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 written 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}




******* Preamble Pending


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]

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]

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}

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)