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(54001) lies on these lines: {2, 3}, {32, 50718}, {49, 18379}, {54, 13851}, {74, 32767}, {112, 39590}, {156, 18430}, {184, 18394}, {265, 11264}, {389, 7722}, {578, 7699}, {946, 31948}, {1112, 12300}, {1147, 18392}, {1173, 11564}, {1199, 18388}, {1614, 18383}, {1986, 10095}, {2914, 3574}, {3043, 10113}, {6152, 11017}, {6153, 6242}, {6241, 23325}, {6344, 14860}, {6696, 12244}, {6746, 45958}, {6748, 18365}, {8537, 18553}, {8744, 43457}, {9707, 18405}, {9820, 12383}, {10110, 32352}, {10312, 39565}, {10632, 42919}, {10633, 42918}, {11438, 11704}, {11464, 34786}, {11561, 12292}, {11572, 14157}, {11597, 22804}, {12133, 22948}, {12254, 32395}, {12289, 18376}, {15012, 43836}, {15031, 44146}, {15081, 26879}, {16223, 46847}, {17854, 32184}, {18488, 46686}, {18504, 46261}, {20417, 34563}, {22330, 32234}, {23292, 43818}, {23324, 34224}, {25739, 43831}, {32171, 52863}, {34545, 43821}, {38140, 41722}, {40640, 44795}, {43846, 46849}, {43865, 52416}
X(54001) = midpoint of X(4) and X(6143)
X(54001) = orthocentroidal-circle-inverse of X(34797)}
X(54001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 34797}, {2, 34797, 17506}, {3, 18567, 10296}, {4, 5, 186}, {4, 235, 26863}, {4, 403, 34484}, {4, 1594, 14865}, {4, 3090, 35471}, {4, 3091, 16868}, {4, 3544, 3147}, {4, 3545, 7505}, {4, 7505, 18559}, {4, 7577, 3520}, {4, 14940, 6240}, {4, 16868, 3518}, {4, 21844, 35480}, {4, 35473, 382}, {4, 35475, 35490}, {4, 35482, 1885}, {4, 35487, 47486}, {4, 37943, 3575}, {4, 44879, 12173}, {4, 44958, 52294}, {4, 52295, 13596}, {5, 3627, 10125}, {5, 3845, 45971}, {5, 6240, 14940}, {5, 18403, 14118}, {5, 18563, 2}, {5, 18567, 3}, {24, 18386, 4}, {378, 3843, 4}, {381, 7507, 35488}, {381, 7547, 4}, {381, 7564, 3832}, {382, 52296, 35473}, {403, 23047, 4}, {427, 7533, 37777}, {546, 1594, 4}, {546, 5066, 13163}, {546, 25402, 5}, {1594, 1885, 35482}, {1656, 35480, 21844}, {1885, 35482, 14865}, {3091, 3832, 7528}, {3091, 7404, 3545}, {3153, 10024, 7512}, {3541, 3839, 4}, {3575, 5066, 35487}, {3575, 35487, 37943}, {3575, 37943, 47486}, {3845, 18560, 4}, {3850, 23047, 403}, {3850, 50137, 3091}, {3851, 18386, 24}, {5094, 35490, 35475}, {6240, 14940, 186}, {7404, 52069, 35500}, {7507, 35488, 4}, {7528, 52295, 3518}, {7547, 35488, 7507}, {10151, 15559, 4}, {10254, 18377, 7488}, {10255, 44263, 22467}, {13163, 48411, 44802}, {13371, 50009, 7464}, {13406, 31724, 23}
X(54002) lies on these lines: {2, 3}, {211, 7867}, {233, 40601}, {1506, 20965}, {3051, 7746}, {3589, 20021}, {3613, 22062}, {3917, 27375}, {7786, 39906}, {11272, 51481}, {11675, 33873}, {14061, 22735}, {18024, 40410}, {18358, 25046}, {21352, 45937}, {31279, 45692}, {40643, 43650}
X(54002) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 237}, {2, 14957, 140}, {2, 32961, 33734}, {2, 37988, 14096}, {3628, 21531, 2}
X(54003) lies on these lines: {2, 3}, {32, 11424}, {39, 185}, {64, 5013}, {160, 36990}, {216, 12294}, {248, 1970}, {511, 23635}, {570, 34146}, {574, 3331}, {577, 19124}, {578, 34396}, {682, 51869}, {1105, 6394}, {1350, 22062}, {1503, 20775}, {3095, 5889}, {3398, 13434}, {5158, 11470}, {5167, 18860}, {5191, 11430}, {5480, 40981}, {5907, 36212}, {5921, 20794}, {7783, 39355}, {8266, 29181}, {8550, 53246}, {9155, 15030}, {9737, 23098}, {11171, 15072}, {11550, 23195}, {11674, 35002}, {13334, 46850}, {13367, 42671}, {13474, 44437}, {14135, 52006}, {15062, 32464}, {15270, 17845}, {15815, 38297}, {16264, 19189}, {16659, 51255}, {20975, 50649}, {22089, 41167}, {23105, 42660}, {23181, 45303}, {23200, 51739}, {37575, 45932}, {39871, 41008}, {40079, 43278}, {41328, 44882}, {41716, 50645}, {44489, 46327}
X(54003) = crossdifference of every pair of points on line {647, 53345}
X(54003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 237}, {3, 441, 417}, {3, 6660, 7488}, {3, 11479, 37344}, {3, 31952, 20}, {3, 32444, 4}, {4, 37121, 5}, {4, 44893, 235}, {5013, 32445, 43718}, {14118, 37183, 3}, {35934, 47620, 14096}, {42789, 42790, 37124}
X(54004) lies on these lines: {2, 3}, {39, 3289}, {95, 17984}, {160, 10516}, {182, 14575}, {211, 30270}, {216, 2211}, {511, 22062}, {569, 34396}, {570, 44716}, {574, 45938}, {1352, 20775}, {1503, 41328}, {3095, 11412}, {3398, 43651}, {5013, 40805}, {5188, 27375}, {5191, 37513}, {5480, 8266}, {5907, 13334}, {6146, 51869}, {6292, 46094}, {6394, 40448}, {9155, 10170}, {9475, 42441}, {9605, 12160}, {9967, 23635}, {10984, 37479}, {11171, 11459}, {11675, 35002}, {11793, 36212}, {14561, 40981}, {15030, 21163}, {20975, 44479}, {22087, 50648}, {37575, 45937}, {39201, 40550}, {44437, 44870}
X(54004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5, 237}, {3, 6660, 7512}, {3, 11328, 37114}, {3, 31952, 376}, {3, 32444, 20}, {3090, 37114, 11328}, {14096, 35934, 47620}, {37126, 37183, 3}
X(54005) lies on these lines: {2, 3}, {115, 3574}, {217, 5475}, {3331, 43457}, {7697, 11444}, {11197, 47328}, {18424, 45938}, {22682, 27375}, {23635, 39530}, {26883, 40643}, {42862, 44145}
X(54005) = midpoint of X(4) and X(37121)
X(54005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5, 237}, {4, 44893, 3575}, {3843, 32444, 4}
X(54006) lies on these lines: {2, 3}, {52, 15047}, {54, 32142}, {95, 339}, {113, 32600}, {115, 2963}, {128, 46654}, {143, 12834}, {182, 15087}, {195, 1216}, {216, 52166}, {252, 51255}, {323, 44324}, {389, 12307}, {399, 5092}, {511, 15038}, {567, 3917}, {568, 43650}, {1154, 15037}, {1173, 13421}, {1199, 12316}, {1209, 44862}, {1351, 37283}, {1511, 5888}, {2917, 32767}, {3455, 15561}, {3581, 5892}, {3763, 52990}, {3819, 22115}, {5012, 15067}, {5085, 18445}, {5096, 45923}, {5309, 50660}, {5447, 37472}, {5562, 37471}, {5650, 18475}, {5890, 33533}, {5898, 21357}, {6101, 14627}, {6243, 15004}, {7691, 12006}, {7753, 11063}, {7999, 32046}, {8553, 15484}, {8589, 34866}, {8718, 45958}, {9703, 15066}, {9730, 32608}, {10170, 10540}, {10601, 13321}, {10627, 13434}, {11258, 15563}, {11381, 33539}, {11464, 44299}, {11898, 32621}, {11935, 40913}, {12188, 41328}, {12325, 32165}, {13336, 18436}, {13339, 13754}, {13364, 15107}, {13470, 48675}, {14128, 52525}, {15033, 37496}, {15108, 50708}, {15567, 31843}, {15801, 36153}, {16030, 40631}, {18350, 44110}, {18451, 53094}, {18493, 37557}, {19596, 24206}, {21230, 43808}, {21975, 51477}, {22121, 53026}, {26879, 32333}, {32063, 44883}, {33541, 46850}, {33879, 34513}, {34783, 37515}, {37779, 45969}, {38402, 46267}, {43150, 45730}, {43704, 44325}, {51175, 53019}
X(54006) = midpoint of X(7550) and X(15246)
X(54006) = reflection of X(i) in X(j) for these {i,j}: {3, 15246}, {37349, 5}
X(54006) = X(22454)-isoconjugate of X(44706)
X(54006) = barycentric quotient X(8882)/X(22454)
X(54006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 2070}, {2, 46450, 5}, {3, 5, 13564}, {3, 140, 43809}, {3, 1656, 2937}, {3, 3526, 45735}, {3, 3843, 10323}, {3, 5055, 22}, {3, 5070, 26}, {3, 5899, 6636}, {3, 7393, 1656}, {3, 7395, 382}, {3, 7484, 5054}, {3, 9818, 3534}, {3, 13621, 7512}, {3, 14118, 35498}, {3, 15694, 6644}, {3, 18378, 7525}, {3, 21308, 34006}, {3, 21312, 14093}, {3, 34864, 14130}, {3, 35452, 8703}, {3, 46219, 24}, {3, 49671, 35001}, {5, 6636, 5899}, {22, 5055, 7545}, {23, 547, 21308}, {24, 13154, 46219}, {140, 37126, 3}, {140, 37938, 2}, {182, 23039, 15087}, {186, 1594, 25}, {548, 45308, 3}, {549, 35921, 3}, {1216, 13353, 195}, {1656, 2937, 18369}, {2071, 12100, 3}, {3090, 7525, 18378}, {3520, 15712, 3}, {3524, 18570, 3}, {3530, 14118, 3}, {3628, 7512, 13621}, {3819, 37513, 22115}, {5012, 15067, 50461}, {5054, 30771, 3526}, {5562, 37471, 43845}, {5899, 6636, 13564}, {6101, 43651, 14627}, {6644, 40916, 15694}, {7484, 32216, 40916}, {7485, 7509, 7514}, {7485, 7514, 3}, {7496, 35921, 549}, {7502, 31723, 12083}, {7509, 7516, 3}, {7514, 7516, 7485}, {7527, 8703, 35452}, {7555, 13595, 37956}, {7555, 15699, 13595}, {7574, 37347, 381}, {10170, 22352, 10540}, {10601, 37494, 13321}, {11250, 15717, 3}, {21308, 34006, 23}, {35500, 45308, 548}, {36439, 36457, 37901}, {37848, 37850, 15109}, {44832, 50135, 12083}
X(54007) lies on these lines: {2, 3}, {49, 48675}, {110, 22804}, {156, 7699}, {265, 3574}, {389, 38724}, {567, 10274}, {578, 18430}, {1568, 15137}, {5562, 6153}, {5895, 18550}, {6145, 43821}, {6288, 50461}, {7703, 32138}, {7728, 11559}, {9630, 38458}, {10095, 14644}, {11430, 52863}, {11591, 32196}, {11801, 11805}, {12902, 37472}, {13851, 43835}, {14128, 41590}, {14676, 18502}, {14860, 14978}, {15033, 18379}, {15038, 32341}, {18424, 38463}, {20299, 43807}, {23325, 37481}, {25739, 43845}, {32340, 44516}, {32608, 34826}, {36753, 40285}
X(54007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 5, 2070}, {4, 3091, 13406}, {4, 10254, 18378}, {4, 18562, 3830}, {4, 18570, 382}, {4, 39504, 14130}, {5, 3153, 34864}, {5, 3627, 34577}, {5, 31724, 3}, {5, 35921, 1656}, {265, 3574, 14627}, {381, 7507, 3}, {546, 33332, 4}, {3851, 18378, 10254}, {5576, 23047, 18403}, {6143, 45971, 37955}, {7547, 7564, 381}, {7574, 13160, 3}, {11563, 50135, 10254}
See Thanassis Gakopoulos, Antreas Hatzipolakis and Ivan Pavlov, euclid 5843.
X(54008) lies on these lines: {4,1903}, {6,1826}, {8,21871}, {9,355}, {10,37062}, {11,3554}, {19,1146}, {34,10366}, {37,5252}, {48,46835}, {56,24005}, {71,3691}, {77,21239}, {80,1743}, {92,5928}, {198,515}, {219,5179}, {281,2182}, {282,5514}, {346,5176}, {391,5086}, {519,21068}, {604,21044}, {610,5787}, {950,10367}, {966,5794}, {1012,11434}, {1212,26063}, {1229,21286}, {1436,6245}, {1449,5722}, {1737,5120}, {1741,37468}, {1836,1899}, {1839,5895}, {1855,3197}, {1856,2192}, {1864,7102}, {1901,5155}, {2082,5090}, {2267,17303}, {2270,5691}, {2276,21860}, {2285,21933}, {2324,5881}, {2994,7381}, {2995,23978}, {3419,3686}, {3553,10950}, {3731,37710}, {4254,10572}, {4863,17362}, {5227,40997}, {5307,13567}, {5786,46878}, {5816,40937}, {5942,21279}, {6611,8808}, {8573,22760}, {11375,50036}, {15817,22758}, {16667,37702}, {17134,25000}, {17299,21801}, {17314,32049}, {18621,28044}, {20927,21277}, {21244,24266}, {21270,30807}, {21853,41687}, {24914,36743}, {46344,51424}
X(54008) = midpoint of X(5942) and X(21279)
X(54008) = reflection of X(i) in X(j) for these {i,j}: {77, 21239}, {198, 20262}
X(54008) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 34411}
X(54008) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 34411}, {46836, 69}
X(54008) = X(i)-Waw conjugate of X(j) for these {i, j}: {4, 1836}
X(54008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 20262, 198}, {2267, 21011, 17303}, {5942, 21279, 34371}
See Thanassis Gakopoulos, Antreas Hatzipolakis and Ivan Pavlov, euclid 5843.
X(54009) lies on these lines: {4,1903}, {9,119}, {19,12679}, {48,12678}, {198,6260}, {208,429}, {221,53009}, {226,6611}, {322,329}, {342,10402}, {610,6259}, {1436,20263}, {1532,1741}, {1826,1836}, {1863,1864}, {2182,37414}, {2199,46836}, {2325,8804}, {2331,38357}, {2899,4645}, {6335,34408}, {7101,33650}, {12572,37320}
X(54009) = reflection of X(1436) in X(20263)
X(54009) = X(i)-Dao conjugate of X(j) for these {i, j}: {281, 34408}
X(54009) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6335, 6129}
See Thanassis Gakopoulos, Antreas Hatzipolakis and Ivan Pavlov, euclid 5843.
X(54010) lies on these lines: {4,7149}, {34,12679}, {73,12678}, {223,6259}, {225,2192}, {1035,20264}, {1118,17832}, {1836,1854}, {1837,1899}, {1895,10361}, {3342,13612}, {7037,47441}, {7103,10374}, {7952,40658}, {8812,10400}
X(54010) = reflection of X(1035) in X(20264)
X(54010) = X(i)-Waw conjugate of X(j) for these {i, j}: {4, 1837}
See Thanassis Gakopoulos, Antreas Hatzipolakis and Ivan Pavlov, euclid 5843.
X(54011) lies on these lines: {6,1885}, {146,45245}, {393,1562}, {647,18890}, {1033,15311}, {1249,5878}, {2331,12940}, {3087,35717}, {3344,13613}, {4846,15851}, {7129,12950}, {15341,15905}, {28783,33546}, {34980,41762}
X(54011) = reflection of X(1033) in X(20265)
X(54011) = X(i)-Waw conjugate of X(j) for these {i, j}: {4, 1899}
X(54011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1562, 14642, 393}, {15311, 20265, 1033}
See Thanassis Gakopoulos, Antreas Hatzipolakis and Ivan Pavlov, euclid 5843.
XX(54012) lies on the circumconic {{A, B, C, X(98), X(45088)}} and these lines: {2,98}, {3,16657}, {4,373}, {6,30739}, {20,34417}, {25,44882}, {30,3066}, {51,7386}, {66,19132}, {68,3526}, {69,5650}, {122,5158}, {140,35602}, {141,26869}, {185,6804}, {290,46328}, {343,16419}, {381,5544}, {394,1353}, {427,17825}, {468,5085}, {511,46336}, {574,6388}, {575,37645}, {597,32216}, {599,5646}, {631,11430}, {632,18952}, {858,14561}, {1350,43957}, {1368,10601}, {1370,5943}, {1495,25406}, {1503,11284}, {1656,45303}, {1853,37439}, {1995,46264}, {2549,3124}, {3090,14216}, {3292,14912}, {3524,32225}, {3525,18912}, {3534,20192}, {3542,37515}, {3580,40916}, {3589,5094}, {3618,15812}, {3796,6677}, {3819,6515}, {3832,44300}, {3917,11433}, {4232,35268}, {4846,7728}, {5020,31383}, {5050,11064}, {5054,44569}, {5067,11457}, {5092,7493}, {5159,38110}, {5480,31152}, {5640,16063}, {5810,17529}, {5892,7706}, {6090,8550}, {6353,22352}, {6617,26905}, {6688,6997}, {6816,9729}, {6819,42400}, {7391,11451}, {7392,11550}, {7395,26937}, {7484,13567}, {7499,26958}, {7500,48896}, {7519,10545}, {7539,23332}, {7605,31857}, {7667,17810}, {7734,41588}, {7998,37644}, {8721,37338}, {9815,15028}, {9822,41256}, {10113,50008}, {10170,18917}, {10300,21850}, {10301,48905}, {10519,41586}, {10691,33586}, {10744,30513}, {11245,17811}, {11484,16655}, {11585,15805}, {11793,18916}, {12017,13394}, {12045,18553}, {13363,14791}, {13366,37669}, {14853,51360}, {15018,44493}, {15024,47528}, {15082,34507}, {15106,25329}, {15448,47597}, {15873,37198}, {16111,37470}, {17508,32223}, {17704,37201}, {18440,35283}, {19130,31099}, {20266,26890}, {21015,52424}, {22111,43448}, {23292,31255}, {25738,46219}, {26255,32237}, {26898,45200}, {30771,37649}, {31860,37899}, {31884,47582}, {33879,41724}, {34608,44106}, {34664,37475}, {34944,45979}, {35259,48906}, {38072,47311}, {38136,47315}, {39691,43620}, {40911,50967}, {44210,53094}, {46517,53023}, {47097,47352}
X(54012) = anticomplement of X(16187)
X(54012) = X(i)-Dao conjugate of X(j) for these {i, j}: {16187, 16187}
X(54012) = X(i)-Ceva conjugate of X(j) for these {i, j}: {46326, 2}
X(54012) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {46326, 6327}
X(54012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18911, 1352}, {2, 6776, 5651}, {125, 22112, 2}, {1352, 18911, 1899}, {5640, 16063, 31670}, {7386, 18928, 51}, {7484, 13567, 43653}, {15028, 37444, 9815}, {25406, 40132, 1495}
See Thanassis Gakopoulos, Antreas Hatzipolakis and Ivan Pavlov, euclid 5843.
X(54013) lies on these lines: {2,98}, {4,15066}, {5,6090}, {6,35283}, {20,7998}, {23,10519}, {24,11487}, {25,48876}, {69,1995}, {107,44134}, {140,26864}, {141,7493}, {193,5640}, {323,14853}, {376,11472}, {394,5480}, {524,3066}, {599,26255}, {631,6800}, {858,47474}, {1216,37122}, {1370,17811}, {1503,46336}, {1993,7392}, {2478,26637}, {2979,6995}, {3060,7398}, {3089,43614}, {3090,6193}, {3167,37439}, {3292,14561}, {3426,46349}, {3522,41462}, {3523,10282}, {3541,44080}, {3545,40112}, {3547,43598}, {3564,11284}, {3580,40132}, {3619,5596}, {3620,4232}, {3763,13394}, {3785,37465}, {3818,31099}, {3819,31383}, {3917,7500}, {3926,37335}, {4549,5891}, {4550,35485}, {4563,11185}, {4576,32815}, {4648,7474}, {5020,6515}, {5032,32127}, {5094,18358}, {5133,37669}, {5646,43273}, {5650,46264}, {5656,15052}, {6353,37636}, {6803,11441}, {6804,14516}, {6815,17814}, {6816,18396}, {7383,10539}, {7426,21356}, {7485,11206}, {7487,11444}, {7494,35264}, {7499,8780}, {7519,33884}, {7550,40913}, {7605,9716}, {7703,30769}, {7999,31305}, {9777,10128}, {10301,33878}, {10516,11064}, {10545,20080}, {10601,12007}, {11402,51732}, {11422,51171}, {11427,37990}, {11821,31304}, {12121,49669}, {12302,44834}, {13416,15060}, {15019,51170}, {15069,37648}, {15106,50008}, {15107,52301}, {15435,20806}, {15533,20192}, {16042,37644}, {17928,18931}, {18440,30739}, {18916,31831}, {18919,26206}, {18928,45968}, {21358,35266}, {25406,40916}, {30221,50149}, {31133,51537}, {31152,39884}, {32113,37980}, {32237,50977}, {32971,46900}, {33926,40680}, {35311,40138}, {35325,41370}, {35486,43586}
X(54013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3410, 23291}, {2, 5921, 18911}, {141, 35259, 7493}, {376, 44833, 21766}, {1352, 5651, 2}, {3619, 35260, 7495}, {22112, 24981, 11179}, {40916, 46818, 25406}
X(54014) lies on these lines: {30, 511}, {1734, 50439}, {4560, 5240}
X(54014) = isogonal conjugate of X(36073)
X(54014) = crossdifference of every pair of points on line {6, 2152}
X(54014) = barycentric quotient X(4488)/X(34380)
X(54015) lies on these lines: {30, 511}, {1734, 50438}, {4560, 5239}
X(54015) = isogonal conjugate of X(36072)
X(54015) = crossdifference of every pair of points on line {6, 2151}
X(54016) lies on the circumcircle and these lines: {102, 2066}, {103, 6502}, {104, 18460}, {105, 16232}, {163, 39383}, {675, 13390}, {692, 2498}, {1311, 14121}, {1783, 6135}, {2362, 53069}, {9099, 13388}, {13389, 43363}, {26703, 30556}, {32726, 53065}
X(56016) = isogonal conjugate of X(56017)
X(54016) = X(7115)-Ceva conjugate of X(34125)
X(54016) = X(i)-isoconjugate of X(j) for these (i,j): {514, 30557}, {521, 1659}, {522, 13388}, {693, 5414}, {905, 7090}, {1577, 1805}, {2067, 4391}, {2362, 6332}, {3261, 53066}, {4025, 7133}, {6365, 14121}, {35519, 53063}
X(54016) = X(13388)-Dao conjugate of X(15413)
X(54016) = trilinear pole of line {6, 34125}
X(54016) = barycentric product X(i)*X(j) for these {i,j}: {100, 16232}, {101, 13390}, {108, 30556}, {109, 14121}, {651, 42013}, {653, 2066}, {1783, 13389}, {1897, 6502}, {6136, 13388}, {6335, 53064}, {18026, 53065}
X(54016) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 30557}, {1415, 13388}, {1576, 1805}, {2066, 6332}, {6502, 4025}, {8750, 7090}, {13389, 15413}, {13390, 3261}, {14121, 35519}, {16232, 693}, {30556, 35518}, {32674, 1659}, {32739, 5414}, {42013, 4391}, {53063, 6365}, {53064, 905}, {53065, 521}
X(54017) lies on this line: {30, 511}
X(54017) = isogonal conjugate of X(54016)
X(54017) = crossdifference of every pair of points on line {6, 34125}
X(54017) = barycentric quotient X(i)/X(j) for these {i,j}: {11918, 9346}, {14689, 20831}
X(54018) lies on the circumcircle and these lines: {102, 5414}, {103, 2067}, {104, 7133}, {105, 2362}, {163, 39384}, {675, 1659}, {692, 2498}, {1311, 7090}, {1783, 6136}, {9098, 13389}, {13388, 43363}, {16232, 53070}, {26703, 30557}, {32726, 53066}
X(54018) = X(7115)-Ceva conjugate of X(34121)
X(54018) = X(i)-isoconjugate of X(j) for these (i,j): {514, 30556}, {521, 13390}, {522, 13389}, {693, 2066}, {905, 14121}, {1577, 1806}, {3261, 53065}, {4025, 42013}, {4391, 6502}, {6332, 16232}, {6364, 7090}, {35519, 53064}
X(54018) = X(13389)-Dao conjugate of X(15413)
X(54018) = trilinear pole of line {6, 34121}
X(54018) = barycentric product X(i)*X(j) for these {i,j}: {100, 2362}, {101, 1659}, {108, 30557}, {109, 7090}, {651, 7133}, {653, 5414}, {1783, 13388}, {1897, 2067}, {6135, 13389}, {6335, 53063}, {18026, 53066}
X(54018) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 30556}, {1415, 13389}, {1576, 1806}, {1659, 3261}, {2067, 4025}, {2362, 693}, {5414, 6332}, {7090, 35519}, {7133, 4391}, {8750, 14121}, {13388, 15413}, {30557, 35518}, {32674, 13390}, {32739, 2066}, {53063, 905}, {53064, 6364}, {53066, 521}
X(54019) lies on these lines: {30, 511}, {4025, 30193}
X(54019) = isogonal conjugate of X(54018)
X(54019) = crossdifference of every pair of points on line {6, 34121}
X(54019) = barycentric product X(20945)*X(41146)
X(54020) lies on the circumcircle and these lines: {104, 7126}, {105, 7052}, {106, 7051}, {163, 16806}, {663, 692}, {840, 19373}, {1311, 7043}, {1415, 36072}, {4559, 36073}
X(54020) = isogonal conjugate of X(54021)
X(54020) = X(i)-isoconjugate of X(j) for these (i,j): {514, 5239}, {522, 37772}, {693, 7127}, {3904, 33655}, {3960, 7026}, {4391, 7051}, {4453, 19551}, {23838, 36668}
X(54020) = trilinear pole of line {6, 42624}
X(54020) = barycentric product X(i)*X(j) for these {i,j}: {100, 7052}, {109, 7043}, {651, 7126}, {2222, 5240}, {19373, 51562}
X(54020) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 5239}, {1415, 37772}, {7043, 35519}, {7052, 693}, {7126, 4391}, {19373, 4453}, {32739, 7127}
X(54021) lies on these lines: {30, 511}, {4453, 36668}, {36930, 49274}
X(54021) = isogonal conjugate of X(54020)
X(54021) = crossdifference of every pair of points on line {6, 42624}
X(54022) lies on the circumcircle and these lines: {104, 19551}, {105, 33655}, {106, 19373}, {163, 16807}, {663, 692}, {840, 7051}, {953, 7127}, {1311, 7026}, {1415, 36073}, {4559, 36072}
X(54022) = X(i)-isoconjugate of X(j) for these (i,j): {514, 5240}, {522, 37773}, {3904, 7052}, {3960, 7043}, {4391, 19373}, {4453, 7126}, {23838, 36669}
X(54022) = barycentric product X(i)*X(j) for these {i,j}: {100, 33655}, {109, 7026}, {651, 19551}, {655, 7127}, {2222, 5239}, {7051, 51562}
X(54022) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 5240}, {1415, 37773}, {7026, 35519}, {7051, 4453}, {7127, 3904}, {19551, 4391}, {33655, 693}
X(54023) lies on these lines: {30, 511}, {4453, 36669}, {36931, 49274}
X(54023) = isogonal conjugate of X(54022)
X(54024) lies on the circumcircle and these lines: {14, 10647}, {5995, 32678}, {19305, 36298}
X(54024) = isogonal conjugate of X(54025)
X(54024) = trilinear pole of line {6, 2154}
X(54025) lies on this lines: {30, 511}
X(54025) = isogonal conjugate of X(54024)
X(54025) = crossdifference of every pair of points on line {6, 2154}
X(54025) = barycentric quotient X(52318)/X(3812)
X(54026) lies on the circumcircle and these lines: {13, 10648}, {5994, 32678}, {11080, 42623}, {19304, 36299}
X(54026) = isogonal conjugate of X(54027)
X(54026) = trilinear pole of line {6, 2153}
X(54027) lies on this line: {30, 511}
X(54027) = isogonal conjugate of X(54026)
X(54027) = crossdifference of every pair of points on line {6, 2153}
X(54028 lies on these lines: {30, 511}, {647, 14334}, {1328, 2394}, {2501, 14333}, {5664, 13821}, {6563, 14326}, {9131, 13316}, {9979, 13319}, {13807, 42733}, {14237, 43673}, {14325, 31296}, {17431, 47122}, {48539, 48955}, {48540, 48986}
X(54028) = isogonal conjugate of X(39384)
X(54028) = crossdifference of every pair of points on line {6, 3155}
X(54028) = {X(2501),X(17432)}-harmonic conjugate of X(14333)
X(54029 lies on these lines: {30, 511}, {647, 14333}, {1327, 2394}, {2501, 14334}, {5664, 13701}, {6563, 14325}, {9131, 13317}, {9979, 13320}, {13687, 42733}, {14232, 43673}, {14326, 31296}, {17432, 47122}, {48539, 48956}, {48540, 48987}
X(54029) = isogonal conjugate of X(39383)
X(54029) = crossdifference of every pair of points on line {6, 3156}
X(54029) = barycentric quotient X(33022)/X(7613)
X(54029) = {X(2501),X(17431)}-harmonic conjugate of X(14334)
X(54030) lies on the Steiner circumellipse and these lines: {99, 39384}, {110, 925}, {290, 6414}, {486, 490}, {488, 13429}, {491, 24245}, {492, 35142}, {1494, 11091}, {1992, 21464}, {3228, 8576}, {5860, 13428}, {6396, 48986}, {8940, 45420}, {10962, 34391}, {16037, 46138}, {18878, 54029}
X(54030) = isotomic conjugate of X(54028)
X(54030) = isotomic conjugate of the isogonal conjugate of X(39384)
X(54030) = X(i)-isoconjugate of X(j) for these (i,j): {31, 54028}, {372, 661}, {491, 798}, {656, 5412}, {810, 1586}, {1924, 45806}, {13461, 51641}, {24006, 26920}
X(54030) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 54028}, {486, 17432}, {5409, 52584}, {9428, 45806}, {10962, 924}, {24245, 523}, {31998, 491}, {33365, 14326}, {36830, 372}, {39062, 1586}, {40596, 5412}
X(54030) = cevapoint of X(i) and X(j) for these (i,j): {2, 54028}, {372, 14326}, {488, 14325}, {523, 615}, {5408, 54029}
X(54030) = trilinear pole of line {2, 371}
X(54030) = barycentric product X(i)*X(j) for these {i,j}: {76, 39384}, {99, 486}, {110, 34392}, {371, 46134}, {492, 925}, {648, 11091}, {670, 8576}, {4563, 41516}, {5408, 30450}, {6331, 6414}, {6528, 26922}, {8940, 35136}, {14570, 16037}, {32734, 45805}
X(54030) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 54028}, {99, 491}, {110, 372}, {112, 5412}, {371, 924}, {486, 523}, {492, 6563}, {645, 13461}, {648, 1586}, {670, 45806}, {925, 485}, {3069, 14326}, {4558, 5409}, {5408, 52584}, {5413, 6753}, {6414, 647}, {8576, 512}, {8911, 30451}, {8940, 3566}, {11091, 525}, {13428, 54029}, {16037, 15412}, {24245, 17432}, {26922, 520}, {32661, 26920}, {32734, 8577}, {34392, 850}, {39383, 44192}, {39384, 6}, {41516, 2501}, {46134, 34391}
X(54031) lies on the Steiner circumellipse and these lines: {99, 39383}, {110, 925}, {290, 6413}, {485, 489}, {487, 13440}, {491, 35142}, {492, 24246}, {1494, 11090}, {1992, 21463}, {3228, 8577}, {5861, 13439}, {6200, 48987}, {8944, 45421}, {10960, 34392}, {13455, 35144}, {16032, 46138}, {18878, 54028}
X(54031) = isotomic conjugate of X(54029)
X(54031) = isotomic conjugate of the isogonal conjugate of X(39383)
X(54031) = X(i)-isoconjugate of X(j) for these (i,j): {31, 54029}, {371, 661}, {492, 798}, {656, 5413}, {810, 1585}, {1924, 45805}, {8911, 24006}
X(54031) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 54029}, {485, 17431}, {5408, 52584}, {9428, 45805}, {10960, 924}, {24246, 523}, {31998, 492}, {33364, 14325}, {36830, 371}, {39062, 1585}, {40596, 5413}
X(54031) = cevapoint of X(i) and X(j) for these (i,j): {2, 54029}, {371, 14325}, {487, 14326}, {523, 590}, {5409, 54028}
X(54031) = trilinear pole of line {2, 372}
X(54031) = barycentric product X(i)*X(j) for these {i,j}: {76, 39383}, {99, 485}, {110, 34391}, {372, 46134}, {491, 925}, {648, 11090}, {670, 8577}, {4563, 41515}, {4625, 13455}, {5409, 30450}, {6331, 6413}, {8944, 35136}, {14570, 16032}, {32734, 45806}
X(54031) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 54029}, {99, 492}, {110, 371}, {112, 5413}, {372, 924}, {485, 523}, {491, 6563}, {648, 1585}, {670, 45805}, {925, 486}, {3068, 14325}, {4558, 5408}, {5409, 52584}, {5412, 6753}, {6413, 647}, {8577, 512}, {8944, 3566}, {11090, 525}, {13439, 54028}, {13455, 4041}, {16032, 15412}, {24246, 17431}, {26920, 30451}, {32661, 8911}, {32734, 8576}, {34391, 850}, {39383, 6}, {39384, 44193}, {41515, 2501}, {46134, 34392}
X(54032) lies on the cubic K1326 and these lines: {2, 51}, {3, 217}, {4, 276}, {20, 39682}, {52, 22270}, {69, 53174}, {97, 184}, {182, 5481}, {389, 31400}, {394, 418}, {520, 53173}, {577, 17974}, {1073, 6638}, {1092, 28724}, {1214, 3784}, {1216, 14376}, {1217, 15644}, {1297, 3098}, {1350, 40801}, {2706, 6037}, {3346, 13348}, {3522, 38256}, {3796, 34003}, {3926, 5562}, {4549, 15421}, {5171, 43652}, {6243, 22268}, {6389, 42487}, {6784, 7612}, {9418, 37114}, {9730, 46412}, {9821, 51997}, {11206, 32319}, {11427, 37872}, {11821, 46735}, {12122, 15429}, {14489, 33878}, {14938, 37484}, {21843, 31850}, {23039, 34897}, {34579, 52926}, {39683, 51350}, {45301, 46730}
X(54032) = isogonal conjugate of X(33971)
X(54032) = isogonal conjugate of the anticomplement of X(42353)
X(54032) = isogonal conjugate of the polar conjugate of X(42313)
X(54032) = isotomic conjugate of the polar conjugate of X(43718)
X(54032) = X(42313)-Ceva conjugate of X(43718)
X(54032) = X(i)-isoconjugate of X(j) for these (i,j): {1, 33971}, {6, 51315}, {19, 458}, {92, 10311}, {158, 182}, {183, 1096}, {393, 52134}, {823, 3288}, {1973, 44144}, {2190, 39530}, {2207, 3403}, {6784, 23999}, {23878, 24019}
X(54032) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 33971}, {5, 39530}, {6, 458}, {9, 51315}, {1147, 182}, {6337, 44144}, {6338, 20023}, {6503, 183}, {22391, 10311}, {35071, 23878}
X(54032) = trilinear pole of line {520, 42293}
X(54032) = barycentric product X(i)*X(j) for these {i,j}: {3, 42313}, {69, 43718}, {262, 394}, {263, 3926}, {326, 2186}, {327, 577}, {343, 51444}, {3265, 26714}, {5562, 42300}, {6394, 51543}, {15414, 52926}, {17974, 46807}, {35911, 36885}, {37188, 40803}
X(54032) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 51315}, {3, 458}, {6, 33971}, {69, 44144}, {184, 10311}, {216, 39530}, {255, 52134}, {262, 2052}, {263, 393}, {326, 3403}, {327, 18027}, {394, 183}, {520, 23878}, {577, 182}, {2186, 158}, {3402, 1096}, {3926, 20023}, {3998, 42711}, {14585, 34396}, {17974, 46806}, {26714, 107}, {32716, 20031}, {39201, 3288}, {42300, 8795}, {42313, 264}, {43718, 4}, {46319, 2207}, {51386, 51373}, {51394, 51372}, {51444, 275}, {51543, 6530}
X(54033) lies on the cubic K1326 and these lines: {2, 15265}, {4, 276}, {20, 76}, {99, 20023}, {183, 47620}, {290, 376}, {1350, 44144}, {6528, 52283}, {8920, 10008}, {10519, 17984}, {11185, 14957}, {11206, 34384}, {18022, 33522}, {44152, 51438}
X(54034) lies on these lines: {3, 54}, {4, 34449}, {5, 96}, {6, 2351}, {25, 8745}, {32, 44077}, {49, 3133}, {50, 23195}, {51, 1576}, {95, 325}, {98, 275}, {137, 50210}, {160, 184}, {228, 2148}, {237, 10547}, {570, 8603}, {878, 2623}, {1141, 50471}, {1370, 43768}, {1410, 52440}, {1994, 14652}, {2167, 35614}, {2200, 52426}, {3051, 14600}, {3425, 19189}, {3456, 42671}, {3575, 8884}, {5576, 36842}, {7399, 19179}, {9792, 45832}, {10558, 14586}, {15958, 42065}, {16032, 49356}, {16037, 49355}, {18420, 19176}, {19161, 21638}, {19188, 37454}, {20975, 34448}, {23286, 34291}, {23292, 51458}, {26864, 33629}, {33581, 44080}, {34093, 38861}, {34986, 39805}, {37347, 40631}, {41205, 45793}
X(54034) = isogonal conjugate of X(311)
X(54034) = isogonal conjugate of the anticomplement of X(570)
X(54034) = isogonal conjugate of the isotomic conjugate of X(54)
X(54034) = isogonal conjugate of the polar conjugate of X(8882)
X(54034) = isotomic conjugate of the isogonal conjugate of X(14573)
X(54034) = polar conjugate of the isotomic conjugate of X(14533)
X(54034) = X(i)-Ceva conjugate of X(j) for these (i,j): {54, 14533}, {933, 2623}, {1166, 6}, {14587, 14586}
X(54034) = X(i)-isoconjugate of X(j) for these (i,j): {1, 311}, {2, 14213}, {4, 18695}, {5, 75}, {19, 28706}, {27, 42698}, {51, 561}, {52, 20571}, {53, 304}, {63, 324}, {76, 1953}, {91, 39113}, {92, 343}, {95, 1087}, {99, 2618}, {158, 52347}, {163, 15415}, {216, 1969}, {264, 44706}, {274, 21011}, {305, 2181}, {310, 21807}, {313, 18180}, {321, 17167}, {326, 13450}, {328, 51801}, {336, 39569}, {662, 18314}, {668, 21102}, {799, 12077}, {811, 6368}, {850, 2617}, {1225, 2216}, {1273, 2166}, {1393, 3596}, {1502, 2179}, {1577, 14570}, {1625, 20948}, {1928, 40981}, {1930, 17500}, {1959, 53245}, {2167, 45793}, {2290, 20573}, {2600, 46405}, {3199, 40364}, {4592, 23290}, {6063, 7069}, {6369, 35174}, {7017, 44708}, {8800, 33808}, {13157, 18750}, {14208, 35360}, {18156, 27364}, {20565, 35194}, {20879, 31610}, {23999, 35442}, {24037, 41221}, {32680, 41078}, {33805, 52945}, {40703, 53174}, {41586, 46277}
X(54034) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 311}, {6, 28706}, {115, 15415}, {206, 5}, {512, 41221}, {1084, 18314}, {1147, 52347}, {1209, 1225}, {3162, 324}, {5139, 23290}, {11597, 1273}, {15259, 13450}, {15261, 27364}, {17423, 6368}, {22391, 343}, {32664, 14213}, {34116, 39113}, {36033, 18695}, {38986, 2618}, {38996, 12077}, {40368, 51}, {40369, 40981}, {40588, 45793}, {46604, 25043}
X(54034) = cevapoint of X(i) and X(j) for these (i,j): {32, 14575}, {184, 52435}, {34952, 41213}
X(54034) = trilinear pole of line {3049, 19627}
X(54034) = crossdifference of every pair of points on line {12077, 18314}
X(54034) = barycentric product X(i)*X(j) for these {i,j}: {1, 2148}, {3, 8882}, {4, 14533}, {6, 54}, {19, 2169}, {25, 97}, {31, 2167}, {32, 95}, {47, 2168}, {48, 2190}, {50, 1141}, {53, 46089}, {64, 33629}, {76, 14573}, {96, 571}, {98, 41270}, {107, 46088}, {110, 2623}, {112, 23286}, {115, 14587}, {163, 2616}, {184, 275}, {186, 11077}, {248, 19189}, {251, 16030}, {252, 2965}, {276, 14575}, {288, 13366}, {393, 19210}, {512, 18315}, {523, 14586}, {570, 1166}, {577, 8884}, {604, 44687}, {647, 933}, {654, 36078}, {661, 36134}, {924, 32692}, {1157, 14579}, {1298, 1971}, {1400, 35196}, {1501, 34384}, {1576, 15412}, {1974, 34386}, {1988, 26887}, {1990, 46090}, {1993, 41271}, {2081, 46966}, {2383, 52968}, {2501, 15958}, {2963, 25044}, {3049, 18831}, {3051, 39287}, {6748, 20574}, {8794, 23606}, {8795, 14585}, {8901, 23357}, {9247, 40440}, {10311, 51444}, {13622, 40633}, {14371, 51936}, {14642, 38808}, {16035, 41890}, {16813, 39201}, {19306, 51804}, {19627, 46138}, {34385, 52436}, {34394, 51275}, {34395, 51268}, {34396, 42300}, {40352, 43768}, {41331, 41488}, {43753, 43917}, {50463, 52418}
X(54034) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 28706}, {6, 311}, {25, 324}, {31, 14213}, {32, 5}, {48, 18695}, {50, 1273}, {51, 45793}, {54, 76}, {95, 1502}, {97, 305}, {184, 343}, {228, 42698}, {275, 18022}, {276, 44161}, {512, 18314}, {523, 15415}, {560, 1953}, {570, 1225}, {571, 39113}, {577, 52347}, {669, 12077}, {798, 2618}, {933, 6331}, {1084, 41221}, {1141, 20573}, {1501, 51}, {1576, 14570}, {1917, 2179}, {1918, 21011}, {1919, 21102}, {1974, 53}, {1976, 53245}, {2148, 75}, {2167, 561}, {2168, 20571}, {2169, 304}, {2179, 1087}, {2190, 1969}, {2205, 21807}, {2206, 17167}, {2207, 13450}, {2211, 39569}, {2489, 23290}, {2616, 20948}, {2623, 850}, {3049, 6368}, {3202, 41480}, {8882, 264}, {8884, 18027}, {8901, 23962}, {9233, 40981}, {9247, 44706}, {9407, 52945}, {9447, 7069}, {9697, 21230}, {11077, 328}, {14270, 41078}, {14533, 69}, {14567, 41586}, {14573, 6}, {14574, 1625}, {14575, 216}, {14585, 5562}, {14586, 99}, {14587, 4590}, {14600, 53174}, {15412, 44173}, {15958, 4563}, {16030, 8024}, {18315, 670}, {19189, 44132}, {19210, 3926}, {19627, 1154}, {23286, 3267}, {25044, 7769}, {27369, 27371}, {32692, 46134}, {33581, 13157}, {33629, 14615}, {34384, 40362}, {34386, 40050}, {34394, 33529}, {34395, 33530}, {34397, 14918}, {35196, 28660}, {36078, 46405}, {36134, 799}, {36417, 14569}, {39287, 40016}, {40373, 217}, {40981, 36412}, {41270, 325}, {41271, 5392}, {44077, 467}, {44162, 3199}, {44687, 28659}, {46088, 3265}, {46089, 34386}, {46288, 17500}, {46680, 27356}, {52435, 52032}, {52436, 52}, {52438, 5891}, {53059, 27364}
X(54034) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 97, 16030}, {54, 8883, 3}, {184, 571, 3135}, {23606, 34396, 11402}
X(54035) lies on the cubic K and these lines: {2, 29069}, {9, 1746}, {37, 10478}, {40, 1089}, {72, 10454}, {75, 21363}, {92, 21361}, {101, 28950}, {165, 29057}, {190, 21375}, {192, 9535}, {312, 1764}, {321, 573}, {329, 21078}, {515, 5692}, {516, 3971}, {517, 3175}, {572, 26223}, {1215, 10434}, {1490, 30266}, {1699, 29054}, {1766, 21376}, {2051, 28606}, {2292, 50037}, {3219, 13478}, {3718, 10437}, {3731, 10888}, {3869, 22022}, {3882, 20928}, {4415, 19542}, {4647, 9548}, {4656, 10445}, {8680, 28609}, {9554, 21333}, {10246, 19722}, {10440, 29347}, {10444, 30568}, {10446, 41839}, {10465, 19582}, {13244, 32853}, {17134, 28997}, {17861, 28387}, {18229, 24336}, {18750, 21362}, {20927, 29418}, {29311, 32915}, {29369, 37521}, {35635, 41229}
X(54035) = reflection of X(32860) in X(10440)
X(54035) = {X(190),X(23512)}-harmonic conjugate of X(21375)
X(54036) lies on these lines: {2, 6030}, {20, 45185}, {22, 38397}, {30, 54}, {69, 41464}, {110, 52397}, {376, 11487}, {550, 16835}, {597, 1176}, {1657, 43599}, {2916, 21358}, {3524, 18488}, {3529, 44866}, {3534, 11459}, {5012, 48901}, {5059, 34563}, {5064, 15080}, {6636, 18553}, {7500, 15019}, {7714, 10545}, {9019, 15531}, {9544, 48896}, {14641, 43846}, {14927, 23293}, {15055, 48368}, {15321, 34573}, {15681, 32139}, {15686, 18442}, {15689, 33541}, {17800, 43585}, {20063, 33749}, {22948, 52093}, {26881, 48905}, {31383, 41462}, {49139, 53779}
X(54036) = midpoint of X(15681) and X(52100)
X(54036) = reflection of X(i) in X(j) for these {i,j}: {15062, 376}, {18442, 15686}
X(54037) lies on these lines: {2, 5655}, {54, 7527}, {69, 146}, {74, 5891}, {110, 2071}, {113, 5890}, {323, 45019}, {378, 399}, {403, 7722}, {541, 11459}, {542, 15305}, {1154, 7728}, {1597, 52124}, {1986, 6623}, {2393, 10296}, {2777, 2979}, {2854, 51023}, {3091, 12099}, {3543, 14984}, {3819, 15055}, {3839, 45237}, {5056, 16270}, {5609, 18439}, {5622, 19140}, {5642, 15072}, {5889, 38791}, {5907, 15054}, {5972, 17853}, {6053, 12270}, {6241, 16534}, {9140, 15030}, {9818, 12308}, {9970, 37784}, {10575, 15034}, {10706, 13754}, {10733, 32062}, {10990, 11444}, {11206, 46349}, {11440, 16219}, {11451, 36518}, {11455, 17702}, {11793, 15021}, {11806, 14845}, {12111, 12827}, {12168, 32063}, {12273, 13202}, {12284, 46686}, {12290, 30714}, {12292, 14683}, {12317, 18537}, {14677, 44324}, {14855, 15035}, {15020, 46850}, {15027, 45958}, {15056, 20417}, {15057, 44321}, {15058, 16003}, {15738, 18909}, {15760, 21357}, {38727, 44299}, {41614, 51941}, {43808, 45959}
X(54037) = reflection of X(i) in X(j) for these {i,j}: {74, 5891}, {5890, 113}, {9140, 15030}, {10733, 32062}, {14677, 44324}, {15072, 5642}, {17853, 5972}, {20126, 15060}
X(54037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {146, 12825, 12219}, {5972, 17853, 20791}
X(54038) lies on these lines: {2, 34146}, {20, 36982}, {54, 64}, {69, 41736}, {110, 1619}, {1899, 12294}, {5878, 5907}, {7391, 41738}, {9914, 11444}, {11459, 15311}, {12058, 41735}, {12085, 34966}, {12111, 46373}, {13567, 32125}, {17811, 34778}
X(54039) lies on these lines: {2, 5656}, {4, 45088}, {54, 1593}, {64, 15056}, {69, 6225}, {110, 1498}, {235, 6241}, {1503, 15531}, {1619, 13445}, {2781, 50973}, {2883, 7729}, {2979, 15311}, {3522, 30443}, {5878, 5889}, {5895, 44668}, {6759, 52093}, {6776, 11381}, {6823, 18439}, {7691, 9914}, {9968, 41744}, {10996, 11487}, {11412, 48672}, {11439, 12324}, {11444, 12250}, {11455, 12022}, {12086, 18882}, {12174, 43812}, {13093, 15058}, {13380, 43766}, {15683, 34750}, {19149, 52028}, {23328, 33879}, {41468, 46373}
X(54039) = reflection of X(i) in X(j) for these {i,j}: {7729, 2883}, {15072, 5656}, {15683, 34750}
X(54039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1498, 36983, 12279}, {6225, 36982, 12111}
X(54040) lies on these lines: {2, 16657}, {3, 3580}, {4, 15066}, {5, 37477}, {20, 64}, {30, 2979}, {74, 550}, {141, 7527}, {185, 5965}, {343, 2071}, {376, 44665}, {378, 37636}, {394, 44440}, {511, 38323}, {539, 14855}, {548, 44076}, {858, 23325}, {1216, 18560}, {1368, 50435}, {1657, 16659}, {1885, 11444}, {1906, 43614}, {2777, 5562}, {2883, 17847}, {2888, 6247}, {3091, 35283}, {3146, 16654}, {3410, 37944}, {3522, 6146}, {3523, 12241}, {3529, 12134}, {3564, 15072}, {3917, 52069}, {5059, 16655}, {5654, 40112}, {5656, 11441}, {5889, 31829}, {5890, 41628}, {6240, 10625}, {6815, 14853}, {6823, 34148}, {7387, 40914}, {7495, 11430}, {7503, 26156}, {7544, 53023}, {7555, 34153}, {7998, 34664}, {8550, 41617}, {9306, 47096}, {9833, 33524}, {10018, 38793}, {10182, 51394}, {10295, 37478}, {10304, 12024}, {10323, 12118}, {10564, 37118}, {10605, 45794}, {10627, 12358}, {10996, 14912}, {11245, 20791}, {11424, 38317}, {11442, 21312}, {11454, 44683}, {11464, 16618}, {11585, 14644}, {12225, 15644}, {12290, 31831}, {12293, 47528}, {12302, 12359}, {12412, 13564}, {13142, 15043}, {13160, 13346}, {13348, 21659}, {13352, 14389}, {13391, 38321}, {13434, 38110}, {13488, 15056}, {13754, 44458}, {14643, 15761}, {15035, 34351}, {15053, 41588}, {15068, 32111}, {15107, 37458}, {15360, 44273}, {15760, 43574}, {16063, 18396}, {16621, 49135}, {16656, 50691}, {16977, 18466}, {18400, 36987}, {18405, 37444}, {18430, 47341}, {21167, 37126}, {23293, 47090}, {23332, 44450}, {33878, 37196}, {34799, 50693}, {35471, 37486}, {35473, 44201}, {37475, 37644}, {41171, 43576}, {43575, 44682}, {44245, 45731}, {45970, 46853}
X(54040) = reflection of X(i) in X(j) for these {i,j}: {3146, 16654}, {12022, 3}, {41628, 5890}, {52069, 3917}, {52397, 36987}
X(54040) = anticomplement of X(16657)
X(54041) lies on these lines: {2, 14845}, {3, 54}, {4, 3819}, {5, 44299}, {20, 5447}, {30, 7998}, {51, 631}, {52, 15717}, {140, 9781}, {154, 10323}, {184, 44832}, {185, 21735}, {186, 1974}, {373, 15709}, {376, 3917}, {389, 10299}, {511, 3524}, {548, 12111}, {549, 3060}, {550, 11444}, {568, 12100}, {569, 45308}, {1173, 15805}, {1199, 13347}, {1216, 3522}, {1370, 41171}, {1657, 15056}, {2393, 10519}, {2781, 15035}, {3523, 3567}, {3525, 6688}, {3526, 11592}, {3528, 5562}, {3529, 11793}, {3530, 15043}, {3533, 10110}, {3534, 15067}, {3538, 18950}, {3543, 10170}, {3545, 5650}, {4550, 37944}, {5054, 5640}, {5055, 33879}, {5067, 13598}, {5446, 10303}, {5651, 37925}, {5663, 15688}, {5876, 52093}, {5899, 10546}, {5907, 17538}, {5943, 15702}, {5946, 15693}, {6243, 15712}, {6636, 11464}, {6800, 43572}, {7485, 15033}, {7492, 51393}, {7512, 11202}, {7514, 41462}, {7525, 11449}, {7699, 51392}, {7731, 15051}, {8703, 15072}, {8718, 32063}, {9730, 15692}, {9818, 21766}, {10263, 15028}, {10304, 13754}, {10539, 16661}, {10691, 12022}, {11001, 15030}, {11002, 15708}, {11188, 50977}, {11414, 43598}, {11439, 15704}, {11561, 15042}, {11591, 12279}, {11704, 37452}, {12082, 17811}, {12088, 44082}, {12162, 50693}, {12220, 47090}, {12281, 38726}, {12283, 48876}, {12284, 41673}, {13321, 15707}, {13352, 15246}, {13363, 15701}, {13451, 15713}, {14094, 41463}, {14128, 17800}, {14156, 52300}, {14157, 15066}, {14810, 41716}, {14831, 15715}, {15036, 38446}, {15053, 37494}, {15060, 15681}, {15080, 22115}, {15081, 44321}, {15683, 16194}, {15698, 16836}, {15719, 21969}, {15759, 45956}, {16063, 25739}, {16192, 31738}, {16386, 35254}, {16976, 18438}, {17504, 40280}, {17834, 43597}, {18378, 33542}, {18436, 33923}, {18439, 44245}, {18859, 33533}, {21734, 40647}, {33524, 33543}, {34783, 46853}, {35921, 37480}, {37481, 44682}, {37498, 43651}, {37913, 43586}, {40916, 44413}, {44870, 49138}, {45958, 49137}, {46849, 49140}, {46852, 50690}
X(54041) = midpoint of X(i) and X(j) for these {i,j}: {2979, 20791}, {10304, 33884}
X(54041) = reflection of X(i) in X(j) for these {i,j}: {3545, 5650}, {5640, 5054}, {5890, 20791}, {15045, 3524}, {20791, 3}, {40280, 17504}
X(54041) = anticomplement of X(14845)
X(54041) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 2979, 5890}, {3, 6101, 10574}, {3, 10627, 5889}, {20, 5447, 7999}, {20, 5891, 11455}, {20, 7999, 15058}, {376, 3917, 11459}, {549, 13340, 3060}, {550, 11444, 12290}, {550, 44324, 18435}, {1216, 3522, 6241}, {1657, 32142, 15056}, {2979, 5890, 11412}, {3523, 10625, 3567}, {3530, 37484, 15043}, {3534, 15067, 15305}, {3819, 13348, 36987}, {3819, 36987, 4}, {5446, 10303, 11465}, {5891, 11455, 15058}, {7485, 37483, 15033}, {7999, 11455, 5891}, {8703, 23039, 15072}, {10263, 15720, 15028}, {11591, 15696, 12279}, {15066, 35243, 14157}, {18435, 44324, 11444}
X(54042) lies on these lines: {2, 13340}, {3, 54}, {4, 11017}, {5, 3819}, {20, 11591}, {30, 3917}, {51, 140}, {52, 3530}, {141, 43129}, {143, 631}, {156, 10323}, {185, 33923}, {206, 1511}, {323, 44832}, {373, 10124}, {376, 5663}, {378, 33533}, {381, 7998}, {382, 7999}, {389, 15712}, {511, 549}, {547, 5650}, {548, 5562}, {550, 1216}, {567, 15246}, {568, 3524}, {632, 5446}, {1092, 5944}, {1350, 6644}, {1370, 34514}, {1498, 33543}, {1539, 44440}, {1656, 44299}, {1657, 11444}, {1658, 43652}, {1994, 13339}, {2393, 48876}, {2889, 12325}, {3060, 5054}, {3146, 45958}, {3313, 52262}, {3522, 18436}, {3523, 6243}, {3525, 32205}, {3526, 10095}, {3528, 34783}, {3529, 32137}, {3534, 11459}, {3538, 18951}, {3567, 13421}, {3627, 11793}, {3628, 14845}, {3845, 10170}, {5070, 18874}, {5073, 15056}, {5188, 44221}, {5453, 50597}, {5462, 14869}, {5495, 16287}, {5499, 37536}, {5640, 15694}, {5907, 15704}, {5943, 11539}, {6030, 43572}, {6636, 22115}, {7484, 39522}, {7512, 32171}, {7514, 37483}, {7516, 37498}, {7530, 17811}, {7555, 51393}, {7771, 51440}, {7811, 51383}, {8681, 50978}, {8703, 13754}, {9019, 44287}, {9703, 15080}, {9729, 44682}, {9730, 12100}, {9781, 46219}, {10113, 13416}, {10264, 17710}, {10282, 44544}, {10298, 38898}, {10303, 16982}, {10519, 44441}, {10575, 31834}, {10982, 13154}, {11002, 15702}, {11064, 25337}, {11245, 43934}, {11439, 49137}, {11561, 15051}, {11624, 41943}, {11626, 41944}, {11812, 21969}, {12041, 41673}, {12083, 15066}, {12099, 34128}, {12103, 12162}, {12108, 14449}, {12111, 15696}, {12236, 18438}, {12308, 33544}, {13201, 15040}, {13321, 15701}, {13336, 36153}, {13358, 38728}, {13490, 29181}, {13565, 52295}, {13624, 31737}, {14216, 42021}, {14540, 48366}, {14541, 48365}, {14810, 18475}, {14831, 14891}, {14881, 52042}, {14915, 15686}, {14929, 51386}, {15033, 37496}, {15045, 15693}, {15058, 17800}, {15068, 32063}, {15072, 15688}, {15101, 34153}, {15122, 44201}, {15305, 15681}, {15330, 38793}, {15532, 52104}, {15606, 40647}, {15684, 16261}, {15692, 40280}, {15703, 33879}, {15713, 21849}, {15717, 37481}, {15721, 16981}, {15760, 51391}, {16226, 41983}, {16241, 36978}, {16242, 36980}, {16836, 17504}, {17538, 18439}, {17714, 44082}, {18281, 43653}, {18451, 33532}, {18570, 37480}, {20299, 21230}, {21243, 21357}, {23329, 44668}, {23332, 34826}, {31663, 31738}, {31805, 31836}, {31829, 34798}, {31831, 34750}, {31884, 34513}, {32139, 37198}, {32196, 32348}, {32609, 34006}, {33542, 47748}, {33699, 46847}, {34380, 40673}, {34579, 52926}, {35921, 37477}, {37126, 37495}, {37471, 45308}, {37814, 46728}, {37936, 43586}, {39504, 51360}, {44241, 45118}, {45759, 45956}, {46029, 51392}, {47751, 52100}
X(54042) = midpoint of X(i) and X(j) for these {i,j}: {2, 13340}, {3, 2979}, {20, 18435}, {51, 10625}, {376, 23039}, {1657, 11455}, {3534, 11459}, {3819, 15644}, {5562, 14855}, {5891, 36987}, {15305, 15681}
X(54042) = reflection of X(i) in X(j) for these {i,j}: {5, 3819}, {51, 140}, {2979, 10627}, {3060, 13363}, {3819, 5447}, {3845, 10170}, {5446, 6688}, {5891, 44324}, {5946, 549}, {6101, 2979}, {9730, 12100}, {10263, 51}, {11455, 45959}, {13451, 10124}, {13491, 14855}, {14855, 548}, {15060, 15067}, {15067, 3917}, {16226, 41983}, {18435, 11591}, {33699, 46847}
X(54042) = anticomplement of X(13364)
X(54042) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6101, 6102}, {3, 10627, 6101}, {3, 11412, 13630}, {140, 10263, 15026}, {140, 10625, 10263}, {143, 11592, 631}, {376, 33884, 23039}, {382, 7999, 14128}, {548, 5562, 13491}, {550, 1216, 5876}, {631, 37484, 143}, {1092, 7525, 5944}, {1216, 13348, 550}, {1657, 11444, 45959}, {2979, 20791, 11412}, {3060, 5054, 13363}, {3523, 6243, 12006}, {3917, 5891, 44324}, {3917, 36987, 5891}, {5447, 15644, 5}, {5891, 44324, 15067}, {10124, 13451, 373}, {15033, 41462, 54006}, {31834, 44245, 10575}, {34553, 34555, 6101}, {37496, 54006, 15033}
X(54043) lies on these lines: {4, 15066}, {2979, 33971}
X(54044) lies on the cubic K and these lines: {3, 54}, {5, 11592}, {20, 14128}, {30, 3819}, {51, 549}, {52, 44682}, {140, 6688}, {143, 3530}, {343, 20379}, {373, 15713}, {376, 15067}, {381, 44299}, {511, 12100}, {548, 5447}, {550, 5891}, {568, 15692}, {631, 10095}, {632, 14845}, {1216, 33923}, {1368, 20304}, {1511, 6636}, {2781, 14810}, {3060, 15693}, {3098, 19136}, {3522, 5876}, {3523, 10263}, {3524, 5946}, {3526, 18874}, {3528, 13491}, {3534, 7998}, {3538, 18952}, {3845, 5650}, {3917, 5663}, {5054, 11451}, {5446, 12108}, {5482, 11277}, {5562, 46853}, {5640, 15701}, {5907, 44245}, {5943, 11812}, {6030, 32609}, {6243, 10299}, {7525, 11202}, {7731, 15042}, {7999, 15696}, {9730, 17504}, {10109, 15082}, {10193, 44668}, {10304, 23039}, {10625, 12006}, {11002, 15719}, {11459, 15688}, {11793, 12103}, {11801, 44321}, {13321, 15718}, {13416, 44249}, {13570, 47478}, {13598, 16239}, {13754, 34200}, {14093, 15072}, {14641, 41981}, {14869, 32205}, {14891, 16836}, {14915, 15690}, {15026, 15720}, {15030, 15686}, {15036, 38898}, {15045, 15700}, {15246, 37477}, {15305, 15689}, {15685, 16261}, {15698, 40280}, {15704, 32062}, {15714, 45956}, {15717, 37484}, {16168, 47509}, {16194, 19710}, {17811, 33532}, {18324, 31884}, {18436, 21735}, {19708, 33884}, {19709, 33879}, {19711, 21969}, {21734, 34783}, {21849, 44580}, {22115, 44832}, {28190, 52796}, {32171, 43652}, {32416, 40670}, {34584, 44458}, {37472, 45308}, {40111, 44108}, {45118, 47114}
X(54044) = midpoint of X(i) and X(j) for these {i,j}: {5, 36987}, {376, 15067}, {548, 44324}, {550, 5891}, {3534, 15060}, {3917, 8703}, {5890, 6101}, {5892, 15644}, {5946, 13340}, {7691, 44325}, {15030, 15686}, {15704, 32062}, {16194, 19710}
X(54044) = reflection of X(i) in X(j) for these {i,j}: {143, 5892}, {5891, 32142}, {5892, 3530}, {5943, 11812}, {11591, 44324}, {11801, 44321}, {13363, 549}, {13364, 140}, {16836, 14891}, {32062, 45958}, {44324, 5447}, {45959, 5891}
X(54044) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10627, 13630}, {548, 5447, 11591}, {550, 32142, 45959}, {3524, 13340, 5946}, {3530, 15644, 143}, {3534, 7998, 15060}, {10625, 12006, 13421}, {10625, 15712, 12006}, {11793, 12103, 32137}, {14869, 45186, 32205}, {34553, 34555, 11412}
X(54045) lies on these lines: {51, 47065}, {184, 47064}, {1141, 1303}, {1154, 13504}, {2979, 25150}, {11202, 34418}, {11412, 38683}, {14073, 44324}, {18435, 32423}, {20791, 38618}
X(54045) = reflection of X(i) in X(j) for these {i,j}: {5890, 1141}, {13505, 5890}, {14073, 44324}
X(54046) lies on these lines: {3, 54}, {23, 114}, {684, 1510}, {930, 32428}, {1291, 1297}, {3518, 16336}, {5965, 14652}, {10594, 35718}, {12107, 14140}, {14981, 37183}, {17714, 18355}, {18875, 44890}
X(54046) = circumcircle-inverse of X(2979)
X(54046) = crossdifference of every pair of points on line {7755, 12077}
X(54047) lies on these lines: {2, 13451}, {3, 54}, {4, 44324}, {30, 33884}, {51, 3526}, {154, 13564}, {381, 3917}, {382, 5891}, {399, 35243}, {511, 5054}, {568, 15693}, {1216, 1657}, {1350, 2070}, {1656, 3819}, {1986, 15042}, {2781, 32609}, {3060, 15694}, {3098, 22115}, {3534, 6000}, {3830, 15067}, {3843, 7999}, {3851, 32142}, {5055, 7998}, {5070, 13364}, {5073, 11444}, {5079, 45186}, {5562, 15696}, {5663, 15689}, {5892, 6243}, {5899, 15066}, {5907, 49137}, {5943, 15723}, {5946, 15701}, {6636, 9703}, {7484, 15038}, {7492, 40111}, {7514, 37496}, {7545, 17811}, {9730, 15700}, {9914, 32063}, {10263, 11451}, {10303, 14449}, {10620, 41673}, {11002, 11539}, {11455, 11591}, {11459, 15681}, {11465, 16982}, {11592, 15043}, {11935, 14810}, {13348, 14855}, {13421, 15028}, {13754, 15688}, {15045, 15707}, {15058, 49134}, {15060, 15684}, {15072, 15695}, {15305, 15685}, {15606, 34783}, {15706, 40280}, {15709, 16981}, {15716, 16836}, {17538, 31834}, {19708, 45956}, {21766, 39522}, {23327, 44751}, {32062, 49136}, {34380, 43934}, {35434, 46847}, {37486, 43809}, {43957, 45967}, {45959, 49139}, {46114, 52300}
X(54047) = midpoint of X(10625) and X(14845)
X(54047) = reflection of X(i) in X(j) for these {i,j}: {5055, 7998}, {11002, 11539}, {13321, 5054}, {14845, 3819}, {45967, 43957}
X(54047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1216, 36987, 18435}, {2979, 5890, 6101}, {3917, 13340, 381}, {5447, 37484, 3526}, {13364, 44299, 5070}, {18435, 36987, 1657}
X(54048) lies on these lines: {2, 13321}, {3, 54}, {4, 15108}, {6, 54006}, {20, 44748}, {22, 50461}, {49, 46728}, {51, 1216}, {52, 3526}, {69, 31723}, {143, 5070}, {154, 2937}, {155, 13564}, {159, 399}, {323, 7502}, {378, 37496}, {381, 511}, {382, 5562}, {389, 15720}, {394, 2070}, {547, 11002}, {549, 33884}, {568, 3917}, {1350, 18445}, {1351, 15038}, {1482, 31738}, {1657, 5925}, {2393, 11898}, {3060, 5055}, {3090, 14449}, {3146, 31834}, {3313, 39899}, {3519, 18381}, {3525, 16881}, {3534, 13340}, {3567, 32142}, {3830, 11459}, {3843, 11591}, {3851, 10263}, {5071, 13451}, {5072, 5446}, {5073, 5876}, {5076, 5907}, {5079, 11793}, {5447, 14531}, {5640, 15703}, {5650, 15723}, {5663, 15681}, {5899, 15068}, {5946, 7998}, {6090, 51519}, {6800, 34006}, {7485, 15037}, {7509, 14627}, {7512, 9704}, {7545, 33586}, {7555, 9544}, {7556, 40111}, {7574, 34118}, {8681, 51175}, {9019, 50955}, {9641, 11189}, {9730, 15693}, {9781, 13421}, {10170, 21969}, {10304, 45956}, {10564, 35495}, {10606, 18859}, {10620, 21312}, {11202, 22115}, {11381, 49133}, {11403, 33539}, {11649, 15533}, {11935, 18475}, {12111, 17800}, {12162, 49136}, {12290, 49139}, {12308, 13201}, {12325, 18356}, {12702, 31737}, {13169, 14984}, {13432, 21660}, {13512, 20477}, {14070, 32609}, {14130, 37498}, {14269, 15060}, {14791, 45794}, {14831, 15700}, {14855, 15644}, {15030, 38335}, {15033, 33533}, {15040, 41673}, {15045, 15701}, {15047, 37493}, {15072, 15689}, {15305, 15684}, {15706, 16836}, {16261, 35403}, {16644, 36979}, {16645, 36981}, {17538, 45957}, {17834, 45735}, {17853, 38788}, {18350, 44082}, {18438, 18536}, {18439, 49137}, {18451, 37924}, {18534, 41716}, {21230, 52295}, {21357, 39504}, {21850, 50135}, {24474, 31816}, {31180, 38724}, {32139, 47748}, {32359, 34785}, {33542, 37198}, {34864, 36747}, {35264, 37956}, {37347, 48876}, {41597, 44108}
X(54048) = midpoint of X(i) and X(j) for these {i,j}: {2979, 11412}, {18435, 37484}
X(54048) = reflection of X(i) in X(j) for these {i,j}: {3, 2979}, {51, 1216}, {52, 3819}, {381, 23039}, {382, 18435}, {568, 3917}, {2979, 6101}, {3060, 15067}, {3534, 13340}, {3819, 15606}, {3830, 11459}, {5073, 11455}, {6243, 51}, {11455, 5876}, {14855, 15644}, {15684, 15305}, {18435, 5562}, {21969, 10170}, {34783, 14855}
X(54048) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12160, 43845}, {3, 12316, 7592}, {143, 7999, 5070}, {323, 7502, 9703}, {394, 37494, 2070}, {568, 3917, 5054}, {1216, 6243, 1656}, {3060, 15067, 5055}, {3567, 32142, 46219}, {5071, 16981, 13451}, {5447, 14531, 37481}, {5562, 37484, 382}, {5889, 10627, 3}, {5946, 7998, 15694}, {6101, 11412, 3}, {10263, 11444, 3851}, {10625, 18436, 1657}, {15644, 34783, 15696}
X(54049) lies on the circumcircle and these lines: {2, 35591}, {3, 15907}, {4, 33333}, {55, 44053}, {930, 1510}, {1141, 1154}, {7691, 14979}, {11671, 52110}, {12219, 39431}, {12226, 53959}, {24772, 32142}, {30481, 33643}, {46966, 52603}
X(54049) = reflection of X(i) in X(j) for these {i,j}: {4, 33333}, {11671, 52110}, {15907, 3}, {24772, 32142}
X(54049) = isogonal conjugate of X(25149)
X(54049) = anticomplement of X(35591)
X(54049) = isogonal conjugate of the anticomplement of X(25149)
X(54049) = isogonal conjugate of the complement of X(25149)
X(54049) = Thomson-isogonal conjugate of X(25150)
X(54049) = Collings transform of X(i) for these i: {1154, 1510, 32142, 33333}
X(54049) = X(1)-isoconjugate of X(25149)
X(54049) = cevapoint of X(i) and X(j) for these (i,j): {526, 32142}, {1154, 1510}
X(54049) = trilinear pole of line {6, 39018}
X(54049) = barycentric product X(18315)*X(38899)
X(54049) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 25149}, {35324, 24147}, {38899, 18314}
X(54050) lies on the cubic K1327 and these lines: {2, 10606}, {3, 5656}, {4, 74}, {5, 40920}, {20, 64}, {30, 32064}, {140, 48672}, {146, 11598}, {154, 10304}, {185, 14912}, {376, 3917}, {378, 11427}, {459, 34170}, {541, 5654}, {548, 12315}, {550, 13093}, {631, 5878}, {962, 12262}, {1073, 27089}, {1092, 43813}, {1370, 13445}, {1498, 3522}, {1593, 14853}, {1853, 3543}, {1885, 18913}, {1992, 2781}, {2071, 37669}, {2883, 3523}, {2935, 37645}, {3090, 22802}, {3091, 5895}, {3146, 3580}, {3147, 11468}, {3183, 14249}, {3426, 37458}, {3524, 10182}, {3528, 6759}, {3529, 14216}, {3545, 23329}, {3564, 34622}, {3618, 7527}, {3619, 12379}, {3832, 40686}, {3839, 23332}, {4232, 37487}, {4293, 10060}, {4294, 10076}, {4297, 9899}, {5056, 5893}, {5067, 25563}, {5218, 12940}, {5889, 31978}, {5907, 30443}, {6001, 9778}, {6241, 18925}, {6353, 21663}, {6459, 49251}, {6460, 49250}, {6624, 51892}, {6640, 38789}, {6815, 15062}, {7288, 12950}, {7395, 40918}, {7487, 16654}, {7493, 11454}, {7503, 15740}, {7714, 32062}, {8549, 41617}, {8703, 32063}, {8718, 44679}, {8780, 47114}, {9545, 46374}, {9833, 17538}, {9914, 17928}, {9919, 12106}, {10192, 15692}, {10193, 15702}, {10282, 21735}, {10385, 32065}, {10605, 11433}, {10620, 18917}, {10991, 48991}, {11001, 18400}, {11202, 19708}, {11250, 12412}, {11430, 35483}, {11440, 37201}, {11441, 53050}, {11444, 36982}, {11456, 35485}, {11541, 34786}, {12022, 18909}, {12111, 30552}, {12163, 18934}, {12358, 18439}, {12825, 27082}, {12964, 42638}, {12970, 42637}, {13568, 53023}, {14118, 40913}, {14530, 33923}, {14826, 44241}, {15072, 25406}, {15138, 16063}, {15438, 22528}, {15640, 50709}, {15704, 34780}, {15717, 16252}, {16253, 51358}, {16658, 18533}, {16775, 29181}, {17813, 51028}, {17821, 21734}, {17835, 37644}, {18381, 33703}, {18396, 49670}, {20125, 25564}, {20791, 41580}, {22467, 40914}, {23049, 51538}, {23291, 44438}, {23324, 50687}, {23326, 52028}, {26944, 43719}, {31305, 34801}, {32111, 35486}, {32346, 34938}, {32423, 34350}, {33522, 35513}, {34286, 35711}, {34782, 50693}, {34944, 40196}, {35864, 42261}, {35865, 42260}, {36201, 51023}, {36876, 40664}, {37196, 41584}, {37197, 43903}, {37200, 46034}, {38282, 51403}, {41362, 49135}, {49138, 52102}
X(54050) = midpoint of X(i) and X(j) for these {i,j}: {5656, 12250}, {5925, 18405}
X(54050) = reflection of X(i) in X(j) for these {i,j}: {2, 10606}, {146, 15131}, {3146, 18405}, {3543, 1853}, {5656, 3}, {6225, 5656}, {11206, 376}, {15131, 11598}, {18405, 6247}, {32063, 8703}, {51028, 17813}
X(54050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5656, 35260}, {3, 12250, 6225}, {4, 74, 18931}, {4, 18931, 37643}, {20, 64, 12324}, {64, 5894, 20}, {550, 13093, 34781}, {1885, 34469, 18913}, {2883, 8567, 3523}, {3357, 20427, 4}, {5895, 6696, 3091}, {5907, 30443, 36983}, {5925, 6247, 3146}, {6225, 35260, 5656}, {40686, 51491, 3832}
X(54051) lies on the cubic K1327 and these lines: {1, 50700}, {2, 515}, {3, 5273}, {4, 4313}, {7, 18446}, {8, 411}, {20, 78}, {30, 5658}, {40, 20007}, {72, 9960}, {84, 3219}, {101, 27382}, {355, 6988}, {376, 971}, {548, 12684}, {550, 12246}, {551, 38150}, {631, 5787}, {912, 28610}, {934, 5932}, {936, 4297}, {938, 944}, {962, 6261}, {997, 43161}, {1006, 18230}, {1012, 36991}, {1060, 3160}, {1064, 4344}, {1210, 13462}, {1385, 6864}, {1750, 4304}, {1807, 36640}, {1895, 18283}, {2287, 7415}, {2800, 34632}, {2947, 22350}, {3146, 6260}, {3485, 6253}, {3487, 20420}, {3488, 19541}, {3523, 6245}, {3528, 34862}, {3529, 6259}, {3601, 37434}, {3616, 6835}, {3868, 9942}, {3876, 12664}, {3940, 5759}, {4305, 5691}, {4323, 21740}, {5049, 7967}, {5080, 6836}, {5126, 5704}, {5175, 6838}, {5328, 6827}, {5435, 5768}, {5550, 6991}, {5603, 8236}, {5720, 6987}, {5734, 40257}, {5748, 6840}, {5758, 6869}, {5811, 6868}, {5815, 17857}, {5817, 16418}, {5842, 9812}, {5927, 11111}, {6001, 9778}, {6256, 6895}, {6705, 15717}, {6764, 22770}, {6796, 7688}, {6828, 18242}, {6831, 10592}, {6849, 24299}, {6855, 18480}, {6865, 18481}, {6880, 31188}, {6894, 40259}, {6904, 10884}, {6909, 10430}, {6918, 34773}, {6985, 12536}, {6986, 12114}, {7971, 20070}, {7992, 12512}, {8166, 18527}, {8726, 17580}, {9776, 18444}, {9910, 33524}, {9948, 35242}, {10304, 52027}, {10580, 22753}, {12528, 12671}, {15704, 48664}, {18391, 44425}, {18525, 52265}, {18623, 46974}, {19067, 43511}, {19068, 43512}, {22792, 33703}, {26062, 35979}, {28381, 48923}, {30332, 37000}, {42637, 49235}, {42638, 49234}, {50702, 52676}
X(54051) = reflection of X(2) in X(52026)
X(54051) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 33597, 5703}, {20, 1490, 6223}, {936, 4297, 37423}, {944, 3149, 938}, {5720, 6987, 18228}, {5768, 6905, 5435}, {5787, 40262, 631}, {6869, 37700, 5758}, {18446, 50701, 7}, {34772, 50695, 962}
X(54052) lies on the cubic K1327 and these lines: {2, 21164}, {3, 5658}, {4, 5435}, {7, 104}, {8, 20}, {21, 10309}, {30, 5770}, {90, 10429}, {140, 48664}, {144, 6282}, {329, 6909}, {376, 971}, {377, 7705}, {516, 34625}, {517, 14646}, {550, 12684}, {631, 6259}, {962, 12114}, {997, 5732}, {1071, 4313}, {1320, 52116}, {1490, 3522}, {1699, 3086}, {1709, 4293}, {1737, 53056}, {1768, 18391}, {2800, 3241}, {2829, 14647}, {2950, 12648}, {3090, 22792}, {3091, 6705}, {3146, 6245}, {3306, 15239}, {3358, 5825}, {3421, 17613}, {3523, 6260}, {3529, 5787}, {3576, 50742}, {3600, 12705}, {3616, 5450}, {3868, 18238}, {3869, 17649}, {3876, 18239}, {3877, 5731}, {4294, 10085}, {4297, 7992}, {4304, 9819}, {4305, 15071}, {4308, 12672}, {4311, 7995}, {4652, 37421}, {5129, 37526}, {5218, 12678}, {5226, 6935}, {5273, 6916}, {5328, 37822}, {5550, 12608}, {5657, 37429}, {5703, 6906}, {5744, 6925}, {5748, 6966}, {5766, 18446}, {5768, 6938}, {5790, 31775}, {5804, 26877}, {5815, 10310}, {5818, 40267}, {5887, 9960}, {6256, 9780}, {6459, 49235}, {6460, 49234}, {6912, 9776}, {6969, 31188}, {6987, 7171}, {7288, 12679}, {8158, 28174}, {8726, 11106}, {9809, 48695}, {9841, 37423}, {9859, 14872}, {9910, 17928}, {9965, 38460}, {10164, 18250}, {10167, 11111}, {10304, 52026}, {10591, 52860}, {10884, 17576}, {10916, 28158}, {11037, 11496}, {11246, 22760}, {12528, 51379}, {12650, 20070}, {12666, 12671}, {12676, 26129}, {16418, 21151}, {21165, 37427}, {21735, 40262}, {24477, 34742}, {24929, 36996}, {25005, 37435}, {26927, 28029}, {30282, 41561}, {35844, 42261}, {35845, 42260}, {37600, 41706}
X(54052) = midpoint of X(5658) and X(12246)
X(54052) = reflection of X(i) in X(j) for these {i,j}: {2, 52027}, {5658, 3}, {6223, 5658}
X(54052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12246, 6223}, {20, 84, 9799}, {1012, 2096, 7}
X(54053) lies on the cubic K1327 and these lines: {3, 42452}, {4, 20329}, {20, 394}, {253, 1294}, {376, 15312}, {550, 36965}, {3146, 33546}, {3183, 3522}, {3523, 6523}, {3543, 10714}, {5056, 51342}, {10304, 51877}
X(54053) = reflection of X(42452) in X(3)
X(54054) lies on the cubic K1327 and these lines: {20, 78}, {189, 972}, {3146, 47441}, {3182, 3522}, {4313, 44696}, {9778, 11206}
X(54055) lies on the cubic K1327 and these lines: {2, 52053}, {20, 3413}, {30, 32443}, {376, 39158}, {3522, 40851}, {3543, 39163}, {5059, 40852}, {10304, 39162}
X(54055) = reflection of X(i) in X(j) for these {i,j}: {{2, 52053}, {3543, 39163}, {39158, 376}, {54056, 20}
fX(54056) lies on the cubic K1327 and these lines: {2, 52054}, {20, 3413}, {30, 39158}, {376, 39159}, {3522, 40852}, {3543, 39162}, {5059, 40851}, {10304, 39163}
X(54056) = reflection of X(i) in X(j) for these {i,j}: {{2, 52054}, {3543, 39162}, {39159, 376}, {54055, 20}
See HG130623.
X(54057) lies on the cubic K630 and these lines: {3, 250}, {5, 23582}, {249, 1092}, {1968, 23964}, {4230, 5502}, {7750, 18020}, {23109, 39299}, {23110, 39298}
X(54057) = circumcircle inverse of X(250)
X(54057) = X(110)-Ceva conjugate of X(250)
X(54057) = X(i)-isoconjugate of X(j) for these (i,j): {{125, 9390}, {523, 9392}, {3708, 15351}}
X(54057) = X(648)-Dao conjugate of X(850)
X(54057) = barycentric product X(i)*X(j) for these {i,j}: {{110, 39062}, {250, 39352}, {662, 2633}}
X(54057) = barycentric quotient X(i)/X(j) for these {i,j}: {{163, 9392}, {250, 15351}, {2629, 20902}, {2633, 1577}, {19208, 53576}, {39062, 850}, {39352, 339}}
X(54058) lies on these lines: {3, 48}, {101, 2253}, {104, 35182}, {163, 2074}, {652, 663}, {1172, 1731}, {1319, 32660}, {2176, 36033}, {2249, 53925}, {2323, 14963}, {3215, 9310}, {39006, 52407}
X(54058) = circumcircle-inverse of X(48)
X(54058) = crossdifference of every pair of points on line {226, 7649}
X(54058) = barycentric product X(78)*X(5137)
X(54058) = barycentric quotient X(5137)/X(273)
X(54059) lies on these lines: {3, 63}, {35, 5197}, {46, 7163}, {55, 6505}, {100, 914}, {103, 6099}, {501, 1800}, {662, 2073}, {1326, 4575}, {1364, 22128}, {1813, 2078}, {2071, 4511}, {3733, 8646}, {4184, 6061}, {5285, 35980}, {9436, 36003}, {14018, 47106}, {26702, 53952}
X(54059) = reflection of X(51629) in X(51632)
X(54059) = circumcircle-inverse of X(63)
X(54059) = X(43363)-Ceva conjugate of X(63)
X(54059) = crossdifference of every pair of points on line {6591, 16583}
X(54059) = barycentric product X(63)*X(37782)
X(54059) = barycentric quotient X(37782)/X(92)
X(54060) lies on the cubic K039 and these lines: {3, 66}, {22, 5523}, {23, 37801}, {74, 46967}, {186, 1289}, {935, 37978}, {1176, 34137}, {5961, 40079}, {6091, 14909}, {6636, 18018}, {7488, 43678}, {7503, 51940}, {7512, 41377}, {9019, 10317}, {10316, 12220}, {13509, 15080}, {13754, 40080}, {14961, 15388}, {17407, 21213}, {27373, 44884}, {28405, 33802}
X(54060) = isogonal conjugate of X(11605)
X(54060) = circumcircle-inverse of X(66)
X(54060) = isogonal conjugate of the polar conjugate of X(37801)
X(54060) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11605}, {1760, 8791}, {2157, 17907}, {2172, 46105}, {37221, 40938}
X(54060) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 11605}, {40583, 17907}
X(54060) = crossdifference of every pair of points on line {2485, 40938}
X(54060) = barycentric product X(i)*X(j) for these {i,j}: {3, 37801}, {23, 14376}, {66, 22151}, {2353, 37804}, {9019, 40404}, {9517, 44766}, {10317, 18018}
X(54060) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11605}, {23, 17907}, {66, 46105}, {2353, 8791}, {8744, 52448}, {9517, 33294}, {10317, 22}, {14376, 18019}, {18374, 8743}, {22151, 315}, {37801, 264}, {37804, 40073}, {42659, 2485}, {46765, 9076}
X(54060) = {X(3),X(2353)}-harmonic conjugate of X(14376)
X(54061) lies on the cubic K039 and these lines: {3, 68}, {24, 16172}, {26, 8906}, {74, 46969}, {131, 50435}, {186, 925}, {847, 22467}, {2071, 5962}, {5392, 45170}, {5963, 7488}, {6644, 14593}, {11589, 15469}, {12095, 44174}, {12364, 13557}, {16178, 37951}, {27087, 32123}, {32734, 51393}, {37814, 46200}, {39986, 40082}, {45781, 52504}
X(54061) = circumcircle-inverse of X(68)
X(54061) = X(45781)-Ceva conjugate of X(68)
X(54061) = X(52557)-Dao conjugate of X(52505)
X(54061) = crossdifference of every pair of points on line {6753, 40939}
X(54061) = barycentric product X(37951)*X(52350)
X(54061) = barycentric quotient X(37951)/X(11547)
X(54062) lies on these lines: {3, 54}, {23, 18315}, {110, 52887}, {323, 933}, {511, 15958}, {1291, 1298}, {1297, 46966}, {10625, 46089}, {11424, 16337}, {18350, 19552}, {34186, 43768}, {37477, 50463}
X(54062) = circumcircle-inverse of X(97)
X(54063) lies on the tangential circle and these lines: {3, 116}, {22, 675}, {24, 917}, {25, 5190}, {199, 34429}, {2079, 47234}, {2931, 8053}, {10117, 20999}, {14729, 23399}, {16681, 39828}, {16873, 39857}, {19165, 23383}
X(54063) = circumcircle-inverse of X(116)
X(54063) = tangential-isogonal conjugate of X(8676)
X(54063) = X(46107)-Ceva conjugate of X(6)
X(54063) = X(32656)-Dao conjugate of X(1331)
X(54064) lies on the tangential circle and these lines: {3, 119}, {22, 1295}, {23, 34550}, {24, 108}, {25, 25640}, {36, 1455}, {40, 2778}, {186, 47149}, {378, 10731}, {1512, 20989}, {2070, 38578}, {2791, 39857}, {2798, 39828}, {2804, 39200}, {2817, 11249}, {2823, 35238}, {2834, 6644}, {2845, 14703}, {2850, 2931}, {2851, 14657}, {2937, 38592}, {6087, 39478}, {6642, 6717}, {7488, 34188}, {7517, 33566}, {9570, 34456}, {10323, 38715}, {10715, 44837}, {12332, 52731}, {13558, 20832}, {13589, 18862}, {15177, 50917}, {17928, 38696}, {47270, 53761}
X(54064) = circumcircle-inverse of X(119)
X(54064) = Stammler-circle-inverse of X(38756)
X(54064) = tangential-isogonal conjugate of X(6001)
X(54065) lies on the tangential circle and these lines: {3, 119}, {11, 25}, {19, 8428}, {22, 100}, {23, 149}, {24, 104}, {26, 952}, {56, 1866}, {80, 8185}, {153, 7488}, {159, 5848}, {186, 12248}, {378, 10728}, {513, 10016}, {528, 9909}, {659, 14667}, {1145, 8193}, {1317, 8192}, {1387, 11365}, {1484, 37440}, {1593, 52836}, {1603, 17100}, {1610, 6224}, {1768, 3220}, {1993, 3045}, {1995, 31272}, {2070, 12773}, {2079, 21004}, {2217, 20832}, {2771, 2931}, {2783, 39828}, {2787, 39857}, {2800, 3556}, {2802, 49553}, {2828, 14703}, {2830, 14657}, {2831, 3185}, {2915, 23361}, {2932, 2933}, {2937, 12331}, {3032, 9571}, {3036, 9712}, {3517, 20418}, {4185, 9658}, {4186, 9672}, {4996, 11337}, {5020, 6667}, {5083, 22769}, {5096, 38472}, {5541, 9591}, {5840, 7387}, {5854, 12410}, {5899, 48680}, {6264, 9625}, {6326, 9626}, {6642, 6713}, {6644, 38602}, {7484, 31235}, {7502, 11698}, {7517, 10738}, {7526, 22799}, {7529, 23513}, {7530, 22938}, {8276, 13913}, {8277, 13977}, {8674, 10117}, {9570, 34458}, {9659, 12763}, {9673, 13274}, {9714, 26308}, {9715, 10830}, {10058, 13730}, {10090, 37034}, {10323, 34474}, {10711, 44837}, {10776, 46588}, {10831, 10834}, {11249, 51628}, {11414, 24466}, {12088, 13199}, {12329, 14740}, {12751, 15177}, {13205, 20872}, {13558, 23860}, {17928, 38693}, {18378, 51517}, {19459, 51198}, {20095, 37913}, {23304, 35973}, {34189, 48391}, {37123, 38657}, {37485, 51007}
X(54065) = midpoint of X(i) and X(j) for these {i,j}: {3, 9913}, {9798, 9912}
X(54065) = circumcircle-inverse of X(123)
X(54065) = tangential-isogonal conjugate of X(513)
X(54065) = X(4391)-Ceva conjugate of X(6)
X(54065) = X(1415)-Dao conjugate of X(651)
X(54065) = crossdifference of every pair of points on line {13006, 34977}
X(54066) lies on the tangential circle and these lines: {3, 126}, {22, 99}, {23, 7665}, {24, 2374}, {25, 1560}, {157, 13558}, {159, 2930}, {186, 47170}, {1495, 5104}, {1995, 11643}, {2882, 35901}, {2931, 32121}, {2934, 15959}, {5938, 37928}, {8428, 14273}, {9909, 11641}, {14667, 18610}, {14729, 21284}, {16316, 37969}, {19165, 45687}, {34131, 47206}
X(54066) = reflection of X(3) in X(14655)
X(54066) = circumcircle-inverse of X(126)
X(54066) = isogonal conjugate of the isotomic conjugate of X(34518)
X(54066) = tangential-isogonal conjugate of X(2393)
X(54066) = X(44146)-Ceva conjugate of X(6)
X(54066) = X(14908)-Dao conjugate of X(895)
X(54066) = barycentric product X(6)*X(34518)
X(54066) = barycentric quotient X(34518)/X(76)
X(54067) lies on the tangential circle and these lines: {3, 128}, {4, 11587}, {22, 18401}, {24, 933}, {25, 18402}, {26, 53808}, {160, 2934}, {378, 44977}, {399, 2917}, {571, 2079}, {2070, 8157}, {3432, 14367}, {5899, 43919}, {6069, 12383}, {6644, 38616}, {7731, 38897}, {14657, 52036}, {14703, 44809}, {34131, 42731}
X(54067) = reflection of X(38585) in X(8157)
X(54067) = circumcircle-inverse of X(128)
X(54067) = tangential-isogonal conjugate of X(18400)
X(54067) = X(14918)-Ceva conjugate of X(6)
X(54068) lies on the tangential circle and these lines: {3, 133}, {22, 5897}, {24, 64}, {25, 50937}, {186, 34178}, {2079, 47228}, {2935, 46587}, {3515, 13558}, {6644, 38624}, {14059, 45735}, {14703, 53255}, {15959, 44879}, {33582, 39857}, {37917, 47215}
X(54068) = circumcircle-inverse of X(133)
X(54068) = tangential isogonal conjugate of X(15311)
X(54068) = X(51358)-Ceva conjugate of X(6)
X(54069) lies on the tangential circle and these lines: {3, 136}, {4, 14769}, {22, 3563}, {24, 110}, {25, 114}, {26, 15478}, {186, 47324}, {2070, 13557}, {2079, 47230}, {2493, 8428}, {3447, 15470}, {3515, 14703}, {7669, 15959}, {10132, 48792}, {10133, 48790}, {13558, 16230}, {14729, 47627}, {18127, 20957}, {19165, 21213}, {34131, 47200}, {37954, 44057}
X(54069) = reflection of X(39119) in X(135)
X(54069) = circumcircle-inverse of X(136)
X(54069) = polar-circle-inverse of X(14769)
X(54070) lies on these lines: {3, 142}, {55, 5011}, {514, 23865}, {758, 23398}, {1308, 41341}, {1323, 1617}, {1324, 20875}, {1621, 5195}, {2175, 4253}, {2195, 3002}, {2942, 5527}, {3322, 5172}, {4251, 21746}, {4262, 23868}, {4314, 20836}, {5030, 17798}, {5088, 23407}, {7742, 53617}, {12651, 20838}, {20988, 36014}, {23850, 23852}, {34179, 40910}
X(54070) = circumcircle-inverse of X(142)
X(54070) = Stammler-circle-inverse of X(31671)
X(54070) = X(19624)-Dao conjugate of X(3935)
X(54070) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 51621, 5144}, {20875, 23402, 1324}
X(54071) lies on these lines: {2, 13558}, {3, 147}, {22, 14673}, {23, 3258}, {110, 3917}, {186, 2080}, {511, 19575}, {827, 1297}, {7496, 30789}, {7527, 44943}, {9479, 44822}, {13335, 22467}, {13372, 14652}, {15915, 19165}, {35375, 52128}, {37126, 46654}, {37978, 51458}
X(54071) = circumcircle-inverse of X(147)
X(54071) = 2nd-Brocard-circle-inverse of X(9863)
X(54072) lies on these lines: {3, 148}, {23, 31655}, {111, 6636}, {186, 2971}, {3565, 5966}, {5092, 5622}, {5104, 5166}, {5940, 37940}, {7492, 33998}, {7496, 10163}, {7512, 15564}, {7527, 45151}, {22467, 34217}, {31843, 37126}, {44821, 53272}
X(54072) = midpoint of X(3) and X(15567)
X(54072) = reflection of X(14671) in X(15567)
X(54072) = circumcircle-inverse of X(148)
X(54073) lies on these lines: {3, 74}, {5, 3043}, {49, 125}, {54, 20304}, {113, 18350}, {182, 32272}, {184, 15061}, {195, 12236}, {265, 1147}, {381, 15463}, {567, 23515}, {1092, 12121}, {1112, 13621}, {1209, 5972}, {1351, 38851}, {1568, 17702}, {1656, 12228}, {1658, 12219}, {1986, 45735}, {2072, 32423}, {2777, 10540}, {2914, 44802}, {2937, 20773}, {3044, 15535}, {3047, 10264}, {3292, 15091}, {3448, 6640}, {3548, 14683}, {3843, 15472}, {5012, 34128}, {5462, 32226}, {5504, 12902}, {6293, 13289}, {6593, 45973}, {6723, 13353}, {6759, 20127}, {7506, 19504}, {7542, 13392}, {7687, 37472}, {7722, 37814}, {7728, 10539}, {9306, 10254}, {9545, 15081}, {9652, 10081}, {9667, 10065}, {9703, 38724}, {9704, 13198}, {9705, 20379}, {9706, 20396}, {9934, 48672}, {10024, 10272}, {10113, 34148}, {10114, 43817}, {10628, 51393}, {11746, 14627}, {11806, 43844}, {11898, 19138}, {12038, 21650}, {12227, 37481}, {12292, 25487}, {12295, 37495}, {12383, 18404}, {12584, 18438}, {12893, 18436}, {13201, 26882}, {13293, 18439}, {13434, 15088}, {13754, 17701}, {14157, 34584}, {14708, 43809}, {15059, 32046}, {15087, 46430}, {15089, 36253}, {15140, 41714}, {16223, 43586}, {18441, 19381}, {18563, 34153}, {19122, 32249}, {19129, 32275}, {19154, 32244}, {21649, 41597}, {22109, 23039}, {22955, 25711}, {25740, 44452}, {32205, 47117}, {32245, 53091}, {33565, 47360}, {35240, 38726}, {44234, 52417}
X(54073) = circumcircle-inverse of X(156)
X(54073) = crossdifference of every pair of points on line {1637, 1879}
X(54073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 110, 156}, {110, 15132, 399}, {1511, 7723, 3}
X(54074) lies on these lines: {2, 13509}, {3, 66}, {113, 625}, {127, 6000}, {193, 41363}, {297, 525}, {325, 1625}, {620, 51393}, {626, 12162}, {2715, 31635}, {2764, 51939}, {3618, 34137}, {3734, 18474}, {3788, 10539}, {6720, 8779}, {7778, 18451}, {13567, 44909}, {14961, 15595}, {15341, 37648}, {18337, 41377}, {25711, 34827}, {35937, 37636}, {44377, 51425}, {44380, 45016}, {45198, 50678}
X(54074) = midpoint of X(i) and X(j) for these {i,j}: {66, 34107}, {2764, 51939}, {18337, 41377}
X(54074) = reflection of X(8779) in X(6720)
X(54074) = complement of X(13509)
X(54074) = circumcircle-inverse of X(157)
X(54074) = complement of the isogonal conjugate of X(34579)
X(54074) = X(i)-complementary conjugate of X(j) for these (i,j): {1953, 138}, {34579, 10}
X(54074) = X(2764)-Ceva conjugate of X(525)
X(54074) = crossdifference of every pair of points on line {184, 2485}
X(54075) lies on the cubic K038 and these lines: {2, 5523}, {3, 66}, {20, 51940}, {30, 127}, {36, 18637}, {76, 28697}, {126, 5159}, {131, 36471}, {187, 15526}, {216, 7820}, {230, 339}, {232, 44340}, {325, 15013}, {441, 525}, {524, 10317}, {577, 7801}, {620, 10257}, {625, 10297}, {626, 12605}, {631, 41377}, {858, 935}, {988, 24780}, {1213, 22366}, {1384, 40995}, {1511, 47085}, {1975, 28405}, {2072, 44377}, {2366, 2715}, {2482, 40349}, {2549, 37073}, {2972, 47526}, {3284, 7813}, {3314, 35952}, {3631, 18472}, {3734, 15760}, {3788, 11585}, {3793, 40996}, {3926, 20806}, {3933, 10316}, {3934, 7542}, {5024, 44909}, {6337, 28406}, {6643, 53033}, {6676, 8891}, {6720, 16318}, {6760, 8724}, {7761, 44249}, {7763, 28695}, {7778, 18531}, {7783, 28433}, {7807, 41009}, {7836, 28723}, {7863, 22401}, {8369, 41005}, {9155, 44888}, {10745, 35002}, {12095, 47082}, {13509, 15066}, {14001, 41363}, {28717, 32831}, {28719, 34254}, {28721, 32837}, {34147, 35282}, {34366, 47286}, {40856, 46942}, {44252, 47105}
X(54075) = midpoint of X(i) and X(j) for these {i,j}: {20, 51940}, {858, 935}, {44252, 47105}
X(54075) = reflection of X(i) in X(j) for these {i,j}: {16318, 6720}, {38971, 5159}
X(54075) = complement of X(5523)
X(54075) = circumcircle-inverse of X(159)
X(54075) = complement of the isogonal conjugate of X(18876)
X(54075) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 1560}, {63, 15116}, {1177, 226}, {2373, 20305}, {18876, 10}, {36095, 520}, {37220, 21243}, {41511, 4892}
X(54075) = X(i)-Ceva conjugate of X(j) for these (i,j): {858, 524}, {935, 525}
crossdifference of every pair of points on line {25, 2485}
X(54075) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 23172, 15270}, {441, 6390, 14961}, {3926, 28696, 23115}
X(54076) lies on these lines: {2, 15340}, {3, 66}, {127, 18400}, {128, 36471}, {290, 2367}, {323, 401}, {339, 1971}, {458, 5523}, {626, 11750}, {1625, 15013}, {3331, 40856}, {6720, 51363}, {7512, 36952}, {7816, 10575}, {9418, 46544}, {14767, 19176}, {22121, 51740}, {30737, 32661}, {35474, 47105}, {37124, 41377}, {37200, 51940}, {41334, 41363}
X(54076) = reflection of X(51363) in X(6720)
X(54076) = complement of X(15340)
X(54076) = circumcircle-inverse of X(160)
X(54076) = crossdifference of every pair of points on line {51, 2485}
X(54077) lies on these lines: {3, 49}, {24, 21396}, {30, 13558}, {125, 15781}, {186, 5667}, {378, 2351}, {539, 13496}, {924, 42658}, {933, 32710}, {1516, 5961}, {1593, 21268}, {1624, 37917}, {5890, 52435}, {7722, 8154}, {11410, 44200}, {12085, 15512}, {14917, 42848}, {21659, 45842}, {35225, 37196}
X(54077) = circumcircle-inverse of X(185)
X(54078) lies on these lines: {1, 13204}, {3, 191}, {35, 110}, {100, 21081}, {399, 26285}, {404, 13605}, {1511, 10902}, {2077, 5663}, {2778, 5538}, {2836, 5096}, {2915, 13146}, {3448, 25440}, {3733, 8674}, {3746, 11720}, {4256, 6126}, {5259, 5972}, {5563, 7984}, {5881, 19478}, {6796, 12383}, {7280, 22586}, {7991, 22583}, {9904, 10310}, {11012, 12778}, {11101, 46816}, {11499, 12407}, {11699, 11849}, {14798, 49203}, {15035, 15931}, {15051, 35202}, {17702, 44425}, {19470, 49204}, {32609, 32613}
X(54078) = circumcircle-inverse of X(191)
X(54079) lies on the curve Q071 and these lines: {3, 9}, {41, 46830}, {102, 5011}, {214, 5199}, {515, 5514}, {650, 663}, {820, 836}, {910, 34591}, {1055, 3119}, {1146, 1319}, {1385, 23058}, {1855, 37080}, {2202, 28044}, {2262, 22753}, {2646, 46835}, {3207, 7079}, {3306, 25931}, {5179, 50371}, {5440, 40869}, {5513, 46415}, {6911, 23840}, {10165, 20262}, {14571, 16777}, {14733, 37763}, {17614, 41006}, {25917, 32561}, {26932, 51775}, {34522, 46344}, {35342, 51376}, {38015, 54008}, {40555, 51364}
X(54079) = reflection of X(51364) in X(40555)
X(54079) = circumcircle-inverse of X(198)
X(54079) = Stevanovic-circle-inverse of X(51361)
X(54079) = crossdifference of every pair of points on line {57, 6129}
X(54079) = barycentric product X(7046)*X(52977)
X(54079) = barycentric quotient X(52977)/X(7056)
X(54080) lies on the cubic K904 and these lines: {3, 206}, {25, 35211}, {339, 44089}, {468, 2373}, {647, 8673}, {2070, 13115}, {2072, 6033}, {2936, 14961}, {3162, 5020}, {9909, 34427}, {10316, 23172}, {10547, 26926}, {10749, 34129}, {14376, 20968}
X(54080) = circumcircle-inverse of X(206)
X(54080) = Moses-radical-circle-inverse of X(46243)
X(54080) = X(52513)-Ceva conjugate of X(6)
X(54080) = crossdifference of every pair of points on line {427, 47125}
X(54080) = {X(20993),X(52041)}-harmonic conjugate of X(3)
X(54081) lies on the 2nd Evans circe, the Moses isodynomic circle (cf. X(41183)) these lines: {1, 1283}, {3, 214}, {10, 36558}, {25, 1845}, {28, 52167}, {36, 23205}, {55, 10703}, {56, 106}, {80, 52242}, {100, 6790}, {101, 102}, {104, 1633}, {110, 38568}, {117, 22753}, {124, 958}, {149, 36171}, {399, 2779}, {517, 1324}, {692, 34586}, {859, 5127}, {952, 53279}, {953, 1618}, {956, 13532}, {960, 34868}, {993, 2792}, {995, 2175}, {999, 1486}, {1001, 11734}, {1015, 5019}, {1064, 2317}, {1364, 10966}, {1387, 53302}, {1411, 15906}, {1468, 53542}, {1473, 1795}, {1482, 23843}, {1626, 10246}, {1718, 42753}, {1960, 8677}, {2099, 11334}, {2178, 8649}, {2217, 12699}, {2305, 9259}, {2390, 52407}, {2773, 22586}, {2785, 8301}, {2817, 9798}, {2818, 3556}, {2819, 41186}, {2842, 22148}, {2849, 3960}, {2852, 41184}, {2853, 19162}, {2932, 23832}, {2933, 12702}, {2975, 33650}, {3149, 50899}, {3738, 4491}, {5541, 23858}, {5584, 38691}, {5903, 37259}, {6224, 13589}, {6718, 25524}, {6788, 28083}, {7373, 47115}, {8158, 39600}, {9321, 20672}, {9532, 19159}, {10269, 38607}, {10573, 28077}, {10680, 22654}, {10747, 22758}, {10777, 13744}, {13730, 26437}, {15507, 51506}, {16064, 37525}, {16370, 50918}, {16680, 23402}, {18393, 34300}, {19297, 21781}, {20676, 22744}, {20842, 37567}, {22141, 23344}, {22144, 53290}, {22765, 38579}, {22769, 47038}, {23981, 51236}, {26321, 38780}, {28194, 51637}, {28348, 52129}, {35239, 38600}
X(54081) = circumcircle-inverse of X(214)
X(54081) = Stammler-circle-inverse of X(48667)
X(54081) = isogonal conjugate of the anticomplement of X(15898)
X(54081) = tangential isogonal conjugate of X(1324)
X(54081) = X(3218)-Ceva conjugate of X(6)
X(54081) = X(2161)-Dao conjugate of X(18359)
X(54081) = crossdifference of every pair of points on line {1639, 53522}
X(54081) = barycentric product X(i)*X(j) for these {i,j}: {56, 28829}, {3218, 15898}
X(54081) = barycentric quotient X(i)/X(j) for these {i,j}: {15898, 18359}, {28829, 3596}
X(54081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {692, 53294, 34586}, {3556, 11249, 15654}
X(54082) lies on these lines: {3, 6}, {23, 3331}, {24, 11674}, {25, 5167}, {26, 32445}, {186, 3289}, {217, 7488}, {316, 458}, {401, 3580}, {512, 34983}, {691, 51222}, {1154, 32661}, {1625, 2070}, {1971, 13754}, {2387, 39857}, {2715, 18401}, {3269, 10313}, {5207, 34850}, {5523, 5667}, {5889, 14585}, {6644, 40805}, {7517, 38297}, {8571, 18377}, {10312, 22416}, {10985, 15030}, {10986, 11459}, {13322, 33664}, {19627, 39839}, {20998, 45938}, {22146, 32608}, {34360, 44146}, {35324, 50461}, {35941, 51224}, {37644, 51350}
X(54082) = reflection of X(39849) in X(1971)
X(54082) = circumcircle-inverse of X(216)
X(54082) = isogonal conjugate of the isotomic conjugate of X(44363)
X(54082) = isogonal conjugate of the polar conjugate of X(41203)
X(54082) = crossdifference of every pair of points on line {523, 23292}
X(54082) = barycentric product X(i)*X(j) for these {i,j}: {3, 41203}, {6, 44363}, {99, 42651}
X(54082) = barycentric quotient X(i)/X(j) for these {i,j}: {41203, 264}, {42651, 523}, {44363, 76}
X(54082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {187, 50387, 1691}, {1379, 1380, 216}
X(54083) lies on these lines: {3, 102}, {185, 603}, {1415, 35072}, {1433, 1795}, {1455, 2817}, {1459, 1946}, {1935, 3042}, {2199, 53853}, {2800, 46974}, {2816, 34050}, {2829, 10017}, {2968, 51422}, {10740, 34030}, {11700, 17102}, {34029, 38776}
X(54083) = circumcircle-inverse of X(221)
X(54083) = {X(102),X(109)}-harmonic conjugate of X(221)
X(54084) lies on these lines: {3, 242}, {4, 2077}, {24, 1324}, {25, 5205}, {28, 1792}, {34, 1054}, {35, 37055}, {1829, 37304}, {1851, 4188}, {1870, 24046}, {3518, 45767}, {4874, 23383}, {11383, 37253}, {13739, 19642}, {14192, 30733}, {16066, 52427}, {19842, 37101}
X(54084) = circumcircle-inverse of X(242)
X(54084) = polar-circle-inverse of X(3814)
X(54085) lies on these lines: {3, 74}, {112, 1112}, {125, 1316}, {247, 2777}, {526, 7669}, {1510, 30715}, {1976, 2781}, {2079, 3569}, {3124, 50363}, {3269, 13198}, {3447, 20188}, {3448, 4226}, {5621, 46130}, {5622, 51335}, {7422, 12244}, {9409, 13558}, {13417, 31850}, {14683, 18331}, {14984, 38873}, {15107, 38582}, {15535, 36181}, {15920, 37457}, {24981, 35022}, {39857, 42663}
X(54085) = circumcircle-inverse of X(246)
X(54085) = crossdifference of every pair of points on line {1637, 5972}
X(54085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 110, 246}, {246, 5191, 110}, {5621, 52162, 46130}
X(54086) lies on the cubic K039 and these lines: {3, 76}, {115, 10684}, {186, 22456}, {187, 2966}, {237, 38947}, {287, 5026}, {1976, 39292}, {2076, 39941}, {5661, 40866}, {6037, 35298}, {8289, 46806}, {13586, 48452}, {13754, 17932}, {26613, 37858}, {34536, 35296}, {35297, 51404}, {43187, 47635}, {47388, 52992}
X(54086) = isogonal conjugate of X(52446)
X(54086) = circumcircle-inverse of X(290)
X(54086) = X(1)-isoconjugate of X(52446)
X(54086) = X(3)-Dao conjugate of X(52446)
X(54086) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 52446}, {2966, 53603}
X(54086) = {X(98),X(99)}-harmonic conjugate of X(290)
X(54087) lies on these lines: {3, 323}, {160, 669}, {325, 6031}, {376, 14731}, {842, 7492}, {5191, 8724}, {5467, 11002}, {5939, 14360}, {5941, 11580}, {9155, 51800}, {10298, 10420}, {11004, 52603}, {14652, 52124}, {34417, 47053}, {40604, 52169}
X(54087) = circumcircle-inverse of X(323)
X(54087) = psi-transform of X(1511)
X(54088) lies on these lines: {3, 315}, {22, 669}, {183, 37930}, {187, 52036}, {323, 353}, {3148, 34245}, {5939, 7669}, {5941, 22329}, {5976, 19165}, {7492, 38940}, {7761, 35936}, {12584, 50567}, {28724, 38525}
X(54088) = circumcircle-inverse of X(325)
X(54088) = 2nd-Brocard-circle-inverse of X(7750)
X(54089) lies on these lines: {3, 76}, {115, 6720}, {148, 4235}, {620, 40484}, {804, 39857}, {5026, 41255}, {6699, 14928}, {7669, 35522}, {8178, 14966}, {9862, 13219}, {23285, 30715}, {24284, 46253}
X(54089) = circumcircle-inverse of X(339)
X(54089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 99, 339}, {115, 53737, 40856}
X(54090) lies on these lines: {3, 10}, {24, 1785}, {35, 37116}, {36, 1772}, {58, 31760}, {100, 45396}, {186, 45766}, {522, 39200}, {946, 37259}, {1399, 31825}, {2077, 37311}, {2222, 9590}, {2708, 29095}, {2932, 51632}, {3417, 5903}, {3465, 5010}, {5172, 14667}, {7488, 10538}, {8069, 51616}, {14127, 41698}, {24042, 52242}, {35013, 39478}
X(54090) = midpoint of X(3) and X(1324)
X(54090) = circumcircle-inverse of X(355)
X(54090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 2933, 6796}, {3, 23843, 5450}
X(54091) lies on these lines: {3, 6}, {25, 38227}, {186, 47158}, {316, 7395}, {385, 39803}, {842, 37920}, {1513, 9861}, {1607, 7684}, {1608, 7685}, {3425, 20885}, {3515, 21396}, {5899, 30715}, {6642, 14693}, {6644, 38230}, {7503, 14712}, {9876, 37461}, {10003, 53485}, {10323, 43453}, {11479, 13449}, {11676, 39832}, {14575, 19123}, {14853, 37457}, {16188, 37972}, {20854, 34218}, {37928, 47584}, {39231, 44668}, {40947, 52276}
X(54091) = reflection of X(3) in X(32762)
X(54091) = circumcircle-inverse of X(389)
X(54091) = Stammler-circle-inverse of X(6243)
X(54091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1379, 1380, 389}, {38596, 38597, 6243}
X(54092) lies on these lines: {3, 49}, {23, 4558}, {25, 44899}, {114, 468}, {122, 11064}, {154, 6503}, {235, 21268}, {669, 684}, {1297, 10420}, {1495, 23181}, {3003, 23357}, {3291, 5941}, {3542, 5962}, {6031, 37668}, {6800, 9723}, {10539, 16391}, {12420, 34853}, {13558, 34382}, {14567, 47406}, {14981, 42671}, {15512, 17836}
X(54092) = circumcircle-inverse of X(394)
X(54092) = crossdifference of every pair of points on line {2501, 3767}
X(54092) = {X(3),X(41615)}-harmonic conjugate of X(47195)
X(54093) lies on these lines: {2, 3}, {100, 2695}, {102, 1290}, {484, 1725}, {517, 5494}, {523, 53277}, {1292, 53926}, {1311, 2691}, {2099, 10149}, {2687, 33637}, {2766, 41904}, {3871, 17479}, {5160, 37567}, {5176, 51629}, {15945, 40582}, {32706, 53952}, {40214, 48897}, {53916, 53941}
X(54093) = reflection of X(i) in X(j) for these {i,j}: {1325, 186}, {3153, 30447}, {37976, 15646}
X(54093) = circumcircle-inverse of X(411)
X(54093) = polar-circle-inverse of X(37368)
X(54093) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 1114, 411}
X(54094) lies on these lines: {2, 3}, {107, 43654}, {250, 1974}, {523, 3186}, {571, 38861}, {935, 53704}, {1304, 2698}, {2452, 40981}, {3563, 53937}, {5106, 51324}, {6037, 40118}, {9513, 44127}, {9998, 35325}, {22239, 48259}, {46426, 46432}
X(54094) = circumcircle-inverse of X(419)
X(54094) = polar-circle-inverse of X(21531)
X(54094) = X(i)-isoconjugate of X(j) for these (i,j): {336, 52446}, {656, 53603}
X(54094) = X(40596)-Dao conjugate of X(53603)
X(54094) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 53603}, {2211, 52446}
X(54094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 4230, 4}, {237, 1316, 37918}, {1113, 1114, 419}, {1316, 37918, 37991}, {5000, 5001, 15915}, {21525, 44895, 2}
X(54095) lies on these lines: {2, 3}, {476, 51760}, {1290, 41345}, {1324, 23860}, {3447, 20872}, {4640, 9591}, {5903, 34435}, {6001, 9625}, {11496, 51883}, {20875, 39857}, {20989, 51632}, {23406, 30715}, {36152, 41495}, {37579, 39751}
X(54095) = reflection of X(7580) in X(37979)
X(54095) = circumcircle-inverse of X(442)
X(54095) = tangential-circle-inverse of X(2915)
X(54095) = tangential-isogonal conjugate of X(2948)
X(54095) = X(19622)-Dao conjugate of X(37783)
X(54095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 20831, 11101}, {23, 186, 51635}, {23, 37919, 5899}, {186, 36001, 3}, {1113, 1114, 442}, {1325, 37919, 36171}, {2074, 30447, 405}, {2074, 37959, 30447}
X(54096) lies on these lines: {2, 3}, {250, 19118}, {523, 1609}, {1304, 23700}, {2079, 47200}, {2452, 8573}, {2453, 8553}, {3053, 47213}, {11063, 47284}, {12828, 53735}, {14729, 47220}, {20987, 30715}, {41584, 41758}
X(54096) = circumcircle-inverse of X(460)
X(54096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {24, 4230, 25}, {1113, 1114, 460}
Contributed by Clark Kimberling and Peter Moses June 29, 2023.
Let SCE be Steiner circumellipse of a triangle ABC, and Let P = p : q : r be a point not on a sideline of ABC. Let A' be the point, other than A, where the line AP meets line BC. Define B' and C' cyclically. The triangle A'B'C' is here named the Steiner-circumcevian triangle of P, denoted by SCC(P). The vertices of SCC(P) are given by
A' = -q r : q (q + r) : r (q + r)
B' = p (r + p) : - r p : r (r + p)
C' = p (p + q) : q (p + q) : - p q
The triangle SCC(P) is perspective to the anticomplementary. Let SC(P) denote the perspector. Then
SC(P) = P2-Ceva conjugate of X(2)
SC(P) = anticomplement of isotomic conjugate of P2.
The appearance of (i,j) in the following list means that SC(X(i)) = X(j).
(2996, 54097), (330, 54098), (7035, 54099), (276, 54100), (291, 54101), (514, 54102). (8781, 54103), (523, 54104), (40410, 54105), (262, 54106), (333, 54107), (18020, 54108), (314, 54109), (4998, 54110), (253, 54111), (310, 54112), (312, 54113)
The triangle SCC(X(2)) is the triangle Gemini 107, and the triangle SCC(4) is the 9th Brocard triangle.
Let Ta be the line tangent to SCC at A', and define Tb and Tc cyclically. Let A* = Tb ^ Tc and define B* and C* cyclically. Then A*B*C* is perspective to ABC, and the perspector is given by the point T(P) = 1 / (-q*r + r*p + p*q) : : . The transformation T maps curves to curves, as in these examples:
T(Kiepert hyperbola) = Kiepert hyperbola
T(K184) = K007
T(K1023) = K1000
T(K868) = K1002
T(K1014) = K1037)
T(K342a) = K1053a)
T(K342b) = K1053n)
X(54097) lies on these lines: {2, 3}, {193, 44518}, {316, 6392}, {543, 32825}, {2996, 20080}, {5023, 39143}, {5254, 51170}, {5395, 18845}, {7748, 32827}, {7760, 43448}, {7781, 32816}, {7825, 32815}, {7842, 32828}, {7848, 32868}, {7873, 46951}, {7898, 32834}, {8589, 32884}, {11185, 32027}, {14023, 39563}, {15301, 32876}, {18424, 32838}, {20094, 32841}, {32829, 43619}, {32883, 39601}, {33684, 39874}, {34505, 41895}, {34803, 44519}, {44377, 51579}
X(54097) = reflection of X(439) in X(32972)
X(54097) = anticomplement of X(439)
X(54097) = X(8769)-anticomplementary conjugate of X(19583)
X(54097) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 19691, 50693}, {2, 33209, 21734}, {2, 50690, 6658}, {2, 50692, 33244}, {3, 52250, 2}, {4, 7841, 32971}, {4, 16045, 11317}, {4, 32974, 32979}, {4, 32982, 2}, {4, 33229, 32974}, {20, 14041, 32980}, {20, 32980, 2}, {377, 33050, 2}, {381, 33238, 32990}, {382, 16041, 32973}, {439, 32972, 2}, {546, 32986, 32987}, {1657, 32969, 35287}, {1657, 37350, 32969}, {2996, 32006, 20080}, {2996, 53419, 38259}, {3091, 33017, 33023}, {3091, 33023, 2}, {3146, 14063, 2}, {3146, 33205, 33193}, {3522, 32966, 2}, {3529, 33228, 32989}, {3543, 5025, 32981}, {3543, 33181, 33280}, {3832, 6655, 2}, {3839, 7791, 32991}, {3850, 5077, 32978}, {5025, 32981, 2}, {5025, 33280, 33181}, {5068, 32965, 2}, {5177, 33051, 2}, {5395, 53418, 18845}, {6658, 33290, 2}, {7791, 14044, 3839}, {7791, 32991, 2}, {7841, 32956, 32974}, {7887, 33703, 35927}, {8597, 16925, 49135}, {11303, 11304, 15702}, {14035, 33200, 2}, {14041, 33279, 20}, {14042, 33251, 33198}, {14045, 33007, 33199}, {14062, 33017, 3091}, {15022, 33004, 2}, {15640, 33203, 33257}, {15717, 32963, 2}, {16044, 33025, 2}, {16044, 33278, 33025}, {17685, 37161, 2}, {20080, 38259, 2996}, {32006, 53419, 2996}, {32963, 33264, 15717}, {32966, 33192, 3522}, {32967, 33271, 10304}, {32971, 32974, 32956}, {32974, 32979, 2}, {32974, 33229, 32982}, {32979, 32982, 32974}, {32993, 32997, 2}, {32993, 33019, 32997}, {32996, 32997, 32993}, {32996, 33019, 2}, {32998, 33267, 15692}, {33006, 33256, 3523}, {33181, 33280, 32981}, {33199, 50691, 33007}, {33200, 50687, 14035}, {33201, 33283, 2}
X(54098) lies on these lines: {1, 2}, {75, 31999}, {149, 33019}, {192, 17448}, {194, 4788}, {319, 26143}, {330, 1278}, {350, 21219}, {391, 16515}, {495, 33060}, {496, 33061}, {536, 32005}, {956, 16914}, {999, 33062}, {1056, 33030}, {1058, 17685}, {1107, 4704}, {1191, 20158}, {1616, 20142}, {3295, 33063}, {3759, 27291}, {3871, 33004}, {4366, 12513}, {4452, 30662}, {4772, 31997}, {4821, 17143}, {5082, 17565}, {5839, 24761}, {6658, 20076}, {6767, 33047}, {7187, 17158}, {7373, 16917}, {9263, 20081}, {16722, 30939}, {16884, 20146}, {16969, 17349}, {16975, 32026}, {17178, 33296}, {17373, 27106}, {20060, 33018}, {20075, 33260}, {20530, 40598}, {24524, 30998}, {25573, 26135}, {26823, 48333}, {26852, 30941}, {27107, 34063}
X(54098) = anticomplement of X(53675)
X(54098) = anticomplement of the isogonal conjugate of X(53146)
X(54098) = anticomplement of the isotomic conjugate of X(53677)
X(54098) = isotomic conjugate of the isogonal conjugate of X(41397)
X(54098) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7121, 21219}, {7153, 20350}, {32039, 21301}, {53146, 8}, {53677, 6327}, {53678, 69}, {53679, 315}
X(54098) = X(53677)-Ceva conjugate of X(2)
X(54098) = barycentric product X(76)*X(41397)
X(54098) = barycentric quotient X(41397)/X(6)
X(54098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 16826, 23511}, {330, 17144, 1278}, {1107, 32095, 4704}, {1278, 38247, 330}, {4393, 29570, 5256}, {20055, 26821, 2}
X(54099) lies on these lines: {2, 32016}, {190, 17494}, {660, 799}, {668, 20295}, {889, 50520}, {4555, 4608}, {4562, 31290}, {4568, 48082}, {4579, 35356}, {9362, 47763}, {17154, 32030}, {32937, 33798}
X(54099) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6632, 149}, {42372, 320}
X(54099) = {X(3952),X(7192)}-harmonic conjugate of X(7035)
X(54100) lies on these lines: {2, 46394}, {3, 95}, {4, 290}, {5, 16089}, {30, 9291}, {32, 16081}, {76, 37200}, {83, 458}, {297, 34850}, {308, 51252}, {315, 18022}, {324, 401}, {393, 37337}, {1078, 1629}, {1235, 35474}, {3785, 44144}, {6331, 7752}, {8794, 52253}, {14246, 46111}, {16264, 17984}, {18831, 34148}, {36794, 41334}, {37124, 44142}
X(54100) = reflection of X(9291) in X(42368)
X(54100) = isotomic conjugate of X(42487)
X(54100) = anticomplement of X(46394)
X(54100) = isotomic conjugate of the isogonal conjugate of X(1629)
X(54100) = polar conjugate of the isogonal conjugate of X(36794)
X(54100) = X(23582)-Ceva conjugate of X(6528)
X(54100) = X(i)-isoconjugate of X(j) for these (i,j): {31, 42487}, {255, 27375}, {3613, 52430}, {9247, 36952}
X(54100) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 42487}, {850, 15526}, {6523, 27375}, {52591, 3269}
X(54100) = cevapoint of X(1629) and X(36794)
X(54100) = barycentric product X(i)*X(j) for these {i,j}: {76, 1629}, {158, 33764}, {264, 36794}, {276, 30506}, {393, 33769}, {1078, 2052}, {1096, 33778}, {5012, 18027}, {6528, 31296}, {10312, 18022}, {23582, 36901}, {37125, 46104}
X(54100) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 42487}, {264, 36952}, {393, 27375}, {1078, 394}, {1629, 6}, {2052, 3613}, {3050, 39201}, {5012, 577}, {6528, 11794}, {7668, 3269}, {10312, 184}, {18042, 255}, {23582, 27867}, {27010, 1364}, {30506, 216}, {31296, 520}, {33764, 326}, {33769, 3926}, {36794, 3}, {36901, 15526}, {37125, 3917}, {38352, 34980}, {41296, 28724}, {41334, 418}
X(54100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 264, 276}, {4, 18027, 6528}
X(54101) lies on these lines: {2, 1978}, {37, 39028}, {42, 19579}, {145, 194}, {190, 25054}, {192, 17794}, {291, 740}, {346, 2998}, {668, 1500}, {812, 23656}, {1015, 17143}, {2276, 52044}, {3802, 30667}, {4360, 52637}, {6542, 40858}, {8264, 17314}, {39786, 40094}
X(54101) = reflection of X(i) in X(j) for these {i,j}: {668, 1500}, {17143, 1015}
X(54101) = anticomplement of the isogonal conjugate of X(51856)
X(54101) = anticomplement of the isotomic conjugate of X(52205)
X(54101) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {292, 20554}, {1911, 20345}, {1922, 17794}, {1927, 30668}, {14598, 33888}, {18267, 2}, {18897, 30667}, {30663, 315}, {40098, 21275}, {51856, 8}, {52205, 6327}
X(54101) = X(52205)-Ceva conjugate of X(2)
X(54101) = {X(17759),X(39925)}-harmonic conjugate of X(291)
X(54102) lies on these lines: {2, 1016}, {8, 19950}, {145, 18343}, {148, 39362}, {149, 21301}, {190, 45213}, {239, 908}, {514, 4440}, {519, 4645}, {1086, 6631}, {1278, 30225}, {1320, 31129}, {4473, 32094}, {6542, 17495}, {6646, 35957}, {9263, 17496}, {17152, 46707}, {17487, 32106}, {20042, 33922}, {26806, 36226}, {27191, 34024}, {32028, 35092}, {39348, 39368}
X(54102) = midpoint of X(4440) and X(6630)
X(54102) = reflection of X(i) in X(j) for these {i,j}: {190, 45213}, {1016, 6547}, {6631, 1086}, {32028, 35092}, {39349, 6630}
X(54102) = anticomplement of X(1016)
X(54102) = anticomplement of the isogonal conjugate of X(1015)
X(54102) = anticomplement of the isotomic conjugate of X(1086)
X(54102) = isotomic conjugate of the isogonal conjugate of X(41395)
X(54102) = anticomplementary isogonal conjugate of X(668)
X(54102) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 668}, {6, 3952}, {11, 21286}, {31, 190}, {56, 21272}, {57, 3888}, {58, 53332}, {81, 53338}, {86, 53363}, {87, 1978}, {163, 50351}, {244, 69}, {292, 23354}, {513, 20295}, {514, 21301}, {560, 46725}, {593, 21295}, {604, 100}, {649, 513}, {663, 4462}, {667, 514}, {693, 21304}, {739, 53340}, {741, 874}, {757, 4576}, {764, 150}, {798, 31290}, {849, 99}, {873, 670}, {875, 812}, {876, 21303}, {1014, 53355}, {1015, 8}, {1019, 512}, {1027, 3766}, {1086, 6327}, {1106, 664}, {1110, 32028}, {1111, 315}, {1178, 799}, {1333, 4427}, {1357, 7}, {1358, 21285}, {1395, 651}, {1397, 4552}, {1398, 4566}, {1400, 3909}, {1402, 3882}, {1408, 17136}, {1416, 883}, {1438, 53358}, {1474, 53349}, {1911, 42720}, {1919, 17494}, {1973, 3732}, {1977, 192}, {1980, 21225}, {2087, 21290}, {2149, 39185}, {2170, 3436}, {2203, 14543}, {2279, 3799}, {2350, 4553}, {2665, 27853}, {2969, 21270}, {3063, 4468}, {3120, 21287}, {3121, 1654}, {3122, 2895}, {3125, 1330}, {3248, 2}, {3249, 9263}, {3271, 329}, {3572, 46403}, {3669, 21302}, {3675, 20552}, {3733, 7192}, {3768, 44008}, {3937, 4329}, {3942, 1370}, {4117, 46714}, {4607, 33917}, {4817, 788}, {6545, 21293}, {6591, 20293}, {7023, 35312}, {7117, 52366}, {7121, 33946}, {7192, 17217}, {7199, 44445}, {7203, 4374}, {8027, 4440}, {8034, 21221}, {8054, 18133}, {9315, 4499}, {9456, 17780}, {16726, 17135}, {16727, 17138}, {17205, 17137}, {17925, 21300}, {18191, 20245}, {21143, 149}, {21762, 41840}, {22096, 6360}, {22383, 20294}, {23345, 21297}, {23349, 47776}, {23892, 891}, {23989, 21275}, {27846, 20345}, {27918, 20554}, {28607, 4781}, {32665, 6550}, {34445, 25310}, {36598, 36863}, {37129, 41314}, {38247, 25312}, {38266, 3699}, {38986, 21219}, {39748, 27808}, {39798, 8050}, {40148, 4033}, {40735, 3807}, {42067, 5905}, {43921, 20347}, {43922, 320}, {43923, 46400}, {43924, 693}, {43925, 7253}, {43929, 53343}, {43932, 46402}, {46289, 33951}, {51866, 660}, {52619, 21305}, {52633, 20355}, {53538, 3434}, {53540, 2893}, {53541, 30660}, {53678, 18830}
X(54102) = X(i)-Ceva conjugate of X(j) for these (i,j): {1086, 2}, {6631, 514}
X(54102) = barycentric product X(i)*X(j) for these {i,j}: {75, 1052}, {76, 41395}
X(54102) = barycentric quotient X(i)/X(j) for these {i,j}: {1052, 1}, {41395, 6}
X(54102) = {X(1016),X(6547)}-harmonic conjugate of X(2)
X(54103) lies on these lines: {2, 39764}, {20, 99}, {69, 114}, {76, 38383}, {98, 325}, {115, 6392}, {316, 10723}, {491, 19056}, {492, 19055}, {524, 44534}, {538, 671}, {542, 46236}, {620, 3785}, {1007, 6036}, {1078, 3314}, {1494, 53367}, {1569, 7818}, {1975, 10722}, {2023, 9766}, {2782, 7776}, {3329, 7886}, {3767, 7752}, {3933, 6033}, {3964, 9861}, {4027, 7897}, {5149, 7895}, {5152, 7871}, {5182, 12830}, {5319, 6722}, {5468, 30789}, {5976, 6054}, {5989, 45018}, {6337, 38749}, {6390, 38741}, {6721, 34229}, {7750, 21166}, {7763, 34473}, {7767, 15561}, {7773, 14639}, {7778, 12829}, {7779, 36849}, {7811, 8182}, {7856, 37665}, {7925, 36864}, {7946, 39652}, {8290, 33276}, {9862, 32818}, {10754, 50771}, {10991, 32825}, {14651, 32823}, {23234, 37671}, {23698, 32006}, {30786, 31127}, {32815, 39838}, {32828, 36519}, {32829, 38737}, {32954, 41675}, {35136, 39352}, {43150, 46318}
X(54103) = reflection of X(i) in X(j) for these {i,j}: {99, 3926}, {6392, 115}
X(54103) = isotomic conjugate of the isogonal conjugate of X(38873)
X(54103) = barycentric product X(76)*X(38873)
X(54103) = barycentric quotient X(38873)/X(6)
X(54103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 325, 8781}, {147, 32458, 99}, {147, 37668, 32458}
X(54104) lies on the cubic K079 and these lines: {2, 4590}, {99, 45212}, {115, 31998}, {148, 523}, {385, 858}, {524, 5207}, {892, 31372}, {2854, 32528}, {3221, 31513}, {6625, 24345}, {7665, 36168}, {8596, 18823}, {14588, 44398}, {17162, 20536}, {20094, 23992}, {25051, 39346}, {25054, 39359}, {33915, 45291}, {40429, 40553}, {40511, 44397}
X(54104) = midpoint of X(148) and X(35511)
X(54104) = reflection of X(i) in X(j) for these {i,j}: {99, 45212}, {4590, 23991}, {14588, 44398}, {20094, 33799}, {31372, 892}, {31998, 115}, {33799, 23992}, {35511, 44373}, {39356, 35511}
X(54104) = anticomplement of X(4590)
X(54104) = anticomplement of the isogonal conjugate of X(3124)
X(54104) = anticomplement of the isotomic conjugate of X(115)
X(54104) = isotomic conjugate of the isogonal conjugate of X(33704)
X(54104) = anticomplementary isogonal conjugate of X(4576)
X(54104) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 4576}, {6, 21295}, {10, 53363}, {19, 53350}, {31, 99}, {32, 6758}, {37, 53338}, {42, 53332}, {65, 53355}, {75, 670}, {115, 6327}, {181, 21272}, {213, 4427}, {244, 17143}, {338, 21275}, {512, 7192}, {513, 17159}, {523, 17217}, {560, 14570}, {649, 17166}, {661, 512}, {667, 17161}, {669, 4560}, {756, 668}, {798, 523}, {810, 6563}, {850, 21305}, {872, 190}, {897, 53367}, {923, 5468}, {1015, 17140}, {1084, 192}, {1101, 33799}, {1109, 315}, {1356, 3210}, {1365, 21285}, {1402, 17136}, {1500, 3952}, {1577, 44445}, {1910, 53371}, {1917, 46726}, {1924, 31296}, {1967, 2396}, {1973, 110}, {2170, 35614}, {2171, 3888}, {2179, 50947}, {2333, 53349}, {2489, 7253}, {2501, 21300}, {2643, 69}, {2971, 5905}, {3120, 17137}, {3121, 1}, {3122, 75}, {3123, 34086}, {3124, 8}, {3125, 17135}, {3248, 4360}, {3271, 21273}, {3572, 4155}, {3708, 1370}, {4017, 4374}, {4024, 21301}, {4036, 21304}, {4079, 513}, {4092, 21286}, {4117, 194}, {4516, 20245}, {4705, 20295}, {7063, 3177}, {7143, 35312}, {7148, 1978}, {8029, 21294}, {8754, 21270}, {9406, 14611}, {9427, 17486}, {16732, 17138}, {18070, 688}, {18210, 18659}, {18757, 4610}, {18832, 4609}, {20975, 4329}, {21043, 21287}, {21131, 21293}, {21725, 30660}, {21833, 1330}, {22260, 21221}, {23099, 21220}, {23894, 53365}, {23994, 33796}, {34294, 21278}, {36142, 33919}, {38252, 4563}, {40525, 25295}, {41683, 53366}, {42068, 21216}, {43763, 880}, {46289, 10330}, {50487, 514}, {51641, 4467}, {51906, 17165}, {53540, 20244}, {53581, 17494}
X(54104) = X(i)-Ceva conjugate of X(j) for these (i,j): {115, 2}, {31998, 523}
X(54104) = barycentric product X(i)*X(j) for these {i,j}: {76, 33704}, {99, 13187}
X(54104) = barycentric quotient X(i)/X(j) for these {i,j}: {13187, 523}, {33704, 6}
X(54104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {148, 44373, 39356}, {4590, 23991, 2}
X(54105) lies on these lines: {2, 36422}, {4, 46724}, {5, 95}, {69, 3855}, {99, 33643}, {233, 40853}, {264, 339}, {311, 15031}, {317, 3091}, {340, 3850}, {467, 19188}, {546, 45198}, {648, 17035}, {1232, 7809}, {3832, 6527}, {3839, 40680}, {3843, 20477}, {3854, 44134}, {3858, 41005}, {5066, 41008}, {5072, 52712}, {7773, 44149}, {14644, 19166}, {32001, 41106}, {36794, 52247}, {40897, 43982}
X(54105) = isotomic conjugate of X(43970)
X(54105) = anticomplement of X(36422)
X(54105) = isotomic conjugate of the isogonal conjugate of X(38848)
X(54105) = X(31)-isoconjugate of X(43970)
X(54105) = X(2)-Dao conjugate of X(43970)
X(54105) = barycentric product X(i)*X(j) for these {i,j}: {76, 38848}, {34987, 42405}
X(54105) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43970}, {34987, 17434}, {38848, 6}
X(54105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 95, 40410}, {5, 32002, 95}, {17035, 36412, 648}
X(54106) lies on these lines: {2, 5034}, {147, 193}, {148, 44434}, {194, 315}, {262, 1352}, {385, 9744}, {1992, 43450}, {2548, 7760}, {2896, 10513}, {3767, 39101}, {3832, 6392}, {7615, 19570}, {7796, 7800}, {7837, 20423}, {8721, 20065}, {9890, 39652}, {15993, 51580}
X(54106) = X(3402)-anticomplementary conjugate of X(6194)
X(54107) lies on these lines: {2, 6354}, {8, 6253}, {9, 20921}, {19, 27}, {40, 52346}, {144, 5739}, {190, 329}, {238, 24218}, {322, 3719}, {347, 37669}, {394, 664}, {489, 46421}, {490, 46422}, {527, 45206}, {653, 15466}, {908, 33116}, {1043, 3869}, {1121, 2994}, {1214, 1944}, {1726, 6996}, {1782, 37088}, {1948, 40152}, {2184, 5931}, {2975, 11101}, {3218, 17862}, {3219, 30807}, {4360, 18662}, {6180, 18663}, {6335, 18736}, {6350, 18134}, {6508, 40882}, {6515, 20078}, {6604, 9965}, {10025, 49514}, {12848, 18928}, {13567, 17950}, {17080, 28950}, {17086, 23292}, {17147, 40571}, {22001, 23512}, {25091, 27420}, {30695, 41821}, {33673, 47848}, {35614, 38480}, {44447, 52365}
X(54107) = anticomplement of X(6354)
X(54107) = anticomplement of the isogonal conjugate of X(7054)
X(54107) = anticomplement of the isotomic conjugate of X(7058)
X(54107) = isotomic conjugate of the isogonal conjugate of X(1630)
X(54107) = polar conjugate of the isogonal conjugate of X(3561)
X(54107) = X(7058)-Ceva conjugate of X(2)
X(54107) = cevapoint of X(1630) and X(3561)
X(54107) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {21, 2893}, {60, 7}, {250, 4566}, {261, 21285}, {283, 2897}, {284, 2475}, {593, 36845}, {757, 6604}, {849, 4452}, {1021, 3448}, {1043, 21287}, {1098, 69}, {1101, 664}, {1253, 46707}, {2150, 145}, {2185, 3434}, {2189, 12649}, {2193, 3152}, {2194, 17778}, {2287, 1330}, {2326, 4}, {2327, 52364}, {2328, 2895}, {4556, 3900}, {4612, 21302}, {4636, 693}, {6061, 329}, {7054, 8}, {7058, 6327}, {7253, 21294}, {21789, 21221}, {23609, 63}, {24000, 18026}, {36069, 36038}, {36421, 5906}, {52379, 21280}, {52914, 46400}, {52935, 46402}
X(54107) = barycentric product X(i)*X(j) for these {i,j}: {75, 411}, {76, 1630}, {264, 3561}, {312, 34035}, {561, 44087}
X(54107) = barycentric quotient X(i)/X(j) for these {i,j}: {411, 1}, {1630, 6}, {3561, 3}, {34035, 57}, {44087, 31}
X(54107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 92, 333}, {63, 20223, 75}, {63, 45738, 18750}, {394, 6360, 664}
X(54108) lies on these lines: {99, 6563}, {110, 685}, {184, 44155}, {250, 47258}, {316, 33803}, {647, 40866}, {648, 23964}, {892, 4577}, {2966, 23357}, {3047, 23962}, {5641, 9143}, {9514, 23878}, {14480, 41298}, {16077, 18831}, {36830, 36900}
X(54108) = isotomic conjugate of the isogonal conjugate of X(38861)
X(54108) = X(14966)-Dao conjugate of X(11672)
X(54108) = barycentric product X(i)*X(j) for these {i,j}: {76, 38861}, {6331, 13198}, {21525, 43187}
X(54108) = barycentric quotient X(i)/X(j) for these {i,j}: {13198, 647}, {21525, 3569}, {38861, 6}
X(54108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 850, 18020}, {23357, 31296, 2966}
X(54109) lies on these lines: {2, 31643}, {19, 27}, {261, 2975}, {314, 2995}, {668, 21286}, {894, 24993}, {1409, 1944}, {3436, 3596}, {4329, 14615}, {6335, 18747}, {10447, 12526}, {17137, 20245}, {17143, 21273}, {20345, 20348}, {24547, 38000}
X(54109) = isotomic conjugate of X(42485)
X(54109) = anticomplement of the isogonal conjugate of X(7058)
X(54109) = isotomic conjugate of the anticomplement of X(15267)
X(54109) = isotomic conjugate of the isogonal conjugate of X(1610)
X(54109) = X(31)-isoconjugate of X(42485)
X(54109) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 42485}, {19608, 42550}
X(54109) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {21, 17778}, {60, 3210}, {200, 46707}, {261, 7}, {270, 30699}, {283, 18667}, {314, 2893}, {332, 2897}, {333, 2475}, {593, 17480}, {757, 4452}, {849, 46716}, {873, 6604}, {1021, 148}, {1043, 2895}, {1098, 2}, {1253, 46714}, {1509, 36845}, {1792, 3151}, {1812, 3152}, {2185, 145}, {2287, 1654}, {2326, 193}, {2327, 18666}, {2328, 1655}, {4610, 3900}, {4612, 522}, {4623, 46402}, {4631, 21302}, {4636, 17496}, {6061, 3177}, {6064, 21272}, {6628, 17158}, {7054, 192}, {7058, 8}, {7253, 21221}, {7259, 31290}, {7340, 35312}, {18020, 4566}, {18021, 21285}, {21789, 21220}, {23999, 18026}, {24041, 664}, {46103, 12649}, {52379, 3434}, {52380, 37759}, {52935, 4025}
X(54109) = barycentric product X(i)*X(j) for these {i,j}: {75, 23512}, {76, 1610}
X(54109) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 42485}, {1610, 6}, {23512, 1}, {34267, 34434}
X(54109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2995, 3869, 314}, {20245, 20246, 17137}
X(54110) lies on these lines: {2, 31611}, {99, 901}, {100, 693}, {101, 48008}, {106, 24191}, {190, 4468}, {320, 50744}, {514, 41405}, {650, 40865}, {664, 4025}, {666, 1252}, {4762, 14589}, {5375, 31150}, {6606, 35157}, {8047, 18821}, {14513, 20295}, {26692, 30610}, {26824, 43986}, {31615, 43991}, {35119, 41395}
X(54110) = isotomic conjugate of X(43974)
X(54110) = isotomic conjugate of the isogonal conjugate of X(1618)
X(54110) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2149, 17036}, {4619, 149}, {31615, 33650}
X(54110) = X(i)-isoconjugate of X(j) for these (i,j): {31, 43974}, {663, 43947}
X(54110) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 43974}, {2284, 6184}
X(54110) = cevapoint of X(100) and X(43991)
X(54110) = barycentric product X(i)*X(j) for these {i,j}: {76, 1618}, {190, 24203}
X(54110) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43974}, {651, 43947}, {1618, 6}, {24203, 514}
X(54110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 693, 4998}, {1252, 17494, 666}, {17494, 51357, 1252}
X(54111) lies on these lines: {2, 6}, {20, 40995}, {253, 3146}, {264, 50689}, {297, 17037}, {315, 30698}, {317, 17578}, {340, 5059}, {1494, 52443}, {3522, 41005}, {3785, 38437}, {3832, 32000}, {3854, 44134}, {15717, 41008}, {20218, 39352}, {21734, 40680}, {22468, 32830}, {32879, 52347}, {32882, 34007}, {44334, 45245}, {46724, 50693}
X(54111) = anticomplement of X(36413)
X(54111) = isotomic conjugate of the isogonal conjugate of X(1620)
X(54111) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2155, 17037}, {2184, 6225}, {31942, 5905}, {52559, 4329}, {53886, 7192}
X(54111) = X(38253)-Dao conjugate of X(33893)
X(54111) = barycentric product X(76)*X(1620)
X(54111) = barycentric quotient X(1620)/X(6)
X(54111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {253, 32001, 3146}, {253, 40996, 35510}, {1270, 1271, 37669}, {3146, 35510, 253}, {32001, 40996, 253}
X(54112) lies on these lines: {1, 17208}, {2, 1258}, {69, 9054}, {310, 2388}, {668, 40007}, {3051, 26810}, {4360, 30941}, {4576, 35614}, {6327, 20554}, {6653, 32863}, {20290, 20561}, {20347, 44139}, {21280, 33796}, {27152, 40728}, {29824, 34020}, {30109, 40586}
X(54112) = anticomplement of X(7109)
X(54112) = isotomic conjugate of the isogonal conjugate of X(23374)
X(54112) = anticomplementary isogonal conjugate of X(46714)
X(54112) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 46714}, {75, 46707}, {86, 1655}, {261, 3177}, {274, 1654}, {310, 2895}, {552, 3210}, {593, 17486}, {757, 194}, {763, 17148}, {799, 31290}, {849, 8264}, {873, 2}, {1019, 25054}, {1098, 46706}, {1509, 192}, {2185, 21218}, {4610, 17494}, {4623, 514}, {4631, 4468}, {6385, 1330}, {6628, 17147}, {7192, 21220}, {7199, 148}, {7304, 41840}, {7307, 32937}, {7340, 4552}, {17206, 18666}, {18021, 329}, {24037, 190}, {24041, 46725}, {30940, 39367}, {34537, 3952}, {46254, 3732}, {52379, 144}, {52612, 513}, {52619, 21221}, {52935, 21225}
X(54112) = barycentric product X(i)*X(j) for these {i,j}: {75, 33792}, {76, 23374}
X(54112) = barycentric quotient X(i)/X(j) for these {i,j}: {23374, 6}, {33792, 1}
X(54112) = {X(8049),X(17135)}-harmonic conjugate of X(310)
X(54113) lies on these lines: {2, 1407}, {4, 29958}, {7, 18928}, {8, 12688}, {63, 2183}, {69, 189}, {144, 5739}, {222, 27539}, {223, 40880}, {321, 5942}, {534, 17781}, {651, 27540}, {664, 20211}, {908, 1997}, {1265, 52366}, {2390, 3436}, {2895, 30695}, {5658, 7360}, {5905, 6604}, {6223, 52346}, {6515, 17484}, {10327, 11678}, {12324, 52345}, {14361, 18026}, {17074, 28794}, {20554, 20557}, {21361, 36698}, {27509, 34048}, {30566, 37781}
X(54113) = isotomic conjugate of X(34546)
X(54113) = anticomplement of X(1407)
X(54113) = anticomplement of the isogonal conjugate of X(346)
X(54113) = isotomic conjugate of the anticomplement of X(6609)
X(54113) = isotomic conjugate of the isogonal conjugate of X(1604)
X(54113) = anticomplementary isogonal conjugate of X(4452)
X(54113) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 4452}, {2, 36845}, {6, 17480}, {8, 7}, {9, 145}, {19, 11851}, {21, 3875}, {31, 46716}, {33, 30699}, {55, 3210}, {75, 6604}, {78, 347}, {86, 17158}, {100, 4025}, {190, 3900}, {200, 2}, {210, 17778}, {220, 192}, {281, 12649}, {312, 3434}, {314, 20244}, {333, 3873}, {341, 69}, {345, 52365}, {346, 8}, {480, 3177}, {643, 4467}, {644, 522}, {646, 21302}, {657, 9263}, {668, 46402}, {728, 144}, {765, 664}, {1021, 17154}, {1043, 75}, {1098, 4360}, {1222, 39126}, {1253, 194}, {1257, 3668}, {1260, 6360}, {1261, 57}, {1265, 4329}, {1320, 1266}, {1792, 17134}, {1802, 3164}, {1897, 17896}, {2287, 1}, {2318, 18667}, {2321, 2475}, {2322, 3868}, {2327, 20222}, {2328, 17147}, {3119, 17036}, {3239, 149}, {3596, 21285}, {3680, 4373}, {3689, 30577}, {3692, 20}, {3693, 52164}, {3694, 3152}, {3699, 693}, {3701, 2893}, {3710, 2897}, {3900, 4440}, {3939, 17496}, {3965, 5484}, {4076, 21272}, {4082, 2895}, {4102, 20292}, {4110, 20350}, {4130, 39351}, {4163, 37781}, {4171, 148}, {4183, 3187}, {4397, 150}, {4420, 41808}, {4511, 41803}, {4515, 1654}, {4524, 21220}, {4578, 514}, {4607, 30704}, {4998, 35312}, {5423, 329}, {6061, 18662}, {6065, 4552}, {6555, 8055}, {6556, 21296}, {6558, 513}, {6559, 518}, {6602, 21218}, {6605, 3870}, {6726, 16018}, {6731, 7057}, {6735, 36918}, {7046, 5905}, {7058, 17140}, {7071, 21216}, {7079, 193}, {7080, 5932}, {7101, 4}, {7256, 7192}, {7257, 4374}, {7258, 512}, {7259, 523}, {8641, 21224}, {14427, 39349}, {14827, 17486}, {15742, 4566}, {23617, 36846}, {27398, 20221}, {27538, 20537}, {28071, 239}, {28659, 21280}, {30681, 52366}, {30693, 3436}, {31343, 3676}, {32008, 30628}, {32635, 3879}, {36802, 53357}, {36916, 12648}, {39959, 51351}, {40435, 16465}, {41798, 26015}, {44693, 41804}, {51562, 36038}, {52371, 37759}, {52406, 1370}, {52549, 14923}, {52622, 21293}, {52663, 38460}
X(54113) = X(i)-isoconjugate of X(j) for these (i,j): {31, 34546}, {604, 2123}
X(54113) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 34546}, {3161, 2123}
X(54113) = barycentric product X(i)*X(j) for these {i,j}: {76, 1604}, {2122, 3596}
X(54113) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 34546}, {8, 2123}, {1604, 6}, {2122, 56}, {6609, 1407}
X(54113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {189, 329, 312}, {651, 27540, 37669}, {908, 26871, 18141}, {5905, 11433, 6604}
X(54114) lies on the cubics K146 and K1010 and on these lines: {2, 9291}, {3, 3164}, {4, 14941}, {20, 39682}, {97, 46717}, {194, 17974}, {324, 34287}, {394, 401}, {458, 1073}, {1972, 40815}, {2052, 35061}, {3346, 43981}, {3682, 25252}, {3926, 44137}, {14376, 37337}, {18027, 35071}, {38256, 40896}
X(54114) = reflection of X(4) in X(46033)
X(54114) = isogonal conjugate of X(32445)
X(54114) = isotomic conjugate of X(3164)
X(54114) = polar conjugate of X(3168)
X(54114) = cyclocevian conjugate of X(44175)
X(54114) = anticomplement of the isotomic conjugate of X(40800)
X(54114) = isotomic conjugate of the anticomplement of X(264)
X(54114) = isotomic conjugate of the complement of X(40896)
X(54114) = isotomic conjugate of the isogonal conjugate of X(1988)
X(54114) = isotomic conjugate of the polar conjugate of X(43710)
X(54114) = polar conjugate of the isogonal conjugate of X(40800)
X(54114) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1988, 21270}, {40800, 6327}, {44828, 21300}
X(54114) = X(40800)-Ceva conjugate of X(2)
X(54114) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32445}, {19, 6638}, {31, 3164}, {48, 3168}, {1953, 26887}, {2148, 42453}
X(54114) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 3164}, {3, 32445}, {6, 6638}, {216, 42453}, {1249, 3168}
X(54114) = cevapoint of X(i) and X(j) for these (i,j): {2, 40896}, {525, 35071}, {1988, 40800}, {2799, 38974}
X(54114) = trilinear pole of line {520, 6130}
X(54114) = barycentric product X(i)*X(j) for these {i,j}: {69, 43710}, {76, 1988}, {264, 40800}, {850, 44828}
X(54114) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3164}, {3, 6638}, {4, 3168}, {5, 42453}, {6, 32445}, {54, 26887}, {1988, 6}, {40800, 3}, {43710, 4}, {44828, 110}
X(54115) lies on the Kiepert circumhyperbola and these lines: {2, 53463}, {4, 5615}, {13, 3181}, {17, 623}, {69, 5103}, {76, 34540}, {148, 627}, {193, 22235}, {194, 43538}, {298, 11122}, {302, 7783}, {621, 7793}, {626, 40706}, {3091, 43954}, {3180, 43542}, {3391, 33395}, {3392, 33393}, {3552, 11489}, {6658, 53441}, {7862, 11129}, {9886, 42063}, {16001, 16626}, {32961, 34541}, {32993, 40900}, {33477, 42062}, {37172, 43543}, {40693, 50211}, {43447, 47518}
X(54115) = isotomic conjugate of the anticomplement of X(302)
X(54115) = isotomic conjugate of the complement of X(40900)
X(54115) = X(619)-Dao conjugate of X(10616)
X(54115) = cevapoint of X(i) and X(j) for these (i,j): {2, 40900}, {115, 23872}
X(54115) = trilinear pole of line {523, 44384}
X(54115) = barycentric quotient X(395)/X(10616)
X(54116) lies on the Kiepert circumhyperbola and these lines: {2, 53452}, {4, 5611}, {14, 3180}, {18, 624}, {69, 5103}, {76, 34541}, {148, 628}, {193, 22237}, {194, 43539}, {299, 11121}, {303, 7783}, {622, 7793}, {626, 40707}, {3091, 43953}, {3181, 43543}, {3366, 33392}, {3367, 33394}, {3552, 11488}, {6658, 53429}, {7862, 11128}, {9885, 42062}, {16002, 16627}, {32961, 34540}, {32993, 40901}, {33476, 42063}, {37173, 43542}, {40694, 50212}, {43446, 47520}
X(54116) = isotomic conjugate of the anticomplement of X(303)
X(54116) = isotomic conjugate of the complement of X(40901)
X(54116) = X(618)-Dao conjugate of X(10617)
X(54116) = cevapoint of X(i) and X(j) for these (i,j): {2, 40901}, {115, 23873}
X(54116) = trilinear pole of line {523, 44385}
X(54116) = barycentric quotient X(396)/X(10617)
X(54117) lies on the circumconic {{A,.B,C, X(2),X(6)}}, the cubic K132, and these lines: {1, 9403}, {2, 34021}, {6, 2669}, {25, 16998}, {37, 1655}, {42, 894}, {75, 25054}, {111, 53631}, {192, 39926}, {193, 45966}, {194, 941}, {694, 18827}, {1400, 7176}, {1654, 30669}, {2054, 30667}, {2248, 33295}, {2998, 34284}, {3572, 16710}, {6625, 17493}, {6646, 21220}, {8033, 40729}, {8770, 16992}, {9263, 24437}, {25457, 39798}, {27318, 39956}, {37632, 39967}
X(54117) = isogonal conjugate of X(21779)
X(54117) = isotomic conjugate of X(1655)
X(54117) = anticomplement of X(34021)
X(54117) = isotomic conjugate of the anticomplement of X(274)
X(54117) = isotomic conjugate of the complement of X(40908)
X(54117) = isotomic conjugate of the isogonal conjugate of X(40770)
X(54117) = isogonal conjugate of the isotomic conjugate of X(43684)
X(54117) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {40737, 17137}, {40770, 17135}
X(54117) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21779}, {2, 18756}, {6, 1045}, {19, 23079}, {31, 1655}, {32, 51863}, {37, 51330}, {58, 21883}, {213, 39915}, {662, 9402}, {869, 40752}, {1918, 34021}, {7104, 27890}, {40728, 40743}
X(54117) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 1655}, {3, 21779}, {6, 23079}, {9, 1045}, {10, 21883}, {1084, 9402}, {6376, 51863}, {6626, 39915}, {32664, 18756}, {40589, 51330}
X(54117) = cevapoint of X(i) and X(j) for these (i,j): {2, 40908}, {513, 1084}, {514, 16592}, {650, 3023}
X(54117) = trilinear pole of line {512, 4369}
X(54117) = barycentric product X(i)*X(j) for these {i,j}: {1, 18298}, {6, 43684}, {75, 40737}, {76, 40770}, {523, 53631}, {18827, 39926}
X(54117) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1045}, {2, 1655}, {3, 23079}, {6, 21779}, {31, 18756}, {37, 21883}, {58, 51330}, {75, 51863}, {86, 39915}, {274, 34021}, {512, 9402}, {870, 40743}, {1909, 27890}, {14621, 40752}, {18298, 75}, {39926, 740}, {40737, 1}, {40770, 6}, {40778, 2276}, {43684, 76}, {53631, 99}
X(54117) = {X(37),X(46714)}-harmonic conjugate of X(1655)
X(54118) lies on these lines: {2, 40216}, {37, 16727}, {100, 17494}, {149, 14947}, {190, 4576}, {192, 13476}, {321, 16728}, {335, 3995}, {693, 26795}, {835, 43076}, {1025, 4552}, {1026, 3952}, {1897, 4238}, {2350, 17027}, {2481, 27190}, {3177, 44005}, {3939, 43190}, {4033, 42720}, {4080, 17244}, {4427, 4613}, {4554, 26985}, {4671, 25242}, {5701, 26846}, {6184, 23989}, {7192, 46148}, {17198, 22032}, {18359, 25244}, {23988, 27009}, {24484, 25049}, {25257, 46802}, {25264, 39698}, {27115, 30610}, {31100, 31125}, {31615, 51357}, {32041, 47869}
X(54118) = isogonal conjugate of X(21007)
X(54118) = isotomic conjugate of X(17494)
X(54118) = anticomplement of X(40619)
X(54118) = isotomic conjugate of the anticomplement of X(693)
X(54118) = isotomic conjugate of the complement of X(26824)
X(54118) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1252, 40007}, {23990, 16552}
X(54118) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21007}, {6, 4040}, {19, 22160}, {31, 17494}, {32, 20954}, {100, 38346}, {109, 38347}, {163, 2486}, {513, 4251}, {593, 21727}, {649, 1621}, {651, 38365}, {657, 38859}, {667, 17277}, {692, 17761}, {1333, 4151}, {1919, 17143}, {1980, 18152}, {2149, 42454}, {3294, 3733}, {8641, 33765}, {14004, 22383}, {27168, 34248}, {32739, 40619}
X(54118) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17494}, {3, 21007}, {6, 22160}, {9, 4040}, {11, 38347}, {37, 4151}, {115, 2486}, {650, 42454}, {1086, 17761}, {5375, 1621}, {6376, 20954}, {6631, 17277}, {8054, 38346}, {9296, 17143}, {32746, 27168}, {38991, 38365}, {39026, 4251}
X(54118) = cevapoint of X(i) and X(j) for these (i,j): {2, 26824}, {37, 514}, {39, 513}, {522, 1212}, {523, 16589}, {525, 18591}, {650, 3058}, {693, 40216}, {918, 6184}
X(54118) = trilinear pole of line {10, 141}
X(54118) = crossdifference of every pair of points on line {38346, 38365}
X(54118) = barycentric product X(i)*X(j) for these {i,j}: {10, 53649}, {100, 40216}, {190, 17758}, {313, 43076}, {668, 13476}, {1018, 40004}, {1978, 2350}, {3952, 39734}, {4033, 39950}
X(54118) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4040}, {2, 17494}, {3, 22160}, {6, 21007}, {10, 4151}, {11, 42454}, {75, 20954}, {100, 1621}, {101, 4251}, {190, 17277}, {194, 27168}, {514, 17761}, {523, 2486}, {649, 38346}, {650, 38347}, {658, 33765}, {663, 38365}, {668, 17143}, {693, 40619}, {756, 21727}, {934, 38859}, {1018, 3294}, {1897, 14004}, {1978, 18152}, {2350, 649}, {3699, 3996}, {3952, 4651}, {4033, 4043}, {4583, 40094}, {6386, 40088}, {13476, 513}, {14549, 46385}, {17494, 26846}, {17496, 26847}, {17758, 514}, {21859, 20616}, {39734, 7192}, {39950, 1019}, {40004, 7199}, {40216, 693}, {40521, 40607}, {43076, 58}, {53649, 86}
X(54118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 46725, 17494}, {693, 35310, 26795}, {4554, 27134, 26985}, {6184, 23989, 27072}
X(54119) lies on the Kiepert circumhyperbola and these lines: {2, 5110}, {4, 2651}, {8, 42066}, {10, 846}, {63, 148}, {76, 37653}, {81, 6625}, {98, 19642}, {115, 7058}, {226, 1943}, {312, 26081}, {321, 1654}, {1029, 16704}, {1947, 17950}, {2051, 32431}, {2895, 4080}, {2996, 14552}, {3896, 5086}, {4049, 21192}, {4362, 20558}, {4388, 11599}, {19734, 33030}, {21935, 26051}, {24789, 26147}, {26109, 30588}, {31290, 43669}, {40718, 40751}
X(54119) = isogonal conjugate of X(2305)
X(54119) = isotomic conjugate of X(17778)
X(54119) = anticomplement of X(40605)
X(54119) = polar conjugate of X(3144)
X(54119) = isotomic conjugate of the anticomplement of X(333)
X(54119) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1247, 20245}, {36934, 21286}
X(54119) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2305}, {6, 1046}, {31, 17778}, {48, 3144}, {1333, 3178}, {1402, 40605}, {1409, 2907}
X(54119) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17778}, {3, 2305}, {9, 1046}, {37, 3178}, {1249, 3144}
X(54119) = cevapoint of X(i) and X(j) for these (i,j): {6, 20836}, {115, 522}, {513, 16613}, {514, 17058}, {521, 16573}
X(54119) = trilinear pole of line {523, 8045}
X(54119) = barycentric product X(i)*X(j) for these {i,j}: {75, 1247}, {86, 36934}, {850, 53633}
X(54119) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1046}, {2, 17778}, {4, 3144}, {6, 2305}, {10, 3178}, {29, 2907}, {333, 40605}, {1247, 1}, {6740, 36927}, {36934, 10}, {53633, 110}
X(54120) lies on these lines: {8, 1757}, {85, 26806}, {257, 6646}, {312, 3765}, {333, 1931}, {1146, 6645}, {2170, 16044}, {3959, 6650}, {4518, 40794}, {4997, 5718}, {5252, 31359}, {5308, 38255}, {6557, 17316}, {10950, 14942}, {18031, 26541}, {21272, 33820}, {24247, 53675}, {24735, 30608}, {26223, 34527}, {28660, 52137}, {39351, 40845}, {42030, 50048}
X(54120) = isogonal conjugate of X(21008)
X(54120) = isotomic conjugate of X(6646)
X(54120) = isotomic conjugate of the anticomplement of X(894)
X(54120) = isotomic conjugate of the complement of X(31300)
X(54120) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21008}, {6, 17596}, {19, 22161}, {31, 6646}, {32, 20955}, {692, 21212}
X(54120) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6646}, {3, 21008}, {6, 22161}, {9, 17596}, {1086, 21212}, {6376, 20955}
X(54120) = cevapoint of X(i) and X(j) for these (i,j): {2, 31300}, {1146, 3907}, {3805, 53823}
X(54120) = trilinear pole of line {522, 4874}
X(54120) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17596}, {2, 6646}, {3, 22161}, {6, 21008}, {75, 20955}, {514, 21212}
X(54121) lies on these lines: {1, 2995}, {63, 53081}, {75, 3869}, {92, 18662}, {261, 2975}, {286, 40440}, {311, 313}, {321, 908}, {329, 34262}, {388, 8048}, {693, 41007}, {1441, 4357}, {2171, 4858}, {2517, 44412}, {2861, 53702}, {2997, 3875}, {3112, 11688}, {3436, 30479}, {3596, 11681}, {4360, 14616}, {5253, 31643}, {10447, 11682}, {17861, 40619}, {18698, 40216}, {20060, 52442}, {24220, 40624}, {30807, 49516}
X(54121) = isogonal conjugate of X(20986)
X(54121) = isotomic conjugate of X(2975)
X(54121) = isotomic conjugate of the anticomplement of X(12)
X(54121) = isotomic conjugate of the complement of X(20060)
X(54121) = isotomic conjugate of the isogonal conjugate of X(34434)
X(54121) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {60, 1764}, {20028, 2893}, {46880, 1330}, {52150, 17778}, {53083, 2475}
X(54121) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20986}, {6, 572}, {19, 22118}, {31, 2975}, {32, 14829}, {41, 17074}, {58, 52139}, {184, 11109}, {692, 21173}, {849, 14973}, {1169, 52087}, {1333, 21061}, {2149, 11998}, {2194, 37558}, {2206, 17751}, {4264, 34278}, {7115, 38344}, {8750, 23187}, {14586, 52322}, {17496, 32739}, {23990, 24237}
X(54121) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2975}, {3, 20986}, {6, 22118}, {9, 572}, {10, 52139}, {37, 21061}, {650, 11998}, {693, 26847}, {1086, 21173}, {1214, 37558}, {1577, 34589}, {2051, 23361}, {2092, 46879}, {3160, 17074}, {4075, 14973}, {6376, 14829}, {26932, 23187}, {40603, 17751}, {40619, 17496}, {40622, 51662}, {40628, 38344}
X(54121) = cevapoint of X(i) and X(j) for these (i,j): {2, 20060}, {523, 4858}, {525, 34588}, {6370, 46398}, {16732, 50330}
X(54121) = trilinear pole of line {1577, 3910}
X(54121) = barycentric product X(i)*X(j) for these {i,j}: {75, 2051}, {76, 34434}, {274, 51870}, {313, 53083}, {321, 20028}, {1228, 40453}, {1441, 46880}, {27801, 52150}
X(54121) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 572}, {2, 2975}, {3, 22118}, {6, 20986}, {7, 17074}, {10, 21061}, {11, 11998}, {37, 52139}, {75, 14829}, {92, 11109}, {226, 37558}, {321, 17751}, {514, 21173}, {594, 14973}, {693, 17496}, {905, 23187}, {960, 46879}, {1111, 24237}, {1441, 52358}, {2051, 1}, {2292, 52087}, {2618, 52322}, {4858, 34589}, {6354, 20617}, {6358, 52357}, {7004, 38344}, {7178, 51662}, {16732, 53566}, {20028, 81}, {20906, 27346}, {34267, 1610}, {34387, 40624}, {34434, 6}, {40453, 1169}, {40619, 26847}, {46880, 21}, {51870, 37}, {52150, 1333}, {53083, 58}, {53702, 32641}
X(54122) lies on the Kiepert circumhyperbola and these lines: {2, 12215}, {3, 46323}, {4, 385}, {69, 1916}, {76, 2549}, {83, 3767}, {98, 17008}, {148, 6194}, {193, 14484}, {194, 3399}, {262, 1352}, {376, 9302}, {459, 37187}, {598, 7615}, {671, 7811}, {2052, 17984}, {2996, 6655}, {3314, 40824}, {3407, 7735}, {3424, 37667}, {4019, 43534}, {5152, 9890}, {5304, 5395}, {5485, 32986}, {6392, 37336}, {7394, 30505}, {7612, 17004}, {7777, 14494}, {7783, 16043}, {7795, 10159}, {7828, 43527}, {7875, 18841}, {7897, 35005}, {8587, 23055}, {9740, 41895}, {9755, 37348}, {9770, 10484}, {10155, 17005}, {10302, 52691}, {11177, 32528}, {14492, 20423}, {16925, 38907}, {16987, 32957}, {16988, 32960}, {17006, 53103}, {18842, 32983}, {18845, 33018}, {33019, 38259}, {33279, 53105}, {37242, 47286}
X(54122) = isogonal conjugate of X(5017)
X(54122) = isotomic conjugate of X(7774)
X(54122) = anticomplement of X(51580)
X(54122) = isotomic conjugate of the anticomplement of X(183)
X(54122) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5017}, {31, 7774}, {662, 50550}, {3402, 51580}
X(54122) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 7774}, {3, 5017}, {1084, 50550}
X(54122) = cevapoint of X(115) and X(23878)
X(54122) = trilinear pole of line {523, 24284}
X(54122) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 7774}, {6, 5017}, {183, 51580}, {512, 50550}
X(54122) = {X(262),X(54106)}-harmonic conjugate of X(7774)
X(54123) lies on the circumconic {{A,B,C,X(1),X(2)}} and these lines: {1, 4899}, {8, 39954}, {28, 20009}, {57, 3208}, {81, 29585}, {88, 29583}, {105, 145}, {192, 279}, {330, 346}, {985, 37588}, {1022, 49277}, {1219, 17280}, {1390, 3622}, {1432, 51058}, {3672, 39724}, {3912, 8056}, {4462, 30694}, {15474, 30699}, {17776, 39696}, {25430, 26626}, {29573, 36603}, {29574, 39980}, {29579, 39963}
X(54123) = isogonal conjugate of X(16781)
X(54123) = isotomic conjugate of the anticomplement of X(344)
X(54123) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16781}, {6, 5272}, {58, 16605}
X(54123) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 16781}, {9, 5272}, {10, 16605}
X(54123) = cevapoint of X(i) and X(j) for these (i,j): {37, 4028}, {1015, 3309}
X(54123) = trilinear pole of line {513, 2977}
X(54123) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 5272}, {6, 16781}, {37, 16605}
X(54124) lies on the Jerabek circumhyperbola and these lines: {2, 248}, {3, 315}, {6, 297}, {66, 264}, {67, 44134}, {68, 76}, {69, 40073}, {70, 1235}, {71, 4150}, {72, 42703}, {83, 46765}, {184, 34405}, {265, 11185}, {290, 1899}, {311, 18124}, {316, 4846}, {327, 1352}, {340, 5486}, {491, 6413}, {492, 6414}, {850, 879}, {1176, 20022}, {1177, 52486}, {1987, 39931}, {5012, 44175}, {5504, 15920}, {5641, 11179}, {7768, 42021}, {7774, 22240}, {7792, 52251}, {8840, 43722}, {9723, 42407}, {9766, 35937}, {11003, 13485}, {11005, 34802}, {14498, 43448}, {15740, 32006}, {16774, 32000}, {16989, 43706}, {17040, 32001}, {18125, 44135}, {32002, 43726}, {32618, 44781}, {32619, 44780}, {34765, 35909}, {37190, 43711}
X(54124) = isogonal conjugate of X(3148)
X(54124) = isotomic conjugate of X(1352)
X(54124) = isotomic conjugate of the anticomplement of X(182)
X(54124) = isotomic conjugate of the complement of X(6776)
X(54124) = isotomic conjugate of the isogonal conjugate of X(3425)
X(54124) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3148}, {6, 16567}, {31, 1352}
X(54124) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 1352}, {3, 3148}, {9, 16567}
X(54124) = cevapoint of X(i) and X(j) for these (i,j): {2, 6776}, {125, 23878}
X(54124) = trilinear pole of line {647, 2799}
X(54124) = barycentric product X(76)*X(3425)
X(54124) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16567}, {2, 1352}, {6, 3148}, {3425, 6}
X(54125) lies on the Jerabek circumhyperbola and these lines: {1, 43693}, {2, 40602}, {3, 18134}, {6, 2907}, {8, 43708}, {65, 5174}, {71, 1761}, {72, 1330}, {73, 3152}, {286, 8044}, {349, 2893}, {2475, 52391}, {5764, 26131}, {7108, 24851}, {10693, 33650}, {17515, 34435}, {18123, 51978}, {38535, 52367}
X(54125) = isogonal conjugate of X(3145)
X(54125) = isotomic conjugate of X(2893)
X(54125) = anticomplement of X(40602)
X(54125) = polar conjugate of X(18679)
X(54125) = cyclocevian conjugate of X(92)
X(54125) = isotomic conjugate of the anticomplement of X(284)
X(54125) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3145}, {6, 1762}, {31, 2893}, {48, 18679}, {65, 40602}
X(54125) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2893}, {3, 3145}, {9, 1762}, {1249, 18679}
X(54125) = cevapoint of X(i) and X(j) for these (i,j): {125, 522}, {513, 8286}, {521, 34846}
X(54125) = trilinear pole of line {647, 4458}
X(54125) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1762}, {2, 2893}, {4, 18679}, {6, 3145}, {284, 40602}
X(54126) lies on the Kiepert circumhyperbola and these lines: {2, 53480}, {4, 43133}, {20, 14229}, {69, 7885}, {83, 13829}, {98, 26441}, {148, 488}, {193, 1131}, {385, 12322}, {485, 637}, {486, 11294}, {489, 17008}, {1270, 2996}, {1352, 14245}, {3069, 14035}, {3091, 45101}, {3128, 37892}, {3317, 11292}, {3406, 21737}, {5025, 5491}, {5395, 7586}, {5591, 33283}, {7612, 10851}, {7783, 32805}, {8781, 13653}, {12221, 14244}, {13759, 53101}, {14234, 45510}, {32820, 45472}, {32996, 53512}
X(54126) = isogonal conjugate of X(12968)
X(54126) = isotomic conjugate of the anticomplement of X(492)
X(54126) = X(1)-isoconjugate of X(12968)
X(54126) = X(3)-Dao conjugate of X(12968)
X(54126) = cevapoint of X(115) and X(54029)
X(54126) = trilinear pole of line {523, 44391}
X(54126) = barycentric quotient X(6)/X(12968)
X(54127) lies on the Kiepert circumhyperbola and these lines: {2, 53479}, {4, 43134}, {20, 14244}, {69, 7885}, {83, 13709}, {98, 8982}, {148, 487}, {193, 1132}, {385, 12323}, {485, 11293}, {486, 638}, {490, 17008}, {598, 31411}, {1271, 2996}, {1352, 14231}, {3068, 14035}, {3091, 45102}, {3127, 37892}, {3316, 11291}, {5025, 5490}, {5395, 7585}, {5590, 33283}, {7612, 10852}, {7783, 32806}, {8781, 13773}, {12221, 44368}, {12222, 14229}, {13639, 53101}, {14238, 45511}, {26620, 43536}, {32820, 45473}, {32996, 53515}
X(54127) = isogonal conjugate of X(12963)
X(54127) = isotomic conjugate of the anticomplement of X(491)
X(54127) = X(1)-isoconjugate of X(12963)
X(54127) = X(3)-Dao conjugate of X(12963)
X(54127) = cevapoint of X(115) and X(54028)
X(54127) = trilinear pole of line {523, 44390}
X(54127) = barycentric quotient X(6)/X(12963)
X(54128) lies on the cubics K998 and K1037, and also on these lines: {2, 52657}, {4, 7224}, {7, 1851}, {31, 3212}, {38, 41527}, {63, 194}, {69, 350}, {77, 614}, {81, 31905}, {561, 7155}, {1444, 5324}, {1814, 6654}, {1965, 7033}, {2162, 21138}, {3112, 24349}, {3271, 6063}, {4124, 33930}, {7035, 27538}, {7056, 7195}, {7226, 27807}, {24451, 40087}
X(54128) = isogonal conjugate of X(34247)
X(54128) = isotomic conjugate of X(32937)
X(54128) = anticomplement of X(52657)
X(54128) = isotomic conjugate of the anticomplement of X(982)
X(54128) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34247}, {2, 51949}, {6, 3501}, {31, 32937}, {32, 17786}, {42, 13588}, {100, 23655}, {101, 21348}, {163, 21958}, {662, 22229}, {692, 17072}, {1110, 23772}, {1783, 22443}, {2329, 51986}, {4551, 23864}, {4559, 21388}, {4876, 51956}, {8927, 51928}, {21438, 32739}, {39930, 51858}
X(54128) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 32937}, {3, 34247}, {9, 3501}, {115, 21958}, {514, 23772}, {1015, 21348}, {1084, 22229}, {1086, 17072}, {6376, 17786}, {8054, 23655}, {32664, 51949}, {39006, 22443}, {40592, 13588}, {40619, 21438}, {40625, 21300}, {41771, 51840}
X(54128) = cevapoint of X(i) and X(j) for these (i,j): {513, 21138}, {514, 3271}, {3808, 35119}, {3810, 26932}
X(54128) = trilinear pole of line {812, 905}
X(54128) = crossdifference of every pair of points on line {22229, 23655}
X(54128) = barycentric product X(i)*X(j) for these {i,j}: {75, 3500}, {7249, 39936}, {10030, 43748}, {17170, 30688}, {18033, 51995}
X(54128) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3501}, {2, 32937}, {6, 34247}, {31, 51949}, {75, 17786}, {81, 13588}, {512, 22229}, {513, 21348}, {514, 17072}, {523, 21958}, {649, 23655}, {693, 21438}, {982, 52657}, {1086, 23772}, {1428, 51956}, {1431, 51986}, {1447, 39930}, {1459, 22443}, {1473, 30689}, {3500, 1}, {3662, 51840}, {3737, 21388}, {4560, 21300}, {7167, 8927}, {7195, 28110}, {7252, 23864}, {18155, 21610}, {21138, 5518}, {23189, 23145}, {39914, 14199}, {39936, 7081}, {43748, 4876}, {51995, 7077}
X(54128) = {X(1965),X(18906)}-harmonic conjugate of X(32937)
X(54129) lies on the cubic K1000 and these lines: {2, 51948}, {4, 2998}, {69, 194}, {710, 6655}, {804, 2514}, {880, 7836}, {1031, 39953}, {1966, 18905}, {3926, 53147}, {4388, 9285}, {5207, 19566}, {7261, 19565}, {7779, 14946}, {7797, 41178}, {18904, 39044}, {20021, 40847}, {20022, 39939}, {33796, 40382}
X(54129) = anticomplement of the isogonal conjugate of X(14946)
X(54129) = anticomplement of the isotomic conjugate of X(51982)
X(54129) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {711, 38844}, {1967, 37889}, {9236, 8782}, {9288, 25332}, {14946, 8}, {40847, 21275}, {51982, 6327}
X(54129) = X(51982)-Ceva conjugate of X(2)
X(54129) = X(i)-isoconjugate of X(j) for these (i,j): {384, 1967}, {694, 1582}, {1581, 1915}, {1916, 1932}, {1925, 8789}, {1927, 9230}, {1965, 9468}, {41517, 51904}
X(54129) = X(i)-Dao conjugate of X(j) for these (i,j): {8290, 384}, {19576, 1915}, {39030, 1925}, {39031, 1932}, {39043, 1582}, {39044, 1965}, {41178, 782}, {53981, 12143}
X(54129) = cevapoint of X(804) and X(41178)
X(54129) = barycentric product X(i)*X(j) for these {i,j}: {385, 9229}, {695, 3978}, {1580, 9239}, {1926, 9288}, {1966, 9285}, {4027, 40847}, {12215, 37892}, {14603, 51948}
X(54129) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 384}, {695, 694}, {732, 4074}, {1580, 1582}, {1691, 1915}, {1926, 1925}, {1933, 1932}, {1966, 1965}, {3505, 3493}, {3978, 9230}, {4027, 16985}, {9229, 1916}, {9236, 1927}, {9239, 1934}, {9285, 1581}, {9288, 1967}, {12215, 37894}, {16985, 36432}, {41178, 35971}, {44089, 11380}, {51318, 51320}, {51903, 51904}, {51948, 9468}, {51982, 41517}
X(54130) lies on the cubic K1000 and these lines: {2, 3114}, {4, 147}, {6, 20027}, {69, 694}, {292, 7018}, {315, 42061}, {316, 51494}, {334, 893}, {733, 35567}, {805, 14712}, {1031, 14570}, {1581, 4645}, {2896, 8871}, {4496, 43262}, {5207, 19566}, {6655, 47648}, {7245, 43263}, {7736, 8842}, {7777, 45146}, {7779, 14970}, {7787, 8789}, {7791, 47642}, {17970, 20065}, {20021, 39939}, {38382, 45914}
on K1000
X(54130) = anticomplement of the isotomic conjugate of X(41517)
X(54130) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1927, 8782}, {1967, 25332}, {41517, 6327}
X(54130) = X(41517)-Ceva conjugate of X(2)
X(54130) = X(i)-isoconjugate of X(j) for these (i,j): {385, 9288}, {695, 1580}, {1691, 9285}, {1933, 9229}, {1966, 51948}, {3978, 9236}, {9239, 14602}, {51903, 51982}
X(54130) = X(i)-Dao conjugate of X(j) for these (i,j): {9467, 51948}, {35971, 804}, {37895, 385}, {39092, 695}
X(54130) = cevapoint of X(782) and X(35971)
X(54130) = barycentric product X(i)*X(j) for these {i,j}: {384, 1916}, {694, 9230}, {1581, 1965}, {1582, 1934}, {1915, 18896}, {1925, 1967}, {3493, 16101}, {4074, 14970}, {36432, 40847}
X(54130) = barycentric quotient X(i)/X(j) for these {i,j}: {384, 385}, {694, 695}, {1581, 9285}, {1582, 1580}, {1915, 1691}, {1916, 9229}, {1925, 1926}, {1927, 9236}, {1932, 1933}, {1934, 9239}, {1965, 1966}, {1967, 9288}, {3493, 3505}, {4074, 732}, {9230, 3978}, {9468, 51948}, {11380, 44089}, {16985, 4027}, {35971, 41178}, {36432, 16985}, {37894, 12215}, {41517, 51982}, {51320, 51318}, {51904, 51903}
X(54130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1916, 38947, 148}, {9468, 18896, 2}, {17493, 30669, 1581}
See Ivan Pavlov, euclid 5829.
X(54131) lies on these lines: {2, 1350}, {3, 5476}, {4, 524}, {5, 21358}, {6, 30}, {20, 51737}, {25, 5642}, {51, 31152}, {69, 3839}, {113, 5648}, {115, 11173}, {141, 3545}, {182, 3534}, {193, 50687}, {262, 42849}, {317, 42854}, {355, 50783}, {376, 597}, {381, 511}, {382, 576}, {383, 9763}, {403, 47556}, {428, 37672}, {515, 47356}, {518, 31162}, {541, 16010}, {542, 1351}, {547, 38136}, {549, 14561}, {550, 10541}, {551, 38035}, {575, 1657}, {578, 34726}, {631, 48310}, {946, 47358}, {1003, 47619}, {1080, 9761}, {1181, 34613}, {1352, 3845}, {1353, 33699}, {1386, 50811}, {1469, 11238}, {1482, 50790}, {1503, 1992}, {1513, 11184}, {1656, 52987}, {1853, 2781}, {1993, 9143}, {2777, 23048}, {2810, 10710}, {2854, 10706}, {2930, 5655}, {3056, 11237}, {3091, 21356}, {3094, 44422}, {3098, 5054}, {3146, 5032}, {3242, 3656}, {3416, 50796}, {3524, 3589}, {3564, 15687}, {3580, 31105}, {3618, 10304}, {3620, 50982}, {3629, 50974}, {3630, 50958}, {3631, 50960}, {3654, 38087}, {3655, 38315}, {3679, 38144}, {3751, 50865}, {3763, 5055}, {3818, 14269}, {3828, 38146}, {3843, 34507}, {3851, 40107}, {3860, 51189}, {4663, 41869}, {5017, 6034}, {5026, 12117}, {5028, 14537}, {5038, 44519}, {5050, 15681}, {5052, 11648}, {5064, 12294}, {5066, 48876}, {5071, 10519}, {5073, 11482}, {5092, 15688}, {5093, 15684}, {5094, 32225}, {5097, 48904}, {5104, 37637}, {5201, 32444}, {5446, 37473}, {5846, 34627}, {5847, 34648}, {5864, 37333}, {5865, 37332}, {5894, 15741}, {5895, 8549}, {5965, 35403}, {5969, 6054}, {6144, 18440}, {6173, 38143}, {6329, 50971}, {6623, 41585}, {6776, 8584}, {6800, 37901}, {6816, 52518}, {7464, 37827}, {7500, 17809}, {7530, 19596}, {7540, 36747}, {7610, 13860}, {7745, 10542}, {7778, 9993}, {7788, 18906}, {7840, 44434}, {7841, 22486}, {8537, 35490}, {8540, 12943}, {8541, 44438}, {8546, 37946}, {8593, 10723}, {8703, 18583}, {9024, 10711}, {9053, 34631}, {9530, 41145}, {9745, 13192}, {9752, 44401}, {9756, 22329}, {9760, 41070}, {9762, 41071}, {9830, 10753}, {9880, 11646}, {9969, 16072}, {9974, 35821}, {9975, 35820}, {9976, 38790}, {10056, 10387}, {10151, 47551}, {10295, 47544}, {10510, 51993}, {10606, 23327}, {10733, 41720}, {10989, 11002}, {11001, 44882}, {11008, 51215}, {11064, 26255}, {11164, 41137}, {11177, 14614}, {11216, 36201}, {11295, 51017}, {11296, 51019}, {11305, 51753}, {11306, 51754}, {11470, 12173}, {11898, 48889}, {12007, 14927}, {12017, 15689}, {12100, 38079}, {12101, 39884}, {12233, 34621}, {12571, 50787}, {12584, 25566}, {12953, 19369}, {13169, 32274}, {13321, 52989}, {13330, 44518}, {13352, 18374}, {13598, 50649}, {13857, 34417}, {14093, 17508}, {14136, 49947}, {14137, 49948}, {14492, 24256}, {14787, 37486}, {14810, 15693}, {14831, 34146}, {14881, 44453}, {14893, 34380}, {14912, 20583}, {15033, 19127}, {15107, 47596}, {15274, 37200}, {15303, 32233}, {15360, 37638}, {15516, 48896}, {15520, 29323}, {15683, 25406}, {15685, 48898}, {15690, 51732}, {15694, 38317}, {15695, 48885}, {15696, 20190}, {15702, 21167}, {15703, 25565}, {15706, 51137}, {15709, 50966}, {15710, 50969}, {15811, 31802}, {16475, 34628}, {16509, 40927}, {16981, 44555}, {17702, 34319}, {17800, 53092}, {17825, 43957}, {17845, 34117}, {18358, 23046}, {18579, 47453}, {18911, 47314}, {19106, 51203}, {19107, 51200}, {19149, 34603}, {19161, 21849}, {19709, 24206}, {19925, 50781}, {20080, 51214}, {22165, 41099}, {22234, 49137}, {22330, 49136}, {22491, 41016}, {22492, 41017}, {22579, 41023}, {22580, 41022}, {23698, 51798}, {25154, 33517}, {25164, 33518}, {25335, 32273}, {26958, 45311}, {28194, 47359}, {28204, 51000}, {30270, 33237}, {30273, 50779}, {30775, 47296}, {31489, 40248}, {32113, 47332}, {32216, 51360}, {32455, 39874}, {33749, 49134}, {34200, 38110}, {34573, 50970}, {35228, 37940}, {35259, 40112}, {35266, 37645}, {35707, 37925}, {35822, 36719}, {35823, 36733}, {36194, 46124}, {36969, 51207}, {36970, 51206}, {37077, 41614}, {37196, 44102}, {37459, 50571}, {37907, 48912}, {37984, 47473}, {38021, 51003}, {38023, 51705}, {38071, 50964}, {38073, 51151}, {38074, 50949}, {38147, 45310}, {39899, 48884}, {40330, 41106}, {40885, 47740}, {41038, 51483}, {41039, 51482}, {41447, 47454}, {42126, 44498}, {42127, 44497}, {43150, 50954}, {44265, 47581}, {44268, 51734}, {44280, 51742}, {44285, 51744}, {44961, 47448}, {46333, 50975}, {47031, 47457}, {47276, 47336}, {47280, 47309}, {47308, 47458}, {47333, 47455}, {47334, 47450}, {47598, 50980}, {47745, 50789}, {48879, 50664}, {48883, 51677}, {49481, 51044}, {49496, 51065}, {49509, 51038}, {49511, 50802}, {49524, 50810}, {49536, 51120}, {50818, 51147}, {50862, 51196}, {50864, 51192}, {50976, 51171}, {50992, 51537}, {51029, 51170}
X(54131) = midpoint of X(i) in X(j) for these {i,j}: {2, 51212}, {6, 51024}, {69, 51028}, {141, 51166}, {193, 51023}, {1351, 3830}, {1353, 33699}, {1992, 3543}, {3618, 51211}, {3629, 51022}, {3751, 50865}, {6144, 51027}, {6776, 15682}, {8584, 51163}, {8593, 10723}, {10733, 41720}, {11008, 51215}, {11477, 47353}, {12294, 21969}, {14927, 15640}, {15534, 36990}, {18440, 50962}, {20080, 51214}, {20423, 31670}, {32455, 51026}, {43273, 48910}, {44456, 50955}, {48884, 51140}, {49496, 51065}, {49536, 51120}, {50862, 51196}, {50864, 51192}, {51029, 51170}
X(54131) = reflection of X(i) in X(j) for these {i,j}: {2, 5480}, {3, 5476}, {6, 20423}, {20, 51737}, {69, 47354}, {141, 50959}, {193, 51132}, {376, 597}, {599, 381}, {1350, 2}, {1352, 3845}, {1853, 23049}, {2930, 5655}, {3094, 44422}, {3242, 3656}, {3416, 50796}, {3534, 182}, {3589, 51130}, {3620, 51129}, {3630, 50958}, {3631, 50960}, {3763, 50963}, {3830, 48901}, {5085, 14853}, {5648, 113}, {5655, 32271}, {6144, 50962}, {6776, 8584}, {8703, 18583}, {10295, 47544}, {10516, 53023}, {10606, 23327}, {11001, 44882}, {11646, 9880}, {12117, 5026}, {12584, 25566}, {13169, 32274}, {15069, 47353}, {15533, 1352}, {15534, 1351}, {15682, 51163}, {15685, 48898}, {15690, 51732}, {19161, 21849}, {20423, 21850}, {30273, 50779}, {31884, 14561}, {32113, 47332}, {32233, 15303}, {33706, 24256}, {33878, 50977}, {36990, 3830}, {39874, 51136}, {39884, 12101}, {39899, 51140}, {40341, 50955}, {43273, 6}, {44265, 47581}, {44268, 51734}, {44280, 51742}, {44285, 51744}, {46264, 50979}, {47031, 47457}, {47353, 4}, {47355, 51173}, {47358, 946}, {47473, 37984}, {48872, 3534}, {48873, 8703}, {48874, 12100}, {48876, 5066}, {48881, 50983}, {48905, 43273}, {48910, 51024}, {49509, 51038}, {49511, 50802}, {50781, 19925}, {50783, 355}, {50787, 12571}, {50789, 47745}, {50790, 1482}, {50810, 49524}, {50811, 1386}, {50818, 51147}, {50955, 3818}, {50962, 37517}, {50965, 3589}, {50966, 51126}, {50967, 141}, {50968, 3618}, {50970, 34573}, {50971, 6329}, {50973, 69}, {50974, 3629}, {50976, 51171}, {50977, 19130}, {50978, 18358}, {51024, 31670}, {51027, 18440}, {51044, 49481}, {51136, 32455}, {51179, 3630}, {51188, 11898}
X(54131) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2986), X(43273)}}, {{A, B, C, X(4846), X(5485)}}, {{A, B, C, X(14484), X(18575)}}
X(54131) = perspector of circumconic {{A,B,C, X(1302), X(36886)}}
X(54131) = reflection of the anticomplement of X(2) in the Hatzipolakis-Moses image of X(2)
X(54131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5480, 38072}, {3, 5476, 47352}, {4, 11477, 15069}, {4, 524, 47353}, {6, 30, 43273}, {6, 31670, 48910}, {6, 48910, 48905}, {6, 51024, 30}, {30, 20423, 6}, {30, 21850, 20423}, {30, 31670, 51024}, {30, 43273, 48905}, {30, 50979, 46264}, {30, 51024, 48910}, {69, 3839, 47354}, {141, 50959, 3545}, {182, 14848, 51185}, {193, 50687, 51023}, {376, 14853, 597}, {376, 597, 5085}, {381, 511, 599}, {381, 599, 10516}, {511, 53023, 10516}, {524, 47353, 15069}, {542, 1351, 15534}, {542, 3830, 36990}, {542, 48901, 3830}, {597, 29181, 376}, {599, 53023, 381}, {1350, 38072, 2}, {1351, 3830, 542}, {1351, 48901, 36990}, {1992, 3543, 1503}, {1992, 51538, 3543}, {2781, 23049, 1853}, {3589, 50965, 3524}, {3618, 10304, 50983}, {3818, 44456, 40341}, {3839, 51028, 69}, {5055, 33878, 50977}, {5055, 50963, 19130}, {5055, 50977, 3763}, {5071, 10519, 20582}, {5476, 19924, 3}, {5480, 51212, 1350}, {8703, 38064, 53094}, {10304, 48881, 50968}, {10653, 10654, 18907}, {11477, 47353, 524}, {13857, 34417, 47597}, {14269, 44456, 50955}, {14269, 50955, 3818}, {14853, 29181, 5085}, {15534, 36990, 542}, {18358, 23046, 50956}, {18440, 37517, 6144}, {18583, 48873, 53094}, {19130, 33878, 3763}, {19130, 50977, 5055}, {20423, 31670, 30}, {20423, 51024, 43273}, {21850, 31670, 6}, {23046, 50978, 18358}, {33878, 50963, 5055}, {37517, 38335, 51027}, {37517, 48895, 18440}, {38064, 48873, 8703}, {38079, 48874, 12100}, {38335, 50962, 18440}, {43273, 48910, 30}, {47354, 51028, 50973}, {48881, 50983, 10304}, {50959, 51166, 50967}
See Ivan Pavlov, euclid 5829.
X(54132) lies on these lines: {2, 51}, {3, 19661}, {4, 524}, {5, 21356}, {6, 376}, {20, 576}, {30, 1351}, {52, 18913}, {69, 381}, {114, 50639}, {141, 5071}, {146, 148}, {182, 10304}, {186, 47544}, {403, 47473}, {528, 10759}, {530, 44459}, {531, 44463}, {541, 895}, {543, 10753}, {544, 10758}, {547, 3619}, {548, 53092}, {549, 3618}, {550, 11482}, {575, 3522}, {597, 1350}, {599, 3545}, {611, 10385}, {631, 47352}, {944, 47356}, {1007, 51438}, {1352, 3839}, {1503, 15534}, {1513, 9770}, {2393, 5656}, {3090, 21358}, {3091, 11178}, {3098, 15053}, {3146, 11645}, {3292, 52301}, {3416, 38074}, {3523, 10168}, {3525, 48310}, {3528, 53093}, {3529, 8550}, {3534, 5093}, {3564, 3830}, {3589, 15702}, {3620, 19130}, {3629, 39874}, {3656, 50999}, {3751, 28194}, {3785, 37345}, {3817, 50787}, {3818, 20080}, {3832, 34507}, {3845, 34380}, {3860, 50957}, {3926, 48673}, {4232, 5642}, {4293, 8540}, {4294, 19369}, {4663, 6361}, {5050, 8703}, {5052, 7739}, {5054, 18583}, {5055, 48876}, {5056, 40107}, {5066, 50963}, {5085, 19708}, {5097, 48873}, {5102, 8584}, {5107, 7737}, {5182, 35927}, {5286, 13330}, {5477, 43618}, {5587, 50781}, {5603, 47358}, {5655, 14984}, {5864, 37172}, {5865, 37173}, {5878, 34788}, {5921, 48901}, {5965, 36324}, {5969, 32474}, {6193, 7540}, {6210, 48830}, {6329, 15715}, {6459, 9974}, {6460, 9975}, {6515, 31133}, {6770, 22580}, {6773, 22579}, {7426, 37645}, {7487, 11470}, {7519, 9143}, {7552, 43841}, {7714, 37672}, {7735, 11173}, {7757, 35439}, {8549, 12250}, {8586, 43453}, {8591, 12177}, {8593, 23698}, {9041, 34631}, {9140, 31099}, {9530, 10766}, {9737, 35287}, {9777, 43957}, {9880, 11161}, {9993, 37668}, {10295, 47545}, {10303, 25555}, {10516, 22165}, {10541, 21735}, {10605, 18919}, {10606, 23326}, {10653, 51207}, {10654, 51206}, {10982, 11821}, {10989, 37644}, {11004, 37901}, {11008, 15687}, {11148, 23235}, {11427, 44210}, {11433, 31152}, {11540, 50981}, {11898, 14269}, {11916, 12257}, {11917, 12256}, {12007, 46333}, {12017, 34200}, {12082, 32621}, {12101, 51174}, {12117, 18800}, {12150, 13355}, {12236, 44441}, {12243, 46034}, {12383, 34319}, {13142, 34725}, {13172, 51798}, {13639, 45511}, {13674, 36719}, {13759, 45510}, {13794, 36733}, {14449, 18281}, {14810, 15705}, {14881, 32828}, {14994, 32874}, {14995, 47076}, {15073, 34621}, {15303, 18533}, {15311, 17813}, {15520, 15697}, {15533, 41099}, {15577, 37939}, {15640, 29012}, {15681, 48906}, {15683, 46264}, {15684, 39899}, {15688, 48874}, {15693, 38110}, {15694, 38079}, {15698, 31884}, {15710, 53094}, {15759, 50987}, {15988, 31156}, {16200, 51089}, {16226, 52520}, {16279, 36163}, {16475, 51705}, {17504, 51732}, {17702, 41720}, {18553, 50689}, {18860, 37809}, {18906, 32836}, {18925, 34726}, {19136, 43574}, {19709, 38136}, {19766, 48936}, {19783, 48939}, {19905, 41135}, {20126, 25320}, {20190, 21734}, {20192, 40132}, {20583, 44882}, {21167, 50970}, {22112, 40911}, {22330, 50693}, {23234, 50567}, {25898, 50407}, {26255, 40112}, {26864, 47312}, {26869, 47311}, {28204, 51192}, {28538, 34627}, {28708, 44211}, {30769, 45311}, {30775, 44569}, {31105, 44555}, {31162, 39898}, {31400, 44453}, {32255, 48679}, {32455, 48905}, {32815, 39099}, {33187, 39141}, {33237, 40268}, {33699, 50986}, {34613, 34781}, {34628, 39870}, {34648, 39885}, {35260, 37904}, {35474, 40138}, {35908, 36890}, {36757, 42511}, {36758, 42510}, {37460, 44102}, {37643, 47097}, {37669, 44212}, {37907, 47581}, {37984, 47551}, {38021, 49511}, {38035, 51003}, {38073, 47595}, {38143, 51151}, {38144, 50949}, {38155, 50786}, {38335, 39884}, {38734, 41895}, {41149, 51136}, {41586, 52284}, {41614, 44413}, {42085, 51200}, {42086, 51203}, {43511, 44657}, {43512, 44656}, {44265, 52238}, {44654, 49039}, {44655, 49038}, {44704, 52282}, {47359, 50810}, {48857, 50600}, {50796, 50950}, {50802, 51004}, {50811, 51005}, {50818, 51000}, {50827, 50953}, {50862, 51197}, {50864, 51001}, {50865, 50952}, {50954, 50985}, {50968, 51138}, {50982, 50993}, {50989, 51129}, {50991, 51130}, {51027, 51187}, {51085, 51153}, {51087, 51146}, {52198, 52450}
X(54132) = midpoint of X(i) in X(j) for these {i,j}: {2, 51028}, {193, 3543}, {381, 44456}, {1992, 51212}, {3830, 50962}, {8584, 51166}, {15534, 51024}, {15682, 50974}, {15684, 39899}, {33699, 50986}, {50862, 51197}, {50864, 51001}, {50865, 50952}, {50992, 51214}, {51027, 51187}
X(54132) = reflection of X(i) in X(j) for these {i,j}: {2, 20423}, {20, 11179}, {69, 381}, {376, 6}, {381, 21850}, {599, 5480}, {944, 47356}, {1350, 597}, {1992, 1351}, {3534, 50979}, {3543, 31670}, {6770, 22580}, {6773, 22579}, {6776, 1992}, {7426, 47571}, {7757, 35439}, {8591, 12177}, {9143, 9970}, {10295, 47545}, {10519, 14853}, {10606, 23326}, {11001, 43273}, {11160, 1352}, {11161, 9880}, {11179, 576}, {11180, 4}, {12117, 18800}, {12383, 34319}, {13172, 51798}, {14912, 5102}, {15533, 47354}, {15534, 51132}, {15681, 48906}, {15682, 51024}, {15683, 46264}, {18440, 15687}, {22165, 50959}, {25406, 5093}, {32247, 9140}, {33878, 549}, {34628, 39870}, {36163, 16279}, {39885, 34648}, {39898, 31162}, {43273, 8584}, {44882, 20583}, {47551, 37984}, {50639, 114}, {50810, 47359}, {50811, 51005}, {50818, 51000}, {50950, 50796}, {50955, 3845}, {50966, 51185}, {50967, 2}, {50973, 22165}, {50974, 15534}, {50978, 5066}, {50989, 51129}, {50990, 50963}, {50991, 51130}, {50992, 50955}, {50994, 51173}, {50999, 3656}, {51004, 50802}, {51023, 3830}, {51136, 41149}, {51179, 15533}, {52987, 10168}
X(54132) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(182), X(15082)}}, {{A, B, C, X(262), X(44556)}}, {{A, B, C, X(263), X(3531)}}, {{A, B, C, X(290), X(50967)}}, {{A, B, C, X(373), X(40803)}}, {{A, B, C, X(5485), X(42313)}}
X(54132) = reflection of the anticomplement of X(6) in the Hatzipolakis-Moses image of X(6)
X(54132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20423, 14853}, {2, 50967, 10519}, {2, 51028, 511}, {2, 511, 50967}, {4, 524, 11180}, {20, 5032, 11179}, {30, 1351, 1992}, {30, 1992, 6776}, {141, 38072, 5071}, {193, 3543, 542}, {511, 14853, 10519}, {511, 20423, 2}, {542, 31670, 3543}, {549, 14848, 3618}, {576, 11179, 5032}, {576, 19924, 11179}, {597, 1350, 3524}, {599, 3545, 40330}, {599, 5480, 3545}, {1351, 51212, 6776}, {1353, 14927, 6776}, {1503, 15534, 50974}, {1503, 51024, 15682}, {1503, 51132, 15534}, {1992, 51212, 30}, {3098, 38064, 15692}, {3534, 25406, 50975}, {3534, 50979, 25406}, {3534, 51172, 5093}, {3564, 3830, 51023}, {3830, 50962, 3564}, {3839, 11160, 1352}, {3845, 34380, 50955}, {5085, 50965, 19708}, {5102, 43273, 8584}, {5102, 51166, 11001}, {8584, 29181, 43273}, {8584, 51166, 29181}, {10516, 50959, 41106}, {11001, 14912, 43273}, {11179, 19924, 20}, {14561, 50977, 2}, {14848, 33878, 549}, {14853, 50967, 2}, {15533, 53023, 47354}, {15534, 51024, 1503}, {15682, 50974, 1503}, {15698, 50966, 31884}, {19709, 51173, 38136}, {20423, 51028, 50967}, {21850, 44456, 69}, {22165, 50959, 10516}, {29181, 43273, 11001}, {31670, 37517, 193}, {31884, 50983, 15698}, {31884, 51185, 50983}, {33750, 50969, 8703}, {34380, 50955, 50992}, {47354, 53023, 41099}, {50962, 51023, 51178}, {50992, 51214, 34380}, {51023, 51538, 3830}, {51024, 51132, 50974}
See Ivan Pavlov, euclid 5829.
X(54133) lies on these lines: {7, 3428}, {55, 5762}, {144, 7680}, {517, 4312}, {528, 34617}, {2951, 37569}, {5696, 37625}, {5735, 15733}, {5759, 8255}, {5805, 42014}, {6361, 38454}, {6690, 21168}, {15096, 31671}, {31245, 38107}
X(54133) = reflection of X(i) in X(j) for these {i,j}: {144, 7680}, {3428, 7}, {5759, 8255}, {36999, 31671}, {42014, 5805}
X(54133) = reflection of the anticomplement of X(7) in the Hatzipolakis-Moses image of X(7)
See Ivan Pavlov, euclid 5829.
X(54134) lies on these lines: {4, 5854}, {8, 6909}, {56, 952}, {145, 7681}, {355, 2098}, {382, 517}, {944, 8256}, {1482, 12611}, {2829, 12531}, {3036, 10785}, {5790, 31246}, {6691, 7967}, {6737, 47745}, {8069, 37706}, {10085, 28204}, {10591, 38156}, {10711, 34710}, {11236, 50907}, {12666, 14923}, {18526, 32612}, {30323, 37712}, {31141, 50798}, {34627, 34706}, {35448, 51515}, {37705, 37821}, {37709, 50196}, {37714, 45035}, {40293, 41684}, {44784, 49163}
X(54134) = reflection of X(i) in X(j) for these {i,j}: {145, 7681}, {944, 8256}, {2098, 355}, {10310, 8}, {18526, 32612}, {31141, 50798}, {36972, 12645}, {37001, 18525}, {37821, 37705}
X(54134) = reflection of the anticomplement of X(8) in the Hatzipolakis-Moses image of X(8)
X(54134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 12645, 36972}, {517, 18525, 37001}, {3632, 5881, 14872}
See Ivan Pavlov, euclid 5829.
X(54135) lies on these lines: {1, 52684}, {4, 527}, {7, 7682}, {9, 1012}, {57, 971}, {80, 2093}, {84, 5729}, {142, 6969}, {517, 4915}, {999, 30330}, {1490, 10394}, {1532, 6173}, {1709, 41700}, {2951, 3359}, {3339, 6259}, {3452, 5785}, {4312, 41698}, {5220, 12705}, {5732, 6905}, {6692, 21151}, {6830, 38075}, {6844, 52457}, {6848, 43177}, {6930, 50836}, {6950, 21153}, {6968, 38150}, {7489, 37611}, {7956, 38036}, {7991, 34606}, {7992, 36279}, {8727, 30326}, {10388, 15298}, {12848, 36991}, {20196, 38108}, {37787, 52027}
X(54135) = midpoint of X(i) in X(j) for these {i,j}: {2093, 3062}, {12848, 36991}
X(54135) = reflection of X(i) in X(j) for these {i,j}: {7, 7682}, {2951, 3359}, {5732, 8257}, {6282, 9}, {36973, 5779}
X(54135) = reflection of the anticomplement of X(9) in the Hatzipolakis-Moses image of X(9)
X(54135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 5779, 36973}, {5732, 8257, 21164}
See Ivan Pavlov, euclid 5829.
X(54136) lies on these lines: {1, 7683}, {4, 758}, {8, 37456}, {10, 3430}, {58, 515}, {355, 511}, {382, 29097}, {1046, 5691}, {2792, 31673}, {2825, 12784}, {2842, 12368}, {3454, 5587}, {3576, 6693}, {4297, 8258}, {5252, 10544}, {7474, 24987}, {10974, 50037}, {12702, 29032}, {13442, 21677}, {15971, 47033}, {18391, 35650}, {18480, 37823}
X(54136) = midpoint of X(i) in X(j) for these {i,j}: {1046, 5691}
X(54136) = reflection of X(i) in X(j) for these {i,j}: {1, 7683}, {3430, 10}, {4297, 8258}, {36974, 355}, {37823, 18480}
X(54136) = reflection of the anticomplement of X(10) in the Hatzipolakis-Moses image of X(10)
X(54136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {355, 511, 36974}
See Ivan Pavlov, euclid 5829.
X(54137) lies on these lines: {4, 521}, {59, 5840}, {24466, 33562}, {34474, 40531}
X(54137) = reflection of the anticomplement of X(11) in the Hatzipolakis-Moses image of X(11)
See Ivan Pavlov, euclid 5829.
X(54138) lies on these lines: {2, 49939}, {3, 16267}, {4, 532}, {13, 14538}, {15, 5472}, {16, 37637}, {30, 22495}, {62, 5309}, {298, 5478}, {396, 5473}, {511, 13103}, {530, 1080}, {576, 41108}, {616, 7684}, {1351, 36970}, {3180, 44666}, {3543, 36327}, {3564, 36961}, {3830, 11477}, {5340, 14540}, {5463, 52266}, {5474, 6783}, {5615, 37835}, {5617, 41036}, {5864, 42813}, {5865, 42431}, {5984, 41023}, {6055, 22571}, {6774, 34755}, {11542, 21156}, {13102, 37517}, {14539, 42155}, {14541, 16965}, {16001, 42973}, {16629, 47066}, {22890, 42152}, {22997, 23698}, {23005, 51206}, {23006, 41406}, {25154, 50855}, {31670, 36962}, {36765, 52194}, {42158, 44250}, {43633, 47068}
X(54138) = reflection of X(i) in X(j) for these {i,j}: {15, 20425}, {298, 5478}, {616, 7684}, {5473, 396}, {5474, 6783}, {14538, 13}, {36969, 13103}, {50855, 25154}
X(54138) = reflection of the anticomplement of X(13) in the Hatzipolakis-Moses image of X(13)
X(54138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {396, 5473, 21158}, {511, 13103, 36969}
See Ivan Pavlov, euclid 5829.
X(54139) lies on these lines: {2, 49940}, {3, 16268}, {4, 533}, {14, 14539}, {15, 37637}, {16, 5471}, {30, 22496}, {61, 5309}, {299, 5479}, {383, 531}, {395, 5474}, {511, 13102}, {576, 41107}, {617, 7685}, {1351, 36969}, {3181, 44667}, {3543, 35749}, {3564, 36962}, {3830, 11477}, {5339, 14541}, {5464, 52263}, {5473, 6782}, {5611, 37832}, {5613, 41037}, {5864, 42432}, {5865, 42814}, {5984, 41022}, {6055, 22572}, {6771, 34754}, {11543, 21157}, {13103, 37517}, {14538, 42154}, {14540, 16964}, {16002, 42972}, {16628, 47068}, {16963, 44250}, {22843, 42149}, {22998, 23698}, {23004, 51207}, {23013, 41407}, {25164, 50858}, {31670, 36961}, {36329, 44219}, {43632, 47066}
X(54139) = reflection of X(i) in X(j) for these {i,j}: {16, 20426}, {299, 5479}, {617, 7685}, {5473, 6782}, {5474, 395}, {14539, 14}, {36329, 44219}, {36970, 13102}, {50858, 25164}
X(54139) = reflection of the anticomplement of X(14) in the Hatzipolakis-Moses image of X(14)
X(54139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {395, 5474, 21159}, {511, 13102, 36970}
See Ivan Pavlov, euclid 5829.
X(54140) lies on these lines: {3, 3412}, {4, 533}, {5, 21359}, {13, 511}, {14, 1351}, {15, 5473}, {16, 21843}, {17, 5864}, {30, 22495}, {61, 44465}, {62, 5306}, {298, 7684}, {381, 11477}, {383, 34509}, {396, 14538}, {397, 14541}, {524, 41016}, {532, 1080}, {621, 5478}, {634, 51753}, {1350, 42974}, {2080, 6779}, {3180, 41022}, {5092, 43030}, {5102, 42975}, {5463, 52650}, {5474, 9117}, {5611, 36967}, {5615, 16242}, {5858, 41040}, {5865, 16965}, {5965, 41024}, {6321, 25166}, {6771, 16960}, {6778, 13103}, {6780, 23698}, {7809, 51754}, {9733, 35731}, {9735, 42528}, {10653, 14539}, {11127, 44466}, {11486, 21157}, {12155, 35917}, {12817, 16002}, {14540, 40693}, {16808, 44456}, {16809, 20426}, {20416, 42507}, {20423, 50858}, {21158, 42912}, {22843, 42158}, {22890, 36836}, {33458, 41034}, {34380, 41036}, {36770, 52648}, {36776, 36784}, {41107, 44461}, {44223, 50860}, {48656, 48901}
X(54140) = reflection of X(i) in X(j) for these {i,j}: {13, 20425}, {298, 7684}, {621, 5478}, {5473, 15}, {5474, 9117}, {6779, 2080}, {14538, 396}, {19106, 13103}, {22493, 381}, {25166, 6321}, {36967, 5611}
X(54140) = reflection of the anticomplement of X(15) in the Hatzipolakis-Moses image of X(15)
X(54140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {298, 7684, 36765}, {396, 14538, 21156}, {511, 20425, 13}
See Ivan Pavlov, euclid 5829.
X(54141) lies on these lines: {3, 3411}, {4, 532}, {5, 21360}, {13, 1351}, {14, 511}, {15, 21843}, {16, 5474}, {18, 5865}, {30, 22496}, {61, 5306}, {62, 44461}, {299, 7685}, {381, 11477}, {383, 533}, {395, 14539}, {398, 14540}, {524, 41017}, {622, 5479}, {633, 51754}, {1080, 34508}, {1350, 42975}, {2080, 6780}, {3181, 41023}, {5092, 43031}, {5102, 42974}, {5464, 44223}, {5473, 9115}, {5611, 16241}, {5615, 36968}, {5859, 41041}, {5864, 16964}, {5965, 41025}, {6321, 25156}, {6774, 16961}, {6777, 13102}, {6779, 23698}, {7809, 51753}, {9736, 42529}, {10654, 14538}, {11126, 44462}, {11485, 21156}, {12154, 35918}, {12816, 16001}, {14541, 40694}, {16808, 20425}, {16809, 44456}, {20415, 42506}, {20423, 50855}, {21159, 42913}, {22843, 36843}, {22890, 42157}, {33459, 41035}, {34380, 41037}, {35731, 45489}, {36765, 51388}, {36776, 41071}, {41108, 44465}, {48655, 48901}, {50859, 52650}
X(54141) = reflection of X(i) in X(j) for these {i,j}: {14, 20426}, {299, 7685}, {622, 5479}, {5473, 9115}, {5474, 16}, {6780, 2080}, {14539, 395}, {19107, 13102}, {22494, 381}, {25156, 6321}, {36776, 41071}, {36968, 5615}
X(54141) = reflection of the anticomplement of X(16) in the Hatzipolakis-Moses image of X(16)
X(54141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 20426, 14}, {42157, 47066, 22890}
See Ivan Pavlov, euclid 5829.
X(54142) lies on these lines: {17, 14540}, {511, 16629}, {627, 5979}, {3627, 36962}, {7684, 44030}, {8259, 22890}, {22832, 44776}
X(54142) = reflection of X(i) in X(j) for these {i,j}: {627, 51753}, {14540, 17}, {22890, 8259}, {44776, 22832}
X(54142) = reflection of the anticomplement of X(17) in the Hatzipolakis-Moses image of X(17)
See Ivan Pavlov, euclid 5829.
X(54143) lies on these lines: {18, 14541}, {511, 16628}, {628, 5978}, {3627, 36961}, {7685, 44032}, {8260, 22843}, {22831, 44777}
X(54143) = reflection of X(i) in X(j) for these {i,j}: {628, 51754}, {14541, 18}, {22843, 8260}, {44777, 22831}
X(54143) = reflection of the anticomplement of X(18) in the Hatzipolakis-Moses image of X(18)
See Ivan Pavlov, euclid 5829.
X(54144) lies on these lines: {19, 18446}, {4329, 51755}, {21165, 30265}
X(54144) = reflection of X(i) in X(j) for these {i,j}: {4329, 51755}, {18446, 19}, {30265, 34176}
X(54144) = reflection of the anticomplement of X(19) in the Hatzipolakis-Moses image of X(19)
X(54144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30265, 34176, 21165}
See Ivan Pavlov, euclid 5829.
X(54145) lies on these lines: {21, 14110}, {30, 65}, {40, 37292}, {191, 517}, {354, 33858}, {382, 13126}, {758, 4301}, {942, 16132}, {1071, 47319}, {2475, 7686}, {2771, 7728}, {2778, 41723}, {3651, 8261}, {3901, 31162}, {3962, 22798}, {4311, 10122}, {5426, 31786}, {5887, 16160}, {5902, 16143}, {6001, 37433}, {6841, 44782}, {6912, 18259}, {7701, 37625}, {7957, 16139}, {10051, 13129}, {11551, 33668}, {13145, 41853}, {16117, 34339}, {16125, 17653}, {18242, 41550}, {22937, 37585}, {37308, 50371}
X(54145) = midpoint of X(i) in X(j) for these {i,j}: {7701, 37625}
X(54145) = reflection of X(i) in X(j) for these {i,j}: {1071, 47319}, {2475, 7686}, {3651, 8261}, {5887, 16160}, {7957, 16139}, {14110, 21}, {16117, 34339}, {16132, 942}, {17653, 16125}, {37585, 22937}, {44782, 6841}
X(54145) = reflection of the anticomplement of X(21) in the Hatzipolakis-Moses image of X(21)
See Ivan Pavlov, euclid 5829.
X(54146) lies on these lines: {22, 36989}, {30, 66}, {378, 34177}, {382, 34118}, {1352, 2781}, {1498, 15069}, {1503, 12083}, {1899, 5621}, {7391, 51756}, {11442, 36201}, {23041, 25337}, {34146, 44440}, {39571, 51739}, {49116, 49669}
X(54146) = reflection of X(i) in X(j) for these {i,j}: {378, 34177}, {7391, 51756}, {36989, 22}
X(54146) = reflection of the anticomplement of X(22) in the Hatzipolakis-Moses image of X(22)
See Ivan Pavlov, euclid 5829.
X(54147) lies on these lines: {4, 9019}, {23, 32233}, {30, 67}, {141, 35484}, {382, 19924}, {511, 7728}, {524, 14094}, {542, 37924}, {1350, 41583}, {1503, 15107}, {1533, 51941}, {5085, 32223}, {5189, 32274}, {7387, 10116}, {7464, 8262}, {8550, 52525}, {9971, 50008}, {10510, 11799}, {10516, 51360}, {10564, 47450}, {10620, 29012}, {10625, 18553}, {15035, 32218}, {15462, 25338}, {16010, 41586}, {16619, 18374}, {19596, 30714}, {25555, 45034}, {35001, 49116}, {37901, 52191}, {51739, 52300}
X(54147) = reflection of X(i) in X(j) for these {i,j}: {1350, 41583}, {5189, 32274}, {7464, 8262}, {10510, 11799}, {16010, 41586}, {32233, 23}, {35001, 49116}, {43576, 141}, {51941, 1533}
X(54147) = reflection of the anticomplement of X(23) in the Hatzipolakis-Moses image of X(23)
See Ivan Pavlov, euclid 5829.
X(54148) lies on these lines: {4, 45780}, {24, 12118}, {30, 64}, {235, 5654}, {3542, 5504}, {6193, 9143}, {6243, 7728}, {7517, 44665}, {9927, 10625}, {11413, 33563}, {11425, 16238}, {17702, 35471}, {18404, 23039}, {19467, 44259}, {21841, 51933}, {31815, 44271}, {37814, 39571}, {44232, 47391}
X(54148) = reflection of X(i) in X(j) for these {i,j}: {11413, 33563}, {12118, 24}, {37444, 9927}, {44752, 235}
X(54148) = reflection of the anticomplement of X(24) in the Hatzipolakis-Moses image of X(24)
X(54148) = reflection of the anticomplement of X(24) in the Hatzipolakis-Moses image of X(24)= {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {235, 44752, 5654}
See Ivan Pavlov, euclid 5829.
X(54149) lies on these lines: {4, 2393}, {25, 6776}, {30, 69}, {542, 6515}, {1352, 1370}, {1368, 40330}, {1495, 11179}, {1503, 10605}, {1596, 10602}, {1992, 18445}, {3542, 8549}, {3564, 18534}, {5050, 44233}, {5622, 6353}, {5921, 7500}, {6403, 41735}, {6644, 25406}, {6815, 43130}, {7530, 32358}, {7728, 14984}, {8263, 10519}, {10249, 35486}, {11487, 14791}, {11898, 44454}, {12244, 36201}, {12324, 37196}, {14157, 41719}, {14912, 19136}, {15069, 16655}, {18909, 37458}, {18928, 44212}, {20423, 51403}, {20987, 37951}, {25739, 36851}, {34621, 53021}, {35260, 40114}, {39898, 44662}, {44276, 51538}
X(54149) = midpoint of X(i) in X(j) for these {i,j}: {5921, 7500}, {11898, 44454}
X(54149) = reflection of X(i) in X(j) for these {i,j}: {1370, 1352}, {6776, 25}, {10602, 1596}, {10605, 41585}, {21312, 8263}
X(54149) = reflection of the anticomplement of X(25) in the Hatzipolakis-Moses image of X(25)
X(54149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1503, 41585, 10605}, {1596, 10602, 14853}, {8263, 21312, 10519}, {39871, 39879, 6776}
See Ivan Pavlov, euclid 5829.
X(54150) lies on these lines: {28, 1071}, {30, 72}, {5777, 52364}, {10167, 44220}, {12528, 31293}, {12672, 44661}, {18446, 20831}
X(54150) = midpoint of X(i) in X(j) for these {i,j}: {12528, 31293}
X(54150) = reflection of X(i) in X(j) for these {i,j}: {1071, 28}, {52364, 5777}
X(54150) = reflection of the anticomplement of X(28) in the Hatzipolakis-Moses image of X(28)
See Ivan Pavlov, euclid 5829.
X(54151) lies on these lines: {31, 30273}, {18805, 30269}, {29054, 49500}
X(54151) = reflection of X(i) in X(j) for these {i,j}: {30269, 18805}, {30273, 31}
X(54151) = reflection of the anticomplement of X(31) in the Hatzipolakis-Moses image of X(31)
See Ivan Pavlov, euclid 5829.
X(54152) lies on these lines: {4, 69}, {20, 35430}, {32, 11257}, {39, 9753}, {194, 35436}, {262, 1506}, {1513, 3095}, {2458, 3406}, {2782, 7754}, {3053, 38642}, {3096, 22677}, {5017, 39646}, {6309, 14981}, {6776, 35432}, {7470, 35387}, {7592, 42548}, {7709, 13357}, {7760, 35431}, {7810, 33706}, {7815, 18806}, {7906, 9772}, {7912, 22503}, {9744, 46305}, {10350, 35930}, {11171, 20576}, {12110, 43183}, {12203, 35424}, {13860, 49111}, {32451, 35389}, {36998, 46321}, {38383, 38743}
X(54152) = reflection of X(i) in X(j) for these {i,j}: {20, 35430}, {194, 35436}, {315, 6248}, {6776, 35432}, {11257, 32}, {30270, 18806}, {32451, 35389}, {36998, 46321}
X(54152) = reflection of the anticomplement of X(32) in the Hatzipolakis-Moses image of X(32)
X(54152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 6248, 315}, {18806, 30270, 22712}
See Ivan Pavlov, euclid 5829.
X(54153) lies on these lines: {30, 37733}, {35, 16113}, {79, 517}, {2475, 37625}, {3649, 11014}, {4301, 10698}, {5499, 5535}, {7982, 16159}, {11009, 16153}, {11012, 14526}, {13995, 31789}, {16118, 37826}, {16125, 52367}, {16154, 33596}, {33557, 49178}
X(54153) = reflection of X(i) in X(j) for these {i,j}: {11012, 14526}, {11014, 3649}, {16113, 35}, {52367, 16125}
X(54153) = reflection of the anticomplement of X(35) in the Hatzipolakis-Moses image of X(35)
See Ivan Pavlov, euclid 5829.
X(54154) lies on these lines: {1, 6842}, {3, 5441}, {4, 758}, {5, 47033}, {8, 13729}, {10, 6920}, {30, 1768}, {36, 10073}, {40, 1728}, {80, 517}, {140, 5426}, {191, 37290}, {200, 3419}, {355, 546}, {484, 5840}, {515, 13279}, {519, 1519}, {912, 41698}, {946, 5086}, {950, 10902}, {1210, 37561}, {1482, 10895}, {1532, 6326}, {1537, 5855}, {1737, 2077}, {1749, 7491}, {2095, 12943}, {2475, 31870}, {3576, 5722}, {3585, 24474}, {3679, 12703}, {4880, 52851}, {5046, 31806}, {5057, 24042}, {5080, 6246}, {5081, 15499}, {5172, 12743}, {5176, 28234}, {5252, 16200}, {5445, 26285}, {5534, 41709}, {5536, 5841}, {5538, 6882}, {5559, 10284}, {5691, 12704}, {5692, 6929}, {5697, 10953}, {5730, 10893}, {5794, 8227}, {5842, 12690}, {5881, 12629}, {5883, 6951}, {5884, 37437}, {5885, 47032}, {5902, 6923}, {5903, 10525}, {5904, 37821}, {6256, 12649}, {6850, 15016}, {6853, 35016}, {6863, 37571}, {6907, 33857}, {6909, 10265}, {6912, 48698}, {6937, 30143}, {6941, 22836}, {6958, 15079}, {6965, 10176}, {6980, 37701}, {7951, 37533}, {10483, 37532}, {10543, 52265}, {10572, 11012}, {10771, 36175}, {10826, 37531}, {10950, 11014}, {11248, 18395}, {11545, 51768}, {11827, 24468}, {12608, 41575}, {12619, 35000}, {12625, 17857}, {12700, 41687}, {14110, 17604}, {14988, 34789}, {15908, 37730}, {18513, 37826}, {18529, 37712}, {22765, 36975}, {35457, 51517}, {37735, 46920}
X(54154) = midpoint of X(i) in X(j) for these {i,j}: {4880, 52851}
X(54154) = reflection of X(i) in X(j) for these {i,j}: {40, 40663}, {2077, 1737}, {5057, 24042}, {5080, 6246}, {5538, 6882}, {6326, 1532}, {6909, 10265}, {12119, 36}, {16113, 1749}, {35000, 12619}, {36975, 22765}
X(54154) = reflection of the anticomplement of X(36) in the Hatzipolakis-Moses image of X(36)
X(54154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 49168, 5693}, {8, 13729, 20117}, {1532, 44669, 6326}, {5538, 37718, 6882}, {5884, 37437, 49178}
See Ivan Pavlov, euclid 5829.
X(54155) lies on these lines: {3, 12206}, {4, 732}, {5, 42006}, {20, 3095}, {39, 12122}, {76, 6249}, {83, 511}, {98, 41755}, {262, 6292}, {754, 13085}, {1916, 7762}, {5188, 9751}, {6287, 9866}, {6308, 37334}, {6704, 22712}, {7900, 22803}, {9821, 10359}, {10357, 11272}, {12836, 18983}, {12837, 13078}, {13111, 35930}, {22728, 48674}, {31168, 44422}
X(54155) = midpoint of X(i) in X(j) for these {i,j}: {13111, 48673}
X(54155) = reflection of X(i) in X(j) for these {i,j}: {76, 6249}, {5188, 51827}, {6287, 14881}, {9821, 49112}, {12122, 39}, {31168, 44422}, {32476, 3095}
X(54155) = reflection of the anticomplement of X(39) in the Hatzipolakis-Moses image of X(39)
X(54155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5188, 51827, 9751}
See Ivan Pavlov, euclid 5829.
X(54156) lies on these lines: {1, 104}, {3, 7971}, {4, 2093}, {9, 31788}, {10, 5811}, {40, 64}, {57, 12672}, {65, 10396}, {80, 52860}, {84, 517}, {165, 6261}, {392, 37526}, {515, 3529}, {516, 49168}, {518, 17649}, {758, 6769}, {912, 6765}, {936, 3359}, {944, 14646}, {946, 3339}, {952, 52116}, {960, 37560}, {962, 6245}, {971, 12702}, {997, 10270}, {1012, 3340}, {1071, 1697}, {1103, 45269}, {1482, 34862}, {1537, 50443}, {1698, 12608}, {1699, 10598}, {1706, 5777}, {1709, 5903}, {2096, 10106}, {2771, 5534}, {2818, 52117}, {2829, 5881}, {2956, 21147}, {3062, 31673}, {3149, 5128}, {3333, 45776}, {3358, 24474}, {3428, 12330}, {3555, 18238}, {3576, 19535}, {3577, 7285}, {3579, 52026}, {3679, 6256}, {3869, 6282}, {3885, 13243}, {3927, 31798}, {3928, 22770}, {3951, 6223}, {4018, 7982}, {4295, 5715}, {4312, 26332}, {4324, 37000}, {4853, 49171}, {4866, 38127}, {4882, 12666}, {5119, 15071}, {5223, 11362}, {5250, 8726}, {5603, 6705}, {5657, 6260}, {5690, 6259}, {5691, 41684}, {5697, 10085}, {5720, 40266}, {5729, 7686}, {5730, 17613}, {5768, 10624}, {5787, 28174}, {5790, 22792}, {5818, 30326}, {5837, 6916}, {5882, 9819}, {6736, 10309}, {6890, 51423}, {6909, 11682}, {7171, 12687}, {7330, 9623}, {7987, 40257}, {7997, 37714}, {8580, 20117}, {9589, 48482}, {9612, 10599}, {9709, 31821}, {9799, 9804}, {9841, 31786}, {9856, 36279}, {9942, 37551}, {9948, 28194}, {10268, 12520}, {10273, 37234}, {10306, 11523}, {10310, 18237}, {10582, 15016}, {10826, 34789}, {10857, 40249}, {10860, 14110}, {10980, 13464}, {11373, 13226}, {11496, 11529}, {11665, 52851}, {11822, 12457}, {11823, 12456}, {12514, 30503}, {12515, 45770}, {12528, 46685}, {12651, 37625}, {12675, 31393}, {12679, 40663}, {12688, 37567}, {12699, 33899}, {12700, 24392}, {13607, 30337}, {14988, 37531}, {17650, 41539}, {17706, 30330}, {18239, 34790}, {18260, 50190}, {18529, 31871}, {19067, 35775}, {19068, 35774}, {19861, 21164}, {21740, 30282}, {33597, 35445}, {35242, 37837}
X(54156) = midpoint of X(i) in X(j) for these {i,j}: {7991, 7992}, {9799, 20070}, {12245, 12246}
X(54156) = reflection of X(i) in X(j) for these {i,j}: {1, 1158}, {962, 6245}, {1482, 34862}, {1490, 40}, {3555, 18238}, {6259, 5690}, {6261, 40256}, {6765, 49163}, {7971, 3}, {7982, 12114}, {9589, 48482}, {11523, 10306}, {12650, 84}, {12667, 11362}, {12699, 33899}, {13253, 48695}, {18239, 34790}, {43166, 3358}
X(54156) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(104), X(44692)}}, {{A, B, C, X(318), X(52027)}}, {{A, B, C, X(1795), X(38271)}}, {{A, B, C, X(2184), X(34051)}}, {{A, B, C, X(3680), X(15501)}}
X(54156) = reflection of the anticomplement of X(40) in the Hatzipolakis-Moses image of X(40)
X(54156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1158, 52027}, {40, 5693, 200}, {40, 6001, 1490}, {84, 517, 12650}, {1158, 2800, 1}, {2093, 7995, 4}, {2800, 48695, 13253}, {7991, 7992, 515}, {12245, 12246, 515}
See Ivan Pavlov, euclid 5829.
X(54157) lies on circumconics {A,B,C,X(5),X(38006)}, {A,B,C,X(54),X(14128)} and on these lines: {3, 22051}, {4, 12175}, {5, 51}, {30, 195}, {54, 550}, {113, 16982}, {140, 12307}, {235, 6242}, {381, 12325}, {495, 6286}, {496, 7356}, {539, 15687}, {546, 2888}, {549, 7691}, {567, 10203}, {632, 30531}, {1141, 31674}, {1493, 15704}, {1595, 12300}, {1596, 6152}, {2914, 6240}, {2917, 37936}, {3519, 3858}, {3627, 7728}, {3845, 6288}, {3853, 11271}, {5446, 13368}, {5965, 21850}, {6247, 10628}, {6284, 35197}, {6689, 14869}, {6823, 12606}, {7354, 51803}, {7502, 32333}, {7574, 32165}, {8703, 10610}, {9833, 17824}, {9905, 28174}, {10066, 10386}, {10115, 43583}, {10263, 43893}, {10272, 30551}, {10677, 42117}, {10678, 42118}, {11539, 32348}, {11563, 14449}, {11566, 22750}, {11702, 34153}, {11804, 13371}, {11805, 22660}, {12160, 44288}, {12242, 15712}, {12785, 38138}, {12965, 42215}, {12971, 42216}, {13421, 43831}, {13431, 32340}, {13482, 18442}, {15134, 47341}, {15137, 38323}, {15760, 22815}, {16163, 47117}, {16625, 51391}, {18400, 44762}, {19150, 48906}, {19710, 20585}, {20584, 38071}, {22791, 31803}, {26879, 32339}, {27196, 46454}, {27246, 35729}, {31724, 36853}, {32273, 32365}, {32346, 34780}
X(54157) = midpoint of X(i) in X(j) for these {i,j}: {4, 12316}, {11271, 48675}, {13431, 32340}, {15800, 15801}
X(54157) = reflection of X(i) in X(j) for these {i,j}: {3, 22051}, {5, 20424}, {54, 11803}, {550, 54}, {1141, 31674}, {2888, 546}, {3627, 15800}, {7691, 8254}, {12307, 140}, {13368, 5446}, {16163, 47117}, {21230, 3574}, {32352, 44056}, {34153, 11702}, {35729, 27246}, {36966, 195}, {48675, 3853}, {48906, 19150}
X(54157) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(5), X(38006)}}, {{A, B, C, X(54), X(14128)}}
X(54157) = reflection of the anticomplement of X(54) in the Hatzipolakis-Moses image of X(54)
X(54157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 12316, 50708}, {30, 195, 36966}, {1154, 20424, 5}, {1154, 3574, 21230}, {1154, 44056, 32352}, {3574, 21230, 5}, {7691, 8254, 549}, {15800, 15801, 32423}, {15800, 32423, 3627}, {20424, 21230, 3574}
See Ivan Pavlov, euclid 5829.
X(54158) lies on these lines: {4, 15733}, {7, 517}, {55, 5759}, {390, 37533}, {516, 18446}, {528, 10698}, {553, 41338}, {3419, 38149}, {3428, 8255}, {3434, 5805}, {5119, 10059}, {5603, 52457}, {5696, 26332}, {5761, 8543}, {5762, 10679}, {5784, 10532}, {5817, 7680}, {6361, 38454}, {6827, 7671}, {6947, 10177}, {7982, 17647}, {11372, 28609}, {31140, 38073}
X(54158) = reflection of X(i) in X(j) for these {i,j}: {390, 37533}, {3428, 8255}, {3434, 5805}, {5759, 55}, {18446, 41570}, {36976, 10679}, {42014, 7680}
X(54158) = reflection of the anticomplement of X(55) in the Hatzipolakis-Moses image of X(55)
X(54158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 41570, 18446}, {3428, 8255, 21151}, {7680, 42014, 5817}
See Ivan Pavlov, euclid 5829.
X(54159) lies on these lines: {4, 527}, {9, 374}, {57, 5728}, {329, 1699}, {452, 7991}, {516, 2093}, {954, 7962}, {971, 2095}, {1006, 6282}, {1445, 6909}, {1708, 41166}, {1728, 12651}, {1750, 2801}, {2094, 30304}, {3421, 38154}, {4512, 7994}, {5785, 6843}, {6173, 6907}, {8226, 31142}, {9965, 36991}, {10399, 12565}, {24474, 52684}, {30223, 41712}, {30330, 43161}, {37421, 43177}, {37569, 47375}
X(54159) = midpoint of X(i) in X(j) for these {i,j}: {9965, 36991}
X(54159) = reflection of X(i) in X(j) for these {i,j}: {5732, 57}, {6282, 8257}, {52457, 7682}
X(54159) = reflection of the anticomplement of X(57) in the Hatzipolakis-Moses image of X(57)
X(54159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2093, 10398, 12848}, {6282, 8257, 21153}, {7682, 52457, 38150}
See Ivan Pavlov, euclid 5829.
X(54160) lies on these lines: {4, 17770}, {10, 511}, {58, 4297}, {387, 24728}, {516, 1046}, {540, 34648}, {758, 4301}, {1330, 19925}, {2392, 31849}, {2792, 51118}, {3430, 8258}, {3817, 7683}, {5691, 20077}, {36974, 38155}
X(54160) = midpoint of X(i) in X(j) for these {i,j}: {5691, 20077}
X(54160) = reflection of X(i) in X(j) for these {i,j}: {1330, 19925}, {3430, 8258}, {4297, 58}
X(54160) = reflection of the anticomplement of X(58) in the Hatzipolakis-Moses image of X(58)
X(54160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3430, 8258, 10164}
See Ivan Pavlov, euclid 5829.
X(54161) lies on these lines: {4, 758}, {21, 517}, {30, 9961}, {65, 3651}, {411, 33858}, {944, 39772}, {2476, 33592}, {2771, 4018}, {3486, 4302}, {3869, 6841}, {5086, 37230}, {5692, 6873}, {5818, 40661}, {5887, 52269}, {5902, 6876}, {6261, 16126}, {6852, 31806}, {6853, 26725}, {7098, 10058}, {7680, 21677}, {7686, 44782}, {8261, 14110}, {21740, 24474}, {31660, 37533}, {40266, 44258}
X(54161) = reflection of X(i) in X(j) for these {i,j}: {944, 39772}, {3651, 65}, {3869, 6841}, {14110, 8261}, {34195, 24474}, {40266, 44258}, {44782, 7686}
X(54161) = reflection of the anticomplement of X(65) in the Hatzipolakis-Moses image of X(65)
X(54161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8261, 14110, 21161}
See Ivan Pavlov, euclid 5829.
X(54162) lies on these lines: {4, 524}, {5, 22151}, {23, 542}, {30, 32247}, {67, 7464}, {69, 49669}, {186, 8262}, {323, 1352}, {399, 3564}, {511, 10296}, {1503, 12317}, {2071, 49116}, {3580, 6776}, {5921, 7519}, {5965, 32271}, {7527, 34507}, {7552, 8550}, {7565, 18553}, {10295, 47558}, {10510, 32274}, {10540, 27085}, {11064, 40330}, {11179, 52300}, {11645, 15054}, {12383, 32113}, {13169, 34802}, {13754, 41737}, {14118, 40107}, {17702, 41721}, {19510, 43574}, {25321, 47581}, {31861, 50955}, {44267, 48679}, {44961, 45016}
X(54162) = midpoint of X(i) in X(j) for these {i,j}: {5921, 37779}
X(54162) = reflection of X(i) in X(j) for these {i,j}: {323, 1352}, {6776, 3580}, {7464, 67}, {10295, 47558}, {10510, 32274}, {11061, 11799}, {12383, 32113}, {32233, 8262}, {48679, 44267}
X(54162) = reflection of the anticomplement of X(67) in the Hatzipolakis-Moses image of X(67)
X(54162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3564, 11799, 11061}
See Ivan Pavlov, euclid 5829.
X(54163) lies on these lines: {3, 22533}, {24, 41587}, {30, 11411}, {68, 11413}, {235, 6193}, {3167, 44235}, {3564, 31725}, {9927, 44752}, {9937, 44269}, {10733, 12111}, {12118, 15078}, {12164, 44271}, {12420, 47096}, {12421, 44440}, {14852, 31282}, {15316, 50435}, {18555, 41619}, {18913, 44240}
X(54163) = reflection of X(i) in X(j) for these {i,j}: {6193, 235}, {11413, 68}, {12118, 33563}, {12164, 44271}, {35490, 12293}, {44752, 9927}
X(54163) = reflection of the anticomplement of X(68) in the Hatzipolakis-Moses image of X(68)
X(54163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12118, 33563, 15078}
See Ivan Pavlov, euclid 5829.
X(54164) lies on these lines: {25, 3564}, {30, 5921}, {69, 21312}, {110, 47597}, {193, 1596}, {542, 10605}, {1352, 10602}, {1568, 17813}, {2393, 5562}, {5093, 46030}, {5094, 12827}, {5181, 10249}, {5654, 11405}, {6644, 18932}, {6677, 14912}, {6776, 8263}, {10733, 12133}, {11442, 31152}, {11443, 14848}, {14516, 37196}, {18534, 46442}, {20772, 32234}, {23293, 31255}, {33878, 40317}, {34966, 39588}, {39874, 44241}, {44212, 50974}, {44276, 44456}
X(54164) = reflection of X(i) in X(j) for these {i,j}: {193, 1596}, {6776, 8263}, {10602, 1352}, {21312, 69}, {31152, 50955}, {32234, 20772}, {39874, 44241}, {39899, 6644}, {44438, 18440}, {44456, 44276}, {50974, 44212}
X(54164) = reflection of the anticomplement of X(69) in the Hatzipolakis-Moses image of X(69)
X(54164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1352, 10602, 16072}, {14984, 18440, 44438}
See Ivan Pavlov, euclid 5829.
X(54165) lies on these lines: {31, 29010}, {75, 30269}, {18805, 30273}, {31134, 51040}
X(54165) = reflection of X(i) in X(j) for these {i,j}: {30269, 75}, {30273, 18805}, {31134, 51040}
X(54165) = reflection of the anticomplement of X(75) in the Hatzipolakis-Moses image of X(75)
See Ivan Pavlov, euclid 5829.
X(54166) lies on these lines: {4, 18768}, {32, 2782}, {39, 37071}, {76, 5999}, {194, 14981}, {382, 511}, {3095, 38743}, {6248, 32452}, {6680, 7709}, {7697, 7867}, {7754, 35386}, {7935, 52996}, {9873, 12251}, {11257, 18806}, {13355, 17130}, {35385, 39646}, {38737, 40923}
X(54166) = reflection of X(i) in X(j) for these {i,j}: {11257, 18806}, {30270, 76}, {32452, 6248}, {37004, 13108}
X(54166) = reflection of the anticomplement of X(76) in the Hatzipolakis-Moses image of X(76)
X(54166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 13108, 37004}
See Ivan Pavlov, euclid 5829.
X(54167) lies on these lines: {39, 550}, {83, 5188}, {511, 13111}, {6249, 44772}, {6287, 22682}, {12122, 21163}, {20088, 35437}, {29012, 35439}
X(54167) = reflection of X(i) in X(j) for these {i,j}: {5188, 83}, {12122, 51827}, {44772, 6249}
X(54167) = reflection of the anticomplement of X(83) in the Hatzipolakis-Moses image of X(83)
X(54167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12122, 51827, 21163}
See Ivan Pavlov, euclid 5829.
X(54168) lies on these lines: {4, 525}, {249, 23698}, {8754, 44769}, {12244, 51258}, {18331, 46982}
X(54168) = reflection of the anticomplement of X(115) in the Hatzipolakis-Moses image of X(115)
See Ivan Pavlov, euclid 5829.
X(54169) lies on these lines: {2, 1350}, {3, 524}, {4, 21358}, {5, 19924}, {6, 3524}, {20, 11164}, {30, 141}, {40, 47358}, {69, 10304}, {74, 5648}, {140, 5476}, {182, 8584}, {187, 20194}, {193, 15705}, {343, 9140}, {376, 599}, {378, 41585}, {381, 20582}, {395, 16940}, {396, 16941}, {511, 549}, {542, 8703}, {548, 34507}, {550, 11645}, {575, 15712}, {576, 3530}, {631, 47352}, {944, 50783}, {1351, 15693}, {1352, 3534}, {1353, 15711}, {1368, 45311}, {1386, 50828}, {1469, 4995}, {1619, 15577}, {1992, 5085}, {2393, 23328}, {2781, 3917}, {3056, 5298}, {3094, 5306}, {3242, 50810}, {3416, 50811}, {3522, 15069}, {3523, 11477}, {3543, 10516}, {3545, 3763}, {3564, 34200}, {3576, 47356}, {3589, 5054}, {3618, 15708}, {3619, 3839}, {3620, 48905}, {3629, 5092}, {3630, 45759}, {3631, 15688}, {3653, 51006}, {3654, 9041}, {3655, 5846}, {3815, 5104}, {3819, 44212}, {3830, 48873}, {3844, 50796}, {3845, 24206}, {4265, 21161}, {4297, 50781}, {5017, 9300}, {5032, 15717}, {5050, 15700}, {5055, 31670}, {5066, 48901}, {5071, 53023}, {5093, 15718}, {5097, 19711}, {5188, 8369}, {5447, 34351}, {5651, 37904}, {5893, 11821}, {5921, 50990}, {5965, 15714}, {5969, 6055}, {5989, 11177}, {6144, 51179}, {6194, 22329}, {6329, 15707}, {6393, 7811}, {6636, 9143}, {6696, 34787}, {6776, 15533}, {7426, 7998}, {7771, 51438}, {8359, 30270}, {8722, 27088}, {9019, 44218}, {9053, 34718}, {9756, 42850}, {9771, 37451}, {10007, 44422}, {10124, 38317}, {10299, 10541}, {10323, 15582}, {10989, 45303}, {11001, 36990}, {11064, 47596}, {11160, 25406}, {11168, 22712}, {11511, 16976}, {11539, 21850}, {11646, 12117}, {11694, 19140}, {11812, 18583}, {12007, 15534}, {12017, 15706}, {12061, 13348}, {12101, 48904}, {12245, 50790}, {12512, 50787}, {13169, 32233}, {13394, 33884}, {13567, 43957}, {13634, 17392}, {13635, 17330}, {14269, 50960}, {14538, 35303}, {14539, 35304}, {14540, 37341}, {14541, 37340}, {14561, 15694}, {14645, 46893}, {14848, 15701}, {14853, 15702}, {14869, 25555}, {14891, 17508}, {14912, 15715}, {14927, 15697}, {14929, 51397}, {15035, 34319}, {15051, 41720}, {15066, 35266}, {15360, 37648}, {15581, 37198}, {15585, 34778}, {15640, 51537}, {15682, 40330}, {15686, 29012}, {15687, 25561}, {15689, 18440}, {15690, 48898}, {15695, 41152}, {15699, 19130}, {15704, 18553}, {15709, 47355}, {15710, 40341}, {15713, 38079}, {15716, 41149}, {15722, 41153}, {15980, 20112}, {16789, 44285}, {17834, 45073}, {18579, 32217}, {19710, 39884}, {20190, 44682}, {21156, 22580}, {21157, 22579}, {21166, 51798}, {21969, 32191}, {22151, 50007}, {22677, 37461}, {23046, 48895}, {23332, 31152}, {25565, 38136}, {28194, 51003}, {28204, 50949}, {28538, 51705}, {29323, 44903}, {29959, 36987}, {30271, 51050}, {30273, 51051}, {30739, 32225}, {32216, 47296}, {33273, 47619}, {33699, 48889}, {34473, 50639}, {34774, 35228}, {36755, 51160}, {36756, 51159}, {37283, 37477}, {37480, 51739}, {37517, 41983}, {38065, 51195}, {38066, 50951}, {38335, 43621}, {39874, 50975}, {39899, 50961}, {40248, 44377}, {40884, 42313}, {41984, 42785}, {42786, 47478}, {44215, 52658}, {44580, 51732}, {47545, 51733}, {48892, 51134}, {49481, 51049}, {49509, 51044}, {49511, 50808}, {49524, 50821}, {50664, 50987}, {50824, 51147}, {50954, 51025}, {51010, 52193}, {51013, 52194}, {51127, 51130}, {51170, 51214}
X(54169) = midpoint of X(i) in X(j) for these {i,j}: {2, 1350}, {6, 50967}, {20, 47353}, {40, 47358}, {69, 43273}, {74, 5648}, {141, 50965}, {193, 50973}, {376, 599}, {944, 50783}, {1352, 3534}, {3094, 33706}, {3098, 50977}, {3242, 50810}, {3416, 50811}, {3589, 50970}, {3620, 50968}, {3630, 51136}, {3631, 50971}, {3763, 50966}, {3830, 48873}, {3845, 48874}, {4297, 50781}, {5476, 52987}, {6144, 51179}, {6776, 15533}, {8703, 48876}, {10519, 31884}, {11001, 36990}, {11646, 12117}, {12245, 50790}, {12512, 50787}, {13169, 32233}, {15682, 48872}, {16789, 44285}, {19710, 39884}, {20423, 33878}, {22165, 44882}, {29959, 36987}, {30271, 51050}, {30273, 51051}, {39874, 51027}, {39899, 50961}, {40341, 50974}, {46264, 50955}, {47354, 48881}, {48905, 51023}, {48906, 50978}, {49509, 51044}, {49511, 50808}
X(54169) = reflection of X(i) in X(j) for these {i,j}: {6, 50983}, {69, 50982}, {141, 50977}, {182, 12100}, {381, 20582}, {597, 549}, {1352, 50991}, {1386, 50828}, {3589, 50984}, {3629, 50979}, {3630, 50978}, {3845, 24206}, {5476, 140}, {5480, 2}, {6329, 51139}, {8550, 51737}, {8584, 182}, {8703, 14810}, {15534, 12007}, {15687, 25561}, {18440, 50958}, {18583, 11812}, {19140, 11694}, {19710, 48885}, {20423, 3589}, {21969, 32191}, {22165, 48876}, {31670, 50959}, {32217, 18579}, {32455, 51138}, {33699, 48889}, {33878, 50970}, {43621, 51026}, {44422, 10007}, {44882, 8703}, {46264, 50971}, {47354, 141}, {48881, 50965}, {48898, 15690}, {48901, 5066}, {48904, 12101}, {49481, 51049}, {49524, 50821}, {50796, 3844}, {50955, 3631}, {50959, 34573}, {50962, 32455}, {50965, 3098}, {50979, 5092}, {51022, 3818}, {51126, 50980}, {51128, 50981}, {51129, 3763}, {51130, 51127}, {51132, 6}, {51133, 3619}, {51136, 48906}, {51147, 50824}, {51163, 3845}, {51166, 21850}, {51732, 44580}, {51737, 3}
X(54169) = complement of X(54131)
X(54169) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(2373), X(51737)}}, {{A, B, C, X(5486), X(14484)}}, {{A, B, C, X(41443), X(43713)}}
X(54169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51212, 38072}, {3, 524, 51737}, {6, 3524, 50983}, {20, 21356, 47353}, {30, 141, 47354}, {30, 3098, 50965}, {30, 3818, 51022}, {30, 50965, 48881}, {30, 50977, 141}, {69, 10304, 43273}, {140, 5476, 48310}, {141, 3098, 48881}, {141, 50965, 30}, {376, 599, 1503}, {511, 549, 597}, {524, 51737, 8550}, {542, 14810, 8703}, {542, 48876, 22165}, {542, 8703, 44882}, {597, 21167, 549}, {599, 31884, 376}, {1992, 15692, 5085}, {3098, 50977, 30}, {3524, 50967, 6}, {3589, 50984, 5054}, {3763, 51024, 3545}, {5054, 20423, 3589}, {5054, 33878, 20423}, {5055, 31670, 50959}, {8703, 48876, 542}, {10519, 31884, 1503}, {14810, 48876, 44882}, {15688, 46264, 50971}, {15688, 50955, 46264}, {15706, 50962, 12017}, {15708, 51028, 3618}, {17504, 50979, 5092}, {20582, 29181, 381}, {22165, 44882, 542}, {24206, 48874, 51163}, {25561, 29317, 15687}, {33533, 47569, 141}, {34573, 50959, 5055}, {38335, 43621, 51026}, {43621, 50956, 38335}, {45759, 50978, 48906}, {47354, 48881, 30}, {50965, 50977, 47354}, {50967, 50983, 51132}, {50970, 50984, 20423}, {51202, 51205, 22165}
See Ivan Pavlov, euclid 5829.
X(54170) lies on circumconic {{A, B, C, X(14484), X(36889)}} and on these lines: {2, 1350}, {3, 19661}, {4, 7883}, {6, 10304}, {20, 524}, {30, 69}, {141, 3839}, {146, 5648}, {182, 13482}, {193, 43273}, {376, 511}, {381, 10519}, {518, 34632}, {542, 11001}, {549, 14853}, {575, 21735}, {576, 3528}, {597, 15692}, {599, 3543}, {631, 5476}, {962, 47358}, {1351, 8703}, {1352, 15682}, {1353, 15690}, {1370, 9140}, {1469, 10385}, {1503, 11160}, {2781, 9143}, {2794, 50639}, {2854, 37749}, {3091, 21358}, {3098, 3524}, {3146, 47353}, {3242, 50872}, {3416, 50864}, {3522, 5032}, {3523, 47352}, {3529, 11645}, {3534, 6776}, {3545, 3619}, {3564, 15681}, {3589, 15708}, {3620, 47354}, {3629, 50971}, {3630, 51027}, {3631, 51022}, {3751, 50808}, {3763, 50959}, {3830, 48876}, {3845, 40330}, {5050, 34200}, {5054, 21850}, {5059, 15069}, {5092, 15710}, {5093, 14093}, {5104, 7735}, {5188, 22486}, {5642, 37669}, {5691, 50781}, {5731, 47356}, {5847, 34628}, {5921, 15533}, {5969, 11177}, {6054, 32458}, {6090, 47312}, {6144, 51136}, {6194, 42850}, {6225, 34787}, {7710, 7840}, {7714, 12294}, {8550, 50693}, {8593, 38738}, {8722, 47061}, {9770, 37182}, {10303, 48310}, {11008, 46264}, {11147, 41137}, {11482, 33923}, {11531, 51089}, {11898, 15685}, {12017, 45759}, {12100, 14848}, {14532, 52229}, {14540, 37172}, {14541, 37173}, {14561, 15702}, {14645, 47102}, {14810, 15698}, {15107, 26255}, {15360, 37643}, {15534, 15697}, {15640, 22165}, {15686, 34380}, {15688, 44456}, {15689, 48906}, {15693, 18583}, {15699, 50963}, {15700, 38110}, {15701, 38079}, {15703, 38136}, {15705, 50983}, {15711, 51732}, {15721, 21167}, {15933, 24471}, {16051, 32225}, {16163, 41720}, {18358, 38335}, {18906, 33706}, {18919, 21663}, {18925, 37484}, {18928, 43957}, {18931, 37494}, {19876, 38146}, {20080, 48905}, {20582, 53023}, {20583, 33748}, {21734, 53093}, {21969, 52520}, {22151, 37483}, {24206, 41106}, {28194, 50999}, {28198, 39898}, {30270, 32985}, {30775, 51360}, {32216, 47582}, {32220, 47031}, {32455, 50972}, {33703, 34507}, {34379, 34638}, {34608, 41716}, {34803, 40248}, {35260, 40112}, {37952, 47544}, {39874, 46333}, {39899, 51178}, {40341, 51215}, {40884, 42287}, {41099, 48901}, {42090, 51200}, {42091, 51203}, {44280, 47545}, {44497, 52080}, {44498, 52079}, {46853, 53092}, {47333, 52238}, {47355, 50984}, {47599, 50981}, {48883, 50430}, {48892, 51140}, {48895, 50956}, {49496, 51042}, {49509, 51064}, {49511, 50865}, {49536, 50814}, {50787, 51118}, {50811, 51192}, {50815, 51196}, {50957, 51184}, {50958, 51216}, {50968, 51132}, {50980, 51173}, {50982, 51217}, {50991, 51163}, {51050, 51063}, {51126, 51130}
X(54170) = midpoint of X(i) in X(j) for these {i,j}: {11160, 15683}, {11898, 15685}, {14927, 50992}, {15533, 48872}, {39874, 51179}, {48905, 50973}
X(54170) = reflection of X(i) in X(j) for these {i,j}: {2, 1350}, {6, 50965}, {69, 50967}, {141, 50970}, {146, 5648}, {193, 43273}, {962, 47358}, {1351, 8703}, {1353, 15690}, {1992, 376}, {3146, 47353}, {3534, 48874}, {3543, 599}, {3618, 50966}, {3629, 50971}, {3751, 50808}, {3830, 48876}, {5691, 50781}, {5921, 15533}, {6144, 51136}, {6776, 3534}, {8593, 38738}, {11001, 48873}, {11008, 50974}, {11477, 51737}, {11531, 51089}, {14927, 11001}, {15534, 44882}, {15640, 36990}, {15682, 1352}, {18440, 50978}, {18906, 33706}, {20080, 50973}, {20423, 3098}, {21969, 52520}, {22486, 5188}, {31670, 50977}, {32220, 47031}, {32455, 50972}, {36990, 22165}, {41720, 16163}, {43273, 48881}, {44456, 50979}, {48910, 47354}, {49496, 51042}, {49536, 50814}, {50864, 3416}, {50865, 49511}, {50872, 3242}, {50962, 48906}, {50967, 33878}, {50974, 46264}, {51022, 3631}, {51023, 69}, {51024, 141}, {51027, 3630}, {51028, 6}, {51029, 3620}, {51063, 51050}, {51064, 49509}, {51118, 50787}, {51140, 48892}, {51163, 50991}, {51166, 3589}, {51170, 50968}, {51178, 39899}, {51192, 50811}, {51196, 50815}, {51211, 3763}, {51212, 2}, {51214, 193}, {51215, 40341}, {51538, 10519}
X(54170) = anticomplement of X(54131)
X(54170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 50965, 10304}, {30, 33878, 50967}, {30, 50967, 69}, {30, 50978, 18440}, {30, 69, 51023}, {141, 51024, 3839}, {376, 1992, 25406}, {376, 511, 1992}, {542, 11001, 14927}, {542, 48873, 11001}, {597, 31884, 15692}, {599, 29181, 3543}, {3098, 20423, 3524}, {3522, 5032, 51737}, {3524, 20423, 3618}, {3524, 50966, 3098}, {3545, 50977, 3619}, {3620, 50687, 47354}, {10304, 51028, 6}, {11160, 15683, 1503}, {11477, 51737, 5032}, {14810, 38064, 15698}, {14927, 50992, 542}, {15689, 48906, 50975}, {15705, 51171, 50983}, {31670, 50977, 3545}, {46333, 51179, 39874}, {47354, 48910, 50687}, {48910, 50687, 51029}
See Ivan Pavlov, euclid 5829.
X(54171) lies on these lines: {183, 3524}, {290, 50967}, {458, 1992}, {9740, 46806}
X(54171) = isotomic conjugate of X(54132)
X(54171) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(2), X(183)}}, {{A, B, C, X(4), X(3524)}}, {{A, B, C, X(69), X(671)}}, {{A, B, C, X(76), X(32836)}}, {{A, B, C, X(95), X(18842)}}, {{A, B, C, X(325), X(9740)}}, {{A, B, C, X(393), X(9302)}}, {{A, B, C, X(511), X(50967)}}, {{A, B, C, X(1494), X(5485)}}, {{A, B, C, X(2996), X(5641)}}, {{A, B, C, X(9154), X(43537)}}, {{A, B, C, X(9214), X(38664)}}, {{A, B, C, X(10519), X(20423)}}, {{A, B, C, X(14853), X(50977)}}, {{A, B, C, X(19222), X(52187)}}, {{A, B, C,
X(37665), X(37671)}}
See Ivan Pavlov, euclid 5829.
X(54172) lies on these lines: {182, 6090}, {183, 3524}, {1384, 1597}, {4232, 33971}, {9755, 11169}, {9756, 45819}
X(54172) = isogonal conjugate of X(54132)
X(54172) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(2), X(1597)}}, {{A, B, C, X(3), X(111)}}, {{A, B, C, X(6), X(95)}}, {{A, B, C, X(22), X(37935)}}, {{A, B, C, X(25), X(3431)}}, {{A, B, C, X(64), X(7607)}}, {{A, B, C, X(74), X(6090)}}, {{A, B, C, X(251), X(44731)}}, {{A, B, C, X(262), X(14490)}}, {{A, B, C, X(468), X(841)}}, {{A, B, C, X(842), X(8770)}}, {{A, B, C, X(1297), X(40103)}}, {{A, B, C, X(1350), X(38010)}}, {{A, B, C, X(1383), X(5481)}}, {{A, B, C, X(3424), X(3531)}}, {{A, B, C, X(3527), X(47586)}}, {{A, B, C, X(3532), X(14388)}}, {{A, B, C, X(3563), X(20421)}}, {{A, B, C, X(7608), X(22334)}}, {{A, B, C, X(11172), X(40802)}}, {{A, B, C, X(11738), X(53103)}}, {{A, B, C, X(13603), X(14494)}}, {{A, B, C, X(14483), X(39951)}}, {{A, B, C, X(14489), X(29180)}}, {{A, B, C, X(28193), X(39954)}}, {{A, B, C, X(52518), X(53100)}}
X(54172) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 3426}, {64, 11181}, {1383, 3424}
See Ivan Pavlov, euclid 5829.
X(54173) lies on these lines: {2, 51}, {3, 524}, {4, 7883}, {5, 21358}, {6, 549}, {20, 11180}, {26, 42021}, {30, 599}, {69, 74}, {98, 50639}, {140, 11477}, {141, 381}, {182, 1992}, {183, 51438}, {193, 5092}, {343, 31152}, {394, 44210}, {515, 50781}, {516, 50787}, {517, 47358}, {518, 3654}, {519, 24257}, {523, 21733}, {530, 44461}, {531, 44465}, {541, 5181}, {543, 19905}, {547, 3763}, {550, 15069}, {575, 3523}, {576, 631}, {597, 1351}, {611, 4995}, {613, 5298}, {754, 35387}, {952, 50783}, {1007, 51396}, {1316, 47585}, {1353, 17504}, {1385, 47356}, {1386, 3653}, {1469, 10056}, {1503, 3534}, {1511, 34319}, {1597, 41585}, {1641, 47570}, {2080, 37809}, {2393, 35704}, {2482, 8722}, {2549, 15993}, {2709, 2770}, {2781, 5655}, {2854, 20126}, {3056, 10072}, {3094, 7739}, {3146, 18553}, {3147, 11470}, {3313, 44441}, {3416, 28204}, {3525, 25555}, {3526, 48310}, {3530, 53093}, {3543, 3620}, {3545, 24206}, {3547, 15606}, {3564, 8703}, {3589, 14848}, {3618, 15702}, {3619, 5071}, {3629, 12017}, {3630, 14093}, {3631, 15681}, {3655, 28538}, {3656, 51003}, {3767, 32521}, {3815, 11173}, {3830, 29181}, {3839, 25561}, {3845, 10516}, {4550, 41583}, {5050, 8584}, {5055, 5480}, {5066, 50964}, {5085, 12100}, {5093, 15701}, {5097, 15708}, {5102, 11812}, {5104, 7737}, {5108, 14694}, {5171, 32985}, {5188, 7801}, {5447, 50649}, {5463, 14539}, {5464, 14538}, {5477, 8588}, {5642, 7493}, {5648, 5663}, {5651, 26255}, {5654, 44262}, {5844, 50790}, {5847, 51705}, {5864, 37341}, {5865, 37340}, {5907, 34621}, {5921, 48898}, {5965, 19708}, {5969, 11632}, {6031, 38940}, {6036, 23055}, {6054, 37182}, {6090, 35266}, {6101, 37473}, {6144, 14891}, {6393, 7788}, {6771, 22580}, {6774, 22579}, {6776, 10304}, {7426, 15066}, {7492, 9143}, {7615, 15980}, {7735, 43456}, {7795, 9821}, {7800, 37345}, {7803, 10357}, {7810, 30270}, {7840, 9744}, {8593, 21166}, {9019, 13340}, {9041, 34718}, {9140, 16063}, {9306, 32267}, {9540, 44502}, {9734, 47061}, {9735, 51012}, {9736, 51015}, {9737, 33215}, {9880, 19662}, {9939, 36998}, {9971, 13391}, {10109, 38136}, {10124, 38079}, {10193, 10250}, {10387, 15170}, {10510, 18580}, {10517, 44471}, {10518, 44472}, {10541, 15712}, {10627, 18281}, {10645, 51200}, {10646, 51203}, {10753, 41134}, {10754, 17008}, {11001, 29012}, {11007, 16279}, {11008, 15715}, {11161, 12117}, {11184, 37451}, {11202, 41719}, {11284, 20192}, {11482, 15720}, {11539, 18583}, {11646, 43619}, {11663, 15644}, {11694, 52697}, {11799, 47556}, {11850, 14530}, {11898, 15688}, {12007, 15706}, {12251, 52996}, {13330, 31401}, {13355, 14645}, {13564, 15582}, {13632, 48908}, {13633, 48875}, {13634, 17378}, {13635, 17346}, {13745, 19782}, {13935, 44501}, {14070, 37485}, {14216, 34787}, {14787, 37484}, {14912, 15698}, {14927, 48885}, {14994, 32836}, {15035, 41720}, {15040, 25329}, {15067, 44275}, {15073, 26937}, {15303, 15462}, {15448, 40912}, {15520, 51141}, {15577, 31166}, {15682, 29317}, {15683, 43150}, {15685, 41152}, {15686, 48905}, {15687, 18358}, {15690, 50968}, {15695, 50971}, {15697, 50969}, {15703, 34573}, {15707, 20583}, {15711, 50986}, {15713, 50981}, {15716, 51174}, {15717, 20190}, {15718, 32455}, {15719, 39561}, {15721, 46267}, {15722, 51139}, {15759, 50985}, {15919, 45662}, {16051, 45311}, {16187, 44833}, {16241, 51206}, {16242, 51207}, {16317, 46949}, {17811, 44212}, {18420, 51993}, {18911, 44555}, {19127, 22115}, {19145, 52045}, {19146, 52046}, {19709, 50959}, {19710, 51189}, {19711, 50987}, {22110, 40248}, {22151, 44493}, {23327, 44751}, {25563, 34788}, {26516, 44484}, {26521, 44483}, {26543, 44217}, {28146, 50792}, {28160, 50784}, {28164, 50788}, {28174, 50791}, {28186, 50785}, {28194, 49511}, {28224, 50782}, {28234, 51089}, {28236, 50786}, {28466, 36740}, {29010, 51051}, {29574, 46475}, {31133, 37636}, {31400, 44500}, {32216, 44569}, {32269, 47597}, {32424, 36883}, {33006, 38228}, {33750, 51178}, {33813, 51798}, {34148, 44491}, {34200, 40341}, {34628, 39885}, {34632, 39898}, {34817, 45088}, {35259, 37904}, {35383, 47102}, {35439, 44562}, {35474, 44134}, {35486, 44102}, {35925, 52994}, {35954, 39656}, {37172, 47068}, {37173, 47066}, {37188, 41145}, {37477, 51739}, {37483, 44218}, {37511, 45118}, {37638, 47097}, {37644, 41462}, {37668, 51397}, {37671, 51374}, {37950, 47276}, {38029, 50828}, {38065, 51150}, {38066, 49524}, {38115, 51002}, {38116, 47359}, {38118, 50829}, {38335, 51163}, {40112, 47596}, {41099, 51538}, {41149, 51138}, {41586, 46336}, {43652, 44470}, {44214, 47544}, {44266, 47450}, {44475, 45522}, {44476, 45523}, {44580, 50988}, {46333, 48896}, {48857, 50591}, {48889, 50687}, {48904, 51537}, {50664, 51170}, {50798, 50949}, {50805, 50998}, {50808, 51004}, {50810, 50999}, {50811, 50950}, {50824, 51000}, {50871, 51168}, {50954, 51022}, {50963, 51166}, {50975, 51215}, {51136, 51175}
X(54173) = midpoint of X(i) in X(j) for these {i,j}: {2, 50967}, {20, 11180}, {69, 376}, {98, 50639}, {381, 33878}, {599, 1350}, {3534, 50955}, {6776, 11160}, {8703, 50978}, {9143, 32247}, {11001, 51023}, {11161, 12117}, {11178, 52987}, {15533, 43273}, {15534, 50973}, {15681, 18440}, {22165, 50965}, {34628, 39885}, {34632, 39898}, {50808, 51004}, {50810, 50999}, {50811, 50950}, {50966, 50990}, {50968, 50989}, {50970, 50991}, {50974, 50992}
X(54173) = reflection of X(i) in X(j) for these {i,j}: {2, 50977}, {4, 11178}, {6, 549}, {376, 3098}, {381, 141}, {576, 10168}, {599, 48876}, {1351, 597}, {1352, 599}, {1992, 182}, {3534, 50965}, {3543, 3818}, {3656, 51003}, {3830, 47354}, {5050, 21167}, {5102, 38110}, {5480, 20582}, {7426, 47569}, {8584, 50983}, {9140, 49116}, {9143, 12584}, {9880, 19662}, {9970, 5642}, {10250, 10193}, {11178, 40107}, {11179, 3}, {11180, 34507}, {11799, 47556}, {12177, 2482}, {14912, 17508}, {15533, 50978}, {15534, 50979}, {15681, 48881}, {15683, 48880}, {15687, 18358}, {16279, 11007}, {20423, 2}, {21850, 547}, {22165, 50982}, {22579, 6774}, {22580, 6771}, {31166, 15577}, {31670, 381}, {31958, 22712}, {34319, 1511}, {35439, 44562}, {41149, 51138}, {41719, 11202}, {43273, 8703}, {43621, 3543}, {46264, 376}, {47354, 50991}, {47356, 1385}, {47359, 50821}, {48901, 25561}, {48905, 15686}, {48906, 34200}, {48910, 15687}, {50798, 50949}, {50805, 50998}, {50954, 51142}, {50955, 22165}, {50956, 50993}, {50958, 41152}, {50959, 51143}, {50961, 15533}, {50962, 8584}, {50964, 51186}, {50979, 12100}, {50993, 51184}, {51000, 50824}, {51005, 50828}, {51024, 3845}, {51185, 50980}, {51187, 50986}, {51188, 50985}, {51798, 33813}
X(54173) = complement of X(54132)
X(54173) = anticomplement of X(5476)
X(54173) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(30), X(14907)}}, {{A, B, C, X(74), X(263)}}, {{A, B, C, X(182), X(373)}}, {{A, B, C, X(262), X(1494)}}, {{A, B, C, X(290), X(20423)}}, {{A, B, C, X(2373), X(11179)}}, {{A, B, C, X(2770), X(53764)}}, {{A, B, C, X(7998), X(40803)}}, {{A, B, C, X(10302), X(42313)}}
X(54173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10519, 50977}, {2, 20423, 14561}, {2, 50967, 511}, {2, 51028, 14853}, {2, 511, 20423}, {3, 524, 11179}, {4, 21356, 11178}, {6, 549, 38064}, {20, 11180, 11645}, {30, 48876, 599}, {30, 599, 1352}, {69, 3098, 46264}, {69, 376, 542}, {141, 33878, 31670}, {376, 542, 46264}, {511, 22712, 31958}, {511, 50977, 2}, {542, 3098, 376}, {547, 21850, 38072}, {599, 1350, 30}, {616, 617, 14907}, {1350, 1352, 48873}, {1350, 36990, 48874}, {1350, 48876, 1352}, {1351, 5054, 597}, {1503, 22165, 50955}, {1503, 50965, 3534}, {1503, 50982, 22165}, {1992, 3524, 182}, {3534, 50955, 1503}, {3564, 15533, 50961}, {3564, 50978, 15533}, {3564, 8703, 43273}, {3631, 48881, 18440}, {3763, 38072, 547}, {3839, 40330, 25561}, {3845, 10516, 50956}, {5050, 50962, 8584}, {5066, 53023, 50964}, {5085, 15534, 50979}, {5085, 50973, 15534}, {5480, 20582, 5055}, {7998, 15360, 2}, {8584, 50983, 5050}, {8703, 50978, 3564}, {10124, 38079, 47355}, {10304, 11160, 6776}, {10516, 51024, 3845}, {10519, 50967, 2}, {11001, 51023, 29012}, {11178, 19924, 4}, {11178, 40107, 21356}, {11178, 52987, 19924}, {11645, 34507, 11180}, {12100, 34380, 50979}, {12100, 50979, 5085}, {14848, 15694, 3589}, {15533, 31884, 43273}, {15533, 43273, 3564}, {15534, 50973, 34380}, {15693, 50962, 5050}, {15694, 44456, 14848}, {15698, 51179, 14912}, {15719, 51214, 39561}, {19708, 50974, 25406}, {19924, 40107, 11178}, {21167, 50983, 15693}, {22165, 50965, 1503}, {25406, 50992, 50974}, {25561, 48901, 3839}, {29181, 47354, 3830}, {29181, 50991, 47354}, {31884, 43273, 8703}, {34380, 50979, 15534}, {38110, 50980, 11812}, {39874, 48892, 46264}, {40107, 52987, 4}, {43273, 50978, 50961}, {50828, 51005, 38029}, {50965, 50982, 50955}, {50966, 50990, 29012}, {50967, 50977, 20423}, {50970, 50991, 29181}, {50974, 50992, 5965}, {50993, 51024, 10516}, {51010, 51013, 69}
See Ivan Pavlov, euclid 5829.
X(54174) lies on these lines: {2, 51}, {3, 5032}, {6, 9542}, {20, 524}, {30, 5921}, {69, 3543}, {147, 50639}, {182, 15705}, {193, 376}, {381, 3620}, {542, 15683}, {549, 44456}, {576, 15717}, {597, 15708}, {599, 3839}, {1350, 1992}, {1351, 3524}, {1352, 50687}, {1353, 15688}, {1503, 50973}, {1699, 50787}, {3091, 21356}, {3098, 51170}, {3146, 11180}, {3522, 11179}, {3523, 11477}, {3534, 34380}, {3545, 48876}, {3564, 11001}, {3618, 15721}, {3619, 38072}, {3830, 50978}, {3832, 11178}, {5050, 15698}, {5056, 21358}, {5059, 11645}, {5068, 40107}, {5071, 21850}, {5085, 51132}, {5093, 12100}, {5102, 50983}, {5999, 9740}, {6776, 48885}, {7809, 10008}, {8359, 40268}, {8584, 31884}, {8703, 14912}, {9737, 11155}, {10109, 51173}, {10299, 11482}, {10303, 47352}, {10516, 50982}, {10753, 52695}, {11008, 48881}, {11173, 37665}, {11412, 34621}, {12017, 15715}, {12101, 50954}, {14848, 15702}, {15069, 49135}, {15078, 37491}, {15531, 36987}, {15533, 15640}, {15534, 25406}, {15681, 39874}, {15682, 50955}, {15685, 51175}, {15686, 39899}, {15690, 50986}, {15697, 43273}, {15701, 51172}, {15707, 51732}, {15709, 18583}, {15716, 50987}, {17504, 53091}, {17578, 34507}, {18906, 32874}, {19708, 50979}, {20583, 53094}, {21167, 51185}, {22165, 51024}, {29012, 50961}, {33751, 35418}, {34638, 39878}, {35513, 44750}, {37483, 37784}, {37488, 37941}, {37517, 38064}, {37668, 51438}, {37712, 50786}, {37907, 47468}, {37952, 47545}, {44280, 47541}, {47354, 50990}, {50801, 51168}, {50808, 50952}, {50811, 51001}, {50815, 51197}, {50864, 50950}, {50865, 51004}, {50872, 50999}, {50958, 50989}, {50959, 50993}, {50960, 51142}, {50969, 51140}, {50991, 51131}, {51077, 51193}, {51136, 51187}, {51174, 51176}
X(54174) = midpoint of X(i) in X(j) for these {i,j}: {11001, 51179}, {15683, 20080}, {15685, 51175}
X(54174) = reflection of X(i) in X(j) for these {i,j}: {2, 50967}, {147, 50639}, {193, 376}, {376, 33878}, {1992, 1350}, {3146, 11180}, {3543, 69}, {3830, 50978}, {5921, 11160}, {8584, 50970}, {11179, 52987}, {15531, 36987}, {15534, 50965}, {15640, 51023}, {15682, 50955}, {39874, 15681}, {39878, 34638}, {39899, 15686}, {44456, 549}, {50864, 50950}, {50865, 51004}, {50872, 50999}, {50952, 50808}, {50962, 8703}, {50974, 3534}, {50986, 15690}, {50992, 50973}, {51001, 50811}, {51023, 15533}, {51024, 22165}, {51028, 2}, {51029, 50989}, {51166, 50991}, {51187, 51136}, {51197, 50815}, {51211, 50990}, {51212, 599}, {51214, 15534}, {51215, 50992}
X(54174) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(182), X(12045)}}, {{A, B, C, X(263), X(14490)}}, {{A, B, C, X(290), X(51028)}}, {{A, B, C, X(15082), X(40803)}}
X(54174) = anticomplement of X(54132)
X(54174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 511, 51028}, {30, 11160, 5921}, {511, 50967, 2}, {599, 51212, 3839}, {1350, 1992, 10304}, {1503, 50973, 50992}, {1503, 50992, 51215}, {3534, 34380, 50974}, {8584, 50970, 31884}, {8703, 50962, 14912}, {10519, 20423, 2}, {11001, 51179, 3564}, {11180, 19924, 3146}, {14853, 50977, 2}, {14912, 50966, 8703}, {15533, 29181, 51023}, {15683, 20080, 542}, {25406, 51214, 15534}, {29181, 51023, 15640}, {50990, 51538, 47354}, {50991, 51166, 53023}
See Ivan Pavlov, euclid 5829.
X(54175) lies on these lines: {9, 7680}, {55, 21168}, {144, 3428}, {517, 51090}, {528, 19914}, {2886, 5762}, {4973, 31657}, {5759, 5842}, {8255, 31658}, {12699, 38454}
X(54175) = midpoint of X(i) in X(j) for these {i,j}: {144, 3428}, {5759, 42014}
X(54175) = reflection of X(i) in X(j) for these {i,j}: {7680, 9}, {8255, 31658}
X(54175) = complement of X(54133)
X(54175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5759, 42014, 5842}
See Ivan Pavlov, euclid 5829.
X(54176) lies on these lines: {1, 1532}, {3, 5854}, {8, 20418}, {46, 7966}, {56, 6942}, {145, 10310}, {355, 3847}, {517, 550}, {529, 4930}, {944, 1317}, {952, 1329}, {1385, 8256}, {3036, 26492}, {3811, 37727}, {3813, 12737}, {5690, 11715}, {6691, 10246}, {6738, 13607}, {7686, 16215}, {11567, 32213}, {12645, 33559}, {12735, 40257}, {18526, 37821}, {31141, 50818}
X(54176) = midpoint of X(i) in X(j) for these {i,j}: {145, 10310}, {944, 2098}, {18526, 37821}, {31141, 50818}
X(54176) = reflection of X(i) in X(j) for these {i,j}: {7681, 1}, {7686, 16215}, {8256, 1385}, {12645, 33559}, {24928, 13607}
X(54176) = complement of X(54134)
X(54176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {944, 2098, 2829}, {3244, 5882, 12675}
See Ivan Pavlov, euclid 5829.
X(54177) lies on these lines: {20, 5854}, {145, 12667}, {517, 3529}, {519, 10085}, {952, 3436}, {2098, 5225}, {3621, 10310}, {3623, 7681}, {12245, 12515}, {12704, 36977}, {18526, 37002}, {25416, 52683}, {28236, 30323}
X(54177) = reflection of X(i) in X(j) for these {i,j}: {3621, 10310}, {37002, 18526}
X(54177) = anticomplement of X(54134)
See Ivan Pavlov, euclid 5829.
X(54178) lies on these lines: {3, 527}, {7, 6282}, {57, 21151}, {142, 6907}, {214, 38759}, {516, 6948}, {517, 5542}, {971, 3452}, {3359, 43151}, {5732, 6987}, {5784, 6245}, {5817, 20196}, {6173, 6916}, {6692, 38122}, {6700, 52684}, {6954, 8257}, {7962, 35514}, {12848, 21164}, {30503, 41570}, {31142, 41561}, {36973, 36996}
X(54178) = midpoint of X(i) in X(j) for these {i,j}: {7, 6282}, {5732, 52457}, {7962, 35514}, {36973, 36996}
X(54178) = reflection of X(i) in X(j) for these {i,j}: {3359, 43151}, {7682, 142}
X(54178) = complement of X(54135)
See Ivan Pavlov, euclid 5829.
X(54179) lies on these lines: {7, 6925}, {20, 527}, {144, 6282}, {329, 971}, {517, 36996}, {2093, 43182}, {2094, 7580}, {5732, 12848}, {5850, 7994}, {6172, 6909}, {6840, 36991}, {27383, 52684}, {37421, 43177}, {37611, 52653}
X(54179) = reflection of X(i) in X(j) for these {i,j}: {144, 6282}, {2093, 43182}, {12848, 5732}, {36991, 52457}
X(54179) = anticomplement of X(54135)
See Ivan Pavlov, euclid 5829.
X(54180) lies on these lines: {1, 3430}, {3, 758}, {58, 602}, {511, 1385}, {515, 3454}, {540, 51705}, {550, 29097}, {944, 36974}, {1046, 7987}, {1125, 7683}, {1319, 10544}, {1330, 5731}, {2825, 11712}, {2842, 11709}, {3743, 30285}, {4221, 16132}, {4228, 19861}, {4653, 8235}, {5429, 30389}, {5538, 37328}, {6326, 37431}, {6693, 10165}, {9840, 35016}, {10176, 13732}, {11573, 11700}, {11713, 31786}, {18481, 37823}, {19544, 30143}, {22791, 29032}, {24309, 37531}, {31803, 49128}, {37620, 51717}
X(54180) = midpoint of X(i) in X(j) for these {i,j}: {1, 3430}, {944, 36974}, {18481, 37823}
X(54180) = reflection of X(i) in X(j) for these {i,j}: {7683, 1125}
X(54180) = complement of X(54136)
See Ivan Pavlov, euclid 5829.
X(54181) lies on these lines: {1, 37443}, {8, 3430}, {20, 758}, {40, 50624}, {58, 5731}, {511, 944}, {515, 1330}, {1046, 4297}, {3476, 10544}, {3529, 29097}, {3616, 7683}, {7385, 30143}, {7987, 8258}, {34195, 48890}
X(54181) = reflection of X(i) in X(j) for these {i,j}: {8, 3430}, {1046, 4297}
X(54181) = anticomplement of X(54136)
See Ivan Pavlov, euclid 5829.
X(54182) lies on these lines: {34, 17520}, {65, 1884}, {429, 1875}, {1866, 1874}
X(54182) = zosma transform of X(54136)
See Ivan Pavlov, euclid 5829.
X(54183) lies on circumconic {{A, B, C, X(14486), X(34288)}} and on these lines: {3, 2393}, {4, 44503}, {6, 30}, {20, 37784}, {22, 5622}, {25, 182}, {154, 15462}, {155, 14791}, {159, 51393}, {376, 41614}, {394, 542}, {511, 10602}, {524, 18917}, {550, 8548}, {575, 10982}, {576, 46850}, {1181, 44469}, {1350, 5621}, {1352, 1368}, {1370, 1993}, {1503, 18451}, {1593, 44479}, {1596, 14561}, {1660, 8780}, {2386, 13355}, {2790, 12177}, {3534, 39562}, {3818, 16072}, {5050, 18534}, {5085, 6644}, {5967, 36192}, {6000, 11511}, {6102, 11477}, {6800, 37980}, {7500, 34545}, {7530, 53093}, {7728, 19149}, {8538, 10575}, {8550, 36747}, {8681, 37480}, {9019, 37489}, {9715, 19360}, {9813, 16836}, {9976, 37853}, {10168, 47597}, {10541, 12106}, {10594, 43815}, {11178, 32216}, {11180, 15066}, {11216, 14855}, {11413, 15073}, {11414, 44470}, {11416, 15072}, {11456, 22151}, {11745, 36752}, {12084, 15074}, {12085, 50649}, {12283, 40228}, {13248, 44573}, {13352, 32621}, {13598, 44489}, {15069, 32140}, {15113, 30771}, {15760, 23327}, {17710, 44883}, {17825, 38064}, {18438, 34778}, {18533, 25406}, {18914, 37498}, {18919, 35513}, {20806, 39874}, {24206, 31255}, {29012, 44438}, {32599, 53097}, {34117, 51491}, {34514, 47353}, {34777, 37511}, {35259, 40114}, {36753, 45034}, {37196, 44480}, {37458, 37514}, {37506, 51739}, {38029, 51695}, {38110, 44233}, {44275, 47352}, {44276, 53023}, {44454, 53091}
X(54183) = midpoint of X(i) in X(j) for these {i,j}: {1370, 6776}, {10602, 21312}
X(54183) = reflection of X(i) in X(j) for these {i,j}: {25, 182}, {1352, 1368}, {18534, 19136}, {39879, 1660}
X(54183) = complement of X(54149)
X(54183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5050, 18534, 19136}, {10602, 21312, 511}, {39522, 50979, 6}
See Ivan Pavlov, euclid 5829.
X(54184) lies on these lines: {20, 2393}, {30, 193}, {1353, 44454}, {1370, 5921}, {3060, 6776}, {5032, 15032}, {5656, 11416}, {11179, 34417}, {12244, 14984}, {13445, 50967}, {14912, 18534}, {18919, 47096}, {19136, 33748}, {34621, 37784}
X(54184) = reflection of X(i) in X(j) for these {i,j}: {5921, 1370}, {7500, 6776}, {44454, 1353}
X(54184) = anticomplement of X(54149)
See Ivan Pavlov, euclid 5829.
X(54185) lies on these lines: {28, 9940}, {30, 553}, {517, 30267}, {1071, 52364}, {5777, 21530}, {11227, 44220}, {12041, 31793}, {18443, 20831}, {31788, 44661}
X(54185) = midpoint of X(i) in X(j) for these {i,j}: {1071, 52364}
X(54185) = reflection of X(i) in X(j) for these {i,j}: {28, 9940}, {5777, 21530}
X(54185) = complement of X(54150)
See Ivan Pavlov, euclid 5829.
X(54186) lies on these lines: {30, 3868}, {1071, 31293}, {12528, 52364}, {18444, 20831}
X(54186) = reflection of X(i) in X(j) for these {i,j}: {12528, 52364}, {31293, 1071}
X(54186) = anticomplement of X(54150)
See Ivan Pavlov, euclid 5829.
X(54187) lies on these lines: {3, 6}, {315, 11257}, {626, 6248}, {2782, 3933}, {3785, 40923}, {6310, 42061}, {7750, 38642}, {7785, 22503}, {7786, 9753}, {7800, 22677}, {7947, 9772}, {10350, 11676}, {11272, 37451}, {15819, 18806}, {20065, 32522}, {20576, 40108}, {32448, 41651}
X(54187) = midpoint of X(i) in X(j) for these {i,j}: {315, 11257}, {30270, 32452}
X(54187) = reflection of X(i) in X(j) for these {i,j}: {32, 13334}, {6248, 626}, {35430, 3}, {35431, 50652}, {35432, 182}, {35436, 39}, {46321, 13335}
X(54187) = complement of X(54152)
X(54187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 35430}, {39, 511, 35436}, {182, 511, 35432}, {511, 13334, 32}, {511, 13335, 46321}, {511, 50652, 35431}, {3095, 11171, 9605}, {5188, 21163, 15513}, {13355, 30270, 3}, {21163, 46321, 13335}, {30270, 32452, 511}
See Ivan Pavlov, euclid 5829.
X(54188) lies on these lines: {20, 185}, {32, 32522}, {1078, 6194}, {2548, 32452}, {3095, 37182}, {3522, 35430}, {5999, 12251}, {7709, 7839}, {7793, 40923}, {9772, 32818}, {14532, 32520}, {22503, 32816}
X(54188) = reflection of X(i) in X(j) for these {i,j}: {20065, 11257}
X(54188) = anticomplement of X(54152)
X(54188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 11257, 20065}
See Ivan Pavlov, euclid 5829.
X(54189) lies on these lines: {4, 69}, {98, 50640}, {183, 3094}, {325, 24256}, {384, 35432}, {3098, 38907}, {3917, 25332}, {5052, 7804}, {5092, 34885}, {5152, 14810}, {5969, 37671}, {6393, 49111}, {7795, 46305}, {10007, 37688}, {11161, 14711}, {12212, 39093}, {12215, 13354}, {43461, 51373}
X(54189) = Cundy-Parry Psi of X(54152)
See Ivan Pavlov, euclid 5829.
X(54190) lies on these lines: {21, 31806}, {30, 51113}, {517, 3647}, {4973, 49107}, {6684, 41542}, {10993, 43174}, {11012, 52126}, {11014, 11684}, {11362, 22937}, {14526, 41547}, {16113, 52367}, {16125, 25639}, {26202, 51118}
X(54190) = midpoint of X(i) in X(j) for these {i,j}: {11012, 52126}, {11014, 11684}, {16113, 52367}
X(54190) = reflection of X(i) in X(j) for these {i,j}: {16125, 25639}
X(54190) = complement of X(54153)
See Ivan Pavlov, euclid 5829.
X(54191) lies on these lines: {517, 3648}, {2475, 5535}, {7330, 52126}, {16113, 20066}
X(54191) = reflection of X(i) in X(j) for these {i,j}: {20066, 16113}
X(54191) = anticomplement of X(54153)
See Ivan Pavlov, euclid 5829.
X(54192) lies on these lines: {1, 6940}, {3, 758}, {30, 21635}, {36, 5083}, {78, 5450}, {140, 35016}, {214, 517}, {404, 31870}, {484, 34474}, {515, 5440}, {519, 11715}, {631, 37571}, {946, 37281}, {1125, 33596}, {1319, 28234}, {1385, 3244}, {1737, 38133}, {2077, 2800}, {2646, 6684}, {3576, 3870}, {3579, 51717}, {3814, 6246}, {3874, 32612}, {3878, 26285}, {3881, 37535}, {3884, 11849}, {3919, 10222}, {4188, 37625}, {4855, 6796}, {4973, 23961}, {5080, 12119}, {5087, 24042}, {5193, 46681}, {5267, 31837}, {5432, 38134}, {5441, 6902}, {5535, 13587}, {5538, 6905}, {5657, 37525}, {5690, 26287}, {5692, 6950}, {5730, 40256}, {5840, 11813}, {5842, 9945}, {5882, 38455}, {6256, 27383}, {6261, 10860}, {6265, 35000}, {6326, 6909}, {6906, 20117}, {6914, 10176}, {6951, 37701}, {6952, 47033}, {6961, 49168}, {10165, 11019}, {10265, 44669}, {10310, 40257}, {11248, 30144}, {11496, 12446}, {11700, 22350}, {12005, 34772}, {12245, 21842}, {12831, 15326}, {13464, 17614}, {14804, 41547}, {14988, 46684}, {24466, 51409}, {26877, 41696}, {27529, 40260}, {31730, 37837}, {33595, 50828}, {35262, 37569}, {40259, 52367}
X(54192) = midpoint of X(i) in X(j) for these {i,j}: {2077, 4511}, {5080, 12119}, {5440, 50371}, {5538, 6905}, {6265, 35000}, {6326, 6909}, {24466, 51409}
X(54192) = reflection of X(i) in X(j) for these {i,j}: {4973, 23961}, {6246, 3814}, {24042, 5087}, {40663, 6684}
X(54192) = complement of X(54154)
X(54192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 22836, 5884}, {2077, 4511, 2800}, {5440, 50371, 515}, {5538, 15015, 6905}, {34772, 37561, 12005}
See Ivan Pavlov, euclid 5829.
X(54193) lies on these lines: {1, 37163}, {8, 6906}, {20, 758}, {30, 9809}, {145, 5884}, {515, 3935}, {517, 6224}, {519, 1768}, {550, 944}, {938, 22768}, {962, 37468}, {1012, 48698}, {1519, 4511}, {3189, 38455}, {3241, 28458}, {3428, 5731}, {3476, 11246}, {3486, 5217}, {3488, 15325}, {3616, 37438}, {5180, 5840}, {5535, 36004}, {5538, 6840}, {5657, 7508}, {5842, 9963}, {6888, 47033}, {6909, 9803}, {6986, 10543}, {8727, 17757}, {10724, 51409}, {11015, 14110}, {12119, 20067}, {12247, 35000}, {15680, 31806}, {22836, 37437}, {31775, 34195}, {34626, 34632}, {37256, 37625}
X(54193) = reflection of X(i) in X(j) for these {i,j}: {6840, 5538}, {9803, 6909}, {10724, 51409}, {12247, 35000}, {20067, 12119}
X(54193) = anticomplement of X(54154)
X(54193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6909, 44669, 9803}
See Ivan Pavlov, euclid 5829.
X(54194) lies on these lines: {34, 40}, {65, 1884}, {108, 1835}, {1845, 1877}, {1870, 32760}
X(54194) = zosma transform of X(54154)
See Ivan Pavlov, euclid 5829.
X(54195) lies on these lines: {3, 732}, {4, 2896}, {76, 12122}, {83, 22712}, {182, 41755}, {262, 31268}, {511, 6292}, {754, 35430}, {3095, 10519}, {3398, 37455}, {3785, 8725}, {3934, 6249}, {5188, 29012}, {5976, 7767}, {6704, 15819}, {12251, 32476}, {16220, 31950}, {22677, 48673}, {31168, 33706}
X(54195) = midpoint of X(i) in X(j) for these {i,j}: {76, 12122}, {5188, 44772}, {6287, 9821}, {12251, 32476}, {31168, 33706}
X(54195) = reflection of X(i) in X(j) for these {i,j}: {6249, 3934}
X(54195) = complement of X(54155)
X(54195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5188, 44772, 29012}, {41650, 49112, 3398}
See Ivan Pavlov, euclid 5829.
X(54196) lies on these lines: {20, 732}, {83, 6194}, {194, 12122}, {511, 2896}, {3091, 42006}, {3146, 12251}, {6249, 31276}, {7893, 8782}, {9821, 12252}, {9866, 45029}, {13111, 32521}
X(54196) = reflection of X(i) in X(j) for these {i,j}: {194, 12122}, {12252, 9821}, {13111, 32521}
X(54196) = anticomplement of X(54155)
See Ivan Pavlov, euclid 5829.
X(54197) lies on circumconics {A,B,C,X(1),X(318)}, {A,B,C,X(3),X(15803)}, {A,B,C,X(4),X(34039)}, {A,B,C,X(20),X(28)}, {A,B,C,X(21),X(37417)}, {A,B,C,X(40),X(104)} and on these lines: {20, 6735}, {318, 52027}, {517, 1394}, {1785, 15803}
X(54197) = isogonal conjugate of X(54156)
X(54197) = X(i)-vertex conjugate of X(j) for these {i, j}: {963, 3345}
X(54197) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(1), X(318)}}, {{A, B, C, X(3), X(15803)}}, {{A, B, C, X(4), X(34039)}}, {{A, B, C, X(20), X(28)}}, {{A, B , C, X(21), X(37417)}} and {{A, B, C, X(40), X(104)}}
See Ivan Pavlov, euclid 5829.
X(54198) lies on these lines: {1, 10309}, {4, 3340}, {10, 119}, {20, 51423}, {40, 6745}, {65, 7682}, {84, 3296}, {221, 51616}, {226, 12672}, {354, 17649}, {382, 515}, {452, 5924}, {496, 942}, {516, 6261}, {517, 6260}, {519, 6256}, {527, 22770}, {551, 5450}, {944, 9580}, {952, 22792}, {962, 1490}, {971, 22791}, {1071, 1537}, {1125, 1158}, {1159, 18483}, {1210, 1519}, {1385, 43177}, {1420, 2096}, {1532, 4848}, {1697, 15239}, {1699, 5804}, {1709, 11045}, {2093, 6848}, {2098, 12678}, {2099, 12679}, {2801, 49600}, {2829, 4342}, {3057, 12831}, {3359, 6700}, {3452, 31788}, {3485, 12705}, {3555, 18239}, {3616, 52027}, {3667, 42757}, {3817, 12616}, {4297, 40257}, {4304, 21740}, {4356, 50189}, {4847, 5693}, {4861, 9809}, {5045, 18238}, {5128, 6927}, {5493, 6796}, {5542, 7373}, {5768, 9614}, {5795, 37822}, {5811, 9623}, {5837, 6907}, {5853, 12700}, {5886, 6705}, {5901, 34862}, {6223, 12650}, {6361, 52026}, {6738, 26333}, {6847, 7995}, {6916, 15829}, {6925, 11682}, {7956, 31794}, {7967, 41864}, {7982, 12667}, {7992, 11034}, {8196, 12457}, {8203, 12456}, {8227, 14647}, {9843, 34339}, {9955, 33899}, {10085, 11046}, {10164, 40256}, {10247, 48664}, {10384, 36996}, {10572, 34789}, {10595, 12246}, {10624, 18446}, {10698, 46435}, {10914, 13257}, {11047, 12686}, {11048, 12687}, {11362, 18242}, {11496, 18237}, {11500, 28194}, {12005, 21625}, {12330, 22753}, {12675, 16215}, {13227, 14872}, {15071, 30384}, {21620, 45776}, {30196, 52354}, {31419, 31821}, {31730, 37837}, {34123, 52116}, {37001, 37740}, {37561, 50908}, {37615, 51724}, {40266, 51755}, {43182, 51577}, {45636, 49170}, {45637, 49171}
X(54198) = midpoint of X(i) in X(j) for these {i,j}: {4, 7971}, {962, 1490}, {1482, 6259}, {3555, 18239}, {6223, 12650}, {7982, 12667}, {10698, 46435}, {37727, 40267}
X(54198) = reflection of X(i) in X(j) for these {i,j}: {10, 12608}, {1158, 1125}, {4297, 40257}, {5493, 6796}, {6245, 946}, {11362, 18242}, {12114, 13464}, {18238, 5045}, {31730, 37837}, {33899, 9955}, {34862, 5901}
X(54198) = complement of X(54156)
X(54198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {946, 5884, 11019}, {946, 6001, 6245}, {1482, 6259, 515}, {2800, 12608, 10}, {9856, 39542, 946}, {37727, 40267, 515}
See Ivan Pavlov, euclid 5829.
X(54199) lies on these lines: {4, 7319}, {7, 12672}, {8, 153}, {20, 7971}, {499, 12767}, {515, 20050}, {517, 6223}, {912, 6764}, {938, 10531}, {944, 30332}, {962, 3868}, {1012, 4323}, {1071, 9785}, {1158, 3616}, {1385, 14646}, {1482, 12246}, {1490, 3935}, {1519, 5704}, {2096, 4308}, {3622, 52027}, {3873, 17649}, {3889, 18238}, {4301, 7992}, {5173, 17650}, {5330, 5731}, {5450, 38314}, {5658, 12702}, {5734, 12114}, {5775, 15908}, {5811, 37562}, {5844, 48664}, {5851, 10912}, {5884, 10580}, {6259, 12245}, {6261, 9778}, {7995, 37434}, {9779, 12616}, {9780, 12608}, {9948, 31162}, {9957, 36996}, {10595, 34862}, {11037, 45776}, {11500, 34632}, {15071, 30305}, {18228, 31788}, {22770, 28610}
X(54199) = reflection of X(i) in X(j) for these {i,j}: {20, 7971}, {7992, 4301}, {9799, 962}, {12245, 6259}, {12246, 1482}, {20070, 1490}
X(54199) = anticomplement of X(54156)
X(54199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {962, 6001, 9799}
See Ivan Pavlov, euclid 5829.
X(54200) lies on circumconic {{A,B,C,X(34),X(104)}} and on these lines: {4, 11}, {29, 5323}, {34, 207}, {57, 21228}, {65, 11436}, {208, 1877}, {318, 3476}, {387, 19365}, {388, 11109}, {393, 604}, {1319, 7952}, {1398, 37226}, {1400, 3087}, {1404, 40138}, {1420, 1785}, {1466, 37028}, {1470, 7412}, {1788, 5081}, {1828, 51399}, {1870, 14257}, {1875, 37566}, {1981, 41785}, {5204, 37410}, {6987, 22341}, {7011, 31789}, {7046, 10944}, {7195, 36118}, {7288, 17555}, {8283, 12667}, {11471, 37550}, {35014, 38517}, {37305, 37579}, {43053, 52283}
X(54200) = X(i)-isoconjugate-of-X(j) for these {i, j}: {78, 945}
X(54200) = barycentric product X(i)*X(j) for these (i, j): {273, 2261}, {278, 944}
X(54200) = barycentric quotient X(i)/X(j) for these (i, j): {608, 945}, {944, 345}, {2261, 78}
X(54200) = zosma transform of X(54156)
X(54200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {207, 1842, 1118}
See Ivan Pavlov, euclid 5829.
X(54201) lies on these lines: {3, 12325}, {4, 21357}, {5, 7693}, {30, 6288}, {54, 3530}, {140, 389}, {195, 549}, {539, 34200}, {546, 1209}, {547, 3574}, {548, 12041}, {550, 2888}, {631, 12316}, {2917, 7555}, {3519, 33923}, {3628, 20424}, {3850, 15800}, {3856, 47582}, {5066, 13565}, {5498, 32338}, {5562, 34577}, {6153, 13391}, {6286, 15325}, {6343, 38706}, {8703, 12254}, {9920, 12324}, {10096, 11591}, {10125, 23039}, {10203, 22115}, {10257, 22815}, {10299, 13432}, {10610, 12100}, {10625, 13368}, {10627, 25563}, {10628, 16252}, {11271, 44682}, {11487, 12106}, {11804, 37452}, {12103, 18400}, {12108, 15801}, {12226, 47090}, {12291, 43607}, {12300, 21841}, {12606, 16196}, {12785, 28224}, {12965, 35255}, {12971, 35256}, {13340, 13423}, {13365, 13451}, {14140, 34804}, {15035, 34483}, {15067, 43581}, {15605, 15690}, {15704, 48675}, {17834, 50136}, {18916, 32333}, {22466, 52073}, {23336, 41590}, {27552, 32358}, {31674, 34837}, {32396, 47599}, {35197, 52793}, {37126, 50476}, {43598, 44264}, {43615, 48876}, {47117, 48378}
X(54201) = midpoint of X(i) in X(j) for these {i,j}: {5, 12307}, {550, 2888}, {7691, 21230}, {10625, 13368}, {12325, 36966}, {15704, 48675}
X(54201) = reflection of X(i) in X(j) for these {i,j}: {54, 3530}, {546, 1209}, {8254, 32348}, {11803, 6689}, {15800, 3850}, {20424, 3628}, {22051, 140}, {31674, 34837}, {32358, 27552}, {47117, 48378}
X(54201) = complement of X(54157)
X(54201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12325, 36966}, {140, 1154, 22051}, {1154, 32348, 8254}, {1154, 6689, 11803}, {7691, 21230, 30}, {8254, 32348, 140}, {12325, 36966, 50708}, {14140, 36837, 34804}
See Ivan Pavlov, euclid 5829.
X(54202) lies on these lines: {3, 54}, {4, 18551}, {20, 50708}, {30, 12325}, {376, 36966}, {378, 12175}, {381, 20584}, {382, 2888}, {539, 15681}, {550, 13432}, {631, 22051}, {999, 6286}, {1209, 3851}, {1351, 9977}, {1498, 5898}, {1593, 6242}, {1597, 6152}, {1598, 12300}, {1656, 20424}, {1657, 12244}, {2914, 32534}, {2917, 14530}, {3091, 21357}, {3295, 7356}, {3357, 35452}, {3426, 3519}, {3532, 37483}, {3534, 12254}, {3574, 5055}, {3830, 6288}, {3843, 15800}, {5054, 8254}, {5070, 32396}, {5204, 51803}, {5217, 35197}, {5562, 13621}, {5663, 15086}, {5899, 18436}, {5925, 13093}, {5965, 33878}, {6000, 17846}, {6221, 12965}, {6398, 12971}, {6767, 18984}, {7373, 13079}, {7517, 41726}, {8717, 34783}, {9935, 44457}, {10282, 17824}, {10539, 37923}, {10605, 21660}, {10677, 42116}, {10678, 42115}, {10982, 32352}, {11271, 15696}, {11413, 11999}, {11444, 22462}, {11591, 21308}, {11597, 15748}, {11702, 15040}, {11802, 15805}, {11803, 15720}, {12017, 19150}, {12111, 37949}, {12164, 44515}, {12226, 21312}, {12702, 15071}, {13321, 44056}, {13391, 13423}, {13565, 19709}, {13754, 47748}, {14049, 38723}, {14531, 14627}, {14926, 18874}, {15051, 47117}, {15072, 47751}, {15644, 43807}, {15694, 32348}, {15750, 52417}, {17834, 18378}, {23039, 43581}, {23409, 44834}, {32609, 43580}, {37922, 46730}
X(54202) = reflection of X(i) in X(j) for these {i,j}: {3, 12307}, {195, 7691}, {382, 2888}, {5073, 48675}, {12308, 5898}, {12316, 3}, {48675, 3519}
X(54202) = anticomplement of X(54157)
X(54202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1154, 12316}, {195, 12307, 7691}, {195, 7691, 3}, {1154, 12307, 3}, {1154, 7691, 195}, {5898, 10628, 12308}, {6101, 32608, 3}
See Ivan Pavlov, euclid 5829.
X(54203) lies on these lines: {3, 15348}, {9, 374}, {55, 15299}, {516, 34176}, {528, 3654}, {971, 3428}, {1001, 37533}, {1006, 7671}, {2099, 15298}, {2886, 5805}, {3358, 10860}, {3434, 5759}, {3929, 11372}, {5119, 10384}, {5220, 5887}, {5657, 37787}, {5696, 11012}, {5698, 26921}, {5709, 52682}, {5784, 11249}, {5880, 37532}, {6210, 20601}, {6883, 10177}, {7082, 9580}, {7680, 38108}, {8255, 38122}, {8257, 26446}, {8545, 39542}, {9856, 41229}, {11362, 15297}, {12699, 38454}, {14100, 40292}, {18407, 52835}, {21153, 32613}, {21168, 36976}, {24929, 38031}, {38117, 47373}
X(54203) = midpoint of X(i) in X(j) for these {i,j}: {3428, 42014}, {3434, 5759}, {11372, 41338}
X(54203) = reflection of X(i) in X(j) for these {i,j}: {55, 31658}, {5805, 2886}, {37533, 1001}, {52835, 18407}
X(54203) = complement of X(54158)
X(54203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3428, 42014, 971}
See Ivan Pavlov, euclid 5829.
X(54204) lies on these lines: {20, 15733}, {144, 517}, {5759, 20075}, {6992, 7671}, {10572, 30332}, {10679, 21168}, {11372, 17781}, {28610, 41338}, {37569, 52653}
X(54204) = reflection of X(i) in X(j) for these {i,j}: {20075, 5759}
X(54204) = anticomplement of X(54158)
See Ivan Pavlov, euclid 5829.
X(54205) lies on these lines: {3, 527}, {9, 6935}, {57, 3475}, {142, 517}, {329, 5732}, {443, 4301}, {516, 997}, {2095, 38122}, {2801, 21060}, {3452, 8727}, {3576, 41570}, {5220, 6705}, {5735, 6904}, {6881, 7682}, {6992, 7675}, {12848, 21153}, {37407, 43174}, {37611, 43175}
X(54205) = midpoint of X(i) in X(j) for these {i,j}: {329, 5732}, {6282, 52457}
X(54205) = reflection of X(i) in X(j) for these {i,j}: {43175, 37611}
X(54205) = complement of X(54159)
X(54205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6282, 52457, 516}
See Ivan Pavlov, euclid 5829.
X(54206) lies on these lines: {7, 517}, {20, 527}, {329, 10431}, {962, 5784}, {1012, 6172}, {2094, 7411}, {2095, 21151}, {2801, 10430}, {3870, 5732}, {5735, 37435}, {5766, 37531}, {5809, 6827}, {6282, 7675}, {6839, 52457}, {7991, 43177}
X(54206) = reflection of X(i) in X(j) for these {i,j}: {9965, 5732}, {12848, 6282}, {36991, 329}
X(54206) = anticomplement of X(54159)
See Ivan Pavlov, euclid 5829.
X(54207) lies on these lines: {19, 1877}, {33, 42289}, {65, 28076}, {1119, 15934}, {1876, 4307}, {4196, 11406}
X(54207) = zosma transform of X(54159)
See Ivan Pavlov, euclid 5829.
X(54208) lies on these lines: {3, 17770}, {511, 1125}, {516, 3430}, {758, 31788}, {1046, 10164}, {1330, 4297}, {2784, 41014}, {2792, 12512}, {3454, 19925}, {7683, 10171}, {7987, 20077}, {12563, 35650}, {28164, 37823}, {28236, 36974}
X(54208) = midpoint of X(i) in X(j) for these {i,j}: {1330, 4297}
X(54208) = reflection of X(i) in X(j) for these {i,j}: {19925, 3454}
X(54208) = complement of X(54160)
See Ivan Pavlov, euclid 5829.
X(54209) lies on these lines: {1, 256}, {20, 17770}, {58, 7987}, {72, 18788}, {165, 1046}, {540, 34628}, {758, 6765}, {962, 49458}, {1330, 5691}, {1695, 10884}, {1750, 10381}, {2392, 5538}, {3454, 7989}, {3794, 8583}, {4297, 20077}, {5429, 30389}, {7683, 7988}, {11531, 35665}, {12635, 53097}, {20018, 24728}, {36974, 37712}, {43159, 48878}
X(54209) = reflection of X(i) in X(j) for these {i,j}: {1046, 3430}, {5691, 1330}, {20077, 4297}
X(54209) = anticomplement of X(54160)
X(54209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1046, 3430, 165}, {8235, 48909, 1}
See Ivan Pavlov, euclid 5829.
X(54210) lies on these lines: {29, 1876}, {1426, 4213}, {1829, 1874}
X(54210) = zosma transform of X(54160)
See Ivan Pavlov, euclid 5829.
X(54211) lies on these lines: {2, 3357}, {4, 3426}, {20, 394}, {25, 32601}, {64, 3091}, {376, 14530}, {541, 34621}, {1503, 11008}, {1559, 3183}, {2071, 32605}, {2777, 5059}, {2883, 3523}, {3090, 35450}, {3146, 5889}, {3522, 5656}, {3529, 12315}, {3543, 5895}, {3832, 22802}, {3839, 6247}, {3854, 20299}, {5056, 15105}, {5261, 10060}, {5274, 10076}, {5894, 10304}, {5921, 34146}, {6523, 51892}, {6616, 36965}, {6622, 34469}, {6696, 7486}, {6759, 50693}, {6815, 11469}, {7408, 13474}, {7488, 9914}, {7691, 52404}, {9833, 15683}, {10303, 10606}, {12950, 14986}, {14216, 17578}, {15072, 30443}, {15682, 34780}, {15692, 16252}, {17538, 32063}, {18381, 50687}, {18400, 50692}, {20725, 27082}, {23249, 35864}, {23259, 35865}, {32064, 50688}, {41736, 50009}
X(54211) = reflection of X(i) in X(j) for these {i,j}: {4, 48672}, {20, 6225}, {3529, 12315}, {5059, 34781}, {12250, 5878}, {12324, 5895}
X(54211) = anticomplement of X(12250)
X(54211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2777, 34781, 5059}, {5656, 20427, 3522}, {5878, 12250, 2}, {5895, 12324, 3543}, {5925, 11206, 20}, {6225, 15311, 20}, {32064, 51491, 50688}
See Ivan Pavlov, euclid 5829.
X(54212) lies on these lines: {3, 758}, {30, 5887}, {65, 5719}, {355, 40661}, {442, 517}, {960, 6841}, {1385, 39772}, {2646, 5428}, {2771, 3650}, {3647, 35459}, {3651, 3869}, {3654, 10197}, {3878, 5794}, {5499, 39542}, {6917, 49177}, {8261, 28465}, {11281, 24474}, {13750, 52793}, {21677, 31837}, {22766, 41697}, {26725, 37625}, {31786, 39783}, {37820, 47033}
X(54212) = midpoint of X(i) in X(j) for these {i,j}: {3651, 3869}, {14110, 44782}
X(54212) = reflection of X(i) in X(j) for these {i,j}: {355, 40661}, {6841, 960}, {21677, 31837}, {24474, 11281}, {39772, 1385}
X(54212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14110, 44782, 30}
X(54212) = complement of X(54161)
See Ivan Pavlov, euclid 5829.
X(54213) lies on these lines: {20, 758}, {517, 2475}, {3428, 34195}, {3651, 3871}, {3869, 37433}, {4189, 16139}, {5709, 39778}, {6888, 31806}
X(54213) = reflection of X(i) in X(j) for these {i,j}: {37433, 3869}
X(54213) = anticomplement of X(54161)
See Ivan Pavlov, euclid 5829.
X(54214) lies on these lines: {65, 1884}, {407, 1877}, {40644, 49745}, {40950, 44840}
X(54214) = zosma transform of X(54161)
See Ivan Pavlov, euclid 5829.
X(54215) lies on these lines: {3, 524}, {4, 22151}, {6, 50008}, {30, 9970}, {67, 3564}, {155, 14791}, {182, 3580}, {323, 6776}, {325, 52772}, {399, 1503}, {468, 15462}, {511, 1986}, {542, 858}, {576, 38323}, {599, 18580}, {1092, 34507}, {1352, 5094}, {1511, 32113}, {1568, 32250}, {1594, 18553}, {2071, 32247}, {2072, 32274}, {2393, 30714}, {5622, 41724}, {5965, 32285}, {6240, 11470}, {6593, 11799}, {7464, 11061}, {7579, 47354}, {8262, 44214}, {9019, 25711}, {11645, 15063}, {12177, 47526}, {13160, 25555}, {13292, 43810}, {14912, 41617}, {14984, 47280}, {15035, 41721}, {15069, 18281}, {15138, 47337}, {15140, 44267}, {16619, 18374}, {18325, 45016}, {19140, 32111}, {19510, 32275}, {32234, 43574}, {32273, 34470}, {37784, 44480}, {38064, 44569}, {41729, 48873}, {46817, 52697}, {47335, 47546}, {47581, 52699}
X(54215) = midpoint of X(i) in X(j) for these {i,j}: {323, 6776}, {7464, 11061}, {10510, 32233}
X(54215) = reflection of X(i) in X(j) for these {i,j}: {67, 15122}, {1352, 11064}, {3580, 182}, {11799, 6593}, {32111, 19140}, {32113, 1511}, {32275, 19510}, {41721, 47569}
X(54215) = complement of X(54162)
X(54215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3564, 15122, 67}, {10510, 32233, 30}
See Ivan Pavlov, euclid 5829.
X(54216) lies on these lines: {20, 524}, {323, 5921}, {511, 12270}, {542, 5189}, {576, 34007}, {3091, 22151}, {3153, 10510}, {3564, 7464}, {6776, 7492}, {7592, 37784}, {9970, 52403}, {11160, 35485}, {11180, 31857}, {32275, 43574}, {33532, 39899}, {37952, 47558}, {40112, 52284}
X(54216) = reflection of X(i) in X(j) for these {i,j}: {5921, 323}, {37779, 6776}
X(54216) = anticomplement of X(54162)
See Ivan Pavlov, euclid 5829.
X(54217) lies on these lines: {3, 12421}, {5, 5504}, {30, 155}, {68, 16196}, {185, 16163}, {235, 1147}, {1092, 11585}, {3167, 31725}, {5654, 44226}, {6193, 11413}, {12038, 33563}, {12420, 21312}, {12901, 43903}, {13292, 37814}, {14516, 43894}, {15078, 18916}, {16238, 39571}, {21841, 51933}, {31804, 44247}, {32263, 43898}, {34148, 45179}
X(54217) = midpoint of X(i) in X(j) for these {i,j}: {6193, 11413}, {12118, 44752}
X(54217) = reflection of X(i) in X(j) for these {i,j}: {68, 16196}, {235, 1147}, {33563, 12038}
X(54217) = complement of X(54163)
X(54217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12118, 44752, 30}
See Ivan Pavlov, euclid 5829.
X(54218) lies on these lines: {3, 53021}, {6, 1596}, {25, 14912}, {30, 1351}, {182, 8263}, {184, 35266}, {193, 21312}, {381, 18919}, {389, 2393}, {394, 1368}, {524, 37480}, {549, 5622}, {550, 15073}, {974, 6467}, {1595, 8549}, {2790, 5477}, {5050, 6677}, {5486, 10249}, {5921, 16072}, {6146, 8538}, {6644, 19459}, {6823, 8548}, {10250, 23292}, {11179, 37475}, {12007, 19136}, {13568, 34788}, {13851, 39884}, {15760, 39562}, {16196, 18910}, {18388, 23326}, {18440, 18918}, {18531, 18935}, {18534, 19119}, {18914, 37498}, {19125, 44233}, {23291, 50955}, {31152, 50974}, {32621, 44274}, {33851, 51737}, {39874, 44438}
X(54218) = midpoint of X(i) in X(j) for these {i,j}: {193, 21312}, {6776, 10602}, {18531, 39899}, {31152, 50974}, {39874, 44438}
X(54218) = reflection of X(i) in X(j) for these {i,j}: {1596, 6}, {8263, 182}, {18440, 44920}, {19136, 12007}, {44212, 50979}, {44241, 48906}, {44273, 11179}
X(54218) = complement of X(54164)
X(54218) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6776, 10602, 30}, {14984, 48906, 44241}
See Ivan Pavlov, euclid 5829.
X(54219) lies on these lines: {1370, 3564}, {1596, 51170}, {2393, 5889}, {5921, 10602}, {6677, 33748}, {9544, 14912}, {14984, 39874}, {18533, 39899}, {20080, 21312}, {31152, 51215}
X(54219) = reflection of X(i) in X(j) for these {i,j}: {5921, 10602}, {18533, 39899}, {20080, 21312}, {51215, 31152}
X(54219) = anticomplement of X(54164)
See Ivan Pavlov, euclid 5829.
X(54220) lies on these lines: {192, 30269}, {2887, 29010}, {31134, 51043}
X(54220) = midpoint of X(i) in X(j) for these {i,j}: {192, 30269}, {31134, 51043}
X(54220) = complement of X(54165)
See Ivan Pavlov, euclid 5829.
X(54221) lies on these lines: {1278, 30269}, {6327, 29010}, {42058, 51043}
X(54221) = reflection of X(i) in X(j) for these {i,j}: {1278, 30269}, {42058, 51043}
X(54221) = anticomplement of X(54165)
See Ivan Pavlov, euclid 5829.
X(54222) lies on these lines: {32, 7709}, {39, 1513}, {76, 11623}, {194, 12203}, {511, 550}, {626, 2782}, {1569, 2794}, {6680, 11171}, {7781, 13355}, {7830, 52996}, {7839, 35386}, {13334, 18806}, {13335, 32516}, {38642, 46283}
X(54222) = midpoint of X(i) in X(j) for these {i,j}: {194, 30270}, {11257, 32452}
X(54222) = reflection of X(i) in X(j) for these {i,j}: {13335, 32516}, {18806, 13334}
X(54222) = complement of X(54165)
X(54222) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11257, 32452, 2794}
See Ivan Pavlov, euclid 5829.
X(54223) lies on these lines: {194, 8721}, {315, 2782}, {511, 3529}, {5999, 18768}, {9753, 32448}, {11257, 35430}, {14931, 20081}, {18806, 32522}
X(54223) = reflection of X(i) in X(j) for these {i,j}: {20081, 30270}
X(54223) = anticomplement of X(54165)
See Ivan Pavlov, euclid 5829.
X(54224) lies on these lines: {546, 3934}, {2896, 5188}, {12122, 44772}, {13111, 15819}
X(54224) = midpoint of X(i) in X(j) for these {i,j}: {2896, 5188}, {12122, 44772}
X(54224) = complement of X(54167)
See Ivan Pavlov, euclid 5829.
X(54225) lies on these lines: {76, 382}, {511, 7847}, {732, 53097}, {754, 9764}, {5188, 20088}, {12252, 22676}, {13111, 22712}
X(54225) = reflection of X(i) in X(j) for these {i,j}: {20088, 5188}
X(54225) = anticomplement of X(54167)
See Ivan Pavlov, euclid 5829.
X(54226) lies on these lines: {40, 22117}, {165, 7952}, {7080, 9778}, {7991, 15501}, {7992, 44692}
X(54226) = isogonal conjugate of X(7992)
X(54226) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(1), X(40)}}, {{A, B, C, X(3), X(165)}}, {{A, B, C, X(28), X(53086)}}, {{A, B, C, X(46), X(6282)}}, {{A, B, C, X(58), X(34432)}}, {{A, B, C, X(84), X(972)}}, {{A, B, C, X(102), X(43719)}}, {{A, B, C, X(200), X(775)}}, {{A, B, C, X(267), X(3062)}}, {{A, B, C, X(517), X(7991)}}, {{A, B, C, X(921), X(29374)}}, {{A, B, C, X(1243), X(31793)}}, {{A, B, C, X(1394), X(7992)}}, {{A, B, C, X(2093), X(14110)}}, {{A, B, C, X(2745), X(32899)}}, {{A, B, C, X(3361), X(6244)}}, {{A, B, C, X(3579), X(7987)}}, {{A, B, C, X(6769), X(41338)}}, {{A, B, C, X(9357), X(39946)}}, {{A, B, C, X(9819), X(31798)}}, {{A, B, C, X(10310), X(15803)}}, {{A, B, C, X(11531), X(12702)}}, {{A, B, C, X(16192), X(35242)}}, {{A, B, C, X(16208), X(35239)}}, {{A, B, C, X(16209), X(35238)}}, {{A, B, C, X(30337), X(31797)}}
X(54226) = X(i)-vertex conjugate of X(j) for these {i, j}: {1, 34432}
X(54226) = X(i)-cross conjugate of X(j) for these {i, j}: {1394, 1}
See Ivan Pavlov, euclid 5829.
X(54227) lies on these lines: {1, 6223}, {2, 7992}, {3, 43182}, {4, 3671}, {5, 9948}, {10, 5777}, {40, 5658}, {56, 41706}, {84, 1125}, {221, 16870}, {226, 12688}, {329, 12565}, {382, 515}, {516, 1490}, {519, 7971}, {551, 12114}, {581, 4356}, {908, 9961}, {944, 4342}, {946, 971}, {950, 12679}, {993, 18237}, {997, 10309}, {1071, 11019}, {1158, 10164}, {1210, 15071}, {1699, 9799}, {1709, 13411}, {1750, 4295}, {2800, 4067}, {2801, 18239}, {2829, 33337}, {3062, 37434}, {3085, 7995}, {3086, 30304}, {3333, 36996}, {3358, 38059}, {3452, 9943}, {3487, 11372}, {3576, 12246}, {3634, 14647}, {3646, 21151}, {3741, 12547}, {3812, 9842}, {3817, 6245}, {3947, 9949}, {4297, 6261}, {4300, 4656}, {4311, 41690}, {4312, 50700}, {4314, 18446}, {4847, 12528}, {5439, 10863}, {5493, 11500}, {5603, 10864}, {5787, 18483}, {5811, 18250}, {5882, 15172}, {5884, 7682}, {5886, 12684}, {5930, 38357}, {6705, 19862}, {6737, 6925}, {6796, 50808}, {6849, 38151}, {6908, 18249}, {6916, 12447}, {7959, 34048}, {8074, 18913}, {8983, 49234}, {9843, 17649}, {9856, 21620}, {9942, 21616}, {9960, 12047}, {10085, 44675}, {10106, 12678}, {10165, 34862}, {10175, 33899}, {10884, 40998}, {10916, 12666}, {11220, 41012}, {11249, 34646}, {12053, 12680}, {12330, 25440}, {12512, 52026}, {12520, 12572}, {12526, 37421}, {12609, 12664}, {12672, 41543}, {12676, 17647}, {12705, 13405}, {13257, 21075}, {13971, 49235}, {14646, 35242}, {16112, 28628}, {18481, 48664}, {19855, 30326}, {20103, 37560}, {22792, 31673}, {28645, 38454}, {31821, 37424}
X(54227) = midpoint of X(i) in X(j) for these {i,j}: {1, 6223}, {6261, 16127}, {7971, 12667}, {18481, 48664}
X(54227) = reflection of X(i) in X(j) for these {i,j}: {10, 6260}, {84, 1125}, {4297, 6261}, {5493, 11500}, {5787, 18483}, {6245, 12608}, {6260, 18243}, {9948, 5}, {12664, 31871}, {31673, 22792}
X(54227) = complement of X(7992)
X(54227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {226, 12688, 21628}, {946, 12675, 21625}, {6001, 18243, 6260}, {6001, 6260, 10}, {6245, 12608, 3817}
See Ivan Pavlov, euclid 5829.
X(54228) lies on these lines: {2, 7992}, {4, 5556}, {7, 10429}, {8, 6001}, {84, 3616}, {144, 12565}, {329, 9961}, {388, 41706}, {392, 10307}, {515, 20050}, {651, 7959}, {938, 15071}, {962, 971}, {1071, 10580}, {1490, 4420}, {1709, 5703}, {2801, 6764}, {3062, 3671}, {3091, 9948}, {3146, 41575}, {3241, 7971}, {3427, 10266}, {4295, 18412}, {4342, 9851}, {5290, 9949}, {5558, 5603}, {5584, 6172}, {5731, 12246}, {5905, 9800}, {5927, 11024}, {6245, 9779}, {6260, 9780}, {7995, 41561}, {9785, 12680}, {9799, 9812}, {9856, 11037}, {9943, 18228}, {9960, 10430}, {10453, 12547}, {10578, 12705}, {10884, 52653}, {11036, 11372}, {12114, 38314}, {14647, 18243}, {14986, 30304}, {16112, 28629}, {16127, 18406}, {28647, 38454}, {40267, 50864}
X(54228) = reflection of X(i) in X(j) for these {i,j}: {8, 6223}
X(54228) = anticomplement of X(7992)
X(54228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9856, 36996, 11037}
X(54229) lies on these lines: {4, 4444}, {25, 16695}, {34, 51642}, {162, 39054}, {419, 4369}, {513, 1835}, {814, 6591}, {2049, 52599}, {2533, 3287}, {4504, 7009}, {7103, 7216}, {17103, 47736}, {17924, 29051}
X(54229) = zosma transform of X(512)
X(54229) = polar conjugate of X(27805)
X(54229) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(4), X(419)}}, {{A, B, C, X(171), X(18838)}}, {{A, B, C, X(513), X(3287)}}, {{A, B, C, X(804), X(6002)}}, {{A, B, C, X(1876), X(7119)}}, {{A, B, C, X(1877), X(7009)}}, {{A, B, C, X(1884), X(14006)}}, {{A, B, C, X(2533), X(4369)}}, {{A, B, C, X(3805), X(29051)}}, {{A, B, C, X(4128), X(51641)}}, {{A, B, C, X(4504), X(4922)}}, {{A, B, C, X(18155), X(48400)}}, {{A, B, C, X(20981), X(22093)}}
X(54229) = perspector of circumconic {{A,B,C,X(278), X(7009)}}
X(54229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3903}, {48, 27805}, {71, 4603}, {78, 29055}, {100, 7015}, {190, 7116}, {219, 37137}, {228, 4594}, {256, 1331}, {257, 906}, {692, 7019}, {874, 17970}, {893, 1332}, {904, 4561}, {1431, 4571}, {1432, 4587}, {2200, 7260}, {3573, 36214}, {3781, 30670}, {4451, 36059}, {4558, 52651}, {4563, 40729}, {4574, 40432}, {7018, 32656}
X(54229) = X(i)-Dao conjugate of X(j) for these {i, j}: {1086, 7019}, {1249, 27805}, {3709, 8611}, {4369, 656}, {5190, 257}, {5521, 256}, {8054, 7015}, {16587, 52609}, {16592, 69}, {20620, 4451}, {36103, 3903}, {40597, 1332}
X(54229) = X(i)-cross conjugate of X(j) for these {i, j}: {20981, 4369}
X(54229) = barycentric product X(i)*X(j) for these (i, j): {4, 4369}, {19, 4374}, {27, 2533}, {92, 4367}, {171, 17924}, {172, 46107}, {264, 20981}, {273, 3287}, {278, 3907}, {419, 4444}, {427, 18111}, {514, 7009}, {653, 4459}, {693, 7119}, {811, 16592}, {894, 7649}, {1119, 4529}, {1215, 17925}, {1237, 43925}, {1824, 16737}, {1826, 17212}, {1840, 7192}, {1847, 4477}, {1897, 7200}, {1909, 6591}, {2052, 22093}, {2501, 17103}, {2969, 18047}, {3064, 7176}, {3572, 17984}, {4128, 6331}, {4922, 6336}, {6649, 8735}, {7175, 44426}, {7178, 14006}, {7196, 18344}, {7234, 44129}, {17787, 43923}, {18200, 41013}, {28006, 40446}
X(54229) = barycentric quotient X(i)/X(j) for these (i, j): {4, 27805}, {19, 3903}, {27, 4594}, {28, 4603}, {34, 37137}, {171, 1332}, {172, 1331}, {286, 7260}, {419, 3570}, {444, 3882}, {514, 7019}, {608, 29055}, {649, 7015}, {667, 7116}, {894, 4561}, {1215, 52609}, {1840, 3952}, {2329, 4571}, {2330, 4587}, {2533, 306}, {3064, 4451}, {3287, 78}, {3572, 36214}, {3907, 345}, {4128, 647}, {4140, 3710}, {4164, 20769}, {4367, 63}, {4369, 69}, {4374, 304}, {4444, 40708}, {4459, 6332}, {4477, 3692}, {4529, 1265}, {4922, 3977}, {6591, 256}, {7119, 100}, {7122, 906}, {7175, 6516}, {7200, 4025}, {7234, 71}, {7649, 257}, {14006, 645}, {16592, 656}, {17103, 4563}, {17212, 17206}, {17924, 7018}, {17925, 32010}, {17984, 27853}, {18111, 1799}, {18200, 1444}, {20964, 4574}, {20981, 3}, {21755, 810}, {22093, 394}, {22373, 822}, {24533, 22370}, {40608, 8611}, {43923, 1432}, {43925, 1178}, {45882, 3781}, {46107, 44187}
See Ivan Pavlov, euclid 5829.
X(54230) lies on cubic K661 and these lines: {1, 6163}, {100, 6161}, {513, 6162}, {764, 5376}, {1083, 2975}, {5548, 36238}, {5592, 39185}, {6631, 24093}
X(54230) = eigentransform of X(513)
X(54230) = reflection of X(i) in X(j) for these {i,j}: {100, 6551}
X(54230) = trilinear pole of line {1052, 41395}
X(54230) = X(i)-Dao conjugate of X(j) for these {i, j}: {1016, 668}
X(54230) = barycentric product X(i)*X(j) for these (i, j): {190, 1052}, {668, 41395}
X(54230) = barycentric quotient X(i)/X(j) for these (i, j): {1052, 514}
See Ivan Pavlov, euclid 5829.
X(54231) lies on these lines: {1, 9323}, {101, 14825}, {595, 6788}, {21201, 36086}, {23100, 39293}, {24047, 41405}, {31273, 35967}
X(54231) = barycentric product X(i)*X(j) for these (i, j): {190, 38863}
X(54231) = eigentransform of X(514)
See Ivan Pavlov, euclid 5829.
X(54232) lies on cubic K028 and on these lines: {3, 101}, {4, 514}, {76, 18025}, {15634, 17181}, {17170, 44040}, {40116, 41320}
X(54232) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(3), X(514)}}, {{A, B, C, X(4), X(101)}}, {{A, B, C, X(76), X(48381)}}, {{A, B, C, X(103), X(53150)}}, {{A, B, C, X(118), X(50734)}}, {{A, B, C, X(220), X(1736)}}, {{A, B, C, X(847), X(3730)}}, {{A, B, C, X(8608), X(42316)}}
X(54232) = Cundy-Parry Psi of X(514)
X(54232) = perspector of circumconic {A,B,C,X(278), X(52781)}
X(54232) = X(i)-isoconjugate-of-X(j) for these {i, j}: {910, 2989}, {15380, 24014}, {36107, 39470}
X(54232) = X(i)-Dao conjugate of X(j) for these {i, j}: {118, 516}, {39003, 39470}
X(54232) = X(i)-cross conjugate of X(j) for these {i, j}: {916, 103}
X(54232) = barycentric product X(i)*X(j) for these (i, j): {103, 48381}, {916, 52781}, {1736, 36101}, {8608, 18025}
X(54232) = barycentric quotient X(i)/X(j) for these (i, j): {103, 2989}, {916, 26006}, {1736, 30807}, {8608, 516}, {32642, 35182}, {48381, 35517}
See Ivan Pavlov, euclid 5829.
X(54233) lies on the cubic K009 and on these lines: {3, 514}, {4, 101}, {32, 23972}, {1147, 14377}, {2724, 35182}
X(54233) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(3), X(101)}}, {{A, B, C, X(4), X(279)}}, {{A, B, C, X(56), X(44408)}}, {{A, B, C, X(14376), X(26006)}}, {{A, B, C, X(31852), X(41321)}}
X(54233) = Cundy-Parry Phi of X(514)
X(54233) = X(i)-isoconjugate-of-X(j) for these {i, j}: {103, 1736}, {911, 48381}, {916, 36122}, {2253, 52781}, {8608, 36101}
X(54233) = X(i)-Dao conjugate of X(j) for these {i, j}: {516, 118}, {23972, 48381}, {46095, 916}
X(54233) = barycentric product X(i)*X(j) for these (i, j): {516, 2989}, {917, 26006}
X(54233) = barycentric quotient X(i)/X(j) for these (i, j): {516, 48381}, {910, 1736}, {917, 52781}, {2989, 18025}, {23972, 118}, {32699, 40116}, {35182, 677}, {47407, 34335}
See Ivan Pavlov, euclid 5829.
X(54234) lies on these lines: {4, 9}, {25, 1626}, {28, 42326}, {29, 17171}, {33, 1851}, {34, 1458}, {225, 4186}, {513, 1835}, {1119, 19604}, {1465, 33302}, {1633, 1738}, {1785, 5146}, {1827, 1828}, {1836, 17810}, {1838, 4222}, {1848, 14004}, {1856, 11393}, {1886, 2201}, {1891, 5342}, {2310, 2385}, {2969, 23710}, {3008, 20780}, {4196, 5338}, {4207, 24943}, {5101, 53008}, {5307, 6995}, {7071, 11400}, {11109, 25966}, {12053, 33587}, {19372, 28104}, {34823, 36557}, {35993, 52427}, {37168, 40509}
X(54234) = isogonal conjugate of X(1810)
X(54234) = intersection, other than A, B, C, of circumconics:, {{A, B, C, X(9), X(513)}}, {{A, B, C, X(10), X(3008)}}, {{A, B, C, X(19), X(43923)}}, {{A, B, C, X(34), X(7719)}}, {{A, B, C, X(71), X(20780)}}, {{A, B, C, X(281), X(7649)}}, {{A, B, C, X(516), X(6084)}}, {{A, B, C, X(1119), X(15742)}}, {{A, B, C, X(1512), X(51419)}}, {{A, B, C, X(1706), X(51839)}}, {{A, B, C, X(1861), X(36124)}}, {{A, B, C, X(2183), X(48032)}}, {{A, B, C, X(2550), X(52210)}}, {{A, B, C, X(7079), X(18344)}}
X(54234) = zosma transform of X(518)
X(54234) = perspector of circumconic {{A,B,C,X(278), X(1897)}}
X(54234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1810}, {3, 1280}, {48, 36807}, {78, 1477}, {212, 35160}, {219, 43760}, {905, 6078}, {1331, 35355}, {4587, 37626}
X(54234) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 1810}, {1249, 36807}, {5521, 35355}, {16593, 69}, {35111, 345}, {36103, 1280}, {39048, 63}, {40837, 35160}
X(54234) = barycentric product X(i)*X(j) for these (i, j): {4, 3008}, {92, 1279}, {273, 2348}, {278, 5853}, {331, 8647}, {1861, 52210}, {1897, 6084}, {2052, 20780}, {6335, 48032}, {16593, 36124}, {36123, 51419}
X(54234) = barycentric quotient X(i)/X(j) for these (i, j): {4, 36807}, {6, 1810}, {19, 1280}, {34, 43760}, {278, 35160}, {608, 1477}, {1279, 63}, {2348, 78}, {3008, 69}, {5853, 345}, {6084, 4025}, {6591, 35355}, {8647, 219}, {8659, 1459}, {8750, 6078}, {20662, 1818}, {20780, 394}, {23704, 4571}, {43923, 37626}, {48032, 905}, {52210, 31637}
X(54234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1890, 1839}, {4, 242, 1861}, {4, 7713, 1869}, {242, 1861, 8756}, {1878, 1884, 1877}
See Ivan Pavlov, euclid 5829.
X(54235) lies on circumconics {{A,B,C,X(2),X(344)}}, {{A,B,C,X(4),X(31926)}}, {{A,B,C,X(19),X(33)}}, {{A,B,C,X(27),X(14004)}}, {{A,B,C,X(29),X(37389)}}, {{A,B,C,X(75),X(20173)}} and on these lines: {4, 42071}, {19, 273}, {33, 92}, {105, 107}, {242, 52480}, {243, 14197}, {264, 281}, {278, 13149}, {286, 648}, {666, 46133}, {927, 20624}, {1861, 33676}, {3673, 39273}, {5307, 51846}, {6331, 31623}, {7017, 42384}, {8735, 18026}, {8764, 23696}, {13576, 52167}, {16813, 32658}, {46106, 46784}
X(54235) = isogonal conjugate of X(20752)
X(54235) = trilinear pole of line {4, 885}
X(54235) = polar conjugate of X(518)
X(54235) = intersection, other than A, B, C, of these circumconics: {{A, B, C, X(2), X(344)}}, {{A, B, C, X(4), X(31926)}}, {{A, B, C, X(19), X(33)}}, {{A, B, C, X(27), X(14004)}}, {{A, B, C, X(29), X(37389)}}, {{A, B, C, X(75), X(20173)}}, {{A, B, C, X(92), X(264)}}, {{A, B, C, X(105), X(1814)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(158), X(331)}}, {{A, B, C, X(242), X(1861)}}, {{A, B, C, X(274), X(9311)}}, {{A, B, C, X(279), X(24590)}}, {{A, B, C, X(308), X(18825)}}, {{A, B, C, X(318), X(1847)}}, {{A, B, C, X(514), X(1952)}}, {{A, B, C, X(523), X(47212)}}, {{A, B, C, X(525), X(2833)}}, {{A, B, C, X(673), X(14942)}}, {{A, B, C, X(1311), X(37202)}}, {{A, B, C, X(1821), X(18816)}}, {{A, B, C, X(2006), X(3512)}}, {{A, B, C, X(2989), X(40450)}}, {{A, B, C, X(4560), X(34056)}}, {{A, B, C, X(5089), X(42071)}}, {{A, B, C, X(17925), X(36125)}}, {{A, B, C, X(27475), X(31618)}}, {{A, B, C, X(36123), X(46102)}}, {{A, B, C, X(37790), X(37805)}}, {{A, B, C, X(40573), X(46103)}}
X(54235) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 20752}, {3, 672}, {6, 1818}, {31, 25083}, {48, 518}, {63, 2223}, {69, 9454}, {71, 3286}, {78, 52635}, {184, 3912}, {190, 23225}, {212, 241}, {219, 1458}, {222, 2340}, {228, 18206}, {255, 5089}, {292, 20778}, {304, 9455}, {394, 2356}, {577, 1861}, {603, 3693}, {652, 2283}, {665, 1331}, {673, 20776}, {822, 4238}, {906, 2254}, {918, 32656}, {926, 1813}, {1025, 1946}, {1026, 22383}, {1437, 3930}, {1444, 39258}, {1459, 2284}, {1790, 20683}, {1802, 34855}, {1810, 20662}, {1814, 42079}, {1876, 2289}, {2196, 8299}, {2200, 30941}, {3252, 7193}, {3263, 9247}, {3717, 52411}, {4055, 15149}, {4088, 32661}, {4447, 7116}, {4575, 24290}, {4712, 32658}, {5236, 6056}, {6184, 36057}, {6516, 46388}, {9436, 52425}, {9502, 36056}, {20769, 40730}, {31637, 39686}, {32657, 50441}, {32660, 50333}, {37908, 40152}, {46108, 52430}
X(54235) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 25083}, {3, 20752}, {9, 1818}, {105, 20740}, {120, 20728}, {136, 24290}, {1249, 518}, {3162, 2223}, {5190, 2254}, {5521, 665}, {6523, 5089}, {7952, 3693}, {19557, 20778}, {20621, 6184}, {20622, 9502}, {33675, 69}, {36103, 672}, {38966, 52614}, {39048, 20749}, {39053, 1025}, {39060, 883}, {40837, 241}
X(54235) = X(i)-cross conjugate of X(j) for these {i, j}: {105, 2481}, {242, 286}, {5089, 4}, {48408, 668}
X(54235) = barycentric product X(i)*X(j) for these (i, j): {4, 2481}, {19, 18031}, {75, 36124}, {76, 8751}, {92, 673}, {105, 264}, {158, 31637}, {273, 14942}, {278, 36796}, {281, 34018}, {286, 13576}, {294, 331}, {666, 17924}, {885, 18026}, {927, 44426}, {1024, 46404}, {1438, 1969}, {1462, 7017}, {1814, 2052}, {1847, 6559}, {2973, 5377}, {3064, 34085}, {6185, 46108}, {6528, 10099}, {6591, 36803}, {7649, 51560}, {13149, 28132}, {18027, 32658}, {18344, 46135}, {18785, 44129}, {23696, 52938}, {36086, 46107}, {36146, 46110}, {40717, 52030}, {46104, 46149}, {46133, 52456}
X(54235) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1818}, {2, 25083}, {4, 518}, {6, 20752}, {19, 672}, {25, 2223}, {27, 18206}, {28, 3286}, {33, 2340}, {34, 1458}, {92, 3912}, {105, 3}, {107, 4238}, {108, 2283}, {158, 1861}, {238, 20778}, {242, 8299}, {264, 3263}, {273, 9436}, {278, 241}, {281, 3693}, {286, 30941}, {294, 219}, {318, 3717}, {331, 40704}, {393, 5089}, {608, 52635}, {653, 1025}, {666, 1332}, {667, 23225}, {673, 63}, {884, 1946}, {885, 521}, {919, 906}, {927, 6516}, {1024, 652}, {1027, 1459}, {1096, 2356}, {1118, 1876}, {1119, 34855}, {1279, 20749}, {1416, 603}, {1438, 48}, {1462, 222}, {1783, 2284}, {1814, 394}, {1824, 20683}, {1826, 3930}, {1861, 4712}, {1876, 1362}, {1886, 9502}, {1897, 1026}, {1973, 9454}, {1974, 9455}, {2052, 46108}, {2195, 212}, {2223, 20776}, {2333, 39258}, {2356, 42079}, {2402, 24562}, {2481, 69}, {2501, 24290}, {2969, 3675}, {3290, 20728}, {5089, 6184}, {5342, 4684}, {6185, 1814}, {6335, 42720}, {6559, 3692}, {6591, 665}, {6654, 20769}, {7009, 4447}, {7476, 42747}, {7649, 2254}, {8735, 17435}, {8751, 6}, {8756, 14439}, {9503, 1815}, {10099, 520}, {13576, 72}, {14267, 34381}, {14625, 4047}, {14942, 78}, {15149, 16728}, {15344, 34159}, {17924, 918}, {18026, 883}, {18031, 304}, {18344, 926}, {18785, 71}, {23710, 35293}, {24006, 4088}, {28071, 1260}, {31637, 326}, {32658, 577}, {32666, 32656}, {32735, 36059}, {34018, 348}, {34337, 23102}, {36057, 255}, {36086, 1331}, {36118, 41353}, {36123, 36819}, {36124, 1}, {36125, 34230}, {36146, 1813}, {36796, 345}, {36802, 4571}, {39534, 42758}, {40754, 20741}, {41013, 3932}, {41934, 32658}, {42071, 23612}, {43921, 3937}, {43929, 22383}, {44129, 18157}, {44426, 50333}, {46108, 4437}, {46149, 3917}, {51560, 4561}, {51838, 36057}, {51866, 2196}, {52029, 3781}, {52030, 295}, {52456, 912}
See Ivan Pavlov, euclid 5829.
X(54236) lies on circumconics {A,B,C,X(3),X(105)}, {A,B,C,X(4),X(218)}, {A,B,C,X(32),X(8642)}, cubic K009 (Lemoine cubic), and on these lines: {3, 518}, {4, 105}, {1147, 34159}, {4712, 11517}, {28914, 35185}, {39173, 51471}
X(54236) = Cundy-Parry Phi of X(518)
X(54236) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14268}, {169, 277}, {1292, 21185}, {2191, 3434}, {6601, 34036}
X(54236) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14268}, {3309, 5511}
X(54236) = barycentric product X(i)*X(j) for these (i, j): {218, 13577}, {344, 3433}, {3870, 44178}, {6604, 40141}, {24562, 26706}
X(54236) = barycentric quotient X(i)/X(j) for these (i, j): {6, 14268}, {218, 3434}, {1617, 37800}, {3309, 26546}, {3433, 277}, {3870, 20927}, {4878, 21073}, {21059, 169}, {40141, 6601}
See Ivan Pavlov, euclid 5829.
X(54237) lies on circumconics {A,B,C,X(1),X(3913)}, {A,B,C,X(3),X(106)}, {A,B,C,X(4),X(145)}, {A,B,C,X(32),X(8643)}, cubic K009 (Lemoine cubic), and on these lines: {3, 519}, {4, 106}, {32, 40621}, {140, 2885}, {572, 3161}, {4487, 4855}, {35186, 44873}
X(54237) = Cundy-Parry Phi of X(519)
X(54237) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 14261}, {3445, 14923}
X(54237) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 14261}, {3667, 5510}, {45036, 14923}
X(54237) = barycentric quotient X(i)/X(j) for these (i, j): {6, 14261}, {1743, 14923}, {33628, 7419}, {40621, 5510}
See Ivan Pavlov, euclid 5829.
X(54238) lies on these lines: {4, 656}, {28, 23226}, {29, 8062}, {34, 51641}, {513, 1835}, {650, 16228}, {4086, 39585}, {5520, 20620}, {7253, 7518}, {7497, 23189}, {7510, 30212}, {17924, 48340}, {44426, 46385}
X(54238) = zosma transform of X(520)
X(54238) = X(i)-isoconjugate-of-X(j) for these {i, j}: {856, 6080}
X(54238) = X(i)-Dao conjugate of X(j) for these {i, j}: {16595, 69}
X(54238) = barycentric product X(i)*X(j) for these (i, j): {19, 23683}, {16595, 36126}, {26888, 46110}
X(54238) = barycentric quotient X(i)/X(j) for these (i, j): {23683, 304}, {26888, 1813}
See Ivan Pavlov, euclid 5829.
X(54239) lies on these lines: {4, 522}, {19, 657}, {24, 39226}, {25, 39199}, {27, 47785}, {33, 42756}, {34, 1459}, {406, 48186}, {427, 47806}, {469, 47787}, {475, 48228}, {513, 1835}, {514, 16231}, {523, 10151}, {661, 3064}, {1528, 8058}, {1826, 4036}, {1841, 6586}, {1851, 21119}, {2849, 21186}, {2969, 3259}, {3667, 44428}, {4194, 48173}, {4196, 47828}, {4200, 48243}, {4207, 47832}, {4212, 47830}, {4213, 47831}, {5521, 13999}, {6087, 6129}, {6994, 27486}, {6995, 47798}, {7378, 47808}, {7408, 48239}, {7409, 48169}, {7490, 46919}, {20315, 44928}, {20316, 46878}, {23741, 48398}, {28161, 39532}, {40950, 42750}, {42403, 45745}, {46107, 47995}
X(54239) = zosma transform of X(521)
X(54239) = perspector of circumconic {A,B,C,X(158), X(196)}
X(54239) = reflection of X(i) in X(j) for these {i,j}: {7649, 39534}, {20315, 44928}, {44426, 16231}
X(54239) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 13138}, {48, 44327}, {63, 36049}, {69, 32652}, {78, 8059}, {84, 1331}, {100, 1433}, {101, 41081}, {109, 271}, {110, 52389}, {189, 906}, {219, 37141}, {268, 651}, {280, 36059}, {282, 1813}, {285, 23067}, {309, 32656}, {394, 40117}, {662, 41087}, {664, 2188}, {1332, 1436}, {1413, 4571}, {1415, 44189}, {1422, 4587}, {1903, 4558}, {2192, 6516}, {2208, 4561}, {2357, 4592}, {4556, 53010}, {4575, 39130}, {5546, 52037}, {6081, 46974}, {6517, 7008}, {32660, 34404}
X(54239) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 271}, {57, 6516}, {136, 39130}, {244, 52389}, {281, 190}, {1015, 41081}, {1084, 41087}, {1146, 44189}, {1249, 44327}, {3162, 36049}, {5139, 2357}, {5190, 189}, {5514, 63}, {5521, 84}, {8054, 1433}, {14837, 52616}, {16596, 69}, {20620, 280}, {36103, 13138}, {38991, 268}, {39025, 2188}, {40615, 34400}
X(54239) = X(i)-cross conjugate of X(j) for these {i, j}: {38362, 7952}
X(54239) = barycentric product X(i)*X(j) for these (i, j): {4, 14837}, {19, 17896}, {40, 17924}, {92, 6129}, {196, 522}, {198, 46107}, {208, 4391}, {221, 46110}, {223, 44426}, {273, 14298}, {278, 8058}, {322, 6591}, {329, 7649}, {342, 650}, {347, 3064}, {514, 7952}, {523, 41083}, {653, 38357}, {663, 40701}, {693, 2331}, {905, 47372}, {1577, 3194}, {1817, 24006}, {2360, 14618}, {2501, 8822}, {3195, 3261}, {3209, 35519}, {5514, 36118}, {6087, 52780}, {7149, 8063}, {7192, 53009}, {16596, 36127}, {17925, 21075}, {18344, 40702}, {24002, 40971}
X(54239) = barycentric quotient X(i)/X(j) for these (i, j): {4, 44327}, {19, 13138}, {25, 36049}, {34, 37141}, {40, 1332}, {196, 664}, {198, 1331}, {208, 651}, {221, 1813}, {223, 6516}, {329, 4561}, {342, 4554}, {512, 41087}, {513, 41081}, {522, 44189}, {608, 8059}, {649, 1433}, {650, 271}, {661, 52389}, {663, 268}, {1096, 40117}, {1817, 4592}, {1973, 32652}, {2187, 906}, {2199, 36059}, {2324, 4571}, {2331, 100}, {2360, 4558}, {2489, 2357}, {2501, 39130}, {3063, 2188}, {3064, 280}, {3194, 662}, {3195, 101}, {3209, 109}, {3676, 34400}, {4017, 52037}, {4705, 53010}, {6129, 63}, {6591, 84}, {7011, 6517}, {7074, 4587}, {7649, 189}, {8058, 345}, {8822, 4563}, {10397, 1259}, {14298, 78}, {14837, 69}, {16596, 52616}, {17896, 304}, {17924, 309}, {18344, 282}, {21075, 52609}, {38357, 6332}, {40701, 4572}, {40971, 644}, {41083, 99}, {43923, 1422}, {44426, 34404}, {46107, 44190}, {47372, 6335}, {53009, 3952}
X(54239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {513, 39534, 7649}
See Ivan Pavlov, euclid 5829.
X(54240) lies on these lines: {1, 8764}, {4, 3270}, {92, 52780}, {107, 108}, {109, 681}, {225, 1896}, {264, 37800}, {273, 4858}, {278, 2052}, {431, 43746}, {450, 41349}, {648, 651}, {653, 1020}, {1068, 1093}, {1415, 16813}, {1441, 6330}, {1577, 39053}, {1758, 41497}, {1813, 1981}, {1880, 16081}, {1897, 4551}, {1948, 22464}, {2405, 52607}, {4552, 6335}, {4554, 6331}, {6528, 32038}, {7952, 14249}, {14165, 37799}, {16080, 40149}, {17924, 23984}, {26704, 52775}, {26705, 52776}, {37798, 46106}, {43035, 52982}, {51358, 51365}
X(54240) = isogonal conjugate of X(36054)
X(54240) = trilinear pole of line {4, 65}
X(54240) = polar conjugate of X(521)
X(54240) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(2), X(2405)}}, {{A, B, C, X(92), X(24035)}}, {{A, B, C, X(107), X(648)}}, {{A, B, C, X(108), X(651)}}, {{A, B, C, X(190), X(1309)}}, {{A, B, C, X(278), X(23706)}}, {{A, B, C, X(523), X(47203)}}, {{A, B, C, X(525), X(2845)}}, {{A, B, C, X(644), X(40117)}}, {{A, B, C, X(650), X(2637)}}, {{A, B, C, X(655), X(26704)}}, {{A, B, C, X(658), X(15455)}}, {{A, B, C, X(681), X(823)}}, {{A, B, C, X(1086), X(39534)}}, {{A, B, C, X(4565), X(36067)}}, {{A, B, C, X(4612), X(30610)}}, {{A, B, C, X(4858), X(24002)}}, {{A, B, C, X(26705), X(27833)}}, {{A, B, C, X(26706), X(32041)}}, {{A, B, C, X(31628), X(46605)}}, {{A, B, C, X(32691), X(37137)}}
X(54240) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36054}, {3, 652}, {9, 23224}, {21, 822}, {29, 32320}, {32, 52616}, {41, 4131}, {48, 521}, {55, 4091}, {63, 1946}, {71, 23189}, {73, 23090}, {78, 22383}, {101, 1364}, {109, 35072}, {184, 6332}, {212, 905}, {219, 1459}, {255, 650}, {283, 647}, {284, 520}, {326, 3063}, {332, 3049}, {333, 39201}, {394, 663}, {512, 6514}, {513, 2289}, {522, 577}, {651, 2638}, {656, 2193}, {657, 1804}, {664, 39687}, {667, 3719}, {810, 1812}, {906, 7004}, {1021, 22341}, {1092, 3064}, {1264, 1919}, {1331, 7117}, {1415, 24031}, {1433, 10397}, {1437, 8611}, {1794, 52306}, {1795, 52307}, {1813, 3270}, {2175, 30805}, {2194, 24018}, {2287, 51641}, {2299, 52613}, {2318, 7254}, {2968, 32660}, {3239, 7335}, {3269, 4636}, {3682, 7252}, {3737, 3990}, {3900, 7125}, {3937, 4587}, {4025, 52425}, {4041, 18604}, {4055, 4560}, {4100, 44426}, {4391, 52430}, {6507, 18344}, {6517, 14936}, {7016, 22382}, {7065, 52919}, {7128, 23614}, {7183, 8641}, {9247, 35518}, {14331, 14379}, {14395, 35200}, {14585, 35519}, {17434, 35196}, {20752, 23696}, {21789, 40152}, {23606, 46110}, {26932, 32656}, {34591, 36059}, {35071, 52921}, {36055, 46391}, {37754, 52914}
X(54240) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36054}, {11, 35072}, {123, 47410}, {133, 14395}, {223, 4091}, {226, 52613}, {478, 23224}, {1015, 1364}, {1146, 24031}, {1214, 24018}, {1249, 521}, {3160, 4131}, {3162, 1946}, {5190, 7004}, {5375, 1259}, {5521, 7117}, {6376, 52616}, {6523, 650}, {6631, 3719}, {9296, 1264}, {10001, 326}, {15259, 3063}, {20620, 34591}, {25640, 52307}, {36103, 652}, {38991, 2638}, {39025, 39687}, {39026, 2289}, {39052, 283}, {39053, 63}, {39054, 6514}, {39060, 69}, {39062, 1812}, {40590, 520}, {40593, 30805}, {40596, 2193}, {40611, 822}, {40624, 23983}, {40625, 16731}, {40837, 905}, {47345, 656}, {51221, 46391}
X(54240) = X(i)-cross conjugate of X(j) for these {i, j}: {108, 18026}, {158, 24032}, {278, 23984}, {650, 4}, {3064, 1896}, {6129, 7}, {17924, 2052}, {21348, 1041}, {44426, 273}, {52607, 653}
X(54240) = X(i)-Zayin conjugate of X(j) for these {i, j}: {1, 36054}, {3, 822}, {1745, 652}
X(54240) = X(i)-Ceva conjugate of X(j) for these {i, j}: {823, 653}, {24032, 158}
X(54240) = barycentric product X(i)*X(j) for these (i, j): {1, 52938}, {4, 18026}, {19, 46404}, {65, 6528}, {75, 36127}, {92, 653}, {107, 1441}, {108, 264}, {112, 52575}, {158, 664}, {225, 811}, {226, 823}, {273, 1897}, {278, 6335}, {281, 13149}, {307, 36126}, {318, 36118}, {331, 1783}, {349, 24019}, {393, 4554}, {522, 24032}, {648, 40149}, {651, 2052}, {668, 1118}, {1093, 6516}, {1096, 4572}, {1214, 15352}, {1231, 6529}, {1415, 18027}, {1813, 6521}, {1857, 4569}, {1880, 6331}, {1896, 4566}, {1969, 32674}, {4391, 23984}, {6358, 52919}, {6386, 7337}, {7012, 46107}, {7017, 32714}, {7128, 46110}, {17073, 42389}, {17924, 46102}, {24033, 35519}, {24035, 52780}, {31623, 52607}, {34388, 52920}, {40117, 40701}, {46104, 46152}
X(54240) = barycentric quotient X(i)/X(j) for these (i, j): {4, 521}, {6, 36054}, {7, 4131}, {19, 652}, {25, 1946}, {28, 23189}, {34, 1459}, {56, 23224}, {57, 4091}, {65, 520}, {75, 52616}, {85, 30805}, {92, 6332}, {100, 1259}, {101, 2289}, {107, 21}, {108, 3}, {109, 255}, {112, 2193}, {158, 522}, {162, 283}, {190, 3719}, {225, 656}, {226, 24018}, {264, 35518}, {273, 4025}, {278, 905}, {331, 15413}, {393, 650}, {513, 1364}, {522, 24031}, {608, 22383}, {648, 1812}, {650, 35072}, {651, 394}, {653, 63}, {658, 7183}, {662, 6514}, {663, 2638}, {664, 326}, {668, 1264}, {692, 6056}, {811, 332}, {823, 333}, {934, 1804}, {1020, 40152}, {1042, 51641}, {1093, 44426}, {1096, 663}, {1172, 23090}, {1214, 52613}, {1231, 4143}, {1309, 1809}, {1396, 7254}, {1400, 822}, {1402, 39201}, {1409, 32320}, {1415, 577}, {1441, 3265}, {1461, 7125}, {1783, 219}, {1813, 6507}, {1826, 8611}, {1841, 52306}, {1857, 3900}, {1875, 8677}, {1880, 647}, {1896, 7253}, {1897, 78}, {1981, 6518}, {1990, 14395}, {2052, 4391}, {2207, 3063}, {2331, 10397}, {3063, 39687}, {3064, 34591}, {3270, 23614}, {4036, 7068}, {4077, 17216}, {4391, 23983}, {4551, 3682}, {4552, 3998}, {4554, 3926}, {4559, 3990}, {4560, 16731}, {4565, 18604}, {4566, 52385}, {4569, 7055}, {5317, 7252}, {6059, 8641}, {6335, 345}, {6516, 3964}, {6520, 3064}, {6521, 46110}, {6524, 18344}, {6528, 314}, {6529, 1172}, {6588, 47410}, {6591, 7117}, {7012, 1331}, {7017, 15416}, {7045, 6517}, {7103, 51646}, {7115, 906}, {7120, 22382}, {7128, 1813}, {7337, 667}, {7649, 7004}, {8747, 3737}, {8748, 1021}, {8750, 212}, {8755, 46391}, {8756, 14418}, {13149, 348}, {13437, 6365}, {13459, 6364}, {14571, 52307}, {15352, 31623}, {15742, 4571}, {17924, 26932}, {18026, 69}, {18344, 3270}, {19366, 680}, {21859, 52386}, {23582, 4612}, {23706, 22350}, {23710, 14414}, {23984, 651}, {23985, 1415}, {23987, 46974}, {24000, 4636}, {24019, 284}, {24021, 52921}, {24032, 664}, {24033, 109}, {31623, 15411}, {32230, 52914}, {32660, 4100}, {32674, 48}, {32702, 14578}, {32713, 2194}, {32714, 222}, {36059, 1092}, {36067, 36055}, {36110, 1795}, {36118, 77}, {36123, 37628}, {36124, 23696}, {36126, 29}, {36127, 1}, {36797, 1792}, {39534, 35014}, {40097, 39167}, {40117, 268}, {40149, 525}, {41013, 52355}, {41321, 51376}, {43923, 3937}, {44426, 2968}, {46102, 1332}, {46107, 17880}, {46152, 3917}, {46404, 304}, {47372, 8058}, {52575, 3267}, {52607, 1214}, {52776, 37741}, {52919, 2185}, {52920, 60}, {52921, 1098}, {52938, 75}
See Ivan Pavlov, euclid 5829.
X(54241) lies on circumconics {A,B,C,X(3),X(8)}, {A,B,C,X(4),X(108)}, cubic K028, and on these lines: {3, 108}, {4, 521}, {8, 14249}, {1118, 2745}, {22350, 23706}, {39267, 39268}
X(54241) = Cundy-Parry Psi of X(521)
X(54241) = trilinear pole of line {14571, 52307}
X(54241) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 39175}, {1795, 6001}, {1809, 51662}
X(54241) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 39175}, {2804, 52114}, {25640, 6001}
X(54241) = X(i)-cross conjugate of X(j) for these {i, j}: {517, 1295}
X(54241) = barycentric quotient X(i)/X(j) for these (i, j): {6, 39175}, {1875, 43058}, {14571, 6001}, {32647, 2720}, {36044, 37136}, {42072, 47434}
See Ivan Pavlov, euclid 5829.
X(54242) lies on circumconics {A,B,C,X(3),X(522)}, {A,B,C,X(4),X(109)}, cubic K028, and on these lines: {3, 102}, {4, 522}, {76, 34393}, {953, 35183}
X(54242) = Cundy-Parry Psi of X(522)
X(54242) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2182, 2988}, {14304, 35187}, {15379, 24034}, {32706, 46974}, {36113, 39471}
X(54242) = X(i)-Dao conjugate of X(j) for these {i, j}: {117, 515}
X(54242) = barycentric product X(i)*X(j) for these (i, j): {1735, 36100}, {8607, 34393}
X(54242) = barycentric quotient X(i)/X(j) for these (i, j): {102, 2988}, {8607, 515}, {32643, 35187}, {32667, 36113}
See Ivan Pavlov, euclid 5829.
X(54243) lies on circumconics {A,B,C,X(3),X(109)}, {A,B,C,X(4),X(280)}, {A,B,C,X(56),X(39199)}, cubic K009 (Lemoine cubic), and on these lines: {3, 522}, {4, 109}, {32, 23986}, {952, 1147}, {2734, 35187}
X(54243) = Cundy-Parry Phi of X(522)
X(54243) = X(i)-isoconjugate-of-X(j) for these {i, j}: {102, 1735}, {8607, 36100}
X(54243) = X(i)-Dao conjugate of X(j) for these {i, j}: {515, 117}
X(54243) = X(i)-cross conjugate of X(j) for these {i, j}: {38554, 515}
X(54243) = barycentric product X(i)*X(j) for these (i, j): {515, 2988}
X(54243) = barycentric quotient X(i)/X(j) for these (i, j): {2182, 1735}, {2988, 34393}, {23986, 117}, {32706, 52780}, {32707, 36067}
See Ivan Pavlov, euclid 5829.
X(54244) lies on these lines: {4, 6003}, {19, 35347}, {24, 39210}, {25, 3733}, {34, 4017}, {108, 34921}, {162, 250}, {186, 14838}, {340, 18160}, {427, 31946}, {513, 1835}, {656, 14192}, {661, 35993}, {759, 32710}, {798, 44103}, {830, 48340}, {1112, 1830}, {1474, 20981}, {1510, 1831}, {1829, 4132}, {2806, 52355}, {2812, 48303}, {2850, 44409}, {3064, 15313}, {3738, 44426}, {6591, 48026}, {7265, 35057}, {15309, 17925}, {17104, 38936}, {17171, 42327}, {23189, 39212}
X(54244) = zosma transform of X(523)
X(54244) = reflection of X(i) in X(j) for these {i,j}: {7649, 18344}
X(54244) = trilinear pole of line {2611, 47230}
X(54244) = perspector of circumconic {A,B,C,X(278), X(6198)}
X(54244) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(4), X(186)}}, {{A, B, C, X(35), X(18838)}}, {{A, B, C, X(162), X(24006)}}, {{A, B, C, X(445), X(35993)}}, {{A, B, C, X(513), X(2605)}}, {{A, B, C, X(526), X(6003)}}, {{A, B, C, X(1876), X(7282)}}, {{A, B, C, X(1877), X(6198)}}, {{A, B, C, X(1884), X(11107)}}, {{A, B, C, X(2611), X(4017)}}, {{A, B, C, X(2614), X(7178)}}, {{A, B, C, X(3678), X(38938)}}, {{A, B, C, X(35235), X(37964)}}, {{A, B, C, X(37305), X(46468)}}
X(54244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 6742}, {48, 15455}, {72, 13486}, {78, 26700}, {79, 1331}, {100, 7100}, {110, 52388}, {219, 38340}, {643, 52390}, {664, 8606}, {758, 36061}, {906, 30690}, {1332, 2160}, {1789, 4551}, {1813, 7110}, {3615, 23067}, {3936, 32662}, {4558, 8818}, {4561, 6186}, {4571, 52372}, {4574, 52393}, {4575, 6757}, {4587, 52374}, {6516, 7073}, {8611, 35049}, {20565, 32656}, {36059, 52344}
X(54244) = X(i)-Dao conjugate of X(j) for these {i, j}: {136, 6757}, {244, 52388}, {1015, 52381}, {1249, 15455}, {5190, 30690}, {5521, 79}, {8054, 7100}, {8287, 69}, {14838, 14208}, {16221, 758}, {20620, 52344}, {36103, 6742}, {39025, 8606}
X(54244) = X(i)-Zayin conjugate of X(j) for these {i, j}: {110, 656}
X(54244) = X(i)-Waw conjugate of X(j) for these {i, j}: {4, 1830}
X(54244) = X(i)-Ceva conjugate of X(j) for these {i, j}: {14775, 7649}
X(54244) = barycentric product X(i)*X(j) for these (i, j): {4, 14838}, {19, 4467}, {25, 18160}, {28, 7265}, {35, 17924}, {92, 2605}, {112, 17886}, {162, 8287}, {273, 9404}, {278, 35057}, {319, 6591}, {513, 52412}, {514, 6198}, {648, 2611}, {650, 7282}, {759, 44427}, {811, 20982}, {823, 22094}, {1399, 46110}, {1442, 3064}, {1824, 16755}, {1825, 4560}, {1897, 7202}, {2003, 44426}, {2052, 23226}, {2174, 46107}, {3219, 7649}, {3261, 14975}, {3678, 17925}, {4077, 41502}, {5379, 21141}, {7178, 11107}, {14616, 47230}, {14618, 17104}, {14775, 16585}, {17095, 18344}, {24006, 40214}, {35235, 37140}, {42033, 43923}
X(54244) = barycentric quotient X(i)/X(j) for these (i, j): {4, 15455}, {19, 6742}, {34, 38340}, {35, 1332}, {186, 4585}, {513, 52381}, {608, 26700}, {649, 7100}, {661, 52388}, {1399, 1813}, {1474, 13486}, {1825, 4552}, {2003, 6516}, {2174, 1331}, {2501, 6757}, {2605, 63}, {2611, 525}, {3063, 8606}, {3064, 52344}, {3219, 4561}, {3678, 52609}, {4467, 304}, {6591, 79}, {7180, 52390}, {7202, 4025}, {7252, 1789}, {7265, 20336}, {7282, 4554}, {7649, 30690}, {8287, 14208}, {9404, 78}, {11107, 645}, {14838, 69}, {14975, 101}, {17104, 4558}, {17886, 3267}, {17924, 20565}, {18160, 305}, {18344, 7110}, {20982, 656}, {21741, 23067}, {21824, 4064}, {22094, 24018}, {23226, 394}, {34079, 36061}, {34397, 1983}, {35057, 345}, {40214, 4592}, {41502, 643}, {43923, 52374}, {43925, 52375}, {44427, 35550}, {47230, 758}, {52405, 4571}, {52412, 668}, {52418, 4242}
X(54244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {513, 18344, 7649}
See Ivan Pavlov, euclid 5829.
X(54245) lies on these lines: {4, 28612}, {25, 21009}, {34, 51655}, {210, 430}, {513, 1835}, {4206, 5338}, {16611, 23230}
X(54245) = zosma transform of X(524)
X(54245) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 51561}, {1444, 34893}, {1790, 34892}
X(54245) = X(i)-Dao conjugate of X(j) for these {i, j}: {16597, 69}, {36103, 51561}
X(54245) = barycentric product X(i)*X(j) for these (i, j): {4, 16611}, {19, 4442}, {92, 39688}, {278, 24394}, {1824, 37756}, {1826, 7292}, {2052, 23230}, {16597, 36128}, {16784, 41013}
X(54245) = barycentric quotient X(i)/X(j) for these (i, j): {19, 51561}, {1824, 34892}, {2333, 34893}, {2832, 15419}, {4442, 304}, {7292, 17206}, {8650, 7254}, {16611, 69}, {16784, 1444}, {23230, 394}, {24394, 345}, {39688, 63}
See Ivan Pavlov, euclid 5829.
X(54246) lies on cubic K1156 and these lines: {2, 8877}, {6, 41404}, {576, 52474}, {7312, 7313}, {23106, 39296}
X(54246) = eigentransform of X(524)
X(54246) = X(i)-Dao conjugate of X(j) for these {i, j}: {10630, 671}
See Ivan Pavlov, euclid 5829.
X(54247) lies on these lines: {4, 1577}, {19, 4041}, {25, 21789}, {28, 14838}, {34, 51640}, {513, 1835}, {830, 17924}, {1891, 3907}, {2299, 21761}, {3064, 8678}, {4198, 4560}, {6591, 50517}, {7497, 39212}, {20620, 46671}, {24019, 32673}, {44705, 47124}
X(54247) = zosma transform of X(525)
X(54247) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1331, 15314}, {4561, 8615}
X(54247) = X(i)-Dao conjugate of X(j) for these {i, j}: {5521, 15314}, {34846, 69}
X(54247) = barycentric product X(i)*X(j) for these (i, j): {4, 16612}, {3064, 4296}, {5279, 7649}, {5285, 17924}, {6591, 7270}, {24019, 34846}
X(54247) = barycentric quotient X(i)/X(j) for these (i, j): {5279, 4561}, {5285, 1332}, {6591, 15314}, {16612, 69}
See Ivan Pavlov, euclid 5829.
X(54248) lies on these lines: {3, 525}, {30, 14850}, {249, 21166}, {512, 46634}, {524, 35383}, {826, 46633}, {3564, 38723}, {3566, 46987}, {12041, 47293}, {15061, 34953}, {38728, 51258}
See Ivan Pavlov, euclid 5918.
X(54249) lies on these lines {37, 513}, {241, 514}, {512, 4162}, {647, 49293}, {649, 4083}, {654, 1938}, {661, 3777}, {784, 48397}, {1449, 3063}, {1743, 20980}, {3287, 43924}, {3310, 47768}, {3709, 4778}, {3766, 4885}, {3912, 23828}, {4378, 16975}, {4394, 21832}, {4501, 48293}, {4526, 6006}, {4699, 20906}, {4751, 20949}, {4817, 25425}, {4820, 8714}, {4850, 47762}, {4905, 24290}, {4932, 25098}, {4977, 6586}, {5029, 48331}, {6372, 48026}, {6588, 29120}, {6591, 29025}, {7234, 22319}, {8632, 48330}, {8659, 48328}, {14433, 31197}, {14991, 23815}, {16671, 39521}, {16884, 21007}, {17092, 24002}, {17461, 41162}, {17756, 47824}, {20952, 23807}, {21791, 22383}, {21894, 47881}, {23780, 30804}, {24635, 33570}, {28374, 49282}, {29029, 47227}, {30665, 50336}, {40549, 47802}, {44307, 45658}
X(54249) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(37), X(16609)}}, {{A, B, C, X(241), X(3252)}}, {{A, B, C, X(513), X(43041)}}, {{A, B, C, X(649), X(43051)}}, {{A, B, C, X(876), X(3676)}}, {{A, B, C, X(1323), X(4334)}}, {{A, B, C, X(3572), X(3669)}}, {{A, B, C, X(3911), X(17754)}}, {{A, B, C, X(10566), X(21348)}}, {{A, B, C, X(19586), X(39957)}}, {{A, B, C, X(20358), X(39742)}}, {{A, B, C, X(20507), X(24002)}}, {{A, B, C, X(20917), X(40881)}}, {{A, B, C, X(24349), X(43037)}}, {{A, B, C, X(40773), X(40787)}}
X(54249) = reflection of X(i) in X(j) for these {i,j}: {20507, 3676}, {21832, 4394}, {3766, 4885}, {650, 665}
X(54249) = complement of isotomic conjugate of of isogonal conjugate of X(4782)
X(54249) = perspector of circumconic {{A, B, C, X(7), X(87)}}
X(54249) = center of circumconic {{A, B, C, X(4817), X(24720)}}
X(54249) = X(i)-isoconjugate-of-X(j) for these {i, j} {101, 41527}, {651, 7220}
X(54249) = X(i)-Dao conjugate of X(j) for these {i, j} {984, 3807}, {1015, 41527}, {24720, 4762}, {38991, 7220}
X(54249) = X(i)-Zayin conjugate of X(j) for these {i, j}: {43077, 4782}
X(54249) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4817, 513}
X(54249) = X(i)-complementary conjugate of X(j) for these {i, j}: {32739, 27481}, {34475, 53575}, {40735, 11}, {43077, 141}, {51449, 53564}, {52654, 21252}, {53648, 626}
X(54249) = (polar of X(1) wrt inconic with perspector X(2)) ∩ (polar of X(2) wrt inconic with perspector X(1))
X(54249) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {513, 41527}, {663, 7220}, {4334, 664}, {8926, 51614}, {19584, 3807}, {19586, 3799}, {20917, 1978}, {21010, 100}, {21101, 4033}, {22163, 1332}, {24349, 668}, {24720, 75}, {45902, 40785}
X(54249) = barycentric product X(i)*X(j) for these (i, j): {1, 24720}, {1019, 21101}, {4334, 522}, {4458, 8926}, {17754, 514}, {17924, 22163}, {19584, 4817}, {20917, 649}, {21010, 693}, {24349, 513}
X(54249) = barycentric quotient X(i)/X(j) for these (i, j): {513, 41527}, {663, 7220}, {4334, 664}, {8926, 51614}, {17754, 190}, {19584, 3807}, {19586, 3799}, {20917, 1978}, {21010, 100}, {21101, 4033}, {22163, 1332}, {24349, 668}, {24720, 75}, {45902, 40785}
X(54249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 3676, 20507}, {649, 4449, 4435}, {4394, 29226, 21832}, {43060, 48276, 650}
See Ivan Pavlov, euclid 5918.
X(54250) lies on circumconics {{A, B, C, X(9503), X(51839)}} and on these lines: {6, 513}, {523, 47454}, {650, 4449}, {665, 2516}, {676, 14330}, {3669, 4394}, {6589, 10581}, {6591, 40137}, {33630, 44426}, {37689, 47803}
X(54250) = perspector of circumconic {{A, B, C, X(105), X(3062)}}
X(54250) = (polar of X(1) wrt inconic with perspector X(57)) ∩ (polar of X(57) wrt inconic with perspector X(1))
See Ivan Pavlov, euclid 5918.
X(54251) lies on these lines: {1, 4785}, {42, 649}, {43, 45313}, {513, 663}, {514, 53553}, {667, 6373}, {798, 9010}, {810, 50515}, {812, 4449}, {1919, 21003}, {3052, 23865}, {3221, 8639}, {3720, 31147}, {3768, 8656}, {3835, 24666}, {4455, 8643}, {4481, 48023}, {4724, 4817}, {9313, 21143}, {16569, 24749}, {20295, 29814}, {21191, 21301}, {23751, 50503}, {24533, 43931}, {25128, 27345}, {25502, 45339}, {25889, 25924}, {28360, 28398}, {29328, 48303}, {29362, 48342}
X(54251) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(875), X(43924)}}, {{A, B, C, X(1319), X(21010)}}, {{A, B, C, X(1458), X(4334)}}, {{A, B, C, X(1463), X(24349)}}, {{A, B, C, X(3572), X(3669)}}, {{A, B, C, X(4017), X(24720)}}, {{A, B, C, X(4785), X(43077)}}, {{A, B, C, X(17754), X(52896)}}, {{A, B, C, X(18108), X(23655)}}, {{A, B, C, X(20459), X(39966)}}, {{A, B, C, X(25426), X(40760)}}
X(54251) = reflection of X(i) in X(j) for these {i,j}: {20979, 667}, {21301, 21191}, {48023, 4481}
X(54251) = perspector of circumconic {{A, B, C, X(57), X(292)}}
X(54251) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 41527}, {664, 7220}, {3799, 47647}, {23605, 51614}
X(54251) = X(i)-Dao conjugate of X(j) for these {i, j}: {984, 4505}, {8054, 41527}, {39025, 7220}
X(54251) = X(i)-Zayin conjugate of X(j) for these {i, j}: {32041, 4724}
X(54251) = (polar of X(1) wrt inconic with perspector X(6)) ∩ (polar of X(6) wrt inconic with perspector X(1))
X(54251) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {649, 41527}, {3063, 7220}, {4334, 4554}, {17754, 668}, {19584, 4505}, {19586, 3807}, {19587, 3799}, {20917, 6386}, {21101, 27808}, {22163, 4561}, {24349, 1978}, {24720, 76}
X(54251) = barycentric product X(i)*X(j) for these (i, j): {4334, 650}, {17754, 513}, {19586, 4817}, {20917, 667}, {21010, 514}, {21101, 3733}, {22163, 7649}, {24349, 649}, {24720, 6}
X(54251) = barycentric quotient X(i)/X(j) for these (i, j): {649, 41527}, {3063, 7220}, {17754, 668}, {19584, 4505}, {19586, 3807}, {19587, 3799}, {20917, 6386}, {21010, 190}, {21101, 27808}, {22163, 4561}, {24349, 1978}, {24720, 76}
X(54251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {667, 6373, 20979}, {7234, 50514, 649}, {50517, 51641, 663}
See Ivan Pavlov, euclid 5918.
X(54252) lies on these lines: {38, 661}, {240, 522}, {798, 4083}
X(54252) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(860), X(11328)}}, {{A, B, C, X(7649), X(45907)}}, {{A, B, C, X(18906), X(52651)}}
X(54252) = perspector of circumconic {{A, B, C, X(92), X(1581)}}
X(54252) = X(i)-isoconjugate-of-X(j) for these {i, j}: {99, 47643}, {110, 19222}
X(54252) = X(i)-Dao conjugate of X(j) for these {i, j}: {244, 19222}, {38986, 47643}
X(54252) = (polar of X(1) wrt inconic with perspector X(75)) ∩ (polar of X(75) wrt inconic with perspector X(1))
X(54252) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {661, 19222}, {798, 47643}, {6234, 37134}, {11328, 662}, {18906, 799}, {45907, 1}
X(54252) = barycentric product X(i)*X(j) for these (i, j): {11328, 1577}, {18906, 661}, {19591, 523}, {45907, 75}
X(54252) = barycentric quotient X(i)/X(j) for these (i, j): {661, 19222}, {798, 47643}, {6234, 37134}, {11328, 662}, {18906, 799}, {19591, 99}, {45907, 1}
See Ivan Pavlov, euclid 5918.
X(54253) lies on these lines: {239, 514}, {513, 1100}, {650, 47922}, {661, 4367}, {663, 2520}, {3250, 4378}, {4024, 17166}, {4079, 16777}, {4435, 4979}, {4826, 48292}, {4893, 14419}, {6372, 8632}, {8672, 20981}, {8678, 50454}, {28195, 50455}, {29212, 47873}, {48019, 48336}, {48026, 48330}, {48266, 48301}
X(54253) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(514), X(9279)}}, {{A, B, C, X(661), X(21196)}}, {{A, B, C, X(16704), X(40750)}}, {{A, B, C, X(18206), X(18791)}}
X(54253) = perspector of circumconic {{A, B, C, X(86), X(1929)}}
X(54253) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 40776}
X(54253) = X(i)-Dao conjugate of X(j) for these {i, j}: {8054, 40776}
X(54253) = X(i)-Ceva conjugate of X(j) for these {i, j}: {28840, 4724}
X(54253) = (polar of X(1) wrt inconic with perspector X(81)) ∩ (polar of X(81) wrt inconic with perspector X(1))
X(54253) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {649, 40776}, {9279, 10}, {18791, 32041}, {24342, 668}
X(54253) = barycentric product X(i)*X(j) for these (i, j): {86, 9279}, {18791, 4762}, {24342, 513}, {40750, 514}
X(54253) = barycentric quotient X(i)/X(j) for these (i, j): {649, 40776}, {9279, 10}, {18791, 32041}, {24342, 668}, {40750, 190}
X(54253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4367, 5029}, {1019, 21832, 649}
See Ivan Pavlov, euclid 5918.
X(54254) lies on these lines: {36, 238}, {43, 7234}, {649, 2666}, {798, 4367}, {804, 52602}, {812, 50512}, {1125, 4785}, {3741, 45313}, {4762, 4782}, {8631, 48136}, {17018, 50487}, {23506, 50500}, {24948, 50489}, {25502, 29487}, {30116, 30203}
X(54254) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2248), X(3286)}}, {{A, B, C, X(40721), X(52897)}}, {{A, B, C, X(40749), X(52680)}}
X(54254) = midpoint of X(i) in X(j) for these {i,j}: {1019, 4455}, {798, 4367}
X(54254) = perspector of circumconic {{A, B, C, X(81), X(2665)}}
X(54254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 40775}
X(54254) = X(i)-Dao conjugate of X(j) for these {i, j}: {8054, 40775}
X(54254) = (polar of X(1) wrt inconic with perspector X(86)) ∩ (polar of X(86) wrt inconic with perspector X(1))
X(54254) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {649, 40775}, {40721, 668}
X(54254) = barycentric product X(i)*X(j) for these (i, j): {40721, 513}, {40749, 514}
X(54254) = barycentric quotient X(i)/X(j) for these (i, j): {649, 40775}, {40721, 668}, {40749, 190}
X(54254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 4455, 513}
See Ivan Pavlov, euclid 5918.
X(54255) lies on these lines: {36, 30235}, {55, 650}, {390, 4762}, {497, 45320}, {513, 4162}, {2820, 3669}, {3057, 9443}, {4885, 5274}, {5281, 44567}, {5284, 25925}, {6767, 8760}, {9819, 14077}, {10589, 31250}, {28042, 44842}
X(54255) = perspector of circumconic {{A, B, C, X(294), X(8056)}}
X(54255) = (polar of X(1) wrt inconic with perspector X(9)) ∩ (polar of X(9) wrt inconic with perspector X(1))
See Ivan Pavlov, euclid 5918.
X(54256) lies on these lines: {514, 661}, {523, 1213}, {649, 48392}, {690, 4931}, {2321, 22044}, {2533, 4024}, {2610, 47873}, {2642, 4777}, {4041, 4838}, {4142, 48277}, {4979, 29150}, {7192, 46192}, {21832, 48393}, {27081, 47792}, {27710, 47659}, {46390, 48120}, {48265, 50522}
X(54256) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(514), X(9279)}}, {{A, B, C, X(693), X(18014)}}, {{A, B, C, X(3936), X(40750)}}, {{A, B, C, X(14210), X(24342)}}, {{A, B, C, X(32679), X(42666)}}
X(54256) = perspector of circumconic {{A, B, C, X(75), X(8818)}}
X(54256) = X(i)-isoconjugate-of-X(j) for these {i, j}: {110, 40776}
X(54256) = X(i)-Dao conjugate of X(j) for these {i, j}: {244, 40776}
X(54256) = (polar of X(2) wrt inconic with perspector X(10)) ∩ (polar of X(10) wrt inconic with perspector X(2))
X(54256) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {661, 40776}, {9279, 1}, {40750, 662}
X(54256) = barycentric product X(i)*X(j) for these (i, j): {75, 9279}, {1577, 40750}, {24342, 523}
X(54256) = barycentric quotient X(i)/X(j) for these (i, j): {661, 40776}, {9279, 1}, {24342, 99}, {40750, 662}
See Ivan Pavlov, euclid 5918.
X(54257) lies on these lines: {216, 520}, {441, 525}, {2485, 5421}, {22089, 32320}, {45907, 52631}
X(54257) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(11064), X(40805)}}, {{A, B, C, X(44436), X(47739)}}
X(54257) = perspector of circumconic {{A, B, C, X(69), X(14941)}}
X(54257) = X(i)-isoconjugate-of-X(j) for these {i, j}: {162, 40815}, {24019, 43711}
X(54257) = X(i)-Dao conjugate of X(j) for these {i, j}: {125, 40815}, {35071, 43711}
X(54257) = (polar of X(2) wrt inconic with perspector X(3)) ∩ (polar of X(3) wrt inconic with perspector X(2))
X(54257) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {520, 43711}, {647, 40815}, {40805, 648}, {47739, 15352}
X(54257) = barycentric product X(i)*X(j) for these (i, j): {40805, 525}, {47739, 52613}
X(54257) = barycentric quotient X(i)/X(j) for these (i, j): {520, 43711}, {647, 40815}, {40805, 648}, {47739, 15352}
See Ivan Pavlov, euclid 5918.
X(54258) lies on these lines: {44, 513}, {512, 16589}, {1213, 4806}, {9402, 50487}, {20691, 22320}, {21834, 50483}, {27075, 48049}
X(54258) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(896), X(40749)}}, {{A, B, C, X(2238), X(40721)}}
X(54258) = reflection of X(i) in X(j) for these {i,j}: {661, 46390}
X(54258) = perspector of circumconic {{A, B, C, X(1), X(40749)}}
X(54258) = X(i)-isoconjugate-of-X(j) for these {i, j}: {662, 40775}
X(54258) = X(i)-Dao conjugate of X(j) for these {i, j}: {1084, 40775}
X(54258) = X(i)-Zayin conjugate of X(j) for these {i, j}: {661, 40775}
X(54258) = (polar of X(2) wrt inconic with perspector X(37)) ∩ (polar of X(37) wrt inconic with perspector X(2))
X(54258) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {512, 40775}, {40721, 799}
X(54258) = barycentric product X(i)*X(j) for these (i, j): {40721, 661}, {40749, 523}
X(54258) = barycentric quotient X(i)/X(j) for these (i, j): {512, 40775}, {40721, 799}, {40749, 99}
X(54258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {513, 46390, 661}
See Ivan Pavlov, euclid 5918.
X(54259) lies on circumconic {{A, B, C, X(5203), X(5921)}} and on these lines: {6, 523}, {525, 3239}, {647, 2506}, {2501, 3566}, {6792, 46982}, {7652, 46425}, {8673, 14346}, {9007, 47138}, {9476, 41254}, {16040, 52588}, {37643, 53374}
X(54259) = perspector of circumconic {{A, B, C, X(98), X(253)}}
X(54259) = X(i)-complementary conjugate of X(j) for these {i, j}: {47735, 21253}
X(54259) = (polar of X(2) wrt inconic with perspector X(4)) ∩ (polar of X(4) wrt inconic with perspector X(2))
X(54259) = barycentric product X(i)*X(j) for these (i, j): {523, 5921}
X(54259) = barycentric quotient X(i)/X(j) for these (i, j): {5921, 99}
X(54259) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14333, 14334, 14341}
See Ivan Pavlov, euclid 5918.
X(54260) lies on these lines: {3, 525}, {523, 4885}, {684, 40494}, {1499, 6334}, {3091, 44705}, {3265, 8057}, {14341, 16230}, {16051, 53383}
X(54260) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3167), X(21910)}}, {{A, B, C, X(5921), X(35912)}}, {{A, B, C, X(14638), X(53173)}}, {{A, B, C, X(16096), X(34156)}}
X(54260) = reflection of X(i) in X(j) for these {i,j}: {16230, 14341}
X(54260) = perspector of circumconic {{A, B, C, X(287), X(2996)}}
X(54260) = X(i)-Dao conjugate of X(j) for these {i, j}: {6776, 35278}
X(54260) = X(i)-complementary conjugate of X(j) for these {i, j}: {4575, 7710}, {42287, 21253}
X(54260) = (polar of X(2) wrt inconic with perspector X(69)) ∩ (polar of X(69) wrt inconic with perspector X(2))
X(54260) = barycentric product X(i)*X(j) for these (i, j): {525, 5921}
X(54260) = barycentric quotient X(i)/X(j) for these (i, j): {5921, 648}
See Ivan Pavlov, euclid 5918.
X(54261) lies on these lines: {1, 514}, {522, 676}, {650, 28161}, {2254, 4962}, {2496, 6084}, {3239, 47695}, {3617, 4546}, {3667, 3676}, {3960, 30235}, {4765, 47798}, {4778, 39540}, {6362, 52596}, {6608, 21189}, {8058, 21179}, {9780, 44448}, {11019, 24720}, {14350, 48547}, {21104, 28225}, {30723, 34958}, {44551, 50356}, {47800, 48187}, {47801, 53558}, {48239, 48268}
X(54261) = midpoint of X(i) in X(j) for these {i,j}: {3239, 47695}, {3676, 53523}
X(54261) = reflection of X(i) in X(j) for these {i,j}: {30723, 34958}, {7658, 676}
X(54261) = perspector of circumconic {{A, B, C, X(673), X(7319)}}
X(54261) = X(i)-complementary conjugate of X(j) for these {i, j}: {42315, 116}
X(54261) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {26716, 8055}
X(54261) = (polar of X(2) wrt inconic with perspector X(7)) ∩ (polar of X(7) wrt inconic with perspector X(2))
X(54261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {522, 676, 7658}, {3676, 53523, 3667}
See Ivan Pavlov, euclid 5918.
X(54262) lies on these lines: {2, 3288}, {125, 6071}, {126, 33330}, {141, 523}, {193, 2451}, {297, 525}, {512, 625}, {669, 30217}, {804, 50550}, {1499, 9148}, {1637, 50547}, {2435, 43710}, {2492, 9030}, {3005, 3800}, {3049, 3618}, {3050, 47355}, {5027, 44451}, {6333, 12077}, {7703, 32120}, {9210, 31296}, {11186, 53365}, {14317, 14318}, {17921, 21300}, {23297, 30491}, {23878, 45336}, {30209, 47206}, {31072, 53331}, {32455, 39520}, {37648, 45327}
X(54262) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(141), X(43715)}}, {{A, B, C, X(297), X(11328)}}, {{A, B, C, X(882), X(2501)}}, {{A, B, C, X(18906), X(44146)}}
X(54262) = midpoint of X(i) in X(j) for these {i,j}: {11186, 53365}, {6333, 12077}, {850, 3569}
X(54262) = reflection of X(i) in X(j) for these {i,j}: {14316, 2501}, {24284, 30476}, {45335, 2}, {5027, 44451}
X(54262) = complement of X(3288)
X(54262) = perspector of circumconic {{A, B, C, X(264), X(1916)}}
X(54262) = center of circumconic {{A, B, C, X(39680), X(45907)}}
X(54262) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 19222}, {662, 47643}
X(54262) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 19222}, {1084, 47643}, {45907, 25423}
X(54262) = X(i)-complementary conjugate of X(j) for these {i, j}: {75, 46656}, {262, 8287}, {263, 16592}, {327, 21253}, {662, 15819}, {799, 52658}, {1755, 39009}, {2186, 115}, {3402, 1084}, {6037, 16609}, {26714, 37}, {36132, 230}, {39681, 19563}, {42313, 34846}, {43718, 16573}
X(54262) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {25424, 4329}, {51844, 13219}
X(54262) = (polar of X(2) wrt inconic with perspector X(76)) ∩ (polar of X(76) wrt inconic with perspector X(2))
X(54262) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {512, 47643}, {523, 19222}, {6234, 805}, {11328, 110}, {19591, 662}, {45907, 6}, {51997, 26714}
X(54262) = barycentric product X(i)*X(j) for these (i, j): {1577, 19591}, {11328, 850}, {14295, 6234}, {18906, 523}, {45907, 76}
X(54262) = barycentric quotient X(i)/X(j) for these (i, j): {512, 47643}, {523, 19222}, {6234, 805}, {11328, 110}, {18906, 99}, {19591, 662}, {45907, 6}, {51997, 26714}
X(54262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {512, 30476, 24284}, {525, 2501, 14316}, {850, 3569, 525}
See Ivan Pavlov, euclid 5918.
X(54263) lies on these lines: {316, 512}, {523, 3589}, {647, 7950}, {826, 4142}, {2528, 50542}, {3288, 20965}, {3906, 14420}, {7927, 24284}, {23597, 23878}, {45692, 50549}
X(54263) = midpoint of X(i) in X(j) for these {i,j}: {2528, 50542}
X(54263) = perspector of circumconic {{A, B, C, X(308), X(1031)}}
X(54263) = X(i)-complementary conjugate of X(j) for these {i, j}: {43357, 21249}
X(54263) = (polar of X(2) wrt inconic with perspector X(83)) ∩ (polar of X(83) wrt inconic with perspector X(2))
X(54263) = barycentric product X(i)*X(j) for these (i, j): {24273, 523}
X(54263) = barycentric quotient X(i)/X(j) for these (i, j): {24273, 99}
See Ivan Pavlov, euclid 5918.
X(54264) lies on these lines: {2, 45755}, {142, 522}, {144, 46402}, {514, 661}, {594, 45659}, {657, 18230}, {885, 47832}, {1734, 6608}, {3261, 17233}, {3309, 4369}, {3676, 24290}, {3700, 43042}, {3887, 47779}, {3900, 4885}, {4171, 24002}, {4431, 20907}, {4928, 14077}, {4932, 42325}, {5316, 14330}, {6362, 46396}, {7155, 35355}, {8713, 50352}, {17239, 20316}, {17241, 20954}, {22019, 22042}, {22229, 43051}, {26985, 53357}, {28161, 40474}, {29571, 33570}, {31019, 47790}, {40551, 47831}
X(54264) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(514), X(9443)}}, {{A, B, C, X(3835), X(35355)}}
X(54264) = midpoint of X(i) in X(j) for these {i,j}: {3700, 43042}, {4171, 24002}
X(54264) = reflection of X(i) in X(j) for these {i,j}: {21195, 46399}
X(54264) = complement of X(45755)
X(54264) = X(i)-complementary conjugate of X(j) for these {i, j}: {651, 3789}, {1002, 26932}, {2279, 1146}, {8693, 9}, {27475, 124}, {32041, 1329}, {36138, 40869}, {37138, 3452}, {40779, 5514}, {42290, 11}, {42302, 34589}, {51443, 4858}, {51563, 21246}, {52635, 39012}
X(54264) = (polar of X(2) wrt inconic with perspector X(85)) ∩ (polar of X(85) wrt inconic with perspector X(2))
X(54264) = X(9443)-reciprocal conjugate of X(1)
X(54264) = barycentric product X(i)*X(j) for these (i, j): {75, 9443}
X(54264) = barycentric quotient X(i)/X(j) for these (i, j): {9443, 1}
X(54264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {522, 46399, 21195}
See Ivan Pavlov, euclid 5918.
X(54265) lies on these lines: {2, 4824}, {8, 2533}, {10, 45332}, {320, 350}, {514, 1125}, {523, 2487}, {649, 48120}, {650, 4802}, {659, 47672}, {661, 4963}, {662, 36239}, {1019, 48393}, {1491, 4379}, {1698, 4705}, {2254, 48253}, {3244, 29298}, {3716, 4977}, {3720, 4724}, {3741, 24720}, {4024, 50342}, {4036, 18154}, {4122, 4789}, {4367, 50457}, {4448, 47969}, {4500, 29078}, {4750, 4777}, {4761, 48291}, {4762, 4782}, {4763, 28179}, {4784, 4804}, {4800, 48021}, {4806, 28840}, {4810, 4979}, {4841, 47799}, {4885, 48030}, {4893, 47928}, {4926, 7659}, {4927, 47989}, {4928, 47992}, {4932, 29328}, {4948, 45691}, {4960, 4983}, {6367, 21192}, {6545, 47968}, {14419, 47683}, {17292, 35352}, {20317, 47922}, {21116, 28195}, {21183, 48007}, {23770, 48276}, {23864, 48382}, {24666, 46385}, {24924, 47827}, {25128, 47843}, {25380, 48233}, {25666, 48002}, {26248, 47797}, {26985, 47945}, {27527, 48209}, {28147, 31286}, {28151, 46915}, {28165, 48254}, {28175, 48000}, {28191, 48214}, {28199, 47773}, {28213, 48001}, {29144, 47123}, {29238, 50515}, {29274, 50517}, {29362, 48399}, {29833, 47691}, {30795, 47810}, {30835, 47909}, {31209, 48176}, {31287, 48194}, {45320, 48027}, {45746, 48227}, {47659, 48241}, {47660, 48326}, {47666, 47822}, {47675, 47804}, {47698, 48185}, {47699, 48177}, {47703, 50340}, {47760, 47953}, {47777, 48608}, {47779, 48010}, {47788, 48047}, {47789, 48062}, {47812, 48153}, {47821, 47946}, {47823, 47975}, {47824, 50341}, {47826, 47910}, {47831, 47996}, {47832, 48024}, {47837, 48407}, {47839, 50449}, {47872, 47918}, {47875, 47959}, {47881, 48088}, {47889, 48131}, {47891, 50348}, {47917, 48162}, {47926, 48226}, {47943, 48414}, {47944, 50522}, {47964, 48197}, {47986, 48547}, {47993, 48183}, {48020, 48167}, {48023, 48184}, {48028, 48202}, {48032, 48251}, {48119, 48578}, {48144, 48392}, {48349, 49283}, {48409, 48569}, {48579, 50359}, {49286, 49296}, {49293, 49295}
X(54265) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(513), X(9279)}}, {{A, B, C, X(523), X(50451)}}, {{A, B, C, X(693), X(18014)}}, {{A, B, C, X(24342), X(30939)}}, {{A, B, C, X(30941), X(40750)}}
X(54265) = midpoint of X(i) in X(j) for these {i,j}: {1019, 48393}, {1491, 48142}, {2533, 17166}, {21146, 47694}, {23770, 48276}, {3716, 49291}, {4010, 7192}, {4024, 50342}, {4367, 50457}, {4369, 49292}, {4724, 48143}, {4761, 48291}, {4782, 48127}, {4784, 4804}, {4810, 4979}, {4932, 48394}, {4960, 4983}, {47660, 48326}, {47703, 50340}, {47704, 48103}, {47944, 50522}, {48024, 48141}, {48029, 48133}, {48119, 50358}, {48144, 48392}, {48153, 50328}, {48349, 49283}, {49286, 49296}, {49293, 49295}, {649, 48120}, {650, 48134}, {659, 47672}, {7662, 43067}
X(54265) = reflection of X(i) in X(j) for these {i,j}: {4948, 45691}, {45676, 2}, {47922, 20317}, {48002, 25666}, {48030, 4885}, {9508, 4369}
X(54265) = complement of X(4824)
X(54265) = perspector of circumconic {{A, B, C, X(79), X(274)}}
X(54265) = X(i)-isoconjugate-of-X(j) for these {i, j}: {101, 40776}
X(54265) = X(i)-Dao conjugate of X(j) for these {i, j}: {1015, 40776}
X(54265) = X(i)-complementary conjugate of X(j) for these {i, j}: {163, 31336}, {25426, 8287}, {27483, 21253}, {28841, 1211}, {30571, 125}
X(54265) = (polar of X(2) wrt inconic with perspector X(86)) ∩ (polar of X(86) wrt inconic with perspector X(2))
X(54265) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {513, 40776}, {9279, 37}, {18791, 37138}, {40750, 100}
X(54265) = barycentric product X(i)*X(j) for these (i, j): {274, 9279}, {24342, 514}, {40750, 693}
X(54265) = barycentric quotient X(i)/X(j) for these (i, j): {513, 40776}, {9279, 37}, {18791, 37138}, {24342, 190}, {40750, 100}
X(54265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 4369, 9508}, {3716, 49291, 4977}, {4369, 49292, 523}, {4379, 48142, 1491}, {4782, 48127, 4762}, {4804, 31148, 4784}, {4932, 48394, 29328}, {7192, 47834, 4010}, {21146, 47694, 513}, {24924, 47934, 47827}, {47672, 47813, 659}, {47694, 47780, 21146}, {47704, 48103, 4802}, {47812, 48153, 50328}, {47832, 48141, 48024}, {48002, 48206, 25666}, {48029, 48133, 28195}, {48119, 48578, 50358}, {48133, 48220, 48029}, {48143, 48234, 4724}
See Ivan Pavlov, euclid 5918.
X(54266) lies on circumconic {{A, B, C, X(522), X(9443)}} and on these lines: {522, 650}, {1212, 3900}, {2254, 4171}, {33570, 50356}
X(54266) = reflection of X(i) in X(j) for these {i,j}: {650, 52614}
X(54266) = perspector of circumconic {{A, B, C, X(8), X(14943)}}
X(54266) = (polar of X(2) wrt inconic with perspector X(9)) ∩ (polar of X(9) wrt inconic with perspector X(2))
X(54266) = X(9443)-reciprocal conjugate of X(7)
X(54266) = barycentric product X(i)*X(j) for these (i, j): {8, 9443}
X(54266) = barycentric quotient X(i)/X(j) for these (i, j): {9443, 7}
X(54266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {522, 52614, 650}
See Ivan Pavlov, euclid 5918.
X(54267) lies on these lines: {230, 231}, {684, 7736}, {694, 804}, {2549, 2797}, {2799, 14316}, {2881, 51431}, {3815, 45319}, {5304, 53345}, {6330, 16081}, {9517, 18907}, {21843, 44818}, {23878, 45336}, {37637, 45682}, {46777, 48540}
X(54267) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(232), X(694)}}, {{A, B, C, X(468), X(5999)}}, {{A, B, C, X(2491), X(34212)}}, {{A, B, C, X(6103), X(47737)}}, {{A, B, C, X(16081), X(16318)}}, {{A, B, C, X(38947), X(47110)}}
X(54267) = midpoint of X(i) in X(j) for these {i,j}: {2395, 3569}
X(54267) = complement of isogonal conjugate of X(32716)
X(54267) = complement of isotomic conjugate of X(6037)
X(54267) = perspector of circumconic {{A, B, C, X(4), X(5999)}}
X(54267) = X(i)-isoconjugate-of-X(j) for these {i, j}: {662, 43702}
X(54267) = X(i)-Dao conjugate of X(j) for these {i, j}: {1084, 43702}
X(54267) = X(i)-complementary conjugate of X(j) for these {i, j}: {560, 39009}, {1910, 46656}, {2186, 36471}, {3402, 35088}, {6037, 2887}, {32716, 10}, {36084, 52658}, {36132, 141}, {53196, 21235}
X(54267) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {512, 43702}, {47737, 2966}
X(54267) = (polar of X(2) wrt inconic with perspector X(98)) ∩ (polar of X(98) wrt inconic with perspector X(2))
X(54267) = barycentric product X(i)*X(j) for these (i, j): {523, 5999}, {2799, 47737}
X(54267) = barycentric quotient X(i)/X(j) for these (i, j): {512, 43702}, {5999, 99}, {47737, 2966}
See Ivan Pavlov, euclid 5918.
X(54268) lies on circumconics {{A, B, C, X(184), X(5921)}} and on these lines: {184, 647}, {512, 1570}, {520, 11589}, {686, 8644}, {1899, 31174}, {2065, 5622}, {6776, 23878}, {23291, 30476}
X(54268) = perspector of circumconic {{A, B, C, X(248), X(1073)}}
X(54268) = (polar of X(3) wrt inconic with perspector X(6)) ∩ (polar of X(6) wrt inconic with perspector X(3))
X(54268) = X(5921)-reciprocal conjugate of X(6331)
X(54268) = barycentric product X(i)*X(j) for these (i, j): {5921, 647}
X(54268) = barycentric quotient X(i)/X(j) for these (i, j): {5921, 6331}
See Ivan Pavlov, euclid 5918.
X(54269) lies on these lines: {30, 511}, {51, 647}, {850, 2979}, {2451, 39201}, {3060, 36900}, {3819, 30476}, {3917, 31174}, {5943, 44560}, {9420, 45907}, {12099, 22264}, {42293, 52590}, {42331, 44173}
X(54269) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(51), X(32428)}}, {{A, B, C, X(520), X(53175)}}, {{A, B, C, X(524), X(40805)}}, {{A, B, C, X(3504), X(3564)}}
X(54269) = perspector of circumconic {{A, B, C, X(2), X(1987)}}
X(54269) = X(i)-isoconjugate-of-X(j) for these {i, j}: {162, 43711}, {662, 40815}
X(54269) = X(i)-Dao conjugate of X(j) for these {i, j}: {125, 43711}, {1084, 40815}
X(54269) = X(i)-complementary conjugate of X(j) for these {i, j}: {40815, 8287}, {43711, 34846}
X(54269) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {40815, 21221}
X(54269) = (polar of X(4) wrt inconic with perspector X(6)) ∩ (polar of X(6) wrt inconic with perspector X(4))
X(54269) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {512, 40815}, {647, 43711}, {47739, 6528}
X(54269) = barycentric product X(i)*X(j) for these (i, j): {40805, 523}, {47739, 520}
X(54269) = barycentric quotient X(i)/X(j) for these (i, j): {512, 40815}, {647, 43711}, {40805, 99}, {47739, 6528}
X(54269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 39469, 512}
See Ivan Pavlov, euclid 5918.
X(54270) lies on these lines: {11, 1146}, {1018, 11814}, {1647, 4120}, {4928, 24228}, {21013, 24003}, {46101, 52338}
X(54270) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(11), X(24131)}}, {{A, B, C, X(1647), X(4124)}}, {{A, B, C, X(2170), X(4919)}}
X(54270) = X(i)-isoconjugate-of-X(j) for these {i, j}: {651, 53682}
X(54270) = X(i)-Dao conjugate of X(j) for these {i, j}: {24188, 30725}, {38991, 53682}
X(54270) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4582, 21132}, {52338, 4530}
X(54270) = (polar of X(8) wrt inconic with perspector X(11)) ∩ (polar of X(11) wrt inconic with perspector X(8))
X(54270) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {663, 53682}, {4530, 6630}, {4919, 5376}, {14122, 7045}, {24131, 7}, {52338, 42555}
X(54270) = barycentric product X(i)*X(j) for these (i, j): {1639, 21204}, {4440, 4530}, {14122, 24026}, {24131, 8}, {52338, 6631}
X(54270) = barycentric quotient X(i)/X(j) for these (i, j): {663, 53682}, {4530, 6630}, {4919, 5376}, {14122, 7045}, {24131, 7}, {52338, 42555}
See Ivan Pavlov, euclid 5918.
X(54271) lies on these lines: {30, 511}, {210, 650}, {354, 45320}, {649, 4477}, {663, 3287}, {667, 3508}, {693, 3873}, {875, 43931}, {905, 24462}, {2488, 3239}, {3158, 16557}, {3669, 53553}, {3681, 31150}, {3709, 52594}, {3740, 44567}, {3742, 4885}, {3794, 39924}, {3868, 47721}, {3877, 47729}, {3892, 48295}, {3894, 47724}, {3898, 48285}, {4024, 50519}, {4134, 48284}, {4164, 48330}, {4374, 52621}, {4430, 47869}, {4502, 50508}, {4512, 8641}, {4524, 4765}, {4661, 17494}, {4820, 50518}, {5902, 50764}, {6050, 17990}, {10030, 21302}, {15280, 24386}, {17072, 21195}, {18081, 48109}, {21003, 48387}, {21183, 30704}, {21260, 40474}, {21388, 21789}, {49285, 53550}
X(54271) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(210), X(740)}}, {{A, B, C, X(516), X(4334)}}, {{A, B, C, X(517), X(21010)}}, {{A, B, C, X(518), X(24349)}}, {{A, B, C, X(522), X(24720)}}, {{A, B, C, X(527), X(17754)}}, {{A, B, C, X(650), X(812)}}, {{A, B, C, X(663), X(4083)}}, {{A, B, C, X(726), X(33676)}}, {{A, B, C, X(732), X(39936)}}, {{A, B, C, X(2344), X(19584)}}, {{A, B, C, X(2784), X(8926)}}, {{A, B, C, X(3287), X(25576)}}, {{A, B, C, X(3709), X(4139)}}, {{A, B, C, X(3794), X(52211)}}, {{A, B, C, X(3808), X(43931)}}, {{A, B, C, X(3810), X(52621)}}, {{A, B, C, X(4162), X(4964)}}, {{A, B, C, X(9025), X(53219)}}, {{A, B, C, X(9443), X(53227)}}, {{A, B, C, X(20917), X(46180)}}
X(54271) = perspector of circumconic {{A, B, C, X(2), X(2319)}}
X(54271) = X(i)-isoconjugate-of-X(j) for these {i, j}: {109, 41527}, {934, 7220}
X(54271) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 41527}, {14714, 7220}
X(54271) = X(i)-Ceva conjugate of X(j) for these {i, j}: {100, 19584}
X(54271) = X(i)-complementary conjugate of X(j) for these {i, j}: {109, 19584}, {7220, 5514}, {41527, 124}
X(54271) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {41527, 33650}
X(54271) = (polar of X(8) wrt inconic with perspector X(9)) ∩ (polar of X(9) wrt inconic with perspector X(8))
X(54271) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {650, 41527}, {657, 7220}, {4334, 658}, {17754, 664}, {20917, 4572}, {21010, 651}, {22163, 6516}, {24349, 4554}, {24720, 85}
X(54271) = barycentric product X(i)*X(j) for these (i, j): {3239, 4334}, {17754, 522}, {20917, 663}, {21010, 4391}, {21101, 3737}, {22163, 44426}, {24349, 650}, {24720, 9}
X(54271) = barycentric quotient X(i)/X(j) for these (i, j): {650, 41527}, {657, 7220}, {4334, 658}, {17754, 664}, {20917, 4572}, {21010, 651}, {22163, 6516}, {24349, 4554}, {24720, 85}
X(54271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {513, 29226, 3808}, {518, 4762, 9443}, {522, 926, 3900}
See Ivan Pavlov, euclid 5918.
X(54272) lies on these lines: {30, 511}, {51, 31174}, {647, 3917}, {850, 3060}, {2524, 3049}, {2979, 36900}, {3819, 44560}, {5943, 30476}, {16695, 23145}
X(54272) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(3), X(32515)}}, {{A, B, C, X(30), X(11328)}}, {{A, B, C, X(511), X(18906)}}, {{A, B, C, X(523), X(45907)}}, {{A, B, C, X(647), X(804)}}, {{A, B, C, X(732), X(3917)}}, {{A, B, C, X(1503), X(1988)}}, {{A, B, C, X(2782), X(6234)}}, {{A, B, C, X(3049), X(3221)}}, {{A, B, C, X(8680), X(19591)}}, {{A, B, C, X(19602), X(43722)}}
X(54272) = perspector of circumconic {{A, B, C, X(2), X(3504)}}
X(54272) = X(i)-isoconjugate-of-X(j) for these {i, j}: {162, 19222}, {811, 47643}
X(54272) = X(i)-Dao conjugate of X(j) for these {i, j}: {125, 19222}, {17423, 47643}
X(54272) = X(i)-Ceva conjugate of X(j) for these {i, j}: {110, 19602}, {25424, 3}
X(54272) = X(i)-complementary conjugate of X(j) for these {i, j}: {162, 19602}, {19222, 34846}, {47643, 16573}
X(54272) = (polar of X(3) wrt inconic with perspector X(69)) ∩ (polar of X(69) wrt inconic with perspector X(3))
X(54272) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {647, 19222}, {3049, 47643}, {11328, 648}, {18906, 6331}, {19591, 811}, {45907, 4}
X(54272) = barycentric product X(i)*X(j) for these (i, j): {11328, 525}, {18906, 647}, {19591, 656}, {24284, 6234}, {45907, 69}
X(54272) = barycentric quotient X(i)/X(j) for these (i, j): {647, 19222}, {3049, 47643}, {11328, 648}, {18906, 6331}, {19591, 811}, {45907, 4}
X(54272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {525, 39469, 520}
See Ivan Pavlov, euclid 5918.
X(54273) lies on these lines: {460, 512}, {882, 1843}, {5113, 6753}, {17994, 50549}
X(54273) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(460), X(11328)}}, {{A, B, C, X(882), X(2501)}}, {{A, B, C, X(3221), X(5027)}}, {{A, B, C, X(5140), X(18906)}}, {{A, B, C, X(27375), X(51997)}}
X(54273) = polar conjugate of isotomic conjugate of X(45907)
X(54273) = perspector of circumconic {{A, B, C, X(393), X(17980)}}
X(54273) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4592, 19222}
X(54273) = X(i)-Dao conjugate of X(j) for these {i, j}: {5139, 19222}
X(54273) = (polar of X(4) wrt inconic with perspector X(25)) ∩ (polar of X(25) wrt inconic with perspector X(4))
X(54273) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {2489, 19222}, {11328, 4563}, {18906, 52608}, {45907, 69}
X(54273) = barycentric product X(i)*X(j) for these (i, j): {4, 45907}, {11328, 2501}, {18906, 2489}
X(54273) = barycentric quotient X(i)/X(j) for these (i, j): {2489, 19222}, {11328, 4563}, {18906, 52608}, {45907, 69}
See Ivan Pavlov, euclid 5918.
X(54274) lies on these lines: {6, 512}, {110, 39527}, {184, 8644}, {351, 39689}, {520, 3167}, {523, 8584}, {524, 11183}, {526, 6593}, {542, 18309}, {575, 9175}, {597, 11182}, {599, 45693}, {688, 11205}, {690, 15303}, {804, 8787}, {888, 9135}, {1499, 50979}, {1649, 8030}, {1992, 5652}, {2086, 38988}, {3049, 3051}, {5027, 9023}, {5050, 21733}, {5467, 44814}, {5653, 52699}, {9137, 11422}, {21906, 35507}, {34290, 45690}, {39469, 47405}, {45692, 47352}, {45914, 52721}
X(54274) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(6), X(8030)}}, {{A, B, C, X(110), X(9171)}}, {{A, B, C, X(187), X(17964)}}, {{A, B, C, X(351), X(1649)}}, {{A, B, C, X(512), X(33915)}}, {{A, B, C, X(2482), X(14609)}}, {{A, B, C, X(5095), X(51980)}}, {{A, B, C, X(8430), X(23992)}}, {{A, B, C, X(14443), X(44814)}}, {{A, B, C, X(14567), X(52197)}}, {{A, B, C, X(17414), X(18311)}}, {{A, B, C, X(22260), X(46049)}}, {{A, B, C, X(36792), X(36821)}}, {{A, B, C, X(45143), X(51927)}}
X(54274) = midpoint of X(i) in X(j) for these {i,j}: {1992, 5652}
X(54274) = reflection of X(i) in X(j) for these {i,j}: {11182, 597}, {22260, 9171}, {34290, 45690}, {599, 45693}, {9171, 6}, {9175, 575}, {9208, 9188}
X(54274) = perspector of circumconic {{A, B, C, X(111), X(187)}}
X(54274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 34574}, {671, 36085}, {691, 46277}, {799, 10630}, {811, 15398}, {892, 897}, {923, 53080}, {1577, 34539}, {4602, 41936}, {18023, 36142}, {20944, 39413}, {23894, 52940}
X(54274) = X(i)-Dao conjugate of X(j) for these {i, j}: {206, 34574}, {524, 670}, {690, 850}, {1648, 76}, {1649, 52632}, {2482, 53080}, {6593, 892}, {17423, 15398}, {21905, 5466}, {23992, 18023}, {38988, 671}, {38996, 10630}, {48317, 46111}
X(54274) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6, 21906}, {110, 187}, {512, 351}, {5095, 23992}
X(54274) = (polar of X(6) wrt inconic with perspector X(187)) ∩ (polar of X(187) wrt inconic with perspector X(6))
X(54274) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {32, 34574}, {187, 892}, {351, 671}, {524, 53080}, {669, 10630}, {690, 18023}, {922, 36085}, {1576, 34539}, {1648, 52632}, {1649, 76}, {2482, 670}, {2642, 46277}, {3049, 15398}, {5095, 6331}, {5467, 52940}, {9426, 41936}, {14273, 46111}, {14443, 338}, {14444, 35522}, {14567, 691}, {21906, 5466}, {23992, 850}, {24038, 4602}, {33915, 3266}, {35507, 17414}, {36792, 4609}, {42081, 799}, {46049, 52628}, {52068, 1978}, {52629, 1502}
X(54274) = barycentric product X(i)*X(j) for these (i, j): {32, 52629}, {110, 23992}, {111, 33915}, {187, 690}, {351, 524}, {1366, 3709}, {1648, 5467}, {1649, 6}, {2482, 512}, {2642, 896}, {3049, 34336}, {5095, 647}, {7067, 7180}, {8030, 9178}, {11183, 18872}, {14273, 3292}, {14417, 44102}, {14419, 21839}, {14443, 249}, {14444, 691}, {14567, 35522}, {16733, 50487}, {17414, 20380}, {20382, 9145}, {21905, 34161}, {21906, 5468}, {24038, 798}, {30454, 6137}, {30455, 6138}, {33921, 48450}, {36792, 669}, {39689, 523}, {42081, 661}, {52038, 9155}, {52068, 649}
X(54274) = barycentric quotient X(i)/X(j) for these (i, j): {32, 34574}, {187, 892}, {351, 671}, {524, 53080}, {669, 10630}, {690, 18023}, {922, 36085}, {1576, 34539}, {1648, 52632}, {1649, 76}, {2482, 670}, {2642, 46277}, {3049, 15398}, {5095, 6331}, {5467, 52940}, {9426, 41936}, {14273, 46111}, {14443, 338}, {14444, 35522}, {14567, 691}, {21906, 5466}, {23992, 850}, {24038, 4602}, {33915, 3266}, {35507, 17414}, {36792, 4609}, {39689, 99}, {42081, 799}, {46049, 52628}, {52068, 1978}, {52629, 1502}
X(54274) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 512, 9171}, {512, 9171, 22260}, {526, 9188, 9208}, {9188, 9208, 14428}
See Ivan Pavlov, euclid 5918.
X(54275) lies on these lines: {6, 4782}, {213, 667}, {649, 854}, {659, 20980}, {798, 50514}, {1919, 8640}, {2484, 50510}, {4501, 50343}, {4784, 16782}, {16969, 48330}, {20979, 23569}, {21389, 50516}, {24512, 24719}
X(54275) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(875), X(43924)}}, {{A, B, C, X(17754), X(51864)}}
X(54275) = perspector of circumconic {{A, B, C, X(56), X(1911)}}
X(54275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {190, 41527}, {3807, 47647}, {4554, 7220}
X(54275) = (polar of X(6) wrt inconic with perspector X(31)) ∩ (polar of X(31) wrt inconic with perspector X(6))
X(54275) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {667, 41527}, {4334, 4572}, {17754, 1978}, {19586, 4505}, {19587, 3807}, {21010, 668}, {24349, 6386}, {24720, 561}
X(54275) = barycentric product X(i)*X(j) for these (i, j): {1919, 20917}, {4334, 663}, {17754, 649}, {19587, 4817}, {21010, 513}, {22163, 6591}, {24349, 667}, {24720, 31}, {40758, 45902}
X(54275) = barycentric quotient X(i)/X(j) for these (i, j): {667, 41527}, {4334, 4572}, {17754, 1978}, {19586, 4505}, {19587, 3807}, {21010, 668}, {24349, 6386}, {24720, 561}
See Ivan Pavlov, euclid 5918.
X(54276) lies on these lines: {6, 25423}, {512, 1692}, {669, 881}, {804, 2451}, {1613, 45317}, {9426, 9429}, {20965, 31176}, {21001, 44451}
X(54276) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(32), X(33874)}}, {{A, B, C, X(881), X(2489)}}, {{A, B, C, X(11328), X(46522)}}, {{A, B, C, X(18906), X(34238)}}
X(54276) = reflection of X(i) in X(j) for these {i,j}: {9491, 9426}
X(54276) = perspector of circumconic {{A, B, C, X(25), X(9468)}}
X(54276) = X(i)-isoconjugate-of-X(j) for these {i, j}: {799, 19222}, {4602, 47643}
X(54276) = X(i)-Dao conjugate of X(j) for these {i, j}: {38996, 19222}
X(54276) = X(i)-Ceva conjugate of X(j) for these {i, j}: {26714, 51997}
X(54276) = (polar of X(6) wrt inconic with perspector X(32)) ∩ (polar of X(32) wrt inconic with perspector X(6))
X(54276) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {669, 19222}, {9426, 47643}, {11328, 670}, {18906, 4609}, {19591, 4602}, {45907, 76}
X(54276) = barycentric product X(i)*X(j) for these (i, j): {3288, 51997}, {5027, 6234}, {11328, 512}, {18906, 669}, {19591, 798}, {45907, 6}
X(54276) = barycentric quotient X(i)/X(j) for these (i, j): {669, 19222}, {9426, 47643}, {11328, 670}, {18906, 4609}, {19591, 4602}, {45907, 76}
X(54276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9426, 9429, 9491}
See Ivan Pavlov, euclid 5918.
X(54277) lies on these lines: {44, 513}, {512, 18001}, {1019, 6626}, {4079, 7234}, {4369, 18160}, {4826, 8663}, {17731, 29487}, {25820, 25822}, {26983, 27194}
X(54277) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(512), X(9508)}}, {{A, B, C, X(513), X(9279)}}, {{A, B, C, X(2234), X(24342)}}, {{A, B, C, X(2238), X(40750)}}, {{A, B, C, X(6626), X(46195)}}
X(54277) = perspector of circumconic {{A, B, C, X(1), X(2054)}}
X(54277) = X(i)-Dao conjugate of X(j) for these {i, j}: {38986, 40776}
X(54277) = X(i)-Zayin conjugate of X(j) for these {i, j}: {1019, 40776}
X(54277) = (polar of X(6) wrt inconic with perspector X(42)) ∩ (polar of X(42) wrt inconic with perspector X(6))
X(54277) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {798, 40776}, {9279, 75}, {24342, 670}, {40750, 799}
X(54277) = barycentric product X(i)*X(j) for these (i, j): {1, 9279}, {24342, 512}, {40750, 661}
X(54277) = barycentric quotient X(i)/X(j) for these (i, j): {798, 40776}, {9279, 75}, {24342, 670}, {40750, 799}
X(54277) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 46390, 798}
See Ivan Pavlov, euclid 5918.
X(54278) lies on these lines: {9, 24720}, {44, 513}, {71, 4824}, {514, 3177}, {663, 1475}, {3207, 44408}, {3709, 53539}, {3835, 10025}, {4253, 4794}, {4379, 30988}, {8641, 20980}, {8642, 20981}, {20974, 42771}, {21390, 48073}, {31605, 49296}, {45755, 50356}, {48043, 53395}
X(54278) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(513), X(9443)}}, {{A, B, C, X(2053), X(2348)}}
X(54278) = reflection of X(i) in X(j) for these {i,j}: {649, 46388}
X(54278) = (polar of X(6) wrt inconic with perspector X(57)) ∩ (polar of X(57) wrt inconic with perspector X(6))
X(54278) = X(9443)-reciprocal conjugate of X(75)
X(54278) = barycentric product X(i)*X(j) for these (i, j): {1, 9443}
X(54278) = barycentric quotient X(i)/X(j) for these (i, j): {9443, 75}
X(54278) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {513, 46388, 649}
See Ivan Pavlov, euclid 5918.
X(54279) lies on these lines: {36, 238}, {55, 7234}, {512, 20981}, {649, 2308}, {824, 4378}, {2786, 4367}, {3063, 4834}, {4038, 18200}, {4775, 50459}, {4785, 33682}, {8639, 23467}, {8646, 50454}, {17212, 50451}, {23472, 50509}, {29487, 37604}
X(54279) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(513), X(9279)}}, {{A, B, C, X(18792), X(24342)}}, {{A, B, C, X(40750), X(52897)}}
X(54279) = reflection of X(i) in X(j) for these {i,j}: {4775, 50459}, {50451, 52601}
X(54279) = perspector of circumconic {{A, B, C, X(81), X(2248)}}
X(54279) = (polar of X(6) wrt inconic with perspector X(58)) ∩ (polar of X(58) wrt inconic with perspector X(6))
X(54279) = X(i)-reciprocal conjugate of X(j) for these {i, j}: {667, 40776}, {9279, 321}, {24342, 1978}, {40750, 668}
X(54279) = barycentric product X(i)*X(j) for these (i, j): {81, 9279}, {18791, 4724}, {24342, 649}, {40750, 513}
X(54279) = barycentric quotient X(i)/X(j) for these (i, j): {667, 40776}, {9279, 321}, {24342, 1978}, {40750, 668}
X(54279) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3733, 4455, 667}
X(54280) lies on these lines: {1, 1992}, {2, 44}, {6, 4364}, {7, 17277}, {8, 190}, {9, 69}, {10, 24695}, {37, 193}, {45, 524}, {63, 2183}, {75, 144}, {85, 12848}, {86, 5296}, {141, 16885}, {145, 4664}, {192, 5839}, {198, 1444}, {200, 24708}, {220, 1332}, {239, 4419}, {281, 317}, {302, 30415}, {303, 30414}, {312, 14552}, {319, 346}, {322, 28974}, {329, 333}, {345, 3219}, {348, 651}, {390, 49450}, {491, 30412}, {492, 30413}, {527, 3707}, {536, 20073}, {545, 17119}, {597, 17325}, {599, 4422}, {645, 34016}, {648, 7952}, {666, 46136}, {894, 966}, {948, 17950}, {956, 15507}, {984, 51192}, {1007, 36407}, {1100, 51170}, {1150, 28808}, {1211, 26065}, {1266, 16833}, {1278, 4371}, {1441, 41563}, {1654, 2345}, {1707, 4104}, {1743, 3618}, {1757, 29659}, {1944, 28827}, {1997, 14829}, {2267, 20769}, {2287, 26647}, {2321, 25728}, {2325, 17294}, {2895, 17776}, {2911, 15988}, {3008, 17274}, {3161, 17233}, {3246, 47358}, {3305, 4001}, {3416, 15481}, {3488, 49753}, {3578, 42032}, {3589, 17253}, {3616, 46922}, {3619, 3973}, {3620, 15492}, {3621, 50077}, {3625, 50089}, {3626, 50118}, {3629, 16777}, {3630, 17311}, {3631, 17267}, {3633, 50110}, {3662, 29607}, {3672, 3759}, {3678, 52609}, {3686, 3729}, {3687, 3929}, {3691, 21281}, {3696, 24280}, {3730, 3882}, {3731, 3879}, {3782, 19723}, {3785, 25066}, {3875, 50019}, {3883, 5223}, {3886, 51090}, {3943, 50079}, {3945, 4687}, {4000, 6646}, {4029, 29605}, {4033, 25278}, {4034, 4431}, {4346, 24599}, {4359, 20078}, {4361, 17334}, {4363, 17330}, {4370, 17269}, {4389, 5222}, {4395, 49747}, {4398, 4402}, {4405, 28297}, {4407, 50300}, {4417, 5273}, {4432, 50316}, {4440, 16816}, {4445, 17340}, {4461, 5564}, {4473, 17230}, {4478, 53664}, {4480, 4659}, {4488, 32087}, {4517, 9025}, {4645, 38057}, {4648, 17260}, {4651, 44447}, {4655, 25351}, {4657, 16669}, {4665, 49721}, {4667, 16831}, {4690, 17281}, {4699, 7222}, {4700, 16834}, {4701, 50100}, {4703, 33137}, {4749, 17018}, {4753, 50282}, {4758, 5257}, {4759, 50311}, {4851, 16814}, {4869, 17263}, {4875, 20111}, {4896, 31211}, {4969, 17318}, {5032, 16666}, {5224, 5749}, {5232, 17289}, {5233, 5744}, {5271, 17781}, {5278, 5905}, {5308, 17378}, {5361, 26792}, {5463, 11791}, {5464, 11790}, {5686, 32850}, {5714, 25446}, {5759, 48878}, {6144, 16675}, {6376, 41316}, {6542, 50074}, {6604, 8545}, {6666, 17298}, {7232, 17337}, {7277, 15668}, {7313, 17744}, {7321, 20059}, {7774, 36405}, {9723, 15817}, {9780, 31144}, {9801, 16112}, {9965, 19804}, {11160, 17374}, {11269, 25378}, {11679, 24705}, {12322, 31561}, {12323, 31562}, {12530, 21867}, {14912, 46475}, {15534, 16672}, {16496, 49783}, {16552, 21362}, {16670, 17023}, {16676, 29574}, {16706, 17329}, {16815, 50128}, {16825, 53601}, {16832, 50116}, {16884, 32455}, {17014, 17320}, {17120, 17248}, {17121, 17247}, {17152, 30616}, {17160, 49748}, {17183, 29767}, {17234, 18230}, {17243, 40341}, {17251, 17369}, {17252, 17368}, {17254, 17367}, {17255, 17366}, {17259, 17365}, {17261, 17314}, {17262, 17362}, {17264, 17360}, {17270, 17355}, {17271, 17354}, {17273, 17352}, {17275, 17351}, {17276, 17348}, {17278, 17345}, {17280, 17343}, {17282, 53598}, {17284, 21356}, {17287, 17339}, {17288, 17338}, {17297, 29627}, {17300, 29599}, {17308, 50115}, {17379, 29592}, {17387, 29621}, {17395, 24441}, {17740, 37656}, {17770, 25352}, {18156, 42724}, {18743, 37655}, {19742, 19785}, {20050, 50121}, {20090, 27268}, {20930, 25001}, {21061, 29497}, {24597, 26580}, {24693, 28558}, {26039, 29610}, {26104, 29630}, {28333, 34824}, {29569, 50133}, {29573, 50992}, {29624, 51488}, {30854, 37788}, {30946, 30997}, {31035, 31303}, {31156, 49687}, {32847, 51297}, {36479, 49712}, {36480, 49710}, {41008, 42018}, {45789, 48629}, {49448, 50030}, {49709, 50075}, {49714, 50835}, {49722, 52709}, {49766, 50950}, {49770, 50090}, {50022, 50080}
X(54280) = reflection of X(i) in X(j) for these {i,j}: {4384, 3707}, {4896, 31211}, {17316, 45}, {29605, 4029}, {42697, 4384}
X(54280) = anticomplement of X(4675)
X(54280) = barycentric product X(i)*X(j) for these {i,j}: {75, 35258}, {190, 47785}
X(54280) = barycentric quotient X(i)/X(j) for these {i,j}: {35258, 1}, {47785, 514}
X(54280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4747, 41847}, {2, 20072, 4644}, {6, 4364, 26626}, {6, 17257, 17321}, {6, 17332, 17257}, {8, 190, 50107}, {8, 6172, 190}, {9, 69, 344}, {9, 4416, 69}, {9, 17296, 25101}, {44, 4643, 2}, {141, 16885, 26685}, {144, 391, 75}, {190, 17346, 8}, {239, 4419, 50101}, {239, 17333, 4419}, {319, 17336, 346}, {320, 17335, 2}, {599, 4422, 29579}, {894, 17331, 966}, {894, 29576, 4470}, {966, 4470, 29576}, {1150, 31018, 28808}, {1654, 17350, 2345}, {1743, 4357, 3618}, {3161, 32099, 17233}, {3219, 5739, 345}, {3305, 4001, 18141}, {3416, 15481, 27549}, {3686, 3729, 42696}, {3758, 17256, 2}, {3759, 17258, 3672}, {3973, 17272, 17353}, {4346, 24599, 37756}, {4364, 26626, 17321}, {4419, 37654, 239}, {4480, 50095, 4659}, {4657, 16669, 51171}, {4699, 31300, 7222}, {4795, 16590, 2}, {4798, 52706, 2}, {4969, 17318, 50129}, {4969, 49742, 17318}, {6144, 16675, 17390}, {6172, 17346, 50107}, {6646, 17349, 4000}, {11160, 29583, 17374}, {14829, 18228, 1997}, {15492, 17344, 17279}, {17257, 26626, 4364}, {17260, 17364, 4648}, {17261, 17363, 17314}, {17263, 17361, 4869}, {17264, 17360, 29616}, {17271, 17354, 29611}, {17272, 17353, 3619}, {17277, 17347, 7}, {17279, 17344, 3620}, {17288, 17338, 53665}, {17289, 17328, 5232}, {17333, 37654, 50101}, {17374, 41313, 29583}, {18230, 21296, 17234}, {36480, 49710, 50303}, {49712, 50296, 36479}
X(54283) lies on these lines: {1, 3052}, {2, 7238}, {6, 2243}, {7, 31187}, {44, 57}, {45, 63}, {88, 4383}, {89, 940}, {678, 41711}, {896, 4860}, {1086, 2094}, {1150, 17118}, {1376, 49712}, {1407, 3173}, {1707, 3246}, {2441, 4498}, {3219, 37682}, {3306, 16885}, {3666, 39254}, {3742, 16570}, {3752, 16670}, {3772, 4887}, {3873, 21000}, {3973, 31197}, {3977, 17311}, {3999, 36277}, {4031, 17278}, {4346, 37642}, {4415, 28610}, {4849, 53056}, {4896, 5745}, {5021, 36283}, {5096, 26866}, {5744, 17365}, {5905, 37691}, {9965, 37646}, {15533, 33077}, {16490, 16558}, {16675, 37633}, {17122, 51297}, {17160, 37683}, {17262, 37684}, {17601, 32913}, {17740, 40341}, {18134, 26070}, {19732, 30564}, {20050, 42049}, {20078, 37634}, {26934, 37567}, {29579, 44416}, {30579, 37639}, {33151, 35596}, {38000, 41847}
X(54281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {45, 37520, 37674}, {63, 37520, 45}
X(54282) lies on these lines: {1, 3}, {2, 3230}, {6, 536}, {31, 10800}, {32, 52134}, {38, 760}, {42, 14839}, {63, 1572}, {75, 2300}, {81, 99}, {83, 213}, {194, 712}, {333, 16829}, {350, 41232}, {519, 37676}, {730, 24259}, {894, 20228}, {981, 41527}, {992, 4967}, {1107, 29529}, {1258, 32017}, {1574, 28254}, {1580, 12194}, {1918, 17445}, {2176, 4384}, {2238, 50095}, {2295, 17023}, {2481, 39940}, {2703, 9081}, {2783, 12177}, {3051, 8621}, {3210, 24282}, {3663, 28369}, {3735, 28606}, {3739, 16685}, {3747, 21352}, {3752, 21888}, {3765, 4721}, {3780, 49770}, {3997, 50114}, {4039, 12263}, {4359, 24254}, {4366, 23660}, {4383, 14535}, {4389, 4503}, {4641, 45751}, {4649, 18794}, {4688, 52897}, {5256, 9620}, {5283, 19735}, {6033, 33106}, {7109, 24592}, {8616, 16497}, {10436, 21769}, {14621, 21760}, {15989, 50167}, {16514, 25368}, {16526, 40750}, {16782, 24326}, {16826, 27002}, {16831, 16969}, {16973, 34377}, {17049, 40934}, {17117, 27644}, {17448, 18206}, {17472, 46903}, {17475, 39714}, {17750, 26626}, {20172, 40728}, {20913, 40886}, {24199, 28350}, {24268, 29069}, {25590, 28365}, {28371, 31198}, {29055, 29352}, {29580, 37633}, {29597, 37674}, {36816, 51987}, {37662, 51390}, {40153, 42051}, {46264, 50629}, {51121, 51122}
X(54282) = crossdifference of every pair of points on line {650, 9010}
X(54282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20367, 37596}, {1, 37555, 980}, {81, 29584, 16971}, {1429, 5255, 5337}, {10800, 24264, 31}, {25590, 41418, 28365}
X(54283) lies on these lines: {2, 2006}, {4, 9}, {6, 10573}, {8, 2323}, {37, 91}, {78, 2321}, {198, 11499}, {219, 594}, {220, 7359}, {226, 53816}, {345, 4494}, {346, 5552}, {355, 2182}, {499, 8609}, {1146, 17369}, {1352, 24332}, {1737, 8557}, {1899, 21028}, {1944, 3661}, {2171, 5747}, {2172, 2329}, {2359, 10570}, {2915, 9712}, {3247, 13411}, {3436, 21066}, {3939, 28118}, {4000, 24209}, {4007, 6737}, {4363, 26932}, {4671, 28836}, {4873, 6745}, {5227, 21074}, {5285, 7102}, {5554, 5749}, {5745, 19822}, {5746, 15556}, {5750, 19860}, {6708, 32777}, {7085, 7140}, {8257, 26001}, {17075, 40903}, {17281, 46835}, {17286, 27384}, {17303, 19854}, {17314, 22836}, {17359, 34852}, {17754, 26013}, {21091, 24315}, {21871, 31837}, {23676, 33127}, {24149, 45794}, {24958, 25679}, {27059, 28731}, {27382, 52405}, {28125, 52335}, {28796, 31025}, {29611, 52457}, {29828, 50366}
X(54283) = X(7284)-complementary conjugate of X(2886)
X(54283) = X(i)-isoconjugate of X(j) for these (i,j): {57, 3422}, {222, 1061}, {905, 36076}
X(54283) = X(i)-Dao conjugate of X(j) for these (i,j): {5452, 3422}, {38964, 514}
X(54283) = crossdifference of every pair of points on line {1459, 8648}
X(54283) = barycentric product X(i)*X(j) for these {i,j}: {8, 1478}, {10, 11103}, {318, 1060}, {4351, 52409}
X(54283) = barycentric quotient X(i)/X(j) for these {i,j}: {33, 1061}, {55, 3422}, {1060, 77}, {1478, 7}, {4351, 1443}, {8750, 36076}, {11103, 86}
X(54283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {281, 2345, 9}, {17355, 20262, 9}
X(54284) lies on these lines: {2, 37}, {7, 11433}, {11, 20276}, {27, 42467}, {56, 20220}, {57, 92}, {85, 2994}, {239, 394}, {241, 6360}, {242, 1473}, {244, 17871}, {273, 2052}, {314, 24556}, {318, 1210}, {320, 6515}, {341, 25005}, {343, 3662}, {469, 12610}, {614, 4008}, {894, 10601}, {938, 23661}, {982, 26013}, {990, 14004}, {1086, 13567}, {1088, 23989}, {1119, 14361}, {1230, 25003}, {1441, 9776}, {1445, 20223}, {1726, 24618}, {1733, 5272}, {1851, 26929}, {1993, 3759}, {3086, 17869}, {3218, 18750}, {3219, 30854}, {3262, 18141}, {3305, 20879}, {3306, 14213}, {3580, 48629}, {3673, 26001}, {3703, 25973}, {3758, 5422}, {3782, 26005}, {3944, 26010}, {4191, 30273}, {4292, 5342}, {4361, 17811}, {4363, 17825}, {4384, 20882}, {4385, 24982}, {4395, 53415}, {4647, 8583}, {5222, 11427}, {5256, 18690}, {5262, 24537}, {5437, 6358}, {5695, 25893}, {5740, 33672}, {5905, 20921}, {7283, 25875}, {9965, 30807}, {10072, 23580}, {10444, 39592}, {11019, 17860}, {12649, 52346}, {14986, 23528}, {16059, 29010}, {16284, 32863}, {16817, 37228}, {17227, 37636}, {17361, 45794}, {17366, 23292}, {17367, 37649}, {17555, 23537}, {17616, 48878}, {17763, 25938}, {17861, 24177}, {17880, 41081}, {17923, 20266}, {18156, 26639}, {18928, 42697}, {20237, 30567}, {20430, 37355}, {20881, 30568}, {20895, 34255}, {20909, 25955}, {20927, 32939}, {20940, 25954}, {23541, 33131}, {23978, 34404}, {24163, 24186}, {24175, 24209}, {24415, 40688}, {25941, 32860}, {26531, 26550}, {26534, 26565}, {26609, 27792}, {26871, 53994}, {26872, 52457}, {30679, 42050}, {37648, 48627}, {37881, 38487}
X(54284) = isotomic conjugate of the isogonal conjugate of X(3554)
X(54284) = X(649)-complementary conjugate of X(47601)
X(54284) = X(i)-isoconjugate of X(j) for these (i,j): {6, 42019}, {55, 53995}, {837, 4055}, {2175, 34401}
X(54284) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 42019}, {223, 53995}, {3086, 2324}, {3554, 10310}, {24005, 3682}, {38015, 1}, {38357, 14298}, {40593, 34401}, {40650, 3084}, {49171, 6}
X(54284) = cevapoint of X(i) and X(j) for these (i,j): {3086, 53994}, {17869, 24005}
X(54284) = barycentric product X(i)*X(j) for these {i,j}: {75, 3086}, {76, 3554}, {85, 53994}, {86, 17869}, {92, 26871}, {274, 24005}, {1519, 18816}, {6063, 30223}
X(54284) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 42019}, {57, 53995}, {85, 34401}, {309, 34413}, {836, 3990}, {1519, 517}, {3086, 1}, {3554, 6}, {17869, 10}, {19354, 212}, {24005, 37}, {26871, 63}, {26955, 201}, {30223, 55}, {38003, 1124}, {38015, 2324}, {40650, 3083}, {49171, 10310}, {53994, 9}
X(54284) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 28605, 26591}, {2, 48380, 312}, {57, 4858, 92}, {1210, 20320, 318}, {3752, 26011, 2}, {4359, 20905, 2}, {20921, 39126, 5905}
X(54285) lies on these lines: {1, 21853}, {3, 37}, {6, 31}, {9, 35}, {19, 37601}, {21, 2345}, {36, 3247}, {44, 4254}, {45, 198}, {48, 1334}, {56, 2171}, {75, 16367}, {100, 966}, {218, 584}, {219, 2278}, {220, 2174}, {284, 2911}, {344, 21511}, {346, 4189}, {405, 17303}, {478, 2197}, {498, 50036}, {572, 10267}, {573, 11248}, {574, 17053}, {579, 24047}, {594, 958}, {595, 5105}, {604, 11510}, {943, 5746}, {956, 17299}, {993, 2321}, {999, 3723}, {1001, 1009}, {1100, 3295}, {1213, 1376}, {1259, 3713}, {1333, 17524}, {1400, 11509}, {1436, 3207}, {1444, 17316}, {1449, 3746}, {1486, 37586}, {1500, 5019}, {1575, 16058}, {1593, 1841}, {1696, 16675}, {1697, 3554}, {1743, 37503}, {2071, 16307}, {2092, 31451}, {2176, 5110}, {2183, 11434}, {2245, 11507}, {2256, 7113}, {2262, 37568}, {2270, 35445}, {2285, 37579}, {2298, 16452}, {2303, 4184}, {2305, 15592}, {2324, 30282}, {2335, 37120}, {2646, 21871}, {2975, 17314}, {3097, 16800}, {3169, 8668}, {3204, 17454}, {3290, 7484}, {3303, 16884}, {3553, 3601}, {3686, 8715}, {3693, 20835}, {3709, 48391}, {3731, 5010}, {3772, 21483}, {3871, 5839}, {3913, 17362}, {3940, 21873}, {3950, 5267}, {3973, 51817}, {4007, 5258}, {4034, 48696}, {4068, 4497}, {4171, 23226}, {4261, 16287}, {4265, 50995}, {4268, 11508}, {4270, 33771}, {4276, 4877}, {4421, 17330}, {4526, 39200}, {4657, 21477}, {4687, 11329}, {4698, 16412}, {5036, 14882}, {5069, 16502}, {5153, 16466}, {5204, 16672}, {5248, 5750}, {5257, 25440}, {5279, 37285}, {5687, 17275}, {5747, 17732}, {5816, 11499}, {5819, 7676}, {6351, 16441}, {6352, 16440}, {6580, 33635}, {6684, 24005}, {7280, 16673}, {7373, 46845}, {7485, 26242}, {7824, 26107}, {8273, 37519}, {8607, 36751}, {8609, 26357}, {8610, 15815}, {9310, 22054}, {9598, 37225}, {9724, 20793}, {10310, 37499}, {10895, 53421}, {10966, 17452}, {11194, 50113}, {11285, 25505}, {11343, 17279}, {11350, 44307}, {11383, 44103}, {12513, 17388}, {13455, 44192}, {13615, 44798}, {16064, 23847}, {16286, 46838}, {16289, 19845}, {16290, 41508}, {16368, 32777}, {16370, 17281}, {16431, 41312}, {16436, 41313}, {16439, 24789}, {16523, 23370}, {16972, 36741}, {17321, 21495}, {17334, 24328}, {17357, 21514}, {17384, 21526}, {17750, 37547}, {17776, 27174}, {18491, 32431}, {19308, 27268}, {20846, 27396}, {21231, 24268}, {21348, 48390}, {21509, 41310}, {21539, 41311}, {21801, 22768}, {22769, 49509}, {25099, 37344}, {31993, 37323}, {35238, 37508}, {40292, 40937}, {41230, 52241}
X(54285) = crossdifference of every pair of points on line {514, 51648}
X(54285) = barycentric product X(1)*X(41229)
X(54285) = barycentric quotient X(41229)/X(75)
X(54285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 37, 2178}, {9, 35, 36744}, {45, 1030, 198}, {71, 2268, 6}, {198, 5217, 1030}, {220, 37504, 2174}, {284, 3730, 2911}, {346, 4189, 38871}, {2267, 2269, 6}, {2268, 41423, 71}, {3295, 5120, 1100}, {5124, 16777, 56}, {16675, 19297, 1696}
X(54286) lies on these lines: {1, 88}, {2, 5119}, {3, 5836}, {4, 9}, {5, 37828}, {7, 34619}, {8, 46}, {31, 4695}, {33, 45269}, {35, 19860}, {36, 3872}, {37, 31433}, {55, 3753}, {56, 10914}, {57, 519}, {63, 484}, {65, 3689}, {72, 3711}, {78, 4867}, {145, 3338}, {165, 993}, {191, 16558}, {200, 758}, {210, 5183}, {226, 45701}, {355, 1158}, {377, 10039}, {381, 5123}, {388, 10915}, {392, 4413}, {405, 3698}, {474, 3057}, {495, 5856}, {498, 39599}, {515, 3359}, {517, 997}, {518, 36279}, {528, 5722}, {551, 5437}, {595, 1722}, {612, 4424}, {614, 1739}, {643, 11116}, {655, 51975}, {920, 5086}, {936, 3878}, {942, 3913}, {946, 6944}, {956, 1155}, {958, 3579}, {960, 9709}, {962, 5328}, {975, 37598}, {999, 3880}, {1000, 34711}, {1012, 13528}, {1018, 40131}, {1056, 49626}, {1100, 4646}, {1107, 1571}, {1125, 1697}, {1145, 5252}, {1319, 16371}, {1329, 12699}, {1339, 40151}, {1377, 49226}, {1378, 49227}, {1387, 17564}, {1420, 22837}, {1454, 41687}, {1476, 3361}, {1478, 6735}, {1479, 24982}, {1572, 1575}, {1574, 39248}, {1698, 4193}, {1699, 3814}, {1708, 3419}, {1728, 5175}, {1730, 48863}, {1737, 3434}, {1768, 15863}, {1770, 3436}, {1781, 3692}, {1788, 5082}, {1836, 17757}, {1837, 12690}, {2082, 16549}, {2098, 17614}, {2099, 5440}, {2136, 3244}, {2160, 3704}, {2320, 3612}, {2328, 17519}, {2475, 10827}, {2800, 5720}, {2886, 6882}, {2932, 17636}, {3035, 5886}, {3085, 12609}, {3086, 26062}, {3158, 3919}, {3174, 30329}, {3219, 53620}, {3241, 27003}, {3245, 5692}, {3295, 3812}, {3303, 5439}, {3305, 19875}, {3336, 3632}, {3337, 3633}, {3339, 3874}, {3340, 22836}, {3421, 3474}, {3452, 28194}, {3488, 34607}, {3550, 37817}, {3555, 5221}, {3582, 31224}, {3584, 31266}, {3587, 5745}, {3601, 30147}, {3617, 31295}, {3624, 37563}, {3625, 6762}, {3626, 5128}, {3634, 31435}, {3636, 37556}, {3646, 51073}, {3647, 5234}, {3654, 28452}, {3678, 12526}, {3683, 4731}, {3696, 5774}, {3715, 3921}, {3729, 51284}, {3742, 6767}, {3743, 16673}, {3749, 30117}, {3820, 24703}, {3822, 31434}, {3825, 9614}, {3828, 7308}, {3833, 10582}, {3838, 31479}, {3870, 5902}, {3884, 8583}, {3890, 17531}, {3892, 10980}, {3893, 32636}, {3898, 9819}, {3911, 45700}, {3918, 5248}, {3922, 37080}, {3927, 4662}, {3928, 4669}, {3929, 4745}, {3931, 16777}, {3940, 44663}, {3968, 4512}, {3987, 5264}, {4015, 12446}, {4084, 11523}, {4187, 12701}, {4188, 4861}, {4253, 50022}, {4271, 37150}, {4292, 6736}, {4295, 7080}, {4297, 37560}, {4301, 6700}, {4386, 9620}, {4421, 24929}, {4428, 51787}, {4498, 28591}, {4511, 25415}, {4640, 9708}, {4652, 5258}, {4658, 17207}, {4668, 6763}, {4691, 41348}, {4714, 5271}, {4723, 32933}, {4737, 32939}, {4848, 37550}, {4853, 8666}, {4882, 41228}, {4915, 4973}, {5122, 11194}, {5180, 27131}, {5187, 9780}, {5223, 30353}, {5249, 10056}, {5251, 35258}, {5255, 24440}, {5267, 35242}, {5272, 40091}, {5288, 37524}, {5426, 51817}, {5435, 34625}, {5438, 7982}, {5534, 5884}, {5552, 12047}, {5554, 10572}, {5563, 36846}, {5573, 24168}, {5603, 12703}, {5690, 5794}, {5697, 19861}, {5705, 6943}, {5708, 34791}, {5709, 6885}, {5726, 8545}, {5777, 17646}, {5791, 9710}, {5795, 31730}, {5881, 12247}, {5882, 37534}, {6174, 15950}, {6205, 45751}, {6261, 11499}, {6684, 6891}, {6691, 11373}, {6797, 13205}, {6890, 19843}, {6918, 45776}, {6973, 10175}, {6986, 16208}, {7183, 25719}, {7289, 49529}, {7330, 40256}, {7681, 12700}, {7686, 10306}, {7702, 26482}, {7969, 9679}, {7987, 51111}, {7995, 31871}, {8170, 34862}, {8580, 10176}, {8582, 10624}, {9843, 12575}, {9945, 37728}, {9957, 25524}, {10106, 49169}, {10197, 25525}, {10199, 21630}, {10200, 12053}, {10270, 12650}, {10528, 13407}, {10609, 37740}, {10826, 25005}, {10860, 28164}, {10896, 17619}, {10912, 24928}, {11236, 51362}, {11274, 51767}, {11376, 13747}, {11500, 12520}, {11508, 37282}, {11518, 33815}, {11530, 51570}, {11552, 31164}, {11813, 30827}, {11826, 45080}, {12019, 15297}, {12245, 12704}, {12513, 37582}, {12635, 50193}, {12647, 51433}, {12767, 47320}, {14798, 37301}, {14974, 16605}, {15843, 37401}, {16483, 16610}, {16611, 16970}, {16669, 21896}, {17064, 17734}, {17284, 24590}, {17573, 33895}, {17594, 30116}, {17668, 18908}, {17754, 50287}, {17784, 18391}, {18228, 34632}, {18393, 30852}, {18540, 50796}, {18990, 32049}, {19537, 37605}, {20085, 37711}, {20103, 28228}, {21370, 29673}, {21952, 42657}, {22300, 31778}, {22791, 25681}, {23537, 28402}, {23958, 31145}, {24174, 37588}, {24390, 24914}, {24473, 41711}, {24715, 37716}, {25092, 31426}, {25413, 45770}, {25466, 32157}, {26066, 31419}, {27529, 37692}, {29007, 50736}, {29529, 48812}, {30331, 34639}, {30556, 35610}, {30557, 35611}, {31443, 31449}, {31458, 37551}, {31803, 54156}, {31855, 49500}, {32760, 37300}, {32912, 49984}, {33709, 50443}, {34720, 51463}, {35004, 37700}, {36480, 37555}, {37274, 40863}, {37612, 37727}, {37829, 50239}, {39148, 52140}, {40726, 51788}, {46684, 52027}, {48882, 49734}, {48915, 49728}, {50581, 50633}, {51093, 51786}, {51103, 51779}
X(54286) = midpoint of X(i) and X(j) for these {i,j}: {8, 4293}, {200, 2093}, {3421, 3474}, {5223, 30353}, {17784, 18391}
X(54286) = reflection of X(i) in X(j) for these {i,j}: {997, 1376}, {4342, 1125}, {24703, 3820}
X(54286) = complement of X(30305)
X(54286) = X(i)-Dao conjugate of X(j) for these (i,j): {17595, 17274}, {38962, 514}
X(54286) = crossdifference of every pair of points on line {1459, 1635}
X(54286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5541, 3895}, {8, 4190, 45287}, {10, 40, 12514}, {10, 5493, 12572}, {40, 1706, 10}, {65, 3811, 12559}, {65, 5687, 3811}, {165, 9623, 993}, {404, 14923, 1}, {484, 3679, 63}, {936, 7991, 3878}, {1145, 11112, 5252}, {1276, 1277, 1766}, {1698, 11010, 5250}, {1739, 37610, 614}, {1788, 5082, 10916}, {2136, 3333, 3244}, {2550, 5657, 10}, {3241, 27003, 51816}, {3306, 3895, 1}, {3339, 6765, 3874}, {3698, 37568, 405}, {3754, 8715, 1}, {3885, 5253, 1}, {4188, 4861, 37618}, {4295, 7080, 21077}, {4386, 21888, 9620}, {4853, 15803, 8666}, {5258, 37572, 4652}, {5437, 31393, 551}, {5438, 7982, 30144}, {5657, 48363, 40}, {5883, 25439, 1}, {5902, 48696, 3870}, {6691, 13463, 11373}, {9709, 12702, 960}, {10199, 21630, 37704}, {11499, 37562, 6261}, {11500, 31788, 12520}, {22791, 47742, 25681}, {25005, 52367, 10826}, {30827, 31162, 11813}, {31190, 37704, 10199}, {34612, 40663, 3419}
X(54287) lies on these lines: {1, 6}, {2, 7283}, {3, 44307}, {10, 968}, {21, 975}, {25, 35}, {33, 30733}, {34, 16577}, {36, 27802}, {43, 4204}, {46, 846}, {57, 16290}, {58, 5287}, {75, 37035}, {78, 4653}, {165, 37320}, {192, 16817}, {312, 11110}, {344, 13725}, {386, 3305}, {406, 498}, {429, 7951}, {440, 9612}, {536, 51676}, {612, 5248}, {756, 3811}, {936, 16346}, {940, 31445}, {988, 3624}, {990, 6986}, {993, 27784}, {997, 10448}, {1010, 4687}, {1125, 4011}, {1224, 39954}, {1698, 3712}, {1707, 37559}, {1745, 37324}, {1860, 39585}, {1961, 37316}, {2218, 7322}, {2276, 53387}, {2345, 19857}, {2901, 5271}, {2915, 5010}, {3175, 11357}, {3216, 7308}, {3293, 37553}, {3338, 26102}, {3465, 3612}, {3587, 52524}, {3601, 36011}, {3616, 26223}, {3646, 49979}, {3666, 11108}, {3672, 17554}, {3679, 3695}, {3683, 5711}, {3685, 19853}, {3739, 50044}, {3752, 16842}, {3868, 33761}, {3916, 37674}, {3953, 10582}, {3989, 28082}, {4000, 17552}, {4195, 27268}, {4239, 25440}, {4292, 14021}, {4306, 8545}, {4340, 5308}, {4358, 16342}, {4420, 9330}, {4423, 37592}, {4512, 5264}, {4664, 51595}, {4689, 9709}, {4693, 31327}, {4698, 16458}, {4704, 19851}, {4755, 16394}, {4850, 17536}, {4851, 49716}, {5016, 14020}, {5044, 19765}, {5047, 28606}, {5100, 49746}, {5119, 13724}, {5250, 30116}, {5262, 16859}, {5272, 25542}, {5295, 19732}, {5313, 5506}, {5438, 19287}, {6675, 17720}, {6886, 53599}, {6913, 37528}, {7069, 10393}, {7270, 48814}, {7741, 37315}, {8728, 50065}, {9534, 17260}, {9708, 37548}, {11512, 34595}, {12047, 21062}, {13411, 27413}, {13728, 17279}, {13732, 46475}, {13734, 16389}, {13735, 51488}, {13742, 17321}, {13745, 41313}, {15803, 21483}, {15976, 48883}, {16050, 16831}, {16343, 44417}, {16418, 37539}, {16602, 16854}, {16610, 16853}, {16828, 50314}, {16844, 31993}, {16856, 31197}, {16865, 37817}, {17022, 31424}, {17243, 49728}, {17263, 33833}, {17278, 17590}, {17281, 51679}, {17289, 37039}, {17303, 17514}, {17322, 37036}, {17342, 51680}, {17588, 31035}, {17916, 41227}, {18540, 48897}, {18743, 19270}, {19273, 30818}, {19758, 25066}, {19766, 26685}, {19767, 27065}, {19784, 50290}, {19785, 31259}, {19854, 24210}, {19871, 50126}, {19874, 32929}, {20077, 29569}, {24512, 31442}, {24789, 50067}, {24936, 31053}, {25091, 37224}, {25430, 37322}, {26064, 32858}, {26127, 29680}, {29573, 49723}, {30282, 37052}, {31658, 37537}, {33116, 52258}, {37317, 37552}, {37327, 37603}, {41310, 51677}, {50068, 50202}
X(54287) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 405, 1}, {958, 6051, 1}, {1453, 3247, 1}, {4205, 32777, 1698}, {4698, 50054, 16458}, {5251, 27785, 1}, {17022, 31424, 37522}, {17776, 37314, 10}, {27802, 37246, 36}, {50067, 50205, 24789}
X(54288) lies on these lines: {2, 4867}, {8, 35}, {10, 12}, {63, 484}, {80, 3219}, {191, 5086}, {214, 51113}, {321, 15065}, {333, 759}, {515, 550}, {516, 54175}, {519, 5745}, {527, 4745}, {912, 4662}, {956, 5172}, {960, 3825}, {997, 6681}, {1125, 17706}, {1145, 4669}, {1478, 3617}, {1512, 15064}, {1737, 10176}, {2801, 24393}, {2802, 4847}, {3245, 33110}, {3452, 6702}, {3476, 8666}, {3488, 5248}, {3585, 11684}, {3586, 12514}, {3632, 4917}, {3647, 10572}, {3814, 5692}, {3869, 18393}, {3874, 24987}, {3876, 18395}, {3878, 6734}, {3881, 24391}, {3884, 5837}, {3898, 26015}, {3899, 11680}, {3951, 10827}, {4364, 25390}, {4511, 5444}, {4691, 8256}, {4732, 8680}, {4868, 25080}, {5178, 11010}, {5180, 31159}, {5220, 5790}, {5341, 17275}, {5435, 5775}, {5657, 7688}, {5791, 30147}, {5881, 21165}, {5902, 27186}, {5905, 53620}, {6175, 11552}, {6788, 17123}, {8728, 33815}, {9803, 15931}, {10039, 18389}, {11362, 37585}, {11813, 31165}, {15228, 47033}, {17051, 51108}, {17056, 53114}, {17057, 31053}, {17461, 33141}, {18253, 37730}, {19875, 31266}, {20013, 31452}, {21014, 21078}, {22758, 35000}, {22836, 26066}, {26065, 48826}, {26792, 31160}, {29046, 50308}, {31164, 51066}, {35016, 41575}, {35466, 49682}, {51071, 51463}
X(54288) = midpoint of X(i) and X(j) for these {i,j}: {8, 993}, {11362, 51755}
X(54288) = reflection of X(3822) in X(10)
X(54288) = barycentric product X(321)*X(37525)
X(54288) = barycentric quotient X(37525)/X(81)
X(54288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 65, 3841}, {10, 3919, 3925}, {10, 4067, 12}, {10, 4084, 442}, {10, 4134, 17757}, {10, 4848, 3918}, {3878, 6734, 24387}, {5837, 10916, 3884}
X(54289) lies on these lines: {1, 21}, {3, 6511}, {4, 2000}, {8, 1943}, {20, 36850}, {29, 18750}, {34, 6734}, {40, 11413}, {42, 8895}, {56, 24476}, {69, 73}, {72, 394}, {224, 4303}, {241, 37282}, {270, 1760}, {271, 1257}, {279, 6904}, {377, 1448}, {936, 32782}, {1040, 4652}, {1062, 3916}, {1071, 22129}, {1214, 1259}, {1427, 37229}, {1763, 11337}, {1798, 43708}, {1800, 6507}, {1829, 37581}, {3616, 27509}, {3682, 6505}, {3870, 36706}, {3876, 37659}, {3912, 28769}, {3927, 18447}, {3928, 33178}, {4347, 4847}, {5256, 24609}, {5262, 37666}, {5271, 15149}, {5287, 37169}, {6769, 37048}, {6872, 37782}, {7085, 37613}, {7291, 7520}, {7360, 26027}, {10527, 34036}, {11363, 24320}, {14054, 36742}, {14206, 39585}, {16454, 20235}, {16465, 36746}, {17181, 26120}, {18634, 26167}, {18651, 37179}, {19860, 24570}, {21370, 37231}, {21406, 50314}, {24537, 52345}, {34028, 41228}, {37094, 52346}, {41538, 45729}
X(54289) = X(i)-isoconjugate of X(j) for these (i,j): {393, 45127}, {13395, 18344}
X(54289) = X(405)-Dao conjugate of X(39585)
X(54289) = barycentric product X(i)*X(j) for these {i,j}: {63, 377}, {304, 37538}, {345, 1448}, {4592, 47124}, {17206, 43214}
X(54289) = barycentric quotient X(i)/X(j) for these {i,j}: {255, 45127}, {377, 92}, {1448, 278}, {1813, 13395}, {37538, 19}, {43214, 1826}, {46038, 7040}, {47124, 24006}
X(54289) = {X(63),X(52362)}-harmonic conjugate of X(1)
X(54290) lies on these lines: {1, 3052}, {3, 12526}, {8, 20}, {9, 46}, {10, 3474}, {21, 11529}, {35, 11523}, {36, 15829}, {55, 41863}, {57, 1125}, {65, 31424}, {72, 165}, {78, 11684}, {100, 3951}, {144, 21075}, {200, 3579}, {329, 6684}, {376, 6737}, {392, 3361}, {405, 3339}, {443, 18249}, {474, 53056}, {484, 1706}, {498, 28609}, {527, 3085}, {595, 3677}, {610, 4047}, {758, 3601}, {908, 31423}, {920, 10396}, {936, 1155}, {942, 4512}, {946, 5744}, {956, 7991}, {958, 2093}, {960, 15803}, {986, 1453}, {993, 3340}, {1046, 17594}, {1071, 10268}, {1210, 5698}, {1259, 7688}, {1420, 3878}, {1697, 3244}, {1722, 7262}, {1768, 9841}, {1788, 12572}, {1836, 5705}, {2136, 11010}, {2270, 3707}, {2292, 37554}, {2975, 7982}, {3146, 5775}, {3158, 5904}, {3218, 3333}, {3219, 37161}, {3243, 3746}, {3247, 31320}, {3306, 3646}, {3336, 5437}, {3359, 10942}, {3421, 43174}, {3428, 12330}, {3496, 16572}, {3555, 53053}, {3576, 3869}, {3587, 16139}, {3623, 31393}, {3624, 51409}, {3633, 5119}, {3648, 18492}, {3652, 18540}, {3670, 7290}, {3678, 46917}, {3679, 10483}, {3680, 5288}, {3683, 5221}, {3697, 15587}, {3701, 25734}, {3712, 10319}, {3753, 5234}, {3811, 35445}, {3847, 24703}, {3868, 35258}, {3874, 10389}, {3895, 20014}, {3899, 37618}, {3911, 25522}, {3925, 31446}, {3940, 31663}, {3962, 5217}, {4293, 5837}, {4294, 24391}, {4295, 5745}, {4302, 12625}, {4330, 41709}, {4333, 47033}, {4480, 6211}, {4654, 10198}, {4677, 34626}, {4691, 41348}, {4847, 6361}, {4853, 12702}, {5057, 5535}, {5082, 5493}, {5084, 51090}, {5175, 28150}, {5204, 31165}, {5223, 5687}, {5231, 5709}, {5247, 16570}, {5248, 11518}, {5262, 36277}, {5264, 7174}, {5267, 13384}, {5325, 19855}, {5436, 5902}, {5438, 5692}, {5440, 16192}, {5530, 24695}, {5552, 17781}, {5560, 6597}, {5657, 12527}, {5693, 52026}, {5708, 10582}, {5730, 7987}, {6734, 41869}, {6738, 11111}, {6743, 50808}, {6745, 37560}, {6765, 37568}, {6974, 12704}, {7308, 51073}, {7330, 18480}, {7580, 7992}, {7701, 52841}, {7962, 8666}, {7971, 11012}, {8227, 11415}, {8583, 37582}, {9580, 10916}, {9588, 17757}, {9589, 24390}, {9623, 37567}, {9624, 51423}, {9965, 21620}, {10404, 37550}, {10461, 52352}, {10527, 31162}, {10624, 24477}, {10882, 23206}, {12635, 30282}, {12717, 16566}, {14110, 52027}, {14450, 31266}, {15172, 31146}, {15446, 30323}, {16209, 41389}, {16418, 31794}, {18398, 38316}, {18493, 37532}, {18499, 37584}, {19535, 53054}, {21616, 31231}, {23085, 37620}, {24467, 34773}, {25728, 46937}, {26364, 31142}, {27065, 46930}, {31053, 31888}, {31249, 34753}, {31445, 36279}
X(54290) = reflection of X(i) in X(j) for these {i,j}: {5229, 10}, {9612, 26066}
X(54290) = X(43533)-Ceva conjugate of X(1)
X(54290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 51576, 16370}, {40, 1158, 10860}, {46, 191, 9}, {57, 12514, 31435}, {484, 41229, 1706}, {986, 1707, 1453}, {3218, 5250, 3333}, {3579, 3927, 200}, {3869, 4652, 3576}, {3929, 5128, 10}, {4018, 16370, 1}, {5119, 6763, 6762}, {5880, 18253, 1698}, {6734, 44447, 41869}
X(54291) lies on these lines: {1, 76}, {2, 11}, {8, 2176}, {42, 312}, {43, 3886}, {75, 40934}, {238, 18900}, {291, 3923}, {518, 24514}, {672, 4676}, {740, 33931}, {982, 24259}, {984, 4368}, {1279, 21264}, {1281, 4376}, {1386, 17027}, {1479, 52256}, {1575, 49484}, {1914, 52133}, {2239, 30942}, {2263, 7196}, {2276, 3685}, {3242, 4713}, {3246, 17028}, {3416, 31027}, {3616, 26978}, {3720, 31005}, {3741, 3883}, {3783, 32941}, {3974, 20012}, {4307, 30962}, {4335, 10436}, {4363, 36222}, {4441, 32922}, {4443, 24425}, {4465, 36534}, {4514, 31330}, {4645, 30945}, {4872, 24723}, {5695, 17759}, {6327, 30965}, {7290, 17026}, {10453, 37676}, {15171, 37148}, {15569, 17032}, {16720, 32117}, {17018, 32926}, {17147, 31115}, {17233, 18082}, {17793, 49473}, {21299, 28369}, {21904, 28581}, {24210, 25385}, {24260, 29668}, {24330, 24349}, {24549, 48900}, {29706, 50637}, {30545, 42289}, {30953, 33106}, {30961, 33126}, {30966, 50295}, {30969, 33104}, {30985, 33124}, {31006, 33112}, {31028, 50289}, {36844, 37193}, {37580, 41236}, {41142, 50126}, {41794, 49483}, {48822, 48841}
X(54291) = crossdifference of every pair of points on line {665, 46386}
X(54291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40718, 37632}, {2, 13576, 4429}, {3242, 4713, 17794}, {14942, 32942, 5263}
X(54292) lies on these lines: {1, 4}, {12, 37983}, {56, 5262}, {58, 7098}, {65, 81}, {86, 664}, {109, 4424}, {201, 5247}, {221, 37614}, {227, 37539}, {284, 32674}, {517, 3955}, {534, 2263}, {551, 1421}, {603, 986}, {758, 2003}, {975, 10588}, {1038, 1788}, {1060, 18391}, {1061, 18533}, {1062, 4305}, {1319, 7191}, {1390, 34056}, {1393, 37607}, {1450, 29821}, {1455, 3666}, {1468, 37591}, {1470, 4850}, {1610, 1829}, {1735, 37469}, {1758, 5429}, {1774, 5119}, {1880, 2303}, {1935, 2292}, {1993, 3869}, {2006, 3822}, {2078, 49480}, {2099, 4318}, {2594, 34772}, {2831, 44302}, {3057, 41733}, {3256, 4868}, {3340, 4347}, {3891, 38460}, {3920, 5252}, {3924, 37523}, {4297, 33178}, {4351, 5902}, {4354, 5441}, {4367, 42751}, {4417, 4511}, {4551, 30115}, {4861, 4968}, {5251, 16577}, {5724, 51421}, {5919, 30621}, {8614, 45288}, {9578, 30142}, {9627, 10543}, {17011, 44733}, {17074, 18838}, {17869, 37157}, {18447, 37361}, {24806, 49487}, {30145, 37709}, {34046, 37549}, {37399, 41600}, {37558, 52564}, {37736, 49686}, {39766, 52358}, {41575, 52362}, {47057, 49682}
X(54292) = barycentric product X(226)*X(17512)
X(54292) = barycentric quotient X(17512)/X(333)
X(54292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34, 3485}, {1, 581, 45230}, {1, 10572, 6198}, {1, 21147, 388}, {4296, 17016, 65}, {4318, 17015, 2099}
X(54293) lies on these lines: {1, 475}, {4, 990}, {6, 19}, {11, 33}, {25, 3752}, {75, 11109}, {318, 32922}, {378, 37817}, {975, 52252}, {1040, 26052}, {1086, 1892}, {1104, 1593}, {1191, 1902}, {1279, 7071}, {1452, 24443}, {1722, 46878}, {1870, 11041}, {1878, 38530}, {1890, 4312}, {2332, 16780}, {2550, 34231}, {2999, 3192}, {3914, 11393}, {4008, 36123}, {4200, 5262}, {4429, 5081}, {5480, 23982}, {5728, 23052}, {5819, 40065}, {7290, 8750}, {9593, 41320}, {11392, 23536}, {16706, 17555}, {17720, 26020}, {24789, 25985}, {24989, 32774}, {37305, 41230}, {40987, 54234}
X(54293) = barycentric product X(i)*X(j) for these {i,j}: {34, 28795}, {92, 22769}
X(54293) = barycentric quotient X(i)/X(j) for these {i,j}: {22769, 63}, {28795, 3718}
X(54293) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1861, 23050}, {6, 1876, 42856}, {2362, 16232, 20613}
X(54294) lies on these lines: {1, 7490}, {4, 9}, {8, 27}, {28, 55}, {65, 278}, {196, 225}, {270, 17126}, {377, 3101}, {380, 5717}, {407, 52082}, {443, 10319}, {469, 9780}, {515, 37379}, {607, 3194}, {938, 37389}, {944, 7554}, {1119, 3339}, {1172, 5711}, {1715, 14647}, {1782, 3474}, {1788, 41342}, {1824, 7952}, {1829, 4196}, {1838, 2093}, {1841, 4646}, {1871, 31788}, {2282, 2357}, {2355, 28076}, {2475, 9536}, {3085, 3198}, {3189, 31900}, {3197, 5706}, {3332, 40660}, {3487, 18673}, {3617, 6994}, {3925, 5142}, {4185, 11406}, {4198, 5174}, {4219, 5584}, {4329, 25015}, {4761, 17926}, {4972, 5125}, {5084, 9816}, {5146, 5183}, {5230, 18678}, {5261, 7282}, {5603, 7543}, {5687, 37377}, {5690, 7534}, {5790, 7546}, {5799, 37381}, {6047, 37567}, {6353, 39586}, {6826, 8251}, {6839, 9537}, {6851, 15941}, {6917, 8141}, {6995, 39570}, {7497, 10306}, {7498, 19859}, {7501, 10902}, {10268, 37028}, {11445, 41723}, {12702, 15762}, {14017, 37601}, {17917, 28629}, {17924, 50499}, {18453, 44229}, {21677, 31902}, {30503, 37417}, {30686, 39579}, {31922, 46883}, {37383, 44695}, {37550, 44696}
X(54294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19, 1869, 4}, {19, 11471, 7713}, {1824, 37384, 7952}, {4185, 11406, 41227}
X(54295) lies on these lines: {1, 3}, {6, 12711}, {8, 3100}, {9, 607}, {10, 33}, {20, 21147}, {34, 516}, {42, 10393}, {72, 1854}, {73, 12520}, {78, 27379}, {108, 8899}, {200, 3704}, {212, 12514}, {222, 9943}, {223, 12565}, {227, 7580}, {255, 1158}, {355, 36985}, {388, 990}, {390, 5262}, {614, 12053}, {651, 9961}, {728, 2324}, {774, 1708}, {950, 3755}, {962, 34036}, {971, 9370}, {975, 5218}, {997, 22072}, {1074, 26332}, {1103, 1490}, {1253, 2292}, {1394, 10860}, {1448, 3474}, {1455, 37022}, {1486, 44545}, {1616, 17622}, {1698, 9817}, {1699, 19372}, {1709, 1935}, {1717, 10827}, {1721, 9579}, {1722, 9581}, {1724, 30223}, {1745, 12940}, {1763, 3556}, {1766, 20613}, {1852, 41869}, {1870, 6361}, {2331, 8804}, {2817, 36986}, {3208, 7105}, {3465, 17857}, {3554, 5301}, {3617, 9539}, {3679, 9576}, {3702, 27394}, {3868, 8271}, {4200, 45281}, {4296, 9778}, {4300, 45126}, {4313, 17016}, {4318, 20070}, {4329, 8900}, {4342, 30148}, {4347, 5493}, {4354, 10573}, {5179, 17905}, {5272, 50443}, {5657, 6198}, {5687, 51361}, {5690, 8144}, {5930, 30265}, {6001, 7078}, {6261, 22350}, {7191, 9785}, {7719, 25087}, {8256, 9639}, {9643, 11362}, {9906, 12910}, {9907, 12911}, {9911, 11398}, {10167, 34046}, {10703, 11682}, {11495, 15832}, {12527, 45275}, {12688, 34048}, {12699, 37697}, {13724, 15503}, {16870, 21075}, {17903, 21062}, {23528, 27378}, {24430, 41229}, {26446, 37696}, {49553, 52427}
X(54295) = reflection of X(1) in X(1062)
X(54295) = X(i)-Ceva conjugate of X(j) for these (i,j): {345, 9}, {4329, 1763}
X(54295) = X(i)-isoconjugate of X(j) for these (i,j): {7, 7169}, {28, 47344}, {56, 7219}, {57, 7097}, {77, 40169}, {604, 40015}
X(54295) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 7219}, {19, 278}, {3161, 40015}, {5452, 7097}, {40180, 7197}, {40591, 47344}
X(54295) = crossdifference of every pair of points on line {650, 51644}
X(54295) = barycentric product X(i)*X(j) for these {i,j}: {1, 27540}, {8, 1763}, {9, 4329}, {21, 21062}, {55, 20914}, {78, 17903}, {312, 3556}, {318, 22119}, {333, 52359}, {345, 36103}, {644, 21174}, {3718, 21148}
X(54295) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 40015}, {9, 7219}, {41, 7169}, {55, 7097}, {71, 47344}, {607, 40169}, {1763, 7}, {3556, 57}, {4329, 85}, {8900, 7365}, {17903, 273}, {20914, 6063}, {21062, 1441}, {21148, 34}, {21174, 24002}, {22119, 77}, {27540, 75}, {36103, 278}, {40183, 7197}, {52359, 226}
X(54295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40, 8270}, {1, 165, 1038}, {1, 30503, 37558}, {1103, 1490, 4551}, {1697, 33178, 1}, {1854, 7074, 72}, {3556, 52359, 1763}
X(54296) lies on these lines: {3, 74}, {6, 31}, {21, 48917}, {199, 1495}, {228, 52405}, {323, 4184}, {394, 19346}, {405, 12702}, {464, 39874}, {572, 44109}, {573, 34417}, {1985, 33108}, {2194, 17454}, {2249, 28841}, {3098, 16064}, {5235, 46521}, {5278, 49719}, {7430, 12112}, {13632, 14389}, {13738, 35239}, {15018, 37510}, {15032, 37120}, {15107, 20834}, {17524, 51340}, {19732, 32947}, {20835, 33878}, {30944, 37633}, {37499, 41424}
X(54296) = crossdifference of every pair of points on line {514, 1637}
X(54296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1495, 22080, 37508}, {1495, 37508, 199}, {2328, 22080, 199}, {2328, 37508, 1495}
X(54297) lies on these lines: {2, 34395}, {3, 6}, {5, 46054}, {13, 83}, {14, 14880}, {18, 98}, {76, 22689}, {202, 10799}, {298, 619}, {384, 22687}, {395, 47610}, {397, 47859}, {550, 22522}, {616, 12214}, {627, 7836}, {628, 7779}, {629, 22894}, {636, 6783}, {729, 39637}, {1506, 6771}, {2004, 10601}, {3170, 44109}, {3171, 15066}, {3181, 7793}, {3200, 3203}, {3406, 43539}, {3457, 15018}, {3458, 15080}, {3643, 10351}, {4027, 5980}, {5012, 34394}, {5182, 5463}, {5254, 46855}, {5321, 31703}, {5699, 32115}, {5868, 41041}, {5872, 10104}, {5978, 34508}, {6115, 6694}, {6151, 41472}, {6636, 21462}, {6774, 7749}, {6778, 37825}, {7006, 12835}, {7746, 46053}, {7748, 46854}, {7787, 10653}, {7808, 11306}, {7815, 43274}, {8150, 33482}, {10358, 42813}, {10359, 40693}, {10788, 42151}, {10796, 16965}, {11295, 41107}, {11307, 36766}, {12110, 42158}, {12150, 35931}, {12192, 36209}, {12203, 16964}, {12204, 36967}, {13084, 33274}, {13196, 52194}, {13881, 22891}, {17128, 42675}, {18501, 42155}, {18502, 36969}, {22846, 39565}, {22855, 44777}, {22862, 42099}, {23006, 42990}, {32134, 42148}, {32465, 32467}, {33388, 37334}, {34540, 42089}, {37340, 51159}, {37835, 48655}
X(54297) = midpoint of X(3364) and X(3365)
X(54297) = Brocard-circle-inverse of X(3104)
X(54297) = isogonal conjugate of the polar conjugate of X(16250)
X(54297) = barycentric product X(3)*X(16250)
X(54297) = barycentric quotient X(16250)/X(264)
X(54297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 3104}, {15, 62, 39}, {15, 1691, 36759}, {15, 10646, 36756}, {16, 61, 3105}, {62, 3398, 36759}, {182, 36760, 36759}, {371, 372, 3107}, {1342, 1343, 15}, {1506, 6771, 52642}, {1687, 1688, 62}, {3104, 3107, 32452}, {3107, 39750, 36759}, {3389, 3390, 3106}, {53430, 53464, 5}
X(54298) lies on these lines: {2, 34394}, {3, 6}, {5, 46053}, {13, 14880}, {14, 83}, {17, 98}, {76, 22687}, {203, 10799}, {299, 618}, {384, 22689}, {396, 47611}, {398, 47860}, {550, 22523}, {617, 12213}, {627, 7779}, {628, 7836}, {630, 22850}, {635, 6782}, {729, 39636}, {1506, 6774}, {2005, 10601}, {2981, 41473}, {3170, 15066}, {3171, 44109}, {3180, 7793}, {3201, 3203}, {3406, 43538}, {3457, 15080}, {3458, 15018}, {3642, 10351}, {4027, 5981}, {5012, 34395}, {5182, 5464}, {5254, 46854}, {5318, 31704}, {5700, 32115}, {5869, 41040}, {5873, 10104}, {5979, 34509}, {6114, 6695}, {6636, 21461}, {6771, 7749}, {6777, 37824}, {7005, 12835}, {7746, 46054}, {7748, 46855}, {7787, 10654}, {7808, 11305}, {7815, 43275}, {8150, 33483}, {10358, 42814}, {10359, 40694}, {10788, 42150}, {10796, 16964}, {11296, 41108}, {12110, 42157}, {12150, 35932}, {12192, 36208}, {12203, 16965}, {12205, 36968}, {13083, 33274}, {13196, 52193}, {13881, 22846}, {17128, 42674}, {18501, 42154}, {18502, 36970}, {22891, 39565}, {22901, 44776}, {22906, 42100}, {23013, 42991}, {32134, 42147}, {32466, 32467}, {33389, 37334}, {34541, 42092}, {36772, 42433}, {37341, 51160}, {37832, 48656}, {41018, 42238}
X(54298) = midpoint of X(3389) and X(3390)
X(54298) = Brocard-circle-inverse of X(3105)
X(54298) = isogonal conjugate of the polar conjugate of X(16249)
X(54298) = barycentric product X(3)*X(16249)
X(54298) = barycentric quotient X(16249)/X(264)
X(54298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 3105}, {15, 62, 3104}, {16, 61, 39}, {16, 1691, 36760}, {16, 10645, 36755}, {61, 3398, 36760}, {182, 36759, 36760}, {371, 372, 3106}, {1342, 1343, 16}, {1506, 6774, 52643}, {1687, 1688, 61}, {3105, 3106, 32452}, {3106, 39750, 36760}, {3364, 3365, 3107}, {53442, 53453, 5}
X(54299) lies on these lines: {2, 3}, {33, 72}, {55, 39585}, {92, 3295}, {281, 5687}, {318, 1260}, {954, 7952}, {1001, 1838}, {1096, 3931}, {1708, 1887}, {1712, 5728}, {1859, 12514}, {1871, 5250}, {1940, 37541}, {3075, 10396}, {3419, 46878}, {3697, 7079}, {3753, 11471}, {4254, 8748}, {5174, 9708}, {7008, 9844}, {7071, 41013}, {9709, 52412}, {10267, 39529}, {11500, 39574}, {12699, 30687}, {36744, 46835}
X(54299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 29, 37393}, {4, 25, 37377}, {4, 406, 442}, {4, 4183, 405}, {4, 4194, 37321}, {4, 7412, 7580}, {4, 16845, 4200}, {4, 30733, 4185}, {21, 7518, 7497}, {29, 1013, 3}, {4186, 11323, 4}, {4219, 7498, 474}, {17516, 37318, 4}, {28044, 37194, 406}
X(54300) lies on these lines: {1, 16287}, {2, 12}, {3, 6}, {8, 35999}, {36, 3216}, {42, 19339}, {55, 16452}, {73, 28274}, {78, 2352}, {238, 23383}, {241, 1410}, {283, 44085}, {333, 404}, {387, 3428}, {474, 5737}, {604, 46879}, {859, 1724}, {956, 5793}, {960, 1402}, {976, 16687}, {978, 20470}, {999, 16286}, {1001, 16289}, {1011, 19765}, {1043, 4203}, {1107, 37609}, {1125, 16288}, {1191, 23853}, {1193, 16678}, {1211, 37255}, {1376, 9534}, {1470, 16295}, {1737, 15232}, {1764, 18178}, {1834, 4192}, {3145, 5347}, {3149, 5786}, {3454, 19258}, {3868, 28936}, {3911, 34831}, {3913, 20018}, {3941, 37552}, {4184, 5331}, {4188, 37652}, {4225, 32911}, {4383, 13738}, {4417, 37030}, {4426, 36025}, {4641, 22345}, {4719, 37575}, {5143, 23844}, {5204, 16451}, {5248, 16300}, {5255, 15621}, {5292, 11249}, {5293, 20990}, {5313, 39578}, {5329, 23843}, {5438, 21384}, {5563, 16296}, {5687, 16400}, {5718, 37225}, {5747, 16848}, {5788, 6911}, {7373, 48855}, {7420, 37732}, {7428, 39748}, {8053, 37573}, {8583, 16878}, {8666, 50605}, {8715, 50588}, {9709, 48852}, {10449, 12513}, {11344, 37538}, {13731, 37662}, {15509, 37264}, {15622, 37570}, {15668, 19518}, {16294, 37579}, {16357, 25526}, {16374, 37522}, {16414, 17749}, {16454, 19769}, {16455, 22766}, {17277, 37442}, {18397, 20803}, {19247, 48867}, {19259, 43531}, {19283, 19701}, {19513, 37646}, {19841, 41258}, {20142, 27656}, {21935, 40109}, {22765, 45939}, {27622, 35466}, {27649, 37681}, {27659, 37694}, {28238, 37663}, {30362, 33096}, {34280, 40453}, {34281, 40153}, {35239, 48857}, {37195, 37537}, {37231, 40980}, {37539, 40956}, {47521, 49745}
X(54300) = Brocard-circle-inverse of X(4267)
X(54300) = crossdifference of every pair of points on line {523, 52326}
X(54300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 4267}, {3, 386, 5132}, {3, 19762, 3286}, {3, 37502, 19760}, {3, 37507, 4252}, {36, 3216, 16453}, {36, 5247, 23361}, {1220, 2975, 958}, {4255, 19759, 3}, {4256, 4278, 3}, {16452, 19767, 55}
X(54301) lies on these lines: {1, 6}, {3, 2003}, {34, 5903}, {35, 47}, {36, 54}, {43, 1771}, {46, 223}, {57, 3157}, {58, 1167}, {78, 1993}, {80, 40950}, {81, 13411}, {155, 5720}, {201, 8555}, {221, 2093}, {222, 15803}, {255, 386}, {394, 936}, {404, 22128}, {498, 5712}, {595, 40958}, {651, 4292}, {692, 42450}, {908, 3193}, {912, 33178}, {937, 42019}, {942, 23071}, {965, 51507}, {970, 3955}, {1046, 1735}, {1155, 8614}, {1181, 1490}, {1210, 3562}, {1399, 2077}, {1427, 3336}, {1451, 5563}, {1466, 23072}, {1498, 1750}, {1745, 1754}, {1772, 6126}, {1785, 3194}, {1870, 15556}, {1936, 37732}, {1994, 34772}, {2078, 5399}, {2183, 2360}, {2361, 2594}, {2964, 32760}, {3072, 4551}, {3075, 3216}, {3100, 41562}, {3145, 23202}, {3340, 44414}, {3601, 36742}, {3746, 14547}, {4303, 13329}, {4383, 41344}, {4641, 17102}, {5044, 22136}, {5219, 5707}, {5285, 5752}, {5312, 11507}, {5313, 8071}, {5396, 52408}, {5398, 37583}, {5537, 38857}, {5584, 38293}, {5703, 37685}, {5704, 14997}, {5706, 9612}, {5711, 31434}, {5713, 7951}, {5716, 12647}, {5717, 10039}, {6149, 52544}, {6282, 37498}, {7066, 11428}, {7193, 29958}, {7592, 18446}, {8726, 37514}, {8757, 9579}, {9370, 9613}, {10573, 34231}, {11010, 15852}, {11429, 40944}, {12161, 37700}, {14557, 40660}, {16577, 26878}, {16853, 22142}, {16948, 17010}, {18443, 36752}, {22072, 37469}, {22076, 26890}, {23070, 37582}, {23154, 26889}, {24929, 36750}, {30282, 36746}, {36747, 37531}, {36749, 37533}, {36753, 37615}, {37530, 37694}, {41227, 52413}
X(54301) = barycentric product X(63)*X(6197)
X(54301) = barycentric quotient X(6197)/X(92)
X(54301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1743, 1728}, {6, 7078, 1}, {73, 580, 36}, {212, 581, 35}, {222, 36745, 15803}, {223, 19349, 34043}, {942, 37509, 52423}, {1124, 1335, 2256}, {2361, 2594, 10902}, {3157, 36754, 57}, {3562, 32911, 1210}, {5706, 34048, 9612}, {23071, 37509, 942}
X(54302) lies on these lines: {1, 21}, {3, 2949}, {7, 11263}, {9, 6675}, {10, 15932}, {20, 1768}, {30, 84}, {35, 16465}, {40, 44238}, {46, 10042}, {56, 44782}, {57, 442}, {72, 37308}, {78, 27086}, {79, 5231}, {224, 7280}, {377, 3336}, {518, 10902}, {936, 1708}, {942, 15823}, {958, 8261}, {1004, 37524}, {1012, 37625}, {1071, 11012}, {1259, 5904}, {1445, 5785}, {1729, 21384}, {1761, 40979}, {1998, 35989}, {2323, 37565}, {2475, 3218}, {2771, 11249}, {3065, 43740}, {3219, 15674}, {3306, 31254}, {3333, 11281}, {3337, 5249}, {3338, 26725}, {3359, 11919}, {3648, 26015}, {3651, 5732}, {3870, 31660}, {3916, 10391}, {3929, 15670}, {4269, 18598}, {4304, 41575}, {5131, 35976}, {5252, 21677}, {5273, 10198}, {5428, 11523}, {5535, 33961}, {5536, 10916}, {5692, 37248}, {5693, 37302}, {5715, 6841}, {5735, 7701}, {5784, 37582}, {5902, 37228}, {6264, 12513}, {6597, 16159}, {6700, 37787}, {6762, 7966}, {6765, 10268}, {9965, 10527}, {10267, 22937}, {10399, 11344}, {10529, 31888}, {10680, 13465}, {12535, 13131}, {12540, 49193}, {12625, 37584}, {12649, 15680}, {12660, 33668}, {12671, 37623}, {12695, 13743}, {13243, 48713}, {15803, 31938}, {16113, 45632}, {16143, 30304}, {17637, 26357}, {18165, 45038}, {18219, 21669}, {18259, 24541}, {22836, 37106}, {24299, 28443}, {24477, 48482}, {25440, 41228}, {28610, 45700}, {31446, 37719}, {34744, 40256}, {37230, 37532}, {37579, 41542}, {37611, 54212}
X(54302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 63, 191}, {21, 39772, 1}, {7701, 12704, 49177}
X(54303) lies on these lines: {2, 6}, {8, 77}, {75, 279}, {269, 4847}, {271, 307}, {309, 321}, {314, 32830}, {326, 20007}, {346, 24635}, {1014, 6904}, {1444, 3522}, {2893, 37421}, {3086, 17272}, {3663, 34625}, {3664, 19843}, {3926, 34282}, {3964, 4189}, {4194, 32001}, {4200, 32000}, {4357, 14986}, {4416, 27508}, {7080, 32099}, {8232, 28797}, {9723, 17548}, {10432, 10446}, {10527, 21296}, {11679, 18623}, {14615, 34284}, {17360, 27525}, {18738, 44147}, {24471, 24477}, {31995, 36595}, {32834, 44139}, {45700, 53598}
X(54303) = isotomic conjugate of the isogonal conjugate of X(37501)
X(54303) = isotomic conjugate of the polar conjugate of X(37276)
X(54303) = barycentric product X(i)*X(j) for these {i,j}: {69, 37276}, {76, 37501}
X(54303) = barycentric quotient X(i)/X(j) for these {i,j}: {37276, 4}, {37501, 6}
X(54303) = {X(1270),X(1271)}-harmonic conjugate of X(5739)
X(54304) lies on these lines: {1, 37438}, {3, 1737}, {7, 8}, {10, 11509}, {30, 90}, {46, 355}, {56, 3419}, {57, 47033}, {72, 18961}, {80, 38761}, {200, 26482}, {224, 41552}, {442, 997}, {517, 10043}, {519, 41540}, {758, 7702}, {950, 52769}, {1155, 6934}, {1158, 37468}, {1210, 22768}, {1319, 10529}, {1454, 11112}, {1470, 6734}, {1478, 41538}, {1788, 4190}, {1836, 5887}, {1858, 6850}, {1898, 6925}, {2099, 12609}, {2245, 54008}, {2646, 3086}, {3358, 5691}, {3476, 5178}, {3486, 37112}, {3612, 5433}, {4863, 37738}, {4930, 17528}, {5260, 25005}, {5704, 37600}, {5787, 15326}, {6833, 17606}, {6897, 18391}, {6984, 17605}, {7098, 17579}, {9579, 41705}, {10044, 31794}, {10573, 34339}, {10826, 37356}, {12666, 41706}, {12701, 14110}, {13273, 18254}, {14988, 41688}, {17728, 22766}, {18838, 49168}, {18962, 41539}, {26475, 37611}, {31231, 37702}, {34447, 41506}, {37730, 44222}
X(54304) = {X(65),X(5794)}-harmonic conjugate of X(5252)
X(54305) lies on these lines: {1, 6}, {3, 1763}, {10, 34}, {20, 5813}, {28, 169}, {33, 12572}, {40, 1593}, {63, 580}, {73, 997}, {78, 581}, {200, 5814}, {212, 12514}, {223, 936}, {241, 16410}, {443, 948}, {474, 1427}, {612, 5717}, {908, 5713}, {910, 37408}, {964, 52345}, {975, 5712}, {976, 40958}, {1040, 31424}, {1060, 5044}, {1062, 31445}, {1260, 37528}, {1773, 5329}, {2000, 2478}, {2267, 18673}, {2551, 34231}, {3073, 42012}, {3198, 37062}, {3305, 52362}, {3421, 5716}, {3488, 15954}, {3682, 45126}, {3811, 14547}, {3920, 5815}, {3929, 33178}, {5130, 5587}, {5285, 7713}, {5687, 15852}, {5705, 19372}, {5720, 5810}, {5752, 37531}, {5783, 30456}, {5791, 37697}, {6282, 14557}, {6554, 7498}, {6986, 24635}, {11396, 26867}, {17441, 37246}, {18443, 47371}, {18607, 37282}, {19843, 34036}, {21060, 30142}, {21370, 37431}, {26893, 37569}
X(54305) = {X(1829),X(7085)}-harmonic conjugate of X(40)
X(54306) lies on these lines: {2, 3}, {13, 35712}, {53, 61}, {62, 6748}, {389, 5318}, {396, 52670}, {398, 37505}, {578, 5321}, {4994, 51268}, {5334, 11426}, {5335, 11432}, {6116, 42598}, {6117, 42163}, {9786, 42094}, {9833, 41038}, {10662, 36747}, {11425, 42093}, {11430, 42101}, {11438, 42102}, {14216, 41039}, {16001, 16625}, {16002, 35715}, {20415, 35714}, {20416, 31688}, {32002, 52194}
X(54306) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 473, 5}
X(54307) lies on these lines: {2, 3}, {14, 35713}, {53, 62}, {61, 6748}, {389, 5321}, {395, 52671}, {397, 37505}, {578, 5318}, {4994, 51275}, {5334, 11432}, {5335, 11426}, {6116, 42166}, {6117, 42599}, {9786, 42093}, {9833, 41039}, {10661, 36747}, {11425, 42094}, {11430, 42102}, {11438, 42101}, {14216, 41038}, {16001, 35714}, {16002, 16625}, {20415, 31687}, {20416, 35715}, {32002, 52193}
X(54307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 472, 5}
X(54308) lies on these lines: {1, 75}, {2, 5105}, {6, 980}, {7, 10571}, {9, 27644}, {21, 7290}, {37, 52897}, {42, 3879}, {43, 17270}, {57, 77}, {58, 988}, {69, 386}, {141, 5153}, {142, 16752}, {193, 4270}, {239, 16738}, {261, 1178}, {269, 1434}, {319, 3293}, {333, 2999}, {524, 4272}, {614, 10458}, {664, 31643}, {757, 763}, {940, 16700}, {969, 994}, {995, 17321}, {1019, 21143}, {1100, 16726}, {1193, 4357}, {1386, 3286}, {1429, 18724}, {1442, 17016}, {2092, 3882}, {2300, 3666}, {2663, 18787}, {3187, 27163}, {3216, 5224}, {3240, 32099}, {3305, 27643}, {3589, 5109}, {3629, 4285}, {3663, 17139}, {3664, 16714}, {3672, 17183}, {3677, 5208}, {3759, 29767}, {3786, 7174}, {3945, 6904}, {3946, 17197}, {4184, 16688}, {4264, 21511}, {4267, 4719}, {4281, 17206}, {4384, 27164}, {4393, 17178}, {4596, 4674}, {4967, 10459}, {5037, 37685}, {5110, 5337}, {5145, 18906}, {5222, 16713}, {5269, 13588}, {5283, 27623}, {5287, 5333}, {5313, 17272}, {7032, 17017}, {7146, 18177}, {8025, 17011}, {10461, 37592}, {10477, 50598}, {16589, 28252}, {16666, 18198}, {16667, 18186}, {16704, 17012}, {16710, 17379}, {16711, 50116}, {16712, 17274}, {16736, 37674}, {16742, 28358}, {16750, 40719}, {16753, 37633}, {16755, 21173}, {16831, 25508}, {17013, 26860}, {17014, 26818}, {17019, 31025}, {17022, 25507}, {17167, 19785}, {17173, 33150}, {17174, 33155}, {17179, 17378}, {17202, 17302}, {17212, 48281}, {17296, 30965}, {17322, 49997}, {17594, 38832}, {18171, 20963}, {18190, 18208}, {18204, 18207}, {19717, 39747}, {21796, 29429}, {24557, 25930}, {26042, 30114}, {26149, 26813}, {26819, 45222}, {26979, 29456}, {31855, 32025}, {33297, 50581}, {34020, 37678}, {50178, 53476}
X(54308) = isogonal conjugate of the isotomic conjugate of X(16739)
X(54308) = X(i)-Ceva conjugate of X(j) for these (i,j): {86, 4357}, {664, 7192}, {4610, 1019}, {7260, 18197}, {16705, 17185}, {37215, 52615}
X(54308) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14624}, {37, 2298}, {42, 1220}, {210, 961}, {213, 30710}, {512, 8707}, {523, 32736}, {594, 1169}, {661, 36147}, {756, 2363}, {1240, 1918}, {1500, 14534}, {1791, 1824}, {1798, 7140}, {1826, 2359}, {3700, 8687}, {3709, 6648}, {4041, 36098}, {4557, 4581}, {7109, 40827}, {14973, 40453}
X(54308) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 14624}, {960, 756}, {1193, 14973}, {1211, 10}, {2092, 2321}, {3125, 4024}, {3666, 1089}, {4357, 3963}, {6626, 30710}, {17197, 522}, {17419, 3700}, {34021, 1240}, {36830, 36147}, {38992, 4041}, {39015, 661}, {39054, 8707}, {40589, 2298}, {40592, 1220}, {52087, 37}
X(54308) = cevapoint of X(i) and X(j) for these (i,j): {1193, 3666}, {4267, 40153}
X(54308) = crossdifference of every pair of points on line {798, 4041}
X(54308) = barycentric product X(i)*X(j) for these {i,j}: {1, 16705}, {6, 16739}, {7, 17185}, {21, 3674}, {58, 20911}, {60, 45196}, {75, 40153}, {81, 4357}, {85, 4267}, {86, 3666}, {99, 48131}, {110, 4509}, {274, 1193}, {279, 46877}, {286, 22097}, {310, 2300}, {333, 24471}, {552, 21033}, {593, 18697}, {662, 3004}, {757, 1211}, {763, 20653}, {799, 6371}, {849, 1228}, {873, 2092}, {960, 1434}, {1014, 3687}, {1019, 53332}, {1088, 46889}, {1414, 3910}, {1444, 1848}, {1509, 2292}, {1829, 17206}, {2185, 41003}, {3882, 7192}, {4573, 17420}, {4610, 50330}, {4625, 52326}, {6628, 21810}, {7199, 53280}, {7303, 27697}, {7304, 45197}, {21124, 52935}, {22345, 44129}, {27455, 33296}, {28369, 32010}
X(54308) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14624}, {58, 2298}, {81, 1220}, {86, 30710}, {110, 36147}, {163, 32736}, {274, 1240}, {444, 1840}, {593, 2363}, {662, 8707}, {757, 14534}, {849, 1169}, {873, 40827}, {960, 2321}, {1019, 4581}, {1193, 37}, {1211, 1089}, {1412, 961}, {1414, 6648}, {1434, 31643}, {1437, 2359}, {1634, 35334}, {1682, 21033}, {1790, 1791}, {1829, 1826}, {1848, 41013}, {2092, 756}, {2269, 210}, {2292, 594}, {2300, 42}, {2354, 1824}, {3004, 1577}, {3666, 10}, {3674, 1441}, {3687, 3701}, {3725, 1500}, {3882, 3952}, {3910, 4086}, {3965, 4082}, {4267, 9}, {4357, 321}, {4509, 850}, {4565, 36098}, {4719, 5257}, {6371, 661}, {16705, 75}, {16739, 76}, {17185, 8}, {17420, 3700}, {18235, 4095}, {18697, 28654}, {20911, 313}, {20967, 1334}, {21033, 6057}, {21124, 4036}, {21810, 6535}, {22074, 2318}, {22076, 3949}, {22097, 72}, {22345, 71}, {24471, 226}, {27455, 42027}, {28369, 1215}, {40153, 1}, {41003, 6358}, {41581, 21073}, {41591, 21065}, {41600, 21074}, {45196, 34388}, {45218, 7148}, {46877, 346}, {46889, 200}, {48131, 523}, {50330, 4024}, {52087, 14973}, {52326, 4041}, {53280, 1018}, {53332, 4033}
X(54308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 980, 16574}, {6, 16696, 18206}, {75, 86, 10455}, {81, 25059, 18163}, {86, 274, 10436}, {86, 4360, 30939}, {86, 16709, 17175}, {86, 33296, 314}, {314, 33296, 3875}, {1100, 16726, 18166}, {1449, 18164, 81}, {2092, 28369, 3882}, {3666, 40153, 17185}, {16726, 18166, 17207}, {27644, 40773, 9}
X(54309) lies on these lines: {1, 2}, {44, 100}, {88, 518}, {89, 3751}, {238, 678}, {390, 52429}, {536, 4767}, {1155, 14513}, {1443, 4551}, {1757, 9324}, {2177, 35595}, {3100, 52371}, {3218, 21805}, {3219, 17601}, {3243, 39963}, {3246, 3689}, {3681, 17595}, {3699, 17160}, {3711, 4850}, {4152, 28503}, {4414, 51297}, {4702, 4954}, {4724, 6006}, {4849, 37520}, {4893, 48352}, {4956, 30566}, {9330, 16676}, {9350, 27003}, {14410, 48244}, {15569, 40434}, {16670, 17126}, {17067, 33148}, {21060, 33102}, {21870, 37633}, {24344, 50127}, {24594, 51055}, {28580, 30578}, {37138, 37222}, {52959, 52966}
X(54309) = crossdifference of every pair of points on line {649, 14421}
X(54309) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {899, 3935, 7292}, {899, 5524, 3935}, {5212, 49991, 32842}, {5529, 49984, 38460}
X(54310) lies on these lines: {1, 89}, {3, 2177}, {6, 41}, {8, 37608}, {21, 8296}, {31, 999}, {32, 17474}, {35, 16490}, {36, 42}, {57, 49487}, {58, 106}, {81, 37617}, {145, 37603}, {187, 16971}, {213, 8649}, {392, 896}, {404, 3214}, {519, 37639}, {529, 37634}, {551, 8025}, {595, 16489}, {601, 1480}, {602, 16203}, {603, 26437}, {672, 2242}, {750, 956}, {840, 2701}, {940, 11194}, {976, 16496}, {978, 14997}, {993, 3720}, {995, 2308}, {997, 32912}, {1015, 21764}, {1064, 22765}, {1125, 19740}, {1334, 33863}, {1376, 49984}, {1385, 2650}, {1478, 29662}, {1616, 41436}, {1724, 28352}, {2975, 37607}, {3073, 45977}, {3241, 3550}, {3304, 3915}, {3333, 16485}, {3336, 15955}, {3338, 3924}, {3600, 5230}, {3616, 6646}, {3679, 5372}, {3722, 37589}, {3750, 17549}, {3751, 35262}, {3877, 4650}, {3973, 8583}, {3976, 16498}, {4188, 50581}, {4234, 32943}, {4273, 22357}, {4293, 11269}, {4300, 11249}, {4315, 5773}, {4317, 5292}, {4322, 37583}, {4383, 40726}, {4424, 4973}, {4511, 32913}, {4642, 37582}, {4656, 34646}, {4694, 29818}, {5021, 9310}, {5030, 16785}, {5165, 22356}, {5247, 5253}, {5251, 30950}, {5270, 45939}, {5280, 23649}, {5298, 37662}, {5303, 37573}, {5429, 7191}, {5434, 37646}, {5886, 24725}, {6048, 17572}, {7267, 49481}, {8162, 21000}, {8616, 38314}, {8626, 20985}, {8666, 10459}, {9340, 51788}, {9350, 16417}, {9708, 17124}, {11112, 33136}, {11114, 24217}, {11115, 50608}, {12577, 28027}, {15492, 25917}, {15950, 17365}, {16393, 32941}, {16466, 23070}, {16487, 28011}, {16493, 17109}, {16797, 33844}, {17015, 17596}, {17056, 31157}, {17117, 27368}, {17178, 49482}, {17455, 28658}, {17579, 33141}, {18990, 21935}, {21242, 50171}, {22361, 34471}, {24165, 39766}, {24443, 32636}, {25524, 28257}, {29571, 31039}, {33104, 45700}, {33771, 41434}, {34605, 37716}, {37539, 49465}, {37599, 46904}, {37600, 49478}, {37602, 40091}, {37817, 51816}, {41011, 44675}
X(54310) = isogonal conjugate of the isotomic conjugate of X(50116)
X(54310) = crossdifference of every pair of points on line {522, 4120}
X(54310) = barycentric product X(i)*X(j) for these {i,j}: {1, 37520}, {6, 50116}, {101, 47891}, {2163, 27747}
X(54310) = barycentric quotient X(i)/X(j) for these {i,j}: {37520, 75}, {47891, 3261}, {50116, 76}
X(54310) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2163, 4257}, {1, 4257, 902}, {31, 999, 1149}, {36, 16474, 4256}, {56, 1468, 1193}, {58, 106, 5315}, {58, 5315, 21747}, {58, 5563, 1201}, {106, 5315, 1201}, {1201, 21747, 5315}, {2067, 6502, 1405}, {3304, 4252, 3915}, {4256, 16474, 42}, {4694, 49480, 29818}, {5247, 5253, 27627}, {5315, 5563, 106}, {7051, 19373, 1400}, {8666, 37522, 10459}
X(54311) lies on these lines: {1, 26034}, {2, 7}, {6, 4001}, {10, 38}, {21, 7293}, {31, 1125}, {42, 49511}, {69, 5256}, {75, 18739}, {81, 5299}, {88, 31247}, {141, 306}, {191, 19881}, {239, 37653}, {312, 4389}, {313, 18136}, {319, 50306}, {321, 3663}, {333, 16706}, {345, 3619}, {354, 4026}, {386, 4101}, {404, 5314}, {405, 1473}, {474, 7085}, {516, 24552}, {519, 33074}, {551, 17469}, {594, 42051}, {614, 50295}, {846, 29637}, {896, 19862}, {899, 4104}, {902, 29686}, {940, 2214}, {942, 13728}, {950, 17676}, {958, 25904}, {964, 4292}, {982, 24163}, {984, 33174}, {993, 19869}, {1009, 22060}, {1038, 1457}, {1086, 31993}, {1150, 32774}, {1210, 5051}, {1211, 3752}, {1266, 28605}, {1698, 33163}, {1707, 3624}, {1738, 31330}, {1764, 12610}, {1999, 17302}, {2239, 43223}, {2308, 29684}, {2321, 17147}, {2887, 6682}, {2895, 17012}, {2999, 5739}, {3008, 5278}, {3011, 26128}, {3120, 31241}, {3175, 17246}, {3187, 3946}, {3210, 3661}, {3220, 37325}, {3416, 17599}, {3419, 11359}, {3488, 51665}, {3586, 50055}, {3589, 4641}, {3616, 37554}, {3617, 41915}, {3634, 26061}, {3664, 19684}, {3672, 34255}, {3687, 4850}, {3703, 3844}, {3717, 7226}, {3720, 50290}, {3739, 40688}, {3741, 3821}, {3744, 44419}, {3755, 17135}, {3763, 3977}, {3772, 37660}, {3782, 4054}, {3840, 4425}, {3879, 17011}, {3883, 7191}, {3891, 4353}, {3912, 28606}, {3916, 17698}, {3920, 33086}, {3944, 29827}, {3966, 49987}, {3969, 29594}, {3989, 4078}, {3998, 37597}, {4000, 5271}, {4028, 33081}, {4030, 49465}, {4035, 31017}, {4138, 33105}, {4205, 5439}, {4358, 4656}, {4360, 50292}, {4364, 44307}, {4383, 4643}, {4384, 24790}, {4392, 29667}, {4398, 42029}, {4414, 24943}, {4415, 30818}, {4416, 32911}, {4429, 25006}, {4431, 50106}, {4438, 30768}, {4640, 35263}, {4650, 25539}, {4652, 37176}, {4655, 25496}, {4660, 29652}, {4667, 19717}, {4675, 19701}, {4683, 32944}, {4684, 17018}, {4712, 24988}, {4847, 4972}, {4851, 20182}, {4855, 37339}, {4863, 48829}, {4886, 17271}, {4966, 37593}, {4970, 49560}, {4980, 53594}, {5119, 48803}, {5121, 25960}, {5192, 12572}, {5222, 14552}, {5224, 19804}, {5235, 26724}, {5241, 16602}, {5252, 48801}, {5263, 33068}, {5283, 29988}, {5287, 17321}, {5302, 25992}, {5550, 36277}, {5722, 50056}, {5737, 17290}, {5743, 16610}, {5847, 17017}, {6057, 49523}, {6536, 30950}, {6685, 33064}, {6703, 37520}, {6734, 16062}, {7174, 10327}, {8025, 21764}, {8362, 25083}, {8616, 29660}, {10468, 11679}, {10479, 23537}, {10856, 37419}, {12436, 16454}, {12514, 19836}, {12609, 19863}, {13369, 50324}, {13405, 33122}, {14213, 26538}, {14829, 17305}, {15315, 50605}, {15523, 46901}, {16060, 20769}, {16349, 25500}, {16368, 18650}, {16570, 34595}, {16815, 26044}, {16818, 18206}, {17020, 37656}, {17045, 37595}, {17046, 26601}, {17056, 48632}, {17123, 24697}, {17126, 29648}, {17127, 29666}, {17165, 26251}, {17185, 17192}, {17197, 27163}, {17227, 18134}, {17238, 17490}, {17247, 41839}, {17249, 18743}, {17253, 37679}, {17273, 33066}, {17278, 19732}, {17284, 17776}, {17285, 42033}, {17288, 17778}, {17289, 32939}, {17293, 50048}, {17307, 19808}, {17308, 19822}, {17320, 34064}, {17323, 50068}, {17325, 37674}, {17348, 49724}, {17355, 32933}, {17367, 37652}, {17376, 37631}, {17383, 37683}, {17392, 37869}, {17449, 29685}, {17526, 31424}, {17591, 32778}, {17592, 33087}, {17593, 33160}, {17594, 33171}, {17596, 32783}, {17598, 33076}, {17600, 32846}, {17811, 26006}, {18044, 19807}, {18139, 21255}, {18229, 23681}, {19857, 52782}, {19864, 21616}, {20043, 32099}, {20106, 33113}, {20582, 50104}, {20879, 26665}, {21075, 26030}, {21529, 23089}, {21620, 26115}, {22031, 26844}, {22230, 23636}, {23790, 47763}, {24175, 24589}, {24178, 31339}, {24210, 30942}, {24231, 32771}, {24239, 25760}, {24470, 50318}, {24564, 31359}, {24598, 29991}, {24723, 32942}, {24987, 37591}, {25058, 30965}, {25065, 42700}, {25101, 33761}, {25354, 25501}, {25881, 25914}, {25896, 25918}, {25958, 29680}, {25959, 29664}, {25982, 26066}, {26015, 32773}, {26091, 41012}, {26098, 29826}, {26104, 37642}, {26563, 45196}, {27162, 28254}, {28516, 48644}, {29596, 33157}, {29633, 32913}, {29650, 32946}, {29663, 32912}, {29819, 49684}, {29821, 33082}, {29828, 33144}, {29833, 37639}, {29841, 37684}, {29960, 40773}, {31136, 50091}, {31237, 50752}, {31264, 32856}, {32772, 33067}, {32775, 32918}, {32859, 53598}, {32917, 33123}, {32920, 50285}, {33078, 49476}, {33089, 39597}, {33091, 49527}, {34573, 44416}, {41711, 47358}
X(54311) = midpoint of X(i) and X(j) for these {i,j}: {17017, 33080}, {24552, 32950}
X(54311) = complement of X(26223)
X(54311) = X(15315)-complementary conjugate of X(141)
X(54311) = X(37218)-Ceva conjugate of X(514)
X(54311) = X(37592)-Dao conjugate of X(2345)
X(54311) = crossdifference of every pair of points on line {663, 50496}
X(54311) = barycentric product X(75)*X(37592)
X(54311) = barycentric quotient X(37592)/X(1)
X(54311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 63, 5294}, {2, 3219, 17353}, {2, 3662, 5249}, {2, 6646, 27064}, {2, 9965, 5749}, {2, 17184, 226}, {2, 17236, 27184}, {2, 17257, 3305}, {2, 26132, 31266}, {2, 26580, 3452}, {2, 26840, 894}, {2, 27184, 908}, {10, 24177, 4359}, {38, 32781, 10}, {57, 17306, 2}, {141, 3666, 306}, {226, 50092, 17184}, {333, 16706, 26723}, {1150, 32774, 40940}, {2308, 29684, 38049}, {2887, 6682, 29639}, {2999, 17272, 5739}, {3741, 3821, 3914}, {3752, 17237, 1211}, {3782, 44417, 4054}, {3989, 29687, 4078}, {4655, 25496, 41011}, {4850, 32782, 3687}, {4972, 46909, 4847}, {5737, 17290, 24789}, {6646, 27064, 17781}, {7191, 33083, 3883}, {7226, 29679, 3717}, {11679, 17304, 19785}, {14829, 17305, 19786}, {17011, 32863, 3879}, {17165, 26251, 53663}, {17235, 44417, 3782}, {17291, 38000, 2}, {17321, 18141, 5287}, {25914, 25917, 25881}, {26128, 32916, 3011}, {28606, 33172, 3912}, {30942, 32776, 24210}, {31330, 33125, 1738}, {32772, 33067, 50307}, {33081, 46904, 4028}
X(54312) lies on these lines: {1, 25}, {3, 42}, {8, 37090}, {10, 16353}, {22, 17018}, {27, 388}, {31, 37492}, {41, 25941}, {43, 7484}, {55, 63}, {56, 4719}, {81, 1460}, {197, 940}, {284, 1037}, {306, 958}, {405, 33171}, {497, 14004}, {519, 16403}, {899, 16419}, {956, 33088}, {968, 24320}, {993, 4028}, {999, 17017}, {1013, 3486}, {1057, 3478}, {1072, 1860}, {1400, 1617}, {1473, 17594}, {1478, 1889}, {1621, 7083}, {1757, 26867}, {1995, 29814}, {2292, 3295}, {3220, 37553}, {3240, 7485}, {3436, 50400}, {3475, 41230}, {3556, 37548}, {3666, 22769}, {3720, 5020}, {3750, 7295}, {3751, 7085}, {4265, 37577}, {4267, 37579}, {4471, 18613}, {4649, 5329}, {5132, 37578}, {5247, 37246}, {6600, 36559}, {7373, 29819}, {7395, 37699}, {7742, 19763}, {8897, 19860}, {9708, 15523}, {10601, 23638}, {11108, 24943}, {11269, 19544}, {11284, 26102}, {11414, 37529}, {14547, 16541}, {16352, 43223}, {16408, 29663}, {16678, 36744}, {17596, 26866}, {19313, 26037}, {19714, 37079}, {19765, 22654}, {20973, 37503}, {21620, 37396}, {21746, 33586}, {25494, 29839}, {29642, 50715}, {37257, 37607}, {37576, 42042}
X(54312) = crossdifference of every pair of points on line {2522, 29142}
X(54312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22, 17018, 37580}, {3295, 42461, 2292}, {4649, 5329, 44094}
X(54313) lies on these lines: {1, 60}, {3, 24883}, {8, 21}, {11, 13746}, {28, 1068}, {36, 37405}, {56, 1325}, {58, 5903}, {81, 37227}, {229, 999}, {270, 14015}, {284, 40968}, {355, 24624}, {409, 3616}, {496, 3109}, {499, 37158}, {501, 21842}, {643, 3885}, {976, 4653}, {993, 27368}, {1010, 33108}, {1098, 3877}, {1175, 37533}, {1385, 40214}, {1478, 37369}, {1479, 7424}, {1793, 5727}, {1834, 37311}, {1837, 6740}, {2082, 5546}, {2099, 46441}, {2185, 3897}, {2217, 2363}, {2218, 40430}, {2646, 35195}, {2975, 17512}, {3057, 35193}, {3615, 11376}, {4184, 33137}, {4188, 25459}, {4221, 35239}, {4225, 5230}, {4234, 49719}, {4299, 5196}, {4311, 18653}, {5006, 53165}, {5127, 5697}, {5204, 37294}, {5251, 20653}, {5253, 11116}, {5267, 50755}, {5358, 7419}, {5730, 37783}, {5754, 32911}, {7478, 10072}, {11010, 52680}, {11115, 33110}, {12030, 47274}, {12053, 51382}, {12702, 15952}, {13589, 38511}, {13733, 19767}, {13739, 41227}, {14127, 38497}, {15792, 37525}, {17539, 20095}, {21004, 23903}, {24928, 51420}, {26363, 37152}, {29658, 33325}, {33139, 34868}, {36927, 37740}, {37587, 52375}
X(54313) = crossdifference of every pair of points on line {2610, 7180}
X(54313) = barycentric product X(21)*X(33133)
X(54313) = barycentric quotient X(33133)/X(1441)
X(54313) = {X(1),X(759)}-harmonic conjugate of X(11101)
X(54314) lies on these lines: {2, 92}, {4, 75}, {7, 8048}, {19, 4384}, {25, 26234}, {27, 4359}, {28, 242}, {29, 5262}, {33, 3875}, {34, 10436}, {85, 1119}, {86, 1870}, {239, 1172}, {264, 1969}, {297, 26538}, {313, 1235}, {318, 20895}, {321, 469}, {322, 32000}, {350, 4213}, {406, 17321}, {427, 3263}, {429, 1228}, {451, 17322}, {458, 26665}, {515, 17859}, {857, 26165}, {946, 17858}, {1269, 44146}, {1699, 18691}, {1826, 20236}, {1829, 20911}, {1838, 18698}, {1841, 3739}, {1848, 3687}, {1861, 4967}, {1921, 44129}, {2969, 34336}, {3264, 44142}, {3672, 4194}, {3766, 44428}, {4198, 5342}, {4207, 4441}, {4357, 45196}, {4360, 6198}, {4858, 39039}, {5279, 30807}, {7019, 40717}, {7140, 52787}, {7282, 52442}, {7378, 31130}, {7490, 19804}, {7713, 33945}, {7718, 39731}, {8822, 45797}, {8889, 30758}, {11109, 24993}, {11337, 17134}, {12047, 18692}, {16732, 40941}, {17442, 29960}, {17555, 24547}, {17861, 39585}, {18147, 20926}, {18483, 18699}, {18650, 18690}, {20891, 31909}, {20905, 37448}, {20906, 44426}, {20907, 54239}, {21579, 42714}, {23661, 52364}, {25001, 26003}, {26042, 37337}, {28653, 52252}, {30044, 31916}, {34231, 44735}, {41005, 41007}
X(54314) = isotomic conjugate of X(1791)
X(54314) = polar conjugate of X(2298)
X(54314) = isotomic conjugate of the isogonal conjugate of X(1829)
X(54314) = polar conjugate of the isotomic conjugate of X(20911)
X(54314) = polar conjugate of the isogonal conjugate of X(3666)
X(54314) = X(6331)-Ceva conjugate of X(17924)
X(54314) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2359}, {31, 1791}, {42, 1798}, {48, 2298}, {71, 1169}, {184, 1220}, {212, 961}, {228, 2363}, {652, 8687}, {1240, 14575}, {1459, 32736}, {1946, 36098}, {2200, 14534}, {4581, 32656}, {9247, 30710}, {15420, 32739}, {22383, 36147}
X(54314) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 1791}, {9, 2359}, {429, 197}, {960, 228}, {1211, 3}, {1249, 2298}, {2092, 219}, {3125, 647}, {3666, 72}, {17197, 23189}, {17419, 652}, {38992, 1946}, {39015, 22383}, {39053, 36098}, {39060, 6648}, {40592, 1798}, {40619, 15420}, {40837, 961}, {46878, 5285}, {52087, 48}
X(54314) = cevapoint of X(i) and X(j) for these (i,j): {1829, 3666}, {1848, 46878}
X(54314) = barycentric product X(i)*X(j) for these {i,j}: {4, 20911}, {27, 18697}, {28, 1228}, {29, 45196}, {75, 1848}, {76, 1829}, {85, 46878}, {92, 4357}, {264, 3666}, {273, 3687}, {274, 429}, {286, 1211}, {318, 3674}, {331, 960}, {444, 44187}, {561, 2354}, {811, 21124}, {1193, 1969}, {1826, 16739}, {1897, 4509}, {2292, 44129}, {2300, 18022}, {3004, 6335}, {3882, 46107}, {3910, 18026}, {4267, 52575}, {6331, 50330}, {6385, 44092}, {7017, 24471}, {16705, 41013}, {16747, 27067}, {17420, 46404}, {17924, 53332}, {18027, 22345}, {20567, 40976}, {31623, 41003}
X(54314) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2359}, {2, 1791}, {4, 2298}, {27, 2363}, {28, 1169}, {81, 1798}, {92, 1220}, {108, 8687}, {264, 30710}, {278, 961}, {286, 14534}, {331, 31643}, {429, 37}, {444, 172}, {653, 36098}, {693, 15420}, {960, 219}, {1193, 48}, {1211, 72}, {1228, 20336}, {1682, 22074}, {1783, 32736}, {1829, 6}, {1848, 1}, {1897, 36147}, {1969, 1240}, {2092, 228}, {2269, 212}, {2292, 71}, {2300, 184}, {2354, 31}, {3004, 905}, {3666, 3}, {3674, 77}, {3687, 78}, {3704, 3694}, {3725, 2200}, {3882, 1331}, {3910, 521}, {3965, 1260}, {4267, 2193}, {4357, 63}, {4509, 4025}, {6335, 8707}, {6371, 22383}, {16705, 1444}, {16739, 17206}, {17185, 283}, {17420, 652}, {17924, 4581}, {17981, 53689}, {18026, 6648}, {18697, 306}, {20653, 3949}, {20911, 69}, {20967, 52425}, {21033, 2318}, {21124, 656}, {21810, 3690}, {22074, 6056}, {22076, 3990}, {22097, 255}, {22345, 577}, {24471, 222}, {27455, 23086}, {28369, 3955}, {32714, 52928}, {40153, 1437}, {40966, 52370}, {40976, 41}, {41003, 1214}, {41013, 14624}, {41581, 22131}, {41591, 22122}, {41600, 22132}, {41609, 2911}, {41611, 218}, {44092, 213}, {45196, 307}, {45218, 22381}, {46877, 2327}, {46878, 9}, {48131, 1459}, {50330, 647}, {51407, 51379}, {51414, 46974}, {52326, 1946}, {52567, 2197}, {53280, 906}, {53332, 1332}
X(54314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1826, 20883, 46108}, {1841, 3739, 15149}
X(54315) lies on these lines: {1, 88}, {4, 7986}, {8, 141}, {10, 32775}, {21, 986}, {30, 33102}, {36, 49682}, {43, 49454}, {55, 4218}, {65, 82}, {81, 1325}, {222, 18419}, {354, 17015}, {377, 7613}, {386, 34195}, {392, 7292}, {484, 49480}, {495, 33148}, {517, 7191}, {519, 24169}, {614, 3877}, {644, 9620}, {758, 32911}, {846, 16858}, {942, 17016}, {956, 4392}, {964, 7155}, {976, 24440}, {982, 49487}, {988, 3897}, {1086, 5724}, {1159, 17025}, {1201, 5330}, {1203, 4084}, {1403, 4216}, {1478, 33146}, {1482, 19514}, {1621, 4424}, {1722, 3876}, {1724, 11684}, {1737, 33133}, {1739, 30115}, {1963, 35991}, {2292, 5047}, {2722, 53926}, {2975, 3670}, {3120, 17577}, {3125, 5276}, {3210, 49492}, {3241, 17597}, {3419, 33131}, {3496, 39251}, {3616, 17054}, {3677, 3872}, {3735, 33854}, {3751, 3868}, {3752, 4511}, {3753, 3920}, {3782, 5080}, {3944, 37375}, {3953, 15955}, {3961, 4695}, {3980, 51669}, {4217, 24280}, {4393, 24610}, {4427, 13735}, {4720, 32860}, {4906, 5919}, {4968, 26538}, {5082, 36579}, {5086, 23537}, {5256, 11529}, {5300, 50582}, {5563, 24167}, {5657, 26228}, {5687, 36565}, {5692, 37680}, {5697, 30148}, {5721, 9803}, {5722, 33134}, {5725, 31019}, {6175, 17889}, {7226, 9708}, {9593, 25082}, {9791, 14020}, {10176, 37687}, {11043, 28238}, {11113, 33100}, {11114, 24248}, {11533, 17534}, {13407, 26729}, {13605, 36250}, {13740, 17164}, {13741, 25253}, {14829, 39766}, {15934, 16056}, {16485, 35258}, {16519, 21951}, {16821, 46909}, {17061, 40663}, {17074, 18838}, {17126, 36279}, {17531, 24174}, {17537, 44006}, {17549, 17596}, {17679, 50591}, {17757, 33153}, {18343, 36154}, {18391, 19785}, {19860, 26635}, {19869, 32779}, {24982, 34937}, {25248, 33821}, {25270, 33817}, {26446, 29665}, {28082, 37598}, {33067, 38456}, {33107, 39542}, {33143, 37716}, {33155, 37715}, {33815, 37559}, {48696, 49686}
X(54315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4642, 3871}, {1, 5883, 37633}, {1, 24046, 5253}, {1, 24443, 404}, {986, 3924, 21}, {3120, 37717, 17577}, {4424, 30117, 1621}, {9620, 26242, 644}, {17054, 37614, 3616}, {17757, 39544, 33153}
X(54316) lies on these lines: {1, 19285}, {6, 43}, {8, 48}, {9, 35}, {10, 284}, {19, 78}, {37, 1247}, {41, 2345}, {42, 2303}, {55, 965}, {69, 1958}, {71, 100}, {72, 1761}, {75, 18162}, {101, 2321}, {159, 197}, {198, 3713}, {219, 3362}, {220, 7038}, {238, 5301}, {281, 2289}, {306, 1474}, {312, 2201}, {319, 662}, {326, 18161}, {380, 936}, {391, 2267}, {404, 2260}, {480, 5781}, {524, 7175}, {572, 3686}, {573, 6796}, {579, 25440}, {584, 17303}, {594, 2174}, {604, 1788}, {608, 37694}, {908, 1839}, {958, 37504}, {966, 2268}, {992, 1914}, {1018, 52405}, {1100, 3812}, {1107, 5110}, {1172, 3682}, {1213, 6690}, {1248, 3990}, {1259, 15656}, {1333, 5247}, {1429, 4361}, {1441, 24435}, {1449, 37559}, {1582, 3783}, {1630, 6737}, {1731, 25078}, {1762, 3998}, {1765, 2077}, {1781, 22021}, {1802, 27382}, {1826, 2327}, {1935, 1950}, {1940, 7120}, {1943, 6359}, {1953, 4511}, {2173, 3949}, {2182, 3965}, {2256, 3913}, {2257, 5438}, {2271, 34261}, {2278, 17275}, {2280, 26040}, {2294, 34772}, {2302, 6734}, {2304, 9534}, {2326, 52412}, {2330, 15984}, {2893, 20305}, {2911, 3501}, {2975, 22054}, {3033, 11574}, {3204, 17281}, {3216, 16470}, {3434, 27395}, {3579, 4047}, {3694, 38903}, {3826, 16503}, {3841, 24937}, {3912, 40530}, {4000, 25940}, {4053, 5341}, {4251, 5750}, {4254, 5783}, {4861, 17438}, {5086, 21011}, {5432, 5742}, {5440, 40937}, {5552, 26063}, {5564, 18042}, {5776, 10310}, {5778, 11248}, {6700, 40963}, {7113, 17362}, {7119, 7270}, {7145, 8681}, {9310, 17314}, {12513, 37519}, {14543, 45744}, {16488, 49997}, {16548, 21078}, {16685, 37588}, {17117, 27950}, {21061, 35342}, {21384, 36743}, {21388, 48391}, {21933, 44669}, {25993, 26006}, {28604, 40744}, {42696, 52134}
X(54316) = isotomic conjugate of the polar conjugate of X(7076)
X(54316) = X(i)-Ceva conjugate of X(j) for these (i,j): {1943, 1935}, {40406, 1}
X(54316) = X(i)-isoconjugate of X(j) for these (i,j): {7, 7106}, {56, 7108}, {57, 7105}, {273, 7107}, {278, 7016}
X(54316) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 7108}, {5452, 7105}, {8062, 4466}, {16573, 693}
X(54316) = cevapoint of X(43) and X(2939)
X(54316) = trilinear pole of line {21761, 21831}
X(54316) = crossdifference of every pair of points on line {4083, 51648}
X(54316) = barycentric product X(i)*X(j) for these {i,j}: {1, 7283}, {8, 1935}, {9, 1943}, {69, 7076}, {75, 26885}, {78, 1940}, {99, 21831}, {100, 8062}, {101, 17899}, {200, 6359}, {219, 1947}, {281, 7364}, {312, 1950}, {345, 7120}, {668, 21761}, {6335, 22382}
X(54316) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 7108}, {41, 7106}, {55, 7105}, {212, 7016}, {1935, 7}, {1940, 273}, {1943, 85}, {1947, 331}, {1950, 57}, {6359, 1088}, {7076, 4}, {7120, 278}, {7283, 75}, {7364, 348}, {8062, 693}, {16573, 4466}, {17899, 3261}, {21761, 513}, {21831, 523}, {22382, 905}, {26885, 1}, {44096, 1430}, {52425, 7107}
X(54316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 20769, 18162}, {100, 2287, 71}, {200, 610, 5227}, {584, 17303, 41239}, {594, 2174, 2329}, {2173, 3949, 5279}, {4420, 5279, 3949}
X(54317) lies on these lines: {1, 39}, {2, 16968}, {6, 78}, {9, 172}, {31, 39244}, {37, 56}, {40, 3727}, {41, 36404}, {46, 3735}, {55, 39255}, {57, 3721}, {63, 33863}, {72, 5021}, {77, 28391}, {86, 25918}, {169, 5277}, {171, 3061}, {200, 3780}, {213, 997}, {241, 37674}, {304, 16061}, {348, 4648}, {392, 14974}, {474, 16583}, {583, 2215}, {604, 22061}, {612, 1107}, {614, 16604}, {750, 17451}, {936, 2238}, {968, 17798}, {975, 5283}, {976, 1475}, {988, 41269}, {1038, 18591}, {1193, 16972}, {1212, 5275}, {1376, 41015}, {1468, 33299}, {1571, 4424}, {1572, 5264}, {1743, 7296}, {1914, 37552}, {2082, 4386}, {2176, 19861}, {2177, 39247}, {2242, 17742}, {2250, 40401}, {2271, 5440}, {3290, 25524}, {3306, 20271}, {3333, 3726}, {3496, 37603}, {3509, 37608}, {3665, 4675}, {3666, 5013}, {3744, 16781}, {3811, 20963}, {3905, 24631}, {3931, 31448}, {3938, 17474}, {3997, 30144}, {4253, 30115}, {4372, 4384}, {4413, 16605}, {4447, 5268}, {4855, 18755}, {5089, 22479}, {5250, 17735}, {5253, 26242}, {5254, 17720}, {5266, 16502}, {5269, 9575}, {5276, 26690}, {5287, 19715}, {5293, 21384}, {5308, 17081}, {5336, 5750}, {5364, 22065}, {5530, 31497}, {5716, 7736}, {5725, 31460}, {7198, 17276}, {7293, 21771}, {8583, 16970}, {8666, 28594}, {9300, 50070}, {9597, 13161}, {9598, 24210}, {10436, 16720}, {17016, 17756}, {17103, 18055}, {17124, 21921}, {17368, 27954}, {21008, 35262}, {21029, 29662}, {21965, 24914}, {28043, 40133}, {31477, 37548}, {34261, 40937}, {37589, 39254}, {37634, 40997}
X(54317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16549, 9620}, {31, 39244, 39248}, {976, 1475, 16973}, {16604, 16974, 614}
X(54318) lies on these lines: {1, 2}, {3, 3812}, {4, 12520}, {5, 6261}, {9, 758}, {21, 46}, {30, 5880}, {33, 860}, {34, 5136}, {35, 37300}, {36, 3306}, {37, 9620}, {40, 1006}, {41, 21921}, {55, 3753}, {56, 5439}, {57, 993}, {63, 4880}, {65, 405}, {72, 3715}, {86, 998}, {142, 515}, {158, 11109}, {165, 37106}, {169, 41239}, {171, 37817}, {210, 44840}, {214, 13384}, {224, 4197}, {236, 18456}, {281, 1870}, {354, 956}, {355, 6881}, {377, 10572}, {381, 3838}, {388, 34489}, {392, 2099}, {404, 3612}, {442, 1837}, {443, 3486}, {452, 4295}, {474, 2646}, {484, 35258}, {516, 6987}, {517, 1001}, {518, 9708}, {529, 25557}, {535, 6173}, {756, 49454}, {940, 16344}, {942, 958}, {944, 6854}, {946, 6827}, {960, 11108}, {962, 6992}, {968, 4424}, {988, 24046}, {990, 3821}, {996, 2191}, {999, 3742}, {1056, 38053}, {1058, 49600}, {1060, 6703}, {1104, 5711}, {1155, 16370}, {1158, 3560}, {1159, 15254}, {1214, 19727}, {1329, 11281}, {1376, 24929}, {1385, 6911}, {1420, 51111}, {1448, 2647}, {1467, 4298}, {1478, 5249}, {1490, 6843}, {1573, 16973}, {1621, 5119}, {1656, 45770}, {1699, 6840}, {1706, 3918}, {1709, 6912}, {1738, 48837}, {1743, 53114}, {1770, 6872}, {1788, 6857}, {1812, 4658}, {1836, 11113}, {2082, 16783}, {2093, 3919}, {2177, 4695}, {2185, 11116}, {2263, 48866}, {2271, 16605}, {2320, 4881}, {2324, 3986}, {2476, 10826}, {2478, 12047}, {2550, 3488}, {2551, 3487}, {2802, 31393}, {2886, 5722}, {2951, 28158}, {2975, 3338}, {3090, 21740}, {3158, 3968}, {3185, 4245}, {3295, 5836}, {3303, 10914}, {3305, 5425}, {3333, 8666}, {3336, 4652}, {3339, 31424}, {3340, 3878}, {3419, 3925}, {3421, 3475}, {3436, 13407}, {3474, 11111}, {3485, 5084}, {3543, 41860}, {3553, 5257}, {3576, 3833}, {3577, 52769}, {3579, 28466}, {3601, 25440}, {3646, 15829}, {3671, 12572}, {3678, 11523}, {3689, 4731}, {3694, 16777}, {3698, 5687}, {3711, 3921}, {3740, 3940}, {3772, 37715}, {3814, 5219}, {3816, 5886}, {3817, 6844}, {3820, 5719}, {3822, 5587}, {3824, 18480}, {3825, 6830}, {3826, 44669}, {3848, 10246}, {3868, 5260}, {3869, 5047}, {3874, 11518}, {3876, 34195}, {3877, 5284}, {3880, 6600}, {3881, 6762}, {3884, 7982}, {3890, 30323}, {3892, 44841}, {3897, 5253}, {3898, 7962}, {3901, 3951}, {3916, 5221}, {3922, 37568}, {3927, 5302}, {3984, 41696}, {3997, 16970}, {4004, 37567}, {4038, 28920}, {4084, 12526}, {4187, 11375}, {4193, 37692}, {4293, 9776}, {4297, 8726}, {4305, 6904}, {4313, 11024}, {4321, 30275}, {4333, 15680}, {4359, 49492}, {4413, 5440}, {4640, 16418}, {4653, 17594}, {4657, 16608}, {4670, 44664}, {4676, 33309}, {4679, 51409}, {4694, 16499}, {4855, 37571}, {4868, 37553}, {5010, 5426}, {5044, 12635}, {5045, 12513}, {5054, 35459}, {5080, 31019}, {5123, 31479}, {5126, 40726}, {5178, 41709}, {5250, 5259}, {5252, 50208}, {5258, 18398}, {5267, 15803}, {5269, 16485}, {5288, 50190}, {5289, 8167}, {5333, 6505}, {5429, 37604}, {5450, 37534}, {5493, 12651}, {5535, 21165}, {5542, 52457}, {5603, 6947}, {5657, 6878}, {5691, 6839}, {5709, 31870}, {5720, 6858}, {5725, 17056}, {5727, 41867}, {5728, 42014}, {5730, 16842}, {5732, 28164}, {5794, 8728}, {5795, 21620}, {5805, 33558}, {5818, 6877}, {5884, 7330}, {5885, 24467}, {5904, 11520}, {5905, 11551}, {6001, 6913}, {6051, 37614}, {6265, 6667}, {6282, 10164}, {6326, 6702}, {6666, 14563}, {6668, 37733}, {6675, 26066}, {6681, 31190}, {6684, 37531}, {6690, 26446}, {6692, 6954}, {6701, 16132}, {6708, 37697}, {6769, 43174}, {6824, 12616}, {6846, 12617}, {6856, 45230}, {6859, 40257}, {6893, 12608}, {6918, 37837}, {6963, 9624}, {6993, 18444}, {7028, 18454}, {7073, 52388}, {7308, 10176}, {7373, 11260}, {7483, 24914}, {7675, 38052}, {7719, 17442}, {7951, 26725}, {7993, 33812}, {8000, 12756}, {8953, 30557}, {9352, 17549}, {9581, 25639}, {9593, 25092}, {9612, 11263}, {9619, 16604}, {9817, 45272}, {9940, 12114}, {9956, 37700}, {10051, 51432}, {10107, 12702}, {10129, 37375}, {10202, 22758}, {10389, 25439}, {10436, 17861}, {10448, 24443}, {10571, 19372}, {10912, 12260}, {11103, 25526}, {11114, 20292}, {11235, 18527}, {11373, 15842}, {11496, 31788}, {11499, 24299}, {11507, 37248}, {11682, 25542}, {12081, 53034}, {12433, 31419}, {12560, 12848}, {12563, 18250}, {12565, 51118}, {12575, 51724}, {12699, 28459}, {12736, 51506}, {12739, 34122}, {13161, 24159}, {13369, 18761}, {13374, 22770}, {13750, 37228}, {14988, 15297}, {15079, 31262}, {15668, 50317}, {15863, 37736}, {16371, 37600}, {16417, 37606}, {16616, 37411}, {16788, 40131}, {16968, 17750}, {17054, 37592}, {17063, 37617}, {17398, 21933}, {17527, 25681}, {17529, 37724}, {17542, 31165}, {17556, 17605}, {17575, 24954}, {17614, 34471}, {17706, 24391}, {17718, 17757}, {17742, 21808}, {18165, 19259}, {18421, 37787}, {18465, 25507}, {18481, 28452}, {18528, 50796}, {19701, 45126}, {21147, 37523}, {21161, 35242}, {21627, 40270}, {21888, 31433}, {23518, 25017}, {24440, 37573}, {24703, 39542}, {24723, 48814}, {24806, 25496}, {26728, 33144}, {28228, 43166}, {28849, 50290}, {28850, 50302}, {30852, 37701}, {31156, 44447}, {31359, 37035}, {31445, 31794}, {31673, 41854}, {32784, 37796}, {32950, 49735}, {33068, 37038}, {33111, 37717}, {33130, 37716}, {33145, 50066}, {35262, 37525}, {36027, 48900}, {36404, 49758}, {36819, 40437}, {37224, 44547}, {37695, 51421}, {40249, 49170}, {40659, 42871}, {41340, 44545}, {41859, 47033}, {42064, 50441}, {44734, 46883}, {48833, 50116}, {48841, 50080}, {48863, 50314}
X(54318) = midpoint of X(i) and X(j) for these {i,j}: {1, 9623}, {9, 11529}, {2550, 3488}, {6767, 40587}, {9708, 15934}
X(54318) = reflection of X(6767) in X(42819)
X(54318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 997}, {1, 10, 3811}, {1, 936, 22836}, {1, 1698, 78}, {1, 1722, 386}, {1, 3624, 19861}, {1, 3679, 3870}, {1, 4853, 3244}, {1, 5268, 30115}, {1, 5272, 995}, {1, 8583, 30144}, {1, 10582, 551}, {1, 12629, 3635}, {2, 18391, 10}, {4, 28629, 12609}, {8, 3616, 10587}, {8, 19855, 10}, {10, 551, 13405}, {10, 1125, 10198}, {10, 3244, 6743}, {10, 6738, 49168}, {10, 10197, 31434}, {10, 13405, 45701}, {10, 30143, 1}, {40, 5436, 5248}, {65, 405, 12514}, {443, 3486, 17647}, {938, 19843, 10916}, {993, 5883, 57}, {1125, 9843, 10200}, {1125, 30147, 1}, {1329, 11281, 11374}, {2099, 4423, 392}, {2551, 3487, 21077}, {3241, 29817, 1}, {3340, 31435, 3878}, {3485, 5084, 21616}, {3560, 34339, 1158}, {3622, 4861, 1}, {3634, 22836, 936}, {3636, 22837, 1}, {3698, 37080, 5687}, {3720, 49487, 1}, {3754, 5248, 40}, {3868, 5260, 41229}, {3872, 4666, 1}, {3897, 5253, 37618}, {3918, 8715, 1706}, {4666, 19860, 3872}, {5136, 40149, 39585}, {5251, 5902, 63}, {5259, 5903, 5250}, {5269, 16485, 49480}, {5587, 25525, 3822}, {5730, 16842, 25917}, {5836, 51715, 3295}, {7951, 26725, 31266}, {8582, 13411, 26364}, {8728, 37730, 5794}, {10459, 28082, 1}, {16418, 36279, 4640}, {17015, 29814, 1}, {17527, 37737, 25681}, {19862, 30144, 8583}, {25440, 35016, 3601}, {30116, 30117, 1}, {38314, 38460, 1}
X(54319) lies on these lines: {1, 2}, {3, 15663}, {40, 106}, {244, 30323}, {517, 3445}, {988, 3898}, {999, 45219}, {1191, 51788}, {1279, 36280}, {1319, 1406}, {1385, 1480}, {1420, 40091}, {1616, 24928}, {2802, 11512}, {3680, 10700}, {4256, 37556}, {4694, 11682}, {5119, 32577}, {7962, 24046}, {8666, 11717}, {9327, 9575}, {10595, 26728}, {12843, 37611}, {15839, 31393}, {16483, 20323}, {37552, 51714}
X(54319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5272, 22837}, {1, 8583, 50637}, {1, 46943, 12629}, {1, 47623, 3811}, {1, 49997, 36846}, {1616, 24928, 37817}, {12629, 46943, 17749}
X(54320) lies on these lines: {1, 3}, {2, 225}, {9, 37694}, {19, 27621}, {20, 40950}, {21, 34}, {33, 411}, {58, 45126}, {63, 73}, {77, 283}, {78, 201}, {212, 3561}, {216, 2277}, {221, 4640}, {222, 3916}, {223, 1935}, {227, 958}, {255, 21165}, {278, 6857}, {348, 6337}, {386, 1708}, {405, 1465}, {631, 1068}, {859, 7713}, {968, 3485}, {970, 19366}, {975, 16577}, {978, 40679}, {993, 21147}, {1042, 4414}, {1072, 7400}, {1074, 6889}, {1076, 6833}, {1254, 10448}, {1368, 26481}, {1410, 22060}, {1441, 16342}, {1448, 18593}, {1449, 2193}, {1451, 5256}, {1452, 4225}, {1455, 15832}, {1457, 5250}, {1490, 24430}, {1728, 37732}, {1745, 7330}, {1785, 6825}, {1825, 20243}, {1829, 52271}, {1838, 6824}, {1870, 6875}, {1877, 6872}, {2006, 7561}, {2067, 19216}, {2197, 5227}, {2594, 3751}, {3011, 7494}, {3149, 9817}, {3193, 17074}, {3523, 23710}, {3524, 38295}, {3911, 5292}, {4000, 7288}, {4189, 4296}, {4267, 18603}, {4292, 5713}, {4331, 18589}, {4551, 41229}, {5159, 47271}, {5248, 34036}, {5253, 26635}, {5433, 11512}, {5705, 18641}, {5745, 5930}, {5752, 20122}, {6198, 6876}, {6349, 24541}, {6350, 24987}, {6502, 19215}, {6509, 30674}, {6675, 37695}, {6734, 34822}, {6988, 7952}, {7004, 10884}, {7289, 18606}, {7386, 29639}, {7508, 32047}, {7741, 37361}, {8609, 36751}, {9816, 28258}, {9843, 43068}, {10257, 11809}, {10527, 17077}, {10538, 26027}, {10571, 12514}, {13323, 19365}, {15829, 34588}, {16272, 16976}, {17321, 22464}, {18446, 44706}, {20277, 22361}, {25490, 39585}, {26066, 51421}, {26377, 37257}, {28034, 54234}, {31445, 34048}, {34033, 51576}, {34977, 51236}, {39751, 44906}
X(54320) = X(11110)-Ceva conjugate of X(3485)
X(54320) = X(i)-isoconjugate of X(j) for these (i,j): {33, 969}, {281, 967}
X(54320) = X(38960)-Dao conjugate of X(44426)
X(54320) = barycentric product X(i)*X(j) for these {i,j}: {63, 3485}, {77, 966}, {348, 968}, {1214, 11110}, {1441, 4288}, {1813, 7650}, {2271, 7182}, {4207, 7183}, {6516, 45745}
X(54320) = barycentric quotient X(i)/X(j) for these {i,j}: {222, 969}, {603, 967}, {966, 318}, {968, 281}, {2271, 33}, {3485, 92}, {4288, 21}, {7650, 46110}, {11110, 31623}, {45745, 44426}, {48099, 3064}
X(54320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1758, 37550}, {1, 15803, 37530}, {3, 1214, 1038}, {3, 17102, 1040}, {3, 37565, 1}, {21, 17080, 34}, {77, 4652, 603}, {223, 31424, 1935}, {405, 1465, 19372}, {6350, 25876, 34823}, {8758, 26357, 1}
X(54321) lies on these lines: {6, 31}, {25, 2260}, {28, 34}, {33, 2257}, {41, 2352}, {48, 5320}, {56, 44098}, {65, 40970}, {73, 1617}, {165, 580}, {171, 26040}, {218, 2318}, {223, 16469}, {238, 5712}, {354, 1104}, {581, 602}, {595, 10389}, {604, 2194}, {609, 38849}, {748, 17056}, {910, 4275}, {1193, 37578}, {1212, 3745}, {1427, 1471}, {1449, 2328}, {1472, 37575}, {1475, 37538}, {1497, 7078}, {1723, 40967}, {1724, 5717}, {1936, 37666}, {2212, 16470}, {2221, 3423}, {3215, 37541}, {3748, 3915}, {4253, 5285}, {5247, 5716}, {5269, 16572}, {7069, 8557}, {7964, 15852}, {10857, 37469}, {16485, 44841}, {16968, 20985}, {22097, 37492}, {28272, 34281}, {28274, 36740}, {34879, 52544}, {41858, 45924}
X(54321) = X(i)-isoconjugate of X(j) for these (i,j): {8, 8814}, {281, 8813}
X(54321) = crossdifference of every pair of points on line {514, 8611}
X(54321) = barycentric product X(57)*X(13615)
X(54321) = barycentric quotient X(i)/X(j) for these {i,j}: {603, 8813}, {604, 8814}, {13615, 312}
X(54321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 31, 212}, {31, 42, 21059}, {58, 1453, 1451}, {2308, 40958, 6}, {5320, 40956, 48}
X(54322) lies on these lines: {1, 5120}, {3, 9}, {6, 31}, {10, 37062}, {19, 1212}, {21, 5749}, {35, 1743}, {36, 3731}, {37, 56}, {40, 2262}, {41, 37504}, {44, 5217}, {45, 1696}, {48, 220}, {100, 391}, {101, 28193}, {144, 24328}, {165, 374}, {197, 44798}, {218, 284}, {219, 572}, {226, 21483}, {228, 26867}, {281, 37305}, {344, 1444}, {346, 2975}, {380, 16572}, {404, 5296}, {405, 5750}, {474, 5257}, {478, 1035}, {480, 15624}, {573, 10310}, {574, 21796}, {579, 16287}, {604, 1334}, {851, 1213}, {859, 4877}, {894, 16367}, {956, 2321}, {958, 2345}, {966, 1376}, {993, 17355}, {999, 3247}, {1001, 41325}, {1012, 10445}, {1014, 5308}, {1030, 16885}, {1100, 3303}, {1125, 21068}, {1214, 6611}, {1259, 16452}, {1400, 1466}, {1449, 3295}, {1473, 5282}, {1474, 37908}, {1500, 5042}, {1723, 40292}, {1766, 3428}, {1778, 4267}, {1826, 4185}, {1901, 37225}, {1953, 34522}, {2092, 31448}, {2099, 21853}, {2183, 15592}, {2223, 16517}, {2245, 11509}, {2250, 34278}, {2260, 5022}, {2264, 37601}, {2277, 5013}, {2278, 2911}, {2287, 4184}, {2297, 4512}, {2300, 14974}, {2303, 3286}, {2323, 10267}, {2324, 3576}, {2646, 3553}, {3057, 3554}, {3207, 22054}, {3304, 16777}, {3305, 11350}, {3361, 47299}, {3523, 27508}, {3587, 23840}, {3683, 20991}, {3686, 5687}, {3693, 5227}, {3746, 16667}, {3781, 37474}, {3913, 5839}, {3925, 4196}, {3950, 8666}, {3973, 5010}, {4130, 23224}, {4192, 5742}, {4263, 31451}, {4268, 11510}, {4287, 17796}, {4357, 21477}, {4421, 37654}, {4423, 17398}, {4856, 25439}, {5105, 16466}, {5242, 21481}, {5243, 21480}, {5249, 16439}, {5273, 15509}, {5279, 25082}, {5283, 34261}, {5285, 13615}, {5294, 16368}, {5303, 38869}, {5314, 20835}, {5563, 16673}, {5657, 53994}, {5710, 20719}, {5745, 16435}, {5746, 13726}, {5747, 16455}, {5817, 36012}, {5819, 11495}, {5830, 49128}, {5838, 7676}, {6666, 37272}, {6684, 20262}, {6971, 15833}, {6986, 27382}, {7071, 22079}, {7083, 37586}, {7114, 41087}, {7129, 40971}, {7308, 37269}, {7484, 22060}, {7573, 27287}, {7738, 28265}, {8557, 26357}, {8609, 10966}, {9310, 37519}, {9605, 16470}, {10434, 15479}, {10979, 23980}, {11329, 17260}, {11340, 27065}, {11343, 17353}, {11349, 18230}, {11517, 37057}, {12513, 17314}, {12572, 37320}, {13006, 36055}, {13733, 17369}, {14021, 28739}, {14379, 30457}, {14439, 20999}, {16058, 17754}, {16370, 50115}, {16431, 50093}, {16440, 30413}, {16441, 30412}, {16518, 23393}, {16548, 35239}, {16669, 37503}, {16675, 21773}, {16970, 37575}, {17134, 25001}, {17257, 21495}, {17306, 21526}, {19762, 25092}, {20471, 38871}, {20780, 53094}, {20818, 52405}, {21233, 24266}, {21488, 26580}, {21511, 26685}, {21811, 52273}, {22769, 50995}, {23397, 23853}, {24005, 24914}, {24612, 27514}, {25068, 37034}, {26036, 37425}, {26059, 37416}, {26063, 37409}, {28627, 37323}, {34820, 51773}
X(54322) = isogonal conjugate of the isotomic conjugate of X(34255)
X(54322) = X(2297)-Ceva conjugate of X(6)
X(54322) = X(25430)-isoconjugate of X(34244)
X(54322) = crossdifference of every pair of points on line {514, 6129}
X(54322) = barycentric product X(i)*X(j) for these {i,j}: {6, 34255}, {8, 34046}, {936, 14551}, {7050, 28616}
X(54322) = barycentric quotient X(i)/X(j) for these {i,j}: {34046, 7}, {34255, 76}
X(54322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9, 198}, {6, 42316, 71}, {35, 1743, 4254}, {37, 36743, 56}, {45, 2178, 1696}, {45, 5124, 2178}, {55, 20992, 21002}, {71, 2267, 6}, {572, 3730, 219}, {604, 1334, 2256}, {672, 2268, 6}, {1011, 7085, 55}, {1696, 5204, 2178}, {2066, 5414, 7074}, {2178, 5124, 5204}, {8053, 12329, 55}
X(54323) lies on these lines: {1, 1719}, {3, 6}, {10, 37232}, {21, 90}, {35, 283}, {46, 81}, {55, 1437}, {60, 1780}, {65, 1412}, {86, 12609}, {377, 25526}, {501, 2360}, {662, 11110}, {849, 44119}, {859, 22768}, {940, 37063}, {975, 2268}, {993, 6514}, {1010, 2185}, {1098, 37296}, {1408, 11509}, {1812, 12514}, {1819, 30282}, {2174, 31445}, {2194, 17524}, {2327, 31424}, {2328, 17104}, {3193, 5119}, {3746, 23059}, {4190, 19766}, {4300, 44709}, {5358, 17194}, {7414, 48897}, {10458, 37231}, {10572, 11103}, {18165, 52012}, {18178, 34339}, {21616, 31631}, {28251, 37225}, {28620, 28628}
X(54323) = barycentric product X(81)*X(41229)
X(54323) = barycentric quotient X(41229)/X(321)
X(54323) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 14868, 997}, {58, 15792, 284}, {60, 4184, 1780}, {501, 4653, 2360}, {2193, 36746, 58}, {2646, 37227, 4653}, {4278, 9275, 58}
X(54324) lies on these lines: {1, 1731}, {2, 1762}, {3, 2173}, {4, 9}, {5, 7359}, {6, 2294}, {25, 40967}, {31, 43214}, {37, 41}, {44, 65}, {45, 55}, {48, 1385}, {57, 1732}, {63, 9816}, {101, 2302}, {142, 16551}, {198, 23843}, {209, 375}, {212, 1859}, {219, 1482}, {220, 21801}, {284, 37571}, {307, 40530}, {379, 8680}, {380, 3731}, {405, 18673}, {579, 1781}, {610, 7987}, {692, 28125}, {748, 40959}, {857, 24682}, {910, 32578}, {984, 41230}, {1108, 20323}, {1212, 2182}, {1213, 27687}, {1253, 21867}, {1633, 24341}, {1698, 1782}, {1723, 2260}, {1760, 28287}, {2171, 2911}, {2175, 21804}, {2225, 5282}, {2265, 19350}, {2266, 2348}, {2277, 28246}, {2289, 33596}, {2315, 3652}, {2332, 25087}, {2886, 24329}, {2939, 13726}, {3011, 7735}, {3101, 27065}, {3198, 3683}, {3219, 24310}, {3305, 10319}, {3306, 31232}, {3576, 22357}, {3707, 21373}, {3925, 17369}, {4209, 27472}, {4266, 5540}, {4370, 34612}, {4470, 36483}, {5279, 24349}, {5325, 21375}, {5506, 18598}, {5750, 19846}, {7522, 53036}, {8558, 24411}, {8609, 9310}, {9028, 25935}, {10246, 23073}, {10536, 26890}, {10914, 52978}, {11428, 26885}, {11529, 16670}, {11683, 17277}, {12329, 21039}, {14021, 24683}, {15492, 21866}, {15656, 45255}, {16192, 18594}, {16305, 33329}, {16561, 17784}, {16666, 44840}, {17330, 21677}, {17438, 20818}, {18161, 37659}, {18162, 24554}, {20785, 24409}, {21811, 36744}, {24435, 25252}, {24591, 37788}, {25885, 41581}, {25917, 52092}, {31261, 41010}, {34048, 37755}
X(54324) = X(2)-isoconjugate of X(3418)
X(54324) = X(32664)-Dao conjugate of X(3418)
X(54324) = crossdifference of every pair of points on line {1459, 3960}
X(54324) = barycentric product X(i)*X(j) for these {i,j}: {1, 3419}, {9, 37695}, {10, 36011}
X(54324) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3418}, {3419, 75}, {36011, 86}, {37695, 85}
X(54324) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1762, 26934}, {2, 14543, 24315}, {2, 24316, 4466}, {9, 19, 71}, {9, 169, 2183}, {9, 16547, 573}, {9, 16548, 3730}, {281, 26063, 21011}, {1212, 2182, 2267}, {6191, 6192, 4}
X(54325) lies on these lines: {6, 31}, {100, 109}, {101, 8693}, {595, 16479}, {663, 2427}, {692, 2874}, {750, 4675}, {765, 3570}, {813, 919}, {1110, 1983}, {1362, 20749}, {1414, 51563}, {2283, 53555}, {4557, 35326}, {4559, 46177}, {4712, 20778}, {6016, 26716}, {17943, 23997}, {20752, 23612}, {28899, 43077}, {51329, 53552}
X(54325) = isogonal conjugate of the isotomic conjugate of X(1026)
X(54325) = X(i)-Ceva conjugate of X(j) for these (i,j): {1110, 42079}, {7012, 9502}, {36086, 101}, {39293, 9310}
X(54325) = X(i)-isoconjugate of X(j) for these (i,j): {7, 885}, {8, 43930}, {11, 927}, {75, 1027}, {76, 43929}, {85, 1024}, {105, 693}, {244, 51560}, {273, 23696}, {277, 2402}, {279, 28132}, {286, 10099}, {294, 24002}, {513, 2481}, {514, 673}, {649, 18031}, {650, 34018}, {666, 1086}, {668, 43921}, {812, 52209}, {884, 6063}, {905, 54235}, {918, 6185}, {919, 23989}, {1015, 36803}, {1111, 36086}, {1358, 36802}, {1416, 35519}, {1438, 3261}, {1462, 4391}, {1814, 17924}, {2170, 34085}, {2195, 52621}, {3271, 46135}, {3669, 36796}, {3676, 14942}, {3766, 52030}, {4014, 14727}, {4025, 36124}, {4444, 6654}, {4858, 36146}, {7192, 13576}, {7199, 18785}, {7649, 31637}, {8751, 15413}, {20907, 51845}, {21132, 39293}, {32735, 34387}, {33676, 43041}, {36057, 46107}
X(54325) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 1027}, {5375, 18031}, {6184, 3261}, {17755, 40495}, {20621, 46107}, {38980, 23989}, {38989, 1111}, {39014, 4858}, {39026, 2481}, {39046, 693}, {39063, 52621}, {40609, 35519}
X(54325) = cevapoint of X(926) and X(20683)
X(54325) = trilinear pole of line {2223, 9454}
X(54325) = crossdifference of every pair of points on line {514, 1111}
X(54325) = barycentric product X(i)*X(j) for these {i,j}: {1, 2284}, {6, 1026}, {9, 2283}, {31, 42720}, {41, 883}, {55, 1025}, {71, 4238}, {99, 39258}, {100, 672}, {101, 518}, {109, 3693}, {110, 3930}, {163, 3932}, {190, 2223}, {220, 41353}, {241, 3939}, {644, 1458}, {651, 2340}, {662, 20683}, {665, 765}, {666, 42079}, {668, 9454}, {677, 9502}, {692, 3912}, {813, 8299}, {901, 14439}, {906, 1861}, {918, 1110}, {919, 4712}, {926, 4564}, {1018, 3286}, {1023, 34230}, {1252, 2254}, {1331, 5089}, {1332, 2356}, {1415, 3717}, {1783, 1818}, {1876, 4587}, {1897, 20752}, {1978, 9455}, {2149, 50333}, {2414, 21059}, {2427, 36819}, {2428, 3870}, {3252, 3573}, {3263, 32739}, {3570, 40730}, {3699, 52635}, {4437, 32666}, {4557, 18206}, {4570, 24290}, {4684, 34074}, {4899, 34080}, {4998, 46388}, {5548, 53531}, {6065, 53544}, {6078, 53552}, {6184, 36086}, {7045, 52614}, {8750, 25083}, {17755, 34067}, {32656, 46108}, {36039, 50441}, {39686, 51560}
X(54325) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1027}, {41, 885}, {59, 34085}, {100, 18031}, {101, 2481}, {109, 34018}, {241, 52621}, {518, 3261}, {560, 43929}, {604, 43930}, {665, 1111}, {672, 693}, {692, 673}, {765, 36803}, {883, 20567}, {906, 31637}, {926, 4858}, {1025, 6063}, {1026, 76}, {1110, 666}, {1252, 51560}, {1253, 28132}, {1458, 24002}, {1818, 15413}, {1919, 43921}, {2149, 927}, {2175, 1024}, {2200, 10099}, {2223, 514}, {2254, 23989}, {2283, 85}, {2284, 75}, {2340, 4391}, {2356, 17924}, {3286, 7199}, {3675, 23100}, {3693, 35519}, {3912, 40495}, {3930, 850}, {3932, 20948}, {3939, 36796}, {4238, 44129}, {4564, 46135}, {5089, 46107}, {8638, 2170}, {8750, 54235}, {9447, 884}, {9454, 513}, {9455, 649}, {18206, 52619}, {18900, 29956}, {20683, 1577}, {20752, 4025}, {21059, 2402}, {23225, 3942}, {23612, 53583}, {23990, 36086}, {24290, 21207}, {32642, 9503}, {32656, 1814}, {32666, 6185}, {32739, 105}, {34067, 52209}, {39258, 523}, {39686, 2254}, {40730, 4444}, {42079, 918}, {42720, 561}, {46388, 11}, {52425, 23696}, {52614, 24026}, {52635, 3676}
X(54326) lies on these lines: {1, 3}, {22, 4392}, {25, 38}, {33, 12721}, {63, 7083}, {105, 5273}, {197, 3242}, {221, 50621}, {222, 3056}, {244, 7484}, {291, 16058}, {613, 3955}, {614, 7085}, {748, 26867}, {756, 11284}, {954, 21321}, {976, 37257}, {984, 5020}, {1036, 3868}, {1037, 17080}, {1350, 1401}, {1395, 1496}, {1407, 10387}, {1473, 5310}, {1621, 35261}, {1995, 7226}, {2330, 52424}, {3509, 4254}, {3688, 17811}, {3752, 12329}, {4220, 4310}, {4294, 26929}, {5324, 11102}, {7337, 23052}, {7580, 36509}, {8543, 44843}, {9335, 40916}, {9708, 33169}, {9709, 33174}, {9812, 44842}, {10544, 34046}, {11108, 32780}, {12589, 26942}, {12595, 20986}, {16049, 36579}, {16419, 17063}, {16556, 19588}, {17017, 44094}, {18183, 37485}, {19544, 33144}, {21342, 22769}, {24477, 41230}, {26040, 33833}, {26241, 38000}, {28082, 37246}, {32913, 37492}, {33115, 50715}, {34247, 37269}, {36559, 37309}, {36574, 37415}, {37499, 41264}
X(54326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37581, 1460}, {3677, 5285, 56}, {5329, 17598, 999}, {5597, 5598, 37539}
X(54327) lies on these lines: {1, 4191}, {3, 3555}, {10, 37319}, {19, 25}, {31, 16946}, {35, 3961}, {36, 3979}, {39, 42}, {51, 2293}, {100, 3757}, {184, 1253}, {199, 40910}, {200, 1011}, {210, 8053}, {480, 26867}, {516, 21319}, {518, 22060}, {692, 23201}, {851, 13405}, {902, 20967}, {1402, 2177}, {1622, 12333}, {1961, 3746}, {1999, 3871}, {2000, 10267}, {2194, 19624}, {2304, 52370}, {2340, 3690}, {3085, 4196}, {3295, 5287}, {3683, 4557}, {3689, 52139}, {3744, 5132}, {3748, 20470}, {3913, 17156}, {3935, 4184}, {3938, 37575}, {3939, 26890}, {3957, 4210}, {4105, 22388}, {4219, 11491}, {4314, 13724}, {4362, 8715}, {4421, 42051}, {4666, 16059}, {4847, 30944}, {5010, 23205}, {5217, 22344}, {5256, 37590}, {5271, 5687}, {5311, 40638}, {5320, 21059}, {6194, 17147}, {6600, 7085}, {7074, 22079}, {8580, 16373}, {8731, 25006}, {10578, 37262}, {14547, 51377}, {17018, 37609}, {17524, 34790}, {20075, 31394}, {20243, 31395}, {20760, 35258}, {20986, 23202}, {20990, 37593}, {22369, 40952}, {23207, 32078}, {23853, 35289}, {25440, 29651}
X(54327) = isogonal conjugate of the isotomic conjugate of X(34790)
X(54327) = X(46660)-Dao conjugate of X(693)
X(54327) = crossdifference of every pair of points on line {905, 4801}
X(54327) = barycentric product X(i)*X(j) for these {i,j}: {6, 34790}, {37, 17524}, {101, 50338}, {219, 1887}
X(54327) = barycentric quotient X(i)/X(j) for these {i,j}: {1887, 331}, {17524, 274}, {34790, 76}, {50338, 3261}
X(54327) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 2223, 40956}, {55, 15624, 228}, {55, 34247, 968}
X(54328) lies on these lines: {21, 37}, {41, 49447}, {56, 24486}, {99, 101}, {163, 4628}, {643, 46148}, {644, 1633}, {660, 2284}, {813, 36081}, {883, 36146}, {1438, 24841}, {2178, 16447}, {2329, 24723}, {2345, 16376}, {2975, 5701}, {4389, 16788}, {4676, 9310}, {5291, 39786}, {13589, 42723}, {16706, 17681}, {23344, 23830}, {51568, 53337}
X(54328) = X(i)-isoconjugate of X(j) for these (i,j): {513, 39979}, {649, 39714}
X(54328) = X(i)-Dao conjugate of X(j) for these (i,j): {5375, 39714}, {39026, 39979}
X(54328) = crossdifference of every pair of points on line {3122, 38363}
X(54328) = barycentric product X(i)*X(j) for these {i,j}: {100, 32922}, {190, 33854}, {765, 46403}, {1252, 20950}, {7035, 21003}
X(54328) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 39714}, {101, 39979}, {20950, 23989}, {21003, 244}, {22155, 3942}, {32922, 693}, {33854, 514}, {46403, 1111}
X(54329) lies on these lines: {1, 6}, {32, 2319}, {36, 20471}, {41, 43}, {101, 978}, {172, 17754}, {190, 3905}, {384, 3729}, {385, 17743}, {609, 16549}, {644, 3915}, {672, 20460}, {728, 3749}, {894, 16822}, {910, 24440}, {966, 19879}, {1018, 7031}, {1334, 8616}, {1423, 7132}, {1429, 4383}, {1438, 39969}, {1698, 26244}, {1707, 18788}, {1740, 9454}, {1783, 1973}, {1914, 3208}, {2053, 18758}, {2108, 39651}, {2271, 42043}, {2276, 37574}, {2295, 7296}, {2321, 5037}, {3052, 19589}, {3169, 16946}, {3496, 9620}, {3502, 3551}, {3663, 17691}, {3912, 37683}, {3923, 49545}, {4195, 17355}, {4251, 7220}, {4513, 37588}, {4641, 7146}, {4859, 17682}, {5039, 50635}, {5255, 30435}, {5305, 37716}, {6210, 12197}, {7766, 17752}, {8056, 37272}, {9310, 21214}, {9593, 17596}, {9605, 37617}, {11321, 25590}, {14829, 17284}, {16913, 17116}, {16914, 17261}, {17286, 33954}, {17304, 33827}, {17349, 30038}, {17350, 17760}, {17367, 49612}, {17750, 37604}, {19812, 29598}, {20970, 52651}, {23681, 50200}, {24982, 40128}, {26036, 33138}, {29573, 41629}, {32911, 52134}, {33950, 49487}
X(54329) = X(i)-Ceva conjugate of X(j) for these (i,j): {1423, 3550}, {7132, 1}
X(54329) = X(514)-isoconjugate of X(28469)
X(54329) = barycentric product X(i)*X(j) for these {i,j}: {100, 28470}, {1255, 41656}, {18098, 41657}
X(54329) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 28469}, {28470, 693}, {41656, 4359}, {41657, 16703}
X(54329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2329, 1}, {32, 3501, 3550}, {172, 17754, 37608}, {218, 5247, 1743}, {609, 16549, 37603}, {2319, 51319, 3550}, {3507, 51291, 3550}, {5280, 16788, 1}, {9310, 33854, 21214}, {16783, 16785, 1}
X(54330) lies on these lines: {1, 6}, {8, 5179}, {41, 12514}, {63, 101}, {78, 3730}, {144, 5088}, {165, 35342}, {169, 3869}, {198, 4047}, {200, 1018}, {239, 31018}, {391, 16821}, {517, 37658}, {609, 1707}, {612, 3997}, {644, 3681}, {672, 997}, {728, 4006}, {758, 40131}, {908, 4384}, {936, 16549}, {1334, 3811}, {1482, 4875}, {1759, 12526}, {1766, 2287}, {2082, 3878}, {2238, 9620}, {2348, 31165}, {3207, 3916}, {3216, 9593}, {3295, 4520}, {3419, 17747}, {3501, 50361}, {3684, 5119}, {3686, 21068}, {3693, 3940}, {3729, 27492}, {3899, 5540}, {3958, 42669}, {4051, 30323}, {4251, 5250}, {4253, 19861}, {4262, 35258}, {4512, 5320}, {4513, 34790}, {4559, 8270}, {4855, 24047}, {5022, 17614}, {5030, 35262}, {5219, 5241}, {5271, 22000}, {5440, 42316}, {5687, 21872}, {5739, 21062}, {7176, 41563}, {7719, 41609}, {10436, 46899}, {12047, 26036}, {12559, 21808}, {14829, 30728}, {16819, 27254}, {16833, 31142}, {17143, 20927}, {18206, 26637}, {20236, 32104}, {24578, 52050}, {26074, 27131}
X(54330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {72, 220, 17742}, {72, 41391, 50995}, {220, 50995, 41391}, {3230, 16973, 1}, {5526, 5692, 9}, {41391, 50995, 17742}
X(54331) lies on these lines: {1, 321}, {2, 10448}, {3, 32918}, {4, 25760}, {8, 31}, {9, 10570}, {10, 21}, {12, 29846}, {20, 26034}, {36, 35999}, {42, 1043}, {51, 9565}, {55, 5793}, {56, 16405}, {65, 4418}, {72, 32938}, {75, 3924}, {78, 32931}, {141, 7354}, {145, 4527}, {171, 10457}, {172, 21024}, {213, 24275}, {238, 11319}, {355, 49128}, {377, 25957}, {388, 33171}, {404, 3831}, {405, 31339}, {443, 25961}, {515, 37399}, {740, 17016}, {748, 17697}, {894, 2650}, {936, 27378}, {950, 47511}, {958, 1011}, {960, 32930}, {976, 4385}, {978, 5192}, {986, 32845}, {993, 10479}, {996, 3632}, {997, 25591}, {1010, 10458}, {1089, 30115}, {1104, 32914}, {1125, 33133}, {1193, 13740}, {1201, 32942}, {1203, 48866}, {1215, 34772}, {1222, 37129}, {1329, 37354}, {1376, 28348}, {1428, 50609}, {1441, 2647}, {1468, 10449}, {1698, 16342}, {1738, 25904}, {1834, 29631}, {1891, 4206}, {1909, 33954}, {2049, 19757}, {2268, 2345}, {2292, 7283}, {2298, 2321}, {2309, 5263}, {2475, 2887}, {2478, 25960}, {2551, 30943}, {2646, 44417}, {2975, 3741}, {3057, 43135}, {3419, 36568}, {3454, 3585}, {3601, 29828}, {3616, 37759}, {3701, 5293}, {3704, 5724}, {3714, 17763}, {3822, 25645}, {3840, 5253}, {3846, 5046}, {3868, 32940}, {3869, 3923}, {3925, 49734}, {3961, 4696}, {3962, 17351}, {4189, 32916}, {4201, 32781}, {4216, 25440}, {4292, 33067}, {4642, 32932}, {4712, 9369}, {4972, 19879}, {5016, 32778}, {5174, 14006}, {5178, 29673}, {5230, 37176}, {5262, 32924}, {5271, 50412}, {5285, 40455}, {5295, 27368}, {5434, 48859}, {5691, 19645}, {5695, 37614}, {5711, 16394}, {5716, 33088}, {5772, 12536}, {5794, 13733}, {5835, 10950}, {6284, 32947}, {6327, 50322}, {6645, 31027}, {6734, 33119}, {6737, 17355}, {6872, 50295}, {7270, 14012}, {9350, 26029}, {10404, 33069}, {10483, 48835}, {11321, 29966}, {11354, 16466}, {12437, 53663}, {12514, 21368}, {13161, 32775}, {13741, 27627}, {15338, 44419}, {15680, 33083}, {16062, 19840}, {16393, 37603}, {16785, 21070}, {16824, 21020}, {16827, 33816}, {16915, 24602}, {16919, 24586}, {17033, 17688}, {17122, 19284}, {17128, 31004}, {17155, 37549}, {17531, 46827}, {17541, 29991}, {17647, 37231}, {17676, 32784}, {17686, 29960}, {19133, 49524}, {19271, 29674}, {19784, 48837}, {19808, 27714}, {19860, 26665}, {19869, 23537}, {20060, 33175}, {20172, 30036}, {20911, 24291}, {21674, 33116}, {21677, 44416}, {23536, 33123}, {24549, 34284}, {25466, 29632}, {25524, 30957}, {26035, 41239}, {26115, 37573}, {29611, 37416}, {30175, 33841}, {30969, 52245}, {32776, 50065}, {32920, 36565}, {32929, 37598}, {32949, 49745}, {33086, 37256}, {33169, 36500}, {34605, 50311}, {37542, 48805}, {37583, 52357}, {42031, 49682}
X(54331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 964, 32772}, {1, 4968, 32923}, {8, 4195, 31}, {8, 5247, 32864}, {10, 21, 32917}, {65, 50054, 4418}, {964, 49492, 1}, {976, 4385, 32927}, {1043, 1220, 42}, {1193, 13740, 32944}, {1468, 10449, 32919}, {2292, 7283, 32936}, {3714, 37539, 17763}, {5086, 32779, 10}, {11115, 17751, 171}
X(54332) lies on these lines: {3, 6}, {76, 110}, {184, 538}, {194, 11003}, {691, 38527}, {1975, 40643}, {1976, 13085}, {2387, 35924}, {3203, 7754}, {3734, 9418}, {3934, 5651}, {5012, 7757}, {5969, 19127}, {6248, 46261}, {6683, 22112}, {7801, 36213}, {8369, 51735}, {9306, 9466}, {16187, 31239}, {21766, 52042}, {32217, 36156}, {33706, 43574}, {35704, 37184}, {43650, 44562}
X(54332) = 2nd-Brocard-circle-inverse of X(3001)
X(54332) = {X(1670),X(1671)}-harmonic conjugate of X(3001)
X(54333) lies on these lines: {1, 4557}, {2, 11}, {3, 16686}, {6, 101}, {10, 19244}, {31, 33846}, {35, 19249}, {36, 238}, {43, 18613}, {56, 651}, {214, 16494}, {239, 15571}, {244, 53280}, {536, 33845}, {537, 23343}, {595, 16414}, {748, 16678}, {958, 19238}, {978, 23383}, {993, 19255}, {1054, 23845}, {1086, 15507}, {1120, 20037}, {1125, 4267}, {1193, 3122}, {1421, 23067}, {1646, 5163}, {2093, 45022}, {2223, 3246}, {2308, 40153}, {2836, 3675}, {3052, 16059}, {3185, 5272}, {3248, 16493}, {3295, 19253}, {3720, 18185}, {3742, 20967}, {4216, 8692}, {4432, 4436}, {4649, 37602}, {5010, 8053}, {5096, 51621}, {5217, 19292}, {5264, 16297}, {5400, 15626}, {5563, 16477}, {5701, 18785}, {6767, 19250}, {8168, 49460}, {9355, 53296}, {15254, 37575}, {15621, 16569}, {15668, 25532}, {16468, 19293}, {16484, 19265}, {16495, 53303}, {16560, 53293}, {16602, 37619}, {17123, 52139}, {17259, 19239}, {17277, 18047}, {17278, 31394}, {19242, 32941}, {19243, 24294}, {19550, 35238}, {20468, 36741}, {21214, 23361}, {23844, 24174}, {23853, 37679}, {23981, 43048}, {24841, 52923}, {27623, 27667}, {28365, 28400}, {36740, 38048}
X(54333) = crossdifference of every pair of points on line {37, 665}
X(54333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {238, 20470, 3286}, {238, 49997, 52897}, {859, 52897, 3286}, {1001, 1376, 48805}, {4557, 53307, 1}, {27628, 28393, 11}, {28239, 28353, 3035}, {28250, 28364, 2886}
X(54334) lies on these lines: {2, 9019}, {3, 6}, {22, 18374}, {51, 47352}, {67, 69}, {110, 35707}, {141, 858}, {159, 6090}, {160, 9155}, {206, 2916}, {315, 35549}, {338, 37190}, {373, 9969}, {376, 2781}, {524, 2979}, {542, 23039}, {597, 3060}, {599, 1853}, {888, 14277}, {1154, 11179}, {1176, 19151}, {1205, 2930}, {1216, 15069}, {1249, 53772}, {1352, 14791}, {1368, 16789}, {1503, 11459}, {1576, 46546}, {1594, 3867}, {1843, 3763}, {1974, 21284}, {3589, 5640}, {3618, 11002}, {3619, 41579}, {3631, 12272}, {3818, 7574}, {3819, 21358}, {4549, 5663}, {5596, 12250}, {5890, 51737}, {5891, 47353}, {5946, 38064}, {6144, 32366}, {6403, 37118}, {6467, 9027}, {6593, 7492}, {6636, 19127}, {6787, 36187}, {6800, 20806}, {7467, 18371}, {7493, 40949}, {7499, 51744}, {7502, 15462}, {8177, 46303}, {8546, 23061}, {8550, 11412}, {8584, 44323}, {8681, 15533}, {8717, 51941}, {8889, 51994}, {9220, 15980}, {9306, 19596}, {9822, 15082}, {10170, 10516}, {10295, 48881}, {10300, 47558}, {10323, 34117}, {10519, 44668}, {10627, 15074}, {11443, 15826}, {11451, 48310}, {11645, 18435}, {11649, 50977}, {12294, 37196}, {12367, 15066}, {13201, 25329}, {13391, 20423}, {13451, 38079}, {13754, 43273}, {14173, 44719}, {14179, 44718}, {14915, 48905}, {14984, 54042}, {15030, 36990}, {15035, 35228}, {15045, 50983}, {15072, 16775}, {15122, 47468}, {15138, 34778}, {15140, 19121}, {15270, 22424}, {15302, 30489}, {15534, 40673}, {16051, 32246}, {16111, 35257}, {16285, 23642}, {16981, 51171}, {18358, 47341}, {20987, 26283}, {21969, 51185}, {22078, 23635}, {23326, 54041}, {23327, 34751}, {29181, 38323}, {31670, 50008}, {33879, 34573}, {33962, 43619}, {34118, 36851}, {34725, 46847}, {34990, 37184}, {35921, 51739}, {37440, 43811}, {37978, 52238}, {44280, 50965}, {48906, 54215}
X(54334) = midpoint of X(i) and X(j) for these {i,j}: {11188, 12220}, {15072, 41716}
X(54334) = reflection of X(i) in X(j) for these {i,j}: {568, 182}, {599, 3917}, {1352, 15067}, {3060, 597}, {5890, 51737}, {8584, 44323}, {9971, 2}, {9973, 11188}, {11188, 141}, {15072, 44882}, {15534, 40673}, {19161, 16836}, {29959, 3819}, {34751, 23327}, {36990, 15030}, {40949, 41670}, {47353, 5891}, {52989, 5092}, {54173, 54042}
X(54334) = anticomplement of X(16776)
X(54334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3001, 566}, {141, 12220, 9973}, {1350, 9967, 44439}, {3313, 11574, 6}, {3819, 29959, 21358}, {5092, 52989, 40280}, {6636, 22151, 19127}, {7998, 11188, 141}, {7998, 12220, 11188}, {10625, 44479, 11477}, {15644, 50649, 53097}, {41328, 50645, 13351}
X(54335) lies on these lines: {1, 2}, {3, 28612}, {9, 4115}, {21, 4647}, {36, 4359}, {55, 16430}, {56, 16429}, {58, 4697}, {75, 99}, {98, 8691}, {100, 4714}, {191, 17164}, {321, 5251}, {333, 758}, {404, 28611}, {405, 4387}, {442, 36974}, {540, 33097}, {596, 1247}, {740, 4653}, {958, 52531}, {1001, 42713}, {1043, 35016}, {1089, 5260}, {1150, 5902}, {1324, 16678}, {1325, 2975}, {1330, 11263}, {1739, 32918}, {2886, 37346}, {3304, 16425}, {3454, 24161}, {3576, 24435}, {3649, 49716}, {3685, 4717}, {3696, 24929}, {3699, 3956}, {3702, 5259}, {3704, 6675}, {3712, 15670}, {3729, 24074}, {3743, 11110}, {3841, 7270}, {3936, 26725}, {3980, 4257}, {4001, 11551}, {4418, 46895}, {4424, 32917}, {4442, 49735}, {4643, 50273}, {4680, 33108}, {4683, 49723}, {4689, 50083}, {4703, 48839}, {4854, 13745}, {4968, 5258}, {4975, 5284}, {5253, 6533}, {5263, 49480}, {5278, 5692}, {5426, 17163}, {5429, 24342}, {5563, 16424}, {5695, 16418}, {5741, 37701}, {5814, 28628}, {5883, 14829}, {6757, 8666}, {7283, 42031}, {10176, 17277}, {11281, 41014}, {12699, 46975}, {16052, 17070}, {16132, 48877}, {16137, 49718}, {16611, 26244}, {16992, 33936}, {17491, 50215}, {17889, 48835}, {18481, 46617}, {18661, 52709}, {19623, 24325}, {21076, 24937}, {24390, 30447}, {24697, 49729}, {26117, 36250}, {26728, 49511}, {27784, 37035}, {32922, 46912}, {33132, 48843}, {35028, 46800}, {35148, 35957}, {37817, 50314}, {41002, 51409}, {47040, 50086}, {48935, 49177}, {50296, 50886}, {51111, 52244}
X(54335) = midpoint of X(3757) and X(16821)
X(54335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 39766, 1}, {8, 19854, 30172}, {8, 25446, 10}, {8, 25650, 21081}, {10, 1125, 24931}, {10, 50757, 2}, {1125, 21081, 25650}, {46895, 52680, 4418}
X(54336) lies on these lines: {1, 2206}, {10, 31}, {32, 37}, {58, 75}, {65, 1397}, {171, 20083}, {225, 1395}, {595, 31359}, {596, 1468}, {727, 839}, {1106, 3668}, {1125, 1472}, {1714, 17126}, {2218, 49480}, {2901, 44115}, {3915, 42285}, {5271, 39708}, {7121, 42027}, {18833, 52394}, {23604, 40940}, {29645, 34920}, {30148, 51687}, {32774, 37522}
X(54336) = X(i)-isoconjugate of X(j) for these (i,j): {2, 4261}, {3, 5142}, {6, 32782}, {668, 838}
X(54336) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 32782}, {32664, 4261}, {36103, 5142}
X(54336) = trilinear pole of line {661, 1919}
X(54336) = barycentric product X(649)*X(839)
X(54336) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 32782}, {19, 5142}, {31, 4261}, {839, 1978}, {1919, 838}
X(54337) lies on these lines: {3, 63}, {9, 11337}, {10, 16049}, {21, 5285}, {22, 31424}, {35, 42}, {71, 283}, {100, 37402}, {165, 11413}, {205, 3730}, {333, 19842}, {404, 4357}, {579, 2268}, {970, 26890}, {1444, 52396}, {1782, 7688}, {1790, 3682}, {1791, 3710}, {2915, 31445}, {3305, 37034}, {3663, 19850}, {3955, 22076}, {4292, 7465}, {4663, 5217}, {5249, 7523}, {5251, 11101}, {5271, 19845}, {5273, 7520}, {5302, 20989}, {5745, 37231}, {6734, 37399}, {7485, 15803}, {8193, 35258}, {12572, 35996}, {13323, 26893}, {15592, 37577}, {19547, 30852}, {19841, 32939}, {25440, 35980}, {37246, 37581}, {39582, 41229}, {41340, 52362}
X(54337) = isogonal conjugate of the polar conjugate of X(19808)
X(54337) = crossdifference of every pair of points on line {4988, 6591}
X(54337) = barycentric product X(3)*X(19808)
X(54337) = barycentric quotient X(19808)/X(264)
X(54337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3916, 7293}, {3, 7085, 78}
X(54338) lies on these lines: {1, 6007}, {7, 8}, {9, 39}, {78, 21320}, {142, 3831}, {144, 41834}, {726, 3781}, {899, 5220}, {960, 4419}, {1001, 1201}, {1042, 12513}, {1401, 11679}, {2235, 2275}, {3056, 32922}, {3663, 35628}, {3681, 26840}, {3688, 49446}, {3784, 4362}, {3792, 49493}, {3869, 4440}, {4361, 8679}, {4517, 49447}, {5211, 10394}, {5223, 6048}, {5542, 35620}, {5728, 28078}, {5782, 25524}, {7248, 14829}, {10477, 24231}, {15481, 24530}, {17151, 35104}, {17155, 26893}, {21334, 30699}, {25557, 30942}, {26029, 38057}, {26106, 38053}, {26892, 32914}, {29311, 53594}, {49537, 51192}
X(54338) = reflection of X(35892) in X(5542)
X(54338) = crossdifference of every pair of points on line {3063, 50353}
X(54339) lies on these lines: {1, 3}, {2, 1451}, {6, 37694}, {7, 603}, {12, 5247}, {27, 225}, {31, 3485}, {48, 27621}, {58, 226}, {60, 23692}, {73, 81}, {86, 283}, {109, 3671}, {212, 5703}, {238, 11375}, {255, 3487}, {388, 1468}, {404, 1818}, {411, 14547}, {474, 52424}, {580, 13411}, {601, 4295}, {750, 1788}, {962, 52428}, {975, 1708}, {1068, 7554}, {1106, 7365}, {1393, 5262}, {1399, 3649}, {1400, 2303}, {1408, 7175}, {1450, 5253}, {1453, 19372}, {1469, 36508}, {1471, 4648}, {1496, 3475}, {1497, 5603}, {1724, 5219}, {1745, 36742}, {2292, 7098}, {2594, 4649}, {2647, 5429}, {2887, 26363}, {2982, 3682}, {3073, 12047}, {3074, 5398}, {3216, 52423}, {4292, 37469}, {4298, 34050}, {4645, 10527}, {4652, 7190}, {5244, 43045}, {5292, 37093}, {5293, 41538}, {5434, 9363}, {5705, 37660}, {5719, 52408}, {6147, 52407}, {6734, 7270}, {6817, 11269}, {7513, 40950}, {8557, 15656}, {9817, 10396}, {10404, 29658}, {11501, 50581}, {12649, 37684}, {15556, 30115}, {15844, 37646}, {16577, 41547}, {17122, 24914}, {17792, 45728}, {17811, 25524}, {18162, 22345}, {18962, 37716}, {26131, 37797}, {26481, 33140}, {26889, 28349}, {52440, 52783}
X(54339) = barycentric product X(56)*X(19810)
X(54339) = barycentric quotient X(19810)/X(3596)
X(54339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 57, 37591}, {1, 37530, 1936}, {56, 940, 37523}, {57, 37554, 1038}, {58, 226, 1935}, {5398, 11374, 3074}
X(54340) lies on these lines: {2, 3}, {19, 2287}, {34, 81}, {100, 1869}, {225, 33133}, {270, 3194}, {273, 1014}, {1172, 1880}, {1722, 1780}, {1824, 34772}, {1826, 5260}, {1829, 40571}, {1841, 2303}, {1859, 45230}, {1868, 3219}, {1871, 21740}, {1891, 5086}, {2285, 46884}, {2975, 5307}, {5235, 46878}, {41601, 44545}
X(54340) = X(41087)-isoconjugate of X(46014)
X(54340) = barycentric product X(27)*X(19860)
X(54340) = barycentric quotient X(i)/X(j) for these {i,j}: {3194, 46014}, {19860, 306}, {46012, 52389}
X(54340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 28, 21}, {4, 31900, 14016}, {28, 29, 4233}, {28, 4183, 13739}, {28, 4185, 14014}, {28, 31902, 4227}, {29, 37258, 35981}, {7497, 37377, 4198}
X(54341) lies on these lines: {1, 2}, {6, 22}, {23, 20865}, {31, 4283}, {39, 4184}, {51, 50595}, {58, 6636}, {427, 48847}, {579, 21764}, {583, 39673}, {1194, 20970}, {1203, 5310}, {1627, 18755}, {1834, 5133}, {1914, 4261}, {2176, 26911}, {2271, 5359}, {2979, 50591}, {3192, 6995}, {4220, 5396}, {4251, 34482}, {4255, 7485}, {4256, 15246}, {4272, 5276}, {4279, 20966}, {5153, 33854}, {5314, 16470}, {7391, 48837}, {7465, 52544}, {8024, 33296}, {8267, 17499}, {9605, 20835}, {22090, 44435}, {31133, 48842}, {32911, 37325}, {33774, 33863}, {37662, 37990}, {37678, 39998}, {44210, 48861}
X(54341) = crossdifference of every pair of points on line {649, 826}
X(54341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 15523}
X(54342) lies on these lines: {1, 7}, {30, 37703}, {35, 5722}, {55, 80}, {57, 50812}, {226, 5561}, {484, 3488}, {550, 50190}, {950, 18395}, {1000, 3065}, {1387, 3058}, {1479, 6900}, {1621, 9963}, {1698, 50398}, {1737, 51817}, {2320, 21630}, {3295, 5441}, {3434, 5426}, {3486, 37563}, {3582, 30282}, {3583, 5219}, {3584, 3586}, {3601, 4857}, {3612, 37704}, {3746, 5252}, {3911, 5010}, {4870, 18393}, {4894, 52352}, {5218, 37718}, {5443, 9670}, {5444, 11238}, {5531, 6930}, {5697, 10386}, {5719, 6284}, {5902, 15935}, {6767, 36975}, {7741, 31795}, {7951, 52638}, {7967, 13253}, {9668, 37701}, {10246, 14217}, {12433, 37572}, {12690, 17057}, {12953, 37731}, {13405, 18513}, {15171, 15950}, {15172, 21842}, {15228, 15934}, {15338, 18398}, {16173, 37606}, {17601, 24223}, {20066, 30143}, {29638, 48836}, {32844, 47040}
X(54342) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4304, 30331, 21578}, {4309, 4313, 1}, {10386, 10543, 5697}, {21578, 30331, 1}
X(54343) lies on these lines: {2, 3}, {8, 41227}, {19, 19860}, {34, 63}, {55, 5174}, {56, 17923}, {65, 1748}, {92, 958}, {219, 608}, {240, 3924}, {243, 22760}, {278, 2975}, {281, 5260}, {993, 1838}, {1259, 5081}, {1844, 30143}, {1848, 24541}, {1852, 2886}, {1870, 1993}, {1888, 4640}, {1891, 24987}, {3486, 41230}, {5208, 44105}, {5251, 39585}, {5253, 17917}, {10528, 38300}, {11471, 35258}, {11681, 37799}
X(54343) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 28, 37253}, {3, 5125, 35994}, {4, 21, 1013}, {27, 11109, 37235}, {28, 37305, 37231}, {405, 7497, 29}, {475, 37395, 377}, {3560, 7535, 25516}, {4185, 37228, 37235}, {5047, 17519, 7498}, {5125, 17515, 3}, {7518, 16865, 4183}
X(54344) lies on these lines: {7, 8}, {20, 49470}, {21, 757}, {37, 63}, {56, 3964}, {72, 10436}, {86, 960}, {192, 9965}, {193, 2262}, {264, 1887}, {286, 1859}, {317, 1875}, {326, 12635}, {354, 17321}, {478, 23144}, {517, 3879}, {536, 50292}, {740, 4292}, {758, 3664}, {942, 4205}, {1014, 4511}, {1071, 10441}, {1211, 3739}, {1444, 2646}, {1858, 17139}, {1944, 9119}, {2264, 41610}, {3555, 3875}, {3663, 3874}, {3672, 3873}, {3740, 28653}, {3742, 17322}, {3753, 17270}, {3812, 5224}, {3869, 3945}, {3880, 17377}, {3881, 4021}, {3884, 4909}, {3894, 4862}, {3901, 4888}, {4022, 11031}, {4304, 49471}, {4360, 34791}, {4430, 4452}, {4644, 43216}, {4664, 28610}, {4687, 5273}, {4851, 21853}, {4967, 34790}, {5208, 8822}, {5902, 17272}, {5904, 25590}, {5905, 5928}, {6001, 10446}, {6356, 9436}, {9799, 51063}, {10442, 15071}, {10884, 30271}, {10889, 12711}, {11520, 37614}, {12723, 35892}, {16465, 18655}, {17274, 24473}, {17316, 21871}, {17364, 34371}, {17365, 34377}, {17374, 21863}, {17378, 44663}, {17616, 44671}, {17863, 20347}, {18206, 40937}, {18252, 52020}, {18650, 20718}, {21866, 22370}, {21874, 27623}, {22021, 25083}, {29747, 37597}, {37175, 37593}, {44547, 44735}
X(54344) = crossdifference of every pair of points on line {3063, 48099}
X(54345) lies on these lines: {2, 3}, {8, 88}, {386, 17378}, {519, 3976}, {752, 978}, {936, 17274}, {956, 26073}, {975, 17320}, {1125, 49746}, {3419, 27002}, {3877, 44299}, {4255, 17313}, {4256, 17234}, {4257, 17352}, {4302, 25531}, {5015, 11512}, {5044, 17333}, {5293, 50285}, {6361, 25879}, {9668, 26139}, {12436, 50116}, {15172, 26111}, {18481, 25965}, {18990, 26029}, {25524, 48829}, {25914, 48810}, {37592, 50286}, {37607, 50287}
X(54345) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 33309}, {2, 4190, 4217}, {2, 4217, 13741}, {2, 6904, 51668}, {2, 16454, 51604}, {2, 36004, 11346}, {2, 51668, 13740}, {17582, 37339, 11110}
X(54346) lies on these lines: {1, 6889}, {2, 34}, {3, 40950}, {5, 1076}, {6, 24914}, {10, 73}, {11, 15852}, {12, 1427}, {33, 6908}, {46, 5713}, {56, 29639}, {65, 17056}, {122, 27687}, {142, 1393}, {201, 226}, {212, 1771}, {222, 5791}, {223, 1698}, {225, 442}, {227, 3925}, {241, 15844}, {405, 1877}, {581, 1737}, {603, 5745}, {631, 34231}, {851, 1869}, {948, 10588}, {1040, 37112}, {1042, 21674}, {1074, 37438}, {1104, 5433}, {1210, 14547}, {1211, 26955}, {1212, 5514}, {1213, 30456}, {1442, 24883}, {1451, 3911}, {1453, 31231}, {1455, 24953}, {1465, 8728}, {1714, 45126}, {1770, 45924}, {1785, 6937}, {1788, 5530}, {1825, 41340}, {1826, 3142}, {1838, 6829}, {1861, 26027}, {1891, 7413}, {1943, 25446}, {3600, 29664}, {4197, 17080}, {4303, 51755}, {4322, 29690}, {4332, 29661}, {5081, 7572}, {5249, 37591}, {5265, 29680}, {5716, 7288}, {6245, 22053}, {6260, 7069}, {6734, 37523}, {6838, 9817}, {6842, 20620}, {7078, 26446}, {7098, 50307}, {8270, 10198}, {10106, 16499}, {11392, 26052}, {17095, 30761}, {19349, 26066}, {19854, 21147}, {22341, 37225}, {24537, 34851}, {24806, 24987}, {27577, 42289}, {37275, 52427}
X(54346) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {442, 1214, 225}, {3911, 5717, 1451}, {37438, 37565, 1074}
X(54347) lies on these lines: {2, 6}, {4, 34787}, {5, 5181}, {39, 15526}, {53, 37778}, {54, 67}, {66, 19459}, {125, 40673}, {159, 31383}, {182, 10257}, {264, 53477}, {338, 1235}, {378, 1503}, {389, 40107}, {403, 5480}, {427, 2393}, {441, 5063}, {468, 19136}, {511, 15760}, {542, 11430}, {570, 41005}, {571, 41008}, {575, 32257}, {576, 41587}, {578, 34507}, {1154, 19161}, {1352, 9818}, {1594, 15073}, {1899, 32621}, {2071, 44882}, {2076, 35928}, {2854, 12827}, {2892, 3520}, {2930, 7527}, {3260, 41237}, {3541, 8549}, {3548, 44503}, {3549, 44492}, {3564, 52262}, {3867, 9973}, {5094, 5486}, {5117, 45279}, {5133, 11188}, {5449, 32284}, {5476, 47473}, {5621, 23328}, {5648, 41171}, {5972, 41612}, {6143, 32241}, {6146, 34118}, {6193, 11425}, {6247, 18925}, {6467, 23300}, {6623, 53023}, {6697, 32366}, {6776, 10249}, {7403, 43130}, {7542, 44470}, {7687, 25561}, {7706, 47468}, {7753, 45312}, {8541, 51744}, {8542, 37454}, {8548, 15120}, {8681, 21243}, {9722, 14767}, {9967, 51392}, {9969, 41584}, {10169, 21639}, {10192, 18374}, {10516, 18537}, {11178, 18390}, {11412, 11660}, {11438, 50977}, {11585, 44479}, {11746, 20113}, {12294, 51403}, {13371, 15074}, {13394, 16387}, {13403, 18553}, {15118, 52293}, {15531, 23293}, {15581, 16655}, {15585, 20987}, {16043, 40691}, {16511, 19510}, {18560, 38885}, {18583, 44911}, {18642, 36743}, {18919, 52299}, {19118, 31267}, {20192, 47556}, {21850, 41583}, {23330, 25328}, {26864, 31166}, {27376, 51260}, {27377, 53485}, {29181, 44440}, {30522, 39884}, {34417, 47449}, {37855, 53418}, {37962, 47450}, {41593, 46444}, {41729, 52416}, {44441, 54183}, {44458, 48881}, {44668, 45179}, {49672, 50983}, {51163, 52403}, {52281, 53507}
X(54347) = midpoint of X(69) and X(1993)
X(54347) = reflection of X(i) in X(j) for these {i,j}: {6, 23292}, {343, 141}, {8541, 51744}, {41612, 5972}
X(54347) = complement of X(41614)
X(54347) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 8542}, {661, 14672}, {5486, 18589}, {30247, 4369}, {36115, 690}, {37217, 512}, {51831, 21247}
X(54347) = crossdifference of every pair of points on line {512, 41613}
X(54347) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 8263, 29959}, {6, 21358, 26958}, {5094, 10602, 23327}, {5181, 29959, 8263}, {5480, 41585, 9971}, {5486, 23327, 10602}, {9971, 32113, 41585}, {11427, 37636, 13567}, {16511, 19510, 30739}
X(54348) lies on these lines: {1, 1167}, {2, 11}, {8, 25875}, {21, 84}, {56, 9965}, {63, 7677}, {238, 25941}, {329, 1617}, {343, 33173}, {392, 1006}, {394, 17127}, {404, 946}, {405, 944}, {411, 41012}, {452, 12667}, {480, 20015}, {516, 35977}, {943, 37244}, {960, 1319}, {962, 37282}, {968, 26635}, {997, 42012}, {1004, 9812}, {1005, 15931}, {1058, 11517}, {1259, 14986}, {1260, 36845}, {1279, 25091}, {1470, 3485}, {1699, 35990}, {1848, 35973}, {2078, 3452}, {2346, 42470}, {2551, 11510}, {3052, 25934}, {3149, 26129}, {3256, 6692}, {3428, 37313}, {3475, 42843}, {3550, 25938}, {3616, 37248}, {3685, 17862}, {3746, 8582}, {3757, 26591}, {3871, 24982}, {3885, 19860}, {3957, 5572}, {4184, 24556}, {4187, 11491}, {4193, 48482}, {4430, 12635}, {4511, 16465}, {4512, 10857}, {5047, 24987}, {5084, 10267}, {5248, 8583}, {5249, 8543}, {5250, 6986}, {5259, 10572}, {5330, 31806}, {5603, 37249}, {5658, 13615}, {5698, 37578}, {5919, 33895}, {6796, 25522}, {6904, 11496}, {6906, 17614}, {6909, 35262}, {6914, 35272}, {6919, 11500}, {6950, 52148}, {8273, 17576}, {8641, 26695}, {9614, 25440}, {9776, 15804}, {9778, 37309}, {10306, 26062}, {10601, 17018}, {10806, 16845}, {11015, 24564}, {11108, 38042}, {11248, 17567}, {11849, 52264}, {13588, 24545}, {15485, 25885}, {17527, 37621}, {17564, 35000}, {18861, 19525}, {20835, 52653}, {25568, 33925}, {25962, 52367}, {25970, 29851}, {26010, 29846}, {26013, 32943}, {26611, 33153}, {31394, 37261}, {34647, 48698}
X(54348) = anticomplement of X(25973)
X(54348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55, 25893, 2}, {1260, 42884, 36845}, {15931, 40998, 1005}
X(54349) lies on these lines: {1, 21807}, {3, 54}, {6, 41}, {35, 23202}, {51, 2360}, {81, 27622}, {184, 581}, {199, 5752}, {283, 34986}, {386, 44104}, {389, 20838}, {405, 3897}, {474, 17191}, {500, 16064}, {572, 22076}, {580, 13366}, {859, 36750}, {970, 1790}, {1011, 10267}, {1051, 2939}, {1181, 37195}, {1199, 37115}, {1351, 37250}, {1437, 5396}, {1724, 21842}, {1730, 3337}, {1870, 4185}, {1994, 4225}, {2003, 22345}, {2302, 7066}, {2476, 26141}, {2594, 20986}, {3060, 20836}, {3167, 11344}, {3193, 4192}, {3616, 36942}, {3682, 26890}, {3876, 17976}, {4191, 36754}, {4209, 20145}, {4303, 26889}, {5050, 37282}, {5708, 11347}, {6090, 16293}, {7421, 15032}, {7428, 51340}, {7522, 29833}, {9566, 11340}, {9777, 13737}, {11245, 18641}, {11432, 37310}, {13323, 52273}, {14793, 19763}, {14912, 37180}, {15988, 37255}, {16287, 22136}, {16451, 37510}, {16452, 22139}, {16453, 37509}, {19684, 37056}, {19762, 36152}, {19767, 37397}, {20833, 48907}, {20843, 37469}, {27621, 37685}, {28238, 32911}, {28348, 36742}, {35998, 48921}, {37231, 48909}, {44085, 52544}
X(54349) = crossdifference of every pair of points on line {522, 12077}
X(54349) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {184, 581, 3145}, {1437, 5396, 37259}
X(54350) lies on these lines: {1, 3}, {8, 47}, {10, 2216}, {31, 10573}, {80, 3073}, {109, 45287}, {238, 18395}, {255, 12647}, {498, 33105}, {499, 3915}, {595, 1737}, {952, 1399}, {1201, 10090}, {1331, 10915}, {1935, 37710}, {2190, 5174}, {2361, 5690}, {2964, 5247}, {3085, 33112}, {4317, 9316}, {5398, 41687}, {5790, 7299}, {8070, 33106}, {10944, 52407}, {16473, 50581}, {18360, 18990}, {41686, 49500}
X(54350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 14792, 37617}, {1771, 37610, 1}, {2964, 41684, 5247}, {3075, 37588, 1}, {5264, 37610, 37552}, {5710, 11507, 1}, {22767, 37542, 1}
X(54351) lies on these lines: {6, 31}, {9, 5115}, {35, 4285}, {44, 58}, {45, 1468}, {48, 28607}, {171, 17330}, {213, 5035}, {595, 16666}, {757, 17260}, {1100, 40091}, {1203, 5109}, {1213, 17122}, {1333, 2251}, {1399, 1405}, {1400, 52440}, {1743, 4275}, {2174, 5019}, {2300, 9456}, {3747, 16522}, {4264, 16669}, {4290, 16670}, {4969, 5255}, {5247, 17369}, {5280, 28614}, {5356, 40977}, {15955, 21864}, {16521, 20985}, {17123, 17398}, {17126, 37654}, {19623, 27064}, {28658, 52407}, {37610, 50131}
X(54351) = isogonal conjugate of the isotomic conjugate of X(17021)
X(54351) = barycentric product X(i)*X(j) for these {i,j}: {1, 16474}, {6, 17021}
X(54351) = barycentric quotient X(i)/X(j) for these {i,j}: {16474, 75}, {17021, 76}
X(54351) = {X(213),X(5035)}-harmonic conjugate of X(7113)
X(54352) lies on these lines: {1, 21}, {2, 4407}, {6, 17449}, {7, 33136}, {9, 17450}, {42, 17595}, {43, 88}, {44, 354}, {45, 3720}, {57, 53397}, {89, 171}, {100, 49498}, {145, 32845}, {244, 3751}, {320, 31134}, {518, 750}, {614, 4722}, {678, 3870}, {899, 4860}, {902, 42871}, {982, 17012}, {984, 9345}, {1002, 2239}, {1150, 49479}, {1320, 53115}, {1471, 5083}, {1757, 17125}, {2177, 3218}, {2243, 2280}, {2308, 17597}, {2999, 42040}, {3187, 42055}, {3214, 5708}, {3240, 18201}, {3243, 3722}, {3246, 4641}, {3306, 21805}, {3315, 16468}, {3681, 17124}, {3749, 9340}, {3914, 4887}, {3957, 4650}, {3979, 17782}, {3989, 16672}, {3999, 4663}, {4038, 7226}, {4346, 33145}, {4363, 31136}, {4392, 4649}, {4414, 49478}, {4655, 29835}, {4661, 17122}, {4683, 29843}, {4684, 33156}, {4792, 40215}, {4847, 4896}, {4966, 33161}, {5220, 30950}, {5221, 7248}, {5256, 42038}, {5287, 42039}, {5297, 49503}, {5332, 17599}, {5695, 50001}, {7262, 29817}, {9324, 9352}, {9350, 27003}, {9780, 25961}, {10453, 32940}, {11269, 32856}, {16490, 17461}, {16499, 53114}, {16522, 41269}, {16666, 17017}, {16704, 17146}, {16816, 32864}, {17022, 42041}, {17126, 49675}, {17140, 32853}, {17145, 32941}, {17154, 32921}, {17155, 17160}, {17187, 18198}, {17298, 21026}, {17364, 32844}, {17365, 33104}, {17483, 33141}, {17484, 24217}, {17495, 49497}, {17598, 37685}, {17763, 49499}, {20963, 36283}, {24165, 50018}, {24231, 33128}, {24349, 32919}, {24473, 49487}, {24477, 33105}, {24725, 26015}, {26061, 29596}, {26070, 29839}, {26102, 51297}, {26227, 49491}, {26627, 49457}, {26842, 32865}, {29579, 33163}, {29655, 32859}, {29662, 37691}, {29824, 32935}, {29833, 50285}, {30579, 32934}, {31137, 41242}, {31237, 33069}, {32863, 33169}, {32920, 37639}, {32923, 37683}, {32927, 37684}, {32933, 42057}, {33087, 33170}, {33103, 33142}, {33114, 49676}, {37567, 41682}, {37633, 49448}, {42058, 49700}, {43149, 52434}, {49764, 50105}, {50102, 53601}
X(54352) = barycentric product X(1)*X(17313)
X(54352) = barycentric quotient X(17313)/X(75)
X(54352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {320, 33120, 31134}, {354, 32912, 748}, {3218, 49490, 2177}, {3873, 32913, 31}, {17365, 51463, 33104}, {33069, 33121, 31237}
X(54353) lies on these lines: {1, 21}, {6, 16375}, {55, 3110}, {99, 109}, {100, 43076}, {101, 110}, {162, 37206}, {284, 9319}, {386, 16448}, {579, 24483}, {662, 3939}, {692, 1634}, {1019, 4236}, {1025, 4238}, {1438, 2311}, {1936, 24630}, {2242, 5170}, {2398, 4560}, {2701, 6083}, {3286, 34230}, {3733, 23344}, {4584, 5377}, {6577, 34594}, {16702, 19624}, {17209, 40910}, {17944, 39026}, {18268, 38865}, {28162, 43359}, {30858, 30995}, {53268, 53324}
X(54353) = X(4584)-Ceva conjugate of X(101)
X(54353) = X(i)-isoconjugate of X(j) for these (i,j): {4, 10099}, {10, 1027}, {65, 885}, {105, 523}, {210, 43930}, {225, 23696}, {226, 1024}, {294, 7178}, {321, 43929}, {512, 2481}, {513, 13576}, {514, 18785}, {525, 8751}, {647, 54235}, {656, 36124}, {661, 673}, {666, 3125}, {798, 18031}, {884, 1441}, {919, 16732}, {927, 4516}, {1416, 4086}, {1427, 28132}, {1438, 1577}, {1462, 3700}, {1814, 2501}, {2195, 4077}, {3120, 36086}, {3121, 36803}, {3122, 51560}, {3657, 52456}, {3709, 34018}, {3952, 43921}, {4010, 52030}, {4017, 14942}, {4088, 51838}, {6185, 24290}, {6559, 7216}, {7180, 36796}, {14618, 32658}, {14625, 47915}, {21044, 36146}, {21052, 51845}, {21207, 32666}, {21832, 52209}, {21945, 36041}, {24006, 36057}, {35353, 52902}, {36802, 53540}
X(54353) = X(i)-Dao conjugate of X(j) for these (i,j): {518, 4088}, {5519, 21945}, {6184, 1577}, {17755, 850}, {20621, 24006}, {31998, 18031}, {34961, 14942}, {35094, 21207}, {36033, 10099}, {36830, 673}, {38980, 16732}, {38989, 3120}, {39014, 21044}, {39026, 13576}, {39046, 523}, {39052, 54235}, {39054, 2481}, {39063, 4077}, {40596, 36124}, {40602, 885}, {40609, 4086}
X(54353) = cevapoint of X(1914) and X(53287)
X(54353) = trilinear pole of line {672, 1818}
X(54353) = crossdifference of every pair of points on line {661, 3120}
X(54353) = barycentric product X(i)*X(j) for these {i,j}: {21, 1025}, {58, 42720}, {63, 4238}, {81, 1026}, {86, 2284}, {99, 672}, {100, 18206}, {101, 30941}, {110, 3912}, {162, 25083}, {163, 3263}, {190, 3286}, {241, 643}, {249, 4088}, {284, 883}, {333, 2283}, {518, 662}, {645, 1458}, {648, 1818}, {665, 4600}, {670, 9454}, {692, 18157}, {799, 2223}, {811, 20752}, {918, 4570}, {926, 4620}, {1252, 23829}, {1331, 15149}, {1414, 3693}, {1861, 4558}, {2254, 4567}, {2287, 41353}, {2340, 4573}, {2356, 4563}, {3717, 4565}, {3930, 52935}, {3932, 4556}, {4447, 4603}, {4575, 46108}, {4584, 8299}, {4592, 5089}, {4602, 9455}, {4610, 20683}, {4622, 14439}, {4623, 39258}, {4627, 4684}, {4629, 4966}, {5546, 9436}, {7257, 52635}, {7259, 34855}, {16728, 36086}, {24041, 24290}, {50333, 52378}
X(54353) = barycentric quotient X(i)/X(j) for these {i,j}: {48, 10099}, {99, 18031}, {101, 13576}, {110, 673}, {112, 36124}, {162, 54235}, {163, 105}, {241, 4077}, {284, 885}, {518, 1577}, {643, 36796}, {662, 2481}, {665, 3120}, {672, 523}, {692, 18785}, {883, 349}, {918, 21207}, {926, 21044}, {1025, 1441}, {1026, 321}, {1333, 1027}, {1412, 43930}, {1414, 34018}, {1458, 7178}, {1576, 1438}, {1818, 525}, {1861, 14618}, {2193, 23696}, {2194, 1024}, {2206, 43929}, {2223, 661}, {2254, 16732}, {2283, 226}, {2284, 10}, {2328, 28132}, {2340, 3700}, {2356, 2501}, {3252, 35352}, {3263, 20948}, {3286, 514}, {3693, 4086}, {3912, 850}, {3930, 4036}, {3932, 52623}, {4088, 338}, {4238, 92}, {4558, 31637}, {4567, 51560}, {4570, 666}, {4575, 1814}, {4600, 36803}, {4620, 46135}, {5089, 24006}, {5546, 14942}, {6184, 4088}, {9454, 512}, {9455, 798}, {15149, 46107}, {18157, 40495}, {18206, 693}, {20662, 53558}, {20683, 4024}, {20752, 656}, {20778, 24459}, {23829, 23989}, {24290, 1109}, {25083, 14208}, {30941, 3261}, {32661, 36057}, {32676, 8751}, {34230, 4049}, {37908, 3064}, {39258, 4705}, {41353, 1446}, {42079, 24290}, {42720, 313}, {46388, 4516}, {51329, 7212}, {52378, 927}, {52614, 52335}, {52635, 4017}, {53539, 53545}, {53550, 4466}, {53554, 8287}
X(54354) lies on these lines: {1, 21}, {2, 37603}, {3, 238}, {6, 37573}, {8, 902}, {9, 32}, {10, 3550}, {19, 1247}, {34, 1758}, {35, 43}, {36, 1044}, {40, 49128}, {46, 13733}, {55, 5247}, {57, 28109}, {72, 7262}, {75, 24850}, {78, 2210}, {87, 19762}, {90, 3465}, {100, 6048}, {165, 1722}, {171, 405}, {329, 36573}, {386, 2309}, {404, 748}, {474, 17123}, {497, 22361}, {499, 26091}, {560, 1098}, {579, 40955}, {601, 1006}, {602, 6906}, {609, 3294}, {614, 4652}, {672, 23443}, {750, 5047}, {942, 4650}, {956, 37588}, {958, 3052}, {964, 1698}, {970, 3271}, {976, 3219}, {982, 3916}, {984, 5266}, {986, 1104}, {988, 7290}, {995, 5267}, {1001, 4252}, {1012, 37570}, {1054, 37231}, {1064, 6875}, {1106, 7677}, {1107, 21793}, {1125, 3662}, {1155, 24174}, {1191, 37617}, {1193, 4189}, {1279, 3976}, {1330, 3771}, {1399, 37523}, {1438, 39946}, {1449, 31429}, {1453, 17594}, {1479, 30943}, {1490, 9355}, {1616, 11194}, {1714, 4302}, {1738, 31730}, {1739, 37572}, {1743, 2268}, {1745, 36152}, {1757, 3811}, {1770, 17889}, {1836, 24161}, {1914, 21384}, {1935, 37579}, {1957, 41227}, {1961, 37316}, {2175, 13323}, {2218, 24310}, {2298, 3731}, {2308, 19767}, {2329, 14974}, {2647, 37550}, {2664, 33718}, {2938, 33781}, {3008, 12512}, {3072, 3560}, {3074, 8069}, {3145, 27659}, {3208, 5291}, {3216, 5010}, {3218, 28082}, {3246, 52541}, {3286, 16690}, {3338, 29820}, {3361, 28017}, {3487, 24695}, {3496, 16968}, {3501, 4426}, {3552, 16827}, {3555, 17715}, {3579, 24440}, {3616, 26840}, {3624, 16342}, {3632, 49492}, {3648, 33098}, {3666, 16478}, {3683, 37539}, {3685, 17733}, {3736, 37296}, {3751, 19133}, {3772, 24851}, {3780, 10987}, {3792, 37482}, {3831, 17697}, {3913, 21000}, {3941, 16683}, {3959, 41319}, {3961, 41229}, {3980, 16817}, {4184, 27660}, {4188, 27627}, {4203, 16569}, {4210, 27636}, {4216, 7280}, {4224, 5272}, {4253, 16779}, {4259, 16793}, {4267, 8053}, {4278, 18792}, {4292, 37103}, {4294, 33137}, {4300, 37106}, {4307, 17558}, {4339, 5273}, {4362, 7283}, {4383, 5217}, {4414, 5262}, {4434, 46937}, {4438, 5015}, {4641, 37080}, {4855, 5529}, {4859, 14377}, {5021, 16503}, {5044, 37589}, {5156, 16289}, {5172, 7299}, {5192, 32918}, {5230, 6872}, {5251, 5264}, {5258, 37610}, {5259, 26102}, {5265, 51301}, {5268, 47511}, {5300, 33115}, {5329, 13730}, {5398, 37529}, {5438, 15601}, {5711, 16418}, {5744, 36574}, {5814, 33160}, {6284, 35466}, {6675, 33111}, {6679, 16062}, {6857, 26098}, {7031, 16552}, {7155, 8669}, {7483, 17717}, {7741, 37354}, {8688, 33804}, {8720, 50023}, {10822, 50585}, {11108, 17122}, {11110, 50302}, {11114, 21935}, {11115, 31339}, {11374, 33096}, {12579, 29645}, {12625, 53388}, {13407, 29675}, {13732, 20368}, {13740, 32916}, {14006, 39585}, {14621, 33047}, {15171, 33141}, {15674, 33112}, {16192, 23511}, {16370, 16466}, {16688, 16872}, {16865, 17126}, {16914, 41240}, {17033, 17692}, {17063, 37582}, {17064, 41869}, {17105, 23493}, {17124, 17536}, {17125, 17531}, {17184, 36505}, {17526, 26034}, {17572, 28257}, {17675, 31210}, {17696, 29960}, {17698, 32784}, {19270, 25496}, {19335, 28271}, {19645, 53591}, {19854, 33109}, {20066, 33139}, {20077, 29839}, {21537, 28254}, {24159, 32857}, {24586, 33821}, {24892, 52367}, {25650, 32946}, {26066, 37717}, {26131, 29661}, {26363, 33106}, {27368, 32929}, {27625, 37307}, {28265, 37331}, {29473, 30822}, {32613, 37699}, {33084, 49716}, {33771, 42043}, {35633, 37683}, {37176, 50295}, {37563, 49494}, {37618, 47623}, {37663, 52793}, {37715, 50241}, {39248, 51328}, {49448, 49530}, {49613, 49705}, {50303, 50739}
X(54354) = X(2218)-Ceva conjugate of X(1)
X(54354) = X(2)-isoconjugate of X(45988)
X(54354) = X(32664)-Dao conjugate of X(45988)
X(54354) = crossdifference of every pair of points on line {661, 21348}
X(54354) = barycentric product X(i)*X(j) for these {i,j}: {1, 37652}, {31, 30022}, {63, 37055}
X(54354) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 45988}, {30022, 561}, {37055, 92}, {37652, 75}
X(54354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1707, 1046}, {3, 238, 978}, {9, 37552, 5293}, {21, 31, 1}, {35, 1724, 43}, {36, 1777, 1044}, {55, 5247, 50581}, {58, 5248, 1}, {238, 7295, 1716}, {595, 993, 1}, {958, 3052, 5255}, {964, 32917, 1698}, {1001, 4252, 37607}, {1104, 4640, 986}, {1125, 4257, 37608}, {1468, 1621, 1}, {1621, 16948, 1468}, {2975, 3915, 1}, {4189, 17127, 1193}, {4426, 17735, 3501}, {5172, 7299, 37694}, {5259, 37522, 26102}, {5266, 31445, 984}, {8666, 40091, 1}, {12514, 37817, 1}, {15485, 37608, 1125}, {16342, 32772, 3624}, {16468, 37574, 386}
X(54355) lies on these lines: {1, 2}, {4, 17126}, {5, 33107}, {6, 11681}, {7, 34030}, {12, 81}, {21, 37715}, {31, 5046}, {40, 33134}, {46, 33102}, {58, 5080}, {65, 33133}, {100, 1834}, {149, 5255}, {171, 2475}, {181, 41723}, {238, 37162}, {341, 33114}, {484, 36250}, {601, 37437}, {942, 22321}, {986, 33155}, {1046, 17484}, {1064, 6960}, {1203, 3814}, {1254, 37798}, {1329, 32911}, {1386, 17606}, {1400, 16548}, {1468, 20060}, {1788, 19785}, {2295, 17737}, {2363, 24624}, {2476, 5711}, {2478, 17127}, {2551, 24597}, {2650, 17719}, {2975, 37646}, {3072, 6840}, {3073, 13729}, {3218, 13161}, {3436, 37642}, {3550, 20066}, {3701, 33166}, {3714, 32779}, {3769, 5016}, {3812, 33129}, {3822, 26131}, {3825, 5315}, {3868, 33153}, {3869, 17720}, {4193, 16466}, {4225, 5172}, {4307, 6871}, {4385, 33170}, {4415, 11684}, {4642, 33135}, {4696, 33121}, {4850, 24914}, {5051, 33083}, {5086, 37539}, {5141, 26098}, {5221, 33146}, {5253, 37634}, {5260, 35466}, {5264, 52367}, {5280, 26074}, {5295, 46918}, {5348, 37191}, {5710, 11680}, {5712, 10585}, {5769, 45931}, {10408, 17167}, {11015, 37589}, {13731, 37621}, {16062, 33086}, {17164, 37759}, {17735, 23903}, {17902, 37235}, {18253, 33761}, {19513, 22765}, {23536, 27003}, {24440, 33128}, {24443, 33150}, {25466, 37633}, {26066, 28606}, {31888, 33099}, {33118, 52353}, {37256, 37603}, {37558, 37797}, {37702, 49480}, {38945, 39458}
X(54355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 5292, 33142}, {10, 24883, 33139}, {171, 21935, 2475}, {387, 5552, 3240}, {1468, 37716, 20060}, {2476, 5711, 33112}, {3822, 37559, 26131}
X(54356) lies on these lines: {1, 21}, {2, 581}, {3, 1243}, {4, 17167}, {8, 16713}, {27, 10884}, {28, 1790}, {29, 34}, {33, 3559}, {40, 4184}, {46, 4278}, {51, 13731}, {55, 18178}, {56, 18165}, {65, 3286}, {78, 333}, {270, 2185}, {279, 17169}, {284, 1800}, {285, 1422}, {355, 47515}, {377, 991}, {386, 6910}, {394, 405}, {442, 500}, {452, 3945}, {511, 37225}, {517, 17524}, {572, 37231}, {759, 43345}, {851, 48893}, {855, 48894}, {859, 1385}, {936, 5235}, {940, 11344}, {942, 8021}, {943, 1331}, {946, 14956}, {950, 17197}, {964, 10455}, {970, 30944}, {1010, 19860}, {1011, 10441}, {1014, 1467}, {1043, 3872}, {1064, 24541}, {1100, 46889}, {1104, 40153}, {1412, 34489}, {1437, 36011}, {1464, 11281}, {1730, 16451}, {1745, 31266}, {1754, 37285}, {1764, 16452}, {1778, 3553}, {1789, 4282}, {1816, 3306}, {1817, 8726}, {1838, 4303}, {2360, 4228}, {2475, 17173}, {2478, 17182}, {2594, 6690}, {2646, 4267}, {3136, 48937}, {3145, 37527}, {3191, 3219}, {3560, 18451}, {3576, 4225}, {3601, 18163}, {3612, 4276}, {3615, 17586}, {3616, 10571}, {3720, 41012}, {3736, 37232}, {3737, 21106}, {3924, 17187}, {4185, 37474}, {4216, 10470}, {4296, 37558}, {4337, 12609}, {4511, 46877}, {4720, 4853}, {5046, 17174}, {5047, 37659}, {5256, 37265}, {5396, 7483}, {5400, 7504}, {5439, 52889}, {5453, 6675}, {5482, 16374}, {5495, 5499}, {5706, 20835}, {5707, 37284}, {5721, 47516}, {5752, 16455}, {5886, 37357}, {5943, 28238}, {6176, 13724}, {6198, 52891}, {6668, 45885}, {6734, 14547}, {6883, 36747}, {7032, 28082}, {7190, 8822}, {7289, 41718}, {8025, 51382}, {8227, 14008}, {8583, 17557}, {8731, 22076}, {11103, 25526}, {11110, 18465}, {11518, 18164}, {11553, 17768}, {12111, 33536}, {13323, 13733}, {14953, 27000}, {15149, 25935}, {15680, 52524}, {16053, 25930}, {16132, 37369}, {16287, 37536}, {16696, 37549}, {16699, 34522}, {16700, 17054}, {16704, 34772}, {16705, 17219}, {17168, 37168}, {17171, 26130}, {17175, 17866}, {17188, 17584}, {17202, 26117}, {17440, 23623}, {18185, 37080}, {18444, 37113}, {18446, 25516}, {18646, 30117}, {18653, 31900}, {19684, 27378}, {19767, 37666}, {19782, 37246}, {20846, 37530}, {21319, 29958}, {22080, 48917}, {22769, 41582}, {23154, 23440}, {26102, 37373}, {27412, 31631}, {27506, 46880}, {30503, 37402}, {31156, 48855}, {31660, 53388}, {31902, 41854}, {31938, 40967}, {33586, 37320}, {35258, 37296}, {35262, 37442}, {35466, 52544}, {36746, 37228}, {37292, 45923}, {40937, 46882}, {42443, 53280}
X(54356) = isotomic conjugate of the polar conjugate of X(46884)
X(54356) = X(i)-Ceva conjugate of X(j) for these (i,j): {86, 5249}, {664, 4560}, {4636, 3737}
X(54356) = X(i)-isoconjugate of X(j) for these (i,j): {12, 1175}, {37, 2982}, {55, 52560}, {65, 943}, {71, 40573}, {181, 40412}, {225, 1794}, {226, 2259}, {523, 15439}, {1400, 40435}, {1402, 40422}, {1409, 40447}, {2197, 40395}, {2616, 35320}, {3700, 32651}, {4041, 36048}, {14775, 23067}, {26942, 40570}
X(54356) = X(i)-Dao conjugate of X(j) for these (i,j): {223, 52560}, {442, 10}, {942, 201}, {5249, 40999}, {15607, 4041}, {16585, 1441}, {18591, 226}, {39007, 656}, {40582, 40435}, {40589, 2982}, {40602, 943}, {40605, 40422}, {40937, 6358}, {52544, 40661}
X(54356) = cevapoint of X(i) and X(j) for these (i,j): {942, 4303}, {8021, 46882}, {14547, 40937}
X(54356) = barycentric product X(i)*X(j) for these {i,j}: {21, 5249}, {29, 18607}, {57, 51978}, {69, 46884}, {75, 46882}, {81, 6734}, {85, 8021}, {86, 40937}, {261, 2294}, {274, 14547}, {314, 2260}, {332, 1841}, {333, 942}, {345, 46883}, {442, 2185}, {445, 1789}, {645, 50354}, {811, 52306}, {1234, 2150}, {1509, 40967}, {1812, 1838}, {1859, 17206}, {3615, 16585}, {3718, 46890}, {4303, 31623}, {4612, 23752}, {4625, 33525}, {14597, 44130}, {18021, 40978}, {23207, 44129}, {28660, 40956}, {31938, 52393}, {40952, 52379}, {43740, 46885}
X(54356) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 40435}, {28, 40573}, {29, 40447}, {57, 52560}, {58, 2982}, {163, 15439}, {270, 40395}, {284, 943}, {333, 40422}, {442, 6358}, {500, 16577}, {942, 226}, {1625, 35320}, {1838, 40149}, {1841, 225}, {1859, 1826}, {2150, 1175}, {2185, 40412}, {2193, 1794}, {2194, 2259}, {2260, 65}, {2294, 12}, {4303, 1214}, {4565, 36048}, {5249, 1441}, {6734, 321}, {8021, 9}, {14547, 37}, {14597, 73}, {16585, 40999}, {18591, 201}, {18607, 307}, {23207, 71}, {31938, 3969}, {33525, 4041}, {37993, 2294}, {39791, 37755}, {40937, 10}, {40952, 2171}, {40956, 1400}, {40967, 594}, {40978, 181}, {44095, 1825}, {46882, 1}, {46883, 278}, {46884, 4}, {46887, 41342}, {46890, 34}, {50354, 7178}, {51978, 312}, {52306, 656}
X(54356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17194, 21}, {21, 81, 283}, {21, 3193, 2328}, {81, 24635, 18206}, {2328, 4658, 3193}, {2646, 18191, 4267}, {4184, 41723, 40}, {8731, 48909, 22076}, {11110, 18465, 19861}
X(54377) lies on these lines: {1, 24597}, {2, 7}, {8, 4917}, {10, 21}, {11, 15254}, {12, 5302}, {20, 5587}, {27, 1268}, {37, 27492}, {40, 6837}, {44, 5718}, {45, 17720}, {55, 25006}, {56, 24564}, {65, 18253}, {69, 28627}, {72, 5719}, {75, 3977}, {78, 6857}, {84, 31423}, {88, 42326}, {119, 11231}, {140, 1071}, {165, 10431}, {169, 24611}, {190, 4054}, {191, 11552}, {209, 18165}, {210, 6690}, {224, 936}, {228, 8731}, {238, 17722}, {306, 319}, {345, 5271}, {377, 1698}, {379, 5179}, {392, 1387}, {405, 1259}, {442, 31445}, {443, 4652}, {464, 26063}, {515, 37106}, {516, 10883}, {518, 37703}, {519, 27754}, {551, 4867}, {594, 50104}, {631, 5720}, {658, 2349}, {748, 24239}, {756, 11031}, {846, 3914}, {896, 50307}, {940, 2911}, {946, 6884}, {950, 16865}, {958, 5252}, {960, 15950}, {968, 33137}, {984, 3011}, {993, 21578}, {1000, 3872}, {1001, 26015}, {1004, 4413}, {1006, 51755}, {1012, 1512}, {1013, 1861}, {1125, 3868}, {1150, 3912}, {1155, 3826}, {1210, 5047}, {1212, 5723}, {1214, 6357}, {1323, 24635}, {1329, 15823}, {1376, 20835}, {1441, 14206}, {1621, 4847}, {1738, 4414}, {1748, 30686}, {1757, 29640}, {1770, 3647}, {1803, 32008}, {1891, 13739}, {2177, 49772}, {2308, 29682}, {2321, 32849}, {2325, 4671}, {2476, 12572}, {2478, 5705}, {2550, 35258}, {2886, 3683}, {2895, 4035}, {2975, 4315}, {3006, 3883}, {3008, 4850}, {3035, 5784}, {3074, 3561}, {3187, 4464}, {3220, 7465}, {3241, 36922}, {3294, 35341}, {3419, 16418}, {3434, 4512}, {3436, 5234}, {3487, 3951}, {3488, 17561}, {3523, 6705}, {3526, 37713}, {3553, 5287}, {3579, 37447}, {3586, 31156}, {3616, 11520}, {3617, 4313}, {3634, 4197}, {3663, 33129}, {3666, 17366}, {3671, 11684}, {3678, 10122}, {3681, 11020}, {3686, 33077}, {3687, 5278}, {3696, 3712}, {3707, 27757}, {3717, 26227}, {3740, 5432}, {3755, 33139}, {3828, 17057}, {3869, 18249}, {3876, 13411}, {3879, 16704}, {3916, 8728}, {3925, 4640}, {3935, 24393}, {3936, 4416}, {3962, 11281}, {3984, 5703}, {3993, 50755}, {4001, 17361}, {4021, 28606}, {4028, 32864}, {4078, 17763}, {4101, 25650}, {4104, 29846}, {4138, 4683}, {4208, 19877}, {4224, 5314}, {4228, 5285}, {4307, 36277}, {4314, 5178}, {4358, 25101}, {4359, 20236}, {4370, 27747}, {4384, 17740}, {4422, 30818}, {4423, 42843}, {4428, 4863}, {4431, 50105}, {4432, 21242}, {4438, 25494}, {4641, 7277}, {4643, 30811}, {4656, 31204}, {4666, 24477}, {4667, 37635}, {4678, 12536}, {4679, 5832}, {4684, 29830}, {4751, 27471}, {4798, 19749}, {4989, 17025}, {4999, 25917}, {5044, 7483}, {5057, 51090}, {5121, 17125}, {5175, 11106}, {5208, 43223}, {5218, 7675}, {5220, 17718}, {5224, 18650}, {5233, 17335}, {5250, 19843}, {5259, 10916}, {5263, 35263}, {5284, 11019}, {5361, 32858}, {5436, 12649}, {5439, 50205}, {5526, 29571}, {5550, 11036}, {5660, 13243}, {5709, 6832}, {5735, 7988}, {5737, 17293}, {5816, 37419}, {5847, 29643}, {6245, 6986}, {6282, 6974}, {6326, 10165}, {6536, 29863}, {6735, 9708}, {6745, 41228}, {6762, 10587}, {6763, 51706}, {6826, 21165}, {6839, 10175}, {6852, 26878}, {6861, 26921}, {6878, 18443}, {6889, 7330}, {7085, 25514}, {7174, 26228}, {7226, 29681}, {7227, 31993}, {7262, 33111}, {7283, 25446}, {7293, 37261}, {7411, 10164}, {7580, 31672}, {7741, 41872}, {8167, 17728}, {8226, 18482}, {8822, 28653}, {9623, 51433}, {9710, 37568}, {9843, 17536}, {9956, 37468}, {10176, 18389}, {10198, 41229}, {10527, 31435}, {11064, 52385}, {11509, 24982}, {11679, 17776}, {11680, 40998}, {11681, 18250}, {12437, 15676}, {12514, 19854}, {14021, 17308}, {14418, 36038}, {15485, 29676}, {15670, 24929}, {15674, 34772}, {15803, 37462}, {16056, 22060}, {16368, 19732}, {16468, 29657}, {16610, 17337}, {16617, 37585}, {16815, 26070}, {17127, 29664}, {17244, 37684}, {17245, 37520}, {17246, 50103}, {17256, 30832}, {17261, 37759}, {17277, 32851}, {17278, 17595}, {17279, 37660}, {17529, 37582}, {17576, 46933}, {17724, 49515}, {17862, 20879}, {18406, 31730}, {18480, 44238}, {18491, 37426}, {18655, 40530}, {18747, 19827}, {19804, 20927}, {19861, 30478}, {19862, 37701}, {20045, 49527}, {20106, 32782}, {20880, 24589}, {21015, 37360}, {21061, 25589}, {21677, 41575}, {22128, 37659}, {22464, 37695}, {23708, 26363}, {24177, 26724}, {24210, 24892}, {24231, 36263}, {24542, 46909}, {24620, 29628}, {24703, 31245}, {24914, 25011}, {25057, 41141}, {25440, 37285}, {25729, 37206}, {25760, 50752}, {26037, 37175}, {26251, 50404}, {26885, 37527}, {27164, 41248}, {27479, 51052}, {27628, 37575}, {29596, 37111}, {29631, 50290}, {29632, 49511}, {29661, 32912}, {29675, 49448}, {29857, 50295}, {29862, 33082}, {29873, 33083}, {30564, 31017}, {30608, 30829}, {30768, 32784}, {31165, 39782}, {31197, 43055}, {31286, 45684}, {31658, 37374}, {32916, 37090}, {33066, 41878}, {33166, 53663}, {35445, 38200}, {37322, 41507}, {37435, 46932}, {37646, 44307}, {37687, 45204}, {37770, 53009}, {42819, 51463}, {47785, 53359}, {49450, 50744}, {49470, 50758}, {49506, 50743}, {49510, 50748}
X(54357) = complement of X(31019)
X(54357) = X(15175)-complementary conjugate of X(141)
X(54357) = crossdifference of every pair of points on line {663, 21828}
X(54357) = barycentric product X(i)*X(j) for these {i,j}: {75, 24929}, {1268, 15670}
X(54357) = barycentric quotient X(i)/X(j) for these {i,j}: {15670, 1125}, {15762, 1838}, {24929, 1}
X(54357) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9, 908}, {2, 63, 5249}, {2, 329, 31266}, {2, 3218, 142}, {2, 3219, 226}, {2, 5273, 63}, {2, 5325, 17781}, {2, 5744, 3306}, {2, 5905, 25525}, {2, 18228, 30852}, {2, 27065, 3452}, {2, 31018, 5219}, {2, 35595, 5316}, {9, 5219, 31018}, {45, 31187, 17720}, {84, 31423, 37112}, {226, 3219, 17781}, {226, 5325, 3219}, {333, 33116, 306}, {405, 5791, 6734}, {846, 33138, 3914}, {960, 24953, 24541}, {1698, 31424, 377}, {3634, 4292, 4197}, {3647, 3841, 1770}, {3911, 6666, 2}, {3929, 25525, 5905}, {5044, 7483, 27385}, {5219, 31018, 908}, {5235, 32779, 10}, {5278, 33113, 3687}, {5745, 6666, 3911}, {7262, 33111, 41011}, {29007, 37797, 226}, {31204, 33761, 33133}, {31231, 51780, 2}, {32917, 33115, 10}, {33133, 33761, 4656}
X(54358) lies on these lines: {1, 6}, {3, 2260}, {7, 27}, {11, 5747}, {19, 942}, {31, 4343}, {35, 37500}, {36, 37504}, {42, 6600}, {48, 999}, {55, 579}, {56, 284}, {57, 380}, {71, 3295}, {142, 940}, {144, 37685}, {198, 4251}, {221, 12560}, {226, 40963}, {281, 938}, {347, 17014}, {354, 2264}, {387, 2550}, {388, 5802}, {480, 3190}, {495, 26063}, {497, 5746}, {516, 5706}, {527, 50068}, {572, 3428}, {584, 2178}, {604, 17474}, {607, 5262}, {610, 3333}, {612, 40659}, {946, 5776}, {949, 21346}, {965, 1125}, {971, 36742}, {1126, 2336}, {1202, 15288}, {1214, 1445}, {1249, 17905}, {1400, 1617}, {1409, 34040}, {1433, 7129}, {1475, 2268}, {1479, 1901}, {1498, 11372}, {1714, 3826}, {1754, 11495}, {1765, 11496}, {1781, 18398}, {1826, 5722}, {1861, 5808}, {1953, 19350}, {2214, 5880}, {2262, 44662}, {2271, 2277}, {2285, 5173}, {2287, 3616}, {2294, 3211}, {2298, 6601}, {2303, 22127}, {2334, 2983}, {2335, 2346}, {2354, 37492}, {2393, 18621}, {2982, 12848}, {3059, 3745}, {3173, 8545}, {3174, 5269}, {3197, 11529}, {3304, 23073}, {3668, 3946}, {3686, 10371}, {3694, 3870}, {3713, 4847}, {3873, 5279}, {3920, 34784}, {4047, 5250}, {4289, 21773}, {4321, 34046}, {4326, 7070}, {4360, 25252}, {4361, 18698}, {4383, 6666}, {4640, 41422}, {4667, 6180}, {5045, 22153}, {5119, 21866}, {5257, 37658}, {5271, 19716}, {5542, 5781}, {5563, 37519}, {5707, 5805}, {5710, 5853}, {5732, 36746}, {5738, 16608}, {5742, 10198}, {5749, 24552}, {5755, 10267}, {5778, 5886}, {5779, 36750}, {5783, 19843}, {5798, 48482}, {5930, 12573}, {7190, 23144}, {7191, 11025}, {7373, 20818}, {7672, 17016}, {7676, 17126}, {7678, 33107}, {7742, 36744}, {8232, 34048}, {10443, 43175}, {10580, 27382}, {10980, 18594}, {11019, 40942}, {14828, 25521}, {15733, 20741}, {15851, 38288}, {15931, 37499}, {17189, 18166}, {17321, 23151}, {17366, 24779}, {17391, 26657}, {17398, 19854}, {18230, 32911}, {18734, 39273}, {19133, 37580}, {20182, 25080}, {20195, 37674}, {21153, 36745}, {21617, 37695}, {23146, 48303}, {24512, 33137}, {24937, 31245}, {28082, 40977}, {30456, 34036}, {31658, 36754}, {31671, 45923}, {36743, 40292}, {37559, 38052}, {37672, 39948}, {38107, 45931}
X(54358) = X(i)-isoconjugate of X(j) for these (i,j): {9, 8814}, {33, 8813}
X(54358) = X(478)-Dao conjugate of X(8814)
X(54358) = barycentric product X(7)*X(13615)
X(54358) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 8814}, {222, 8813}, {13615, 8}
X(54358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6, 219}, {1, 1723, 37}, {1, 2257, 40937}, {6, 37, 218}, {6, 16777, 2911}, {6, 16781, 2300}, {1100, 1108, 1}, {1400, 2280, 4254}, {1475, 2268, 5120}, {17321, 41610, 23151}, {53134, 53135, 72}
X(54359) lies on these lines: {1, 572}, {6, 3057}, {8, 9}, {11, 17303}, {19, 25}, {20, 31325}, {40, 1400}, {41, 380}, {57, 3672}, {63, 192}, {71, 8557}, {169, 3731}, {200, 21033}, {220, 2264}, {226, 4329}, {312, 2339}, {392, 5783}, {497, 2345}, {573, 5119}, {594, 1837}, {608, 1902}, {610, 9310}, {672, 2257}, {941, 989}, {960, 3713}, {1055, 3100}, {1100, 2098}, {1253, 3747}, {1445, 37555}, {1449, 7962}, {1723, 3730}, {1743, 9819}, {1753, 37528}, {1760, 4664}, {1763, 4656}, {1781, 16673}, {2176, 22074}, {2182, 2256}, {2263, 8898}, {2267, 3554}, {2277, 22071}, {2280, 10388}, {2330, 16972}, {2331, 21148}, {2646, 7221}, {2901, 12514}, {3056, 42447}, {3058, 17281}, {3085, 39579}, {3217, 6602}, {3305, 17280}, {3306, 17302}, {3486, 5227}, {3496, 41261}, {3553, 21801}, {3663, 28017}, {3723, 34471}, {3729, 10889}, {3811, 21078}, {3913, 3965}, {3930, 10382}, {3950, 4314}, {4032, 18655}, {4294, 49542}, {4307, 12717}, {4313, 5279}, {4327, 12721}, {4335, 18788}, {4419, 7289}, {5048, 16884}, {5341, 16672}, {5405, 8231}, {5540, 53052}, {5749, 9785}, {5750, 12053}, {5816, 10039}, {5831, 24390}, {7297, 16675}, {7347, 30413}, {7348, 30412}, {7675, 51058}, {8609, 26357}, {8897, 27184}, {9789, 30381}, {9848, 53089}, {10387, 14100}, {10393, 22021}, {10445, 10624}, {10827, 32431}, {10950, 17299}, {10966, 36743}, {11376, 17398}, {11683, 20173}, {12575, 17355}, {16547, 16676}, {16577, 26215}, {16580, 31158}, {17388, 37740}, {17481, 31164}, {17754, 29837}, {18785, 28071}, {20227, 28011}, {21389, 42312}, {25505, 28798}, {25590, 53526}, {26242, 30677}, {26789, 31019}, {26837, 31053}, {28043, 40965}, {33635, 39943}, {37499, 37568}, {39273, 51052}
X(54359) = crossdifference of every pair of points on line {905, 17420}
X(54359) = barycentric product X(i)*X(j) for these {i,j}: {1, 2551}, {19, 23600}, {78, 52082}, {100, 47136}, {281, 10319}
X(54359) = barycentric quotient X(i)/X(j) for these {i,j}: {2551, 75}, {10319, 348}, {23600, 304}, {47136, 693}, {52082, 273}
X(54359) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1766, 2285}, {9, 1697, 2269}, {9, 3208, 3692}, {19, 37, 40131}, {37, 910, 1696}, {41, 21809, 2324}, {55, 11997, 4319}, {380, 2324, 41}, {1334, 40968, 9}, {2268, 17452, 1}, {3161, 33950, 9}, {7133, 42013, 612}
X(54360) lies on these lines: {1, 24}, {8, 26090}, {37, 2599}, {42, 65}, {72, 52391}, {201, 41340}, {225, 44661}, {226, 1825}, {603, 18732}, {942, 20277}, {946, 1831}, {950, 1866}, {1193, 28290}, {1214, 22342}, {1400, 18674}, {1439, 52390}, {1451, 40959}, {1830, 6260}, {1835, 5930}, {1905, 2654}, {3215, 26934}, {5903, 18446}, {7114, 18838}, {18210, 22341}, {20280, 49454}, {28787, 40152}
X(54360) = X(i)-isoconjugate of X(j) for these (i,j): {21, 1063}, {29, 7163}, {11103, 18532}
X(54360) = X(i)-Dao conjugate of X(j) for these (i,j): {18588, 317}, {40611, 1063}
X(54360) = barycentric product X(i)*X(j) for these {i,j}: {1, 18588}, {226, 1062}, {1214, 1479}, {5358, 26942}, {17584, 37755}
X(54360) = barycentric quotient X(i)/X(j) for these {i,j}: {1062, 333}, {1400, 1063}, {1409, 7163}, {1479, 31623}, {5358, 46103}, {18588, 75}
X(54360) = {X(65),X(17441)}-harmonic conjugate of X(73)
X(54361) lies on these lines: {1, 3090}, {2, 1837}, {3, 12019}, {4, 46}, {5, 3485}, {7, 10895}, {8, 11}, {10, 497}, {12, 938}, {20, 24914}, {21, 11502}, {33, 1722}, {40, 5225}, {43, 2654}, {55, 5047}, {56, 5704}, {57, 5229}, {65, 3091}, {80, 499}, {116, 277}, {140, 4305}, {145, 11376}, {153, 20118}, {210, 8165}, {226, 7989}, {281, 1731}, {354, 5261}, {355, 3086}, {381, 4295}, {388, 1210}, {390, 17358}, {404, 22760}, {452, 26066}, {496, 5790}, {498, 3488}, {515, 6927}, {516, 41348}, {517, 10591}, {519, 50443}, {546, 36279}, {631, 10572}, {632, 37606}, {942, 10590}, {948, 26012}, {950, 1698}, {960, 6919}, {962, 10896}, {986, 7069}, {999, 18357}, {1056, 10827}, {1058, 10039}, {1111, 24797}, {1118, 7541}, {1125, 5727}, {1155, 3146}, {1159, 5072}, {1317, 38758}, {1376, 5175}, {1387, 12645}, {1478, 3337}, {1479, 5657}, {1482, 10593}, {1610, 37366}, {1633, 17516}, {1656, 37730}, {1699, 4848}, {1732, 1826}, {1836, 3832}, {1854, 23332}, {1857, 5125}, {1858, 6871}, {1864, 3812}, {2093, 18483}, {2099, 7173}, {2345, 21029}, {2348, 27541}, {2362, 31412}, {2475, 16141}, {2476, 10958}, {2550, 24982}, {2551, 6734}, {3057, 3617}, {3085, 5722}, {3189, 5552}, {3295, 38042}, {3340, 3817}, {3419, 17619}, {3421, 10916}, {3434, 25005}, {3436, 24477}, {3487, 7951}, {3525, 3612}, {3545, 12047}, {3582, 34627}, {3583, 6361}, {3586, 6684}, {3600, 17728}, {3601, 3634}, {3614, 5226}, {3616, 7504}, {3621, 5048}, {3622, 37740}, {3626, 7962}, {3632, 50444}, {3679, 12053}, {3683, 18231}, {3689, 27525}, {3698, 17604}, {3753, 31418}, {3814, 49168}, {3826, 5809}, {3828, 4314}, {3851, 39542}, {3869, 5187}, {3911, 5691}, {3947, 11518}, {4000, 20305}, {4208, 10391}, {4292, 18492}, {4293, 18480}, {4294, 26446}, {4297, 31231}, {4302, 5445}, {4304, 31423}, {4313, 5432}, {4316, 5560}, {4333, 15682}, {4342, 4691}, {4511, 6931}, {4654, 38076}, {4662, 17642}, {4731, 9848}, {4853, 24386}, {5046, 5698}, {5055, 37737}, {5056, 11375}, {5067, 37721}, {5068, 17605}, {5071, 37692}, {5123, 7080}, {5128, 51118}, {5176, 10529}, {5204, 7319}, {5219, 6738}, {5231, 5795}, {5252, 14986}, {5260, 26357}, {5281, 46932}, {5298, 50864}, {5400, 10571}, {5433, 5731}, {5435, 7354}, {5550, 34471}, {5554, 11680}, {5603, 7741}, {5687, 34122}, {5690, 9669}, {5693, 12736}, {5714, 5902}, {5716, 37717}, {5730, 17533}, {5748, 12635}, {5768, 18242}, {5770, 37821}, {5804, 7680}, {5806, 41539}, {5815, 31141}, {5825, 17768}, {5828, 6764}, {5881, 44675}, {5887, 6973}, {6256, 10265}, {6261, 6969}, {6554, 21044}, {6702, 26364}, {6736, 24392}, {6737, 30827}, {6745, 12625}, {6788, 24159}, {6843, 44547}, {6844, 7686}, {6856, 45230}, {6912, 11509}, {6920, 11507}, {6946, 22766}, {6981, 45770}, {6982, 34339}, {6984, 13750}, {7004, 24174}, {7486, 37724}, {7967, 37711}, {8256, 11235}, {8287, 27686}, {8582, 26040}, {9352, 31295}, {9578, 11019}, {9580, 43174}, {9613, 50796}, {9614, 11362}, {9655, 34753}, {9656, 52783}, {9778, 12953}, {9785, 11238}, {9812, 37567}, {9947, 17625}, {10072, 37710}, {10106, 37714}, {10157, 12709}, {10303, 37600}, {10385, 19875}, {10392, 38052}, {10525, 12619}, {10580, 15888}, {10592, 15934}, {10595, 23708}, {10707, 34711}, {11037, 11237}, {11230, 37739}, {11415, 34744}, {11522, 30286}, {11681, 12649}, {12245, 30384}, {12246, 41698}, {12247, 39692}, {12433, 31479}, {12447, 20196}, {12528, 18838}, {12607, 36845}, {12647, 37720}, {13226, 40267}, {13384, 19862}, {13405, 37723}, {14011, 51978}, {14100, 40333}, {14257, 32594}, {15016, 41562}, {15017, 41558}, {15299, 38149}, {15325, 18525}, {15803, 31673}, {16232, 42561}, {16569, 22072}, {17531, 22768}, {17541, 28934}, {17567, 17647}, {17603, 37436}, {17784, 37828}, {18228, 21677}, {18397, 31870}, {18908, 50196}, {19065, 44623}, {19066, 44624}, {19872, 53054}, {24430, 24443}, {24987, 26105}, {26358, 53055}, {27383, 44669}, {30852, 41575}, {31399, 31434}, {34700, 45310}, {36574, 37716}, {37001, 54052}, {37709, 38155}, {37734, 38314}
X(54362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10175, 10588}, {2, 1837, 3486}, {4, 1737, 1788}, {4, 1788, 3474}, {4, 14646, 52860}, {5, 18391, 3485}, {8, 26129, 5289}, {10, 9581, 497}, {12, 938, 3475}, {57, 19925, 5229}, {80, 499, 944}, {80, 15079, 499}, {355, 3086, 3476}, {498, 37702, 3488}, {950, 1698, 5218}, {1210, 5587, 388}, {1479, 18395, 5657}, {1737, 10826, 4}, {1837, 17606, 2}, {3036, 10912, 8}, {3617, 5274, 3057}, {3621, 18220, 5048}, {3847, 5289, 26129}, {4313, 19877, 5432}, {5128, 51792, 51118}, {5690, 9669, 30305}, {5722, 9956, 3085}, {7741, 10573, 5603}, {8287, 41501, 27686}, {10593, 11545, 1482}, {10896, 40663, 962}, {11681, 12649, 25568}, {18395, 37718, 1479}
X(54362) lies on these lines: {2, 14}, {6, 25}, {16, 22}, {18, 7495}, {23, 62}, {32, 3130}, {39, 3129}, {61, 1995}, {111, 16807}, {187, 3132}, {251, 3457}, {395, 44210}, {397, 10301}, {398, 468}, {427, 5321}, {428, 5318}, {462, 5254}, {463, 7745}, {566, 11141}, {574, 3131}, {612, 10638}, {614, 7051}, {842, 40156}, {858, 16964}, {1250, 5310}, {1368, 42117}, {1370, 42085}, {1383, 21461}, {1627, 41409}, {1993, 51207}, {2493, 11088}, {3054, 51546}, {3060, 51206}, {3104, 44718}, {4232, 42999}, {5020, 11485}, {5064, 42093}, {5094, 5339}, {5133, 16809}, {5169, 42814}, {5189, 42432}, {5237, 7492}, {5238, 40916}, {5306, 11081}, {5322, 19373}, {5335, 6995}, {5343, 52284}, {5352, 7496}, {5640, 36757}, {6353, 10632}, {6636, 10646}, {6676, 10634}, {6800, 36758}, {6997, 18582}, {7378, 42133}, {7386, 42119}, {7391, 19107}, {7392, 10643}, {7394, 16808}, {7396, 43466}, {7408, 42134}, {7484, 11480}, {7485, 10645}, {7493, 40694}, {7494, 11489}, {7499, 23303}, {7500, 42086}, {7519, 16965}, {7539, 42095}, {7571, 42914}, {7667, 42087}, {8014, 46342}, {9465, 34395}, {9909, 11486}, {10154, 11267}, {10565, 11420}, {10635, 15818}, {10691, 42122}, {11138, 44529}, {11142, 13338}, {11284, 22236}, {11548, 42143}, {13595, 37776}, {16063, 42157}, {16250, 41254}, {16268, 47596}, {16419, 42116}, {16966, 37990}, {18468, 42816}, {19106, 34603}, {20062, 42100}, {20063, 43633}, {21849, 44498}, {23302, 37439}, {30739, 42147}, {31099, 42160}, {31133, 36970}, {31152, 42154}, {34608, 42120}, {34609, 42126}, {34755, 37913}, {34986, 44497}, {37353, 42918}, {37454, 42163}, {37899, 42148}, {37900, 42158}, {37904, 43229}, {37910, 42924}, {41100, 47313}, {42099, 52397}, {42101, 52285}, {42140, 44442}, {42150, 46336}, {42164, 46517}, {42942, 43957}, {42993, 52300}, {42998, 52301}
X(54362) = isogonal conjugate of the isotomic conjugate of X(11304)
X(54362) = crossdifference of every pair of points on line {525, 6138}
X(54362) = barycentric product X(6)*X(11304)
X(54362) = barycentric quotient X(11304)/X(76)
X(54363) lies on these lines: {2, 13}, {6, 25}, {15, 22}, {17, 7495}, {23, 61}, {32, 3129}, {39, 3130}, {62, 1995}, {111, 16806}, {187, 3131}, {251, 3458}, {396, 44210}, {397, 468}, {398, 10301}, {427, 5318}, {428, 5321}, {462, 7745}, {463, 5254}, {566, 11142}, {574, 3132}, {612, 1250}, {614, 19373}, {842, 40157}, {858, 16965}, {1368, 42118}, {1370, 42086}, {1383, 21462}, {1627, 41408}, {1993, 51206}, {2493, 11083}, {3054, 51547}, {3060, 51207}, {3105, 44719}, {4232, 42998}, {5020, 11486}, {5064, 42094}, {5094, 5340}, {5133, 16808}, {5169, 42813}, {5189, 42431}, {5237, 40916}, {5238, 7492}, {5306, 11086}, {5310, 10638}, {5322, 7051}, {5334, 6995}, {5344, 52284}, {5351, 7496}, {5640, 36758}, {6353, 10633}, {6636, 10645}, {6676, 10635}, {6800, 36757}, {6997, 18581}, {7378, 42134}, {7386, 42120}, {7391, 19106}, {7392, 10644}, {7394, 16809}, {7396, 43465}, {7408, 42133}, {7484, 11481}, {7485, 10646}, {7493, 40693}, {7494, 11488}, {7499, 23302}, {7500, 42085}, {7519, 16964}, {7539, 42098}, {7571, 42915}, {7667, 42088}, {8015, 46343}, {9465, 34394}, {9909, 11485}, {10154, 11268}, {10565, 11421}, {10634, 15818}, {10691, 42123}, {11139, 44529}, {11141, 13338}, {11284, 22238}, {11548, 42146}, {13595, 37775}, {16063, 42158}, {16249, 41254}, {16267, 47596}, {16419, 42115}, {16967, 37990}, {18470, 42815}, {19107, 34603}, {20062, 42099}, {20063, 43632}, {21849, 44497}, {23303, 37439}, {30739, 42148}, {31099, 42161}, {31133, 36969}, {31152, 42155}, {34608, 42119}, {34609, 42127}, {34754, 37913}, {34986, 44498}, {37353, 42919}, {37454, 42166}, {37899, 42147}, {37900, 42157}, {37904, 43228}, {37910, 42925}, {41101, 47313}, {42100, 52397}, {42102, 52285}, {42141, 44442}, {42151, 46336}, {42165, 46517}, {42943, 43957}, {42992, 52300}, {42999, 52301}
X(54363) = isogonal conjugate of the isotomic conjugate of X(11303)
X(54363) = crossdifference of every pair of points on line {525, 6137}
X(54363) = barycentric product X(6)*X(11303)
X(54363) = barycentric quotient X(11303)/X(76)
X(54364) lies on these lines: {1, 514}, {31, 57}, {33, 92}, {34, 7128}, {43, 1699}, {77, 927}, {294, 3577}, {517, 2427}, {666, 3872}, {908, 35015}, {919, 2717}, {994, 18785}, {997, 35333}, {998, 1438}, {1193, 14267}, {1465, 23981}, {2191, 36041}, {2999, 52210}, {5256, 6654}, {14190, 41162}, {19861, 40724}, {22144, 38575}, {31019, 46784}, {35258, 36086}
X(54364) = isogonal conjugate of X(36819)
X(54364) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36819}, {104, 518}, {241, 52663}, {665, 13136}, {672, 34234}, {909, 3912}, {918, 32641}, {1309, 53550}, {1458, 51565}, {1795, 1861}, {1809, 1876}, {1818, 36123}, {2223, 18816}, {2250, 18206}, {2254, 36037}, {2283, 43728}, {2284, 2401}, {2342, 9436}, {2423, 42720}, {2720, 50333}, {3263, 34858}, {3286, 38955}, {3693, 34051}, {14578, 46108}, {16082, 20752}, {34159, 51832}, {34230, 36944}, {36795, 52635}, {41933, 51390}
X(54364) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 36819}, {1145, 3717}, {3259, 2254}, {16586, 3263}, {23980, 3912}, {25640, 1861}, {38981, 50333}, {40613, 518}
X(54364) = cevapoint of X(517) and X(15507)
X(54364) = trilinear pole of line {1769, 2183}
X(54364) = barycentric product X(i)*X(j) for these {i,j}: {75, 51987}, {105, 908}, {294, 22464}, {517, 673}, {666, 1769}, {885, 24029}, {919, 36038}, {927, 46393}, {1027, 2397}, {1438, 3262}, {1457, 36796}, {1462, 6735}, {1465, 14942}, {1785, 1814}, {2183, 2481}, {2804, 36146}, {3310, 51560}, {5377, 42754}, {10015, 36086}, {14571, 31637}, {15507, 52209}, {17139, 18785}, {22350, 54235}, {34085, 53549}, {51381, 52030}, {51390, 51838}
X(54364) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 36819}, {105, 34234}, {294, 51565}, {517, 3912}, {673, 18816}, {859, 18206}, {908, 3263}, {919, 36037}, {1024, 43728}, {1027, 2401}, {1416, 34051}, {1438, 104}, {1457, 241}, {1465, 9436}, {1769, 918}, {1785, 46108}, {1875, 5236}, {2183, 518}, {2195, 52663}, {2427, 1026}, {3310, 2254}, {8751, 36123}, {14571, 1861}, {14942, 36795}, {15507, 17755}, {17139, 18157}, {18785, 38955}, {21801, 3932}, {22350, 25083}, {22464, 40704}, {23981, 1025}, {24028, 51390}, {24029, 883}, {32658, 1795}, {32666, 32641}, {32735, 37136}, {36086, 13136}, {36124, 16082}, {42758, 53583}, {46393, 50333}, {51377, 3930}, {51987, 1}, {52480, 46794}
X(54365) lies on these lines: {1, 2}, {32, 69}, {141, 16060}, {384, 1330}, {1043, 6656}, {1654, 4251}, {2271, 5224}, {3430, 6999}, {3620, 4262}, {3936, 17686}, {4417, 7770}, {5741, 17541}, {7789, 17206}, {7807, 14829}, {7819, 41014}, {7832, 33297}, {11321, 18134}, {16930, 26131}, {16931, 26064}, {17234, 33035}, {18266, 33081}, {31023, 52367}, {33033, 41878}, {33172, 33830}, {33181, 37655}
X(54365) = crossdifference of every pair of points on line {649, 2514}
X(54365) = {X(25645),X(29433)}-harmonic conjugate of X(2)
X(54366) lies on these lines: {1, 6908}, {2, 7}, {4, 11}, {12, 19855}, {20, 37583}, {36, 6987}, {46, 5758}, {55, 35514}, {65, 3085}, {72, 1788}, {73, 387}, {145, 18467}, {196, 18687}, {208, 3089}, {218, 52659}, {222, 37642}, {223, 4341}, {241, 17720}, {269, 34050}, {278, 393}, {279, 2006}, {281, 26011}, {342, 17923}, {347, 18593}, {388, 442}, {390, 2078}, {392, 3485}, {405, 7288}, {440, 7011}, {452, 5265}, {496, 37411}, {497, 1617}, {498, 3339}, {499, 3361}, {604, 5802}, {631, 1466}, {651, 24597}, {938, 6838}, {942, 6825}, {943, 11509}, {948, 37695}, {950, 1420}, {954, 5218}, {999, 6907}, {1000, 2099}, {1005, 7677}, {1006, 1470}, {1042, 5230}, {1145, 34619}, {1155, 5759}, {1210, 1467}, {1319, 3488}, {1398, 37376}, {1407, 34032}, {1436, 7490}, {1458, 11269}, {1460, 7413}, {1465, 4000}, {1478, 6843}, {1512, 18391}, {1604, 11347}, {1728, 5811}, {1751, 3451}, {1758, 24248}, {1864, 5658}, {2003, 37666}, {2256, 17056}, {2263, 3011}, {2550, 37240}, {2900, 36845}, {3120, 4331}, {3256, 5281}, {3336, 10320}, {3419, 3476}, {3434, 35990}, {3474, 17613}, {3475, 5173}, {3586, 10072}, {3600, 5177}, {3601, 37108}, {3651, 4294}, {3660, 5728}, {3671, 10198}, {3711, 40663}, {4292, 5715}, {4295, 37550}, {4298, 26363}, {4304, 37427}, {4306, 5292}, {4308, 5175}, {4315, 45700}, {4318, 26228}, {4321, 5231}, {4323, 10587}, {4327, 29639}, {4334, 33140}, {4848, 7080}, {4996, 37313}, {5018, 29658}, {5222, 8776}, {5228, 5718}, {5274, 50696}, {5290, 19854}, {5323, 25516}, {5433, 16845}, {5434, 50741}, {5531, 10573}, {5552, 15556}, {5660, 11570}, {5703, 37112}, {5704, 6953}, {5708, 6863}, {5712, 37543}, {5714, 6832}, {5729, 13257}, {5770, 5777}, {5771, 6147}, {5775, 44848}, {5776, 51365}, {5809, 18450}, {5812, 6891}, {6180, 35466}, {6224, 11240}, {6260, 10396}, {6604, 30828}, {6734, 45039}, {6829, 10590}, {6834, 37566}, {6856, 15844}, {6862, 24470}, {6913, 15325}, {6926, 15803}, {6936, 34880}, {6937, 26437}, {6958, 37545}, {6959, 34753}, {6979, 9964}, {6989, 11374}, {7195, 40615}, {8226, 10589}, {9119, 38015}, {9579, 37434}, {9780, 41824}, {10056, 18421}, {10200, 12572}, {10382, 11019}, {10580, 30284}, {11349, 38900}, {11575, 51489}, {13411, 37407}, {13615, 26105}, {15728, 26007}, {17080, 19785}, {17595, 43056}, {17603, 21151}, {17625, 24477}, {18962, 31410}, {24604, 32625}, {25568, 41539}, {26487, 31794}, {28808, 38468}, {30478, 37224}, {30832, 33298}, {32851, 39126}, {33129, 37800}, {37382, 38461}, {37722, 51773}
X(54366) = X(6350)-Dao conjugate of X(28808)
X(54366) = crossdifference of every pair of points on line {663, 52307}
X(54366) = barycentric product X(i)*X(j) for these {i,j}: {7, 18391}, {85, 8557}, {273, 18446}, {278, 6350}, {331, 19350}
X(54366) = barycentric quotient X(i)/X(j) for these {i,j}: {1512, 6735}, {6350, 345}, {8557, 9}, {18391, 8}, {18446, 78}, {19350, 219}
X(54366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8732, 3911}, {7, 5435, 3218}, {7, 37797, 2}, {226, 1708, 329}, {226, 3911, 9}, {329, 5435, 1708}, {499, 9612, 6846}, {1108, 1427, 43058}, {1427, 3772, 278}, {3487, 6889, 3085}, {3487, 33993, 17718}, {14986, 37421, 950}
X(54367) lies on these lines: {2, 3}, {10, 45}, {387, 37654}, {519, 5814}, {551, 5717}, {752, 5711}, {942, 17274}, {975, 50050}, {1125, 48808}, {1330, 17378}, {1698, 17601}, {1834, 17330}, {2901, 50087}, {3017, 48839}, {3175, 3679}, {3295, 49746}, {3876, 27776}, {3927, 17333}, {3931, 5827}, {4357, 5722}, {5015, 50286}, {5143, 31160}, {5225, 19866}, {5263, 9668}, {5292, 49728}, {5484, 7373}, {5725, 50290}, {5743, 48837}, {5774, 37715}, {5808, 50092}, {9708, 32773}, {10449, 17271}, {10896, 19863}, {12572, 50115}, {13161, 50305}, {14555, 48847}, {15934, 27184}, {16589, 22426}, {17251, 50271}, {17301, 50062}, {18440, 25898}, {19765, 27739}, {24723, 36279}, {26625, 51340}, {35652, 50051}, {37674, 48835}, {37679, 48843}, {42044, 50041}, {42051, 50066}, {47037, 50157}, {48803, 49736}, {50047, 50107}, {50067, 50101}
X(54367) = reflection of X(19276) in X(2)
X(54367) = complement of X(51668)
X(54367) = orthocentroidal-circle-inverse of X(37150)
X(54367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 37150}, {2, 377, 51671}, {2, 452, 51673}, {2, 964, 51603}, {2, 4217, 51672}, {2, 11113, 11354}, {2, 11114, 16394}, {2, 14020, 405}, {2, 17528, 50427}, {2, 17537, 964}, {2, 17579, 19290}, {2, 17677, 17528}, {2, 26117, 37038}, {2, 37038, 3}, {2, 37150, 2049}, {2, 37314, 51679}, {2, 48814, 16418}, {2, 48816, 19332}, {2, 48817, 50059}, {2, 49735, 16370}, {2, 50055, 11112}, {2, 50056, 11359}, {2, 50165, 16393}, {2, 50171, 51602}, {2, 51594, 11110}, {2, 51606, 37176}, {2, 51673, 17698}, {2, 51679, 16844}, {4, 4205, 2049}, {5, 13725, 19273}, {442, 37314, 16844}, {442, 51679, 2}, {4205, 37150, 2}, {4205, 52246, 37150}, {4217, 51672, 11354}, {5051, 14020, 2}, {11113, 51672, 4217}, {17556, 51677, 2}, {26117, 52258, 3}, {37038, 52258, 2}, {37144, 37145, 3}, {37146, 37147, 46219}, {37150, 52246, 4}, {37715, 50295, 5774}
X(54368) lies on these lines: {1, 19}, {3, 1838}, {4, 35}, {5, 1852}, {12, 7511}, {21, 39585}, {22, 1074}, {24, 225}, {25, 1324}, {27, 4276}, {29, 5248}, {33, 36009}, {34, 46}, {36, 278}, {40, 1794}, {55, 7497}, {92, 993}, {102, 3362}, {107, 158}, {165, 37305}, {255, 46883}, {270, 9275}, {281, 5251}, {499, 7521}, {516, 37258}, {517, 6056}, {573, 3074}, {758, 1748}, {994, 2190}, {1001, 37393}, {1076, 17928}, {1096, 37817}, {1118, 37583}, {1125, 30687}, {1430, 4257}, {1478, 37395}, {1621, 17519}, {1699, 37380}, {1737, 1751}, {1829, 13750}, {1842, 14017}, {1859, 24929}, {1870, 5902}, {1871, 2646}, {1888, 3579}, {1890, 47042}, {1891, 10039}, {1905, 2355}, {1957, 52680}, {3085, 4198}, {3144, 54084}, {3422, 12047}, {3560, 39574}, {3583, 37372}, {4185, 5530}, {4219, 5010}, {4227, 5307}, {5125, 25440}, {5174, 8715}, {5259, 7498}, {5903, 6197}, {6284, 15763}, {6690, 37321}, {6912, 39531}, {6914, 39529}, {7510, 32613}, {7537, 7741}, {7952, 17562}, {8071, 37245}, {8757, 37489}, {10037, 13161}, {10056, 38300}, {10058, 51282}, {10523, 37376}, {10629, 37392}, {11399, 17523}, {15931, 37028}, {17923, 37304}, {22766, 37236}, {24611, 37231}, {25540, 34851}, {36744, 37377}, {41859, 52252}
X(54368) = barycentric product X(92)*X(5398)
X(54368) = barycentric quotient X(5398)/X(63)
X(54368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 37799, 7951}, {28, 41227, 1}, {92, 17515, 993}, {278, 7501, 36}
X(54369) lies on these lines: {1, 2}, {6, 1214}, {9, 25080}, {31, 22394}, {41, 1763}, {46, 1817}, {48, 57}, {65, 11347}, {81, 6505}, {219, 3666}, {223, 3668}, {226, 3553}, {278, 52033}, {284, 10319}, {440, 10393}, {611, 20588}, {940, 53996}, {990, 2947}, {1006, 1453}, {1442, 37666}, {1468, 36016}, {1723, 32911}, {1780, 27174}, {2003, 34052}, {2324, 4656}, {2328, 17594}, {2331, 40149}, {2646, 21483}, {3752, 37543}, {3755, 40960}, {4272, 18643}, {4383, 40937}, {5249, 24779}, {5706, 15836}, {6198, 18678}, {6261, 19542}, {6349, 53596}, {7146, 21370}, {7190, 23681}, {8557, 16577}, {9121, 50701}, {10397, 21174}, {10572, 37185}, {12514, 16368}, {12520, 37419}, {14110, 16435}, {16466, 37528}, {18734, 23122}, {19788, 24179}, {19790, 24203}, {25252, 27064}, {31266, 37887}, {37181, 48837}, {37662, 37695}
X(54369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2999, 40940}, {1, 50581, 15954}
X(54370) lies on these lines: {1, 651}, {2, 1709}, {3, 15254}, {4, 9}, {5, 1158}, {7, 90}, {21, 3062}, {36, 8544}, {46, 3091}, {55, 5927}, {57, 1776}, {63, 1699}, {65, 5729}, {72, 42014}, {78, 5696}, {84, 1125}, {109, 9817}, {118, 40131}, {142, 3358}, {144, 11415}, {165, 3305}, {191, 52269}, {200, 15064}, {226, 30223}, {238, 990}, {329, 42012}, {355, 528}, {381, 28534}, {390, 10043}, {405, 12520}, {411, 2951}, {442, 12679}, {499, 30379}, {515, 6930}, {517, 5220}, {518, 1351}, {527, 946}, {920, 1445}, {944, 47357}, {954, 1898}, {958, 9856}, {962, 6172}, {971, 1001}, {997, 1012}, {1005, 1750}, {1006, 50528}, {1071, 10177}, {1376, 10157}, {1490, 5248}, {1698, 6932}, {1708, 1836}, {1721, 13329}, {1723, 3332}, {1728, 4295}, {1736, 2263}, {1737, 6957}, {1741, 5829}, {1768, 3306}, {1770, 6835}, {1858, 5728}, {2346, 36599}, {2475, 52860}, {2476, 38052}, {2950, 6702}, {3100, 15430}, {3218, 9779}, {3219, 9812}, {3333, 43180}, {3359, 6982}, {3361, 9814}, {3434, 20588}, {3485, 5542}, {3486, 10384}, {3587, 28150}, {3616, 10085}, {3634, 37560}, {3646, 9841}, {3652, 5805}, {3671, 10396}, {3678, 6769}, {3683, 7580}, {3685, 48878}, {3740, 6244}, {3754, 54156}, {3811, 5777}, {3826, 6842}, {3869, 4853}, {3878, 54135}, {3884, 12650}, {3895, 37712}, {3911, 10863}, {3913, 9947}, {3928, 50802}, {4067, 7982}, {4294, 5766}, {4297, 11111}, {4301, 36973}, {4413, 17613}, {4423, 10167}, {4466, 6173}, {4640, 19541}, {4672, 48900}, {4676, 13727}, {4679, 37374}, {5047, 9961}, {5086, 38154}, {5119, 30332}, {5219, 21635}, {5250, 5691}, {5259, 10884}, {5284, 11220}, {5437, 10171}, {5693, 12559}, {5709, 18483}, {5715, 12558}, {5762, 40273}, {5811, 21077}, {5843, 20330}, {5851, 5886}, {5853, 47745}, {5903, 41700}, {6001, 6913}, {6259, 25466}, {6260, 10198}, {6282, 10176}, {6666, 6825}, {6684, 9842}, {6838, 18230}, {6846, 12609}, {6847, 21616}, {6852, 20195}, {6856, 38204}, {6857, 38059}, {6860, 17700}, {6872, 36991}, {6888, 37692}, {6893, 12616}, {6915, 30295}, {6939, 12686}, {6945, 30312}, {6985, 11495}, {6988, 43151}, {7069, 8270}, {7098, 38151}, {7171, 10165}, {7308, 10164}, {7411, 41860}, {7491, 31672}, {7675, 37571}, {7680, 37822}, {7705, 7989}, {7971, 30147}, {8167, 11227}, {8255, 11374}, {8581, 20323}, {8715, 47375}, {8727, 24703}, {9778, 27065}, {9809, 31019}, {9943, 11108}, {9955, 24467}, {10179, 30283}, {10398, 12560}, {10582, 30304}, {10595, 51099}, {10826, 13729}, {11376, 38055}, {11662, 36971}, {11729, 25558}, {12526, 54159}, {12635, 31821}, {12699, 38454}, {13257, 17718}, {13743, 45770}, {15296, 34352}, {15481, 51516}, {15803, 30353}, {16209, 17531}, {16617, 31657}, {17728, 41695}, {18450, 37618}, {19862, 37526}, {20116, 30330}, {20117, 37531}, {21740, 38316}, {22758, 42842}, {22793, 26921}, {24248, 53599}, {24430, 34036}, {24723, 36652}, {25524, 34862}, {25917, 37022}, {26202, 32612}, {26333, 51755}, {28236, 31393}, {30340, 51816}, {33179, 42871}, {33596, 42843}, {35258, 44425}, {35664, 39559}, {36663, 52690}, {36996, 38053}, {37360, 42467}, {37624, 42819}, {37695, 38357}, {38036, 41705}
X(54370) = midpoint of X(i) and X(j) for these {i,j}: {4, 5698}, {9, 11372}, {1001, 16112}, {3062, 5732}, {5223, 43166}, {36991, 43161}
X(54370) = reflection of X(i) in X(j) for these {i,j}: {3, 15254}, {5732, 52769}, {5805, 42356}, {5880, 5}, {11495, 31658}, {25558, 11729}, {43177, 1125}, {43178, 3}
X(54370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 5698, 12514}, {200, 30326, 15064}, {390, 29007, 15298}, {405, 12688, 12520}, {1156, 8543, 10394}, {1768, 7988, 3306}, {1836, 7082, 1708}, {3219, 9812, 41338}, {3560, 31937, 6261}, {5057, 10883, 1699}, {5223, 24644, 43166}, {5248, 31871, 1490}, {5777, 11496, 3811}, {5880, 15297, 8257}, {6191, 6192, 169}, {6212, 6213, 5011}, {7308, 10860, 10164}, {8543, 10394, 1}, {10398, 12560, 30329}, {36991, 52653, 43161}
X(54371) lies on these lines: {1, 2915}, {3, 6}, {21, 1211}, {22, 19765}, {28, 17056}, {35, 72}, {36, 4719}, {37, 18598}, {55, 976}, {56, 199}, {229, 37635}, {239, 19841}, {894, 19842}, {896, 5217}, {910, 5277}, {940, 11337}, {958, 32778}, {993, 5814}, {1036, 1191}, {1213, 47512}, {1325, 26131}, {1330, 17512}, {1763, 3601}, {1829, 2646}, {1834, 4220}, {2174, 3682}, {2194, 22076}, {2975, 32842}, {3295, 20918}, {3303, 20851}, {3936, 17521}, {4189, 5739}, {4361, 19844}, {4363, 19845}, {4653, 20831}, {5248, 16686}, {5310, 37080}, {5347, 19767}, {5358, 6675}, {5438, 35342}, {5710, 20847}, {5711, 39582}, {5712, 7520}, {5718, 37231}, {5810, 6914}, {7295, 24697}, {7297, 9895}, {11102, 25650}, {15976, 44517}, {16049, 49745}, {16370, 49723}, {16429, 25526}, {16777, 27802}, {17104, 22136}, {18178, 37527}, {18185, 20844}, {19329, 25524}, {19523, 19744}, {19720, 37151}, {20852, 22654}, {20872, 37573}, {23130, 40214}, {23383, 23868}, {25909, 47296}, {35212, 37594}, {37034, 37674}, {37225, 40980}, {37431, 37662}, {37571, 54095}
X(54371) = X(37539)-Ceva conjugate of X(1191)
X(54371) = crossdifference of every pair of points on line {523, 16612}
X(54371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 386, 5096}, {3, 19762, 5124}, {3, 36740, 4252}, {3, 36744, 19760}, {284, 3430, 52544}
X(54372) lies on these lines: {2, 3}, {53, 86}, {92, 54120}, {264, 17300}, {273, 26806}, {281, 17350}, {317, 1654}, {318, 6542}, {324, 26541}, {393, 17379}, {1249, 37677}, {1785, 16826}, {1897, 29588}, {1990, 46922}, {2052, 6625}, {2202, 40744}, {2322, 27377}, {3087, 17349}, {3945, 43981}, {4393, 34231}, {6646, 7282}, {6748, 17277}, {7046, 20055}, {7952, 29570}, {9308, 20090}, {17343, 32001}, {17375, 32000}
X(54372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 21940, 2}, {297, 11109, 2}, {458, 37448, 2}, {1585, 1586, 4213}, {25986, 37279, 2}
X(54373) lies on these lines: {1, 228}, {2, 2269}, {6, 24310}, {9, 321}, {31, 40}, {43, 26893}, {57, 77}, {63, 194}, {212, 41230}, {226, 4266}, {306, 3169}, {329, 2347}, {380, 41342}, {497, 26013}, {573, 27659}, {978, 22076}, {982, 17441}, {985, 39596}, {986, 1829}, {1193, 9549}, {1278, 3219}, {1423, 19785}, {1621, 1697}, {1745, 50594}, {1763, 36572}, {1764, 2999}, {1851, 24248}, {1914, 10319}, {1999, 21371}, {2262, 3666}, {2270, 5276}, {2286, 45984}, {3057, 25091}, {3061, 3998}, {3208, 17776}, {3501, 5294}, {3772, 4271}, {3882, 25527}, {3914, 6210}, {3929, 50106}, {3969, 4050}, {4000, 22097}, {4254, 37543}, {4384, 10471}, {4640, 40970}, {5119, 8616}, {5222, 28274}, {5230, 9548}, {5250, 16824}, {7308, 53391}, {16503, 19716}, {16572, 36808}, {16609, 19788}, {16779, 19729}, {16826, 39970}, {17451, 28606}, {17595, 18735}, {18178, 37523}, {26723, 27626}, {37400, 40958}
X(54373) = crossdifference of every pair of points on line {4041, 23655}
X(54373) = {X(573),X(40940)}-harmonic conjugate of X(27659)
X(54374) lies on these lines: {3, 6}, {20, 66}, {22, 34146}, {69, 7691}, {141, 3575}, {159, 45813}, {206, 7488}, {427, 29181}, {1092, 32391}, {1204, 26926}, {1352, 45286}, {1370, 23293}, {1503, 16789}, {2781, 22109}, {3357, 48905}, {3917, 21213}, {5562, 15577}, {5576, 48901}, {5907, 20987}, {6697, 32393}, {7499, 21167}, {7503, 9969}, {7667, 50965}, {7689, 46264}, {9019, 19124}, {9715, 19149}, {9968, 38435}, {10516, 18494}, {10519, 18533}, {11414, 34778}, {11440, 14927}, {12225, 51756}, {12270, 52363}, {14790, 48873}, {15107, 51538}, {20806, 38444}, {23335, 48874}, {29317, 31723}, {34417, 37454}, {38321, 50977}, {41362, 48881}
X(54374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 3313}, {3, 19161, 5157}, {3098, 46728, 1350}, {7488, 41716, 206}, {11440, 41464, 14927}
X(54375) lies on these lines: {2, 3}, {51, 97}, {95, 107}, {110, 216}, {157, 35260}, {323, 30258}, {577, 5640}, {3066, 36748}, {3284, 15019}, {5158, 11422}, {6394, 26235}, {10545, 22052}, {10546, 10979}, {13450, 19179}, {18350, 46025}, {23181, 44180}, {23606, 34545}, {26898, 35264}, {26907, 31626}, {33926, 40680}, {34147, 46832}, {34828, 35283}, {35259, 36751}, {37081, 43651}, {44299, 53852}, {51444, 52153}
X(54375) = X(656)-isoconjugate of X(23232)
X(54375) = X(40596)-Dao conjugate of X(23232)
X(54375) = crossdifference of every pair of points on line {647, 42731}
X(54375) = barycentric quotient X(112)/X(23232)
X(54375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 37068, 26874}, {38431, 38432, 7527}
X(54376) lies on these lines: {3, 74}, {5, 43896}, {51, 125}, {66, 67}, {69, 40228}, {113, 7399}, {143, 23294}, {146, 6815}, {184, 15578}, {185, 15151}, {265, 14790}, {468, 34146}, {511, 46517}, {542, 7667}, {974, 10628}, {1205, 2854}, {1370, 3448}, {1899, 44439}, {1986, 3541}, {2393, 47278}, {2777, 3575}, {2979, 11898}, {3269, 35325}, {3357, 44080}, {3917, 24981}, {5157, 6593}, {5462, 38725}, {5576, 18874}, {5621, 13198}, {5622, 19504}, {5972, 7499}, {6000, 37931}, {6053, 11793}, {6101, 11457}, {6699, 25711}, {6723, 37454}, {6746, 20299}, {7505, 44544}, {7687, 16105}, {7728, 18420}, {7731, 46430}, {9140, 13201}, {9826, 15061}, {10113, 31723}, {10117, 21213}, {10264, 23335}, {10627, 34224}, {10721, 18494}, {10938, 35485}, {10990, 15105}, {11432, 19348}, {11557, 20397}, {12006, 43608}, {12058, 32263}, {12236, 20379}, {12244, 12292}, {12824, 15059}, {13289, 44679}, {13391, 25739}, {13630, 14389}, {13754, 47090}, {14708, 52262}, {14915, 47340}, {15081, 15465}, {16111, 44239}, {16223, 38729}, {16981, 31099}, {18435, 54013}, {19208, 54034}, {20126, 44441}, {26926, 32366}, {31152, 41716}, {32125, 32316}, {32226, 34468}, {33884, 39874}, {34783, 37645}, {37453, 41715}, {38356, 44467}, {41580, 52297}, {41671, 45311}
X(54376) = midpoint of X(i) and X(j) for these {i,j}: {7723, 10620}, {10990, 21650}, {12041, 15101}, {12244, 12292}, {12281, 17854}, {12825, 15054}
X(54376) = reflection of X(i) in X(j) for these {i,j}: {110, 13416}, {185, 15151}, {974, 20417}, {1112, 125}, {1986, 16270}, {6053, 11793}, {11557, 20397}, {12133, 15738}, {12236, 20379}, {13148, 974}, {13417, 11746}, {16105, 7687}, {25711, 6699}, {44573, 12041}
X(54376) = circumcircle-inverse of X(13171)
X(54376) = barycentric product X(11832)*X(14919)
X(54376) = barycentric quotient X(11832)/X(46106)
X(54376) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 110, 13171}, {74, 12281, 17854}, {125, 1112, 12099}, {125, 13417, 11746}, {5621, 17847, 13198}, {6241, 7998, 26864}, {11746, 13417, 1112}, {13171, 15106, 110}, {32616, 32617, 12174}
X(54377) lies on these lines: {1, 1404}, {6, 19}, {7, 17120}, {9, 604}, {33, 44085}, {37, 1388}, {44, 56}, {45, 1319}, {57, 88}, {374, 37566}, {572, 3612}, {610, 2347}, {612, 1397}, {978, 1400}, {1100, 38296}, {1399, 4290}, {1428, 4327}, {1429, 8545}, {1445, 7175}, {1449, 2171}, {1766, 5697}, {1788, 37654}, {1950, 16946}, {2099, 16666}, {2265, 8557}, {2267, 22061}, {2317, 3553}, {3589, 10401}, {3660, 22163}, {3697, 5783}, {3707, 3911}, {3758, 41245}, {3870, 4579}, {3943, 37738}, {4643, 43053}, {4700, 4848}, {4969, 41687}, {5069, 40590}, {5252, 17369}, {5933, 51170}, {6180, 28017}, {7397, 53020}, {9957, 54359}, {10106, 50115}, {10944, 17281}, {11509, 37503}, {17237, 31230}, {17330, 24914}, {19297, 34880}
X(54377) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3478}, {6332, 9088}
X(54377) = X(i)-Dao conjugate of X(j) for these (i,j): {32664, 3478}, {53838, 4391}
X(54377) = crossdifference of every pair of points on line {521, 4895}
X(54377) = barycentric product X(i)*X(j) for these {i,j}: {1, 3476}, {56, 4737}, {65, 4234}, {108, 9031}, {651, 47766}, {664, 48327}, {4551, 47845}
X(54377) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3478}, {3476, 75}, {4234, 314}, {4737, 3596}, {9031, 35518}, {47766, 4391}, {47845, 18155}, {48327, 522}
X(54377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2182, 2082}, {57, 16670, 1405}
X(54378) lies on these lines: {1, 6}, {2, 13}, {10, 1250}, {15, 21}, {18, 37162}, {61, 16865}, {62, 5047}, {202, 5284}, {377, 42086}, {396, 15670}, {404, 10646}, {406, 10642}, {442, 5318}, {443, 42120}, {451, 10633}, {452, 5334}, {474, 11481}, {475, 11476}, {993, 7051}, {1125, 19373}, {1276, 54296}, {2306, 3647}, {2475, 19106}, {2476, 16808}, {2478, 18581}, {4187, 23303}, {4189, 10645}, {4190, 42091}, {4193, 16967}, {4197, 16965}, {4208, 43465}, {5046, 16809}, {5084, 11489}, {5141, 42919}, {5154, 42914}, {5177, 42134}, {5187, 42111}, {5237, 17531}, {5248, 10638}, {5260, 7006}, {5277, 19780}, {5278, 40714}, {5321, 11113}, {5351, 17572}, {5352, 17574}, {6175, 36969}, {6675, 11542}, {6856, 42142}, {6857, 11488}, {6871, 42106}, {6872, 42085}, {6910, 42092}, {6933, 42114}, {7483, 23302}, {7504, 42915}, {8728, 42118}, {10654, 31156}, {11095, 32431}, {11097, 37508}, {11108, 11486}, {11111, 42119}, {11112, 42088}, {11114, 19107}, {11480, 16370}, {11485, 16418}, {15671, 16267}, {15672, 16962}, {15673, 42912}, {15674, 16960}, {15677, 36967}, {15680, 42099}, {15988, 51206}, {16408, 42115}, {16773, 17575}, {16842, 22238}, {16862, 36843}, {17525, 42942}, {17527, 42121}, {17528, 42127}, {17529, 42148}, {17530, 42110}, {17532, 42094}, {17536, 34755}, {17556, 42095}, {17561, 37640}, {17571, 42116}, {17579, 42100}, {19526, 22236}, {31295, 42113}, {37325, 54362}, {37375, 42918}, {37462, 42151}, {37675, 41406}, {42096, 50242}, {42097, 50239}, {42112, 50244}, {42117, 50241}, {42145, 50240}, {42155, 44217}
X(54378) = crossdifference of every pair of points on line {513, 6137}
X(54378) = {X(21),X(5362)}-harmonic conjugate of X(15)
X(54379) lies on these lines: {1, 6}, {2, 14}, {10, 10638}, {16, 21}, {17, 37162}, {61, 5047}, {62, 16865}, {203, 5284}, {377, 42085}, {395, 15670}, {404, 10645}, {406, 10641}, {442, 5321}, {443, 42119}, {451, 10632}, {452, 5335}, {474, 11480}, {475, 11475}, {993, 19373}, {1125, 7051}, {1250, 5248}, {1277, 54296}, {2475, 19107}, {2476, 16809}, {2478, 18582}, {3647, 33654}, {4187, 23302}, {4189, 10646}, {4190, 42090}, {4193, 16966}, {4197, 16964}, {4208, 43466}, {5046, 16808}, {5084, 11488}, {5141, 42918}, {5154, 42915}, {5177, 42133}, {5187, 42114}, {5238, 17531}, {5260, 7005}, {5277, 19781}, {5278, 40713}, {5318, 11113}, {5351, 17574}, {5352, 17572}, {6175, 36970}, {6675, 11543}, {6856, 42139}, {6857, 11489}, {6871, 42103}, {6872, 42086}, {6910, 42089}, {6933, 42111}, {7483, 23303}, {7504, 42914}, {8728, 42117}, {10653, 31156}, {11096, 32431}, {11098, 37508}, {11108, 11485}, {11111, 42120}, {11112, 42087}, {11114, 19106}, {11481, 16370}, {11486, 16418}, {15671, 16268}, {15672, 16963}, {15673, 42913}, {15674, 16961}, {15677, 36968}, {15680, 42100}, {15988, 51207}, {16408, 42116}, {16772, 17575}, {16842, 22236}, {16862, 36836}, {17525, 42943}, {17527, 42124}, {17528, 42126}, {17529, 42147}, {17530, 42107}, {17532, 42093}, {17536, 34754}, {17556, 42098}, {17561, 37641}, {17571, 42115}, {17579, 42099}, {19526, 22238}, {31295, 42112}, {37325, 54363}, {37375, 42919}, {37462, 42150}, {37675, 41407}, {42096, 50239}, {42097, 50242}, {42113, 50244}, {42118, 50241}, {42144, 50240}, {42154, 44217}
X(54379) = crossdifference of every pair of points on line {513, 6138}
X(54379) = {X(21),X(5367)}-harmonic conjugate of X(16)
X(54380) lies on these lines: {2, 3}, {112, 6033}, {113, 1560}, {114, 132}, {126, 133}, {127, 38553}, {232, 14356}, {265, 8791}, {325, 877}, {542, 6103}, {648, 6054}, {935, 38953}, {1503, 35912}, {1550, 34761}, {1990, 14995}, {3014, 47228}, {3564, 34211}, {5968, 6530}, {9214, 47172}, {10735, 38741}, {11059, 47392}, {13200, 38744}, {16092, 17986}, {16188, 18312}, {16316, 52472}, {16318, 34810}, {18809, 31655}, {23234, 52094}, {23347, 24975}, {23350, 53156}, {30786, 42308}, {31842, 50938}, {34334, 34336}, {34366, 47105}, {36875, 47155}, {41676, 51872}, {46986, 52464}, {47151, 52772}, {53149, 53266}
X(54380) = midpoint of X(4) and X(4235)
X(54380) = polar-circle-inverse of X(36166)
X(54380) = orthoptic-circle-of-the-Steiner-inellipse-inverse of X(7473)
X(54380) = X(i)-Ceva conjugate of X(j) for these (i,j): {47105, 542}, {47110, 511}
X(54380) = X(i)-isoconjugate of X(j) for these (i,j): {293, 842}, {656, 53691}, {35200, 53866}, {35909, 36084}, {35911, 36104}
X(54380) = X(i)-Dao conjugate of X(j) for these (i,j): {132, 842}, {133, 53866}, {23967, 287}, {38970, 14223}, {38987, 35909}, {39000, 35911}, {39073, 40080}, {40596, 53691}, {42426, 98}
X(54380) = crossdifference of every pair of points on line {248, 647}
X(54380) = barycentric product X(i)*X(j) for these {i,j}: {297, 542}, {325, 6103}, {877, 1640}, {2247, 40703}, {2799, 7473}, {2967, 46786}, {4230, 18312}, {5191, 44132}, {6333, 35907}, {14618, 42743}, {14999, 16230}, {15595, 47105}, {17986, 51389}, {36790, 52491}, {38552, 46787}
X(54380) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 53691}, {232, 842}, {297, 5641}, {542, 287}, {684, 35911}, {877, 6035}, {1640, 879}, {1990, 53866}, {2247, 293}, {2967, 46787}, {3569, 35909}, {4230, 5649}, {5191, 248}, {6041, 878}, {6103, 98}, {7473, 2966}, {9475, 40080}, {14999, 17932}, {16230, 14223}, {17994, 14998}, {34369, 47388}, {35907, 685}, {38552, 46786}, {42743, 4558}, {47105, 9476}, {47427, 40079}, {51334, 52492}, {51428, 51404}, {52491, 34536}
X(54380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 858, 1650}, {2, 4240, 468}, {114, 132, 2967}, {402, 5159, 2}, {427, 468, 35235}, {5000, 5001, 868}, {16188, 42426, 38552}
X(54381) lies on these lines: {2, 3}, {52, 23307}, {53, 136}, {125, 1205}, {126, 135}, {132, 47208}, {1112, 21850}, {1184, 13854}, {1503, 44080}, {1899, 8549}, {2892, 15106}, {3199, 15820}, {3580, 6403}, {3815, 11062}, {3867, 16776}, {5480, 44084}, {5523, 9465}, {7745, 52905}, {8262, 41585}, {8791, 8882}, {11188, 41584}, {12167, 26869}, {12294, 51360}, {13567, 47328}, {14389, 19128}, {14580, 27376}, {15131, 38851}, {15473, 23306}, {16178, 31655}, {16285, 19595}, {18911, 39588}, {19504, 25321}, {20300, 47296}, {20621, 45946}, {21243, 43130}, {23292, 44077}, {23315, 46682}, {30786, 32002}, {31383, 41602}, {32123, 40909}, {32125, 36990}, {34336, 34338}, {40130, 51434}, {42426, 47222}, {50938, 53832}
X(54381) = complement of X(26283)
X(54381) = polar-circle-inverse of X(37980)
X(54381) = polar conjugate of the isotomic conjugate of X(54347)
X(54381) = X(30251)-complementary conjugate of X(8062)
X(54381) = X(39382)-Ceva conjugate of X(523)
X(54381) = barycentric product X(4)*X(54347)
X(54381) = barycentric quotient X(54347)/X(69)
X(54381) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 24, 468}, {2, 858, 11585}, {2, 7401, 11284}, {2, 37977, 10018}, {2, 46336, 7393}, {4, 858, 427}, {4, 35480, 47309}, {25, 37981, 235}, {235, 427, 37981}, {427, 468, 5}, {427, 30739, 5094}, {468, 3575, 25}, {1368, 15809, 427}, {1368, 23335, 858}, {1594, 3147, 7405}, {1594, 7487, 235}, {1995, 16051, 37454}, {1995, 31099, 10297}, {4232, 5169, 403}, {5000, 5001, 15760}, {5159, 16238, 2}, {7576, 45179, 1596}, {12106, 13371, 5}, {15559, 52284, 427}, {34351, 37458, 24}
X(54382) lies on these lines: {1, 32}, {2, 39248}, {6, 19}, {9, 2295}, {10, 9596}, {31, 16968}, {36, 9619}, {37, 5250}, {39, 46}, {40, 2276}, {48, 23623}, {57, 893}, {63, 1107}, {77, 40765}, {78, 4386}, {87, 13610}, {169, 213}, {171, 3061}, {187, 3612}, {191, 31442}, {230, 11375}, {232, 1452}, {257, 14621}, {284, 39598}, {354, 16781}, {386, 5011}, {484, 1571}, {516, 9598}, {612, 20715}, {614, 20271}, {748, 21921}, {750, 39244}, {894, 21281}, {940, 2339}, {942, 16502}, {960, 5275}, {988, 36643}, {997, 5277}, {1015, 3338}, {1046, 21384}, {1100, 37549}, {1155, 5013}, {1159, 43136}, {1191, 3290}, {1210, 9599}, {1333, 54356}, {1400, 23544}, {1454, 43039}, {1468, 2170}, {1500, 5119}, {1573, 41229}, {1707, 21332}, {1722, 21951}, {1737, 2548}, {1766, 31785}, {1770, 2549}, {1788, 7736}, {1836, 5254}, {1837, 7745}, {1899, 41011}, {1905, 2207}, {1909, 52652}, {1965, 21608}, {2093, 9593}, {2176, 40131}, {2280, 2650}, {2646, 3053}, {3306, 16604}, {3340, 7296}, {3474, 7738}, {3485, 7735}, {3550, 39255}, {3579, 31448}, {3751, 3780}, {3752, 24590}, {3767, 12047}, {3772, 5244}, {3815, 24914}, {3868, 16973}, {3869, 5276}, {3915, 21808}, {3916, 31449}, {3924, 21764}, {3970, 37610}, {4000, 27000}, {4136, 4865}, {4252, 34522}, {4264, 5336}, {4275, 17443}, {4292, 9597}, {4295, 5286}, {4333, 7756}, {4338, 7765}, {4383, 16605}, {4426, 19860}, {4641, 4875}, {4644, 6604}, {5021, 43065}, {5023, 37600}, {5128, 9574}, {5228, 40133}, {5256, 18202}, {5280, 5903}, {5282, 10459}, {5283, 12514}, {5299, 5902}, {5305, 39542}, {5322, 21771}, {5332, 11529}, {5445, 31441}, {5475, 10826}, {5657, 31402}, {5697, 16785}, {6684, 31497}, {7737, 10572}, {7746, 37692}, {9331, 37563}, {9592, 15803}, {9605, 36279}, {9650, 10827}, {10039, 31409}, {11010, 31433}, {12526, 16517}, {13881, 17605}, {14974, 16601}, {16466, 16583}, {16552, 49500}, {16606, 27459}, {16716, 40153}, {16784, 18398}, {16974, 21331}, {17365, 30617}, {18907, 37730}, {21029, 33104}, {21387, 32913}, {21874, 37658}, {26066, 37661}, {26446, 31460}, {31422, 37572}, {31429, 54290}, {31459, 49226}, {31477, 37568}, {33950, 36404}, {37588, 51058}, {41826, 50011}
X(54382) = crossdifference of every pair of points on line {521, 1491}
X(54382) = barycentric product X(1)*X(26098)
X(54382) = barycentric quotient X(26098)/X(75)
X(54382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 17451, 16968}, {57, 9575, 2275}, {171, 3061, 54317}, {5280, 5903, 9620}
X(54383) lies on these lines: {1, 28287}, {2, 3786}, {6, 21}, {7, 8}, {20, 185}, {22, 40571}, {42, 63}, {72, 13725}, {78, 1400}, {81, 37090}, {141, 4197}, {145, 9052}, {159, 41739}, {182, 37106}, {209, 345}, {329, 37193}, {386, 10461}, {464, 16465}, {524, 17579}, {674, 51192}, {758, 24248}, {938, 41828}, {942, 37153}, {971, 9962}, {980, 50596}, {991, 18206}, {1010, 51223}, {1012, 1351}, {1210, 29965}, {1284, 12635}, {1350, 7411}, {1352, 6839}, {1423, 11523}, {1714, 35637}, {1812, 37538}, {1843, 4198}, {1992, 37516}, {2269, 7675}, {2287, 19310}, {2810, 9965}, {3056, 4313}, {3098, 37105}, {3218, 35980}, {3242, 9054}, {3564, 37468}, {3620, 4208}, {3781, 17316}, {3794, 37666}, {3876, 5296}, {3901, 32857}, {3940, 19266}, {4189, 5138}, {4292, 34379}, {4304, 51196}, {4335, 12526}, {4343, 5250}, {5032, 50742}, {5249, 31330}, {5480, 10883}, {5728, 37169}, {5751, 36706}, {5757, 13727}, {5767, 37088}, {5847, 25304}, {6007, 24280}, {6403, 37395}, {6646, 17676}, {6837, 14853}, {6884, 14561}, {6993, 40330}, {7102, 37181}, {9024, 9963}, {9047, 11015}, {10431, 51212}, {10444, 29311}, {10459, 11520}, {10519, 37112}, {12294, 37104}, {12649, 37191}, {14054, 37179}, {15988, 37228}, {16704, 50404}, {17153, 36500}, {17558, 51171}, {17576, 51170}, {17778, 37107}, {20080, 37435}, {20683, 27549}, {20835, 37492}, {21850, 37447}, {22277, 26115}, {24391, 30097}, {24473, 50428}, {25494, 32911}, {31670, 37433}, {31775, 34380}, {33088, 52025}, {33878, 37426}, {35628, 52020}, {36740, 37285}, {36741, 37300}, {37103, 37652}, {37109, 45990}, {37180, 45963}, {37467, 37676}, {44238, 48906}, {48013, 50481}
X(54383) = reflection of X(i) in X(j) for these {i,j}: {8, 3779}, {69, 4259}, {10477, 4260}
X(54383) = anticomplement of X(10477)
X(54383) = crossdifference of every pair of points on line {2451, 3063}
X(54383) = {X(4260),X(10477)}-harmonic conjugate of X(2)
X(54384) lies on these lines: {4, 70}, {6, 34436}, {22, 184}, {25, 15139}, {30, 52}, {51, 125}, {251, 10766}, {378, 389}, {542, 27365}, {568, 10605}, {973, 1595}, {974, 14677}, {1147, 44259}, {1181, 6243}, {1495, 41580}, {1539, 16194}, {1899, 3060}, {1994, 13198}, {2056, 35901}, {3051, 38356}, {3292, 44260}, {3313, 19127}, {3567, 26937}, {3629, 6467}, {3796, 18438}, {3845, 15738}, {3917, 6676}, {5133, 23330}, {5446, 31723}, {5562, 15760}, {5622, 53863}, {5889, 44440}, {5890, 35481}, {5891, 46029}, {5899, 43590}, {5943, 31236}, {5946, 44236}, {6000, 35480}, {6101, 25337}, {6152, 16659}, {6240, 41725}, {6247, 6746}, {6293, 12173}, {6403, 31383}, {6776, 20062}, {7502, 10625}, {9730, 18570}, {9967, 22352}, {10282, 37932}, {11002, 23291}, {11381, 11576}, {11402, 44439}, {11438, 44269}, {11550, 34146}, {12058, 51360}, {12162, 44263}, {12293, 34783}, {13366, 50649}, {13413, 14845}, {13564, 19362}, {13598, 52842}, {13851, 44288}, {15644, 44837}, {16226, 44218}, {16655, 44544}, {18445, 45780}, {19357, 37484}, {19467, 44831}, {20299, 43896}, {21213, 34117}, {21849, 31133}, {21851, 34417}, {23217, 52032}, {27372, 27375}, {32184, 43903}, {32285, 40949}, {34565, 51739}, {37969, 44110}, {41716, 43653}
X(54384) = midpoint of X(i) and X(j) for these {i,j}: {5889, 44440}, {6243, 12083}
X(54384) = reflection of X(i) in X(j) for these {i,j}: {378, 389}, {3313, 19127}, {5562, 15760}, {6101, 25337}, {10625, 7502}, {11550, 47328}, {12162, 44263}, {31133, 21849}, {31723, 5446}, {52842, 13598}
X(54384) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {185, 45186, 21659}, {1112, 13567, 51}, {6403, 41715, 31383}, {21213, 34117, 44078}, {34221, 34222, 20300}
X(54385) lies on these lines: {1, 19}, {2, 5227}, {6, 354}, {7, 18589}, {9, 1125}, {34, 2286}, {37, 56}, {57, 71}, {63, 86}, {65, 2256}, {154, 3745}, {169, 1449}, {219, 942}, {226, 1435}, {281, 1056}, {388, 1826}, {474, 3694}, {497, 1839}, {518, 965}, {573, 12704}, {579, 3338}, {604, 21808}, {612, 12329}, {894, 26106}, {936, 3949}, {940, 44101}, {966, 24477}, {968, 2352}, {997, 22021}, {999, 40937}, {1100, 2082}, {1108, 3304}, {1210, 26063}, {1445, 25523}, {1659, 6203}, {1723, 51816}, {1760, 17394}, {1761, 5250}, {1766, 3247}, {1901, 10404}, {1903, 8581}, {2002, 7190}, {2178, 26357}, {2242, 5336}, {2257, 54324}, {2261, 16193}, {2264, 17609}, {2287, 3873}, {2646, 7221}, {3213, 20613}, {3305, 17381}, {3306, 3692}, {3509, 29644}, {3553, 9310}, {3554, 17451}, {3601, 22054}, {3616, 5279}, {3870, 54316}, {3875, 24435}, {3945, 7289}, {4000, 24162}, {4298, 8804}, {4675, 28017}, {5045, 22153}, {5120, 16601}, {5221, 21866}, {5249, 28753}, {5252, 21933}, {5253, 27396}, {5275, 30677}, {5356, 16672}, {5437, 20106}, {5572, 5781}, {5712, 44103}, {5738, 9028}, {5747, 13407}, {5750, 17742}, {5776, 12675}, {6204, 6352}, {7079, 21620}, {7131, 41246}, {8666, 25081}, {9444, 21857}, {9578, 21011}, {11037, 27382}, {11518, 22356}, {15487, 44081}, {15934, 20818}, {16516, 20358}, {16566, 29597}, {17718, 46345}, {17754, 29642}, {18655, 24424}, {21049, 54008}, {24476, 51210}, {27059, 29585}, {28738, 31266}, {30456, 34046}, {32636, 37500}, {37080, 37504}, {37578, 54285}
X(54385) = crossdifference of every pair of points on line {656, 3309}
X(54385) = barycentric product X(i)*X(j) for these {i,j}: {1, 443}, {75, 44094}
X(54385) = barycentric quotient X(i)/X(j) for these {i,j}: {443, 75}, {44094, 1}
X(54385) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 2260, 1732}, {9, 3333, 2260}, {16777, 37519, 2646}
X(54386) lies on these lines: {1, 6}, {3, 1707}, {7, 24178}, {8, 989}, {10, 14555}, {31, 78}, {38, 3951}, {40, 43}, {42, 5250}, {46, 2390}, {56, 4641}, {57, 978}, {58, 997}, {63, 988}, {65, 1722}, {145, 42360}, {171, 936}, {191, 5313}, {200, 5255}, {210, 5710}, {329, 13161}, {377, 41011}, {386, 1245}, {387, 24210}, {443, 50307}, {519, 42032}, {579, 23620}, {580, 6261}, {595, 3749}, {602, 18446}, {612, 3876}, {614, 3868}, {651, 4320}, {748, 2650}, {896, 4652}, {908, 5230}, {920, 46016}, {940, 25917}, {942, 5272}, {946, 33137}, {959, 2285}, {968, 19767}, {975, 10176}, {976, 3984}, {979, 43070}, {986, 2999}, {990, 31803}, {1036, 7085}, {1039, 44086}, {1040, 1858}, {1042, 1445}, {1043, 4676}, {1183, 37399}, {1201, 32912}, {1210, 27411}, {1265, 51192}, {1468, 19861}, {1469, 29958}, {1490, 37570}, {1580, 8235}, {1610, 2261}, {1685, 6213}, {1686, 6212}, {1697, 20683}, {1698, 5743}, {1699, 5799}, {1706, 6048}, {1708, 10571}, {1714, 12047}, {1716, 4260}, {1721, 12688}, {1738, 4295}, {1742, 37551}, {1798, 17104}, {1834, 24703}, {1999, 19582}, {2082, 37657}, {2093, 24440}, {2292, 5256}, {3008, 3671}, {3072, 5720}, {3073, 37531}, {3185, 54300}, {3187, 25253}, {3293, 5119}, {3306, 27627}, {3333, 21214}, {3338, 49997}, {3339, 23511}, {3556, 36741}, {3576, 13323}, {3601, 54354}, {3612, 52680}, {3624, 6703}, {3646, 26102}, {3649, 24789}, {3679, 5835}, {3683, 19765}, {3685, 20018}, {3702, 17156}, {3710, 33088}, {3812, 37679}, {3869, 32911}, {3870, 3915}, {3873, 28011}, {3913, 4849}, {3914, 11415}, {3916, 16570}, {3927, 37592}, {3940, 5266}, {3962, 37549}, {4101, 33171}, {4134, 30145}, {4255, 4640}, {4259, 42450}, {4281, 17185}, {4292, 24695}, {4339, 20007}, {4384, 49598}, {4512, 37573}, {4650, 15803}, {4850, 11684}, {4855, 36277}, {5044, 5268}, {5082, 49772}, {5221, 16610}, {5269, 5293}, {5271, 41249}, {5292, 21616}, {5398, 45770}, {5438, 5529}, {5705, 17717}, {5887, 36754}, {5903, 44545}, {5905, 23536}, {6001, 36745}, {6765, 37588}, {6996, 12544}, {7262, 31424}, {7308, 45897}, {7713, 10974}, {7957, 12652}, {8227, 33140}, {8580, 8951}, {8583, 23151}, {9369, 20037}, {9441, 12565}, {9534, 50314}, {9612, 33096}, {9614, 33141}, {10899, 15932}, {11036, 16020}, {11269, 41012}, {11375, 35466}, {11520, 28082}, {11682, 49487}, {12520, 13329}, {12559, 30117}, {12709, 52424}, {13425, 49592}, {13458, 49593}, {15556, 34036}, {16778, 19762}, {16824, 17349}, {17127, 34772}, {17350, 20036}, {17596, 54290}, {17781, 48818}, {19766, 50290}, {19860, 25885}, {22836, 37817}, {24391, 36574}, {24914, 37663}, {24954, 37634}, {25079, 30567}, {25681, 37646}, {26066, 37662}, {27003, 27625}, {27131, 54355}, {27538, 41261}, {28629, 37650}, {30323, 49494}, {31165, 37614}, {34040, 41539}, {35672, 41422}, {37550, 37694}, {39585, 41234}, {39954, 51223}, {46190, 54352}, {50576, 50617}
X(54386) = reflection of X(1) in X(1191)
X(54386) = X(i)-Ceva conjugate of X(j) for these (i,j): {959, 1}, {2285, 17594}
X(54386) = X(514)-isoconjugate of X(28477)
X(54386) = barycentric product X(i)*X(j) for these {i,j}: {100, 28478}, {941, 39773}
X(54386) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 28477}, {28478, 693}, {39773, 34284}
X(54386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1203, 16475}, {1, 1743, 5247}, {1, 3973, 5234}, {1, 5904, 16496}, {1, 16468, 1453}, {1, 16469, 16478}, {6, 960, 1}, {31, 78, 37552}, {57, 978, 11512}, {63, 1193, 988}, {65, 4383, 1722}, {72, 16466, 1}, {386, 12514, 17594}, {595, 3811, 3749}, {978, 1046, 57}, {1104, 12635, 1}, {1203, 5692, 1}, {1616, 34791, 1}, {1695, 2944, 40}, {1714, 12047, 17064}, {2999, 12526, 986}, {3216, 49500, 46}, {3339, 23511, 24174}, {3555, 16483, 1}, {5044, 5711, 5268}, {5315, 5904, 1}, {5529, 37603, 5438}, {7290, 11523, 1}, {12688, 37537, 1721}, {21214, 32913, 3333}
X(54387) lies on these lines: {1, 3}, {21, 44}, {45, 78}, {89, 17548}, {551, 40688}, {678, 10459}, {1104, 17012}, {1125, 51671}, {1193, 3246}, {3616, 17382}, {3617, 33113}, {4005, 51297}, {4256, 16610}, {4304, 5718}, {4641, 16370}, {4652, 54281}, {4653, 5440}, {4670, 16393}, {4870, 33095}, {5165, 16666}, {5260, 54309}, {5530, 10543}, {5703, 50065}, {13411, 37691}, {17677, 30823}, {19862, 48843}, {27751, 52246}, {30115, 33595}, {32774, 46934}, {37716, 52638}, {39595, 49739}
X(54387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3, 37520}, {1, 17601, 65}, {1, 37574, 17601}, {1, 37599, 3999}, {2646, 37573, 37548}, {3601, 19765, 37539}, {4653, 5440, 44307}
X(54388) lies on these lines: {1, 20594}, {3, 6}, {5, 53423}, {10, 98}, {41, 43}, {74, 30554}, {83, 2051}, {111, 28564}, {165, 40749}, {181, 10799}, {205, 4239}, {213, 893}, {501, 5213}, {604, 37608}, {699, 28469}, {727, 6010}, {729, 1293}, {733, 28486}, {1078, 14829}, {1174, 53005}, {1213, 50418}, {1385, 17448}, {1682, 12835}, {1695, 10789}, {1764, 25059}, {1790, 19308}, {1973, 4231}, {2174, 21857}, {2175, 23863}, {2238, 9840}, {2268, 37574}, {2304, 2319}, {2317, 22066}, {2323, 22065}, {2328, 16372}, {2330, 18758}, {2360, 19329}, {2388, 15621}, {2698, 2702}, {2705, 5970}, {3029, 12176}, {3031, 12192}, {3032, 12199}, {3203, 9562}, {3509, 22061}, {3651, 47641}, {3687, 20769}, {4027, 34454}, {4653, 15981}, {5182, 21937}, {5277, 19522}, {6685, 7413}, {7787, 9535}, {7793, 37683}, {8715, 32468}, {9310, 37675}, {9553, 10797}, {9554, 10798}, {9956, 25629}, {9959, 21879}, {10359, 36697}, {10791, 50037}, {10796, 49129}, {12195, 44039}, {12203, 13727}, {13193, 34453}, {13194, 34458}, {14880, 36477}, {16589, 48894}, {18904, 31394}, {19514, 24512}, {20777, 26890}, {21753, 50423}, {22267, 39141}, {22366, 41255}, {22449, 26889}, {24309, 32462}, {26243, 52134}, {28246, 33138}, {28841, 53900}
X(54388) = crossdifference of every pair of points on line {523, 20508}
X(54388) = barycentric product X(1)*X(11688)
X(54388) = barycentric quotient X(11688)/X(75)
X(54388) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {371, 372, 5145}, {970, 3398, 4279}, {1342, 1343, 572}, {1683, 1684, 573}, {1687, 1688, 58}, {1691, 2092, 4279}, {36759, 36760, 34476}
X(54389) lies on these lines: {1, 2325}, {2, 45}, {4, 9}, {6, 145}, {7, 3834}, {8, 44}, {31, 3974}, {37, 2275}, {69, 17230}, {75, 26685}, {101, 53904}, {141, 144}, {142, 7222}, {192, 3618}, {193, 17233}, {198, 36510}, {220, 5782}, {239, 50107}, {312, 26065}, {320, 17342}, {329, 32777}, {344, 894}, {345, 27064}, {374, 5836}, {390, 49524}, {391, 594}, {497, 16561}, {519, 4873}, {524, 17269}, {527, 17284}, {536, 5222}, {551, 36911}, {597, 17014}, {672, 30942}, {996, 1000}, {997, 36916}, {1018, 4266}, {1100, 20057}, {1125, 16676}, {1213, 46932}, {1215, 25375}, {1219, 1616}, {1265, 4195}, {1266, 3729}, {1376, 1633}, {1441, 28966}, {1449, 3635}, {1575, 36222}, {1731, 5082}, {1732, 24477}, {1743, 2321}, {1897, 40138}, {1978, 44152}, {1992, 6542}, {1999, 42032}, {2161, 3434}, {2173, 24850}, {2178, 38869}, {2182, 30618}, {2245, 27040}, {2265, 24247}, {2267, 2329}, {2295, 27523}, {2999, 42049}, {3008, 4659}, {3052, 7172}, {3061, 21801}, {3210, 46907}, {3217, 54316}, {3241, 4908}, {3247, 3636}, {3285, 17539}, {3589, 3672}, {3617, 17330}, {3619, 6646}, {3620, 17285}, {3621, 4969}, {3622, 16672}, {3623, 50113}, {3624, 3731}, {3629, 17309}, {3661, 54280}, {3679, 3707}, {3685, 36404}, {3686, 3973}, {3710, 5716}, {3739, 7229}, {3751, 49763}, {3758, 17264}, {3763, 17334}, {3770, 29542}, {3790, 51192}, {3871, 37503}, {3912, 4644}, {3932, 4307}, {3945, 17243}, {3948, 41316}, {3986, 19878}, {4007, 4701}, {4011, 26105}, {4034, 4058}, {4069, 41276}, {4072, 4856}, {4081, 28124}, {4082, 5269}, {4188, 19297}, {4357, 25728}, {4360, 51171}, {4361, 4461}, {4371, 4431}, {4402, 4686}, {4416, 17286}, {4418, 26040}, {4429, 24280}, {4432, 36479}, {4439, 50300}, {4452, 17366}, {4480, 17274}, {4488, 17276}, {4512, 53663}, {4641, 34255}, {4643, 6172}, {4664, 26626}, {4667, 29573}, {4670, 5308}, {4671, 24597}, {4675, 29627}, {4687, 49514}, {4693, 50282}, {4702, 47359}, {4727, 20050}, {4740, 29590}, {4741, 21356}, {4747, 17392}, {4748, 17308}, {4754, 27253}, {4755, 4798}, {4869, 17267}, {4871, 17754}, {4896, 41141}, {4942, 17061}, {4982, 51093}, {5218, 14439}, {5225, 36568}, {5232, 17293}, {5263, 27549}, {5273, 44417}, {5296, 16814}, {5325, 18229}, {5712, 17776}, {5744, 30818}, {5772, 52653}, {5905, 33157}, {6541, 50284}, {6666, 25590}, {6687, 52709}, {7046, 8750}, {7227, 17259}, {7228, 17265}, {7232, 20059}, {7277, 17311}, {7288, 25591}, {7321, 17341}, {7397, 29069}, {7735, 37764}, {8557, 26015}, {8609, 26690}, {9780, 24723}, {9791, 26083}, {10436, 25101}, {10589, 33119}, {11008, 17373}, {14039, 30108}, {14543, 24335}, {14953, 30906}, {15254, 39581}, {15492, 17275}, {16020, 49483}, {16086, 48817}, {16669, 17299}, {16675, 17398}, {16720, 27472}, {16989, 33889}, {17054, 37024}, {17116, 17338}, {17118, 17337}, {17119, 24599}, {17120, 17242}, {17132, 31191}, {17229, 32099}, {17231, 21296}, {17232, 31300}, {17246, 47355}, {17250, 17257}, {17254, 29613}, {17255, 34573}, {17258, 17371}, {17261, 17321}, {17266, 50128}, {17268, 17364}, {17277, 20181}, {17278, 31995}, {17292, 17333}, {17295, 20080}, {17302, 25269}, {17323, 51126}, {17348, 32087}, {17349, 42696}, {17362, 20052}, {17367, 50101}, {17377, 51170}, {17378, 29583}, {17395, 47352}, {17484, 30991}, {17756, 53340}, {17790, 28809}, {19822, 27065}, {19867, 51665}, {19998, 37657}, {20078, 33172}, {20106, 28609}, {20471, 38871}, {20927, 26665}, {21076, 21712}, {21689, 27708}, {24248, 33159}, {24331, 38025}, {24411, 40869}, {24485, 36801}, {24695, 29674}, {24817, 36473}, {24821, 29660}, {24864, 53582}, {25243, 26668}, {25734, 54311}, {26098, 33164}, {26244, 42316}, {26799, 27136}, {27013, 53376}, {27058, 27514}, {27334, 28778}, {27382, 46830}, {27508, 34524}, {28739, 41804}, {29585, 46922}, {29679, 44447}, {29713, 34283}, {29834, 32925}, {29860, 33144}, {31018, 32779}, {32034, 33198}, {32847, 50303}, {32938, 33171}, {32941, 49701}, {33068, 44446}, {37640, 37795}, {37641, 37794}, {40859, 48869}, {40940, 42047}, {41241, 50105}, {45789, 48632}, {48864, 52963}, {49458, 49713}, {49462, 49531}, {49491, 51058}, {49688, 49699}, {49712, 50316}, {49756, 50289}, {49768, 51099}, {49770, 50089}, {49772, 50126}, {50019, 50100}
X(54389) = midpoint of X(4873) and X(16670)
X(54389) = reflection of X(i) in X(j) for these {i,j}: {4346, 17290}, {29616, 17269}
X(54389) = complement of X(4346)
X(54389) = anticomplement of X(17290)
X(54389) = X(i)-isoconjugate of X(j) for these (i,j): {57, 3478}, {905, 9088}
X(54389) = X(i)-Dao conjugate of X(j) for these (i,j): {5452, 3478}, {53838, 514}
X(54389) = trilinear pole of line {47766, 48327}
X(54389) = crossdifference of every pair of points on line {1459, 1960}
X(54389) = barycentric product X(i)*X(j) for these {i,j}: {1, 4737}, {8, 3476}, {10, 4234}, {190, 47766}, {668, 48327}, {1897, 9031}, {3952, 47845}
X(54389) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 3478}, {3476, 7}, {4234, 86}, {4737, 75}, {8750, 9088}, {9031, 4025}, {47766, 514}, {47845, 7192}, {48327, 513}
X(54389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 190, 4419}, {2, 4346, 17290}, {2, 4389, 26104}, {2, 4454, 1086}, {2, 17369, 26039}, {2, 20073, 4389}, {6, 346, 17314}, {6, 3943, 145}, {6, 17340, 346}, {7, 17279, 53665}, {8, 44, 37654}, {9, 2345, 966}, {9, 3501, 2183}, {9, 17355, 2345}, {44, 17281, 8}, {45, 17369, 2}, {75, 26685, 37650}, {145, 346, 3943}, {145, 3943, 17314}, {190, 4389, 20073}, {190, 17305, 49748}, {190, 17354, 2}, {312, 26065, 37642}, {320, 17342, 29579}, {344, 894, 4648}, {594, 16885, 391}, {597, 17318, 17014}, {894, 17339, 344}, {1086, 49721, 4454}, {1743, 2321, 5839}, {1743, 3632, 4700}, {2321, 4700, 3632}, {2325, 50115, 1}, {3008, 50118, 4659}, {3161, 5749, 37}, {3589, 17262, 3672}, {3632, 4700, 5839}, {3729, 17353, 4000}, {3758, 17264, 17316}, {3912, 50127, 4644}, {4363, 4422, 2}, {4370, 17369, 45}, {4389, 20073, 4419}, {4419, 26104, 4389}, {4422, 49726, 4363}, {4432, 36479, 47357}, {4432, 50313, 36479}, {4461, 37681, 4361}, {4480, 29596, 17274}, {4643, 17359, 29611}, {4670, 41313, 5308}, {4675, 41310, 29627}, {4727, 50131, 20050}, {4741, 29587, 21356}, {4747, 29621, 17392}, {4969, 50087, 3621}, {5296, 19877, 52706}, {6172, 29611, 4643}, {6646, 17358, 3619}, {7229, 18230, 3739}, {16814, 17303, 5296}, {17230, 17350, 20072}, {17230, 20072, 69}, {17261, 17368, 17321}, {17267, 17365, 4869}, {17279, 17351, 7}, {17280, 17350, 69}, {17280, 20072, 17230}, {17285, 17347, 3620}, {17289, 17336, 17257}, {17293, 17332, 5232}, {17303, 52706, 19877}, {17308, 50093, 4748}, {17776, 26223, 5712}, {29627, 35578, 4675}, {32930, 33163, 497}
X(54390) lies on these lines: {1, 2}, {6, 31197}, {9, 16610}, {38, 30393}, {44, 57}, {45, 3752}, {63, 88}, {77, 31188}, {165, 748}, {210, 5573}, {223, 31231}, {244, 5223}, {269, 3911}, {329, 4887}, {678, 9350}, {750, 16469}, {908, 4859}, {988, 21496}, {1086, 31142}, {1155, 15601}, {1279, 46917}, {1376, 3246}, {1453, 16408}, {1743, 3306}, {2297, 17352}, {2975, 45047}, {3218, 3973}, {3452, 17067}, {3579, 19517}, {3666, 16676}, {3677, 3740}, {3689, 35227}, {3729, 24620}, {3731, 4850}, {3772, 20196}, {3868, 8951}, {3875, 30829}, {3886, 25531}, {4000, 5316}, {4328, 5219}, {4346, 18228}, {4358, 17151}, {4383, 5437}, {4413, 7290}, {4512, 17123}, {4695, 9819}, {4849, 44841}, {4862, 31018}, {4896, 9776}, {4900, 17460}, {4902, 17484}, {5055, 18506}, {5204, 37269}, {5233, 17282}, {5241, 17306}, {5400, 5732}, {5718, 20195}, {8167, 37553}, {8616, 9324}, {10388, 52429}, {10434, 27639}, {10980, 54352}, {12526, 24174}, {16421, 37609}, {16435, 35242}, {16666, 37674}, {16667, 37633}, {16736, 18198}, {16753, 18186}, {16862, 37554}, {17063, 49712}, {17117, 30861}, {17160, 18743}, {17277, 31233}, {17349, 31228}, {17490, 30568}, {17721, 38200}, {21363, 28280}, {21514, 37599}, {21519, 37552}, {21526, 37589}, {21896, 37556}, {24589, 25590}, {24594, 41241}, {24789, 30827}, {25525, 37663}, {25734, 30579}, {26724, 30852}, {28609, 40688}, {31190, 35466}, {36636, 43044}, {37662, 41867}
X(54390) = barycentric product X(75)*X(16486)
X(54390) = barycentric quotient X(16486)/X(1)
X(54390) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2999, 17022}, {2, 17020, 5287}, {2, 23511, 2999}, {3306, 37680, 1743}, {4383, 37520, 16670}, {4384, 16831, 16829}, {5256, 17021, 1}, {5272, 16569, 200}, {5287, 17013, 1}, {5437, 16670, 37520}, {16602, 37679, 57}, {17278, 51415, 5219}
X(54391) lies on these lines: {1, 21}, {2, 495}, {3, 145}, {4, 10529}, {5, 20060}, {8, 56}, {10, 5253}, {11, 529}, {12, 7504}, {20, 22770}, {22, 19993}, {28, 35058}, {30, 149}, {35, 3244}, {36, 100}, {40, 3885}, {42, 37617}, {44, 5548}, {46, 14923}, {55, 3241}, {57, 3872}, {59, 518}, {65, 4861}, {72, 17624}, {75, 1014}, {78, 1420}, {88, 1739}, {92, 17519}, {101, 45751}, {104, 517}, {105, 666}, {106, 24625}, {108, 5081}, {144, 42884}, {153, 1532}, {165, 3895}, {171, 54310}, {172, 17448}, {190, 15571}, {200, 13462}, {238, 1149}, {239, 11349}, {346, 5120}, {355, 6915}, {376, 20075}, {377, 3600}, {385, 9263}, {388, 2476}, {392, 3219}, {405, 3622}, {411, 944}, {474, 3617}, {484, 2802}, {496, 5046}, {497, 11114}, {499, 11681}, {515, 13279}, {523, 1325}, {527, 51423}, {528, 15326}, {535, 3583}, {550, 20066}, {551, 5251}, {631, 10528}, {644, 672}, {651, 1457}, {759, 39697}, {859, 16704}, {908, 44675}, {912, 12776}, {932, 2382}, {934, 2751}, {952, 6905}, {958, 3304}, {960, 20323}, {961, 4968}, {962, 12114}, {978, 32577}, {982, 49487}, {995, 32911}, {997, 3681}, {1001, 6172}, {1005, 3488}, {1006, 4430}, {1010, 27163}, {1012, 9965}, {1015, 5291}, {1018, 5030}, {1042, 9363}, {1043, 29766}, {1054, 4695}, {1055, 3684}, {1058, 6872}, {1100, 38871}, {1108, 5279}, {1125, 5258}, {1155, 3880}, {1201, 5247}, {1259, 6049}, {1260, 37313}, {1280, 2224}, {1317, 4996}, {1318, 3257}, {1385, 3555}, {1387, 17484}, {1388, 12635}, {1398, 4200}, {1444, 4360}, {1447, 30806}, {1455, 4318}, {1475, 2329}, {1478, 11680}, {1482, 6906}, {1573, 37675}, {1617, 37300}, {1633, 49709}, {1697, 4652}, {1727, 12758}, {1737, 5176}, {1743, 38869}, {1757, 47623}, {1770, 49600}, {1778, 16685}, {1791, 5262}, {1817, 3187}, {1897, 37305}, {1999, 37620}, {2077, 13278}, {2170, 3509}, {2178, 5839}, {2217, 34860}, {2218, 39702}, {2238, 9259}, {2242, 5276}, {2251, 50028}, {2320, 2346}, {2352, 49687}, {2475, 18990}, {2478, 14986}, {2646, 34791}, {2886, 5434}, {3035, 5298}, {3058, 15678}, {3086, 3436}, {3243, 13384}, {3245, 41702}, {3294, 9327}, {3295, 3623}, {3303, 17574}, {3306, 9623}, {3315, 4694}, {3333, 19860}, {3337, 3754}, {3361, 4853}, {3419, 35990}, {3428, 5731}, {3434, 4293}, {3478, 9309}, {3485, 18967}, {3486, 10966}, {3552, 54098}, {3560, 10595}, {3576, 3870}, {3582, 3814}, {3585, 24387}, {3621, 4188}, {3624, 17546}, {3632, 25440}, {3633, 7280}, {3635, 3746}, {3636, 5259}, {3651, 34773}, {3666, 17015}, {3670, 15955}, {3678, 51714}, {3679, 36006}, {3680, 5128}, {3683, 10179}, {3685, 4742}, {3701, 9369}, {3753, 27003}, {3780, 21008}, {3811, 37618}, {3813, 7354}, {3816, 34606}, {3876, 19861}, {3902, 32932}, {3911, 5193}, {3913, 5204}, {3916, 9957}, {3924, 3976}, {3928, 7962}, {3935, 4881}, {3940, 4661}, {3951, 15829}, {3957, 24929}, {4018, 10222}, {4084, 11009}, {4190, 5082}, {4191, 20012}, {4197, 19843}, {4203, 10453}, {4210, 20011}, {4216, 20037}, {4220, 29840}, {4221, 17147}, {4225, 20040}, {4245, 19742}, {4252, 37542}, {4257, 37610}, {4265, 51147}, {4297, 11015}, {4302, 34611}, {4315, 4847}, {4321, 10861}, {4342, 34646}, {4345, 28610}, {4359, 16821}, {4390, 17754}, {4393, 21511}, {4413, 40726}, {4428, 8162}, {4434, 9457}, {4513, 5022}, {4585, 34230}, {4586, 35167}, {4640, 5919}, {4678, 9709}, {4720, 13588}, {4723, 5205}, {4855, 6765}, {4867, 51506}, {4880, 10058}, {4969, 19297}, {4975, 47626}, {4999, 15888}, {5010, 25439}, {5044, 15179}, {5048, 44663}, {5049, 29817}, {5051, 5484}, {5057, 30384}, {5084, 10586}, {5086, 10916}, {5096, 9053}, {5124, 17388}, {5131, 5541}, {5141, 9654}, {5178, 17647}, {5180, 17768}, {5187, 47743}, {5211, 33849}, {5218, 11239}, {5223, 53058}, {5261, 6933}, {5263, 51669}, {5264, 50637}, {5265, 6921}, {5270, 25639}, {5372, 5774}, {5432, 34749}, {5433, 12607}, {5450, 7982}, {5525, 24036}, {5529, 21805}, {5535, 6264}, {5550, 17534}, {5552, 7288}, {5584, 9797}, {5603, 5905}, {5657, 10269}, {5690, 6940}, {5698, 42886}, {5725, 29680}, {5727, 34716}, {5734, 11496}, {5790, 6946}, {5836, 32636}, {5841, 37726}, {5854, 17100}, {5882, 11012}, {5884, 11014}, {5886, 31053}, {5901, 6920}, {5903, 22837}, {5904, 30144}, {6001, 13243}, {6079, 8686}, {6224, 22560}, {6360, 36029}, {6542, 21495}, {6550, 13266}, {6645, 17686}, {6647, 9317}, {6690, 31157}, {6691, 21031}, {6734, 10106}, {6767, 16370}, {6824, 10597}, {6825, 10530}, {6828, 10532}, {6857, 10587}, {6868, 10806}, {6875, 16202}, {6876, 35252}, {6914, 10247}, {6924, 12645}, {6930, 10596}, {6932, 12115}, {6943, 10785}, {6949, 10942}, {6950, 10679}, {7176, 20880}, {7269, 54344}, {7270, 19850}, {7437, 47043}, {7447, 14260}, {7451, 36944}, {7465, 29832}, {7485, 20020}, {7489, 10283}, {7491, 32214}, {7548, 26470}, {7580, 30283}, {7688, 51705}, {7718, 22479}, {7762, 20102}, {7951, 34690}, {8025, 19259}, {8158, 20070}, {8192, 11337}, {8543, 42842}, {8583, 30393}, {8692, 41436}, {9037, 10755}, {9310, 21384}, {9312, 38859}, {9318, 35102}, {9352, 54286}, {9668, 34740}, {9710, 26060}, {9780, 17535}, {9960, 12687}, {9961, 10085}, {9963, 21578}, {10090, 12531}, {10449, 35999}, {10459, 37607}, {10538, 14198}, {10572, 49627}, {10609, 36003}, {10698, 14988}, {10902, 13607}, {10912, 37567}, {10914, 37582}, {11036, 37228}, {11108, 46934}, {11112, 33110}, {11115, 26819}, {11235, 12943}, {11343, 17014}, {11350, 20043}, {11362, 37561}, {11415, 22760}, {11491, 26286}, {11604, 33961}, {11813, 16173}, {12005, 20612}, {12029, 53625}, {12127, 16192}, {12527, 41012}, {12532, 12740}, {12543, 14450}, {12629, 15803}, {12690, 28186}, {12702, 37403}, {12746, 32844}, {13589, 20042}, {13738, 20036}, {13996, 32426}, {15170, 15677}, {15171, 15680}, {15185, 30284}, {15287, 37681}, {15383, 47622}, {15507, 20072}, {15733, 18450}, {15808, 25542}, {15934, 37306}, {16049, 20222}, {16061, 26759}, {16212, 22755}, {16367, 29585}, {16371, 31145}, {16408, 46933}, {16451, 20018}, {16465, 18444}, {16483, 17127}, {16499, 30116}, {16693, 53268}, {16862, 46932}, {16863, 46931}, {16864, 46930}, {17016, 37592}, {17024, 37325}, {17074, 24806}, {17152, 17206}, {17230, 21540}, {17314, 36743}, {17349, 19291}, {17362, 21773}, {17364, 31394}, {17474, 41239}, {17480, 37231}, {17483, 39542}, {17547, 25055}, {17551, 19858}, {17614, 34790}, {17681, 26964}, {17683, 27304}, {17734, 24222}, {17742, 26690}, {17798, 50015}, {18042, 41610}, {18047, 37686}, {18391, 22767}, {18398, 30147}, {18481, 33557}, {18491, 34627}, {19065, 44607}, {19066, 44606}, {19245, 37652}, {19258, 31017}, {19260, 37685}, {19308, 20016}, {19314, 39587}, {19537, 20054}, {19704, 51092}, {19789, 37241}, {20007, 37282}, {20013, 37301}, {20014, 37307}, {20015, 37309}, {20017, 37312}, {20045, 37449}, {20085, 28224}, {20095, 36004}, {20101, 37331}, {20347, 24203}, {20999, 37311}, {21010, 36534}, {21161, 50824}, {21222, 53286}, {21477, 29616}, {21620, 24541}, {21669, 22791}, {21842, 22836}, {22769, 51192}, {23361, 23391}, {23858, 30577}, {23958, 36279}, {23961, 34474}, {24391, 37583}, {24473, 50194}, {24558, 25875}, {24599, 37272}, {24602, 49774}, {24841, 53302}, {24914, 32049}, {24927, 31837}, {25416, 35000}, {25466, 31254}, {26088, 26202}, {26140, 51384}, {26877, 37562}, {26878, 31838}, {27086, 41345}, {27368, 35991}, {28174, 51529}, {28190, 38631}, {28236, 44425}, {28376, 42461}, {28377, 32843}, {28797, 41245}, {28813, 43053}, {29662, 37716}, {29824, 35992}, {30143, 50190}, {30305, 44447}, {30392, 52769}, {31159, 34637}, {31393, 35258}, {33129, 50759}, {33812, 35204}, {33950, 40133}, {33956, 36920}, {34631, 44455}, {34880, 41687}, {35238, 50810}, {35984, 48847}, {36001, 46636}, {36090, 36100}, {37251, 37705}, {37254, 39567}, {37564, 37734}, {37919, 54081}, {38570, 47274}, {38901, 40293}, {40910, 49771}, {41555, 45043}, {49712, 52923}, {50608, 54331}, {51816, 54318}
X(54391) = midpoint of X(i) and X(j) for these {i,j}: {149, 20067}, {3218, 38460}, {3245, 41702}, {5535, 6264}
X(54391) = reflection of X(i) in X(j) for these {i,j}: {8, 40663}, {100, 36}, {153, 1532}, {484, 4973}, {908, 44675}, {1320, 38460}, {3935, 5440}, {4511, 1319}, {5057, 30384}, {5080, 11}, {5176, 1737}, {5440, 5126}, {6163, 238}, {6735, 3911}, {6905, 22765}, {6909, 104}, {11684, 1749}, {12531, 41684}, {17484, 51409}, {17757, 15325}, {35000, 38602}, {36001, 46636}, {45043, 41555}, {51409, 1387}
X(54391) = anticomplement of X(17757)
X(54391) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {58, 153}, {104, 1330}, {909, 2895}, {1412, 36918}, {1795, 52364}, {2401, 21294}, {2423, 21221}, {14578, 3151}, {34051, 2893}, {34234, 21287}, {34858, 1654}
X(54391) = X(9268)-Ceva conjugate of X(100)
X(54391) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14554}, {649, 50039}
X(54391) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 14554}, {1769, 35015}, {5375, 50039}, {34590, 523}
X(54391) = cevapoint of X(517) and X(49997)
X(54391) = trilinear pole of line {21786, 21894}
X(54391) = crossdifference of every pair of points on line {661, 2092}
X(54391) = barycentric product X(i)*X(j) for these {i,j}: {75, 5053}, {99, 21894}, {100, 21222}, {668, 21786}, {4554, 53286}, {5376, 34590}, {6335, 23087}
X(54391) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14554}, {100, 50039}, {5053, 1}, {21222, 693}, {21786, 513}, {21894, 523}, {23087, 905}, {53286, 650}
X(54391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63, 3877}, {1, 191, 3884}, {1, 993, 1621}, {1, 2975, 21}, {1, 3869, 5330}, {1, 3874, 34195}, {1, 5429, 17469}, {1, 6763, 3878}, {1, 8666, 2975}, {1, 12514, 3890}, {1, 51111, 51683}, {1, 52680, 40091}, {3, 145, 3871}, {8, 56, 404}, {10, 5253, 17531}, {10, 5563, 5253}, {11, 5080, 37375}, {36, 100, 13587}, {40, 36846, 3885}, {56, 12513, 8}, {65, 11260, 4861}, {200, 13462, 35262}, {388, 10527, 2476}, {405, 7373, 3622}, {551, 5251, 5284}, {944, 11249, 411}, {956, 999, 2}, {958, 3304, 3616}, {958, 3616, 5047}, {982, 49487, 54315}, {993, 1621, 21}, {1015, 5291, 33854}, {1125, 5258, 5260}, {1125, 5260, 17536}, {1385, 3555, 34772}, {1420, 6762, 78}, {1478, 11680, 17577}, {1478, 45700, 11680}, {1482, 32153, 6906}, {1621, 2975, 993}, {2242, 16975, 5276}, {3086, 3436, 4193}, {3241, 11194, 17549}, {3428, 5731, 7411}, {3434, 4293, 17579}, {3476, 24477, 8}, {3560, 12001, 10595}, {3582, 3814, 31272}, {3621, 4188, 5687}, {3623, 4189, 3295}, {3633, 7280, 8715}, {3635, 5267, 3746}, {3685, 38475, 4742}, {3813, 7354, 52367}, {3878, 6763, 11684}, {3881, 51111, 1}, {3889, 3897, 1}, {3935, 4881, 5440}, {4293, 34625, 3434}, {4678, 17572, 9709}, {4694, 30117, 3315}, {5010, 51093, 25439}, {5126, 5440, 4881}, {5251, 5284, 16861}, {5251, 37602, 551}, {5265, 7080, 6921}, {5288, 5563, 10}, {5433, 12607, 27529}, {5552, 7288, 17566}, {5603, 22758, 6912}, {5690, 37535, 6940}, {6645, 26801, 17686}, {8158, 37022, 20070}, {9780, 25524, 17535}, {10529, 20076, 4}, {10916, 45287, 5086}, {11240, 34610, 11114}, {11680, 34605, 1478}, {14511, 36037, 1320}, {15325, 17757, 2}, {18967, 22759, 3485}, {18990, 24390, 2475}, {22791, 26321, 21669}, {26286, 37727, 11491}, {34605, 45700, 17577}
X(54392) lies on these lines: {1, 2}, {3, 3306}, {4, 5249}, {5, 18446}, {7, 452}, {9, 3868}, {11, 28628}, {20, 8726}, {21, 57}, {29, 34}, {33, 5125}, {35, 37301}, {36, 20846}, {37, 37549}, {40, 1621}, {46, 5248}, {55, 3812}, {56, 3742}, {63, 405}, {65, 1001}, {72, 3305}, {73, 19372}, {81, 1453}, {84, 6912}, {140, 31224}, {142, 377}, {169, 16783}, {224, 442}, {226, 2478}, {244, 988}, {269, 32086}, {283, 1451}, {307, 6604}, {329, 5129}, {344, 3710}, {354, 958}, {388, 21617}, {392, 11682}, {404, 3601}, {411, 3576}, {443, 3488}, {474, 4855}, {495, 50206}, {497, 28629}, {515, 6835}, {553, 31156}, {631, 37531}, {728, 3247}, {748, 2650}, {750, 37552}, {894, 17697}, {908, 3487}, {940, 1104}, {944, 6864}, {946, 6836}, {956, 5045}, {960, 4423}, {962, 30503}, {964, 10436}, {965, 1100}, {968, 986}, {990, 17304}, {993, 3338}, {999, 16293}, {1006, 5709}, {1010, 19788}, {1012, 9940}, {1038, 27407}, {1040, 2654}, {1043, 19804}, {1054, 37574}, {1060, 7515}, {1062, 18641}, {1071, 6913}, {1086, 50065}, {1158, 15016}, {1220, 2191}, {1229, 4968}, {1257, 25430}, {1259, 37244}, {1266, 15956}, {1279, 5710}, {1329, 17718}, {1376, 13867}, {1385, 3149}, {1392, 45830}, {1393, 54320}, {1394, 17074}, {1420, 3897}, {1442, 31994}, {1446, 4350}, {1448, 17194}, {1449, 2287}, {1478, 51706}, {1479, 12609}, {1482, 31838}, {1490, 3091}, {1656, 37700}, {1697, 38316}, {1699, 6895}, {1706, 3871}, {1723, 25081}, {1728, 18389}, {1750, 3832}, {1790, 54340}, {1834, 24789}, {1837, 25466}, {1870, 7498}, {1883, 25365}, {1891, 26130}, {1895, 11109}, {2082, 16503}, {2098, 10179}, {2263, 41246}, {2280, 21921}, {2320, 30389}, {2339, 40959}, {2475, 3586}, {2476, 9581}, {2551, 3475}, {2646, 25524}, {2647, 4320}, {2975, 3333}, {3090, 5720}, {3146, 5732}, {3174, 40333}, {3189, 26040}, {3218, 16865}, {3219, 16859}, {3295, 3753}, {3303, 3895}, {3339, 4512}, {3340, 3877}, {3419, 8728}, {3428, 13374}, {3436, 21620}, {3485, 26105}, {3522, 10857}, {3523, 6282}, {3555, 9708}, {3560, 10202}, {3612, 35016}, {3615, 43682}, {3646, 34195}, {3648, 5586}, {3649, 24703}, {3662, 26117}, {3666, 17054}, {3671, 11415}, {3680, 51779}, {3681, 41863}, {3691, 51194}, {3698, 3748}, {3746, 54286}, {3750, 24440}, {3752, 19765}, {3754, 5119}, {3758, 32024}, {3816, 11281}, {3817, 6870}, {3822, 10826}, {3824, 17532}, {3825, 37692}, {3833, 25440}, {3834, 50050}, {3838, 10896}, {3869, 5284}, {3873, 5260}, {3874, 41229}, {3876, 7308}, {3884, 25415}, {3885, 37556}, {3889, 6762}, {3890, 7982}, {3898, 30323}, {3911, 6910}, {3916, 5708}, {3918, 25439}, {3927, 16857}, {3928, 16858}, {3929, 16861}, {3940, 16853}, {3984, 5044}, {4002, 4917}, {4004, 12702}, {4101, 14555}, {4187, 11374}, {4188, 30282}, {4189, 15803}, {4190, 4304}, {4193, 5219}, {4197, 37723}, {4198, 18650}, {4202, 17282}, {4204, 10381}, {4208, 5175}, {4217, 50116}, {4233, 7713}, {4252, 37520}, {4255, 16610}, {4292, 6872}, {4296, 27402}, {4297, 50695}, {4303, 7518}, {4313, 6904}, {4328, 32098}, {4357, 5738}, {4389, 32007}, {4428, 37568}, {4533, 51572}, {4640, 5221}, {4648, 5716}, {4653, 24046}, {4657, 18635}, {4658, 40571}, {4662, 41711}, {4675, 49745}, {4687, 32008}, {4863, 9710}, {4966, 10371}, {4999, 17728}, {5016, 18139}, {5046, 9612}, {5051, 25527}, {5080, 5290}, {5122, 19535}, {5177, 10382}, {5226, 6919}, {5251, 18398}, {5258, 50190}, {5259, 5902}, {5276, 16780}, {5281, 26062}, {5294, 13742}, {5314, 37547}, {5422, 54301}, {5426, 7280}, {5438, 17531}, {5440, 16408}, {5534, 5818}, {5542, 12527}, {5587, 6991}, {5603, 6865}, {5687, 50203}, {5691, 6894}, {5692, 12559}, {5715, 6840}, {5719, 17527}, {5728, 37224}, {5731, 50700}, {5736, 27401}, {5744, 17558}, {5750, 51972}, {5768, 6846}, {5787, 8226}, {5804, 6908}, {5806, 7580}, {5880, 6284}, {5886, 6831}, {5901, 6922}, {5905, 12572}, {5930, 37800}, {6147, 31164}, {6173, 8544}, {6245, 6837}, {6260, 6957}, {6261, 6828}, {6326, 31272}, {6505, 41930}, {6667, 12739}, {6675, 41574}, {6684, 37569}, {6690, 24914}, {6692, 6921}, {6705, 6974}, {6767, 10914}, {6832, 51755}, {6838, 7682}, {6855, 21740}, {6860, 40257}, {6883, 24474}, {6906, 37534}, {6909, 37526}, {6911, 24299}, {6914, 37612}, {6915, 51683}, {6918, 10246}, {6920, 7330}, {6943, 9624}, {6985, 13151}, {6988, 37611}, {7078, 10601}, {7171, 21669}, {7269, 32003}, {7270, 17234}, {7293, 13730}, {7489, 24467}, {7532, 37697}, {7590, 8125}, {7741, 26725}, {7991, 21153}, {8000, 12533}, {8082, 8126}, {8167, 12635}, {8666, 51816}, {9352, 35242}, {9575, 40129}, {9778, 12651}, {9812, 12565}, {9816, 18673}, {9961, 11372}, {10106, 51723}, {10129, 16132}, {10175, 10585}, {10177, 12711}, {10404, 25557}, {10430, 18219}, {10451, 10856}, {10589, 45230}, {10624, 51724}, {11018, 19520}, {11024, 17784}, {11031, 25906}, {11106, 21454}, {11115, 26627}, {11227, 37022}, {11230, 45770}, {11517, 50204}, {12109, 26893}, {12513, 17609}, {12560, 52653}, {12564, 42012}, {12625, 20195}, {12650, 54051}, {12699, 37428}, {12701, 49736}, {13323, 26884}, {13369, 37234}, {13373, 22758}, {13614, 17080}, {13725, 54311}, {14020, 17274}, {14923, 31393}, {15071, 54370}, {16048, 40131}, {16284, 17394}, {16368, 19753}, {16370, 37582}, {16484, 37598}, {16485, 37554}, {16749, 17175}, {16845, 54357}, {16968, 24512}, {17048, 25500}, {17272, 26064}, {17379, 27288}, {17534, 51780}, {17557, 46877}, {17566, 31190}, {17570, 27065}, {17571, 37545}, {17594, 24443}, {17619, 31479}, {18483, 50528}, {18634, 33178}, {19283, 35612}, {19309, 20769}, {19665, 51710}, {19684, 30807}, {20070, 43166}, {20171, 24325}, {20292, 41869}, {20330, 31799}, {20905, 23661}, {21031, 37703}, {21165, 37532}, {22128, 36742}, {22345, 28383}, {23542, 25017}, {24174, 37573}, {24391, 31259}, {24470, 50241}, {24590, 37064}, {25015, 32774}, {25992, 38047}, {26229, 36007}, {26729, 33151}, {27378, 34036}, {27384, 27410}, {27413, 30854}, {28381, 48894}, {31053, 37162}, {31880, 53034}, {34824, 49734}, {37189, 40950}, {37225, 39598}, {37231, 51687}, {37246, 37581}, {37522, 37817}, {37539, 37674}, {37605, 40726}, {38028, 52265}, {40836, 41081}, {40942, 41006}, {43531, 43675}
X(54392) = isotomic conjugate of the isogonal conjugate of X(54321)
X(54392) = X(i)-isoconjugate of X(j) for these (i,j): {55, 8814}, {607, 8813}
X(54392) = X(223)-Dao conjugate of X(8814)
X(54392) = cevapoint of X(13615) and X(54358)
X(54392) = barycentric product X(i)*X(j) for these {i,j}: {75, 54358}, {76, 54321}, {85, 13615}
X(54392) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 8814}, {77, 8813}, {13615, 9}, {54321, 6}, {54358, 1}
X(54392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 78}, {1, 10, 3870}, {1, 936, 34772}, {1, 1125, 19861}, {1, 1698, 3811}, {1, 1722, 42}, {1, 2999, 19767}, {1, 3624, 997}, {1, 4853, 3241}, {1, 5268, 976}, {1, 5272, 1193}, {1, 6765, 3957}, {1, 8583, 4511}, {1, 9623, 145}, {1, 10582, 3616}, {1, 12629, 3623}, {1, 19860, 3872}, {1, 29820, 28011}, {1, 54318, 19860}, {2, 938, 6734}, {2, 3622, 5703}, {2, 5703, 27385}, {2, 12649, 10}, {2, 34772, 936}, {3, 5439, 3306}, {4, 18443, 10884}, {5, 37615, 18446}, {9, 3868, 3951}, {9, 11518, 3868}, {21, 57, 4652}, {34, 37523, 77}, {46, 5248, 35258}, {57, 5436, 21}, {65, 1001, 5250}, {72, 11108, 3305}, {72, 15934, 11520}, {142, 950, 377}, {145, 29817, 1}, {244, 10448, 988}, {405, 942, 63}, {474, 24929, 4855}, {551, 9843, 13411}, {551, 30147, 1}, {936, 12127, 20007}, {936, 34772, 78}, {1125, 1210, 2}, {1125, 30143, 1}, {1706, 10389, 3871}, {2646, 25524, 35262}, {3091, 18444, 1490}, {3218, 16865, 31424}, {3303, 5836, 3895}, {3305, 11520, 72}, {3485, 26105, 41012}, {3487, 5084, 908}, {3601, 5437, 404}, {3617, 3957, 6765}, {3624, 5705, 2}, {3671, 40998, 11415}, {3698, 3748, 3913}, {3720, 3924, 1}, {3812, 51715, 55}, {3816, 11281, 11375}, {3868, 5047, 9}, {3869, 5284, 31435}, {3876, 17536, 7308}, {4187, 11374, 30852}, {4189, 27003, 15803}, {4304, 12436, 4190}, {4420, 19877, 8580}, {4511, 5550, 8583}, {4666, 19860, 1}, {4666, 54318, 3872}, {4861, 38314, 1}, {5046, 31019, 9612}, {5047, 11518, 3951}, {5129, 11036, 329}, {5248, 5883, 46}, {5259, 5902, 12514}, {5554, 10587, 31397}, {5691, 38150, 6894}, {5708, 16418, 3916}, {5836, 42819, 3303}, {6762, 44841, 3889}, {6918, 10246, 33597}, {7308, 11523, 3876}, {8167, 12635, 25917}, {8582, 13405, 5552}, {8728, 12433, 3419}, {9581, 25525, 2476}, {9843, 13411, 2}, {10449, 16817, 5271}, {11108, 15934, 72}, {11529, 31435, 3869}, {17016, 29814, 1}, {25917, 44840, 12635}, {37246, 37581, 54337}
X(54393) lies on these lines: {2, 13335}, {3, 114}, {4, 69}, {5, 32}, {20, 7836}, {30, 7801}, {39, 37242}, {53, 13562}, {83, 3406}, {98, 5025}, {115, 43183}, {125, 41238}, {140, 7867}, {141, 35387}, {147, 6655}, {182, 6656}, {184, 41237}, {187, 37466}, {262, 7785}, {297, 9306}, {325, 9737}, {343, 460}, {355, 760}, {371, 6290}, {372, 6289}, {376, 7870}, {381, 754}, {383, 9989}, {458, 21243}, {517, 4769}, {542, 7841}, {550, 40278}, {575, 7803}, {576, 7762}, {631, 7831}, {736, 3095}, {746, 20430}, {1078, 37446}, {1080, 9988}, {1348, 6178}, {1349, 6177}, {1503, 13355}, {1504, 49356}, {1505, 49355}, {1513, 5171}, {1656, 6680}, {1975, 23698}, {2031, 43620}, {2080, 39603}, {2207, 39569}, {2386, 18531}, {2387, 18474}, {2453, 18375}, {2548, 13357}, {2782, 7748}, {2896, 22712}, {3016, 15068}, {3053, 37071}, {3091, 9753}, {3314, 10722}, {3398, 7834}, {3425, 7503}, {3564, 5028}, {3852, 51756}, {3934, 35430}, {5017, 10516}, {5056, 5395}, {5063, 45921}, {5188, 7873}, {5206, 37459}, {5286, 44499}, {5476, 7812}, {5480, 35389}, {5613, 11304}, {5617, 11303}, {5872, 36252}, {5873, 36251}, {5921, 32982}, {5965, 7754}, {5972, 11331}, {5999, 7885}, {6036, 7887}, {6054, 7833}, {6055, 11318}, {6194, 7929}, {6321, 13108}, {6467, 41757}, {6721, 33233}, {6750, 17814}, {6776, 32974}, {7388, 43120}, {7389, 43121}, {7395, 44200}, {7470, 48898}, {7694, 7800}, {7697, 18806}, {7709, 7847}, {7747, 35930}, {7749, 36519}, {7752, 37334}, {7756, 14981}, {7770, 24206}, {7773, 13860}, {7775, 37345}, {7791, 9744}, {7793, 38227}, {7794, 39838}, {7802, 11676}, {7821, 18860}, {7822, 35385}, {7823, 12110}, {7824, 43461}, {7825, 15980}, {7832, 35925}, {7842, 54187}, {7843, 32189}, {7851, 9755}, {7854, 22505}, {7855, 32515}, {7857, 21445}, {7859, 10359}, {7863, 38738}, {7864, 32467}, {7879, 40107}, {7883, 50977}, {7891, 21166}, {7899, 34473}, {7911, 12177}, {7928, 37455}, {7934, 9862}, {7935, 37479}, {8370, 11178}, {8724, 34504}, {8743, 39604}, {9766, 10983}, {9880, 14645}, {10242, 48663}, {10551, 20022}, {10768, 38521}, {11005, 38523}, {11179, 33190}, {11511, 45279}, {11550, 14957}, {11574, 41761}, {11646, 15069}, {12362, 42353}, {13085, 44422}, {13881, 23514}, {14003, 51372}, {14265, 53174}, {14568, 34623}, {14639, 36849}, {14826, 37174}, {14881, 40250}, {16312, 47339}, {16925, 47113}, {16964, 23013}, {16965, 23006}, {18358, 53418}, {19130, 35431}, {22566, 34510}, {23234, 33274}, {23293, 46571}, {30549, 36245}, {30736, 35894}, {32971, 40330}, {33230, 38064}, {33736, 37527}, {34664, 51611}, {35840, 49087}, {35841, 49086}, {36163, 47213}, {36173, 38528}, {37841, 53797}, {37984, 47577}, {39590, 46321}, {52016, 53477}, {52090, 54222}
X(54393) = midpoint of X(i) and X(j) for these {i,j}: {4, 315}, {30270, 36997}
X(54393) = reflection of X(i) in X(j) for these {i,j}: {3, 626}, {32, 5}, {35387, 141}, {35389, 5480}, {35424, 24206}, {35430, 3934}, {35431, 19130}, {36998, 13335}, {47577, 37984}
X(54393) = complement of X(36998)
X(54393) = anticomplement of X(13335)
X(54393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36998, 13335}, {4, 1352, 6248}, {5, 7745, 10358}, {5, 10104, 7746}, {5, 32151, 10104}, {114, 32152, 3}, {147, 6655, 11257}, {1513, 7750, 5171}, {3091, 20065, 9753}, {5025, 9863, 98}, {6248, 13449, 4}, {7785, 37336, 262}, {7791, 9744, 13334}, {7818, 36997, 30270}, {7823, 13862, 12110}, {10356, 10358, 5}, {20428, 20429, 48901}, {22505, 49111, 40279}, {37824, 37825, 34507}
X(54394) lies on these lines: {1, 1859}, {3, 1838}, {4, 12}, {6, 19}, {25, 225}, {27, 4267}, {28, 56}, {29, 1001}, {33, 37080}, {40, 1888}, {52, 8757}, {92, 958}, {108, 17562}, {201, 54324}, {208, 5338}, {222, 18180}, {226, 37377}, {240, 37549}, {273, 1940}, {388, 4198}, {405, 1882}, {407, 11383}, {475, 3925}, {1012, 40946}, {1038, 9816}, {1068, 11399}, {1074, 11414}, {1096, 1104}, {1125, 37393}, {1214, 7535}, {1376, 5125}, {1393, 26934}, {1426, 1452}, {1430, 4252}, {1435, 32636}, {1466, 7490}, {1470, 37245}, {1478, 7511}, {1479, 15763}, {1593, 37601}, {1598, 1785}, {1621, 7518}, {1715, 1777}, {1724, 41342}, {1753, 7957}, {1762, 37591}, {1826, 37318}, {1844, 15934}, {1846, 28353}, {1848, 11375}, {1865, 37225}, {1869, 1877}, {1872, 37569}, {1875, 7713}, {1891, 5252}, {1894, 26378}, {1935, 24310}, {2181, 3924}, {2332, 11553}, {2550, 4200}, {2911, 15443}, {2969, 22479}, {3149, 53850}, {3485, 54340}, {3560, 39529}, {3616, 17519}, {3913, 5174}, {4219, 5217}, {4423, 7498}, {5142, 37799}, {5146, 5172}, {5204, 7501}, {5236, 10404}, {5248, 54299}, {5323, 14014}, {5433, 7521}, {5584, 37305}, {5706, 11428}, {5752, 7066}, {5930, 51687}, {6197, 37567}, {6254, 11436}, {6913, 39574}, {7354, 37395}, {7510, 10267}, {7952, 17602}, {8273, 37028}, {9122, 23207}, {10198, 37321}, {10319, 19372}, {10536, 19365}, {10896, 37372}, {11237, 34666}, {11347, 22341}, {11392, 37398}, {11393, 37368}, {11471, 37391}, {11502, 37381}, {11509, 14018}, {15975, 49745}, {17923, 25524}, {19366, 34032}, {22759, 37790}, {25514, 54320}, {26481, 37362}, {28628, 30687}, {31387, 37117}, {37194, 52427}, {37231, 37800}, {46884, 54358}
X(54394) = polar conjugate of the isotomic conjugate of X(37543)
X(54394) = X(i)-isoconjugate of X(j) for these (i,j): {63, 2335}, {78, 51223}, {345, 2215}, {6332, 36080}
X(54394) = X(i)-Dao conjugate of X(j) for these (i,j): {3162, 2335}, {38967, 52355}
X(54394) = crossdifference of every pair of points on line {521, 52306}
X(54394) = barycentric product X(i)*X(j) for these {i,j}: {4, 37543}, {34, 5271}, {57, 39585}, {81, 1882}, {92, 1451}, {108, 23882}, {278, 405}, {331, 5320}, {608, 44140}, {653, 46385}, {1396, 5295}
X(54394) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 2335}, {405, 345}, {608, 51223}, {1395, 2215}, {1451, 63}, {1882, 321}, {5271, 3718}, {5320, 219}, {23882, 35518}, {37543, 69}, {39585, 312}, {46385, 6332}
X(54394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 41227, 55}, {19, 34, 65}, {28, 278, 56}, {92, 54343, 958}, {1068, 36009, 11399}, {1426, 2355, 1452}, {1838, 54368, 3}, {2362, 16232, 1841}, {2969, 37238, 22479}, {4214, 11406, 1869}, {17923, 37253, 25524}
X(54395) lies on these lines: {2, 99}, {4, 110}, {5, 9155}, {30, 5191}, {69, 48540}, {76, 94}, {83, 13582}, {98, 36163}, {125, 53346}, {141, 311}, {193, 317}, {246, 10264}, {287, 35902}, {297, 525}, {298, 21468}, {299, 21469}, {316, 323}, {385, 40885}, {524, 50187}, {542, 34174}, {625, 36212}, {858, 44420}, {868, 2782}, {1273, 34827}, {1316, 6321}, {1561, 3543}, {1625, 1993}, {1634, 34981}, {1976, 46264}, {1989, 6148}, {2407, 3018}, {2502, 11064}, {2697, 53691}, {2996, 16080}, {3014, 38393}, {3124, 5254}, {3233, 46982}, {3260, 53416}, {3292, 13449}, {3448, 38664}, {3506, 48884}, {4226, 23698}, {5117, 7703}, {5286, 39024}, {5392, 46105}, {5642, 9880}, {5972, 38734}, {7426, 46999}, {7468, 16188}, {7500, 9157}, {7550, 34837}, {7598, 39660}, {7599, 39661}, {7745, 20976}, {7760, 46723}, {7777, 11672}, {7812, 11004}, {7827, 15018}, {7841, 15066}, {8352, 40112}, {8370, 14389}, {8753, 34518}, {8754, 32114}, {8836, 11131}, {8838, 11130}, {9123, 19912}, {9131, 21731}, {9140, 12243}, {9158, 47103}, {9185, 47348}, {9486, 43291}, {10554, 23334}, {10723, 35278}, {11054, 44555}, {11632, 36194}, {14651, 35922}, {14712, 40853}, {14957, 51360}, {15107, 43453}, {15462, 39120}, {17008, 31635}, {18366, 43676}, {19130, 36213}, {19570, 44577}, {20127, 54085}, {20998, 41238}, {21850, 51335}, {22151, 53507}, {22515, 51430}, {25051, 53569}, {25328, 38361}, {31099, 46034}, {31709, 41888}, {31710, 41887}, {34505, 37638}, {35298, 38227}, {36189, 39528}, {37765, 37784}, {38259, 44877}, {39689, 53418}, {39809, 51431}, {48910, 52162}
X(54395) = reflection of X(i) in X(j) for these {i,j}: {2407, 3018}, {3014, 38393}, {4226, 47200}
X(54395) = polar conjugate of X(40118)
X(54395) = isotomic conjugate of the isogonal conjugate of X(2493)
X(54395) = polar conjugate of the isogonal conjugate of X(14984)
X(54395) = X(842)-anticomplementary conjugate of X(4329)
X(54395) = X(5641)-Ceva conjugate of X(38939)
X(54395) = X(i)-isoconjugate of X(j) for these (i,j): {48, 40118}, {163, 51480}, {1910, 40083}, {2159, 51457}, {2642, 35191}
X(54395) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 51480}, {1249, 40118}, {2493, 542}, {3163, 51457}, {11672, 40083}, {16188, 6}, {23967, 51474}
X(54395) = cevapoint of X(2493) and X(14984)
X(54395) = crossdifference of every pair of points on line {184, 351}
X(54395) = barycentric product X(i)*X(j) for these {i,j}: {76, 2493}, {264, 14984}, {325, 34175}, {340, 51847}, {523, 14221}, {850, 7468}, {5641, 16188}, {51481, 52515}
X(54395) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 40118}, {30, 51457}, {511, 40083}, {523, 51480}, {542, 51474}, {691, 35191}, {2493, 6}, {7468, 110}, {14221, 99}, {14984, 3}, {16188, 542}, {34175, 98}, {38939, 842}, {51847, 265}, {52515, 2987}
X(54395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 51389, 2}, {141, 53495, 338}, {297, 5523, 46106}, {297, 44146, 14918}, {297, 47286, 3580}, {2592, 2593, 51481}, {3569, 41079, 9979}, {3580, 47286, 51481}, {10723, 35278, 36181}
X(54396) lies on these lines: {1, 5136}, {2, 225}, {4, 9}, {8, 28950}, {25, 29828}, {29, 33}, {34, 92}, {56, 26011}, {63, 34831}, {77, 21588}, {208, 1940}, {219, 5295}, {226, 14257}, {321, 27410}, {377, 34823}, {405, 6708}, {406, 498}, {407, 26066}, {427, 29857}, {429, 1329}, {461, 6745}, {475, 1838}, {551, 38295}, {860, 1698}, {958, 1867}, {960, 1824}, {993, 37117}, {1038, 24537}, {1040, 23661}, {1068, 1125}, {1118, 30686}, {1172, 45032}, {1376, 37194}, {1426, 3812}, {1610, 35635}, {1825, 3869}, {1836, 20306}, {1848, 52082}, {1865, 17303}, {1870, 30147}, {1872, 7524}, {1877, 5554}, {1884, 5090}, {1887, 41538}, {1889, 5302}, {1891, 7102}, {1944, 10449}, {2049, 40937}, {2182, 5786}, {2339, 2478}, {2886, 37368}, {2899, 4194}, {3338, 34589}, {3452, 39579}, {3616, 23710}, {3713, 3714}, {4292, 20205}, {5125, 19808}, {5130, 7140}, {5236, 7103}, {5338, 37390}, {5705, 37381}, {5737, 15823}, {5745, 14018}, {5794, 37239}, {6198, 22836}, {6350, 54346}, {6684, 37414}, {6737, 7046}, {6796, 7412}, {6836, 34822}, {7009, 16066}, {7414, 25440}, {7498, 7952}, {7531, 45766}, {8889, 50752}, {10538, 26091}, {11399, 37393}, {11517, 54299}, {11679, 44734}, {17555, 52412}, {17860, 54295}, {20223, 37591}, {20883, 54293}, {25917, 53861}, {37276, 44696}
X(54396) = polar conjugate of X(44733)
X(54396) = polar conjugate of the isotomic conjugate of X(11679)
X(54396) = polar conjugate of the isogonal conjugate of X(2268)
X(54396) = X(i)-isoconjugate of X(j) for these (i,j): {3, 959}, {48, 44733}, {56, 34259}, {73, 5331}, {77, 2258}, {222, 941}, {603, 31359}, {905, 32693}, {1409, 37870}, {2286, 34260}, {22383, 32038}, {23189, 52931}, {34258, 52411}
X(54396) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 34259}, {958, 1038}, {1249, 44733}, {7952, 31359}, {17417, 905}, {34261, 63}, {36103, 959}
X(54396) = barycentric product X(i)*X(j) for these {i,j}: {4, 11679}, {8, 5307}, {10, 44734}, {27, 3714}, {29, 31993}, {33, 34284}, {92, 958}, {264, 2268}, {273, 3713}, {281, 10436}, {312, 4185}, {318, 940}, {333, 1867}, {1468, 7017}, {1897, 23880}, {6335, 17418}, {15742, 53526}, {36797, 50457}
X(54396) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 44733}, {9, 34259}, {19, 959}, {29, 37870}, {33, 941}, {281, 31359}, {318, 34258}, {607, 2258}, {940, 77}, {958, 63}, {1039, 34260}, {1172, 5331}, {1468, 222}, {1867, 226}, {1897, 32038}, {2268, 3}, {3713, 78}, {3714, 306}, {4185, 57}, {5019, 603}, {5307, 7}, {8672, 51664}, {8750, 32693}, {10436, 348}, {11679, 69}, {17418, 905}, {23880, 4025}, {31993, 307}, {34261, 1038}, {34284, 7182}, {44734, 86}, {50457, 17094}, {53526, 1565}, {53561, 7004}
X(54396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 281, 46878}, {29, 318, 33}, {92, 11109, 34}, {1867, 4185, 5307}, {5136, 41013, 1}, {7090, 14121, 1826}, {7140, 37226, 5130}, {23661, 27378, 1040}, {40950, 53008, 8}
X(54397) lies on these lines: {1, 1828}, {4, 9}, {25, 36}, {28, 39963}, {33, 7962}, {34, 106}, {35, 26378}, {46, 37226}, {57, 1877}, {165, 37391}, {406, 25522}, {428, 5155}, {995, 40982}, {1572, 33853}, {1597, 35238}, {1598, 11249}, {1698, 1883}, {1763, 3586}, {1785, 1851}, {1829, 5697}, {1848, 48803}, {1866, 3340}, {1875, 40961}, {3583, 11390}, {3679, 5101}, {3746, 11400}, {4194, 41012}, {4214, 37572}, {5119, 21361}, {5151, 5541}, {5437, 37168}, {5722, 7289}, {6848, 36986}, {9816, 17532}, {10319, 11113}, {11105, 31435}, {11114, 24611}, {13730, 19372}, {15737, 52427}, {18344, 48111}, {26580, 39579}, {28039, 30117}, {28076, 36572}, {37458, 38761}
X(54397) = crossdifference of every pair of points on line {1459, 14418}
X(54397) = barycentric product X(i)*X(j) for these {i,j}: {19, 50101}, {92, 16483}, {278, 3895}
X(54397) = barycentric quotient X(i)/X(j) for these {i,j}: {3895, 345}, {16483, 63}, {50101, 304}
X(54397) = {X(1828),X(4186)}-harmonic conjugate of X(1)
X(54398) lies on these lines: {1, 5273}, {2, 72}, {3, 20007}, {4, 144}, {7, 10}, {8, 20}, {9, 938}, {21, 145}, {57, 17580}, {75, 52345}, {78, 3523}, {100, 37105}, {165, 6743}, {169, 391}, {191, 4294}, {200, 10884}, {210, 1788}, {219, 3562}, {224, 4420}, {307, 14256}, {329, 3091}, {333, 37113}, {346, 3730}, {347, 18631}, {377, 3421}, {387, 3672}, {388, 21677}, {390, 12514}, {412, 7046}, {443, 21454}, {452, 3219}, {517, 37434}, {519, 4313}, {527, 50736}, {631, 3940}, {748, 28080}, {758, 19843}, {908, 5056}, {912, 6908}, {936, 5435}, {950, 3929}, {960, 14986}, {962, 4847}, {997, 5265}, {1012, 12245}, {1046, 4307}, {1071, 5657}, {1125, 31446}, {1145, 13243}, {1210, 18228}, {1219, 10461}, {1259, 2975}, {1260, 6986}, {1265, 14829}, {1697, 6764}, {1698, 21060}, {1706, 24393}, {1707, 4339}, {1737, 8165}, {1834, 4419}, {2095, 6864}, {2318, 37523}, {2475, 20078}, {2551, 5220}, {2895, 26054}, {3059, 9943}, {3085, 5904}, {3086, 5692}, {3090, 46873}, {3146, 3419}, {3189, 4640}, {3218, 6904}, {3361, 12447}, {3434, 11684}, {3436, 6839}, {3452, 5704}, {3485, 3962}, {3488, 11106}, {3522, 3916}, {3543, 5175}, {3555, 11020}, {3616, 11520}, {3621, 17576}, {3622, 5730}, {3632, 4304}, {3654, 9859}, {3679, 4292}, {3681, 7080}, {3695, 14021}, {3697, 9954}, {3710, 34255}, {3786, 27334}, {3811, 5281}, {3812, 38057}, {3839, 17781}, {3869, 6837}, {3871, 20015}, {3874, 11038}, {3878, 34625}, {3901, 19854}, {3950, 35629}, {3984, 10303}, {4005, 24914}, {4067, 26363}, {4134, 26364}, {4189, 20013}, {4197, 17757}, {4220, 42461}, {4293, 6763}, {4346, 23537}, {4430, 10587}, {4454, 43533}, {4461, 5295}, {4641, 5716}, {4651, 37109}, {4652, 10304}, {4661, 10528}, {4662, 5784}, {4677, 34639}, {4678, 37435}, {4853, 18219}, {4855, 15692}, {4882, 5732}, {5046, 43740}, {5082, 10431}, {5119, 12632}, {5177, 5905}, {5178, 44447}, {5187, 26792}, {5221, 26040}, {5226, 5705}, {5234, 6738}, {5249, 9780}, {5250, 36845}, {5262, 54305}, {5274, 10916}, {5325, 5436}, {5440, 15717}, {5552, 15016}, {5687, 7411}, {5690, 6916}, {5703, 5745}, {5708, 17582}, {5709, 50700}, {5711, 39587}, {5731, 6737}, {5735, 19925}, {5748, 7486}, {5758, 51755}, {5759, 5787}, {5763, 5789}, {5768, 37423}, {5770, 6926}, {5771, 6988}, {5774, 37088}, {5806, 5817}, {5836, 34744}, {5837, 6762}, {5882, 36922}, {5902, 19855}, {6172, 12572}, {6765, 7675}, {6846, 24474}, {6871, 17484}, {6884, 10527}, {6919, 31018}, {6944, 31835}, {6987, 26921}, {6989, 24475}, {8822, 42696}, {8951, 45204}, {9122, 20212}, {9370, 34035}, {9534, 20367}, {9797, 31393}, {9840, 22149}, {9945, 21735}, {9960, 14872}, {9964, 46685}, {10381, 26125}, {10477, 26059}, {10578, 41863}, {10580, 31435}, {10586, 41389}, {10883, 24390}, {11015, 20052}, {11851, 19851}, {12125, 12671}, {12528, 37421}, {12635, 30478}, {12710, 30628}, {14646, 31777}, {15394, 40417}, {15934, 16845}, {15935, 16866}, {16368, 20043}, {17054, 37650}, {17127, 36579}, {17284, 39589}, {17746, 27541}, {18220, 45700}, {18221, 54318}, {18391, 41229}, {18650, 32099}, {18655, 32087}, {19262, 22458}, {20009, 37683}, {20012, 37175}, {20059, 37161}, {22131, 52058}, {24635, 37528}, {25524, 45085}, {25568, 26066}, {26446, 27525}, {26685, 37024}, {26842, 50237}, {27549, 28287}, {28605, 41013}, {30340, 51706}, {30852, 46936}, {34619, 50835}, {36996, 37424}, {37254, 37547}, {40661, 54366}, {48890, 49716}
X(54398) = reflection of X(i) in X(j) for these {i,j}: {7, 5833}, {3487, 5791}, {4313, 31424}, {5290, 10}
X(54398) = anticomplement of X(3487)
X(54398) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5273, 17558}, {2, 3868, 11036}, {4, 3927, 144}, {7, 10, 4208}, {8, 63, 20}, {9, 938, 5129}, {9, 24391, 938}, {10, 3339, 11024}, {10, 5223, 5815}, {40, 9799, 20}, {78, 5744, 3523}, {329, 6734, 3091}, {960, 24477, 14986}, {1071, 5657, 37108}, {1071, 34790, 41228}, {1259, 2975, 37106}, {3219, 12649, 452}, {3487, 5791, 2}, {3488, 31445, 11106}, {3617, 9965, 377}, {3632, 4304, 12536}, {3951, 6734, 329}, {4313, 31424, 50742}, {4847, 12526, 962}, {5745, 11523, 5703}, {5770, 31837, 6926}, {5775, 5815, 10}, {11106, 20008, 3488}, {11520, 54357, 3616}
X(54399) lies on these lines: {5, 9275}, {8, 21}, {11, 60}, {12, 24624}, {30, 58}, {79, 33135}, {81, 3649}, {110, 37722}, {140, 15792}, {191, 18163}, {270, 1852}, {284, 1213}, {442, 6703}, {496, 17104}, {501, 15325}, {662, 6691}, {740, 3647}, {758, 18178}, {759, 37730}, {1503, 37447}, {1761, 40979}, {2185, 4999}, {3058, 35193}, {3109, 37702}, {3286, 3651}, {4225, 5427}, {4276, 5428}, {4653, 15174}, {4658, 16137}, {5127, 15171}, {5358, 44253}, {5433, 40214}, {5441, 52680}, {10122, 18165}, {11263, 17197}, {11684, 16704}, {12433, 37816}, {15670, 49730}, {15674, 26044}, {17637, 18191}, {18653, 32636}, {33857, 54356}
X(54399) = reflection of X(3704) in X(18253)
X(54399) = X(6742)-Ceva conjugate of X(3737)
X(54399) = barycentric product X(4560)*X(14985)
X(54399) = barycentric quotient X(14985)/X(4552)
X(54399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 333, 18253}, {81, 37369, 3649}
X(54400) lies on these lines: {1, 104}, {6, 19}, {8, 28968}, {33, 6001}, {40, 73}, {42, 51660}, {46, 10571}, {56, 15854}, {57, 957}, {63, 24806}, {201, 2324}, {208, 1425}, {212, 30503}, {222, 517}, {223, 2093}, {225, 4295}, {227, 37567}, {388, 50307}, {595, 34489}, {614, 18838}, {758, 8270}, {942, 34040}, {960, 25934}, {991, 1697}, {1038, 3869}, {1042, 37550}, {1060, 14988}, {1191, 37566}, {1319, 3052}, {1393, 3339}, {1394, 3340}, {1406, 4320}, {1420, 4257}, {1435, 32065}, {1455, 2099}, {1465, 36279}, {1572, 52635}, {1708, 49500}, {1737, 34029}, {1771, 6261}, {1836, 51421}, {1877, 18391}, {1935, 19860}, {2122, 13601}, {2199, 3553}, {2654, 12705}, {3057, 34046}, {3157, 37562}, {3195, 51399}, {3359, 22350}, {3660, 16483}, {3753, 34048}, {3877, 17074}, {4084, 4347}, {4337, 5119}, {4424, 45126}, {4551, 54286}, {4559, 40131}, {5250, 37523}, {5252, 5848}, {5711, 12709}, {5727, 18328}, {5836, 9370}, {5886, 43043}, {5902, 34036}, {5903, 21147}, {7078, 31788}, {7191, 18419}, {7355, 11471}, {12047, 34030}, {12514, 37558}, {12672, 41344}, {12940, 52840}, {18421, 34033}, {18915, 46878}, {19366, 42448}, {20306, 26955}, {22072, 37560}, {23070, 25413}, {24914, 51415}, {26888, 44121}, {37696, 40266}, {37740, 51422}
X(54400) = crossdifference of every pair of points on line {521, 46393}
X(54400) = barycentric product X(57)*X(5657)
X(54400) = barycentric quotient X(5657)/X(312)
X(54400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 221, 34}, {5903, 34043, 21147}
X(54401) lies on these lines: {1, 2}, {9, 47}, {11, 7405}, {12, 1060}, {24, 33}, {34, 1594}, {36, 7509}, {37, 921}, {38, 17437}, {46, 201}, {55, 6642}, {56, 7393}, {90, 601}, {91, 6358}, {171, 920}, {240, 23050}, {255, 756}, {750, 17700}, {774, 17699}, {984, 3075}, {988, 10090}, {1038, 1478}, {1062, 5432}, {1385, 21479}, {1479, 7401}, {1490, 4337}, {1870, 10588}, {3147, 5218}, {3337, 4327}, {3583, 7544}, {3585, 37444}, {3761, 28706}, {4296, 10590}, {4302, 7487}, {4319, 44802}, {4320, 5270}, {4324, 31304}, {4682, 44547}, {4995, 44211}, {5010, 7488}, {5217, 14070}, {5250, 54350}, {5348, 26921}, {5707, 41538}, {5818, 54292}, {6796, 16577}, {7280, 37126}, {7741, 14788}, {8144, 34351}, {8270, 12047}, {8965, 44590}, {10127, 15171}, {10592, 32047}, {10827, 21147}, {16238, 37729}, {18397, 37559}, {18447, 31479}, {21077, 54289}, {24431, 24467}, {31423, 33178}, {34036, 37692}, {37034, 40635}
X(54401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5268, 498}, {601, 7069, 90}, {750, 44706, 17700}, {1210, 30142, 1}, {3086, 3920, 1}, {30145, 44675, 1}
X(54402) lies on these lines: {1, 6}, {11, 40693}, {12, 40694}, {13, 10896}, {14, 10895}, {15, 5204}, {16, 5217}, {35, 22238}, {36, 22236}, {55, 62}, {56, 61}, {203, 3304}, {222, 7344}, {388, 42999}, {395, 498}, {396, 499}, {397, 1479}, {398, 1478}, {497, 42998}, {559, 6191}, {999, 2307}, {1482, 33655}, {2306, 5708}, {3085, 37641}, {3086, 37640}, {3295, 7127}, {3303, 7006}, {3364, 18996}, {3365, 18995}, {3389, 19038}, {3390, 19037}, {3582, 49947}, {3583, 5340}, {3584, 49948}, {3585, 5339}, {3614, 18581}, {4299, 42147}, {4302, 42148}, {4316, 43194}, {4324, 43193}, {5010, 36843}, {5225, 5335}, {5229, 5334}, {5362, 5550}, {5367, 9780}, {5432, 42149}, {5433, 42152}, {5471, 9650}, {5472, 9665}, {6284, 10653}, {7126, 36750}, {7173, 18582}, {7280, 36836}, {7354, 10654}, {7741, 42156}, {7951, 42153}, {8739, 11398}, {8740, 11399}, {9654, 42975}, {9657, 42991}, {9669, 42974}, {9670, 42990}, {10056, 43229}, {10072, 43228}, {10483, 42154}, {10592, 11543}, {10593, 11542}, {10638, 11486}, {11073, 52186}, {11485, 19373}, {12941, 14137}, {12943, 16964}, {12952, 14136}, {12953, 16965}, {15326, 42150}, {15338, 42151}, {31479, 42989}, {33654, 36279}, {37772, 52424}
X(54402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61, 202, 56}, {62, 7005, 55}
X(54403) lies on these lines: {1, 6}, {3, 2307}, {11, 40694}, {12, 40693}, {13, 10895}, {14, 10896}, {15, 5217}, {16, 5204}, {35, 22236}, {36, 22238}, {55, 61}, {56, 62}, {202, 3304}, {222, 7345}, {388, 42998}, {395, 499}, {396, 498}, {397, 1478}, {398, 1479}, {497, 42999}, {1082, 6192}, {1250, 11485}, {1482, 7052}, {2306, 36279}, {3085, 37640}, {3086, 37641}, {3303, 7005}, {3364, 19038}, {3365, 19037}, {3389, 18996}, {3390, 18995}, {3582, 49948}, {3583, 5339}, {3584, 49947}, {3585, 5340}, {3614, 18582}, {4299, 42148}, {4302, 42147}, {4316, 43193}, {4324, 43194}, {5010, 36836}, {5225, 5334}, {5229, 5335}, {5362, 9780}, {5367, 5550}, {5432, 42152}, {5433, 42149}, {5471, 9665}, {5472, 9650}, {5708, 33654}, {6284, 10654}, {7051, 11486}, {7173, 18581}, {7280, 36843}, {7354, 10653}, {7741, 42153}, {7951, 42156}, {8739, 11399}, {8740, 11398}, {9654, 42974}, {9657, 42990}, {9669, 42975}, {9670, 42991}, {10056, 43228}, {10072, 43229}, {10483, 42155}, {10592, 11542}, {10593, 11543}, {11072, 52186}, {12942, 14136}, {12943, 16965}, {12951, 14137}, {12953, 16964}, {15326, 42151}, {15338, 42150}, {19551, 36750}, {31479, 42988}, {37773, 52424}
X(54403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61, 7006, 55}, {62, 203, 56}, {2307, 7127, 3}
X(54404) lies on these lines: {3, 326}, {7, 37550}, {9, 1760}, {19, 28287}, {22, 18615}, {40, 75}, {46, 10436}, {57, 86}, {63, 69}, {77, 283}, {85, 8822}, {191, 17272}, {269, 1758}, {320, 54290}, {348, 7013}, {394, 14597}, {484, 25590}, {1264, 3785}, {1697, 4360}, {1918, 17594}, {2270, 17277}, {2339, 28274}, {3218, 3945}, {3219, 5232}, {3333, 17394}, {3496, 27626}, {3576, 44179}, {3751, 21035}, {3875, 5119}, {3928, 17378}, {3929, 17271}, {4047, 23151}, {4357, 12514}, {4640, 24471}, {4902, 16558}, {4967, 54286}, {5250, 17321}, {5709, 10446}, {6762, 17377}, {11010, 17151}, {16992, 24310}, {17270, 21277}, {17322, 31435}, {17393, 31393}, {18713, 40937}, {19804, 39592}, {21059, 35258}, {27633, 39248}, {33295, 54373}, {34377, 54285}, {43216, 54322}
X(54404) = isotomic conjugate of the polar conjugate of X(5256)
X(54404) = X(10319)-Dao conjugate of X(52082)
X(54404) = barycentric product X(i)*X(j) for these {i,j}: {63, 17321}, {69, 5256}, {77, 14555}, {304, 16466}, {348, 5250}, {1332, 47995}, {3926, 7713}, {3931, 17206}, {4194, 7183}, {4254, 7182}, {4563, 50332}, {4592, 48402}
X(54404) = barycentric quotient X(i)/X(j) for these {i,j}: {3931, 1826}, {4254, 33}, {5250, 281}, {5256, 4}, {7713, 393}, {14555, 318}, {16466, 19}, {17321, 92}, {47995, 17924}, {48402, 24006}, {50332, 2501}
X(54404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 22370, 5227}, {77, 4652, 1444}
X(54405) lies on these lines: {1, 19}, {2, 7}, {3, 37}, {6, 169}, {10, 5227}, {40, 3332}, {44, 5708}, {45, 5356}, {46, 71}, {56, 40937}, {65, 219}, {72, 965}, {75, 16054}, {77, 18726}, {78, 22021}, {86, 1760}, {101, 3553}, {172, 5336}, {192, 37274}, {198, 37034}, {220, 37544}, {222, 30456}, {281, 388}, {282, 951}, {312, 37092}, {344, 37280}, {346, 6904}, {354, 2264}, {355, 21933}, {379, 17863}, {404, 27396}, {443, 2345}, {517, 2256}, {572, 18443}, {573, 5709}, {604, 17451}, {608, 34036}, {612, 5285}, {614, 16470}, {910, 4254}, {912, 5778}, {938, 5802}, {940, 21370}, {948, 1119}, {950, 4198}, {968, 3724}, {969, 1814}, {993, 25081}, {999, 1108}, {1014, 24635}, {1055, 3100}, {1071, 5776}, {1100, 15934}, {1159, 22147}, {1212, 5120}, {1213, 5791}, {1333, 36011}, {1376, 3694}, {1385, 37519}, {1439, 6180}, {1449, 2082}, {1466, 1696}, {1467, 5053}, {1468, 40977}, {1478, 1826}, {1479, 1839}, {1572, 21769}, {1723, 2260}, {1731, 2257}, {1732, 3337}, {1737, 26063}, {1752, 18398}, {1761, 5327}, {1763, 5712}, {1773, 2333}, {1817, 28606}, {1841, 7497}, {1880, 2286}, {1895, 8748}, {1901, 21530}, {2160, 37584}, {2171, 2289}, {2252, 17700}, {2261, 30274}, {2268, 21808}, {2270, 4266}, {2276, 16056}, {2277, 28258}, {2287, 3868}, {2298, 4224}, {2352, 8021}, {2354, 26098}, {3197, 50195}, {3229, 20370}, {3290, 25514}, {3487, 7521}, {3612, 22054}, {3664, 7289}, {3666, 11347}, {3672, 24604}, {3686, 24391}, {3693, 37270}, {3721, 39598}, {3729, 20336}, {3731, 7523}, {3739, 37075}, {3772, 6678}, {3811, 54316}, {3916, 19523}, {3945, 7291}, {4261, 16415}, {4292, 8804}, {4641, 19728}, {4877, 31424}, {4908, 19706}, {5019, 16968}, {5037, 16780}, {5042, 49758}, {5122, 16675}, {5138, 16972}, {5142, 9612}, {5275, 37581}, {5276, 15487}, {5290, 7079}, {5341, 16777}, {5540, 16667}, {5707, 12417}, {5711, 40660}, {5717, 7713}, {5728, 5781}, {5755, 37532}, {5757, 37151}, {5787, 21049}, {5816, 24005}, {6147, 52259}, {6351, 8231}, {7113, 37615}, {7146, 53996}, {7297, 16884}, {7359, 10404}, {7557, 9581}, {7561, 11374}, {7719, 21620}, {8726, 37431}, {8728, 17303}, {9122, 37528}, {9579, 52364}, {9816, 24162}, {10401, 26932}, {10827, 21011}, {10901, 15830}, {11019, 40963}, {12436, 17355}, {12437, 20009}, {13408, 15945}, {13726, 54287}, {13750, 19350}, {14547, 40983}, {15656, 25516}, {15956, 24608}, {16488, 28011}, {16566, 16831}, {16568, 17394}, {16601, 54322}, {16673, 30282}, {16814, 37545}, {16817, 21384}, {16843, 31445}, {17073, 41003}, {17134, 25255}, {17279, 37326}, {17289, 37097}, {17316, 27059}, {17321, 24609}, {17736, 21061}, {17799, 25528}, {18165, 46882}, {18635, 41004}, {18655, 24606}, {18714, 44179}, {19547, 37623}, {19857, 41229}, {20171, 37233}, {21483, 44307}, {21866, 36279}, {23151, 54344}, {24179, 34830}, {24316, 53596}, {24325, 50198}, {26626, 26998}, {32777, 37266}, {37052, 37539}, {37113, 40979}, {37271, 44798}, {37306, 38871}, {37538, 43214}, {42018, 46830}
X(54405) = polar conjugate of the isotomic conjugate of X(54289)
X(54405) = X(i)-isoconjugate of X(j) for these (i,j): {4, 45127}, {650, 13395}
X(54405) = X(i)-Dao conjugate of X(j) for these (i,j): {405, 5271}, {36033, 45127}
X(54405) = crossdifference of every pair of points on line {656, 663}
X(54405) = barycentric product X(i)*X(j) for these {i,j}: {1, 377}, {4, 54289}, {8, 1448}, {75, 37538}, {86, 43214}, {662, 47124}, {5905, 46038}, {28606, 45999}
X(54405) = barycentric quotient X(i)/X(j) for these {i,j}: {48, 45127}, {109, 13395}, {377, 75}, {1448, 7}, {37538, 1}, {43214, 10}, {46038, 2994}, {47124, 1577}, {54289, 69}
X(54405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 610, 284}, {1, 1781, 19}, {1, 18594, 380}, {2, 5279, 9}, {7, 27382, 5746}, {9, 57, 579}, {28, 2303, 284}, {48, 2294, 1}, {226, 40942, 5747}, {354, 2264, 54358}, {1449, 16547, 2082}, {1723, 3338, 2260}, {1880, 2286, 21147}, {2260, 54324, 1723}, {2285, 40131, 9}, {3247, 16548, 54359}, {6203, 6204, 226}, {16777, 37504, 24929}
X(54406) lies on these lines: {1, 6}, {8, 1572}, {10, 9596}, {19, 10822}, {31, 33299}, {32, 78}, {39, 63}, {43, 3496}, {46, 1575}, {58, 54317}, {169, 2238}, {172, 997}, {187, 4855}, {329, 5286}, {574, 4652}, {579, 21744}, {672, 23620}, {748, 21808}, {908, 3767}, {920, 13006}, {936, 5277}, {976, 21764}, {978, 3509}, {1046, 17754}, {1193, 5282}, {1211, 17308}, {1468, 39244}, {1475, 32912}, {1500, 5250}, {1571, 17756}, {1716, 20861}, {1722, 3125}, {1759, 3216}, {1914, 3811}, {2082, 20683}, {2175, 26924}, {2241, 3870}, {2242, 19861}, {2276, 12514}, {2548, 6734}, {2975, 9619}, {3053, 5440}, {3219, 31442}, {3305, 16589}, {3338, 16604}, {3419, 7745}, {3661, 5739}, {3693, 14974}, {3868, 33854}, {3869, 9620}, {3876, 5276}, {3915, 3930}, {3916, 5013}, {3927, 9605}, {3929, 31429}, {3940, 30435}, {3951, 7772}, {3984, 5007}, {4006, 37610}, {4011, 21071}, {4383, 16583}, {4640, 31448}, {4641, 5021}, {5044, 5275}, {5119, 20691}, {5120, 42461}, {5278, 41249}, {5744, 31400}, {5791, 37661}, {5813, 33867}, {6542, 27523}, {7085, 20967}, {7739, 17781}, {7746, 30852}, {9574, 54290}, {9593, 12526}, {9599, 10916}, {12699, 21956}, {15494, 17798}, {16549, 49500}, {17206, 25918}, {17736, 49997}, {18055, 33295}, {24987, 31409}, {25006, 31416}, {26035, 26223}, {26066, 31460}, {31451, 35258}, {33950, 37657}, {34460, 37532}, {49561, 49710}, {50621, 54359}
X(54406) = barycentric product X(1)*X(33088)
X(54406) = barycentric quotient X(33088)/X(75)
X(54406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {44, 21874, 218}, {5299, 5904, 16973}
X(54407) lies on these lines: {1, 19}, {4, 991}, {21, 1038}, {24, 37530}, {25, 940}, {27, 33}, {29, 34}, {37, 46890}, {58, 30733}, {81, 2299}, {112, 2725}, {162, 37131}, {238, 52413}, {241, 1876}, {242, 514}, {278, 38053}, {386, 7521}, {468, 35466}, {500, 15763}, {518, 5089}, {608, 1001}, {648, 14024}, {859, 46974}, {942, 18734}, {1040, 1817}, {1060, 36011}, {1062, 52012}, {1214, 8021}, {1395, 17185}, {1396, 4183}, {1458, 5236}, {1465, 52889}, {1742, 52840}, {1818, 1861}, {1848, 3720}, {1890, 40983}, {1936, 52427}, {2074, 52680}, {2191, 8747}, {2193, 36017}, {2263, 5327}, {2328, 8270}, {3100, 14953}, {3186, 16066}, {3192, 6353}, {3194, 41790}, {3576, 7436}, {3736, 54293}, {4206, 10458}, {4227, 4653}, {4248, 9311}, {4551, 37799}, {4564, 4570}, {5009, 32676}, {5125, 17234}, {5712, 37394}, {5718, 37432}, {5728, 46882}, {6198, 31900}, {7100, 44290}, {7466, 37633}, {7497, 50317}, {7537, 37732}, {11341, 20131}, {11363, 37539}, {11393, 17167}, {11398, 18180}, {14017, 37522}, {14196, 52460}, {15150, 36797}, {16747, 17175}, {17056, 37362}, {17188, 34036}, {17569, 30663}, {19765, 37245}, {20883, 24325}, {26702, 32688}, {31905, 52209}, {32682, 39439}, {37966, 47185}
X(54407) = polar conjugate of the isotomic conjugate of X(18206)
X(54407) = cevapoint of X(i) and X(j) for these (i,j): {1458, 1876}, {2356, 5089}
X(54407) = crossdifference of every pair of points on line {71, 656}
X(54407) = X(i)-isoconjugate of X(j) for these (i,j): {3, 13576}, {10, 36057}, {37, 1814}, {42, 31637}, {63, 18785}, {71, 673}, {72, 105}, {73, 14942}, {100, 10099}, {228, 2481}, {294, 1214}, {306, 1438}, {307, 2195}, {321, 32658}, {525, 919}, {647, 666}, {656, 36086}, {810, 51560}, {885, 23067}, {1409, 36796}, {1416, 3710}, {1439, 28071}, {1462, 3694}, {2200, 18031}, {3049, 36803}, {3682, 36124}, {3990, 54235}, {3998, 8751}, {4551, 23696}, {4580, 46163}, {5377, 18210}, {6559, 52373}, {8611, 36146}, {14208, 32666}, {17094, 52927}, {28132, 52610}, {32735, 52355}, {34018, 52370}, {43929, 52609}
X(54407) = X(i)-Dao conjugate of X(j) for these (i,j): {3162, 18785}, {6184, 306}, {8054, 10099}, {17755, 20336}, {20621, 10}, {35094, 14208}, {36103, 13576}, {36905, 1231}, {38980, 525}, {38989, 656}, {39014, 8611}, {39046, 72}, {39052, 666}, {39062, 51560}, {39063, 307}, {39077, 51366}, {40589, 1814}, {40592, 31637}, {40596, 36086}, {40609, 3710}
X(54407) = barycentric product X(i)*X(j) for these {i,j}: {1, 15149}, {4, 18206}, {19, 30941}, {21, 5236}, {25, 18157}, {27, 518}, {28, 3912}, {29, 241}, {58, 46108}, {81, 1861}, {85, 37908}, {86, 5089}, {92, 3286}, {162, 918}, {274, 2356}, {286, 672}, {333, 1876}, {514, 4238}, {648, 2254}, {665, 811}, {823, 53550}, {1026, 17925}, {1172, 9436}, {1396, 3717}, {1458, 31623}, {1474, 3263}, {1783, 23829}, {2223, 44129}, {2299, 40704}, {2322, 34855}, {8747, 25083}, {16728, 36124}, {17924, 54353}, {17926, 41353}, {22116, 31905}, {36797, 53544}, {44130, 52635}
X(54407) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 13576}, {25, 18785}, {27, 2481}, {28, 673}, {29, 36796}, {58, 1814}, {81, 31637}, {112, 36086}, {162, 666}, {241, 307}, {286, 18031}, {518, 306}, {648, 51560}, {649, 10099}, {665, 656}, {672, 72}, {811, 36803}, {918, 14208}, {926, 8611}, {1026, 52609}, {1172, 14942}, {1333, 36057}, {1458, 1214}, {1474, 105}, {1818, 3998}, {1861, 321}, {1876, 226}, {2203, 1438}, {2204, 2195}, {2206, 32658}, {2223, 71}, {2254, 525}, {2299, 294}, {2332, 28071}, {2340, 3694}, {2356, 37}, {3263, 40071}, {3286, 63}, {3675, 4466}, {3693, 3710}, {3912, 20336}, {3930, 3695}, {3932, 52369}, {4183, 6559}, {4233, 31638}, {4238, 190}, {4447, 4019}, {5089, 10}, {5236, 1441}, {5317, 36124}, {5338, 14625}, {7252, 23696}, {8747, 54235}, {9436, 1231}, {9454, 228}, {9455, 2200}, {9502, 51366}, {15149, 75}, {18157, 305}, {18206, 69}, {20683, 3949}, {20752, 3682}, {23225, 822}, {23829, 15413}, {24290, 4064}, {25083, 52396}, {30941, 304}, {32676, 919}, {35325, 35333}, {37908, 9}, {39258, 3690}, {42071, 3930}, {43925, 1027}, {46108, 313}, {51400, 20235}, {52635, 73}, {52890, 36816}, {53539, 51664}, {53544, 17094}, {53550, 24018}, {54325, 4574}, {54353, 1332}
X(54407) = {X(81),X(4233)}-harmonic conjugate of X(2299)
X(54408) lies on these lines: {1, 3}, {9, 11}, {33, 38}, {34, 1496}, {48, 53557}, {63, 497}, {84, 6284}, {90, 4857}, {191, 51785}, {200, 11502}, {212, 614}, {244, 1253}, {283, 5324}, {390, 3218}, {496, 26921}, {518, 1998}, {672, 1732}, {984, 9817}, {997, 48713}, {1000, 48363}, {1158, 10624}, {1317, 7966}, {1364, 3056}, {1435, 23710}, {1479, 7330}, {1708, 11019}, {1709, 9580}, {1711, 33141}, {1731, 30224}, {1836, 5735}, {1837, 34606}, {2170, 32578}, {2183, 29639}, {2194, 18163}, {2260, 54359}, {2310, 36263}, {2361, 7290}, {2551, 6734}, {3027, 24469}, {3058, 3928}, {3100, 4392}, {3219, 5274}, {3220, 10833}, {3242, 51361}, {3305, 10589}, {3306, 5218}, {3318, 3321}, {3452, 20588}, {3486, 34610}, {3583, 18540}, {3586, 49176}, {3662, 27542}, {3705, 3719}, {3752, 7074}, {3874, 10393}, {3877, 13279}, {3929, 7082}, {4302, 7171}, {4316, 7284}, {4319, 7004}, {4336, 46901}, {4640, 42842}, {4845, 34925}, {4907, 53524}, {5219, 15298}, {5227, 12589}, {5230, 28272}, {5250, 30478}, {5273, 10527}, {5281, 27003}, {5432, 5437}, {5541, 8275}, {5578, 5579}, {5705, 50206}, {5715, 26481}, {6056, 54373}, {6762, 10950}, {7160, 34485}, {7580, 17625}, {7701, 16142}, {7965, 10957}, {7971, 45288}, {8609, 42316}, {9581, 10953}, {9779, 29007}, {9785, 11240}, {9841, 15338}, {10916, 12572}, {11376, 24953}, {11520, 45230}, {11525, 17636}, {12053, 12514}, {12678, 15239}, {12701, 12705}, {15171, 24467}, {15348, 52457}, {15845, 24703}, {15852, 34046}, {16141, 54302}, {17276, 38357}, {17452, 41423}, {18240, 52769}, {18450, 35986}, {24392, 42012}, {24987, 26040}, {26878, 47743}, {28076, 40950}, {36481, 36483}, {36488, 36540}, {36501, 36504}, {36509, 36572}, {43819, 43856}, {45634, 49170}
X(54408) = X(i)-Ceva conjugate of X(j) for these (i,j): {30237, 513}, {52457, 34526}
X(54408) = X(i)-isoconjugate of X(j) for these (i,j): {57, 34525}, {664, 46006}
X(54408) = X(i)-Dao conjugate of X(j) for these (i,j): {5452, 34525}, {15348, 8}, {39025, 46006}
X(54408) = barycentric product X(i)*X(j) for these {i,j}: {1, 52457}, {7, 34526}
X(54408) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 34525}, {3063, 46006}, {34526, 8}, {52457, 75}
X(54408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 165, 2078}, {1, 5536, 57}, {1, 5709, 37550}, {1, 10268, 11510}, {35, 17437, 37534}, {40, 57, 1155}, {55, 4860, 17603}, {55, 18839, 1}, {63, 497, 30223}, {165, 10388, 55}, {354, 1155, 56}, {1155, 3057, 55}, {1697, 3333, 2646}, {2078, 11012, 37578}, {3333, 24468, 46}, {3576, 35445, 34879}, {3660, 50196, 354}, {5536, 41338, 5709}, {5570, 40292, 18443}, {8186, 8187, 32760}, {32622, 32623, 3359}, {45625, 45626, 10966}
X(54409) lies on these lines: {1, 19297}, {3, 6}, {9, 3467}, {21, 17330}, {23, 5276}, {35, 44}, {36, 16666}, {37, 3746}, {41, 17796}, {45, 55}, {100, 17369}, {141, 21516}, {198, 1953}, {524, 21511}, {546, 50036}, {590, 21553}, {597, 21495}, {599, 11343}, {615, 21492}, {941, 3444}, {966, 16865}, {999, 20997}, {1001, 51550}, {1100, 5563}, {1172, 3518}, {1213, 5047}, {1405, 5172}, {1444, 3629}, {1696, 16674}, {1732, 34879}, {1990, 7412}, {1992, 21508}, {1995, 5275}, {2174, 2269}, {2178, 3304}, {2280, 41341}, {2975, 4969}, {3068, 21565}, {3069, 21568}, {3295, 16672}, {3496, 4053}, {3553, 7991}, {3554, 30389}, {3589, 21540}, {3627, 53421}, {3763, 21496}, {3871, 3943}, {3913, 50087}, {4189, 37654}, {4220, 5306}, {4700, 5267}, {5010, 16670}, {5258, 50082}, {5259, 52706}, {5277, 16427}, {6144, 21517}, {6749, 37305}, {7113, 22357}, {7300, 40937}, {7496, 33854}, {8252, 21549}, {8253, 21546}, {8584, 35276}, {8609, 34486}, {8666, 50131}, {8715, 17281}, {9300, 19649}, {9607, 37328}, {9766, 21485}, {11010, 21864}, {11349, 17392}, {13846, 16433}, {13847, 16432}, {15533, 21509}, {15534, 16436}, {16042, 37675}, {16373, 37673}, {16431, 51185}, {16440, 32788}, {16441, 32787}, {16522, 37609}, {16554, 19302}, {16644, 21481}, {16645, 21480}, {16885, 54285}, {17362, 38871}, {17398, 17531}, {19053, 21567}, {19054, 21566}, {19237, 31144}, {19308, 46922}, {21358, 21514}, {21475, 49948}, {21476, 49947}, {21477, 47352}, {21510, 40341}, {21515, 51186}, {21519, 47355}, {21783, 35216}, {23854, 23868}, {24328, 49747}, {37441, 40138}, {45987, 52555}
X(54409) = isogonal conjugate of the isotomic conjugate of X(37656)
X(54409) = X(39974)-Ceva conjugate of X(6)
X(54409) = crossdifference of every pair of points on line {523, 3960}
X(54409) = barycentric product X(6)*X(37656)
X(54409) = barycentric quotient X(37656)/X(76)
X(54409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4254, 37503}, {3, 37503, 6}, {6, 1030, 5124}, {6, 4258, 4289}, {6, 36744, 1030}, {6, 37504, 4287}, {32, 4277, 6}, {39, 33882, 6}, {55, 4471, 16686}, {58, 4285, 6}, {61, 62, 36750}, {284, 4271, 6}, {371, 372, 51340}, {386, 4290, 6}, {573, 584, 6}, {1333, 4263, 6}, {1953, 46823, 16777}, {2092, 2220, 6}, {2245, 4251, 6}, {2278, 4266, 6}, {4254, 36744, 6}, {4261, 16946, 6}, {4262, 4266, 2278}, {4264, 4272, 6}, {4270, 4275, 6}, {4273, 4274, 6}, {22236, 22238, 36746}, {36744, 37503, 3}
X(54410) lies on these lines: {1, 6}, {3, 75}, {8, 37225}, {10, 34247}, {21, 192}, {25, 92}, {35, 49474}, {55, 740}, {56, 4032}, {183, 1921}, {228, 5271}, {239, 37502}, {312, 16058}, {321, 1011}, {333, 20760}, {345, 8731}, {346, 52241}, {404, 4699}, {474, 3739}, {495, 4205}, {536, 16370}, {716, 47037}, {726, 993}, {742, 36740}, {894, 37507}, {975, 19518}, {976, 3728}, {1009, 2345}, {1078, 10009}, {1278, 4189}, {1284, 12588}, {1403, 32916}, {1621, 37316}, {1631, 2915}, {1999, 37323}, {2053, 2218}, {2178, 19329}, {2223, 50314}, {2352, 11358}, {2975, 13733}, {3145, 4812}, {3286, 4363}, {3295, 49470}, {3303, 49471}, {3428, 29054}, {3560, 20430}, {3564, 15976}, {3644, 17571}, {3685, 23407}, {3695, 10449}, {3696, 5687}, {3741, 4438}, {3746, 49469}, {3781, 28287}, {3797, 16367}, {3883, 31394}, {3913, 49459}, {3923, 20992}, {3993, 5248}, {4184, 28605}, {4188, 4772}, {4191, 4359}, {4358, 16373}, {4361, 5132}, {4421, 50086}, {4423, 29644}, {4664, 16418}, {4672, 36635}, {4681, 19526}, {4686, 19535}, {4687, 11108}, {4688, 16371}, {4698, 16842}, {4704, 16865}, {4709, 8715}, {4739, 19537}, {4740, 17549}, {4751, 16408}, {4755, 17542}, {4821, 17548}, {4980, 19346}, {5047, 27268}, {5192, 27261}, {5263, 33745}, {5267, 50117}, {5282, 20706}, {5695, 8053}, {5719, 16848}, {5739, 21319}, {5762, 10446}, {6284, 21927}, {7193, 52134}, {7295, 8424}, {8666, 49479}, {10436, 37609}, {10453, 17776}, {10479, 17293}, {10892, 53260}, {11194, 31178}, {11322, 31025}, {11344, 20171}, {11679, 21483}, {12329, 49531}, {13615, 20173}, {13723, 38871}, {14021, 20533}, {16059, 19804}, {16286, 18137}, {16292, 18147}, {16368, 19791}, {16846, 17322}, {16850, 17321}, {16857, 51488}, {16862, 31238}, {16998, 19565}, {17524, 50044}, {17718, 43223}, {17740, 30944}, {17894, 22388}, {18042, 23095}, {19533, 37539}, {19785, 37329}, {21010, 50302}, {21161, 51043}, {21330, 28082}, {23093, 35519}, {23863, 25124}, {24320, 49516}, {24789, 50199}, {25524, 40328}, {26107, 37042}, {27282, 37314}, {27491, 31319}, {28453, 51039}, {28463, 51047}, {30271, 37022}, {30699, 37175}, {36011, 36494}, {36280, 36294}, {36741, 49481}, {37492, 49496}, {51062, 51506}
X(54410) = X(6)-isoconjugate of X(45965)
X(54410) = X(9)-Dao conjugate of X(45965)
X(54410) = barycentric quotient X(1)/X(45965)
X(54410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 21061, 10477}, {2352, 31993, 11358}, {3696, 15624, 5687}, {38871, 41230, 13723}
X(54411) lies on these lines: {1, 5327}, {3, 6}, {21, 73}, {28, 4303}, {29, 34}, {81, 1936}, {212, 4184}, {222, 8021}, {223, 17194}, {1001, 10571}, {1427, 18165}, {1437, 40602}, {1745, 25516}, {1790, 2299}, {1817, 22053}, {1818, 2287}, {1838, 34830}, {2328, 3173}, {2360, 22654}, {2659, 31623}, {3145, 44112}, {3194, 44709}, {3330, 15972}, {4215, 26892}, {5712, 10458}, {5784, 16699}, {7078, 17524}, {7532, 15668}, {7538, 17379}, {7572, 17277}, {10391, 18603}, {15852, 18178}, {17056, 37370}, {17187, 40958}, {18166, 41344}, {27164, 34831}, {36020, 45963}
X(54411) = barycentric product X(i)*X(j) for these {i,j}: {85, 36020}, {333, 45963}
X(54411) = barycentric quotient X(i)/X(j) for these {i,j}: {36020, 9}, {45963, 226}
X(54411) = {X(81),X(35981)}-harmonic conjugate of X(1936)
X(54412) lies on the cubics K518 and K620 and also on these lines: {2, 22401}, {4, 69}, {24, 99}, {25, 305}, {30, 41009}, {32, 15014}, {33, 1909}, {34, 350}, {64, 290}, {75, 46878}, {95, 7395}, {112, 6179}, {183, 1593}, {186, 7782}, {190, 41320}, {193, 21447}, {194, 232}, {235, 325}, {274, 406}, {275, 41231}, {297, 3981}, {310, 4207}, {313, 1869}, {331, 40028}, {339, 382}, {378, 1078}, {384, 10311}, {385, 1968}, {393, 6339}, {403, 7752}, {420, 41259}, {427, 40022}, {458, 4074}, {468, 11059}, {475, 18140}, {538, 3199}, {648, 2207}, {671, 43678}, {850, 46371}, {1007, 6622}, {1093, 6528}, {1118, 18026}, {1172, 34283}, {1228, 4198}, {1230, 6994}, {1321, 34391}, {1322, 34392}, {1494, 52646}, {1596, 3933}, {1861, 6376}, {1885, 7750}, {1974, 12215}, {2052, 2996}, {2211, 32451}, {2481, 43742}, {3053, 37199}, {3087, 26214}, {3088, 32828}, {3089, 3926}, {3091, 26166}, {3144, 30022}, {3146, 30737}, {3172, 14614}, {3192, 33296}, {3266, 4232}, {3520, 7771}, {3541, 32832}, {3542, 7763}, {3575, 32819}, {3934, 33843}, {3972, 10312}, {4194, 34284}, {4196, 18152}, {4200, 18135}, {5186, 5976}, {5200, 45805}, {5286, 17907}, {6337, 6353}, {6390, 21841}, {6623, 32816}, {6823, 45198}, {6995, 8024}, {7378, 39998}, {7487, 28706}, {7505, 7769}, {7547, 15031}, {7738, 37187}, {7745, 27377}, {7748, 40889}, {7757, 39575}, {7760, 8743}, {7767, 13488}, {7770, 36794}, {7773, 37197}, {7802, 18560}, {7805, 14581}, {7812, 37855}, {7814, 44958}, {8149, 33874}, {9217, 14382}, {9464, 52301}, {10604, 40050}, {11414, 46724}, {11470, 39099}, {14063, 26179}, {14265, 22456}, {14457, 54124}, {15149, 30830}, {16089, 18913}, {18018, 34603}, {20477, 39568}, {26164, 32974}, {26235, 52284}, {27376, 47286}, {28660, 37384}, {28809, 37102}, {30716, 37915}, {32581, 52570}, {34505, 52282}, {35477, 43459}, {37765, 41361}, {40009, 46140}, {40680, 52404}, {40890, 52628}, {41584, 51374}, {41760, 44518}, {44228, 47392}, {45806, 52291}, {46105, 53105}, {53197, 53205}
X(54412) = isogonal conjugate of X(40319)
X(54412) = isotomic conjugate of X(6391)
X(54412) = anticomplement of X(22401)
X(54412) = polar conjugate of X(8770)
X(54412) = isotomic conjugate of the isogonal conjugate of X(6353)
X(54412) = isotomic conjugate of the polar conjugate of X(21447)
X(54412) = polar conjugate of the isogonal conjugate of X(193)
X(54412) = X(40413)-anticomplementary conjugate of X(4329)
X(54412) = X(i)-Ceva conjugate of X(j) for these (i,j): {2052, 264}, {34537, 648}
X(54412) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40319}, {3, 38252}, {31, 6391}, {48, 8770}, {63, 53059}, {184, 8769}, {255, 14248}, {560, 6340}, {810, 3565}, {2996, 9247}, {34208, 52430}
X(54412) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6391}, {3, 40319}, {69, 394}, {1249, 8770}, {2489, 3124}, {3162, 53059}, {6353, 9924}, {6374, 6340}, {6388, 520}, {6509, 45199}, {6523, 14248}, {15525, 647}, {36103, 38252}, {39062, 3565}, {51579, 3}
cevapoint of X(i) and X(j) for these (i,j): {4, 6392}, {25, 40318}, {193, 6353}
X(54412) = barycentric product X(i)*X(j) for these {i,j}: {69, 21447}, {76, 6353}, {92, 18156}, {193, 264}, {276, 41588}, {308, 41584}, {683, 40326}, {1502, 19118}, {1707, 1969}, {2052, 6337}, {3053, 18022}, {3167, 18027}, {3566, 6331}, {4028, 44129}, {5139, 34537}, {7017, 17081}, {16081, 51374}, {17876, 46254}, {32459, 46111}, {47733, 51843}
X(54412) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6391}, {4, 8770}, {6, 40319}, {19, 38252}, {25, 53059}, {76, 6340}, {92, 8769}, {193, 3}, {264, 2996}, {324, 27364}, {393, 14248}, {439, 3167}, {648, 3565}, {1611, 53068}, {1707, 48}, {2052, 34208}, {3053, 184}, {3167, 577}, {3566, 647}, {3787, 20775}, {3798, 1459}, {4028, 71}, {5139, 3124}, {6331, 35136}, {6337, 394}, {6353, 6}, {6388, 20975}, {8651, 3049}, {8940, 6414}, {8944, 6413}, {10607, 1092}, {13567, 45199}, {17081, 222}, {17876, 3708}, {18156, 63}, {19118, 32}, {21447, 4}, {21874, 228}, {21970, 5158}, {32459, 3292}, {33632, 10547}, {37174, 40809}, {37199, 9306}, {37778, 5203}, {40318, 15261}, {40326, 6467}, {41584, 39}, {41588, 216}, {47733, 3504}, {51374, 36212}
X(54412) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 76, 264}, {4, 3186, 40325}, {4, 32001, 32006}, {4, 44146, 76}, {264, 340, 44133}, {297, 40814, 15466}, {2207, 7754, 648}, {3934, 33843, 37337}, {14615, 44131, 264}, {32001, 44131, 14615}, {37174, 51481, 2052}, {43976, 44132, 264}, {44780, 44781, 14615}
X(54413) lies on the cubics K281 and K731 and also on these lines: {2, 729}, {6, 538}, {32, 3231}, {39, 33705}, {182, 14609}, {187, 46319}, {213, 52893}, {574, 9468}, {1084, 30495}, {1918, 52894}, {1974, 5033}, {3016, 14601}, {3224, 7808}, {3288, 22111}, {5034, 39238}, {5970, 6787}, {7787, 42346}, {7815, 36615}, {9431, 15482}, {9463, 12150}, {9490, 17130}, {9516, 42534}, {19137, 41412}, {40354, 52905}
X(54413) = isogonal conjugate of X(7757)
X(54413) = isogonal conjugate of the anticomplement of X(9466)
X(54413) = isogonal conjugate of the isotomic conjugate of X(9462)
X(54413) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7757}, {2, 36289}, {75, 9463}, {662, 5996}, {799, 9009}, {1966, 11654}, {4602, 9489}
X(54413) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 7757}, {206, 9463}, {1084, 5996}, {9467, 11654}, {32664, 36289}, {38996, 9009}
X(54413) = trilinear pole of line {669, 888}
X(54413) = crossdifference of every pair of points on line {5996, 9009}
X(54413) = barycentric product X(i)*X(j) for these {i,j}: {6, 9462}, {512, 9066}
X(54413) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7757}, {31, 36289}, {32, 9463}, {512, 5996}, {669, 9009}, {9066, 670}, {9426, 9489}, {9462, 76}, {9468, 11654}
X(54414) lies on the cubics K333 and K713 and also on these lines: {1, 1864}, {9, 222}, {57, 23089}, {223, 329}, {226, 2999}, {651, 1422}, {1103, 6260}, {1490, 22350}, {1743, 3173}, {1750, 4551}, {6510, 34032}, {8808, 27508}, {9371, 53087}, {23511, 52659}, {45204, 54366}
X(54414) = X(7)-Ceva conjugate of X(40)
X(54414) = X(2324)-Dao conjugate of X(8)
X(54414) = barycentric product X(347)*X(6765)
X(54414) = barycentric quotient X(6765)/X(280)
X(54415) lies on the cubics K611 and K1169, and on the curve Q066, and on these lines: {2, 38936}, {186, 2931}, {403, 16310}, {3153, 5962}, {3448, 32710}, {5627, 40388}, {10421, 18533}, {12028, 16221}, {14222, 14618}, {51965, 52487}
X(54415) = isogonal conjugate of X(2931)
X(54415) = cyclocevian conjugate of X(94)
X(54415) = isogonal conjugate of the anticomplement of X(23306)
X(54415) = isogonal conjugate of the complement of X(12319)
X(54415) = isotomic conjugate of the anticomplement of X(14910)
X(54415) = X(1)-isoconjugate of X(2931)
X(54415) = X(3)-Dao conjugate of X(2931)
X(54415) = cevapoint of X(i) and X(j) for these (i,j): {512, 39021}, {523, 16221}
X(54415) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 2931}, {40388, 40392}
X(54416) lies on these lines: {1, 6}, {2, 31402}, {3, 172}, {5, 9596}, {8, 5276}, {10, 5275}, {11, 2548}, {12, 3767}, {25, 41}, {30, 9598}, {31, 1334}, {32, 55}, {33, 2207}, {35, 609}, {36, 5013}, {39, 56}, {57, 9593}, {58, 3730}, {65, 9620}, {75, 11321}, {81, 7123}, {86, 27248}, {101, 386}, {115, 9650}, {140, 31497}, {165, 31426}, {169, 41015}, {171, 3501}, {183, 27020}, {187, 5217}, {192, 384}, {194, 6645}, {198, 2092}, {217, 19354}, {222, 3497}, {230, 498}, {232, 11399}, {239, 39731}, {304, 894}, {312, 41236}, {315, 26590}, {321, 19281}, {330, 7839}, {344, 33821}, {346, 2298}, {350, 7770}, {371, 31459}, {388, 5286}, {404, 17756}, {406, 1783}, {474, 1575}, {495, 5305}, {496, 9599}, {499, 3815}, {517, 54382}, {574, 5204}, {604, 4322}, {608, 2171}, {612, 1184}, {631, 31462}, {672, 1468}, {728, 5269}, {904, 41268}, {910, 4646}, {940, 3912}, {949, 36018}, {975, 16849}, {976, 3930}, {986, 3509}, {987, 1922}, {993, 25092}, {999, 2275}, {1010, 2303}, {1015, 3304}, {1018, 5264}, {1030, 37557}, {1060, 23115}, {1155, 1571}, {1172, 7718}, {1193, 9310}, {1213, 19784}, {1278, 16913}, {1319, 9619}, {1333, 17524}, {1376, 5277}, {1415, 11509}, {1420, 9592}, {1429, 52424}, {1438, 2334}, {1478, 5254}, {1479, 7745}, {1504, 18996}, {1505, 18995}, {1570, 5194}, {1572, 3057}, {1574, 4413}, {1580, 37327}, {1611, 5268}, {1613, 40790}, {1672, 12051}, {1673, 12050}, {1692, 5148}, {1696, 21796}, {1759, 4424}, {1909, 7754}, {1914, 3295}, {1930, 4363}, {1975, 25264}, {2023, 10069}, {2066, 6424}, {2067, 6422}, {2162, 3494}, {2172, 2174}, {2178, 4261}, {2179, 20665}, {2221, 28606}, {2238, 4205}, {2241, 3303}, {2251, 4258}, {2285, 2286}, {2292, 5282}, {2295, 3695}, {2304, 9454}, {2330, 40825}, {2344, 43073}, {2476, 17737}, {2549, 7354}, {2915, 18755}, {2975, 31449}, {3027, 10797}, {3063, 48327}, {3085, 7735}, {3086, 7736}, {3125, 16550}, {3157, 23128}, {3172, 7071}, {3175, 50060}, {3204, 4272}, {3207, 4255}, {3208, 5255}, {3240, 4239}, {3287, 48290}, {3496, 37598}, {3585, 44518}, {3614, 43620}, {3616, 33854}, {3666, 11343}, {3670, 17736}, {3672, 17691}, {3674, 6180}, {3684, 50581}, {3693, 37539}, {3735, 37614}, {3746, 7031}, {3752, 37272}, {3758, 18156}, {3774, 34247}, {3780, 36479}, {3911, 31396}, {3915, 21764}, {3920, 5359}, {3924, 21808}, {3991, 5266}, {3993, 49545}, {3995, 11320}, {4000, 17682}, {4204, 21753}, {4252, 42316}, {4254, 12410}, {4257, 24047}, {4262, 33771}, {4263, 51436}, {4293, 7738}, {4316, 44519}, {4317, 9607}, {4366, 7787}, {4372, 24326}, {4383, 17023}, {4386, 5687}, {4390, 10459}, {4441, 17686}, {4513, 5710}, {4644, 17170}, {4699, 16911}, {4704, 16914}, {4972, 26085}, {5010, 5023}, {5019, 54322}, {5058, 19038}, {5062, 19037}, {5122, 31430}, {5206, 9341}, {5229, 43448}, {5262, 16048}, {5271, 19725}, {5306, 10056}, {5309, 11237}, {5319, 15888}, {5332, 6767}, {5341, 16545}, {5364, 40978}, {5414, 6423}, {5422, 26639}, {5433, 31401}, {5434, 7739}, {5452, 20970}, {5475, 10896}, {5703, 40129}, {5706, 39591}, {5724, 40997}, {6161, 43929}, {6198, 8743}, {6284, 7737}, {6421, 6502}, {6602, 10460}, {7079, 20310}, {7083, 40969}, {7085, 44119}, {7109, 37316}, {7173, 31415}, {7232, 17192}, {7280, 15815}, {7288, 31400}, {7368, 16283}, {7746, 31476}, {7747, 9664}, {7748, 12943}, {7749, 31501}, {7753, 9665}, {7763, 26686}, {7765, 9651}, {7778, 30103}, {7803, 26561}, {7951, 13881}, {8193, 36744}, {8588, 46846}, {9300, 10072}, {9336, 37602}, {9548, 37320}, {9574, 15803}, {9597, 15048}, {9661, 31463}, {9669, 15484}, {9780, 37675}, {10053, 12829}, {10311, 11398}, {10483, 44526}, {10527, 31466}, {10589, 31404}, {10592, 43291}, {10802, 34870}, {10987, 21309}, {11174, 26959}, {11269, 37315}, {11333, 41318}, {11337, 32758}, {11358, 21877}, {11363, 45786}, {11392, 27376}, {11501, 21859}, {12150, 53680}, {12836, 46305}, {12948, 31472}, {12949, 44622}, {13006, 22766}, {13733, 39686}, {13898, 31481}, {14986, 37665}, {14996, 29583}, {15171, 18907}, {15325, 31406}, {16394, 17281}, {16458, 17303}, {16549, 37522}, {16583, 40131}, {16818, 17259}, {16912, 27268}, {16915, 17759}, {16992, 27255}, {16995, 53675}, {16997, 26752}, {17015, 33950}, {17018, 37325}, {17143, 20172}, {17144, 20179}, {17233, 33954}, {17280, 17688}, {17284, 37674}, {17302, 33827}, {17398, 19836}, {17451, 49487}, {17592, 21775}, {17698, 24512}, {17743, 41240}, {17754, 37607}, {17976, 50598}, {18140, 26687}, {18166, 33953}, {18447, 22120}, {18596, 37241}, {18993, 45582}, {18994, 45583}, {19030, 31411}, {19231, 20136}, {19349, 39643}, {19785, 50200}, {20181, 32104}, {20227, 54385}, {20861, 50591}, {20980, 48332}, {21007, 48324}, {21070, 48863}, {21348, 22157}, {21789, 21837}, {21843, 52793}, {23151, 37676}, {24914, 31398}, {25066, 54317}, {26036, 33137}, {26223, 42707}, {26363, 37661}, {26437, 43039}, {26626, 32911}, {28594, 30142}, {29579, 37633}, {29585, 37685}, {29598, 37679}, {29633, 37673}, {29674, 40750}, {29815, 34482}, {30130, 33937}, {31231, 31428}, {31433, 37568}, {34046, 52635}, {35768, 45512}, {35769, 45513}, {37314, 37657}, {37546, 54409}, {37589, 39255}, {41323, 50592}, {44103, 51686}, {49771, 50028}
X(54416) = isogonal conjugate of the isotomic conjugate of X(2345)
X(54416) = isogonal conjugate of the polar conjugate of X(7102)
X(54416) = polar conjugate of the isotomic conjugate of X(7085)
X(54416) = X(i)-Ceva conjugate of X(j) for these (i,j): {941, 55}, {2285, 1460}, {2303, 612}, {2345, 7085}, {6574, 667}
X(54416) = X(i)-isoconjugate of X(j) for these (i,j): {7, 2339}, {57, 30479}, {75, 2221}, {76, 1472}, {85, 1036}, {274, 1245}, {304, 51686}, {310, 2281}, {348, 1039}, {513, 37215}, {514, 1310}, {4025, 36099}, {10436, 34260}, {15413, 32691}
X(54416) = X(i)-Dao conjugate of X(j) for these (i,j): {206, 2221}, {958, 34284}, {5452, 30479}, {5515, 3261}, {17421, 15413}, {39026, 37215}, {40125, 4000}, {40181, 75}
X(54416) = trilinear pole of line {2484, 8646}
X(54416) = crossdifference of every pair of points on line {513, 3004}
X(54416) = barycentric product X(i)*X(j) for these {i,j}: {1, 612}, {3, 7102}, {4, 7085}, {6, 2345}, {8, 1460}, {9, 2285}, {10, 44119}, {19, 5227}, {31, 4385}, {33, 1038}, {37, 2303}, {42, 1010}, {55, 388}, {56, 3974}, {72, 4206}, {99, 50494}, {100, 8678}, {101, 6590}, {110, 48395}, {190, 2484}, {200, 4320}, {210, 5323}, {220, 7365}, {281, 2286}, {480, 7197}, {663, 14594}, {668, 8646}, {692, 2517}, {941, 34261}, {1184, 30701}, {1260, 7103}, {1474, 3610}, {1783, 2522}, {1918, 44154}, {1973, 19799}, {2287, 8898}, {4557, 47844}, {5286, 7123}, {7070, 10375}, {8750, 23874}, {8816, 30706}, {17742, 40184}
X(54416) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 2221}, {41, 2339}, {55, 30479}, {101, 37215}, {388, 6063}, {560, 1472}, {612, 75}, {692, 1310}, {1010, 310}, {1038, 7182}, {1184, 4000}, {1460, 7}, {1918, 1245}, {1974, 51686}, {2175, 1036}, {2205, 2281}, {2212, 1039}, {2285, 85}, {2286, 348}, {2303, 274}, {2345, 76}, {2484, 514}, {2517, 40495}, {2522, 15413}, {3610, 40071}, {3974, 3596}, {4206, 286}, {4320, 1088}, {4385, 561}, {5227, 304}, {6590, 3261}, {7085, 69}, {7102, 264}, {8646, 513}, {8678, 693}, {8898, 1446}, {14594, 4572}, {19459, 17170}, {19799, 40364}, {30701, 40831}, {34261, 34284}, {36744, 14258}, {40184, 46740}, {44119, 86}, {47844, 52619}, {48395, 850}, {50494, 523}
X(54416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6, 16502}, {1, 5280, 6}, {1, 5299, 16781}, {1, 17742, 37}, {1, 54329, 41239}, {2, 31402, 31460}, {3, 2276, 31448}, {6, 220, 213}, {6, 2176, 16466}, {6, 2256, 2300}, {6, 16781, 5299}, {31, 1334, 14974}, {32, 1500, 55}, {35, 609, 3053}, {37, 4426, 405}, {39, 2242, 56}, {41, 42, 2271}, {41, 607, 30706}, {41, 51949, 2200}, {115, 9650, 10895}, {172, 2276, 3}, {187, 31451, 5217}, {312, 41258, 41236}, {672, 1468, 5021}, {999, 9605, 2275}, {1124, 1335, 611}, {1914, 7296, 30435}, {2176, 16523, 1}, {2303, 2345, 34261}, {3053, 31477, 35}, {3295, 30435, 1914}, {3767, 31409, 12}, {4386, 20691, 5687}, {5058, 31471, 19038}, {5280, 16785, 1}, {5283, 5291, 958}, {5299, 16781, 16502}, {7031, 9331, 3746}, {7747, 9664, 12953}, {15048, 18990, 9597}
X(54417) lies on these lines: {1, 1437}, {3, 6}, {21, 60}, {28, 1905}, {35, 22276}, {46, 18163}, {55, 283}, {56, 1790}, {65, 81}, {86, 28628}, {184, 19765}, {209, 54337}, {314, 52550}, {333, 26066}, {407, 49745}, {442, 6703}, {501, 34956}, {662, 37442}, {692, 37573}, {859, 22766}, {940, 4185}, {1010, 5794}, {1064, 44709}, {1428, 4719}, {1682, 20959}, {1724, 16455}, {1780, 17524}, {1792, 2330}, {1800, 22768}, {1834, 37527}, {1837, 11103}, {2182, 2303}, {2206, 10457}, {3057, 3193}, {3612, 52680}, {3812, 17518}, {4189, 34259}, {4221, 14110}, {4225, 40214}, {4340, 14018}, {4653, 17104}, {5324, 17603}, {5327, 37422}, {5743, 7483}, {5799, 37468}, {6910, 14555}, {10458, 13733}, {11112, 48845}, {12609, 17197}, {12675, 25713}, {13750, 18180}, {16948, 37600}, {19767, 44085}, {20832, 44092}, {24929, 41608}, {25681, 31631}, {27622, 45897}, {27644, 28275}, {27660, 37225}, {37296, 51290}, {37552, 47373}, {40980, 54356}, {46976, 53421}
X(54417) = isogonal conjugate of the polar conjugate of X(44734)
X(54417) = X(i)-isoconjugate of X(j) for these (i,j): {10, 959}, {12, 5331}, {37, 44733}, {65, 31359}, {225, 34259}, {226, 941}, {522, 52931}, {661, 32038}, {1400, 34258}, {1441, 2258}, {1577, 32693}, {2171, 37870}
X(54417) = X(i)-Dao conjugate of X(j) for these (i,j): {17417, 1577}, {34261, 321}, {36830, 32038}, {40582, 34258}, {40589, 44733}, {40602, 31359}
X(54417) = barycentric product X(i)*X(j) for these {i,j}: {3, 44734}, {21, 940}, {58, 11679}, {60, 31993}, {81, 958}, {86, 2268}, {110, 23880}, {283, 5307}, {284, 10436}, {314, 5019}, {333, 1468}, {593, 3714}, {643, 48144}, {662, 17418}, {1014, 3713}, {1790, 54396}, {1812, 4185}, {2194, 34284}, {4570, 53526}, {4612, 8672}, {4631, 8639}, {4636, 50457}, {5546, 43067}, {16049, 34279}
X(54417) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 34258}, {58, 44733}, {60, 37870}, {110, 32038}, {284, 31359}, {314, 40828}, {940, 1441}, {958, 321}, {1333, 959}, {1415, 52931}, {1468, 226}, {1576, 32693}, {2150, 5331}, {2193, 34259}, {2194, 941}, {2268, 10}, {3713, 3701}, {3714, 28654}, {4185, 40149}, {5019, 65}, {10436, 349}, {11679, 313}, {17418, 1577}, {23880, 850}, {31993, 34388}, {44734, 264}, {48144, 4077}, {52143, 34263}, {53526, 21207}
X(54417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 50597, 33844}, {6, 1030, 50033}, {21, 60, 2194}, {21, 1812, 960}, {58, 284, 4267}, {58, 15792, 4276}, {58, 54323, 3}, {81, 16049, 65}, {333, 37232, 26066}, {1805, 1806, 6}
X(54418) lies on these lines: {1, 2}, {4, 1039}, {6, 19}, {9, 2292}, {12, 3772}, {21, 17594}, {28, 44119}, {31, 40}, {33, 429}, {35, 37817}, {36, 39582}, {46, 58}, {55, 1104}, {56, 197}, {57, 961}, {63, 986}, {75, 1220}, {77, 3212}, {81, 17518}, {100, 37552}, {141, 10371}, {169, 5280}, {171, 24440}, {201, 8557}, {204, 11471}, {208, 17408}, {213, 9620}, {223, 1042}, {238, 5250}, {241, 15832}, {244, 3333}, {294, 5665}, {341, 32926}, {354, 17054}, {377, 1738}, {388, 4000}, {405, 968}, {442, 5725}, {517, 16466}, {518, 37549}, {593, 37405}, {595, 5119}, {601, 3359}, {672, 9593}, {748, 31435}, {750, 37554}, {774, 10396}, {894, 21216}, {896, 54290}, {940, 3812}, {950, 3755}, {956, 19527}, {958, 3666}, {959, 34045}, {960, 4383}, {964, 50314}, {988, 2975}, {990, 5691}, {1001, 37548}, {1038, 1788}, {1040, 3486}, {1046, 21376}, {1054, 37608}, {1056, 23675}, {1062, 37730}, {1086, 10404}, {1155, 4252}, {1191, 3057}, {1203, 5903}, {1253, 1697}, {1279, 3303}, {1329, 17720}, {1334, 16970}, {1376, 37539}, {1386, 5710}, {1394, 9316}, {1402, 13738}, {1403, 22345}, {1448, 3339}, {1451, 37550}, {1455, 1466}, {1458, 1467}, {1469, 16980}, {1478, 23537}, {1497, 24028}, {1575, 54317}, {1616, 5919}, {1706, 4695}, {1716, 26117}, {1721, 3146}, {1724, 4424}, {1739, 37522}, {1743, 12526}, {1751, 2258}, {1757, 3951}, {1763, 35650}, {1764, 34281}, {1772, 17700}, {1854, 1864}, {1891, 5800}, {1902, 3195}, {2092, 5336}, {2093, 2308}, {2099, 40635}, {2170, 9575}, {2176, 52370}, {2177, 16485}, {2191, 2334}, {2197, 2277}, {2274, 37523}, {2276, 16968}, {2280, 16780}, {2295, 16972}, {2300, 10480}, {2475, 33131}, {2476, 17064}, {2478, 24210}, {2550, 5716}, {2646, 4255}, {2650, 11529}, {2901, 42707}, {3052, 37568}, {3058, 34656}, {3120, 9612}, {3304, 52541}, {3306, 24174}, {3338, 24046}, {3340, 34036}, {3361, 54310}, {3436, 13161}, {3485, 19372}, {3553, 26063}, {3589, 5835}, {3610, 17314}, {3612, 4256}, {3646, 17125}, {3663, 12527}, {3664, 41826}, {3671, 5813}, {3677, 6762}, {3685, 17697}, {3691, 16517}, {3698, 3745}, {3702, 5192}, {3704, 32777}, {3727, 39248}, {3729, 17489}, {3735, 54406}, {3736, 37232}, {3743, 54287}, {3744, 3913}, {3749, 3871}, {3751, 3868}, {3753, 5711}, {3780, 16973}, {3813, 17721}, {3869, 32911}, {3880, 37542}, {3891, 4696}, {3895, 37588}, {3946, 5795}, {3987, 5264}, {4195, 32932}, {4217, 28580}, {4260, 39598}, {4295, 41011}, {4296, 37666}, {4298, 24177}, {4300, 30503}, {4332, 10460}, {4339, 17784}, {4348, 4848}, {4361, 5793}, {4414, 31424}, {4429, 7270}, {4652, 17596}, {4656, 18250}, {4673, 32942}, {4674, 54336}, {4749, 6284}, {4868, 5248}, {4917, 16498}, {4972, 5016}, {5018, 23579}, {5046, 33134}, {5252, 17366}, {5253, 11512}, {5255, 16478}, {5260, 28606}, {5266, 5687}, {5275, 16605}, {5290, 23681}, {5310, 8193}, {5315, 5697}, {5322, 9798}, {5338, 44115}, {5429, 37603}, {5436, 37553}, {5584, 15852}, {5587, 21935}, {5706, 7686}, {5712, 28629}, {5718, 28628}, {5724, 5794}, {5727, 7221}, {5838, 12560}, {5880, 49745}, {6051, 11108}, {6203, 18992}, {6204, 18991}, {6210, 23659}, {6261, 37732}, {7174, 21039}, {7194, 39969}, {7354, 34666}, {7986, 40263}, {7991, 16469}, {8715, 49480}, {9548, 27659}, {9605, 43065}, {9619, 53165}, {9643, 37721}, {9817, 54361}, {9895, 37697}, {9957, 16483}, {9958, 48903}, {10315, 52425}, {10375, 41489}, {10436, 20911}, {10448, 46904}, {10572, 48837}, {10822, 26893}, {11114, 50080}, {11236, 50103}, {11319, 32929}, {11354, 50083}, {11375, 37662}, {11523, 49454}, {11681, 33133}, {12607, 17061}, {12652, 20070}, {12709, 34048}, {13407, 24159}, {13601, 34040}, {14014, 46883}, {14110, 36745}, {14529, 44085}, {16451, 16778}, {16473, 53615}, {16474, 18398}, {16583, 40131}, {16600, 17742}, {16610, 25524}, {16974, 20691}, {17164, 26223}, {17185, 27660}, {17277, 31359}, {17279, 25992}, {17301, 34606}, {17597, 34791}, {17602, 21031}, {17863, 27410}, {18178, 40153}, {18446, 37699}, {18623, 41824}, {18732, 23122}, {20060, 33150}, {21075, 34937}, {22119, 41340}, {24161, 31266}, {24474, 44414}, {24789, 25466}, {24914, 37646}, {24954, 51415}, {25681, 37663}, {25917, 37679}, {26066, 35466}, {28076, 40987}, {30380, 31533}, {30381, 31532}, {31426, 41423}, {32860, 54331}, {33094, 41869}, {33781, 50408}, {34046, 37566}, {34339, 36742}, {34720, 50130}, {35258, 54354}, {35635, 51558}, {36752, 37562}, {37314, 50290}, {37529, 42078}, {37558, 45126}, {37615, 37698}, {40941, 54385}, {40959, 52359}, {40985, 44094}, {42051, 48832}, {48812, 50106}, {48821, 50046}, {48826, 50049}, {48827, 49719}, {49732, 50070}, {50055, 50091}
X(54418) = polar conjugate of the isotomic conjugate of X(10319)
X(54418) = X(10319)-Dao conjugate of X(17321)
X(54418) = crossdifference of every pair of points on line {521, 649}
X(54418) = barycentric product X(i)*X(j) for these {i,j}: {4, 10319}, {7, 54359}, {34, 23600}, {57, 2551}, {63, 52082}, {651, 47136}
X(54418) = barycentric quotient X(i)/X(j) for these {i,j}: {2551, 312}, {10319, 69}, {23600, 3718}, {47136, 4391}, {52082, 92}, {54359, 8}
X(54418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 612}, {1, 43, 78}, {1, 200, 976}, {1, 614, 28011}, {1, 978, 19861}, {1, 1698, 975}, {1, 1722, 2}, {1, 2999, 1193}, {1, 3216, 997}, {1, 3293, 3811}, {1, 5272, 3616}, {1, 6048, 5293}, {1, 6765, 3938}, {1, 9623, 10459}, {1, 18395, 54401}, {1, 23511, 8583}, {1, 50581, 3870}, {2, 17016, 1}, {6, 3959, 54382}, {6, 41015, 2082}, {8, 5262, 1}, {8, 26965, 31339}, {10, 40940, 5230}, {31, 4642, 40}, {34, 65, 2263}, {40, 1453, 31}, {42, 3924, 1}, {57, 21147, 4320}, {145, 7191, 1}, {238, 37598, 5250}, {388, 4000, 23536}, {405, 3931, 968}, {950, 54295, 4319}, {976, 3214, 200}, {986, 5247, 63}, {995, 15955, 1}, {1104, 4646, 55}, {1193, 49487, 1}, {1386, 5836, 5710}, {1468, 24443, 57}, {1697, 7290, 3915}, {1724, 4424, 12514}, {1788, 54292, 1038}, {2362, 16232, 2285}, {2975, 4850, 988}, {3244, 30148, 1}, {3436, 19785, 13161}, {3616, 17015, 1}, {3869, 32911, 54386}, {3987, 5264, 54286}, {4383, 37614, 960}, {5256, 19860, 1}, {8583, 23511, 27627}, {10459, 17017, 1}, {22836, 49682, 1}, {24174, 37607, 3306}
X(54419) lies on these lines: {1, 21}, {2, 41}, {6, 28287}, {7, 604}, {27, 1973}, {42, 37090}, {48, 86}, {57, 21511}, {101, 16831}, {172, 940}, {239, 2280}, {284, 1958}, {304, 52379}, {379, 2140}, {405, 23151}, {572, 10444}, {584, 3739}, {662, 41847}, {672, 16367}, {750, 18266}, {894, 2268}, {942, 13723}, {1013, 2356}, {1150, 3912}, {1760, 2294}, {2112, 17397}, {2174, 15668}, {2185, 17103}, {2187, 37103}, {2241, 54282}, {2267, 3758}, {2278, 4670}, {2327, 28627}, {2329, 5273}, {3204, 4698}, {3217, 17260}, {3306, 11349}, {3720, 25494}, {3998, 50716}, {4197, 29633}, {4209, 9776}, {4223, 54392}, {4251, 4384}, {4390, 6542}, {4426, 37676}, {4649, 54383}, {5256, 16780}, {5278, 29960}, {5294, 33819}, {5337, 17750}, {5712, 41243}, {5736, 29967}, {6734, 37149}, {7675, 28071}, {9310, 16826}, {9318, 27907}, {9454, 20131}, {13738, 19716}, {16368, 19714}, {16524, 18278}, {16787, 17011}, {17032, 51949}, {17321, 18162}, {17394, 18042}, {17696, 26065}, {17754, 21495}, {20347, 37076}, {20835, 37580}, {23124, 46882}, {24929, 25083}, {26229, 36021}, {29822, 50404}, {29837, 37443}, {30949, 50200}, {30985, 37086}, {34055, 52394}, {37285, 37576}, {37632, 41258}, {38252, 40737}
X(54419) = X(2)-isoconjugate of X(45966)
X(54419) = X(32664)-Dao conjugate of X(45966)
X(54419) = barycentric product X(i)*X(j) for these {i,j}: {1, 16992}, {63, 11341}, {75, 5138}
X(54419) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 45966}, {5138, 1}, {11341, 92}, {16992, 75}
X(54419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40744, 41}, {284, 10436, 1958}, {1429, 16503, 26626}
X(54410) lies on these lines: {1, 2178}, {3, 2262}, {4, 9}, {6, 46}, {20, 1741}, {30, 54008}, {36, 1609}, {37, 5119}, {48, 12704}, {57, 77}, {63, 3686}, {65, 4254}, {90, 2960}, {142, 24590}, {155, 610}, {198, 517}, {218, 21866}, {219, 910}, {380, 37550}, {484, 1743}, {579, 1195}, {978, 50361}, {1030, 3612}, {1100, 3338}, {1155, 5120}, {1172, 1452}, {1182, 2257}, {1213, 51557}, {1436, 37623}, {1479, 24005}, {1572, 2277}, {1604, 22770}, {1630, 15836}, {1697, 3247}, {1708, 3101}, {1723, 2245}, {1729, 15945}, {1730, 10319}, {1759, 5227}, {1763, 3684}, {1804, 34492}, {1903, 37411}, {2092, 54382}, {2164, 36743}, {2199, 21147}, {2269, 54405}, {2278, 17700}, {2285, 4266}, {2324, 7991}, {2328, 5338}, {2900, 3198}, {2938, 24708}, {3169, 3509}, {3218, 20082}, {3333, 4262}, {3336, 16667}, {3428, 15817}, {3553, 5903}, {3579, 54322}, {3731, 11010}, {3959, 5336}, {4047, 37658}, {4269, 21384}, {4384, 54404}, {4858, 10444}, {5036, 7297}, {5128, 16670}, {5250, 5257}, {5285, 11383}, {7013, 43035}, {7031, 41332}, {7070, 52427}, {7113, 17437}, {7289, 20367}, {7580, 9119}, {7964, 15288}, {10605, 50528}, {11349, 53996}, {11415, 27522}, {12702, 21871}, {15496, 26893}, {16673, 37563}, {16884, 51816}, {17275, 41229}, {19297, 30323}, {20070, 27508}, {21068, 28194}, {21857, 54406}, {22124, 40943}, {25521, 27000}, {31393, 47299}, {36641, 41339}, {37419, 45206}, {37489, 41854}, {37499, 40937}, {37500, 43065}, {50033, 54386}
X(54420) = Bevan-circle-inverse of X(5179)
X(54420) = X(2994)-Ceva conjugate of X(1)
X(54420) = X(2)-isoconjugate of X(34447)
X(54420) = X(i)-Dao conjugate of X(j) for these (i,j): {46, 5905}, {32664, 34447}
X(54420) = crossdifference of every pair of points on line {1459, 4041}
X(54420) = barycentric product X(i)*X(j) for these {i,j}: {1, 11415}, {57, 27522}, {75, 15494}
X(54420) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 34447}, {11415, 75}, {15494, 1}, {27522, 312}
X(54420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19, 573, 9}, {40, 2270, 9}, {71, 169, 9}, {573, 5011, 19}, {966, 12514, 9}, {1766, 2183, 9}
X(54421) lies on these lines: {1, 21}, {2, 54386}, {4, 41011}, {6, 19}, {7, 23536}, {8, 193}, {10, 5739}, {33, 1858}, {40, 42}, {46, 386}, {56, 3185}, {57, 959}, {72, 612}, {73, 37550}, {78, 171}, {86, 969}, {145, 4339}, {172, 52425}, {201, 3553}, {213, 40131}, {222, 4320}, {223, 1254}, {226, 5230}, {238, 54392}, {354, 1191}, {377, 50307}, {387, 1838}, {388, 4644}, {484, 5312}, {517, 36742}, {518, 5710}, {519, 50043}, {524, 5835}, {601, 37531}, {602, 18443}, {604, 23623}, {609, 4291}, {614, 942}, {750, 936}, {757, 44179}, {940, 960}, {946, 11269}, {958, 4641}, {975, 5692}, {976, 5269}, {978, 3306}, {984, 3951}, {986, 5256}, {988, 3218}, {990, 15071}, {995, 3338}, {997, 37522}, {999, 20805}, {1036, 37581}, {1064, 5709}, {1096, 3194}, {1155, 4255}, {1201, 3333}, {1203, 5902}, {1220, 3758}, {1245, 51223}, {1386, 37549}, {1419, 7273}, {1420, 54310}, {1430, 5706}, {1448, 34043}, {1452, 3192}, {1453, 2308}, {1467, 1471}, {1469, 23154}, {1475, 9575}, {1572, 20963}, {1610, 5323}, {1616, 17609}, {1697, 2293}, {1706, 3214}, {1708, 37558}, {1714, 12609}, {1721, 9961}, {1722, 32911}, {1724, 54318}, {1732, 5165}, {1754, 12520}, {1757, 28375}, {1766, 12435}, {1770, 48837}, {1834, 1836}, {1837, 5155}, {1938, 22383}, {2003, 21147}, {2093, 4642}, {2194, 14529}, {2257, 42289}, {2646, 4252}, {2654, 30223}, {2999, 3339}, {3011, 3487}, {3052, 37080}, {3072, 18446}, {3157, 52077}, {3187, 17164}, {3293, 54286}, {3303, 21002}, {3336, 5313}, {3340, 4332}, {3475, 28027}, {3485, 37642}, {3556, 37538}, {3612, 4257}, {3616, 38000}, {3646, 30950}, {3649, 3772}, {3671, 40940}, {3702, 39594}, {3720, 31435}, {3721, 16972}, {3745, 3962}, {3752, 5221}, {3811, 5264}, {3812, 4383}, {3870, 5255}, {3875, 17141}, {3876, 5268}, {3938, 41863}, {3984, 5293}, {3997, 17742}, {4067, 30142}, {4319, 12711}, {4331, 5930}, {4414, 54290}, {4640, 19765}, {4646, 37567}, {4649, 37598}, {4650, 4652}, {4663, 5836}, {4667, 5837}, {4719, 17595}, {4722, 9623}, {4855, 37603}, {4860, 52541}, {5045, 16483}, {5138, 39598}, {5173, 34040}, {5222, 27000}, {5247, 19860}, {5252, 5849}, {5262, 16475}, {5271, 49598}, {5275, 21874}, {5292, 12047}, {5310, 37547}, {5315, 18398}, {5437, 27627}, {5552, 27338}, {5691, 29046}, {5697, 16474}, {5705, 33105}, {5707, 5887}, {5712, 8896}, {5718, 26066}, {5794, 49745}, {5905, 13161}, {6261, 37530}, {6734, 26098}, {7078, 50195}, {7098, 54320}, {7290, 11518}, {8192, 23381}, {8227, 29662}, {8270, 15556}, {8771, 35991}, {9340, 30282}, {9612, 21935}, {9943, 37537}, {10375, 14642}, {10404, 17365}, {10436, 17137}, {10459, 32912}, {10480, 54359}, {10884, 37570}, {11018, 41422}, {11375, 37646}, {11415, 24210}, {11512, 27003}, {11521, 21375}, {11551, 24159}, {12544, 19645}, {12635, 37539}, {12709, 37543}, {13738, 20967}, {14110, 36746}, {15955, 25415}, {16472, 53615}, {16485, 21747}, {16780, 21764}, {16824, 37652}, {16970, 21808}, {17016, 37685}, {17064, 24883}, {17126, 34772}, {17594, 19767}, {17750, 54406}, {17751, 26223}, {17768, 50065}, {18041, 33766}, {18391, 39585}, {19861, 26625}, {20018, 32932}, {22479, 44094}, {24512, 39248}, {24914, 37662}, {25524, 37520}, {25591, 30567}, {25681, 37634}, {25917, 37674}, {28570, 50050}, {28628, 35466}, {30116, 41229}, {30143, 53114}, {31053, 54355}, {32937, 41261}, {34339, 36754}, {34791, 37542}, {35004, 39523}, {35258, 37573}, {35262, 37608}, {36747, 37562}, {36985, 41562}, {37588, 49490}, {37602, 54319}, {37614, 44663}, {37692, 45939}, {40266, 45923}, {40952, 42448}, {44735, 54109}, {50579, 50581}, {50582, 50635}
X(54421) = reflection of X(10371) in X(5835)
X(54421) = X(989)-anticomplementary conjugate of X(1330)
X(54421) = X(5737)-Dao conjugate of X(10447)
X(54421) = crossdifference of every pair of points on line {521, 661}
X(54421) = barycentric product X(i)*X(j) for these {i,j}: {1, 5712}, {28, 8896}, {63, 37384}, {65, 37265}, {225, 23602}
X(54421) = barycentric quotient X(i)/X(j) for these {i,j}: {5712, 75}, {8896, 20336}, {23602, 332}, {37265, 314}, {37384, 92}
X(54421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1046, 63}, {1, 1707, 21}, {1, 12514, 968}, {1, 12526, 2292}, {1, 31424, 10448}, {1, 49500, 12514}, {6, 54382, 2082}, {31, 2650, 1}, {65, 221, 2263}, {72, 5711, 612}, {81, 3869, 1}, {354, 1191, 28011}, {387, 4295, 3914}, {896, 10448, 31424}, {942, 16466, 614}, {1042, 10460, 1193}, {1453, 11529, 3924}, {2308, 3924, 1453}, {2999, 3339, 24443}, {5269, 11523, 976}, {5692, 37559, 975}, {7290, 11518, 28082}, {17126, 34772, 37552}, {21935, 24725, 9612}
X(54422) lies on these lines: {1, 21}, {2, 3951}, {3, 3928}, {4, 527}, {5, 28609}, {7, 10}, {8, 2093}, {9, 942}, {20, 519}, {30, 12625}, {36, 1259}, {40, 518}, {44, 17054}, {46, 200}, {55, 41863}, {56, 3962}, {57, 72}, {65, 9623}, {78, 3218}, {84, 517}, {144, 938}, {145, 4304}, {165, 3811}, {210, 5221}, {223, 37591}, {226, 5705}, {268, 38290}, {269, 52385}, {329, 1210}, {354, 31435}, {376, 12437}, {377, 3679}, {379, 16833}, {380, 1761}, {387, 3663}, {404, 3984}, {405, 3929}, {442, 4654}, {443, 553}, {516, 7992}, {529, 5881}, {537, 37088}, {540, 48890}, {550, 34701}, {551, 17558}, {610, 52012}, {726, 10444}, {908, 6931}, {912, 1490}, {937, 43216}, {946, 24477}, {956, 3340}, {958, 11529}, {960, 3333}, {962, 7995}, {978, 18193}, {982, 54386}, {984, 54344}, {986, 3751}, {997, 3361}, {999, 15829}, {1012, 7982}, {1056, 5837}, {1103, 1735}, {1125, 5273}, {1158, 6769}, {1191, 21342}, {1420, 5730}, {1423, 10381}, {1453, 4641}, {1467, 1708}, {1697, 3555}, {1698, 5249}, {1699, 10916}, {1706, 5784}, {1709, 12651}, {1714, 23681}, {1722, 1757}, {1729, 3509}, {1741, 2324}, {1743, 5279}, {1750, 12528}, {1765, 10441}, {1788, 21075}, {1834, 17276}, {1858, 54408}, {2094, 6904}, {2095, 5777}, {2096, 12245}, {2136, 12702}, {2184, 52889}, {2323, 3157}, {2476, 31164}, {2478, 17781}, {2801, 9960}, {2802, 11519}, {2900, 16117}, {2901, 35629}, {2951, 12669}, {2999, 3670}, {3062, 51118}, {3091, 30326}, {3158, 3579}, {3169, 48917}, {3189, 31730}, {3190, 4303}, {3191, 37523}, {3194, 23052}, {3219, 16859}, {3220, 37547}, {3241, 17576}, {3243, 3295}, {3244, 4313}, {3294, 43220}, {3296, 51723}, {3304, 31165}, {3305, 17534}, {3306, 3876}, {3338, 5692}, {3419, 9579}, {3421, 4848}, {3487, 5745}, {3496, 51194}, {3523, 11407}, {3576, 12635}, {3583, 36599}, {3586, 12649}, {3587, 13369}, {3601, 3916}, {3612, 41696}, {3624, 54357}, {3634, 30393}, {3635, 30337}, {3636, 30343}, {3646, 3742}, {3650, 41864}, {3671, 19843}, {3677, 16466}, {3678, 8580}, {3682, 4306}, {3684, 36643}, {3695, 17296}, {3729, 10449}, {3746, 20835}, {3812, 5220}, {3813, 31162}, {3875, 8822}, {3940, 5438}, {3958, 54385}, {4005, 4413}, {4007, 50042}, {4034, 49718}, {4084, 18421}, {4101, 17740}, {4187, 31142}, {4197, 19875}, {4293, 6737}, {4295, 4847}, {4301, 34625}, {4347, 34033}, {4644, 5717}, {4650, 37552}, {4652, 17548}, {4659, 5295}, {4677, 17579}, {4685, 37109}, {4853, 5903}, {4860, 25917}, {4862, 23537}, {4867, 37618}, {4882, 41228}, {4930, 15178}, {4936, 5525}, {5044, 5437}, {5119, 16465}, {5128, 5687}, {5129, 6172}, {5227, 24476}, {5231, 12047}, {5234, 54318}, {5255, 16496}, {5258, 37228}, {5267, 53054}, {5288, 25415}, {5325, 16845}, {5435, 6700}, {5436, 15934}, {5439, 7308}, {5531, 9964}, {5535, 17857}, {5542, 18249}, {5563, 37248}, {5587, 5852}, {5691, 49168}, {5693, 12704}, {5696, 30353}, {5711, 7174}, {5715, 6866}, {5720, 37251}, {5729, 36973}, {5744, 13411}, {5758, 6245}, {5762, 5787}, {5779, 5806}, {5791, 6147}, {5811, 7682}, {5843, 6259}, {5853, 6361}, {5882, 34610}, {5884, 30503}, {5902, 41229}, {5905, 6734}, {6173, 8728}, {6282, 37403}, {6684, 25568}, {6735, 10940}, {6744, 30330}, {6764, 10430}, {6837, 11522}, {6839, 37714}, {6876, 18446}, {6916, 11362}, {7171, 37585}, {7330, 24474}, {7411, 8715}, {7675, 53053}, {7957, 10860}, {7963, 45763}, {7971, 22770}, {7987, 18444}, {7996, 28526}, {8056, 8951}, {8726, 21153}, {9004, 52359}, {9588, 37112}, {9589, 10431}, {9614, 11415}, {9624, 34647}, {9708, 31794}, {9841, 31793}, {9843, 18228}, {9949, 10429}, {10167, 37551}, {10382, 14054}, {10404, 21677}, {10436, 14007}, {10477, 44421}, {10529, 51423}, {10582, 18398}, {10624, 36845}, {10883, 24387}, {11106, 15933}, {11113, 37723}, {11224, 22837}, {11239, 31436}, {11260, 16200}, {11512, 18201}, {11551, 19854}, {11813, 50444}, {12436, 21454}, {12527, 18391}, {12565, 15071}, {12640, 50810}, {12699, 24392}, {12701, 51463}, {12705, 18219}, {12710, 15185}, {13462, 30144}, {13740, 50127}, {14021, 29573}, {15239, 18239}, {16062, 17274}, {17114, 20683}, {17151, 18655}, {17254, 37164}, {17449, 28011}, {17581, 54405}, {17728, 25522}, {17733, 35621}, {17736, 54330}, {17768, 28646}, {18178, 40979}, {18186, 52564}, {18253, 41870}, {18443, 24475}, {18483, 28647}, {20077, 50582}, {20214, 38271}, {20320, 52345}, {20880, 28612}, {21096, 41325}, {21164, 26877}, {21255, 39589}, {23144, 34043}, {23154, 26893}, {23511, 24046}, {24328, 37320}, {24440, 49712}, {24467, 37531}, {24468, 50528}, {25440, 53056}, {26051, 50128}, {30389, 37106}, {31190, 34753}, {31253, 36835}, {31302, 41261}, {31393, 34791}, {31549, 49592}, {31550, 49593}, {31775, 34742}, {31789, 34695}, {31837, 37534}, {34619, 37108}, {34716, 37727}, {34937, 37642}, {35596, 37256}, {37153, 50116}, {37175, 42042}, {37358, 37720}, {37421, 41561}, {37433, 50865}, {37467, 42043}, {37568, 41711}, {37581, 42461}, {37623, 52026}, {37719, 47516}, {44238, 50811}, {47622, 52181}, {49627, 51785}, {50095, 50735}, {50443, 51409}, {50581, 54383}, {50742, 51071}, {51724, 52653}
X(54422) = midpoint of X(6764) and X(20070)
X(54422) = reflection of X(i) in X(j) for these {i,j}: {4, 24391}, {1490, 5709}, {2136, 12702}, {2900, 37584}, {3189, 31730}, {5691, 49168}, {5758, 6245}, {6765, 40}, {6769, 1158}, {7971, 22770}, {7982, 12513}, {11523, 3}, {12629, 6762}, {37531, 24467}
X(54422) = X(38271)-anticomplementary conjugate of X(1330)
X(54422) = barycentric product X(75)*X(37500)
X(54422) = barycentric quotient X(37500)/X(1)
X(54422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63, 31424}, {1, 191, 4512}, {1, 16570, 54354}, {7, 5223, 5785}, {7, 54398, 10}, {8, 9965, 4292}, {21, 3868, 11520}, {21, 11520, 1}, {40, 1071, 5732}, {46, 5904, 200}, {57, 72, 936}, {63, 3868, 1}, {63, 11520, 21}, {78, 3218, 15803}, {144, 938, 12572}, {191, 3894, 1}, {405, 24473, 11518}, {942, 3927, 9}, {956, 4018, 3340}, {993, 12559, 1}, {3338, 5692, 8583}, {3339, 5223, 10}, {3868, 39772, 3894}, {3873, 5250, 1}, {3873, 11684, 5250}, {3874, 12514, 1}, {3901, 6763, 1}, {3928, 11523, 3}, {3929, 11518, 405}, {3940, 37582, 5438}, {4641, 37549, 1453}, {4652, 34772, 30282}, {4880, 5904, 46}, {5044, 5708, 5437}, {5261, 5775, 10}, {5273, 11036, 1125}, {5686, 11024, 10}, {5791, 6147, 25525}, {5905, 6734, 9612}, {7991, 30304, 20}, {8056, 8951, 17749}, {11415, 26015, 9614}, {11682, 54391, 1}, {15071, 41338, 12565}, {15934, 31445, 5436}, {24467, 37531, 52027}, {24475, 26921, 18443}, {34790, 36279, 1706}, {41863, 54290, 55}, {43174, 43177, 37108}
X(54423) lies on these lines: {1, 19285}, {2, 45129}, {3, 6}, {37, 78}, {42, 48}, {55, 22074}, {213, 54285}, {387, 37151}, {391, 16347}, {518, 19758}, {940, 1100}, {966, 16342}, {967, 28625}, {980, 16973}, {992, 19283}, {1150, 5839}, {1211, 16350}, {1213, 16343}, {1386, 19761}, {1409, 11509}, {1449, 37522}, {1468, 22054}, {1778, 4189}, {2172, 2174}, {2256, 3190}, {2268, 22072}, {2276, 2911}, {2286, 2594}, {2288, 11434}, {2303, 19767}, {2451, 48382}, {3049, 48391}, {3216, 19523}, {3295, 16685}, {3687, 5737}, {3958, 4414}, {4000, 5736}, {4016, 12635}, {4360, 30882}, {4383, 37323}, {4646, 5706}, {5275, 16352}, {5301, 16466}, {5313, 16470}, {5331, 37091}, {5747, 48837}, {8743, 41502}, {8818, 44518}, {11344, 46889}, {11507, 22134}, {15668, 17023}, {16345, 37673}, {16349, 17277}, {16351, 17330}, {16457, 24931}, {16458, 17398}, {16777, 30115}, {16783, 19286}, {16884, 17054}, {20150, 33035}, {20818, 38903}, {21904, 41243}, {25523, 40940}, {37245, 46890}, {39520, 48384}
X(54423) = crossdifference of every pair of points on line {523, 50501}
X(54423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3053, 4275}, {6, 4255, 4261}, {6, 4258, 2220}, {6, 5013, 583}, {6, 5110, 36743}, {6, 5124, 5021}, {6, 18755, 36744}, {6, 37500, 5165}, {6, 37504, 1333}, {216, 2092, 4261}, {284, 386, 6}, {572, 4270, 6}, {584, 5153, 6}, {965, 19765, 37}, {2278, 4272, 6}, {4251, 5105, 6}, {4261, 4273, 6}, {4263, 5114, 6}, {4268, 4285, 6}, {4275, 17454, 3053}, {5019, 20970, 6}, {5747, 48837, 53417}
X(54424) lies on these lines: {1, 19}, {6, 11529}, {7, 25935}, {9, 65}, {37, 40}, {45, 21866}, {55, 3247}, {57, 40937}, {71, 2093}, {86, 18713}, {196, 226}, {200, 22021}, {219, 3340}, {223, 1880}, {269, 18726}, {282, 2358}, {326, 18714}, {579, 3339}, {938, 40963}, {942, 2257}, {1045, 8769}, {1108, 3333}, {1400, 15830}, {1449, 2264}, {1706, 3694}, {1723, 5902}, {1743, 54324}, {1761, 31424}, {1766, 30503}, {1826, 9612}, {1839, 3586}, {1855, 5290}, {1859, 10382}, {2171, 2324}, {2178, 10902}, {2256, 7982}, {2285, 17451}, {2286, 34039}, {2321, 2550}, {2999, 9816}, {3101, 5287}, {3174, 19589}, {3198, 37553}, {3204, 3553}, {3485, 40942}, {3554, 17443}, {3664, 18725}, {3671, 5746}, {4259, 5785}, {4295, 8804}, {5227, 9623}, {5279, 19860}, {5587, 21933}, {5749, 25904}, {5750, 28629}, {5802, 6738}, {6203, 38004}, {7688, 54285}, {9119, 12709}, {9536, 17019}, {9575, 20227}, {10319, 17022}, {10436, 11683}, {10582, 40959}, {11518, 54358}, {12514, 25081}, {14521, 36973}, {15941, 18506}, {16676, 37567}, {18165, 40979}, {18634, 41003}, {18635, 41010}, {18655, 25255}, {20818, 50194}, {21808, 54359}, {27411, 44733}
X(54424) = barycentric product X(1)*X(5177)
X(54424) = barycentric quotient X(5177)/X(75)
X(54424) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 19, 380}, {1, 1781, 610}, {1, 18594, 284}, {19, 2294, 1}, {1953, 54385, 1}, {2093, 3731, 71}, {2171, 40131, 2324}
X(54425) lies on these lines: {1, 5809}, {2, 77}, {6, 7}, {8, 34}, {9, 347}, {73, 3616}, {85, 3618}, {105, 1037}, {142, 1419}, {144, 22464}, {169, 14256}, {212, 9778}, {219, 278}, {222, 9776}, {226, 1449}, {241, 37650}, {269, 3008}, {273, 26668}, {279, 1445}, {281, 36949}, {307, 391}, {342, 1249}, {344, 664}, {348, 17277}, {388, 1386}, {404, 1035}, {452, 5930}, {497, 30621}, {581, 5703}, {658, 30682}, {962, 7078}, {1040, 10430}, {1068, 5811}, {1104, 4308}, {1167, 1777}, {1212, 3160}, {1394, 6904}, {1404, 28081}, {1427, 5435}, {1429, 28015}, {1436, 34813}, {1441, 5749}, {1442, 5308}, {1453, 3600}, {1456, 2550}, {1458, 16020}, {1465, 5744}, {1736, 5825}, {1743, 3668}, {1804, 11349}, {1818, 27383}, {1943, 34255}, {2199, 37274}, {2270, 7013}, {2988, 50442}, {3062, 45275}, {3100, 36991}, {3161, 4552}, {3664, 30275}, {3672, 8545}, {3759, 6604}, {3912, 53997}, {3945, 21617}, {4295, 54301}, {4296, 54305}, {4328, 50114}, {4383, 7365}, {5226, 5712}, {5261, 5717}, {5273, 17080}, {5745, 36636}, {5748, 6510}, {5768, 37697}, {5909, 37417}, {6060, 37104}, {6172, 36640}, {6610, 17278}, {7053, 37272}, {7070, 50696}, {7190, 17014}, {7490, 14557}, {8055, 28996}, {8271, 34036}, {9312, 17353}, {9800, 54295}, {10578, 14547}, {12573, 16469}, {16670, 52819}, {17081, 43062}, {17086, 17257}, {17242, 25726}, {17286, 25719}, {17381, 52422}, {17917, 41883}, {18228, 18624}, {19877, 54346}, {20921, 37669}, {26006, 27508}, {26125, 26626}, {26671, 43045}, {28741, 29627}, {28780, 29611}, {28968, 31995}, {30705, 31638}, {30854, 33673}, {31018, 37798}, {34492, 53996}, {41246, 51171}
X(54425) = X(30705)-Ceva conjugate of X(7)
X(54425) = X(55)-isoconjugate of X(41790)
X(54425) = X(i)-Dao conjugate of X(j) for these (i,j): {223, 41790}, {497, 6554}
X(54425) = cevapoint of X(223) and X(16572)
X(54425) = barycentric product X(i)*X(j) for these {i,j}: {7, 17784}, {651, 25009}, {7131, 41787}, {8817, 43916}
X(54425) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 41790}, {17784, 8}, {25009, 4391}, {43916, 497}
X(54425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 948, 7}, {9, 43035, 347}, {269, 3008, 8732}, {278, 34048, 329}, {279, 37681, 1445}, {651, 37800, 7}, {1743, 3668, 12848}, {4000, 6180, 7}, {4552, 28966, 3161}, {5723, 6180, 4000}, {5819, 39063, 7}, {26668, 30807, 27382}
X(54426) lies on these lines: {1, 2}, {6, 25}, {22, 58}, {31, 579}, {32, 199}, {39, 1011}, {55, 4261}, {228, 2277}, {305, 33296}, {427, 1834}, {430, 5254}, {573, 20966}, {581, 4220}, {942, 24163}, {968, 40934}, {980, 37329}, {991, 17187}, {1180, 4253}, {1184, 2271}, {1196, 20970}, {1245, 51223}, {1368, 48847}, {1370, 48837}, {1468, 5322}, {1627, 4262}, {1724, 37325}, {1848, 3914}, {2082, 40976}, {2176, 3690}, {2177, 16488}, {2221, 37581}, {2223, 19343}, {2258, 39943}, {2273, 26885}, {2275, 40956}, {2300, 26893}, {2332, 3162}, {3052, 4286}, {3060, 50600}, {3198, 3752}, {3291, 20754}, {3736, 37090}, {3917, 50591}, {4204, 5283}, {4207, 5286}, {4251, 5359}, {4255, 7484}, {4256, 7485}, {4257, 6636}, {4259, 40153}, {4270, 5276}, {4272, 5275}, {4281, 19310}, {4749, 5165}, {5105, 33854}, {5153, 37060}, {5156, 5329}, {5396, 19544}, {5721, 37362}, {5943, 50595}, {7453, 9465}, {7494, 37642}, {7499, 37646}, {7772, 47523}, {9605, 13615}, {10319, 22057}, {10565, 37666}, {13588, 24598}, {14547, 20753}, {16368, 19758}, {16466, 37547}, {18147, 32926}, {18697, 32860}, {19309, 19725}, {19792, 32922}, {22021, 22196}, {22090, 47757}, {23536, 37093}, {28606, 37819}, {31152, 48842}, {36000, 37552}, {37439, 37662}, {37678, 40022}, {40941, 43214}, {44212, 48861}, {45962, 54308}
X(54426) = isogonal conjugate of the isotomic conjugate of X(16062)
X(54426) = crossdifference of every pair of points on line {525, 649}
X(54426) = barycentric product X(6)*X(16062)
X(54426) = barycentric quotient X(16062)/X(76)
X(54426) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 306}, {2, 54341, 386}, {6, 37538, 44119}, {39, 40984, 1011}, {42, 5311, 41265}, {5285, 16470, 31}
X(54427) lies on these lines: {1, 2}, {3, 47}, {6, 22766}, {35, 1064}, {36, 54}, {46, 10571}, {56, 7130}, {58, 1800}, {65, 1772}, {100, 54350}, {213, 13006}, {222, 40293}, {255, 14793}, {500, 37600}, {581, 3612}, {595, 32760}, {602, 36152}, {920, 46016}, {1042, 3336}, {1066, 1450}, {1079, 4320}, {1191, 11508}, {1319, 5399}, {1385, 2594}, {1409, 50650}, {1457, 5903}, {1464, 37582}, {1468, 16473}, {1470, 3157}, {1478, 37694}, {1725, 17102}, {1745, 4299}, {1807, 9630}, {2003, 37561}, {2635, 10483}, {2646, 5396}, {2654, 7741}, {3073, 10058}, {3075, 10090}, {3468, 4351}, {3585, 6127}, {3914, 39599}, {4253, 8776}, {4255, 11507}, {4261, 22134}, {4300, 5010}, {4303, 7280}, {4551, 45287}, {5348, 6924}, {5540, 40957}, {6149, 14792}, {6265, 33177}, {6326, 33178}, {6914, 7299}, {7078, 8071}, {7428, 42450}, {8068, 21935}, {8069, 16466}, {8578, 22090}, {10087, 37588}, {10269, 36752}, {10572, 37732}, {14529, 20842}, {14547, 37571}, {14803, 37469}, {16453, 37836}, {17605, 48903}, {18480, 45885}, {22768, 36742}, {23070, 52440}, {24431, 31835}, {24443, 53615}, {24475, 53525}, {26437, 44414}, {31870, 43048}, {34471, 37698}, {37564, 52408}
X(54427) = barycentric product X(63)*X(41722)
X(54427) = barycentric quotient X(41722)/X(92)
X(54427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 10573}, {1, 936, 54401}, {1, 978, 499}, {1, 3216, 1737}, {1064, 22072, 35}, {1066, 1450, 5563}, {1193, 22350, 1}, {31397, 50604, 1}
X(54428) lies on these lines: {1, 25}, {3, 9817}, {4, 36}, {10, 35973}, {11, 6756}, {12, 21841}, {24, 33}, {26, 37696}, {28, 1785}, {34, 5563}, {47, 2212}, {55, 3517}, {56, 1598}, {108, 1838}, {172, 3199}, {225, 36009}, {232, 5280}, {235, 3585}, {297, 30103}, {389, 10535}, {406, 5251}, {428, 3582}, {484, 1902}, {496, 7715}, {498, 6353}, {609, 2207}, {613, 7716}, {993, 4194}, {1038, 7387}, {1040, 6642}, {1060, 7517}, {1062, 7506}, {1192, 10060}, {1210, 7466}, {1398, 37587}, {1452, 5903}, {1478, 3089}, {1479, 7487}, {1593, 7280}, {1595, 5433}, {1596, 7354}, {1597, 5204}, {1737, 4231}, {1824, 32760}, {1827, 20837}, {1859, 10902}, {1870, 34484}, {1871, 2078}, {1872, 2077}, {1876, 3337}, {1885, 4316}, {1906, 4325}, {2067, 35765}, {2299, 54301}, {2964, 14975}, {3075, 3220}, {3083, 15187}, {3084, 15188}, {3085, 4232}, {3086, 5322}, {3100, 44802}, {3299, 5412}, {3301, 5413}, {3515, 5010}, {3518, 3746}, {3542, 7951}, {3567, 9638}, {3575, 3583}, {3614, 37942}, {4233, 13411}, {5090, 18395}, {5160, 44272}, {5258, 46878}, {5299, 10311}, {5353, 10642}, {5357, 10641}, {5530, 7438}, {6152, 51803}, {6284, 37458}, {6285, 11438}, {6502, 35764}, {6759, 19366}, {7352, 46261}, {7497, 37583}, {7529, 19372}, {7714, 10072}, {7718, 10573}, {7952, 17562}, {8144, 12106}, {8946, 45613}, {8948, 45614}, {10076, 15811}, {10110, 19365}, {10282, 11429}, {10896, 18494}, {10985, 16784}, {11109, 19864}, {11393, 37122}, {12135, 41684}, {12137, 53616}, {12146, 18244}, {12173, 18514}, {13488, 15326}, {13621, 18455}, {13861, 37697}, {14803, 37117}, {14986, 52301}, {16472, 44105}, {16473, 44086}, {16655, 26955}, {18378, 18447}, {18513, 37197}, {20831, 46974}, {22479, 54397}, {37440, 37729}, {37935, 52793}
X(54428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {24, 33, 35}, {25, 11399, 1}, {25, 11401, 26378}, {25, 26377, 7713}, {1905, 11363, 1}, {3518, 6198, 52427}, {3542, 11392, 7951}, {6198, 52427, 3746}, {6642, 9645, 1040}, {7952, 17562, 54368}
X(54429) lies on these lines: {1, 4001}, {2, 58}, {3, 5739}, {4, 1150}, {8, 20}, {21, 69}, {72, 26892}, {78, 991}, {81, 13725}, {141, 17526}, {145, 31303}, {193, 19767}, {283, 27505}, {306, 31424}, {307, 1394}, {315, 34016}, {333, 377}, {343, 24538}, {376, 3578}, {387, 16704}, {391, 579}, {404, 14555}, {443, 5278}, {452, 37655}, {524, 19765}, {550, 49718}, {631, 5741}, {940, 37314}, {966, 16454}, {1211, 4252}, {1453, 54311}, {1468, 50295}, {1714, 48835}, {1792, 37285}, {1834, 50055}, {1935, 28739}, {2287, 37180}, {2475, 5361}, {2478, 14829}, {2895, 4189}, {2975, 19262}, {3286, 36000}, {3487, 32859}, {3601, 4101}, {3616, 3945}, {3648, 24280}, {3687, 4652}, {3702, 5698}, {3710, 3929}, {3876, 54280}, {3916, 5814}, {3933, 21982}, {3936, 6857}, {4061, 12512}, {4188, 37656}, {4190, 9534}, {4195, 37653}, {4201, 37652}, {4292, 5271}, {4294, 17135}, {4309, 50625}, {4313, 49687}, {4388, 10527}, {4417, 6910}, {4450, 5082}, {4640, 10371}, {4643, 37539}, {4921, 48813}, {5046, 5372}, {5047, 18141}, {5051, 37642}, {5233, 6921}, {5235, 37153}, {5247, 26034}, {5712, 16342}, {5737, 49745}, {5738, 16346}, {6327, 19843}, {6776, 15983}, {6851, 48935}, {6869, 48877}, {6872, 10449}, {7793, 46707}, {8822, 19848}, {10327, 41229}, {10446, 11415}, {13742, 33172}, {14826, 28376}, {16062, 24597}, {16343, 49743}, {16347, 31034}, {16370, 41014}, {16845, 18139}, {16865, 32863}, {16948, 32782}, {17206, 19310}, {17234, 31259}, {17277, 37462}, {17674, 37650}, {17776, 31445}, {19766, 37685}, {19851, 26840}, {24248, 27368}, {24570, 26540}, {25524, 41002}, {25912, 26657}, {26117, 37683}, {28921, 46878}, {32099, 52396}, {33065, 36573}, {33171, 54354}, {34511, 50272}, {37054, 54303}, {37255, 37507}, {47102, 50275}, {48878, 50695}, {48883, 50698}
X(54429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 49716, 5739}, {20, 14552, 8}, {940, 49728, 37314}, {3916, 5814, 17740}, {16704, 17676, 387}, {16948, 32782, 37176}
X(54430) lies on these lines: {1, 201}, {3, 226}, {4, 35}, {9, 21}, {10, 55}, {33, 30733}, {36, 3487}, {56, 954}, {57, 6986}, {72, 993}, {142, 37282}, {198, 37052}, {228, 13733}, {270, 35192}, {329, 4189}, {388, 15931}, {404, 25525}, {411, 5219}, {442, 5432}, {452, 5281}, {497, 5259}, {499, 6878}, {516, 37601}, {551, 10966}, {581, 3074}, {908, 20846}, {936, 37306}, {946, 40292}, {958, 1260}, {968, 54295}, {991, 1935}, {1001, 12053}, {1125, 26357}, {1210, 6883}, {1259, 5745}, {1376, 37224}, {1453, 1612}, {1479, 6832}, {1490, 6906}, {1621, 1697}, {1724, 14547}, {1726, 18673}, {1792, 11679}, {1836, 12511}, {2077, 6908}, {2330, 10477}, {2975, 11523}, {3057, 30147}, {3085, 6987}, {3452, 11344}, {3485, 5759}, {3486, 5251}, {3488, 3746}, {3522, 8232}, {3523, 54366}, {3560, 4304}, {3583, 6990}, {3586, 6920}, {3612, 5450}, {3616, 5766}, {3634, 11502}, {3651, 4333}, {3683, 12711}, {3822, 10953}, {3871, 12625}, {3916, 17603}, {4183, 54396}, {4276, 25516}, {4294, 6846}, {4295, 7688}, {4298, 37578}, {4313, 16865}, {4428, 8170}, {4995, 11113}, {5047, 9581}, {5128, 5665}, {5217, 7580}, {5249, 37301}, {5257, 16346}, {5260, 5727}, {5267, 22768}, {5284, 50443}, {5316, 16293}, {5541, 53053}, {5692, 45230}, {5703, 37106}, {5715, 6905}, {5728, 15837}, {5746, 37297}, {5750, 37065}, {5758, 11012}, {5777, 6914}, {6284, 8226}, {6598, 31660}, {6684, 11507}, {6690, 47510}, {6745, 13615}, {6889, 10320}, {6907, 26285}, {6913, 11499}, {6936, 31452}, {7354, 34879}, {7411, 9579}, {7513, 40573}, {7522, 19760}, {7538, 27287}, {7676, 52835}, {7742, 21620}, {8071, 10165}, {8666, 34471}, {8804, 54285}, {10056, 14798}, {10164, 11509}, {10267, 31397}, {10382, 30393}, {10383, 31424}, {10391, 31445}, {10589, 25542}, {10831, 39475}, {11491, 31434}, {12572, 37284}, {12664, 33597}, {13405, 37579}, {13738, 51687}, {13739, 40395}, {14799, 37719}, {15865, 31789}, {16342, 27394}, {17549, 28609}, {18389, 26921}, {18397, 26878}, {22361, 37522}, {24929, 31837}, {28606, 33178}, {29828, 47511}, {31266, 35979}, {36018, 40131}, {50317, 52408}
X(54430) = crossdifference of every pair of points on line {4017, 43060}
X(54430) = barycentric product X(9)*X(5736)
X(54430) = barycentric quotient X(5736)/X(85)
X(54430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 78, 40661}, {9, 3601, 10393}, {35, 498, 6796}, {55, 405, 950}, {405, 11517, 10}, {405, 19763, 1751}, {943, 1006, 1}, {5010, 9612, 3651}, {5703, 37106, 37583}
X(54431) lies on these lines: {1, 37284}, {3, 6}, {21, 5712}, {24, 3194}, {25, 34}, {31, 73}, {36, 1453}, {42, 37601}, {47, 7078}, {81, 20846}, {193, 1792}, {223, 37583}, {387, 3651}, {393, 8885}, {405, 17056}, {411, 37642}, {593, 26636}, {937, 37561}, {940, 11344}, {993, 5717}, {1036, 16678}, {1191, 1617}, {1193, 37578}, {1211, 37065}, {1212, 5275}, {1259, 4641}, {1399, 19349}, {1402, 3556}, {1408, 44087}, {1451, 1470}, {1460, 23843}, {1468, 14547}, {1472, 3433}, {1490, 8557}, {1612, 3487}, {1724, 37249}, {1834, 7580}, {1838, 3772}, {2911, 3682}, {2975, 5716}, {3145, 37538}, {3149, 37646}, {3428, 15852}, {3560, 5713}, {3755, 12511}, {3767, 53422}, {3915, 33925}, {4185, 40980}, {4340, 37306}, {4383, 37282}, {4646, 5584}, {5265, 36007}, {5292, 6985}, {5324, 27621}, {5438, 16572}, {5563, 16485}, {7083, 23383}, {7742, 16466}, {16293, 37674}, {16344, 25526}, {16346, 19701}, {16410, 37679}, {16968, 37609}, {17337, 50203}, {18603, 19765}, {19309, 25524}, {19767, 37285}, {22760, 40950}, {24597, 35979}, {28466, 48870}, {30478, 37149}, {32911, 37301}, {35466, 37229}, {37228, 49745}, {37234, 45924}
X(54431) = isogonal conjugate of the isotomic conjugate of X(5738)
X(54431) = isogonal conjugate of the polar conjugate of X(37388)
X(54431) = barycentric product X(i)*X(j) for these {i,j}: {3, 37388}, {6, 5738}, {57, 10393}
X(54431) = barycentric quotient X(i)/X(j) for these {i,j}: {5738, 76}, {10393, 312}, {37388, 264}
X(54431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4254, 19760}, {3, 19762, 36743}, {3, 37492, 4267}, {56, 1035, 1427}, {58, 581, 6}, {19759, 54371, 3}
X(54432) lies on these lines: {1, 21}, {3, 18397}, {5, 57}, {7, 499}, {9, 7483}, {20, 484}, {35, 10391}, {36, 1071}, {40, 10950}, {46, 80}, {56, 5693}, {72, 19525}, {90, 1699}, {91, 267}, {201, 37469}, {224, 15015}, {226, 6852}, {377, 18395}, {405, 30274}, {411, 41562}, {498, 5273}, {515, 7098}, {580, 7004}, {912, 37583}, {942, 7489}, {946, 1776}, {1012, 1727}, {1158, 2093}, {1210, 3218}, {1259, 41686}, {1420, 6265}, {1445, 6915}, {1454, 5587}, {1478, 15932}, {1479, 5536}, {1490, 1708}, {1697, 37728}, {1698, 17700}, {1729, 5540}, {1735, 5247}, {1736, 3075}, {1737, 3336}, {1741, 1743}, {1771, 4650}, {1781, 15656}, {1788, 2096}, {1836, 7701}, {1837, 5535}, {1858, 11012}, {1864, 37623}, {2003, 37565}, {2077, 41538}, {2094, 11023}, {2949, 10393}, {3065, 37433}, {3086, 9965}, {3219, 13411}, {3286, 20803}, {3306, 7504}, {3333, 15950}, {3338, 5443}, {3586, 5709}, {3601, 7508}, {3652, 39542}, {3683, 16193}, {3911, 6949}, {3916, 44547}, {3928, 10396}, {4197, 16763}, {4299, 9799}, {4304, 11010}, {4313, 37563}, {4641, 17102}, {5131, 11220}, {5251, 13750}, {5398, 33178}, {5435, 6979}, {5692, 22766}, {5704, 23958}, {5735, 51768}, {5784, 41700}, {5904, 8069}, {6147, 10021}, {6284, 16113}, {6837, 18393}, {6890, 41563}, {6906, 15556}, {7082, 8227}, {7280, 10884}, {7354, 41697}, {7411, 16767}, {9579, 37230}, {9581, 37532}, {9613, 37550}, {9614, 12704}, {9964, 45764}, {10072, 28610}, {10090, 13243}, {10954, 31434}, {11507, 18412}, {12540, 13089}, {12647, 54398}, {12671, 44425}, {15297, 25522}, {16465, 32760}, {16572, 23972}, {17010, 34772}, {17437, 37358}, {17699, 51784}, {18761, 36279}, {21381, 24432}, {22760, 37625}, {24430, 37530}, {31231, 37612}, {31775, 40663}, {37106, 37616}, {37251, 37582}, {37426, 37572}, {37787, 43177}
X(54432) = barycentric product X(63)*X(7537)
X(54432) = barycentric quotient X(7537)/X(92)
X(54432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 18389, 1}, {57, 7330, 9612}, {58, 44706, 1}, {63, 31424, 191}, {63, 54302, 6763}, {4641, 17102, 54301}, {12704, 30223, 9614}
See HG050723
X(54433) lies on these lines: {1, 2}, {3, 345}, {4, 312}, {5, 28808}, {7, 1930}, {20, 346}, {21, 17776}, {28, 1043}, {30, 42032}, {37, 13725}, {45, 49728}, {56, 3703}, {58, 26065}, {63, 3710}, {69, 72}, {75, 443}, {100, 8193}, {181, 10369}, {189, 51304}, {192, 4201}, {210, 10371}, {315, 33939}, {319, 18156}, {321, 377}, {322, 32000}, {329, 1330}, {332, 14868}, {333, 47512}, {341, 3421}, {344, 405}, {348, 3933}, {376, 42033}, {379, 19838}, {388, 3974}, {404, 17740}, {464, 42706}, {497, 5015}, {631, 32851}, {728, 37551}, {894, 4340}, {942, 18141}, {944, 37431}, {958, 3932}, {960, 3416}, {1010, 2303}, {1058, 4514}, {1089, 1478}, {1104, 13742}, {1191, 5846}, {1228, 44150}, {1229, 6835}, {1257, 18636}, {1376, 3704}, {1453, 17353}, {1468, 33163}, {1479, 4680}, {1724, 26685}, {1770, 24280}, {1792, 11517}, {1801, 11115}, {1959, 26120}, {1973, 54316}, {1997, 4187}, {2289, 2329}, {2292, 26034}, {2321, 54405}, {2327, 16788}, {2475, 4671}, {2478, 4358}, {2551, 46937}, {2899, 36974}, {2901, 48837}, {2975, 32862}, {3058, 48798}, {3061, 53994}, {3159, 48835}, {3161, 17744}, {3175, 48813}, {3189, 41230}, {3191, 22008}, {3303, 4030}, {3434, 3702}, {3436, 3701}, {3487, 18134}, {3610, 5227}, {3685, 4294}, {3693, 36706}, {3712, 5217}, {3714, 5794}, {3729, 4292}, {3751, 41247}, {3767, 34542}, {3790, 4293}, {3797, 7791}, {3820, 5827}, {3869, 33078}, {3876, 5739}, {3883, 31435}, {3940, 21530}, {3949, 18671}, {3951, 4001}, {3966, 25917}, {3977, 4652}, {3984, 4101}, {3995, 17676}, {3998, 37180}, {4000, 33833}, {4019, 52387}, {4037, 9598}, {4082, 12527}, {4123, 6198}, {4133, 8769}, {4188, 33168}, {4189, 32849}, {4195, 17280}, {4198, 49542}, {4202, 19785}, {4252, 44416}, {4295, 4645}, {4296, 28739}, {4299, 7206}, {4320, 8816}, {4329, 51884}, {4359, 37462}, {4387, 6284}, {4388, 19582}, {4417, 5142}, {4513, 37537}, {4664, 51665}, {4673, 5082}, {4684, 41863}, {4869, 11036}, {4894, 4975}, {4901, 6762}, {5044, 5814}, {5084, 18743}, {5088, 32830}, {5175, 7557}, {5253, 33089}, {5280, 5749}, {5423, 5815}, {5434, 48806}, {5687, 12410}, {5690, 19547}, {5716, 13740}, {5788, 19782}, {5839, 16502}, {5847, 54386}, {6057, 7354}, {6327, 11415}, {6604, 37544}, {6857, 33116}, {6910, 33113}, {7046, 52346}, {7230, 7748}, {7386, 19799}, {7520, 52365}, {7523, 14829}, {11111, 17264}, {11112, 50044}, {11359, 50067}, {11374, 30828}, {11523, 17296}, {11681, 37983}, {12572, 30568}, {13728, 17321}, {13736, 54287}, {14210, 32099}, {15170, 48800}, {16284, 20914}, {16454, 19822}, {16466, 51192}, {16781, 17362}, {17095, 32818}, {17181, 37668}, {17263, 17552}, {17281, 50054}, {17289, 37037}, {17299, 40941}, {17342, 51673}, {17350, 20077}, {17359, 51670}, {17526, 33157}, {17559, 30829}, {17582, 19804}, {17678, 42047}, {18719, 20932}, {19844, 37261}, {20237, 20320}, {20928, 41013}, {23537, 30699}, {24701, 33066}, {25516, 51978}, {25527, 34937}, {26117, 41839}, {27509, 34823}, {27539, 46878}, {27549, 41229}, {31359, 34260}, {31993, 37153}, {32777, 37176}, {33079, 37598}, {33167, 37608}, {34791, 49688}, {35652, 50050}, {37093, 44140}, {37162, 46938}, {37231, 49492}, {37655, 54398}, {39731, 42696}, {41313, 50430}, {49716, 54280}, {50073, 51666}
X(54433) = isogonal conjugate of X(51686)
X(54433) = isotomic conjugate of the isogonal conjugate of X(7085)
X(54433) = isotomic conjugate of the polar conjugate of X(2345)
X(54433) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51686}, {4, 1472}, {19, 2221}, {27, 2281}, {28, 1245}, {34, 1036}, {56, 1039}, {513, 32691}, {608, 2339}, {649, 36099}, {1395, 30479}
X(54433) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 1039}, {3, 51686}, {6, 2221}, {958, 4185}, {5375, 36099}, {5515, 7649}, {11517, 1036}, {17421, 513}, {23874, 26933}, {36033, 1472}, {39026, 32691}, {40179, 4000}, {40181, 19}, {40591, 1245}
X(54433) = cevapoint of X(23874) and X(26933)
X(54433) = trilinear pole of line {2522, 23874}
X(54433) = barycentric product X(i)*X(j) for these {i,j}: {1, 19799}, {63, 4385}, {69, 2345}, {71, 44154}, {75, 5227}, {76, 7085}, {86, 3610}, {190, 23874}, {304, 612}, {306, 1010}, {312, 1038}, {345, 388}, {348, 3974}, {646, 51644}, {668, 2522}, {1016, 26933}, {1265, 7365}, {1332, 2517}, {2285, 3718}, {2286, 3596}, {2303, 20336}, {3926, 7102}, {4320, 52406}, {4561, 6590}, {4563, 48395}, {6332, 14594}, {7197, 30681}, {7386, 30701}, {40071, 44119}, {47844, 52609}, {50494, 52608}
X(54433) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 2221}, {6, 51686}, {9, 1039}, {48, 1472}, {71, 1245}, {78, 2339}, {100, 36099}, {101, 32691}, {219, 1036}, {228, 2281}, {345, 30479}, {388, 278}, {612, 19}, {1010, 27}, {1038, 57}, {1332, 1310}, {1460, 608}, {2285, 34}, {2286, 56}, {2303, 28}, {2345, 4}, {2517, 17924}, {2522, 513}, {3610, 10}, {3974, 281}, {4206, 5317}, {4320, 1435}, {4385, 92}, {4561, 37215}, {5227, 1}, {5286, 1851}, {5323, 1396}, {6590, 7649}, {7085, 6}, {7102, 393}, {7365, 1119}, {7386, 4000}, {8678, 6591}, {8898, 1426}, {14594, 653}, {19459, 16502}, {19799, 75}, {23874, 514}, {26933, 1086}, {34259, 34260}, {34261, 4185}, {44119, 1474}, {44154, 44129}, {47844, 17925}, {48395, 2501}, {50494, 2489}, {51644, 3669}
X(54433) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 19836, 3616}, {2, 145, 5262}, {2, 20009, 1}, {3, 3695, 345}, {8, 34255, 10449}, {10, 975, 2}, {10, 17733, 33137}, {20, 346, 7283}, {69, 304, 17170}, {69, 1265, 72}, {145, 33091, 8}, {312, 7270, 4}, {388, 3974, 4385}, {1104, 17279, 13742}, {3702, 5300, 3434}, {3771, 8669, 36573}, {4001, 52354, 3951}, {4358, 5016, 2478}, {4673, 32850, 5082}, {5044, 5814, 14555}, {6327, 25253, 11415}, {10449, 16086, 8}, {17742, 18596, 5279}, {19783, 29585, 1}, {26363, 30172, 30741}, {32777, 37539, 37176}
See HG020723
X(54434) lies on these lines: {2, 15032}, {3, 7712}, {4, 15066}, {5, 323}, {6, 3090}, {23, 15067}, {52, 10545}, {74, 5907}, {110, 7550}, {128, 47064}, {140, 399}, {141, 7552}, {155, 5067}, {186, 5891}, {195, 35018}, {376, 17811}, {394, 3545}, {546, 37496}, {547, 34545}, {568, 16042}, {631, 11456}, {1181, 3533}, {1199, 1656}, {1209, 2914}, {1216, 15107}, {1495, 7512}, {1498, 10299}, {1511, 14118}, {1594, 18358}, {1614, 5092}, {1993, 5071}, {1994, 5055}, {2071, 15060}, {2888, 50143}, {2979, 52294}, {3055, 45769}, {3098, 7999}, {3431, 7503}, {3518, 10546}, {3520, 4550}, {3524, 18451}, {3525, 11441}, {3526, 43605}, {3528, 35237}, {3542, 3620}, {3544, 36747}, {3581, 11591}, {3619, 7558}, {3628, 15037}, {3819, 14157}, {3917, 37925}, {5056, 11004}, {5068, 16266}, {5097, 22233}, {5449, 12364}, {5609, 13339}, {5651, 11438}, {5654, 14789}, {5888, 52525}, {5899, 44324}, {6126, 20117}, {6832, 14996}, {6852, 37633}, {6920, 51340}, {6983, 14997}, {7464, 15030}, {7486, 12161}, {7488, 33533}, {7505, 11487}, {7509, 26864}, {7530, 33884}, {7556, 35259}, {7565, 51391}, {7691, 47486}, {7998, 46261}, {9306, 11464}, {9729, 43596}, {9781, 37517}, {10109, 15038}, {10303, 32139}, {10539, 15080}, {10540, 15246}, {10564, 14865}, {10594, 33878}, {10625, 26863}, {10821, 34826}, {11064, 44834}, {11178, 22151}, {11412, 34417}, {11430, 35500}, {12111, 37470}, {12383, 34664}, {12812, 14627}, {13565, 15091}, {13595, 23039}, {13754, 43584}, {13861, 48912}, {14002, 37494}, {14094, 16836}, {14643, 51882}, {15022, 36749}, {15028, 15083}, {15081, 52124}, {15087, 15699}, {15350, 21357}, {16261, 37480}, {16534, 52171}, {18350, 37126}, {31831, 43808}, {34507, 41617}, {36753, 46936}, {37636, 37943}, {37945, 54042}, {41106, 44413}, {43576, 46847}, {43651, 44109}, {43844, 50664}, {43845, 48154}
X(54434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15068, 15032}, {3, 15052, 12112}, {110, 10170, 7550}, {547, 50461, 34545}, {1216, 43614, 34484}, {3819, 14157, 44832}, {10546, 11444, 37478}, {10546, 37478, 3518}, {11793, 43598, 7512}
X(54435) lies on these lines: {1, 6}, {3, 1250}, {8, 5362}, {11, 18581}, {12, 18582}, {13, 11237}, {14, 11238}, {15, 55}, {16, 56}, {35, 11480}, {36, 11481}, {61, 3303}, {62, 3304}, {115, 10061}, {222, 1082}, {388, 5335}, {395, 10072}, {396, 10056}, {495, 11542}, {496, 11543}, {497, 5334}, {498, 23302}, {499, 23303}, {559, 52424}, {940, 49594}, {999, 7127}, {1069, 10662}, {1277, 37772}, {1478, 5318}, {1479, 5321}, {2306, 12702}, {2307, 3295}, {3058, 10654}, {3085, 11488}, {3086, 11489}, {3157, 10661}, {3582, 16645}, {3583, 42093}, {3584, 16644}, {3585, 42094}, {3614, 42114}, {3616, 5367}, {3638, 5228}, {3639, 6180}, {3746, 22236}, {4293, 42120}, {4294, 42119}, {4299, 42088}, {4302, 42087}, {4309, 42147}, {4317, 42148}, {4325, 43193}, {4330, 43194}, {4383, 53589}, {4857, 5339}, {5204, 10646}, {5217, 10645}, {5225, 42133}, {5229, 42134}, {5270, 5340}, {5432, 42092}, {5433, 42089}, {5434, 10653}, {5471, 10077}, {5472, 10062}, {5563, 22238}, {6114, 12951}, {6115, 12942}, {6284, 42085}, {6782, 12952}, {6783, 12941}, {7173, 42111}, {7354, 42086}, {7741, 42095}, {7951, 42098}, {9654, 42128}, {9655, 42127}, {9656, 42813}, {9657, 16965}, {9668, 42126}, {9669, 42125}, {9670, 16964}, {9671, 42814}, {10483, 42097}, {10590, 42142}, {10591, 42139}, {10592, 42146}, {10593, 42143}, {10641, 11398}, {10642, 11399}, {10895, 16808}, {10896, 16809}, {12943, 19106}, {12953, 19107}, {13075, 23013}, {15171, 42117}, {15325, 42121}, {15326, 42091}, {15338, 42090}, {15888, 40693}, {15934, 33655}, {16772, 31452}, {18972, 22862}, {18974, 23006}, {18990, 42118}, {22860, 31706}, {22904, 31705}, {22906, 22910}, {31479, 42132}, {33653, 51340}, {37719, 42156}, {37720, 42153}, {37722, 40694}
X(54435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5353, 6}, {1, 54403, 54402}, {6, 5353, 54403}, {999, 11486, 19373}, {1124, 1335, 54403}, {1250, 7051, 3}, {2307, 10638, 11485}, {3295, 11485, 10638}, {7127, 19373, 11486}
X(54436) lies on these lines: {1, 6}, {3, 10638}, {8, 5367}, {11, 18582}, {12, 18581}, {13, 11238}, {14, 11237}, {15, 56}, {16, 55}, {35, 11481}, {36, 11480}, {61, 3304}, {62, 3303}, {115, 10062}, {222, 559}, {388, 5334}, {395, 10056}, {396, 10072}, {495, 11543}, {496, 11542}, {497, 5335}, {498, 23303}, {499, 23302}, {940, 49595}, {999, 7051}, {1069, 10661}, {1082, 52424}, {1250, 3295}, {1251, 51340}, {1276, 37773}, {1478, 5321}, {1479, 5318}, {2307, 7373}, {3058, 10653}, {3085, 11489}, {3086, 11488}, {3157, 10662}, {3582, 16644}, {3583, 42094}, {3584, 16645}, {3585, 42093}, {3614, 42111}, {3616, 5362}, {3638, 6180}, {3639, 5228}, {3746, 22238}, {4293, 42119}, {4294, 42120}, {4299, 42087}, {4302, 42088}, {4309, 42148}, {4317, 42147}, {4325, 43194}, {4330, 43193}, {4383, 53588}, {4857, 5340}, {5204, 10645}, {5217, 10646}, {5225, 42134}, {5229, 42133}, {5270, 5339}, {5432, 42089}, {5433, 42092}, {5434, 10654}, {5471, 10061}, {5472, 10078}, {5563, 22236}, {6114, 12941}, {6115, 12952}, {6284, 42086}, {6767, 7127}, {6782, 12942}, {6783, 12951}, {7052, 15934}, {7173, 42114}, {7354, 42085}, {7741, 42098}, {7951, 42095}, {9654, 42125}, {9655, 42126}, {9656, 42814}, {9657, 16964}, {9668, 42127}, {9669, 42128}, {9670, 16965}, {9671, 42813}, {10483, 42096}, {10590, 42139}, {10591, 42142}, {10592, 42143}, {10593, 42146}, {10641, 11399}, {10642, 11398}, {10895, 16809}, {10896, 16808}, {12702, 33654}, {12943, 19107}, {12953, 19106}, {13076, 23006}, {15171, 42118}, {15325, 42124}, {15326, 42090}, {15338, 42091}, {15888, 40694}, {16773, 31452}, {18973, 22906}, {18975, 23013}, {18990, 42117}, {22859, 31706}, {22862, 22865}, {22905, 31705}, {31479, 42129}, {37719, 42153}, {37720, 42156}, {37722, 40693}
X(54436) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5357, 6}, {1, 54402, 54403}, {6, 5357, 54402}, {999, 11485, 7051}, {1124, 1335, 54402}, {3295, 11486, 1250}, {10638, 19373, 3}
X(54437) lies on these lines: {1, 6}, {3, 202}, {11, 42156}, {12, 42153}, {13, 9669}, {14, 9654}, {18, 31479}, {35, 36843}, {36, 36836}, {55, 22238}, {56, 22236}, {61, 999}, {62, 3295}, {203, 7373}, {388, 398}, {395, 3085}, {396, 3086}, {397, 497}, {495, 40694}, {496, 40693}, {498, 16645}, {499, 16644}, {1056, 42999}, {1058, 42998}, {1407, 37773}, {1478, 5339}, {1479, 5340}, {2098, 33655}, {2306, 4860}, {2307, 3304}, {3303, 7127}, {3389, 31474}, {3411, 31480}, {3582, 49905}, {3584, 49906}, {3614, 42095}, {3617, 5367}, {4293, 42147}, {4294, 42148}, {4299, 43194}, {4302, 43193}, {5204, 11480}, {5217, 10638}, {5218, 16773}, {5225, 5318}, {5229, 5321}, {5362, 46934}, {5432, 43239}, {5433, 43238}, {6284, 42155}, {6767, 7006}, {7173, 42098}, {7288, 16772}, {7354, 42154}, {9655, 16964}, {9668, 16965}, {10056, 49948}, {10072, 49947}, {10386, 42924}, {10588, 42599}, {10589, 42598}, {10590, 42163}, {10591, 42166}, {10592, 18581}, {10593, 18582}, {10653, 15171}, {10654, 18990}, {11073, 42019}, {14986, 37640}, {15325, 42152}, {33654, 37567}
X(54437) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5357, 54402}, {1, 54402, 6}, {202, 7005, 3}, {1124, 1335, 5357}
X(54438) lies on these lines: {1, 6}, {3, 203}, {11, 42153}, {12, 42156}, {13, 9654}, {14, 9669}, {17, 31479}, {35, 36836}, {36, 36843}, {55, 2307}, {56, 7127}, {61, 3295}, {62, 999}, {202, 7373}, {388, 397}, {395, 3086}, {396, 3085}, {398, 497}, {495, 40693}, {496, 40694}, {498, 16644}, {499, 16645}, {1056, 42998}, {1058, 42999}, {1250, 5217}, {1407, 37772}, {1478, 5340}, {1479, 5339}, {2098, 7052}, {2306, 37567}, {3364, 31474}, {3412, 31480}, {3582, 49906}, {3584, 49905}, {3614, 42098}, {3617, 5362}, {4293, 42148}, {4294, 42147}, {4299, 43193}, {4302, 43194}, {4860, 33654}, {5204, 7051}, {5218, 16772}, {5225, 5321}, {5229, 5318}, {5367, 46934}, {5432, 43238}, {5433, 43239}, {6284, 42154}, {6767, 7005}, {7173, 42095}, {7288, 16773}, {7354, 42155}, {9655, 16965}, {9668, 16964}, {10056, 49947}, {10072, 49948}, {10386, 42925}, {10588, 42598}, {10589, 42599}, {10590, 42166}, {10591, 42163}, {10592, 18582}, {10593, 18581}, {10653, 18990}, {10654, 15171}, {11072, 42019}, {14986, 37641}, {15325, 42149}
X(54438) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5353, 54403}, {1, 54403, 6}, {55, 2307, 22236}, {56, 7127, 22238}, {203, 7006, 3}, {1124, 1335, 5353}
X(54439) lies on these lines: {2, 99}, {3, 74}, {6, 2987}, {23, 18860}, {32, 11004}, {39, 2981}, {97, 14586}, {114, 36163}, {187, 249}, {237, 15107}, {247, 12900}, {351, 53247}, {394, 5210}, {476, 46634}, {511, 35298}, {694, 12055}, {842, 7468}, {868, 15561}, {895, 9145}, {1003, 50673}, {1297, 37918}, {1316, 33813}, {1384, 1993}, {1495, 37183}, {1634, 9142}, {1976, 5092}, {1989, 44386}, {1994, 5008}, {2080, 23061}, {2502, 53095}, {2979, 41275}, {3003, 41617}, {3053, 20976}, {3098, 36213}, {3124, 5013}, {3148, 10546}, {3292, 47113}, {3448, 14981}, {3569, 8552}, {3580, 6390}, {3581, 44221}, {3619, 14806}, {3620, 10979}, {4226, 21166}, {4235, 41253}, {5012, 26316}, {5024, 9486}, {5467, 52699}, {5642, 53710}, {5649, 46787}, {5651, 9734}, {5653, 44814}, {5888, 14096}, {6337, 37643}, {6636, 7711}, {7471, 46987}, {7496, 21163}, {7813, 37779}, {7925, 40885}, {8182, 10554}, {8289, 46806}, {8369, 14389}, {8588, 32901}, {8722, 33884}, {8724, 9140}, {8836, 37340}, {8838, 37341}, {9160, 9184}, {9216, 46131}, {9737, 34417}, {9775, 9832}, {10545, 11328}, {10564, 52279}, {10718, 35937}, {10752, 15919}, {10991, 14683}, {11007, 30789}, {11064, 32459}, {11416, 22087}, {13335, 44109}, {14417, 39905}, {14480, 46633}, {14570, 48540}, {14611, 46981}, {14649, 54087}, {14850, 53132}, {15019, 32447}, {15462, 40083}, {15815, 20998}, {17811, 46276}, {23234, 53161}, {23235, 53346}, {27088, 40112}, {31626, 34897}, {32456, 35933}, {32985, 37645}, {33215, 40915}, {33878, 51335}, {34511, 37644}, {34840, 52125}, {36181, 38738}, {36188, 47326}, {37114, 37478}, {37483, 52276}, {38736, 51431}, {38748, 47200}, {39785, 44555}, {40078, 48450}, {40349, 44436}, {40916, 44420}, {43460, 50706}, {51882, 53767}
X(54439) = crossdifference of every pair of points on line {351, 1637}
X(54439) = X(53247)-lineconjugate of X(351)
X(54439) = barycentric product X(99)*X(34291)
X(54439) = barycentric quotient X(34291)/X(523)
X(54439) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9155, 110}, {187, 36212, 323}, {237, 35002, 15107}, {323, 35296, 187}, {620, 51389, 2}, {2981, 6151, 39024}, {9145, 46127, 895}, {11130, 11131, 110}, {32456, 51372, 35933}
X(54440) lies on these lines: {31, 16834}, {55, 14839}, {63, 2809}, {99, 109}, {100, 101}, {110, 6013}, {171, 9881}, {190, 522}, {238, 28580}, {516, 24630}, {536, 19624}, {692, 4436}, {833, 29119}, {835, 6577}, {898, 6014}, {901, 29351}, {932, 1293}, {985, 3802}, {993, 2802}, {1229, 47487}, {1253, 3729}, {1331, 2398}, {1332, 35338}, {1438, 24578}, {1633, 3882}, {2161, 2805}, {2195, 17755}, {2242, 37540}, {2316, 24482}, {2328, 32932}, {3241, 17126}, {3685, 13329}, {3875, 21059}, {3888, 6003}, {3912, 9441}, {4238, 32674}, {4414, 4475}, {4424, 4653}, {4482, 29066}, {4553, 15313}, {4586, 32041}, {4781, 35281}, {5091, 8299}, {8694, 8708}, {9070, 29133}, {17475, 38865}, {22370, 24309}, {23845, 53268}, {25083, 41339}, {28226, 29199}, {28916, 32929}, {29159, 43348}, {30664, 43077}, {43076, 46961}
X(54440) = X(43349)-anticomplementary conjugate of X(21293)
X(54440) = X(4586)-Ceva conjugate of X(101)
X(54440) = X(i)-isoconjugate of X(j) for these (i,j): {244, 37138}, {513, 1002}, {514, 2279}, {523, 51443}, {649, 27475}, {650, 42290}, {661, 42302}, {1015, 32041}, {1086, 8693}, {3122, 51563}, {3669, 40779}
X(54440) = X(i)-Dao conjugate of X(j) for these (i,j): {1001, 47123}, {2276, 824}, {3826, 47704}, {5375, 27475}, {36830, 42302}, {39026, 1002}
X(54440) = cevapoint of X(i) and X(j) for these (i,j): {1001, 4724}, {49478, 50336}
X(54440) = trilinear pole of line {1001, 2280}
X(54440) = crossdifference of every pair of points on line {244, 20974}
X(54440) = barycentric product X(i)*X(j) for these {i,j}: {100, 4384}, {101, 4441}, {109, 28809}, {110, 4044}, {190, 1001}, {644, 40719}, {645, 42289}, {646, 1471}, {651, 3886}, {662, 3696}, {664, 37658}, {668, 2280}, {692, 21615}, {765, 4762}, {1016, 4724}, {1492, 27474}, {1897, 23151}, {3257, 4702}, {3699, 5228}, {3789, 4586}, {4567, 4804}, {4578, 42309}, {4998, 45755}, {37133, 40732}
X(54440) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 27475}, {101, 1002}, {109, 42290}, {110, 42302}, {163, 51443}, {692, 2279}, {765, 32041}, {1001, 514}, {1110, 8693}, {1252, 37138}, {1471, 3669}, {2280, 513}, {3696, 1577}, {3789, 824}, {3886, 4391}, {3939, 40779}, {4044, 850}, {4384, 693}, {4441, 3261}, {4567, 51563}, {4702, 3762}, {4724, 1086}, {4762, 1111}, {4804, 16732}, {5228, 3676}, {21615, 40495}, {23151, 4025}, {28044, 3064}, {28809, 35519}, {37658, 522}, {40719, 24002}, {40732, 3250}, {42289, 7178}, {45755, 11}
X(54440) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 644, 1026}, {100, 3573, 101}
X(54441) lies on these lines: {3, 13257}, {4, 11}, {9, 45633}, {72, 74}, {119, 6889}, {153, 6908}, {226, 10058}, {329, 17100}, {405, 38602}, {411, 13243}, {442, 10742}, {950, 10074}, {952, 7580}, {954, 12775}, {971, 5122}, {1006, 37822}, {1035, 38295}, {1490, 1768}, {1728, 10090}, {2800, 5119}, {3149, 13226}, {5450, 37692}, {5658, 18861}, {5851, 21168}, {6223, 52270}, {6713, 6832}, {6878, 21154}, {6906, 11374}, {6976, 10269}, {6990, 31272}, {9945, 37426}, {9946, 10884}, {9957, 10698}, {9963, 33557}, {10393, 11570}, {10936, 12776}, {11523, 25438}, {12690, 12773}, {12750, 48694}, {13615, 34123}, {14803, 48695}, {16127, 36152}, {34122, 37240}, {35979, 40263}, {53252, 53279}
X(54441) = reflection of X(10728) in X(13273)
X(54441) = crossdifference of every pair of points on line {14399, 52307}
X(54441) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1490, 1768, 12691}, {12773, 37411, 12690}
X(54442) lies on these lines: {29, 12616}, {46, 13739}, {100, 110}, {107, 109}, {163, 1021}, {270, 1771}, {759, 12736}, {901, 53683}, {1158, 11107}, {1414, 4566}, {1624, 23845}, {1633, 4246}, {1780, 4248}, {2328, 10164}, {4237, 35278}, {6001, 15776}, {6740, 9803}, {11329, 35259}, {24580, 35260}, {24624, 45043}, {53324, 53761}
X(54442) = trilinear pole of line {8557, 18446}
X(54442) = barycentric product X(i)*X(j) for these {i,j}: {99, 8557}, {162, 6350}, {648, 18446}, {662, 18391}, {811, 19350}
X(54442) = barycentric quotient X(i)/X(j) for these {i,j}: {6350, 14208}, {8557, 523}, {18391, 1577}, {18446, 525}, {19350, 656}
X(54442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 3658, 662}, {653, 7452, 107}
X(54443) lies on these lines: {2, 304}, {75, 499}, {76, 17095}, {85, 32832}, {183, 17181}, {312, 7763}, {345, 32829}, {346, 32835}, {348, 20925}, {498, 18156}, {908, 17206}, {1078, 4872}, {1102, 3305}, {1969, 17923}, {3074, 4592}, {3086, 39731}, {3403, 16706}, {3767, 25918}, {3926, 28808}, {4561, 6734}, {5886, 21281}, {7270, 7752}, {7769, 32851}, {7862, 34542}, {11374, 30962}, {17079, 32885}, {17144, 36542}, {17170, 34229}, {17289, 30103}, {17315, 30125}, {17322, 19864}, {18135, 27187}, {18140, 37758}, {18142, 29793}, {24282, 24914}, {26363, 30758}, {27162, 33133}, {32838, 52422}, {44179, 54401}
X(54443) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {348, 32828, 20925}, {7769, 33939, 32851}
X(54444) lies on these lines: {2, 2003}, {6, 63}, {9, 1993}, {21, 54301}, {31, 50600}, {35, 50593}, {51, 3955}, {57, 5422}, {72, 36750}, {78, 36742}, {81, 908}, {92, 3758}, {182, 7293}, {222, 3306}, {239, 20879}, {275, 1948}, {323, 27065}, {329, 37685}, {394, 3305}, {511, 5314}, {575, 26889}, {576, 26893}, {651, 5249}, {894, 14213}, {914, 5294}, {940, 30852}, {1203, 2975}, {1331, 14547}, {1351, 7085}, {1473, 5050}, {1790, 2183}, {1959, 5280}, {1992, 26872}, {1994, 2323}, {2994, 54283}, {3060, 5285}, {3074, 54356}, {3157, 54392}, {3193, 12572}, {3218, 26740}, {3220, 5012}, {3618, 26871}, {3745, 17615}, {3784, 43650}, {3812, 8614}, {3870, 45729}, {3916, 37509}, {3920, 46685}, {4652, 36754}, {4855, 36746}, {5259, 35197}, {5299, 52134}, {5439, 23070}, {5440, 51340}, {5483, 16585}, {5748, 14996}, {5752, 54337}, {5943, 26884}, {7193, 13366}, {7308, 15066}, {7330, 7592}, {7584, 16028}, {9777, 37581}, {11004, 52405}, {11402, 24320}, {11456, 18540}, {11681, 37559}, {12514, 16473}, {14206, 17120}, {15018, 27003}, {16514, 45843}, {17379, 27287}, {17745, 24635}, {20834, 23202}, {22060, 37510}, {22129, 52424}, {22141, 33595}, {24467, 36753}, {26885, 34986}, {26921, 36749}, {26932, 37649}, {26933, 45298}, {31164, 37543}, {31266, 34048}, {37584, 39522}, {44547, 52362}, {45206, 52351}
X(54444) = reflection of X(5314) in X(26890)
X(54444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2003, 22128}, {182, 26892, 7293}, {222, 10601, 3306}, {1994, 3219, 2323}, {3218, 34545, 52423}
See Ivan Pavlov, Romantics of Geometry 12957.
X(54445) lies on these lines: {1, 3523}, {2, 515}, {3, 962}, {4, 5550}, {7, 36}, {8, 631}, {10, 10303}, {20, 1125}, {21, 10309}, {30, 9779}, {35, 9785}, {40, 3622}, {46, 4323}, {56, 3475}, {104, 6883}, {140, 944}, {145, 6684}, {165, 551}, {214, 9803}, {329, 1006}, {355, 3525}, {376, 5886}, {381, 28190}, {388, 37605}, {390, 30282}, {392, 11227}, {404, 11024}, {405, 5658}, {411, 8273}, {497, 37600}, {499, 4305}, {516, 10304}, {517, 3524}, {519, 15708}, {548, 18493}, {549, 3241}, {572, 5296}, {632, 18525}, {938, 2646}, {946, 3522}, {952, 5054}, {971, 17561}, {991, 49997}, {993, 18228}, {997, 5273}, {999, 10578}, {1000, 25405}, {1001, 6909}, {1012, 5284}, {1056, 5126}, {1151, 13959}, {1152, 13902}, {1319, 5218}, {1388, 52793}, {1478, 5444}, {1479, 37163}, {1482, 3530}, {1483, 12108}, {1698, 38155}, {1737, 31188}, {1788, 34471}, {2094, 21165}, {2320, 6954}, {2771, 31669}, {2807, 20791}, {2975, 5815}, {3085, 4308}, {3086, 3612}, {3090, 18481}, {3091, 3624}, {3146, 8227}, {3244, 9588}, {3361, 11036}, {3474, 15950}, {3476, 5432}, {3485, 5204}, {3486, 5433}, {3488, 15325}, {3526, 5818}, {3528, 12699}, {3529, 9955}, {3533, 9956}, {3534, 38034}, {3543, 3817}, {3545, 28160}, {3579, 10299}, {3600, 13411}, {3601, 14986}, {3617, 5882}, {3620, 39870}, {3621, 13607}, {3623, 11362}, {3654, 15719}, {3655, 11231}, {3656, 15698}, {3679, 15721}, {3753, 10156}, {3816, 6932}, {3828, 37712}, {3839, 7988}, {3845, 50819}, {3869, 9940}, {3876, 12675}, {3890, 31788}, {3892, 15104}, {3897, 6921}, {3904, 44819}, {3911, 13384}, {4188, 10902}, {4189, 37561}, {4293, 5226}, {4295, 7280}, {4300, 21214}, {4301, 16192}, {4304, 5274}, {4311, 5261}, {4342, 31508}, {4345, 5119}, {4423, 6912}, {4511, 5744}, {4539, 38067}, {4666, 6282}, {4677, 51085}, {5010, 30305}, {5047, 12114}, {5049, 33575}, {5055, 28186}, {5056, 5691}, {5059, 18483}, {5067, 18480}, {5068, 31673}, {5080, 6947}, {5092, 39898}, {5175, 6889}, {5180, 23961}, {5250, 24558}, {5298, 15933}, {5304, 9592}, {5333, 7415}, {5428, 14450}, {5436, 37421}, {5450, 6223}, {5690, 15720}, {5758, 26286}, {5768, 13151}, {5770, 28465}, {5840, 32558}, {5881, 46933}, {6001, 35260}, {6049, 21842}, {6176, 30947}, {6224, 6713}, {6245, 24564}, {6256, 37162}, {6693, 54181}, {6796, 17572}, {6853, 26492}, {6857, 17614}, {6872, 26129}, {6875, 11415}, {6897, 52367}, {6904, 24541}, {6925, 26105}, {6940, 10267}, {6943, 25466}, {6960, 10200}, {6967, 27529}, {6972, 10198}, {6989, 10785}, {7406, 29612}, {7411, 22753}, {7486, 19925}, {7492, 9625}, {7586, 9583}, {7984, 48378}, {7989, 19878}, {8583, 10884}, {8715, 12541}, {8726, 19861}, {9615, 13971}, {9624, 21734}, {9708, 38669}, {9746, 11200}, {9799, 37837}, {9802, 33814}, {9809, 38602}, {9933, 20191}, {10124, 38138}, {10167, 33574}, {10186, 28885}, {10247, 15693}, {10283, 12100}, {10519, 38029}, {10527, 37407}, {10580, 24929}, {10590, 21578}, {10624, 18220}, {10916, 12536}, {11001, 50873}, {11019, 53054}, {11038, 21153}, {11194, 25568}, {11224, 51103}, {11500, 17531}, {11522, 12512}, {11539, 28224}, {11735, 15051}, {11812, 38112}, {12104, 16116}, {12245, 15178}, {12246, 19526}, {12263, 32522}, {12528, 25917}, {12571, 50688}, {12702, 15712}, {13405, 13462}, {13464, 20070}, {14890, 38081}, {15022, 18492}, {15177, 15246}, {15626, 19261}, {15640, 30308}, {15676, 16132}, {15688, 28178}, {15689, 28182}, {15690, 50806}, {15694, 34627}, {15696, 40273}, {15701, 50824}, {15705, 28194}, {15709, 28204}, {15710, 28198}, {15713, 50798}, {15722, 50805}, {15726, 38025}, {15759, 50813}, {15837, 51772}, {16370, 21151}, {17127, 37469}, {17183, 37303}, {17504, 28212}, {17538, 22793}, {17576, 41012}, {17777, 38604}, {17923, 37028}, {18357, 46219}, {18391, 37525}, {19003, 42522}, {19004, 42523}, {19708, 51709}, {19875, 28236}, {21164, 35258}, {21167, 38315}, {21168, 38030}, {24386, 34701}, {27625, 37732}, {28150, 38021}, {28172, 50687}, {28216, 45759}, {28466, 38033}, {28858, 53014}, {28866, 44431}, {29648, 50699}, {29666, 50698}, {29817, 37569}, {30332, 30384}, {31145, 38127}, {31399, 46930}, {31657, 51409}, {33748, 34379}, {33923, 48661}, {34474, 38032}, {34862, 54228}, {35202, 37105}, {35239, 45977}, {35271, 38122}, {37306, 52148}, {37557, 45308}, {37714, 51073}, {38053, 38454}, {40333, 43175}, {40998, 50742}, {41869, 50693}, {44299, 52796}, {48893, 50420}, {48923, 50418}, {50808, 51110}, {50814, 51106}, {50818, 51068}, {50829, 51093}, {50865, 51109}, {50872, 51105}, {50977, 51001}, {50983, 50999}, {50984, 51000}, {50998, 51139}, {51045, 51056}, {51049, 51054}, {51071, 51086}, {51137, 51193}, {52705, 53579}
X(54445) = reflection of X(i) in X(j) for these {i,j}: {3839, 7988}, {7988, 19883}
X(54445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3576, 5731}, {2, 51705, 50864}, {3, 3616, 962}, {3, 38028, 5603}, {3, 5603, 9778}, {3, 5901, 6361}, {36, 52769, 37106}, {40, 3622, 5734}, {56, 5703, 11037}, {140, 944, 9780}, {355, 3525, 19877}, {376, 5886, 9812}, {499, 37616, 4305}, {549, 10246, 5657}, {551, 15692, 34632}, {631, 1385, 8}, {631, 7967, 26446}, {1125, 7987, 20}, {1385, 26446, 7967}, {2646, 7288, 938}, {2975, 27383, 5815}, {3085, 37618, 4308}, {3086, 3612, 4313}, {3486, 5433, 5704}, {3522, 46934, 946}, {3524, 3653, 38314}, {3526, 34773, 5818}, {3529, 9955, 10248}, {3576, 10165, 2}, {3576, 5587, 51705}, {3622, 15717, 40}, {3624, 4297, 3091}, {3654, 51084, 15719}, {5603, 38028, 3616}, {5657, 10246, 3241}, {5691, 19862, 5056}, {5886, 17502, 376}, {7988, 28164, 3839}, {7989, 19878, 46936}, {8273, 25524, 411}, {10165, 50828, 3576}, {10299, 10595, 3579}, {11231, 31662, 3655}, {12245, 15178, 20057}, {12512, 15808, 11522}, {13464, 35242, 20070}, {15325, 37606, 3488}, {15712, 51700, 12702}, {19883, 28164, 7988}, {19925, 34595, 7486}, {21151, 38031, 52653}, {30282, 44675, 390}, {30308, 50815, 15640}
See Ivan Pavlov, Romantics of Geometry 12957.
X(54446) lies on these lines: {1482, 4853}, {5902, 7271}, {10310, 17524}
X(54446) = intersection, other than A, B, C, of these circumonics: {{A*, B, C, X(1), X(3304)}}, {{A, B, C, X(3), X(16615)}}, {{A, B, C, X(4), X(963)}}, {{A, B, C, X(6), X(102)}}, {{A, B, C, X(8), X(3477)}}, {{A, B, C, X(55), X(80)}}, {{A, B, C, X(56), X(1389)}}, {{A, B, C, X(64), X(1126)}}, {{A, B, C, X(65), X(10310)}}, {{A, B, C, X(103), X(14490)}}, {{A, B, C, X(104), X(3531)}}, {{A, B, C, X(939), X(17097)}}, {{A, B, C, X(945), X(1173)}}, {{A, B, C, X(947), X(22334)}}, {{A, B, C, X(953), X(14491)}}, {{A, B, C, X(1000), X(10579)}}, {{A, B, C, X(1057), X(24297)}}, {{A, B, C, X(1243), X(1436)}}, {{A, B, C, X(1392), X(52792)}}, {{A, B, C, X(2099), X(10269)}}, {{A, B, C, X(2217), X(44861)}}, {{A, B, C, X(3062), X(28227)}}, {{A, B, C, X(3426), X(14496)}}, {{A, B, C, X(3431), X(28189)}}, {{A, B, C, X(4900), X(13404)}}, {{A, B, C, X(6583), X(11510)}}, {{A, B, C, X(11509), X(35004)}}, {{A, B, C, X(14483), X(14497)}}, {{A, B, C, X(17098), X(42019)}}, {{A, B, C, X(21398), X(33963)}}
X(54446) = isogonal conjugate of X(54445)
See Ivan Pavlov, Romantics of Geometry 12957.
X(54447) lies on these lines: {1, 1656}, {2, 515}, {3, 7989}, {4, 3634}, {5, 40}, {8, 7486}, {9, 3814}, {10, 3090}, {11, 31393}, {12, 3333}, {51, 52796}, {57, 6881}, {80, 13384}, {84, 4197}, {115, 9574}, {119, 11219}, {140, 5691}, {165, 381}, {355, 3624}, {382, 16192}, {442, 7701}, {485, 13947}, {486, 13893}, {496, 51784}, {498, 6887}, {499, 9578}, {516, 3545}, {517, 4731}, {547, 3679}, {549, 28190}, {567, 9586}, {569, 9622}, {631, 19925}, {632, 18481}, {944, 19862}, {946, 5056}, {952, 15699}, {962, 15022}, {993, 6946}, {999, 5726}, {1125, 5067}, {1210, 3475}, {1329, 5705}, {1385, 5070}, {1420, 10827}, {1478, 31231}, {1506, 9575}, {1512, 6879}, {1532, 3826}, {1571, 39565}, {1572, 7603}, {1594, 7713}, {1697, 7741}, {1702, 42262}, {1703, 42265}, {1706, 6975}, {1737, 5219}, {1995, 9625}, {2077, 4413}, {2093, 17605}, {2095, 3715}, {2136, 24387}, {2476, 24991}, {2801, 38093}, {2886, 12703}, {2948, 20304}, {3091, 6684}, {3097, 7697}, {3340, 18395}, {3359, 6980}, {3361, 9654}, {3523, 31673}, {3524, 28164}, {3525, 4297}, {3526, 7987}, {3544, 6361}, {3567, 31752}, {3579, 3851}, {3583, 35445}, {3584, 10389}, {3586, 5432}, {3589, 39885}, {3601, 6861}, {3614, 9612}, {3616, 46936}, {3617, 13464}, {3622, 47745}, {3626, 10595}, {3632, 5901}, {3646, 4187}, {3653, 28224}, {3654, 10109}, {3655, 38138}, {3656, 38112}, {3697, 13374}, {3742, 18908}, {3751, 24206}, {3812, 5693}, {3817, 3828}, {3822, 5437}, {3830, 50812}, {3832, 31425}, {3833, 15064}, {3839, 28150}, {3841, 6941}, {3843, 31663}, {3855, 51118}, {3860, 50825}, {3876, 31870}, {3901, 31835}, {3911, 10590}, {3929, 38109}, {4002, 45776}, {4193, 31435}, {4208, 54052}, {4302, 51792}, {4355, 34753}, {4423, 34486}, {4512, 17556}, {4668, 10222}, {4677, 10247}, {4915, 51362}, {5010, 7489}, {5020, 15177}, {5044, 37625}, {5047, 6796}, {5054, 28160}, {5068, 18483}, {5072, 22793}, {5079, 7991}, {5123, 9623}, {5128, 5445}, {5154, 5250}, {5231, 17757}, {5251, 6911}, {5254, 31428}, {5259, 11499}, {5290, 10592}, {5433, 9613}, {5438, 6852}, {5450, 17531}, {5550, 5882}, {5690, 11522}, {5704, 21620}, {5775, 46873}, {5777, 15016}, {5789, 24645}, {5817, 38204}, {5972, 12407}, {6256, 37462}, {6264, 31272}, {6326, 6702}, {6459, 9618}, {6565, 9616}, {6666, 6844}, {6667, 12751}, {6705, 37436}, {6721, 13178}, {6722, 9864}, {6723, 12368}, {6735, 11525}, {6766, 7958}, {6827, 18406}, {6830, 51780}, {6832, 26364}, {6841, 37551}, {6842, 37560}, {6856, 8582}, {6859, 20196}, {6874, 12514}, {6877, 25525}, {6883, 44425}, {6912, 9342}, {6918, 11012}, {6920, 25440}, {6931, 24987}, {6932, 10860}, {6933, 24982}, {6939, 26040}, {6944, 19854}, {6964, 19855}, {6983, 26363}, {6991, 24468}, {7173, 9614}, {7280, 45976}, {7290, 17734}, {7393, 8185}, {7424, 33538}, {7504, 7705}, {7509, 9626}, {7514, 9590}, {7529, 37557}, {7581, 49619}, {7582, 49618}, {7688, 19541}, {7743, 9819}, {7962, 23708}, {8164, 11019}, {8193, 11484}, {8253, 9583}, {8580, 37569}, {8726, 50726}, {8728, 37526}, {8976, 19004}, {9306, 9621}, {9582, 23261}, {9587, 18350}, {9591, 13861}, {9592, 31489}, {9593, 13881}, {9617, 35255}, {9668, 31508}, {9669, 53053}, {9746, 28866}, {9779, 28194}, {9781, 31737}, {9820, 9896}, {9902, 11272}, {9905, 13565}, {9957, 50444}, {10039, 50443}, {10157, 50740}, {10197, 38316}, {10246, 15703}, {10267, 25542}, {10283, 51093}, {10304, 28172}, {10476, 10887}, {10519, 38146}, {10576, 18991}, {10577, 18992}, {10589, 31397}, {10593, 51785}, {10857, 18529}, {10864, 17529}, {10895, 15803}, {10902, 11108}, {11001, 50803}, {11014, 31262}, {11224, 50817}, {11362, 46933}, {11444, 31760}, {11500, 16842}, {11531, 18493}, {11539, 28186}, {12100, 50799}, {12114, 16862}, {12119, 31235}, {12435, 34466}, {12616, 25011}, {12619, 15017}, {12778, 15088}, {12785, 32396}, {12812, 22791}, {12900, 13211}, {13607, 46934}, {13624, 46219}, {13729, 26060}, {13886, 49547}, {13911, 42583}, {13912, 42561}, {13939, 49548}, {13951, 19003}, {13973, 42582}, {13975, 31412}, {14269, 28154}, {14892, 28216}, {15024, 31732}, {15056, 31728}, {15059, 33535}, {15626, 19275}, {15682, 50829}, {15694, 17502}, {15695, 51088}, {15698, 50862}, {15702, 34648}, {15726, 38075}, {15931, 18491}, {16132, 31254}, {16173, 38319}, {16208, 45630}, {16209, 45631}, {16408, 37561}, {16475, 38317}, {16496, 42786}, {16832, 30849}, {17057, 31263}, {17124, 37469}, {18358, 39878}, {18525, 30389}, {19708, 51081}, {19709, 50865}, {19710, 50866}, {19883, 28236}, {20400, 49176}, {21151, 38158}, {21168, 38151}, {23046, 28182}, {24386, 34619}, {24392, 45701}, {24644, 38121}, {24808, 48854}, {26725, 37713}, {28178, 38071}, {28204, 30392}, {28212, 47478}, {28234, 53620}, {30286, 50194}, {30308, 50821}, {31398, 43620}, {31421, 44518}, {31452, 41864}, {31776, 53057}, {34474, 38161}, {34747, 51515}, {34773, 48154}, {35258, 37375}, {37290, 38411}, {37556, 37720}, {37718, 38182}, {38036, 38057}, {38052, 38108}, {38059, 38149}, {38073, 38101}, {38107, 38179}, {38150, 38454}, {38154, 38758}, {38172, 51516}, {38180, 51768}, {41106, 50808}, {41867, 51755}, {44217, 52027}, {48888, 49993}, {48897, 50416}, {50798, 51110}, {50818, 51109}, {51068, 51077}
X(54447) = midpoint of X(7988) and X(19875)
X(54447) = reflection of X(i) in X(j) for these {i,j}: {38021, 7988}, {7988, 5055}
X(54447) = complement of X(54445)
X(54447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30315, 9956}, {2, 10175, 5587}, {3, 7989, 18492}, {4, 31423, 35242}, {4, 3634, 31423}, {5, 26446, 1699}, {10, 10171, 5603}, {10, 3090, 8227}, {10, 8227, 7982}, {11, 31434, 31393}, {355, 3628, 3624}, {381, 11231, 165}, {517, 5055, 7988}, {547, 38042, 5886}, {1125, 38155, 7967}, {1125, 5818, 5881}, {1385, 5070, 34595}, {1656, 5790, 11230}, {1656, 9956, 1}, {1698, 1699, 26446}, {1699, 26446, 40}, {1737, 5219, 11529}, {3090, 5603, 10171}, {3091, 19877, 6684}, {3091, 6684, 41869}, {3526, 18480, 7987}, {3544, 6361, 12571}, {3614, 24914, 9612}, {3679, 5886, 16200}, {3817, 3828, 5657}, {3817, 5657, 31162}, {4413, 6913, 2077}, {5055, 19875, 38021}, {5055, 38083, 19875}, {5056, 9780, 946}, {5067, 5818, 1125}, {5071, 5657, 3817}, {5818, 7967, 38155}, {5886, 38042, 3679}, {6931, 24987, 25522}, {7486, 31399, 9624}, {7504, 7705, 19860}, {7988, 19875, 517}, {9956, 11230, 5790}, {10165, 50811, 3576}, {10172, 10175, 2}, {15022, 46932, 962}, {18395, 37692, 3340}, {19925, 51073, 631}, {34595, 37714, 1385}, {38182, 38752, 37718}, {51066, 51709, 50817}
See Ivan Pavlov, Romantics of Geometry 12957.
X(54448) lies on these lines: {1, 5068}, {2, 515}, {3, 46932}, {4, 3617}, {5, 3622}, {8, 1699}, {10, 3146}, {20, 5818}, {40, 17578}, {80, 10590}, {119, 20085}, {144, 5080}, {145, 355}, {149, 6957}, {153, 6826}, {165, 15683}, {376, 28190}, {381, 5844}, {516, 50687}, {517, 3839}, {519, 9779}, {546, 12245}, {631, 46930}, {944, 5056}, {946, 3621}, {950, 7319}, {952, 3545}, {962, 4678}, {1056, 12019}, {1131, 19065}, {1132, 19066}, {1385, 7486}, {1478, 21454}, {1482, 3855}, {1483, 5072}, {1698, 15717}, {1837, 3475}, {2551, 6895}, {3090, 18525}, {3241, 3817}, {3436, 6894}, {3522, 5691}, {3523, 9956}, {3524, 28186}, {3534, 50826}, {3543, 5657}, {3544, 5901}, {3579, 49135}, {3600, 17728}, {3616, 7989}, {3623, 5881}, {3632, 12571}, {3679, 9812}, {3698, 9961}, {3753, 50736}, {3830, 38112}, {3850, 12645}, {3851, 10595}, {3858, 8148}, {3868, 9947}, {3877, 10157}, {4297, 19877}, {4309, 5560}, {4661, 18908}, {4677, 50803}, {4691, 9589}, {4731, 15726}, {4745, 51119}, {4886, 45100}, {5055, 28224}, {5059, 31673}, {5066, 10247}, {5067, 34773}, {5071, 10246}, {5086, 6870}, {5154, 24558}, {5177, 5658}, {5226, 5727}, {5229, 11246}, {5252, 5274}, {5265, 17606}, {5686, 38454}, {5704, 9613}, {5726, 10578}, {5734, 20014}, {5787, 37436}, {5794, 8165}, {5886, 34627}, {6246, 20095}, {6361, 50688}, {6684, 50693}, {6835, 20060}, {6839, 9965}, {6884, 10786}, {6920, 18518}, {6946, 18519}, {6990, 10942}, {7377, 24599}, {7384, 29616}, {7982, 20052}, {7988, 28236}, {7991, 10248}, {9654, 11036}, {9708, 36002}, {10283, 19709}, {10303, 18481}, {10304, 28160}, {10580, 51782}, {10591, 37710}, {10826, 14986}, {10883, 17757}, {10944, 18220}, {11038, 11237}, {11111, 38058}, {11224, 50802}, {11231, 15692}, {11235, 32426}, {11239, 38037}, {11500, 16865}, {11522, 20050}, {11551, 18391}, {12111, 23841}, {12114, 17572}, {14269, 28212}, {14646, 15679}, {15056, 16980}, {15626, 19291}, {15640, 50821}, {15708, 28208}, {15721, 17502}, {16200, 20049}, {17547, 38031}, {18444, 18528}, {19875, 28164}, {21734, 31399}, {23249, 35789}, {23259, 35788}, {23675, 28092}, {25005, 37435}, {28178, 38066}, {28216, 38081}, {29621, 36662}, {30308, 50801}, {31730, 50692}, {31888, 37230}, {33697, 49140}, {33699, 50809}, {34632, 38127}, {36926, 39570}, {38034, 41106}, {38158, 52653}, {38176, 50810}, {39885, 51170}, {41099, 50800}, {49524, 51537}, {50865, 51068}
X(54448) = reflection of X(i) in X(j) for these {i,j}: {38314, 7988}, {7988, 38076}
X(54448) = anticomplement of X(54445)
X(54448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3617, 20070}, {8, 19925, 3832}, {20, 5818, 46933}, {355, 3091, 145}, {355, 38140, 5603}, {944, 5056, 46934}, {962, 18492, 50689}, {1699, 37714, 38155}, {3523, 9956, 46931}, {3616, 7989, 15022}, {3621, 3854, 946}, {3851, 37705, 10595}, {4678, 50689, 962}, {5603, 38140, 3091}, {5691, 9780, 3522}, {5731, 10175, 2}, {5818, 18480, 20}, {7988, 28236, 38314}, {19925, 38155, 1699}, {28236, 38076, 7988}
Contributed by Clark Kimberling and Peter Moses, July 11, 2023.
As noted in the Glossary, suppose that P = p : q : r (trilinear coordinates, not barycentric) is a point not on a sideline of ABC, and let A'B'C' be the cevian triangle of P. The circumcircle of A'B'C' meets line BC in two points: A' and A"; pairs B', B", and C',C" are obtained cyclically. The lines AA", BB", CC" concur in the cyclocevian conjugate of P. Let
g(a,b,c) = a/[p(qb + rc)] and f(a,b,c) = bc/[g(b,c,a) + g(c,a,b) - g(a,b,c)].
The cyclocevian conjugate of P is given by
f(a,b,c) : f(b,c,a) : f(c,a,b) (trilinears).
The cyclocevian conjugate of a point is the
isotomic conjuguate
of the anticomplement
of the isogonal conjugate
of the complement
of the isotomic conjugate
of the point
(Darij Grinberg, January 24, 2003)
Now switching to bartycentric coordinates, suppose that p x + q y + r z = 0 is a line. It's image under cyclocevian conjugationj is the octic curve given by
(c^4*p + c^4*q - c^4*r)*x^4*y^4 + (-2*b^2*c^2*p + 2*c^4*p - 2*a^2*c^2*q + 2*c^4*q - 2*c^4*r)*x^4*y^3*z + (-2*b^2*c^2*p + 2*c^4*p - 2*a^2*c^2*q + 2*c^4*q - 2*c^4*r)*x^3*y^4*z + (-(a^4*p) + b^4*p - 4*b^2*c^2*p + c^4*p + a^4*q - b^4*q - 2*a^2*c^2*q + c^4*q + a^4*r - 2*a^2*b^2*r + b^4*r - c^4*r)*x^4*y^2*z^2 + (-2*a^4*p + 2*b^4*p - 6*b^2*c^2*p + 4*c^4*p + 2*a^4*q - 2*b^4*q - 6*a^2*c^2*q + 4*c^4*q + 2*a^4*r - 4*a^2*b^2*r + 2*b^4*r - 4*c^4*r)*x^3*y^3*z^2 + (-(a^4*p) + b^4*p - 2*b^2*c^2*p + c^4*p + a^4*q - b^4*q - 4*a^2*c^2*q + c^4*q + a^4*r - 2*a^2*b^2*r + b^4*r - c^4*r)*x^2*y^4*z^2 + (2*b^4*p - 2*b^2*c^2*p - 2*b^4*q - 2*a^2*b^2*r + 2*b^4*r)*x^4*y*z^3 + (-2*a^4*p + 4*b^4*p - 6*b^2*c^2*p + 2*c^4*p + 2*a^4*q - 4*b^4*q - 4*a^2*c^2*q + 2*c^4*q + 2*a^4*r - 6*a^2*b^2*r + 4*b^4*r - 2*c^4*r)*x^3*y^2*z^3 + (-4*a^4*p + 2*b^4*p - 4*b^2*c^2*p + 2*c^4*p + 4*a^4*q - 2*b^4*q - 6*a^2*c^2*q + 2*c^4*q + 4*a^4*r - 6*a^2*b^2*r + 2*b^4*r - 2*c^4*r)*x^2*y^3*z^3 + (-2*a^4*p + 2*a^4*q - 2*a^2*c^2*q + 2*a^4*r - 2*a^2*b^2*r)*x*y^4*z^3 + (b^4*p - b^4*q + b^4*r)*x^4*z^4 + (2*b^4*p - 2*b^2*c^2*p - 2*b^4*q - 2*a^2*b^2*r + 2*b^4*r)*x^3*y*z^4 + (-(a^4*p) + b^4*p - 2*b^2*c^2*p + c^4*p + a^4*q - b^4*q - 2*a^2*c^2*q + c^4*q + a^4*r - 4*a^2*b^2*r + b^4*r - c^4*r)*x^2*y^2*z^4 + (-2*a^4*p + 2*a^4*q - 2*a^2*c^2*q + 2*a^4*r - 2*a^2*b^2*r)*x*y^3*z^4 + (-(a^4*p) + a^4*q + a^4*r)*y^4*z^4 = 0
For example, the cyclocevian image of the Euler line passes through A, B, C, and the anticevian triangle of ABC, and through X(i) for these i: 2, 4, 1032, 13580, 13581, 54449.
The appearance of (i,j) in the following list means that the cyclocevian conjugate of X(i) is X(j):
(1,1029, (2,4), (5,54449), (6,1031), (7,7), (8,189), (13,13483), (14,13484), (20,1032), (63,54450), (66,2998), (67,46275), (68,34287), (69,253), (75,8044), (76,41513), (80,8046), (92,54125), (94,54415), (99,13485), (110,15351), (190,44184), (254,13579), (280,54451), (290,9473), (329,1034), (330,7357), (471,19157), (648,13573), (668,8047), (670,35511), (671,13574), (1113,13580), (1114,13581), (1138,13582), (2113,6650), (2184,13583), (2986,50480), (2992,19776), (2993,19777), (2994,7219), (2996,13575), (3223,13584), (3346,6504), (3459,13585), (4373,8048), (5395,39978), (5932,41080), (6339,42484), (6553,34546), (6601,42483), (6625,8049), (6630,8050), (7319,8051), (9510,13576), (10405,13577), (11606,41520), (14355,31907), (14361,14365), (15321,40042), (19712,41898), (19713,41897), (34214,39939), (35058,43712), (36606,52803), (41514,43740), (42427,42428), (44175,54114), (24243,55020), (24244,55021), (36917,55022), (38259,55023), (39695,55024), (39719,55025), (39726,55026), (39748,55027), (39953,55028), (41895,55029), (42361,55030), (44177, 55031), (46270,55032), (46271,55033), (46274,55034), (54117,55035), (54119,55036), (54120, 55037)
If "circumcircle" is replaced by "Steiner circumellipse" in the definition of cyclocevian conjugate, the result is here named the Steiner-cevian conjugate of X. The appearance of (i,j) in the following list means that the Steiner-cevian conjugate of of X(i) is X(j):
(1,13610), (2,2), (4,43710), (6,14370), (7,43750), (8,7155), (69,43714), (75,18298), (148,31998), (192,3212), (194,3186), (513,9267), (514,42555), (523,9293), (1654,17762), (1655,1045), (2896,40035), (4440,6631), (8591,39061), (9263,9296), (17487,9460), (25054,9428), (39350,33675), (39351,10001), (39352,39062), (39354,33678), (39355,39058), (39358,9410), (52637,3499), (54104,13187} If "circumcircle" is replaced by "Kiepert circumhyperbola" in the definition of cyclocevian conjugate, the result is here named the Kiepert-cevian conjugate of X. The appearance of (i,j) in the following list means that the Kiepert-cevian conjugate of of X(i) is X(j):
(1,13486), (2,99), (3,110), (4,35360), (6,13578), (13,36839), (14,36840), (30,476), (399,47053), (616,35314), (617,35315), (5667,4240}
X(54449) lies on these lines: (),
X(54449) = cyclocevian conjugate of X(5)
X(54449) = isotomic conjugate of the anticomplement of X(288)
X(54450 ) lies on these lines: (377, 1249), , (1231, 2897), , (4296, 5930), , (5279, 8804), , (6839, 14249), , (7270, 52345), , (10152, 37433), , (10431, 33893), , (37163, 38808), , (37456, 40431),
X(54450 ) = isotomic conjugate of X(2897)
X(54450 ) = polar conjugate of X(18687)
X(54450 ) = cyclocevian conjugate of X(63)
X(54450 ) = isotomic conjugate of the anticomplement of X(1172)
X(54450 ) = X(i)-isoconjugate of X(j) for these (i,j): (:31, 2897), , (48, 18687),
X(54450 ) = X(i)-Dao conjugate of X(j) for these (i,j): (:2, 2897), , (1249, 18687),
X(54450 ) = cevapoint of X(i) and X(j) for these (i,j): (:122, 521), , (522, 34846),
X(54450 ) = trilinear pole of line (6587, 16612),
X(54450 ) = barycentric quotient X(i)/X(j) for these (i,j), : (:2, 2897), , (4, 18687),
X(54451) lies on these lines: (40, 3436), , (196, 5905), , (223, 908), , (329, 20928), , (972, 34188), , (3193, 3194), , (3434, 15499), , (4391, 26871),
X(54451) = cyclocevian conjugate of X(280)
X(54451) = isotomic conjugate of the anticomplement of X(222)
X(54451) = X(42464)-anticomplementary conjugate of X(347)
X(54451) = X(i)-isoconjugate of X(j) for these (i,j): (:6, 1158), , (41, 31600), , (55, 34052), , (8609, 10692),
X(54451) = X(i)-Dao conjugate of X(j) for these (i,j): (:9, 1158), , (223, 34052), , (3160, 31600),
X(54451) = cevapoint of X(i) and X(j) for these (i,j): (:9, 5534), , (513, 6506), , (521, 5514),
X(54451) = trilinear pole of line (2804, 6129),
X(54451) = barycentric product X(75)*X(42464)
X(54451) = barycentric quotient X(i)/X(j) for these (i,j), : (:1, 1158), , (7, 31600), , (57, 34052), , (36052, 10692), , (42464, 1),
X(54452) lies on these lines : : {2, 40595}, {150, 35175}, {320, 517}, {859, 34184}, {1443, 1457}, {2183, 3218}, {3264, 21290}, {4389, 14260}
X(54452) = isogonal conjugate of X(23858)
X(54452) = isotomic conjugate of X(21290)
X(54452) = anticomplement of X(40595)
X(54452) = cyclocevian conjugate of X(903)
X(54452) = isotomic conjugate of the anticomplement of X(106)
X(54452) = isotomic conjugate of the complement of X(20098)
X(54452) = isotomic conjugate of the isogonal conjugate of X(34184)
X(54452) = X(34184)-anticomplementary conjugate of X(17495)
X(54452) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23858}, {6, 16561}, {19, 23135}, {31, 21290}, {32, 21600}, {44, 40595}
X(54452) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 21290}, {3, 23858}, {6, 23135}, {9, 16561}, {6376, 21600}
X(54452) = cevapoint of X(i) and X(j) for these (i,j): {2, 20098}, {514, 3259}
X(54452) = trilinear pole of line {3310, 3960}
X(54452) = barycentric product X(76)*X(34184)
X(54452) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16561}, {2, 21290}, {3, 23135}, {6, 23858}, {75, 21600}, {106, 40595}, {34184, 6}
X(54453) = lies on the cubnic K938 and these lines: {249, 36472}, {323, 9721}, {403, 3564}, {1993, 15538}, {3448, 3566}, {3580, 5866}, {3926, 14253}, {37779, 52504}, {39138, 52451}
X(54453) = reflection of X(249) in X(36472)
X(54453) = isogonal conjugate of X(2079)
X(54453) = antigonal image of X(249)
X(54453) = cyclocevian conjugate of X(925)
X(54453) = isotomic conjugate of the anticomplement of X(4558)
X(54453) = cevapoint of X(i) and X(j) for these (i,j): {6, 12310}, {511, 41181}, {3564, 36472}, {13754, 39021}
X(54453) = trilinear pole of line {5972, 6132}
X(54453) = barycentric quotient X(6)/X(2079)
X(54454) lies on these lines: {2, 40582}, {69, 4189}, {95, 37291}, {253, 6872}, {264, 5046}, {305, 34282}, {306, 2895}, {307, 1442}, {319, 20336}, {328, 14616}, {1029, 30690}, {1441, 2475}, {1494, 15677}, {2893, 21272}, {3448, 41004}, {5154, 8797}, {6340, 45962}, {7054, 15526}, {15674, 40412}, {17576, 35510}, {17791, 21287}, {20846, 40995}
X(54454) = isotomic conjugate of X(2475)
X(54454) = anticomplement of X(40582)
X(54454) = cyclocevian conjugate of X(2995)
X(54454) = isotomic conjugate of the anticomplement of X(21)
X(54454) = isotomic conjugate of the complement of X(15680)
X(54454) = isotomic conjugate of the isogonal conjugate of X(34435)
X(54454) = X(34435)-anticomplementary conjugate of X(63)
X(54454) = X(i)-isoconjugate of X(j) for these (i,j): {6, 1781}, {25, 52362}, {31, 2475}, {41, 18625}, {42, 229}, {213, 52361}, {1400, 40582}, {1402, 52360}, {1973, 28754}
X(54454) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 2475}, {9, 1781}, {3160, 18625}, {6337, 28754}, {6505, 52362}, {6626, 52361}, {40592, 229}, {40605, 52360}
X(54454) = cevapoint of X(i) and X(j) for these (i,j): {2, 15680}, {513, 17058}, {514, 8286}, {521, 15526}, {522, 8287}, {23880, 53829}
X(54454) = trilinear pole of line {525, 14838}
X(54454) = barycentric product X(76)*X(34435)
X(54454) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1781}, {2, 2475}, {7, 18625}, {21, 40582}, {63, 52362}, {69, 28754}, {81, 229}, {86, 52361}, {333, 52360}, {34435, 6}, {37887, 41495}
X(54455) lies on these lines: {2, 39054}, {148, 7265}, {484, 4645}, {1577, 21221}, {2533, 3448}, {3936, 19308}, {17484, 17789}, {26081, 47318}
X(54455) = isogonal conjugate of X(21004)
X(54455) = isotomic conjugate of X(21221)
X(54455) = anticomplement of X(39054)
X(54455) = cyclocevian conjugate of X(3952)
X(54455) = isotomic conjugate of the anticomplement of X(662)
X(54455) = isotomic conjugate of the complement of X(31297)
X(54455) = X(39137)-anticomplementary conjugate of X(7192)
X(54455) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21004}, {6, 21381}, {19, 22156}, {31, 21221}, {32, 20951}, {58, 21890}, {163, 50574}, {512, 39054}, {692, 21209}, {1333, 21098}
X(54455) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 21221}, {3, 21004}, {6, 22156}, {9, 21381}, {10, 21890}, {37, 21098}, {115, 50574}, {1086, 21209}, {6376, 20951}
X(54455) = cevapoint of X(i) and X(j) for these (i,j): {2, 31297}, {523, 24040}
X(54455) = trilinear pole of line {4458, 6370}
X(54455) = barycentric product X(75)*X(39137)
X(54455) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21381}, {2, 21221}, {3, 22156}, {6, 21004}, {10, 21098}, {37, 21890}, {75, 20951}, {514, 21209}, {523, 50574}, {662, 39054}, {39137, 1}
X(54456) lies on the cubic K323 and these lines: {2, 3252}, {6, 6654}, {239, 672}, {350, 518}, {1447, 1458}, {2113, 13576}, {2669, 3286}, {9318, 40721}, {20345, 30941}, {27922, 34230}, {35119, 52205}
X(54456) = reflection of X(52209) in X(35119)
X(54456) = isogonal conjugate of X(2110)
X(54456) = isotomic conjugate of X(17794)
X(54456) = anticomplement of X(36906)
X(54456) = antitomic image of X(52209)
X(54456) = cyclocevian conjugate of X(7261)
X(54456) = isotomic conjugate of the anticomplement of X(291)
X(54456) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2111, 4645}, {33701, 20552}
X(54456) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2110}, {6, 24578}, {19, 20762}, {31, 17794}, {42, 8849}, {55, 52161}, {58, 20694}, {1914, 36906}, {2223, 33674}
X(54456) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17794}, {3, 2110}, {6, 20762}, {9, 24578}, {10, 20694}, {223, 52161}, {40592, 8849}
X(54456) = cevapoint of X(i) and X(j) for these (i,j): {513, 35119}, {514, 38989}, {650, 15615}
X(54456) = trilinear pole of line {665, 812}
X(54456) = barycentric product X(i)*X(j) for these {i,j}: {75, 2111}, {33701, 52209}
X(54456) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 24578}, {2, 17794}, {3, 20762}, {6, 2110}, {37, 20694}, {57, 52161}, {81, 8849}, {291, 36906}, {673, 33674}, {2111, 1}, {33701, 17755}
X(54457) lies on these lines: {2, 36033}, {8, 34242}, {573, 1759}, {1479, 7253}, {1969, 21270}, {3868, 5081}, {3869, 6327}, {4296, 4511}, {7141, 18474}
X(54457) = isogonal conjugate of X(23843)
X(54457) = isotomic conjugate of X(21270)
X(54457) = anticomplement of X(36033)
X(54457) = polar conjugate of X(17902)
X(54457) = cyclocevian conjugate of X(7361)
X(54457) = isotomic conjugate of the anticomplement of X(48)
X(54457) = isotomic conjugate of the complement of X(20074)
X(54457) = X(7094)-anticomplementary conjugate of X(6360)
X(54457) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23843}, {2, 2908}, {4, 36033}, {6, 1726}, {19, 22130}, {31, 21270}, {32, 20926}, {48, 17902}, {692, 21184}, {1333, 21072}
X(54457) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 21270}, {3, 23843}, {6, 22130}, {9, 1726}, {37, 21072}, {1086, 21184}, {1249, 17902}, {6376, 20926}, {32664, 2908}
X(54457) = cevapoint of X(i) and X(j) for these (i,j): {2, 20074}, {124, 521}, {520, 34846}, {525, 21253}
X(54457) = trilinear pole of line {6589, 16612}
X(54457) = barycentric product X(i)*X(j) for these {i,j}: {75, 7094}, {561, 7139}
X(54457) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1726}, {2, 21270}, {3, 22130}, {4, 17902}, {6, 23843}, {10, 21072}, {31, 2908}, {48, 36033}, {75, 20926}, {514, 21184}, {7094, 1}, {7139, 31}
X(54458) lies on these lines: {69, 25048}, {141, 27004}, {883, 46152}, {1332, 46163}, {3882, 46148}, {3888, 4576}, {4553, 53332}, {6386, 21301}, {17137, 46158}
X(54458) = isogonal conjugate of X(21005)
X(54458) = isotomic conjugate of X(21301)
X(54458) = cyclocevian conjugate of X(9295)
X(54458) = isotomic conjugate of the anticomplement of X(667)
X(54458) = isotomic conjugate of the complement of X(31291)
X(54458) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21005}, {6, 21389}, {19, 22157}, {31, 21301}, {32, 20952}, {667, 32926}, {692, 21210}, {1333, 21099}, {1973, 28423}
X(54458) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 21301}, {3, 21005}, {6, 22157}, {9, 21389}, {37, 21099}, {1086, 21210}, {6337, 28423}, {6376, 20952}, {6631, 32926}
X(54458) = cevapoint of X(i) and X(j) for these (i,j): {2, 31291}, {141, 513}, {512, 1211}, {514, 2887}, {522, 21244}, {523, 21245}, {812, 20542}, {4083, 21250}, {6371, 51571}, {6373, 20343}
X(54458) = trilinear pole of line {39, 712}
X(54458) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21389}, {2, 21301}, {3, 22157}, {6, 21005}, {10, 21099}, {69, 28423}, {75, 20952}, {190, 32926}, {514, 21210}
X(54459) lies on these lines: {2, 8792}, {69, 2916}, {99, 42052}, {253, 7519}, {264, 7533}, {287, 37779}, {305, 1369}, {339, 37349}, {1494, 37901}, {1799, 7664}, {2373, 37760}, {5189, 18019}, {6330, 37766}, {13219, 18018}, {14002, 41896}, {15526, 36415}, {15899, 30786}, {31857, 51884}, {37644, 42287}
X(54459) = isogonal conjugate of X(19596)
X(54459) = isotomic conjugate of X(5189)
X(54459) = anticomplement of X(40583)
X(54459) = cyclocevian conjugate of X(14364)
X(54459) = isotomic conjugate of the anticomplement of X(23)
X(54459) = isotomic conjugate of the complement of X(20063)
X(54459) = isotomic conjugate of the isogonal conjugate of X(34437)
X(54459) = X(i)-isoconjugate of X(j) for these (i,j): {1, 19596}, {6, 16546}, {19, 22121}, {31, 5189}, {32, 20916}, {41, 18627}, {692, 21176}, {896, 8877}, {1333, 21064}, {1964, 38946}, {2157, 40583}
X(54459) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 5189}, {3, 19596}, {6, 22121}, {9, 16546}, {37, 21064}, {1086, 21176}, {3160, 18627}, {6376, 20916}, {15899, 8877}, {41884, 38946}
X(54459) = cevapoint of X(i) and X(j) for these (i,j): {2, 20063}, {6292, 9019}, {9517, 15526}
X(54459) = trilinear pole of line {525, 3589}
X(54459) = barycentric product X(76)*X(34437)
X(54459) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16546}, {2, 5189}, {3, 22121}, {6, 19596}, {7, 18627}, {10, 21064}, {23, 40583}, {75, 20916}, {83, 38946}, {111, 8877}, {514, 21176}, {22151, 52363}, {34437, 6}
Let ABC be a right triangle at A. There exists a lot of finite centers in ETC lying on the hypotenuse BC (produced included), in particular, those having first coordinates with a multiplying factor cos(A) or (-a^2+b^2+c^2).
Let denote by ℋ the set of k such that X(k)-of-ABC lies on the hypotenuse BC. As an example, the subset o ℋ for k≤1000 is:
{3, 48, 49, 63, 68, 69, 71, 72, 73, 77, 78, 97, 122, 123, 125, 127, 130, 131, 155, 184, 185, 201, 212, 216, 217, 219, 222, 224, 228, 248, 255, 265, 268, 271, 283, 287, 293, 295, 296, 304, 305, 306, 307, 326, 328, 332, 336, 337, 339, 343, 345, 348, 394, 408, 417, 418, 426, 440, 441, 454, 464, 465, 466, 487, 488, 563, 577, 603, 606, 647, 652, 656, 682, 684, 686, 810, 820, 822, 828, 836, 852, 856, 878, 879, 895, 905, 906, 914, 974}
Application.
Let ABC be an acute triangle. Build the rectangle BCCaBa such that A lies on CaBa. Two right triangles BaBA and CaCA are obtained. Now, for a given k ∈ ℋ, let B'a = X(k)-of-BaBA and C'a = X(k)-of-CaCA, these centers lying on their hipotenuses AB and AC, respectively. Define C'b, A'b and A'c, B'c cyclically. It is not hard to prove that, for any k∈ℋ, these six points lie on an conic 𝒞( X(k) ), here named the H-conic of X(k) (H stands for hypotenuses).
Depending on the chosen k, 𝒞( X(k) ) can degenerate to two lines or to the line at infinity (as with X(3), X(68) and others). Also, every pair of constructed points on a side of ABC can coincide and the H-conic approaches to a circle, as occurs with X(69), for which the Taylor circle is obtained.
X(54460) lies on these lines: {140, 54465}, {394, 10665}, {492, 40697}, {641, 1583}
X(54460) = center of the H-conic of X(n) for these n: {48, 73, 336, 820, 836}
X(54461) lies on these lines: {50, 323}, {252, 32142}, {338, 11140}, {32423, 41590}
X(54461) = center of the H-conic of X(n) for these n: {49, 265}
X(54462) lies on these lines: {1, 3}, {7, 13386}, {222, 16232}, {482, 46017}, {2262, 51841}, {2362, 52424}, {3083, 52420}, {13390, 39795}, {16608, 30380}, {16663, 23839}
X(54462) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(6348)}} and {{A, B, C, X(3), X(13386)}}
X(54462) = X(52286)-of-intouch triangle, when ABC is acute
X(54462) = center of the H-conic of X(n) for these n: {72, 219}
X(54463) lies on these lines: {76, 6504}, {394, 577}, {1216, 12362}, {23292, 46184}
X(54463) = center of the H-conic of X(n) for these n: {125, 130, 184, 185, 217, 287, 296, 686, 974}
X(54464) lies on these lines: {3, 6213}, {3718, 13458}
X(54465) lies on these lines: {140, 54460}, {394, 10666}, {491, 40697}, {642, 1584}
X(54465) = center of the H-conic of X(n) for these n: {563, 652, 656, 822}
X(54466) lies on these lines: {12359, 16196}
X(54467) lies on these lines: {5, 578}, {25, 6750}, {26, 5961}, {216, 2165}, {254, 1093}, {7493, 33495}, {8800, 27087}, {9938, 34840}, {13383, 15508}, {16310, 41587}, {23105, 52585}
See Stanley Rabinowitz and Peter Moses, euclid 5951.
X(54468) lies on these lines: {4, 52164}, {100, 13386}, {105, 1336}, {291, 16232}, {1282, 6212}, {8299, 14121}
See Stanley Rabinowitz and Peter Moses, euclid 5951.
X(54469) lies on these lines: {4,52164}, {100,13387}, {105,1123}, {291,2362}, {1282,6213}, {7090,8299}
See Stanley Rabinowitz and César Lozada, euclid 5956.
X(54470) lies on these lines: {6, 19}, {8048, 13389}, {9042, 23050}
X(54470) = X(13386)-Ceva conjugate of-X(16232)
X(54470) = X(2362)-Dao conjugate of-X(13387)
See Stanley Rabinowitz and César Lozada, euclid 5956.
X(54471) lies on these lines: {6, 19}, {7133, 7595}, {8048, 13388}, {9043, 23050}
X(54471) = X(13387)-Ceva conjugate of-X(2362)
X(54471) = X(16232)-Dao conjugate of-X(13386)
See Elias Hagos and César Lozada, euclid 5957.
X(54472) lies on these lines: {6, 46342}, {13, 511}, {15, 11142}, {51, 512}, {52, 11555}, {187, 3457}, {265, 11139}, {316, 16770}, {373, 52039}, {396, 15929}, {2380, 5995}, {2393, 22826}, {5611, 21310}, {5640, 21466}, {6104, 13350}, {11080, 16247}, {11537, 11624}, {15609, 47026}, {25178, 53793}, {25219, 34373}, {30439, 36970}, {32761, 54363}, {34325, 36978}, {36208, 44498}, {36755, 41474}
X(54472) = X(15295)-Dao conjugate of-X(34374)
X(54472) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (11060, 34374), (34373, 7799)
X(54472) = barycentric product of X(i) and X(j) for these {i, j}: {1989, 34373}
X(54472) = (X(5995), X(16459))-harmonic conjugate of X(11083)
See Elias Hagos and César Lozada, euclid 5957.
X(54473) lies on these lines: {6, 46343}, {14, 511}, {16, 11141}, {51, 512}, {52, 11556}, {187, 3458}, {265, 11138}, {316, 16771}, {373, 52040}, {395, 15930}, {2381, 5994}, {2393, 22827}, {5615, 21311}, {5640, 21467}, {6105, 13349}, {11085, 16248}, {11549, 11626}, {15610, 47027}, {25173, 53793}, {25220, 34375}, {30440, 36969}, {32761, 54362}, {34326, 36980}, {36209, 44497}, {36756, 41475}
X(54473) = X(15295)-Dao conjugate of-X(34376)
Orthology centers related to bicevian conics: X(54474)-X(55009)
X(54473) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (11060, 34376), (34375, 7799)
X(54473) = barycentric product of X(i) and X(j) for these {i, j}: {1989, 34375}
X(54473) = (X(5994), X(16460))-harmonic conjugate of X(11088)
This preamble and centers X(54474)-X(55009) were contributed by Ivan Pavlov, July 19, 2023.
Let (c) be the bicevian conic of P={u,v,w} and Q={p,q,r}. Lines AP, BP, CP intersect (c) at six points, three of which form the cevian triangle of P. Denote the other three with A1, B1, and C1. Similarly, using Q, define A2, B2, and C2. The lines A1A2, B1B2, and C1C2 form a triangle TaTbTc, which is always perspective to ABC.
In the cases when a certain fourth degree relation holds, ABC and TaTbTc are also orthologic.
In the particular case when Q=X(2) and P lies on the Kiepert hyperbola, the orthology center of ABC and TaTbTc also lies on the Kiepert hyperbola.
In the particular case when Q=X(4) and P lies on the circumconic with perspector X(4), the configuration is degenerate becasue Ta=Tb=Tc=H. The orthology center (which exists only in the limit) is the isotomic conjugate of (SB u v+SC u w-a^2 v w : :) and lies on the Steiner circumellipse. When the orthology center of ABC and TaTbTc exists it lies on the Euler line.
For more information on how each center arises see the documents attached to Euclid 5932.
Contributed by Peter Moses, July 21, 2023: The appearance of i in the following list means that X(i) is a major center and lies on the Kiepert hyperbola: 54479, 54480, 54534, 54535, 54536, 54537, 54538, 54542, 54543, 54574, 54575, 54576. 54577. 54578, 54579, 54580, 54581, 54591, 54592, 54593, 54594, 54595, 54596, 54597, 54598, 54599, 54634, 54635, 54636
X(54474) lies on these lines: {1, 3}, {2, 10186}, {37, 1742}, {43, 25075}, {45, 9355}, {77, 9440}, {100, 28125}, {226, 53617}, {515, 44430}, {516, 27475}, {949, 20770}, {954, 5018}, {984, 991}, {1088, 1323}, {1212, 3740}, {1251, 30300}, {1253, 1442}, {1376, 34522}, {1699, 36731}, {1721, 3247}, {1961, 5527}, {1962, 9778}, {2293, 7671}, {2340, 3681}, {2951, 16673}, {3688, 50658}, {3817, 7377}, {3842, 48878}, {3920, 18461}, {3989, 11220}, {4021, 43151}, {4098, 9950}, {4336, 7676}, {4566, 5281}, {4640, 6603}, {4650, 11364}, {4687, 45305}, {5308, 6999}, {5311, 7411}, {5432, 5723}, {5526, 7262}, {5657, 50282}, {5731, 48856}, {5779, 51294}, {5851, 49742}, {5886, 29365}, {5927, 16601}, {6184, 19584}, {6211, 37474}, {6986, 16478}, {7380, 10175}, {7611, 29349}, {8580, 52705}, {8926, 40781}, {9316, 38459}, {9442, 9502}, {10164, 50114}, {11495, 16777}, {14520, 20683}, {15624, 18161}, {16112, 16675}, {16468, 31658}, {16475, 21153}, {16826, 48900}, {17389, 28870}, {17392, 38454}, {24203, 24283}, {24328, 53394}, {24341, 35338}, {25568, 35102}, {26446, 29331}, {28160, 36732}, {28849, 29574}, {29657, 37374}, {29675, 43057}, {30301, 33653}, {31395, 48929}, {38127, 49772}
X(54474) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(1), X(18810)}}, {{A, B, C, X(56), X(28869)}}, {{A, B, C, X(57), X(34521)}}, {{A, B, C, X(1088), X(4860)}}, {{A, B, C, X(5228), X(9442)}}, {{A, B, C, X(9441), X(40779)}}
X(54474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 51300, 41339}
X(54475) lies on these lines: {2, 10723}, {4, 41672}, {30, 10153}, {115, 43537}, {381, 42011}, {542, 32532}, {2794, 47586}, {3424, 39838}, {5480, 45103}, {5485, 9880}, {5503, 6321}, {7607, 14639}, {10722, 53100}, {38259, 38664}
X(54475) = reflection of X(i) in X(j) for these {i,j}: {43537, 115}
X(54475) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(265), X(39446)}}, {{A, B, C, X(2710), X(14498)}}, {{A, B, C, X(3455), X(52518)}}, {{A, B, C, X(3531), X(6323)}}, {{A, B, C, X(3563), X(10630)}}, {{A, B, C, X(9154), X(10723)}}, {{A, B, C, X(14490), X(52239)}}, {{A, B, C, X(35140), X(38738)}}, {{A, B, C, X(39838), X(45031)}}
X(54476) lies on these lines: {2, 5585}, {20, 53098}, {30, 10155}, {76, 23334}, {262, 50687}, {381, 53103}, {524, 43681}, {671, 51170}, {3146, 7608}, {3543, 14494}, {3832, 7607}, {3839, 7612}, {3854, 53859}, {5032, 38259}, {5068, 10185}, {5503, 20094}, {7620, 43676}, {8781, 52695}, {10159, 32979}, {11303, 43444}, {11304, 43445}, {11669, 15683}, {14068, 43529}, {17578, 53099}, {32982, 43527}, {32996, 43528}, {33698, 43448}, {38253, 52281}, {41895, 53418}, {43537, 50689}
X(54476) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11741)}}, {{A, B, C, X(6), X(5585)}}, {{A, B, C, X(428), X(32979)}}, {{A, B, C, X(458), X(50687)}}, {{A, B, C, X(524), X(43726)}}, {{A, B, C, X(1383), X(23334)}}, {{A, B, C, X(3146), X(52281)}}, {{A, B, C, X(3832), X(52282)}}, {{A, B, C, X(3839), X(37174)}}, {{A, B, C, X(5032), X(20080)}}, {{A, B, C, X(5064), X(32982)}}, {{A, B, C, X(7408), X(8370)}}, {{A, B, C, X(7409), X(7841)}}, {{A, B, C, X(11317), X(52301)}}, {{A, B, C, X(13377), X(21765)}}, {{A, B, C, X(14490), X(30535)}}, {{A, B, C, X(46275), X(52223)}}, {{A, B, C, X(52450), X(52695)}}
X(54477) lies on these lines: {2, 48884}, {30, 10159}, {76, 3830}, {83, 3845}, {381, 43527}, {383, 10187}, {428, 16080}, {671, 12101}, {1080, 10188}, {1513, 10185}, {2394, 7927}, {3399, 52854}, {5064, 43530}, {5485, 44678}, {6054, 35005}, {7865, 15682}, {9302, 10722}, {10302, 33699}, {14269, 53102}, {14488, 36990}, {15687, 43676}, {18841, 41099}, {43681, 50687}
X(54477) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(3830)}}, {{A, B, C, X(30), X(428)}}, {{A, B, C, X(74), X(34572)}}, {{A, B, C, X(251), X(13603)}}, {{A, B, C, X(264), X(46204)}}, {{A, B, C, X(381), X(5064)}}, {{A, B, C, X(427), X(3845)}}, {{A, B, C, X(468), X(12101)}}, {{A, B, C, X(1173), X(29316)}}, {{A, B, C, X(1297), X(46848)}}, {{A, B, C, X(1494), X(15321)}}, {{A, B, C, X(1799), X(18550)}}, {{A, B, C, X(1989), X(43458)}}, {{A, B, C, X(3108), X(14487)}}, {{A, B, C, X(3543), X(7714)}}, {{A, B, C, X(4518), X(33696)}}, {{A, B, C, X(5066), X(52285)}}, {{A, B, C, X(6995), X(15682)}}, {{A, B, C, X(7378), X(41099)}}, {{A, B, C, X(7408), X(11001)}}, {{A, B, C, X(7409), X(41106)}}, {{A, B, C, X(7576), X(34603)}}, {{A, B, C, X(7865), X(42037)}}, {{A, B, C, X(10301), X(33699)}}, {{A, B, C, X(11058), X(45819)}}, {{A, B, C, X(11169), X(48911)}}, {{A, B, C, X(11181), X(14490)}}, {{A, B, C, X(11738), X(39955)}}, {{A, B, C, X(13481), X(32085)}}, {{A, B, C, X(14495), X(22334)}}, {{A, B, C, X(16835), X(29322)}}
X(54477) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 10185}
X(54478) lies on these lines: {30, 10185}, {76, 50989}, {98, 12101}, {671, 41149}, {3543, 53859}, {3830, 7607}, {3845, 7608}, {3860, 53108}, {8352, 10159}, {11317, 43527}, {33699, 53104}, {41099, 53098}
X(54478) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11588)}}, {{A, B, C, X(6), X(50989)}}, {{A, B, C, X(297), X(12101)}}, {{A, B, C, X(428), X(8352)}}, {{A, B, C, X(524), X(41149)}}, {{A, B, C, X(3531), X(20251)}}, {{A, B, C, X(3830), X(52282)}}, {{A, B, C, X(3845), X(52281)}}, {{A, B, C, X(5064), X(11317)}}, {{A, B, C, X(13603), X(32901)}}, {{A, B, C, X(15534), X(51187)}}, {{A, B, C, X(41153), X(50991)}}
X(54479) lies on these lines: {2, 42112}, {13, 42520}, {14, 12101}, {17, 3845}, {18, 3830}, {30, 10187}, {381, 10188}, {383, 10185}, {3412, 14269}, {3534, 42611}, {3860, 19107}, {3861, 42976}, {5066, 43443}, {5076, 49904}, {5487, 33622}, {5488, 36346}, {8703, 42597}, {11001, 43444}, {11121, 35749}, {11122, 36330}, {12816, 42101}, {12820, 42093}, {12821, 41107}, {14893, 41973}, {15682, 42505}, {15687, 42503}, {16808, 43369}, {16965, 43557}, {19106, 43429}, {19709, 43441}, {19710, 42493}, {22235, 42160}, {33602, 43368}, {33603, 36969}, {33606, 42125}, {33607, 36970}, {33699, 42100}, {36329, 40706}, {36769, 40707}, {36968, 42953}, {38335, 42533}, {41099, 42581}, {41101, 42106}, {41106, 42434}, {41108, 43540}, {41113, 43553}, {41119, 43196}, {41120, 41972}, {41122, 43365}, {42089, 43003}, {42098, 43544}, {42119, 43554}, {42141, 42510}, {42419, 42813}, {42528, 42931}, {42631, 43324}, {42633, 43226}, {42900, 43229}, {43006, 43541}, {43008, 43017}, {43022, 49903}, {43227, 43327}, {43242, 43399}, {43555, 49908}, {44580, 51915}
X(54479) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(471), X(12101)}}, {{A, B, C, X(472), X(3830)}}, {{A, B, C, X(473), X(3845)}}, {{A, B, C, X(7043), X(33696)}}, {{A, B, C, X(8742), X(46204)}}, {{A, B, C, X(18550), X(40712)}}
X(54479) = X(i)-cross conjugate of X(j) for these {i, j}: {43475, 12816}
X(54480) lies on these lines: {2, 42113}, {13, 12101}, {14, 42521}, {17, 3830}, {18, 3845}, {30, 10188}, {381, 10187}, {1080, 10185}, {3411, 14269}, {3534, 42610}, {3860, 19106}, {3861, 42977}, {5066, 43442}, {5076, 49903}, {5487, 36352}, {5488, 33624}, {8703, 42596}, {11001, 43445}, {11121, 35752}, {11122, 36327}, {12817, 42102}, {12820, 41108}, {12821, 42094}, {14893, 41974}, {15682, 42504}, {15687, 42502}, {16809, 43368}, {16964, 43556}, {19107, 43428}, {19709, 43440}, {19710, 42492}, {22237, 42161}, {33602, 36970}, {33603, 43369}, {33606, 36969}, {33607, 42128}, {33699, 42099}, {35751, 40707}, {36967, 42952}, {38335, 42532}, {40706, 47867}, {41099, 42580}, {41100, 42103}, {41106, 42433}, {41107, 43541}, {41112, 43552}, {41119, 41971}, {41120, 43195}, {41121, 43364}, {42092, 43002}, {42095, 43545}, {42120, 43555}, {42140, 42511}, {42420, 42814}, {42529, 42930}, {42632, 43325}, {42634, 43227}, {42901, 43228}, {43007, 43540}, {43009, 43016}, {43023, 49904}, {43226, 43326}, {43243, 43400}, {43554, 49907}, {44580, 51916}
X(54480) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(470), X(12101)}}, {{A, B, C, X(472), X(3845)}}, {{A, B, C, X(473), X(3830)}}, {{A, B, C, X(7026), X(33696)}}, {{A, B, C, X(8741), X(46204)}}, {{A, B, C, X(18550), X(40711)}}
X(54480) = X(i)-cross conjugate of X(j) for these {i, j}: {43476, 12817}
X(54481) lies on these lines: {30, 10290}, {542, 43688}, {1916, 11645}, {6054, 43529}, {9180, 30217}, {10159, 44224}, {14223, 25423}
X(54481) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(44224)}}, {{A, B, C, X(512), X(14388)}}, {{A, B, C, X(542), X(25423)}}, {{A, B, C, X(543), X(30217)}}, {{A, B, C, X(804), X(11645)}}, {{A, B, C, X(9830), X(32472)}}
X(54482) lies on these lines: {2, 38225}, {30, 10484}, {98, 18424}, {381, 8587}, {1916, 32519}, {5475, 7608}, {5476, 45103}, {7607, 21445}, {7622, 42011}, {9755, 43535}, {11170, 53418}, {14912, 32532}
X(54482) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(38225)}}, {{A, B, C, X(54), X(34154)}}, {{A, B, C, X(592), X(30496)}}, {{A, B, C, X(1173), X(9515)}}, {{A, B, C, X(3425), X(9831)}}, {{A, B, C, X(14356), X(18424)}}, {{A, B, C, X(18550), X(47388)}}
X(54483) lies on these lines: {4, 34319}, {30, 10511}, {94, 8352}, {5466, 32228}, {7550, 10185}, {7578, 11317}
X(54483) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(186), X(8352)}}, {{A, B, C, X(265), X(34319)}}, {{A, B, C, X(477), X(36882)}}, {{A, B, C, X(524), X(11564)}}, {{A, B, C, X(5627), X(6094)}}, {{A, B, C, X(6344), X(18818)}}, {{A, B, C, X(7577), X(11317)}}, {{A, B, C, X(7841), X(18559)}}, {{A, B, C, X(22151), X(34802)}}
X(54484) lies on these lines: {2, 47610}, {14, 9862}, {17, 6770}, {18, 33420}, {20, 5487}, {30, 11121}, {76, 616}, {83, 22796}, {542, 40706}, {621, 40707}, {1916, 46708}, {2986, 14181}, {3438, 34296}, {3457, 40158}, {5478, 43550}, {5617, 10159}, {6582, 42035}, {6773, 43539}, {9302, 53442}, {10188, 41020}, {10210, 13582}, {11122, 12188}, {11603, 41023}, {36961, 43547}, {39874, 43542}
X(54484) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34533)}}, {{A, B, C, X(74), X(616)}}, {{A, B, C, X(621), X(1141)}}, {{A, B, C, X(1494), X(8737)}}, {{A, B, C, X(2379), X(11738)}}, {{A, B, C, X(2980), X(11085)}}, {{A, B, C, X(2992), X(11080)}}, {{A, B, C, X(2993), X(34288)}}, {{A, B, C, X(9141), X(34376)}}, {{A, B, C, X(11270), X(23716)}}, {{A, B, C, X(14491), X(34321)}}
X(54484) = X(i)-vertex conjugate of X(j) for these {i, j}: {3439, 9302}
X(54485) lies on these lines: {2, 47611}, {13, 9862}, {17, 33421}, {18, 6773}, {20, 5488}, {30, 11122}, {76, 617}, {83, 22797}, {542, 40707}, {622, 40706}, {1916, 46709}, {2986, 14177}, {3439, 34295}, {3458, 40159}, {5479, 43551}, {5613, 10159}, {6295, 42036}, {6770, 43538}, {9302, 53430}, {10187, 41021}, {11121, 12188}, {11602, 41022}, {36962, 43546}, {39874, 43543}
X(54485) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34534)}}, {{A, B, C, X(74), X(617)}}, {{A, B, C, X(622), X(1141)}}, {{A, B, C, X(1494), X(8738)}}, {{A, B, C, X(2378), X(11738)}}, {{A, B, C, X(2980), X(11080)}}, {{A, B, C, X(2992), X(34288)}}, {{A, B, C, X(2993), X(11085)}}, {{A, B, C, X(9141), X(34374)}}, {{A, B, C, X(11270), X(23717)}}, {{A, B, C, X(14491), X(34322)}}
X(54485) = X(i)-vertex conjugate of X(j) for these {i, j}: {3438, 9302}
X(54486) lies on these lines: {2, 34514}, {30, 11140}, {94, 7540}, {1503, 9221}, {1510, 2394}, {3518, 16080}, {37939, 42410}, {43530, 52295}
X(54486) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(26), X(18559)}}, {{A, B, C, X(30), X(1510)}}, {{A, B, C, X(70), X(34288)}}, {{A, B, C, X(93), X(1989)}}, {{A, B, C, X(186), X(7540)}}, {{A, B, C, X(252), X(30537)}}, {{A, B, C, X(376), X(37122)}}, {{A, B, C, X(381), X(52295)}}, {{A, B, C, X(1138), X(8884)}}, {{A, B, C, X(1141), X(15321)}}, {{A, B, C, X(1179), X(1494)}}, {{A, B, C, X(2980), X(6344)}}, {{A, B, C, X(3520), X(13490)}}, {{A, B, C, X(5627), X(6145)}}, {{A, B, C, X(6240), X(37939)}}, {{A, B, C, X(7512), X(7576)}}, {{A, B, C, X(11738), X(16263)}}, {{A, B, C, X(13489), X(16620)}}, {{A, B, C, X(13596), X(23410)}}, {{A, B, C, X(16837), X(52154)}}, {{A, B, C, X(31181), X(44958)}}, {{A, B, C, X(32085), X(33565)}}, {{A, B, C, X(34797), X(51519)}}, {{A, B, C, X(43908), X(48911)}}
X(54486) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 9221}
X(54487) lies on these lines: {2, 5104}, {6, 43535}, {30, 11170}, {76, 7775}, {83, 7833}, {98, 5476}, {381, 43532}, {385, 11167}, {597, 3407}, {598, 3329}, {599, 42006}, {671, 5475}, {1916, 11163}, {3314, 8176}, {3406, 32134}, {3815, 10484}, {5395, 33192}, {5466, 11640}, {5485, 7774}, {5503, 7777}, {7766, 42536}, {7824, 43527}, {7912, 18840}, {8592, 11317}, {10159, 16921}, {10717, 34087}, {11184, 42010}, {11648, 17503}, {17005, 42011}, {18841, 33215}, {22110, 43529}, {32995, 43681}, {33256, 53102}, {37665, 41895}
X(54487) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5104)}}, {{A, B, C, X(25), X(33013)}}, {{A, B, C, X(251), X(7775)}}, {{A, B, C, X(385), X(9487)}}, {{A, B, C, X(427), X(7833)}}, {{A, B, C, X(428), X(16921)}}, {{A, B, C, X(597), X(3314)}}, {{A, B, C, X(599), X(3329)}}, {{A, B, C, X(1992), X(7774)}}, {{A, B, C, X(3108), X(9515)}}, {{A, B, C, X(5064), X(7824)}}, {{A, B, C, X(5094), X(8597)}}, {{A, B, C, X(5475), X(51541)}}, {{A, B, C, X(5476), X(14356)}}, {{A, B, C, X(6094), X(22336)}}, {{A, B, C, X(7378), X(33215)}}, {{A, B, C, X(7714), X(32962)}}, {{A, B, C, X(7777), X(22329)}}, {{A, B, C, X(7806), X(22110)}}, {{A, B, C, X(7837), X(41624)}}, {{A, B, C, X(7903), X(34572)}}, {{A, B, C, X(7912), X(42037)}}, {{A, B, C, X(8859), X(11184)}}, {{A, B, C, X(8860), X(17005)}}, {{A, B, C, X(8889), X(33192)}}, {{A, B, C, X(9164), X(45108)}}, {{A, B, C, X(9227), X(38005)}}, {{A, B, C, X(9229), X(46645)}}, {{A, B, C, X(10717), X(14609)}}, {{A, B, C, X(11160), X(37665)}}, {{A, B, C, X(14388), X(20251)}}, {{A, B, C, X(18818), X(45819)}}, {{A, B, C, X(30495), X(39389)}}, {{A, B, C, X(45090), X(52395)}}
X(54487) = trilinear pole of line {9208, 523}
X(54488) lies on these lines: {2, 52771}, {30, 11172}, {98, 46034}, {262, 43448}, {598, 6776}, {3543, 43535}, {5395, 39646}, {7608, 31400}, {7612, 11676}, {7620, 11167}, {14485, 14853}, {15980, 40824}, {36998, 53100}
X(54488) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(52771)}}, {{A, B, C, X(253), X(48259)}}, {{A, B, C, X(265), X(6776)}}, {{A, B, C, X(393), X(9154)}}, {{A, B, C, X(6530), X(46034)}}, {{A, B, C, X(6620), X(15980)}}, {{A, B, C, X(11676), X(37174)}}, {{A, B, C, X(11738), X(23700)}}, {{A, B, C, X(33971), X(43448)}}
X(54489) lies on these lines: {2, 6777}, {4, 5469}, {13, 52649}, {14, 14830}, {17, 542}, {30, 11602}, {76, 5463}, {83, 5460}, {115, 12816}, {148, 33610}, {530, 11122}, {531, 40707}, {533, 35005}, {543, 49901}, {598, 16809}, {671, 48996}, {2996, 22577}, {3457, 48353}, {5466, 22934}, {5470, 43546}, {6582, 11121}, {6778, 33607}, {7607, 41020}, {11603, 11632}, {14223, 23872}, {16530, 43539}, {22566, 46053}, {22570, 36967}, {33461, 42036}, {33623, 41135}, {36766, 48657}
X(54489) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(32906)}}, {{A, B, C, X(542), X(23872)}}, {{A, B, C, X(2378), X(3455)}}, {{A, B, C, X(2380), X(46286)}}, {{A, B, C, X(3439), X(34533)}}
X(54489) = midpoint of X(i) in X(j) for these {i,j}: {148, 33610}
X(54489) = reflection of X(i) in X(j) for these {i,j}: {12816, 115}
X(54489) = trilinear pole of line {43228, 523}
X(54489) = X(i)-vertex conjugate of X(j) for these {i, j}: {13, 3439}
X(54490) lies on these lines: {2, 6778}, {4, 5470}, {13, 14830}, {14, 44289}, {18, 542}, {30, 11603}, {76, 5464}, {83, 5459}, {115, 12817}, {148, 33611}, {530, 40706}, {531, 11121}, {532, 35005}, {543, 49902}, {598, 16808}, {671, 48995}, {2996, 22578}, {3458, 48355}, {5466, 22889}, {5469, 43547}, {6295, 11122}, {6777, 33606}, {7607, 41021}, {11602, 11632}, {14223, 23873}, {16529, 43538}, {22566, 46054}, {22568, 36968}, {33460, 42035}, {33625, 41135}
X(54490) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(32908)}}, {{A, B, C, X(542), X(23873)}}, {{A, B, C, X(2379), X(3455)}}, {{A, B, C, X(2381), X(46286)}}, {{A, B, C, X(3438), X(34534)}}
X(54490) = midpoint of X(i) in X(j) for these {i,j}: {148, 33611}
X(54490) = reflection of X(i) in X(j) for these {i,j}: {12817, 115}
X(54490) = trilinear pole of line {43229, 523}
X(54490) = X(i)-vertex conjugate of X(j) for these {i, j}: {14, 3438}
X(54491) lies on these lines: {30, 11608}, {226, 542}, {415, 16080}, {522, 14223}, {2394, 2785}, {2796, 43683}, {9180, 28292}
X(54491) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(415)}}, {{A, B, C, X(522), X(542)}}, {{A, B, C, X(543), X(28292)}}, {{A, B, C, X(1311), X(9141)}}, {{A, B, C, X(2796), X(6003)}}
X(54492) lies on these lines: {10, 2247}, {30, 11611}, {321, 542}, {422, 16080}, {513, 14223}, {2394, 2787}, {9180, 28475}
X(54492) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(422)}}, {{A, B, C, X(105), X(9141)}}, {{A, B, C, X(513), X(542)}}, {{A, B, C, X(543), X(28475)}}
X(54493) lies on these lines: {30, 11668}, {98, 38335}, {262, 14893}, {381, 53108}, {1657, 10185}, {3627, 7607}, {3843, 7608}, {7827, 18843}, {11303, 43441}, {11304, 43440}, {11669, 23046}, {14044, 43529}, {14066, 43528}, {15684, 53104}, {50691, 53859}
X(54493) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(14490)}}, {{A, B, C, X(297), X(38335)}}, {{A, B, C, X(458), X(14893)}}, {{A, B, C, X(3431), X(11588)}}, {{A, B, C, X(3627), X(52282)}}, {{A, B, C, X(3843), X(52281)}}, {{A, B, C, X(11741), X(32901)}}
X(54494) lies on these lines: {6, 33698}, {30, 11669}, {98, 14269}, {262, 15687}, {381, 53104}, {382, 7608}, {546, 7607}, {597, 53102}, {598, 6329}, {3529, 53098}, {3851, 10185}, {5485, 11008}, {7827, 18845}, {8591, 35005}, {10302, 11317}, {11149, 33257}, {11303, 43442}, {11304, 43443}, {11668, 38071}, {14042, 43529}, {14062, 43528}, {15681, 53108}, {17503, 53418}, {20583, 53105}, {33229, 43527}, {50688, 53099}
X(54494) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(3531)}}, {{A, B, C, X(297), X(14269)}}, {{A, B, C, X(382), X(52281)}}, {{A, B, C, X(458), X(15687)}}, {{A, B, C, X(546), X(52282)}}, {{A, B, C, X(597), X(31360)}}, {{A, B, C, X(599), X(6329)}}, {{A, B, C, X(1992), X(11008)}}, {{A, B, C, X(3431), X(11741)}}, {{A, B, C, X(5064), X(33229)}}, {{A, B, C, X(7841), X(52285)}}, {{A, B, C, X(10301), X(11317)}}, {{A, B, C, X(10630), X(47060)}}, {{A, B, C, X(11588), X(11736)}}, {{A, B, C, X(11738), X(20251)}}, {{A, B, C, X(20583), X(40341)}}, {{A, B, C, X(33696), X(34914)}}
X(54495) lies on these lines: {2, 9717}, {30, 12066}, {74, 671}, {76, 36890}, {1494, 8781}, {2394, 15543}, {2433, 5466}, {2986, 9140}, {5627, 39295}, {9180, 14651}
X(54495) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(12065)}}, {{A, B, C, X(74), X(2433)}}, {{A, B, C, X(476), X(1138)}}, {{A, B, C, X(1494), X(18808)}}, {{A, B, C, X(1989), X(9214)}}, {{A, B, C, X(5627), X(12079)}}, {{A, B, C, X(5641), X(40118)}}, {{A, B, C, X(7418), X(52492)}}, {{A, B, C, X(9140), X(33565)}}, {{A, B, C, X(14582), X(35912)}}, {{A, B, C, X(15454), X(15543)}}, {{A, B, C, X(16092), X(52491)}}, {{A, B, C, X(34174), X(53161)}}
X(54495) = trilinear pole of line {6128, 523}
X(54495) = X(i)-cross conjugate of X(j) for these {i, j}: {542, 5627}
X(54495) = barycentric quotient X(i)/X(j) for these (i, j): {2433, 34291}
X(54496) lies on these lines: {4, 34986}, {30, 13380}, {96, 31180}, {98, 34609}, {317, 459}, {381, 45300}, {671, 37672}, {1368, 7607}, {2052, 27377}, {5020, 7608}, {5392, 14615}, {7396, 43537}, {7398, 53099}, {10159, 41235}, {16072, 40448}, {37874, 53420}
X(54496) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(290), X(34412)}}, {{A, B, C, X(297), X(34609)}}, {{A, B, C, X(317), X(1494)}}, {{A, B, C, X(394), X(43844)}}, {{A, B, C, X(428), X(41235)}}, {{A, B, C, X(467), X(31180)}}, {{A, B, C, X(524), X(37672)}}, {{A, B, C, X(1368), X(52282)}}, {{A, B, C, X(5020), X(52281)}}, {{A, B, C, X(6391), X(27377)}}, {{A, B, C, X(8794), X(40832)}}, {{A, B, C, X(15749), X(37669)}}, {{A, B, C, X(16072), X(52280)}}, {{A, B, C, X(35142), X(41530)}}
X(54497) lies on these lines: {10, 35338}, {30, 13576}, {321, 50154}, {537, 43677}, {542, 43671}, {918, 2394}, {1111, 43682}, {2826, 5466}, {15149, 16080}
X(54497) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(918)}}, {{A, B, C, X(74), X(37128)}}, {{A, B, C, X(84), X(36871)}}, {{A, B, C, X(104), X(2991)}}, {{A, B, C, X(274), X(10308)}}, {{A, B, C, X(348), X(34800)}}, {{A, B, C, X(524), X(2826)}}, {{A, B, C, X(537), X(6002)}}, {{A, B, C, X(651), X(1292)}}, {{A, B, C, X(1111), X(7261)}}, {{A, B, C, X(1138), X(9510)}}, {{A, B, C, X(3065), X(4560)}}, {{A, B, C, X(3426), X(39981)}}, {{A, B, C, X(3431), X(39952)}}, {{A, B, C, X(3512), X(17925)}}, {{A, B, C, X(7313), X(17096)}}, {{A, B, C, X(14483), X(39971)}}, {{A, B, C, X(16615), X(32009)}}, {{A, B, C, X(28840), X(28850)}}, {{A, B, C, X(36800), X(39768)}}, {{A, B, C, X(44129), X(48877)}}, {{A, B, C, X(48897), X(52374)}}
X(54497) = trilinear pole of line {354, 523}
X(54498) lies on these lines: {2, 15032}, {20, 13582}, {30, 13579}, {376, 6504}, {459, 37943}, {3543, 13585}, {3839, 11538}, {7400, 43681}, {7505, 16080}, {34621, 38259}, {37119, 43530}
X(54498) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1989)}}, {{A, B, C, X(20), X(37943)}}, {{A, B, C, X(30), X(7505)}}, {{A, B, C, X(54), X(34288)}}, {{A, B, C, X(64), X(52154)}}, {{A, B, C, X(66), X(13597)}}, {{A, B, C, X(68), X(5627)}}, {{A, B, C, X(69), X(6344)}}, {{A, B, C, X(74), X(2165)}}, {{A, B, C, X(93), X(36889)}}, {{A, B, C, X(252), X(14457)}}, {{A, B, C, X(253), X(5900)}}, {{A, B, C, X(254), X(1138)}}, {{A, B, C, X(264), X(45138)}}, {{A, B, C, X(376), X(3542)}}, {{A, B, C, X(381), X(6145)}}, {{A, B, C, X(393), X(3431)}}, {{A, B, C, X(847), X(1494)}}, {{A, B, C, X(1141), X(4846)}}, {{A, B, C, X(1173), X(22270)}}, {{A, B, C, X(1217), X(3459)}}, {{A, B, C, X(2963), X(3426)}}, {{A, B, C, X(3088), X(5071)}}, {{A, B, C, X(3089), X(3524)}}, {{A, B, C, X(3519), X(48911)}}, {{A, B, C, X(3527), X(30537)}}, {{A, B, C, X(3532), X(18317)}}, {{A, B, C, X(3541), X(3545)}}, {{A, B, C, X(3543), X(14940)}}, {{A, B, C, X(3549), X(18559)}}, {{A, B, C, X(3839), X(6143)}}, {{A, B, C, X(6526), X(45736)}}, {{A, B, C, X(7383), X(7714)}}, {{A, B, C, X(7552), X(18533)}}, {{A, B, C, X(7558), X(7576)}}, {{A, B, C, X(10201), X(35471)}}, {{A, B, C, X(11816), X(14542)}}, {{A, B, C, X(13472), X(52187)}}, {{A, B, C, X(14491), X(46952)}}, {{A, B, C, X(14938), X(22334)}}, {{A, B, C, X(16868), X(44441)}}, {{A, B, C, X(17983), X(46259)}}, {{A, B, C, X(18349), X(36612)}}, {{A, B, C, X(18361), X(44157)}}, {{A, B, C, X(20421), X(51316)}}, {{A, B, C, X(21844), X(46451)}}, {{A, B, C, X(22268), X(52518)}}, {{A, B, C, X(33565), X(34285)}}, {{A, B, C, X(34436), X(51761)}}, {{A, B, C, X(34621), X(38282)}}, {{A, B, C, X(43917), X(45838)}}
X(54498) = X(i)-cross conjugate of X(j) for these {i, j}: {11456, 4}
X(54499) lies on these lines: {10, 16132}, {30, 13583}
X(54499) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(1427)}}, {{A, B, C, X(278), X(2349)}}, {{A, B, C, X(376), X(37388)}}, {{A, B, C, X(1138), X(2184)}}, {{A, B, C, X(1903), X(1989)}}, {{A, B, C, X(5627), X(13853)}}, {{A, B, C, X(10308), X(37887)}}, {{A, B, C, X(16132), X(52374)}}, {{A, B, C, X(28609), X(37797)}}
X(54500) lies on these lines: {2, 15037}, {3, 13582}, {4, 11063}, {30, 13585}, {94, 7552}, {226, 16763}, {275, 1157}, {376, 13579}, {381, 11538}, {2052, 37943}, {3470, 14940}, {3524, 6504}, {6143, 43530}, {6770, 40104}, {6773, 40105}, {7383, 43681}, {7592, 43666}, {9381, 38542}
X(54500) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(16763)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1138)}}, {{A, B, C, X(6), X(15037)}}, {{A, B, C, X(30), X(14940)}}, {{A, B, C, X(54), X(1989)}}, {{A, B, C, X(74), X(2963)}}, {{A, B, C, X(93), X(1494)}}, {{A, B, C, X(95), X(6344)}}, {{A, B, C, X(186), X(7552)}}, {{A, B, C, X(252), X(5627)}}, {{A, B, C, X(264), X(5900)}}, {{A, B, C, X(376), X(7505)}}, {{A, B, C, X(381), X(6143)}}, {{A, B, C, X(631), X(36612)}}, {{A, B, C, X(847), X(13418)}}, {{A, B, C, X(1173), X(22268)}}, {{A, B, C, X(1487), X(6662)}}, {{A, B, C, X(2165), X(3431)}}, {{A, B, C, X(3089), X(15702)}}, {{A, B, C, X(3524), X(3542)}}, {{A, B, C, X(3541), X(5071)}}, {{A, B, C, X(3545), X(37119)}}, {{A, B, C, X(3613), X(13597)}}, {{A, B, C, X(5055), X(35482)}}, {{A, B, C, X(5684), X(16764)}}, {{A, B, C, X(6188), X(20421)}}, {{A, B, C, X(10201), X(21844)}}, {{A, B, C, X(11058), X(17711)}}, {{A, B, C, X(13472), X(22270)}}, {{A, B, C, X(13623), X(20480)}}, {{A, B, C, X(14938), X(16835)}}, {{A, B, C, X(15464), X(46452)}}, {{A, B, C, X(18361), X(18368)}}, {{A, B, C, X(19307), X(34483)}}, {{A, B, C, X(33565), X(45838)}}, {{A, B, C, X(40410), X(45138)}}, {{A, B, C, X(43917), X(53864)}}
X(54500) = X(i)-cross conjugate of X(j) for these {i, j}: {15032, 4}
X(54501) lies on these lines: {30, 14223}, {524, 52459}, {542, 2394}, {543, 43673}, {671, 46982}, {1503, 9180}, {2794, 5466}, {7473, 16080}, {10722, 41392}, {11645, 46040}
X(54501) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(99)}}, {{A, B, C, X(316), X(6054)}}, {{A, B, C, X(511), X(11636)}}, {{A, B, C, X(524), X(2794)}}, {{A, B, C, X(543), X(1503)}}, {{A, B, C, X(1302), X(9141)}}, {{A, B, C, X(2782), X(11645)}}, {{A, B, C, X(5627), X(42345)}}, {{A, B, C, X(6033), X(7809)}}, {{A, B, C, X(7799), X(10722)}}, {{A, B, C, X(11006), X(45774)}}, {{A, B, C, X(46982), X(52475)}}
X(54501) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 9180}, {671, 22455}
X(54502) lies on the Kiepert hyperbola and on these lines: {30, 14228}, {524, 43566}, {591, 1132}, {1131, 5861}, {5860, 43567}, {12322, 43560}, {14243, 36718}
X(54503) lies on these lines: {2, 9675}, {30, 14231}, {76, 591}, {381, 14238}, {486, 35948}, {671, 19108}, {3317, 12322}, {5491, 5861}, {6569, 49229}, {10194, 39388}, {13757, 42023}, {13770, 42024}, {15031, 45575}, {19101, 45420}, {35297, 53488}
X(54503) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(9675)}}, {{A, B, C, X(249), X(589)}}, {{A, B, C, X(1016), X(13390)}}, {{A, B, C, X(1509), X(7090)}}, {{A, B, C, X(3069), X(5861)}}, {{A, B, C, X(5860), X(19053)}}, {{A, B, C, X(18820), X(32085)}}
X(54504) lies on these lines: {30, 14236}, {637, 34091}, {671, 13847}, {1132, 26618}, {5491, 5860}, {6569, 49213}, {13757, 42024}
X(54504) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(494)}}, {{A, B, C, X(589), X(32422)}}, {{A, B, C, X(3069), X(5860)}}
X(54505) lies on these lines: {30, 14240}, {638, 34089}, {671, 13846}, {1131, 26617}, {5490, 5861}, {6568, 49212}, {13637, 42023}
X(54505) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(493)}}, {{A, B, C, X(588), X(32420)}}, {{A, B, C, X(3068), X(5861)}}
X(54506) lies on the Kiepert hyperbola and on these lines: {30, 14243}, {524, 43567}, {1131, 1991}, {1132, 5860}, {5861, 43566}, {12323, 43561}, {14228, 36734}
>X(54507) lies on these lines: {30, 14245}, {76, 1991}, {381, 14234}, {485, 35949}, {671, 19109}, {3316, 12323}, {5490, 5860}, {6568, 49228}, {10195, 39387}, {13637, 42024}, {13651, 42023}, {15031, 45574}, {22541, 45421}, {35297, 53487}
X(54507) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(588)}}, {{A, B, C, X(1016), X(1659)}}, {{A, B, C, X(1509), X(14121)}}, {{A, B, C, X(3068), X(5860)}}, {{A, B, C, X(5861), X(19054)}}, {{A, B, C, X(18819), X(32085)}}
X(54508) lies on these lines: {30, 1446}, {226, 15938}, {2394, 3900}, {4183, 16080}
X(54508) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(3900)}}, {{A, B, C, X(4219), X(11113)}}, {{A, B, C, X(8748), X(15938)}}, {{A, B, C, X(17532), X(37372)}}
X(54509) lies on these lines: {2, 51396}, {6, 11167}, {30, 14485}, {76, 11163}, {83, 8359}, {98, 597}, {262, 42849}, {325, 10302}, {598, 5077}, {671, 3363}, {1506, 18840}, {3329, 8593}, {3424, 11179}, {3815, 5503}, {5461, 9302}, {5466, 44568}, {5485, 7736}, {6054, 43532}, {7737, 18842}, {7840, 42006}, {11648, 32532}, {25555, 43537}, {31489, 42011}, {44401, 53104}
X(54509) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(11163)}}, {{A, B, C, X(183), X(42849)}}, {{A, B, C, X(325), X(597)}}, {{A, B, C, X(427), X(8359)}}, {{A, B, C, X(468), X(3363)}}, {{A, B, C, X(524), X(11169)}}, {{A, B, C, X(599), X(11174)}}, {{A, B, C, X(842), X(30535)}}, {{A, B, C, X(843), X(39389)}}, {{A, B, C, X(1494), X(13377)}}, {{A, B, C, X(1506), X(42037)}}, {{A, B, C, X(1992), X(7736)}}, {{A, B, C, X(3329), X(7840)}}, {{A, B, C, X(3815), X(22329)}}, {{A, B, C, X(4518), X(34914)}}, {{A, B, C, X(5077), X(5094)}}, {{A, B, C, X(7249), X(34892)}}, {{A, B, C, X(7792), X(22110)}}, {{A, B, C, X(8860), X(31489)}}, {{A, B, C, X(9164), X(30537)}}, {{A, B, C, X(9300), X(41624)}}, {{A, B, C, X(9770), X(44556)}}, {{A, B, C, X(18823), X(36897)}}, {{A, B, C, X(23297), X(51224)}}, {{A, B, C, X(35705), X(52094)}}, {{A, B, C, X(36882), X(42286)}}, {{A, B, C, X(37647), X(44401)}}, {{A, B, C, X(43950), X(46316)}}
X(54509) = trilinear pole of line {11186, 523}
X(54510) lies on these lines: {30, 14534}, {381, 34258}, {429, 16080}, {3017, 13478}, {4185, 43530}, {37415, 43527}
X(54510) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(429)}}, {{A, B, C, X(65), X(1494)}}, {{A, B, C, X(381), X(4185)}}, {{A, B, C, X(961), X(1168)}}, {{A, B, C, X(1880), X(44835)}}, {{A, B, C, X(1989), X(51870)}}, {{A, B, C, X(3577), X(13610)}}, {{A, B, C, X(5064), X(37415)}}
X(54511) lies on these lines: {30, 14554}, {226, 1387}, {2827, 4049}, {4080, 38460}
X(54511) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(51788)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(80), X(1387)}}, {{A, B, C, X(104), X(519)}}, {{A, B, C, X(903), X(46435)}}, {{A, B, C, X(1222), X(16005)}}, {{A, B, C, X(1877), X(2161)}}, {{A, B, C, X(3577), X(39704)}}, {{A, B, C, X(3582), X(6735)}}, {{A, B, C, X(3872), X(7284)}}, {{A, B, C, X(5560), X(51709)}}, {{A, B, C, X(14483), X(53114)}}, {{A, B, C, X(16615), X(43972)}}, {{A, B, C, X(36123), X(36910)}}
X(54512) lies on these lines: {2, 7687}, {4, 3163}, {30, 16080}, {275, 3845}, {381, 43530}, {459, 5667}, {2052, 3830}, {2394, 9033}, {10152, 34297}, {10159, 34664}, {11001, 38253}, {12101, 39284}
X(54512) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3830)}}, {{A, B, C, X(5), X(3845)}}, {{A, B, C, X(6), X(22455)}}, {{A, B, C, X(20), X(15682)}}, {{A, B, C, X(30), X(265)}}, {{A, B, C, X(74), X(15051)}}, {{A, B, C, X(95), X(18550)}}, {{A, B, C, X(140), X(12101)}}, {{A, B, C, X(250), X(34802)}}, {{A, B, C, X(253), X(18847)}}, {{A, B, C, X(287), X(53201)}}, {{A, B, C, X(376), X(3543)}}, {{A, B, C, X(381), X(36430)}}, {{A, B, C, X(382), X(3534)}}, {{A, B, C, X(428), X(34664)}}, {{A, B, C, X(546), X(5066)}}, {{A, B, C, X(547), X(14893)}}, {{A, B, C, X(549), X(15687)}}, {{A, B, C, X(550), X(33699)}}, {{A, B, C, X(895), X(2693)}}, {{A, B, C, X(1093), X(46204)}}, {{A, B, C, X(1105), X(21400)}}, {{A, B, C, X(1217), X(18296)}}, {{A, B, C, X(1300), X(5627)}}, {{A, B, C, X(1302), X(52447)}}, {{A, B, C, X(1513), X(8352)}}, {{A, B, C, X(1551), X(36196)}}, {{A, B, C, X(1989), X(7687)}}, {{A, B, C, X(3091), X(41099)}}, {{A, B, C, X(3146), X(11001)}}, {{A, B, C, X(3524), X(50687)}}, {{A, B, C, X(3529), X(15640)}}, {{A, B, C, X(3545), X(3839)}}, {{A, B, C, X(3627), X(8703)}}, {{A, B, C, X(3832), X(41106)}}, {{A, B, C, X(3843), X(19709)}}, {{A, B, C, X(3853), X(12100)}}, {{A, B, C, X(3861), X(10109)}}, {{A, B, C, X(4846), X(36437)}}, {{A, B, C, X(5054), X(38335)}}, {{A, B, C, X(5055), X(14269)}}, {{A, B, C, X(5073), X(15685)}}, {{A, B, C, X(5076), X(15693)}}, {{A, B, C, X(5505), X(50531)}}, {{A, B, C, X(5667), X(10152)}}, {{A, B, C, X(6110), X(11092)}}, {{A, B, C, X(6111), X(11078)}}, {{A, B, C, X(7576), X(52069)}}, {{A, B, C, X(8431), X(50433)}}, {{A, B, C, X(8597), X(11676)}}, {{A, B, C, X(9909), X(34725)}}, {{A, B, C, X(10127), X(44804)}}, {{A, B, C, X(10201), X(18568)}}, {{A, B, C, X(10297), X(47332)}}, {{A, B, C, X(11317), X(13860)}}, {{A, B, C, X(11564), X(43660)}}, {{A, B, C, X(11738), X(41894)}}, {{A, B, C, X(11744), X(48378)}}, {{A, B, C, X(11812), X(12102)}}, {{A, B, C, X(13603), X(41890)}}, {{A, B, C, X(14093), X(35434)}}, {{A, B, C, X(14487), X(41891)}}, {{A, B, C, X(14490), X(15364)}}, {{A, B, C, X(14860), X(17505)}}, {{A, B, C, X(14892), X(41987)}}, {{A, B, C, X(15318), X(15749)}}, {{A, B, C, X(15319), X(18848)}}, {{A, B, C, X(15679), X(21669)}}, {{A, B, C, X(15681), X(15684)}}, {{A, B, C, X(15686), X(35404)}}, {{A, B, C, X(15694), X(35403)}}, {{A, B, C, X(15698), X(50688)}}, {{A, B, C, X(15718), X(35401)}}, {{A, B, C, X(16263), X(34288)}}, {{A, B, C, X(17578), X(19708)}}, {{A, B, C, X(18323), X(44265)}}, {{A, B, C, X(18361), X(46255)}}, {{A, B, C, X(18377), X(44278)}}, {{A, B, C, X(18405), X(41372)}}, {{A, B, C, X(18572), X(44266)}}, {{A, B, C, X(18850), X(36889)}}, {{A, B, C, X(23046), X(38071)}}, {{A, B, C, X(30247), X(48373)}}, {{A, B, C, X(34613), X(52397)}}, {{A, B, C, X(34621), X(44442)}}, {{A, B, C, X(36490), X(36730)}}, {{A, B, C, X(36551), X(36729)}}, {{A, B, C, X(36720), X(36732)}}, {{A, B, C, X(36721), X(36731)}}, {{A, B, C, X(36722), X(36728)}}, {{A, B, C, X(37904), X(47339)}}, {{A, B, C, X(44262), X(44288)}}, {{A, B, C, X(44263), X(44287)}}, {{A, B, C, X(45301), X(46848)}}, {{A, B, C, X(46429), X(48362)}}, {{A, B, C, X(47097), X(47310)}}
X(54512) = trilinear pole of line {14401, 523}
X(54513) lies on these lines: {30, 16277}, {2394, 23881}, {5392, 7841}, {7488, 10511}, {7509, 7607}, {7608, 14788}, {8370, 40393}
X(54513) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(24), X(7841)}}, {{A, B, C, X(30), X(23881)}}, {{A, B, C, X(265), X(6664)}}, {{A, B, C, X(524), X(3519)}}, {{A, B, C, X(599), X(14528)}}, {{A, B, C, X(1300), X(1502)}}, {{A, B, C, X(1594), X(8370)}}, {{A, B, C, X(6094), X(45195)}}, {{A, B, C, X(6656), X(7576)}}, {{A, B, C, X(6662), X(36882)}}, {{A, B, C, X(7487), X(33190)}}, {{A, B, C, X(7509), X(52282)}}, {{A, B, C, X(8352), X(10018)}}, {{A, B, C, X(11317), X(52296)}}, {{A, B, C, X(11585), X(37855)}}, {{A, B, C, X(14262), X(34505)}}, {{A, B, C, X(14788), X(52281)}}, {{A, B, C, X(20806), X(34801)}}, {{A, B, C, X(33565), X(40405)}}
X(54514) lies on the Kiepert hyperbola and these lines: {2, 33708}, {30, 1676}, {524, 3818}, {543, 33707}, {1677, 5309}, {11000, 43527}, {16080, 16246}, {16245, 43530}
X(54514) = reflection of X(i) in X(j) for these {i,j}: {33708, 2}
X(54515) lies on the Kiepert hyperbola and these lines: {2, 33707}, {30, 1677}, {524, 3818}, {543, 33708}, {1676, 5309}, {10999, 43527}
X(54515) = reflection of X(i) in X(j) for these {i,j}: {33707, 2}
X(54516) lies on these lines: {29, 43530}, {30, 1751}, {226, 381}, {4080, 12649}, {5125, 16080}
X(54516) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(15934)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(29), X(381)}}, {{A, B, C, X(30), X(5125)}}, {{A, B, C, X(78), X(36599)}}, {{A, B, C, X(80), X(273)}}, {{A, B, C, X(84), X(903)}}, {{A, B, C, X(158), X(36910)}}, {{A, B, C, X(225), X(34288)}}, {{A, B, C, X(307), X(4846)}}, {{A, B, C, X(519), X(12649)}}, {{A, B, C, X(1257), X(10308)}}, {{A, B, C, X(3345), X(36603)}}, {{A, B, C, X(3426), X(4674)}}, {{A, B, C, X(3545), X(7518)}}, {{A, B, C, X(3839), X(7498)}}, {{A, B, C, X(5136), X(52269)}}, {{A, B, C, X(6734), X(10056)}}, {{A, B, C, X(7319), X(36590)}}, {{A, B, C, X(7513), X(17532)}}, {{A, B, C, X(10429), X(36588)}}, {{A, B, C, X(11114), X(37381)}}, {{A, B, C, X(28193), X(39742)}}, {{A, B, C, X(36721), X(37389)}}, {{A, B, C, X(36889), X(39130)}}
X(54517) lies on these lines: {10, 28854}, {30, 17758}, {226, 3058}, {1446, 7264}, {2394, 4151}, {3309, 4049}, {3870, 4080}, {10159, 13727}, {14004, 16080}, {36652, 43527}, {36721, 43531}
X(54517) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(3748)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(30331)}}, {{A, B, C, X(27), X(36722)}}, {{A, B, C, X(30), X(4151)}}, {{A, B, C, X(79), X(3058)}}, {{A, B, C, X(80), X(21453)}}, {{A, B, C, X(428), X(13727)}}, {{A, B, C, X(461), X(3543)}}, {{A, B, C, X(469), X(36721)}}, {{A, B, C, X(514), X(28854)}}, {{A, B, C, X(516), X(4762)}}, {{A, B, C, X(519), X(3309)}}, {{A, B, C, X(903), X(15909)}}, {{A, B, C, X(996), X(42361)}}, {{A, B, C, X(1088), X(5561)}}, {{A, B, C, X(1280), X(16615)}}, {{A, B, C, X(2736), X(53226)}}, {{A, B, C, X(2788), X(2796)}}, {{A, B, C, X(3017), X(27572)}}, {{A, B, C, X(3062), X(39704)}}, {{A, B, C, X(3426), X(53114)}}, {{A, B, C, X(3668), X(34288)}}, {{A, B, C, X(4847), X(10056)}}, {{A, B, C, X(5064), X(36652)}}, {{A, B, C, X(5556), X(51783)}}, {{A, B, C, X(28194), X(29186)}}, {{A, B, C, X(36124), X(52374)}}
X(54518) lies on these lines: {30, 18366}, {13582, 18403}, {13585, 18566}, {13619, 16080}
X(54518) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(13619)}}, {{A, B, C, X(265), X(1138)}}, {{A, B, C, X(1494), X(6188)}}, {{A, B, C, X(3459), X(17505)}}, {{A, B, C, X(11058), X(16000)}}, {{A, B, C, X(11564), X(18317)}}, {{A, B, C, X(14940), X(18566)}}, {{A, B, C, X(18361), X(45736)}}, {{A, B, C, X(18403), X(37943)}}
X(54519) lies on these lines: {2, 41424}, {20, 10159}, {30, 18840}, {76, 3543}, {83, 3839}, {381, 18841}, {383, 43446}, {428, 459}, {1080, 43447}, {1503, 43951}, {2394, 3800}, {2996, 50687}, {3091, 43527}, {3424, 5306}, {3830, 5485}, {3845, 18842}, {5304, 14458}, {6776, 14488}, {6811, 43564}, {6813, 43565}, {6995, 16080}, {7000, 10194}, {7374, 10195}, {7378, 43530}, {7714, 38253}, {10302, 15640}, {12101, 32532}, {13860, 53098}, {14269, 18843}, {14484, 36990}, {14893, 18844}, {17578, 43681}, {43676, 50688}
X(54519) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34572)}}, {{A, B, C, X(20), X(428)}}, {{A, B, C, X(25), X(3543)}}, {{A, B, C, X(30), X(3800)}}, {{A, B, C, X(66), X(18361)}}, {{A, B, C, X(74), X(39955)}}, {{A, B, C, X(251), X(3426)}}, {{A, B, C, X(253), X(11058)}}, {{A, B, C, X(305), X(43699)}}, {{A, B, C, X(376), X(7408)}}, {{A, B, C, X(381), X(7378)}}, {{A, B, C, X(427), X(3839)}}, {{A, B, C, X(1297), X(22334)}}, {{A, B, C, X(1383), X(13603)}}, {{A, B, C, X(1494), X(52223)}}, {{A, B, C, X(1989), X(8801)}}, {{A, B, C, X(3091), X(5064)}}, {{A, B, C, X(3108), X(3531)}}, {{A, B, C, X(3146), X(7714)}}, {{A, B, C, X(3527), X(29180)}}, {{A, B, C, X(3545), X(7409)}}, {{A, B, C, X(3563), X(46851)}}, {{A, B, C, X(3830), X(4232)}}, {{A, B, C, X(3845), X(52284)}}, {{A, B, C, X(5304), X(7788)}}, {{A, B, C, X(5306), X(37668)}}, {{A, B, C, X(5481), X(52518)}}, {{A, B, C, X(6353), X(50687)}}, {{A, B, C, X(6623), X(31133)}}, {{A, B, C, X(7487), X(34603)}}, {{A, B, C, X(7500), X(7576)}}, {{A, B, C, X(7519), X(18559)}}, {{A, B, C, X(9095), X(39732)}}, {{A, B, C, X(9740), X(41624)}}, {{A, B, C, X(10152), X(40174)}}, {{A, B, C, X(10301), X(15640)}}, {{A, B, C, X(13472), X(29316)}}, {{A, B, C, X(13575), X(16251)}}, {{A, B, C, X(14495), X(16835)}}, {{A, B, C, X(15314), X(36916)}}, {{A, B, C, X(15682), X(52301)}}, {{A, B, C, X(22336), X(48911)}}, {{A, B, C, X(32085), X(36889)}}, {{A, B, C, X(43726), X(52188)}}
X(54519) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43951}
X(54520) lies on these lines: {2, 31860}, {20, 43527}, {30, 18841}, {76, 3839}, {83, 3543}, {381, 18840}, {383, 43447}, {459, 5064}, {1080, 43446}, {1513, 53098}, {2996, 7837}, {3091, 10159}, {3424, 53023}, {3830, 18842}, {3845, 5485}, {5395, 50687}, {6811, 43565}, {6813, 43564}, {6995, 43530}, {7000, 10195}, {7374, 10194}, {7378, 16080}, {8796, 42854}, {9300, 14484}, {14492, 37665}, {15687, 18843}, {18844, 38335}, {43681, 50689}, {50688, 53102}
X(54520) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(5064)}}, {{A, B, C, X(25), X(3839)}}, {{A, B, C, X(30), X(7378)}}, {{A, B, C, X(66), X(52188)}}, {{A, B, C, X(193), X(7837)}}, {{A, B, C, X(251), X(3531)}}, {{A, B, C, X(253), X(43726)}}, {{A, B, C, X(376), X(7409)}}, {{A, B, C, X(381), X(6995)}}, {{A, B, C, X(393), X(43458)}}, {{A, B, C, X(427), X(3543)}}, {{A, B, C, X(428), X(3091)}}, {{A, B, C, X(1297), X(52518)}}, {{A, B, C, X(1383), X(14487)}}, {{A, B, C, X(1494), X(45833)}}, {{A, B, C, X(1799), X(43699)}}, {{A, B, C, X(3087), X(42854)}}, {{A, B, C, X(3108), X(3426)}}, {{A, B, C, X(3527), X(34572)}}, {{A, B, C, X(3545), X(7408)}}, {{A, B, C, X(3830), X(52284)}}, {{A, B, C, X(3832), X(7714)}}, {{A, B, C, X(3845), X(4232)}}, {{A, B, C, X(5481), X(22334)}}, {{A, B, C, X(8801), X(13481)}}, {{A, B, C, X(8889), X(50687)}}, {{A, B, C, X(9300), X(15589)}}, {{A, B, C, X(10002), X(53023)}}, {{A, B, C, X(10304), X(52285)}}, {{A, B, C, X(11058), X(22336)}}, {{A, B, C, X(14483), X(39955)}}, {{A, B, C, X(14490), X(39951)}}, {{A, B, C, X(14583), X(52485)}}, {{A, B, C, X(15321), X(48911)}}, {{A, B, C, X(16251), X(18018)}}, {{A, B, C, X(18361), X(38005)}}, {{A, B, C, X(18575), X(46204)}}, {{A, B, C, X(30537), X(34285)}}, {{A, B, C, X(35512), X(39978)}}, {{A, B, C, X(36889), X(52223)}}, {{A, B, C, X(37665), X(37671)}}, {{A, B, C, X(40174), X(52452)}}, {{A, B, C, X(41099), X(52301)}}
X(54520) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 53098}
X(54521) lies on these lines: {20, 53102}, {30, 18843}, {83, 10304}, {549, 18841}, {598, 15640}, {3091, 43676}, {3534, 18842}, {3543, 53109}, {3839, 53105}, {5055, 18840}, {5066, 5485}, {5306, 43537}, {5395, 15683}, {7000, 43570}, {7374, 43571}, {7486, 10159}, {10303, 43527}, {14458, 37665}, {14853, 53104}, {15684, 18844}
X(54521) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(253), X(18361)}}, {{A, B, C, X(427), X(10304)}}, {{A, B, C, X(428), X(7486)}}, {{A, B, C, X(549), X(7378)}}, {{A, B, C, X(1494), X(52224)}}, {{A, B, C, X(3534), X(52284)}}, {{A, B, C, X(3613), X(52187)}}, {{A, B, C, X(3839), X(37453)}}, {{A, B, C, X(4232), X(5066)}}, {{A, B, C, X(5055), X(6995)}}, {{A, B, C, X(5064), X(10303)}}, {{A, B, C, X(5094), X(15640)}}, {{A, B, C, X(5481), X(43691)}}, {{A, B, C, X(7409), X(15709)}}, {{A, B, C, X(7714), X(15022)}}, {{A, B, C, X(7788), X(37665)}}, {{A, B, C, X(8801), X(11058)}}, {{A, B, C, X(8889), X(15683)}}, {{A, B, C, X(22336), X(46204)}}, {{A, B, C, X(34288), X(45090)}}, {{A, B, C, X(34572), X(40801)}}, {{A, B, C, X(36889), X(45833)}}, {{A, B, C, X(39951), X(43713)}}
X(54522) lies on these lines: {30, 18844}, {83, 15692}, {547, 18840}, {3424, 9300}, {3543, 53107}, {3839, 53106}, {3860, 32532}, {5054, 18841}, {5485, 19709}, {8703, 18842}, {10159, 46936}, {14853, 53108}, {15681, 18843}
X(54522) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(253), X(45090)}}, {{A, B, C, X(427), X(15692)}}, {{A, B, C, X(428), X(46936)}}, {{A, B, C, X(547), X(6995)}}, {{A, B, C, X(3108), X(44731)}}, {{A, B, C, X(3543), X(52298)}}, {{A, B, C, X(3613), X(45833)}}, {{A, B, C, X(3839), X(52297)}}, {{A, B, C, X(4232), X(19709)}}, {{A, B, C, X(5054), X(7378)}}, {{A, B, C, X(8703), X(52284)}}, {{A, B, C, X(8801), X(30537)}}, {{A, B, C, X(9300), X(37668)}}, {{A, B, C, X(36889), X(52224)}}, {{A, B, C, X(45108), X(52187)}}, {{A, B, C, X(45819), X(46212)}}
X(54523) lies on these lines: {2, 44456}, {4, 9606}, {5, 43681}, {30, 18845}, {76, 5071}, {83, 3524}, {376, 5395}, {381, 38259}, {383, 43556}, {598, 11001}, {671, 41106}, {1080, 43557}, {2996, 3545}, {3525, 43527}, {3528, 53102}, {3544, 43676}, {5067, 10159}, {5306, 7612}, {6997, 13582}, {7736, 14458}, {9753, 53108}, {10155, 14853}, {11172, 41624}, {13860, 47586}, {14229, 49263}, {14244, 49260}, {15682, 53101}, {15702, 18841}, {16080, 52299}, {18842, 19708}, {38282, 43530}, {41099, 41895}
X(54523) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(22332)}}, {{A, B, C, X(6), X(44456)}}, {{A, B, C, X(25), X(5071)}}, {{A, B, C, X(30), X(52299)}}, {{A, B, C, X(69), X(11058)}}, {{A, B, C, X(264), X(52188)}}, {{A, B, C, X(376), X(8889)}}, {{A, B, C, X(381), X(38282)}}, {{A, B, C, X(427), X(3524)}}, {{A, B, C, X(428), X(5067)}}, {{A, B, C, X(468), X(41106)}}, {{A, B, C, X(1007), X(5306)}}, {{A, B, C, X(1173), X(14489)}}, {{A, B, C, X(1494), X(46952)}}, {{A, B, C, X(3090), X(7714)}}, {{A, B, C, X(3431), X(39951)}}, {{A, B, C, X(3525), X(5064)}}, {{A, B, C, X(3527), X(36616)}}, {{A, B, C, X(3545), X(6353)}}, {{A, B, C, X(3613), X(17040)}}, {{A, B, C, X(5094), X(11001)}}, {{A, B, C, X(6997), X(37943)}}, {{A, B, C, X(7249), X(18490)}}, {{A, B, C, X(7378), X(15702)}}, {{A, B, C, X(7736), X(7788)}}, {{A, B, C, X(8770), X(14483)}}, {{A, B, C, X(8797), X(34288)}}, {{A, B, C, X(9770), X(41624)}}, {{A, B, C, X(13472), X(40801)}}, {{A, B, C, X(13575), X(45972)}}, {{A, B, C, X(14356), X(36892)}}, {{A, B, C, X(19708), X(52284)}}, {{A, B, C, X(20421), X(39389)}}, {{A, B, C, X(30775), X(35481)}}, {{A, B, C, X(34208), X(52187)}}, {{A, B, C, X(37119), X(44442)}}, {{A, B, C, X(41099), X(52290)}}, {{A, B, C, X(43662), X(52518)}}, {{A, B, C, X(43726), X(52154)}}, {{A, B, C, X(44658), X(48911)}}, {{A, B, C, X(45838), X(52717)}}
X(54524) lies on these lines: {17, 47865}, {30, 21845}, {530, 43548}, {5459, 43545}, {10188, 35751}, {17503, 49947}, {35749, 43447}, {35752, 43544}, {36768, 43443}, {43554, 51482}
X(54524) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(2981), X(32901)}}
X(54525) lies on these lines: {18, 47866}, {30, 21846}, {531, 43549}, {5460, 43544}, {10187, 36329}, {17503, 49948}, {36327, 43446}, {36330, 43545}, {43555, 51483}
X(54525) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6151), X(32901)}}
X(54526) lies on these lines: {2, 45924}, {4, 52956}, {10, 7359}, {29, 16080}, {30, 226}, {381, 1751}, {519, 43683}, {522, 2394}, {542, 11608}, {1446, 15936}, {1784, 40149}, {2785, 14223}, {4049, 6003}, {4080, 34772}, {5125, 43530}, {5466, 28292}, {13576, 18406}, {17758, 37428}, {24624, 52269}, {28580, 43677}
X(54526) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(2341)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(4304)}}, {{A, B, C, X(29), X(30)}}, {{A, B, C, X(74), X(53114)}}, {{A, B, C, X(78), X(17098)}}, {{A, B, C, X(80), X(5719)}}, {{A, B, C, X(84), X(39704)}}, {{A, B, C, X(225), X(1989)}}, {{A, B, C, X(265), X(307)}}, {{A, B, C, X(273), X(2166)}}, {{A, B, C, X(282), X(44693)}}, {{A, B, C, X(376), X(7518)}}, {{A, B, C, X(381), X(5125)}}, {{A, B, C, X(502), X(5627)}}, {{A, B, C, X(519), X(1389)}}, {{A, B, C, X(524), X(28292)}}, {{A, B, C, X(542), X(2785)}}, {{A, B, C, X(860), X(52269)}}, {{A, B, C, X(996), X(39695)}}, {{A, B, C, X(1065), X(15909)}}, {{A, B, C, X(1257), X(16615)}}, {{A, B, C, X(1494), X(39130)}}, {{A, B, C, X(1861), X(18406)}}, {{A, B, C, X(2287), X(15936)}}, {{A, B, C, X(3345), X(39980)}}, {{A, B, C, X(3543), X(7498)}}, {{A, B, C, X(3584), X(6734)}}, {{A, B, C, X(4674), X(44835)}}, {{A, B, C, X(5556), X(40836)}}, {{A, B, C, X(6002), X(28580)}}, {{A, B, C, X(7513), X(11113)}}, {{A, B, C, X(8747), X(52374)}}, {{A, B, C, X(10308), X(43972)}}, {{A, B, C, X(14004), X(37428)}}, {{A, B, C, X(17577), X(37381)}}, {{A, B, C, X(17677), X(37362)}}, {{A, B, C, X(28840), X(28849)}}, {{A, B, C, X(31155), X(44225)}}, {{A, B, C, X(36722), X(37389)}}, {{A, B, C, X(43917), X(45095)}}
X(54526) = trilinear pole of line {14400, 523}
X(54527) lies on these lines: {2, 3233}, {30, 2394}, {524, 43673}, {542, 14223}, {543, 52459}, {671, 10733}, {1503, 5466}, {2794, 9180}, {3081, 12079}, {4240, 9140}, {9141, 34767}, {11645, 43665}, {34761, 53161}
X(54527) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(476)}}, {{A, B, C, X(265), X(9140)}}, {{A, B, C, X(511), X(11645)}}, {{A, B, C, X(524), X(1503)}}, {{A, B, C, X(541), X(17702)}}, {{A, B, C, X(542), X(20404)}}, {{A, B, C, X(543), X(2794)}}, {{A, B, C, X(1494), X(9214)}}, {{A, B, C, X(1989), X(18808)}}, {{A, B, C, X(2697), X(5641)}}, {{A, B, C, X(10733), X(11744)}}, {{A, B, C, X(11050), X(11251)}}, {{A, B, C, X(15454), X(18317)}}, {{A, B, C, X(19924), X(29012)}}, {{A, B, C, X(34765), X(53161)}}, {{A, B, C, X(42308), X(52485)}}
X(54527) = trilinear pole of line {3163, 23967}
X(54527) = X(i)-isoconjugate-of-X(j) for these {i, j}: {35200, 52464}
X(54527) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 5466}
X(54527) = X(i)-Dao conjugate of X(j) for these {i, j}: {133, 52464}, {42426, 52469}
X(54527) = barycentric quotient X(i)/X(j) for these (i, j): {1990, 52464}, {6103, 52469}
X(54528) lies on these lines: {2, 6739}, {10, 36910}, {30, 24624}, {80, 226}, {321, 52409}, {759, 21161}, {860, 16080}, {1446, 18815}, {1834, 1989}, {2166, 43682}, {2394, 6370}, {4080, 36590}, {5136, 43530}, {5397, 5721}, {10706, 19629}
X(54528) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(5425)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(860)}}, {{A, B, C, X(37), X(44835)}}, {{A, B, C, X(74), X(4674)}}, {{A, B, C, X(80), X(2166)}}, {{A, B, C, X(104), X(903)}}, {{A, B, C, X(381), X(5136)}}, {{A, B, C, X(519), X(41558)}}, {{A, B, C, X(655), X(32041)}}, {{A, B, C, X(897), X(2687)}}, {{A, B, C, X(1000), X(14563)}}, {{A, B, C, X(1138), X(5620)}}, {{A, B, C, X(1243), X(39974)}}, {{A, B, C, X(1389), X(40430)}}, {{A, B, C, X(1494), X(38955)}}, {{A, B, C, X(1737), X(39991)}}, {{A, B, C, X(1821), X(35161)}}, {{A, B, C, X(1989), X(45926)}}, {{A, B, C, X(3065), X(4511)}}, {{A, B, C, X(3427), X(36588)}}, {{A, B, C, X(3577), X(3679)}}, {{A, B, C, X(4231), X(17677)}}, {{A, B, C, X(6344), X(15065)}}, {{A, B, C, X(11105), X(28452)}}, {{A, B, C, X(11113), X(37381)}}, {{A, B, C, X(11604), X(33593)}}, {{A, B, C, X(16139), X(41697)}}, {{A, B, C, X(18391), X(36916)}}, {{A, B, C, X(24297), X(36596)}}, {{A, B, C, X(24857), X(34485)}}, {{A, B, C, X(37718), X(51310)}}, {{A, B, C, X(44693), X(52663)}}
X(54528) = trilinear pole of line {17718, 523}
X(54528) = X(i)-isoconjugate-of-X(j) for these {i, j}: {36, 24929}
X(54528) = X(i)-Dao conjugate of X(j) for these {i, j}: {15898, 24929}
X(54528) = X(i)-cross conjugate of X(j) for these {i, j}: {18391, 40437}
X(54528) = barycentric quotient X(i)/X(j) for these (i, j): {2161, 24929}
X(54529) lies on these lines: {30, 30505}, {275, 46511}, {6504, 32983}, {13579, 33016}, {13582, 16044}, {16080, 37125}
X(54529) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(46511)}}, {{A, B, C, X(30), X(37125)}}, {{A, B, C, X(74), X(39968)}}, {{A, B, C, X(308), X(14483)}}, {{A, B, C, X(376), X(37337)}}, {{A, B, C, X(695), X(30537)}}, {{A, B, C, X(1031), X(33565)}}, {{A, B, C, X(1141), X(52395)}}, {{A, B, C, X(1173), X(3228)}}, {{A, B, C, X(2998), X(14491)}}, {{A, B, C, X(3527), X(9462)}}, {{A, B, C, X(3531), X(34816)}}, {{A, B, C, X(3541), X(32986)}}, {{A, B, C, X(3542), X(32983)}}, {{A, B, C, X(7505), X(33016)}}, {{A, B, C, X(15412), X(30535)}}, {{A, B, C, X(16044), X(37943)}}, {{A, B, C, X(33017), X(37119)}}
X(54530) lies on these lines: {30, 30588}, {2394, 4777}, {5466, 28319}
X(54530) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4777)}}, {{A, B, C, X(524), X(28319)}}, {{A, B, C, X(16615), X(46187)}}, {{A, B, C, X(28840), X(28889)}}
X(54531) lies on these lines: {4, 17809}, {25, 53099}, {30, 31363}, {262, 7714}, {376, 13599}, {427, 43537}, {428, 14484}, {459, 3087}, {472, 22235}, {473, 22237}, {1249, 8796}, {1585, 3591}, {1586, 3590}, {2052, 40065}, {2996, 52281}, {3424, 5064}, {3535, 10194}, {3536, 10195}, {3545, 40448}, {5094, 53859}, {5395, 52282}, {5485, 37672}, {6353, 7608}, {7378, 47586}, {7607, 8889}, {10159, 52288}, {38282, 53098}, {43527, 52283}
X(54531) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(17809)}}, {{A, B, C, X(69), X(39286)}}, {{A, B, C, X(70), X(4994)}}, {{A, B, C, X(97), X(13472)}}, {{A, B, C, X(343), X(36809)}}, {{A, B, C, X(394), X(1173)}}, {{A, B, C, X(428), X(52288)}}, {{A, B, C, X(458), X(7714)}}, {{A, B, C, X(1073), X(52518)}}, {{A, B, C, X(1249), X(3087)}}, {{A, B, C, X(1992), X(37672)}}, {{A, B, C, X(2165), X(6748)}}, {{A, B, C, X(3527), X(36609)}}, {{A, B, C, X(3545), X(52280)}}, {{A, B, C, X(5064), X(52283)}}, {{A, B, C, X(5702), X(6749)}}, {{A, B, C, X(6353), X(52281)}}, {{A, B, C, X(8889), X(52282)}}, {{A, B, C, X(13452), X(31626)}}, {{A, B, C, X(15809), X(33190)}}, {{A, B, C, X(36916), X(53817)}}, {{A, B, C, X(39948), X(40396)}}, {{A, B, C, X(39980), X(40397)}}, {{A, B, C, X(42287), X(43726)}}
X(54531) = polar conjugate of X(5056)
X(54531) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 5056}
X(54532) lies on these lines: {30, 32022}, {3839, 6625}, {4196, 16080}, {4207, 43530}, {10159, 36670}
X(54532) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4196)}}, {{A, B, C, X(42), X(3531)}}, {{A, B, C, X(74), X(39965)}}, {{A, B, C, X(381), X(4207)}}, {{A, B, C, X(428), X(36670)}}, {{A, B, C, X(1002), X(10308)}}, {{A, B, C, X(1246), X(52188)}}, {{A, B, C, X(2350), X(3426)}}, {{A, B, C, X(3543), X(4212)}}, {{A, B, C, X(3839), X(4213)}}, {{A, B, C, X(14483), X(39961)}}, {{A, B, C, X(14490), X(39966)}}, {{A, B, C, X(39980), X(45137)}}
X(54533) lies on these lines: {2, 51420}, {4, 52955}, {10, 2173}, {28, 16080}, {30, 321}, {226, 49744}, {513, 2394}, {535, 43683}, {542, 11611}, {752, 43677}, {2787, 14223}, {5142, 43530}, {5466, 28475}, {10159, 37431}
X(54533) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(28), X(30)}}, {{A, B, C, X(74), X(1169)}}, {{A, B, C, X(79), X(49744)}}, {{A, B, C, X(265), X(20336)}}, {{A, B, C, X(376), X(4198)}}, {{A, B, C, X(381), X(5142)}}, {{A, B, C, X(428), X(37431)}}, {{A, B, C, X(524), X(28475)}}, {{A, B, C, X(542), X(2787)}}, {{A, B, C, X(752), X(6002)}}, {{A, B, C, X(1494), X(43712)}}, {{A, B, C, X(1791), X(34800)}}, {{A, B, C, X(1989), X(41013)}}, {{A, B, C, X(3426), X(46010)}}, {{A, B, C, X(3543), X(7521)}}, {{A, B, C, X(7576), X(37231)}}, {{A, B, C, X(15763), X(31154)}}, {{A, B, C, X(20029), X(34288)}}, {{A, B, C, X(28840), X(28845)}}
X(54533) = trilinear pole of line {14399, 523}
X(54534) lies on these lines: {2, 42197}, {13, 32787}, {15, 42639}, {16, 43503}, {17, 18587}, {18, 18585}, {30, 3366}, {381, 3392}, {395, 3845}, {485, 36455}, {486, 16268}, {590, 36967}, {1327, 36970}, {1328, 36450}, {1991, 42036}, {2041, 10195}, {2044, 5351}, {3317, 36465}, {3367, 51854}, {3389, 36436}, {3391, 35822}, {3830, 6221}, {5066, 53439}, {6307, 40706}, {6561, 43475}, {6565, 49948}, {10188, 14814}, {11121, 33441}, {12101, 53438}, {12817, 42284}, {14226, 37641}, {14241, 36446}, {15687, 53459}, {16242, 53444}, {16808, 36466}, {16963, 42235}, {16964, 52217}, {22237, 42248}, {32788, 42507}, {35731, 35786}, {36445, 42256}, {36448, 36968}, {42134, 43567}, {42218, 43542}, {42228, 42813}, {42238, 42587}, {42280, 52214}
X(54534) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(15), X(588)}}, {{A, B, C, X(61), X(5417)}}, {{A, B, C, X(472), X(18585)}}, {{A, B, C, X(473), X(18587)}}, {{A, B, C, X(1585), X(36455)}}, {{A, B, C, X(1659), X(14358)}}, {{A, B, C, X(6221), X(51728)}}
X(54535) lies on these lines: {2, 42195}, {5, 50245}, {6, 50246}, {13, 32788}, {15, 42640}, {16, 43504}, {17, 18586}, {18, 15765}, {30, 3367}, {381, 3391}, {395, 3845}, {485, 16268}, {486, 36437}, {591, 42036}, {615, 36967}, {1327, 36467}, {1328, 36970}, {2042, 10194}, {2043, 5351}, {3316, 36446}, {3366, 51852}, {3390, 36454}, {3392, 35823}, {3830, 6398}, {5066, 53438}, {6303, 40706}, {6560, 43475}, {6564, 49948}, {10188, 14813}, {11121, 33440}, {12101, 53439}, {12817, 42283}, {14226, 36465}, {14241, 37641}, {15687, 53460}, {16242, 53445}, {16808, 36448}, {16963, 42237}, {16964, 52216}, {22237, 42246}, {32787, 42507}, {35731, 36470}, {36463, 42254}, {36466, 36968}, {42134, 43566}, {42220, 43542}, {42227, 42813}, {42236, 42587}, {42281, 52215}
X(54535) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(51728)}}, {{A, B, C, X(15), X(589)}}, {{A, B, C, X(61), X(5419)}}, {{A, B, C, X(472), X(15765)}}, {{A, B, C, X(473), X(18586)}}, {{A, B, C, X(1586), X(36437)}}, {{A, B, C, X(13390), X(14358)}}
X(54536) lies on the Kiepert hyperbola and these lines: {30, 3374}, {381, 3387}, {3373, 35823}, {3830, 12823}, {3845, 6565}, {6451, 43623}, {10194, 14782}, {10195, 14784}
X(54536) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3830, 42728, 12823}, {6565, 32788, 12822}
X(54537) lies on the Kiepert hyperbola and these lines: {30, 3387}, {381, 3374}, {3388, 35822}, {3830, 12822}, {3845, 6564}, {6452, 43622}, {10194, 14784}, {10195, 14782}
X(54537) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3830, 42727, 12822}, {6564, 32787, 12823}
X(54538) lies on these lines: {2, 42196}, {14, 32788}, {15, 43504}, {16, 42640}, {17, 18585}, {18, 18587}, {30, 3392}, {381, 3366}, {396, 3845}, {485, 16267}, {486, 36455}, {591, 42035}, {615, 36968}, {1327, 36449}, {1328, 36969}, {2041, 10194}, {2044, 5352}, {3316, 36464}, {3365, 36436}, {3367, 35823}, {3391, 51853}, {3590, 51727}, {3592, 50245}, {3830, 6398}, {5066, 53450}, {6302, 40707}, {6560, 43476}, {6564, 49947}, {10187, 14814}, {11122, 33442}, {12101, 53451}, {12816, 42283}, {14226, 36447}, {14241, 37640}, {15687, 53471}, {16241, 53433}, {16809, 36466}, {16962, 42238}, {16965, 52215}, {22235, 42247}, {32787, 42506}, {33607, 51728}, {35731, 36445}, {36448, 36967}, {42133, 43566}, {42219, 43543}, {42229, 42814}, {42235, 42586}, {42280, 52216}
X(54538) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(16), X(589)}}, {{A, B, C, X(62), X(5419)}}, {{A, B, C, X(472), X(18587)}}, {{A, B, C, X(473), X(18585)}}, {{A, B, C, X(1586), X(36455)}}, {{A, B, C, X(3592), X(51727)}}, {{A, B, C, X(13390), X(14359)}}, {{A, B, C, X(34754), X(51728)}}
X(54538) = X(i)-cross conjugate of X(j) for these {i, j}: {41107, 50246}
X(54538) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16808, 41101, 50246}
X(54539) lies on these lines: {2, 8627}, {30, 3399}, {76, 754}, {83, 7861}, {98, 48889}, {262, 29012}, {381, 3406}, {384, 10159}, {428, 37892}, {671, 12156}, {732, 43688}, {1916, 12830}, {2896, 14033}, {2996, 20088}, {3849, 10302}, {5025, 43527}, {5306, 43535}, {5503, 8592}, {5999, 7608}, {6292, 14036}, {7607, 13862}, {8290, 8781}, {9751, 53108}, {11057, 14030}, {11606, 12829}, {11645, 14492}, {12206, 18501}, {14042, 43676}, {14062, 53102}, {14068, 43681}, {16041, 18841}, {17766, 34475}, {40163, 42037}, {43534, 50289}
X(54539) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(11361)}}, {{A, B, C, X(251), X(512)}}, {{A, B, C, X(384), X(428)}}, {{A, B, C, X(385), X(41624)}}, {{A, B, C, X(427), X(14041)}}, {{A, B, C, X(699), X(27375)}}, {{A, B, C, X(732), X(25423)}}, {{A, B, C, X(733), X(8601)}}, {{A, B, C, X(1031), X(32085)}}, {{A, B, C, X(2896), X(3866)}}, {{A, B, C, X(3108), X(14498)}}, {{A, B, C, X(3849), X(12073)}}, {{A, B, C, X(4590), X(22336)}}, {{A, B, C, X(4785), X(17766)}}, {{A, B, C, X(5025), X(5064)}}, {{A, B, C, X(5306), X(7840)}}, {{A, B, C, X(5999), X(52281)}}, {{A, B, C, X(6995), X(14033)}}, {{A, B, C, X(7378), X(16041)}}, {{A, B, C, X(7408), X(14039)}}, {{A, B, C, X(7409), X(33285)}}, {{A, B, C, X(7714), X(14035)}}, {{A, B, C, X(7826), X(34572)}}, {{A, B, C, X(7837), X(14614)}}, {{A, B, C, X(7893), X(46287)}}, {{A, B, C, X(8290), X(12829)}}, {{A, B, C, X(9227), X(45819)}}, {{A, B, C, X(9229), X(15321)}}, {{A, B, C, X(12156), X(52898)}}, {{A, B, C, X(13862), X(52282)}}, {{A, B, C, X(14046), X(52285)}}, {{A, B, C, X(14537), X(51541)}}, {{A, B, C, X(23878), X(29012)}}, {{A, B, C, X(34238), X(46320)}}, {{A, B, C, X(39955), X(44557)}}, {{A, B, C, X(44132), X(48889)}}
X(54539) = reflection of X(i) in X(j) for these {i,j}: {12156, 14537}
X(54539) = trilinear pole of line {14428, 523}
X(54540) lies on these lines: {30, 3406}, {76, 7818}, {83, 7748}, {98, 48901}, {381, 3399}, {384, 43527}, {598, 11648}, {671, 7837}, {1916, 9766}, {2996, 7900}, {5025, 10159}, {5064, 37892}, {5999, 7607}, {7608, 13862}, {7914, 14046}, {7938, 16041}, {9302, 41135}, {9765, 10335}, {14033, 18841}, {14042, 53102}, {14062, 43676}, {14614, 43535}, {22728, 38732}, {32996, 43681}
X(54540) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(43098)}}, {{A, B, C, X(25), X(14041)}}, {{A, B, C, X(111), X(18546)}}, {{A, B, C, X(251), X(7818)}}, {{A, B, C, X(384), X(5064)}}, {{A, B, C, X(385), X(9766)}}, {{A, B, C, X(427), X(11361)}}, {{A, B, C, X(428), X(5025)}}, {{A, B, C, X(524), X(7837)}}, {{A, B, C, X(3108), X(30495)}}, {{A, B, C, X(5999), X(52282)}}, {{A, B, C, X(6995), X(16041)}}, {{A, B, C, X(7378), X(14033)}}, {{A, B, C, X(7408), X(33285)}}, {{A, B, C, X(7409), X(14039)}}, {{A, B, C, X(7714), X(14063)}}, {{A, B, C, X(7777), X(13468)}}, {{A, B, C, X(7840), X(9487)}}, {{A, B, C, X(7864), X(9484)}}, {{A, B, C, X(7896), X(34572)}}, {{A, B, C, X(7938), X(42037)}}, {{A, B, C, X(9229), X(43726)}}, {{A, B, C, X(11058), X(18823)}}, {{A, B, C, X(11648), X(42008)}}, {{A, B, C, X(13862), X(52281)}}, {{A, B, C, X(14036), X(52285)}}, {{A, B, C, X(15014), X(31133)}}, {{A, B, C, X(15351), X(18018)}}, {{A, B, C, X(17505), X(51454)}}, {{A, B, C, X(18023), X(45819)}}, {{A, B, C, X(44132), X(48901)}}, {{A, B, C, X(44176), X(53197)}}
X(54540) = X(i)-cross conjugate of X(j) for these {i, j}: {41624, 2}
X(54541) lies on these lines: {30, 34087}, {888, 2394}, {14537, 45092}, {16080, 46522}
X(54541) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(888)}}, {{A, B, C, X(1976), X(53221)}}, {{A, B, C, X(30496), X(48911)}}
X(54542) lies on these lines: {2, 42538}, {20, 43564}, {30, 34089}, {381, 34091}, {485, 43257}, {1131, 42572}, {1132, 6432}, {2043, 43445}, {2044, 43444}, {3091, 43565}, {3146, 10195}, {3316, 3543}, {3317, 3839}, {3590, 17578}, {3591, 50689}, {3830, 43536}, {3832, 10194}, {7000, 53098}, {8972, 41959}, {14226, 42216}, {15683, 43558}, {19054, 43560}, {23249, 43563}, {42275, 43568}, {42284, 42539}, {42418, 43507}, {43378, 50692}, {43503, 43569}, {43888, 52667}
X(54542) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(371), X(46851)}}, {{A, B, C, X(588), X(14490)}}, {{A, B, C, X(1152), X(6432)}}, {{A, B, C, X(1585), X(50687)}}, {{A, B, C, X(3311), X(6449)}}, {{A, B, C, X(5417), X(46848)}}, {{A, B, C, X(6200), X(13603)}}
X(54543) lies on these lines: {2, 42537}, {20, 43565}, {30, 34091}, {381, 34089}, {486, 43256}, {1131, 6431}, {1132, 42573}, {2043, 43444}, {2044, 43445}, {3091, 43564}, {3146, 10194}, {3316, 3839}, {3317, 3543}, {3590, 31454}, {3591, 17578}, {3832, 10195}, {3845, 43536}, {7374, 53098}, {13941, 41960}, {14241, 42215}, {15683, 43559}, {19053, 43561}, {23259, 43562}, {42276, 43569}, {42283, 42540}, {42417, 43508}, {43379, 50692}, {43504, 43568}, {43887, 52666}
X(54543) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(372), X(46851)}}, {{A, B, C, X(589), X(14490)}}, {{A, B, C, X(1151), X(6431)}}, {{A, B, C, X(1586), X(50687)}}, {{A, B, C, X(3312), X(6450)}}, {{A, B, C, X(5419), X(46848)}}, {{A, B, C, X(6396), X(13603)}}
X(54544) lies on these lines: {30, 34258}, {226, 48825}, {381, 14534}, {429, 43530}, {2394, 8672}, {4185, 16080}, {10159, 37415}
X(54544) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4185)}}, {{A, B, C, X(79), X(48825)}}, {{A, B, C, X(381), X(429)}}, {{A, B, C, X(428), X(37415)}}, {{A, B, C, X(961), X(10308)}}, {{A, B, C, X(1494), X(20029)}}, {{A, B, C, X(1880), X(16263)}}, {{A, B, C, X(51870), X(52154)}}
X(54545) lies on these lines: {10, 11645}, {30, 34475}, {2394, 4785}, {3849, 4052}, {5466, 28470}, {9830, 34899}, {16080, 31912}, {28562, 43677}
X(54545) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4785)}}, {{A, B, C, X(514), X(11645)}}, {{A, B, C, X(524), X(28470)}}, {{A, B, C, X(2789), X(9830)}}, {{A, B, C, X(3667), X(3849)}}, {{A, B, C, X(6002), X(28562)}}
X(54546) lies on these lines: {10, 2794}, {30, 34899}, {115, 3429}, {514, 52459}, {542, 4052}, {1503, 11599}, {2394, 2789}, {2784, 43677}, {2786, 43673}, {2792, 43683}, {3667, 14223}, {9180, 28296}, {28470, 46040}, {38309, 39838}
X(54546) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2789)}}, {{A, B, C, X(511), X(727)}}, {{A, B, C, X(514), X(2794)}}, {{A, B, C, X(542), X(3667)}}, {{A, B, C, X(543), X(28296)}}, {{A, B, C, X(1503), X(2786)}}, {{A, B, C, X(2782), X(28470)}}, {{A, B, C, X(2784), X(6002)}}, {{A, B, C, X(2792), X(6003)}}, {{A, B, C, X(9083), X(9141)}}, {{A, B, C, X(23698), X(28529)}}
X(54546) = reflection of X(i) in X(j) for these {i,j}: {3429, 115}
X(54546) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 11599}
X(54547) lies on these lines: {2, 1625}, {4, 7668}, {30, 35098}, {76, 14570}, {96, 32734}, {98, 14157}, {112, 275}, {217, 53576}, {262, 5890}, {2052, 33885}, {7608, 37121}, {13582, 40853}, {13599, 15058}, {16080, 44893}, {32445, 43679}
X(54547) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(50678)}}, {{A, B, C, X(30), X(44893)}}, {{A, B, C, X(74), X(15412)}}, {{A, B, C, X(112), X(1625)}}, {{A, B, C, X(237), X(46511)}}, {{A, B, C, X(276), X(16835)}}, {{A, B, C, X(287), X(45138)}}, {{A, B, C, X(393), X(47383)}}, {{A, B, C, X(1141), X(23582)}}, {{A, B, C, X(1179), X(39454)}}, {{A, B, C, X(1972), X(6344)}}, {{A, B, C, X(2395), X(3455)}}, {{A, B, C, X(3431), X(40815)}}, {{A, B, C, X(4580), X(18876)}}, {{A, B, C, X(7714), X(37186)}}, {{A, B, C, X(14483), X(42300)}}, {{A, B, C, X(14618), X(43917)}}, {{A, B, C, X(14908), X(33885)}}, {{A, B, C, X(17703), X(36952)}}, {{A, B, C, X(27366), X(37125)}}, {{A, B, C, X(34897), X(53246)}}, {{A, B, C, X(37121), X(52281)}}, {{A, B, C, X(37943), X(40853)}}
X(54547) = trilinear pole of line {51, 34093}
X(54547) = X(i)-cross conjugate of X(j) for these {i, j}: {3331, 4}
X(54548) lies on these lines: {30, 35353}, {517, 5466}, {536, 2394}, {2783, 9180}, {14223, 35103}
X(54548) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(536)}}, {{A, B, C, X(517), X(524)}}, {{A, B, C, X(542), X(35103)}}, {{A, B, C, X(543), X(2783)}}, {{A, B, C, X(712), X(11645)}}, {{A, B, C, X(2687), X(35155)}}
X(54549) lies on these lines: {10, 7262}, {30, 3597}, {226, 17394}, {321, 17363}, {6539, 17350}, {7607, 37360}, {7608, 19544}, {10159, 41236}
X(54549) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(2985)}}, {{A, B, C, X(314), X(17394)}}, {{A, B, C, X(428), X(41236)}}, {{A, B, C, X(553), X(17350)}}, {{A, B, C, X(1509), X(2994)}}, {{A, B, C, X(7262), X(9277)}}, {{A, B, C, X(11114), X(44734)}}, {{A, B, C, X(17346), X(42028)}}, {{A, B, C, X(17392), X(19723)}}, {{A, B, C, X(19544), X(52281)}}, {{A, B, C, X(19827), X(42029)}}, {{A, B, C, X(37360), X(52282)}}, {{A, B, C, X(39696), X(43733)}}
X(54549) = trilinear pole of line {47820, 523}
X(54550) lies on these lines: {30, 37874}, {235, 43530}, {381, 801}, {1593, 16080}, {3839, 43670}, {6812, 10194}, {6814, 10195}, {6823, 43527}, {10159, 11479}
X(54550) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(1593)}}, {{A, B, C, X(235), X(381)}}, {{A, B, C, X(265), X(40032)}}, {{A, B, C, X(428), X(11479)}}, {{A, B, C, X(1105), X(34288)}}, {{A, B, C, X(1494), X(14457)}}, {{A, B, C, X(3531), X(16263)}}, {{A, B, C, X(3839), X(6622)}}, {{A, B, C, X(5064), X(6823)}}, {{A, B, C, X(9307), X(45088)}}, {{A, B, C, X(15740), X(52188)}}, {{A, B, C, X(16657), X(41372)}}, {{A, B, C, X(17703), X(52154)}}, {{A, B, C, X(18361), X(52441)}}, {{A, B, C, X(18848), X(52518)}}, {{A, B, C, X(22336), X(46255)}}, {{A, B, C, X(35512), X(45857)}}
X(54551) lies on these lines: {30, 37892}, {275, 14041}, {384, 16080}, {459, 14033}, {2052, 11361}, {3399, 34664}, {5025, 43530}, {14039, 38253}
X(54551) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11361)}}, {{A, B, C, X(5), X(14041)}}, {{A, B, C, X(20), X(14033)}}, {{A, B, C, X(30), X(384)}}, {{A, B, C, X(265), X(9229)}}, {{A, B, C, X(376), X(14035)}}, {{A, B, C, X(381), X(5025)}}, {{A, B, C, X(382), X(14036)}}, {{A, B, C, X(546), X(14046)}}, {{A, B, C, X(547), X(14044)}}, {{A, B, C, X(549), X(14042)}}, {{A, B, C, X(1502), X(18434)}}, {{A, B, C, X(1657), X(14030)}}, {{A, B, C, X(2998), X(16263)}}, {{A, B, C, X(3091), X(16041)}}, {{A, B, C, X(3146), X(14039)}}, {{A, B, C, X(3524), X(14068)}}, {{A, B, C, X(3534), X(14034)}}, {{A, B, C, X(3543), X(14001)}}, {{A, B, C, X(3545), X(14063)}}, {{A, B, C, X(3830), X(7892)}}, {{A, B, C, X(3832), X(33285)}}, {{A, B, C, X(3839), X(14064)}}, {{A, B, C, X(3845), X(7901)}}, {{A, B, C, X(3858), X(33288)}}, {{A, B, C, X(3860), X(33286)}}, {{A, B, C, X(5054), X(14066)}}, {{A, B, C, X(5055), X(14062)}}, {{A, B, C, X(5066), X(14045)}}, {{A, B, C, X(5071), X(32996)}}, {{A, B, C, X(5999), X(8370)}}, {{A, B, C, X(6145), X(43098)}}, {{A, B, C, X(7833), X(35930)}}, {{A, B, C, X(7841), X(13862)}}, {{A, B, C, X(7924), X(44230)}}, {{A, B, C, X(9516), X(46255)}}, {{A, B, C, X(11001), X(14031)}}, {{A, B, C, X(11744), X(40416)}}, {{A, B, C, X(14032), X(15681)}}, {{A, B, C, X(14037), X(15682)}}, {{A, B, C, X(14038), X(15684)}}, {{A, B, C, X(14043), X(15687)}}, {{A, B, C, X(14047), X(14893)}}, {{A, B, C, X(14065), X(14269)}}, {{A, B, C, X(14067), X(38335)}}, {{A, B, C, X(14069), X(50687)}}, {{A, B, C, X(14498), X(41891)}}, {{A, B, C, X(15014), X(38323)}}, {{A, B, C, X(15980), X(33013)}}, {{A, B, C, X(23046), X(33284)}}, {{A, B, C, X(33283), X(41099)}}, {{A, B, C, X(33289), X(38071)}}, {{A, B, C, X(33290), X(41106)}}
X(54552) lies on these lines: {30, 38253}, {459, 3543}, {2052, 50687}, {3146, 16080}, {3832, 43530}
X(54552) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(50687)}}, {{A, B, C, X(20), X(1494)}}, {{A, B, C, X(30), X(3146)}}, {{A, B, C, X(64), X(34570)}}, {{A, B, C, X(253), X(43699)}}, {{A, B, C, X(265), X(16251)}}, {{A, B, C, X(376), X(17578)}}, {{A, B, C, X(381), X(3832)}}, {{A, B, C, X(382), X(15683)}}, {{A, B, C, X(1217), X(17505)}}, {{A, B, C, X(1294), X(52443)}}, {{A, B, C, X(3091), X(3839)}}, {{A, B, C, X(3426), X(41894)}}, {{A, B, C, X(3522), X(3830)}}, {{A, B, C, X(3545), X(50689)}}, {{A, B, C, X(3613), X(38439)}}, {{A, B, C, X(3845), X(5068)}}, {{A, B, C, X(3854), X(41099)}}, {{A, B, C, X(5059), X(15682)}}, {{A, B, C, X(5076), X(15705)}}, {{A, B, C, X(5896), X(38263)}}, {{A, B, C, X(7391), X(34621)}}, {{A, B, C, X(7408), X(34664)}}, {{A, B, C, X(8801), X(38445)}}, {{A, B, C, X(10152), X(36413)}}, {{A, B, C, X(10304), X(50688)}}, {{A, B, C, X(11001), X(50690)}}, {{A, B, C, X(14269), X(15022)}}, {{A, B, C, X(14490), X(41890)}}, {{A, B, C, X(15077), X(31361)}}, {{A, B, C, X(15640), X(49135)}}, {{A, B, C, X(15687), X(15717)}}, {{A, B, C, X(18296), X(18848)}}, {{A, B, C, X(18550), X(46412)}}, {{A, B, C, X(18846), X(21400)}}, {{A, B, C, X(22466), X(52187)}}, {{A, B, C, X(31942), X(36616)}}
X(54553) lies on these lines: {10, 37589}, {30, 38309}, {321, 50118}, {543, 33996}, {597, 2051}, {2482, 34899}, {4049, 29126}, {5485, 37642}, {10302, 14829}, {11611, 50114}
X(54553) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(57), X(37589)}}, {{A, B, C, X(267), X(36603)}}, {{A, B, C, X(333), X(34914)}}, {{A, B, C, X(519), X(29126)}}, {{A, B, C, X(597), X(14829)}}, {{A, B, C, X(897), X(8056)}}, {{A, B, C, X(1992), X(37642)}}, {{A, B, C, X(2363), X(17107)}}, {{A, B, C, X(6703), X(31144)}}, {{A, B, C, X(17763), X(50114)}}, {{A, B, C, X(29574), X(50755)}}, {{A, B, C, X(29594), X(29631)}}, {{A, B, C, X(29600), X(33139)}}
X(54554) lies on these lines: {2, 476}, {4, 38395}, {30, 39295}, {76, 5641}, {94, 9140}, {98, 1989}, {262, 34370}, {265, 671}, {2394, 5627}, {2986, 51228}, {5466, 14582}, {5476, 7578}, {5485, 51835}, {6344, 46105}, {8781, 52094}, {9180, 14639}, {10412, 43665}, {10722, 41392}, {14223, 34368}, {14355, 14560}, {16080, 18384}, {16092, 51847}, {18316, 48453}, {24624, 36096}, {34365, 51345}, {35909, 43707}
X(54554) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(3258)}}, {{A, B, C, X(74), X(9140)}}, {{A, B, C, X(186), X(18867)}}, {{A, B, C, X(265), X(14582)}}, {{A, B, C, X(476), X(5627)}}, {{A, B, C, X(477), X(34312)}}, {{A, B, C, X(842), X(5641)}}, {{A, B, C, X(1138), X(14731)}}, {{A, B, C, X(1494), X(15328)}}, {{A, B, C, X(1550), X(51227)}}, {{A, B, C, X(1989), X(10412)}}, {{A, B, C, X(2501), X(47220)}}, {{A, B, C, X(6344), X(52449)}}, {{A, B, C, X(6530), X(37765)}}, {{A, B, C, X(8599), X(52192)}}, {{A, B, C, X(9161), X(35364)}}, {{A, B, C, X(9214), X(18808)}}, {{A, B, C, X(12065), X(22104)}}, {{A, B, C, X(14254), X(14583)}}, {{A, B, C, X(16092), X(16188)}}, {{A, B, C, X(34174), X(52094)}}, {{A, B, C, X(52492), X(53177)}}, {{A, B, C, X(52763), X(53158)}}
X(54554) = trilinear pole of line {1989, 14998}
X(54554) = X(i)-isoconjugate-of-X(j) for these {i, j}: {323, 2247}, {542, 6149}, {1101, 53132}, {2624, 14999}
X(54554) = X(i)-Dao conjugate of X(j) for these {i, j}: {523, 53132}, {14993, 542}, {15295, 5191}
X(54554) = X(i)-cross conjugate of X(j) for these {i, j}: {1550, 98}, {1640, 39290}, {43090, 6344}, {53132, 523}
X(54554) = barycentric product X(i)*X(j) for these (i, j): {290, 34370}, {842, 94}, {1577, 36096}, {1989, 5641}, {10412, 5649}, {14223, 476}, {14998, 35139}, {15475, 6035}, {23969, 850}, {35909, 46456}, {51228, 5627}
X(54554) = barycentric quotient X(i)/X(j) for these (i, j): {115, 53132}, {476, 14999}, {842, 323}, {1989, 542}, {5627, 51227}, {5641, 7799}, {5649, 10411}, {10412, 18312}, {11060, 5191}, {14223, 3268}, {14998, 526}, {15475, 1640}, {18384, 6103}, {23969, 110}, {34370, 511}, {35909, 8552}, {36096, 662}, {40355, 48451}, {46787, 51383}, {48453, 1511}, {50942, 45808}, {51228, 6148}
X(54555) lies on these lines: {4, 52949}, {21, 16080}, {30, 40149}, {275, 17577}, {459, 11111}, {521, 2394}, {2052, 11114}, {2476, 43530}, {2798, 14223}, {38253, 50739}, {40395, 52269}
X(54555) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11114)}}, {{A, B, C, X(5), X(17577)}}, {{A, B, C, X(20), X(11111)}}, {{A, B, C, X(21), X(30)}}, {{A, B, C, X(265), X(1441)}}, {{A, B, C, X(376), X(6872)}}, {{A, B, C, X(381), X(2476)}}, {{A, B, C, X(411), X(11113)}}, {{A, B, C, X(442), X(52269)}}, {{A, B, C, X(542), X(2798)}}, {{A, B, C, X(941), X(16263)}}, {{A, B, C, X(1005), X(37428)}}, {{A, B, C, X(1175), X(34570)}}, {{A, B, C, X(1494), X(18123)}}, {{A, B, C, X(3146), X(50739)}}, {{A, B, C, X(3543), X(6857)}}, {{A, B, C, X(3545), X(6871)}}, {{A, B, C, X(3560), X(17579)}}, {{A, B, C, X(3839), X(6856)}}, {{A, B, C, X(6175), X(6841)}}, {{A, B, C, X(6828), X(17532)}}, {{A, B, C, X(6842), X(37375)}}, {{A, B, C, X(6869), X(31156)}}, {{A, B, C, X(6870), X(50741)}}, {{A, B, C, X(6912), X(11112)}}, {{A, B, C, X(6932), X(17556)}}, {{A, B, C, X(7491), X(17549)}}, {{A, B, C, X(7548), X(17530)}}, {{A, B, C, X(8229), X(17677)}}, {{A, B, C, X(10883), X(17528)}}, {{A, B, C, X(13587), X(37290)}}, {{A, B, C, X(15670), X(52841)}}, {{A, B, C, X(15679), X(16617)}}, {{A, B, C, X(26737), X(34578)}}
X(54555) = trilinear pole of line {14395, 523}
X(54556) lies on these lines: {4, 51270}, {14, 51254}, {30, 40158}, {15441, 23097}, {16080, 40709}
X(54556) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(298)}}, {{A, B, C, X(265), X(300)}}, {{A, B, C, X(302), X(18550)}}, {{A, B, C, X(5627), X(53029)}}, {{A, B, C, X(8445), X(11131)}}, {{A, B, C, X(40709), X(51254)}}
X(54557) lies on these lines: {4, 51277}, {13, 51254}, {30, 40159}, {15442, 23097}, {16080, 40710}
X(54557) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(299)}}, {{A, B, C, X(265), X(301)}}, {{A, B, C, X(303), X(18550)}}, {{A, B, C, X(5627), X(53030)}}, {{A, B, C, X(8455), X(11130)}}, {{A, B, C, X(40710), X(51254)}}
X(54558) lies on these lines: {30, 40178}, {3424, 34621}, {6504, 7841}, {7383, 7607}, {7400, 43537}, {13582, 32982}, {47586, 52404}
X(54558) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(141), X(45088)}}, {{A, B, C, X(524), X(42021)}}, {{A, B, C, X(1502), X(52487)}}, {{A, B, C, X(3089), X(33190)}}, {{A, B, C, X(3431), X(6339)}}, {{A, B, C, X(3541), X(8370)}}, {{A, B, C, X(3542), X(7841)}}, {{A, B, C, X(3546), X(37855)}}, {{A, B, C, X(4846), X(6664)}}, {{A, B, C, X(7383), X(52282)}}, {{A, B, C, X(9164), X(44157)}}, {{A, B, C, X(14528), X(34898)}}, {{A, B, C, X(32982), X(37943)}}, {{A, B, C, X(34165), X(34505)}}, {{A, B, C, X(34621), X(52283)}}
X(54559) lies on these lines: {30, 40395}, {275, 11113}, {405, 43530}, {442, 16080}, {459, 50741}, {2052, 17532}, {5397, 5796}
X(54559) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(17532)}}, {{A, B, C, X(5), X(11113)}}, {{A, B, C, X(20), X(50741)}}, {{A, B, C, X(30), X(442)}}, {{A, B, C, X(72), X(1494)}}, {{A, B, C, X(265), X(40412)}}, {{A, B, C, X(376), X(5177)}}, {{A, B, C, X(381), X(405)}}, {{A, B, C, X(452), X(3545)}}, {{A, B, C, X(943), X(5627)}}, {{A, B, C, X(1006), X(17577)}}, {{A, B, C, X(1294), X(1441)}}, {{A, B, C, X(3651), X(6175)}}, {{A, B, C, X(3839), X(16845)}}, {{A, B, C, X(5714), X(7319)}}, {{A, B, C, X(6598), X(34303)}}, {{A, B, C, X(6829), X(11114)}}, {{A, B, C, X(6843), X(11111)}}, {{A, B, C, X(6907), X(11112)}}, {{A, B, C, X(6913), X(17556)}}, {{A, B, C, X(6920), X(37375)}}, {{A, B, C, X(6937), X(17579)}}, {{A, B, C, X(7413), X(17677)}}, {{A, B, C, X(7580), X(17528)}}, {{A, B, C, X(13442), X(16052)}}, {{A, B, C, X(17530), X(31789)}}, {{A, B, C, X(19542), X(37150)}}, {{A, B, C, X(21161), X(46870)}}, {{A, B, C, X(25985), X(34664)}}, {{A, B, C, X(30810), X(36722)}}, {{A, B, C, X(37411), X(44217)}}
X(54560) lies on these lines: {30, 4049}, {516, 5466}, {519, 2394}, {2784, 9180}, {2796, 14223}, {16080, 46541}, {17132, 43673}, {28562, 43665}
X(54560) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(519)}}, {{A, B, C, X(511), X(28562)}}, {{A, B, C, X(516), X(524)}}, {{A, B, C, X(542), X(2796)}}, {{A, B, C, X(543), X(2784)}}, {{A, B, C, X(726), X(11645)}}, {{A, B, C, X(1503), X(17132)}}, {{A, B, C, X(2688), X(35153)}}, {{A, B, C, X(17766), X(19924)}}
X(54561) lies on these lines: {2, 22797}, {13, 10722}, {17, 36962}, {18, 41023}, {30, 40706}, {76, 48656}, {262, 41039}, {462, 16080}, {542, 11121}, {5318, 14492}, {5479, 43547}, {5979, 8781}, {6033, 40707}, {6773, 22237}, {11603, 41022}, {43546, 51753}
X(54561) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(14372)}}, {{A, B, C, X(64), X(23717)}}, {{A, B, C, X(74), X(16460)}}, {{A, B, C, X(842), X(51447)}}, {{A, B, C, X(1494), X(11085)}}, {{A, B, C, X(2378), X(13603)}}, {{A, B, C, X(3426), X(3439)}}, {{A, B, C, X(3441), X(11060)}}, {{A, B, C, X(11080), X(32085)}}, {{A, B, C, X(14483), X(34322)}}
X(54561) = isogonal conjugate of X(36756)
X(54562) lies on these lines: {2, 22796}, {14, 10722}, {17, 41022}, {18, 36961}, {30, 40707}, {76, 48655}, {262, 41038}, {463, 16080}, {542, 11122}, {5321, 14492}, {5478, 43546}, {5978, 8781}, {6033, 40706}, {6770, 22235}, {11602, 41023}, {43547, 51754}
X(54562) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(14373)}}, {{A, B, C, X(64), X(23716)}}, {{A, B, C, X(74), X(16459)}}, {{A, B, C, X(842), X(51446)}}, {{A, B, C, X(1494), X(11080)}}, {{A, B, C, X(2379), X(13603)}}, {{A, B, C, X(3426), X(3438)}}, {{A, B, C, X(3440), X(11060)}}, {{A, B, C, X(11085), X(32085)}}, {{A, B, C, X(14483), X(34321)}}
X(54562) = isogonal conjugate of X(36755)
X(54563) lies on these lines: {10, 24705}, {30, 40718}, {226, 50178}, {536, 43677}, {824, 2394}, {5466, 28468}, {6002, 35353}, {16080, 31909}
X(54563) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(824)}}, {{A, B, C, X(79), X(28660)}}, {{A, B, C, X(514), X(20028)}}, {{A, B, C, X(517), X(28840)}}, {{A, B, C, X(524), X(28468)}}, {{A, B, C, X(536), X(6002)}}, {{A, B, C, X(1258), X(16615)}}, {{A, B, C, X(1400), X(47947)}}, {{A, B, C, X(3227), X(28630)}}, {{A, B, C, X(4102), X(43073)}}, {{A, B, C, X(10435), X(36871)}}, {{A, B, C, X(24479), X(35161)}}, {{A, B, C, X(44129), X(48899)}}
X(54564) lies on these lines: {30, 4080}, {900, 2394}, {4049, 11125}, {5466, 28294}, {16080, 37168}
X(54564) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(900)}}, {{A, B, C, X(74), X(34079)}}, {{A, B, C, X(524), X(28294)}}, {{A, B, C, X(903), X(45136)}}, {{A, B, C, X(28840), X(28877)}}
X(54565) lies on these lines: {20, 43529}, {30, 40824}, {76, 11180}, {1916, 3543}, {3091, 43528}, {3407, 3839}, {5503, 10722}, {6620, 16080}, {37334, 53098}
X(54565) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6620)}}, {{A, B, C, X(393), X(5641)}}, {{A, B, C, X(419), X(3543)}}, {{A, B, C, X(1976), X(3426)}}, {{A, B, C, X(3839), X(5117)}}, {{A, B, C, X(6531), X(36889)}}, {{A, B, C, X(10630), X(11738)}}, {{A, B, C, X(40708), X(43699)}}
X(54566) lies on these lines: {30, 42006}, {76, 19924}, {83, 11645}, {671, 48895}, {7470, 10159}, {10168, 43527}, {11170, 36990}, {14492, 39593}, {43528, 44230}
X(54566) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(7470)}}, {{A, B, C, X(512), X(13603)}}, {{A, B, C, X(826), X(11645)}}, {{A, B, C, X(3849), X(32473)}}, {{A, B, C, X(5641), X(15321)}}, {{A, B, C, X(11738), X(44557)}}, {{A, B, C, X(14487), X(43950)}}, {{A, B, C, X(28487), X(28562)}}, {{A, B, C, X(44146), X(48895)}}
X(54567) lies on these lines: {2, 22505}, {30, 42010}, {115, 53100}, {262, 39838}, {2794, 7607}, {5503, 32479}, {7608, 10722}, {9862, 43537}, {11170, 53017}, {14651, 47586}, {35705, 40824}, {38743, 43529}
X(54567) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(2793), X(32479)}}, {{A, B, C, X(3455), X(16835)}}, {{A, B, C, X(8753), X(39644)}}, {{A, B, C, X(9154), X(38741)}}, {{A, B, C, X(10630), X(29011)}}, {{A, B, C, X(11744), X(53605)}}
X(54567) = reflection of X(i) in X(j) for these {i,j}: {53100, 115}
X(54568) lies on these lines: {30, 42011}, {381, 10153}, {671, 53017}, {1503, 17503}, {2794, 8587}, {5475, 53099}, {47586, 53016}
X(54568) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(34154)}}, {{A, B, C, X(3425), X(10630)}}, {{A, B, C, X(9515), X(52518)}}
X(54568) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 17503}
X(54569) lies on these lines: {2, 9749}, {3, 36761}, {10, 49539}, {13, 1503}, {14, 2794}, {17, 5868}, {18, 41034}, {30, 42035}, {76, 41062}, {83, 41064}, {98, 41044}, {115, 36990}, {262, 41052}, {485, 41050}, {486, 41048}, {530, 5485}, {531, 5503}, {542, 42036}, {671, 41023}, {1327, 49972}, {1328, 49974}, {2394, 27551}, {2782, 36784}, {3391, 13749}, {3392, 13748}, {3543, 22574}, {5334, 14484}, {5335, 47853}, {5478, 43540}, {5869, 43546}, {6108, 53015}, {6114, 22664}, {6115, 7710}, {6770, 43542}, {6776, 9112}, {6777, 43539}, {9750, 36776}, {11121, 44667}, {11602, 19106}, {12816, 41028}, {14223, 27550}, {14539, 40824}, {16964, 22693}, {22796, 38317}, {23006, 41021}, {23698, 41458}, {23870, 43673}, {23871, 52459}, {31710, 46034}, {33602, 41030}, {33604, 41032}, {33607, 41026}, {36772, 41035}, {39838, 42093}, {40707, 44666}
X(54569) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(27551)}}, {{A, B, C, X(64), X(3438)}}, {{A, B, C, X(66), X(8741)}}, {{A, B, C, X(67), X(11080)}}, {{A, B, C, X(74), X(16257)}}, {{A, B, C, X(523), X(8737)}}, {{A, B, C, X(530), X(1499)}}, {{A, B, C, X(531), X(2793)}}, {{A, B, C, X(542), X(27550)}}, {{A, B, C, X(1177), X(8739)}}, {{A, B, C, X(1297), X(51446)}}, {{A, B, C, X(1485), X(10642)}}, {{A, B, C, X(1503), X(23870)}}, {{A, B, C, X(2379), X(3426)}}, {{A, B, C, X(2794), X(23871)}}, {{A, B, C, X(2980), X(8742)}}, {{A, B, C, X(3440), X(34130)}}, {{A, B, C, X(3527), X(34321)}}, {{A, B, C, X(11087), X(18575)}}, {{A, B, C, X(32085), X(41897)}}
X(54569) = reflection of X(i) in X(j) for these {i,j}: {36761, 3}, {36776, 9750}, {36961, 41038}
X(54569) = isogonal conjugate of X(14538)
X(54569) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 13}, {23717, 43532}
X(54569) = X(i)-cross conjugate of X(j) for these {i, j}: {22513, 13}
X(54569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2794, 41038, 36961}
X(54570) lies on these lines: {2, 9750}, {3, 41458}, {10, 49541}, {13, 2794}, {14, 1503}, {17, 41035}, {18, 5869}, {30, 42036}, {76, 41063}, {83, 41065}, {98, 41045}, {115, 36990}, {262, 41053}, {485, 41049}, {486, 41051}, {530, 5503}, {531, 5485}, {542, 42035}, {671, 41022}, {1327, 49973}, {1328, 49975}, {2394, 27550}, {3366, 13749}, {3367, 13748}, {3543, 22573}, {5334, 47854}, {5335, 14484}, {5479, 43541}, {5868, 43547}, {6109, 53015}, {6114, 7710}, {6115, 22664}, {6773, 43543}, {6776, 9113}, {6778, 43538}, {11122, 44666}, {11603, 19107}, {12817, 41029}, {14223, 27551}, {14538, 40824}, {16965, 22694}, {22797, 38317}, {23013, 41020}, {23698, 36761}, {23870, 52459}, {23871, 43673}, {31709, 46034}, {33603, 41031}, {33605, 41033}, {33606, 41027}, {39838, 42094}, {40706, 44667}
X(54570) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(27550)}}, {{A, B, C, X(64), X(3439)}}, {{A, B, C, X(66), X(8742)}}, {{A, B, C, X(67), X(11085)}}, {{A, B, C, X(74), X(16258)}}, {{A, B, C, X(523), X(8738)}}, {{A, B, C, X(530), X(2793)}}, {{A, B, C, X(531), X(1499)}}, {{A, B, C, X(542), X(27551)}}, {{A, B, C, X(1177), X(8740)}}, {{A, B, C, X(1297), X(51447)}}, {{A, B, C, X(1485), X(10641)}}, {{A, B, C, X(1503), X(23871)}}, {{A, B, C, X(2378), X(3426)}}, {{A, B, C, X(2794), X(23870)}}, {{A, B, C, X(2980), X(8741)}}, {{A, B, C, X(3441), X(34130)}}, {{A, B, C, X(3527), X(34322)}}, {{A, B, C, X(11082), X(18575)}}, {{A, B, C, X(32085), X(41898)}}
X(54570) = reflection of X(i) in X(j) for these {i,j}: {36962, 41039}, {41458, 3}
X(54570) = isogonal conjugate of X(14539)
X(54570) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14}, {23716, 43532}
X(54570) = X(i)-cross conjugate of X(j) for these {i, j}: {22512, 14}
X(54570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2794, 41039, 36962}
X(54571) lies on these lines: {2, 9736}, {4, 5472}, {13, 44666}, {14, 5478}, {17, 23005}, {18, 22832}, {30, 42062}, {76, 16629}, {98, 5318}, {532, 42035}, {2996, 22113}, {5965, 11121}, {5982, 8781}, {6115, 16652}, {6770, 43540}, {6772, 10611}, {6776, 31683}, {11602, 22900}, {12816, 41022}, {12820, 36961}, {14458, 41039}, {14853, 43541}, {16001, 16626}, {20377, 22890}, {22235, 22532}, {22237, 41056}, {22892, 43554}, {33388, 36969}, {36782, 43544}, {41020, 43550}, {43546, 52838}, {48666, 53105}
X(54571) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(23716)}}, {{A, B, C, X(54), X(34321)}}, {{A, B, C, X(523), X(11139)}}, {{A, B, C, X(532), X(27551)}}, {{A, B, C, X(2379), X(14483)}}, {{A, B, C, X(3438), X(3527)}}, {{A, B, C, X(5966), X(51446)}}, {{A, B, C, X(11080), X(17983)}}, {{A, B, C, X(41897), X(45857)}}
X(54571) = isogonal conjugate of X(13350)
X(54572) lies on these lines: {2, 9735}, {4, 5471}, {13, 5479}, {14, 44667}, {17, 22831}, {18, 23004}, {30, 42063}, {76, 16628}, {98, 5321}, {533, 42036}, {2996, 22114}, {5965, 11122}, {5983, 8781}, {6114, 16653}, {6773, 43541}, {6775, 10612}, {6776, 31684}, {11603, 22856}, {12817, 41023}, {12821, 36962}, {14458, 41038}, {14853, 43540}, {16002, 16627}, {20378, 22843}, {22235, 41057}, {22237, 22531}, {22848, 43555}, {33389, 36970}, {41021, 43551}, {43547, 52839}, {48665, 53105}
X(54572) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(23717)}}, {{A, B, C, X(54), X(34322)}}, {{A, B, C, X(523), X(11138)}}, {{A, B, C, X(533), X(27550)}}, {{A, B, C, X(2378), X(14483)}}, {{A, B, C, X(3439), X(3527)}}, {{A, B, C, X(5966), X(51447)}}, {{A, B, C, X(11085), X(17983)}}, {{A, B, C, X(41898), X(45857)}}
X(54572) = isogonal conjugate of X(13349)
X(54573) lies on these lines: {30, 42410}, {6240, 16080}, {7547, 43530}
X(54573) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6145)}}, {{A, B, C, X(250), X(16835)}}, {{A, B, C, X(381), X(7547)}}, {{A, B, C, X(847), X(38436)}}, {{A, B, C, X(1138), X(15319)}}, {{A, B, C, X(1179), X(21400)}}, {{A, B, C, X(1300), X(13481)}}, {{A, B, C, X(1494), X(16000)}}, {{A, B, C, X(1989), X(38447)}}, {{A, B, C, X(3830), X(32534)}}, {{A, B, C, X(5627), X(8884)}}, {{A, B, C, X(7576), X(12605)}}, {{A, B, C, X(15392), X(15619)}}, {{A, B, C, X(16263), X(43949)}}, {{A, B, C, X(18550), X(45138)}}, {{A, B, C, X(32533), X(34288)}}, {{A, B, C, X(43660), X(46255)}}
X(54574) lies on these lines: {13, 43368}, {14, 42683}, {17, 14893}, {18, 38335}, {30, 43440}, {381, 43441}, {3627, 10187}, {3830, 43549}, {3843, 10188}, {3845, 43548}, {12821, 43475}, {15684, 43442}, {19107, 43554}, {22235, 43492}, {22237, 42436}, {23046, 43443}, {33602, 43476}, {33607, 42117}, {42088, 43545}, {42499, 42543}, {43226, 43542}, {43228, 43472}, {43556, 49827}
X(54574) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(38335)}}, {{A, B, C, X(473), X(14893)}}
X(54575) lies on these lines: {13, 42682}, {14, 43369}, {17, 38335}, {18, 14893}, {30, 43441}, {381, 43440}, {3627, 10188}, {3830, 43548}, {3843, 10187}, {3845, 43549}, {12820, 43476}, {15684, 43443}, {19106, 43555}, {22235, 42435}, {22237, 43491}, {23046, 43442}, {33603, 43475}, {33606, 42118}, {42087, 43544}, {42498, 42544}, {43227, 43543}, {43229, 43471}, {43557, 49826}
X(54575) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(14893)}}, {{A, B, C, X(473), X(38335)}}
X(54576) lies on these lines: {2, 43367}, {4, 42612}, {13, 42781}, {17, 14269}, {18, 15687}, {30, 43442}, {381, 43443}, {382, 10187}, {546, 10188}, {3830, 43545}, {3845, 43544}, {3861, 42952}, {5351, 43446}, {11480, 43548}, {12101, 33606}, {12816, 43030}, {15681, 43440}, {16242, 43398}, {22235, 49876}, {22237, 41100}, {33604, 36970}, {38071, 43441}, {41107, 43553}, {41108, 43550}, {42093, 42480}, {42105, 43543}, {42589, 42976}, {42947, 43447}, {43229, 43547}, {43418, 43552}
X(54576) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(15687)}}, {{A, B, C, X(473), X(14269)}}
X(54577) lies on these lines: {2, 43366}, {4, 42613}, {14, 42782}, {17, 15687}, {18, 14269}, {30, 43443}, {381, 43442}, {382, 10188}, {546, 10187}, {3830, 43544}, {3845, 43545}, {3861, 42953}, {5352, 43447}, {11481, 43549}, {12101, 33607}, {12817, 43031}, {15681, 43441}, {16241, 43397}, {22235, 41101}, {22237, 49875}, {33605, 36969}, {38071, 43440}, {41107, 43551}, {41108, 43552}, {42094, 42481}, {42104, 43542}, {42588, 42977}, {42946, 43446}, {43228, 43546}, {43419, 43553}
X(54577) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(14269)}}, {{A, B, C, X(473), X(15687)}}
X(54578) lies on these lines: {4, 43253}, {18, 50687}, {30, 43444}, {381, 43445}, {3146, 10187}, {3543, 43446}, {3830, 43555}, {3832, 10188}, {3839, 43447}, {3845, 43554}, {12101, 33605}, {15640, 43102}, {15683, 43442}, {17578, 42514}, {33607, 43476}, {42103, 42631}, {42126, 43542}, {42682, 49813}, {42694, 49873}, {43206, 49824}, {43228, 43556}, {43473, 43541}, {43544, 46335}
X(54578) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(50687)}}
X(54579) lies on these lines: {4, 43252}, {17, 50687}, {30, 43445}, {381, 43444}, {3146, 10188}, {3543, 43447}, {3830, 43554}, {3832, 10187}, {3839, 43446}, {3845, 43555}, {12101, 33604}, {15640, 43103}, {15683, 43443}, {17578, 42515}, {33606, 43475}, {42106, 42632}, {42127, 43543}, {42683, 49812}, {42695, 49874}, {43205, 49825}, {43229, 43557}, {43474, 43540}, {43545, 46334}
X(54579) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(473), X(50687)}}
X(54580) lies on these lines: {2, 42096}, {13, 43364}, {14, 43397}, {17, 3839}, {18, 3543}, {20, 10187}, {30, 43446}, {376, 43444}, {381, 43447}, {1080, 53098}, {2043, 43565}, {2044, 43564}, {3091, 10188}, {3146, 42793}, {3545, 43445}, {3830, 43543}, {3845, 43542}, {5321, 43552}, {5334, 12820}, {10304, 43442}, {12101, 33603}, {12816, 42133}, {12821, 41113}, {15640, 43545}, {15682, 42121}, {15692, 43440}, {17578, 42519}, {22235, 49947}, {22237, 42148}, {33604, 42128}, {33606, 43242}, {33607, 42901}, {33699, 42963}, {35750, 42035}, {36327, 42036}, {41099, 42136}, {41106, 42122}, {41108, 43546}, {41112, 43550}, {41120, 50688}, {42093, 43540}, {42109, 49906}, {42161, 43547}, {42509, 43466}, {42589, 43305}, {42591, 46333}, {42635, 49876}, {42899, 43557}, {42905, 49825}, {42919, 43544}, {42956, 43870}, {43229, 43541}, {43551, 49826}
X(54580) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(3543)}}, {{A, B, C, X(473), X(3839)}}, {{A, B, C, X(31361), X(41901)}}, {{A, B, C, X(40711), X(43699)}}
X(54580) = X(i)-cross conjugate of X(j) for these {i, j}: {43477, 43540}