}, {651, 4103}, {664, 40521}, {756, 4998}, {762, 4620}, {1016, 2171}, {1018, 4552}, {1020, 30730}, {1110, 34388}, {1252, 6358}, {1254, 4076}, {2149, 28654}
X(65958) = trilinear quotient X(i)/X(j) for these (i,j): (10, 18191), (12, 244), (59, 849), (85, 61403), (181, 3248), (201, 3937), (226, 16726), (312, 26856), (321, 17197), (349, 16727), (594, 2170), (756, 3271), (765, 60), (1016, 2185), (1018, 7252), (1089, 11), (1091, 1365), (1109, 7336), (1252, 2150), (1254, 1357)

X(65959) = X(4)X(250)∩X(1568)X(39569)

Barycentrics    (a^2-b^2)^2*(a^2-c^2)^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)^2 : :

See Antreas Hatzipolakis and César Lozada, euclid 7129.

X(65959) lies on these lines: {4, 250}, {1568, 39569}, {23290, 35360}, {23582, 47390}

X(65959) = cevapoint of X(5) and X(61195)
X(65959) = X(60828)-cross conjugate of-X(35360)
X(65959) = X(i)-Dao conjugate of-X(j) for these (i, j): (216, 53576), (6663, 125), (14363, 8901), (46394, 38352)
X(65959) = X(i)-isoconjugate of-X(j) for these {i, j}: {1109, 46089}, {2148, 53576}, {2169, 8901}, {2616, 23286}
X(65959) = X(i)-reciprocal conjugate of-X(j), and X(65959) = barycentric quotient X(i)/X(j), for these (i, j): (5, 53576), (53, 8901), (1087, 20902), (1625, 23286), (14570, 62428), (23357, 46089), (35360, 15412), (36412, 125), (45793, 339), (46394, 34980), (52604, 2623), (57195, 5489), (60828, 338), (61194, 58308), (61378, 3269), (62259, 3708), (62260, 20975), (62261, 115)
X(65959) = barycentric product X(i)*X(j) for these {i,j}: {249, 60828}, {250, 45793}, {4590, 62261}, {14570, 35360}, {18020, 36412}, {23181, 65183}, {46254, 62259}
X(65959) = trilinear product X(i)*X(j) for these {i,j}: {250, 1087}, {1101, 60828}, {2617, 35360}, {18020, 62259}, {23999, 61378}, {24041, 62261}, {46254, 62260}
X(65959) = trilinear quotient X(i)/X(j) for these (i,j): (1087, 125), (1101, 46089), (2617, 23286), (14213, 53576), (35360, 2616), (36412, 3708), (45793, 20902), (60828, 1109), (62259, 20975), (62261, 2643)

X(65960) = X(4)X(6072)∩X(69)X(249)

Barycentrics    (b^2+c^2)^2*(a^2-b^2)^2*(a^2-c^2)^2*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :

See Antreas Hatzipolakis and César Lozada, euclid 7129.

X(65960) lies on these lines: {4, 6072}, {69, 249}, {4590, 57655}, {51371, 64724}

X(65960) = X(59995)-cross conjugate of-X(4576)
X(65960) = X(i)-Dao conjugate of-X(j) for these (i, j): (6665, 125), (40938, 34294), (52042, 65751), (59994, 38352)
X(65960) = X(i)-isoconjugate of-X(j) for these {i, j}: {3708, 59996}, {34055, 51906}
X(65960) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (250, 59996), (427, 34294), (1843, 51906), (4175, 15526), (4576, 4580), (7794, 125), (8041, 20975), (18020, 52395), (35325, 18105), (41676, 58784), (52042, 38352), (55270, 52936), (59994, 65751), (59995, 339)
X(65960) = barycentric product X(i)*X(j) for these {i,j}: {250, 59995}, {2528, 55270}, {4175, 23582}, {4576, 41676}, {7794, 18020}
X(65960) = trilinear product X(i)*X(j) for these {i,j}: {4175, 24000}, {8041, 46254}, {35325, 55239}
X(65960) = trilinear quotient X(i)/X(j) for these (i,j): (4175, 2632), (7794, 3708), (17442, 51906), (20883, 34294), (41676, 55240), (46254, 52395), (55239, 4580), (59995, 20902)

X(65961) = X(6528)X(46371)∩X(52779)X(58979)

Barycentrics    (a^2-b^2)^4*(a^2-c^2)^4*(a^2+b^2-c^2)^3*(a^2-b^2+c^2)^3 : :

See Antreas Hatzipolakis and César Lozada, euclid 7129.

X(65961) lies on these lines: {6528, 46371}, {52779, 58979}

X(65961) = polar conjugate of the complement of X(54108)
X(65961) = cevapoint of X(47390) and X(47443)
X(65961) = X(47390)-cross conjugate of-X(47443)
X(65961) = X(i)-Dao conjugate of-X(j) for these (i, j): (9428, 23107), (31998, 23616), (39062, 5489)
X(65961) = X(i)-isoconjugate of-X(j) for these {i, j}: {115, 37754}, {798, 23616}, {810, 5489}, {1109, 34980}, {1924, 23107}, {2632, 20975}, {2643, 2972}, {2970, 42080}, {2971, 24020}, {3269, 3708}, {6507, 61339}, {17879, 65751}
X(65961) = X(i)-reciprocal conjugate of-X(j), and barycentric quotient X(i)/X(j), for these (i, j): (99, 23616), (249, 2972), (250, 3269), (648, 5489), (670, 23107), (1101, 37754), (6524, 61339), (6529, 8029), (15352, 23105), (18020, 15526), (23357, 34980), (23582, 125), (23590, 8754), (23964, 20975), (23975, 2971), (23999, 20902), (24000, 3708), (31614, 4143), (32230, 115), (34538, 2970), (41937, 65751), (46254, 17879), (47389, 23974), (47390, 35071), (47443, 520), (52913, 55269), (52919, 21134), (55270, 3265), (59152, 52613), (59153, 512), (62719, 24020)
X(65961) = trilinear pole of the line {2407, 47443} and intersection, other than {A, B, C}, of every pair of circumconics with perspectors on this line
X(65961) = perspector of the central inconic through X(18020) and X(32230)
X(65961) = pole of the the tripolar of X(23616) with respect to the Steiner-Wallace hyperbola
X(65961) = barycentric product X(i)*X(j) for these {i,j}: {107, 55270}, {670, 59153}, {4590, 32230}, {6528, 47443}, {6529, 31614}, {15352, 59152}, {18020, 23582}, {23590, 47389}, {24000, 46254}, {24021, 62719}, {47390, 57556}, {52913, 55268}
X(65961) = trilinear product X(i)*X(j) for these {i,j}: {250, 23999}, {799, 59153}, {823, 47443}, {18020, 24000}, {23590, 62719}, {23964, 46254}, {24019, 55270}, {24022, 47389}, {24041, 32230}, {36126, 59152}
X(65961) = trilinear quotient X(i)/X(j) for these (i,j): (249, 37754), (799, 23616), (811, 5489), (1101, 34980), (4602, 23107), (6520, 61339), (18020, 2632), (23582, 3708), (23999, 125), (24000, 20975), (24021, 8754), (24022, 2971), (24041, 2972), (32230, 2643), (36126, 8029), (46254, 15526), (47389, 24020), (47390, 42080), (47443, 822), (55270, 24018)

X(65962) = X(520)X(23583)∩X(523)X(5972)

Barycentrics    2*a^14-4*(b^2+c^2)*a^12+12*b^2*c^2*a^10+2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^8+(3*b^8+3*c^8-4*(2*b^4-3*b^2*c^2+2*c^4)*b^2*c^2)*a^6-3*(b^8-c^8)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^8+c^8-4*(b^4+c^4)*b^2*c^2)*a^2+(b^8-c^8)*(b^2-c^2)^3 : :

See Antreas Hatzipolakis and César Lozada, euclid 7129.

X(65962) lies on these lines: {520, 23583}, {523, 5972}, {1503, 38792}, {1990, 59558}, {6530, 51394}, {11064, 47158}, {32300, 65719}, {34947, 53569}

X(65962) = midpoint of X(i) and X(j) for these (i, j): {6530, 51394}, {11064, 47158}, {34947, 53569}
X(65962) = X(59153)-complementary conjugate of-X(8287)
X(65962) = center of the central inconic through X(18020) and X(32230)
X(65962) = pole of the line {2407, 47443} with respect to the Steiner inellipse

X(65963) = ISOGONAL CONJUGATE OF X(61066)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - 2*a^3*c + 2*a^2*b*c + 2*a*b^2*c - 2*b^3*c + a^2*c^2 - 4*a*b*c^2 + b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 2*c^4)^2*(a^4 - 2*a^3*b + a^2*b^2 + 2*a*b^3 - 2*b^4 + 2*a^2*b*c - 4*a*b^2*c + 2*b^3*c - 2*a^2*c^2 + 2*a*b*c^2 + b^2*c^2 - 2*b*c^3 + c^4)^2 : :

X(65963) lies on this line: {43048, 65249}

X(65963) = isogonal conjugate of X(61066)
X(65963) = isogonal conjugate of the complement of X(46136)
X(65963) = X(i)-cross conjugate of X(j) for these (i,j): {6, 953}, {654, 35011}
X(65963) = X(i)-isoconjugate of X(j) for these (i,j): {1, 61066}, {9, 3319}, {952, 2265}
X(65963) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 61066}, {478, 3319}
X(65963) = cevapoint of X(6) and X(953)
X(65963) = trilinear pole of line {953, 65854}
X(65963) = barycentric product X(i)*X(j) for these {i,j}: {953, 46136}, {65249, 65249}
X(65963) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 61066}, {56, 3319}, {953, 952}

X(65964) = X(9)X(2319)∩X(75)X(3617)

Barycentrics    (a - b - c)*(a^3*b - 4*a^2*b^2 + 3*a*b^3 + a^3*c + 3*a^2*b*c + a*b^2*c - 3*b^3*c - 4*a^2*c^2 + a*b*c^2 + 2*b^2*c^2 + 3*a*c^3 - 3*b*c^3) : :

X(65964) lies on the cubic K1373 and these lines: {9, 2319}, {75, 3617}, {144, 6555}, {312, 63600}, {346, 65952}, {1222, 3242}, {3699, 17350}, {5128, 62222}, {6552, 59573}, {63165, 65954}

X(65964) = X(3729)-Ceva conjugate of X(346)

X(65965) = X(7)X(14942)∩X(75)X(65955)

Barycentrics    (a - b - c)*(a^2 + b^2 - a*c - b*c)*(a^2 - a*b - b*c + c^2)*(a^6 - 2*a^5*b + 2*a^4*b^2 - 4*a^3*b^3 + 5*a^2*b^4 - 2*a*b^5 - 2*a^5*c + 3*a^4*b*c + 2*a^3*b^2*c - 4*a^2*b^3*c + b^5*c + 2*a^4*c^2 + 2*a^3*b*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 - 4*b^4*c^2 - 4*a^3*c^3 - 4*a^2*b*c^3 + 2*a*b^2*c^3 + 6*b^3*c^3 + 5*a^2*c^4 - 4*b^2*c^4 - 2*a*c^5 + b*c^5) : :

X(65965) lies on the cubic K1373 and these lines: {7, 14942}, {75, 65955}, {192, 28071}, {885, 42337}, {927, 2951}, {3161, 6559}, {4907, 6185}, {6654, 14100}, {43182, 61436}, {63236, 63600}, {65952, 65956}

X(65965) = X(3729)-Ceva conjugate of X(65956)

X(65966) = X(9)X(9311)∩X(7)X(145)

Barycentrics    (a + b - 3*c)*(a - 3*b + c)*(3*a^2 - 2*a*b - b^2 - 2*a*c + 2*b*c - c^2) : :

X(65966) lies on the cubic K1374 and these lines: {2, 9311}, {7, 145}, {144, 63626}, {350, 40014}, {1002, 10107}, {3912, 6557}, {5222, 8056}, {6556, 18025}, {14942, 33963}, {21272, 36638}, {30827, 30833}

X(65966) = X(6557)-Ceva conjugate of X(4373)
X(65966) = X(64083)-cross conjugate of X(144)
X(65966) = X(i)-isoconjugate of X(j) for these (i,j): {1743, 11051}, {3052, 3062}, {4162, 53622}, {4936, 61380}
X(65966) = X(i)-Dao conjugate of X(j) for these (i,j): {7, 5435}, {7658, 4953}, {13609, 3667}, {24151, 3062}, {62575, 10405}
X(65966) = barycentric product X(i)*X(j) for these {i,j}: {144, 4373}, {165, 40014}, {3160, 6557}, {3680, 31627}, {6556, 9533}, {7658, 53647}, {8056, 16284}, {27818, 64083}, {58794, 62533}
X(65966) = barycentric quotient X(i)/X(j) for these {i,j}: {144, 145}, {165, 1743}, {1419, 1420}, {3160, 5435}, {3207, 3052}, {3445, 11051}, {3680, 19605}, {4373, 10405}, {6557, 63165}, {7658, 3667}, {8056, 3062}, {9533, 62787}, {13609, 4953}, {16284, 18743}, {19604, 64980}, {21060, 3950}, {21872, 4849}, {22117, 20818}, {27818, 36620}, {31627, 39126}, {38828, 53622}, {40014, 44186}, {55285, 14321}, {57064, 4546}, {64083, 3161}, {65173, 61240}
X(65966) = {X(3680),X(27818)}-harmonic conjugate of X(4373)

X(65967) = X(8)X(45252)∩X(346)X(19605)

Barycentrics    (a - b - c)*(3*a - b - c)*(a^2 - 2*a*b + b^2 + 2*a*c + 2*b*c - 3*c^2)*(a^2 + 2*a*b - 3*b^2 - 2*a*c + 2*b*c + c^2) : :

X(65967) lies on the cubic K1374 and these lines: {8, 45252}, {346, 19605}, {1997, 36620}, {3062, 56076}, {3161, 53579}, {3239, 9812}, {3912, 6557}, {5274, 63592}, {8055, 20533}, {20942, 33677}

X(65967) = X(10405)-Ceva conjugate of X(63165)
X(65967) = X(i)-cross conjugate of X(j) for these (i,j): {145, 3161}, {63624, 8}
X(65967) = X(i)-isoconjugate of X(j) for these (i,j): {144, 16945}, {165, 40151}, {1419, 3445}, {3160, 38266}, {3207, 19604}
X(65967) = X(i)-Dao conjugate of X(j) for these (i,j): {8, 144}, {3756, 7658}, {45036, 1419}
X(65967) = barycentric product X(i)*X(j) for these {i,j}: {145, 63165}, {3062, 44720}, {3158, 44186}, {3161, 10405}, {4546, 53640}, {6555, 36620}, {11051, 44723}, {18743, 19605}, {44729, 55284}
X(65967) = barycentric quotient X(i)/X(j) for these {i,j}: {145, 3160}, {1420, 17106}, {1743, 1419}, {3062, 19604}, {3158, 165}, {3161, 144}, {4521, 7658}, {5435, 9533}, {6555, 64083}, {10405, 27818}, {11051, 40151}, {18743, 31627}, {19605, 8056}, {39126, 50561}, {43290, 65165}, {44186, 62528}, {44720, 16284}, {44729, 55285}, {52354, 50563}, {63165, 4373}

X(65968) = X(2)X(9311)∩X(8)X(60812)

Barycentrics    (a - b - c)*(a*b - b^2 - 2*a*c + b*c)*(2*a*b - a*c - b*c + c^2)*(a^3 - a^2*b + 2*a*b^2 - a^2*c - a*b*c - b^2*c + 2*a*c^2 - b*c^2) : :

X(65968) lies on the cubic K1374 and these lines: {2, 9311}, {8, 60812}, {346, 65952}, {3008, 30610}, {3501, 9315}, {4876, 40869}, {6553, 60813}, {9309, 17792}, {17284, 32023}, {33677, 36807}, {51845, 56714}

X(65968) = X(3717)-Dao conjugate of X(40883)
X(65968) = barycentric product X(19589)*X(32023)
X(65968) = barycentric quotient X(i)/X(j) for these {i,j}: {19589, 1376}, {19593, 6168}, {27830, 27829}

X(65969) = X(2)X(1280)∩X(8)X(2170)

Barycentrics    (a - b - c)*(a^4 - a^3*b + 2*a^2*b^2 - 3*a*b^3 + b^4 - a^3*c + a^2*b*c - a*b^2*c - b^3*c + 2*a^2*c^2 - a*b*c^2 + 4*b^2*c^2 - 3*a*c^3 - b*c^3 + c^4) : :

X(65969) lies on the cubic K1374 and these lines: {2, 1280}, {8, 2170}, {11, 3974}, {105, 4578}, {120, 6552}, {147, 2789}, {346, 14942}, {350, 52662}, {1447, 4899}, {1916, 65192}, {3021, 4779}, {3263, 33677}, {3679, 5988}, {3705, 4901}, {3717, 40869}, {4042, 7172}, {6084, 20344}, {6556, 18025}, {7081, 24393}, {7774, 39354}, {7840, 39368}, {9451, 52157}, {11814, 28655}, {18743, 26139}, {24524, 30758}, {27510, 27542}, {31085, 31091}, {32850, 40883}, {36221, 65198}, {37665, 40621}, {42720, 52164}

X(65969) = X(3912)-Ceva conjugate of X(346)
X(65969) = X(56)-isoconjugate of X(9452)
X(65969) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 9452}, {6559, 673}
X(65969) = barycentric product X(i)*X(j) for these {i,j}: {8, 52157}, {312, 9451}
X(65969) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 9452}, {9451, 57}, {9453, 1462}, {52157, 7}

X(65970) = X(7)X(190)∩X(8)X(220)

Barycentrics    (a - b - c)*(a^5 - 4*a^4*b + 5*a^3*b^2 - 3*a^2*b^3 + 2*a*b^4 - b^5 - 4*a^4*c + 3*a^3*b*c - a*b^3*c + 2*b^4*c + 5*a^3*c^2 - 2*a*b^2*c^2 - b^3*c^2 - 3*a^2*c^3 - a*b*c^3 - b^2*c^3 + 2*a*c^4 + 2*b*c^4 - c^5) : :

X(65970) lies on the cubic K1374 and these lines: {7, 190}, {8, 220}, {346, 14943}, {1281, 3501}, {3717, 52507}, {3912, 10025}, {4919, 41006}, {6068, 31722}, {8834, 10699}, {17464, 17794}, {24771, 29641}, {27129, 30625}, {28058, 40869}, {29839, 64579}, {44351, 65195}, {52084, 52164}

X(65970) = X(i)-Ceva conjugate of X(j) for these (i,j): {3912, 8}, {10025, 65953}
X(65970) = X(14942)-Dao conjugate of X(673)
X(65970) = crosssum of X(649) and X(61056)
X(65970) = barycentric product X(i)*X(j) for these {i,j}: {8, 52164}, {312, 52084}
X(65970) = barycentric quotient X(i)/X(j) for these {i,j}: {52084, 57}, {52164, 7}, {56721, 43760}

X(65971) = X(2)X(3119)∩X(7)X(14942)

Barycentrics    (a + b - c)*(a - b + c)*(a^6 - 3*a^5*b + 5*a^4*b^2 - 6*a^3*b^3 + 3*a^2*b^4 + a*b^5 - b^6 - 3*a^5*c + 7*a^4*b*c - 4*a^3*b^2*c - a*b^4*c + b^5*c + 5*a^4*c^2 - 4*a^3*b*c^2 + 2*a^2*b^2*c^2 - 3*b^4*c^2 - 6*a^3*c^3 + 6*b^3*c^3 + 3*a^2*c^4 - a*b*c^4 - 3*b^2*c^4 + a*c^5 + b*c^5 - c^6) : :

X(65971) lies on the cubic K1374 and these lines: {2, 3119}, {7, 14942}, {8, 348}, {279, 28850}, {350, 40704}, {1146, 31994}, {1818, 57768}, {1997, 36620}, {4876, 43750}, {5853, 9436}, {9312, 26531}, {10186, 62705}, {24014, 45276}, {28739, 56310}, {31527, 57477}, {38053, 62674}, {41353, 58035}, {56933, 62669}

X(65971) = reflection of X(i) in X(j) for these {i,j}: {25718, 664}, {39351, 63592}
X(65971) = X(3912)-Ceva conjugate of X(7)
X(65971) = X(56783)-Dao conjugate of X(673)
X(65971) = barycentric product X(40704)*X(56720)
X(65971) = barycentric quotient X(56720)/X(294)
X(65971) = {X(664),X(52156)}-harmonic conjugate of X(50441)

X(65972) = X(2)X(44817)∩X(20)X(62433)

Barycentrics    b^2*(b - c)*c^2*(b + c)*(a^4*b^2 - 2*a^2*b^4 + b^6 + a^4*c^2 + 2*a^2*b^2*c^2 - b^4*c^2 - 2*a^2*c^4 - b^2*c^4 + c^6) : :

X(65972) lies on the cubic K1375 and these lines: {2, 44817}, {20, 62433}, {22, 804}, {69, 40048}, {94, 2394}, {98, 2373}, {99, 925}, {325, 523}, {339, 868}, {525, 62377}, {686, 3580}, {1370, 53365}, {1494, 65267}, {1637, 18312}, {1995, 47206}, {2780, 44440}, {2974, 34336}, {3448, 9517}, {5133, 17994}, {6334, 47236}, {7493, 9147}, {12827, 55121}, {14389, 14397}, {16386, 61776}, {18019, 62645}, {30744, 45689}, {34767, 51967}, {41512, 61188}, {45807, 65710}, {65753, 65756}

X(65972) = reflection of X(41079) in X(14592)
X(65972) = isotomic conjugate of X(10420)
X(65972) = anticomplement of X(47230)
X(65972) = polar conjugate of X(32708)
X(65972) = anticomplement of the isogonal conjugate of X(60053)
X(65972) = isotomic conjugate of the anticomplement of X(16221)
X(65972) = isotomic conjugate of the isogonal conjugate of X(55121)
X(65972) = polar conjugate of the isogonal conjugate of X(6334)
X(65972) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {63, 14731}, {265, 21221}, {328, 21294}, {476, 5905}, {662, 12383}, {4575, 18301}, {4592, 1272}, {14560, 21216}, {32662, 192}, {32678, 193}, {32680, 4}, {35139, 21270}, {36061, 2}, {36096, 54395}, {36129, 6515}, {39295, 7253}, {46456, 5906}, {52153, 21220}, {60053, 8}, {65251, 39118}, {65262, 15454}
X(65972) = X(i)-Ceva conjugate of X(j) for these (i,j): {1494, 339}, {20573, 338}
X(65972) = X(16221)-cross conjugate of X(2)
X(65972) = X(i)-isoconjugate of X(j) for these (i,j): {31, 10420}, {32, 65262}, {48, 32708}, {163, 14910}, {184, 36114}, {560, 18878}, {687, 9247}, {798, 18879}, {1576, 36053}, {1973, 43755}, {5504, 32676}, {15328, 23995}, {32678, 52557}
X(65972) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 10420}, {113, 1576}, {115, 14910}, {338, 60035}, {647, 61216}, {1249, 32708}, {2088, 50}, {3003, 2420}, {3580, 52603}, {4858, 36053}, {5664, 15470}, {6334, 526}, {6337, 43755}, {6374, 18878}, {6376, 65262}, {15526, 5504}, {16178, 25}, {18314, 15328}, {18334, 52557}, {23285, 15421}, {31998, 18879}, {34834, 110}, {35588, 52435}, {36901, 2986}, {39005, 184}, {39021, 6}, {55121, 21731}, {55267, 65762}, {56399, 32662}, {56792, 40352}, {62551, 39371}, {62576, 687}, {62598, 15454}, {62605, 36114}, {65732, 51456}, {65753, 30}, {65905, 32661}
X(65972) = cevapoint of X(6334) and X(55121)
X(65972) = crosspoint of X(264) and X(35139)
X(65972) = crosssum of X(184) and X(14270)
X(65972) = barycentric product X(i)*X(j) for these {i,j}: {76, 55121}, {264, 6334}, {305, 47236}, {338, 61188}, {339, 16237}, {403, 3267}, {525, 44138}, {686, 18022}, {850, 3580}, {1494, 65757}, {1502, 21731}, {1725, 20948}, {3003, 44173}, {3260, 65614}, {3268, 57486}, {5392, 65473}, {6563, 52504}, {14618, 62338}, {15329, 23962}, {20573, 60342}, {41079, 65715}
X(65972) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 10420}, {4, 32708}, {69, 43755}, {75, 65262}, {76, 18878}, {92, 36114}, {99, 18879}, {113, 2420}, {125, 61216}, {264, 687}, {338, 15328}, {339, 15421}, {403, 112}, {523, 14910}, {525, 5504}, {526, 52557}, {686, 184}, {850, 2986}, {868, 65762}, {1577, 36053}, {1725, 163}, {1986, 14591}, {2394, 10419}, {3003, 1576}, {3267, 57829}, {3580, 110}, {5664, 39371}, {6334, 3}, {6563, 52505}, {12827, 61198}, {12828, 61207}, {13754, 32661}, {14264, 32640}, {14592, 12028}, {14618, 1300}, {15329, 23357}, {16221, 47230}, {16237, 250}, {18022, 57932}, {18312, 51456}, {18314, 60035}, {18808, 40388}, {21731, 32}, {24978, 58924}, {34834, 52603}, {39021, 21731}, {39170, 32662}, {41079, 15454}, {44084, 61206}, {44138, 648}, {44173, 40832}, {44427, 38936}, {47236, 25}, {52000, 61208}, {52451, 2715}, {52487, 58959}, {52504, 925}, {55121, 6}, {55265, 1495}, {56403, 14560}, {57486, 476}, {58261, 65615}, {60342, 50}, {60498, 32729}, {61188, 249}, {61209, 57655}, {62338, 4558}, {62361, 32734}, {62551, 15470}, {63735, 1625}, {65473, 1993}, {65614, 74}, {65715, 44769}, {65757, 30}, {65780, 65776}
X(65972) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {850, 3267, 30474}, {22339, 22340, 6563}

X(65973) = X(2)X(525)∩X(30)X(3268)

Barycentrics    (b - c)*(b + c)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4) : :
X(65973) = 3 X[297] - 2 X[58351], 2 X[1637] - 3 X[44576]

X(65973) lies on the cubic K1375 and these lines: {2, 525}, {30, 3268}, {74, 2857}, {99, 1304}, {297, 2799}, {325, 6333}, {339, 850}, {523, 1494}, {868, 34765}, {1637, 44576}, {2419, 47105}, {6563, 13219}, {9155, 47263}, {9979, 44216}, {14380, 54124}, {14417, 40884}, {16080, 52459}, {18022, 44173}, {18311, 58875}, {18808, 55972}, {35088, 62629}, {35908, 52486}, {36875, 62642}, {46751, 64690}, {53383, 65771}

X(65973) = reflection of X(i) in X(j) for these {i,j}: {9979, 44216}, {40884, 14417}, {62629, 35088}
X(65973) = isotomic conjugate of X(65776)
X(65973) = anticomplement of X(65782)
X(65973) = antitomic image of X(62629)
X(65973) = isotomic conjugate of the isogonal conjugate of X(32112)
X(65973) = X(36034)-anticomplementary conjugate of X(65774)
X(65973) = X(65754)-cross conjugate of X(2799)
X(65973) = X(i)-isoconjugate of X(j) for these (i,j): {31, 65776}, {163, 35906}, {248, 56829}, {293, 23347}, {1495, 36084}, {1910, 2420}, {2159, 65777}, {2173, 2715}, {2966, 9406}, {3284, 36104}, {9407, 36036}, {14600, 24001}, {32676, 35912}
X(65973) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 65776}, {115, 35906}, {132, 23347}, {868, 51431}, {2679, 9407}, {2799, 65754}, {3163, 65777}, {5664, 65779}, {5976, 2407}, {9410, 2966}, {11672, 2420}, {15526, 35912}, {23285, 65778}, {35088, 30}, {36896, 2715}, {36901, 60869}, {38970, 1990}, {38987, 1495}, {39000, 3284}, {39039, 56829}, {41167, 9409}, {55267, 1637}, {61505, 51937}, {62595, 4240}, {62606, 43754}, {65760, 3233}, {65763, 58346}
X(65973) = cevapoint of X(2799) and X(65754)
X(65973) = trilinear pole of line {2799, 65756}
X(65973) = barycentric product X(i)*X(j) for these {i,j}: {76, 32112}, {99, 65756}, {297, 34767}, {325, 2394}, {850, 35910}, {1494, 2799}, {2396, 12079}, {3267, 35908}, {6333, 16080}, {6393, 18808}, {14380, 44132}, {31621, 65754}, {34765, 51227}, {36890, 62629}, {44769, 62431}
X(65973) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 65776}, {30, 65777}, {74, 2715}, {232, 23347}, {240, 56829}, {297, 4240}, {325, 2407}, {339, 65778}, {511, 2420}, {523, 35906}, {525, 35912}, {684, 3284}, {850, 60869}, {868, 1637}, {1494, 2966}, {2349, 36084}, {2394, 98}, {2433, 1976}, {2491, 9407}, {2799, 30}, {3569, 1495}, {6333, 11064}, {8749, 32696}, {12079, 2395}, {14223, 53866}, {14356, 41392}, {14380, 248}, {14919, 43754}, {16077, 60179}, {16080, 685}, {16230, 1990}, {17994, 14581}, {18808, 6531}, {23350, 48453}, {32112, 6}, {33752, 52951}, {33805, 36036}, {34765, 51228}, {34767, 287}, {35088, 65754}, {35908, 112}, {35910, 110}, {36119, 36104}, {36875, 60504}, {40703, 24001}, {41172, 9409}, {42703, 42716}, {44114, 14398}, {44769, 57742}, {46787, 51263}, {51227, 34761}, {51389, 3233}, {55267, 51431}, {56792, 60777}, {58351, 3081}, {62431, 41079}, {62551, 65779}, {62555, 51389}, {62629, 9214}, {62645, 65781}, {62665, 17974}, {63856, 60506}, {65614, 52451}, {65754, 3163}, {65755, 58346}, {65756, 523}
X(65973) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34767, 52766, 62363}, {34767, 65710, 36890}

X(65974) = X(98)X(1494)∩X(325)X(877)

Barycentrics    (b - c)^2*(b + c)^2*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)^2 : :

X(65974) lies on the cubic K1375 and these lines: {30, 36890}, {74, 65648}, {98, 1494}, {325, 877}, {524, 65777}, {868, 34765}, {1650, 3268}, {2394, 43673}, {2799, 65756}, {3081, 9141}, {12079, 34767}

X(65974) = X(9406)-isoconjugate of X(57562)
X(65974) = X(i)-Dao conjugate of X(j) for these (i,j): {2799, 30}, {9410, 57562}, {35088, 65776}, {41172, 2420}, {55267, 35906}
X(65974) = barycentric product X(i)*X(j) for these {i,j}: {325, 65756}, {1494, 35088}, {2394, 62555}, {12079, 32458}, {35910, 62431}
X(65974) = barycentric quotient X(i)/X(j) for these {i,j}: {868, 35906}, {1494, 57562}, {2394, 41173}, {2799, 65776}, {12079, 41932}, {32112, 2715}, {35088, 30}, {35910, 57742}, {41167, 2420}, {46052, 65754}, {59805, 1495}, {62431, 60869}, {62555, 2407}, {65754, 65777}, {65756, 98}

X(65975) = X(2)X(60511)∩X(3)X(76)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^8 - 2*a^6*b^2 + a^4*b^4 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 - 4*b^4*c^4 + 2*b^2*c^6) : :

X(65975) lies on the cubic K1375 and these lines: {2, 60511}, {3, 76}, {30, 61188}, {69, 523}, {325, 868}, {538, 2088}, {599, 36790}, {2493, 7778}, {3260, 23342}, {3734, 32761}, {5641, 7788}, {14999, 35906}, {32836, 36890}, {35910, 51389}, {37637, 47406}, {46777, 51481}, {53793, 64687}, {62338, 62551}

X(65975) = isotomic conjugate of the isogonal conjugate of X(47049)
X(65975) = X(1494)-Ceva conjugate of X(325)
X(65975) = X(i)-Dao conjugate of X(j) for these (i,j): {34810, 51820}, {51389, 30}, {55267, 65764}
X(65975) = crossdifference of every pair of points on line {1692, 2491}
X(65975) = barycentric product X(i)*X(j) for these {i,j}: {76, 47049}, {325, 65767}, {1494, 65760}, {2396, 53266}
X(65975) = barycentric quotient X(i)/X(j) for these {i,j}: {868, 65764}, {34810, 35906}, {47049, 6}, {53266, 2395}, {55071, 2088}, {65760, 30}, {65767, 98}
X(65975) = {X(69),X(36891)}-harmonic conjugate of X(65771)

X(65976) = X(2)X(60509)∩X(30)X(6334)

Barycentrics    (b - c)*(b + c)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(-a^4 - a^2*b^2 + 2*b^4 + 2*a^2*c^2 - b^2*c^2 - c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(65976) = 3 X[868] - 2 X[65763], 3 X[16230] - 4 X[65763], 3 X[53161] - X[65775]

X(65976) lies on the cubic K1375 and these lines: {2, 60509}, {30, 6334}, {74, 98}, {325, 6333}, {868, 16230}, {1494, 18808}, {9033, 62639}, {9134, 12079}, {9717, 45687}, {10749, 13556}, {34174, 36875}, {38749, 65723}, {55121, 62551}

X(65976) = reflection of X(16230) in X(868)
X(65976) = X(i)-Ceva conjugate of X(j) for these (i,j): {1494, 65756}, {18808, 32112}
X(65976) = X(i)-isoconjugate of X(j) for these (i,j): {163, 65781}, {9406, 55266}, {36051, 65776}
X(65976) = X(i)-Dao conjugate of X(j) for these (i,j): {114, 65776}, {115, 65781}, {230, 2407}, {868, 30}, {9410, 55266}, {35088, 36891}, {55152, 35906}, {55267, 65758}
X(65976) = trilinear pole of line {41181, 55267}
X(65976) = barycentric product X(i)*X(j) for these {i,j}: {114, 2394}, {1494, 55267}, {2799, 36875}, {4226, 65756}, {16077, 41181}, {18808, 62590}, {32112, 51481}
X(65976) = barycentric quotient X(i)/X(j) for these {i,j}: {114, 2407}, {230, 65776}, {523, 65781}, {868, 65758}, {1494, 55266}, {2394, 40428}, {2433, 2065}, {2799, 36891}, {32112, 2987}, {35908, 32697}, {35910, 10425}, {36875, 2966}, {41181, 9033}, {51335, 2420}, {51431, 65777}, {55122, 35906}, {55267, 30}, {65756, 62645}

X(65977) = X(2)X(2501)∩X(30)X(44427)

Barycentrics    (b - c)*(b + c)*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)*(a^8 - a^6*b^2 + a^4*b^4 - 3*a^2*b^6 + 2*b^8 - a^6*c^2 - a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 5*b^6*c^2 + a^4*c^4 + 3*a^2*b^2*c^4 + 6*b^4*c^4 - 3*a^2*c^6 - 5*b^2*c^6 + 2*c^8) : :
X(65977) = 3 X[2] - 4 X[65758], 2 X[6334] - 3 X[33228]

X(65977) lies on the cubic K1375 and these lines: {2, 2501}, {30, 44427}, {98, 523}, {112, 57065}, {148, 525}, {325, 2799}, {339, 14618}, {1499, 53016}, {1513, 16230}, {1550, 52472}, {2489, 38652}, {2967, 36170}, {3566, 10722}, {6334, 33228}, {12384, 36173}, {23870, 33518}, {23871, 33517}, {47236, 51358}, {50719, 54029}, {50720, 54028}, {59805, 65608}, {65755, 65756}

X(65977) = reflection of X(i) in X(j) for these {i,j}: {1513, 16230}, {65772, 65758}
X(65977) = anticomplement of X(65772)
X(65977) = X(i)-Ceva conjugate of X(j) for these (i,j): {687, 297}, {1494, 868}
X(65977) = X(163)-isoconjugate of X(65783)
X(65977) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 65783}, {55267, 65766}, {65755, 30}
X(65977) = barycentric product X(i)*X(j) for these {i,j}: {868, 65768}, {1494, 65763}, {1550, 34765}
X(65977) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 65783}, {868, 65766}, {1550, 34761}, {52472, 65776}, {65763, 30}, {65768, 57991}
{X(65758),X(65772)}-harmonic conjugate of X(2)

X(65978) = X(2)X(98)∩X(30)X(65774)

Barycentrics    (b - c)^2*(b + c)^2*(-(a^2*b^2) + b^4 - a^2*c^2 + c^4)*(3*a^8 - 5*a^6*b^2 + 3*a^4*b^4 - 3*a^2*b^6 + 2*b^8 - 5*a^6*c^2 + 5*a^4*b^2*c^2 + a^2*b^4*c^2 - b^6*c^2 + 3*a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 - b^2*c^6 + 2*c^8) : :

X(65978) lies on the cubic K1375 and these lines: {2, 98}, {30, 65774}, {115, 46416}, {523, 15526}, {868, 2799}, {1494, 9214}, {2972, 40470}, {9033, 62551}, {14356, 35908}, {14995, 64923}, {36471, 53832}, {65754, 65756}

X(65978) = midpoint of X(1494) and X(9214)
X(65978) = complement of X(65776)
X(65978) = complement of the isogonal conjugate of X(32112)
X(65978) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 65782}, {240, 57128}, {1755, 5664}, {2159, 2799}, {2349, 24284}, {2433, 16609}, {5360, 57046}, {23997, 31945}, {32112, 10}, {35908, 8062}, {35910, 4369}, {36119, 6130}, {57653, 14401}, {65756, 21253}
X(65978) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 65782}, {1494, 2799}
X(65978) = X(i)-Dao conjugate of X(j) for these (i,j): {55267, 65765}, {65754, 30}, {65782, 2}
X(65978) = barycentric product X(2799)*X(53383)
X(65978) = barycentric quotient X(i)/X(j) for these {i,j}: {868, 65765}, {53383, 2966}, {65782, 65776}

X(65979) = X(2)X(41392)∩X(30)X(74)

Barycentrics    (a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4) : :

X(65979) lies on the cubic K1375 and these lines: {2, 41392}, {30, 74}, {94, 2394}, {339, 57486}, {1494, 1989}, {14356, 35908}, {14919, 18883}, {16080, 39295}, {17986, 53768}, {30529, 62730}, {35910, 51389}, {56395, 60870}, {56399, 64923}, {57482, 60502}

X(65979) = X(i)-isoconjugate of X(j) for these (i,j): {163, 65779}, {248, 35201}, {293, 39176}, {1511, 1910}, {2173, 14355}, {2624, 65776}, {6149, 35906}, {36084, 52743}
X(65979) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 65779}, {132, 39176}, {5976, 6148}, {11672, 1511}, {14993, 35906}, {35088, 5664}, {36896, 14355}, {38970, 62172}, {38987, 52743}, {39039, 35201}, {41167, 47414}, {55267, 3258}, {62595, 14920}
X(65979) = cevapoint of X(2799) and X(65756)
X(65979) = trilinear pole of line {14356, 32112}
X(65979) = barycentric product X(i)*X(j) for these {i,j}: {94, 35910}, {325, 5627}, {328, 35908}, {1494, 14356}, {2799, 39290}, {11079, 44132}, {15395, 62431}, {32112, 35139}, {39295, 65756}
X(65979) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 14355}, {94, 60869}, {232, 39176}, {240, 35201}, {265, 35912}, {297, 14920}, {325, 6148}, {476, 65776}, {511, 1511}, {523, 65779}, {868, 3258}, {1989, 35906}, {2433, 60777}, {2799, 5664}, {3569, 52743}, {5627, 98}, {11079, 248}, {14356, 30}, {14592, 65778}, {15395, 57742}, {16230, 62172}, {32112, 526}, {34370, 48453}, {35908, 186}, {35910, 323}, {39290, 2966}, {40355, 1976}, {41172, 47414}, {41392, 65777}, {50464, 17974}, {54554, 53866}, {57486, 65780}, {65756, 62551}

X(65980) = X(2)X(35907)∩X(98)X(468)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :

X(65980) lies on the cubic K1375 and these lines: {2, 35907}, {98, 468}, {232, 65756}, {297, 2799}, {523, 50188}, {868, 6530}, {1494, 6330}, {1503, 2409}, {1637, 51358}, {1990, 62551}, {2394, 5523}, {4235, 65774}, {14919, 34129}, {34138, 35910}, {36875, 41204}, {41676, 65719}, {54074, 62665}, {60527, 62376}

X(65980) = X(i)-Ceva conjugate of X(j) for these (i,j): {1494, 35908}, {16080, 63856}
X(65980) = X(i)-isoconjugate of X(j) for these (i,j): {293, 51937}, {2173, 15407}, {9406, 57761}
X(65980) = X(i)-Dao conjugate of X(j) for these (i,j): {132, 51937}, {232, 30}, {441, 11064}, {9410, 57761}, {23976, 35912}, {36896, 15407}, {39073, 3284}, {50938, 35906}, {55267, 65759}
X(65980) = barycentric product X(i)*X(j) for these {i,j}: {132, 1494}, {297, 63856}, {15595, 16080}, {17875, 36119}, {30737, 35908}, {35910, 60516}
X(65980) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 15407}, {132, 30}, {232, 51937}, {868, 65759}, {1494, 57761}, {1503, 35912}, {2409, 65776}, {6530, 52485}, {9475, 3284}, {15595, 11064}, {16080, 9476}, {16318, 35906}, {32112, 2435}, {35908, 1297}, {35910, 64975}, {55275, 1637}, {60516, 60869}, {63856, 287}

X(65981) = X(2)X(60503)∩X(30)X(935)

Barycentrics    (a^4 - a^2*b^2 + b^4 - c^4)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^4 - b^4 - a^2*c^2 + c^4)*(a^8 - a^6*b^2 + a^4*b^4 + a^2*b^6 - 2*b^8 - a^6*c^2 - a^4*b^2*c^2 - a^2*b^4*c^2 + 3*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6 + 3*b^2*c^6 - 2*c^8) : :

X(65981) lies on the cubic K1375 and these lines: {2, 60503}, {30, 935}, {67, 98}, {132, 35908}, {325, 36884}, {339, 39269}, {2794, 14357}, {10415, 12079}, {10766, 34366}, {17708, 30789}, {18019, 62645}, {57799, 65269}

X(65982) = X(2)X(60504)∩X(98)X(868)

Barycentrics    (a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(2*a^12 - 5*a^10*b^2 + 6*a^8*b^4 - 6*a^6*b^6 + 2*a^4*b^8 + 3*a^2*b^10 - 2*b^12 - 5*a^10*c^2 + 6*a^8*b^2*c^2 - a^6*b^4*c^2 - a^4*b^6*c^2 - 2*a^2*b^8*c^2 + 3*b^10*c^2 + 6*a^8*c^4 - a^6*b^2*c^4 + 2*a^4*b^4*c^4 - a^2*b^6*c^4 - 6*b^8*c^4 - 6*a^6*c^6 - a^4*b^2*c^6 - a^2*b^4*c^6 + 10*b^6*c^6 + 2*a^4*c^8 - 2*a^2*b^2*c^8 - 6*b^4*c^8 + 3*a^2*c^10 + 3*b^2*c^10 - 2*c^12) : :

X(65982) lies on the cubic K1375 and these lines: {2, 60504}, {98, 868}, {287, 2395}, {325, 441}, {339, 57490}, {2794, 60506}, {5967, 51431}, {10722, 40820}, {35906, 63856}, {41145, 51963}

X(65982) = X(1494)-Ceva conjugate of X(98)
X(65982) = X(35906)-Dao conjugate of X(30)
X(65982) = barycentric product X(98)*X(65771)
X(65982) = barycentric quotient X(65771)/X(325)
X(65982) = {X(287),X(65781)}-harmonic conjugate of X(65767)

X(65983) = (name pending)

Barycentrics    (2 a^12 - 8 a^10 b^2 + 14 a^8 b^4 - 16 a^6 b^6 + 14 a^4 b^8 - 8 a^2 b^10 + 2 b^12 - 6 a^10 c^2 + 13 a^8 b^2 c^2 - 7 a^6 b^4 c^2 - 7 a^4 b^6 c^2 + 13 a^2 b^8 c^2 - 6 b^10 c^2 + 4 a^8 c^4 - 9 a^6 b^2 c^4 - 5 a^4 b^4 c^4 - 9 a^2 b^6 c^4 + 4 b^8 c^4 + 4 a^6 c^6 + 13 a^4 b^2 c^6 + 13 a^2 b^4 c^6 + 4 b^6 c^6 - 6 a^4 c^8 - 11 a^2 b^2 c^8 - 6 b^4 c^8 + 2 a^2 c^10 + 2 b^2 c^10) (2 a^12 - 6 a^10 b^2 + 4 a^8 b^4 + 4 a^6 b^6 - 6 a^4 b^8 + 2 a^2 b^10 - 8 a^10 c^2 + 13 a^8 b^2 c^2 - 9 a^6 b^4 c^2 + 13 a^4 b^6 c^2 - 11 a^2 b^8 c^2 + 2 b^10 c^2 + 14 a^8 c^4 - 7 a^6 b^2 c^4 - 5 a^4 b^4 c^4 + 13 a^2 b^6 c^4 - 6 b^8 c^4 - 16 a^6 c^6 - 7 a^4 b^2 c^6 - 9 a^2 b^4 c^6 + 4 b^6 c^6 + 14 a^4 c^8 + 13 a^2 b^2 c^8 + 4 b^4 c^8 - 8 a^2 c^10 - 6 b^2 c^10 + 2 c^12) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 7145.

X(65983) lies on this line: {14683, 37943}

X(65983) = isogonal conjugate X(65984)

X(65984) = X(6)X(3200)∩X(232)X(11063)

Barycentrics    a^2 (2 a^10 b^2 - 6 a^8 b^4 + 4 a^6 b^6 + 4 a^4 b^8 - 6 a^2 b^10 + 2 b^12 + 2 a^10 c^2 - 11 a^8 b^2 c^2 + 13 a^6 b^4 c^2 - 9 a^4 b^6 c^2 + 13 a^2 b^8 c^2 - 8 b^10 c^2 - 6 a^8 c^4 + 13 a^6 b^2 c^4 - 5 a^4 b^4 c^4 - 7 a^2 b^6 c^4 + 14 b^8 c^4 + 4 a^6 c^6 - 9 a^4 b^2 c^6 - 7 a^2 b^4 c^6 - 16 b^6 c^6 + 4 a^4 c^8 + 13 a^2 b^2 c^8 + 14 b^4 c^8 - 6 a^2 c^10 - 8 b^2 c^10 + 2 c^12) : :

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 7145.

X(65984) lies on these lines: {6, 3200}, {232, 11063}, {2493, 15302}, {3018, 7749}, {8745, 36423}, {8791, 52154}

X(65984) = isogonal conjugate X(65983)



leftri

Points releated to the extouch-of-Fuhrmann triangle: X(65985)-X(66071)

rightri

This preamble and centers X(65985)-X(66071) were contributed by Ivan Pavlov on October 30, 2024.

For more information and constructions of the extouch-of-Fuhrmann triangle see this Euclid thread.

X(65985) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND ANTI-URSA MINOR

Barycentrics    a^5*(b^2+c^2)+a^3*b*c*(b^2+c^2)-(b-c)^2*(b+c)^3*(b^2+c^2)-a*(b^2-c^2)^2*(b^2+b*c+c^2)+a^4*(b^3+b^2*c+b*c^2+c^3) : :

X(65985) lies on these lines: {2, 3}, {11, 33178}, {12, 63319}, {81, 43712}, {115, 16716}, {125, 18180}, {339, 16747}, {495, 30142}, {496, 23304}, {946, 2778}, {1717, 7741}, {1853, 5707}, {3444, 53421}, {3574, 34462}, {3695, 19839}, {3739, 25639}, {5090, 37729}, {5130, 32047}, {10593, 17070}, {13605, 47319}, {21243, 37536}, {21260, 65492}, {24470, 26933}, {44316, 59750}

X(65985) = inverse of X(44898) in nine-point circle
X(65985) = inverse of X(44898) in MacBeath inconic
X(65985) = complement of X(2915)
X(65985) = X(i)-Ceva conjugate of X(j) for these {i, j}: {59075, 523}
X(65985) = X(i)-complementary conjugate of X(j) for these {i, j}: {43712, 10}
X(65985) = pole of line {523, 8043} with respect to the nine-point circle
X(65985) = pole of line {6, 3444} with respect to the Kiepert hyperbola
X(65985) = pole of line {523, 8043} with respect to the MacBeath inconic
X(65985) = intersection, other than A, B, C, of circumconics {{A, B, C, X(451), X(43712)}}, {{A, B, C, X(2915), X(57695)}}, {{A, B, C, X(3613), X(52252)}}, {{A, B, C, X(37305), X(61133)}}

X(65986) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND ANTI-INNER-YFF

Barycentrics    (a+b-c)*(a-b+c)*(a^7+a^5*b*c-2*a^6*(b+c)-5*a^2*b*(b-c)^2*c*(b+c)+(b-c)^4*(b+c)^3-2*a*(b^2-c^2)^2*(b^2-b*c+c^2)+a^4*(b^3+c^3)+a^3*(b^4+5*b^3*c+5*b*c^3+c^4)) : :

X(65986) lies on these lines: {1, 5812}, {56, 64345}, {57, 2886}, {65, 49176}, {497, 60895}, {946, 48694}, {1836, 30304}, {2078, 13405}, {3254, 61021}, {3337, 65994}, {3485, 51111}, {4295, 5768}, {4298, 11263}, {5082, 12432}, {7702, 45632}, {10165, 37583}, {17637, 49177}, {24470, 65987}, {26437, 61716}, {34789, 66020}, {37625, 45634}, {49170, 64119}, {66015, 66046}

X(65987) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND ANTI-OUTER-YFF

Barycentrics    (a+b-c)*(a-b+c)*(a^8-a^7*(b+c)+a^6*(-2*b^2+5*b*c-2*c^2)+(b^2-c^2)^4-a*(b-c)^2*(b+c)^3*(b^2-4*b*c+c^2)-a^2*(b^2-c^2)^2*(2*b^2-b*c+2*c^2)+a^5*(b^3+b^2*c+b*c^2+c^3)+2*a^4*(b^4-3*b^3*c-3*b*c^3+c^4)+a^3*(b^5-3*b^4*c+6*b^3*c^2+6*b^2*c^3-3*b*c^4+c^5)) : :

X(65987) lies on these lines: {1, 11826}, {57, 7681}, {65, 12751}, {79, 24465}, {388, 49169}, {946, 48695}, {1210, 46435}, {3337, 65995}, {5553, 61114}, {5880, 60937}, {5884, 6256}, {7702, 9612}, {9581, 12676}, {11023, 26333}, {11263, 12436}, {11509, 64345}, {12761, 65998}, {17637, 18838}, {24470, 65986}, {64155, 66020}

X(65988) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND AQUILA

Barycentrics    3*a^4+5*a^3*(b+c)-5*a*(b-c)^2*(b+c)-2*(b^2-c^2)^2-a^2*(b^2-5*b*c+c^2) : :
X(65988) = -5*X[1698]+4*X[51573]

X(65988) lies on these lines: {1, 550}, {2, 191}, {7, 11010}, {46, 64345}, {65, 9897}, {79, 546}, {382, 5902}, {484, 3982}, {946, 1768}, {1698, 51573}, {2306, 42779}, {3244, 6224}, {3338, 16767}, {3339, 7702}, {3474, 63255}, {3530, 3649}, {3585, 30424}, {3626, 5270}, {3632, 3868}, {3671, 37616}, {3820, 34501}, {3833, 63285}, {3851, 5221}, {4298, 64896}, {4317, 20057}, {4338, 5586}, {5010, 57283}, {5079, 61716}, {5223, 5852}, {5248, 5303}, {5441, 62151}, {5442, 61853}, {5535, 49107}, {5563, 65991}, {5691, 5884}, {5883, 64289}, {5885, 16150}, {6154, 66006}, {6906, 37587}, {7992, 64119}, {8727, 13865}, {10543, 62141}, {11531, 28458}, {11544, 35018}, {11551, 12512}, {14869, 37701}, {15687, 37702}, {15688, 37571}, {15720, 37524}, {16137, 62087}, {18221, 49135}, {18398, 48661}, {18990, 64766}, {24465, 45764}, {28198, 36946}, {31423, 38114}, {31870, 66048}, {32635, 43732}, {33102, 63310}, {33654, 42780}

X(65988) = reflection of X(i) in X(j) for these {i,j}: {1, 5557}, {5506, 9782}, {5557, 34502}
X(65988) = X(5557) of Aquila triangle
X(65988) = pole of line {4977, 8043} with respect to the Suppa-Cucoanes circle
X(65988) = pole of line {3982, 17011} with respect to the dual conic of Yff parabola
X(65988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5557, 28174, 1}, {28174, 34502, 5557}

X(65989) = TRIPOLE OF PERSPECTIVITY AXIS OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND FUHRMANN

Barycentrics    (a^3+3*b^3-b^2*c-3*b*c^2+c^3+a^2*(-3*b+c)+a*(-b^2+b*c+c^2))*(a^3+b^3+a^2*(b-3*c)-3*b^2*c-b*c^2+3*c^3+a*(b^2+b*c-c^2)) : :

X(65989) lies on these lines: {149, 519}, {1016, 30578}, {1086, 8046}, {3911, 37771}, {4080, 6630}, {4358, 18151}, {4440, 16704}, {5226, 14628}, {17484, 62231}, {21454, 40218}, {37635, 60692}

X(65989) = trilinear pole of line {12019, 21180}
X(65989) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 15015}
X(65989) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 15015}
X(65989) = X(i)-cross conjugate of X(j) for these {i, j}: {14028, 903}, {16173, 7}
X(65989) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(514)}}, {{A, B, C, X(27), X(54794)}}, {{A, B, C, X(57), X(64896)}}, {{A, B, C, X(88), X(12653)}}, {{A, B, C, X(89), X(44559)}}, {{A, B, C, X(92), X(1029)}}, {{A, B, C, X(149), X(673)}}, {{A, B, C, X(278), X(3583)}}, {{A, B, C, X(908), X(4801)}}, {{A, B, C, X(1086), X(30578)}}, {{A, B, C, X(2006), X(9897)}}, {{A, B, C, X(2226), X(58794)}}, {{A, B, C, X(3218), X(5226)}}, {{A, B, C, X(4080), X(4440)}}, {{A, B, C, X(4564), X(27789)}}, {{A, B, C, X(4608), X(8047)}}, {{A, B, C, X(4654), X(17484)}}, {{A, B, C, X(4671), X(4956)}}, {{A, B, C, X(26142), X(27070)}}, {{A, B, C, X(26749), X(36588)}}, {{A, B, C, X(37635), X(40882)}}, {{A, B, C, X(39705), X(46275)}}

X(65990) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND HEXYL

Barycentrics    a*(a^9+9*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)+a^3*(b^2-c^2)^2*(8*b^2-13*b*c+8*c^2)-2*a^2*b*(b-c)^2*c*(b^3-7*b^2*c-7*b*c^2+c^3)+a^6*(8*b^3-6*b^2*c-6*b*c^2+8*c^3)-a*(b^2-c^2)^2*(3*b^4-11*b^3*c+8*b^2*c^2-11*b*c^3+3*c^4)-a^5*(6*b^4+7*b^3*c-10*b^2*c^2+7*b*c^3+6*c^4)-2*a^4*(3*b^5-8*b^4*c+7*b^3*c^2+7*b^2*c^3-8*b*c^4+3*c^5)) : :
X(65990) = -5*X[8227]+4*X[31936]

X(65990) lies on these lines: {1, 5787}, {4, 11263}, {40, 993}, {65, 1768}, {84, 5884}, {550, 30503}, {952, 66006}, {1012, 37625}, {1490, 65949}, {3244, 6264}, {3333, 64334}, {3872, 12842}, {5538, 21677}, {5691, 64345}, {5732, 5880}, {5855, 12629}, {6326, 6831}, {7411, 19860}, {7508, 10268}, {7702, 9579}, {8227, 31936}, {9856, 44840}, {12672, 66009}, {12705, 45632}, {15071, 17637}, {18406, 41540}, {21669, 47319}, {37434, 64324}, {37728, 64288}, {37736, 64291}, {41854, 41865}, {54193, 63146}, {64676, 65991}

X(65991) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND HUTSON-INTOUCH

Barycentrics    (a-b-c)*(4*a^3-7*a*(b-c)^2-a^2*(b+c)-2*(b-c)^2*(b+c)) : :
X(65991) = X[8]+3*X[1392]

X(65991) lies on these lines: {1, 381}, {8, 1392}, {11, 3244}, {55, 17573}, {65, 1387}, {79, 24928}, {354, 5884}, {390, 2646}, {946, 52836}, {1125, 3057}, {1319, 4299}, {1385, 4330}, {1698, 2098}, {1837, 3623}, {3058, 3636}, {3303, 61275}, {3304, 59372}, {3582, 11278}, {3584, 13606}, {3633, 50443}, {3656, 32636}, {3748, 12859}, {4995, 15808}, {5045, 39782}, {5154, 33956}, {5563, 65988}, {5603, 10404}, {5734, 17728}, {5886, 10051}, {5901, 5919}, {6745, 17648}, {7962, 34595}, {7982, 61649}, {8581, 64160}, {9624, 61648}, {9670, 64952}, {9957, 52638}, {10043, 11011}, {10107, 25414}, {10222, 16173}, {10283, 64345}, {10543, 11263}, {10572, 64848}, {10595, 64322}, {10609, 41540}, {11038, 63275}, {15950, 64703}, {16137, 17609}, {17636, 27385}, {17660, 66013}, {18253, 64046}, {20014, 54361}, {28645, 54391}, {30384, 34773}, {30424, 38055}, {31231, 63209}, {31730, 37605}, {33179, 37720}, {34471, 41864}, {37080, 61276}, {37722, 63257}, {47319, 64042}, {50906, 62617}, {64676, 65990}

X(65991) = midpoint of X(i) and X(j) for these {i,j}: {1, 45035}, {1392, 7705}
X(65991) = reflection of X(i) in X(j) for these {i,j}: {39781, 1}
X(65991) = inverse of X(3244) in Feuerbach hyperbola
X(65991) = pole of line {3244, 3873} with respect to the Feuerbach hyperbola
X(65991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 28204, 39781}, {1, 45035, 28204}, {5048, 11376, 17606}

X(65992) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND 6TH-MIXTILINEAR

Barycentrics    a*(a^9+5*a^7*b*c-3*a^8*(b+c)+10*a^2*b*(b-c)^2*c*(b+c)^3+(b-c)^4*(b+c)^3*(b^2-6*b*c+c^2)+2*a^6*(4*b^3+b^2*c+b*c^2+4*c^3)-a*(b^2-c^2)^2*(3*b^4-9*b^3*c-20*b^2*c^2-9*b*c^3+3*c^4)-a^5*(6*b^4+b^3*c+22*b^2*c^2+b*c^3+6*c^4)+a^3*(b-c)^2*(8*b^4+3*b^3*c-6*b^2*c^2+3*b*c^3+8*c^4)-2*a^4*(3*b^5+b^4*c+8*b^3*c^2+8*b^2*c^3+b*c^4+3*c^5)) : :

X(65992) lies on these lines: {1, 7965}, {65, 12767}, {1467, 7702}, {1699, 10884}, {2951, 5880}, {3062, 12669}, {3244, 7993}, {3927, 64369}, {5234, 6912}, {5531, 66006}, {5538, 12447}, {5884, 7992}, {8001, 11531}, {10980, 18219}, {11518, 17637}, {41860, 41865}, {64264, 66009}

X(65993) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND SUBMEDIAL

Barycentrics    3*a^2*(b-c)^2+a^3*(b+c)-(b+c)^2*(b^2-4*b*c+c^2)+a*(b^3-7*b^2*c-7*b*c^2+c^3) : :

X(65993) lies on these lines: {1, 42020}, {2, 988}, {3, 50535}, {10, 496}, {65, 16594}, {121, 10915}, {946, 11814}, {996, 1125}, {1210, 24003}, {1722, 1997}, {3090, 39605}, {3452, 46827}, {3756, 59577}, {3823, 3847}, {3831, 5316}, {3885, 60443}, {4187, 62673}, {4193, 60423}, {4432, 59675}, {4871, 21075}, {5121, 46937}, {5530, 30829}, {8582, 25079}, {9026, 49511}, {9843, 59511}, {10916, 59684}, {17054, 59731}, {17308, 33042}, {17385, 25354}, {17675, 30826}, {21616, 49993}, {24171, 58467}, {24174, 62297}, {25011, 25591}, {28018, 52353}, {45204, 63800}, {49529, 59666}, {49627, 59669}, {58405, 59544}, {59587, 62630}

X(65993) = midpoint of X(i) and X(j) for these {i,j}: {1, 42020}, {2899, 11512}
X(65993) = reflection of X(i) in X(j) for these {i,j}: {10, 2885}, {3445, 1125}
X(65993) = complement of X(11512)
X(65993) = X(2899) of Gemini 110 triangle
X(65993) = X(i)-complementary conjugate of X(j) for these {i, j}: {42360, 141}
X(65993) = pole of line {4462, 28478} with respect to the Steiner inellipse
X(65993) = pole of line {11679, 16602} with respect to the dual conic of Yff parabola
X(65993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2899, 11512}, {1210, 24003, 59685}, {2885, 3880, 10}

X(65994) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND INNER-YFF

Barycentrics    a^10-a^9*(b+c)-(b-c)^6*(b+c)^4+a*(b-c)^4*(b+c)^3*(b^2+c^2)-3*a^8*(b^2-b*c+c^2)+a^2*(b-c)^4*(b+c)^2*(3*b^2+b*c+3*c^2)+a^6*(b-c)^2*(4*b^2+b*c+4*c^2)+2*a^7*(b^3+c^3)+2*a^5*b*c*(b^3+b^2*c+b*c^2+c^3)-a^4*(4*b^6-7*b^5*c+4*b^4*c^2+2*b^3*c^3+4*b^2*c^4-7*b*c^5+4*c^6)-2*a^3*(b^7-b^4*c^3-b^3*c^4+c^7) : :

X(65994) lies on these lines: {1, 48519}, {11, 65995}, {46, 7702}, {65, 10057}, {79, 8068}, {100, 41540}, {377, 12647}, {946, 10058}, {1478, 5884}, {1709, 6831}, {2886, 17437}, {3337, 65986}, {3585, 65998}, {5880, 15298}, {10043, 10532}, {10073, 66013}, {10826, 41688}, {11263, 13411}, {11507, 64345}, {12736, 47319}, {13750, 16152}, {16113, 59321}, {20292, 39599}, {32760, 63262}, {47033, 53615}, {53616, 66017}, {64155, 66009}, {64191, 66003}

X(65994) = inverse of X(65995) in Feuerbach hyperbola

X(65995) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND OUTER-YFF

Barycentrics    a^10-a^9*(b+c)-(b-c)^6*(b+c)^4+a*(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)-3*a^8*(b^2-b*c+c^2)+a^2*(b-c)^4*(b+c)^2*(3*b^2+5*b*c+3*c^2)+a^6*(b-c)^2*(4*b^2+5*b*c+4*c^2)+2*a^7*(b^3+c^3)-2*a^5*b*c*(b^3-3*b^2*c-3*b*c^2+c^3)-2*a^3*(b-c)^2*(b^5-2*b^4*c-b^3*c^2-b^2*c^3-2*b*c^4+c^5)-a^4*(4*b^6+b^5*c-12*b^4*c^2+18*b^3*c^3-12*b^2*c^4+b*c^5+4*c^6) : :

X(65995) lies on these lines: {1, 37290}, {11, 65994}, {65, 10073}, {79, 5533}, {946, 10074}, {1479, 5884}, {1537, 66003}, {3337, 65987}, {3338, 7702}, {3434, 10573}, {3583, 64292}, {5570, 16153}, {5880, 15299}, {6246, 66046}, {10052, 10531}, {10057, 64042}, {10085, 64119}, {10122, 13129}, {11263, 16152}, {15845, 17437}, {22766, 64345}, {23708, 41688}, {32760, 59719}, {34789, 65998}

X(65995) = inverse of X(65994) in Feuerbach hyperbola
X(65995) = pole of line {34339, 65994} with respect to the Feuerbach hyperbola

X(65996) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND INNER-YFF TANGENTS

Barycentrics    a^10-a^9*(b+c)+16*a^5*b^2*c^2*(b+c)+a*(b-c)^6*(b+c)^3-(b-c)^6*(b+c)^4+a^8*(-3*b^2+7*b*c-3*c^2)+2*a^7*(b^3+c^3)+a^2*(b^2-c^2)^2*(3*b^4-7*b^3*c+12*b^2*c^2-7*b*c^3+3*c^4)+a^6*(4*b^4-17*b^3*c+6*b^2*c^2-17*b*c^3+4*c^4)-2*a^3*(b-c)^2*(b^5+7*b^3*c^2+7*b^2*c^3+c^5)-a^4*(4*b^6-15*b^5*c+12*b^4*c^2+10*b^3*c^3+12*b^2*c^4-15*b*c^5+4*c^6) : :

X(65996) lies on these lines: {46, 1532}, {65, 12749}, {79, 119}, {80, 65998}, {946, 10090}, {2077, 16155}, {3337, 65997}, {5884, 10573}, {6246, 66048}, {11263, 59719}, {11509, 45976}, {13407, 56120}, {14803, 44675}, {16154, 17637}, {64155, 65132}

X(65997) = PERSPECTOR OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN AND OUTER-YFF TANGENTS

Barycentrics    a^10-a^9*(b+c)+24*a^5*b^2*c^2*(b+c)+a*(b-c)^6*(b+c)^3-(b-c)^6*(b+c)^4+a^2*(b-c)^2*(b+c)^4*(3*b^2-5*b*c+3*c^2)-a^8*(3*b^2+b*c+3*c^2)+2*a^7*(b^3+c^3)+a^6*(4*b^4+7*b^3*c-18*b^2*c^2+7*b*c^3+4*c^4)-2*a^3*(b-c)^2*(b^5+11*b^3*c^2+11*b^2*c^3+c^5)-a^4*(4*b^6+9*b^5*c-28*b^4*c^2+42*b^3*c^3-28*b^2*c^4+9*b*c^5+4*c^6) : :

X(65997) lies on these lines: {65, 12750}, {79, 37726}, {946, 12776}, {999, 64345}, {3337, 65996}, {3338, 5880}, {5563, 41540}, {5884, 12116}, {12687, 64119}, {16155, 17637}, {37701, 42842}

X(65998) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN WRT EXTOUCH

Barycentrics    a*(a^8*(b+c)-2*a^6*(b-c)^2*(b+c)-6*a^4*b*(b-c)^2*c*(b+c)-2*a^7*(b^2+c^2)-(b-c)^4*(b+c)^3*(b^2+c^2)+2*a*(b^2-c^2)^2*(b^4-3*b^3*c+2*b^2*c^2-3*b*c^3+c^4)-2*a^3*(b-c)^2*(3*b^4-2*b^2*c^2+3*c^4)+a^5*(6*b^4-6*b^3*c+4*b^2*c^2-6*b*c^3+6*c^4)+2*a^2*(b-c)^2*(b^5+3*b^4*c+3*b*c^4+c^5)) : :
X(65998) = -3*X[2]+X[12666], -3*X[5886]+4*X[18260], -3*X[26446]+2*X[32159]

X(65998) lies on these lines: {1, 84}, {2, 12666}, {4, 5553}, {65, 2829}, {72, 2077}, {79, 46435}, {80, 65996}, {104, 64042}, {119, 12616}, {404, 48697}, {513, 53047}, {515, 37562}, {517, 64076}, {518, 49163}, {912, 1158}, {938, 5555}, {942, 26333}, {946, 15528}, {971, 5880}, {1470, 1858}, {1490, 59333}, {1519, 12688}, {1737, 41560}, {1768, 59327}, {1898, 26476}, {2771, 34862}, {2778, 51490}, {2800, 3244}, {2801, 10915}, {2950, 66006}, {3057, 54176}, {3358, 42843}, {3359, 9943}, {3585, 65994}, {3817, 6245}, {3868, 64078}, {5450, 5887}, {5552, 12528}, {5554, 12667}, {5693, 41389}, {5722, 12676}, {5777, 26364}, {5842, 64707}, {5884, 6738}, {5885, 22792}, {5886, 18260}, {6261, 10269}, {6705, 31803}, {6735, 14872}, {6906, 56941}, {6938, 64043}, {6959, 18856}, {7681, 37566}, {7686, 9579}, {9856, 58588}, {9940, 10200}, {9942, 37534}, {10167, 16132}, {10399, 15239}, {10531, 63962}, {10826, 41704}, {10942, 33899}, {11570, 66013}, {12005, 21625}, {12115, 64358}, {12332, 56176}, {12664, 64345}, {12669, 60925}, {12703, 54156}, {12761, 65987}, {13278, 66002}, {15016, 41865}, {16209, 52026}, {18239, 18242}, {19904, 49207}, {22753, 64132}, {24475, 66009}, {24927, 40257}, {26446, 32159}, {30424, 31870}, {34381, 49165}, {34772, 66055}, {34789, 65995}, {37002, 64721}, {44547, 56889}, {54290, 63976}, {64021, 64120}

X(65998) = midpoint of X(i) and X(j) for these {i,j}: {84, 15071}, {1071, 17649}, {3868, 64190}, {64021, 64120}
X(65998) = reflection of X(i) in X(j) for these {i,j}: {72, 64118}, {5887, 5450}, {6256, 34339}, {6261, 13369}, {9856, 58588}, {11500, 9943}, {12114, 18238}, {12688, 63980}, {18239, 18242}, {22792, 5885}, {31803, 6705}, {40263, 12616}, {54198, 12005}, {54227, 40249}, {64119, 942}
X(65998) = complement of X(12666)
X(65998) = X(1071) of anti-outer-Yff
X(65998) = pole of line {56, 1519} with respect to the Feuerbach hyperbola
X(65998) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1433), X(5553)}}, {{A, B, C, X(12686), X(44692)}}
X(65998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7992, 12686}, {971, 34339, 6256}, {1071, 12711, 12675}, {1071, 17649, 6001}, {6001, 18238, 12114}

X(65999) = ORTHOLOGY CENTER OF THESE TRIANGLES: EXTOUCH-OF-FUHRMANN WRT 1ST-SCHIFFLER

Barycentrics    4*a^7+a^6*(b+c)-3*(b-c)^4*(b+c)^3-2*a*(b^2-c^2)^2*(b^2-b*c+c^2)-2*a^5*(5*b^2-2*b*c+5*c^2)-5*a^4*(b^3+b^2*c+b*c^2+c^3)+a^3*(8*b^4-6*b^3*c-8*b^2*c^2-6*b*c^3+8*c^4)+a^2*(7*b^5+b^4*c-7*b^3*c^2-7*b^2*c^3+b*c^4+7*c^5) : :
X(65999) = -3*X[2]+X[12769]

X(65999) lies on these lines: {1, 5180}, {2, 12769}, {79, 6595}, {404, 48702}, {2771, 66046}, {3627, 5884}, {5880, 12745}, {7483, 64345}, {11263, 15325}, {12600, 16128}, {18985, 52783}

X(65999) = midpoint of X(i) and X(j) for these {i,j}: {12409, 14450}
X(65999) = reflection of X(i) in X(j) for these {i,j}: {12267, 18244}
X(65999) = complement of X(12769)

X(66000) = ORTHOLOGY CENTER OF THESE TRIANGLES: 1ST MOSES-MIYAMOTO-APOLLONIUS TRIANGLE WRT EXTOUCH-OF-FUHRMANN

Barycentrics    a*(a^3-a^2*(b+c)+(b-c)^2*(b+c)-a*(b^2+c^2))*(a^4*(b+c)+a^2*b*c*(b+c)-2*a^3*(b^2+c^2)+2*a*(b-c)^2*(b^2+b*c+c^2)-(b-c)^2*(b+c)*(b^2+b*c+c^2))+2*a*(a^2-b^2+b*c-c^2)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+c^2))*S : :

X(66000) lies on these lines: {7, 80}, {104, 18460}, {1387, 30347}, {1768, 30401}, {2771, 63283}, {2800, 52805}, {5083, 30342}, {6204, 6326}, {6224, 52811}, {6264, 30320}, {6265, 30386}, {9946, 30277}, {9952, 30289}, {10265, 30381}, {11571, 30426}, {12515, 30297}, {12611, 30307}, {12619, 30314}, {12691, 30325}, {12758, 30334}, {12767, 30355}, {12770, 30361}, {12771, 30369}, {12772, 30419}, {12774, 30407}, {17638, 30376}, {18254, 30413}, {18458, 35775}, {49240, 52807}

X(66000) = reflection of X(i) in X(j) for these {i,j}: {66001, 11570}
X(66000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2801, 11570, 66001}




This is the end of PART 33: Centers X(64001) - X(66000)

PART 1: Introduction and Centers X(1) - X(1000) PART 2: Centers X(1001) - X(3000) PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000) PART 5: Centers X(7001) - X(10000) PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000) PART 8: Centers X(14001) - X(16000) PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000) PART 11: Centers X(20001) - X(22000) PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000) PART 14: Centers X(26001) - X(28000) PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000) PART 17: Centers X(32001) - X(34000) PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000) PART 20: Centers X(38001) - X(40000) PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000) PART 23: Centers X(44001) - X(46000) PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000) PART 26: Centers X(50001) - X(52000) PART 27: Centers X(52001) - X(54000)
PART 28: Centers X(54001) - X(56000) PART 29: Centers X(56001) - X(58000) PART 30: Centers X(58001) - X(60000)
PART 31: Centers X(60001) - X(62000) PART 32: Centers X(62001) - X(64000) PART 33: Centers X(64001) - X(66000)
PART 34: Centers X(66001) - X(68000) PART 35: Centers X(68001) - X(70000) PART 36: Centers X(70001) - X(72000)