| 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(18001) lies on the cubic K978 and these lines: {42, 8663}, {351, 2054}, {514, 1125}, {649, 2308}, {659, 1929}, {661, 1962}, {804, 11599}, {875, 9506}, {4983, 6155}
X(18001) = X(i)-cross conjugate of X(j) for these (i,j): {3121, 9506}, {4455, 512}
X(18001) = crossdifference of every pair of points on line {1931, 6157}
X(18001) = X(3882)-zayin conjugate of X(9508)
X(18001) = X(i)-isoconjugate of X(j) for these (i,j): {99, 1757}, {100, 17731}, {190, 1931}, {423, 1332}, {662, 6542}, {668, 1326}, {799, 17735}, {2786, 4567}, {4584, 6651}, {4589, 8298}, {4600, 9508}, {4601, 5029}
X(18001) = barycentric product X(i)*X(j) for these {i,j}: {512, 6650}, {513, 9278}, {514, 2054}, {649, 11599}, {661, 1929}, {2702, 3120}, {3733, 6543}, {4010, 9506}
X(18001) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 6542}, {649, 17731}, {667, 1931}, {669, 17735}, {798, 1757}, {1919, 1326}, {1929, 799}, {2054, 190}, {2702, 4600}, {3121, 9508}, {3122, 2786}, {4079, 6541}, {4455, 6651}, {6650, 670}, {9278, 668}, {9505, 4639}, {9506, 4589}, {11599, 1978}
X(18002) lies on the cubic K978 and these lines: {512, 2092}, {513, 3666}, {667, 2300}, {798, 3725}, {804, 11611}, {893, 2483}, {900, 11609}
X(18002) = crossdifference of every pair of points on line {5209, 5291}
X(18002) = X(i)-isoconjugate of X(j) for these (i,j): {99, 17763}, {100, 5209}, {422, 4561}, {662, 17790}, {799, 5291}, {1978, 5006}, {2787, 4600}, {5061, 7257}
X(18002) = barycentric product X(i)*X(j) for these {i,j}: {667, 11611}, {2703, 3125}, {7180, 11609}
X(18002) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 17790}, {649, 5209}, {669, 5291}, {798, 17763}, {1980, 5006}, {2703, 4601}, {3121, 2787}, {11611, 6386}
X(18003) lies on the cubic K979 and these lines: {321, 690}, {523, 1577}, {668, 891}, {756, 14430}, {1089, 3762}
X(18003) = crossdifference of every pair of points on line {1333, 1977}
X(18003) = X(58)-isoconjugate of X(2703)
X(18003) = X(523)-Hirst inverse of X(4036)
X(18003) = barycentric product X(i)*X(j) for these {i,j}: {321, 2787}, {523, 17790}, {850, 5291}, {1577, 17763}, {4024, 5209}
X(18003) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 2703}, {2680, 3310}, {2787, 81}, {3700, 11609}, {4036, 11611}, {5040, 1333}, {5061, 4565}, {5209, 4610}, {5291, 110}, {17763, 662}, {17790, 99}
X(18004) lies on the cubic K979 and these lines: {10, 690}, {100, 190}, {313, 14295}, {513, 4522}, {523, 661}, {756, 2254}, {826, 4129}, {918, 3837}, {1089, 3762}, {1215, 3716}, {1826, 16230}, {2786, 9508}, {3239, 4874}, {3678, 3887}, {4080, 5466}, {4170, 4808}, {4500, 4802}, {4705, 7265}, {4707, 14431}, {4922, 14432}, {4944, 7662}, {6366, 13272}, {6370, 12078}
X(18004) = midpoint of X(i) and X(j) for these {i,j}: {661, 4122}, {4010, 4088}, {4024, 4824}, {4170, 4808}, {4705, 7265}
X(18004) = reflection of X(i) in X(j) for these {i,j}: {4806, 14321}, {4874, 3239}
X(18004) = X(4562)-Ceva conjugate of X(594)
X(18004) = crosspoint of X(i) and X(j) for these (i,j): {100, 15168}, {321, 4583}, {4444, 4608}
X(18004) = crossdifference of every pair of points on line {58, 1015}
X(18004) = crosssum of X(3733) and X(5009)
X(18004) = X(i)-isoconjugate of X(j) for these (i,j): {81, 2702}, {110, 1929}, {163, 6650}, {4556, 9278}
X(18004) = X(i)-Hirst inverse of X(j) for these (i,j): {523, 4024}, {3943, 4062}
X(18004) = barycentric product X(i)*X(j) for these {i,j}: {10, 2786}, {313, 5029}, {321, 9508}, {423, 4064}, {514, 6541}, {523, 6542}, {850, 17735}, {1577, 1757}, {1931, 4036}, {4024, 17731}
X(18004) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 2702}, {523, 6650}, {661, 1929}, {1326, 4556}, {1757, 662}, {2681, 676}, {2786, 86}, {4024, 11599}, {4079, 2054}, {4705, 9278}, {5029, 58}, {6541, 190}, {6542, 99}, {9508, 81}, {17731, 4610}, {17735, 110}
{X(4088),X(4120)}-harmonic conjugate of X(4010)
X(18005) lies on the cubic K979 and these lines: {523, 3120}, {690, 4049}, {900, 903}, {4080, 5466}
X(18005) = barycentric product X(2796)*X(4049)
X(18006) lies on the cubic K979 and these lines: {100, 658}, {225, 16230}, {226, 690}, {349, 14295}, {523, 656}, {900, 13273}, {1254, 2254}, {7234, 17094}
X(18006) = crossdifference of every pair of points on line {284, 14936}
X(18006) = X(i)-isoconjugate of X(j) for these (i,j): {21, 2701}, {110, 2648}, {2652, 4636}
X(18006) = barycentric product X(i)*X(j) for these {i,j}: {226, 2785}, {349, 5075}, {1577, 1758}
X(18006) = barycentric quotient X(i)/X(j) for these {i,j}: {661, 2648}, {1400, 2701}, {1758, 662}, {2651, 4612}, {2785, 333}, {5060, 4636}, {5075, 284}
X(18007) = 3 X[9166] - X[9168], 3 X[115] - 2 X[9183], 4 X[10189] - X[15300]
X(18007) lies on the cubic K979 and these lines: {111, 9189}, {115, 523}, {543, 8371}, {671, 690}, {1499, 9880}, {1649, 5461}, {2793, 6094}, {5465, 9214}, {9166, 9168}, {10189, 15300}
X(18007) = midpoint of X(671) and X(5466)
X(18007) = reflection of X(1649) in X(5461)
X(18007) = X(922)-isoconjugate of X(9170)
X(18007) = barycentric product X(i)*X(j) for these {i,j}: {543, 5466}, {671, 8371}
X(18007) = barycentric quotient X(i)/X(j) for these {i,j}: {543, 5468}, {671, 9170}, {2502, 5467}, {8371, 524}, {9171, 187}, {9178, 843}
X(18008) lies oon the cubic K979 and the line {523, 14603}
X(18009) lies on the cubic K979 and these lines: {523, 1086}, {690, 4444}
X(18009) = X(3573)-isoconjugate of X(12031)
X(18009) = barycentric quotient X(3572)/X(12031)
X(18010) lies on the cubic K979 and these lines: {23, 385}, {83, 690}, {308, 14295}, {804, 11606}, {882, 14970}, {4577, 4630}, {8290, 9479}, {9185, 10130}
X(18010) = cevapoint of X(5113) and X(9479)
X(18010) = crosspoint of X(4577) and X(14970)
X(18010) = crosssum of X(3005) and X(8623)
X(18010) = barycentric product X(i)*X(j) for these {i,j}: {83, 9479}, {308, 5113}, {420, 4580}
X(18010) = barycentric quotient X(i)/X(j) for these {i,j}: {2076, 1634}, {5113, 39}, {7779, 4576}, {9479, 141}
X(18011) lies on the cubic K979 and these lines: {10, 523}, {690, 4080}, {4555, 4618}
X(18012) lies on the cubic K979 and these lines: {523, 7625}, {690, 5485}
X(18012) = barycentric product X(2793)*X(5485)
X(18012) = barycentric quotient X(i)/X(j) for these {i,j}: {2793, 1992}, {9135, 1384}
X(18013) lies on the cubic K979 and these lines: {522, 5745}, {523, 17056}, {690, 11608}, {2689, 2701}
X(18013) = X(i)-isoconjugate of X(j) for these (i,j): {109, 2651}, {110, 1758}, {651, 5060}
X(18013) = barycentric product X(i)*X(j) for these {i,j}: {522, 11608}, {1577, 2648}, {2652, 4391}
X(18013) = barycentric quotient X(i)/X(j) for these {i,j}: {650, 2651}, {661, 1758}, {663, 5060}, {2648, 662}, {2652, 651}, {3064, 415}, {11608, 664}
X(18014) lies on the cubic K979 and these lines: {10, 6367}, {86, 4977}, {514, 1125}, {523, 1213}, {690, 4049}, {900, 6650}, {1269, 3261}, {1577, 4647}, {1839, 7649}, {2690, 2702}, {3649, 4806}
X(18014) = X(4010)-cross conjugate of X(523)
X(18014) = crossdifference of every pair of points on line {1326, 17735}
X(18014) = X(i)-isoconjugate of X(j) for these (i,j): {100, 1326}, {101, 1931}, {110, 1757}, {163, 6542}, {423, 906}, {662, 17735}, {692, 17731}, {4567, 5029}, {4570, 9508}
X(18014) = trilinear pole of line {3120, 4988}
X(18014) = barycentric product X(i)*X(j) for these {i,j}: {514, 11599}, {523, 6650}, {693, 9278}, {1577, 1929}, {2054, 3261}, {6543, 7192}
X(18014) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 17735}, {513, 1931}, {514, 17731}, {523, 6542}, {649, 1326}, {661, 1757}, {1929, 662}, {2054, 101}, {2702, 4570}, {3120, 2786}, {3122, 5029}, {3125, 9508}, {4010, 6651}, {4024, 6541}, {6543, 3952}, {6650, 99}, {7649, 423}, {9278, 100}, {9505, 4584}, {11599, 190}
X(18015) lies on the cubic K979 and these lines: {81, 6371}, {513, 3666}, {523, 1211}, {661, 2292}, {690, 11611}, {1290, 2703}, {1829, 6591}
X(18015) = X(i)-isoconjugate of X(j) for these (i,j): {110, 17763}, {163, 17790}, {190, 5006}, {422, 1331}, {643, 5061}, {662, 5291}, {692, 5209}, {2787, 4570}, {4600, 5040}
X(18015) = crossdifference of every pair of points on line {5006, 5291}
X(18015) = barycentric product X(i)*X(j) for these {i,j}: {513, 11611}, {2703, 16732}, {7178, 11609}
X(18015) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 5291}, {514, 5209}, {523, 17790}, {661, 17763}, {667, 5006}, {2703, 4567}, {3121, 5040}, {3125, 2787}, {6591, 422}, {7180, 5061}, {11609, 645}, {11611, 668}
See Tran Quang Hung and César Lozada, Hyacinthos 27560.
X(18016) lies on these lines: {3, 54}, {30, 13856}, {140, 6592}, {539, 14143}, {1209, 14072}, {13434, 15770}
X(18016) = midpoint of X(3) and X(15345)
X(18016) = {X(3), X(54)}-harmonic conjugate of X(6150)
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27570.
X(18017) lies on this line: {2,3}
X(18017) = reflection of X(20) in X(16273)
X(18018) lies on the cubics K141 and K555 and on these lines: {2, 1235}, {4, 13575}, {22, 76}, {25, 339}, {66, 69}, {95, 7485}, {253, 7378}, {264, 5133}, {287, 1993}, {305, 858}, {401, 9983}, {850, 2419}, {2052, 6330}, {3266, 6340}, {7396, 9464}
X(18018) = isogonal conjugate of X(206)
X(18018) = isotomic conjugate of X(22)
X(18018) = polar conjugate of X(8743)
X(18018) = complement of polar conjugate of isogonal conjugate of X(23172)
X(18018) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2156, 8878}, {16277, 5905}
X(18018) = X(i)-cross conjugate of X(j) for these (i,j): {6, 76}, {427, 2}, {523, 1289}, {1853, 2052}, {1899, 5392}, {11245, 11140}
X(18018) = X(i)-isoconjugate of X(j) for these (i,j): {1, 206}, {2, 17453}, {6, 2172}, {9, 7251}, {19, 10316}, {22, 31}, {32, 1760}, {37, 17186}, {48, 8743}, {57, 4548}, {63, 17409}, {163, 2485}, {315, 560}, {798, 4611}, {1333, 4456}, {1397, 4123}, {1755, 11610}, {2175, 7210}, {2206, 4463}, {9247, 17907}, {9447, 17076}
X(18018) = X(2)-Hirst inverse of X(16097)
X(18018) = cevapoint of X(i) and X(j) for these (i,j): {2, 7391}, {6, 2353}, {66, 14376}, {339, 523}, {826, 15526}, {13854, 17407}
X(18018) = barycentric product X(i)*X(j) for these {i,j}: {66, 76}, {264, 14376}, {305, 13854}, {561, 2156}, {1289, 3267}, {1502, 2353}, {8024, 16277}
X(18018) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2172}, {2, 22}, {3, 10316}, {4, 8743}, {6, 206}, {10, 4456}, {25, 17409}, {31, 17453}, {55, 4548}, {56, 7251}, {58, 17186}, {66, 6}, {75, 1760}, {76, 315}, {85, 7210}, {98, 11610}, {99, 4611}, {141, 3313}, {264, 17907}, {312, 4123}, {313, 4150}, {321, 4463}, {339, 127}, {523, 2485}, {525, 8673}, {693, 16757}, {1289, 112}, {2156, 31}, {2353, 32}, {6063, 17076}, {9033, 14396}, {13854, 25}, {14376, 3}, {16097, 15013}, {16277, 251}, {16747, 16715}, {17407, 3162}
X(18018) = cevapoint of circumcircle intercepts of de Longchamps line
X(18018) = {X(13854),X(14376)}-harmonic conjugate of X(2)
X(18019) lies on the hyperbola {{A,B,C,X(2),X(69)}} and these lines: {2, 339}, {23, 935}, {67, 69}, {76, 7664}, {95, 7496}, {99, 1799}, {264, 5169}, {287, 323}, {306, 4568}, {325, 328}, {1236, 3266}, {1494, 10989}, {7391, 11605}
X(18019) = isogonal conjugate of X(18374)
X(18019) = isotomic conjugate of X(23)
X(18019) = polar conjugate of X(8744)
X(18019) = X(i)-cross conjugate of X(j) for these (i,j): {524, 76}, {858, 2}, {9140, 94}
X(18019) = X(i)-isoconjugate of X(j) for these (i,j): {19, 10317}, {23, 31}, {32, 16568}, {48, 8744}, {163, 2492}, {316, 560}, {922, 14246}, {923, 6593}, {9447, 17088}
X(18019) = X(23)-vertex conjugate of X(8791)
X(18019) = cevapoint of X(i) and X(j) for these (i,j): {2, 5189}, {6, 5938}, {39, 2393}, {524, 14357}, {3266, 8024}
X(18019) = trilinear pole of line {141, 525} (the line through the symmedian points of the 1st and 2nd Ehrmann inscribed triangles)
X(18019) = barycentric product X(i)*X(j) for these {i,j}: {67, 76}, {305, 8791}, {561, 2157}, {599, 10512}, {850, 17708}, {935, 3267}, {1502, 3455}, {3266, 10415}, {8024, 9076}, {9464, 10511}
X(18019) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 23}, {3, 10317}, {4, 8744}, {67, 6}, {75, 16568}, {76, 316}, {141, 9019}, {523, 2492}, {524, 6593}, {525, 9517}, {599, 10510}, {671, 14246}, {850, 9979}, {935, 112}, {2157, 31}, {3266, 7664}, {3455, 32}, {3580, 12824}, {5466, 10561}, {6063, 17088}, {8791, 25}, {9076, 251}, {10415, 111}, {10511, 1383}, {10512, 598}, {11064, 16165}, {11605, 8743}, {14357, 187}, {17708, 110}
Line X(99)X(112) (the trilinear polar of X(18020) is the locus of the trilinear pole of the tangent at P to hyperbola {{A,B,C,X(4),P}}, as P moves on the Euler line. (Randy Hutson, June 27, 2018)
X(18020) lies on these lines: {99, 1304}, {107, 10425}, {110, 685}, {112, 9150}, {249, 297}, {250, 325}, {327, 5651}, {415, 4620}, {422, 4601}, {423, 4600}, {450, 3260}, {460, 5203}, {647, 2966}, {648, 892}, {877, 4240}, {1098, 7045}, {2396, 2409}, {4230, 17941}, {4235, 9170}, {5641, 5642}, {6563, 7471}, {7769, 14366}
X(18020) = isogonal conjugate of X(20975)
X(18020) = isotomic conjugate of X(125)
X(18020) = polar conjugate of X(115)
X(18020) = X(5539)-zayin conjugate of X(656)
X(18020) = X(i)-cross conjugate of X(j) for these (i,j): {2, 6331}, {4, 648}, {24, 16813}, {69, 99}, {76, 4577}, {186, 687}, {249, 4590}, {315, 670}, {316, 892}, {317, 6528}, {340, 16077}, {403, 15459}, {419, 685}, {451, 6335}, {511, 2966}, {1092, 4558}, {1330, 190}, {1974, 112}, {2893, 664}, {3043, 14590}, {3144, 653}, {3542, 15352}, {4213, 1897}, {5095, 4235}, {5972, 2}, {6353, 107}, {7058, 4610}, {9306, 110}, {15462, 5649}, {15595, 2396}, {16163, 2407}
X(18020) = pole wrt polar circle of trilinear polar of X(115) (line X(1648)X(8029))
X(18020) = X(i)-isoconjugate of X(j) for these (i,j): {3, 2643}, {6, 3708}, {19, 3269}, {25, 2632}, {31, 125}, {48, 115}, {63, 3124}, {71, 3125}, {72, 3122}, {73, 4516}, {181, 7004}, {184, 1109}, {201, 3271}, {212, 1365}, {213, 4466}, {228, 3120}, {244, 3690}, {255, 8754}, {304, 1084}, {305, 4117}, {306, 3121}, {326, 2971}, {338, 9247}, {339, 560}, {512, 656}, {523, 810}, {525, 798}, {603, 4092}, {647, 661}, {667, 4064}, {669, 14208}, {756, 3937}, {822, 2501}, {872, 1565}, {905, 4079}, {1015, 3949}, {1096, 2972}, {1254, 3270}, {1356, 3718}, {1367, 2212}, {1395, 7068}, {1425, 2310}, {1459, 4705}, {1500, 3942}, {1562, 2155}, {1577, 3049}, {1924, 3267}, {1973, 15526}, {1974, 17879}, {2084, 4580}, {2170, 2197}, {2171, 7117}, {2200, 16732}, {2433, 2631}, {2616, 15451}, {2624, 14582}, {2642, 10097}, {3248, 3695}, {4575, 8029}, {7063, 7182}, {7180, 8611}
X(18020) = cevapoint of X(i) and X(j) for these (i,j): {2, 110}, {4, 648}, {69, 99}, {107, 11547}, {112, 1974}, {249, 250}, {662, 1098}, {1092, 4558}, {1113, 8116}, {1114, 8115}, {2407, 16163}, {2409, 15595}, {3043, 14590}, {3233, 11064}, {4235, 5095}, {4240, 14920}, {5468, 7664}, {6148, 10411}, {15164, 15165}
X(18020) = trilinear pole of line {99, 112}
X(18020) = barycentric product X(i)*X(j) for these {i,j}: {4, 4590}, {27, 4600}, {28, 4601}, {29, 4620}, {76, 250}, {99, 648}, {107, 4563}, {108, 4631}, {110, 6331}, {112, 670}, {162, 799}, {249, 264}, {274, 5379}, {278, 6064}, {281, 7340}, {286, 4567}, {662, 811}, {685, 2396}, {823, 4592}, {877, 2966}, {892, 4235}, {1101, 1969}, {1509, 15742}, {1783, 4623}, {1897, 4610}, {2407, 16077}, {4558, 6528}, {6035, 7473}
X(18020) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3708}, {2, 125}, {3, 3269}, {4, 115}, {19, 2643}, {20, 1562}, {25, 3124}, {27, 3120}, {28, 3125}, {59, 2197}, {60, 7117}, {63, 2632}, {69, 15526}, {76, 339}, {86, 4466}, {92, 1109}, {99, 525}, {107, 2501}, {110, 647}, {112, 512}, {162, 661}, {163, 810}, {186, 2088}, {190, 4064}, {249, 3}, {250, 6}, {264, 338}, {270, 2170}, {275, 8901}, {278, 1365}, {281, 4092}, {286, 16732}, {297, 868}, {304, 17879}, {315, 127}, {323, 16186}, {345, 7068}, {348, 1367}, {393, 8754}, {394, 2972}, {468, 1648}, {476, 14582}, {525, 5489}, {593, 3937}, {643, 8611}, {648, 523}, {662, 656}, {670, 3267}, {685, 2395}, {687, 15328}, {691, 10097}, {757, 3942}, {765, 3949}, {799, 14208}, {811, 1577}, {877, 2799}, {892, 14977}, {933, 2623}, {1016, 3695}, {1101, 48}, {1172, 4516}, {1252, 3690}, {1262, 1425}, {1275, 6356}, {1304, 2433}, {1474, 3122}, {1509, 1565}, {1576, 3049}, {1625, 15451}, {1783, 4705}, {1897, 4024}, {1974, 1084}, {2052, 2970}, {2185, 7004}, {2189, 3271}, {2203, 3121}, {2207, 2971}, {2326, 2310}, {2396, 6333}, {2407, 9033}, {2420, 9409}, {2421, 684}, {2501, 8029}, {2715, 878}, {2966, 879}, {3233, 14401}, {4213, 6627}, {4230, 3569}, {4232, 6791}, {4235, 690}, {4240, 1637}, {4242, 2610}, {4556, 1459}, {4558, 520}, {4563, 3265}, {4564, 201}, {4567, 72}, {4570, 71}, {4573, 17094}, {4575, 822}, {4576, 2525}, {4577, 4580}, {4590, 69}, {4600, 306}, {4610, 4025}, {4611, 8673}, {4612, 521}, {4620, 307}, {4623, 15413}, {4636, 652}, {5094, 8288}, {5379, 37}, {5468, 14417}, {6064, 345}, {6331, 850}, {6335, 4036}, {6353, 6388}, {6528, 14618}, {7012, 2171}, {7054, 3270}, {7058, 2968}, {7115, 181}, {7128, 1254}, {7340, 348}, {7473, 1640}, {8750, 4079}, {10311, 6784}, {10411, 8552}, {11064, 1650}, {11547, 136}, {14129, 137}, {14570, 6368}, {14587, 14533}, {14590, 526}, {14591, 14270}, {14920, 3258}, {15329, 686}, {15388, 2353}, {15395, 11079}, {15460, 15166}, {15461, 15167}, {15742, 594}, {16077, 2394}, {16080, 12079}, {17206, 17216}
X(18020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (647, 9514, 2966), (4240, 5468, 877)
X(18021) lies on these lines: {76, 940}, {86, 310}, {99, 16678}, {171, 5209}, {274, 3666}, {286, 6385}, {305, 16992}, {313, 17731}, {314, 3706}, {333, 3691}, {561, 670}, {799, 14829}, {1909, 2668}, {3596, 4042}, {3996, 7257}, {4631, 7058}
X(18021) = isotomic conjugate of X(181)
X(18021) = X(i)-cross conjugate of X(j) for these (i,j): {3271, 4560}, {3794, 2185}
X(18021) = X(i)-isoconjugate of X(j) for these (i,j): {12, 560}, {31, 181}, {32, 2171}, {42, 1402}, {56, 872}, {57, 7109}, {65, 1918}, {201, 1974}, {213, 1400}, {226, 2205}, {604, 1500}, {669, 4551}, {756, 1397}, {762, 16947}, {765, 1356}, {798, 4559}, {1084, 4564}, {1106, 7064}, {1253, 7143}, {1254, 2175}, {1395, 3690}, {1409, 2333}, {1415, 4079}, {1425, 2212}, {1501, 6358}, {1880, 2200}, {1924, 4552}, {1973, 2197}, {2149, 3124}, {4117, 4998}, {6059, 7138}, {6354, 9447}, {7045, 7063}, {7147, 14827}, {7235, 14598}, {8736, 9247}
X(18021) = cevapoint of X(3271) and X(4560)
X(18021) = barycentric product X(i)*X(j) for these {i,j}: {21, 6385}, {60, 1502}, {76, 261}, {274, 314}, {310, 333}, {312, 873}, {561, 2185}, {670, 4560}, {693, 4631}, {1509, 3596}, {1928, 2150}, {3705, 7307}, {3737, 4602}, {4391, 4623}, {4609, 7252}, {6063, 7058}, {7199, 7257}
X(18021) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 181}, {8, 1500}, {9, 872}, {11, 3124}, {21, 213}, {29, 2333}, {55, 7109}, {60, 32}, {69, 2197}, {75, 2171}, {76, 12}, {81, 1402}, {85, 1254}, {86, 1400}, {99, 4559}, {261, 6}, {264, 8736}, {270, 1973}, {274, 65}, {279, 7143}, {283, 2200}, {284, 1918}, {286, 1880}, {304, 201}, {310, 226}, {312, 756}, {314, 37}, {332, 71}, {333, 42}, {345, 3690}, {346, 7064}, {348, 1425}, {522, 4079}, {552, 1407}, {561, 6358}, {593, 1397}, {645, 4557}, {670, 4552}, {757, 604}, {763, 1408}, {799, 4551}, {873, 57}, {1015, 1356}, {1043, 1334}, {1088, 7147}, {1098, 41}, {1434, 1042}, {1444, 1409}, {1509, 56}, {1812, 228}, {1920, 7211}, {1921, 7235}, {2150, 560}, {2185, 31}, {2189, 1974}, {2194, 2205}, {2326, 2212}, {3271, 1084}, {3596, 594}, {3701, 762}, {3718, 3949}, {3737, 798}, {3786, 3774}, {3794, 16584}, {3926, 7066}, {4087, 4037}, {4391, 4705}, {4560, 512}, {4572, 4605}, {4590, 59}, {4610, 109}, {4612, 692}, {4623, 651}, {4625, 1020}, {4631, 100}, {4858, 2643}, {4976, 8663}, {6061, 14827}, {6063, 6354}, {6064, 1252}, {6385, 1441}, {6514, 4055}, {6628, 1412}, {7017, 7140}, {7054, 2175}, {7058, 55}, {7155, 6378}, {7183, 7138}, {7192, 7180}, {7199, 4017}, {7252, 669}, {7253, 3709}, {7257, 1018}, {7258, 4069}, {7304, 1403}, {7340, 1262}, {8735, 2971}, {14936, 7063}, {17096, 7250}, {17185, 3725}, {17197, 3122}, {17206, 73}, {17880, 3708}
X(18022) lies on these lines: {2, 6331}, {25, 8840}, {69, 8795}, {76, 297}, {183, 16089}, {264, 305}, {276, 7763}, {290, 1899}, {308, 13854}, {324, 8024}, {393, 1241}, {458, 3978}, {683, 6524}, {685, 2001}, {1235, 5117}, {1975, 9291}, {3410, 13485}, {6528, 11185}, {9230, 9308}
X(18022) = isogonal conjugate of X(14575)
X(18022) = isotomic conjugate of X(184)
X(18022) = polar conjugate of X(32)
X(18022) = X(i)-cross conjugate of X(j) for these (i,j): {76, 1502}, {311, 76}, {850, 6331}, {1235, 264}, {8754, 14618}, {17864, 75}
X(18022) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14575}, {3, 560}, {6, 9247}, {19, 14585}, {31, 184}, {32, 48}, {63, 1501}, {69, 1917}, {77, 9448}, {163, 3049}, {212, 1397}, {217, 2148}, {222, 9447}, {228, 2206}, {248, 9417}, {255, 1974}, {293, 9418}, {304, 9233}, {577, 1973}, {603, 2175}, {656, 14574}, {669, 4575}, {810, 1576}, {906, 1919}, {922, 14908}, {1176, 1923}, {1331, 1980}, {1333, 2200}, {1395, 6056}, {1437, 1918}, {1755, 14600}, {1790, 2205}, {1924, 4558}, {1933, 17970}, {1964, 10547}, {2179, 14533}, {2196, 14599}, {2203, 4055}, {2207, 4100}, {2212, 7335}, {4592, 9426}, {7099, 14827}, {7193, 14598}
X(18022) = cevapoint of X(i) and X(j) for these (i,j): {2, 11442}, {4, 17907}, {69, 7763}, {76, 264}, {8754, 14618}
X(18022) = trilinear pole of line {2799, 3267}
X(18022) = pole wrt polar circle of trilinear polar of X(32) (line X(669)X(688))
X(18022) = perspector of ABC and orthoanticevian triangle of X(1502)
X(18022) = barycentric product X(i)*X(j) for these {i,j}: {4, 1502}, {19, 1928}, {75, 1969}, {76, 264}, {92, 561}, {276, 311}, {305, 2052}, {308, 1235}, {331, 3596}, {670, 14618}, {850, 6331}, {2501, 4609}, {3267, 6528}, {6063, 7017}, {6386, 17924}
X(18022) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 9247}, {2, 184}, {3, 14585}, {4, 32}, {5, 217}, {6, 14575}, {10, 2200}, {19, 560}, {25, 1501}, {27, 2206}, {33, 9447}, {69, 577}, {75, 48}, {76, 3}, {83, 10547}, {85, 603}, {92, 31}, {95, 14533}, {98, 14600}, {112, 14574}, {158, 1973}, {232, 9418}, {240, 9417}, {242, 14599}, {253, 14642}, {264, 6}, {273, 604}, {274, 1437}, {276, 54}, {278, 1397}, {281, 2175}, {286, 1333}, {290, 248}, {297, 237}, {304, 255}, {305, 394}, {306, 4055}, {308, 1176}, {310, 1790}, {311, 216}, {312, 212}, {313, 71}, {314, 2193}, {315, 10316}, {316, 10317}, {317, 571}, {318, 41}, {321, 228}, {324, 51}, {325, 3289}, {326, 4100}, {331, 56}, {334, 2196}, {339, 3269}, {340, 50}, {341, 1802}, {342, 2199}, {343, 418}, {345, 6056}, {348, 7335}, {349, 73}, {393, 1974}, {419, 14602}, {427, 3051}, {468, 14567}, {492, 8911}, {523, 3049}, {561, 63}, {607, 9448}, {626, 4173}, {648, 1576}, {668, 906}, {670, 4558}, {671, 14908}, {799, 4575}, {811, 163}, {850, 647}, {877, 14966}, {1088, 7099}, {1093, 2207}, {1235, 39}, {1236, 14961}, {1240, 2359}, {1441, 1409}, {1446, 1410}, {1502, 69}, {1577, 810}, {1784, 9406}, {1824, 2205}, {1826, 1918}, {1847, 1106}, {1861, 9454}, {1896, 2204}, {1916, 17970}, {1920, 3955}, {1921, 7193}, {1928, 304}, {1930, 4020}, {1969, 1}, {1973, 1917}, {1974, 9233}, {1978, 1331}, {1990, 9407}, {2052, 25}, {2489, 9426}, {2501, 669}, {2888, 8565}, {2967, 9419}, {2969, 1977}, {2970, 3124}, {2971, 9427}, {2973, 1015}, {2998, 15389}, {3260, 3284}, {3261, 1459}, {3266, 3292}, {3267, 520}, {3596, 219}, {3718, 2289}, {3926, 1092}, {4391, 1946}, {4572, 1813}, {4602, 4592}, {4609, 4563}, {5089, 9455}, {5117, 3117}, {5254, 682}, {5392, 2351}, {6063, 222}, {6143, 9697}, {6331, 110}, {6335, 692}, {6344, 11060}, {6384, 15373}, {6385, 1444}, {6386, 1332}, {6521, 1096}, {6528, 112}, {6530, 2211}, {6531, 14601}, {6591, 1980}, {7017, 55}, {7018, 7116}, {7020, 7118}, {7046, 14827}, {7101, 1253}, {7140, 7109}, {7141, 1500}, {7182, 7125}, {7649, 1919}, {7763, 1147}, {7769, 49}, {8024, 3917}, {8039, 4121}, {8754, 1084}, {8756, 9459}, {8795, 8882}, {8882, 14573}, {9291, 1970}, {13450, 3199}, {14208, 822}, {14249, 3172}, {14603, 12215}, {14615, 15905}, {14618, 512}, {15415, 6368}, {15466, 154}, {16081, 1976}, {16089, 1971}, {16230, 2491}, {17442, 1923}, {17907, 206}, {17980, 8789}, {17984, 1691}
X(18023) lies on these lines: {67, 316}, {76, 338}, {111, 308}, {264, 2970}, {290, 892}, {313, 1978}, {349, 4572}, {691, 2367}, {1502, 4609}, {2453, 5152}, {3978, 17948}, {5466, 14295}, {7771, 11643}, {9211, 9214}
X(18023) = isogonal conjugate of X(14567)
X(18023) = isotomic conjugate of X(187)
X(18023) = X(i)-cross conjugate of X(j) for these (i,j): {625, 2}, {3266, 76}, {14977, 892}
X(18023) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14567}, {6, 922}, {19,23200}, {31, 187}, {32, 896}, {163, 351}, {468, 9247}, {524, 560}, {798, 5467}, {1501, 14210}, {1576, 2642}, {1917, 3266}, {1918, 16702}, {1924, 5468}, {1927, 5026}, {1973, 3292}, {2205, 6629}, {4760, 14598}, {5967, 9417}, {7181, 9447}, {9406, 9717}
X(18023) = cevapoint of X(i) and X(j) for these (i,j): {2, 316}, {76, 3266}, {115, 9134}
X(18023) = trilinear pole of line {76, 850}
X(18023) = barycentric product X(i)*X(j) for these {i,j}: {76, 671}, {111, 1502}, {305, 17983}, {561, 897}, {670, 5466}, {850, 892}, {923, 1928}, {4609, 9178}, {6331, 14977}
X(18023) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 922}, {2, 187}, {6, 14567}, {69, 3292}, {75, 896}, {76, 524}, {99, 5467}, {111, 32}, {264, 468}, {274, 16702}, {290, 5967}, {305, 6390}, {310, 6629}, {313, 4062}, {316, 6593}, {325, 9155}, {338, 1648}, {523, 351}, {561, 14210}, {670, 5468}, {671, 6}, {691, 1576}, {693, 14419}, {850, 690}, {892, 110}, {895, 184}, {897, 31}, {923, 560}, {1236, 5181}, {1494, 9717}, {1502, 3266}, {1577, 2642}, {1920, 7267}, {1921, 4760}, {2408, 8644}, {3260, 5642}, {3261, 4750}, {3266, 2482}, {3267, 14417}, {3596, 3712}, {3978, 5026}, {5380, 692}, {5466, 512}, {5547, 2175}, {5968, 237}, {6063, 7181}, {6331, 4235}, {6385, 16741}, {7316, 1397}, {8024, 7813}, {8430, 2491}, {8753, 1974}, {9154, 1976}, {9178, 669}, {9213, 14270}, {9214, 1495}, {10097, 3049}, {10415, 3455}, {14295, 11183}, {14364, 10417}, {14618, 14273}, {14908, 14575}, {14977, 647}, {15398, 14908}, {16092, 5191}, {17948, 2502}, {17983, 25}, {18007, 9171}
X(18023) = polar conjugate of isogonal conjugate of X(30786)
X(18024) lies on the hyperbola {{A,B,C,X(2),X(69)}} and these lines: {2, 6331}, {69, 290}, {95, 6394}, {98, 689}, {237, 17984}, {287, 3978}, {305, 4609}, {306, 1978}, {307, 4572}, {1976, 14382}
X(18024) = isogonal conjugate of X(9418)
X(18024) = isotomic conjugate of X(237)
X(18024) = polar conjugate of X(2211)
X(18024) = X(325)-cross conjugate of X(76)
X(18024) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9418}, {6, 9417}, {31, 237}, {32, 1755}, {48, 2211}, {163, 2491}, {232, 9247}, {240, 14575}, {325, 1917}, {511, 560}, {798, 14966}, {1501, 1959}, {1910, 9419}, {1924, 2421}, {1933, 14251}, {1973, 3289}, {2205, 17209}, {2206, 5360}
X(18024) = cevapoint of X(i) and X(j) for these (i,j): {2, 14957}, {76, 325}, {1502, 14603}
X(18024) = trilinear pole of line {76, 525}
X(18024) = barycentric product X(i)*X(j) for these {i,j}: {76, 290}, {98, 1502}, {305, 16081}, {336, 1969}, {561, 1821}, {1910, 1928}, {2395, 4609}
X(18024) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 9417}, {2, 237}, {4, 2211}, {6, 9418}, {69, 3289}, {75, 1755}, {76, 511}, {98, 32}, {99, 14966}, {248, 14575}, {264, 232}, {287, 184}, {290, 6}, {293, 9247}, {310, 17209}, {321, 5360}, {325, 11672}, {336, 48}, {511, 9419}, {523, 2491}, {561, 1959}, {670, 2421}, {850, 3569}, {879, 3049}, {1502, 325}, {1821, 31}, {1910, 560}, {1916, 14251}, {1969, 240}, {1976, 1501}, {2395, 669}, {2422, 9426}, {2715, 14574}, {2966, 1576}, {3266, 9155}, {3267, 684}, {3404, 1923}, {4609, 2396}, {5967, 14567}, {6331, 4230}, {6394, 577}, {6531, 1974}, {14265, 1692}, {14382, 1691}, {14601, 9233}, {14603, 5976}, {14618, 17994}, {15630, 9427}, {16081, 25}, {17974, 14585}
X(18025) lies on the Steiner circumellipse and these lines: {7, 4081}, {8, 348}, {69, 144}, {75, 4569}, {85, 318}, {86, 648}, {99, 103}, {280, 6604}, {304, 341}, {319, 6606}, {337, 4562}, {350, 14727}, {658, 2968}, {666, 2338}, {903, 2400}, {911, 4586}, {1121, 3904}, {1222, 6613}, {2424, 3226}, {2966, 17731}, {4555, 15634}
X(18025) = isotomic conjugate of X(516)
X(18025) = X(i)-cross conjugate of X(j) for these (i,j): {516, 2}, {4872, 86}, {9436, 75}, {15634, 2400}
X(18025) = polar conjugate of X(1886)
X(18025) = X(314)-beth conjugate of X(4569)
X(18025) = X(43)-zayin conjugate of X(910)
X(18025) = X(i)-isoconjugate of X(j) for these (i,j): {6, 910}, {31, 516}, {48, 1886}, {55, 1456}, {213, 14953}, {513, 2426}, {667, 2398}, {676, 692}, {810, 4241}, {1333, 17747}, {1438, 9502}
X(18025) = cevapoint of X(i) and X(j) for these (i,j): {1, 7291}, {2, 516}, {8, 3912}, {103, 1815}, {2340, 3730}, {2400, 15634}
X(18025) = trilinear pole of line {2, 2400}
X(18025) = barycentric product X(i)*X(j) for these {i,j}: {76, 103}, {190, 2400}, {264, 1815}, {561, 911}, {677, 3261}, {1016, 15634}, {1978, 2424}, {2338, 6063}, {3263, 9503}
X(18025) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 910}, {2, 516}, {4, 1886}, {10, 17747}, {57, 1456}, {86, 14953}, {101, 2426}, {103, 6}, {190, 2398}, {514, 676}, {518, 9502}, {648, 4241}, {677, 101}, {911, 31}, {1815, 3}, {2338, 55}, {2398, 3234}, {2400, 514}, {2424, 649}, {9503, 105}, {15634, 1086}
X(18026) lies on the Steiner circumellipse and these lines: {4, 150}, {7, 264}, {30, 16090}, {34, 3226}, {65, 290}, {75, 342}, {76, 14257}, {85, 318}, {92, 1121}, {99, 108}, {101, 1981}, {107, 13395}, {190, 653}, {196, 7017}, {226, 1947}, {273, 903}, {278, 3227}, {286, 7282}, {324, 17483}, {329, 15466}, {348, 7952}, {458, 5228}, {527, 1948}, {648, 651}, {664, 1897}, {666, 1783}, {693, 934}, {1305, 13589}, {1415, 2966}, {1441, 1494}, {1785, 9436}, {1861, 10030}, {1880, 3228}, {2052, 5905}, {6180, 9308}
X(18026) = isogonal conjugate of X(1946)
X(18026) = isotomic conjugate of X(521)
X(18026) = anticomplement of X(35072)
X(18026) = polar conjugate of X(650)
X(18026) = X(2)-Ceva conjugate of X(39060)
X(18026) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 1946}, {43, 652}, {1754, 822}, {2947, 649}
X(18026) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7045, 6527}, {7128, 20}
X(18026) = X(9394)-complementary conjugate of X(141)
X(18026) = X(811)-Ceva conjugate of X(664)
X(18026) = X(i)-cross conjugate of X(j) for these (i,j): {521, 2}, {651, 4554}, {653, 13149}, {693, 264}, {1897, 6335}, {3868, 4564}, {4391, 85}, {4566, 664}, {5905, 1275}, {12649, 1016}, {14544, 15455}, {17496, 276}, {17896, 75}, {17924, 331}
X(18026) = cevapoint of X(i) and X(j) for these (i,j): {2, 521}, {4, 17924}, {7, 693}, {108, 651}, {226, 522}, {318, 4391}, {342, 17896}, {442, 525}, {513, 3772}, {514, 1210}, {653, 1897}
X(18026) = crosspoint of X(i) and X(j) for these (i,j): {811, 6528}
X(18026) = trilinear pole of line {2, 92}
X(18026) = pole wrt polar circle of trilinear polar of X(650) (line X(926)X(2170))
X(18026) = Brianchon point (perspector) of inscribed parabola with focus X(108)
X(18026) = crossdifference of PU(101)
X(18026) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1946}, {3, 663}, {6, 652}, {21, 810}, {31, 521}, {32, 6332}, {41, 905}, {48, 650}, {55, 1459}, {63, 3063}, {71, 7252}, {77, 8641}, {78, 667}, {101, 7117}, {108, 2638}, {109, 3270}, {184, 522}, {212, 513}, {219, 649}, {222, 657}, {228, 3737}, {283, 512}, {284, 647}, {332, 669}, {333, 3049}, {345, 1919}, {520, 2299}, {577, 3064}, {603, 3900}, {607, 4091}, {656, 2194}, {661, 2193}, {692, 7004}, {798, 1812}, {822, 1172}, {884, 1818}, {906, 2170}, {1015, 4587}, {1021, 1409}, {1331, 3271}, {1333, 8611}, {1334, 7254}, {1364, 8750}, {1436, 10397}, {1437, 4041}, {1790, 3709}, {1802, 3669}, {1803, 10581}, {1807, 8648}, {1808, 4455}, {1813, 14936}, {1980, 3718}, {2159, 14395}, {2175, 4025}, {2188, 6129}, {2196, 4435}, {2200, 4560}, {2212, 4131}, {2289, 6591}, {2318, 3733}, {2327, 7180}, {2342, 8677}, {2489, 6514}, {2605, 8606}, {3248, 4571}, {3287, 7116}, {3937, 3939}, {4105, 7053}, {4130, 7099}, {4391, 9247}, {4516, 4575}, {5075, 17973}, {6056, 7649}, {9447, 15413}, {9456, 14418}, {14331, 14642}, {14432, 14908}
X(18026) = barycentric product X(i)*X(j) for these {i,j}: {4, 4554}, {7, 6335}, {8, 13149}, {19, 4572}, {34, 1978}, {65, 6331}, {75, 653}, {76, 108}, {85, 1897}, {92, 664}, {100, 331}, {107, 1231}, {109, 1969}, {162, 349}, {190, 273}, {225, 799}, {226, 811}, {264, 651}, {278, 668}, {281, 4569}, {286, 4552}, {307, 823}, {318, 658}, {608, 6386}, {646, 1119}, {648, 1441}, {670, 1880}, {934, 7017}, {1214, 6528}, {1783, 6063}, {1826, 4625}, {1847, 3699}, {1874, 4639}, {2052, 6516}, {3261, 7012}, {4623, 8736}, {4624, 5342}, {4626, 7101}, {4998, 17924}, {6517, 6521}, {7282, 15455}
X(18026) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 652}, {2, 521}, {4, 650}, {6, 1946}, {7, 905}, {10, 8611}, {19, 663}, {25, 3063}, {27, 3737}, {28, 7252}, {29, 1021}, {30, 14395}, {33, 657}, {34, 649}, {40, 10397}, {57, 1459}, {59, 906}, {65, 647}, {73, 822}, {75, 6332}, {77, 4091}, {85, 4025}, {92, 522}, {99, 1812}, {100, 219}, {101, 212}, {107, 1172}, {108, 6}, {109, 48}, {110, 2193}, {112, 2194}, {158, 3064}, {162, 284}, {190, 78}, {196, 6129}, {225, 661}, {226, 656}, {242, 4435}, {264, 4391}, {273, 514}, {278, 513}, {281, 3900}, {286, 4560}, {314, 15411}, {331, 693}, {342, 14837}, {348, 4131}, {349, 14208}, {388, 2522}, {461, 4827}, {513, 7117}, {514, 7004}, {519, 14418}, {527, 14414}, {607, 8641}, {643, 2327}, {644, 1260}, {645, 1792}, {646, 1265}, {648, 21}, {650, 3270}, {651, 3}, {652, 2638}, {653, 1}, {655, 1807}, {658, 77}, {662, 283}, {664, 63}, {668, 345}, {765, 4587}, {799, 332}, {811, 333}, {823, 29}, {905, 1364}, {906, 6056}, {927, 1814}, {934, 222}, {1014, 7254}, {1016, 4571}, {1018, 2318}, {1020, 73}, {1025, 1818}, {1118, 6591}, {1119, 3669}, {1214, 520}, {1231, 3265}, {1275, 6516}, {1295, 2431}, {1331, 2289}, {1332, 1259}, {1395, 1919}, {1396, 3733}, {1400, 810}, {1402, 3049}, {1414, 1790}, {1415, 184}, {1426, 7180}, {1441, 525}, {1446, 17094}, {1461, 603}, {1465, 8677}, {1633, 7124}, {1783, 55}, {1784, 14400}, {1813, 255}, {1824, 3709}, {1826, 4041}, {1827, 10581}, {1847, 3676}, {1848, 17420}, {1855, 6608}, {1870, 654}, {1875, 3310}, {1876, 665}, {1877, 1635}, {1880, 512}, {1895, 14331}, {1896, 17926}, {1897, 9}, {1947, 8062}, {1978, 3718}, {1981, 1936}, {2405, 6001}, {2501, 4516}, {2635, 2637}, {2639, 2636}, {2720, 14578}, {3064, 2310}, {3261, 17880}, {3596, 15416}, {3669, 3937}, {3676, 3942}, {3699, 3692}, {3732, 1040}, {3939, 1802}, {3952, 3694}, {4033, 3710}, {4077, 4466}, {4242, 2323}, {4391, 2968}, {4551, 71}, {4552, 72}, {4554, 69}, {4559, 228}, {4561, 3719}, {4564, 1331}, {4565, 1437}, {4566, 1214}, {4569, 348}, {4572, 304}, {4573, 1444}, {4584, 1808}, {4592, 6514}, {4605, 201}, {4617, 7053}, {4620, 4592}, {4625, 17206}, {4626, 7177}, {4998, 1332}, {5089, 926}, {5236, 2254}, {5307, 17418}, {5342, 4765}, {5379, 5546}, {6063, 15413}, {6198, 9404}, {6331, 314}, {6335, 8}, {6358, 4064}, {6516, 394}, {6517, 6507}, {6591, 3271}, {6614, 7099}, {6648, 1791}, {7009, 3287}, {7012, 101}, {7017, 4397}, {7045, 1813}, {7046, 4130}, {7079, 4105}, {7101, 4163}, {7115, 692}, {7128, 109}, {7199, 17219}, {7282, 14838}, {7649, 2170}, {7952, 14298}, {8736, 4705}, {8750, 41}, {8751, 884}, {8756, 4895}, {10404, 2523}, {13136, 1809}, {13138, 268}, {13149, 7}, {14257, 6588}, {14594, 5227}, {15352, 1896}, {15742, 644}, {17896, 16596}, {17905, 11934}, {17906, 3057}, {17923, 3738}, {17924, 11}
X(18027) lies on these lines: {2, 276}, {3, 9291}, {4, 290}, {5, 264}, {68, 317}, {76, 297}, {107, 2367}, {308, 393}, {327, 1235}, {349, 1969}, {685, 2909}, {1968, 10684}, {2207, 3114}, {3767, 16081}, {6331, 7763}
X(18027) = isogonal conjugate of X(14585)
X(18027) = isotomic conjugate of X(577)
X(18027) = X(i)-cross conjugate of X(j) for these (i,j): {324, 264}, {6334, 16077}, {14618, 6528}, {15526, 850}
X(18027) = cevapoint of X(i) and X(j) for these (i,j): {2, 317}, {264, 2052}, {850, 15526}
X(18027) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14585}, {3, 9247}, {25, 4100}, {31, 577}, {32, 255}, {41, 7335}, {48, 184}, {63, 14575}, {217, 2169}, {326, 1501}, {394, 560}, {418, 2148}, {563, 2351}, {604, 6056}, {822, 1576}, {1092, 1973}, {1333, 4055}, {1397, 2289}, {1437, 2200}, {1804, 9447}, {1917, 3926}, {1974, 6507}, {2175, 7125}, {2206, 3990}, {3049, 4575}, {4020, 10547}, {7183, 9448}, {9417, 17974}
X(18027) = trilinear pole of line {850, 6368}
X(18027) = barycentric square of X(264)
X(18027) = {X(9291),X(16089)}-harmonic conjugate of X(3)
X(18027) = barycentric product X(i)*X(j) for these {i,j}: {76, 2052}, {92, 1969}, {158, 561}, {264, 264}, {276, 324}, {304, 6521}, {305, 1093}, {311, 8795}, {331, 7017}, {393, 1502}, {850, 6528}, {1096, 1928}, {3267, 15352}, {6331, 14618}, {15415, 16813}
X(18027) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 577}, {4, 184}, {5, 418}, {6, 14585}, {7, 7335}, {8, 6056}, {10, 4055}, {19, 9247}, {25, 14575}, {53, 217}, {63, 4100}, {69, 1092}, {75, 255}, {76, 394}, {85, 7125}, {92, 48}, {107, 1576}, {158, 31}, {253, 14379}, {264, 3}, {273, 603}, {275, 14533}, {276, 97}, {286, 1437}, {290, 17974}, {297, 3289}, {304, 6507}, {305, 3964}, {311, 5562}, {312, 2289}, {313, 3682}, {317, 1147}, {318, 212}, {321, 3990}, {324, 216}, {331, 222}, {338, 3269}, {339, 2972}, {342, 7114}, {393, 32}, {459, 14642}, {561, 326}, {811, 4575}, {823, 163}, {847, 2351}, {850, 520}, {1093, 25}, {1096, 560}, {1118, 1397}, {1235, 3917}, {1367, 1363}, {1502, 3926}, {1577, 822}, {1585, 8911}, {1748, 563}, {1826, 2200}, {1847, 7099}, {1857, 2175}, {1896, 2194}, {1969, 63}, {2052, 6}, {2207, 1501}, {2501, 3049}, {2973, 3937}, {3261, 4091}, {3596, 1259}, {4572, 6517}, {6059, 9448}, {6063, 1804}, {6331, 4558}, {6335, 906}, {6520, 1973}, {6521, 19}, {6524, 1974}, {6528, 110}, {6530, 237}, {6531, 14600}, {6747, 6752}, {7017, 219}, {7020, 2188}, {7068, 7065}, {7101, 1802}, {7141, 3690}, {8747, 2206}, {8794, 8882}, {8795, 54}, {11547, 571}, {13450, 51}, {14165, 50}, {14249, 154}, {14618, 647}, {15352, 112}, {15466, 15905}, {16081, 248}, {16082, 14578}, {16813, 14586}, {17858, 820}, {17907, 10316}, {17983, 14908}
X(18028) lies on the cubic K221 and this line: {1, 561}
X(18028) = isogonal conjugate of X(17956)
X(18028) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17956}, {2, 17965}
X(18028) = barycentric product X(i)*X(j) for these {i,j}: {662, 18008}, {799, 17995}
X(18028) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17956}, {31, 17965}, {17995, 661}, {18008, 1577}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27574.
X(18029) lies on these lines: {185, 9033}, {5562, 7723}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27574.
X(18030) lies on this line: {185, 10111}
X(18031) lies on the cubic K986 and these lines:
{2, 4554}, {8, 76}, {29, 811}, {75, 4712}, {85, 17451}, {105, 789}, {264, 1863}, {310, 333}, {312, 561}, {349, 6559}, {350, 14942}, {672, 10030}, {927, 1311}, {1438, 4593}, {1921, 3263}, {4572, 4858}
X(18031) = isogonal conjugate of X(9454)
X(18031) = isotomic conjugate of X(672)
X(18031) = polar conjugate of X(2356)
X(18031) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 9454}, {1740, 672}
X(18031) = X(18031) = X(i)-cross conjugate of X(j) for these (i,j): {350, 310}, {3912, 75}
X(18031) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9454}, {2, 9455}, {6, 2223}, {31, 672}, {32, 518}, {41, 1458}, {48, 2356}, {184, 5089}, {213, 3286}, {241, 2175}, {560, 3912}, {604, 2340}, {651, 8638}, {665, 692}, {667, 2284}, {926, 1415}, {1026, 1919}, {1397, 3693}, {1501, 3263}, {1818, 1973}, {1861, 9247}, {1922, 8299}, {2206, 3930}, {2210, 3252}, {2283, 3063}, {2428, 8642}, {3049, 4238}, {4447, 7104}, {9436, 9447}, {14598, 17755}
X(18031) = cevapoint of X(i) and X(j) for these (i,j): {75, 3912}, {76, 1921}
X(18031) = trilinear pole of line {75, 522}
X(18031) = barycentric product X(i)*X(j) for these {i,j}: {75, 2481}, {76, 673}, {105, 561}, {310, 13576}, {666, 3261}, {885, 4572}, {1027, 6386}, {1438, 1502}, {1814, 1969}, {6063, 14942}
X(18031) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2223}, {2, 672}, {4, 2356}, {6, 9454}, {7, 1458}, {8, 2340}, {31, 9455}, {69, 1818}, {75, 518}, {76, 3912}, {85, 241}, {86, 3286}, {92, 5089}, {105, 31}, {190, 2284}, {264, 1861}, {273, 1876}, {294, 41}, {312, 3693}, {313, 3932}, {321, 3930}, {331, 5236}, {335, 3252}, {350, 8299}, {514, 665}, {522, 926}, {561, 3263}, {663, 8638}, {664, 2283}, {666, 101}, {668, 1026}, {673, 6}, {693, 2254}, {811, 4238}, {850, 4088}, {885, 663}, {927, 109}, {1024, 3063}, {1027, 667}, {1111, 3675}, {1269, 4966}, {1416, 1397}, {1438, 32}, {1462, 604}, {1814, 48}, {1909, 4447}, {1921, 17755}, {2195, 2175}, {2481, 1}, {3261, 918}, {3263, 4712}, {3596, 3717}, {3912, 6184}, {4358, 14439}, {4554, 1025}, {4572, 883}, {4858, 17435}, {5377, 1110}, {5936, 14626}, {6063, 9436}, {6185, 1438}, {6559, 220}, {6654, 1914}, {8751, 1973}, {9436, 1362}, {9503, 911}, {10099, 810}, {13576, 42}, {14942, 55}
X(18032) lies on the cubic K986 and these lines:
{75, 1654}, {76, 4485}, {85, 11375}, {274, 1111}, {286, 2905}, {334, 3948}, {668, 4647}, {767, 2702}, {870, 17962}, {1218, 2054}, {3766, 18014}, {4623, 16709}
X(18032) = isotomic conjugate of X(1757)
X(18032) = X(i)-cross conjugate of X(j) for these (i,j): {350, 75}, {11599, 6650}
X(18032) = X(i)-isoconjugate of X(j) for these (i,j): {6, 17735}, {25, 17976}, {31, 1757}, {32, 6542}, {42, 1326}, {101, 5029}, {110, 17990}, {184, 17927}, {213, 1931}, {423, 2200}, {512, 17943}, {669, 17934}, {692, 9508}, {1576, 18004}, {1911, 8298}, {1918, 17731}, {1922, 6651}, {2206, 6541}
X(18032) = cevapoint of X(i) and X(j) for these (i,j): {1111, 3766}, {3948, 4647}
X(18032) = trilinear pole of line {693, 4359}
X(18032) = barycentric product X(i)*X(j) for these {i,j}: {75, 6650}, {76, 1929}, {274, 11599}, {304, 17982}, {310, 9278}, {561, 17962}, {799, 18014}, {873, 6543}, {1577, 17930}, {1921, 9505}, {1969, 17972}, {2054, 6385}, {4602, 18001}
X(18032) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17735}, {2, 1757}, {63, 17976}, {75, 6542}, {81, 1326}, {86, 1931}, {92, 17927}, {239, 8298}, {274, 17731}, {286, 423}, {321, 6541}, {350, 6651}, {513, 5029}, {514, 9508}, {661, 17990}, {662, 17943}, {693, 2786}, {799, 17934}, {1577, 18004}, {1929, 6}, {2054, 213}, {2702, 692}, {6543, 756}, {6650, 1}, {9278, 42}, {9505, 292}, {9506, 1911}, {11599, 37}, {17930, 662}, {17940, 163}, {17962, 31}, {17972, 48}, {17982, 19}, {18001, 798}, {18014, 661}
X(18033) lies on the cubics K865 and K986 and these lines:
{7, 871}, {75, 4073}, {76, 85}, {241, 4554}, {310, 7249}, {561, 3212}, {982, 3673}, {1088, 6384}, {1443, 4625}, {1921, 3975}, {1926, 4087}, {4059, 18021}
X(18033) = isotomic conjugate of X(7077)
X(18033) = X(i)-beth conjugate of X(j) for these (i,j): {799, 241}, {3766, 3676}, {4623, 1443}
X(18033) = X(350)-cross conjugate of X(1921)
X(18033) = X(i)-isoconjugate of X(j) for these (i,j): {8, 14598}, {9, 1922}, {31, 7077}, {32, 4876}, {41, 292}, {55, 1911}, {213, 2311}, {291, 2175}, {295, 2212}, {334, 9448}, {335, 9447}, {560, 4518}, {607, 2196}, {813, 3063}, {875, 3939}, {1927, 7081}, {1967, 2330}, {2329, 9468}, {8789, 17787}
X(18033) = X(85)-Hirst inverse of X(6063)
X(18033) = cevapoint of X(350) and X(10030)
X(18033) = X(18033) = barycentric product X(i)*X(j) for these {i,j}: {7, 1921}, {75, 10030}, {76, 1447}, {85, 350}, {239, 6063}, {279, 4087}, {310, 16609}, {561, 1429}, {670, 7212}, {812, 4572}, {1088, 3975}, {1284, 6385}, {1428, 1502}, {1431, 14603}, {1432, 1926}, {3766, 4554}, {3978, 7249}, {7205, 17493}
X(18033) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 7077}, {7, 292}, {56, 1922}, {57, 1911}, {75, 4876}, {76, 4518}, {77, 2196}, {85, 291}, {86, 2311}, {238, 41}, {239, 55}, {242, 607}, {348, 295}, {350, 9}, {385, 2330}, {604, 14598}, {659, 3063}, {664, 813}, {740, 1334}, {812, 663}, {874, 644}, {1284, 213}, {1428, 32}, {1429, 31}, {1431, 9468}, {1432, 1967}, {1434, 741}, {1447, 6}, {1874, 2333}, {1914, 2175}, {1921, 8}, {1926, 17787}, {1966, 2329}, {2201, 2212}, {2210, 9447}, {3570, 3939}, {3669, 875}, {3676, 3572}, {3684, 1253}, {3685, 220}, {3716, 657}, {3766, 650}, {3797, 4517}, {3948, 210}, {3975, 200}, {3978, 7081}, {4010, 3709}, {4037, 7064}, {4087, 346}, {4124, 14936}, {4148, 4105}, {4435, 8641}, {4495, 4390}, {4554, 660}, {4572, 4562}, {4625, 4584}, {4839, 8653}, {6063, 335}, {6654, 2195}, {7179, 3862}, {7212, 512}, {7235, 1500}, {7249, 694}, {9436, 3252}, {10030, 1}, {12835, 14599}, {14024, 2332}, {14295, 4140}, {14296, 3287}, {14599, 9448}, {16591, 5360}, {16609, 42}, {17206, 1808}, {17755, 2340}
X(18034) lies on the cubic K986 and these lines:
{334, 3948}, {335, 350}, {1921, 3263}
X(18034) = isotomic conjugate of X(9472)
X(18034) = X(76)-Ceva conjugate of X(335)
X(18034) = X(i)-isoconjugate of X(j) for these (i,j): {31, 9472}, {2113, 2210}
X(18034) = X(334)-Hirst inverse of X(17789)
X(18034) = barycentric product X(i)*X(j) for these {i,j}: {76, 9470}, {334, 17738}
X(18034) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9472}, {335, 2113}, {2112, 2210}, {8301, 1914}, {9470, 6}, {17738, 238}
X(18035) lies on the cubic K986 and these lines:
{76, 4485}, {310, 321}, {350, 740}, {874, 1281}, {4505, 4518}
X(18035) = isotomic conjugate of X(9506)
X(18035) = X(76)-Ceva conjugate of X(1921)
X(18035) = X(i)-isoconjugate of X(j) for these (i,j): {31, 9506}, {32, 9505}, {875, 2702}, {1911, 17962}, {1922, 1929}, {6650, 14598}
X(18035) = barycentric product X(i)*X(j) for these {i,j}: {76, 6651}, {561, 8298}, {1921, 6542}
X(18035) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9506}, {75, 9505}, {239, 17962}, {350, 1929}, {740, 2054}, {1757, 1911}, {1921, 6650}, {2786, 3572}, {3570, 2702}, {3948, 9278}, {4010, 18001}, {6542, 292}, {6651, 6}, {8298, 31}, {8843, 7121}, {9508, 875}, {17731, 741}, {17735, 1922}
X(18036) lies on the cubic K986 and these lines:
{76, 3496}, {314, 7261}
X(18036) = isotomic conjugate of X(17798)
X(18036) = X(350)-cross conjugate of X(76)
X(18036) = X(i)-isoconjugate of X(j) for these (i,j): {31, 17798}, {32, 3509}, {560, 4645}, {1281, 14598}, {1501, 17789}, {2175, 5018}
X(18036) = barycentric product X(i)*X(j) for these {i,j}: {76, 7261}, {561, 3512}, {1502, 8852}
X(18036) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 17798}, {75, 3509}, {76, 4645}, {85, 5018}, {313, 4071}, {561, 17789}, {1269, 4987}, {1921, 1281}, {3261, 4458}, {3512, 31}, {7061, 172}, {7261, 6}, {7281, 41}, {8852, 32}
X(18037) lies on the cubics K356 and K986 and these lines:
{69, 17788}, {71, 190}, {75, 1654}, {76, 3496}, {239, 732}, {257, 335}, {310, 333}, {321, 6653}, {350, 385}, {1086, 15985}, {1921, 3975}, {1966, 3948}, {4645, 17789}, {16696, 16706}
X(18037) = X(3975)-beth conjugate of X(6651)
X(18037) = X(76)-Ceva conjugate of X(350)
X(18037) = X(i)-isoconjugate of X(j) for these (i,j): {292, 8852}, {1911, 3512}, {1922, 7261}, {7061, 9468}
X(18037) = X(i)-Hirst inverse of X(j) for these (i,j): {1921, 3978}, {4645, 17789}
X(18037) = crosspoint of X(3509) and X(8868)
X(18037) = X(18037) = crosssum of X(3512) and X(8875)
X(18037) = barycentric product X(i)*X(j) for these {i,j}: {75, 1281}, {239, 17789}, {350, 4645}, {874, 4458}, {1921, 3509}, {4087, 5018}
X(18037) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 8852}, {239, 3512}, {350, 7261}, {1281, 1}, {1966, 7061}, {3509, 292}, {3685, 7281}, {4458, 876}, {4645, 291}, {17789, 335}, {17798, 1911}
X(18037) = {X(17738),X(17739)}-harmonic conjugate of X(3512)
X(18038) lies on the cubic K987 and these lines:
{6, 8852}, {31, 3121}, {42, 1976}, {58, 163}, {239, 16985}, {291, 825}, {1428, 1691}, {1580, 8847}, {1922, 1967}, {2210, 14602}, {4027, 16364}, {8300, 8853}
X(18038) = X(6)-Ceva conjugate of X(2210)
X(18038) = X(i)-isoconjugate of X(j) for these (i,j): {334, 3512}, {335, 7261}, {1916, 7061}
X(18038) = X(1691)-Hirst inverse of X(1914)
X(18038) = crosspoint of X(6) and X(17798)
X(18038) = crosssum of X(2) and X(7261)
X(18038) = barycentric product X(i)*X(j) for these {i,j}: {31, 1281}, {238, 17798}, {1914, 3509}, {2210, 4645}, {14599, 17789}
X(18038) = barycentric quotient X(i)/X(j) for these {i,j}: {1281, 561}, {1933, 7061}, {2210, 7261}, {14599, 3512}, {17798, 334}
At the suggestion of Seiichi Kirikami, the line H through X(5) perpendicular to the Euler line of a triangle ABC is here named the Hatzipolakis axis of ABC. In the plane of a triangle ABDC, let
L = Euler line of ABC;
H = Hatzipolakis axis of ABC;
D = L∩BC, and define E and F cyclically;
LA = L-of-AEF, and define LB and LC cyclically;
MA = H-of-AEF, and define MB and MC cyclically.
The lines MA, MB, MC concur in X(18039).
See Seiichi Kirikami and Angel Montesdeoca, Hyacinthos 27589.
The Hatzipolakis axis H is parallel to orthic axis and the De Londchamps axis; they meet in X(523). An equation for H, in barycentric coordinates, follows:
h(a,b,c) x + h(b,c,a) y + h(c,a,b) = 0, where h(a,b,c) = a2(b2c2 - (a2 - b2 - c2)2 .
H passes through X(i) for these i: 5, 523, 6757, 8151, 10287, 10288, 10412, 14254, 14356, 14566, 14592, 14670, 15475, and X(18114) - X(18122). (Peter Moses, April 27, 2018)
The isogonal conjugate of H is the circumconic with center X(11597), perspector X(50). An equation for this conic follows:
g(a,b,c) y z + g(b,c,a) z x + g(c,a,b) x y = 0, where g(a,b,c) = a4(b2c2 - (a2 - b2 - c2)2.
The conic passes through X(i) for these i: 54, 110, 10411, 14355, 14385, 14591, 17104. (Peter Moses, April 27, 2018)
X(18039) lies on these lines: {3,16171}, {4,526}, {5,523}, {1510,3521}, {5448,9033}
X(18040) lies on these lines: {1, 18044}, {10, 4022}, {75, 141}, {76, 4043}, {142, 3264}, {308, 18053}, {312, 1230}, {313, 3912}, {314, 17295}, {320, 17787}, {321, 17229}, {341, 495}, {350, 17315}, {561, 18045}, {668, 17277}, {1269, 2321}, {1909, 17289}, {3596, 17234}, {3759, 3780}, {3761, 17286}, {3765, 17279}, {3770, 17280}, {3836, 4710}, {3948, 17243}, {3975, 17263}, {4377, 17231}, {4494, 17298}, {4687, 6376}, {16709, 17303}, {17300, 17790}, {17788, 17791}, {18041, 18055}, {18042, 18047}, {18057, 18059}, {18067, 18069}
X(18041) lies on these lines: {1, 82}, {2, 17443}, {19, 662}, {48, 16568}, {63, 17471}, {75, 1953}, {192, 17444}, {561, 18051}, {1740, 2643}, {1964, 17472}, {2170, 3759}, {2171, 3758}, {2234, 17891}, {2294, 17394}, {3061, 17289}, {4053, 17363}, {4664, 17452}, {4687, 17451}, {7146, 16706}, {7202, 17364}, {18040, 18055}, {18044, 18061}, {18058, 18060}
X(18042) lies on these lines: {1, 82}, {38, 1933}, {41, 3759}, {48, 75}, {63, 2148}, {101, 17277}, {190, 572}, {192, 2278}, {239, 2174}, {284, 4360}, {584, 4393}, {604, 3758}, {894, 7113}, {897, 17891}, {922, 1582}, {1429, 16706}, {1580, 1964}, {1918, 11364}, {1953, 16568}, {1959, 17438}, {2173, 17868}, {2267, 17336}, {2268, 4664}, {2302, 11683}, {2304, 17144}, {2329, 17289}, {3204, 17349}, {3573, 8053}, {4268, 17350}, {4287, 17262}, {4687, 9310}, {8772, 17446}, {12195, 18082}, {16788, 17381}, {18040, 18047}, {18053, 18062}, {18064, 18079}
X(18043) lies on these lines: {1, 18045}, {69, 674}, {75, 7243}, {673, 2319}, {3262, 7788}, {4417, 4766}, {16284, 17294}, {18044, 18056}
X(18044) lies on these lines: {1, 18040}, {2, 313}, {75, 4494}, {76, 17289}, {190, 1423}, {273, 6335}, {308, 561}, {312, 17285}, {314, 17228}, {321, 17293}, {344, 349}, {350, 17233}, {646, 3644}, {668, 3759}, {1269, 2345}, {1909, 17381}, {3264, 4000}, {3589, 3765}, {3596, 16706}, {3662, 17790}, {3760, 4043}, {3770, 17368}, {3875, 4033}, {3912, 4150}, {3948, 17279}, {3963, 4657}, {3975, 17352}, {4110, 17160}, {4358, 17267}, {4360, 17786}, {4377, 17384}, {4389, 17787}, {6376, 17277}, {6381, 17353}, {18041, 18061}, {18043, 18056}, {18045, 18078}
X(18045) lies on these lines: {1, 18043}, {75, 3703}, {561, 18040}, {1233, 5249}, {1760, 18046}, {6063, 17234}, {18044, 18078}, {18057, 18066}
X(18046) lies on these lines: {1, 18040}, {2, 37}, {76, 17381}, {141, 17202}, {313, 17023}, {314, 17307}, {872, 17793}, {1269, 5750}, {1760, 18045}, {3264, 3946}, {3589, 3948}, {3596, 17380}, {3759, 6376}, {3963, 17045}, {4033, 4360}, {7377, 17234}, {8060, 18070}, {16709, 17398}, {17393, 17786}, {18057, 18058}
X(18047) lies on these lines: {1, 83}, {2, 9259}, {6, 9263}, {8, 8301}, {48, 17786}, {75, 4390}, {99, 813}, {100, 932}, {101, 668}, {172, 17752}, {190, 644}, {344, 3476}, {660, 3903}, {662, 4033}, {718, 8625}, {815, 835}, {894, 7200}, {1237, 14382}, {1909, 2329}, {1914, 10027}, {1958, 4110}, {1975, 4513}, {2275, 17743}, {2295, 6645}, {3759, 9457}, {3807, 4561}, {4128, 4154}, {4164, 4579}, {4551, 8707}, {4554, 4621}, {4919, 17738}, {5773, 14829}, {6224, 17233}, {6376, 9310}, {16720, 17741}, {16916, 16969}, {18040, 18042}
X(18048) lies on these lines: {2, 6}, {75, 7225}, {100, 17142}, {1078, 16574}, {1760, 18055}, {18040, 18042}
X(18049) lies on these lines: {1, 82}, {92, 304}, {662, 16545}, {2172, 16568}
X(18050) lies on these lines: {1, 18091}, {39, 75}, {257, 312}, {321, 1107}, {350, 17489}, {561, 18055}, {984, 3159}, {1237, 17451}, {4613, 16681}, {17144, 17475}
X(18051) lies on these lines: {1, 75}, {561, 18041}, {1760, 18062}, {4118, 18058}, {18060, 18069}
X(18052) lies on these lines: {1, 18057}, {2, 16707}, {75, 15523}, {76, 85}, {141, 16739}, {305, 17234}, {561, 18040}, {3720, 17149}, {18059, 18066}, {18065, 18078}
X(18053) lies on these lines: {1, 18058}, {75, 1581}, {82, 18079}, {308, 18040}, {561, 18041}, {18042, 18062}
X(18054) lies on these lines: {1, 18066}, {561, 18040}
X(18055) lies on these lines: {1, 83}, {2, 3721}, {169, 3570}, {312, 1237}, {335, 2275}, {344, 3485}, {561, 18050}, {1078, 1759}, {1760, 18048}, {1909, 3061}, {1953, 17786}, {2140, 4568}, {2243, 7793}, {2896, 4799}, {3096, 17211}, {3662, 16720}, {3670, 7786}, {3702, 17233}, {3876, 17277}, {3930, 17144}, {3954, 17030}, {4110, 17868}, {4561, 17682}, {4595, 14923}, {4950, 7785}, {6376, 17451}, {18040, 18041}
X(18056) lies on these lines: {1, 561}, {38, 3403}, {63, 1966}, {75, 16750}, {612, 1920}, {614, 1921}, {799, 1707}, {811, 1096}, {982, 4495}, {984, 7244}, {1740, 1926}, {1760, 18058}, {3305, 6376}, {3306, 6384}, {4011, 6381}, {18043, 18044}
X(18057) lies on these lines: {1, 18052}, {75, 4972}, {257, 312}, {305, 4429}, {319, 350}, {799, 6043}, {17027, 17149}, {18040, 18059}, {18043, 18044}, {18045, 18066}, {18046, 18058}
X(18058) lies on these lines:
{1, 18053}, {38, 75}, {82, 18064}, {560, 18062}, {1760, 18056}, {4118, 18051}, {6376, 17371}, {6384, 17370}, {18041, 18060}, {18046, 18057}
X(18059) lies on these lines:
{1, 561}, {2, 3121}, {42, 1920}, {75, 3873}, {81, 1966}, {310, 740}, {321, 1909}, {334, 4972}, {668, 756}, {799, 846}, {874, 4418}, {1215, 1978}, {1621, 1965}, {1921, 3720}, {2667, 6385}, {3770, 4037}, {3936, 7018}, {4038, 4495}, {4649, 7244}, {4850, 6384}, {18040, 18057}, {18052, 18066}
X(18060) lies on these lines: {1, 18062}, {75, 1581}, {18041, 18058}, {18051, 18069}
X(18061) lies on these lines: {1, 83}, {2, 3125}, {75, 4568}, {76, 3061}, {99, 17738}, {257, 3934}, {335, 1015}, {344, 5603}, {668, 2170}, {673, 4561}, {986, 7786}, {1016, 4919}, {1078, 3496}, {2087, 9263}, {2802, 4595}, {3570, 5540}, {3807, 4986}, {3944, 7790}, {4518, 14839}, {10176, 17277}, {18041, 18044}
X(18062) lies on these lines:
{1, 18060}, {75, 2640}, {304, 16563}, {560, 18058}, {662, 799}, {1760, 18051}, {4593, 18063}, {18042, 18053}
X(18063) lies on these lines: {662, 811}, {4593, 18062}
X(18064) lies on these lines: {1, 561}, {31, 799}, {38, 1966}, {82, 18058}, {92, 811}, {310, 5263}, {748, 6376}, {750, 6384}, {874, 17147}, {1920, 3920}, {1921, 7191}, {1926, 1964}, {1965, 17469}, {3891, 6382}, {4495, 17598}, {18042, 18079}
X(18064) = isotomic conjugate of isogonal conjugate of X(33760)
X(18065) lies on these lines: {1, 18040}, {76, 17286}, {313, 17284}, {344, 6381}, {1826, 3912}, {3264, 4859}, {3596, 17282}, {3662, 4494}, {3760, 17233}, {3761, 17289}, {3763, 4377}, {3875, 17786}, {3963, 17306}, {4033, 17151}, {10447, 17228}, {17274, 17787}, {17298, 17790}, {18052, 18078}, {18067, 18068}
X(18066) lies on these lines: {1, 18054}, {2, 18037}, {76, 3120}, {149, 350}, {561, 18067}, {3952, 6376}, {18045, 18057}, {18052, 18059}
X(18067) lies on these lines:
{1, 18052}, {76, 2887}, {226, 6381}, {305, 3836}, {350, 4865}, {561, 18066}, {1215, 6376}, {18040, 18069}, {18065, 18068}
X(18068) lies on these lines: {1, 561}, {9, 7244}, {57, 4495}, {92, 14210}, {799, 16570}, {1707, 1966}, {1920, 5268}, {1921, 5272}, {1926, 16571}, {3403, 17149}, {18065, 18067}
X(18069) lies on these lines:
{1, 18053}, {561, 4118}, {17149, 17445}, {18040, 18067}, {18051, 18060}
X(18070) lies on these lines: {75, 8061}, {82, 2618}, {308, 3572}, {523, 3963}, {661, 786}, {798, 812}, {1086, 4374}, {2084, 18080}, {4010, 4036}, {4079, 4129}, {4580, 7212}, {8060, 18046}, {18071, 18072}
X(18071) lies on these lines: {2, 650}, {75, 16892}, {514, 17789}, {2526, 4397}, {4106, 4391}, {18070, 18072}, {18077, 18081}
X(18072) lies on these lines: {522, 4389}, {693, 4036}, {2517, 4828}, {3261, 3596}, {18070, 18071}
X(18073) lies on these lines: {1, 18040}, {3264, 17067}, {4033, 17160}, {18070, 18071}
X(18074) lies on this line: {18070, 18071}
X(18075) lies on these lines: {1, 561}, {799, 896}, {1920, 5297}, {1921, 7292}, {1926, 2234}, {18070, 18071}
X(18076) lies on this line: {18070, 18071}
X(18077) lies on these lines: {75, 826}, {514, 1921}, {814, 7255}, {2533, 7192}, {4560, 16705}, {18071, 18081}
X(18078) lies on these lines: {1, 561}, {1920, 17022}, {1921, 2999}, {1966, 4512}, {4495, 17594}, {18044, 18045}, {18052, 18065}
X(18079) lies on these lines: {1, 75}, {82, 18053}, {560, 18058}, {18042, 18064}
X(18080) lies on these lines: {1, 10566}, {192, 513}, {514, 4079}, {786, 7199}, {2084, 18070}
X(18081) lies on these lines: {75, 2530}, {76, 514}, {693, 2533}, {812, 1019}, {2084, 18070}, {3766, 4992}, {4398, 4406}, {18071, 18077}
X(18082) lies on these lines:
{1, 18040}, {2, 16684}, {10, 82}, {12, 1284}, {42, 308}, {86, 334}, {141, 17153}, {190, 256}, {513, 894}, {528, 18101}, {560, 10791}, {594, 2238}, {740, 872}, {827, 2372}, {1010, 1224}, {1176, 15232}, {1826, 2201}, {4366, 18092}, {4972, 18090}, {5046, 17500}, {5846, 17751}, {9903, 16556}, {12195, 18042}, {15523, 17285}, {16890, 18100}, {17045, 17724}, {18004, 18010}, {18083, 18084}
X(18083) lies on these lines: {2, 18095}, {7363, 18097}, {16889, 18090}, {18082, 18084}
X(18084) lies on these lines: {1176, 15320}, {5244, 6354}, {18082, 18083}, {18088, 18089}
X(18085) lies on this line: {18082, 18083}
X(18086) lies on these lines: {83, 226}, {1334, 3975}, {5046, 17500}, {17192, 17681}
(18087) lies on these lines: {2, 16684}, {83, 226}, {673, 4599}, {1176, 15320}, {1233, 1475}, {3925, 17672}
X(18088) lies on these lines: {2, 16683}, {83, 13576}, {3112, 4388}, {3434, 18098}, {5046, 17500}, {18084, 18089}
X(18089) lies on these lines: {2, 16684}, {81, 6385}, {83, 213}, {3891, 7770}, {4972, 6656}, {18084, 18088}, {18096, 18100}
X(18090) lies on these lines: {4972, 18082}, {16889, 18083}, {16890, 18104}
X(18091) lies on these lines: {1, 18050}, {2, 16683}, {10, 82}, {384, 16689}, {904, 7018}, {2176, 18098}, {8299, 18101}, {16918, 18092}, {17685, 18100}
X(18092) lies on these lines: {2, 3613}, {6, 76}, {183, 251}, {297, 10550}, {1799, 15271}, {4366, 18082}, {10549, 17907}, {16918, 18091}
X(18092) = isogonal conjugate of X(31613)
X(18093) lies on these lines: {2, 18103}, {31, 83}, {594, 2238}, {16889, 18083}
X(18094) lies on these lines: {2, 16684}, {308, 16606}, {2295, 3589}, {16819, 17385}, {16889, 16890}, {18100, 18103}
X(18095) lies on these lines: {2, 18083}, {16889, 16890}
X(18096) lies on these lines: {2, 3613}, {16889, 18083}, {18089, 18100}
X(18097) lies on these lines: {12, 1284}, {56, 18102}, {82, 225}, {83, 226}, {308, 349}, {664, 1432}, {3669, 7176}, {5244, 6354}, {6358, 16609}, {7363, 18083}, {7557, 17500}, {18006, 18010}
X(18098) lies on these lines: {6, 3891}, {37, 82}, {81, 335}, {83, 213}, {100, 733}, {171, 649}, {292, 16717}, {594, 2238}, {756, 3294}, {894, 16707}, {2161, 4628}, {2176, 18091}, {2240, 16587}, {2295, 4972}, {3434, 18088}, {3914, 3997}, {3995, 4366}, {5244, 6354}, {17989, 17997}
X(18098) = isogonal conjugate of X(16696)
X(18098) = isotomic conjugate of X(16703)
X(18099) lies on these lines: {1, 83}, {12, 1284}, {1215, 1580}, {1237, 1966}, {4367, 6645}
X(18100) lies on these lines: {2, 18083}, {16890, 18082}, {17685, 18091}, {18089, 18096}, {18094, 18103}
X(18101) lies on these lines: {82, 17500}, {83, 13576}, {528, 18082}, {2170, 3907}, {3120, 4107}, {4124, 11988}, {8299, 18091}, {9448, 10798}, {16889, 18102}
X(18102) lies on these lines: {10, 82}, {56, 18097}, {667, 18107}, {16889, 18101}
X(18103) lies on these lines: {2, 18093}, {83, 14621}, {308, 3765}, {4366, 18082}, {18094, 18100}
X(18104) lies on these lines: {2, 16683}, {3589, 4972}, {16890, 18090}
X(18105) lies on these lines: {6, 688}, {23, 385}, {82, 876}, {251, 9178}, {512, 1691}, {689, 9150}, {691, 827}, {733, 5970}, {1176, 1510}, {1634, 4577}, {2451, 9009}, {2489, 3804}, {2492, 2514}, {2770, 9076}, {3267, 4108}, {4455, 4705}, {4630, 14560}, {14041, 18107}
X(18105) = isogonal conjugate of X(4576)
X(18106) lies on this line: {18107, 18108}
X(18107) lies on these lines: {667, 18102}, {798, 812}, {3669, 7176}, {4083, 17752}, {14041, 18105}, {18106, 18108}
X(18108) lies on these lines: {23, 385}, {171, 649}, {513, 1980}, {661, 830}, {667, 693}, {812, 8635}, {827, 1290}, {1176, 3657}, {1633, 4628}, {2752, 9076}, {3803, 6591}, {4380, 8646}, {4401, 6590}, {18106, 18107}
X(18109) lies on this line:{2, 16684}, {18106, 18107}
X(18110) lies on these lines: {2530, 17686}, {18106, 18107}
X(18111) lies on these lines: {83, 1019}, {2533, 4164}, {4367, 6645}, {7178, 10566}, {18106, 18107}
X(18112) lies on these lines: {12, 1284}, {18106, 18107}
X(18113) lies on this line:
{3120, 4107}
The Hatzipolakis axis is defined at X(18039).
Let P'1 and U'1 be the circle-{{X(2043),X(2044),PU(5)}}-inverses of PU(1). Then X(18114) = P(1)U'1∩U(1)P'1. (Randy Hutson, March 29, 2020)
X(18114) lies on these lines: {1,7136}, {2,16186}, {3,6}, {4,16237}, {5,523}, {30,15358}, {51,15329}, {54,14587}, {237,11649}, {381,15356}
X(18114) = crossdifference of every pair of points on line {50, 523}
X(18114) = X(i)-line conjugate of X(j) for these (i,j): {3, 50}, {5, 523}
X(18114) = X(i)-isoconjugate of X(j) for these (i,j): {54, 2621}, {110, 2627}
X(18114) = X(i)-Hirst inverse of X(j) for these (i,j): {5, 523}
X(18114) = barycentric product X(i)*X(j) for these {i,j}: {1577, 2626}, {2620, 14213}
X(18114) = barycentric quotient X(i)/X(j) for these {i,j}: {661, 2627}, {1953, 2621}, {2620, 2167}, {2626, 662}
X(18114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 18121, 14356), (3557, 3558, 568), (18121, 18122, 5)
X(18115) lies on these lines: {1,3}, {5,523}, {442,16186}
X(18115) = crossdifference of every pair of points on line {50, 650}
X(18116) lies on these lines: {5,523}, {44,513}
X(18116) = X(9221)-Ceva conjugate of X(11)
X(18116) = crossdifference of every pair of points on line {1, 50}
X(18116) = X(567)-zayin conjugate of X(4551)
X(18116) = barycentric product X(7951)*X(14838)
X(18116) = barycentric quotient X(7951)/X(15455)
X(18117) lies on these lines: {5,523}, {187,237}
X(18117) = reflection of X(i) in X(j) for these {i,j}: (669, 6140), (14270, 647)
X(18117) = crossdifference of every pair of points on line {2, 50}
X(18117) = crosssum of X(523) and X(14389)
X(18117) = X(662)-isoconjugate of X(7578)
X(18117) = barycentric product X(i*X(j) for these {i,j}: {523, 566}, {647, 7577}
X(18117) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 7578}, {566, 99}, {7577, 6331}
X(18118) lies on these lines: {5,523}, {241,514}
X(18118) = crosssum of X(2278) and X(9404)
X(18118) = crossdifference of every pair of points on line {50, 55}
X(18119) lies on these lines: {1,7}, {5,523}
X(18119) = crossdifference of every pair of points on line {50, 657}
X(18120) lies on these lines: {1,2}, {5,523}
X(18120) = crossdifference of every pair of points on line {50, 649}
X(18121) lies on these lines: {4,6}, {5,523}, {136,11746}, {567,14560}
X(18121) = crossdifference of every pair of points on line {50, 520}
X(18121) = PU(5)-harmonic conjugate of X(14566)
X(18122) lies on these lines: {2,6}, {5,523}, {53,16237}, {114,2854}, {297,16328}
X(18122) = midpoint of X(6033) and X(9142)
X(18122) = crossdifference of every pair of points on line {50, 512}
X(18122) = X(2)-daleth conjugate of X(3580)
X(18122) = X(9160)-complementary conjugate of X(4369)
X(18122) = barycentric product X(i)*X(j) for these {i,j}: {76, 15544}
X(18122) = barycentric quotient X(i)/X(j) for these {i,j}: {15544, 6}
X(18122) = {X(5),X(18114)}-harmonic conjugate of X(18121)
See Kadir Altintas and César Lozada, Hyacinthos 27592.
X(18123) lies on the Jerabek hyperbola and these lines: {6, 2476}, {54, 6853}, {65, 2475}, {3448, 3869}, {5080, 15232}, {8044, 17139}
X(18123) = isogonal conjugate of X(20832)
X(18123) = isotomic conjugate of anticomplement of X(2193)
See Kadir Altintas and César Lozada, Hyacinthos 27592.
X(18124) lies on the Jerabek hyperbola and these lines: {6, 5133}, {54, 1352}, {66, 7391}, {70, 511}, {74, 1286}, {1176, 1899}, {1177, 3448}, {3431, 3619}, {3564, 15317}, {7544, 14542}
X(18124) = isogonal conjugate of X(21213)
X(18124) = isotomic conjugate of anticomplement of X(10316)
See Kadir Altintas and César Lozada, Hyacinthos 27592.
X(18125) lies on the Jerabek hyperbola and these lines: {6, 3448}, {54, 542}, {66, 13203}, {67, 5189}, {74, 1287}, {125, 1176}, {1173, 9970}, {1177, 9140}, {1352, 3431}, {2781, 6145}, {2854, 13622}, {2930, 3410}, {3519, 14984}, {3818, 15102}, {5486, 11442}
X(18125) = isogonal conjugate of X(21284)
X(18125) = isotomic conjugate of anticomplement of X(10317)
X(18125) = antigonal conjugate of X(1176)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27594.
X(18126) lies on these lines: {3, 15317}, {20, 13579}, {26, 2165}, {186, 254}
X(18126) = barycentric product X(i)*X(j) for these {i,j}: {155, 13579}, {1993, 15242}, {6515, 15317}
X(18126) = barycentric quotient X(i)/X(j) for these (i,j): (1609, 7505), (15242, 5392), (15317, 6504)
X(18126) = trilinear product X(i)*X(j) for these {i,j}: {47, 15242}, {920, 15317}
X(18126) = trilinear quotient X(i)/X(j) for these (i,j): (920, 7505), (15242, 91), (15317, 921)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27594.
X(18127) lies on these lines: {50, 2070}, {186, 14731}, {6644, 14385}, {12028, 12091}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27606.
X(18128) lies on these lines: {3, 539}, {4, 15019}, {30, 11565}, {49, 14156}, {68, 7400}, {140, 542}, {184, 6640}, {389, 11819}, {511, 17712}, {548, 11264}, {550, 10112}, {569, 11457}, {575, 14864}, {974, 6146}, {1147, 3546}, {1181, 5448}, {1209, 3448}, {1503, 5462}, {1899, 3549}, {3564, 5447}, {5012, 6689}, {5446, 11245}, {5890, 11750}, {5892, 12134}, {5946, 13419}, {5965, 10627}, {6643, 15083}, {6699, 13367}, {7386, 9936}, {10114, 12041}, {10263, 11225}, {10264, 10610}, {10575, 12022}, {11442, 13336}, {12241, 14915}, {12362, 13754}, {13399, 14130}, {13403, 13491}
X(18128) = midpoint of X(i) and X(j) for these {i,j}: {3, 10116}, {548, 11264}, {550, 10112}, {10114, 12041}, {10575, 12897}, {13403, 13491}
X(18128) = {X(10575), X(12022)}-harmonic conjugate of X(12897)
See César Lozada, Hyacinthos 27607.
X(18129) lies on these lines: {32, 127}, {626, 11574}
See César Lozada, Hyacinthos 27607.
X(18130) lies on these lines: {25, 5593}, {53, 571}, {136, 216}, {6751, 8754}
X(18130) = X(5593)-of-anti-Ara triangle
X(18130) = (2nd anti-Conway)-isotomic conjugate of X(235)
See César Lozada, Hyacinthos 27607.
X(18131) lies on these lines: {226, 15497}, {1445, 15487}
As a point on the Euler line, X(18132) has Shinagawa coefficients (7*R*r+8*r^2-E-3*F, 3*R*r-3*F).
See Tran Quang Hung and César Lozada, Hyacinthos 27608.
X(18132) lies on this line: {2,3}
X(18133) lies on these lines: {2, 3770}, {6, 18046}, {9, 18044}, {10, 75}, {37, 18040}, {45, 18073}, {69, 2478}, {86, 13741}, {141, 3948}, {192, 4033}, {312, 17228}, {314, 17196}, {319, 350}, {321, 17239}, {668, 4360}, {757, 799}, {908, 17241}, {1909, 17322}, {1964, 17793}, {3644, 4110}, {3661, 4043}, {3701, 3844}, {3720, 17149}, {3731, 18065}, {3760, 17270}, {3765, 4657}, {3963, 4364}, {3975, 16706}, {4358, 17231}, {4664, 17786}, {6646, 17790}, {14994, 15991}, {17195, 17378}, {17234, 18150}, {17258, 17787}, {18072, 18158}
X(18134) lies on these lines: {1, 977}, {2, 6}, {7, 345}, {8, 3475}, {19, 8897}, {42, 4429}, {43, 3836}, {55, 4645}, {57, 3719}, {63, 320}, {75, 306}, {76, 85}, {92, 914}, {120, 3699}, {142, 3687}, {171, 3771}, {189, 1997}, {190, 5905}, {192, 3782}, {209, 3868}, {223, 7210}, {224, 5174}, {278, 664}, {286, 469}, {305, 18157}, {319, 5271}, {321, 17233}, {329, 344}, {354, 3705}, {377, 1043}, {404, 1792}, {405, 1330}, {442, 10449}, {464, 8822}, {551, 16498}, {643, 1754}, {740, 17889}, {752, 8616}, {846, 4655}, {857, 18135}, {908, 17241}, {986, 3178}, {1001, 4388}, {1086, 3210}, {1125, 16478}, {1352, 7413}, {1434, 3926}, {1621, 6327}, {1730, 3882}, {1738, 4028}, {1836, 3685}, {1848, 18156}, {1999, 3772}, {2550, 3996}, {2886, 4966}, {2893, 7522}, {2999, 17282}, {3006, 3873}, {3011, 3769}, {3060, 3909}, {3175, 17242}, {3187, 17377}, {3219, 17347}, {3262, 17862}, {3305, 17263}, {3416, 3757}, {3662, 3666}, {3695, 6147}, {3712, 11246}, {3729, 4654}, {3750, 4660}, {3752, 3834}, {3758, 5294}, {3821, 17592}, {3823, 4849}, {3824, 5295}, {3840, 17717}, {3944, 4892}, {3957, 5014}, {3966, 16823}, {4001, 17361}, {4054, 17240}, {4259, 5208}, {4384, 4886}, {4385, 13407}, {4389, 17184}, {4398, 17147}, {4415, 17243}, {4641, 17364}, {4684, 4847}, {4972, 17018}, {5256, 16706}, {5287, 17317}, {5814, 16817}, {6505, 17923}, {6626, 16349}, {7081, 17718}, {7262, 17770}, {7377, 10478}, {8728, 9534}, {10371, 16824}, {11679, 17296}, {16787, 17023}, {16826, 16974}, {17011, 17380}, {17312, 17720}, {17336, 17781}, {17715, 17766}
X(18134) = complement of X(37652)
X(18135) lies on these lines: {1, 6381}, {2, 39}, {6, 17541}, {7, 2899}, {8, 350}, {10, 3760}, {21, 183}, {32, 16920}, {69, 2478}, {75, 3701}, {85, 5226}, {86, 5192}, {99, 4188}, {141, 17550}, {145, 668}, {192, 1921}, {264, 4194}, {279, 4554}, {304, 4358}, {308, 941}, {313, 17321}, {314, 5232}, {315, 5046}, {325, 4193}, {331, 6335}, {344, 349}, {348, 1997}, {384, 16997}, {385, 16916}, {404, 1975}, {406, 1235}, {452, 15589}, {497, 18057}, {857, 18134}, {1007, 6931}, {1078, 4189}, {1125, 3761}, {1278, 10009}, {1909, 3616}, {2176, 4465}, {2295, 4713}, {2475, 11185}, {3161, 10030}, {3214, 3875}, {3263, 3673}, {3314, 17669}, {3403, 17261}, {3596, 3672}, {3617, 17143}, {3618, 18046}, {3619, 18137}, {3691, 17026}, {3718, 17863}, {3734, 5277}, {3785, 6872}, {3933, 4187}, {3975, 5222}, {3992, 7264}, {4044, 17308}, {4396, 4426}, {4410, 4798}, {4419, 17790}, {4648, 18144}, {4721, 17750}, {5047, 16992}, {5051, 5224}, {5154, 7752}, {5275, 17686}, {5276, 7770}, {5305, 17540}, {5712, 18052}, {6337, 6921}, {6390, 13747}, {7750, 11114}, {7751, 17002}, {7767, 11113}, {7771, 17548}, {7776, 17556}, {7793, 17692}, {14907, 15680}, {16915, 16999}, {16918, 16998}, {17777, 18066}
X(18136) lies on these lines: {2, 3770}, {63, 18044}, {76, 16739}, {81, 18046}, {141, 312}, {321, 17237}, {333, 17681}, {341, 4202}, {940, 18148}, {2185, 18048}, {4033, 17147}, {8033, 18140}, {17027, 17149}, {18139, 18150}
X(18137) lies on these lines: {2, 37}, {76, 17234}, {141, 3948}, {142, 1269}, {190, 16574}, {239, 16685}, {313, 3912}, {314, 17277}, {319, 3975}, {341, 10449}, {392, 4673}, {518, 3701}, {668, 17295}, {740, 3216}, {984, 4075}, {1230, 18139}, {1909, 17317}, {1921, 18050}, {2300, 3759}, {2321, 3264}, {3230, 17144}, {3250, 18080}, {3596, 4033}, {3619, 18135}, {3685, 5132}, {3696, 3702}, {3760, 17282}, {3765, 4851}, {3770, 17300}, {3840, 4022}, {3963, 17243}, {4417, 14615}, {4676, 5156}, {4828, 18154}, {6376, 17228}, {6385, 18138}, {7283, 16453}, {13476, 17165}, {15668, 16709}, {17232, 18144}, {17240, 17786}, {17284, 18044}, {17307, 18140}, {17788, 18151}
X(18138) lies on these lines: {2, 16703}, {42, 75}, {76, 85}, {210, 3263}, {305, 4417}, {314, 14828}, {1215, 1930}, {2887, 18057}, {3266, 5741}, {3475, 4441}, {3936, 8024}, {6385, 18137}
X(18139) lies on these lines: {1, 4202}, {2, 6}, {7, 17776}, {8, 8728}, {37, 17184}, {42, 3836}, {51, 3909}, {63, 17298}, {75, 3969}, {92, 2973}, {100, 16056}, {142, 306}, {190, 17483}, {226, 4358}, {264, 445}, {312, 17241}, {320, 3219}, {321, 1930}, {344, 5905}, {354, 3006}, {386, 17674}, {553, 3977}, {750, 3771}, {1001, 6327}, {1086, 17147}, {1230, 18137}, {1330, 5047}, {1621, 4450}, {1738, 3896}, {1962, 3821}, {1999, 17312}, {2321, 4980}, {2325, 3982}, {2887, 3720}, {3187, 4851}, {3475, 10327}, {3616, 13728}, {3664, 5294}, {3666, 3834}, {3701, 13407}, {3702, 12609}, {3703, 17140}, {3782, 3995}, {3826, 4651}, {3873, 4260}, {3925, 4966}, {3932, 17165}, {3933, 17169}, {4197, 10449}, {4340, 17526}, {4388, 5284}, {4427, 11246}, {4429, 17018}, {4442, 17889}, {4641, 17376}, {4884, 17154}, {5256, 17282}, {5271, 17296}, {8024, 18052}, {9776, 17740}, {16706, 17011}, {16752, 17670}, {17019, 17317}, {17174, 18046}, {18136, 18150}
X(18139) = complement of X(19742)
X(18140) lies on these lines: {1, 668}, {2, 39}, {10, 350}, {21, 1078}, {32, 16916}, {37, 308}, {69, 5084}, {75, 1089}, {83, 5276}, {85, 4554}, {86, 13741}, {99, 404}, {148, 17565}, {183, 405}, {187, 17692}, {190, 16549}, {192, 10009}, {264, 406}, {286, 5142}, {304, 17284}, {312, 17308}, {313, 17322}, {314, 5224}, {315, 2478}, {316, 5046}, {325, 4187}, {377, 11185}, {384, 5277}, {385, 16918}, {451, 1235}, {452, 3785}, {474, 1975}, {626, 17669}, {646, 4664}, {799, 1509}, {894, 4721}, {940, 11353}, {1125, 1909}, {1574, 17759}, {1577, 18077}, {1961, 1965}, {1969, 6335}, {2238, 17034}, {2295, 4465}, {2896, 17685}, {3096, 17550}, {3230, 17752}, {3247, 17786}, {3264, 17320}, {3293, 4360}, {3403, 3731}, {3570, 4251}, {3596, 17321}, {3624, 3761}, {3679, 17144}, {3734, 16915}, {3765, 17397}, {3770, 17398}, {3831, 4357}, {3875, 6048}, {3912, 4109}, {3931, 4087}, {3933, 17527}, {3952, 17141}, {3972, 16920}, {3975, 17023}, {4188, 7782}, {4189, 7771}, {4193, 7752}, {4358, 17292}, {4364, 17790}, {4441, 9780}, {4482, 9327}, {4687, 18044}, {5129, 15589}, {5209, 6626}, {5254, 17670}, {5275, 7770}, {5284, 18064}, {6179, 17001}, {6337, 17567}, {6872, 14907}, {7750, 11113}, {7751, 16998}, {7773, 17556}, {7787, 16995}, {7789, 17694}, {7792, 17540}, {7793, 16914}, {7802, 11114}, {7815, 17684}, {7816, 17693}, {8033, 18136}, {11108, 16992}, {14296, 14431}, {15031, 17577}, {15668, 18144}, {16917, 17128}, {17000, 17129}, {17048, 17755}, {17234, 17671}, {17277, 18046}, {17283, 18157}, {17307, 18137}, {17451, 18061}
X(18141) lies on these lines: {2, 6}, {7, 312}, {8, 354}, {57, 345}, {58, 13742}, {63, 344}, {75, 9776}, {142, 11679}, {145, 17597}, {190, 9965}, {200, 4684}, {226, 17298}, {306, 3306}, {320, 329}, {443, 10449}, {487, 16433}, {488, 16432}, {497, 4645}, {553, 3729}, {908, 1997}, {938, 7270}, {980, 16043}, {1043, 6904}, {1265, 3868}, {1330, 5084}, {1376, 4966}, {1445, 3719}, {1999, 4000}, {2094, 17264}, {2550, 10453}, {2999, 3879}, {3210, 3726}, {3218, 17776}, {3305, 4001}, {3416, 3742}, {3474, 3685}, {3475, 7081}, {3616, 3745}, {3666, 17316}, {3687, 5437}, {3695, 5708}, {3703, 4860}, {3752, 4851}, {3772, 3834}, {3785, 11343}, {3819, 10477}, {3873, 10327}, {3883, 10582}, {4035, 6692}, {4188, 5347}, {4340, 13740}, {4357, 17022}, {4358, 5905}, {4387, 11246}, {4415, 7232}, {4416, 7308}, {4514, 10580}, {4656, 17274}, {5272, 5847}, {5287, 17321}, {5308, 17137}, {5324, 16048}, {5337, 14001}, {5744, 17241}, {5918, 9801}, {6542, 17490}, {6776, 16434}, {6862, 11487}, {6890, 12324}, {6958, 11411}, {7172, 11038}, {7195, 17789}, {9534, 17582}, {10452, 18229}, {16602, 17374}, {18135, 18136}
X(18141) = anticomplement of X(37679)
X(18142) lies on these lines: {2, 16708}, {75, 210}, {76, 2051}, {85, 5226}, {226, 18045}, {908, 1233}, {1699, 18043}, {6385, 18137}, {17234, 18153}
X(18143) lies on these lines: {2, 3770}, {75, 141}, {76, 17234}, {86, 18046}, {142, 313}, {274, 17307}, {308, 3572}, {310, 18052}, {312, 17241}, {314, 17297}, {321, 17231}, {341, 8728}, {350, 17317}, {662, 18048}, {1269, 3912}, {1909, 16706}, {3761, 17282}, {3765, 17278}, {3823, 4696}, {3844, 4968}, {3948, 17245}, {4359, 17239}, {4410, 17357}, {4553, 17142}, {4648, 18147}, {4751, 6376}, {7321, 17787}, {8024, 16708}, {10436, 18044}, {17143, 17295}, {17144, 17386}
X(18144) lies on these lines: {2, 3770}, {7, 17790}, {75, 4377}, {76, 141}, {142, 6381}, {192, 18040}, {274, 17327}, {312, 17231}, {313, 3662}, {314, 599}, {321, 17228}, {341, 3823}, {350, 4851}, {513, 7155}, {536, 17786}, {668, 4361}, {894, 18044}, {1086, 3596}, {1269, 3661}, {1278, 4033}, {1909, 4657}, {2228, 17157}, {2278, 18048}, {3729, 18065}, {3739, 6376}, {3760, 17296}, {3761, 17306}, {3765, 16706}, {3844, 4385}, {3948, 17234}, {3963, 4389}, {3975, 17278}, {4043, 17230}, {4110, 4686}, {4112, 18209}, {4358, 17241}, {4410, 17385}, {4445, 17143}, {4494, 4862}, {4648, 18135}, {6383, 6386}, {9464, 16727}, {15668, 18140}, {17144, 17372}, {17232, 18137}, {17276, 17787}, {17300, 18147}, {17313, 18145}, {17379, 18046}, {17788, 18159}
X(18145) lies on these lines: {2, 39}, {75, 3992}, {99, 13587}, {183, 16370}, {313, 17320}, {314, 17196}, {325, 17533}, {350, 519}, {536, 1921}, {545, 17790}, {551, 1909}, {1078, 17549}, {1577, 4960}, {1975, 16371}, {3679, 3760}, {3734, 16997}, {3972, 17001}, {4193, 7796}, {4358, 4945}, {4554, 17078}, {4677, 17144}, {4740, 10009}, {5046, 7768}, {5154, 7814}, {5277, 17128}, {6179, 16920}, {7751, 16916}, {7760, 17541}, {7780, 17692}, {7788, 17556}, {7794, 17669}, {7811, 11114}, {14210, 18159}, {16857, 16992}, {16915, 17130}, {16998, 17131}, {17313, 18144}, {17342, 18044}, {17378, 18147}
X(18146) lies on these lines: {2, 39}, {10, 4479}, {75, 3828}, {99, 16371}, {183, 16418}, {350, 3679}, {519, 6376}, {536, 10009}, {551, 6381}, {668, 3241}, {1078, 16370}, {1921, 4664}, {1975, 16417}, {2478, 7768}, {3596, 17320}, {3734, 16999}, {3972, 16997}, {4187, 7796}, {4193, 7814}, {4554, 17079}, {4669, 17144}, {5046, 7860}, {6179, 16916}, {7751, 16918}, {7752, 17533}, {7771, 17549}, {7780, 16914}, {7782, 13587}, {7804, 16995}, {7809, 17556}, {7811, 11113}, {7854, 17685}, {7856, 17540}, {7878, 17541}, {7922, 17669}, {11057, 11114}, {16917, 17130}, {16992, 17542}, {17000, 17131}, {17195, 17378}, {17271, 18147}
X(18147) lies on these lines: {1, 313}, {2, 37}, {6, 3948}, {29, 264}, {69, 2478}, {76, 86}, {190, 579}, {239, 16520}, {286, 469}, {314, 5224}, {319, 5722}, {320, 18148}, {326, 1226}, {341, 387}, {386, 3596}, {668, 17377}, {1100, 3765}, {1228, 5192}, {1234, 5736}, {1269, 3760}, {1333, 11320}, {1441, 11375}, {1909, 17394}, {3216, 3264}, {3718, 5292}, {3723, 4377}, {3759, 3975}, {3770, 17379}, {3879, 6381}, {3912, 4150}, {3963, 16777}, {4033, 17314}, {4044, 5750}, {4286, 17262}, {4648, 18143}, {4869, 18150}, {5165, 17350}, {5564, 9534}, {14615, 18153}, {17160, 17749}, {17271, 18146}, {17300, 18144}, {17315, 17786}, {17316, 18040}, {17378, 18145}
X(18148) lies on these lines: {2, 330}, {38, 1237}, {75, 3670}, {76, 16887}, {86, 13741}, {313, 3831}, {320, 18147}, {350, 17137}, {668, 3216}, {940, 18136}, {986, 4485}, {1966, 16574}, {3721, 18050}, {3760, 17274}, {4261, 17786}, {10449, 17144}
X(18149) lies on these lines: {2, 3121}, {11, 334}, {75, 244}, {312, 335}, {693, 18066}, {874, 1054}, {1920, 3840}, {1921, 4871}, {3226, 17477}, {3766, 4927}, {4728, 18150}, {5718, 6376}, {6382, 17063}, {7033, 17597}
X(18150) lies on these lines: {2, 16723}, {75, 141}, {312, 4080}, {646, 903}, {3762, 18151}, {4043, 17231}, {4417, 14554}, {4728, 18149}, {4869, 18147}, {6376, 17758}, {16709, 17307}, {17232, 18137}, {17234, 18133}, {17298, 18044}, {17300, 18046}, {17790, 18073}, {18136, 18139}
X(18151) lies on these lines: {2, 16732}, {9, 75}, {92, 4997}, {239, 17796}, {312, 3969}, {319, 1229}, {322, 17240}, {645, 14616}, {765, 1090}, {1121, 16284}, {1441, 17263}, {2607, 5150}, {3262, 17264}, {3673, 7827}, {3762, 18150}, {3912, 17791}, {4422, 4957}, {6996, 16568}, {17352, 17861}, {17788, 18137}
X(18152) lies on these lines: {2, 39}, {32, 16955}, {42, 308}, {43, 3760}, {69, 6818}, {75, 756}, {99, 4210}, {183, 1011}, {264, 4207}, {312, 561}, {321, 1921}, {385, 16957}, {668, 17135}, {799, 14829}, {870, 5311}, {1078, 4184}, {1235, 4213}, {1240, 2296}, {1255, 17032}, {1909, 3720}, {1920, 4358}, {1965, 17763}, {1975, 4191}, {3596, 4441}, {3734, 16954}, {3741, 6381}, {3765, 17027}, {3972, 16959}, {4651, 17143}, {4671, 6382}, {5226, 6063}, {6385, 18137}, {16956, 17128}
X(18153) lies on these lines: {2, 39}, {75, 4082}, {183, 13615}, {200, 350}, {264, 461}, {1909, 10582}, {1997, 4554}, {3760, 8580}, {4847, 6376}, {6381, 11019}, {14615, 18147}, {17234, 18142}
X(18154) lies on these lines: {2, 650}, {75, 4024}, {661, 7199}, {850, 4789}, {1019, 1577}, {2517, 7662}, {3261, 6590}, {3700, 4374}, {4057, 4874}, {4359, 17161}, {4811, 7659}, {4815, 4913}, {4828, 18137}, {9534, 14077}
X(18155) lies on these lines: {2, 16751}, {75, 850}, {85, 17094}, {99, 2222}, {312, 3700}, {320, 350}, {333, 1021}, {522, 4087}, {643, 799}, {650, 3975}, {811, 1414}, {812, 18071}, {814, 7255}, {1019, 1577}, {2787, 7234}, {3004, 3766}, {3261, 4025}, {3676, 18033}, {3716, 3737}, {3733, 4874}, {3835, 4481}, {4036, 9508}, {4086, 4913}, {4170, 5216}, {4374, 4897}, {4960, 4978}, {7203, 17218}, {14208, 18160}, {16754, 17496}, {18070, 18106}
X(18155) = isotomic conjugate of X(4551)
X(18156) lies on these lines: {1, 75}, {2, 16605}, {19, 2128}, {34, 664}, {47, 4592}, {69, 960}, {85, 350}, {92, 18056}, {145, 3263}, {158, 811}, {192, 7187}, {239, 16781}, {312, 1909}, {320, 17170}, {330, 3797}, {344, 1212}, {491, 14121}, {492, 7090}, {662, 1973}, {742, 16969}, {1848, 18134}, {1959, 6508}, {1975, 3685}, {3061, 3452}, {3633, 4986}, {3718, 3879}, {3759, 16502}, {3760, 4975}, {3761, 7278}, {3811, 4561}, {3877, 17137}, {3889, 17141}, {3890, 17152}, {6337, 17081}, {6384, 7146}, {12514, 17206}, {16503, 16822}, {16524, 16827}, {17336, 17742}, {17442, 18041}, {18049, 18058}
X(18156) = isogonal conjugate of X(38252)
X(18156) = cevapoint of X(1) and X(2128)
X(18156) = anticomplement of X(16605)
X(18156) = {[trilinear product of PU(116)],[trilinear product of PU(117)]}-harmonic conjugate of X(75)
X(18157) lies on these lines: {1, 75}, {2, 16703}, {37, 16705}, {38, 17208}, {76, 17234}, {85, 6385}, {99, 2725}, {241, 16728}, {305, 18134}, {310, 312}, {321, 16748}, {514, 1921}, {518, 3263}, {536, 16711}, {537, 17179}, {726, 17205}, {984, 16887}, {1434, 2285}, {2887, 17203}, {3006, 17198}, {3266, 3936}, {3739, 17497}, {3842, 17210}, {4358, 16727}, {4564, 4601}, {4639, 17789}, {4664, 16712}, {4751, 16611}, {5233, 11059}, {8024, 18052}, {8025, 16707}, {13476, 17141}, {16704, 16741}, {16891, 18057}, {17283, 18140}, {17755, 18206}
X(18157) = isotomic conjugate of X(18785)
X(18158) lies on these lines: {2, 16755}, {75, 4036}, {76, 3261}, {522, 5224}, {1577, 4960}, {4140, 4664}, {4828, 15413}, {18072, 18133}
X(18159) lies on these lines: {2, 7200}, {12, 85}, {75, 537}, {76, 4485}, {80, 17361}, {150, 320}, {350, 4742}, {514, 18061}, {1909, 5484}, {2481, 3680}, {3570, 9317}, {3753, 7321}, {3762, 18150}, {3766, 4927}, {4919, 6631}, {9318, 18047}, {14210, 18145}, {17788, 18144}
X(18160) lies on these lines: {2, 15419}, {69, 7253}, {75, 4086}, {86, 8062}, {190, 4529}, {656, 5224}, {693, 4806}, {799, 4590}, {816, 8632}, {918, 3261}, {1577, 4960}, {2517, 4406}, {3762, 4509}, {4036, 4374}, {4171, 17233}, {4625, 15455}, {5641, 14616}, {6002, 18077}, {6003, 18076}, {7799, 14838}, {14208, 18155}
X(18161) lies on these lines: {1, 159}, {6, 2114}, {7, 1953}, {19, 77}, {48, 1442}, {57, 2164}, {69, 1959}, {86, 423}, {141, 3061}, {189, 6508}, {241, 2262}, {320, 18041}, {394, 1762}, {982, 18168}, {984, 8679}, {986, 16696}, {1423, 8609}, {1565, 16608}, {1633, 4336}, {1726, 2003}, {2170, 4000}, {2171, 4644}, {2294, 3945}, {2323, 16551}, {3056, 17447}, {3879, 9028}, {4051, 4361}, {4419, 17452}, {4475, 7032}, {4648, 17451}, {4675, 17443}, {5845, 17390}, {5902, 18164}, {7087, 17716}, {7119, 7210}, {7201, 17365}, {7204, 8608}, {8680, 10446}, {14963, 17052}, {17170, 17442}, {17197, 17861}, {17276, 17444}, {17592, 18185}, {18194, 18208}
X(18162) lies on these lines: {1, 159}, {6, 1423}, {7, 48}, {19, 7190}, {37, 16560}, {41, 4000}, {57, 2178}, {101, 142}, {141, 2329}, {144, 2267}, {171, 18209}, {198, 5228}, {222, 8761}, {284, 3663}, {320, 18042}, {527, 572}, {584, 17301}, {604, 4644}, {610, 4328}, {651, 2317}, {662, 7321}, {692, 9440}, {1086, 2174}, {1442, 3942}, {1565, 17043}, {1633, 2293}, {1953, 7269}, {2187, 3475}, {2261, 8545}, {2266, 3598}, {2268, 4419}, {2278, 17276}, {2304, 17753}, {3204, 17278}, {3423, 10934}, {3684, 4361}, {3946, 4251}, {4073, 16799}, {4357, 9028}, {4648, 9310}, {4649, 8679}, {5563, 18164}, {5845, 16503}, {7113, 7175}, {7119, 7247}, {9441, 15624}, {16788, 17306}, {17787, 18048}
X(18163) lies on these lines: {1, 859}, {2, 3882}, {6, 1764}, {9, 312}, {21, 1697}, {40, 58}, {55, 17194}, {57, 77}, {63, 3187}, {86, 5437}, {165, 3286}, {239, 16722}, {940, 1730}, {1010, 1706}, {1043, 2136}, {1334, 5325}, {1396, 8829}, {1420, 4225}, {2170, 16579}, {2185, 4612}, {2193, 10319}, {2257, 4269}, {2269, 5745}, {2270, 2303}, {2328, 5324}, {2347, 3452}, {3158, 3794}, {3243, 5208}, {3306, 8025}, {3333, 4658}, {3576, 4276}, {3666, 18177}, {3750, 18174}, {3928, 9311}, {3929, 4921}, {4281, 10476}, {4516, 17611}, {4603, 6654}, {5219, 17167}, {5235, 7308}, {5535, 9275}, {5802, 14552}, {6762, 10461}, {8056, 16736}, {9580, 14956}, {14010, 15845}, {14936, 16721}, {17594, 18169}, {17596, 18192}
X(18164) lies on these lines: {1, 3286}, {6, 16726}, {7, 17197}, {9, 86}, {21, 10390}, {40, 4658}, {57, 77}, {58, 2191}, {63, 8025}, {65, 18177}, {142, 1475}, {165, 18185}, {239, 16710}, {314, 4659}, {333, 5437}, {354, 17194}, {527, 17183}, {579, 3945}, {583, 17392}, {738, 1434}, {757, 2150}, {876, 13610}, {894, 17178}, {940, 5120}, {942, 18176}, {1010, 6762}, {1018, 17390}, {1400, 4667}, {1437, 3338}, {2257, 17189}, {2260, 3664}, {2999, 16700}, {3158, 13588}, {3306, 16704}, {3339, 18178}, {3361, 4267}, {3928, 17185}, {3946, 17474}, {4000, 17205}, {4184, 10389}, {4253, 4648}, {4384, 16709}, {4654, 17167}, {4851, 16549}, {4860, 18191}, {5228, 7053}, {5333, 7308}, {5563, 18162}, {5902, 18161}, {10436, 16738}, {10980, 18165}, {15668, 16552}, {16574, 17379}, {16723, 17313}, {16887, 17306}, {17202, 17274}, {17296, 17754}
X(18165) lies on these lines: {1, 859}, {2, 4259}, {11, 17167}, {21, 65}, {25, 940}, {27, 243}, {28, 1905}, {29, 1875}, {37, 4269}, {46, 17524}, {51, 5718}, {57, 3286}, {58, 942}, {81, 105}, {86, 1431}, {171, 1283}, {181, 6690}, {210, 5235}, {244, 16700}, {284, 910}, {333, 518}, {511, 17056}, {517, 4653}, {958, 10461}, {960, 11110}, {982, 16696}, {1001, 10473}, {1010, 3812}, {1043, 5836}, {1155, 4184}, {1412, 3660}, {1730, 5132}, {1755, 2294}, {1817, 17603}, {1836, 14956}, {1887, 3559}, {2245, 8731}, {2328, 5173}, {2360, 16193}, {2646, 4225}, {3666, 4215}, {3736, 3752}, {3740, 3786}, {3784, 4675}, {3816, 17182}, {3819, 17245}, {3838, 14009}, {3869, 17588}, {3873, 16704}, {3924, 10457}, {4224, 5135}, {4229, 10178}, {4650, 5902}, {4658, 5045}, {5737, 10477}, {6675, 10974}, {7195, 17169}, {7289, 18166}, {7290, 11021}, {9335, 16753}, {10980, 18164}, {11019, 17197}, {11680, 17173}, {14008, 17605}, {16699, 17451}, {16736, 17063}, {18175, 18181}
X(18166) lies on these lines: {1, 3286}, {2, 6}, {37, 18206}, {58, 1001}, {110, 9110}, {171, 18185}, {239, 16709}, {274, 4361}, {314, 4363}, {320, 17202}, {354, 18182}, {894, 4043}, {942, 18179}, {1014, 5228}, {1100, 16726}, {2295, 17390}, {2663, 4557}, {2667, 4436}, {2999, 16736}, {3293, 4649}, {3664, 17197}, {3736, 3913}, {3739, 17175}, {3946, 17205}, {4000, 17169}, {4038, 18169}, {4057, 18196}, {4393, 16710}, {4644, 17183}, {4653, 11194}, {4657, 16887}, {4670, 10455}, {4833, 18199}, {4851, 17750}, {4852, 16971}, {5256, 16700}, {7289, 18165}, {16685, 17394}, {16705, 17045}, {16752, 17366}, {16753, 17012}, {17139, 17365}, {17179, 17382}
X(18167) lies on these lines: {1, 16681}, {81, 18182}, {257, 274}, {626, 3118}, {762, 4469}, {982, 18171}, {1437, 18187}, {2085, 4118}, {3670, 16696}, {3721, 16887}, {3735, 16705}, {3953, 18172}, {3981, 17203}, {18168, 18195}, {18175, 18203}
X(18167) = isotomic conjugate of isogonal conjugate of X(16717)
X(18168) lies on these lines: {1, 2916}, {6, 18207}, {75, 4475}, {982, 18161}, {3554, 18193}, {3662, 4118}, {4389, 17470}, {4443, 17447}, {7202, 18194}, {7237, 17227}, {7263, 17891}, {16696, 18190}, {18167, 18195}
X(18169) lies on these lines: {1, 21}, {2, 5145}, {42, 16704}, {43, 333}, {86, 87}, {171, 3286}, {261, 1178}, {572, 5276}, {741, 1961}, {873, 17175}, {940, 16058}, {980, 11328}, {982, 16696}, {986, 18180}, {1019, 8027}, {1054, 8849}, {1107, 1197}, {1185, 16552}, {1201, 17588}, {1613, 5283}, {2185, 5009}, {2267, 2303}, {2309, 3741}, {3120, 17173}, {3216, 5278}, {3550, 4184}, {3666, 18191}, {3720, 4368}, {3737, 4448}, {3742, 16726}, {3750, 18185}, {3944, 17167}, {4038, 18166}, {4425, 17202}, {5235, 16569}, {5255, 17524}, {10459, 11115}, {10980, 18186}, {13323, 13732}, {15569, 18211}, {16700, 17063}, {17594, 18163}, {17600, 18170}, {18182, 18204}, {18190, 18203}
X(18170) lies on these lines: {1, 6}, {36, 8266}, {75, 7032}, {82, 7122}, {86, 670}, {87, 4363}, {171, 16679}, {183, 614}, {239, 1964}, {308, 1909}, {330, 8264}, {385, 7191}, {571, 10801}, {612, 11174}, {869, 3759}, {872, 17121}, {894, 3248}, {982, 18161}, {1015, 17049}, {1045, 4852}, {1086, 7184}, {1333, 12194}, {1429, 18209}, {1582, 7113}, {1740, 4361}, {2170, 17446}, {2174, 8300}, {2210, 18042}, {2220, 11364}, {2234, 17117}, {2275, 4446}, {2309, 4360}, {2664, 17348}, {3009, 17277}, {3056, 4443}, {3329, 3920}, {3661, 7189}, {3770, 12263}, {3783, 17362}, {5019, 10800}, {5069, 12782}, {5201, 5563}, {5272, 15271}, {7202, 18183}, {7766, 17024}, {9359, 17351}, {10802, 13345}, {16571, 17119}, {16696, 18205}, {17600, 18169}
X(18171) lies on these lines: {1, 3286}, {32, 81}, {86, 5283}, {194, 17178}, {213, 4641}, {274, 330}, {982, 18167}, {1015, 16705}, {1107, 16726}, {2275, 16887}, {3670, 18184}, {4384, 16700}, {16604, 17210}, {16709, 16819}, {16736, 16832}, {16753, 16815}, {17050, 17205}
X(18172) lies on these lines: {1, 3286}, {81, 172}, {86, 1107}, {239, 16700}, {274, 670}, {330, 17178}, {980, 3053}, {982, 18189}, {1015, 16744}, {2176, 18206}, {3953, 18167}, {3976, 18176}, {4384, 16736}, {16746, 17208}, {16753, 16816}, {16975, 17175}, {18178, 18205}
X(18173) lies on these lines: {1, 994}, {43, 5208}, {244, 16753}, {667, 18197}, {982, 16696}, {1647, 17174}, {3286, 18201}, {3976, 18180}, {3999, 18191}, {10458, 17591}, {16704, 17449}, {17194, 18193}
X(18174) lies on these lines: {1, 18191}, {171, 17194}, {354, 18192}, {982, 16696}, {3750, 18163}, {10458, 17592}, {16497, 18206}, {16753, 17063}
X(18175) lies on these lines: {81, 18210}, {982, 18177}, {18165, 18181}, {18167, 18203}
X(18176) lies on these lines: {1, 16680}, {81, 16787}, {942, 18164}, {982, 18167}, {986, 16696}, {3061, 16887}, {3501, 16728}, {3673, 17197}, {3976, 18172}, {7146, 18206}, {16708, 17050}, {17046, 17177}, {17169, 17451}, {18192, 18208}
X(18177) lies on these lines: {65, 18164}, {75, 17197}, {81, 16947}, {982, 18175}, {986, 16696}, {2170, 16713}, {3666, 18163}, {17183, 17452}, {18184, 18186}
X(18178) lies on these lines: {1, 859}, {4, 5820}, {6, 10441}, {10, 4553}, {12, 17167}, {21, 643}, {40, 3286}, {58, 517}, {65, 81}, {86, 3812}, {284, 501}, {314, 3714}, {333, 960}, {387, 4259}, {511, 1834}, {524, 10381}, {958, 10480}, {986, 16696}, {1010, 5836}, {1043, 3794}, {1071, 2831}, {1108, 4269}, {1319, 4225}, {1329, 17182}, {1385, 4276}, {1682, 4999}, {1697, 17194}, {2170, 16699}, {2194, 3193}, {2262, 2303}, {2551, 17183}, {3339, 18164}, {3579, 4278}, {3698, 14005}, {3736, 4646}, {3786, 4662}, {3869, 16704}, {3890, 17588}, {3893, 4720}, {3959, 16716}, {4256, 5482}, {4271, 13731}, {4642, 17187}, {4653, 9957}, {5119, 17524}, {5123, 14011}, {5292, 5752}, {5324, 17642}, {5562, 5721}, {5706, 11414}, {5885, 15792}, {8679, 13161}, {10461, 12513}, {11115, 14923}, {11681, 17174}, {12701, 14956}, {18172, 18205}
X(18179) lies on these lines: {1, 1631}, {6, 1760}, {141, 3721}, {343, 3782}, {674, 17446}, {942, 18166}, {982, 18161}, {2228, 7237}, {3122, 17470}, {3125, 3739}, {3666, 18202}, {3670, 16696}, {3726, 17390}, {3727, 17045}, {3735, 4657}, {3778, 4118}, {3954, 17239}, {3959, 4361}, {4016, 4357}, {4022, 4475}, {18181, 18190}
X(18180) lies on these lines: {1, 859}, {2, 5752}, {3, 1243}, {5, 51}, {21, 517}, {25, 5707}, {27, 1071}, {28, 60}, {40, 17194}, {46, 3286}, {58, 65}, {72, 333}, {79, 513}, {86, 5439}, {110, 6583}, {185, 8727}, {284, 2262}, {354, 2360}, {373, 17527}, {389, 6831}, {392, 11110}, {394, 7535}, {404, 5482}, {405, 10441}, {442, 511}, {495, 16980}, {500, 851}, {573, 16455}, {946, 2779}, {956, 10461}, {957, 3622}, {970, 7483}, {986, 18169}, {1010, 3753}, {1043, 10914}, {1155, 4278}, {1210, 17197}, {1216, 6881}, {1325, 5885}, {1385, 4225}, {1532, 10110}, {1714, 4259}, {1715, 7416}, {1730, 16453}, {1764, 16287}, {1790, 10202}, {1817, 9940}, {1824, 14016}, {1872, 3559}, {1884, 13408}, {1953, 2179}, {2194, 5358}, {2392, 11263}, {2476, 3060}, {2646, 4276}, {2771, 12826}, {2979, 4197}, {3057, 4653}, {3125, 16716}, {3193, 4228}, {3555, 5208}, {3567, 6830}, {3579, 4184}, {3670, 16696}, {3697, 3786}, {3791, 3874}, {3819, 17529}, {3868, 16704}, {3877, 17588}, {3917, 8728}, {3931, 10458}, {3976, 18173}, {4183, 5908}, {4187, 5943}, {4193, 5640}, {5044, 5235}, {5084, 17183}, {5141, 11002}, {5173, 5324}, {5249, 11573}, {5398, 13733}, {5446, 6842}, {5462, 6882}, {5499, 13391}, {5663, 16160}, {5706, 13730}, {5709, 8021}, {5751, 14018}, {5810, 6515}, {5889, 6828}, {5890, 6845}, {5907, 8226}, {6688, 17575}, {6829, 11412}, {6841, 13754}, {6941, 9781}, {6943, 15043}, {6963, 15024}, {6990, 11459}, {6991, 11444}, {7419, 10222}, {8679, 13407}, {9955, 14008}, {10473, 16466}, {10883, 12111}, {11113, 15488}, {12699, 14956}, {13374, 17188}, {13587, 14131}, {14011, 17619}, {14964, 16699}, {15329, 18115}, {16608, 17171}
X(18181) lies on these lines: {81, 1576}, {1634, 16701}, {3675, 16726}, {7202, 18191}, {17197, 17463}, {18165, 18175}, {18179, 18190}
X(18182) lies on these lines: {81, 18167}, {354, 18166}, {3125, 16707}, {17193, 17456}, {18169, 18204}
X(18183) lies on these lines: {1, 2916}, {6, 982}, {38, 141}, {69, 4392}, {244, 3589}, {354, 18166}, {518, 3293}, {522, 3663}, {742, 4022}, {984, 3763}, {986, 3242}, {1086, 17446}, {1193, 9021}, {1386, 3953}, {1401, 3313}, {1634, 16696}, {3619, 7226}, {3677, 7289}, {4475, 17445}, {4642, 9053}, {7202, 18170}, {7263, 17872}, {12329, 17595}
X(18184) lies on these lines: {1, 16680}, {81, 163}, {86, 3732}, {116, 17198}, {1018, 16728}, {1111, 3942}, {2087, 16742}, {2170, 7208}, {3125, 7202}, {3670, 18171}, {3675, 18191}, {3953, 18167}, {4424, 16696}, {5902, 18161}, {16727, 17761}, {18177, 18186}
X(18185) lies on these lines: {1, 859}, {3, 4658}, {6, 16058}, {21, 3241}, {55, 81}, {58, 3052}, {86, 1376}, {100, 8025}, {165, 18164}, {171, 18166}, {284, 11051}, {333, 1001}, {518, 17185}, {524, 4199}, {584, 9306}, {846, 4068}, {940, 4191}, {999, 4276}, {1010, 3913}, {1191, 4281}, {1621, 16704}, {1961, 4557}, {2177, 17187}, {3058, 14956}, {3304, 4225}, {3666, 18210}, {3746, 17524}, {3748, 18191}, {3750, 18169}, {3791, 16684}, {4413, 5333}, {4421, 13588}, {4423, 5235}, {4436, 4697}, {4640, 18206}, {4653, 6767}, {5396, 5891}, {10389, 17194}, {11235, 14009}, {11238, 14008}, {13405, 17197}, {16056, 17392}, {16696, 17594}, {17167, 17718}, {17592, 18161}, {17601, 18198}
X(18186) lies on these lines: {1, 3286}, {9, 16726}, {86, 3731}, {333, 8056}, {1743, 18206}, {3729, 17178}, {4384, 16710}, {4859, 16713}, {4862, 17197}, {10980, 18169}, {16673, 17207}, {16709, 16832}, {18177, 18184}, {18192, 18193}
X(18187) lies on these lines: {918, 1086}, {1437, 18167}
X(18188) lies on this line: {1, 16873}
X(18189) lies on these lines: {1, 16681}, {274, 3959}, {942, 18166}, {982, 18172}, {986, 16696}, {3125, 17175}, {3670, 18171}, {3727, 16705}, {3735, 16887}
X(18190) lies on these lines: {982, 18175}, {4475, 16738}, {16696, 18168}, {17202, 17470}, {18169, 18203}, {18179, 18181}, {18206, 18207}
X(18191) lies on these lines: {1, 18174}, {2, 3909}, {11, 124}, {21, 643}, {28, 1408}, {55, 17194}, {58, 65}, {81, 105}, {86, 9432}, {140, 10035}, {210, 333}, {244, 659}, {255, 2218}, {284, 17603}, {314, 4519}, {513, 3120}, {518, 16704}, {654, 2170}, {859, 1319}, {867, 8286}, {940, 5020}, {982, 18192}, {1010, 3698}, {1014, 4637}, {1043, 3893}, {1086, 2969}, {1122, 17189}, {1155, 3286}, {1333, 2262}, {1351, 4383}, {1357, 1358}, {1437, 5358}, {2328, 17642}, {2646, 4267}, {2810, 17724}, {3011, 8679}, {3025, 7336}, {3030, 6174}, {3056, 16713}, {3216, 5482}, {3220, 5137}, {3666, 18169}, {3675, 18184}, {3683, 17185}, {3733, 15635}, {3737, 14115}, {3742, 8025}, {3748, 18185}, {3752, 17187}, {3838, 17173}, {3952, 16729}, {3999, 18173}, {4003, 16696}, {4653, 5919}, {4658, 17609}, {4679, 17183}, {4860, 18164}, {5087, 17174}, {5650, 17337}, {5836, 11115}, {7192, 16727}, {7202, 18181}, {13751, 17104}, {14204, 15343}, {14923, 17539}, {17167, 17605}
X(18191) = complement of X(3909)
X(18192) lies on these lines: {1, 21}, {43, 16704}, {87, 16738}, {333, 16569}, {354, 18174}, {741, 8706}, {979, 1698}, {982, 18191}, {984, 18211}, {1613, 16552}, {2162, 16975}, {3248, 6682}, {3286, 3550}, {3840, 17178}, {3944, 17197}, {7184, 16713}, {16696, 17591}, {16726, 17063}, {17596, 18163}, {18176, 18208}, {18186, 18193}
X(18193) lies on these lines: {1, 3}, {9, 17063}, {38, 3306}, {45, 3848}, {63, 244}, {72, 11512}, {88, 3681}, {200, 1054}, {226, 14494}, {238, 3928}, {240, 1435}, {291, 5223}, {329, 5121}, {511, 7248}, {612, 4392}, {613, 1407}, {614, 1707}, {846, 10582}, {984, 5437}, {1086, 17064}, {1111, 7182}, {1357, 3784}, {1376, 16496}, {1743, 3509}, {3052, 4906}, {3062, 3551}, {3219, 9335}, {3403, 6384}, {3554, 18168}, {3729, 3840}, {3731, 17754}, {3751, 3752}, {3782, 17728}, {3816, 17276}, {3817, 4887}, {3846, 17274}, {3870, 17449}, {3929, 17123}, {3944, 4862}, {4310, 5435}, {4414, 4666}, {4421, 4864}, {4438, 17282}, {4650, 7290}, {4654, 17717}, {5220, 16602}, {5231, 17889}, {6682, 10436}, {7174, 17122}, {7204, 7271}, {7293, 7298}, {11246, 17721}, {17156, 17495}, {17194, 18173}, {18186, 18192}
X(18194) lies on these lines: {1, 6}, {43, 1964}, {48, 8300}, {75, 87}, {183, 5272}, {239, 1740}, {308, 3761}, {330, 2998}, {385, 614}, {386, 4991}, {513, 3551}, {577, 10801}, {604, 1582}, {612, 3329}, {869, 17121}, {978, 4974}, {979, 4385}, {982, 18207}, {1015, 17065}, {1045, 16834}, {1333, 10789}, {2309, 4393}, {3009, 17349}, {3097, 5069}, {3510, 17026}, {3550, 3941}, {3729, 9359}, {3758, 17445}, {3783, 5839}, {4000, 7184}, {4361, 16571}, {5019, 12194}, {5042, 10800}, {5268, 11174}, {7189, 17363}, {7191, 7766}, {7202, 18168}, {7280, 8266}, {11364, 16946}, {16569, 17348}, {16696, 17591}, {18161, 18208}
X(18195) lies on these lines: {81, 560}, {244, 16709}, {982, 16696}, {1386, 3953}, {3122, 17202}, {4022, 16738}, {18167, 18168}, {18179, 18181}
X(18196) lies on these lines: {1, 16692}, {81, 1919}, {798, 17212}, {1019, 4762}, {3733, 4782}, {4057, 18166}
X(18197) lies on these lines: {1, 669}, {57, 7180}, {239, 514}, {650, 4481}, {659, 3737}, {667, 18173}, {798, 4369}, {812, 18071}, {1054, 9361}, {1635, 16751}, {2978, 4040}, {3733, 4782}, {3835, 17217}, {4083, 8640}, {4375, 17185}, {4784, 8672}
X(18198) lies on these lines: {1, 3286}, {37, 17207}, {44, 16726}, {45, 86}, {81, 89}, {88, 16704}, {330, 4361}, {3733, 4782}, {3834, 16723}, {4286, 17378}, {4395, 16711}, {4480, 17195}, {4887, 17197}, {16709, 16815}, {16710, 16816}, {16714, 17366}, {17067, 17205}, {17601, 18185}
X(18199) lies on these lines: {6, 4369}, {81, 6654}, {222, 4077}, {514, 7254}, {661, 940}, {1019, 8712}, {1021, 7203}, {1396, 17926}, {3733, 4782}, {4160, 5711}, {4833, 18166}, {4885, 17218}, {15419, 17069}
X(18200) lies on these lines: {1, 16874}, {81, 649}, {86, 3835}, {171, 7234}, {385, 4369}, {661, 9810}, {1019, 1429}, {1412, 3676}, {1580, 4367}, {1919, 4932}, {3733, 4782}, {3776, 4817}, {4107, 16737}
X(18201) lies on these lines: {1, 3}, {7, 17717}, {38, 5297}, {44, 1052}, {45, 17754}, {58, 17513}, {63, 17063}, {88, 291}, {89, 985}, {100, 17449}, {190, 4871}, {226, 7608}, {238, 244}, {511, 1357}, {518, 1054}, {527, 5121}, {535, 6788}, {537, 5205}, {614, 4650}, {748, 9335}, {750, 4392}, {752, 5211}, {846, 3742}, {902, 3315}, {984, 3306}, {1086, 17070}, {1647, 5057}, {1707, 5573}, {1757, 16610}, {2243, 16786}, {3286, 18173}, {3733, 4782}, {3752, 4663}, {3756, 17768}, {3911, 17719}, {3928, 5272}, {3938, 9352}, {3944, 17728}, {4031, 17722}, {4310, 17725}, {4414, 16484}, {4495, 18075}, {4649, 4850}, {4661, 9350}, {4716, 17162}, {4722, 17020}, {4887, 9436}, {4902, 7988}, {6384, 7244}, {7064, 15082}, {7226, 17124}, {7293, 7302}, {9324, 9451}, {17767, 17777}
X(18202) lies on these lines: {1, 199}, {2, 3125}, {306, 3721}, {982, 18210}, {1211, 4016}, {3666, 18179}, {3670, 18203}, {3782, 14213}, {3959, 5271}, {6155, 17011}
X(18203) lies on these lines: {1, 22}, {982, 18161}, {2887, 4118}, {3670, 18202}, {3741, 4475}, {4137, 17184}, {4425, 17470}, {18167, 18175}, {18169, 18190}
X(18204) lies on these lines: {1, 16876}, {982, 18167}, {3670, 18202}, {16696, 18168}, {18169, 18182}, {18206, 18208}
X(18205) lies on these lines: {1, 16683}, {81, 4586}, {1100, 16726}, {3670, 18171}, {16696, 18170}, {18172, 18178}
X(18206) lies on these lines: {1, 21}, {2, 2350}, {6, 980}, {7, 16713}, {9, 86}, {37, 18166}, {40, 4229}, {44, 16726}, {57, 85}, {69, 579}, {71, 3879}, {110, 2725}, {141, 583}, {144, 17183}, {193, 573}, {194, 1764}, {200, 13588}, {213, 4641}, {239, 514}, {284, 1444}, {310, 17026}, {314, 3729}, {329, 17182}, {518, 2223}, {524, 2245}, {527, 17139}, {553, 17050}, {599, 5043}, {660, 1757}, {666, 2311}, {672, 3912}, {869, 17187}, {894, 10455}, {940, 5021}, {982, 16476}, {988, 4281}, {1014, 1445}, {1018, 6542}, {1020, 17950}, {1026, 4447}, {1043, 6762}, {1282, 8849}, {1333, 16973}, {1400, 4416}, {1412, 1708}, {1475, 16705}, {1723, 17189}, {1724, 16048}, {1730, 4209}, {1743, 18186}, {1756, 17770}, {1765, 10446}, {1778, 16970}, {1992, 4266}, {2111, 17738}, {2149, 4564}, {2176, 18172}, {2260, 4357}, {2303, 16517}, {2323, 6518}, {3008, 16752}, {3219, 3294}, {3285, 16702}, {3305, 5333}, {3306, 5235}, {3333, 11110}, {3501, 17294}, {3555, 17524}, {3629, 4271}, {3661, 16549}, {3666, 6155}, {3730, 17316}, {3736, 3751}, {3786, 5223}, {3811, 4278}, {3870, 4184}, {3928, 9311}, {4258, 16436}, {4269, 7289}, {4282, 4558}, {4383, 16700}, {4640, 18185}, {4715, 16723}, {4921, 16833}, {5036, 6144}, {5228, 16699}, {5231, 14009}, {5236, 9436}, {5247, 16735}, {5278, 17683}, {5905, 17167}, {6646, 17202}, {6904, 9534}, {7146, 18176}, {7719, 14013}, {9965, 17753}, {10471, 11679}, {13476, 16684}, {16050, 17742}, {16497, 18174}, {16709, 17277}, {16710, 17349}, {17173, 17483}, {17174, 17484}, {17178, 17350}, {17308, 17754}, {17755, 18157}, {18190, 18207}, {18204, 18208}
X(18206) = isogonal conjugate of X(18785)
X(18206) = cevapoint of X(518) and X(672)
X(18206) = crosssum of X(37) and X(2238)
X(18206) = crosspoint of X(81) and X(37128)
X(18206) = crossdifference of every pair of points on line X(42)X(661)
X(18206) = trilinear pole of line X(2254)X(8299)
X(18207) lies on these lines: {1, 159}, {6, 18168}, {256, 17447}, {320, 4118}, {894, 4475}, {982, 18194}, {1582, 7291}, {2643, 7321}, {3942, 7184}, {6646, 17470}, {7202, 18170}, {7237, 17288}, {18190, 18206}
X(18208) lies on these lines: {1, 3}, {6, 18168}, {58, 17517}, {226, 3399}, {238, 17799}, {239, 4475}, {244, 1959}, {304, 6384}, {335, 726}, {518, 3507}, {1111, 18033}, {1580, 3218}, {1920, 1930}, {3061, 16604}, {3673, 3944}, {3674, 3865}, {3726, 4876}, {3752, 17795}, {3840, 17760}, {4118, 16706}, {7237, 17291}, {7291, 8300}, {17302, 17470}, {18161, 18194}, {18176, 18192}, {18204, 18206}
X(18209) lies on these lines: {1, 2916}, {6, 7166}, {141, 1580}, {171, 18162}, {320, 7122}, {560, 3662}, {982, 1631}, {1030, 17596}, {1086, 1582}, {1429, 18170}, {2210, 16706}, {3821, 5009}, {4112, 18144}, {7113, 7184}, {8300, 17366}
X(18210) lies on these lines: {1, 1283}, {2, 16100}, {4, 2828}, {11, 2969}, {56, 11383}, {63, 17972}, {65, 1410}, {77, 17973}, {81, 18175}, {122, 125}, {228, 1214}, {244, 665}, {517, 15626}, {982, 18202}, {1364, 3270}, {1365, 2611}, {1427, 1824}, {1437, 7100}, {1565, 2968}, {1566, 4988}, {2631, 2632}, {2771, 18115}, {3122, 17476}, {3666, 18185}, {3827, 8758}, {7202, 18181}, {8731, 16585}
X(18210) = isogonal conjugate of X(5379)
X(18210) = isotomic conjugate of polar conjugate of X(3125)
X(18210) = X(19)-isoconjugate of X(4567)
X(18211) lies on these lines: {81, 643}, {244, 659}, {984, 18192}, {15569, 18169}
In the plane of a triangle ABC, let P be a point. Let
(BCP) = cirumcircle of BCP, and define (CAP) and (ABP) cyclically;
A' = the point of interection, other than P, or AP and (BCP), and define B' and C' cyclically;
A'' = reflection of A' in the center of (BCP), and define B'' and C'' cyclically.
Then A''B''C'' is perspective to ABC. (Thanh Oai Dao, April 29, 2018)
X(18212) and X(18213) were contributed by César Lozada, April 30, 2018, with the following notes. The perspector of ABC and A''B''C'' is here named the Dao perspector of P, denoted by D(P). The appearance of (i,j) in the following list means that D(X(i)) = X(j): (1, 1), (2, 13608), (3, 24), (4, 68), (5,18212), (6, 14262), (13, 18), (14,17), (15, 62), (16, 61), (20,18213), (36, 35), (59, 11247), (80, 79), (249, 10279), (265, 14111). In general, if P = x : y : z (barycentrics), then
D(P) = (-x^2*SA+SB*x*y+SC*x*z+2*a^2*y*z)*(-SC*c^2*x*y+SB*b^2*x*z-2*a^2*c^2*y^2-SA*a^2*y*z)*(SC*c^2*x*y-SB*b^2*x*z-SA*a^2*y*z-2*a^2*b^2*z^2) : :
X(18212) lies on these lines: {3, 12325}, {5, 10227}, {49, 6150}, {186, 3432}, {1141, 3520}, {15620, 17506}
See X(18212).
X(18213) lies on these lines: {3, 1661}, {5896, 6622}
Zaniah triangles and related centers: X(18214)-X(18261)
This preamble and centers X(18214)-X(18261) were contributed by César Eliud Lozada, May 01, 2018.
In a triangle ABC, let AmBmCm be the medial triangle, I the incenter and A' the touchpoint of the incircle with the side BC. Then the lines AA', IAm and BmCm are concurrent at a point A1. Denote B1 and C1 cyclically. The triangle A1B1C1 is here named the 1st Zaniah triangle of ABC.
Continuing with the previous construction, let Ja be the A-excenter and A" the touchpoint of the A-excircle with the side BC. Then the lines AA", JaAm and BmCm are concurrent at a point A2. Denote B2 and C2 cyclically. The triangle A2B2C2 is here named the 2nd Zaniah triangle of ABC. [See note (*) below.]
Barycentric coordinates of the first vertex of each triangle are:
A1 = 2*a : a+b-c : a-b+c
A2 = 2*a : a-b+c : a+b-c
The vertices of both triangles lie on a conic with center X(18214) and perspector X(18215).
(*) Note: the 1st Zaniah triangle is the cevian triangle of X(1) wrt the medial triangle, or equivalently, the extouch triangle of the medial triangle, or the complement of the extouch triangle. The 2nd Zaniah triangle is the cevian triangle of X(9) wrt the medial triangle, or equivalently, the intouch triangle of the medial triangle, or the complement of the intouch triangle. (Randy Hutson, June 27, 2018)
This circumconic, as the complement of the Privalov conic, is an ellipse for all ABC.
X(18214) lies on these lines: {2,1814}, {141,3740}, {1376,17060}, {3035,15260}, {3816,4885}, {3827,15497}, {4682,13405}
X(18214) = complement of X(5452)
X(18214) = X(14713) of 2nd Zaniah triangle
X(18214) = {X(2), X(13577)}-harmonic conjugate of X(5452)
X(18216) lies on these lines: {1,6}, {7,4907}, {57,4319}, {77,7671}, {241,4326}, {269,14100}, {354,4328}, {497,3668}, {938,3755}, {950,7273}, {990,3333}, {1418,2951}, {2263,10384}, {3672,3677}, {4000,5573}, {4356,6744}, {7190,11025}, {7271,15726}, {7322,10578}, {9442,10390}
X(18217) lies on these lines: {1,3522}, {65,8275}, {142,1698}, {191,3338}, {354,5586}, {942,4355}, {944,14563}, {946,7992}, {1387,1768}, {1699,11544}, {3296,7991}, {3339,9898}, {3624,5273}, {3671,18220}, {3679,11024}, {3894,10855}, {4298,18221}, {4312,5572}, {5045,11034}, {9897,12736}, {10122,11220}, {10543,11518}, {10609,12653}, {10825,11021}, {12409,12917}
X(18217) = reflection of X(1) in X(5558)
X(18217) = X(5558) of Aquila triangle
X(18217) = (inverse-in-incircle)-isotomic conjugate of-X(3945)
X(18217) = {X(354), X(5586)}-harmonic conjugate of X(9589)
X(18219) lies on these lines: {1,9799}, {4,142}, {20,11024}, {40,958}, {63,12651}, {84,942}, {515,12855}, {517,12654}, {936,6847}, {952,12658}, {1490,8727}, {1768,3339}, {3062,9960}, {3295,7966}, {4292,11023}, {5261,7675}, {6001,18241}, {6837,8583}, {7992,12560}, {9624,11281}, {9948,14563}, {10431,12565}, {10582,10884}
X(18220) lies on these lines: {1,3091}, {2,3057}, {4,1387}, {7,11522}, {10,4345}, {11,145}, {55,17572}, {142,390}, {496,6830}, {497,2475}, {519,5828}, {551,4313}, {938,13464}, {942,5603}, {944,7704}, {946,3600}, {962,5265}, {999,11544}, {1000,1656}, {1058,5901}, {1125,5281}, {1210,5734}, {1319,3146}, {1320,6931}, {1388,5225}, {1420,9812}, {1482,6978}, {1697,5550}, {1699,4308}, {1837,3623}, {1854,3315}, {1898,3485}, {2098,3617}, {3086,5903}, {3241,9581}, {3295,6946}, {3476,3832}, {3486,10129}, {3487,9844}, {3522,12701}, {3621,5048}, {3624,4342}, {3671,18217}, {3742,10866}, {3876,5686}, {3877,18231}, {4293,16118}, {4295,18223}, {4301,5435}, {4321,18222}, {4323,11019}, {4678,17606}, {4853,5328}, {4861,6919}, {5056,10051}, {5068,5252}, {5119,10303}, {5691,6049}, {5703,9624}, {5704,7982}, {5731,9614}, {5886,6964}, {6745,12541}, {7080,17648}, {7486,10039}, {7962,9780}, {7967,9669}, {9779,10106}, {10122,11036}, {10966,16865}, {11375,13867}
X(18220) = X(3532) of Hutson intouch triangle
X(18220) = X(15077) of inverse-in-incircle triangle
X(18220) = (inverse-in-incircle)-isotomic conjugate of-X(4862)
Let A'B'C' be the intouch triangle and let A"B"C" be the Euler triangle of A'B'C'. The finite fixed point of the affine transformation that carries ABC onto A''B''C'' is X(18221), i.e. X(18221) = ATFF(ABC, A"B"C"); see the preamble just before X(10129)). (Angel Montesdeoca, March 25, 2022)
X(18221) lies on these lines: {1,3523}, {2,11281}, {4,11544}, {7,5691}, {8,142}, {20,5441}, {40,15933}, {65,390}, {100,3304}, {145,354}, {519,11024}, {758,5129}, {938,946}, {942,944}, {952,3296}, {999,6942}, {1056,12645}, {1058,1159}, {1125,5775}, {1387,6833}, {2136,3241}, {3086,5425}, {3090,16137}, {3091,9803}, {3212,3945}, {3333,7966}, {3336,10304}, {3339,4313}, {3340,10580}, {3475,3617}, {3487,9956}, {3522,5221}, {3528,15174}, {3543,18244}, {3616,5837}, {3649,3832}, {4295,18224}, {4298,18217}, {4308,7990}, {4323,11019}, {4678,15888}, {4778,14812}, {4848,10578}, {5056,15079}, {5059,11246}, {5226,12563}, {5261,6993}, {5665,5809}, {5690,6989}, {5883,17580}, {6744,9785}, {6872,12917}, {7972,12736}, {7991,8236}, {8000,12855}, {8422,11033}, {9949,12560}, {10890,11021}, {11023,11037}
X(18221) = midpoint of X(65) and X(13867)
X(18221) = reflection of X(8) in X(11530)
X(18221) = X(7320) of 5th mixtilinear triangle
X(18221) = X(15740) of inverse-in-incircle triangle
X(18221) = X(16936) of Hutson intouch triangle
X(18221) = (inverse-in-incircle)-isotomic conjugate of-X(4888)
X(18221) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8, 11518, 11038), (11529, 17706, 938)
X(18222) lies on these lines: {4,12855}, {9,5836}, {142,1699}, {516,5129}, {942,7992}, {1750,11218}, {3062,5572}, {4312,11023}, {4321,18220}, {4326,5226}, {4626,7271}, {5223,8001}, {5691,15006}, {9580,12859}, {9949,12560}, {11281,16143}, {12736,12767}
X(18223) lies on these lines: {1,4190}, {4,15528}, {7,10591}, {11,10052}, {56,1387}, {63,499}, {65,10043}, {142,498}, {354,10044}, {553,946}, {942,1478}, {1479,7702}, {1737,11023}, {3086,14450}, {3333,10042}, {3874,10057}, {4295,18220}, {4860,11544}, {5045,11045}, {5836,12647}, {5902,10532}, {8071,11281}, {10039,11024}, {10045,10980}, {10059,12855}, {10090,11517}, {10106,14563}, {10122,16152}, {11019,18224}, {12917,13128}
X(18223) = X(10940) of outer-Yff triangle
X(18223) = (inverse-in-incircle)-isotomic conjugate of-X(77)
X(18224) lies on these lines: {1,5905}, {11,10044}, {65,10051}, {142,499}, {354,10052}, {498,3305}, {942,1479}, {946,3982}, {950,14563}, {1387,3304}, {1478,1898}, {1737,11024}, {2099,15171}, {3333,10050}, {3419,5836}, {4295,18221}, {5045,11046}, {10056,10075}, {10073,12736}, {10092,10980}, {10122,16153}, {10531,15528}, {11019,18223}, {12647,15862}, {12917,13129}
X(18224) = X(10941) of inner-Yff triangle
X(18224) = (outer-Yff)-isogonal conjugate of-X(8071)
X(18224) = (inverse-in-incircle)-isotomic conjugate of-X(7190)
X(18225) lies on these lines: {65,10935}, {142,5552}, {354,10940}, {942,12115}, {946,12686}, {1387,12775}, {5045,11047}, {5261,11023}, {5836,12648}, {7956,11544}, {10122,16154}, {10915,11024}, {10970,10971}, {12736,12749}, {12855,12874}, {12917,13130}
X(18225) = (inner-Yff tangents)-isogonal conjugate of-X(3303)
X(18226) lies on these lines: {1,6992}, {65,10936}, {142,10527}, {354,10941}, {942,12116}, {946,12687}, {1387,12776}, {3304,11281}, {3333,11920}, {4863,5836}, {5045,11048}, {10122,16155}, {10916,11024}, {10970,10971}, {12736,12750}, {12855,12875}, {12917,13131}
X(18227) lies on these lines: {1,18247}, {2,8581}, {8,210}, {9,165}, {10,9842}, {57,8169}, {65,8165}, {188,11858}, {200,10384}, {226,1329}, {236,11860}, {354,5328}, {515,5044}, {516,10241}, {518,3452}, {936,10864}, {958,1420}, {1125,11035}, {1699,5836}, {2886,10863}, {3035,13227}, {3036,9951}, {3742,10569}, {3820,6001}, {3925,5123}, {5204,5302}, {5658,9943}, {5745,10855}, {5777,9948}, {7028,11859}, {9949,18251}, {9950,18252}, {9952,18254}, {9953,18255}, {10862,18229}, {10865,18230}, {10868,18235}, {11519,15829}, {12386,18248}, {12446,18249}, {12449,18257}, {12450,18258}, {12451,18259}, {16120,18253}
X(18227) = X(13567) of Atik triangle
X(18227) = X(13567) of 2nd Zaniah triangle
X(18227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11678, 8581), (8, 10866, 12448), (9, 18236, 3740), (210, 17604, 8), (210, 18228, 960), (3740, 15587, 8580), (5044, 9947, 12447), (5927, 8580, 15587), (8580, 10860, 1376)
X(18228) is the homothetic center of the complement of the intouch triangle and the anticomplement of the excentral triangle. (Randy Hutson, June 27, 2018)
Let A'B'C' be as defined at X(5658). A'B'C' is homothetic to the medial triangle and the orthic-of-intouch triangle at X(226), and to the anticomplementary triangle at X(18228). (Randy Hutson, June 27, 2018)
Let A"B"C" be the Hutson-extouch triangle. Let La be the tangent to the A-excircle at A", and define Lb and Lc cyclically. Let A* = Lb∩Lc, B* = Lc∩La, C* = La∩Lb. Then A*B*C* is homothetic to ABC and the orthic-of-intouch triangle at X(57), to the anticomplementary triangle at X(144), and to the medial triangle at X(18228). (Randy Hutson, June 27, 2018)
X(18228) lies on these lines: {1,5129}, {2,7}, {3,5658}, {4,5044}, {8,210}, {10,962}, {11,3715}, {20,936}, {72,938}, {78,452}, {145,3984}, {188,9793}, {200,390}, {220,4383}, {223,3160}, {236,11891}, {281,469}, {333,6557}, {344,4417}, {345,3161}, {346,3687}, {391,11679}, {392,3421}, {405,5703}, {516,8580}, {517,6939}, {518,10580}, {612,4344}, {651,17811}, {857,1211}, {942,17559}, {946,6766}, {950,12536}, {958,3304}, {997,5731}, {1001,10578}, {1058,6764}, {1125,5234}, {1212,5308}, {1260,5766}, {1329,2476}, {1376,5698}, {1532,3820}, {1698,4295}, {1737,5775}, {1848,7079}, {1997,14829}, {2324,5256}, {2345,5743}, {2550,3740}, {2886,9779}, {2999,3672}, {3030,3038}, {3035,9809}, {3036,9802}, {3058,3711}, {3061,17316}, {3083,17805}, {3084,17802}, {3090,5791}, {3241,5289}, {3434,18236}, {3474,4413}, {3487,11108}, {3488,3940}, {3522,5438}, {3523,6700}, {3600,8583}, {3601,11106}, {3617,5837}, {3683,5218}, {3689,10385}, {3697,5082}, {3752,4419}, {3816,5220}, {3869,13601}, {3870,8236}, {3878,15104}, {3883,7172}, {3890,7320}, {3916,17567}, {3927,17527}, {3945,17022}, {3983,12701}, {4000,4415}, {4023,4387}, {4187,5704}, {4208,9612}, {4292,17580}, {4307,5268}, {4310,5272}, {4339,5293}, {4342,4915}, {4358,5739}, {4512,5281}, {4847,5274}, {4855,17576}, {4882,12575}, {5046,5175}, {5056,5705}, {5086,7319}, {5123,5180}, {5195,5199}, {5223,11019}, {5241,7229}, {5250,7080}, {5302,5550}, {5440,11111}, {5603,9708}, {5691,12447}, {5709,6964}, {5714,8728}, {5719,16857}, {5720,6987}, {5741,17776}, {5768,6947}, {5777,6865}, {5784,10430}, {5804,6898}, {5812,6864}, {5817,8727}, {5828,10039}, {5850,10980}, {6147,16853}, {6349,16596}, {6361,9709}, {6734,6919}, {6838,12514}, {6840,10176}, {6910,15823}, {6926,7330}, {7028,9795}, {8582,12526}, {9789,18234}, {9791,18235}, {9797,18247}, {9800,18251}, {9801,18252}, {9803,18254}, {9804,18255}, {9807,18258}, {10446,18229}, {10582,11038}, {11374,16845}, {12391,18248}, {12542,18257}, {12543,18259}, {13411,17558}, {14450,18253}, {16020,17123}, {16602,17276}, {16713,17182}, {16832,17753}, {17170,17284}, {17358,17482}
X(18228) = polar conjugate of X(11546)
X(18228) = anticomplement of X(5437)
X(18228) = X(17810) of 2nd Conway triangle
X(18228) = X(17810) of 2nd Zaniah triangle
X(18228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 9, 5273), (2, 63, 5435), (2, 144, 57), (2, 329, 7), (2, 908, 5226), (2, 3219, 5744), (2, 3305, 18230), (2, 3452, 5328), (9, 3452, 2), (57, 5316, 2), (226, 7308, 2), (329, 9776, 5905), (908, 3305, 2), (3306, 17781, 9965), (5273, 5328, 2), (5435, 6172, 63)
X(18229) lies on these lines: {1,2}, {9,1764}, {40,2050}, {188,11894}, {210,10473}, {226,17272}, {236,11896}, {312,3731}, {333,1743}, {518,11021}, {940,5783}, {958,10882}, {960,12435}, {966,3452}, {1211,5219}, {1215,5223}, {1329,10887}, {1376,10434}, {1402,4413}, {2297,16713}, {2345,5745}, {2886,10886}, {3035,13244}, {3036,12550}, {3305,5235}, {3666,17151}, {3739,5437}, {3740,10439}, {3772,17306}, {3928,4363}, {4417,17270}, {4859,10468}, {5044,10441}, {5226,5232}, {5234,6996}, {5273,10444}, {5438,10470}, {5777,12547}, {7028,11895}, {10436,14829}, {10446,18228}, {10862,18227}, {10889,18230}, {10891,18234}, {10892,18235}, {11521,15829}, {12126,18247}, {12392,18248}, {12544,18249}, {12545,18250}, {12548,18251}, {12551,18254}, {12552,18255}, {12553,18257}, {12554,18258}, {12557,18259}, {16124,18253}, {17056,17296}, {17617,18236}
X(18229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 8, 12546), (2, 5271, 2999), (2, 11679, 1), (9, 10472, 10456), (1764, 10888, 10442), (2999, 5271, 16833), (4384, 16831, 16827)
X(18230) lies on these lines: {1,4924}, {2,7}, {3,5817}, {5,5759}, {6,5308}, {8,344}, {10,390}, {37,5222}, {43,4343}, {44,4648}, {45,4000}, {69,17241}, {72,17552}, {75,3161}, {140,5779}, {149,6594}, {188,7022}, {192,4402}, {193,17244}, {210,5572}, {220,5543}, {238,4344}, {239,4460}, {346,4384}, {391,3912}, {392,4345}, {405,4313}, {427,7717}, {497,15837}, {516,1698}, {518,3616}, {631,971}, {632,5843}, {673,2345}, {857,1213}, {936,7675}, {938,954}, {958,4308}, {960,4323}, {962,6886}, {966,5838}, {984,16020}, {1125,5223}, {1156,3035}, {1212,3160}, {1329,7679}, {1376,7676}, {1621,6600}, {1656,5762}, {1743,3945}, {1992,17317}, {2287,16053}, {2324,7269}, {2325,4461}, {2476,3826}, {2478,2550}, {2886,7678}, {2951,10164}, {3008,3672}, {3036,12730}, {3059,3740}, {3085,15299}, {3086,15298}, {3090,5805}, {3241,3759}, {3243,3622}, {3247,17014}, {3358,6223}, {3475,3715}, {3488,16857}, {3523,5732}, {3600,5234}, {3601,10392}, {3617,5853}, {3619,17256}, {3620,17266}, {3624,5542}, {3646,14986}, {3664,3973}, {3681,15185}, {3683,9778}, {3707,17296}, {3739,7229}, {3757,5423}, {3763,4748}, {3816,6067}, {3925,9812}, {3943,4371}, {3946,16676}, {3950,16833}, {4208,12572}, {4321,5265}, {4326,5281}, {4335,16569}, {4346,4859}, {4370,17118}, {4413,11495}, {4416,4869}, {4419,16814}, {4423,10580}, {4473,4699}, {4488,17336}, {4644,16885}, {4657,6687}, {4675,15492}, {4679,9779}, {4853,7320}, {4877,14953}, {4916,4969}, {5044,5703}, {5084,5766}, {5218,14100}, {5220,5550}, {5232,17284}, {5251,5731}, {5261,12573}, {5440,17561}, {5704,5791}, {5729,6675}, {5735,7486}, {5758,6887}, {5777,12669}, {5784,6910}, {5785,6700}, {5811,6989}, {5825,6857}, {5832,6931}, {5836,7673}, {5839,17243}, {6068,6667}, {6684,11372}, {6840,17057}, {6921,10861}, {7028,8388}, {7288,8581}, {7670,18258}, {8167,17051}, {8237,18234}, {8238,18235}, {8582,18231}, {9846,18247}, {9945,16418}, {10398,13411}, {10865,18227}, {10889,18229}, {11008,17387}, {11024,12514}, {11526,15829}, {12399,18248}, {12536,16859}, {12560,18249}, {12649,17570}, {12706,18251}, {12718,18252}, {12755,18254}, {12846,18255}, {12847,18257}, {12850,18259}, {16133,18253}, {16675,17366}, {16677,17395}, {16815,17339}, {16832,17355}, {17265,17332}, {17267,17330}, {17314,17348}, {17316,17349}, {17321,17352}, {17620,18236}
X(18230) = anticomplement of X(20195)
X(18230) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 9, 7), (2, 144, 142), (2, 3219, 9776), (2, 3305, 18228), (2, 5273, 5435), (2, 17260, 5296), (2, 18228, 5226), (7, 9, 6172), (8, 1001, 8236), (9, 142, 144), (9, 6666, 2), (142, 144, 7), (480, 1001, 2346), (1445, 8232, 7), (8545, 8732, 7), (17260, 17338, 2)
X(18231) lies on these lines: {1,5775}, {2,65}, {8,3158}, {9,5128}, {10,20}, {12,144}, {46,4208}, {63,5261}, {100,958}, {191,10590}, {390,6734}, {452,10395}, {962,5705}, {997,10303}, {1212,17756}, {1698,4295}, {1737,5129}, {1770,18250}, {1837,11106}, {2475,2551}, {2550,6895}, {3085,5904}, {3091,12514}, {3146,4640}, {3522,5794}, {3555,11018}, {3600,5744}, {3616,5837}, {3622,4999}, {3634,5328}, {3651,9709}, {3672,5230}, {3679,4305}, {3820,6937}, {3832,5698}, {3877,18220}, {3927,8164}, {4847,12632}, {5082,12732}, {5086,17576}, {5226,12526}, {5231,9785}, {5250,5274}, {5550,15829}, {5657,5791}, {5658,5777}, {5659,6888}, {5660,18254}, {5686,7080}, {5690,6892}, {6850,10742}, {6906,9708}, {8580,12520}, {8582,18230}, {10198,11036}, {10304,17647}, {10527,15558}, {10585,11684}, {12671,14647}
X(18231) = X(14528) of 2nd Zaniah triangle
X(18231) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9, 9780, 8165), (1698, 18249, 18228)
Let (Oa) be the reflection of the A-excircle in line BC. Define (Ob) and (Oc) cyclically. Then X(18232) is the radical center of circles (Oa), (Ob), (Oc).
X(18232) lies on these lines: {2,10052}, {3,18254}, {8,90}, {9,2252}, {10,6923}, {63,499}, {912,960}, {956,2098}, {1376,3652}, {1727,5552}, {1776,3811}, {3036,5690}, {3647,5217}, {3814,7702}, {3820,5499}, {5692,15446}, {5745,18233}, {7082,10916}, {7330,17647}, {10395,12572}, {12849,18259}
X(18232) = complement of X(10052)
X(18232) = X(15317) of 2nd Zaniah triangle
X(18233) lies on these lines: {2,10044}, {5,18253}, {8,7162}, {9,6832}, {10,6928}, {191,6933}, {405,10176}, {498,3305}, {958,6265}, {993,5777}, {1158,6825}, {3091,12514}, {3149,3647}, {5745,18232}, {6987,17647}
X(18233) = complement of X(10044)
X(18234) lies on these lines: {2,8243}, {8,7090}, {9,7595}, {10,7596}, {37,615}, {210,17610}, {236,11996}, {518,11030}, {936,8234}, {958,8225}, {960,9808}, {1125,11042}, {1329,8230}, {1376,8224}, {2886,8228}, {3036,12744}, {3452,12610}, {5273,10885}, {5745,10858}, {7028,8248}, {8237,18230}, {8244,8580}, {8246,18235}, {9789,18228}, {10891,18229}, {11532,15829}, {13090,18258}, {16144,18253}, {17627,18236}
X(18234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11687, 8243), (8, 8239, 12638)
X(18235) lies on these lines: {2,1284}, {8,21}, {9,43}, {10,9840}, {63,1469}, {71,1755}, {100,8852}, {165,3501}, {171,172}, {188,8249}, {198,1376}, {210,17611}, {236,8425}, {518,11031}, {851,4418}, {936,8235}, {960,1193}, {1125,11043}, {1329,5051}, {2886,8229}, {3035,13265}, {3036,12746}, {3061,17592}, {3214,4689}, {3452,4425}, {3740,11203}, {3741,4154}, {3923,4192}, {3980,16056}, {4685,5325}, {5044,9959}, {5289,17599}, {5777,12683}, {7028,8250}, {7081,17787}, {8238,18230}, {8245,8580}, {8246,18234}, {9791,18228}, {10868,18227}, {10892,18229}, {11533,15829}, {12405,18248}, {12567,18249}, {12579,18250}, {12713,18251}, {12725,18252}, {12770,18254}, {12869,18255}, {13071,18257}, {13091,18258}, {13123,18259}, {17628,18236}
X(18235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11688, 1284), (8, 21, 8240), (8, 8240, 12642), (43, 846, 256), (1376, 8424, 4220)
X(18236) lies on these lines: {2,3660}, {8,17622}, {9,165}, {10,1532}, {11,210}, {72,1329}, {188,17629}, {236,17631}, {355,2551}, {392,12647}, {517,6973}, {518,17626}, {936,12114}, {958,17614}, {960,3679}, {1125,17624}, {1864,6745}, {2550,10157}, {2886,17618}, {3035,10167}, {3036,17652}, {3434,18228}, {3555,10072}, {3681,5328}, {3753,3838}, {3876,8165}, {3967,4858}, {3983,5837}, {4662,4915}, {4679,10947}, {5173,5748}, {5220,8169}, {5273,17616}, {5435,11678}, {5552,12711}, {5745,17612}, {5777,12666}, {5784,15064}, {5795,10944}, {5811,12676}, {5836,7989}, {5853,17604}, {6692,8581}, {6700,14872}, {7028,17630}, {10177,13405}, {10866,12640}, {11826,12572}, {17617,18229}, {17620,18230}, {17627,18234}, {17628,18235}, {17644,18247}, {17645,18248}, {17646,18249}, {17647,18250}, {17650,18251}, {17651,18252}, {17653,18253}, {17654,18254}, {17655,18255}, {17656,18257}, {17657,18258}, {17659,18259}
X(18236) = midpoint of X(5435) and X(11678)
X(18236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 17615, 17625), (8, 17622, 17648), (11, 210, 17658), (210, 17642, 14740), (1376, 5927, 17668), (1709, 8580, 1376), (3740, 18227, 9)
X(18237) lies on these lines: {1,1035}, {3,960}, {36,7992}, {55,7971}, {56,84}, {64,102}, {104,10309}, {382,2829}, {474,14647}, {515,12513}, {946,999}, {956,12667}, {958,6260}, {971,11249}, {1001,5450}, {1012,3485}, {1490,3428}, {1498,10571}, {1728,12664}, {1788,3149}, {2800,10306}, {2886,6256}, {6743,11362}, {6913,12608}, {6918,12616}, {8071,15071}, {9708,18242}, {10966,12680}, {11281,13743}
X(18237) = X(7971) of anti-Mandart-incircle triangle
X(18237) = X(9937) of 2nd circumperp triangle
X(18237) = X(12301) of 1st circumperp triangle
X(18237) = X(12330) of ABC-X3 reflections triangle
X(18237) = {X(1158), X(6261)}-harmonic conjugate of X(960)
X(18238) lies on these lines: {1,84}, {2,18239}, {4,10305}, {5,142}, {7,10309}, {20,14923}, {63,10310}, {65,2096}, {377,9799}, {474,1490}, {515,5836}, {518,1158}, {960,5450}, {1387,9856}, {1902,3937}, {2800,13600}, {2823,5908}, {2829,4292}, {2949,3916}, {3742,12608}, {3812,6256}, {5123,12616}, {5252,12680}, {5572,12005}, {5658,6983}, {5732,11500}, {5777,6700}, {5787,6923}, {5884,14563}, {6223,6957}, {6259,10202}, {6833,12664}, {6837,9960}, {6966,12528}, {7080,14647}, {8582,18242}, {9948,12855}, {11376,12688}
X(18238) = midpoint of X(1) and X(17649)
X(18238) = reflection of X(i) in X(j) for these (i,j): (960, 5450), (5777, 6705)
X(18238) = complement of X(18239)
X(18238) = X(4) of 1st Zaniah triangle
X(18238) = X(9820) of Conway triangle
X(18238) = X(12420) of 2nd Zaniah triangle
X(18238) = X(15316) of inverse-in-incircle triangle
X(18238) = X(17649) of anti-Aquila triangle
X(18238) = (1st Zaniah)-isogonal conjugate of-X(12608)
X(18238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (9799, 11220, 12671), (12608, 18260, 3742)
X(18239) lies on the Mandart hyperbola and these lines: {1,10092}, {2,18238}, {3,9}, {8,6001}, {10,17649}, {65,6256}, {210,1158}, {354,12608}, {515,3057}, {912,6259}, {946,8581}, {1145,17661}, {1319,1898}, {1858,12678}, {2057,10310}, {2478,9799}, {2829,14110}, {4187,5927}, {5658,6834}, {5691,16007}, {5787,6929}, {5882,9848}, {6838,9960}, {6921,11220}, {6959,13369}, {7971,12629}, {8545,11496}, {9856,12650}, {10167,13747}, {10306,12686}, {10394,12675}, {11500,13528}, {12330,17857}
X(18239) = reflection of X(i) in X(j) for these (i,j): (65, 6256), (1071, 6260)
X(18239) = anticomplement of X(18238)
X(18239) = X(4)-of-extouch-triangle
X(18239) = X(12420)-of-intouch-triangle
X(18239) = X(12421)-of-excentral-triangle
X(18239) = X(17649)-of-outer-Garcia-triangle
X(18239) = extouch-isogonal conjugate of X(1158)
X(18239) = X(8)-Ceva conjugate of X(1210)
X(18240) lies on these lines: {1,88}, {2,14740}, {11,118}, {65,15558}, {80,938}, {104,3333}, {149,10580}, {153,11037}, {165,7673}, {496,12005}, {499,3678}, {516,3660}, {518,6667}, {528,11018}, {676,3738}, {758,5570}, {942,1387}, {946,15528}, {952,5045}, {999,11715}, {1056,12751}, {1058,14217}, {1145,5439}, {1210,3881}, {1317,17609}, {1537,3671}, {1736,17449}, {1768,10980}, {2829,4298}, {3035,3742}, {3086,3874}, {3338,10058}, {3488,12119}, {3812,5854}, {3878,5744}, {3887,14760}, {3892,15863}, {3968,12647}, {5049,6797}, {5531,14151}, {5533,10122}, {5536,7677}, {5660,11038}, {5708,12515}, {5840,13373}, {5880,13271}, {5884,11373}, {5902,12758}, {6147,12611}, {6265,15934}, {6713,12432}, {6744,16193}, {7373,12737}, {8083,8104}, {8227,12665}, {9940,12575}, {10164,17642}, {10404,12764}, {10589,15064}, {10698,11529}, {10707,11020}, {11033,13267}, {11570,14986}
X(18240) = midpoint of X(i) and X(j) for these {i,j}: {1, 12736}, {11, 5083}, {65, 15558}, {942, 1387}, {946, 15528}
X(18240) = complement of X(14740)
X(18240) = incircle-inverse-of X(1054)
X(18240) = X(113) of incircle-circles triangle
X(18240) = X(125) of inverse-in-incircle triangle
X(18240) = X(5972) of intouch triangle
X(18240) = X(6723) of Ursa-minor triangle
X(18240) = X(12736) of anti-Aquila triangle
X(18240) = X(15473) of 2nd circumperp triangle
X(18240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11, 354, 5083), (354, 17626, 11019), (3742, 12915, 13405), (5049, 6797, 12735)
X(18241) lies on these lines: {1,5920}, {2,12670}, {142,5045}, {354,11023}, {5173,10122}, {5687,12658}, {5785,15185}, {5836,17706}, {6001,18219}, {9804,11024}
X(18241) = complement of X(12670)
X(18242) lies on these lines: {1,1532}, {2,12114}, {3,119}, {4,12}, {5,515}, {8,6932}, {10,5777}, {11,944}, {20,11681}, {30,6796}, {40,17757}, {56,6834}, {65,1512}, {84,1698}, {100,11826}, {104,5433}, {140,5450}, {153,2975}, {198,15849}, {226,7686}, {227,1785}, {355,2886}, {381,16202}, {388,6848}, {411,5080}, {442,1490}, {495,946}, {496,5882}, {497,10893}, {498,1012}, {517,10915}, {528,10525}, {529,11249}, {908,14110}, {952,3813}, {958,6825}, {971,3826}, {1001,6893}, {1158,3652}, {1210,3660}, {1376,6850}, {1478,3149}, {1519,3057}, {1537,5697}, {1621,13729}, {1768,5445}, {2098,10956}, {2099,10955}, {2551,6908}, {2800,3678}, {3086,6969}, {3303,10531}, {3304,10805}, {3419,17857}, {3428,3436}, {3475,5804}, {3545,7958}, {3560,6690}, {3576,4187}, {3612,5691}, {3614,6830}, {3616,6945}, {3634,6705}, {3679,7971}, {3814,4297}, {3820,6684}, {3829,10943}, {3925,5658}, {4193,5731}, {4197,9799}, {4293,6927}, {4413,6897}, {4423,6898}, {4999,6863}, {5123,9943}, {5204,6880}, {5217,6938}, {5253,6979}, {5432,6906}, {5552,6925}, {5603,15888}, {5693,13257}, {5720,5794}, {5787,6881}, {5790,9710}, {5791,12677}, {6223,9780}, {6245,8728}, {6668,6862}, {6691,6959}, {6734,14872}, {6837,10585}, {6847,10588}, {6905,7354}, {6913,10198}, {6923,11499}, {6929,10267}, {6934,12943}, {6942,15326}, {6947,8273}, {6968,10896}, {6985,10526}, {7682,12915}, {7705,11220}, {7952,10271}, {7956,13464}, {8227,12650}, {8582,18238}, {8727,10592}, {9708,18237}, {9709,12330}, {10039,12672}, {10165,17527}, {10167,17619}, {10523,10572}, {10532,11237}, {10598,10806}, {10711,12762}, {10864,17529}, {10902,11113}, {10954,12047}, {11014,12751}, {12680,17606}
X(18242) = midpoint of X(i) and X(j) for these {i,j}: {3, 6256}, {4, 11500}, {10, 6260}, {100, 12761}, {355, 6261}, {1158, 6259}, {6985, 10526}
X(18242) = complement of X(12114)
X(18242) = X(155)-of-4th-Euler-triangle
X(18242) = X(5504)-of-K798i-triangle
X(18242) = X(7680)-of-outer-Johnson-triangle
X(18242) = X(9932)-of-2nd-Zaniah-triangle
X(18242) = X(11500)-of-Euler-triangle
X(18242) = X(12163)-of-3rd-Euler-triangle
X(18242) = (K798i)-isogonal conjugate of-X(6713)
X(18242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1532, 7681), (2, 12667, 12114), (3, 119, 1329), (4, 12, 7680), (4, 3085, 11496), (4, 10590, 10894), (4, 10786, 55), (4, 11491, 6284), (5, 1385, 3816), (8, 6932, 15908), (104, 6949, 5433), (153, 6960, 2975), (355, 6842, 2886), (944, 6941, 11), (6834, 12115, 56)
X(18243) lies on these lines: {3,16127}, {4,3649}, {5,3833}, {10,5777}, {40,13257}, {84,3624}, {145,12667}, {226,12710}, {411,3648}, {515,1483}, {944,9670}, {946,5049}, {971,9955}, {1490,5842}, {1519,12680}, {1532,15071}, {1768,5442}, {2800,4127}, {2829,6259}, {3616,6223}, {3671,16616}, {3816,13369}, {5087,9942}, {5658,6361}, {5768,10893}, {6147,6744}, {6824,16112}, {6985,17768}, {7483,7701}, {7680,12688}, {7956,12005}, {9960,10129}, {11113,16132}, {11246,16116}, {12528,15908}, {12701,12831}
X(18243) = midpoint of X(3) and X(16127)
X(18244) lies on these lines: {1,5180}, {2,12682}, {35,13080}, {56,13126}, {79,942}, {142,12444}, {191,3584}, {498,12535}, {499,12849}, {946,16116}, {1387,3649}, {1479,12255}, {1749,14526}, {2475,3919}, {2771,5270}, {3065,12047}, {3543,18221}, {3582,11263}, {3585,12600}, {3746,13995}, {4325,16132}, {4857,16159}, {5441,11011}, {5572,16153}, {5836,16152}, {6869,16143}, {7280,12556}, {7741,12919}, {7951,12947}, {10572,11552}, {11024,12543}, {12660,17700}
X(18244) = reflection of X(3746) in X(13995)
X(18244) = complement of X(12682)
X(18244) = X(13418) of inverse-in-incircle triangle
X(18244) = (inverse-in-incircle)-isotomic conjugate of-X(7269)
X(18244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (79, 17637, 3583), (10266, 13129, 1)
X(18245) lies on these lines: {84,493}, {515,12636}, {971,10669}, {1490,11828}, {1709,11951}, {2829,12741}, {6001,12440}, {6223,6462}, {6245,8212}, {6257,8218}, {6258,8216}, {6259,8220}, {6260,8222}, {6461,18246}, {7971,8210}, {7992,8188}, {8194,9910}, {8201,12456}, {8208,12457}, {8214,12667}, {8987,13899}, {10085,11953}, {10875,12496}, {10945,12676}, {10951,12677}, {11377,12114}, {11394,12136}, {11503,12330}, {11840,12196}, {11846,12246}, {11907,12668}, {11930,12678}, {11932,12679}, {11947,12680}, {11949,12684}, {11955,12686}, {11957,12687}, {13956,13974}
X(18245) = X(84) of Lucas homothetic triangle
X(18246) lies on these lines: {84,494}, {515,12637}, {971,10673}, {1490,11829}, {1709,11952}, {2829,12742}, {6001,12441}, {6223,6463}, {6245,8213}, {6257,8219}, {6258,8217}, {6259,8221}, {6260,8223}, {6461,18245}, {7971,8211}, {7992,8189}, {8195,9910}, {8202,12456}, {8209,12457}, {8215,12667}, {8987,13900}, {10085,11954}, {10876,12496}, {10946,12676}, {10952,12677}, {11378,12114}, {11395,12136}, {11504,12330}, {11841,12196}, {11847,12246}, {11908,12668}, {11931,12678}, {11933,12679}, {11948,12680}, {11950,12684}, {11956,12686}, {11958,12687}, {13957,13974}
X(18246) = X(84) of Lucas(-1) homothetic triangle
X(18247) lies on these lines: {1,18227}, {2,9850}, {4,5836}, {8,9848}, {9,3913}, {10,971}, {188,9853}, {210,3486}, {354,8165}, {518,938}, {519,960}, {936,958}, {1125,12128}, {1329,3742}, {1376,9841}, {1706,15726}, {2886,9842}, {3333,8169}, {3697,5234}, {3812,5290}, {3820,12675}, {3983,5273}, {4711,5837}, {5044,5882}, {5123,8728}, {5328,17609}, {5745,9858}, {6261,9708}, {6738,9954}, {7028,9854}, {8580,9851}, {9797,18228}, {9846,18230}, {9852,18235}, {12126,18229}, {12127,15829}, {17644,18236}
X(18247) = midpoint of X(8) and X(9848)
X(18247) = complement of X(9850)
X(18247) = {X(2), X(12125)}-harmonic conjugate of X(9850)
X(18248) lies on these lines: {2,12389}, {8,12400}, {9,12396}, {210,17633}, {518,12403}, {936,12398}, {958,12388}, {1125,12401}, {1329,12394}, {1376,12387}, {2886,12393}, {5273,12390}, {5745,12385}, {8580,12404}, {12386,18227}, {12391,18228}, {12392,18229}, {12395,15829}, {12399,18230}, {12405,18235}, {17645,18236}
X(18248) = midpoint of X(8) and X(12400)
X(18248) = complement of X(12402)
X(18248) = {X(2), X(12389)}-harmonic conjugate of X(12402)
X(18249) lies on these lines: {1,5273}, {2,3339}, {3,9948}, {4,9}, {8,4314}, {21,6737}, {55,6743}, {63,4298}, {72,13405}, {144,5290}, {188,12568}, {191,4292}, {210,12711}, {220,3997}, {236,12570}, {270,2328}, {329,3947}, {387,4356}, {388,3929}, {405,6738}, {518,12564}, {519,958}, {551,12559}, {758,942}, {936,10164}, {946,5791}, {950,3683}, {986,3008}, {997,8726}, {1001,6744}, {1046,3664}, {1212,3931}, {1329,3828}, {1376,12511}, {1698,4295}, {1788,7308}, {2325,3714}, {2886,12558}, {3219,12527}, {3305,8582}, {3452,3634}, {3626,5302}, {3636,5289}, {3647,15823}, {3679,4294}, {3686,3704}, {3740,18251}, {3812,6666}, {3817,5705}, {3876,6745}, {3911,12709}, {3927,5850}, {4047,5750}, {4208,4312}, {4297,9799}, {4326,4882}, {4357,10521}, {4640,12512}, {4656,5230}, {4662,15733}, {4847,5250}, {5044,6001}, {5129,5775}, {5220,12855}, {5249,11684}, {5261,6172}, {5692,13411}, {5744,8583}, {5785,7992}, {6700,10176}, {7028,12569}, {8580,9949}, {9708,11362}, {9858,10178}, {11529,16845}, {12446,18227}, {12544,18229}, {12560,18230}, {12567,18235}, {12607,15481}, {17646,18236}
X(18249) = midpoint of X(8) and X(4314)
X(18249) = complement of X(3671)
X(18249) = X(578) of 2nd Zaniah triangle
X(18249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 12526, 3671), (8, 4512, 4314), (9, 10, 18250), (10, 5493, 2550), (960, 5745, 1125), (960, 18253, 5745), (4847, 5250, 12575), (5325, 5837, 958), (18228, 18231, 1698)
X(18250) lies on these lines: {1,5129}, {2,3361}, {4,9}, {8,4082}, {20,8580}, {21,6745}, {56,5316}, {63,8582}, {72,6738}, {144,3339}, {188,12580}, {200,452}, {210,950}, {236,12582}, {329,3671}, {341,3883}, {388,7308}, {390,4882}, {405,13405}, {515,5044}, {518,6744}, {519,960}, {527,3812}, {908,5260}, {936,4297}, {938,5223}, {942,5850}, {946,8158}, {958,999}, {993,6700}, {1056,3646}, {1212,5717}, {1329,3634}, {1376,12512}, {1698,4208}, {1722,3663}, {1770,18231}, {1788,3929}, {1837,3715}, {2325,3704}, {2478,4847}, {2886,12571}, {2899,11679}, {3008,13161}, {3059,9844}, {3244,15829}, {3305,3436}, {3333,17559}, {3624,5328}, {3626,5837}, {3679,10624}, {3686,3714}, {3697,11113}, {3820,6684}, {3828,5325}, {3876,6737}, {3983,6284}, {4301,9623}, {4312,11024}, {4315,8583}, {4342,4853}, {4512,7080}, {4538,4662}, {4640,9711}, {4679,12053}, {4915,9785}, {5084,11019}, {5123,18253}, {5231,6919}, {5250,6736}, {5251,13411}, {5261,12573}, {5716,7322}, {5779,9948}, {5785,9799}, {5791,10175}, {6685,16850}, {7028,12581}, {8169,16408}, {12545,18229}, {12579,18235}, {12607,15254}, {17647,18236}
X(18250) = midpoint of X(i) and X(j) for these {i,j}: {8, 12575}, {72, 6738}
X(18250) = complement of X(4298)
X(18250) = X(389) of 2nd Zaniah triangle
X(18250) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 12527, 4298), (9, 10, 18249), (9, 2551, 10), (10, 5493, 1706), (200, 452, 4314), (210, 950, 6743), (958, 3452, 1125), (1329, 5302, 5745), (1329, 5745, 3634), (1706, 5698, 5493), (5129, 5815, 1), (5273, 8165, 1698)
X(18251) lies on these lines: {1,5696}, {2,12529}, {8,12709}, {9,5584}, {10,5777}, {20,17668}, {72,2550}, {210,1706}, {236,12716}, {392,4294}, {516,960}, {517,5794}, {518,3671}, {758,3626}, {936,10310}, {942,2886}, {958,971}, {1125,12710}, {1329,10157}, {1376,3579}, {1818,6051}, {1858,3925}, {2551,5927}, {2975,17616}, {3059,11523}, {3600,10861}, {3617,17615}, {3660,10527}, {3740,18249}, {3742,12564}, {3813,12915}, {4292,5857}, {4326,9848}, {4512,5217}, {4640,12511}, {4662,9954}, {4999,11227}, {5087,12558}, {5248,9858}, {5273,9961}, {5436,14100}, {5745,9943}, {5842,17647}, {6762,8581}, {7288,17612}, {9623,14872}, {9800,18228}, {9949,18227}, {11036,15185}, {12527,16120}, {12548,18229}, {12651,15829}, {12706,18230}, {12713,18235}, {17650,18236}
X(18251) = midpoint of X(i) and X(j) for these {i,j}: {8, 12709}, {72, 4295}, {3059, 12560}
X(18251) = reflection of X(942) in X(12609)
X(18251) = complement of X(12711)
X(18251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 12529, 12711), (210, 17634, 12526)
X(18252) lies on these lines: {2,12530}, {8,12721}, {9,1721}, {188,12726}, {210,3729}, {236,12728}, {354,17304}, {516,960}, {517,4660}, {518,3663}, {936,12717}, {942,3821}, {958,990}, {1125,12722}, {1155,16566}, {1329,12618}, {1376,1766}, {1716,16583}, {1742,3061}, {2805,17229}, {2886,12610}, {3740,17355}, {3912,11997}, {3923,5044}, {4523,4655}, {5273,9962}, {5745,9944}, {5784,10444}, {7028,12727}, {7996,8580}, {9004,17345}, {9564,10445}, {9801,18228}, {9950,18227}, {9957,17766}, {12652,15829}, {12718,18230}, {12725,18235}, {17651,18236}
X(18252) = midpoint of X(i) and X(j) for these {i,j}: {8, 12721}, {4523, 4655}
X(18252) = reflection of X(i) in X(j) for these (i,j): (942, 3821), (3923, 5044)
X(18252) = complement of X(12723)
X(18252) = X(317) of 2nd Zaniah triangle
X(18252) = (2nd Zaniah)-isotomic conjugate of-X(5777)
X(18252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 12530, 12723), (210, 17635, 3729)
X(18253) lies on these lines: {1,15670}, {2,3649}, {5,18233}, {8,21}, {9,46}, {10,30}, {12,3219}, {40,9710}, {44,5530}, {63,10404}, {72,6690}, {140,5694}, {145,15672}, {188,16146}, {210,17637}, {236,16151}, {517,16617}, {518,10122}, {519,15174}, {524,3178}, {758,942}, {846,1834}, {908,6668}, {936,16132}, {946,5771}, {952,12104}, {993,5428}, {1046,17056}, {1158,3652}, {1210,15254}, {1376,3651}, {1749,17757}, {2475,2551}, {2771,3035}, {2795,3039}, {2886,5791}, {2975,5427}, {3036,4691}, {3085,5220}, {3241,15675}, {3244,5837}, {3305,16140}, {3336,17529}, {3452,11263}, {3474,3648}, {3616,15671}, {3617,15677}, {3622,5289}, {3623,15676}, {3633,5426}, {3634,6701}, {3679,5441}, {3683,6734}, {3715,5552}, {3740,5777}, {3813,5250}, {3820,5499}, {3829,16155}, {3831,4422}, {3876,5432}, {3878,10021}, {3927,10198}, {3951,17718}, {4067,5719}, {4197,11246}, {4420,4995}, {4913,6362}, {5123,18250}, {5506,17575}, {5587,16113}, {5692,7483}, {5852,13407}, {6745,14454}, {6857,12635}, {7028,16147}, {8256,9708}, {8580,16143}, {9588,10860}, {9709,16117}, {9948,10164}, {10175,16125}, {12607,17699}, {14450,18228}, {15829,16126}, {16120,18227}, {16124,18229}, {16133,18230}, {16142,17606}, {16144,18234}, {17653,18236}
X(18253) = midpoint of X(i) and X(j) for these {i,j}: {8, 10543}, {10, 3647}, {1749, 17757}, {3679, 17525}
X(18253) = complement of X(3649)
X(18253) = X(54) of 2nd Zaniah triangle
X(18253) = X(6152) of 4th Euler triangle
X(18253) = (2nd Zaniah)-isogonal conjugate of-X(5044)
X(18253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11684, 3649), (8, 21, 10543), (10, 5325, 5302), (79, 191, 3650), (79, 1698, 442), (191, 1698, 79), (442, 3650, 79), (960, 5745, 4999), (1125, 16137, 11281), (3648, 9780, 6175), (5745, 18249, 960), (5791, 12514, 2886), (6675, 16137, 1125)
Let A'B'C' be the Inner Garcia triangle. Let A" be the orthogonal projection of A on line B'C', and define B", C" cyclically. Triangle A"B"C" is perpsective to the extouch triangle at X(18254). (Randy Hutson, June 27, 2018)
X(18254) lies on these lines: {2,11570}, {3,18232}, {8,80}, {9,48}, {10,119}, {11,72}, {63,10090}, {78,90}, {100,3876}, {188,12771}, {210,1145}, {236,12774}, {392,1317}, {405,12739}, {517,3036}, {518,1387}, {519,15558}, {758,908}, {912,6713}, {936,1768}, {942,6667}, {952,960}, {956,12740}, {958,6265}, {1125,5083}, {1158,5720}, {1320,3681}, {1329,5694}, {1376,12515}, {1698,11571}, {2478,10073}, {2551,12247}, {2771,3035}, {2829,5777}, {2886,12611}, {3032,4115}, {3086,3874}, {3219,4996}, {3419,12764}, {3436,10057}, {3452,10265}, {3647,17100}, {3754,7951}, {3877,12531}, {3968,17057}, {4533,13996}, {5123,14988}, {5219,5883}, {5250,10087}, {5273,9964}, {5289,12737}, {5660,18231}, {5698,13199}, {5705,15017}, {5745,9946}, {5794,10742}, {5904,10529}, {6127,16586}, {6264,15829}, {7028,12772}, {8580,12767}, {8666,12059}, {9623,13253}, {9803,18228}, {9952,18227}, {11113,12743}, {11813,16174}, {12447,13227}, {12551,18229}, {12755,18230}, {12770,18235}, {17654,18236}
X(18254) = midpoint of X(i) and X(j) for these {i,j}: {8, 12758}, {11, 72}
X(18254) = reflection of X(942) in X(6667)
X(18254) = complement of X(11570)
X(18254) = X(265)-of-2nd-Zaniah-triangle
X(18254) = X(10)-of-A"B"C", as described at X(8068)
X(18254) = 2nd Zaniah-isogonal conjugate of-X(5123)
X(18254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 12532, 11570), (104, 997, 214), (210, 17638, 1145)
X(18255) lies on these lines: {2,12533}, {8,5920}, {9,3295}, {10,12864}, {210,17639}, {518,12855}, {936,12842}, {958,12521}, {1125,12853}, {1329,12620}, {1376,12516}, {2886,12612}, {3555,11018}, {4882,9898}, {5273,12537}, {5745,12439}, {8001,8580}, {9804,18228}, {9953,18227}, {12552,18229}, {12654,15829}, {12846,18230}, {12869,18235}, {17655,18236}
X(18255) = midpoint of X(8) and X(5920)
X(18255) = complement of X(12854)
X(18255) = (2nd Zaniah)-isogonal conjugate of-X(9710)
X(18255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 12533, 12854), (6765, 7160, 12631)
X(18256) lies on these lines: {145,188}, {483,7028}, {557,16017}, {2090,14121}
X(18257) lies on these lines: {2,12534}, {8,12876}, {9,12659}, {19,7359}, {210,17640}, {518,12914}, {522,596}, {936,12843}, {958,12522}, {1125,12907}, {1329,12621}, {1376,12517}, {2886,12613}, {5273,12538}, {5745,12442}, {8580,13069}, {12449,18227}, {12542,18228}, {12553,18229}, {12655,15829}, {12847,18230}, {13071,18235}, {17656,18236}
X(18257) = midpoint of X(8) and X(12876)
X(18257) = complement of X(12912)
X(18257) = {X(2), X(12534)}-harmonic conjugate of X(12912)
X(18258) lies on these lines: {1,188}, {2,177}, {8,7048}, {9,164}, {10,2090}, {142,178}, {145,11234}, {167,8580}, {210,17641}, {236,13092}, {518,5571}, {936,12844}, {958,12523}, {1125,12908}, {1329,12622}, {1376,12518}, {2886,12614}, {3616,11191}, {5273,12539}, {7670,18230}, {9807,18228}, {11530,12879}, {12450,18227}, {12554,18229}, {12656,15829}, {13090,18234}, {13091,18235}, {17657,18236}
X(18258) = {8, 8422}, {164, 12694}, {177, 11691}
X(18258) = reflection of X(12908) in X(1125)
X(18258) = complement of X(177)
X(18258) = X(i)-complementary conjugate of X(j) for these (i,j): {260, 10}, {10492, 116}
X(18258) = X(1)-of-2nd-Zaniah-triangle
X(18258) = X(12262)-of-Hutson-intouch-triangle
X(18258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11691, 177), (188, 7028, 1), (188, 12646, 10233)
X(18259) lies on these lines: {2,10044}, {8,6597}, {9,10266}, {10,191}, {20,7701}, {21,60}, {63,14450}, {210,17643}, {518,12917}, {936,12845}, {958,12524}, {1125,12909}, {1329,12623}, {1376,12519}, {1749,14526}, {2886,12615}, {3218,11263}, {3647,17100}, {3651,3652}, {3715,12342}, {3876,12745}, {4189,12786}, {5273,12540}, {5745,12444}, {6734,11604}, {8580,13101}, {12451,18227}, {12514,15680}, {12543,18228}, {12557,18229}, {12657,15829}, {12849,18232}, {12850,18230}, {13123,18235}, {17659,18236}
X(18259) = midpoint of X(8) and X(12877)
X(18259) = complement of X(12913)
X(18259) = {X(2), X(12535)}-harmonic conjugate of X(12913)
X(18260) lies on these lines: {104,13750}, {354,1158}, {495,12616}, {515,3812}, {942,5450}, {946,3660}, {2800,5045}, {3742,12608}, {5439,6256}, {5570,6906}, {5884,16193}, {5901,6001}, {6705,11018}, {6796,11227}, {10202,12114}
X(18260) = midpoint of X(i) and X(j) for these {i,j}: {942, 5450}, {6705, 12005}
X(18260) = complement of X(32159)
X(18260) = X(5) of 1st Zaniah triangle
X(18260) = {X(3742), X(18238)}-harmonic conjugate of X(12608)
X(18261) lies on these lines: {1,142}, {527,3554}, {1449,7269}, {4667,7190}, {4861,17306}
X(18261) = X(6) of 1st Zaniah triangle
X(18261) = (1st Zaniah)-isogonal conjugate of-X(3742)
X(18262) lies on the cubic K988 and theselines: {1, 3492}, {31, 184}, {32, 1917}, {385, 1492}, {692, 17735}, {846, 3955}, {1911, 1933}, {1980, 3063}, {3506, 3510}
X(18262) = isogonal conjugate of X(18036)
X(18262) = X(1911)-Ceva conjugate of X(32)
X(18262) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18036}, {75, 7261}, {76, 3512}, {561, 8852}, {6063, 7281}, {7018, 7061}
X(18262) = X(31)-Hirst inverse of X(7122)
X(18262) = barycentric product X(i)*X(j) for these {i,j}: {6, 17798}, {31, 3509}, {32, 4645}, {41, 5018}, {291, 18038}, {560, 17789}, {1281, 1922}, {2206, 4071}, {14598, 18037}
X(18262) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18036}, {32, 7261}, {560, 3512}, {1501, 8852}, {3509, 561}, {4645, 1502}, {9447, 7281}, {17789, 1928}, {17798, 76}, {18038, 350}
X(18263) lies on the cubic K988 and these lines: {741, 1326}, {9505, 17962}
X(18263) = isogonal conjugate of X(18035)
X(18263) = X(32)-cross conjugate of X(1922)
X(18263) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18035}, {75, 6651}, {76, 8298}, {350, 6542}, {874, 2786}, {1757, 1921}, {3948, 17731}, {6382, 8843}
X(18263) = barycentric product X(i)*X(j) for these {i,j}: {6, 9506}, {31, 9505}, {292, 17962}, {741, 2054}, {1911, 1929}, {1922, 6650}, {2702, 3572}, {14598, 18032}
X(18263) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18035}, {32, 6651}, {560, 8298}, {1922, 6542}, {9505, 561}, {9506, 76}, {14598, 1757}, {17962, 1921}
X(18264) lies on the cubic K988
X(18264) = isogonal conjugate of X(18034)
X(18264) = X(32)-cross conjugate of X(1914)
X(18264) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18034}, {75, 9470}, {334, 8301}, {335, 17738}
X(18264) = barycentric product X(i)*X(j) for these {i,j}: {6, 9472}, {1914, 2113}
X(18264) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18034}, {32, 9470}, {2210, 17738}, {9472, 76}, {14599, 8301}
X(18265) lies on the cubics K866 and K988 and on these lines: {3, 291}, {21, 4518}, {32, 1922}, {35, 3864}, {55, 2344}, {284, 2311}, {292, 1438}, {604, 1911}, {983, 1582}, {1918, 1927}, {3862, 15624}
X(18265) = isogonal conjugate of X(18033)
X(18265) = X(1253)-beth conjugate of X(3939)
X(18265) = X(1911)-Ceva conjugate of X(1922)
X(18265) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18033}, {2, 10030}, {7, 350}, {57, 1921}, {75, 1447}, {76, 1429}, {85, 239}, {238, 6063}, {242, 7182}, {269, 4087}, {274, 16609}, {279, 3975}, {310, 1284}, {561, 1428}, {659, 4572}, {664, 3766}, {799, 7212}, {812, 4554}, {873, 7235}, {874, 3676}, {1088, 3685}, {1431, 1926}, {1432, 3978}, {1434, 3948}, {1966, 7249}, {3716, 4569}, {4010, 4625}, {7196, 17493}
X(18265) = X(2330)-Hirst inverse of X(7077)
X(18265) = crosssum of X(350) and X(10030)
X(18265) = X(18264) = barycentric product X(i)*X(j) for these {i,j}: {6, 7077}, {8, 1922}, {9, 1911}, {31, 4876}, {32, 4518}, {33, 2196}, {41, 291}, {42, 2311}, {55, 292}, {295, 607}, {312, 14598}, {334, 9447}, {335, 2175}, {644, 875}, {660, 3063}, {663, 813}, {694, 2330}, {741, 1334}, {1808, 2333}, {1927, 17787}, {1967, 2329}, {2195, 3252}, {3572, 3939}, {4140, 17938}, {7081, 9468}, {7233, 14827}
barycentric quotient X(i)/X(j) for these {i,j}: {6, 18033}, {31, 10030}, {32, 1447}, {41, 350}, {55, 1921}, {220, 4087}, {292, 6063}, {560, 1429}, {669, 7212}, {813, 4572}, {1253, 3975}, {1501, 1428}, {1911, 85}, {1918, 16609}, {1922, 7}, {1927, 1432}, {2175, 239}, {2196, 7182}, {2205, 1284}, {2311, 310}, {2329, 1926}, {2330, 3978}, {3063, 3766}, {4518, 1502}, {4876, 561}, {7077, 76}, {7081, 14603}, {7109, 7235}, {8789, 1431}, {9447, 238}, {9448, 1914}, {9468, 7249}, {14598, 57}, {14827, 3685}
X(18266) lies on the cubic K988 and these lines: {21, 756}, {31, 32}, {36, 386}, {42, 172}, {48, 2209}, {100, 1580}, {101, 3747}, {239, 11364}, {244, 11349}, {560, 15624}, {692, 922}, {872, 1333}, {976, 13723}, {1326, 1757}, {1691, 7077}, {1914, 2109}, {1918, 2174}, {1964, 2220}, {2177, 4262}, {3285, 4557}, {6542, 8298}, {7032, 16946}
X(18266) = isogonal conjugate of X(18032)
X(18266) = X(55)-beth conjugate of X(17798)
X(18266) = X(i)-Ceva conjugate of X(j) for these (i,j): {1326, 17735}, {1911, 31}
X(18266) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18032}, {2, 6650}, {69, 17982}, {75, 1929}, {76, 17962}, {86, 11599}, {99, 18014}, {264, 17972}, {274, 9278}, {310, 2054}, {350, 9505}, {523, 17930}, {670, 18001}, {850, 17940}, {1509, 6543}, {1921, 9506}, {2702, 3261}
X(18266) = X(31)-Hirst inverse of X(213)
X(18266) = crossdifference of every pair of points on line {693, 4359}
X(18266) = crosssum of X(i) and X(j) for these (i,j): {1111, 3766}, {3948, 4647}
X(18266) = barycentric product X(i)*X(j) for these {i,j}: {1, 17735}, {6, 1757}, {19, 17976}, {31, 6542}, {37, 1326}, {42, 1931}, {48, 17927}, {100, 5029}, {101, 9508}, {163, 18004}, {213, 17731}, {228, 423}, {292, 8298}, {661, 17943}, {662, 17990}, {692, 2786}, {798, 17934}, {1333, 6541}, {1911, 6651}, {14598, 18035}
X(18266) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18032}, {31, 6650}, {32, 1929}, {163, 17930}, {213, 11599}, {560, 17962}, {798, 18014}, {872, 6543}, {1326, 274}, {1757, 76}, {1918, 9278}, {1922, 9505}, {1924, 18001}, {1931, 310}, {1973, 17982}, {2205, 2054}, {5029, 693}, {6542, 561}, {8298, 1921}, {9247, 17972}, {9508, 3261}, {14598, 9506}, {17731, 6385}, {17735, 75}, {17927, 1969}, {17934, 4602}, {17943, 799}, {17976, 304}, {17990, 1577}
X(18266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (32, 869, 31), (2210, 2223, 31), (2223, 2251, 2210)
X(18267) lies on the cubic K988 and these lines: {1911, 1914}, {1922, 9454}, {9455, 14598}
X(18268) lies on the cubics K988 and K997 and on these lines: {6, 662}, {32, 163}, {58, 101}, {81, 4586}, {83, 1509}, {99, 17475}, {110, 1977}, {593, 3051}, {643, 1979}, {692, 1333}, {694, 1169}, {875, 923}, {876, 1910}, {1408, 1415}, {1931, 16514}, {3114, 7307}, {4876, 16785}
X(18269) lies on the cubic K988 and these lines: {604, 1403}, {1922, 1927}
X(18269) = barycentric product X(7121)*X(17792)
X(18270) lies on the cubic K989 and these lines: {1581, 1965}, {1923, 4602}
X(18270) = X(31)-Ceva conjugate of X(1966)
X(18271) lies on the cubic K990 and these lines: {1, 1965}, {38, 1925}, {256, 9230}, {291, 3978}
X(18271) = X(1967)-Ceva conjugate of X(75)
X(18271) = X(1)-Hirst inverse of X(1965)
X(18271) = barycentric product X(1926)*X(8871)
X(18271) = barycentric quotient X(8871)/X(1967)
X(18272) lies on the cubic K991 and these lines: {1, 1925}, {31, 1582}, {384, 904}, {385, 1911}, {1964, 1965}, {1967, 2236}, {5999, 8927}
X(18272) = X(1967)-aleph conjugate of X(17799)
X(18272) = X(560)-he conjugate of X(1740)
X(18272) = X(1927)-Ceva conjugate of X(1)
X(18272) = X(31)-Hirst inverse of X(1582)
X(18272) = barycentric product X(1966)*X(8871)
X(18272) = barycentric quotient X(8871)/X(1581)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3510, 7168, 385), (6196, 7346, 384)
X(18273) lies on the cubic K992 and these lines: {1925, 1934}
X(18273) = X(1)-Ceva conjugate of X(1926)
X(18274) lies on the cubics K788 and K993 and on these lines: {31, 1979}, {32, 6196}, {100, 699}, {172, 694}, {238, 8623}, {350, 385}, {662, 1333}, {1580, 8845}, {1691, 2210}
X(18274) = X(32)-Ceva conjugate of X(1914)
X(18274) = crosspoint of X(3510) and X(8875)
X(18274) = crosssum of X(7168) and X(8868)
X(18274) = X(335)-isoconjugate of X(7168)
X(18274) = X(1691)-Hirst inverse of X(2210)
X(18274) = barycentric product X(238)*X(3510)
X(18274) = barycentric quotient X(i)/X(j) for these {i,j}: {2210, 7168}, {3510, 334}, {18038, 8868}
X(18275) lies on the cubic K994 and these lines: {1, 7346}, {75, 982}, {76, 1928}, {335, 1926}, {561, 3662}, {1978, 17759}, {3261, 3835}
X(18275) = X(335)-Ceva conjugate of X(76)
X(18275) = X(32)-isoconjugate of X(7168)
X(18275) = X(75)-Hirst inverse of X(1920)
X(18275) = barycentric product X(561)*X(3510)
X(18275) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 7168}, {3510, 31}, {17789, 8868}
X(18276) lies on the cubic K995 and these lines: {75, 1925}, {334, 14603}
X(18275) = X(1581)-Ceva conjugate of X(561)
X(18275) = X(75)-Hirst inverse of X(1925)
X(18275) = barycentric quotient X(8871)/X(1927)
X(18277) lies on the cubic K996 and these lines: {37, 6386}, {75, 3122}, {76, 3061}, {274, 4602}, {334, 1581}, {350, 3978}, {1921, 14603}, {1926, 3948}
X(18277) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1921}, {3510, 141}
X(18277) = X(2)-Ceva conjugate of X(1921)
X(18277) = X(1922)-isoconjugate of X(7168)
X(18277) = X(350)-Hirst inverse of X(3978)
X(18277) = crosssum of circumcircle intercepts of line PU(12) (line X(1918)X(1919))
X(18277) = complementary conjugate of complement of X(18278)
X(18277) = barycentric quotient X(i)/X(j) for these {i,j}: {350, 7168}, {3510, 1911}, {18037, 8868}
X(18278) lies on the cubics K432 and K997 and on these lines: {1, 3495}, {6, 75}, {31, 172}, {171, 213}, {292, 1755}, {825, 14602}, {1403, 3224}, {1429, 2111}, {1580, 1922}, {1911, 3747}, {1967, 16365}, {1979, 2223}, {2231, 17790}
X(18278) = X(i)-Ceva conjugate of X(j) for these (i,j): {1580, 17798}, {1922, 6}
X(18278) = crosspoint of X(i) and X(j) for these (i,j): {813, 5383}
X(18278) = crossdifference of every pair of points on line {788, 3741}
X(18278) = crosssum of X(812) and X(6377)
X(18278) = X(i)-isoconjugate of X(j) for these (i,j): {2, 7168}, {7261, 8868}
X(18278) = X(i)-Hirst inverse of X(j) for these (i,j): {31, 172}
X(18278) = anticomplement of complementary conjugate of X(18277)
X(18278) = X(18278) = barycentric product X(i)*X(j) for these {i,j}: {1, 3510}, {3509, 8875}
X(18278) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 7168}, {3510, 75}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27613.
X(18279) lies on these lines: {3,16177}, {4,74}, {5,523}, {402,7740}, {5502,11911}, {5972,15454}, {6000,11251}, {6070,14264}, {6640,14379}, {10255,14059}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27614.
X(18280) lies on this line: {1,3}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27615.
X(18281) lies on these lines: {2,3}, {49,11457}, {68,13561}, {70,16867}, {125,13352}, {156,14216}, {499,8144}, {524,8548}, {541,3357}, {542,1147}, {568,15061}, {576,15118}, {2888,15124}, {5418,11265}, {5420,11266}, {5449,13346}, {5462,5476}, {5562,13857}, {5642,10539}, {5654,5663}, {5878,15138}, {6102,16270}, {6247,9820}, {6662,9214}, {6699,11438}, {9306,14156}, {9630,10072}, {9927,15123}, {10264,15106}, {10282,11645}, {10510,11255}, {11064,15068}, {12038,15126}, {12118,15114}, {12161,15120}, {12325,15137}, {13363,14561}, {15113,17702}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27612 and Hyacinthos 27612.
X(18282) lies on these lines: {2, 3}, {17, 11268}, {18, 11267}, {51, 8254}, {52, 11803}, {110, 3519}, {143, 12242}, {5562, 10272}, {5663, 14862}, {5944, 10619}, {5972, 10627}, {6689, 13364}, {6723, 17712}, {7691, 11805}, {8718, 15061}, {8960, 11266}, {10192, 10274}, {13561, 14864}
X(18282) = midpoint of X(i) and X(j), for these {i, j}: {5,12107}, {26,10224}, {1658,13406}, {10020,13383}, {15331,15761}
X(18282) = reflection of X(i) in X(j), for these {i, j}: {5,12010}, {5498,10125}, {10125,10020} , {11250,10212}
See Telv Cohl and Angel Montesdeoca, Hyacinthos 27620 and HG040518.
X(18283) lies on these lines: {1,4}, {3,280}, {20,1897}, {24,1604}, {104,963}, {108,3176}, {198,7003}, {318,5731}, {451,10786}, {1071,5908}, {3183,3198}
X(18283) = reflection of X(i) in X(j) for these (i,j): (4, 7952), (280, 3)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27630.
X(18284) lies on these lines: {5,13289}, {107,7488}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27632.
X(18285) lies on these lines: {5,1117}, {30,146}
X(18285) = midpoint of X(399) and X(1138)
X(18285) = reflection of X(i) in X(j) for these {i,j}: {11749, 1138}, {14993,10272}
X(18285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3470, 3471, 5)
X(18285) = X(484)-aleph conjugate of X(1048)
X(18285) = X(i)-Ceva conjugate of X(j) for these (i,j): {10272, 5}, {14993, 30}
X(18285) = barycentric quotient X(i)/X(j) for these {i,j}: {5671, 13582}, {11063, 8487}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27638.
X(18286) lies on this line: {25, 193}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27638.
X(18287) lies on these lines: {2, 1975}, {4, 8892}, {25, 193}, {385, 17037}, {439, 1611}, {3164, 10565}, {6353, 6392}, {6462, 8854}, {6995, 8878}, {7398, 17035}
X(18287) = isogonal conjugate of X(39128)
X(18287) = anticomplement of X(6340)
X(18287) = polar conjugate of isotomic conjugate of X(39127)
X(18287) = crossdifference of every pair of points on line X(2519)X(8651)
X(18287) = trilinear product X(193)*X(19213)
X(18287) = {X(6337), X(8770)}-harmonic conjugate of X(2)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27638.
X(18288) lies on these lines: {2, 107}, {4, 17830}, {25, 64}, {232, 1033}, {3183, 6353}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27638.
X(18289) lies on these lines: {2, 371}, {4, 8280}, {6, 6676}, {22, 6560}, {25, 485}, {372, 7494}, {427, 6561}, {590, 5020}, {858, 9681}, {1151, 1368}, {1587, 10565}, {3068, 5413}, {3070, 9909}, {4232, 8960}, {5013, 8964}, {5159, 6425}, {5420, 7499}, {6200, 7386}, {6409, 10691}, {6423, 8944}, {6453, 16051}, {6459, 8889}, {6564, 6995}, {6677, 8981}, {7392, 10576}, {7396, 9541}, {7583, 10154}
X(18289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1588, 8281), (6, 6676, 18290), (3068, 6353, 8854)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27638.
X(18290) lies on these lines: {2, 372}, {4, 8281}, {6, 6676}, {22, 6561}, {25, 486}, {371, 7494}, {427, 6560}, {1152, 1368}, {1588, 10565}, {3053, 8964}, {3069, 5412}, {3071, 9909}, {5159, 6426}, {5418, 7499}, {6410, 10691}, {6424, 8940}, {6454, 16051}, {6460, 8889}, {6677, 13966}, {7392, 10577}, {7584, 10154}
X(18290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1587, 8280), (6, 6676, 18289), (3069, 6353, 8855)
X(18291) lies on these lines: {1, 164}, {40, 20114}, {168, 3973}, {361, 1743}, {8076, 45087}, {8092, 52797}, {10023, 30420}, {24242, 53001}
X(18291) = X(24242)-Ceva conjugate of X(1)
X(18291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {164, 10231, 1}, {258, 266, 1}, {8078, 53119, 1}
X(18292) lies on these lines: {1, 359}, {2, 3}
X(18293) lies on these lines: {1, 360}, {2, 3}
X(18294) lies on this line: {2, 360}
X(18294) = midpoint of X(360) and X(1115)
X(18294) = complement X(1115)
X(18294) = X(i)-complementary conjugate of X(j) for these (i,j): {7021, 10}, {7041, 141}
X(18294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 360, 1115)
X(18295) lies on this line: {2, 360}
See Angel Montesdeoca, Hyacinthos 27653.
X(18296) lies on these lines:
{65,5556}, {3091,14528}, {3146,3532}, {3426,12102}, {3431,3544}, {11270,11541}, {13851,15740}
X(18297) lies on the cubics K744, K766, and the line {510, 1759}
X(18297) = isogonal conjugate of X(18753)
X(18297) = isotomic conjugate of X(366)
X(18297) = X(4179)-cross conjugate of X(366)
X(18297) = X(i)-isoconjugate of X(j) for these (i,j): {6, 365}, {31, 366}, {56, 4166}, {604, 4182}, {1333, 4179}
X(18297) = cevapoint of X(i) and X(j) for these (i,j): {1, 510}, {366, 4182}
X(18297) = barycentric product X(i)*X(j) for these {i,j}: {75, 366}, {76, 365}, {85, 4182}, {274, 4179}, {508, 556}, {4166, 6063}
X(18297) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 365}, {2, 366}, {8, 4182}, {9, 4166}, {10, 4179}, {174, 509}, {365, 6}, {366, 1}, {508, 174}, {509, 266}, {4146, 508}, {4166, 55}, {4179, 37}, {4181, 4180}, {4182, 9}
X(18298) lies on the cubic K744 and these lines: {1, 2668}, {10, 1920}, {37, 1655}, {65, 7196}
X(18298) = isogonal conjugate of X(18756)
X(18298) = isotomic conjugate of X(1045)
X(18298) = X(i)-cross conjugate of X(j) for these (i,j): {257, 85}, {310, 75}
X(18298) = X(i)-isoconjugate of X(j) for these (i,j): {31, 1045}, {32, 1655}, {110, 9402}
X(18298) = trilinear pole of line {661, 4374}
X(18298) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1045}, {75, 1655}, {661, 9402}
X(18299) lies on the the Feuerbach hyperbola, the cubic K744, and these lines:
{8, 3978}, {9, 1966}, {76, 7155}, {256, 10030}, {1909, 4876}, {3551, 3673}
X(18299) = isogonal conjugate of X(18758)
X(18299) = isotomic conjugate of X(17792)
X(18299) = X(i)-cross conjugate of X(j) for these (i,j): {257, 274}, {18033, 2481}
X(18299) = X(i)-isoconjugate of X(j) for these (i,j): {31, 17792}, {32, 17760}, {192, 18269}, {1911, 8844}
X(18299) = cevapoint of X(i) and X(j) for these (i,j): {2, 3056}, {693, 4459}
X(18299) = trilinear pole of line {650, 14296}
X(18299) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 17792}, {75, 17760}, {239, 8844}, {7121, 18269}
Triangles and centers related to the Ehrmann pivots (PU(5)): X(18300)-X(18587)
Let TC1=A1B1C1 be the triangle obtained by rotating ABC about the 1st Ehrmann pivot, P(5), by an angle of 2π/3, so that TC1 circumscribes ABC. Triangle TC1 is here named the 1st Ehrmann circumscribing triangle. Let TC2=A2B2C2 be the triangle obtained by rotating ABC about the 2nd Ehrmann pivot, U(5), by an angle of -2π/3, so that TC2 circumscribes ABC. Triangle TC2 is here named the 2nd Ehrmann circumscribing triangle. TC1 and TC2 are inscribed in the Johnson circle (centered at X(4)).
Let TI1=A'1B'1C'1 be the triangle obtained by rotating ABC about the 1st Ehrmann pivot, P(5), by an angle of -2π/3, so that TI1 is inscribed in ABC. Triangle TI1 is here named the 1st Ehrmann inscribed triangle. Let TI2=A'2B'2C'2 be the triangle obtained by rotating ABC about the 2nd Ehrmann pivot, U(5), by an angle of 2π/3, so that TI2 is inscribed in ABC. Triangle TI2 is here named the 2nd Ehrmann inscribed triangle. TI1 and TI2 are inscribed in a common conic, here named the Ehrmann conic. The center of the Ehrmann conic is X(14993).
The orthocenter of TC1 is the circumcenter of TI1, and is here introduced (and at Bicentric Pairs) as P(173). P(173) is therefore the intersection of the Euler lines of TC1 and TI1. The orthocenter of TC2 is the circumcenter of TI2, and is here introduced as U(173). U(173) is therefore the intersection of the Euler lines of TC2 and TI2. PU(173) lie on the Hatzipolakis axis (line PU(5) or X(5)X(523)). The midpoint of PU(173) is X(5). P(173), X(3) and X(4) are the vertices of an equilateral triangle with center P(5). U(173), X(3) and X(4) are the vertices of an equilateral triangle with center U(5).
The vertex-triangle of TC1 and TC2 is here named the Ehrmann vertex-triangle. The Ehrmann vertex-triangle is the Kosnita triangle of the Johnson triangle (or equivalently, the reflection of the Kosnita triangle in X(5)), and the tangential triangle of the Ehrmann mid-triangle (defined below). The vertex-triangle of TI1 and TI2 is ABC.
Let VAVBVC be the Ehrmann vertex-triangle. Then VA is the isogonal conjugate of A'1 wrt TC1, and the isogonal conjugate of A'2 wrt TC2, and cyclically for VB and VC.
The A-vertex of the Ehrmann vertex-triangle has barycentric coordinates:
VA = a^6 - a^4(b^2 + c^2) - a^2(b^4 + c^4) + (b^2 - c^2)^2(b^2 + c^2) : -(a^2 + b^2 - c^2)[(a^2 - b^2 - c^2)^2 - b^2c^2] : -(a^2 - b^2 + c^2)[(a^2 - b^2 - c^2)^2 - b^2c^2]
The Ehrmann vertex-triangle is orthologic to ABC with orthology center X(4).
The Ehrmann vertex-triangle is Eulerologic to ABC at X(7577).
The Ehrmann vertex-triangle is perspective to the reflections-of-P triangle for all P.
The appearance of (T,i) in the following list means that the Ehrmann vertex-triangle is perspective to triangle T at X(i). An asterisk indicates the triangles are homothetic.
(ABC, 4), (anticomplementary, 18387), (anti-Ara, 18385), (anti-Ascella*, 18386), (1st anti-Conway*, 18388), (2nd anti-Conway*, 18390), (anti-Euler, 4), (3rd anti-Euler*, 18392), (4th anti-Euler*, 18394), (anti-excenters-incenter reflections*, 4), (2nd anti-extouch*, 18396), (anti-Hutson intouch*, 382), (anti-incircle-circles*, 3843), (anti-inverse-in-incircle*, 4), (6th anti-mixtilinear*, 18531), (anti-tangential midarc*, 3585), (circumorthic*, 4), (dual of orthic*, 3153), (2nd Ehrmann*, 542), (X(2)-Ehrmann*, 7574), (X(3)-Ehrmann*, 18400), (X(4)-Ehrmann*, 18403), (Ehrmann mid, 3818), (Ehrmann side*, 18403), (Euler, 4), (2nd Euler*, 18404), (1st excosine*, 18405), (extangents*, 18406), (2nd extouch, 4), (3rd extouch, 4), (intangents*, 3583), (Johnson, 6288), (1st Kenmotu diagonals*, 6564), (2nd Kenmotu diagonals*, 6565), (Kosnita*, 5), (Lucas antipodal tangents*, 18414), (Lucas(-1) antipodal tangents*, 18415), (midheight, 4), (mid-triangle of 1st and 2nd Kenmotu diagonals*, 115), (mid-triangle of inner and outer tri-equilateral*, 18424), (orthic*, 4), (orthoanticevian of X(3)*, 18418), (orthocentroidal, 4), (orthocevian of X(3)*, 18416), (1st orthosymmedial, 4), (reflection, 4), (reflections-of-X(1), 18426), (reflections-of-X(2), 18427), (reflections-of-X(5), 18428), (reflections-of-X(6), 18429), (submedial*, 18420), (tangential*, 381), (inner tri-equilateral*, 16808), (outer tri-equilateral*, 16809), (Trinh*, 30)
The side-triangle of TI1 and TI2 is here named the Ehrmann side-triangle. The Ehrmann side-triangle is the circumorthic triangle of the Johnson triangle (or equivalently, the reflection of the circumorthic triangle in X(5)), and also the 2nd isogonal triangle of X(4) (see X(36)). It is inscribed (along with TC1 and TC2) in the Johnson circle. The side-triangle of TC1 and TC2 is ABC.
The A-vertex of the Ehrmann side-triangle has barycentric coordinates:
SA = a^2[a^4 + a^2(b^2 + c^2) - 2(b^2 - c^2)^2] : -(a^2 - b^2 + c^2)[(a^2 + b^2 - c^2)^2 - a^2b^2] : -(a^2 + b^2 - c^2)[(a^2 - b^2 + c^2)^2 - a^2c^2]
The Ehrmann side-triangle is orthologic to ABC with orthology center X(3).
The Ehrmann side-triangle is Eulerologic to ABC at X(3). ABC is Eulerologic to the Ehrmann side-triangle at X(18403).
The appearance of (T,i) in the following list means that the Ehrmann side-triangle is perspective to triangle T at X(i). An asterisk indicates the triangles are homothetic.
(AAOA, 18441), (ABC, 265), (ABC-X3 reflections, 18442), (anti-Ascella*, 9818), (1st anti-Conway*, 567), (2nd anti-Conway*, 568), (3rd anti-Euler*, 11459), (4th anti-Euler*, 12111), (anti-excenters-incenter reflections*, 382), (2nd anti-extouch*, 18445), (anti-Hutson intouch*, 3), (anti-incircle-circles*, 3), (anti-inverse-in-incircle*, 18531), (6th anti-mixtilinear*, 3), (anti-tangential midarc*, 18447), (Ara, 3), (Ascella, 3), (circumorthic*, 5), (1st circumperp, 3), (2nd circumperp, 3), (dual of orthic*, 30), (2nd Ehrmann*, 18449), (X(3)-Ehrmann*, 10540), (X(4)-Ehrmann*, 18403), (Ehrmann vertex*, 18403), (2nd Euler*, 3), (1st excosine*, 18451), (extangents*, 18453), (Fuhrmann, 3), (intangents*, 18455), (Johnson, 3), (1st Kenmotu diagonals*, 18457), (2nd Kenmotu diagonals*, 18459), (Kosnita*, 3), (Lucas antipodal tangents*, 18462), (Lucas(-1) antipodal tangents*, 18462), (medial, 3), (mid-triangle of 1st and 2nd Kenmotu diagonals*, 10317), (mid-triangle of inner and outer tri-equilateral*, 18472), (orthic, 381), (orthoanticevian of X(3)*, 18466), (orthocevian of X(3)*, 18464), (submedial*, 5055), (tangential*, 3), (inner tri-equilateral*, 18468), (outer tri-equilateral*, 18470), (Trinh*, 3), (X3-ABC reflections, 12429)
The mid-triangle of TC1 and TC2 is here named the Ehrmann mid-triangle. The Ehrmann mid-triangle is the Johnson triangle of the Euler triangle (or equivalently, the reflection of the Euler triangle in X(546)), and the intouch triangle of the Ehrmann vertex-triangle if ABC is acute. The mid-triangle of TI1 and TI2 is the medial triangle.
The A-vertex of the Ehrmann mid-triangle has barycentric coordinates:
MA = 2a^4 - b^4 - c^4 - a^2b^2 - a^2c^2 + 2b^2c^2 : -2a^4 + b^4 - 2c^4 + a^2b^2 + 4a^2c^2 + b^2c^2 : -2a^4 - 2b^4 + c^4 + 4a^2b^2 + a^2c^2 + b^2c^2
ABC is Eulerologic to the Ehrmann mid-triangle at X(4).
The appearance of (T,i) in the following list means that the Ehrmann mid-triangle is perspective to triangle T at X(i). An asterisk indicates the triangles are homothetic.
(ABC*, 381), (ABC-X3 reflections*, 382), (anticomplementary*, 4), (anti-Ara*, 4), (anti-Aquila*, 9955), (5th anti-Brocard*, 18502), (anti-Euler*, 3091), (anti-excenters-incenter reflections, 18488), (anti-inverse-in-incircle, 18489), (anti-Mandart-incircle*, 18491), (3rd antipedal of X(1)*, 18529), (3rd antipedal of X(3)*, 18535), (3rd antipedal of X(4)*, 18537), (Ara*, 9818), (Aquila*, 18492), (1st Auriga*, 18495), (2nd Auriga*, 18497), (5th Brocard*, 18500), (circumorthic, 18504), (Danneels-Bevan*, 18505), (Ehrmann vertex, 3818), (Euler*, 546), (3rd Euler, 5), (4th Euler, 5), (outer Garcia*, 12699), (Gossard*, 18507), (inner Grebe*, 18509), (outer Grebe*, 18511), (2nd isogonal of X(1)*, 18513), (Johnson*, 4), (inner Johnson*, 18516), (outer Johnson*, 18517), (1st Johnson-Yff*, 1479), (2nd Johnson-Yff*, 1478), (Lucas homothetic*, 18520), (Lucas(-1) homothetic*, 18522), (Mandart-incircle*, 3583), (medial*, 30), (5th mixtilinear*, 18525), (orthic, 113), (orthocevian of X(2)*, 5), (3rd pedal of X(1)*, 18527), (3rd pedal of X(3)*, 18531), (3rd pedal of X(4)*, 1596), (X3-ABC reflections*, 3843), (submedial, 5), (inner Yff*, 10895), (outer Yff*, 10896), (inner Yff tangents*, 18542), (outer Yff tangents*, 18544)
The cross-triangle of TI1 and TI2 is here named the Ehrmann cross-triangle. The Ehrmann cross-triangle is degenerate, its vertices lying on line X(3)X(523) (the trilinear polar of X(2986)). It is perspective to the Johnson triangle at X(10745). The vertices of the cross triangle of TC1 and TC2 are the infinite points of lines BC, CA, AB.
The A-vertex of the Ehrmann cross-triangle has barycentric coordinates:
XA = (b^2 - c^2)(2a^4 - b^4 - c^4 - a^2b^2 - a^2c^2 + 2b^2c^2) : -(a^2 - b^2 + c^2)[(a^2 + b^2 - c^2)^2 - a^2b^2] : (a^2 + b^2 - c^2)[(a^2 - b^2 + c^2)^2 - a^2c^2]
Let A1B1C1 and A2B2C2 be the 1st and 2nd Ehrmann circumscribing triangles. X(18300) is the radical center of the circumcircles of AA1A2, BB1B2, CC1C2.
X(18300) lies on these lines: {4,94}, {328,3153}, {381,7578}, {476,10296}, {1989,3839} et al
Let A'1B'1C'1 and A'2B'2C'2 be the 1st and 2nd Ehrmann inscribed triangles. X(18301) is the radical center of circumcircles of AA'1A'2, BB'1B'2, CC'1C'2.
X(18301) lies on these lines: {2,94}, {20,5663}, {147,5189}, {148,13582}, {194,11004}, {6194,7492} et al
X(18301) = anticomplement of X(94)
X(18302) is the radical center of the incircles of ABC and the 1st and 2nd Ehrmann circumscribing triangles.
X(18302) lies on these lines: {4,8}, {6265,18342}
X(18303) is the radical center of the incircles of ABC and the 1st and 2nd Ehrmann inscribed triangles.
X(18303) lies on these lines: {3,10}, {2800,18341}
X(18304) is the radical center of the Brocard circles of ABC and the 1st and 2nd Ehrmann circumscribing triangles.
X(18304) lies on these lines: {4,69}, {39,6794}, {110,1316}, {194,5654}, {262,2394}, {868,7697}, {4549,6194} et al
X(18305) is the radical center of the Brocard circles of ABC and the 1st and 2nd Ehrmann inscribed triangles.
X(18305) lies on these lines: {3,2916}, {690,6033}, {2420,11646}
X(18306) is the radical center of the orthosymmedial circles of ABC and the 1st and 2nd Ehrmann circumscribing triangles.
X(18306) lies on these lines: {4,141}, {1499,5664}, {2088,2548} et al
X(18307) is the radical center of the orthosymmedial circles of ABC and the 1st and 2nd Ehrmann inscribed triangles.
X(18307) lies on these lines: {3,66}, {1316,6792}, {2088,2453} et al
X(18308) is the intersection, other than X(4), of the Lester circles of the 1st and 2nd Ehrmann circumscribing triangles.
X(18308) lies on these lines: {5, 1116}, {113, 114}, {381, 15475}, {512, 14566}, {523, 546}, {826, 2394}
X(18309) is the intersection, other than X(4), of circles {{X(2),X(3),X(6),X(111),X(691)}} of the 1st and 2nd Ehrmann circumscribing triangles.
X(18309) lies on these lines: {2,8644}, {5,9175}, {381,9178}, {512,3818}, {523,3845}, {4108,10033} et al
X(18310) is the intersection, other than X(3), of circles {{X(2),X(4),X(6)}} of the 1st and 2nd Ehrmann inscribed triangles.
X(18310) lies on these lines: {2,523}, {141,525}, {599,1640}, {2492,6719} et al
X(18310) = complement of X(18311)
X(18311) lies on these lines: {2,523}, {6,525}, {126,1560}, {233,13162}, {597,1640}, {648,5649}, {690,15303}, {804,14443}, {826,9171}, {1196,2485} et al
X(18311) = anticomplement of X(18310)
X(18311) = radical center of polar circle and circles O(13,14) and O(15,16) (the latter being the Schoute circle)
X(18311) = barycentric product X(10)*X(514)*X(316)*X(524)
X(18311) = barycentric product X(i)*X(j) for these {i,j}: {316,690}, {523,7664}, {524,9979}
X(18312) lies on these lines: {2,647}, {5,523}, {76,2394}, {115,127}, {141,525}, {264,8430}, {512,3818}, {804,12042}, {879,1352}, {2485,7746} et al
X(18312) = isotomic conjugate of X(5649)
X(18312) = intersection, other than X(4), of circles {{X(3),X(4),X(6),X(112),X(842)}} of the 1st and 2nd Ehrmann circumscribing triangles
X(18312) = intersection, other than X(3), of circles {{X(3),X(4),X(6),X(112),X(842)}} of the 1st and 2nd Ehrmann inscribed triangles
X(18313) is the intersection, other than X(4), of circles {{X(3),X(5),X(6),X(115)}} of the 1st and 2nd Ehrmann circumscribing triangles.
X(18313) lies on these lines: {512,3818}, {523,546}, {647,15820}, {804,6140}, {924,18553}, {3566,18358} et al
X(18314) is the intersection, other than X(3), of circles {{X(4),X(15),X(16),X(186),X(3484),X(15412)}} of the 1st and 2nd Ehrmann inscribed triangles.
The trilinear polar of X(18314) passes through X(137).
X(18314) lies on the circumconic centered at X(12077), and these lines: {2,2413}, {5,15451}, {83,2422}, {128,16188}, {233,13162}, {297,525}, {512,13449}, {523,2072}, {826,1209}, {1510,11583}, {1577,6358} et al
X(18314) = pole wrt polar circle of trilinear polar of X(933) (line X(6)X(24))
X(18314) = polar conjugate of X(933)
X(18314) = isogonal conjugate of X(14586)
X(18314) = isotomic conjugate of X(18315)
X(18314) = complement of X(15412)
X(18314) = X(i)-isoconjugate of X(j) for these {i,j}: {1,14586}, {31,18315}, {48,933}, {54,163}
X(18314) = barycentric product X(5)*X(10)*X(76)*X(514)
X(18314) = barycentric product X(i)*X(j) for these {i,j}: {5,850}, {76,12077}, {311,523}
Line X(3)X(54) is the isogonal conjugate of hyperbola {{A,B,C,X(4),X(5)}}.
X(18315) lies on the MacBeath circumconic and these lines: {54,575}, {95,141}, {97,6509}, {110,933}, {249,14570}, {275,2986}, {648,16813}, {1141,12383} et al
X(18315) = isogonal conjugate of X(12077)
X(18315) = isotomic conjugate of X(18314)
X(18315) = trilinear pole of line X(3)X(54)
X(18315) = X(i)-isoconjugate of X(j) for these {i,j}: {1,12077}, {19,6368}, {31,18314}, {51,1577}, {92,15451}
X(18315) = barycentric product X(6)*X(86)*X(95)*X(190)
X(18315) = barycentric product X(i)*X(j) for these {i,j}: {54,99}, {95,110}
Let A1B1C1 and A2B2C2 be the 1st and 2nd Ehrmann circumscribing triangles. Let A' be the cevapoint of A1 and A2, and define B', C' cyclically. The lines AA', BB', CC' concur in X(18316).
X(18316) lies on the Kiepert hyperbola and these lines: {2,265}, {4,1989}, {30,94}, {76,328}, {186,5627}, {275,1141}, {381,7578}, {526,2394}, {598,14356}, {1513,10511}, {3839,18576} et al
X(18316) = barycentric quotient X(1989)/X(381)
Let A'1B'1C'1 and A'2B'2C'2 be the 1st and 2nd Ehrmann inscribed triangles. Let A' be the intersection of the tangents to the Ehrmann conic at A'1 and A'2. Define B', C' cyclically. The lines AA', BB', CC' concur in X(18317).
X(18317) lies on these lines: {3,3163}, {30,14919}, {97,8703}, {394,399}, {1073,3830}, {1272,3926} et al
X(18317) = isogonal conjugate of X(12112)
X(18317) = perspector of Ehrmann conic
X(18318) lies on these lines: {3,14993}, {265,6334}, {476,12113}, {1650,5627}
Let A'1B'1C'1 and A'2B'2C'2 be the 1st and 2nd Ehrmann inscribed triangles. Let P1 be the intersection, other than A'1, B'1, C'1, of the Ehrmann conic and the circumcircle of A'1B'1C'1. Let P2 be the intersection, other than A'2, B'2, C'2, of the Ehrmann conic and the circumcircle of A'2B'2C'2. X(18319) is the midpoint of P1 and P2.
Let LA, LB, LC be the lines through A, B, C, resp. parallel to the Euler line. Let MA, MB, MC be the reflections of BC, CA, AB in LA, LB, LC, resp. Let A' = MB∩MC, and define B' and C' cyclically. Triangle A'B'C' is inversely similar to, and 3 times the size of, ABC. X(18319) = X(5)-of-A'B'C'. (See Hyacinthos #16741/16782, Sep 2008.)
X(18319) lies on these lines: {5,3258}, {30,74}, {140,477}, {381,14731}, {1117,1291}, {12091,15760}, {14851,15059}
X(18319) = reflection of X(477) in X(140)
X(18319) = X(14731)-of-Ehrmann-mid-triangle
Let P1 and P2 be as at X(18319). X(18320) is the crossdifference of P1 and P2.
X(18320) lies on these lines: {3,6}, {647,2436}, {6128,10413}
X(18321) lies on these lines: {3,512}, {5,6787}, {382,511}, {3111,3526}, {13449,18322}
X(18321) = reflection of X(18322) in X(13449)
X(18321) = reflection of X(3) in line X(4)X(69)
X(18322) lies on these lines: {3,6}, {265,290}, {385,1154}, {13449,18321}
X(18322) = reflection of X(18321) in X(13449)
X(18322) = reflection of X(3) in line X(512)X(13449)
X(18323) lies on these lines: {2,3}, {476,18576}, {1503,7728}, {3018,3284}, {8705,18438}, {11557,13202}, {13376,15012}, {14537,15860}
X(18323) = reflection of X(3) in X(10297)
X(18323) = reflection of X(3) in line X(523)X(6334)
X(18323) = inverse-in-circumcircle of X(18324)
X(18323) = {X(1113),X(1114)}-harmonic conjugate of X(18324)
X(18323) = X(10297)-of-X3-ABC-reflections-triangle
X(18324) lies on these lines: {2,3}, {143,11425}, {154,5663}, {156,12163}, {159,13680}, {394,1511}, {539,9932}, {541,13289}, {542,15577}, {569,16226}, {1151,11266}, {1152,11265} et al
X(18324) = midpoint of X(3) and X(14070)
X(18324) = reflection of X(18568) in X(5)
X(18324) = harmonic center of Kosnita and tangential circles
X(18324) = inverse-in-circumcircle of X(18323)
X(18324) = {X(1113),X(1114)}-harmonic conjugate of X(18323)
X(18324) = X(18568)-of-Johnson-triangle
X(18324) = X(3576)-of-Kosnita-triangle if ABC is acute
X(18324) = X(10246)-of-tangential-triangle if ABC is acute
X(18324) = orthic-to-Kosnita similarity image of X(381)
X(18324) = orthic-to-tangential similarity image of X(3845)
X(18324) = Ehrmann-mid-to-ABC similarity image of X(18566)
X(18324) = X(26)-Gibert-Moses centroid; see the preamble just before X(21153)
X(18325) lies on these lines: {2,3}, {265,10293}, {1478,5160}, {1479,7286}, {1503,12902}, {2777,3581}, {3521,5446}, {3580,10620}, {5270,9628}, {18358,18551} et al
X(18325) = reflection of X(3) in X(11799)
X(18325) = reflection of X(3) in line X(523)X(11799)
X(18325) = X(11799)-of-X3-ABC-reflections-triangle
X(18326) lies on these lines: {3,3667}, {30,6790}, {381,6788}, {519,3830} et al
X(18326) = reflection of X(3) in line X(355)X(381)
X(18327) lies on these lines: {3,142}, {381,8074}, {5179,7687}
X(18327) = Stammler-circle-inverse of X(36641)
X(18328) lies on the Fuhrmann circle and these lines: {8,144}, {103,1146}, {118,664}, {382,18329}, {1308,18491} et al
X(18328) = reflection of X(4) in line X(355)X(382)
X(18328) = X(99)-of-Fuhrmann-triangle
X(18328) = intersection of Soddy lines of anticevian triangles of PU(4)
X(18329) lies on these lines: {3,514}, {382,18328}, {516,4701}, {5252,18340} et al
X(18329) = reflection of X(3) in line X(355)X(382)
X(18330) lies on these lines: {1,3}, {568,5722}, {5787,18439}, {8679,10742} et al
X(18331) lies on these lines: {2,18332}, {4,690}, {69,74}, {114,15342}, {115,15081}, {147,5663}, {246,2782}, {1511,14850}, {3545,9144}, {3569,6792}, {9140,12243}
X(18331) = reflection of X(4) in X(11005)
X(18331) = reflection of X(4) in line X(2)X(98)
X(18331) = anticomplement of X(18332)
X(18331) = intersection, other than X(4), of X(2)-, X(15)-, and X(16)-Fuhrmann circles (aka Hagge circles)
X(18331) = X(11005)-of-anti-Euler-triangle
X(18331) = circummedial-to-X(2)-Fuhrmann similarity image of X(842)
X(18331) = intersection of Fermat axes of anticevian triangles of PU(4)
X(18332) lies on the Brocard circle, the Brocard (seventh) cubic (K023), and these lines: {2,18331}, {3,690}, {6,13}, {30,9144}, {74,12042}, {98,5663}, {110,1316}, {146,9862}, {3023,10091}, {3448,14651}, {5642,8724}, {5972,15561}
X(18332) = reflection of X(3) in line X(2)X(98)
X(18332) = isogonal conjugate of X(18333)
X(18332) = complement of X(18331)
X(18332) = inverse-in-circumcircle of X(14270)
X(18332) = inverse-in-orthocentroidal-circle of X(14356)
X(18332) = crossdifference of every pair of points on line X(526)X(2493)
X(18332) = X(842)-of-1st-Brocard-triangle
X(18332) = 1st-Brocard-isogonal conjugate of X(30)
X(18332) = intersection, other than X(6), of Brocard circle and Fermat axis
X(18332) = intersection, other than X(3), of circles O(3,13) and O(3,14)
X(18332) = similitude center of X(13)- and X(14)-Brocard triangles
X(18332) = {X(1113),X(1114)}-harmonic conjugate of X(14270)
X(18332) = intersection of Fermat axes of antipedal triangles of PU(1)
X(18332) = {P15,P16}-harmonic conjugate of X(6), where P15 and P16 are the orthogonal projections of X(15) and X(16) on the Fermat axis
X(18333) lies on hyperbola {{A,B,C,X(2),X(15),X(16)}} and these lines: {323,7468}, {842,18334}, {7799,14221}
X(18333) = reflection of X(842) in X(18334)
X(18333) = isogonal conjugate of X(18332)
X(18333) = antitomic conjugate of X(842)
X(18333) = antipode of X(842) in hyperbola {{A,B,C,X(2),X(15),X(16)}}
X(18333) = trilinear pole of line X(526)X(2493)
Hyperbola {{A,B,C,X(2),X(15),X(16)}} is the isogonal conjugate of the Fermat axis and the isotomic conjugate of line X(2)X(94), and intersects the circumcircle, other than at A, B, and C, at X(842). The perspector of hyperbola {{A,B,C,X(2),X(15),X(16)}} is X(526).
Let A'B'C' be the orthic triangle. Let La be the Fermat axis of triangle AB'C', and define Lb and Lc cyclically. Let A" = Lb∩Lc, and define B" and C" cyclically. Triangle A"B"C" is inversely similar to ABC, with similicenter X(18334). (Randy Hutson, July 31 2018)
X(18334) lies on the Steiner inellipse and these lines: {32,14385}, {115,647}, {187,1511}, {842,18333}, {2088,16186} et al
X(18334) = complement of X(35139)
X(18334) = perspector of circumparabola centered at X(526)
X(18334) = X(2)-Ceva conjugate of X(526)
X(18334) = barycentric square of X(526)
X(18334) = crossdifference of every pair of points on line X(476)X(10412) (the tangent to circumcircle at X(476))
X(18335) lies on these lines: {54,69}, {3091,18336}
X(18335) = reflection of X(4) in line X(193)X(576)
X(18335) = intersection of Napoleon axes of anticevian triangles of PU(4)
X(18336) lies on these lines: {3091,18335}, {5076,5965}
X(18336) = reflection of X(3) in line X(193)X(576)
X(18337) lies on these lines: {2,18338}, {4,525}, {5,6794}, {20,64}, {110,14981}, {2421,11441} et al
X(18337) = reflection of X(4) in line X(3)X(66)
X(18337) = anticomplement of X(18338)
X(18337) = X(12384)-of-1st-Brocard-triangle
X(18337) = intersection, other than X(4), of X(2)- and X(3)-Fuhrmann circles (aka -Hagge circles)
X(18337) = X(112)-of-X(3)-Fuhrmann-triangle
X(18337) = circummedial-to-X(2)-Fuhrmann similarity image of X(1297)
X(18337) = intersection of van Aubel lines of anticevian triangles of PU(4)
X(18338) lies on the Brocard circle and these lines: {{2, 18337}, {3, 525}, {4, 6}, {20, 30227}, {76, 15407}, {98, 3269}, {125, 11623}, {154, 2409}, {183, 36893}, {184, 1316}, {185, 31850}, {287, 38664}, {648, 10762}, {868, 1899}, {935, 11464}, {1562, 2794}, {1640, 35901}, {2697, 2713}, {2710, 9289}, {2715, 11257}, {2777, 14900}, {2782, 17974}, {3172, 15639}, {5622, 22265}, {7422, 10605}, {9512, 34980}, {12203, 39941}, {13516, 14003}, {13567, 36191}, {14249, 34538}, {14685, 15000}
X(18338) = midpoint of X(i) and X(j) for these {i,j}: {6776, 35902}, {13509, 41377}
X(18338) = complement of X(18337)
X(18338) = circumcircle-inverse of X(39201)
X(18338) = polar-circle-inverse of X(6530)
X(18338) = psi-transform of X(107)
X(18338) = crossdifference of every pair of points on line {232, 520}
X(18338) = intersection, other than X(6), of van Aubel line and Brocard circle
X(18338) = orthogonal projection of X(3) on van Aubel line
X(18338) = X(1297)-of-1st-Brocard-triangle
X(18338) = intersection of van Aubel lines of antipedal triangles of PU(1)
X(18338) = {X(35913),X(35914)}-harmonic conjugate of X(10002)
X(18339) lies on the Fuhrmann circle and these lines: {4,522}, {8,20}, {102,2968}, {109,952}, {117,1897}, {355,18340}, {1785,10826} et al
X(18339) = reflection of X(18340) in X(355)
X(18339) = reflection of X(4) in line X(3)X(10)
X(18339) = X(925)-of-Fuhrmann-triangle
X(18339) = X(109)-of-X(3)-Fuhrmann-triangle
X(18339) = antipode in Fuhrmann circle of X(18340)
X(18339) = intersection, other than X(4), of Fuhrman circle and X(3)-Fuhrmann circle
X(18340) lies on the Fuhrmann circle, circle {{X(1),X(3),X(355)}}, and these lines: {1,4}, {3,2222}, {8,522}, {11,106}, {55,13744}, {80,1772}, {109,2829}, {153,4551}, {355,18339}, {535,1936}, {952,10703}, {1324,7428}, {1388,3319}, {1647,9581}, {1837,6788}, {1854,18525}, {2098,3326}, {5252,18328}, {5587,15737}, {5727,18343} et al
X(18340) = reflection of X(18339) in X(355)
X(18340) = reflection of X(4) in line X(355)X(522)
X(18340) = X(1300)-of-Fuhrmann-triangle
X(18340) = antipode in Fuhrmann circle of X(18339)
X(18340) = intersection of lines X(1)X(522) of 1st and 2nd Ehrmann circumscribing triangles
X(18341) lies on the Fuhrmann circle, the circle O(3,4), the circle {{X(1),X(3),X(355)}}, and these lines: {3,8}, {4,900}, {5,18342}, {80,1772}, {108,12832}, {119,15343}, {1769,6788}, {2800,18303} et al
X(18341) = reflection of X(4) in line X(1)X(5)
X(18341) = reflection of X(18342) in X(5)
X(18341) = X(476)-of-Fuhrmann-triangle
X(18341) = X(18342)-of-Johnson-triangle
X(18341) = intersection of lines X(1)X(5) of anticevian triangles of PU(4)
X(18342) lies on these lines: {3,900}, {4,145}, {5,18341}, {6265,18302}
X(18342) = reflection of X(18341) in X(5)
X(18342) = reflection of X(3) in line X(1)X(5)
X(18342) = X(18341)-of-Johnson-triangle
X(18343) lies on the Fuhrmann circle and these lines: {2,1083}, {4,885}, {7,8}, {10,9318}, {105,4904}, {120,644}, {150,13576}, {279,3323}, {840,929}, {1352,7613}, {2711,2864}, {2784,9317}, {5727,18340} et al
X(18343) = reflection of X(4) in line X(355)X(518)
X(18343) = X(112)-of-Fuhrmann-triangle
X(18343) = X(20344)-of-1st-Brocard-triangle
X(18343) = inverse-in-polar-circle of X(18344)
X(18343) = intersection, other than X(4), of Fuhrmann circle and X(2)-Fuhrmann circle (aka Hagge circle)
X(18343) = circummedial-to-X(2)-Fuhrmann similarity image of X(105)
X(18443) = {X(1),X(3)}-harmonic conjugate of X(37531)
The trilinear polar of X(18344) passes through X(4516). (Randy Hutson, October 15, 2018)
X(18344) lies on these lines: {4,885}, {25,667}, {33,4162}, {34,2424}, {107,2714}, {108,7128}, {112,9090}, {460,512}, {468,10006}, {513,1835}, {521,1948}, {650,1946}, {657,4041}, {661,663}, {905,8760}, {1146,11988}, {2432,7008}, {3064,3700} et al
X(18344) = isogonal conjugate of X(6516)
X(18344) = pole wrt polar circle of trilinear polar of X(4554) (line X(7)X(8))
X(18344) = polar conjugate of X(4554)
X(18344) = polar-circle-inverse of X(18343)
X(18344) = crossdifference of every pair of points on line X(63)X(77)
X(18344) = X(i)-isoconjugate of X(j) for these {i,j}: {1, 6516}, {48, 4554}, {63, 651}
X(18344) = trilinear product X(i)*X(j) for these {i,j}: {9,6591}, {19,650}, {33,513}
X(18344) = barycentric product X(4)*X(650)
X(18344) = barycentric product of Feuerbach-hyperbola-intercepts of orthic axis
X(18344) = intersection of perspectrices of [ABC and Gemini triangle 37] and [ABC and Gemini triangle 38]
X(18345) lies on these lines: {3,667}, {518,18440}
X(18345) = reflection of X(3) in line X(355)X(518)
X(18346) lies on these lines: {3,669}, {381,6792}, {524,3830}, {3534,14916}, {9169,15703} et al
X(18346) = reflection of X(3) in line X(381)X(524)
X(18347) lies on these lines: {3,69}, {4,3566}, {5,18348}, {5622,15357} et al
X(18347) = reflection of X(18348) in X(5)
X(18347) = reflection of X(4) in line X(5)X(6)
X(18347) = X(18348)-of-Johnson-triangle
X(18348) lies on these lines: {3,3566}, {4,193}, {5,18347}, {1975,10425}, {4226,8780} et al
X(18348) = reflection of X(3) in line X(5)X(6)
X(18348) = reflection of X(18347) in X(5)
X(18348) = X(18347)-of-Johnson-triangle
X(18349) lies on these lines: {20,1154}, {94,18351}, {1249,11062}, {1273,14615}, {3238,7661}
X(18349) = isogonal conjugate of X(18350)
X(18350) lies on these lines: {2,156}, {3,64}, {5,49}, {17,11137}, {18,11134}, {23,6101}, {24,3581}, {25,6243}, {30,13489}, {51,195}, {52,12316}, {115,9603}, {140,1614}, {143,13595}, {155,568}, {182,5070}, {184,1656}, {185,399}, {186,5876}, {215,7741}, {323,10263}, {373,15047}, {381,1147}, {382,1092}, {394,7517}, {436,14978}, {499,9652}, {550,14157}, {569,5055}, {578,3851}, {1154,3518}, {1199,15026}, {1216,1495}, {1352,6639}, {1437,7489}, {1493,13364}, {1506,9604}, {1511,3520}, {3167,3527}, {3521,5655}, {3526,5651}, {6642,18445}, {7488,11591}, {10255,18474}, {12038,12302}, {12121,18560} et al
X(18350) = isogonal conjugate of X(18349)
X(18351) lies on these lines: {5,93}, {94,18349}, {382,6243}
X(18351) = barycentric product X(18353)*X(18354)
X(18352) lies on these lines: {1,564}, {63,2962}, {91,6149}, {92,2964}, {2169,9377} et al
X(18353) lies on these lines: {3,2963}, {4,2965}, {5,13351}, {6,13}, {50,2165}, {566,13160}, {7387,8553} et al
X(18353) = barycentric quotient X(18351)/X(18354)
X(18354) lies on these lines: {20,64}, {30,1238}, {95,99}, {264,14865}, {317,18559}, {1225,7488}, {3260,13489} et al
X(18354) = barycentric quotient X(18351)/X(18353)
X(18355) lies on these lines: {}
X(18355) = isogonal connjugate of X(18356)
X(18356) lies on these lines: {3,2888}, {4,16880}, {5,5422}, {30,64}, {140,1899}, {155,10224}, {156,542}, {265,12111}, {343,7525}, {550,11457}, {578,11264}, {973,6102}, {1147,13561}, {1154,18381}, {5655,18504}, {10226,12118}, {11411,18569}, {11818,16881}, {13754,18377}, {13861,18440}, {18379,18566} et al
X(18356) = isogonal conjugate of X(18355)
X(18357) is the centroid of the incenters of the 1st and 2nd Ehrmann circumscribing triangles and the 1st and 2nd Ehrmann inscribed triangles.
X(18357) lies on these lines: {1,5}, {2,18525}, {3,5260}, {4,5690}, {8,381}, {10,30}, {21,18524}, {40,3627}, {45,5816}, {65,11544}, {100,13743}, {140,515}, {145,3545}, {153,6901}, {165,15704}, {382,5657}, {403,12135}, {405,18518}, {474,18519}, {484,3652}, {516,3853}, {517,546}, {518,18358}, {519,5066}, {547,1125}, {548,6684}, {549,1698}, {550,5691}, {551,10109}, {632,3576}, {912,9947}, {943,6913}, {944,1656}, {946,3625}, {958,18491}, {962,3843}, {1159,5714}, {1385,3628}, {1482,3091}, {1699,3858}, {1706,18540}, {3090,10246}, {3584,10543}, {3586,10386}, {3616,5055}, {3622,5071}, {3624,3655}, {3654,15687}, {3679,3845}, {3839,4678}, {3851,5603}, {4188,18515}, {5056,7967}, {5554,18542}, {5599,18497}, {5600,18495}, {5694,15064}, {5704,6918}, {5708,6826}, {6147,9654}, {7354,18395}, {7969,18538}, {16210,18507} et al
X(18357) = midpoint of X(i) and X(j) for these {i,j}: {5,355}, {10,18480}
X(18357) = reflection of X(5901) in X(5)
X(18357) = complement of X(34773)
X(18357) = X(140)-of-Fuhrmann-triangle
X(18357) = X(5901)-of-Johnson-triangle
X(18358) is the centroid of the symmedian points of the 1st and 2nd Ehrmann circumscribing triangles and the 1st and 2nd Ehrmann inscribed triangles.
X(18358) lies on these lines: {2,8780}, {3,14927}, {4,3620}, {5,6}, {30,141}, {69,381}, {114,3055}, {140,1503}, {156,182}, {159,7514}, {184,11548}, {193,3545}, {323,5133}, {382,10519}, {427,15066}, {428,15107}, {468,10546}, {495,12589}, {496,12588}, {511,546}, {518,18357}, {524,5066}, {542,547}, {549,3763}, {575,12812}, {576,12811}, {597,10109}, {599,3845}, {611,10592}, {613,10593}, {632,5085}, {1154,9969}, {1176,10540}, {1495,6676}, {3054,5033}, {3090,5050}, {3544,11482}, {3566,18313}, {3580,10545}, {3618,5055}, {3630,3850}, {3851,11008}, {3857,11477}, {5056,14912}, {5072,5093}, {5181,10113}, {7687,14913}, {10297,11188}, {10691,11550}, {15435,18420}, {18325,18551} et al
X(18358) = midpoint of X(5) and X(1352)
X(18359) is the trilinear pole of the line through the incenters of the 1st and 2nd Ehrmann inscribed triangles (line X(10)X(522)).
Let A38B38C38 be Gemini triangle 38. Let LA be the line through A38 parallel to BC, and define LB and LC cyclically. Let A'38 = LB∩LC, and define B'38 and C'38 cyclically. Triangle A'38B'38C'38 is homothetic to ABC at X(18359). (Randy Hutson, January 15, 2019)
X(18359) lies on these lines: {2,2006}, {8,80}, {29,1807}, {92,324}, {94,226}, {189,5905}, {190,321}, {312,3969}, {329,2994}, {476,15168}, {655,3218}, {759,835}, {1220,1411} et al
X(18359) = isogonal conjugate of X(7113)
X(18359) = isotomic conjugate of X(3218)
X(18359) = anticomplement of X(16586)
X(18359) = complement of anticomplementary conjugate of X(21277)
X(18359) = polar conjugate of X(1870)
X(18359) = trilinear pole of line X(10)X(522)
X(18359) = X(i)-isoconjugate of X(j) for these {i,j}: {1,7113}, {31,3218}, {48,1870}
X(18360) is the crosssum of the incenters of the 1st and 2nd Ehrmann inscribed triangles.
X(18360) lies on these lines: {6,8775}, {31,5221}, {35,1464}, {42,8614}, {46,582}, {55,1066}, {56,1149}, {58,65}, {73,14882}, {171,3649}, {221,4255}, {603,2099}, {1042,5172} et al
X(18361) is the cevapoint of the centroids of the 1st and 2nd Ehrmann inscribed triangles.
X(18361) lies on these lines: {468,5306}, {523,11648}, {524,3098}, {3266,7788}
X(18361) = isogonal conjugate of X(10546)
X(18362) is the barycentric product of the centroids of the 1st and 2nd Ehrmann inscribed triangles.
X(18362) lies on these lines: {2, 99}, {5, 5309}, {30, 5206}, {32, 381}, {39, 5055}, {187, 3830}, {230, 3845}, {376, 7749}, {547, 5254}, {549, 7748}, {591, 13850}, {625, 7788}, {631, 12815}, {1506, 5071}, {1989, 5158}, {1991, 13932}, {3053, 14269}, {3054, 12100}, {3090, 7765}, {3091, 7755}, {3406, 14458}, {3524, 7756}, {3534, 8588}, {3545, 3767}, {3815, 10109}, {3839, 7747}, {3851, 5007}, {4995, 9664}, {5013, 15703}, {5023, 15684}, {5025, 7865}, {5028, 6034}, {5033, 11645}, {5054, 15515}, {5056, 9698}, {5066, 5306}, {5068, 5319}, {5107, 15533}, {5210, 15685}, {5298, 9651}, {5305, 11737}, {5569, 8353}, {6781, 15682}, {7703, 11647}, {7751, 7809}, {7775, 7837}, {7799, 7862}, {7808, 7884}, {7810, 16041}, {7811, 7825}, {7815, 7924}, {7880, 7887}, {7902, 16921}, {8354, 15597}, {8589, 15701}, {9466, 11318}, {9606, 12812}, {10979, 18353}, {11057, 14041}, {11121, 11132}, {11122, 11133}, {14075, 15484}, {15513, 15681}, {15544, 18435}
X(18362) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 115, 11648), (2, 11648, 574), (3545, 3767, 7753), (5066, 5306, 5475), (5071, 7739, 1506), (6034, 11178, 5028)
X(18363) is the cevapoint of the nine-point centers of the 1st and 2nd Ehrmann circumscribing triangles.
X(18363) lies on the Jerabek hyperbola and these lines: {546,11559}, {3153,14861}, {3532,7577}, {7283,14471}
X(18363) = isogonal conjugate of X(18364)
X(18364) is the crosssum of the nine-point centers of the 1st and 2nd Ehrmann circumscribing triangles.
X(18364) lies on these lines: {2,3}, {74,10610}, {110,11559}, {195,11430}, {399,13367}, {1204,14805}, {1209,12121} et al
X(18364) = isogonal conjugate of X(18363)
X(18365) is the crossdifference of the nine-point centers of the 1st and 2nd Ehrmann circumscribing triangles.
X(18365) lies on these lines: {3,6}, {2493,10313}, {14579,14910}, {16310,18572}
X(18365) = isogonal conjugate of X(18366)
X(18365) = crossdifference of every pair of points on line X(523)X(546)
Line X(523)X(546) is the line through the nine-point centers of the 1st and 2nd Ehrmann circumscribing triangles.
X(18366) lies on the Kiepert hyperbola and these lines: {4,10264}, {98,16166}, {801,15108}, {3580,13582} et al
X(18366) = isogonal conjugate of X(18365)
X(18366) = polar conjugate of X(13619)
X(18366) = trilinear pole of line X(523)X(546)
X(18366) = X(i)-isoconjugate of X(j) for these {i,j}: {1,18365}, {48,13619}
X(18367) is the barycentric product of the nine-point centers of the 1st and 2nd Ehrmann circumscribing triangles.
X(18367) lies on these lines: {6,17505}, {53,112}, {577,18562}
X(18368) is the cevapoint of the nine-point centers of the 1st and 2nd Ehrmann inscribed triangles.
X(18368) lies on the Jerabek hyperbola and these lines: {3, 2889}, {4, 12291}, {54, 13420}, {64, 12254}, {74, 10619}, {140, 10821}, {265, 14128}, {1154, 14861}, {1173, 12242}, {1994, 18282}, {3519, 15108}, {3521, 12226}, {13582, 18370}, {15002, 15047}
X(18368) = isogonal conjugate of X(18369)
X(18369) is the crosssum of the nine-point centers of the 1st and 2nd Ehrmann inscribed triangles.
X(18369) lies on these lines: {2,3}, {49,15038}, {51,195}, {54,13364}, {107,14978}, {110,1173}, {143,15801}, {155,13321}, {156,5640}, {389,399}, {568,15083}, {669,10280}, {1495,13353}, {5609,13358}, {10282,14845} et al
X(18369) = isogonal conjugate of X(18368)
X(18370) is the crosspoint of the nine-point centers of the 1st and 2nd Ehrmann inscribed triangles.
Let P17 be the X(17)-Ceva conjugate of X(18). Let P18 be the X(18)-Ceva conjugate of X(17). Then X(18370) = X(17)P17 ∩ X(18)P18.
X(18370) lies on these lines: {4,93}, {140,930}, {252,550}, {13582,18368} et al
X(18371) is the crossdifference of the symmedian points of the 1st and 2nd Ehrmann circumscribing triangles.
X(18371) lies on these lines: {2,6}, {50,237}, {186,2076}, {526,3049}, {566,14096}, {694,14910}, {1691,15462} et al
X(18371) = isogonal conjugate of X(18372)
X(18371) = crossdifference of every pair of points on line X(512)X(3818)
Line X(512)X(3818) is the line through the symmedian points of the 1st and 2nd Ehrmann circumscribing triangles.
X(18372) lies on these lines: {25,12188}, {385,14910}, {694,3580}, {850,14998}
X(18372) = isogonal conjugate of X(18371)
X(18372) = trilinear pole of line X(512)X(3818)
X(18472) = Schoute-circle-inverse of X(37473)
X(18472) = {X(15),X(16)}-harmonic conjugate of X(37473)
X(18373) is the crosssum of the symmedian points of the 1st and 2nd Ehrmann inscribed triangles.
X(18373) lies on these lines: {32,381}, {112,251}, {1384,5020} et al
X(18374) is the crossdifference of the symmedian points of the 1st and 2nd Ehrmann inscribed triangles.
X(18374) lies on these lines: {6,25}, {23,6593}, {30,15462}, {49,576}, {50,237}, {67,468}, {110,524}, {182,381}, {186,2781}, {215,8540}, {338,419}, {403,1503}, {511,2070}, {512,1691}, {542,10540}, {566,3148}, {567,5476}, {575,7545}, {597,5012}, {599,9306}, {1084,14602}, {15356,18487} et al
X(18374) = isogonal conjugate of X(18019)
X(18374) = crossdifference of every pair of points on line X(141)X(525)
X(18375) is the barycentric product of the symmedian points of the 1st and 2nd Ehrmann inscribed triangles.
X(18375) lies on these lines: {3,67}, {50,69}, {141,566}, {338,5025}, {7574,7818}, {10510,14003}
X(18376) lies on these lines: {4,51}, {5,11202}, {6,18429}, {64,5076}, {265,18434}, {1154,9927}, {2393,3818}, {3534,10193}, {5663,18566}, {13754,18568}, {18403,18430} et al
X(18376) = reflection of X(11202) in X(5)
X(18376) = X(2)-of-Ehrmann-vertex-triangle
X(18376) = X(154)-of-Ehrmann-mid-triangle
X(18376) = X(11202)-of-Johnson-triangle
X(18377) lies on these lines: {2,3}, {68,18434}, {143,18390}, {155,18405}, {1154,9927}, {3564,18382}, {5876,18474}, {6564,11265}, {13754,18356}, {18430,18436} et al
X(18377) = midpoint of X(4) and X(18569)
X(18377) = reflection of X(i) in X(j) for these (i,j): (4,18567), (1658,5), (15761,546), (18566,18568)
X(18377) = anticomplement of X(15331)
X(18377) = Ehrmann-side-to-Ehrmann-vertex similarity image of X(4)
X(18377) = orthic-to-Ehrmann-side similarity image of X(13406)
X(18377) = X(3)-of-Ehrmann-vertex-triangle
X(18377) = X(26)-of-Ehrmann-mid-triangle
X(18377) = X(1658)-of-Johnson-triangle
X(18377) = X(18569)-of-Euler-triangle
X(18377) = X(18567)-of-anti-Euler-triangle
X(18377) = {X(381),X(382)}-harmonic conjugate of X(18378)
X(18378) is the intersection of the Euler lines of ABC and the reflection triangle.
X(18378) lies on these lines: {2,3}, {49,1495}, {52,10540}, {64,9919}, {110,10263}, {143,1614}, {154,9920}, {155,5898}, {156,195}, {159,5093}, {161,14530}, {184,14627}, {399,5889}, {511,18350}, {567,10110}, {568,6759}, {999,9658}, {1482,8185}, {6243,10539}, {6767,10037}, {7373,10046}, {9591,9956}, {9625,18480}, {9626,9955}, {10117,18381} et al
X(18378) = {X(381),X(382)}-harmonic conjugate of X(18377)
X(18379) lies on these lines: {3,18392}, {4,94}, {5,13367}, {26,18405}, {30,5449}, {68,18568}, {1154,9927}, {5876,18403}, {10095,18390}, {14852,18434}, {18356,18566} et al
X(18379) = X(5)-of-Ehrmann-vertex-triangle
X(18379) = X(156)-of-Ehrmann-mid-triangle
X(18379) = {X(18392),X(18394)}-harmonic conjugate of X(3)
X(18380) lies on these lines: {4,6}, {157,381}, {2871,3818}, {6751,13851}, {18403,18437} et al
X(18380) = X(6)-of-Ehrmann-vertex-triangle
X(18380) = X(157)-of-Ehrmann-mid-triangle
X(18381) lies on these lines: {2,9833}, {4,51}, {5,182}, {17,11243}, {18,11244}, {24,125}, {26,5449}, {30,3357}, {64,265}, {154,1656}, {155,542}, {156,10224}, {221,9654}, {381,1498}, {546,2883}, {576,13292}, {1147,13371}, {1154,18356}, {3521,18434}, {3575,11438}, {5446,18382}, {13491,18428}, {14915,18431}, {18403,18439} et al
X(18381) = midpoint of X(4) and X(14216)
X(18381) = reflection of X(i) in X(j) for these (i,j): (2883,546), (6759,5)
X(18381) = complement of X(9833)
X(18381) = anticomplement of X(10282)
X(18381) = X(8)-of-Ehrmann-vertex-triangle if ABC is acute
X(18381) = X(1498)-of-Ehrmann-mid-triangle
X(18381) = X(3811)-of-orthic-triangle if ABC is acute
X(18381) = X(6759)-of-Johnson-triangle
X(18381) = X(14216)-of-Euler-triangle
X(18382) lies on these lines: {2,18427}, {4,6}, {5,15577}, {20,15578}, {66,265}, {69,3153}, {141,18531}, {154,7394}, {159,381}, {161,5133}, {182,18428}, {206,11818}, {511,9927}, {542,12596}, {546,15581}, {1352,6288}, {1843,13851}, {2393,3818}, {3564,18377}, {3589,18420}, {3827,18480}, {5446,18381}, {6403,18394}, {9969,18390}, {12220,18392}, {15585,18537} et al
X(18382) = reflection of X(i) in X(j) for these (i,j): (20,15578), (15577,5)
X(18382) = X(9)-of-Ehrmann-vertex-triangle if ABC is acute
X(18382) = X(159)-of-Ehrmann-mid-triangle
X(18382) = X(15577)-of-Johnson-triangle
X(18383) lies on these lines: {3,18405}, {4,51}, {5,5944}, {20,18392}, {30,5449}, {52,265}, {64,3830}, {125,6240}, {154,3851}, {184,7547}, {235,7687}, {381,569}, {382,1853}, {427,13403}, {511,9927}, {546,575}, {548,10193}, {567,10274}, {578,7507}, {924,10412}, {1181,18386}, {5663,18567}, {5876,18572}, {5907,18404}, {6146,18388}, {7355,18513}, {11695,18420}, {11793,18531}, {12162,18403}, {13754,18356} et al
X(18383) = midpoint of X(382) and X(3357)
X(18383) = reflection of X(10282) in X(5)
X(18383) = complement of X(34785)
X(18383) = X(10)-of-Ehrmann-vertex-triangle if ABC is acute
X(18383) = X(6759)-of-Ehrmann-mid-triangle
X(18383) = X(10282)-of-Johnson-triangle
X(18384) lies on these lines: {4,94}, {25,1989}, {51,11138}, {403,14993}, {460,8753}, {468,476}, {1990,14560} et al
X(18384) = pole wrt polar circle of trilinear polar of X(7799) (line X(526)X(3268))
X(18384) = polar conjugate of X(7799)
X(18384) = isogonal conjugate of isotomic conjugate of X(6344)
X(18384) = barycentric product X(4)*X(79)*X(80)
X(18384) = barycentric product X(i)*X(j) for these {i,j}: {4,1989}, {6,6344}
X(18384) = barycentric quotient X(4)/X(7799)
X(18385) lies on these lines: {25,265}, {235,9927}, {1843,13851}, {3575,11438}, {6623,18387}
X(18385) = X(18532)-of-anti-Ara-triangle
X(18386) lies on these lines: {2,3} {184,18405}, {1181,18383}, {1498,11572}, {1853,13399}, {1986,13321}, {3172,18429}, {9777,18390} et al
X(18386) = {X(381),X(382)}-harmonic conjugate of X(10254)
X(18387) lies on these lines: {2,265}, {4,14449}, {5,11935}, {20,11454}, {146,11442}, {193,3818}, {3091,5654}, {3543,18474}, {6623,18385} et al
X(18387) = anticomplement of X(3431)
X(18387) = perspector of Johnson circle wrt Ehrmann vertex-triangle
X(18387) = X(5561)-of-Ehrmann-vertex-triangle if ABC is acute
X(18388) lies on these lines: {2,1568}, {4,54}, {5,389}, {6,13}, {20,6030}, {30,11430}, {51,403}, {125,5890}, {140,13568}, {154,18494}, {182,18531}, {185,1594}, {186,10182}, {567,18403}, {1181,7507}, {6146,18383}, {17809,18405}, {18439,18488} et al
X(18388) = midpoint of X(4) and X(184)
X(18388) = {X(6),X(381)}-harmonic conjugate of X(18390)
X(18388) = X(993)-of-orthic-triangle if ABC is acute
X(18388) = X(18389)-of-Ehrmann-vertex-triangle if ABC is acute
X(18388) = X(18389)-of-1st-anti-Conway-triangle if ABC is acute
X(18388) = X(1478)-of-2nd-anti-Conway-triangle if ABC is acute
X(18388) = X(18474)-of-Ehrmann-mid-triangle
X(18388) = X(184)-of-Euler-triangle
X(18388) = X(11430)-of-orthocentroidal-triangle
X(18388) = Ehrmann-side-to-orthic similarity image of X(18474)
The homothetic center of these triangles is X(18388).
X(18389) lies on these lines: {1, 21}, {2, 18397}, {3, 15556}, {5, 226}, {7, 80}, {10, 343}, {20, 5903}, {36, 18444}, {41, 1729}, {42, 1735}, {46, 10884}, {56, 12005}, {57, 6905}, {65, 515}, {72, 5745}, {84, 1389}, {158, 1844}, {224, 17700}, {377, 3754}, {484, 7411}, {496, 6583}, {498, 3678}, {517, 4304}, {518, 8255}, {519, 16465}, {527, 5728}, {938, 5046}, {946, 1858}, {950, 7491}, {960, 16193}, {999, 5083}, {1012, 2099}, {1159, 18519}, {1454, 6796}, {1470, 15528}, {1708, 18443}, {1737, 3822}, {1741, 3553}, {1765, 2171}, {1777, 4332}, {1788, 15016}, {1870, 2003}, {1898, 18483}, {2093, 5732}, {2096, 11041}, {3085, 5904}, {3086, 5443}, {3419, 5832}, {3485, 5693}, {3487, 6852}, {3586, 5735}, {3679, 5833}, {3753, 5784}, {3911, 10202}, {3919, 17616}, {4197, 18395}, {4295, 9799}, {4306, 7138}, {4311, 12675}, {4312, 12669}, {4313, 5697}, {4973, 14793}, {5119, 7675}, {5173, 6001}, {5273, 5692}, {5434, 17660}, {5570, 11019}, {5691, 9960}, {5709, 10393}, {6284, 17637}, {6830, 12691}, {6911, 9946}, {6920, 11518}, {7098, 10902}, {7489, 15934}, {7508, 17010}, {7548, 9612}, {7951, 15064}, {8545, 10398}, {10247, 15558}, {10624, 12711}, {10883, 18393}, {11571, 13243}, {11888, 18399}, {11889, 18409}, {11890, 18408}, {13601, 18238}, {13739, 17104}
X(18389) = reflection of X(72) in X(5745)
X(18389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 920, 5248), (5902, 18391, 12736), (5902, 18412, 18391)
X(18390) lies on these lines: {2,11430}, {3,2929}, {4,51}, {5,578}, {6,13}, {25,18396}, {30,11438}, {52,18404}, {68,5907}, {125,378}, {143,18377}, {155,10112}, {182,15760}, {184,403}, {235,6146}, {382,9786}, {394,16072}, {468,11202}, {511,18531}, {539,15068}, {546,12233}, {567,10254}, {568,18403}, {569,10024}, {576,10297}, {800,18437}, {1173,16000}, {1204,18560}, {1350,18536}, {1352,8681}, {1593,15121}, {1620,15696}, {2888,15056}, {3448,15305}, {3531,15321}, {3581,18564}, {5446,18569}, {5449,7526}, {5640,16223}, {5943,18420}, {6653,15644}, {6756,15873}, {7507,10982}, {7577,14644}, {9777,18386}, {9969,18382}, {10095,18379}, {10201,18475}, {10625,18555}, {10733,15053}, {11435,18406}, {11442,15030}, {11444,15108}, {13364,15465}, {13561,15807}, {15019,15044}, {15078,16163}, {17810,18405} et al
X(18390) = midpoint of X(4) and X(1899)
X(18390) = reflection of X(9306) in X(5)
X(18390) = {X(6),X(381)}-harmonic conjugate of X(18388)
X(18390) = orthic-to-2nd-Euler similarity image of X(9306)
X(18390) = X(997)-of-orthic-triangle if ABC is acute
X(18390) = X(18391)-of-Ehrmann-vertex-triangle if ABC is acute
X(18390) = X(18391)-of-2nd-anti-Conway-triangle if ABC is acute
X(18390) = X(1899)-of-Euler-triangle
X(18390) = X(9306)-of-Johnson-triangle
X(18390) = X(11438)-of-orthocentroidal-triangle
The homothetic center of these triangles is X(18390).
X(18391) lies on these lines: {1,2}, {3,1788}, {4,65}, {5,3485}, {6,281}, {7,80}, {11,2099}, {12,3487}, {19,5802}, {20,46}, {21,11507}, {30,3474}, {35,4313}, {36,5435}, {40,950}, {55,1006}, {56,944}, {57,515}, {58,1771}, {72,2551}, {79,7319}, {81,11103}, {100,8069}, {104,1470}, {1512,18446}, {2771,18516}, {3871,11508}, {5708,18525}, {6147,9654} et al
X(18391) = anticomplement of X(997)
X(18391) = polar conjugate of isotomic conjugate of X(6350)
X(18392) lies on these lines: {3,18379}, {4,52}, {5,11449}, {20,18383}, {22,18405}, {110,381}, {10539,18504}, {12220,18382}, {18436,18567} et al
X(18392) = X(18393)-of-Ehrmann-vertex-triangle if ABC is acute
X(18392) = X(18393)-of-3rd-anti-Euler-triangle if ABC is acute
X(18392) = {X(3),X(18379)}-harmonic conjugate of X(18394)
The homothetic center of these triangles is X(18392).
X(18393) lies on these lines: {1,4}, {2,484}, {5,5903}, {7,3065}, {8,11280}, {10,3899}, {11,11571}, {12,5697}, {13,7052}, {30,15950}, {35,11375}, {36,1836}, {40,6863}, {46,6862}, {56,79}, {57,1727}, {65,7741}, {80,381}, {165,6954} et al
X(18393) = {X(5),X(5903)}-harmonic conjugate of X(18395)
X(18394) lies on these lines: {3,18379}, {4,51}, {5,10546}, {24,14644}, {64,10721}, {186,11704}, {381,1614}, {6403,18382}, {10540,18504}, {12111,18403}, {15058,18474}, {18436,18572} et al
X(18394) = X(18395)-of-Ehrmann-vertex-triangle if ABC is acute
X(18394) = X(18395)-of-4th-anti-Euler-triangle if ABC is acute
X(18394) = {X(3),X(18379)}-harmonic conjugate of X(18392)
The homothetic center of these triangles is X(18394).
X(18395) lies on these lines: {1,2}, {3,80}, {4,484}, {5,5903}, {11,5690}, {12,5902}, {18,7052}, {35,1837}, {36,355}, {40,3583}, {46,3585}, {56,5790}, {57,5270}, {65,5694}, {72,5123}, {79,10895}, {90,3359}, {119,5693}, {140,10950}, {5204,5442}, {7354,18357}, {7701,18516} et al
X(18395) = {X(5),X(5903)}-harmonic conjugate of X(18393)
X(18396) lies on these lines: {3,125}, {4,6}, {20,3580}, {24,12289}, {25,18390}, {30,1899}, {51,18494}, {64,11457}, {68,4549}, {113,12419}, {184,381}, {185,382}, {378,1853}, {394,18531}, {974,10733}, {1568,3167}, {5562,11898}, {6467,15030}, {9818,18474}, {18403,18445} et al
X(18396) = X(18397)-of-Ehrmann-vertex-triangle if ABC is acute
X(18396) = X(18397)-of-2nd-anti-extouch-triangle if ABC is acute
The homothetic center of these triangles is X(18396).
X(18397) lies on these lines: {1,6}, {2,18389}, {4,80}, {35,920}, {36,1708}, {40,1858}, {43,1735}, {46,1490}, {56,6326}, {57,912}, {65,5587}, {191,11507}, {201,581}, {226,1737}, {329,758}, {452,3878} et al
The homothetic center of these triangles is X(3843).
X(18398) lies on these lines: {1,3}, {2,3678}, {4,5557}, {7,79}, {8,3881}, {10,3873}, {11,6147}, {37,5043}, {63,5259}, {72,3624}, {80,388}, {81,5358}, {104,15173}, {145,3754}, {1210,3947} et al
The anti-tangential midarc triangle is the reflection of the intangents triangle in X(1).
The homothetic center of these triangles is X(3585).
X(18399) lies on these lines: {1,164}, {46,8081}, {65,8099}, {80,177}, {188,5692}, {484,8075}, {517,10503}, {758,11690}, {942,10506}, {2089,5902} et al
The X(3)-Ehrmann triangle is the medial triangle of the tangential triangle, and also the cross-triangle of the following pairs of triangles: {1st and 2nd Kenmotu diagonals}, {inner and outer tri-equilateral}, {1st and 2nd anti-Conway}. It is also the anti-inner-Conway triangle and the reflection of the Kosnita triangle in X(10282). See X(25) for a generalization.
X(18400) lies on these (parallel) lines: {2,10182}, {3,161}, {4,54}, {5,5944}, {13,11243}, {14,11244}, {20,2888}, {25,18390}, {26,9927}, {30,511}, {51,7576}, {52,10112}, {64,1657}, {66,3098}, {74,10421}, {107,6761}, {110,1568}, {113,10540}, {115,1971}, {125,186}, {140,13470}, {143,11262}, {154,381}, {195,382}, {265,2070} et al
X(18400) = isogonal conjugate of X(18401)
X(18400) = X(758)-of-orthic-triangle if ABC is acute
X(18401) lies on the circumcircle and these lines: {2,18402}, {3,933}, {5,107}, {110,5562}, {112,216}, {476,3153}, {925,12225}, {1289,7576}, {1291,2071}, {1301,3518}, {1304,2070}, {3520,6799} et al
X(18401) = circumcircle antipode of X(933)
X(18401) = reflection of X(933) in X(3)
X(18401) = anticomplement of X(18402)
X(18401) = Λ(X(4), X(54))
X(18401) = the point of intersection, other than A, B, and C, of the circumcircle and conic {{A,B,C,X(3),X(5)}}
X(18401) = Collings transform of X(2972)
X(18402) lies on the nine-point circle and these lines: {2,18401}, {4,137}, {11,1944}, {115,6748}, {122,140}, {125,389}, {127,14767}, {130,6752}, {136,3575}, {139,571}, {186,3258}, {216,8439}, {403,10214}, {1540,18400} et al
X(18402) = complement of X(18401)
X(18402) = inverse-in-polar-circle of X(1141)
X(18402) = Λ(X(4), X(54)), wrt orthic triangle
X(18403) is the perspector of ABC and the reflection of the circumorthic tangential triangle in line X(403)X(523) (which is the perspectrix of ABC and the circumorthic tangential triangle).
X(18403) lies on these lines: {2,3}, {49,5448}, {113,10540}, {115,10317}, {156,12289}, {265,1531}, {389,13376}, {541,13399}, {542,18449}, {567,18388}, {568,18390}, {577,9220}, {1060,18513}, {1989,3284}, {3581,7687}, {3583,9629}, {3585,18447}, {5446,15800}, {5876,18379}, {5964,9927}, {6000,7728}, {6564,18457}, {6565,18459}, {10721,13445}, {11440,13561}, {12022,15087}, {12111,18394}, {12162,18383}, {12358,13391}, {14156,16163}, {14915,16223}, {16808,18468}, {16809,18470}, {18376,18430}, {18380,18437}, {18381,18439}, {18382,18440}, {18396,18445}, {18406,18453}, {18414,18462}, {18415,18463}, {18416,18464}, {18418,18466}, {18424,18472}
X(18403) = midpoint of X(4) and X(3153)
X(18403) = reflection of X(i) in X(j) for these (i,j): (3,2072), (23,11563), (186,5), (2070,403), (11563,546)
X(18403) = complement of X(13619)
X(18403) = anticomplement of X(15646)
X(18403) = inverse-in-Johnson-circle of X(3)
X(18403) = inverse-in-circumcircle of X(1658)
X(18403) = inverse-in-nine-point-circle of X(10024)
X(18403) = inverse-in-polar-circle of X(6240)
X(18403) = inverse-in-2nd-Droz-Farny-circle of X(15761)
X(18403) = pole wrt Johnson circle of line X(3)X(523) (the line of the Ehrmann cross-triangle)
X(18403) = homothetic center of Ehrmann vertex-triangle and X(4)-Ehrmann triangle
X(18403) = homothetic center of Ehrmann side-triangle and X(4)-Ehrmann triangle
X(18403) = X(36)-of-Ehrmann-vertex-triangle if ABC is acute
X(18403) = X(36)-of-Ehrmann-side-triangle if ABC is acute
X(18403) = X(36)-of-X(4)-Ehrmann-triangle if ABC is acute
X(18403) = X(3153)-of-Euler-triangle
X(18403) = X(2072)-of-X3-ABC-reflections-triangle
X(18403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381,382,25), (1113,1114,1658), (1312,1313,10024), (10750,10751,3)
X(18403) = barycentric product X(69)*X(3583)*X(3585)
X(18403) = Eulerologic center of these triangles: ABC to Ehrmann side
X(18404) lies on these lines: {2,3}, {52,18390}, {113,6759}, {125,7689}, {127,7825}, {485,18457}, {486,18459}, {1062,3583}, {1147,1568}, {1352,6288}, {3521,4846}, {5878,7728}, {5907,18383}, {7748,14961}, {14216,18439}, {17814,18405} et al
X(18404) = reflection of X(24) in X(5)
X(18404) = complement of X(35471)
X(18404) = anticomplement of X(37814)
X(18404) = inverse-in-Johnson-circle of X(2072)
X(18404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (1,j,k): (381,382,1598), (10750,10751,2072)
X(18404) = X(46)-of-Ehrmann-vertex-triangle if ABC is acute
X(18404) = X(46)-of-2nd-Euler-triangle if ABC is acute
X(18404) = X(24)-of-Johnson-triangle
X(18404) = X(7517)-of-Ehrmann-mid-triangle
X(18405) lies on these lines: {3,18383}, {4,6}, {5,17821}, {22,18392}, {24,14644}, {25,13851}, {26,18379}, {30,1853}, {64,265}, {154,381}, {155,18377}, {161,9818}, {184,18386}, {221,3585}, {389,10938}, {394,3153}, {542,17813}, {546,9833}, {567,3843}, {568,3830}, {1192,6240}, {1619,18535}, {3197,18406}, {5907,18438}, {6145,9927}, {6288,17846}, {6564,17819}, {6565,17820}, {12293,18569}, {15068,18572}, {16808,17826}, {16809,17827}, {17809,18388}, {17810,18390}, {17811,18531}, {17814,18404}, {17825,18420}, {18403,18451} et al
X(18405) = reflection of X(154) in X(381)
X(18405) = orthic-to-Ehrmann-vertex similarity image of X(12022)
X(18405) = X(5692)-of-Ehrmann-vertex-triangle if ABC is acute
X(18405) = X(5692)-of-1st-excosine-triangle if ABC is acute
X(18406) lies on these lines: {1,18517}, {4,9}, {55,381}, {65,79}, {908,4420}, {1478,4654}, {1479,5219}, {2093,18513}, {3197,18405}, {5270,18525}, {9816,18420}, {11435,18390}, {18403,18453} et al
X(18406) = X(18408)-of-Ehrmann-vertex-triangle if ABC is acute
X(18406) = X(18408)-of-extangents-triangle if ABC is acute
X(18406) = {X(381),X(18407)}-harmonic conjugate of X(3583)
X(18407) lies on these lines:
{4,8}, {5,5248}, {30,993}, {55,381}, {56,18544}, {149,3656}, {377,13624}, {382,3428}, {528,3845}, {546,7680}, {674,3818}, {1385,3824}, {1479,9955}, {1699,6326}, {1836,2771}, {2099,3585}, {2475,3897}, {3304,18543}, {3715,5790}, {3843,10679}, {3868,16159}, {3873,11604}, {3874,16125}, {4294,6866}, {4316,18515}, {4857,18493}, {5119,18492}, {5172,7741}, {5225,6849}, {5270,18526}, {5840,8727}, {5886,6839}, {6253,6842}, {6284,6841}, {6681,6924}, {6826,11230}, {6827,11231}, {6928,9956}, {7548,11491}, {8069,10896}, {9656,18545}, {9897,10742}, {10537,18400}, {10895,18518}, {11018,18527}, {11366,18496}, {11367,18498}, {12116,15178}, {12943,18519}, {15733,18482}
X(18407) = midpoint of X(i) and X(j) for these {i,j}: {55, 18499}, {382, 3428}, {2099, 18525}, {3419, 12699}, {12943, 18519}
X(18407) = reflection of X(i) in X(j) for these {i,j}: {7680, 546}
X(18407) = X(55)-of-Ehrmann-mid-triangle
X(18407) = X(174)-of-Ehrmann-vertex-triangle
X(18407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 18517, 18480), (355, 12699, 3869), (381, 18499, 55), (381, 18524, 7951), (3583, 18406, 381)
The homothetic center of these triangles is X(18406).
X(18408) lies on these lines: {1, 168}, {36, 18454}, {46, 7590}, {65, 12491}, {80, 177}, {174, 5902}, {236, 5692}, {484, 7589}, {517, 10502}, {758, 8126}, {942, 10501}, {2093, 8423}, {3337, 7588}, {5425, 18456}, {5691, 12685}, {5697, 11924}, {5883, 8125}, {5903, 8351}, {7593, 18397}, {8092, 18398}, {8129, 15016}, {8379, 18393}, {8382, 18395}, {11571, 13267}, {11890, 18389}, {11891, 18391}
X(18408) = {X(174),X(5902)}-harmonic conjugate of X(18409)
The homothetic center of these triangles is X(3583).
X(18409) lies on these lines: {1,164}, {46,8082}, {65,8100}, {80,12772}, {174,5902}, {484,8076}, {517,10501}, {758,8125}, {942,10502}, {2093,8090} et al
X(18409) = {X(174),X(5902)}-harmonic conjugate of X(18408)
The homothetic center of these triangles is X(6564).
X(18410) lies on these lines: {1,372}, {7,80}, {36,18458}
X(18410) = {X(7),X(18413)}-harmonic conjugate of X(18411)
X(18410) = {X(5902),X(18412)}-harmonic conjugate of X(18411)
The homothetic center of these triangles is X(6565).
X(18411) lies on these lines: {1,371}, {7,80}, {36,18460}
X(18411) = {X(7),X(18413)}-harmonic conjugate of X(18410)
X(18411) = {X(5902),X(18412)}-harmonic conjugate of X(18413)
X(18412) lies on these lines: {1,6}, {4,15909}, {7,80}, {20,12432}, {35,7675}, {36,1445}, {46,5732}, {55,15104}, {57,11502}, {65,971}, {142,1737}, {144,758}, {165,10391}, {200,16465}, {210,11018}, {354,5219}, {390,5697}, {484,11495}, {516,5903}, {517,14100}, {908,3873}, {912,11529}, {938,3874}, {942,5290}, {946,10392}, {999,6326}, {1002,11028}, {1210,3947}, {3062,3577}, {3826,18395}, {5708,18491} et al
X(18412) = reflection of X(1) in X(5728)
X(18412) = {X(18410),X(18411)}-harmonic conjugate of X(5902)
The homothetic center of these triangles is X(115).
X(18413) lies on these lines: {1,41}, {7,80}, {36,11714}, {46,103}, {65,2808}, {72,3041}, {116,1737}, {118,12047}, {152,4295}, {354,5723}, {517,3022}, {518,1146}, {758,10025}, {926,10015}, {942,1362}, {1721,2093}, {3033,5530} et al
X(18413) = reflection of X(1) in X(11028)
X(18413) = {X(18410),X(18411)}-harmonic conjugate of X(7)
X(18414) lies on these lines: {381, 8939}, {382, 13021}, {3818, 12590}, {9723, 18415}, {18403, 18462}
X(18415) lies on these lines: {381, 8943}, {382, 13022}, {3818, 12591}, {9723, 18414}, {18403, 18463}
X(18416) lies on these lines: {4,54}, {265,8612}, {18403,18464}
X(18416) = X(18417)-of-Ehrmann-vertex-triangle if ABC is acute
X(18416) = X(18417)-of-orthocevian-triangle-of-X(3) if ABC is acute
The homothetic center of these triangles is X(18416).
X(18417) lies on these lines: {1,21}, {5,1211}, {80,313}, {86,5902}, {333,5692}, {484,13588}, {524,10477}, {859,5289}, {1010,5903} et al
X(18418) lies on these lines: {5,3357}, {6,13}, {185,3091}, {1568,2063}, {3858,12370}, {18403,18466} et al
X(18418) = X(18419)-of-Ehrmann-vertex-triangle if ABC is acute
X(18418) = X(18419)-of-orthoanticevian-triangle-of-X(3) if ABC is acute
The homothetic center of these triangles is X(18418).
X(18419) lies on these lines: {7,80}, {57,4511}, {65,145}, {758,5435}, {938,5884}, {942,5603}, {999,10698}, {1476,1482} et al
X(18420) lies on these lines: {2,3}, {66,3818}, {68,389}, {69,1154}, {571,7737}, {1352,7706}, {1568,5651}, {1899,9730}, {3589,18382}, {5422,12022}, {5462,9815}, {5943,18390}, {6193,12161}, {9816,18406}, {9895,18517}, {10574,11457}, {11487,11591}, {11695,18383}, {12163,13568}, {12324,13491}, {14826,15068}, {17825,18405} et al
X(18420) = reflection of X(i) in X(j) for these (i,j): (4,11818), (9818,5)
X(18420) = anticomplement of X(7514)
X(18420) = inverse-in-orthocentroidal-circle of X(18531)
X(18420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,4,18531), (3,4,14790)
X(18420) = X(18421)-of-Ehrmann-vertex-triangle if ABC is acute
X(18420) = X(18421)-of-submedial-triangle if ABC is acute
X(18420) = X(1597)-of-Ehrmann-mid-triangle
X(18420) = X(9818)-of-Johnson-triangle
X(18420) = X(11818)-of-anti-Euler-triangle
X(18420) = Johnson-circle-inverse of anticomplement of X(37934)
The homothetic center of these triangles is X(18420).
X(18421) lies on these lines: {1,3}, {7,519}, {8,3671}, {10,5226}, {72,4866}, {145,4298}, {226,3679}, {3062,3577} et al
X(18421) = trilinear product X(57)*X(16676)
X(18421) = trilinear quotient X(16676)/X(9)
The homothetic center of these triangles is X(16808).
X(18422) lies on these lines: {1,16}, {7,80}, {36,18469}
X(18422) = {X(7),X(18425)}-harmonic conjugate of X(18423)
The homothetic center of these triangles is X(16809).
X(18423) lies on these lines: {1,15}, {7,80}, {36,18471}
X(18423) = {X(7),X(18425)}-harmonic conjugate of X(18422)
X(18424) lies on these lines: {2,8589}, {3,11742}, {4,187}, {5,574}, {6,13}, {32,546}, {39,3091}, {69,7615}, {111,5169}, {230,3845}, {316,9939}, {325,18546}, {382,5210}, {577,10297}, {625,7801}, {631,11614}, {671,7777}, {858,8585}, {1003,6722}, {1078,14062}, {1352,5107}, {1384,3843}, {1506,3851}, {2548,3855}, {2549,3545}, {18403,18472} et al
X(18424) = midpoint of X(6564) and X(6565)
X(18424) = X(18425)-of-Ehrmann-vertex-triangle if ABC is acute
X(18424) = X(8588)-of-orthocentroidal-triangle
The homothetic center of these triangles is X(18424).
X(18425) lies on these lines: {1,1055}, {7,80}, {36,18473}, {4336,5119} et al
X(18425) = {X(18422),X(18423)}-harmonic conjugate of X(7)
X(18426) lies on these lines: {46,1749}, {109,3585}, {15430,18514} et al
X(18427) lies on these lines: {2,18382}, {110,7533}, {265,5946}, {381,5898}, {3060,3410}, {5169,12310}, {5189,7703} et al
X(18428) lies on these lines: {4,14860}, {52,6288}, {110,3574}, {143,9927}, {182,18382}, {265,389}, {3818,5876}, {13491,18381} et al
X(18429) lies on these lines: {6,18376}, {381,3053}, {1989,3845}, {3172,18386} et al
X(18430) lies on these lines: {3,18383}, {4,94}, {5,10546}, {6,3843}, {30,11454}, {49,7547}, {184,381}, {382,3581}, {1352,6288}, {3521,11457}, {6243,9927}, {11442,18568}, {13449,18321}, {18376,18403}, {18377,18436}, {18440,18449} et al
X(18430) = reflection of X(11464) in X(5)
X(18430) = X(7951)-of-Ehrmann-vertex-triangle if ABC is acute
X(18430) = X(11464)-of-Johnson-triangle
X(18431) lies on these lines: {4,10293}, {5,64}, {30,8548}, {541,3357}, {5894,12084}, {6000,18553}, {6288,12324}, {10606,15122}, {14915,18381}, {15311,15579}
X(18432) lies on these lines: {265,576}, {569,6145}, {1147,15133}, {2888,18569}, {2904,7507}, {6243,9927}, {7574,11649}
X(18433) lies on these lines: {54,15760}, {265,1885}, {5449,7526}, {12370,13198}
Let VAVBVC be the Ehrmann vertex-triangle. Let A' be the center of conic {{A,B,C,VB,VC}} and define B', C' cyclically. The lines AA', BB', CC' concur in X(18434).
Let AA1A2 be the equilateral triangle, with A1, A2 on BC. Define BB1B2 and CC1C2 cyclically. The points A1, A2, B1, B2, C1, C2 lie on a conic with center X(6) and perspector X(18434); see the preamble just before X(34433).
X(18434) lies on the Jerabek hyperbola and these lines: {3,18383}, {6,13851}, {54,7547}, {64,11572}, {68,18377}, {69,3153}, {74,1853}, {265,18376}, {3521,18381}, {14852,18379} et al
X(18434) = X(17057)-of-Ehrmann-vertex-triangle is ABC is acute
X(18435) lies on these lines: {2,5655}, {3,64}, {4,93}, {5,5890}, {25,3581}, {30,2979}, {51,381}, {110,18570}, {140,6241}, {389,3851}, {547,15045}, {548,7999}, {550,11444}, {631,13491}, {1971,18472}, {2393,18438}, {11190,18453}, {11241,18457}, {11242,18459}, {18376,18403} et al
X(18435) = reflection of X(i) in X(j) for these (i,j): (2,15060), (3,5891), (381,15030), (568,381), (5890,5)
X(18435) = X(2)-of-Ehrmann-side-triangle
X(18435) = X(5890)-of-Johnson-triangle
X(18435) = X(5891)-of-X3-ABC-reflections-triangle
X(18436) lies on these lines: {2,6102}, {3,49}, {4,93}, {5,568}, {20,5663}, {24,3581}, {26,10540}, {30,11412}, {52,381}, {54,14805}, {68,265}, {69,3521}, {110,1658}, {140,5890}, {143,3091}, {156,7488}, {195,578}, {323,3520}, {382,511}, {389,1656}, {399,2917}, {539,18564}, {542,11750}, {546,3060}, {547,15024}, {548,15072}, {549,7999}, {550,2979}, {1657,5925}, {1986,7505}, {1993,7526}, {2070,10539}, {2072,12359}, {2781,5878}, {2807,12702}, {3090,5946}, {3534,10575}, {3545,10095}, {3548,12358}, {3564,12605}, {3627,15305}, {3819,13382}, {5076,13598}, {5964,9927}, {6237,18453}, {7352,18447}, {7517,17834}, {10665,18457}, {10666,18459}, {11442,18569}, {11449,15331}, {11465,15699}, {11592,15692}, {12118,18442}, {12270,15332}, {12279,15704}, {14585,18472}, {15033,15801}, {15133,18441}, {15606,15696}, {18377,18430}, {18392,18567}, {18394,18572} et al
X(18436) = reflection of X(i) in X(j) for these (i,j): (3,5562), (4,5876), (20,6101), (52,5907), (382,12162), (5889,5), (6243,4)
X(18436) = anticomplement of X(6102)
X(18436) = Cundy-Parry Phi transform of X(49)
X(18436) = Cundy-Parry Psi transform of X(93)
X(18436) = X(4)-of-Ehrmann-side-triangle
X(18436) = X(5889)-of-Johnson-triangle
X(18436) = X(5562)-of-X3-ABC-reflections-triangle
X(18436) = X(5876)-of-anti-Euler-triangle
X(18436) = orthic-to-circumorthic similarity image of X(5876)
X(18437) lies on these lines: {3,66}, {4,3164}, {30,317}, {53,381}, {147,14941}, {216,3818}, {418,11442}, {542,577}, {800,18390}, {1899,6638}, {2871,18438}, {17849,18451}, {18380,18403} et al
X(18437) = X(6)-of-Ehrmann-side-triangle
X(18437) = perspector of Johnson circle wrt Ehrmann side-triangle
X(18438) lies on these lines: {3,6}, {5,6403}, {30,12220}, {67,18441}, {69,265}, {141,2072}, {159,10540}, {193,1154}, {206,11597}, {376,1986}, {381,1843}, {382,12294}, {542,18564}, {1112,7493}, {1352,6288}, {1353,5889}, {1469,18447}, {1503,18439}, {2393,18435}, {2871,18437}, {3056,18455}, {3091,11576}, {3564,12605}, {3779,18453}, {5562,11898}, {5907,18405}, {6776,15074}, {7502,12228}, {8705,18323}, {9924,18451}, {10297,11188}, {11645,18561}, {12590,18462}, {12591,18463} et al
X(18438) = reflection of X(i) in X(j) for these (i,j): (3,9967), (382,12294), (6403,5)
X(18438) = X(7)-of-Ehrmann-side-triangle if ABC is acute
X(18438) = X(6403)-of-Johnson-triangle
X(18438) = X(9967)-of-X3-ABC-reflections-triangle
X(18439) lies on these lines: {2, 13491}, {3, 64}, {4, 94}, {5, 6241}, {20, 5876}, {30, 11412}, {49, 378}, {52, 3830}, {70, 3521}, {110, 11250}, {113, 7729}, {140, 15058}, {156, 3520}, {184, 14130}, {185, 381}, {376, 11591}, {382, 6243}, {389, 3843}, {399, 1147}, {511, 5073}, {546, 5890}, {548, 11444}, {549, 15056}, {550, 11459}, {567, 1181}, {631, 15060}, {1154, 3146}, {1204, 10620}, {1216, 3534}, {1503, 18438}, {1593, 18445}, {1614, 15062}, {1656, 15030}, {1657, 5562}, {1658, 11440}, {2070, 7689}, {2072, 6247}, {2777, 18565}, {2807, 18525}, {2883, 10024}, {2979, 15704}, {3060, 3853}, {3091, 13630}, {3426, 12164}, {3522, 15067}, {3523, 14128}, {3529, 6101}, {3543, 10263}, {3545, 12006}, {3549, 5656}, {3567, 3845}, {3581, 7517}, {3627, 5889}, {3832, 5946}, {3839, 10095}, {3850, 15043}, {3851, 9730}, {3855, 15026}, {3858, 5640}, {3861, 9781}, {3917, 14641}, {4550, 10984}, {5055, 9729}, {5066, 15024}, {5068, 13363}, {5071, 11017}, {5076, 5446}, {5079, 5892}, {5448, 15063}, {5655, 18281}, {5787, 18330}, {5878, 6288}, {6254, 18453}, {6285, 18455}, {6293, 18474}, {6640, 14643}, {6699, 17856}, {7355, 18447}, {7395, 13339}, {7488, 12112}, {7506, 10605}, {7525, 8718}, {7526, 11456}, {7540, 16621}, {7999, 8703}, {8549, 18449}, {9704, 11430}, {9818, 12174}, {10110, 14269}, {10170, 15720}, {10224, 12270}, {10226, 11449}, {10625, 17800}, {11413, 15068}, {11424, 15087}, {11441, 12084}, {11451, 12811}, {11454, 15331}, {11468, 15646}, {11750, 18564}, {11799, 12359}, {11819, 16658}, {12106, 15054}, {12121, 12825}, {12134, 15311}, {12308, 13352}, {12324, 18531}, {13561, 16868}, {14216, 18404}, {14845, 15012}, {15061, 17854}, {15462, 15579}, {15463, 16867}, {15644, 15681}, {18381, 18403}, {18388, 18488}, {18400, 18562}
X(18439) = reflection of X(i) in X(j) for these (i,j): (3, 12162), (20, 5876), (52, 13474), (382, 11381), (1657, 5562), (3529, 6101), (12121, 12825)
X(18439) = anticomplement of X(13491)
X(18439) = X(8)-of-Ehrmann-side-triangle if ABC is acute
X(18439) = X(20)-of-OAOBOC, as described at X(7666)
X(18439) = X(6241)-of-Johnson-triangle
X(18439) = X(12162)-of-X3-ABC-reflections-triangle
X(18439) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 12162, 18435), (3, 18451, 18350), (52, 13474, 3830), (64, 18451, 3), (389, 16194, 3843), (1539, 18379, 4), (1614, 15062, 18570), (3357, 10539, 3), (5890, 11439, 546), (5907, 10575, 3), (6241, 15305, 5), (10575, 12162, 5907), (11459, 12279, 550), (11793, 14855, 3), (15058, 15072, 140)
X(18440) lies on these lines: {2,8780}, {3,66}, {4,193}, {5,3618}, {6,13}, {22,3410}, {25,3580}, {30,69}, {67,10620}, {68,1598}, {110,5094}, {114,9756}, {147,7777}, {182,1656}, {206,10540}, {317,16264}, {343,9909}, {376,3620}, {378,12168}, {382,511}, {394,11550}, {427,3167}, {428,6515}, {518,18345}, {524,3830}, {546,1353}, {550,10519}, {674,18499}, {1350,1657}, {1386,18493}, {1843,13754}, {2393,18435}, {3091,7920}, {3094,18503}, {3242,18526}, {3751,18480}, {5039,18502}, {5076,5965}, {5891,11574}, {6467,15030}, {12212,18501}, {12329,18524}, {12583,18508}, {12586,18519}, {12587,18518}, {12594,18545}, {12595,18543}, {13562,18531}, {13861,18356}, {15141,18441}, {18382,18403}, {18430,18449} et al
X(18440) = midpoint of X(i) and X(j) for these {i,j}: {4,5921}, {382,11898}
X(18440) = reflection of X(i) in X(j) for these (i,j): (3,1352), (6,3818), (1351,4), (6776,5), (10620,67)
X(18440) = X(9)-of-Ehrmann-side-triangle if ABC is acute
X(18440) = X(6776)-of-Johnson-triangle
X(18440) = X(5921)-of-Euler-triangle
X(18440) = X(1352)-of-X3-ABC-reflections-triangle
X(18441) lies on these lines: {67,18438}, {265,15136}, {15133,18436}, {15141,18440}
X(18442) lies on these lines: {3,1568}, {20,5876}, {30,6288}, {110,550}, {265,12359}, {548,6030}, {1350,1657}, {6776,15074}, {9927,18561}, {12118,18436} et al
X(18442) = reflection of X(3521) in X(3)
X(18442) = X(1389)-of-Ehrmann-side-triangle
X(18442) = X(3521)-of-ABC-X3-reflections-triangle
The homothetic center of these triangles is X(9818).
X(18443) lies on these lines: {1,3}, {2,5720}, {4,5249}, {5,1490}, {7,6987}, {9,912}, {10,5534}, {28,1790}, {30,5732}, {34,4303}, {63,1006}, {77,1119}, {78,631}, {84,3560}, {104,9946}, {990,18506}, {997,5745}, {1001,3358}, {1012,7171} et al
X(18443) = X(11818)-of-excentral-triangle
The homothetic center of these triangles is X(567).
X(18444) lies on these lines: {1,7}, {2,5720}, {3,3218}, {8,224}, {10,5531}, {21,104}, {35,11570}, {36,18389}, {40,11520}, {63,3576}, {72,6986}, {78,3523}, {84,2320}, {200,5775}, {226,6840}, {329,6992}, {355,4197}, {377,944}, {404,9940}, {405,5779}, {411,942}, {412,6198}, {515,5249}, {517,3957}, {572,5279}, {581,5262}, {631,5770}, {758,15931}, {912,1006}, {936,10303}, {938,6838}, {946,16132}, {971,6912}, {997,5273}, {999,11020}, {1001,12669}, {1012,10246}, {2094,6282}, {2801,5251}, {2894, 4861}, {2975,12675}, {3487,6836}, {3616,6261}, {5248,15071}, {5260,14872}, {5761,6899}, {5787,6828}, {5884,10902}, {5905,6987}, {7580,15934}, {11012,12005}, {11888,18448}, {11889,18456}, {11890,18454} et al
X(18445) lies on these lines: {2, 15032}, {3, 49}, {4, 1994}, {5, 5422}, {6, 13}, {20, 16266}, {22, 1154}, {24, 156}, {25, 568}, {26, 1614}, {30, 1993}, {52, 161}, {54, 7526}, {64, 16867}, {68, 10024}, {110, 5890}, {143, 10594}, {146, 2914}, {154, 2070}, {182, 5891}, {186, 9544}, {195, 382}, {235, 13292}, {323, 376}, {378, 5663}, {389, 7506}, {511, 12083}, {549, 15066}, {567, 9818}, {569, 5907}, {578, 12162}, {1069, 18447}, {1199, 3091}, {1351, 2393}, {1353, 1596}, {1495, 14831}, {1511, 15078}, {1593, 18439}, {1656, 15038}, {1658, 9707}, {1899, 2072}, {1995, 5609}, {2192, 9642}, {2875, 10679}, {2937, 17834}, {3047, 7722}, {3060, 7530}, {3095, 14917}, {3157, 18455}, {3448, 7577}, {3520, 9545}, {3521, 15316}, {3532, 16665}, {3543, 11004}, {3545, 15052}, {3549, 11411}, {3564, 15760}, {3567, 13861}, {3580, 10201}, {3581, 14070}, {3843, 10982}, {4846, 12364}, {5012, 7514}, {5054, 17811}, {5055, 10601}, {5070, 15805}, {5071, 15018}, {5076, 15811}, {5079, 15047}, {5093, 8541}, {5448, 10116}, {5651, 5892}, {5876, 7503}, {5986, 13860}, {6000, 13352}, {6101, 10323}, {6146, 18404}, {6241, 12084}, {6243, 7387}, {6639, 12359}, {6640, 9820}, {6642, 18350}, {6776, 18531}, {6800, 7502}, {7395, 13353}, {7464, 9716}, {7484, 13339}, {7485, 15067}, {7509, 11591}, {7516, 11444}, {7529, 11432}, {7545, 13321}, {7723, 13198}, {9306, 9730}, {9705, 11449}, {9706, 11440}, {9714, 14530}, {9955, 16472}, {10254, 14852}, {10575, 13346}, {10602, 18449}, {10606, 10620}, {11413, 13491}, {11422, 14094}, {11423, 13434}, {11425, 14130}, {11457, 13371}, {11464, 18324}, {11472, 12308}, {11477, 11649}, {11597, 12168}, {11793, 13336}, {12082, 13391}, {12085, 12174}, {12134, 12233}, {12165, 12412}, {12228, 12825}, {12291, 15801}, {12827, 14643}, {13366, 15030}, {13630, 17928}, {14480, 15111}, {14528, 18364}, {14912, 18537}, {16473, 18480}, {18386, 18430}, {18396, 18403}
X(18445) = reflection of X(i) in X(j) for these (i,j): (3,184)
X(18445) = X(18446)-of-Ehrmann-side-triangle
X(18445) = X(18446)-of-2nd-anti-extouch-triangle
X(18445) = X(184)-of-X3-ABC-reflections-triangle
X(18445) = X(11442)-of-Johnson-triangle
X(18445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 12164, 18436), (6, 18451, 381), (113, 10111, 265), (113, 18390, 381), (155, 1181, 3), (156, 6102, 24), (185, 1147, 3), (381, 399, 18451), (381, 15087, 6), (399, 15087, 381), (1204, 12038, 3), (1216, 10984, 3), (7592, 11441, 5), (7689, 13367, 3), (18388, 18474, 381)
The homothetic center of these triangles is X(18445).
X(18446) lies on these lines: {1,4}, {2,5720}, {3,63}, {8,5534}, {9,48}, {10,6889}, {20,5758}, {21,7330}, {35,1158}, {36,1708}, {37,5776}, {40,758}, {46,5884}, {55,6001}, {56,12675}, {57,6905}, {65,11500}, {77,1060}, {84,943}, {100,3359}, {142,6854}, {198,9119}, {200,5657}, {207,1148}, {218,7124}, {284,4227}, {329,4511}, {355,442}, {376,527}, {392,13615}, {405,1385}, {411,3868}, {452,5811}, {474,9940}, {498,12616}, {499,10395}, {500,13442}, {517,3870}, {518,3428}, {519,2900}, {549,13226}, {1389,5665}, {1512,18391}, {1538,18527}, {3295,12672}, {3358,12669}, {5881,6937}, {5927,6913}, {6843,18528}, {6912,18540}, {6983,9843}, {7593,18454}, {8079,18448}, {8080,9837}, {12848,18450} et al
X(18446) = midpoint of X(20) and X(5905)
X(18446) = reflection of X(i) in X(j) for these (i,j): (4,226), (63,3)
X(18446) = X(184)-of-hexyl-triangle
X(18446) = X(226)-of-anti-Euler-triangle
X(18446) = X(18474)-of-excentral-triangle
X(18446) = Ehrmann-mid-to-ABC similarity image of X(18388)
X(18446) = hexyl-isogonal conjugate of X(6210)
X(18446) = Cundy-Parry Phi transform of X(78)
X(18446) = Cundy-Parry Psi transform of X(34)
X(18446) = trilinear product X(63)*X(8557)
X(18447) lies on these lines: {1,3}, {5,1870}, {11,10024}, {12,2072}, {20,8144}, {33,382}, {34,381}, {73,265}, {172,10317}, {221,18451}, {227,18524}, {603,18477}, {1442,5453}, {1469,18438}, {3585,18403}, {7352,18436}, {7355,18439} et al
X(18447) = X(18448)-of-Ehrmann-side-triangle if ABC is acute
X(18447) = X(18448)-of-anti-tangential-midarc-triangle if ABC is acute
X(18447) = trilinear product X(63)*X(5341)
The homothetic center of these triangles is X(18447).
X(18448) lies on these lines: {1,167}, {3,8093}, {40,11534}, {104,12771}, {188,997}, {355,8087}, {517,8075}, {999,11032}, {1319,10503}, {8079,18446}, {11888,18444} et al
X(18449) lies on these lines: {3,6}, {4,11255}, {5,8537}, {30,11416}, {265,895}, {1503,7728}, {1986,7464}, {8539,18453}, {8549,18439}, {17813,18451}, {18430,18440} et al
X(18449) = X(18450)-of-Ehrmann-side-triangle if ABC is acute
X(18449) = X(18450)-of-2nd-Ehrmann-triangle if ABC is acute
X(18449) = 2nd-Lemoine-circle-inverse of X(32761)
The homothetic center of these triangles is X(18449).
X(18450) lies on these lines: {1,7}, {9,1055}, {36,2801}, {56,10394}, {100,518}, {104,971}, {517,14151}, {527,4511}, {663,6006}, {997,6172}, {999,7671}, {1319,15726}, {12848,18446} et al
X(18451) lies on these lines: {2,11456}, {3,64}, {4,155}, {5,1181}, {6,13}, {22,11459}, {24,12111}, {25,13754}, {26,5876}, {30,394}, {33,3157}, {34,1069}, {49,11425}, {52,1598}, {68,235}, {70,13160}, {74,15078}, {110,378}, {156,7526}, {184,9818}, {185,6642}, {221,18447}, {323,3543}, {376,12112}, {382,13419}, {389,7529}, {403,11442}, {427,5654}, {511,18534}, {541,15106}, {546,10982}, {567,17809}, {568,17810}, {569,11479}, {1092,11381}, {1351,8681}, {1503,18531}, {2003,18540}, {2192,18455}, {3197,18453}, {4550,18475}, {5055,17825}, {6288,17824}, {6776,18537}, {7517,17834}, {7728,17847}, {9924,18438}, {12429,17836}, {17813,18449}, {17819,18457}, {17826,18468}, {17827,18470}, {17845,18563}, {17849,18437}, {18403,18405} et al
X(18451) = reflection of X(i) in X(j) for these (i,j): (3,9306), (1899,5)
X(18451) = X(18452)-of-Ehrmann-side-triangle
X(18451) = X(18452)-of-1st-excosine-triangle
X(18451) = X(1899)-of-Johnson-triangle
The homothetic center of these triangles is X(18451).
X(18452) lies on these lines: {1,1864}, {20,519}, {145,7995}, {200,2975}, {952,2093}, {1320,2801}, {10980,18391} et al
X(18453) lies on these lines: {1,3}, {4,8141}, {5,6197}, {19,381}, {30,3101}, {71,265}, {382,11471}, {567,11428}, {568,11435}, {2550,18531}, {3197,18451}, {3198,18524}, {3779,18438}, {5415,18457}, {5416,18459}, {6237,18436}, {6253,18563}, {6254,18439}, {8539,18449}, {10636,18468}, {10637,18470}, {10988,18472}, {11190,18435}, {18403,18406} et al
X(18453) = X(18454)-of-Ehrmann-side-triangle
X(18453) = X(18454)-of-extangents-triangle
The homothetic center of these triangles is X(18453).
X(18454) lies on these lines: {1,167}, {3,12445}, {40,11535}, {104,7707}, {173,3576}, {236,997}, {258,11529}, {355,8382}, {517,7589}, {758,1130}, {942,7588}, {999,8083}, {1319,10502}, {7593,18446}, {11890,18444} et al
X(18454) = {X(1),X(174)}-harmonic conjugate of X(18456)
X(18455) lies on these lines: {1,3}, {4,8144}, {21,2906}, {212,18477}, {339,350}, {1398,12085}, {2192,18451}, {3056,18438}, {6285,18439}, {10987,18472} et al
X(18455) = {X(9627),X(9630)}-harmonic conjugate of X(1)
X(18455) = X(18456)-of-Ehrmann-side-triangle
X(18455) = X(18456)-of-intangents-triangle
The homothetic center of these triangles is X(18455).
X(18456) lies on these lines: {1,167}, {3,8094}, {40,11899}, {104,12772}, {173,11529}, {214,10231}, {258,3576}, {355,8088}, {517,8076}, {942,7587}, {997,7028}, {999,11033}, {1319,10501}, {8080,9837}, {11889,18444} et al
X(18456) = {X(1),X(174)}-harmonic conjugate of X(18454)
X(18457) lies on these lines: {3,6}, {4,11265}, {5,10880}, {30,11417}, {49,10666}, {265,6413}, {381,5412}, {382,11473}, {485,18404}, {486,6639}, {590,2072}, {1658,10881}, {2070,5413}, {3092,7517}, {5055,10961}, {5415,18453}, {5418,6640}, {6564,18403}, {6565,10254}, {7488,11266}, {7502,11418}, {7728,13287}, {10255,10576}, {10533,10540}, {10665,18436}, {10962,11597}, {11241,18435}, {11447,11459}, {11448,11464}, {11462,12111}, {11474,14130}, {12424,12429}, {17819,18451} et al
X(18457) = {X(3),X(6)}-harmonic conjugate of X(18459)
X(18457) = X(18458)-of-Ehrmann-side-triangle
X(18457) = X(18458)-of-1st-Kenmotu-diagonals-triangle
The homothetic center of these triangles is X(18457).
X(18458) lies on these lines: {1,7}, {36,18410}, {104,7133}, {3576,6204} et al
X(18459) lies on these lines: {3,6}, {4,11266}, {5,10881}, {30,11418}, {49,10665}, {265,6414}, {381,5413}, {382,11474}, {485,6639}, {486,18404}, {615,2072}, {1658,10880}, {2070,5412}, {3093,7517}, {5055,10963}, {5416,18453}, {5420,6640}, {6564,10254}, {6565,18403}, {7488,11265}, {7502,11417}, {7728,13288}, {10255,10577}, {10534,10540}, {10666,18436}, {10960,11597}, {11242,18435}, {11447,11464}, {11448,11459}, {11463,12111}, {11473,14130}, {12425,12429} et al
X(18459) = {X(3),X(6)}-harmonic conjugate of X(18457)
X(18459) = X(18460)-of-Ehrmann-side-triangle
X(18459) = X(18460)-of-2nd-Kenmotu-diagonals-triangle
The homothetic center of these triangles is X(18459).
X(18460) lies on these lines: {1,7}, {36,18411}, {3576,6203} et al
The homothetic center of these triangles is X(10317).
X(18461) lies on these lines: {1,7}, {104,294}, {515,9317}, {517,840}, {1055,3576} et al
X(18462) lies on these lines: {3,485}, {9723,18463}, {12590,18438}, {18403,18414}
X(18463) lies on these lines: {3,486}, {9723,18462}, {12591,18438}, {18403,18415}
X(18464) lies on these lines: {3,8612}, {5,49}, {18403,18416}
X(18464) = X(18465)-of-Ehrmann-side-triangle
X(18464) = X(18465)-of-orthocevian-triangle-of-X(3)
The homothetic center of these triangles is X(18464).
X(18465) lies on these lines: {1,75}, {2,5396}, {21,104}, {81,4511}, {214,4276}, {333,997}, {355,14011}, {517,13588}, {859,3794}, {956,3786}, {999,5208}, {1420,10461} et al
X(18466) lies on these lines: {3,6}, {265,3548}, {1147,10938}, {18403,18418} et al
X(18466) = X(18467)-of-Ehrmann-side-triangle
X(18466) = X(18467)-of-orthoanticevian-triangle-of-X(3)
The homothetic center of these triangles is X(18466).
X(18467) lies on these lines: {1,7}, {56,4996}, {997,5775}, {1319,3877} et al
X(18468) lies on these lines: {3, 6}, {5, 10632}, {13, 18564}, {30, 11420}, {381, 10641}, {382, 11475}, {465, 3580}, {466, 14389}, {1658, 10633}, {2070, 10642}, {3166, 10640}, {3549, 5334}, {5055, 10643}, {5318, 18563}, {5321, 10024}, {6639, 18581}, {7051, 18447}, {7502, 11421}, {7542, 11543}, {9818, 11408}, {10254, 16809}, {10255, 16966}, {10636, 18453}, {10638, 18455}, {10661, 18436}, {11409, 14070}, {11452, 11459}, {11453, 11464}, {11466, 12111}, {11476, 14130}, {11488, 18531}, {11542, 12605}, {16808, 18403}, {18404, 18582}
X(18468) = Brocard-circle-inverse-of X(18470)
X(18468) = X(18469)-of-Ehrmann-side-triangle
X(18468) = X(18469)-of-inner-tri-equilateral-triangle
X(18468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 18470), (15, 10634, 3), (18438, 18472, 18470)
The homothetic center of these triangles is X(18468).
X(18469) lies on these lines: {1,7}, {36,18422}, {1653,3576}
X(18470) lies on these lines: {3, 6}, {5, 10633}, {14, 18564}, {30, 11421}, {49, 10661}, {381, 10642}, {382, 11476}, {465, 14389}, {466, 3580}, {1250, 18455}, {1658, 10632}, {2070, 10641}, {3549, 5335}, {5055, 10644}, {5318, 10024}, {5321, 18563}, {6639, 18582}, {7502, 11420}, {7542, 11542}, {9818, 11409}, {10254, 16808}, {10255, 16967}, {10637, 18453}, {11408, 14070}, {11452, 11464}, {11453, 11459}, {11467, 12111}, {11475, 14130}, {11489, 18531}, {11543, 12605}, {16809, 18403}, {18404, 18581}
X(18470) = Brocard circle-inverse-of X(18468)
X(18470) = X(18471)-of-Ehrmann-side-triangle
X(18470) = X(18471)-of-outer-tri-equilateral-triangle
X(18470) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 18468), (16, 10635, 3), (18438, 18472, 18468)
The homothetic center of these triangles is X(18470).
X(18471) lies on these lines: {1,7}, {36,18423}, {104,1251}, {1652,3576}
X(18472) lies on these lines: {3,6}, {5,10986}, {112,7502}, {115,18564}, {550,5523}, {1968,2937}, {1971,18435}, {2072,3054}, {10987,18455}, {10988,18453}, {14585,18436}, {18403,18424} et al
X(18472) = X(18473)-of-Ehrmann-side-triangle if ABC is acute
The homothetic center of these triangles is X(18472).
X(18473) lies on these lines: {1,7}, {36,18425}, {5902,11714}
X(18474) lies on these lines: {2,11464}, {3,161}, {4,52}, {5,156}, {6,13}, {30,343}, {51,11818}, {128,6069}, {578,5576}, {973,6102}, {1092,13371}, {1352,2393}, {1531,18568}, {1593,9937}, {1899,9730}, {3543,18387}, {5562,11572}, {5876,18377}, {5907,18383}, {6293,18439}, {7574,11649}, {9818,18396}, {10255,18350}, {15058,18394}, {18376,18403} et al
X(18474) = midpoint of X(4) and X(11442)
X(18474) = reflection of X(184) in X(5)
X(18474) = anticomplement of X(18475)
X(18474) = X(18446)-of-orthic-triangle if ABC is acute
X(18474) = X(993)-of-Ehrmann-side-triangle if ABC is acute
X(18474) = X(184)-of-Johnson-triangle
X(18474) = X(11442)-of-Euler-triangle
X(18474) = X(18445)-of-Ehrmann-mid-triangle
X(18474) = Ehrmann-side-to-orthic similarity image of X(18445)
X(18474) = orthic-to-Ehrmann-side similarity image of X(18388)
Let OAOBOC be the Kosnita triangle. Let A' be the trilinear pole, wrt OAOBOC, of line BC, and define B', C' cyclically. The lines OAA', OBB', OCC' concur in X(18475).
X(18475) lies on these lines: {2,11464}, {3,49}, {5,5944}, {6,14070}, {22,13352}, {23,15033}, {24,569}, {26,578}, {30,11430}, {51,567}, {52,54}, {110,5891}, {140,13561}, {141,542}, {143,12107}, {154,9818}, {156,5907}, {161,6642}, {1531,18564}, {4550,18451}, {10201,18390} et al
X(18475) = midpoint of X(i) and X(j) for these {i,j}: {3,184}, {22,13352}
X(18475) = complement of X(18474)
X(18475) = {X(24),X(569)}-harmonic conjugate of X(5462)
X(18475) = X(226)-of-Kosnita-triangle if ABC is acute
X(18476) lies on these lines: {110,1173}, {1598,2904}, {1657,5889}, {9937,15047}, {11935,15024}
Let SASBSC be the Ehrmann side-triangle. Let A' be the trilinear product SB*SC, and define B', C' cyclically. The lines AA', BB', CC' concur in X(18477).
X(18477) lies on these lines: {1,21}, {34,18540}, {40,9643}, {48,3708}, {75,811}, {158,1087}, {212,18455}, {603,18447} et al
X(18477) = barycentric product X(75)*X(5158)
X(18477) = barycentric quotient X(5158)/X(1)
X(18478) lies on these lines: {3,125}, {328,1494}, {476,10296}, {6344,14860} et al
X(18478) = barycentric product X(69)^2*X(381)*X(1989)
X(18479) lies on these lines: {30,74}, {184,5158}
X(18479) = barycentric product X(6)*X(69)^2*X(381)*X(1989)
X(18480) lies on these lines: {1,381}, {2,13624}, {3,1698}, {4,8}, {5,515}, {10,30}, {12,6841}, {20,5818}, {35,13743}, {40,382}, {55,10827}, {56,10826}, {57,9655}, {65,79}, {140,4297}, {518,3818}, {519,3845}, {1482,1699}, {3751,18440}, {3827,18382}, {7713,18494}, {9941,18500}, {11852,18508}, {12438,18507}, {12440,18520}, {12441,18522} et al
X(18480) = midpoint of X(i) and X(j) for these {i,j}: {1,18525}, {3,5691}, {4,355}, {8,12699}, {40,382}
X(18480) = reflection of X(i) in X(j) for these (i,j): (1,9955), (3,9956), (10,18357), (140,4297), (946,546), (1385,5), (3579,12)
X(18480) = complement of X(18481)
X(18480) = anticomplement of X(13624)
X(18480) = inverse-in-Johnson-circle of X(5080)
X(18480) = X(1)-of-Ehrmann-mid-triangle
X(18480) = X(355)-of-Euler-triangle
X(18480) = X(1385)-of-Johnson-triangle
X(18480) = X(177)-of-Ehrmann-vertex-triangle if ABC is acute
X(18480) = X(3579)-of-outer-Garcia-triangle
X(18480) = X(9955)-of-Aquila-triangle
X(18480) = X(9956)-of-X3-ABC-reflections-triangle
X(18480) = X(18525)-of-anti-Aquila-triangle
X(18480) = X(1511)-of-Fuhrmann-triangle
X(18480) = orthic-to-Ehrmann-side similarity image of X(9955)
X(18480) = orthic-to-2nd-Euler similarity image of X(1385)
X(18480) = excentral-to-Fuhrmann similarity image of X(12515)
X(18480) = endo-homothetic center of these triangles: Ehrmann mid and anti-Aquila; The homothetic center is X(9955).
X(18480) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,381,9955), (4,8,12699), (10750,10751,5080), (18495,18497,55), (18516,18517,4)
X(18481) lies on these lines: {1,30}, {2,13624}, {3,10}, {4,1385}, {5,3576}, {8,376}, {12,3612}, {20,145}, {140,5587}, {381,1125}, {549,1698} et al
X(18481) = midpoint of X(i) and X(j) for these {i,j}: {20,944}, {145,6361}
X(18481) = reflection of X(i) in X(j) for these (i,j): (3,4297), (4,1385), (8,3579), (355,3), (3654,376), (5691,5), (12699,1), (18525,10)
X(18481) = X(5876)-of-excentral-triangle
X(18481) = X(12902)-of-Fuhrmann-triangle
X(18481) = X(1385)-of-anti-Euler-triangle
X(18481) = X(355)-of-ABC-X3-reflections-triangle
X(18481) = X(4297)-of-X3-ABC-reflections-triangle
X(18481) = X(5691)-of-Johnson-triangle
X(18482) lies on these lines: {4,7}, {5,516}, {9,381}, {30,142}, {46,11372}, {55,1538}, {80,15909}, {144,3839}, {518,3818}, {3243,18525} et al
X(18482) = midpoint of X(4) and X(5805)
X(18482) = X(9)-of-Ehrmann-mid-triangle
X(18482) = X(5805)-of-Euler-triangle
X(18483) lies on these lines: {1,4}, {3,3817}, {5,516}, {8,3839}, {10,381}, {11,1354}, {12,10624}, {20,5550}, {30,1125}, {40,3091}, {45,10445}, {57,10591}, {79,553}, {84,5556}, {124,133}, {140,10171}, {142,6851}, {165,3090}, {355,3625}, {376,3624}, {382,4297}, {495,12575}, {496,4298}, {517,546}, {519,3845} et al
X(18483) = midpoint of X(4) and X(946)
X(18483) = reflection of X(i) in X(j) for these (i,j): (1125,9955), (6684,5)
X(18483) = complement of X(31730)
X(18483) = QA-P33 (Centroid of the Orthocenter Quadrangle) of quadrangle ABCX(1)
X(18483) = X(10)-of-Ehrmann-mid-triangle
X(18483) = X(6684)-of-Johnson-triangle
X(18483) = X(946)-of-Euler-triangle
X(18484) lies on this line: {1495,14254}
X(18484) = barycentric product X(30)*X(76)*X(381)^2
X(18485) lies on these lines: {1990,3081}, {9407,14583}
X(18485) = barycentric product X(30)*X(381)^2
Let A'B'C' be the Ehrmann mid-triangle. Let A" be the trilinear product B'*C', and define B", C" cyclically. The lines AA", BB", CC" concur in X(18486).
X(18486) lies on these lines: {75,158}, {1099,1784}, {1725,2166} et al
X(18486) = barycentric product X(30)*X(75)*X(381)
X(18486) = barycentric product X(381)*X(14206)
Let A'B'C' be the Ehrmann mid-triangle. Let A" be the barycentric product B'*C', and define B", C" cyclically. The lines AA", BB", CC" concur in X(18487).
X(18487) lies on these lines: {2,216}, {4,15860}, {6,3830}, {30,1990}, {53,3845}, {115,16303}, {187,3018}, {233,10109}, {381,5158}, {577,3534}, {1249,15682}, {6748,12101}, {6749,15687}, {10979,15693}, {15356,18374}, {15685,15905} et al
X(18487) = barycentric product X(30)*X(381)
X(18488) lies on these lines: {2,8718}, {3,2916}, {4,5449}, {5,10575}, {30,1209}, {52,1595}, {64,381}, {113,1594}, {125,546}, {378,8907}, {389,16003}, {1593,9937}, {7577,11439}, {18388,18439} et al
X(18488) = midpoint of X(4) and X(15062)
X(18488) = X(3521)-of-Ehrmann-mid-triangle
X(18488) = X(1389)-of-anti-excenters-incenter-reflections-triangle
X(18488) = X(15062)-of-Euler-triangle
X(18489) lies on these lines: {4,5447}, {5,5544}, {8,6849}, {69,381}, {113,3545}, {376,5888}, {3544,18504}, {3818,18537} et al
X(18489) = perspector of Johnson circle wrt Ehrmann mid-triangle
X(18489) = X(3531)-of-Ehrmann-mid-triangle
X(18489) = X(18490)-of-anti-inverse-in-incircle-triangle
X(18489) = X(5544)-of-Johnson-triangle
The trilinear polar of X(18490) passes through X(650).
X(18490) lies on the Feuerbach hyperbola and these lines: {1,3528}, {7,5049}, {8,4002}, {9,551}, {79,1058}, {80,1056}, {84,10595}, {354,1000}, {388,5560} et al
X(18490) = isogonal conjugate of X(6767)
X(18491) lies on these lines: {1,18518}, {3,1698}, {4,100}, {5,1001}, {30,1376}, {55,381}, {56,80}, {57,18528}, {113,12334}, {165,18529}, {355,956}, {382,10310}, {515,6692}, {958,18357}, {1308,18328}, {1466,9655}, {1479,11501}, {3585,11509}, {7741,11510}, {8068,10896}, {11504,18522}, {11848,18507} et al
X(18491) = midpoint of X(57) and X(18528)
X(18491) = X(9668)-of-Ehrmann-mid-triangle
X(18491) = X(9668)-of-anti-Mandart-incircle-triangle
X(18491) = {X(381),X(18499)}-harmonic conjugate of X(3583)
X(18492) lies on these lines: {1,381}, {3,7989}, {4,9}, {5,3576}, {12,3586}, {20,10175}, {30,1698}, {46,1749}, {57,3585}, {84,6839}, {113,12407}, {145,946}, {165,382}, {354,9656}, {355,546}, {376,3634}, {515,3091}, {517,3843}, {944,3636}, {950,10590}, {962,4678}, {1385,3851}, {1478,3333}, {1479,9578}, {1656,7987}, {1697,3583}, {1837,3649}, {2478,3646}, {3090,4297}, {3361,9655}, {3488,3947}, {3529,10164}, {3543,9780}, {3601,5441}, {3653,11737}, {3654,14893}, {3679,3845}, {3715,12702}, {3814,5438}, {3822,5436}, {3828,15682}, {3854,5882}, {3857,5901}, {3861,5690}, {4004,6001}, {4314,8164}, {4677,8148}, {4746,12245}, {5010,13743}, {5055,13624}, {5090,10151}, {5219,6866}, {5252,9614}, {5290,5722}, {8188,18520}, {8189,18522}, {11852,18507} et al
X(18492) = midpoint of X(4) and X(5818)
X(18492) = reflection of X(1) in X(18493)
X(18492) = X(18493)-of-Ehrmann-mid-triangle
X(18492) = X(18493)-of-Aquila-triangle
X(18492) = {X(381),X(18525)}-harmonic conjugate of X(9955)
X(18492) = X(5818)-of-Euler-triangle
The homothetic center of these triangles is X(18492).
X(18493) lies on these lines: {1,381}, {2,12702}, {3,142}, {4,3622}, {5,8}, {10,3656}, {30,3616}, {40,3526}, {55,5443}, {56,79}, {140,962}, {145,3545}, {149,6900}, {165,15720}, {226,7373}, {265,11723}, {355,3244}, {382,1385}, {388,1387}, {399,12261}, {403,11396}, {496,3485}, {515,3843}, {517,1656}, {546,944}, {547,9780}, {549,5550}, {550,9812}, {551,3830}, {952,3091}, {958,11813}, {982,5492}, {999,10404}, {1058,5719}, {1386,18440}, {1388,3585}, {1657,3576}, {3241,5066}, {3295,11375}, {3487,5809}, {3560,5057}, {7687,12898}, {7704,18549}, {11720,12902}, {11831,18508}, {12164,12259} et al
X(18493) = midpoint of X(1) and X(18492)
X(18493) = {X(1),X(381)}-harmonic conjugate of X(18525)
The homothetic center of these triangles is X(9818).
X(18494) lies on these lines: {2,3}, {6,18400}, {34,9655}, {51,18396}, {52,12429}, {53,7737}, {66,3426}, {154,18388}, {1829,18525}, {1843,13754}, {7713,18480}, {11383,18524}, {17810,18390}
X(18495) lies on these lines: {4,5601}, {5,9834}, {30,5599}, {55,10827}, {113,12466}, {355,8204}, {381,5597}, {382,11822}, {5598,18525}, {5600,18357}, {8201,18520}, {8202,18522), {11865,18516} et al
X(18495) = {X(55),X(18480)}-harmonic conjugate of X(18497)
X(18495) = X(18496)-of-Ehrmann-mid-triangle
X(18495) = X(18496)-of-1st-Auriga-triangle
The homothetic center of these triangles is X(18495).
X(18496) lies on these lines: {1,18498}, {381,5597}
X(18496) = {X(1),X(18499)}-harmonic conjugate of X(18498)
X(18497) lies on these lines: {4,5602}, {5,9835}, {30,5600}, {55,10827}, {113,12467}, {355,8197}, {381,5598}, {382,11823}, {5597,18525}, {5599,18357}, {8208,18520}, {8209,18522}, {11866,18516} et al
X(18497) = {X(55),X(18480)}-harmonic conjugate of X(18495)
X(18497) = X(18498)-of-Ehrmann-mid-triangle
X(18497) = X(18498)-of-2nd-Auriga-triangle
The homothetic center of these triangles is X(18497).
X(18498) lies on these lines: {1,18496}, {381,5598}
X(18498) = {X(1),X(18499)}-harmonic conjugate of X(18496)
X(18499) lies on these lines: {1, 18496}, {3, 2886}, {4, 3871}, {9, 5790}, {30, 956}, {55, 381}, {56, 18543}, {79, 2099}, {382, 517}, {528, 3830}, {674, 18440}, {952, 5905}, {1656, 5259}, {1657, 3428}, {1824, 18494}, {3149, 11928}, {3419, 12702}, {3534, 18515}, {3585, 18545}, {3814, 11499}, {3820, 6928}, {3843, 7680}, {4294, 6841}, {5055, 6690}, {5119, 12953}, {5173, 18541}, {5249, 10246}, {5535, 11661}, {6253, 10525}, {6284, 18517}, {6917, 16202}, {6934, 10943}, {8069, 9669}, {9614, 18493}, {9670, 9955}, {11018, 18530}, {12116, 16203}, {12635, 12699}
X(18499) = reflection of X(i) in X(j) for these (i,j): (1657, 3428), (5119, 18480)
X(18499) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 18518, 18542), (3583, 18491, 381), (18496, 18498, 1)
X(18500) lies on these lines: {3,7914}, {4,2896}, {5,7846}, {30,3096}, {32,381}, {113,12501}, {382,3098}, {1479,10873}, {3091,9862}, {3545,10583}, {3583,10877}, {3830,7842}, {3851,9756}, {7899,10000}, {7918,14458}, {7923,10345}, {9941,18480}, {9997,18525}, {10047,10896}, {10871,18516}, {10872,18517}, {10875,18520}, {10876,18522}, {10878,18542}, {10879,18544}, {11885,18507} et al
X(18500) = X(18501)-of-Ehrmann-mid-triangle
X(18500) = X(18501)-of-5th-Brocard-triangle
The homothetic center of these triangles is X(18500).
X(18501) lies on these lines: {3,83}, {4,11842}, {5,7793}, {30,7787}, {32,381}, {98,3843}, {182,1657}, {382,3398}, {399,12201}, {9766,18548}, {11490,18524}, {11839,18508}, {12194,18525}, {12212,18440} et al
X(18502) lies on these lines: {3,6683}, {4,3398}, {5,316}, {30,83}, {32,381}, {98,546}, {113,12201}, {182,382}, {384,14881}, {538,18548}, {1478,10798}, {1656,5171}, {2782,7839}, {3583,10799}, {3843,11842}, {3849,8150}, {5039,18440}, {5476,7748}, {7770,9821}, {10113,13193}, {10792,18509}, {10793,18511}, {10794,18516}, {10800,18525}, {10802,10896}, {11839,18507}, {11840,18520}, {11841,18522}
X(18502) = X(18503)-of-Ehrmann-mid-triangle
X(18502) = X(18503)-of-5th-anti-Brocard-triangle
The homothetic center of these triangles is X(18502).
X(18503) lies on these lines: {3,3096}, {4,9301}, {5,9862}, {30,2896}, {32,381}, {382,6248}, {399,12501}, {3094,18440}, {9941,18525}, {11494,18524}, {11885,18508} et al
X(18504) lies on these lines: {3,1539}, {4,11449}, {5,6241}, {54,156}, {110,12293}, {113,5449}, {235,6403}, {3544,18489}, {5655,18356}, {7577,11439}, {10539,18392}, {10540,18394}
X(18504) = X(21400)-of-Ehrmann-mid-triangle
X(18505) lies on these lines: {10,30}, {381,2999}, {2270,18540}
X(18505) = X(18506)-of-Ehrmann-mid-triangle
X(18505) = X(18506)-of-Danneels-Bevan-triangle
The homothetic center of these triangles is X(18505).
X(18506) lies on these lines: {1,30}, {4,5256}, {6,18540}, {37,3587}, {42,18528}, {84,5707}, {376,5287}, {381,2999}, {517,7174}, {940,7171}, {942,3182}, {990,18443}, {1103,9654} et al
X(18507) lies on these lines: {2,3}, {113,12790}, {1478,11906}, {1479,11905}, {1539,12369}, {3818,12583}, {9955,11831}, {10113,13212}, {10895,11912}, {10896,11913}, {11839,18502}, {11848,18491}, {11852,18492}, {11863,18495}, {11864,18497}, {11885,18500}, {11900,12699}, {11901,18509}, {11902,18511}, {11903,18516}, {11904,18517}, {11907,18520}, {11908,18522}, {11910,18525}, {11914,18542}, {11915,18544}, {12438,18480}, {12611,12729}, {12794,14881}, {16210,18357}
X(18507) = X(18508)-of-Ehrmann-mid-triangle
X(18507) = X(18508)-of-Gossard-triangle
X(18507) = X(12113)-of-Johnson-triangle
The homothetic center of these triangles is X(18507).
X(18508) lies on these lines: {2,3}, {399,12790}, {999,11906}, {2777,5502}, {3295,11905}, {8148,12626}, {9033,12121}, {9654,11912}, {11831,18493}, {11839,18501}, {11848,18524}, {11852,18480}, {11885,18503}, {11900,12702}, {12164,12418}, {12438,18525}, {12583,18440}, {12902,13212}, {15526,16111}
X(18509) lies on these lines: {3,10261}, {4,1161}, {5,5871}, {6,13}, {30,5591}, {1478,10925}, {1479,10923}, {3583,10927}, {5605,18525}, {8216,18520}, {8217,18522}, {9955,11370}, {10048,10896}, {10792,18502}, {10919,18516}, {10929,18542}, {10931,18544}, {11901,18507}
X(18509) = {X(381),X(3818)}-harmonic conjugate of X(18511)
X(18509) = X(18510)-of-Ehrmann-mid-triangle
X(18509) = X(18510)-of-inner-Grebe-triangle
The homothetic center of these triangles is X(18509).
X(18510) lies on these lines: {2,6199}, {3,1588}, {4,6418}, {5,6417}, {6,13}, {30,6395}, {371,3526}, {372,1657}, {376,6446}, {382,3071}, {485,5072}, {486,590}, {546,1132}, {547,8972}, {549,6445}, {550,6408}, {615,5054}, {631,6407}, {632,3317}, {1131,3858}, {1151,15720}, {1152,15696} et al
X(18510) = {X(6),X(381)}-harmonic conjugate of X(18512)
X(18510) = X(6395)-of-orthocentroidal-triangle
X(18511) lies on these lines: {3,10262}, {4,1160}, {5,5870}, {6,13}, {30,5590}, {1478,10926}, {1479,10924}, {3583,10928}, {8218,18520}, {8219,18522}, {9955,11371}, {10049,10896}, {10793,18502}, {10920,18516}, {10930,18542}, {10932,18544}, {11902,18507}
X(18511) = {X(381),X(3818)}-harmonic conjugate of X(18509)
X(18511) = X(18512)-of-Ehrmann-mid-triangle
X(18511) = X(18512)-of-outer-Grebe-triangle
The homothetic center of these triangles is X(18511).
X(18512) lies on these lines: {2,6395}, {3,1587}, {4,6417}, {5,6418}, {6,13}, {30,6199}, {371,1657}, {372,3526}, {376,6445}, {382,3070}, {485,615}, {486,5072}, {546,1131}, {549,6446}, {550,6407}, {590,5054}, {631,6408}, {632,3316}, {1132,3858}, {1151,15696}, {1152,8960} et al
X(18512) = {X(6),X(381)}-harmonic conjugate of X(18510)
X(18512) = X(6199)-of-orthocentroidal-triangle
X(18513) lies on these lines: {1,4}, {5,7280}, {8,4525}, {11,3845}, {30,5010}, {35,382}, {36,381}, {46,1749}, {55,3830}, {56,3843}, {57,13273}, {79,1837}, {80,1836}, {498,3146}, {1060,18403}, {1709,12761}, {2093,18406}, {3295,9656}, {3336,9579}, {3337,9581}, {3543,3584}, {3746,5076}, {3822,11114}, {3853,6284}, {4214,8185}, {4309,5261}, {4317,10591}, {5073,5217}, {5141,5267}, {5268,7391}, {5272,7394}, {5326,8703}, {5441,11374}, {5563,9655}, {6645,14044}, {7355,18383}, {9897,10742}, {10037,11403}, {10827,11010}, {11009,18525}, {12102,15171} et al
X(18513) = X(18515)-of-Ehrmann-mid-triangle
X(18513) = X(18515)-2nd-isogonal-triangle-of-X(1)
X(18514) lies on these lines: {1,4}, {2,4324}, {5,5010}, {8,4537}, {11,3627}, {12,3845}, {30,5433}, {35,381}, {36,382}, {46,12764}, {65,18550}, {15430,18426} et al
X(18514) = {X(1),X(4)}-harmonic conjugate of X(18513)
The homothetic center of these triangles is X(18513).
X(18515) lies on these lines: {2,10742}, {3,10}, {30,11680}, {35,18526}, {36,381}, {55,7972}, {56,79}, {104,1621}, {952,6950}, {999,11551}, {1385,15071}, {4188,18357} et al
X(18516) lies on these lines: {4,8}, {5,6256}, {10,16004}, {11,381}, {12,18542}, {30,1376}, {57,3585}, {104,6945}, {113,12889}, {119,1012}, {153,5603}, {382,6244}, {388,9955}, {498,13743}, {546,7956}, {1385,6893}, {1479,10944}, {1709,3359}, {2093,18406}, {2096,6839}, {2551,3579}, {2771,18391}, {3091,10785}, {3545,10584}, {3560,6690}, {3583,7962}, {3586,18528}, {3843,11928}, {4302,18524}, {5084,13624}, {5450,6681}, {5731,6965}, {5886,6957}, {6282,18529}, {6284,18518}, {6841,10523}, {6850,9956}, {6916,11231}, {6939,11230}, {7701,18395}, {10629,12915}, {10794,18502}, {10871,18500}, {10896,10948}, {10919,18509}, {10920,18511}, {10942,11496}, {10945,18520}, {10946,18522}, {10949,18544}, {11865,18495}, {11866,18497}, {11903,18507}, {12619,14647}, {15888,18545} et al
X(18516) = reflection of X(i) in X(j) for these (i,j): (7956,546), (10269,5)
X(18516) = X(999)-of-Ehrmann-mid-triangle
X(18516) = X(999)-of-inner-Johnson-triangle
X(18516) = X(10269)-of-Johnson-triangle
X(18516) = {X(4),X(18480)}-harmonic conjugate of X(18517)
X(18517) lies on these lines: {1,18406}, {3,3925}, {4,8}, {5,1001}, {11,18544}, {12,381}, {30,958}, {55,6841}, {113,12890}, {443,13624}, {497,6849}, {498,18524}, {515,6917}, {1385,6826}, {1478,3649}, {1621,6990}, {1697,3583}, {2550,3579}, {2771,4295}, {3091,10786}, {3340,3585}, {3545,10585}, {3616,6900}, {3818,9052}, {3832,10599}, {3843,10738}, {4302,13743}, {4317,12773}, {4846,15232}, {5603,6894}, {5657,6895}, {5731,6901}, {5768,5885}, {5880,13369}, {5886,6835}, {6691,6911}, {6796,6862}, {6827,9956}, {6861,10902}, {6864,11230}, {6865,11231}, {6903,9780}, {9895,18420}, {10523,10896}, {10872,18500}, {10895,10954}, {10951,18520}, {10952,18522}, {10955,18542}, {11904,18507} et al
X(18517) = X(3295)-of-Ehrmann-mid-triangle
X(18517) = X(3295)-of-outer-Johnson-triangle
X(18517) = {X(4),X(18480)}-harmonic conjugate of X(18516)
The homothetic center of these triangles is X(1479).
X(18518) lies on these lines: {1,18491}, {3,10}, {4,3871}, {5,10585}, {8,6985}, {11,18543}, {12,381}, {30,3436}, {40,18528}, {55,10827}, {72,3426}, {405,18357}, {6284,18516}, {12587,18440} et al
X(18518) = inner-Johnson-to-outer-Johnson similarity image of X(3)
X(18518) = {X(3),X(18525)}-harmonic conjugate of X(18519)
The homothetic center of these triangles is X(1478).
X(18519) lies on these lines: {1,1898}, {3,10}, {4,10529}, {5,10584}, {11,381}, {12,18545}, {30,956}, {36,18491}, {56,10826}, {63,10914}, {80,1470}, {104,6911}, {153,6830}, {226,7373}, {382,5841}, {388,6841}, {399,12889}, {474,18357}, {5927,6913}, {12586,18440} et al
X(18519) = outer-Johnson-to-inner-Johnson similarity image of X(3)
X(18519) = {X(3),X(18525)}-harmonic conjugate of X(18518)
X(18520) lies on these lines: {4,6462}, {5,9838}, {30,8222}, {113,12894}, {381,493}, {546,8212}, {1478,11932}, {1479,11930}, {3091,11846}, {3583,11947}, {3818,12590}, {3843,11949}, {6461,18522}, {8188,18492}, {8194,9818}, {8201,18495}, {8208,18497}, {8210,18525}, {8214,12699}, {8216,18509}, {8218,18511}, {9955,11377}, {10113,13215}, {10875,18500}, {10895,11951}, {10896,11953}, {10945,18516}, {10951,18517}, {11503,18491}, {11840,18502}, {11907,18507}, {11955,18542}, {11957,18544}, {12440,18480}
X(18520) = X(18521)-of-Ehrmann-mid-triangle
X(18520) = X(18521)-of-Lucas-homothetic-triangle
The homothetic center of these triangles is X(18520).
X(18521) lies on these lines: {3,5490}, {381,493}, {6464,18523}
X(18522) lies on these lines: {4,6463}, {5,9839}, {30,8223}, {113,12895}, {381,494}, {546,8213}, {1478,11933}, {1479,11931}, {3091,11847}, {3583,11948}, {3818,12591}, {3843,11950}, {6461,18520}, {8189,18492}, {8195,9818}, {8202,18495}, {8209,18497}, {8211,18525}, {8215,12699}, {8217,18509}, {8219,18511}, {9955,11378}, {10113,13216}, {10876,18500}, {10895,11952}, {10896,11954}, {10946,18516}, {10952,18517}, {11504,18491}, {11841,18502}, {11908,18507}, {11956,18542}, {11958,18544}, {12441,18480}
X(18522) = X(18523)-of-Ehrmann-mid-triangle
X(18522) = X(18523)-of-Lucas(-1)-homothetic-triangle
The homothetic center of these triangles is X(18522).
X(18523) lies on these lines: {3,5491}, {381,494}, {6464,18521}
The homothetic center of these triangles is X(3583).
X(18524) lies on these lines: {3,10}, {4,11849}, {5,1621}, {21,18357}, {30,100}, {35,13743}, {36,9897}, {40,5694}, {55,381}, {56,18526}, {80,5172}, {119,5842}, {140,9342}, {165,18528}, {191,210}, {227,18447}, {382,11248}, {399,12334}, {411,5690}, {474,3897}, {484,2771}, {498,18517}, {517,3689}, {547,5284}, {692,10540}, {758,12738}, {859,6740}, {944,6924}, {952,6905}, {999,11502}, {1001,5055}, {1482,3149}, {1656,4423}, {3198,18453}, {3295,11375}, {3869,3940}, {4302,18516}, {4413,5054}, {5531,5535}, {9654,11507}, {9655,11509}, {11231,15931}, {11249,12645}, {11383,18494}, {11490,18501}, {11494,18503}, {11510,18543}, {11848,18508}, {12164,12328}, {12329,18440} et al
X(18525) lies on these lines: {1,381}, {3,10}, {4,145}, {5,944}, {8,30}, {20,4678}, {40,1657}, {55,5441}, {56,80}, {65,9655}, {104,6924}, {113,12898}, {140,5731}, {382,517}, {399,12368}, {495,3486}, {496,3476}, {516,4701}, {518,18345}, {519,3830}, {546,1483}, {547,5550}, {942,5727}, {950,6767}, {956,5086}, {999,1837}, {1012,11015}, {1056,6849}, {1071,4004}, {1125,3655}, {1385,1656}, {1387,10591}, {1478,3649}, {1479,10944}, {1697,18540}, {1829,18494}, {1854,18340}, {2099,3585}, {2807,18439}, {3241,3845}, {3242,3818}, {3243,18482}, {3244,3656}, {5204,5442}, {5270,18406}, {5597,18497}, {5598,18495}, {5604,18511}, {5605,18509}, {5708,18391}, {8210,18520}, {8211,18522}, {9941,18503}, {9997,18500}, {10800,18502}, {11009,18513}, {11910,18507}, {12194,18501}, {12410,18534}, {12438,18508} et al
X(18525) = reflection of X(i) in X(j) for these (i,j): (1,18480), (1483,546)
X(18525) = anticomplement of X(34773)
X(18525) = X(18526)-of-Ehrmann-mid-triangle
X(18525) = X(18526)-of-5th-mixtilinear-triangle
X(18525) = anti-Aquila-to-ABC similarity image of X(18480)
X(18525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1,381,18493), (9955,18492,381), (18518,18519,3), (18527,18529,381), (18542,18544,381)
The homothetic center of these triangles is X(18525).
X(18526) lies on these lines: {1,381}, {3,8}, {4,1483}, {5,3622}, {10,3655}, {20,5844}, {30,145}, {35,18515}, {40,15696}, {56,18524}, {79,2099}, {80,1388}, {119,3847}, {355,1125}, {376,3621}, {382,515}, {399,12898}, {517,1657}, {519,3534}, {3242,18440}, {3616,5055}, {7984,12902}, {11928,12737} et al
X(18526) = anticomplement of X(37705)
X(18526) = {X(18543),X(18545)}-harmonic conjugate of X(381)
X(18527) lies on these lines: {1,381}, {4,5045}, {8,7317}, {30,11019}, {65,14861}, {355,1058}, {382,3333}, {497,517}, {942,1479}, {999,3586}, {1478,5049}, {1538,18446} et al
X(18527) = midpoint of X(i) and X(j) for these {i,j}: {497,5722}, {999,3586}
X(18527) = {X(381),X(18525)}-harmonic conjugate of X(18529)
X(18527) = X(18528)-of-Ehrmann-mid-triangle
X(18527) = X(18528)-of-3rd-pedal-triangle-of-X(1)
The homothetic center of these triangles is X(18527).
X(18528) lies on these lines: {1,381}, {3,5234}, {4,3870}, {5,10582}, {30,200}, {40,18518}, {42,18506}, {55,18540}, {57,18491}, {84,11499}, {165,18524}, {210,3587}, {3586,18516}, {6843,18446} et al
X(18528) = reflection of X(57) in X(18491)
X(18529) lies on these lines: {1,381}, {4,200}, {30,8580}, {40,3715}, {165,18491}, {1490,6843}, {1750,3925}, {6282,18516} et al
X(18529) = {X(381),X(18525)}-harmonic conjugate of X(18527)
X(18529) = X(18530)-of-Ehrmann-mid-triangle
X(18529) = X(18530)-of-3rd-antipedal-triangle-of-X(1)
The homothetic center of these triangles is X(18529).
X(18530) lies on these lines: {1,381}, {3,4314}, {5,10578}, {30,10580}, {80,8162}, {382,5045} et al
X(18531) lies on these lines: {2, 3}, {68, 5562}, {69, 265}, {113, 206}, {115, 577}, {125, 4549}, {127, 131}, {141, 18382}, {155, 6146}, {156, 13470}, {182, 18388}, {184, 1568}, {216, 5475}, {343, 14852}, {388, 18447}, {394, 18396}, {486, 10898}, {497, 18455}, {511, 18390}, {542, 11511}, {567, 11427}, {568, 11433}, {626, 14376}, {1038, 3585}, {1040, 3583}, {1060, 1478}, {1062, 1479}, {1092, 12118}, {1154, 6515}, {1216, 9927}, {1352, 2393}, {1503, 18451}, {1531, 4846}, {1660, 9833}, {1899, 13754}, {1992, 18449}, {1993, 12022}, {2549, 14961}, {2550, 18453}, {2790, 6033}, {2834, 10743}, {2888, 12606}, {2971, 13556}, {2974, 10748}, {3068, 18457}, {3069, 18459}, {3098, 7687}, {3284, 5309}, {3448, 7723}, {3519, 15077}, {3521, 15740}, {3564, 10602}, {3767, 10316}, {3818, 11574}, {3819, 18376}, {5158, 7753}, {5512, 15560}, {5878, 10575}, {5892, 7706}, {5907, 18381}, {5972, 11202}, {6288, 11487}, {6564, 11513}, {6565, 11514}, {6776, 18445}, {7728, 13203}, {7735, 10317}, {7748, 15075}, {7818, 15526}, {7998, 18392}, {7999, 18394}, {9306, 18400}, {9969, 15812}, {10113, 13416}, {10116, 15083}, {10319, 18406}, {10540, 11206}, {10634, 18582}, {10635, 18581}, {11411, 18436}, {11442, 11459}, {11457, 12111}, {11488, 18468}, {11489, 18470}, {11515, 16808}, {11516, 16809}, {11550, 15030}, {11793, 18383}, {12091, 14731}, {12134, 17814}, {12160, 13292}, {12162, 14216}, {12318, 12429}, {12324, 18439}, {12370, 16266}, {13346, 13403}, {13562, 18440}, {14649, 14689}, {14841, 14843}, {14912, 15087}, {15133, 15738}, {17811, 18405}
X(18531) = midpoint of X(4) and X(1370)
X(18531) = reflection of X(i) in X(j) for these (i,j): (3,1368), (25,5)
X(18531) = isogonal conjugate of X(18532)
X(18531) = complement of X(18533)
X(18531) = anticomplement of X(6644)
X(18531) = complementary conjugate of complement of X(34801)
X(18531) = inverse-in-Johnson-circle of X(10297)
X(18531) = inverse-in-orthocentroidal-circle of X(18420)
X(18531) = inverse-in-orthoptic-circle-of-Steiner-inellipse of X(16387)
X(18531) = homothetic center of Ehrmann vertex-triangle and 6th anti-mixtilinear
X(18531) = homothetic center of Ehrmann side-triangle and anti-inverse-in-incircle triangle
X(18531) = X(18534)-of-Ehrmann-mid-triangle
X(18531) = X(18534)-of-3rd-pedal-triangle-of-X(3)
X(18531) = X(2093)-of-Ehrmann-vertex-triangle if ABC is acute
X(18531) = X(999)-of-Ehrmann-side-triangle if ABC is acute
X(18531) = X(25)-of-Johnson-triangle
X(18531) = X(1370)-of-Euler-triangle
X(18531) = X(1368)-of-X3-ABC-reflections-triangle
X(18531) = X(6282)-of-orthic-triangle if ABC is acute
X(18531) = orthic-to-Ehrmann-vertex similarity image of X(18533)
X(18531) = barycentric product X(69)*X(1478)*X(1479)
X(18531) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18563, 20), (4, 3545, 7394), (4, 18537, 381), (5, 7502, 10201), (381, 382, 18535), (381, 12083, 11799), (381, 18534, 1596), (382, 7529, 6756), (1597, 1598, 16542), (3091, 3547, 10024), (6826, 6851, 7490), (7502, 10201, 7493), (7526, 13371, 3541), (10297, 15760, 381), (10750, 10751, 10297), (14807, 14808, 7464)
X(18532) lies on the Jerabek hyperbola and these lines: {24,68}, {25,265}, {65,1061}, {69,186}, {73,3422}, {378,4846} et al
X(18532) = isogonal conjugate of X(18531)
X(18532) = anti-Ara-to-ABC similarity image of X(18385)
X(18533) lies on these lines: {2,3}, {33,4302}, {34,4299}, {35,11392}, {36,11393}, {52,12118}, {54,14542}, {64,16655}, {66,74}, {99,317}, {112,393}, {132,14649}, {185,9833}, {193,1986}, {232,7737}, {254,8883}, {264,14907}, {477,10423}, {570,3087}
X(18533) = midpoint of X(i) and X(j) for these {i,j}: {20,7500}, {183,18440)
X(18533) = reflection of X(i) in X(j) for these (i,j): (4,25), (1370,3)
X(18533) = isogonal conjugate of X(34801)
X(18533) = anticomplement of X(18531)
X(18533) = crossdifference of every pair of points on line X(647)X(14396)
X(18533) = inverse-in-polar-circle of X(10297)
X(18533) = {X(3),X(4)}-harmonic conjugate of X(3541)
X(18533) = X(25)-of-anti-Euler-triangle
X(18533) = X(57)-of-circumorthic-triangle if ABC is acute
X(18533) = X(1370)-of-ABC-X3-reflections-triangle
X(18533) = X(2093)-of-orthic-triangle if ABC is acute
X(18533) = orthic-to-circumorthic similarity image of X(25)
X(18533) = Ehrmann-vertex-to-orthic similarity image of X(18531)
X(18533) = perspector of ABC and cross-triangle of 1st and 2nd Lemoine-Dao triangles
X(18533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (381, 15069, 576), (10516, 18440, 182)
The homothetic center of these triangles is X(18531).
X(18534) lies on these lines: {2,3}, {34,9645}, {49,1660}, {52,1498}, {115,1609}, {154,13352}, {265,9919}, {511,18451}, {12410,18525} et al
X(18534) = {X(381),X(382)}-harmonic conjugate of X(31723)
X(18534) = {X(381),X(1657)}-harmonic conjugate of X(18536)
Given a triangle ABC and a point P, let c(P) be the circumconic having perspector P, and let A' be the center of the conic that passes through P and is tangent to c(P) at B and C. Define points B' and C' cyclically. The triangles ABC and A'B'C' are orthologic if and only P is on the sextic (passing through X(2), X(6)) having this barycentric equation:
Cyclic sum [ y z(17(b^2-c^2) x^4- ((15a^2+31b^2-19c^2) y-(15a^2-19b^2+31c ^2) z)x^3+ a^2(y+z)(y-z)^3) ]= 0.
If P is the centroid then the orthologic center of A'B'C' with respect to ABC is X(15692). The reciprocal orthologic center is X(4). If P is the symmedian then the orthologic center of ABC with respect to A'B'C' is X(18535). The reciprocal orthologic center is X(3). (Angel Montesdeoca, December 12, 2022)
X(18535) lies on these lines: {2,3}, {6,3531}, {33,6767}, {34,7373}, {115,8573}, {182,13570}, {389,12315}, {399,2971}, {1112,12308}, {1159,1905}, {1181,3527}, {1351,8681}, {1619,18405}, {3066,11820}, {3092,6417}, {3093,6418}, {3199,9605} et al
X(18535) = {X(381),X(382)}-harmonic conjugate of X(18531)
X(18535) = X(18536)-of-Ehrmann-mid-triangle
X(18535) = X(18536)-of-3rd-antipedal-triangle-of-X(3)
X(18535) = endo-homothetic center of these triangles: Ehrmann mid and 3rd antipedal of X(4); The homothetic center is X(18537).
X(18535) = trilinear product X(4)*X(999)*X(3295)
The homothetic center of these triangles is X(18535).
X(18536) lies on these lines: {2,3}, {216,15484}, {1038,9655}, {1216,11850}, {1350,18390}, {5891,11574} et al
X(18536) = {X(381),X(1657)}-harmonic conjugate of X(18534)
X(18537) lies on these lines: {2,3}, {113,3618}, {146,9826}, {800,5475}, {1352,8681}, {1899,15030}, {3818,18489}, {6337,15505}, {6776,18451}, {15585,18382} et al
X(18537) = {X(3),X(381)}-harmonic conjugate of X(1596)
X(18537) = X(18535)-of-Ehrmann-mid-triangle
X(18537) = X(18535)-of-3rd-antipedal-triangle-of-X(4)
X(18538) lies on these lines: {2,6398}, {4,3590}, {5,6}, {20,3316}, {30,590}, {140,3070}, {371,546}, {372,3628}, {381,3068}, {631,1131}, {632,1152}, {1151,3627}, {3069,5055}, {3071,3850}, {3090,3312}, {3091,3311}, {7969,18357} et al
X(18538) = X(18539)-of-Ehrmann-mid-triangle
X(18538) = X(18539)-of-X(2)-quadsquares-triangle
The homothetic center of these triangles is X(18538).
X(18539) lies on these lines: {4,193}, {30,492}, {230,6565}, {381,3068}, {3830,5860} et al
X(18540) lies on these lines: {1,1898}, {2,7171}, {3,1750}, {4,63}, {5,84}, {6,18506}, {9,30}, {34,18477}, {40,382}, {46,1749}, {55,18528}, {57,381}, {165,18491}, {515,6930}, {517,5223}, {1697,18525}, {1706,18357}, {1709,3359}, {2003,18451}, {2270,18505}, {6912,18446} et al
X(18540) = X(18541)-of-Ehrmann-mid-triangle
X(18540) = X(18541)-of-tangential-of-excentral-triangle
The homothetic center of these triangles is X(18540).
X(18541) lies on these lines: {1,1657}, {3,226}, {4,5708}, {5,5435}, {7,30}, {20,6147}, {46,9654}, {55,15228}, {56,79}, {57,381}, {65,9655}, {140,5714}, {376,5719}, {377,3927}, {382,942}, {388,12702} et al
X(18542) lies on these lines: {1,381}, {3,119}, {4,3871}, {5,10584}, {8,10711}, {12,18516}, {30,5552}, {113,12905}, {382,11248}, {546,10531}, {944,11729}, {1470,9655}, {1478,10958}, {1479,10956}, {1656,10269}, {1657,2077}, {2098,12611}, {3091,10805}, {3545,10586}, {3583,10965}, {3585,11509}, {3818,12594}, {3832,10596}, {3843,12000}, {3845,11239}, {5055,10200}, {5554,18357}, {5587,15071}, {5687,11698}, {5777,5790}, {6735,12702}, {6841,10590}, {6882,12667}, {6929,16202}, {6968,10943}, {7681,12001}, {9818,10834}, {10113,13217}, {10878,18500}, {10929,18509}, {10930,18511}, {10955,18517}, {11231,16209}, {11914,18507}, {11955,18520}, {11956,18522}, {12645,12751}
X(18542) = {X(381),X(18525)}-harmonic conjugate of X(18544)
X(18542) = X(18543)-of-Ehrmann-mid-triangle
X(18542) = X(18543)-of-inner-Yff-tangents-triangle
X(18542) = endo-homothetic center of these triangles: Ehrmann mid and outer Yff; The homothetic center is X(10896).
The homothetic center of these triangles is X(18542).
X(18543) lies on these lines: {1,381}, {3,3434}, {4,12001}, {5,10587}, {11,18518}, {30,10529}, {56,18499}, {382,2829}, {6831,12000}, {11510,18524}, {12595,18440} et al
X(18543) = {X(381),X(18526)}-harmonic conjugate of X(18545)
X(18544) lies on these lines: {1,381}, {3,2886}, {4,10529}, {5,10585}, {11,18517}, {30,10527}, {56,18407}, {113,12906}, {382,11249}, {497,6841}, {546,10532}, {1478,10959}, {1479,10957}, {1656,4423}, {1657,11012}, {3091,10806}, {3526,10902}, {3545,10587}, {3583,10966}, {3818,12595}, {3832,10597}, {3843,10742}, {3845,11240}, {3847,5055}, {5044,5790}, {6734,12702}, {6917,16203}, {7548,7967}, {7680,12000}, {7741,11510}, {8148,13463}, {9655,12773}, {9818,10835}, {10113,13218}, {10879,18500}, {10916,11235}, {10931,18509}, {10932,18511}, {10949,18516}, {11231,16208}, {11915,18507}, {11957,18520}, {11958,18522}, {12611,12750}
X(18544) = {X(381),X(18525)}-harmonic conjugate of X(18542)
X(18544) = X(18545)-of-Ehrmann-mid-triangle
X(18544) = X(18545)-of-outer-Yff-tangents-triangle
X(18544) = endo-homothetic center of these triangles: Ehrmann mid and inner Yff; The homothetic center is X(10895).
The homothetic center of these triangles is X(18544).
X(18545) lies on these lines: {1,381}, {3,3436}, {4,12000}, {5,10586}, {12,18519}, {30,10528}, {119,1656}, {153,3560}, {355,12609}, {382,5842}, {399,12905}, {1478,10955}, {1482,12608}, {1532,12001}, {1657,11248}, {9655,11509}, {12594,18440}, {15888,18516} et al
X(18545) = {X(381),X(18526)}-harmonic conjugate of X(18543)
X(18546) lies on these lines: {2,99}, {4,754}, {5,7781}, {30,5171}, {32,11361}, {76,7818}, {194,15031}, {316,17131}, {325,18424}, {381,538}, {382,7780}, {524,3818}, {546,7759}, {591,6565}, {625,7908}, {626,16041}, {1007,14148} et al
X(18546) = reflection of X(7775) in X(381)
X(18546) = X(9766)-of-Ehrmann-mid-triangle
X(18546) = X(9766)-of-1st-Brocard-triangle
X(18547) lies on these lines: {194,3818}, {3845,7812}, {9166,14880}
X(18548) lies on these lines: {2,32}, {538,18502}, {576,732}, {3095,7781}, {3398,7843}, {3849,12054}, {5034,7872}, {7697,7751}, {7759,10796}, {7764,12110}, {8178,14881}, {9766,18501}
X(18549) lies on these lines: {3,15079}, {8,10738}, {517,5560}, {1482,1699}, {5076,16150}, {6246,12645}, {6913,11517}, {6980,10543}, {7704,18493}, {11928,12737}
X(18550) lies on these lines: {3,1531}, {4,15003}, {5,11270}, {6,3830}, {30,3431}, {54,382}, {64,3843}, {65,18514}, {67,3818}, {74,381} et al
X(18551) lies on these lines: {3,5888}, {6,12308}, {146,381}, {399,11702}, {599,3818}, {3426,5055}, {18325,18358} et al
X(18552) lies on these lines: {30,3589}, {264,3545}, {381,5158}, et al
X(18553) lies on these lines: {3, 11178}, {4, 69}, {5, 542}, {6, 3851}, {39, 6287}, {51, 3410}, {67, 3521}, {98, 16984}, {114, 5939}, {140, 1503}, {141, 550}, {182, 1656}, {343, 10301}, {373, 3448}, {381, 576}, {382, 599}, {524, 546}, {924, 18313}, {1350, 5073}, {1351, 18555}, {1657, 3098}, {1899, 6688}, {1992, 3855}, {2030, 7746}, {2393, 18383}, {3090, 11179}, {3091, 5032}, {3292, 5169}, {3519, 11808}, {3529, 7936}, {3564, 3850}, {3619, 10299}, {3628, 10168}, {3763, 15720}, {3819, 11550}, {3843, 11477}, {3854, 14853}, {3858, 5480}, {3917, 5189}, {5012, 7570}, {5038, 7603}, {5056, 6776}, {5059, 10519}, {5068, 5921}, {5070, 10541}, {5094, 9306}, {5891, 7574}, {5943, 11442}, {6000, 18431}, {6054, 7608}, {6102, 16776}, {6249, 7762}, {7401, 15012}, {7514, 15581}, {7527, 12584}, {7528, 16625}, {7547, 8541}, {7607, 8590}, {7747, 15993}, {8675, 18039}, {8681, 9927}, {8786, 10486}, {9019, 11591}, {9140, 16042}, {9225, 15820}, {9730, 14982}, {9751, 16988}, {9822, 13382}, {9971, 18436}, {9976, 14644}, {9977, 15052}, {10991, 13335}, {11257, 11261}, {11572, 15056}, {11649, 15060}, {11793, 14791}, {13108, 18500}, {13851, 15073}, {14216, 17704}, {14269, 15533}, {14866, 15098}, {16194, 18325}
X(18553) = midpoint of X(576) and X(15069)
X(18553) = reflection of X(1) in X(j) for these (i,j): (575,5), (14810,141)
X(18553) = X(575)-of-Johnson-triangle
Let MAMBMC be the Ehrmann mid-triangle. Let A' be the center of conic {{A,B,C,MB,MC}} and define B', C' cyclically. The lines AA', BB', CC' concur in X(18554).
X(18554) lies on these lines: {30,16240}, {264,3545}
X(18554) = barycentric quotient X(30)*X(381)/X(376)
X(18554) = barycentric quotient X(18487)/X(376)
Let MAMBMC be the Ehrmann mid-triangle and JAJBJC the Johnson triangle. Let A' be the center of conic {{JA,JB,JC,MB,MC}} and define B', C' cyclically. The lines AA', BB', CC' concur in X(4). The lines JAA', JBB', JCC', concur in X(18555).
X(18555) lies on these lines: {4,52}, {113,13431}, {265,13598}, {382,14864}, {1216,2889}, {10619,12370}, {10625,18390}, {13421,18572} et al
X(18556) lies on these lines: {3,523}, {20,2394}, {122,127}, {512,5891}, {1640,2420}, {1649,11007}, {3268,9517}, {7493,9209}
X(18556) = midpoint of X(20) and X(2394)
X(18556) = reflection of X(5664) in X(3)
X(18556) = X(2)-of-Ehrmann-cross-triangle
X(18556) = X(14566)-of-anti-Euler-triangle
X(18556) = X(5664)-of-ABC-X3-reflections-triangle
X(18557) lies on these lines: {265,8673}, {343,525}, {648,14618}, {1568,9033} et al
X(18557) = barycentric product X(30)*X(69)^2*X(76)*X(523)*X(1989)
X(18557) = barycentric product X(i)*X(j) for these {i,j}: {76,18558}, {328,9033}, {3265,14254}, {11064,14592}
X(18557) = barycentric quotient X(18558)/X(6)
X(18558) lies on these lines: {112,476}, {216,647}, {850,5664}, {1989,6587} et al
X(18558) = barycentric product X(30)*X(69)^2*X(523)*X(1989)
X(18558) = barycentric product X(i)*X(j) for these {i,j}: {6,18557}, {265,9033}, {3265,14583}, {11064,14582}
X(18558) = barycentric quotient X(i)/X(j) for these (i,j): (9033,340), (14583,107), (18557,76)
X(18559) lies on these lines: {2,3}, {13,10632}, {14,10633}, {52,12278}, {74,11550}, {115,10986}, {232,14537}, {264,11057}, {317,18354}, {389,12289}, {539,5889}, {541,12140}, {542,6403}, {1235,7811} et al
X(18559) = reflection of X(18564) in X(5)
X(18559) = inverse-in-polar-circle of X(18572)
X(18559) = X(18564)-of-Johnson-triangle
X(18560) lies on these lines: {2,3}, {33,10483}, {49,7728}, {54,10721}, {64,11457}, {74,5894}, {112,5254}, {113,12038}, {185,1986}, {232,7756}, {541,10116}, {567,3521}, {1105,1300}, {1204,18390}, {12121,18350} et al
X(18560) = Kosnita-to-orthic similarity image of X(20)
X(18560) = harmonic center of polar and second Droz-Farny circles
X(18560) = inverse-in-2nd-Droz-Farny-circle of X(186)
X(18560) = X(5697)-of-orthic-triangle if ABC is acute
X(18560) = {X(3),X(4)}-harmonic conjugate of X(403)
X(18561) lies on these lines: {2,3}, {339,11057}, {9927,18442}, {10317,11648}, {11645,18438}, {12111,12291}, {12902,15085}
X(18561) = midpoint of X(18562) and X(18564)
X(18561) = reflection of X(i) in X(j) for these (i,j): (3,18564), (18564,18563)
X(18561) = {X(18562),X(18563)}-harmonic conjugate of X(3)
X(18561) = Ehrmann-mid-to-ABC similarity image of X(18559)
X(18561) = X(18564)-of-X3-ABC-reflections-triangle
X(18561) = X(18559)-of-Ehrmann-side-triangle
X(18562) lies on these lines: {2,3}, {68,11559}, {265,7689}, {339,7802}, {568,13403}, {1092,12121}, {18439,18400} et al
X(18562) = reflection of X(i) in X(j) for these (i,j): (3,18563), (1209,18561), (18565,3)
X(18562) = X(5903)-of-Ehrmann-side-triangle if ABC is acute
X(18562) = X(18563)-of-X3-ABC-reflections-triangle
X(18562) = {X(3),X(4)}-harmonic conjugate of X(10254)
X(18563) lies on these lines: {2,3}, {52,13403}, {113,10282}, {127,7842}, {131,14103}, {265,12359}, {339,7750}, {567,12233}, {568,12241}, {1060,10483}, {1503,18438}, {6253,18453}, {17845,18451} et al
X(18563) = midpoint of X(i) and X(j) for these {i,j}: {3,18562}, {18561,18564}
X(18563) = reflection of X(i) in X(j) for these (i,j): (3,12605), (6240,5)
X(18563) = complement of X(34797)
X(18563) = X(65)-of-Ehrmann-side-triangle if ABC is acute
X(18563) = X(6240)-of-Johnson-triangle
X(18563) = X(12605)-of-X3-ABC-reflections-triangle
X(18563) = {X(3),X(4)}-harmonic conjugate of X(10024)
X(18564) lies on these lines: {2,3}, {13,18468}, {14,18470}, {115,18472}, {339,7811}, {539,18436}, {542,18438}, {577,1989}, {1531,18475}, {3581,18390}, {11750,18439} et al
X(18564) = midpoint of X(3) and X(18561)
X(18564) = reflection of X(i) in X(j) for these (i,j): (1207,18561), (18559,5), (18561,18563)
X(18564) = X(5902)-of-Ehrmann-side-triangle if ABC is acute
X(18564) = X(18559)-of-Johnson-triangle
X(18564) = {X(3),X(18562)}-harmonic conjugate of X(18565)
X(18565) lies on these lines: {2,3}, {184,3521}, {265,1204}, {1147,12121}, {2777,18439}, {4846,15002} et al
X(18565) = reflection of X(18562) in X(3)
X(18565) = X(5697)-of-Ehrmann-side-triangle if ABC is acute
X(18565) = {X(3),X(4)}-harmonic conjugate of X(10255)
X(18565) = {X(3),X(18562)}-harmonic conjugate of X(18564)
X(18566) lies on these lines: {2,3}, {1539,11550}, {5663,18376}, {18356,18379}
X(18566) = midpoint of X(4) and X(18568)
X(18566) = reflection of X(i) in X(j) for these (i,j): (18377,18568), (18568,18567)
X(18566) = orthic-to-Ehrmann-vertex similarity image of X(3845)
X(18566) = X(18568)-of-Euler-triangle
X(18566) = X(10246)-of-Ehrmann-vertex-triangle if ABC is acute
X(18566) = X(18324)-of-Ehrmann-mid-triangle
X(18567) lies on these lines: {2,3}, {52,10113}, {1531,5876}, {1539,11381}, {3818,12061}, {5663,18383}, {18392,18436} et al
X(18567) = midpoint of X(i) and X(j) for these {i,j}: {4,18377}, {18566,18568}
X(18567) = reflection of X(15331) in X(5)
X(18567) = X(1385)-of-Ehrmann-vertex-triangle if ABC is acute
X(18567) = X(1658)-of-Ehrmann-mid-triangle
X(18567) = X(15331)-of-Johnson-triangle
X(18567) = circumorthic-to-orthic similarity image of X(18377)
X(18568) lies on these lines: {2,3}, {68,18379}, {542,12596}, {1531,18474}, {11442,18430}, {13754,18376}, {13851,14831}
X(18568) = midpoint of X(18377) and X(18566)
X(18568) = reflection of X(i) in X(j) for these (i,j): (4,18566), (10201,381), (18324,5), (18566,18567)
X(18568) = X(3576)-of-Ehrmann-vertex-triangle if ABC is acute
X(18568) = X(14070)-of-Ehrmann-mid-triangle
X(18568) = X(18324)-of-Johnson-triangle
X(18568) = X(18566)-of-anti-Euler-triangle
X(18568) = inverse-in-Johnson-circle of X(10295)
X(18568) = {X(10750),X(10751)}-harmonic conjugate of X(10295)
X(18569) lies on these lines: {2,3}, {50,2165}, {68,1154}, {70,265}, {156,5654}, {184,11750}, {485,11265}, {486,11266}, {511,9927}, {542,15083}, {568,15800}, {569,3574}, {1147,18400}, {1352,9973}, {1479,8144}, {1531,11381}, {1568,10539}, {1853,12163}, {1899,6102}, {2888,18432}, {5446,18390}, {5448,6759}, {5562,11572}, {6146,12161}, {6193,12319}, {7706,9729}, {11411,18356}, {12293,18405} et al
X(18569) = midpoint of X(i) and X(j) for these {i,j}: {4,14790}, {382,12085}
X(18569) = reflection of X(i) in X(j) for these (i,j): (3,13371), (4,18377), (20,11250), (26,5)
X(18569) = anticomplement of X(1658)
X(18569) = X(40)-of-Ehrmann-vertex-triangle if ABC is acute
X(18569) = X(11249)-of-Ehrmann-side-triangle if ABC is acute
X(18569) = X(7387)-of-Ehrmann-mid-triangle
X(18569) = X(26)-of-Johnson-triangle
X(18569) = X(14790)-of-Euler-triangle
X(18569) = X(18377)-of-anti-Euler-triangle
X(18569) = X(18377)-of-circumorthic-triangle if ABC is acute
X(18569) = X(13371)-of-X3-ABC-reflections-triangle
X(18569) = inverse-in-Johnson-circle of X(403)
X(18569) = X(37531)-of-orthic-triangle if ABC is acute
X(18569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,5,11818), (5,26,10201), (10750,10751,403)
Let A'1B'1C'1, A'2B'2C'2 be the 1st and 2nd Ehrmann inscribed triangles, and VAVBVC the Ehrmann vertex-triangle. X(18570) is the radical center of the circumcircles of A'1B'1C'1, A'2B'2C'2, and VAVBVC.
X(18570) lies on these lines: {2, 3}, {36, 37729}, {49, 12111}, {51, 32110}, {54, 11440}, {74, 5012}, {99, 14558}, {110, 18435}, {143, 11424}, {154, 11472}, {156, 12162}, {182, 2781}, {184, 5663}, {185, 32046}, {265, 23293}, {399, 3431}, {566, 38872}, {567, 5890}, {568, 15033}, {569, 1204}, {574, 19220}, {578, 6102}, {1092, 11591}, {1147, 5876}, {1154, 13352}, {1181, 45957}, {1352, 12302}, {1495, 16194}, {1511, 4550}, {1539, 13289}, {1614, 15062}, {1899, 10264}, {2001, 38650}, {2079, 43620}, {2549, 34866}, {2935, 4846}, {2979, 37477}, {3043, 22584}, {3060, 3581}, {3098, 9019}, {3357, 10274}, {3410, 12383}, {3818, 35228}, {3917, 10564}, {4045, 6720}, {5010, 37697}, {5092, 19127}, {5158, 39176}, {5449, 13403}, {5621, 11179}, {5651, 16165}, {5664, 22089}, {5889, 37472}, {5907, 12038}, {5944, 6759}, {5946, 11438}, {6000, 18475}, {6101, 13346}, {6288, 12278}, {6293, 40441}, {6689, 43577}, {6699, 10193}, {7280, 37696}, {7691, 37484}, {8157, 38616}, {8546, 16510}, {8567, 37476}, {8588, 10314}, {9659, 15171}, {9672, 18990}, {9682, 18538}, {9704, 43605}, {9729, 43604}, {9730, 21663}, {9826, 37470}, {9927, 34826}, {10113, 12893}, {10192, 46817}, {10263, 46730}, {10313, 18472}, {10386, 10831}, {10539, 32171}, {10540, 11464}, {10574, 11468}, {10605, 37506}, {10620, 11003}, {11202, 46261}, {11265, 11474}, {11266, 11473}, {11267, 11476}, {11268, 11475}, {11412, 37495}, {11416, 18438}, {11425, 12161}, {11430, 13754}, {11439, 26882}, {11442, 32423}, {11449, 15058}, {11455, 26881}, {11459, 22115}, {11587, 38585}, {11597, 12270}, {11645, 35707}, {12042, 39860}, {12133, 20773}, {12241, 44158}, {12284, 15089}, {12294, 19154}, {12358, 25487}, {12359, 12370}, {13339, 20791}, {13391, 37478}, {13434, 37481}, {13496, 33813}, {13858, 36362}, {13859, 36363}, {14216, 32345}, {14566, 39228}, {14767, 32456}, {14793, 15252}, {14855, 22352}, {14915, 34513}, {15055, 40280}, {15061, 26913}, {15068, 40111}, {15177, 28174}, {15534, 32599}, {15577, 39884}, {16881, 37490}, {17702, 21243}, {17811, 32620}, {18308, 39481}, {18356, 44076}, {18400, 34514}, {18436, 34148}, {18474, 30522}, {18912, 43575}, {18913, 43905}, {18952, 26937}, {19163, 34217}, {19357, 32139}, {19467, 32140}, {22505, 39854}, {22515, 39825}, {22804, 23358}, {23039, 43574}, {24206, 38726}, {25738, 45970}, {26883, 32137}, {26917, 43821}, {32142, 43652}, {32196, 46728}, {32333, 36966}, {32358, 43595}, {32392, 34114}, {34292, 45997}, {35257, 45839}, {37489, 39522}, {39477, 44921}, {43601, 43651}, {43619, 44521}
X(18570) = midpoint of X(i) and X(j) for these {i,j}: {3, 378}, {20, 31723}, {427, 44249}, {3534, 31133}, {44218, 44285}
X(18570) = reflection of X(i) in X(j) for these {i,j}: {4, 39504}, {427, 44236}, {7502, 3}, {12083, 7555}, {15760, 140}, {19127, 5092}, {25337, 3530}, {37969, 18571}, {44210, 12100}, {44239, 548}, {44259, 43615}, {44261, 34200}, {44262, 549}, {44263, 5}, {44271, 45179}, {44287, 44218}, {44288, 427}
X(18570) = orthocentroidal circle inverse of X(10254)
X(18570) = anticomplement of X(46029)
X(18570) = X(55)-of-Trinh-triangle if ABC is acute
X(18570) = harmonic center of nine-point circle and Trinh circle
X(18570) = Trinh-isogonal conjugate of X(3098)
X(18570) = center of circle that is the circumperp conjugate of the de Longchamps line
X(18570) = circumperp conjugate of X(7574)
X(18570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 10254}, {2, 35473, 3}, {3, 4, 1658}, {3, 5, 37814}, {3, 20, 7525}, {3, 24, 15331}, {3, 25, 18324}, {3, 381, 186}, {3, 382, 7488}, {3, 1593, 26}, {3, 1597, 14070}, {3, 1656, 22467}, {3, 1657, 7512}, {3, 1995, 18571}, {3, 2070, 10298}, {3, 3516, 12084}, {3, 3520, 11250}, {3, 3534, 6636}, {3, 6644, 15646}, {3, 7485, 12100}, {3, 7503, 140}, {3, 7506, 32534}, {3, 7509, 3530}, {3, 7514, 549}, {3, 7516, 15712}, {3, 7517, 38444}, {3, 7526, 5}, {3, 7527, 12106}, {3, 7529, 15750}, {3, 9818, 6644}, {3, 11413, 548}, {3, 12083, 44837}, {3, 12084, 550}, {3, 14130, 4}, {3, 14865, 17714}, {3, 15078, 37968}, {3, 15688, 44832}, {3, 17928, 43615}, {3, 18859, 376}, {3, 31861, 7575}, {3, 34864, 631}, {3, 35001, 7492}, {3, 35477, 10226}, {3, 35495, 37948}, {3, 35496, 35497}, {3, 35501, 9909}, {3, 35502, 12107}, {3, 38335, 13620}, {3, 44218, 44274}, {3, 45735, 21844}, {4, 1658, 37440}, {4, 6639, 13406}, {4, 10201, 11563}, {4, 10298, 2070}, {5, 549, 44452}, {5, 15646, 6644}, {22, 7484, 6676}, {22, 31236, 13595}, {23, 13596, 3830}, {25, 18324, 7575}, {25, 31861, 3845}, {26, 1593, 3627}, {26, 18534, 37947}, {54, 11440, 34783}, {140, 10226, 3}, {140, 13406, 6639}, {140, 16976, 549}, {140, 44920, 44911}, {140, 46031, 34330}, {186, 381, 12106}, {186, 7527, 381}, {378, 37970, 4}, {378, 44269, 427}, {378, 44281, 44274}, {381, 31236, 13413}, {382, 7488, 17714}, {427, 44218, 44236}, {427, 44236, 44287}, {427, 44269, 44274}, {427, 44281, 44269}, {427, 44285, 44249}, {468, 46030, 44270}, {546, 15331, 24}, {549, 34152, 3}, {569, 1204, 13630}, {578, 7689, 6102}, {1511, 15060, 9306}, {1594, 18563, 18377}, {1594, 34005, 18563}, {1597, 7530, 15687}, {1597, 14070, 7530}, {1614, 15062, 18439}, {1885, 7542, 15761}, {1885, 15761, 44271}, {2070, 10298, 1658}, {2071, 14118, 35921}, {2071, 35921, 3}, {3091, 21844, 45735}, {3520, 14118, 3}, {3520, 35921, 2071}, {3526, 35496, 3}, {3543, 7556, 5899}, {3627, 37947, 18534}, {3628, 43615, 17928}, {3832, 44879, 13621}, {3845, 7575, 25}, {3853, 12107, 7517}, {4550, 9306, 15060}, {5054, 35495, 3}, {5133, 10295, 38321}, {5876, 43394, 1147}, {6636, 7464, 3534}, {6644, 7526, 9818}, {6644, 9818, 5}, {6644, 15646, 37814}, {6676, 13413, 44282}, {7488, 14865, 382}, {7503, 35477, 3}, {7512, 12086, 1657}, {7512, 35478, 12086}, {7514, 11410, 34152}, {7517, 35502, 3853}, {7517, 38444, 12107}, {7530, 14070, 37936}, {7555, 44837, 7502}, {10024, 18560, 44279}, {10125, 44235, 7505}, {11425, 12163, 12161}, {11449, 15058, 18350}, {11464, 15305, 10540}, {11818, 18533, 38322}, {12083, 44837, 7555}, {12162, 13367, 156}, {13630, 32210, 1204}, {14130, 18364, 3}, {14130, 37970, 39504}, {14782, 14783, 14940}, {14784, 14785, 34007}, {15068, 47391, 40111}, {15332, 45971, 35471}, {15682, 37913, 37924}, {15687, 37936, 7530}, {18281, 18531, 37938}, {18324, 31861, 25}, {18404, 37119, 10224}, {19467, 32140, 45731}, {22467, 35500, 1656}, {31236, 35480, 381}, {32046, 32138, 185}, {32171, 45959, 10539}, {34477, 46030, 468}, {34864, 35498, 3}, {35231, 35232, 47335}, {35502, 38444, 7517}, {37347, 44246, 38323}, {42789, 42790, 7577}, {42807, 42808, 10018}, {44218, 44249, 427}, {44236, 44249, 44288}, {44281, 44285, 3}, {44287, 44288, 427}, {44911, 44920, 5}
Let A'1B'1C'1, A'2B'2C'2 be the 1st and 2nd Ehrmann inscribed triangles, and MAMBMC the Ehrmann mid-triangle. X(18571) is the radical center of the circumcircles of A'1B'1C'1, A'2B'2C'2, and MAMBMC.
X(18571) lies on these lines: {2,3}, {182,15826}, {187,16308}, {323,15040}, {1511,3292} et al
X(18571) = complement of X(18572)
X(18571) = inverse-in-circumcircle of X(3830)
X(18571) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3,1995,18570), (1113,1114,3830)
X(18572) lies on these lines: {2,3}, {265,11564}, {323,12902}, {511,10113}, {542,15826}, {1154,13851}, {5876,18383}, {13421,18555}, {15068,18405}, {18394,18436} et al
X(18572) = midpoint of X(4) and X(7574)
X(18572) = reflection of X(7575) in X(5)
X(18571) = isogonal conjugate of anticomplement of X(39083)
X(18572) = anticomplement of X(18571)
X(18572) = inverse-in-Johnson-circle of X(2)
X(18572) = inverse-in-polar-circle of X(18559)
X(18572) = {X(10750),X(10751)}-harmonic conjugate of X(2)
X(18572) = X(1155)-of-Ehrmann-vertex-triangle if ABC is acute
X(18572) = X(23)-of-Ehrmann-mid-triangle
X(18572) = X(7575)-of-Johnson-triangle
X(18572) = X(7574)-of-Euler-triangle
X(18571) = crossdifference of every pair of points on line X(647)X(18573)
X(18571) = orthoptic-circle-of-Steiner-inellipe-inverse of X(31857)
X(18571) = {X(3),X(23)}-harmonic conjugate of X(37950)
Let SASBSC be the Ehrmann side-triangle and MAMBMC the Ehrmann mid-triangle. X(18573) is the radical center of the circumcircles of ASAMA, BSBMB, and CSCMC.
X(18573) lies on these lines: {2,16308}, {3,6}, {4,16328}, {140,16303}, {393,14940}, {1989,7746}, {3018,7749}, {6128,7756}, {7495,16306}
Let VAVBVC, SASBSC, MAMBMC be the Ehrmann vertex-triangle, Ehrmann side-triangle, and Ehrmann mid-triangle, resp. X(18574) is the radical center of the circumcircles of VASAMA, VBSBMB, and VCSCMC.
X(18574) lies on these lines: {4,18575}, {5,11456}
X(18575) lies on hyperbola {{A,B,C,X(4),X(381)}} and these lines: {2,11594}, {4,18574}, {67,5475}, {232,566}, {250,458}, {262,338}, {325,5169}, {378,8719}, {381,511} et al
X(18575) = isogonal conjugate of X(11003)
X(18575) = isotomic conjugate of X(7771)
X(18575) = trilinear pole of line X(3569)X(3906)
X(18575) = perspector of orthocentroidal circle
X(18575) = pole of Lemoine axis wrt orthocentroidal circle
Let A1B1C1 and A2B2C2 be the 1st and 2nd Ehrmann circumscribing triangles, resp., and VAVBVC be the Ehrmann vertex-triangle. X(18576) is the radical center of the circumcircles of A1A2VA, B1B2VB, and C1C2VC.
X(18576) lies on these lines: {4,94}, {476,18323}, {1989,3845}, {3839,18316}, {5961,7526}
Let A1B1C1 and A2B2C2 be the 1st and 2nd Ehrmann circumscribing triangles, resp., and XAXBXC be the Ehrmann cross-triangle. X(18577) is the radical center of the circumcircles of A1A2XA, B1B2XB, and C1C2XC.
X(18577) lies on these lines: {4,477}, {113,10540}, {1553,3153}
X(18578) lies on these lines: {3,6}, {94,3580}, {1986,11062} et al
X(18578) = crossdifference of the isogonal conjugates of PU(5)
X(18579) lies on these lines: {2,3}, {523,9126}, {524,1511}, {3292,11693}, {3564,5648}, {5892,11649} et al
X(18579) = QA-P2 (Euler-Poncelet Point) of quadrangle PU(4)PU(5)
X(18579) = anticenter of cyclic quadrilateral PU(4)PU(5)
X(18580) lies on these lines: {2,3}, {67,11179}, {182,6699}, {184,15132}, {1352,1511} et al
X(18580) = midpoint of X(3) and X(5094)
X(18580) = center of conic {{X(3),X(5094),PU(4),PU(5)}}
X(18581) is the PU(5)PU(45) trapezoid point - the point in which the extended legs P(5)U(45) and U(5)P(45) of the trapezoid PU(5)PU(45) meet.
X(18581) lies on these lines: {2,14}, {3,5321}, {4,16}, {5,6}, {13,3545}, {17,5056}, {20,10646}, {30,11481}, {61,3090}, {62,3091}, {69,624}, {115,5617}, {140,5339}, {141,11306}, {381,395}, {393,6116}, {396,5055}, {397,3851}, {398,1656}, {498,10638}, {499,7051}, {631,10645}, {1250,1479}, {3850,5340}, {3589,11305}, {5471,5613}, {6783,9113} et al
X(18581) = {X(5),X(6)}-harmonic conjugate of X(18582)
X(18581) = {X(18583),X(18584)}-harmonic conjugate of X(18582)
X(18582) is the diagonal crosspoint of trapezoid PU(5)PU(45) - the point in which the diagonals P(5)P(45) and U(5)U(45) of the trapezoid PU(5)PU(45) intersect.
X(18582) lies on these lines: {2,13}, {3,5318}, {4,15}, {5,6}, {14,3545}, {18,5056}, {20,10645}, {30,11480}, {61,3091}, {62,3090}, {69,623}, {115,5613}, {140,5340}, {141,11305}, {381,396}, {393,6117}, {395,5055}, {397,1656}, {398,3851}, {498,1250}, {631,10646}, {1478,7051}, {1479,10638}, {3850,5339}, {3589,11306}, {5472,5617}, {6782,9112} et al
X(18582) = {X(5),X(6)}-harmonic conjugate of X(18581)
X(18582) = {X(18583),X(18584)}-harmonic conjugate of X(18581)
X(18583) lies on these lines: {2,1351}, {3,3618}, {4,5050}, {5,6}, {20,12017}, {30,182}, {69,1656}, {114,9300}, {140,143}, {141,576}, {524,547}, {546,575}, {548,5092}, {549,1350}, {550,5085}, {3091,7920} et al
X(18583) = midpoint of X(i) and X(j) for these {i,j}: {5,6}, {141,576}, {182,5480}
X(18583) = reflection of X(i) in X(j) for these (i,j): (140,3589), (141,3628), (548,5092)
X(18583) = complement of complement of X(1351)
X(18583) = centroid of PU(5)PU(45)
X(18583) = {X(14136),X(14137)}-harmonic conjugate of X(9300)
X(18583) = {X(18581),X(18582)}-harmonic conjugate of X(18584)
X(18584) lies on these lines: {2, 5210}, {4, 3055}, {5, 6}, {32, 5079}, {39, 5072}, {140, 5585}, {182, 14162}, {187, 1656}, {230, 5071}, {381, 574}, {382, 8589}, {546, 15815}, {547, 7737}, {599, 8176}, {625, 3763}, {1383, 7570}, {1384, 5055}, {1506, 3851}, {2079, 5020}, {2549, 5066}, {3053, 3054}, {3091, 5013}, {3526, 8588}, {3545, 3815}, {3628, 5023}, {5008, 15484}, {5056, 7745}, {5068, 5254}, {5070, 7747}, {5076, 15515}, {5206, 11614}, {6671, 11306}, {6672, 11305}, {6781, 15694}, {7530, 15109}, {7617, 15534}, {7739, 14892}, {7773, 7929}, {7784, 16921}, {7844, 10485}, {8375, 10576}, {8376, 10577}, {11184, 11185}, {11737, 15048}, {15491, 16041}
X(18584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (382, 8589, 11742), (1506, 18424, 5024), (3851, 5024, 18424), (18581, 18582, 18583)
The Euler line intersects the circle O(PU(5)) (the circle with segment PU(5) as diameter) in two points, X(15765) and X(18585). Of the two, X(18585) is the farthest from X(3).
Let A'B'C' be the triangle obtained by rotaing ABC about the 1st Ehrmann pivot, P(5), by π/2. Let A"B"C" be the triangle obtained by rotaing ABC about the 2nd Ehrmann pivot, U(5), by -π/2. Then A', B', C', A", B", C" lie on a common ellipse, with center X(18585). Also, the lines A'A", B'B", C'C" concur in X(18585) and X(18585) is the similitude center of A'B'C' and A"B"C".
X(18585) lies on these lines: {2,3}, {13,3071}, {14,3070}, {15,590}, {16,615}, {371,396}, {372,395}, {485,10654}, {486,10653}, {618,641}, {619,642}, {629,13701}, {630,13821}, {639,3643}, {640,3642}, {3068,11485}, {3069,11486}, {5318,6565}, {5321,6564}, {5334,13665}, {5335,13785}, {5478,6251}, {5479,6250}, {6221,11488}, {6303,6774}, {6306,6771}, {6398,11489}, {8252,11481}, {8253,11480}
X(18585) = reflection of X(15765) in X(5)
X(18585) = X(15765)-of-Johnson-triangle
X(18585) = X(18586)-of-Ehrmann-mid-triangle
X(18585) = {X(i)X(j)}-harmonic conjugate of X(15765) for these {i,j}: {2,3}, {4,381}, {20,5055}, {140,549}, {376,1656}, {382,3545}, {546,3845}, {547,550}, {548,15699}, {631,5054}, {632,12100} et al
X(18585) = {X(2043),X(2044)}-harmonic conjugate of X(18586)
X(18586) is the intersection nearest to X(2) of the Euler line and the circle centered at X(4) and passing through PU(5).
X(18586) lies on these lines: {2,3}, {13,372}, {14,371}, {15,6565}, {16,6564}, {395,485}, {396,486}, {590,18581}, {615,18582}, {3068,11543}, {3069,11542} et al
X(18586) = reflection of X(i) in X(j) for these (i,j): (3,15765), (2044,5), (18587,4)
X(18586) = X(1) of X(2)PU(5)
X(18586) = X(2044)-of-Johnson-triangle
X(18586) = X(15765)-of-X3-ABC-reflections-triangle
X(18586) = Ehrmann-mid-to-ABC similarity image of X(18585)
X(18586) = {X(i),X(j)}-harmonic conjugate of X(18587) for these {i,j}: {2,5}, {3,381}, {20,3845}, {140,3545}, {376,546}, {382,3830}, {547,3090}, {549,3091}, {550,3839}, {2043,18585}, {2044,15765}
X(18586) = {X(2043),X(2044)}-harmonic conjugate of X(18585)
X(18587) is the intersection farthest from X(2) of the Euler line and the circle centered at X(4) and passing through PU(5).
X(18587) lies on these lines: {2,3}, {13,371}, {14,372}, {15,6564}, {16,6565}, {395,486}, {396,485}, {590,18582}, {615,18581}, {3068,11542}, {3069,11543}, {5318,6561}, {5321,6560} et al
X(18587) = reflection of X(i) in X(j) for these (i,j): (3,18585), (2043,5), (18586,4)
X(18587) = X(2043)-of-Johnson-triangle
X(18587) = X(18585)-of-X3-ABC-reflections-triangle
X(18587) = Ehrmann-mid-to-ABC similarity image of X(15765)
X(18587) = {X(i),X(j)}-harmonic conjugate of X(18586) for these {i,j}: {2,5}, {3,381}, {20,3845}, {140,3545}, {376,546}, {382,3830}, {547,3090}, {549,3091}, {550,3839}, {2043,18585}, {2044,15765}
X(18587) = X(2043),X(2044)}-harmonic conjugate of X(15765)
Collineations inverse-images: X(18588)-X(18752)
This preamble and centers X(18588)-X(18752) were contributed by César Eliud Lozada, May 4, 2018.
Suppose that m is a collination. If P = m(Q), then P is the m collineation-image of Q, as in the preambles just before X(16286) and X(16504), and Q is here named the m inverse colllineation-image of P. Explicitly, if
P = (A',B',C',U; A'',B'',C''V) collineation image of Q, then Q = (A'',B'',C'',V; A',B',c",U) collination inverse-image of P.
Let Q be the (T1, X1; T2, X2)-collineation image of P, where T1 and T2 are two central triangles, and X1 and X2 two centers. The following table shows the general expressions of the first trilinear coordinate of the image Q when P = u : v : w (trilinears) is given, and the first trilinear coordinate of the inverse-image P, when Q = u : v : w (trilinears) is given.
| Collineation | image of u:v:w | inverse-image of u:v:w |
|---|---|---|
| (ABC, X(2); excentral, X(1)) | -u*a+v*b+w*c | b*c*(v+w) |
| (excentral, X(1); ABC, X(2)) | b*c*(v+w) | -u*a+v*b+w*c |
| (ABC, X(2); tangential, X(1)) | (u*(b+c)*a^2-v*(a+c)*b^2-w*(a+b)*c^2)*a | b*c*(w*b+v*c)*(a+c)*(a+b) |
| (tangential, X(1); ABC, X(2)) | b*c*(w*b+v*c)*(a+c)*(a+b) | a*(u*(b+c)*a^2-v*(a+c)*b^2-w*(a+b)*c^2) |
| (ABC, X(2); medial, X(1)) | b*c*((a-b+c)*b*v+c*(a+b-c)*w) | b*c*(u*a-v*b-w*c)*(a+b-c)*(a-b+c) |
| (medial, X(1); ABC, X(2)) | b*c*(u*a-v*b-w*c)*(a+b-c)*(a-b+c) | b*c*((a-b+c)*b*v+c*(a+b-c)*w) |
| (ABC, X(2); anticomplementary, X(1)) | b*c*(-(b+c)*a*u+b*(a+c)*v+(a+b)*c*w) | b*c*(v*b+w*c)*(a+c)*(a+b) |
| (anticomplementary, X(1); ABC, X(2)) | b*c*(v*b+w*c)*(a+c)*(a+b) | b*c*(-(b+c)*a*u+b*(a+c)*v+(a+b)*c*w) |
| (ABC, X(2); incentral, X(1)) | v*b+w*c | b*c*(u-v-w) |
| (incentral, X(1); ABC, X(2)) | b*c*(u-v-w) | v*b+w*c |
| (ABC, X(2); cevian-of-X(75), X(1)) | b^2*c^2*(b*(a^2-b^2+c^2)*v+c*(a^2+b^2-c^2)*w) | b*c*(u*a^2-v*b^2-w*c^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) |
| (cevian-of-X(75), X(1); ABC, X(2)) | b*c*(u*a^2-v*b^2-w*c^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) | b^2*c^2*(b*(a^2-b^2+c^2)*v+c*(a^2+b^2-c^2)*w) |
| (ABC, X(2); anticevian-of-X(75), X(1)) | b^2*c^2*(-(b^2+c^2)*u*a+(a^2+c^2)*v*b+(a^2+b^2)*w*c) | b*c*(v*b^2+w*c^2)*(a^2+c^2)*(a^2+b^2) |
| (anticevian-of-X(75), X(1); ABC, X(2)) | b*c*(v*b^2+w*c^2)*(a^2+c^2)*(a^2+b^2) | b^2*c^2*(-(b^2+c^2)*u*a+(a^2+c^2)*v*b+(a^2+b^2)*w*c) |
| (ABC, X(1); anticevian-of-X(75), X(2)) | b^2*c^2*((-b-c)*u+(a+c)*v+(a+b)*w) | (v*b^2+w*c^2)*(a+c)*(a+b) |
| (anticevian-of-X(75), X(2); ABC, X(1)) | (v*b^2+w*c^2)*(a+c)*(a+b) | b^2*c^2*((-b-c)*u+(a+c)*v+(a+b)*w) |
X(18588) lies on these lines: {2,1748}, {3,1770}, {5,1859}, {37,226}, {222,18651}, {343,18638}, {498,8251}, {1040,1699}, {1062,1479}, {2193,17167}, {5219,10319}, {5249,17073}, {12609,18641}, {18604,18647}
X(18588) = complement of X(1748)
X(18588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 18664, 1748), (226, 18589, 1214), (226, 18590, 16580)
X(18589) lies on these lines: {1,5800}, {2,19}, {3,142}, {10,4523}, {21,17171}, {37,226}, {40,18634}, {48,18650}, {63,18651}, {65,18635}, {71,307}, {141,960}, {219,9028}, {306,3610}, {344,908}, {347,5236}, {379,1839}, {464,5249}, {497,614}, {517,16608}, {828,16591}, {857,1441}, {1038,2263}, {1062,3946}, {1279,12053}, {1368,2886}, {1385,17043}, {1444,18648}, {1890,4223}, {2193,17197}, {2385,6389}, {2822,10741}, {2876,11574}, {2883,9943}, {3452,17279}, {3579,18644}, {3812,5799}, {4026,18641}, {4075,4078}, {4851,12635}, {4859,9614}, {5316,17357}, {6684,8251}, {6706,6823}, {7289,17170}, {7536,17384}, {8062,8768}, {10691,17382}, {16593,16596}, {18671,18733}
X(18589) = isotomic conjugate of isogonal conjugate of X(23620)
X(18589) = complement of X(19)
X(18589) = complementary conjugate of X(226)
X(18589) = polar conjugate of isogonal conjugate of X(22057)
X(18589) = barycentric product X(10)*X(17170)
X(18589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 4329, 19), (37, 16580, 226), (37, 16581, 16580), (71, 4466, 307), (857, 1441, 1826), (1214, 18588, 226), (16577, 18590, 226)
X(18590) lies on these lines: {2,18665}, {37,226}, {16607,16609}, {18605,18649}
X(18590) = complement of isogonal conjugate of X(2158)
X(18590) = complement of complement of X(18665)
X(18590) = complementary conjugate of complement of X(2158)
X(18590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (226, 18589, 16577), (16580, 18588, 226)
X(18591) lies on these lines: {2,286}, {3,6}, {9,1745}, {19,851}, {37,226}, {45,15831}, {53,6907}, {71,73}, {198,5452}, {199,2299}, {212,8606}, {232,4220}, {233,6882}, {241,18635}, {393,6908}, {408,2183}, {442,1838}, {464,5712}, {478,1035}, {1108,1834}, {1172,3651}, {1212,1213}, {1474,3145}, {1826,3142}, {2260,14547}, {2276,10319}, {2335,3487}, {2345,6350}, {3087,6987}, {4303,14597}, {5179,14873}, {5929,18161}, {6184,15526}, {7515,17398}, {8963,16440}, {18210,18674}, {18606,18650}
X(18591) = complement of X(286)
X(18591) = complementary conjugate of complement of X(228)
X(18591) = crosspoint of X(2) and X(72)
X(18591) = crosssum of X(6) and X(28)
X(18591) = perspector of circumconic centered at X(942)
X(18591) = center of circumconic that is locus of trilinear poles of lines passing through X(942)
X(18591) = X(2)-Ceva conjugate of X(942)
X(18591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 18666, 286), (71, 73, 3990), (440, 1214, 18592), (579, 581, 6)
X(18592) lies on these lines: {2,216}, {3,4653}, {33,851}, {37,226}, {81,3284}, {223,3330}, {225,3142}, {408,2654}, {441,6703}, {442,1785}, {464,4648}, {577,940}, {856,5437}, {857,17080}, {1210,1834}, {1211,15526}, {1465,1865}, {1856,3136}, {2092,18642}, {3666,18635}, {3772,17053}, {4383,5158}, {11064,16697}, {16588,16589}, {18608,18652}
X(18592) = complement of X(31623)
X(18592) = complementary conjugate of complement of X(1409)
X(18592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (440, 1214, 18591), (440, 18643, 17056)
X(18593) lies on these lines: {1,3651}, {2,7110}, {36,186}, {37,226}, {56,2915}, {57,77}, {65,4868}, {73,15556}, {109,1758}, {223,1708}, {227,4848}, {241,514}, {278,18679}, {323,1443}, {500,10122}, {516,8758}, {553,3664}, {580,3468}, {758,1464}, {851,18210}, {908,16578}, {942,5453}, {1418,4031}, {1421,7677}, {1458,5083}, {1735,12016}, {1736,2635}, {1787,5053}, {1795,3466}, {1873,7741}, {2078,4318}, {2594,12432}, {3649,3743}, {3998,4035}, {4292,13408}, {4892,16598}, {5249,16579}, {5427,7286}, {5745,18607}, {7799,17078}, {8143,11544}, {14165,17923}
X(18593) = midpoint of X(851) and X(18210)
X(18593) = isogonal conjugate of X(2341)
X(18593) = complement of X(14206)
X(18593) = complementary conjugate of complement of X(2159)
X(18593) = X(19)-isoconjugate of X(1793)
X(18593) = trilinear pole of the line {526, 3028}
X(18593) = isotomic conjugate of polar conjugate of X(1835)
X(18593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 18668, 14206), (36, 4351, 11700), (226, 1214, 16577), (241, 1465, 3911), (1214, 1427, 226), (4850, 17092, 57), (17080, 17092, 4850)
X(18594) lies on these lines: {1,19}, {6,3339}, {9,165}, {35,198}, {36,1436}, {46,1743}, {57,2264}, {200,5279}, {219,7991}, {269,7291}, {281,5691}, {579,2272}, {662,18713}, {1108,13462}, {1580,8769}, {1604,8069}, {1707,2312}, {1723,15803}, {1741,1768}, {1755,16570}, {1944,10442}, {1959,8771}, {2093,3197}, {2183,3973}, {2256,9819}, {2257,3361}, {2262,5902}, {2287,12526}, {2324,16548}, {3207,3247}, {3496,15479}, {3553,5341}, {3554,7297}, {4312,5746}, {4882,5227}, {5223,5781}, {5750,5819}, {5776,7992}, {6197,9121}, {7271,7289}, {8809,11347}, {9119,15071}, {14543,18655}
X(18594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19, 610, 1), (19, 2173, 610), (2182, 2270, 1743)
X(18595) lies on these lines: {1,19}, {63,17865}, {662,18716}, {1748,17858}, {1760,18695}, {1763,5219}, {1820,2158}, {14543,18658}
X(18595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19, 18596, 610), (19, 18597, 16545)
X(18596) lies on the cubic K605 and these lines: {1,19}, {2,169}, {6,18732}, {20,346}, {37,13730}, {63,1930}, {77,18727}, {194,5088}, {255,2312}, {304,1760}, {662,18717}, {920,1755}, {921,1910}, {1448,2285}, {1490,16550}, {1759,1764}, {2082,5299}, {2128,14210}, {4020,16567}, {5089,9798}, {7297,16781}, {14543,18659}, {14953,17147}, {16551,16552}, {16568,18156}
X(18596) = anticomplement of X(36907)
X(18596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 610, 2172), (1, 16545, 19), (1, 16546, 16545), (48, 17442, 1), (48, 18597, 19), (610, 18595, 19), (1755, 2083, 920), (1973, 18671, 1), (2172, 18669, 1), (2173, 18671, 1973)
X(18597) lies on these lines: {1,19}, {662,18718}, {1755,1820}, {2083,2180}
X(18597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19, 18596, 48), (16545, 18595, 19)
X(18598) lies on these lines: {1,19}, {9,440}, {40,1503}, {71,191}, {223,2285}, {306,2897}, {573,2949}, {662,18720}, {1045,1719}, {1490,1766}, {2264,16470}, {2831,6326}, {2941,2951}, {3198,5285}, {4329,14543}, {7291,18650}, {11683,18697}
X(18598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1474, 18674, 1), (2173, 18674, 1474), (2939, 18599, 610)
X(18599) lies on these lines: {1,19}, {6,3468}, {9,1745}, {37,3465}, {191,2956}, {219,1761}, {223,1708}, {347,14543}, {662,18721}, {846,1709}, {978,1047}, {1046,1744}, {1108,15854}, {1214,1762}, {1490,3731}, {1940,5930}, {3682,5279}, {8915,9121}
X(18599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (610, 18598, 2939), (1172, 18675, 1), (2173, 18675, 1172)
X(18600) lies on these lines: {1,17136}, {2,39}, {7,10571}, {8,16887}, {41,18723}, {81,279}, {85,4850}, {86,3445}, {99,9109}, {192,18157}, {304,17147}, {314,4452}, {347,1014}, {348,16697}, {1201,3663}, {1444,17521}, {1509,4610}, {1975,11319}, {2170,18176}, {2275,16742}, {3210,16703}, {3241,17179}, {3598,4225}, {3616,17175}, {3666,16708}, {3736,4310}, {3933,4202}, {3945,4190}, {3946,17474}, {4000,16696}, {4059,4719}, {4267,7195}, {4346,17139}, {4653,17201}, {4868,7278}, {5088,5262}, {5222,18206}, {7176,17016}, {7225,18724}, {7774,16910}, {7891,17003}, {7906,16906}, {9780,17210}, {10453,17208}, {16347,16992}, {16704,17206}, {16709,17321}, {16710,17302}, {16726,17301}, {16737,18081}, {16739,17490}, {16919,17379}, {16931,17000}, {17141,17154}
X(18600) = complement of X(27040)
X(18600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 17205, 17169), (274, 16705, 2), (274, 16712, 16705), (274, 16750, 16749), (4000, 16696, 16713), (16705, 16711, 274), (16711, 16712, 2)
X(18601) lies on these lines: {2,3770}, {57,77}, {239,18171}, {244,18169}, {274,561}, {321,16720}, {348,16697}, {982,17187}, {1086,17173}, {2275,16717}, {2999,18186}, {3210,17178}, {3286,7191}, {3666,4760}, {3736,3873}, {3752,16704}, {3782,17174}, {4359,16738}, {4393,18172}, {5249,17205}, {5333,16831}, {16714,16743}, {16725,16727}, {16735,16752}, {17011,18166}, {17012,18198}, {17863,18608}
X(18601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 16700, 16753), (3666, 16726, 8025), (5256, 18164, 81), (16696, 16700, 2)
X(18602) lies on these lines: {2,16698}, {86,16697}, {333,3752}, {8025,18609}, {16577,18645}, {16579,18646}, {16714,16743}
X(18602) = {X(2), X(16698)}-harmonic conjugate of X(16701)
X(18603) lies on these lines: {1,8021}, {2,16699}, {27,1427}, {58,17102}, {81,593}, {241,1817}, {284,1214}, {440,3002}, {774,820}, {800,6509}, {859,1763}, {1040,3286}, {2194,8758}, {4000,16700}, {4215,17441}, {16745,16746}, {18175,18180}
X(18603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (81, 16697, 16696), (81, 18609, 16697)
X(18604) lies on these lines: {2,18746}, {58,8071}, {81,593}, {222,1790}, {255,820}, {283,1433}, {394,577}, {967,5019}, {1412,4282}, {1455,16049}, {1800,7078}, {1812,4558}, {1817,4565}, {3286,10832}, {18588,18647}
X(18604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (81, 1444, 16697), (81, 18605, 1333)
X(18605) lies on these lines: {2,18748}, {58,14793}, {81,593}, {571,1993}, {1396,4565}, {1790,4282}, {18590,18649}
X(18605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (81, 1444, 16698), (1333, 18604, 81)
X(18606) lies on these lines: {2,18749}, {37,5736}, {48,1214}, {63,3990}, {75,3164}, {77,14597}, {81,593}, {216,307}, {255,3916}, {348,2275}, {1804,5228}, {2197,9028}, {3739,16699}, {3827,16872}, {7193,18734}, {18210,18733}, {18591,18650}
X(18606) = {X(16697), X(18607)}-harmonic conjugate of X(18608)
X(18607) lies on these lines: {2,85}, {3,6511}, {27,5088}, {37,5905}, {57,1804}, {63,77}, {69,3998}, {75,6360}, {81,593}, {169,16438}, {283,1789}, {306,3933}, {307,343}, {440,1565}, {464,17170}, {469,17181}, {500,14054}, {517,7416}, {527,16577}, {536,17479}, {553,16579}, {942,8021}, {960,1464}, {967,980}, {991,16465}, {1445,10601}, {1455,2975}, {1763,11350}, {1817,7291}, {2000,7580}, {2895,3965}, {3151,4872}, {3219,6610}, {3739,18668}, {3782,8609}, {3827,16678}, {3945,9965}, {4359,16713}, {4640,8758}, {4652,17102}, {5249,16585}, {5744,17080}, {5745,18593}, {6708,14206}, {9776,17092}, {10319,18733}, {11064,18652}, {12649,15852}
X(18607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (63, 77, 394), (63, 6505, 219), (440, 1565, 18651), (18606, 18608, 16697)
X(18608) lies on these lines: {2,18751}, {81,593}, {348,4352}, {603,17102}, {940,1804}, {1107,16721}, {1214,7125}, {16700,16749}, {17863,18601}, {18592,18652}
X(18608) = {X(16697), X(18607)}-harmonic conjugate of X(18606)
X(18609) lies on these lines: {2,16718}, {58,1789}, {81,593}, {110,8758}, {693,905}, {1736,2617}, {3003,3580}, {8025,18602}, {16701,16704}, {16734,16741}
X(18609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (81, 16697, 16698), (16697, 18603, 81)
X(18610) lies on these lines: {1,159}, {3,3739}, {21,5263}, {22,1602}, {25,1841}, {75,16876}, {157,14017}, {885,4057}, {1576,2189}, {1633,17220}, {16685,16686}
X(18610) = X(1841) of Ara triangle
X(18610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18611, 18612), (1, 18615, 18611), (1, 18616, 18619), (16682, 16684, 16678), (18611, 18615, 18622), (18611, 18618, 18619), (18612, 18620, 18619), (18612, 18622, 18611), (18616, 18618, 18620)
X(18611) lies on these lines: {1,159}, {154,2352}, {206,2175}, {595,3941}, {1503,15976}, {1619,16678}, {1630,2328}, {1633,17134}, {3692,4557}, {5250,8053}, {8618,15270}, {16679,18613}
X(18611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18615, 18610), (3556, 18621, 159), (18610, 18612, 1), (18610, 18619, 18618), (18610, 18622, 18615), (18612, 18622, 18610)
X(18612) lies on these lines: {1,159}, {1633,17221}, {3877,8053}
X(18612) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18611, 18610), (16680, 18614, 8053), (18610, 18611, 18622), (18610, 18619, 18620)
X(18613) lies on these lines: {1,859}, {2,15621}, {3,551}, {22,3007}, {55,750}, {56,1149}, {86,1621}, {228,3748}, {404,15625}, {519,4245}, {528,16056}, {851,3058}, {855,5434}, {946,15622}, {1001,16058}, {1279,1402}, {1376,3840}, {1486,1617}, {1497,14529}, {1699,15626}, {2318,9049}, {3286,8616}, {3303,13738}, {3746,16453}, {3750,5132}, {3870,4557}, {3941,16878}, {4362,15571}, {4421,16059}, {5563,7428}, {7373,15654}, {8227,15623}, {8715,16414}, {10389,15624}, {13724,15888}, {16679,18611}
X(18613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1486, 1617, 1626), (1621, 16678, 8053)
X(18614) lies on these lines: {1,18177}, {3877,8053}, {16679,16691}
X(18614) = {X(8053), X(18612)}-harmonic conjugate of X(16680)
X(18615) lies on these lines: {1,159}, {31,1474}, {154,14597}, {326,16876}, {610,3185}, {1633,18655}, {1661,2352}, {16690,16778}
X(18615) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18610, 18611, 1), (18610, 18622, 18611)
X(18616) lies on these lines: {1,159}, {25,16583}, {304,16876}, {1633,18656}, {3696,8193}
X(18616) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18617, 18619), (18610, 18619, 1), (18610, 18620, 18618)
X(18617) lies on these lines: {1,159}, {23,17497}, {1019,16874}, {1633,18657}, {14210,16876}
X(18617) = {X(18616), X(18619)}-harmonic conjugate of X(1)
X(18618) lies on these lines: {1,159}, {1633,18658}
X(18618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18610, 18619, 18611), (18610, 18620, 18616)
X(18619) lies on these lines: {1,159}, {1043,1610}, {1633,18659}, {2393,4749}, {16876,18156}
X(18619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18616, 18610), (1, 18617, 18616), (18611, 18618, 18610), (18612, 18620, 18610)
X(18620) lies on the line {1,159}
X(18620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18610, 18619, 18612), (18616, 18618, 18610)
X(18621) lies on these lines: {1,159}, {3,12335}, {6,2212}, {25,2262}, {48,55}, {64,8273}, {197,7070}, {198,9502}, {206,219}, {221,1458}, {347,1633}, {478,8750}, {1001,1503}, {1108,7083}, {1319,10934}, {1376,10192}, {1495,11383}, {1498,8053}, {1617,3433}, {1621,11206}, {1631,3428}, {1661,3185}, {1853,4423}, {2328,7169}, {3126,15313}, {5584,7973}, {6759,10267}, {10282,11248}, {10310,17821}, {11500,16252}, {12328,13383}
X(18621) = X(2262) of Ara triangle
X(18621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (154, 2192, 10537), (159, 18611, 3556)
X(18622) lies on these lines: {1,159}, {669,2106}, {1633,18661}
X(18622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18610, 18611, 18612), (18611, 18615, 18610)
X(18623) lies on these lines: {1,9799}, {2,77}, {6,7365}, {7,27}, {8,1943}, {20,1394}, {34,938}, {56,5324}, {57,279}, {63,347}, {73,5703}, {109,9778}, {221,962}, {226,1419}, {307,14552}, {329,394}, {333,348}, {345,664}, {387,1448}, {388,3745}, {411,1035}, {497,1456}, {934,7011}, {940,948}, {1079,10321}, {1118,7335}, {1214,3160}, {1407,4000}, {1433,6223}, {1435,7289}, {1439,7490}, {1455,5731}, {1465,5435}, {1804,1817}, {1870,5768}, {1895,6616}, {2264,7197}, {3100,10430}, {3157,5758}, {3616,10571}, {3772,6610}, {4573,7055}, {4644,6354}, {5287,8232}, {5423,14594}, {5658,15252}, {5744,17080}, {5811,8757}, {5815,9370}, {6358,7229}, {6611,15509}, {7053,11347}, {9776,17074}, {17081,17082}
X(18623) = isogonal conjugate of X(30457)
X(18623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7, 18624, 278), (222, 278, 7), (222, 6357, 278), (223, 1422, 77), (278, 6357, 18624), (278, 18629, 18628), (1394, 5930, 20), (3160, 5273, 1214), (16662, 16663, 14256), (18631, 18633, 18632)
X(18624) lies on these lines: {2,3160}, {7,27}, {189,17923}, {223,1442}, {347,5273}, {934,11347}, {1068,6223}, {1118,7338}, {1422,1443}, {1435,7291}, {1456,9812}, {4313,5930}, {5222,7365}, {5748,6505}, {7055,17088}, {7490,14256}
X(18624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (278, 6357, 18623), (278, 18623, 7)
X(18625) lies on these lines: {2,7110}, {7,27}, {85,17087}, {226,1029}, {323,5905}, {651,6354}, {857,948}, {1068,13408}, {1443,5249}, {1478,3153}, {3193,14450}, {3487,5453}, {3616,17584}, {3772,7200}, {4854,16133}, {5435,7365}
X(18626) lies on these lines: {7,27}, {4000,7297}
X(18626) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7, 18627, 18629), (278, 18629, 7), (278, 18630, 18628)
X(18627) lies on the line {7,27}
X(18627) = {X(18626), X(18629)}-harmonic conjugate of X(7)
X(18628) lies on the line {7,27}
X(18628) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (278, 18629, 18623), (278, 18630, 18626)
X(18629) lies on these lines: {7,27}, {85,16706}, {4000,7291}
X(18629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7, 18626, 278), (7, 18627, 18626), (222, 18630, 278), (18623, 18628, 278)
X(18630) lies on the line {7,27}
X(18630) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (278, 18629, 222), (18626, 18628, 278)
X(18631) lies on these lines: {7,27}, {73,1442}, {307,1943}, {2260,7291}, {2897,14544}, {3160,5932}, {3212,7105}
X(18631) = {X(18623), X(18632)}-harmonic conjugate of X(18633)
X(18632) lies on these lines: {7,27}, {347,18697}, {4296,5930}, {7291,10521}, {7365,14256}
X(18632) = {X(18631), X(18633)}-harmonic conjugate of X(18623)
X(18633) lies on these lines: {7,27}, {938,15763}, {1375,5435}, {5226,5932}, {5273,6349}, {5603,9799}
X(18633) = {X(18623), X(18632)}-harmonic conjugate of X(18631)
X(18634) lies on these lines: {1,16608}, {2,7}, {19,4466}, {29,9579}, {40,18589}, {78,17296}, {141,936}, {223,13567}, {269,282}, {273,4858}, {278,459}, {281,3668}, {610,1375}, {857,18655}, {938,3946}, {965,17272}, {1119,8894}, {1210,1861}, {1439,9119}, {1449,5738}, {1565,18725}, {1736,4859}, {3086,3341}, {3739,5705}, {4292,7498}, {4648,13411}, {4851,17044}, {5125,9581}, {5704,17067}, {5742,16832}, {6706,17327}, {7515,15803}, {7532,9612}, {9843,12618}, {17064,17065}
X(18634) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 307, 9), (16608, 17073, 1), (16608, 18644, 17073)
X(18635) lies on these lines: {1,16608}, {2,6}, {3,5803}, {5,5751}, {7,857}, {37,307}, {57,440}, {65,18589}, {78,4851}, {142,442}, {226,1439}, {241,18591}, {273,1865}, {284,1375}, {429,1876}, {936,17296}, {938,1834}, {948,5932}, {1086,17863}, {1445,2245}, {1565,18726}, {2092,17058}, {2262,5929}, {2294,4466}, {2893,16054}, {3142,15844}, {3330,6180}, {3454,9843}, {3666,18592}, {3739,6734}, {3946,4904}, {4205,5808}, {4340,7498}, {4361,12649}, {5051,5807}, {5244,16580}, {17171,18165}
X(18635) = complement of X(2287)
X(18635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 69, 965), (2, 5738, 6), (7, 857, 1901), (142, 17052, 442)
X(18636) lies on these lines: {1,16608}, {56,14376}, {57,7198}, {72,141}, {220,3763}, {427,16607}, {857,18656}, {1375,2172}, {1565,18727}, {1902,12610}, {3912,3998}, {4466,17442}, {4904,17054}, {11517,17060}, {13567,14557}
X(18636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18637, 18639), (16608, 18639, 1), (16608, 18640, 18638)
X(18637) lies on these lines: {1,16608}, {141,5692}, {857,18657}, {1565,18728}, {1734,17069}, {4466,18669}
X(18637) = {X(18636), X(18639)}-harmonic conjugate of X(1)
X(18638) lies on these lines: {1,16608}, {343,18588}, {857,18658}, {1565,18729}, {4466,18670}
X(18638) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16608, 18639, 17073), (16608, 18640, 18636)
X(18639) lies on these lines: {1,16608}, {2,607}, {3,8299}, {141,960}, {304,6393}, {857,18659}, {1214,3912}, {1368,3741}, {1375,1973}, {1565,18730}, {3061,16596}, {3742,18214}, {4466,18671}, {6349,17316}
X(18639) = complement of X(607)
X(18639) = complementary conjugate of polar conjugate of X(34398)
X(18639) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18636, 16608), (1, 18637, 18636), (17043, 18640, 16608), (17073, 18638, 16608)
X(18640) lies on these lines: {1,16608}, {1565,18731}
X(18640) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16608, 18639, 17043), (18636, 18638, 16608)
X(18641) lies on these lines: {1,16608}, {2,3}, {8,6349}, {9,3182}, {10,227}, {72,307}, {78,1060}, {117,122}, {223,936}, {283,11064}, {388,7011}, {392,10373}, {581,13567}, {960,16596}, {1210,1834}, {1212,1213}, {1503,2360}, {1565,18732}, {1838,6708}, {1901,4292}, {2968,6734}, {3160,5932}, {3454,6700}, {3695,3998}, {4026,18589}, {4340,15905}, {4466,18673}, {5044,10380}, {5250,15941}, {5296,15831}, {5777,10379}, {6350,9780}, {8885,18687}, {12609,18588}, {13411,17056}
X(18641) = isotomic conjugate of polar conjugate of X(1901)
X(18641) = complement of X(29)
X(18641) = complementary conjugate of X(34831)
X(18641) = inverse of X(7532) in the orthocentroidal circle
X(18641) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3, 7515), (2, 4, 7532), (2, 20, 7498), (2, 3152, 29), (2, 5125, 5), (2, 7572, 140), (2, 13725, 16416), (1375, 13442, 28), (17073, 18642, 18643)
X(18642) lies on these lines: {1,16608}, {2,1172}, {3,66}, {9,440}, {10,4523}, {119,127}, {281,857}, {306,307}, {441,2193}, {442,1861}, {1038,17296}, {1040,17306}, {1060,4851}, {1062,4657}, {1368,10472}, {1375,1474}, {1565,18733}, {1848,6708}, {2092,18592}, {3454,6260}, {4254,13567}, {4466,18674}, {6184,15526}, {6882,14767}, {14961,16696}
X(18642) = complementary conjugate of X(6708)
X(18642) = complement of X(1172)
X(18642) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 2897, 1172), (18641, 18643, 17073)
X(18643) lies on these lines: {1,16608}, {2,253}, {3,3332}, {37,226}, {86,441}, {127,16052}, {142,17102}, {216,17245}, {347,857}, {442,7952}, {577,17392}, {1172,1375}, {1213,15526}, {1565,18734}, {2968,3739}, {3945,15905}, {4466,18675}, {5158,17337}, {6389,15668}, {14376,17698}
X(18643) = complement of X(2322)
X(18643) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17056, 18592, 440), (17073, 18642, 18641)
X(18644) lies on these lines: {1,16608}, {2,7359}, {142,3647}, {522,676}, {857,18661}, {1375,2173}, {1565,18735}, {3579,18589}, {10200,17290}
X(18644) = midpoint of X(1375) and X(4466)
X(18644) = complement of X(7359)
X(18644) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16608, 17073, 17043), (17073, 18634, 16608)
X(18645) lies on these lines: {2,17168}, {86,142}, {575,13747}, {1790,17182}, {16577,18602}, {16578,16701}
X(18645) = {X(2), X(17168)}-harmonic conjugate of X(18646)
X(18646) lies on these lines: {2,17168}, {21,551}, {86,226}, {1010,5882}, {2185,17197}, {3218,8025}, {16577,16701}, {16579,18602}, {17183,17483}
X(18646) = {X(2), X(17168)}-harmonic conjugate of X(18645)
X(18647) lies on these lines: {27,86}, {18588,18604}
X(18647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17167, 18648, 1790), (17167, 18649, 17171)
X(18648) lies on these lines: {27,86}, {1368,6467}, {1444,18589}, {16738,17177}, {17170,17175}
X(18648) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (86, 17171, 17167), (86, 17172, 17171), (1790, 18647, 17167), (17168, 18649, 17167)
X(18649) lies on these lines: {27,86}, {18590,18605}
X(18649) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17167, 18648, 17168), (17171, 18647, 17167)
X(18650) lies on these lines: {1,7}, {2,610}, {3,307}, {9,14021}, {21,3220}, {27,86}, {48,18589}, {57,5738}, {63,69}, {85,1891}, {142,379}, {159,1626}, {224,326}, {226,2268}, {320,8822}, {377,10436}, {412,7282}, {511,14053}, {515,1441}, {534,1953}, {553,15936}, {674,3313}, {950,17863}, {1266,11015}, {1439,10167}, {1565,16163}, {2269,15982}, {2278,16580}, {2772,12825}, {2893,6734}, {3868,3879}, {3911,5740}, {3912,5279}, {3942,18674}, {5232,5273}, {5285,7411}, {6467,17441}, {7291,18598}, {10452,10461}, {10572,17861}, {17647,18698}, {17880,18697}, {18591,18606}
X(18650) = X(570) of Conway triangle
X(18650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7, 20, 18655), (7, 3188, 3668), (7, 4313, 3672), (1790, 18651, 18652), (3664, 4292, 7), (3668, 4297, 17134), (3942, 18674, 18733)
X(18651) lies on these lines: {1,1370}, {2,169}, {27,86}, {63,18589}, {77,226}, {85,469}, {222,18588}, {304,305}, {348,464}, {440,1565}, {908,17241}, {940,16580}, {946,4666}, {1125,4228}, {1368,17441}, {3007,18662}, {3151,5088}, {3687,17880}, {3720,4303}, {5236,7210}, {5311,13407}, {7573,17095}, {17183,17184}
X(18651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (440, 1565, 18607), (18650, 18652, 1790)
X(18652) lies on these lines: {2,77}, {27,86}, {63,348}, {222,17073}, {226,7125}, {306,326}, {307,394}, {1125,4303}, {1445,11427}, {1812,4001}, {3616,10430}, {4359,17880}, {6357,6708}, {9776,17023}, {11064,18607}, {18592,18608}
X(18652) = {X(1790), X(18651)}-harmonic conjugate of X(18650)
X(18653) lies on these lines: {2,17190}, {27,86}, {30,113}, {60,4292}, {81,553}, {99,3977}, {110,516}, {229,950}, {239,514}, {501,12047}, {515,1325}, {662,908}, {1326,3011}, {1770,17104}, {1817,5235}, {2173,14206}, {2617,2635}, {4001,7058}, {4225,5267}, {4297,11101}, {11350,17259}, {13407,15792}, {16049,17647}, {17173,18646}, {17174,18645}, {17199,17204}, {18593,18609}
X(18653) = midpoint of X(110) and X(5196)
X(18653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (27, 1790, 17167), (1790, 17167, 17168)
X(18654) lies on these lines: {1,17183}, {75,17136}, {2975,4360}, {3869,17393}, {4460,5744}, {5176,17322}, {14543,18042}, {14953,17868}
X(18654) = {X(75), X(17221)}-harmonic conjugate of X(17136)
X(18655) lies on these lines: {1,7}, {2,8804}, {4,307}, {9,379}, {19,27}, {21,10436}, {40,1441}, {46,17861}, {57,17863}, {84,2997}, {142,14021}, {150,2822}, {273,412}, {326,17139}, {377,4357}, {464,5249}, {484,17885}, {553,15956}, {610,14953}, {857,18634}, {950,5738}, {1445,6996}, {1486,16678}, {1633,18615}, {1741,4858}, {1958,2327}, {3187,4452}, {3601,5736}, {3729,5279}, {3868,3875}, {4360,11520}, {5128,17895}, {5740,9581}, {6356,10400}, {9436,10431}, {10447,10461}, {12514,18698}, {14543,18594}, {17156,17157}, {17274,17579}
X(18655) = anticomplement of X(8804)
X(18655) = X(571) of Conway triangle
X(18655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (7, 20, 18650), (7, 3188, 269), (7, 4313, 3945), (75, 8822, 63), (3663, 4292, 7), (5088, 10446, 77), (17134, 17220, 1), (17220, 18661, 17134)
X(18656) lies on these lines: {1,7}, {2,4456}, {4,349}, {75,16747}, {150,2825}, {304,17139}, {517,1231}, {857,18636}, {1369,17135}, {1633,18616}, {2172,14953}, {7391,17492}, {8680,17442}, {14543,16545}
X(18656) = anticomplement of X(4456)
X(18656) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18657, 18659), (17220, 18659, 1), (17220, 18660, 18658)
X(18657) lies on these lines: {1,7}, {857,18637}, {1633,18617}, {8680,18669}, {14210,17139}, {14543,16546}, {14712,17482}
X(18657) = {X(18656), X(18659)}-harmonic conjugate of X(1)
X(18658) lies on these lines: {1,7}, {857,18638}, {1633,18618}, {8680,18670}, {14543,18595}
X(18658) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17220, 18659, 17134), (17220, 18660, 18656)
X(18659) lies on these lines: {1,7}, {2,2333}, {857,18639}, {1370,17135}, {1633,18619}, {1973,14953}, {5307,7406}, {8680,18671}, {14543,18596}, {17139,18156}
X(18659) = anticomplement of X(2333)
X(18659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18656, 17220), (1, 18657, 18656), (17134, 18658, 17220), (17221, 18660, 17220)
X(18660) lies on these lines: {}
X(18661) lies on these lines: {1,7}, {523,4467}, {857,18644}, {1155,17895}, {1441,3579}, {1633,18622}, {2173,8680}, {3647,18698}, {5307,8756}, {8822,11684}, {10543,15936}, {17136,17139}
X(18661) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17134, 17220, 17221), (17134, 18655, 17220)
X(18662) lies on these lines: {2,2006}, {7,6360}, {63,3187}, {92,18677}, {192,329}, {908,3995}, {914,17184}, {1214,17862}, {1790,17221}, {2167,4560}, {2185,14570}, {2975,17512}, {3007,18651}, {3210,5744}, {6758,17140}, {17483,18668}
X(18662) = anticomplement of X(6358)
X(18662) = isotomic conjugate of isogonal conjugate of X(21770)
X(18662) = anticomplementary conjugate of anticomplement of X(2150)
X(18662) = polar conjugate of isogonal conjugate of X(20803)
X(18662) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4858, 16577, 2), (6358, 16579, 2)
X(18663) lies on these lines: {2,85}, {20,17441}, {192,3151}, {193,3210}, {1763,5088}, {3218,17490}, {3732,11347}, {7500,17480}
X(18663) = anticomplement of X(18750)
X(18663) = anticomplementary conjugate of anticomplement of X(2155)
X(18663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1427, 18750, 2), (5905, 6360, 192), (5905, 18668, 6360)
X(18664) lies on these lines: {2,1748}, {7,7125}, {192,3151}, {347,17483}, {3152,4295}, {7538,11415}
X(18664) = anticomplement of X(1748)
X(18664) = anticomplementary conjugate of anticomplement of X(1820)
X(18664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1748, 18588, 2), (4329, 5905, 6360), (5905, 18665, 17481)
X(18665) lies on these lines: {2,18590}, {192,3151}
X(18665) = anticomplement of isogonal conjugate of X(2158)
X(18665) = anticomplement of anticomplement of X(18590)
X(18665) = anticomplementary conjugate of anticomplement of X(2158)
X(18665) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4329, 5905, 17479), (17481, 18664, 5905)
X(18666) lies on these lines: {2,286}, {20,185}, {22,16998}, {192,3151}, {401,15988}, {1654,3152}, {3101,17759}, {4269,7560}, {6840,17035}, {7538,17379}, {7580,9308}
X(18666) = anticomplement of X(286)
X(18666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (286, 18591, 2), (3151, 6360, 18667)
X(18667) lies on these lines: {2,216}, {20,5208}, {81,401}, {192,3151}, {1214,1947}, {2897,17950}, {3152,3210}
X(18667) = anticomplement of X(31623)
X(18667) = anticomplementary conjugate of anticomplement of X(1409)
X(18667) = {X(3151), X(6360)}-harmonic conjugate of X(18666)
X(18668) lies on these lines: {2,7110}, {192,3151}, {239,514}, {3739,18607}, {4552,17484}, {6758,17491}, {14956,18210}, {17147,17364}, {17483,18662}
X(18668) = reflection of X(14956) in X(18210)
X(18668) = anticomplement of X(14206)
X(18668) = anticomplementary conjugate of anticomplement of X(2159)
X(18668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5905, 6360, 17479), (6360, 18663, 5905), (14206, 18593, 2)
X(18669) lies on these lines: {1,19}, {163,2312}, {304,18717}, {514,661}, {896,2157}, {1725,1755}, {1763,5287}, {1930,17865}, {2170,16784}, {2171,16785}, {3002,18210}, {3942,18728}, {4466,18637}, {5497,17464}, {6149,16562}, {8680,18657}, {9406,17468}, {17170,18727}, {17466,17472}
X(18669) = isotomic conjugate of X(37220)
X(18669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16545, 1973), (1, 18596, 2172), (1755, 3708, 1725), (2576, 2577, 2172), (14210, 18715, 1959), (17442, 18671, 1)
X(18670) lies on these lines: {1,19}, {255,1820}, {774,2180}, {1959,18716}, {2314,4100}, {3942,18729}, {4466,18638}, {6508,14206}, {8680,18658}
X(18670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1953, 18671, 48), (1953, 18672, 17442)
X(18671) lies on these lines: {1,19}, {38,17473}, {255,2083}, {326,2128}, {336,9239}, {774,1755}, {775,1910}, {820,17462}, {1107,17447}, {1496,16567}, {1959,6508}, {2170,7124}, {2171,2286}, {3061,6554}, {3708,4020}, {3720,17441}, {3942,17170}, {4466,18639}, {7146,7365}, {8680,18659}, {16716,17872}, {18589,18733}
X(18671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 17442, 1953), (1, 18596, 1973), (1, 18669, 17442), (48, 18670, 1953), (1973, 18596, 2173), (17170, 18730, 3942), (17438, 18672, 1953), (18156, 18717, 1959)
X(18672) lies on these lines: {1755,17473}, {1959,18718}
X(18673) lies on these lines: {1,19}, {20,8680}, {21,1762}, {35,1782}, {40,758}, {42,65}, {55,976}, {63,1792}, {71,72}, {78,10319}, {100,1257}, {201,228}, {226,1869}, {678,2632}, {684,14414}, {740,3189}, {774,3185}, {950,1842}, {960,8299}, {1043,11683}, {1104,2264}, {1191,7124}, {1490,11471}, {1715,5884}, {1763,10393}, {1829,14547}, {1859,2654}, {1888,2635}, {1959,18719}, {2265,3074}, {2357,10901}, {3057,17832}, {3251,4139}, {3611,7066}, {3827,4300}, {3869,6508}, {3942,4303}, {4101,8896}, {4267,11031}, {4466,18641}, {5494,10902}, {5584,12329}, {6986,16560}, {7289,10884}, {7971,17831}, {17164,17784}
X(18673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 2939, 28), (28, 2939, 2173), (48, 18674, 18675), (4303, 18732, 3942)
X(18674) lies on these lines: {1,19}, {37,17441}, {73,2171}, {192,3151}, {306,3610}, {516,4065}, {740,11677}, {1486,1962}, {1959,18720}, {2099,2286}, {2292,3827}, {3057,4016}, {3159,3950}, {3942,18650}, {3951,3958}, {4431,18697}, {4466,18642}, {18210,18591}
X(18674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18598, 1474), (1474, 18598, 2173), (18650, 18733, 3942), (18673, 18675, 48)
X(18675) lies on these lines: {1,19}, {37,73}, {71,1214}, {201,3990}, {219,3157}, {221,2256}, {347,8680}, {500,971}, {1060,2289}, {1108,1201}, {1826,5930}, {1841,2654}, {1959,18721}, {1962,2293}, {2285,7114}, {3682,3949}, {3743,12705}, {3942,18734}, {4466,18643}, {7004,14597}, {8803,10901}
X(18675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18599, 1172), (48, 18674, 18673), (1172, 18599, 2173)
X(18676) lies on these lines: {2,17906}, {4,2181}, {92,4850}, {281,17902}, {653,17074}, {1148,2658}, {17892,17915}, {17912,17914}
X(18676) = polar conjugate of isotomic conjugate of X(21271)
X(18676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (281, 17903, 17902), (17902, 17903, 18688), (17902, 18683, 18684), (17906, 18677, 2)
X(18677) lies on these lines: {2,17906}, {19,18163}, {92,18662}, {7952,10056}
X(18677) = polar conjugate of isogonal conjugate of X(23846)
X(18677) = {X(2), X(18676)}-harmonic conjugate of X(17906)
X(18678) lies on these lines: {2,280}, {4,204}, {33,2999}, {108,11347}, {196,8755}, {223,7129}, {225,7490}, {226,1249}, {278,393}, {281,17902}, {469,5222}
X(18678) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (393, 3772, 278), (17902, 17903, 281), (17902, 18688, 17903)
X(18679) lies on these lines: {2,216}, {4,580}, {27,1865}, {29,1834}, {33,43}, {81,445}, {92,3772}, {199,14192}, {225,1247}, {278,18593}, {281,17902}, {297,333}, {440,8748}, {442,8747}, {451,498}, {469,4383}, {648,17778}, {653,6354}, {1211,2322}, {1249,5712}, {1990,17056}, {4641,7282}, {6530,7413}, {9308,18134}, {17911,17919}
X(18680) lies on these lines: {281,17902}, {386,6198}
X(18680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (281, 18681, 18683), (17902, 18683, 281), (17902, 18684, 18682)
X(18681) lies on these lines: {281,17902}, {17908,17925}
X(18681) = {X(18680), X(18683)}-harmonic conjugate of X(281)
X(18682) lies on the line {281,17902}
X(18682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17902, 18683, 17903), (17902, 18684, 18680)
X(18683) lies on the line {281,17902}
X(18683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (281, 18680, 17902), (281, 18681, 18680), (17903, 18682, 17902), (18676, 18684, 17902)
X(18684) lies on the line {281,17902}
X(18684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17902, 18683, 18676), (18680, 18682, 17902)
X(18685) lies on these lines: {4,6}, {37,451}, {281,17902}, {2322,5051}, {2345,7952}, {4220,16318}
X(18685) = {X(17903), X(18686)}-harmonic conjugate of X(18687)
X(18686) lies on these lines: {2,1235}, {27,5523}, {42,4213}, {112,3151}, {281,17902}, {440,16318}, {469,8743}
X(18686) = {X(18685), X(18687)}-harmonic conjugate of X(17903)
X(18687) lies on these lines: {2,253}, {81,15262}, {281,17902}, {451,3085}, {1075,6853}, {3183,6908}, {4383,8743}, {6964,8888}, {8885,18641}
X(18687) = {X(17903), X(18686)}-harmonic conjugate of X(18685)
X(18688) lies on these lines: {281,17902}, {693,905}
X(18688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (17902, 17903, 18676), (17903, 18678, 17902)
X(18689) lies on these lines: {1,17877}, {8,4566}, {75,77}, {339,6739}, {1441,17859}, {4453,4986}, {4858,9317}
X(18689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (75, 664, 17880), (1441, 17859, 18690)
X(18690) lies on these lines: {7,5906}, {75,78}, {86,17880}, {284,4858}, {1441,17859}, {3687,3936}, {4511,18697}
X(18690) = {X(1441), X(17859)}-harmonic conjugate of X(18689)
X(18691) lies on these lines: {1,75}, {269,17880}, {1441,17860}, {4081,6046}, {8769,17901}, {17861,17869}, {17890,17891}
X(18691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (75, 17858, 1), (17858, 18699, 75)
X(18692) lies on these lines: {1,75}, {1441,12609}, {3664,17880}, {17860,17874}, {17863,17877}
X(18693) lies on these lines: {1,75}, {774,17879}, {1748,16545}
X(18693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18694, 1930), (1930, 17858, 1), (17858, 18696, 18695)
X(18694) lies on these lines: {1,75}, {1725,17879}, {14208,17901}
X(18694) = {X(1930), X(18693)}-harmonic conjugate of X(1)
X(18695) lies on these lines: {1,75}, {63,1820}, {69,17880}, {92,18713}, {1760,18595}, {1953,14213}, {1959,17865}
X(18695) = isotomic conjugate of X(2190)
X(18695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (75, 304, 326), (1930, 17858, 75), (17858, 18696, 18693)
X(18696) lies on the line {1,75}
X(18696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1930, 17858, 17859), (18693, 18695, 17858)
X(18697) lies on these lines: {1,75}, {7,17164}, {8,2893}, {69,758}, {141,4016}, {226,306}, {239,16470}, {312,17286}, {313,1089}, {322,4385}, {347,18632}, {1111,1269}, {1231,3668}, {1240,1978}, {1848,3687}, {2292,4357}, {2294,3912}, {2650,3879}, {3263,4967}, {3596,6382}, {3702,17863}, {3718,17270}, {3729,5227}, {3743,17321}, {3946,4359}, {3952,4538}, {3958,4416}, {4021,4065}, {4085,4714}, {4137,7237}, {4431,18674}, {4511,18690}, {4980,17133}, {4986,5564}, {5285,17797}, {10319,11679}, {11683,18598}, {17880,18650}
X(18697) = isotomic conjugate of X(2363)
X(18697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (75, 304, 10436), (75, 17762, 314), (4647, 18698, 75)
X(18698) lies on these lines: {1,75}, {2,17861}, {7,758}, {9,8680}, {10,307}, {63,1744}, {85,17272}, {142,2294}, {191,8822}, {219,4363}, {273,5705}, {313,3992}, {321,3950}, {322,3679}, {519,15936}, {523,3126}, {527,3958}, {993,17134}, {1086,4016}, {1089,4078}, {1108,4688}, {1111,4357}, {1125,17863}, {1213,16732}, {1214,6358}, {1698,17885}, {1723,4384}, {1754,3980}, {1781,11683}, {1962,4021}, {2256,17118}, {2292,3663}, {2328,4418}, {2650,3664}, {3262,4967}, {3634,17895}, {3672,3743}, {3718,3761}, {3739,4858}, {3878,17220}, {3879,7278}, {4466,17052}, {4847,17874}, {5235,14206}, {5496,7269}, {5936,6757}, {7264,17321}, {12514,18655}, {17647,18650}
X(18698) = complement of X(25255)
X(18698) = anticomplement of X(25081)
X(18698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (75, 304, 10447), (75, 18697, 4647), (11683, 16054, 1781)
X(18699) lies on these lines: {1,75}, {1443,17880}, {4397,14208}
X(18699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (75, 17858, 17859), (75, 18691, 17858)
X(18700) lies on these lines: {2,18085}, {4557,18099}, {18082,18095}
X(18700) = {X(2), X(18085)}-harmonic conjugate of X(18701)
X(18701) lies on these lines: {2,18085}, {3112,6654}, {18084,18095}
X(18701) = {X(2), X(18085)}-harmonic conjugate of X(18700)
X(18702) lies on these lines: {2,18086}, {13853,18097}, {17500,18087}, {18082,18083}
X(18702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18083, 18084, 18082), (18083, 18712, 18084)
X(18703) lies on these lines: {2,3613}, {83,1751}, {308,18134}, {857,18086}, {18082,18083}, {18087,18095}
X(18704) lies on the line {18082,18083}
X(18704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18082, 18705, 18707), (18083, 18707, 18082), (18083, 18708, 18706)
X(18705) lies on the line {18082,18083}
X(18705) = {X(18704), X(18707)}-harmonic conjugate of X(18082)
X(18706) lies on the line {18082,18083}
X(18706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18083, 18707, 18084), (18083, 18708, 18704)
X(18707) lies on these lines: {18082,18083}, {18091,18095}
X(18707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18082, 18704, 18083), (18082, 18705, 18704), (18084, 18706, 18083), (18085, 18708, 18083)
X(18708) lies on the line {18082,18083}
X(18708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18083, 18707, 18085), (18704, 18706, 18083)
X(18709) lies on these lines: {4,83}, {18082,18083}
X(18709) = {X(18084), X(18710)}-harmonic conjugate of X(18711)
X(18710) lies on these lines: {2,15270}, {83,469}, {18082,18083}
X(18710) = {X(18709), X(18711)}-harmonic conjugate of X(18084)
X(18711) lies on these lines: {2,66}, {18082,18083}
X(18711) = {X(18084), X(18710)}-harmonic conjugate of X(18709)
X(18712) lies on these lines: {18082,18083}, {18106,18107}
X(18712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18083, 18084, 18085), (18084, 18702, 18083)
X(18713) lies on these lines: {1,82}, {19,326}, {63,1953}, {92,18695}, {320,18725}, {610,16568}, {662,18594}, {1707,17472}, {2234,8769}, {18040,18043}, {18068,18069}
X(18713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19, 1959, 326), (1760, 18041, 1), (18041, 18722, 1760)
X(18714) lies on these lines: {1,82}, {86,1959}, {190,2171}, {239,17443}, {284,16568}, {320,18726}, {662,1781}, {1045,2643}, {1654,4053}, {1953,4360}, {2667,17472}, {3061,17381}, {3970,17315}, {4137,10458}, {7146,17234}, {17160,17868}, {17233,17762}, {17277,17451}, {17319,17444}, {17378,18161}, {18040,18050}, {18043,18059}, {18044,18055}
X(18714) = {X(1959), X(2294)}-harmonic conjugate of X(86)
X(18715) lies on these lines: {1,82}, {320,18728}, {514,661}, {662,16546}, {1930,16747}, {2644,17799}, {17019,17456}
X(18715) = isotomic conjugate of X(37221)
X(18715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1959, 18669, 14210), (18049, 18717, 1)
X(18716) lies on these lines: {1,82}, {320,18729}, {662,18595}, {1959,18670}
X(18716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18041, 18717, 1760), (18041, 18718, 18049)
X(18717) lies on these lines: {1,82}, {75,17442}, {304,18669}, {320,18730}, {662,18596}, {1959,6508}, {18052,18055}
X(18717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18049, 18041), (1, 18715, 18049), (1760, 18716, 18041), (1959, 18671, 18156), (18042, 18718, 18041)
X(18718) lies on these lines: {1,82}, {320,18731}, {662,18597}, {1959,18672}
X(18718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18041, 18717, 18042), (18049, 18716, 18041)
X(18719) lies on these lines: {1,82}, {20,2831}, {28,16568}, {72,319}, {75,16747}, {320,18732}, {662,2939}, {1046,6043}, {1098,1762}, {1959,18673}, {3868,18178}, {3869,4673}, {4463,7270}, {5692,18747}
X(18719) = reflection of X(3868) in X(18178)
X(18719) = {X(1760), X(18720)}-harmonic conjugate of X(18721)
X(18720) lies on these lines: {1,82}, {75,17171}, {320,18733}, {662,18598}, {1474,16568}, {1959,18674}
X(18720) = {X(18719), X(18721)}-harmonic conjugate of X(1760)
X(18721) lies on these lines: {1,82}, {75,15149}, {320,18734}, {662,18599}, {1172,16568}, {1761,16599}, {1959,18675}
X(18721) = {X(1760), X(18720)}-harmonic conjugate of X(18719)
X(18722) lies on these lines: {1,82}, {320,18735}, {662,1959}, {896,2644}, {897,1581}, {1580,17472}, {2349,14206}, {2643,17799}, {18070,18071}
X(18722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1760, 18041, 18042), (1760, 18713, 18041)
X(18723) lies on these lines: {1,16680}, {6,16742}, {41,18600}, {101,17205}, {999,18164}, {1429,18206}, {2329,16887}, {7225,16713}, {7289,18177}, {9259,16726}, {9267,9299}, {9310,17169}, {9317,16727}, {16696,18162}
X(18723) = {X(16696), X(18162)}-harmonic conjugate of X(18724)
X(18724) lies on these lines: {1,18177}, {41,16713}, {56,18164}, {81,1400}, {86,142}, {940,1730}, {2268,17183}, {4267,18166}, {7083,17194}, {7225,18600}, {7289,18176}, {16696,18162}
X(18724) = {X(16696), X(18162)}-harmonic conjugate of X(18723)
X(18725) lies on these lines: {1,159}, {19,269}, {57,1422}, {77,610}, {142,2391}, {189,2184}, {222,3197}, {241,2270}, {320,18713}, {513,3062}, {1086,5575}, {1108,2097}, {1419,2182}, {1467,1829}, {1565,18634}, {1743,16560}, {1953,4328}, {2385,4312}, {2809,3174}, {3554,7202}, {4445,7323}, {4851,5845}, {5223,8679}, {6245,13156}, {8680,10442}, {16696,18163}, {18164,18180}, {18193,18194}
X(18725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19, 3942, 269), (77, 7291, 610), (7289, 18161, 1), (18161, 18735, 7289)
X(18726) lies on these lines: {1,159}, {6,16551}, {9,7146}, {37,4503}, {57,1804}, {81,2150}, {142,17451}, {284,7291}, {320,18714}, {527,2171}, {942,18164}, {1086,17443}, {1100,7202}, {1266,17868}, {1565,18635}, {1953,3663}, {1959,4357}, {2170,3946}, {2294,3664}, {2309,4475}, {3061,17306}, {3665,16608}, {3666,18163}, {3670,16696}, {3970,4851}, {4006,4445}, {4053,17344}, {4389,18041}, {17197,17863}, {17246,17444}, {18166,18184}, {18169,18190}
X(18726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2294, 3942, 3664), (16696, 18179, 3670)
X(18727) lies on these lines: {1,159}, {77,18596}, {81,17186}, {1565,18636}, {2003,5280}, {2172,7291}, {3942,17442}, {17170,18669}
X(18727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18728, 18730), (18161, 18730, 1), (18161, 18731, 18729)
X(18728) lies on these lines: {1,159}, {320,18715}, {1565,18637}, {3942,18669}, {7202,16784}, {18200,18208}
X(18728) = {X(18727), X(18730)}-harmonic conjugate of X(1)
X(18729) lies on these lines: {1,159}, {320,18716}, {1565,18638}, {3942,18670}
X(18729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18161, 18730, 7289), (18161, 18731, 18727)
X(18730) lies on these lines: {1,159}, {7,17442}, {222,3497}, {320,18717}, {1565,18639}, {1973,7291}, {3942,17170}, {7202,16781}, {18169,18176}
X(18730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18727, 18161), (1, 18728, 18727), (3942, 18671, 17170), (7289, 18729, 18161), (18162, 18731, 18161)
X(18731) lies on these lines: {1,159}, {320,18718}, {1565,18640}
X(18731) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18161, 18730, 18162), (18727, 18729, 18161)
X(18732) lies on these lines: {1,159}, {3,6511}, {6,18596}, {20,145}, {28,60}, {65,222}, {69,72}, {279,1439}, {320,18719}, {511,14054}, {518,3313}, {912,5562}, {960,2836}, {971,1902}, {1062,1473}, {1364,10544}, {1385,8907}, {1565,18641}, {1828,5722}, {2771,12825}, {2835,10624}, {3074,16560}, {3670,18163}, {3937,13369}, {3942,4303}, {5045,17024}, {5249,9895}, {5728,7717}, {5904,9004}
X(18732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3942, 18673, 4303), (7289, 18733, 18734)
X(18733) lies on these lines: {1,159}, {320,18720}, {1474,7291}, {1565,18642}, {3942,18650}, {10319,18607}, {16696,18175}, {18178,18179}, {18210,18606}, {18589,18671}
X(18733) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3942, 18674, 18650), (18732, 18734, 7289)
X(18734) lies on these lines: {1,159}, {63,77}, {81,2189}, {241,579}, {284,3666}, {320,18721}, {1172,7291}, {1437,16696}, {1565,18643}, {2175,8758}, {3942,18675}, {4357,15595}, {5089,16608}, {7193,18606}, {18179,18187}
X(18734) = {X(7289), X(18733)}-harmonic conjugate of X(18732)
X(18735) lies on these lines: {1,159}, {44,16560}, {320,18722}, {1429,7202}, {1443,2173}, {1565,18644}, {2391,17067}, {3733,4782}
X(18735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1443, 7291, 2173), (2173, 3942, 1443), (7289, 18161, 18162), (7289, 18725, 18161)
X(18736) lies on these lines: {2,16697}, {76,7182}, {333,18738}, {908,17241}, {1577,1764}, {4417,18740}, {17234,18741}, {18135,18136}
X(18736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18133, 18742, 18134), (18134, 18737, 18133), (18134, 18747, 18746), (18134, 18752, 18742), (18737, 18752, 18134), (18749, 18751, 18750)
X(18737) lies on these lines: {2,16698}, {908,17241}
X(18737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18133, 18736, 18134), (18134, 18736, 18752), (18134, 18747, 18748), (18740, 18741, 2)
X(18738) lies on these lines: {2,16699}, {69,2478}, {75,225}, {85,2476}, {183,16048}, {333,18736}, {469,18750}, {811,1098}, {1577,16552}, {3061,3452}, {5224,14615}, {5701,17263}, {14829,18148}, {17346,18740}
X(18738) = {X(349), X(6734)}-harmonic conjugate of X(75)
X(18739) lies on these lines: {2,3770}, {57,18044}, {226,17234}, {312,17184}, {321,17235}, {940,18046}, {3210,4033}, {3666,18040}, {4359,4377}, {14829,18148}, {17595,18073}, {18134,18150}, {18141,18147}
X(18739) = {X(2), X(18136)}-harmonic conjugate of X(18133)
X(18740) lies on these lines: {2,16698}, {190,653}, {645,4585}, {1577,3882}, {3936,18752}, {4417,18736}, {17234,18133}, {17346,18738}
X(18740) = {X(2), X(18737)}-harmonic conjugate of X(18741)
X(18741) lies on these lines: {2,16698}, {4417,18133}, {14829,18136}, {17234,18736}, {18139,18752}
X(18741) = {X(2), X(18737)}-harmonic conjugate of X(18740)
X(18742) lies on these lines: {2,16699}, {76,1088}, {908,17241}, {4869,18136}, {18141,18147}
X(18742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18134, 18736, 18133), (18134, 18752, 18736)
X(18743) lies on the cubic K972 and these lines: {1,341}, {2,37}, {7,8051}, {8,3740}, {9,14829}, {10,4673}, {55,5205}, {57,190}, {63,17336}, {69,18228}, {85,5226}, {86,2297}, {92,4997}, {100,9083}, {145,4487}, {171,4011}, {210,10453}, {226,17234}, {238,3769}, {239,16969}, {304,17284}, {306,5233}, {314,18229}, {319,14555}, {320,329}, {322,5328}, {333,3305}, {354,4009}, {388,2899}, {474,7283}, {668,14759}, {726,17063}, {740,16569}, {748,17763}, {908,17241}, {936,1043}, {938,1265}, {940,3758}, {975,13740}, {982,3971}, {984,3840}, {1001,7081}, {1088,4554}, {1089,3624}, {1125,4125}, {1211,17228}, {1376,3685}, {1698,4714}, {1836,17777}, {1909,5308}, {1999,3759}, {2051,18061}, {2325,6692}, {2403,4462}, {2478,7270}, {2901,17749}, {2999,4360}, {3008,17158}, {3061,3452}, {3158,4939}, {3161,5435}, {3241,4723}, {3304,9369}, {3550,4432}, {3616,3701}, {3622,4696}, {3661,5743}, {3662,4415}, {3679,4975}, {3687,5316}, {3695,17527}, {3699,3870}, {3702,9780}, {3705,3816}, {3717,11019}, {3718,17353}, {3729,5437}, {3742,3967}, {3756,4884}, {3757,4423}, {3836,3944}, {3873,3952}, {3886,8580}, {3891,7292}, {3923,17122}, {3948,17056}, {3975,17316}, {3985,17754}, {3993,6686}, {3994,17155}, {4033,16594}, {4095,4384}, {4110,17242}, {4248,4855}, {4362,17123}, {4387,4413}, {4388,4679}, {4389,4656}, {4418,17124}, {4427,9352}, {4434,8616}, {4514,10327}, {4968,5550}, {4981,9330}, {5044,10449}, {5219,18044}, {5256,17393}, {5263,5268}, {5287,17394}, {5423,10580}, {5712,17317}, {5718,18040}, {5722,16086}, {5737,17260}, {5739,17360}, {6063,18153}, {6703,17368}, {7308,11679}, {7321,9776}, {8167,16823}, {16593,18045}, {16817,16842}, {16832,17143}, {17149,18149}, {17243,17786}, {17266,17789}, {17267,17788}, {17308,17762}, {17387,17778}, {18136,18139}
X(18743) = isogonal conjugate of X(38266)
X(18743) = cevapoint of X(i) and X(j) for these {i,j}: {2, 8055}, {145, 3161}, {1743, 4855}
X(18743) = crosssum of X(6) and X(21785)
X(18743) = isotomic conjugate of X(8056)
X(18743) = anticomplement of X(16602)
X(18743) = complement of X(17490)
X(18743) = trilinear pole of the line {3667, 4404}
X(18743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3992, 4737), (2, 192, 3752), (2, 312, 75), (2, 3210, 16610), (2, 3995, 4850), (2, 4358, 312), (2, 4671, 4359), (2, 17490, 16602), (344, 1997, 2), (3175, 3210, 3644), (3175, 16610, 3210), (3992, 4737, 341), (4043, 4751, 75), (4687, 18137, 75), (4849, 4891, 145)
X(18744) lies on these lines: {2,1333}, {75,4150}, {857,18147}, {908,17241}, {5224,17335}, {13741,17283}, {16062,17370}
X(18744) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18133, 18745, 18747), (18134, 18747, 18133), (18134, 18748, 18746)
X(18745) lies on these lines: {2,16702}, {908,17241}, {4129,4481}
X(18745) = {X(18744), X(18747)}-harmonic conjugate of X(18133)
X(18746) lies on these lines: {2,18604}, {908,17241}
X(18746) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18134, 18747, 18736), (18134, 18748, 18744)
X(18747) lies on these lines: {2,1444}, {9,1760}, {69,857}, {75,1826}, {76,5179}, {86,5747}, {333,469}, {908,17241}, {3718,4150}, {5692,18719}, {5816,7377}, {17234,17671}, {18142,18143}
X(18747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18133, 18744, 18134), (18133, 18745, 18744), (18736, 18746, 18134), (18737, 18748, 18134)
X(18748) lies on these lines: {2,18605}, {908,17241}
X(18748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18134, 18747, 18737), (18744, 18746, 18134)
X(18749) lies on these lines: {2,18606}, {75,225}, {319,16090}, {320,18147}, {326,4554}, {908,17241}, {1760,16560}, {7013,18026}
X(18749) = isotomic conjugate of X(3362)
X(18749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (264, 307, 75), (18736, 18750, 18751)
X(18750) lies on the cubic K605 and these lines: {2, 85}, {8, 7957}, {19, 27}, {20, 3198}, {69, 189}, {76, 19814}, {77, 27413}, {100, 41905}, {144, 321}, {158, 255}, {190, 3719}, {204, 1097}, {219, 1943}, {222, 1944}, {223, 27411}, {242, 37581}, {278, 27509}, {304, 2184}, {306, 16284}, {319, 26872}, {320, 26871}, {322, 345}, {326, 27398}, {341, 1370}, {346, 30698}, {440, 44150}, {469, 18738}, {651, 28950}, {662, 6507}, {799, 20641}, {896, 17871}, {908, 17241}, {1229, 37655}, {1441, 5273}, {1707, 4008}, {1733, 16570}, {1746, 16551}, {1763, 3732}, {1821, 20939}, {1959, 6508}, {1966, 33787}, {1999, 10025}, {2000, 14004}, {2064, 3718}, {2349, 20941}, {2975, 4228}, {3187, 17158}, {3673, 19790}, {3797, 32747}, {3869, 4673}, {3928, 4858}, {3929, 6358}, {3952, 11678}, {3975, 19583}, {4296, 27410}, {4385, 12527}, {4687, 27287}, {5088, 11347}, {5179, 21621}, {5287, 14828}, {5342, 6734}, {5739, 5942}, {5744, 19804}, {5748, 30829}, {6350, 20930}, {6708, 27339}, {6996, 21370}, {7009, 24320}, {7017, 35516}, {7112, 7182}, {7291, 19645}, {7360, 7580}, {7490, 20235}, {8804, 14615}, {9535, 14557}, {9965, 17862}, {11679, 30625}, {14544, 20221}, {14829, 20927}, {15466, 44697}, {17074, 28951}, {17441, 30943}, {17781, 42034}, {17811, 27420}, {17863, 37666}, {17884, 36277}, {18041, 45224}, {18141, 20946}, {18151, 28956}, {18623, 27382}, {19788, 24597}, {20171, 37683}, {20445, 37206}, {20760, 30273}, {20905, 21454}, {20940, 36101}, {20942, 39996}, {21286, 42709}, {21600, 27834}, {21856, 28054}, {22149, 29010}, {24584, 24612}, {26543, 27184}, {32851, 40697}, {32859, 37781}, {37216, 37220}, {39732, 41916}, {40616, 45200}
X(18750) = reflection of X(18663) in X(1427)
X(18750) = isogonal conjugate of X(2155)
X(18750) = isotomic conjugate of X(2184)
X(18750) = anticomplement of X(1427)
X(18750) = complement of X(18663)
X(18750) = anticomplement of the isogonal conjugate of X(2287)
X(18750) = isotomic conjugate of the anticomplement of X(36908)
X(18750) = isotomic conjugate of the isogonal conjugate of X(610)
X(18750) = isotomic conjugate of the polar conjugate of X(1895)
X(18750) = X(7038)-complementary conjugate of X(141)
X(18750) = X(304)-Ceva conjugate of X(75)
X(18750) = X(i)-cross conjugate of X(j) for these (i,j): {20, 33673}, {610, 1895}, {1895, 75}, {8804, 20}, {36908, 2}
X(18750) = cevapoint of X(i) and X(j) for these (i,j): {20, 27382}, {8057, 40616}
X(18750) = crosspoint of X(799) and X(23999)
X(18750) = trilinear pole of line {17898, 21172}
X(18750) = crossdifference of every pair of points on line {810, 8641}
X(18750) = trilinear product X(2)*X(20)
X(18750) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {8, 2893}, {9, 2475}, {21, 7}, {55, 17778}, {58, 4452}, {60, 3875}, {78, 2897}, {81, 36845}, {86, 6604}, {99, 46402}, {110, 4025}, {162, 17896}, {200, 2895}, {212, 18667}, {219, 3152}, {220, 1654}, {261, 20244}, {283, 347}, {284, 145}, {314, 21285}, {333, 3434}, {341, 21287}, {346, 1330}, {643, 693}, {645, 21302}, {657, 148}, {662, 3900}, {757, 17158}, {1021, 149}, {1043, 69}, {1098, 75}, {1172, 12649}, {1253, 1655}, {1260, 3151}, {1333, 17480}, {1474, 11851}, {1792, 4329}, {1802, 18666}, {2185, 3873}, {2194, 3210}, {2206, 46716}, {2287, 8}, {2299, 30699}, {2322, 4}, {2326, 3868}, {2327, 20}, {2328, 2}, {2332, 193}, {3239, 3448}, {3900, 21221}, {4183, 5905}, {4397, 21294}, {4570, 664}, {4636, 4467}, {5379, 4566}, {5546, 522}, {6061, 63}, {6065, 3882}, {7054, 1}, {7058, 17135}, {7253, 150}, {7256, 20295}, {7258, 21301}, {7259, 513}, {8641, 21220}, {21789, 4440}, {23609, 18662}, {28660, 21280}, {35193, 41808}, {36797, 46400}, {46889, 5484}
X(18750) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2155}, {2, 33581}, {3, 41489}, {4, 14642}, {6, 64}, {19, 19614}, {25, 1073}, {31, 2184}, {32, 253}, {41, 8809}, {56, 30457}, {184, 459}, {393, 14379}, {512, 46639}, {577, 6526}, {604, 44692}, {647, 1301}, {657, 36079}, {669, 44326}, {1436, 41088}, {1501, 41530}, {1973, 19611}, {1974, 34403}, {2207, 15394}, {3269, 15384}, {3346, 47437}, {5896, 40135}, {8749, 11589}, {8798, 8882}, {14092, 34426}, {14390, 43695}, {15905, 31942}, {28783, 41085}, {28785, 31956}, {33585, 37672}, {38956, 40353}
X(18750) = barycentric product X(i)*X(j) for these {i,j}: {1, 14615}, {8, 33673}, {20, 75}, {27, 42699}, {63, 15466}, {69, 1895}, {76, 610}, {85, 27382}, {92, 37669}, {99, 17898}, {122, 23999}, {154, 561}, {204, 305}, {253, 1097}, {274, 8804}, {304, 1249}, {310, 3198}, {312, 18623}, {314, 5930}, {322, 41084}, {326, 14249}, {336, 44704}, {345, 44697}, {668, 21172}, {799, 6587}, {811, 8057}, {823, 20580}, {1394, 3596}, {1562, 46254}, {1577, 36841}, {1969, 15905}, {3172, 40364}, {3718, 44696}, {4554, 14331}, {4625, 14308}, {6063, 7070}, {7182, 44695}, {15291, 46234}, {17880, 44699}, {18695, 38808}, {20322, 34412}, {20336, 44698}, {28660, 30456}
X(18750) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 64}, {2, 2184}, {3, 19614}, {6, 2155}, {7, 8809}, {8, 44692}, {9, 30457}, {19, 41489}, {20, 1}, {31, 33581}, {40, 41088}, {48, 14642}, {63, 1073}, {69, 19611}, {75, 253}, {92, 459}, {122, 2632}, {154, 31}, {158, 6526}, {162, 1301}, {204, 25}, {255, 14379}, {304, 34403}, {314, 5931}, {326, 15394}, {388, 10375}, {561, 41530}, {610, 6}, {662, 46639}, {799, 44326}, {934, 36079}, {1097, 20}, {1099, 38956}, {1249, 19}, {1394, 56}, {1562, 3708}, {1712, 41085}, {1895, 4}, {2883, 774}, {3079, 204}, {3172, 1973}, {3198, 42}, {3213, 608}, {5930, 65}, {6060, 7070}, {6525, 1096}, {6587, 661}, {6616, 1712}, {7070, 55}, {7156, 607}, {7338, 1394}, {8057, 656}, {8804, 37}, {8822, 41082}, {10152, 36119}, {14213, 13157}, {14249, 158}, {14308, 4041}, {14331, 650}, {14345, 2631}, {14615, 75}, {14944, 8767}, {15291, 2159}, {15466, 92}, {15905, 48}, {17898, 523}, {18623, 57}, {18671, 45207}, {20322, 1853}, {20580, 24018}, {21172, 513}, {23999, 44181}, {24000, 15384}, {27382, 9}, {30456, 1400}, {33629, 2148}, {33673, 7}, {35602, 255}, {36043, 39464}, {36413, 610}, {36841, 662}, {36908, 1427}, {37669, 63}, {38808, 2190}, {40616, 34591}, {40933, 1042}, {41084, 84}, {41086, 2357}, {42459, 1953}, {42658, 810}, {42699, 306}, {44695, 33}, {44696, 34}, {44697, 278}, {44698, 28}, {44699, 7012}, {44704, 240}, {44706, 8798}, {45200, 6508}, {45239, 1044}, {45245, 18594}, {47409, 37754}
X(18750) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18663, 1427}, {2, 30807, 20921}, {63, 92, 75}, {63, 14206, 92}, {63, 14212, 14213}, {63, 20223, 32939}, {189, 329, 69}, {1760, 21582, 75}, {3673, 40940, 19790}, {3732, 23512, 1763}, {3869, 20220, 4673}, {6554, 7365, 2}, {9965, 17862, 39126}, {14206, 14213, 14212}, {14206, 20879, 14211}, {14212, 14213, 92}, {18623, 27382, 37669}, {18749, 18751, 18736}, {36850, 37185, 4872}
X(18751) lies on these lines: {2,18608}, {63,6335}, {75,7017}, {312,343}, {908,17241}, {4391,17080}
X(18751) = {X(18736), X(18750)}-harmonic conjugate of X(18749)
X(18752) lies on these lines: {2,16718}, {908,17241}, {1019,1577}, {3936,18740}, {18139,18741}
X(18752) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (18134, 18736, 18737), (18736, 18742, 18134)
X(18753) lies on the cubics K771 and K1006, and on these lines: {1, 510}, {365, 4166}
X(18753) = isogonal conjugate of X(18297)
X(18753) = X(i)-isoconjugate of X(j) for these (i,j): {2, 366}, {7, 4182}, {75, 365}, {85, 4166}, {86, 4179}, {188, 508}, {509, 556}
X(18753) = crosssum of X(i) and X(j) for these (i,j): {1, 510}, {366, 4182}
X(18753) = barycentric product X(i)*X(j) for these {i,j}: {1, 365}, {6, 366}, {56, 4182}, {57, 4166}, {58, 4179}, {259, 509}
X(18753) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 366}, {32, 365}, {41, 4182}, {213, 4179}, {365, 75}, {366, 76}, {2175, 4166}, {4166, 312}, {4179, 313}, {4182, 3596}
X(18754) lies on the cubic K1006 and these lines: {1, 257}, {32, 6196}, {41, 43}, {56, 2665}, {58, 87}, {171, 213}, {172, 3510}, {609, 18272}, {1045, 8424}, {4116, 6179}
X(18754) = X(i)-aleph conjugate of X(j) for these (i,j): {1, 3496}, {365, 17596}, {366, 16566}
X(18754) = X(894)-he conjugate of X(2664)
X(18754) = X(171)-Hirst inverse of X(18278)
X(18754) = barycentric product X(239)*X(16362)
X(18754) = barycentric quotient X(16362)/X(335)
X(18754) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (385, 904, 1)
X(18755) lies on the cubics K1003 and K1006, and on and these lines: {1, 1929}, {3, 6}, {21, 2238}, {35, 213}, {37, 1247}, {41, 2276}, {42, 172}, {43, 4426}, {55, 869}, {65, 17966}, {86, 16917}, {99, 17499}, {100, 2295}, {101, 1500}, {141, 16060}, {197, 3207}, {230, 1834}, {232, 2332}, {332, 15985}, {524, 17206}, {609, 5312}, {940, 11329}, {988, 16973}, {995, 2241}, {1045, 8424}, {1078, 17034}, {1100, 4719}, {1107, 3684}, {1126, 9341}, {1193, 1914}, {1213, 11110}, {1330, 10026}, {1415, 2594}, {1654, 6626}, {1655, 3570}, {1792, 15984}, {1968, 3192}, {2110, 16683}, {2174, 2200}, {2177, 5168}, {2251, 5280}, {2275, 2280}, {2329, 3507}, {2975, 3780}, {3230, 3746}, {3293, 5291}, {3295, 16969}, {3589, 16061}, {3601, 16968}, {3666, 16519}, {3727, 4511}, {3915, 10987}, {4383, 16367}, {4559, 14882}, {4653, 16589}, {5254, 13727}, {5306, 13634}, {5313, 7031}, {5563, 16971}, {6996, 7745}, {8649, 9327}, {9300, 13635}, {16054, 17056}, {16503, 16604}, {17103, 17693}, {17337, 17687}
X(18755) = isogonal conjugate of X(6625)
X(18755) = isogonal conjugate of isotomic conjugate of X(1654)
X(18755) = X(i)-Ceva conjugate of X(j) for these (i,j): {42, 6}, {172, 2176}
X(18755) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6625}, {2, 13610}, {75, 2248}, {286, 15377}
X(18755) = X(213)-Hirst inverse of X(17735)
X(18755) = cevapoint of X(8298) and X(8845)
X(18755) = crosspoint of X(i) and X(j) for these (i,j): {101, 249}, {1654, 4213}
X(18755) = crossdifference of every pair of points on line {523, 2487}
X(18755) = crosssum of X(i) and X(j) for these (i,j): {115, 514}, {513, 16592}, {523, 6627}
X(18755) = tangential-isogonal conjugate of X(16681)
X(18755) = Brocard-circle-inverse of X(33863)
X(18755) = polar conjugate of isotomic conjugate of X(22139)
X(18755) = barycentric product X(i)*X(j) for these {i,j}: {1, 846}, {3, 4213}, {6, 1654}, {31, 17762}, {35, 14844}, {42, 6626}, {55, 17084}, {71, 2905}, {249, 6627}, {2664, 8937}
X(18755) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6625}, {31, 13610}, {32, 2248}, {846, 75}, {1654, 76}, {2200, 15377}, {4213, 264}, {6626, 310}, {6627, 338}, {17084, 6063}, {17762, 561}
X(18755) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 2271, 6), (6, 1030, 2305), (6, 5023, 4252), (6, 15815, 5022), (32, 386, 6), (35, 213, 17735), (39, 4251, 6), (284, 2092, 6), (386, 4262, 32), (572, 4263, 6), (584, 4261, 6), (1333, 4272, 6), (1654, 17689, 6626), (2220, 5153, 6), (2245, 4273, 6), (2278, 4277, 6), (4251, 4256, 39), (4255, 4258, 6), (4266, 5114, 6), (4270, 5019, 6), (4272, 17454, 1333), (4285, 5035, 6), (5105, 16946, 6)
X(18756) lies on the cubic K1006 and these lines: {1, 21}, {6, 9403}, {41, 904}, {42, 16372}, {172, 1918}, {237, 2187}, {748, 17030}, {5255, 8622}
X(18756) = isogonal conjugate of X(18298)
X(18756) = X(i)-Ceva conjugate of X(j) for these (i,j): {172, 41}, {1918, 31}
X(18756) = crossdifference of every pair of points on line {661, 4374}
X(18756) = X(55)-beth conjugate of X(16372)
X(18756) = barycentric product X(i)*X(j) for these {i,j}: {6, 1045}, {31, 1655}, {662, 9402}
X(18756) = barycentric quotient X(i)/X(j) for these {i,j}: {1045, 76}, {1655, 561}, {9402, 1577}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (595, 1923, 31)
X(18757) lies on the cubic K1006 and these lines: {1, 1326}, {42, 172}, {213, 7122}, {1967, 18268}, {2107, 2112}
X(18757) = isogonal conjugate of X(17762)
X(18757) = X(i)-cross conjugate of X(j) for these (i,j): {904, 7121}, {1333, 31}
X(18757) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17762}, {2, 1654}, {8, 17084}, {10, 6626}, {69, 4213}, {75, 846}, {306, 2905}, {319, 14844}, {4590, 6627}
X(18757) = barycentric product X(i)*X(j) for these {i,j}: {1, 2248}, {6, 13610}, {28, 15377}, {31, 6625}
X(18757) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17762}, {31, 1654}, {32, 846}, {604, 17084}, {1333, 6626}, {1973, 4213}, {2203, 2905}, {2248, 75}, {6625, 561}, {13610, 76}
X(18758) lies on the cubic K1006 and these lines: {1, 3}, {32, 2209}, {39, 2309}, {42, 237}, {43, 11328}, {100, 17752}, {172, 18265}, {213, 904}, {1197, 3117}, {1755, 4531}, {1923, 8022}, {2200, 9417}, {3720, 14096}, {8844, 17760}, {16604, 16683}
X(18758) = isogonal conjugate of X(18299)
X(18758) = X(i)-Ceva conjugate of X(j) for these (i,j): {172, 213}, {18265, 2223}
X(18758) = crossdifference of every pair of points on line {650, 14296}
X(18758) = crosssum of X(i) and X(j) for these (i,j): {2, 3056}, {693, 4459}
X(18758) = X(643)-beth conjugate of X(17752)
X(18758) = barycentric product X(i)*X(j) for these {i,j}: {6, 17792}, {31, 17760}, {292, 8844}, {6376, 18269}
X(18758) = barycentric quotient X(i)/X(j) for these {i,j}: {8844, 1921}, {17760, 561}, {17792, 76}, {18269, 87}
X(18759) lies on the cubic K1006 and these lines: {1, 3506}, {32, 904}, {41, 18038}, {56, 58}, {101, 10799}, {172, 18262}, {213, 7122}, {1492, 6645}, {1691, 2175}, {2174, 4531}
X(18759) = isogonal conjugate of X(18760)
X(18759) = X(172)-Ceva conjugate of X(32)
X(18759) = X(334)-isoconjugate of X(16366)
X(18759) = barycentric product X(i)*X(j) for these {i,j}: {6, 8424}, {31, 17739}
X(18759) = barycentric quotient X(i)/X(j) for these {i,j}: {8424, 76}, {14599, 16366}, {17739, 561}
X(18759) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (904, 1933, 32)
X(18760) lies on the cubic K744 and these lines: {1909, 3509}, {2321, 17760}
X(18760) = isogonal conjugate of X(18759)
X(18760) = isotomic conjugate of X(8424)
X(18760) = X(257)-cross conjugate of X(76)
X(18760) = X(i)-isoconjugate of X(j) for these (i,j): {31, 8424}, {32, 17739}
X(18760) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8424}, {75, 17739}, {16366, 1914}
Centers X(18761)-X(18770) were contributed by César Lozada, May 10, 2018.
X(18761) lies on these lines: {1,1898}, {3,1698}, {4,2975}, {5,6256}, {30,958}, {35,18518}, {36,18492}, {55,5441}, {56,381}, {80,11509}, {104,3091}, {119,6833}, {191,12702}, {355,1012}, {376,5260}, {382,3428}, {405,18481}, {515,3560}, {517,3927}, {912,12559}, {944,6912}, {952,11496}, {956,12699}, {993,6985}, {999,9612}, {1376,18357}, {1385,1490}, {1470,10826}, {1478,6841}, {1482,5693}, {1657,5584}, {1699,10680}, {1706,3579}, {2829,6917}, {3303,18526}, {3304,12611}, {3545,5253}, {3556,18400}, {3583,10966}, {3587,5234}, {3601,18528}, {3845,11194}, {4293,6849}, {4297,6883}, {4857,18543}, {5080,6845}, {5204,18515}, {5217,18524}, {5229,6866}, {5450,6911}, {5694,5779}, {5731,6920}, {5790,10310}, {5818,6909}, {5881,10679}, {5887,11682}, {5903,7701}, {6668,6862}, {6713,6944}, {6824,12667}, {6837,12115}, {6900,12248}, {6906,11499}, {6914,11500}, {6957,10785}, {6974,10786}, {7951,18542}, {7987,18529}, {8068,10742}, {8227,16203}, {8666,18483}, {8727,10526}, {10058,11501}, {10085,10202}, {10198,16617}, {10483,18406}, {10864,18443}, {11108,13624}, {11492,18497}, {11493,18495}, {11495,15704}, {11522,12001}
X(18761) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18480, 18491), (5, 12114, 10269), (355, 1012, 11248), (12773, 18493, 3304), (13743, 18525, 55)
X(18762) lies on these lines: {2,6221}, {4,3591}, {5,6}, {20,3317}, {140,3071}, {323,15233}, {371,3628}, {372,546}, {381,3069}, {382,6446}, {547,590}, {549,6411}, {550,5420}, {631,1132}, {632,1151}, {640,3631}, {1124,10592}, {1152,3627}, {1328,8703}, {1335,10593}, {1478,13955}, {1479,13954}, {1587,3851}, {1588,1656}, {1592,15066}, {3068,5055}, {3070,3850}, {3090,3311}, {3091,3312}, {3146,6450}, {3299,3614}, {3301,7173}, {3367,10646}, {3392,10645}, {3525,6449}, {3526,6445}, {3529,6456}, {3544,6428}, {3545,7586}, {3583,13958}, {3594,3857}, {3619,11314}, {3845,6438}, {3853,6481}, {5054,9541}, {5056,7582}, {5066,6564}, {5068,7581}, {5070,9540}, {5071,7585}, {5072,6418}, {5076,6408}, {5079,6417}, {5418,6437}, {6409,14869}, {6410,15704}, {6419,12812}, {6420,12811}, {6427,13886}, {6433,11539}, {6435,10109}, {6441,13846}, {6454,12102}, {6455,10303}, {6477,12101}, {6480,16239}, {6497,17538}, {6677,8281}, {7968,18357}, {8253,15699}, {9818,13943}, {9955,13936}, {10194,15712}, {10297,18459}, {10895,13962}, {10896,13963}, {11316,12322}, {11488,18586}, {12699,13947}, {13938,18502}, {13940,18491}, {13942,18492}, {13946,18500}, {13952,18516}, {13959,18525}, {13964,18542}, {13965,18544}, {13971,18480}, {15018,15234}
X(18762) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 13941, 6398), (4, 13951, 13966), (5, 6, 18538), (5, 486, 7584), (5, 5874, 6290), (5, 7584, 7583), (6, 18538, 7583), (546, 13993, 372), (1588, 1656, 8981), (3071, 10577, 140), (6398, 13941, 13966), (6398, 13951, 13941), (6561, 8252, 549), (7584, 18538, 6), (11542, 11543, 7584)
X(18763) lies on these lines: {40,6127}, {3869,3940}
X(18764) lies on the line {16806,16808}
X(18765) lies on the line {16807,16809}
X(18766) lies on these lines: {672,6244}, {991,999}
X(18767) lies on the line {220,6244}
X(18768) lies on these lines: {2,39}, {98,7781}, {543,9873}, {698,1352}, {736,12251}, {1569,6337}, {7694,7758}, {7747,14645}
X(18768) = {X(76), X(194)}-harmonic conjugate of X(3767)
X(18769) lies on these lines: {2,32}, {5480,13111}, {11257,12252}
X(18769) = {X(2896), X(8150)}-harmonic conjugate of X(13086)
X(18770) lies on the line {1157,8154}
X(18770) = reflection of X(1157) in X(8154)
Suppose that P = p : q : r (barycentyrics) is a point in the plane of a triangle ABC, and let A'B'C' be the cevian triangle of P. Let A'' be the point, other than P, of the interserction of the circumcircles of PBC' and PCB', and define B'' and C'' cyclically. Then A''B''C'' is perspective to ABC, and the perspector is the point
f(P) = a2(p + q)(p + r) : b2(q + r)(q + p) : c2(r + p)(r + q).
The appearance of (i,j) in the following list means that f(X(i)) = X(j): (1,58), (2,6), (3,54), (4,4), (5,1173), (6,251), (7,57), (8,1), (9,1174), (10,1126), (11,18771), (12,18772), (13,16459), (14,16460), (20,3), (21,1175), (22,1176), (23,1177), (30,74), (38,1178), (40,947), (52,1179), (54,1166), (55,3449), (56,3450), (57,3451), (58,3453), (63,284), (65,961), (66,18018), (67,10415), (68,847), (69,2), (72,943), (74,10419), (75,81), (76,83), (78,1167), (80,1168), (81,1169), (85,1170), (86,1171), (92,1172), (95,288), (98,2065), (99,249), (100,59), (101,15378), (102,15379), (103,15380), (104,15381), (105,15382), (106,15383), (107,15384), (108,15385), (109,15386), (110,250), (111,15387), (112,15388), etc.
Let "conj" abbreviate "conjugate"; then
f(P) = complement of isotomic conj of cyclocevian conj of isotomic conj of P
f(P) = complement of anticomplementary conj of P
f(P) = isogonal conj of midpoint of X(2) and (reflection of P in X(2))
f(P) = isogonal conj of midpoint of X(3) and (reflection of P in X(5))
f(P) = isogonal conj of midpoint of X(4) and (reflection of P in X(3))
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27654.
X(18771) lies on these lines: {6, 1618}, {7, 7336}, {59, 3271}, {518, 5048}, {672, 5537}, {1458, 5193}, {5091, 9309}
X(18771) = isogonal conjugate of X(3035)
X(18771) = trilinear pole of the line {665, 9259}
See X(18771) and Antreas Hatzipolakis and César Lozada, Hyacinthos 27654.
X(18772) lies on these lines: {8, 6058}, {60, 181}, {960, 5260}, {2269, 3746}, {4267, 5172}
X(18772) = isogonal conjugate of X(4999)
X(18772) = X(92)-isoconjugate of X(22056)
See Bernard Gibert, Q142.
If you have GeoGebra, you can view X(18773)&X(18774) .
X(18773) lies on the Feuerbach hyperbola of the tangential triangle (i.e., the Stammler hypoerbola), the Salmon quartic Q142, the cubics K035 and K150, and on this line: {187,237}
X(18773) = reflection of X(18774) in X(5027)
X(18773) = X(99)-Ceva conjugate of X(18774)
X(18773) = X(9427)-cross conjugate of X(18774)
X(18773) = X(4602)-isoconjugate of X(18774)
X(18773) = X(3231)-Hirst inverse of X(18774)
X(18773) = X(6)-vertex conjugate of X(18774)
X(18773) = barycentric quotient X(9426)/X(18774)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (187, 5106, 18774), (669, 887, 18774)
See X(18774) and Bernard Gibert, Q142.
X(18774) lies on the Feuerbach hyperbola of the tangential triangle, the curve Q142, the cubics K035 and K150, and on this line: {187,237}
X(18774) = reflection of X(18773) in X(5027)
X(18774) = X(99)-Ceva conjugate of X(18773)
X(18774) = X(9427)-cross conjugate of X(18773)
X(18774) = X(4602)-isoconjugate of X(18773)
X(18774) = X(3231)-Hirst inverse of X(18773)
X(18774) = X(6)-vertex conjugate of X(18773)
X(18774) = barycentric quotient X(9426)/X(18773)
X(18774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (187, 5106, 18773), (669, 887, 18773)
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27657.
X(18775) lies on these lines: {2,6082}, {6,2482}, {597,1499}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27657.
X(18776) lies on these lines: {3,11659}, {6,13}, {15,15743}, {396,523}, {5917,6775}, {5994,6772}, {9214,11085}, {11485,15442}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27657.
X(18777) lies on these lines: {3,11658}, {6,13}, {16,11586}, {395,523}, {5916,6772}, {5995,6775}, {9214,11080}, {11486,15441}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27657.
X(18778) lies on these lines: {6,15526}, {525,5894}
See Tran Quang Hung and Angel Montesdeoca, Hyacinthos 27657.
X(18779) lies on these lines: {6,281}, {522,1158}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27662.
X(18780) lies on these lines: {30, 113}, {74, 1989}, {1986, 1990}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27662.
X(18781) lies on these lines: {30, 146}, {74, 1989}, {94, 10264}
X(18782) lies on these lines: {4,7}, {46,12764}, {55,381}, {1479,17718}, {3579,6928}, {5122,10431}, {7742,10896}, {12611,13274}
X(18782) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3583, 18406, 9668)
X(18783) lies on the cubics K771 and K1025 and on these lines:
{350, 3509}, {672, 1282}, {846, 8934}, {1914, 18262}, {2223, 16514}, {8868, 17739}, {17731, 18206}
X(18783) = isogonal conjugate of X(17738)
X(18783) = X(1911)-cross conjugate of X(1)
X(18783) = crosspoint of X(2109) and X(9500)
X(18783) = X(i)-he conjugate of X(j) for these (i,j): {238, 1757}, {291, 2108}
X(18783) = X(2113)-Hirst inverse of X(9472)
X(18783) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17738}, {2, 8301}, {75, 2112}, {239, 9470}, {1914, 18034}
X(18783) = barycentric product X(i)*X(j) for these {i,j}: {1, 2113}, {291, 9472}, {334, 18264}
X(18783) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17738}, {31, 8301}, {32, 2112}, {291, 18034}, {1911, 9470}, {2113, 75}, {9472, 350}, {18264, 238}
X(18784) lies on the cubics K1006 and K1025 and on these lines:
{9, 6626}, {172, 18262}, {846, 1334}, {1282, 8937}, {1909, 3509}, {8868, 17738}, {18755, 18758}
X(18784) = isogonal conjugate of X(17739)
X(18784) = X(904)-cross conjugate of X(1)
X(18784) = X(7061)-he conjugate of X(9)
X(18784) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17739}, {2, 8424}, {76, 18759}
X(18784) = barycentric product X(i)*X(j) for these {i,j}: {31, 18760}, {291, 16366}
X(18784) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17739}, {31, 8424}, {560, 18759}, {16366, 350}, {18760, 561}
X(18785) lies on the cubic K1025 and these lines:
{1, 41}, {6, 13476}, {9, 75}, {10, 1018}, {19, 2195}, {37, 4068}, {57, 2279}, {65, 213}, {82, 4628}, {158, 7719}, {225, 2333}, {292, 659}, {596, 5282}, {666, 2311}, {672, 3008}, {759, 919}, {897, 16548}, {910, 2223}, {969, 1814}, {1020, 1400}, {1024, 2161}, {1026, 4876}, {1416, 1451}, {1462, 2285}, {1581, 2664}, {1697, 14942}, {1730, 5364}, {1766, 8769}, {1781, 13610}, {2214, 16972}, {2217, 16968}, {3124, 6044}, {3290, 16782}, {3730, 14267}, {3731, 17038}, {4674, 16611}, {9278, 16369}, {17739, 18298}
X(18785) = isogonal conjugate of X(18206)
X(18785) = isotomic conjugate of X(18157)
X(18785) = X(i)-Ceva conjugate of X(j) for these (i,j): {666, 1027}, {673, 13576}, {919, 1024}
X(18785) = X(3747)-cross conjugate of X(1)
X(18785) = cevapoint of X(37) and X(2238)
X(18785) = crosspoint of X(105) and X(673)
X(18785) = trilinear pole of line {42, 661}
X(18785) = crossdifference of every pair of points on line {2254, 8299}
X(18785) = crosssum of X(518) and X(672)
X(18785) = X(9)-beth conjugate of X(4557)
X(18785) = X(105)-daleth conjugate of X(1)
X(18785) = X(i)-he conjugate of X(j) for these (i,j): {2481, 672}, {7233, 3509}
X(18785) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 18206}, {2, 672}, {661, 2254}, {3252, 1757}, {17451, 17799}, {17719, 1025}
X(18785) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18206}, {2, 3286}, {3, 15149}, {21, 241}, {27, 1818}, {31, 18157}, {58, 3912}, {81, 518}, {86, 672}, {99, 665}, {105, 16728}, {110, 918}, {274, 2223}, {283, 5236}, {284, 9436}, {310, 9454}, {333, 1458}, {593, 3932}, {662, 2254}, {741, 17755}, {757, 3930}, {883, 7252}, {905, 4238}, {926, 4573}, {1014, 3693}, {1019, 1026}, {1025, 3737}, {1171, 4966}, {1333, 3263}, {1412, 3717}, {1434, 2340}, {1444, 5089}, {1790, 1861}, {1812, 1876}, {2283, 4560}, {2284, 7192}, {2356, 17206}, {3675, 4567}, {4088, 4556}, {6385, 9455}
X(18785) = barycentric product X(i)*X(j) for these {i,j}: {1, 13576}, {10, 105}, {37, 673}, {42, 2481}, {65, 14942}, {213, 18031}, {226, 294}, {306, 8751}, {321, 1438}, {661, 666}, {885, 4551}, {919, 1577}, {927, 4041}, {1024, 4552}, {1027, 3952}, {1416, 3701}, {1427, 6559}, {1441, 2195}, {1462, 2321}, {1814, 1826}, {1897, 10099}, {3120, 5377}, {3709, 4528}, {9503, 17747}
X(18785) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 18157}, {6, 18206}, {10, 3263}, {19, 15149}, {31, 3286}, {37, 3912}, {42, 518}, {65, 9436}, {105, 86}, {210, 3717}, {213, 672}, {228, 1818}, {294, 333}, {512, 2254}, {661, 918}, {666, 799}, {672, 16728}, {673, 274}, {756, 3932}, {798, 665}, {884, 3737}, {885, 18155}, {919, 662}, {927, 4625}, {1024, 4560}, {1027, 7192}, {1334, 3693}, {1400, 241}, {1402, 1458}, {1416, 1014}, {1438, 81}, {1462, 1434}, {1500, 3930}, {1814, 17206}, {1824, 1861}, {1880, 5236}, {1918, 2223}, {1962, 4966}, {2195, 21}, {2205, 9454}, {2238, 17755}, {2333, 5089}, {2481, 310}, {3122, 3675}, {3747, 8299}, {3930, 4437}, {4551, 883}, {4557, 1026}, {4559, 1025}, {4705, 4088}, {4729, 4925}, {4849, 4899}, {5377, 4600}, {8750, 4238}, {8751, 27}, {10099, 4025}, {13576, 75}, {14942, 314}, {18031, 6385}
X(18785) = {X(105),X(294)}-harmonic conjugate of X(1438)
X(18786) lies on the cubics K1025 and K1026 and on these lines:
{1, 257}, {9, 43}, {57, 87}, {200, 4451}, {261, 1178}, {659, 3737}, {694, 3509}, {695, 3496}, {978, 3865}, {1282, 16363}, {1581, 2664}, {1697, 7220}, {1740, 3863}, {1757, 1967}, {1759, 2233}, {2236, 17596}, {2665, 18206}, {2999, 4835}, {3570, 3961}, {3684, 16514}, {3685, 3783}, {4076, 5524}, {5272, 7249}
X(18786) = isogonal conjugate of X(18787)
X(18786) = X(694)-Ceva conjugate of X(1)
X(18786) = X(4366)-cross conjugate of X(1)
X(18786) = cevapoint of X(2238) and X(4093)
X(18786) = crossdifference of every pair of points on line {2295, 4367}
X(18786) = crosssum of X(385) and X(6645)
X(18786) = X(i)-he conjugate of X(j) for these (i,j): {2, 43}, {6, 9}, {893, 17596}, {3224, 46}
X(18786) = X(i)-zayin conjugate of X(j) for these (i,j): {511, 43}, {665, 3287}, {2086, 5539}, {3229, 9}, {5113, 3737}
X(18786) = trilinear product of vertices of 1st Sharygin triangle
X(18786) = X(i)-isoconjugate of X(j) for these (i,j): {171, 291}, {172, 335}, {292, 894}, {295, 7009}, {334, 7122}, {660, 4367}, {694, 6645}, {741, 1215}, {813, 4369}, {876, 4579}, {1909, 1911}, {1920, 1922}, {1926, 18267}, {2311, 4032}, {2330, 7233}, {3572, 18047}, {3963, 18268}, {4589, 7234}, {4876, 7175}, {7077, 7176}, {7205, 18265}
X(18786) = X(256)-Hirst inverse of X(893)
X(18786) = X(i)-he conjugate of X(j) for these (i,j): {2, 43}, {6, 9}, {893, 17596}, {3224, 46}
X(18786) = X(i)-zayin conjugate of X(j) for these (i,j): {511, 43}, {665, 3287}, {2086, 5539}, {3229, 9}, {5113, 3737}
X(18786) = barycentric product X(i)*X(j) for these {i,j}: {1, 17493}, {238, 257}, {239, 256}, {350, 893}, {812, 3903}, {904, 1921}, {1178, 3948}, {1429, 4451}, {1431, 3975}, {1432, 3685}, {1581, 4366}, {1914, 7018}, {1916, 8300}, {2201, 7019}, {3684, 7249}, {4010, 4603}, {4037, 7303}, {4455, 7260}
X(18786) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 894}, {239, 1909}, {256, 335}, {257, 334}, {350, 1920}, {659, 4369}, {740, 3963}, {812, 4374}, {862, 1840}, {893, 291}, {904, 292}, {1284, 4032}, {1428, 7175}, {1429, 7176}, {1432, 7233}, {1447, 7196}, {1580, 6645}, {1914, 171}, {2201, 7009}, {2210, 172}, {2238, 1215}, {3573, 18047}, {3684, 7081}, {3685, 17787}, {3747, 2295}, {3903, 4562}, {3948, 1237}, {4093, 16587}, {4366, 1966}, {4375, 14296}, {4433, 4095}, {4435, 3907}, {4594, 4639}, {4603, 4589}, {4810, 4842}, {7104, 1911}, {7116, 295}, {8300, 385}, {8632, 4367}, {8789, 18267}, {10030, 7205}, {14599, 7122}, {17493, 75}
X(18786) = {X(257),X(904)}-harmonic conjugate of X(1)
X(18787) lies on the cubic K1025 and K1026 and on these lines:
{1, 335}, {9, 87}, {43, 57}, {269, 7233}, {334, 10436}, {660, 1757}, {694, 3509}, {741, 1961}, {813, 6015}, {846, 16362}, {894, 7184}, {1018, 5539}, {1045, 13610}, {1215, 8033}, {1740, 3862}, {4128, 4154}, {4518, 5268}, {5018, 9416}, {5378, 7312}
X(18787) = isogonal conjugate of X(18786)
X(18787) = X(i)-cross conjugate of X(j) for these (i,j): {385, 1}, {2236, 17103}, {4447, 171}
X(18787) = cevapoint of X(385) and X(6645)
X(18787) = crosssum of X(2238) and X(4093)
X(18787) = trilinear pole of line {2295, 4367}
X(18787) = X(i)-aleph conjugate of X(j) for these (i,j): {291, 9}, {292, 43}, {335, 1759}, {660, 1018}, {4876, 10860}, {7077, 170}
X(18787) = X(i)-he conjugate of X(j) for these (i,j): {291, 2664}, {292, 1757}, {2113, 43}
X(18787) = X(i)-zayin conjugate of X(j) for these (i,j): {39, 2238}, {512, 659}, {3252, 2664}
X(18787) = X(i)-isoconjugate of X(j) for these (i,j): {6, 17493}, {238, 256}, {239, 893}, {242, 7015}, {257, 1914}, {350, 904}, {659, 3903}, {694, 4366}, {740, 1178}, {1428, 4451}, {1431, 3685}, {1432, 3684}, {1581, 8300}, {1921, 7104}, {2210, 7018}, {4455, 4594}
X(18787) = barycentric product X(i)*X(j) for these {i,j}: {171, 335}, {172, 334}, {291, 894}, {292, 1909}, {337, 7119}, {660, 4369}, {741, 3963}, {813, 4374}, {876, 18047}, {1237, 18268}, {1581, 6645}, {1911, 1920}, {2329, 7233}, {2533, 4584}, {4367, 4562}, {4444, 4579}, {4518, 7175}, {4639, 7234}, {4876, 7176}, {5378, 7200}, {7077, 7196}, {14603, 18267}
X(18787) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17493}, {171, 239}, {172, 238}, {291, 257}, {292, 256}, {335, 7018}, {813, 3903}, {894, 350}, {1215, 3948}, {1580, 4366}, {1691, 8300}, {1909, 1921}, {1911, 893}, {1922, 904}, {2196, 7015}, {2295, 740}, {2329, 3685}, {2330, 3684}, {3287, 3716}, {3805, 4486}, {4164, 4375}, {4367, 812}, {4369, 3766}, {4447, 17755}, {4477, 4148}, {4579, 3570}, {4584, 4594}, {4589, 7260}, {4876, 4451}, {6645, 1966}, {7081, 3975}, {7119, 242}, {7122, 1914}, {7175, 1447}, {7176, 10030}, {7196, 18033}, {14598, 7104}, {17787, 4087}, {18047, 874}, {18267, 9468}, {18268, 1178}
X(18787) = {X(335),X(1911)}-harmonic conjugate of X(1)
X(18788) lies on the cubic K1025 and these lines:
{1, 3}, {9, 17792}, {10, 7379}, {37, 8245}, {43, 2082}, {100, 1959}, {511, 1757}, {516, 3685}, {674, 16560}, {846, 1334}, {984, 1350}, {1282, 2340}, {1376, 3061}, {1580, 9323}, {1581, 2664}, {1698, 7380}, {1699, 2887}, {1709, 17742}, {1742, 1766}, {1961, 4220}, {2329, 4640}, {2784, 6542}, {2938, 13610}, {2944, 4300}, {2947, 18596}, {2951, 7996}, {3309, 4790}, {3430, 5293}, {3509, 4447}, {3674, 13405}, {3769, 3905}, {4039, 9860}, {4219, 17442}, {5691, 7270}, {7081, 17739}, {9004, 18735}, {9746, 16831}, {9778, 17316}, {10164, 17023}, {10860, 16557}, {12329, 18161}
X(18788) = reflection of X(1757) in X(6211)
X(18788) = X(i)-Ceva conjugate of X(j) for these (i,j): {3509, 1757}, {4447, 2664}, {4876, 1}
X(18788) = crosspoint of X(660) and X(7045)
X(18788) = crosssum of X(659) and X(2310)
X(18788) = X(i)-he conjugate of X(j) for these (i,j): {8, 165}, {9, 40}, {2319, 9}, {17787, 8931}
X(18788) = X(i)-zayin conjugate of X(j) for these (i,j): {3693, 165}, {7077, 1757}
X(18788) = X(9)-Hirst inverse of X(17792)
X(18788) = barycentric product X(335)*X(8932)
X(18788) = barycentric quotient X(8932)/X(239)
X(18788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (55, 7146, 1), (2340, 7291, 1282), (3507, 17799, 1757)
X(18789) lies on the cubic K1025 and this line: {57, 846}
X(18790) lies on the cubic K1025) and these lines:
{1, 3506}, {9, 8245}, {57, 1929}, {846, 8847}, {1282, 8853}, {1757, 17798}, {1768, 5150}, {1781, 13610}, {9499, 18206}
X(18790) = X(3509)-Ceva conjugate of X(1)
X(18790) = barycentric product X(i)*X(j) for these {i,j}: {239, 8933}, {894, 8936}
X(18790) = barycentric quotient X(i)/X(j) for these {i,j}: {8933, 335}, {8936, 257}
X(18791) lies on the cubic K1025 and these lines: {9, 86}, {1002, 1282}, {2938, 13610}
X(18791) = barycentric quotient X(9279)/X(4804)
X(18792) lies on the cubic K1026 and these lines:
{1, 75}, {2, 5145}, {6, 474}, {8, 17178}, {10, 16738}, {21, 3551}, {36, 238}, {38, 18601}, {42, 8025}, {43, 81}, {58, 87}, {244, 16753}, {284, 16779}, {333, 16569}, {386, 17379}, {404, 4279}, {518, 16726}, {596, 17142}, {660, 1757}, {662, 5009}, {726, 3009}, {741, 3510}, {899, 16704}, {982, 16700}, {984, 16696}, {1014, 4334}, {1125, 2309}, {1201, 11115}, {1738, 17197}, {2106, 2108}, {2229, 3231}, {3061, 16716}, {3097, 4476}, {3120, 17174}, {3248, 4974}, {3293, 4649}, {3550, 13588}, {3576, 10892}, {3725, 4697}, {3751, 18164}, {3821, 17202}, {3944, 17182}, {4184, 8616}, {4383, 16409}, {4551, 5061}, {5223, 18186}, {5253, 10457}, {5272, 17194}, {5333, 10458}, {7032, 16825}, {10459, 17589}, {16610, 18191}, {16736, 17063}, {16748, 17176}, {17167, 17889}, {17185, 17596}, {17349, 17749}
X(18792) = cevapoint of X(1575) and X(3009)
X(18792) = crossdifference of every pair of points on line {37, 798}
X(18792) = crosssum of X(i) and X(j) for these (i,j): {42, 2238}, {659, 8054}
X(18792) = X(i)-Ceva conjugate of X(j) for these (i,j): {741, 1}, {4589, 1019}
X(18792) = X(i)-aleph conjugate of X(j) for these (i,j): {1, 13174}, {4584, 3570}
X(18792) = X(86)-daleth conjugate of X(1)
X(18792) = X(i)-he conjugate of X(j) for these (i,j): {58, 6}, {81, 3216}, {9506, 2664}, {12031, 3737}
X(18792) = X(i)-zayin conjugate of X(j) for these (i,j): {292, 2238}, {1755, 1743}, {3286, 3216}, {3747, 43}, {8632, 661}
X(18792) = X(17793)-cross conjugate of X(1)
X(18792) = X(i)-isoconjugate of X(j) for these (i,j): {10, 727}, {42, 3226}, {65, 8851}, {512, 8709}
X(18792) = X(i)-vertex conjugate of X(j) for these (i,j): {1, 16695}, {16695, 1}
X(18792) = barycentric product X(i)*X(j) for these {i,j}: {81, 726}, {86, 1575}, {274, 3009}, {333, 1463}, {662, 3837}, {799, 6373}
X(18792) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 3226}, {284, 8851}, {662, 8709}, {726, 321}, {1333, 727}, {1463, 226}, {1575, 10}, {3009, 37}, {3837, 1577}, {6373, 661}, {8850, 16609}, {17475, 740}, {17793, 3948}
X(18792) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 17187, 18169), (86, 3736, 1), (87, 978, 16468), (2667, 5625, 1), (16569, 18192, 333), (16736, 18165, 17063)
X(18793) lies on the cubic K1026 and these lines:L
{1, 668}, {2, 8050}, {31, 43}, {42, 3952}, {213, 1018}, {291, 659}, {741, 3510}, {923, 5380}, {1042, 4566}, {1402, 4551}, {1743, 3402}, {1757, 1967}, {1783, 1973}, {3112, 18093}, {3216, 16476}, {16569, 16576}, {18754, 18757}
X(18793) = cevapoint of X(i) and X(j) for these (i,j): {42, 2238}, {659, 8054}
X(18793) = crosssum of X(1575) and X(3009)
X(18793) = X(3226)-daleth conjugate of X(1)
X(18793) = X(i)-he conjugate of X(j) for these (i,j): {727, 1575}, {2109, 43}
X(18793) = X(6)-zayin conjugate of X(1575)
X(18793) = X(i)-cross conjugate of X(j) for these (i,j): {740, 1}, {4455, 1018}
X(18793) = X(i)-isoconjugate of X(j) for these (i,j): {21, 1463}, {58, 726}, {81, 1575}, {86, 3009}, {99, 6373}, {110, 3837}, {741, 17793}
X(18793) = trilinear pole of line {37, 798}
X(18793) = barycentric product X(i)*X(j) for these {i,j}: {37, 3226}, {226, 8851}, {321, 727}, {661, 8709}
X(18793) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 726}, {42, 1575}, {213, 3009}, {661, 3837}, {727, 81}, {798, 6373}, {1400, 1463}, {2238, 17793}, {3226, 274}, {3747, 17475}, {8709, 799}, {8851, 333}
X(18794) lies on the cubics K771 and K1026 and on these lines:
{1, 335}, {6, 1045}, {31, 43}, {32, 6196}, {87, 572}, {171, 1979}, {238, 2110}, {1914, 3510}, {2209, 4579}, {3972, 4116}
X(18794) = X(i)-Ceva conjugate of X(j) for these (i,j): {1914, 1}, {3510, 18754}
X(18794) = X(1581)-isoconjugate of X(16361)
X(18794) = X(i)-aleph conjugate of X(j) for these (i,j): {1, 3509}, {6, 2664}, {365, 1757}, {18753, 3510}
X(18794) = X(i)-he conjugate of X(j) for these (i,j): {6, 2108}, {238, 43}, {2210, 1740}, {9472, 2664}
X(18794) = X(3747)-zayin conjugate of X(2108)
X(18794) = X(31)-Hirst inverse of X(8300)
X(18794) = barycentric product X(894)*X(16363)
X(18794) = barycentric quotient X(i)/X(j) for these {i,j}: {1691, 16361}, {16363, 257}
X(18794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (32, 6196, 18754), (1911, 4366, 1), (7168, 18274, 18754)
X(18795) lies on the cubics K766 and K1026, and on these lines:
{350, 18275}, {726, 3783}, {1575, 2664}, {1914, 3510}, {2106, 2108}, {2111, 2665}, {8875, 18754}
X(18795) = X(335)-cross conjugate of X(1)
X(18795) = X(171)-isoconjugate of X(16363)
X(18795) = X(i)-he conjugate of X(j) for these (i,j): {239, 2664}, {2145, 43}
X(18795) = barycentric product X(1916)*X(16361)
X(18795) = barycentric quotient X(i)/X(j) for these {i,j}: {893, 16363}, {16361, 385}
X(18796) lies on the cubic K1027 and these lines:
{1, 7096}, {5, 182}, {32, 14820}, {49, 3095}, {110, 7796}, {184, 3456}, {211, 14575}, {1092, 8922}, {3492, 3734}, {3506, 7751}, {7869, 9306}, {9544, 13571}, {14574, 15270}
X(18796) = X(76)-Ceva conjugate of X(32)
X(18796) = barycentric product X(2206)X(4174)
X(18797) lies on the cubic K1027 and on this line: {2979, 7768}
X(18797) = X(32)-cross conjugate of X(76)
X(18797) = barycentric quotient X(313)/X(4174)
X(18798) lies on the cubic K1027 and these lines: {1, 1670}, {76, 1423}, {1676, 1759}
X(18798) = isogonal conjugate of X(18799)
X(18798) = X(67)-isoconjugate of X(1672)
X(18798) = barycentric product X(561)*X(1673)
X(18798) = barycentric quotient X(i)/X(j) for these {i,j}: {560, 1672}, {1673, 31}
X(18798) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (76, 3403, 18799), (1423, 3503, 18799), (3501, 3508, 18799)
X(18799) lies on the cubic K1027 and these lines: {1, 1671}, {76, 1423}, {1677, 1759}
X(18799) = isogonal conjugate of X(18798)
X(18799) = X(76)-isoconjugate of X(1673)
X(18799) = barycentric product X(561)*X(1672)
X(18799) = barycentric quotient X(i)/X(j) for these {i,j}: {560, 1673}, {1672, 31}
X(18799) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (76, 3403, 18798), (1423, 3503, 18798), (3501, 3508, 18798)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18800) lies on these lines: {2, 98}, {6, 543}, {99, 1285}, {115, 597}, {126, 1641}, {141, 9167}, {187, 524}, {376, 10753}, {511, 8598}, {575, 8370}, {576, 10992}, {599, 620}, {690, 15303}, {754, 12151}, {1384, 16508}, {1569, 5052}, {1995, 9966}, {2434, 15304}, {2502, 9172}, {2682, 8352}, {2793, 9135}, {2794, 5077}, {2796, 4991}, {3589, 14971}, {3618, 9166}, {4235, 5095}, {5017, 14645}, {5032, 8591}, {5050, 11632}, {5461, 10488}, {5468, 12036}, {5476, 9880}, {6321, 14848}, {7735, 9877}, {8182, 15483}, {8359, 10991}, {8369, 8550}, {9169, 10418}, {10554, 14916}, {17952, 17979}
X(18800) = midpoint of X(i) and X(j) for these {i,j}: {2, 8593}, {99, 1992}, {376, 10753}
X(18800) = reflection of X(i) in X(j) for these (i,j): (115, 597), (599, 620)
X(18800) = complement of X(11161)
X(18800) = orthoptic-circle-of-Steiner-inellipse-inverse-of X(9759)
X(18800) = barycentric quotient X(524)/X(5503)
X(18800) = X(115)-of-anti-Artzt-triangle
X(18800) = X(597)-of-anti-McCay-triangle
X(18800) = X(8370)-of-6th-anti-Brocard-triangle
X(18800) = X(8598)-of-1st-Brocard-triangle
X(18800) = center of circle {{X(i), X(j), X(k)}} for these {i, j, k}: {67, 10488, 11646}, {99, 1992, 15342}, {5026, 6593, 8787}
X(18800) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5032, 8591, 10754), (5182, 8593, 2), (13642, 13761, 2)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18801) lies on these lines: {7, 528}, {11, 7671}, {55, 5851}, {100, 12848}, {119, 15607}, {3660, 10427}, {12831, 15726}
X(18801) = reflection of X(11) in X(8255)
X(18801) = {X(12730), X(14151)}-harmonic conjugate of X(3241)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18802) lies on these lines: {8, 2829}, {11, 8256}, {56, 100}, {57, 12641}, {119, 517}, {1210, 2802}, {2098, 3035}, {3036, 3434}, {3880, 12832}, {4855, 12735}, {5083, 12640}, {12531, 17784}
X(18802) = reflection of X(i) in X(j) for these (i,j): (11, 8256), (2098, 3035)
X(18802) = {X(1145), X(1537)}-harmonic conjugate of X(6735)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18803) lies on these lines: {115, 6783}, {396, 15609}, {3180, 10409}, {5612, 11601}, {11600, 16267}
X(18803) = midpoint of X(3180) and X(10409)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18804) lies on these lines: {115, 6782}, {395, 15610}, {3181, 10410}, {5616, 11600}, {11601, 16268}
X(18804) = midpoint of X(3181) and X(10410)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18805) lies on these lines: {31, 75}, {37, 6679}, {752, 4688}, {2210, 4836}, {2887, 3739}, {4412, 5019}, {4699, 6327}
X(18805) = midpoint of X(31) and X(75)
X(18805) = reflection of X(i) in X(j) for these (i,j): (37, 6679), (2887, 3739)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27670.
X(18806) lies on the cubic K459 and these lines: {5, 141}, {6, 8149}, {32, 76}, {39, 620}, {194, 5319}, {262, 7862}, {315, 16044}, {538, 5306}, {698, 5305}, {732, 7805}, {754, 8370}, {760, 12263}, {1078, 5162}, {1916, 7828}, {2023, 7886}, {2458, 8150}, {2782, 7816}, {2794, 6248}, {3094, 7834}, {3095, 3788}, {3398, 5149}, {5028, 7808}, {5052, 7838}, {5188, 7830}, {5969, 7817}, {6194, 7800}, {6309, 7798}, {7759, 13330}, {7760, 9865}, {7761, 9821}, {7795, 9753}, {7797, 8782}, {7920, 10335}
X(18806) = midpoint of X(32) and X(76)
X(18806) = reflection of X(39) in X(6680)
X(18806) = complement of X(32452)
X(18806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (76, 6179, 9983), (5403, 5404, 5031)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27674.
X(18807) lies on these lines: {5, 128}, {1154, 14071}
See Angel Montesdeoca, HG160518.
X(18808) lies on these lines: {4,523}, {74,1300}, {93,18039}, {264,850}, {297,14977}, {393,2433}, {476,1304}, {512,16263}, {520,12111}, {525,16253}, {685,879}, {847,11704}, {877,892}, {924,12290}, {1105,6368}, {1826,4024}, {2395,6531}, {5466,16080}, {6344,10412}, {9033,10152}
See Angel Montesdeoca, HG160518.
X(18809) lies on the nine-point circle and these lines: {2,2693}, {4,477}, {5,16177}, {30,122}, {113,520}, {115,1990}, {125,403}, {127,11799}, {133,523}, {136,10151}, {235,16221}, {1552,2777}, {1553,7480}, {1560,9209}, {1596,5099}, {5520,15763}, {6761,11792}
X(18809) = reflection of X(16177) in X(5)
X(18809) = reflection of X(133) in Euler line
X(18809) = complement of X(2693)
X(18809) = inverse-in-polar-circle of X(477)
X(18809) = X(107) of reflection of Euler triangle in Euler line
Perspectors of Inconics: X(18810)-X(18831)
Let P be a point in the plane of a triangle ABC. Let
A' = reflection of P in BC, and define B' and C' cyclically;
Q = circumcenter of A'B'C' = isogonal conjugate of P;
A'' = QA'∩BC, and define B'' and C'' cyclically.
The triangle A''B''C'' is perspective to ABC. Let D(P) denote the perspector. The points P and Q are the foci of the inconic tangent to BC, CA, AB at A'', B'', C'', respectively. (Based on notes from Thanh Oai Dao, May 17, 2018)
If P = p : q : r (barycentrics), then D(P) = q r/(b2r2+ c2q2 + (b2 - c2 - a2) q r) : : , and
D(P) = isotomic conjugate of the anticomplement of (midpoint of P and isogonal conjugate of P)
D(P) = cevapoint of P and the orthocorrespondent of P
D(P) = cross conjugate of (midpoint of P and isogonal conjugate of P) and G
If P is on the infinity line, then D(P) = isotomic conjugate of P
If P on the circumcircle or infinity line, then D(P) lies on the Steiner circumellipse.
(Peter Moses, May 21, 2018)
The appearance of (i,j) in the following list means that D(X(i)) = X(j):
(67,10512), (69,10604), (74,1494), (98,290), (99,670), (100,668), (101,190), (103,18025), (105,2481}
{106,903), (107,6528), (108,18026), (109,664), (110,99), (111,671), (112,648), (511,290), (512,670), (513,668), (514,190), (516,18025), (518,2481), (519,903), (520,6528), (521,18026), (522,664), (523,99), (524,671), (525,648), (527,1121), (532,11117), (533,11118), (536,3227), (538,3228), (542,5641), (690,892), (691,892), (698,3225), (699,3225), (726,3226), (727,3226), (729,3228), (732,14970), (733,14970), (739,3227), (758,14616), (759,14616), (812,4562), (813,4562), (824,4586), (825,4586), (826,4577), (827,4577), (842,5641), (888,886), (891,889), (898,889), (900,4555), (901,4555), (918,666), (919,666), (934,4569), (1113,15164), (1114,15165), (1304,16077), (1379,6190), (1380,6189), (2291,1121), (2380,11117), (2381,11118), (2574,15164), (2575,15165), (2715,2966), (2799,2966), (3413,6190), (3414,6189), (3900,4569), (3910,6648), (4588,4597), (4777,4597), (4977,6540), (6362,6606), (6550,6635), (6551,6635), (8687,6648), (8701,6540), (9033,16077), (9136,9487), (9150,886)
X(18810) lies on these lines: {85, 527}, {1088, 1323}
X(18810) = isotomic conjugate of the anticomplement X(8255)
X(18810) = X(8255)-cross conjugate of X(2)
X(18810) = cevapoint of X(7) and X(1996)
X(18810) = Brianchon point (perspector) of inconic centered at X(8255)
X(18810) = isotomic conjugate of isogonal conjugate of vertex conjugate of X(7) and X(55)
X(18810) = barycentric quotient X(i)/X(j) for these {i,j}: {85, 5231}, {279, 4860}, {513, 17425}, {1088, 6173}, {1996, 15346}
X(18810) = X(i)-isoconjugate of X(j) for these (i,j): {101, 17425}, {1253, 4860}, {2175, 5231}, {6173, 14827}
X(18811) lies on this line: {312, 3911}
X(18811) = isotomic conjugate of X(2098)
X(18811) = cevapoint of X(8) and X(1997)
X(18811) = X(8256)-cross conjugate of X(2)
X(18811) = X(i)-cross conjugate of X(j) for these (i,j): {4462, 4554}, {8256, 2}
X(18811) = Brianchon point (perspector) of inconic centered at X(8256)
X(18811) = isotomic conjugate of isogonal conjugate of vertex conjugate of X(8) and X(56)
X(18811) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2098}, {101, 17424}, {2175, 4862}
X(18811) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2098}, {85, 4862}, {513, 17424}, {1997, 15347}
X(18812) lies on these lines: {6, 6543}, {10, 261}, {12, 86}, {313, 17731}, {314, 1089}, {333, 594}
X(18812) = isotomic conjugate of the anticomplement X(8258)
X(18812) = isotomic conjugate of the complement X(1046)
X(18812) = X(8258)-cross conjugate of X(2)
X(18812) = X(i)-isoconjugate of X(j) for these (i,j): {81, 9560}, {662, 17411}
X(18812) = cevapoint of X(i) and X(j) for these (i,j): {2, 1046}, {10, 1999}
X(18812) = trilinear pole of line {4024, 4560}
X(18812) = Brianchon point (perspector) of inconic centered at X(8258)
X(18812) = isotomic conjugate of isogonal conjugate of vertex conjugate of X(10) and X(58)
X(18812) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 9560}, {512, 17411}, {1999, 15349}
X(18813) lies on this line: {17, 622}
X(18813) = isotomic conjugate of the anticomplement X(8259)
X(18813) = X(8259)-cross conjugate of X(2)
X(18813) = cevapoint of X(61) and X(2004)
X(18814) lies on this line: {18, 621}
X(18814) = isotomic conjugate of the anticomplement X(8260)
X(18814) = X(8260)-cross conjugate of X(2)
X(18814) = cevapoint of X(62) and X(2005)
X(18815) lies on the conic {{A,B,C,X(2),X(7)}} and on these lines:
{2, 2006}, {7, 80}, {27, 653}, {75, 311}, {77, 17885}, {85, 14584}, {86, 664}, {272, 759}, {273, 2973}, {310, 4572}, {347, 7318}, {651, 16732}, {655, 673}, {675, 1447}, {1325, 14194}, {1443, 17895}, {1807, 7269}, {1944, 2989}, {2166, 3668}, {3262, 4511}, {4957, 5723}, {5936, 15065}, {6650, 17950}
X(18815) = isogonal conjugate of X(2361)
X(18815) = isotomic conjugate of X(4511)
X(18815) = cevapoint of X(i) and X(j) for these (i,j): {11, 10015}, {36, 2003}, {65, 1465}, {80, 2006}, {912, 1214}, {3911, 14584}, {4858, 14304}
X(18815) = X(i)-cross conjugate of X(j) for these (i,j): {80, 18359}, {515, 92}, {1737, 2}, {3911, 85}
X(18815) = X(75)-beth conjugate of X(664)
X(18815) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 2361}, {4040, 654}
X(18815) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2361}, {6, 2323}, {9, 7113}, {21, 3724}, {31, 4511}, {36, 55}, {37, 4282}, {41, 3218}, {50, 7110}, {80, 215}, {100, 8648}, {101, 654}, {184, 5081}, {186, 8606}, {212, 1870}, {228, 17515}, {284, 2245}, {320, 2175}, {650, 1983}, {692, 3738}, {758, 2194}, {1253, 1443}, {1464, 2328}, {1946, 4242}, {2150, 4053}, {2316, 17455}, {3063, 4585}, {3689, 16944}, {4089, 6066}, {4996, 6187}, {6149, 7073}, {14827, 17078}
X(18815) = trilinear pole of line {226, 514}
X(18815) = barycentric product X(i)*X(j) for these {i,j}: {7, 18359}, {75, 2006}, {76, 1411}, {80, 85}, {94, 1442}, {226, 14616}, {331, 1807}, {349, 759}, {655, 693}, {903, 14628}, {1434, 15065}, {1446, 6740}, {2161, 6063}, {2166, 17095}, {2222, 3261}
X(18815) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2323}, {2, 4511}, {6, 2361}, {7, 3218}, {12, 4053}, {27, 17515}, {56, 7113}, {57, 36}, {58, 4282}, {65, 2245}, {80, 9}, {85, 320}, {92, 5081}, {109, 1983}, {226, 758}, {273, 17923}, {278, 1870}, {279, 1443}, {513, 654}, {514, 3738}, {553, 4973}, {649, 8648}, {653, 4242}, {655, 100}, {664, 4585}, {693, 3904}, {759, 284}, {1088, 17078}, {1168, 2316}, {1319, 17455}, {1399, 50}, {1400, 3724}, {1411, 6}, {1427, 1464}, {1441, 3936}, {1442, 323}, {1793, 2327}, {1807, 219}, {1989, 7073}, {2003, 6149}, {2006, 1}, {2161, 55}, {2166, 7110}, {2222, 101}, {2341, 2328}, {3218, 4996}, {3668, 18593}, {3676, 3960}, {3911, 214}, {4077, 4707}, {4654, 4880}, {5219, 4867}, {5435, 4881}, {6187, 41}, {6740, 2287}, {7113, 215}, {7146, 3792}, {14584, 44}, {14616, 333}, {14628, 519}, {15065, 2321}, {18359, 8}
X(18816) lies on the Steiner circumellipse and on these lines:
{7, 264}, {63, 190}, {69, 150}, {75, 77}, {76, 14266}, {81, 648}, {99, 104}, {286, 6528}, {317, 8048}, {666, 1814}, {889, 15635}, {909, 4586}, {2401, 3227}, {2966, 14578}, {3262, 4555}, {4124, 9432}, {4569, 6063}, {4597, 17143}, {10538, 14198}
X(18816) = isotomic conjugate of X(517)
X(18816) = cevapoint of X(i) and X(j) for these (i,j): {2, 517}, {8, 4358}, {75, 320}, {2401, 15635}
X(18816) = X(i)-cross conjugate of X(j) for these (i,j): {104, 16082}, {517, 2}, {2804, 6335}, {3218, 274}, {3904, 4554}, {15635, 2401}
X(18816) = X(314)-beth conjugate of X(664)
X(18816) = X(43)-zayin conjugate of X(2183)
X(18816) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2183}, {31, 517}, {32, 908}, {41, 1465}, {42, 859}, {48, 14571}, {55, 1457}, {101, 3310}, {184, 1785}, {212, 1875}, {560, 3262}, {649, 2427}, {692, 1769}, {810, 4246}, {902, 14260}, {1361, 2342}, {1397, 6735}, {1911, 15507}, {1918, 17139}, {1919, 2397}, {2206, 17757}, {8677, 8750}
X(18816) = trilinear pole of line {2, 905}
X(18816) = polar conjugate of X(14571)
X(18816) = barycentric product X(i)*X(j) for these {i,j}: {69, 16082}, {76, 104}, {310, 2250}, {331, 1809}, {561, 909}, {668, 2401}, {693, 13136}, {1309, 15413}, {1795, 1969}, {2423, 6386}, {14578, 18022}
X(18816) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2183}, {2, 517}, {4, 14571}, {7, 1465}, {57, 1457}, {75, 908}, {76, 3262}, {81, 859}, {88, 14260}, {92, 1785}, {100, 2427}, {104, 6}, {239, 15507}, {274, 17139}, {278, 1875}, {312, 6735}, {320, 16586}, {321, 17757}, {513, 3310}, {514, 1769}, {648, 4246}, {668, 2397}, {693, 10015}, {905, 8677}, {909, 31}, {1309, 1783}, {1465, 1361}, {1795, 48}, {1809, 219}, {2250, 42}, {2342, 41}, {2397, 15632}, {2401, 513}, {2423, 667}, {2720, 1415}, {4358, 1145}, {4391, 2804}, {10428, 9456}, {13136, 100}, {14266, 8609}, {14578, 184}, {15501, 198}, {15635, 1015}, {16082, 4}, {17862, 1532}, {17923, 1845}
X(18817) lies on these lines: {94, 2052}, {264, 328}, {265, 6528}, {476, 16089}, {1989, 16081}, {14254, 18027}
X(18817) = isotomic conjugate of the isogonal conjugate of X(6344)
X(18817) = cevapoint of X(i) and X(j) for these (i,j): {5, 3580}, {94, 6344}, {186, 1994}
X(18817) = X(i)-isoconjugate of X(j) for these (i,j): {48, 50}, {184, 6149}, {323, 9247}, {822, 14591}, {2290, 14533}, {4575, 14270}
X(18817) = trilinear pole of line {324, 14592}
X(18817) = polar conjugate of X(50)
X(18817) = barycentric product X(i)*X(j) for these {i,j}: {76, 6344}, {94, 264}, {265, 18027}, {328, 2052}, {1502, 18384}, {1969, 2166}, {1989, 18022}, {6331, 10412}, {6528, 14592}
X(18817) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 50}, {92, 6149}, {94, 3}, {107, 14591}, {264, 323}, {265, 577}, {324, 1154}, {328, 394}, {338, 16186}, {850, 8552}, {1141, 14533}, {1989, 184}, {2052, 186}, {2166, 48}, {2501, 14270}, {2970, 2088}, {6331, 10411}, {6344, 6}, {6528, 14590}, {10412, 647}, {11060, 14575}, {13450, 11062}, {14165, 3043}, {14254, 3284}, {14356, 3289}, {14592, 520}, {14618, 526}, {14859, 11077}, {15475, 3049}, {16080, 14385}, {16081, 14355}, {18022, 7799}, {18027, 340}, {18384, 32}
X(18818) lies on the conic {{A,B,C,X(2),X(56)) and these lines: {2, 18023}, {6, 598}, {25, 17983}, {111, 8859}, {263, 9214}, {524, 8785}, {694, 17948}, {1976, 9154}, {4590, 11162}, {6094, 14568}
X(18818) = isotomic conjugate of the complement X(11054)
X(18818) = X(i)-cross conjugate of X(j) for these (i,j): {2408, 892}, {6088, 670}, {9465, 10630}, {9485, 99}
X(18818) = cevapoint of X(i) and X(j) for these (i,j): {2, 11054}, {187, 11422}
X(18818) = X(i)-isoconjugate of X(j) for these (i,j): {574, 896}, {599, 922}, {2642, 9145}
X(18818) = trilinear pole of line {512, 598}
X(18818) = barycentric product X(i)*X(j) for these {i,j}: {598, 671}, {892, 8599}, {1383, 18023}, {10512, 14246}
X(18818) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 574}, {598, 524}, {671, 599}, {691, 9145}, {892, 9146}, {1383, 187}, {5380, 3908}, {5466, 3906}, {8599, 690}, {8753, 8541}, {9178, 17414}, {9214, 13857}, {10511, 14357}, {11636, 5467}, {14246, 10510}, {17983, 5094}, {18023, 9464}
X(18819) lies on this line: {485, 490}
X(18819) = isogonal conjugate of X(32568)
X(18819) = cevapoint of X(371) and X(8577)
X(18819) = trilinear pole of line {9131, 13320}
X(18819) = barycentric quotient X(8577)/X(1504)
X(18820) lies on this line: {486, 489}
X(18820) = isogonal conjugate of X(32575)
X(18820) = cevapoint of X(372) and X(8576)
X(18820) = trilinear pole of line {9131, 13319}
X(18820) = barycentric quotient X(8576)/X(1505)
X(18821) lies on the Steiner circumellipse and these lines:
{2, 666}, {8, 4555}, {99, 840}, {190, 320}, {514, 1121}, {519, 664}, {522, 903}, {648, 15149}, {668, 3263}, {693, 2481}, {4076, 6635}, {4562, 17294}, {4597, 10031}, {4998, 6174}, {7199, 14616}
X(18821) = reflection of X(666) in X(2)
X(18821) = isotomic conjugate of X(528)
X(18821) = complement of X(39363)
X(18821) = anticomplement of X(35113)
X(18821) = X(43)-zayin conjugate of X(2246)
X(18821) = X(528)-cross conjugate of X(2)
X(18821) = cevapoint of X(i) and X(j) for these (i,j): {2, 528}
X(18821) = trilinear pole of line {2, 918}
X(18821) = barycentric product X(76)*X(840)
X(18821) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2246}, {2, 528}, {7, 5723}, {88, 14190}, {513, 1643}, {518, 1642}, {840, 6}, {926, 14411}, {5723, 3322}, {14191, 44}
X(18821) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2246}, {31, 528}, {41, 5723}, {101, 1643}, {902, 14190}, {1438, 1642}
X(18822) lies on the Steiner circumellipse and these lines:
{1, 4555}, {2, 4562}, {44, 190}, {75, 889}, {99, 2382}, {350, 519}, {513, 903}, {514, 3227}, {664, 1319}, {666, 6654}, {765, 6635}, {1877, 18026}
X(18822) = reflection of X(4562) in X(2)
X(18822) = isotomic conjugate of X(537)
X(18822) = anticomplement of X(35123)
X(18822) = X(537)-cross conjugate of X(2)
X(18822) = cevapoint of X(2) and X(537)
X(18822) = X(314)-beth conjugate of X(889)
X(18822) = trilinear pole of line {2, 812}
X(18822) = barycentric product X(76)*X(2382)
X(18822) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 537}, {2382, 6}
X(18823) lies on the Steiner circumellipse and these lines:
{2, 892}, {30, 16103}, {76, 14255}, {99, 524}, {190, 4062}, {468, 648}, {523, 671}, {670, 3266}, {1992, 2966}, {2482, 4590}, {5461, 14728}, {9164, 9182}, {9165, 14061}, {9166, 17948}, {13479, 16092}
X(18823) = reflection of X(892) in X(2)
X(18823) = isogonal conjugate of X(2502)
X(18823) = isotomic conjugate of X(543)
X(18823) = anticomplement of X(35087)
X(18823) = cevapoint of X(2) and X(543)
X(18823) = X(9170)-Ceva conjugate of X(9180)
X(18823) = X(i)-cross conjugate of X(j) for these (i,j): {543, 2}, {9168, 99}, {9180, 9170}
X(18823) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2502}, {31, 543}, {163, 8371}, {187, 17955}, {661, 9181}, {662, 9171}, {798, 9182}, {896, 17964}, {922, 17948}, {923, 1641}
X(18823) = trilinear pole of line {2, 690}
X(18823) = barycentric product X(i)*X(j) for these {i,j}: {76, 843}, {99, 9180}, {523, 9170}
X(18823) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 543}, {6, 2502}, {99, 9182}, {110, 9181}, {111, 17964}, {512, 9171}, {523, 8371}, {524, 1641}, {671, 17948}, {843, 6}, {897, 17955}, {5466, 18007}, {9170, 99}, {9178, 17993}, {9180, 523}
X(18824) lies on the Steiner circumellipse and these lines:
{31, 668}, {32, 190}, {58, 670}, {99, 697}, {664, 1397}, {1106, 4569}, {1395, 18026}, {1922, 4562}
X(18824) = isogonal conjugate of X(8619)
X(18824) = isotomic conjugate of X(696)
X(18824) = X(696)-cross conjugate of X(2)
X(18824) = cevapoint of X(2) and X(696)
X(18824) = trilinear pole of line {2, 1919}
X(18824) = barycentric product X(76)*X(697)
X(18824) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 696}, {6, 8619}, {697, 6}
X(18825) lies on the Steiner circumellipse and these lines:
{6, 668}, {31, 190}, {81, 670}, {99, 713}, {385, 17961}, {604, 664}, {608, 18026}, {648, 2203}, {739, 889}, {1407, 4569}, {1911, 4562}, {2162, 4363}, {4555, 9456}, {5317, 6528}
X(18825) = isogonal conjugate of X(8620)
X(18825) = isotomic conjugate of X(712)
X(18825) = cevapoint of X(i) and X(j) for these (i,j): {2, 712}
X(18825) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 8620}, {43, 2228}
X(18825) = X(712)-cross conjugate of X(2)
X(18825) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8620}, {6, 2228}, {31, 712}, {190, 9297}
X(18825) = trilinear pole of line {2, 667}
X(18825) = barycentric product X(i)*X(j) for these {i,j}: {76, 713}
X(18825) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2228}, {2, 712}, {6, 8620}, {667, 9297}, {713, 6}
X(18826) lies on the Steiner circumellipse and these lines:
{1, 670}, {31, 99}, {42, 668}, {190, 213}, {648, 1973}, {664, 1402}, {892, 923}, {1042, 4569}, {1096, 6528}
X(18826) = isotomic conjugate of X(714)
X(18826) = X(43)-zayin conjugate of X(2229)
X(18826) = X(i)-cross conjugate of X(j) for these (i,j): {714, 2}, {3768, 799}
X(18826) = cevapoint of X(2) and X(714)
X(18826) = trilinear pole of line {2, 798}
X(18826) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2229}, {31, 714}
X(18826) = barycentric product X(76)*X(715)
X(18826) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2229}, {2, 714}, {715, 6}
X(18827) lies on the Steiner circumellipse, the cubics K768 and K769, and on these lines:
on lines {1, 99}, {10, 274}, {19, 648}, {37, 86}, {38, 873}, {65, 664}, {75, 670}, {81, 4586}, {82, 757}, {158, 6528}, {225, 18026}, {239, 9278}, {244, 799}, {518, 2669}, {596, 17143}, {666, 2311}, {671, 4444}, {813, 2368}, {870, 982}, {876, 18009}, {889, 4639}, {892, 897}, {1910, 2966}, {1916, 6625}, {2106, 16514}, {2481, 4458}, {2588, 15165}, {2589, 15164}, {2663, 18787}, {2668, 3666}, {3228, 3572}, {3668, 4569}, {4360, 13476}, {4555, 4589}, {4562, 6542}, {4576, 17154}, {6540, 17175}, {6626, 16823}, {9505, 17770}, {10436, 17038}
X(18827) = isogonal conjugate of X(3747)
X(18827) = isotomic conjugate of X(740)
X(18827) = complement of X(39367)
X(18827) = anticomplement of X(35068)
X(18827) = cevapoint of X(i) and X(j) for these (i,j): {1, 18206}, {2, 740}, {86, 17731}, {244, 812}, {291, 335}, {4155, 16592}
X(18827) = X(i)-cross conjugate of X(j) for these (i,j): {740, 2}, {812, 799}, {876, 4562}, {1959, 85}, {2227, 87}, {2254, 662}, {4645, 14534}
X(18827) = X(314)-beth conjugate of X(670)
X(18827) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 3747}, {43, 2238}
X(18827) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3747}, {3, 862}, {6, 2238}, {10, 2210}, {31, 740}, {32, 3948}, {37, 1914}, {41, 16609}, {42, 238}, {55, 1284}, {56, 4433}, {71, 2201}, {82, 4093}, {100, 4455}, {110, 4155}, {210, 1428}, {212, 1874}, {213, 239}, {228, 242}, {321, 14599}, {350, 1918}, {512, 3573}, {604, 3985}, {659, 4557}, {669, 874}, {692, 4010}, {741, 4094}, {756, 5009}, {798, 3570}, {904, 4039}, {1018, 8632}, {1333, 4037}, {1334, 1429}, {1400, 3684}, {1402, 3685}, {1824, 7193}, {1911, 4368}, {1921, 2205}, {1967, 4154}, {2054, 8298}, {2194, 7235}, {3903, 5027}, {4435, 4559}
X(18827) = X(741)-Hirst inverse of X(17103)
X(18827) = trilinear pole of line {2, 661}
X(18827) = areal center of cevian triangles of PU(6)
X(18827) = areal center of cevian triangles of PU(10)
X(18827) = barycentric product X(i)*X(j) for these {i,j}: {27, 337}, {76, 741}, {81, 334}, {86, 335}, {99, 4444}, {274, 291}, {292, 310}, {331, 1808}, {333, 7233}, {513, 4639}, {514, 4589}, {561, 18268}, {660, 7199}, {670, 3572}, {693, 4584}, {799, 876}, {875, 4602}, {1019, 4583}, {1434, 4518}, {1581, 8033}, {1911, 6385}, {1916, 17103}, {2311, 6063}, {4562, 7192}, {5378, 16727}
X(18827) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2238}, {2, 740}, {6, 3747}, {7, 16609}, {8, 3985}, {9, 4433}, {10, 4037}, {19, 862}, {21, 3684}, {27, 242}, {28, 2201}, {39, 4093}, {57, 1284}, {58, 1914}, {75, 3948}, {81, 238}, {86, 239}, {99, 3570}, {226, 7235}, {239, 4368}, {274, 350}, {278, 1874}, {291, 37}, {292, 42}, {295, 71}, {310, 1921}, {314, 3975}, {333, 3685}, {334, 321}, {335, 10}, {337, 306}, {385, 4154}, {514, 4010}, {593, 5009}, {649, 4455}, {660, 1018}, {661, 4155}, {662, 3573}, {741, 6}, {799, 874}, {813, 4557}, {875, 798}, {876, 661}, {894, 4039}, {1014, 1429}, {1019, 659}, {1333, 2210}, {1412, 1428}, {1434, 1447}, {1790, 7193}, {1808, 219}, {1911, 213}, {1922, 1918}, {1931, 8298}, {2196, 228}, {2206, 14599}, {2238, 4094}, {2311, 55}, {3572, 512}, {3616, 4771}, {3676, 7212}, {3733, 8632}, {3736, 16514}, {3737, 4435}, {4128, 2086}, {4358, 4783}, {4369, 804}, {4444, 523}, {4518, 2321}, {4560, 3716}, {4562, 3952}, {4583, 4033}, {4584, 100}, {4589, 190}, {4639, 668}, {4649, 16369}, {4778, 4839}, {4876, 210}, {4960, 4810}, {5235, 4693}, {5257, 4829}, {5333, 4716}, {6629, 4760}, {7077, 1334}, {7192, 812}, {7199, 3766}, {7233, 226}, {7253, 4148}, {8025, 4974}, {8033, 1966}, {9505, 9278}, {9506, 2054}, {14598, 2205}, {16609, 3027}, {16704, 4432}, {16737, 14296}, {17103, 385}, {17197, 4124}, {17212, 4107}, {17731, 6651}, {18200, 4164}, {18206, 8299}, {18268, 31}, {18787, 2295}, {18792, 17475}
X(18828) lies on the Steiner circumellipse and these lines: {99, 783}, {688, 4577}, {754, 14946}
X(18828) = isotomic conjugate of X(782)
X(18828) = X(782)-cross conjugate of X(2)
X(18828) = cevapoint of X(i) and X(j) for these (i,j): {2, 782}, {882, 14970}
X(18828) = X(i)-isoconjugate of X(j) for these (i,j): {31, 782}, {2084, 16985}
X(18828) = trilinear pole of line {2, 14946}
X(18828) = barycentric product X(76)*X(783)
X(18828) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 782}, {783, 6}, {4577, 16985}, {14946, 688}
X(18829) lies on the Steiner circumellipse and these lines: {76, 14251}, {99, 512}, {190, 4079}, {290, 325}, {351, 9150}, {385, 3225}, {523, 670}, {524, 694}, {538, 671}, {648, 2489}, {664, 4589}, {668, 4705}, {881, 886}, {882, 2396}, {892, 9178}, {1634, 4577}, {1934, 14616}, {2421, 2422}, {3226, 17731}, {3493, 3933}, {4584, 4586}, {5641, 7788}, {7779, 14970}, {9467, 12215}, {9487, 11163}
X(18829) = reflection of X(i) in X(j) for these {i,j}: {385, 3229}, {3978, 325}
X(18829) = isogonal conjugate of X(5027)
X(18829) = isotomic conjugate of X(804)
X(18829) = cevapoint of X(i) and X(j) for these (i,j): {2, 804}, {69, 684}, {325, 523}, {512, 3229}, {694, 881}, {732, 3005}, {812, 6682}, {1634, 2421}, {3569, 14251}
X(18829) = X(i)-cross conjugate of X(j) for these (i,j): {804, 2}, {876, 1581}, {881, 694}, {882, 14970}, {2395, 8781}, {2396, 99}, {3569, 76}, {5207, 18020}, {7779, 4590}
X(18829) = crossdifference of every pair of points on line {2086, 2679}
X(18829) = crosssum of X(2491) and X(9429)
X(18829) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5027}, {31, 804}, {42, 4164}, {171, 4455}, {213, 4107}, {238, 7234}, {385, 798}, {419, 810}, {512, 1580}, {523, 1933}, {560, 14295}, {661, 1691}, {662, 2086}, {667, 4039}, {669, 1966}, {875, 4154}, {880, 4117}, {923, 11183}, {1577, 14602}, {1918, 14296}, {1924, 3978}, {1926, 9426}, {2210, 2533}, {2236, 18105}, {2295, 8632}, {3573, 4128}, {3747, 4367}, {4010, 7122}
X(18829) = X(99)-Hirst inverse of X(805)
X(18829) = X(17938)-vertex conjugate of X(17941)
X(18829) = trilinear pole of line {2, 694}
X(18829) = barycentric product X(i)*X(j) for these {i,j}: {76, 805}, {99, 1916}, {256, 4639}, {257, 4589}, {291, 7260}, {334, 4603}, {335, 4594}, {662, 1934}, {670, 694}, {799, 1581}, {1502, 17938}, {1967, 4602}, {4576, 14970}, {4584, 7018}, {4609, 9468}
X(18829) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 804}, {6, 5027}, {76, 14295}, {81, 4164}, {86, 4107}, {99, 385}, {110, 1691}, {163, 1933}, {190, 4039}, {257, 4010}, {274, 14296}, {292, 7234}, {335, 2533}, {512, 2086}, {524, 11183}, {648, 419}, {660, 2295}, {662, 1580}, {670, 3978}, {694, 512}, {733, 18105}, {799, 1966}, {805, 6}, {876, 16592}, {881, 1084}, {882, 3124}, {893, 4455}, {1178, 8632}, {1576, 14602}, {1581, 661}, {1634, 8623}, {1916, 523}, {1927, 1924}, {1934, 1577}, {1967, 798}, {2396, 5976}, {3569, 2679}, {3570, 4154}, {3572, 4128}, {3903, 2238}, {4074, 782}, {4226, 12829}, {4518, 4140}, {4562, 1215}, {4563, 12215}, {4576, 732}, {4583, 3963}, {4584, 171}, {4589, 894}, {4590, 17941}, {4594, 239}, {4602, 1926}, {4603, 238}, {4609, 14603}, {4639, 1909}, {4835, 4839}, {5468, 5026}, {6331, 17984}, {7249, 7212}, {7260, 350}, {8789, 9426}, {9468, 669}, {11654, 9009}, {14251, 2491}, {15391, 878}, {17938, 32}, {17941, 4027}, {17970, 3049}, {17980, 2489}
X(18830) lies on the Steiner circumellipse and these lines: {75, 87}, {76, 4014}, {99, 932}, {190, 4598}, {330, 3227}, {350, 4947}, {513, 6386}, {646, 4562}, {664, 874}, {666, 5383}, {668, 3888}, {894, 3225}, {903, 4479}, {1221, 7168}, {1930, 3494}, {2162, 4363}, {2481, 6383}, {3228, 16606}
X(18830) = isogonal conjugate of X(8640)
X(18830) = isotomic conjugate of X(4083)
X(18830) = X(4598)-Ceva conjugate of X(668)
X(18830) = X(i)-cross conjugate of X(j) for these (i,j): {513, 87}, {649, 274}, {1978, 668}, {4083, 2}, {7155, 5383}, {10453, 1016}, {17144, 7035}
X(18830) = cevapoint of X(i) and X(j) for these (i,j): {2, 4083}, {75, 513}, {321, 2533}, {514, 3840}
X(18830) = X(4598)-aleph conjugate of X(15966)
X(18830) = X(314)-beth conjugate of X(3226)
X(18830) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8640}, {31, 4083}, {32, 3835}, {42, 16695}, {43, 667}, {101, 6377}, {192, 1919}, {213, 18197}, {513, 2209}, {649, 2176}, {663, 1403}, {692, 3123}, {1397, 4147}, {1423, 3063}, {1918, 17217}, {1977, 4595}, {1980, 6376}, {2200, 17921}, {3051, 18107}, {9456, 14408}
X(18830) = trilinear pole of line {2, 330}
X(18830) = barycentric product X(i)*X(j) for these {i,j}: {75, 4598}, {76, 932}, {87, 1978}, {100, 6383}, {190, 6384}, {330, 668}, {670, 16606}, {693, 5383}, {2162, 6386}, {2319, 4572}, {3699, 7209}, {4554, 7155}
X(18830) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 4083}, {6, 8640}, {75, 3835}, {81, 16695}, {86, 18197}, {87, 649}, {100, 2176}, {101, 2209}, {190, 43}, {274, 17217}, {286, 17921}, {312, 4147}, {330, 513}, {513, 6377}, {514, 3123}, {519, 14408}, {536, 14426}, {651, 1403}, {664, 1423}, {668, 192}, {932, 6}, {1978, 6376}, {2053, 3063}, {2162, 667}, {2319, 663}, {3112, 18107}, {3699, 3208}, {4033, 3971}, {4359, 4992}, {4554, 3212}, {4598, 1}, {4623, 7304}, {5383, 100}, {6383, 693}, {6384, 514}, {6386, 6382}, {7035, 4595}, {7121, 1919}, {7148, 4079}, {7155, 650}, {7192, 16742}, {7209, 3676}, {7275, 4502}, {16606, 512}
X(18831) lies on the Steiner circumellipse, the bianticevian conic of X(2) and X(3), and on these lines: {49, 9291}, {54, 276}, {95, 549}, {99, 933}, {110, 6528}, {275, 671}, {648, 16813}, {877, 4577}, {1147, 18027}, {2966, 14586}, {3228, 8882}, {5504, 8795}
X(18831) = isogonal conjugate of X(15451)
X(18831) = isotomic conjugate of X(6368)
X(18831) = anticomplement of X(39019)
X(18831) = X(i)-cross conjugate of X(j) for these (i,j): {110, 18315}, {264, 18020}, {933, 16813}, {1993, 4590}, {5012, 250}, {6368, 2}, {15412, 276}
X(18831) = cevapoint of X(i) and X(j) for these (i,j): {2, 6368}, {54, 15412}, {110, 648}, {140, 525}, {933, 18315}, {9033, 14920}
X(18831) = X(i)-vertex conjugate of X(j) for these (i,j): {4, 14586}, {1576, 6528}
X(18831) = trilinear pole of line {2, 95}
X(18831) = center of bianticevian conic of X(2) and X(3)
X(18831) = polar conjugate of X(12077)
X(18831) = orthic-to-ABC barycentric image of X(130)
X(18831) = barycentric product X(i)*X(j) for these {i,j}: {54, 6331}, {69, 16813}, {76, 933}, {95, 648}, {97, 6528}, {99, 275}, {110, 276}, {264, 18315}, {670, 8882}, {799, 2190}, {811, 2167}, {4558, 8795}, {4563, 8884}, {14586, 18022}, {15412, 18020}, {15958, 18027}
X(18831) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6368}, {3, 17434}, {4, 12077}, {6, 15451}, {30, 14391}, {54, 647}, {92, 2618}, {95, 525}, {97, 520}, {99, 343}, {107, 53}, {110, 216}, {112, 51}, {162, 1953}, {186, 2081}, {250, 1625}, {264, 18314}, {275, 523}, {276, 850}, {648, 5}, {799, 18695}, {811, 14213}, {933, 6}, {1141, 14582}, {1576, 217}, {2148, 810}, {2167, 656}, {2169, 822}, {2190, 661}, {2407, 1568}, {2616, 3708}, {4558, 5562}, {6331, 311}, {6528, 324}, {6529, 14569}, {8795, 14618}, {8882, 512}, {8884, 2501}, {14586, 184}, {14590, 1154}, {15352, 13450}, {15412, 125}, {15422, 8754}, {15958, 577}, {16813, 4}, {17515, 2600}, {18020, 14570}, {18022, 15415}, {18315, 3}
X(18831) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15451}, {5, 810}, {19, 17434}, {31, 6368}, {48, 12077}, {51, 656}, {53, 822}, {184, 2618}, {216, 661}, {217, 1577}, {343, 798}, {520, 2181}, {525, 2179}, {647, 1953}, {669, 18695}, {1625, 3708}, {2159, 14391}, {2290, 14582}, {3049, 14213}, {4079, 16697}, {9247, 18314}
X(18832) lies on the cubics K995 and K1028 and on these lines:
{1, 1965}, {10, 6382}, {19, 1966}, {37, 2998}, {75, 1925}, {304, 1581}, {759, 3222}, {2186, 18156}, {3403, 8769}
X(18832) = isotomic conjugate of X(1740)
X(18832) = X(3223)-Ceva conjugate of X(75)
X(18832) = X(i)-cross conjugate of X(j) for these (i,j): {561, 75}, {4117, 18070}
X(18832) = X(i)-isoconjugate of X(j) for these (i,j): {3, 11325}, {6, 1613}, {31, 1740}, {32, 194}, {41, 1424}, {99, 9491}, {110, 3221}, {112, 2524}, {184, 3186}, {560, 17149}, {604, 7075}, {1501, 6374}, {2175, 17082}
X(18832) = cevapoint of X(693) and X(3123)
X(18832) = trilinear pole of line {661, 17893}
X(18832) = barycentric product X(i)*X(j) for these {i,j}: {75, 2998}, {76, 3223}, {561, 3224}, {1577, 3222}, {1969, 3504}
X(18832) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1613}, {2, 1740}, {7, 1424}, {8, 7075}, {19, 11325}, {75, 194}, {76, 17149}, {85, 17082}, {92, 3186}, {561, 6374}, {656, 2524}, {661, 3221}, {798, 9491}, {2998, 1}, {3222, 662}, {3223, 6}, {3224, 31}, {3504, 48}, {15389, 9247}
X(18833) lies on the cubics K865 and K1028 and on these lines: {1, 561}, {19, 1969}, {37, 308}, {65, 18033}, {75, 1928}, {82, 1966}, {304, 2186}, {310, 596}, {689, 759}, {1581, 1925}, {1910, 4593}, {1923, 1965}, {6385, 13476}
X(18833) = isogonal conjugate of X(1923)
X(18833) = isotomic conjugate of X(1964)
X(18833) = cevapoint of X(75) and X(561)
X(18833) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 1923}, {18272, 2236}
X(18833) = X(i)-cross conjugate of X(j) for these (i,j): {75, 3112}, {1237, 76}, {1577, 4602}, {16889, 83}, {17446, 92}
X(18833) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1923}, {6, 3051}, {31, 1964}, {32, 39}, {38, 560}, {99, 9494}, {110, 688}, {141, 1501}, {163, 2084}, {184, 1843}, {427, 14575}, {669, 1634}, {732, 8789}, {826, 14574}, {827, 2531}, {1397, 3688}, {1401, 2175}, {1576, 3005}, {1917, 1930}, {1918, 17187}, {1927, 2236}, {1973, 4020}, {1974, 3917}, {1980, 4553}, {2205, 16696}, {3404, 9417}, {3665, 9448}, {4576, 9426}, {8024, 9233}, {8623, 9468}, {9247, 17442}
X(18833) = X(1)-Hirst inverse of X(18028)
X(18833) = trilinear pole of line {661, 786}
X(18833) = barycentric product X(i)*X(j) for these {i,j}: {75, 308}, {76, 3112}, {82, 1502}, {83, 561}, {251, 1928}, {670, 18070}, {689, 1577}, {850, 4593}, {1799, 1969}, {1926, 14970}, {3405, 18024}, {6385, 18082}, {6386, 10566}
X(18833) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3051}, {2, 1964}, {6, 1923}, {69, 4020}, {75, 39}, {76, 38}, {82, 32}, {83, 31}, {85, 1401}, {92, 1843}, {251, 560}, {264, 17442}, {274, 17187}, {290, 3404}, {304, 3917}, {308, 1}, {310, 16696}, {312, 3688}, {313, 3954}, {523, 2084}, {561, 141}, {661, 688}, {689, 662}, {733, 1927}, {798, 9494}, {799, 1634}, {850, 8061}, {1176, 9247}, {1237, 16587}, {1502, 1930}, {1577, 3005}, {1799, 48}, {1925, 4074}, {1926, 732}, {1928, 8024}, {1930, 8041}, {1966, 8623}, {1969, 427}, {1978, 4553}, {3112, 6}, {3261, 2530}, {3403, 14096}, {3405, 237}, {3948, 4093}, {3978, 2236}, {4118, 3118}, {4577, 163}, {4580, 810}, {4593, 110}, {4599, 1576}, {4602, 4576}, {6385, 16887}, {6386, 4568}, {8061, 2531}, {10566, 667}, {14970, 1967}, {16889, 16584}, {16890, 2085}, {17500, 2179}, {18041, 211}, {18042, 3203}, {18070, 512}, {18082, 213}, {18091, 1197}, {18097, 1402}, {18098, 1918}, {18105, 1924}, {18107, 8640}, {18108, 1919}, {18156, 3787}
X(18833) = {X(1925),X(1930)}-harmonic conjugate of X(4602)
X(18834) lies on the cubic K1028 and these lines: {1031, 17788}, {1930, 1965}
X(18834) = isotomic conjugate of X(16556)
X(18834) = X(3112)-cross conjugate of X(75)
X(18834) = X(i)-isoconjugate of X(j) for these (i,j): {6, 10329}, {31, 16556}, {32, 2896}, {39, 14885}, {2175, 17083}
X(18834) = barycentric product X(i)*X(j) for these {i,j}: {75, 1031}, {561, 14370}
X(18834) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 10329}, {2, 16556}, {75, 2896}, {82, 14885}, {85, 17083}, {1031, 1}, {14370, 31}
X(18835) lies on the cubic K1028 and on these lines: {1, 76}, {264, 1969}, {305, 3705}, {313, 3178}, {1848, 2064}, {1928, 18036}, {1930, 7018}, {4109, 17788}
X(18835) = isotomic conjugate of X(34250)
X(18835) = isotomic conjugate of the isogonal conjugate of X(4388)
X(18835) = X(i)-isoconjugate of X(j) for these (i,j): {32, 3497}, {560, 7224}
X(18835) = barycentric product X(i)*X(j) for these {i,j}: {75, 17788}, {76, 4388}, {310, 4109}, {561, 3496}, {1978, 4142}, {3596, 17086}
X(18835) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 3497}, {76, 7224}, {3496, 31}, {4109, 42}, {4142, 649}, {4388, 6}, {17086, 56}, {17788, 1}, {17797, 172}
X(18836) lies on the cubic K1028 and these lines: {1, 18036}, {76, 3497}, {304, 17786}, {4385, 7182}
X(18836) = isotomic conjugate of the isogonal conjugate of X(7224)
X(18836) = X(1909)-cross conjugate of X(76)
X(18836) = X(i)-isoconjugate of X(j) for these (i,j): {32, 3496}, {560, 4388}, {1501, 17788}, {9447, 17086}
X(18836) = barycentric product X(i)*X(j) for these {i,j}: {76, 7224}, {561, 3497}
X(18836) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 3496}, {76, 4388}, {313, 4109}, {561, 17788}, {1920, 17797}, {3261, 4142}, {3497, 31}, {6063, 17086}, {7224, 6}
X(18837) lies on the cubic K1028 and on these lines: {1, 4602}, {75, 1925}, {76, 3662}, {304, 1926}, {305, 3705}, {561, 1928}, {6376, 6386}
X(18837) = isotomic conjugate of X(34248)
X(18837) = isotomic conjugate of the isogonal conjugate of X(17149)
X(18837) = X(75)-Ceva conjugate of X(561)
X(18837) = crosspoint of X(75) and X(17149)
X(18837) = X(i)-isoconjugate of X(j) for these (i,j): {25, 15389}, {32, 3224}, {560, 3223}, {1501, 2998}, {1974, 3504}, {3222, 9426}
X(18837) = X(304)-Hirst inverse of X(1926)
X(18837) = barycentric product X(i)*X(j) for these {i,j}: {75, 6374}, {76, 17149}, {194, 561}, {1502, 1740}, {1613, 1928}
X(18837) = barycentric quotient X(i)/X(j) for these {i,j}: {63, 15389}, {75, 3224}, {76, 3223}, {194, 31}, {304, 3504}, {561, 2998}, {1424, 1397}, {1613, 560}, {1740, 32}, {3186, 1973}, {3221, 1924}, {4602, 3222}, {6374, 1}, {7075, 2175}, {17082, 604}, {17149, 6}
X(18837) = {X(1928),X(1930)}-harmonic conjugate of X(561)
See Mihajlon, Angel Montesdeoca, and César Lozada, Hyacinthos 27693 and Hyacinthos 27694.
X(18838) lies on these lines: {1, 3}, {2, 18419}, {4, 5553}, {7, 5080}, {11, 1519}, {12, 3812}, {34, 1406}, {119, 912}, {221, 17054}, {226, 3814}, {244, 1457}, {388, 5176}, {499, 5887}, {513, 1835}, {515, 12736}, {518, 6735}, {519, 5083}, {535, 553}, {603, 3924}, {758, 3911}, {915, 1870}, {960, 5433}, {971, 13273}, {1042, 1393}, {1104, 1399}, {1118, 5146}, {1210, 1858}, {1317, 3880}, {1357, 3319}, {1359, 3025}, {1361, 14027}, {1404, 2173}, {1408, 18180}, {1411, 1455}, {1426, 14593}, {1428, 3827}, {1464, 1465}, {1739, 4551}, {1788, 3868}, {1790, 18178}, {1898, 9581}, {2170, 2272}, {2252, 8609}, {3290, 4559}, {3582, 11571}, {3649, 5087}, {3671, 11813}, {3742, 15950}, {3753, 5252}, {3754, 10106}, {3869, 7288}, {3873, 12648}, {3874, 4848}, {3919, 4315}, {3922, 9850}, {4295, 10531}, {5225, 9961}, {5439, 10200}, {5440, 12739}, {5777, 17606}, {5836, 10944}, {6173, 8581}, {6284, 9943}, {7335, 18732}, {7354, 7686}, {7672, 11239}, {10122, 17706}, {10572, 13369}, {10896, 12688}, {10940, 12649}, {10950, 12675}, {11219, 17638}, {11376, 12672}, {11502, 18446}, {11729, 14988}, {12115, 18391}, {12679, 17649}, {12740, 17654}, {12751, 17660}, {15904, 16869}
X(18838) = midpoint of X(i) and X(j), for these {i, j}: {65,1319}, {1737,11570}
X(18838) = reflection of X(i) in X(j), for these (i,j): (1319,3660), (5123,3812), (5570,942), (17615,5123), (18839,5570)
X(18838) = incircle-inverse-of X(56)
X(18838) = X(403)-of-intouch-triangle
X(18838) = X(2071)-of-inverse-in-incircle-triangle
X(18838) = X(10257)-of-Ursa-minor-triangle
X(18838) = X(13528)-of-Mandart-incircle-triangle
X(18838) = X(16386)-of-Hutson-intouch-triangle
X(18838) = X(17615)-of-1st-Johnson-Yff-triangle
X(18838) = inverse-in-{circumcircle, incircle}-inverter of X(1617)
X(18838) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 46, 11248), (1, 57, 1470), (1, 2093, 12703), (1, 5193, 1319), (36, 5535, 1155), (36, 11529, 5048), (56, 5221, 1454), (57, 5902, 65), (65, 354, 2099), (65, 11011, 13601), (65, 13751, 11011), (1155, 1319, 5172), (2446, 2447, 56), (5045, 13601, 11011), (5172, 11509, 2077), (11011, 13751, 5045)
See César Lozada, Hyacinthos 27694.
X(18839) lies on these lines: {1, 3}, {11, 518}, {12, 13374}, {72, 11376}, {105, 2990}, {210, 5231}, {497, 3873}, {513, 11934}, {516, 5083}, {535, 950}, {672, 8609}, {840, 3100}, {971, 13274}, {1279, 2361}, {1362, 3326}, {1364, 3322}, {1512, 10956}, {1797, 14190}, {1830, 1876}, {1836, 10947}, {1837, 3555}, {1858, 3874}, {1864, 11238}, {1898, 9614}, {2323, 2348}, {2342, 15635}, {3021, 3025}, {3058, 10391}, {3193, 5324}, {3254, 15733}, {3328, 5580}, {3486, 3889}, {3583, 12750}, {3681, 10589}, {3742, 5432}, {3814, 10916}, {3827, 10535}, {3848, 5326}, {3868, 11240}, {3870, 11502}, {3876, 10527}, {3911, 18240}, {4018, 17622}, {4430, 5274}, {4511, 13279}, {4662, 5123}, {5176, 12649}, {6284, 12675}, {7004, 17449}, {7686, 10944}, {7965, 10949}, {8540, 9004}, {9657, 9850}, {10529, 18220}, {10624, 12005}, {10896, 14872}, {11813, 14054}, {11997, 13476}, {12680, 12953}, {17626, 17728}
X(18839) = reflection of X(3911) in X(18240)
X(18839) = incircle-inverse-of X(55)
X(18839) = X(23)-of-inverse-in-incircle-triangle
X(18839) = X(468)-of-Ursa-minor-triangle
X(18839) = X(858)-of-intouch-triangle
X(18839) = X(1155)-of-Mandart-incircle-triangle
X(18839) = X(7574)-of-incircle-circles triangle
X(18839) = X(10295)-of-Hutson-intouch-triangle
X(18839) = X(17615)-of-2nd-Johnson-Yff triangle
X(18839) = reflection of X(18838) in X(5570)
X(18839) = inverse-in-{circumcircle, incircle}-inverter of X(3)
X(18839) = anticomplement, wrt intouch triangle, of X(3660)
X(18839) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 5536, 2078), (1, 5709, 11510), (57, 5537, 1155), (65, 354, 4860), (354, 3057, 17603), (354, 3748, 11018), (354, 17642, 55), (2078, 5536, 1155), (2098, 4860, 55), (2446, 2447, 55), (3057, 17603, 55), (5173, 12915, 354), (5597, 5598, 8069), (6583, 9957, 13750), (17603, 17642, 3057)
Dao-bipedal-perspectors: X(18840)-X(18855)
This preamble and centers X(18840)-X(18855) were contributed by César Eliud Lozada, May 26, 2018.
Let ABC be a triangle, P, Q two isogonal conjugate points and PaPbPc, QaQbQc their respective pedal triangles. Let t be a real number, P′a the point on PPa such that PP′a/PPa=t and Q'a the point on QQa such that QQ'a/QQa=t; define P′b, P′c, Q′b, Q′c cyclically. Denote A′=PQ′a ∩ QP′a and similarly B' and C'. Then A′B′C′ and ABC are perspective and, for given P, Q, the locus of the perspectors is a rectangular hyperbola. (Dao Thanh Oai, May 22, 2018)
Suppose P=U:V:W (trilinears). Vertex A' has trilinear coordinates:
A' = -(t-2)*u*v*w : (u^2+v^2+t*cos(C)*u*v)*w : (u^2+w^2+t*cos(B)*u*w)*v
The perspector A′B′C′, ABC is:
Z(P, t) = V*W*(U^2+t*cos(C)*U*V+V^2) *(U^2+t*cos(B)*U*W+W^2) : : (trilinears)
When P is fixed and t varies, the perspector Z(P, t) lies on the rectangular hyperbola Κ(P) with trilinear equation:
Κ(P) = ∑ ( ((U^2+V^2)*W*cos(B)-(U^2+W^2)*V*cos(C))*v*w )= 0
Κ(P) has center:
O*(P) = b*c*((U^2+W^2)*V*a*b-(U^2+V^2)*W*a*c+(b^2-c^2)*U*(V^2+W^2))*((U^2+V^2)*W*cos(B)-(U^2+W^2)*V*cos(C)) : :
and perspector:
P*(P) = (U^2+V^2)*W*cos(B)-(U^2+W^2)*V*cos(C) : :
Κ(P) is the isogonal conjugate of the line:
∑(((U^2+V^2)*W*cos(B)-(U^2+W^2)*V*cos(C)) u ) = 0
The perspector Z(P, t) is here named here the Dao-bipedal-perspector-of-(P, t) and the conic Κ(P) is here named here the Dao-bipedal-conic-of-P.
The appearance of (i, t, j) in the following list means that the Dao-bipedal-perspector-of-(X(i), t)=X(j):
(2, -3, 2996), (2, -5/2, 5485), (2, -2, 76), (2, -3/2, 18840), (2, -1, 2), (2, -1/2, 18841), (2, 0, 83), (2, 1/2, 18842), (2, 1, 5395), (2, 3/2, 18843), (2, 2, 598), (2, 5/2, 18844), (2, 3, 18845), (3, -3, 18846), (3, -5/2, 18847), (3, -2, 18848), (3, -3/2, 18849), (3, -1, 18850), (3, -1/2, 18851), (3, 0, 1105), (3, 1/2, 18852), (3, 1, 1217), (3, 3/2, 18853), (3, 2, 264), (3, 5/2, 18854), (3, 3, 18855)
The appearance of (i, j) in the following list means that the O*(X(i)) = X(j): (1, 11), (2, 115), (3, 136)
Let BA, CA be the anticomplementary circle intercepts of line BC. Let B'A, C'A be the {B,C}-harmonic conjugates of BA, CA resp. Define C'B, A'B, A'C, B'C cyclically. Then B'A, C'A, C'B, A'B, A'C, B'C lie on a common ellipse, and X(18840) is both its center and perspector. (Randy Hutson, October 8, 2019)
X(18840) lies on the Kiepert hyperbola and these lines: {2,3933}, {3,3424}, {4,141}, {5,14484}, {6,18841}, {10,4000}, {69,83}, {76,3619}, {98,620}, {183,14069}, {226,7195}, {262,3090}, {297,8796}, {315,598}, {321,3673}, {376,7800}, {485,5591}, {486,5590}, {599,18842}, {626,3545}, {671,3096}, {1131,7389}, {1132,7388}, {1235,2052}, {1285,7767}, {1916,14064}, {2051,7402}, {2896,14033}, {2996,6656}, {3406,14912}, {3407,7793}, {3524,7789}, {3525,7612}, {3529,3734}, {3533,3788}, {3618,7894}, {3620,5395}, {3763,5286}, {3785,14039}, {3855,7849}, {4869,13740}, {5067,7778}, {5082,13576}, {5232,17681}, {5254,5485}, {5503,7867}, {6292,7738}, {6625,17232}, {7397,13478}, {7608,7869}, {7735,7822}, {7736,7794}, {7745,18843}, {7783,16043}, {7791,11606}, {7801,11167}, {7803,10159}, {7819,15589}, {7865,15682}, {7878,11008}, {7879,18845}, {7880,15709}, {7895,9770}, {7938,16041}, {8889,8891}, {14534,18141}
X(18840) = isogonal conjugate of X(30435)
X(18840) = isotomic conjugate of X(3618)
X(18840) = polar conjugate of X(6995)
X(18840) = trilinear pole of the line {523, 2525}
X(18841) lies on the Kiepert hyperbola and these lines: {2,7762}, {3,14484}, {4,3589}, {5,3424}, {6,18840}, {10,7290}, {69,10159}, {76,3618}, {98,3090}, {262,631}, {321,5222}, {376,14492}, {458,8796}, {459,8743}, {485,7376}, {486,7375}, {598,7859}, {671,7803}, {1131,7388}, {1132,7389}, {1285,8362}, {1916,14001}, {2051,7397}, {2996,7770}, {3091,14535}, {3407,14064}, {3525,14494}, {3529,7804}, {3533,6680}, {3545,7834}, {3619,7878}, {3855,12252}, {5067,7612}, {5286,5485}, {5395,6656}, {5503,9167}, {7402,13478}, {7736,7888}, {7745,18842}, {7746,11167}, {7846,8781}, {7915,9770}, {10155,15491}, {10357,15709}, {10358,14485}, {11174,14069}, {11606,16924}
X(18841) = isogonal conjugate of X(9605)
X(18841) = isotomic conjugate of X(3619)
X(18841) = polar conjugate of X(7378)
X(18841) = trilinear pole of the line {523, 3804}
X(18842) lies on the Kiepert hyperbola and these lines: {2,1285}, {4,597}, {6,5485}, {10,15601}, {30,14484}, {69,10302}, {76,1992}, {98,3545}, {182,14485}, {262,376}, {381,3424}, {543,14482}, {598,3618}, {599,18840}, {631,7608}, {671,18800}, {1916,8591}, {2394,18311}, {2444,5466}, {2482,5503}, {2996,8370}, {3317,13783}, {3407,16041}, {3524,14494}, {3590,7388}, {3591,7389}, {3855,7817}, {4080,17014}, {5071,7612}, {5395,7841}, {5490,13757}, {5491,13637}, {7375,10194}, {7376,10195}, {7735,11167}, {7745,18841}, {7770,11160}, {7804,9770}, {7812,10159}, {8787,14912}, {10155,15702}, {11163,14039}, {11669,15709}, {14492,15682}
X(18842) = reflection of X(2) in X(14535)
X(18842) = isogonal conjugate of X(5024)
X(18842) = trilinear pole of the line {523, 8644} (the orthic axis of the Thomson triangle)
X(18843) lies on the Kiepert hyperbola and these lines: {4,6329}, {76,11008}, {98,3855}, {262,3529}, {382,14484}, {546,3424}, {631,11669}, {3528,14494}, {3544,7612}, {7608,10299}, {7745,18840}
X(18844) lies on the Kiepert hyperbola and these lines: {3090,11668}, {3424,3843}, {3627,14484}, {5485,7745}, {14494,17538}
X(18845) lies on the Kiepert hyperbola and these lines: {2,5023}, {3,10155}, {20,14494}, {98,3832}, {262,3146}, {315,10302}, {439,5475}, {1916,14068}, {2996,7745}, {3091,7612}, {3522,7608}, {5068,7607}, {5485,7754}, {7879,18840}, {11669,15717}, {14484,17578}
X(18845) = isogonal conjugate of X(15815)
X(18846) lies on these lines: {30,6526}, {382,393}, {1093,3146}, {1885,18855}, {3543,8884}, {8801,13488}, {16263,17578}
X(18846) = trilinear pole of the line {2501, 14345}
X(18847) lies on these lines: {393,15682}, {1885,18854}, {3529,6526}, {9007,18808}
X(18848) lies on th3e hyperbola {{A,B,C,X(4),X(93)}} these lines: {4,18418}, {20,6526}, {30,1093}, {264,1885}, {382,8884}, {393,3146}, {520,12111}, {648,5895}, {847,18560}, {1593,14860}, {3627,16263}, {10152,11441}
X(18848) = isogonal conjugate of X(1204)
X(18848) = anticomplement of X(33553)
X(18848) = cevapoint of X(4) and X(20)
X(18848) = trilinear pole of the line {1636, 2501}
X(18849) lies on these lines: {376,6526}, {1093,3529}, {1885,18853}, {8884,15682}
X(18850) lies on these lines: {3,6526}, {4,11064}, {20,1093}, {30,393}, {254,18560}, {525,16253}, {1217,1885}, {1593,18855}, {1597,8801}, {1826,15942}, {3088,14860}, {3146,8884}, {3543,16263}
X(18850) = isogonal conjugate of X(10605)
X(18850) = trilinear pole of the line {2501, 9033}
X(18851) lies on these lines: {376,1093}, {393,3529}, {631,6526}, {1593,18854}, {1885,18852}
X(18852) lies on these lines: {4,6090}, {376,393}, {631,1093}, {1593,18853}, {1885,18851}, {3088,18854}, {3090,6526}, {3147,15424}, {3529,8884}, {15682,16263}
X(18852) = trilinear pole of the line {2501, 9007}
X(18853) lies on these lines: {376,8884}, {393,631}, {427,18854}, {847,8889}, {1093,3090}, {1593,18852}, {1885,18849}, {3545,6526}
X(18854) lies on these lines: {254,8889}, {393,3090}, {427,18853}, {631,8884}, {1093,3545}, {1179,6353}, {1593,18851}, {1885,18847}, {3088,18852}, {3529,16263}, {3855,6526}
X(18855) lies on these lines: {2,8884}, {4,343}, {5,393}, {20,16263}, {68,3087}, {254,1594}, {324,1093}, {381,6526}, {427,1217}, {1105,3088}, {1179,3542}, {1300,3541}, {1593,18850}, {1885,18846}, {6525,7528}
X(18855) = polar conjugate of X(11427)
X(18855) = trilinear pole of the line {2501, 6368}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27696.
X(18856) lies on these lines: {1, 3}, {912, 3035}, {6001, 6713}, {13369, 18242}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27696.
X(18857) lies on these lines: {1, 3}, {104, 4881}, {140, 5123}, {214, 912}, {355, 6921}, {513, 17099}, {515, 6681}, {631, 5176}, {3582, 12119}, {3814, 10165}, {5080, 6947}, {5731, 6880}, {5886, 6938}, {6834, 18481}, {6929, 11230}, {6959, 18480}, {9956, 13747}
X(18857) = midpoint of X(3) and X(1319)
X(18857) = circumcircle-inverse-of X(10680)
X(18857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 10246, 5119), (3, 16203, 10966), (1381, 1382, 10680), (3576, 10269, 1385)
See Angel Montesdeoca, HG260518.
X(18858) lies on these lines: {98,446}, {805,2966}, {1297,1916}, {2698,12176}, {6037,17938}
Circumperp conjugates: X(18859)-X(18864)
This preamble and centers X(18859)-X(18864) were contributed by César Eliud Lozada, May 28, 2018.
Let ABC be a triangle and P a point. The perpendicular bisectors of BC, CA, AB intersect the circumcircle at (A1, A2), (B1, B2), (C1, C2) ,respectively. Then the circumcircles of PA1A2, PB1B2, PC1C2 are coaxial. (Antreas Hatzipolakis, May 26, 2018, Anopolis 7568)
Let Q be the point of intersection (other than P) of the three indicated circles. Then:
For P other than X(3), the mapping P → Q is a conjugacy. The point Q is here named the Q=circumperp conjugate of P (as A1, A2, B1, B2, C1, C2 are the vertices of the circumperp triangles). For P= u:v:w (trilinears), coordinates of Q(P) are:
Q(P) = (-a*(-b*c*SC*SB*u^2+2*w*v*SA^3)-SA*a*b*c*(b^2*v^2+c^2*w^2)+b*((SA+SB)*S^2-2*SA*SB^2)*w*u+c*((SA+SC)*S^2-2*SA*SC^2)*u*v)*a : :
Some properties:
The appearance of (i,j) in the following list means that the circumperp conjugate of X(i) is X(j), for X(i) not on the circumcircle of ABC:
(1,2077), (2,7464), (4,2071), (5,18859), (6,18860), (8,18861), (11,18862), (13,18863), (14,18864), (15,14539), (16,14538), (20,186), (22,10295), (23,376), (24,16386), (36,40), (40,36), (56,13528), (64,12096), (122,2935), (131,12302), (186,20), (187,1350), (265,13496), (376,23), (378,858), (399,12041), (403,11413), (484,11012), (548,5899), (550,2070), (858,378), (944,17100), (1155,3428), (1157,7691), (1319,10310), (1324,4297), (1325,3651), (1326,3430), (1350,187), (1498,11589), (1511,10620), (1657,15646), (2070,550), (2071,4), (2072,12084), (2076,5188), (2077,1), (2078,6282), (2080,3098), (2456,9737), (2459,11825), (2460,11824), (2482,16010), (2935,122), (3098,2080), (3153,3520), (3184,10117), (3357,6760), (3428,1155), (3430,1326), (3520,3153), (3534,7575), (3576,5537), (3651,1325), (4297,1324), (4996,12247), (5104,8722), (5126,6244), (5144,11495), (5152,11257), (5172,14110), (5188,2076), (5196,7430), (5473,6104), (5474,6105), (5536,7688), (5537,3576), (5538,10902), (5609,15041), (5621,14981), (5866,6776), (5899,548), (5961,12121), (6150,12307), (6244,5126), (6282,2078), (6566,12305), (6567,12306), (6760,3357), (6770,14368), (6773,14369), (6776,5866), (7418,7472), (7421,7424), (7422,7468), (7424,7421), (7425,7475), (7429,7477), (7430,5196), (7440,7479), (7464,2), (7468,7422), (7472,7418), (7475,7425), (7477,7429), (7479,7440), (7488,13619), (7574,18570), (7575,3534), (7688,5536), (7689,13557), (7691,1157), (8722,5104), (9301,14810), (9737,2456), (10117,3184), (10257,12085), (10260,12119), (10295,22), (10310,1319), (10564,14687), (10620,1511), (10745,13293), (10902,5538), (11012,484), (11250,18403), (11257,5152), (11413,403), (11495,5144), (11589,1498), (11643,12117), (11676,15915), (11713,12332), (11824,2460), (11825,2459), (12041,399), (12042,13188), (12084,2072), (12085,10257), (12095,12163), (12096,64), (12105,15689), (12117,11643), (12119,10260), (12121,5961), (12163,12095), (12247,4996), (12302,131), (12305,6566), (12306,6567), (12307,6150), (12332,11713), (12383,14652), (12584,14830), (13188,12042), (13293,10745), (13496,265), (13528,56), (13557,7689), (13558,16163), (13619,7488), (14094,15055), (14110,5172), (14538,16), (14539,15), (14652,12383), (14687,10564), (14703,16111), (14810,9301), (14830,12584), (14981,5621), (15035,15054), (15041,5609), (15054,15035), (15055,14094), (15646,1657), (15681,18571), (15689,12105), (15915,11676), (16010,2482), (16111,14703), (16163,13558), (16386,24), (17100,944), (18403,11250), (18570,7574), (18571,15681), (18859,5), (18860,6), (18861,8), (18862,11), (18863,13), (18864,14)
As a point on the Euler line, X(18859) has Shinagawa coefficients (3*E-8*F, -7*E+8*F).
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27704.
X(18859) is the crosspoint of the intersections of the circumcircle and Trinh circle. (Randy Hutson, June 27, 2018)
Let P and Q be circumcircle antipodes. X(18859) is the Euler line intercept, other than X(5), of circle {{X(5),P,Q}} for all P, Q. (Randy Hutson, August 13, 2020)
X(18859) lies on these lines: {2, 3}, {36, 9629}, {39, 18373}, {49, 10575}, {56, 9641}, {74, 1154}, {156, 12279}, {185, 195}, {399, 2935}, {477, 930}, {511, 5621}, {539, 13399}, {933, 2693}, {999, 10149}, {1092, 18439}, {1204, 6243}, {1350, 11649}, {1511, 14157}, {1568, 7728}, {2696, 9076}, {3098, 9973}, {3357, 18436}, {5663, 13445}, {5944, 8718}, {6101, 11440}, {6128, 11063}, {9703, 11456}, {9729, 15047}, {10540, 14915}, {10620, 12302}, {10625, 12307}, {11381, 18350}, {11430, 14855}, {11591, 15062}, {12006, 12834}, {12041, 13358}, {12099, 15107}, {12121, 13293}, {12242, 14861}, {13352, 15087}, {13367, 14641}, {13630, 14627}, {13863, 18401}, {14156, 14643}, {14581, 14961}, {15033, 15037}, {15089, 17855}, {18863, 18864}
X(18859) = reflection of X(2070) in X(3)
X(18859) = reflection of X(382) in X(18403)
X(18859) = anticomplement of X(11563)
X(18859) = circumcircle-inverse of X(550)
X(18859) = Stammler circle-inverse of X(1657)
X(18859) = Stammler circles radical circle-inverse of X(3)
X(18859) = X(2070)-of ABC-X3-reflections-triangle
X(18859) = X(2071)-of-X3-ABC-reflections-triangle
X(18859) = anti-Hutson intouch-isogonal conjugate of X(10620)
X(18859) = pole wrt circumcircle of line X(523)X(550)
X(18859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1593, 1656), (3, 3830, 6644), (3, 3843, 17928), (3, 5073, 24), (3, 5899, 186), (3, 9818, 5054), (20, 18569, 18565), (186, 5899, 2070), (1113, 1114, 550), (3830, 6644, 7545), (7488, 10226, 3), (7502, 18569, 25), (12087, 17506, 12107), (15122, 18325, 1656), (15154, 15155, 1657), (18565, 18569, 382)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27704.
Let P and Q be circumcircle antipodes. X(18860) is the Brocard axis intercept, other than X(6), of circle {{X(6),P,Q}} for all P, Q. (Randy Hutson, August 13, 2020)
X(18860) lies on these lines: {3, 6}, {4, 625}, {5, 7820}, {20, 316}, {30, 114}, {55, 5194}, {56, 5148}, {74, 2709}, {98, 538}, {99, 5999}, {103, 2705}, {110, 2710}, {122, 441}, {140, 7852}, {147, 7799}, {165, 5184}, {262, 7804}, {325, 2794}, {376, 3849}, {512, 684}, {549, 5215}, {620, 1513}, {631, 7834}, {691, 1297}, {842, 1296}, {1007, 7694}, {1092, 2909}, {1293, 2700}, {1352, 7801}, {1495, 9155}, {1503, 6390}, {1593, 5140}, {2393, 9145}, {2936, 6000}, {2967, 14581}, {3148, 5651}, {3292, 5191}, {3455, 13754}, {3522, 14712}, {3523, 7803}, {3564, 7813}, {3734, 13860}, {3926, 5921}, {5031, 7789}, {5071, 10150}, {5149, 11676}, {5207, 6337}, {5480, 8369}, {6194, 7771}, {7575, 11642}, {7780, 12251}, {7796, 9863}, {7798, 9755}, {7835, 13862}, {8149, 11257}, {8719, 14532}, {8724, 11645}, {9027, 9142}, {9890, 13172}, {10011, 10256}, {10352, 13586}, {10723, 14041}, {11799, 16760}, {13241, 14388}, {15122, 16188}
X(18860) = midpoint of X(i) and X(j) for these {i,j}: {20, 316}, {99, 5999}, {842,7464}
X(18860) = reflection of X(i) in X(j) for these (i,j): (4, 625), (187,3), (11799, 16760)
X(18860) = circumcircle-inverse of X(1350)
X(18860) = Moses-circle-inverse of X(5028)
X(18860) = X(187)-of ABC-X3-reflections-triangle
X(18860) = X(625)-of-anti-Euler-triangle
X(18860) = X(5148)-of-2nd-circumperp-tangential-triangle
X(18860) = X(5194)-of-anti-Mandart-incircle-triangle
X(18860) = (ABC-X3 reflections)-isogonal conjugate of X(12117)
X(18860) = X(187)-of-circumcevian-triangle-of-X(511)
X(18860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 1350, 8722), (3, 3095, 13335), (3, 5024, 5085), (3, 5171, 15513), (3, 9734, 8589), (3, 9737, 39), (3, 11171, 5092), (15, 16, 2030), (1350, 8722, 5188), (1379, 1380, 1350), (3095, 13335, 5007), (3098, 9734, 3), (5097, 13335, 11842), (6566, 6567, 1692), (10631, 15513, 187), (12305, 12306, 11477)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27704.
X(18861) lies on these lines: {3, 8}, {4, 10090}, {11, 6906}, {21, 6713}, {35, 11715}, {36, 2800}, {56, 10698}, {80, 5450}, {119, 404}, {149, 10785}, {153, 4188}, {497, 5533}, {953, 2841}, {1320, 11248}, {1385, 17654}, {1470, 5603}, {1768, 6261}, {2077, 2802}, {2829, 6905}, {3035, 6940}, {3149, 10728}, {3885, 12737}, {5253, 11729}, {5840, 6909}, {5884, 14800}, {6667, 6920}, {6830, 13273}, {6924, 10742}, {6941, 12761}, {6942, 12248}, {6952, 8068}, {6977, 10629}, {7967, 10087}, {10265, 10572}, {10711, 16371}, {12116, 13199}, {14803, 15528}, {15015, 18446}
X(18861) = circumcircle-inverse of X(944)
X(18861) = X(17100)-of-ABC-X3-reflections-triangle
X(18861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (56, 12332, 10698), (100, 104, 944)
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27704.
X(18862) lies on these lines: {3, 11}, {40, 12302}, {378, 915}, {1295, 11413}, {1593, 5521}, {3428, 11714}
X(18862) = X(14667)-of ABC-X3-reflections-triangle
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27704.
X(18863) lies on these lines: {3, 13}, {7691, 14541}, {12041, 14539}, {18859, 18864}
X(18863) = circumcircle-inverse of X(5473)
X(18863) = X(6104)-of-ABC-X3-reflections-triangle
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27704.
X(18864) lies on these lines: {3, 14}, {7691, 14540}, {12041, 14538}, {18859, 18863}
X(18864) = circumcircle-inverse of X(5474)
X(18864) = X(6105)-of-ABC-X3-reflections-triangle
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27705.
X(18865) lies on the Fuhrmann circle, the cubic K800, and these lines: {4, 5535}, {5, 580}, {355, 13514}, {502, 5587}
X(18865) = Fuhrmann-circle-antipode of X(13514)
X(18865) = X(6798)-of-excentral-triangle
See Tran Quang Hung and Angel Montesdeoca, ADGEOM 4608.
X(18866) lies on this line: {2,3}
See Tran Quang Hung and Angel Montesdeoca, ADGEOM 4608.
X(18867) lies on these lines: {2,3}, {94,9140}, {2088,14846}
X(18867) = reflection of X(2) in X(13448)
See Tran Quang Hung and Angel Montesdeoca, ADGEOM 4608.
X(18868) lies on this line: {2,3}
See Tran Quang Hung and Angel Montesdeoca, ADGEOM 4608.
X(18869) lies on this line: {2,3}
See Tran Quang Hung and Angel Montesdeoca, ADGEOM 4608.
X(18870) lies on these lines: {2,3}, {125,9530}, {523,1853}, {1899,2452}, {2972,10714}, {3258,11550}
See Tran Quang Hung and Francisco Javier García Capitán, ADGEOM 4585.
X(18871) lies on this line: {2,3}
See Tran Quang Hung and Randy Hutson, ADGEOM 4613.
X(18872) lies on these lines: {3,9217}, {6,694}, {32,249}, {39,512}, {543,598}, {574,805}, {733,12074}, {2086,3229}
See Tran Quang Hung and Randy Hutson, ADGEOM 4613.
X(18873) lies on these lines: {262,6036}, {523,3629}, {576,2065}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27715.
X(18874) lies on these lines: {4,7693}, {5,51}, {30,11695}, { 140,13598}, {156,17809}, {185, 3857}, {373,550}, {381,6241}, { 382,11451}, {389,5066}, {546, 5943}, {547,5446}, {568,5068}
X(18874) = midpoint of X(i) and X(j) for these {i,j}: {5,10095}, {143,14128}, {546, 12006}, {1216,16982}, {3628, 10110}, {3850,5462}, {3861,9729}
X(18874) = reflection of X(i) in X(j) for these {i,j}: {3628,12046}, {11017,12811}, { 11592,16239}
X(18874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 51, 11591), (5, 143, 14128), (5, 13364, 10095), (381, 15026, 13630), (546, 5943, 12006), (10095, 14128, 143)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27718.
X(18875) lies on this line: {5,51}
X(18875) = midpoint of X(11583) and X(16336)
X(18876) lies on the cubics K039, K043, K113, K938 and these lines: {2, 112}, {3, 1177}, {32, 14376}, {97, 14586}, {132, 18420}, {186, 1297}, {248, 6334}, {276, 16813}, {524, 10317}, {577, 2482}, {858, 11605}, {906, 3998}, {1073, 1384}, {1214, 1415}, {2072, 10749}, {2080, 6760}, {2794, 18531}, {2799, 14910}, {2966, 11610}, {3153, 10735}, {3926, 4558}, {5866, 10766}, {9517, 14908}, {10422, 15899}, {10745, 14830}, {13310, 14489}, {13754, 17974}
X(18876) = isogonal conjugate of X(5523)
X(18876) = complement of X(34163)
X(18876) = X(2373)-Ceva conjugate of X(1177)
X(18876) = X(i)-cross conjugate of X(j) for these (i,j): {187, 3}, {14417, 4558}
X(18876) = X(2)-line conjugate of X(1560)
X(18876) = X(1177)-vertex conjugate of X(9517)
X(18876) = cevapoint of X(i) and X(j) for these (i,j): {3, 10317}, {6, 15139}, {577, 3292}
X(18876) = trilinear pole of line {184, 520}
X(18876) = circumcircle-inverse of X(1177)
X(18876) = crosssum of X(i) and X(j) for these (i,j): {6, 8428}, {2393, 14580}
X(18876) = barycentric product X(i)*X(j) for these {i,j}: {3, 2373}, {69, 1177}, {3265, 10423}, {6390, 10422}
X(18876) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 858}, {6, 5523}, {32, 14580}, {48, 18669}, {69, 1236}, {184, 2393}, {187, 1560}, {577, 14961}, {1177, 4}, {1204, 15126}, {1790, 17172}, {2373, 264}, {3292, 5181}, {10422, 17983}, {10423, 107}, {13754, 12827}
X(18876) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5523}, {4, 18669}, {19, 858}, {75, 14580}, {92, 2393}, {158, 14961}, {897, 1560}, {1236, 1973}, {1824, 17172}
Let P and U be the touchpoints of the tangents to the polar circle from X(74). Then X(18877) is the crossdifference of P and U. (Randy Hutson, October 15, 2018)
X(18877) lies on the cubic K381 and these lines: {6, 74}, {53, 10152}, {125, 6128}, {184, 1576}, {248, 14380}, {275, 6749}, {287, 524}, {394, 4558}, {526, 686}, {541, 3163}, {571, 14642}, {906, 3990}, {1304, 1971}, {1409, 1415}, {1562, 3018}, {1636, 2430}, {1989, 18320}, {1990, 15311}, {2871, 10602}, {3284, 11079}, {5467, 17974}, {14385, 14585}, {14533, 14586}
Let A'B'C' be the circumcevian triangle of X(6000). Let A" be the barycentric product B'*C', and define B" and C" cyclically. A", B", C" are collinear on the trilinear polar of the Cundy-Parry Phi transform of X(520). The lines AA", BB", CC" concur in X(18877). (Randy Hutson, August 19, 2019)
X(18877) = X(50)-cross conjugate of X(14533)
X(18877) = cevapoint of X(686) and X(3269)
X(18877) = crosspoint of X(i) and X(j) for these (i,j): {74, 14919}, {1294, 2986}
X(18877) = crossdifference of every pair of points on line {113, 133}
X(18877) = crosssum of X(i) and X(j) for these (i,j): {6, 14703}, {30, 1990}, {186, 15262}, {1650, 14391}, {3003, 6000}
X(18877) = trilinear pole of line X(184)X(39201)
X(18877) = barycentric product of circumcircle intercepts of line X(3)X(520)
X(18877) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1784}, {4, 14206}, {19, 3260}, {30, 92}, {75, 1990}, {158, 11064}, {264, 2173}, {273, 7359}, {318, 6357}, {561, 14581}, {811, 1637}, {823, 9033}, {1099, 16080}, {1495, 1969}, {1577, 4240}, {2166, 14920}, {2631, 6528}, {6335, 11125}, {9406, 18022}, {14400, 18026}
X(18877) = X(1726)-zayin conjugate of X(2173)
X(18877) = barycentric product X(i)*X(j) for these {i,j}: {3, 74}, {6, 14919}, {48, 2349}, {63, 2159}, {110, 14380}, {184, 1494}, {265, 14385}, {323, 11079}, {394, 8749}, {520, 1304}, {577, 16080}, {895, 9717}, {1073, 15291}, {2433, 4558}, {3292, 9139}, {5504, 14264}, {6000, 15404}, {10152, 14379}, {10419, 13754}, {15395, 16186}
X(18877) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3260}, {31, 1784}, {32, 1990}, {48, 14206}, {50, 14920}, {74, 264}, {184, 30}, {418, 1568}, {577, 11064}, {1304, 6528}, {1494, 18022}, {1501, 14581}, {1576, 4240}, {2159, 92}, {2349, 1969}, {2433, 14618}, {3049, 1637}, {5627, 18817}, {8749, 2052}, {9247, 2173}, {9407, 16240}, {11079, 94}, {14380, 850}, {14385, 340}, {14575, 1495}, {14585, 3284}, {14908, 9214}, {14919, 76}, {15291, 15466}, {16080, 18027}
X(18877) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (74, 15291, 8749), (8749, 15291, 6)
X(18878) lies on the Steiner circumellipse, the cubic K256, and on these lines: {99, 6563}, {249, 648}, {290, 1236}, {315, 5641}, {316, 1300}, {671, 2986}, {892, 15328}, {1494, 7799}, {2966, 15421}, {3228, 14910}, {4590, 15470}, {6528, 18020}
X(18878) = isogonal conjugate of X(21731)
X(18878) = isotomic conjugate of crosspoint of X(4) and X(476)
X(18878) = anticomplement of X(39021)
X(18878) = trilinear pole of line {2, 2986}
X(18878) = X(i)-cross conjugate of X(j) for these (i,j): {323, 4590}, {3260, 18020}, {10420, 687}, {15328, 2986}
X(18878) = cevapoint of X(i) and X(j) for these (i,j): {69, 3268}, {99, 10411}, {110, 2407}, {323, 15470}, {523, 11064}, {525, 10257}, {2986, 15328}, {5504, 15421}
X(18878) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1784}, {4, 14206}, {19, 3260}, {30, 92}, {75, 1990}, {158, 11064}, {264, 2173}, {273, 7359}, {318, 6357}, {561, 14581}, {811, 1637}, {823, 9033}, {1099, 16080}, {1495, 1969}, {1577, 4240}, {2166, 14920}, {2631, 6528}, {6335, 11125}, {9406, 18022}, {14400, 18026}
X(18878) = barycentric product X(i)*X(j) for these {i,j}: {69, 687}, {76, 10420}, {99, 2986}, {670, 14910}, {1300, 4563}, {4590, 15328}, {5504, 6331}, {15421, 18020}
X(18878) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 686}, {69, 6334}, {99, 3580}, {110, 3003}, {249, 15329}, {648, 403}, {662, 1725}, {687, 4}, {1300, 2501}, {2407, 113}, {2986, 523}, {4235, 12828}, {4558, 13754}, {4575, 2315}, {5504, 647}, {10419, 2433}, {10420, 6}, {12028, 14582}, {14590, 1986}, {14910, 512}, {15328, 115}, {15421, 125}, {15454, 1637}, {15470, 2088}, {18020, 16237}
X(18879) lies on these lines: {24, 250}, {249, 1993}, {687, 2407}, {691, 10420}, {1300, 10723}, {2966, 15421}, {4590, 7763}, {4611, 5649}
X(18879) = X(i)-cross conjugate of X(j) for these (i,j): {186, 99}, {3003, 110}, {14910, 10420}
X(18879) = cevapoint of X(i) and X(j) for these (i,j): {110, 3003}, {323, 4558}, {10420, 14910}
X(18879) = X(i)-isoconjugate of X(j) for these (i,j): {115, 1725}, {403, 3708}, {1109, 3003}, {2315, 2970}, {2643, 3580}
X(18879) = polar conjugate of {X(39240),X(39241)}-harmonic conjugate of X(136)
X(18879) = trilinear pole of line {110, 924}
X(18879) = barycentric product X(i)*X(j) for these {i,j}: {99, 10420}, {249, 2986}, {687, 4558}, {4590, 14910}, {5504, 18020}
X(18879) = barycentric quotient X(i)/X(j) for these {i,j}: {186, 16221}, {249, 3580}, {250, 403}, {687, 14618}, {1101, 1725}, {1300, 2970}, {2986, 338}, {4558, 6334}, {5504, 125}, {10419, 12079}, {10420, 523}, {14910, 115}
X(18880) lies on the cubic K375
X(18881) = isogonal conjugate of X(19221)
X(18881) = barycentric product X(6)*X(18880)
X(18881) = barycentric quotient X(32)/X(19220)
X(18881) = trilinear product X(31)*X(18880)
X(18881) = trilinear quotient X(31)/X(19220)
X(18881) = lies on the circumconic with center X(113)
X(18881) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(110)}} and {{A, B, C, X(111), X(2353)}}
X(18881) = X(75)-isoconjugate-of-X(19220)
X(18881) = X(32)-reciprocal conjugate of-X(19220)
X(18882) lies on the cubic K428 and these lines: {20, 49}, {23, 206}, {69, 11003}, {110, 3818}, {184, 323}, {378, 399}, {1147, 11459}, {2916, 6800}, {3047, 17847}, {7391, 9544}, {9704, 10323}, {11597, 12383}, {12219, 18445}
X(18882) = barycentric product X(6)X(14558)
X(18882) = barycentric quotient X(14558)/X(76)
X(18883) lies on the cubic K491 and these lines: {2, 94}, {5, 49}, {24, 136}, {254, 6344}, {381, 18576}, {403, 12028}, {468, 476}, {626, 11060}, {1995, 3425}, {2006, 7110}, {3091, 18300}, {3545, 18316}, {3580, 16310}, {6132, 10412}
X(18883) = isotomic conjugate of X(37802)
X(18883) = cevapoint of X(5) and X(16310)
X(18883) = crossdifference of every pair of points on line {2081, 14270}
X(18883) = trilinear pole of line {52, 924}
X(18883) = X(18127)-complementary conjugate of X(18589)
X(18883) = X(18817)-Ceva conjugate of X(265)
X(18883) = polar conjugate of X(5962)
X(18883) = X(i)-isoconjugate of X(j) for these (i,j): {48, 5962}, {50, 91}, {96, 2290}, {186, 1820}, {925, 2624}, {1154, 2168}, {2165, 6149}
X(18883) = {X(8836),X(8838)}-harmonic conjugate of X(265)
X(18883) = barycentric product X(i)*X(j) for these {i,j}: {24, 328}, {94, 1993}, {264, 5961}, {265, 317}, {476, 6563}, {1147, 18817}, {1989, 7763}, {6344, 9723}
X(18883) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 5962}, {24, 186}, {47, 6149}, {52, 1154}, {94, 5392}, {265, 68}, {317, 340}, {467, 14918}, {476, 925}, {571, 50}, {924, 526}, {1141, 96}, {1989, 2165}, {1993, 323}, {2166, 91}, {2180, 2290}, {5961, 3}, {6344, 847}, {6563, 3268}, {7763, 7799}, {11547, 14165}, {14111, 562}, {14576, 11062}, {18384, 14593}
X(18884) lies on the conic {{A, B, C, X(2), X(7)}}, the cubic K745, and on this line: {7, 10500}
Let (Oa), (Ob), (Oc) be the circles centered at A, B, C, resp., and externally tangent to the incircle. Let A' be the insimilicenter of (Ob) and (Oc), and define B' and C' cyclically. The lines AA', BB', CC' concur in X(18885). (Randy Hutson, June 27, 2018)
X(18885) lies on the cubics K745, K746, K972, and these lines: {37,2089}, {173,13443}, {178,10489}, {1400,12809}, {1418,7371}, {7707,10502}
X(18885) = X(555)-Ceva conjugate of X(7)
X(18885) = X(i)-cross conjugate of X(j) for these (i,j): {173, 7057}, {2089, 7}
X(18885) = cevapoint of X(i) and X(j) for these (i,j): {234, 14596}
X(18885) = X(i)-isoconjugate of X(j) for these (i,j): {41, 7048}, {55, 258}, {289, 6726}
X(18885) = barycentric product X(i)*X(j) for these {i,j}: {7, 7057}, {85, 173}, {236, 555}, {2089, 4146}, {7022, 7048}
X(18885) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 7048}, {57, 258}, {173, 9}, {174, 7028}, {234, 2090}, {236, 6731}, {2089, 188}, {7022, 7057}, {7057, 8}, {7370, 289}, {7371, 1488}, {10490, 15997}, {13444, 3659}, {14596, 16015}
X(18886) lies on these lines: {1, 10489}, {2, 4146}, {7, 174}, {177, 11192}, {279, 555}, {2089, 7022}, {5435, 7371}, {8113, 8387}, {10499, 13092}
X(18886) = X(10489)-Ceva conjugate of X(10502)
X(18886) = crosspoint of X(i) and X(j) for these (i,j): {10490, 14596}
X(18886) = X(i)-isoconjugate of X(j) for these (i,j): {1252, 10491}, {4564, 10501}
X(18886) = barycentric product X(i)*X(j) for these {i,j}: {1, 10489}, {7, 10502}, {177, 177}, {178, 10490}, {234, 7707}, {14596, 16016}
X(18886) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 10491}, {3271, 10501}, {10489, 75}, {10502, 8}
X(18887) lies on the cubic K746 and these lines: {37, 259}, {234, 14596}, {7707, 10500}, {8965, 10232}
X(18887) = crosspoint of X(i) and X(j) for these (i,j): {7707, 16016}, {15997, 16015}
X(18887) = barycentric product X(i)*X(j) for these {i,j}: {178, 15997}, {2090, 7707}, {7048, 10502}, {16015, 16016}
X(18887) = barycentric quotient X(10502)/X(7057)
X(18888) lies on these lines: {6, 266}, {9, 173}, {55, 259}, {57, 7371}, {284, 6727}, {2291, 13444}, {7707, 10500}
X(18888) = X(i)-Ceva conjugate of X(j) for these (i,j): {57, 10490}, {173, 7707}, {177, 16012}
X(18888) = X(i)-isoconjugate of X(j) for these (i,j): {2, 260}, {100, 10492}
X(18888) = crosspoint of X(i) and X(j) for these (i,j): {57, 266}, {177, 14596}, {8372, 16015}
X(18888) = trilinear pole of line {663, 6729}
X(18888) = crosssum of X(i) and X(j) for these (i,j): {9, 188}, {258, 7028}
X(18888) = barycentric product X(i)*X(j) for these {i,j}: {1, 177}, {7, 16012}, {9, 14596}, {57, 16016}, {173, 16015}, {174, 7707}, {178, 266}, {188, 10490}, {234, 259}, {260, 10489}, {522, 13444}, {2089, 15997}, {7057, 16011}, {8372, 13443}
X(18888) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 260}, {177, 75}, {649, 10492}, {7707, 556}, {10490, 4146}, {13444, 664}, {14596, 85}, {16011, 7048}, {16012, 8}, {16016, 312}
X(18888) = {X(173),X(8078)}-harmonic conjugate of X(9)
X(18889) lies on these lines: {6, 109}, {41, 692}, {44, 294}, {220, 3939}, {607, 8750}, {643, 2287}, {911, 7113}
X(18889) = isogonal conjugate of X(37780)
X(18889) = crosspoint of X(2291) and X(4845)
X(18889) = crossdifference of every pair of points on line {6366, 10427}
X(18889) = crosssum of X(527) and X(1323)
X(18889) = trilinear pole of line {41, 8641}
X(18889) = X(169)-zayin conjugate of X(1155)
X(18889) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1323}, {7, 527}, {75, 6610}, {63,38461}, {85, 1155}, {273, 6510}, {279, 6745}, {658, 6366}, {664, 1638}, {1055, 6063}, {1088, 6603}, {1121, 3321}, {4554, 14413}, {6647, 7249}, {13149, 14414}
X(18889) = barycentric product X(i)*X(j) for these {i,j}: {1, 4845}, {9, 2291}, {41, 1121}, {55, 1156}, {3900, 14733}, {5526, 15734}, {10426, 15733}
X(18889) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 1323}, {32, 6610}, {41, 527}, {1156, 6063}, {1253, 6745}, {2175, 1155}, {2291, 85}, {3063, 1638}, {4845, 75}, {8641, 6366}, {9447, 1055}, {14733, 4569}, {14827, 6603}
X(18890) lies on the cubic K307 and these lines: {154, 160}, {216, 631}, {577, 14371}
X(18890) = X(51)-cross conjugate of X(3)
X(18890) = crosspoint of X(1073) and X(13855)
X(18890) = crosssum of X(1075) and X(1249)
X(18890) = isotomic conjugate of the polar conjugate of X(32319)
X(18890) = X(i)-isoconjugate of X(j) for these (i,j): {92, 6759}, {2167, 14363}
X(18890) = barycentric product X(i)*X(j) for these {i,j}: {3, 15318}, {5, 14371}
X(18890) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 14363}, {184, 6759}, {14371, 95}, {15318, 264}
X(18891) lies on the cubic K1024 and these lines:
{10, 18833}, {75, 700}, {76, 321}, {239, 3978}, {305, 3705}, {308, 17289}, {310, 3741}, {318, 18022}, {320, 670}, {693, 784}, {894, 9230}, {1269, 6385}, {1281, 8783}, {1921, 3797}, {1926, 4087}, {1978, 3912}, {3264, 6386}, {3662, 6374}, {4044, 18152}, {6063, 7185}, {6376, 7034}
X(18891) = isogonal conjugate of X(14598)
X(18891) = isotomic conjugate of X(1911)
X(18891) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14598}, {6, 1922}, {31, 1911}, {32, 292}, {56, 18265}, {171, 1927}, {172, 9468}, {213, 18268}, {238, 18267}, {291, 560}, {295, 1974}, {334, 1917}, {335, 1501}, {660, 1980}, {692, 875}, {741, 1918}, {813, 1919}, {894, 8789}, {1397, 7077}, {1920, 14604}, {1924, 4584}, {1967, 7122}, {1973, 2196}, {4589, 9426}, {7233, 9448}, {7234, 17938}, {17735, 18263}
X(18891) = X(76)-Hirst inverse of X(561)
X(18891) = cevapoint of X(1921) and X(4087)
X(18891) = crossdifference of every pair of points on line {1980, 2205}
X(18891) = X(i)-isoconjugate of X(j) for these (i,j): {92, 6759}, {2167, 14363}
X(18891) = barycentric product X(i)*X(j) for these {i,j}: {75, 1921}, {76, 350}, {85, 4087}, {238, 1502}, {239, 561}, {256, 14603}, {257, 1926}, {310, 3948}, {312, 18033}, {740, 6385}, {812, 6386}, {871, 3797}, {874, 3261}, {1914, 1928}, {1978, 3766}, {3596, 10030}, {3975, 6063}, {3978, 7018}, {4010, 4602}, {7260, 14295}, {18032, 18035}, {18036, 18037}
X(18891) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1922}, {2, 1911}, {6, 14598}, {9, 18265}, {69, 2196}, {75, 292}, {76, 291}, {86, 18268}, {238, 32}, {239, 31}, {242, 1973}, {256, 9468}, {257, 1967}, {274, 741}, {292, 18267}, {304, 295}, {312, 7077}, {314, 2311}, {350, 6}, {385, 7122}, {514, 875}, {561, 335}, {659, 1919}, {668, 813}, {670, 4584}, {693, 3572}, {740, 213}, {874, 101}, {893, 1927}, {904, 8789}, {1429, 1397}, {1447, 604}, {1502, 334}, {1914, 560}, {1920, 18787}, {1921, 1}, {1926, 894}, {1929, 18263}, {1966, 172}, {1978, 660}, {2201, 1974}, {2210, 1501}, {2238, 1918}, {3261, 876}, {3263, 3252}, {3570, 692}, {3596, 4876}, {3684, 2175}, {3685, 41}, {3716, 3063}, {3747, 2205}, {3766, 649}, {3797, 869}, {3948, 42}, {3975, 55}, {3978, 171}, {4010, 798}, {4037, 872}, {4087, 9}, {4148, 8641}, {4366, 2210}, {4432, 2251}, {4455, 1924}, {4486, 788}, {4495, 2242}, {4602, 4589}, {4603, 17938}, {4609, 4639}, {4760, 922}, {6385, 18827}, {6386, 4562}, {6651, 18266}, {7018, 694}, {7193, 9247}, {7260, 805}, {8299, 9454}, {8300, 14599}, {8632, 1980}, {10030, 56}, {14024, 2204}, {14433, 890}, {14599, 1917}, {14603, 1909}, {16609, 1402}, {17493, 904}, {17755, 2223}, {17984, 7119}, {18032, 9506}, {18033, 57}, {18035, 1757}, {18037, 17798}, {18277, 3510}, {18786, 7104}
X(18891) = {X(76),X(6382)}-harmonic conjugate of X(3661)
X(18892) lies on these lines: {32, 1917}, {172, 1932}, {560, 1501}, {1914, 1933}, {4161, 18759}, {6066, 9459}
X(18892) = X(i)-isoconjugate of X(j) for these (i,j): {75, 334}, {76, 335}, {264, 337}, {291, 561}, {292, 1502}, {295, 18022}, {313, 18827}, {693, 4583}, {850, 4589}, {871, 3864}, {876, 6386}, {1577, 4639}, {1909, 1934}, {1911, 1928}, {1916, 1920}, {1978, 4444}, {3261, 4562}, {3596, 7233}, {4518, 6063}
X(18892) = X(560)-Hirst inverse of X(1501)
X(18892) = barycentric product X(i)*X(j) for these {i,j}: {1, 14599}, {6, 2210}, {31, 1914}, {32, 238}, {41, 1428}, {163, 4455}, {184, 2201}, {213, 5009}, {239, 560}, {242, 9247}, {256, 14602}, {350, 1501}, {692, 8632}, {893, 1933}, {904, 1691}, {1333, 3747}, {1397, 3684}, {1429, 2175}, {1447, 9447}, {1580, 7104}, {1917, 1921}, {1919, 3573}, {1922, 8300}, {1973, 7193}, {1980, 3570}, {2112, 18264}, {2206, 2238}, {4366, 14598}, {4433, 16947}, {6652, 18267}, {6654, 9455}, {8852, 18038}, {9448, 10030}
X(18892) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 334}, {238, 1502}, {239, 1928}, {560, 335}, {1501, 291}, {1576, 4639}, {1914, 561}, {1917, 292}, {1933, 1920}, {1980, 4444}, {2201, 18022}, {2210, 76}, {5009, 6385}, {7104, 1934}, {9233, 1911}, {9247, 337}, {9447, 4518}, {9448, 4876}, {14574, 4584}, {14599, 75}, {14602, 1909}
X(18893) lies on these lines: {291, 7122}, {560, 1922}, {1911, 2206}
X(18893) = X(i)-isoconjugate of X(j) for these (i,j): {76, 1921}, {238, 1928}, {239, 1502}, {257, 14603}, {350, 561}, {1926, 7018}, {3596, 18033}, {3766, 6386}, {3948, 6385}, {4010, 4609}, {4087, 6063}
X(18893) = barycentric product X(i)*X(j) for these {i,j}: {6, 14598}, {31, 1922}, {32, 1911}, {171, 8789}, {172, 1927}, {291, 1501}, {292, 560}, {334, 9233}, {335, 1917}, {604, 18265}, {741, 2205}, {813, 1980}, {1909, 14604}, {1914, 18267}, {1918, 18268}, {1974, 2196}, {4584, 9426}, {7122, 9468}, {18263, 18266}
X(18893) = barycentric quotient X(i)/X(j) for these {i,j}: {292, 1928}, {560, 1921}, {1501, 350}, {1911, 1502}, {1917, 239}, {1922, 561}, {7122, 14603}, {8789, 7018}, {9233, 238}, {9447, 4087}, {9448, 3975}, {14598, 76}, {14604, 256}
X(18894) lies on these lines: {560, 9233}, {1501, 1917}, {2210, 14602}
X(18894) = X(1501)-Hirst inverse of X(1917)
X(18894) = X(i)-isoconjugate of X(j) for these (i,j): {76, 334}, {291, 1502}, {292, 1928}, {335, 561}, {337, 1969}, {850, 4639}, {1920, 1934}, {3261, 4583}, {4444, 6386}
X(18894) = barycentric product X(i)*X(j) for these {i,j}: {6, 14599}, {31, 2210}, {32, 1914}, {238, 560}, {239, 1501}, {242, 14575}, {350, 1917}, {893, 14602}, {904, 1933}, {1428, 2175}, {1429, 9447}, {1447, 9448}, {1576, 4455}, {1691, 7104}, {1918, 5009}, {1921, 9233}, {1974, 7193}, {1980, 3573}, {2201, 9247}, {2206, 3747}, {4010, 14574}, {8300, 14598}, {12835, 18265}
X(18894) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 1928}, {560, 334}, {1501, 335}, {1914, 1502}, {1917, 291}, {2210, 561}, {9233, 292}, {9448, 4518}, {14574, 4589}, {14575, 337}, {14599, 76}, {14602, 1920}
X(18895) lies on these lines: {75, 291}, {76, 334}, {274, 292}, {295, 4589}, {304, 4876}, {310, 321}, {337, 16747}, {561, 8024}, {789, 1281}, {894, 1922}, {1921, 3263}, {3978, 17789}, {4459, 18830}, {4639, 18359}, {6063, 6358}, {6386, 16732}, {10471, 18827}
X(18895) = isogonal conjugate of X(14599)
X(18895) = isotomic conjugate of X(1914)
X(18895) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14599}, {6, 2210}, {31, 1914}, {32, 238}, {41, 1428}, {163, 4455}, {184, 2201}, {213, 5009}, {239, 560}, {242, 9247}, {256, 14602}, {350, 1501}, {692, 8632}, {893, 1933}, {904, 1691}, {1333, 3747}, {1397, 3684}, {1429, 2175}, {1447, 9447}, {1580, 7104}, {1917, 1921}, {1919, 3573}, {1922, 8300}, {1973, 7193}, {1980, 3570}, {2112, 18264}, {2206, 2238}, {4366, 14598}, {4433, 16947}, {6652, 18267}, {6654, 9455}, {8852, 18038}, {9448, 10030}
X(18895) = X(i)-Hirst inverse of X(j) for these (i,j): {76, 334}, {335, 1920}, {1921, 18034}
X(18895) = cevapoint of X(i) and X(j) for these (i,j): {75, 17789}, {321, 3263}, {335, 337}
X(18895) = trilinear pole of line {313, 3261}
X(18895) = barycentric product X(i)*X(j) for these {i,j}: {75, 334}, {76, 335}, {264, 337}, {291, 561}, {292, 1502}, {295, 18022}, {313, 18827}, {693, 4583}, {850, 4589}, {871, 3864}, {876, 6386}, {1577, 4639}, {1909, 1934}, {1911, 1928}, {1916, 1920}, {1978, 4444}, {3261, 4562}, {3596, 7233}, {4518, 6063}
X(18895) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2210}, {2, 1914}, {6, 14599}, {7, 1428}, {10, 3747}, {69, 7193}, {75, 238}, {76, 239}, {85, 1429}, {86, 5009}, {92, 2201}, {171, 1933}, {172, 14602}, {264, 242}, {291, 31}, {292, 32}, {295, 184}, {312, 3684}, {313, 740}, {321, 2238}, {334, 1}, {335, 6}, {337, 3}, {349, 16609}, {350, 8300}, {514, 8632}, {523, 4455}, {561, 350}, {660, 692}, {668, 3573}, {693, 659}, {694, 7104}, {741, 2206}, {850, 4010}, {875, 1980}, {894, 1691}, {1237, 4039}, {1269, 4974}, {1441, 1284}, {1447, 12835}, {1502, 1921}, {1581, 904}, {1909, 1580}, {1911, 560}, {1916, 893}, {1920, 385}, {1921, 4366}, {1922, 1501}, {1934, 256}, {1978, 3570}, {2113, 18264}, {2196, 9247}, {2533, 5027}, {3252, 9454}, {3261, 812}, {3262, 15507}, {3263, 8299}, {3264, 4432}, {3266, 4760}, {3509, 18038}, {3572, 1919}, {3596, 3685}, {3661, 16514}, {3701, 4433}, {3864, 869}, {4036, 4155}, {4374, 4164}, {4391, 4435}, {4444, 649}, {4518, 55}, {4562, 101}, {4583, 100}, {4584, 163}, {4589, 110}, {4639, 662}, {4876, 41}, {5378, 1110}, {6063, 1447}, {6386, 874}, {7018, 18786}, {7077, 2175}, {7233, 56}, {7245, 2242}, {14598, 1917}, {15523, 4093}, {16720, 8623}, {18031, 6654}, {18034, 8301}, {18265, 9448}, {18760, 16366}, {18787, 7122}, {18827, 58}
Let A'B'C' and A"B"C" be the 1st Brocard and 1st anti-Brocard triangles, resp. Let A* be the barycentric product A'*A", and define B*, C* cyclically. The lines AA*, BB*, CC* concur in X(18896). (Randy Hutson, June 27, 2018)
X(18896) lies on the cubic K1023 and these lines: {2, 3114}, {5, 6234}, {76, 115}, {83, 3115}, {141, 308}, {264, 5117}, {290, 325}, {313, 1934}, {315, 17970}, {316, 805}, {334, 1581}, {338, 1502}, {733, 6572}, {880, 11646}, {882, 14295}, {2086, 3225}, {5031, 14603}, {5207, 9467}, {7752, 14251}, {7937, 11654}
X(18896) = isogonal conjugate of X(14602)
X(18896) = isotomic conjugate of X(1691)
X(18896) = X(5031)-cross conjugate of X(2)
X(18896) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14602}, {6, 1933}, {31, 1691}, {32, 1580}, {163, 5027}, {171, 14599}, {172, 2210}, {385, 560}, {419, 9247}, {1101, 2086}, {1501, 1966}, {1914, 7122}, {1917, 3978}, {1924, 17941}, {1926, 9233}, {1927, 4027}, {9236, 16985}
X(18896) = X(i)-Hirst inverse of X(j) for these (i,j): {76, 1916}, {694, 9230}
X(18896) = cevapoint of X(i) and X(j) for these (i,j): {2, 5207}, {141, 325}
X(18896) = trilinear pole of line {850, 2528}
X(18896) = {X(334),X(7018)}-harmonic conjugate of X(1581)
X(18896) = barycentric product X(i)*X(j) for these {i,j}: {75, 1934}, {76, 1916}, {327, 8842}, {334, 7018}, {561, 1581}, {694, 1502}, {850, 18829}, {882, 4609}, {1928, 1967}, {8024, 14970}
X(18896) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1933}, {2, 1691}, {6, 14602}, {75, 1580}, {76, 385}, {115, 2086}, {141, 8623}, {256, 2210}, {257, 1914}, {264, 419}, {291, 7122}, {305, 12215}, {313, 4039}, {334, 171}, {335, 172}, {337, 3955}, {523, 5027}, {561, 1966}, {670, 17941}, {693, 4164}, {694, 32}, {805, 1576}, {850, 804}, {868, 2679}, {881, 9426}, {882, 669}, {893, 14599}, {1502, 3978}, {1581, 31}, {1916, 6}, {1927, 1917}, {1928, 1926}, {1930, 2236}, {1934, 1}, {1967, 560}, {3261, 4107}, {3266, 5026}, {3978, 4027}, {4518, 2330}, {4583, 4579}, {4609, 880}, {7018, 238}, {7019, 7193}, {7249, 1428}, {8024, 732}, {8789, 9233}, {8842, 182}, {9230, 16985}, {9468, 1501}, {14251, 9418}, {14970, 251}, {15391, 14600}, {17938, 14574}, {17970, 14575}, {17980, 1974}, {18022, 17984}, {18024, 14382}, {18276, 18270}, {18829, 110}
X(18897) lies on these lines: {32, 1911}, {172, 335}, {292, 1333}, {560, 14598}, {609, 18787}, {697, 813}, {741, 769}, {1492, 18274}, {1922, 2205}, {1927, 14604}
X(18897) = isogonal conjugate of isotomic conjugate of X(1922)
X(18897) = X(i)-isoconjugate of X(j) for these (i,j): {75, 1921}, {76, 350}, {85, 4087}, {238, 1502}, {239, 561}, {256, 14603}, {257, 1926}, {310, 3948}, {312, 18033}, {740, 6385}, {812, 6386}, {871, 3797}, {874, 3261}, {1914, 1928}, {1978, 3766}, {3596, 10030}, {3975, 6063}, {3978, 7018}, {4010, 4602}, {7260, 14295}, {18032, 18035}, {18036, 18037}
X(18897) = X(i)-Hirst inverse of X(j) for these (i,j): {560, 14598}
X(18897) = barycentric product X(i)*X(j) for these {i,j}: {1, 14598}, {6, 1922}, {31, 1911}, {32, 292}, {56, 18265}, {171, 1927}, {172, 9468}, {213, 18268}, {238, 18267}, {291, 560}, {295, 1974}, {334, 1917}, {335, 1501}, {660, 1980}, {692, 875}, {741, 1918}, {813, 1919}, {894, 8789}, {1397, 7077}, {1920, 14604}, {1924, 4584}, {1967, 7122}, {1973, 2196}, {4589, 9426}, {7233, 9448}, {7234, 17938}, {17735, 18263}
X(18897) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1921}, {172, 14603}, {291, 1928}, {292, 1502}, {560, 350}, {1397, 18033}, {1501, 239}, {1911, 561}, {1917, 238}, {1922, 76}, {1927, 7018}, {1980, 3766}, {2175, 4087}, {2205, 3948}, {7122, 1926}, {8789, 257}, {9233, 1914}, {9426, 4010}, {9447, 3975}, {9448, 3685}, {14598, 75}, {14604, 893}, {18265, 3596}, {18267, 334}, {18268, 6385}
X(18898) lies on the conic {{A,B,C,X(2),X(6)}}, the cubic K1013, and on these lines: {2, 1501}, {6, 6660}, {32, 694}, {37, 983}, {251, 3981}, {263, 12212}, {308, 3114}, {2987, 13330}, {3108, 5012}, {5038, 11175}
X(18898) = isogonal conjugate of X(3314)
X(18898) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3314}, {63, 5117}, {75, 3094}, {76, 3116}, {561, 3117}, {824, 3888}, {982, 3661}, {984, 3662}, {1581, 9865}, {3061, 7179}, {3705, 7146}, {3776, 3799}, {3777, 3807}, {3786, 16888}, {3794, 16603}, {4602, 17415}
X(18898) = barycentric product X(i)*X(j) for these {i,j}: {6, 3407}, {31, 3113}, {32, 3114}, {251, 14617}, {983, 985}, {1976, 8840}, {2344, 7132}, {9063, 9426}
X(18898) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3314}, {25, 5117}, {32, 3094}, {560, 3116}, {1501, 3117}, {1691, 9865}, {3113, 561}, {3114, 1502}, {3407, 76}, {9426, 17415}, {14617, 8024}
X(18899) lies on the cubic K1016 and these lines: {2, 6}, {32, 8789}, {39, 1186}, {110, 707}, {194, 3499}, {1207, 7786}, {1501, 9233}, {3116, 7032}
X(18899) = crosssum of X(1502) and X(10010)
X(18899) = crossdifference of every pair of points on line {512, 14295}
X(18899) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3114}, {76, 3113}, {561, 3407}, {661, 9063}, {871, 17743}, {7034, 14621}, {14617, 18833}
X(18899) = {X(6),X(1613)}-harmonic conjugate of X(385)
X(18899) = barycentric product X(i)*X(j) for these {i,j}: {6, 3117}, {31, 3116}, {32, 3094}, {99, 9006}, {110, 17415}, {869, 7032}, {1501, 3314}, {3888, 8630}, {5117, 14575}, {8789, 9865}
X(18899) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3114}, {110, 9063}, {560, 3113}, {869, 7034}, {1501, 3407}, {3094, 1502}, {3116, 561}, {3117, 76}, {7032, 871}, {9006, 523}, {9418, 8840}, {17415, 850}
X(18900) lies on these lines: {6, 31}, {32, 1922}, {100, 701}, {101, 717}, {314, 983}, {560, 1501}, {595, 3802}, {872, 1185}, {985, 4279}, {2175, 7104}, {2176, 18756}, {2236, 4376}, {3187, 3797}, {3510, 3550}, {4386, 8622}, {7032, 16693}
X(18900) = isogonal conjugate of X(871)
X(18900) = X(2175)-beth conjugate of X(31)
X(18900) = X(i)-isoconjugate of X(j) for these (i,j): {1, 871}, {75, 870}, {76, 14621}, {561, 985}, {693, 789}, {1086, 5388}, {1978, 4817}, {3114, 3662}, {3261, 4586}
X(18900) = barycentric product X(i)*X(j) for these {i,j}: {6, 869}, {31, 2276}, {32, 984}, {41, 1469}, {58, 3774}, {101, 788}, {190, 8630}, {213, 3736}, {560, 3661}, {604, 4517}, {692, 3250}, {901, 14436}, {983, 3117}, {1911, 16514}, {1919, 3799}, {1922, 3783}, {1973, 3781}, {1980, 3807}, {2175, 7146}, {2210, 3862}, {3797, 14598}, {3864, 14599}, {7179, 9447}, {7204, 14827}
X(18900) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 871}, {32, 870}, {560, 14621}, {788, 3261}, {869, 76}, {984, 1502}, {1110, 5388}, {1501, 985}, {1980, 4817}, {2276, 561}, {3661, 1928}, {3736, 6385}, {3774, 313}, {8630, 514}, {9448, 2344}
X(18900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (31, 2209, 1914), (2205, 9455, 560)
X(18901) lies on these lines: {76, 14820}, {325, 4609}, {1502, 3314}, {9865, 14603}, {10010, 16986}
X(18901) = isogonal conjugate of X(14604)
X(18901) = isotomic conjugate of X(8789)
X(18901) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14604}, {31, 8789}, {32, 1927}, {560, 9468}, {694, 1917}, {1501, 1967}, {1581, 9233}, {1924, 17938}, {7104, 14598}
X(18901) = barycentric product X(i)*X(j) for these {i,j}: {76, 14603}, {561, 1926}, {1502, 3978}, {1928, 1966}, {4609, 14295}
X(18901) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8789}, {6, 14604}, {75, 1927}, {76, 9468}, {305, 17970}, {385, 1501}, {561, 1967}, {670, 17938}, {804, 9426}, {850, 881}, {880, 1576}, {1502, 694}, {1580, 1917}, {1691, 9233}, {1909, 14598}, {1920, 1922}, {1921, 7104}, {1926, 31}, {1928, 1581}, {1966, 560}, {3978, 32}, {4609, 805}, {5976, 9418}, {12215, 14575}, {14295, 669}, {14296, 1980}, {14382, 14601}, {14603, 6}, {17941, 14574}, {17984, 1974}, {18022, 17980}
X(18902) lies on these lines: {32, 14820}, {50, 3289}, {1501, 9233}
X(18902) = X(i)-Hirst inverse of X(j) for these (i,j): {1501, 9233}
X(18902) = X(i)-isoconjugate of X(j) for these (i,j): {76, 1934}, {561, 1916}, {694, 1928}, {1502, 1581}
X(18902) = barycentric product X(i)*X(j) for these {i,j}: {6, 14602}, {31, 1933}, {32, 1691}, {172, 14599}, {385, 1501}, {419, 14575}, {560, 1580}, {804, 14574}, {1576, 5027}, {1917, 1966}, {2210, 7122}, {3978, 9233}, {4027, 8789}, {9426, 17941}
X(18902) = barycentric quotient X(i)/X(j) for these {i,j}: {560, 1934}, {1501, 1916}, {1580, 1928}, {1691, 1502}, {1917, 1581}, {1933, 561}, {9233, 694}, {14574, 18829}, {14602, 76}
X(18903) lies on these lines: {1501, 9468}, {8789, 14574}, {9233, 14604}
X(18903) = X(i)-Hirst inverse of X(j) for these (i,j): {9233, 14604}
X(18903) = X(i)-isoconjugate of X(j) for these (i,j): {561, 14603}, {1502, 1926}, {1928, 3978}
X(18903) = barycentric product X(i)*X(j) for these {i,j}: {6, 14604}, {32, 8789}, {560, 1927}, {694, 9233}, {881, 14574}, {1501, 9468}, {1917, 1967}, {9426, 17938}
X(18903) = barycentric quotient X(i)/X(j) for these {i,j}: {1501, 14603}, {1917, 1926}, {1927, 1928}, {8789, 1502}, {9233, 3978}, {14604, 76}
X(18904) lies on the cubic K1035 and these lines: {2, 893}, {10, 37}, {39, 3821}, {142, 16604}, {226, 16606}, {238, 1691}, {292, 4645}, {722, 2887}, {732, 1107}, {804, 3709}, {812, 14838}, {874, 17279}, {1001, 18755}, {1100, 15989}, {1279, 9423}, {1284, 2238}, {1575, 1738}, {1716, 16968}, {1921, 14603}, {2229, 3120}, {2240, 3724}, {2275, 3662}, {3006, 8620}, {3061, 3094}, {3121, 3936}, {3721, 3778}, {3777, 3808}, {4657, 17030}, {4892, 16592}, {16591, 16609}, {16886, 16889}
X(18904) = midpoint of X(1966) and X(17493)
X(18904) = complement X(1966)
X(18904) = X(i)-complementary conjugate of X(j) for these (i,j): {32, 5976}, {512, 2679}, {694, 141}, {733, 3934}, {805, 512}, {881, 115}, {882, 125}, {904, 17793}, {1581, 2887}, {1916, 626}, {1927, 37}, {1967, 10}, {7104, 17755}, {8789, 39}, {9468, 2}, {14251, 114}, {14604, 8265}, {14946, 6656}, {17938, 523}, {17970, 3}, {17980, 5}
X(18904) = X(13576)-Ceva conjugate of X(4531)
X(18904) = crosspoint of X(i) and X(j) for these (i,j): {2, 1581}, {238, 1921}
X(18904) = crossdifference of every pair of points on line {983, 3733}
X(18904) = crosssum of X(i) and X(j) for these (i,j): {6, 1580}, {291, 1922}
X(18904) = X(i)-isoconjugate of X(j) for these (i,j): {741, 17743}, {813, 7255}, {1019, 8684}, {7033, 18268}
X(18904) = X(3721)-Hirst inverse of X(3778)
X(18904) = barycentric product X(i)*X(j) for these {i,j}: {238, 2887}, {239, 3721}, {350, 3778}, {740, 982}, {812, 7239}, {1284, 3705}, {1429, 4136}, {1921, 16584}, {2238, 3662}, {2275, 3948}, {3061, 16609}, {3573, 3801}, {3684, 16888}, {3794, 7235}, {3808, 3952}, {3865, 4039}, {3888, 4010}, {4433, 7185}, {4531, 18033}
X(18904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 17493, 1966), (1921, 18277, 14603)
X(18905) lies on the cubic K1036 and these lines: {2, 292}, {10, 16606}, {37, 226}, {171, 1691}, {722, 2887}, {893, 4645}, {982, 3094}, {1215, 16587}, {1575, 3687}, {1920, 14603}, {2229, 15523}, {2275, 3705}, {3121, 4972}, {3663, 17459}, {4847, 17448}, {7187, 9865}, {8620, 17184}
X(18905) = midpoint of X(1965) and X(17485)
X(18905) = complement X[1965]
X(18905) = X(i)-complementary conjugate of X(j) for these (i,j): {695, 141}, {9229, 626}, {9236, 37}, {9285, 2887}, {9288, 10}, {14946, 325}
X(18905) = crosspoint of X(i) and X(j) for these (i,j): {2, 9285}, {171, 1920}, {7184, 7187}
X(18905) = crosssum of X(i) and X(j) for these (i,j): {6, 1582}, {256, 7104}
X(18905) = X(1178)-isoconjugate of X(17743)
X(18905) = barycentric product X(i)*X(j) for these {i,j}: {10, 7184}, {37, 7187}, {171, 2887}, {894, 3721}, {982, 1215}, {1237, 7032}, {1909, 3778}, {1920, 16584}, {2275, 3963}, {2295, 3662}, {2329, 16888}, {2533, 3888}, {3061, 4032}, {3794, 7211}, {3801, 4579}, {4136, 7175}, {4369, 7239}, {4531, 7205}, {7237, 17103}
X(18905) = barycentric quotient X(i)/X(j) for these {i,j}: {1215, 7033}, {1237, 7034}, {2295, 17743}, {2887, 7018}, {3721, 257}, {3778, 256}, {3888, 4594}, {4367, 7255}, {7032, 1178}, {7184, 86}, {7187, 274}, {7188, 17103}, {8033, 7307}, {16584, 893}
X(18905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 17485, 1965), (16587, 16592, 1215)
X(18906) lies on the cubics K677, K708, K757, K1014, K1037 and these lines: {2, 694}, {4, 69}, {5, 6393}, {6, 194}, {9, 16822}, {39, 3618}, {51, 305}, {99, 182}, {141, 5025}, {183, 1350}, {184, 16276}, {193, 732}, {262, 1007}, {325, 5480}, {350, 1469}, {373, 11059}, {385, 5017}, {518, 17144}, {524, 11361}, {538, 1992}, {597, 14036}, {599, 14041}, {670, 10010}, {726, 3751}, {736, 7737}, {1078, 3098}, {1431, 1966}, {1569, 5182}, {1691, 3552}, {1692, 7816}, {1909, 3056}, {1965, 7033}, {2021, 13085}, {2076, 7793}, {2548, 8149}, {2782, 6776}, {3060, 8024}, {3095, 3926}, {3102, 11292}, {3103, 11291}, {3266, 5640}, {3329, 10335}, {3407, 7766}, {3564, 13108}, {3589, 7892}, {3619, 3934}, {3620, 14063}, {3629, 14034}, {3630, 14066}, {3631, 14062}, {3734, 5028}, {3763, 7901}, {3767, 18806}, {3785, 9821}, {4176, 7392}, {4563, 5651}, {5034, 7781}, {5039, 7760}, {5092, 7782}, {5103, 7912}, {5476, 7799}, {5490, 13877}, {5491, 13930}, {5847, 9902}, {6329, 14038}, {6376, 17792}, {6384, 17082}, {6390, 18583}, {6664, 16285}, {7615, 9466}, {7697, 10008}, {7757, 9741}, {7763, 14561}, {7771, 14810}, {7774, 9865}, {7786, 14069}, {8584, 14030}, {9464, 11002}, {10330, 11003}, {11257, 13354}, {13331, 14037}
X(18906) = reflection of X(i) in X(j) for these {i,j}: {69, 76}, {193, 13330}, {194, 6}, {11257, 13354}
X(18906) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3113, 69}, {3114, 6327}, {3407, 8}
X(18906) = X(i)-Ceva conjugate of X(j) for these (i,j): {458, 1007}, {3114, 2}
X(18906) = X(183)-Hirst inverse of X(5999)
X(18906) = cevapoint of X(194) and X(6194)
X(18906) = crossdifference of every pair of points on line {3049, 3221}
X(18906) = anticomplement of X(3094)
X(18906) = X(194)-of-1st-Brocard-triangle
X(18906) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 69, 5207), (6, 1975, 12215), (2076, 8177, 7793), (3212, 7155, 1966), (3981, 4074, 2)
X(18906) = barycentric product X(i)*X(j) for these {i,j}: {76, 11328}, {3978, 6234}
X(18906) = barycentric quotient X(i)/X(j) for these {i,j}: {6234, 694}, {11328, 6}
See Antreas Hatzipolakis and Angel Montesdeoca, Hyacinthos 27722.
X(18907) lies on these lines: {2,1285}, {3,7736}, {4,3172}, {5,32}, {6,30}, {11,609}, {12,7031}, {20,9605}, {39,550}, {51,15510}, {53,14581}, {69,11286}, {83,7750}, {98,14485}, {99,12156}, {112,251}, {115,3845}, {140,2548}, {141,754}, {172,496}, {183,3793}, {187,549}, {193,14033}, {235,10312}, {315,7819}, {316,7792}, {325,3972}, {376,5024}, {381,7735}, {382,5286}, {384,3933}, {385,8370}, {393,18494}, {428,5359}, {468,9745}, {495,1914}, {524,3734}, {538,3629}, {543,8584}, {546,3767}, {548,5013}, {574,8703}, {597,2030}, {598,3363}, {632,1506}, {952,1572}, {966,11354}, {1003,6390}, {1007,11288}, {1316,6792}, {1353,2782}, {1383,7426}, {1500,10386}, {1503,5039}, {1513,10788}, {1555,8779}, {1595,1968}, {1596,10311}, {1597,3087}, {1609,7514}, {1611,10128}, {1625,3051}, {1657,7738}, {1901,5037}, {1992,11159}, {1995,16317}, {2207,6756}, {2386,9969}, {2393,16983}, {2420,11007}, {2794,5480}, {2896,16988}, {3054,7603}, {3055,11539}, {3058,16785}, {3199,7715}, {3314,6661}, {3329,8356}, {3524,15655}, {3530,5023}, {3541,8778}, {3552,7921}, {3575,8743}, {3589,7761}, {3618,11287}, {3627,5007}, {3820,4386}, {3850,13881}, {3853,5319}, {3858,7755}, {3934,15598}, {5041,7756}, {5103,16385}, {5206,15712}, {5210,12100}, {5276,11113}, {5277,17527}, {5280,6284}, {5299,7354}, {5309,15687}, {5434,16784}, {5471,14137}, {5472,14136}, {5585,14891}, {6423,7584}, {6424,7583}, {6656,7787}, {6658,7839}, {6680,7843}, {6772,9112}, {6775,9113}, {6823,10316}, {7575,9699}, {7576,8744}, {7754,14035}, {7759,7789}, {7766,11361}, {7767,7770}, {7772,15704}, {7773,8361}, {7776,14001}, {7778,8368}, {7784,8364}, {7785,7807}, {7802,7878}, {7803,8357}, {7816,7838}, {7820,7845}, {7829,7842}, {7841,16989}, {7846,7860}, {7873,7889}, {7879,16898}, {7881,14037}, {7885,8363}, {7892,7900}, {7897,14036}, {7929,16895}, {8359,11174}, {8367,15271}, {8573,9818}, {8588,17504}, {8981,12963}, {9465,10301}, {9575,18481}, {9599,15325}, {9698,15513}, {9939,16986}, {10109,18584}, {10317,15760}, {10547,11380}, {11001,14482}, {11163,12040}, {11185,14614}, {11297,11488}, {11298,11489}, {11646,12212}, {11648,14075}, {11842,15980}, {12006,15575}, {12968,13966}, {13357,14881}, {13785,18539}, {15480,17131}, {15603,15700}, {15809,17409}, {16306,18572}
X(18907) = midpoint of X(i) and X(j) for these {i,j}: {6,7737}, {1992,11159}
X(18907) = reflection of X(i) in X(j) for these {i,j}: {5,10796}, {141,7804}, {7761,3589}, {14929,141}, {15048,6}
X(18907) = X(6)-of-1st-orthosymmedial-triangle
X(18907) = X(6)-of-pedal-triangle-of-X(6)
X(18907) = pedal isogonal conjugate of X(6)
See Kadir Altintas and Angel Montesdeoca, ADGEOM 4650.
X(18908) lies on these lines: {3,3697}, {4,8}, {5,3555}, {10,1071}, {12,354}, {40,4662}, {84,165}, {200,1012}, {210,515}, {392,952}, {405,5534}, {495,5728}, {518,5587}, {519,15064}, {912,3753}, {936,958}, {942,5261}, {944,5044}, {956,5720}, {960,5881}, {971,5657}, {997,18236}, {1385,5260}, {1532,4847}, {1698,12675}, {1737,17625}, {2836,13214}, {3036,12665}, {3086,17624}, {3090,5045}, {3295,9844}, {3617,12528}, {3621,13600}, {3678,14110}, {3679,6001}, {3698,5884}, {3870,6913}, {3889,5056}, {3892,10171}, {3916,11499}, {3921,10167}, {3935,6912}, {3956,10164}, {3983,6684}, {4015,4297}, {4533,18525}, {4882,12705}, {5049,11374}, {5173,10590}, {5251,5531}, {5290,5902}, {5302,10902}, {5439,9956}, {5603,10157}, {5687,7330}, {5693,5836}, {5726,18412}, {5770,17612}, {5780,10246}, {5791,10786}, {5886,11240}, {5904,7686}, {5919,10950}, {6927,12125}, {6965,18527}, {7580,18528}, {7989,13374}, {8164,11018}, {8168,12703}, {8728,10202}, {9004,12587}, {9708,18446}, {9780,9940}, {10039,12711}, {10176,18250}, {10573,12709}, {10588,16193}, {11362,12688}, {12599,12692}, {12629,12635}
X(18908) = reflection of X(i) in X(j) for these {i,j}: {354,10175}, {3576,3740}, {3753,5790}, {3892,10171}, {5603,10157}, {10164,3956}
anti-triangles: X(18909)-X(19212)
This preamble and centers X(18909)-X(19212) were contributed by César Eliud Lozada, June 4, 2018.
Let T=AtBtCt be a triangle perspective and orthologic to ABC. Suppose Pt is the perspector (ABC, T) and Ot is the orthologic center ABC to T, both expressed with respect to T. The anti-triangle-of-T is ABC and, if T is taken as the reference triangle, then its anti-triangle T'=A'tB'tC't is given by:
A't = PtA ∩ (perpendicular to BC through Ot)
and cyclically for B't and C't.
Several triangles T satisfying the above conditions are given in the following table, together with the (ABC, T) perspector, the ABC-to-T orthologic center and its anti-triangle:
| Triangle T | Perspector (ABC,T) (w/r to T) |
Orthologic center ABC to T (w/r to T) |
Anti-triangle A' barycentric coordinates |
Notes |
| Atik | X(69) | X(18909) | anti-Atik triange: A' = S^2*(4*R^2-SA)/SA^2 : SB : SC |
Only for ABC acute |
| 2nd circumperp-tangential | X(56) | X(7354) | 2nd anti-circumperp-tangential triangle: A' = (b+c)^2/(-a+b+c) : b^2/(a-b+c) : c^2/(a+b-c) |
For any ABC |
| inner Grebe | X(6) | X(1588) | anti-inner-Grebe triangle: A' = a^2-S : b^2 : c^2 |
For any ABC |
| outer Grebe | X(6) | X(1587) | anti-outer-Grebe triangle: A' = a^2+S : b^2 : c^2 |
For any ABC |
| Honsberger | X(6) | X(182) | anti-Honsberger triangle: A' = -a^4/(b^2+c^2) : b^2 : c^2 |
Only for ABC acute |
| 1st orthosymmedial | X(1297) | X(19158) | 1st anti-orthosymmedial triangle: A' = (S^4+3*SA^2*S^2+2*(SA^2-SB*SC-SW^2)*SA^2)*a^2/(2*SA+SB+SC) : ((SA-SB)*S^2-2*(SA*SC-SB^2)*SA)*b^2 : ((SA-SC)*S^2-2*(SA*SB-SC^2)*SA)*c^2 |
Only for ABC acute |
| 1st Sharygin | X(8795) | X(8884) | 1st anti-Sharygin triangle:
A' = -a^2*SB*SC/(S^2+SB*SC) : SC^2*(SA+SB)/(S^2+SA*SC) : SB^2*(SA+SC)/(S^2+SA*SB) |
Only for ABC acute |
| 3rd tri-squares | X(1328) | X(486) | 3rd anti-tri-squares triangle: A' = 2*S*(2*S^2-(18*R^2+SA-4*SW)*S-3*SB*SC)/((3*SA-S)*(SA-S)) : 3*SC-S : 3*SB-S |
Only for ABC acute |
| 4th tri-squares | X(1327) | X(485) | 4th anti-tri-squares triangle: A' = -2*S*(2*S^2+(18*R^2+SA-4*SW)*S-3*SB*SC)/((3*SA+S)*(SA+S)) : 3*SC+S : 3*SB+S |
Only for ABC acute |
Centers X(18909)-X(19212) are perspectors, homothetic centers, orthologic centers and parallelogic centers of these anti-triangles and other triangles. For a complete list, see X(18909) Anti-triangles.pdf.
X(18909) lies on these lines: {1,18915}, {2,1181}, {3,69}, {4,51}, {5,18920}, {6,3088}, {15,18929}, {16,18930}, {20,6146}, {24,11206}, {30,18945}, {40,18921}, {64,12241}, {68,15740}, {125,3090}, {140,11487}, {155,3546}, {182,19119}, {184,631}, {217,7736}, {235,5656}, {287,14001}, {343,7400}, {371,18923}, {372,18924}, {376,1204}, {511,18935}, {569,5622}, {576,18919}, {578,14912}, {942,10360}, {974,3448}, {1056,1425}, {1058,3270}, {1154,18946}, {1217,9308}, {1352,6803}, {1368,12164}, {1370,5889}, {1498,3089}, {1503,7487}, {1593,11245}, {1595,11432}, {1596,12315}, {1614,3147}, {1853,12233}, {1885,12250}, {1907,9777}, {1986,13203}, {2777,18947}, {2883,6623}, {3043,13198}, {3146,18396}, {3167,16196}, {3269,7738}, {3521,15749}, {3524,13367}, {3538,3917}, {3541,7592}, {3542,11456}, {3547,12359}, {3548,18445}, {3618,7404}, {3818,9815}, {4846,9927}, {5072,18489}, {5562,7386}, {5663,18933}, {5739,6908}, {5907,6804}, {6102,14790}, {6353,6759}, {6467,15644}, {6643,13754}, {6696,8550}, {6815,10574}, {6816,12111}, {6825,14555}, {6891,18141}, {6995,16655}, {6997,15043}, {7401,9730}, {7494,10984}, {7689,18128}, {8884,19166}, {9825,18440}, {9833,11438}, {10116,12118}, {10619,12325}, {10625,15073}, {10938,13491}, {11424,13399}, {12085,13292}, {12162,18537}, {12319,18948}, {13093,13488}, {13630,18420}, {15134,18569}, {15811,15873}, {16621,17810}, {17702,18932}, {18296,18550}, {18926,18980}, {18927,18981}, {18937,18944}, {18938,18943}
X(18909) = reflection of X(15811) in X(15873)
X(18909) = anticomplement of X(17814)
X(18909) = excentral-to-ABC functional image of X(4882)
X(18909) = X(4882)-of-orthic-triangle if ABC is acute
X(18909) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 11411, 69), (3, 18913, 18931), (3, 18914, 6776), (3, 18917, 11411), (4, 1075, 6524), (4, 6241, 6225), (4, 14361, 1093), (4, 18916, 11433), (487, 488, 3964), (5878, 18390, 4), (6241, 18912, 4), (6776, 18913, 3), (11433, 12324, 4), (18913, 18914, 18925), (18915, 18922, 1), (18925, 18931, 3)
X(18910) lies on these lines: {3,18934}, {4,14457}, {20,6146}, {24,159}, {125,11487}, {376,18936}, {631,5181}, {974,15740}, {1181,3089}, {1899,5562}, {3313,15073}, {3448,12825}, {7387,18914}, {8907,18925}, {12250,18560}, {12324,18396}, {12605,18917}, {16063,18946}, {16163,18932}
X(18910) = reflection of X(4) in X(14457)
X(18911) lies on these lines: {2,98}, {3,3580}, {4,4846}, {5,11456}, {6,858}, {20,11438}, {22,13567}, {51,7391}, {54,3548}, {66,3618}, {68,631}, {69,3266}, {70,13353}, {141,8546}, {193,11511}, {343,7485}, {373,3818}, {376,15360}, {427,5422}, {468,6800}, {511,16063}, {567,18281}, {568,14791}, {632,18356}, {850,879}, {852,18437}, {1353,1368}, {1370,3060}, {1503,1995}, {1648,9832}, {1853,5133}, {2088,2549}, {2888,10303}, {2979,6515}, {3091,5643}, {3398,14003}, {3541,13434}, {3564,15066}, {3620,5888}, {4197,5810}, {4550,16003}, {5050,5094}, {5085,7495}, {5169,14561}, {5189,11002}, {5297,12588}, {5449,7558}, {5654,15032}, {5889,6643}, {5890,18531}, {5892,18474}, {5943,7394}, {6030,10565}, {6146,17928}, {6804,15056}, {6816,12111}, {6997,11451}, {7292,12589}, {7378,12834}, {7401,15028}, {7493,15080}, {7509,12359}, {7528,15024}, {7529,16659}, {7544,18381}, {7592,11585}, {7728,12824}, {8550,11064}, {9707,16238}, {9786,12225}, {10113,12099}, {10539,18128}, {11284,18440}, {11411,11444}, {11412,18951}, {11413,12241}, {11422,14912}, {11439,12324}, {11440,18913}, {11441,18914}, {11443,18919}, {11445,18921}, {11446,18922}, {11447,18923}, {11448,18924}, {11449,18925}, {11452,18929}, {11453,18930}, {11454,18931}, {11459,18917}, {12270,18933}, {12271,18934}, {12272,18935}, {12273,18932}, {12274,18937}, {12275,18938}, {12276,18941}, {12277,18942}, {12278,18945}, {12280,18946}, {12828,16111}, {13015,18943}, {13016,18944}, {13201,18947}, {13630,18404}, {14788,15805}, {14805,15061}, {14853,15019}, {15045,18420}, {15053,18533}, {15305,18537}, {18124,19151}, {18392,18918}, {19119,19122}, {19166,19167}
X(18911) = anticomplement of X(5651)
X(18911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1899, 11442), (2, 3448, 1352), (3, 18952, 18912), (125, 182, 2), (1352, 1899, 3448), (1352, 3448, 11442), (1368, 11245, 1993), (1370, 11433, 3060), (1853, 10601, 5133), (5050, 5094, 14389), (5169, 15018, 14561), (5449, 13336, 7558), (6515, 7386, 2979), (6643, 18916, 5889), (7386, 18950, 6515)
X(18912) lies on these lines: {2,54}, {3,3580}, {4,51}, {5,5422}, {6,70}, {20,17712}, {24,161}, {66,1173}, {69,7999}, {74,14457}, {110,10111}, {113,3091}, {125,578}, {182,7558}, {184,7505}, {193,8538}, {206,1614}, {235,11456}, {265,14708}, {317,19166}, {343,7509}, {378,6696}, {403,1181}, {468,9707}, {568,18569}, {575,1352}, {1092,10112}, {1192,10295}, {1199,7577}, {1204,13403}, {1503,10594}, {1598,16659}, {1656,11402}, {1853,10982}, {1993,11585}, {1995,12134}, {2072,12161}, {2548,16837}, {3087,4994}, {3089,14157}, {3147,11464}, {3410,5056}, {3518,9833}, {3527,5064}, {3541,15033}, {3549,5012}, {3855,18418}, {5094,11426}, {5198,16658}, {5446,7391}, {5462,7544}, {5640,7528}, {5810,6829}, {5889,18531}, {5925,10605}, {6102,18404}, {6240,9786}, {6243,14791}, {6247,16657}, {6515,6643}, {6642,14516}, {6800,13383}, {6815,15045}, {6816,11411}, {7401,15024}, {7503,12359}, {7507,11432}, {7547,12233}, {7552,11179}, {7731,18947}, {9730,9927}, {9815,16223}, {10116,10539}, {10255,15087}, {10601,14788}, {10619,11202}, {10625,16063}, {11458,18919}, {11460,18921}, {11461,18922}, {11462,18923}, {11463,18924}, {11465,18928}, {11466,18929}, {11467,18930}, {11468,18931}, {12099,15026}, {12111,18917}, {12164,16072}, {12227,15081}, {12278,15053}, {12281,18933}, {12282,18934}, {12283,18935}, {12284,18932}, {12285,18937}, {12286,18938}, {12287,18941}, {12288,18942}, {12289,18533}, {12291,18946}, {13017,18943}, {13018,18944}, {13160,14852}, {14542,16000}, {14627,15135}, {14855,18555}, {15032,16868}, {15043,18420}, {15058,18537}, {15121,18281}, {15873,16655}, {18948,19161}, {19119,19123}
X(18912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18952, 18911), (4, 1899, 11457), (4, 11433, 3567), (4, 12324, 11455), (4, 18909, 6241), (4, 18916, 5890), (4, 18918, 18394), (4, 18950, 18916), (5, 11245, 7592), (51, 18381, 4), (185, 18390, 4), (569, 5449, 2), (6146, 13567, 24), (8538, 12585, 193), (10110, 11550, 4)
X(18913) lies on these lines: {1,10360}, {2,185}, {3,69}, {4,64}, {6,6696}, {20,1204}, {24,1619}, {25,12324}, {55,18915}, {56,18922}, {74,14457}, {125,146}, {155,2063}, {184,3523}, {193,13346}, {235,6225}, {343,10996}, {376,6146}, {378,18916}, {382,18918}, {389,3088}, {468,12174}, {578,5095}, {631,1181}, {974,7722}, {1151,18923}, {1152,18924}, {1192,1503}, {1350,18935}, {1498,6353}, {1593,11433}, {1596,13093}, {2883,6622}, {2935,18947}, {3089,6000}, {3147,11456}, {3269,5286}, {3270,14986}, {3346,9307}, {3515,11206}, {3516,11245}, {3529,18396}, {3541,5890}, {3542,5656}, {3546,13754}, {4846,5449}, {5085,19119}, {5584,18921}, {5878,6623}, {6392,9289}, {6467,13348}, {6515,11413}, {6643,12163}, {6823,15740}, {6995,13399}, {7386,11821}, {7404,9730}, {7487,11438}, {7714,16621}, {8889,12233}, {9545,13198}, {10606,12241}, {10620,18933}, {11425,14912}, {11440,18911}, {11457,18533}, {11477,18919}, {11479,18928}, {11480,18929}, {11481,18930}, {12084,18951}, {12164,16196}, {12301,18934}, {12302,18932}, {12303,18937}, {12304,18938}, {12305,18941}, {12306,18942}, {12307,18946}, {13021,18926}, {13022,18927}, {13367,15717}, {13851,17578}, {14561,15012}, {14826,17928}, {15073,15644}, {15128,16270}, {19166,19172}
X(18913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18909, 6776), (3, 18914, 18925), (3, 18917, 6193), (20, 1899, 18945), (64, 13567, 4), (389, 3088, 14853), (1204, 1899, 20), (1853, 13568, 4), (3542, 6241, 5656), (6247, 9786, 4), (11438, 14216, 7487), (18909, 18925, 18914), (18909, 18931, 3), (18914, 18925, 6776)
X(18914) lies on these lines: {3,69}, {4,3527}, {5,1181}, {6,1595}, {25,18916}, {30,52}, {49,10257}, {51,16655}, {68,6823}, {125,3628}, {140,184}, {155,1368}, {156,16238}, {182,13562}, {235,11456}, {287,7819}, {343,10984}, {382,18945}, {389,1503}, {427,7592}, {428,3567}, {468,1614}, {524,15644}, {542,9729}, {548,1204}, {550,10605}, {568,7553}, {578,6247}, {999,18915}, {1147,16196}, {1199,15559}, {1216,10691}, {1351,18935}, {1370,12160}, {1498,1596}, {1594,15032}, {1597,12324}, {1598,11433}, {1885,6241}, {2777,12024}, {2883,18390}, {3088,11426}, {3089,18950}, {3167,3546}, {3270,15172}, {3295,18922}, {3311,18923}, {3312,18924}, {3448,13160}, {3517,11206}, {3530,13367}, {3541,11402}, {3575,5890}, {3627,18396}, {3843,18918}, {3861,13851}, {4846,12293}, {5050,7404}, {5159,9820}, {5480,9968}, {5622,13353}, {5708,10360}, {5848,12675}, {5921,6803}, {5965,13348}, {6000,12241}, {6353,14530}, {6467,10625}, {6515,11414}, {6643,12164}, {6676,12359}, {6677,10539}, {6696,11430}, {6759,13567}, {7387,18910}, {7399,11442}, {7401,18440}, {7403,18583}, {7405,18358}, {7667,11412}, {9730,9825}, {9781,16658}, {9786,9833}, {9919,18947}, {10110,16621}, {10114,17855}, {10127,12006}, {10264,13198}, {10295,12254}, {10306,18921}, {10574,14516}, {10937,12278}, {11225,13598}, {11232,14641}, {11381,16657}, {11441,18911}, {11482,18919}, {11484,18928}, {11485,18929}, {11486,18930}, {11487,16419}, {11550,16198}, {11585,18445}, {12038,16976}, {12118,12421}, {12233,18381}, {12308,18933}, {12309,18934}, {12310,18932}, {12311,18937}, {12312,18938}, {12313,18941}, {12314,18942}, {12316,18946}, {12362,13754}, {13023,18943}, {13024,18944}, {13382,13568}, {13403,15311}, {14786,19125}, {19166,19173}
X(18914) = midpoint of X(i) and X(j) for these {i,j}: {1885, 6241}, {10114, 17855}, {12118, 12421}
X(18914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 14216, 1595), (343, 10984, 16197), (389, 13419, 11745), (1181, 1899, 5), (3088, 14912, 11426), (3567, 16659, 428), (6241, 12022, 1885), (6247, 8550, 578), (6776, 18909, 3), (7592, 11457, 427), (9730, 12134, 9825), (11456, 18912, 235), (11745, 13419, 6756), (18909, 18925, 18913), (18913, 18925, 3)
X(18915) lies on these lines: {1,18909}, {4,65}, {33,12324}, {34,11433}, {35,18931}, {36,18925}, {55,18913}, {56,6776}, {69,73}, {125,10588}, {184,7288}, {185,497}, {221,13567}, {388,1425}, {966,1409}, {999,18914}, {1060,11411}, {1181,3086}, {1398,11245}, {1428,19119}, {1469,18935}, {1870,18916}, {2067,18923}, {3157,3546}, {3585,18918}, {4293,6146}, {4294,10605}, {4296,6515}, {6502,18924}, {6643,7352}, {7051,18929}, {7353,18942}, {7354,18945}, {7356,18946}, {7362,18941}, {18447,18917}, {19166,19175}
X(18915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18909, 18922), (1425, 1899, 388)
X(18916) lies on these lines: {2,155}, {3,6515}, {4,51}, {5,18917}, {6,3541}, {20,12022}, {24,159}, {25,18914}, {52,1370}, {54,69}, {64,16657}, {68,6815}, {74,18947}, {110,18932}, {140,11402}, {184,3147}, {186,18925}, {343,7383}, {378,18913}, {427,11432}, {568,14790}, {1181,3542}, {1199,11427}, {1353,16196}, {1368,12160}, {1595,9777}, {1596,12174}, {1614,6353}, {1870,18915}, {1906,12315}, {1907,3527}, {1993,3546}, {3089,11456}, {3090,18928}, {3292,3525}, {3448,7544}, {3518,11206}, {3520,18931}, {3538,11574}, {3547,3580}, {3548,12161}, {3855,12317}, {5071,11704}, {5422,7404}, {5462,6997}, {5739,6889}, {5889,6643}, {5894,10605}, {5946,7528}, {6102,18531}, {6146,9786}, {6197,18921}, {6198,18922}, {6239,18941}, {6240,18945}, {6242,18946}, {6247,10982}, {6400,18942}, {6403,18935}, {6640,15087}, {6803,15045}, {6804,11459}, {6816,13754}, {6853,14555}, {6897,9534}, {6995,16659}, {7386,11412}, {7392,15024}, {7401,11442}, {7505,15032}, {7699,18920}, {7722,18933}, {8537,18919}, {9815,16226}, {9935,12254}, {10632,18929}, {10633,18930}, {10880,18923}, {10881,18924}, {11225,13346}, {11431,14853}, {12111,18537}, {12509,18937}, {12510,18938}, {13035,18943}, {13036,18944}, {13568,18396}, {14787,15047}, {15135,18281}, {16655,17810}, {19119,19128}
X(18916) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18951, 6515), (4, 14361, 13450), (4, 18950, 18912), (51, 14216, 4), (68, 9730, 6815), (389, 1899, 4), (631, 14912, 54), (1181, 13567, 3542), (3567, 11457, 4), (5889, 18911, 6643), (5890, 18912, 4), (6102, 18952, 18531), (6146, 9786, 18533), (11433, 18909, 4), (11442, 15043, 7401)
X(18917) lies on these lines: {2,15032}, {3,69}, {4,94}, {5,18916}, {30,6515}, {49,631}, {52,14216}, {68,185}, {74,10111}, {125,5654}, {140,6090}, {155,3548}, {156,3147}, {381,11433}, {382,12324}, {389,3818}, {542,11438}, {567,14912}, {1092,9936}, {1147,6699}, {1154,1370}, {1181,3549}, {1204,12118}, {1352,9730}, {1593,13292}, {1899,13754}, {2070,11206}, {3167,10257}, {3357,10112}, {3526,11487}, {3528,12325}, {3541,12161}, {3580,11456}, {3589,14786}, {3618,14787}, {3629,6247}, {3851,18489}, {5055,18928}, {5656,11799}, {5876,6816}, {5889,11457}, {5890,11442}, {5900,16867}, {5946,6997}, {6146,12163}, {6353,10540}, {6643,18436}, {6815,13630}, {7403,11432}, {7592,14389}, {7689,10116}, {9786,12134}, {10264,15106}, {11427,15087}, {11459,18911}, {11472,16657}, {11550,14831}, {11579,13352}, {11585,12164}, {12111,18912}, {12301,12421}, {12429,18934}, {12605,18910}, {13567,18451}, {15077,18550}, {15108,15692}, {18403,18918}, {18435,18537}, {18437,18953}, {18438,18935}, {18447,18915}, {18449,18919}, {18453,18921}, {18455,18922}, {18457,18923}, {18459,18924}, {18462,18926}, {18463,18927}, {18468,18929}, {18470,18930}, {18563,18945}, {19119,19129}, {19166,19176}
X(18917) = anticomplement of X(15068)
X(18917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1181, 12359, 3549), (5876, 18952, 6816), (5889, 11457, 14790), (5890, 11442, 18420), (6193, 18913, 3), (11411, 18909, 3), (12317, 18932, 265), (14787, 15037, 3618)
X(18918) lies on these lines: {2,18396}, {3,15749}, {4,51}, {5,8780}, {30,18931}, {68,15077}, {69,265}, {125,376}, {184,3545}, {287,16041}, {381,6776}, {382,18913}, {403,11206}, {542,18919}, {1181,3832}, {1503,6623}, {1853,15153}, {3091,6146}, {3147,12289}, {3153,6515}, {3521,18296}, {3543,10605}, {3546,12293}, {3583,18922}, {3585,18915}, {3818,18935}, {3843,18914}, {5067,13367}, {5447,6643}, {5656,10151}, {5891,15073}, {5946,10938}, {6288,18946}, {6353,18400}, {6564,18923}, {6565,18924}, {6622,9833}, {7378,16657}, {10201,11801}, {10519,18536}, {10602,11180}, {11245,18386}, {11411,18404}, {11427,12022}, {12024,17809}, {12118,14156}, {13363,18420}, {13567,18405}, {14449,18569}, {14826,16072}, {14912,18388}, {16808,18929}, {16809,18930}, {18377,18951}, {18379,18952}, {18380,18953}, {18392,18911}, {18403,18917}, {18406,18921}, {18414,18926}, {18415,18927}, {18474,18537}, {19119,19130}, {19166,19177}
X(18918) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6761, 6524), (4, 11457, 6225), (5, 18945, 18925), (1899, 13851, 4), (18394, 18912, 4)
X(18919) lies on these lines: {2,8263}, {4,6}, {69,125}, {193,858}, {373,3618}, {376,5622}, {511,18931}, {542,18918}, {575,9815}, {576,18909}, {631,15073}, {1899,1992}, {2393,6353}, {6515,11416}, {6643,8548}, {7714,19136}, {8537,18916}, {8538,11411}, {8539,18921}, {8540,18922}, {8541,11433}, {9813,18928}, {9924,15448}, {9926,18934}, {9974,18941}, {9975,18942}, {9976,18933}, {9977,18946}, {11216,18950}, {11245,11405}, {11255,18951}, {11443,18911}, {11458,18912}, {11470,12324}, {11477,18913}, {11482,18914}, {11585,11898}, {12596,18932}, {12597,18937}, {12598,18938}, {13037,18943}, {13038,18944}, {13248,18947}, {13567,17813}, {18449,18917}, {19166,19178}
X(18919) = {X(6), X(18935)}-harmonic conjugate of X(19119)
X(18920) lies on these lines: {5,18909}, {125,6622}, {1352,6804}, {1598,18931}, {3089,6247}, {3574,11433}, {5447,6643}, {7699,18916}, {10113,14790}
X(18921) lies on these lines: {4,65}, {19,11433}, {40,18909}, {55,6776}, {63,69}, {1409,5712}, {1899,2550}, {3101,6515}, {3197,13567}, {3779,18935}, {5415,18923}, {5416,18924}, {5584,18913}, {6197,18916}, {6252,18941}, {6253,18945}, {6255,18946}, {6353,10536}, {6404,18942}, {7688,18931}, {7724,18933}, {8141,18951}, {8251,11411}, {8539,18919}, {9816,18928}, {10119,18947}, {10306,18914}, {10636,18929}, {10637,18930}, {10902,18925}, {11190,18950}, {11245,11406}, {11428,14912}, {11445,18911}, {11460,18912}, {11471,12324}, {12417,18934}, {12661,18932}, {12662,18937}, {12663,18938}, {13041,18943}, {13042,18944}, {18406,18918}, {18453,18917}, {19119,19133}, {19166,19181}
X(18921) = {X(1899), X(3611)}-harmonic conjugate of X(2550)
X(18922) lies on these lines: {1,18909}, {4,6285}, {33,11433}, {35,18925}, {36,18931}, {55,6776}, {56,18913}, {69,1040}, {125,10589}, {184,5218}, {185,388}, {354,10360}, {497,1899}, {1062,11411}, {1069,3546}, {1181,3085}, {1250,18930}, {2066,18923}, {2192,13567}, {2330,19119}, {3056,18935}, {3100,6515}, {3147,9638}, {3295,18914}, {3583,18918}, {4293,10605}, {4294,6146}, {5414,18924}, {6198,18916}, {6238,6643}, {6283,18941}, {6284,18945}, {6286,18946}, {6353,10535}, {6405,18942}, {7071,11245}, {7727,18933}, {8144,18951}, {8540,18919}, {9817,18928}, {9931,18934}, {10118,18947}, {10638,18929}, {11189,18950}, {11429,14912}, {11446,18911}, {11461,18912}, {12888,18932}, {12910,18937}, {12911,18938}, {13043,18943}, {13044,18944}, {18455,18917}, {19166,19182}
X(18922) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 18909, 18915), (1899, 3270, 497)
X(18923) lies on these lines: {4,6}, {69,1589}, {184,3069}, {185,6459}, {216,12256}, {371,18909}, {372,18925}, {577,12257}, {1151,18913}, {1899,3068}, {2066,18922}, {2067,18915}, {3156,18997}, {3311,18914}, {3546,8909}, {5410,11245}, {5412,11433}, {5413,11206}, {5415,18921}, {6353,10533}, {6458,11514}, {6515,11417}, {6564,18918}, {6643,10665}, {9541,10605}, {10116,19062}, {10880,18916}, {10897,11411}, {10961,18928}, {11241,18950}, {11265,18951}, {11447,18911}, {11462,18912}, {11473,12324}, {12375,18933}, {12424,18934}, {12891,18932}, {12960,18937}, {12961,18938}, {12962,18941}, {12963,18942}, {12965,18946}, {13045,18943}, {13046,18944}, {13287,18947}, {13567,17819}, {18457,18917}, {19166,19183}
X(18923) = {X(6), X(6776)}-harmonic conjugate of X(18924)
X(18924) lies on these lines: {4,6}, {69,1590}, {184,3068}, {185,6460}, {216,12257}, {371,18925}, {372,18909}, {577,12256}, {1152,18913}, {1589,8911}, {1899,3069}, {3155,18998}, {3312,18914}, {5411,11245}, {5412,11206}, {5413,11433}, {5414,18922}, {5416,18921}, {6353,10534}, {6396,18931}, {6457,11513}, {6502,18915}, {6515,11418}, {6565,18918}, {6643,10666}, {10116,19061}, {10881,18916}, {10898,11411}, {10963,18928}, {11242,18950}, {11266,18951}, {11448,18911}, {11463,18912}, {11474,12324}, {12376,18933}, {12425,18934}, {12892,18932}, {12966,18937}, {12967,18938}, {12968,18941}, {12969,18942}, {12971,18946}, {13047,18943}, {13048,18944}, {13288,18947}, {13567,17820}, {18459,18917}, {19166,19184}
X(18924) = {X(6), X(6776)}-harmonic conjugate of X(18923)
X(18925) lies on these lines: {2,6146}, {3,69}, {4,54}, {5,8780}, {6,7487}, {15,18930}, {16,18929}, {20,1181}, {24,11433}, {35,18922}, {36,18915}, {49,18531}, {52,1992}, {68,18475}, {70,3431}, {110,6816}, {125,3525}, {154,3089}, {182,6803}, {185,376}, {186,18916}, {193,17834}, {287,16043}, {371,18924}, {372,18923}, {378,12324}, {389,6403}, {511,19119}, {567,7528}, {569,3618}, {575,9815}, {631,1899}, {1092,7386}, {1093,6618}, {1147,6643}, {1204,3528}, {1503,3088}, {1596,14530}, {1658,18951}, {1853,14528}, {1885,5656}, {2055,14575}, {3091,14389}, {3135,16035}, {3147,11464}, {3167,12362}, {3515,11245}, {3522,10605}, {3527,7715}, {3542,9707}, {3575,11402}, {3796,7400}, {3855,13851}, {4549,15083}, {5012,6815}, {5050,9825}, {5622,13336}, {5876,10938}, {6225,11456}, {6353,10282}, {6515,7488}, {6622,18390}, {6623,16252}, {6642,18928}, {6676,12429}, {6756,11426}, {6804,9306}, {6995,10982}, {6997,13434}, {7395,14826}, {7404,12134}, {7514,11487}, {7592,18533}, {7714,10110}, {7735,14585}, {8550,9786}, {8797,19176}, {8889,18381}, {8907,18910}, {9143,15738}, {9704,18404}, {9729,11179}, {9909,13142}, {9932,18934}, {9969,11387}, {10539,18537}, {10602,11432}, {10902,18921}, {10984,10996}, {11202,18950}, {11430,14216}, {11449,18911}, {11577,12226}, {12118,12318}, {12174,12250}, {12233,17809}, {12363,18436}, {12383,13198}, {12893,18932}, {12972,18937}, {12973,18938}, {12974,18941}, {12975,18942}, {13049,18943}, {13050,18944}, {13203,15463}, {13289,18947}, {13292,14070}, {13352,14927}, {13567,17821}, {14852,15077}, {15316,15740}, {19166,19185}
X(18925) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6193, 69), (3, 6776, 18909), (3, 18909, 18931), (3, 18914, 18913), (4, 54, 11427), (5, 18945, 18918), (154, 12241, 3089), (569, 7401, 3618), (578, 9833, 4), (1899, 13367, 631), (6756, 11426, 14853), (6776, 18913, 18914), (9707, 12022, 3542), (11464, 18912, 3147), (18913, 18914, 18909)
X(18926) lies on these lines: {3,18938}, {3070,11846}, {6643,18939}, {6776,8939}, {9723,18927}, {12257,13889}, {12590,18935}, {13021,18913}, {18414,18918}, {18462,18917}, {18909,18980}, {19119,19134}, {19166,19186}
X(18927) lies on these lines: {3,18937}, {3071,11847}, {6643,18940}, {6776,8943}, {9723,18926}, {12256,13943}, {12591,18935}, {13022,18913}, {18415,18918}, {18463,18917}, {18909,18981}, {19119,19135}, {19166,19187}
X(18928) lies on these lines: {2,6}, {4,5943}, {5,18909}, {20,17810}, {51,7386}, {83,459}, {182,6353}, {264,14361}, {329,6604}, {373,1899}, {389,6804}, {631,13346}, {637,3539}, {638,3540}, {641,18938}, {642,18937}, {1352,6688}, {1368,14853}, {1370,5640}, {1503,7398}, {1656,11411}, {1660,5012}, {1853,2883}, {1995,11206}, {2052,6819}, {3066,6995}, {3090,18916}, {3547,15805}, {3628,11487}, {3796,4232}, {3981,7738}, {4176,11059}, {5014,5554}, {5020,6776}, {5050,6677}, {5055,18917}, {5085,10565}, {5462,6643}, {5480,7396}, {5644,18583}, {6225,10574}, {6642,18925}, {6723,18947}, {6803,11695}, {6805,12322}, {6806,12323}, {6815,15028}, {6816,15043}, {6997,11451}, {7401,18474}, {8889,14561}, {9306,14912}, {9730,18537}, {9813,18919}, {9816,18921}, {9817,18922}, {9820,18934}, {9822,18935}, {9823,18941}, {9824,18942}, {9825,18945}, {10128,18440}, {10154,12017}, {10519,16419}, {10643,18929}, {10644,18930}, {10961,18923}, {10963,18924}, {11225,16187}, {11245,11284}, {11431,12160}, {11465,18912}, {11479,18913}, {11484,18914}, {12900,18932}, {13053,18943}, {13054,18944}, {13363,18420}, {14557,17170}, {14790,15026}, {19119,19137}, {19166,19188}
X(18928) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 193, 17811), (2, 343, 3619), (2, 5422, 11427), (2, 10601, 3618), (2, 11433, 69), (4, 9729, 15740), (373, 1899, 7392), (3628, 18951, 11487), (11245, 11284, 14826), (11451, 18911, 6997), (13567, 17825, 2), (14555, 18141, 4417)
X(18929) lies on these lines: {4,6}, {15,18909}, {16,18925}, {69,11515}, {184,11489}, {1899,11488}, {6515,11420}, {6643,10661}, {7051,18915}, {10632,18916}, {10634,11411}, {10636,18921}, {10638,18922}, {10641,11433}, {10642,11206}, {10643,18928}, {10645,18931}, {10657,18933}, {10659,18934}, {10663,18932}, {10667,18941}, {10671,18942}, {10677,18946}, {10681,18947}, {11243,18950}, {11245,11408}, {11267,18951}, {11452,18911}, {11466,18912}, {11475,12324}, {11480,18913}, {11485,18914}, {12980,18937}, {12982,18938}, {13057,18943}, {13058,18944}, {13567,17826}, {16808,18918}, {18468,18917}, {19166,19190}
X(18929) = {X(6), X(6776)}-harmonic conjugate of X(18930)
X(18930) lies on these lines: {4,6}, {15,18925}, {16,18909}, {69,11516}, {184,11488}, {1250,18922}, {1899,11489}, {6515,11421}, {6643,10662}, {10633,18916}, {10635,11411}, {10637,18921}, {10641,11206}, {10642,11433}, {10644,18928}, {10646,18931}, {10658,18933}, {10660,18934}, {10664,18932}, {10668,18941}, {10672,18942}, {10678,18946}, {10682,18947}, {11244,18950}, {11245,11409}, {11268,18951}, {11453,18911}, {11467,18912}, {11476,12324}, {11481,18913}, {11486,18914}, {12981,18937}, {12983,18938}, {13059,18943}, {13060,18944}, {13567,17827}, {16809,18918}, {18470,18917}, {19166,19191}
X(18930) = {X(6), X(6776)}-harmonic conjugate of X(18929)
X(18931) lies on these lines: {2,10605}, {3,69}, {4,74}, {20,3580}, {24,12324}, {30,18918}, {35,18915}, {36,18922}, {64,3089}, {184,3524}, {185,631}, {186,11206}, {235,12250}, {376,1899}, {378,11433}, {468,5656}, {511,18919}, {550,18945}, {568,16270}, {974,12219}, {1181,3523}, {1192,6247}, {1498,15448}, {1598,18920}, {1992,5622}, {2071,6515}, {3088,5480}, {3098,18935}, {3147,6241}, {3167,16976}, {3269,7735}, {3520,18916}, {3522,6146}, {3542,6225}, {3546,12163}, {3547,15740}, {3618,9730}, {4549,6643}, {5092,19119}, {5654,6699}, {5878,6622}, {5890,11427}, {6000,6353}, {6396,18924}, {6623,15311}, {6816,11440}, {6997,15053}, {7493,15072}, {7688,18921}, {7690,18941}, {7691,18946}, {7692,18942}, {7729,15151}, {8567,12241}, {9938,18934}, {10299,13367}, {10564,11008}, {10606,13567}, {10645,18929}, {10646,18930}, {11204,18950}, {11245,11410}, {11250,18951}, {11425,12007}, {11430,14912}, {11454,18911}, {11468,18912}, {12293,15077}, {12901,18932}, {12984,18937}, {12985,18938}, {13061,18943}, {13062,18944}, {13293,18947}, {13851,15682}, {19166,19192}
X(18931) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18909, 18925), (3, 18913, 18909), (1192, 6247, 7487), (6696, 9786, 3088)
The reciprocal orthologic center of these triangles is X(15136)
X(18932) lies on these lines: {4,94}, {52,13203}, {68,11806}, {69,5504}, {74,6515}, {110,18916}, {113,11433}, {125,11411}, {193,10264}, {1899,12319}, {2931,6776}, {3047,3147}, {5900,15317}, {6723,11487}, {10111,12383}, {10663,18929}, {10664,18930}, {11245,12168}, {11800,14216}, {12228,14912}, {12273,18911}, {12284,18912}, {12295,12324}, {12302,18913}, {12310,18914}, {12325,15089}, {12596,18919}, {12661,18921}, {12825,18537}, {12888,18922}, {12891,18923}, {12892,18924}, {12893,18925}, {12900,18928}, {12901,18931}, {13567,17838}, {13754,18933}, {14984,18935}, {16163,18910}, {17702,18909}, {19119,19138}, {19166,19193}
X(18932) = orthologic center of the anti-Atik triangle to these triangles: AOA, 1st Hyacinth
X(18932) = {X(265), X(18917)}-harmonic conjugate of X(12317)
The reciprocal orthologic center of these triangles is X(3581)
X(18933) lies on these lines: {4,74}, {5,12412}, {69,265}, {110,6816}, {113,3618}, {146,974}, {235,13171}, {399,6776}, {542,18935}, {1370,10733}, {1596,9919}, {1899,12317}, {1986,11433}, {3089,10117}, {3153,3580}, {3448,12825}, {3546,12302}, {5621,6623}, {5663,18909}, {5878,17855}, {5972,6804}, {6146,14683}, {6225,17854}, {6353,13289}, {6515,12219}, {6643,17702}, {6723,6803}, {6815,15059}, {7386,16163}, {7722,18916}, {7723,11411}, {7724,18921}, {7727,18922}, {7728,16270}, {9976,18919}, {10113,14790}, {10620,18913}, {10628,18947}, {10657,18929}, {10658,18930}, {11245,12165}, {11744,15151}, {11801,18569}, {12227,14912}, {12241,17847}, {12270,18911}, {12281,18912}, {12292,12324}, {12308,18914}, {12310,12362}, {12375,18923}, {12376,18924}, {13567,17835}, {13754,18932}, {15066,18396}, {18945,18946}, {19119,19140}, {19166,19195}
X(18933) = orthologic center of these triangles: anti-Atik to orthocentroidal
X(18933) = {X(265), X(18531)}-harmonic conjugate of X(12319)
The reciprocal orthologic center of these triangles is X(7387)
X(18934) lies on these lines: {3,18910}, {4,52}, {69,3546}, {155,11433}, {1147,14912}, {1899,12318}, {3564,6642}, {5449,11487}, {6776,9937}, {9820,18928}, {9926,18919}, {9931,18922}, {9932,18925}, {9938,18931}, {10659,18929}, {10660,18930}, {11245,12166}, {12118,18128}, {12271,18911}, {12282,18912}, {12293,12324}, {12301,18913}, {12309,18914}, {12417,18921}, {12424,18923}, {12425,18924}, {12429,18917}, {13567,17836}, {19119,19141}, {19166,19196}
X(18934) = orthologic center of these triangles: anti-Atik to 2nd Hyacinth
X(18934) = {X(12359), X(15316)}-harmonic conjugate of X(3546)
The reciprocal orthologic center of these triangles is X(576)
X(18935) lies on these lines: {4,6}, {66,17040}, {69,305}, {125,3619}, {159,6353}, {182,6803}, {184,3618}, {193,1370}, {511,18909}, {542,18933}, {800,8721}, {1350,18913}, {1351,18914}, {1352,6804}, {1353,14790}, {1469,18915}, {1843,11433}, {1974,11206}, {2393,18950}, {2871,18953}, {3056,18922}, {3098,18931}, {3313,15073}, {3538,10519}, {3564,6643}, {3589,15435}, {3779,18921}, {3818,18918}, {5050,7401}, {5095,13203}, {5157,5622}, {5486,16774}, {5839,11677}, {5921,6816}, {5965,18946}, {6403,18916}, {6515,12220}, {6997,19125}, {9822,18928}, {9924,13567}, {9967,11411}, {10996,19126}, {11245,12167}, {11513,12257}, {11514,12256}, {12272,18911}, {12283,18912}, {12294,12324}, {12590,18926}, {12591,18927}, {14984,18932}, {18438,18917}, {18440,18537}, {19166,19197}
X(18935) = reflection of X(69) in X(15812)
X(18935) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 3867, 14853), (6, 6776, 19119), (1181, 18396, 16654), (1899, 6467, 69), (6776, 14853, 1181), (18919, 19119, 6)
The reciprocal orthologic center of these triangles is X(9729)
X(18936) lies on these lines: {376,18910}, {2929,6776}, {13567,17837}, {19119,19142}, {19166,19198}
The reciprocal orthologic center of these triangles is X(3)
X(18937) lies on these lines: {3,18927}, {4,12237}, {69,486}, {487,1584}, {642,18928}, {1598,3564}, {1899,12320}, {6515,12221}, {6776,12978}, {11245,12169}, {11411,12601}, {12229,14912}, {12274,18911}, {12285,18912}, {12296,12324}, {12303,18913}, {12311,18914}, {12509,18916}, {12597,18919}, {12662,18921}, {12910,18922}, {12960,18923}, {12966,18924}, {12972,18925}, {12980,18929}, {12981,18930}, {12984,18931}, {13567,17839}, {18909,18944}, {19119,19143}, {19166,19199}
The reciprocal orthologic center of these triangles is X(3)
X(18938) lies on these lines: {3,18926}, {4,12238}, {69,485}, {488,1583}, {641,18928}, {1598,3564}, {1899,12321}, {6515,12222}, {6776,12979}, {11245,12170}, {11411,12602}, {12230,14912}, {12275,18911}, {12286,18912}, {12297,12324}, {12304,18913}, {12312,18914}, {12510,18916}, {12598,18919}, {12663,18921}, {12911,18922}, {12961,18923}, {12967,18924}, {12973,18925}, {12982,18929}, {12983,18930}, {12985,18931}, {13567,17842}, {18909,18943}, {19119,19144}, {19166,19200}
The reciprocal orthologic center of these triangles is X(6643)
X(18939) lies on these lines: {155,371}, {3564,12426}, {5408,11198}, {6643,18926}, {9723,18940}, {9927,18414}, {12163,13021}, {13754,18980}, {18436,18462}, {19134,19139}, {19186,19194}
The reciprocal orthologic center of these triangles is X(6643)
X(18940) lies on these lines: {155,372}, {3564,12427}, {6643,18927}, {9723,18939}, {9927,18415}, {12163,13022}, {13754,18981}, {18436,18463}, {19135,19139}, {19187,19194}
The reciprocal orthologic center of these triangles is X(3)
X(18941) lies on these lines: {4,12239}, {69,12360}, {511,18909}, {1151,6776}, {1899,12322}, {6239,18916}, {6252,18921}, {6283,18922}, {6291,11433}, {6515,12223}, {7362,18915}, {7690,18931}, {9823,18928}, {9974,18919}, {10667,18929}, {10668,18930}, {11245,12171}, {11411,12603}, {12231,14912}, {12276,18911}, {12287,18912}, {12298,12324}, {12305,18913}, {12313,18914}, {12962,18923}, {12968,18924}, {12974,18925}, {13567,17840}, {19119,19145}, {19166,19201}
X(18941) = {X(18909), X(18935)}-harmonic conjugate of X(18942)
The reciprocal orthologic center of these triangles is X(3)
X(18942) lies on these lines: {4,12240}, {69,12361}, {511,18909}, {1152,6776}, {1899,12323}, {6400,18916}, {6404,18921}, {6405,18922}, {6406,11433}, {6515,12224}, {7353,18915}, {7692,18931}, {9824,18928}, {9975,18919}, {10671,18929}, {10672,18930}, {11245,12172}, {11411,12604}, {12232,14912}, {12277,18911}, {12288,18912}, {12299,12324}, {12306,18913}, {12314,18914}, {12963,18923}, {12969,18924}, {12975,18925}, {13567,17843}, {19119,19146}, {19166,19202}
The reciprocal orthologic center of these triangles is X(10670)
X(18943) lies on these lines: {4,13013}, {69,13027}, {1899,13025}, {6515,13009}, {6776,13055}, {11245,13007}, {11411,13039}, {11433,13051}, {12324,13019}, {13011,14912}, {13015,18911}, {13017,18912}, {13021,18913}, {13023,18914}, {13035,18916}, {13037,18919}, {13041,18921}, {13043,18922}, {13045,18923}, {13047,18924}, {13049,18925}, {13053,18928}, {13057,18929}, {13059,18930}, {13061,18931}, {13567,17841}, {18909,18938}, {19119,19147}, {19166,19203}
The reciprocal orthologic center of these triangles is X(10674)
X(18944) lies on these lines: {4,13014}, {69,13028}, {1899,13026}, {6515,13010}, {6776,13056}, {11245,13008}, {11411,13040}, {11433,13052}, {12324,13020}, {13012,14912}, {13016,18911}, {13018,18912}, {13022,18913}, {13024,18914}, {13036,18916}, {13038,18919}, {13042,18921}, {13044,18922}, {13046,18923}, {13048,18924}, {13050,18925}, {13054,18928}, {13058,18929}, {13060,18930}, {13062,18931}, {13567,17844}, {18909,18937}, {19119,19148}, {19166,19204}
The reciprocal orthologic center of these triangles is X(4)
X(18945) lies on these lines: {2,11449}, {3,15077}, {4,6}, {5,8780}, {20,1204}, {30,18909}, {69,11821}, {125,3523}, {154,6622}, {184,3091}, {185,3060}, {193,10112}, {235,11206}, {265,3549}, {382,18914}, {550,18931}, {1885,12324}, {3088,18381}, {3089,9833}, {3525,15748}, {3529,10605}, {3541,15126}, {3546,12118}, {3547,9927}, {3575,11433}, {3832,13851}, {4292,10360}, {4846,18128}, {5056,10619}, {5562,8681}, {5622,10984}, {5907,5921}, {6102,10938}, {6240,18916}, {6253,18921}, {6284,18922}, {6288,14786}, {6515,12225}, {6623,6759}, {6816,14516}, {7354,18915}, {7378,11424}, {7396,13346}, {7404,18474}, {7487,18400}, {7505,12254}, {7507,11427}, {7714,15873}, {8889,11425}, {9786,18950}, {9825,18928}, {10519,15812}, {10602,12164}, {11245,12173}, {11411,12605}, {12134,18537}, {12250,18560}, {12278,18911}, {12289,18533}, {12370,14790}, {13403,14216}, {13567,17845}, {18563,18917}, {18933,18946}, {19166,19205}
X(18945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6146, 6776), (4, 14912, 12233), (20, 1899, 18913), (69, 12362, 11821), (6146, 18396, 4), (6816, 14516, 14826), (9833, 18390, 3089), (12024, 18405, 14912), (12233, 18405, 4), (12289, 18912, 18533), (12362, 12429, 69), (18918, 18925, 5)
The reciprocal orthologic center of these triangles is X(6243)
X(18946) lies on these lines: {4,54}, {69,3519}, {70,18368}, {195,6776}, {323,6146}, {539,6643}, {1154,18909}, {1209,3619}, {1370,15801}, {1493,14790}, {1899,12325}, {2888,11577}, {2914,13203}, {5965,18935}, {6152,11433}, {6242,18916}, {6255,18921}, {6286,18922}, {6288,18918}, {6403,13433}, {6515,12226}, {7356,18915}, {7691,18931}, {9977,18919}, {10677,18929}, {10678,18930}, {11245,12175}, {11411,12606}, {12234,14912}, {12280,18911}, {12291,18912}, {12300,12324}, {12307,18913}, {12316,18914}, {12319,15089}, {12965,18923}, {12971,18924}, {13567,17846}, {16063,18910}, {18933,18945}, {19119,19150}, {19166,19207}
The reciprocal parallelogic center of these triangles is X(15139)
X(18947) lies on these lines: {4,94}, {25,14683}, {52,12319}, {68,11557}, {69,5095}, {74,18916}, {110,6353}, {113,11411}, {125,8889}, {235,12165}, {399,3089}, {542,7714}, {631,15463}, {1177,19119}, {1596,12308}, {1899,13203}, {2777,18909}, {2781,18950}, {2904,14940}, {2914,7505}, {2935,18913}, {3043,3147}, {3088,10264}, {6143,15018}, {6723,18928}, {6776,10117}, {6804,12358}, {6816,12219}, {7401,16222}, {7723,18537}, {7731,18912}, {9833,10114}, {9919,18914}, {10118,18922}, {10119,18921}, {10628,18933}, {10681,18929}, {10682,18930}, {11245,13171}, {11487,12900}, {11807,14216}, {12241,17835}, {12324,13202}, {12412,13292}, {13198,14912}, {13201,18911}, {13248,18919}, {13287,18923}, {13288,18924}, {13289,18925}, {13293,18931}, {13567,17847}, {19166,19208}
X(18947) = parallelogic center of these triangles: anti-Atik to AOA
X(18947) = parallelogic center of these triangles: anti-Atik to 1st Hyacinth
X(18947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1112, 3448, 4), (1899, 13417, 13203)
X(18948) lies on these lines: {10619,16063}, {12319,18909}, {18912,19161}
X(18949) lies on the line {1147,6804}
X(18950) lies on these lines: {2,3167}, {4,51}, {5,5644}, {6,8889}, {54,3525}, {68,5892}, {69,3819}, {125,11427}, {154,6353}, {193,1368}, {343,631}, {376,12022}, {436,459}, {1154,6643}, {1181,6622}, {1351,7396}, {1352,6688}, {1503,7714}, {1853,14853}, {1992,11225}, {1993,16051}, {2393,18935}, {2781,18947}, {2979,6515}, {3089,18914}, {3090,7592}, {3448,6997}, {3546,13292}, {3580,7494}, {3620,16419}, {5020,5921}, {5891,6804}, {7378,9777}, {7392,11442}, {7398,18440}, {9786,18945}, {10606,12241}, {11189,18922}, {11190,18921}, {11202,18925}, {11204,18931}, {11216,18919}, {11241,18923}, {11242,18924}, {11243,18929}, {11244,18930}, {15012,15077}, {18435,18537}, {19119,19153}, {19166,19209}
X(18950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 11245, 14912), (1899, 11433, 4), (6515, 18911, 7386), (6776, 13567, 6353), (18912, 18916, 4), (18951, 18952, 6643)
X(18951) lies on these lines: {2,1199}, {3,6515}, {4,94}, {5,11411}, {6,12359}, {20,12370}, {26,6776}, {30,18909}, {49,3147}, {52,1899}, {68,389}, {69,140}, {141,15805}, {155,13567}, {156,6353}, {193,3546}, {195,6640}, {578,11225}, {631,13353}, {1147,5181}, {1154,6643}, {1352,5462}, {1370,6243}, {1493,3525}, {1658,18925}, {1992,18281}, {1993,3548}, {2895,6989}, {3060,11457}, {3167,16238}, {3542,18445}, {3549,3580}, {3564,6642}, {3567,7528}, {3627,12324}, {3628,11487}, {4846,13382}, {5422,14786}, {5446,14216}, {5876,18537}, {5889,18531}, {5946,7401}, {6101,7386}, {6639,15087}, {6803,12006}, {6804,11591}, {6816,18436}, {7387,18910}, {7392,15026}, {7403,9777}, {7542,11402}, {8141,18921}, {8144,18922}, {8889,13561}, {9306,9936}, {9833,10116}, {10071,11436}, {10112,11438}, {10821,11004}, {11250,18931}, {11255,18919}, {11265,18923}, {11266,18924}, {11267,18929}, {11268,18930}, {11412,18911}, {11585,12160}, {11818,16881}, {12084,18913}, {12085,13142}, {12163,12241}, {12233,14852}, {12235,19161}, {12293,13568}, {14791,15134}, {14912,19129}, {16625,18381}, {18377,18918}, {19119,19154}, {19166,19210}
X(18951) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (52, 1899, 14790), (68, 389, 18420), (193, 3546, 16266), (3567, 11442, 7528), (3580, 7592, 3549), (5889, 18912, 18531), (6515, 18916, 3), (6643, 18950, 18952), (10112, 11438, 12118), (11411, 11433, 5), (11487, 18928, 3628), (16881, 18356, 11818)
X(18952) lies on these lines: {2,49}, {3,3580}, {4,3521}, {5,1181}, {6,13371}, {26,13567}, {30,9786}, {52,14791}, {54,6640}, {66,18583}, {68,140}, {70,14389}, {125,569}, {143,11433}, {156,6776}, {182,5449}, {343,7516}, {381,11457}, {389,18569}, {546,14216}, {578,18281}, {1154,6643}, {1352,3628}, {1368,13292}, {1370,10263}, {1503,13861}, {1656,11442}, {2072,7592}, {2888,3525}, {3090,3448}, {3147,5944}, {3410,5067}, {3548,15121}, {5012,6639}, {5422,5576}, {5462,11818}, {5663,18909}, {5876,6816}, {5890,18404}, {6101,6515}, {6102,18531}, {6146,6644}, {6759,18128}, {6804,14128}, {7386,10627}, {7393,12166}, {7401,13363}, {7514,12359}, {7528,15026}, {7706,15012}, {8550,9820}, {9140,14787}, {9306,10116}, {9729,9927}, {9833,12106}, {9968,19130}, {11003,14940}, {11245,11585}, {11411,11591}, {11511,12585}, {11572,16226}, {12006,18420}, {12084,12241}, {12289,15053}, {12319,13358}, {15114,15128}, {18379,18918}, {19119,19155}, {19166,19211}
X(18952) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1368, 13292, 16266), (3628, 18356, 1352), (5462, 18381, 11818), (6643, 18950, 18951), (6816, 18917, 5876), (11245, 11585, 12161), (11433, 14790, 143), (15012, 18383, 7706), (18531, 18916, 6102), (18911, 18912, 3)
X(18953) lies on these lines: {53,11433}, {69,10607}, {157,6776}, {1503,7487}, {1899,6751}, {2871,18935}, {13567,17849}, {18380,18918}, {18437,18917}, {19119,19156}, {19166,19212}
X(18954) lies on these lines: {1,7387}, {3,12}, {4,10832}, {11,1598}, {22,388}, {23,3600}, {24,4293}, {25,34}, {26,18990}, {36,6642}, {55,11414}, {57,8185}, {65,9798}, {159,1469}, {161,221}, {197,10834}, {390,12087}, {496,7530}, {499,7529}, {529,9712}, {999,7517}, {1056,12088}, {1317,13222}, {1319,11365}, {1399,1460}, {1454,1473}, {1470,15654}, {1479,18534}, {1486,11510}, {1593,9672}, {1909,15574}, {1935,5329}, {1995,7288}, {2099,8192}, {3023,9861}, {3027,13175}, {3028,12310}, {3057,9911}, {3085,10323}, {3086,10594}, {3167,9652}, {3295,4354}, {3304,9673}, {3320,11641}, {3324,14673}, {3327,15960}, {4185,10829}, {4214,13273}, {4294,12082}, {4317,9714}, {5020,5433}, {5198,10896}, {5229,7503}, {5252,8193}, {5261,6636}, {5265,13595}, {5281,16661}, {5347,9370}, {5434,9909}, {5594,18960}, {5595,18959}, {5899,7373}, {6020,12413}, {6284,16541}, {6285,9914}, {7071,9628}, {7352,9937}, {7393,7951}, {7395,10895}, {7485,10588}, {7509,10590}, {7516,10592}, {8190,18955}, {8191,18956}, {8194,18963}, {8195,18964}, {9613,15177}, {9657,9659}, {9667,14530}, {9876,18969}, {9908,18970}, {9910,12688}, {9912,18976}, {9915,18975}, {9916,18974}, {9917,18982}, {9918,18983}, {9920,18984}, {9921,18989}, {9922,18988}, {10483,12085}, {10790,12835}, {10828,18957}, {10830,18962}, {10835,18967}, {10944,12410}, {11853,18958}, {12168,12373}, {12411,18979}, {12412,18968}, {12414,18985}, {12903,13171}, {13680,18986}, {13800,18987}, {13861,15325}, {13889,18965}, {13943,18966}, {16119,18977}, {18995,19005}, {18996,19006}
X(18954) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7387, 10833), (22, 388, 10831), (34, 5322, 56), (56, 9658, 25), (999, 7517, 10046), (9672, 12943, 1593)
X(18955) lies on these lines: {1,3}, {4,11871}, {8,11870}, {11,8196}, {12,5599}, {34,11384}, {80,18497}, {388,5601}, {1317,13228}, {1469,12452}, {1478,8200}, {3023,12179}, {3027,13176}, {3028,13208}, {3320,13229}, {3585,18495}, {4293,11843}, {5252,8197}, {5434,11207}, {6020,12478}, {6285,12468}, {8190,18954}, {8198,18959}, {8199,18960}, {8201,18963}, {8202,18964}, {8207,10573}, {10944,12454}, {11837,12835}, {11861,18957}, {11863,18958}, {11865,18961}, {11867,18962}, {11872,18391}, {12345,18969}, {12415,18970}, {12456,12688}, {12460,18976}, {12464,18979}, {12466,18968}, {12470,18975}, {12472,18974}, {12474,18982}, {12476,18983}, {12480,18984}, {12482,18985}, {12484,18989}, {12486,18988}, {13682,18986}, {13802,18987}, {13890,18965}, {13944,18966}, {16121,18977}, {18995,19007}, {18996,19008}
X(18955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 11252, 11873), (55, 65, 18956), (388, 5601, 11869), (999, 11875, 11879)
X(18956) lies on these lines: {1,3}, {4,11872}, {8,11869}, {11,8203}, {12,5600}, {34,11385}, {80,18495}, {388,5602}, {1317,13230}, {1469,12453}, {1478,8207}, {3023,12180}, {3027,13177}, {3320,13231}, {3585,18497}, {4293,11844}, {5252,8204}, {5434,11208}, {6020,12479}, {6285,12469}, {8191,18954}, {8200,10573}, {8205,18959}, {8206,18960}, {8208,18963}, {8209,18964}, {10944,12455}, {11838,12835}, {11862,18957}, {11864,18958}, {11866,18961}, {11868,18962}, {11871,18391}, {12346,18969}, {12416,18970}, {12457,12688}, {12461,18976}, {12465,18979}, {12467,18968}, {12471,18975}, {12473,18974}, {12475,18982}, {12477,18983}, {12481,18984}, {12483,18985}, {12485,18989}, {12487,18988}, {13683,18986}, {13803,18987}, {13891,18965}, {13945,18966}, {16122,18977}, {18995,19009}, {18996,19010}
X(18956) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 11253, 11874), (55, 65, 18955), (388, 5602, 11870), (999, 11876, 11880)
X(18957) lies on these lines: {1,9821}, {3,10038}, {4,10874}, {11,9993}, {12,3096}, {32,56}, {34,11386}, {55,3098}, {57,3099}, {65,9941}, {388,2896}, {999,9301}, {1317,13235}, {1319,11368}, {1401,1403}, {1469,2276}, {1478,9996}, {2099,9997}, {3023,4293}, {3027,8782}, {3028,13210}, {3057,12497}, {3085,10357}, {3320,13236}, {3585,18500}, {5252,9857}, {5433,7846}, {5434,7811}, {6020,12503}, {6285,12502}, {7288,10583}, {7333,9998}, {7354,9873}, {7865,11237}, {9655,18503}, {9878,18969}, {9923,18970}, {9981,18975}, {9982,18974}, {9983,18982}, {9985,18984}, {9986,18989}, {9987,18988}, {9994,18959}, {9995,18960}, {10345,10797}, {10356,10895}, {10828,18954}, {10871,18961}, {10872,18962}, {10875,18963}, {10876,18964}, {10878,11494}, {10879,18967}, {10944,12495}, {11861,18955}, {11862,18956}, {11885,18958}, {12496,12688}, {12498,18976}, {12500,18979}, {12501,18968}, {12504,18985}, {13685,18986}, {13805,18987}, {13892,18965}, {13946,18966}, {16123,18977}, {18995,19011}, {18996,19012}
X(18957) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 9821, 10877), (388, 2896, 10873), (999, 9301, 10047)
X(18958) lies on these lines: {1,11251}, {3,11912}, {4,11906}, {11,11897}, {12,1650}, {30,55}, {34,11832}, {56,402}, {57,11852}, {65,12438}, {388,4240}, {999,11911}, {1317,13268}, {1319,11831}, {1469,12583}, {1651,5434}, {2099,11910}, {3023,12181}, {3027,13179}, {3028,13212}, {3057,12696}, {3476,16212}, {3585,18507}, {4293,11845}, {5252,11900}, {5433,15183}, {6020,12796}, {6285,12791}, {7354,12113}, {9655,18508}, {9657,15774}, {10944,12626}, {11509,11848}, {11839,12835}, {11853,18954}, {11863,18955}, {11864,18956}, {11885,18957}, {11901,18959}, {11902,18960}, {11903,18961}, {11904,18962}, {11907,18963}, {11908,18964}, {11915,18967}, {12347,18969}, {12418,18970}, {12668,12688}, {12729,18976}, {12789,18979}, {12790,18968}, {12792,18975}, {12793,18974}, {12794,18982}, {12795,18983}, {12797,18984}, {12798,18985}, {12799,18989}, {12800,18988}, {13689,18986}, {13809,18987}, {13894,18965}, {13948,18966}, {15326,16190}, {16129,18977}, {18995,19017}, {18996,19018}
X(18958) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 11251, 11909), (999, 11911, 11913)
X(18959) lies on these lines: {1,1161}, {3,10040}, {4,10925}, {6,41}, {11,6202}, {12,5591}, {34,11388}, {55,11824}, {57,5589}, {65,3641}, {388,1271}, {999,10048}, {1317,13269}, {1319,11370}, {1478,6215}, {2099,5605}, {3023,6227}, {3027,6319}, {3028,7732}, {3057,12697}, {3085,10517}, {3303,7353}, {3320,13282}, {3585,18509}, {4293,10783}, {5252,5689}, {5434,5861}, {5595,18954}, {5871,7354}, {5875,18990}, {6020,12805}, {6258,12688}, {6263,18976}, {6267,6285}, {6270,18974}, {6271,18975}, {6273,18982}, {6275,18983}, {6277,18984}, {6279,18988}, {6281,9657}, {8198,18955}, {8205,18956}, {8216,18963}, {8217,18964}, {8396,19038}, {8974,18965}, {9882,18969}, {9929,18970}, {9994,18957}, {10513,10924}, {10514,10895}, {10792,12835}, {10919,18961}, {10921,18962}, {10929,11497}, {10931,18967}, {10944,12627}, {11901,18958}, {12801,18979}, {12803,18968}, {12807,18985}, {13690,18986}, {13810,18987}, {13949,18966}, {16130,18977}
X(18959) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1161, 10927), (56, 1469, 18960), (388, 1271, 10923), (999, 11916, 10048)
X(18960) lies on these lines: {1,1160}, {3,10041}, {4,10926}, {6,41}, {11,6201}, {12,5590}, {34,11389}, {55,11825}, {57,5588}, {65,3640}, {388,1270}, {999,10049}, {1317,13270}, {1319,11371}, {1478,6214}, {2099,5604}, {3023,6226}, {3027,6320}, {3028,7733}, {3057,12698}, {3085,10518}, {3303,7362}, {3320,13283}, {3585,18511}, {4293,10784}, {5252,5688}, {5434,5860}, {5594,18954}, {5870,7354}, {5874,18990}, {6020,12806}, {6257,12688}, {6262,18976}, {6266,6285}, {6268,18974}, {6269,18975}, {6272,18982}, {6274,18983}, {6276,18984}, {6278,9657}, {6280,18989}, {8199,18955}, {8206,18956}, {8218,18963}, {8219,18964}, {8416,19037}, {9883,18969}, {9930,18970}, {9995,18957}, {10513,10923}, {10515,10895}, {10793,12835}, {10920,18961}, {10922,18962}, {10930,11498}, {10932,18967}, {10944,12628}, {11902,18958}, {12802,18979}, {12804,18968}, {12808,18985}, {13691,18986}, {13811,18987}, {13950,18966}, {16131,18977}
X(18960) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1160, 10928), (56, 1469, 18959), (388, 1270, 10924), (999, 11917, 10049)
X(18961) lies on these lines: {1,6923}, {3,10320}, {4,11}, {5,1470}, {12,377}, {20,5172}, {28,9658}, {34,11390}, {36,6928}, {46,10526}, {55,6850}, {57,3585}, {65,68}, {145,388}, {226,17647}, {382,1617}, {497,1388}, {499,6929}, {999,10948}, {1317,13271}, {1319,1479}, {1399,5230}, {1415,3767}, {1420,3583}, {1454,4292}, {1466,6826}, {1469,12586}, {1709,9579}, {1788,5080}, {1836,12672}, {1887,5101}, {1898,6259}, {2478,5433}, {3023,12182}, {3027,13180}, {3028,13213}, {3057,12700}, {3085,6951}, {3320,13294}, {3340,5270}, {3361,18513}, {3614,6854}, {3913,10956}, {3916,17619}, {4185,10829}, {4190,10524}, {5046,7288}, {5204,6827}, {5217,6916}, {5221,5229}, {5252,10914}, {5432,6897}, {5434,10949}, {5697,16153}, {5840,11508}, {5903,10057}, {6020,12925}, {6284,6925}, {6285,12920}, {6836,15326}, {6842,8071}, {6863,14793}, {6901,10590}, {6948,10321}, {6957,7173}, {6958,8068}, {6959,10090}, {7491,7742}, {9581,10085}, {9655,18519}, {10043,16159}, {10404,17625}, {10589,13729}, {10742,12832}, {10794,12835}, {10871,18957}, {10919,18959}, {10920,18960}, {10943,18990}, {10945,18963}, {10946,18964}, {10950,12115}, {10966,15908}, {11375,17614}, {11502,18242}, {11604,18467}, {11865,18955}, {11866,18956}, {11903,18958}, {12348,18969}, {12422,18970}, {12676,12688}, {12701,17622}, {12737,18976}, {12857,18979}, {12889,18968}, {12921,18975}, {12922,18974}, {12923,18982}, {12924,18983}, {12926,18984}, {12927,18985}, {12928,18989}, {12929,18988}, {13462,18514}, {13693,18986}, {13813,18987}, {13895,18965}, {13952,18966}, {16138,18977}, {18995,19023}, {18996,19024}
X(18961) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10525, 10947), (11, 7354, 12114), (56, 13273, 4), (65, 1478, 18962), (377, 10522, 1376), (388, 3434, 10944), (999, 11928, 10948), (3086, 10598, 11), (3585, 10826, 18516), (6850, 10629, 55), (10893, 12761, 4)
X(18962) lies on these lines: {1,6928}, {2,12}, {3,10954}, {4,1389}, {10,1454}, {11,10532}, {20,14882}, {34,11391}, {55,6868}, {57,5270}, {65,68}, {72,5252}, {153,5229}, {999,6971}, {1056,1388}, {1259,11501}, {1317,13272}, {1319,11374}, {1466,6885}, {1469,12587}, {1470,6924}, {1479,3656}, {1482,10947}, {1836,6256}, {1875,5130}, {2478,15950}, {3023,12183}, {3027,13181}, {3028,13214}, {3057,5812}, {3085,5172}, {3086,10599}, {3256,10483}, {3320,13295}, {3340,3585}, {3485,5080}, {4293,6942}, {5173,18480}, {5221,6901}, {5708,12832}, {5903,6923}, {6020,12935}, {6253,12667}, {6285,12930}, {6867,10895}, {6874,10590}, {6934,7354}, {6936,11510}, {9613,17857}, {9655,18518}, {10404,18838}, {10522,10944}, {10795,12835}, {10830,18954}, {10872,18957}, {10921,18959}, {10922,18960}, {10948,12001}, {10951,18963}, {10952,18964}, {10957,12513}, {11867,18955}, {11868,18956}, {11904,18958}, {12349,18969}, {12423,18970}, {12677,12688}, {12738,18976}, {12858,18979}, {12890,18968}, {12931,18975}, {12932,18974}, {12933,18982}, {12934,18983}, {12936,18984}, {12937,18985}, {12938,18989}, {12939,18988}, {13694,18986}, {13814,18987}, {13896,18965}, {13953,18966}, {16139,18977}, {18995,19025}, {18996,19026}
X(18962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10526, 10953), (65, 1478, 18961), (388, 3436, 12), (999, 11929, 10523), (1478, 10573, 6917), (7354, 10955, 11500), (15843, 15844, 12)
X(18963) lies on these lines: {1,10669}, {3,11951}, {4,11932}, {11,8212}, {12,8222}, {34,11394}, {55,11828}, {56,493}, {57,8188}, {65,12440}, {388,6462}, {999,11949}, {1317,13275}, {1319,11377}, {1469,12590}, {1478,8220}, {2099,8210}, {3023,12186}, {3027,13184}, {3028,13215}, {3320,13298}, {3585,18520}, {4293,11846}, {5252,8214}, {5434,12152}, {6020,12996}, {6285,12986}, {6339,11931}, {6461,18964}, {7354,9838}, {8194,18954}, {8201,18955}, {8208,18956}, {8216,18959}, {8218,18960}, {10875,18957}, {10944,12636}, {10945,18961}, {10951,18962}, {10981,11948}, {11503,11509}, {11840,12835}, {11907,18958}, {11957,18967}, {12352,18969}, {12426,18970}, {12688,18245}, {12741,18976}, {12861,18979}, {12894,18968}, {12988,18975}, {12990,18974}, {12992,18982}, {12994,18983}, {12998,18984}, {13000,18985}, {13002,18989}, {13004,18988}, {13697,18986}, {13817,18987}, {13899,18965}, {13956,18966}, {16161,18977}, {18995,19031}, {18996,19032}
X(18963) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10669, 11947), (388, 6462, 11930)
X(18964) lies on these lines: {1,10673}, {3,11952}, {4,11933}, {11,8213}, {12,8223}, {34,11395}, {55,11829}, {56,494}, {57,8189}, {65,12441}, {388,6463}, {999,11950}, {1317,13276}, {1319,11378}, {1469,12591}, {1478,8221}, {2099,8211}, {3023,12187}, {3027,13185}, {3028,13216}, {3320,13299}, {3585,18522}, {4293,11847}, {5252,8215}, {5434,12153}, {6020,12997}, {6285,12987}, {6339,11930}, {6461,18963}, {7354,9839}, {8195,18954}, {8202,18955}, {8209,18956}, {8217,18959}, {8219,18960}, {10876,18957}, {10944,12637}, {10946,18961}, {10952,18962}, {10981,11947}, {11504,11509}, {11841,12835}, {11908,18958}, {11958,18967}, {12353,18969}, {12427,18970}, {12688,18246}, {12742,18976}, {12862,18979}, {12895,18968}, {12989,18975}, {12991,18974}, {12993,18982}, {12995,18983}, {12999,18984}, {13001,18985}, {13003,18989}, {13005,18988}, {13698,18986}, {13818,18987}, {13900,18965}, {13957,18966}, {16162,18977}, {18995,19033}, {18996,19034}
X(18964) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 10673, 11948), (388, 6463, 11931)
X(18965) lies on these lines: {1,8981}, {2,13954}, {3,13904}, {4,13898}, {6,5433}, {11,371}, {12,590}, {34,13884}, {36,7583}, {55,9540}, {56,3068}, {57,13888}, {65,8983}, {140,3301}, {388,8972}, {485,7354}, {499,3311}, {615,7294}, {631,19037}, {999,13903}, {1151,6284}, {1317,13922}, {1319,13883}, {1335,5418}, {1388,19066}, {1469,13910}, {1478,8976}, {1479,6221}, {1587,5204}, {1702,11376}, {1837,9583}, {2099,13902}, {3023,8980}, {3027,8997}, {3028,8998}, {3057,13912}, {3058,9648}, {3070,15326}, {3071,7173}, {3086,19038}, {3299,15325}, {3316,10590}, {3320,13923}, {3526,13963}, {3585,18538}, {3614,10576}, {4293,13886}, {4299,13665}, {4302,6449}, {5160,9631}, {5252,13893}, {5298,6502}, {5434,13846}, {6020,13918}, {6285,8991}, {6417,13962}, {6453,9660}, {6459,10896}, {6564,9647}, {7288,7585}, {7582,13955}, {8974,18959}, {8987,12688}, {8988,18976}, {8992,18982}, {8993,18983}, {8995,18984}, {9541,12953}, {9616,12701}, {9646,15888}, {10944,13911}, {11509,13887}, {12835,13885}, {13848,18987}, {13879,18988}, {13889,18954}, {13890,18955}, {13891,18956}, {13892,18957}, {13894,18958}, {13895,18961}, {13896,18962}, {13899,18963}, {13900,18964}, {13907,18967}, {13908,18969}, {13909,18970}, {13914,18979}, {13915,18968}, {13916,18975}, {13917,18974}, {13919,18985}, {13920,18986}, {13921,18989}, {13925,18990}, {15950,16232}, {16148,18977}
X(18965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 8981, 13901), (2, 18996, 19027), (3, 13904, 19030), (6, 5433, 18966), (56, 3068, 19028), (140, 3301, 13958), (371, 9661, 11), (388, 8972, 13897), (499, 3311, 19029), (590, 2067, 12), (999, 13903, 13905), (1335, 5418, 5432), (6284, 9663, 1151), (6453, 9660, 9662), (7288, 7585, 18995)
X(18966) lies on these lines: {1,13958}, {2,13897}, {3,13962}, {4,13955}, {6,5433}, {11,372}, {12,615}, {34,13937}, {36,7584}, {55,13935}, {56,3069}, {57,13942}, {65,13971}, {140,3299}, {388,13941}, {486,7354}, {499,3312}, {590,7294}, {631,19038}, {999,13961}, {1124,5420}, {1152,6284}, {1317,13991}, {1319,13936}, {1388,19065}, {1469,13972}, {1478,13951}, {1479,6398}, {1588,5204}, {1703,11376}, {2067,5298}, {2099,13959}, {2362,15950}, {3023,13967}, {3027,13989}, {3028,13990}, {3057,13975}, {3070,7173}, {3071,15326}, {3086,19037}, {3301,15325}, {3317,10590}, {3320,13992}, {3526,13905}, {3585,18762}, {3592,9663}, {3614,10577}, {4293,13939}, {4299,13785}, {4302,6450}, {5252,13947}, {5326,9646}, {5434,13847}, {6020,13985}, {6285,13980}, {6396,15338}, {6418,13904}, {6420,9661}, {6460,10896}, {7288,7586}, {7581,13898}, {10944,13973}, {11509,13940}, {12688,13974}, {12835,13938}, {13849,18987}, {13880,18988}, {13933,18989}, {13943,18954}, {13944,18955}, {13945,18956}, {13946,18957}, {13948,18958}, {13949,18959}, {13950,18960}, {13952,18961}, {13953,18962}, {13956,18963}, {13957,18964}, {13965,18967}, {13968,18969}, {13970,18970}, {13976,18976}, {13978,18979}, {13979,18968}, {13981,18975}, {13982,18974}, {13983,18982}, {13984,18983}, {13986,18984}, {13987,18985}, {13988,18986}, {13993,18990}, {16149,18977}
X(18966) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 13966, 13958), (2, 18995, 19028), (3, 13962, 19029), (6, 5433, 18965), (56, 3069, 19027), (140, 3299, 13901), (388, 13941, 13954), (499, 3312, 19030), (615, 6502, 12), (999, 13961, 13963), (1124, 5420, 5432), (7288, 7586, 18996)
X(18967) lies on these lines: {1,3}, {4,10959}, {11,10532}, {12,6933}, {34,11401}, {145,11501}, {149,3600}, {388,6871}, {956,11375}, {958,15950}, {1149,1451}, {1191,15306}, {1317,13279}, {1398,1887}, {1469,12595}, {1478,10943}, {1696,2323}, {2178,17438}, {3023,12190}, {3027,13190}, {3028,13218}, {3086,6879}, {3320,13314}, {3585,18544}, {3649,10941}, {3890,7098}, {4293,10806}, {4298,7702}, {5219,5288}, {5252,10916}, {5434,10949}, {6020,13119}, {6285,13095}, {6834,10955}, {7288,10587}, {7354,12116}, {9655,18543}, {9657,13273}, {10530,10956}, {10804,12835}, {10835,18954}, {10879,18957}, {10931,18959}, {10932,18960}, {10944,12649}, {11237,17530}, {11915,18958}, {11957,18963}, {11958,18964}, {12357,18969}, {12431,18970}, {12687,12688}, {12750,18976}, {12875,18979}, {12906,18968}, {13106,18975}, {13107,18974}, {13110,18982}, {13113,18983}, {13122,18984}, {13131,18985}, {13133,18989}, {13135,18988}, {13717,18986}, {13840,18987}, {13907,18965}, {13965,18966}, {16155,18977}, {18393,18761}, {18995,19049}, {18996,19050}
X(18967) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 36, 16202), (1, 56, 11510), (1, 10680, 10966), (1, 11249, 55), (1, 12704, 3057), (56, 2099, 11509), (56, 3303, 5172), (56, 14882, 5204), (65, 999, 56), (388, 10529, 10957), (999, 12001, 1), (1470, 5563, 56), (3340, 5563, 1470)
The reciprocal orthologic center of these triangles is X(7574)
X(18968) lies on these lines: {1,12888}, {3,12903}, {4,10091}, {11,10113}, {12,1511}, {20,10065}, {30,3024}, {34,12140}, {35,16163}, {36,125}, {46,13211}, {55,12121}, {56,265}, {57,12407}, {74,4299}, {79,1365}, {80,1354}, {110,1478}, {113,3585}, {382,12374}, {388,10088}, {498,15035}, {499,14644}, {542,1469}, {999,12902}, {1319,12261}, {1479,10733}, {2099,12898}, {2771,18976}, {2777,6285}, {2948,9613}, {3028,3327}, {3448,4293}, {3583,12295}, {4311,13605}, {4316,16111}, {4325,16003}, {5204,15061}, {5252,12778}, {5663,7354}, {5972,7951}, {6699,7280}, {7288,15081}, {7343,13202}, {7687,7741}, {7728,12943}, {9651,14901}, {10074,10778}, {10089,11005}, {10895,14643}, {11392,15472}, {11509,12334}, {11720,12047}, {11723,18393}, {11801,15325}, {12041,15326}, {12201,12835}, {12412,18954}, {12466,18955}, {12467,18956}, {12501,18957}, {12790,18958}, {12803,18959}, {12804,18960}, {12889,18961}, {12890,18962}, {12894,18963}, {12895,18964}, {12906,18967}, {13182,18332}, {13915,18965}, {13979,18966}, {18995,19051}, {18996,19052}
X(18968) = reflection of X(3028) in X(18990)
X(18968) = orthologic center of these triangles: 2nd anti-circumperp-tangential to AOA
X(18968) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 1st Hyacinth
X(18968) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 12383, 10088), (999, 12902, 12904), (3448, 4293, 10081)
The reciprocal orthologic center of these triangles is X(9855)
X(18969) lies on these lines: {1,12354}, {2,13182}, {3,10054}, {4,12351}, {11,9880}, {12,2482}, {30,3023}, {34,12132}, {55,12117}, {56,671}, {57,9875}, {99,11237}, {115,5298}, {381,10089}, {388,8591}, {530,18975}, {531,18974}, {542,7354}, {543,3027}, {999,10070}, {1319,12258}, {1469,9830}, {1478,8724}, {2099,9884}, {2782,18971}, {2796,10106}, {3534,10053}, {3543,12185}, {3600,8596}, {4293,12243}, {4299,14830}, {4870,11711}, {5182,10797}, {5252,9881}, {5433,5461}, {5969,18982}, {6034,9597}, {6321,10072}, {9114,12941}, {9116,12942}, {9876,18954}, {9878,18957}, {9882,18959}, {9883,18960}, {10056,15452}, {10992,15888}, {11006,12903}, {11152,12837}, {11509,12326}, {12191,12835}, {12345,18955}, {12346,18956}, {12347,18958}, {12348,18961}, {12349,18962}, {12352,18963}, {12353,18964}, {12357,18967}, {13908,18965}, {13968,18966}, {18995,19057}, {18996,19058}
X(18969) = orthologic center of these triangles: McCay to 2nd anti-circumperp-tangential
X(18969) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 8591, 12350), (999, 12355, 10070)
The reciprocal orthologic center of these triangles is X(9833)
X(18970) lies on these lines: {1,9931}, {3,10055}, {4,1069}, {11,9927}, {12,1147}, {30,6238}, {34,12134}, {36,12359}, {55,12118}, {56,68}, {57,9896}, {155,1478}, {388,3157}, {499,14852}, {539,5434}, {999,10071}, {1060,6146}, {1319,12259}, {1469,3564}, {1479,12293}, {1870,14516}, {2099,9933}, {3167,9654}, {4293,11411}, {4299,12163}, {5252,9928}, {5432,12038}, {5433,5449}, {5504,12903}, {5654,10895}, {7354,13754}, {7689,15326}, {7951,9820}, {9655,12164}, {9657,9936}, {9908,18954}, {9923,18957}, {9929,18959}, {9930,18960}, {11509,12328}, {12193,12835}, {12415,18955}, {12416,18956}, {12418,18958}, {12422,18961}, {12423,18962}, {12426,18963}, {12427,18964}, {12431,18967}, {13909,18965}, {13970,18966}, {18995,19061}, {18996,19062}
X(18970) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 2nd Hyacinth
X(18970) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 6193, 3157), (999, 12429, 10071)
The reciprocal orthologic center of these triangles is X(3)
X(18971) lies on these lines: {1,13078}, {12,15819}, {56,262}, {76,9657}, {388,6194}, {511,5434}, {1469,3023}, {2782,18969}, {3095,4317}, {3600,12836}, {4293,7709}, {5188,15888}, {5563,14881}, {7354,13077}, {9655,10079}, {9772,12184}, {11246,14839}, {18982,18990}, {18995,19063}, {18996,19064}
The reciprocal orthologic center of these triangles is X(3)
X(18972) lies on these lines: {1,13075}, {12,630}, {18,56}, {388,628}, {533,5434}, {999,16628}, {1319,11740}, {1469,5965}, {1478,16627}, {5433,6674}, {11603,13182}, {12942,14145}, {18974,18990}, {18995,19069}, {18996,19072}
The reciprocal orthologic center of these triangles is X(3)
X(18973) lies on these lines: {1,13076}, {12,629}, {17,56}, {388,627}, {532,5434}, {1319,11739}, {1469,5965}, {1478,16626}, {5433,6673}, {11602,13182}, {12941,14144}, {18975,18990}, {18995,19071}, {18996,19070}
The reciprocal orthologic center of these triangles is X(13)
X(18974) lies on these lines: {1,13076}, {3,10062}, {4,12952}, {11,5478}, {12,618}, {13,56}, {14,13182}, {34,12142}, {36,6771}, {55,5473}, {57,9901}, {99,12941}, {388,616}, {530,5434}, {531,18969}, {542,1469}, {999,10078}, {1081,1365}, {1319,11705}, {1478,5617}, {2099,7975}, {4293,6770}, {5252,12781}, {5298,5459}, {5433,6669}, {5463,11237}, {5472,7051}, {5563,16001}, {5613,10089}, {6268,18960}, {6270,18959}, {6321,10077}, {9116,12350}, {9916,18954}, {9982,18957}, {11509,12337}, {12205,12835}, {12472,18955}, {12473,18956}, {12793,18958}, {12922,18961}, {12932,18962}, {12990,18963}, {12991,18964}, {13107,18967}, {13917,18965}, {13982,18966}, {18972,18990}, {18995,19073}, {18996,19074}
X(18974) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 7th Fermat-Dao
X(18974) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 11th Fermat-Dao
X(18974) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 15th Fermat-Dao
X(18974) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 1st isodynamic-Dao
X(18974) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 1st Lemoine-Dao
X(18974) = orthologic center of these triangles: outer-Napoleon to 2nd anti-circumperp-tangential
X(18974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 616, 12942), (999, 13103, 10078)
The reciprocal orthologic center of these triangles is X(14)
X(18975) lies on these lines: {1,13075}, {3,10061}, {4,12951}, {11,5479}, {12,619}, {13,13182}, {14,56}, {34,12141}, {36,6774}, {55,5474}, {57,9900}, {99,12942}, {115,7051}, {388,617}, {530,18969}, {531,5434}, {542,1469}, {554,1365}, {999,10077}, {1319,11706}, {1478,5613}, {2099,7974}, {4293,6773}, {5252,12780}, {5298,5460}, {5433,6670}, {5464,11237}, {5563,16002}, {5617,10089}, {6269,18960}, {6271,18959}, {6321,10078}, {9114,12350}, {9915,18954}, {9981,18957}, {11509,12336}, {12204,12835}, {12470,18955}, {12471,18956}, {12792,18958}, {12921,18961}, {12931,18962}, {12988,18963}, {12989,18964}, {13106,18967}, {13916,18965}, {13981,18966}, {18973,18990}, {18995,19075}, {18996,19076}
X(18975) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 8th Fermat-Dao
X(18975) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 12th Fermat-Dao
X(18975) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 16th Fermat-Dao
X(18975) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 2nd isodynamic-Dao
X(18975) = orthologic center of these triangles: 2nd anti-circumperp-tangential to 2nd Lemoine-Dao
X(18975) = orthologic center of these triangles: inner-Napoleon to 2nd anti-circumperp-tangential
X(18975) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 617, 12941), (999, 13102, 10077)
The reciprocal orthologic center of these triangles is X(3)
X(18976) lies on these lines: {1,10738}, {3,10057}, {4,12740}, {11,515}, {12,214}, {30,12758}, {34,12137}, {36,12619}, {55,12119}, {56,80}, {57,9897}, {65,952}, {100,5252}, {149,3476}, {244,14584}, {355,10090}, {388,6224}, {528,8581}, {999,10073}, {1145,17647}, {1317,1365}, {1385,8068}, {1387,10572}, {1388,9669}, {1470,12751}, {1836,10698}, {2098,14217}, {2099,7972}, {2771,18968}, {2800,7354}, {2802,10944}, {2829,12688}, {2932,11501}, {3057,5840}, {3585,12611}, {4293,12247}, {4299,12515}, {4311,10265}, {4973,15863}, {5083,5434}, {5433,6702}, {5691,12764}, {6262,18960}, {6263,18959}, {6284,15558}, {6326,9613}, {6797,18838}, {8988,18965}, {9578,15015}, {9579,13253}, {9912,18954}, {10058,18481}, {10609,10956}, {10724,12701}, {10950,12005}, {11509,12331}, {11729,17605}, {12198,12835}, {12460,18955}, {12461,18956}, {12498,18957}, {12729,18958}, {12737,18961}, {12738,18962}, {12741,18963}, {12742,18964}, {12750,18967}, {13976,18966}, {18995,19077}, {18996,19078}
X(18976) = reflection of X(i) in X(j) for these (i,j): (1145, 17647), (1317, 10106), (6284, 15558), (10950, 12736)
X(18976) = orthologic center of these triangles: 2nd anti-circumperp-tangential to K798e
X(18976) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 6224, 12739), (999, 12747, 10073), (6326, 9613, 12763)
The reciprocal orthologic center of these triangles is X(3)
X(18977) lies on these lines: {1,16142}, {3,16152}, {4,16141}, {11,1354}, {12,3647}, {21,11375}, {30,65}, {34,16114}, {55,16113}, {56,79}, {57,16118}, {191,9578}, {382,5221}, {388,3648}, {758,10944}, {999,16150}, {1319,3636}, {1361,3327}, {1454,10826}, {1478,3652}, {1621,10404}, {1788,2475}, {2099,5441}, {2771,18968}, {3065,13273}, {3485,15677}, {3884,5434}, {4293,16116}, {4308,14450}, {4870,17525}, {5183,16004}, {5252,11684}, {5427,11263}, {5428,14526}, {5433,6701}, {5901,11544}, {8581,17768}, {10543,10624}, {11373,16159}, {11509,16117}, {12835,16115}, {16119,18954}, {16121,18955}, {16122,18956}, {16123,18957}, {16129,18958}, {16130,18959}, {16131,18960}, {16138,18961}, {16139,18962}, {16148,18965}, {16149,18966}, {16155,18967}, {16161,18963}, {16162,18964}, {16617,17605}, {18995,19079}, {18996,19080}
X(18977) = orthologic center of these triangles: 2nd anti-circumperp-tangential to K798i
X(18977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 3648, 16140), (999, 16150, 16153)
The reciprocal orthologic center of these triangles is X(12241)
X(18978) lies on these lines: {18995,19083}, {18996,19084}
The reciprocal orthologic center of these triangles is X(40)
X(18979) lies on these lines: {1,12863}, {3,10059}, {4,12860}, {11,12599}, {12,12864}, {34,12139}, {55,12120}, {56,7160}, {57,9898}, {65,1056}, {388,9874}, {999,10075}, {1319,12260}, {1478,12856}, {1864,12853}, {2099,7971}, {3340,5696}, {3649,12854}, {4293,12249}, {5173,9578}, {5252,12777}, {11509,12333}, {12200,12835}, {12411,18954}, {12464,18955}, {12465,18956}, {12500,18957}, {12789,18958}, {12801,18959}, {12802,18960}, {12857,18961}, {12858,18962}, {12861,18963}, {12862,18964}, {12875,18967}, {13914,18965}, {13978,18966}, {18995,19085}, {18996,19086}
X(18979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 9874, 12859), (999, 12872, 10075)
The reciprocal orthologic center of these triangles is X(1)
X(18980) lies on these lines: {3,485}, {4,18414}, {182,19134}, {511,10669}, {7395,9723}, {8884,19186}, {13754,18939}, {18909,18926}
The reciprocal orthologic center of these triangles is X(1)
X(18981) lies on these lines: {3,486}, {4,18415}, {182,19135}, {511,10673}, {7395,9723}, {8884,19187}, {13754,18940}, {18909,18927}
The reciprocal orthologic center of these triangles is X(3)
X(18982) lies on these lines: {1,2782}, {3,10063}, {4,12836}, {6,10797}, {11,6248}, {12,39}, {34,12143}, {55,11257}, {56,76}, {57,9902}, {65,730}, {194,388}, {262,10895}, {384,12835}, {498,11171}, {499,7697}, {511,7354}, {538,5434}, {726,10106}, {732,1469}, {999,10079}, {1319,12263}, {1478,3095}, {1916,13182}, {2099,7976}, {3085,7709}, {3094,9597}, {3097,9578}, {3202,9652}, {3585,14881}, {3934,5433}, {4293,12251}, {4299,9821}, {5188,15326}, {5252,12782}, {5298,9466}, {5432,13334}, {5969,18969}, {6272,18960}, {6273,18959}, {7757,11237}, {7951,11272}, {8992,18965}, {9917,18954}, {9983,18957}, {10944,14839}, {11152,12350}, {11509,12338}, {12474,18955}, {12475,18956}, {12794,18958}, {12923,18961}, {12933,18962}, {12992,18963}, {12993,18964}, {13110,18967}, {13983,18966}, {18971,18990}, {18995,19089}, {18996,19090}
X(18982) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (194, 388, 12837), (999, 13108, 10079)
The reciprocal orthologic center of these triangles is X(3)
X(18983) lies on these lines: {1,13078}, {3,10064}, {4,12954}, {11,6249}, {12,6292}, {34,12144}, {55,12122}, {56,83}, {57,9903}, {388,2896}, {732,1469}, {754,5434}, {999,10080}, {1319,12264}, {1463,10106}, {1478,6287}, {2099,7977}, {3023,18990}, {4293,12252}, {4299,8725}, {5204,9751}, {5252,12783}, {5433,6704}, {6274,18960}, {6275,18959}, {7333,7334}, {8993,18965}, {9918,18954}, {11509,12339}, {11606,13182}, {12206,12835}, {12476,18955}, {12477,18956}, {12795,18958}, {12924,18961}, {12934,18962}, {12994,18963}, {12995,18964}, {13113,18967}, {13984,18966}, {18995,19091}, {18996,19092}
X(18983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 2896, 12944), (999, 13111, 10080)
The reciprocal orthologic center of these triangles is X(4)
X(18984) lies on these lines: {1,1154}, {3,10066}, {4,12956}, {11,3574}, {12,942}, {34,11576}, {36,10610}, {54,56}, {55,7691}, {57,9905}, {195,999}, {388,2888}, {517,17705}, {539,5434}, {1056,12325}, {1060,12363}, {1319,12266}, {1425,10619}, {1478,6288}, {1493,5563}, {1870,6152}, {2099,7979}, {3028,3327}, {3295,12307}, {3304,15801}, {4293,12254}, {5252,12785}, {5433,6689}, {6198,12300}, {6255,11529}, {6276,18960}, {6277,18959}, {7354,18400}, {7373,12316}, {7951,13565}, {8254,15325}, {8995,18965}, {9920,18954}, {9985,18957}, {11509,12341}, {12208,12835}, {12480,18955}, {12481,18956}, {12606,18447}, {12797,18958}, {12926,18961}, {12936,18962}, {12998,18963}, {12999,18964}, {13122,18967}, {13986,18966}, {18995,19095}, {18996,19096}
X(18984) = midpoint of X(1) and X(7356)
X(18984) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (195, 999, 10082), (388, 2888, 12946)
The reciprocal orthologic center of these triangles is X(79)
X(18985) lies on these lines: {1,13080}, {3,13128}, {4,12957}, {11,79}, {12,13089}, {34,12146}, {55,12556}, {56,10266}, {57,12409}, {65,17643}, {388,12849}, {999,13126}, {1319,12267}, {1478,12919}, {2099,13100}, {4293,12255}, {5252,12786}, {5563,18244}, {6595,13273}, {11509,12342}, {12209,12835}, {12414,18954}, {12482,18955}, {12483,18956}, {12504,18957}, {12798,18958}, {12807,18959}, {12808,18960}, {12927,18961}, {12937,18962}, {13000,18963}, {13001,18964}, {13131,18967}, {13919,18965}, {13987,18966}, {18995,19097}, {18996,19098}
X(18985) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 12849, 12947), (999, 13126, 13129)
The reciprocal orthologic center of these triangles is X(13665)
X(18986) lies on these lines: {1,13699}, {3,13714}, {4,13696}, {11,13687}, {12,13701}, {30,7362}, {55,13666}, {56,1327}, {57,13679}, {388,13678}, {999,13713}, {1319,13667}, {1469,18987}, {1478,13692}, {2099,13702}, {4293,13674}, {5252,13688}, {11237,13712}, {11509,13675}, {12835,13672}, {13680,18954}, {13682,18955}, {13683,18956}, {13685,18957}, {13689,18958}, {13690,18959}, {13691,18960}, {13693,18961}, {13694,18962}, {13697,18963}, {13698,18964}, {13717,18967}, {13920,18965}, {13988,18966}, {18995,19099}
X(18986) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 13678, 13695), (999, 13713, 13715)
The reciprocal orthologic center of these triangles is X(13785)
X(18987) lies on these lines: {1,13819}, {3,13837}, {4,13816}, {11,13807}, {12,13821}, {30,7353}, {34,13788}, {55,13786}, {56,1328}, {57,13799}, {388,13798}, {999,13836}, {1319,13787}, {1469,18986}, {1478,13812}, {2099,13822}, {4293,13794}, {5252,13808}, {11237,13835}, {11509,13795}, {12835,13792}, {13800,18954}, {13802,18955}, {13803,18956}, {13805,18957}, {13809,18958}, {13810,18959}, {13811,18960}, {13813,18961}, {13814,18962}, {13817,18963}, {13818,18964}, {13840,18967}, {13848,18965}, {13849,18966}, {18995,19101}, {18996,19100}
X(18987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 13798, 13815), (999, 13836, 13838)
The reciprocal orthologic center of these triangles is X(485)
X(18988) lies on these lines: {1,12911}, {3,10068}, {4,12959}, {11,6250}, {12,641}, {30,7362}, {34,12148}, {55,12124}, {56,485}, {57,9907}, {388,488}, {497,12297}, {999,10084}, {1056,12510}, {1319,12269}, {1469,3564}, {1478,6289}, {2099,7981}, {3600,12222}, {4293,12257}, {5252,12788}, {5433,6118}, {6278,9657}, {6279,18959}, {6337,12948}, {9922,18954}, {9987,18957}, {11509,12344}, {12211,12835}, {12304,16541}, {12486,18955}, {12487,18956}, {12800,18958}, {12929,18961}, {12939,18962}, {13004,18963}, {13005,18964}, {13135,18967}, {13879,18965}, {13880,18966}, {18995,19102}, {18996,19103}
X(18988) = orthologic center of these triangles: 2nd anti-circumperp-tangential to outer-Vecten
X(18988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 488, 12949), (999, 12602, 10084), (1469, 18990, 18989)
The reciprocal orthologic center of these triangles is X(486)
X(18989) lies on these lines: {1,12910}, {3,10067}, {4,12958}, {11,6251}, {12,642}, {30,7353}, {34,12147}, {55,12123}, {56,486}, {57,9906}, {388,487}, {497,12296}, {999,10083}, {1056,12509}, {1319,12268}, {1469,3564}, {1478,6290}, {2099,7980}, {3600,12221}, {4293,12256}, {5252,12787}, {5433,6119}, {6280,18960}, {6281,9657}, {6337,12949}, {9921,18954}, {9986,18957}, {11509,12343}, {12210,12835}, {12303,16541}, {12484,18955}, {12485,18956}, {12799,18958}, {12928,18961}, {12938,18962}, {13002,18963}, {13003,18964}, {13133,18967}, {13921,18965}, {13933,18966}, {18995,19104}, {18996,19105}
X(18989) = orthologic center of these triangles: 2nd anti-circumperp-tangential to inner-Vecten
X(18989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (388, 487, 12948), (999, 12601, 10083), (1469, 18990, 18988)
X(18990) lies on these lines: {1,30}, {2,9654}, {3,388}, {4,496}, {5,56}, {7,944}, {8,2094}, {10,529}, {11,546}, {12,36}, {20,1056}, {26,18954}, {33,13488}, {34,6756}, {35,548}, {46,5252}, {55,550}, {57,355}, {65,952}, {80,3337}, {104,6831}, {145,17579}, {150,1434}, {153,6915}, {172,5305}, {202,398}, {203,397}, {221,9833}, {226,1385}, {229,3109}, {278,7511}, {330,7762}, {354,10572}, {377,956}, {381,3086}, {382,497}, {390,3529}, {404,17757}, {428,7191}, {442,2975}, {443,9708}, {474,3436}, {498,549}, {515,942}, {516,9957}, {517,4292}, {518,17647}, {519,4757}, {528,3244}, {535,1125}, {547,3614}, {612,10691}, {631,5261}, {908,17614}, {946,1387}, {950,5045}, {958,8728}, {971,12573}, {988,5725}, {993,6675}, {1010,5484}, {1012,10532}, {1015,7745}, {1058,3146}, {1060,4320}, {1111,7198}, {1155,10039}, {1159,18526}, {1210,12019}, {1317,11009}, {1319,5901}, {1376,17563}, {1388,10283}, {1420,5886}, {1425,6146}, {1428,18583}, {1466,11499}, {1469,3564}, {1470,6924}, {1479,3304}, {1482,3476}, {1483,2099}, {1484,10074}, {1565,4911}, {1595,11392}, {1596,11399}, {1617,3560}, {1656,7288}, {1657,4294}, {1699,11373}, {1737,18357}, {1770,3057}, {1788,5790}, {1837,3338}, {1870,3575}, {1885,6198}, {1909,7767}, {2066,9647}, {2067,7583}, {2192,5878}, {2242,5254}, {2551,16408}, {2646,5719}, {2886,8666}, {3023,18983}, {3028,3327}, {3090,5265}, {3149,12115}, {3297,6561}, {3298,6560}, {3303,4302}, {3333,5691}, {3339,5881}, {3361,5587}, {3421,6904}, {3474,12702}, {3475,4305}, {3485,7491}, {3486,15934}, {3487,5731}, {3488,11037}, {3523,8164}, {3526,10588}, {3528,5281}, {3530,5432}, {3576,5290}, {3582,5066}, {3583,3853}, {3584,12100}, {3612,17718}, {3616,5714}, {3622,11114}, {3628,5433}, {3654,5128}, {3665,7272}, {3670,5724}, {3671,5842}, {3746,4316}, {3814,6691}, {3815,9650}, {3822,4999}, {3830,5225}, {3843,10591}, {3845,10072}, {3850,7741}, {3851,10589}, {3861,18513}, {3878,17768}, {3911,9956}, {3920,7667}, {3925,5258}, {3947,10165}, {3957,11015}, {4067,5852}, {4084,5855}, {4187,5080}, {4190,5687}, {4308,5603}, {4312,7982}, {4321,5805}, {4355,6253}, {5044,12527}, {5049,12577}, {5083,6583}, {5088,7247}, {5122,6684}, {5134,9327}, {5217,8703}, {5221,10573}, {5260,17529}, {5267,6690}, {5268,7734}, {5272,10128}, {5322,6676}, {5427,10021}, {5435,5818}, {5450,7680}, {5552,16371}, {5693,5843}, {5708,18391}, {5730,5905}, {5762,8581}, {5795,12436}, {5840,12735}, {5844,5903}, {5874,18960}, {5875,18959}, {5902,10950}, {6502,7584}, {6644,10037}, {6645,6656}, {6907,11249}, {6920,7677}, {6922,10269}, {6923,10680}, {6928,16203}, {6934,10805}, {6938,10597}, {6948,10306}, {6958,11929}, {7051,11542}, {7284,17700}, {7502,9659}, {7526,10832}, {7530,10046}, {7737,16781}, {7743,18483}, {8227,13462}, {8727,12114}, {8757,16466}, {9578,15803}, {9597,15048}, {9661,18538}, {9672,18570}, {10065,14677}, {10069,13182}, {10081,10264}, {10089,12184}, {10090,11698}, {10091,12373}, {10385,15681}, {10527,17532}, {10826,17728}, {10943,18961}, {10954,14793}, {11236,17564}, {11238,15687}, {11681,13747}, {12085,16541}, {12102,18514}, {12605,18447}, {12616,13226}, {12945,13312}, {13117,13296}, {13411,13624}, {13925,18965}, {13993,18966}, {18971,18982}, {18972,18974}, {18973,18975}, {18995,19116}, {18996,19117}
X(18990) = midpoint of X(i) and X(j) for these {i,j}: {1, 7354}, {1770, 3057}, {3028, 18968}
X(18990) = reflection of X(i) in X(j) for these (i,j): (950, 5045), (5795, 12436)
X(18990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6147, 16137), (1, 6284, 15172), (1, 9579, 12699), (1, 10404, 6147), (1, 10483, 6284), (1, 15171, 15170), (2, 9654, 10592), (3, 388, 495), (4, 999, 496), (4, 3600, 999), (4, 14986, 9669), (388, 4293, 3), (3600, 9655, 496), (5434, 7354, 1), (6284, 7354, 10483), (6284, 15172, 15171)
X(18991) lies on these lines: {1,6}, {2,8983}, {3,1703}, {8,7585}, {10,3068}, {11,19077}, {30,19080}, {40,371}, {55,19010}, {57,2067}, {58,606}, {65,6415}, {81,3084}, {165,1151}, {171,8941}, {176,5222}, {214,19112}, {355,7583}, {372,3576}, {481,4644}, {482,4000}, {485,5587}, {486,8227}, {515,1587}, {516,6459}, {517,1702}, {519,19054}, {551,13959}, {590,1698}, {595,605}, {615,3624}, {631,13975}, {730,19090}, {936,1377}, {944,7581}, {946,1588}, {952,19078}, {999,19013}, {1086,1373}, {1125,3069}, {1132,9779}, {1152,7987}, {1319,18995}, {1371,17366}, {1372,7277}, {1374,17365}, {1378,9623}, {1385,3312}, {1420,6502}, {1468,6203}, {1482,6417}, {1504,9620}, {1505,9619}, {1572,5058}, {1685,9549}, {1686,9548}, {1697,2066}, {1699,3071}, {1737,13904}, {1829,5410}, {1837,19030}, {2646,19037}, {2800,19082}, {2802,19113}, {2999,13389}, {3057,19038}, {3070,5691}, {3295,18999}, {3340,16232}, {3579,6221}, {3592,7991}, {3601,5414}, {3616,7586}, {3649,19079}, {3679,13911}, {4297,6460}, {5252,19028}, {5393,7090}, {5411,11363}, {5412,7713}, {5550,13941}, {5603,7582}, {5657,13912}, {5818,13886}, {5886,7584}, {5901,19116}, {6001,19068}, {6175,16148}, {6398,13624}, {6409,16192}, {6418,10246}, {6419,7982}, {6421,9592}, {6422,9593}, {6428,15178}, {6429,9584}, {6431,11531}, {6450,17502}, {6500,10247}, {6564,18492}, {6684,9540}, {8396,12697}, {8972,9780}, {8976,9956}, {8987,14647}, {9798,19006}, {9941,19012}, {9955,13785}, {10039,13905}, {10165,13935}, {11230,13951}, {11364,18993}, {11365,19005}, {11366,19007}, {11367,19009}, {11368,19011}, {11373,19023}, {11374,19025}, {11375,19027}, {11376,19029}, {11377,19031}, {11378,19033}, {11705,19073}, {11706,19075}, {11709,19059}, {11710,19055}, {11711,19108}, {11715,19081}, {11720,19110}, {11722,19114}, {11739,19071}, {11740,19069}, {11831,19017}, {12114,19067}, {12194,18994}, {12258,19057}, {12259,19061}, {12260,19085}, {12261,19051}, {12262,19087}, {12263,19089}, {12264,19091}, {12265,19093}, {12266,19095}, {12267,19097}, {12268,19104}, {12269,19102}, {12438,19018}, {12440,19032}, {12441,19034}, {13665,18480}, {13667,19099}, {13787,19101}, {13895,17619}, {13898,17606}, {18493,18510}, {18512,18525}
X(18991) = midpoint of X(1) and X(5589)
X(18991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 18992), (1, 3751, 3640), (1, 16475, 11370), (1, 19003, 7968), (1, 19004, 6), (6, 7968, 19003), (6, 7969, 1), (6, 19048, 3301), (6, 19050, 3299), (1203, 3554, 18992), (1453, 2257, 18992), (3641, 11371, 1), (7968, 19003, 18992), (7969, 19004, 18992), (9575, 16475, 18992)
X(18992) lies on these lines: {1,6}, {2,13883}, {3,1702}, {8,7586}, {10,3069}, {11,19078}, {30,19079}, {40,372}, {55,19007}, {57,6502}, {58,605}, {65,6416}, {81,3083}, {165,1152}, {171,8945}, {175,5222}, {214,19113}, {355,7584}, {371,3576}, {481,4000}, {482,4644}, {485,8227}, {486,5587}, {515,1588}, {516,6460}, {517,1703}, {519,19053}, {551,13902}, {590,3624}, {595,606}, {615,1698}, {631,13912}, {730,19089}, {936,1378}, {944,7582}, {946,1587}, {952,19077}, {999,19014}, {1086,1374}, {1125,3068}, {1131,9779}, {1151,7987}, {1319,18996}, {1371,7277}, {1372,17366}, {1373,17365}, {1377,9623}, {1385,3311}, {1420,2067}, {1482,6418}, {1505,9620}, {1685,9548}, {1686,9549}, {1697,5414}, {1699,3070}, {1737,13962}, {1829,5411}, {1837,19029}, {2066,3601}, {2362,3340}, {2646,19038}, {2800,19081}, {2802,19112}, {2999,13388}, {3057,19037}, {3071,5691}, {3295,19000}, {3579,6398}, {3594,7991}, {3616,7585}, {3649,19080}, {3679,13973}, {4297,6459}, {5252,19027}, {5405,14121}, {5410,11363}, {5413,7713}, {5550,8972}, {5603,7581}, {5657,13975}, {5818,13939}, {5886,7583}, {5901,19117}, {6001,19067}, {6175,16149}, {6221,13624}, {6395,12702}, {6410,16192}, {6417,10246}, {6420,7982}, {6421,9593}, {6422,9592}, {6427,15178}, {6432,11531}, {6437,9585}, {6449,17502}, {6501,10247}, {6565,18492}, {6684,13935}, {8416,12698}, {8976,11230}, {9540,10165}, {9780,13941}, {9798,19005}, {9941,19011}, {9955,13665}, {9956,13951}, {10039,13963}, {11364,18994}, {11365,19006}, {11366,19008}, {11367,19010}, {11368,19012}, {11373,19024}, {11374,19026}, {11375,19028}, {11376,19030}, {11377,19032}, {11378,19034}, {11705,19074}, {11706,19076}, {11709,19060}, {11710,19056}, {11711,19109}, {11715,19082}, {11720,19111}, {11722,19115}, {11739,19070}, {11740,19072}, {11831,19018}, {12114,19068}, {12194,18993}, {12258,19058}, {12259,19062}, {12260,19086}, {12261,19052}, {12262,19088}, {12263,19090}, {12264,19092}, {12265,19094}, {12266,19096}, {12267,19098}, {12268,19105}, {12269,19103}, {12438,19017}, {12440,19031}, {12441,19033}, {13785,18480}, {13787,19100}, {13952,17619}, {13955,17606}, {13974,14647}, {18493,18512}, {18510,18525}
X(18992) = midpoint of X(1) and X(5588)
X(18992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 18991), (1, 3751, 3641), (1, 16475, 11371), (1, 19003, 6), (1, 19004, 7969), (6, 7968, 1), (6, 7969, 19004), (6, 19047, 3299), (6, 19049, 3301), (1203, 3554, 18991), (1453, 2257, 18991), (3640, 11370, 1), (7968, 19003, 18991), (7969, 19004, 18991), (9575, 16475, 18991)
X(18993) lies on these lines: {2,13938}, {3,6}, {83,3069}, {98,1587}, {183,8992}, {384,19089}, {385,19090}, {486,10358}, {590,7815}, {615,7808}, {641,3815}, {1078,3068}, {1194,8577}, {1588,12110}, {1703,12197}, {3299,10801}, {3301,10802}, {4027,19108}, {5411,11380}, {7582,10788}, {7583,10104}, {7584,10796}, {7585,7793}, {7586,7787}, {7770,13983}, {7968,10800}, {10352,13989}, {10789,19003}, {10790,19005}, {10791,13936}, {10794,19023}, {10795,19025}, {10797,19027}, {10798,19029}, {10799,19037}, {10803,19047}, {11364,18991}, {11490,18999}, {11837,19007}, {11838,19009}, {11839,19017}, {11840,19031}, {11841,19033}, {12150,19053}, {12176,19055}, {12191,19057}, {12192,19059}, {12193,19061}, {12194,18992}, {12195,19065}, {12196,19067}, {12198,19077}, {12199,19081}, {12200,19085}, {12201,19051}, {12202,19087}, {12204,19075}, {12205,19073}, {12206,19091}, {12207,19093}, {12208,19095}, {12209,19097}, {12210,19104}, {12211,19102}, {12835,18995}, {13193,19110}, {13194,19112}, {13195,19114}, {13672,19099}, {13785,18502}, {13792,19101}, {16115,19079}, {18501,18510}
X(18993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 32, 18994), (32, 5039, 10792), (39, 372, 9995), (182, 13356, 18994), (577, 1207, 18994), (1342, 1343, 6423), (7585, 7793, 13885)
X(18994) lies on these lines: {2,13885}, {3,6}, {83,3068}, {98,1588}, {183,13983}, {384,19090}, {385,19089}, {485,10358}, {590,7808}, {615,7815}, {642,3815}, {1078,3069}, {1194,8576}, {1587,12110}, {1702,12197}, {3299,10802}, {3301,10801}, {4027,19109}, {5410,11380}, {7581,10788}, {7583,10796}, {7584,10104}, {7585,7787}, {7586,7793}, {7770,8992}, {7969,10800}, {8997,10352}, {10789,19004}, {10790,19006}, {10791,13883}, {10794,19024}, {10795,19026}, {10797,19028}, {10798,19030}, {10799,19038}, {10803,19048}, {10804,19050}, {11364,18992}, {11490,19000}, {11837,19008}, {11838,19010}, {11839,19018}, {11840,19032}, {11841,19034}, {12150,19054}, {12176,19056}, {12191,19058}, {12192,19060}, {12193,19062}, {12194,18991}, {12195,19066}, {12196,19068}, {12198,19078}, {12199,19082}, {12200,19086}, {12201,19052}, {12202,19088}, {12204,19076}, {12205,19074}, {12206,19092}, {12207,19094}, {12208,19096}, {12209,19098}, {12210,19105}, {12211,19103}, {12835,18996}, {13193,19111}, {13194,19113}, {13195,19115}, {13665,18502}, {13792,19100}, {16115,19080}, {18501,18512}
X(18994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 32, 18993), (32, 5039, 10793), (39, 371, 9994), (182, 13356, 18993), (577, 1207, 18993), (1342, 1343, 6424), (7586, 7793, 13938)
X(18995) lies on these lines: {1,3312}, {2,13897}, {3,3299}, {4,19029}, {5,13955}, {6,41}, {11,1587}, {12,3069}, {34,5411}, {35,6398}, {36,3311}, {55,372}, {57,19003}, {65,6416}, {140,13905}, {371,5204}, {388,7586}, {486,10895}, {495,13963}, {498,13966}, {499,7583}, {605,1399}, {631,13901}, {999,3301}, {1152,2066}, {1155,1702}, {1317,19112}, {1319,18991}, {1335,3304}, {1378,4413}, {1388,7969}, {1420,19004}, {1478,7584}, {1588,7354}, {1703,3057}, {2099,2362}, {2361,3076}, {3023,19055}, {3027,19108}, {3028,19110}, {3068,5433}, {3070,10896}, {3071,12943}, {3085,13958}, {3086,7581}, {3295,6395}, {3297,3303}, {3298,6432}, {3320,19114}, {3585,13785}, {4293,7582}, {4641,13389}, {5010,6450}, {5219,13942}, {5221,16232}, {5252,13936}, {5298,19054}, {5420,9646}, {5432,13935}, {5434,19053}, {5563,6428}, {6020,19093}, {6221,7280}, {6284,6460}, {6285,19087}, {6459,15326}, {6471,8162}, {6560,12953}, {7288,7585}, {7741,13665}, {7951,13951}, {8416,10928}, {9655,18510}, {10588,13941}, {10590,13939}, {10592,13993}, {10881,11398}, {10944,19065}, {11375,13971}, {11510,19000}, {12688,19067}, {12835,18993}, {13904,15325}, {13959,15950}, {18954,19005}, {18955,19007}, {18956,19009}, {18957,19011}, {18958,19017}, {18961,19023}, {18962,19025}, {18963,19031}, {18964,19033}, {18967,19049}, {18968,19051}, {18969,19057}, {18970,19061}, {18971,19063}, {18972,19069}, {18973,19071}, {18974,19073}, {18975,19075}, {18976,19077}, {18977,19079}, {18978,19083}, {18979,19085}, {18982,19089}, {18983,19091}, {18984,19095}, {18985,19097}, {18986,19099}, {18987,19101}, {18988,19102}, {18989,19104}, {18990,19116}
X(18995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3312, 19037), (2, 19028, 13897), (3, 3299, 19038), (5, 13962, 13955), (6, 56, 18996), (6, 6502, 56), (12, 3069, 13954), (372, 1124, 55), (388, 7586, 19027), (499, 7583, 13898), (999, 6418, 3301), (1152, 2066, 5217), (2362, 7968, 2099), (3086, 7581, 19030), (18966, 19028, 2)
X(18996) lies on these lines: {1,3311}, {2,13954}, {3,3301}, {4,19030}, {5,13898}, {6,41}, {11,1588}, {12,3068}, {34,5410}, {35,6221}, {36,3312}, {55,371}, {57,19004}, {65,6415}, {140,13963}, {372,5204}, {388,7585}, {485,10895}, {486,9661}, {495,13905}, {498,8981}, {499,7584}, {606,1399}, {631,13958}, {999,3299}, {1124,3304}, {1151,5217}, {1155,1703}, {1317,19113}, {1319,18992}, {1377,4413}, {1388,7968}, {1420,19003}, {1478,7583}, {1587,7354}, {1702,3057}, {2066,3298}, {2099,7969}, {2361,3077}, {2362,5221}, {2646,9583}, {3023,19056}, {3027,19109}, {3028,19111}, {3069,5433}, {3070,12943}, {3071,10896}, {3085,13901}, {3086,7582}, {3297,6431}, {3320,19115}, {3585,13665}, {4293,7581}, {4641,13388}, {4995,9648}, {5010,6449}, {5219,13888}, {5252,13883}, {5298,19053}, {5432,9540}, {5434,19054}, {5563,6427}, {6020,19094}, {6284,6459}, {6285,19088}, {6398,7280}, {6460,15326}, {6470,8162}, {6560,9647}, {6561,12953}, {7288,7586}, {7741,13785}, {7951,8976}, {8396,10927}, {8972,10588}, {8983,11375}, {9541,15338}, {9655,18512}, {10590,13886}, {10592,13925}, {10880,11398}, {10944,19066}, {11509,19000}, {11510,18999}, {12688,19068}, {12835,18994}, {13902,15950}, {13962,15325}, {18954,19006}, {18955,19008}, {18956,19010}, {18957,19012}, {18958,19018}, {18961,19024}, {18962,19026}, {18963,19032}, {18964,19034}, {18967,19050}, {18968,19052}, {18969,19058}, {18970,19062}, {18971,19064}, {18972,19072}, {18973,19070}, {18974,19074}, {18975,19076}, {18976,19078}, {18977,19080}, {18978,19084}, {18979,19086}, {18982,19090}, {18983,19092}, {18984,19096}, {18985,19098}, {18987,19100}, {18988,19103}, {18989,19105}, {18990,19117}
X(18996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3311, 19038), (2, 19027, 13954), (3, 3301, 19037), (5, 13904, 13898), (6, 56, 18995), (6, 2067, 56), (12, 3068, 13897), (371, 1335, 55), (388, 7585, 19028), (499, 7584, 13955), (999, 6417, 3299), (1151, 5414, 5217), (2066, 3298, 3303), (3298, 3592, 2066), (18965, 19027, 2)
X(18997) lies on these lines: {3,19061}, {25,19039}, {1181,3312}, {1588,1593}, {1899,18998}, {3156,18923}, {19005,19041}
X(18998) lies on these lines: {3,19062}, {25,19040}, {1181,3311}, {1587,1593}, {1899,18997}, {3155,18924}, {19006,19042}
X(18999) lies on these lines: {1,19014}, {2,13940}, {3,1702}, {6,31}, {35,19003}, {56,7968}, {100,7586}, {197,19005}, {372,10310}, {405,13883}, {474,13971}, {590,4423}, {615,4413}, {958,19066}, {1001,3068}, {1151,8273}, {1376,3069}, {1466,6502}, {1486,19006}, {1587,11496}, {1588,11500}, {1621,7585}, {1703,10306}, {3295,18991}, {3299,11507}, {3301,11508}, {3303,7969}, {3311,10267}, {3312,11248}, {3746,19004}, {3913,19065}, {4421,19053}, {4428,19054}, {5284,8972}, {5411,11383}, {5687,13936}, {6418,11849}, {7582,11491}, {7584,11499}, {9709,13947}, {11108,13893}, {11490,18993}, {11492,19007}, {11493,19009}, {11494,19011}, {11501,19027}, {11502,19029}, {11503,19031}, {11504,19033}, {11510,18996}, {11848,19017}, {12178,19055}, {12326,19057}, {12327,19059}, {12328,19061}, {12330,19067}, {12331,19077}, {12332,19081}, {12333,19085}, {12335,19087}, {12336,19075}, {12337,19073}, {12338,19089}, {12339,19091}, {12340,19093}, {12341,19095}, {12342,19097}, {12343,19104}, {12344,19102}, {13173,19108}, {13204,19110}, {13205,19112}, {13206,19114}, {13675,19099}, {13785,18491}, {13795,19101}, {16117,19079}, {17819,18621}, {18510,18524}
X(18999) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18992, 19013), (6, 55, 19000), (6, 3052, 606), (1621, 7585, 13887)
X(19000) lies on these lines: {1,19013}, {2,13887}, {3,1703}, {6,31}, {35,19004}, {56,2362}, {100,7585}, {197,19006}, {371,10310}, {405,13936}, {474,8983}, {590,4413}, {615,4423}, {958,19065}, {1001,3069}, {1108,7133}, {1152,8273}, {1376,3068}, {1466,2067}, {1486,19005}, {1587,11500}, {1588,11496}, {1621,7586}, {1702,10306}, {3295,18992}, {3299,11508}, {3301,11507}, {3303,7968}, {3311,11248}, {3312,10267}, {3746,19003}, {3913,19066}, {4421,19054}, {4428,19053}, {5284,13941}, {5410,11383}, {5687,13883}, {6244,9616}, {6417,11849}, {7581,11491}, {7583,11499}, {9709,13893}, {11108,13947}, {11490,18994}, {11492,19008}, {11493,19010}, {11494,19012}, {11501,19028}, {11502,19030}, {11503,19032}, {11504,19034}, {11509,18996}, {11510,18995}, {11848,19018}, {12178,19056}, {12326,19058}, {12327,19060}, {12328,19062}, {12330,19068}, {12331,19078}, {12332,19082}, {12333,19086}, {12334,19052}, {12335,19088}, {12336,19076}, {12337,19074}, {12338,19090}, {12339,19092}, {12340,19094}, {12341,19096}, {12342,19098}, {12343,19105}, {12344,19103}, {13173,19109}, {13204,19111}, {13205,19113}, {13206,19115}, {13665,18491}, {13795,19100}, {16117,19080}, {17820,18621}, {18512,18524}
X(19000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18991, 19014), (6, 55, 18999), (6, 3052, 605), (1621, 7586, 13940)
X(19001) lies on these lines: {74,1588}, {125,19002}, {399,3312}, {2914,19095}, {3581,19051}, {7720,10814}, {12112,19059}, {13288,17812}
X(19002) lies on these lines: {74,1587}, {125,19001}, {399,3311}, {2914,19096}, {3581,19052}, {7721,10815}, {12112,19060}, {13287,17812}
X(19003) lies on these lines: {1,6}, {2,13942}, {10,7586}, {35,18999}, {36,19013}, {40,3312}, {57,18995}, {165,372}, {355,19116}, {371,7987}, {481,5222}, {485,7988}, {486,7989}, {515,7582}, {517,6418}, {615,13893}, {946,7581}, {1125,7585}, {1131,12571}, {1152,9616}, {1373,4644}, {1374,4000}, {1378,8580}, {1385,6417}, {1420,18996}, {1482,6501}, {1504,9592}, {1505,9593}, {1587,1699}, {1588,5691}, {1697,19037}, {1698,3069}, {1703,6420}, {1768,19081}, {2067,13462}, {2362,18421}, {2948,19110}, {3068,3624}, {3099,19011}, {3311,3576}, {3317,10172}, {3339,16232}, {3361,6502}, {3579,6395}, {3592,9615}, {3601,19038}, {3634,13941}, {3679,13936}, {3746,19000}, {5219,19028}, {5411,7713}, {5541,19112}, {5563,19014}, {5587,7584}, {5886,19117}, {6396,9582}, {6409,9584}, {6419,9583}, {6428,7982}, {6447,9617}, {6455,9618}, {6500,10246}, {7583,8227}, {7992,19067}, {8185,19005}, {8187,19009}, {8188,19031}, {8189,19033}, {8983,13959}, {9578,19027}, {9581,19029}, {9588,13975}, {9860,19055}, {9875,19057}, {9896,19061}, {9897,19077}, {9898,19085}, {9899,19087}, {9900,19075}, {9901,19073}, {9902,19089}, {9903,19091}, {9904,19059}, {9905,19095}, {9906,19104}, {9907,19102}, {9955,18512}, {10175,13939}, {10789,18993}, {10826,19023}, {10827,19025}, {11231,13961}, {11852,19017}, {12407,19051}, {12408,19093}, {12409,19097}, {13174,19108}, {13221,19114}, {13679,19099}, {13785,18492}, {13799,19101}, {13911,13947}, {13912,13935}, {15015,19113}, {16118,19079}, {18480,18510}
X(19003) = reflection of X(1) in X(11370)
X(19003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 19004), (6, 7968, 18991), (6, 18992, 1), (372, 1702, 165), (1125, 7585, 13888), (1152, 9616, 16192), (1386, 3640, 1), (3068, 13971, 3624), (3069, 13883, 1698), (7968, 18991, 1), (13936, 19066, 3679), (13959, 19054, 8983), (18991, 18992, 7968), (19053, 19066, 13936)
X(19004) lies on these lines: {1,6}, {2,13888}, {10,7585}, {35,19000}, {36,19014}, {40,3311}, {57,18996}, {165,371}, {355,19117}, {372,7987}, {482,5222}, {485,7989}, {486,7988}, {515,7581}, {517,6417}, {590,13947}, {946,7582}, {1125,7586}, {1132,12571}, {1151,16192}, {1152,9615}, {1373,4000}, {1374,4644}, {1377,8580}, {1385,6418}, {1420,18995}, {1482,6500}, {1504,9593}, {1505,9592}, {1587,5691}, {1588,1699}, {1697,19038}, {1698,3068}, {1702,6419}, {1768,19082}, {2067,3361}, {2362,3339}, {2948,19111}, {3069,3624}, {3099,19012}, {3312,3576}, {3316,10172}, {3592,9616}, {3601,19037}, {3634,8972}, {3679,13883}, {3746,18999}, {5219,19027}, {5410,7713}, {5541,19113}, {5563,19013}, {5587,7583}, {5886,19116}, {6395,13624}, {6425,9584}, {6427,7982}, {6447,9618}, {6455,9617}, {6501,10246}, {6502,13462}, {7584,8227}, {7992,19068}, {8185,19006}, {8187,19010}, {8188,19032}, {8189,19034}, {9540,13975}, {9578,19028}, {9581,19030}, {9588,13912}, {9860,19056}, {9875,19058}, {9896,19062}, {9897,19078}, {9898,19086}, {9899,19088}, {9900,19076}, {9901,19074}, {9902,19090}, {9903,19092}, {9904,19060}, {9905,19096}, {9906,19105}, {9907,19103}, {9955,18510}, {10175,13886}, {10789,18994}, {10826,19024}, {10827,19026}, {11231,13903}, {11852,19018}, {12407,19052}, {12408,19094}, {12409,19098}, {13174,19109}, {13221,19115}, {13665,18492}, {13799,19100}, {13893,13973}, {13902,13971}, {15015,19112}, {16118,19080}, {16232,18421}, {18480,18512}
X(19004) = reflection of X(1) in X(11371)
X(19004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 19003), (6, 7969, 18992), (6, 18991, 1), (371, 1703, 165), (372, 9583, 7987), (1125, 7586, 13942), (1386, 3641, 1), (3068, 13936, 1698), (3069, 8983, 3624), (7969, 18992, 1), (13883, 19065, 3679), (13902, 19053, 13971), (18991, 18992, 7969), (19054, 19065, 13883)
X(19005) lies on these lines: {2,13943}, {3,1588}, {6,25}, {22,7586}, {24,7582}, {26,19116}, {197,18999}, {371,8277}, {372,11414}, {486,7395}, {492,1583}, {590,11284}, {605,1460}, {606,7083}, {615,7484}, {1486,19000}, {1587,1598}, {1593,3071}, {1703,9911}, {1995,7585}, {3068,5020}, {3070,5198}, {3156,8573}, {3299,10037}, {3301,10046}, {3311,6642}, {3312,7387}, {3524,9695}, {6395,12083}, {6414,6421}, {6417,7506}, {6418,7517}, {6419,8276}, {6424,8911}, {6501,18378}, {7393,13951}, {7485,13941}, {7509,13939}, {7516,13993}, {7529,7583}, {7581,10594}, {7968,8192}, {8185,19003}, {8190,19007}, {8191,19009}, {8193,13936}, {8194,19031}, {8195,19033}, {8564,8943}, {9798,18992}, {9861,19055}, {9876,19057}, {9908,19061}, {9909,19053}, {9910,19067}, {9912,19077}, {9913,19081}, {9914,19087}, {9915,19075}, {9916,19073}, {9917,19089}, {9918,19091}, {9919,19059}, {9920,19095}, {9921,19104}, {9922,19102}, {10666,12166}, {10790,18993}, {10828,19011}, {10829,19023}, {10830,19025}, {10831,19027}, {10832,19029}, {10833,19037}, {10834,19047}, {10835,19049}, {11365,18991}, {11427,15200}, {11433,15199}, {11641,19114}, {11853,19017}, {12310,19110}, {12410,19065}, {12411,19085}, {12412,19051}, {12413,19093}, {12414,19097}, {13175,19108}, {13222,19112}, {13567,15211}, {13680,19099}, {13800,19101}, {13861,19117}, {18954,18995}, {18997,19041}
X(19005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 25, 19006), (1995, 7585, 13889)
X(19006) lies on these lines: {2,13889}, {3,1587}, {6,25}, {22,7585}, {24,7581}, {26,19117}, {197,19000}, {371,11414}, {372,8276}, {485,7395}, {491,1584}, {590,7484}, {605,7083}, {606,1460}, {615,11284}, {1486,18999}, {1588,1598}, {1593,3070}, {1702,9911}, {1995,7586}, {3069,5020}, {3071,5198}, {3155,8573}, {3299,10046}, {3301,10037}, {3311,7387}, {3312,6642}, {3522,9694}, {6413,6422}, {6417,7517}, {6418,7506}, {6420,8277}, {6500,18378}, {7393,8976}, {7485,8972}, {7509,13886}, {7516,13925}, {7529,7584}, {7582,10594}, {7969,8192}, {8185,19004}, {8190,19008}, {8191,19010}, {8193,13883}, {8194,19032}, {8195,19034}, {8563,8939}, {9798,18991}, {9861,19056}, {9876,19058}, {9908,19062}, {9909,19054}, {9910,19068}, {9912,19078}, {9913,19082}, {9914,19088}, {9915,19076}, {9916,19074}, {9917,19090}, {9918,19092}, {9919,19060}, {9920,19096}, {9921,19105}, {9922,19103}, {10665,12166}, {10790,18994}, {10828,19012}, {10829,19024}, {10830,19026}, {10831,19028}, {10832,19030}, {10833,19038}, {10834,19048}, {10835,19050}, {11365,18992}, {11427,15199}, {11433,15200}, {11641,19115}, {11853,19018}, {12410,19066}, {12411,19086}, {12412,19052}, {12413,19094}, {12414,19098}, {13175,19109}, {13222,19113}, {13567,15212}, {13800,19100}, {13861,19116}, {16119,19080}, {18954,18996}, {18998,19042}
X(19006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 25, 19005), (1995, 7586, 13943)
X(19007) lies on these lines: {1,19010}, {2,13944}, {6,5597}, {55,18992}, {372,11822}, {1587,8196}, {1703,12458}, {3299,11877}, {3301,11879}, {3312,11252}, {3616,13891}, {5411,11384}, {5598,7968}, {5600,19066}, {5601,7586}, {6418,11875}, {7582,11843}, {7584,8200}, {7585,13890}, {8190,19005}, {8197,13936}, {8201,19031}, {8202,19033}, {11207,19053}, {11366,18991}, {11492,18999}, {11493,19013}, {11837,18993}, {11861,19011}, {11863,19017}, {11865,19023}, {11867,19025}, {11869,19027}, {11871,19029}, {11873,19037}, {11881,19047}, {11883,19049}, {12179,19055}, {12345,19057}, {12365,19059}, {12415,19061}, {12454,19065}, {12456,19067}, {12460,19077}, {12462,19081}, {12464,19085}, {12466,19051}, {12468,19087}, {12470,19075}, {12472,19073}, {12474,19089}, {12476,19091}, {12478,19093}, {12480,19095}, {12482,19097}, {12484,19104}, {12486,19102}, {13176,19108}, {13208,19110}, {13228,19112}, {13229,19114}, {13682,19099}, {13785,18495}, {13802,19101}, {16121,19079}, {18955,18995}
X(19007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5597, 19008), (55, 18992, 19009)
X(19008) lies on these lines: {1,19009}, {2,13890}, {6,5597}, {55,18991}, {371,11822}, {1588,8196}, {1702,12458}, {3068,5599}, {3299,11879}, {3301,11877}, {3311,11252}, {3616,13945}, {5410,11384}, {5598,7969}, {5600,19065}, {5601,7585}, {6417,11875}, {7581,11843}, {7583,8200}, {7586,13944}, {8190,19006}, {8197,13883}, {8201,19032}, {8202,19034}, {11366,18992}, {11492,19000}, {11493,19014}, {11837,18994}, {11861,19012}, {11863,19018}, {11865,19024}, {11867,19026}, {11869,19028}, {11871,19030}, {11873,19038}, {11881,19048}, {11883,19050}, {12179,19056}, {12345,19058}, {12365,19060}, {12415,19062}, {12454,19066}, {12456,19068}, {12460,19078}, {12462,19082}, {12464,19086}, {12466,19052}, {12468,19088}, {12470,19076}, {12472,19074}, {12474,19090}, {12476,19092}, {12478,19094}, {12480,19096}, {12482,19098}, {12484,19105}, {12486,19103}, {13176,19109}, {13208,19111}, {13228,19113}, {13665,18495}, {13802,19100}, {16121,19080}, {18955,18996}
X(19008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5597, 19007), (55, 18991, 19010)
X(19009) lies on these lines: {1,19008}, {2,13945}, {6,5598}, {55,18992}, {372,11823}, {1587,8203}, {1703,12459}, {3069,5600}, {3299,11878}, {3301,11880}, {3312,11253}, {3616,13890}, {5411,11385}, {5597,7968}, {5599,19066}, {5602,7586}, {6418,11876}, {7582,11844}, {7584,8207}, {7585,13891}, {8187,19003}, {8191,19005}, {8204,13936}, {8208,19031}, {8209,19033}, {11208,19053}, {11367,18991}, {11492,19013}, {11493,18999}, {11838,18993}, {11862,19011}, {11864,19017}, {11866,19023}, {11868,19025}, {11870,19027}, {11872,19029}, {11874,19037}, {11882,19047}, {11884,19049}, {12180,19055}, {12346,19057}, {12366,19059}, {12455,19065}, {12457,19067}, {12461,19077}, {12463,19081}, {12465,19085}, {12467,19051}, {12469,19087}, {12471,19075}, {12473,19073}, {12475,19089}, {12477,19091}, {12479,19093}, {12481,19095}, {12483,19097}, {12485,19104}, {12487,19102}, {13177,19108}, {13209,19110}, {13230,19112}, {13231,19114}, {13683,19099}, {13785,18497}, {13803,19101}, {16122,19079}, {18956,18995}
X(19009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5598, 19010), (55, 18992, 19007)
X(19010) lies on these lines: {1,19007}, {2,13891}, {6,5598}, {55,18991}, {371,11823}, {1588,8203}, {1702,12459}, {3068,5600}, {3299,11880}, {3301,11878}, {3311,11253}, {3616,13944}, {5410,11385}, {5597,7969}, {5599,19065}, {5602,7585}, {6417,11876}, {7581,11844}, {7583,8207}, {7586,13945}, {8187,19004}, {8191,19006}, {8204,13883}, {8208,19032}, {8209,19034}, {11208,19054}, {11367,18992}, {11492,19014}, {11493,19000}, {11838,18994}, {11862,19012}, {11864,19018}, {11866,19024}, {11868,19026}, {11870,19028}, {11872,19030}, {11874,19038}, {11882,19048}, {11884,19050}, {12180,19056}, {12346,19058}, {12366,19060}, {12416,19062}, {12455,19066}, {12457,19068}, {12461,19078}, {12463,19082}, {12465,19086}, {12467,19052}, {12469,19088}, {12471,19076}, {12473,19074}, {12475,19090}, {12477,19092}, {12479,19094}, {12481,19096}, {12483,19098}, {12485,19105}, {12487,19103}, {13177,19109}, {13209,19111}, {13230,19113}, {13231,19115}, {13665,18497}, {13803,19100}, {16122,19080}, {18956,18996}
X(19010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5598, 19009), (55, 18991, 19008)
X(19011) lies on these lines: {2,13946}, {3,6}, {486,10356}, {615,7914}, {1587,9993}, {1588,9873}, {1703,12497}, {2896,7586}, {3068,7846}, {3069,3096}, {3099,19003}, {3299,10038}, {3301,10047}, {5411,11386}, {7582,9862}, {7584,9996}, {7585,10583}, {7811,19053}, {7968,9997}, {8782,19108}, {9857,13936}, {9878,19057}, {9923,19061}, {9941,18992}, {9981,19075}, {9982,19073}, {9983,19089}, {9984,19059}, {9985,19095}, {9986,19104}, {9987,19102}, {10828,19005}, {10871,19023}, {10872,19025}, {10873,19027}, {10874,19029}, {10875,19031}, {10876,19033}, {10877,19037}, {10878,19047}, {10879,19049}, {11368,18991}, {11494,18999}, {11861,19007}, {11862,19009}, {11885,19017}, {12495,19065}, {12496,19067}, {12498,19077}, {12499,19081}, {12500,19085}, {12501,19051}, {12502,19087}, {12503,19093}, {12504,19097}, {13210,19110}, {13235,19112}, {13236,19114}, {13685,19099}, {13785,18500}, {13805,19101}, {16123,19079}, {18503,18510}, {18957,18995}
X(19011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 32, 19012), (372, 5007, 10793), (7585, 10583, 13892)
X(19012) lies on these lines: {2,13892}, {3,6}, {485,10356}, {590,7914}, {1587,9873}, {1588,9993}, {1702,12497}, {2896,7585}, {3068,3096}, {3069,7846}, {3099,19004}, {3299,10047}, {3301,10038}, {5410,11386}, {7581,9862}, {7583,9996}, {7586,10583}, {7811,19054}, {7969,9997}, {8782,19109}, {9857,13883}, {9878,19058}, {9923,19062}, {9941,18991}, {9981,19076}, {9982,19074}, {9983,19090}, {9984,19060}, {9985,19096}, {9986,19105}, {9987,19103}, {10828,19006}, {10871,19024}, {10872,19026}, {10873,19028}, {10874,19030}, {10875,19032}, {10876,19034}, {10877,19038}, {10878,19048}, {10879,19050}, {11368,18992}, {11494,19000}, {11861,19008}, {11862,19010}, {11885,19018}, {12495,19066}, {12496,19068}, {12498,19078}, {12499,19082}, {12500,19086}, {12501,19052}, {12502,19088}, {12503,19094}, {12504,19098}, {13210,19111}, {13235,19113}, {13236,19115}, {13665,18500}, {13805,19100}, {16123,19080}, {18503,18512}, {18957,18996}
X(19012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 32, 19011), (371, 5007, 10792), (7586, 10583, 13946)
X(19013) lies on these lines: {1,19000}, {3,1702}, {6,41}, {21,13940}, {36,19003}, {55,7968}, {104,7582}, {372,3428}, {405,13971}, {474,13883}, {605,4252}, {606,1191}, {956,13936}, {958,3069}, {999,18991}, {1001,13959}, {1152,5416}, {1376,19066}, {1466,16232}, {1588,12114}, {2975,7586}, {3297,5415}, {3304,7969}, {3311,10269}, {3312,11249}, {3556,17820}, {3616,13887}, {4413,13911}, {5251,13942}, {5253,7585}, {5260,13941}, {5563,19004}, {9708,13947}, {10966,19037}, {11194,19053}, {11492,19009}, {11493,19007}, {12513,19065}, {12773,19077}, {13743,19079}, {13785,18761}, {13893,16408}, {18237,19067}, {19038,19047}, {19093,19159}, {19114,19162}
X(19013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18992, 18999), (6, 56, 19014)
X(19014) lies on these lines: {1,18999}, {3,1703}, {6,41}, {21,13887}, {36,19004}, {55,7969}, {104,7581}, {371,3428}, {405,8983}, {474,13936}, {605,1191}, {606,4252}, {956,13883}, {958,3068}, {999,18992}, {1001,13902}, {1151,5415}, {1376,19065}, {1466,2362}, {1587,12114}, {2975,7585}, {3298,5416}, {3304,7968}, {3311,11249}, {3312,10269}, {3556,17819}, {3616,13940}, {4413,13973}, {5251,13888}, {5253,7586}, {5260,8972}, {5563,19003}, {9708,13893}, {10966,19038}, {11194,19054}, {11492,19010}, {11493,19008}, {12513,19066}, {12773,19078}, {13665,18761}, {13743,19080}, {13947,16408}, {18237,19068}, {19037,19048}, {19094,19159}, {19115,19162}
X(19014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18991, 19000), (6, 56, 19013)
X(19015) lies on these lines: {64,1588}, {1498,3312}, {1853,19016}, {6218,17810}, {17812,19059}, {17824,19095}, {17834,19061}, {17835,19051}
X(19016) lies on these lines: {64,1587}, {1498,3311}, {1853,19015}, {6217,17810}, {17812,19060}, {17824,19096}, {17834,19062}, {17835,19052}
X(19017) lies on these lines: {2,13948}, {6,402}, {30,372}, {615,15184}, {1587,11897}, {1588,12113}, {1650,3069}, {1651,19053}, {1703,12696}, {3068,15183}, {3299,11912}, {3301,11913}, {3312,11251}, {4240,7586}, {5411,11832}, {6418,11911}, {6459,16190}, {7582,11845}, {7585,13894}, {7968,11910}, {11049,13847}, {11831,18991}, {11839,18993}, {11848,18999}, {11852,19003}, {11853,19005}, {11863,19007}, {11864,19009}, {11885,19011}, {11900,13936}, {11903,19023}, {11904,19025}, {11905,19027}, {11906,19029}, {11907,19031}, {11908,19033}, {11909,19037}, {11914,19047}, {11915,19049}, {12181,19055}, {12347,19057}, {12369,19059}, {12418,19061}, {12438,18992}, {12626,19065}, {12668,19067}, {12729,19077}, {12752,19081}, {12789,19085}, {12790,19051}, {12791,19087}, {12792,19075}, {12793,19073}, {12794,19089}, {12795,19091}, {12796,19093}, {12797,19095}, {12798,19097}, {12799,19104}, {12800,19102}, {13179,19108}, {13212,19110}, {13268,19112}, {13281,19114}, {13689,19099}, {13785,18507}, {13809,19101}, {16129,19079}, {16210,19066}, {18508,18510}, {18958,18995}
X(19017) = {X(6), X(402)}-harmonic conjugate of X(19018)
X(19018) lies on these lines: {2,13894}, {6,402}, {30,371}, {590,15184}, {1587,12113}, {1588,11897}, {1650,3068}, {1651,19054}, {1702,12696}, {3069,15183}, {3299,11913}, {3301,11912}, {3311,11251}, {4240,7585}, {5410,11832}, {6417,11911}, {6460,16190}, {7581,11845}, {7586,13948}, {7969,11910}, {11049,13846}, {11831,18992}, {11839,18994}, {11848,19000}, {11852,19004}, {11853,19006}, {11863,19008}, {11864,19010}, {11885,19012}, {11900,13883}, {11903,19024}, {11904,19026}, {11905,19028}, {11907,19032}, {11908,19034}, {11909,19038}, {11914,19048}, {11915,19050}, {12181,19056}, {12347,19058}, {12369,19060}, {12418,19062}, {12438,18991}, {12626,19066}, {12668,19068}, {12729,19078}, {12752,19082}, {12789,19086}, {12790,19052}, {12791,19088}, {12792,19076}, {12793,19074}, {12794,19090}, {12795,19092}, {12796,19094}, {12797,19096}, {12798,19098}, {12799,19105}, {12800,19103}, {13179,19109}, {13212,19111}, {13268,19113}, {13281,19115}, {13665,18507}, {13809,19100}, {16129,19080}, {16210,19065}, {18508,18512}, {18958,18996}
X(19018) = {X(6), X(402)}-harmonic conjugate of X(19017)
X(19019) lies on these lines: {3312,13630}, {12241,19083}
X(19020) lies on these lines: {3311,13630}, {12241,19084}
X(19021) lies on these lines: {185,3312}, {372,17818}, {1588,1885}, {1899,6416}, {5411,19039}, {6146,19061}, {6415,13198}, {6467,10133}, {15851,19022}
X(19022) lies on these lines: {185,3311}, {371,17818}, {1587,1885}, {1899,6415}, {5410,19040}, {6146,19062}, {6416,13198}, {6467,10132}, {15851,19021}
X(19023) lies on these lines: {2,13952}, {6,11}, {12,19047}, {355,7584}, {372,11826}, {1376,3069}, {1587,10893}, {1588,12114}, {1703,12700}, {3299,10523}, {3301,10948}, {3312,10525}, {3434,7586}, {5411,11390}, {6418,11928}, {7581,10598}, {7582,10785}, {7585,10584}, {7968,10944}, {10794,18993}, {10826,19003}, {10829,19005}, {10871,19011}, {10912,19065}, {10914,13936}, {10943,19116}, {10945,19031}, {10946,19033}, {10947,19037}, {10949,19049}, {11235,19053}, {11373,18991}, {11865,19007}, {11866,19009}, {11903,19017}, {12182,19055}, {12348,19057}, {12371,19059}, {12422,19061}, {12676,19067}, {12737,19077}, {12761,19081}, {12857,19085}, {12889,19051}, {12920,19087}, {12921,19075}, {12922,19073}, {12923,19089}, {12924,19091}, {12925,19093}, {12926,19095}, {12927,19097}, {12928,19104}, {12929,19102}, {13180,19108}, {13213,19110}, {13271,19112}, {13294,19114}, {13693,19099}, {13785,18516}, {13813,19101}, {13883,17619}, {13971,17614}, {16138,19079}, {18510,18519}, {18961,18995}
X(19023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 11, 19024), (7584, 18992, 19025), (7585, 10584, 13895)
X(19024) lies on these lines: {2,13895}, {6,11}, {12,19048}, {355,7583}, {371,11826}, {1376,3068}, {1587,12114}, {1588,10893}, {1702,12700}, {3299,10948}, {3301,10523}, {3311,10525}, {3434,7585}, {5410,11390}, {6417,11928}, {7581,10785}, {7582,10598}, {7586,10584}, {7969,10944}, {8983,17614}, {10794,18994}, {10826,19004}, {10829,19006}, {10871,19012}, {10912,19066}, {10914,13883}, {10943,19117}, {10945,19032}, {10946,19034}, {10947,19038}, {10949,19050}, {11235,19054}, {11373,18992}, {11865,19008}, {11866,19010}, {11903,19018}, {12182,19056}, {12348,19058}, {12371,19060}, {12422,19062}, {12676,19068}, {12737,19078}, {12761,19082}, {12857,19086}, {12889,19052}, {12920,19088}, {12921,19076}, {12922,19074}, {12923,19090}, {12924,19092}, {12925,19094}, {12926,19096}, {12927,19098}, {12928,19105}, {12929,19103}, {13180,19109}, {13213,19111}, {13271,19113}, {13294,19115}, {13665,18516}, {13813,19100}, {13936,17619}, {16138,19080}, {18512,18519}, {18961,18996}
X(19024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 11, 19023), (7583, 18991, 19026), (7586, 10584, 13952)
X(19025) lies on these lines: {2,13953}, {6,12}, {11,19049}, {72,13936}, {355,7584}, {372,11827}, {958,3069}, {1001,13965}, {1587,10894}, {1588,11500}, {1703,5812}, {3071,5416}, {3299,10954}, {3301,10523}, {3312,10526}, {3436,7586}, {5411,11391}, {5791,13947}, {6418,11929}, {7581,10599}, {7582,10786}, {7585,10585}, {7968,10950}, {10795,18993}, {10827,19003}, {10830,19005}, {10872,19011}, {10942,19116}, {10951,19031}, {10952,19033}, {10953,19037}, {10955,19047}, {11236,19053}, {11374,18991}, {11867,19007}, {11868,19009}, {11904,19017}, {12183,19055}, {12349,19057}, {12372,19059}, {12423,19061}, {12635,19065}, {12677,19067}, {12738,19077}, {12762,19081}, {12858,19085}, {12890,19051}, {12930,19087}, {12931,19075}, {12932,19073}, {12933,19089}, {12934,19091}, {12935,19093}, {12936,19095}, {12937,19097}, {12938,19104}, {12939,19102}, {13181,19108}, {13214,19110}, {13272,19112}, {13295,19114}, {13694,19099}, {13785,18517}, {13814,19101}, {15888,19050}, {16139,19079}, {18510,18518}, {18962,18995}
X(19025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 12, 19026), (7584, 18992, 19023), (7585, 10585, 13896)
X(19026) lies on these lines: {2,13896}, {6,12}, {11,19050}, {72,13883}, {355,7583}, {371,11827}, {958,3068}, {1001,13907}, {1587,11500}, {1588,10894}, {1702,5812}, {3070,5415}, {3299,10523}, {3301,10954}, {3311,10526}, {3436,7585}, {5410,11391}, {5791,13893}, {6417,11929}, {7581,10786}, {7582,10599}, {7586,10585}, {7969,10950}, {10795,18994}, {10827,19004}, {10830,19006}, {10872,19012}, {10942,19117}, {10951,19032}, {10952,19034}, {10953,19038}, {10955,19048}, {11236,19054}, {11374,18992}, {11867,19008}, {11868,19010}, {11904,19018}, {12183,19056}, {12349,19058}, {12372,19060}, {12423,19062}, {12635,19066}, {12677,19068}, {12738,19078}, {12762,19082}, {12858,19086}, {12890,19052}, {12930,19088}, {12931,19076}, {12932,19074}, {12933,19090}, {12934,19092}, {12935,19094}, {12936,19096}, {12937,19098}, {12938,19105}, {12939,19103}, {13181,19109}, {13214,19111}, {13272,19113}, {13295,19115}, {13665,18517}, {13814,19100}, {15888,19049}, {16139,19080}, {18512,18518}, {18962,18996}
X(19026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 12, 19025), (7583, 18991, 19024), (7586, 10585, 13953)
X(19027) lies on these lines: {1,7584}, {2,13954}, {3,13958}, {4,19037}, {5,3301}, {6,12}, {11,486}, {36,13966}, {55,1588}, {56,3069}, {65,13936}, {371,5432}, {372,7354}, {388,7586}, {485,3614}, {495,3299}, {498,3311}, {499,13951}, {606,7299}, {615,2067}, {999,13962}, {1124,15888}, {1132,5225}, {1152,15326}, {1155,13975}, {1319,13971}, {1377,3925}, {1388,13959}, {1420,13942}, {1428,13972}, {1478,3312}, {1479,13785}, {1587,10895}, {1656,13904}, {1686,10406}, {1703,1836}, {2099,19065}, {2362,3649}, {3071,5414}, {3077,5348}, {3085,7582}, {3086,13939}, {3090,13898}, {3157,19061}, {3295,18510}, {4299,6398}, {5204,13935}, {5217,6459}, {5219,19004}, {5252,18992}, {5298,13847}, {5326,5418}, {5411,11392}, {5434,6502}, {6174,9679}, {6203,10911}, {6395,9655}, {6396,9647}, {6409,9649}, {6417,13905}, {6418,9654}, {6419,9646}, {6460,12943}, {6561,15338}, {7288,13941}, {7294,8252}, {7581,10590}, {7583,7951}, {7585,10588}, {7741,18762}, {7968,10944}, {7969,15950}, {9578,19003}, {9661,10577}, {10088,19051}, {10592,19117}, {10797,18993}, {10831,19005}, {10873,19011}, {10956,19047}, {10957,19049}, {11237,19053}, {11375,18991}, {11501,18999}, {11510,13940}, {11869,19007}, {11870,19009}, {11905,19017}, {11930,19031}, {11931,19033}, {12184,19055}, {12350,19057}, {12373,19059}, {12678,19067}, {12739,19077}, {12763,19081}, {12837,19089}, {12859,19085}, {12903,19110}, {12940,19087}, {12941,19075}, {12942,19073}, {12944,19091}, {12945,19093}, {12946,19095}, {12947,19097}, {12948,19104}, {12949,19102}, {13182,19108}, {13273,19112}, {13296,19114}, {13695,19099}, {13815,19101}, {13973,16232}, {13993,15325}, {16140,19079}
X(19027) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7584, 19029), (2, 18996, 18965), (3, 13963, 13958), (5, 3301, 19030), (6, 12, 19028), (56, 3069, 18966), (388, 7586, 18995), (486, 1335, 11), (495, 19116, 3299), (498, 3311, 13901), (615, 2067, 5433), (3071, 5414, 6284), (3085, 7582, 19038), (3086, 13939, 13955), (13954, 18996, 2)
X(19028) lies on these lines: {1,7583}, {2,13897}, {3,13901}, {4,19038}, {5,3299}, {6,12}, {11,485}, {36,8981}, {55,1587}, {56,3068}, {65,13883}, {371,7354}, {372,5432}, {388,7585}, {486,3614}, {495,3301}, {498,3312}, {499,8976}, {590,5433}, {605,7299}, {999,13904}, {1131,5225}, {1151,15326}, {1155,13912}, {1319,8983}, {1335,15888}, {1378,3925}, {1388,13902}, {1428,13910}, {1478,3311}, {1479,13665}, {1588,10895}, {1656,13962}, {1685,10406}, {1702,1836}, {2066,3070}, {2067,5434}, {2099,19066}, {2362,13911}, {3076,5348}, {3085,7581}, {3086,13886}, {3090,13955}, {3157,19062}, {3295,18512}, {3649,16232}, {4299,6221}, {5204,9540}, {5217,6460}, {5219,19003}, {5252,18991}, {5298,13846}, {5326,5420}, {5410,11392}, {6204,10910}, {6417,9654}, {6418,13963}, {6425,9649}, {6459,12943}, {6560,15338}, {7288,8972}, {7294,8253}, {7582,10590}, {7584,7951}, {7586,10588}, {7741,18538}, {7968,15950}, {7969,10944}, {8960,9661}, {9578,19004}, {10088,19052}, {10592,19116}, {10797,18994}, {10831,19006}, {10873,19012}, {10956,19048}, {10957,19050}, {11237,19054}, {11375,18992}, {11501,19000}, {11510,13887}, {11869,19008}, {11870,19010}, {11905,19018}, {11930,19032}, {11931,19034}, {12184,19056}, {12350,19058}, {12373,19060}, {12678,19068}, {12739,19078}, {12763,19082}, {12837,19090}, {12859,19086}, {12903,19111}, {12940,19088}, {12941,19076}, {12942,19074}, {12944,19092}, {12945,19094}, {12946,19096}, {12947,19098}, {12948,19105}, {12949,19103}, {13182,19109}, {13273,19113}, {13296,19115}, {13815,19100}, {13925,15325}, {16140,19080}
X(19028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7583, 19030), (2, 18995, 18966), (3, 13905, 13901), (5, 3299, 19029), (6, 12, 19027), (56, 3068, 18965), (372, 9646, 5432), (388, 7585, 18996), (485, 1124, 11), (495, 19117, 3301), (498, 3312, 13958), (590, 6502, 5433), (2066, 3070, 6284), (3085, 7581, 19037), (13897, 18995, 2)
X(19029) lies on these lines: {1,7584}, {2,13901}, {3,13962}, {4,18995}, {5,3299}, {6,11}, {12,486}, {35,13966}, {55,3069}, {56,1588}, {371,5433}, {372,6284}, {485,7173}, {496,3301}, {497,7586}, {498,13951}, {499,3311}, {605,5348}, {615,2066}, {999,18510}, {1069,19061}, {1132,5229}, {1152,15338}, {1478,13785}, {1479,3312}, {1587,10896}, {1656,13905}, {1703,12701}, {1837,18992}, {2098,19065}, {2330,13972}, {2646,13971}, {3057,13936}, {3058,5414}, {3071,6502}, {3076,7299}, {3085,13939}, {3086,7582}, {3090,13897}, {3295,13963}, {3297,15888}, {3601,13942}, {4302,6398}, {4995,13847}, {5204,6459}, {5217,13935}, {5218,13941}, {5326,8252}, {5411,11393}, {5418,7294}, {6395,9668}, {6396,9660}, {6409,9662}, {6417,13904}, {6418,9669}, {6419,9661}, {6460,12953}, {6561,15326}, {7581,10591}, {7583,7741}, {7585,10589}, {7951,18762}, {7968,10950}, {9581,19003}, {9646,10577}, {10091,19051}, {10593,19117}, {10798,18993}, {10832,19005}, {10874,19011}, {10958,19047}, {10959,19049}, {11238,19053}, {11376,18991}, {11502,18999}, {11871,19007}, {11872,19009}, {11906,19017}, {11932,19031}, {11933,19033}, {12185,19055}, {12351,19057}, {12374,19059}, {12679,19067}, {12740,19077}, {12764,19081}, {12836,19089}, {12904,19110}, {12950,19087}, {12951,19075}, {12952,19073}, {12954,19091}, {12955,19093}, {12956,19095}, {12957,19097}, {12958,19104}, {12959,19102}, {13183,19108}, {13274,19112}, {13297,19114}, {13696,19099}, {13816,19101}, {13883,17606}, {13989,15452}, {16141,19079}
X(19029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7584, 19027), (2, 19038, 13901), (3, 13962, 18966), (5, 3299, 19028), (6, 11, 19030), (55, 3069, 13958), (486, 1124, 12), (496, 19116, 3301), (497, 7586, 19037), (499, 3311, 18965), (615, 2066, 5432), (3071, 6502, 7354), (3085, 13939, 13954), (3086, 7582, 18996), (13955, 19038, 2)
X(19030) lies on these lines: {1,7583}, {2,13898}, {3,13904}, {4,18996}, {5,3301}, {6,11}, {12,485}, {35,8981}, {55,3068}, {56,1587}, {371,6284}, {372,5433}, {486,7173}, {496,3299}, {497,7585}, {498,8976}, {499,3312}, {590,5414}, {606,5348}, {999,18512}, {1069,19062}, {1131,5229}, {1151,15338}, {1478,13665}, {1479,3311}, {1588,10896}, {1656,13963}, {1702,12701}, {1837,18991}, {2066,3058}, {2067,3070}, {2098,19066}, {2330,13910}, {2646,8983}, {3057,13883}, {3077,7299}, {3085,13886}, {3086,7581}, {3090,13954}, {3295,13905}, {3298,15888}, {3601,13888}, {4302,6221}, {4995,13846}, {5204,6460}, {5217,9540}, {5218,8972}, {5326,8253}, {5410,11393}, {5420,7294}, {6417,9669}, {6418,13962}, {6425,9662}, {6459,12953}, {6560,15326}, {7582,10591}, {7584,7741}, {7586,10589}, {7951,18538}, {7969,10950}, {8960,9646}, {8997,15452}, {9581,19004}, {10091,19052}, {10593,19116}, {10798,18994}, {10832,19006}, {10874,19012}, {10958,19048}, {10959,19050}, {11238,19054}, {11376,18992}, {11502,19000}, {11871,19008}, {11872,19010}, {11906,19018}, {11932,19032}, {11933,19034}, {12185,19056}, {12351,19058}, {12374,19060}, {12679,19068}, {12740,19078}, {12764,19082}, {12836,19090}, {12860,19086}, {12904,19111}, {12950,19088}, {12951,19076}, {12952,19074}, {12954,19092}, {12955,19094}, {12956,19096}, {12957,19098}, {12958,19105}, {12959,19103}, {13183,19109}, {13274,19113}, {13297,19115}, {13816,19100}, {13936,17606}, {16141,19080}
X(19030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 7583, 19028), (2, 19037, 13958), (3, 13904, 18965), (5, 3301, 19027), (6, 11, 19029), (55, 3068, 13901), (372, 9661, 5433), (485, 1335, 12), (496, 19117, 3299), (497, 7585, 19038), (499, 3312, 18966), (590, 5414, 5432), (2067, 3070, 7354), (3085, 13886, 13897), (13898, 19037, 2)
X(19031) lies on these lines: {2,13956}, {6,493}, {39,8408}, {372,11828}, {800,19034}, {1587,8212}, {1588,9838}, {3069,8222}, {3299,11951}, {3301,11953}, {3312,10669}, {5411,11394}, {6418,11949}, {6461,19033}, {6462,7586}, {7582,11846}, {7584,8220}, {7585,13899}, {7968,8210}, {8188,19003}, {8194,19005}, {8201,19007}, {8208,19009}, {8214,13936}, {10875,19011}, {10945,19023}, {10951,19025}, {11377,18991}, {11503,18999}, {11840,18993}, {11907,19017}, {11930,19027}, {11932,19029}, {11947,19037}, {11955,19047}, {11957,19049}, {12152,19053}, {12186,19055}, {12352,19057}, {12377,19059}, {12426,19061}, {12440,18992}, {12636,19065}, {12741,19077}, {12765,19081}, {12861,19085}, {12894,19051}, {12986,19087}, {12988,19075}, {12990,19073}, {12992,19089}, {12994,19091}, {12996,19093}, {12998,19095}, {13000,19097}, {13002,19104}, {13004,19102}, {13184,19108}, {13215,19110}, {13275,19112}, {13298,19114}, {13697,19099}, {13785,18520}, {13817,19101}, {16161,19079}, {18245,19067}, {18963,18995}
X(19031) = {X(6), X(493)}-harmonic conjugate of X(19032)
X(19032) lies on these lines: {2,13899}, {6,493}, {32,8408}, {194,6462}, {371,11828}, {1587,9838}, {1588,8212}, {3068,8222}, {3301,11951}, {3311,10669}, {5410,11394}, {6417,11949}, {6461,19034}, {7581,11846}, {7583,8220}, {7586,13956}, {7969,8210}, {8188,19004}, {8194,19006}, {8201,19008}, {8208,19010}, {8214,13883}, {8393,17475}, {10875,19012}, {10945,19024}, {10951,19026}, {11377,18992}, {11503,19000}, {11840,18994}, {11907,19018}, {11930,19028}, {11932,19030}, {11947,19038}, {11955,19048}, {11957,19050}, {12152,19054}, {12186,19056}, {12352,19058}, {12377,19060}, {12426,19062}, {12440,18991}, {12636,19066}, {12741,19078}, {12765,19082}, {12861,19086}, {12894,19052}, {12986,19088}, {12988,19076}, {12990,19074}, {12994,19092}, {12996,19094}, {12998,19096}, {13000,19098}, {13002,19105}, {13004,19103}, {13184,19109}, {13215,19111}, {13275,19113}, {13298,19115}, {13341,19033}, {13665,18520}, {13817,19100}, {16161,19080}, {18245,19068}, {18963,18996}
X(19032) = {X(6), X(493)}-harmonic conjugate of X(19031)
X(19033) lies on these lines: {2,13957}, {6,494}, {32,8420}, {194,6463}, {372,11829}, {1587,8213}, {1588,9839}, {3069,8223}, {3299,11952}, {3301,11954}, {3312,10673}, {5411,11395}, {6418,11950}, {6461,19031}, {7582,11847}, {7584,8221}, {7585,13900}, {7968,8211}, {8189,19003}, {8195,19005}, {8202,19007}, {8209,19009}, {8215,13936}, {8394,17475}, {10876,19011}, {10946,19023}, {10952,19025}, {11378,18991}, {11504,18999}, {11841,18993}, {11908,19017}, {11931,19027}, {11933,19029}, {11948,19037}, {11956,19047}, {11958,19049}, {12153,19053}, {12187,19055}, {12353,19057}, {12378,19059}, {12427,19061}, {12441,18992}, {12637,19065}, {12742,19077}, {12766,19081}, {12862,19085}, {12895,19051}, {12987,19087}, {12989,19075}, {12991,19073}, {12995,19091}, {12997,19093}, {12999,19095}, {13001,19097}, {13003,19104}, {13005,19102}, {13185,19108}, {13216,19110}, {13276,19112}, {13299,19114}, {13341,19032}, {13698,19099}, {13785,18522}, {13818,19101}, {16162,19079}, {18246,19067}, {18964,18995}
X(19033) = {X(6), X(494)}-harmonic conjugate of X(19034)
X(19034) lies on these lines: {2,13900}, {6,494}, {39,8420}, {371,11829}, {800,19031}, {1587,9839}, {1588,8213}, {3068,8223}, {3299,11954}, {3301,11952}, {3311,10673}, {5410,11395}, {6417,11950}, {6461,19032}, {6463,7585}, {7581,11847}, {7583,8221}, {7586,13957}, {7969,8211}, {8189,19004}, {8195,19006}, {8202,19008}, {8209,19010}, {8215,13883}, {10876,19012}, {10946,19024}, {10952,19026}, {11378,18992}, {11504,19000}, {11841,18994}, {11908,19018}, {11931,19028}, {11933,19030}, {11948,19038}, {11956,19048}, {11958,19050}, {12153,19054}, {12187,19056}, {12353,19058}, {12378,19060}, {12427,19062}, {12441,18991}, {12637,19066}, {12742,19078}, {12766,19082}, {12862,19086}, {12895,19052}, {12987,19088}, {12989,19076}, {12991,19074}, {12993,19090}, {12995,19092}, {12997,19094}, {12999,19096}, {13001,19098}, {13003,19105}, {13005,19103}, {13185,19109}, {13216,19111}, {13276,19113}, {13299,19115}, {13665,18522}, {13818,19100}, {16162,19080}, {18246,19068}, {18964,18996}
X(19034) = {X(6), X(494)}-harmonic conjugate of X(19033)
X(19035) lies on the line {65,6416}
X(19036) lies on the line {65,6415}
X(19037) lies on these lines: {1,3312}, {2,13898}, {3,3301}, {4,19027}, {5,13954}, {6,31}, {11,3069}, {12,1587}, {33,5411}, {35,3311}, {36,6398}, {56,372}, {65,1703}, {140,13904}, {371,5217}, {486,10896}, {496,13962}, {497,7586}, {498,7583}, {499,13966}, {631,18965}, {999,6395}, {1100,7133}, {1124,3303}, {1152,2067}, {1317,19081}, {1399,3077}, {1479,7584}, {1588,6284}, {1697,19003}, {1837,13936}, {2098,7968}, {2646,18991}, {3023,19108}, {3027,19055}, {3028,19059}, {3057,18992}, {3058,19053}, {3068,5432}, {3070,10895}, {3071,12953}, {3085,7581}, {3086,18966}, {3295,3299}, {3297,6432}, {3298,3304}, {3320,19093}, {3583,13785}, {3601,19004}, {3746,6428}, {4294,7582}, {4995,19054}, {5010,6221}, {5218,7585}, {5420,9661}, {5433,13935}, {6020,19114}, {6450,7280}, {6459,15338}, {6460,7354}, {6560,12943}, {7355,19087}, {7741,13951}, {7951,13665}, {8416,18960}, {9645,11266}, {9668,18510}, {10535,17820}, {10589,13941}, {10591,13939}, {10593,13993}, {10799,18993}, {10833,19005}, {10877,19011}, {10881,11399}, {10947,19023}, {10950,19065}, {10953,19025}, {10965,19047}, {10966,19013}, {11376,13971}, {11873,19007}, {11874,19009}, {11909,19017}, {11947,19031}, {11948,19033}, {12354,19057}, {12428,19061}, {12680,19067}, {12743,19077}, {12863,19085}, {12896,19051}, {13075,19075}, {13076,19073}, {13077,19089}, {13078,19091}, {13079,19095}, {13080,19097}, {13081,19104}, {13082,19102}, {13699,19099}, {13819,19101}, {13905,19117}, {13947,17606}, {15171,19116}, {15452,19109}, {16142,19079}, {19014,19048}
X(19037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3312, 18995), (2, 19030, 13898), (3, 3301, 18996), (5, 13963, 13954), (6, 55, 19038), (6, 5414, 55), (11, 3069, 13955), (372, 1335, 56), (497, 7586, 19029), (498, 7583, 13897), (1152, 2067, 5204), (3085, 7581, 19028), (3295, 6418, 3299), (3298, 3594, 6502), (3298, 6502, 3304), (13958, 19030, 2)
X(19038) lies on these lines: {1,3311}, {2,13901}, {3,3299}, {4,19028}, {5,13897}, {6,31}, {11,3068}, {12,1588}, {33,5410}, {35,3312}, {36,6221}, {44,7133}, {56,371}, {65,1702}, {140,13962}, {372,5217}, {485,10896}, {486,9646}, {496,13904}, {497,7585}, {498,7584}, {499,8981}, {631,18966}, {1151,5204}, {1155,9616}, {1317,19082}, {1319,9583}, {1335,3303}, {1399,3076}, {1479,7583}, {1587,6284}, {1697,19004}, {1837,13883}, {2067,3297}, {2098,7969}, {2646,18992}, {3023,19109}, {3027,19056}, {3028,19060}, {3057,18991}, {3058,19054}, {3069,5432}, {3070,12953}, {3071,10895}, {3085,7582}, {3086,18965}, {3295,3301}, {3298,6431}, {3320,19094}, {3583,13665}, {3601,19003}, {3746,6427}, {4294,7581}, {4995,19053}, {5010,6398}, {5218,7586}, {5298,9663}, {5433,9540}, {6020,19115}, {6449,7280}, {6459,7354}, {6460,15338}, {6560,9660}, {6561,12943}, {7355,19088}, {7741,8976}, {7951,13785}, {8396,18959}, {8972,10589}, {8983,11376}, {9541,15326}, {9645,11265}, {9668,18512}, {10535,17819}, {10591,13886}, {10593,13925}, {10799,18994}, {10833,19006}, {10877,19012}, {10880,11399}, {10947,19024}, {10950,19066}, {10953,19026}, {10965,19048}, {10966,19014}, {11873,19008}, {11874,19010}, {11909,19018}, {11947,19032}, {11948,19034}, {12354,19058}, {12428,19062}, {12680,19068}, {12743,19078}, {12863,19086}, {12896,19052}, {13075,19076}, {13076,19074}, {13077,19090}, {13078,19092}, {13079,19096}, {13080,19098}, {13081,19105}, {13082,19103}, {13819,19100}, {13893,17606}, {13963,19116}, {15171,19117}, {15452,19108}, {16142,19080}, {19013,19047}
X(19038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3311, 18996), (2, 19029, 13955), (3, 3299, 18995), (5, 13905, 13897), (6, 55, 19037), (6, 2066, 55), (11, 3068, 13898), (371, 1124, 56), (497, 7585, 19030), (498, 7584, 13954), (1151, 6502, 5204), (2067, 3297, 3304), (3085, 7582, 19027), (3297, 3592, 2067), (13901, 19029, 2)
X(19039) lies on these lines: {4,19087}, {5,1587}, {6,3536}, {25,18997}, {51,19041}, {125,19042}, {389,1588}, {3092,17822}, {5411,19021}, {5413,5871}, {6218,17810}, {7582,11431}, {7687,19059}, {10783,17820}, {12235,19061}, {12236,19051}, {12242,19095}, {13567,19040}
X(19040) lies on these lines: {4,19088}, {5,1588}, {6,3535}, {25,18998}, {51,19042}, {125,19041}, {389,1587}, {3091,8969}, {3093,17822}, {5410,19022}, {5412,5870}, {6217,17810}, {7581,11431}, {7687,19060}, {10784,17819}, {12235,19062}, {12236,19052}, {12242,19096}, {13567,19039}
X(19041) lies on these lines: {4,1132}, {6,3128}, {25,1163}, {51,19039}, {52,19061}, {125,19040}, {185,1588}, {193,1586}, {427,5304}, {1271,3536}, {1587,3574}, {1843,5200}, {1986,19051}, {3069,10133}, {3071,5895}, {3087,3127}, {13202,19059}, {13431,13440}, {18997,19005}
X(19041) = polar conjugate of the isotomic conjugate of X(33365)
X(19042) lies on these lines: {4,1131}, {6,3127}, {25,1162}, {51,19040}, {52,19062}, {125,19039}, {185,1587}, {193,1585}, {427,5304}, {1270,3535}, {1588,3574}, {1986,19052}, {3068,5200}, {3070,5895}, {3087,3128}, {13202,19060}, {13429,13431}, {18998,19006}
X(19042) = polar conjugate of the isotomic conjugate of X(33364)
X(19043) lies on these lines: {4,19059}, {125,19044}, {381,486}, {568,19051}, {1587,7699}, {1588,5890}, {7581,19095}, {7720,10814}
X(19044) lies on these lines: {4,19060}, {125,19043}, {381,485}, {1587,5890}, {1588,7699}, {7582,19096}, {7721,10815}
X(19045) lies on these lines: {4,19095}, {6,10261}, {184,6220}, {382,3071}, {1588,6241}
X(19046) lies on these lines: {4,19096}, {6,10262}, {184,6219}, {382,3070}, {1587,6241}
X(19047) lies on these lines: {1,6}, {2,13964}, {12,19023}, {119,486}, {371,10269}, {372,11248}, {590,10200}, {615,1378}, {1152,2077}, {1470,6502}, {1587,10531}, {1588,12115}, {1703,12703}, {3069,5552}, {3071,6256}, {3311,16203}, {3312,10679}, {5411,11400}, {5554,19066}, {6418,12000}, {6735,13973}, {7581,10596}, {7582,10805}, {7584,10942}, {7585,10586}, {7586,10528}, {9616,16209}, {10803,18993}, {10834,19005}, {10878,19011}, {10915,13936}, {10955,19025}, {10956,19027}, {10958,19029}, {10965,19037}, {11239,19053}, {11881,19007}, {11882,19009}, {11914,19017}, {11955,19031}, {11956,19033}, {12189,19055}, {12356,19057}, {12381,19059}, {12430,19061}, {12648,19065}, {12686,19067}, {12749,19077}, {12775,19081}, {12874,19085}, {12905,19051}, {13094,19087}, {13104,19075}, {13105,19073}, {13109,19089}, {13112,19091}, {13118,19093}, {13121,19095}, {13130,19097}, {13132,19104}, {13134,19102}, {13189,19108}, {13217,19110}, {13278,19112}, {13313,19114}, {13716,19099}, {13785,18542}, {13839,19101}, {16154,19079}, {16232,18838}, {18510,18545}, {19013,19038}
X(19047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 19048), (6, 1124, 19050), (6, 3297, 7969), (6, 7968, 19049), (3299, 18992, 6), (3640, 10048, 12595), (7585, 10586, 13906)
X(19048) lies on these lines: {1,6}, {2,13906}, {12,19024}, {119,485}, {371,11248}, {372,10269}, {590,1377}, {615,10200}, {1151,2077}, {1470,2067}, {1587,12115}, {1588,10531}, {1702,12703}, {2362,18838}, {3068,5552}, {3070,6256}, {3311,10679}, {3312,16203}, {5410,11400}, {5554,19065}, {6417,12000}, {6735,13911}, {7581,10805}, {7582,10596}, {7583,10942}, {7585,10528}, {7586,10586}, {10803,18994}, {10834,19006}, {10878,19012}, {10915,13883}, {10955,19026}, {10956,19028}, {10958,19030}, {10965,19038}, {11239,19054}, {11509,18996}, {11881,19008}, {11882,19010}, {11914,19018}, {11955,19032}, {11956,19034}, {12189,19056}, {12356,19058}, {12381,19060}, {12430,19062}, {12648,19066}, {12686,19068}, {12749,19078}, {12775,19082}, {12874,19086}, {12905,19052}, {13094,19088}, {13104,19076}, {13105,19074}, {13109,19090}, {13112,19092}, {13118,19094}, {13121,19096}, {13130,19098}, {13132,19105}, {13134,19103}, {13189,19109}, {13217,19111}, {13278,19113}, {13313,19115}, {13665,18542}, {13839,19100}, {16154,19080}, {18512,18545}, {19014,19037}
X(19048) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 19047), (6, 1335, 19049), (6, 3298, 7968), (6, 7969, 19050), (3301, 18991, 6), (3641, 10049, 12595), (7586, 10586, 13964)
X(19049) lies on these lines: {1,6}, {2,13965}, {11,19025}, {371,10267}, {372,11249}, {590,10198}, {615,1377}, {1151,10902}, {1152,11012}, {1587,10532}, {1588,12116}, {1703,12704}, {2067,5416}, {3311,16202}, {3312,10680}, {5411,11401}, {6283,19133}, {6418,12001}, {6734,13973}, {7581,10597}, {7582,10806}, {7584,10943}, {9616,16208}, {10835,19005}, {10879,19011}, {10949,19023}, {10957,19027}, {10959,19029}, {10966,19013}, {11510,18996}, {11883,19007}, {11884,19009}, {11915,19017}, {11957,19031}, {11958,19033}, {12190,19055}, {12357,19057}, {12382,19059}, {12431,19061}, {12649,19065}, {12687,19067}, {12750,19077}, {12776,19081}, {12875,19085}, {12906,19051}, {13095,19087}, {13106,19075}, {13107,19073}, {13110,19089}, {13119,19093}, {13122,19095}, {13131,19097}, {13133,19104}, {13135,19102}, {13190,19108}, {13218,19110}, {13279,19112}, {13314,19114}, {13717,19099}, {13785,18544}, {13840,19101}, {15888,19026}, {16155,19079}, {18510,18543}, {18967,18995}
X(19049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 19050), (6, 1335, 19048), (6, 3298, 7969), (6, 7968, 19047), (3301, 18992, 6), (3640, 10040, 12594)
X(19050) lies on these lines: {1,6}, {2,13907}, {11,19026}, {371,11249}, {372,10267}, {590,1378}, {615,10198}, {1151,11012}, {1152,10902}, {1587,12116}, {1588,10532}, {1702,12704}, {3068,10527}, {3311,10680}, {3312,16202}, {5410,11401}, {5415,6502}, {6405,19133}, {6417,12001}, {6734,13911}, {7581,10806}, {7582,10597}, {7583,10943}, {7585,10529}, {7586,10587}, {10804,18994}, {10835,19006}, {10879,19012}, {10916,13883}, {10949,19024}, {10957,19028}, {10959,19030}, {10966,19014}, {11240,19054}, {11510,18995}, {11883,19008}, {11884,19010}, {11915,19018}, {11957,19032}, {11958,19034}, {12190,19056}, {12357,19058}, {12382,19060}, {12431,19062}, {12649,19066}, {12687,19068}, {12750,19078}, {12776,19082}, {12906,19052}, {13095,19088}, {13106,19076}, {13107,19074}, {13110,19090}, {13113,19092}, {13119,19094}, {13122,19096}, {13131,19098}, {13133,19105}, {13135,19103}, {13190,19109}, {13218,19111}, {13279,19113}, {13314,19115}, {13665,18544}, {13840,19100}, {15888,19025}, {16155,19080}, {18512,18543}, {18967,18996}
X(19050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6, 19049), (6, 1124, 19047), (6, 3297, 7968), (6, 7969, 19048), (3299, 18991, 6), (3641, 10041, 12594), (7586, 10587, 13965)
The reciprocal orthologic center of these triangles is X(7574)
X(19051) lies on these lines: {2,13979}, {3,13969}, {5,19111}, {6,13}, {30,19059}, {110,7584}, {125,3311}, {371,15061}, {372,12121}, {486,14643}, {568,19043}, {615,10819}, {1511,3069}, {1587,10113}, {1588,5663}, {1656,8998}, {1986,19041}, {2777,19087}, {3071,7728}, {3299,12903}, {3301,12904}, {3312,17702}, {3448,7582}, {3581,19001}, {5411,12140}, {5972,13951}, {6221,6699}, {6398,16163}, {6418,12902}, {6419,15027}, {6459,12041}, {7583,14644}, {7585,13915}, {7586,12383}, {7968,12898}, {8981,15059}, {10088,19027}, {10091,19029}, {10264,19060}, {11801,19117}, {11804,19096}, {12201,18993}, {12236,19039}, {12261,18991}, {12407,19003}, {12412,19005}, {12466,19007}, {12467,19009}, {12501,19011}, {12778,13936}, {12790,19017}, {12889,19023}, {12890,19025}, {12894,19031}, {12895,19033}, {12896,19037}, {12905,19047}, {12906,19049}, {13961,15040}, {13966,15035}, {13972,15462}, {15535,19056}, {17835,19015}, {18968,18995}, {19095,19110}
X(19051) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 265, 19052), (7585, 15081, 13915)
The reciprocal orthologic center of these triangles is X(7574)
X(19052) lies on these lines: {2,13915}, {3,8994}, {6,13}, {110,7583}, {125,3312}, {371,12121}, {372,15061}, {485,14643}, {568,19044}, {590,10820}, {1511,3068}, {1587,5663}, {1588,10113}, {1656,13990}, {1986,19042}, {2771,19078}, {2777,19088}, {3070,7728}, {3299,12904}, {3301,12903}, {3311,17702}, {3448,7581}, {3581,19002}, {5410,12140}, {5972,8976}, {6221,16163}, {6395,13969}, {6398,6699}, {6417,12902}, {6420,15027}, {6460,12041}, {7584,14644}, {7585,12383}, {7586,13979}, {7969,12898}, {8981,15035}, {10088,19028}, {10091,19030}, {10264,19059}, {11801,19116}, {11804,19095}, {12201,18994}, {12236,19040}, {12261,18992}, {12334,19000}, {12407,19004}, {12412,19006}, {12466,19008}, {12467,19010}, {12501,19012}, {12778,13883}, {12790,19018}, {12889,19024}, {12890,19026}, {12894,19032}, {12895,19034}, {12896,19038}, {12905,19048}, {12906,19050}, {13903,15040}, {13910,15462}, {13966,15059}, {15535,19055}, {17835,19016}, {18968,18996}
X(19052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 265, 19051), (7586, 15081, 13979)
The reciprocal orthologic center of these triangles is X(2)
X(19053) lies on these lines: {2,6}, {4,1328}, {5,6428}, {20,3594}, {30,1588}, {115,19058}, {140,6427}, {371,3524}, {372,376}, {381,1587}, {428,5411}, {485,5071}, {486,3545}, {511,19063}, {519,18992}, {528,19112}, {530,19073}, {531,19075}, {532,19071}, {533,19069}, {538,19089}, {539,19061}, {541,19059}, {542,19055}, {543,19057}, {547,13951}, {548,6448}, {549,3311}, {551,13959}, {631,6419}, {754,19091}, {1151,15692}, {1152,10304}, {1267,17120}, {1327,6436}, {1505,7739}, {1589,5158}, {1590,3284}, {1651,19017}, {2482,19109}, {3058,19037}, {3070,3839}, {3071,3543}, {3241,7968}, {3299,10056}, {3301,10072}, {3317,10576}, {3522,6426}, {3523,3592}, {3528,6454}, {3534,6395}, {3536,5702}, {3582,13962}, {3584,13963}, {3679,13936}, {3828,13947}, {3830,18510}, {3845,13785}, {4421,18999}, {4428,19000}, {4995,19038}, {5007,11291}, {5054,6417}, {5055,6501}, {5066,13665}, {5067,8960}, {5298,18996}, {5391,17121}, {5405,16670}, {5413,7714}, {5414,10385}, {5418,15709}, {5420,15702}, {5434,18995}, {5459,19074}, {5460,19076}, {5642,19111}, {6055,19056}, {6174,19113}, {6221,12100}, {6398,8703}, {6409,15705}, {6423,13798}, {6425,15717}, {6431,15708}, {6442,15640}, {6445,15716}, {6447,15712}, {6449,17504}, {6451,15711}, {6452,15759}, {6453,10299}, {6455,14891}, {6471,15683}, {6497,15714}, {6499,13925}, {6500,8981}, {6560,15682}, {6561,11001}, {7000,8550}, {7738,12969}, {7772,11292}, {7811,19011}, {8976,13993}, {8983,13942}, {9166,13968}, {9466,19090}, {9530,19093}, {9909,19005}, {10577,13886}, {11194,19013}, {11206,11242}, {11207,19007}, {11208,19009}, {11235,19023}, {11236,19025}, {11237,19027}, {11238,19029}, {11239,19047}, {11240,19049}, {11485,15764}, {12150,18993}, {12152,19031}, {12153,19033}, {13701,13769}, {13712,14482}, {13782,13832}, {13833,13843}, {13902,13971}, {13908,14061}, {18512,18762}
X(19053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 6, 19054), (2, 1992, 5861), (2, 7585, 13846), (2, 13759, 591), (2, 19054, 3068), (6, 615, 7585), (6, 3069, 3068), (6, 7586, 3069), (395, 396, 8252), (591, 597, 2), (615, 13846, 2), (1588, 3312, 6460), (3069, 19054, 2), (3312, 19116, 1588), (5032, 5306, 19054), (5304, 8584, 19054)
The reciprocal orthologic center of these triangles is X(2)
X(19054) lies on these lines: {2,6}, {4,1327}, {5,6427}, {20,3592}, {30,1587}, {115,19057}, {140,6428}, {371,376}, {372,3524}, {381,1588}, {428,5410}, {485,3545}, {486,5071}, {511,19064}, {519,18991}, {528,19113}, {530,19074}, {531,19076}, {532,19070}, {533,19072}, {538,19090}, {539,19062}, {541,19060}, {542,19056}, {543,19058}, {547,8976}, {548,6447}, {549,3312}, {551,13902}, {631,6420}, {754,19092}, {1151,10304}, {1152,15692}, {1267,17121}, {1328,6435}, {1504,7739}, {1589,3284}, {1590,5158}, {1651,19018}, {2066,10385}, {2482,19108}, {3058,19038}, {3070,3543}, {3071,3839}, {3090,8960}, {3241,7969}, {3299,10072}, {3301,10056}, {3316,10577}, {3522,6425}, {3523,3594}, {3528,6453}, {3535,5702}, {3582,13904}, {3584,13905}, {3679,13883}, {3828,13893}, {3830,18512}, {3845,13665}, {4421,19000}, {4428,18999}, {4995,19037}, {5007,11292}, {5054,6418}, {5055,6500}, {5066,13785}, {5298,18995}, {5391,17120}, {5393,16670}, {5412,7714}, {5418,15702}, {5420,15709}, {5434,18996}, {5459,19073}, {5460,19075}, {5642,19110}, {6055,19055}, {6174,19112}, {6221,8703}, {6395,15693}, {6396,15698}, {6398,12100}, {6410,15705}, {6424,13678}, {6426,15717}, {6432,15708}, {6441,15640}, {6446,15716}, {6448,15712}, {6450,17504}, {6451,15759}, {6452,15711}, {6454,9680}, {6456,14891}, {6470,15683}, {6496,15714}, {6498,13993}, {6501,13903}, {6560,11001}, {6561,15682}, {7374,8550}, {7738,12962}, {7772,11291}, {7811,19012}, {8963,13341}, {8983,13959}, {9166,13908}, {9466,19089}, {9530,19094}, {9681,17538}, {9909,19006}, {10576,13939}, {11194,19014}, {11206,11241}, {11207,19008}, {11208,19010}, {11235,19024}, {11236,19026}, {11237,19028}, {11238,19030}, {11239,19048}, {11240,19050}, {11486,15764}, {12150,18994}, {12152,19032}, {12153,19034}, {13662,13831}, {13720,13769}, {13821,13833}, {13835,14482}, {13888,13971}, {13925,13951}, {13968,14061}, {18510,18538}
X(19054) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 6, 19053), (2, 1992, 5860), (2, 7586, 13847), (2, 13639, 1991), (2, 19053, 3069), (6, 590, 7586), (6, 3068, 3069), (6, 7585, 3068), (395, 396, 8253), (590, 13847, 2), (597, 1991, 2), (1587, 3311, 6459), (3068, 19053, 2), (3311, 19117, 1587), (5032, 5306, 19053), (5304, 8584, 19053)
The reciprocal orthologic center of these triangles is X(5999)
X(19055) lies on these lines: {2,13967}, {3,19109}, {6,98}, {30,19057}, {99,372}, {114,3069}, {115,1587}, {147,7586}, {485,14061}, {486,6569}, {491,8781}, {542,19053}, {620,13935}, {631,8997}, {690,19059}, {1327,6568}, {1588,2794}, {2782,3312}, {2783,19112}, {2787,19081}, {2799,19093}, {3023,18995}, {3027,19037}, {3068,6036}, {3070,14639}, {3071,10722}, {3299,10053}, {3301,10069}, {3311,12042}, {3545,13968}, {5182,19146}, {5411,12131}, {6033,7584}, {6055,19054}, {6230,13773}, {6231,13760}, {6320,8416}, {6395,13188}, {6418,12188}, {6560,10723}, {7581,14651}, {7582,9862}, {7585,8980}, {7968,7970}, {9767,13926}, {9860,19003}, {9861,19005}, {9864,13936}, {11632,19058}, {11710,18991}, {11724,13959}, {12176,18993}, {12178,18999}, {12179,19007}, {12180,19009}, {12181,19017}, {12182,19023}, {12183,19025}, {12184,19027}, {12185,19029}, {12186,19031}, {12187,19033}, {12189,19047}, {12190,19049}, {13640,13790}, {13966,15561}, {15535,19052}, {19091,19116}
X(19055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 98, 19056), (98, 10753, 6227)
The reciprocal orthologic center of these triangles is X(5999)
X(19056) lies on these lines: {2,8980}, {3,19108}, {6,98}, {30,19058}, {99,371}, {114,3068}, {115,1588}, {147,7585}, {485,6568}, {486,14061}, {492,8781}, {542,19054}, {620,9540}, {631,13989}, {690,19060}, {1328,6569}, {1587,2794}, {2782,3311}, {2783,19113}, {2787,19082}, {2799,19094}, {3023,18996}, {3027,19038}, {3069,6036}, {3070,10722}, {3071,14639}, {3299,10069}, {3301,10053}, {3312,12042}, {3545,13908}, {5182,19145}, {5410,12131}, {6033,7583}, {6055,19053}, {6230,13640}, {6231,13653}, {6319,8396}, {6417,12188}, {6561,10723}, {7581,9862}, {7582,14651}, {7586,13967}, {7969,7970}, {8981,15561}, {9583,11711}, {9768,13873}, {9860,19004}, {9861,19006}, {9864,13883}, {11632,19057}, {11710,18992}, {11724,13902}, {12176,18994}, {12178,19000}, {12179,19008}, {12180,19010}, {12181,19018}, {12182,19024}, {12183,19026}, {12184,19028}, {12185,19030}, {12186,19032}, {12187,19034}, {12189,19048}, {12190,19050}, {13670,13760}, {15535,19051}, {19092,19117}
X(19056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 98, 19055), (98, 10753, 6226)
The reciprocal orthologic center of these triangles is X(9855)
X(19057) lies on these lines: {2,8997}, {6,598}, {30,19055}, {115,19054}, {372,12117}, {530,19075}, {531,19073}, {542,1588}, {543,19053}, {1587,9880}, {2482,3069}, {2782,19063}, {3068,5461}, {3299,10054}, {3301,10070}, {3524,13967}, {5411,12132}, {5465,19111}, {5969,19089}, {6418,12355}, {7582,12243}, {7584,8724}, {7585,13908}, {7586,8591}, {7968,9884}, {9875,19003}, {9876,19005}, {9878,19011}, {9881,13936}, {9892,13761}, {11632,19056}, {12158,13927}, {12191,18993}, {12258,18991}, {12326,18999}, {12345,19007}, {12346,19009}, {12347,19017}, {12348,19023}, {12349,19025}, {12350,19027}, {12351,19029}, {12352,19031}, {12353,19033}, {12354,19037}, {12356,19047}, {12357,19049}, {13642,13796}, {13846,14061}, {18969,18995}
X(19057) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 671, 19058), (671, 8593, 9882)
The reciprocal orthologic center of these triangles is X(9855)
X(19058) lies on these lines: {2,13908}, {6,598}, {30,19056}, {115,19053}, {371,12117}, {530,19076}, {531,19074}, {542,1587}, {543,19054}, {1588,9880}, {2482,3068}, {2782,19064}, {3069,5461}, {3299,10070}, {3301,10054}, {3524,8980}, {5410,12132}, {5465,19110}, {5969,19090}, {6417,12355}, {7581,12243}, {7583,8724}, {7585,8591}, {7586,13968}, {7969,9884}, {9875,19004}, {9876,19006}, {9878,19012}, {9881,13883}, {9894,13642}, {11632,19055}, {12159,13874}, {12191,18994}, {12258,18992}, {12326,19000}, {12345,19008}, {12346,19010}, {12347,19018}, {12348,19024}, {12349,19026}, {12350,19028}, {12351,19030}, {12352,19032}, {12353,19034}, {12354,19038}, {12356,19048}, {12357,19050}, {13676,13761}, {13847,14061}, {18969,18996}
X(19058) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 671, 19057), (671, 8593, 9883)
The reciprocal orthologic center of these triangles is X(12112)
X(19059) lies on these lines: {2,13969}, {3,19111}, {4,19043}, {6,74}, {30,19051}, {110,372}, {113,3069}, {125,1587}, {146,7586}, {371,10817}, {381,13979}, {399,6395}, {485,15059}, {541,19053}, {542,19108}, {631,8998}, {690,19055}, {1152,15035}, {1511,6398}, {1539,13785}, {1588,2777}, {2771,19112}, {3028,19037}, {3068,6699}, {3070,14644}, {3071,10721}, {3299,10065}, {3301,10081}, {3311,12041}, {3312,5663}, {3594,14094}, {5411,12133}, {5972,13935}, {6396,10818}, {6410,15036}, {6417,15041}, {6418,10620}, {6419,15021}, {6420,15054}, {6426,15034}, {6454,15020}, {6459,16111}, {6460,17702}, {6560,10733}, {7582,12244}, {7583,15061}, {7584,7728}, {7585,8994}, {7687,19039}, {7733,8416}, {7968,7978}, {8674,19081}, {9517,19093}, {9904,19003}, {9919,19005}, {9984,19011}, {10264,19052}, {10628,19095}, {11709,18991}, {11723,13959}, {12112,19001}, {12192,18993}, {12327,18999}, {12365,19007}, {12366,19009}, {12368,13936}, {12369,19017}, {12371,19023}, {12372,19025}, {12373,19027}, {12374,19029}, {12377,19031}, {12378,19033}, {12381,19047}, {12382,19049}, {13202,19041}, {13915,18512}, {13966,14643}, {17812,19015}
X(19059) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 74, 19060), (74, 10752, 7725), (372, 12375, 10820)
The reciprocal orthologic center of these triangles is X(12112)
X(19060) lies on these lines: {2,8994}, {3,19110}, {4,19044}, {6,74}, {110,371}, {113,3068}, {125,1588}, {146,7585}, {372,10818}, {381,13915}, {486,15059}, {541,19054}, {542,19109}, {631,13990}, {690,19056}, {1151,15035}, {1511,6221}, {1539,13665}, {1587,2777}, {2771,19113}, {3028,19038}, {3069,6699}, {3070,10721}, {3071,14644}, {3299,10081}, {3301,10065}, {3311,5663}, {3312,12041}, {3592,14094}, {5410,12133}, {5972,9540}, {6409,15036}, {6417,10620}, {6418,15041}, {6419,15054}, {6420,15021}, {6425,15034}, {6453,15020}, {6459,17702}, {6460,16111}, {6561,10733}, {7581,12244}, {7583,7728}, {7584,15061}, {7586,13969}, {7687,19040}, {7732,8396}, {7969,7978}, {8674,19082}, {8981,14643}, {9517,19094}, {9541,16163}, {9583,11720}, {9904,19004}, {9919,19006}, {9984,19012}, {10264,19051}, {10628,19096}, {11709,18992}, {11723,13902}, {12112,19002}, {12192,18994}, {12327,19000}, {12365,19008}, {12366,19010}, {12368,13883}, {12369,19018}, {12371,19024}, {12372,19026}, {12373,19028}, {12374,19030}, {12377,19032}, {12378,19034}, {12381,19048}, {12382,19050}, {13202,19042}, {13979,18510}, {17812,19016}
X(19060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 74, 19059), (74, 10752, 7726), (371, 12376, 10819)
The reciprocal orthologic center of these triangles is X(9833)
X(19061) lies on these lines: {2,13970}, {3,18997}, {5,6}, {30,19087}, {52,19041}, {372,12118}, {539,19053}, {615,8909}, {1069,19029}, {1147,3069}, {1587,9927}, {1588,13754}, {3068,5449}, {3157,19027}, {3299,10055}, {3301,10071}, {3311,12359}, {3536,6515}, {5054,8912}, {5411,12134}, {6146,19021}, {6418,12429}, {6458,10898}, {6459,7689}, {6460,17702}, {7505,11447}, {7582,11411}, {7585,13909}, {7968,9933}, {9820,13951}, {9833,11266}, {9896,19003}, {9908,19005}, {9923,19011}, {9928,13936}, {10116,18924}, {12038,13935}, {12164,18510}, {12193,18993}, {12235,19039}, {12259,18991}, {12328,18999}, {12415,19007}, {12418,19017}, {12422,19023}, {12423,19025}, {12426,19031}, {12427,19033}, {12428,19037}, {12430,19047}, {12431,19049}, {13383,17819}, {17834,19015}, {18970,18995}
X(19061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 68, 19062), (486, 10665, 5654)
The reciprocal orthologic center of these triangles is X(9833)
X(19062) lies on these lines: {2,13909}, {3,18998}, {5,6}, {30,19088}, {52,19042}, {371,12118}, {539,19054}, {1069,19030}, {1147,3068}, {1587,13754}, {1588,9927}, {3069,5449}, {3157,19028}, {3299,10071}, {3301,10055}, {3312,12359}, {3535,6515}, {5410,12134}, {6146,19022}, {6417,12429}, {6457,10897}, {6459,17702}, {6460,7689}, {7505,11448}, {7581,11411}, {7586,13970}, {7969,9933}, {8976,9820}, {9540,12038}, {9833,11265}, {9896,19004}, {9908,19006}, {9923,19012}, {9928,13883}, {10116,18923}, {12164,18512}, {12193,18994}, {12235,19040}, {12259,18992}, {12328,19000}, {12415,19008}, {12416,19010}, {12418,19018}, {12422,19024}, {12423,19026}, {12426,19032}, {12427,19034}, {12428,19038}, {12430,19048}, {12431,19050}, {13383,17820}, {17834,19016}, {18970,18996}
X(19062) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 68, 19061), (485, 10666, 5654)
The reciprocal orthologic center of these triangles is X(3)
X(19063) lies on these lines: {6,98}, {511,19053}, {2782,19057}, {3069,15819}, {3312,19091}, {6194,7586}, {6419,7786}, {6427,11272}, {6428,14881}, {7582,7709}, {7584,7697}, {8992,13939}, {18971,18995}, {19089,19116}
X(19063) = {X(6), X(262)}-harmonic conjugate of X(19064)
The reciprocal orthologic center of these triangles is X(3)
X(19064) lies on these lines: {6,98}, {511,19054}, {2782,19058}, {3068,15819}, {3311,19092}, {6194,7585}, {6420,7786}, {6427,14881}, {6428,11272}, {7581,7709}, {7583,7697}, {13886,13983}, {18971,18996}, {19090,19117}
X(19064) = {X(6), X(262)}-harmonic conjugate of X(19063)
The reciprocal orthologic center of these triangles is X(10)
X(19065) lies on these lines: {1,1123}, {2,7969}, {6,8}, {10,3068}, {40,6459}, {145,7586}, {355,1587}, {371,5657}, {372,944}, {388,2362}, {485,5818}, {486,5603}, {515,1703}, {517,1588}, {519,18992}, {590,9780}, {605,5255}, {606,5247}, {615,3616}, {758,19079}, {938,3298}, {952,3312}, {958,19000}, {962,3071}, {1125,13947}, {1145,19113}, {1152,5731}, {1335,18391}, {1376,19014}, {1385,13935}, {1388,18966}, {1482,7584}, {1698,8983}, {1702,11362}, {1788,2067}, {1999,13458}, {2098,19029}, {2099,19027}, {2802,19077}, {3189,5416}, {3299,12647}, {3303,13940}, {3311,5690}, {3476,6502}, {3486,5414}, {3576,13975}, {3579,9541}, {3617,7585}, {3622,13941}, {3679,13883}, {3913,18999}, {5411,12135}, {5413,7718}, {5550,8252}, {5554,19048}, {5599,19010}, {5600,19008}, {5790,7583}, {5844,19116}, {5901,13951}, {6361,6561}, {6395,18526}, {6418,12645}, {6684,9583}, {7582,12245}, {8148,18510}, {9615,10164}, {10246,13966}, {10283,13993}, {10595,13939}, {10912,19023}, {10944,18995}, {10950,19037}, {12195,18993}, {12410,19005}, {12454,19007}, {12455,19009}, {12495,19011}, {12513,19013}, {12626,19017}, {12635,19025}, {12636,19031}, {12637,19033}, {12648,19047}, {12649,19049}, {13665,18357}, {13904,18395}, {13954,15950}, {13976,16173}, {14839,19089}, {15863,19078}, {16210,19018}, {18493,18762}
X(19065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3069, 13959), (1, 7090, 6351), (1, 13936, 3069), (2, 7969, 13902), (6, 8, 19066), (10, 18991, 3068), (145, 7586, 7968), (3617, 7585, 13911), (3679, 19004, 13883), (7969, 13973, 2), (13883, 19004, 19054)
The reciprocal orthologic center of these triangles is X(10)
X(19066) lies on these lines: {1,1336}, {2,7968}, {6,8}, {10,3069}, {40,6460}, {145,7585}, {355,1588}, {371,944}, {372,5657}, {388,16232}, {485,5603}, {486,5818}, {515,1702}, {517,1587}, {519,18991}, {590,3616}, {605,5247}, {606,5255}, {615,9780}, {758,19080}, {938,3297}, {952,3311}, {958,18999}, {962,3070}, {1124,18391}, {1125,13893}, {1145,19112}, {1151,5731}, {1376,19013}, {1385,9540}, {1388,18965}, {1482,7583}, {1698,13971}, {1703,11362}, {1788,6502}, {1999,13425}, {2066,3486}, {2067,3476}, {2098,19030}, {2099,19028}, {2802,19078}, {3189,5415}, {3299,10573}, {3301,12647}, {3303,13887}, {3312,5690}, {3576,13912}, {3617,7586}, {3622,8972}, {3679,13936}, {3913,19000}, {4297,9616}, {5410,12135}, {5412,7718}, {5550,8253}, {5554,19047}, {5599,19009}, {5600,19007}, {5790,7584}, {5844,19117}, {5882,9583}, {5901,8976}, {6361,6560}, {6417,12645}, {7581,12245}, {8148,18512}, {8981,10246}, {9541,18481}, {10283,13925}, {10595,13886}, {10912,19024}, {10944,18996}, {10950,19038}, {12195,18994}, {12410,19006}, {12454,19008}, {12455,19010}, {12495,19012}, {12513,19014}, {12626,19018}, {12635,19026}, {12636,19032}, {12637,19034}, {12648,19048}, {12649,19050}, {13785,18357}, {13897,15950}, {13962,18395}, {14839,19090}, {15863,19077}, {16210,19017}, {18493,18538}
X(19066) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3068, 13902), (1, 13883, 3068), (1, 14121, 6352), (2, 7968, 13959), (6, 8, 19065), (10, 18992, 3069), (145, 7585, 7969), (3617, 7586, 13973), (3679, 19003, 13936), (7968, 13911, 2), (13936, 19003, 19053)
The reciprocal orthologic center of these triangles is X(40)
X(19067) lies on these lines: {2,13974}, {6,84}, {372,1490}, {515,1703}, {971,3312}, {1124,12705}, {1158,1702}, {1587,6245}, {1709,3299}, {2829,19077}, {3068,6705}, {3069,6260}, {3301,10085}, {5411,12136}, {5450,9583}, {6001,18992}, {6259,7584}, {6418,12684}, {7582,12246}, {7585,8987}, {7968,7971}, {7992,19003}, {9910,19005}, {12114,18991}, {12196,18993}, {12330,18999}, {12456,19007}, {12457,19009}, {12496,19011}, {12608,13964}, {12667,13936}, {12668,19017}, {12676,19023}, {12677,19025}, {12678,19027}, {12679,19029}, {12680,19037}, {12686,19047}, {12687,19049}, {12688,18995}, {13883,14647}, {13947,18242}, {18237,19013}, {18245,19031}, {18246,19033}
X(19067) = {X(6), X(84)}-harmonic conjugate of X(19068)
The reciprocal orthologic center of these triangles is X(40)
X(19068) lies on these lines: {2,8987}, {6,84}, {371,1490}, {515,1702}, {971,3311}, {1158,1703}, {1335,12705}, {1588,6245}, {1709,3301}, {2829,19078}, {3068,6260}, {3069,6705}, {3299,10085}, {5410,12136}, {6001,18991}, {6259,7583}, {6261,9583}, {6417,12684}, {6796,9582}, {7581,12246}, {7586,13974}, {7969,7971}, {7992,19004}, {9616,11500}, {9910,19006}, {12114,18992}, {12196,18994}, {12330,19000}, {12456,19008}, {12457,19010}, {12496,19012}, {12608,13906}, {12667,13883}, {12668,19018}, {12676,19024}, {12677,19026}, {12678,19028}, {12679,19030}, {12680,19038}, {12686,19048}, {12687,19050}, {12688,18996}, {13893,18242}, {13936,14647}, {18237,19014}, {18245,19032}, {18246,19034}
X(19068) = {X(6), X(84)}-harmonic conjugate of X(19067)
The reciprocal orthologic center of these triangles is X(3)
X(19069) lies on these lines: {6,17}, {533,19053}, {628,7586}, {630,3069}, {3068,6674}, {3312,19075}, {6418,16628}, {7584,16627}, {10612,19076}, {11740,18991}, {18972,18995}, {19073,19116}
X(19069) = {X(6), X(18)}-harmonic conjugate of X(19072)
The reciprocal orthologic center of these triangles is X(3)
X(19070) lies on these lines: {6,17}, {532,19054}, {627,7585}, {629,3068}, {3069,6673}, {3311,19074}, {6417,16629}, {7583,16626}, {10611,19073}, {11739,18992}, {18973,18996}, {19076,19117}
X(19070) = {X(6), X(17)}-harmonic conjugate of X(19071)
The reciprocal orthologic center of these triangles is X(3)
X(19071) lies on these lines: {6,17}, {532,19053}, {627,7586}, {629,3069}, {3068,6673}, {3312,19073}, {6418,16629}, {7584,16626}, {10611,19074}, {11739,18991}, {18973,18995}, {19075,19116}
X(19071) = {X(6), X(17)}-harmonic conjugate of X(19070)
The reciprocal orthologic center of these triangles is X(3)
X(19072) lies on these lines: {6,17}, {533,19054}, {628,7585}, {630,3068}, {3069,6674}, {3311,19076}, {6417,16628}, {7583,16627}, {10612,19075}, {11740,18992}, {18972,18996}, {19074,19117}
X(19072) = {X(6), X(18)}-harmonic conjugate of X(19069)
The reciprocal orthologic center of these triangles is X(3)
X(19073) lies on these lines: {2,13982}, {6,13}, {372,5473}, {530,19053}, {531,19057}, {616,7586}, {618,3069}, {619,19109}, {1587,5478}, {3068,6669}, {3299,10062}, {3301,10078}, {3311,6771}, {3312,19071}, {5411,12142}, {5459,19054}, {5617,7584}, {6302,13765}, {6418,13103}, {6428,16001}, {6770,7582}, {7585,13917}, {7968,7975}, {9901,19003}, {9916,19005}, {9982,19011}, {10611,19070}, {11705,18991}, {12205,18993}, {12337,18999}, {12472,19007}, {12473,19009}, {12781,13936}, {12793,19017}, {12922,19023}, {12932,19025}, {12942,19027}, {12952,19029}, {12990,19031}, {12991,19033}, {13076,19037}, {13105,19047}, {13107,19049}, {13646,13825}, {13916,14061}, {18974,18995}, {19069,19116}
X(19073) = {X(6), X(13)}-harmonic conjugate of X(19074)
The reciprocal orthologic center of these triangles is X(3)
X(19074) lies on these lines: {2,13917}, {6,13}, {371,5473}, {530,19054}, {531,19058}, {616,7585}, {618,3068}, {619,19108}, {1588,5478}, {3069,6669}, {3299,10078}, {3301,10062}, {3311,19070}, {3312,6771}, {5410,12142}, {5459,19053}, {5617,7583}, {6306,13646}, {6417,13103}, {6427,16001}, {6770,7581}, {7586,13982}, {7969,7975}, {9901,19004}, {9916,19006}, {9982,19012}, {10611,19071}, {11705,18992}, {12205,18994}, {12337,19000}, {12472,19008}, {12473,19010}, {12781,13883}, {12793,19018}, {12922,19024}, {12932,19026}, {12942,19028}, {12952,19030}, {12990,19032}, {12991,19034}, {13076,19038}, {13105,19048}, {13107,19050}, {13705,13765}, {13981,14061}, {18974,18996}, {19072,19117}
X(19074) = {X(6), X(13)}-harmonic conjugate of X(19073)
The reciprocal orthologic center of these triangles is X(14)
X(19075) lies on these lines: {2,13981}, {6,13}, {372,5474}, {530,19057}, {531,19053}, {617,7586}, {618,19109}, {619,3069}, {1587,5479}, {3068,6670}, {3299,10061}, {3301,10077}, {3311,6774}, {3312,19069}, {5411,12141}, {5460,19054}, {5613,7584}, {6303,13764}, {6418,13102}, {6428,16002}, {6773,7582}, {7585,13916}, {7968,7974}, {9900,19003}, {9915,19005}, {9981,19011}, {10612,19072}, {11706,18991}, {12204,18993}, {12336,18999}, {12470,19007}, {12471,19009}, {12780,13936}, {12792,19017}, {12921,19023}, {12931,19025}, {12941,19027}, {12951,19029}, {12988,19031}, {12989,19033}, {13075,19037}, {13104,19047}, {13106,19049}, {13645,13823}, {13917,14061}, {18975,18995}, {19071,19116}
X(19075) = {X(6), X(14)}-harmonic conjugate of X(19076)
The reciprocal orthologic center of these triangles is X(14)
X(19076) lies on these lines: {2,13916}, {6,13}, {371,5474}, {530,19058}, {531,19054}, {617,7585}, {618,19108}, {619,3068}, {1588,5479}, {3069,6670}, {3299,10077}, {3301,10061}, {3311,19072}, {3312,6774}, {5410,12141}, {5460,19053}, {5613,7583}, {6307,13645}, {6417,13102}, {6427,16002}, {6773,7581}, {7586,13981}, {7969,7974}, {9900,19004}, {9915,19006}, {9981,19012}, {10612,19069}, {11706,18992}, {12204,18994}, {12336,19000}, {12470,19008}, {12471,19010}, {12780,13883}, {12792,19018}, {12921,19024}, {12931,19026}, {12941,19028}, {12951,19030}, {12988,19032}, {12989,19034}, {13075,19038}, {13104,19048}, {13106,19050}, {13703,13764}, {13982,14061}, {18975,18996}, {19070,19117}
X(19076) = {X(6), X(14)}-harmonic conjugate of X(19075)
The reciprocal orthologic center of these triangles is X(3)
X(19077) lies on these lines: {2,13976}, {6,80}, {10,19113}, {11,18991}, {100,13936}, {214,3069}, {372,12119}, {515,19081}, {952,18992}, {1588,2800}, {1698,13922}, {1703,5840}, {2802,19065}, {2829,19067}, {3035,13947}, {3068,6702}, {3299,10057}, {3301,10073}, {3311,12619}, {3576,13977}, {5411,12137}, {6224,7586}, {6265,7584}, {6418,12747}, {6713,9583}, {7582,12247}, {7585,8988}, {7968,7972}, {7969,16173}, {9897,19003}, {9912,19005}, {10265,19082}, {12198,18993}, {12331,18999}, {12460,19007}, {12461,19009}, {12498,19011}, {12611,13785}, {12729,19017}, {12737,19023}, {12738,19025}, {12739,19027}, {12740,19029}, {12741,19031}, {12742,19033}, {12743,19037}, {12749,19047}, {12750,19049}, {12773,19013}, {13991,15015}, {15863,19066}, {18976,18995}
X(19077) = {X(6), X(80)}-harmonic conjugate of X(19078)
The reciprocal orthologic center of these triangles is X(3)
X(19078) lies on these lines: {2,8988}, {6,80}, {10,19112}, {11,18992}, {100,13883}, {214,3068}, {371,12119}, {515,19082}, {952,18991}, {1587,2800}, {1698,13991}, {1702,5840}, {2771,19052}, {2802,19066}, {2829,19068}, {3035,13893}, {3069,6702}, {3299,10073}, {3301,10057}, {3312,12619}, {3576,13913}, {5410,12137}, {6224,7585}, {6265,7583}, {6417,12747}, {7581,12247}, {7586,13976}, {7968,16173}, {7969,7972}, {9897,19004}, {9912,19006}, {10265,19081}, {12198,18994}, {12331,19000}, {12460,19008}, {12461,19010}, {12498,19012}, {12611,13665}, {12729,19018}, {12737,19024}, {12738,19026}, {12739,19028}, {12740,19030}, {12741,19032}, {12742,19034}, {12743,19038}, {12749,19048}, {12750,19050}, {12773,19014}, {13922,15015}, {15863,19065}, {18976,18996}
X(19078) = {X(6), X(80)}-harmonic conjugate of X(19077)
The reciprocal orthologic center of these triangles is X(3)
X(19079) lies on these lines: {2,16149}, {6,79}, {21,13971}, {30,18992}, {372,16113}, {442,13893}, {758,19065}, {1587,16125}, {3068,6701}, {3069,3647}, {3299,16152}, {3301,16153}, {3648,7586}, {3649,18991}, {3652,7584}, {5411,16114}, {5441,7968}, {6175,13883}, {6418,16150}, {7582,16116}, {7585,16148}, {11684,13936}, {13743,19013}, {13947,18253}, {16115,18993}, {16117,18999}, {16118,19003}, {16121,19007}, {16122,19009}, {16123,19011}, {16129,19017}, {16138,19023}, {16139,19025}, {16140,19027}, {16141,19029}, {16142,19037}, {16154,19047}, {16155,19049}, {16161,19031}, {16162,19033}, {18977,18995}
X(19079) = {X(6), X(79)}-harmonic conjugate of X(19080)
The reciprocal orthologic center of these triangles is X(3)
X(19080) lies on these lines: {2,16148}, {6,79}, {21,8983}, {30,18991}, {371,16113}, {442,13947}, {758,19066}, {1588,16125}, {2771,19052}, {3068,3647}, {3069,6701}, {3299,16153}, {3301,16152}, {3648,7585}, {3649,18992}, {3652,7583}, {5410,16114}, {5441,7969}, {6175,13936}, {6417,16150}, {7581,16116}, {7586,16149}, {11684,13883}, {13743,19014}, {13893,18253}, {16115,18994}, {16117,19000}, {16118,19004}, {16119,19006}, {16121,19008}, {16122,19010}, {16123,19012}, {16129,19018}, {16138,19024}, {16139,19026}, {16140,19028}, {16141,19030}, {16142,19038}, {16154,19048}, {16155,19050}, {16161,19032}, {16162,19034}, {18977,18996}
X(19080) = {X(6), X(79)}-harmonic conjugate of X(19079)
The reciprocal orthologic center of these triangles is X(40)
X(19081) lies on these lines: {2,13977}, {3,19113}, {6,104}, {11,1587}, {100,372}, {119,3069}, {153,7586}, {515,19077}, {631,13922}, {952,3312}, {1317,19037}, {1588,2829}, {1703,2802}, {1768,19003}, {2771,19110}, {2783,19108}, {2787,19055}, {2800,18992}, {2806,19093}, {2831,19114}, {3035,13935}, {3068,6713}, {3071,10728}, {3299,10058}, {3301,10074}, {5411,12138}, {5587,13976}, {5840,6460}, {6395,12331}, {6418,12773}, {6560,10724}, {7582,12248}, {7584,10742}, {7585,13913}, {7968,10698}, {8416,13270}, {8674,19059}, {9913,19005}, {10265,19078}, {11715,18991}, {11729,13959}, {12199,18993}, {12332,18999}, {12462,19007}, {12463,19009}, {12499,19011}, {12751,13936}, {12752,19017}, {12761,19023}, {12762,19025}, {12763,19027}, {12764,19029}, {12765,19031}, {12766,19033}, {12775,19047}, {12776,19049}, {13942,15017}
X(19081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 104, 19082), (104, 10759, 12753)
The reciprocal orthologic center of these triangles is X(40)
X(19082) lies on these lines: {2,13913}, {3,19112}, {6,104}, {11,1588}, {100,371}, {119,3068}, {153,7585}, {214,9583}, {515,19078}, {631,13991}, {952,3311}, {1317,19038}, {1587,2829}, {1702,2802}, {1768,19004}, {2771,19111}, {2783,19109}, {2787,19056}, {2800,18991}, {2806,19094}, {2831,19115}, {3035,9540}, {3069,6713}, {3070,10728}, {3299,10074}, {3301,10058}, {5410,12138}, {5587,8988}, {5840,6459}, {6417,12773}, {6561,10724}, {7581,12248}, {7583,10742}, {7586,13977}, {7969,10698}, {8396,13269}, {8674,19060}, {9913,19006}, {10265,19077}, {11715,18992}, {11729,13902}, {12199,18994}, {12332,19000}, {12462,19008}, {12463,19010}, {12499,19012}, {12751,13883}, {12752,19018}, {12761,19024}, {12762,19026}, {12763,19028}, {12764,19030}, {12765,19032}, {12766,19034}, {12775,19048}, {12776,19050}, {13888,15017}
X(19082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 104, 19081), (104, 10759, 12754)
The reciprocal orthologic center of these triangles is X(12241)
X(19083) lies on these lines: {6,17837}, {12241,19019}, {18978,18995}
The reciprocal orthologic center of these triangles is X(12241)
X(19084) lies on these lines: {6,17837}, {12241,19020}, {18978,18996}
The reciprocal orthologic center of these triangles is X(40)
X(19085) lies on these lines: {2,13978}, {6,7160}, {372,12120}, {1587,12599}, {3069,12864}, {3299,10059}, {3301,10075}, {5411,12139}, {6418,12872}, {7582,12249}, {7584,12856}, {7585,13914}, {7586,9874}, {7968,8000}, {9898,19003}, {12200,18993}, {12260,18991}, {12333,18999}, {12411,19005}, {12464,19007}, {12465,19009}, {12500,19011}, {12777,13936}, {12789,19017}, {12857,19023}, {12858,19025}, {12859,19027}, {12860,19029}, {12861,19031}, {12862,19033}, {12863,19037}, {12874,19047}, {12875,19049}, {18979,18995}
X(19085) = {X(6), X(7160)}-harmonic conjugate of X(19086)
The reciprocal orthologic center of these triangles is X(40)
X(19086) lies on these lines: {2,13914}, {6,7160}, {371,12120}, {1588,12599}, {3068,12864}, {3299,10075}, {3301,10059}, {5410,12139}, {6417,12872}, {7581,12249}, {7583,12856}, {7585,9874}, {7586,13978}, {7969,8000}, {9898,19004}, {12200,18994}, {12260,18992}, {12333,19000}, {12411,19006}, {12464,19008}, {12465,19010}, {12500,19012}, {12777,13883}, {12789,19018}, {12857,19024}, {12858,19026}, {12859,19028}, {12860,19030}, {12861,19032}, {12862,19034}, {12863,19038}, {12874,19048}, {18979,18996}
X(19086) = {X(6), X(7160)}-harmonic conjugate of X(19085)
The reciprocal orthologic center of these triangles is X(4)
X(19087) lies on these lines: {2,13980}, {3,17819}, {4,19039}, {6,64}, {30,19061}, {154,1152}, {221,5414}, {371,10606}, {372,1498}, {1151,8567}, {1192,5412}, {1204,5410}, {1503,6460}, {1587,6247}, {1588,15311}, {1703,6001}, {1853,3070}, {1854,2362}, {2192,6502}, {2777,19051}, {2883,3069}, {3068,6696}, {3071,5895}, {3093,9786}, {3299,10060}, {3301,10076}, {3311,3357}, {3312,6000}, {3594,12970}, {5411,11381}, {5413,15811}, {5878,7584}, {5894,6459}, {5925,6561}, {6225,7586}, {6285,18995}, {6395,12315}, {6396,17821}, {6398,6759}, {6409,11241}, {6410,10533}, {6418,13093}, {6426,10534}, {6449,11204}, {6450,10282}, {6456,11202}, {7355,19037}, {7582,12250}, {7585,8991}, {7968,7973}, {9899,19003}, {9914,19005}, {11598,19111}, {12202,18993}, {12262,18991}, {12335,18999}, {12468,19007}, {12469,19009}, {12502,19011}, {12779,13936}, {12791,19017}, {12920,19023}, {12930,19025}, {12940,19027}, {12950,19029}, {12986,19031}, {12987,19033}, {13094,19047}, {13095,19049}, {13288,17812}, {13935,16252}
X(19087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 64, 19088), (372, 1498, 17820), (1152, 12964, 154)
The reciprocal orthologic center of these triangles is X(4)
X(19088) lies on these lines: {2,8991}, {3,17820}, {4,19040}, {6,64}, {30,19062}, {154,1151}, {221,2066}, {371,1498}, {372,10606}, {1152,8567}, {1192,5413}, {1204,5411}, {1503,6459}, {1587,15311}, {1588,6247}, {1660,9686}, {1702,6001}, {1853,3071}, {1854,16232}, {2067,2192}, {2777,19052}, {2883,3068}, {2917,9683}, {3069,6696}, {3070,5895}, {3092,9786}, {3299,10076}, {3301,10060}, {3311,6000}, {3312,3357}, {3592,12964}, {5410,11381}, {5412,15811}, {5878,7583}, {5894,6460}, {5925,6560}, {6221,6759}, {6225,7585}, {6285,18996}, {6409,10534}, {6410,11242}, {6417,13093}, {6425,10533}, {6449,10282}, {6450,11204}, {6455,11202}, {7355,19038}, {7581,12250}, {7586,13980}, {7969,7973}, {9540,16252}, {9899,19004}, {9914,19006}, {11598,19110}, {12202,18994}, {12262,18992}, {12335,19000}, {12468,19008}, {12469,19010}, {12502,19012}, {12779,13883}, {12791,19018}, {12920,19024}, {12930,19026}, {12940,19028}, {12950,19030}, {12986,19032}, {12987,19034}, {13094,19048}, {13095,19050}, {13287,17812}
X(19088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 64, 19087), (371, 1498, 17819), (1151, 12970, 154)
The reciprocal orthologic center of these triangles is X(3)
X(19089) lies on these lines: {2,13983}, {3,13938}, {6,76}, {39,3069}, {183,13885}, {194,6463}, {262,486}, {372,11257}, {384,18993}, {385,18994}, {511,1588}, {538,19053}, {615,7786}, {637,2548}, {730,18992}, {1587,6248}, {2782,3312}, {3068,3934}, {3095,7584}, {3299,10063}, {3301,10079}, {5188,6459}, {5411,12143}, {5969,19057}, {5976,19109}, {6318,13766}, {6418,13108}, {7582,12251}, {7583,7697}, {7585,8992}, {7968,7976}, {9466,19054}, {9540,15819}, {9902,19003}, {9917,19005}, {9983,19011}, {11171,13966}, {11272,13951}, {12263,18991}, {12338,18999}, {12474,19007}, {12475,19009}, {12782,13936}, {12794,19017}, {12836,19029}, {12837,19027}, {12923,19023}, {12933,19025}, {12992,19031}, {13077,19037}, {13109,19047}, {13110,19049}, {13331,13972}, {13334,13935}, {13647,13827}, {13785,14881}, {14839,19065}, {18982,18995}, {19063,19116}
X(19089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 76, 19090), (486, 3103, 262)
The reciprocal orthologic center of these triangles is X(3)
X(19090) lies on these lines: {2,8992}, {3,13885}, {6,76}, {39,3068}, {183,13938}, {194,6462}, {262,485}, {371,11257}, {384,18994}, {385,18993}, {511,1587}, {538,19054}, {590,7786}, {638,2548}, {730,18991}, {1588,6248}, {2782,3311}, {3069,3934}, {3095,7583}, {3299,10079}, {3301,10063}, {5188,6460}, {5410,12143}, {5969,19058}, {5976,19108}, {6314,13647}, {6417,13108}, {7581,12251}, {7584,7697}, {7586,13983}, {7969,7976}, {8976,11272}, {8981,11171}, {9466,19053}, {9540,13334}, {9902,19004}, {9917,19006}, {9983,19012}, {12263,18992}, {12338,19000}, {12474,19008}, {12475,19010}, {12782,13883}, {12794,19018}, {12836,19030}, {12837,19028}, {12923,19024}, {12933,19026}, {12993,19034}, {13077,19038}, {13109,19048}, {13110,19050}, {13331,13910}, {13665,14881}, {13707,13766}, {13935,15819}, {14839,19066}, {18982,18996}, {19064,19117}
X(19090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 76, 19089), (485, 3102, 262)
The reciprocal orthologic center of these triangles is X(3)
X(19091) lies on these lines: {2,13984}, {6,76}, {371,9751}, {372,12122}, {754,19053}, {1587,6249}, {2896,7586}, {3068,6704}, {3069,6292}, {3299,10064}, {3301,10080}, {3312,19063}, {5411,12144}, {6287,7584}, {6308,13938}, {6317,13767}, {6418,13111}, {7582,12252}, {7585,8993}, {7968,7977}, {8290,19109}, {9903,19003}, {9918,19005}, {12206,18993}, {12264,18991}, {12339,18999}, {12476,19007}, {12477,19009}, {12783,13936}, {12795,19017}, {12924,19023}, {12934,19025}, {12944,19027}, {12954,19029}, {12994,19031}, {12995,19033}, {13078,19037}, {13112,19047}, {13113,19049}, {13648,13829}, {18983,18995}, {19055,19116}
X(19091) = {X(6), X(83)}-harmonic conjugate of X(19092)
The reciprocal orthologic center of these triangles is X(3)
X(19092) lies on these lines: {2,8993}, {6,76}, {371,12122}, {372,9751}, {754,19054}, {1588,6249}, {2896,7585}, {3068,6292}, {3069,6704}, {3299,10080}, {3301,10064}, {3311,19064}, {5410,12144}, {6287,7583}, {6308,13885}, {6313,13648}, {6417,13111}, {7581,12252}, {7586,13984}, {7969,7977}, {8290,19108}, {9903,19004}, {9918,19006}, {12206,18994}, {12264,18992}, {12339,19000}, {12476,19008}, {12477,19010}, {12783,13883}, {12795,19018}, {12924,19024}, {12934,19026}, {12944,19028}, {12954,19030}, {12994,19032}, {12995,19034}, {13078,19038}, {13112,19048}, {13113,19050}, {13709,13767}, {18983,18996}, {19056,19117}
X(19092) = {X(6), X(83)}-harmonic conjugate of X(19091)
The reciprocal orthologic center of these triangles is X(4)
X(19093) lies on these lines: {2,13985}, {3,19115}, {6,1297}, {112,372}, {127,1587}, {132,3069}, {631,13923}, {2781,19110}, {2794,6460}, {2799,19055}, {2806,19081}, {2831,19112}, {3299,13116}, {3301,13117}, {3312,19114}, {3320,19037}, {5411,12145}, {6020,18995}, {6395,13310}, {6418,13115}, {6560,10735}, {6720,13935}, {7582,12253}, {7584,12918}, {7585,13918}, {7586,12384}, {7968,13099}, {8416,13283}, {9517,19059}, {9530,19053}, {12207,18993}, {12265,18991}, {12340,18999}, {12408,19003}, {12413,19005}, {12478,19007}, {12479,19009}, {12503,19011}, {12784,13936}, {12796,19017}, {12925,19023}, {12935,19025}, {12945,19027}, {12955,19029}, {12996,19031}, {12997,19033}, {13118,19047}, {13119,19049}, {13785,19160}, {19013,19159}
The reciprocal orthologic center of these triangles is X(4)
X(19094) lies on these lines: {2,13918}, {3,19114}, {6,1297}, {112,371}, {127,1588}, {132,3068}, {631,13992}, {2781,19111}, {2794,6459}, {2799,19056}, {2806,19082}, {2831,19113}, {3299,13117}, {3301,13116}, {3311,19115}, {3320,19038}, {5410,12145}, {6020,18996}, {6417,13115}, {6561,10735}, {6720,9540}, {7581,12253}, {7583,12918}, {7585,12384}, {7586,13985}, {7969,13099}, {8396,13282}, {9517,19060}, {9530,19054}, {9541,14689}, {9583,11722}, {12207,18994}, {12265,18992}, {12340,19000}, {12408,19004}, {12413,19006}, {12478,19008}, {12479,19010}, {12503,19012}, {12784,13883}, {12796,19018}, {12925,19024}, {12935,19026}, {12945,19028}, {12955,19030}, {12996,19032}, {12997,19034}, {13118,19048}, {13119,19050}, {13665,19160}, {19014,19159}
The reciprocal orthologic center of these triangles is X(4)
X(19095) lies on these lines: {2,13986}, {4,19045}, {6,24}, {195,6418}, {372,7691}, {539,19053}, {1154,3312}, {1209,3069}, {1493,6428}, {1587,3574}, {1588,18400}, {2888,7586}, {2914,19001}, {3068,6689}, {3299,10066}, {3301,10082}, {3311,10610}, {5411,11576}, {6288,7584}, {6395,12307}, {6420,12971}, {7581,19043}, {7582,12254}, {7585,8995}, {7968,7979}, {8254,19117}, {9905,19003}, {9920,19005}, {9985,19011}, {10628,19059}, {11597,19111}, {11804,19052}, {12208,18993}, {12242,19039}, {12266,18991}, {12341,18999}, {12480,19007}, {12481,19009}, {12785,13936}, {12797,19017}, {12926,19023}, {12936,19025}, {12946,19027}, {12956,19029}, {12998,19031}, {12999,19033}, {13079,19037}, {13121,19047}, {13122,19049}, {13565,13951}, {17824,19015}, {18984,18995}, {19051,19110}
X(19095) = {X(6), X(54)}-harmonic conjugate of X(19096)
The reciprocal orthologic center of these triangles is X(4)
X(19096) lies on these lines: {2,8995}, {4,19046}, {6,24}, {195,6417}, {371,7691}, {539,19054}, {1154,3311}, {1209,3068}, {1493,6427}, {1587,18400}, {1588,3574}, {2888,7585}, {2914,19002}, {3069,6689}, {3299,10082}, {3301,10066}, {3312,10610}, {5410,11576}, {6288,7583}, {6419,12965}, {7581,12254}, {7582,19044}, {7586,13986}, {7969,7979}, {8254,19116}, {8976,13565}, {9905,19004}, {9920,19006}, {9985,19012}, {10628,19060}, {11597,19110}, {11804,19051}, {12208,18994}, {12242,19040}, {12266,18992}, {12341,19000}, {12480,19008}, {12481,19010}, {12785,13883}, {12797,19018}, {12926,19024}, {12936,19026}, {12946,19028}, {12956,19030}, {12998,19032}, {12999,19034}, {13079,19038}, {13121,19048}, {13122,19050}, {17824,19016}, {18984,18996}, {19052,19111}
X(19096) = {X(6), X(54)}-harmonic conjugate of X(19095)
The reciprocal orthologic center of these triangles is X(79)
X(19097) lies on these lines: {2,13987}, {6,10266}, {372,12556}, {1587,12600}, {3069,13089}, {3299,13128}, {3301,13129}, {5411,12146}, {6418,13126}, {7582,12255}, {7584,12919}, {7585,13919}, {7586,12849}, {7968,13100}, {12209,18993}, {12267,18991}, {12342,18999}, {12409,19003}, {12414,19005}, {12482,19007}, {12483,19009}, {12504,19011}, {12786,13936}, {12798,19017}, {12927,19023}, {12937,19025}, {12947,19027}, {12957,19029}, {13000,19031}, {13001,19033}, {13080,19037}, {13130,19047}, {13131,19049}, {18985,18995}
The reciprocal orthologic center of these triangles is X(79)
X(19098) lies on these lines: {2,13919}, {6,10266}, {371,12556}, {1588,12600}, {3068,13089}, {3299,13129}, {3301,13128}, {5410,12146}, {6417,13126}, {7581,12255}, {7583,12919}, {7585,12849}, {7586,13987}, {7969,13100}, {12209,18994}, {12267,18992}, {12342,19000}, {12409,19004}, {12414,19006}, {12482,19008}, {12483,19010}, {12504,19012}, {12786,13883}, {12798,19018}, {12927,19024}, {12937,19026}, {12947,19028}, {12957,19030}, {13000,19032}, {13001,19034}, {13080,19038}, {13130,19048}, {13131,19050}, {18985,18996}
The reciprocal orthologic center of these triangles is X(13665)
X(19099) lies on these lines: {2,13988}, {6,1327}, {30,19102}, {372,13666}, {1587,13687}, {3069,13701}, {3299,13714}, {3301,13715}, {5306,6424}, {5309,19105}, {5411,13668}, {6418,13713}, {7582,13674}, {7584,13692}, {7585,13920}, {7586,13678}, {7968,13702}, {13662,13831}, {13667,18991}, {13672,18993}, {13675,18999}, {13679,19003}, {13680,19005}, {13682,19007}, {13683,19009}, {13685,19011}, {13688,13936}, {13689,19017}, {13693,19023}, {13694,19025}, {13695,19027}, {13696,19029}, {13697,19031}, {13698,19033}, {13699,19037}, {13711,13932}, {13712,13769}, {13716,19047}, {13717,19049}, {13834,13846}, {14232,14492}, {18986,18995}
The reciprocal orthologic center of these triangles is X(13665)
X(19100) lies on these lines: {2,13848}, {6,1327}, {30,19105}, {371,13786}, {1588,13807}, {3068,13821}, {3299,13838}, {3301,13837}, {5306,6423}, {5309,19102}, {5410,13788}, {6417,13836}, {7581,13794}, {7583,13812}, {7585,13798}, {7586,13849}, {7969,13822}, {13711,13847}, {13782,13832}, {13787,18992}, {13792,18994}, {13795,19000}, {13799,19004}, {13800,19006}, {13802,19008}, {13803,19010}, {13805,19012}, {13808,13883}, {13809,19018}, {13813,19024}, {13814,19026}, {13815,19028}, {13816,19030}, {13817,19032}, {13818,19034}, {13819,19038}, {13833,13835}, {13834,13850}, {13839,19048}, {13840,19050}, {14237,14492}, {18987,18996}
X(19100) = {X(6), X(1328)}-harmonic conjugate of X(19101)
The reciprocal orthologic center of these triangles is X(13785)
X(19101) lies on these lines: {2,13782}, {6,1327}, {30,19104}, {372,13786}, {1384,13835}, {1587,13807}, {3069,13821}, {3299,13837}, {3301,13838}, {5411,13788}, {6418,13836}, {7582,13794}, {7584,13812}, {7585,13848}, {7586,13798}, {7753,19103}, {7968,13822}, {11055,13789}, {11147,12158}, {13651,13850}, {13770,13847}, {13787,18991}, {13792,18993}, {13795,18999}, {13799,19003}, {13800,19005}, {13802,19007}, {13803,19009}, {13805,19011}, {13808,13936}, {13809,19017}, {13813,19023}, {13814,19025}, {13815,19027}, {13816,19029}, {13817,19031}, {13818,19033}, {13819,19037}, {13839,19047}, {13840,19049}, {18987,18995}
X(19101) = {X(6), X(1328)}-harmonic conjugate of X(19100)
The reciprocal orthologic center of these triangles is X(485)
X(19102) lies on these lines: {2,13880}, {5,6}, {30,19099}, {187,9681}, {372,7738}, {488,7586}, {491,7899}, {492,7905}, {615,13882}, {641,3069}, {1504,5418}, {1587,6250}, {3068,6118}, {3299,10068}, {3301,10084}, {3594,15048}, {3618,5490}, {5062,6560}, {5286,6420}, {5304,9757}, {5309,19100}, {5411,12148}, {5420,6422}, {6418,12602}, {6419,7735}, {6423,6561}, {7582,12257}, {7585,13879}, {7739,12969}, {7968,7981}, {9907,19003}, {9922,19005}, {9987,19011}, {12211,18993}, {12269,18991}, {12344,18999}, {12486,19007}, {12487,19009}, {12788,13936}, {12800,19017}, {12929,19023}, {12939,19025}, {12949,19027}, {12959,19029}, {13004,19031}, {13005,19033}, {13082,19037}, {13134,19047}, {13135,19049}, {14229,14853}, {18988,18995}
X(19102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 485, 19103), (6, 5305, 19105), (6, 13834, 13651), (6, 19116, 19104), (485, 19103, 13651), (7584, 14561, 486), (13834, 19103, 485)
The reciprocal orthologic center of these triangles is X(485)
X(19103) lies on these lines: {5,6}, {371,12124}, {488,7585}, {491,7909}, {641,3068}, {1504,6560}, {1588,6250}, {1992,5490}, {3069,6118}, {3299,10084}, {3301,10068}, {5062,5418}, {5410,12148}, {6417,12602}, {6431,18907}, {7581,12257}, {7586,13880}, {7753,19101}, {7969,7981}, {9907,19004}, {9922,19006}, {9987,19012}, {12211,18994}, {12269,18992}, {12344,19000}, {12486,19008}, {12487,19010}, {12788,13883}, {12800,19018}, {12929,19024}, {12939,19026}, {12949,19028}, {12959,19030}, {13004,19032}, {13005,19034}, {13082,19038}, {13134,19048}, {13135,19050}, {18988,18996}
X(19103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 485, 19102), (6, 13651, 13834), (6, 19117, 19105), (485, 19102, 13834), (6289, 7583, 485), (13651, 19102, 485)
The reciprocal orthologic center of these triangles is X(486)
X(19104) lies on these lines: {2,13933}, {5,6}, {30,19101}, {372,12123}, {487,7586}, {492,7909}, {642,3069}, {1505,6561}, {1587,6251}, {1992,5491}, {3068,6119}, {3299,10067}, {3301,10083}, {5058,5420}, {5411,12147}, {6418,12601}, {6432,18907}, {7582,12256}, {7585,13921}, {7968,7980}, {9906,19003}, {9921,19005}, {9986,19011}, {12210,18993}, {12268,18991}, {12343,18999}, {12484,19007}, {12485,19009}, {12787,13936}, {12799,19017}, {12928,19023}, {12938,19025}, {12948,19027}, {12958,19029}, {13002,19031}, {13003,19033}, {13081,19037}, {13132,19047}, {13133,19049}, {18989,18995}
X(19104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 486, 19105), (6, 13770, 13711), (6, 19116, 19102), (486, 19105, 13711), (6290, 7584, 486), (13770, 19105, 486)
The reciprocal orthologic center of these triangles is X(486)
X(19105) lies on these lines: {2,13921}, {5,6}, {30,19100}, {371,7738}, {487,7585}, {491,7905}, {492,7899}, {574,9680}, {590,13934}, {642,3068}, {1505,5420}, {1588,6251}, {3069,6119}, {3299,10083}, {3301,10067}, {3592,15048}, {3618,5491}, {5058,6561}, {5286,6419}, {5304,9758}, {5309,19099}, {5410,12147}, {5418,6421}, {6417,12601}, {6420,7735}, {6424,6560}, {7581,12256}, {7586,13933}, {7736,8960}, {7739,12962}, {7969,7980}, {8375,9681}, {9906,19004}, {9921,19006}, {9986,19012}, {12210,18994}, {12268,18992}, {12343,19000}, {12484,19008}, {12485,19010}, {12787,13883}, {12799,19018}, {12928,19024}, {12938,19026}, {12948,19028}, {12958,19030}, {13002,19032}, {13003,19034}, {13081,19038}, {13132,19048}, {13133,19050}, {14244,14853}, {18989,18996}
X(19105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 486, 19104), (6, 5305, 19102), (6, 13711, 13770), (6, 19117, 19103), (486, 19104, 13770), (7583, 14561, 485), (13711, 19104, 486)
The reciprocal orthologic center of these triangles is X(19073)
X(19106) lies on these lines: {2,12820}, {3,16808}, {4,16}, {5,10646}, {6,382}, {13,15}, {14,3830}, {17,1657}, {20,10645}, {61,3146}, {62,3627}, {381,11481}, {395,15687}, {530,621}, {546,5237}, {550,5350}, {623,5463}, {1250,3585}, {3091,5351}, {3200,14157}, {3411,3853}, {3457,10210}, {3529,5238}, {3534,12816}, {3543,5334}, {3861,16773}, {5059,5366}, {5073,5340}, {5076,16961}, {5352,15704}, {5611,16001}, {6240,10641}, {6777,10722}, {6778,13103}, {7051,10483}, {7728,10658}, {7937,11303}, {8597,12155}, {10634,18563}, {10654,15682}, {10657,10661}, {10675,10677}, {11475,18560}, {11515,12605}, {14269,16645}, {15681,16644}, {18468,18562}
X(19106) = reflection of X(5611) in X(16001)
X(19106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 16808, 16966), (4, 16, 16809), (6, 382, 19107), (6, 19107, 16964), (13, 15, 16960), (15, 5318, 13), (15, 16960, 16962), (16, 16809, 18), (20, 18582, 10645), (381, 11481, 16967), (382, 16965, 16964), (11481, 16967, 16242), (16965, 19107, 6)
The reciprocal orthologic center of these triangles is X(19074)
X(19107) lies on these lines: {2,12821}, {3,16809}, {4,15}, {5,10645}, {6,382}, {13,3830}, {14,16}, {18,1657}, {20,10646}, {61,3627}, {62,3146}, {381,11480}, {396,15687}, {531,622}, {546,5238}, {550,5349}, {624,5464}, {3091,5352}, {3201,14157}, {3412,3853}, {3529,5237}, {3534,12817}, {3543,5335}, {3583,7051}, {3585,10638}, {3861,16772}, {5059,5365}, {5073,5339}, {5076,16960}, {5351,15704}, {5615,16002}, {6240,10642}, {6777,13102}, {6778,10722}, {7728,10657}, {7937,11304}, {8597,12154}, {10635,18563}, {10653,15682}, {10658,10662}, {10676,10678}, {11476,18560}, {11516,12605}, {14269,16644}, {15681,16645}, {18470,18562}
X(19107) = reflection of X(5615) in X(16002)
X(19107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 16809, 16967), (4, 15, 16808), (6, 382, 19106), (6, 19106, 16965), (14, 16, 16961), (15, 16808, 17), (16, 5321, 14), (16, 16961, 16963), (20, 18581, 10646), (381, 11480, 16966), (382, 16964, 16965), (11480, 16966, 16241), (16964, 19106, 6)
The reciprocal parallelogic center of these triangles is X(385)
X(19108) lies on these lines: {2,13908}, {3,19056}, {6,99}, {98,372}, {114,1587}, {115,3069}, {148,7586}, {486,14639}, {542,19059}, {543,19053}, {615,14061}, {618,19076}, {619,19074}, {620,3068}, {631,8980}, {690,19110}, {2482,19054}, {2782,3312}, {2783,19081}, {2787,19112}, {2794,6460}, {2799,19114}, {3023,19037}, {3027,18995}, {3071,10723}, {3299,10086}, {3301,10089}, {4027,18993}, {5186,5411}, {5469,13981}, {5470,13982}, {5976,19090}, {6034,13972}, {6036,13935}, {6054,13773}, {6226,8416}, {6321,7584}, {6395,12188}, {6398,12042}, {6418,13188}, {6560,10722}, {7582,13172}, {7583,15561}, {7585,8997}, {7968,7983}, {8290,19092}, {8782,19011}, {9166,13847}, {11711,18991}, {11725,13959}, {13173,18999}, {13174,19003}, {13175,19005}, {13176,19007}, {13177,19009}, {13178,13936}, {13179,19017}, {13180,19023}, {13181,19025}, {13182,19027}, {13183,19029}, {13184,19031}, {13185,19033}, {13189,19047}, {13190,19049}, {13653,13758}, {13967,14651}, {15452,19038}
X(19108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 99, 19109), (99, 10754, 6319)
The reciprocal parallelogic center of these triangles is X(385)
X(19109) lies on these lines: {2,8997}, {3,19055}, {6,99}, {98,371}, {114,1588}, {115,3068}, {148,7585}, {485,14639}, {542,19060}, {543,19054}, {590,14061}, {618,19075}, {619,19073}, {620,3069}, {690,19111}, {2482,19053}, {2782,3311}, {2783,19082}, {2787,19113}, {2794,6459}, {2799,19115}, {3023,19038}, {3027,18996}, {3070,10723}, {3299,10089}, {3301,10086}, {5186,5410}, {5469,13916}, {5470,13917}, {5976,19089}, {6034,13910}, {6036,9540}, {6054,13653}, {6221,12042}, {6227,8396}, {6321,7583}, {6417,13188}, {6561,10722}, {7581,13172}, {7584,15561}, {7586,13989}, {7969,7983}, {8290,19091}, {8782,19012}, {8980,14651}, {9166,13846}, {9583,11710}, {11711,18992}, {11725,13902}, {13173,19000}, {13174,19004}, {13175,19006}, {13176,19008}, {13177,19010}, {13178,13883}, {13179,19018}, {13180,19024}, {13181,19026}, {13182,19028}, {13183,19030}, {13184,19032}, {13185,19034}, {13189,19048}, {13190,19050}, {13638,13773}, {15452,19037}
X(19109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 99, 19108), (99, 10754, 6320)
The reciprocal parallelogic center of these triangles is X(323)
X(19110) lies on these lines: {2,13990}, {3,19060}, {5,19052}, {6,110}, {74,372}, {113,1587}, {125,3069}, {265,7584}, {399,6418}, {486,14644}, {542,19053}, {615,15059}, {631,8994}, {690,19108}, {1112,5411}, {1151,15051}, {1152,15055}, {1511,3311}, {1588,17702}, {1656,13915}, {2771,19081}, {2777,6460}, {2781,19093}, {2948,19003}, {3028,18995}, {3068,5972}, {3071,10733}, {3299,10088}, {3301,10091}, {3312,5663}, {3448,7586}, {3592,15020}, {3594,15054}, {5465,19058}, {5609,6428}, {5622,19146}, {5642,19054}, {6395,10620}, {6398,12041}, {6409,10817}, {6419,10819}, {6420,12376}, {6426,10818}, {6459,16163}, {6560,10721}, {6699,13935}, {7582,12383}, {7583,14643}, {7585,8998}, {7726,8416}, {7968,7984}, {8674,19112}, {9517,19114}, {10113,13785}, {10272,19117}, {11242,13287}, {11597,19096}, {11598,19088}, {11720,18991}, {11735,13959}, {12310,19005}, {12902,18510}, {12903,19027}, {12904,19029}, {13193,18993}, {13204,18999}, {13208,19007}, {13209,19009}, {13210,19011}, {13211,13936}, {13212,19017}, {13213,19023}, {13214,19025}, {13215,19031}, {13216,19033}, {13217,19047}, {13218,19049}, {13654,13758}, {13939,15081}, {13966,15061}, {15647,17820}, {19051,19095}
X(19110) = reflection of X(19051) in X(19116)
The reciprocal parallelogic center of these triangles is X(323)
X(19111) lies on these lines: {2,8998}, {3,19059}, {5,19051}, {6,110}, {74,371}, {113,1588}, {125,3068}, {265,7583}, {372,10819}, {399,6417}, {485,14644}, {542,19054}, {590,15059}, {631,13969}, {690,19109}, {1112,5410}, {1151,15055}, {1152,15051}, {1511,3312}, {1587,17702}, {1656,13979}, {2771,19082}, {2777,6459}, {2781,19094}, {2948,19004}, {3028,18996}, {3069,5972}, {3070,10733}, {3299,10091}, {3301,10088}, {3311,5663}, {3448,7585}, {3592,15054}, {3594,15020}, {5465,19057}, {5609,6427}, {5622,19145}, {5642,19053}, {6221,12041}, {6395,15040}, {6396,15036}, {6410,10818}, {6419,12375}, {6420,10820}, {6425,10817}, {6460,16163}, {6561,10721}, {6699,9540}, {7581,12383}, {7584,14643}, {7586,13990}, {7725,8396}, {7969,7984}, {8674,19113}, {8981,15061}, {9517,19115}, {9541,16111}, {9583,11709}, {10113,13665}, {10272,19116}, {11241,13288}, {11597,19095}, {11598,19087}, {11720,18992}, {11735,13902}, {12902,18512}, {12903,19028}, {12904,19030}, {13193,18994}, {13204,19000}, {13208,19008}, {13209,19010}, {13210,19012}, {13211,13883}, {13212,19018}, {13213,19024}, {13214,19026}, {13215,19032}, {13216,19034}, {13217,19048}, {13218,19050}, {13638,13774}, {13886,15081}, {15647,17819}
X(19111) = reflection of X(19052) in X(19117)
X(19111) = {X(372), X(10819)}-harmonic conjugate of X(15035)
The reciprocal parallelogic center of these triangles is X(1)
X(19112) lies on these lines: {2,13991}, {3,19082}, {6,100}, {10,19078}, {11,3069}, {80,13936}, {104,372}, {119,1587}, {149,7586}, {214,18991}, {528,19053}, {631,13913}, {952,3312}, {1145,19066}, {1317,18995}, {1320,7968}, {1387,13959}, {1588,5840}, {1698,8988}, {1703,2800}, {1862,5411}, {2771,19059}, {2783,19055}, {2787,19108}, {2802,18992}, {2806,19114}, {2829,6460}, {2831,19093}, {3035,3068}, {3071,10724}, {3299,10087}, {3301,10090}, {5533,13962}, {5541,19003}, {6174,19054}, {6395,12773}, {6418,12331}, {6560,10728}, {6702,13947}, {6713,13935}, {7582,13199}, {7584,10738}, {7585,13922}, {8068,13963}, {8416,12754}, {8674,19110}, {13194,18993}, {13205,18999}, {13222,19005}, {13228,19007}, {13230,19009}, {13235,19011}, {13268,19017}, {13271,19023}, {13272,19025}, {13273,19027}, {13274,19029}, {13275,19031}, {13276,19033}, {13278,19047}, {13279,19049}, {13971,16173}, {15015,19004}
X(19112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 100, 19113), (100, 10755, 13269)
The reciprocal parallelogic center of these triangles is X(1)
X(19113) lies on these lines: {2,13922}, {3,19081}, {6,100}, {10,19077}, {11,3068}, {80,13883}, {104,371}, {119,1588}, {149,7585}, {214,18992}, {528,19054}, {631,13977}, {952,3311}, {1145,19065}, {1317,18996}, {1320,7969}, {1387,13902}, {1587,5840}, {1698,13976}, {1702,2800}, {1862,5410}, {2771,19060}, {2783,19056}, {2787,19109}, {2802,18991}, {2806,19115}, {2829,6459}, {2831,19094}, {3035,3069}, {3070,10724}, {3299,10090}, {3301,10087}, {5533,13904}, {5541,19004}, {6174,19053}, {6417,12331}, {6561,10728}, {6702,13893}, {6713,9540}, {7581,13199}, {7583,10738}, {7586,13991}, {8068,13905}, {8396,12753}, {8674,19111}, {8983,16173}, {9583,11715}, {13194,18994}, {13205,19000}, {13222,19006}, {13228,19008}, {13230,19010}, {13235,19012}, {13268,19018}, {13271,19024}, {13272,19026}, {13273,19028}, {13274,19030}, {13275,19032}, {13276,19034}, {13278,19048}, {13279,19050}, {15015,19003}
X(19113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 100, 19112), (100, 10755, 13270)
The reciprocal parallelogic center of these triangles is X(6)
X(19114) lies on these lines: {2,13992}, {3,19094}, {6,74}, {127,3069}, {132,1587}, {372,1297}, {631,13918}, {1588,2794}, {2799,19108}, {2806,19112}, {2831,19081}, {3068,6720}, {3071,10735}, {3299,13311}, {3301,13312}, {3312,19093}, {3320,18995}, {5411,13166}, {6020,19037}, {6395,13115}, {6418,13310}, {6459,14689}, {7582,13200}, {7584,10749}, {7585,13923}, {7586,13219}, {7968,10705}, {8416,12806}, {9517,19110}, {11641,19005}, {11722,18991}, {13195,18993}, {13206,18999}, {13221,19003}, {13229,19007}, {13231,19009}, {13236,19011}, {13280,13936}, {13281,19017}, {13294,19023}, {13295,19025}, {13296,19027}, {13297,19029}, {13298,19031}, {13299,19033}, {13313,19047}, {13314,19049}, {13785,19163}, {19013,19162}
The reciprocal parallelogic center of these triangles is X(6)
X(19115) lies on these lines: {2,13923}, {3,19093}, {6,74}, {127,3068}, {132,1588}, {371,1297}, {631,13985}, {1587,2794}, {2799,19109}, {2806,19113}, {2831,19082}, {3069,6720}, {3299,13312}, {3301,13311}, {3311,19094}, {3320,18996}, {5410,13166}, {6020,19038}, {6417,13310}, {6460,14689}, {7581,13200}, {7583,10749}, {7585,13219}, {7586,13992}, {7969,10705}, {8396,12805}, {9517,19111}, {9583,12265}, {11641,19006}, {11722,18992}, {13195,18994}, {13206,19000}, {13221,19004}, {13231,19010}, {13236,19012}, {13280,13883}, {13281,19018}, {13294,19024}, {13295,19026}, {13296,19028}, {13297,19030}, {13298,19032}, {13299,19034}, {13313,19048}, {13314,19050}, {13665,19163}, {19014,19162}
X(19116) lies on these lines: {2,6417}, {3,7582}, {4,6418}, {5,6}, {20,6395}, {26,19005}, {30,1588}, {140,3069}, {193,11314}, {355,19003}, {371,549}, {372,550}, {381,1131}, {495,3299}, {496,3301}, {546,1587}, {547,8976}, {548,6398}, {597,639}, {615,632}, {640,3629}, {952,18992}, {1132,3843}, {1151,15712}, {1152,8703}, {1483,7968}, {1505,15048}, {1592,1994}, {1656,3316}, {1993,15235}, {3068,3628}, {3070,3845}, {3071,3627}, {3091,18512}, {3317,5070}, {3526,13941}, {3528,6446}, {3530,6221}, {3592,5420}, {3594,6561}, {3850,13665}, {3857,6564}, {3858,6565}, {5055,13886}, {5062,18907}, {5411,6756}, {5413,7715}, {5414,10386}, {5418,6431}, {5422,15236}, {5690,13936}, {5844,19065}, {5886,19004}, {5901,18991}, {6409,17504}, {6432,6560}, {6445,15717}, {6449,12100}, {6450,9541}, {6470,15713}, {6472,15718}, {6475,15695}, {6496,14891}, {6498,10109}, {7969,10283}, {8254,19096}, {10154,11265}, {10272,19111}, {10577,15699}, {10592,19028}, {10593,19030}, {10880,13937}, {10942,19025}, {10943,19023}, {11801,19052}, {13861,19006}, {13904,13955}, {13905,13954}, {13962,15325}, {13963,19038}, {15171,19037}, {18990,18995}, {19051,19095}, {19055,19091}, {19063,19089}, {19069,19073}, {19071,19075}
X(19116) = midpoint of X(19051) and X(19110)
X(19116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 6, 19117), (5, 1353, 5875), (6, 486, 7583), (6, 7584, 5), (371, 13966, 549), (381, 6501, 7581), (485, 18762, 5), (486, 7583, 5), (1588, 19053, 3312), (3069, 3311, 140), (6214, 14561, 5), (6418, 18510, 4), (7582, 7586, 3), (7583, 7584, 486), (19102, 19104, 6)
X(19117) lies on these lines: {2,6418}, {3,7581}, {4,6417}, {5,6}, {26,19006}, {30,1587}, {140,3068}, {193,11313}, {355,19004}, {371,550}, {372,549}, {376,9543}, {381,1132}, {495,3301}, {496,3299}, {546,1588}, {547,13951}, {548,6221}, {590,632}, {597,640}, {615,8960}, {631,6395}, {639,3629}, {952,18991}, {1131,3843}, {1151,8703}, {1152,15712}, {1483,7969}, {1504,15048}, {1591,1994}, {1656,3317}, {1993,15236}, {2066,10386}, {3069,3628}, {3070,3627}, {3071,3845}, {3091,18510}, {3316,5070}, {3526,8972}, {3528,6445}, {3530,6398}, {3592,6560}, {3594,5418}, {3850,13785}, {3857,6565}, {3858,6564}, {5055,13939}, {5058,18907}, {5410,6756}, {5412,7715}, {5420,6432}, {5422,15235}, {5690,13883}, {5844,19066}, {5886,19003}, {5901,18992}, {6410,17504}, {6431,6561}, {6446,15717}, {6450,12100}, {6471,15713}, {6473,15718}, {6474,15695}, {6497,14891}, {6499,10109}, {7968,10283}, {8254,19095}, {9541,12103}, {9691,15688}, {10154,11266}, {10272,19110}, {10576,15699}, {10592,19027}, {10593,19029}, {10881,13884}, {10942,19026}, {10943,19024}, {11801,19051}, {13861,19005}, {13897,13963}, {13898,13962}, {13904,15325}, {13905,19037}, {15171,19038}, {18990,18996}, {19056,19092}, {19064,19090}, {19070,19076}, {19072,19074}
X(19117) = midpoint of X(19052) and X(19111)
X(19117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5, 6, 19116), (5, 1353, 5874), (6, 485, 7584), (6, 7583, 5), (372, 8981, 549), (381, 6500, 7582), (485, 7584, 5), (486, 18538, 5), (1587, 19054, 3311), (3068, 3312, 140), (6215, 14561, 5), (6417, 18512, 4), (7581, 7585, 3), (7583, 7584, 485), (19103, 19105, 6)
Let A'B'C' be the cevian triangle of X(25). Let A" be the inverse-in-circumcircle of A', and define B" and C" cyclically. The lines AA", BB", CC" concur in X(19118). (Randy Hutson, January 15, 2019)
X(19118) lies on the conic {{X(3),X(6),X(24),X(60),X(143),X(1511),X(1986)}} and these lines: {3,19121}, {4,5050}, {6,25}, {24,1351}, {69,468}, {143,3517}, {182,1593}, {193,3167}, {235,6776}, {237,15905}, {378,12017}, {393,460}, {403,18440}, {419,9308}, {427,3618}, {511,3515}, {575,5198}, {597,5064}, {1177,13171}, {1249,6620}, {1350,11470}, {1386,11396}, {1398,1428}, {1576,1609}, {1691,8778}, {1692,2207}, {1829,16475}, {1986,12168}, {1993,19122}, {2211,3172}, {2330,7071}, {3089,14912}, {3516,5085}, {3518,11482}, {3542,3564}, {3575,14853}, {3589,5094}, {3629,15471}, {3751,11363}, {3867,6329}, {5092,11410}, {5095,6144}, {5182,5186}, {5480,12173}, {5622,12133}, {5921,6622}, {6391,8780}, {7395,19131}, {7484,19126}, {7487,11426}, {7507,14561}, {7576,14848}, {7592,19123}, {8573,14575}, {9715,9967}, {9909,12220}, {11245,19119}, {11284,19137}, {11403,19124}, {11406,19133}, {12160,19139}, {12161,19155}, {12165,19140}, {12166,19141}, {12169,19143}, {12170,19144}, {12171,19145}, {12172,19146}, {12174,19149}, {12175,19150}, {13007,19147}, {13008,19148}, {14070,18438}, {16030,19171}, {18386,19130}
X(19118) = isogonal conjugate of X(6340)
X(19118) = X(3565)-isoconjugate of X(14208)
X(19118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 25, 12167), (6, 154, 6467), (6, 159, 10602), (6, 1974, 25), (6, 7716, 8541), (6, 9973, 11216), (6, 12167, 11405), (6, 18374, 159), (6, 19125, 11402), (6, 19132, 184), (6, 19153, 19125), (3517, 5093, 6403), (5085, 12294, 3516)
X(19119) lies on these lines: {2,13562}, {4,6}, {22,193}, {66,8889}, {69,184}, {182,18909}, {185,11574}, {206,6353}, {376,3313}, {511,18925}, {631,5157}, {1177,18947}, {1353,7387}, {1428,18915}, {1843,11206}, {1899,3618}, {1974,11433}, {1992,6467}, {2330,18922}, {3547,3564}, {3620,7495}, {5050,7404}, {5085,18913}, {5092,18931}, {5093,7553}, {5622,12317}, {5921,13160}, {6515,19121}, {6643,19139}, {7500,10602}, {7714,9969}, {11061,13198}, {11245,19118}, {11411,19131}, {11513,12256}, {11514,12257}, {12324,19124}, {13567,19132}, {18911,19122}, {18912,19123}, {18916,19128}, {18917,19129}, {18918,19130}, {18921,19133}, {18926,19134}, {18927,19135}, {18928,19137}, {18932,19138}, {18933,19140}, {18934,19141}, {18936,19142}, {18937,19143}, {18938,19144}, {18941,19145}, {18942,19146}, {18943,19147}, {18944,19148}, {18946,19150}, {18950,19153}, {18951,19154}, {18952,19155}, {18953,19156}, {19166,19171}
X(19119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 5596, 4), (6, 6776, 18935), (6, 18935, 18919), (69, 1176, 7494), (6776, 14853, 6146)
X(19120) lies on these lines: {6,1916}, {32,5969}, {83,597}, {98,141}, {99,698}, {110,13518}, {182,2782}, {542,626}, {732,2458}, {1503,2456}, {1975,10131}, {3094,5152}, {3589,10352}, {3618,10353}, {5976,8177}, {7753,18800}, {7789,8724}, {7809,8593}, {7919,11646}, {10754,12212}
X(19120) = midpoint of X(6) and X(5989)
X(19120) = inverse of X(5149) in the 1st Lemoine circle
X(19120) = {X(4027), X(14931)}-harmonic conjugate of X(3407)
X(19121) lies on these lines: {2,1974}, {3,19118}, {4,19131}, {6,22}, {20,182}, {23,1843}, {26,6403}, {30,19129}, {54,1351}, {69,110}, {74,19138}, {97,19171}, {111,8869}, {141,18374}, {156,11898}, {159,12272}, {160,4558}, {184,193}, {376,15472}, {394,19132}, {511,7488}, {729,3565}, {858,3589}, {1239,18018}, {1370,3618}, {1428,4296}, {1495,14913}, {1576,8266}, {1614,3564}, {1976,2998}, {1993,19125}, {2071,5092}, {2330,3100}, {2937,8537}, {2979,19122}, {3044,14645}, {3098,10298}, {3101,19133}, {3146,19124}, {3153,19130}, {3620,9306}, {5027,13232}, {5050,11414}, {5085,11413}, {5135,16049}, {5138,7520}, {5480,12225}, {5596,11442}, {5622,10733}, {5921,6759}, {6101,19155}, {6515,19119}, {6636,11574}, {6800,15531}, {7492,11511}, {7502,12228}, {7512,9967}, {7555,18449}, {7760,14247}, {8548,12283}, {8588,15596}, {9822,13595}, {9909,12167}, {11411,19141}, {11412,19123}, {12058,15246}, {12111,19149}, {12219,19140}, {12221,19143}, {12222,19144}, {12223,19145}, {12224,19146}, {12226,19150}, {13009,19147}, {13010,19148}, {13201,15141}, {14157,18440}
X(19121) = isogonal conjugate of the isotomic conjugate of X(33651)
X(19121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19154, 19128), (6, 22, 12220), (6, 1176, 5012), (6, 2916, 17710), (6, 12220, 11416), (6, 19127, 1176), (182, 14853, 13434), (1974, 19126, 2), (5157, 19136, 3618), (11412, 19123, 19139)
X(19122) lies on these lines: {3,19123}, {6,110}, {22,19132}, {156,12283}, {159,11416}, {182,12111}, {206,12220}, {511,11449}, {575,5921}, {1177,13201}, {1974,3060}, {1993,19118}, {2330,11446}, {2979,19121}, {3618,11442}, {5012,19125}, {5050,11441}, {5085,11440}, {5092,11454}, {5480,12278}, {5889,19128}, {5890,12168}, {6467,9544}, {7998,19126}, {11412,19154}, {11439,19124}, {11444,19131}, {11445,19133}, {11451,19137}, {11459,19129}, {11464,18438}, {11574,15080}, {12270,19140}, {12271,19141}, {12273,19138}, {12274,19143}, {12275,19144}, {12276,19145}, {12277,19146}, {12279,19149}, {12280,19150}, {13015,19147}, {13016,19148}, {14516,18583}, {18392,19130}, {18911,19119}, {19167,19171}
X(19122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19155, 19123), (6, 12272, 11443), (19128, 19139, 5889)
X(19123) lies on these lines: {3,19122}, {6,1173}, {54,19125}, {74,5085}, {156,12272}, {159,8537}, {182,6241}, {206,6403}, {511,11464}, {1177,7731}, {1351,9707}, {1974,3567}, {2330,11461}, {3618,11457}, {5034,13509}, {5050,11456}, {5092,11468}, {5093,11422}, {5480,12289}, {5889,19154}, {5890,19128}, {7592,19118}, {7999,19126}, {11412,19121}, {11455,19124}, {11459,19131}, {11460,19133}, {11465,19137}, {12111,19129}, {12281,19140}, {12282,19141}, {12284,19138}, {12285,19143}, {12286,19144}, {12287,19145}, {12288,19146}, {12290,19149}, {12291,19150}, {13018,19148}, {18394,19130}, {18912,19119}, {19168,19171}
X(19123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19155, 19122), (6, 1614, 12283), (6, 12283, 11458), (19121, 19139, 11412)
X(19124) lies on these lines: {3,1843}, {4,83}, {6,64}, {20,19126}, {24,5092}, {25,373}, {30,19131}, {33,1428}, {34,2330}, {51,10249}, {69,13346}, {110,15431}, {112,5039}, {159,13367}, {184,427}, {186,17508}, {193,16622}, {206,7507}, {235,3589}, {264,12215}, {378,511}, {382,19129}, {542,15463}, {569,1595}, {576,14865}, {578,3088}, {1092,1352}, {1147,18440}, {1177,13202}, {1204,19161}, {1350,3516}, {1351,12163}, {1386,1902}, {1498,19125}, {1594,3818}, {1597,5050}, {1598,12017}, {1691,10311}, {1885,5480}, {2071,9813}, {2211,5034}, {2777,5622}, {3091,19137}, {3092,12299}, {3093,12298}, {3098,3520}, {3146,19121}, {3515,7716}, {3564,13352}, {3575,3867}, {3627,19154}, {4219,5138}, {5012,7378}, {5026,12131}, {5094,5651}, {5095,11579}, {5102,11405}, {5198,10541}, {6467,8549}, {6593,12133}, {6756,13336}, {7503,11574}, {7526,9967}, {7527,11511}, {8889,9306}, {9822,17928}, {11381,19149}, {11403,19118}, {11439,19122}, {11455,19123}, {11471,19133}, {12162,19139}, {12292,19140}, {12293,19141}, {12295,19138}, {12296,19143}, {12297,19144}, {12300,19150}, {12324,19119}, {13019,19147}, {13020,19148}, {13488,18583}, {14130,18438}, {14912,15033}, {15811,19132}, {18374,18386}, {19169,19171}
X(19124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 182, 1974), (6, 1593, 12294), (6, 12294, 11470), (3516, 12167, 1350), (3520, 6403, 3098), (11579, 15472, 5095)
X(19125) lies on these lines: {2,13562}, {3,1176}, {5,3618}, {6,25}, {26,1351}, {54,19123}, {66,5094}, {69,3167}, {141,6090}, {155,19131}, {182,1181}, {185,5085}, {193,7493}, {394,19126}, {399,5622}, {427,5596}, {511,9715}, {974,12168}, {1350,13367}, {1353,13383}, {1498,19124}, {1503,7507}, {1593,19149}, {1899,3589}, {1992,10154}, {1993,19121}, {3515,19161}, {3542,14912}, {3549,3564}, {3796,11574}, {5012,19122}, {5092,10605}, {5093,9714}, {5157,7484}, {5938,9407}, {6146,14561}, {6403,9707}, {6593,13198}, {6756,11426}, {6800,12220}, {6997,18935}, {7514,12017}, {7528,18583}, {7592,19128}, {10132,11514}, {10133,11513}, {10601,19137}, {11064,15812}, {11179,16072}, {11425,12294}, {11427,15809}, {12161,19154}, {12228,12412}, {13171,15141}, {13490,14848}, {14786,18914}, {18396,19130}, {18445,19129}, {19170,19171}
X(19125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 1843), (6, 159, 12167), (6, 206, 25), (6, 9924, 8541), (6, 19132, 1974), (6, 19153, 19118), (11402, 19118, 6)
X(19126) lies on these lines: {2,1974}, {3,6}, {20,19124}, {22,1843}, {25,9822}, {30,3867}, {69,184}, {95,19171}, {110,3620}, {140,19154}, {141,206}, {159,14913}, {193,5012}, {394,19125}, {485,19144}, {486,19143}, {597,10691}, {631,19128}, {1038,1428}, {1040,2330}, {1092,10519}, {1177,5972}, {1216,19139}, {1352,3547}, {1368,3589}, {1503,6823}, {1660,8263}, {1976,6394}, {2916,9973}, {3506,15526}, {3564,12229}, {3618,7386}, {3619,5651}, {3763,18374}, {3796,8681}, {3818,15760}, {3819,19153}, {3955,7289}, {5227,7193}, {5480,12362}, {5622,16163}, {5907,19149}, {6403,7512}, {6593,13416}, {6636,8541}, {6643,14561}, {6699,19138}, {6776,7400}, {7467,10311}, {7484,19118}, {7503,12294}, {7716,9909}, {7998,19122}, {7999,19123}, {9969,15818}, {10319,19133}, {10996,18935}, {12272,15080}, {12358,19140}, {12359,19141}, {12363,19150}, {13027,19147}, {13028,19148}, {15471,15712}, {17811,19132}, {18531,19130}
X(19126) = inverse of X(11574) in the Brocard circle
X(19126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1974, 19137), (2, 19121, 1974), (3, 6, 11574), (3, 1578, 12361), (3, 1579, 12360), (3, 19131, 182), (6, 5157, 182), (6, 11574, 11511), (69, 1176, 184), (141, 206, 9306), (141, 19127, 206), (182, 13347, 5085), (571, 8266, 5171), (5050, 13336, 182), (11513, 11514, 216), (11515, 11516, 10979)
X(19127) lies on these lines: {2,18374}, {3,1177}, {6,22}, {23,9971}, {25,16776}, {30,182}, {54,11477}, {69,9544}, {76,4577}, {110,599}, {112,13238}, {141,206}, {184,524}, {378,5085}, {427,1974}, {511,7502}, {574,9515}, {575,5446}, {576,7555}, {1352,10540}, {1503,15760}, {1614,15069}, {1976,9462}, {1992,11003}, {2854,6800}, {3618,7391}, {5050,12083}, {5092,18570}, {5621,15072}, {5622,18396}, {7492,10510}, {7493,8262}, {7668,14880}, {7712,12367}, {8266,14575}, {8541,8705}, {8547,10602}, {8550,13292}, {9407,14096}, {9426,11183}, {10575,15579}, {10982,12082}, {10984,12241}, {13394,16387}, {14060,18573}, {18382,19129}
X(19127) = midpoint of X(6) and X(22)
X(19127) = reflection of X(i) in X(j) for these (i,j): (141, 6676), (427, 3589)
X(19127) = center of pedal circle of X(6) wrt tangential triangle
X(19127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 2916, 12220), (182, 19136, 597), (206, 19126, 141), (1176, 19121, 6), (1974, 5157, 3589)
X(19128) lies on these lines: {2,19131}, {3,19118}, {4,83}, {5,19129}, {6,24}, {25,5012}, {26,12220}, {49,1353}, {69,3147}, {74,1177}, {110,468}, {112,1691}, {141,10018}, {159,12283}, {184,6353}, {186,249}, {193,1147}, {206,1614}, {232,1692}, {378,5085}, {403,1503}, {419,685}, {569,7487}, {575,1843}, {592,5038}, {597,7576}, {631,19126}, {1112,15107}, {1181,19132}, {1351,3515}, {1352,7505}, {1428,1870}, {1495,13198}, {1593,12017}, {1594,3589}, {1658,18438}, {1968,5033}, {1986,6593}, {2030,8744}, {2070,11416}, {2203,4231}, {2330,6198}, {2445,7418}, {3043,5095}, {3088,13336}, {3090,19137}, {3098,11470}, {3517,12167}, {3520,5092}, {3541,5157}, {3575,13434}, {3818,16868}, {4232,11003}, {5034,10311}, {5138,7501}, {5476,18559}, {5480,6240}, {5596,11457}, {5889,19122}, {5890,19123}, {5921,10539}, {6102,19155}, {6197,19133}, {6239,19145}, {6241,19149}, {6242,19150}, {6400,19146}, {6467,10282}, {6622,6759}, {6756,13353}, {7488,9967}, {7512,11574}, {7556,11511}, {7575,12228}, {7592,19125}, {7722,19140}, {7731,15141}, {8548,12272}, {9418,17974}, {10203,14940}, {10295,15472}, {10313,14965}, {12140,15118}, {12509,19143}, {12510,19144}, {13035,19147}, {13036,19148}, {14483,19151}, {14810,17506}, {14853,15033}, {15579,16835}, {18916,19119}
X(19128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19154, 19121), (6, 24, 6403), (6, 6403, 8537), (6, 15577, 15073), (182, 1974, 4), (206, 6776, 1614), (5092, 12294, 3520), (5622, 18374, 14157), (5889, 19122, 19139)
X(19129) lies on these lines: {3,6}, {4,19154}, {5,19128}, {30,19121}, {49,3564}, {54,1353}, {141,11597}, {156,5921}, {206,10540}, {265,1176}, {381,1974}, {382,19124}, {549,12228}, {895,15089}, {1147,11898}, {1177,7728}, {1352,6639}, {1368,14389}, {1428,18447}, {1503,10024}, {1658,6403}, {1843,2070}, {2072,3589}, {2330,18455}, {2931,6467}, {3549,6776}, {3580,5012}, {3618,18531}, {3818,10254}, {3867,7540}, {5055,19137}, {5422,15818}, {5476,18564}, {5480,18563}, {5876,19155}, {6593,7723}, {6746,7488}, {6823,12022}, {7496,13416}, {7502,12220}, {10984,18396}, {11459,19122}, {11464,12272}, {12111,19123}, {12167,14070}, {12294,14130}, {12429,19141}, {12605,18583}, {13198,13394}, {14561,18404}, {14912,18951}, {18382,19127}, {18403,19130}, {18435,19153}, {18436,19139}, {18437,19156}, {18439,19149}, {18445,19125}, {18451,19132}, {18453,19133}, {18462,19134}, {18463,19135}, {18917,19119}, {19171,19176}
X(19129) = inverse of X(18438) in the Brocard circle
X(19129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 18438), (6, 12017, 14805), (6, 18438, 18449), (182, 5050, 13353), (182, 5157, 12017), (182, 19131, 3), (206, 18440, 10540), (568, 13353, 567), (5157, 12017, 13339), (5622, 19138, 265)
X(19130) lies on these lines: {2,3098}, {3,7889}, {4,83}, {5,141}, {6,13}, {20,17508}, {30,3589}, {51,3580}, {69,1568}, {110,7533}, {114,262}, {125,5169}, {126,13518}, {140,14810}, {184,7394}, {193,576}, {206,11818}, {302,5979}, {303,5978}, {315,10356}, {373,858}, {378,15473}, {382,5085}, {383,6771}, {389,7403}, {403,1843}, {427,5943}, {518,9955}, {524,5066}, {546,575}, {569,13419}, {578,7528}, {597,3845}, {611,10896}, {613,10895}, {698,7764}, {754,8177}, {1080,6774}, {1350,1656}, {1351,3851}, {1353,3857}, {1368,6688}, {1386,18480}, {1428,3585}, {1469,7741}, {1495,14389}, {1506,3094}, {1594,12294}, {1595,9729}, {1596,3867}, {1691,7747}, {1995,5972}, {2072,14845}, {2076,7749}, {2330,3583}, {2679,16188}, {2777,7706}, {2781,6697}, {2794,10796}, {2916,5899}, {3056,7951}, {3066,5094}, {3071,18539}, {3088,9815}, {3090,7944}, {3095,7813}, {3153,19121}, {3242,18493}, {3398,15870}, {3448,15019}, {3564,3850}, {3619,5071}, {3631,11737}, {3763,5055}, {3767,5039}, {3814,17792}, {3830,12017}, {3832,6776}, {3839,11179}, {3843,5050}, {3854,5921}, {3855,15520}, {3856,12007}, {3858,8550}, {4260,6841}, {5017,7746}, {5056,10519}, {5064,10601}, {5072,11477}, {5076,10541}, {5093,15069}, {5096,13743}, {5102,11898}, {5116,7756}, {5158,18437}, {5189,7605}, {5422,11550}, {5449,10095}, {5512,13234}, {5576,19161}, {5642,10546}, {5846,18357}, {5946,10264}, {6032,6791}, {6036,13860}, {6055,7806}, {6247,15012}, {6288,19150}, {6292,9821}, {6403,16868}, {6593,10113}, {6698,15088}, {6990,10477}, {6997,9306}, {7399,13598}, {7401,13346}, {7405,15644}, {7470,7859}, {7544,11424}, {7690,11292}, {7692,11291}, {7699,11188}, {7752,18906}, {7755,12212}, {7765,13331}, {7787,9873}, {7810,9301}, {7829,14880}, {7937,10292}, {8705,16511}, {9171,18309}, {9753,17008}, {9862,12150}, {9880,14928}, {9927,19139}, {9967,10024}, {9968,18952}, {9970,14644}, {9971,10254}, {10182,12106}, {10224,18874}, {10301,13394}, {10539,12242}, {10733,15462}, {10991,11842}, {11225,11442}, {11563,17710}, {11574,15760}, {12110,14712}, {12177,14639}, {12383,15033}, {12584,14643}, {13354,15980}, {13490,18475}, {13861,15577}, {15063,16261}, {16475,18492}, {18376,19153}, {18377,19154}, {18379,19155}, {18380,19156}, {18381,19149}, {18386,19118}, {18392,19122}, {18394,19123}, {18396,19125}, {18403,19129}, {18404,19131}, {18405,19132}, {18406,19133}, {18414,19134}, {18415,19135}, {18420,19137}, {18531,19126}, {18918,19119}, {19171,19177}
X(19130) = midpoint of X(i) and X(j) for these {i,j}: {4, 182}, {5, 5480}, {6, 3818}, {206, 18382}, {546, 18583}, {597, 3845}, {1386, 18480}, {6288, 19150}, {6593, 10113}, {9171, 18309}, {9927, 19139}, {18376, 19153}, {18377, 19154}, {18379, 19155}, {18380, 19156}, {18381, 19149}
X(19130) = reflection of X(6698) in X(15088)
X(19130) = complement of X(3098)
X(19130) = inverse of X(12188) in the orthocentroidal circle
X(19130) = inverse-in-Kiepert-hyperbola of X(7753)
X(19130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 7693, 10545), (4, 14561, 182), (5, 14881, 626), (6, 381, 3818), (13, 14, 7753), (262, 13862, 114), (381, 18510, 18511), (381, 18512, 18509), (623, 624, 626), (639, 640, 7849), (3589, 5092, 10168), (3818, 5476, 6), (5103, 5480, 14881), (5403, 5404, 14881), (6564, 6565, 5475)
X(19131) lies on these lines: {2,19128}, {3,6}, {4,19121}, {5,1974}, {26,1843}, {30,19124}, {49,11898}, {51,15818}, {54,193}, {68,1176}, {69,1147}, {113,1177}, {125,19138}, {141,7542}, {155,19125}, {184,343}, {206,1209}, {1060,1428}, {1062,2330}, {1503,15760}, {1614,5921}, {1656,19137}, {2070,9813}, {3524,15463}, {3548,15812}, {3589,11585}, {3618,6643}, {3818,10024}, {3867,7553}, {5012,6515}, {5095,12228}, {5480,12605}, {5562,19139}, {5622,17702}, {5891,19153}, {6146,6823}, {6403,7488}, {6467,8548}, {6593,12358}, {6759,18440}, {7395,19118}, {7502,8541}, {7506,9822}, {7512,12220}, {7526,12294}, {7716,9714}, {7723,19140}, {8251,19133}, {9715,12167}, {10249,14855}, {10282,14913}, {10516,18374}, {11411,19119}, {11444,19122}, {11459,19123}, {11591,19155}, {12162,19149}, {12362,18583}, {12601,19143}, {12602,19144}, {12606,19150}, {13039,19147}, {13040,19148}, {13292,16197}, {14561,18531}, {17814,19132}, {18404,19130}, {19171,19179}
X(19131) = inverse of X(9967) in the Brocard circle
X(19131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6, 9967), (3, 19129, 182), (5, 19154, 1974), (6, 182, 569), (6, 9967, 8538), (6, 17834, 1351), (182, 5157, 13336), (182, 19126, 3), (206, 1352, 10539), (577, 5034, 14965)
X(19132) lies on these lines: {6,25}, {22,19122}, {64,1176}, {69,10192}, {155,19154}, {182,1498}, {193,15585}, {221,1428}, {394,19121}, {511,17821}, {1177,17847}, {1181,19128}, {1351,10282}, {1503,3618}, {1853,3589}, {2192,2330}, {2935,15462}, {3053,14575}, {3197,19133}, {5013,9407}, {5050,6759}, {5092,10606}, {5480,17845}, {5893,14927}, {6000,12017}, {6593,10117}, {8780,14913}, {9833,18583}, {11206,15583}, {11477,15577}, {13567,19119}, {15811,19124}, {17811,19126}, {17814,19131}, {17825,19137}, {17834,19139}, {17835,19140}, {17836,19141}, {17837,19142}, {17838,19138}, {17839,19143}, {17840,19145}, {17842,19144}, {17843,19146}, {17844,19148}, {17846,19150}, {17849,19156}, {18405,19130}, {18451,19129}, {19171,19180}
X(19132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 9924), (6, 206, 154), (6, 9924, 17813), (184, 19118, 6), (206, 19153, 6), (1974, 19125, 6), (3589, 5596, 1853), (5085, 19149, 64)
X(19133) lies on these lines: {1,2175}, {6,31}, {19,1974}, {21,518}, {35,4260}, {40,182}, {65,82}, {81,9455}, {110,1963}, {141,16792}, {171,1582}, {172,560}, {206,10536}, {284,2223}, {294,2264}, {354,4224}, {511,10902}, {584,15624}, {612,5320}, {692,1100}, {1177,10119}, {1203,10822}, {2194,2303}, {2259,7077}, {2260,17798}, {2278,3941}, {2294,5202}, {2302,16872}, {2550,3618}, {2911,4517}, {3101,19121}, {3178,5847}, {3189,4195}, {3197,19132}, {3242,10448}, {3573,17319}, {3589,3925}, {3746,9052}, {3946,5091}, {4343,8647}, {4579,17120}, {5050,10306}, {5085,5584}, {5092,7688}, {5248,10477}, {5480,6253}, {5526,7064}, {5711,7535}, {6154,6329}, {6197,19128}, {6252,19145}, {6254,19149}, {6255,19150}, {6283,19049}, {6404,19146}, {6405,19050}, {7113,16679}, {7724,19140}, {8141,19154}, {8251,19131}, {9025,15988}, {9816,19137}, {10319,19126}, {11190,19153}, {11406,19118}, {11445,19122}, {11460,19123}, {11471,19124}, {12417,19141}, {12661,19138}, {12662,19143}, {12663,19144}, {13041,19147}, {13042,19148}, {18406,19130}, {18453,19129}, {18921,19119}, {19171,19181}
X(19133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 55, 3779), (6, 3779, 8539), (1386, 5135, 1428)
X(19134) lies on these lines: {3,19144}, {6,493}, {182,18980}, {5085,13021}, {9723,19135}, {11514,13889}, {18414,19130}, {18462,19129}, {18926,19119}, {18939,19139}, {19171,19186}
X(19134) = {X(6), X(8939)}-harmonic conjugate of X(12590)
X(19135) lies on these lines: {3,19143}, {6,494}, {182,18981}, {5085,13022}, {9723,19134}, {11513,13943}, {18415,19130}, {18463,19129}, {18927,19119}, {18940,19139}, {19171,19187}
X(19136) lies on the cubic K055 and these lines: {4,1177}, {6,25}, {30,182}, {32,1084}, {49,11482}, {110,1992}, {141,6677}, {143,576}, {157,800}, {160,5065}, {185,9968}, {218,692}, {237,5063}, {263,14910}, {511,6644}, {524,8263}, {567,14848}, {575,7530}, {578,11745}, {599,5651}, {895,14002}, {1092,11477}, {1176,7500}, {1368,3589}, {1370,3618}, {1503,1596}, {1597,10249}, {1598,8549}, {1995,8542}, {2781,11438}, {2929,11470}, {3003,3148}, {3066,12039}, {3518,15073}, {4232,5486}, {5032,9544}, {5050,18534}, {5093,9703}, {6759,8550}, {6776,14157}, {7493,16511}, {7714,18919}, {8548,13861}, {9019,11511}, {9171,9426}, {9813,16776}, {10541,16936}, {11188,13595}, {13345,14575}, {13352,15462}, {14561,18531}, {14853,15033}, {16098,18898}, {19139,19141}
X(19136) = midpoint of X(6) and X(25)
X(19136) = reflection of X(i) in X(j) for these (i,j): (141, 6677), (1368, 3589)
X(19136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 1974, 206), (6, 9971, 8541), (6, 18374, 184), (184, 1974, 18374), (184, 18374, 206), (597, 19127, 182), (3618, 19121, 5157), (18583, 19154, 182)
X(19137) lies on these lines: {2,1974}, {5,182}, {6,1196}, {25,11574}, {32,6375}, {69,5651}, {141,6677}, {184,3618}, {511,6642}, {577,11328}, {578,7401}, {597,10128}, {641,19144}, {642,19143}, {1092,14853}, {1147,18583}, {1177,6723}, {1656,19131}, {1660,15583}, {1843,1995}, {2330,9817}, {3090,19128}, {3091,19124}, {3098,6644}, {3628,19154}, {3763,16187}, {5039,16285}, {5050,10539}, {5055,19129}, {5085,11479}, {5138,7535}, {5157,18374}, {5462,19139}, {5476,10127}, {5480,9825}, {6688,19153}, {7506,9967}, {7526,17508}, {7687,15462}, {8265,13356}, {9729,19149}, {9816,19133}, {9820,19141}, {9823,19145}, {9824,19146}, {10601,19125}, {11284,19118}, {11451,19122}, {11465,19123}, {12220,13595}, {12294,17928}, {13053,19147}, {13054,19148}, {13562,13567}, {17825,19132}, {18420,19130}, {18928,19119}, {19171,19188}
X(19137) = complement of X(15812)
X(19137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 1974, 19126), (6, 5020, 9822), (6, 9822, 9813), (206, 3589, 182)
The reciprocal orthologic center of these triangles is X(15136)
X(19138) lies on these lines: {6,1511}, {74,19121}, {110,468}, {113,1974}, {125,19131}, {182,15118}, {193,3043}, {206,542}, {265,1176}, {511,12893}, {1177,5663}, {1351,15463}, {1986,12168}, {2330,12888}, {2854,8548}, {3581,10752}, {3618,12319}, {5050,12310}, {5085,12302}, {5092,12901}, {6593,19139}, {6699,19126}, {11579,14852}, {12273,19122}, {12284,19123}, {12295,19124}, {12661,19133}, {12900,19137}, {13754,19140}, {14982,18374}, {17838,19132}, {18932,19119}, {19171,19193}
X(19138) = midpoint of X(6) and X(2931)
X(19138) = reflection of X(1177) in X(19154)
X(19138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 15462, 12228), (265, 19129, 5622)
The reciprocal orthologic center of these triangles is X(12160)
X(19139) lies on these lines: {3,1176}, {5,6}, {25,110}, {26,206}, {30,19149}, {49,18438}, {52,1974}, {66,13371}, {69,3549}, {141,9820}, {143,9937}, {156,159}, {182,7514}, {184,9967}, {193,2904}, {195,5093}, {323,7493}, {394,6676}, {524,10201}, {539,5476}, {575,15083}, {576,9925}, {611,1069}, {613,3157}, {912,1386}, {1154,19153}, {1173,6391}, {1181,12362}, {1216,19126}, {1350,7502}, {1428,7352}, {1503,18569}, {1614,12220}, {1843,10539}, {1994,6997}, {2330,6238}, {2854,12596}, {3098,12038}, {3173,15253}, {3589,12359}, {3618,11411}, {3818,5448}, {5050,7395}, {5085,12163}, {5092,7689}, {5097,8681}, {5157,7516}, {5422,7539}, {5462,19137}, {5480,11818}, {5504,9970}, {5562,19131}, {5596,14790}, {5622,7723}, {5663,15141}, {5889,19122}, {6090,15135}, {6467,8538}, {6593,19138}, {6643,19119}, {6644,19161}, {6776,18445}, {6816,14912}, {7507,11441}, {8537,12272}, {8705,15580}, {9715,11464}, {9927,19130}, {10003,10104}, {10601,11548}, {11412,19121}, {11416,12283}, {11819,12118}, {12160,19118}, {12162,19124}, {12294,13352}, {14708,15462}, {14926,15087}, {14982,15140}, {17702,19140}, {17834,19132}, {18436,19129}, {18939,19134}, {18940,19135}, {19136,19141}, {19171,19194}
X(19139) = midpoint of X(i) and X(j) for these {i,j}: {5504, 9970}, {5596, 14790}
X(19139) = reflection of X(i) in X(j) for these (i,j): (26, 206), (66, 13371), (141, 9820), (3098, 12038), (3818, 5448), (9927, 19130)
X(19139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (155, 5654, 15068), (5889, 19122, 19128), (11412, 19123, 19121), (19154, 19155, 19153)
The reciprocal orthologic center of these triangles is X(3581)
X(19140) lies on the cubic K263 and these lines: {6,13}, {23,110}, {67,14643}, {74,827}, {141,10272}, {182,4550}, {206,1511}, {262,5987}, {518,11699}, {575,11579}, {576,2854}, {895,5097}, {1177,10628}, {1351,2930}, {1352,11061}, {1386,2771}, {1503,18572}, {1531,10706}, {1843,2914}, {1974,1986}, {2330,7727}, {2777,15141}, {3448,14561}, {3581,18374}, {3589,10264}, {3618,12317}, {5050,12308}, {5085,10620}, {5480,19150}, {5611,13858}, {5615,13859}, {5621,12017}, {5642,15066}, {5972,15106}, {7722,19128}, {7723,19131}, {7724,19133}, {8681,12364}, {9140,15018}, {9142,18114}, {9143,11004}, {9759,11580}, {9977,15052}, {10540,11649}, {11456,15063}, {11898,16176}, {12041,17508}, {12165,19118}, {12177,15342}, {12219,19121}, {12270,19122}, {12281,19123}, {12292,19124}, {12294,15463}, {12358,19126}, {13754,19138}, {14683,14853}, {14810,15035}, {15068,16534}, {17702,19139}, {17835,19132}, {18933,19119}, {19171,19195}
X(19140) = midpoint of X(i) and X(j) for these {i,j}: {6, 399}, {1351, 2930}, {1352, 11061}, {11898, 16176}, {12177, 15342}
X(19140) = reflection of X(i) in X(j) for these (i,j): (74, 5092), (141, 10272), (182, 6593), (895, 5097)
X(19140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (74, 15462, 5092), (5050, 12308, 16010)
The reciprocal orthologic center of these triangles is X(7387)
X(19141) lies on these lines: {6,1147}, {49,6391}, {68,1176}, {110,6353}, {155,1974}, {156,206}, {511,9932}, {569,6803}, {2330,9931}, {3618,12318}, {5050,12309}, {5085,12301}, {5092,9938}, {9820,19137}, {11411,19121}, {12166,19118}, {12271,19122}, {12282,19123}, {12293,19124}, {12359,19126}, {12417,19133}, {12429,19129}, {13754,19149}, {17836,19132}, {18934,19119}, {19136,19139}, {19171,19196}
X(19141) = midpoint of X(6) and X(9937)
The reciprocal orthologic center of these triangles is X(9729)
X(19142) lies on these lines: {6,2929}, {110,13567}, {206,1614}, {17837,19132}, {18936,19119}, {19171,19198}
X(19142) = midpoint of X(6) and X(2929)
The reciprocal orthologic center of these triangles is X(3)
X(19143) lies on these lines: {3,19135}, {6,12229}, {182,9687}, {486,19126}, {487,1974}, {511,12972}, {642,19137}, {2330,12910}, {3564,6759}, {3618,12320}, {5050,12311}, {5085,12303}, {5092,12984}, {12169,19118}, {12221,19121}, {12274,19122}, {12285,19123}, {12296,19124}, {12509,19128}, {12601,19131}, {12662,19133}, {17839,19132}, {18937,19119}, {19171,19199}
X(19143) = midpoint of X(6) and X(12978)
The reciprocal orthologic center of these triangles is X(3)
X(19144) lies on these lines: {3,19134}, {6,12230}, {182,13030}, {485,19126}, {488,1974}, {511,8909}, {641,19137}, {2330,12911}, {3564,6759}, {3618,12321}, {5050,12312}, {5085,12304}, {5092,12985}, {12170,19118}, {12222,19121}, {12275,19122}, {12286,19123}, {12297,19124}, {12510,19128}, {12602,19131}, {12663,19133}, {17842,19132}, {18938,19119}, {19171,19200}
X(19144) = midpoint of X(6) and X(12979)
The reciprocal orthologic center of these triangles is X(3)
X(19145) lies on these lines: {3,6}, {69,9540}, {141,5418}, {154,8854}, {159,8276}, {485,1503}, {486,3589}, {493,1976}, {542,8980}, {590,1352}, {611,2067}, {613,2066}, {1124,1428}, {1335,2330}, {1513,13638}, {1588,3618}, {1702,16475}, {1853,8280}, {1974,3092}, {2854,10819}, {3068,6776}, {3071,14561}, {3093,12298}, {3564,8909}, {3751,9583}, {5182,19056}, {5480,6561}, {5622,19111}, {5847,13912}, {5848,13913}, {5921,8972}, {6239,19128}, {6252,19133}, {6391,8912}, {6459,14853}, {7374,8975}, {8855,17825}, {8962,10133}, {8976,18440}, {9646,12588}, {9661,12589}, {9679,17792}, {9682,15577}, {9823,19137}, {10168,13847}, {10516,10576}, {10533,13889}, {12171,19118}, {12223,19121}, {12276,19122}, {12287,19123}, {12375,16010}, {17840,19132}, {18941,19119}, {19171,19201}
X(19145) = reflection of X(485) in X(13910)
X(19145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 371, 15883), (3, 3311, 6422), (6, 182, 19146), (6, 5085, 372), (371, 2460, 6221), (1151, 5023, 12974), (1151, 12962, 12313), (1151, 12968, 3), (1350, 2030, 19146), (2459, 6200, 3), (3311, 5050, 6), (3311, 12017, 13331), (3311, 12313, 12962), (3385, 3386, 11825), (5034, 5058, 6), (6221, 15655, 6200)
The reciprocal orthologic center of these triangles is X(3)
X(19146) lies on these lines: {3,6}, {69,13935}, {141,5420}, {154,8855}, {159,8277}, {485,3589}, {486,1503}, {494,1976}, {542,13847}, {611,6502}, {613,5414}, {615,1352}, {1124,2330}, {1335,1428}, {1513,13758}, {1587,3618}, {1703,16475}, {1853,8281}, {1974,3093}, {2854,10820}, {3069,6776}, {3070,14561}, {3092,12299}, {3564,13934}, {5182,19055}, {5480,6560}, {5622,19110}, {5847,13975}, {5848,13977}, {5921,13941}, {6400,19128}, {6404,19133}, {6460,14853}, {7000,13949}, {8854,17825}, {8970,15235}, {9824,19137}, {10168,13846}, {10516,10577}, {10534,13943}, {12172,19118}, {12224,19121}, {12277,19122}, {12288,19123}, {12376,16010}, {13951,18440}, {17843,19132}, {18942,19119}, {19171,19202}
X(19146) = reflection of X(486) in X(13972)
X(19146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 372, 15884), (3, 3312, 6421), (6, 182, 19145), (6, 1691, 6424), (6, 5085, 371), (372, 2459, 6398), (1152, 12963, 3), (1152, 12969, 12314), (1350, 2030, 19145), (1505, 1692, 6), (2460, 6396, 3), (3312, 5050, 6), (3312, 12017, 13331), (3312, 12314, 12969), (3371, 3372, 11824), (5034, 5062, 6)
The reciprocal orthologic center of these triangles is X(10670)
X(19147) lies on these lines: {6,13011}, {182,13030}, {511,13049}, {1974,13051}, {2330,13043}, {3618,13025}, {5050,13023}, {5085,13021}, {5092,13061}, {13007,19118}, {13009,19121}, {13015,19122}, {13017,19123}, {13019,19124}, {13027,19126}, {13035,19128}, {13039,19131}, {13041,19133}, {13053,19137}, {17841,19132}, {18943,19119}, {19171,19203}
X(19147) = midpoint of X(6) and X(13055)
The reciprocal orthologic center of these triangles is X(10674)
X(19148) lies on these lines: {6,13012}, {182,9687}, {511,13050}, {1974,13052}, {2330,13044}, {3618,13026}, {5050,13024}, {5085,13022}, {5092,13062}, {13008,19118}, {13010,19121}, {13016,19122}, {13018,19123}, {13020,19124}, {13028,19126}, {13036,19128}, {13040,19131}, {13042,19133}, {13054,19137}, {17844,19132}, {18944,19119}, {19171,19204}
X(19148) = midpoint of X(6) and X(13056)
The reciprocal orthologic center of these triangles is X(389)
X(19149) lies on these lines: {3,206}, {4,6}, {5,66}, {22,110}, {25,19161}, {30,19139}, {64,1176}, {69,11441}, {132,3162}, {141,3547}, {155,159}, {182,6000}, {184,1619}, {185,1974}, {399,11898}, {1177,5663}, {1351,2393}, {1352,15760}, {1386,6001}, {1428,7355}, {1469,10535}, {1593,19125}, {1598,9969}, {1656,6697}, {1660,3167}, {1853,5133}, {1971,5017}, {1993,7500}, {2330,6285}, {2777,15141}, {2854,17838}, {3098,10282}, {3313,11414}, {3357,5092}, {3556,7193}, {3589,6247}, {3618,12324}, {3763,7558}, {3955,7169}, {5050,12315}, {5097,11216}, {5102,15531}, {5157,7395}, {5621,17854}, {5622,12292}, {5878,12605}, {5895,12225}, {5907,19126}, {6241,19128}, {6254,19133}, {6288,18440}, {6403,14157}, {6467,11470}, {6823,13562}, {7403,14216}, {7494,10192}, {7512,17821}, {7553,9833}, {7669,10608}, {9729,19137}, {9914,11574}, {9924,11477}, {9934,9970}, {10250,15516}, {10516,13160}, {10541,15579}, {10605,18374}, {10606,15578}, {11202,14810}, {11381,19124}, {12017,13093}, {12088,15582}, {12111,19121}, {12162,19131}, {12174,19118}, {12279,19122}, {12290,19123}, {13754,19141}, {14643,15116}, {15068,16618}, {18381,19130}, {18400,19150}, {18439,19129}, {19171,19206}
X(19149) = midpoint of X(i) and X(j) for these {i,j}: {4, 5596}, {9924, 11477}, {9934, 9970}
X(19149) = reflection of X(i) in X(j) for these (i,j): (3, 206), (141, 16252), (3098, 10282), (3357, 5092), (9924, 15581), (18381, 19130)
X(19149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (64, 19132, 5085), (154, 1350, 15577), (1176, 7503, 5085), (5656, 11456, 1498), (7592, 14853, 6)
The reciprocal orthologic center of these triangles is X(6243)
X(19150) lies on these lines: {6,17}, {51,110}, {54,511}, {141,8254}, {182,1154}, {206,576}, {539,5476}, {575,15801}, {1353,10169}, {1428,7356}, {1974,6152}, {2330,6286}, {2854,11702}, {2888,14561}, {2914,9976}, {3098,10610}, {3574,3818}, {3618,12325}, {3629,11536}, {5050,12316}, {5085,12307}, {5092,7691}, {5480,19140}, {6242,19128}, {6255,19133}, {6288,19130}, {8550,11803}, {9972,14913}, {10116,12161}, {11597,12584}, {12175,19118}, {12226,19121}, {12280,19122}, {12291,19123}, {12300,19124}, {12363,19126}, {12606,19131}, {15520,16776}, {17846,19132}, {18400,19149}, {18946,19119}, {19171,19207}
X(19150) = midpoint of X(6) and X(195)
X(19150) = reflection of X(i) in X(j) for these (i,j): (141, 8254), (3098, 10610), (6288, 19130)
X(19151) lies on the Jerabek hyperbola and these lines: {2,18125}, {4,18374}, {66,15139}, {67,184}, {68,11179}, {69,11003}, {74,15578}, {182,265}, {206,15321}, {248,566}, {895,5012}, {1177,15140}, {3050,10097}, {5505,13198}, {5622,11564}, {7492,10510}, {14483,19128}, {18124,18911}
X(19151) = isogonal conjugate of X(5169)
X(19152) lies on these lines: {}
X(19153) lies on these lines: {3,1177}, {6,25}, {64,9968}, {66,3589}, {156,8548}, {160,15905}, {182,6000}, {381,597}, {403,6776}, {511,11202}, {524,3167}, {542,14852}, {575,6759}, {576,10282}, {599,5642}, {924,7633}, {1154,19139}, {1203,3556}, {1351,2070}, {1609,14575}, {1619,5012}, {1992,7426}, {2330,11189}, {2979,19121}, {3148,9407}, {3564,10201}, {3618,5133}, {3629,15585}, {3819,19126}, {3827,5902}, {5085,10606}, {5092,11204}, {5476,18400}, {5480,18494}, {5486,15471}, {5621,17853}, {5622,11456}, {5890,19123}, {5891,19131}, {6329,15583}, {6688,19137}, {6800,12824}, {7493,16789}, {7545,14530}, {7576,14853}, {8547,13248}, {8550,16252}, {9019,9909}, {9707,15073}, {9914,10984}, {9921,11265}, {9922,11266}, {10169,11206}, {10254,18440}, {11190,19133}, {11284,15139}, {11470,13367}, {11477,17821}, {11482,15582}, {11818,18583}, {13093,15579}, {18376,19130}, {18435,19129}, {18950,19119}, {19171,19209}
X(19153) = midpoint of X(6) and X(154)
X(19153) = reflection of X(18376) in X(19130)
X(19153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 206, 159), (6, 18374, 25), (6, 19132, 206), (575, 6759, 8549), (1177, 6593, 15141), (19118, 19125, 6), (19154, 19155, 19139)
X(19154) lies on these lines: {3,19118}, {4,19129}, {5,1974}, {6,26}, {22,1112}, {30,182}, {49,193}, {54,5093}, {66,13561}, {110,11898}, {140,19126}, {141,10020}, {155,19132}, {156,206}, {159,8548}, {184,1353}, {511,1658}, {575,17714}, {576,12107}, {1154,19139}, {1176,3527}, {1177,5663}, {1350,15462}, {1351,14070}, {1352,10201}, {1503,15761}, {2070,6403}, {2330,8144}, {2937,12220}, {3098,15331}, {3589,13371}, {3618,14790}, {3627,19124}, {3628,19137}, {3818,13406}, {5012,9777}, {5085,12084}, {5092,11250}, {5622,10113}, {5889,19123}, {5921,10540}, {7488,18438}, {7502,9967}, {7525,11574}, {7555,11511}, {7556,18449}, {8141,19133}, {9714,12167}, {10226,17508}, {10516,13565}, {10984,16657}, {11412,19122}, {12017,12085}, {12161,19125}, {12294,18570}, {14561,18569}, {14984,15577}, {18377,19130}, {18951,19119}, {19171,19210}
X(19154) = midpoint of X(i) and X(j) for these {i,j}: {6, 26}, {159, 8548}, {1177, 19138}
X(19154) = reflection of X(i) in X(j) for these (i,j): (66, 13561), (141, 10020), (156, 206), (3098, 15331), (3818, 13406), (18377, 19130)
X(19154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (182, 19136, 18583), (1974, 19131, 5), (19121, 19128, 3), (19139, 19153, 19155)
X(19155) lies on these lines: {3,19122}, {6,156}, {26,19132}, {143,1974}, {159,11255}, {182,4550}, {511,12107}, {575,12811}, {1154,19139}, {1493,5093}, {3589,13561}, {5609,5921}, {5876,19129}, {5944,18438}, {6101,19121}, {6102,19128}, {11591,19131}, {12161,19118}, {18379,19130}, {18952,19119}, {19171,19211}
X(19155) = midpoint of X(i) and X(j) for these {i,j}: {6, 156}, {159, 11255}
X(19155) = reflection of X(18379) in X(19130)
X(19155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19122, 19123, 3), (19139, 19153, 19154)
X(19156) lies on these lines: {5,182}, {6,157}, {53,460}, {184,3815}, {263,2965}, {264,685}, {325,2001}, {1176,18092}, {1692,9233}, {3202,11272}, {5012,11174}, {9756,17974}, {17849,19132}, {18380,19130}, {18437,19129}, {18953,19119}, {19171,19212}
X(19156) = midpoint of X(6) and X(157)
X(19156) = reflection of X(18380) in X(19130)
X(19157) lies on these lines: {112,3575}, {11610,16081}
The reciprocal orthologic center of these triangles is X(1297)
X(19158) lies on these lines: {4,251}, {22,1498}, {112,1529}, {1180,1181}, {1503,10313}, {3424,10311}, {6000,9157}
The reciprocal orthologic center of these triangles is X(19158)
X(19159) lies on these lines: {3,11722}, {36,12408}, {55,13099}, {56,1297}, {104,12253}, {112,3428}, {132,958}, {517,13206}, {956,12784}, {999,12265}, {2975,12384}, {3149,13280}, {3320,10966}, {9530,11194}, {11249,19162}, {12114,12925}, {18761,19160}, {19013,19093}, {19014,19094}
The reciprocal orthologic center of these triangles is X(19158)
X(19160) lies on these lines: {4,339}, {30,132}, {112,382}, {127,546}, {381,1297}, {550,6720}, {1478,12955}, {1479,12945}, {1539,9517}, {2781,10113}, {2794,3627}, {3091,12253}, {3320,3583}, {3543,13200}, {3585,6020}, {3830,10735}, {3843,13115}, {3845,9530}, {7530,19165}, {9955,12265}, {10575,16225}, {10718,14269}, {10895,13116}, {10896,13117}, {12207,18502}, {12340,18491}, {12408,18492}, {12478,18495}, {12479,18497}, {12503,18500}, {12699,12784}, {12796,18507}, {12805,18509}, {12806,18511}, {12925,18516}, {12935,18517}, {12943,13312}, {12953,13311}, {12996,18520}, {12997,18522}, {13099,18525}, {13118,18542}, {13119,18544}, {13630,16224}, {13665,19094}, {13785,19093}, {13918,18538}, {13985,18762}, {18761,19159}
X(19160) = midpoint of X(i) and X(j) for these {i,j}: {4, 12918}, {112, 382}, {12699, 12784}, {12796, 18507}, {13099, 18525}
X(19160) = reflection of X(i) in X(j) for these (i,j): (127, 546), (550, 6720)
X(19160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 12384, 10749), (3830, 13310, 10735), (10749, 12918, 12384)
The reciprocal orthologic center of these triangles is X(1297)
X(19161) lies on these lines: {3,6}, {4,66}, {24,206}, {25,19149}, {51,125}, {67,10628}, {69,5889}, {141,5562}, {159,1181}, {184,15577}, {185,1503}, {251,1297}, {524,14831}, {542,11562}, {597,16226}, {1176,7488}, {1204,19124}, {1352,7706}, {1353,14708}, {1370,3060}, {1469,11436}, {1498,7716}, {1594,6697}, {2393,5890}, {2979,11427}, {3515,19125}, {3541,3567}, {3564,6102}, {3618,15043}, {3619,11444}, {3763,11793}, {3818,12162}, {3867,6247}, {3917,7499}, {5446,14790}, {5462,14561}, {5576,19130}, {5596,7487}, {5622,13248}, {5876,18358}, {5891,18388}, {5907,9822}, {5921,11188}, {5946,18583}, {6000,9971}, {6291,14233}, {6406,14230}, {6467,8550}, {6593,16223}, {6644,19139}, {7383,10519}, {7687,15432}, {7728,16194}, {8549,12167}, {9825,13562}, {9968,10594}, {9970,11557}, {9973,13382}, {10574,12220}, {11579,11806}, {12227,12584}, {12235,18951}, {12893,15462}, {13310,18373}, {14912,15073}, {14913,15069}, {14927,15072}, {15030,16776}, {18912,18948}
X(19161) = midpoint of X(i) and X(j) for these {i,j}: {69, 5889}, {185, 1843}
X(19161) = reflection of X(i) in X(j) for these (i,j): (4, 9969), (5876, 18358), (5907, 9822), (6467, 8550), (9970, 11557), (11579, 11806), (15030, 16776)
X(19161) = X(4)-of-1st-orthosymmedial-triangle
X(19161) = inverse-in-circle-{{X(371)X(372),PU(1),PU(39)}} of X(10316)
X(19161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 1192, 5085), (6, 2076, 1970), (51, 12294, 5480), (371, 372, 10316), (389, 11438, 9730), (5890, 6403, 6776), (5907, 9822, 10516), (9729, 11574, 5085), (9730, 9967, 182)
The reciprocal parallelogic center of these triangles is X(10313)
X(19162) lies on these lines: {3,12265}, {36,13221}, {55,10705}, {56,112}, {104,13200}, {127,958}, {517,12340}, {956,13280}, {999,11722}, {1297,3428}, {2794,12114}, {2975,13219}, {3149,12784}, {6020,10966}, {11249,19159}, {11492,13231}, {11493,13229}, {18761,19163}, {19013,19114}, {19014,19115}
The reciprocal parallelogic center of these triangles is X(10313)
X(19163) lies on these lines: {3,10735}, {4,339}, {5,2794}, {30,127}, {112,381}, {132,546}, {140,14689}, {382,1297}, {1478,13297}, {1479,13296}, {1539,2781}, {2881,18312}, {3091,13200}, {3320,3585}, {3543,12253}, {3583,6020}, {3830,10718}, {3843,13310}, {3850,14900}, {7526,19165}, {9517,10113}, {9530,15687}, {9955,11722}, {10095,16224}, {10742,10780}, {10766,18440}, {10895,13311}, {10896,13312}, {12699,13280}, {12943,13117}, {12953,13116}, {13195,18502}, {13206,18491}, {13221,18492}, {13229,18495}, {13231,18497}, {13236,18500}, {13281,18507}, {13282,18509}, {13283,18511}, {13294,18516}, {13295,18517}, {13298,18520}, {13299,18522}, {13313,18542}, {13314,18544}, {13665,19115}, {13785,19114}, {13923,18538}, {13992,18762}, {18761,19162}
X(19163) = midpoint of X(i) and X(j) for these {i,j}: {3, 10735}, {4, 10749}, {382, 1297}, {3830, 10718}, {10705, 18525}, {10742, 10780}, {10766, 18440}, {12699, 13280}, {13281, 18507}
X(19163) = reflection of X(132) in X(546)
X(19163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 13219, 12918), (10749, 12918, 13219)
X(19164) lies on these lines: {4,32}, {22,110}, {127,3547}, {147,4558}, {251,5480}, {577,7710}, {1503,10313}, {2831,3744}, {2967,9861}, {5133,10276}, {6720,7404}, {7387,11641}, {7500,12384}, {7553,12918}, {9512,12131}, {9748,13345}, {10002,17409}, {10749,15760}, {11258,13310}, {11642,14649}, {11674,14157}, {12088,15562}, {14689,18876}
X(19164) = {X(1297), X(9157)}-harmonic conjugate of X(19165)
X(19165) lies on the tangential circle and these lines: {3,114}, {6,3425}, {22,110}, {23,12384}, {24,112}, {25,132}, {98,338}, {157,9756}, {186,13200}, {378,10735}, {842,3447}, {1576,2967}, {1661,9530}, {2070,2080}, {2076,13236}, {2352,14667}, {2799,11616}, {2831,3185}, {2848,14703}, {2871,17974}, {2881,6132}, {2916,8925}, {2931,9517}, {2937,9821}, {3515,14900}, {5078,10016}, {5621,11005}, {6642,6720}, {6644,14649}, {7488,7750}, {7517,12918}, {7526,19163}, {7530,19160}, {8185,12784}, {8276,13923}, {8277,13992}, {8989,9732}, {9590,13221}, {9591,12408}, {9609,10766}, {9658,12945}, {9659,13296}, {9672,13297}, {9673,12955}, {12088,12253}, {13280,15177}, {14070,14655}
X(19165) = midpoint of X(3) and X(11641)
X(19165) = circumcircle-inverse of X(114)
X(19165) = isogonal conjugate of anticomplement of X(39085)
X(19165) = circumperp conjugate of X(38749)
X(19165) = Stammler-circle-inverse of X(38744)
X(19165) = X(105)-of-tangential-triangle if ABC is acute
X(19165) = 1st-orthosymmedial-to-ABC similarity image of X(5)
X(19165) = 2nd-Brocard-circle-inverse of X(32152)
X(19165) = orthoptic-circle-of-Steiner-inellipse-inverse of X(14769)
X(19165) = {X(1297), X(9157)}-harmonic conjugate of X(19164)
X(19166) lies on these lines: {2,19170}, {4,6752}, {54,69}, {97,6515}, {264,5890}, {275,459}, {317,18912}, {417,16035}, {1899,19174}, {6643,19194}, {6776,19189}, {8794,14361}, {8884,18909}, {11245,16030}, {11411,19179}, {12324,19169}, {13567,19180}, {18911,19167}, {18913,19172}, {18914,19173}, {18915,19175}, {18917,19176}, {18918,19177}, {18919,19178}, {18921,19181}, {18922,19182}, {18923,19183}, {18924,19184}, {18925,19185}, {18926,19186}, {18927,19187}, {18928,19188}, {18929,19190}, {18930,19191}, {18931,19192}, {18932,19193}, {18933,19195}, {18934,19196}, {18935,19197}, {18936,19198}, {18937,19199}, {18938,19200}, {18941,19201}, {18942,19202}, {18943,19203}, {18944,19204}, {18945,19205}, {18946,19207}, {18947,19208}, {18950,19209}, {18951,19210}, {18952,19211}, {18953,19212}, {19119,19171}
X(19167) lies on these lines: {3,54}, {22,19180}, {95,7998}, {110,19189}, {275,3060}, {340,520}, {476,1298}, {3580,8901}, {8884,12111}, {11439,19169}, {11440,19172}, {11441,19173}, {11442,19174}, {11443,19178}, {11444,19179}, {11445,19181}, {11446,19182}, {11447,19183}, {11448,19184}, {11449,19185}, {11451,19188}, {11452,19190}, {11453,19191}, {11454,19192}, {11459,19176}, {12270,19195}, {12271,19196}, {12272,19197}, {12273,19193}, {12274,19199}, {12275,19200}, {12276,19201}, {12277,19202}, {12278,19205}, {12279,19206}, {12280,19207}, {13015,19203}, {13016,19204}, {13201,19208}, {18392,19177}, {18911,19166}, {19122,19171}
X(19167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19211, 19168), (54, 19194, 5889)
X(19168) lies on these lines: {3,54}, {24,19180}, {74,19172}, {95,7999}, {275,3567}, {317,18912}, {1614,19189}, {4993,15024}, {4994,9781}, {6241,8884}, {7731,19208}, {11455,19169}, {11456,19173}, {11457,19174}, {11458,19178}, {11459,19179}, {11460,19181}, {11461,19182}, {11462,19183}, {11463,19184}, {11464,19185}, {11465,19188}, {11466,19190}, {11467,19191}, {11468,19192}, {12111,19176}, {12281,19195}, {12282,19196}, {12283,19197}, {12284,19193}, {12285,19199}, {12286,19200}, {12287,19201}, {12288,19202}, {12289,19205}, {12290,19206}, {12291,19207}, {13017,19203}, {13018,19204}, {18394,19177}, {19123,19171}
X(19168) = inverse of X(5618) in the nine-point circle
X(19168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19211, 19167), (97, 19194, 11412), (4994, 9792, 9781), (7592, 16030, 54)
X(19169) lies on these lines: {3,10184}, {4,54}, {20,95}, {24,19192}, {25,19172}, {30,19179}, {33,19175}, {34,19182}, {64,8795}, {96,7576}, {97,3146}, {107,8887}, {185,9792}, {378,19185}, {382,19176}, {1498,19170}, {1593,19189}, {1597,19173}, {1885,19205}, {1906,8901}, {1968,8882}, {3091,19188}, {3575,6801}, {3627,19210}, {3832,4993}, {5198,16035}, {8794,14249}, {11381,19206}, {11403,16030}, {11439,19167}, {11455,19168}, {11470,19178}, {11471,19181}, {11473,19183}, {11474,19184}, {11475,19190}, {11476,19191}, {12162,19194}, {12292,19195}, {12293,19196}, {12294,19197}, {12295,19193}, {12296,19199}, {12297,19200}, {12298,19201}, {12299,19202}, {12300,19207}, {12307,14978}, {12324,19166}, {13019,19203}, {13020,19204}, {13202,19208}, {15811,19180}, {19124,19171}
X(19169) = {X(4), X(8884)}-harmonic conjugate of X(275)
X(19170) lies on these lines: {2,19166}, {3,54}, {6,275}, {25,9792}, {95,394}, {155,19179}, {184,19189}, {185,19172}, {1181,8884}, {1498,19169}, {1593,19206}, {1994,8613}, {4993,5422}, {6776,19174}, {8901,11245}, {10601,19188}, {10602,19178}, {10605,19192}, {10665,16032}, {10666,16037}, {18396,19177}, {18445,19176}, {19125,19171}
X(19170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 19180, 275), (54, 19209, 16030), (11402, 16030, 54)
X(19171) lies on these lines: {6,24}, {95,19126}, {97,19121}, {182,8884}, {275,1974}, {511,19185}, {1176,8795}, {1177,19208}, {1428,19175}, {2330,19182}, {3618,19174}, {5050,19173}, {5085,19172}, {5092,19192}, {5480,19205}, {16030,19118}, {19119,19166}, {19122,19167}, {19123,19168}, {19124,19169}, {19125,19170}, {19129,19176}, {19130,19177}, {19131,19179}, {19132,19180}, {19133,19181}, {19134,19186}, {19135,19187}, {19137,19188}, {19138,19193}, {19139,19194}, {19140,19195}, {19141,19196}, {19142,19198}, {19143,19199}, {19144,19200}, {19145,19201}, {19146,19202}, {19147,19203}, {19148,19204}, {19149,19206}, {19150,19207}, {19153,19209}, {19154,19210}, {19155,19211}, {19156,19212}
X(19171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 19189, 19197), (6, 19197, 19178)
X(19172) lies on these lines: {3,95}, {20,19174}, {25,19169}, {54,64}, {55,19175}, {56,19182}, {74,19168}, {97,11413}, {185,19170}, {275,1593}, {382,19177}, {1151,19183}, {1152,19184}, {1350,19197}, {1885,8901}, {2935,19208}, {3053,8882}, {3516,16030}, {5085,19171}, {5584,19181}, {9786,9792}, {10606,19209}, {10620,19195}, {11440,19167}, {11477,19178}, {11479,19188}, {11480,19190}, {11481,19191}, {12084,19210}, {12163,19194}, {12301,19196}, {12302,19193}, {12303,19199}, {12304,19200}, {12305,19201}, {12306,19202}, {12307,19207}, {13021,19186}, {13022,19187}, {14533,17849}, {15202,16032}, {15205,16037}, {18913,19166}
X(19172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 8884, 19189), (3, 19173, 19185), (20, 19174, 19205), (54, 19206, 19180), (64, 19180, 19206), (1593, 16035, 275), (8884, 19185, 19173), (8884, 19192, 3), (19173, 19185, 19189)
X(19173) lies on these lines: {3,95}, {4,16030}, {5,19174}, {24,16035}, {25,54}, {97,11414}, {275,1598}, {382,19205}, {999,19175}, {1351,19197}, {1597,19169}, {3295,19182}, {3311,19183}, {3312,19184}, {3542,8901}, {3843,19177}, {4994,5198}, {5050,19171}, {5412,16034}, {5413,16029}, {6759,19180}, {7387,19210}, {9792,11432}, {9919,19208}, {10306,19181}, {11441,19167}, {11456,19168}, {11482,19178}, {11484,19188}, {11485,19190}, {11486,19191}, {12164,19194}, {12308,19195}, {12309,19196}, {12310,19193}, {12311,19199}, {12312,19200}, {12313,19201}, {12314,19202}, {12315,19206}, {12316,19207}, {13023,19203}, {13024,19204}, {15199,16037}, {15200,16032}, {18914,19166}
X(19173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8884, 19185, 19172), (8884, 19189, 3), (19172, 19185, 3), (19172, 19189, 19185)
X(19174) lies on these lines: {2,19189}, {4,54}, {5,19173}, {20,19172}, {25,8901}, {69,8795}, {95,7386}, {97,1370}, {263,6524}, {376,19192}, {388,19175}, {427,16030}, {497,19182}, {631,19185}, {1235,3917}, {1503,19180}, {1899,19166}, {1992,19178}, {2052,6403}, {2550,19181}, {3068,19183}, {3069,19184}, {3575,16035}, {3618,19171}, {4993,6997}, {6643,19179}, {6776,19170}, {7392,19188}, {7735,8882}, {9792,11433}, {11411,19194}, {11442,19167}, {11457,19168}, {11488,19190}, {11489,19191}, {12317,19195}, {12318,19196}, {12319,19193}, {12320,19199}, {12321,19200}, {12322,19201}, {12323,19202}, {12324,19206}, {12325,19207}, {12363,14978}, {13025,19203}, {13026,19204}, {13203,19208}, {14790,19210}, {18531,19176}
X(19174) = {X(19172), X(19205)}-harmonic conjugate of X(20)
X(19175) lies on these lines: {1,8884}, {33,19169}, {34,275}, {35,19192}, {36,19185}, {54,65}, {55,19172}, {56,19189}, {73,8795}, {95,1038}, {97,4296}, {172,8882}, {221,19180}, {388,19174}, {999,19173}, {1060,19179}, {1398,16030}, {1428,19171}, {1469,19197}, {2067,19183}, {3585,19177}, {6502,19184}, {7051,19190}, {7352,19194}, {7353,19202}, {7354,19205}, {7355,19206}, {7356,19207}, {7362,19201}, {18447,19176}, {18915,19166}
X(19175) = {X(1), X(8884)}-harmonic conjugate of X(19182)
X(19176) lies on these lines: {3,95}, {4,19210}, {5,49}, {30,97}, {96,6642}, {275,381}, {382,19169}, {546,4994}, {568,9792}, {2980,9833}, {5055,19188}, {5876,19211}, {7728,19208}, {8797,18925}, {8882,10317}, {11459,19167}, {12111,19168}, {12429,19196}, {18403,19177}, {18435,19209}, {18436,19194}, {18437,19212}, {18438,19197}, {18439,19206}, {18445,19170}, {18447,19175}, {18449,19178}, {18451,19180}, {18453,19181}, {18455,19182}, {18457,19183}, {18459,19184}, {18462,19186}, {18463,19187}, {18468,19190}, {18470,19191}, {18531,19174}, {18563,19205}, {18917,19166}, {19129,19171}
X(19176) = {X(8884), X(19179)}-harmonic conjugate of X(3)
X(19177) lies on these lines: {4,54}, {5,19185}, {30,19192}, {95,18531}, {97,3153}, {115,8882}, {265,6528}, {381,19189}, {382,19172}, {542,19178}, {3583,19182}, {3585,19175}, {3818,19197}, {3843,19173}, {5962,14111}, {6288,19207}, {6564,19183}, {6565,19184}, {9792,18390}, {9927,19194}, {16030,18386}, {16808,19190}, {16809,19191}, {18376,19209}, {18377,19210}, {18379,19211}, {18380,19212}, {18381,19206}, {18392,19167}, {18394,19168}, {18396,19170}, {18403,19176}, {18404,19179}, {18405,19180}, {18406,19181}, {18414,19186}, {18415,19187}, {18420,19188}, {18918,19166}, {19130,19171}
X(19177) = {X(5), X(19205)}-harmonic conjugate of X(19185)
X(19178) lies on these lines: {6,24}, {95,11511}, {97,11416}, {275,8541}, {511,19192}, {542,19177}, {575,19185}, {576,8884}, {895,8795}, {1992,19174}, {8538,19179}, {8539,19181}, {8540,19182}, {8548,19194}, {8549,19206}, {8550,19205}, {9813,19188}, {9926,19196}, {9974,19201}, {9975,19202}, {9976,19195}, {9977,19207}, {10602,19170}, {11216,19209}, {11255,19210}, {11405,16030}, {11443,19167}, {11458,19168}, {11470,19169}, {11477,19172}, {11482,19173}, {12596,19193}, {12597,19199}, {12598,19200}, {13037,19203}, {13038,19204}, {13248,19208}, {17813,19180}, {18449,19176}, {18919,19166}
X(19178) = {X(6), X(19197)}-harmonic conjugate of X(19171)
X(19179) lies on these lines: {2,54}, {3,95}, {4,97}, {5,275}, {30,19169}, {52,9792}, {113,19208}, {125,19193}, {140,6760}, {155,19170}, {1060,19175}, {1062,19182}, {1656,19188}, {3090,4993}, {3091,4994}, {5562,19194}, {5891,19209}, {6643,19174}, {6815,8883}, {7395,16030}, {7401,8882}, {7723,19195}, {8251,19181}, {8538,19178}, {9967,19197}, {10634,19190}, {10635,19191}, {10897,19183}, {10898,19184}, {11411,19166}, {11444,19167}, {11459,19168}, {11591,19211}, {12161,13599}, {12162,19206}, {12601,19199}, {12602,19200}, {12603,19201}, {12604,19202}, {12605,19205}, {12606,19207}, {13039,19203}, {13040,19204}, {17814,19180}, {18404,19177}, {19131,19171}
X(19179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 19176, 8884), (5, 19210, 275), (95, 8884, 3)
X(19180) lies on these lines: {6,275}, {22,19167}, {24,19168}, {26,19211}, {54,64}, {95,17811}, {97,394}, {154,19189}, {155,19210}, {184,16030}, {185,16035}, {221,19175}, {1498,8884}, {1503,19174}, {1899,8901}, {2192,19182}, {3197,19181}, {4993,10601}, {4994,10982}, {6759,19173}, {8716,9289}, {9792,17810}, {9924,19197}, {10606,19192}, {13567,19166}, {15811,19169}, {17813,19178}, {17814,19179}, {17819,19183}, {17820,19184}, {17821,19185}, {17825,19188}, {17826,19190}, {17827,19191}, {17834,19194}, {17835,19195}, {17836,19196}, {17837,19198}, {17838,19193}, {17839,19199}, {17840,19201}, {17841,19203}, {17842,19200}, {17843,19202}, {17844,19204}, {17845,19205}, {17846,19207}, {17847,19208}, {17849,19212}, {18405,19177}, {18451,19176}, {19132,19171}
X(19180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 19206, 19172), (275, 19170, 6), (19172, 19206, 64)
X(19181) lies on these lines: {19,275}, {40,8884}, {54,65}, {55,19182}, {71,8795}, {95,10319}, {97,3101}, {2550,19174}, {3197,19180}, {3779,19197}, {5415,19183}, {5416,19184}, {5584,19172}, {6252,19201}, {6253,19205}, {6254,19206}, {6255,19207}, {6404,19202}, {7688,19192}, {7724,19195}, {8141,19210}, {8251,19179}, {8539,19178}, {8882,10315}, {9792,11435}, {9816,19188}, {10119,19208}, {10306,19173}, {10636,19190}, {10637,19191}, {10902,19185}, {11190,19209}, {11406,16030}, {11445,19167}, {11460,19168}, {11471,19169}, {12417,19196}, {12661,19193}, {12662,19199}, {12663,19200}, {13041,19203}, {13042,19204}, {18406,19177}, {18453,19176}, {18921,19166}, {19133,19171}
X(19182) lies on these lines: {1,8884}, {33,275}, {34,19169}, {35,19185}, {36,19192}, {54,6198}, {55,19181}, {56,19172}, {95,1040}, {97,3100}, {497,19174}, {1062,19179}, {1250,19191}, {1914,8882}, {2066,19183}, {2190,8883}, {2192,19180}, {2330,19171}, {3056,19197}, {3295,19173}, {3583,19177}, {5414,19184}, {6238,19194}, {6283,19201}, {6284,19205}, {6285,19206}, {6286,19207}, {6405,19202}, {7071,16030}, {7727,19195}, {8144,19210}, {8540,19178}, {9792,11436}, {9817,19188}, {9931,19196}, {10118,19208}, {10638,19190}, {11189,19209}, {11446,19167}, {11461,19168}, {12888,19193}, {12910,19199}, {12911,19200}, {13043,19203}, {13044,19204}, {18455,19176}, {18922,19166}
X(19182) = {X(1), X(8884)}-harmonic conjugate of X(19175)
X(19183) lies on these lines: {6,24}, {95,11513}, {97,11417}, {275,5412}, {371,8884}, {372,19185}, {1151,19172}, {2066,19182}, {2067,19175}, {3068,19174}, {3070,19205}, {3311,19173}, {5410,16030}, {5415,19181}, {6413,8795}, {6564,19177}, {8901,13884}, {10665,19194}, {10897,19179}, {10961,19188}, {11241,19209}, {11265,19210}, {11447,19167}, {11462,19168}, {11473,19169}, {12375,19195}, {12424,19196}, {12891,19193}, {12960,19199}, {12961,19200}, {12962,19201}, {12963,19202}, {12964,19206}, {12965,19207}, {13045,19203}, {13046,19204}, {13287,19208}, {17819,19180}, {18457,19176}, {18923,19166}
X(19183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 19189, 19184), (8882, 19197, 19184)
X(19184) lies on these lines: {6,24}, {95,11514}, {97,11418}, {275,5413}, {371,19185}, {372,8884}, {1152,19172}, {3069,19174}, {3071,19205}, {3312,19173}, {5411,16030}, {5414,19182}, {5416,19181}, {6396,19192}, {6414,8795}, {6502,19175}, {6565,19177}, {8901,13937}, {10666,19194}, {10898,19179}, {10963,19188}, {11242,19209}, {11266,19210}, {11448,19167}, {11463,19168}, {11474,19169}, {12376,19195}, {12425,19196}, {12892,19193}, {12966,19199}, {12967,19200}, {12968,19201}, {12969,19202}, {12970,19206}, {12971,19207}, {13047,19203}, {13048,19204}, {13288,19208}, {17820,19180}, {18459,19176}, {18924,19166}
X(19184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 19189, 19183), (8882, 19197, 19183)
X(19185) lies on these lines: {3,95}, {4,16837}, {5,19177}, {15,19191}, {16,19190}, {24,275}, {35,19182}, {36,19175}, {39,8882}, {54,186}, {97,7488}, {110,19195}, {182,19197}, {371,19184}, {372,19183}, {378,19169}, {511,19171}, {575,19178}, {578,9792}, {631,19174}, {1147,19194}, {1658,19210}, {3515,16030}, {3518,4994}, {6642,19188}, {6759,19206}, {9932,19196}, {10902,19181}, {11202,19209}, {11449,19167}, {11464,19168}, {12893,19193}, {12972,19199}, {12973,19200}, {12974,19201}, {12975,19202}, {13049,19203}, {13050,19204}, {13289,19208}, {15207,16037}, {15208,16032}, {15750,16035}, {17821,19180}, {18925,19166}
X(19185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 8884, 19192), (3, 19173, 19172), (3, 19189, 8884), (5, 19205, 19177), (19172, 19173, 8884), (19172, 19189, 19173)
X(19186) lies on these lines: {3,19200}, {8884,18980}, {8939,19189}, {9723,19187}, {12590,19197}, {13021,19172}, {18414,19177}, {18462,19176}, {18926,19166}, {18939,19194}, {19134,19171}
X(19187) lies on these lines: {3,19199}, {8884,18981}, {8943,19189}, {9723,19186}, {12591,19197}, {13022,19172}, {18415,19177}, {18463,19176}, {18927,19166}, {18940,19194}, {19135,19171}
X(19188) lies on these lines: {2,95}, {3,14635}, {5,8884}, {54,3090}, {96,7569}, {264,8794}, {276,1073}, {288,14389}, {631,4994}, {641,19200}, {642,19199}, {1656,19179}, {3091,19169}, {3628,19210}, {5020,19189}, {5055,19176}, {5462,19194}, {5943,9792}, {6642,19185}, {6688,19209}, {6723,19208}, {7392,19174}, {8795,15466}, {9729,19206}, {9813,19178}, {9816,19181}, {9817,19182}, {9820,19196}, {9822,19197}, {9823,19201}, {9824,19202}, {9825,19205}, {10601,19170}, {10643,19190}, {10644,19191}, {10961,19183}, {10963,19184}, {11284,16030}, {11451,19167}, {11465,19168}, {11479,19172}, {11484,19173}, {12900,19193}, {13053,19203}, {13054,19204}, {17825,19180}, {18420,19177}, {18928,19166}, {19137,19171}
X(19188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 275, 95), (2, 4993, 275)
X(19189) lies on these lines: {2,19174}, {3,95}, {4,160}, {6,24}, {22,97}, {25,262}, {26,19210}, {55,19181}, {56,19175}, {110,19167}, {154,19180}, {155,19194}, {156,19211}, {157,19212}, {184,19170}, {186,523}, {195,19207}, {237,6530}, {250,2070}, {378,8719}, {381,19177}, {399,19195}, {468,8901}, {842,933}, {935,1141}, {1151,19201}, {1152,19202}, {1498,19206}, {1593,19169}, {1614,19168}, {1995,4993}, {2929,19198}, {2931,19193}, {3135,11547}, {3515,9307}, {4230,14356}, {4994,10594}, {5020,19188}, {6776,19166}, {8939,19186}, {8943,19187}, {9937,19196}, {10117,19208}, {12978,19199}, {12979,19200}, {13055,19203}, {13056,19204}, {15203,16037}, {15204,16032}
X(19189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 8884, 19172), (3, 19173, 8884), (25, 16030, 275), (54, 9792, 6), (8884, 19185, 3), (19171, 19197, 6), (19173, 19185, 19172), (19183, 19184, 6), (19190, 19191, 6)
X(19190) lies on these lines: {6,24}, {15,8884}, {16,19185}, {95,11515}, {97,11420}, {275,10641}, {5318,19205}, {7051,19175}, {10634,19179}, {10636,19181}, {10638,19182}, {10643,19188}, {10645,19192}, {10657,19195}, {10659,19196}, {10661,19194}, {10663,19193}, {10667,19201}, {10671,19202}, {10675,19206}, {10677,19207}, {10681,19208}, {11243,19209}, {11267,19210}, {11408,16030}, {11452,19167}, {11466,19168}, {11475,19169}, {11480,19172}, {11485,19173}, {11488,19174}, {16808,19177}, {17826,19180}, {18468,19176}, {18929,19166}
X(19190) = {X(6), X(19189)}-harmonic conjugate of X(19191)
X(19191) lies on these lines: {6,24}, {15,19185}, {16,8884}, {95,11516}, {97,11421}, {275,10642}, {1250,19182}, {5321,19205}, {10635,19179}, {10637,19181}, {10644,19188}, {10646,19192}, {10658,19195}, {10660,19196}, {10662,19194}, {10664,19193}, {10668,19201}, {10672,19202}, {10676,19206}, {10678,19207}, {10682,19208}, {11244,19209}, {11268,19210}, {11409,16030}, {11453,19167}, {11467,19168}, {11476,19169}, {11481,19172}, {11486,19173}, {11489,19174}, {16809,19177}, {17827,19180}, {18470,19176}, {18930,19166}
X(19191) = {X(6), X(19189)}-harmonic conjugate of X(19190)
X(19192) lies on these lines: {3,95}, {24,19169}, {30,19177}, {35,19175}, {36,19182}, {54,74}, {97,2071}, {187,8882}, {275,378}, {376,19174}, {511,19178}, {550,19205}, {3098,19197}, {3357,19206}, {3516,16035}, {4993,7527}, {4994,14865}, {5092,19171}, {6396,19184}, {7688,19181}, {7689,19194}, {7690,19201}, {7691,19207}, {7692,19202}, {9792,11438}, {9938,19196}, {10605,19170}, {10606,19180}, {10645,19190}, {10646,19191}, {11204,19209}, {11250,19210}, {11410,16030}, {11454,19167}, {11468,19168}, {12901,19193}, {12984,19199}, {12985,19200}, {13061,19203}, {13062,19204}, {15206,16032}, {15209,16037}, {18931,19166}
X(19192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 8884, 19185), (3, 19172, 8884)
The reciprocal orthologic center of these triangles is X(15136)
X(19193) lies on these lines: {5,49}, {74,97}, {95,6699}, {113,275}, {125,19179}, {399,3484}, {2931,19189}, {5504,8795}, {5663,19206}, {8884,17702}, {9792,12236}, {10663,19190}, {10664,19191}, {12168,16030}, {12273,19167}, {12284,19168}, {12295,19169}, {12302,19172}, {12310,19173}, {12319,19174}, {12596,19178}, {12661,19181}, {12888,19182}, {12891,19183}, {12892,19184}, {12893,19185}, {12900,19188}, {12901,19192}, {13754,19195}, {14984,19197}, {17838,19180}, {18932,19166}, {19138,19171}
The reciprocal orthologic center of these triangles is X(12160)
X(19194) lies on these lines: {3,54}, {5,9792}, {30,19206}, {52,275}, {68,317}, {95,1216}, {155,19189}, {539,19207}, {1147,19185}, {3060,4994}, {3564,19197}, {3567,4993}, {5462,19188}, {5562,19179}, {6238,19182}, {6643,19166}, {7352,19175}, {7689,19192}, {8548,19178}, {8884,13754}, {9927,19177}, {10661,19190}, {10662,19191}, {10665,19183}, {10666,19184}, {11411,19174}, {12162,19169}, {12163,19172}, {12164,19173}, {17702,19195}, {17834,19180}, {18436,19176}, {18939,19186}, {18940,19187}, {19139,19171}
X(19194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5889, 19167, 54), (11412, 19168, 97), (19210, 19211, 19209)
The reciprocal orthologic center of these triangles is X(3581)
X(19195) lies on these lines: {54,74}, {95,12358}, {97,12219}, {110,19185}, {265,6528}, {275,1986}, {399,19189}, {542,19197}, {2777,19206}, {5663,8884}, {7687,9792}, {7723,19179}, {7724,19181}, {7727,19182}, {8882,14901}, {9976,19178}, {10620,19172}, {10657,19190}, {10658,19191}, {12165,16030}, {12270,19167}, {12281,19168}, {12292,19169}, {12308,19173}, {12317,19174}, {12375,19183}, {12376,19184}, {13754,19193}, {17702,19194}, {17835,19180}, {18933,19166}, {19140,19171}, {19205,19207}
The reciprocal orthologic center of these triangles is X(7387)
X(19196) lies on these lines: {2,54}, {95,12359}, {97,11411}, {155,275}, {3564,19210}, {8795,15316}, {9792,12235}, {9820,19188}, {9926,19178}, {9931,19182}, {9932,19185}, {9937,19189}, {9938,19192}, {10659,19190}, {10660,19191}, {12166,16030}, {12271,19167}, {12282,19168}, {12293,19169}, {12301,19172}, {12309,19173}, {12318,19174}, {12417,19181}, {12424,19183}, {12425,19184}, {12429,19176}, {13754,19206}, {17836,19180}, {18934,19166}, {19141,19171}
The reciprocal orthologic center of these triangles is X(576)
X(19197) lies on these lines: {6,24}, {69,8795}, {95,11574}, {97,12220}, {182,19185}, {275,1843}, {511,8884}, {542,19195}, {1350,19172}, {1351,19173}, {1469,19175}, {1503,19205}, {2393,19209}, {2871,19212}, {3056,19182}, {3098,19192}, {3564,19194}, {3779,19181}, {3818,19177}, {5965,19207}, {9822,19188}, {9924,19180}, {9967,19179}, {12167,16030}, {12272,19167}, {12283,19168}, {12294,19169}, {12590,19186}, {12591,19187}, {14984,19193}, {18438,19176}, {18935,19166}
X(19197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 19189, 19171), (19171, 19178, 6), (19183, 19184, 8882), (19201, 19202, 8884)
The reciprocal orthologic center of these triangles is X(9729)
X(19198) lies on these lines: {54,403}, {2929,19189}, {3260,8795}, {17837,19180}, {18936,19166}, {19142,19171}
The reciprocal orthologic center of these triangles is X(3)
X(19199) lies on these lines: {3,19187}, {54,12229}, {95,486}, {97,12221}, {275,487}, {642,19188}, {3564,19200}, {8884,19204}, {9792,12237}, {12169,16030}, {12274,19167}, {12285,19168}, {12296,19169}, {12303,19172}, {12311,19173}, {12320,19174}, {12597,19178}, {12601,19179}, {12662,19181}, {12910,19182}, {12960,19183}, {12966,19184}, {12972,19185}, {12978,19189}, {12980,19190}, {12981,19191}, {12984,19192}, {17839,19180}, {18937,19166}, {19143,19171}
The reciprocal orthologic center of these triangles is X(3)
X(19200) lies on these lines: {3,19186}, {54,12230}, {95,485}, {97,12222}, {275,488}, {641,19188}, {3564,19199}, {8884,19203}, {9792,12238}, {12170,16030}, {12275,19167}, {12286,19168}, {12297,19169}, {12304,19172}, {12312,19173}, {12321,19174}, {12598,19178}, {12602,19179}, {12663,19181}, {12911,19182}, {12961,19183}, {12967,19184}, {12973,19185}, {12979,19189}, {12982,19190}, {12983,19191}, {12985,19192}, {17842,19180}, {18938,19166}, {19144,19171}
The reciprocal orthologic center of these triangles is X(3)
X(19201) lies on these lines: {54,6239}, {95,12360}, {97,12223}, {275,6291}, {511,8884}, {1151,19189}, {6252,19181}, {6283,19182}, {7362,19175}, {7690,19192}, {9792,12239}, {9823,19188}, {9974,19178}, {10667,19190}, {10668,19191}, {12171,16030}, {12276,19167}, {12287,19168}, {12298,19169}, {12305,19172}, {12313,19173}, {12322,19174}, {12603,19179}, {12962,19183}, {12968,19184}, {12974,19185}, {17840,19180}, {18941,19166}, {19145,19171}
X(19201) = {X(8884), X(19197)}-harmonic conjugate of X(19202)
The reciprocal orthologic center of these triangles is X(3)
X(19202) lies on these lines: {54,6400}, {95,12361}, {97,12224}, {275,6406}, {511,8884}, {1152,19189}, {6404,19181}, {6405,19182}, {7353,19175}, {7692,19192}, {9792,12240}, {9824,19188}, {9975,19178}, {10671,19190}, {10672,19191}, {12172,16030}, {12277,19167}, {12288,19168}, {12299,19169}, {12306,19172}, {12314,19173}, {12323,19174}, {12604,19179}, {12963,19183}, {12969,19184}, {12975,19185}, {17843,19180}, {18942,19166}, {19146,19171}
The reciprocal orthologic center of these triangles is X(10670)
X(19203) lies on these lines: {54,13011}, {95,13027}, {97,13009}, {275,13051}, {8884,19200}, {9792,13013}, {13007,16030}, {13015,19167}, {13017,19168}, {13019,19169}, {13021,19172}, {13023,19173}, {13025,19174}, {13037,19178}, {13039,19179}, {13041,19181}, {13043,19182}, {13045,19183}, {13047,19184}, {13049,19185}, {13053,19188}, {13055,19189}, {13061,19192}, {17841,19180}, {18943,19166}, {19147,19171}
The reciprocal orthologic center of these triangles is X(10674)
X(19204) lies on these lines: {54,13012}, {95,13028}, {97,13010}, {275,13052}, {8884,19199}, {9792,13014}, {13008,16030}, {13016,19167}, {13018,19168}, {13020,19169}, {13022,19172}, {13024,19173}, {13026,19174}, {13038,19178}, {13040,19179}, {13042,19181}, {13044,19182}, {13046,19183}, {13048,19184}, {13050,19185}, {13054,19188}, {13056,19189}, {13062,19192}, {17844,19180}, {18944,19166}, {19148,19171}
The reciprocal orthologic center of these triangles is X(4)
X(19205) lies on these lines: {4,160}, {5,19177}, {20,19172}, {30,1105}, {54,6240}, {95,12362}, {97,12225}, {275,3575}, {382,19173}, {550,19192}, {1503,19197}, {1885,19169}, {3070,19183}, {3071,19184}, {4994,7576}, {5254,8882}, {5318,19190}, {5321,19191}, {5480,19171}, {6253,19181}, {6284,19182}, {7354,19175}, {8550,19178}, {8795,9291}, {9792,12241}, {9825,19188}, {12173,16030}, {12278,19167}, {12289,19168}, {12605,19179}, {17845,19180}, {18563,19176}, {18945,19166}, {19195,19207}
X(19205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (20, 19174, 19172), (19177, 19185, 5)
The reciprocal orthologic center of these triangles is X(389)
X(19206) lies on these lines: {4,6752}, {30,19194}, {54,64}, {95,5907}, {97,12111}, {99,1298}, {185,275}, {1498,19189}, {1503,19197}, {1593,19170}, {2777,19195}, {3357,19192}, {4993,10574}, {4994,5890}, {5663,19193}, {6000,8884}, {6254,19181}, {6285,19182}, {6759,19185}, {7355,19175}, {8549,19178}, {9729,19188}, {10675,19190}, {10676,19191}, {11381,19169}, {12162,19179}, {12174,16030}, {12279,19167}, {12290,19168}, {12315,19173}, {12324,19174}, {12964,19183}, {12970,19184}, {13754,19196}, {18381,19177}, {18400,19207}, {18439,19176}, {19149,19171}
X(19206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (64, 19180, 19172), (19172, 19180, 54)
The reciprocal orthologic center of these triangles is X(6243)
X(19207) lies on these lines: {54,186}, {95,12363}, {97,12226}, {195,19189}, {275,6152}, {340,3519}, {539,19194}, {1154,8884}, {5965,19197}, {6255,19181}, {6286,19182}, {6288,19177}, {7356,19175}, {7691,19192}, {9792,12242}, {9977,19178}, {10677,19190}, {10678,19191}, {12175,16030}, {12280,19167}, {12291,19168}, {12300,19169}, {12307,19172}, {12316,19173}, {12325,19174}, {12606,19179}, {12965,19183}, {12971,19184}, {17846,19180}, {18400,19206}, {18946,19166}, {19150,19171}, {19195,19205}
The reciprocal parallelogic center of these triangles is X(15139)
X(19208) lies on these lines: {54,74}, {95,5972}, {97,110}, {113,19179}, {125,275}, {1112,9792}, {1177,19171}, {2777,8884}, {2781,19209}, {2935,19172}, {3484,12281}, {4993,15059}, {4994,14644}, {5663,19193}, {6723,19188}, {7728,19176}, {7731,19168}, {9919,19173}, {10117,19189}, {10118,19182}, {10119,19181}, {10681,19190}, {10682,19191}, {13171,16030}, {13201,19167}, {13202,19169}, {13203,19174}, {13248,19178}, {13287,19183}, {13288,19184}, {13289,19185}, {17847,19180}, {18947,19166}
X(19209) lies on these lines: {3,54}, {51,107}, {95,3819}, {154,19180}, {2393,19197}, {2781,19208}, {4993,11451}, {5891,19179}, {6000,8884}, {6688,19188}, {10606,19172}, {11189,19182}, {11190,19181}, {11202,19185}, {11204,19192}, {11216,19178}, {11241,19183}, {11242,19184}, {11243,19190}, {11244,19191}, {18376,19177}, {18435,19176}, {18950,19166}, {19153,19171}
X(19209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (16030, 19170, 54), (19210, 19211, 19194)
Let L be the line through X(3) parallel to BC. Let Ab = L∩AB, and Ac = L∩AC, and let D = midpoint of AX(4). Let A' be the point, other than A, in which the circles {{B,D,Ab}} and {{C, D,Ac}} meet. Define B' and C' cyclically. The finite fixed point of the affine transformation that carries ABC onto A'B'C' is X(19210). (Angel Montesdeoca, April 13, 2021)
X(19210) lies on these lines: {3,54}, {4,19176}, {5,275}, {26,19189}, {30,1105}, {49,418}, {95,140}, {96,2986}, {143,9792}, {155,19180}, {381,4994}, {394,16391}, {417,15958}, {539,10600}, {550,933}, {577,1147}, {648,15912}, {1576,10282}, {1656,4993}, {1658,19185}, {3284,5462}, {3484,5876}, {3564,19196}, {3627,19169}, {3628,19188}, {3933,6394}, {5663,19193}, {6638,13855}, {6642,8882}, {6760,14371}, {7387,19173}, {8141,19181}, {8144,19182}, {8154,12254}, {11250,19192}, {11255,19178}, {11265,19183}, {11266,19184}, {11267,19190}, {11268,19191}, {11591,15781}, {12084,19172}, {12605,13557}, {14790,19174}, {18377,19177}, {18951,19166}, {19154,19171}
X(19210) = isogonal conjugate of X(13450)
X(19210) = X(53)-isoconjugate of X(92)
X(19210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 97, 3), (54, 8883, 16035), (275, 19179, 5), (19194, 19209, 19211)
X(19211) lies on these lines: {3,54}, {26,19180}, {143,275}, {156,19189}, {4993,15026}, {5663,8884}, {5876,19176}, {9792,10095}, {11591,19179}, {18379,19177}, {18952,19166}, {19155,19171}
X(19211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (19167, 19168, 3), (19194, 19209, 19210)
X(19212) lies on these lines: {53,275}, {157,19189}, {1503,8884}, {2871,19197}, {8795,14533}, {17849,19180}, {18380,19177}, {18437,19176}, {18953,19166}, {19156,19171}
X(19213) lies on the cubic K1039 and these lines: {1, 2129}, {63, 8769}
X(19213) = X(19)-Ceva conjugate of X(8769)
X(19213) = barycentric product X(8769)*X(18287)
X(19213) = barycentric quotient X(18287)/X(18156)
X(19214) lies on the cubic K1039 and this line: {1707, 2128}
X(19214) = X(63)-cross conjugate of X(1707)
X(19214) = X(i)-isoconjugate of X(j) for these (i,j): {8770, 18287}
X(19214) = barycentric quotient X(i)/X(j) for these {i,j}: {1707, 18287}
X(19215) lies on the Feuerbach hyperbola of the tangential triangle, the cubic K1039 and these lines:
{1, 1805}, {3, 6212}, {6, 6203}, {48, 63}, {155, 6213}, {159, 9043}, {2164, 7348}, {2178, 6204}
X(19215) = X(i)-isoconjugate of X(j) for these (i,j): {2, 8948}, {4, 493}, {25, 5490}, {1306, 2501}
X(19215) = barycentric product X(i)*X(j) for these {i,j}: {1, 488}, {19, 8222}, {63, 3068}, {75, 10132}, {304, 6423}, {326, 5200}, {662, 17431}
X(19215) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 8948}, {48, 493}, {63, 5490}, {488, 75}, {3068, 92}, {4575, 1306}, {5200, 158}, {6423, 19}, {8222, 304}, {10132, 1}, {17431, 1577}
X(19215) = {X(48),X(63)}-harmonic conjugate of X(19216)
X(19216) lies on the Feuerbach hyperbola of the tangential triangle, the cubic K1039, and these lines:
{1, 1806}, {3, 6213}, {6, 6204}, {48, 63}, {155, 6212}, {159, 9042}, {2164, 7347}, {2178, 6203}
X(19216) = X(i)-isoconjugate of X(j) for these (i,j): {2, 8946}, {4, 494}, {25, 5491}, {1307, 2501}, {5200, 6464}
X(19216) = barycentric product X(i)*X(j) for these {i,j}: {1, 487}, {19, 8223}, {63, 3069}, {75, 10133}, {304, 6424}, {662, 17432}
X(19216) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 8946}, {48, 494}, {63, 5491}, {487, 75}, {3069, 92}, {4575, 1307}, {6424, 19}, {8223, 304}, {10133, 1}, {17432, 1577}
X(19216) = {X(48),X(63)}-harmonic conjugate of X(19215)
X(19217) lies on the cubic K1039, the curve Q066, and these lines:
{494, 1880}, {1707, 3377}, {1824, 6212}, {1826, 13386}, {2128, 17442}
X(19217) = X(i)-isoconjugate of X(j) for these (i,j): {2, 10133}, {3, 3069}, {6, 487}, {25, 8223}, {69, 6424}, {110, 17432}
X(19217) = barycentric product X(i)*X(j) for these {i,j}: {19, 5491}, {75, 8946}, {92, 494}
X(19217) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 487}, {19, 3069}, {31, 10133}, {63, 8223}, {494, 63}, {661, 17432}, {1307, 4592}, {1973, 6424}, {5491, 304}, {8946, 1}
X(19218) lies on the cubic K1039, the curve Q066, and these lines:
{493, 1880}, {1707, 3378}, {1824, 6213}, {1826, 13387}, {2128, 17442}
X(19218) = X(i)-isoconjugate of X(j) for these (i,j): {2, 10132}, {3, 3068}, {6, 488}, {25, 8222}, {69, 6423}, {110, 17431}, {394, 5200}
X(19218) = barycentric product X(i)*X(j) for these {i,j}: {19, 5490}, {75, 8948}, {92, 493}
X(19218) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 488}, {19, 3068}, {31, 10132}, {63, 8222}, {493, 63}, {661, 17431}, {1096, 5200}, {1306, 4592}, {1973, 6423}, {5490, 304}, {8948, 1}
X(19219) lies on these lines:
{2, 3}, {6, 6218}, {51, 7581}, {154, 1588}, {184, 7582}, {459, 14237}, {1163, 1165}, {1249, 5412}, {1587, 17810}, {1899, 14242}, {3068, 8383}, {5871, 13567}, {6515, 9929}, {7585, 11388}, {10783, 11433}, {10784, 11206}
X(19219) = X(1163)-cross conjugate of X(4)
X(19219) = barycentric product X(i)*X(j) for these {i,j}: {4, 7586}
X(19219) = barycentric quotient X(i)/X(j) for these {i,j}: {1163, 5591}, {1165, 5590}, {7586, 69}
X(19219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4, 6353, 3536), (428, 3127, 4), (1585, 6995, 4)
X(19220) lies on these lines:
{6,18373}, {22,187}, {30,32}, {39,378}, {50,3534}, {112,2549}, {184,512}, {251,7391}, {427,5475}, {571,6781}, {574,18570}, {2781,5028}, {3016,9306}, {3053,12083}, {3163,5063}, {5206,7502}, {7746,15760}, {7756,10316}, {10314,18424}
X(19220) = isogonal conjugate of X(18880)
X(19220) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18880}, {75, 18881}
X(19220) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18880}, {32, 18881}
X(19221) lies on these lines:
{2,16306}, {3,523}, {6,3260}, {141,1990}, {183,2493}, {315,524}, {1235,2207}, {6248,8542}, {7887,18122}, {8547,12203}, {10358,12039}
X(19221) = isogonal conjugate of X(18881)
X(19221) = isotomic conjugate of X(18880)
X(19221) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18881}, {31, 18880}
X(19221) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 18880}, {6, 18881}
X(19222) lies on the Jerabek hyperbola, the cubics K790, K1012, K1037, and these lines: {3,194}, {6,419}, {69,3978}, {71,4039}, {327,6784}, {695,5286}, {3114,18906}, {3117,7735}
X(19222) = isogonal conjugate of X(11328)
X(19222) = isotomic conjugate of X(18906)
X(19222) = cevapoint of X(523) and X(6784)
X(19222) = X(3094)-cross conjugate of X(2)
X(19222) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11328}, {31, 18906}, {1580, 6234}
X(19222) = trilinear pole of line {647, 804}
X(19222) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 18906}, {6, 11328}, {694, 6234}
At X(1138), it is noted that "There are only two points X siuch that the pedal triangle of X is similar to the cevian triangle of X. They are X(4) and X(1138)." (Jean-Pierre Ehrmann, January 4, 2003). In the case that X = X(1138), the center of similitude is X(19223). See Angel Montesdeoca, HG040618.
X(19223) lies on this line: {477,1138}
X(19224) lies on these lines: {2, 3}, {238, 16826}
X(19225) lies on this line: {2, 3}
X(19226) lies on this line: {2, 3}
X(19227) lies on this line: {2, 3}
X(19228) lies on this line: {2, 3}
X(19229) lies on these lines: {2, 3}, {1203, 16826}
X(19230) lies on this line: {2, 3}
X(19231) lies on this line: {2, 3}
X(19232) lies on these lines: {2, 3}, {5259, 16827}
X(19233) lies on this line: {2,3}
X(19234) lies on this line: {2,3}
X(19235) lies on this line: {2,3}
X(19236) lies on these lines: this line: {2,3}
X(19237) lies on these lines: {2, 3}, {239, 5251}, {958, 4393}, {993, 17397}, {1621, 6542}, {3661, 5248}, {5247, 17011}, {5259, 16826}
X(19238) lies on these lines: {2, 3}, {956, 17349}, {993, 17123}, {995, 5247}
X(19239) lies on these lines: {2, 3}, {956, 995}
X(19240) lies on these lines: {2, 3}, {667, 993}
X(19241) lies on these lines: {1, 4557}, {2, 3}, {373, 5396}, {956, 17277}, {995, 3304}, {3679, 18613}, {4279, 16483}, {5247, 5563}, {5398, 5651}, {5587, 15626}, {7989, 15622}, {9956, 15623}
X(19242) lies on this line: {2,3}
X(19243) lies on these lines: {2, 3}, {958, 995}, {1001, 4279}, {5251, 17123}, {5255, 5259}, {9708, 17277}
X(19244) lies on these lines: {2, 3}, {995, 12513}
X(19245) lies on these lines: {2, 3}, {36, 748}, {56, 651}, {110, 5398}, {957, 2990}, {995, 1203}, {3241, 18613}, {5253, 15654}, {5396, 5640}
X(19246) lies on these lines: {2, 3}, {9, 995}
X(19247) lies on these lines: {2, 3}, {58, 11194}, {519, 4267}, {956, 4921}, {3794, 10246}, {4276, 4421}, {4428, 4653}
X(19248) lies on these lines: {2, 3}, {995, 6767}, {999, 16499}, {1125, 15621}
X(19249) lies on these lines: {2, 3}, {995, 3303}, {5396, 5650}, {10165, 15626}
X(19250) lies on these lines: {2, 3}, {10, 18613}, {995, 1126}, {996, 9708}, {999, 4383}, {3828, 15621}, {5396, 6688}
X(19251) lies on these lines: {2, 3}, {154, 2818}, {995, 4252}, {4669, 15621}, {11194, 15654}
X(19252) lies on this line: {2, 3}
X(19253) lies on these lines: {2, 3}, {3828, 18613}, {5398, 16187}
X(19254) lies on these lines: {2, 3}, {995, 5204}, {1631, 14793}, {4677, 15621}
X(19255) lies on these lines: {2, 3}, {995, 11194}
X(19256) lies on these lines: {1, 957}, {2, 3}, {73, 995}, {198, 5802}, {228, 3488}, {391, 956}, {1697, 2654}, {1724, 2360}, {1745, 7963}, {3185, 18391}, {7288, 15654}
X(19257) lies on these lines: {1, 4277}, {2, 3}, {392, 573}, {581, 17614}, {956, 966}, {999, 5739}, {1724, 5035}
X(19258) lies on these lines: {2, 3}, {999, 18134}, {1376, 17734}, {4680, 16687}, {5224, 9708}
X(19259) lies on these lines: {2, 3}, {10, 4267}, {58, 958}, {81, 956}, {86, 999}, {171, 5251}, {284, 5783}, {332, 1057}, {333, 5774}, {517, 17185}, {519, 18185}, {759, 831}, {942, 10461}, {993, 3286}, {995, 1001}, {1043, 3295}, {1376, 4276}, {2099, 18417}, {3786, 3940}, {4658, 12513}, {4803, 8168}, {5208, 15934}, {5603, 17183}, {5886, 17182}, {9623, 18163}, {10246, 18465}
X(19260) lies on these lines: {2, 3}, {238, 993}, {999, 17379}, {2975, 16466}, {4112, 5251}, {4267, 10449}, {4279, 4653}, {5248, 5255}
X(19261) lies on these lines: {2, 3}, {386, 18185}, {551, 15621}, {995, 1616}, {1125, 18613}, {3819, 5396}, {4267, 17749}
X(19262) lies on these lines: {2, 3}, {56, 4340}, {104, 1310}, {333, 5767}, {345, 5657}, {387, 4267}, {515, 10434}, {581, 10470}, {946, 10882}, {956, 14552}, {991, 995}, {993, 3220}, {999, 3945}, {3332, 3428}, {4293, 16678}, {5361, 5769}, {5603, 10446}
X(19263) lies on these lines: {2, 3}, {39, 995}, {4660, 8053}
X(19264) lies on these lines: {2, 3}, {284, 995}, {999, 2303}, {16699, 18596}
X(19265) lies on these lines: {2, 3}, {1698, 15621}, {10175, 15626}
X(19266) lies on these lines: {2, 3}, {69, 999}, {995, 1386}, {997, 4259}, {1402, 5252}, {3931, 5836}
X19267) lies on these lines: {2, 3}, {518, 995}, {999, 3618}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27743.
X(19268) lies on these lines: {5,930}, {128,1154}, {10615,14071}
X(19269) lies on these lines: {2, 3}, {238, 3739}, {16466, 16825}
X(19270) lies on these lines: {1,3769}, {2,3}, {10,4256}, {35,5263}, {86,5156}, {95,2190}, {145,5774}, {171,595}, {332,5224}, {333,386}, {495,5484}, {894,3916}, {993,1220}, {1043,10479}, {1213,5110}, {1222,16499}, {1330,5718}, {1460,7288}, {2305,17398}, {3216,3736}, {3616,5711}, {3624,15485}, {3752,16817}, {4026,4999}, {4255,5737}, {4357,13411}, {4420,4981}, {4646,16821}, {5247,6685}, {5296,5783}, {10436,15803}, {14828,16887}, {17592,17733}
X(19271) lies on these lines: {2, 3}, {31, 3980}, {894, 5138}, {1468, 4362}
X(19272) lies on these lines: {2, 3}, {3624, 5737}, {15668, 16468}
X(19273) lies on these lines: {1, 5774}, {2, 3}, {10, 4255}, {171, 3624}, {386, 5737}, {1125, 1191}, {1460, 5433}, {3736, 17259}, {4042, 5312}, {4357, 11374}, {4413, 16828}, {5156, 15668}, {5257, 5783}, {5295, 18229}, {5530, 5827}, {5765, 17306}
X(19274) lies on these lines: {2, 3}, {171, 3632}, {996, 3626}, {3244, 5711}, {3445, 3636}
X(19275) lies on these lines: {2, 3}, {995, 2334}, {1698, 18613}
X(19276) lies on these lines: {2, 3}, {10, 4252}, {171, 3679}, {519, 5711}, {551, 4356}, {894, 3940}, {999, 5263}, {1220, 9709}, {1460, 5434}, {4257, 5737}, {4653, 15668}, {4720, 14996}, {5827, 5955}
X(19277) lies on these lines: {2, 3}, {519, 4923}, {540, 17251}, {1460, 11237}, {3679, 5711}, {4357, 18541}, {5263, 6767}, {8583, 18506}, {10436, 15934}
X() lies on these lines: {2, 3}, {145, 5372}, {171, 3616}, {332, 5232}, {333, 4255}, {386, 18169}, {894, 4652}, {966, 5110}, {988, 3757}, {1125, 8616}, {1460, 5265}, {3085, 5484}, {3621, 5774}, {3622, 5711}, {3736, 17349}, {4256, 9534}, {4673, 4689}, {5156, 17379}, {5217, 5263}
X(19279) lies on these lines: {2, 3}, {519, 5774}, {551, 1616}, {1125, 3052}, {1460, 5298}, {4256, 5737}, {5122, 10436}
X(19280) lies on these lines: {2, 3}, {10, 4886}, {86, 10479}, {171, 3634}, {1460, 10588}, {1698, 16468}, {1714, 17381}, {3746, 5263}, {5711, 9780}, {10436, 10466}
X(19281) lies on these lines: {2, 3}, {6, 75}, {608, 1441}, {1724, 4384}, {2221, 4359}, {3187, 4968}, {3661, 7270}, {3948, 5275}, {5247, 5271}
X(19282) lies on these lines: {2, 3}, {940, 5247}, {958, 15668}, {978, 4423}, {3831, 5737}
X(19283) lies on these lines: {2, 3}, {41, 965}, {56, 15668}, {940, 958}, {978, 5259}, {1001, 1193}, {1150, 5260}, {3980, 12567}, {8583, 10470}, {9708, 17751}
X(19284) lies on these lines: {1, 17495}, {2, 3}, {145, 940}, {750, 17751}, {975, 3995}, {976, 17140}, {1150, 3617}, {1468, 4651}, {3753, 5482}, {3980, 17164}, {3989, 8720}, {4252, 5278}, {4855, 10436}, {4881, 10470}, {5253, 5263}, {5267, 16828}, {5293, 17165}, {9534, 16704}, {16948, 17277}, {17163, 17733}
X(19285) lies on these lines: {2, 3}, {72, 965}, {940, 5439}, {975, 5440}, {1453, 5437}, {3753, 5706}, {5279, 15650}
X(19286) lies on these lines: {2, 3}, {940, 3555}, {3295, 4359}
X(19287) lies on these lines: {2, 3}, {37, 5440}, {1104, 5439}, {1125, 2218}, {1754, 3753}
X(19288) lies on these lines: {2, 3}, {3873, 16830}
X(19289) lies on these lines: {2, 3}, {940, 3636}
X(19290) lies on these lines: {2, 3}, {519, 940}, {975, 3175}, {4859, 15668}, {5440, 10436}
X(19291) lies on these lines: {2, 3}, {8, 18613}, {36, 17125}, {5396, 11451}
X(19292) lies on these lines: {2, 3}, {36, 17124}, {995, 3746}, {5396, 7998}
X(19293) lies on thie line: {2, 3}
X(19294) lies on the cubics K390 and K752 and these lines: {6, 2981}, {15, 1154}, {16, 1511}, {50, 323}, {62, 11624}, {395, 6128}, {396, 532}, {526, 6137}, {3171, 11135}, {5357, 6149}, {6151, 14579}, {10410, 11089}
X(19294) = midpoint of X(11126) and X(17403)
X(19294) = X(11600)-complementary conjugate of X(2887)
X(19294) = X(i)-Ceva conjugate of X(j) for these (i,j): {11126, 1154}, {11131, 1511}, {17403, 526}
X(19294) = X(i)-isoconjugate of X(j) for these (i,j): {75, 11084}, {2153, 11117}, {2154, 11119}, {2166, 2981}
X(19294) = crosspoint of X(i) and X(j) for these (i,j): {2, 11600}, {16, 323}
X(19294) = crossdifference of every pair of points on line {13, 15475}
X(19294) = crosssum of X(i) and X(j) for these (i,j): {6, 6104}, {14, 1989}
X(19294) = X(16)-daleth conjugate of X(1511)
X(19294) = barycentric product X(i)*X(j) for these {i,j}: {6, 14922}, {15, 532}, {16, 618}, {323, 396}, {3479, 14369}, {14446, 17402}
X(19294) = barycentric quotient X(i)/X(j) for these {i,j}: {15, 11117}, {16, 11119}, {32, 11084}, {50, 2981}, {396, 94}, {463, 6344}, {532, 300}, {618, 301}, {14922, 76}
X(19294) = {X(50),X(323)}-harmonic conjugate of X(19295)
X(19295) lies on the cubics K390 and K752 and these lines: {6, 6151}, {15, 1511}, {16, 1154}, {50, 323}, {61, 11626}, {395, 533}, {396, 6128}, {526, 6138}, {2981, 14579}, {3170, 11136}, {5353, 6149}, {10409, 11084}
X(19295) = midpoint of X(11127) and X(17402)
X(19295) = X(11601)-complementary conjugate of X(2887)
X(19295) = X(i)-Ceva conjugate of X(j) for these (i,j): {11127, 1154}, {11130, 1511}, {17402, 526}
X(19295) = crosspoint of X(i) and X(j) for these (i,j): {2, 11601}, {15, 323}
X(19295) = crossdifference of every pair of points on line {14, 15475}
X(19295) = crosssum of X(i) and X(j) for these (i,j): {6, 6105}, {13, 1989}
X(19295) = X(15)-daleth conjugate of X(1511)
X(19295) = barycentric product X(i)*X(j) for these {i,j}: {15, 619}, {16, 533}, {323, 395}, {3480, 14368}, {14447, 17403}
X(19295) = {X(50),X(323)}-harmonic conjugate of X(19294)
X(19295) = X(i)-isoconjugate of X(j) for these (i,j): {75, 11089}, {2153, 11120}, {2154, 11118}, {2166, 6151}
X(19295) = barycentric quotient X(i)/X(j) for these {i,j}: {15, 11120}, {16, 11118}, {32, 11089}, {50, 6151}, {395, 94}, {462, 6344}, {533, 301}, {619, 300}
X(19296) lies on the conic {{A,B,C,X(1),X(7)}}, the cubic K745, and on these lines: {2, 18884}, {7, 16015}
X(19296) = barycentric product X(1)*X(18884)
X(19296) = barycentric quotient X(18884)/X(75)
X(19297) lies on the cubic K1042 and these lines: {3, 45}, {6, 41}, {9, 5124}, {35, 37}, {36, 44}, {50, 1415}, {55, 16672}, {100, 3943}, {101, 2245}, {108, 1990}, {218, 5043}, {219, 5036}, {404, 17369}, {579, 3204}, {649, 4057}, {859, 3285}, {910, 2078}, {995, 4290}, {1014, 7277}, {1086, 11349}, {1108, 7300}, {1126, 4272}, {1213, 5260}, {1333, 9341}, {1444, 17332}, {1604, 1609}, {1696, 16675}, {1817, 4415}, {1914, 8610}, {2153, 11142}, {2154, 11141}, {2160, 2171}, {2161, 2173}, {2220, 17053}, {2223, 16686}, {2242, 4277}, {2243, 5078}, {2975, 17330}, {3052, 15494}, {3122, 18266}, {3295, 5011}, {3339, 3553}, {3509, 4053}, {3724, 6187}, {4254, 7373}, {4286, 16453}, {4363, 11329}, {4370, 13587}, {4557, 17798}, {5010, 16676}, {5563, 16666}, {11343, 17325}
X(19297) = isogonal conjugate of X(21739)
X(19297) = X(2161)-Ceva conjugate of X(6)
X(19297) = cevapoint of X(1030) and X(3196)
X(19297) = crosspoint of X(i) and X(j) for these (i,j): {759, 1171}, {1262, 2222}
X(19297) = crossdifference of every pair of points on line {522, 1125}
X(19297) = crosssum of X(i) and X(j) for these (i,j): {758, 1213}, {1146, 3738}, {3943, 4015}
X(19297) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3065}, {320, 11075}, {4453, 14147}
X(19297) = X(i)-beth conjugate of X(j) for these (i,j): {9, 16548}, {5546, 17796}
X(19297) = X(4120)-zayin conjugate of X(513)
X(19297) = polar conjugate of isotomic conjugate of X(23071)
X(19297) = barycentric product X(i)*X(j) for these {i,j}: {1, 484}, {6, 17484}, {31, 17791}, {80, 6126}, {3219, 11076}, {3678, 14158}
X(19297) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3065}, {484, 75}, {6126, 320}, {17484, 76}, {17791, 561}
X(19297) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3065}, {320, 11075}, {4453, 14147}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (37, 15586, 16548), (101, 2245, 17796), (198, 2178, 6), (910, 8609, 7297), (1055, 2183, 7113), (1400, 2174, 6), (2183, 7113, 6)
X(19298) lies on the Feuerbach hyperbola of the tangential triangle, the cubic K1042, and on these lines: {1, 1094}, {3, 5672}, {6, 1653}, {63, 662}, {195, 7345}, {399, 1277}, {2154, 2640}, {2173, 15772}, {2945, 15789}
X(19298) = X(15772)-Ceva conjugate of X(3)
X(19298) = X(366)-aleph conjugate of X(3179)
X(19298) = X(2)-isoconjugate of X(3440)
X(19298) = barycentric product X(1)*X(616)
X(19298) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3440}, {616, 75}
X(19298) = {X(662),X(2247)}-harmonic conjugate of X(19299)
X(19299) lies on the Feuerbach hyperbola of the tangential triangle, the cubic K1042, and on these lines: {1, 1095}, {3, 5673}, {6, 1652}, {63, 662}, {195, 7344}, {399, 1276}, {2153, 2640}, {2173, 15771}, {2946, 15788}
X(19299) = X(15771)-Ceva conjugate of X(3)
X(19299) = X(2)-isoconjugate of X(3441)
X(19299) = barycentric product X(1)X(617)
X(19299) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3441}, {617, 75}
X(19299) = {X(662),X(2247)}-harmonic conjugate of X(19298)
X(19300) lies on the cubic K1042 and these lines: {}
X(19300) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3479}, {396, 2993}, {14373, 14922}
X(19300) = barycentric product X(i)*X(j) for these {i,j}: {1, 1337}
X(19300) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3479}, {1337, 75}
X(19301) lies on the cubic K1042 and these lines:
X(19301) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3480}, {395, 2992}
X(19301) = barycentric product X(1)*X(1338)
X(19301) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3480}, {1338, 75}
X(19302) lies on the cubic K1042 and these lines: {6, 19303}, {9, 1030}, {36, 7297}, {57, 7202}, {101, 17454}, {284, 17455}, {2160, 2170}, {2161, 2173}, {2245, 2316}, {5124, 5540}
X(19302) = isogonal conjugate of X(17484)
X(19302) = X(11075)-Ceva conjugate of X(6)
X(19302) = X(7113)-cross conjugate of X(6)
X(19302) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17484}, {2, 484}, {6, 17791}, {92,23071}, {319, 11076}, {3969, 14158}, {6126, 18359}
X(19302) = cevapoint of X(8648) and X(14936)
X(19302) = trilinear pole of line {663, 2308}
X(19302) = crosssum of X(9) and X(13146)
X(19302) = barycentric product X(i)*X(j) for these {i,j}: {1, 3065}, {79, 7343}, {3218, 11075}, {3960, 14147}
X(19302) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17791}, {6, 17484}, {31, 484}, {3065, 75}, {7343, 319}, {11075, 18359}
X(19303) lies on the cubic K1042 and these lines: {6, 19302}, {31, 2153}, {48, 163}, {1953, 16562}, {2173, 6149}, {2315, 9406}
X(19303) = X(i)-Ceva conjugate of X(j) for these (i,j): {2173, 48}, {6149, 31}
X(19303) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1138}, {1494, 11070}, {2986, 18781}, {13582, 14451}
X(19303) = X(1094)-Hirst inverse of X(1095)
X(19303) = barycentric product X(i)*X(j) for these {i,j}: {1, 399}, {31, 1272}, {163, 14566}, {6149, 14993}
X(19303) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 1138}, {399, 75}, {1272, 561}, {9406, 11070}
X(19304) lies on the cubic K1042 and these lines: {3, 5672}, {6, 2151}, {19, 25}, {2154, 11141}, {2173, 3130}, {2183, 7127}
X(19304) = X(i)-Ceva conjugate of X(j) for these (i,j): {7126, 6}, {15771, 1276}
X(19304) = X(2)-isoconjugate of X(7060)
X(19304) = barycentric product X(i)*X(j) for these {i,j}: {1, 1276}, {37, 15771}
X(19304) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 7060}, {1276, 75}, {15771, 274}
X(19305) lies on the cubic K1042 and these lines: {3, 5673}, {6, 2152}, {19, 25}, {48, 7127}, {2153, 11142}, {2173, 3129}
X(19305) = X(15772)-Ceva conjugate of X(1277)
X(19305) = X(2)-isoconjugate of X(7059)
X(19305) = barycentric product X(i)*X(j) for these {i,j}: {1, 1277}, {37, 15772}
X(19305) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 7059}, {1277, 75}, {15772, 274}
X(19306) lies on and these lines: {47, 48}, {2167, 18722}
on K1042
X(19306) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1263}, {5, 13582}, {311, 14579}, {1273, 11071}, {1291, 18314}, {14918, 15392}
X(19306) = barycentric product X(i)*X(j) for these {i,j}: {1, 1157}, {54, 1749}, {2167, 11063}
X(19306) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 1263}, {1157, 75}, {1749, 311}, {2148, 13582}, {6140, 2618}, {11063, 14213}
See Tran Quang Hung and Angel Montesdeoca, ADGEOM 4654.
X(19307) lies on this line: {381,14483}
See Angel Montesdeoca, HG050618.
X(19308) lies on these lines: {2,3}, {35,16826}, {36,239}, {56,4393}, {81,18755}, {86,1030}, {99,3948}, {100,4433}, {192,2178}, {198,17350}, {291,18266}, {662,2245}, {757,4272}, {1284,6650}, {1444,1654}, {1931,2238}, {2160,18714}, {2895,17206}, {4384,7280}, {5010,16831}, {5124,17277}, {5204,16816}, {6511,18663}, {8715,17389}, {15586,16568}
X(19309) lies on these lines: {1, 2271}, {2, 3}, {105, 14625}, {965, 10477}, {999, 16823}, {1453, 5272}, {1724, 5021}, {3295, 16830}, {5584, 9746}, {8193, 16828}
X(19310) lies on these lines: {2, 3}, {55, 16830}, {56, 85}, {105, 1036}, {614, 16478}, {958, 17798}, {965, 3786}, {1001, 17322}, {1486, 5263}, {2271, 5276}, {2339, 5338}, {3220, 10436}, {3290, 16974}, {4265, 15668}, {5096, 17259}, {5253, 16020}, {5275, 18755}
X(19311) lies on these lines: {1, 16992}, {2, 3}, {2271, 9534}, {4340, 17206}, {4357, 4655}, {5711, 16830}
X(19312) lies on these lines: {1, 257}, {2, 3}, {325, 6626}, {1043, 18755}, {1220, 17798}, {1724, 3329}, {3747, 5255}, {5145, 17000}, {5988, 12579}
X(19313) lies on these lines: {2, 3}, {612, 3555}, {999, 16830}, {1001, 1738}, {2271, 3216}, {3295, 16823}, {5021, 5275}
X(19314) lies on these lines: {2, 3}, {55, 16823}, {56, 16830}, {1001, 16706}, {1447, 1466}, {1621, 16020}, {3889, 3920}, {4265, 17259}, {5021, 5276}, {5096, 15668}, {5250, 9441}
X(19315) lies on this lines: {2,3}
X(19316) lies on these lines: {2, 3}, {3303, 16830}, {3304, 16823}
X(19317) lies on this line: {2,3}
X(19318) lies on these lines: {2, 3}, {229, 6626}, {385, 3304}, {3746, 16830}, {5260, 17798}, {5563, 16823}
X(19319) lies on these lines: {2, 3}, {2271, 17749}, {3646, 9441}, {6767, 16823}, {7373, 16830}
X(19320) lies on these lines: {2, 3}, {3303, 16823}, {3304, 16830}
X(19321) lies on these lines: {2, 3}, {6767, 16830}, {7373, 16823}, {12410, 16828}
X(19322) lies on this line: {2,3}
X(19323) lies on this line: {2,3}
X(19324) lies on this line: {2,3}
X(19325) lies on these lines: {2, 3}, {5204, 16830}, {5217, 16823}
X(19326) lies on these lines: {2, 3}, {5204, 16823}, {5217, 16830}, {11194, 17798}
X(19327) lies on these lines: {2, 3}, {3746, 16823}, {5563, 16830}
X(19328) lies on this line: {2,3}
X(19329) lies on these lines: {1, 1929}, {2, 3}, {10, 17798}, {55, 10180}, {56, 16609}, {72, 3509}, {238, 2305}, {985, 16466}, {1001, 1030}, {1453, 11512}, {2248, 5247}, {4433, 5687}, {5282, 15650}
See Antreas Hatzipolakis and César Lozada, Hyacinthos 27749.
X(19330) lies on these lines: {3, 15899}, {23, 895}, {111, 468}, {5486, 13574}, {7493, 10416}
X(19331) lies on these lines: {2, 3}, {58, 19750}, {386, 19739}, {940, 3244}, {3636, 19765}, {4255, 19747}, {4256, 19746}, {4257, 19751}
X(19332) lies on these lines: {2, 3}, {551, 3946}, {940, 3679}, {3828, 5737}, {3940, 10436}, {4257, 19744}, {9708, 19870}
X(19333) lies on these lines: {2, 3}, {58, 19740}, {145, 5737}, {1150, 3622}, {3617, 19765}, {5550, 17127}
X(19334) lies on these lines: {2, 3}, {748, 19862}, {940, 5550}, {1125, 1150}, {3616, 5737}, {3746, 19858}, {4252, 19749}, {9780, 19765}
X(19335) lies on these lines: {2, 3}, {244, 517}, {500, 14131}, {3813, 15625}, {5844, 20039}
X(19336) lies on these lines: {2, 3}, {386, 19738}, {940, 3241}, {993, 19870}, {996, 1150}, {1468, 4685}, {3445, 19765}, {4252, 19723}, {4255, 19722}, {4256, 19684}, {4257, 5278}, {4921, 9534}, {5303, 19853}
X(19337) lies on these lines: {2, 3}, {386, 19741}, {940, 3621}, {4255, 19740}
X(19338) lies on these lines: {2, 3}, {42, 5132}, {228, 16574}
X(19339) lies on these lines: {2, 3}, {31, 5132}, {3720, 16678}
X(19340) lies on these lines: {2, 3}, {42, 5156}
X(19341) lies on these lines: {2, 3}, {3052, 5132}
X(19342) lies on these lines: {2, 3}, {16569, 16678}
X(19343) lies on these lines: {2, 3}, {42, 2260}, {228, 579}, {2252, 3185}
X(19344) lies on these lines: {2, 3}, {43, 16778}
X(19345) lies on these lines: {2, 3}
X(19346) lies on these lines: {2, 3}, {42, 4252}, {55, 14969}, {228, 3929}, {3720, 5204}, {4428, 16678}, {5303, 10453}
Hutson triangles and related centers: X(19347)-X(19511)
This preamble and centers X(19347)-X(19511) were contributed by César Eliud Lozada, June 10, 2018.
The following triangles were referenced in ETC by Randy Hutson: AAOA and AOA (at the preamble of X(15015) and 2nd anti-extouch, anti-tangential-midarc and Lucas(±1) antipodal tangents (at the preamble of X(18300)). For definitions of these triangles, see index of triangles referenced in ETC.
Centers X(19347)-X(19511) are perspectors, homothetic centers, orthologic centers and parallelogic centers of these triangles and other triangles. For a complete list, see X(19347)-Hutson-triangles.pdf.
X(19347) lies on these lines: {2,18914}, {3,49}, {4,11402}, {5,3618}, {6,1598}, {22,12160}, {24,15032}, {25,1614}, {30,18925}, {52,9909}, {54,1593}, {64,11430}, {69,16197}, {110,16270}, {125,5070}, {140,11487}, {154,389}, {156,6642}, {182,17814}, {195,11577}, {378,12174}, {381,6146}, {399,13198}, {468,18916}, {546,18945}, {549,18913}, {568,9714}, {569,11479}, {578,1498}, {631,6090}, {999,19349}, {1192,11202}, {1199,9777}, {1351,7387}, {1384,14585}, {1595,11427}, {1656,1899}, {1872,2261}, {1993,11414}, {3089,14912}, {3295,19354}, {3311,19355}, {3312,19356}, {3515,5890}, {3516,6241}, {3530,18931}, {3542,11245}, {3547,3564}, {3843,18396}, {3850,18918}, {5012,7395}, {5020,10539}, {5064,16659}, {5073,10619}, {5085,11793}, {5093,5446}, {5094,11457}, {5198,11423}, {5422,19361}, {5544,19360}, {5609,5622}, {5656,13488}, {5889,6800}, {6000,11425}, {6102,14070}, {6152,9920}, {6391,12309}, {6676,11411}, {6756,11206}, {7393,12017}, {7503,11003}, {7517,15087}, {7529,10540}, {7530,10602}, {7542,18917}, {7583,18924}, {7584,18923}, {8550,16252}, {9544,17928}, {9545,11413}, {9706,15072}, {9786,10282}, {9833,12233}, {9936,11898}, {10116,14852}, {10117,12227}, {10245,14831}, {10306,19350}, {10601,11484}, {10606,14528}, {10938,12162}, {10982,13366}, {11004,12087}, {11403,15033}, {11438,17821}, {11464,15750}, {11485,19363}, {11486,19364}, {11542,18930}, {11543,18929}, {11820,13352}, {12007,15873}, {12429,15760}, {13336,16419}, {13383,18951}, {15325,18915}, {16543,19149}, {18583,18935}, {19170,19173}
X(19347) = isogonal conjugate of X(18853)
X(19347) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 18445, 12164), (4, 11402, 11426), (6, 1598, 3527), (6, 6759, 1598), (25, 7592, 11432), (184, 185, 19357), (184, 1181, 3), (185, 19357, 3), (394, 10984, 3), (1181, 19357, 185), (1614, 7592, 25), (3796, 5562, 3), (6776, 19125, 5050), (10605, 13367, 3), (11432, 14530, 25), (12163, 18475, 3)
X(19348) lies on these lines: {74,1112}, {125,399}, {403,12112}, {974,5644}, {1511,5622}, {1597,15151}, {2914,15106}, {3581,18859}, {3618,10264}, {6053,17825}, {6395,18998}, {7687,17812}, {9919,12099}, {10620,11557}, {11064,12364}, {11438,11808}, {11456,11704}, {15037,19362}, {15061,15115}
X(19349) lies on these lines: {1,1181}, {2,18915}, {3,73}, {6,19}, {12,1899}, {25,19366}, {33,1498}, {35,10605}, {36,19357}, {46,223}, {54,19368}, {55,185}, {56,184}, {72,3173}, {109,581}, {155,1060}, {201,219}, {225,5706}, {377,651}, {378,10076}, {388,611}, {389,11398}, {394,1038}, {495,18914}, {580,10571}, {974,10088}, {999,19347}, {1035,8614}, {1069,18445}, {1204,5217}, {1394,2003}, {1398,11402}, {1406,1427}, {1428,19125}, {1451,1457}, {1478,6146}, {1503,11392}, {1593,7355}, {1708,16471}, {1788,10360}, {1870,7592}, {1885,12940}, {1993,4296}, {2067,19355}, {2286,3990}, {3028,13198}, {3085,18909}, {3194,14257}, {3270,3303}, {3562,6836}, {3585,18396}, {4293,18925}, {5012,19367}, {5204,13367}, {5218,18913}, {5229,18945}, {5794,9370}, {6198,11456}, {6241,10060}, {6285,7071}, {6502,19356}, {6759,11399}, {6910,17074}, {6917,8757}, {7051,19363}, {7066,7085}, {9637,11413}, {10071,15760}, {10601,19372}, {10602,19369}, {11393,12233}, {19170,19175}, {19358,19370}, {19359,19371}, {19364,19373}
X(19349) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1181, 19354), (6, 221, 34), (73, 3215, 3), (184, 1425, 56), (222, 7078, 73), (1398, 11402, 19365), (7071, 12174, 6285), (7355, 11429, 1593), (18445, 18447, 1069)
X(19350) lies on these lines: {2,18921}, {3,48}, {6,19}, {9,5693}, {25,10536}, {40,1181}, {46,610}, {54,11460}, {55,184}, {155,8251}, {185,5584}, {197,209}, {198,2245}, {218,2183}, {222,3942}, {224,3692}, {284,11507}, {296,949}, {394,10319}, {572,15830}, {579,1630}, {584,11434}, {1195,8573}, {1436,2259}, {1498,11471}, {1593,6254}, {1826,5776}, {1869,5706}, {1899,3925}, {1993,3101}, {1994,9536}, {2256,2646}, {2266,2272}, {2286,14597}, {2301,4266}, {2982,7490}, {3207,17796}, {5012,11445}, {5415,19355}, {5416,19356}, {5781,5880}, {6197,7592}, {7078,18673}, {7688,10605}, {8141,12161}, {8539,10602}, {9816,10601}, {10306,19347}, {10636,19363}, {10637,19364}, {10902,19357}, {11190,11402}, {18396,18406}, {18445,18453}, {19125,19133}, {19170,19181}
X(19350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 3197, 19), (48, 2252, 3), (65, 2182, 19), (184, 3611, 55), (10536, 11435, 25), (11190, 11428, 11406), (11402, 11406, 11428)
X(19351) lies on these lines: {3,9929}, {25,6218}, {184,8903}, {1161,1181}, {1163,5595}, {1593,5871}, {11916,19362}
X(19352) lies on these lines: {3,9930}, {25,6217}, {184,8904}, {1160,1181}, {1162,5594}, {1593,5870}, {11917,19362}
X(19353) lies on these lines: {156,1181}, {974,2929}, {1147,11806}, {1593,15121}, {7529,7706}
X(19354) lies on these lines: {1,1181}, {2,18922}, {3,1069}, {6,33}, {11,1899}, {24,9638}, {25,10535}, {34,1498}, {35,19357}, {36,10605}, {52,9645}, {54,11461}, {55,184}, {56,185}, {155,1062}, {195,9641}, {212,219}, {222,7004}, {378,10060}, {389,11399}, {394,1040}, {496,18914}, {497,613}, {603,1433}, {974,10091}, {1204,5204}, {1250,19364}, {1364,1473}, {1398,7355}, {1425,3304}, {1479,6146}, {1503,11393}, {1593,6285}, {1854,17824}, {1870,11456}, {1885,12950}, {1993,3100}, {1994,9539}, {2066,19355}, {2264,17832}, {2323,2900}, {2330,19125}, {3086,18909}, {3157,18445}, {3295,19347}, {3583,18396}, {3689,7074}, {4294,18925}, {5012,11446}, {5217,13367}, {5225,18945}, {5414,19356}, {6198,7592}, {6241,10076}, {6759,11398}, {7071,11189}, {7072,7082}, {7288,18913}, {8144,12161}, {8540,10602}, {9642,15087}, {9817,10601}, {10055,15760}, {10638,19363}, {11392,12233}, {12595,17642}, {14986,18915}, {19170,19182}
X(19354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 1181, 19349), (6, 2192, 33), (184, 3270, 55), (1398, 12174, 7355), (6285, 19365, 1593), (7071, 11402, 11429), (10535, 11436, 25), (11189, 11429, 7071), (18445, 18455, 3157)
X(19355) lies on these lines: {2,18923}, {3,6413}, {6,25}, {54,11462}, {125,8253}, {155,10897}, {185,1151}, {216,10133}, {217,6424}, {371,1181}, {372,19357}, {394,11513}, {485,6146}, {577,10132}, {578,3093}, {590,1899}, {974,10819}, {1092,1578}, {1152,13367}, {1204,6409}, {1498,11473}, {1579,10984}, {1584,10960}, {1587,18925}, {1593,12964}, {1993,11417}, {2066,19354}, {2067,19349}, {3068,6776}, {3070,12231}, {3092,6759}, {3269,9600}, {3284,8908}, {3311,19347}, {3796,11514}, {3964,5409}, {5012,11447}, {5415,19350}, {6414,6415}, {6423,14585}, {6564,18396}, {6800,11418}, {7585,18924}, {7592,10880}, {8911,15905}, {8981,18914}, {9540,18909}, {9707,10881}, {9974,15073}, {10116,13909}, {10601,10961}, {11245,13884}, {11265,12161}, {11425,11474}, {14533,15846}, {18445,18457}, {19170,19183}
X(19355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 5413), (6, 184, 19356), (6, 10533, 25), (6, 10534, 5411), (6, 11241, 5410), (6, 17819, 5412), (5410, 11402, 6)
X(19356) lies on these lines: {2,18924}, {3,6414}, {6,25}, {49,8909}, {54,11463}, {125,8252}, {155,10898}, {185,1152}, {216,8908}, {217,6423}, {371,19357}, {372,1181}, {394,11514}, {486,6146}, {577,10133}, {578,3092}, {615,1899}, {974,10820}, {1092,1579}, {1151,13367}, {1204,6410}, {1498,11474}, {1578,10984}, {1583,10962}, {1588,18925}, {1593,12970}, {1993,11418}, {3069,6776}, {3071,12232}, {3093,6759}, {3312,19347}, {3796,11513}, {3964,5408}, {5012,11448}, {5414,19354}, {5416,19350}, {6396,10605}, {6413,6416}, {6424,14585}, {6502,19349}, {6565,18396}, {6800,11417}, {7586,18923}, {7592,10881}, {9707,10880}, {9975,15073}, {10116,13970}, {10601,10963}, {11245,13937}, {11266,12161}, {11425,11473}, {13935,18909}, {13966,18914}, {14533,15847}, {18445,18459}, {19170,19184}
X(19356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 5412), (6, 184, 19355), (6, 10533, 5410), (6, 10534, 25), (6, 11242, 5411), (6, 17820, 5413), (216, 8908, 10132), (5411, 11402, 6), (6414, 8911, 3)
X(19357) lies on these lines: {2,6146}, {3,49}, {4,154}, {5,18396}, {6,24}, {15,19364}, {16,19363}, {20,6800}, {25,578}, {26,5944}, {35,19354}, {36,19349}, {51,3517}, {52,14070}, {64,3431}, {68,7542}, {110,7503}, {125,3526}, {140,1899}, {141,631}, {156,7526}, {182,14913}, {186,7592}, {215,9659}, {216,10608}, {217,3053}, {287,11285}, {371,19356}, {372,19355}, {378,1498}, {382,1533}, {389,3515}, {427,9833}, {511,9715}, {549,18914}, {567,3066}, {569,6642}, {575,10602}, {974,12284}, {1192,5890}, {1350,7512}, {1351,16195}, {1495,1598}, {1503,3541}, {1511,13198}, {1593,6759}, {1597,14530}, {1656,6288}, {1658,12161}, {1970,2207}, {1993,7488}, {1995,13434}, {2192,9638}, {2477,9672}, {2930,5622}, {3043,17847}, {3047,17838}, {3088,11206}, {3089,16657}, {3090,18945}, {3092,10534}, {3093,10533}, {3147,13567}, {3269,15815}, {3357,11410}, {3516,6000}, {3518,17810}, {3523,18909}, {3524,18913}, {3542,10192}, {3547,13394}, {3574,18494}, {3851,13851}, {5012,11449}, {5050,6467}, {5056,18918}, {5064,13419}, {5094,18381}, {5446,9714}, {5654,12605}, {5889,9706}, {6090,11793}, {6102,18324}, {6241,10606}, {6639,14852}, {6643,11064}, {6644,12006}, {7387,13352}, {7395,9306}, {7487,11427}, {7502,16266}, {7505,12022}, {7507,18400}, {7509,17811}, {7514,10610}, {7544,14389}, {7547,12289}, {7556,11477}, {7577,12254}, {7712,12087}, {7738,15341}, {8550,18916}, {8779,9605}, {8780,11479}, {8909,10898}, {9540,18924}, {9544,11441}, {9590,16473}, {9705,11459}, {9820,18531}, {10018,18912}, {10024,12293}, {10117,15463}, {10154,13142}, {10201,12370}, {10249,11457}, {10519,19119}, {10574,15078}, {10594,15033}, {10902,19350}, {11398,19365}, {11399,11429}, {11414,13346}, {11432,13366}, {11438,15750}, {11472,14130}, {11935,19362}, {12118,15760}, {12173,18388}, {12233,18533}, {13353,15805}, {13935,18923}, {14157,15811}, {14805,18350}, {15038,19361}, {15448,15873}, {15472,15647}, {15717,18931}, {15806,18377}, {19170,19185}
X(19357) = isogonal conjugate of X(18855)
X(19357) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 18925, 6146), (3, 49, 155), (3, 184, 1181), (3, 1147, 394), (3, 1181, 10605), (3, 3167, 5562), (3, 9704, 18445), (3, 18445, 12163), (3, 19347, 185), (4, 9707, 154), (154, 11425, 4), (154, 14528, 11425), (184, 185, 19347), (184, 13367, 3), (185, 19347, 1181), (1147, 18475, 3)
X(19358) lies on these lines: {2,18926}, {3,18939}, {182,9723}, {184,8939}, {185,13021}, {371,1843}, {1181,18980}, {8414,12590}, {10132,13889}, {18396,18414}, {18445,18462}, {19125,19134}, {19170,19186}, {19349,19370}
X(19359) lies on these lines: {2,18927}, {3,18940}, {182,9723}, {184,8943}, {185,13022}, {372,1843}, {1181,18981}, {8406,12591}, {10133,13943}, {18396,18415}, {18445,18463}, {19125,19135}, {19170,19187}, {19349,19371}
X(19360) lies on these lines: {2,18910}, {3,12235}, {5,1181}, {6,3541}, {24,5622}, {64,974}, {125,155}, {182,14913}, {184,15805}, {185,11472}, {389,1593}, {394,3548}, {973,9786}, {3311,18997}, {3312,18998}, {3538,18919}, {5094,12242}, {5422,18909}, {5544,19347}, {6146,6815}, {6776,15435}, {7687,18381}, {8548,16196}, {10257,15316}, {10263,12041}, {11064,17836}, {11431,18913}, {11457,19149}, {11596,15318}, {13488,18431}, {15061,15317}, {15752,15811}, {17810,17823}
X(19361) lies on these lines: {125,195}, {143,5622}, {184,15047}, {381,1181}, {568,1204}, {1199,1594}, {1593,5890}, {1899,19362}, {1992,18281}, {2452,6662}, {5050,6642}, {5422,19347}, {5654,10255}, {5892,13353}, {6146,15037}, {6417,18997}, {6418,18998}, {6746,7730}, {7592,7699}, {7666,17701}, {9971,10250}, {15038,19357}, {15811,18376}
X(19362) lies on these lines: {5,9512}, {6,18381}, {24,15135}, {54,7731}, {125,15047}, {155,11898}, {184,195}, {185,567}, {382,1181}, {394,11850}, {399,6288}, {578,6293}, {1199,15559}, {1351,7387}, {1593,6241}, {1614,9920}, {1899,19361}, {1993,9706}, {2904,11402}, {6143,15106}, {6146,14627}, {6417,18998}, {6418,18997}, {6759,9973}, {10605,11999}, {10938,11424}, {11576,14157}, {11916,19351}, {11917,19352}, {11935,19357}, {12234,13419}, {12429,18445}, {13434,15100}, {15032,18560}, {15037,19348}, {17824,18388}
X(19363) lies on these lines: {2,18929}, {3,10661}, {6,25}, {15,1181}, {16,19357}, {54,11466}, {155,10634}, {185,11480}, {394,11515}, {1498,11475}, {1593,10675}, {1993,11420}, {3796,11516}, {5012,11452}, {5335,18925}, {5340,8741}, {6146,18582}, {6776,11488}, {6800,11421}, {7051,19349}, {7592,10632}, {9707,10633}, {10601,10643}, {10605,10645}, {10636,19350}, {10638,19354}, {11267,12161}, {11425,11476}, {11481,13367}, {11485,19347}, {16808,18396}, {18445,18468}, {19170,19190}
X(19363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 10642), (6, 184, 19364), (6, 11243, 11408), (6, 17826, 10641), (6, 17827, 8739), (11402, 11408, 6)
X(19364) lies on these lines: {2,18930}, {3,10662}, {6,25}, {15,19357}, {16,1181}, {54,11467}, {155,10635}, {185,11481}, {394,11516}, {1250,19354}, {1498,11476}, {1593,10676}, {1993,11421}, {3796,11515}, {5012,11453}, {5334,18925}, {5339,8742}, {6146,18581}, {6776,11489}, {6800,11420}, {7592,10633}, {9707,10632}, {10601,10644}, {10605,10646}, {10637,19350}, {11268,12161}, {11425,11475}, {11480,13367}, {11486,19347}, {16809,18396}, {18445,18470}, {19170,19191}, {19349,19373}
X(19364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 10641), (6, 184, 19363), (6, 11244, 11409), (6, 17826, 8740), (6, 17827, 10642), (11402, 11409, 6)
X(19365) lies on these lines: {1,578}, {3,11436}, {4,9638}, {5,18970}, {6,41}, {11,12241}, {33,11424}, {34,184}, {35,11430}, {36,389}, {54,65}, {55,11425}, {57,3468}, {182,1038}, {208,5320}, {221,17809}, {388,11427}, {567,18447}, {569,1060}, {999,11426}, {1040,13346}, {1062,13352}, {1181,7355}, {1398,11402}, {1425,13366}, {1437,1465}, {1593,6285}, {1875,2194}, {1914,1970}, {1935,7193}, {2323,7066}, {3056,10831}, {3583,13403}, {3585,18388}, {4296,5012}, {5204,9786}, {5270,12242}, {5433,13567}, {6198,15033}, {6238,7526}, {7280,11438}, {7288,11433}, {7352,12161}, {7353,12232}, {7354,12233}, {7356,12234}, {7362,12231}, {7741,18390}, {9306,19372}, {10118,15472}, {10982,11399}, {11398,19357}, {11422,19367}, {11423,19368}, {13568,15326}, {14912,18915}
X(19365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 578, 11429), (6, 56, 19366), (1398, 11402, 19349), (1451, 7114, 56), (1593, 19354, 6285)
X(19366) lies on these lines: {1,389}, {3,11429}, {4,65}, {5,7352}, {6,41}, {9,7066}, {11,12233}, {12,13567}, {25,19349}, {33,185}, {34,51}, {35,11438}, {36,578}, {52,1060}, {55,9786}, {57,1745}, {221,17810}, {388,11433}, {511,1038}, {568,18447}, {851,1454}, {974,10118}, {999,11432}, {1040,9729}, {1062,9730}, {1181,10535}, {1192,5217}, {1214,5752}, {1361,3340}, {1398,9777}, {1597,10076}, {1708,10974}, {1870,3567}, {1899,11392}, {2003,7335}, {2099,2654}, {2285,3330}, {2330,10831}, {2635,5221}, {3028,11746}, {3056,19161}, {3060,4296}, {3100,10574}, {3145,3215}, {3157,6642}, {3585,18390}, {5204,11425}, {5640,19367}, {5890,6198}, {5907,9817}, {5943,19372}, {6102,6238}, {6284,13568}, {7280,11430}, {7288,11427}, {7353,12240}, {7354,12241}, {7356,12242}, {7362,12239}, {7741,18388}, {8144,13630}, {9638,15032}, {9781,19368}, {9792,19175}, {10055,18951}, {10071,18420}, {10483,13403}, {12888,14708}, {13292,18970}
X(19366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 389, 11436), (6, 56, 19365), (33, 185, 6285), (51, 1425, 34), (65, 1864, 1887), (1181, 11399, 10535)
X(19367) lies on these lines: {1,11446}, {2,1425}, {3,19368}, {7,16749}, {22,221}, {33,11439}, {34,3060}, {35,11454}, {36,11449}, {55,11440}, {56,110}, {65,11445}, {331,4566}, {388,11442}, {942,6828}, {999,11441}, {1038,7998}, {1060,11444}, {1062,15072}, {1398,1993}, {1428,19122}, {1469,12272}, {1870,5889}, {2067,11447}, {2979,4296}, {3100,7355}, {3585,18392}, {3868,5125}, {4225,10571}, {5012,19349}, {5640,19366}, {5663,11461}, {5905,7103}, {6000,9538}, {6198,15305}, {6241,18455}, {6502,11448}, {7051,11452}, {7353,12277}, {7354,12278}, {7356,12280}, {7362,12276}, {8144,12290}, {9539,11381}, {9657,18984}, {10076,13445}, {11422,19365}, {11443,19369}, {11451,19372}, {11453,19373}, {11459,18447}, {14516,18990}, {18911,18915}, {19167,19175}
X(19367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 12111, 11446), (1870, 7352, 5889), (3100, 7355, 12279)
X(19368) lies on these lines: {1,6241}, {3,19367}, {4,1425}, {24,221}, {33,11455}, {34,3567}, {35,11468}, {36,11464}, {54,19349}, {55,74}, {56,1614}, {65,11460}, {388,11457}, {942,6845}, {999,11456}, {1038,7999}, {1060,11459}, {1398,7592}, {1428,19123}, {1469,12283}, {1870,5890}, {2067,11462}, {2242,13509}, {4296,7352}, {5563,9638}, {5663,11446}, {6198,7355}, {6502,11463}, {7051,11466}, {7353,12288}, {7354,12289}, {7356,12291}, {7362,12287}, {7373,12174}, {8144,12279}, {9538,10575}, {9539,14915}, {9781,19366}, {11423,19365}, {11458,19369}, {11465,19372}, {11467,19373}, {12111,18447}, {15072,18455}, {18912,18915}, {19168,19175}
X(19368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6241, 11461), (4296, 7352, 11412), (6198, 7355, 12290)
X(19369) lies on these lines: {1,576}, {6,41}, {12,524}, {33,11470}, {34,8541}, {35,511}, {36,575}, {55,11477}, {57,17779}, {65,651}, {69,10588}, {181,2003}, {182,7280}, {193,5261}, {221,17813}, {388,1992}, {518,4861}, {542,3585}, {597,5433}, {611,1351}, {613,5093}, {614,15004}, {894,7235}, {999,11482}, {1038,11511}, {1060,8538}, {1124,7353}, {1126,1431}, {1284,4649}, {1335,7362}, {1398,11405}, {1500,5107}, {1692,9341}, {1870,8537}, {1914,12837}, {1943,7211}, {2477,18374}, {2647,3340}, {3589,7294}, {3600,5032}, {4296,11416}, {4299,11179}, {5135,9037}, {5194,16785}, {5260,15988}, {5322,13366}, {5434,8584}, {5476,7741}, {7286,15826}, {7292,15019}, {7352,8548}, {7354,8550}, {7355,8549}, {7356,9977}, {8787,18969}, {9813,19372}, {10591,12589}, {10602,19349}, {10895,15069}, {11237,15534}, {11443,19367}, {11458,19368}, {18447,18449}, {18915,18919}, {19175,19178}
X(19369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 576, 8540), (6, 1469, 1428), (611, 1351, 3056)
X(19370) lies on these lines: {55,13021}, {56,8939}, {1428,19134}, {1469,12590}, {3585,18414}, {7352,18939}, {9723,19371}, {18447,18462}, {18915,18926}, {19175,19186}, {19349,19358}
X(19371) lies on these lines: {1,18981}, {55,13022}, {56,8943}, {1428,19135}, {1469,12591}, {3585,18415}, {7352,18940}, {9723,19370}, {18447,18463}, {18915,18927}, {19175,19187}, {19349,19359}
X(19372) lies on these lines: {1,5}, {2,34}, {4,1040}, {33,3091}, {36,6642}, {55,11479}, {56,5020}, {57,1724}, {63,1393}, {65,1722}, {172,10314}, {201,3305}, {208,4223}, {221,3812}, {222,5439}, {223,7532}, {225,2478}, {227,1001}, {278,5084}, {354,9370}, {373,1425}, {377,1877}, {381,1062}, {388,614}, {405,1465}, {498,7404}, {603,3306}, {612,10588}, {748,1254}, {899,4332}, {978,2647}, {999,11484}, {1060,1656}, {1068,6898}, {1076,6947}, {1214,11108}, {1394,5437}, {1396,17581}, {1398,11284}, {1428,19137}, {1441,5192}, {1448,3911}, {1454,1707}, {1466,16610}, {1469,9822}, {1470,11512}, {1478,7401}, {1479,18537}, {1698,8270}, {1745,18443}, {1785,6893}, {1788,2263}, {1838,6827}, {1870,3090}, {2067,10961}, {2635,10884}, {2999,7522}, {3074,5709}, {3100,3832}, {3340,9895}, {3545,6198}, {3553,9596}, {3585,18420}, {3600,7292}, {3634,4347}, {3749,11501}, {3850,8144}, {3851,18455}, {3854,9539}, {3855,9643}, {4318,9780}, {4319,5225}, {4320,7288}, {5010,7526}, {5047,17080}, {5055,18447}, {5226,5262}, {5261,7191}, {5345,9658}, {5433,6677}, {5434,10128}, {5462,7352}, {5907,11436}, {5943,19366}, {6250,12911}, {6251,12910}, {6502,10963}, {6644,7280}, {6816,11393}, {6913,17102}, {6939,7952}, {6997,11392}, {7051,10643}, {7353,9824}, {7354,9825}, {7355,9729}, {7362,9823}, {7395,11398}, {8167,15832}, {8757,10202}, {9306,19365}, {9813,19369}, {9842,16870}, {10601,19349}, {10644,19373}, {11451,19367}, {11465,19368}, {18915,18928}, {19175,19188}
X(19372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 5, 9817), (2, 34, 1038), (1421, 9578, 1), (1454, 7299, 1707)
X(19373) lies on these lines: {1,16}, {3,10638}, {6,41}, {11,5318}, {13,3582}, {15,36}, {18,5270}, {33,11476}, {34,10642}, {35,10646}, {55,11481}, {57,7052}, {62,5353}, {65,10637}, {115,18974}, {221,17827}, {388,11489}, {395,5434}, {396,5298}, {499,18582}, {999,7127}, {1038,11516}, {1060,10635}, {1082,17011}, {1398,11409}, {1464,2151}, {1478,18581}, {1870,10633}, {2975,5367}, {3086,5335}, {3218,5240}, {3583,19106}, {3584,16242}, {3585,16809}, {3639,17729}, {3746,5237}, {4293,5334}, {4296,11421}, {4325,16964}, {5204,11480}, {5253,5362}, {5321,7354}, {5471,18975}, {7005,7280}, {7126,7284}, {7288,11488}, {7352,10662}, {7353,10672}, {7355,10676}, {7356,10678}, {7362,10668}, {7741,16808}, {7951,16967}, {10072,10653}, {10483,19107}, {10535,10675}, {10644,19372}, {11237,16645}, {11453,19367}, {11467,19368}, {11542,15325}, {11543,18990}, {15888,16773}, {18447,18470}, {18915,18930}, {19175,19191}, {19349,19364}
X(19373) = isogonal conjugate of X(7026)
X(19373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 16, 1250), (6, 56, 7051), (6, 7051, 2307), (15, 202, 5357), (36, 5357, 15), (1055, 1458, 7051)
X(19374) lies on these lines: {3,16219}, {20,16165}, {67,3431}, {110,15138}, {1350,15141}, {1511,4549}, {2935,11820}, {5655,10282}, {7574,10564}, {10226,15132}, {11935,19403}, {12118,15114}, {12901,19376}, {17702,18434}
X(19375) lies on these lines: {67,1916}, {858,9479}, {1281,19400}, {2781,5999}, {2782,7574}, {4027,15140}, {5989,15141}, {8289,19379}, {8302,19382}, {8303,19383}, {8304,19384}, {8305,19385}, {8306,19386}, {8307,19387}, {8308,19388}, {8309,19389}, {8310,19392}, {8311,19393}, {8312,19394}, {8313,19395}, {8314,19396}, {8315,19397}, {8316,19398}, {8317,19399}, {9772,15182}
X(19376) lies on these lines: {3,15738}, {64,541}, {67,1350}, {68,12307}, {113,5094}, {399,19381}, {4549,19380}, {5663,15141}, {7574,10620}, {10117,14915}, {10510,13754}, {10564,12302}, {12163,15133}, {12901,19374}, {15041,19402}
X(19377) lies on these lines: {3,12824}, {67,1351}, {7574,12308}, {12164,15133}, {12310,15136}
X(19378) lies on these lines: {67,11574}, {141,15141}, {1216,15133}, {6699,15136}, {7574,12358}
X(19379) lies on these lines: {3,19392}, {6,67}, {98,15182}, {110,8705}, {6221,19386}, {6395,19385}, {6396,19394}, {6398,19387}, {6433,19388}, {6434,19389}, {6435,19396}, {6436,19397}, {6593,7492}, {7728,19140}, {8289,19375}, {8296,19400}, {8297,19401}, {8375,19382}, {8376,19383}, {10752,19128}, {13248,15139}
X(19379) = {X(15140), X(15141)}-harmonic conjugate of X(67)
X(19380) lies on these lines: {67,9967}, {125,15136}, {1352,15141}, {4549,19376}, {5562,15133}, {7574,7723}, {15138,16111}
X(19381) lies on these lines: {54,9140}, {67,182}, {110,7574}, {399,19376}, {1147,15133}, {3043,5094}, {3581,12893}, {5655,6759}, {5663,19402}, {10510,11649}, {13293,15138}, {15135,19403}, {15141,15577}
X(19382) lies on these lines: {67,6421}, {574,19383}, {1151,15141}, {5058,15140}, {6443,15106}, {8302,19375}, {8318,19400}, {8334,19401}, {8375,19379}, {8396,19384}, {8397,19386}, {8398,19392}, {8399,19396}, {8400,19385}, {8401,19387}, {8402,19389}, {8403,19393}, {8404,19395}, {8405,19397}, {8406,19399}, {10837,15182}, {11937,19390}, {11939,19391}
X(19383) lies on these lines: {67,6422}, {574,19382}, {1152,15141}, {5062,15140}, {6444,15106}, {8303,19375}, {8319,19400}, {8335,19401}, {8376,19379}, {8407,19384}, {8409,19386}, {8410,19388}, {8411,19392}, {8412,19394}, {8413,19396}, {8414,19398}, {8416,19385}, {8417,19387}, {8418,19393}, {8419,19397}, {10838,15182}, {11938,19390}, {11940,19391}
X(19384) lies on these lines: {3,67}, {371,15141}, {372,19389}, {3311,15140}, {3312,19399}, {6221,19398}, {6446,19387}, {6447,19394}, {6449,19396}, {6451,19397}, {6453,19388}, {8304,19375}, {8320,19400}, {8336,19401}, {8396,19382}, {8407,19383}, {9682,13654}, {10839,15182}, {11941,19390}, {11943,19391}
X(19385) lies on these lines: {3,67}, {371,19388}, {372,15141}, {3311,19398}, {3312,15140}, {6395,19379}, {6396,15106}, {6398,19399}, {6445,19386}, {6448,19395}, {6450,19397}, {6452,19396}, {6454,19389}, {8305,19375}, {8321,19400}, {8337,19401}, {8400,19382}, {8416,19383}, {10840,15182}, {11942,19390}, {11944,19391}
X(19386) lies on these lines: {3,19387}, {67,1151}, {371,19399}, {6221,19379}, {6425,15140}, {6429,15141}, {6439,15106}, {6445,19385}, {6453,19398}, {6468,19388}, {6470,19389}, {6472,19392}, {6474,19393}, {6476,19394}, {6478,19395}, {6480,19396}, {6482,19397}, {8306,19375}, {8322,19400}, {8338,19401}, {8397,19382}, {8409,19383}, {10841,15182}, {11959,19390}, {11961,19391}
X(19387) lies on these lines: {3,19386}, {67,1152}, {372,19398}, {6398,19379}, {6426,15140}, {6430,15141}, {6440,15106}, {6446,19384}, {6454,19399}, {6469,19389}, {6471,19388}, {6473,19393}, {6475,19392}, {6477,19395}, {6479,19394}, {6481,19397}, {6483,19396}, {8307,19375}, {8323,19400}, {8339,19401}, {8401,19382}, {8417,19383}, {10842,15182}, {11960,19390}, {11962,19391}
X(19388) lies on these lines: {3,19389}, {67,6425}, {371,19385}, {1151,15141}, {6221,15106}, {6409,15140}, {6433,19379}, {6453,19384}, {6468,19386}, {6471,19387}, {6484,19392}, {6486,19393}, {6488,19395}, {6490,19396}, {6492,19397}, {8308,19375}, {8324,19400}, {8340,19401}, {8410,19383}, {10843,15182}, {11963,19390}, {11965,19391}
X(19389) lies on these lines: {3,19388}, {67,6426}, {372,19384}, {1152,15141}, {6398,15106}, {6410,15140}, {6434,19379}, {6454,19385}, {6469,19387}, {6470,19386}, {6485,19393}, {6487,19392}, {6489,19394}, {6491,19397}, {6493,19396}, {8309,19375}, {8325,19400}, {8341,19401}, {8402,19382}, {10844,15182}, {11964,19390}, {11966,19391}
X(19390) lies on these lines: {67,6401}, {542,10670}, {11937,19382}, {11938,19383}, {11941,19384}, {11942,19385}, {11959,19386}, {11960,19387}, {11963,19388}, {11964,19389}, {11967,19392}, {11969,19393}, {11971,19394}, {11973,19395}, {11975,19396}, {11977,19397}, {11979,19398}, {11981,19399}, {11983,19391}, {11984,15140}, {11986,15141}, {14167,15182}
X(19391) lies on these lines: {67,6402}, {542,10674}, {11939,19382}, {11940,19383}, {11943,19384}, {11944,19385}, {11961,19386}, {11962,19387}, {11965,19388}, {11966,19389}, {11968,19393}, {11970,19392}, {11972,19395}, {11974,19394}, {11976,19397}, {11978,19396}, {11980,19399}, {11982,19398}, {11983,19390}, {11985,15140}, {11987,15141}, {14168,15182}
X(19392) lies on these lines: {3,19379}, {67,6417}, {371,15141}, {3312,15140}, {6419,15106}, {6449,19398}, {6456,19399}, {6472,19386}, {6475,19387}, {6484,19388}, {6487,19389}, {6494,19396}, {6496,19395}, {6498,19397}, {8310,19375}, {8326,19400}, {8342,19401}, {8398,19382}, {8411,19383}, {10845,15182}, {11967,19390}, {11970,19391}
X(19393) lies on these lines: {3,19379}, {67,6418}, {372,15141}, {3311,15140}, {6420,15106}, {6450,19399}, {6455,19398}, {6473,19387}, {6474,19386}, {6485,19389}, {6486,19388}, {6495,19397}, {6497,19394}, {6499,19396}, {8311,19375}, {8327,19400}, {8343,19401}, {8403,19382}, {8418,19383}, {10846,15182}, {11968,19391}, {11969,19390}
X(19394) lies on these lines: {3,19395}, {67,6419}, {1151,15141}, {3312,15140}, {6396,19379}, {6441,15106}, {6447,19384}, {6476,19386}, {6479,19387}, {6489,19389}, {6497,19393}, {6500,19397}, {8312,19375}, {8328,19400}, {8344,19401}, {8412,19383}, {10847,15182}, {11971,19390}, {11974,19391}
X(19395) lies on these lines: {3,19394}, {67,6420}, {1152,15141}, {3311,15140}, {6395,19397}, {6442,15106}, {6448,19385}, {6477,19387}, {6478,19386}, {6488,19388}, {6496,19392}, {6501,19396}, {8313,19375}, {8329,19400}, {8345,19401}, {8404,19382}, {10848,15182}, {11972,19391}, {11973,19390}
X(19396) lies on these lines: {3,19397}, {67,372}, {6425,19398}, {6427,15140}, {6431,15141}, {6435,19379}, {6449,19384}, {6452,19385}, {6480,19386}, {6483,19387}, {6490,19388}, {6493,19389}, {6494,19392}, {6499,19393}, {6501,19395}, {8314,19375}, {8330,19400}, {8346,19401}, {8399,19382}, {8413,19383}, {10849,15182}, {11975,19390}, {11978,19391}
X(19397) lies on these lines: {3,19396}, {67,371}, {6395,19395}, {6426,19399}, {6428,15140}, {6432,15141}, {6436,19379}, {6450,19385}, {6451,19384}, {6481,19387}, {6482,19386}, {6491,19389}, {6492,19388}, {6495,19393}, {6498,19392}, {6500,19394}, {8315,19375}, {8331,19400}, {8347,19401}, {8405,19382}, {8419,19383}, {10850,15182}, {11976,19391}, {11977,19390}
X(19398) lies on these lines: {3,15140}, {67,371}, {372,19387}, {1151,15141}, {3311,19385}, {6221,19384}, {6425,19396}, {6437,15106}, {6449,19392}, {6453,19386}, {6455,19393}, {8316,19375}, {8332,19400}, {8348,19401}, {8414,19383}, {10851,15182}, {11979,19390}, {11982,19391}
X(19399) lies on these lines: {3,15140}, {67,372}, {371,19386}, {1152,15141}, {3312,19384}, {6396,19379}, {6398,19385}, {6426,19397}, {6438,15106}, {6450,19393}, {6454,19387}, {6456,19392}, {8317,19375}, {8333,19400}, {8349,19401}, {8406,19382}, {10852,15182}, {11980,19391}, {11981,19390}
X(19400) lies on these lines: {67,256}, {1281,19375}, {1580,15140}, {2781,9840}, {8296,19379}, {8318,19382}, {8319,19383}, {8320,19384}, {8321,19385}, {8322,19386}, {8323,19387}, {8324,19388}, {8325,19389}, {8326,19392}, {8327,19393}, {8328,19394}, {8329,19395}, {8330,19396}, {8331,19397}, {8332,19398}, {8333,19399}, {8424,15141}, {10853,15182}
X(19401) lies on these lines: {67,291}, {1281,19375}, {8297,19379}, {8300,15140}, {8301,15141}, {8334,19382}, {8335,19383}, {8336,19384}, {8337,19385}, {8338,19386}, {8339,19387}, {8340,19388}, {8341,19389}, {8342,19392}, {8343,19393}, {8344,19394}, {8345,19395}, {8346,19396}, {8347,19397}, {8348,19398}, {8349,19399}, {10854,15182}
X(19402) lies on these lines: {67,3098}, {74,7574}, {4550,14643}, {5663,19381}, {7689,15133}, {10620,15141}, {10706,15062}, {12219,15137}, {12901,15136}, {13289,15138}, {15041,19376}
X(19403) lies on these lines: {1351,15141}, {7506,12824}, {7574,12902}, {10620,15138}, {11935,19374}, {12429,15133}, {15135,19381}
X(19404) lies on these lines: {3,12170}, {4,19418}, {25,8939}, {184,19430}, {427,19420}, {1398,19370}, {1593,18980}, {1993,19412}, {3515,19440}, {3516,13007}, {5410,19436}, {5411,19439}, {7071,19434}, {7395,19428}, {7484,9723}, {7592,19414}, {9777,19410}, {11245,18926}, {11284,19448}, {11402,19358}, {11403,19416}, {11405,19426}, {11406,19432}, {11408,19450}, {11409,19452}, {11410,19454}, {12160,18939}, {12167,12590}, {16030,19186}, {18386,18414}, {19118,19134}
X(19404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8939, 19446, 25), (9723, 19422, 7484), (19358, 19408, 11402)
X(19405) lies on these lines: {3,12169}, {4,19419}, {25,8943}, {184,19431}, {427,19421}, {1398,19371}, {1593,18981}, {1993,19413}, {3515,19441}, {3516,13008}, {5410,19438}, {5411,19437}, {7071,19435}, {7395,19429}, {7484,9723}, {7592,19415}, {9777,19411}, {11245,18927}, {11284,19449}, {11402,19359}, {11403,19417}, {11405,19427}, {11406,19433}, {11408,19451}, {11409,19453}, {11410,19455}, {12160,18940}, {12167,12591}, {16030,19187}, {18386,18415}, {19118,19135}
X(19405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8943, 19447, 25), (9723, 19423, 7484), (19359, 19409, 11402)
X(19406) lies on these lines: {2,19422}, {3,12170}, {4,19428}, {20,18980}, {22,8939}, {30,18462}, {97,19186}, {183,1232}, {394,19430}, {1370,19420}, {1993,19358}, {2071,19454}, {2979,19412}, {3060,19410}, {3100,19434}, {3101,19432}, {3146,19416}, {3153,18414}, {4296,19370}, {5012,19408}, {6515,18926}, {7488,19440}, {11412,18939}, {11413,13009}, {11414,19418}, {11416,19426}, {11417,19436}, {11418,19439}, {11420,19450}, {11421,19452}, {12220,12590}, {19121,19134}
X(19406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11412, 19414, 18939), (19422, 19446, 2)
X(19407) lies on these lines: {2,19423}, {3,12169}, {4,19429}, {20,18981}, {22,8943}, {30,18463}, {97,19187}, {183,1232}, {394,19431}, {1370,19421}, {1993,19359}, {2071,19455}, {2979,19413}, {3060,19411}, {3100,19435}, {3101,19433}, {3146,19417}, {3153,18415}, {4296,19371}, {5012,19409}, {6515,18927}, {7488,19441}, {11412,18940}, {11413,13010}, {11414,19419}, {11416,19427}, {11417,19438}, {11418,19437}, {11420,19451}, {11421,19453}, {12220,12591}, {19121,19135}
X(19407) = {X(19423), X(19447)}-harmonic conjugate of X(2)
X(19408) lies on these lines: {3,12230}, {6,493}, {54,19186}, {97,394}, {182,19422}, {184,19446}, {372,13889}, {389,19440}, {488,590}, {567,18462}, {569,19428}, {578,18980}, {641,8966}, {1579,17836}, {5012,19406}, {8253,11090}, {9306,19448}, {10533,12305}, {10961,12314}, {11402,19358}, {11422,19412}, {11423,19414}, {11424,19416}, {11425,13011}, {11426,19418}, {11427,19420}, {11428,19432}, {11429,19434}, {11430,19454}, {12161,18939}, {14912,18926}, {17809,19430}, {18388,18414}, {19365,19370}
X(19408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 8939, 19410), (11402, 19404, 19358)
X(19409) lies on these lines: {3,8908}, {6,494}, {54,19187}, {97,394}, {182,19423}, {184,19447}, {371,13943}, {389,19441}, {487,615}, {567,18463}, {569,19429}, {578,18981}, {642,13960}, {1578,17836}, {5012,19407}, {8252,11091}, {9306,19449}, {10534,12306}, {10963,12313}, {11402,19359}, {11422,19413}, {11423,19415}, {11424,19417}, {11425,13012}, {11426,19419}, {11427,19421}, {11428,19433}, {11429,19435}, {11430,19455}, {12161,18940}, {14912,18927}, {17809,19431}, {18388,18415}, {19365,19371}
X(19409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 8943, 19411), (11402, 19405, 19359)
X(19410) lies on these lines: {3,12238}, {4,18926}, {5,18939}, {6,493}, {25,19358}, {51,19446}, {52,19428}, {53,3068}, {185,19416}, {371,1598}, {389,18980}, {487,590}, {511,19422}, {578,19440}, {3060,19406}, {3567,19424}, {5640,19412}, {5943,19448}, {9723,10601}, {9777,19404}, {9781,19414}, {9786,13013}, {9792,19186}, {10669,12360}, {11432,19418}, {11433,19420}, {11435,19432}, {11436,19434}, {11438,19454}, {17810,19430}, {18390,18414}, {19366,19370}
X(19410) = {X(6), X(8939)}-harmonic conjugate of X(19408)
X(19411) lies on these lines: {3,12237}, {4,18927}, {5,18940}, {6,494}, {25,19359}, {51,19447}, {52,19429}, {53,3069}, {185,19417}, {372,1598}, {389,18981}, {488,615}, {511,19423}, {568,18463}, {578,19441}, {3060,19407}, {3567,19425}, {5640,19413}, {5943,19449}, {9723,10601}, {9777,19405}, {9781,19415}, {9786,13014}, {9792,19187}, {10673,12361}, {11432,19419}, {11433,19421}, {11435,19433}, {11436,19435}, {11438,19455}, {17810,19431}, {18390,18415}, {19366,19371}
X(19412) lies on these lines: {3,12275}, {22,19430}, {110,8939}, {1993,19404}, {2979,19406}, {3060,19446}, {5012,19358}, {5640,19410}, {5889,18939}, {7998,19422}, {9723,19413}, {11422,19408}, {11439,19416}, {11440,13015}, {11441,19418}, {11442,19420}, {11443,19426}, {11444,19428}, {11445,19432}, {11446,19434}, {11447,19436}, {11448,19439}, {11449,19440}, {11451,19448}, {11452,19450}, {11453,19452}, {11454,19454}, {11459,18462}, {12111,18980}, {12272,12590}, {18392,18414}, {18911,18926}, {19122,19134}, {19167,19186}, {19367,19370}
X(19412) = {X(18939), X(19424)}-harmonic conjugate of X(5889)
X(19413) lies on these lines: {3,12274}, {22,19431}, {110,8943}, {1993,19405}, {2979,19407}, {3060,19447}, {5012,19359}, {5640,19411}, {5889,18940}, {7998,19423}, {9723,19412}, {11422,19409}, {11439,19417}, {11440,13016}, {11441,19419}, {11442,19421}, {11443,19427}, {11444,19429}, {11445,19433}, {11446,19435}, {11447,19438}, {11448,19437}, {11449,19441}, {11451,19449}, {11452,19451}, {11453,19453}, {11454,19455}, {11459,18463}, {12111,18981}, {12272,12591}, {18392,18415}, {18911,18927}, {19122,19135}, {19167,19187}, {19367,19371}
X(19414) lies on these lines: {3,12275}, {24,19430}, {54,19358}, {74,13017}, {1614,8939}, {3567,19446}, {5890,19424}, {6241,18980}, {7592,19404}, {7999,19422}, {9723,19415}, {9781,19410}, {11412,18939}, {11423,19408}, {11455,19416}, {11456,19418}, {11457,19420}, {11458,19426}, {11459,19428}, {11460,19432}, {11461,19434}, {11462,19436}, {11463,19439}, {11464,19440}, {11465,19448}, {11466,19450}, {11467,19452}, {11468,19454}, {12111,18462}, {12283,12590}, {18394,18414}, {18912,18926}, {19123,19134}, {19168,19186}, {19368,19370}
X(19414) = {X(18939), X(19406)}-harmonic conjugate of X(11412)
X(19415) lies on these lines: {3,12274}, {24,19431}, {54,19359}, {74,13018}, {1614,8943}, {3567,19447}, {5890,19425}, {6241,18981}, {7592,19405}, {7999,19423}, {9723,19414}, {9781,19411}, {11412,18940}, {11423,19409}, {11455,19417}, {11456,19419}, {11457,19421}, {11458,19427}, {11459,19429}, {11460,19433}, {11461,19435}, {11462,19438}, {11463,19437}, {11464,19441}, {11465,19449}, {11466,19451}, {11467,19453}, {11468,19455}, {12111,18463}, {12283,12591}, {18394,18415}, {18912,18927}, {19123,19135}, {19168,19187}, {19368,19371}
X(19416) lies on these lines: {3,12297}, {4,18414}, {20,19422}, {24,19454}, {25,13019}, {30,19428}, {33,19370}, {34,19434}, {185,19410}, {378,19440}, {382,18462}, {1498,19358}, {1593,8939}, {1597,19418}, {3091,19448}, {3146,19406}, {8797,9723}, {11403,19404}, {11424,19408}, {11439,19412}, {11455,19414}, {11470,19426}, {11471,19432}, {11473,19436}, {11474,19439}, {11475,19450}, {11476,19452}, {12162,18939}, {12294,12590}, {12324,18926}, {15811,19430}, {19124,19134}, {19169,19186}
X(19417) lies on these lines: {3,12296}, {4,18415}, {20,19423}, {24,19455}, {25,13020}, {30,19429}, {33,19371}, {34,19435}, {185,19411}, {378,19441}, {382,18463}, {1498,19359}, {1593,8943}, {1597,19419}, {3091,19449}, {3146,19407}, {8797,9723}, {11403,19405}, {11424,19409}, {11439,19413}, {11455,19415}, {11470,19427}, {11471,19433}, {11473,19438}, {11474,19437}, {11475,19451}, {11476,19453}, {12162,18940}, {12294,12591}, {12324,18927}, {15811,19431}, {19124,19135}, {19169,19187}
X(19418) lies on these lines: {3,485}, {4,19404}, {5,19420}, {25,19424}, {999,19370}, {1351,11949}, {1597,19416}, {1598,19446}, {3295,19434}, {3311,19436}, {3312,19439}, {3843,18414}, {5050,19134}, {6759,19430}, {9723,19419}, {10306,19432}, {11414,19406}, {11426,19408}, {11432,19410}, {11441,19412}, {11456,19414}, {11482,19426}, {11484,19448}, {11485,19450}, {11486,19452}, {12164,18939}, {18914,18926}, {19173,19186}, {19347,19358}
X(19418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (8939, 13021, 19440), (13021, 19440, 3)
X(19419) lies on these lines: {3,486}, {4,19405}, {5,19421}, {25,19425}, {999,19371}, {1351,11950}, {1597,19417}, {1598,19447}, {3295,19435}, {3311,19438}, {3312,19437}, {3843,18415}, {5050,19135}, {6759,19431}, {9723,19418}, {10306,19433}, {11414,19407}, {11426,19409}, {11432,19411}, {11441,19413}, {11456,19415}, {11482,19427}, {11484,19449}, {11485,19451}, {11486,19453}, {12164,18940}, {18914,18927}, {19173,19187}, {19347,19359}
X(19420) lies on these lines: {2,6503}, {3,12321}, {4,18414}, {5,19418}, {20,13021}, {69,6462}, {376,19454}, {388,19370}, {427,19404}, {491,19442}, {497,19434}, {631,19440}, {1370,19406}, {1503,19430}, {1589,13889}, {1899,18926}, {1992,19426}, {2550,19432}, {3068,19436}, {3069,19439}, {3618,19134}, {6643,19428}, {6776,19358}, {7386,19422}, {7392,19448}, {11411,18939}, {11427,19408}, {11433,19410}, {11442,19412}, {11457,19414}, {11488,19450}, {11489,19452}, {18462,18531}, {19174,19186}
X(19421) lies on these lines: {2,6503}, {3,12320}, {4,18415}, {5,19419}, {20,13022}, {69,6463}, {376,19455}, {388,19371}, {427,19405}, {492,19443}, {497,19435}, {631,19441}, {1370,19407}, {1503,19431}, {1590,13943}, {1899,18927}, {1992,19427}, {2550,19433}, {3068,19438}, {3069,19437}, {3618,19135}, {6643,19429}, {6776,19359}, {7386,19423}, {7392,19449}, {11411,18940}, {11427,19409}, {11433,19411}, {11442,19413}, {11457,19415}, {11488,19451}, {11489,19453}, {18463,18531}, {19174,19187}
X(19422) lies on these lines: {2,19406}, {3,485}, {20,19416}, {69,18926}, {95,19186}, {182,19408}, {394,19358}, {511,19410}, {631,19424}, {1038,19370}, {1040,19434}, {1216,18939}, {1599,19449}, {7386,19420}, {7484,9723}, {7998,19412}, {7999,19414}, {10319,19432}, {11511,19426}, {11513,19436}, {11514,19439}, {11515,19450}, {11516,19452}, {11574,12590}, {17811,19430}, {18414,18531}, {19126,19134}
X(19422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 19406, 19446), (2, 19446, 19448), (7484, 19404, 9723)
X(19423) lies on these lines: {2,19407}, {3,486}, {20,19417}, {69,18927}, {95,19187}, {182,19409}, {394,19359}, {511,19411}, {631,19425}, {1038,19371}, {1040,19435}, {1216,18940}, {1600,19448}, {7386,19421}, {7484,9723}, {7998,19413}, {7999,19415}, {10319,19433}, {11511,19427}, {11513,19438}, {11514,19437}, {11515,19451}, {11516,19453}, {11574,12591}, {17811,19431}, {18415,18531}, {19126,19135}
X(19423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 19407, 19447), (7484, 19405, 9723)
X(19424) lies on these lines: {2,19428}, {3,12170}, {4,18414}, {5,18462}, {24,8939}, {25,19418}, {54,19186}, {76,95}, {186,19440}, {378,13021}, {631,19422}, {1181,19430}, {1870,19370}, {3090,19448}, {3520,19454}, {3567,19410}, {5889,18939}, {5890,19414}, {6197,19432}, {6403,12590}, {7592,19358}, {8537,19426}, {10632,19450}, {10633,19452}, {10880,19436}, {10881,19439}, {18916,18926}, {19128,19134}
X(19424) = {X(5889), X(19412)}-harmonic conjugate of X(18939)
X(19425) lies on these lines: {2,19429}, {3,12169}, {4,18415}, {5,18463}, {24,8943}, {25,19419}, {54,19187}, {76,95}, {186,19441}, {378,13022}, {631,19423}, {1181,19431}, {1870,19371}, {3090,19449}, {3520,19455}, {3567,19411}, {5889,18940}, {5890,19415}, {6197,19433}, {6198,19435}, {6403,12591}, {7592,19359}, {8537,19427}, {10632,19451}, {10633,19453}, {10880,19438}, {10881,19437}, {18916,18927}, {19128,19135}
X(19426) lies on these lines: {3,12598}, {6,493}, {511,19454}, {542,18414}, {575,19440}, {576,18980}, {1992,19420}, {8537,19424}, {8538,19428}, {8539,19432}, {8540,19434}, {8541,19446}, {8548,18939}, {9723,19427}, {9813,19448}, {10602,19358}, {11405,19404}, {11416,19406}, {11443,19412}, {11458,19414}, {11470,19416}, {11477,13021}, {11482,19418}, {11511,19422}, {17813,19430}, {18449,18462}, {18919,18926}, {19178,19186}, {19369,19370}
X(19426) = {X(6), X(12590)}-harmonic conjugate of X(19134)
X(19427) lies on these lines: {3,12597}, {6,494}, {511,19455}, {542,18415}, {575,19441}, {576,18981}, {1992,19421}, {8537,19425}, {8538,19429}, {8539,19433}, {8540,19435}, {8541,19447}, {8548,18940}, {9723,19426}, {9813,19449}, {10602,19359}, {11405,19405}, {11416,19407}, {11443,19413}, {11458,19415}, {11470,19417}, {11477,13022}, {11482,19419}, {11511,19423}, {17813,19431}, {18449,18463}, {18919,18927}, {19178,19187}, {19369,19371}
X(19428) lies on these lines: {2,19424}, {3,485}, {4,19406}, {5,19446}, {30,19416}, {52,19410}, {155,19358}, {569,19408}, {1060,19370}, {1062,19434}, {1656,19448}, {5562,18939}, {6643,19420}, {7393,9723}, {7395,19404}, {8251,19432}, {8538,19426}, {8962,12314}, {9967,12590}, {10634,19450}, {10635,19452}, {10897,19436}, {10898,19439}, {11411,18926}, {11444,19412}, {11459,19414}, {17814,19430}, {18404,18414}, {19131,19134}, {19179,19186}
X(19429) lies on these lines: {2,19425}, {3,486}, {4,19407}, {5,19447}, {30,19417}, {52,19411}, {155,19359}, {569,19409}, {1060,19371}, {1062,19435}, {1656,19449}, {5562,18940}, {6643,19421}, {7393,9723}, {7395,19405}, {8251,19433}, {8538,19427}, {9967,12591}, {10634,19451}, {10635,19453}, {10897,19438}, {10898,19437}, {11411,18927}, {11444,19413}, {11459,19415}, {17814,19431}, {18404,18415}, {19131,19135}, {19179,19187}
X(19430) lies on these lines: {3,17842}, {6,19358}, {22,19412}, {24,19414}, {64,13021}, {154,8939}, {184,19404}, {221,19370}, {394,19406}, {1181,19424}, {1498,18980}, {1503,19420}, {2192,19434}, {3197,19432}, {5085,9723}, {6759,19418}, {10606,19454}, {13567,18926}, {15811,19416}, {17809,19408}, {17810,19410}, {17811,19422}, {17813,19426}, {17814,19428}, {17819,19436}, {17820,19439}, {17821,19440}, {17825,19448}, {17826,19450}, {17827,19452}, {17834,18939}, {18405,18414}, {18451,18462}, {19132,19134}, {19180,19186}
X(19430) = {X(19358), X(19446)}-harmonic conjugate of X(6)
X(19431) lies on these lines: {3,17839}, {6,19359}, {22,19413}, {24,19415}, {64,13022}, {154,8943}, {184,19405}, {221,19371}, {394,19407}, {1181,19425}, {1498,18981}, {1503,19421}, {2192,19435}, {3197,19433}, {5085,9723}, {6759,19419}, {10606,19455}, {13567,18927}, {15811,19417}, {17809,19409}, {17810,19411}, {17811,19423}, {17813,19427}, {17814,19429}, {17819,19438}, {17820,19437}, {17821,19441}, {17825,19449}, {17826,19451}, {17827,19453}, {17834,18940}, {18405,18415}, {18451,18463}, {19132,19135}, {19180,19187}
X(19431) = {X(19359), X(19447)}-harmonic conjugate of X(6)
X(19432) lies on these lines: {3,12663}, {19,19446}, {40,18980}, {55,8939}, {65,19370}, {2550,19420}, {3101,19406}, {3197,19430}, {3779,12590}, {5415,19436}, {5416,19439}, {5584,13021}, {6197,19424}, {7688,19454}, {8251,19428}, {8539,19426}, {9723,19433}, {9816,19448}, {10306,19418}, {10319,19422}, {10636,19450}, {10637,19452}, {10902,19440}, {11406,19404}, {11428,19408}, {11435,19410}, {11445,19412}, {11460,19414}, {11471,19416}, {18406,18414}, {18453,18462}, {18921,18926}, {19133,19134}, {19181,19186}, {19350,19358}
X(19433) lies on these lines: {3,12662}, {19,19447}, {40,18981}, {55,8943}, {65,19371}, {2550,19421}, {3101,19407}, {3197,19431}, {3779,12591}, {5415,19438}, {5416,19437}, {5584,13022}, {6197,19425}, {7688,19455}, {8251,19429}, {8539,19427}, {9723,19432}, {9816,19449}, {10306,19419}, {10319,19423}, {10636,19451}, {10637,19453}, {10902,19441}, {11406,19405}, {11428,19409}, {11435,19411}, {11445,19413}, {11460,19415}, {11471,19417}, {18406,18415}, {18453,18463}, {18921,18927}, {19133,19135}, {19181,19187}, {19350,19359}
X(19434) lies on these lines: {1,18980}, {3,12911}, {33,19446}, {34,19416}, {35,19440}, {36,19454}, {55,8939}, {56,13021}, {497,19420}, {1040,19422}, {1062,19428}, {1250,19452}, {2066,19436}, {2192,19430}, {2330,19134}, {3056,11947}, {3100,19406}, {3295,19418}, {3583,18414}, {5414,19439}, {6238,18939}, {7071,19404}, {8540,19426}, {9723,19435}, {9817,19448}, {10638,19450}, {11429,19408}, {11436,19410}, {11446,19412}, {11461,19414}, {18455,18462}, {18922,18926}, {19182,19186}, {19354,19358}
X(19435) lies on these lines: {1,18981}, {3,12910}, {33,19447}, {34,19417}, {35,19441}, {36,19455}, {55,8943}, {56,13022}, {497,19421}, {1040,19423}, {1062,19429}, {1250,19453}, {2066,19438}, {2192,19431}, {2330,19135}, {3056,11948}, {3100,19407}, {3295,19419}, {3583,18415}, {5414,19437}, {6198,19425}, {6238,18940}, {7071,19405}, {8540,19427}, {9723,19434}, {9817,19449}, {10638,19451}, {11429,19409}, {11436,19411}, {11446,19413}, {11461,19415}, {18455,18463}, {18922,18927}, {19182,19187}, {19354,19359}
X(19436) lies on these lines: {3,12961}, {6,493}, {371,18980}, {372,19440}, {577,13889}, {1151,13021}, {2066,19434}, {2067,19370}, {3068,19420}, {3311,19418}, {5063,19437}, {5410,19404}, {5412,19446}, {5415,19432}, {6564,18414}, {9723,19438}, {10665,18939}, {10880,19424}, {10897,19428}, {10961,19448}, {11417,19406}, {11447,19412}, {11462,19414}, {11473,19416}, {11513,19422}, {17819,19430}, {18457,18462}, {18923,18926}, {19183,19186}, {19355,19358}
X(19436) = {X(6), X(8939)}-harmonic conjugate of X(19439)
X(19437) lies on these lines: {3,12966}, {6,494}, {371,19441}, {372,18981}, {577,13943}, {1152,13022}, {3069,19421}, {3312,19419}, {5063,19436}, {5411,19405}, {5413,19447}, {5414,19435}, {5416,19433}, {6396,19455}, {6502,19371}, {6565,18415}, {9723,19439}, {10666,18940}, {10881,19425}, {10898,19429}, {10963,19449}, {11418,19407}, {11448,19413}, {11463,19415}, {11474,19417}, {11514,19423}, {17820,19431}, {18459,18463}, {18924,18927}, {19184,19187}, {19356,19359}
X(19437) = {X(6), X(8943)}-harmonic conjugate of X(19438)
X(19438) lies on these lines: {3,12960}, {6,494}, {216,13943}, {371,18981}, {372,19441}, {570,19439}, {1151,13022}, {2066,19435}, {2067,19371}, {3068,19421}, {3311,19419}, {5410,19405}, {5412,19447}, {5415,19433}, {6564,18415}, {9723,19436}, {10665,18940}, {10880,19425}, {10897,19429}, {10961,19449}, {11417,19407}, {11447,19413}, {11462,19415}, {11473,19417}, {11513,19423}, {17819,19431}, {18457,18463}, {18923,18927}, {19183,19187}, {19355,19359}
X(19438) = {X(6), X(8943)}-harmonic conjugate of X(19437)
X(19439) lies on these lines: {3,12967}, {6,493}, {216,13889}, {371,19440}, {372,18980}, {570,19438}, {1152,13021}, {3069,19420}, {3312,19418}, {5411,19404}, {5413,19446}, {5414,19434}, {5416,19432}, {6396,19454}, {6502,19370}, {6565,18414}, {9723,19437}, {10666,18939}, {10881,19424}, {10898,19428}, {10963,19448}, {11418,19406}, {11448,19412}, {11463,19414}, {11474,19416}, {11514,19422}, {17820,19430}, {18459,18462}, {18924,18926}, {19184,19186}, {19356,19358}
X(19439) = {X(6), X(8939)}-harmonic conjugate of X(19436)
X(19440) lies on these lines: {3,485}, {5,18414}, {15,19452}, {16,19450}, {24,19446}, {35,19434}, {36,19370}, {182,12590}, {186,19424}, {371,19439}, {372,19436}, {378,19416}, {389,19408}, {511,19134}, {575,19426}, {578,19410}, {631,19420}, {1147,18939}, {3515,19404}, {6642,19448}, {7488,19406}, {9723,19441}, {10902,19432}, {11449,19412}, {11464,19414}, {17821,19430}, {18925,18926}, {19185,19186}, {19357,19358}
X(19440) = {X(3), X(19418)}-harmonic conjugate of X(13021)
X(19441) lies on these lines: {3,486}, {5,18415}, {15,19453}, {16,19451}, {24,19447}, {35,19435}, {36,19371}, {182,12591}, {186,19425}, {371,19437}, {372,19438}, {378,19417}, {389,19409}, {511,19135}, {575,19427}, {578,19411}, {631,19421}, {1147,18940}, {3515,19405}, {6642,19449}, {7488,19407}, {9723,19440}, {10902,19433}, {11449,19413}, {11464,19415}, {17821,19431}, {18925,18927}, {19185,19187}, {19357,19359}
X(19442) lies on these lines: {6,493}, {491,19420}, {1991,3785}, {9732,18980}, {12306,13021}
X(19443) lies on these lines: {6,494}, {492,19421}, {591,3785}, {9733,18981}, {12305,13022}
X(19444) lies on these lines: {}
X(19445) lies on these lines: {}
X(19446) lies on these lines: {2,19406}, {3,69}, {4,18414}, {5,19428}, {6,19358}, {19,19432}, {24,19440}, {25,8939}, {33,19434}, {34,19370}, {51,19410}, {52,18939}, {160,5594}, {184,19408}, {275,19186}, {378,19454}, {381,18462}, {1593,13021}, {1598,19418}, {1843,11394}, {1974,19134}, {3060,19412}, {3156,13889}, {3567,19414}, {5412,19436}, {5413,19439}, {8541,19426}, {10641,19450}, {10642,19452}, {11433,18926}, {12170,13055}
X(19446) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 19406, 19422), (6, 19430, 19358), (25, 19404, 8939), (19422, 19448, 2)
X(19447) lies on these lines: {2,19407}, {3,69}, {4,18415}, {5,19429}, {6,19359}, {19,19433}, {24,19441}, {25,8943}, {33,19435}, {34,19371}, {51,19411}, {52,18940}, {160,5595}, {184,19409}, {275,19187}, {378,19455}, {381,18463}, {1593,13022}, {1598,19419}, {1843,11395}, {1974,19135}, {3060,19413}, {3155,13943}, {3567,19415}, {5412,19438}, {5413,19437}, {8541,19427}, {10641,19451}, {10642,19453}, {11433,18927}, {12169,13056}
X(19447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 19407, 19423), (6, 19431, 19359), (25, 19405, 8943), (19423, 19449, 2)
X(19448) lies on these lines: {2,19406}, {3,639}, {5,18980}, {25,1007}, {1600,19423}, {1656,19428}, {3090,19424}, {3091,19416}, {5020,8939}, {5055,18462}, {5462,18939}, {5943,19410}, {6642,19440}, {7392,19420}, {8943,8944}, {9306,19408}, {9813,19426}, {9816,19432}, {9817,19434}, {9822,12590}, {10601,19358}, {10643,19450}, {10644,19452}, {10961,19436}, {10963,19439}, {11284,19404}, {11451,19412}, {11465,19414}, {11479,13021}, {11484,19418}, {17825,19430}, {18414,18420}, {18926,18928}, {19134,19137}, {19186,19188}, {19370,19372}
X(19448) = {X(2), X(19446)}-harmonic conjugate of X(19422)
X(19449) lies on these lines: {2,19407}, {3,640}, {5,18981}, {25,1007}, {1599,19422}, {1656,19429}, {3090,19425}, {3091,19417}, {5020,8943}, {5055,18463}, {5462,18940}, {5943,19411}, {6642,19441}, {7392,19421}, {8939,8940}, {9306,19409}, {9813,19427}, {9816,19433}, {9817,19435}, {9822,12591}, {10601,19359}, {10643,19451}, {10644,19453}, {10961,19438}, {10963,19437}, {11284,19405}, {11451,19413}, {11465,19415}, {11479,13022}, {11484,19419}, {17825,19431}, {18415,18420}, {18927,18928}, {19135,19137}, {19187,19188}, {19371,19372}
X(19449) = {X(2), X(19447)}-harmonic conjugate of X(19423)
X(19450) lies on these lines: {3,12982}, {6,493}, {15,18980}, {16,19440}, {7051,19370}, {9723,19451}, {10632,19424}, {10634,19428}, {10636,19432}, {10638,19434}, {10641,19446}, {10643,19448}, {10645,19454}, {10661,18939}, {11408,19404}, {11420,19406}, {11452,19412}, {11466,19414}, {11475,19416}, {11480,13021}, {11485,19418}, {11488,19420}, {11515,19422}, {16808,18414}, {17826,19430}, {18462,18468}, {18926,18929}, {19186,19190}, {19358,19363}
X(19450) = {X(6), X(8939)}-harmonic conjugate of X(19452)
X(19451) lies on these lines: {3,12980}, {6,494}, {15,18981}, {16,19441}, {7051,19371}, {9723,19450}, {10632,19425}, {10634,19429}, {10636,19433}, {10638,19435}, {10641,19447}, {10643,19449}, {10645,19455}, {10661,18940}, {11408,19405}, {11420,19407}, {11452,19413}, {11466,19415}, {11475,19417}, {11480,13022}, {11485,19419}, {11488,19421}, {11515,19423}, {16808,18415}, {17826,19431}, {18463,18468}, {18927,18929}, {19187,19190}, {19359,19363}
X(19451) = {X(6), X(8943)}-harmonic conjugate of X(19453)
X(19452) lies on these lines: {3,12983}, {6,493}, {15,19440}, {16,18980}, {1250,19434}, {9723,19453}, {10633,19424}, {10635,19428}, {10637,19432}, {10642,19446}, {10644,19448}, {10646,19454}, {10662,18939}, {11409,19404}, {11421,19406}, {11453,19412}, {11467,19414}, {11476,19416}, {11481,13021}, {11486,19418}, {11489,19420}, {11516,19422}, {16809,18414}, {17827,19430}, {18462,18470}, {18926,18930}, {19186,19191}, {19358,19364}, {19370,19373}
X(19452) = {X(6), X(8939)}-harmonic conjugate of X(19450)
X(19453) lies on these lines: {3,12981}, {6,494}, {15,19441}, {16,18981}, {1250,19435}, {9723,19452}, {10633,19425}, {10635,19429}, {10637,19433}, {10642,19447}, {10644,19449}, {10646,19455}, {10662,18940}, {11409,19405}, {11421,19407}, {11453,19413}, {11467,19415}, {11476,19417}, {11481,13022}, {11486,19419}, {11489,19421}, {11516,19423}, {16809,18415}, {17827,19431}, {18463,18470}, {18927,18930}, {19187,19191}, {19359,19364}, {19371,19373}
X(19453) = {X(6), X(8943)}-harmonic conjugate of X(19451)
X(19454) lies on these lines: {3,485}, {24,19416}, {30,18414}, {35,19370}, {36,19434}, {376,19420}, {378,19446}, {511,19426}, {2071,19406}, {3098,12590}, {3520,19424}, {5092,19134}, {6396,19439}, {7688,19432}, {7689,18939}, {9723,19455}, {10605,19358}, {10606,19430}, {10645,19450}, {10646,19452}, {11410,19404}, {11430,19408}, {11438,19410}, {11454,19412}, {11468,19414}, {18926,18931}, {19186,19192}
X(19454) = {X(12985), X(13061)}-harmonic conjugate of X(3)
X(19455) lies on these lines: {3,486}, {24,19417}, {30,18415}, {35,19371}, {36,19435}, {376,19421}, {378,19447}, {511,19427}, {2071,19407}, {3098,12591}, {3520,19425}, {5092,19135}, {6396,19437}, {7688,19433}, {7689,18940}, {9723,19454}, {10605,19359}, {10606,19431}, {10645,19451}, {10646,19453}, {11410,19405}, {11430,19409}, {11438,19411}, {11454,19413}, {11468,19415}, {18927,18931}, {19187,19192}
The reciprocal orthologic center of these triangles is X(15136)
X(19456) lies on these lines: {2,18932}, {3,974}, {6,13}, {24,3047}, {25,12236}, {49,9730}, {52,10117}, {54,12284}, {74,1993}, {110,6642}, {125,155}, {146,1994}, {156,13358}, {184,2931}, {185,12302}, {195,2935}, {382,11744}, {394,6699}, {576,11807}, {1147,11806}, {1181,17702}, {1351,9919}, {1498,12295}, {1593,5663}, {1594,3448}, {1986,12412}, {2904,12292}, {2914,12317}, {5012,12273}, {5622,12358}, {5654,10255}, {6759,11800}, {6776,12319}, {7529,11746}, {7544,14683}, {7723,12164}, {9714,15647}, {9934,18534}, {10264,15106}, {10601,12900}, {10602,12596}, {10605,12901}, {10663,19363}, {10664,19364}, {10733,11456}, {11064,12364}, {11402,12168}, {11432,16222}, {11441,14644}, {11579,15141}, {11935,19374}, {12041,16266}, {12085,17854}, {12140,12419}, {12160,13171}, {12310,19347}, {12368,16473}, {12383,15032}, {12661,19350}, {12888,19354}, {12891,19355}, {12892,19356}, {12893,19357}, {12902,19362}, {13201,15801}, {13346,17855}, {13754,19457}, {14627,16657}, {14984,19459}, {16003,17847}, {18396,19479}, {19125,19138}, {19170,19193}, {19349,19469}, {19358,19482}, {19359,19483}
X(19456) = midpoint of X(12160) and X(13171)
X(19456) = reflection of X(3) in X(13198)
X(19456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17838, 113), (113, 17838, 399), (265, 18445, 399), (974, 5504, 3), (11402, 12168, 12228)
The reciprocal orthologic center of these triangles is X(3581)
X(19457) lies on these lines: {2,18933}, {3,125}, {4,10117}, {6,74}, {22,10733}, {24,14644}, {25,7687}, {26,10113}, {54,12281}, {64,17854}, {110,7503}, {141,12383}, {146,7527}, {155,7723}, {184,399}, {185,567}, {186,15081}, {338,1300}, {394,5504}, {542,12168}, {568,1204}, {569,11562}, {578,10628}, {1092,18466}, {1112,10982}, {1181,5663}, {1205,19124}, {1498,12292}, {1511,7514}, {1593,2777}, {1597,9919}, {1658,11801}, {1899,10264}, {1993,12219}, {2070,13851}, {2071,3580}, {2917,12289}, {2929,16013}, {3047,11441}, {3088,13203}, {3092,13288}, {3093,13287}, {3357,17855}, {3448,6146}, {3516,13293}, {3520,12022}, {3581,18859}, {5012,12270}, {5972,7395}, {6776,8546}, {7387,12295}, {7485,15051}, {7509,15035}, {7592,7722}, {7689,11806}, {7724,19350}, {7727,19354}, {9659,12904}, {9672,12903}, {9934,12133}, {9976,10602}, {10170,13367}, {10263,12041}, {10298,18918}, {10657,19363}, {10658,19364}, {11250,19353}, {11402,12165}, {11413,15055}, {11424,13417}, {11425,15463}, {11426,14448}, {11430,15106}, {11744,18532}, {12085,16111}, {12244,14865}, {12308,19347}, {12375,19355}, {12376,19356}, {12803,19351}, {12804,19352}, {12825,17838}, {13093,17856}, {13754,19456}, {14683,18925}, {15040,17701}, {15059,17928}, {15089,18436}, {18382,18533}, {18997,19051}, {18998,19052}, {19125,19140}, {19170,19195}, {19349,19470}, {19358,19484}, {19359,19485}, {19467,19468}
X(19457) = midpoint of X(1593) and X(13171)
X(19457) = reflection of X(1181) in X(13198)
X(19457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 265, 2931), (6, 17835, 1986), (74, 378, 2935), (74, 974, 10605), (74, 1986, 17835), (74, 5622, 974), (74, 15033, 7731), (1597, 9919, 13202), (2935, 5621, 74), (5504, 12358, 394), (6699, 12901, 3), (7687, 13289, 25), (10938, 14805, 184), (11402, 12165, 12227), (11598, 15151, 74)
The reciprocal orthologic center of these triangles is X(7387)
X(19458) lies on these lines: {2,18934}, {3,15316}, {5,6}, {25,12235}, {52,9908}, {54,12282}, {184,9937}, {185,12301}, {394,3548}, {1147,5892}, {1154,10606}, {1498,12293}, {1593,12160}, {1993,3541}, {2393,7387}, {2931,17821}, {3157,13750}, {3796,19468}, {5012,12271}, {5446,12167}, {5504,16270}, {6391,12309}, {6776,12318}, {8549,14790}, {9820,10601}, {9926,10602}, {9927,18451}, {9931,19354}, {9932,19357}, {9938,10605}, {10659,19363}, {10660,19364}, {12134,12420}, {12164,18435}, {12417,19350}, {12424,19355}, {12425,19356}, {12429,18445}, {15061,15115}, {15317,18436}, {19125,19141}, {19170,19196}, {19349,19471}, {19358,19486}, {19359,19487}
X(19458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17836, 155), (155, 14852, 17814), (394, 19360, 3548), (6391, 19347, 12309), (11402, 12166, 1147)
The reciprocal orthologic center of these triangles is X(576)
X(19459) lies on these lines: {2,18935}, {3,69}, {6,25}, {22,193}, {24,14912}, {26,1353}, {54,12283}, {125,2930}, {141,1899}, {155,9967}, {160,1609}, {182,14913}, {185,1350}, {197,4849}, {237,8573}, {394,11574}, {511,1181}, {518,8192}, {542,12168}, {895,12310}, {1040,1473}, {1100,1486}, {1176,6391}, {1205,17847}, {1351,7387}, {1352,6146}, {1469,19349}, {1498,12294}, {1503,1593}, {1511,5622}, {1598,14853}, {1992,9909}, {1993,12220}, {1995,18919}, {2781,12165}, {2854,13198}, {2916,6144}, {3056,19354}, {3094,6751}, {3098,10605}, {3131,18930}, {3132,18929}, {3155,18924}, {3156,18923}, {3270,10387}, {3515,8550}, {3516,10619}, {3547,12309}, {3589,8546}, {3618,5020}, {3619,16419}, {3620,7485}, {3689,12329}, {3751,9798}, {3779,19350}, {3796,8681}, {3818,18396}, {3827,11396}, {4185,5800}, {5012,12272}, {5017,6752}, {5039,10790}, {5050,6642}, {5085,13367}, {5093,7517}, {5095,10117}, {5198,5480}, {5227,7085}, {5847,8193}, {5921,7503}, {5965,19468}, {5972,15128}, {6403,7592}, {6800,15531}, {7529,18583}, {8406,12591}, {8414,12590}, {8547,17710}, {8593,9876}, {9707,19128}, {9822,10601}, {9861,10753}, {9913,10759}, {9919,10752}, {9937,19131}, {10132,11513}, {10133,11514}, {10754,13175}, {10755,13222}, {10762,14673}, {10766,11641}, {11365,16475}, {11425,19124}, {11479,18945}, {12007,15582}, {13567,15585}, {14575,15905}, {14984,19456}, {15074,19139}, {18382,18386}, {18438,18445}, {19170,19197}
X(19459) = reflection of X(1351) in X(12161)
X(19459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 154, 1974), (6, 159, 25), (6, 184, 19125), (6, 206, 19118), (6, 6467, 10602), (6, 7716, 51), (6, 9924, 1843), (6, 9969, 9777), (184, 6467, 6), (5594, 19006, 25), (5595, 19005, 25), (6776, 10519, 18909), (10602, 19125, 6), (11402, 12167, 6), (19463, 19464, 1181)
The reciprocal orthologic center of these triangles is X(9729)
X(19460) lies on these lines: {2,18936}, {5,19361}, {6,17837}, {184,2929}, {9729,19353}, {11487,19348}, {19125,19142}, {19170,19198}, {19349,19472}, {19358,19488}, {19359,19489}
The reciprocal orthologic center of these triangles is X(3)
X(19461) lies on these lines: {2,18937}, {3,18940}, {6,487}, {25,12237}, {54,12285}, {155,12601}, {184,12978}, {185,12303}, {394,486}, {642,10601}, {1181,19466}, {1498,12296}, {1578,6463}, {1595,3564}, {1993,3092}, {5012,12274}, {6290,10982}, {6776,12320}, {7592,12509}, {9733,10608}, {10602,12597}, {10605,12984}, {11402,12169}, {12311,19347}, {12662,19350}, {12910,19354}, {12960,19355}, {12966,19356}, {12972,19357}, {12980,19363}, {12981,19364}, {19125,19143}, {19170,19199}, {19349,19473}, {19358,19490}
X(19461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17839, 487), (11402, 12169, 12229)
The reciprocal orthologic center of these triangles is X(3)
X(19462) lies on these lines: {2,18938}, {3,18939}, {6,488}, {25,12238}, {54,12286}, {155,12602}, {184,12979}, {185,12304}, {394,485}, {641,10601}, {1181,19465}, {1498,12297}, {1579,6462}, {1595,3564}, {1993,3093}, {5012,12275}, {6289,10982}, {6776,12321}, {7592,12510}, {9732,10608}, {10602,12598}, {10605,12985}, {11402,12170}, {12312,19347}, {12663,19350}, {12911,19354}, {12961,19355}, {12967,19356}, {12973,19357}, {12982,19363}, {12983,19364}, {19125,19144}, {19170,19200}, {19349,19474}, {19359,19491}
X(19462) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17842, 488), (11402, 12170, 12230)
The reciprocal orthologic center of these triangles is X(3)
X(19463) lies on these lines: {2,18941}, {3,8825}, {6,6291}, {25,12239}, {54,12287}, {155,12603}, {184,1151}, {185,12305}, {394,12360}, {511,1181}, {1498,12298}, {1993,12223}, {5012,12276}, {6239,7592}, {6252,19350}, {6283,19354}, {6776,12322}, {7362,19349}, {7690,10605}, {9823,10601}, {9974,10602}, {10667,19363}, {10668,19364}, {11402,12171}, {12313,19347}, {12962,19355}, {12968,19356}, {12974,19357}, {19125,19145}, {19170,19201}, {19358,19492}, {19359,19494}
X(19463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17840, 6291), (1181, 19459, 19464), (11402, 12171, 12231)
The reciprocal orthologic center of these triangles is X(3)
X(19464) lies on these lines: {2,18942}, {6,6406}, {25,12240}, {54,12288}, {155,12604}, {184,1152}, {185,12306}, {394,12361}, {511,1181}, {1498,12299}, {1993,12224}, {5012,12277}, {6400,7592}, {6404,19350}, {6405,19354}, {6776,12323}, {7353,19349}, {7692,10605}, {9824,10601}, {9975,10602}, {10671,19363}, {10672,19364}, {11402,12172}, {12314,19347}, {12963,19355}, {12969,19356}, {12975,19357}, {19125,19146}, {19170,19202}, {19358,19495}, {19359,19493}
X(19464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17843, 6406), (1181, 19459, 19463), (11402, 12172, 12232)
The reciprocal orthologic center of these triangles is X(10670)
X(19465) lies on these lines: {2,18943}, {6,13051}, {25,13013}, {54,13017}, {155,13039}, {184,13055}, {185,13021}, {394,13027}, {1181,19462}, {1498,13019}, {1993,13009}, {5012,13015}, {6776,13025}, {7592,13035}, {10601,13053}, {10602,13037}, {10605,13061}, {11402,13007}, {13023,19347}, {13041,19350}, {13043,19354}, {13045,19355}, {13047,19356}, {13049,19357}, {13057,19363}, {13059,19364}, {19125,19147}, {19170,19203}, {19349,19475}, {19359,19497}
X(19465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17841, 13051), (11402, 13007, 13011)
The reciprocal orthologic center of these triangles is X(10670)
X(19466) lies on these lines: {2,18944}, {6,13052}, {25,13014}, {54,13018}, {155,13040}, {184,13056}, {185,13022}, {394,13028}, {1181,19461}, {1498,13020}, {1993,13010}, {5012,13016}, {6776,13026}, {7592,13036}, {10601,13054}, {10602,13038}, {10605,13062}, {11402,13008}, {13024,19347}, {13042,19350}, {13044,19354}, {13046,19355}, {13048,19356}, {13050,19357}, {13058,19363}, {13060,19364}, {19125,19148}, {19170,19204}, {19349,19476}, {19358,19496}
X(19466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17844, 13052), (11402, 13008, 13012)
The reciprocal orthologic center of these triangles is X(4)
X(19467) lies on these lines: {2,11449}, {3,68}, {4,54}, {5,18396}, {6,3575}, {20,185}, {24,12022}, {25,12241}, {26,12370}, {30,1181}, {49,5654}, {51,7487}, {64,5486}, {125,631}, {154,235}, {155,12605}, {182,6815}, {186,18912}, {217,7737}, {265,6639}, {287,7791}, {376,1204}, {378,14216}, {382,19347}, {389,18533}, {394,12362}, {403,9707}, {418,15653}, {427,11425}, {468,17821}, {550,10605}, {569,18420}, {895,15740}, {974,12121}, {1092,6643}, {1147,18531}, {1199,18559}, {1352,7503}, {1370,13346}, {1425,4293}, {1495,3089}, {1498,1885}, {1503,1593}, {1597,16655}, {1598,16657}, {1993,12225}, {2165,14533}, {3070,12231}, {3071,12232}, {3088,11550}, {3090,18918}, {3091,13851}, {3146,11422}, {3147,11202}, {3153,9545}, {3270,4294}, {3431,6143}, {3515,13567}, {3516,6247}, {3520,11457}, {3522,18913}, {3528,18931}, {3541,11430}, {3542,10282}, {3548,12038}, {3549,9927}, {3767,14585}, {3796,6823}, {4549,9936}, {4846,15317}, {5012,12278}, {5286,8779}, {5318,19363}, {5321,19364}, {5422,9815}, {5480,19125}, {5596,12294}, {5651,6804}, {5878,11456}, {5944,10201}, {6240,7592}, {6253,19350}, {6284,19354}, {6288,14805}, {6459,18924}, {6460,18923}, {6515,10112}, {6696,11410}, {6756,10982}, {6816,9306}, {7354,19349}, {7500,13598}, {7505,11464}, {7542,14852}, {7544,13434}, {7689,10116}, {8537,14912}, {8550,10602}, {9704,18403}, {9777,11745}, {9786,11245}, {9825,10601}, {10996,18935}, {11392,11429}, {11393,19365}, {11402,12173}, {11403,16621}, {11426,18494}, {11438,18916}, {11750,13352}, {12024,15750}, {12174,15311}, {12293,15760}, {13198,17702}, {13470,14791}, {13561,18580}, {16163,18910}, {18445,18563}, {18457,19062}, {18459,19061}, {19170,19205}, {19358,19498}, {19359,19499}, {19457,19468}
X(19467) = reflection of X(4) in X(578)
X(19467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 6146, 1899), (3, 12429, 343), (4, 11427, 3574), (4, 18925, 184), (6, 17845, 3575), (20, 6776, 185), (49, 18404, 5654), (54, 12289, 4), (184, 10619, 18925), (376, 18909, 1204), (550, 18914, 10605), (6759, 13403, 4), (7503, 14516, 1352), (11430, 18381, 3541), (18396, 19357, 5)
The reciprocal orthologic center of these triangles is X(6243)
X(19468) lies on these lines: {2,18946}, {3,539}, {6,24}, {22,15801}, {25,12242}, {26,1493}, {125,5898}, {155,12606}, {184,195}, {185,12307}, {394,12363}, {524,7512}, {1154,1181}, {1209,7393}, {1498,12300}, {1593,18400}, {1598,3574}, {1993,12226}, {2888,6146}, {2914,10117}, {2931,15089}, {3520,6247}, {3796,19458}, {5012,12280}, {5892,13353}, {5965,19459}, {6242,7592}, {6255,19350}, {6286,19354}, {6288,18396}, {6776,12325}, {7356,19349}, {7691,10605}, {9935,10982}, {9977,10602}, {10610,19360}, {10677,19363}, {10678,19364}, {11402,12175}, {11803,17714}, {12316,19347}, {12965,19355}, {12971,19356}, {19125,19150}, {19170,19207}, {19358,19502}, {19359,19503}, {19457,19467}
X(19468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17846, 6152), (54, 6152, 6), (54, 12380, 3567), (11402, 12175, 12234)
The reciprocal orthologic center of these triangles is X(15136)
X(19469) lies on these lines: {1,12888}, {30,10118}, {33,12295}, {34,113}, {35,12901}, {36,12893}, {55,12302}, {56,2931}, {65,5504}, {73,265}, {74,4296}, {110,1870}, {125,1060}, {388,12319}, {399,1069}, {999,12310}, {1038,6699}, {1062,16163}, {1398,12168}, {1428,19138}, {1469,14984}, {2067,12891}, {3028,7352}, {3448,10055}, {3585,19479}, {4318,7978}, {4351,10081}, {5663,6238}, {6198,10733}, {6502,12892}, {7051,10663}, {10664,19373}, {11436,14708}, {12121,18455}, {12228,19365}, {12236,19366}, {12273,19367}, {12284,19368}, {12428,19472}, {12596,19369}, {12900,19372}, {12903,15133}, {13754,19470}, {18915,18932}, {19175,19193}, {19349,19456}, {19370,19482}, {19371,19483}
The reciprocal orthologic center of these triangles is X(3581)
X(19470) lies on these lines: {1,3024}, {12,10264}, {33,12292}, {34,1986}, {35,73}, {36,110}, {46,2948}, {55,10620}, {56,399}, {65,79}, {113,7741}, {125,7951}, {146,1479}, {172,14901}, {221,17835}, {388,12317}, {484,4551}, {517,11670}, {542,1469}, {611,16010}, {999,12308}, {1038,12358}, {1060,7723}, {1319,11699}, {1398,12165}, {1428,19140}, {1478,3448}, {1511,7280}, {1539,18514}, {1870,7722}, {2067,12375}, {2772,5425}, {2777,7355}, {2842,3214}, {2935,10076}, {3157,12302}, {3582,5655}, {3583,7728}, {3746,10065}, {4293,14683}, {4296,12219}, {4299,12383}, {4302,12244}, {4316,12121}, {4857,12374}, {5010,12041}, {5119,9904}, {5217,15041}, {5270,12903}, {5433,10272}, {5563,10091}, {6000,10118}, {6286,10628}, {6502,12376}, {7051,10657}, {7352,10483}, {7354,7356}, {7687,19366}, {7972,8674}, {7984,11009}, {9976,19369}, {10069,15342}, {10113,18513}, {10658,19373}, {12047,13605}, {12184,15545}, {12227,19365}, {12261,18393}, {12270,19367}, {12281,19368}, {12902,12943}, {13754,19469}, {14677,15338}, {18915,18933}, {19175,19195}, {19349,19457}, {19370,19484}, {19371,19485}
X(19470) = reflection of X(1) in X(3028)
X(19470) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (35, 6126, 10088), (74, 10088, 35), (265, 12373, 3585), (7728, 12904, 3583)
The reciprocal orthologic center of these triangles is X(7387)
X(19471) lies on these lines: {1,9931}, {33,12293}, {34,155}, {35,9938}, {36,9932}, {55,12301}, {56,9937}, {65,921}, {68,73}, {221,17836}, {388,12318}, {999,12309}, {1038,12359}, {1062,12118}, {1079,4551}, {1147,19365}, {1398,12166}, {1428,19141}, {2067,12424}, {4296,11411}, {6502,12425}, {7051,10659}, {7355,13754}, {9820,19372}, {9926,19369}, {10118,17702}, {10660,19373}, {12235,19366}, {12271,19367}, {12282,19368}, {12429,18447}, {18915,18934}, {19175,19196}, {19349,19458}, {19370,19486}, {19371,19487}
The reciprocal orthologic center of these triangles is X(9729)
X(19472) lies on these lines: {1,18978}, {56,2929}, {65,775}, {221,17837}, {1428,19142}, {7354,10118}, {12428,19469}, {18915,18936}, {19175,19198}, {19349,19460}, {19370,19488}, {19371,19489}
The reciprocal orthologic center of these triangles is X(3)
X(19473) lies on these lines: {1,12910}, {3,19371}, {33,12296}, {34,487}, {35,12984}, {36,12972}, {55,12303}, {56,12978}, {65,12662}, {221,17839}, {388,12320}, {486,1038}, {642,19372}, {999,12311}, {1040,12123}, {1060,12601}, {1398,12169}, {1428,19143}, {1870,12509}, {2067,12960}, {3564,19474}, {4296,12221}, {6251,9817}, {6502,12966}, {7051,12980}, {8270,9906}, {12229,19365}, {12237,19366}, {12274,19367}, {12285,19368}, {12597,19369}, {12981,19373}, {18915,18937}, {19175,19199}, {19349,19461}, {19370,19490}
The reciprocal orthologic center of these triangles is X(3)
X(19474) lies on these lines: {1,12911}, {3,19370}, {33,12297}, {34,488}, {35,12985}, {36,12973}, {55,12304}, {56,12979}, {65,12663}, {221,17842}, {388,12321}, {485,1038}, {641,19372}, {999,12312}, {1040,12124}, {1060,12602}, {1398,12170}, {1428,19144}, {1870,12510}, {2067,12961}, {3564,19473}, {4296,12222}, {6250,9817}, {6502,12967}, {7051,12982}, {8270,9907}, {12230,19365}, {12238,19366}, {12275,19367}, {12286,19368}, {12598,19369}, {12983,19373}, {18915,18938}, {19175,19200}, {19349,19462}, {19371,19491}
The reciprocal orthologic center of these triangles is X(10670)
X(19475) lies on these lines: {1,12911}, {33,13019}, {34,13051}, {35,13061}, {36,13049}, {55,13021}, {56,13055}, {65,13041}, {221,17841}, {388,13025}, {999,13023}, {1038,13027}, {1060,13039}, {1398,13007}, {1428,19147}, {1870,13035}, {2067,13045}, {4296,13009}, {6502,13047}, {7051,13057}, {13011,19365}, {13013,19366}, {13015,19367}, {13017,19368}, {13037,19369}, {13053,19372}, {13059,19373}, {18915,18943}, {19175,19203}, {19349,19465}, {19371,19497}
The reciprocal orthologic center of these triangles is X(10670)
X(19476) lies on these lines: {1,12910}, {33,13020}, {34,13052}, {35,13062}, {36,13050}, {55,13022}, {56,13056}, {65,13042}, {221,17844}, {388,13026}, {999,13024}, {1038,13028}, {1060,13040}, {1398,13008}, {1428,19148}, {1870,13036}, {2067,13046}, {4296,13010}, {6502,13048}, {7051,13058}, {13012,19365}, {13014,19366}, {13016,19367}, {13018,19368}, {13038,19369}, {13054,19372}, {13060,19373}, {18915,18944}, {19175,19204}, {19349,19466}, {19370,19496}
The reciprocal orthologic center of these triangles is X(12419)
X(19477) lies on these lines: {3,68}, {1147,15134}, {3448,19376}, {3564,15141}, {15123,15128}, {15138,17702}
The reciprocal orthologic center of these triangles is X(7574)
X(19478) lies on these lines: {1,399}, {3,12334}, {36,12407}, {55,12898}, {56,265}, {104,3448}, {113,18761}, {125,10269}, {952,13204}, {956,12778}, {958,1511}, {999,12261}, {2975,12383}, {3428,12121}, {3560,11720}, {5253,15081}, {5663,12114}, {10966,12896}, {11249,17702}, {11492,12467}, {11493,12466}, {12368,18519}, {19013,19051}, {19014,19052}
The reciprocal orthologic center of these triangles is X(15136)
X(19479) lies on these lines: {4,110}, {5,12893}, {30,12901}, {74,3153}, {125,7689}, {155,12902}, {265,1531}, {381,2931}, {382,12302}, {542,12596}, {546,18428}, {2777,18569}, {3047,12289}, {3410,18387}, {3583,12888}, {3585,19469}, {3818,14984}, {3843,12310}, {4550,7687}, {5449,14644}, {5663,18377}, {5876,9927}, {6288,15030}, {6564,12891}, {6565,12892}, {6699,18531}, {7728,11381}, {10264,18572}, {10663,16808}, {10664,16809}, {11744,14915}, {11801,12359}, {12038,12121}, {12168,18386}, {12228,18388}, {12236,18390}, {12273,18392}, {12284,18394}, {12661,18406}, {12825,18474}, {12900,18420}, {13293,13371}, {15061,18442}, {17838,18405}, {18396,19456}, {18414,19482}, {18415,19483}, {18918,18932}, {19130,19138}, {19177,19193}
X(19479) = midpoint of X(i) and X(j) for these {i,j}: {155, 12902}, {382, 12302}, {7728, 15133}
X(19479) = reflection of X(13293) in X(13371)
X(19479) = {X(113), X(12295)}-harmonic conjugate of X(12140)
The reciprocal orthologic center of these triangles is X(19481)
X(19480) lies on the line {3,2929}
The reciprocal orthologic center of these triangles is X(19480)
X(19481) lies on these lines: {6,13}, {30,16108}, {54,5972}, {125,10112}, {1493,11804}, {1986,11225}, {2777,6102}, {3448,11424}, {5449,6723}, {5462,13365}, {5965,12358}, {6146,11800}, {10113,10116}, {10628,13292}, {11264,11801}, {11806,12370}, {12236,18400}, {13358,13630}
X(19481) = midpoint of X(i) and X(j) for these {i,j}: {125, 10112}, {6146, 11800}, {10113, 10116}, {11264, 11801}, {11806, 12370}
X(19481) = {X(265), X(15087)}-harmonic conjugate of X(113)
The reciprocal orthologic center of these triangles is X(15136)
X(19482) lies on these lines: {74,19406}, {110,19424}, {113,19446}, {125,19428}, {265,18462}, {5663,19500}, {6699,19422}, {9723,19483}, {10663,19450}, {10664,19452}, {12168,19404}, {12228,19408}, {12236,19410}, {12273,19412}, {12284,19414}, {12295,19416}, {12302,13021}, {12310,19418}, {12319,19420}, {12590,14984}, {12596,19426}, {12661,19432}, {12888,19434}, {12891,19436}, {12892,19439}, {12893,19440}, {12900,19448}, {12901,19454}, {13754,19484}, {17702,18980}, {17838,19430}, {18414,19479}, {18926,18932}, {19134,19138}, {19186,19193}, {19358,19456}, {19370,19469}
The reciprocal orthologic center of these triangles is X(15136)
X(19483) lies on these lines: {74,19407}, {110,19425}, {113,19447}, {125,19429}, {265,18463}, {2931,8943}, {5663,19501}, {6699,19423}, {9723,19482}, {10663,19451}, {10664,19453}, {12168,19405}, {12228,19409}, {12236,19411}, {12273,19413}, {12284,19415}, {12295,19417}, {12302,13022}, {12310,19419}, {12319,19421}, {12591,14984}, {12596,19427}, {12661,19433}, {12888,19435}, {12891,19438}, {12892,19437}, {12893,19441}, {12900,19449}, {12901,19455}, {13754,19485}, {17702,18981}, {17838,19431}, {18415,19479}, {18927,18932}, {19135,19138}, {19187,19193}, {19359,19456}, {19371,19469}
The reciprocal orthologic center of these triangles is X(3581)
X(19484) lies on these lines: {74,19454}, {110,19440}, {265,18414}, {399,6221}, {542,12590}, {1986,19446}, {2777,19500}, {5663,18980}, {7687,19410}, {7722,19424}, {7723,19428}, {7724,19432}, {7727,19434}, {9723,19485}, {9976,19426}, {10620,13021}, {10628,19507}, {10657,19450}, {10658,19452}, {12165,19404}, {12219,19406}, {12227,19408}, {12270,19412}, {12281,19414}, {12292,19416}, {12308,19418}, {12317,19420}, {12358,19422}, {12375,19436}, {12376,19439}, {13754,19482}, {17702,18939}, {17835,19430}, {18926,18933}, {19134,19140}, {19186,19195}, {19358,19457}, {19370,19470}, {19498,19502}
The reciprocal orthologic center of these triangles is X(3581)
X(19485) lies on these lines: {74,19455}, {110,19441}, {265,18415}, {399,6398}, {542,12591}, {1986,19447}, {2777,19501}, {5663,18981}, {7687,19411}, {7722,19425}, {7723,19429}, {7724,19433}, {7727,19435}, {9723,19484}, {9976,19427}, {10620,13022}, {10628,19508}, {10657,19451}, {10658,19453}, {12165,19405}, {12219,19407}, {12227,19409}, {12270,19413}, {12281,19415}, {12292,19417}, {12308,19419}, {12317,19421}, {12358,19423}, {12375,19438}, {12376,19437}, {13754,19483}, {17702,18940}, {17835,19431}, {18927,18933}, {19135,19140}, {19187,19195}, {19359,19457}, {19371,19470}, {19499,19503}
The reciprocal orthologic center of these triangles is X(7387)
X(19486) lies on these lines: {3,12426}, {68,19428}, {155,19446}, {1147,19408}, {2079,8276}, {3053,8909}, {8939,9937}, {9723,19487}, {9820,19448}, {9926,19426}, {9931,19434}, {9932,19440}, {9938,19454}, {10659,19450}, {10660,19452}, {11411,19406}, {12166,19404}, {12235,19410}, {12271,19412}, {12282,19414}, {12293,19416}, {12301,13021}, {12309,19418}, {12318,19420}, {12359,19422}, {12417,19432}, {12424,19436}, {12425,19439}, {12429,18462}, {13754,19500}, {17836,19430}, {18926,18934}, {19134,19141}, {19186,19196}, {19358,19458}, {19370,19471}
The reciprocal orthologic center of these triangles is X(7387)
X(19487) lies on these lines: {3,12427}, {68,19429}, {155,19447}, {1147,19409}, {2079,8277}, {8943,9937}, {9723,19486}, {9820,19449}, {9926,19427}, {9931,19435}, {9932,19441}, {9938,19455}, {10659,19451}, {10660,19453}, {11411,19407}, {12166,19405}, {12235,19411}, {12271,19413}, {12282,19415}, {12293,19417}, {12301,13022}, {12309,19419}, {12318,19421}, {12359,19423}, {12417,19433}, {12424,19438}, {12425,19437}, {12429,18463}, {13754,19501}, {17836,19431}, {18927,18934}, {19135,19141}, {19187,19196}, {19359,19458}, {19371,19471}
The reciprocal orthologic center of these triangles is X(9729)
X(19488) lies on these lines: {2929,8939}, {9723,19489}, {17837,19430}, {18926,18936}, {19134,19142}, {19186,19198}, {19358,19460}, {19370,19472}
The reciprocal orthologic center of these triangles is X(9729)
X(19489) lies on these lines: {2929,8943}, {9723,19488}, {17837,19431}, {18927,18936}, {19135,19142}, {19187,19198}, {19359,19460}, {19371,19472}
The reciprocal orthologic center of these triangles is X(3)
X(19490) lies on these lines: {3,69}, {486,19422}, {642,19448}, {8939,12978}, {12169,19404}, {12221,19406}, {12229,19408}, {12237,19410}, {12274,19412}, {12285,19414}, {12296,19416}, {12303,13021}, {12311,19418}, {12320,19420}, {12509,19424}, {12597,19426}, {12601,19428}, {12662,19432}, {12910,19434}, {12960,19436}, {12966,19439}, {12972,19440}, {12980,19450}, {12981,19452}, {12984,19454}, {17839,19430}, {18926,18937}, {18980,19496}, {19134,19143}, {19186,19199}, {19358,19461}, {19370,19473}
The reciprocal orthologic center of these triangles is X(3)
X(19491) lies on these lines: {3,69}, {485,19423}, {641,19449}, {8943,12979}, {12170,19405}, {12222,19407}, {12230,19409}, {12238,19411}, {12275,19413}, {12286,19415}, {12297,19417}, {12304,13022}, {12312,19419}, {12321,19421}, {12510,19425}, {12598,19427}, {12602,19429}, {12663,19433}, {12911,19435}, {12961,19438}, {12967,19437}, {12973,19441}, {12982,19451}, {12983,19453}, {12985,19455}, {17842,19431}, {18927,18938}, {18981,19497}, {19135,19144}, {19187,19200}, {19359,19462}, {19371,19474}
The reciprocal orthologic center of these triangles is X(3)
X(19492) lies on these lines: {3,8854}, {30,12976}, {371,12164}, {511,10669}, {1151,1498}, {1181,8414}, {5013,7395}, {5907,15883}, {6239,19424}, {6252,19432}, {6283,19434}, {6291,19446}, {7362,19370}, {7690,19454}, {8408,12986}, {8821,11825}, {9723,19494}, {9823,19448}, {9974,19426}, {10667,19450}, {10668,19452}, {12171,19404}, {12223,19406}, {12231,19408}, {12239,19410}, {12276,19412}, {12287,19414}, {12298,19416}, {12305,13021}, {12313,19418}, {12322,19420}, {12360,19422}, {12603,19428}, {12962,19436}, {12964,13045}, {12968,19439}, {12974,19440}, {17840,19430}, {18926,18941}, {19134,19145}, {19186,19201}, {19358,19463}
X(19492) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (5013, 7395, 19493), (12590, 18980, 19495)
The reciprocal orthologic center of these triangles is X(3)
X(19493) lies on these lines: {3,8855}, {30,13067}, {372,12164}, {511,10673}, {1152,1498}, {1181,8406}, {5013,7395}, {5907,15884}, {6400,19425}, {6404,19433}, {6405,19435}, {6406,19447}, {7353,19371}, {7692,19455}, {8420,12987}, {8820,11824}, {9723,19495}, {9824,19449}, {9975,19427}, {10671,19451}, {10672,19453}, {12172,19405}, {12224,19407}, {12232,19409}, {12240,19411}, {12277,19413}, {12288,19415}, {12299,19417}, {12306,13022}, {12314,19419}, {12323,19421}, {12361,19423}, {12604,19429}, {12963,19438}, {12969,19437}, {12970,13048}, {12975,19441}, {17843,19431}, {18927,18942}, {19135,19146}, {19187,19202}, {19359,19464}
The reciprocal orthologic center of these triangles is X(3)
X(19494) lies on these lines: {511,10673}, {1151,8943}, {6239,19425}, {6252,19433}, {6283,19435}, {6291,19447}, {7362,19371}, {7690,19455}, {9723,19492}, {9823,19449}, {9974,19427}, {10667,19451}, {10668,19453}, {12171,19405}, {12223,19407}, {12231,19409}, {12239,19411}, {12276,19413}, {12287,19415}, {12298,19417}, {12305,13022}, {12313,19419}, {12322,19421}, {12360,19423}, {12603,19429}, {12962,19438}, {12968,19437}, {12974,19441}, {17840,19431}, {18927,18941}, {19135,19145}, {19187,19201}, {19359,19463}
X(19494) = {X(12591), X(18981)}-harmonic conjugate of X(19493)
The reciprocal orthologic center of these triangles is X(3)
X(19495) lies on these lines: {511,10669}, {1152,8939}, {6400,19424}, {6404,19432}, {6405,19434}, {6406,19446}, {7353,19370}, {7692,19454}, {9723,19493}, {9824,19448}, {9975,19426}, {10671,19450}, {10672,19452}, {12172,19404}, {12224,19406}, {12232,19408}, {12240,19410}, {12277,19412}, {12288,19414}, {12299,19416}, {12306,13021}, {12314,19418}, {12323,19420}, {12361,19422}, {12604,19428}, {12963,19436}, {12969,19439}, {12975,19440}, {17843,19430}, {18926,18942}, {19134,19146}, {19186,19202}, {19358,19464}
X(19495) = {X(12590), X(18980)}-harmonic conjugate of X(19492)
The reciprocal orthologic center of these triangles is X(10674)
X(19496) lies on these lines: {311,1975}, {8939,13056}, {13008,19404}, {13010,19406}, {13012,19408}, {13014,19410}, {13016,19412}, {13018,19414}, {13020,19416}, {13024,19418}, {13026,19420}, {13028,19422}, {13036,19424}, {13038,19426}, {13040,19428}, {13042,19432}, {13044,19434}, {13046,19436}, {13048,19439}, {13050,19440}, {13052,19446}, {13054,19448}, {13058,19450}, {13060,19452}, {13062,19454}, {17844,19430}, {18926,18944}, {18980,19490}, {19134,19148}, {19186,19204}, {19358,19466}
The reciprocal orthologic center of these triangles is X(10670)
X(19497) lies on these lines: {311,1975}, {8943,13055}, {13007,19405}, {13009,19407}, {13011,19409}, {13013,19411}, {13015,19413}, {13017,19415}, {13019,19417}, {13023,19419}, {13025,19421}, {13027,19423}, {13035,19425}, {13037,19427}, {13039,19429}, {13041,19433}, {13043,19435}, {13045,19438}, {13047,19437}, {13049,19441}, {13051,19447}, {13053,19449}, {13057,19451}, {13059,19453}, {13061,19455}, {17841,19431}, {18927,18943}, {18981,19491}, {19135,19147}, {19187,19203}, {19359,19465}
The reciprocal orthologic center of these triangles is X(4)
X(19498) lies on these lines: {4,8939}, {5,18414}, {20,13021}, {30,18980}, {382,19418}, {550,19454}, {1503,9838}, {1885,19416}, {3070,19436}, {3071,19439}, {3575,19446}, {5318,19450}, {5321,19452}, {5480,19134}, {6240,19424}, {6253,19432}, {6284,19434}, {6815,9723}, {7354,19370}, {8550,19426}, {9825,19448}, {12173,19404}, {12225,19406}, {12233,19408}, {12241,19410}, {12278,19412}, {12289,19414}, {12362,19422}, {12605,19428}, {13749,19442}, {17845,19430}, {18462,18563}, {18926,18945}, {19186,19205}, {19358,19467}, {19484,19502}
X(19498) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (20, 19420, 13021), (18414, 19440, 5)
The reciprocal orthologic center of these triangles is X(4)
X(19499) lies on these lines: {4,8943}, {5,18415}, {20,13022}, {30,18981}, {382,19419}, {550,19455}, {1503,9839}, {1885,19417}, {3070,19438}, {3071,19437}, {3575,19447}, {5318,19451}, {5321,19453}, {5480,19135}, {6240,19425}, {6253,19433}, {6284,19435}, {6815,9723}, {7354,19371}, {8550,19427}, {9825,19449}, {12173,19405}, {12225,19407}, {12233,19409}, {12241,19411}, {12278,19413}, {12289,19415}, {12362,19423}, {12605,19429}, {13748,19443}, {17845,19431}, {18463,18563}, {18927,18945}, {19187,19205}, {19359,19467}, {19485,19503}
X(19499) = {X(20), X(19421)}-harmonic conjugate of X(13022)
The reciprocal orthologic center of these triangles is X(389)
X(19500) lies on these lines: {4,18926}, {30,18939}, {64,13021}, {185,19446}, {1151,1498}, {1181,19408}, {1503,9838}, {1593,19358}, {2777,19484}, {3070,12257}, {3357,19454}, {5663,19482}, {5907,19422}, {6000,18980}, {6241,19424}, {6254,19432}, {6285,19434}, {6759,19440}, {7355,19370}, {8549,19426}, {9723,19501}, {9729,19448}, {10675,19450}, {10676,19452}, {11381,19416}, {12111,19406}, {12162,19428}, {12174,19404}, {12279,19412}, {12290,19414}, {12315,19418}, {12324,19420}, {12964,19436}, {12970,19439}, {13754,19486}, {18381,18414}, {18400,19502}, {18439,18462}, {19134,19149}, {19186,19206}
X(19500) = {X(64), X(19430)}-harmonic conjugate of X(13021)
The reciprocal orthologic center of these triangles is X(389)
X(19501) lies on these lines: {4,18927}, {30,18940}, {64,13022}, {185,19447}, {1152,1498}, {1181,19409}, {1503,9839}, {1593,19359}, {2777,19485}, {3071,12256}, {3357,19455}, {5663,19483}, {5907,19423}, {6000,18981}, {6241,19425}, {6254,19433}, {6285,19435}, {6759,19441}, {7355,19371}, {8549,19427}, {9723,19500}, {9729,19449}, {10675,19451}, {10676,19453}, {11381,19417}, {12111,19407}, {12162,19429}, {12174,19405}, {12279,19413}, {12290,19415}, {12315,19419}, {12324,19421}, {12964,19438}, {12970,19437}, {13754,19487}, {18381,18415}, {18400,19503}, {18439,18463}, {19135,19149}, {19187,19206}
X(19501) = {X(64), X(19431)}-harmonic conjugate of X(13022)
The reciprocal orthologic center of these triangles is X(6243)
X(19502) lies on these lines: {54,19440}, {195,3311}, {539,18939}, {1154,18980}, {5965,12590}, {6152,19446}, {6242,19424}, {6255,19432}, {6286,19434}, {6288,18414}, {7356,19370}, {7691,19454}, {9723,19503}, {9977,19426}, {10677,19450}, {10678,19452}, {12175,19404}, {12226,19406}, {12234,19408}, {12242,19410}, {12280,19412}, {12291,19414}, {12300,19416}, {12307,13021}, {12316,19418}, {12325,19420}, {12363,19422}, {12606,19428}, {12965,19436}, {12971,19439}, {17846,19430}, {18400,19500}, {18926,18946}, {19134,19150}, {19186,19207}, {19358,19468}, {19484,19498}
The reciprocal orthologic center of these triangles is X(6243)
X(19503) lies on these lines: {54,19441}, {195,3312}, {539,18940}, {1154,18981}, {5965,12591}, {6152,19447}, {6242,19425}, {6255,19433}, {6286,19435}, {6288,18415}, {7356,19371}, {7691,19455}, {9723,19502}, {9977,19427}, {10677,19451}, {10678,19453}, {12175,19405}, {12226,19407}, {12234,19409}, {12242,19411}, {12280,19413}, {12291,19415}, {12300,19417}, {12307,13022}, {12316,19419}, {12325,19421}, {12363,19423}, {12606,19429}, {12965,19438}, {12971,19437}, {17846,19431}, {18400,19501}, {18927,18946}, {19135,19150}, {19187,19207}, {19359,19468}, {19485,19499}
The reciprocal parallelogic center of these triangles is X(15139)
X(19504) lies on the cubic K944 and these lines: {2,18947}, {3,1986}, {4,195}, {6,67}, {24,3043}, {25,110}, {52,2931}, {54,7731}, {74,3516}, {112,246}, {113,155}, {146,1885}, {184,10117}, {185,2935}, {186,15040}, {247,1625}, {265,7507}, {323,468}, {378,7722}, {394,5972}, {427,1353}, {428,9143}, {542,5064}, {576,11800}, {578,10628}, {648,2970}, {1092,16223}, {1147,11557}, {1177,19125}, {1181,2777}, {1398,3028}, {1498,13202}, {1511,3515}, {1570,14580}, {1593,5663}, {1594,14627}, {1597,12292}, {1829,2948}, {1843,2930}, {2781,11402}, {2854,12167}, {3088,12317}, {3092,12376}, {3093,12375}, {3518,15039}, {3520,15041}, {3541,10264}, {3542,10272}, {3575,12383}, {5012,13201}, {5186,15342}, {5198,5609}, {5422,15059}, {5621,13366}, {5898,6152}, {6143,15047}, {6243,11597}, {6593,19118}, {6642,16222}, {6723,10601}, {6759,11807}, {6776,13203}, {7395,12358}, {7484,13416}, {7503,12219}, {7687,10982}, {7728,18445}, {8901,9512}, {9777,11746}, {9919,19347}, {9934,16105}, {10113,18386}, {10114,18381}, {10118,19354}, {10119,19350}, {10263,11702}, {10602,13248}, {10605,13293}, {10681,19363}, {10682,19364}, {10721,11456}, {11403,12133}, {11410,12041}, {11425,14448}, {11562,12302}, {12160,12168}, {12164,12825}, {12173,17702}, {12236,15132}, {12244,15032}, {12273,15801}, {12281,15033}, {13211,16473}, {13287,19355}, {13288,19356}, {13289,19357}, {15035,15750}, {15042,17506}, {15046,16868}, {15063,17838}, {16010,19124}, {18396,19506}, {19170,19208}, {19349,19505}, {19358,19507}, {19359,19508}
X(19504) = midpoint of X(i) and X(j) for these {i,j}: {1593, 12165}, {12160, 12168}
X(19504) = reflection of X(i) in X(j) for these (i,j): (3, 12228), (1181, 12227), (1593, 15472)
X(19504) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 17847, 125), (125, 17847, 15106), (184, 13417, 10117), (378, 7722, 10620), (1597, 12308, 12292), (1986, 15463, 3), (11402, 13171, 13198), (11562, 13352, 12302)
The reciprocal parallelogic center of these triangles is X(15139)
X(19505) lies on these lines: {1,2777}, {30,12888}, {33,13202}, {34,125}, {35,13293}, {36,13289}, {55,2935}, {56,10117}, {65,2906}, {74,1870}, {110,4296}, {113,1060}, {146,12940}, {221,17847}, {388,13203}, {974,11436}, {999,9919}, {1038,5972}, {1062,16111}, {1112,19366}, {1177,1428}, {1398,13171}, {1425,13417}, {1456,10693}, {1503,7286}, {2067,13287}, {2192,17812}, {2778,3057}, {2781,3028}, {2892,12588}, {3585,19506}, {4318,7984}, {4351,9934}, {5663,6238}, {6000,7727}, {6198,10721}, {6286,10628}, {6502,13288}, {6723,19372}, {7051,10681}, {7728,18447}, {7731,19368}, {9931,17702}, {10076,10620}, {10682,19373}, {11429,15472}, {11744,12374}, {13198,19365}, {13201,19367}, {13248,19369}, {18915,18947}, {19175,19208}, {19349,19504}, {19370,19507}, {19371,19508}
X(19505) = {X(9934), X(10091)}-harmonic conjugate of X(10535)
The reciprocal parallelogic center of these triangles is X(15139)
X(19506) lies on these lines: {4,74}, {5,13289}, {30,12893}, {52,265}, {110,1568}, {113,6759}, {146,14216}, {381,10117}, {382,2935}, {541,18568}, {542,13248}, {1112,18390}, {1177,19130}, {1503,18572}, {1539,13491}, {1853,10620}, {2781,10113}, {3043,12289}, {3098,15116}, {3521,9730}, {3583,10118}, {3585,19505}, {3843,9919}, {5663,18377}, {5972,11202}, {6000,7728}, {6146,12227}, {6247,18567}, {6564,13287}, {6565,13288}, {6696,14677}, {6723,18420}, {7507,19457}, {7574,10564}, {7706,13364}, {7723,18474}, {7731,18394}, {10119,18406}, {10274,12228}, {10282,14643}, {10681,16808}, {10682,16809}, {11204,16111}, {11550,12292}, {11566,15873}, {12901,13371}, {12902,17847}, {13171,18386}, {13198,18388}, {13201,18392}, {13346,15132}, {13403,15472}, {13417,13851}, {18396,19504}, {18414,19507}, {18415,19508}, {18918,18947}, {19177,19208}
X(19506) = midpoint of X(i) and X(j) for these {i,j}: {146, 14216}, {382, 2935}, {12902, 17847}
X(19506) = reflection of X(i) in X(j) for these (i,j): (1177, 19130), (3098, 15116), (12901, 13371)
X(19506) = {X(17847), X(18405)}-harmonic conjugate of X(12902)
The reciprocal parallelogic center of these triangles is X(15139)
X(19507) lies on these lines: {74,19424}, {110,19406}, {113,19428}, {125,19446}, {1112,19410}, {1177,19134}, {2777,18980}, {2935,13021}, {5663,19482}, {5972,19422}, {6723,19448}, {7728,18462}, {7731,19414}, {8939,10117}, {9723,19508}, {9919,19418}, {10118,19434}, {10119,19432}, {10628,19484}, {10681,19450}, {10682,19452}, {13171,19404}, {13198,19408}, {13201,19412}, {13202,19416}, {13203,19420}, {13248,19426}, {13287,19436}, {13288,19439}, {13289,19440}, {13293,19454}, {17847,19430}, {18414,19506}, {18926,18947}, {19186,19208}, {19358,19504}, {19370,19505}
The reciprocal parallelogic center of these triangles is X(15139)
X(19508) lies on these lines: {74,19425}, {110,19407}, {113,19429}, {125,19447}, {1112,19411}, {1177,19135}, {2777,18981}, {2935,13022}, {5663,19483}, {5972,19423}, {6723,19449}, {7728,18463}, {7731,19415}, {8943,10117}, {9723,19507}, {9919,19419}, {10118,19435}, {10119,19433}, {10628,19485}, {10681,19451}, {10682,19453}, {13171,19405}, {13198,19409}, {13201,19413}, {13202,19417}, {13203,19421}, {13248,19427}, {13287,19438}, {13288,19437}, {13289,19441}, {13293,19455}, {17847,19431}, {18415,19506}, {18927,18947}, {19187,19208}, {19359,19504}, {19371,19505}
The reciprocal orthologic center of these triangles is X(12419)
X(19509) lies on these lines: {5,578}, {3564,15116}, {5094,19477}, {6640,15316}, {10257,15115}, {11064,15123}, {15125,17702}
The reciprocal orthologic center of these triangles is X(12584)
X(19510) lies on these lines: {5,141}, {67,3292}, {69,11443}, {125,9027}, {524,5159}, {542,15122}, {599,5094}, {858,2393}, {1092,15069}, {1350,1531}, {1352,10564}, {2072,15117}, {2781,15125}, {3564,15115}, {5486,16051}, {12585,15120}, {14984,15123}, {17416,17429}
X(19510) = midpoint of X(i) and X(j) for these {i,j}: {67, 3292}, {599, 13857}, {858, 5181}, {1350, 1531}, {1352, 10564}
X(19510) = {X(599), X(5094)}-harmonic conjugate of X(8542)
The reciprocal orthologic center of these triangles is X(19481)
X(19511) lies on these lines: {5,12897}, {511,15119}, {5094,19480}
X(19512) lies on these lines: {2, 3}, {239, 5844}, {355, 17284}, {517, 3008}, {572, 17245}, {573, 17337}, {952, 3912}, {1482, 5222}, {1483, 17316}, {1766, 17278}, {2548, 4258}, {3763, 5816}, {3767, 5022}, {4253, 5305}, {4384, 5690}, {5144, 6667}, {5308, 10246}, {5901, 17023}, {10247, 17014}, {10446, 17352}, {12610, 17356}
X(19513) lies on these lines: {2, 3}, {10, 15825}, {40, 978}, {43, 10476}, {386, 10441}, {500, 5482}, {515, 3831}, {517, 1193}, {573, 992}, {952, 17751}, {970, 1764}, {1054, 2944}, {1698, 10882}, {1745, 3784}, {1766, 2277}, {3075, 3955}, {3624, 10434}, {3813, 15621}, {5230, 11249}, {5312, 10439}, {5313, 12435}, {5433, 16678}, {5844, 20040}, {6176, 10470}, {9548, 16569}, {12245, 20036}
X(19514) lies on these lines: {2, 3}, {40, 1054}, {511, 3216}, {517, 1201}, {528, 15625}, {572, 5277}, {1385, 10459}, {1403, 11043}, {1423, 15803}, {1764, 15489}, {4255, 19782}, {5396, 5482}, {5844, 20041}
X(19515) lies on these lines: {2, 3}, {355, 9458}, {517, 1647}, {952, 17780}, {5844, 20042}
X(19516) lies on these lines: {2, 3}, {517, 1961}, {1482, 5311}, {5707, 9566}, {5844, 20069}, {10246, 17017}
X(19517) lies on these lines: {2, 3}, {165, 17123}, {517, 2999}, {1385, 17022}, {1482, 5256}, {1764, 4383}, {1766, 3752}, {3452, 15509}, {4423, 10434}, {5222, 8158}, {5287, 10246}, {5844, 20043}, {7308, 10856}, {8148, 17012}, {9708, 18229}, {10247, 17011}
X(19518) lies on these lines: {2, 3}, {956, 9345}, {978, 1001}, {992, 2271}, {4267, 17259}, {4281, 4383}, {6767, 20036}
X(19519) lies on these lines: {2, 3}, {958, 17122}, {3753, 10476}
X(19520) lies on these lines: {1, 17811}, {2, 3}, {56, 142}, {57, 958}, {78, 954}, {942, 956}, {993, 12436}, {1001, 3601}, {1466, 5745}, {1467, 7091}, {1708, 15823}, {1724, 17825}, {2975, 9776}, {2979, 19771}, {3303, 12437}, {3753, 5709}, {3819, 19782}, {3889, 15934}, {5120, 5323}, {5251, 15803}, {5260, 5744}, {5436, 10383}, {5784, 10393}, {6282, 11496}, {8071, 19854}, {8726, 12114}, {11518, 12513}
X(19521) lies on these lines: {2, 3}, {392, 6769}, {936, 954}, {956, 3333}, {958, 3361}, {1001, 5438}, {3646, 11496}, {5045, 19860}, {5440, 8583}, {7675, 9858}, {8257, 15823}, {10855, 10884}
X(19522) lies on these lines: {2, 3}, {511, 18792}, {517, 3009}, {667, 17072}, {1929, 18788}, {2238, 2311}, {2664, 8924}, {2782, 3948}, {5844, 20044}, {8850, 18208}
X(19523) lies on these lines: {2, 3}, {72, 940}, {197, 16828}, {386, 19728}, {392, 5706}, {1376, 19857}, {4255, 19753}, {5259, 17064}, {10472, 11517}
X(19524) lies on these lines: {2, 3}, {35, 392}, {36, 3812}, {55, 3884}, {56, 5883}, {956, 8071}, {958, 14793}, {1125, 5172}, {3753, 11012}, {3877, 11849}, {3878, 14882}, {3913, 5559}, {4996, 5260}, {4999, 10090}, {5251, 14792}, {5506, 16761}, {5730, 11507}, {10902, 17614}
X(19525) lies on these lines: {2, 3}, {35, 5836}, {36, 392}, {55, 2802}, {56, 3878}, {80, 1376}, {191, 14804}, {956, 8069}, {993, 5172}, {1001, 14793}, {1387, 1621}, {1389, 10306}, {1470, 15950}, {1727, 14800}, {1749, 5692}, {1836, 11813}, {2077, 3753}, {2886, 10058}, {3816, 10090}, {4257, 5127}, {5123, 5251}, {5248, 11376}, {5259, 14792}, {5440, 10391}, {5687, 10950}, {5745, 17010}, {6001, 17614}, {6265, 10269}, {6599, 15175}
X(19526) lies on these lines: {2, 3}, {55, 3626}, {56, 3982}, {392, 5693}, {956, 3244}, {958, 3632}, {993, 3304}, {1001, 5563}, {1621, 20057}, {3295, 20050}, {3612, 15254}, {3683, 5730}, {3916, 5436}, {3984, 15650}, {4423, 5267}, {4428, 5258}, {4512, 7982}, {5250, 10222}, {5251, 5687}, {5426, 12635}, {7280, 8167}, {16112, 17614}, {19746, 19762}, {19751, 19763}, {19829, 19844}, {19837, 19845}
X(19527) lies on these lines: {2, 3}, {958, 988}, {1472, 5711}
X(19528) lies on these lines: {2, 3}, {941, 9605}, {956, 5266}, {988, 1001}
X(19529) lies on these lines: {2, 3}, {956, 3924}, {958, 982}
X(19530) lies on these lines: {2, 3}, {171, 956}, {3217, 5783}
X(19531) lies on these lines: {2, 3}, {58, 956}, {284, 5782}, {958, 5264}, {1001, 18792}, {4267, 5687}, {5711, 10457}, {7373, 8025}, {10914, 18163}, {17174, 18493}
X(19532) lies on these lines: {2, 3}, {87, 1001}, {956, 3915}, {958, 8616}, {996, 5248}
X(19533) lies on these lines: {2, 3}, {41, 5783}, {171, 958}, {956, 1468}, {1001, 1740}, {3736, 19765}, {10457, 19734}, {15654, 19858}
X(19534) lies on these lines: {2, 3}
X(19535) lies on these lines: {2, 3}, {35, 956}, {55, 3244}, {56, 3636}, {392, 7987}, {958, 5010}, {993, 3626}, {999, 5303}, {1001, 7280}, {2975, 20050}, {3295, 20057}, {3601, 3916}, {3612, 4640}, {3838, 4333}, {3871, 20054}, {3897, 12702}, {4257, 4658}, {4299, 6690}, {4302, 4999}, {4330, 11235}, {4421, 5258}, {4428, 5563}, {4512, 17614}, {4652, 11520}, {5023, 5283}, {5204, 5248}, {5206, 5275}, {5210, 5277}, {5250, 13624}, {5440, 15650}, {7782, 16992}, {8588, 16589}, {9657, 10197}, {10198, 15326}, {10386, 10529}, {17502, 19861}, {19739, 19762}, {19747, 19759}, {19750, 19763}, {19820, 19844}, {19830, 19841}, {19833, 19845}
X(19536) lies on these lines: {2, 3}, {392, 11224}, {519, 4423}, {956, 8167}, {1001, 19875}, {1698, 4428}, {3303, 4745}, {3624, 11194}, {3828, 5687}, {3929, 5439}, {4421, 5259}
X(19737) lies on these lines: {2, 3}, {36, 3632}, {55, 3636}, {56, 3244}, {78, 5122}, {100, 20050}, {165, 17614}, {956, 3626}, {999, 20057}, {1155, 5730}, {1376, 5258}, {1466, 4031}, {1482, 4881}, {1788, 10609}, {2932, 6154}, {3035, 4299}, {3753, 7987}, {3916, 5438}, {4004, 13384}, {4302, 6691}, {4325, 11236}, {4333, 5087}, {4413, 5267}, {4421, 5563}, {4652, 15650}, {5217, 15808}, {5277, 15815}, {5303, 9708}, {5440, 11523}, {5704, 12690}, {6681, 10896}, {8688, 16489}, {9670, 10199}, {9945, 12649}, {10200, 15338}, {10386, 10586}, {12635, 15015}, {17502, 19860}, {19739, 19763}, {19747, 19760}, {19750, 19762}, {19820, 19845}, {19830, 19842}, {19833, 19844}
X(19538) lies on these lines: {2, 3}, {55, 4691}, {956, 3635}, {958, 3633}, {3295, 20053}, {3625, 5248}, {3913, 4668}, {5250, 11278}
X(19539) lies on these lines: {2, 3}, {55, 4701}
X(19540) lies on these lines: {2, 3}, {40, 16569}, {42, 1482}, {43, 517}, {55, 17717}, {355, 3741}, {386, 15488}, {515, 3840}, {516, 6686}, {899, 12702}, {946, 6685}, {952, 10453}, {1376, 3846}, {1403, 3944}, {1575, 1766}, {1764, 5400}, {2635, 3784}, {3185, 5087}, {3240, 8148}, {3720, 10246}, {3771, 11500}, {4871, 18481}, {5844, 20012}, {7988, 10434}, {7989, 10882}, {10247, 17018}, {10680, 11269}, {11235, 15621}, {12645, 17135}, {15489, 17749}
X(19541) lies on these lines: {2, 3}, {7, 5658}, {8, 8158}, {9, 10157}, {11, 1617}, {33, 1465}, {40, 5044}, {46, 12688}, {55, 1538}, {56, 5691}, {57, 971}, {63, 5779}, {100, 5748}, {165, 3683}, {200, 517}, {222, 2635}, {226, 5805}, {278, 15252}, {329, 5762}, {355, 4847}, {497, 7956}, {515, 999}, {516, 1376}, {908, 1260}, {912, 2095}, {942, 1490}, {944, 5804}, {946, 3295}, {954, 5226}, {958, 19925}, {962, 5687}, {975, 15852}, {990, 3752}, {1001, 3817}, {1071, 5708}, {1155, 1709}, {1172, 15851}, {1210, 5787}, {1214, 9817}, {1385, 10582}, {1437, 11424}, {1454, 1898}, {1466, 9579}, {1470, 12943}, {1479, 6253}, {1482, 3870}, {1512, 5790}, {1519, 10679}, {1537, 12331}, {1565, 17093}, {1621, 9779}, {1698, 5584}, {1742, 17122}, {1754, 4383}, {1770, 12679}, {1836, 11502}, {2932, 10724}, {3303, 4870}, {3306, 10167}, {3338, 12680}, {3361, 10864}, {3428, 5587}, {3579, 12705}, {3583, 8069}, {3585, 8071}, {3624, 8273}, {3634, 12511}, {3711, 15104}, {3812, 12520}, {3913, 4301}, {3927, 5709}, {3935, 8148}, {3957, 10247}, {4254, 5747}, {4292, 6259}, {4423, 7988}, {4650, 9355}, {4666, 10246}, {4882, 6766}, {4930, 7982}, {5128, 7995}, {5220, 15064}, {5221, 15071}, {5231, 11249}, {5248, 12571}, {5273, 5817}, {5274, 8166}, {5432, 7965}, {5435, 13226}, {5437, 5732}, {5439, 10884}, {5603, 5719}, {5752, 5907}, {5759, 18228}, {5780, 12672}, {5841, 18516}, {5842, 9668}, {5843, 9965}, {5844, 20015}, {5905, 13257}, {6256, 9655}, {6261, 7686}, {6666, 10164}, {6745, 10306}, {6796, 11496}, {7681, 9669}, {7741, 7742}, {7744, 11809}, {7967, 15935}, {8167, 10171}, {8257, 15726}, {9441, 16569}, {9654, 18242}, {9842, 12572}, {9955, 10267}, {10156, 10857}, {10241, 10860}, {10382, 11018}, {10680, 18525}, {10738, 18499}, {11012, 18492}, {11501, 12701}, {12001, 18526}, {12667, 18990}, {12704, 14872}, {14793, 18513}, {15299, 17604}, {15934, 18446}, {16202, 18493}
X(19541) = anticomplement of X(37364)
X(19542) lies on these lines: {1, 5799}, {2, 3}, {9, 5743}, {11, 2352}, {63, 5755}, {72, 970}, {141, 1764}, {226, 1465}, {306, 517}, {329, 4488}, {355, 5271}, {515, 5721}, {516, 2887}, {573, 1211}, {908, 3998}, {944, 5797}, {946, 6051}, {952, 3187}, {1214, 1848}, {1490, 2999}, {1503, 1754}, {1708, 5928}, {1714, 5786}, {1715, 6247}, {1730, 13567}, {1750, 5400}, {1751, 13478}, {1826, 6708}, {1834, 10454}, {1901, 4261}, {2893, 14829}, {3419, 11679}, {3452, 8804}, {3772, 5336}, {3912, 15488}, {4023, 10440}, {4026, 10434}, {4383, 5776}, {4417, 9535}, {4657, 10888}, {4966, 10439}, {5256, 5396}, {5435, 5740}, {5658, 5796}, {5742, 5745}, {5816, 19732}, {5844, 20017}, {6356, 17080}, {10446, 18134}, {10478, 17056}, {10856, 17306}, {12555, 17296}
X(19543) lies on these lines: {2, 3}, {35, 17717}, {40, 3216}, {355, 10479}, {386, 517}, {499, 16678}, {952, 10449}, {991, 5482}, {1482, 19767}, {1714, 3428}, {1745, 11573}, {1764, 5752}, {1766, 4261}, {3579, 5956}, {5132, 11248}, {5292, 11249}, {5396, 10441}, {5587, 10882}, {5690, 9534}, {5844, 20018}, {8227, 10434}, {12116, 15623}
X(19544) lies on these lines: {2, 3}, {40, 5268}, {55, 17720}, {81, 1351}, {98, 931}, {165, 12717}, {171, 6210}, {182, 2194}, {183, 314}, {197, 2886}, {262, 14534}, {498, 8193}, {511, 940}, {517, 612}, {573, 5275}, {614, 1385}, {908, 7085}, {956, 3705}, {970, 5706}, {986, 8235}, {1007, 1444}, {1036, 5230}, {1038, 1875}, {1211, 1352}, {1350, 18165}, {1376, 3185}, {1482, 3920}, {1483, 19993}, {1486, 6690}, {1503, 5743}, {1859, 9817}, {2000, 17441}, {2193, 10311}, {2792, 4703}, {2895, 11898}, {3011, 10267}, {3085, 12410}, {3430, 19782}, {3564, 5739}, {3576, 5272}, {4254, 7735}, {4413, 15494}, {4414, 11203}, {5120, 7736}, {5219, 5285}, {5297, 12702}, {5329, 17717}, {5480, 6703}, {5687, 7081}, {5690, 10327}, {5707, 5752}, {5844, 20020}, {6776, 14555}, {7191, 10246}, {7262, 7609}, {8192, 10527}, {8245, 17596}, {10198, 11365}, {10519, 18141}
X(19544) = {X(2),X(3)}-harmonic conjugate of X(16434)
X(19545) lies on these lines: {2, 3}, {40, 2664}, {517, 869}, {5844, 19994}
X(19546) lies on these lines: {2, 3}, {42, 10222}, {43, 7982}, {511, 5400}, {515, 4871}, {517, 899}, {1482, 3240}, {3216, 15488}, {3720, 15178}, {3829, 15621}, {5087, 15507}, {5844, 19998}, {7991, 16569}
X(19547) lies on these lines: {2, 3}, {56, 5725}, {198, 5831}, {517, 975}, {940, 5752}, {956, 5827}, {970, 5707}, {1350, 5482}, {3035, 9912}, {4999, 9798}, {5262, 10246}, {5432, 8193}, {5743, 5810}, {5844, 20009}, {6690, 11365}, {11573, 19366}
X(19548) lies on these lines: {2, 3}, {35, 3944}, {40, 5293}, {517, 976}, {601, 15310}, {970, 1754}, {1376, 3556}, {1626, 4999}, {1745, 3955}, {3075, 3784}, {3357, 3359}, {3430, 10441}, {5844, 20035}
X(19549) lies on these lines: {2, 3}, {355, 3831}, {517, 978}, {970, 17749}, {1193, 1482}, {1764, 9566}, {3216, 9567}, {3814, 15654}, {5230, 10680}, {5844, 20036}, {10476, 16569}, {12645, 17751}
X(19550) lies on these lines: {2, 3}, {386, 18178}, {517, 995}, {581, 5482}, {1329, 15654}, {3216, 5752}, {5769, 14829}, {5844, 20037}, {10785, 15623}, {11230, 17384}
X(19551) is the result of the substitution S → -S in the barycentrics for X(7126).
X(19551) lies on the Feuerbach hyperbola and these lines: {1, 62}, {6, 11073}, {8, 7026}, {9, 10638}, {13, 79}, {15, 3065}, {37, 1250}, {45, 55}, {80, 14358}, {651, 1082}, {1320, 5240}, {2154, 8015}, {2173, 3129}, {2320, 5239}, {7051, 7284}
X(19551) = X(44)-cross conjugate of X(7126)
X(19551) = X(i)-isoconjugate of X(j) for these (i,j): {15, 1081}, {57, 5240}, {554, 5357}, {1082, 3179}, {1443, 7126}, {1790, 1832}, {3218, 7052}
X(19551) = barycentric product X(i)X(j) for these {i,j}: {1, 7026}, {80, 5239}, {1793, 1833}, {5240, 14358}, {7127, 18359}
X(19551) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 5240}, {1824, 1832}, {2153, 1081}, {3457, 2306}, {5239, 320}, {6187, 7052}, {7026, 75}, {7051, 1443}, {7127, 3218}, {11073, 554}
X(19551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (37, 1250, 1251), (45, 55, 7126), (2246, 2310, 7126)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27760.
X(19552) lies on the cubics K025, K465, the sextic Q114, and these lines: {2,6150},{3,3432},{4,93},{5,252},{30,930},{265,14859},{381,16337},{571,2963},{1487,3850},{1510,11583},{1656,10615},{3447,5899},{3627,14141}
X(19552) = midpoint of X(3627) and X(14141)
X(19552) = reflection of X(i) in X(j) for these {i,j}: {{3, 16336}, {1157, 5}, {14980, 18403}
X(19552) = isogonal conjugate of X(34418)
X(19552) = anticomplement X(6150)
X(19552) = polar-circle-inverse of X(6152)
X(19552) = (anticomplement of circumcircle)-inverse of X(12325)
X(19552) = antigonal image of X(2070)
X(19552) = barycentric product X(2070)*X(11140)
X(19552) = barycentric quotient X(i)/X(j) for these {i,j}: {{93, 9381}, {2070, 1994}, {9380, 49}
X(19552) = {X(4),X(3519)}-harmonic conjugate of X(18370)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27760.
X(19553) lies on these lines: {5,195},{30,11671},{252,15345},{382,15619},{523,2070},{539,16337},{930,6150},{1141,1154}
X(19553) = reflection of X(i) in X(j) for these (i,j): (930,6150), (14140,12026)
X(19554) lies on the cubics K772 and K789, and on these lines:
{2, 7224}, {6, 41}, {31, 1501}, {32, 7032}, {101, 1757}, {184, 5364}, {213, 7122}, {238, 2112}, {292, 1691}, {663, 1919}, {672, 7193}, {741, 919}, {984, 9310}, {1911, 18263}, {1966, 4586}, {1973, 3010}, {2268, 3100}, {2352, 9447}, {3508, 4579}, {18038, 18262}
X(19554) = X(5546)-beth conjugate of X(1757)
X(19554) = X(292)-Ceva conjugate of X(31)
X(19554) = X(i)-isoconjugate of X(j) for these (i,j): {2, 7261}, {6, 18036}, {75, 3512}, {76, 8852}, {85, 7281}, {257, 7061}
X(19554) = X(i)-Hirst inverse of X(j) for these (i,j): {6, 172}, {7122, 18759}, {18038, 18262}
X(19554) = X(172)-vertex conjugate of X(663)
X(19554) = crossdifference of every pair of points on line {522, 4357}
X(19554) = crosssum of X(i) and X(j) for these (i,j): {3766, 4858}, {3948, 18697}
X(19554) = barycentric product X(i)*X(j) for these {i,j}: {1, 17798}, {6, 3509}, {31, 4645}, {32, 17789}, {55, 5018}, {75, 18262}, {335, 18038}, {692, 4458}, {1281, 1911}, {1333, 4071}, {1922, 18037}, {8868, 18278}
X(19554) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18036}, {31, 7261}, {32, 3512}, {560, 8852}, {1281, 18891}, {2175, 7281}, {3509, 76}, {4645, 561}, {5018, 6063}, {7122, 7061}, {17789, 1502}, {17798, 75}, {18038, 239}, {18262, 1}
X(19555) lies on the cubic K863 and these lines: {1, 1917}, {19, 27}, {38, 1582}, {163, 18715}, {257, 384}, {335, 385}, {798, 14208}, {1581, 2236}, {1654, 5282}, {1759, 3761}, {1959, 2312}, {2227, 2640}, {2247, 18722}, {3329, 7249}, {3401, 3404}, {3760, 7096}, {4518, 5999}, {9247, 18049}, {17471, 18042}
X(19555) = X(i)-aleph conjugate of X(j) for these (i,j): {694, 18272}, {1916, 17799}
X(19555) = X(i)-he conjugate of X(j) for these (i,j): {75, 1760}, {561, 63}
X(19555) = X(1934)-Ceva conjugate of X(1)
X(19555) = X(75)-Hirst inverse of X(1965)
X(19555) = cevapoint of X(i) and X(j) for these (i,j): {16556, 16559}
X(19555) = barycentric product X(i)*X(j) for these {i,j}: {1, 5207}, {75, 6660}, {662, 14316}, {1965, 3505}, {1966, 3493}, {1967, 8783}
X(19555) = barycentric quotient X(i)/X(j) for these {i,j}: {1965, 16101}, {3493, 1581}, {3505, 9285}, {5207, 75}, {6660, 1}, {8783, 1926}, {14316, 1577}
X(19555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1760, 16567, 63), (3496, 3497, 384), (3509, 3512, 385), (6211, 7351, 5999)
X(19556) lies on the cubic K1034 and these lines: {32, 682}, {1576, 2076}, {2531, 3049}, {8743, 10828}
X(19556) = X(9468)-Ceva conjugate of X(1501)
X(19556) = X(9239)-isoconjugate of X(16101)
X(19556) = barycentric product X(i)*X(j) for these {i,j}: {32, 6660}, {1501, 5207}, {3493, 14602}, {8783, 14604}, {14316, 14574}
X(19556) = barycentric quotient X(6660)/X(1502)
Let A'B'C' be the medial triangle. Let A1 and A2 be the 1st and 2nd bicentrics of A', resp., and define B1, B2, C1, C2 cyclically. Let VaVbVc be the vertex-triangle of A1B1C1 and A2B2C2. Then VaVbVc is perspective to ABC at X(893) and to the medial triangle at X(19557). (Randy Hutson, August 29, 2018)
X(19557) is the perspector of the unary cofactor triangles of the obverse triangle of X(1) and the N-obverse triangle of X(1). (Randy Hutson, October 15, 2018)
X(19557) lies on the cubics K251, K252, K1035, the Feuerbach hyperbola of the medial triangle, and on these lines:
{1, 1929}, {2, 2112}, {3, 3061}, {6, 7166}, {9, 8245}, {10, 98}, {86, 142}, {100, 4876}, {171, 292}, {214, 5011}, {238, 1691}, {239, 385}, {334, 4586}, {419, 2201}, {1375, 17060}, {1580, 2238}, {1914, 8623}, {1959, 19308}, {1973, 3144}, {2092, 2670}, {2247, 3647}, {3126, 9508}, {3509, 17798}, {3716, 8632}, {5029, 16158}, {6184, 9441}, {7146, 11329}, {8299, 8853}, {16788, 17057}
X(19557) = complement X(7261)
X(19557) = isogonal conjugate of X(24479)
X(19557) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 238}, {1911, 5988}, {3509, 141}, {4645, 2887}, {5018, 2886}, {7121, 18208}, {17789, 626}, {17798, 10}, {18038, 17755}, {18262, 37}
X(19557) = X(2)-Ceva conjugate of X(238)
X(19557) = X(i)-isoconjugate of X(j) for these (i,j): {291, 3512}, {292, 7261}, {335, 8852}, {694, 7061}, {1922, 18036}
X(19557) = X(i)-Hirst inverse of X(j) for these (i,j): {1, 8301}, {239, 385}, {3509, 17798}, {8424, 18790}
X(19557) = X(3126)-line conjugate of X(9508)
X(19557) = cevapoint of X(8298) and X(8932)
X(19557) = crosspoint of X(2) and X(4645)
X(19557) = crosssum of X(6) and X(8852)
X(19557) = barycentric product X(i)*X(j) for these {i,j}: {1, 1281}, {6, 18037}, {76, 18038}, {238, 4645}, {239, 3509}, {350, 17798}, {1914, 17789}, {3573, 4458}, {3685, 5018}, {18262, 18891}
X(19557) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 7261}, {350, 18036}, {1281, 75}, {1580, 7061}, {1914, 3512}, {2210, 8852}, {3509, 335}, {4645, 334}, {5018, 7233}, {17789, 18895}, {17798, 291}, {18037, 76}, {18038, 6}, {18262, 1911}, {18274, 8875}
X(19557) = center of hyperbola {{A,B,C,X(100),PU(8)}}
X(19557) = crosssum of circumcircle intercepts of line PU(6) (line X(37)X(513))
X(19557) = {X(1691),X(18904)}-harmonic conjugate of X(238)
X(19558) lies on the cubic K532 and these lines: {6, 25}, {32, 14820}, {110, 7779}, {182, 7875}, {384, 3492}, {385, 3506}, {647, 9426}, {733, 2715}, {904, 1932}, {1911, 1933}, {2242, 18759}, {3289, 9407}, {3314, 9306}, {5651, 7868}
X(19558) = X(694)-Ceva conjugate of X(32)
X(19558) = X(9285)-isoconjugate of X(16101)
X(19558) = X(6)-Hirst inverse of X(1915)
X(19558) = X(i)-vertex conjugate of X(j) for these (i,j): {647, 1915}, {1915, 647}
X(19558) = cevapoint of X(3492) and X(3506)
X(19558) = crosspoint of X(694) and X(3493)
X(19558) = crossdifference of every pair of points on line {525, 6656}
X(19558) = crosssum of X(339) and X(14295)
X(19558) = barycentric product X(i)*X(j) for these {i,j}: {6, 6660}, {32, 5207}, {1576, 14316}, {1691, 3493}, {1915, 3505}, {8783, 8789}
X(19558) = barycentric quotient X(i)/X(j) for these {i,j}: {1915, 16101}, {3493, 18896}, {5207, 1502}, {6660, 76}, {8783, 18901}
X(19559) lies on the cubic K864 and these lines: {1, 19}, {292, 1691}, {656, 1924}, {893, 1915}, {1431, 12212}, {1932, 1964}, {2112, 18904}
X(19559) = X(1581)-Ceva conjugate of X(31)
X(19559) = X(695)-isoconjugate of X(16101)
X(19559) = X(1)-Hirst inverse of X(1582)
X(19559) = X(1)-line conjugate of X(17446)
X(19559) = crossdifference of every pair of points on line {656, 17446}
X(19559) = barycentric product X(i)*X(j) for these {i,j}: {1, 6660}, {31, 5207}, {163, 14316}, {1580, 3493}, {1582, 3505}, {1927, 8783}
X(19559) = barycentric quotient X(i)/X(j) for these {i,j}: {1582, 16101}, {3493, 1934}, {3505, 9239}, {5207, 561}, {6660, 75}
X(19560) lies on the cubic K866 and these lines: {31, 1932}, {163, 17799}, {1922, 14602}
X(19560) = X(1967)-Ceva conjugate of X(560)
X(19560) = X(9229)-isoconjugate of X(16101)
X(19560) = X(31)-Hirst inverse of X(1932)
X(19560) = barycentric product X(i)*X(j) for these {i,j}: {31, 6660}, {560, 5207}, {1932, 3505}, {1933, 3493}
X(19560) = barycentric quotient X(i)/X(j) for these {i,j}: {1932, 16101}, {5207, 1928}, {6660, 561}
X(19561) lies on the cubics K774 and K861, and on these lines: {1, 3506}, {6, 2054}, {37, 692}, {48, 3056}, {81, 105}, {101, 7077}, {172, 694}, {182, 7611}, {238, 1284}, {335, 1492}, {1691, 3747}, {1914, 1933}, {2294, 5202}, {3509, 18262}, {3573, 6651}, {3725, 5147}, {4155, 4435}, {4366, 18264}, {5191, 17454}, {8298, 8853}, {8540, 17455}
X(19561) = X(1)-Ceva conjugate of X(1914)
X(19561) = X(i)-isoconjugate of X(j) for these (i,j): {291, 7261}, {334, 8852}, {335, 3512}, {1581, 7061}, {1911, 18036}, {7233, 7281}
X(19561) = X(i)-Hirst inverse of X(j) for these (i,j): {6, 2112}, {238, 1580}
X(19561) = X(2112)-vertex conjugate of X(5029)
X(19561) = crosspoint of X(1) and X(3509)
X(19561) = crosssum of X(i) and X(j) for these (i,j): {1, 3512}, {2, 5992}
X(19561) = barycentric product X(i)*X(j) for these {i,j}: {6, 1281}, {31, 18037}, {75, 18038}, {238, 3509}, {239, 17798}, {1914, 4645}, {1921, 18262}, {2210, 17789}, {3684, 5018}, {4071, 5009}
X(19561) = barycentric quotient X(i)/X(j) for these {i,j}: {239, 18036}, {1281, 76}, {1691, 7061}, {1914, 7261}, {2210, 3512}, {3509, 334}, {4645, 18895}, {14599, 8852}, {17798, 335}, {18037, 561}, {18038, 1}, {18262, 292}
X(19561) = {X(1),X(18790)}-harmonic conjugate of X(3512)
X(19562) lies on the cubic K659 and these lines: {2, 2998}, {315, 1899}, {670, 1613}, {689, 1501}, {3981, 14603}, {7467, 8920}, {7878, 9490}
X(19562) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1740, 2896}, {4593, 3221}, {4599, 669}, {17149, 1369}
X(19562) = X(6)-Ceva conjugate of X(76)
X(19562) = barycentric product X(76)X(8264)
X(19562) = barycentric quotient X(8264)/X(6)
X(19563) lies on the cubic K1035 and these lines: {2, 1581}, {10, 4531}, {238, 1921}, {960, 17793}, {1125, 5976}
X(19563) = complement X(1581)
X(19563) = X(i)-complementary conjugate of X(j) for these (i,j): {2, 5031}, {6, 325}, {31, 18904}, {32, 3229}, {110, 804}, {171, 3836}, {172, 3912}, {238, 3846}, {249, 11052}, {251, 732}, {385, 141}, {419, 5}, {804, 125}, {827, 5113}, {1429, 17062}, {1576, 2491}, {1580, 10}, {1691, 2}, {1914, 4357}, {1933, 37}, {1966, 2887}, {1976, 2023}, {2210, 1107}, {3978, 626}, {4039, 3454}, {4107, 116}, {4164, 11}, {4579, 3837}, {5009, 6682}, {5026, 126}, {5027, 115}, {7122, 1575}, {8623, 6292}, {11183, 5099}, {12215, 1368}, {14602, 39}, {17941, 512}, {18902, 8265}
X(19563) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 18904}, {3952, 804}
X(19563) = crosspoint of X(i) and X(j) for these (i,j): {2, 1966}, {18904, 18905}
X(19563) = crosssum of X(6) and X(1967)
X(19563) = barycentric product X(i)*X(j) for these {i,j}: {1966, 18904}, {3662, 4154}, {4368, 7187}
X(19563) = barycentric quotient X(i)/X(j) for these {i,j}: {4154, 17743}, {18904, 1581}
X(19564) lies on the cubic K1036 and these lines: {2, 9285}, {171, 1920}, {16583, 16606}
X(19564) = complement X(9285)
X(19564) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 6656}, {31, 18905}, {384, 141}, {1582, 10}, {1915, 2}, {1932, 37}, {1965, 2887}, {9230, 626}, {11380, 6}
X(19564) = X(2)-Ceva conjugate of X(18905)
X(19564) = crosspoint of X(2) and X(1965)
X(19564) = crosssum of X(6) and X(9288)
X(19564) = barycentric product X(1965)X(18905)
X(19564) = barycentric quotient X(18905)/X(9285)
X(19565) lies on the cubics K136 and K985, and on these lines: {1, 87}, {2, 561}, {37, 1655}, {75, 2275}, {241, 10030}, {291, 740}, {292, 1966}, {334, 18904}, {335, 1959}, {518, 9263}, {1400, 2998}, {1432, 4032}, {1581, 4645}, {1691, 4586}, {1978, 2229}, {3210, 17027}, {4388, 17485}, {4687, 18073}, {4699, 17030}, {7018, 18905}, {17026, 17490}, {17029, 17495}
X(19565) = anticomplement X(1921)
X(19565) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {32, 17794}, {291, 315}, {292, 6327}, {741, 17137}, {875, 150}, {1911, 69}, {1922, 8}, {1927, 6646}, {2196, 1370}, {9468, 4388}, {14598, 2}, {18265, 329}, {18267, 6542}, {18268, 17135}, {18893, 194}, {18897, 192}
X(19565) = X(i)-Ceva conjugate of X(j) for these (i,j): {292, 2}, {1966, 4645}
X(19565) = X(18277)-cross conjugate of X(2)
X(19565) = X(i)-isoconjugate of X(j) for these (i,j): {6, 7168}, {8852, 8868}
X(19565) = X(1)-Hirst inverse of X(894)
X(19565) = X(1)-line conjugate of X(2309)
X(19565) = crossdifference of every pair of points on line {2309, 8630}
X(19565) = polar conjugate of isogonal conjugate of X(23186)
X(19565) = barycentric product X(i)*X(j) for these {i,j}: {6, 18275}, {75, 3510}, {76, 18278}, {292, 18277}, {8875, 17789}, {18274, 18895}
X(19565) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7168}, {3509, 8868}, {3510, 1}, {8875, 3512}, {18274, 1914}, {18275, 76}, {18277, 1921}, {18278, 6}
X(19565) = {X(1920),X(16584)}-harmonic conjugate of X(2)
X(19566) lies on the cubic K787 and these lines: {2, 14603}, {6, 194}, {39, 8790}, {232, 17984}, {292, 1966}, {523, 9491}, {694, 732}, {893, 1965}, {17126, 17486}
X(19566) = anticomplement X(14603)
X(19566) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1917, 8782}, {1927, 69}, {1967, 315}, {8789, 8}, {9468, 6327}, {14604, 192}, {17938, 17217}, {18903, 17486}
X(19566) = X(9468)-Ceva conjugate of X(2)
X(19566) = X(i)-Hirst inverse of X(j) for these (i,j): {6, 384}, {8790, 9230}
X(19566) = X(i)-vertex conjugate of X(j) for these (i,j): {384, 9491}, {9491, 384}
X(19566) = barycentric product X(i)*X(j) for these {i,j}: {1, 18271}, {31, 18276}, {75, 18272}, {1581, 18270}, {1967, 18273}, {3978, 8871}
X(19566) = barycentric quotient X(i)/X(j) for these {i,j}: {8871, 694}, {18270, 1966}, {18271, 75}, {18272, 1}, {18273, 1926}, {18276, 561}
X(19566) = {X(194),X(2998)}-harmonic conjugate of X(18906)
X(19567) lies on the cubics K738 and K768, and on these lines: {2, 330}, {10, 1920}, {65, 18832}, {75, 700}, {76, 982}, {291, 3978}, {325, 334}, {335, 3948}, {668, 2664}, {693, 2533}, {714, 6386}, {789, 1580}, {1916, 17789}, {3912, 18149}, {5989, 16364}, {9436, 18033}, {18275, 18277}
X(19567) = isotomic conjugate of X(7168)
X(19567) = X(i)-Ceva conjugate of X(j) for these (i,j): {291, 75}, {3978, 17789}
X(19567) = X(31)-isoconjugate of X(7168)
X(19567) = X(i)-Hirst inverse of X(j) for these (i,j): {2, 1909}, {18275, 18277}
X(19567) = crossdifference of every pair of points on line {1197, 8640}
X(19567) = barycentric product X(i)*X(j) for these {i,j}: {1, 18275}, {76, 3510}, {291, 18277}, {561, 18278}
X(19567) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 7168}, {3510, 6}, {4645, 8868}, {8875, 8852}, {18274, 2210}, {18275, 75}, {18277, 350}, {18278, 31}
{X(1502),X(4446)}-harmonic conjugate of X(75)
X(19568) lies on the cubic K517 and these lines: {2, 39}, {22, 7781}, {51, 698}, {141, 4175}, {251, 7816}, {524, 3313}, {536, 3058}, {732, 3917}, {1369, 7882}, {1370, 7758}, {1627, 7805}, {1799, 7783}, {3787, 4576}, {5007, 16949}, {5064, 9766}, {5133, 7764}, {5359, 7798}, {6379, 7837}, {7391, 7759}, {7485, 7751}, {7760, 16951}, {7779, 16275}, {7780, 15246}, {7905, 8878}, {8041, 14994}, {9909, 15652}
X(19568) = X(4)-Ceva conjugate of X(141)
X(19568) = orthic-isogonal conjugate of X(141)
X(19568) = barycentric product X(i)*X(j) for these {i,j}: {38, 18056}, {141, 7754}
X(19568) = barycentric quotient X(i)/X(j) for these {i,j}: {7754, 83}, {18056, 3112}
X(19568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (39, 8024, 8891), (194, 305, 1194), (3266, 8267, 1196)
X(19569) lies on the cubic K104 and these lines: {2, 187}, {30, 194}, {148, 15682}, {193, 11645}, {376, 7785}, {381, 7793}, {385, 3830}, {2794, 9878}, {2996, 3543}, {3529, 13571}, {3552, 7809}, {3729, 4677}, {3793, 12101}, {5066, 17004}, {6658, 7946}, {6661, 7938}, {7747, 7811}, {7753, 7802}, {7754, 15684}, {7766, 11648}, {7774, 11001}, {7777, 8703}, {7783, 15681}, {7787, 7924}, {7799, 7900}, {7833, 9300}, {7842, 7884}, {7860, 7880}, {7865, 10159}, {8597, 14614}, {9766, 9855}, {9774, 15697}, {9939, 11361}, {15679, 16998}, {15693, 17005}
X(19569) = reflection of X(i) in X(j) for these {i,j}: {7802, 7753}, {7811, 7747}, {9939, 11361}, {11057, 14537}, {14976, 2}
X(19569) = anticomplement X(11057)
X(19569) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {11058, 6327}, {14479, 8}
X(19569) = X(11058)-Ceva conjugate of X(2)
X(19569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (11057, 14537, 2)
X(19570) lies on the cubic K278 and these lines: {2, 39}, {5, 13571}, {13, 533}, {14, 532}, {30, 148}, {99, 14658}, {115, 7779}, {192, 10056}, {193, 3818}, {330, 10072}, {376, 7793}, {381, 7754}, {384, 5306}, {524, 5207}, {549, 7783}, {671, 754}, {732, 6034}, {1916, 9302}, {2896, 5254}, {2996, 3543}, {3017, 17499}, {3407, 5485}, {3524, 17008}, {3545, 7774}, {3642, 16267}, {3643, 16268}, {3830, 7823}, {3845, 7762}, {5025, 7788}, {5054, 17004}, {5055, 7777}, {5305, 6661}, {5965, 14639}, {5989, 8591}, {6179, 6658}, {6655, 7751}, {7665, 9870}, {7748, 11057}, {7752, 18362}, {7753, 7760}, {7766, 11185}, {7790, 7865}, {7805, 14537}, {7812, 18546}, {7813, 14061}, {7833, 8667}, {7838, 15031}, {7839, 9300}, {7856, 17130}, {7906, 13881}, {7926, 18424}, {7946, 14063}, {11361, 14614}, {11539, 17006}, {15699, 17005}
X(19570) = midpoint of X(11054) and X(14568)
X(19570) = reflection of X(i) in X(j) for these {i,j}: {2, 14568}, {7779, 7809}, {7809, 115}, {8591, 13586}
X(19570) = anticomplement X(7799)
X(19570) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 1272}, {476, 17217}, {560, 18301}, {798, 14731}, {1973, 12383}, {1989, 6327}, {2166, 315}, {11060, 8}, {14560, 7192}
X(19570) = X(1989)-Ceva conjugate of X(2)
X(19570) = crossdifference of every pair of points on line {669, 10567}
X(19570) = crosssum of X(9427) and X(14270)
X(19570) = barycentric product X(94)*X(14972)
X(19570) = barycentric quotient X(14972)/X(323)
X(19570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 5309, 7797), (76, 5309, 2), (148, 385, 14712), (148, 11177, 9878), (381, 7754, 7837), (381, 7837, 7785), (3180, 11121, 621), (3181, 11122, 622), (5254, 17129, 2896), (5305, 17128, 10583), (7751, 11648, 7811), (7811, 11648, 6655), (7827, 9466, 2), (7828, 7880, 2)
X(19571) lies on the cubic K356 and these lines: {2, 4048}, {76, 3492}, {110, 8024}, {290, 308}, {384, 694}, {385, 18902}, {419, 3978}, {732, 16985}, {782, 5027}, {3124, 16950}, {3148, 8788}, {3727, 4366}, {5207, 6660}, {5976, 8784}, {9998, 16949}
X(19571) = X(76)-Ceva conjugate of X(385)
X(19571) = X(i)-Hirst inverse of X(j) for these (i,j): {2, 5989}, {5207, 6660}
X(19571) = crosspoint of X(3493) and X(3505)
X(19571) = barycentric product X(i)*X(j) for these {i,j}: {6, 8783}, {385, 5207}, {3978, 6660}, {14316, 17941}
X(19571) = barycentric quotient X(i)/X(j) for these {i,j}: {5207, 1916}, {6660, 694}, {8783, 76}
X(19572) lies on the cubic K862 and these lines: {1, 14821}, {163, 1930}, {239, 16985}, {894, 4027}, {1281, 8784}, {1582, 1967}, {1821, 3112}
X(19572) = X(75)-Ceva conjugate of X(1580)
X(19572) = X(14946)-isoconjugate of X(16101)
X(19572) = barycentric product X(i)*X(j) for these {i,j}: {31, 8783}, {1580, 5207}, {1966, 6660}
X(19572) = barycentric quotient X(i)/X(j) for these {i,j}: {5207, 1934}, {6660, 1581}, {8783, 561}
X(19573) lies on the cubic K322 and these lines: {2, 2998}, {76, 14820}, {257, 1925}, {335, 1926}, {384, 8790}, {850, 3221}, {1502, 3981}
X(19573) = X(694)-Ceva conjugate of X(76)
X(19573) = X(2)-Hirst inverse of X(9230)
X(19573) = crosspoint of X(694) and X(8871)
X(19573) = barycentric product X(i)*X(j) for these {i,j}: {1, 18276}, {75, 18271}, {561, 18272}, {1581, 18273}, {1934, 18270}, {8871, 14603}
X(19573) = barycentric quotient X(i)/X(j) for these {i,j}: {8871, 9468}, {18270, 1580}, {18271, 1}, {18272, 31}, {18273, 1966}, {18276, 75}
X(19574) lies on the cubic K865 and these lines: {75, 2640}, {304, 16559}, {1581, 1965}, {1910, 4593}
X(19574) = X(561)-Ceva conjugate of X(1966)
X(19574) = barycentric product X(i)*X(j) for these {i,j}: {1, 8783}, {1926, 6660}, {1966, 5207}
X(19574) = barycentric quotient X(i)/X(j) for these {i,j}: {5207, 1581}, {6660, 1967}, {8783, 75}
X(19575) lies on the cubic K1033 and these lines: {39, 14574}, {51, 251}, {1576, 17970}, {1691, 2679}, {4027, 8784}, {8789, 14946}
X(19575) = X(6)-Ceva conjugate of X(14602)
X(19575) = crosspoint of X(6) and X(6660)
X(19575) = barycentric product X(i)*X(j) for these {i,j}: {1501, 8783}, {1691, 6660}, {5207, 14602}
X(19575) = barycentric quotient X(6660)/X(18896)
X(19576) lies on the Jerabek hyperbola of the medial triangle, the cubic K252, and on these lines: {3, 3492}, {5, 83}, {6, 3506}, {141, 1576}, {385, 419}, {1147, 3095}, {1915, 9468}, {1971, 11672}, {8290, 8784}
X(19576) = complementary conjugate of X(21536)
X(19576) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1691}, {5207, 2887}, {6660, 10}
X(19576) = crosssum of circumcircle intercepts of line PU(11) (line X(141)X(523))
X(19576) = center of hyperbola {{A,B,C,X(110),X(251)}}
X(19576) = X(2)-Ceva conjugate of X(1691)
X(19576) = X(i)-Hirst inverse of X(j) for these (i,j): {6, 3506}, {385, 16985}
X(19576) = X(3506)-vertex conjugate of X(5113)
X(19576) = crosspoint of X(2) and X(5207)
X(19576) = barycentric product X(i)*X(j) for these {i,j}: {32, 8783}, {385, 6660}, {1691, 5207}, {3493, 4027}, {3505, 16985}
X(19576) = barycentric quotient X(i)/X(j) for these {i,j}: {5207, 18896}, {6660, 1916}, {8783, 1502}, {16985, 16101}
X(19577) lies on the cubic K533 and these lines: {2, 39}, {23, 148}, {193, 7703}, {230, 14588}, {385, 858}, {427, 7762}, {468, 7665}, {691, 5189}, {850, 2489}, {1799, 7830}, {2996, 4232}, {5094, 7754}, {5169, 7785}, {5986, 16985}, {7495, 7783}, {7793, 16063}, {7805, 15820}, {7847, 15822}
X(19577) = anticomplement of X(37804)
X(19577) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {935, 17217}, {1973, 11061}, {2157, 1370}, {3455, 4329}, {8791, 6327}
X(19577) = X(8791)-Ceva conjugate of X(2)
X(19577) = cevapoint of X(7665) and X(8878)
X(19577) = barycentric quotient X(8869)/X(895)
X(19577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 9464, 7836), (39, 11056, 2), (7746, 11059, 2)
X(19578) lies on the cubic K861 and these lines: {82, 1910}, {1927, 1932}
X(19578) = X(1)-Ceva conjugate of X(1933)
X(19578) = barycentric product X(i)*X(j) for these {i,j}: {560, 8783}, {1580, 6660}, {1933, 5207}
X(19578) = barycentric quotient X(i)/X(j) for these {i,j}: {6660, 1934}, {8783, 1928}
X(19579) lies on the cubics K673 and K739, and on these lines: {1, 1655}, {2, 7167}, {81, 799}, {194, 6196}, {213, 668}, {238, 385}, {239, 3978}, {256, 291}, {294, 18299}, {350, 732}, {789, 1922}, {1580, 16360}, {1966, 2238}, {2210, 16985}, {4027, 16364}, {8300, 16361}
X(19579) = X(6)-Ceva conjugate of X(239)
X(19579) = X(292)-isoconjugate of X(7168)
X(19579) = X(238)-Hirst inverse of X(385)
X(19579) = crosspoint of X(6) and X(18278)
X(19579) = barycentric product X(i)*X(j) for these {i,j}: {6, 18277}, {76, 18274}, {350, 3510}, {1914, 18275}, {1921, 18278}, {8875, 18037}
X(19579) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 7168}, {3510, 291}, {18274, 6}, {18275, 18895}, {18277, 76}, {18278, 292}
X(19580) is the perspector of the unary cofactor triangles of the trilinear obverse triangle of X(2) and the trilinear N-obverse triangle of X(2). (Randy Hutson, October 15, 2018)
X(19580) lies on the cubics K773 and K989 and these lines: {1, 3511}, {6, 1045}, {58, 99}, {171, 292}, {190, 1918}, {238, 1921}, {239, 2236}, {385, 3747}, {659, 5027}, {1580, 1914}, {2176, 18754}, {3510, 18278}, {4586, 14598}, {5255, 8298}, {16696, 18170}
X(19580) = X(31)-Ceva conjugate of X(238)
X(19580) = X(291)-isoconjugate of X(7168)
X(19580) = X(i)-Hirst inverse of X(j) for these (i,j): {6, 18794}, {1580, 1914}, {3510, 18278}
X(19580) = crosssum of X(6) and X(16365)
X(19580) = barycentric product X(i)*X(j) for these {i,j}: {31, 18277}, {75, 18274}, {239, 3510}, {350, 18278}, {1281, 8875}, {2210, 18275}
X(19580) = barycentric quotient X(i)/X(j) for these {i,j}: {1914, 7168}, {3510, 335}, {18274, 1}, {18277, 561}, {18278, 291}
X(19581) lies on the cubics K770 and K992 and these lines: {1, 7168}, {2, 3121}, {42, 1978}, {75, 3056}, {86, 670}, {239, 1966}, {257, 335}, {350, 1926}, {740, 3978}, {804, 3766}, {3510, 18275}
X(19581) = isotomic conjugate of X(24576)
X(19581) = X(1)-Ceva conjugate of X(350)
X(19581) = X(1911)-isoconjugate of X(7168)
X(19581) = X(239)-Hirst inverse of X(1966)
X(19581) = crosspoint of X(1) and X(3510)
X(19581) = crosssum of X(1) and X(7168)
X(19581) = barycentric product X(i)*X(j) for these {i,j}: {1, 18277}, {238, 18275}, {561, 18274}, {1921, 3510}, {18278, 18891}
X(19581) = barycentric quotient X(i)/X(j) for these {i,j}: {239, 7168}, {1281, 8868}, {3510, 292}, {18274, 31}, {18275, 334}, {18277, 75}, {18278, 1911}
X(19582) lies on the cubic K157 and these lines: {1, 979}, {2, 986}, {4, 17777}, {8, 210}, {10, 17461}, {21, 2053}, {37, 2275}, {40, 5205}, {56, 190}, {65, 18743}, {72, 10453}, {78, 3685}, {145, 3952}, {192, 1193}, {344, 3485}, {386, 4065}, {392, 4385}, {644, 2176}, {846, 19278}, {978, 3210}, {995, 3159}, {997, 7283}, {1043, 4387}, {1149, 17480}, {1468, 17350}, {1479, 16086}, {1682, 3596}, {1788, 1997}, {3061, 3985}, {3212, 18135}, {3241, 8834}, {3305, 16824}, {3622, 17165}, {3649, 17234}, {3699, 3913}, {3704, 5233}, {3705, 3710}, {3717, 12053}, {3725, 4734}, {3729, 8583}, {3869, 4358}, {3890, 4696}, {3992, 5697}, {4003, 5550}, {4115, 4253}, {4188, 4427}, {4209, 17738}, {4419, 16720}, {4645, 11415}, {4737, 9957}, {4975, 5904}, {5250, 7081}, {5692, 10449}, {6555, 12632}, {6557, 9780}, {6651, 17696}, {6731, 8242}, {7080, 9368}, {8616, 8669}, {9371, 9375}, {9534, 10176}, {17464, 17794}
X(19582) = X(1)-Ceva conjugate of X(8)
X(19582) = X(3169)-cross conjugate of X(3210)
X(19582) = X(56)-isoconjugate of X(979)
X(19582) = X(40)-Hirst inverse of X(5205)
X(19582) = crosspoint of X(1) and X(978)
X(19582) = crosssum of X(1) and X(979)
X(19582) = barycentric product X(i)*X(j) for these {i,j}: {8, 3210}, {75, 3169}, {312, 978}
X(19582) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 979}, {978, 57}, {3169, 1}, {3210, 7}, {16614, 1357}
X(19582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 4011, 17697), (8, 4903, 3701), (8, 8055, 2899), (210, 4673, 8), (312, 960, 8), (341, 3057, 8), (497, 1265, 8), (3057, 4009, 341), (3701, 3877, 8), (3702, 3876, 8), (3885, 4723, 8), (5423, 9785, 8)
X(19583) is the intersection of the tangents at X(487) and X(488) to the orthocubic K006. (Randy Hutson, March 29, 2020)
X(19583) lies on the cubic K170 and these lines: {2, 1975}, {22, 5866}, {69, 305}, {75, 497}, {99, 6353}, {325, 6527}, {388, 7196}, {427, 1007}, {1368, 3926}, {1369, 16063}, {1370, 3266}, {1611, 6392}, {3265, 11123}, {3618, 11324}, {3785, 10691}, {3975, 18750}, {4576, 6515}, {6331, 6524}, {7391, 14360}, {7392, 11059}, {7484, 9723}, {7763, 8889}, {18906, 18928}
X(19583) = isogonal conjugate of X(15369)
X(19583) = isotomic conjugate of cyclocevian conjugate of X(38259)
X(19583) = anticomplement X(8770)
X(19583) = orthic-isogonal conjugate of X(69)
X(19583) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 2996}, {63, 7396}, {81, 17156}, {162, 2501}, {193, 8}, {662, 3566}, {823, 16229}, {1707, 2}, {3053, 192}, {3167, 6360}, {3798, 149}, {4028, 2895}, {6337, 4329}, {6353, 5905}, {17081, 7}, {18156, 69}
X(19583) = X(4)-Ceva conjugate of X(69)
X(19583) = X(6461)-cross conjugate of X(6338)
X(19583) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15369}, {6, 2129}, {1973, 6339}
X(19583) = barycentric product X(i)*X(j) for these {i,j}: {4, 6338}, {69, 6392}, {75, 2128}, {264, 6461}, {305, 1611}, {670, 2519}
X(19583) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2129}, {6, 15369}, {69, 6339}, {1611, 25}, {2128, 1}, {2519, 512}, {6338, 69}, {6392, 4}, {6461, 3}
X(19583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (305, 7386, 69), (1899, 4176, 69), (6337, 6340, 2)
X(19584) lies on the Feuerbach hyperbola of the medial triangle, the cubics K1012 and K1038, and on these lines: {1, 1575}, {2, 4876}, {3, 2329}, {6, 3507}, {9, 17792}, {10, 262}, {75, 142}, {100, 2344}, {870, 4562}, {982, 16587}, {984, 3094}, {1215, 19222}, {1755, 3647}, {1964, 5105}, {2276, 3117}, {3169, 6600}, {3314, 3661}, {3930, 17230}, {4266, 6594}, {6374, 17786}, {6376, 17760}, {13089, 17744}
X(19584) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 984}, {4334, 2886}, {17754, 141}
X(19584) = X(2)-Ceva conjugate of X(984)
X(19584) = barycentric product X(i)*X(j) for these {i,j}: {3661, 17754}, {3790, 4334}
X(19584) = barycentric quotient X(i)/X(j) for these {i,j}: {4517, 7220}, {17754, 14621}
X(19585) lies on the cubic K788 and these lines: {32, 8790}, {251, 689}, {384, 694}, {385, 18901}, {710, 3978}, {1691, 16985}, {4161, 4366}, {8290, 16951}
X(19585) = X(32)-Ceva conjugate of X(385)
X(19585) = X(1691)-Hirst inverse of X(16985)
X(19585) = barycentric product X(i)*X(j) for these {i,j}: {1, 18270}, {31, 18273}, {1580, 18271}, {1933, 18276}, {1966, 18272}
X(19585) = barycentric quotient X(i)/X(j) for these {i,j}: {18270, 75}, {18271, 1934}, {18272, 1581}, {18273, 561}
X(19586) lies on the cubics K1015 and K1017 and these lines: {1, 7077}, {2, 210}, {6, 3009}, {37, 263}, {48, 2330}, {192, 17792}, {237, 15624}, {611, 17976}, {660, 14621}, {984, 1469}, {2276, 3116}, {2294, 3728}, {3117, 3774}
X(19586) = X(1)-Ceva conjugate of X(2276)
X(19586) = crosspoint of X(1) and X(17754)
X(19586) = barycentric product X(984)X(17754)
X(19586) = barycentric quotient X(17754)/X(870)
X(19587) lies on the cubics K1016 and K1019 and these lines: {1, 672}, {2, 3508}, {41, 18758}, {42, 263}, {194, 3501}, {813, 985}, {869, 3117}, {1469, 2276}, {3116, 3774}
X(19587) = X(6)-Ceva conjugate of X(869)
X(19587) = barycentric product X(i)*X(j) for these {i,j}: {2276, 17754}, {4334, 4517}
X(19588) lies on the Feuerbach hyperbola of the tangential triangle, the cubics K171 and K707, and on these lines: {1, 7083}, {3, 69}, {6, 1196}, {25, 193}, {110, 19118}, {141, 16419}, {155, 1351}, {159, 524}, {195, 5093}, {206, 9027}, {371, 12590}, {372, 12591}, {394, 6467}, {399, 10752}, {511, 1498}, {542, 2935}, {576, 14914}, {610, 3684}, {1033, 15143}, {1147, 5050}, {1350, 16936}, {1352, 11479}, {1353, 6642}, {1368, 18935}, {1460, 1740}, {1593, 5921}, {1597, 18440}, {1599, 19404}, {1600, 19405}, {1609, 1634}, {1974, 8780}, {1993, 12167}, {2854, 13248}, {2917, 5965}, {2918, 9908}, {2930, 6144}, {3186, 7754}, {3360, 5017}, {3517, 9937}, {3620, 7484}, {5847, 12410}, {6090, 15531}, {6403, 12160}, {8053, 9028}, {8548, 15047}, {8939, 8940}, {8943, 8944}, {8996, 12978}, {11484, 18583}, {11513, 19409}, {11514, 19408}, {13175, 14645}, {17836, 19347}
X(19588) = midpoint of X(i) and X(j) for these {i,j}: {6403, 12271}
X(19588) = reflection of X(i) in X(j) for these {i,j}: {1351, 155}, {6391, 6}, {12310, 2930}, {12429, 1352}
X(19588) = isogonal conjugate of cyclocevian conjugate of X(38259)
X(19588) = isotomic conjugate of X(3) wrt anticevian triangle of X(3)
X(19588) = tangential-isogonal conjugate of X(9909)
X(19588) = X(i)-Ceva conjugate of X(j) for these (i,j): {25, 3}, {193, 6}, {6392, 1611}
X(19588) = X(i)-isoconjugate of X(j) for these (i,j): {2, 2129}, {19, 6339}, {75, 15369}
X(19588) = X(1033)-Hirst inverse of X(15143)
X(19588) = crossdifference of every pair of points on line {2489, 2506}
X(19588) = crosssum of X(i) and X(j) for these (i,j): {512, 15525}, {523, 5139}
X(19588) = barycentric product X(i)*X(j) for these {i,j}: {1, 2128}, {3, 6392}, {4, 6461}, {25, 6338}, {69, 1611}, {99, 2519}
X(19588) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 6339}, {31, 2129}, {32, 15369}, {1611, 4}, {2128, 75}, {2519, 523}, {6338, 305}, {6392, 264}, {6461, 69}
X(19588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (69, 19459, 3), (155, 12309, 1598), (193, 18287, 6339), (1993, 12272, 12167), (3167, 6391, 6), (6193, 12166, 3)
X(19589) lies on the cubic K980 and these lines: {1, 474}, {9, 10387}, {55, 2053}, {100, 1429}, {200, 3061}, {238, 3507}, {241, 9451}, {294, 2340}, {518, 18788}, {519, 13635}, {644, 8647}, {667, 3900}, {673, 3912}, {678, 8772}, {1959, 3935}, {3169, 6600}, {3212, 3905}, {3870, 7146}, {3939, 16786}, {9441, 14839}
X(19589) = X(105)-Ceva conjugate of X(9)
X(19589) = X(1)-Hirst inverse of X(1376)
X(19589) = X(1)-line conjugate of X(3752)
X(19589) = crossdifference of every pair of points on line {3752, 4394}
X(19590) lies on the cubic K739 and these lines: {83, 3225}, {194, 8790}, {782, 14295}, {1916, 8783}, {3051, 4609}, {8789, 9063}
X(19590) = X(6)-Ceva conjugate of X(3978)
X(19590) = barycentric product X(i)*X(j) for these {i,j}: {1, 18273}, {75, 18270}, {1580, 18276}, {1926, 18272}, {1966, 18271}
X(19590) = barycentric quotient X(i)/X(j) for these {i,j}: {18270, 1}, {18271, 1581}, {18272, 1967}, {18273, 75}, {18276, 1934}
X(19591) lies on the cubic K1031 and these lines: {1, 1581}, {19, 27}, {31, 1582}, {38, 17868}, {55, 17792}, {192, 7075}, {304, 2179}, {330, 1424}, {384, 3500}, {385, 1423}, {672, 17349}, {1575, 4383}, {1707, 2236}, {3329, 14621}, {3402, 3403}, {5999, 6210}
X(19591) = X(3114)-aleph conjugate of X(3403)
X(19591) = X(i)-isoconjugate of X(j) for these (i,j): {6, 19222}
X(19591) = barycentric product X(i)*X(j) for these {i,j}: {1, 18906}, {75, 11328}, {1966, 6234}
X(19591) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19222}, {6234, 1581}, {11328, 1}, {18906, 75}
X(19591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (31, 2227, 1740), (75, 1755, 63), (1423, 2319, 385), (1707, 16571, 2236), (1740, 3223, 18272), (3500, 3501, 384), (6210, 7350, 5999)
X(19592) lies on the cubic K653 and these lines: {5, 83}, {11205, 14153}
X(19592) = X(76)-Ceva conjugate of X(1691)
X(19593) lies on the cubic K981 and these lines: {1, 39}, {7, 190}, {56, 644}, {120, 1329}, {241, 6168}, {294, 1376}, {659, 3126}, {672, 4447}, {2170, 5836}, {2347, 17792}, {3693, 17464}
X(19593) = X(57)-Ceva conjugate of X(518)
X(19593) = X(i)-Hirst inverse of X(j) for these (i,j): {1, 9451}, {241, 6168}
X(19593) = X(i)-line conjugate of X(j) for these (i,j): {3126, 659}
X(19594) lies on the cubic K927 and these lines: {514, 17451}, {693, 1734}, {905, 4762}, {3309, 4077}
X(19594) = X(1)-Ceva conjugate of X(1111)
X(19594) = X(10)-isoconjugate of X(2141)
X(19594) = barycentric product X(693)X(2140)
X(19594) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 2141}, {2140, 100}
X(19595) lies on the cubic K140 and these lines: {6, 66}, {5596, 8879}
X(19595) = X(69)-Ceva conjugate of X(1843)
X(19595) = barycentric product X(i)*X(j) for these {i,j}: {141, 8879}, {427, 5596}
X(19595) = barycentric quotient X(i)/X(j) for these {i,j}: {5596, 1799}, {8879, 83}
X(19596) lies on the cubic K531 and these lines: {3, 11178}, {4, 15582}, {6, 25}, {22, 599}, {23, 524}, {24, 15581}, {26, 15069}, {110, 9019}, {141, 2916}, {160, 15109}, {186, 1503}, {237, 7669}, {378, 15577}, {511, 5899}, {512, 2076}, {542, 2070}, {575, 13621}, {576, 18378}, {597, 13595}, {1350, 12083}, {1352, 7502}, {1576, 18365}, {1634, 6660}, {1976, 14579}, {2781, 14157}, {3098, 18435}, {3129, 14173}, {3130, 14179}, {3455, 5938}, {3518, 8550}, {3763, 7485}, {4265, 4653}, {5012, 16776}, {5104, 11641}, {5476, 7545}, {5655, 12584}, {6593, 11416}, {6642, 10541}, {6776, 15580}, {7514, 10516}, {7517, 11477}, {7556, 11180}, {7575, 16010}, {8546, 14002}, {8681, 12310}, {9909, 15533}, {11179, 12106}, {11188, 19127}, {15091, 19140}
X(19596) = midpoint of X(i) and X(j) for these {i,j}: {12367, 18374}
X(19596) = reflection of X(i) in X(j) for these {i,j}: {6, 18374}, {5621, 186}, {11416, 6593}, {18374, 1495}
X(19596) = X(67)-Ceva conjugate of X(6)
X(19596) = isogonal conjugate of isotomic conjugate of X(5189)
X(19596) = polar conjugate of isotomic conjugate of X(22121)
X(19596) = crosspoint, wrt excentral or tangential triangle, of X(2916) and X(2930)
X(19596) = cevapoint of X(2916) and X(2930)
X(19596) = crossdifference of every pair of points on line {525, 3589}
X(19596) = crosssum of X(i) and X(j) for these (i,j): {6292, 9019}, {9517, 15526}
X(19596) = barycentric product X(i)*X(j) for these {i,j}: {1, 16546}, {6, 5189}, {55, 18627}, {524, 8877}
X(19596) = barycentric quotient X(i)/X(j) for these {i,j}: {5189, 76}, {8877, 671}, {16546,
75}, {18627, 6063}
X(19596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (184, 9971, 6), (206, 9973, 6), (237, 7669, 11063), (1495, 12367, 6)
X(19597) lies on the cubic K411 and these lines: {3, 69}, {22, 7893}, {25, 7762}, {32, 15371}, {39, 8681}, {155, 3511}, {394, 4173}, {524, 9917}, {525, 14824}, {1147, 3398}, {1634, 3053}, {1995, 7921}, {3051, 3167}, {3504, 10547}, {6287, 9927}, {6391, 9605}, {6638, 10316}, {7754, 10340}, {7773, 9149}, {9821, 13754}
X(19597) = reflection of X(9917) in X(15270)
X(19597) = X(32)-Ceva conjugate of X(3)
X(19597) = X(1969)-isoconjugate of X(15371)
X(19597) = barycentric quotient X(15371)/X(14575)
X(19597) = {X(682),X(3926)}-harmonic conjugate of X(3)
X(19598) lies on the circumcircle of the Steiner triangle, the cubic K602, and these lines: {2, 12076}, {114, 8151}, {115, 523}, {620, 11123}, {690, 14683}, {2482, 13187}, {2799, 11641}, {6722, 8029}
X(19598) = reflection of X(i) in X(j) for these {i,j}: {114, 8151}
X(19598) = anticomplement X[12076]
X(19598) = X(99)-Ceva conjugate of X(620)
X(19598) = crosspoint of X(99) and X(14061)
X(19598) = barycentric product X(11123)X(14061)
X(19599) lies on the cubic K776 and these lines: {2, 1975}, {3, 3504}, {99, 419}, {287, 12215}, {669, 3265}, {5117, 7763}, {13586, 16985}
X(19599) = X(98)-Ceva conjugate of X(69)
X(19599) = X(2)-Hirst inverse of X(1975)
X(19599) = crossdifference of every pair of points on line {1196, 8651}
X(19599) = crosssum of X(2211) and X(3080)
X(19599) = X(2)-daleth conjugate of X(7789)
X(19600) lies on the cubic K1032 and these lines: {1, 2227}, {561, 14213}, {7179, 9865}
X(19600) = X(18898)-isoconjugate of X(19222)
barycentric quotient X(18906)/X(3113)
X(19601) lies on the cubic K485 and these lines: {2, 11058}, {597, 3845}, {5306, 7426}
X(19601) = complement X(11058)
X(19601) = medial-isogonal conjugate of X(7703)
X(19601) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 7703}, {31, 14537}, {7712, 10}, {11057, 2887}
X(19601) = X(2)-Ceva conjugate of X(14537)
X(19601) = crosspoint of X(2) and X(11057)
X(19601) = crosssum of X(6) and X(14479)
X(19601) = barycentric product X(11057)X(14537)
X(19601) = barycentric quotient X(14537)/X(11058)
X(19602) lies on the Jerabek hyperbola of the medial triangle, the cubic K1012 and these lines: {2, 19222}, {3, 3491}, {5, 76}, {6, 3229}, {1147, 3398}, {1511, 13210}, {3114, 18829}, {3314, 5117}, {4550, 5167}, {6234, 18906}, {6786, 11171}
X(19602) = complement X(19222)
X(19602) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3094}, {11328, 10}, {18906, 2887}
X(19602) = X(2)-Ceva conjugate of X(3094)
X(19602) = crosspoint of X(2) and X(18906)
X(19602) = barycentric product X(i)*X(j) for these {i,j}: {3094, 18906}, {3314, 11328}, {6234, 9865}
X(19602) = barycentric quotient X(i)/X(j) for these {i,j}: {3094, 19222}, {11328, 3407}, {18906, 3114}
X(19603) lies on the cubic K1015 and these lines: {75, 1953}
X(19603) = X(1)-Ceva conjugate of X(3116)
X(19603) = X(3407)-isoconjugate of X(19222)
X(19603) = barycentric product X(3116)X(18906)
X(19603) = barycentric quotient X(i)/X(j) for these {i,j}: {3116, 19222}, {11328, 3113}
X(19604) lies on the cubics K365 and K970, and on these lines: {7, 145}, {57, 1122}, {226, 6557}, {269, 1279}, {1014, 16945}, {1293, 15728}, {1358, 4862}, {1419, 1462}, {2089, 2091}, {3663, 14261}, {4014, 4907}, {4052, 4654}, {4888, 11518}, {5193, 7023}, {5573, 9309}, {6556, 9578}
X(19604) = isogonal conjugate of X(3158)
X(19604) = cevapoint of X(1) and X(8056)
X(19604) = X(86)-beth conjugate of X(3875)
X(19604) = X(i)-zayin conjugate of X(j) for these (i,j): {1, 3158}, {3309, 4394}
X(19604) = X(i)-cross conjugate of X(j) for these (i,j): {1, 57}, {3445, 8056}, {3742, 1432}, {3752, 279}, {4906, 7132}, {17054, 1422}
X(19604) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3158}, {6, 3161}, {8, 3052}, {9, 1743}, {21, 4849}, {33, 4855}, {41, 18743}, {55, 145}, {56, 6555}, {57, 4936}, {59, 4953}, {100, 4162}, {101, 4521}, {109, 4546}, {200, 1420}, {210, 16948}, {220, 5435}, {284, 3950}, {643, 4729}, {644, 4394}, {1110, 4939}, {1252, 4534}, {2195, 4899}, {2318, 4248}, {2328, 4848}, {3445, 15519}, {3667, 3939}, {3699, 8643}, {3756, 6065}, {5546, 14321}, {5548, 14425}
X(19604) = barycentric product X(i)*X(j) for these {i,j}: {7, 8056}, {57, 4373}, {76, 16945}, {85, 3445}, {105, 10029}, {269, 6557}, {279, 3680}, {738, 6556}, {1014, 4052}, {1358, 5382}, {1743, 16078}, {16079, 18743}
X(19604) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3161}, {6, 3158}, {7, 18743}, {9, 6555}, {55, 4936}, {56, 1743}, {57, 145}, {65, 3950}, {222, 4855}, {241, 4899}, {244, 4534}, {269, 5435}, {513, 4521}, {604, 3052}, {649, 4162}, {650, 4546}, {1086, 4939}, {1293, 644}, {1396, 4248}, {1400, 4849}, {1407, 1420}, {1412, 16948}, {1427, 4848}, {1743, 15519}, {2170, 4953}, {3445, 9}, {3669, 3667}, {3676, 4462}, {3680, 346}, {3752, 12640}, {3911, 4487}, {4017, 14321}, {4052, 3701}, {4373, 312}, {5221, 4898}, {5382, 4076}, {6557, 341}, {7178, 4404}, {7180, 4729}, {8056, 8}, {10029, 3263}, {16079, 8056}, {16945, 6}
X(19604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1122, 7271, 57), (5575, 6180, 57)
X(19605) lies on the cubics K363 and K972 and these lines: {2, 3160}, {9, 165}, {57, 3119}, {200, 4513}, {281, 1886}, {282, 1449}, {972, 11372}, {1699, 13609}, {2125, 10939}, {3243, 14943}, {5514, 8727}, {13388, 15892}, {13389, 15891}
X(19605) = isogonal conjugate of X(1419)
X(19605) = isotomic conjugate of X(31627)
X(19605) = complement of X(31527)
X(19605) = X(i)-complementary conjugate of X(j) for these (i,j): {41, 17113}, {2125, 141}, {8917, 2886}
X(19605) = X(10405)-Ceva conjugate of X(3062)
X(19605) = X(i)-cross conjugate of X(j) for these (i,j): {1, 9}, {4907, 3680}, {10939, 7}, {12688, 7003}, {14100, 8}
X(19605) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1419}, {6, 3160}, {7, 3207}, {9, 17106}, {55, 9533}, {56, 144}, {57, 165}, {109, 7658}, {604, 16284}, {7339, 13609}
X(19605) = cevapoint of X(i) and X(j) for these (i,j): {1, 3062}, {650, 3119}
X(19605) = barycentric product X(i)*X(j) for these {i,j}: {8, 3062}, {9, 10405}, {312, 11051}
X(19605) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3160}, {6, 1419}, {8, 16284}, {9, 144}, {41, 3207}, {55, 165}, {56, 17106}, {57, 9533}, {650, 7658}, {3062, 7}, {3119, 13609}, {10405, 85}, {11051, 57}
X(19606) lies on the cubics K368 and K975 and these lines: {6, 194}, {703, 3222}, {1501, 15389}, {3504, 18899}
X(19606) = X(39)-cross conjugate of X(3051)
X(19606) = X(i)-isoconjugate of X(j) for these (i,j): {82, 6374}, {83, 17149}, {194, 3112}, {251, 18837}, {308, 1740}, {1613, 18833}
X(19606) = crosssum of X(194) and X(6374)
X(19606) = barycentric product X(i)*X(j) for these {i,j}: {39, 3224}, {427, 15389}, {688, 3222}, {1843, 3504}, {1923, 18832}, {1964, 3223}, {2998, 3051}
X(19606) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 18837}, {39, 6374}, {1923, 1740}, {1964, 17149}, {3051, 194}, {3223, 18833}, {3224, 308}, {9494, 3221}, {15389, 1799}
X(19606) = {X(6),X(3224)}-harmonic conjugate of X(2998)
X(19607) lies on the cubic K379 and these lines: {2, 572}, {8, 283}, {21, 1610}, {29, 60}, {81, 92}, {85, 17074}, {257, 7291}, {285, 7020}, {312, 1812}, {1220, 1798}, {1311, 2206}, {1437, 5136}, {1805, 7090}, {1806, 14121}, {1808, 4518}, {1999, 18359}, {2399, 4560}, {2994, 16704}
X(19607) = X(i)-cross conjugate of X(j) for these (i,j): {6, 21}, {1837, 314}
X(19607) = X(i)-isoconjugate of X(j) for these (i,j): {37, 10571}, {42, 17080}, {65, 573}, {226, 3185}, {1214, 3192}, {1400, 3869}, {1402, 4417}, {1409, 17555}, {2171, 4225}, {4551, 6589}
X(19607) = cevapoint of X(6) and X(2217)
X(19607) = barycentric product X(i)*X(j) for these {i,j}: {21, 2995}, {86, 10570}, {261, 15232}, {314, 2217}, {333, 13478}
X(19607) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 3869}, {29, 17555}, {58, 10571}, {60, 4225}, {81, 17080}, {284, 573}, {333, 4417}, {2194, 3185}, {2217, 65}, {2299, 3192}, {2995, 1441}, {7252, 6589}, {10570, 10}, {13478, 226}, {15232, 12}
X(19608) lies on the cubic K253 and these lines: {2, 2995}, {3, 10}
X(19608) = X(284)-complementary conjugate of X(15267)
X(19608) = X(2092)-cross conjugate of X(960)
X(19608) = X(i)-isoconjugate of X(j) for these (i,j): {573, 961}, {2298, 10571}
X(19608) = barycentric product X(i)*X(j) for these {i,j}: {960, 2995}, {3687, 13478}, {4357, 10570}
X(19608) = barycentric quotient X(i)/X(j) for these {i,j}: {960, 3869}, {1193, 10571}, {2217, 961}, {2269, 573}, {3666, 17080}, {3687, 4417}, {4267, 4225}, {10570, 1220}
X(19609) lies on the cubic K035 and these lines: {39, 14990}
X(19609) = X(512)-cross conjugate of X(39)
X(19609) = X(4593)-isoconjugate of X(14990)
X(19609) = barycentric quotient X(688)/X(14990)
X(19610) lies on the cubic K367 and these lines: {6, 9217}, {1648, 11123}, {2645, 9396}
X(19610) = X(512)-cross conjugate of X(3124)
X(19610) = X(i)-isoconjugate of X(j) for these (i,j): {99, 2644}, {799, 9218}, {2640, 4590}
X(19610) = X(6)-Hirst inverse of X(9217)
X(19610) = X(i)-line conjugate of X(j) for these (i,j): {6, 9218}, {9217, 9218}
X(19610) = barycentric product X(i)*X(j) for these {i,j}: {115, 9217}, {512, 9293}, {661, 9396}, {2643, 9395}
X(19610) = barycentric quotient X(i)/X(j) for these {i,j}: {669, 9218}, {798, 2644}, {3124, 148}, {9217, 4590}, {9293, 670}, {9396, 799}
X(19611) lies on the cubic K034 and these lines: {7, 1034}, {8, 253}, {63, 610}, {75, 1895}, {77, 271}, {78, 7013}, {326, 1792}, {1073, 3692}, {1259, 2062}, {1804, 7111}, {6355, 7358}, {17879, 18691}
X(19611) = isogonal conjugate of X(204)
X(19611) = isotomic conjugate of X(1895)
X(19611) = X(i)-beth conjugate of X(j) for these (i,j): {69, 5932}, {5931, 8809}
X(19611) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1817, 6225}, {3194, 14361}
X(19611) = X(5931)-Ceva conjugate of X(253)
X(19611) = X(i)-cross conjugate of X(j) for these (i,j): {1, 63}, {1439, 69}, {6508, 304}
X(19611) = X(i)-isoconjugate of X(j) for these (i,j): {1, 204}, {2, 3172}, {3, 6525}, {4, 154}, {6, 1249}, {9, 3213}, {19, 610}, {20, 25}, {28, 3198}, {31, 1895}, {32, 15466}, {33, 1394}, {34, 7070}, {57, 7156}, {64, 3079}, {112, 6587}, {184, 14249}, {393, 15905}, {607, 18623}, {1033, 3344}, {1474, 8804}, {1495, 10152}, {1973, 18750}, {1974, 14615}, {1990, 15291}, {2131, 17833}, {2299, 5930}
X(19611) = cevapoint of X(i) and X(j) for these (i,j): {1, 2184}, {525, 7358}
X(19611) = barycentric product X(i)*X(j) for these {i,j}: {63, 253}, {64, 304}, {69, 2184}, {75, 1073}, {92, 15394}, {162, 14638}, {305, 2155}, {326, 459}, {345, 8809}, {561, 14642}, {1102, 6526}, {1214, 5931}, {1969, 14379}
X(19611) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1249}, {2, 1895}, {3, 610}, {6, 204}, {19, 6525}, {31, 3172}, {48, 154}, {55, 7156}, {56, 3213}, {63, 20}, {64, 19}, {69, 18750}, {71, 3198}, {72, 8804}, {75, 15466}, {77, 18623}, {92, 14249}, {219, 7070}, {222, 1394}, {253, 92}, {255, 15905}, {304, 14615}, {459, 158}, {521, 14331}, {525, 17898}, {610, 3079}, {656, 6587}, {1073, 1}, {1214, 5930}, {2155, 25}, {2184, 4}, {2349, 10152}, {2632, 1562}, {3343, 1712}, {6508, 2883}, {6526, 6520}, {8611, 14308}, {8798, 1953}, {8809, 278}, {11589, 2173}, {14379, 48}, {14638, 14208}, {14642, 31}, {15394, 63}
X(19612) lies on the cubic K1027 and these lines: {}
X(19612) = X(32)-cross conjugate of X(18796)
X(19613) lies on the cubic K141 and these lines: {22, 8793}
X(19613) = X(6)-cross conjugate of X(22)
X(19613) = X(i)-isoconjugate of X(j) for these (i,j): {66, 16544}, {2156, 5596}
X(19613) = barycentric quotient X(i)/X(j) for these {i,j}: {22, 5596}, {2172, 16544}, {8743, 8879}
X(19614) lies on the cubic K175 and these lines: {1, 204}, {6, 7367}, {48, 820}, {55, 64}, {56, 7037}, {92, 821}, {212, 7114}, {326, 1792}, {336, 18156}, {603, 2188}, {775, 1958}, {943, 8809}, {1073, 1260}, {1106, 2638}, {1253, 7138}, {1802, 3990}, {3811, 15501}, {8606, 11589}
X(19614) = isogonal conjugate of X(1895)
X(19614) = X(i)-beth conjugate of X(j) for these (i,j): {3, 1035}, {1301, 34}
X(19614) = X(2184)-Ceva conjugate of X(2155)
X(19614) = X(i)-cross conjugate of X(j) for these (i,j): {31, 48}, {1410, 3}
X(19614) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1895}, {2, 1249}, {3, 14249}, {4, 20}, {6, 15466}, {19, 18750}, {25, 14615}, {27, 8804}, {29, 5930}, {30, 10152}, {69, 6525}, {75, 204}, {76, 3172}, {85, 7156}, {92, 610}, {107, 8057}, {154, 264}, {162, 17898}, {253, 3079}, {273, 7070}, {281, 18623}, {286, 3198}, {312, 3213}, {318, 1394}, {648, 6587}, {653, 14331}, {1105, 2883}, {1294, 1559}, {1503, 14944}, {2052, 15905}, {3183, 14365}, {3344, 14361}, {3346, 6616}, {5895, 18848}, {14345, 15459}
X(19614) = cevapoint of X(31) and X(2155)
X(19614) = crossdifference of every pair of points on line {14331, 17898}
X(19614) = crosssum of X(i) and X(j) for these (i,j): {1, 1712}, {204, 610}, {3176, 7952}
X(19614) = barycentric product X(i)*X(j) for these {i,j}: {1, 1073}, {3, 2184}, {19, 15394}, {48, 253}, {63, 64}, {69, 2155}, {75, 14642}, {92, 14379}, {219, 8809}, {255, 459}, {1409, 5931}, {2167, 8798}, {2169, 13157}, {2349, 11589}, {6507, 6526}, {15400, 18594}
X(19614) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 15466}, {3, 18750}, {6, 1895}, {19, 14249}, {31, 1249}, {32, 204}, {48, 20}, {63, 14615}, {64, 92}, {184, 610}, {228, 8804}, {253, 1969}, {560, 3172}, {603, 18623}, {647, 17898}, {810, 6587}, {822, 8057}, {1073, 75}, {1301, 823}, {1397, 3213}, {1409, 5930}, {1946, 14331}, {1973, 6525}, {2155, 4}, {2159, 10152}, {2175, 7156}, {2184, 264}, {2200, 3198}, {6526, 6521}, {8798, 14213}, {8809, 331}, {9247, 154}, {11589, 14206}, {14379, 63}, {14642, 1}, {15394, 304}, {15905, 1097}
X(19614) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (820, 1496, 48)
X(19615) lies on the cubic K177 and these lines: {3, 3162}
X(19615) = X(32)-cross conjugate of X(206)
X(19615) = X(16544)-isoconjugate of X(18018)
X(19615) = barycentric quotient X(i)/X(j) for these {i,j}: {206, 5596}, {17409, 8879}, {17453, 16544}
X(19616) lies on the cubic K968 and these lines: {}
X(19616) = X(31)-cross conjugate of X(2172)
X(19616) = X(i)-isoconjugate of X(j) for these (i,j): {66, 5596}, {8879, 14376}
X(19616) = barycentric quotient X(i)/X(j) for these {i,j}: {206, 16544}, {2172, 5596}
X(19617) lies on this cubic: K167
X(19617) = X(3)-cross conjugate of X(3167)
X(19618) lies on this cubic: K453
X(19618) = X(44)-cross conjugate of X(214)
X(19618)-isoconjugate of X(16554)
X(19618) = barycentric quotient X(i)/X(j) for these {i,j}: {214, 6224}, {17455, 16554}
X(19619) lies on the cubic K454 and these lines: {44, 1465}, {106, 2342}
X(19619) = isogonal conjugate of complement of X(36917)
X(19619) = X(6)-cross conjugate of X(36)
X(19619) = X(i)-isoconjugate of X(j) for these (i,j): {80, 16554}, {2161, 6224}
X(19619) = barycentric quotient X(i)/X(j) for these {i,j}: {36, 6224}, {7113, 16554}
X(19620) lies on this cubic: K637
X(19620) = X(1100)-cross conjugate of X(3647)
X(19620) = barycentric quotient X(i)/X(j) for these {i,j}: {3647, 3648}, {17454, 16553}
X(19621) lies on the cubic K1050 and this line:
{6, 100}
X(19622) lies on the cubic K1050 and these lines: {3, 6}, {37, 7054}, {44, 5546}, {112, 2687}, {163, 7113}, {448, 16732}, {647, 2605}, {759, 7297}, {1325, 15586}, {1576, 2223}, {2150, 2174}, {4558, 16702}, {4565, 6610}, {5127, 17796}
X(19622) = X(759)-Ceva conjugate of X(2194)
X(19622) = X(i)-isoconjugate of X(j) for these (i,j): {2, 5620}, {226, 11604}, {1290, 1577}
X(19622) = crossdifference of every pair of points on line {442, 523}
X(19622) = crosssum of X(i) and X(j) for these (i,j): {3218, 5483}, {4707, 16732}
X(19622) = barycentric product X(i)*X(j) for these {i,j}: {1, 5127}, {3, 2074}, {21, 5172}, {74, 16164}, {81, 17796}, {110, 8674}
X(19622) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 5620}, {1576, 1290}, {2074, 264}, {2194, 11604}, {5127, 75}, {5172, 1441}, {8674, 850}, {16164, 3260}, {17796, 321}
X(19622) = {X(3825),X(4282)}-harmonic conjugate of X(1333)
X(19623) lies on the cubic K1050 and these lines: {2, 6}, {37, 261}, {44, 645}, {58, 4672}, {99, 536}, {190, 1931}, {239, 662}, {314, 1333}, {321, 593}, {335, 2161}, {523, 1325}, {527, 6629}, {648, 14571}, {740, 1326}, {757, 894}, {799, 4396}, {892, 3227}, {1178, 18170}, {1509, 4670}, {1999, 2185}, {2235, 18268}, {2966, 14578}, {3110, 6007}, {4363, 17103}, {4364, 6626}, {4442, 5196}, {4567, 4590}, {4573, 6610}, {5209, 5291}, {5695, 11104}, {6043, 7081}, {11611, 17929}, {16560, 18206}, {18825, 18829}
X(19623) = reflection of X(99) in X(16702)
X(19623) = isotomic conjugate of X(11611)
X(19623) = antitomic conjugate of X(17790)
X(19623) = X(2)-daleth conjugate of X(6703)
X(19623) = X(i)-cross conjugate of X(j) for these (i,j): {5006, 422}, {17763, 5209}
X(19623) = X(i)-isoconjugate of X(j) for these (i,j): {10, 17961}, {31, 11611}, {37, 17954}, {42, 17946}, {71, 17981}, {101, 18015}, {190, 18002}, {661, 2703}, {1400, 11609}, {1826, 17971}, {4024, 17939}, {4079, 17929}
X(19623) = X(2)-Hirst inverse of X(81)
X(19623) = cevapoint of X(5291) and X(17763)
X(19623) = trilinear pole of line {2787, 5040}
X(19623) = crossdifference of every pair of points on line {512, 2092}
X(19623) = barycentric product X(i)*X(j) for these {i,j}: {1, 5209}, {69, 422}, {76, 5006}, {81, 17790}, {86, 17763}, {99, 2787}, {274, 5291}, {286, 17977}, {314, 5061}, {513, 17935}, {670, 5040}, {693, 17944}, {1444, 17987}, {4623, 17989}
X(19623) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 11611}, {21, 11609}, {28, 17981}, {58, 17954}, {81, 17946}, {110, 2703}, {422, 4}, {513, 18015}, {667, 18002}, {1333, 17961}, {1437, 17971}, {2787, 523}, {5006, 6}, {5040, 512}, {5061, 65}, {5209, 75}, {5291, 37}, {17763, 10}, {17790, 321}, {17935, 668}, {17944, 100}, {17977, 72}, {17989, 4705}, {18003, 4036}
X(19623) = {X(6189),X(6190)}-harmonic conjugate of X(81)
X(19624) lies on the cubic K1050 and these lines: {6, 31}, {35, 3792}, {44, 3939}, {109, 6610}, {171, 17392}, {238, 528}, {517, 1279}, {595, 4646}, {663, 6586}, {692, 2223}, {1086, 9441}, {1110, 2251}, {1458, 3446}, {1471, 2099}, {2161, 2195}, {2174, 2175}, {2183, 8647}, {2340, 17796}, {2643, 3747}, {2886, 17123}, {2911, 6600}, {3053, 7084}, {4268, 16688}, {5119, 7290}, {6690, 17122}, {8255, 9440}, {8750, 14571}, {9459, 18266}
X(19624) = X(2291)-Ceva conjugate of X(41)
X(19624) = X(i)-isoconjugate of X(j) for these (i,j): {7, 3254}, {693, 1308}
X(19624) = crosspoint of X(i) and X(j) for these (i,j): {1170, 15728}, {1252, 2742}, {2078, 5526}
X(19624) = crossdifference of every pair of points on line {142, 514}
X(19624) = crosssum of X(i) and X(j) for these (i,j): {1086, 2826}, {1212, 15733}
X(19624) = isogonal conjugate of isotomic conjugate of X(3935)
X(19624) = barycentric product X(i)*X(j) for these {i,j}: {1, 5526}, {6, 3935}, {9, 2078}, {31, 17264}, {101, 3887}, {190, 8645}, {2291, 6594}, {4845, 15730}
X(19624) = barycentric quotient X(i)/X(j) for these {i,j}: {41, 3254}, {2078, 85}, {3887, 3261}, {3935, 76}, {5526, 75}, {8645, 514}, {17264, 561}
X(19624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (692, 2223, 7113), (2175, 15624, 2174), (2183, 8647, 16686)
X(19625) lies on the cubic K1050 and these lines: {6, 75}, {4586, 7113}
X(19626) lies on the cubic K1048 and these lines: {6, 2936}, {32, 1084}, {111, 251}, {187, 5166}, {671, 3407}, {691, 699}, {895, 5007}, {1501, 9427}, {3115, 18023}, {8753, 14581}, {14609, 19220}
X(19626) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3266}, {76, 14210}, {187, 1928}, {313, 16741}, {524, 561}, {690, 4602}, {896, 1502}, {1969, 6390}, {2642, 4609}, {4062, 6385}, {4750, 6386}, {7813, 18833}
X(19626) = trilinear pole of line {1501, 9426}
X(19626) = barycentric product X(i)*X(j) for these {i,j}: {25, 14908}, {31, 923}, {32, 111}, {184, 8753}, {560, 897}, {669, 691}, {671, 1501}, {892, 9426}, {895, 1974}, {1397, 5547}, {1576, 9178}, {1980, 5380}, {2175, 7316}, {5466, 14574}, {5968, 14601}, {9139, 9407}, {9154, 9418}, {9233, 18023}, {10630, 14567}, {14575, 17983}
X(19626) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3266}, {111, 1502}, {560, 14210}, {691, 4609}, {897, 1928}, {923, 561}, {1501, 524}, {1917, 896}, {8753, 18022}, {9233, 187}, {9426, 690}, {9427, 1648}, {9448, 3712}, {9494, 14424}, {14574, 5468}, {14575, 6390}, {14604, 18872}, {14908, 305}, {18894, 4760}, {18902, 5026}
X(19626) = isogonal conjugate of isotomic conjugate of X(32740)
X(19627) lies on the cubic K1049 and these lines: {6, 2070}, {32, 184}, {39, 18475}, {50, 18334}, {115, 1971}, {186, 2088}, {187, 13754}, {249, 13586}, {542, 1691}, {1495, 11060}, {1692, 2393}, {1915, 7753}, {1970, 7747}, {2021, 3455}, {3016, 10540}, {3053, 18445}, {3289, 9696}, {7746, 18474}, {9418, 14574}
X(19627) = X(14591)-Ceva conjugate of X(14270)
X(19627) = X(i)-isoconjugate of X(j) for these (i,j): {63, 18817}, {75, 94}, {76, 2166}, {92, 328}, {265, 1969}, {304, 6344}, {561, 1989}, {799, 10412}, {811, 14592}, {1928, 11060}, {4602, 15475}
X(19627) = crossdifference of every pair of points on line {311, 850}
X(19627) = crosssum of X(94) and X(328)
X(19627) = barycentric product X(i)*X(j) for these {i,j}: {6, 50}, {31, 6149}, {32, 323}, {110, 14270}, {163, 2624}, {184, 186}, {237, 14355}, {340, 14575}, {526, 1576}, {647, 14591}, {669, 10411}, {1273, 14573}, {1399, 2361}, {1495, 14385}, {1501, 7799}, {2081, 14586}, {2148, 2290}, {2151, 2152}, {2174, 7113}, {3049, 14590}, {3268, 14574}, {3724, 17104}, {8603, 11135}, {8604, 11136}, {11062, 14533}, {14165, 14585}
X(19627) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 18817}, {32, 94}, {50, 76}, {184, 328}, {186, 18022}, {323, 1502}, {560, 2166}, {669, 10412}, {1501, 1989}, {1974, 6344}, {2081, 15415}, {3049, 14592}, {6149, 561}, {9233, 11060}, {9407, 14254}, {9418, 14356}, {9426, 15475}, {10411, 4609}, {14270, 850}, {14355, 18024}, {14573, 1141}, {14574, 476}, {14575, 265}, {14591, 6331}
X(19628) lies on the circumcircke, the cubic K1051, and these lines: {11, 110}, {80, 101}, {99, 4996}, {100, 14204}, {109, 2006}, {112, 8735}, {759, 8648}, {827, 18101}, {2222, 3724}
X(19629) lies on the cubic K1051 and these lines: {6, 13}, {7, 3028}, {11, 110}, {80, 7727}, {516, 14194}, {528, 6740}, {759, 16686}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27769.
X(19630) lies on these lines: {1,2687}, {1325,2771}
X(19631) lies on the cubic K1051 and this line: {80, 145}
X(19632) lies on the cubic K1051 and this line: {80, 3244}
X(19633) lies on the cubic K1051 and this line: {80, 3241}
X(19634) lies on the cubic K1051 and these lines: {2, 901}, {7, 14027}, {11, 3257}, {80, 519}, {88, 5057}, {106, 535}, {516, 14193}, {1318, 5080}, {4080, 5211}, {4582, 17777}, {4997, 5087}, {10199, 16944}, {14260, 17556}
X(19634) = {X(5087),X(14190)}-harmonic conjugate of X(4997)
X(19635) lies on the cubic K1051 and these lines: {7, 3027}, {80, 291}, {99, 8299}, {516, 14196}, {543, 11355}
X(19636) lies on the cubic K1051 and these lines:{7, 528}, {11, 88}, {30, 1168}, {80, 900}, {100, 4080}, {106, 1086}, {516, 14190}, {545, 1145}, {653, 1846}, {901, 19628}, {952, 4792}, {2161, 12515}, {2796, 4013}, {3035, 4997}, {3257, 17768}, {3932, 4582}, {4945, 6174}
X(19636) = {X(4997),X(14193)}-harmonic conjugate of X(3035)
X(19637) lies on the cubic K1051 and these lines: {7, 3023}, {80, 256}, {98, 1284}, {528, 3903}, {694, 804}, {874, 18896}, {893, 3914}, {1423, 9860}, {1431, 2792}, {1916, 5992}, {4603, 19642}, {7260, 19643}
X(19638) lies on the cubic K1051 and this line: {80, 551}
X(19639) lies on the cubic K1051 and this line: {80, 1125}
X(19640) lies on the cubic K1051 and these lines: {2, 80}, {11, 4604}, {89, 11269}, {4588, 10707}
X(19641) lies on the cubic K1051 and this line: {80, 1698}
X(19642) lies on the cubic K1051 and these lines: {7, 1365}, {10, 21}, {11, 662}, {27, 295}, {63, 13174}, {81, 3914}, {110, 149}, {284, 14009}, {333, 3696}, {409, 950}, {516, 2651}, {528, 643}, {645, 17777}, {1012, 14663}, {1098, 6284}, {1834, 2363}, {2185, 2886}, {3017, 17579}, {3109, 12690}, {3218, 5196}, {3419, 17512}, {4388, 7058}, {4603, 19637}, {4631, 19643}, {5722, 11116}, {6011, 7411}, {13576, 14534}
X(19643) lies on the cubic K1051 and these lines: {7, 1356}, {11, 799}, {80, 313}, {86, 741}, {516, 14195}, {528, 7257}, {752, 5209}, {3122, 18827}, {4388, 18021}, {4594, 18896}, {4631, 19642}, {5539, 10436}, {7260, 19637}
X(19644) lies on the cubic K1051 and this line: {528, 644}
X(19645) lies on these lines: {2, 3}, {7, 940}, {8, 5786}, {31, 516}, {40, 5271}, {57, 17863}, {63, 321}, {81, 10446}, {92, 3101}, {226, 2268}, {278, 4329}, {306, 515}, {312, 5279}, {329, 5776}, {386, 19752}, {517, 3187}, {572, 10478}, {573, 1746}, {952, 20017}, {962, 5706}, {965, 18228}, {991, 10458}, {1030, 19721}, {1076, 4292}, {1214, 17134}, {1427, 3188}, {1441, 5307}, {1468, 12545}, {1999, 3868}, {2345, 5273}, {2975, 10465}, {3687, 5016}, {4297, 10448}, {4313, 5716}, {5124, 19720}, {5287, 10884}, {5294, 10445}, {5732, 17022}, {5844, 20046}, {6044, 19642}, {7291, 18750}, {8822, 14829}, {10437, 17185}, {17019, 18444}, {17316, 19782}
X(19646) lies on these lines: {2, 3}, {517, 3214}, {970, 3030}, {3303, 5718}, {5396, 10222}, {5844, 20047}, {6668, 8053}, {7173, 16678}, {7982, 15488}
X(10647) lies on these lines: {2, 3}, {40, 899}, {42, 7982}, {43, 7991}, {228, 5748}, {517, 3240}, {573, 5400}, {1766, 17756}, {3817, 10434}, {4297, 4871}, {5844, 20048}, {10222, 17018}, {10589, 16678}, {10882, 19925}, {12245, 19998}, {15488, 19767}
X(19648) lies on these lines: {2, 3}, {40, 5400}, {517, 3293}, {970, 12702}, {1482, 5396}, {2051, 12699}, {2635, 11573}, {3295, 5718}, {3654, 9568}, {5687, 5741}, {5743, 9709}, {5844, 20051}, {7741, 16678}, {10882, 18492}, {15315, 17595}
X(19649) lies on these lines: {2, 3}, {38, 6211}, {40, 614}, {81, 182}, {100, 3705}, {104, 9059}, {105, 165}, {183, 1444}, {230, 5124}, {329, 1473}, {517, 7191}, {572, 5276}, {612, 3576}, {651, 3784}, {748, 6210}, {908, 7293}, {940, 5085}, {944, 10327}, {956, 7172}, {982, 983}, {1030, 3815}, {1214, 5481}, {1295, 9088}, {1350, 4383}, {1353, 20086}, {1385, 3920}, {1482, 17024}, {1621, 9751}, {1764, 13329}, {2077, 5310}, {2692, 2752}, {2975, 4696}, {3006, 11491}, {3011, 11012}, {3086, 8193}, {3216, 3430}, {3220, 3452}, {3579, 7292}, {3911, 5285}, {3955, 17074}, {5120, 5304}, {5268, 7987}, {5297, 13624}, {5358, 17749}, {5584, 16020}, {5739, 10519}, {5744, 7085}, {7080, 8192}, {7967, 20020}, {12017, 14996}, {12245, 19993}, {12410, 14986}, {19767, 19782}
X(19650) lies on these lines: {2, 3}
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27777.
X(19651) lies on these lines: {30,54},{93,186},{476,1141},{477,933},{1173,16106},{5899,16035},{15646,19176}
X(19651) = crosssum of X(1154) and X(14128)
X(19651) = barycentric product X(95)*X(19656)
X(19652) lies on these lines: {3, 18343}, {186, 17924}, {245, 3724}, {929, 19628}, {1284, 5172}
X(19652) = circumcircle-invere of X(18343)
X(19652) = singular focus of the cubic K1052
X(19653) lies on the cubic K1052 and these lines {36, 106}, {55, 4638}, {14190, 14193}
X(19654) lies on the cubic K1052 and these lines: {6, 36}, {55, 4588}, {1001, 1156}, {8692, 9353}
X(19654) = isogonal conjugate of X(32631)
X(19654) = barycentric product X(i)*X(j) for these {i,j}: {89, 5220}, {2163, 17294}
X(19654) = barycentric quotient X(5220)/X(4671)
X(19655) lies on the cubic K1052 and these lines: {36, 58}, {55, 4556}, {110, 846}
X(19655) = crosssum of X(4705) and X(6627)
See X(19651).
X(19656) lies on these lines: {6,382},{50,112},{93,393},{566,18281},{1879,18367},{1989,3003},{3018,11063},{3163,18365},{8553,15750}
X(19656) = barycentric product X(5)*X(19651)
X(19656) = barycentric quotient X(19651) / X(95)
See Alexandr Skutin, Peter Moses, and Angel Montesdeoca, Hyacinthos 27780 and Hyacinthos 27781.
X(19657) lies on the circumcircle
See Alexandr Skutin, Peter Moses, and Angel Montesdeoca, Hyacinthos 27780 and Hyacinthos 27781.
X(19658) lies on the cubic K060 and these lines: {5,79},{30,5685},{265,14452}
X(19658) = antigonal image of X(484)
X(19658) = symgonal image of X(11813)
X(19658) = X(i)-isoconjugate of X(j) for these (i,j): {3336, 7343}, {6149, 14452}
X(19658) = cevapoint of X(3467) and X(5685)
X(19658) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 14452}, {11076, 3336}
See Angel Montesdeoca, HG180618.
X(19659) lies on these lines: {2,3}, {32,6178}, {39,3414}, {141,1380}, {187,2040}, {524,3558}, {574,1349}, {597,14630}, {1340,3589}, {1341,1503}, {1379,5480}, {3933,6189}, {8550,14631}
X(19659) = reflection of X(19660) in X(37345)
X(19659) = {X(i),X(j)}-harmonic conjugate of X(19660) for these {i,j}: {2,8369}, {3,5}
See Angel Montesdeoca, HG180618.
X(19660) lies on these lines: {2,3}, {32,6177}, {39,3413}, {141,1379}, {187,2039}, {524,3557}, {574,1348}, {597,14631}, {1340,1503}, {1341,3589}, {1380,5480}, {3933,6190}, {8550,14630}
X(19660) = reflection of X(19659) in X(37345)
X(19660) = {X(i),X(j)}-harmonic conjugate of X(19659) for these {i,j}: {2,8369}, {3,5}
See Angel Montesdeoca, HG180618.
X(19661) lies on these lines: {2,1285}, {5,598}, {6,7618}, {30,9753}, {32,524}, {187,597}, {230,3363}, {315,8365}, {489,7584}, {490,7583}, {543,5306}, {549,2080}, {550,7827}, {599,3793}, {1353,8724}, {1992,6390}, {2482,5008}, {3053,8182}, {3815,7619}, {3845,9166}, {5032,11165}, {5182,16508}, {5215,7753}, {6329,8588}, {7620,7735}, {7622,9300}, {7745,8176}, {7804,11168}, {7806,8352}, {7812,7940}, {7856,15704}, {7878,15712}, {8362,15810}, {8370,8859}, {8598,15048}, {9740,14039}, {9770,11288}, {14537,14971}
See Angel Montesdeoca, HG180618.
X(19662) lies on these lines: {2,98}, {6,14971}, {69,9166}, {115,599}, {141,543}, {524,625}, {597,6722}, {620,9830}, {690,18310}, {1992,14061}, {2482,11646}, {3619,14928}, {3763,9167}, {3818,11159}, {5071,10753}, {6034,15533}, {8360,11623}, {8369,18553}
See Angel Montesdeoca, HG180618.
X(19663) lies on these lines: {39, 597}, {384, 11638}
X(19664) lies on these lines: {2, 3}
X(19665) lies on these lines: {2, 3}, {4366, 12701}
X(19666) lies on these lines: {2, 3}, {4366, 9580}
X(19667) lies on these lines: {2, 3}
X(19668) lies on these lines: {2, 3}
X(19669) lies on these lines: {2, 3}, {698, 940}
X(19670) lies on these lines: {2, 3}, {385, 18144}, {698, 4383}
X(19671) lies on these lines: {2, 3}
X(19672) lies on these lines: {2, 3}
X(19673) lies on these lines: {2, 3}
X(19674) lies on these lines: {2, 3}
X(19675) lies on these lines: {2, 3}
X(19676) lies on these lines: {2, 3}
X(19677) lies on these lines: {2, 3}
X(19678) lies on these lines: {2, 3}
X(19679) lies on these lines: {2, 3}
X(19680) lies on these lines: {2, 3}, {698, 3936}
X(19681) lies on these lines: {2, 3}
X(19682) lies on these lines: {2, 3}, {736, 3948}
X(19683) lies on these lines: {2, 3}
X(19684) lies on these lines: {1, 321}, {2, 6}, {3, 19769}, {7, 16368}, {8, 2049}, {21, 19762}, {55, 11322}, {58, 16342}, {63, 10466}, {75, 17011}, {92, 1870}, {100, 11358}, {226, 604}, {306, 5750}, {312, 17019}, {329, 405}, {330, 1255}, {377, 19752}, {379, 2140}, {386, 16454}, {404, 19763}, {445, 17907}, {452, 19753}, {551, 4656}, {572, 10478}, {594, 20017}, {748, 1125}, {750, 6685}, {961, 3485}, {980, 18601}, {1010, 19767}, {1011, 1621}, {1100, 3187}, {1215, 5311}, {1230, 18147}, {1449, 5271}, {1730, 3306}, {1751, 2364}, {1962, 3923}, {2296, 14621}, {2345, 3969}, {2476, 19755}, {3175, 3723}, {3219, 3758}, {3305, 16552}, {3622, 11319}, {3666, 4376}, {3681, 16830}, {3751, 4981}, {3782, 17045}, {3840, 9345}, {3873, 10477}, {3875, 4980}, {3948, 5192}, {3995, 16777}, {4001, 4667}, {4026, 6327}, {4188, 19760}, {4189, 19759}, {4193, 19754}, {4195, 19757}, {4198, 19756}, {4252, 16347}, {4255, 19284}, {4256, 19336}, {4307, 4450}, {4358, 5287}, {4359, 5256}, {4363, 17147}, {4389, 17483}, {4414, 4697}, {4418, 17592}, {4470, 19825}, {4657, 17184}, {4658, 10479}, {4672, 10180}, {4703, 6536}, {4747, 9965}, {5016, 5717}, {5021, 16349}, {5145, 10458}, {5253, 13738}, {5263, 17018}, {5283, 11342}, {5439, 14557}, {5550, 16844}, {5749, 17776}, {5813, 7535}, {5905, 17321}, {6904, 19764}, {7081, 9347}, {9534, 14005}, {9776, 11347}, {11115, 19765}, {11321, 16752}, {11343, 17169}, {17012, 19804}, {17021, 18743}, {17140, 17599}, {17155, 17600}, {19281, 19785}
X(19685) lies on these lines: {2, 3}
X(19686) lies on these lines: {2, 3}, {6, 20094}, {32, 19570}, {99, 7753}, {148, 3972}, {315, 19569}, {316, 7880}, {543, 4027}, {698, 1992}, {1975, 7837}, {2896, 11057}, {3058, 6645}, {3734, 7811}, {4366, 5434}, {7737, 7779}, {7739, 7787}, {7747, 7809}, {7748, 7884}, {7757, 8591}, {7783, 9300}, {7785, 7799}, {7788, 7823}, {7797, 11648}, {7802, 7865}, {7857, 18362}, {8716, 11164}, {9878, 11606}, {10351, 18501}, {10352, 12117}, {10353, 10796}
X(19686) = midpoint of X(2) and X(6658)
X(19686) = reflection of X(2) in X(384)
X(19686) = reflection of X(6655) in X(2)
X(19686) = anticomplement of X(7924)
X(19687) lies on these lines: {2, 3}, {99, 7745}, {141, 7802}, {148, 5305}, {194, 18907}, {316, 7789}, {325, 7747}, {543, 5007}, {698, 3629}, {1285, 6392}, {1975, 7737}, {3053, 11185}, {3589, 7847}, {3631, 5104}, {3734, 7750}, {3793, 17129}, {3815, 7782}, {3849, 7794}, {3933, 7823}, {3934, 6781}, {3972, 5254}, {4366, 18990}, {5038, 6329}, {6390, 7785}, {6645, 15171}, {7748, 7792}, {7756, 7804}, {7764, 14537}, {7767, 14712}, {7787, 15048}, {7820, 7842}, {7839, 20094}, {7878, 9607}, {10352, 18502}, {11008, 11173}
X(19687) = complement of X(33256)
X(19687) = anticomplement of X(8357)
X(19687) = {X(2),X(20)}-harmonic conjugate of X(33226)
X(19688) lies on these lines: {2, 3}
X(19689) lies on these lines: {2, 3}, {76, 5346}, {83, 7764}, {99, 7889}, {148, 7834}, {316, 7915}, {698, 3618}, {1975, 7875}, {2548, 7945}, {2896, 3972}, {3053, 16986}, {3096, 14712}, {3314, 20088}, {3329, 7789}, {3589, 7783}, {3734, 7797}, {3763, 7904}, {4372, 17280}, {5475, 7930}, {5965, 12208}, {7737, 7938}, {7745, 7931}, {7747, 7944}, {7748, 7943}, {7753, 7909}, {7779, 7787}, {7785, 7804}, {7792, 17128}, {7794, 12150}, {7801, 7878}, {7802, 7914}, {7808, 7835}, {7810, 10159}, {7812, 7869}, {7816, 7859}, {7823, 7868}, {7856, 17130}, {7858, 7880}, {7864, 20094}, {7881, 7921}, {7891, 11174}, {7932, 11185}, {7939, 18907}, {16989, 20081}
X(19690) lies on these lines: {2, 3}, {148, 3096}, {698, 3620}, {2549, 7938}, {2896, 7751}, {4045, 7785}, {5254, 7928}, {5286, 7929}, {5309, 7936}, {5319, 9939}, {5346, 6179}, {7738, 7897}, {7739, 7946}, {7748, 7937}, {7750, 7923}, {7756, 7944}, {7765, 7883}, {7779, 7784}, {7795, 20094}, {7802, 7913}, {7803, 7898}, {7811, 7902}, {7818, 13571}, {7827, 7873}, {7830, 7919}, {7831, 7861}, {7834, 7910}, {7836, 7847}, {7840, 9607}, {7842, 7859}, {7851, 7904}, {7854, 19570}, {7932, 14907}, {7939, 15048}
X(19691) lies on these lines: {2, 3}, {148, 7751}, {315, 20094}, {698, 20080}, {2549, 20088}, {2896, 17130}, {6179, 7748}, {7756, 7785}, {7796, 8591}, {7836, 7842}, {7872, 10583}, {8596, 9939}, {14023, 14976}
X(19691) = anticomplement of X(6658)
X(19692) lies on these lines: {2, 3}, {83, 7863}, {148, 7846}, {3734, 7856}, {3972, 7854}, {7758, 7787}, {7785, 7820}, {7795, 7946}, {7803, 20094}, {7804, 7836}, {7822, 7936}, {7832, 7843}
X(19693) lies on these lines: {2, 3}, {148, 7856}, {3972, 5346}, {7737, 7946}, {7747, 7909}, {7758, 20088}, {7772, 8591}, {7785, 7863}, {7787, 20094}, {7816, 7858}, {7836, 7843}, {7854, 14712}, {7902, 10583}
X(19694) lies on these lines: {2, 3}, {39, 16987}, {83, 7821}, {141, 10583}, {385, 7822}, {597, 13571}, {1078, 16988}, {3329, 7764}, {3589, 7836}, {3618, 7906}, {3734, 7923}, {3763, 7793}, {3934, 16984}, {3972, 7914}, {6704, 7769}, {7780, 10159}, {7783, 7820}, {7787, 7868}, {7792, 17129}, {7795, 7839}, {7804, 7885}, {7808, 7925}, {7834, 17128}, {7840, 7869}, {7849, 12150}, {7874, 17005}, {7884, 17130}, {7945, 11174}
X(19695) lies on these lines: {2, 3}, {141, 7910}, {148, 7767}, {325, 7756}, {543, 7873}, {698, 3630}, {2549, 7762}, {3849, 7765}, {3933, 7898}, {5254, 6179}, {5305, 14712}, {6390, 7885}, {6781, 7861}, {7745, 7847}, {7748, 7750}, {7761, 17130}, {7789, 7911}, {7792, 7872}, {7812, 9607}, {7823, 15048}, {7864, 18907}, {7939, 20094}, {14929, 20081}
X(19696) lies on these lines: {2, 3}, {99, 7843}, {316, 7863}, {698, 6144}, {1975, 7946}, {3329, 7756}, {3734, 7936}, {3972, 7902}, {4366, 10483}, {7737, 7839}, {7747, 7783}, {7748, 7856}, {7758, 7823}, {7762, 20094}, {7802, 7854}, {7816, 7885}, {7842, 7931}, {11057, 17130}, {14712, 17129}, {15031, 15513}
X(19697) lies on these lines: {2, 3}, {83, 6390}, {597, 7781}, {698, 6329}, {3589, 7816}, {3629, 5039}, {3734, 5305}, {3972, 7767}, {5306, 17130}, {7745, 7820}, {7764, 7789}, {7795, 18907}, {7863, 9300}
X(19697) = complement of X(8357)
X(19697) = orthocentroidal-circle-inverse of X(33241)
X(19697) = {X(2),X(4)}-harmonic conjugate of X(33241)
X(19698) lies on these lines: {2, 3}
X(19699) lies on these lines: {2, 3}, {698, 14829}
X(19700) lies on these lines: {2, 3}
X(19701) lies on these lines: {1, 2049}, {2, 6}, {3, 10478}, {4, 19753}, {21, 19759}, {55, 11358}, {56, 226}, {63, 4670}, {142, 11347}, {223, 7532}, {278, 5136}, {306, 17303}, {312, 16826}, {321, 16777}, {354, 10477}, {386, 16458}, {404, 19760}, {442, 19755}, {443, 19764}, {474, 19763}, {964, 3616}, {980, 16700}, {1001, 1011}, {1010, 19765}, {1100, 5271}, {1255, 4671}, {1333, 16350}, {1621, 11322}, {1724, 3624}, {1730, 5437}, {1848, 4185}, {1889, 3838}, {1962, 5695}, {1985, 3816}, {1999, 17394}, {2274, 3720}, {3175, 3247}, {3187, 16884}, {3286, 16343}, {3305, 4698}, {3576, 10888}, {3666, 10436}, {3715, 3842}, {3739, 5256}, {3782, 17321}, {3923, 10180}, {3995, 16672}, {4042, 4649}, {4187, 19754}, {4208, 19752}, {4252, 16342}, {4255, 16454}, {4256, 19290}, {4257, 16351}, {4361, 17011}, {4364, 5905}, {4413, 6685}, {4472, 19822}, {4653, 16394}, {4657, 5249}, {4758, 5745}, {4860, 6682}, {5283, 16831}, {5814, 19857}, {7308, 16552}, {9534, 14007}, {10449, 19280}, {11374, 16843}, {13615, 17188}, {13740, 19768}, {14005, 19767}, {17045, 19785}, {17118, 17147}, {17184, 17325}, {17255, 17483}, {17369, 17776}, {17395, 19789}, {17396, 19796}, {17397, 19281}
X(19702) lies on these lines: {2, 3}, {7792, 17130}
X(19703) lies on these lines: {2, 3}
X(19704) lies on these lines: {2, 3}, {35, 11194}, {36, 4428}, {392, 10178}, {519, 5217}, {551, 5204}, {956, 4421}, {993, 4745}, {3241, 5303}, {3829, 4302}, {3929, 5440}, {4265, 15534}, {4669, 5267}, {5275, 8588}, {5276, 15655}
X(19705) lies on these lines: {2, 3}, {36, 4421}, {519, 5204}, {551, 5217}, {956, 4669}, {3928, 5440}, {4428, 5010}, {4677, 5288}, {5096, 15534}, {5275, 8589}, {16192, 17614}
X(19706) lies on these lines: {2, 3}, {57, 4677}, {519, 5708}, {529, 9709}, {4260, 15534}, {9776, 9802}
X(19707) lies on these lines: {2, 3}
X(19708) lies on these lines: {2, 3}, {36, 10385}, {98, 15300}, {165, 7967}, {182, 13482}, {491, 13678}, {492, 13798}, {541, 15051}, {551, 6361}, {574, 1285}, {590, 14241}, {615, 14226}, {944, 4677}, {962, 3653}, {1056, 5010}, {1058, 7280}, {1350, 8584}, {1384, 14482}, {1992, 3098}, {2482, 9862}, {3241, 3579}, {3618, 19924}, {3654, 5731}, {3655, 12245}, {3656, 9778}, {3748, 18490}, {4293, 4995}, {4294, 5298}, {4297, 4745}, {4669, 5657}, {5206, 5368}, {5210, 5306}, {5304, 15655}, {5346, 7738}, {5485, 13468}, {5590, 13691}, {5591, 13810}, {5642, 12244}, {5650, 11455}, {6055, 13172}, {6174, 12248}, {6200, 19054}, {6337, 7811}, {6396, 19053}, {6409, 7581}, {6410, 7582}, {6412, 9541}, {6418, 9543}, {6419, 9693}, {6451, 7585}, {6452, 7586}, {6776, 15533}, {7735, 8588}, {7736, 8589}, {7987, 10595}, {7998, 14855}, {8164, 15326}, {8182, 9741}, {8591, 12042}, {9143, 12041}, {9167, 10722}, {9734, 12156}, {11055, 12251}, {11178, 14927}, {11179, 14810}, {11204, 11206}, {11257, 14711}, {11592, 18439}, {12112, 17811}, {12117, 14651}, {12254, 15605}, {13348, 14831}, {14458, 15810}, {14677, 15042}, {14912, 15534}, {15023, 16534}, {16226, 17704}
X(19708) = midpoint of X(376) and X(631)
X(19708) = anticomplement of X(19709)
X(19708) = {X(2),X(3)}-harmonic conjugate of X(15698)
As a point on the Euler line, X(19709) has Shinagawa coefficients (7,9).
X(19709) lies on these lines: {2, 3}, {6, 18362}, {13, 16961}, {14, 16960}, {115, 18584}, {399, 5422}, {485, 6500}, {486, 6501}, {519, 18493}, {551, 18525}, {568, 14845}, {590, 1328}, {597, 18440}, {599, 19130}, {615, 1327}, {946, 4745}, {1131, 13993}, {1132, 13925}, {1159, 17605}, {1351, 11178}, {1352, 8584}, {1384, 14537}, {1482, 4677}, {1992, 18358}, {3095, 14711}, {3241, 18357}, {3579, 19876}, {3582, 10895}, {3584, 10896}, {3614, 9669}, {3654, 10175}, {3655, 19925}, {3656, 3817}, {3679, 8148}, {3763, 19924}, {3828, 12699}, {4428, 18524}, {4870, 10826}, {4995, 9668}, {5024, 7603}, {5093, 5476}, {5298, 9655}, {5306, 15484}, {5339, 16962}, {5340, 16963}, {5346, 7753}, {5461, 6033}, {5587, 10247}, {5640, 15060}, {5642, 12902}, {5644, 5655}, {5663, 11451}, {5889, 18874}, {5943, 18435}, {6199, 6565}, {6321, 15300}, {6395, 6564}, {6445, 8253}, {6446, 8252}, {6459, 6474}, {6460, 6475}, {6472, 9540}, {6473, 13935}, {6561, 9690}, {6688, 16194}, {6767, 7951}, {7173, 9654}, {7373, 7741}, {7585, 14226}, {7586, 14241}, {7617, 8667}, {7699, 9777}, {7703, 18551}, {7844, 14535}, {7988, 10246}, {8176, 9766}, {8556, 9301}, {9140, 12308}, {9143, 11801}, {9166, 12188}, {9169, 18346}, {9781, 14128}, {9880, 15561}, {10095, 15056}, {10591, 15170}, {10620, 15088}, {11017, 12111}, {11055, 13108}, {11180, 18583}, {11184, 18546}, {11402, 14644}, {11459, 13321}, {11465, 12046}, {11645, 12017}, {12355, 14639}, {12702, 19875}, {12816, 16967}, {12817, 16966}, {13363, 15305}, {13691, 18511}, {13810, 18509}, {14627, 17814}, {14830, 14971}, {15026, 15058}, {15037, 18451}, {15038, 15068}, {15362, 17810}, {16644, 16809}, {16645, 16808}, {18481, 19883}, {18489, 18928}, {18510, 18538}, {18512, 18762}
X(19709) = complement of X(19708)
X(19709) = anticomplement of X(15713)
X(19710) lies on these lines: {2, 3}, {553, 15935}, {3058, 4316}, {3579, 4745}, {4299, 15170}, {4302, 8162}, {4324, 5434}, {5306, 6781}, {7737, 11742}, {8584, 19924}, {8725, 12156}, {10645, 12816}, {10646, 12817}, {11057, 14929}
X(19711) lies on these lines: {2, 3}, {3653, 11531}, {4669, 13624}, {6429, 19116}, {6430, 19117}, {6484, 13966}, {6485, 8981}, {7581, 10138}, {7582, 10137}, {15048, 15602}
X(19712) lies on the curves {{A,B,C,X(4),X(5)}}, K420b, K1053b, Q111, Q124, and these lines:
{5,302},{53,396},{617,1263},{3181,11143}
X(19712) = isotomic conjugate of X(627)
X(19712) = X(17)-cross conjugate of X(2)
X(19712) = X(31)-isoconjugate of X(627)
X(19712) = barycentric product X(76)*X(3489)
X(19712) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 627}, {396, 15802}, {3489, 6}, {13483, 8495}
X(19713) lies on the curves {{A,B,C,X(4),X(5)}}, K420a, K1053a, Q111, Q124, and these lines: {5,303},{53,395},{616,1263},{3180,11144}
X(19713) = isotomic conjugate of X(628)
X(19713) = X(18)-cross conjugate of X(2)
X(19713) = X(31)-isoconjugate of X(628)
X(19713) = barycentric product X(76)*X(3490)
X(19713) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 628}, {395, 15778}, {3490, 6}, {13484, 8496}
X(19714) lies on these lines: {1, 1011}, {2, 6}, {42, 5687}, {58, 16343}, {306, 17750}, {405, 1468}, {964, 10453}, {969, 2339}, {3136, 19755}, {4184, 19759}, {4191, 19763}, {4192, 5707}, {4210, 19760}, {4340, 6817}, {4658, 16405}, {5283, 5287}, {5710, 11322}, {5902, 18202}, {13588, 19767}, {16057, 19770}, {16552, 17022}, {17027, 19281}
X(19715) lies on these lines: {1, 11358}, {2, 6}, {56, 1011}, {58, 16345}, {2049, 3741}, {4191, 19760}, {4199, 19753}, {4203, 19757}, {4252, 16343}, {5283, 17022}, {13588, 19765}, {16056, 19764}, {16058, 19762}, {16059, 19763}, {19281, 19803}
X(19716) lies on these lines: {1, 3998}, {2, 6}, {21, 19753}, {57, 16368}, {58, 16346}, {63, 405}, {72, 16843}, {142, 1751}, {379, 9776}, {404, 19764}, {411, 19769}, {938, 964}, {1125, 16471}, {1407, 1446}, {1730, 16783}, {2049, 6734}, {3306, 11347}, {4260, 16353}, {5138, 16352}, {5249, 7522}, {5320, 19309}, {5439, 7535}, {5932, 17074}, {6904, 19752}, {11344, 19762}, {12649, 19822}, {19281, 19788}
X(19716) = isotomic conjugate of polar conjugate of X(37377)
X(19717) lies on these lines: {1, 3159}, {2, 6}, {8, 1126}, {58, 16347}, {145, 964}, {226, 1404}, {261, 1171}, {321, 1100}, {386, 19284}, {405, 3622}, {497, 11330}, {894, 17011}, {1449, 3187}, {1724, 3616}, {1962, 4672}, {2049, 3617}, {2345, 20017}, {3210, 17013}, {3219, 17120}, {3952, 5311}, {3969, 17369}, {4080, 9456}, {4188, 19763}, {4189, 19762}, {4359, 4670}, {4393, 17143}, {4427, 17592}, {4430, 10477}, {4649, 17135}, {4663, 4981}, {4852, 4980}, {5141, 19755}, {5154, 19754}, {5256, 17495}, {5263, 20011}, {5271, 16667}, {5905, 16783}, {6872, 19783}, {8049, 14621}, {9534, 17589}, {9965, 16368}, {11115, 19767}, {16552, 16826}, {16707, 18138}, {17014, 19281}, {17017, 17140}, {17023, 17184}, {17146, 17598}, {17154, 17599}, {17302, 17483}, {17539, 19765}, {17548, 19759}, {17676, 19766}, {19825, 20043}
X(19717) = {X(2),X(6)}-harmonic conjugate of X(19742)
X(19718) lies on these lines: {2, 6}, {58, 16348}, {405, 3333}, {964, 10580}, {1763, 5439}, {2049, 4847}, {7411, 19769}, {11347, 16783}, {13615, 19753}, {19281, 19790}
X(19719) lies on these lines: {1, 19281}, {2, 6}, {58, 16349}, {405, 16826}, {964, 17316}, {1011, 17032}, {1724, 16831}, {2049, 3661}, {4649, 5271}, {5249, 19834}, {5308, 11342}, {6645, 11320}, {11329, 19763}, {14621, 16368}, {16367, 19762}, {19308, 19760}, {19752, 19783}
X(19720) lies on these lines: {2, 6}, {3, 19755}, {4, 19759}, {5, 19762}, {11, 1011}, {140, 19763}, {405, 499}, {631, 19760}, {1656, 19754}, {1746, 4268}, {2245, 10478}, {2476, 19769}, {2886, 11358}, {5124, 19645}, {5433, 13738}, {6989, 19764}, {10200, 16844}, {11322, 11680}, {19281, 19794}
X(19721) lies on these lines: {2, 6}, {3, 19754}, {4, 19760}, {5, 19763}, {12, 13738}, {37, 6708}, {55, 1985}, {140, 19762}, {405, 498}, {631, 19759}, {1011, 5432}, {1030, 19645}, {1656, 19755}, {1730, 5219}, {1746, 2278}, {3035, 11358}, {4271, 10478}, {6824, 19764}, {6884, 19752}, {10198, 16844}, {17566, 19769}, {19281, 19795}
X(19722) lies on these lines: {1, 3175}, {2, 6}, {58, 16351}, {321, 16884}, {386, 19290}, {405, 551}, {519, 2334}, {964, 3241}, {1011, 4428}, {1429, 4654}, {1724, 11357}, {2049, 3679}, {3058, 11355}, {3782, 11352}, {4011, 5625}, {4234, 19765}, {4255, 19336}, {4363, 17011}, {4470, 20043}, {4670, 5256}, {4795, 16368}, {5271, 16666}, {5905, 17045}, {7478, 19771}, {13587, 19760}, {16370, 19762}, {16371, 19763}, {16405, 18185}, {17323, 17483}, {17530, 19755}, {17533, 19754}, {17549, 19759}, {19281, 19796}
X(19723) lies on these lines: {1, 11357}, {2, 6}, {8, 11346}, {9, 3175}, {44, 5271}, {45, 3187}, {55, 4685}, {58, 19290}, {63, 17348}, {238, 4042}, {321, 16885}, {386, 16351}, {405, 519}, {545, 19819}, {1011, 4421}, {1714, 16052}, {1724, 3679}, {1730, 3928}, {1751, 4052}, {1985, 3829}, {1999, 17335}, {2049, 19875}, {3052, 4651}, {3219, 4361}, {3715, 4096}, {3749, 4113}, {3929, 16552}, {4001, 17278}, {4234, 9534}, {4252, 19336}, {4384, 4641}, {4974, 17599}, {5283, 16834}, {5294, 17275}, {5711, 19870}, {7263, 20078}, {11194, 13738}, {11351, 16816}, {13587, 19759}, {15254, 17156}, {16370, 19763}, {16371, 19762}, {17331, 19786}, {17332, 19785}, {17333, 19796}, {17334, 19789}, {17362, 17776}, {17530, 19754}, {17533, 19755}, {17549, 19760}, {17553, 19767}, {19281, 19797}
X(19724) lies on these lines: {2, 6}, {22, 19759}, {25, 19756}, {58, 16352}, {386, 16353}, {405, 614}, {427, 19755}, {1724, 3338}, {2221, 10436}, {2999, 16783}, {3187, 16781}, {5271, 16502}, {7484, 19763}, {7485, 19760}, {19281, 19798}, {19753, 19757}
X(19725) lies on these lines: {2, 6}, {22, 19760}, {25, 19763}, {58, 16353}, {386, 16352}, {405, 612}, {427, 19754}, {980, 16438}, {1724, 5268}, {2355, 17594}, {4224, 19757}, {4228, 19765}, {5256, 16583}, {5283, 16368}, {5337, 16439}, {7484, 19762}, {7485, 19759}, {11347, 15487}, {16783, 17022}, {19281, 19799}
X(19726) lies on these lines: {2, 6}, {36, 1011}, {58, 16355}, {3720, 11358}, {4257, 16343}, {4653, 16395}, {5253, 11322}, {5271, 16971}, {16373, 19762}, {16405, 19757}, {19281, 19801}
X(19727) lies on these lines: {2, 6}, {3, 19753}, {57, 405}, {58, 16416}, {142, 7522}, {474, 19764}, {942, 16843}, {1210, 2049}, {1396, 7498}, {1413, 7532}, {3306, 16368}, {3624, 16471}, {3666, 17054}, {3812, 10319}, {3998, 16777}, {4252, 16346}, {5437, 11347}, {11344, 19759}, {16293, 19762}, {16410, 19763}, {17580, 19752}, {19281, 19802}
X(19728) lies on these lines: {1, 16843}, {2, 6}, {57, 1724}, {58, 19285}, {345, 11342}, {386, 19523}, {405, 3666}, {1396, 7521}, {1722, 10319}, {1751, 3008}, {2221, 3739}, {3752, 16368}, {5711, 19857}, {7523, 19764}, {11320, 17490}, {11337, 19759}, {11347, 16610}, {11375, 16471}, {19281, 19804}, {19753, 19765}
X(19729) lies on these lines: {2, 6}, {38, 405}, {58, 16356}, {291, 1011}, {1724, 18398}, {3145, 19762}, {19281, 19805}
X(19730) lies on these lines: {2, 6}, {55, 2654}, {57, 5283}, {58, 19282}, {171, 405}, {404, 19757}, {750, 1011}, {978, 4038}, {1730, 17022}, {2049, 3831}, {4252, 19283}, {5156, 16345}, {5268, 10477}, {5711, 16844}, {11358, 17122}, {19281, 19806}, {19753, 19761}
X(19731) lies on these lines: {1, 4245}, {2, 6}, {58, 16357}, {405, 595}, {859, 19763}, {1724, 5711}, {1730, 3666}, {4216, 19757}, {4641, 16552}, {5132, 10458}, {16374, 19762}, {19246, 19753}, {19263, 19761}, {19281, 19807}
X(19732) lies on these lines: {1, 4042}, {2, 6}, {3, 1746}, {9, 1730}, {10, 55}, {21, 19760}, {37, 5271}, {45, 321}, {57, 4059}, {58, 16458}, {63, 3739}, {171, 1698}, {210, 10477}, {306, 17275}, {312, 17260}, {379, 5273}, {404, 19759}, {442, 19754}, {474, 19762}, {594, 17776}, {958, 13738}, {964, 9780}, {968, 3696}, {1011, 1376}, {1215, 3715}, {1407, 17077}, {1453, 19859}, {1714, 4205}, {1861, 11323}, {1889, 2355}, {1936, 5705}, {1985, 2886}, {1999, 4687}, {3175, 3731}, {3187, 16777}, {3216, 19273}, {3219, 4363}, {3242, 4981}, {3550, 11354}, {3617, 3996}, {3624, 4038}, {3666, 4384}, {3679, 3750}, {3741, 4423}, {3782, 17257}, {3842, 4362}, {3948, 19792}, {3965, 11679}, {3995, 16675}, {4001, 4675}, {4104, 17718}, {4185, 5155}, {4187, 19755}, {4245, 9708}, {4252, 16454}, {4255, 16342}, {4256, 16351}, {4257, 19290}, {4261, 16350}, {4267, 19283}, {4364, 19785}, {4413, 11358}, {4641, 10436}, {4643, 5249}, {4698, 5287}, {5132, 16343}, {5256, 17348}, {5260, 5793}, {5294, 17303}, {5347, 19310}, {5710, 19853}, {5711, 16828}, {5745, 11347}, {5788, 13731}, {5791, 7535}, {5816, 19542}, {5905, 17332}, {6857, 19764}, {7308, 18229}, {7521, 19756}, {9458, 16500}, {9534, 11110}, {10472, 17185}, {10479, 11108}, {13741, 19770}, {15569, 17156}, {16349, 18755}, {16466, 19858}, {16471, 19854}, {16783, 17284}, {16815, 17595}, {16823, 17597}, {16825, 17599}, {16845, 19753}, {17119, 17147}, {17184, 17253}, {17246, 19789}, {17247, 19796}, {17248, 19786}, {17531, 19769}, {17555, 18679}, {17557, 19767}, {17558, 19752}, {17698, 19761}, {19281, 19808}
X(19733) lies on these lines: {2, 6}, {19281, 19809}, {19760, 19770}
X(19734) lies on these lines: {1, 228}, {2, 6}, {3, 10458}, {31, 405}, {58, 19283}, {63, 5283}, {171, 1011}, {612, 10477}, {750, 11358}, {1621, 5710}, {2295, 17776}, {3142, 19754}, {4225, 19760}, {5156, 16343}, {5294, 17750}, {5707, 13731}, {10457, 19533}, {16466, 16844}, {18169, 19762}, {19281, 19810}
X(19735) lies on these lines: {2, 6}, {405, 3915}, {474, 17187}, {1011, 3550}, {2308, 5711}, {4191, 18169}, {4279, 16343}, {5260, 5710}, {7419, 19765}, {11357, 16483}, {19281, 19811}, {19757, 19763}
X(19736) lies on these lines: {2, 6}, {867, 19754}, {2049, 9458}, {13589, 19760}
X(19737) lies on these lines: {2, 6}, {199, 19759}, {1616, 17150}, {19281, 19813}
X(19738) lies on these lines: {1, 11346}, {2, 6}, {321, 1449}, {386, 19336}, {519, 964}, {551, 1724}, {1100, 3175}, {3187, 16666}, {3241, 11354}, {3616, 11357}, {3758, 17011}, {3969, 5749}, {3995, 16884}, {4096, 5311}, {4234, 19767}, {4421, 11322}, {4658, 5192}, {4980, 16834}, {13587, 19763}, {16371, 19769}, {16783, 17781}, {17369, 20017}, {17380, 17483}, {17549, 19762}, {17579, 19752}, {19281, 19819}
X(19739) lies on these lines: {2, 6}, {58, 19289}, {386, 19331}, {405, 3636}, {964, 20050}, {3840, 14969}, {5271, 16668}, {19281, 19820}, {19535, 19762}, {19537, 19763}
X(19740) lies on these lines: {2, 6}, {58, 19333}, {106, 835}, {145, 2049}, {321, 3723}, {551, 4054}, {964, 3622}, {1724, 5550}, {3247, 3995}, {4189, 19769}, {4255, 19337}, {4256, 19284}, {4257, 16347}, {4699, 17013}, {6539, 20017}, {10436, 17495}, {16865, 19762}, {17011, 17117}, {17116, 17147}, {17572, 19763}, {17589, 19767}, {19281, 19823}
X(19741) lies on these lines: {2, 6}, {386, 19337}, {964, 3623}, {2049, 4678}, {3723, 3995}, {4670, 17495}, {17011, 17116}, {19281, 19824}
X(19742) lies on these lines: {2, 6}, {8, 595}, {9, 3187}, {10, 2308}, {31, 4651}, {38, 4974}, {44, 321}, {55, 19998}, {58, 19284}, {63, 17495}, {144, 19789}, {145, 405}, {238, 17135}, {239, 3219}, {329, 1751}, {379, 9965}, {386, 16347}, {756, 3791}, {902, 4685}, {958, 20040}, {964, 3617}, {984, 17150}, {1386, 4981}, {1621, 20011}, {1730, 3218}, {1743, 5271}, {1757, 17165}, {1778, 17587}, {2003, 17077}, {2345, 6539}, {2550, 20064}, {3008, 4001}, {3175, 15492}, {3216, 17187}, {3295, 20051}, {3434, 11330}, {3681, 20045}, {3683, 3896}, {3686, 5294}, {3891, 5220}, {3923, 17163}, {3952, 4362}, {3969, 17362}, {4188, 19762}, {4189, 19763}, {4359, 4641}, {4393, 5283}, {4416, 17184}, {4427, 7262}, {4454, 19826}, {4661, 10477}, {4720, 13735}, {4980, 17351}, {5141, 19754}, {5154, 19755}, {5686, 20020}, {5839, 17776}, {9534, 11115}, {16783, 17316}, {16825, 17140}, {16865, 20018}, {16948, 19770}, {17011, 17121}, {17019, 17260}, {17314, 20046}, {17483, 20072}, {17491, 17889}, {17548, 19760}, {17572, 19769}, {17576, 19752}, {17588, 19767}, {19281, 19825}
X(19742) = anticomplement of X(18139)
X(19742) = {X(2),X(6)}-harmonic conjugate of X(19717)
X(19743) lies on these lines: {2, 6}, {321, 16666}, {964, 3621}, {1051, 4418}, {1100, 3995}, {1126, 20051}, {1724, 3622}, {3187, 16667}, {3623, 11319}, {3758, 17147}, {5749, 20017}, {6539, 17362}, {17011, 17120}, {17017, 17154}, {17539, 19767}, {17548, 19762}, {19281, 19826}
X() lies on these lines: {2, 6}, {10, 16844}, {35, 405}, {58, 16456}, {321, 16675}, {386, 16457}, {474, 19759}, {964, 19877}, {1011, 4413}, {1104, 19859}, {1191, 19858}, {1714, 17514}, {1724, 17122}, {1730, 7308}, {1985, 3925}, {2049, 3634}, {3175, 16677}, {3740, 10477}, {3752, 5283}, {3772, 5257}, {3828, 11357}, {4252, 16458}, {4257, 19332}, {4265, 16353}, {4267, 19282}, {4415, 5296}, {4698, 11679}, {5096, 16352}, {5132, 16345}, {5249, 17253}, {5271, 16777}, {5437, 16552}, {6675, 19764}, {7522, 8804}, {8728, 19754}, {9342, 11322}, {11108, 19763}, {16408, 19762}, {17527, 19755}, {17535, 19769}, {17557, 19765}, {19281, 19827}
X(19745) lies on these lines: {2, 6}, {2049, 4668}, {19281, 19828}
X(19746) lies on these lines: {2, 6}, {405, 15808}, {2049, 3632}, {4256, 19331}, {4257, 19289}, {17574, 19759}, {19281, 19829}, {19526, 19762}
X(19747) lies on these lines: {2, 6}, {964, 20057}, {2049, 3626}, {4252, 19289}, {4255, 19331}, {17011, 17118}, {17563, 19764}, {17571, 19762}, {17573, 19763}, {19281, 19830}, {19535, 19759}, {19537, 19760}
X(19748) lies on these lines: {1, 4942}, {2, 6}, {2049, 4691}, {19281, 19831}
X(19749) lies on these lines: {2, 6}, {58, 19272}, {321, 16674}, {405, 5204}, {1011, 8167}, {2049, 3624}, {3286, 16355}, {4252, 19334}, {4256, 16458}, {4423, 11358}, {5047, 19759}, {14007, 19765}, {16842, 19762}, {16862, 19763}, {17529, 19755}, {17531, 19760}, {17536, 19769}, {17575, 19754}, {19281, 19832}
X(19750) lies on these lines: {2, 6}, {58, 19331}, {386, 19289}, {405, 3244}, {1724, 3632}, {3175, 3973}, {3187, 16885}, {3715, 3791}, {4042, 16468}, {4395, 20078}, {4706, 16570}, {4969, 17776}, {5271, 16669}, {19281, 19833}, {19535, 19763}, {19537, 19762}
X(19751) lies on these lines: {2, 6}, {405, 3626}, {3187, 16674}, {4042, 16484}, {4256, 19289}, {4257, 19331}, {5271, 16814}, {9332, 19872}, {14969, 19862}, {17574, 19760}, {19281, 19837}, {19526, 19763}
X(19752) lies on these lines: {1, 379}, {2, 19753}, {6, 20}, {8, 16368}, {21, 5278}, {27, 19767}, {377, 19684}, {386, 19645}, {405, 4313}, {938, 11347}, {1004, 19769}, {1724, 4304}, {1751, 3601}, {3488, 7535}, {4197, 19755}, {4208, 19701}, {4294, 16471}, {5703, 7522}, {6884, 19721}, {6904, 19716}, {7411, 19762}, {10883, 19754}, {17558, 19732}, {17576, 19742}, {17579, 19738}, {17580, 19727}, {19719, 19783}
X(19753) lies on these lines: {1, 6}, {2, 19752}, {3, 19727}, {4, 19701}, {21, 19716}, {284, 16416}, {452, 19684}, {950, 2049}, {1005, 19769}, {1125, 7522}, {1751, 16844}, {3419, 19857}, {4199, 19715}, {4255, 19523}, {9534, 16053}, {11323, 11363}, {13615, 19718}, {14022, 19754}, {16845, 19732}, {19246, 19731}, {19724, 19757}, {19728, 19765}, {19730, 19761}
X(19754) lies on these lines: {1, 1985}, {2, 19762}, {3, 19721}, {4, 19763}, {5, 6}, {12, 405}, {30, 19760}, {140, 19759}, {226, 19366}, {427, 19725}, {442, 19732}, {498, 1011}, {867, 19736}, {964, 11681}, {1329, 2049}, {1478, 13738}, {1656, 19720}, {1714, 3136}, {1724, 7951}, {1730, 9612}, {2476, 2651}, {3142, 19734}, {3814, 5061}, {4187, 19701}, {4193, 19684}, {4245, 9654}, {5141, 19742}, {5142, 14873}, {5154, 19717}, {5179, 5283}, {5705, 16552}, {7532, 15844}, {8727, 19764}, {8728, 19744}, {9534, 14009}, {10883, 19752}, {14008, 19767}, {14022, 19753}, {17530, 19723}, {17533, 19722}, {17575, 19749}, {19281, 19839}
X(19755) lies on these lines: {2, 19763}, {3, 19720}, {4, 19762}, {5, 6}, {10, 10480}, {11, 405}, {30, 19759}, {140, 19760}, {427, 19724}, {442, 19701}, {499, 13738}, {964, 11680}, {1011, 1479}, {1656, 19721}, {1713, 5715}, {1714, 3142}, {1724, 1985}, {2049, 2886}, {2475, 19769}, {2476, 19684}, {3136, 19714}, {3816, 16844}, {3829, 11354}, {4187, 19732}, {4193, 5278}, {4197, 19752}, {5141, 19717}, {5154, 19742}, {8728, 19764}, {9534, 14011}, {10477, 10916}, {10478, 10974}, {17527, 19744}, {17529, 19749}, {17530, 19722}, {17533, 19723}
X(19756) lies on these lines: {1, 1824}, {4, 19701}, {6, 28}, {25, 19724}, {1891, 2049}, {4198, 19684}, {4206, 19757}, {5130, 19857}, {7466, 19769}, {7490, 19764}, {7521, 19732}, {9534, 14013}, {14014, 19767}, {14017, 19759}, {14018, 17056}
X(19757) lies on these lines:
X(19758) lies on these lines: {1, 3}, {2, 19768}, {6, 13723}, {39, 405}, {194, 19312}, {274, 19311}, {386, 11343}, {965, 984}, {1008, 1975}, {1009, 5013}, {1434, 4340}, {1724, 9605}, {3314, 4201}, {3926, 13725}, {4195, 7783}, {4310, 5736}, {5275, 19329}, {5283, 19309}, {7795, 13728}, {8721, 13442}, {9534, 16060}, {14001, 19766}, {16349, 16823}
X(19759) lies on these lines: {3, 6}, {4, 19720}, {21, 19701}, {22, 19724}, {30, 19755}, {36, 405}, {56, 1011}, {140, 19754}, {199, 19737}, {377, 15447}, {404, 19732}, {474, 19744}, {631, 19721}, {940, 16452}, {958, 11358}, {960, 16778}, {993, 2049}, {1191, 16678}, {1724, 7280}, {1985, 5433}, {2635, 5204}, {2975, 11322}, {3763, 16298}, {4184, 19714}, {4188, 5278}, {4189, 19684}, {4383, 16451}, {5047, 19749}, {5438, 16552}, {7485, 19725}, {11337, 19728}, {11344, 19727}, {13587, 19723}, {13726, 17056}, {14017, 19756}, {15668, 16289}, {16294, 17811}, {16295, 17825}, {17548, 19717}, {17549, 19722}, {17574, 19746}, {19281, 19841}, {19535, 19747}
X(19760) lies on these lines: {3, 6}, {4, 19721}, {21, 19732}, {22, 19725}, {30, 19754}, {35, 405}, {55, 2654}, {140, 19755}, {404, 19701}, {631, 19720}, {899, 1011}, {910, 5283}, {940, 16451}, {1724, 5010}, {1730, 3601}, {1985, 6284}, {3763, 16299}, {4188, 19684}, {4189, 5278}, {4191, 19715}, {4210, 19714}, {4216, 19731}, {4225, 19734}, {4383, 16452}, {4646, 10434}, {5248, 16844}, {7485, 19724}, {13587, 19722}, {13589, 19736}, {16289, 17259}, {16294, 17825}, {16295, 17811}, {17531, 19749}, {17548, 19742}, {17549, 19723}, {17574, 19751}, {19281, 19842}, {19308, 19719}, {19537, 19747}, {19733, 19770}
X(19761) lies on these lines: {1, 3}, {6, 1009}, {32, 405}, {183, 1008}, {238, 965}, {384, 19768}, {385, 4195}, {1001, 5301}, {1010, 16992}, {1104, 4386}, {1453, 3684}, {1975, 11104}, {3053, 13723}, {3694, 3751}, {3785, 13725}, {4026, 15668}, {4201, 7904}, {4307, 5736}, {4340, 14828}, {5277, 19309}, {7379, 9863}, {7793, 19312}, {7800, 13728}, {9534, 16061}, {16043, 19766}, {16349, 16830}, {17698, 19732}, {19263, 19731}, {19730, 19753}
X(19762) lies on these lines: {1, 1011}, {2, 19754}, {3, 6}, {4, 19755}, {5, 19720}, {8, 11322}, {10, 11358}, {21, 19684}, {25, 19724}, {36, 978}, {56, 226}, {72, 2352}, {81, 16452}, {86, 16289}, {140, 19721}, {141, 16298}, {184, 1780}, {185, 1779}, {394, 16294}, {404, 5278}, {474, 19732}, {499, 1985}, {672, 3682}, {851, 1714}, {936, 16552}, {940, 16287}, {958, 2049}, {964, 2975}, {975, 5283}, {1397, 7066}, {1402, 12514}, {1490, 1713}, {1730, 15803}, {1838, 4185}, {2223, 3811}, {3008, 11347}, {3145, 19729}, {3149, 13478}, {3216, 4191}, {3589, 16299}, {3911, 14058}, {3941, 5266}, {4184, 19767}, {4188, 19742}, {4189, 19717}, {4192, 5292}, {4203, 10449}, {4216, 16948}, {4383, 16453}, {5712, 13726}, {5718, 16455}, {7411, 19752}, {7484, 19725}, {7742, 16471}, {9534, 13588}, {10479, 16405}, {10601, 16295}, {11194, 11354}, {11323, 11399}, {11344, 19716}, {13615, 19718}, {15668, 16288}, {16058, 19715}, {16059, 17749}, {16290, 17056}, {16293, 19727}, {16367, 19719}, {16368, 17023}, {16370, 19722}, {16371, 19723}, {16373, 19726}, {16374, 19731}, {16408, 19744}, {16466, 16678}, {16842, 19749}, {16848, 17398}, {16865, 19740}, {17030, 19281}, {17524, 19765}, {17548, 19743}, {17549, 19738}, {17571, 19747}, {18169, 19734}, {19526, 19746}, {19535, 19739}, {19537, 19750}
X(19763) lies on these lines: {1, 228}, {2, 19755}, {3, 6}, {4, 19754}, {5, 19721}, {10, 55}, {21, 5278}, {25, 19725}, {35, 43}, {37, 9895}, {81, 16451}, {100, 964}, {140, 19720}, {141, 16299}, {169, 5283}, {380, 1713}, {394, 16295}, {404, 19684}, {411, 9535}, {469, 14873}, {474, 19701}, {859, 19731}, {940, 16453}, {1001, 16844}, {1036, 1794}, {1043, 19260}, {1213, 16848}, {1259, 3687}, {1376, 2049}, {1479, 1985}, {1621, 19853}, {1682, 6056}, {1780, 5320}, {2051, 3149}, {2269, 3682}, {2276, 4456}, {2915, 9571}, {3185, 3931}, {3295, 4245}, {3589, 16298}, {3811, 10477}, {4185, 5530}, {4188, 19717}, {4189, 19742}, {4191, 19714}, {4225, 19767}, {4383, 16287}, {4421, 11354}, {4428, 11357}, {5266, 15624}, {5292, 13731}, {5706, 7420}, {6685, 11358}, {7428, 19770}, {7484, 19724}, {7713, 17594}, {9548, 10902}, {9549, 11012}, {10601, 16294}, {11108, 19744}, {11329, 19719}, {11330, 20066}, {13587, 19738}, {16059, 19715}, {16288, 17259}, {16289, 17277}, {16370, 19723}, {16371, 19722}, {16410, 19727}, {16415, 17056}, {16862, 19749}, {17572, 19740}, {17573, 19747}, {19281, 19845}, {19526, 19751}, {19535, 19750}, {19537, 19739}, {19735, 19757}
X(19764) lies on these lines: {1, 3198}, {2, 19752}, {3, 6}, {28, 19765}, {35, 16471}, {55, 3682}, {78, 16368}, {379, 5703}, {404, 19716}, {405, 936}, {443, 19701}, {474, 19727}, {950, 7532}, {975, 7535}, {1817, 19767}, {1819, 11344}, {4224, 19725}, {4383, 13726}, {5718, 14018}, {6675, 19744}, {6824, 19721}, {6857, 19732}, {6904, 19684}, {6989, 19720}, {7490, 19756}, {7522, 13411}, {7523, 19728}, {8727, 19754}, {8728, 19755}, {16056, 19715}, {17563, 19747}
X(19765) lies on these lines: {1, 3}, {2, 1043}, {4, 5718}, {6, 21}, {8, 5737}, {20, 5712}, {28, 19764}, {37, 78}, {42, 958}, {43, 16345}, {45, 3876}, {58, 16370}, {73, 6180}, {81, 4189}, {145, 1150}, {200, 16348}, {239, 16349}, {306, 16350}, {333, 20018}, {376, 4340}, {377, 17056}, {386, 405}, {387, 6857}, {474, 4256}, {519, 16351}, {551, 19290}, {581, 1012}, {612, 16352}, {614, 4719}, {859, 19731}, {869, 16354}, {899, 16355}, {936, 16416}, {960, 968}, {975, 5440}, {976, 16356}, {978, 4423}, {995, 16357}, {997, 6051}, {1001, 1193}, {1010, 19701}, {1026, 16358}, {1036, 1486}, {1064, 11496}, {1104, 5256}, {1125, 16458}, {1181, 6906}, {1191, 1621}, {1211, 13725}, {1434, 3522}, {1468, 1918}, {1500, 4513}, {1509, 7782}, {1698, 16457}, {1714, 6675}, {1724, 16418}, {1837, 5530}, {2050, 10454}, {2177, 3913}, {2271, 5283}, {2292, 12635}, {2303, 7520}, {2594, 9370}, {2650, 4414}, {2975, 17018}, {2999, 5436}, {3100, 17966}, {3216, 11108}, {3240, 5260}, {3244, 19289}, {3293, 9708}, {3445, 19336}, {3486, 5724}, {3487, 3782}, {3560, 5396}, {3589, 17526}, {3616, 4000}, {3617, 19333}, {3622, 19284}, {3624, 16456}, {3634, 19272}, {3636, 19331}, {3672, 5736}, {3736, 19533}, {3886, 10472}, {3897, 17015}, {3915, 4428}, {3936, 17676}, {4028, 10371}, {4101, 4643}, {4184, 19714}, {4201, 18134}, {4225, 19734}, {4228, 19725}, {4234, 19722}, {4257, 4658}, {4258, 5276}, {4267, 10458}, {4304, 5717}, {4313, 5716}, {4352, 14828}, {4646, 19860}, {4648, 6904}, {4703, 12579}, {4850, 17054}, {4855, 5287}, {4999, 11269}, {5132, 13738}, {5230, 6690}, {5248, 16466}, {5251, 5312}, {5259, 5313}, {5275, 18755}, {5278, 17588}, {5292, 7483}, {5438, 17022}, {5714, 17775}, {5721, 6824}, {5725, 10572}, {5776, 10393}, {5788, 10950}, {6914, 12161}, {7419, 19735}, {7783, 17379}, {7904, 17300}, {9534, 11110}, {9605, 16783}, {9780, 19334}, {10449, 19270}, {10479, 19273}, {10896, 17717}, {11115, 19684}, {13161, 17718}, {13411, 17720}, {13588, 19715}, {13736, 14555}, {14007, 19749}, {14829, 19278}, {14996, 17548}, {16020, 19288}, {16842, 17749}, {17265, 17674}, {17524, 19762}, {17539, 19717}, {17557, 19744}, {19728, 19753}
X(19766) lies on these lines: {1, 2}, {6, 13725}, {20, 572}, {69, 13728}, {72, 17321}, {86, 443}, {377, 19684}, {405, 3618}, {631, 19782}, {999, 16299}, {1008, 5286}, {1043, 17381}, {1246, 18656}, {1724, 13736}, {3295, 16298}, {3487, 19786}, {3589, 13742}, {4201, 4340}, {4205, 14555}, {4255, 6703}, {5712, 16062}, {5749, 7283}, {7493, 19771}, {8193, 16452}, {9840, 14853}, {12410, 16287}, {14001, 19758}, {16043, 19761}, {16045, 19768}, {16989, 19312}, {17352, 17552}, {17676, 19717}
X(19767) lies on these lines: {1, 2}, {3, 81}, {4, 5396}, {6, 21}, {7, 73}, {20, 581}, {27, 19752}, {35, 17126}, {37, 3876}, {55, 16452}, {56, 5132}, {58, 4189}, {60, 184}, {65, 17080}, {69, 16705}, {86, 16454}, {100, 5711}, {284, 7520}, {333, 16342}, {354, 4719}, {376, 500}, {377, 5712}, {388, 2594}, {391, 4270}, {404, 940}, {411, 5706}, {443, 16752}, {573, 10470}, {579, 1449}, {810, 4560}, {942, 4850}, {959, 1402}, {962, 1064}, {964, 1043}, {966, 4272}, {986, 2650}, {991, 3522}, {999, 16453}, {1010, 19684}, {1013, 3194}, {1038, 1442}, {1046, 4414}, {1056, 5399}, {1066, 11037}, {1100, 2275}, {1150, 19270}, {1203, 5248}, {1330, 17676}, {1386, 3779}, {1457, 4323}, {1466, 17074}, {1468, 2209}, {1482, 19543}, {1621, 16289}, {1724, 4653}, {1817, 19764}, {1834, 2476}, {1870, 14018}, {2051, 10454}, {2177, 5255}, {2271, 5276}, {2278, 2363}, {2287, 16346}, {2292, 17592}, {2334, 12513}, {2667, 19582}, {2901, 4671}, {3100, 5746}, {3192, 4194}, {3295, 16287}, {3487, 19785}, {3618, 17526}, {3666, 3868}, {3735, 6155}, {3736, 17379}, {3743, 5692}, {3750, 3915}, {3869, 3931}, {3871, 5710}, {3874, 4392}, {3936, 16062}, {3940, 16848}, {3945, 6904}, {4101, 4357}, {4184, 19762}, {4188, 4256}, {4190, 4340}, {4197, 17056}, {4201, 17778}, {4202, 18134}, {4216, 4267}, {4225, 19763}, {4228, 19771}, {4234, 19738}, {4252, 17549}, {4257, 17548}, {4281, 10458}, {4300, 9778}, {4313, 14547}, {4383, 5047}, {4417, 5051}, {4551, 5261}, {4868, 5903}, {4921, 16351}, {5068, 5400}, {5086, 5725}, {5165, 16666}, {5247, 10448}, {5278, 11110}, {5333, 16458}, {5398, 6875}, {5707, 6905}, {5713, 6839}, {5721, 6828}, {5739, 13725}, {5752, 19262}, {5904, 7226}, {6198, 7102}, {6767, 16286}, {6906, 7592}, {7373, 16414}, {8025, 19284}, {8666, 16474}, {9275, 11003}, {9544, 17104}, {9566, 14636}, {9567, 13731}, {11115, 19717}, {13588, 19714}, {14005, 19701}, {14008, 19754}, {14014, 19756}, {14624, 17314}, {14997, 16859}, {15488, 19647}, {15934, 16415}, {16347, 16704}, {16370, 16948}, {17234, 17674}, {17393, 18147}, {17539, 19743}, {17553, 19723}, {17557, 19732}, {17588, 19742}, {17589, 19740}, {17750, 17756}, {19281, 19848}, {19649, 19782}
X(19768) lies on these lines: {1, 7770}, {2, 19758}, {4, 18134}, {76, 405}, {183, 13723}, {384, 19761}, {1009, 1975}, {1724, 7754}, {3673, 7283}, {3948, 16048}, {4195, 17128}, {4201, 16986}, {4223, 18135}, {4385, 16817}, {5286, 13742}, {9534, 17681}, {13740, 19701}, {16045, 19766}, {16062, 19838}, {18140, 19309}
X(19769) lies on these lines: {1, 11322}, {2, 19754}, {3, 19684}, {6, 404}, {8, 11358}, {21, 19701}, {56, 964}, {86, 16452}, {405, 5253}, {411, 19716}, {474, 5278}, {1004, 19752}, {1005, 19753}, {1011, 3616}, {2049, 2975}, {2475, 19755}, {2476, 19720}, {3286, 16342}, {3658, 19771}, {4188, 19717}, {4189, 19740}, {4203, 19715}, {5333, 16289}, {7411, 19718}, {7466, 19756}, {13587, 19722}, {13588, 19714}, {16298, 18139}, {16371, 19738}, {17531, 19732}, {17535, 19744}, {17536, 19749}, {17566, 19721}, {17572, 19742}, {19281, 19850}
X(19770) lies on these lines: {1, 4245}, {6, 404}, {940, 16297}, {3617, 5278}, {4234, 9534}, {7419, 19735}, {7428, 19763}, {13741, 19732}, {16057, 19714}, {16948, 19742}, {19733, 19760}
X(19771) lies on these lines: {1, 1995}, {2, 19782}, {6, 11101}, {405, 5640}, {1012, 10574}, {1183, 17018}, {2979, 19520}, {3560, 3567}, {3658, 19769}, {4228, 19767}, {4232, 19783}, {5422, 13733}, {6883, 11465}, {7419, 19735}, {7474, 9534}, {7478, 19722}, {7493, 19766}, {13442, 18911}
X(19772) lies on the cubic K1053a and these lines:
{2, 3}, {323, 10661}, {616, 5668}, {628, 8837}, {2992, 3180}, {8836, 19713}, {10217, 16770}, {10639, 11130}
X(19772) = isotomic conjugate of X(19774)
X(19772) = anticomplement X(470)
X(19772) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 616}, {2152, 12383}, {2153, 4}, {3457, 5905}, {5995, 7253}, {8737, 5906}
X(19772) = X(621)-Ceva conjugate of X(3180)
X(19772) = crosssum of X(3269) and X(6137)
X(19772) = barycentric product X(i)*X(j) for these {i,j}: {76, 11243}, {298, 8919}, {300, 3165}, {303, 8175}
X(19772) = barycentric quotient X(i)/X(j) for these {i,j}: {62, 8479}, {3165, 15}, {8175, 18}, {8919, 13}, {11243, 6}
X(19772) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 20, 19773), (3, 471, 2), (5, 8613, 19773), (465, 472, 2)
X(19773) lies on the cubic K1053b and these lines:
{2, 3}, {323, 10662}, {617, 5669}, {627, 8839}, {2993, 3181}, {8838, 19712}, {10218, 16771}, {10640, 11131}
X(19773) = isotomic conjugate of X(19775)
X(19773) = anticomplement X(471)
X(19773) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 617}, {2151, 12383}, {2154, 4}, {3458, 5905}, {5994, 7253}, {8738, 5906}
X(19773) = X(622)-Ceva conjugate of X(3181)
X(19773) = crosssum of X(3269) and X(6138)
X(19773) = barycentric product X(i)*X(j) for these {i,j}: {76, 11244}, {299, 8918}, {301, 3166}, {302, 8174}
X(19773) = barycentric quotient X(i)/X(j) for these {i,j}: {61, 8471}, {3166, 16}, {8174, 17}, {8918, 14}, {11244, 6}
X(19773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 20, 19772), (3, 470, 2), (5, 8613, 19772), (466, 473, 2)
X(19774) lies on the cubic K1053a and these lines: on lines {4, 19775}, {616, 8174}, {628, 8918}
X(19774) = isogonal conjugate of X(11243)
X(19774) = isotomic conjugate of X(19772)
X(19774) = polar conjugate of X(36302)
X(19774) = X(i)-cross conjugate of X(j) for these (i,j): {470, 2}, {2992, 11121}
X(19774) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11243}, {2151, 8919}, {2153, 3165}
X(19774) = trilinear pole of line {525, 11543}
X(19774) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11243}, {13, 8919}, {15, 3165}, {18, 8175}, {8479, 62}
X(19775) lies on these lines: {4, 19774}, {617, 8175}, {627, 8919}
X(19775) = isotomic conjugate of X(19773)
X(19775) = polar conjugate of X(36303)
X(19775) = isogonal conjugate of X(11244)
X(19775) = X(i)-cross conjugate of X(j) for these (i,j): {471, 2}, {2993, 11122}
X(19775) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11244}, {2152, 8918}, {2154, 3166}
X(19775) = trilinear pole of line {525, 11542}
X(19775) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11244}, {14, 8918}, {16, 3166}, {17, 8174}, {8471, 61}
X(19776) lies on the curves Q100,Q124,K264a,K276,K419b,K860,K1053a and on these lines:
{30, 298}, {301, 14254}, {396, 470}, {617, 15454}, {628, 3471}, {2993, 10653}, {3180, 11092}, {10217, 11119}
X(19776) = isotomic conjugate of X(616)
X(19776) = cyclocevian conjugate of X(2992)
X(19776) = antitomic conjugate of X(36308)
X(19776) = X(i)-cross conjugate of X(j) for these (i,j): {13, 2}, {2992, 19713}
X(19776) = X(i)-isoconjugate of X(j) for these (i,j): {6, 19298}, {31, 616}
X(19776) = barycentric product X(76)X(3440)
X(19776) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19298}, {2, 616}, {396, 15768}, {3440, 6}
X(19777) lies on the curves Q100,Q124,K264b,K276,K419a,K860,K1053b and on these lines:
{30, 299}, {300, 14254}, {395, 471}, {616, 15454}, {627, 3471}, {2992, 10654}, {3181, 11078}, {10218, 11120}
X(19777) = isotomic conjugate of X(617)
X(19777) = cyclocevian conjugate of X(2993)
X(19777) = antitomic conjugate of X(36311)
X(19777) = X(i)-cross conjugate of X(j) for these (i,j): {14, 2}, {2993, 19712}
X(19777) = X(i)-isoconjugate of X(j) for these (i,j): {6, 19299}, {31, 617}
X(19777) = barycentric product X(76)*X(3441)
X(19777) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19299}, {2, 617}, {395, 15769}, {3441, 6}
X(19778) lies on the cubics K267 and K1053a and on these lines:
{2, 18}, {4, 93}, {69, 301}, {298, 11146}, {323, 470}, {511, 10210}, {616, 8173}, {621, 11581}, {2963, 11488}, {3180, 11082}, {3181, 8604}, {10678, 11004}, {11489, 19295}
X(19778) = isogonal conjugate of X(11142)
X(19778) = isotomic conjugate of X(16770)
X(19778) = anticomplement X(11127)
X(19778) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2153, 628}, {11082, 8}
X(19778) = pedal antipodal perspector of X(13)
X(19778) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11142}, {6, 3383}, {31, 16770}, {62, 2153}, {2166, 11134}, {2964, 11139}
X(19778) = barycentric product X(i)*X(j) for these {i,j}: {18, 298}, {75, 3384}, {7799, 11138}, {11082, 11129}, {11140, 11146}
X(19778) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3383}, {2, 16770}, {6, 11142}, {15, 62}, {18, 13}, {50, 11134}, {298, 303}, {323, 11145}, {470, 472}, {533, 6672}, {2963, 11139}, {3384, 1}, {8175, 8919}, {8604, 11081}, {8739, 10641}, {8742, 8737}, {10678, 6104}, {11082, 11080}, {11086, 11088}, {11092, 8836}, {11129, 11133}, {11131, 11127}, {11137, 2965}, {11138, 1989}, {11143, 8838}, {11146, 1994}, {16807, 5995}
X(19778) = {X(3519),X(11140)}-harmonic conjugate of X(19779)
X(19779) lies on the cubics K267 and K1053b and on these lines:
{2, 17}, {4, 93}, {69, 300}, {299, 11145}, {323, 471}, {617, 8172}, {622, 11582}, {2963, 11489}, {3180, 8603}, {3181, 11087}, {10210, 11442}, {10677, 11004}, {11488, 19294}
X(19779) = isogonal conjugate of X(11141)
X(19779) = isotomic conjugate of X(16771)
X(19779) = anticomplement X(11126)
X(19779) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2154, 627}, {11087, 8}
X(19779) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11141}, {6, 3376}, {31, 16771}, {61, 2154}, {2166, 11137}, {2964, 11138}
X(19779) = pedal antipodal perspector of X(14)
X(19779) = barycentric product X(i)*X(j) for these {i,j}: {17, 299}, {75, 3375}, {7799, 11139}, {11087, 11128}, {11140, 11145}
X(19779) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3376}, {2, 16771}, {6, 11141}, {16, 61}, {17, 14}, {50, 11137}, {299, 302}, {323, 11146}, {471, 473}, {532, 6671}, {2963, 11138}, {3375, 1}, {8174, 8918}, {8603, 11086}, {8740, 10642}, {8741, 8738}, {10677, 6105}, {11078, 8838}, {11081, 11083}, {11087, 11085}, {11128, 11132}, {11130, 11126}, {11134, 2965}, {11139, 1989}, {11144, 8836}, {11145, 1994}, {16806, 5994}
X(19779) = {X(3519),X(11140)}-harmonic conjugate of X(19778)
X(19780) lies on the cubic 1054a and these lines:
{2, 10617}, {3, 6}, {112, 10633}, {115, 19106}, {172, 1250}, {230, 1080}, {303, 10616}, {395, 621}, {396, 616}, {623, 11298}, {1501, 11130}, {1914, 19373}, {1968, 10642}, {1971, 10675}, {1989, 15441}, {2151, 19305}, {2381, 5995}, {3129, 3457}, {3438, 11081}, {3440, 9412}, {3643, 6671}, {5340, 7684}, {5472, 16960}, {5475, 16967}, {5479, 16942}, {5859, 11128}, {6105, 11060}, {7006, 9341}, {7737, 18581}, {7745, 11289}, {7746, 16808}, {7747, 16809}, {7749, 16966}, {7753, 16242}, {8778, 11409}, {10311, 11476}
X(19780) = isogonal conjugate of X(11121)
X(19780) = X(i)-Ceva conjugate of X(j) for these (i,j): {3129, 11243}, {3457, 6}
X(19780) = X(3170)-cross conjugate of X(6)
X(19780) = crosspoint of X(249) and X(5995)
X(19780) = barycentric product X(i)*X(j) for these {i,j}: {6, 3180}, {13, 3170}
X(19780) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11121}, {3170, 298}, {3180, 76}
X(19780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 3053, 19781), (6, 5023, 11480), (16, 32, 6), (16, 187, 2076)
X(19781) lies on the cubic 1054b and these lines:
{2, 10616}, {3, 6}, {112, 10632}, {115, 19107}, {172, 10638}, {230, 383}, {302, 10617}, {395, 617}, {396, 622}, {624, 11297}, {1501, 11131}, {1914, 7051}, {1968, 10641}, {1971, 10676}, {1989, 15442}, {2152, 19304}, {2380, 5994}, {3130, 3458}, {3439, 11086}, {3441, 9412}, {3642, 6672}, {5339, 7685}, {5471, 16961}, {5475, 16966}, {5478, 16943}, {5858, 11129}, {6104, 11060}, {7005, 9341}, {7737, 18582}, {7745, 11290}, {7746, 16809}, {7747, 16808}, {7749, 16967}, {7753, 16241}, {8778, 11408}, {10311, 11475}
X(19781) = isogonal conjugate of X(11122)
X(19781) = X(i)-Ceva conjugate of X(j) for these (i,j): {3130, 11244}, {3458, 6}
X(19781) = X(3171)-cross conjugate of X(6)
X(19781) = crosspoint of X(249) and X(5994)
X(19781) = barycentric product X(i)*X(j) for these {i,j}: {6, 3181}, {14, 3171}
X(19781) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11122}, {3171, 299}, {3181, 76}
X(19781) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (6, 3053, 19780), (6, 5023, 11481), (15, 32, 6), (15, 187, 2076)
X(19782) lies on these lines: {1, 3}, {2, 19771}, {4, 18134}, {6, 13732}, {20, 17300}, {224, 1824}, {386, 16434}, {394, 13733}, {405, 511}, {631, 19766}, {914, 5130}, {958, 3781}, {965, 3061}, {1012, 5907}, {1216, 3560}, {1350, 9840}, {1351, 1724}, {1352, 13442}, {3314, 7379}, {3430, 19544}, {3523, 19783}, {3819, 19520}, {4255, 19514}, {5462, 5752}, {6194, 19312}, {6795, 13869}, {7413, 10449}, {7580, 15488}, {9049, 12513}, {10519, 13725}, {11101, 15066}, {13742, 14853}, {15978, 19838}, {16352, 19861}, {16353, 19860}, {17316, 19645}, {19649, 19767}
X(19783) lies on these lines: {1, 2}, {6, 13736}, {20, 17379}, {193, 13725}, {1008, 6392}, {1246, 18659}, {1265, 16777}, {3523, 19782}, {3620, 13728}, {3945, 4201}, {4190, 8025}, {4232, 19771}, {5032, 13745}, {5304, 19312}, {6767, 16298}, {6872, 19717}, {7373, 16299}, {11036, 17302}, {11106, 16783}, {12410, 16452}, {19719, 19752}
X(19784) lies on these lines: {1, 2}, {19, 475}, {55, 17698}, {197, 474}, {341, 19812}, {405, 1486}, {451, 7718}, {958, 13728}, {964, 4972}, {966, 5280}, {1010, 4429}, {1203, 3618}, {1220, 1478}, {1224, 1930}, {1479, 13740}, {2049, 3925}, {2345, 4647}, {3247, 3610}, {3589, 16466}, {3619, 16474}, {3743, 17776}, {3826, 16458}, {4195, 4302}, {4201, 4299}, {4295, 5749}, {4385, 19786}, {4673, 17371}, {4680, 5716}, {5248, 17526}, {5251, 13725}, {5257, 17742}, {5259, 13742}, {5294, 12514}, {5296, 17744}, {6051, 17279}, {6284, 11354}, {7354, 11359}, {10895, 16052}, {11108, 12410}, {15988, 16473}, {16299, 16678}, {16502, 17398}, {19886, 19946}, {19888, 19891}, {19895, 19900}, {19896, 19928}
X(19785) lies on these lines: {1, 224}, {2, 37}, {3, 19850}, {4, 5262}, {6, 3782}, {7, 27}, {8, 3891}, {21, 19844}, {55, 7465}, {56, 16049}, {57, 16548}, {63, 1723}, {69, 3187}, {92, 3673}, {142, 5287}, {145, 5014}, {149, 17024}, {218, 329}, {226, 3946}, {239, 5739}, {277, 1255}, {306, 3875}, {333, 4389}, {348, 16697}, {387, 3868}, {388, 17016}, {404, 19845}, {497, 1370}, {612, 1738}, {908, 2999}, {938, 5125}, {940, 1086}, {942, 1068}, {948, 7247}, {964, 19838}, {982, 11269}, {986, 5230}, {990, 10431}, {995, 17182}, {1001, 4854}, {1010, 3616}, {1056, 17015}, {1104, 6872}, {1108, 18607}, {1211, 4361}, {1376, 17602}, {1386, 1836}, {1449, 4654}, {1479, 1717}, {1743, 17781}, {1834, 12649}, {1999, 3662}, {2475, 5716}, {2478, 19852}, {2550, 3920}, {2886, 17599}, {2895, 5839}, {3008, 3305}, {3011, 17594}, {3120, 17017}, {3219, 4419}, {3241, 17678}, {3315, 10580}, {3436, 13161}, {3474, 17126}, {3475, 13576}, {3485, 11553}, {3487, 19767}, {3670, 5292}, {3729, 5294}, {3744, 20075}, {3745, 5880}, {3755, 3870}, {3771, 4970}, {3791, 4655}, {3821, 4362}, {3838, 17723}, {3873, 4310}, {3982, 4667}, {4001, 17274}, {4188, 19842}, {4189, 19841}, {4193, 19839}, {4195, 19840}, {4346, 9965}, {4353, 4847}, {4357, 5271}, {4360, 18134}, {4364, 19732}, {4383, 4415}, {4393, 17778}, {4395, 5743}, {4425, 16825}, {4429, 10327}, {4514, 19993}, {4641, 17276}, {4644, 17483}, {4646, 10528}, {4648, 17019}, {4703, 4974}, {4719, 11375}, {4859, 17022}, {4868, 10056}, {5101, 5722}, {5228, 6354}, {5278, 17257}, {5284, 16020}, {5530, 10585}, {5698, 17127}, {5712, 17011}, {5737, 17323}, {6063, 16750}, {6327, 17150}, {6350, 18662}, {6703, 7263}, {7283, 17526}, {7613, 9347}, {9598, 16974}, {10468, 11679}, {11415, 16466}, {14213, 17861}, {16757, 17896}, {17045, 19701}, {17056, 17395}, {17316, 18139}, {17332, 19723}, {17860, 17884}, {19281, 19684}
X(19786) lies on these lines: {1, 977}, {2, 37}, {21, 19841}, {27, 86}, {33, 5125}, {36, 17512}, {57, 16566}, {63, 1732}, {81, 320}, {83, 226}, {85, 278}, {92, 17907}, {141, 1999}, {171, 3821}, {190, 5294}, {238, 4425}, {239, 1211}, {306, 4360}, {319, 3187}, {329, 3618}, {333, 4357}, {377, 497}, {404, 19842}, {405, 19844}, {442, 19852}, {474, 19845}, {551, 17678}, {612, 4429}, {846, 6679}, {894, 3782}, {940, 3662}, {964, 19840}, {1010, 1125}, {1086, 6703}, {1100, 17778}, {1220, 13161}, {1386, 4388}, {1427, 17086}, {1621, 7465}, {1909, 18057}, {1961, 3836}, {2049, 19838}, {2308, 4683}, {2999, 5233}, {3120, 14012}, {3219, 17258}, {3305, 17352}, {3487, 19766}, {3589, 4415}, {3683, 9791}, {3685, 4854}, {3687, 3946}, {3705, 17599}, {3745, 4645}, {3755, 3996}, {3757, 4026}, {3758, 5905}, {3759, 5739}, {3771, 17592}, {3816, 16067}, {3914, 5263}, {3920, 4972}, {3925, 16830}, {3936, 17011}, {3961, 4085}, {3974, 9780}, {4001, 17273}, {4187, 19839}, {4205, 16817}, {4383, 17367}, {4385, 19784}, {4417, 5256}, {4641, 6646}, {4656, 17353}, {4660, 17716}, {4703, 16468}, {5051, 5262}, {5222, 14555}, {5224, 5271}, {5253, 16049}, {5278, 17256}, {5287, 17234}, {5737, 17325}, {5741, 17012}, {5743, 17366}, {6685, 17719}, {7081, 17602}, {7283, 17698}, {11679, 17306}, {14005, 19848}, {14829, 17305}, {16700, 16744}, {17019, 17317}, {17022, 17282}, {17045, 17056}, {17248, 19732}, {17331, 19723}, {17397, 19281}
X(19787) lies on these lines: {2, 37}, {27, 310}, {76, 5271}, {306, 17143}, {314, 5249}, {333, 1269}, {377, 10453}, {1010, 3720}, {1011, 19838}, {1230, 3975}, {1909, 3187}, {4184, 19841}, {4191, 19845}, {4204, 16817}, {4210, 19842}, {5178, 7270}, {13588, 19848}, {14012, 17031}, {17027, 19281}
X(19788) lies on these lines: {2, 37}, {27, 57}, {63, 3673}, {81, 85}, {92, 17861}, {322, 3187}, {377, 938}, {411, 19850}, {1104, 7538}, {1108, 6360}, {1210, 1785}, {1453, 5342}, {2221, 11341}, {3086, 6349}, {3914, 4008}, {5736, 17011}, {6734, 16062}, {7182, 16750}, {7270, 12649}, {11344, 19844}, {16346, 16817}, {19281, 19716}
X(19789) lies on these lines: {2, 37}, {7, 1943}, {8, 17184}, {27, 4373}, {63, 1266}, {144, 19742}, {145, 377}, {149, 1370}, {193, 17483}, {239, 5813}, {306, 17151}, {329, 4402}, {333, 4398}, {497, 4442}, {940, 7263}, {1010, 3622}, {1211, 17119}, {1738, 10327}, {2550, 3891}, {2999, 4054}, {3434, 19993}, {3475, 3896}, {3617, 16062}, {3621, 7270}, {3663, 5271}, {3782, 4361}, {3875, 5249}, {4001, 4862}, {4188, 19845}, {4189, 19844}, {4307, 17150}, {4310, 17135}, {4346, 14552}, {4383, 4395}, {4419, 5278}, {4440, 20078}, {4659, 5294}, {5154, 19839}, {6539, 18840}, {6872, 19851}, {11115, 19848}, {11319, 19838}, {17014, 19281}, {17160, 18134}, {17246, 19732}, {17314, 18139}, {17334, 19723}, {17395, 19701}, {17548, 19841}, {17784, 20045}
X(19790) lies on these lines: {2, 37}, {27, 1088}, {306, 17158}, {377, 10580}, {1010, 10582}, {3187, 16284}, {3673, 18750}, {4847, 16062}, {7411, 19850}, {13615, 19844}, {19281, 19718}
X(19791) lies on these lines: {1, 19281}, {2, 37}, {27, 295}, {72, 239}, {306, 740}, {377, 17316}, {518, 3187}, {742, 3782}, {984, 5271}, {1010, 16826}, {1104, 11320}, {1108, 17148}, {2901, 3912}, {3008, 3159}, {3661, 5295}, {3696, 4972}, {3896, 13576}, {3948, 16583}, {4044, 16600}, {5014, 20017}, {6542, 7270}, {7283, 16050}, {11329, 19845}, {16367, 19844}, {17310, 17678}, {19308, 19842}
X(19792) lies on these lines: {2, 37}, {3, 19838}, {27, 264}, {57, 349}, {63, 1269}, {76, 333}, {313, 5271}, {314, 18134}, {377, 18141}, {404, 19848}, {940, 19281}, {1150, 1234}, {1230, 5278}, {1714, 4385}, {1726, 16574}, {3419, 7270}, {3948, 19732}, {7283, 16290}, {10479, 16062}, {16287, 19844}, {16451, 19842}, {16452, 19840}, {16453, 19845}, {16817, 16848}
X(19793) lies on these lines: {2, 37}, {4, 19838}, {27, 69}, {278, 1231}, {377, 1043}, {5712, 19281}, {7009, 10449}, {13726, 19844}
X(19794) lies on these lines: {2, 37}, {4, 19841}, {5, 19844}, {140, 19845}, {377, 7288}, {499, 1010}, {631, 19842}, {1656, 19839}, {2476, 19850}, {7270, 10527}, {7465, 11680}, {19281, 19720}
X(19795) lies on these lines: {2, 37}, {3, 19839}, {4, 19842}, {5, 19845}, {55, 16067}, {140, 19844}, {377, 10588}, {498, 1010}, {631, 19841}, {5552, 7270}, {11681, 16049}, {17566, 19850}, {19281, 19721}
X(19796) lies on these lines: {2, 37}, {27, 648}, {63, 4398}, {81, 7321}, {239, 3782}, {306, 17160}, {319, 17184}, {320, 3187}, {333, 3663}, {377, 3241}, {519, 5100}, {551, 1010}, {1086, 1999}, {1211, 17117}, {3679, 16062}, {3759, 5905}, {3875, 18134}, {3914, 4514}, {3979, 4743}, {4360, 5249}, {4361, 4886}, {4389, 5271}, {4395, 4415}, {4402, 14555}, {4440, 4641}, {4442, 7191}, {4654, 7247}, {4734, 17718}, {4852, 17778}, {4854, 16823}, {5278, 17258}, {11354, 19838}, {13587, 19842}, {16370, 19844}, {16371, 19845}, {17247, 19732}, {17315, 18139}, {17333, 19723}, {17396, 19701}, {17533, 19839}, {17549, 19841}, {19281, 19722}
X(19797) lies on these lines: {2, 37}, {10, 17678}, {27, 8756}, {81, 5564}, {333, 4967}, {519, 1010}, {553, 7247}, {894, 4886}, {1211, 17116}, {1999, 4665}, {3679, 7270}, {3829, 16067}, {3969, 17317}, {4234, 19849}, {7229, 14555}, {11357, 19838}, {13587, 19841}, {16062, 19875}, {16370, 19845}, {16371, 19844}, {17328, 20078}, {17530, 19839}, {17549, 19842}, {17553, 19848}, {19281, 19723}
X(19798) lies on these lines: {2, 37}, {22, 19841}, {25, 16817}, {27, 274}, {614, 1010}, {5272, 6533}, {7484, 19845}, {7485, 19842}, {19281, 19724}, {19838, 19852}
X(19799) lies on these lines: {2, 37}, {22, 19842}, {25, 7283}, {63, 3718}, {85, 8024}, {92, 2064}, {304, 305}, {341, 1370}, {377, 3701}, {427, 19839}, {612, 1010}, {1089, 5268}, {1259, 7081}, {1368, 3695}, {3705, 16067}, {4224, 19840}, {4494, 6358}, {7365, 8816}, {7484, 19844}, {7485, 19841}, {19281, 19725}
X(19800) lies on these lines: {2, 37}, {27, 871}, {1921, 5271}, {16372, 19844}
X(19801) lies on these lines: {2, 37}, {27, 811}, {16373, 19844}, {16405, 19840}, {19281, 19726}
X(19802) lies on these lines: {2, 37}, {27, 3306}, {57, 17048}, {85, 18623}, {377, 17603}, {938, 7270}, {1210, 16062}, {11344, 19841}, {16293, 19844}, {16410, 19845}, {19281, 19727}
X(19803) lies on these lines: {2, 37}, {27, 6384}, {306, 17144}, {1011, 19841}, {3741, 16062}, {4191, 19842}, {4203, 19840}, {5271, 6376}, {7270, 10453}, {11358, 19838}, {16058, 19844}, {16059, 19845}, {19281, 19715}
X(19804) lies on these lines: {1, 3996}, {2, 37}, {3, 16817}, {7, 14555}, {8, 354}, {10, 982}, {55, 16823}, {56, 16824}, {57, 85}, {63, 17277}, {69, 4886}, {81, 3759}, {86, 5256}, {92, 8756}, {100, 9105}, {142, 3687}, {145, 4883}, {171, 16825}, {190, 3305}, {226, 5233}, {238, 3980}, {239, 940}, {304, 17023}, {306, 17234}, {320, 5739}, {322, 3306}, {341, 4003}, {404, 2352}, {443, 7270}, {553, 4416}, {614, 5263}, {673, 2339}, {748, 4418}, {750, 3769}, {756, 17155}, {894, 4383}, {942, 9534}, {978, 3725}, {980, 16819}, {999, 16821}, {1086, 5743}, {1125, 17592}, {1211, 3662}, {1215, 16569}, {1220, 1722}, {1266, 4656}, {1268, 18044}, {1376, 3757}, {1429, 16822}, {1441, 5435}, {1449, 4771}, {1698, 3992}, {1920, 10009}, {1999, 4361}, {2550, 4514}, {2895, 17361}, {2999, 10436}, {3008, 17789}, {3218, 5278}, {3219, 17335}, {3616, 4673}, {3617, 3999}, {3624, 4647}, {3632, 4457}, {3634, 4125}, {3673, 16832}, {3681, 17140}, {3685, 4423}, {3696, 3742}, {3699, 8580}, {3701, 19877}, {3702, 5550}, {3705, 3925}, {3718, 17306}, {3729, 7308}, {3741, 17063}, {3782, 5241}, {3846, 17889}, {3873, 4651}, {3875, 17022}, {3886, 10582}, {3891, 5297}, {3923, 17123}, {3966, 4645}, {3969, 17240}, {4001, 17346}, {4042, 4860}, {4061, 4684}, {4110, 4967}, {4360, 5287}, {4362, 17122}, {4388, 5880}, {4392, 4981}, {4413, 7081}, {4415, 7263}, {4417, 5249}, {4641, 17349}, {4652, 5338}, {4675, 17778}, {4692, 19875}, {4697, 16468}, {4717, 19883}, {5262, 16454}, {5294, 17352}, {5308, 17158}, {5372, 17791}, {5437, 11679}, {5439, 10449}, {5695, 8167}, {5744, 18750}, {5905, 7321}, {6376, 18136}, {6703, 17366}, {7283, 11108}, {8056, 18229}, {8758, 10527}, {9347, 17150}, {9816, 11683}, {11337, 19841}, {16700, 16738}, {16815, 17595}, {16826, 17144}, {16830, 17599}, {16831, 17143}, {16843, 19838}, {17011, 17394}, {17012, 19684}, {17019, 17393}, {17069, 18155}, {17077, 17080}, {17124, 17763}, {17386, 20017}, {17397, 17762}, {19281, 19728}
X(19805) lies on these lines: {2, 37}, {38, 16062}, {3145, 19844}, {3873, 7270}, {7283, 19852}, {19281, 19729}
X(19806) lies on these lines: {2, 37}, {333, 6376}, {341, 5230}, {404, 19840}, {750, 14012}, {1837, 7270}, {1966, 10319}, {1999, 17786}, {2064, 17861}, {3831, 16062}, {5273, 18135}, {13738, 19842}, {14829, 18044}, {19281, 19730}
X(19807) lies on these lines: {2, 37}, {8, 18178}, {27, 7017}, {63, 313}, {333, 3596}, {355, 7270}, {859, 19845}, {940, 3963}, {1230, 2245}, {3264, 5271}, {3702, 11376}, {3765, 4641}, {4216, 19840}, {4245, 19838}, {4494, 11679}, {15315, 16062}, {16374, 19844}, {19281, 19731}
X(19808) lies on these lines: {2, 37}, {6, 4886}, {8, 3745}, {10, 58}, {21, 19842}, {27, 1268}, {57, 7247}, {63, 5224}, {81, 319}, {86, 306}, {209, 3786}, {377, 1155}, {404, 19841}, {405, 19845}, {442, 19839}, {474, 19844}, {594, 1999}, {894, 1211}, {940, 3661}, {1125, 17600}, {1214, 17095}, {1441, 18625}, {1654, 4641}, {1698, 16062}, {1961, 3773}, {2245, 3219}, {2886, 16067}, {2899, 19877}, {3187, 5564}, {3305, 17354}, {3619, 9776}, {3634, 17593}, {3687, 5750}, {3703, 16830}, {3758, 5739}, {3782, 17116}, {3828, 17678}, {3931, 19865}, {3969, 17019}, {4001, 17271}, {4058, 4102}, {4205, 7283}, {4383, 17368}, {4415, 7227}, {4472, 17056}, {4514, 5263}, {4670, 17778}, {4872, 10319}, {5153, 17011}, {5251, 17512}, {5256, 17381}, {5260, 16049}, {5287, 17233}, {5294, 17277}, {5743, 17369}, {5749, 14555}, {6533, 19881}, {7321, 17184}, {10436, 18134}, {11110, 19857}, {16342, 19840}, {16817, 17698}, {16844, 19838}, {17022, 17286}, {17329, 20078}, {17531, 19850}, {17557, 19848}, {17590, 19852}, {19281, 19732}
X(19809) lies on these lines: {2, 37}, {19281, 19733}
X(19810) lies on these lines: {2, 37}, {3, 19840}, {27, 1240}, {63, 76}, {81, 1909}, {171, 14012}, {306, 314}, {313, 333}, {1010, 10458}, {1230, 3219}, {1999, 3963}, {2221, 7770}, {3142, 19839}, {3596, 5271}, {3770, 4641}, {3975, 5278}, {4225, 19842}, {4385, 5230}, {5086, 7270}, {13738, 19838}, {19281, 19734}
X(19811) lies on these lines: {2, 37}, {57, 4494}, {63, 3596}, {305, 3403}, {333, 3264}, {668, 4001}, {1010, 10459}, {2064, 14213}, {3219, 3975}, {5176, 7270}, {7283, 13724}, {8024, 10030}, {19281, 19735}, {19840, 19845}
X(19812) lies on these lines: {2, 37}, {57, 17305}, {63, 17249}, {81, 17361}, {85, 17087}, {226, 17381}, {306, 17393}, {333, 17250}, {341, 19784}, {377, 5225}, {405, 19841}, {474, 19842}, {940, 17227}, {1010, 3624}, {1125, 16062}, {1211, 3759}, {1999, 17228}, {3616, 7270}, {3662, 6703}, {3687, 17380}, {4415, 17368}, {4417, 17023}, {4425, 4676}, {4641, 17329}, {4656, 17354}, {5047, 19850}, {5226, 7247}, {5284, 7465}, {5287, 17241}, {5294, 17336}, {5737, 17326}, {5743, 17367}, {11108, 19844}, {11679, 17307}, {14829, 17306}, {16408, 19845}, {17022, 17283}, {17056, 17397}, {17394, 18134}, {17527, 19839}, {17551, 19848}
X(19813) lies on these lines: {2, 37}, {199, 19841}, {19281, 19737}
X(19814) lies on these lines: {2, 37}, {76, 18750}, {306, 4673}, {341, 5271}, {1010, 17022}, {5175, 7270}, {11347, 19838}, {11350, 19842}
X(19815) lies on these lines: {2, 37}, {27, 1810}, {264, 18044}, {306, 4514}, {950, 3912}, {1265, 5222}, {1999, 4437}, {4872, 18134}, {11349, 19842}, {16062, 17284}, {17244, 19281}
X(19816) lies on these lines: {2, 37}, {27, 6331}, {5271, 10009}
X(19817) lies on these lines: {2, 37}
X(19818) lies on these lines: {2, 37}, {5271, 6381}, {11322, 19838}
X(19819) lies on these lines: {2, 37}, {8, 17678}, {27, 4921}, {377, 519}, {545, 19723}, {1266, 5271}, {2895, 4371}, {3782, 17119}, {4234, 19848}, {4361, 5905}, {4373, 14552}, {4421, 7465}, {5249, 17151}, {5739, 17117}, {5839, 17483}, {11194, 16049}, {11346, 19838}, {13587, 19845}, {16371, 19850}, {16833, 17781}, {17549, 19844}, {19281, 19738}
X(19820) lies on these lines: {2, 37}, {333, 1266}, {377, 20050}, {903, 4001}, {1010, 3636}, {1999, 7263}, {3187, 7321}, {3632, 7270}, {3782, 4886}, {3982, 7247}, {4398, 5271}, {5249, 17160}, {5564, 17184}, {17151, 18134}, {19281, 19739}, {19535, 19844}, {19537, 19845}
X(19821) lies on these lines: {2, 37}, {1999, 18143}, {5271, 18133}, {11679, 18739}, {17524, 19841}
X(19822) lies on these lines: {2, 37}, {8, 81}, {10, 46}, {21, 19845}, {27, 281}, {306, 10436}, {329, 7229}, {404, 19844}, {474, 19850}, {594, 940}, {894, 5739}, {958, 16049}, {966, 3219}, {967, 1150}, {1211, 4363}, {1370, 2550}, {1376, 7465}, {1867, 5791}, {2321, 5287}, {2476, 19839}, {2895, 4644}, {2995, 6350}, {3305, 17355}, {3617, 7270}, {3695, 16458}, {3758, 4886}, {3782, 17118}, {3969, 17316}, {3974, 5297}, {4001, 17270}, {4042, 4733}, {4188, 19841}, {4189, 19842}, {4383, 17369}, {4384, 5294}, {4470, 5712}, {4472, 19701}, {4641, 17275}, {4643, 20078}, {4665, 6703}, {4967, 5271}, {5232, 9965}, {5256, 5750}, {5278, 19281}, {5552, 5955}, {5554, 5793}, {5743, 7227}, {5782, 10601}, {7222, 17483}, {8025, 20017}, {9780, 16062}, {11110, 19848}, {11680, 16067}, {12649, 19716}, {16817, 17526}, {17019, 17314}
X(19823) lies on these lines: {2, 37}, {27, 8025}, {145, 16062}, {149, 377}, {3623, 7270}, {4080, 18841}, {4189, 19850}, {4310, 17146}, {4972, 20020}, {5905, 17120}, {6871, 19852}, {16865, 19844}, {17572, 19845}, {17589, 19848}, {19281, 19740}
X(19824) lies on these lines: {2, 37}, {377, 3623}, {3914, 19993}, {4310, 17145}, {4346, 16704}, {4678, 16062}, {5905, 17121}, {7270, 20014}, {17678, 20049}, {19281, 19741}
X(19825) lies on these lines: {2, 37}, {8, 4340}, {63, 4967}, {145, 1010}, {169, 3219}, {377, 3421}, {940, 4665}, {1211, 17118}, {1654, 20078}, {3679, 4001}, {3945, 20017}, {3969, 4648}, {4188, 19844}, {4189, 19845}, {4363, 5739}, {4383, 7227}, {4431, 5287}, {4470, 19684}, {4678, 7270}, {5141, 19839}, {5263, 19993}, {5905, 17116}, {17548, 19842}, {17572, 19850}, {17588, 19848}, {19281, 19742}, {19717, 20043}
X(19826) lies on these lines: {2, 37}, {377, 1159}, {4310, 17163}, {4454, 19742}, {5739, 17119}, {5905, 17117}, {7270, 20052}, {17539, 19848}, {17548, 19844}, {19281, 19743}
X(19827) lies on these lines: {2, 37}, {10, 3769}, {57, 17307}, {63, 17250}, {81, 17360}, {306, 17394}, {377, 19877}, {405, 19842}, {474, 19841}, {940, 17228}, {1010, 1698}, {1211, 3758}, {3634, 16062}, {3661, 6703}, {3687, 17381}, {3925, 16067}, {4417, 5750}, {4438, 19856}, {4641, 17328}, {5287, 17240}, {5294, 17335}, {5435, 7247}, {5743, 17368}, {7270, 9780}, {7465, 9342}, {8728, 19839}, {11108, 19845}, {14829, 17308}, {16408, 19844}, {17022, 17285}, {17535, 19850}, {17678, 19876}, {19281, 19744}
X(19828) lies on these lines: {2, 37}, {3633, 7270}, {3782, 17121}, {4668, 16062}, {19281, 19745}
X(19829) lies on these lines: {2, 37}, {1010, 15808}, {3244, 7270}, {3632, 16062}, {3782, 17120}, {17574, 19841}, {19281, 19746}, {19526, 19844}
X(19830) lies on these lines: {2, 37}, {377, 20057}, {3187, 17361}, {3626, 16062}, {3759, 3782}, {5249, 17393}, {5271, 17249}, {7270, 20050}, {17184, 17360}, {17571, 19844}, {17573, 19845}, {19281, 19747}, {19535, 19841}, {19537, 19842}
X(19831) lies on these lines: {2, 37}, {4691, 16062}, {7270, 20053}, {19281, 19748}
X(19832) lies on these lines: {2, 37}, {1010, 19862}, {1125, 7270}, {1211, 17121}, {3624, 16062}, {5047, 19841}, {5219, 7247}, {16842, 19844}, {16862, 19845}, {17531, 19842}, {17536, 19850}, {17575, 19839}, {19281, 19749}
X(19833) lies on these lines: {2, 37}, {1010, 3244}, {3626, 7270}, {4363, 4886}, {19281, 19750}, {19535, 19845}, {19537, 19844}
X(19834) lies on these lines: {2, 37}, {27, 2203}, {239, 5814}, {1010, 17397}, {3187, 3416}, {4393, 7270}, {5249, 19719}, {17023, 19281}
X(19835) lies on these lines: {2, 37}, {8, 1370}, {22, 19845}, {306, 1930}, {377, 4385}, {712, 18202}, {1010, 3920}, {3701, 16062}, {3702, 7191}, {4228, 19848}, {4673, 19993}, {4696, 7270}, {5016, 7391}, {5133, 19839}, {6636, 19842}, {7081, 7465}, {7485, 19844}, {15246, 19841}
X(19836) lies on these lines: {1, 2}, {36, 15434}, {56, 17698}, {69, 1203}, {141, 16466}, {304, 17322}, {442, 17111}, {443, 11677}, {474, 8193}, {966, 5299}, {993, 17526}, {1001, 13728}, {1191, 3763}, {1213, 16502}, {1478, 13740}, {1479, 16062}, {1930, 17321}, {3619, 5315}, {3695, 17599}, {4000, 4647}, {4195, 4299}, {4201, 4302}, {4205, 4423}, {4657, 6051}, {4673, 17370}, {5251, 13742}, {5259, 13725}, {5749, 17744}, {5750, 17742}, {5955, 16610}, {6284, 11359}, {7354, 11354}, {10896, 16052}, {12410, 16408}, {15988, 16472}, {16298, 16678}, {17306, 18589}, {19873, 19946}, {19888, 19896}, {19891, 19928}
X(19837) lies on these lines: {2, 37}, {1010, 3626}, {1268, 3977}, {4031, 7247}, {4886, 17120}, {17574, 19842}, {19281, 19751}, {19526, 19845}
X(19838) lies on these lines: {1, 19281}, {2, 19848}, {3, 19792}, {4, 19793}, {27, 10449}, {75, 405}, {312, 7535}, {377, 18139}, {964, 19785}, {1003, 19849}, {1010, 15668}, {1011, 19787}, {1724, 3729}, {1985, 19839}, {2049, 19786}, {4245, 19807}, {11319, 19789}, {11320, 19851}, {11322, 19818}, {11346, 19819}, {11347, 19814}, {11354, 19796}, {11357, 19797}, {11358, 19803}, {13738, 19810}, {15978, 19782}, {16062, 19768}, {16843, 19804}, {16844, 19808}, {18147, 19285}, {19798, 19852}
X(19839) lies on these lines: {1, 16067}, {2, 19844}, {3, 19795}, {4, 19845}, {5, 75}, {12, 1010}, {30, 19842}, {140, 19841}, {345, 5142}, {377, 10590}, {427, 19799}, {429, 7283}, {442, 19808}, {1329, 16062}, {1370, 5552}, {1656, 19794}, {1985, 19838}, {2476, 19822}, {3142, 19810}, {4187, 19786}, {4193, 19785}, {5080, 16049}, {5133, 19835}, {5141, 19825}, {5154, 19789}, {7270, 17757}, {8728, 19827}, {14008, 19848}, {17527, 19812}, {17530, 19797}, {17533, 19796}, {17575, 19832}, {19281, 19754}
X(19840) lies on these lines: {1, 14012}, {3, 19810}, {21, 75}, {404, 19806}, {964, 19786}, {1010, 10448}, {1011, 19787}, {1468, 17157}, {4195, 19785}, {4203, 19803}, {4216, 19807}, {4224, 19799}, {7283, 13733}, {16342, 19808}, {16405, 19801}, {16452, 19792}, {19281, 19757}, {19811, 19845}
X(19841) lies on these lines: {3, 75}, {4, 19794}, {21, 19786}, {22, 19798}, {36, 1010}, {140, 19839}, {199, 19813}, {404, 19808}, {405, 19812}, {474, 19827}, {631, 19795}, {993, 16062}, {1011, 19803}, {2915, 16817}, {2975, 3006}, {3682, 18042}, {4184, 19787}, {4188, 19822}, {4189, 19785}, {5047, 19832}, {5267, 17512}, {5303, 16049}, {5433, 16067}, {7485, 19799}, {9895, 16568}, {11337, 19804}, {11344, 19802}, {13587, 19797}, {15246, 19835}, {16452, 19792}, {17524, 19821}, {17548, 19789}, {17549, 19796}, {17574, 19829}, {19281, 19759}, {19535, 19830}
X(19842) lies on these lines: {3, 75}, {4, 19795}, {10, 17512}, {21, 19808}, {22, 19799}, {30, 19839}, {35, 1010}, {42, 2363}, {71, 1098}, {100, 1792}, {197, 341}, {312, 11337}, {345, 7520}, {377, 5218}, {404, 19786}, {405, 19827}, {474, 19812}, {631, 19794}, {662, 3682}, {987, 3764}, {1043, 5285}, {2915, 7283}, {3101, 18719}, {4188, 19785}, {4189, 19822}, {4191, 19803}, {4210, 19787}, {4216, 19807}, {4225, 19810}, {6284, 16067}, {6636, 19835}, {7485, 19798}, {11349, 19815}, {11350, 19814}, {13587, 19796}, {13738, 19806}, {16451, 19792}, {17531, 19832}, {17548, 19825}, {17549, 19797}, {17574, 19837}, {19281, 19760}, {19308, 19791}, {19537, 19830}
X(19843) lies on these lines: {1, 2}, {3, 1602}, {4, 958}, {5, 2551}, {7, 12609}, {9, 946}, {11, 5084}, {12, 3421}, {20, 993}, {21, 3434}, {35, 17784}, {36, 6904}, {40, 5745}, {46, 5744}, {55, 5082}, {56, 443}, {58, 4307}, {63, 4295}, {72, 3485}, {75, 3926}, {100, 6910}, {104, 6897}, {140, 9709}, {142, 3333}, {149, 16865}, {210, 11375}, {219, 966}, {278, 475}, {280, 17860}, {329, 12047}, {347, 18698}, {355, 6825}, {377, 2975}, {388, 442}, {390, 5248}, {404, 7742}, {405, 497}, {452, 1479}, {474, 1617}, {496, 11108}, {515, 6908}, {516, 5833}, {517, 5791}, {518, 3487}, {631, 1376}, {943, 1001}, {944, 5794}, {960, 5603}, {962, 5273}, {988, 1738}, {999, 8728}, {1000, 10912}, {1006, 12116}, {1056, 12513}, {1071, 18251}, {1107, 5286}, {1108, 17303}, {1213, 2256}, {1329, 3090}, {1377, 3069}, {1378, 3068}, {1385, 6989}, {1389, 6852}, {1468, 4340}, {1478, 5177}, {1482, 6861}, {1486, 17560}, {1573, 3767}, {1612, 5263}, {1656, 3820}, {1699, 5234}, {1706, 6684}, {1723, 5749}, {1788, 3753}, {1792, 11110}, {1838, 4200}, {1861, 3088}, {2257, 5750}, {2345, 5831}, {2476, 3436}, {2478, 5260}, {3035, 3525}, {3058, 17561}, {3219, 11415}, {3295, 6675}, {3338, 9776}, {3361, 8732}, {3419, 3486}, {3427, 12616}, {3452, 8227}, {3474, 3916}, {3475, 3555}, {3518, 9713}, {3522, 5267}, {3523, 15931}, {3600, 3841}, {3646, 6666}, {3678, 5686}, {3683, 12701}, {3702, 17776}, {3814, 5056}, {3816, 17559}, {3817, 18250}, {3822, 5261}, {3826, 17582}, {3838, 5714}, {3874, 11036}, {3878, 6884}, {3881, 11038}, {3913, 6690}, {4005, 4870}, {4187, 10589}, {4220, 9798}, {4223, 11365}, {4224, 8193}, {4301, 18249}, {4302, 17576}, {4413, 5433}, {4423, 17552}, {4512, 10624}, {4640, 6361}, {5044, 5761}, {5045, 15185}, {5067, 9711}, {5080, 6871}, {5123, 6983}, {5129, 5274}, {5175, 10572}, {5218, 5687}, {5223, 8232}, {5225, 11113}, {5226, 5815}, {5229, 17532}, {5265, 17580}, {5278, 16471}, {5281, 8715}, {5289, 10595}, {5435, 11024}, {5438, 10165}, {5542, 5785}, {5587, 5795}, {5657, 5836}, {5659, 6888}, {5690, 6862}, {5698, 12699}, {5706, 5737}, {5721, 5793}, {5731, 17647}, {5784, 12675}, {5790, 6863}, {5811, 12608}, {5818, 6834}, {5832, 15823}, {5837, 7982}, {5936, 7318}, {6284, 11111}, {6459, 9678}, {6763, 9965}, {6826, 11249}, {6829, 10532}, {6842, 18542}, {6853, 10786}, {6855, 7680}, {6867, 10526}, {6869, 18517}, {6874, 10599}, {6877, 10597}, {6878, 10806}, {6881, 10680}, {6883, 10943}, {6886, 18228}, {6892, 11248}, {6907, 12667}, {6916, 12114}, {6919, 7741}, {6920, 10531}, {6930, 10525}, {6933, 11681}, {6935, 10310}, {6937, 12115}, {6939, 7681}, {6944, 9956}, {6952, 8256}, {6954, 11499}, {6964, 10175}, {6965, 10598}, {6988, 11500}, {7512, 9712}, {8164, 12607}, {9612, 12527}, {9799, 12520}, {9961, 17646}, {10385, 15670}, {10473, 10822}, {10519, 17792}, {10588, 17757}, {11376, 17642}, {11525, 12640}, {13161, 17064}, {13464, 15829}, {14450, 20078}, {15171, 16418}, {15325, 16408}, {16699, 17905}, {17528, 18990}, {19884, 19888}, {19927, 19946}
X(19844) lies on these lines: {2, 19839}, {3, 75}, {5, 19794}, {8, 7465}, {21, 19785}, {25, 16817}, {56, 1010}, {140, 19795}, {345, 7523}, {377, 2975}, {404, 19822}, {405, 19786}, {443, 1791}, {474, 19808}, {499, 16067}, {956, 7270}, {958, 16062}, {975, 19314}, {1011, 19787}, {1370, 10527}, {1760, 9895}, {3145, 19805}, {3428, 10465}, {3757, 8193}, {4184, 19848}, {4188, 19825}, {4189, 19789}, {4359, 11337}, {7484, 19799}, {7485, 19835}, {8192, 16821}, {9798, 16824}, {11108, 19812}, {11344, 19788}, {11365, 16823}, {13615, 19790}, {13726, 19793}, {16058, 19803}, {16287, 19792}, {16293, 19802}, {16367, 19791}, {16370, 19796}, {16371, 19797}, {16372, 19800}, {16373, 19801}, {16374, 19807}, {16408, 19827}, {16842, 19832}, {16843, 17322}, {16865, 19823}, {17030, 19281}, {17548, 19826}, {17549, 19819}, {17571, 19830}, {19526, 19829}, {19535, 19820}, {19537, 19833}
X(19845) lies on these lines: {3, 75}, {4, 19839}, {5, 19795}, {8, 16049}, {21, 19822}, {22, 19835}, {25, 7283}, {27, 1259}, {28, 345}, {55, 1010}, {100, 377}, {140, 19794}, {197, 4385}, {321, 11337}, {404, 19785}, {405, 19808}, {474, 19786}, {859, 19807}, {958, 17512}, {1376, 16062}, {1479, 16067}, {1958, 3682}, {3685, 11365}, {4188, 19789}, {4189, 19825}, {4191, 19787}, {4225, 19848}, {5687, 7270}, {7085, 9534}, {7484, 19798}, {11108, 19827}, {11329, 19791}, {13587, 19819}, {13738, 19810}, {16059, 19803}, {16370, 19797}, {16371, 19796}, {16408, 19812}, {16410, 19802}, {16453, 19792}, {16862, 19832}, {17572, 19823}, {17573, 19830}, {19281, 19763}, {19526, 19837}, {19535, 19833}, {19537, 19820}, {19811, 19840}
X(19846) lies on these lines: {1, 2}, {35, 4429}, {475, 1842}, {750, 6693}, {964, 3841}, {993, 4202}, {1089, 3772}, {1104, 4680}, {1213, 2273}, {1479, 13742}, {1724, 2887}, {2218, 3925}, {3338, 17282}, {3583, 17697}, {3662, 6763}, {3670, 4438}, {4972, 5248}, {5251, 16062}, {5264, 6679}, {5294, 12609}, {5506, 17338}, {6533, 17278}, {7741, 13741}, {9591, 17522}, {10483, 17678}, {12047, 17353}, {19873, 19927}, {19884, 19896}
X(19847) lies on these lines: {1, 2}, {36, 13741}, {3777, 19947}, {3825, 4202}, {4647, 16610}, {7280, 17697}
X(19848) lies on these lines: {2, 19838}, {8, 27}, {21, 75}, {28, 321}, {377, 1043}, {404, 19792}, {1010, 3616}, {4184, 19844}, {4225, 19845}, {4228, 19835}, {4234, 19819}, {4358, 17581}, {4720, 7270}, {10538, 16049}, {11110, 19822}, {11115, 19789}, {13588, 19787}, {14005, 19786}, {14008, 19839}, {16046, 19849}, {17539, 19826}, {17551, 19812}, {17553, 19797}, {17557, 19808}, {17588, 19825}, {17589, 19823}, {19281, 19767}
X(19849) lies on these lines: {1, 849}, {27, 3011}, {28, 3290}, {75, 11104}, {1003, 19838}, {2218, 14015}, {4234, 19797}, {4236, 19850}, {16046, 19848}
X(19850) lies on these lines: {1, 7465}, {2, 19839}, {3, 19785}, {21, 19786}, {36, 16049}, {56, 377}, {75, 404}, {81, 11573}, {108, 5125}, {411, 19788}, {474, 19822}, {1010, 5253}, {1370, 3086}, {1791, 4202}, {2476, 19794}, {2975, 16062}, {3193, 5137}, {4000, 11337}, {4188, 19789}, {4189, 19823}, {4203, 19803}, {4220, 5262}, {4236, 19849}, {4239, 16817}, {5047, 19812}, {5303, 17512}, {7411, 19790}, {11322, 19818}, {13587, 19796}, {13588, 19787}, {16371, 19819}, {17531, 19808}, {17535, 19827}, {17536, 19832}, {17566, 19795}, {17572, 19825}, {19281, 19769}
X(19851) lies on these lines: {1, 2}, {3, 17490}, {7, 20077}, {21, 3210}, {28, 330}, {72, 17349}, {75, 1104}, {192, 405}, {193, 11036}, {321, 17697}, {748, 19582}, {894, 1453}, {956, 17480}, {966, 16519}, {1010, 4699}, {1043, 4361}, {1278, 7283}, {1279, 4673}, {1724, 17350}, {1851, 4198}, {2345, 16974}, {3672, 13736}, {3769, 3812}, {3875, 5436}, {3891, 5260}, {3995, 16859}, {4000, 4201}, {4189, 17495}, {4313, 4402}, {4452, 11106}, {4740, 13735}, {4850, 19278}, {6872, 19789}, {11320, 19838}, {13725, 17302}, {13728, 17383}, {13742, 17280}, {14829, 17054}, {16485, 17117}, {16865, 17147}, {17127, 17164}
X(19852) lies on these lines: {75, 11108}, {442, 19786}, {2478, 19785}, {4204, 16817}, {6871, 19823}, {7283, 19805}, {13615, 19790}, {16410, 19802}, {17590, 19808}, {19798, 19838}
P(10) = b : c : a (barycentrics) and U(10) = c : a : b are a bicentric pair.
X(19853) lies on these lines: {1, 2}, {55, 11110}, {100, 16342}, {181, 3485}, {192, 4647}, {213, 966}, {274, 3596}, {330, 1224}, {333, 5711}, {405, 5263}, {573, 962}, {726, 17038}, {946, 9535}, {956, 16458}, {958, 1010}, {964, 5260}, {970, 5603}, {1107, 5069}, {1191, 17259}, {1203, 17349}, {1213, 2176}, {1220, 2049}, {1376, 19270}, {1621, 19763}, {1695, 4301}, {1756, 4295}, {2345, 5283}, {2550, 13725}, {2975, 16454}, {3295, 16844}, {3476, 9552}, {3486, 9555}, {3600, 17077}, {3868, 4981}, {3871, 17557}, {3925, 16062}, {4026, 9710}, {4195, 5251}, {4276, 17588}, {4294, 13736}, {4357, 17753}, {4429, 13728}, {4673, 4687}, {5226, 10408}, {5303, 19336}, {5584, 13727}, {5710, 19732}, {5734, 9568}, {5749, 16552}, {5901, 9567}, {8192, 16353}, {8193, 19310}, {9549, 13464}, {9709, 19273}, {12410, 19309}, {16466, 17277}, {17050, 17306}, {17143, 17321}, {17144, 17322}, {19891, 19937}
X(19854) lies on these lines: {1, 2}, {3, 3925}, {4, 5251}, {5, 3428}, {7, 6763}, {9, 12047}, {11, 11108}, {12, 9708}, {21, 4302}, {35, 2550}, {36, 443}, {40, 6824}, {46, 5745}, {55, 6675}, {56, 8728}, {63, 12609}, {65, 5791}, {120, 19313}, {140, 4413}, {142, 3338}, {165, 6847}, {191, 4295}, {210, 11374}, {219, 1213}, {278, 1224}, {345, 4647}, {377, 993}, {388, 5258}, {405, 1479}, {442, 958}, {452, 3583}, {474, 3826}, {475, 1838}, {496, 4423}, {497, 5259}, {515, 6889}, {516, 6837}, {517, 6861}, {631, 6796}, {946, 6832}, {962, 6884}, {1001, 11517}, {1056, 5288}, {1376, 7483}, {1377, 13963}, {1378, 13905}, {1617, 5433}, {1699, 6846}, {1723, 5750}, {2077, 6892}, {2476, 5260}, {2551, 6856}, {2975, 4197}, {3336, 5744}, {3337, 9776}, {3434, 4309}, {3436, 3822}, {3485, 5692}, {3487, 5904}, {3576, 6989}, {3585, 5177}, {3649, 3927}, {3683, 12699}, {3698, 6862}, {3746, 5082}, {3814, 6933}, {3816, 16842}, {3817, 6886}, {3824, 10404}, {3829, 17542}, {3838, 5302}, {3894, 11036}, {3916, 5880}, {4190, 5267}, {4208, 4293}, {4220, 8185}, {4294, 17558}, {4313, 5426}, {4324, 17576}, {4429, 19270}, {4679, 9955}, {4699, 7836}, {4972, 16342}, {5044, 5173}, {5047, 11680}, {5084, 7741}, {5129, 10591}, {5234, 9612}, {5274, 17554}, {5432, 9709}, {5450, 6897}, {5506, 18230}, {5584, 8727}, {5587, 6825}, {5603, 5659}, {5657, 6852}, {5687, 6690}, {5691, 6908}, {5759, 15909}, {5770, 15016}, {5795, 10827}, {5818, 6853}, {5905, 11263}, {6256, 6937}, {6284, 16418}, {6668, 9711}, {6684, 6833}, {6691, 16862}, {6826, 11012}, {6834, 10175}, {6838, 19925}, {6848, 7989}, {6851, 7688}, {6863, 9956}, {6869, 18406}, {6877, 10532}, {6878, 12116}, {6881, 11249}, {6887, 7308}, {6890, 10164}, {6904, 7280}, {6913, 15908}, {6958, 11231}, {6983, 10172}, {7288, 17582}, {7354, 17528}, {7489, 10525}, {8071, 19520}, {8167, 17590}, {9342, 17566}, {9668, 16866}, {9669, 16857}, {10165, 10785}, {10431, 12511}, {10589, 17559}, {15338, 17571}, {15676, 20066}, {16415, 16678}, {16471, 19732}, {19884, 19930}
X(19855) lies on these lines: {1, 2}, {4, 3925}, {9, 4295}, {11, 17559}, {20, 5251}, {35, 17558}, {36, 17580}, {40, 6846}, {46, 5273}, {55, 16845}, {56, 17582}, {149, 17570}, {197, 7523}, {210, 3487}, {218, 966}, {220, 1213}, {277, 3739}, {279, 1224}, {281, 475}, {329, 12609}, {346, 4647}, {355, 6989}, {377, 5260}, {388, 8728}, {390, 5259}, {391, 17745}, {405, 2550}, {442, 2551}, {443, 958}, {496, 16853}, {497, 11108}, {517, 6887}, {631, 4413}, {946, 7308}, {956, 17529}, {962, 6886}, {993, 6904}, {1001, 5082}, {1058, 4423}, {1191, 17337}, {1329, 6856}, {1376, 6857}, {1478, 4208}, {1479, 5129}, {1656, 8158}, {1724, 4307}, {1788, 5791}, {2093, 18249}, {2345, 16601}, {2886, 5084}, {3090, 7680}, {3428, 6864}, {3434, 5047}, {3436, 4197}, {3485, 5044}, {3525, 10785}, {3600, 5258}, {3646, 12053}, {3649, 3715}, {3671, 8232}, {3683, 6361}, {3698, 5657}, {3813, 8167}, {3820, 10588}, {3841, 5177}, {3983, 17718}, {4223, 8193}, {4292, 5234}, {4298, 8732}, {4302, 11106}, {4340, 5247}, {4429, 13725}, {4472, 7960}, {4673, 17263}, {4999, 17567}, {5218, 6675}, {5229, 17528}, {5248, 17784}, {5263, 13742}, {5302, 5880}, {5316, 6766}, {5587, 6908}, {5686, 5904}, {5692, 12432}, {5750, 16572}, {5815, 13407}, {5817, 12688}, {5818, 6889}, {6247, 7959}, {6600, 17590}, {6684, 6847}, {6825, 9956}, {6848, 10175}, {6878, 11491}, {6891, 11231}, {6921, 9342}, {6939, 15908}, {7288, 16408}, {7951, 8165}, {9612, 18250}, {10589, 17527}, {12047, 18228}, {12260, 15998}, {12756, 12854}, {13726, 18610}, {15171, 16857}, {15325, 16863}, {17158, 17322}, {19888, 19900}, {19930, 19937}
X(19856) lies on these lines: {1, 2}, {35, 16850}, {55, 16846}, {86, 3775}, {238, 1213}, {291, 1224}, {350, 4647}, {514, 19882}, {740, 17322}, {966, 16468}, {984, 17303}, {1009, 5251}, {1010, 6626}, {1011, 8185}, {1203, 2238}, {1757, 5750}, {3789, 5904}, {3821, 17326}, {3836, 17307}, {3842, 17289}, {3923, 17248}, {4438, 19827}, {4649, 17398}, {4655, 17250}, {4672, 17256}, {4716, 4733}, {4966, 6707}, {5259, 8299}, {13632, 18480}, {16477, 17330}, {17252, 17770}, {19886, 19933}, {19888, 19944}, {19898, 19943}
X(19857) lies on these lines: {1, 2}, {28, 1224}, {37, 17514}, {55, 16843}, {72, 1213}, {209, 5044}, {405, 17303}, {958, 19285}, {1043, 1268}, {1376, 19523}, {1724, 5750}, {1869, 5142}, {3419, 19753}, {3739, 13728}, {5130, 19756}, {5302, 7359}, {5711, 19728}, {5814, 19701}, {7270, 14007}, {11110, 19808}, {17357, 17590}, {19930, 19932}
X(19858) lies on these lines: {1, 2}, {3, 16682}, {35, 16342}, {36, 16454}, {39, 17303}, {56, 16458}, {181, 11375}, {474, 16678}, {475, 5307}, {573, 946}, {596, 17038}, {958, 2049}, {964, 5251}, {970, 5886}, {993, 1010}, {994, 3878}, {999, 16456}, {1001, 16844}, {1191, 19744}, {1203, 5278}, {1220, 19280}, {1319, 9552}, {1376, 19273}, {1621, 17557}, {1682, 11376}, {1695, 11522}, {2051, 8227}, {2140, 17306}, {2646, 9555}, {2886, 4205}, {2975, 14005}, {3032, 16173}, {3295, 16457}, {3303, 19272}, {3361, 17077}, {3746, 19334}, {3841, 16062}, {3925, 13728}, {4253, 5750}, {4276, 5248}, {4279, 16690}, {4357, 12609}, {4366, 16929}, {4981, 5904}, {5010, 16347}, {5204, 19290}, {5217, 16351}, {5219, 10408}, {5711, 5737}, {6284, 13745}, {6645, 16928}, {6846, 10445}, {7280, 19284}, {7288, 16878}, {8193, 16352}, {8666, 14007}, {9549, 9568}, {9553, 17605}, {9566, 18493}, {10436, 16887}, {11365, 19309}, {12511, 13727}, {15654, 19533}, {16466, 19732}, {19884, 19886}, {19891, 19893}, {19933, 19953}
X(19859) lies on these lines: {1, 2}, {4, 5257}, {9, 2049}, {29, 4512}, {35, 16346}, {55, 16416}, {57, 16458}, {63, 14005}, {307, 5290}, {942, 16456}, {965, 5711}, {966, 5717}, {1104, 19744}, {1453, 19732}, {1781, 12514}, {2901, 16673}, {3247, 5295}, {3419, 17514}, {3576, 5786}, {3868, 17551}, {4208, 18655}, {5285, 19285}, {5296, 12572}, {5436, 16844}, {5438, 19273}, {5725, 5742}, {5799, 8227}, {7532, 9816}, {8728, 17306}, {9593, 17303}, {10436, 14007}, {11024, 17220}, {15803, 16454}, {16410, 16678}, {19885, 19886}
X(19860) lies on these lines: {1, 2}, {3, 3753}, {6, 4875}, {9, 1405}, {21, 40}, {33, 5174}, {34, 92}, {37, 3692}, {46, 993}, {55, 5836}, {56, 3306}, {57, 2975}, {63, 65}, {72, 9708}, {77, 1441}, {85, 4350}, {86, 322}, {100, 1706}, {142, 10106}, {144, 12560}, {165, 4189}, {169, 16788}, {210, 3984}, {224, 3925}, {226, 3436}, {354, 12513}, {355, 442}, {377, 515}, {388, 5249}, {392, 1482}, {404, 3576}, {405, 517}, {443, 944}, {452, 962}, {474, 1385}, {516, 6872}, {518, 11520}, {529, 10404}, {758, 3951}, {894, 2263}, {908, 2551}, {942, 956}, {946, 2478}, {950, 3434}, {952, 8728}, {960, 2099}, {966, 3553}, {990, 17676}, {999, 5439}, {1001, 3057}, {1013, 11471}, {1038, 6350}, {1104, 5710}, {1155, 3922}, {1159, 3927}, {1191, 17825}, {1203, 5422}, {1222, 2191}, {1320, 7160}, {1329, 11375}, {1376, 2646}, {1420, 5253}, {1457, 19372}, {1467, 3600}, {1478, 12609}, {1490, 5177}, {1512, 6825}, {1519, 6893}, {1621, 1697}, {1656, 17619}, {1699, 5046}, {1790, 17518}, {1837, 2886}, {2098, 4423}, {2136, 10389}, {2294, 5227}, {2295, 16968}, {2322, 2331}, {2324, 5296}, {2346, 3680}, {2475, 5691}, {2476, 5587}, {2550, 3486}, {2650, 3751}, {2951, 5059}, {3036, 12739}, {3146, 12565}, {3158, 11530}, {3174, 12536}, {3218, 3339}, {3219, 5234}, {3295, 3895}, {3303, 3880}, {3304, 3742}, {3338, 5883}, {3359, 6906}, {3421, 3487}, {3428, 7686}, {3488, 5082}, {3555, 15934}, {3579, 16370}, {3612, 3918}, {3646, 5330}, {3654, 15670}, {3662, 4327}, {3671, 5905}, {3681, 11523}, {3697, 3940}, {3729, 17164}, {3731, 4936}, {3748, 3893}, {3816, 11376}, {3817, 5187}, {3822, 10827}, {3838, 10895}, {3868, 11529}, {3873, 6762}, {3877, 5047}, {3890, 5284}, {3916, 4004}, {3929, 11684}, {3953, 16499}, {3962, 5220}, {4002, 5440}, {4051, 16503}, {4187, 5886}, {4188, 7987}, {4190, 4297}, {4193, 8227}, {4197, 5881}, {4208, 18444}, {4225, 10434}, {4298, 20076}, {4311, 12436}, {4313, 17784}, {4314, 20075}, {4318, 5749}, {4323, 18228}, {4357, 7190}, {4512, 7991}, {4640, 10107}, {4642, 10448}, {4646, 19765}, {4848, 5745}, {4881, 17572}, {4968, 17862}, {5044, 5730}, {5045, 19521}, {5048, 8167}, {5080, 9612}, {5084, 5603}, {5086, 5727}, {5119, 5248}, {5141, 7989}, {5154, 7988}, {5175, 10382}, {5176, 9578}, {5178, 12625}, {5219, 11681}, {5251, 5903}, {5258, 5902}, {5259, 5697}, {5283, 9620}, {5288, 18398}, {5289, 11011}, {5290, 20060}, {5303, 9352}, {5425, 5904}, {5438, 13384}, {5538, 9588}, {5657, 6857}, {5690, 6675}, {5706, 16346}, {5707, 16344}, {5720, 5818}, {5731, 6904}, {5748, 8165}, {5880, 7354}, {5901, 17527}, {5919, 10912}, {5985, 9860}, {6175, 16132}, {6264, 17535}, {6361, 11111}, {6667, 12740}, {6684, 6910}, {6690, 8256}, {6769, 17558}, {6871, 19925}, {6912, 12705}, {6913, 12672}, {6921, 10165}, {6933, 10175}, {7308, 15829}, {7504, 7705}, {7674, 8236}, {7967, 17582}, {8148, 16857}, {8545, 12709}, {9581, 11680}, {9778, 17576}, {9955, 17556}, {10222, 16842}, {10246, 16408}, {10247, 16853}, {10394, 12529}, {10441, 19283}, {10595, 17559}, {10601, 16466}, {10864, 11220}, {11106, 12651}, {11112, 18481}, {11113, 12699}, {11115, 17194}, {11224, 17570}, {11278, 17542}, {11281, 12607}, {11374, 17757}, {11415, 12572}, {11531, 16859}, {12245, 16845}, {12435, 17185}, {12680, 17616}, {12702, 16418}, {13369, 18519}, {13624, 16371}, {14007, 18465}, {14828, 16284}, {15066, 16474}, {15178, 16862}, {16192, 17548}, {16295, 16678}, {16353, 19782}, {17502, 19537}, {17528, 18525}, {17532, 18480}, {17577, 18492}, {18180, 19259}, {19884, 19890}, {19885, 19893}
See Dasari Naga Vijay Krishna, On a Conic Through Twelve Notable Points, Int. J. Adv. Math. and Mech. 7(2) (2019) 1-15.
X(19861) lies on these lines: {1, 2}, {3, 392}, {9, 604}, {11, 5794}, {21, 84}, {33, 11109}, {34, 17555}, {36, 4652}, {37, 5782}, {40, 404}, {46, 3878}, {55, 4855}, {56, 63}, {57, 3869}, {65, 3306}, {72, 999}, {77, 4357}, {100, 1697}, {104, 7330}, {144, 4321}, {165, 4188}, {205, 572}, {210, 12513}, {214, 3612}, {224, 1001}, {283, 602}, {326, 17321}, {329, 3600}, {348, 4350}, {354, 11520}, {355, 4187}, {377, 946}, {388, 908}, {394, 16466}, {405, 1385}, {442, 5886}, {443, 5603}, {452, 1490}, {474, 517}, {496, 3419}, {500, 13745}, {515, 2478}, {516, 4190}, {518, 3304}, {632, 19907}, {758, 3338}, {894, 4327}, {912, 16203}, {942, 5730}, {944, 5084}, {952, 17527}, {956, 5044}, {958, 1319}, {962, 6282}, {965, 1108}, {966, 3554}, {988, 2292}, {990, 11115}, {1038, 1457}, {1064, 13725}, {1191, 2221}, {1203, 1993}, {1329, 5252}, {1331, 1496}, {1376, 3057}, {1448, 17184}, {1458, 17257}, {1467, 5265}, {1479, 17647}, {1482, 3753}, {1512, 6944}, {1519, 6850}, {1572, 5277}, {1616, 3744}, {1621, 3601}, {1699, 2475}, {1706, 7962}, {1837, 3816}, {2098, 4413}, {2099, 3812}, {2256, 3692}, {2257, 2287}, {2263, 3662}, {2322, 7129}, {2324, 5749}, {2476, 8227}, {2551, 3476}, {2886, 11376}, {3035, 12740}, {3174, 8236}, {3218, 3361}, {3219, 13462}, {3242, 3445}, {3243, 11025}, {3295, 5440}, {3303, 10179}, {3333, 3868}, {3336, 3899}, {3340, 5437}, {3359, 6940}, {3430, 4239}, {3434, 12053}, {3436, 3452}, {3485, 5249}, {3522, 12565}, {3555, 3940}, {3556, 7293}, {3579, 16371}, {3646, 3897}, {3653, 15670}, {3681, 6762}, {3689, 4917}, {3698, 5048}, {3702, 17862}, {3740, 11260}, {3814, 10827}, {3817, 6871}, {3825, 10826}, {3873, 11523}, {3884, 5119}, {3895, 5687}, {3898, 8715}, {3911, 5837}, {3913, 5919}, {3928, 11684}, {3951, 5563}, {4018, 5708}, {4101, 11433}, {4189, 4512}, {4193, 5587}, {4197, 9624}, {4225, 10882}, {4292, 11415}, {4297, 6872}, {4298, 5905}, {4308, 18228}, {4311, 12572}, {4315, 12527}, {4334, 6646}, {4355, 17483}, {4640, 5204}, {4848, 6692}, {4867, 12559}, {5018, 17236}, {5046, 5691}, {5057, 9579}, {5080, 9613}, {5086, 9581}, {5087, 10895}, {5128, 9352}, {5141, 7988}, {5154, 7989}, {5175, 5274}, {5187, 19925}, {5260, 7308}, {5261, 5748}, {5266, 16483}, {5276, 9575}, {5283, 9619}, {5284, 5436}, {5315, 15066}, {5316, 5795}, {5330, 7982}, {5534, 7967}, {5538, 11522}, {5657, 17567}, {5698, 8544}, {5732, 17576}, {5734, 11024}, {5752, 19257}, {5780, 10246}, {5790, 17619}, {5882, 17857}, {5887, 10269}, {5901, 8728}, {6265, 6713}, {6684, 6921}, {6769, 17580}, {6857, 18443}, {6909, 12705}, {6910, 10165}, {6919, 12650}, {6931, 10175}, {7174, 15839}, {7190, 10436}, {7991, 17572}, {8158, 16411}, {8666, 10176}, {9578, 11681}, {9709, 10914}, {9785, 17784}, {9841, 9961}, {9945, 10386}, {9954, 12128}, {9955, 17532}, {10074, 18254}, {10222, 16862}, {10247, 16863}, {10444, 17183}, {10595, 17582}, {10861, 11372}, {11014, 17566}, {11110, 18465}, {11112, 12699}, {11113, 18481}, {11533, 17591}, {12114, 18239}, {12575, 20075}, {12688, 17616}, {12702, 16417}, {13624, 16370}, {15178, 16842}, {15677, 16143}, {15988, 16475}, {16200, 17535}, {16294, 16678}, {16352, 19782}, {17194, 17588}, {17502, 19535}, {17528, 18493}, {17556, 18480}, {17558, 18444}, {19884, 19889}, {19885, 19894}
X(19862) lies on these lines: {1, 2}, {3, 3817}, {4, 10171}, {5, 4297}, {9, 5551}, {11, 3841}, {12, 4315}, {20, 7988}, {35, 5284}, {36, 5047}, {40, 3525}, {44, 5257}, {45, 3986}, {55, 16862}, {56, 3947}, {58, 17123}, {65, 3833}, {79, 15671}, {86, 16477}, {140, 946}, {142, 3647}, {165, 10303}, {210, 3881}, {214, 6667}, {226, 5433}, {321, 6533}, {354, 3678}, {355, 5070}, {392, 3754}, {404, 5259}, {405, 5204}, {442, 3825}, {443, 5225}, {474, 4423}, {496, 3826}, {515, 1656}, {516, 631}, {517, 632}, {527, 4798}, {546, 17502}, {547, 18480}, {549, 9955}, {590, 13971}, {595, 17122}, {596, 3971}, {615, 8983}, {620, 11599}, {726, 4687}, {748, 19334}, {756, 3953}, {758, 5439}, {940, 19272}, {942, 3848}, {956, 16856}, {958, 16853}, {960, 4084}, {993, 11108}, {999, 16855}, {1001, 16408}, {1010, 19832}, {1155, 6681}, {1213, 16666}, {1376, 16863}, {1385, 3628}, {1420, 10588}, {1621, 17535}, {1699, 3523}, {1724, 17125}, {1738, 17370}, {2345, 4098}, {2802, 3698}, {2975, 17534}, {3035, 14150}, {3057, 3918}, {3090, 3576}, {3091, 7987}, {3159, 6532}, {3219, 3337}, {3246, 3836}, {3247, 4072}, {3305, 3338}, {3361, 5226}, {3452, 4999}, {3454, 17514}, {3526, 4301}, {3533, 5603}, {3555, 4015}, {3589, 4663}, {3601, 10589}, {3614, 3822}, {3619, 16475}, {3646, 5437}, {3653, 15703}, {3654, 15723}, {3663, 17322}, {3671, 3911}, {3697, 17609}, {3739, 3993}, {3740, 5045}, {3742, 3874}, {3743, 3752}, {3753, 3884}, {3763, 5847}, {3812, 3878}, {3814, 5126}, {3816, 8728}, {3821, 17400}, {3824, 5087}, {3868, 4525}, {3869, 4744}, {3876, 4537}, {3898, 5836}, {3931, 16602}, {3946, 4133}, {3950, 16672}, {3968, 10914}, {4002, 5919}, {4058, 16777}, {4065, 10180}, {4066, 4358}, {4078, 17357}, {4125, 4968}, {4197, 4304}, {4298, 5219}, {4308, 5726}, {4311, 7951}, {4342, 11376}, {4349, 17245}, {4356, 17278}, {4357, 4896}, {4364, 4912}, {4413, 8715}, {4470, 17132}, {4643, 4758}, {4653, 14007}, {4657, 17067}, {4662, 5049}, {4667, 4708}, {4709, 15569}, {4848, 15950}, {4860, 15650}, {4887, 10436}, {4909, 17270}, {4991, 17394}, {5010, 17572}, {5054, 12699}, {5055, 18481}, {5056, 5691}, {5067, 5587}, {5071, 18492}, {5084, 5229}, {5218, 12575}, {5220, 5542}, {5234, 5328}, {5251, 5253}, {5260, 5563}, {5261, 13462}, {5264, 17124}, {5265, 5290}, {5303, 16861}, {5316, 17590}, {5325, 6147}, {5432, 12053}, {5444, 10572}, {5625, 17348}, {5657, 9624}, {5708, 5745}, {5714, 12572}, {5731, 7486}, {5749, 15828}, {5790, 13607}, {5850, 18230}, {5882, 9956}, {5901, 11231}, {5972, 13605}, {6051, 16610}, {6245, 6861}, {6361, 15702}, {6541, 17385}, {6683, 12263}, {6701, 15670}, {6715, 11814}, {6721, 11710}, {6722, 11711}, {6723, 11720}, {6852, 12617}, {6857, 12436}, {6915, 15931}, {6946, 10902}, {7280, 16865}, {7561, 18589}, {7585, 13942}, {7586, 13888}, {7958, 12558}, {8148, 13464}, {8252, 13936}, {8253, 13883}, {8666, 16854}, {8972, 19003}, {9579, 17561}, {9591, 15246}, {9779, 15717}, {9782, 11552}, {9812, 16192}, {9819, 18220}, {9943, 10156}, {10481, 17095}, {11365, 16419}, {11573, 15049}, {11709, 12900}, {12675, 15064}, {13893, 13959}, {13902, 13947}, {13941, 19004}, {14969, 19751}, {15066, 16472}, {15601, 17306}, {15668, 16457}, {15672, 16118}, {15694, 18493}, {16296, 16678}, {16589, 16604}, {16676, 17355}, {16948, 17557}, {17326, 17770}, {17384, 17764}, {19886, 19985}, {19933, 19962}, {19935, 19936}
X(19862) = midpoint of X(1) and X(3617)
X(19862) = complement of X(1698)
X(19862) = anticomplement of X(31253)
X(19862) = {X(1),X(2)}-harmonic conjugate of X(3634)
X(19863) lies on these lines: {1, 2}, {4, 10882}, {11, 4205}, {12, 10475}, {35, 5263}, {36, 1010}, {55, 19273}, {56, 2049}, {86, 10452}, {314, 17322}, {333, 1203}, {350, 10471}, {631, 10434}, {894, 6763}, {946, 1764}, {964, 993}, {1213, 2300}, {1220, 5258}, {1402, 5433}, {1479, 13725}, {1756, 4357}, {2183, 5257}, {2260, 5750}, {2886, 13728}, {3090, 10887}, {3091, 10465}, {3159, 3989}, {3338, 10436}, {3487, 11021}, {3576, 10454}, {3666, 4647}, {3670, 6682}, {3678, 4981}, {3702, 3743}, {3739, 6533}, {3817, 12545}, {3841, 4202}, {3846, 15825}, {3953, 4022}, {4423, 16844}, {4657, 10472}, {4975, 6051}, {5010, 19278}, {5204, 19276}, {5217, 19279}, {5248, 16342}, {5249, 10461}, {5251, 13740}, {5253, 14005}, {5259, 11110}, {5267, 11115}, {5270, 5484}, {5284, 17557}, {5443, 18417}, {5506, 17260}, {5563, 19280}, {5603, 12435}, {5737, 16466}, {5814, 17723}, {5886, 10441}, {6837, 10444}, {6846, 10888}, {6847, 10856}, {8227, 10476}, {10165, 10470}, {10447, 17321}, {10473, 11375}, {10474, 15950}, {10480, 11376}, {11263, 17184}, {11365, 16352}, {11521, 13464}, {19884, 19891}, {19886, 19927}, {19894, 19929}
X(19863) = complement of X(26115)
X(19864) lies on these lines: {1, 2}, {36, 13740}, {894, 3337}, {993, 5192}, {1203, 14829}, {1215, 3953}, {1220, 5563}, {2530, 4874}, {3583, 4201}, {3752, 4647}, {3816, 13728}, {3825, 5051}, {3841, 17674}, {3931, 4975}, {4195, 7280}, {4423, 19273}, {4894, 17721}, {5204, 11354}, {5251, 13741}, {5259, 19270}, {5267, 11319}, {5433, 17698}, {7173, 16052}, {7741, 16062}, {8610, 17303}, {10896, 11359}, {19891, 19927}
X(19865) lies on these lines: {1, 2}, {1010, 4026}, {1220, 4205}, {1224, 4647}, {2886, 19280}, {2891, 3775}, {3925, 14007}, {3931, 19808}, {4429, 16458}, {4972, 14005}, {6051, 17289}, {11110, 17798}, {16466, 17381}
X(19866) lies on these lines: {1, 2}, {388, 2049}, {391, 1203}, {497, 4205}, {966, 16466}, {1010, 1444}, {1191, 1213}, {1219, 1224}, {2270, 5257}, {2550, 13728}, {3672, 4647}, {4026, 5082}, {4294, 5263}, {4295, 4357}, {4366, 16904}, {4673, 17322}, {5218, 19273}, {6645, 16903}, {6857, 15509}, {12410, 16852}, {18481, 18505}, {18990, 19277}, {19886, 19928}
X(19867) lies on these lines: {1, 2}, {72, 17237}, {443, 4470}, {1224, 2224}, {2174, 16788}, {3987, 5835}, {4364, 13728}, {4422, 13745}, {11112, 17369}
X(19868) lies on these lines: {1, 2}, {55, 16851}, {69, 4349}, {75, 4353}, {86, 4684}, {307, 12573}, {391, 16469}, {392, 8074}, {461, 7713}, {516, 4357}, {518, 5750}, {740, 4021}, {760, 960}, {894, 5850}, {956, 8568}, {964, 12527}, {966, 7290}, {984, 17355}, {1001, 4254}, {1010, 1434}, {1213, 1279}, {1224, 1280}, {1386, 3686}, {2345, 7174}, {2550, 17306}, {3242, 17303}, {3671, 10521}, {3696, 3946}, {3717, 17289}, {3755, 4657}, {3775, 5847}, {3883, 5224}, {3886, 4356}, {4026, 5853}, {4307, 17272}, {4314, 13725}, {4344, 5232}, {4407, 4672}, {4981, 5294}, {4989, 17348}, {5144, 19329}, {5223, 5749}, {5542, 10436}, {5846, 17239}, {6051, 16600}, {7498, 7719}, {9798, 13615}, {10106, 16603}, {12575, 14942}, {13740, 18250}
X(19869) lies on these lines: {1, 2}, {65, 17698}, {405, 3556}, {758, 5294}, {894, 11551}, {964, 12609}, {1220, 13407}, {1770, 4195}, {1836, 11354}, {1842, 5136}, {2294, 5750}, {4202, 17647}, {4357, 5251}, {4684, 16474}, {5257, 16788}, {5692, 17353}, {5880, 16394}, {8756, 17442}, {10572, 16062}, {12047, 13740}, {12514, 17526}
X(19870) lies on these lines: {1, 2}, {37, 4714}, {55, 11357}, {100, 17553}, {958, 19290}, {993, 19336}, {1018, 5257}, {1376, 16351}, {3175, 4647}, {3739, 4692}, {3842, 4424}, {3925, 16052}, {4234, 5251}, {4737, 4751}, {4981, 5883}, {5711, 19723}, {9708, 19332}
X(19871) lies on these lines: {1, 2}, {3746, 16844}, {3894, 4981}, {4330, 13736}, {4647, 4664}, {5251, 16394}, {5258, 16458}, {5315, 17259}, {8185, 16403}, {8715, 17557}, {9710, 17514}, {11552, 17257}, {15668, 16474}, {19886, 19937}
X(19872) lies on these lines: {1, 2}, {35, 16842}, {36, 16862}, {40, 3628}, {46, 5506}, {55, 16855}, {140, 5691}, {165, 3090}, {191, 7308}, {355, 16239}, {515, 3533}, {516, 7486}, {549, 18492}, {631, 7989}, {632, 3576}, {958, 16864}, {993, 17535}, {1001, 16856}, {1213, 16670}, {1376, 16854}, {1420, 7294}, {1656, 1699}, {2948, 6723}, {3035, 17590}, {3055, 9575}, {3091, 16192}, {3305, 3336}, {3361, 10588}, {3525, 7987}, {3526, 5587}, {3601, 5326}, {3614, 8728}, {3697, 3848}, {3740, 18398}, {3746, 8167}, {3763, 4663}, {3826, 7741}, {3833, 3876}, {3868, 4532}, {3889, 3956}, {3890, 3968}, {3894, 4539}, {3901, 5044}, {3911, 4355}, {3925, 10593}, {4312, 6666}, {4413, 5259}, {4512, 6931}, {4862, 17249}, {5010, 5047}, {5020, 9591}, {5056, 10164}, {5067, 6684}, {5068, 12512}, {5070, 8227}, {5204, 5251}, {5217, 11108}, {5219, 5221}, {5225, 17559}, {5229, 17582}, {5248, 9342}, {5426, 5438}, {5437, 6668}, {5541, 6667}, {5726, 7288}, {6683, 9902}, {6721, 9860}, {6722, 13174}, {6978, 10268}, {7173, 17527}, {7280, 17531}, {7393, 9590}, {7951, 17529}, {8148, 11230}, {8185, 16419}, {8252, 13893}, {8253, 13888}, {9332, 19751}, {9573, 9816}, {9576, 9817}, {9624, 11278}, {9904, 12900}, {9955, 15703}, {10303, 19925}, {11539, 18481}, {12019, 15015}, {12699, 15699}, {15694, 18480}, {15723, 18525}, {16477, 17259}, {16676, 17303}, {16948, 17551}
X(19872) = Spieker-circle-inverse of X(1)
Barycentrics a^5-(b+c)*a^4+(2*b^2-7*b*c+2*c^2)*a^3+3*(b+c)*(b^2+c^2)*a^2-(2*b^4+2*c^4+b*c*(5*b^2-2*b*c+5*c^2))*a+(b+c)*(b^4+c^4-2*b*c*(b-c)^2) : :
X(19873) lies on these lines: {2, 3675}, {1125, 3242}, {1698, 19942}, {19836, 19946}, {19846, 19927}, {19896, 19900}
X(19874) lies on these lines: {1, 2}, {35, 17588}, {71, 5296}, {100, 11110}, {388, 17077}, {942, 4981}, {958, 16454}, {993, 19284}, {1010, 5260}, {1213, 2295}, {1220, 14005}, {1334, 5257}, {1376, 16342}, {1826, 4200}, {1869, 4194}, {1909, 16709}, {2292, 3842}, {2901, 17163}, {3691, 5750}, {3739, 4968}, {3743, 4714}, {3780, 17398}, {3826, 4202}, {3925, 5051}, {3995, 4647}, {4097, 12632}, {4205, 4972}, {4472, 4754}, {5047, 5263}, {5224, 17137}, {5251, 11115}, {5278, 5711}, {5687, 16844}, {5710, 17259}, {6284, 14020}, {8192, 19313}, {9568, 11521}, {9708, 16458}, {19929, 19937}
X(19874) = anticomplement of X(25512)
X(19875) lies on these lines: {1, 2}, {4, 9588}, {5, 3654}, {9, 484}, {11, 9819}, {12, 3339}, {30, 165}, {35, 9709}, {36, 4413}, {40, 381}, {46, 3929}, {55, 16857}, {57, 5726}, {75, 3992}, {80, 6174}, {99, 9875}, {100, 16858}, {115, 9881}, {119, 12767}, {140, 3655}, {171, 19277}, {191, 6175}, {210, 5902}, {291, 13466}, {312, 4714}, {329, 11552}, {355, 549}, {376, 5691}, {405, 4421}, {442, 9711}, {443, 5270}, {452, 4330}, {474, 5258}, {495, 10980}, {515, 3524}, {516, 3839}, {517, 4731}, {518, 3921}, {535, 5131}, {538, 3097}, {547, 3656}, {553, 1788}, {594, 16673}, {597, 3416}, {599, 3751}, {671, 13174}, {894, 17488}, {903, 17250}, {942, 3983}, {944, 15702}, {946, 5071}, {952, 3653}, {958, 7280}, {960, 4002}, {966, 3973}, {984, 1739}, {993, 13587}, {1001, 19536}, {1054, 10713}, {1213, 3731}, {1268, 10436}, {1282, 10708}, {1329, 17530}, {1376, 5010}, {1385, 15694}, {1482, 15703}, {1571, 11648}, {1621, 17547}, {1656, 7982}, {1697, 11238}, {1699, 3545}, {1706, 11010}, {1743, 17303}, {1757, 3823}, {1768, 10711}, {1770, 18231}, {1837, 4995}, {2049, 19723}, {2093, 3820}, {2100, 10719}, {2101, 10720}, {2482, 13178}, {2550, 3583}, {2551, 3585}, {2886, 17533}, {2948, 9140}, {3035, 9897}, {3058, 9581}, {3090, 11362}, {3091, 9589}, {3099, 7865}, {3303, 16853}, {3304, 16863}, {3336, 3928}, {3340, 4870}, {3361, 5434}, {3452, 18393}, {3525, 5882}, {3534, 18480}, {3543, 19925}, {3550, 11354}, {3576, 5054}, {3579, 3830}, {3628, 9624}, {3646, 15079}, {3647, 15679}, {3663, 5936}, {3678, 3901}, {3681, 3894}, {3696, 4755}, {3697, 3812}, {3698, 5044}, {3701, 4980}, {3711, 15934}, {3740, 3753}, {3746, 11108}, {3754, 3876}, {3760, 18146}, {3826, 5223}, {3829, 4187}, {3832, 5493}, {3833, 3873}, {3841, 11681}, {3842, 4664}, {3848, 4711}, {3868, 4015}, {3869, 3918}, {3874, 4540}, {3899, 3968}, {3913, 16842}, {3940, 5425}, {3984, 16126}, {4034, 17398}, {4085, 17286}, {4256, 9350}, {4297, 15692}, {4301, 5056}, {4309, 5129}, {4312, 6172}, {4317, 17580}, {4325, 6904}, {4338, 5177}, {4355, 5261}, {4428, 5259}, {4472, 4795}, {4479, 18140}, {4643, 10022}, {4658, 17551}, {4659, 4708}, {4662, 5439}, {4663, 15533}, {4674, 4945}, {4687, 4732}, {4692, 19804}, {4848, 10588}, {4857, 5084}, {4866, 5557}, {4880, 5220}, {4888, 5232}, {4900, 13602}, {4902, 5224}, {4908, 16676}, {4921, 14005}, {4937, 9330}, {5047, 8715}, {5064, 7713}, {5066, 12699}, {5067, 13464}, {5070, 10222}, {5119, 7308}, {5128, 10895}, {5219, 18421}, {5234, 11112}, {5248, 16861}, {5250, 5506}, {5252, 5298}, {5260, 17549}, {5309, 9593}, {5426, 15671}, {5432, 5727}, {5441, 15673}, {5445, 5791}, {5459, 12781}, {5460, 12780}, {5463, 9901}, {5464, 9900}, {5531, 12619}, {5537, 6913}, {5540, 10712}, {5541, 6702}, {5563, 16408}, {5603, 10172}, {5642, 13211}, {5731, 15708}, {5735, 6993}, {5737, 19290}, {5775, 11551}, {5886, 11224}, {6054, 9860}, {6055, 9864}, {6534, 17155}, {7688, 18491}, {7757, 9902}, {7992, 18242}, {8165, 18249}, {8666, 17531}, {8703, 18357}, {9466, 12782}, {9904, 10706}, {10164, 10304}, {10165, 15709}, {10718, 13221}, {11049, 12438}, {11230, 16200}, {11235, 17619}, {11274, 12531}, {11280, 15829}, {11359, 17596}, {12100, 18481}, {12258, 14061}, {12512, 15683}, {12513, 16862}, {12514, 17577}, {12607, 17529}, {12645, 15723}, {12702, 19709}, {13624, 15701}, {13679, 13712}, {13799, 13835}, {13846, 18991}, {13847, 18992}, {13883, 19053}, {13888, 19065}, {13893, 13973}, {13911, 13947}, {13936, 19054}, {13942, 19066}, {15485, 17259}, {15621, 19241}, {15693, 18525}, {15707, 17502}, {16062, 19797}, {16118, 18253}, {16487, 17337}, {16667, 17275}, {16712, 17210}, {17151, 17320}, {17239, 17313}, {17270, 17378}, {17327, 17382}, {18613, 19265}
X(19875) = complement of X(38314)
X(19875) = anticomplement of X(19883)
X(19875) = centroid of X(1)X(2)X(8)
X(19876) lies on these lines: {1, 2}, {30, 7989}, {35, 16857}, {40, 5055}, {165, 381}, {355, 11539}, {376, 10175}, {484, 7308}, {515, 15702}, {517, 15703}, {537, 4751}, {547, 7988}, {549, 5587}, {553, 10588}, {632, 3653}, {903, 17249}, {1213, 3973}, {1268, 17151}, {1376, 17542}, {1571, 18362}, {1656, 7991}, {1699, 5071}, {3090, 9588}, {3097, 9466}, {3336, 3929}, {3361, 11237}, {3524, 5691}, {3534, 18492}, {3543, 10164}, {3545, 6684}, {3576, 15694}, {3579, 19709}, {3628, 3656}, {3654, 8227}, {3655, 10124}, {3740, 4539}, {3746, 16853}, {3826, 17530}, {3833, 3894}, {3848, 3921}, {3889, 4540}, {3901, 4536}, {3913, 16856}, {4297, 15708}, {4325, 17580}, {4330, 5129}, {4370, 17303}, {4413, 5010}, {4421, 5259}, {4428, 16842}, {4532, 5883}, {4857, 17559}, {4870, 18421}, {4995, 9581}, {5054, 7987}, {5056, 9589}, {5067, 11522}, {5070, 7982}, {5248, 17547}, {5251, 16371}, {5258, 16862}, {5270, 17582}, {5298, 9578}, {5316, 18393}, {5326, 5727}, {5434, 5726}, {5493, 15022}, {5563, 16863}, {5790, 15723}, {5818, 15709}, {5852, 6173}, {6702, 9963}, {7280, 16417}, {8715, 17534}, {9166, 13174}, {9167, 13178}, {9342, 17549}, {9881, 14971}, {10109, 12699}, {10304, 19925}, {11049, 11852}, {11224, 11230}, {11552, 18228}, {11812, 18481}, {13846, 19004}, {13847, 19003}, {15621, 19275}, {15693, 18480}, {15713, 18357}, {17248, 17487}, {17678, 19827}
X(19877) lies on these lines: {1, 2}, {3, 9342}, {4, 11231}, {5, 6361}, {7, 10588}, {12, 5435}, {20, 10175}, {21, 4413}, {35, 16859}, {40, 5056}, {55, 17536}, {56, 17535}, {100, 11108}, {140, 5731}, {165, 3832}, {333, 17551}, {355, 3525}, {377, 19827}, {442, 3648}, {443, 5080}, {474, 5260}, {515, 10303}, {516, 5068}, {517, 5067}, {547, 12702}, {631, 9956}, {632, 5790}, {942, 4533}, {944, 3526}, {956, 5828}, {958, 17531}, {960, 3922}, {962, 3090}, {964, 19744}, {966, 16669}, {993, 17572}, {999, 16864}, {1001, 17534}, {1132, 9616}, {1150, 16456}, {1213, 5749}, {1268, 5936}, {1329, 4197}, {1376, 5047}, {1385, 3533}, {1478, 5442}, {1621, 9709}, {1656, 5657}, {1699, 15022}, {1788, 3649}, {2345, 16675}, {2476, 3826}, {2550, 17371}, {2899, 19808}, {2975, 16408}, {3091, 6684}, {3146, 7989}, {3161, 5257}, {3295, 16854}, {3434, 17559}, {3436, 17582}, {3452, 18231}, {3474, 3614}, {3522, 19925}, {3523, 5587}, {3524, 18480}, {3545, 3579}, {3618, 3844}, {3628, 5603}, {3681, 5439}, {3697, 3873}, {3698, 3877}, {3701, 19804}, {3740, 3868}, {3742, 3983}, {3812, 3876}, {3817, 9588}, {3820, 17529}, {3833, 4547}, {3836, 20072}, {3841, 5141}, {3842, 4699}, {3869, 4004}, {3871, 4423}, {3889, 4662}, {3911, 5261}, {3921, 5045}, {3925, 4193}, {3943, 16674}, {3968, 5697}, {3988, 5883}, {4002, 14923}, {4015, 4661}, {4018, 5044}, {4127, 5902}, {4188, 5251}, {4295, 5445}, {4308, 5433}, {4313, 5432}, {4344, 17337}, {4470, 4708}, {4472, 4748}, {4757, 5692}, {5054, 18357}, {5059, 16192}, {5070, 5690}, {5071, 12699}, {5087, 5180}, {5175, 16845}, {5217, 16858}, {5218, 17606}, {5235, 14007}, {5247, 17124}, {5248, 17570}, {5253, 9708}, {5255, 17125}, {5265, 9578}, {5281, 9581}, {5284, 5687}, {5296, 16814}, {5303, 16417}, {5441, 15674}, {5691, 15717}, {5744, 8728}, {5745, 8165}, {5758, 6877}, {5772, 15590}, {5791, 9776}, {5905, 9782}, {6666, 6919}, {6667, 13996}, {6701, 14450}, {6856, 10129}, {6857, 17619}, {6910, 7705}, {7229, 17248}, {7585, 13947}, {7586, 13893}, {7679, 15844}, {7991, 10171}, {8164, 11037}, {8185, 15246}, {8252, 19066}, {8253, 19065}, {8972, 13936}, {9591, 14002}, {9785, 10589}, {9961, 10157}, {10246, 16239}, {11230, 12245}, {11680, 17527}, {12512, 17578}, {13624, 15702}, {13883, 13941}, {14647, 18243}, {15699, 18493}, {16589, 17756}
X(19877) = anticomplement of X(34595)
X(19878) lies on these lines: {1, 2}, {3, 10171}, {5, 17502}, {35, 17535}, {36, 17536}, {40, 3533}, {55, 16864}, {56, 16854}, {140, 516}, {354, 4533}, {392, 3922}, {515, 3628}, {517, 16239}, {518, 4547}, {547, 13624}, {549, 18483}, {631, 3817}, {632, 6684}, {726, 4698}, {942, 4127}, {946, 3526}, {958, 16855}, {960, 3833}, {993, 16842}, {1001, 16863}, {1213, 4700}, {1266, 17322}, {1385, 10172}, {1656, 10165}, {1699, 10303}, {2784, 6721}, {3090, 4297}, {3218, 5506}, {3523, 7988}, {3525, 6361}, {3576, 5067}, {3579, 11539}, {3649, 3911}, {3664, 17250}, {3678, 3742}, {3697, 3892}, {3698, 3898}, {3740, 3881}, {3743, 16610}, {3746, 9342}, {3814, 17575}, {3816, 3841}, {3822, 17527}, {3825, 8728}, {3834, 6693}, {3848, 3988}, {3874, 4005}, {3878, 4004}, {3894, 4537}, {3946, 4527}, {3947, 7288}, {3962, 5439}, {3968, 9957}, {3993, 4751}, {4015, 5045}, {4018, 5883}, {4029, 16674}, {4066, 18743}, {4134, 18398}, {4298, 5433}, {4314, 10589}, {4315, 10588}, {4358, 6533}, {4423, 16862}, {4472, 17132}, {4706, 10180}, {4708, 4758}, {4999, 18250}, {5047, 5267}, {5056, 7987}, {5070, 10175}, {5087, 5122}, {5204, 17542}, {5248, 8167}, {5251, 17534}, {5253, 17546}, {5257, 16885}, {5259, 17531}, {5303, 17547}, {5432, 12575}, {5435, 5586}, {5442, 12047}, {5691, 7486}, {5750, 16814}, {5850, 6666}, {6705, 18243}, {7280, 16859}, {7496, 9591}, {8252, 8983}, {8253, 13971}, {8972, 13942}, {9779, 16192}, {11231, 13464}, {12577, 15325}, {12699, 15694}, {12702, 15723}, {13888, 13941}, {15674, 16118}, {15699, 18480}, {16669, 17398}, {16675, 17355}, {19933, 19968}
X(19878) = midpoint of X(1) and X(4691)
X(19878) = complement of X(3634)
X(19879) lies on these lines: {1, 2}, {1043, 4085}, {1213, 2329}, {1220, 2887}, {1224, 1432}, {3061, 17303}, {3710, 11533}, {3763, 12513}, {3925, 15973}, {4195, 4660}, {4647, 17787}, {5247, 15985}, {5251, 9840}, {5255, 17698}, {8616, 17526}, {13742, 15485}
X(19880) lies on these lines: {1, 2}, {3763, 6762}
X(19881) lies on these lines: {1, 2}, {36, 17698}, {141, 1203}, {1213, 5299}, {1224, 17385}, {1930, 17322}, {3583, 16062}, {3585, 13740}, {3763, 16466}, {4195, 4316}, {4201, 4324}, {4647, 16706}, {5259, 13728}, {5280, 17398}, {5294, 6763}, {5750, 17744}, {6051, 17384}, {6533, 19808}, {8193, 16408}, {10483, 11354}, {11552, 17291}, {12410, 16863}, {17192, 17326}
X(19882) lies on these lines: {1, 4444}, {514, 19856}, {1125, 7192}
X(19883) lies on these lines: {1, 2}, {30, 3817}, {36, 16858}, {40, 15702}, {56, 17542}, {79, 15675}, {140, 4301}, {142, 5122}, {165, 15708}, {226, 5298}, {354, 4134}, {355, 15703}, {376, 8227}, {381, 4297}, {392, 3833}, {515, 3653}, {516, 3524}, {517, 11539}, {547, 1385}, {549, 946}, {553, 11375}, {620, 12258}, {631, 5493}, {632, 11362}, {962, 15721}, {993, 8167}, {1001, 16417}, {1482, 15723}, {1656, 3655}, {1699, 10304}, {2482, 11599}, {3303, 16864}, {3304, 16854}, {3525, 9624}, {3526, 3654}, {3533, 7982}, {3534, 18483}, {3543, 7987}, {3545, 3576}, {3579, 11812}, {3628, 5882}, {3646, 3928}, {3656, 6684}, {3671, 4870}, {3740, 3892}, {3742, 4525}, {3746, 17535}, {3821, 11149}, {3822, 17533}, {3825, 17530}, {3829, 8728}, {3839, 7988}, {3845, 13624}, {3848, 4744}, {3874, 4537}, {3947, 5434}, {3968, 5919}, {3971, 6534}, {3986, 15828}, {3993, 4688}, {4015, 17609}, {4052, 17698}, {4072, 17303}, {4084, 5439}, {4098, 16674}, {4304, 5444}, {4314, 11238}, {4315, 11237}, {4342, 5432}, {4421, 16408}, {4423, 16370}, {4654, 7288}, {4717, 19804}, {4742, 4793}, {4758, 4795}, {4848, 7294}, {4868, 16602}, {4973, 15254}, {4995, 12053}, {4999, 5325}, {5054, 5886}, {5071, 19925}, {5183, 6681}, {5248, 16371}, {5251, 17547}, {5253, 16861}, {5257, 16590}, {5258, 17534}, {5259, 17549}, {5267, 16418}, {5284, 13587}, {5461, 11711}, {5542, 15325}, {5563, 17536}, {5603, 15709}, {5642, 13605}, {5750, 16675}, {5901, 10124}, {6174, 12732}, {6701, 17525}, {6707, 17382}, {8666, 16842}, {8692, 15668}, {8703, 9955}, {8715, 16862}, {9812, 15705}, {10109, 18480}, {10172, 10246}, {10175, 15699}, {10222, 16239}, {11108, 11194}, {11263, 15670}, {12512, 15692}, {12513, 16855}, {12699, 15693}, {15701, 18493}, {16668, 17330}, {17248, 17488}, {18481, 19709}, {18613, 19248}, {19933, 20004}
X(19883) = complement of X(19875)
X(19883) = centroid of X(1)X(2)X(10)
X(19883) = {X(1),X(2)}-harmonic conjugate of X(3828)
X(19884) lies on these lines: {1, 19885}, {2, 19893}, {3, 142}, {1698, 19937}, {2283, 11375}, {17913, 17927}, {19843, 19888}, {19846, 19896}, {19854, 19930}, {19858, 19886}, {19860, 19890}, {19861, 19889}, {19863, 19891}, {19934, 19936}
X(19885) lies on these lines: {1, 19884}, {4, 1125}, {10, 19888}, {1060, 5293}, {8583, 19889}, {19859, 19886}, {19860, 19893}, {19861, 19894}, {19890, 19900}, {19932, 19934}
X(19886) lies on these lines: {1, 19932}, {2, 3675}, {6, 1125}, {551, 19992}, {3624, 19991}, {3634, 19978}, {3828, 19990}, {16828, 19891}, {19784, 19946}, {19856, 19933}, {19858, 19884}, {19859, 19885}, {19862, 19985}, {19863, 19927}, {19866, 19928}, {19871, 19937}, {19943, 19944}
X(19887) lies on these lines: {1, 19888}, {7, 1125}, {1698, 19931}, {3624, 19927}, {3679, 19890}
X(19888) lies on these lines: {1, 19887}, {2, 3675}, {9, 1125}, {10, 19885}, {1025, 3485}, {1083, 3616}, {3085, 19931}, {3086, 19927}, {3126, 19947}, {10527, 19894}, {18391, 19890}, {19784, 19891}, {19836, 19896}, {19843, 19884}, {19855, 19900}, {19856, 19944}, {19933, 19943}
X(19889) lies on these lines: {1, 6547}, {2, 6075}, {11, 214}, {8583, 19885}, {19861, 19884}
X(19890) lies on these lines: {1, 19927}, {2, 6075}, {8, 19928}, {10, 19931}, {12, 1125}, {513, 4026}, {3679, 19887}, {5176, 16830}, {10573, 19930}, {18391, 19888}, {19860, 19884}, {19885, 19900}
X(19891) lies on these lines: {2, 19896}, {31, 1125}, {16828, 19886}, {19784, 19888}, {19836, 19928}, {19853, 19937}, {19858, 19893}, {19863, 19884}, {19864, 19927}, {19898, 19946}
X(19892) lies on these lines: {32, 1125}, {19858, 19884}
X(19893) lies on these lines: {2, 19884}, {10, 19937}, {35, 404}, {16828, 19929}, {19858, 19891}, {19860, 19885}
X(19894) lies on these lines: {2, 19884}, {12, 16830}, {21, 36}, {2530, 19947}, {3634, 19937}, {10527, 19888}, {19861, 19885}, {19863, 19929}
X(19895) lies on these lines: {1, 19933}, {2, 3675}, {37, 39}, {876, 19947}, {4568, 9507}, {16828, 19946}, {19784, 19900}, {19935, 19943}
X(19896) lies on these lines: {1, 1016}, {2, 19891}, {38, 1125}, {19784, 19928}, {19836, 19888}, {19846, 19884}, {19873, 19900}
X(19897) lies on these lines: {1, 19934}, {37, 39}, {1909, 16830}, {17794, 18827}, {19858, 19884}
X(19898) lies on these lines: {2, 3675}, {44, 1125}, {1491, 19947}, {19856, 19943}, {19891, 19946}
X(19899) lies on these lines: {1, 19943}, {2, 3675}, {45, 1125}
X(19900) lies on these lines: {1, 6547}, {2, 19884}, {55, 474}, {16828, 19886}, {19784, 19895}, {19855, 19888}, {19873, 19896}, {19885, 19890}
Polar co-centers: X(19901)-X(19926)
This preamble and centers X(19901)-X(19926) were contributed by César Eliud Lozada, June 26, 2018.
Let T1=A1B1C1 and T2=A2B2C2 be two triangles not inscribed in the same circle and such that the perpendicular bisectors of A1A2, B1B2 and C1C2 concur at a point O. The point O provides a common center for handling T1 and T2 in polar coordinates. In such cases, triangles T1 and T2 are called polar co-centric and the point O is here named the polar co-center of T1 and T2.
The appearance of (T1, T2, n) in the following list means that triangles T1 and T2 are polar co-centric with X(n) as polar co-center (Note: n=0 indiates a not-yet calculated center):
(ABC, Aries, 26), (ABC, inner-Conway, 355), (ABC, outer-Garcia, 10), (ABC, Gossard, 402), (ABC, Johnson, 5), (ABC, 5th mixtilinear, 1), (ABC, 1st Parry, 19901), (ABC, 2nd Parry, 19902), (ABC, Schroeter, 30), (ABC, 2nd Sharygin, 19903), (ABC-X3 reflections, Artzt, 7618), (ABC-X3 reflections, outer-Garcia, 522), (ABC-X3 reflections, Gossard, 523), (ABC-X3 reflections, intangents, 19904), (ABC-X3 reflections, Johnson, 523), (ABC-X3 reflections, 5th mixtilinear, 513), (ABC-X3 reflections, 1st Parry, 19902), (ABC-X3 reflections, 2nd Parry, 19901), (anti-Aquila, Ehrmann-mid, 9955), (anti-Aquila, Euler, 522), (anti-Aquila, excenters-midpoints, 3), (anti-Aquila, medial, 1125), (anti-Ara, 2nd anti-Conway, 546), (anti-Ara, 2nd Hyacinth, 5), (anti-Artzt, circumsymmedial, 19905), (4th anti-Brocard, anti-McCay, 19906), (4th anti-Brocard, anti-orthocentroidal, 2780), (2nd anti-circumperp-tangential, Euler, 19907), (1st anti-circumperp, Aries, 19908), (1st anti-circumperp, inner-Conway, 40), (1st anti-circumperp, Ehrmann-side, 523), (1st anti-circumperp, 1st Parry, 19909), (2nd anti-Conway, 6th anti-mixtilinear, 512), (2nd anti-Conway, 2nd Hyacinth, 140), (anti-Euler, anticomplementary, 3), (anti-Euler, Aquila, 522), (anti-Euler, 5th Brocard, 19910), (anti-Euler, reflection, 3), (anti-Euler, X3-ABC reflections, 523), (3rd anti-Euler, 4th anti-Euler, 3), (anti-excenters-reflections, 2nd Euler, 523), (anti-excenters-reflections, orthic, 4), (anti-Honsberger, Ehrmann-vertex, 19130), (anti-Honsberger, 2nd Ehrmann, 6), (anti-Honsberger, Kosnita, 512), (anti-Honsberger, Trinh, 5092), (anti-Hutson intouch, tangential, 3), (anti-incircle-circles, anti-inverse-in-incircle, 5), (anti-incircle-circles, 1st excosine, 6759), (anti-inverse-in-incircle, 1st excosine, 525), (anti-Mandart-incircle, 2nd circumperp tangential, 3), (6th anti-mixtilinear, midheight, 5), (6th anti-mixtilinear, 1st Zaniah, 1125), (6th anti-mixtilinear, 2nd Zaniah, 6684), (1st anti-Sharygin, Lucas(-1) inner, 0), (anti-tangential-midarc, intangents, 1), (anticomplementary, Aquila, 10), (anticomplementary, 2nd Fuhrmann, 355), (anticomplementary, reflection, 3), (anticomplementary, Steiner, 30), (anticomplementary, X3-ABC reflections, 5), (anticomplementary, Yff contact, 516), (Aquila, X3-ABC reflections, 513), (Aries, 1st Parry, 0), (Artzt, circummedial, 11184), (Artzt, circumsymmedial, 19911), (1st Auriga, 2nd Auriga, 55), (1st Brocard-reflected, Ehrmann-side, 3818), (1st Brocard, 1st orthosymmedial, 5), (2nd Brocard, 4th Brocard, 5), (2nd Brocard, 2nd orthosymmedial, 5), (4th Brocard, 2nd orthosymmedial, 5), (4th Brocard, 3rd Parry, 19912), (5th Brocard, 1st Parry, 19913), (5th Brocard, 2nd Parry, 0), (circumorthic, Ehrmann-side, 5), (1st circumperp, inner-Conway, 19914), (1st circumperp, 2nd Sharygin, 19915), (2nd circumperp, 2nd Sharygin, 19916), (inner-Conway, Honsberger, 9), (inner-Conway, 2nd Sharygin, 19917), (inner-Conway, Ursa-minor, 3309), (2nd Conway, 6th mixtilinear, 514), (Ehrmann-mid, Euler, 546), (Ehrmann-mid, medial, 523), (Ehrmann-mid, X-parabola-tangential, 19918), (Ehrmann-vertex, 2nd Ehrmann, 690), (Ehrmann-vertex, Kosnita, 5), (Ehrmann-vertex, Trinh, 523), (2nd Ehrmann, Kosnita, 575), (2nd Ehrmann, Trinh, 512), (3rd Euler, extouch, 19919), (3rd Euler, intouch, 19907), (3rd Euler, Mandart-incircle, 19920), (4th Euler, Hutson intouch, 19907), (excenters-reflections, excentral, 1), (excenters-reflections, hexyl, 513), (excentral, hexyl, 3), (excentral, 2nd Schiffler, 6265), (excentral, 2nd Sharygin, 19921), (extouch, Feuerbach, 191), (extouch, intouch, 3), (extouch, Mandart-excircles, 1), (extouch, Mandart-incircle, 6261), (extouch, medial, 3579), (extouch, orthic, 10), (7th Fermat-Dao, 8th Fermat-Dao, 187), (11th Fermat-Dao, outer-Napoleon, 5), (12th Fermat-Dao, inner-Napoleon, 5), (Feuerbach, incentral, 19922), (inner-Garcia, 2nd Schiffler, 104), (outer-Garcia, Garcia-reflection, 4), (outer-Garcia, Gossard, 0), (outer-Garcia, Johnson, 513), (outer-Garcia, 5th mixtilinear, 3667), (Garcia-reflection, Pelletier, 518), (Garcia-reflection, 2nd Schiffler, 11), (Gossard, Johnson, 523), (Gossard, 5th mixtilinear, 19923), (Honsberger, Ursa-minor, 5572), (incircle-circles, inverse-in-incircle, 5045), (incircle-circles, 2nd Zaniah, 1125), (intouch, medial, 1385), (intouch, orthic, 946), (inverse-in-incircle, 2nd Zaniah, 3309), (Johnson, 5th mixtilinear, 900), (1st Johnson-Yff, inner-Yff, 495), (2nd Johnson-Yff, outer-Yff, 496), (Kosnita, Trinh, 3), (Lemoine, X-parabola-tangential, 19924), (Mandart-excircles, orthic, 517), (Mandart-incircle, medial, 19907), (medial, X-parabola-tangential, 30), (midheight, 1st Zaniah, 18483), (midheight, 2nd Zaniah, 19925), (orthic, X-parabola-tangential, 511), (orthocentroidal, 1st orthosymmedial, 597), (Pelletier, Ursa-minor, 517), (1st Sharygin, 2nd Sharygin, 19926), (tangential-midarc, 2nd tangential-midarc, 1), (1st Zaniah, 2nd Zaniah, 5)
X(19901) lies on these lines: {3,6088}, {110,1296}, {111,9126}, {2482,2793}, {2854,19902}
X(19901) = reflection of X(111) in X(9126)
X(19901) = X(19902)-of-circumsymmedial triangle
X(19902) lies on these lines: {3,526}, {74,111}, {110,9126}, {351,5663}, {541,19912}, {690,6055}, {1499,7426}, {2088,9175}, {2854,19901}, {5655,11176}, {9023,11579}, {9188,9970}, {9828,11006}, {11615,15054}
X(19902) = midpoint of X(74) and X(9138)
X(19902) = reflection of X(i) in X(j) for these (i,j): (110, 9126), (5655, 11176)
X(19902) = X(19901)-of-circumsymmedial triangle
X(19903) lies on these lines: {101,1293}, {2783,19916}
X(19904) lies on these lines: {3,9}, {33,5908}, {55,1720}, {208,942}, {517,1854}, {990,9786}, {1062,5909}, {1385,1455}, {1535,17555}, {11745,12610}, {17616,17928}
X(19905) lies on these lines: {2,98}, {3,9830}, {30,5104}, {69,12243}, {74,14833}, {141,8724}, {511,671}, {524,11632}, {599,2782}, {1469,10054}, {1503,14830}, {1992,14651}, {3056,10070}, {3098,9878}, {5026,5054}, {5050,8787}, {5085,10488}, {5207,9302}, {5461,14561}, {5465,9970}, {5476,9166}, {7775,11623}, {8591,10519}, {11645,11676}
X(19905) = midpoint of X(i) and X(j) for these {i,j}: {69, 12243}, {74, 14833}
X(19905) = X(19911)-of-anti-Artzt triangle
X(19905) = {X(9166), X(10753)}-harmonic conjugate of X(5476)
X(19906) lies on these lines: {111,11632}, {543,2080}
X(19907) lies on these lines: {1,5}, {2,19914}, {3,5330}, {30,1537}, {100,1482}, {104,1621}, {145,6959}, {149,6917}, {153,6929}, {155,1616}, {214,517}, {381,10031}, {515,12611}, {551,10265}, {900,7623}, {944,10742}, {946,11567}, {1125,12619}, {1145,4511}, {1191,12161}, {1319,11570}, {1320,6911}, {1385,2800}, {1388,10074}, {2098,10087}, {2099,10090}, {2646,12758}, {2771,5609}, {2932,10679}, {2951,15686}, {3035,5690}, {3560,12773}, {3576,12515}, {3616,12247}, {3622,6862}, {3623,6944}, {3655,12678}, {3656,14217}, {3877,7508}, {5541,16200}, {5603,6224}, {5790,12531}, {5887,17660}, {6690,6713}, {6702,11230}, {7982,15015}, {9946,15558}, {9956,15863}, {10202,17654}, {10269,12332}, {11849,17100}, {12047,18976}, {12119,12699}, {12747,18493}, {12832,15325}
X(19907) = midpoint of X(i) and X(j) for these {i,j}: {1, 6265}, {3, 10698}, {100, 1482}, {381, 10031}, {944, 10742}, {1320, 12331}, {5887, 17660}, {9946, 15558}, {12119, 12699}
X(19907) = reflection of X(6246) in X(9955)
X(19907) = complement of X(19914)
X(19907) = X(6265)-of-anti-Aquila triangle
X(19907) = X(10113)-of-2nd circumperp triangle
X(19907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 6326, 12737), (1, 12739, 12735), (1, 12740, 1387), (1484, 10283, 1387), (3576, 13253, 12515), (5603, 6224, 10738), (6265, 12737, 6326), (10247, 12331, 1320)
X(19908) lies on these lines: {3,49}, {22,12118}, {24,68}, {25,9927}, {30,9938}, {186,11411}, {539,2917}, {1069,9672}, {1658,3564}, {2070,12429}, {3157,9659}, {5449,6642}, {5654,7503}, {5894,12084}, {5925,12085}, {5961,15512}, {6288,7506}, {6644,12359}, {6689,7395}, {7387,10117}, {7514,9820}, {7517,12293}, {8276,13909}, {8277,13970}, {9590,9896}, {9928,15177}, {12309,16195}, {12893,15750}, {12901,13171}, {15316,17834}
X(19908) = midpoint of X(i) and X(j) for these {i,j}: {3, 9908}, {7387, 12301}, {15316, 17834}
X(19908) = X(9927)-of-Ara triangle
X(19908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (155, 12163, 18436), (155, 19357, 1147), (1147, 7689, 1216)
X(19909) lies on these lines: {}
X(19910) lies on these lines: {3,8150}, {20,2782}, {99,3095}, {511,13188}, {1569,13330}, {1916,8350}, {2080,5989}, {5188,12188}, {5969,11179}, {5976,6321}, {8290,10796}, {9466,12355}
X(19910) = {X(5976), X(6321)}-harmonic conjugate of X(7697)
X(19911) lies on these lines: {2,99}, {3,9830}, {98,5569}, {187,8593}, {524,2080}, {542,8182}, {1384,8787}, {2021,8859}, {2782,7610}, {3849,6054}, {5038,8369}, {5210,10488}, {5503,11170}, {5969,11165}, {6390,8586}, {7606,11171}, {8592,13586}, {9169,9486}, {9771,15561}, {11632,15597}, {12117,18860}
X(19911) = reflection of X(i) in X(j) for these (i,j): (98, 5569), (11632, 15597)
X(19911) = X(19905)-of-Artzt triangle
X(19911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 2482, 15483), (2482, 9890, 9888), (9885, 9886, 99), (9892, 9894, 8591)
X(19912) lies on these lines: {2,2780}, {3,11176}, {4,9147}, {5,9148}, {30,351}, {98,729}, {113,114}, {115,2793}, {262,9180}, {376,9126}, {381,804}, {523,11799}, {526,5655}, {541,19902}, {647,1555}, {1499,1513}, {1596,17994}, {1637,16220}, {2485,11620}, {5926,15724}, {9138,10706}, {9188,11179}, {13306,14041}, {14397,16657}
X(19912) = midpoint of X(i) and X(j) for these {i,j}: {4, 9147}, {9138, 10706}
X(19912) = reflection of X(i) in X(j) for these (i,j): (3, 11176), (376, 9126), (9148, 5)
X(19912) = anticomplement of X(16235)
X(19912) = X(9147)-of-Euler triangle
X(19912) = X(9148)-of-Johnson triangle
X(19912) = X(11176)-of-X3-ABC reflections triangle
X(19913) lies on these lines: {}
X(19914) lies on these lines: {1,12619}, {2,19907}, {3,8}, {5,10698}, {10,6265}, {11,1482}, {40,9897}, {46,18976}, {65,10057}, {80,517}, {119,2886}, {145,6958}, {149,6928}, {153,6923}, {355,2800}, {381,1537}, {515,12515}, {519,10265}, {549,10031}, {912,17654}, {999,12832}, {1317,5432}, {1320,1484}, {1385,7972}, {1387,10247}, {1656,5554}, {1737,12740}, {1768,5881}, {1837,12758}, {2098,5533}, {2099,8068}, {2771,12751}, {2829,18525}, {3057,10073}, {3419,12691}, {3579,12119}, {3617,6863}, {3621,6891}, {3626,12738}, {3632,6264}, {3653,11274}, {3656,16174}, {3679,6326}, {3689,11219}, {4668,5531}, {4677,7993}, {4678,6825}, {5119,12743}, {5176,12532}, {5252,11570}, {5587,12611}, {5697,13274}, {5722,15558}, {5840,11827}, {5886,6702}, {5903,13273}, {6842,11698}, {8148,12019}, {8200,12463}, {8207,12462}, {10039,12739}, {10058,10950}, {10074,10944}, {11362,16139}, {11571,12763}, {11715,13497}, {12749,17660}, {12775,13743}, {18237,18518}
X(19914) = midpoint of X(i) and X(j) for these {i,j}: {40, 9897}, {149, 12245}, {1768, 5881}, {3632, 6264}
X(19914) = reflection of X(i) in X(j) for these (i,j): (1, 12619), (119, 3036), (355, 15863), (1317, 6713), (1320, 1484), (10698, 5)
X(19914) = anticomplement of X(19907)
X(19914) = circumcircle-inverse of X(38722)
X(19914) = X(6265)-of-outer-Garcia triangle
X(19914) = X(10698)-of-Johnson triangle
X(19914) = X(12619)-of-Aquila triangle
X(19914) = inner-Garcia-to-outer-Garcia similarity image of X(355)
X(19914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (100,104,38722), (119, 3036, 5790), (1317, 6713, 10246), (5587, 13253, 12611)
X(19915) lies on these lines: {3,6084}, {100,1292}, {528,19916}, {2832,14664}
X(19916) lies on these lines: {3,900}, {104,105}, {528,19915}, {659,952}, {891,12737}, {1155,3309}, {1960,6265}, {2783,19903}, {2821,12515}
X(19916) = midpoint of X(104) and X(13266)
X(19917) lies on the line {100,932}
X(19918) lies on these lines: {30,10279}, {403,8151}, {8029,18325}, {10280,15122}
X(19919) lies on these lines: {5,17768}, {21,10246}, {30,40}, {214,960}, {381,10032}, {547,3336}, {758,11260}, {846,5453}, {896,5492}, {920,6147}, {956,8148}, {1749,3337}, {1768,3530}, {1776,12433}, {3579,4015}, {3650,5057}, {3820,5499}, {3850,5535}, {5506,10124}, {5660,11277}, {5693,7508}, {5708,16133}, {6914,12635}, {15174,16141}, {16137,16140}
X(19919) = midpoint of X(i) and X(j) for these {i,j}: {21, 13465}, {381, 10032}, {3650, 6841}
X(19919) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (191, 7701, 16139), (3652, 16139, 7701)
X(19920) lies on these lines: {1,1399}, {100,1389}, {946,11567}, {7704,18493}
X(19921) lies on these lines: {40,926}, {659,2808}, {1054,2821}
X(19922) lies on these lines: {115,119}, {952,8143}, {2771,5609}, {2800,9959}, {5492,6265}
X(19922) = midpoint of X(5492) and X(6265)
X(19923) lies on the line {30,511}
X(19924) lies on these lines: {2,3098}, {3,5476}, {4,7883}, {6,3534}, {20,576}, {23,5642}, {30,511}, {69,13603}, {115,5104}, {125,10989}, {141,3845}, {182,376}, {381,1350}, {549,5480}, {550,575}, {597,5092}, {599,3818}, {671,9302}, {1176,13482}, {1351,15681}, {1352,3543}, {1533,10706}, {1657,11477}, {1992,11001}, {2076,6034}, {3094,7753}, {3146,11180}, {3524,14561}, {3589,12100}, {3627,18553}, {3839,10519}, {4316,8540}, {4324,19369}, {5017,5309}, {5039,7739}, {5050,15689}, {5073,15069}, {5085,14848}, {5097,15686}, {5171,8182}, {5181,18325}, {5188,15810}, {5189,9140}, {5477,8586}, {5648,7728}, {5655,12584}, {5972,7426}, {5999,6055}, {6699,15361}, {6776,15683}, {6791,11647}, {7470,7827}, {7540,10625}, {7576,12294}, {7618,9737}, {7756,13330}, {7810,9821}, {7811,18906}, {8262,18572}, {8550,15704}, {9301,14830}, {9855,18800}, {9873,9939}, {10304,14853}, {10510,15303}, {10516,14269}, {10754,14712}, {11160,15640}, {11634,14811}, {12017,15695}, {12101,18358}, {12117,12177}, {12242,13564}, {13168,14856}, {13414,15158}, {13415,15159}, {13421,18128}, {14449,17712}, {14862,15582}, {15516,15691}, {15533,18440}, {15534,15685}, {15678,15988}
X(19924) = circumnormal isogonal conjugate of X(12074)
X(19924) = anticomplement of X(19924)
X(19924) = complement of X(19924)
X(19925) lies on these lines: {1,3091}, {2,4297}, {3,3634}, {4,9}, {5,515}, {8,1699}, {11,10106}, {12,950}, {20,1698}, {30,3828}, {35,6912}, {36,6915}, {57,5229}, {65,5927}, {72,15064}, {78,6870}, {80,7548}, {115,118}, {140,10172}, {142,5787}, {145,3854}, {153,5270}, {165,3146}, {200,5175}, {226,1837}, {355,381}, {377,8582}, {388,9581}, {411,5251}, {497,9578}, {498,4304}, {499,4311}, {517,546}, {518,5806}, {550,11231}, {551,944}, {632,17502}, {726,6248}, {758,5777}, {908,5086}, {938,5290}, {942,2801}, {952,3850}, {958,19541}, {960,10157}, {962,3679}, {971,3812}, {990,1722}, {993,3149}, {997,6844}, {1158,18540}, {1193,5400}, {1210,1478}, {1254,1736}, {1319,7173}, {1323,17181}, {1329,8727}, {1420,10589}, {1479,6957}, {1490,6843}, {1537,15863}, {1656,10165}, {1697,5225}, {1737,3336}, {1750,5177}, {1770,18395}, {1788,9579}, {1836,4848}, {1838,7541}, {1848,7559}, {1853,12779}, {1902,10151}, {2646,3614}, {2654,4551}, {2771,11801}, {2796,9880}, {2829,6702}, {2886,5795}, {3008,7377}, {3070,13936}, {3071,13883}, {3085,3586}, {3086,4315}, {3090,3576}, {3244,3855}, {3306,10085}, {3339,9814}, {3361,5704}, {3419,6743}, {3434,6736}, {3436,4847}, {3452,5794}, {3485,5727}, {3486,5219}, {3544,15808}, {3560,6796}, {3579,3627}, {3583,10039}, {3601,10588}, {3612,6860}, {3616,5068}, {3617,7991}, {3621,11224}, {3624,5056}, {3625,7982}, {3628,13624}, {3633,5734}, {3636,3851}, {3649,13257}, {3654,14269}, {3671,9612}, {3697,7957}, {3753,12688}, {3754,6001}, {3813,7956}, {3814,6700}, {3829,11260}, {3833,9940}, {3841,6907}, {3843,4691}, {3845,4745}, {3856,5844}, {3858,4701}, {3874,14872}, {3881,13374}, {3911,7354}, {3912,7384}, {4058,7323}, {4084,5693}, {4208,5732}, {4245,15622}, {4342,9614}, {4353,13161}, {4669,12245}, {4911,10521}, {5047,15931}, {5066,5901}, {5072,10246}, {5080,5536}, {5198,8193}, {5232,10442}, {5248,6913}, {5252,10863}, {5267,6905}, {5437,10864}, {5439,12680}, {5450,6911}, {5480,5847}, {5506,6840}, {5550,15022}, {5714,11529}, {5720,6866}, {5722,6744}, {5805,5850}, {5836,9856}, {5853,12607}, {5880,6259}, {5902,12528}, {6147,17706}, {6224,15017}, {6245,6256}, {6249,17766}, {6253,11113}, {6260,12609}, {6261,6867}, {6459,13893}, {6460,13947}, {6560,13975}, {6561,13912}, {6745,10883}, {6828,7951}, {6846,10198}, {6849,7682}, {6864,9843}, {6896,12115}, {6917,12616}, {6918,12114}, {6919,8583}, {6920,10902}, {6929,18517}, {6945,7741}, {6964,10200}, {6993,10884}, {7247,10520}, {7406,17308}, {7503,8185}, {7620,17132}, {7680,12558}, {7705,17579}, {7967,9624}, {8165,8580}, {8273,16842}, {8715,11496}, {9588,9778}, {9656,10404}, {9657,17728}, {9798,11479}, {9803,11551}, {9850,17626}, {9864,11599}, {9911,18535}, {10019,12135}, {10176,14110}, {10197,10786}, {10199,10785}, {10265,10742}, {10454,10887}, {10479,12545}, {10594,15177}, {10599,17857}, {10944,17618}, {10950,17605}, {11112,17619}, {11441,16473}, {12368,13605}, {12811,15178}
X(19925) = midpoint of X(i) and X(j) for these {i,j}: {4, 10}, {5, 18480}, {8, 4301}, {119, 6246}, {355, 946}, {1537, 15863}, {3244, 5881}, {3579, 3627}, {3625, 7982}, {3874, 14872}, {4084, 5693}, {5836, 9856}, {6245, 6256}, {9864, 11599}, {10265, 10742}, {12368, 13605}
X(19925) = reflection of X(i) in X(j) for these (i,j): (3, 3634), (3881, 13374), (1125, 5)
X(19925) = complement of X(4297)
X(19925) = X(10)-of-Euler triangle
X(19925) = X(185)-of-3rd Euler triangle
X(19925) = X(946)-of-Ehrmann-mid triangle
X(19925) = X(1125)-of-Johnson triangle
X(19925) = X(3634)-of-X3-ABC reflections triangle
X(19925) = X(5562)-of-4th Euler triangle
X(19925) = X(5972)-of-Fuhrmann triangle
X(19925) = X(13405)-of-outer-Johnson triangle
X(19925) = X(16625)-of-excentral triangle
X(19925) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (1, 3091, 3817), (1, 10590, 3947), (2, 5691, 4297), (3, 10175, 3634), (4, 5587, 10), (4, 5818, 40), (5, 1125, 10171), (5, 18242, 3822), (10, 5493, 5657), (10, 12572, 18249), (40, 5587, 5818), (40, 5818, 10), (5587, 18406, 1512), (5587, 18492, 4), (5691, 7989, 2)
X(19926) lies on these lines: {659,2782}, {804,9840}, {2789,9147}, {6002,11676}
X(19927) lies on these lines: {1, 19890}, {2, 19884}, {56, 226}, {499, 19930}, {3086, 19888}, {3624, 19887}, {8583, 19885}, {11681, 16830}, {11813, 17798}, {19843, 19946}, {19846, 19873}, {19863, 19886}, {19864, 19891}
X(19928) lies on these lines: {1, 19887}, {2, 19884}, {8, 19890}, {57, 1125}, {392, 17095}, {3436, 16830}, {3573, 3616}, {19784, 19896}, {19836, 19891}, {19866, 19886}
X(19929) lies on these lines: {2, 19891}, {58, 86}, {16828, 19893}, {19858, 19884}, {19863, 19894}, {19874, 19937}
X(19930) lies on these lines: {1, 19887}, {2, 19891}, {63, 1125}, {498, 19931}, {499, 19927}, {10573, 19890}, {19854, 19884}, {19855, 19937}, {19857, 19932}
X(19931) lies on these lines: {2, 19884}, {10, 19890}, {65, 392}, {191, 3294}, {405, 2283}, {498, 19930}, {1212, 1329}, {1698, 19887}, {2975, 16830}, {3085, 19888}
X(19932) lies on these lines: {1, 19886}, {69, 1125}, {1698, 19887}, {3624, 16479}, {19857, 19930}, {19885, 19934}
X(19933) lies on these lines: {1, 19895}, {2, 19935}, {10, 19934}, {75, 1125}, {519, 20001}, {551, 20000}, {1698, 19887}, {3244, 20010}, {3624, 19996}, {3634, 19951}, {3828, 19969}, {5550, 20003}, {15808, 19999}, {19856, 19886}, {19858, 19953}, {19862, 19962}, {19878, 19968}, {19883, 20004}, {19888, 19943}
X(19934) lies on these lines: {1, 19897}, {10, 19933}, {76, 1125}, {19884, 19936}, {19885, 19932}
X(19935) lies on these lines: {1, 19886}, {2, 19933}, {58, 86}, {620, 1929}, {3624, 19887}, {14349, 19947}, {19862, 19936}, {19895, 19943}
X(19936) lies on these lines: {99, 1125}, {19862, 19935}, {19884, 19934}, {19941, 19943}
X(19937) lies on these lines: {1, 6547}, {10, 19893}, {100, 1125}, {1308, 2752}, {1698, 19884}, {3634, 19894}, {19853, 19891}, {19855, 19930}, {19871, 19886}, {19874, 19929}
X(19938) lies on these lines: {10, 75}
See Antreas Hatzipolakis, César Lozada, and Peter Moses, Hyacinthos 27802 and Hyacinthos 27803.
X(19939) = reflection of X(137) in the line X(5501)X(13856)
See Antreas Hatzipolakis and Peter Moses, Hyacinthos 27809.
X(19940) lies of these lines: {2, 3}, {3574, 14051}
X(19940) = midpoint of X(546) and X(5501)
X(19940) = reflection of X(i) in X(j) for these {i, j}: {140, 13469}, {3530, 12056}, {10289, 5}, {15333, 10109}, {15334, 3628}, {15335, 3850}, {15336, 3530}
X(19941) lies on these lines: {101, 1125}, {927, 17095}, {19936, 19943}
X(19942) lies on these lines: {1, 19886}, {141, 1125}, {620, 8301}, {1698, 19873}
X(19943) lies on these lines: {1, 19899}, {10, 4555}, {190, 1125}, {19856, 19898}, {19886, 19944}, {19888, 19933}, {19895, 19935}, {19936, 19941}
X(19944) lies on these lines: {1, 19895}, {192, 1125}, {19856, 19888}, {19886, 19943}
X(19945) lies on these lines: {10, 75}, {11, 244}, {190, 4947}, {291, 903}, {513, 16507}, {764, 2087}, {1646, 14434}, {3248, 4014}, {4392, 4443}, {4941, 17234}
X(19946) lies on these lines: {10, 19890}, {210, 1125}, {16828, 19895}, {19784, 19886}, {19836, 19873}, {19843, 19927}, {19855, 19888}, {19891, 19898}
X(19947) lies on these lines: {2, 764}, {8, 14421}, {12, 3669}, {274, 693}, {513, 1125}, {514, 3634}, {667, 5253}, {876, 19895}, {1022, 1698}, {1491, 19898}, {2530, 19894}, {2787, 3837}, {3126, 19888}, {3244, 9269}, {3251, 3622}, {3309, 5901}, {3616, 6161}, {3624, 4448}, {3626, 9260}, {3754, 4083}, {3777, 19847}, {3934, 4885}, {4378, 16830}, {4905, 5443}, {10006, 14475}, {14349, 19935}
X(19948) lies on this line: {647, 1125}
X(19949) lies on these lines: {514, 19856}, {649, 1125}, {1491, 19898}
X(19950) lies on these lines: {1, 16377}, {2, 19933}, {10, 75}, {291, 1111}, {1447, 11364}, {2108, 2795}, {5883, 6788}, {16497, 16823}
X(19951) lies on these lines: {1, 6631}, {2, 4124}, {10, 75}, {291, 18159}, {3634, 19933}
X(19952) lies on these lines: {10, 75}
X(19953) lies on these lines: {10, 75}, {19858, 19933}
X(19954) lies on these lines: {10, 75}
X(19955) lies on these lines: {2, 19976}, {10, 75}, {239, 3570}
X(19956) lies on these lines: {10, 75}
X(19957) lies on these lines: {10, 75}, {876, 4049}
X(19958) lies on these lines: {10, 75}
X(19959) lies on these lines: {10, 75}
X(19960) lies on these lines: {10, 75}
X(19961) lies on these lines: {10, 75}
X(19962) lies on these lines: {10, 75}, {4142, 8714}, {4655, 19987}, {17770, 19992}, {19862, 19933}
X(19963) lies on these lines: {1, 19895}, {10, 75}, {291, 4986}
X(19964) lies on these lines: {10, 75}, {899, 3570}
X(19965) lies on these lines: {10, 75}, {1642, 3008}
X(19966) lies on these lines: {10, 75}
X(19967) lies on these lines: {10, 75}
X(19968) lies on these lines: {10, 75}
X(19969) lies on these lines: {10, 75}
X(19970) lies on these lines: {10, 75}
X(19971) lies on these lines: {10, 75}
X(19972) lies on these lines: {10, 75}
X(19973) lies on these lines: {2, 4562}, {10, 75}, {244, 334}, {2087, 19974}
X(19974) lies on these lines: {1, 2}, {334, 1015}, {1724, 6652}, {2087, 19973}, {9318, 17499}
X(19975) lies on these lines: {2, 19933}, {75, 19976}, {335, 3120}
X(19976) lies on these lines: {2, 19955}, {6, 9318}, {75, 19975}
X(19977) lies on these lines: {1, 7829}, {2, 3675}, {6, 10}
X(19978) lies on these lines: {6, 10}, {3634, 19886}
X(19979) lies on these lines: {6, 10}
X(19980) lies on these lines: {6, 10}, {19858, 19884}
X(19981) lies on these lines: {6, 10}
X(19982) lies on these lines: {2, 19955}, {6, 10}, {37, 19997}
X(19983) lies on these lines: {6, 10}
X(19984) lies on these lines: {6, 10}
X(19985) lies on these lines: {6, 10}, {19862, 19886}
X(19986) lies on these lines: {6, 10}
X(19987) lies on these lines: {1, 19886}, {6, 10}, {8, 14947}, {4655, 19962}
X(19988) lies on these lines: {6, 10}
X(19989) lies on these lines: {6, 10}
X(19990) lies on these lines: {6, 10}, {3828, 19886}
X(19991) lies on these lines: {6, 10}, {3624, 19886}
X(19992) lies on these lines: {6, 10}, {551, 19886}, {17770, 19962}
X(19993) lies on these lines: {1, 2}, {144, 20068}, {149, 7391}, {193, 4430}, {390, 17147}, {497, 3891}, {1279, 17776}, {1483, 19544}, {1848, 7409}, {1891, 7408}, {2835, 9965}, {3210, 20075}, {3242, 5739}, {3315, 18141}, {3434, 19789}, {3744, 17740}, {3871, 7485}, {3914, 19824}, {4000, 5014}, {4220, 7967}, {4307, 17140}, {4310, 6327}, {4329, 4452}, {4383, 9053}, {4514, 19785}, {4673, 19835}, {5263, 19825}, {5310, 8666}, {5324, 16704}, {5844, 16434}, {5846, 17597}, {7394, 20060}, {7500, 17480}, {12245, 19649}, {17495, 17784}, {20062, 20067}
X(19994) lies on these lines: {1, 2}, {193, 9016}, {766, 20064}, {5844, 19545}
X(19995) lies on these lines: {10, 75}
X(19996) lies on these lines: {10, 75}, {3624, 19933}
X(19997) lies on these lines: {10, 75}, {37, 19982}
X(19998) lies on these lines: {1, 2}, {55, 19742}, {100, 3286}, {209, 17784}, {210, 3896}, {244, 17145}, {321, 4849}, {513, 4380}, {518, 4706}, {672, 4700}, {740, 3952}, {896, 4753}, {1215, 17163}, {1757, 4427}, {1783, 14954}, {2238, 3943}, {2533, 9260}, {3210, 4661}, {3681, 17147}, {3722, 4974}, {3930, 4771}, {3932, 4819}, {4080, 4442}, {4090, 4365}, {4113, 4981}, {4430, 17490}, {4465, 4971}, {4734, 7226}, {5069, 5839}, {5247, 17539}, {5687, 11322}, {5752, 6361}, {5844, 19546}, {12245, 19647}
X(19998) = anticomplement of X(29824)
X(19999) lies on these lines: {10, 75}, {15808, 19933}
X(20000) lies on these lines: {10, 75}, {551, 19933}
| 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) |